{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Whitening versus standardizing" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, just read in data, and take a peek. The data can be found on [GitHub](https://github.com/ppham27/MLaPP-solutions/blob/master/chap04/heightWeightData.txt)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 210 entries, 0 to 209\n", "Data columns (total 3 columns):\n", "gender 210 non-null int64\n", "height 210 non-null int64\n", "weight 210 non-null int64\n", "dtypes: int64(3)\n", "memory usage: 5.0 KB\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " gender height weight\n", "0 1 67 125\n", "1 2 68 140\n", "2 2 67 142\n", "3 2 60 110\n", "4 2 64 97" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "raw_data = pd.read_csv(\"heightWeightData.txt\", header=None, names=[\"gender\", \"height\", \"weight\"])\n", "raw_data.info()\n", "raw_data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're told that for gender, 1 is male, and 2 is female. Part (a) says to extract the height/weight data corresponding to the males. Then, we fit a 2d Gaussian to the male data, using the empirical mean and covariance. Then, we'll plot this data.\n", "\n", "Let's extract the males first." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " gender height weight\n", "0 1 67 125\n", "6 1 79 210\n", "8 1 71 150\n", "11 1 71 175\n", "12 1 72 145" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "male_data = raw_data[raw_data.gender == 1]\n", "male_data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we'll calculate the empirical mean and covariance." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 71.65753425 175.61643836]\n", "[[ 9.6498405 46.93713642]\n", " [ 46.93713642 1035.277538 ]]\n" ] } ], "source": [ "mu_male = male_data.mean(axis=0)[1:].as_matrix() # remove gender\n", "male_mean_diff = male_data.iloc[:,1:].as_matrix() - mu_male\n", "covariance_male = np.dot(male_mean_diff.T, male_mean_diff)/len(male_data)\n", "print(mu_male)\n", "print(covariance_male)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the data now." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QsqxmuA8dmn4fW93hw4db1tN6aEzcd11m9bgkQUFB2lq0aFHb8lKp1LKe1kNj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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "plt.plot(male_data.height, male_data.weight, 'ko')\n", "plt.axis([60,80,120,285])\n", "plt.title('raw')\n", "plt.xlabel('height')\n", "plt.ylabel('weight')\n", "plt.axes().set_aspect(0.2)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Let $\\mathbf{x} \\sim \\mathcal{N}\\left(\\boldsymbol\\mu, \\Sigma\\right)$, where $\\mathbf{x} \\in \\mathbb{R}^p$. We can write $\\Sigma = SDS^\\intercal$ by the spectral theorem, where the columns of $S$ are orthonormal eigenvectors, and $D$ is a diagonal matrix of eigenvectors, $\\lambda_1, \\lambda_2,\\ldots,\\lambda_n$.\n", "\n", "$\\mathbf{x}$ has probability mass function,\n", "\n", "\\begin{equation}\n", "f(\\mathbf{x}) = \\frac{1}{(2\\pi)^{p/2}\\sqrt{\\det{\\Sigma}}}\\exp\\left(-\\frac{1}{2}\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)^\\intercal\\Sigma^{-1}\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)\\right).\n", "\\end{equation}\n", "\n", "Note that $S^\\intercal S = I$, and $S^{-1} = S^\\intercal$. This implies that \n", "\n", "\\begin{equation}\n", "\\Sigma^{-1} = \\left(SDS^\\intercal\\right)^{-1} = \\left(S^\\intercal\\right)^{-1}D^{-1}S^{-1} = SD^{-1}S^\\intercal.\n", "\\end{equation}\n", "\n", "Let $\\mathbf{y} = S^\\intercal\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)$.\n", "\n", "Then, we have that \n", "\n", "\\begin{align}\n", "\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)^\\intercal\\Sigma^{-1}\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)\n", "&= \\left(\\mathbf{x}-\\boldsymbol\\mu\\right)^\\intercal S D^{-1} S^\\intercal\\left(\\mathbf{x}-\\boldsymbol\\mu\\right) \\\\\n", "&= \\left(S^\\intercal\\left(\\mathbf{x}-\\boldsymbol\\mu\\right)\\right)^\\intercal D^{-1} S^\\intercal\\left(\\mathbf{x}-\\boldsymbol\\mu\\right) \\\\\n", "&= \\mathbf{y}^\\intercal D^{-1} \\mathbf{y}.\n", "\\end{align}\n", "\n", "Moreover, $\\mathbf{x} = S\\mathbf{y} + \\boldsymbol\\mu$, so $D\\mathbf{x}(\\mathbf{y}) = S$, and so $\\det D\\mathbf{x}(\\mathbf{y}) = 1$. Changing variables, the probability density function for $\\mathbf{y}$ is\n", "\n", "\\begin{equation}\n", "f(\\mathbf{y}) = \\frac{1}{(2\\pi)^{p/2}\\sqrt{\\det D}}\\exp\\left(-\\frac{1}{2}\\mathbf{y}^\\intercal D^{-1} \\mathbf{y}\\right)\n", "= \\frac{1}{(2\\pi)^{p/2}\\sqrt{\\prod_{j=1}^p\\lambda_j}}\\exp\\left(-\\frac{1}{2}\\sum_{j=1}^p \\frac{y_j^2}{\\lambda_j}\\right) = \\prod_{j=1}^p\\frac{1}{\\sqrt{2\\pi\\lambda_j}}\\exp\\left(-\\frac{1}{2}\\frac{y_j^2}{\\lambda_j}\\right).\n", "\\end{equation}\n", "\n", "Thus, $\\mathbf{y} \\sim \\mathcal{N}\\left(\\mathbf{0}, D\\right)$, and the coordinates of $\\mathbf{y}$ are independent, with $y_i \\mathcal{N}\\left(0, \\lambda_j\\right)$. Now, the level curves of $f$ correspond to the hyperellipsoids\n", "\n", "\\begin{equation}\n", "\\sum_{j=1}^p \\frac{y_j^2}{\\lambda_j} = \\sum_{j=1}^p \\left(\\frac{y_j}{\\sqrt{\\lambda_j}}\\right)^2 = c.\n", "\\end{equation}\n", "\n", "$\\frac{y_j}{\\sqrt{\\lambda_j}} \\sim \\mathcal{N}(0, 1)$, so $\\sum_{j=1}^p \\frac{y_j^2}{\\lambda_j} \\sim \\chi^2_p$, and so a $95\\%$ confidence region would be\n", "\n", "\\begin{equation}\n", "\\sum_{j=1}^p \\frac{y_j^2}{\\lambda_j} \\leq F_{\\chi^2_p}^{-1}(0.95), \n", "\\end{equation}\n", "\n", "where $F$ is the cumulative distribution function. For our $p = 2$ case, $F_{\\chi^2_p}^{-1}(0.95) \\approx 5.991.$ Now $\\mathbf{y}$ our coordinates with respect to a orthonormal eigenbasis. Since $\\mathbf{x} = S\\mathbf{y} + \\boldsymbol\\mu$, the confidence region is a rotated hyperellipsoid centered at $\\boldsymbol\\mu$ with semi-axes along the eigenvectors of $\\Sigma$. Let's plot this hyperellipsoid along with the indexed data." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tpIguwaFDhwgMDGTUqFEkJyfz0P79mIMqbP2OiIjLbbrYiiqzbJkI6FvDhiJ5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\n0bVrV55++mmWL1/OokWLHHFhvqDyGCvHpB06dMjRXrJkiSP04+TJk5w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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def calculate_2d_gaussian_confidence_region(mu, Sigma, p = 0.95, points = 200):\n", " \"\"\"\n", " Returns a points x 2 numpy.ndarray of the confidence region.\n", " \n", " Keyword arguments:\n", " mu -- mean\n", " Sigma -- covariance matrix\n", " p -- percent confidence\n", " points -- number of points to interpolate\n", " \"\"\"\n", " assert(len(mu) == len(Sigma))\n", " assert(np.all(Sigma == Sigma.T))\n", " eigenvalues, S = np.linalg.eig(Sigma)\n", " S = S[:,eigenvalues.argsort()[::-1]]\n", " eigenvalues = eigenvalues[eigenvalues.argsort()[::-1]]\n", " theta = np.linspace(0, 2*np.pi, num = points)\n", " x = np.sqrt(eigenvalues[0]*stats.chi2.ppf(p, df=2))*np.cos(theta)\n", " y = np.sqrt(eigenvalues[1]*stats.chi2.ppf(p, df=2))*np.sin(theta)\n", " return np.dot(S, np.array([x,y])).T + mu\n", "def plot_raw_males(ax=None):\n", " if ax == None:\n", " ax = plt.gca()\n", " gaussian_fit_male = calculate_2d_gaussian_confidence_region(mu_male, covariance_male, p = 0.95, points = 100) \n", " ax.axis([60,80,90,285])\n", " ax.set_title('raw')\n", " ax.set_xlabel('height')\n", " ax.set_ylabel('weight')\n", " for row in male_data.itertuples():\n", " ax.text(row.height, row.weight, row.Index, horizontalalignment='center', verticalalignment='center')\n", " ax.set_aspect(0.2)\n", " ax.plot(gaussian_fit_male[:,0], gaussian_fit_male[:,1], linewidth=3, color='red')\n", " ax.plot(mu_male[0], mu_male[1], 'rx', markersize=10, markeredgewidth=3) \n", " ax.grid(True)\n", "plt.figure(figsize=(8,8))\n", "plot_raw_males(plt.gca())\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For part (b) says to do the same thing with standardized data." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UBKaU2wMPuLf9eMHMTJrE/EAwtwtcsuxHj1rJ6+WX3YtWVqtmLQT4z3/65Niv\n/Ajmaw9afq+U//773dtffw3Hjxf8exQiTWLKf23cCDfcAEuWuI/dfrtVVXLzzfbFpZQvq14dmja1\nttPSrBUc/Ji2iSn/NGcO9OoFqanuY889Z92RhYbaF5dS/mDcOHjqKWu7XbvsXwR9iCdtYprElH8R\nsdZFeuEF97GyZa3u8+3b2xeX8oqoqCjKli1LSEgIRYsWZd26dbzwwgssWLAAYwwVK1ZkxowZhGeu\nm6U8s28fREZa26GhVpWiDy6YqR07AkQwtwtkK/uff1rd5LMmsNq1Yd26gE1gwXztAc6fP4/D4SAp\nKYl169YBMGTIEDZv3symTZvo2LEjL730kr1BepHXrn9EBMTGWtvp6bB6tXfepxBoElP+4eBBiI+3\nBitnat0a1qyxEpkKSCJCRkZGtmOlsvQ2PXPmDBUrVizssAJDy5bu7ZUr7YvjCml1ovJ9mzdbd1r7\n9rmP/eMfVhf6okXti0t5XY0aNShXrhyhoaEMGDCA/v37AzBs2DDef/99SpQowdq1aymbOZ2S8ty8\nedaK5mAtnOmDd2PaJqb838KF0L07nDlj7YeEwFtvwWOP+X33eXVpBw4coGrVqhw5coS2bdvyzjvv\n0CLLvJdjxozh119/ZXqATKFUqI4cgcqVre2iReHECShRwt6YctA2sQARlO0iIjB2LI6OHd0JrHRp\n+OIL+Ne/giaBBeW1z2Lbtm0AVKpUifvuu8/VLpape/fubNiwwY7QCoVXr3+lStaUbAAXLsDatd57\nLy/SJKZ8T1qaNYHvkCHuY9Wrww8/wF132ReXKlRnz54l1TmE4syZM3z99dc0aNCAHVlWJZg/fz4x\nMTF2hej/brvNve2n7WJanah8y9mz8OCD2ZeJaNECPvvM+uaogsbu3bu57777MMaQlpZGjx49GDp0\nKF26dGH79u2EhoZSo0YN/vOf/1A5s1pM5c/MmdZ8o2B1lFq+3N54ctA2MeVfjh+HDh2yNzD37GnN\nSF+8uH1xKRWoso4XK1UKTp3yqap6bRMLEEHRLrJ/v1W1kTWBDR2KIyEhqBNYUFz7i9DyO7z7BuHh\n7vX1/vgDDhzw7vt5gSYxZb+tW60uvj//7D721lswapRPfStUKuAYA3XquPedHWn8iVYnKnutWWPN\nQp85k3aRItYaR9272xuXUsGiVy94/31re9IkeOQRe+PJwpPqxCKFFYxSf7FoEXTp4p7Et2RJqwNH\nu3b2xqVEkVmkAAAgAElEQVRUMKlb173th3diWp3oBwKyXeD9961OHJkJrGJFWLHiLwksIMueD1p+\nh90h2KpQyp+1OvHXX73/fgVMk5gqfG++aVVhpKdb+1FRVoeOG2+0NSylgpKf34lpm5gqXKNGWet+\nZWrUCBYvhmuvtS8mpYLZuXPWdFMZGVZHjzNn4Oqr7Y4K0C72yte8/HL2BHbrrfDtt5rAlLJT8eLW\njDhgTfe2e7e98eSTJjE/4PftAiIwfDi8+KL7WOvW1h1Y5hiVPPh92a+Qlt9hdwi2KrTyh4W5t48d\nK5z3LCDaO1F5lwgMHQqvv+4+1q6dtQyEj82YrVTQuuYa97afJTFtE1PeIwKDB8O//+0+dvfd8Omn\ncNVV9sWllMouIQFmzLC2p06Fvn1tDSeTtokp+2RkWGt+ZU1gHTta48A0geXb9u3biY2NJS4ujtjY\nWMqWLcv48eOZO3cuDRo0IDQ0lMTERLvDVP6qQgX3tp/diWkS8wN+1y6QkWGN+p840X2sc2eYMyff\n8yD6XdkLWGb5a9euTVJSEomJiWzcuJGSJUty33330bBhQ+bNm0fLrEvNBxC9/o7CeSM/rk7UNjFV\nsNLToX9/yLrS7oMPwgcfWFNKqSu2bNkyatasSUREhOuYVrerK+LHSUzvxPxAfHy83SF4RgQGDsye\nwHr2vKIE5jdl95Lcyv/JJ5/QrVu3wg/GBnr94wvnjbImscx5TP2EJjFVMETg6adhyhT3sYQEK6Hp\nHViBuXDhAgsXLqRr1652h6ICibaJKW/yi3aBkSNh3Dj3fs+eVi+n0NArOq1flN2LcpZ/8eLF3HDD\nDVQKklWu9fo7CueNsg53OXeucN6zgGgSU1furbeyD2S+7z6YNg1C9M+roH388cd5ViVqu5gKRjpO\nTF2Zd9+FAQPc++3awcKFQb0as7ecPXuW6667jl27dlG6dGkA5s+fz2OPPcbRo0cpV64cMTExLF68\n2OZIld9ZswZuvtnavukma98HeDJOTJOYunwffww9eljtYQAtWsCSJToTh1L+xo+TmNb3+AGfbBdY\nuNBq98pMYDfcAF98UeAJzCfLXoi0/A67Q7BVoZXfj28SNImp/Fu+HO6/370eWHQ0fPUVlC1rb1wB\nLioqisaNGxMbG0vTpk0BSElJoV27dtSpU4c77riDkydP2hyl8gcnT56ka9eu1KtXj/r167P255/d\nT5qL3vj4HK1OVPmzZg3cfjucPWvt16wJK1fqciqFoEaNGmzcuJHy5cu7jj3zzDNcc801DBkyhDFj\nxpCSksLo0aNtjFL5g969e9OyZUsSEhJIS0vjrMNBmbZtrSebNYMffrA3QCetTlQF67ff4J573Ams\nWjVYtkwTWCERETIyMrIdW7BgAb169QKgV69ezJ8/347QlB85deoUq1atIiEhAYAiRYpQpmRJm6O6\nfJrE/IBPtAscOQJ33eUeCFmxopXAoqK8+rY+UXYbZS2/MYa2bdty4403MnXqVAAOHTpEmHMtqCpV\nqnD48GE7wvQavf6OAj/n7t27qVixIgkJCcTFxTFgwABSU1ML/H0KiyYxdWlnz0L79rBzp7V/9dXw\n+edQt669cQWZ1atXk5iYyKJFi5g4cSKrVq3C5Gi/yLmvVE5paWkkJiby6KOPkpiYSIkSJRj9v/+5\nX1CmjH3BXQbbk5gx5n/GmEPGmC12x+KrbJ0/Lj3d6ka/dq21bwzMnGnVmxcCnTsv3rVdtWpVACpV\nqsS9997LunXrCAsL49ChQwAcPHiQypUr2xGm1+j1jy/wc4aHhxMREUGTJk0A6NKlC4lbt7pfkHUK\nKj9gexIDpgN32B2EyoUIDBoEWdtZ3n4b7r3XvpiC1NmzZ/njjz8AOHPmDF9//TUNGzakQ4cOzHAu\nZvjee+/RsWNHG6NU/iAsLIyIiAi2b98OwPLly4nOmrg0ieWPiHwHpNgdhy+zrV3grbdgwgT3/pNP\nWgtdFiJtE3EAVttXixYtiI2NpVmzZrRv35527drxzDPPsHTpUurUqcPy5csZOnSovQEXML3+Dq+c\nd/z48fTo0YOYmBg2b97Mczfe6H7Sz5KYTi+ucjdnjpW0MnXpAq+/bl88Qa569eps2rTpL8crVKjA\nsmXLbIhI+bPGjRuzfv1694HHH3dvaxLzjt69exPl7AmXOUdcZn1x5reVQN3PPFZo7z9hAjz5JJnv\n7mjQAPr3J945oW9hlj8+Pt7237+d+1p+LX+hvN8vv7j/vx86BIX5eZNl3+FwuKrHozzs+ewTg52N\nMdcBn4tIozye18HOhWX7dmsOtcyF8WrXhu+/z75onvJLffv25YsvviAsLIwtW6x+VOvXr+fRRx/l\nwoULFC1alEmTJrka/AGSk5OpX78+I0aMYPDgwXaFrrztb3+DRYus7YULrd7IPsCfBjsb50PlIvOb\nitedPAkdOrgTWOXKsHixrQms0Mruowqy/AkJCSxZsiTbsSFDhvDKK6+QlJTEiBEjePrpp7M9/+ST\nT3L33XcXWAz5pdffUThvlHU1Zz+rTrQ9iRljZgLfA7WNMcnGmAS7YwpKmV3pt22z9q+6yhoLVqOG\nvXGpAtOiRYtsU1aB1W0/c77FEydOUK1aNddzCxYsoEaNGtSvX79Q41Q2OHrUve1nScwnqhMvRasT\nC8Hzz8Nrr7n3P/oIune3Lx7lFXv37qV9+/au6sTk5GSaN2+eWW3D999/T0REBGfOnKFdu3YsXbqU\nsWPHUrp0aa1ODFTp6dbqE+fPW/unToFzvTq7+VN1orLT7NnZE9iQIZrAgkTfvn2ZMGECycnJvPXW\nW/Tp0weAl156iUGDBlHCubSOfokMYL//7k5glSr5TALzmIj4/MMKM3itWLHCeyfftEmkRAkRa2iz\nyJ13iqSlee/98smrZfcDBV3+PXv2SMOGDV37pUuXzvZ82bJlRUTk1ltvlerVq0v16tWlXLlycs01\n18jEiRMLNBZP6PVf4f03+eYb9///Zs28/3754Pzsv2h+8Jsu9soLjh6Fjh3ds9LXqmVNKRUaam9c\nymvE/cUQgFq1avHtt9/SsmVLli9fTq1atQBYuXKl6zUjRoygdOnSDBw4sNDjVYUgc05UsJZW8jOa\nxPxA5niKAnXhAnTtCnv3WvulS8OCBZCj4d9uXim7HynI8nfv3h2Hw8GxY8eIjIxkxIgRTJkyhYED\nB3L+/HmuuuoqpkyZUmDvVxD0+sd7/0127XJv+2FHLu3YEaz+9S/3lFLGWAnMR8aGKKUK0QMPWO3i\nADNmgHN9Ol+gHTsCRIGPFZk2LfuciCNH+mwC03FCDrtDsJWW3+H9N/Hz6kRNYsEmKQmytm106QLP\nPWdfPErl4dy5czzyyCPExsZSv359nsvxdzpu3DhCQkI4nnWgrso/P09iWp0YTE6dghtugB07rP2G\nDa0ppUqVsjcupfJw9uxZSpQoQXp6Os2bN2fcuHE0b96c/fv3069fP7Zt28bGjRup4GcDdH3G8ePu\nGXlKlIA//rCaF3yEVicqNxEYMMCdwEqVgrlzNYEpn5Y5Tu3cuXNkZGS4ZhwZNGgQY8eOtTO0wLB5\ns3u7dm2fSmCe0iTmBwqkXnzKFPjkk+z7tWtf+Xm9TNtEHHaHYKtvvvmG2NhYqlSpQnx8PNHR0Sxc\nuJCIiAgaNmxod3he5/Xrv3Gje/uGG7z7Xl6iXeyDwaZN2dcLGjAAunWzLx6lPBQSEkJSUhKnTp3i\njjvuYNGiRbz22mssXbrU9RptargCWZNYXJx9cVwBbRMLdKdPW9+wfvvN2m/UCNasgauvtjcupfJp\n5MiRGGN45513KFGiBCLC/v37qVatGuvWraNy5cp2h+h/atd2fzasWQM33WRvPDkUWJuYMeZxT44p\nHyMC//iH+4+0ZElrPIgmMOUHjh496pphPzU1laVLl3LzzTdz8OBBdu3axe7duwkPDycpKUkT2OU4\nedL92RAaan3B9UOetonlNvqtdwHGoS7isuvFp06Fjz9270+eDHXqFEhMhSXY24SCufwHDhzgxhtv\nJDY2lmbNmtGhQwduv/32bK/JnH0/UHn1+iclubfr1/fbL7cXbRMzxnQDugPVjTELszxVGtDBGb5s\nyxZrVo5Mffta64Up5ScaNmzIlClTLjr10q6sUyap/ElMdG/7aacOuESbmDHmOqA6MAoYmuWp08AW\nEUnzbniuOLRNLD/OnrUaaTMXuGzQANautcaBKKUUWF9qZ860tt95Bx591N54cuFJm9hF78REZC+w\nF7i5IANTXvbMM+4EVqKE1Q6mCeyiTp48Sb9+/fjpp58ICQlh2rRpvPXWW2zbtg1jDCkpKZQvX57E\nrN9elfJnAdC9Hjzv2NHJGPObMeakMeaUMea0MeaUt4NTlnzViy9dan2ryjR+PNSrV+AxFZbCahN6\n/PHHufvuu9m6dSubN2+mXr16zJo1i6SkJBITE+ncuTOdOnUqlFiyCuY2MdDye638x47B9u3Wdmgo\nNG7snfcpBJ6OE3sdaC8iW70ZjLpCKSmQkODeb98enCv1qrydOnWKVatWMWPGDACKFClCmTJlsr1m\n9uzZrFixwobolPICh8PqvQxw441+26kDPO+deEgTmH08XlPoX/+ylhoHqFgR3n3XL6eRyaow1lPa\nvXs3FStWJCEhgbi4OAYMGEBqaqrr+VWrVlGlShVq2jA5qq6nFW93CLbyWvm/+ca93bq1d96jkFw0\niTmrETsBG4wxnxhjumUecx5XvmLuXPjwQ/f+f/8LYWH2xeNFo0aNon79+jRq1IgePXpw7tw5RowY\nQXh4OHFxccTFxfHVV195fL60tDQSExN59NFHSUxMpESJEowaNcr1/Mcff0w3neFEBZKsSSzHsAV/\nc6k7sfbORxngLNAuy7F7vBuaynTJevGDB+Hhh937PXtC585ejamw5Cz73r17effdd0lKSmLLli2k\npaUxa9YsAAYPHkxiYiKJiYnceeedHr9HeHg4ERERNGnSBIAuXbqQ5BxDk56ezmeffcYDDzxQMAXK\nJ20Tctgdgq28Uv7/+z/49Vdru3hxuNm/++1dqndiwsWeVz4gc3b6Y8es/fBwqzNHgCpTpgzFihXj\nzJkzhISEcPbsWapVq8aePXsue9BrWFgYERERbN++ndq1a7N8+XKio6MBWLp0KfXq1ePaa68tyGIo\nZZ+sd2G33OLX7WHgYccOY0xun4ongQ0isqBgQ1I5XbRefPp0+Pzz7Pvlynk9psKSs+zly5fnySef\nJDIykhIlStCuXTvatGnD6tWreeedd/jggw9o0qQJ48aNo2zZsh6/z/jx4+nRowcXLlygRo0aTJ8+\nHYBPPvnE1qpEbROKtzsEW3ml/AFUlQgeTgBsjJkC1AXmOA91BnYD1wC7ROQJr0WIDnbO0+7d1nxn\nf/xh7T/2WEDfhYE1Q8M999zDd999R9myZenSpQtdu3albdu2VKxYEWMMw4YN48CBA/zvf/+zO1yl\nfIsIREVBcrK1//33Pl2dWJCLYjYCWonIBBGZALTBSmr3YbWTKS/KtV5cBPr3dyew2rVh9OhCjasw\n5Cz7hg0baN68ORUqVCA0NJROnTrx/fffU6lSJYyzJ2b//v1Zv369DdEWPG0Tctgdgq0KvPy7d7sT\nWKlS4GwH9meeJrHyQNYlgEsCFUQkHThX4FGpS/vgA1i+3NoOCYH33/fZWTkyMjKIi4ujQ4cO2Y6P\nGzeOkJAQjh/3fBrOOnXqsGbNGv78809EhOXLl1OvXj0OHjzoes1nn31GgwYNCix+lbe+ffsSFhZG\noywzoL/wwgs0btyYmJgY2rRpw/79+13PjRo1ilq1alGvXj2+/vprO0L2CydPnqRr16706tWL+vXr\ns3btWlJSUmjXrh116tThjjvucM3wny+ZnxkALVtC0aIFF7RdROSSD6AvVvXhdGAGsAvoh5XMxnpy\njit5WGEqlyNHRK65RsS6HxMZNMjuiC7qzTfflB49ekj79u1dx/bt2yd33HGHREVFybFjx/J1vtdf\nf12io6OlYcOG0qtXLzl//rz07NlTGjZsKI0bN5aOHTvKwYMHC7oYKherVq2SpKQkadiwoevY6dOn\nXdvjx4+Xfv36iYjIzz//LDExMXLhwgXZvXu31KxZUzIyMgo9Zn/Qq1cvmTZtmoiIXLhwQU6cOCFD\nhgyRMWPGiIjI6NGj5Zlnnsn/ie+5x/258eabBRmyVzg/+y+eHy71AnEnkqpAR+fjWk9/riAemsRy\n6NXL/YcYGSmS5UPD1+zbt0/atGkjK1asyJbEunTpIlu2bLmsJKZ8y549e7IlsaxGjRrl+rAdNWqU\njB492vXcnXfeKWvWrCmUGP3JyZMnpUaNGn85XqdOHdeXswMHDkidOnXyd+JTp0SKF3d/duzcWRDh\nepUnSexSg53rOv+Ncyaxfc5HFecxVQiy1Yt/8w289557f+JEq27bRw0aNIixY8e62qsAFixYQERE\nBA0bNrzkz2ubiMPuEC7LsGHDiIyMZMaMGTz77LMA/P7770RERLheU61aNX7PnGEmD/5a/iuRdQaZ\n2rVrM2DAAM6ePcuhQ4cIc05gUKVKFQ4fPpy/Ey9eDOecrT+NG0ONGgUcuT0u1SY22PnvuFweb3gx\nLpWbP//MPqi5Sxe4x3fHnH/55ZeEhYURExPjGsOVmprKqFGjGDFihOt1mc+pwPHKK6+QnJxMQkIC\nTzzh1c7LASfrDDJTpkyhZMmSjB49OtsXQeAv+5c0b557+777CiBS33Cpwc4DnP+2KpxwVG5cY0Ve\nfdW9nHiZMvD227bF5InVq1ezcOFCFi1aRGpqKqdPn+ahhx5iz549NG7cGBFh//793HDDDaxbty7X\nJeZ1nFC83SFcke7du3P33XcD1p3Xvn37XM/t37+fatWqXfTn/b38lyPnDDJFihRh9OjRhIWFue7G\nDh48mOv/lzydOwdffuneD6Ak5ulSLCWMMcOc48UwxtQyxvjuLUAg+uUXGDPGvT96NPj4LBKvvfYa\nycnJ7Nq1i1mzZtG6dWvmzJnDwYMH2bVrF7t37yY8PJykpKT8/YdUPkXcbdcA7Nixw7U9f/58YmJi\nAOjQoQOzZs3i/Pnz7N69mx07dtC0adNCj9fXZZ1BBmD58uXUr1+fDh06uFZaeO+99+jYsaPnJ/3m\nGzh92tquUQM8qMr3F54uxTId2Ajc4tz/HWvg8xfeCEpl5/jmG+JfeAEuXLAO3Hwz/OMf9gZVQJyD\nGfN83uFwBOW38Uy+Xv7u3bvjcDg4duwYkZGRjBgxgi+//JJt27ZRpEgRatSowX/+8x8AoqOjuf/+\n+4mOjqZo0aJMmjTpklVivl5+b8mcQSYlJYVGjRoxffp00tPTuf/++5k2bRrXXXcds2fP9vyEn33m\n3r7vPr9f3SIrT2fs2CAiTYwxSSIS6zy2WUQKZSW1YJ+xw/Hkk8S/+aa1U6QIJCVBkIyDCtYPsUxa\nfi3/FZc/PR2qVoUjR6z91autORP9gCczdniaxL4HbgdWi0icMaYm8LGIFEpdQFAnsePHoVYt61+A\nZ5+F116zNyallP9YtQpuu83arlLFWnMwxNN5LuxVkNNOvQh8BUQYYz4ClgNDrjA+5YmXX3YnsKgo\nGD7c1nACwf79+2ndujX169enYcOGDBs2jNjYWBo1akSZMmUIDQ2lXr16nDx5kgkTJlC3bl3Kly9P\n5cqViY2N5dtvv83X+cfnmM/ycmYqCRa5zQBysZkqtmzZwi233EKDBg1o3Lgx58+f9+icmT/XuHFj\nOnbsyB/O6duOHz9O69atKV26NP/617+8WNJCNHeue7tjR79JYB671EAy5x3Qh1hJ6zHgb0BFT36u\noB4E62DnrVtFihSRFZmDE+fOtTuiQrdixYoCP+eBAwckKSlJRKzZJWrXri1bt26VIUOGyOjRo6Vq\n1aoydOhQefDBB6Vt27Yyfvx46dOnjxw5ckQOHz4sN9xww2WdXyT/M5V4o/y+LOcMICtWrMhzpoq0\ntDRp1KiR/PjjjyIicvz48VxnAMltVpEbb7xRVq1aJSIi06dPl+HDh4uIyJkzZ2T16tUyefJkeeyx\nx7xXUA9d8fU/d06kYkX3AOelSwskrsLClQ52zuJ/wFVAB2ACMNkY83hBJ1SVw1NPQVqatX3bbdBJ\nF9MuCFWqVHH1mCtVqhT16tVj//79LFiwgKioKGrWrMnjjz/Ol19+ydChQ9m2bRutW7emYsWKVKpU\niXLlyrFhw4Z8nT9zUG/m4G+VuxYtWlC+fPlsxxYsWECvXr0A6NWrF/Pnzwfg66+/pnHjxq55MsuX\nL59rR5Hczvnbb7/RokULANq0acOnn34KQIkSJbjlllsoXrx4wRbMLosWwdGj1nZ4OLQKvNFSHiUx\nEVkBvAoMB94FmgCPeDEutWSJa1xHvDHw738HVI8iT3m7UX/Pnj1s2rSJZs2acejQIb7++mu6d+9O\nlSpVOHv2LCtXrmTRokUMGjSItWvXsnv3bjZu3JhtvJMn57/ppptYuHChxzOVZArmTg1glf/w4cO5\nzlSR2QX9zjvvpEmTJvn6clC/fn0WLlwIwOzZs7NNUuxLrvj6O7vkA/DQQxAaemXn80GejhNbDqwG\nHgC2ATeKSF1vBhbU0tJg0CD3fp8+EBtrXzwB6o8//qBLly68/fbblCpVCmMMCxcupGvXrq7XpKSk\n8Ntvv9GmTRtuu+02Bg8eTPPmzQn14MMg6/lDQ0N57bXXdKaSApB5t5WWlsbq1av5+OOPWbVqFfPm\nzWPFihUenWPatGlMnDiRG2+8kTNnzlCsWDFvhmyPI0eyD3B23s0GGk+rE7cA54EGWGuLNTDG+Pea\n1r5s8mTYutXaLlUKh3PGg2Dkrbnz0tLS6NKlCz179nQNGi1ZsiQNGjSgYsWKHDx4kKuuuopOnToR\nGhrKzJkziYiIYOrUqaSkpFC7du18nX/nzp2umUqqV6/umqnkUvPfBePcgVk5HA7XTBVAtpkqwsPD\nue222yhfvjxXX301d999N4mJiR6dt3bt2ixZsoT169fz4IMPUrNmTa+V4Upc0fWfOdPdHHHLLdaa\ngwHI0+rEQSJyG9AJOIY1+PmENwMLWikp8MIL7v3nn4cKFeyLJ0D16dOH6OhoHn/c3bRbqlQpKlWq\nBFgzIrRo0YJvvvmG1NRUNm/ezIULF0hMTKRo0aLUrXvxioic52/QoEG+Zyrp27cvnTp1ytarbsiQ\nIdSrV4+YmBg6d+7MqVOnAJg5cyaxsbHExcURGxtLaGgoW7Zsuezfj53E3aELIM+ZKu644w5+/PFH\n/vzzT9LS0vj222+Jjo726JxHnGOmMjIyeOWVV3g465ykWX7Gr2WtSuzd264ovO9SPT+cF/KfwCfA\nDmAZVpf71p78bEE8CKbeiY8/7u5JVL26SGqq3REFnO+++05CQkKkcePGEhMTI7GxsTJv3jypUKGC\nxMfHS+3ataVt27Zy+PBh+fvf/y61a9eW4sWLS1RUlLRt21aSk5Pzff7Fixdne0316tUv2Tsxt151\nS5culfT0dBEReeaZZ2To0KF/+bkff/xRrr/+ek9/HT6lW7duUrVqVSlWrJhERETItGnT5Pjx43L7\n7be7rktKSorr9R999JHUr19fGjZsmOvvIq9zvv3221K7dm2pU6eOPPvss9leHxUVJddcc42ULl1a\nIiIiXD1L/UpSkvtz5KqrRE6csDuiy4IHvRM9Hez8FLAK2CgiaV7Kpxd7f/EkTr+3bZs1E0dmFcDc\nudC5s70xKVvt3buX9u3b53pXNX/+fD799FM++OCDbMeff/55QkJCGDlyZGGFqXzNoEFWZzCA7t3h\no4/sjecyFdhgZxF5Q0TW2pHAgsrw4bl2qQ/mdpFgLjvADz/8kOdz06ZN46677vrL8U8++YRu3bp5\nM6xCE+zX/7LKf/48fPihez+QqxLxvGOH8rZNm2DOHPf+uHFB2aU+N7nNuLB+/XqaNm1KbGwsTZs2\ndY3bOnfuHN27d6dRo0bUr1+f0aNH2xW2V7366qsULVqU7t27Zzu+bt06SpYsmWfbUEHLeW0yMjII\nCwujdOnSxMTEEB0dzbXXXktcXBxxcXH85z//uegMG7ld6xdeeIHGjRsTExNDmzZtXN3hA3J2jYKw\ncCEcPUpfICwkhEZPPul6Kq/ZT/z6d3mp+kZfeBAMbWLt27vrsO+91+5ofEpubUPx8fGyZMkSERFZ\ntGiRxMfHi4jIjBkzpFu3biIicvbsWYmKipK9e/cWftAFZM+ePdnKLWLNMHHLLbfIn3/++ZfXDxo0\nSEaNGlVY4f3l2rz55pvSunVrueeee0REpHnz5tKqVSsR8WyGjdyu9enTp13b48ePl759+4qI782u\n4TNatBABWQWS1L9/tt9lXrOf+OrvkgKcsUN509q18Pnn1rYx1nyJyiW3GReqVq3q+hZ54sQJ1+KK\nVapU4cyZM6Snp3P27FmKFy9OmTJlCj3mgiLuL3IAfPXVV4wdO5aFCxf+ZVYJEWH27Nk8+OCDhRZf\n1muzf/9+Fi1axPDhw11jucLDw13XyZMZNnK71qVKlXJtnzlzhooVKwIBOLtGQUhMhO++A6BFkSKU\n79cv29N5zX7iz79LTWK+IGuX+gce+MuCdcHcLpBX2UePHs3gwYOJjIxkyJAhjBo1CrC6XZcpU4aq\nVasSFRXFU089Rbly5Qox4oLTvXt3mjRpwvbt24mMjGT69Ok89thj/PHHH7Rt25a4uDgGDhzoev3K\nlSuJjIwkKirKlngzp9TKmpiSkpJITk4mJiaGESNGcP78+XzNsJF5/YcNG0ZkZCQzZszg2Wef9VYR\nfE6+/+9PmODe7toVnDOdZMpr9hN/pknMbitXwtdfW9shIfDSS7aG4y/69u3LhAkTSE5O5q233qJP\nnz4AfPjhh6SmprrGZL3xxhvs2bOnUOLxdKb0Cxcu0KdPHxo1anTRWfFnzpzJ3LlzOXfuHMuWLWP8\n+ESFiCEAACAASURBVPGULl2aChUqsHPnTnr37k1CQoKrbfDpp5/+y4z5l5KRkUFsbCwdOnQAYO7c\nuTRo0IDQ0FCPBw4DnD59mrCwMGJiYlx3jq+++iq1atXi8OHDbNq0iVKlSrFo0aLLmmHjlVdeITk5\nmYSEBJ544ol8lTFoHD5sDXDO5EHb1qUWJfULl6pv9IUHgdomlpEhcuut7raw3r3tjshn5WwbKl26\ndLbny5YtKyIijzzyiHz44Yeu43369JE5c+Z4Pb78zJQ+ceJE6dOnj4iIR7Pi55Seni5Vq1aV5OTk\nPNsGPfXmm29Kjx49pH379iIi8uuvv8r27dulVatWsnHjRo/OsWfPHqlUqZJERERI9erVpUqVKlKs\nWDGpVKlStna7CRMmSPny5V37I0eOlDfeeCPX8+VsB8yUnJwsDRo0yHZsxowZPtWOY5uRI92fJU2b\nishff5d169aVgwcPioi12kLdunWzncLXfpdom5iPW7bMWrAOrBWbs1YrqmzE/YUGgFq1arnuYJYv\nX06tWrUAqFu3LsuXLwes9pM1a9ZccnaNguDJTOmfOZeI/+WXX2jdujXAX2fFX7AAMjJyf5OMDFiw\ngGXLllGzZk0iIiLybBv0RGYbVr8s7SZ16tShVq1a2X7XlyIihIWFkZyczK5duxg0aBDFihVj69at\npKSkuF536tQpjDGXnGEj57XesWOHa3v+/PmuFQJy/kxQO38eJk1y7zvvwnL+LvOa/SQrv/tdXirL\n+cKDQLwTy8iwvi1lfnN6+OE8Xxpsa0pltWLFilxnXNiwYYM0bdpUYmJipFmzZpKYmCgiIn/++af0\n6NFDGjRoIPXr15dx48YVWqw5v/U2b95cFixYICIi48aNkzJlyoiIyJQpU+T++++XtLQ02bVrl5Qr\nV04+++wzkRdftP4WEhJEnLNyuK59erp1HKRPTIxMnDhRRET27t0r4eHhEhERIeHh4ZecTSSrLl26\nSFJSkjgcDtedWKb4+HiP7sRyuzbVqlWTq6++WmJjY6VChQpSoUIFady4sXTs2FEmTZp00Rk2cp5v\nyJAh0rlzZ2nQoIHExMRIp06d5NChQ67XB8TsGhfh8f/9mTPdnyVVqoicO5fv2U988XeJB3divpCg\n7gR+BbYDz+TxGm/8fuy1cKH7j654cZF9+/J8abAnMX+RM4lt27ZN2rVrJ02aNJGXX35ZKlasKCJW\nV/NBgwZJbGys3HvvvfK3v/1NFjz3nPvvIUsiW7FiRbYEdh6kIsiR998XEZE2bdrIvHnzRERkzpw5\n0qZNG49i/eKLL+TRRx8VEet3nNklPpOnSczb/On6e4PH5W/WzP23M2KEV2MqTD6fxLA6luwArgOK\nApuAurm8zju/IbtkZGT/o3viCbsjUgXgYm0527dvl5tuuinX52655RbZ+vPPrkSVLZFduJDt+AKQ\nO6pVc92p5WwbzLzbu5Rnn302WxtWyZIlpWfPnq7nfSWJKQ+sXev+mylaVMTZ5hUI/CGJNQMWZ9kf\nmtvdWMAlsVWr3H90xYqJ/N//2R2RukJ9+vSRa665RooXL+7ar1ChgpQqVUpq1aolVatWlb59+0r9\n+vUFkDp16kijRo2kVq1a0rhxY+skWe648no8WL26zJg2zfW+cXFx4nA4RERk2bJl0qRJk3zHnld1\n4oYNGy7zt6EKVefO7r+RLF9EAoEnSczujh3VgKxL5O53HgtsWcfH/P3vULXqRV+u48R831dffcXx\n48c5d+4ckZGRVK5cmeuvv57U1FROnDjBgQMHOH/+PPPmzaNRo0acOXOG1NRUdu7cyc6dO62ThITA\n1KmQkOA6ryPLe5zt2ZNlp0/TqUsX17HJkyczZMgQYmNjGTZsGFOmTLmicsyfP5+IiAjWrFnDPffc\nk+vcjIXJX66/t1yy/D//DJ9+6t4fPNir8fiiInYH4KnevXu7BnGWK1eOmJgY19LdmRfaL/a3bsXh\nXBY9HuCppy7585s2bfKd+HU/1/2hQ4dSs2ZNOnfuzPvvvw9Yy95HRUVRoUIFjDH88MMP1KpVi5CQ\nEIYPH87SpUuJjY1lgbPHYZs2bSAkBEePHjB9uvX3gTuRxU+bxpEiRbK9f5MmTRgzZswVxS8iDHZ+\n+N17772uweG+9PvV/Tz2X3vN/fdxzz0QE+Nb8eVz3+FwuHpPejpo36OlWLzFGNMMeElE7nTuD8W6\nfRyT43ViZ5wFql8/+N//rO327a3JOlVAWL16NW3atCE1NRWwvmyJCN999x0dOnQgJSWFEydO0KpV\nK9q3b8+hQ4fYs2cPmzZtYtu2bdZJMjKsv5Hp0//6BgkJ1p1aiN0VKMon/PYb1K3rHpKxdi00bWpv\nTAWswJZi8aL1wPXGmOuMMcWAB4HA/VQ/cACyrv00ZIh9sSivu3DhAkWLFqWhcxqxzNkR0tPTef/9\n9+natSvLli2ja9eu1g9cLIGBdbxfv7zHkangMmqU+2+hXbuAS2CesjWJiUg61qrRXwM/A7NEZKud\nMXnV+PHWoESAZs2geXOPfizzdjsY+WvZU1NTSU9Pp0KFCoCVuCpVqgTAnj17+Nvf/kaPHj3o1KmT\nNUg6twSWkIBj2bJsbWS+lshym24rr6mrLmeZHH+9/gUlz/Lv2ZP9C/GwYYURjk+y+04MEflKROqI\nSC0RCczFnwBOn4b//Me9P2SIrhcWYMTdm5adO3cSEhLCrl27qF69Or///juHDh3i8OHDnDx5krFj\nx3Ly5Enmzp3LqFGjmPTII39JYEydCqGhf+nswfTp7lUPbJaQkMCSJUuyHWvYsCHz5s2jZcuW2Y7P\nmjULsOaU3LBhA5MnTyY5ObnQYg0oY8a4F9Bt2RJuvdXeeOx0qe6LvvAgELrYjxvn7gZbq5ZIWprd\nEakC1K1bN6lUqZIYYyQiIkJuuukmCQsLE2OMFClSRIoWLSqTJ0+W8PBw+f/2zjM8qmprwO+ZNAIh\n9CQYEjoJKaQA0lQi0hUQRcCoSFG8YkO6ylVRr0ZUrOCH3ktRmqgIKEVpQZDeRLqAEEABqdJT2N+P\nkykJKZOQmTOTWe/z5OHsM2f2WWv2MOvsvdZey9vbW2mapgIDA1VISIgKDQ1Vf//9d54ZOyzYht+/\n8ooRKuZLfvvjknLtNVu8eLHq2rWryszMVKdOnVIRERE5MkYIdnL0qL41x/x7snSp0RI5DNwgxN4z\nyMiA99+3tocN05+whVKFt7c3Pj4+ADzxxBMcP36c69evk5GRQY0aNejRowdHjhwhIyOD69evc/78\nef71r38xZMgQvUbWq6/C3Ll5B2+YssPv585120oHpalMjqGMHZvTLZGdh9NTESPmDL7/HrJLqhMU\nBH36FOntnuwXSE1NLZLfBawlUGJiYoiLiyPd/B/egYwdO5bIyEjq1atHhQoVuHDhAmAtB+/j48OD\nDz5oSdY7Y8YMS3j9l19+iZeXF9u3b4du3XIYsBxjbzLpr7sp06dPL3KZHE/+7kMe+p84AbZ7Af/9\nb493S4gRcwYTJ1qPH38cypQxThY3pCh+l6ysLB555BE+++wzduzYQWpqqmV25Ei8vb0ZN24cO3fu\nZO3atYwfP549e/aQkpJC27Zt2bt3L23atLEU70xOTmbr1q1s2bKFL7/8kjp16uQw0qWRX375he7d\nu2MymahWrRqtWrWyZu8X7OP11+HqVf24cWMweDO6KyBGzNEcPGgteqlpuhErIuZNgZ5IUlJSnmVO\n8isZ8tNPPxEXF0dMTAwAlSpVckrhv5CQEEuJkICAABo2bMjRo0fzLQdvy8yZM+ndu3ee/brD2Cur\n7zrP18wUp0yOO+jvSHLo//vvOR+IX33V42dhIEbM8Xz+ufW4Y0eoWdM4WTyAffv2AdCxY0eaNGnC\nO7YpvpyEeQNz8+bNOXHiRKHl4L/66isefPBBZ4tZIiQnJ9OyZUv27dtHeHg4kydPzjd11RNPPEF6\nejqxsbE0a9aMAQMGWB42BDt46SVrROIdd8Dddxsrj6tQWOSHK/zhrtGJ164pFRRkjSKaO7dY3Xhy\nOQqz7rYRcOfOnVM9evRQkZGRqmzZsmrKlClqw4YNqmnTpuqWW25Rfn5+atmyZery5cuqRYsWavny\n5U6T98KFC6px48ZqbvZY21YyVkqpypUr52ivX79eNWrUKN/+PHnslRL9LfrbZqoHpdatM1QuZ4FE\nJxrM3LlgfvIODZUnpxLiueeeo3PnzuzevZumTZtSq1YtRowYwRtvvMG4ceO4/fbbef311/H396dz\n5843BH44iszMTHr06MEjjzxiqZgbHBzMiRMnADh+/DhBQUE53jNr1iy3nYUJTkKpnNl9evSAZs2M\nk8fFECPmSGzXrx97DLyLl2/Zk/0CtklqlVL8888/rFq1in7Zm381TSMgIIDq1atz/vx5OnTowIED\nBwgJCSEzM5OVK1cSFRVV4D0+/PBDYmNjiY2N5aOPPgJgw4YN3HrrrSQkJHDrrbfaFYDQv39/oqKi\neO655yznCioHr5Ri9uzZ+frDbPX3VET/JFi4EFau1E94e8Obbxoqk8tR2FTNFf5wx+XEffusU3+T\nqcDKzULB2JZZDwkJUbVr11Z33nmn8vHxUV5eXio4OFi1bt1a1ahRQ4WFhanKlSurBg0aqNjYWDVq\n1KgC+96xY4eKjY1VV69eVZmZmapdu3Zq//79KikpSf34449KKaUWLlyokpKSCuxn9erVymQyqbi4\nOBUfH68SEhLUokWL1OnTp/MtB5+amqpatGhx8x+QUHrJzFQqOtr6WzJokNESORXsWE50m1Isboft\nXo6774YaNYrdVWpqqsc+kaampjJjxgxLe/PmzTRv3pzZs2fTpEkTnn/+ecqXL8/atWv5+OOPuffe\ne/nmm2+YOHEiS5YsKbT/3bt306xZM/z8/AC44447mDNnDtWrV+fcuXMAnDt3jtDQgsvctWrViqys\nrDxfW7p0aZ7nW7duzZo1awrs15PHHkT/1BdeIGnnTr0REAAvv2ysQC6ILCc6gvR0yF5CAuCJJwwT\npbRRo0YNwsLCaNKkCQD3338/W7ZsYcOGDdx7770A9OjRgw0bNtjVX0xMDKtWreLs2bNcvnyZhQsX\ncvToUVJSUhg6dCjh4eGMGDHCsr9LEJzG5cs582kOHw7Zka6CFTFijuDHH+HUKf04LEwPrb8J3O1J\nNK8MGy+//DJxcXHEx8fTtm1bjpozmGSTlpZG+fLlGTduXI7zuXUPDg4mLCzMEkq/bNkyoqOjqVev\nHiuz/QbLli2jQYMGdskaGRnJyJEjadeuHZ07dyYhIQGTycSAAQP4+OOPSUtL4/3336d///5F/RhK\nhJIc+969e+Pr60uZMmUs/r/hw4fj5+eHt7c35cuXJzg42LLPzmQyUbZsWWJiYvD19b1hbJyBu333\nS5QPPyTJ/DsSHFykqs1Hjx6lTZs2REdH5/D1mjPIRERE0KFDB0sGmcOHD1O2bFkSExNJTExk0KBB\nJa6OwyhsvdEV/nA3n9iDD1rXsEeONFoap7Nq1Sq1devWHElhL1y4YDn+6KOP1IABA3K8p0ePHqpn\nz57qvffeK7T/bdu2qSZNmqi4uDjVvXt3de7cObVx40Z16623qvj4eNW8eXO1ZcuWYsn+4osvqgkT\nJqjAwMAc53O33ZG5c+eqWbNmqdjYWHXhwgXVoEED1atXL9WwYUPVsGFDNXLkSJWUlKRGjhypDh06\npKpWrapef/31Io2NUEIcOaJUuXLW35FPPy3S2//66y+1detWpZSyjPXu3bvViBEj1Ntvv62UUiol\nJUWNzP59yi+Js9EgIfYGcOkSzJtnbZdA+LS75Y/LK8NGQECA5fjSpUt6wtts5s2bR506dYiOjr6h\nr7x0j4uLY+PGjWzbto05c+ZQoUIFmjRpwvr169m6dStr164lISHBbnn//vtvQJ8Nfvfddzz00EPF\nntmVNCU59t26daN58+aAPh61atVi3759XLx4kbCwMJo3b06VKlUsWUXOnz9P1apV8x0bZ+Bu3/0S\nY+hQuHSJVICYGBgwoEhvL04GGd1muB8S2FHS/PCDvpYNeunwUp4PryiMHj2aL774grJly7J+/XpA\nN2hjx45lyZIlhmTXAN2vdubMGXx8fJgwYQKBgYFMnDiRp556ivT0dMqUKcNntoE6pYBDhw6xevVq\nlixZQocOHfDz82PSpEn07t2bZcuWsWHDBjIzMxk2bBiJiYnUr1/fMEPmcSxbBrNnW9vjx8NN5P+0\nN4PMoUOHSExMpEKFCrz++uvcdtttxb6nUylsquYKf7jTcuK991qXAMaMMVoawyhoeSIlJUX17dtX\nKaXUsGHD1Ndff62UUurVV19V7777rtNk9EQOHTqkoqKiVL169VSnTp2UUkqVL19eRUREqPvuu08p\npWcVGThwoLrtttvU119/rTZv3qwCAwPVf/7zHyNF9wyuXVMqMtL6G/LQQzfVnb0ZZK5du6bOnDmj\nlFJq8+bNKiwsLIcLwCiwYznRcANlz5/bGLGzZ3MWq9u712iJDKMgI5aWlqZiYmKUUkrdfvvtqnbt\n2qp27dqqYsWKqkqVKmr8+PHOFNWj2L9/vwoICFBt27ZVYWFhqnbt2spkMilN01RycrL666+/VGRk\npAoODlbNmjWzjI23t7eqUKGCjI2jGTvW+vtRvrxSf/5Z7K4yMjJUhw4d1AcffGA5FxkZqY4fP66U\nUpaxzovcBU2Nwh4jJj6xkuS776zF6hIToYT8KO7oF1DWBxAA9u/fbzmeO3euZb3+559/5uDBgxw8\neJDBgwfz4osv5oiMchfd84rI3LhxY55ZP86cOUObNm0oX748zz77bIH9lrT+5mjEJUuWkJaWxoQJ\nEwgICKBevXpMnz6dqVOnEhsbS926dVmzZg0HDx5k6dKllC1bluHDhzs9as1dxr9EOHoUxoyxtseM\nIXXv3mJ3V5QMMqdOneL69esAHDx4kP3791OnTp1i39uZiE+sJJk1y3rswfnwkpOTSU1N5fTp04SH\nhzNmzBgWLFjA3r178fb2pk6dOnz66adGi1mi9OvXj2eeeYY+NgVPzfkc27dvz6JFixg+fDgrVqyg\nTJkyvPHGG+zYsYMdO3Y4TcZ27dqxdOlSNE3D19eX6tWrk5GRgZ+fHwcPHqRMmTJUq1aN22+/ndjY\nWBo1aoSvry8mk4kuXbrg7+/vNFk9kmHD9MAwgOhoePpp+OWXYnX1yy+/MH36dGJjY0lISEDTNN58\n801GjhxJz549mTRpEjVr1mR2tu/t559/5uWXX7aM98SJE92m6rZm+7TsqmiaplxezpMn4ZZbwJy1\n4fBhCA83VibBqRw+fJguXbroFZrRjXn37t154IEHmDlzJgsWLGDatGmW66dOncrmzZste3gED2bZ\nMmjb1tpOTYVcBV89EU3TUEoVWDRNZmIlxbffWg3YbbeJARNISUmhVatWDB06FKVUoSmmBA8lPR2e\necbaTk4WA1YExCdWUvzwg/W4Z88S7dqj/AK5cGfdbzbrR4MGDTCZTPj7+1syMFSrVg0fHx98fHwI\nCAigSZMmlkwoYWFhlClTBj8/P+rUqUO62T+bR39mRowYQXBwMGXKlKFChQo8//zzAFy+fJkGDRrg\n7+9P2bJl+fDDD2/+A7GD3Jkmnsn+cc8v0wTA9u3badmyJTExMcTFxd2gt8vz/vuwe7d+XL482Gw1\ncefvv7MQI1YSXLkCK1ZY21I3TADWr19frHyOZgYPHszo0aMB8Pb2Zty4cXzxxRfccccd1K5dm8GD\nB1O3bl1+/fVXpk2bxvHjx+nYsSN7s4MBvHOV/hk8eDAzZ87Mcc4cjHLx4kWefPJJi3PfbHCvXLnC\n5s2befHFF4v+ARQDs547d+5k7dq1zJs3jz179pCSkkLbtm3Zu3cvbdq0seSyzMrK4pFHHuGzzz5j\nx44dpKam4nMTe6qczp498Mor1varr+puCcFuxIiVBCtX6oYM9A3OJRzV48n549xJ99wRmfXr1y80\n60dBvt5BgwbRoUMHwJqBYcqUKbz00ktERUVx/PhxateuDcB7771HUFAQkZGR1KpVi4iICDZu3HhD\nfzVyVVPYsGEDL7zwAt7e3jRv3pwzZ84AsGvXLtpm+2gaNmyIn58fX3zxRVE/kiKTO9NEYmJigZkm\nfvrpJ0uuR4BKlSqhaQW6UFyHrCzo3x+uXdPbiYk5lxVxr++/UYhPrCRYuNB63LmzcXIIhpFXROZn\nn33GoEGD8sz6Ubt2bS5cuEB6ejrz5s3jp59+IjIystD77Nu3j1GjRrFx40b8/f1ZtGgRo0ePZsaM\nGXh5ebFp0yaaNGmCyWTi2LFjdvX3888/8+KLL7J//34GDx4MQHx8PD/88AMffPAB69at49y5c+w0\nlwRxEvZkmjAngu7YsSOnTp2iV69eDB8+3KlyFptPPoG1a/Vjb289Y707zSJdBDFiN4tSsGCBte0A\nI+bJNZXcRXfbmme2mNNr5eaPP/6wq98tW7bkaKenp/Pnn38yd+5clixZwj333MOFCxdITU1l27Zt\nBAUF8f3331OrVi1+++037rvvvgL7z8zM5OzZs3Tp0oWlS5cyadIkRo8ezX//+19atGhBxYoVqVix\nItWqVbthedKRXLx4kR49evDYY48REBBww+zK3M7MzOSXX35h06ZNlClThrvuuosmTZpw5513Ok3W\nYnHgALzwgrX90kt5pqhzl++/kchy4s3y++9w8KB+HBCgRyYKggPIzMzk5MmT9OzZk27dujFy5EjS\n09Mts786derw22+/4e/vT2BgIKdPny60z7CwMPz9/Vm4cCGLFy/GZDJx+vRpfH192bx5M5cvX+bP\nP//kypUrtGrVygla6nr26NGDRx55xJK/Lzg4mBMnTgBw/PhxgoKCAL2+3B133EGlSpXw9/enc+fO\nNxh+l+P6dXjsMasLIjYWnORzLI2IEbtZbJcS77oLsisElySe/CTmyboDJCQkWPxm/fv3p0GDBlSu\nXBmAzz77DC8vL6pUqcKzzz7Lnj17iIqK4vfff+fYsWN0zKOOXW6/Xb169fjf//7H/PnzOXz4MBkZ\nGVSpUoUzZ85wKruWVUpKCiaTic5OWiq3zTRhHv/8Mk106NCB3377jatXr5KZmcnKlSuJiopyipzF\nZuJEfR8YgJeXvozo65vnpZ7+/beLwvJSucIfrpw7sV07a66ziRONlkYoRdSsWVOZTCYFWP4NDAy0\n5DosV66cat68uYqJiVHx8fEqNDRU+fj4KD8/P9WrV68C+/Py8lL9+vVTdevWVWXLllVlypRR/v7+\nqlu3bkoppVavXq18fX2Vn5+fqly5slq3bp1TdF69erUymUwqLi5OxcfHq4SEBLVo0SJ1+vRpdddd\nd6kGDRqodu3aqbNnz1reM336dBUdHa1iY2PVqFGjnCJnsTl0SKmAAOtvxgsvGC2RS4MkAHYwFy7k\nTPibluaQ26xYscIh/boDjtK9f//+KigoKEeS4jNnzqh27dqpBg0aqPbt26tz584ppfRkxv7+/ioh\nIUElJCSoJ5980iEy5YUnj71SpUz/69eVat/e+nsRGanUlSsFvqVU6V8M7DFispx4M/z8szXhb2ws\nhIUZK49gN/369ePHH3/McS6/vUigL7tt2bKFLVu2MGHCBGeLK5QGJk+Gn37SjzUNJk2CMmWMlak0\nUJiVc4U/XHUm9sIL1qeqwYONlqbUUr9+faVpmipTpozl3Ndff61CQkIUoOrWrWsps/7tt9+q8uXL\nK5PJpIKCgtTy5cvz7Td3uZiIiIgcZSoiIiIs15lLx9jD1atX1a233qri4+NVVFSUeiF7ySi/mZ6z\nyGv2qZRSH330kYqMjFQxMTGWz3H69OmW5bz4+HhlMpnUr7/+6lR5SxUHDyoVGGj9vRgyxGiJ3AJk\nOdHB3HGH9UuZXdhRKHnGjx+vZs2alcOITZ06VbVq1Uq1bt1abd68Wf39999KKaXWrl2r5s+fryZO\nnKiSk5NVaGhovv3mNmK5Cwaa24cOHVIBAQEqISFBJSUlqVWrVhUq86VLl5RSSmVmZqpmzZqp1atX\nqxEjRqi3335bKaUXBjUbDGexatUqtXXr1hw6r1ixQrVr105lZGQopZTlc7Tlt99+U/Xq1XOanKWO\njAylWrSw/lbUq6dU9vdDKBh7jJgsJxaXjAywTSPUsqXDbuXJ+dNSU1PzzDSxYMECXnvtNct+oapV\nqwLQvHlzunTpgp+fH1WqVOHq1atkZGQU697mvqtXr05aWhpbtmzhvffeIzk5mYsXLxb43rJlywJw\n7do1rl+/TqVKlfLNOlEQJTn2t912G5UqVcpx7tNPP2XUqFGWPWDmz9GWmTNn0rt37xKToyiUiu/+\n66/n3NQ8fTpkfz8Ko1To72DEiBWXrVvh6lX9uFYtyXfmZMyZJjZv3szAgQMtBSdt2b9/P4mJiXbn\n0stvL5Kvr6/lxz8xMZG6detaMkXkx/Xr10lISCAkJISkpCSioqLyzTphJObPsXnz5tx55515fo5f\nffUVD3pwfbybYtUqeOMNa/u11+DWW42TpxQiRqy42JbVcPAmUE/eK5Kf7uZME40bN+a5556jZ67K\nAceOHWPNmjU5Uj3lRlmXq4GSrXprMpnYunUrR48eZdWqVaSmpuabdaIgHD325s9x3bp1jB079obP\nccOGDZQrV86wvVdu/d0/dw4efljf3AyQlAQjRhSpC7fW30mIESsuthVXnZTJQLASFhZmSakUHR1t\nyTQBejmPjz/+mPbt21OrVq0835+cnEzLli3Zt28f4eHhTJ48mVGjRrFkyRIiIiJYtmwZo0aNAvSq\nt40aNSIxMZGePXsWqeptYGAgnTt3ZtOmTfnO9IzE9nNs2rRpjs8RYNasWTILKw5KwRNPQFqa3q5U\nCb78Ut/cLJQokjuxOCiV04g50B8Gnp0/zax77lnTvffey/LlywE9Uaw508S5c+e45557eOCBHnBQ\nhQAAIABJREFUB3Jcn5v8ch0uXbr0hnP33XdfoTkIbTl16hTPP/88P/30E9WqVaNy5cq88sorNG/e\nnFtvvZWKFSuSkZFBp06dCu2rpMc+v8+xdevW7Nu3z/I5mq+dPXs2q1evLrH7FxW3/e5PnQqzZ1vb\n//0v5PLr2oPb6u9EZCZWHA4fhr/+0o8DAyG7DITgGGrVqkXr1q25du0a3t7e9O/fnypVqvDuu++y\ncuVKevXqRUhICADjx49n+/btTJgwgQkTJuDr68tas1PdSfz111+sX7+eSpUqceDAAbp27cpdd93F\nr7/+SrVq1bh69Somk8mpCXUh79ln//79OXjwILGxsSQnJ+cot/Lzzz8THh6e72xWyIf9++Hpp63t\nxx+HIjwECUVDK+hp1VXQNE25lJzTp+tr3QDt20OuTbOCAHD48GG6dOnC9u3bAb3W1dmzZwF9ybND\nhw5OL28iOJj0dN29YA6QiYiAzZuhXDlj5XJTNE1DKVWg81hmYsXBNkt28+bGySG4FdHR0cyfPx+A\n2bNnc/ToUYMlEkqcf//basB8fGDmTDFgDkaMWHGwfXrOowZQXly7do1mzZqRkJBAdHS0pdz7mDFj\nqFGjBomJiSQmJrJ48eIb3mu7V2TAgAGWkvK5ee+99zCZTJbqvBkZGfTv359GjRqRkJBgqTLsTjhq\nn0xen2N+Y3Ht2jWSk5Np1KgR0dHRpKSkFOleb731FtHR0fz999888cQTNGnShEuXLuGbT+ZyWzx9\nn5Bb6T93Lowda22/9RYkJNxUl26lv0FIYEdxsDVi0dF2vcXPz48VK1ZQtmxZsrKyaNWqFb9kB4cM\nGTKEIUOG2NVPv379eOaZZ+jTp0+O80ePHmXJkiXUrFnTcu7zzz9H0zS2b9/O33//TadOnfLcB+SJ\n5Pc55jUWs2bNAmD79u1cuXKFqKgokpOTCQ8PL/Q+GRkZfP755+zZswdfX1969erF3XffTYsWLVhg\nW0xVcG9+/x2yN7ID0KkTPP+8cfJ4EDITKyrnz4N5GcjXF+rVs/uteWVxAAqMooOce0XyyroA8Pzz\nz/POO+/kOLdr1y7atGkDQLVq1ahYsaLbGTFHRWbl9znmNRYhISFcunSJrKwsLl++jJ+fH4GBgYXe\nQymFpmn4+vpy6dIl/vrrLy5fvkxISAhvvPEG//rXvwrtw9Mj09xC/0uX9MCNf/7R27VqwbRpYLr5\nn1e30N9gxIgVlV27rMcREXoaGTvJK4sDwCeffEJ8fDyPPfYY58+fL7JI8+fPJywsjNjY2Bzn4+Li\nmD9/PllZWfzxxx9s3ryZI0eOFLl/T8J2LM6dOwfohRcDAwOpXr06tWrVYtiwYYXuEzNHAh44cICT\nJ09SvXp1GjRowMqVK3n22WcJDQ2lb9++TtBIcChKwcCBsGOH3vbzg2+/hezCpYLjESNWVGyXEouY\nxcA2i8PPP//MypUrGTRoEAcPHmTbtm2EhITkuaxY0Lr4lStXePPNNxkzZozlnHk20b9/f0JDQ2na\ntClDhgyhVatWeLnZZktn+gRyj8XQoUMBmDZtGleuXOH48eMcPHiQd999l0OHDhXYV2xsLJUqVaJ2\n7dqWh4jOnTtjMpm4du0aM2fOJDExsVCZPN0n4vL6jx8PtnsOJ0wAO8bVXlxefxdAfGJFpRj+sNwE\nBgZy9913s2nTJlq3bm05//jjj9OlS5ci9XXgwAEOHTpEXFwcSimOHj1K48aN2bBhA0FBQYwbN85y\nbatWrWjQoEGxZPYEqlWrZjm2HYs1a9bQvXt3TCYT1apVo1WrVmzatCnf/VOHDx+2+MHmzp1ryQTy\n1Vdf8eWXX7J+/XrKlCljd9YPwUVZsyan3+uxx6B/f+Pk8VBkJlZUimDEbCPgTp06xfnz5/nmm2+I\njo7m5Zdfply5chw/fhzQAwB69uxJWlraDZGEudfFbbMuxMTEWGYIf/zxBzVq1GDr1q0EBQVx5coV\nLl++DMCSJUvw8fEhMjKyBD4E5+FIn0Du7BXmsQCYM2cOMdmb2CMjI1m2bBkAly5dYt26dQV+joGB\ngRY/WN26dTl16hRVq1ZFKcWyZcto2LAhs2fPtiudk6f7RFxW/xMn4IEHIDNTbzduDB9/XOK3cVn9\nXYnCarW4wh+uVE/sllusdYH27CnwUtv6Tdu3b1cJCQkqMjJSRUREqLp166rNmzerRx55RMXGxqrQ\n0FAVHh6ujh8/rk6ePKkaN26cZ58PPvigql69uvL19VVhYWFq0qRJOV6vXbu2On36tFJKr4MVERGh\noqKiVLt27VRaWlrJfAalgLw+R/NYxMXFqW7dulkKZF69elU99NBDKiYmRkVHR6v33nuv0P4/++wz\nFRAQoIKCglRiYqKKiopSsbGxqk+fPmr58uWqadOmjlZRcBQZGUolJVl/BypXVuqPP4yWqlSCFMUs\nYc6ft35xfX31L3Mh5C68aCYpKUlt3rzZ0n7qqafUtGnTLO277rpLbdy4USmlFy70VNxR9wMHDqiG\nDRuq06dPq8zMTHXvvfeq6dOnW15/8skn1bhx4+zqyx31L0lcUv/hw62/A5qm1OLFDruVS+rvROwx\nYrKcWBSOHbMeh4UVKTKxMCSSsPSwadMmWrVqReXKlfHy8uK+++5jTXbpnqysLObMmUOvXr0MllIo\nFl9+CbZbWcaMgQ4djJNHECNWJGyNWGhoiXZdUCRhfuvi5kwQjRo14qGHHiI9PZ2zZ8/Svn17IiIi\n6NChQ5FD9nP3ee3aNV5++WXi4uKIj4+nbdu2Tk2X5I4+gYiICNatW8fVq1dz+MFA9002bNiQW+ws\nomrWP68MIyNGjKBhw4bEx8dz//338495n1IpwqXGf/VqPXjDzN13w0svOfSWLqW/iyJGrCjYGrES\nruTs5eXFuHHj2LJlC9999x1nz54tMJLQHAG3detWtm/fTmZmJjNnziQlJYW2bduyd+9e2rRpw1tv\nvWW3DHn1+dVXXzFixAh+/fVXtm3bRrdu3Xj11VdLQOPSS1xcHH369KFx48aWqNGBAwcCxa+S3K9f\nP37MlWi6ffv27Ny5k23btlG/fv0ijbVQRA4ehO7d9QS/oAd1zZhRIhuahZtDRqAo/Pmn9djOmZiy\n+vXyfM1MQZGEee0VsY2Ay8zM5MqVK4SGhjJv3jwezU5/8+ijjzJ37ly75Myrz8uXL3PLLbcQEBBg\nuebSpUtUrVrV7j5vFnfdJzN8+HB27tzJ9u3bmTp1Kj4+PgBMnjzZYtDswax/XhlG2rZtiyn7R7R5\n8+alMqGwS4z/+fNwzz1w6pTerlYNfvhBL8PkYFxCfxfHsH1imqb1AF4FGgJNlVJbCn6HC1DE5cTk\n5GRSU1M5ffo04eHhjBkzhkqVKvHMM89w6tQp7rnnHuLj41m0aBEnT56kQ4cOeHl5ERoaypdffllg\n35UqVWLo0KGEh4dTtmxZ2rdvT9u2bTlx4gTBwcGAni7p5MmTdquXX58Ao0eP5osvvqBs2bKsX7/e\n7j4F5zBp0iR69+5ttBilj8xM6NkTdu/W235+eqJfqbHmOhQW+eGoPyACqA8sBxILubZkQ16KS/fu\n1qikWbMMFSV3BFz37t3VtGnTVKVKlXJcV7ly5WL3mTuqTimlUlJSVN++fUtEB1fhyJEj6s4771RR\nUVEqJiZGffjhh0oppb7++msVHR2tTCZTjkhSo8gv0vWNN95Q9913nwESeQBPPWX9Pw9K5fr/IDgW\nXDk6USm1Vyn1O1BgwTOXwoGBHUUldwRc9+7dWbNmDcHBwZw4cQLQN+8GBQUVu0/bqDozycnJbpdE\nuDC8vb0ZN24cO3fuZO3atYwfP549e/YQGxvLd999lyOriqsxZcoUFi5cyAzb1EdCyfDJJ3paKTMv\nvwzJycbJI+SJ+MSKggMDOwoir3XxvCLgoqKi6Nq1K1OmTAFg6tSpdOvWze775BdVt3//fss1c+fO\nJT4+/mZVshtn+ARCQkIsOgUEBNCwYUOOHTtGREQE9evXz9en6Qxs9VfWlQkAFi9ezDvvvMP8+fPx\n8/MzQDrHY5hPaPFieO45a7tnT3jlFaeLIT6xwnGoT0zTtCVAsO0pQAEvKaW+L0pfffv2teSqq1ix\nIvHx8ZbwU/NAO7R9/TpJ2WmJUgH27yepTh2n3H/btm15vm6OgLt69Sr16tVj4MCBXLhwgXbt2jF+\n/HgiIyOZPXt2ke7Xp08fIiMj8fLy4vbbb2fgwIGWsPrAwEDq1KnDww8/TGpqqnM/fye1Dx06xLp1\n63jiiScwc+7cOTZt2mRJ2GuEfK+//jq7d+/m9OnTBAcH07dvX+bMmUN6ejotWrQA9ECPCRMmuNTn\n6ZbtyZPhqadIun5db0dGQv/+JGUH0RguXylup6amWh7C88tNmhvNyKdMAE3TVgBDVQGBHZqmKaPl\n5NIlMEfplSkDV64YK49Q4ly8eJGkpCT+/e9/55jB3nnnnbz33nt2ZZ0X3JwjR6BlS2vNwLAw2LAB\nQkKMlctD0TQNpVSBLidXWU50fb+YrdHy9zdODsEhZGZm0qNHDx555JEiLcEKpYjTp/XsG2YDVq4c\nfP+9GDAXxzAjpmnavZqmHQGaAz9omrbIKFnswtaIZVdodhbm6bYjyCsTRH5ZP65du0ZycjKNGjUi\nOjqalJQUh8llxpG629K/f3+ioqJ4ztYPYoNRKwHO0t9VcZr+ly7pGTjMofQ+PvDddxAX55z754On\nj789GBmdOFcpFaaU8ldKVVdKdTJKFrsopTOxvDJB5Jf1Y9asWQBs376dTZs2MXHiRNLS0pwuc0nz\nyy+/MH36dJYvX05CQgKJiYksXryYuXPnEhYWxrp167jnnnvo1Mm1v6JCMcnI0MuqmPc/ahp88QW0\na2esXIJ9FBaD7wp/uMI+sW3brHtF8tir487k3n8UERFhKUPy119/qYiICKWUUosXL1Zdu3ZVmZmZ\n6tSpUyoiIkKdPXvWEJkFoUTIylLq4Ydz7gX76COjpRKywZX3ibkd2SmhAKcvJzqbkydP5sj6Yd53\n1qFDBwIDA6levTq1atVi2LBhUp1YcF+UgmHDYNo067nRo+GZZ4yTSSgyYsTsxcDlRKPXxc35+aZN\nm8aVK1cslaTfffddDh065NB7G6270Yj+qY7rfOxYeP99a3vgQHjtNcfdrxh4+vjbgxgxeymlPrG8\nyC/rx5o1a+jevTsmk4lq1arRqlWrUpe9Q/AQJk2CUaOs7fvugwkTdH+Y4FaIEbOXq1etx2XKOPXW\n5k2BjkJZfY8AObJ+TJkyxRJyHhkZybJlywA9m/26dessmfYdhaN1d3VE/6SS73T+fHj8cdubwPTp\nkF2/z5Xw9PG3BzFi9pJdSgPQo5lKCcnJybRs2ZJ9+/YRHh7O5MmTGTVqFEuWLCEiIoLly5czKvuJ\n9YknniA9PZ3Y2FiaNWvGgAEDiImJMVgDQSgCixbpkYjZ2TiIj9ez0jv5wVQoOQzP2GEPLpGxY8kS\naN9eP77rLli61Gm3TrVJ8eRpeLLuIPqXqP4//QRdu8K1a3q7bl29WrMLb2b29PF3p4wdro+tH0xS\nTgmCe7FsGXTrZjVgtWrB8uUubcAE+xAjZi8GGjF3fhJ76623iI6Oxt/fnxo1anDt2jWeffZZAgIC\nKFOmDMHBwRw5ciTf97uL7nllPhkzZgw1atQgMTHRsoEaICMjg/79+9OoUSMSEhJYuXJlvv26i/6O\nokT0T02FLl2sfu3wcFixQv/XxfH08bcHMWL2IjOxInP48GE+//xz+vbty/33349Siq+++ooTJ04w\nevRorl69SsOGDenZs6fRot40eWU+ARgyZAhbtmxhy5YtdOzYEYDPP/8cTdPYvn07P/30E0OHDnW2\nuJ7DqlVwzz3W/7M1augzMKnMXGoQI2YvBhoxd90rEhgYiMlkYsGCBfTr14+srCxuueUWfv31V/r1\n6wfAo48+yq5du/Ltw110v+2226hUqdIN5/Py5e7atYs2bdoAUK1aNSpWrJjvVgV30d9R3JT+a9ZA\n5856XkTQawAuX677wtwETx9/exAjZi+2Rsw2e4eQL5UqVaJChQps3LiRBx54AG9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def standardize(x, mean, sd):\n", " \"\"\"Standardizes assuming x is normally distributed.\"\"\"\n", " return (x - mean)/sd\n", "def plot_standardized_males(ax=None):\n", " if ax == None:\n", " ax = plt.gca()\n", " gaussian_fit_male = calculate_2d_gaussian_confidence_region(mu_male, covariance_male, p = 0.95, points = 100) \n", " ax.set_title('standardized')\n", " ax.set_xlabel('height')\n", " ax.set_ylabel('weight')\n", " ax.plot(standardize(male_data.height, mu_male[0], np.sqrt(covariance_male[0,0])), \n", " standardize(male_data.weight, mu_male[1], np.sqrt(covariance_male[1,1])),\n", " \" \")\n", " for row in male_data.itertuples():\n", " ax.text(standardize(row.height, mu_male[0], np.sqrt(covariance_male[0,0])), \n", " standardize(row.weight, mu_male[1], np.sqrt(covariance_male[1,1])),\n", " row.Index, horizontalalignment='center', verticalalignment='center')\n", " ax.set_aspect('equal')\n", " ax.plot(standardize(gaussian_fit_male[:,0], mu_male[0], np.sqrt(covariance_male[0,0])), \n", " standardize(gaussian_fit_male[:,1], mu_male[1], np.sqrt(covariance_male[1,1])), \n", " linewidth=3, color='red')\n", " ax.plot(0, 0, 'rx', markersize=10, markeredgewidth=3) \n", " ax.grid(True)\n", "plt.figure(figsize=(8,8))\n", "plot_standardized_males()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Part (c) deals with *whitening* or *sphereing* the data. This involves transforming the data so that the dimensions are uncorrelated and have equal variances along the axes. Recall that\n", "\n", "\\begin{equation}\n", "\\mathbf{y} = S^\\intercal\\left(\\mathbf{x} - \\boldsymbol\\mu\\right) \\sim \\mathcal{N}\\left(\\mathbf{0}, D\\right),\n", "\\end{equation}\n", "\n", "so this transformation accomplishes the tasks of making the dimensions uncorrelated. Now, to make the variances equal simply multiply by $\\sqrt{D^{-1}}$, which is easy to compute since $D$ is diagonal and positive definite, so our transformation is\n", "\n", "\\begin{equation}\n", "\\mathbf{y}^\\prime = \\sqrt{D^{-1}}\\mathbf{y} = \\sqrt{D^{-1}}S^\\intercal\\left(\\mathbf{x} - \\boldsymbol\\mu\\right)\n", "\\sim \\mathcal{N}\\left(\\mathbf{0}, I\\right).\n", "\\end{equation}\n", "\n", "Let's plot this." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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o2LAho0ePLvLref0sPufO2XqjA9ClC/ToAfhA7tfg7PwDAwMpVaoUmZmZZGdn\nc/bsWWrVqgXgFtOM6v5PsjoESyUlJUHz5vDss/aNgwaZEyIpQIt4sTt16hTffvstycnJAJQoUYKK\nFSvSoUMH/PzMP3erVq3Yv3+/lWG6l1dfhZ07zeXAQHNuYe2N7hKVKlVi0KBBhIWFUatWLYKCguiQ\n15FwypQpxMfH89hjj3Hy5EmLI1U+bfhw8xpyMJvcXn3V0nDciRbxYrZ7926qVq1KcnIyiYmJPPHE\nE2RlZRV4zPTp07nrrruK/Jpe3S72yy8wdqx9/fXXIe9IELw89yJwdv5paWlMnDiRPXv2cPDgQc6c\nOcOcOXMYMGAAaWlpbNq0iRo1ajBw4ECnxnEluv9TrA7BUrb8K1aEcePsd0ycCNu3WxKTu9EiXsyy\ns7NJTU3l6aefJjU1lbJlyxY4dT5q1ChKlixJbx+axOOqBg2C7Gxz+bbb4IknrI3Hx2zYsIE2bdpQ\nuXJl/P39ue+++1izZg3VqlXDyDsb8vjjj7N+/XqLI/VOhXUq/Oc//0lcXBzx8fEMGjRIz9rl69PH\n/I4A8zvjmWe0kxuY7V7ufjPD9AyHDx+W8PBw2/q3334r99xzj4iIzJgxQ1q3bi3nzp2zKjz3smSJ\niPnfUMTPT+Tnn62OyOds2rRJmjRpIllZWZKbmyt9+/aVKVOmyKFDh2yPmTBhgvTq1cvCKL1Tenq6\nhIeHy/nz50VEpGfPnjJr1iw5ffq07TFvvfWW9O/f36oQ3c/mzSL+/vbvjY8/tjoip8mre9esj3ok\nXsyCg4MJDQ1lZ14b7/Lly2ncuDFLlixh3LhxLFq0iNKlS1scpRvIyYEXX7Sv9+9vTnygXCouLo5H\nHnmEpk2bEhcXB8ATTzzBkCFDiI2NJT4+nlWrVjFx4kSLIy26/v37ExwcTKzDWPuOR7cdOnS47Oh2\n7969VKhQgQkTJrgszsI6FdasWZPy5cvbHpOZmUnVqlVdFpPbi401j8DzDRyoM50VpdJbfcODjsRF\nzKObZs2aSVxcnHTv3l1OnDghDRo0kLCwMElISJCEhAR56qmnivx6K1eudF6wVnn3Xfuv6XLlRByO\n/Bx5Ze7XQfNfed3P+fbbb2Xjxo0SExNj23ato9sePXpIz549Zfz48Tcc642YNm2alC9fXqpXry5/\n/etfbdtffvllCQ0NldDQUDlx4oRLY3Inhe7/EydEgoPt3x9Dh7o8LldAj8StExcXx/r169m0aRPz\n58+nYsWSgq8fAAAgAElEQVSK/Pbbb+zZs8d23e3UqVOtDtM6Z87A//2ffX3oUHvPU6Vu0q233kql\nSpUKbLva0e3ChQupV68e0dHRLosRrtypEGDkyJHs3buXu+66i7/97W8ujcvtVaxYsDPsxImwb591\n8VhMi7gH8LprRceNs89KVLOm2bntCrwu9+uk+ScV22v94x//ICwsjJkzZ/L3v/8dMAv62LFjeeWV\nV1x+XfyVOhWCvUlg9erVbNiwAYCMjAw6depEZGQknTt3tl32d/78eXr37k1sbCzR0dGMGTPGpXk4\n0xX3/8MPQ8uW5vKFCzBqlMticjdaxJVrHThQ8FKRUaOgbFnr4lE+I//oNjk52XZ0O3z4cF544QXK\n5n0GXVnIIyMjWbt2LefOnUNEWL58OY0aNWLXrl0kJyezdOlSTp06RXx8PABjxoyhQ4cO/Prrr7Rv\n39521Uv+CHtbtmxhw4YN/Oc//2Hv3r0uy8MShgEjR9rX338f0tKsi8dKRTnnbvUND2sTL25e1S6a\nnGxvy4qPF8nOvurDvSr3G6D5r7yh56WnpxdoE3e0d+9eadKkiYiI3HbbbRIeHi7h4eESFBQkVapU\nkbfffvtGw71uY8eOlcaNG0tMTIz07dtXLly4IPfff7/ExMRI48aNpWzZsnLkyBEREYmMjJTDhw+L\niMihQ4ckMjJSRESWLFkiXbp0kezsbDl27JhERkZKRkaGy3Jwpqvu/9xckbZt7d8nffu6KCrXoIht\n4iUs/g2hfMn27TBzpn39jTfsYyIrVYzEfgAAwK5du2jQoAEAn3/+ue3odvXq1bbHjBgxggoVKjBg\nwACXxTl48GAGDx5cYNu8efMAc1z79u3bU716dQCOHj1KcHAwADVq1ODIkSMAdO7cmQ8++ICQkBCy\nsrKYOHEiQUFBLsvBMoZhjtx2++3m+uzZMGwYREVZG5eL6el0D+A17aJjxtgHZ7jrLrjjjms+xWty\nv0GenH9hl3qtX7+eFi1akJCQQIsWLWztvVdq172R/Hv37k3r1q3ZuXMnYWFhzJgxg2HDhhETE0NC\nQgIpKSmMHz++WHJ0tnLlyl3xvvxhnD/44AOysrI4fPgwaWlpvPHGG6Snp7soQue65v6/7Tbo3Nlc\nzs01h2f1NUU5XLf6ho+fTvcKu3cXHKThhx+sjkg5WWGXeiUlJcnSpUtFROTLL7+UpKQkERGZOXOm\nbUCZs2fPSt26dWXPnj2uD9qNXNokEBUVVeB0elRUlIiIPPXUU/LBBx/YHtevXz/59NNPXRusldat\ns3+vgDkgjBdALzHzHl4xfvK4ceYALwDt2kGrVkV6mlfkfhM8Of/CLvUKCQmx9ao+ceKEbca0GjVq\nkJmZSU5ODmfPnqV06dIEBgZ6dP43S0Q44zCQSZcuXZiZ1xw1c+ZMunbtCkBUVBTLly8HzN72a9eu\nJcpLTikXaf83bw55fwsA/vlPp8Xjjiwv4oZhvG8YxhHDMLZYHYtyksOHzd6j+V56ybpYlKXGjBnD\nwIEDCQsLY8iQIbYe1p07dyYwMJCQkBDq1q3Liy++6BvtuleQ3ySwf//+Ak0Cy5YtIzIykhUrVjBs\n2DAAnnzySS5cuEBMTAwtW7akf//+NPG10Q//9S/78sKF4Etj/RflcN2ZN+BWIB7YcpXHFPupCuVC\nQ4bYT3U1b272KlU+4dJTwh06dJAFCxaIiMinn34qHTp0EBGR2bNny/333y85OTly9OhRiYyMlN27\nd1sRsvJUDz5o/57p2dPqaG4annI6XUS+AzKsjkM5SUYGvPOOff2ll3SucB/2448/0q1bNwB69Ohh\nmx1tzZo1dO/eHT8/P6pVq0abNm1snd6UKhLHM3yffQbefq18HsuLuLo2j24XfPttOH3aXG7cGLp0\nua6ne3TuxcDT8xf72TQAGjZsyKpVqwBzcqCGDRsCV27X9fT8b5bmn1L0B8fGQvv25nJOjvnd4wO0\niCvnycyEN9+0rw8bBn76kbPayZMneeCBB2jUqBHR0dH8+OOPPPTQQyQkJJCYmEh4eDiJiYk3/T6F\nXeo1bdo0hgwZQkJCAv/4xz+YNm0aoO26qpg4jjM/bZr5HeTlDMdfyZYFYRh1gC9EJPYK90vfvn2p\nW7cuAEFBQcTHx9uuIcz/tabrbra+dSs88wwpAMHBJO3bByVLuk98Prp+5513EhcXx+uvv052djZL\nly6lXLlytvsffPBBypcvz/t5nRGtjlfXdb3I67m5pISGwsGDJAFMnUpKo0buE99V1vOX86/xnzVr\nFiJyzbZHdynidTGLeMwV7hd3iFNdBxHz9NYvv5jrkycXnAdYWeLUqVMkJCTw+++/X/ExYWFhrFy5\nkvr167swMqWKyeTJ8Nxz5nJkJGzb5pFnAA3DKFIRtzwzwzDmAGuACMMw9hqGkWx1TNersJGprjTj\nEMDo0aNp2LAhjRo14uuvv77m6zv+UvMYa9faC3jZsuasQzfAI3MvRsWd/+7du6latSrJyckkJiby\nxBNPkJWVZbv/22+/pUaNGm5TwHX/p1gdgqVuKP9HH4XAQHP5119h6dLiDMntWF7ERaS3iNQUkdIi\nEiYiM6yO6Xrlzzjk6EozDm3bto1PPvmE7du389VXXzFgwAC88izDf/5jX+7Vy5wDWFkuOzub1NRU\nnn76aVJTUylbtqztswkwd+5cevXqZWGEV1bYj+V58+bRpEkT/P39SU1NLfD4LVu20Lp1a5o0aUJc\nXBwXLlxwdcjKChUqwGOP2dcd++V4o6Jch2b1DQ+4TvzS62GvNOPQ6NGjZcyYMbbH3XnnnbJ27VrX\nButsx4+LBATYr9lct87qiFSew4cPS3h4uG3922+/lXvuuUdERLKzsyU4OFgOHDhgVXhXVdgwrjt2\n7JCdO3dKu3bt5KeffrJtz87OltjYWPn5559FROT48eOSq+MT3JSvvvpKIiMjpWHDhgW+w9xSWpqI\nn5/9O+iXX6yO6LrhKdeJe6tLZxw6evQoAAcOHCA0NNT2uFq1anHgwAFLYnSaDz6Ac+fM5fh4aNbM\n2niUTXBwMKGhoezcuRMwL/Nq3LgxAMuWLaNRo0bUrFnTyhCvqLBhXCMjI2nYsCEiwunTp2297sPD\nw6lVqxZZWVm0aNGC9u3b07JlS732/Abl5ubyzDPPsHTpUrZu3crcuXPZsWOH1WFdWXg45I1HAMB7\n71kXi5NpEXcR4yYGOPGodjER89KOfE8+eVODu3hU7k7gjPzfeust+vTpQ3x8PJs3b+alvEEyPv74\nY7c7lX49+b/xxhvcfffdbN++nb/97W8EBgbSuXNnTpw4Qe/evRkxYsRl0366O3f5/K9bt46GDRtS\np04dSpYsyUMPPcTChQud/r43lf+TT9qX586F7Oybjscd6XziThIcHMyRI0cIDg7m8OHDtjmBa9Wq\nxb59+2yP279/v20SCK/www/2Dm3lykHv3tbGoy4TFxdnGynN0YwZHtcdxSYnJ4eNGzfyxRdfAGYz\n4fr162nfvj3du3fn7bff