{ "metadata": { "name": "3b - Linear regression 2D" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Loading data\n", "=====================================================\n", "We will work with \"Parkinsons Telemonitoring\" dataset of the University of Oxford. The original study used a range of linear regression methods to predict the clinician's Parkinson's disease symptom score on the UPDRS scale\n", "\n", "We load the dataset \"Parkinsons Telemonitoring\" using the numpy loadtxt function.\n", "\n", "The columns are separated by ',' delimiter, which we pass to the loadtxt function." ] }, { "cell_type": "code", "collapsed": true, "input": [ "data = np.loadtxt(\"data/artifical_lin.txt\")" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want to work now with 2-dim data, in order to plot it in 3d space. Therefore we select 2 columns (attributes) from total of 12 columns. \n", "\n", "In this example we will select attributes \"Clinician's motor UPDRS score\" and \"Clinician's total UPDRS score\", which are 4th and 5th columns. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = data[:, :-1]\n", "y = data[:, -1]\n", "print X[:10, :]\n", "print y[:10]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[ 0.00747581 0.43208362]\n", " [ 0.49910584 0.20943748]\n", " [ 0.11935362 0.59634898]\n", " [ 0.47691878 0.91091956]\n", " [ 0.73039367 0.88576849]\n", " [ 0.96646013 0.75029941]\n", " [ 0.0254202 0.74285026]\n", " [ 0.17781366 0.59303845]\n", " [ 0.44925923 0.89314114]\n", " [ 0.08370431 0.26143735]]\n", "[ 1.45054918 1.1025327 1.33827336 2.6022192 2.2101526 2.6110778\n", " 1.71069895 2.23335293 3.10281928 0.86406978]\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We shuffle examples:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.utils import shuffle\n", "X, y = shuffle(X, y, random_state=1)\n", "print X.shape\n", "print y.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(500, 2)\n", "(500,)\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we split the data into train and test set:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "train_set_size = X.shape[0] / 2\n", "print train_set_size\n", "X_train = X[:train_set_size, :] # selects first train_set_size rows (examples) for train set\n", "X_test = X[train_set_size:, :] # selects from row train_set_size until the last one for test set\n", "print(X_train.shape)\n", "print(X_test.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "250\n", "(250, 2)\n", "(250, 2)\n" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we split the targets into train and test set in similar way as we splitted data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_train = y[:train_set_size] # selects first 15 rows (targets) for train set\n", "y_test = y[train_set_size:] # selects from row 250 until the last one for test set\n", "print(y_train.shape)\n", "print(y_test.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(250,)\n", "(250,)\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the data in the 3d plot. There is some linear relationship in the data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ax.scatter3D(X_train[:500, 0], X_train[:500, 1], y_train[:500])\n", "ax.view_init(6,-20)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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LP6WcNencuTP79u27pGWojQg+4bJ0qXs2XoyyeRN9UavL/rwMBhN5eWULoFY3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\n9HBTkXcH+M+itbt27eXrry9gNnchIyOec+dW8uyzYzh37g/S0rKpXbs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5LfHze4LY2Bie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\n9xtN4n8AAAAASUVORK5CYII=\n" } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear regression\n", "=================\n", "Create linear regression object, which we use later to apply linear regression on data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn import linear_model\n", "regr = linear_model.LinearRegression()\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fit the model using the training set" ] }, { "cell_type": "code", "collapsed": false, "input": [ "regr.fit(X_train, y_train);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We found the coefficients and the bias (the intercept)" ] }, { "cell_type": "code", "collapsed": true, "input": [ "print(regr.coef_)\n", "print(regr.intercept_)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 0.08241879 2.96344602]\n", "0.0970358170677\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we calculate the mean square error on the test set" ] }, { "cell_type": "code", "collapsed": true, "input": [ "# The mean square error\n", "print(\"Training error: \", np.mean((regr.predict(X_train) - y_train) ** 2))\n", "print(\"Test error: \", np.mean((regr.predict(X_test) - y_test) ** 2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "('Training error: ', 0.15277146364596908)\n", "('Test error: ', 0.16965042383819595)\n" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting data and linear model\n", "==============================\n", "Now we want to plot the train data and teachers in 3d plot (marked as dots). \n", "\n", "With plane we represents the data and predictions (linear model that we found).