5uTJk971f82FLj2DWLt2bdatW2dhREVwxx0QEgKHDsGRI7BsmTkFspfR\nI/FiIvb2e6DgjEOzZs2yzTjUpUsXPvroIy5cuMDu3bvZtWsXLVq0uOpr519P6BEcj8J79bL3Er1B\nHpW7E2j+SUV6XFZWFkFBQbZe919++SWtW7dmwoQJDBs2jK1btzJlypQCnfg8ge7/pBt/sr9/wYOI\n2bNvOh53pEW8GBQ2MpXjjEPLly+3zTjUuHFjevbsSePGjbn77ruZOnXqTZ1qdysnT8LHH9vXn3jC\nuliUV7r0x7Lj9h07dth63UdERLB8+XIeffRR3nzzTVq0aMHTTz9Nv379LIja89WqVYu9DmORe8wZ\nxEcesS9//jmcOmVdLM5SlN5vVt/wgN7pzrRy5UqrQyia2bPtvUHj4opltjKPyd1J3DH/ffv2Sbt2\n7aRx48YSEREhtWrVkoSEBGnSpIn4+/tL9erVpVOnTvL6669LVFSUREdHS0xMjMTExEh8fLykpKQU\n+b0c8+/Vq5eEhIRIqVKlJDQ0VKZPny4LFiyQ2rVrS0BAgPj7+8udd94pImZP9vj4ePHz85OYmBgZ\nNmyYiIgEBgYW69/C2dxl/2dnZ0v9+vUlPT1dzp8/L3FxcbJt2zanv2+x5B8ba/9emj795l/PRShi\n73RtE1c3ZdKkSbyX1/PzceA5YDPwVEYGmfHx1K1blw8//JDy5ctbGaYqRiVKlGDChAnEx8dz5swZ\nmjZtypw5c5g+fTp79uxhw4YNvPrqq7zzzjv89ttvTJs2je+//54PP/yQP/74g7vuuuuGeonPmTOn\n0O35s6K1bduWSZMmAWav+06dOuHn58eECRNo27Yty5cvJyIi4sYT92H+/v5MmTKFTp06kZubS//+\n/WmUN5yp23v4Ycjv0Dh7NiR73HhiV1eUSm/1DR8/EndXv/zyi8TExMi5c+ckOyNDOhqG7AJpDvLt\nnDkiIjJjxgz5v//7P4sjVc7UtWtXWbZsmdSuXVtatGghIiL33nuvhIWFiYjI008/LR988IHt8Xfc\ncYesX7++2OPYtGmTNGvWTOLi4qR79+5y4sQJWb9+vbRo0ULi4+OlVatWkpqaWuzvq9zcgQP2a8YN\nQ2TvXqsjKhKKeCRueYEuUpBaxN3Sp59+Ko899pi5MneuvAoyFiTI39/2mH379knjxo0tilA52+7d\nu6VOnTpy+vRpKVWqlEydOlVEROLj4yUgIEBatmwpERER0qFDB8nOzpa0tDQJCgqS+fPnWxy58ikd\nO9pPqY8ebXU0RVLUIq4d2zyAu1wreqkmTZrw7bffkpGRQd+hQ/kX8DoQXasWCxcuZN68eTRv3pxt\n27YVGBJzzpw5tmkvExIS8Pf3Z8uWLYW+h7vm7irunP+ZM2fo0aMHkyZNonTp0ly8eJEHHngAMId3\nBVi7di2zZs1i3bp1NG/enIEDB9KmTRv8/f2L9B7unL8raP4pxfNCjh3crtAs46m0iKsbFhUVxdCh\nQ+l4xx1s2beP7oABTP/3v5k6dSojRozgwQcfpGTJkgWe17t3bzZu3EhqaiqzZ8+mXr16BcbDVu4v\nOzubHj168PDDD9O1a1e++uorypYtS05ODgDVq1e3jY3QqlUrqlWrxrJly1iwYAEZGRnaNq1cq1s3\nKFXKXP75Z3Doae/ptIh7AHe+VjQ5OZkNL73ERhGqAaVLlCDirrtYunQpP//8M08//TQBAQFXfP7c\nuXN56KGHrni/O+fuCu6af79+/WjcuDHPP/88YO7Htm3b2sZGqFixIrVr1wbMiUjOnz9PlSpVWLZs\nGSVLliQqKqpI7+Ou+buK5p9UPC9Uvjw4vtbixcXzum5Ai7i6KX/88QfMm8deYCkQVKmSuQ1zvOWR\nI0de9XpSdxzqU11dfk/zFStWkJCQQHx8PF9++SVTp061jY1w+vRpateuTUxMDH369MEwDKKjoxk3\nbhyzvXTQDXcwevRooqOjKVOmDLVr1+b8+fM899xzlC9fnoCAAIKDgwuMGOlT/vIX+7IXFXHLO60V\n5YaPd2xzl2tFC3NbmzYSbRgSDzIXJKZhQ5k0aZJERERIZGSk/P3vf5ekpKQCM0zl+/HHHyU2Nvaq\nr+/OubuC5r/S6hAsdT35p6enS3h4uIwdO1b69OkjNWvWlFmzZknPnj1ldF5nrrZt20qrVq2cFG3x\nK9b9v2uXvXNbmTIiZ88W32s7AdqxTbnC6pdf5hcRNgK3hIdDQADPPfccv/76Kzt27OC111674nM/\n+ugjPQpXbi8iIgI/Pz/KlClj2zZv3jxCQkIwDIMGDRrYRmScP38+gYGB+Pv7ExwczMqVK10WZ2Bg\nIH5+fixevJjk5GRycnKoWbMmmzdvJjnv2ui+ffuybds2l8XkVurXh/xmnKwscOG+cSYd7MUDuHW7\n2PLltkVp1w65wqQI5g/LguuffPIJ33333VVf3q1zdwHNP8nqEPjb3/5GlSpVePTRR23bzp49S/36\n9YmMjGTChAmEhYUBULNmTT788EMOHTrEqlWrePjhh9m/f/8Nv/f15F+pUiUqVqzI+vXreeCBByhb\ntiwdOnSwTcQEsGDBAlvnQ09Q7Pv/L3+B/ClUFy+Gu+8u3te3gB6Jq5uzYgUAvYHWn39eYPz4zz//\nnNDQUNauXcs999zDXQ4zCK1evZqwsDDq1q1rTdxKFdGAAQNsnfTyLV68mH/961+2eQ+qVq0KmD3x\n7733XkqXLk2VKlU4d+4cFy9edEmc77//Prt372bfvn18+umn5OTkFBjlbtSoUZQsWZLSpUu7JB63\ndGm7uFw+Dr/HKco5d6tvaJu41SEU7tgxcwQkEPH3Fzl5stjfwm1zdxHNf6XVIYiIyHfffScBAQG2\n9fj4eHnllVekQoUK0rRp08tGoJs5c6bcdddd0rFjx5t63+vJv1u3blKuXDkJDw+XGjVqSKlSpSQi\nIkKioqLkzTfflNatW0t6erpERUXdVEyuVOz7/8IFkcBAe9v4L78U7+sXI7RNXDldSor9l2yLFjc9\n7ahSniI7O5uMjAyaNm3K888/T8+ePQvcf+DAAdasWcM0x6l5nWz48OGEh4ezbds25s6dS/Xq1Xnu\nuedo0qQJr732GosWLeKjjz6yTYvsk0qWhE6d7Ote0Etdi7gHcId2wULlnUoHoH17p7yF2+buIpp/\nktUhFCo0NJT77rsPgOjoaPz8/Pjzzz8Bc5rOyZMn06lTp5tuLrqe/OPi4njkkUdo2rQp/fv3B+CJ\nJ54gNTWVU6dOUatWLUaNGmW7BNQTOGX/O7aDe0HnNu3Ypm6cQ6c2ZxVxT7Rz504efPBBDMNAREhL\nS+PVV1+lZs2aDB8+nO3bt7N+/XoSExOtDlUVkdib9gBz5rQVeT9i09PTuXjxIlWqVOHEiRPcc889\nPPDAA5d15nSFwYMHMzh/xq48v//+u8vjcGu3325f/uEHyM0FPw8+ni3KOXerb2ibuNUhXG7/fnu7\nUunSIllZTnkbt8z9OuTk5EhISIjs3btXduzYITt37pR27doVet18YTw9/5vlDvnXqVNH/Pz8BBB/\nf39JTk6WefPmSdmyZcUwDClRooRt9raRI0eKYRji7+8vfn5+UrJkSVmzZs0Nv7c75G8lp+SfmytS\nvbrbt4uj84krp3I8ld6mDVxlaFVf9s0331C/fn1CQ0Nt28QbesT6kPT09EK333///Zdte/nll3n5\n5ZedHJG6KYYBrVvD55+b6z/8ANHR1sZ0Ezz4HILvcMt2QccifscdTnsbt8z9OtzssLKenv/N0vyT\nrA7BUk7L/5Zb7Mtr1jjnPVxEi7i6MY6DurRta10cbuzixYssWrTINj2ncr5JkyYRExNDTEwMb731\nFgDr1q2jRYsWJCQk0KJFCzZs2GBxlMpyrVvbl7WIK2dzuzmFz561j3pkGBAf77S3crvcr8NXX31F\n06ZNqVatWqH3161bl7i4OFtxAcjIyKBTp05ERkbSuXNn/ve//7kyZLdzPft/69atvP/++2zYsIFN\nmzbxv//9j99//52hQ4cycuRINm7cyIgRIy7r+OXOPPnzXxycln/TpublZgC//grHjjnnfVxAi7i6\nflu2mD06ASIjoVw5a+NxU3Pnzr3iqXQRwc/Pj5SUFDZu3Mi6vDMbY8aMoUOHDvz666+0b9++wIhb\n6uq2b99Oy5YtKV26NP7+/tx+++3Mnz+fkJAQTpw4AcCJEyeuOque8hFlyoDj1SFr11oXy80qSu83\nq2/4eO90tzN1qr1nZ+/eVkfjljIzM6Vq1apy6tQp27YFCxZI7dq1JSAgQGrUqCFlypSRY8eOFXhe\nZGSkHD58WEREDh06JJGRkS6N25Nt375dIiMj5fjx45KZmSm33HKLPPfcc7Jnzx6pXbu2hIaGSu3a\ntWXv3r1Wh6rcwQsv2L/H/v53q6O5DDpim3Ka1FT7ckKCdXG4sbJly/LHH39QoUIF27Zu3bqxb98+\nsrKyOHToEDVq1KBjx440b96c9957D6DAZBU1atTg6NGjlsRfVPv376d9+/ZER0cXaIfON378ePz8\n/Dh+/LjTY4mKimLo0KF07NiRu+++m4SEBPz8/Ojfvz+TJ09m7969TJw4kX79+jk9FuUBHDu3/fCD\ndXHcrKJUeqtv+PiRuNtdK9q0qf0X7DffOPWt3C73YnTw4EERETl69KjEx8fL6tWrpVKlSgUeExgY\naEVoRXbo0CHZuHGjiIicPn1aIiIiZPv27SIism/fPuncubPUrVtX/vzzzxt6/ZvZ/y+99JJMnTr1\nsr+hu/9NHXnz578onJr/7t3277GqVZ33PjcIPRJXTnHxIvz8s31dj8RvWEhICADVqlWjW7durFu3\njuDgYI4cOQLA4cOHCQoKsjLEa6pRowbxeR0by5cvT6NGjThw4AAAL7zwAuPGjXNpPPlDiu7du5cF\nCxbQp08fGjRowKpVqwBYvnw5ERERLo1JuamwMChb1lw+dsxjO7cZ4gEDTxiGIZ4Qp0/YvNneG71O\nHbjCQBjq6s6ePUtubi7ly5cnMzOTTp068corr7B8+XIqV67M0KFDef3118nIyGDMmDFWh1sk6enp\nJCUl8csvv7BixQpSUlKYMGEC4eHh/PTTT1SuXNnpMdx+++0cP36ckiVLMnHiRJKSktiwYQNPP/00\nFy5cICAggKlTp5KgPz4VmJ3bNm40l1evhttuszYeB3nDNhvXepyO2KauT/4HHvQo/CYcOXKE7t27\nYxgG2dnZ9OnTh06dOtGsWTN69uzJ9OnTqVOnDp988onVoRbJmTNn6NGjB5MmTcLf35/XXnuNZcuW\n2e531Y/w1atXX7atWbNm/Pjjjy55f+VhGjWyf6dt3+5WRbyo9HS6B3Cra0U3bbIvu2ACD7fKvRiF\nh4ezadMmNm7cyM8//8ywYcMAqFy5Mt988w2//vorX3/9NZsc/95uKjs7mx49evDwww/TtWtXfv/9\nd9LT04mLiyM8PJz9+/fTtGnTG+qk5637v6g0/xTnvkGjRvbl7dud+15Ookfi6vrs2mVfdvwPoHxW\nv379aNy4Mc8//zwATZo04fDhw7b7w8PDSU1NpVKlSlaFqFThvKCIa5u4uj5NmsDWrebyhg3myEfK\nZ33//ffcfvvtxMTEYBgGhmHw2muvceedd9oeU69ePTZs2OCSNnGlrsu2bfbJT8LCYM8ea+NxUNQ2\ncT2dropOBHbvtq+Hh1sXi3ILbdq0IScnx9Y0kJqaWqCAA6SlpVG5cmX69+9PcHAwsbGxtvu2bNlC\n69atiYuLo2vXrpw5cwYwx53v168fsbGxJCQk2HqXu1Jh8V46LO7JkycB2LNnD2XLliUxMZHExEQG\nDBjg8njVDWjQAPz9zeW9eyHv8+dJtIh7ALdpF/vjD3PcdIDAQHDB6VG3yd0i3pR/cnIyS5cuLbDt\nscceY+zYsWzevJnu3bszduxYAN59910Mw+Ctt97i66+/ZtCgQW4R76XD4o4ePdp2X4MGDUhNTSU1\nNZWpU6cWSwzetP9vhNPzL1XKLOT5fv3Vue/nBFrEVdE5Xk5Wt645+YlSRXTrrbde1i7+22+/ceut\ntwLQoUMH5s+fD8C2bdto3749YF5HHxQU5PLZxwqLd+HChfTt2xeAvn378nn+nNToPPEey7Fd3AOL\nuHZs8wBuM6ewBafS3SZ3i3h7/tHR0XTs2JEtW7bg5+fHn3/+SXBwMP7+/sybN4/AwED8/f3ZuXMn\nLVq04O233+b999/n4sWLlCpVirFjx9KuXTuXxXv06NErDoubnp5OYmIiFStW5NVXX7X9OLkZ3r7/\nr8Ul+deta18+eND571fM9EhcFZ22h6tiNn36dE6ePEnVqlU5ceIE2dnZVKxYkQsXLtCwYUPKly9P\ndnY2gYGBiAglS5bkf//7H5s3b2bmzJn06tWLChUqMGHCBEviN/LORoWEhLB3715SU1MZP348vXv3\ntrXvKzdXo4Z9+dAh6+K4QVrEPYDbtItdejrdBdwmd4t4e/4RERGsW7eOL7/8kmrVqtGkSRP8/f05\nc+YM8+bNY8KECXz88cecOnWKUqVKUb9+fWrkfelGR0eTkZFxWUc6Z7p0WNzq1asDUKpUKdup98TE\nROrXr8/OnTtv+v28ff9fi0vyzxv+GACHSyM9hRZxVXR6JK5uktgnNQLsY53n5uZy+vRpHnnkEcDs\nnZ4/A9zf/vY3DMPAz6/g19XQoUOpWbMmMTExLou3S5cuzJw5E4BZs2bRtWtXAPr06WPryZ6Wlsau\nXbv49NNPqV27tq3H+pIlSwA4f/48vXv3JjY2lujoaI8ZVtdrefiReFFnEXu+KNucdcPHZzFzG5GR\n9ll/Nm+2OhrlYXr16iUhISFSqlQpCQ0NlenTp8ukSZMkIiJC6tWrJ9WqVZP09HSJiooSPz8/iYyM\nlNDQUAkLC5OKFStKQECArFixQkRE1q1bJwEBAbJt2zYZPny4jB8/3iXxHj9+XO644w6JiIiQjh07\nSkZGhoiIjBw5UurVqycBAQHStGlTWbx48RXjmjlzpvTq1UtERM6ePSt169aVPXv2FHv8qog2b7Z/\nrzVqZHU0NhRxFrOiFtHUQrZtLMpzi+OmRdxNVKtm/7AfOmR1NMqLpKenS0xMjK2Ily5dWnbv3i0t\nW7aU3377TerXry9+fn5Sp04diYyMlDJlysioUaPk+PHjth8AnTp1khMnToiIyIcffijx8fGSkJAg\n8fHx4ufnJ5ud/MMzP4d8w4cPlzfeeOOyxy1ZskS6dOki2dnZcuzYMYmMjLT9GFAWOHrU/r0WFGR1\nNDZFLeJXPZ1uGEYvwzC+AMINw1jkcFsJHHfW2QFVkFu0i4nAiRP2dRdNkekWuVvIV/IX+w92RIQK\nFSowadIkdu7cScuWLTl69Ci5ubmcO3cOwzDIyclh6tSphIeHc/DgQXJzcylTpoztuu3evXvbBp+Z\nPW9XIwwAACAASURBVHs29erVKzBoi6tMmTKF+Ph4HnvsMU7k/f/p3LkzgYGBhISEULduXV588cUr\nTjnrK/v/SlySf5UqUCLvQq0TJ+DcOee/ZzG6Vpv4GmA8sCPv3/zbIKCzc0NTbiUry5xLHKB0aQgI\nsDYe5TV69+5N69at2blzJ1FRUfz222+cPHmSd955B4DQ0FAqVKiAYRicOXOG3377jTJlyhAQEMC5\nc+fo378/L730Ev/+978LXLedb+7cuTz00EOuTosBAwaQlpbGpk2bqFGjhm3Amg8++ICsrCwOHz5M\nWloab7zxBuk6pa91/Pwg77JBwOM6t121iIvIHhFJEZFbRGSVwy1VRLJdFaSvc4trRR2Pwl04kYVb\n5G4hX8h/zpw5HDx4kPvvv59KlSpRokQJatSowTvvvMPx48fZtGkTBw4coG7duuzdu5ddu3YRFBTE\npk2bKFOmDNWqVQMuv24738cff0yvXr1cnRbVqlWzXYL2+OOPs379egDWrFlD9+7d8fPzo1q1arRp\n0+aKA9n4wv6/Gpfl79i5zcOKeJEGezEM4z7gdaA6YOTdREQCnRibcicZGfZlF51KV75lzpw5V70/\nLS2twLzl5cuXxzAMXnnlFdtjjEtGEVy3bh3lypWjcePGTonZkWOTAJiXoOVfDjd//nyaNGkCQFRU\nFMuXL6dPnz5kZmaydu1aXnjhBafHp67CsYjnXULoKYp6idlYoIuIVBSRQBGpoAXcddyiXcyC9nBw\nk9wtpPmn2JYvnbccrnzddr6PPvrIJUfhjk0CYWFhzJgxgyFDhhAbG0t8fDyrVq1i4sSJADz55JNc\nuHCBmJgYWrZsSf/+/W0F/lK6/1Nc80bly9uX8+eH8BBFHXb1iIh45mSrqnhYVMSVynfpvOVgv257\n6NChBa7bBvPI+JNPPuG7775zemyFnUVITk4u9LGlS5fmgw8+uGz7/v37eeSRRzhy5Ah+fn48/vjj\nxMbGMm/ePIYPH8727dtZv349iYmJxR6/z3Ps4+NhHduuWsTzTqMDbDAM42Pgc+B8/v0iMt+Jsak8\nbtEupm3iltD8kwBz3vIPP/yQmJgYEhISbPOWDx06lJ49ezJ9+nTq1KnDJ598Ynvu6tWrCQsLo66L\nRhe8WSVKlGDChAnEx8dz5swZmjZtysKFCwkJCWHBggU8+eSTVofoci77/HtrEQfudVg+C3RyWBdA\ni7iv0DZx5QoLF8K995o9hh20adOGnIsX4YsvwOFoG+Cbb74p9KXatm3LmjVrnBZqcatRo4atDb18\n+fI0atSIAwcOcMcddwA6S5pTeXARv1bv9OSr3Pq5Kkhf5xbtYqdO2ZcDXdcdwi1yt5BP5T98OHTr\nBo89Brm5gEP+ubnm9m7dzMfdgP79