\n", "\n", "We first scatter the 3d points using mplot3d:\n" ] }, { "cell_type": "code", "collapsed": true, "input": [ "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "\n", "\n", "ax.scatter3D(X_train[:500, 0], X_train[:500, 1], y_train[:500]) # plots 3d points, 500 is number of points which are visualized\n", "\n", "# here we create plane which we want to plot, using the train data and predictions (you don't need to understand it)\n", "range_x = np.linspace(X_train[:, 0].min(), X_train[:, 0].max(), num=10)\n", "range_y = np.linspace(X_train[:, 1].min(), X_train[:, 1].max(), num=10)\n", "xx, yy = np.meshgrid(range_x, range_y)\n", "zz = np.vstack([xx.ravel(), yy.ravel()]).T\n", "pred = regr.predict(zz)\n", "pred = pred.reshape(10, 10)\n", "\n", "ax.plot_surface(xx, yy, pred, alpha=.1) # plots the plane\n", "ax.view_init(6,-20)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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3xGrNRa1OxWy+vNWGFouFTz75hKlTp3Lzzb2YO3cpsbFVN9q4GFarlbS0NLZv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\nuBUkfARBEIRbQcJHEARBuBX/D/+rs8+tFlGdAAAAAElFTkSuQmCC\n" } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the data and the plane in similar way for test data:" ] }, { "cell_type": "code", "collapsed": true, "input": [ "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure()\n", "ax = Axes3D(fig)\n", "ax.scatter3D(X_test[:500, 0], X_test[:500, 1], y_test[:500]) # plots 3d points 500 is number of points which are visualized\n", "\n", "# here we create plane which we want to plot, using the train data and predictions (you don't need to understand it)\n", "range_x = np.linspace(X_test[:, 0].min(), X_test[:, 0].max(), num=10)\n", "range_y = np.linspace(X_test[:, 1].min(), X_test[:, 1].max(), num=10)\n", "xx, yy = np.meshgrid(range_x, range_y)\n", "zz = np.vstack([xx.ravel(), yy.ravel()]).T\n", "pred = regr.predict(zz)\n", "pred = pred.reshape(10, 10)\n", "\n", "ax.plot_surface(xx, yy, pred, alpha=.1) # plots the plane\n", "ax.view_init(6,-20)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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X6vVeWK2NzwWs6corx5CS8j+Sk98FJHr2VDN9+gyMRiNWq/WMtdoDB46iUo1D\np6tafs7b+zp27/6YO+9schEaZTab+eKLj0lO3oSPz3Q6ddqOwdANs/kZIiMjGTgwiYSE25GkSNTq\nrbz00out88TNVD230G6343JVrWXaVojgE4Q2Ij4+hj171pKdLSNJKmR5F0OHXt6kfZOSkpg/fy9h\nYbPRaj1Zv/47PDxWMXXq5Ab3KSsro7i4GH9/f/fKKMePH+ell15i5cqV3HHHfWzYsKvOyh5BQUEM\nH96RrVvnodXG4XDsZ+jQICIiImptV1RUxHvvfUNhoR+yXEl5eRrDh1+DWq0iNrYbKtVx+vd3MHx4\nfK3BKA25+up4PvpoBVbrYFwuC35+iUhST2Q5Cq3WgY9PF8rK0pGkzRiNdsrKMtBoDBQWbmTMmKZP\nk9Dr9cye/RdOnTqFoiiEhYU1q0nSZPLG5Upz37Za0zGZ6q4801xWq4Wvv17Ap59+yGWXjSImZjDl\n5TPQ6brgdBaiKLvo3n0yX3xxLVu3bqWiooIBA+4844jSc0WWZQYOHMixY8d48MEHiYmJuSDlqI8I\nPqFNu9RrpydPnnTPOQsLC+PBB69i794kFAViYkZy5EgamzYdJDzch+HD4xochn/kyAm02sEYDFVN\ncMHBY9i372umTq3/eQ8ePMSCBVuR5SDU6gLGju3MDz98x48//sjMmfewfv0OfHzq71utGsRxNzEx\nGzlx4gidOnVk3Lgr6vSdff/9eoqLBxMWNhhFkdm//00OHFhGz55XYbOV07FjGVdccU2T55R169aN\nWbN0HD6cik6nZuDAqezceZDIyHj8/IrJyPgeRTETG2tk8uSrWbNmI3a7ixtv7MbQoYOwWCxNeh6o\nWux7wYJvKS+3MGZMHBMnXt3kftGrr76STZteITPzdcALT8/93HXXo01+7tPZ7TaWLl3ERx+9R3z8\nIH78cTm9e/fm0KFD3H33P6ms/ACnM5sOHQK4556nCQryZ86cR7jiiita/JytQaVSkZCQQGlpKePH\nj2fTpk2MGTPmgpapmgg+oc261OcYff/9KjZtKkSjCQa2c/fdo4iJ6cWECaHIsszixStJT4/Axyea\n9PQ0cnM3cMstV9dpUiwsLGTHjl0kJnojy1FERkZSUZFNjx71B0plZSX/+98WAgJuw2YrZ+3aOXz8\n8VPceefdrFv3O35+/mcsu1qtZvz4xpdCO3WqFG/vTkDVYtkhIZcRE7OfoKDDeHnpGTx4XLMnUkdF\nRREVFeV7ieuSAAAgAElEQVS+HRkZxK5dR4mKGkfHjgPJytrEyJHe9OjRvc6Fcw8cSOTQoXSMRh1X\nXDHYPen9dNnZ2cya9TwWy62o1d7s3PkJx44d5+GHm3Yldy8vL1577Wn27duH0+kkNnZyk5v5CgsL\n+e2331AUhcGD49m8eT3z5r1N7969WbLkm1oT53v37s3atV+TmprKG2/M58CB3nh7/4Xs7MPcf/9/\n+OGHeYSHhzfpeU/Xmh84fX19mThxIrt37xbBJwjtWXp6Ops3FxAZeRtqtQazuZAvv/yKF1+MRpIk\nSkpKSEtT6NBhIADe3kGcPLmc0tJS/P3/DKby8nKefXYeeXlDkeXf2LJlHl27htKjRwW33HJbvc9d\nXl5OaanMzp3/x/79S+jf/3ZuuOFF/vKXqxoNvapVUoqRJKlJI0O7dQtm27YEjMYrcbnsOBxJDBs2\niL59+7bgHatfdHRPLr+8nK1bFwMweHAH4uP7YbFY+PbblSQlZREc7EN0dDg//JCGr+84HI4KDhz4\nlscfv4WgoKA6x/z11+2YzWPw8oojPf0ZnM4g5s//lezsIp5++pEmjdw1Go0MHz68Wa8lOzubBx74\nF2Vlg7BYDlFePhuTycS4ceP597+fqNOUDFX9aJ07d2b//iP4+89HktR4eY2ivHwY+/fvb1HwtUbo\nFRQUoNFo8PPzw2KxsHbtWp599tmzPm5rEcEnCBdAZWUlKlUAanXVv6Cnp4nCwqqh+zqd7o9andM9\nnLxqjpWzTm3v4MGD5Od3p2PHCXToMI7c3J1UVHzOiy++Wu/Iw9zcXD788EMWL/4fMTHTuPfeqtpF\nWdkPbNmyj9JSJxERPlx2WVythY8tFgtLl64hM1NCUZzExnozadLYRkf9TZ58JYWF35KU9A4qlYsJ\nE2Lo06dP67yBf5AkieHD4xkypOoDQnVf3OefLyUhIRiT6Q5SU9NZvXoevXs/ib9/F0AiK6ucxMTD\nXH756HqPCQq5uR/hck1EpZqEJGWwe/cC1qxZx/XXN9xveja++GIJeXmRmM3LAH8U5Q4sljK2bRvE\nLbf8le+//6TeoNZoNOh0GhyOHHS6DiiKjCxn4uU1okXlkGX5rC9nlJOTwx133IEsy8iyzMyZMxk7\nduxZHbM1ieAThAsgNDQUjWYzZWU5eHuHkp29hy5dfN2jMH19fenXz489ezZjNHbAas1g0KCABuY0\nVoWPWq3DZOqDThdaJ/Ryc3N54403WLBgAVOmTGPx4uWsXn2Q0tJ16PUW/P21FBX1wtc3jJMn0ygv\n38ZNN13prtVt27abzMxIwsPjkWWZAwc20KlTIv36NVx7MxqNPPjgbVRUVKDRaDAajY2+JxUVFeTl\n5aHT6YiIiGhWU3fNE7XNZmP//mzCw+9CklQYDIEkJ3tTXl7On9f5bbhWM2rUSL788mny860oyi0o\nSg7BwQHAQLKyjtfZ3uFwsHjxUo4cSad79wimT7+lWaNpq65XuJrvv5+P1RpIWNjbnDrVHbX6GGr1\nj/j53U9xcT7r1q1j+vTpdfZXqVQ89dT9vPDCg5SXX4NancTAgWqGDRvW5DLU1NilppqqT58+7N27\n96yOcS6J4BOEC8DPz48HHriShQu/JyPDRvfugdx22yT345IkcfXVlxEZmUR+fi7BwcHExETXOU7v\n3r0JCFhPZuZ6tNogzOaNzJgxxP14QUEBb775Jp9//jnXXXcTS5b8QrduPZAkid69Y6moqMBisfDd\nd0cJDOwEQHBwD3JyjmM2m91TGHJySvHxqRqVp1KpMBiiyMvLOePrlCSpSdd7y87O5ssvN2GzhSPL\nZQwYkMSkSS27nJJarUatVnA6LWi1VZcFMpk8sVhWUVioxemswNNzL3371g0RqFrk+/33n2PWrKc5\nceInTKYH8PLSUF6+hR49ateizGYz9933KMnJ/qjV41m/fhs7dz7D3LmvNBoe1c2JW7ZsYO7c15Fl\nJzNn3sby5acwGHoDmSjKZ3h7V/9N6BtdNOOmm26gS5eOHDx4kICAkYwfP77Fiym4XK5L/gK2Ivja\nGTGPr+3o0qUL//nP/Q2eaFQqFX369G70GL6+vvz979N59dUvKChw0LlzIP3796aoqIi3336bTz75\nhIkTr+fnnzcRFhZOSUmJe9/qPpiqvwnrH/MG1TidDsBe68QZEeFPRsYxvLyCkWUXFstJQkKCW+29\n+OWX31CrxxAeHomiyOzbt4LevY+3aMk2jUbDjTcOY8mSz1Gp+uF0pjN8eCTDhsWSnHwIg0HD6NFT\nG51CERERweefv8O//vUKKSkPYTbbmDx5BKNHj3bXRCsqKpg9+2n27TsFvI9K5cLXdxz799/GyZMn\nGy37zp2/8dFH71JRUcbTT/+L6667DkmSiIyczxdfzMDHpxiHwxOtNorS0qV4eq5izJh5dY5Tc+mz\ngQMHMnDgwGa/X6cTwSfU61IfbSicX2d7ktm9+ziDBz+EydSBwsJMZs9+kl271nLNNZP48cf1REQ0\nPo/L19eXgQNN7N69BZUqGFnOZtSojrWmTowcOYjc3LWcOLEUSXIxaFAgsbH1h/KpU6fYsSMVm81J\np04B9O3bA61W2+jrLCoy4+9fdRkhSVKhUgViNpsb3L5acXEx27b9it3uIi6un3tdzLFjRxMeHszJ\nk5kEBEQSFxeH3W4nPr7pC0b7+voyd+6LFBQUoNPp3AM1qm3ZsoWMjEhUqmIkyQ9FsVNRYcbHx4Dd\nbq/3mHv27GTu3NfIycniqaeeYurUqbXel4ceupeHHroXWZZZtGgJq1Z9gb+/F4888iYdOnRoctnP\nRms0dbZ1IvgE4SJmt9spKHDg7+/Nt9++wKpV79O9ezyffLKIuLj4evep/uDmcDj46qvv2bEjCV9f\nD665ZgjBwRI+Pr3qjAbU6/VMnz6R0tJS1Gp1g82XZWVlbNiQirf3AHx9PVi37hdWrdpLZGQEvXsH\nEx/ft94Pjt26BXP48H7Cw+OxWstRlOMEB48mOzubzMxMAgMDa01jgKoJ8k8++QZFRfGAF99++zHP\nPDODmJgYkpOT+fnnbTidLsaNG4RGo2kwjBqjUqkIDq6/Zltebkani8ZoTKOy8k3gcpzOlURESHTt\nWnvC/MGDCcyd+zrHj6fw5JNPMnnyZLy9vRsMGJVKxcyZ05g5c1qzy3y2WmNwS1sngk8QLmJWq5Wt\nW79l/fp7iY29isce+wXIpFu3Hmfcd8GCJaxcaSUg4GEyM0/x8ceLeO21WQ3Ob5Mk6YyLmxcXF2Ox\n+GKzFVNYeJDCwiA8PDoREtKbgwf34eOTSmVlBQsX/kJlpZ2RI2O59dYbueaay7DZNpCa+hl6vcSU\nKfEkJx9l3rxVKEoXZPkEt902jGuv/fMCuxs3bqWoaBihoVMAKCmJYPHi1dx+u44XX1yMWn0TKpWe\nAweW8dhjSoM11Jbq2zcWtfpTOnZ8iNzc5ZSV/YsePfyYN+9192WCkpMPMXfu6yQm7ucf//gHt99+\nO3q9vkm12QtFNHUKwkXK4XCQl5eHXq8n8M+hfJeMiooKPvzwQ95++20GDRrK3Xf/H35+PZHlTIYO\nDa939OfpfbtbtuwnKOg5tFpvDIYQTp06QnJycoPB1xRFRUVs2bIXo3E0eXnZSFIg/fv7oVKp8fLq\nSELCryxfvhsPj7vR6fz56aelqFQ/MGPGTdx667U4HA40Gg2VlZU8//xneHs/jVYbgNNZzldfPc+Q\nIQPdQ/otFjsqVYj7ubVaX8xmK1u27AKuwd+/qllTklSsXr2q1YOvV69ePPHEDcyf/zlqtYXp06/l\nnntuQ6fTcexYCu+//wY7d/7O3/72GIsWLTzjqNa2QgSfIFyEiouLef/9JeTmGpHlSsaM6cBNN028\nJPpmKysr+fjjj3nzzTcZMmQEixb9QPfuPbFarVRUVGAwGNwjMc/EYNDjcJSi1VY3Wxaj14eeVfn2\n708nICACh6MST08PsrJO4OVVdUyLpYjy8mxkeSTe3l0pLy8HLmPt2k+YMeMmAHdNKSMjg+LiUlyu\n/fj6DkCr9UOlCqK0tNQdfIMG9eGnnxZRXh6JRuNJWdkSbryxH0VFZciyw10mWXagVp+bPquRI0cw\ncuSfIz3T0k7wwQdvsXXrJmbPnsX8+R81e3WaC000dQrCRWjp0tXk58fToUM8LpeT9eu/Jjo6sdUn\nT5+NlJQUfvjhNyor7Qwa1Jnx40c3OvzcYrEwf/583njjDQYOjOeLL5YSHf3nor8Gg6HBdTwbcscd\nE3jnnXmUlY1ClnPp3PkUAwfWv9pLNafTSX5+Pj4+PvWe0C0WFz16jMDprMRm80atzqa8PJGcnFIC\nAy2EhnZi69YC0tMzOX48D5crH43mOMuXr+C66yYAVXMOn3/+Q3JyIsnKSsRgWE7XrtPQanMJCfmz\nhhcdHc0TT9zA4sXfYLU6mDRpABMnjicrK4tNmz4hL0+FSqVHUX5m8uQpzXpvmisrK5MPP3yHdetW\ncv/99zN37lsXxXUk6yMGtwjCBdaSqRcZGcUEBFT1canVGtTqruTnF7V20VosOzubjz/ego/PtXh6\n+rJu3UYkaQsTJtRdVNhms/HZZ5/x6quv0qfPAObP/4qYmD8DPCMjk6SkLDQaiT59Ote7skdDRowY\nhsnkz+HDyXh5BTNy5A31hqeiKGRlZZGWlsa7735JaakORSnlwQdv4vrrr621ba9eYWzduo/w8GGo\n1Xq6dvXk+uu7ExISgslkwmaz8fPPr7BhQwoazUA0ml1ERv6T+fM/Z/To4fj5+fHNNz9RVjaeXr3G\ncfx4BmbzOvLyXufdd/9dZ1BNXNxA4uJqD+GPjIzkuefuYd26X3E6XYwadQvR0dFUVlY2+b1pqtzc\nU3z88Vx++eUH7rrrLvbu3dumLr/TEqKpU7jkVDf31Zz/01a1tHwdO5o4cOAwERHDcDrtuFwphIQM\nOPOO50l6ejqK0gdf36qRk2Fhl7F37zdMmPDnNna7nQULFvDKK68QHR3Lhx/+jz59+p12nAxWrTqO\nj08sLpeTkycPct11/Zp0iZ9q0dHRREfXnRhfzeVysXTpSpKSZDZs+JbKypvo2PFaJKmcDz54it69\ne9K9+5+LQY8cGY/L9TsJCUsxGLRMmzaQbt26kZSURGpqKmFhYTzwwFQOHXoHg2E43t4PYDB0pKTk\nB0pLS/Hz86OoqAKdLhwPDyO9e/egqKiIAQMqGi0nVDXR7dyZQGJiJnq9hnHjRrhHgrb23NXCwgLm\nz3+f7777hhkzZrB79+5mfehoy0RTpyBchG6+eTxFRcvIyDiIoliYMKE7vXu37sCGs6HX63G58ty3\nLZYSfH2rlrhyOBx8+eWXvPzyy3Tp0p333vuMfv3qn5R8+HAWPj598PGpGryTl2clLS27WcF3JklJ\nSRw6pCM8fByVlV+j0YymqKiMkJBAVKq+pKen1wo+jUbD2LEjqV6WUVEUvv76BzZsKECl6oii/MSU\nKTEEB+ux28PR6cLIyvoUjSbF/UFn6NAYdu/+GYejMwBO50oGD65/akZNu3btZ/PmCkJCrsJiqWTZ\nsm3MmGFocDpCS5SWlrBo0ecsWbKIm2++iR07drRoMFBrffA8Fx9gq9eHvZSJ4BMuOVWrmdxJUVER\nOp3uvPW1NLVWERMTQ5cuhzhx4hdUKh/U6sPceutoFi5cyIsvvkRUVCfeeGMecXGDGz2ORiMhy38u\nY6UorlYfxFFeXolaHUpJSToOhwaL5TOsVl/8/CYgy8mEhDS+EHJVf1sGYWGzUKu12O2j+OGHt3nm\nmft56aV5JCQcwunsiJ9fH+6442988MHzjB9/JcXF5Xz33b8AuPXWkYwbd+YL8iYlZREYOAadzgu9\n3ouKiu5kZeW0SvCVl5exYMEnfPnlZ0yaNIlff912wS7weq6Jpk5BuEip1erz2vTUnE/der2e+++f\nSnJyMmazmYQEB9dddz2hoeG8+upc4uOH1rtfSkoq27cfweGQ6d8/itjYjqxYkUh+vhVZdqDTnaBL\nl8bDsrnCw0OwWreSmOiiW7dnOXJkFy5XJZmZj3LffVefsSZttVpRqUyo1VWjNXU6bxRFT1RUFFOn\njuXECROeni8iSRJm8zpefvkDFi6cy7RpNzJt2o1AVbPvmWogsiyTlJTMwYMWtNoAevXqgMlkRq/3\naHS/MzGbzSxa9Dmff/4RV111JStWrCA6OrpWMGRkZJCcnIyiKPTq1euiD0QRfIIgnBNqtZqkpCRe\neOFFAgJMPP/86wwbNrLB7TMzM/npp1RMpsswGDRs3ryTK6/UcN11fTlxIgu1WkW3boPrXVHl9Jqo\noiju+2o+Vt/PYWFhDB7sxf79aRiNxQwb1puQkAAqKy3cfPNkrFZrvc9RfZ+Pjw86XTq5ufvx8elC\nYeFuwsKqPiRkZGTjdPZ0l0ejiSYnJ7/WeqLVJElCpVKhUqmQJMl9u/rnLVt+JSvLiF6vQZZD2Lnz\nN0aNKic/vx8zZjxKZaWFIUN68+ij96PX6xt8n6tZrRYWL/4f8+d/wMiRI1i9ehU9e/asM0Dmu++W\n88wz88jPD0KWj+Hvr+Xhh6fzyCP3t/k+9IaIUZ2CILg1FhKKouByuWoNHqpvO1mW+eGHH3j55Zfx\n8vLhySf/w9ChVYFXvQ5kfSGSnHwcSeqMSmVAUcDDoycHDuyhc+coevTo5N6vtLS0wWNUKysrc5ez\n5sm5vp8lScJk8sdqXYHZnIFG04mOHcdjNBrR6/Xu7WqeKGvuq9PpeOyxaSxc+As5Od8RHR3GHXfM\nwMvLi0GDBrB48UfI8tWo1QE4HIu57LI+7qbp6gXVq5caq7omoVLnu0qlYv/+E5hMVxMREURlZRZm\nczhqdRL//e9itNon0GiCWbv2EwyGBTzyyH0Nvjd2u41ly77mww/fJS4ujuXLfyA2NrbW77D69RUV\nFTFnzocUFr4K9EWtLqekZBqffrqZkSMHMWhQ09cFbUvE4BZBOEfOVNOoeWJzOByNbnc+76t2ekjI\nsozVaq0TKNXfZVlm5cqVvPLKK+h0Bv72t6cZMWK0OzBqHq+++3x8PJFli3uunyxb8fX1xMPDo8Hw\nOv2+6mBsrM/T4XBQUFCA0WjEz8+PkpISvvxyEwEB91BaGkhWVgIVFW8wd+4TtS5U25jOnTvz7LMP\n17l/+PDhPPxwFh98MBOLRWHo0P489dS/6ryGmjW801X/nQQGenHoUDa+vj3R6fyxWE5RVpaPw3EF\nXl49kSTw8bmTbdv+xezZdQeEOBwOli9fxrx5bxMdHc033yw+45UOCgoKkKRQXK5A1GpPwAtJikSW\nTWRmZorga8NE8F0CWnICv9BhUlNDNY1q1TWhM21X3331hUhT9z1TraimsrIyjEaje+WRaoqi8PPP\nP/P888+jKBKPP/5/XH75uGY3g/XpE8ORIxvIyXGgUukxGE4yfPiIVj1B5efn8847X1FYqEdRKrj2\n2r5ERYVit3eiS5fhWK1WHI5QSkv3ttoliW699WamT78Jp9NZ571rCkmSUKvVTJx4BYcPLyAvLw9F\nkQkPz6Zv3/4cOHAKSQJFAbs9B5NJT2VlpbuZVFEUVq78iQ8/fJuOHaP4/PPPGDJkyJmfGAgPD0en\nK0CtTsblCkWSjgOZaDTFdOp0c7NfS1vhdDpFU6dQV81aSPXtmt/P9301NfUEXl07aeqJvqGmrNPv\na04ZznTyl2WZ0tJSfHx8Gt2uLVIUhVWrVjFnzhxsNgePPPIE48Zd3eJ+H6PRyNSp40hPT0eWZYKC\nRrb6ROkFC5ZTUjKa0NA4nE4rP/44n2nTNLhc+ciyA4PBgCRVotcrzV4lpjGSJLUo9Gry8/Pj6afv\nJSUlBYDu3SeiKAqrV/+H9PTXUZRQ1Oq1zJ59Px4eHjidTlav/oUPPngLf38/3njjdYYPH44kSe5g\nrPl1+v8KgJeXF++//yz33fcvMjL+jaJUEhTky+zZt9C/f/+zej0XkhjcItTL6XTWui5Xc0/0TQ2R\n5gRHc06oxcXFeHl5XfKf6i4ERVFYu3Ytc+bMoaKiktmz/8FVV01olfdar9cTHBzM4sWrSEsrwdNT\nw7RpY9yXwKlvTpfdbuezz75ix47DmEzezJgxqcGT8okTuRQWJnPkyE8YjSYCAsLQ6/WMGRPOxo1z\nUak6Aoe4994JLb66d02KopCQsJ+DB0/g7W1kzJgh+Pv7t/h4Hh4e9OtXe5L/O+88x9atWzGbzfTs\n+QgxMTFs2LCG9957HZ1Ox6uvvsK4cePctb/T+xAdDof7ds0+R7VajUqlIi4ujh07fiEnJ4fKykqC\ng4PP68ot5+Ki0iL4hHrpdLqLshYiNI/T6URRlCbVRhRFYePGjbz44osUFZXw178+RlBQOGZzJenp\n6e4LpNbHarWSlpaGy+UiIiKi0T64r75aSXZ2b0ymXpSV5fDZZ6uZOdPBxo2JlJRY6djRn0mTLnOP\n7nz33U9YvdqOp+dscnJO8swzc/n881fqnepx6tQxkpKKUatvRlESycj4FE/PF7j77ukMGZJISUkJ\nPj4TMZlMWCyWs77awLZtv7NkSQqensOw2YpJSPiaf/zj9iYvst0UHh4ejB8/HpfLxcaNa3nuuSdw\nOGw888wzTJw4sc6HxzP1JVosFiRJwuVyuUMRIDAw0F07rG4qrK+WeC6ciwnsIvgE4RJXUVHB+vW/\nkp9fTo8eYYwYMZRt23aybdtxFEUiLi6cq64a1eDJYMuWLfz73/8mP7+AWbP+wdVXX8tbb31KUpIV\nCEWlWsJf/zqWQYPicDqdFBYWotFo3AGyZMk68vPDUKl06PUbmTp1RL3BZLfbycgoQ5LC2LfvJCqV\ngdJSGx999Avdut1OeHgw2dnJfP/9Bm6//ToURWHduh34+3+KSuWBXt+ZwsIDJCQkcOWVV9Y6tsPh\nIDs7D73+RVwuTySpJ2p1EuXl5UiSRJ8+fdiwYRvffLMflcoXD49i7rzzqjoXrG2ONWv2ERw8E4Oh\n6hp/mZklJCcn1xoUsnnzFl599WPMZjMjR8bzxBMPN3lQTbUdO7bzzjuvUlJSxL///QzXX399s2vg\n1X2J1c2y1ftX1xKrg7G+WmJ9zaZtmVi5RRAucTabjffeW0xWVjQeHj3Ys2cfe/d+SklJR6KipiFJ\nanbs2IKf3z6GDas9Sm/btm3MmfM86enp3Hvvw9xww1QMBgMJCQkkJRkJD7/9jz6jfixc+BE9e/bg\nf//7hbw8PbJsJS7ORIcOIRQWRhEZWbWWaGGhP9u3J3LddXVXKqmqedpITU3741pzCkVFNjIyDAwY\nUHXVguDgXmRl7cNms6HT6dBqNTidZeh01WFRgU6nq3NsRVFQq1UEBwchyxokSYXd/uecwMzMTNat\nyyA09DbUah3FxSdZsmQDjz46o8XvfVUznVTjtlSr6S45OZl//WsuNttEFEVmxYrdwHv85z9PNOn4\n+/bt5t13XyM7O5Mnn/wn1157bau31NSs1Z3+wej0QDy9lmixWOoEYlsIxvbQ1Hlpx7pwUavuUzmX\n0tPTycryIzJyNF5eofj6DmL16oMYjZ1Rq6s+2QcERHP8eL57n99//51rrpnAX/5yF9deO4U1a7Yz\nadKN7n4vm82GShXgPoHp9QGYzTZWr/6V/PwYwsJuIixsOjt2ODlyJAWt9s/L++j1XlRWOqiPJEmM\nH98Xm209paXrKSlZTHR0ZyTJ6h5sZbWWodPJ6HQ6JEnirrtuoLz8RQoLf6ao6H3CwzMZPLju6i46\nnY5rrhmD2TwHh2MPlZVfEhBw0j2kv6SkBEkKR62uCk1//47k5ZWf1e9n3Lh+5Ob+QHFxCjk5O/Hz\nS6Fnz57ux3ft2kVJiS/l5blUVERgNgexYsX6Mx43MfEADzwwk8cff4jp06eyZ89upk2bVu/J3OVy\n1XOE1lEdZBqNBp1Oh8FgwMPDw11j1ev1qNVq92A5q9WK2WzGbDZjsViw2Ww4HA5cLpe7Bnk+tIfg\nEzU+oV2rCieFkpJ0Dh3ajcsVQE4OpKT8Smho1dUAystz6dnTk127djFnzvMcPpzEww8/xrx5t9Rb\ne+rcuTM63XpKSmIxGsMoKFjN8OE9OXWqFF/f4QCoVGp0uigMhuPY7UeoqDCh0egpLt5PXFzDix73\n79+fESNyUasD8fbuCSh4e2eSm7sSlcqEJGVxww3x7tC94YZJhIcHs3fvIQICAhg58p8N9s3NmDGF\nvLy5pKXNJTa2B48++pr7mnsmkwlFScBuN6PTeVJQkExkpP9Z1U5Gjx6Bh4eBgwf34uNj4IorbqlV\nI6s68dvQaJ5CkrS4XMOwWvdQUlKCn59fneMdOZLEe++9wf79e7nvvntZtOh/7v7C6lpWtZSUFB54\n4EmOHz9GeHgH3n//hfM2ErNmDbG5tcTTm01Pf12tQQSfIFzioqKiiIjYyKpVizAab8DlKmXUqDso\nKNhAcvJiPD0DsFoTeP/9LSQmHuLBBx/l3Xc/a3TZq+DgYB5//GYWLvyZkhIzo0d35dZbp7By5Rb2\n70/BaByMy+XE4ThBr17d6ddPz6+/bsfhkBkzJpJ+/WIbPLavry833DCItWsTsdmy8fNTeOSRmZjN\nZiorKwkI6FHn6gxDhgxhyJAhtVZ2OV1KSgoPP/w8FstYwEJi4o5aJ9WwsDBuvLE3y5cvQlGMmEwu\npk6dUO+xmkqSJAYPHsTgwfVP9I6Pj0en+xWnMx3QAwUEB4e7l0mrdvx4Ku+//yY7dmz/Y4SmHx9/\nvJJvvlnNwoXvEhMTU2t7u93OjBmzKCx8BC+v68nL28gddzzGpk3fndWo0tbQlAE2NfsSq2usZrO5\nwWbT5n44EYNbhEvS+WhCvNAURaGoqAiNRtPoKEmdTsd9903h6NFP0OlKCQ31p0ePbmRlWTEY9vHl\nl2+Qnp7BQw89yjvvfIpe37T5a927d+f55x+pdd/48SMpKlpJenoqYGPUqCiio6ORJImuXbs0+bV1\n60oIDBoAACAASURBVNaFTp2isNls7pVb6qsBNcdHHy3Gbv8L/v5XAVBU5MPSpcv561/vdW8zaNAA\nYmN7YbVa8fHxOecDIHr27MmAAT6cOPEbanUsanUCPXsGugf+ZGSk8cEHb7F58wYefvivPP30P7nh\nhgeB5eh03Sgq+ok77niEHTtW1zpuRkYGpaU6PDxuAsBovBKH4xNSU1OJ/3/2zjuuqvKP4+9zN5c9\nZIMCKg5E0cSdO1MzzZmZllnZMCtt/LK0NPfIbaamuUeWmrnTUnMPAreIgmzZcLn3ctf5/UGgCCgq\nmtl9v16+rnDOee5zrt7nc77PdzW+c/ujf7KPZVGAza2iZDAYsFgKt7ZvtRKLtkaLSrrdLoh38iVa\nhc+KlX8h+fn5TJw4n8jIdETRyHPPNWDo0IHlLtQuLi60aVOXrCw33N0DuXLlCOvXjyQu7jJeXt0J\nCnqZCxeSMJnMVKC+cbmo1Wpee60n2dnZyOXyBwrbl8lklZJLV0RurhaZzLP458JWRGdKnadSqVCp\nVGRkZPDjj7+RlJSNn58LvXq1r/T8NZVKxfTpnzF79jKuXz9CzZq+vPPOCG7cSGHhwtns3r2dN998\nk9mzZ+Do6Mju3buRSJ5CKq0OgI1NNzIzR5OVlVXCknN2dsZiycBsTkMqrYLFkofJFI+LiwsGg4Hk\n5GScnJweWTurB+VWMbud261Es9lc/LvbRVAikRT7G61RnVas/MtYvnwjERH++Ph8hsViYMuW2QQH\nH6BduzblXvP88y1ZuHAdM2asJzb2PAEBoTRp8hNubs0AiI9fz4EDB+nc+dkHmpsgCCUW4djYWPbt\nO47FYqF160Ylmro+Stq3f4pvv12B0fghFoseUfyR1q3Ljtg0Go0sW/YrGk0zXF2rEx9/iR9++JX3\n3x9Q6ZaCh4cHY8eORBAEbtxIZf78GWzd+jOvvvoqp0+fLiG23t7emM1nEYQcJBJHDIYoFAqxlIC5\nuLjw4YeDmTmzF0bj08AxXn75GQwGA61bv0BurgJRzOKLL97mpZf6Ver9PAzuZIGWZSVCaV9ikSge\nOHCAt956CxcXF06ePMnUqVOpWrXqw76FR45V+Kw8cZw/H4+T06t/f+mVKBRNiI6+Srt2ZZ9/+fJl\nJkyYwG+/7eXVV9/klVfW8OWXC8jPv/mFl8nc0WjSK3WecXFxTJy4DuiIIMg4fHgTH3/cDaPRzPHj\nF1EopLRr1xhfX98Kj5mWlkZCQipyuZSgoGoVTjLv0+cFNBodv/wyCqlUwrvv9qBly7KbzGZkZJCZ\nqcbbuzYA7u4hJCX9RVZWFm5ubhWea0XJzMxg6dJv2bhxHQMGvMSJEyfKbC4bEhLCkCFdWLKkE3J5\nLSSSKObOHYdMJiv2V2q1WvR6PW+9NYTw8DDOnTvHxYv1MBgs9Ov3OgUF47Cz64bJlMj48QNo2LA+\ntWrVqvR7qizud+u1PF9ip06d+Oabb7hy5QoNGza8b6s3Pj6eQYMGcePGDQRB4M0332T48OH3NdbD\nwCp8Vv71mM1mrly5QkFBAVWrVqVqVTfi4s5iZ1cNUbRgMJzFz6/0U2tMTAwTJ05k+/YdBAWFUavW\nC1y+rOPatViaNg3mp5+2Igjdyc+/hl6/g5CQgcXX5uXlERUVhclkok6dOvdVxeSPP04gih