+9uGRs23fv16WrRoQUJCAi1atLD1Ej9+/Djt27enQoUKPPfc\nczeR1I1JT09n06ZNXLhwweXv7U5c9vkvU8a+7E1FPJ9hGG8VcnvVMIyu1372NV/7TsMwdhiGsdMw\njKE3+3rKSRyPAvz9rYvDB1xPscm3d+9eS2fzumkLF8KIEebyjBkFCrmtgM+YYa6PGGE+/jolJyez\ndOnSAtuGDBnCyJEj2bhxIyNGjGDw4MEABAQEMHLkSMaPH3/DKd0oxx74ZRyLi3Iebz0SdxAAxAO/\n5d1igdpAf8Mw3rzRNzcMww+YgjlwTDTQyzCMqBt9PW/ly+2ivpi7Y7HJz/9KxSbfoEGDuPvuu10d\nagGF/fgYMmQIjRo1Ij4+nvvvv59TeWd05syZQ0JCAomJiSQkJOB/331scTxNnlfIk269tWABB0hO\nNk+5X6dbb73VNtNYvpCQEE6ePAnAiRMnqFWrFgBly5aldevWlC5d+rrf52Zc2gPfFz//jixpE8/K\ncs17FpOiFvFYoJ2ITBaRyUAHIAroTsF28uvVAvgtb1CZi8BHwE0f3Svlya6n2AAsXLiQevXqER0d\n7dI4L1XYkW6nTp3YunUrmzZtomHDhlcfFnX+fLNA55sxA0qWvLyAv/feZW3mN2rMmDEMHDiQsLAw\nhgwZYovPKoX1wHek7eJO4nh20UuPxCsBDhfSUQ6oLCI5OPRWvwG1gH0O6/vztikHPtUueglfzh3s\n+V+p2GRmZjJ27FheeeUVy7/gC/vx0aFDB9sUoq1atWL//v2XPc82LKqfn1mgHQp5iuMDi7mAg3n2\nYPLkyezdu5eJEyfSr591XX3ye+CvWLHCdpZi7NixfP7554SGhrJ27Vruuece7rrrLstidDWX/f//\n8kv78uTJrnnPYlLU68THApsMw0jBHK3tduA1wzDKAYV3DS1mjz76qO1SkaCgIOLj422nWvJ3tLeu\nb9q0yfp40tIw1yBlzx5ISXGbv483rh92GPoxJSWFF198kcmTJ9OtWzdGjBhB9+7d2bBhA8OHD6dT\np06sW7cOMI/UrI4/MzOTlEI+H9OnT+ehhx667PEzZ85k1KhRZrJ+fqT06QMzZtg/b3n/Jk2bZt5f\njPH9+OOPvPzyy6SkpNCjRw/69+9/2eP3799faD7OWM/JySmwnr88e/bsAo93VTw+s56RUfDzZsHf\nN3/5usfRL8pUZ3m/8EMwT3V3BWoW9XnXeM1WwBKH9WHA0EIed72zuKniNnKkfbq+l16yOhqvd+m0\nlhUqVChwf8WKFUVE5LbbbpPw8HAJDw+XoKAgqVKlirz99tsujdXRpXHnGzlypNx333229V9//VXi\n4+MlIiJCAgICJDAwUCZNmiTr1q6V5lWrSjxIc5D1+Z85EElOFsnJuan4du/eLU2aNLGtJyYmSkpK\nioiIfPPNN9KsWbMCj585c6Y888wzN/WeygO0a2f/nLlJvaGIU5Fea7CXKBHZYRhG/hBB+ae+axiG\nUUNEUq/vJ8Nl1gMNDMOoAxwCHgJcP1OBUm5G7D9gAWjYsCGrVq2ibdu2LF++nIYNGwLmgCb5RowY\nQYUKFRgwYIDL472amTNn8uWXX7JixQrbtoiICDZu3MjAgQOpVq0akydPpnvXrjzSqhUjjx2jE/AV\nMBhYmf+k/LbxGzyl3rt3b1JSUvjzzz8JCwvj/7d353E21v3jx1+fWQzTWMY2ZBtkG8YsUUIZIpK1\nFOkWg+pOiyhEWpREWpSWL3Wj/BLuynJH1gyTVDIGU4RkmbIb+zLb5/fHZ+acGQYznHOus7yfj8d5\nuK5rzsx5vzvTec/1WceMGcPUqVMZNGgQ6enpFC9enKlTp9qeX7NmTU6dOkV6ejoLFizg22+/5ZFH\nHiE9PZ309HS6du3KuHHjSEtLo2fPnuzZs4fw8HDmzp1L6dKlr/U/l7BCp06wKuc3zYIphdfjas3p\nQ4FHMduPXkwDba7nxbXWWUqpJ4FlmP75/2hZ3vUSeZvOfI0v5p632ISFhTF+/PgrFht3cvEfH0uW\nLGHixImsWbPmkpHeOmdZ1HHjxlG7dm2qjRlD5QMHOJHz9eOtWhEQEADVq9sL+HUU8sttsPLzzz8X\neP2vv/665NqqVasIDg4mKyuLFi1asHbtWhYuXEjbtm0ZPnw4EyZM4I033mD8+PFFiu1yfPH3Py+X\n5Z93Pr6HbbN8xSKutX4059/WzgpAa70EqOesny+Ep8lbbPJ+iF2u2OTKu5uXFQq60x03bhzp6em0\na9cOMIPbPvroI8C+LOrq1at5MCICpk5lPNACePaGG9B//mnmaffoYV4gbyHv2vWSldtcITg4GIAL\nFy6QnZ1NaGgoCxYsYPXq1QD07duXuLg4hxVx4SJ5R6R7WBEvbN91MDAamJpzXgfoVJjvdcQDN+mj\n8Gnjxtn7i0aMcMpLnD9/Xt9yyy06OjpaR0RE6JEjR2qttf75559106ZNdXR0tG7atKlev369U15f\nuF56erouX768Pnz4sNYvv6zbgp7Xpo3WWVn6v//9r27btq15YlaW6RMHrV9+2bJ4s7KydHR0tC5Z\nsqQeNmyY1lrrMmXK6P79++uKFSvqyMhIHRoaqrXWetOmTfq2227TjRs31l26dNGnTp2yLG5xFSNG\n2D/fxo2zOhqtdeH7xAtbROcAw4EUbS/qyYX5Xkc8pIi7gQ8+sP+S//vfTnuZM2fOaK21zszM1Lfe\neqtOTEzUcXFxeunSpVprrRcvXqzj4uKc9vrCtRYsWKDbt29vOy9ZokS+wWulSpWyPzkrS+v5810Z\n3mWdOHFCN2vWTK9atUqHhobqxMREvXHjRh0ZGanLli2rtda6adOmOjExUWut9fTp0/WLL75oZcji\nSgYPtn++vfOO1dForQtfxAvbqVRba/0mkJFTUc9ippoJF8g7BcEyeTc9ybujmYNd3Fy5c+dOKleu\nzPGc17x4oRNv5xbvvRN9+eWX+fb7rtOgAasTEwFYuXIllStXtj/Zz8+SJvSClCpVio4dO/Lrr78S\nFhZGnTp1CA0NJSMjw7an+Y4dO2jZsiVvvPEG48aN48033+Shhx4q0nro3v7+X43L8vfg5vTCFvF0\npVQJzGA2lFK1ub5FXoSncVERz87OJiYmhkqVKhEXF0d4eDjjx4/n2WefdZtVtYRjnD17lhUrVnDv\nvffark2ZMoXhw4cTExPD6NGjefbZZy2MML8jR47YVs07d+4cy5cvJyYmxranOZg/MnP3NG/YsCGf\nfvopn3zyCQMHDiQoKIjMzExmz55tVQricjy4iBe2ObsdsBo4DHwB7AbiCvO9jnggzenWW7vW3tzU\nrJnTXy5vc2Xbtm31vHnztNY6fz+pEC60efNmHRMTo6Ojo3Xjxo31xIkTtdZaHz16VN955526Vq1a\nOiQkRKelpWmtzVz41q1b6+LFi+uRI0fq8uXL606dOunly5dbmYYoSM+e9s+3WbOsjkZrXfjmdGWe\ne2VKqf8HbAbOAbuAn7XWR5zxR8VlXl8XJk7hRL//Drlrc9erB9u2Of0lX3vtNUqUKMFrr71muwMC\nKF26dL5zIdzBnj176Ny5M5s3b853/ZNPPuGJJ54gIyODMmXK0LFjR6ZNm0bfvn3Zvn07AGlpaYSG\nhpKUdL1Lb4hrcs899qVX5893i24bpRRa66t2Wxe2Of0/mJ3MugCTgSlKqYJX6BcO5xb9Yi5oTi+o\nuVIpxU033WSbwrNy5Urq1q3rlNd3R27x3lvIk/LX9pZDAA4fPsyuXbuYMGECxYoVY8qUKcTFxfHn\nn38yZ84cZs+eTVJSEklJSdx33335uhVyeVL+zuCy/A8etB+HhbnmNR2kUGuna61XKaXWAE2B1sC/\nMVuHvufE2IQ7cUER379/P3379kVrTXZ2Nn369OHmm2+mVatWPPHEE26/0InwXQXNkT916hTjx4/n\nzJkzBAUFcf/991OsWDHGjBnDjTfemO/7586dy6rcFcOE6+3fbz/OO5jSAxS2OX0lZueydUAi8IPW\n+pCTY8v7+tKcbjWtISgIMjLM+blznjcARAgX27RpE//61794/PHHGTFiBJmZmURGRto2rAFITEzk\n2WefzXdNuFB2NhQrBllZ5txNPtsc3Zy+GUgHGmH2Fm+UM1pd+AqlIO82k2lp1sUihIeIiorinnvu\nYciQIVSrVo0ePXpQuXLlfKvyXTzNTrjYkSP2Ah4a6hYFvCgKVcS11kO01ncA9wJHgemA8+YZiXzc\npl+sbFn78SHXNMS4Te4WkfwTrA7husXGxvLwww/z+++/M3PmTHr06MGPP/4IQFZWFt988w09e/Ys\n8Hu9If/r4ZL882z7S6VKzn89BytUEVdKPamUmgNsxGxFOg3wnZ3phVGjhv24qHveCuGj6tWrx08/\n/cT58+fRWrNy5UoaNGgAwPLly2nQoMElfeTChTy4PxwKObANMzL9HWCD1jrTifGIArjNLkY1a9qP\nC9jhyRncJneLSP5xVodw3aKionj44Ye5+eab8ff3JyYmhkcffRSAOXPmXLEp3Rvyvx4uyd/D78QL\nOzr9LWcHIjxAeLj9WO7EhSi0YcOGMWzYsEuuT8/dmU1Yx8PvxIu2Ia+whNv0i1lwJ+42uVtE8k+w\nOgRLSf4Jzn8RD78TlyIuCs+CIi6EM9StWxc/Pz9KlChBamoqbdq0oUKFCgQGBhIYGEhISAhNmjQh\nKiqK6OhoqlWrRvHixQkKCqJWrVpF2sREuLm8rYoeuLlSoeaJW03mibuJw4chZ4cmSpaEEyfM1DMP\nFx4eTunSpfHz8yMwMJBffvmFl156iQULFqCUonz58syYMYOqVataHapwkI8++ohy5crRr18//vrr\nLw4cOMD+/ft566232LdvHw888AA7duxgzpw5pKSkEBMTwz333MOkSZNo06YNO3fuxM9P7oG8Qr16\nkLP8LUlJEBNjbTw5HD1PXAgoXx5uuMEcnzoFx45ZG4+D+Pn5kZCQwMaNG20LbgwfPpxNmzaRnJxM\n165deeWVV6wNUjjUoEGDbH+UVapUiejoaGbMmMELL7xAREQEBw4coGZOy9Pbb79NxYoVqV+/PuHh\n4dSrV4/169dbGb5wlPR0+PNP+7kHLuksRdwDuE2/mFIub1J3Re65y7zmFRISYjs+c+YM5cuXd3oc\nBXGb994irsx/+/btPP/88yxYsIBZs2Zx9913M3r0aGbNmkVaWhq//vorTZo04ejRo/z9998uielq\n+Q8YMICwsDAaN25suzZmzBiqVq1KbGwssbGxLFmyBICMjAz69+9P48aNiYmJse1H4M6c/v7v2GFf\n6KVGDftNigeRIi6KJu8IdS/pF1dK0a5dO5o2bconn3xiuz569GiqV6/OjBkzGDlypIUReqfcveO7\ndOkCwFdffUWjRo3w9/e3ZDev9PR09uzZw/z58+nfvz+dOnVi7NixNG3aFD8/PypWrEhiYiJ79uxh\ny5YtLo+vIPHx8SxduvSS60OHDrVtrtKhQwfA7KamlGLz5s0sW7bMrfZqt8zWrfbjnLn7nkaKuAdw\nq7miN91kP/79d6e/nCtyX7t2LUlJSSxevJgPP/yQH374AYCxY8eyd+9e4uPjeeaZZ5weR0Hc6r13\nsPfee4+GudvbApGRkcybN49WrVrZrrkq/8zMTA4dOsQDDzxA165dGTFiBOnp6bYNTWrVqsWWLVso\nUaIEpUqV4ujRoy6J62r5t2zZktC8yyHnKGgM0e+//06bNm0AqFChAmXKlOHXX391SJzO4vT3X4q4\n8DnR0fbjjRuti8OBKufMDa1QoQLdu3e/ZCOK3r17u/2HnadJTU1l8eLFDBw40HatXr161KlTp8AC\n5Ax5tw7t378/devWpWzO0sJTp07F39+fcuXK8fTTT7Nt2zYiIiLYsWMHf//9t+3u1l198MEHREdH\nM3DgQNv2vlFRUSxcuJCsrCz++usvNmzYwL59+yyO1GJSxIUruFW/aGys/dgFTZ7Ozv3s2bOcPn0a\nMH3fy5Yto1GjRuzcudP2nPnz5xOd948XF3Kr996BhgwZwsSJE1FXmd3grPzDw8Np1aoVFy5cwN/f\nn5kzZ5KSksLYsWPx8/Pj3XffJSoqisjISB5//HEqVqzIvHnziIyMpEuXLnTs2NEpcV3sWvIfNGgQ\nu3btIjk5mUqVKjF06FDA/KFSpUoVmjZtytChQ2nRogX+/v4OjtixnP777wVFvLDLrgph1K9vtiS9\ncAH27YOjR6FcOaujumYHDx6ke/fuKKXIzMzkoYce4q677qJHjx5s374df39/atWqxccff2x1qF5j\n0aJFhIWFER0dTUJCgsvuvPPa7cUrDlaoUMF2/Mgjj9C5c2cA/P39eeedd2xfa9GiBXU9cDS2w2Rn\nwx9/2M+liAtncat+0cBAiIyE3ObljRuhbVunvZyzc69ZsybJycmXXP/qq6+c+rqF5VbvvYOsXbuW\nhQsXsnjxYs6dO8epU6d4+OGH+fzzzy95rjfmXxSFyT9vtwDAgQMHqJSz8tg333xDo0aNADh37hxa\na4KDg1m+fDmBgYHUr1/fKXE7ilPf/z17zN7hABUqeOzNiBRxUXSxsS4r4sL7jBs3jnHjxgGwevVq\n3n777UsKuCzuVDi9e/cmISHBNgBvzJgxrFq1iuTkZPz8/AgPD2fKlCkAHDp0iPbt2+Pv70+VKlWY\nOXOmxdFbLO9c/5w/dDyRFHEPkJCQ4F53JHlXNHJyv7jb5e5ivpT//Pnzeeqppzhy5AidOnUiOjqa\nESNG+Ez+Bbna+z9r1qxLrsXHxxf43Bo1arBt2zZHheYSTv39z9nTHYDmzZ3zGi4gRVwUXd7BbV4y\nQl1Yo1WrVrYpZd26daNbt275vu6tA/uEG/CSIi5rp4uiO3fOrJ2elWVWcTt5EvKscCaEEG7t7Fko\nXRoyM8350aOQM73QXcja6cJ5SpQwo9QBtJa7cSGEZ/n1V3sBb9DA7Qp4UUgR9wBu2aR46632Yyeu\nweyWubuQK/MvaB3ul156ybYdZ9u2bUlNTbV97Y033qBOnTo0aNCAZcuWOSUmef8TrA7BUk7Lf906\n+/FttznnNVxEiri4NjnLNwKwcqV1cQiHKWgd7ot3cxszZgxglvCcO3cuW7du5bvvvmPQoEEyoryI\nCvqjafjw4TRo0IDo6Gjuu+8+zpw5Y2GEXsxL+sNBirhHcMvRuXmL+I8/2udbOphb5u5Crsy/oHW4\nL97NrVzOXNqFCxfSq1cvAgICCA8Pp06dOpcsV+sI3vz+F/RH01133cVvv/1GcnIyderUsa3j76uc\n8v5rLUVcCCpXtq9wlJ4Oa9daG49wmoJ2c/v777+pVq2a7TlVqlRx2facV9KrVy+KFStG8eLFiYyM\n5P3332fYsGEEBQUREBBAyZIlCQsLIyoqikaNGuHn50dwcDCNGjWiWLFi+VY0c7aC/mhq27Ytfn7m\nY7lZs2b5ui+Eg+zcCUeOmOPQUKhXz9p4rpMUcQ/gtv1iee/Gv//eKS/htrm7iDvkb+VubkXN/8EH\nH2TmzJnUrVuXdevW8eGHH7Jv3z5q165N3bp1eeKJJ4iIiODuu+9m0aJFlCtXjlGjRtGgQQO6d+/u\nnCSu0bRp06hRo4bVYVjKKb//a9bYj2+7Dfw8uwx6dvTCWnfeaT+WfnGvl3c3typVquTbASs1NZUq\nVapYFZpN165dadasGWC6AsLDw9m+fTunT5+mWrVqNGvWjHLlyjF//nwATpw4Qfny5alVq1a+bVGt\n9vrrrxMYGEhbWQ3R8RYvth+3bm1dHA4iRdwDuG2/YKtWZp44mCkbOVseOpLb5u4irs7/4nW4L7eb\nW5cuXZg9ezbp6en89ddf7Ny5k1tuucXh8VxP/rt37+aHH37ggw8+IC0tjaCgIKZNm8a9997LwYMH\n+eWXX8jMzOS5555j3bp17Nmzx3GBX4cZM2awePFiZs2aJb//js4/PR2WL7ef33OPY3++BWTFNnHt\nypY1q7dt2GB2BFqzBnJ2TBKep6B1uBctWsQff/xBQEBAvt3cIiIieOCBB4iIiCAwMJCPPvroqtuK\nulJWVhbt2rWjVatWNG/eHKUU27dvp2HDhvTu3ZunnnqKFStW0KJFCwYPHkytWrVo3bo1tWvXdmmc\nF//RtGTJEiZOnMiaNWsICgpyaSw+ITERTp0yxzVr2te78GS5v0Tu/DBh+q5Vq1ZZHcLlDRumtRnv\nqfXgwQ7/8W6duwtI/quK/D07d+7UISEhum3btrpatWq6Zs2a2s/PTyuldO/evfX+/ft1YGCgBrRS\nStesWVPXrFlTK6W0UkoHBAToUqVK6WeeeUZrrfWZM2d0nTp1dPHixXWJEiX0pEmTHJLbgw8+qCtX\nrqyLFSumq1WrpqdNm6ZvuukmXb16dR0TE6NjYmJ0ly5dHPJansrhv/9Dhtg/r5580rE/28Fy6t5V\n66PciYvrc+edMHGiOV60CN59197ELoQFckejL89pNl2yZAk9e/YkLCyML774ggkTJtCoUSPOnDnD\n3r172bVrF7t27SIiIoKqVauybds2Ro8ezbmcaZP9+/cHzFaeW7dupUmTJgwePPi64yzM5iXuMLDR\nq3z7rf3YC5rSQdZOF9fr/HmzF+/p0+Z80ybIs3iF8F0DBgzg22+/JSwsjM2bN5OdnU3lypU5e/Ys\ntWvXJj09nePHj9v2vn7kkUeYOXMmJ0+exN/fn/Xr11OsWLEivWa7du1YsWIFSikCAgKoXLkyGRkZ\nZGZmcuzYMQICAqhQoQK33347Z8+eZeHChURHR+Pn58fhw4fp2LEjH3/8MfPnz+frr79m5syZNG7c\nmJYtW/LRRx8BULZsWSZNmsTDDz/s8P9mwol27