1wdQ0l\nJ+cqOl0wS5ZswGj0xc6uLSaTnjNntjBiRE+8vMqP9CwiMTGRnTujkUoDMZsLOH/+MC1b1mbSpLn8\n9dc53NxcGTHiNVq1alXqWolEwpAhLzNkyJ3z8vR6PRs3bub48Qv4+VWnQYMwRNEEaCu1fidATk42\n33+/gFWrfqB3714cPXrkrgnz//vfB7zwQmeSk5OpWfPz4vMtFgtz5nzH0qUbADmhodVZsGAys2Yt\n5cyZakAD4uMjcHA4h51dN2QyH8zmxly5cuWxFr6HgUwmo1q1arz00kv3PYZcLmfmzJk0aNAAjUZD\no0aN6NixI7Vr167Emd4/VuGz8q/GZDIxd+4KoqL4u6LILt54oxNXrmwgKekMFouWpk3t6dDhprkX\nGxvLpEmT2Lp1K6+88gbdur1JYmJz3N1botUmM2/eMr78ciA3bmxn/fpPEUVfAgOdiY1Npnbt2uTk\n5PD11wtJS6sJqFCrF/H++72oXr16mXMs2lIqvd0EZnMBMTF70Ot90OudSEhIITy8Oy4uhVueiYla\nIiPPV0j4Tp++hp1dfeztC6M6k5LMjBjxFbGxTVGrx5CWdp5RoyawYUP1Co13O2azmfff/5yzZz3Q\n64NJSlpHXNwhGjd2oUuX2pVWaiwvL4/lyxexfPlinnuuGwcPHii13ZaQkMD8+atITs4iPDyYIUMG\nFEfaBgcHl8gHBNizZw/Llh1FpdqPROJEZOR43nvvf8TEqHF2HoMgQGKiH3l5w3F2fgcQMZsj8fPr\nWSn39G+iMiq3eHp64ulZ6DO2s7Ojdu3aJCUlWYXPipXK4NSpU/z1l5pq1V5CEATS0s6yffufzJ79\nBXFxccjlcqpWrYpUKuX69etMnjyFTZt+ZuDAIezdewwbGzVvvz0ZT8+WCIKAra03Gk11UlNT0enk\ntG//JU5OAZjNJvbuXUvt2rFERJwjLS0MH5/CcP60NC9+/fUAH3xQWviio69y6NBlTCYICHCiVauG\nxbl/Tz/dkO3bF5CZ2Qm12gOZLJUqVVqRkhKNl1ejv0eo+CJkMpmRyRS3/GwiOjoWZ+fvEQQJNjZN\n0ekacu7cuQoLX15eHvPm/UBUVAxqtYzz55Oxs5uFra2EgoJLZGS8hlbbkosXjYSEBJdKpbgXtNp8\nVq1axpIl8+nYsSMHDhwgMDCwuBFtEdnZ2bzzzjhyc/thY1OTNWs2kZY2jy+/HFnu2H/9dQ6j8XnU\n6kKfoFI5iIsXe6FQNCneKgwICOLKlSwMhjcRxWRef/25UkWvK4N/MjK0IlR2Hl9sbCwREREVbvf0\nKLAKn5V/NTk5GqRSn+KFxN7elxs38lCpVMVP/QkJCUyZMpWNG3+kf/9X+O23ozg7Fy6AoiiiVkvQ\nalOwtfXCYjFhNidjZxfKjRu5eHsXWhpSqQyp1IecnBw0Gj1y+c0ISKXSldxcPbeTlpbGvn3XqVKl\nLXK5imvXLqBURtGyZWHeWmBgIP37t+bnn3Oxtb1OrVqhaLXZHD++ihs36mI261GpThAW1rd4zNjY\nWJYtW4dGo6dz51Z06NC++FidOt4cOBCFo2MdjEY9CkUSKpUckykFudwbUTRjsSTcU9muiRPnEhkZ\ngKPjIOLjI8nKmoRanYNU6oxOF4FOV4u4uOe5fv0Gx45NYfbs0cUFsitKQYGetWtXsHDhHFq2bMGe\nPXuKLYOyErTPnDlDbm5t3NyeA8DGZgR79/Zl1ChjuQXF/fw8kUpPIoqvIwhSDIYT1K0bSEFBMikp\ny1AqG2EwbKFHjxYMHdqfKlWqEBhY8RSTJwmTyfTABciL0Gg09O7dm9mzZ1dq8fEHxSp898Hj/LRW\nER73PL6CggKysrIqVIw4IMAfi2Unen0YSqU9KSkHadPGD4CkpCSmT5/OmjVrePHFgezefRhX15LB\nF4Ig8MYb3Zk3bykaTQ3M5mTatPGkevXqBAS4ER8fhYdHAwyGPETxKlWqdKJ+fQm//bYHrdYfiURF\nbu5uOnQIKjW3rKwspFIfFIrCRcTVNZDr1/eXOKdZs8bExp7EwSEIqVSByXSRN95oSV7eVRQKKS1a\n9C7OW0tISGDgwOHk5/dHIqnCwYNLyMvL44UXegAQHFwDiURCdPQ5lEopDRo0wtl5KDNmfIBe3xap\n9CINGthXuDO4VqslMvI6bm6jEQQJnp5tSU7eQnb2NNTq3mRnr8bB4QuqVAlHECAtLZnIyEhatmxZ\nofENBgMbN65lwYKZhIU1YOvWXypkYcnlckQxv9hyMpu1SCTc0TLu1asXv/zyO1FRPZFI3LC3P8+0\nad9ib2/PjBmLuH79IGFhNRg+fOI9F8F+0iis2/rgFp/RaKRXr168/PLL9OjRoxJmVnlYhc/KY0VC\nQgLLl+9Fp3NAFHNo3z6Adu1al3t+jRo1GDIkjVWrZmM0ioSHV6VNm1Z8/PHHrFy5kt69X2L37kO4\nuZXfMTw0tB7jx3uQkJCAg0MoQUFBCILAiy8+y/LlW0lOPoHFoqV9+1o4OjoiiiJhYQ4cOzYNOzsV\nvXo1o02b5qXGzcnJ4fLlGHJzBQIDA8nPz8LZuWQAiKenJ716hXLo0EkMBjMdOhRWbinr4WrHjl3k\n53fG1vYVAAwGP5YunVAsfIWfRxA1atwU4RdeeJ5q1fy4fPkyLi6daNiwYYW3ThUKBVKpGZMpF7m8\nMEHe19eGWrUKyMpahskkEBRUg5tTrdgDlclkYvPmH5k7dzrBwcGsX7/ujonjubm5zJu3nFOnLuPm\n5siwYf0ICsri8uU5yGTBmEw7GDKk6x0Xa4VCwZIlM7lw4QJarZb69b8qToWYNm1MhT6P/wqVsdUp\niiJDhgyhTp06fPDBB5U0s8rDKnxWHhtEUWT16r1Ipc/g6+tDQYGWX39dSWho3TuGybdq1ZwWLZqS\nmprK7Nmzadr0E154oQ87d/6Ju7tHhd7b3d29VIi8s7Mz778/kIsXL7Jly0lOnTKyf/8KFApHfHw6\n4ejoS1LSEU6evEjNmtVK5OBdvHiRWbM2kZ7uxtGjv+DmJvL883Vp3ry0n8Pf3x9/f/+7ztFkMiOK\nN314hfUry6/VmJCQwOjRM4iNTcLV1ZExY4bd04Imk8l47bVuLFkyHoulOXCZxo0d+eqrkUgkEpYv\nX8fGjQsxGJ6loCARZ+dL1K/ft9zxzGYzv/66mblzp+Hj48MPPyyjRYuyUyZuZcqUbzl2zB83t9dJ\nSrrK558vZO7cjzh06BjJyedp2LATbdu2qdD9PE5+pseVyhC+Q4cOsWrVKkJDQwkLK+w8MmnSJJ59\n9sHyYCsLq/BZeWzQ6/Xk5Ij4+/sAoFSqEQQPcnJy7ih8GRkZzJw5k++//57nnnuBbdv+wMvr/vvE\n3YrZbGb79gjs7J7D1taN8+f/IDY2h5SUWNLSArGxqc3162dYtGgHn39epXieS5f+gkLxKrVq1Uav\nv0FKymp8fKQPVAuyU6cOrFr1PlqtJ1JpFWAB/ft3LfNci8XCJ59MIi2tNy4uHcjPP8Nnn01j/vwv\n76m8WZHFeOXKVdzcGtKqVatii3HQoH64ue3i5MnfcXW1pV+/T8r0H1osFnbv3sasWVNxdnZkwYL5\ntGnTpkLvbzAYOHbsMl5eoxEEKQqFC6mpocTHxzNgwOOfXP6wKSpJVplURsmyli1bPpQC2pWFVfis\nPDaoVCpcXKRkZV3H2dkfvT4PQUjFyalsqyAzM5PZs2ezaNEiunTpzi+/7MPHp+LJ3hWhMOFZiYtL\noaApFGrMZi0JCZl4eLRBp4vD3t6bzMxEfvxxKyEhtWjUqD65uVpUKk9MJhO5uQJarTt//RWJnZ0z\n7u7OVKtWjWvXrmGxWAgICKhQl/fAwEAWLZrMwoWr0Wh0dO3anV69Crc5MzIyWLRoLbGxKdSo4UOP\nHh1JSzPh6FhYe9PWtj55eYHExcXdsRt8WYSFhREWFoZOp+Po0aPodHpq166Fr68vXbs+S9euZT/F\nF3al38PMmZORy6VMmzaFZ5555p585DKZDKVSisGQgVLpjihasFhuYGPT8J7uoTJ4nP3ilYm1O4MV\nK48QQRAYMKADK1bsISFBhSDk0717nVI1ILOzs5k7dy7ffvstHTt2YcuW3/D1vftW4f2gVCqJjj7O\n3r3HUCrtCAysBcQAnuTmnkMmi0MU1cTEJOHg0Im4OAunTm2kQYMA9uzZRHp6I/Lzjeh0e9mypQq5\nuWZUqstcvDiLtDQlgqDAz8/EtGmfV6hKRt26dZk7d2KJ3xkMBj7/fAZJSc1Rq3uyf/8R4uKWA/kY\nDKkoFB6YzToslqT7Lmat1WoZP34B16/7IQguyGTL+eijHtStW7fUuaIocujQfmbOnEJBgZavvvqK\nbt263VdQmEQiYdiw3nzzzVhE8WkghqeekjyyFkJl8W8Pbrsb1iLVVqw8Yry8vBgxoj85OTnY2tqi\n0+mKj+Xm5jJ//nzmzZtHu3bP8NNPO6laNeChzmfbtj1oNEEola0xGk1ERi5j2LDGFBQI7Ny5DkfH\np7h06Vf8/J6jRo1mSKUy4uP19OnjREzMVmJj92Nj44GDQwPs7V8kNvY8rq45nD/vQ1DQZwiClNjY\nFSxdupYPP3yr3HnodDpUKtXfUYxmcnJysLOzQ6FQEB8fT0qKElfXQutPpfIjLu4kAwd2ZuXKz9Dp\n6gOX6dHjqfuuu3jy5EmuX/fDx2cAALm5NVi9+mcmTiwpfMePH2HmzElkZmYwZsxoevXq9cBbcZ07\nP4O/vw+XL1/GyakBrVq1qtQC3VZKYjabrUWqrTx5PO7pDHK5vNhXptPp0Gg0fPvtt8yZM4dWrdqx\nYcM2AgJKpg88rKTgkyev4O7eDxsbH0wmI5mZPbFYUnjllZ60b59AfHw8Gza44uFRr/j9BaGws3b7\n9s3JyuqAk1MtLl8+h0ymxmAwk5mZhiA0AArrJapUjbh2bV2Z75+amsobb3xIdPQFZDIZ7703lMuX\ns8jJkaJQ6Bg69HmcnZ2wWLRYLCYkEhmiaAT0dO78DM2bNyE2NhZ395aEhISQl5d3X5+DXl+AINxM\nTlcqXdBobuYuRkScZNasKVy/Hsvo0V/w4osvVqo4hYSEEBJSfp9CK5WHVfisWPkHyc/PZ8GCBXz3\n3Xc0a9aKadMWkJJSwPHj0QiClGrVqpGens6SJT8SHZ2Cp6cTQ4f2qlCEZHlkZGTw559n0Wj0BAS4\n4uCgJDk5GVtbPxQKJRZLKs7OtmRkZPDZZ+OJiopGIjFTvbqGhg3fpaAgFxuby1Sr1hNnZ2cE4UcM\nBi+k0lQyM7cSFlaN3FwRmewogtAJUQSdbj/BwWX7JocN+5To6BYIwo8YjZeZPv11mjadRtWq4Wi1\nKSxY8D0TJ75Bs2Y+/PnnTKTSBpjNJ+nYsRZuboW964pKqT3Iw07t2rWQSleQm1sDpdKF9PRf6NKl\nNufOnWHWrMlcunSeUaNGMXDgwAr5K//LPO6VWywWyxNvUT/Zd2flX4lWq2Xx4sV888031K/fiBUr\nfsLGxpYVK45ja1vYJmjlyiMMHAhLl24mNbUFHh6NycmJZvr0NUya9B62trb3/L75+fls2XICqI9a\n7URExCWqV/cnNvZXUlKuATr8/ZNo2fJtBg/+mPPn66FQ/A+T6S8uXFhIcLADtWrVoGPHrjg5OeHk\n5MT773fm5593IZdrcHJSUbWqHT4+jfjzzyMcPvw2IKV+fXcGD/641HxEUeTMmdNIJMsAAYnEHZOp\nBgUFhb5AtdqTvDxvMjIy+OSTd2nUaB/XrycQENCIdu3aVuri6ufnx8iRz7N69Uby8/U0auTIwYO/\nMW/eKT799FN+/vnHO3alh8L8PalU+lgv+laswS1WrDxS9Ho933//PdOmTaN+/YYsXboOLy9fHB0d\n2br1D1Sqp3B29kejyUOnC2Dv3qMkJZnw9CwUQyen2qSmepGUlFSqr51Op+PatWtIJBICAwOL62VC\nYRmwb75ZzrVrCYADPXs2QKm0xc2tDocO/Yafnw863XWaNw+mXbveZGZmEh0NKtUbgBJRdMZgOIK/\nvyMvv9ydhIQEzp8/T5UqVQgJqUtISOkAkHbtmpORkYHZbMbd3b1MMSjsrO5OdnYkEkk4oqhCEJKQ\nSDQAGI15iGIKTk5OSKVSnnmmY7mfbXp6Onl5edja2nLlyhWys7OpVq3aPbURqlevHkOHqpkzZxrr\n1q1m5MiRrF278q6VTrKzs5k5cxl//RWHg4OS4cP70LhxxarHVCZWwa0YlVGk+nHHKnxW/nEKCgr4\n4YcfmDJlCrVr12PRotWEhIQChYsmgEwmwWIxcvlyDKdOXaOgIJszZw6hVqtwcclFLrdHFE1YLBml\nFuLIyEg+/3wBeXn+uLnZ0qiRkg8+eAW1Wo1Wq2Xs2O/Q6/vj4lKDq1cPsmnTPAYNGkdExG8kJXlR\no0YvlMoMIiP/oGVLAxaLBZVKjUZzEYMhBotFhijGkprqyJ49+/n992QEwQNBOEnfvg0JDS3tmxIE\noUKiM23alwwbNgxBaIEoxhAS4oSj4w5SU6MQxRReeqlpcUmzshBFkSVLVvLTT4eRSBzJz4/B1tYP\nlaoGEslqRo9+tUJlwuLj45g3bwb79u1m+PDhLFmysMI1OWfPXk5UVC18fUei1SYzadIcZs/2wM/P\nr0LXVwaPs0/7ccNq8Vn5z3OvT3/34r8wGAysWLGCyZMnU6NGLRYs+IHQ0MIqD2azmdWrN3Ds2EUC\nArzp3Lklx48f5PBhKSpVQ9TqVDw9B5GYuIDDhz/FbK6BrW0qAwaElOjZlpiYyMiR35CV1Rcbm9Yk\nJMRgNkfxxx+H6NKlI4mJiWi1rri4NEQURdzcwklL201MzGGuXDlJo0bvolTaolTakpRUlaSkJIKC\ngujcuRqrVq3DYumOIKShUrXmyJEoMjOdCQgYilQqR6/P5aef1lKnTq379pm0atWKrVvX8Ndff+Hi\n0o0WLVqQk5NDWloaTk5OdxQ9KIzG3LjxAk5Oc9HpLCQlrQNO4+DQDh+f1kybtoSVK78p998sOTmJ\nBQtmsn37Ft5++23mzj13TykRoigSEXEVb+/3EQQJtrY+ZGeHcu3atUcqfE8qD8NfaBU+K088BoOB\nffv+JCEhg6pVq9CmTQvkcjkZGRls3LiPxMQ8qlSxoU+ftsX9tcrixo0brFy5ndjYDPz8nBk4sHO5\nrW+MRiOrV69m4sRJVKsWxOzZiwkLK7n1NWrUBHbvBomkLUePxhEVtYLXXutMZOR+FAoncnI0xMVd\nJznZwlNPtcLJyR+NJgGttqDEQnDqVARarR82NvVRKJwRhFqkpV0iPb0wutHOzg6zOQOzWYdUaoOr\nqwKTSUfbtkr0eg9sbCSkpd1AFKGgIBuFwhu5XM7gwd357bcxiGIiSqUrnp5vkpU1Db1eRCotDO5Q\nqRzIzJSj1+sfqDL97SXNivyHFSEhIQGLJQyJRE1y8hXM5ibAfnJy3MnLiyEgIAej0Vhi6xcgLS2V\nhQvnsHnzj7z22mucPXv2vloOCYKAi4sd+fnxqFTuZGREkJl5BKWyf7EVdqdXi8VSvBBbtyofDdY8\nPitl8qR8AUVRZPHi9fz1lzN2dg04duwCV69uYMiQfqxZsxuNJhx//xpkZcWzYsVehg/vVWaXbZPJ\nxHffbSInpxW+vnXJyIhmwYLNfPHFayUCHkwmE2vXrmXChIn4+Pgxbdo8GjduWmq8xMREfvvtIvb2\nyxAENaJYwLlzk7BYLLi5SYiLS0et7ktengaJJA+Nxkzt2uFIJM25cmVGiSdWmUyKjY0t+flHkct9\nEcV8LJZIgoO7A4V5gz16NGLTpslATeAcr7/elfDwxshkcsaOnYVWG4ooZuDjcxUXl5bF1/n4OABP\noVYHotOlIpUm4ehoS25uAg4OPqSlncPDQ8r27Ts5ciQSb283hgwZWCoh/2Hi4+ODRLIZi6UnOTl5\nQBTgjlTqicn0G3K5EalUitlsRhRFMjMzWLJkARs3rqF///4cP3682KosyqmsiGDd+jp4cGcmTZpC\nZGQ0BQX+2NpamDhxIbNne+Dg4HBLGkjZr0Vzk0gkJf5YxfDhYBU+K080qampREXlU7XqKwiCgKtr\nMKdPz6VDhzgyMmT4+hYGiDg7+5GQ4ERmZmaJbcQiMjMzSUtT4udXDwA3t2ASEo6Tnp6Oj48PZrOZ\nDRs2MH78BKpUcWfSpFk0aVK6m0ERubm5CIISQSis9SeT2QCFX8aXX27NuHG/odOdRi7X4+kZiMmU\nicGgQRRNqNXyEluzTZqEU7XqQa5evUhu7seIYgr9+zcmPPxmN4ABA3oRFnaetLQ0fHwaFgfG3LiR\nibd3Q+ztqyGThVBQEML+/cfo3r0TCoWCTz99jYkTp5Od7YXJlMjQoc8RFhbCunW7SUzU4ufnRFpa\nAsuXX8Fs7osgXGTv3rdYv35xcdTpvYpIEWX9vqxratasyTPP+LBz5zAgB0GwIAh2mM3vIJHE07Zt\nc7RaLbm5uaxa9T3r16+kR48e7N+/Hx+fwpqpZrMZKC1IRZ/z3YSrefNm1KnzG9euheLmNgg7OzsS\nEubzyy+7GD58aLn/D6BwETYYDAiCgMViKf5jMBT6WgVBKBbBIkEUBMEqiA+ANY/Pyr+arVu38cMP\nvyIIAq+++hzPPVfYMbxkAvvtC4SAUqlEEHQUFOSjVNpiMhmwWHLKjd5Tq9UIggaDQYtCocZkKkAU\ns1GpVMWC5+DgyNixU2nWrOVdFyUvLy88PSWkpCxEJmuL0XgZe/tonnrqIwRBoH37BGxs6uHg4MqJ\nE0e5evUEaWkKpNI4hgxpC9xsYOrk5MSECe+xa9cf5OVpadKkD2FhYRiNRuCmSAQFBREUFIQoiuh0\nOkRRJDk5C0fHEFxcaiCKkJ0tJSkpDo1GgyiK1KhRnVmzPiE1NRUnJ6fircDXX+9eLBYdOryATLYD\nmcwR6EJ6eix//PEH7dvfbCB7u1CU9ftbF/N7fR0x4h3690/mxx9/YtmyPRiNLyIIV3Fyukjv3r1Z\nvnwxy5cvomvXrhw9evSea3lWhOxsPa6uTbGzKwyIkctDiI//vcLXC4KAVCotYYmIolhiO9RoNGKx\nWIr7yd1qHVZGcMvjnn9XWVh9fFb+tezZs5fRozdiY1OYH/bFF1NRqVR06NCu+Bx3d3fq1FFx9uw2\nHBxqkZd3ngYN7PHx8aF79zA2bdoC+GCxpNCpU1CxX+l2y8LGxobu3euzceNyJJIAzOZruLreoH37\n9iiVNnzyyRhatCjsqWcwGO5qzcjlcr788i0mTFhIZmYEnp4yxowZUbyodegQzI4dv5Kb64S32d3T\n6gAAIABJREFUdxZduzbD2dkBD48OuLu7/20x3lz87ezs6N27W/HPRRbErZRlzVSv7kVERCROTgFI\nJAJabRR16vgXlw4DsLW1xdvbm/z8fJRKZYnk7SLxlUiUxU/QoqhCqVQ+8m7U3t7eDB8+jGrVqnLk\nyF/Y2SlRq1vTp09n2rdvxx9//FEqBaQyady4FhERv2BrWw9RNGMwbKNx40YPNGbRw4BEIikRPHSr\nZWg2m0v8n9Pr9aWsQyslsQqflX+cu21llfe6adM+ZLIhqNX1EEUwGIbw8887ad68KWazGb1ej0Qi\n4eWXn/s7uGU/fn4utGnTmdzcXAIC/Bk40IasrCzs7ELw9PQkMzOzxNxuFYuGDevh7u7M1q1bWb16\nDSqVDcOGfczTT7crri9Z3rVlWTMNGjRg3br5pKen4+7uXvxFFASBp54Ko1atGqSmpnLlyhUUCgWh\noaFltsR5EFq2bEZe3l5+//07ANq3r0mrVs3K3AYqWoBvXUilUimdO3dk165PgUFYLOdwdDxLkyal\nk9UfFc2aNSU7uzBwpXnzZuzevYs6deoAcPnyZaKionBycqJNmzaVWr1j8OCXiI+fwY4dPQGRPn3a\nFHeWqGyKRO1WjEYjRqMRiURSwjossiRv9x8+TB53y9Hq47NSLkajsXirBSruc7mf1yLuZYtLpZJh\nNGYWj2E2Z6FWK4rPkUqlyGQy5HI53bt3LnMcOzs7AgICytyKu/Xvoiiyfft2xo0bh8lk4dNPv6Rd\nu3trP1MWcrkce3t75HJ5qbFMJhMffzyB9HQ/QI6T0zKWLJl+x8jTe0UQBLp06UCnToXbp/ezGIwd\n+z+8vJZy+PBCPD1dGDlywQP15LtfDAYDGzeuYf78mTRoUJ8tWzaX6HDw++9/MGLEXMzmNsAhmjbd\nwYIFUypN/BQKBePHf8aoUVokEkmZQVIPk6KHq1ujV4u2SYv+GI1GzGZz8UPMrb7Dx1moKhur8Fkp\nF73+ZoHeuwlRRYMA7vZ6L7z11gCOHPmc9PTCKh+2tpt4880J2NjYYDKZkMvlpULY7xVRFNm9ezdj\nx45Fq9UzfPjHPPNMl0fiGF+6dA2pqa2wsyvsaJCZuZIFC5Yzbtynd71Wo9Fw6dIlBEGgZs2ad912\nvH0RuHjxIqtX7yA/X0+rVqHFDw5lIZfLee+9obz3XgVu6iFgMpnYsmUjc+dOp3r1IJYsWVzCv1jE\n6NFzKCgYjSBUw8ZGxdGjn3Hw4EHatm1bqfO5W5WXR8m9+g2LfIVFluOTKojW4BYr5VLRqhX/FDVr\n1mT16ils27YbQRDo2nUqAQGV08JHFEX27dvH2LFjycrKYfjwj+ncudsDfVlEUWTnzj0cOXIeR0cb\n+vXriq9v+U1lU1IykUja3XJ9EGfP7uXgwaOEhtYut7ddZmYm33yzhuzsIEDE1fUIH344oMJ5cbGx\nsXzxxRKk0pdQq91ZtepnzOatPPtse0RRZOvWbezZcwQHBzVvvDHgvtsAaTQazp07hyAIhISE3LNg\nWCwWfv11M3PnTsPT05OlS7+nefPm5OTklDrXbDYTHR2DRqMAdEAyrq7OxVVz/kuU5zcURRGTyURB\nQUEJQbw9veJRi6E1gf3+sArfffK4t/aBwo7d771Xfo+3+2H//v189dVYbtxIY/jwj+nS5flK+ZJs\n2LCZNWtisLPrhsGQSmTkHGbO/LTcrbYmTUI4fPhnLJZGGI2Qm7saP7+a7Nmj4NixX3jjjefLFL+9\new+j0YTj61tY3zM5+RD79h2mZ88ud52jXq9n/vzlJCQ0xNbWB3t7Ka6uL7J377c8+2x71qz5kXnz\ndmCxvI4oJnHgwHusW7ewzBSQO5Gens7nn88iKysQMOPpuYPx4z+skA9TFEV27drGnDnTsLe3Ze7c\nObRt27Y4HaAsoqKi0OkMiOIBBOFNRDGb9PSNVK/e857m/SRTZB0WuhEKt2lv3So1m82YTKYnIsXC\nKnxWrPzNwYMHGTduHAkJiQwbNpJu3XpWiv9HFEW2bdvF1KkrkUg+w8fHDU/PuqSmJhEREUHjxo3L\nvK5Xrx7ExyezcWNv8vP1BAU9TZs2HyGVykhIEDl79iItWjQpdV12tg6l8ta+cq7k5CSWOa8zZ85w\n8WI8jo5qWrYM59ixv8jOdkMul2Nj40te3g0kkiSqVi38HFat2oRUOh2lsjA6UqO5wZ49v/HKK4NK\njJ2Tk8Po0ZM5eTICV1c3xo4dQcOGDYuPr1//K9nZbXF37wRAcvJP/PLLLl5+uc8dP8fff/+N2bOn\nIJHApEkTePbZZyu02Kanp+PgUI/c3HhMpq5IJE6oVAX3Vanlv8StW6VF0bxFW6Vms7lcv+Gt5z2O\nYmhtS2TlieRerNUjR44wduw4rl69yrBhI+nRo0+lfikOHjzMypXnkEiqAX5cv56LXC4DTHfcOpVI\nJIwY8S7vv/8Wixf/hEbTFqm0cF5SqRKjUV/mdfXqVSUi4ii2tl6IoohGc6TM7gkHDhxm48arqNVP\nYTCkERGxBk9Pd2rWfJbExOXk5v6I2WyDIGznpZdeBoqCkW59Ui77cxo58ktOnvRBJltHQsIF3n57\nFD/9tKR4azc9PQ+V6maJMrncn7S002WOJYoihw8fYObMyeh0+Xz55Zd07979nhbUevXqIQgXUCqH\nY2s7CaPxB3x8EvHw8KjwGFYKuXWrtIhb/YYWi6XYMszPzy+1Tfo4+A2t3Rms/Gc5fvw448Z9zcWL\nlxg2bAQvvND3oTQYPX78PDY2z1KtWhIxMUuwWFqRkPA7detG06hRt7teL5VKadq0Fhs2/Am0wGQq\nACKoWbN0AAdAkyaNycvTsWfPIgRBoFevBjz1VMMS54iiyI4dp/D0fB2lstCXm5CQg7d3HgUFN3ju\nuY+Ijv6D1NTj9O3bnsaNG6PRaOjXryuLFo3BZHoFs/katrY7aN9+YYmxjUYjJ06cQKmcjSDIkUrd\nMZubc/r06WLha9AgiMjI3ajVAYiiiYKCfaVqmQKcOHGUmTMnk5aWypgxo+ndu/d9bVF5enqybt1C\nXn99BDduJBIcXI9Vq5Y/Udtd/6R1dbsYSiQSjEYjKpWqeJu0PL/hP1GazbrVaeU/x6lTpxg37msi\nIyPp0KEHHTq8SvXqng/ti+DoqMZgSEcud0QiuYFePxcfHzkTJ87G0dGxzGCM2wkMrEb9+peIjt6A\nj48P7du3LtevJggCHTu2pmPH1ncc02y2IJHcFHpBkFO3bjBqdRqXLu2iShULzzzTkk6dbo7zyisD\nSExMZPPmGUilTvj7B5UatzCFRIHZnIxM5o8oWoAk7O1bFZ/TrduzZGSsY9eujwCBPn1a0br108XH\nIyNPM3PmFGJjYxg9+gv69+//wFZ4ixYtuHDh2H/iaf9xobyo0juVZnsUQTRW4bPynyEyMpJx48Zx\n6tRp+vQZgJdXU5TKlmRne7N370Xy8k7QunVpn9mD0r17R/btG8e5c3Lk8oE4OBhQKiM4evQ0zz//\n7F2vT0hIYMyYBeTnB2Cx6BDF63h5PfdAcxIEgTZt6rJz5xacnJqi06Xj4HCN4OCWNGzYEI1Gg0Qi\nKdHlXRAE4uLiiIzMo379lSiVrmRlHWby5EXMmzeuxHkffzyMqVPfQqfrglx+gdq1oWXLlsXnSCQS\nXnvtJQYP7l98DcD582eYNWsqFy6c4bPPPmPQoEEPnJJyO1bR+2e51xQLoJSl+KCCaBU+K088Z8+e\n5euvv+bo0WMMHfoe9eq1Yc2a39BoaqNSnaVnT098fFpy4MAPuLs74OnpWakJ2O7u7rRrF05urgtO\nTgG4uLhgNFbj6NENdOvWiXXrNrJjx58olUreffclnn766RLXL1q0AZ3uBdzcmiGKFiIivuXw4cO0\nbn1ni+5udO7cHju7I5w9exBnZxs6depbnO9XXipLUlISglC7OHjGyakZ168vw2g0ltgm7tevF4GB\n/kRGRuLq+jRdunQpcxu5aAGLjr7EnDlTOXnyGJ988gkbN6575AngVipvu/Rex7lTabaijhm3lmZ7\n0BQLawK7lSeWixcvMnXqVA4cOMgbb7zLxIlziIu7znvvLcDO7iuMxhQsliC2bt1Ls2ahHDsWRXy8\nEqk0gXfe6UK9eqW7it8vHh6uODhYiquuaDQZ2NsrWbVqHYsW/YlE8gmimMdHH03g229tadToZo3H\n1NRsbG0LtxQFQYIgBJKenlnm+9wLEomE1q1b0Lp1iwpf4+bmhsWyB5NJi0ymRqO5gKurfZnbkI0b\nNy43YrWIa9euMnfudA4d+oMPP/yQFSuWlbAyrfy3KRI0uVxeLFR3SrGoaGm2/8J295N9d1ZKcenS\nJd544026dOlK9ep12bfvGK+//g42NmqSk5MRhGBUqurI5RogjczMOA4f/oWAgP54eg7C1vY1Fi36\npVTtzQehTZtWeHj8RVLSGpKStgA/0a/fs2zevBdBGIlCEYpK1RKjcRA7dpSs6F+vXjWys/chihaM\nxlzgGEFBlZOof6/UrFmT3r3rk5U1hqysqQjCd/zvf0PKfNpOSEjg7NmzaLXaMo5d57PPPqBPn87U\nr1+H8+fPM2LECKvoWSnF7dZjkcDJ5XJUKhVqtRpbW1tUKhVSqbS48oxWqyU/Px+dTkdBQUGxQBal\nYlgtPitPBDExMUyYMIFdu3bx8stD2L17Es7OJRui+vn5IYrrMZtzcXN7hhs31uDmFoGHRwu8vAoT\nvtVqT3Jy5Gi12kqrXuPg4MD48R9y6tQpTCYTdeu+jaenJyqVAlHMveXMbNRqZYlrBw/uR1bWEiIj\nP0AqFRk0qGOJGpSPmpdf7kObNs3Izc3F19e3VNK5KIpMnDiDdeu2IJd7olBksWLFAmrWrElKSjIL\nFsxk27bNDB06lHPnzv0jdT2tPFnczW9YlG9osVgYOXIkcXFxfPLJJ7Rt25Y+fcrPHf03YxW+J5xr\n164xadIkfv31V1599U327j2OTCYr9USn1+vRarU891w9fv11GBKJC56eekaNGsXChbvR6W6gVnuQ\nmXkWNzdJpbfVsbOzK+WXGzZsIMOHTyQ//zqCkIud3Vb69v22xDm2traMHv0+Op0OuVxebnRjTk4O\nJ0+eRCaTER4ejo2NzR3nU1SiSi6XExUVRUxMDN7e3oSHh9/VX3KnUmuHDh1iw4YDmM27sVgc0Wo3\n8dZbI2jXLoxNm9bz6quvcubMGdzc3O74HlasPAhl5RsCTJgwgUGDBlGtWjXi4uLue/zXXnuNbdu2\n4e7uzpkzZx50upWOVfieUOLi4pg8eTKbN2/m5ZeHsHfvMRwdC+tR3r69ptFomD59GYmJVZBIPKhX\nrzaDBz9HcHAwCoWCd96RsmjRd+TkKHBzExg27MVHklfUrFkzZs/+jIMHj2Fjo6Bnz2/LFZU7CVlC\nQgL9+7+JTlcTUdTh5fUta9cuLtdiPXbsGKNGTSE7Owd7ezvy8yXIZG0QhF/p2vUQo0Z9eN/3f/Xq\nVczmFgiCI6KYicVyitjY49jYPEVERESldpewYuVecXV1Lbb8HmS7c/Dgwbz33nsMGjTo7if/A1iF\n7wkjPj6eKVOm8tNPGxkwYDB79x7DyenO22X79v1JUlIwPj6F9SpTUg5y+vQl6tWrB0BoaD1mzapd\nvL35KJNpQ0JCaNq06QM52ydNmkN2dn8UiiGIokh8/FgWL/6BESNKt0xITU1l5MiJmM2TUKlqc/36\ncmSyXXh7j0AUC9i2bSB9+16576atQUFBSCTr0OtNmEwrkUhCqV49lBkzZtz3/VmxUtk86He8VatW\nxMbGVs5kHgJW4XtCSEpKYtq0aaxbt44XXxzInj1HcHGpWK3FjAwNCkXt4p9tbLzJyLhU4hyZTFbp\njV7vhEajYe3an7hyJYGwsFr07t39vpO0ExNvIAiFfr/Cprj1SUg4Wuq8hIQENm/eTEFBMApFHTIz\nc4FumEw/k5kZh6trAFKpL1lZWfc1j/x8DZGRJzCZzgLncXSsgVqdyPr1a+9rPCtWrNwfVuH7l5OS\nksL06dNZvXo1vXv3Z9euQ7i5VbmnMWrX9uPPP49iNFZHEGTk5h6ibt37a6dTGRgMBkaOHEdMTC0k\nkvacPPk7sbHz+d//3i/3msTERCIiIrC1taVFixYlErvDw0OJjV2NKIYgigXI5T8RHl6yh96JEyeY\nMmU9Go0HOTmXgGRkMk/gApBLQYENubl/YG8fc8/Wnl6vY9WqZSxePJ+2bdtw/PgxlEolWVlZ1KhR\nwxqtacXKI8YqfPfJP92W6MaNG8yYMYMfflhOeHgLhg8fS3h4g3sSPa1Wy86dfxITk4G9fRqJiWNQ\nqezo1CmUDh2evvsAD4mLFy8SG6vAxeXNvyvbh7N372u8+25emX65qKgohg37CpOpOZBCUNCPLF78\nTXGS94cfvk1CwhgOHmwBiPTt25N+/XoXXy+KInPmrEWlGomzsz9a7WQSEt5BEBqiVJ5CJnOmoKAH\ntrbOzJkzvsKRlgUFBaxfv4qFC2fTpEk4O3fuoG7dmwWx77dX33+Jx731l5V/J1bh+5eRnp7OzJkz\n+f77pXTt2p3Ond8gK6sBp0+7c/ToQQYOzKV584qVFtu580+uXvXG27sTjo6Z5OXt47XX2j1QCL3Z\nbGbv3v1cu5aCr68rHTu2rVBZrTNnznDuXDTOznY4OTkC0r97yJmQSASg/AeNiRMXYDR+jI3N04ii\nSHT0F2zfvp2ePQv7ydnY2LBgwTS0Wi1SqRSlsmRKhMViITdXh7u7L4IgEBz8P/Lz30epjCM4eBpK\npTtZWbP5+usXqVmz5l3vxWg08vPP65g37xvq1avHpk0/ExYWdtfrrPw3qMyC2Q/rweCf7hDxsLEK\n378Ao9FIfHw8y5YtY8mSJXTp0p2tW/eRlpbOokXX8PMr3LbT6wPYsmXZXYWv0M9lJiYmA2/vTgiC\ngJ2dKzk5vmRkZNy38ImiyOLFazhyRIJKVZ/Dhy9y4cIyRox4447BKXv37mfRoj8RhJaYzYlUrXoC\nV9cbnDnTF73+BmCgSZOa5foYMzKykMtrFN+byVSD9PTSfrjyuphLpVJCQ4M4c+YX3Ny6odfH4+8v\nUrt2IDExCzGZJLz9dre7ip7ZbGbr1p+ZO3c6gYGBrF69iqZNm97xGiuPhse1911l8DjeV//+/dm/\nfz8ZGRn4+fkxbtw4Bg8e/E9Pqxir8D3mnD59mhEjviIi4hBBQfX47rtVPPVUOADJySkIws0wfpnM\nhrw8U4XGlUgk2Nkp0GqzsLV1+TuRNQuVyue+55qdnc3Rowl4eX2GRCJDFOtz7tw3JCUllZuGIIoi\nK1fuxNn5E1Sqwm3a+PhvsbGJRxTrolTORqnUcPXqlxw/fpzw8PBSYzRp0oA9e35AKh2JyXQDhWI7\nYWEf3NPcR458nRkzlnDmzHYcHW0ZPXogDRs2xGg0IpPJ7ri4WCwWdu7cysKFc/DwcGfx4kWlaopa\n+ffzJItnZbN27eMdsGUVvseU3NxcZs6cycyZcwgMfJbBgw8ilSr5/ffd1K8fhlwup3r16tjaHiIt\nzRcbGzcyMw/QqVPppqrl0axZEBs2rEalqoFKZaF+fRvc3d3ve86FNQElCMJN604QZFgsljteZzAY\nMRpNxMbGIJVKUCgUJCZep0qVCUgk7kgkXuTkdOLMmbNlCt9nnw1Hq53MoUOdUCiUfPTRkFJ1MKOj\no1myZC0ajZ4uXVrRpUvJ7uROTk58/fVHpRa3O/UgFEWRPXt2MHv2FFQqJdOnT61w13MrVqz8c1iF\n7zEjLy+PBQsWMGfOHJ56qilduowmOPjN4uPJyTbk5eXh4uKCk5MTH37Yl19++YPcXD1PP12Njh0r\nZmkcP36KLVvOYTJ5kZ4eRfPmHhw8mMmWLUfx9rbnjTd63nMytYuLC6Ghrvz110bs7MLQaC5QvboZ\nH5/yrUhBEAgIcGbLloUoFH0xmxORSrfi7+9GWtpFVCp3RFFEKr2Ei0vZpchsbW355puvi4vx3i48\n169fZ/Dgkeh0g5FI3Dhx4ju0Wh19+vQscz53QxRF9u/fy+zZU7FYTIwf/zWtWrVCpVI91qJntVis\nWCnEKnyPCfn5+SxcuJBZs2bRvHlr1q3bioeHFzNnbqKgIA+l0h6tNguZLL9E+LuXlxdDh/a/p/fS\naDRs2hSBu/sQFAo7NJoUfvhhNGFhH+PtXYPMzHPMn/8jX331zj1VbxAEgXfeGcjWrbu5eHEHWm0q\n1arVICYm5o7+sYICCZ6eTuh0m1Ao7FCru9OyZRbbts1Erz+AIKRRp46FLl263PH9y/Mjbt++C632\neWxt+wFgNHqyYsX4MoXvbhw+fJBZsyaTl5fLmDGjeeGFF5BIJOTl5d3zWFasWPlnsArfP4xWq2Xx\n4sXMmDGD8PDmrFq1iRo1gouPv/BCIzZt+hlRdEUiSadfv2alohIrgtlsZv36zRw6dBaJxIRO54iv\nr93fx/SYzT7Y2BRGNbq6hpCc/DvZ2dm4ulYsCb4IpVJJ164d2LHjc2Jj/Tl6VM6KFdMZO3YwzZs3\nK/MaQZDi7f0sdnaF952auhMvLxVr187j2LFjODk50bx58ztuOz5sTp48xqxZU0hOTmTMmNH07dv3\nia9gb8XKk4pV+P4h9Ho9S5YsYfr06TRs2JgffviRWrXqlDovJKQO/v6+5Obm4uTkdN/FoVesWM9P\nP6ViZ/caWm0Sycnf4OR0Ai+vxuh0mUil6Uilhb44gyEXiURbHAVpMpm4du0aoigSGBh41woq+/fv\nJzbWFxeXjwHQahsxZ86sEsKXn5/Ptm27SUvLoVo1B2JiVmEy9cRs1qJQ7OHpp4fh6elJu3btUKvV\nDyQyXbp0YtWqYWi1rkgkbgjCdwwaVDFrLyoqglmzpnD1ajSjRo1iwIAB/6gA/xexbs8+OorSI570\nz9wqfI+YgoICli1bxtSpUwkJacCSJWuoU6de8fHo6Gji4pJwdFTToEED5HI5Dg4OD1wubNeu4zg7\nj0Uud0WprIpO15WMjJVYLEdwdpYxdGgrDhxYikTijyheY+DAp7GxsUGr1fLZZ5O5csWEKAoEBIhM\nmTLqjgKs0+kQxZv+Qbnck/z8m4Wx9Xo9X3wxndjYYOTy2hiNv9O4sRqL5QAqlYwXXngTPz+/B7rf\nW/H392fZshl8//068vJ0dOkygC5dnr3jNX/+eYApU8aSmHidjz/+mPfe21ShfEQrVqw8/liF7xFh\nMBhYvnw5U6ZMITi4DgsWLCc0tGSwxpEjx9mw4QIyWShGYwonT/7Im2/2q5QtNaVSjsGgQS53RRBA\noTDSv39nWrZsiY2NDYIg0KpVAhkZGVSp0ghvb28A1q3bxMWLVXFxGQrAlStLWbnyR95+u/ycnPr1\n6yOTTSQ/Pwy53Iu8vOV07nyza/rZs2e5ft0NV9fnMRjSsbV9i4iI0WzYMKfUk2Z2djYrVmwgOTmH\n0NAAevbsdl81O2vUqMHkyaPvet6VK5eZNOkrDhz4A7W6NWp1O1as2Erfvn0rVYyfZIqshrJe7/VY\nUURwUT+5J90SuResVW3uH6vwPWSMRiOrVq1i0qRJBARUZ86cJTRo0KjUeaIosmXLMTw8hqBQ2P9d\ngWQ9V69eve9OALfyyitdmTVrHvn5z2AyJePhcYHmzfuVSOr29fUtlW8XG5uCXN62eMFRKsOIjd12\nx/cKDAxkwoShzJ27iLw8LV26hDJs2JDi42azmbS0i0RFPYMguCCV6qhWzQuLxVJC5HU6HePGzSM1\ntRk2Ns2JitpHUtJSPvjgzbLe9oGIjb3KvHnfsH//b/j718DZeRYODm8DkJU1hzlzljBt2thKf9+H\nye1CYjabi/sM3k1w7lWgbv8d3Nwuu/W1rN+Vd0wikSCRSDCZTBiNRvR6fYmmqkVC+G8Uw8qc87/x\n/v9prML3kDCZTKxdu5bx4yfg71+NGTO+pVGj0jloRVgsFkwmEZmsUIgKm0TaYTQaK2U+7dq1wcXF\niVOnzqJSyejY8ZMK+Qtr1arK0aN/IoqNAAG9/gC1a/uXOi89PZ2YmBjc3NwICgqicePGrFjRuPSA\nFObGJSefxmLZiETih8Gwg6SksaWiMi9fvkxqahXc3Xv9XV2mFr///h5vvaUvrsP5oCQmxjN//kx2\n797Gu+++y8KFcxk8eCQpKTe7VQhCIOnpF+9r/AcVkPs5/3ZL4FZBEUWR/Pz8u4rRreJT3rGKCNqD\nYjabkUgkxXMv6hhuNpsxGAx/p7oUiqBEIvlXWIXWtJJ/HqvwVTKF0ZPrGT9+Au7unkyZMofw8LKj\nGW9FKpXSsKE/J07sxs0tnPz8FGxtr+Pv36rS5hYYGMiJE+eJikoiO3s7Awb0wMnJ6Y7X9OnTnejo\n2Rw9+jaiKNC4sR/9+79e4pyjR48yYsTXCEJNDIarDBjwLB988Ha5Y6akpGBn1xydzhOLxYhS2RGz\n+Uvy8vLK8GXeTH4XxcK/3+uicbsQiKJIamoKCxfO5tdfNzFkyBBOnz6Ni4sLoijSoUM4p07Nx2gM\nAszAQtq27UV+fn7x9bcLjslkwmQyodVqH8j6KU9Aihb/exnj9s/KbDaTl5eHo6PjPX1+jwu3WntF\nAUa3C6HFYikWwH+LED5u/Bc+L6vwVSKpqal06NCRhIQEJk6cQffuve9+0S307t0FpXI3R458i729\nkpde6nbfUZy3YzabmT17BXFxdbG378CpU+dIS1vBF1+8c0efmVwuZ8yYkWRkZCCKIm5ubiW+GKIo\n8tFH4zCZZqBQ1Ecuz2XNmkF06NCKkJCQEmMVCYGvry+ieBa5XItE4ozJdByVSo5KpSq2cEVRJCAg\nAG/vbBITV6FQBFNQ8AfPPBOK2Wwu7iJfUSupiKysTJYvX8SWLRt56aWXOPj/9s48vqkq7//vpE26\nUChdGMpWKKVQaqEF6SayiCIUFaGi8gzggIqOyIzbjCg+/BR1ABEVB1xwFDcEoSAiiMVqxrW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hpANBdXp7D4aoknWZ1lZWUUFBSg0WiIiYmp04ov7rJ//34OHTpEWFgYN910k8Po0tnic4XVamXv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\nTkSuQmCC\n" } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Playing with this Notebook\n", "==========================\n", "\n", "Do linear regression on dataset named 'artifical_lin\".\n", "\n", "Try to see what happens with the error, if you change the sizes of train set and test set. \n", "\n", "Add noise to the data, and fit the model again. How does the error changes when you add more noise?\n", "\n", "You add noise using normal distribution, with mean 0 and width 0.4 (you can vary this parameters).\n", "noise = np.random.normal(0,0.4, (train_set_size,2))\n", "\n", "Add noise to data:\n", "X = X + noise\n" ] } ], "metadata": {} } ] }