IC6dc1xcLBZL714cWtjugJZO124RvHi+fvBv/oK\nKHg1qjFjxlC1alViY2OJjY1lyZIlAOzZs4fg4GDb9UGDBrk0BeEcFy9m8t5779GoUSPi4uJITk6m\nbNmy1K9fn6SkJNavX8///d//MXXqVFJSUkhISCAwMLDIr7l8+XK01mRnZ5Oens6ePXv4559/OHTo\nEJmZmZw/f559+/Yxa9Ys2x17UlISv/76K2XLliUsLIxmzZoxcOBA6uXMH46Ojubbb78lPT2dNWvW\ncPz4cX777TeH/XcSLrJokf24bVu3LuBFIUXcA7h9k1qPHvbjnCJe0GpUAEOHDiUpKYmkpCQ6dOhg\nu37TTTfZrufe8YAH5O5khc3/woUL3HrrrcTExNCwYUNGjRqV7+tvv/02fn5+HDt2zAlRFizvYiap\nqaksXryYF1980TYArmrVqpzImdGwbNky2wIsAKGhoSilXPr+Z2ZmkpaWRufOnYmMjGTatGkAfPrp\np1SoUIEyZcrQq1cvKlSoQECAa3oi5fc/wXE/LG8R95KmdJDR6cIROnQwzVNnz8LWrfD777Rs2bLA\nKTuX6xaR7pLrExQUxKpVqwgODiYrK4sWLVqwdu1aWrRoQWpqKsuXL7d04ZAhQ4YwceJEW9EG2Lhx\nI8eOHSM6OprixYsTHh5Ohw4dOHLkCD179mTYsGEujbFatWqUKFGCxYsX8/3339OwYUOOHj1Ktnrw\n7QAAIABJREFUuXLl2LBhg+15pUqVokWLFi6NTVynU6fyb9TUsaN1sTiY3Il7ALefKxocnP8v25y7\n8YJ88MEHREdHM3DgQI4fP267vnv3bmJjY2ndunW+9aLdPncnK0r+wcHBgLkrz87Ott0F5xZQq5w6\ndYqwsDCio6Ntf6y9/vrr1KlTh0OHDpGcnExISAiLFy/myy+/JDExkXnz5rFq1Sqnvv/aPvsFMK1B\n//nPf1i4cCF79uwhIyOD4cOHU7FiRSIiIgAYP348fn5+/PnnnzRo0IDIyEief/55wAxUi4mJITY2\nlpiYGPz9/dm8efN1xSi//3GO+UHffAMZGeY4OhqqVnXMz3UHhRnCbvUDH59i5hHmzLFP3YiM1Fpr\nvXv3bh2Zc6y11ocOHdLZ2dlaa61feOEF3b9/f6211hcuXNDHjh3TWmu9YcMGXa1aNX3q1CkXJ+D5\nsrKydHR0tC5ZsqQeNmyY1lrrBQsW6CFDhmittQ4PD9dHjx51aUy7d+/WFSpUsE31qlSpki5WrJiu\nUKGCPn/+vO15kydP1qGhobbz1157Tb/11ltOi6tGjRraz89PA9rf31/Hx8fr2rVr6+DgYNtUsq5d\nu+rExEQ9ffp0DeigoCBdtmxZ/eGHH+p27drpjIwMrbXWhw8fvuTnb9myRd90001Oi18U0Z132j+f\nJkywOppCoZBTzCwv0IUK0seLuEfMFT51Suvixe3/o2zbdkkRz+tKX4uLi9MbNmzQWntI7k50Lfmf\nOHFCN2vWTC9atEjfeuut+uTJk1prU8SPHDni4Aiv7K+//tKNGjWynU+YMEGHhIToI0eO6P3799uu\nv/7667ps2bL63LlzOiMjQ7dt21YvXrzYLd7/i39XH3jgAb1y5corfs+oUaP06NGjr/u13SF/Kzkk\n/337tFbKfC4ppXVq6vX/TBcobBGX5nThGCEhcPfd9vOvv76kufLAgQO242+++cY2iOnIkSNkZ2cD\nsGvXLnbu3EmtWrVcE7cXKlWqFB07diQpKYndu3cTFRVFzZo1SU1N5eabb+bQoUMuiaN37940b96c\n7du3U716daZPn877779vW02tYcOGlCtXjujoaH755RfGjh1LkyZNiI2NpUmTJtyd9/fJjWzfvp01\na9bQrFkzWrdubVtPPq85c+bw4IMPWhCduMQXX5hbCzDrWrjBGv8OVZhKb/UDH78T9xhffGG7E3+w\ndOlLVqPq06ePjoyM1FFRUbpr1676wIEDWmutv/76a92wYUMdExOjb775Zr1o0SKLE/E8hw8f1seP\nH9daa3327Fl9++236xUrVuR7Tnh4uK3bQhTexXfijRo10k8//bTWWutffvlF16xZM9/zf/75Z924\ncWOXxiguIztb64YN7S2En31mdUSFhqzYJlyuUyfbKPVZJ07AkiWQs6MUXLoaVa57772Xe++911VR\neqX9+/fTt29ftDZzpPv06cOdeXeZw7Z4hEURFt3Fi8UAfPXVV7zyyits3bqV9evXExsbC5jBfPHx\n8aSkpJCVlUWfPn1sA84crVq1arbf16ZNm+Ln52cbxQ4we/ZsuQt3F8nJkDunPzgYvPBzRprTPYDH\nzBUtVQp69rSfT5163T/SY3J3ksLmHxkZSVJSEhs3bmTTpk0899xzlzxn165dlC1b1sEROk98fDyv\nv/56vmuRkZHMmzePVq1a5bs+e/ZsADZv3syvv/7KlClT2Lt3r0Pi0PYWQQC6devG999/D5im9YyM\nDFsB11ozd+5cevXq5ZDXlt//hOv7ATNn2o+7dzfdfl5GirhwrMcesx/Png15ppEJURQtW7Yk5KIP\n3Xr16lGnTp1LWhQqVarEmTNnyMrK4uzZswQFBVGqVKnrjqGgfv3+/fuza9cuIiMj6d27N59//rnt\n+WvWrKF69eqEh4df92uL65SZCXnXp/fSZXJl7XThWFqbeZi582M/+ACeeMLamITH2rNnD507d75k\nvnXr1q15++23bc3pAH369GHp0qWcO3eOd999l4EDB7o6XOFOvvvOvqhL5cqwbx/4+1sbUxHI2unC\nGkrlvxufMsU+MlQIJ/niiy84d+4cBw4cYNeuXbz11lvs3r3b6rCElaZMsR/37u1RBbwoLCviSqke\nSqkUpVSWUir26t/huzyuX+yhh8wgEoAtW+Dnn6/5R3lc7g7m6/mvW7euUM9bu3Yt3bt3x8/PjwoV\nKtCiRYsCp355Gl9//685/z//hIUL7ede3Cpj5Z34FqA7sPpqTxQepnRpyDuwJ+9fxEIU0eW60vJe\nr1+/PitXrgTgzJkz/PTTT9SvX98l8Qk3NHmyvQXw7rvBi38XLO8TV0qtAp7VWidd4TnSJ+5pfvkF\nbr3VHJcoAf/8A2XKWBuT8Ci9e/cmISGBo0ePEhYWxpgxYwgNDeWpp57iyJEjlClThujoaL777jsu\nXLjAgAED2LRpE1pr+vfvz9ChQ61OQVjh5EmzNvqpU+Z86VK46y5rY7oGhe0TlyIunENriImBTZvM\n+aRJMHiwtTEJIbzfpEkwZIg5btDAzBNXV62FbsctBrYppZYrpTbneWzJ+bezM1/X23hkv5hS8O9/\n28/ffhvS04v8Yzwydwdyx/wHDBhAWFgYjRs3tl1LS0vjrrvuol69erRv3z7flqObN2+mefPmNGrU\niKioKNKL8Hvgjvm7kuSfULRvyMqC99+3nz/zjEcW8KJw6optWut2jvpZ/fr1s829zG1Gy92mLveN\n9tbz5ORkt4qn0OcPPwwvvUTC4cOwbx9xs2ZBv37uE5+cX9N5dHQ0t912G+/nfFgmJCQwZcoU2rZt\ny/Dhw3nsscd4/PHHmTVrFllZWXTv3p3Ro0cTHx9PWloaa9euRSnlNvnIuRed/+9/JPz1lzkvWxb+\n9S/3iu8K57nHRZ1V4S7N6c9prTdc4TnSnO6p3ngDRo0yx/XqmaYtL53q4Usunr9dv359Vq9eTVhY\nGAcOHCAuLo5t27bx3Xff8eWXX+ZbEEUIp4mLg9U5Y6VHjoRx4ywN53q4RXP6lSiluiml9gHNgG+V\nUt9ZFYtwokGDzHKsAH/8AfPmWRuPcIpDhw4RFhYGmNXTcndK2759OwAdOnSgSZMmTJw40bIYhZfb\nuNFewAMCzGePD7CsiGut52utq2mtS2itK2ut3XPfQTeQt7nF45QuDU8+aT8fN65Ii794dO4O4Kn5\nq5x+yMzMTNauXcuXX35JYmIi8+bNY9WqVYX+OZ6av6NI/gmFf3Ledfbvv9+MUPcBsmKbcL7Bg800\nMzB/LS9bZm08wuHCwsI4ePAgYPaNr1ixIgBVq1bljjvuIDQ0lBIlStj2ORfCoZKS4Ouv7ecFbADk\nrSzvEy8M6RP3AoMH20eN3nGHvdlLeKTdu3fTuXNntmzZAsCIESMoW7YsI0aMYMKECaSlpXH48GH+\n97//cfr0aY4dO0ZAQAB169YFoFSpUpQvX54ZM2ZQtWpVjh07Ro8ePVi/fj3x8fG2QXNCFEqnTrBo\nkTm+7z746itr43EAj5knXhhSxL3A3r1Qu7bZWQggMRFatrQ2JnFNClqEpVu3btx///3s27ePGjVq\nMHfuXFJSUggJCaFLly6UKlUKPz8/2rVrx9tvvw3A5MmT2bRpE59++ilnz54lOTmZlJQUUlJSpIiL\nwlu3Dpo3N8dKmaWeGza0NiYHcPuBbaLwvKJfrHp16NPHfv7qq4X6Nq/I/Tq4Y/6zZs3in3/+4cKF\nC+zdu5f4+HhCQ0NZsWIFf/zxB8uWLaNMmTK0bNmS0NBQypQpQ0pKCps3b7YVcDDLo5YvXx6A4OBg\nmjdvTlBQUL7Xcsf8XUnyT7j6k1580X7cu7dXFPCikCIuXGfECPDL+ZVbvtwshyh8zujRo6levToz\nZsxg5MiRVocjPNmqVZCzZj7+/vDyy9bGYwFpTheu9eij8Mkn5rhRI0hOlnnjXuxy+4EDTJgwgW3b\ntjF9+nTbtc8++4wNGzZIc7q4Oq3h9tth7VpzPmAAfPqptTE5kDSnC/f06qtwww3mOCUF8nyAC9/S\nu3dvr9guVFhk6VJ7AQ8MzN+s7kOkiHsAr+oXq1TJNKvnevFFOH36sk/3qtyvgafnr7XOt2Xozp07\nbcfz588nOjq6wO/J5en5Xy/JP6HgL2Rnw+jR9vNHH4UaNVwSk7tx6trpQhTo2Wfh//7PbE964ABM\nnAhjxlgdlXCwvKPYq1evzpgxY1i0aBF//PEHAQEB1KpVi48//tj2/Jo1a3Lq1CnS09NZsGABy2Q9\nAXE5M2bAhpyVuosXty/t7IOkT1xYY8YMiI83xyVKwI4dUKWKpSEJITzAsWNmH4YjR8z5Cy/A2LHW\nxuQE0icu3FufPhAVZY7PnfPZ/iwhRBG9+KK9gFev7tN34SBF3CN4Zb+Yv7/ZYzzXjBmwadMlT/PK\n3ItA8k+wOgRLSf4J+S9s3Gi64nJNmgTBwS6Nyd1IERfWufNO6NjRHGsNjz8OWVnWxiSEDxswYABh\nYWE0btzYdi0tLY277rqLevXq0b59e06cOJHve/bu3UvJkiV55513nBtcdjY88YT5F6B9e+jWzbmv\n6QGkT1xYa+tW06yekWHOJ0/Ov+uZEMJlfvjhB0JCQnj44Ydtc/tHjBhBuXLlGD58uG1d/PHjx9u+\n5/7778fPz49bb72VoUOHOi+46dOhf39zHBhopqjmrMXvjaRPXHiGBg0g76pdI0eaddaFEC6Xu1Ru\nXgsWLKBv374A9O3bl/nz5+f7Wq1atWjo7KVO09LyT00dNsyrC3hRSBH3AF7fLzZqlCnmYOaMP/64\nbc9xr8/9KiT/BKtDsJQ75H/o0CHCwsIAqFSpkm3L2dOnT/Pmm2/y8ssv46yWUlv+L70Ehw+b42rV\nfH4wW15SxIX1goLgP/8xOxABLF4MX35pbUxCiAL55ex/MGbMGIYMGUJwzsAyp3V5/vgjfPSR/fzd\nd+2rPgrpExdu5Kmn4IMPzHH58qa/PGeXKyGEa1y83n2DBg1ISEggLCyMAwcO0Lp1a7Zu3codd9xB\namoqYAa/+fv78+qrrzJo0CDHBXP6NERHw59/mvO77oIlS+x/8Hsx6RMXnmfcONNUBmYe6JAh1sYj\nhA+6eKncLl26MGPGDMBsUNO1a1cA1qxZw65du9i1axfPPPMMo0aNcmwBBxg+3F7AS5c2G5z4QAEv\nCiniHsAd+sVcomTJ/HNA/9//I+HNN62Lxw2443tf0DSkzZs307x5c6KioujatSunc9bDP3bsGG3a\ntKFkyZI8/fTTRX4td8zflVydf+/evWnevDnbt2+nevXqTJ8+neeff57ly5dTr149Vq5cyfPPP++a\nYJYsISHPsrxMnmz/I1/Y5f7V5c4PE6bvWrVqldUhuFbv3lqboW16VfnyWh89anVElnHH9z4xMVFv\n3LhRR0ZG2q41bdpUJyYmaq21nj59un7xxRe11lqfOXNGr127Vk+ZMkU/9dRTRX4td8zflXw2/6NH\nta5cWa/K+RzQ996rdXa21VG5VE7du2p9lD5x4X4OHzaj1Y8eNeddusD8+dKM5kYu7jcNDQ0lLS0N\ngNTUVNq3b89vv/1me77sEy6K5MEHYfZsc1yxopkTXqGCtTG5mPSJC89VoQJMm2Y/X7jQPuBNuKWG\nDRuycOFCAObOnWsb8OSuUlNTadOmDQ0bNiQyMtL2x8WVVifL7TJo1KgRUVFRpKenWxW+d5s9217A\nAT75xOcKeFFIEfcAPtkv2KULDB5MQu75c89BUpKFAVnDU977adOm8eGHH9K0aVPOnDlDsWLFHPJz\nnZV/QEAA77zzDr/99hvr1q3jww8/ZNu2bYwfP562bdvyxx9/0KZNG9544w0AsrKy6NOnD1OnTiUl\nJYWEhAQCAwOdEltenvL+O8w//0CewXEJd99tPgvEZUkRF+5rwgSoU8ccp6dDr15w6pS1MYkC1a1b\nl6VLl7J+/Xp69epF7dq1rQ7piipVqkR0dDQAISEhNGjQgNTU1MuuTrZs2TKioqJo1KgRYLoPlHTv\nOFZmptndMKdbhho1zFrp4oqkiHuAuLg4q0OwRlAQcYsWQUiIOd+xw/yV7kPjI9z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def whiten(X, mu, Sigma):\n", " assert(len(mu) == len(Sigma))\n", " assert(np.all(Sigma == Sigma.T))\n", " eigenvalues, S = np.linalg.eig(Sigma)\n", " S = S[:,eigenvalues.argsort()[::-1]]\n", " eigenvalues = eigenvalues[eigenvalues.argsort()[::-1]] \n", " inverse_precision = np.diag(1/np.sqrt(eigenvalues))\n", " return np.dot(np.dot(X - mu, S), inverse_precision)\n", "def plot_whitened_males(ax=None):\n", " if ax == None:\n", " ax = plt.gca()\n", " gaussian_fit_male = calculate_2d_gaussian_confidence_region(mu_male, covariance_male, p = 0.95, points = 100) \n", " whitened_gaussian_fit_male = whiten(gaussian_fit_male, mu_male, covariance_male)\n", " ax.set_title('whitened')\n", " ax.set_xlabel('height')\n", " ax.set_ylabel('weight')\n", " whitened_male_data = whiten(np.array([male_data.height, male_data.weight]).T, mu_male, covariance_male)\n", " ax.plot(whitened_male_data[:,0], whitened_male_data[:,1], \" \")\n", " for i in range(len(whitened_male_data)):\n", " ax.text(whitened_male_data[i, 0], whitened_male_data[i, 1], \n", " male_data.index[i], horizontalalignment='center', verticalalignment='center')\n", " ax.set_aspect('equal')\n", " ax.plot(whitened_gaussian_fit_male[:,0], whitened_gaussian_fit_male[:,1],\n", " linewidth=3, color='red')\n", " ax.plot(0, 0, 'rx', markersize=10, markeredgewidth=3) \n", " ax.grid(True)\n", "plt.figure(figsize=(8,8))\n", "plot_whitened_males()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can plot all three figures together just like in the textbook." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bit0bfo69sOcJJWIkGD7/3PX62LPHLVeoAP/+N/Tpk7NJRkYGl19+Od9++22e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\nktQnJmIkSZIkSZL6xESMJEmSJElSn/w/r8ISblQRiu4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(20,8))\n", "ax1 = fig.add_subplot(1,3,1)\n", "ax2 = fig.add_subplot(1,3,2)\n", "ax3 = fig.add_subplot(1,3,3)\n", "plot_raw_males(ax1)\n", "plot_standardized_males(ax2)\n", "plot_whitened_males(ax3)" ] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }