{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Copyright (c) 2015, 2016 [Sebastian Raschka](sebastianraschka.com)\n", "\n", "https://github.com/rasbt/python-machine-learning-book\n", "\n", "[MIT License](https://github.com/rasbt/python-machine-learning-book/blob/master/LICENSE.txt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Python Machine Learning - Code Examples" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 10 - Predicting Continuous Target Variables with Regression Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sebastian Raschka \n", "last updated: 2016-09-29 \n", "\n", "CPython 3.5.2\n", "IPython 5.1.0\n", "\n", "numpy 1.11.1\n", "pandas 0.18.1\n", "matplotlib 1.5.1\n", "sklearn 0.18\n", "seaborn 0.7.0\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,sklearn,seaborn" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "*The use of `watermark` is optional. You can install this IPython extension via \"`pip install watermark`\". For more information, please see: https://github.com/rasbt/watermark.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Overview" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [Introducing a simple linear regression model](#Introducing-a-simple-linear-regression-model)\n", "- [Exploring the Housing Dataset](#Exploring-the-Housing-Dataset)\n", " - [Visualizing the important characteristics of a dataset](#Visualizing-the-important-characteristics-of-a-dataset)\n", "- [Implementing an ordinary least squares linear regression model](#Implementing-an-ordinary-least-squares-linear-regression-model)\n", " - [Solving regression for regression parameters with gradient descent](#Solving-regression-for-regression-parameters-with-gradient-descent)\n", " - [Estimating the coefficient of a regression model via scikit-learn](#Estimating-the-coefficient-of-a-regression-model-via-scikit-learn)\n", "- [Fitting a robust regression model using RANSAC](#Fitting-a-robust-regression-model-using-RANSAC)\n", "- [Evaluating the performance of linear regression models](#Evaluating-the-performance-of-linear-regression-models)\n", "- [Using regularized methods for regression](#Using-regularized-methods-for-regression)\n", "- [Turning a linear regression model into a curve - polynomial regression](#Turning-a-linear-regression-model-into-a-curve---polynomial-regression)\n", " - [Modeling nonlinear relationships in the Housing Dataset](#Modeling-nonlinear-relationships-in-the-Housing-Dataset)\n", " - [Dealing with nonlinear relationships using random forests](#Dealing-with-nonlinear-relationships-using-random-forests)\n", " - [Decision tree regression](#Decision-tree-regression)\n", " - [Random forest regression](#Random-forest-regression)\n", "- [Summary](#Summary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from IPython.display import Image\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Added version check for recent scikit-learn 0.18 checks\n", "from distutils.version import LooseVersion as Version\n", "from sklearn import __version__ as sklearn_version" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Introducing a simple linear regression model" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1JFgfCo67UQkEp/CuOGVAzE3bjAIvOPd/8gGMRSuTrkNfBjbxQoqXSIAESIAE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"text/plain": [ "" ] }, "execution_count": 4, "metadata": { "image/png": { "width": 500 } }, "output_type": "execute_result" } ], "source": [ "Image(filename='./images/10_01.png', width=500) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exploring the Housing dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Source: [https://archive.ics.uci.edu/ml/datasets/Housing](https://archive.ics.uci.edu/ml/datasets/Housing)\n", "\n", "Attributes:\n", " \n", "
\n",
    "1. CRIM      per capita crime rate by town\n",
    "2. ZN        proportion of residential land zoned for lots over \n",
    "                 25,000 sq.ft.\n",
    "3. INDUS     proportion of non-retail business acres per town\n",
    "4. CHAS      Charles River dummy variable (= 1 if tract bounds \n",
    "                 river; 0 otherwise)\n",
    "5. NOX       nitric oxides concentration (parts per 10 million)\n",
    "6. RM        average number of rooms per dwelling\n",
    "7. AGE       proportion of owner-occupied units built prior to 1940\n",
    "8. DIS       weighted distances to five Boston employment centres\n",
    "9. RAD       index of accessibility to radial highways\n",
    "10. TAX      full-value property-tax rate per $10,000\n",
    "11. PTRATIO  pupil-teacher ratio by town\n",
    "12. B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks \n",
    "                 by town\n",
    "13. LSTAT    % lower status of the population\n",
    "14. MEDV     Median value of owner-occupied homes in $1000's\n",
    "
" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTATMEDV
00.0063218.02.3100.5386.57565.24.09001296.015.3396.904.9824.0
10.027310.07.0700.4696.42178.94.96712242.017.8396.909.1421.6
20.027290.07.0700.4697.18561.14.96712242.017.8392.834.0334.7
30.032370.02.1800.4586.99845.86.06223222.018.7394.632.9433.4
40.069050.02.1800.4587.14754.26.06223222.018.7396.905.3336.2
\n", "
" ], "text/plain": [ " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", "0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296.0 \n", "1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242.0 \n", "2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242.0 \n", "3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222.0 \n", "4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222.0 \n", "\n", " PTRATIO B LSTAT MEDV \n", "0 15.3 396.90 4.98 24.0 \n", "1 17.8 396.90 9.14 21.6 \n", "2 17.8 392.83 4.03 34.7 \n", "3 18.7 394.63 2.94 33.4 \n", "4 18.7 396.90 5.33 36.2 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/'\n", " 'housing/housing.data',\n", " header=None,\n", " sep='\\s+')\n", "\n", "df.columns = ['CRIM', 'ZN', 'INDUS', 'CHAS', \n", " 'NOX', 'RM', 'AGE', 'DIS', 'RAD', \n", " 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "### Note:\n", "\n", "\n", "If the link to the Housing dataset provided above does not work for you, you can find a local copy in this repository at [./../datasets/housing/housing.data](./../datasets/housing/housing.data).\n", "\n", "Or you could fetch it via" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTATMEDV
00.0063218.02.3100.5386.57565.24.09001296.015.3396.904.9824.0
10.027310.07.0700.4696.42178.94.96712242.017.8396.909.1421.6
20.027290.07.0700.4697.18561.14.96712242.017.8392.834.0334.7
30.032370.02.1800.4586.99845.86.06223222.018.7394.632.9433.4
40.069050.02.1800.4587.14754.26.06223222.018.7396.905.3336.2
\n", "
" ], "text/plain": [ " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", "0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296.0 \n", "1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242.0 \n", "2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242.0 \n", "3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222.0 \n", "4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222.0 \n", "\n", " PTRATIO B LSTAT MEDV \n", "0 15.3 396.90 4.98 24.0 \n", "1 17.8 396.90 9.14 21.6 \n", "2 17.8 392.83 4.03 34.7 \n", "3 18.7 394.63 2.94 33.4 \n", "4 18.7 396.90 5.33 36.2 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv('https://raw.githubusercontent.com/rasbt/python-machine-learning-book/master/code/datasets/housing/housing.data',\n", " header=None, sep='\\s+')\n", "\n", "df.columns = ['CRIM', 'ZN', 'INDUS', 'CHAS', \n", " 'NOX', 'RM', 'AGE', 'DIS', 'RAD', \n", " 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']\n", "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualizing the important characteristics of a dataset" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OXkjhjFJXacTrY9USgUgUTyLhxubVgO5eO0acXly22CDheKyujjkywmEee3Y3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H+Ocm9AJ3mUvLiCSnz/yNzTLmkYn7IUsAwj1uRpVHKwDHWqKYtPZ6sNh/e14dzV\nEWhUcvzs7csoMWnoijeFQlk0pH4YywD/8OLcFNQpqwM6yaPkxTkeI7Znm3ZJw/iUpaBv2EfU5FVa\n9Ni4jtogZXFhWQbBcBxnejNy9zRlnUKhLCZSP+zl41eIvw84fWgwL8WZURYb2kKBkhd7qYrYpmmX\nlOUMTROmLBeoLVIolOUEHZPuXWgkb5Uy31YGNn18XmmXtJUCZTG5v9GCQ3tacGckiCqLHu2NlqU+\nJcoqRRjb+p0+GHRKRKMJVFiM4hhXKKVOCoVCKQTTKahLfbX2ZivOXnZT322VsOwmeePj49i/fz9e\nfPFF1NbWLvXprFjm28qAS6fnlXZJWylQFpMTpwfwk7d6xW2FQoY9D9ct4RlRVivSsa1rvQM/PXpF\nHOMKpdRJoVAohWC6MhrpeHZ4Xxt+kNUGhvpuK5tlla6ZTCbxwgsvQK1WL/WprHjySejeS59PubcY\nkLRQkG5TKIVCOpZFYsm8r1MoFMpyJ8dXkz5L6bi2ollWk7x/+qd/wjPPPAOLhaZazZelzsFe6s+n\n3FvUSFso2GgLBcrCIB3bNCo+IYaOcRQKZaUhHc9qbNJ2RHRcW8ksm3TNX//61zCbzXjooYfwH//x\nH0t9OiuepW5lsNSfT7m32LGxBhzHr0JW24zY+fmapT4lyiole2zTa5WIxhJ4+L5OOsZRKJQVh9RX\n62i2osSkob7bKoHhOI5b6pMAgGeffRbMZG+rK1euoLa2Ft///vdhNufXee3u7l7M06Msc9rb25f6\nFGYNtV1KNivFdqndUqRQ250/AwMD+P/eckFf7Jh2v5H+c9CarIu+X9AzhP9rjw3V1dXT7reSWCl2\nCyxv26UsPnO13WUTyfv5z38u/v/gwYP4+7//+ykneAILcaN2d3cv6nHnq0K52Oe7XI+70ijUNSjk\n9VyOx5rtcWZzHy3H77fSWI7XbyGPNZ/xeaV8x3uF5Xj9uru7sW7dOuAtV0GOt1CsW7cOa9eunfP7\nqN0WhpXkixVyDJ3uuIVipR13riybSV42QkTvXoCqUFIo84feR5SFgNoV5V6HS6fR19c3435r1qyB\nTCZbhDOirCToGLq0LMtJ3ksvvbTUp7Bo5FOhpDcAhTI36H1EWQioXVHudSKBUfzdD8egNd2ccp+w\nbwQ/+8cDdxXto6xu6Bi6tCzLSd69BFWhpFDmD72PKAsBtSsKBdCaLDPW7lEo+aBj6NJCJ3lLDFWh\npFDmD72PKAsBtSsKhUK5e+gYurTQSd4Sw7IMNrXZafiaQpkH9D6iLATUrigUCuXuoWPo0kIneQWi\nUApCFApl7tD7j7IcoXZJoVAoM0PHyoWBTvIKBFUQolCWDnr/UZYj1C7vXVKpFG7enFqsBOB75Ol0\nukU6Iwpl+ULHyoWBTvIKBFUQolCWDnr/UZYj1C7vXW7evImD3/pvaE2W/5+9O4+O6rzvx/++V6PZ\nF21oZjSgXaAFhchaMOAKQwRG2D2YYLuxa1ynOQ12vs3pL256il0amj8aJzk5Pm3zbRP3fE/iGLt2\nk3ghcYBQvClmsZAgFEsCDFoQkmaE1tnXe39/jOZq7tVoH0kj6fP6x56Ze68uM59777N8nueZcrvB\nO21IX1uySGe1MCZbZqGrqws6nU70Hi21QGKhe+XCoEpenNAMQoQsHbr+SCKiuFzdZjIrpXvUtkhn\ns3CmXGYhaqF3WmqBTIbulQuDKnlxQjMIEbJ06PojiYjikqwWtMwCmQ+6Vy4MquTFCc0gRMjSoeuP\nJCKKS0LGTZbWGQulda4udK9cGFTJI4QQQgghC2rKtM4olNZJSHxQJY8QQgghhCw4SuskZPGwS30C\nhBBCCCGEEELiJ2F68jiOw5EjR9DR0QGWZfHd734XhYWFS31ahBBCCCEAwuvf3bhxY9rtZjr2jBBC\nFkrCVPI++OADMAyDN954A42NjXjppZfwH//xH0t9WoQQQgghAIA7d+7gmz84sSrWvyOELG8JU8mr\nq6vDzp07AQA9PT0wGGiNDEIIIYQsjt+ceB9X2rqm3Ob6tRaoDQWrYv07QsjyljCVPABgWRaHDx/G\nmTNn8G//9m9LfTqEEEIIWSUutXSg2bpmym2coQK4R/unPZbHMQSAWRXbxftvzuT7JYRMj+F5nl/q\nk5AaHBzEo48+ir4AVfsAACAASURBVBMnTkCpVMbcprm5eZHPiiS6ysrKpT6FGaHYJVLLIXYpbkks\nFLtkOVoOcQtQ7JKJZhO7CVPJO378OGw2G77+9a/D6XTi4YcfxokTJyCXy5f61AghhBBCCCFk2UiY\nSp7H48Hzzz+PgYEBBINBHDp0CDt27Fjq0yKEEEIIIYSQZSVhKnmEEEIIIYQQQuaPFkMnhBBCCCGE\nkBWEKnmEEEIIIYQQsoJQJY8QQgghhBBCVhCq5BFCCCGEEELICkKVPEIIIYQQQghZQaiSRwghhBBC\nCCErCFXyCCGEEEIIIWQFoUoeIYQQQgghhKwgVMkjhBBCCCGEkBWEKnmEEEIIIYQQsoJQJY8QQggh\nhBBCVhCq5BFCCCGEEELICkKVPEIIIYQQQghZQaiSRwghhBBCCCErCFXyCCGEEEIIIWQFoUoeIYQQ\nQgghhKwgVMkjhBBCCCGEkBWEKnmEEEIIIYQQsoJQJY8QQgghhBBCVhCq5BFCCCGEEELICkKVPEII\nIYQQQghZQaiSRwghhBBCCCErCFXyCCGEEEIIIWQFoUoeIYQQQgghhKwgVMkjhBBCCCGEkBWEKnmE\nEEIIIYQQsoLIluKP/ud//ic++OADBAIBPPHEE6iursbhw4fBsiyKiopw9OjRpTgtQgghhBBCCFn2\nFr0nr7GxEZcvX8abb76JY8eOoa+vDy+++CKee+45vPbaa+A4DmfOnFns0yKEEEIIIYSQFWHRK3mf\nfPIJ1q9fj2984xt49tlncf/996O1tRVVVVUAgNraWpw/f36xT4sQQgghhBBCVoRFT9ccHh5Gb28v\nXn75ZXR3d+PZZ58Fx3HC5xqNBg6HY7FPixBCCCGEEEJWhEWv5KWkpKCgoAAymQx5eXlQKBSw2WzC\n5y6XC3q9ftrjNDc3L+RpkmWmsrJyqU9hxih2SbTlErsUt0SKYpcsR8slbgGKXSI269jlF9mHH37I\n/+Vf/iXP8zxvtVr5Xbt28c888wz/6aef8jzP89/5znf4EydOTHucpqamBTk/Ou7yPO5yEs/vYKUf\nKxHPKd7HWi4S9fujYy3dsZaLRP3+VvqxEvGclpvlVhaj4y7scWdr0Xvy7r//fjQ1NeGRRx4Bz/P4\np3/6J1gsFhw5cgSBQAAFBQXYs2fPYp8WIYQQQgghhKwIS7KEwre//e0J7x07dmwJzoQQQgghhBBC\nVhZaDJ0QQgghhBBCVhCq5BFCCCGEEELICkKVPEIIIYQQQghZQaiSRwghhBBCCCErCFXyCCGEEEII\nIWQFoUoeIYQQQgghhKwgVMkjhBBCCCGEkBWEKnmEEEIIIYQQsoJQJY8QQgghhBBCVhCq5BFCCCGE\nEELICkKVPEIIIYQQQghZQaiSRwghhBBCCCErCFXyCCGEEEIIIWQFoUoeIYQQQgghhKwgVMkjhBBC\nCCGEkBVEtlR/+Mtf/jK0Wi0AYO3atXjmmWdw+PBhsCyLoqIiHD16dKlOjRBCCCGEEDKJUCiEW7du\nid7r6uqCTqebsG1BQQGSkpIW69TImCWp5Pn9fgDAq6++Krz37LPP4rnnnkNVVRWOHj2KM2fOoK6u\nbilOjxBCCCGEEDKJW7du4eDz/wW1IVP8wXtW0Uv3aD+OvfgE1q9fv4hnR4AlquRdu3YNbrcbX/va\n1xAKhfCtb30Lra2tqKqqAgDU1tbi3LlzS1rJC3E8LrZYcdtmB8vy4MGif9CNjBQVHG4/UvUKhII8\n7G4/yvLTsbnMDB5AY4sVXX2jyDMbEOJ5tHYMQa9JhkGlAsfxYFlmyf5NZGUJcTxsLiXePH0NeWYD\nOPDo6rMj12xATZkJPCDEsN0VQFl+GjaXmRHkeJy+0Ikuqx25Zj0e2JwLmYwVHTcSx5FjJXrcOtwB\nnDrXgZ4BJ9au0WLvljyo1clweYM4cbYdPXfD75d5g1AqlyyBgWA8bt84fQ06jRyDIx6oFDLkmvSo\nKp0+1qLjM89swJBbhTdPX5txrE4W3y5vEO3DWvzhzUtYt0aLB7flIwSI4ic/S4cb3eH9KkuMaGqz\nLavrhCy96PjTq5RzKhfEiuGpPpMef7JtIu+33mYQkPfNal9/kMOZxi6MOr0IhXg43AFkpmjR8f51\nrM3UC8+kT1v60NoeLhdJr3l/kJvy2UQSj9qQCW2qZalPg0xiSUo7SqUSX/va1/Doo4+is7MTf/VX\nfwWe54XPNRoNHA7HUpyaoLHFik+u9KDhcg8O7inGsVNtwme1FRYcb2hHbYUFDZd7cLyhHS88XQMA\n+N4rjcI2DZd7RPvo9VZsKTcv7j+ErFiNLVb85PhNABPjLRKPkRgGgOMNt/DC0zUYHPXg5XeuCtvy\nPPDQffmi40biOHKsRI/bU+c68OrJ8WuU54FH69bjxNl2vHoi6n0wePRL1Jq4lKLjFhiP3doKC0I8\npo216PiMFfez2T96nxNn2/HqyWvC+9zYf6Pj5+CeYrz+++sAgEP7y0XX0XK4TsjSk8ZfakrarOMm\nVgzLp/hMevzJtol+/91Pume17+kLnWjrHAKACWWfX5y4JjyTXnzlouiz6Gv+9IXOKZ9NhJDZWZJK\nXm5uLnJycoT/T0lJQWtrq/C5y+WCXq+f9jjNzc0Lcn7Nzc1ovc3A4wsCAHoHXaLPI+9H/gsArTf7\nYm4T/br1Zh/k/t4FOd+FsJyOW1lZGfdjLqR4fAett8dbWKXxFonHWO+7/eLjdPSMCOcTiX3pPnOJ\n23j9zjM5Ts8AI3ntRHNzM3ruSt6/61zU85qJ5RS78Y5bQHw/nUmsTRf3s9k/ep9YsSIV/Szo6BmZ\n9m/H816XiMdabbEbj2PF4/4a6xhfzJ75/Xuybeazb0cPM+F6BMavUWkZKfJZ9N/o6BEfO/rZBKzO\nuAUStyzW1dU1420/++yzeXfeJOr3sJjHnW3sLkkl76233sKNGzdw9OhR2Gw2OJ1ObNu2DY2Njaip\nqUFDQwPuvffeaY+zEBdqc3MzKisrEZD3YfhKuDUqK0Mj2kalCH9tWlUyaiss8PiCMGamIF2vxLuf\ndAMA1ArZhH1KC82ojHNLb+R84225HXe5icd3EJD3TRpvpYVmMIAQw9HvD9k9QGO38F6+JQWVlfmi\n2I8cN7LPbOM2Xr/zTI/TMXJD9NqSoUVl5Xp0St9fE35/sc5rpYl33ALj99OZ3iOni/vZ7B+9T6xY\nkSaKZWVoUF1qhFohQ/7aFNF1JP3b8YyRRD3WcpIo31887q+xjgF/74zv35NtM599rd52tHUMTTjX\nyPUdeSZF75uVoYUxQ42KijywLAOrt110TeWNPZuA1Ru3wMKWdedDp9NNGH83mY0bN85rTN5yK5Mm\nSrwuSSXvkUcewfPPP48nnngCLMvi+9//PlJSUnDkyBEEAgEUFBRgz549S3FqgpoyExgGyDbpIGN5\n/MWDJbANupFuUMLu8uPpB0vAMMDP3wun8lxsteHIV2vwwtM14bEiWQZs/ULW+Jg8ZQibo/LmCZmv\nmjITnt1XCLs3CXlZBmzblIWuPjtyzAYh1tixGLYNuZGXZUB1iRHN16xC44RKIUNGilJ03MoSIw7t\nL0eX1Y4csx7VJcal+OfNyt4teeD5cA+eJUOLB7fmAQAe3JYPDuFeGUuGBn+6jVJ/llokbke9SZAn\nJ+HusBsH64uRZ9ajsmT6e2RNmUl0ny3P02DUw8LuCgDgpx3jFL1/9LXy4LZ8cDyPngEXLGu0QqyM\nx48W5//3Dj7vCbdG/8kXs2Ieh5CpRMeffo7lglgxfPly76SfzWT/6Pdbb/ahtNA8q30f2JwLWRIL\nh8uHzLQiuDwBrElVAjxw36YaVJUYcemaDQfrizEw4oXLG8CZxi64vEGk61XYUm7GA5tzwfMIP3tM\neuy5N3fW3w0hZNySVPKSk5Pxox/9aML7x44dW4KziY1lGWzeaMbmjeOtWO990i7KF9+7LVe0T0fv\nKL6yu1iUw771C1kAwrV6GpRP4ollGRg1XuytHW8t2lKeJdomxAPHosYZpRtU6Oqzi8ZMrMvUYvPG\n8f2a2myiOI88gBOZWp2MR+smthIqlTJhDF5zczNNupIAInGbmpo1YWzPTO6RLMtgS7lZiMkTDUM4\ndjLcCxcZdzpVvEr3j1AqZchPdeLROnHrayR+3jx9TajgAUBHr33C/Z6Q6UTH31zLBZPF8HSfTbdN\n5H25v3fS3sXJ9pXJWOg1CvzfX10R3nt2XyH21pYBAM5f7ROu9+pSIy622oTtuvpGsaXcDJmMpTF4\nhMQRTVs0C11Wu+i1TiUXvc4xGxbzdAiZVlff6ITXuZI4lcZtrH0Iibd4xVnfoC8ux5nOdNcNIaud\n9NqLvjajP5OmWdO1RMjCoGbtWcg1iyeDSTcoKV2HJLRYBdPp0nmoMEsWQ7zizJyhiMtxpjOTNDhC\nVjPpNW1OV8T8rKnNhkP7y+F0++laImQBUSVvFuqqc+D1h3Cn34m1mVp8qSobcnkSpeuQhBWrYDpd\nOk/0mLxc0/IYk0eWn3hUmkIcjySGwcH64qi1IBemwDiTNDhCVhPpmnlVJUbRNa0Ijk/KMdmziBCy\ncKiSNwuXrvfjlffGl3rIytDSA58ktLkUTKVj8tIMiT8mjyw/8ag0NbZY8X/f+Vx4XZafTgVHQhbJ\nZGvmRa7p5ubx5ReokYSQxUdj8mYgxPE4f7UPl67bsL3CAs3Y5A00VoksF5EYfvP0NVy42geO4yfd\nlsbkkaUymzgFKFYJWUp3+u2orbCgutSI7RUW9PTbp9+JELJoqCdvBqStVftqCzDi8CIvi8YqkeXh\n05Y+vPjKReH1C09XT5iJM4LG5JGlMps4BShWCVlKakWyaKbmPEsp3jx9DbljY78JIUuLKnkzIG0d\n7h1w4mKrTVgegZBE19ouXqS2pX1o0sIzjckjS2U2cQqEY/WrD25A35CXYpWQReZw+0WvW9oHhaUR\nXni6BtHzj0vH79XQmDxCFhxV8mZA2lqsGpv+t7VjiCp6ZFnQa5KnfB2NxuSRpTKbOAXCsfrz310X\nXlOsErJ4JisbAeHG8aL08c8mG79HCFk4VMmbAaFno88Oty+I5rZwS9V0BRBCEkWuSY/aCgs8viBU\nChlkSQwuXO2L2Zoaa5wTPYzJfEW35OtVSnAcPyH2pHGaY9JPcrQwilVCFs9Us2nq1HIcO9kmbJtj\nNgB+l/CarlVCFh9V8maguc2Gts4hhDgOpjQN7i03IxDkpi2AEJIIQhwPHkCOSYchuxdubxDdNic+\nax/CgN2DvVvyRIVtGudEFoK0JT81JW1CIa+q1IQgz6O1fQh6TTIYIGZlMGIusUppY4TMzcUWKz65\n0gOPL4g7/U4wDIQZMwNBDjwgSvO/cmV8dk16rhCy+KiSNwO3bXbR4OIDOwuRYVChunR8YDEVHEii\nii5cV5caoVUl48zFbgDAxVYb0vVK0bgnWvSZLISZtOSzLAMGDI433BLemyqtq6bMhGf3FcLuTZpx\nrM41bYzu8WS1k5aFsk06VJeGr4NYaf7RY/LouULI4qNK3gzYXQHRa4fLD61SJnrAU745SVTRhWu1\nQgaGERdMoye3oIIsWShTteRHxx3LMtAoZXB5gwCmTutiWQZGjRd7aytnfB5zTRujezxZ7aRloWtd\nw/i0xYot5eaY11X0mLzoxVDoiULI4qBK3gyU5qWJWpYDQQ5KhXg8HuWbk0QhrajlRy310dRmw0N/\nki/aPnpsKRVkyUKJbsnXK0OoKjHi/NU+YTzPT6N6AWorLEKPQbzTuuaaNkb3eLLaleWLy0IqhQyX\nrtvAAKLnDDBxTB49WwhZfFTJm4EklsG+2gL0DjihUsjQ2GJFVoZGtA3lm5NEMfFhWi1Kk2EZftLJ\nLaggSxYKyzLC+J3m5mY0tdlEacTRUnVK/PkDGxYkrWuuaWN0jyer3eYyM57ZX47m6/1QKWRobrOh\nssSIf36lccJzZnOZCZcvj4/Jo2cLIYuPKnnTCHE8uqx2MAyE9V+AiQ94yjcniWLiw9SOr+wuFh6o\nHMeD4xkhVqPHlkoLsjq1fMqJLwiZK2kacbSy/PQZFwAZhhV6BGeSYhxd2ZwNuseT1Y5lGdRvzUOa\nQYVL18MVvMhs49LnjJT02cKyk8/wTAiJD6rkTaOxxYpjJ69Bo5ShtsICWRKLbJMOPf12XLgK4QY1\n14IDIfE2XY/DVLFaU2bCof3luDTWUnvsZNuyXntsJtP2k6URHadNbTYc2l8Op9s/6wqU1SnHT47P\nPw0sxPGwuZR48/S1mJVFuseTlUqa4i9n2Um3jVwHDIB/jsoYma5nO9JI0tI+iGGHF29/eBMub5DS\nNglZQEtWyRscHMSBAwfw85//HElJSTh8+DBYlkVRURGOHj26VKc1QaS12eUNouFyD/Zuy8WvztwQ\nJgWgGxRJNPPpcWBZBk63X9RrvZzTamYybT9ZGrHidC4V8L5Bn+j1XOO1scWKnxy/KbymeztZLaT3\nyWf3FU67z2yfM5HKYVffKI43jM/QuZyfL4QkusmbaxZQMBjE0aNHoVQqAQAvvvginnvuObz22mvg\nOA5nzpxZitOKSdorkq5XChU8YGJqHCFLLfIwjaTOzLbgvJLGHsUaB0ISw3zjNMKcoRC9nmu8UqyQ\n1Uoa69KGk1jmev2upOcLIYluSXryfvCDH+Dxxx/Hyy+/DJ7n0draiqqqKgBAbW0tzp07h7q6uqU4\ntQmkrVVJkvvYZNOA0/TzZKnNNR5X0tgjKlCsPNK4NuuDcYlXihWyWklj35yumGTL2GbzrFlJzxdC\nEt2iV/LefvttpKenY9u2bfjpT38KAOA4Tvhco9HA4XAs9mlNSjoOg+P4SW9QNEUwSSRzjceVNPZI\nOm0/FSiWv1ipZXtr5x+vc1lYnZCVQFrxUgSts9p/Ns+alfR8ISTRMTzP89NvFj9PPvmksBjz9evX\nkZOTg7a2Nnz22WcAgPfffx/nz5/HkSNHpjxOc3Pzgp/rbP3xNoN3P+kWXj983zp8MXtRv95Vq7Jy\n5oshL7XFil2Kx+VhucRuotxzKa4TB8UuAZbfNblc4hZI7Njt6urCj9+zQptqmXI753APvvmQCTk5\nOYt0ZivXbGN30XvyXnvtNeH/n3rqKXz3u9/FD3/4Q1y8eBHV1dVoaGjAvffeO6NjLcSF2tzcPOVx\np0pLCMj7RDe60kIzKsdaq6Y77kKd72o57nITr+9gqu9TGo86nQYBuX7SVJp4/jbxOlYinlO8j7Wc\nLMb3N13qlzSuzekKVFaWLfh50bGWt0T8/lbKsSYr+1y6dBm+ZFNchrCs1rgFlqasOxM6nQ54b2a9\nvhs3bsT69evn/LeWW5k0UeI1IZZQ+Pu//3v84z/+IwKBAAoKCrBnz56lPqVJTZWWQLnmJJHQlNVk\nOZou9Wu+qWWEkPiarOwTr+VNCCFzs6SVvFdffVX4/2PHji3hmUwtumWZZRlkGBQozc+AxxdEt80u\nTP1NueYkkUSSZXyBIKLbTqebspomECJLKdYsl9HxGp0ExgKwORWTrm1HCJk9hmFx/mrfjJ8Bsco+\nIY7HiJtBdakRaoUMTW02Wi6BkEWWED15ia6xxYp/ffMSKkuM8PiC2H1vLo5/fAsubxAXW21YZ9Rh\nS3nWUp8mISKftvThxVcuCq93VK7Fh813Jp0RNrJYOE0gRBbaVIXI6Wa5jI7r2goLGi6Pr7lFsUrI\n3EQ/C1QKNW5098DjC+JOvxMMA2zeOLvrqrHFijf+53PhdW2FhWasJWSRUSVvBrr6RlFZYhQKExdb\nbdhRuRYhjofHF0RHrx2by+a+zhMhC6G1fUj0WqtOxqH95ejqGwWDcIpNrMXCp+tJIWS+YqVxReKx\nq28Uh75cDq83AEumfkLae3Rce3xB0WcUq4TMzcUWKz65Eq7YFVpSRI0n2SbdrCt50udIqk5JQ1gI\nWWRUyZuBHLMeN7pHRO8xDIOGy3cAhCt9eVkGbCk3U6obSRh6TbLodbpBibbOIYQ4Dl5/CJ+1D07Y\nJxK30aj1lcSbdLHlSMNDpJCpVsjwJ1+0xCxYRse1WiF+hC1krNK9naxkt212UcUu2uCIF8EgB5mM\nnfHxpM+Rsvx0ul4IWWRUyZsBlmGQbdThYqtNeC9NrxRtc6ffjnNXeVz5/C5c7gCa2mxweYM4tL8c\nTrdfSIWjmxxZDP4gh2RZEnZvzoZeI4eMZeDzcWi43IMdlWvx1oc3AQDbK8RTH+eMFV5pAiGykMwZ\n4sWWc8yGCYXMbJMOHB+uAOaZDeDAo6vPDr1Gjq/UFcE65IEpTYWv/ekGeP1Y8FiVpj+/8HQ1pemT\nhDHbcXRSdldA+P9I44lGKUNliRHeQAjvfnwTAI+1mZPP0ByN1p0kZOlRJW8GOnpHcep8J2orLPD4\ngijOSYVSniTahmVZUQEgMlbk0vV+oXKYmpJGqURkUZy+0Imf/bZFeF1bYYFWHe4BiaxTCQBNbTY8\nvmsDWBbCYuE0gRBZaCatf0JDQoukZ3nQ7sWxk9cATBx7F/36Gw8X4eHdpQt+ztL055b2IarkkYQx\n35ksy/LTcLzhFoDwc+HRnUXwBznhPSB83f3ixLUZHZtlGRg1XuytXfpp5AlZraiSNwO5ZgNc3iAa\nLvdAo5Thng2ZuG114LEvFSEpiYHD5Ydt0CXaJzJWRBWVTkTjRchCkaaS3bbaRZ8Hghwy9Ercf89a\nZK3RIMOgwMCoDy5vEDIZg8fqNqC5uXlC6yylqJF4C3E8rA457F5xTJXlp+HslTvYfs86DI56kWFQ\nYt0aNfLWpoJlxDEXPRavd8C7KOctTX+WviZkKcVKgZ6uvCG+v+vxzP5ydFrtyEhRIRTi0Gl1iraP\nXHfRx6ZnBCGJa06VvB/84Ad45JFHUFBQEO/zSSiRm1dPvx3P7C+H3e2HQi7Dy+9cFbaprbAgx6TD\nbatDtG9WhhZffSgdvzxzQ3iPxjaRhdLYYsV/vnMF2+9Zh7P/24sck070eZ5Zj1fHekUA4IndG/D5\nnRGoFDLkmPSTHpdS1Ei8NbVY0W8HBkdd8PpDSGKBe0pMSGIY1G/NE3rvgHCc/tfp6xPSiqMbz8zp\n4tTPhZJr0gvZHNNdN4Qstlgp0NOJnnhL2lv+xO71KMlNFQ1TiVx30cem2ZgJSVxzquRpNBp84xvf\nQEpKCg4cOIAHH3wQGo0m3ue25KQ3r0P7y/G5ZAIWjy+I3gEXmtpsQgEg16zHhuxUVBYbYc7Qhqen\nH0uFI2QhdPWNYvs964SxdhqlDE/tLUH/sBsGjRzDDnFvh23YjawMLcry01FdOnlcUooaibcum12I\nUwBQK4sR5MKTrkh77GzDbgAQ7q8sw6A4JxUZKSqsy9Qu6mLoVaUmhMbGCOaYDVNeN4Qstlgp0NOJ\nngFTOlPtwKgXZ6/04sCOQvT0O2HJ1MI65MKh/eWiY9NszIQkrplPlRTlr//6r/H73/8ehw8fRktL\nC/bu3YvDhw+jqakp3ue3pCbcvKzhQf/RVAoZMlPUQjrnxVYblPIkbN5oBhOdskDZC2QB5ZoNGBwd\nr8i5vEH0D7vxfx75ImRJLNRKcWqZMVU9YZH0WChFjcSbbcg94XVX3yg8viDSDeIJrbKN4R7pyP2V\n43k43H5s3mjGV3YXY0u5GTzHLcp5Ry/CTrdzkmh4jsOW8vHrYiYpk9EzYEpnqjVoFagsMWJw1AuF\nPAmnznfi7JU+ON1+0bFpNmZCEte8xuRVVFSgoqICgUAAH330EY4dO4YjR47g1KlT8Tq/JSW9eWUY\nVGDZ8KLSDMNAp5ZDJWfh9vpxYEchBke9SDcokWcOp/HEWoOMWrjIQqgpM6FvwImPLoVfa5QyZKaq\n8e+//iOy0jVouNSNJ3ZvQO+AC1kZGpz+tBMDoz6cOt81ZXoNpaiReMvLMkx4nWFQ4U6/Ex9f6hbu\npblZeuQYtXh81wYMO7zQqJPRY3NCq5EvyUzFlJZGVpromZQNWgVYloHTE4BKIYNKniRK36yrXgd/\nkIPTE8CFq33C2DuajZmQxBWXiVcuX76MhoYGtLa2YsuWLfE4ZEKI3Lxa2gcx7PCi564TN28P4f6q\nbHh9ITg9AaTrFVAqZHjld23CfmtSyvHm6WtwemihXrI4WJbB2kwNnti9AbYhN7LWaPDqifGYfGpv\nCYYd4YKzddCFgdHxQfrSuAxxPD79rA9Xbt6FTiXHhuwUcBwHY7qOUtTIvJlSVUKcGtPVYMCBB4/7\nKyzINulwd9iDbJMO/YMu+AMhfPLHbuStTcWpC10AgAstVqTrVYt+L6W0NLLSRPdOgwHWpKjAsgws\nGRoMO8PPiMgyCqk6JX71wecAgOMN7cL4bJqNmZDENedKXmtrK37729/i5MmTyMvLw/79+3HkyBEo\nFIszCH4xRG5eXX2jON7Qg+pSI2o2ZqHL6kBzmw2VJUZcbR9ErlkPjVIGlzdcqWseWzYh1hpkhCyU\n9l4H7tx1wuMLQueWi2LyTr8Tn37WF1678cvlov2kcdnYYsWLvxAvB1KSS73QJD7a++z4r9PXhdf7\nagvw03dacGh/Od7+8CYqS4xo6xxCtlGH4x/fwr7aAnx+RzwWuqV9UJjNT87OadTBrFFaGlnOYs2C\nOdXEKwd2FEKjlGHPllzctjkQCHGiZwqNzyYk8c2pkldfXw+/34/9+/fj9ddfh8VimX6nZSzXbIBG\nKUO2UYcRhw8eXxCVJUbhhnix1Sa6QUbGkSQlsfjqQyXwBziaeIUsOH8wNB6TEMdkqk6BzRvNCIU4\nBAPBKdNrpD0WHl8QXZIlGQiZixDHIxjkUV1qhFohQ1ObDQ63H0B4zHOs+6pt2D1hvNCww4vjDeHt\nnt1XuCjnTmlpZDmTphv/w1iWUoR04pWhUS/21RYIDTLSZwqNzyYk8c2pkved73xnRaVlTqeyxIhH\n69ajpX0Q2UYdgiEObskNUZbEorrUiJKcNLz14edCa9eh/eX48o78mGuQERJPLk9A9FqtlKG61Ihs\now6nzncKy2AZFQAAIABJREFUMZmVoQUD4LG6DTFjMlsy7k6lkMGcvvJmzyWLr7HFijf+Z7wXr7bC\nAp4PJ43lmvVovtYv2t7jCyLXlIZskw7bNmWhq88OlmXw9tjsnBkGBRy+JPz7r/+IXLMeD2zOhUy2\nMD17lJZGljNp4123zY6RqFmXpQ0pIZ6f0IMuS2Kxe3M2dGq5MPcAISRxzamSt2XLFpw/fx5vvPEG\n2tvboVAoUFhYiCeeeAKbNm2K9zkuuaY2G155rxUA0NEzggfuzcWg3YvtFRY0tdng8gaRplciGOLQ\nM+AUCtMA4BxrpSZkoUV6kCOyMrQ4dT48jikSkxqlDG5fEKcbuzBg92DvlrwJFT2n24+D9cWwDbmh\n08iRzDKQJS3Ov4GsbNKCplKeBJc3gEP7y5FhUCLbqBOty1W0NgUKOYPNG8MVq5oyM06d60BpfjrU\nChmyMjR456NbqCwxovlaP/z+EPZtL6QGNUIk8swGYRIttUKGQbsXTW02fKWuCB4/B6fHj0d2FsLj\nC8LhDqC5zYaqEqPoGMZUNQZG3Dh1vhMbclKX5h9CCJmxOVXy3n33Xbz00kt46qmncODAATAMg+vX\nr+Nb3/oWDh8+jN27d0+5P8dxOHLkCDo6OsCyLL773e9CLpfj8OHDYFkWRUVFOHr06Jz+QQshumBS\nmp+B138vHk8iS2LQN+jE2St9eHi7eIH46HEbsXLiqTBC4sXtDYhmwmTA4YWna3Cn3y4UnCtLjDje\ncAtAOB2O4YH6reKKnm3YjYERLz5o6hbe21crjmtC5kI6rk2nluPslV7kmPSwDrpxprELj+wsQpfV\nDpVChuMNt1BXkyNs39hixU/fuSq8fqyuaEKKpylDuyC9bXT/JssZB1405u7J+mK4vEF4/JzwTACA\ng/XF+N3ZTgDhBu4DOwox4vQhRavA7X47ZCw7NleBncbkEZLg5lTJ+9nPfobXX38d69atE96rra3F\nrl278Hd/93fTVvI++OADMAyDN954A42NjXjppZfA8zyee+45VFVV4ejRozhz5gzq6urmcnpxF10w\nkeat9w44AYRT2oBwL8ih/eVwuv0Txm1MNwU3FSLIfKzN1OMXJ64Jr+/bZMGWcjNOnvMKlT9ZkjiV\n7Ub3CDJarUJPCQDYnRN7n8vy0xbuxMmqUVNmwqH95bh0vR8qhQynzneissQInVqOu0NuVJYYwfG8\nqDcvOvakPYF2p3/CPXmhZr282GLFJ1d64PEFcaffCYaB6LohJJF19YnHVQ+OePDE7g0YGPWI3h+y\ne/H4riLY3QG4vUGcOt+JupocvDWWIg2EG/1o4iFCEt+cZ9eMruBF5ObmIhgMxtharK6uDjt37gQA\n9Pb2wmAw4Ny5c6iqqgIQrjCeO3cuYSp540spDEAlT4JKIRNSHpJlLMwZGgSDQRysL8bgiBd2lx+p\negV6+u1oHNsfmH4KblqHicxHZYkRh/aXo3fAiXSDCp19o2AAdPc7hBZc6YyvwRCHLqtdVFjNzdLj\n2Ik2oWK4MT8dm8soDsn8sSwDjy8Ag0YOjUqOzRvNMKWrEQwGEeTCPQ0apQy1FRak6hQoy88QNZRJ\newJzzXpoVMmiSqF0TGm83LbZRT0h2SYdVfLIshF97WiUMmSkqHDnrhNrDCrRrJlub1DoyTtYXwy9\nJgeBUEh0rECIJpIjZDmYUyUvKWn+A3RYlsXhw4dx5swZ/Ou//ivOnj0rfKbRaOBwOOb9N+IlsuAn\nwKOjZ1T0oH90ZxFkSQzUShVejkojqh0rTP/ixDW88HQN5BifpbOyxAiPLwitRo5PP+tDR2+4547W\nYSLz0dRmw8vvXEVthQW//UOH8P6Te4pF2zxWV4SO3nA6XHObDRrl+CxpIS48Cca2TVnQa+SQsQzW\nZWoTvkeZesGXD7UiGf4ghzNRKWLP7C9HilYhmnXz4e0FE+5/NWUmPP90NVrbh6DXJMOYqkIgGMS+\n2gI43H7wPI9Rp0/6J2dlslgatHtF20lfE7LUproPVpYY8dTeEmF5kmMnx7M+DuwohHXIhexMPTp6\nR4X5Bq51DeNiqw3PSJbd+WLRGrq/ErIMMHxkarNZ2LFjB/7mb/5mwvs8z+PHP/4xPvjggxkfa3Bw\nEI888gjcbjc+/fRTAMD777+P8+fP48iRI5Pu19zcPNvTnhebS4mfHL+J6lKjqNX4S9XrkG/WoHfQ\nA4c7KPTwBTkO/gCHi602PHzfOnwxmwfDsugcVuHnvxPPLhepNP7lQxvws/fGP3t2XyGMGipIzERl\nZeVSn8KMLVTs/vE2g3c/6Z4Qo1vKzcjK0GDU5YdBIwcY4K0PxlNv/qyuCCWZ4ZSdSJxHGiNkSSyM\nqUoUG33gOW5BzjseIucdsZyuneUSu/GK2z92s+gZ9Ili9MGtOfjdufAkQZG1uTzeAHKMyTBp/aLY\nk/7We+7NERZKB4Ddm9dha8GsH2uTHj8SS58PqvH6728I7//57iIUZXhiHWLVWG2xm+gmi12GYdE1\nokJHnwscz8PnD+FCi1XYrrrUCJVCJmrAjjRUN1zuwaP35yDDkIy+QR/M6QqYdP6Efh5MZ7nELZDY\nsdvV1YUfv2eFNnXqZdScwz345kMm5OTkTLkdmd5sY3dOPXmbN28WKmSxPpvO8ePHYbPZ8PWvfx0K\nhQIsy2Ljxo1obGxETU0NGhoacO+99057nIW4UJubm2Me983T4VYv6TTDWRkavPNxB/ZuzcfvzrYJ\n7z++awP8wRA6ekZgXJOCP94eQVmhCf7gxDXIIkIcM2EdpulayyY73/labsddbuL1HUR/nwF5H979\npHtCjOaZ9TjecEtIxzlYXyyaoEWnkaOyshTNzc2we8O99NGTWQCzTx2e7e88WQv0TI8TuT4j7N4k\n7K0V7xfP2FutcTzff3OI49FpvwmwybiI8UpemkE1/jdKjKLxPwfri5Ft1Asx8Ybkt04zKEWzBmab\n9KisHF87bza9vNHXQEQklkKf9YmumzxLKio3lk76b03UeKPYnZ9E/S0mi90H7rsHJ8914Ge/G880\nemRnIdAyvl1kCEq0cI96uCJYlGucU1ZRon5Xy02ilsV0Oh3wnnX6DQFs3LgR69evn/PfWm5l0kSJ\n1zlV8r7//e/P64/u3r0bzz//PJ588kkEg0EcOXIE+fn5OHLkCAKBAAoKCrBnz555/Y14i0w/HOQ4\nPLF7Az6/MwKVQoa3P7yJPVty0TPgxK7qdQhyPJyeAPzBEEadPlSXmnGtcwhNbTa8+0k3DknSHlRR\nBXJLpp7WYSJzFhk72tNvR56lBL13XdBp5OA4DtsrLDgxtpxCe+8oklgWqToF0nQKBIIc3jx9DXqV\nEvlZ4XEbizWZRcR8J7WQjtWiSQESU2OLFa+81yqMu1PJZTCmqZBn1gu9xyzDiJan+fz2CE6e60DP\ngBPWQReMqWpkGBQYGA2nZSaxEDVI5GbpJ/zN2Yx1niyWqkpNCPEQGuGqS2lMEkkssWK3scWKS9fD\n609qlDLUlJng9Yfw+K4N6B9xQ5HMwpSmgcMTEPWuu31BbNu0FqZ0NY2/I2SZmlMl74UXXsD3vvc9\nAMA777yD/fv3C589/vjjeOONN6bcX6VS4V/+5V8mvH/s2LG5nM6iiJ5+OFQmnv3tts2Bi602Uepl\n5PWZi+Fp6COfeb0B0ZgSnUaOPLMOlkw93UjJvEQWawbMePP0NZz+9Lbw2eO7Ngj/n5WhhW3IjbNX\nerGl3Ax/kBN6Qe5L4XGwvhgOd0DU0zLbShPDsDh/tW/GY+TmO6lFZNKZLqsduSY9qiXrO5HEEBl3\n7PIG0XC5B/ffsxZdVgd0ajkO7CjEq1HjhCL3TEumFpZMrbBWKQAc3FOM7n4n0g1KDI6I03JHHOLZ\nYWc71jnSWBKdUQGMX181ZSY0tljxyzPXafwnWXCz6YmWxm5ViRHvfPQ5LGu0uAgbKkuM+LD5jrB9\nbYUFpjQ1fhbV8CJLYhEMcWhus6E0Px1alYzim5Blak6VvNbW8Yftq6++KqrkeTwrc4xC9PTDlkzt\nhFQHjVKGVJ1SNHFAdG9IpHV6nVEPjodoXZq5zKIZufG33mYQkPdRQYOI9A+Lr8P+Ebcw7mJgxA0A\nqKvJgVLO4r/PfC5sl5WhRZ5Fj39987KQmnbPhswJDRDTFTysTjl+cnzmvSd2V2DK19NparOirXMI\nHl8QHm8QGSlKbN5IazglGmlPA8eHG89SdEphOZoIlmFQW2GBdciFZMlkX939Tnx0KVxYffqhYtFn\nKTo5LlwdvyfOpJdXfD+1YnOZadJ4nU3PIE0ItHwk6m81m3iLNEREPj9/tQ/HTl4TKnDyZPF15PEF\nMWQfX2KHAeALBHH2Sh+AcNmGsiLIfPEch46Ojuk3BFBQUBCXyR1J2JyXUIiQztvCMEt/U1wI0QUF\n65BLuClmG3XCWk/RFbdayVT1kcLMtk1ZE9armW0qXIjjcfJchzCb57ufdNNyC0Qk3yJ+MKfoFHh/\nrFf5YH0x1hnDPcc/efuKaLthpxcFjEGYAValkGFNigosy4gKQTq1XLQotTT++gbFMxxOF+Mb89Mw\n7PAKPYrlBbNbl6+jR9wTmJWhxeaNWaJz1quU4Dg+IQpuq1Wkp+Fiax98gXBvAQA43H6kaOSisXWy\nJAZnLt7BwfpiyJJYfHRp/DjpBqXw/6EgJxor19PvxC9+14Zn9pejfmvepD1z0aIL0u9+0i3sGytW\nZtMzSMviLB+J+lvNJt5CHI+LLVbcttnHGsrC5TOXN4jmNhv2318o2l6lCC+lcDKqB/2p+hKkaJKR\nZlAjx6SntORVKBQK4datW9NuN9OKm8dxF9/5zwGoDVMf0z3aj2MvPjGvsXtEbE6VvOiK3Eqt1ElF\nFxS0GjlefvsqNEoZtKpkbNuUBVbyPSTLWOQYtUhiGIR4XijMdPXZ5z1+KDrHPoKWW1jdpK3Qu2vC\ns1h1We3IMelhTFVB+cAG0YQ+IY5HVoZWdJxckx7tveJlQlJ1SnT0huP+tRNtcHmD2LbJLCqQ9/Tb\nAYzHnzlDITrudDHOQzyuatum2fXCDTu9MV9LC26pKWl0nSyhSE/DyMgw/uPd8R7k5CQGWo0ct60O\nIRPiT/8kH4/v2oAckw4V642QJyehy2qHOV2D3/5hvLAw7PCJYmdH1Vpsr7DgavsA0gwqoWdjqt9d\nWpBuvt4v7Cs1m/s3LYuzfCTqbzWbeGscG9sca13UyhIj3vnopnDfLrSk4O6IG3dHJmZ9FJoV2LVl\nPTWIrVK3bt3Cwef/C2pD5pTbDd5pQ/rakhkdU23InHYWThJ/c6rkBQIB9PX1geM44f8jPXqBwOzS\nrJaL6DSITz/rw/7tBaK0S+ki0ylaBbr7XVhr1OLtD28KMxtq1fKYefOzGb/U1Tc6YQZFSqlY3WK1\nQtdvzRMqfhkGFR6r2yCKq8YWK/77f64LD/2S3FTU1eTg5IUOYd0xAFDJWbz++/DSHpFxUqY0jWgG\nxOJc8YRCJq1/2t6TaBN7t+3YUj7zil6eWTzZRu7YgtiJWnBb7YxaX1R86DE06hX1DB/YUYjufoeQ\nNvbC0zV46L58AEAgyAkVvlyTHn7JMydNp8RbH97EgR2FM/69pQVplUI26b4z6Rmc7Lh0n05cifpb\nzWa8cVffqGiYSFObDQfri8EwQCDAw5MfTslsbR+EXiOHViWHTp0sOobbG8T/dgSh11vpXrmKzaRS\n5h61Tfk5WXpzquS53W48+eSTAMLpmtH/vxp69jp6RzFk98ItuZk+srMIXVa7kMIZqdgd2FGI2zYH\nVAoZvL5AzLz52c7+9u7Ht6YcM0VWl1iVGQBTxlVX36gwAQYAWNLkuHS9H5/fHhH1jESn+EQKED39\n4vFTTrd4sgue42Y1U+x8C1i7N+eC48d7Lh+4NzcuxyULQxof/+/4Z6LPb9scyDbqhNfRFa6mNpuQ\nqg4AD9fmitI1rUMuAOEY3VmdPaPzqSkz4Zn95Wi+3g+VQobmNhvu2xS7gCO9f0933Nk0dpClk6i/\nlTTeJ+thBsL3uztR92aXN4h1xnCDV/SzoLbCgkCQw/GGW9AoZXj0S0Xo7LMLsV+an04NYoSsAHOq\n5H3zm9+c9LPVUMmLVLLqt+YKs2y6vEEMjnqgUsgw4vAJFTxgfPZNALhvU82E481l9re/+co94XFG\nyhD2TDJ2hKwesSoz08WVdB9zumJCSzAAuDx+YUKhsvx0rF+XAq1GLlpMd76Vp/kWsGQyVujpmey4\nemUoYQpuREyvEfcmRMbWRUTHlzSuVYpkNDR0Cq8j46E3rV8z49+bZRnUb80Dw3lg9ybhvk2WuMTK\nbCqEZGkl6m81m/JBZYkRww4vjOlqOD0BbCoMXwO/PHNdtJ1SnoSzV3oBhMsugSAnmjGcJlwhZGWY\nUyXv+eefR3p6OrZs2YLk5OQJnz/88MPzPrFEEz3mKcesx3OP34M7dx147EtFcLgDSNHKkZychP4h\nNwxaBXZVr8O5q31weYPINemxITsVaTpFzFSL2fY2RD+MmpubqYJHYqYAD416RLO9SuOqpsw0tpzH\nIHRqOZx+HsMOH4rWpYge+AaNAi5vABkpKvTcdWJjfgaqSoxI16smrZTNdgmFWAWsEMfD5lLizdPX\npj2GP8jh9IXOcEqTWY8HNudCJmMhmhaKLpMlF+J4fNrSh//tZHFr+DpyTXpUFBth0ClE6482t9nw\n5fsLkWFQIs2gwqXrNgzZPXhgcy7yzAbUVa+DRiWHw+2HVpWEbxz4Atp7R2FO1yBZBpTkpsHp9qOx\nxTrjWRKjY2WxQyVRZ3YkS2+m5QOGYfE/jV0YHHYDDAMuxOPuqAvvfnwT/cMeHNhRiI8vdWNg1AdT\nmkbYT6OUIU2nwJN7ijHk8MKYqgIDDl19o2AAikVClrE5VfLeeecdnDhxAmfPnkVxcTH27t2LrVu3\ngmXZeJ9fwpCOeXr2wBfQbXNCpZRBrZTB6w/hjf+5IXxeW2HBQ/floW/QjRPnOuDyBvFUfTH+32+u\nYlPRGmwuMwuTX/Dgsa+2AAZtMrQqOd1cyaxIC4iVJUb8/kInLl3vFyp4T9aXCBWx6O21GjnONN5G\nZYlRSNHUKGVCivGG7BRYB90wp2vQP+yBxxfEiMMHhoGoUhbieFGlzu5R4sevj18vz/9FNbZ+YXaT\nqTS2WPGT4+Pj/qZKYz59oVOU0sTzwEP35dPEKwmmscWKF1+5KLyurbDgzl0n+u460XTNhu33rMPg\nqBcHdhTixLkO1FVno9NqF5bGYBkGeo0cAITZWG90c0iWscKapIf2l4tiYbK4kV43DIMZx1u8JerM\njmTpTZblEGkwaW0fgkGbDFmSBoOjLgw7vMK9/MCOQtHY6Sf3FGNo1IPufgfu22SBSimDXp2Mn0Wt\nQTnT64cQkvjmVMkrKSlBSUkJ/vZv/xZXr17FiRMn8NJLL2Hjxo148MEHsXnz5nif55KTpkyMOLzw\nBzlwniDsIT98/pDoc48viEG7eNa3/mEPRhw+XO8axo3bw9iQnQYePL4nKfRE9qGbK5mJ6AKiRinD\nY3Xr8Vn7oFDBqywxwun2Cw0G0gJlZDxThMsbFFKMc016nLnYjX21BVMuVi495p/VFYnO8cqNu7h3\no1k4h5n0XMwmTanLao/5upMmXkkokd9Uo5ShssQIlmHg9ASQLE9CaX6GqEC6o3ItAhwvijtjuhqd\nVjs0KjnORC1Zs6+2QPj/jl7xb97SPijMKBtNGrMH68Xr7S1mrNAEQWQyk6WRShtM/vyBDZDJGCTL\nxhvbB0fFsw7f7B5BvsWAu3dGoFbw+ORKD/ZszRVtM+FeSrFIyLI173XyysvLUV5ejqamJvzoRz/C\nb3/7W1y+fDke55ZQpCkTIS68LEJkPbGidSm4emtAGIuXbdRBqUjCgR2F6Ol3QiFPQqpegVMXuoCW\ncMH61x804sFtuaLjRhe2F/vmSmuKLU/RBcTKEiN+HtUqG6nAadVyYQ2lW3eGhTTO9jvDWJupjTkm\nAwAcnvCEKk6PeGIVu0v8WlpIHXX5oVHKhOtBo05GY4sV/Ni20csxAMA/PF0jfBap9M0mjTl3ktk1\nUw1KHNhRiMFRL9INSqTplbF2J4sk8ptG9xwD4QLq3SHxVO6K5CS43OKZM32BEFJ1ClgH3dheYUFT\nmw0ub1AUn+Z0jWgflmVw4nwH9m7JE633eOm6TXSMYbtvyWKFJggi0aZrBAtxPFraB0X7WIfcCAQ5\nyJJYIa6j15MEAEumFv91Ojw+T6OUYc+WXIw6/dhZtQ7/+3k/SvMzwIIRXRcUi4QsX3Ou5PE8j4sX\nL+LUqVNoaGhASUkJDh48iB07dsTz/BJGdMpEEsvg7ohHVFC52GrDEw9swOfd4TElp853Yu/WPLz1\n4U2h1XrY4RNunpHKnFIu/gnWZuqixlCFC6rS8YAsw6CjN3zzl8cxRZZS25an6AKidNKUyHpIgWAQ\nJ891oK1zSGiccPuCuL8qG29/eBOqsQaJUZcfmSkq9A06UVthgSlNDQDIMKhEx03VKXDhap9Q+Mgz\nG0Tr5qVo5PjT+/Jwqzc8Y5tWKUO3zY5Xoxbdje61ln72wtPV2FxmxrP7CmH3Jk07GUuqXiGaYTHN\nEF6nz+H0i3qHnto7szV9yMKoLDHimf3luNkjbhQYdvhQlJ0imsxHo0qG3eUTbWdK04hSySIxlJWh\nRnWpESqFDBwnXhw9iQWudQzB7w8iK0M3IXtiX20BRhxeZKYq8bP32oT3n6ovntNYucg+rbcZBOR9\nM9onnjM70vi++In1XS6GWMNDnG4/7K4AyvLTwDKMsMRNhDldg+u3h4Xyw96teUhPkeOrD5VgxOGH\nyxtAEssIjW+VJUbRvfFgfTGORd2D99UWwJSupsmqCFnG5lTJO3r0KP7whz+gtLQU9fX1+Pa3vw21\nWh3vc0sokZSJmjITjn98E3qNAgOSVAjbkFvUGxJZZLSyxCgUrP3+EPZtL8DQqBfbKyzQqmSorbBA\nlsQiGApPHuHyBnFgR6GwwHqs9LpI4fjZfYWIF0oZWp5qykz4h6drcNtmRzDEi2Iw26jD3RE3Ctam\n4NL1fgCY0Dixo3ItQhwveuAf2FkI8MCw3Yun9paA4zlRL4fPH8Q/v9IopBRzEKfV7ahcixStQjiX\nQJBDml68QHp0hXTQLr6WWtqHUFM2HnvTFVGv3BgQ/X2tKhlbyi3oG3CJtpO+pgLx4mpqs6G1c2jC\n75mRokK3zYGdVeug18ihTGbRfdeJ651DOLCjECNOH4rWpsAuKdgmJ7E4sKMQwaie6PotOaJYuLfM\nhAstVmSkqtB+pQcpOnHvRu+AExdbbTCli59h1iE3Tp7rEFUqD+0vh9PtnzJWou/X737SPaO0+3hO\n+kLj++In1ncpX4S/K01r7h92460Pwvfn4w23cLC+GCwzvjxT0doUvPNReD1ejVKGfbUFsA27oVQk\nwecL4p2Px1ObI+UHaYOgdFH03gEntCoZ3Q8JWcbmVMn77//+b6SkpKC1tRWtra146aWXRJ+///77\ncTm5RNTYYsXP32sVUh2iC9QpWnEhdk2KChqlDKk6JTZvNCMU4nD11gAutFixo3IteAB37rrQcLkH\n1aVG0bF6+p1QK2Xo6B2F0zOxdyaib1Dc0j0flDK0PLEsAx7AsZPXoFGGGw106mSk6pQYdflQuC4F\n/kB4llcwQKdk4XGGYRDiQqKeOLcnAK1aDkumDrtqcvDLMzdElcBHdobH3EUaAqSLmTs9AdHYEIM6\nGQbJ9VG5IRPr16Ugx2zAnX7x/npN8qwmXkmVFNxTdeG/tdaoEf271maKU/moQLy47vTbkW5QweMN\n4PFdG9A/4kaGQYlgKIQPm+8I2+2rLYApTSOa8KetcwgleWmi4wVCHN768CYeqyvCzqp14Hke6ZJe\nZ0umFmgBHC4/Pr7cg7+Q9OZqVeEZoh3ugCRWtELDSMSl6/3CfXqyWJlLY9nFFis+uRIueN/pd4Jh\nIBrzOhvUWBc/sb7LovSF/7vStObqUvGs3AMjXvAATp3vRGWJEX1DLiH1vbLEKKRkAmMNdmM0Shky\nU9Woq85GZpoKre2Dwn45kpR3WkaBkOVvTpW8lVyJm070Td/p9uPRLxXB4fJDo05G710X/nxPMQZH\nPPAFQlAqWHx5R6EoBSLSisYwDBou38H2sTWd1ArxT2HJ1Ar7RbaJUEVta04XF5zng9YUW74icRlZ\n3HxfbT5eOzUed199qBS/+uDzmI0TmakqJMtYXOsKp/q0tA+gfksebMNuYUxHIBQUFYBdY2OgIoUA\naQOBSiFDml4ppNBlpqkhl7Oi3sDMVBUeHFvb7he/GxKl2Hl8wVkVVh1uv2h/x9hYrkCAE/XqrDNq\nY35vM/kbUtQLOHORmQB9/hDe+Wi84l5bYQHLsBiS9OT6AyEEAjxUqmTR75dv0eMvHixB710X9Bo5\nrEMubK+wwOsLIhji4PEFMeryxVwcXTc2Kycz1gMSiUOPNxwrGSkqnDjXKfytrDWaCffl6HvvZLEi\nvRaSk5Pw77/+o2hpD6nbNvuUExvNBjXWxU/M79LvmmTrmZnJ2PfIs/jS9fB9WhqHLm8ADMbv9zur\n1gmfSXvoHFHjpytLjPj1B58Lr5/cUwxfIASnOwAWwFcfKoFt2INUTTLyLKmoLl38MgDdVwmJnzlV\n8iwWy/QbrVDRLWy///Q2gHBB5dSFLgDA+at9QkVuz705GHGIe9pkSSwyDAoYU9XYUm6GJVOL+i05\nSNMr8fiu9ejotSN/rQHOqAkHmtps+LO6Igw7fNCp5UhOYlC/JQcVG4xQBMNjWOJxY6T195YvaWFE\nrRCvX3lnbGFplzeIU+c7sa+2AL0DznChledFDREHdhTiWFQF0R/goFYko+HyeMrPn+/ZgK8+VCos\n91GxIRN/8WAJ7vQ7YUxTI7JCXaQyKa/JxhqDUtQbKJdtwK2ecLwWZaeifzicLsQA2JCdCmni2lSF\nVVNH0YL4AAAgAElEQVSGCiNOn7C/OT1cOXW4xRN3SF/Pp0Acz96XlS4yE6C0R8LjC2LI7sGaNHGq\npNcfRIpOKSqgAuEZiv0BDgatQlRYPVhfjN/8oQMAsKt6vMDLAFiXqcWBHYVQJYcrVz5/SBSHj+4s\nwlcfKoXXF46NSIrcwIgXSUks6qrXYdTlR1l+Ot77w63xyYw08ikL6K03+5CSosOvztwQeksiS3tI\nSScykr6ejcoSIw7tLw+vGWnSx1yblcxMrLGSly/3zuuYMxn7HnkWMwBOne9CU1s4rV6lkEGrTgbP\n8XC4A9i7JQcGrQLyZBaP7CxCl9WO/CyDqBEvXa/EozuLMGj3gpE80h3uAI43TEzlfHZf4ZLdyyi7\ngpD4mffsmqtNTZkJz+wvx7WuYeE9acuZLIlFdakRGlUydBq5aDIBnVqOvVvz8OpYal2yjIUsicWd\nfifM6WpcaLFCrUpGKMQJ+7i8QQRDPE6PVSqB8NiQcGUs/MChG+PqJi2M9A04RJ9npIynsLm8QciS\nGGiUyUhPUaJ3wCXqpZMWrHsHnAgEOdF7A8MeoZEDCE8M0NEbXs8sGORgTleD48ZHGpnT1RN6awbt\nHgw7fLjT70TB2hRRT0ZJbhrqt+bNeOKVQEB8foFg+G+bM8TpmdKZF+cz4UU8e19WukiPaayeMbVK\njsERj1BIVSlkaGyxxvwuff4QstZocKNrRPR+/6BbiOEUnRK/iqoA7r+/EEOjHpgz1KitsEwY1zfq\n8qF/2I2N+eE8POnMnwfri1FTZkZ1iRGK5CRhjN7FVhvS9apJC+hyfy8udIyn0QETp6ePmC5OZ6Op\nzSYaR5hmmHiOZGYmW75gPmaTPRB9f9Kq5RMmHcpMVYNlAX+Ah93lg1ohQ3JS+LMQx8GUpsGwwweP\nL4imNhv2bS8QHd8XiD0UJJ7DQGaL0o0JiZ9Fr+QFg0G88MIL6OnpQSAQwDPPPIPCwkIcPnwYLMui\nqKgIR48eXezTmjGWZVC/NQ88A3x0KTyGRFpw4XkeBo0cwRAPnzeAJx7YgKFRL9y+IM5euYMvFGUC\niD2N+K7qdTDoFDh5LtzbMur0geN59Iz1xEQ43VNPYU83xtUlujAS4nicOucRJrFwuv0YdXiF1lyd\nWg670wfLGjV4MLCs0aInakKStZKURrc3OGEyCKWkp3Bw1COK5X21BZAns0K65m2bA3mSMR8cNz5J\nTHJykuizTqt9VpNR+AKhmK893oAkDVTckzefQpzdFZjyNRkX6TGN9EgokpOQalAgGODRbXMgf60B\ngUBI1AOhU8vh9Yl/P7mMxajTL4yzizBmqNHZF27YkE7ic6c/vObjIzuL0HC5B08/KB6Tx3E8Pr7c\ng6wMDZ7dV4jO/sCEzyPxEeu+O1XsSJf2yDHpY27nDwRFKaSBYDDmdjNBz4LENl32gDQrZ3OZCTVl\nJvz8ty2i7ZJlLBgAgRCPX565IfRA3x3xgQGgkstEPda1FRYMjXpF15NOLZ5GJpKOHM9hILNF6caE\nxM+iV/J+85vfIDU1FT/84Q9ht9uxb98+FBcX47nnnkNVVRWOHj2KM2fOoK6ubrFPbcZYlsHeLXkA\nHx6InyxjsaNyLRiGgU4th8vjhz/ITVis99SFrnAL21gvnbQH8MbY8gtJLDO2/l4Aa1JVOHG2A1WS\nlBvpIGm6MZKIxhYrfhrV4vvVh0rxyzM3UFNmEk1u8fxTVUiWsbh+e1hUQTOlq7GvtgAOtx/peiVO\nnOsQllgYcfqQolXAL6lUOT3StEg/GGY8XbO2wgK1MllUwMgwKIX1+iyZ4glS8rMMs5p4JRQSz+4Z\nWYx9baYevzgxnnp636aaGX+P0ynJSxOlOpXmpsbt2CtNTZkJh/aX49L1foQ4Hn/4Yw8e3l6AX31w\nAwBwocWKpx8smTBWLiD5XXdvzkZ2hga/fv+GsO06oxYeb0jYbrIxzMOOcOVPGocRw04fNqwJgTOL\nf0dtVEF4NvdZhmGRqlNi77Zc6FRypBuU2FWTE3NbuUyGtz4cX77h0P7ySY87HXoWJLbpxr5Ls3Ke\n2V+ONIMSIw5x40WKVoFfffC5kAItbTTeVyvutZMlsQAD5Jp0uNUbbgj4sOk2DtYXg+N4aMcaVe7b\nVCMMA1kK8VxOhJDVbtErefX19dizZw8AIBQKISkpCa2traiqqgIA1NbW4ty5cwldyQPCFT2n2y9q\nea4uNSIU4uD2TWyFjfQgeHxBtLYPorbCgjS9Ehchnu7eHwhhyO5DbpYeLk8Ag6Ne/NmuDfB4/cLC\n6nJ5krC8AhBu+ePBY19tAfSaZGSbdGAAvHn6Gg1cXmViLZLrD4Tw/33lHnwetQh6U5sNt20OPFq3\nAY1RMQyE1yyLpAY/9qWimGsq/VldkahAbkwVz2jIMoBljRZ1Ndkwp6uRZ9bjVs+oqBASPaNsXpZe\n9NnWL2TNqkdi1OmP+XohJxOyO8UTfIxGpbnS5AHjhO/Cahdiz+UNoveueAKL7n4n3r/YLbz+yq71\nSGEZUeU/3aBEXXUOvP4QXnmvVdj2gXvHK09NbTY8VheeEMvl/f/bO/P4pqr0/3+SZk+arjQNpbTQ\nlm4gllIWgWqRrYhAWVRW+ep3Rv3OOI4rIIz7xujob0Zxxtl0RL/6RUUYHUBkUBBElrIMtAUFSoHS\npnuzN9v9/RFyk3uTbmm68rxfL14vbnPvk3NvnnvOec55FgeKy9w6po1RYNWcLDQbW/z0EHBnZBUI\nrLBY7JxdcKvP7q9vvFuStu14N51Rire3eevxPbkqL2DSFQB+LqT8GmidgSbJfZu2Yt+dLgY/Xmrg\n6PypC3WIjVCg5EId7rg1Dc1GG9RKCa7WG6GUiTBUE44jpTq/ReMWG/fY4XRhz1H3+1WQO4Rd8EvU\nqP36VU8YSG/QHS6yBHG90uNGnlzungwajUY89NBDePjhh7Fhwwb2c6VSCYPB0NrlfYpAGQWPlumw\noCAVl6q592B3uLyGXakO+45XQikTYUVhBs5UNLIF1GdNTMYX+8s5tfAAYMn0EfjsG2+cSVS4jM18\n5V75804m7isahXc+P8W6b5y+UI+Rw2Ou64nm9cLhkmq/Fd8kbQRcDIPNu736U5A7BEla924Zv7RB\nVLi3sLhY5E484XAynHOaTTaYrQ5YWhxgGAZqpf8und3pRLOxBXa7E0nx6oDvi4dK3oT/UrW+UzsS\n/BpnmmvHDheD+mYL6vVWSMX+mey6YoxduMo1WhUy7/1QjKyX1up8Rkdwy16olVLO5FZvsmFQlJzz\njO+5PRvHz9b49a+aaO4ig1QcBj3cZWxuTB+EMKEQLoYB43L56dXgWBXyc0RQycWoNrrwPi8bsosB\nfjjlLmrOj3cLFJPn4VId11ArudCAiaMGBzzXk/mTPVYEX43NV+fDW0kOQ/RNDpdUAxBwdP6OW9Mg\nk4Yha3gsNv/b3YffnJMAkVCI3EwNdh68GHDRWC4TY0VhBqrqzIiJkOLL/eU+n4mwbGY6LQIQxACn\nVxKvVFVV4Ze//CWWL1+O2267Da+++ir7mclkglodOG6BT3Fxcbe0r6NyJUIhHpiXiqqGFkSpFWg0\ntGDWxGTs+L4cN46Iw7z8FLTYHYhRy7B173m2UOnCqW4jcKgmHOeuNHN2A5uMLcjL0iBaLYNSJmKD\n9mubrOxOnlQSBpPFhp37S6FRAqXnqzjtunjNFcPXfWPbvvN4YF4qNEquARCK59BZukNubm5uyGV2\nJ6F8Br6ySi8JcLRMx06WUxPUkDqqceg8d5Ink4Thp4s6mG0MBAJuaQOJSMgplr5waiqcPCMvRi3D\nzoPeWkwyqchvdyQq3FsMfXCsAhmaFvf7Ut+C8HAFtnzjdXXkG2lqmRMSRzV7vjZGCqmjuo0VZhWW\nzkiHrsHMZvcsLi7GFaMKP142wNLigMXqwPYDPyFB5Y1vrTHJ8fY2r/H7P/PTEKewBPoCPwbHcI0U\nbbSM/S1KL3Gfd+m5Kkhsgdven3Q3GL3lPwuhQICC3CGwWO24Y1oajCYboiNkcDi45S6Wz8pgs8J6\n0DUYYbHaOImpAHfcnEeHB8cqA5atmTF+KIbEyiFxVGPxrWmoa7LA6WKw+3AFTFYHYsLDwNv8gChM\niC3fuItM/8/8NNQ22TiG6E8Xda3+rpFqbmxruELU6vNraAjjLJI0NOr9zu3os69oVuLdf3nfzZYW\nG5IiuIsooep/Brru9rSs0ksC8BJyw2C24V8HKjFptHeB4GiZDrfdlIxms50to6CUiXDHre6460iV\nFHuPXUZds9vboLrezEkAFKEQIy3GBNhMrWYLDdU99sXn3p/0Fuj5uVhFRUW3fF9HOH36dKsbPf1p\nTtpdcjuruz1u5NXV1eHee+/FU089hQkTJgAAMjMzceTIEeTl5WHfvn3s39ujO17U4uLioOXaHS58\nsvtHDEuIhN3hwoGTVzBjQjIuVusxa2IyKmuMSBkSAafTBYlYiEZDCyQ89x27w4UjpTocgY6zmxeh\nkvgVozbb3ckqNIMiAXjdnAYPck8u+O4bemsYZud37N668hx6Q25/I1TPgP88HZIqNJhc7CQ0ZUgU\nxozUorS6jHOdQi7GJ3vO4eacBGiipahuMLO7cvyC4ZeqDSivbOLE5PETmETydgPlUhGUMm9yFnOL\nC2Nyctjjw6errsWduie1w7RqPxczoVCA4uLiDuls2Y5S/J/PTuUd09KQm5uL0h2lHMNBE5OGuTd7\n5f1122mOnMoGFwqntP99xcXFmD0pDS6E4UqNEYlxKsyZNBwSifudtEuqsHW/953MStUidwDs5AWj\nt/xn4WIYFJfqkJupgbnFCYZhkJYkx9mLjZzr6potbFF7D9FqOfQmO0ou1HmNukEqOJxO1Da5i6ZX\nN5g513j6QaVMjHqDHUVTc3Cx6Se4XAynTw1XKVFRxc1+6XC62MlxZYML2hg1PvnWu5N3X9Eo5Ob6\nl0QAgBPbTnIMN6vN2erzs0uq8Alv59dXXzrTb/7w6QnOcVWDFQumeq+9Xvvg7upzQynLLqlCSTnX\n3V6tlCA3U8PpY01WB5wMYPUZ401Wt+57+jvP/METIuK7uJwyJAq5I7O6/R6781ldT/T0XCw8PBz4\nsnfiMkeOHIkRI0b4/b2/zUn7ir72uJH3zjvvQK/X4+2338bGjRshEAiwbt06vPDCC7Db7UhJSWFj\n9vobR8t0+Od3569NXhyYMSEZ267t4AHuTvfHy004UqpjE7AcLdNhWl4ilHIJrDYH7A4Xu4Mnl4pw\na14i7A4XW9DXQ0W1HmPS3Vk6rbwMgi6XC0+uGofLOj1nl5AC8Ac+LjAoLtOxOljbbIHLxSA2UsbR\nEfE1962jZTrMmTyM6x50LWmJB7lUhKzhsZwJ8crZ3AyFEeFi/NecLFzSGRAXpUCzwcqJK8oeHs05\nf2xWPJwMWKMuNzOejcUIBn5Mnv7asYmXEIafICY2SsrZxYxWd9xN7tjZGk5cmDZWxbaf4qK8+D6L\ncIUEm3aUITdTw+qppcWBRr3Vb3euxeaE85qbu0dvk+LVcDEMGg1Wjj7eMS2t1cQrHndMg9mGmGsu\notYWO5wuF+e3bza2cHbBhw9WQwDgljFDWN3gx8rxs21yvjdajK37LrLHT67Ka9U9OJT60tGMnkTf\nY1x2PGobTRydV8rFKC7T4fbJw1B0SypsdgciVVLoGiycOo5D48Ox8/uLrCzP4oZc6p5PCCHAkVId\nNFFy5GZQ7USCuB7ocSNv3bp1WLdund/fN23a1NNNCTkVVc0cF0mPMec59s3m5lldm3VTMkRCAWcX\nwnNNXJQcZqsDn31zzm/iMlQT7t5NkQfOIDhxlBbjs+ORqFG3O3EINPFoD0os0TepqNL76WCMWo5p\neUlwOBlUVOuhjVHii+/crpImq8PPQGoytPi4e0YiSi3Fj5e5dcmq6kxYMSsDV+tNGByjhMPuwrtf\nencLVxRmgHG5UDgxCTnpGj/dC3VwfWsxeaNSB+FfBy6yfx+dEss5j2HA7gAxDIPI8I4beW0lhqHk\nAV58n4XLxSA6Qo4jpVV+elqQO4TVu2StGtsPuGOIcjM1iImQYUy6ho1DLrnQwPmOZqPXx82TeKXZ\n0AJNtBK1TWYkDFKh2WCF7NpOq0gUhjAHdydvZWEmsobHQACg9EI9soZFs7UfPbrRmThRrdqJVXOy\n2J3e3HRNq7GanSkX0h6exDSe753RSkZPonvp6BjJP2/mhGEQCCvcyX3i1Wg22pCbqcHH1+YI+TkJ\nnD4tPycBR0p1GKoJ57hkDhmkwtCp4bC2ODAvPwWiMEApE0EqEeFIma7TfRON+f0fp9OJ8+fdY39F\nRYV7xy4A5eXlAf9O9D+oGHoISdZG+E2Gva5CIqQNicSFymbcnJPAJkVp1HMd8JUyEQZFyTF1bCIE\nAmDvscvIz0mAw+XC8lkZOHe5CQlxKuw8eBGLp7m3tH0zviXHezO+8WunHSqpxpUaPRRSMQxmG9tR\nB5p4tDfVpcQSfZNAOugxPuZMdruVuVwMEmJVqNDp2Ri22Agp6prduhihlGLXIfeEInt4DGZOSEZU\neDV2H/YWP1crJdi007uwsGhqKidW6cLVZsRHKyEWhfWIXiikQo7RqZS63aDFQgFnt0bMc482me1+\n5SM6Cr+MCf+Y8MfTJzU1NeHIj1wj2Wixo7yyCTePSUTTtfjmvccuY9/xSr/+ZeTwGE75Cm2sN/7N\nZHWAcblLH7y/w7vwsLAgFY0G94JGUnw4jp2p4ehshY/nw723Z8PhdPjpxrgpHd9xu1Avxnv/8u70\nSsRhrdbZC2V/2tYOM9FzdPQ3DXSep692uhhs23ceMkkY5t+cApPZBoOZ640gFgmxbGY6TFa7O9FK\nvRk2uxO7DlX4lVVYWJCKBr0Fl3X6ThtrNOb3f86fP48Va/8Xigi3F1hrLpn1V8oQMyQz4GdE/4KM\nvBAyLjsedXoLx0VyTHocBseqoJKL8OFX3mD4ZTPTsf1a4gpfo08UJkRdowVHy3TYY3VwdgKlYhF+\nKKnGJJEWuZkaXKkxQi6S4dgZbsa36Aj/jG+eDpqftdMzYfGloqoZaTFt3ysV3O2bBNJB/m6DUChA\nbbOFk5xiZWEmKuuMGByrhN7YwtbJ05tsOFJazbqTHT9bA5PVzi4+KGVi5KTHodFgRU2jN2FJ4iAV\nzl/VY9rYxO6/aQA/XjZg9xGvETotbygK4XZr9t2tUcoykJft1VP+hIl/3BZCgYDjVuVb1oRoG6GA\nYVO/e0iOVyN9aBQ+8Fk8WFGYgUSN2s+Y4pfGmDZhOKTiMJRfbYYmWgG5JAz/OceNbbqkM/joowAx\nkXIYfbJ0aqO9Bv7lGoNfPKDBbO/UDm1lLTc20NfF3oNnYeBKjZ5jcFbW6AEE15+GUhYRPB0dI9s6\n73BJNacIen5OAoZoVIBPXfS4SDmu1pkgEAjQqG9BwiAl/neXu/4kPy6/ydiC2AgFp+/vqLFGY/7A\nQBERB1VUQpvnmJt1bX5O9B/IyAshniLp0WoZSi80QK0UIy5SjlkTkvHXbSc55+p8JsRHy3SYf3MK\nxwj0GGNCgQA35yTgaJkO4jD3pFImCUOLzYmD/7mK3YcduGNaGnuOyeoI2Pl6Omh+p+9ZzfNFpZDg\nxCUz7JKqVlf5qOBu30QoFGDm+GSAgd/Ori8V1dwEEzVNZkxJY2CXqPFddSVnIUA6PR3lV5uRpFUj\nPlqKFrsU4jAhNNEKhCvcO3Wbd5/lXFN0cwrGpMdhQisp40NNklbFmdgmad07O/V6bjbZOt5xLC+N\nfwzvuC3KeSUUEuNUGD+SJj0d4UqtFV8frWJ/s4ykKFTVmfxKdegazFg0dYRfH8SvNSaRhKHwpmE4\nVFKF0gsNYBgGmcOi8EOJd6XaVx/LrzbDbOXu1C2emoa8LA0ilRIMipJD12Dh9Kud0Q0AfgmMBseq\nIBQg4MKAQirmtCUjOfhi6KGURQRPR8fIYdoITt81bLD3PL5hZWlxl63x1SGHk2Fr3gHuBWTP52mJ\nkThSqmMXkcUiIQQCIDZCiqzhsbC0OHBZp2cTXYXifgiC6DuQkRdihEIBBBBwXImeXDUOQ+O8DpBK\nmQjaGAWnMHVdM3fy6THGXAyDfccrsXRmOgRAQEOw/KqeE/8XqPP1dNAKKfcnT7rmruFZFVcpJPhg\nRxlMVge27r/c6iofJZbou/BreQXa2eUnZ4iPUeLEJQNGpQEqhZjzma7RzBbRXTojHf+7y6uD9xW5\nJ5B6E3cHzGpzYMa4pB6L2bDbuen3k+LdsQbRap4Rxzs2t3CTFvGzhrYFTXqCRxsrZVO/A8DM8UnQ\nm+wQhXH1JUYtx/aD5Zg9cVi7unS4pBov+9QLnTV+KFtWI2GQiqOPydoI/FDCLT3TYLCy/eiHO706\nPi8/BY0Ga6d0AwCUEm7SmOo6I+qbrQEXBjqT0KU9QimLCJ7Wxkjf2Da1XIZIMcPRCd9SCYFqi4rC\nwrDv+EX2b7eMGcI5p7rBDIlIiPgYNZoMLVhYkAqXi8Hne71zkoUFqayHw5FSXcCC6B29H4Ig+i5k\n5HUDgdwaRgyy4clV41ByoR6iMAHHXWJhQSrCeRProfHhkEtFKC5zb5v/xIuzArjZswB3MeYnV40L\n2Pl6OujKGj0yk0ehqt4EhVSMqjoDjpYC47PjMXGUFh/vOsMJ3m7NJYMSS/RdOuJWM3N8Mphru33x\nMUp8+d151DW3YOv+y7h/AXfln2G8uytV9dwsr54JZfbwaM7ChtXmxK7DFWxsSXdztd4c8DgpPpwT\nk5cczw00HxSpwKd7vO3m33tb+MbCJmkD75gSgYlX2TgTxryseDAM8M7nJzn17nYduoi65pY2i457\n4Ou9C+AsSMhlIlYfczM1qKzj1uCLDncvAPC9Ha7WGXGkVNcp3QCAC9Vcg27q2ETERHL7ec/CQCgX\nDJK0as7OEH9Bh+gZWhsj+bFt8/JTOJ9XVOkxcdRgOF0MBAJgZWEGapusUCvFqG+2wmzhGu1D4rj1\nGNVKKYQCYLNPMrepPLf5Jp9ERe7vbN/1ksZ8guh/kJHXDQQasBmbCRNHaVFR1eyXGKPR0ALAhRWF\nGThT0Qi5VAS9oYUzQYhQShBxrU6OZ/dvRGIkIpQSHDzlXpFOindn0hQAfm6W3vT0Whw8VYU/+ez0\n5OckwMkAE0dpaXdiANCR31AkErIT3o93nWGTrgCAxWr3S3nvQRvLdUELV7h3qMdna3HHtDSUX9VD\nLhXhcEk1pNcyGfYE8dG87JpRcgBAVb2ZE5MXNTebc57VxnV9auFXw24D/o6pryFCmejahnG5/CaM\n47LjwQAouVCPCJUU2/Z5y890ZBLK1/twJTd9lK+L8tEyHX663Mj57a/WG6GUiTBU414I8PSznhIM\nHdUNz2+vknNj+iKUEiTHqwMuDIRyl0TnUysNANISI4OWRYQe/mKEQubvXeN0MdjxfTmOna1BuEKC\nuEgZDGY7IlRSNBisWDozHfXNFkSHy7HzYDnycxIgFglhd7iw64eLyBrODaqPjuDqoobXX9I4TxAD\nEzLyugH+gD02U4Ovv2/Ax7vOIFwpYSfGHqLCpbDaHBAKHFDJxTBa7FDJZFg2Mx3VDWZEqqQwmW2c\nyeqymemoaTBjaLwKIlECtDFK1s0SaDuYOpCff0VV87VJFoN5+SlQSIVIGRLFpiwn+g+dnTDyJ8cJ\ncWq/lPcVVc0YGq9GeWUjZ2dMb3S7GQuFAkSrZZzV456szxWllmBFYQau1pmQEKtE1LVSCJW13N2a\nK7zjBr2NMyGOCu943FV7CRMoE13n8CxEjc+Ox/aD5RyPgo5MQsdlx2Pt3Xk4ea4WEUoJWy6BleGj\njxVVzRAJhdjr89uvmpOFwbEqfPJvrw4vnZHO7ibydaM1Q97z2989O511F9VEKxAVLoGLYVB2scEd\nW2V1YFCEHONHakO6S9KezhO9h9PFQMVbfKhtNOO+olEwmm1sf32opJqzgJSfk4BBkXLsPHgRuZka\n/HS5CWmJkWg2tqCu2b0gnJelQemFejb2bmFBKqobTBAJhVDLxSjIHQKjxY6hmnB8d+wy2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FIpHgxRdfRGJiYpfaefLkSbz22mvYtGkTLl26hDVr1kAoFCItLQ1PP/10p+U5HA48+eST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\nBhBk5BEEQRAEQRAEQQwg/j+cO4pz7d/IwgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "\n", "sns.set(style='whitegrid', context='notebook')\n", "cols = ['LSTAT', 'INDUS', 'NOX', 'RM', 'MEDV']\n", "\n", "sns.pairplot(df[cols], size=2.5)\n", "plt.tight_layout()\n", "# plt.savefig('./figures/scatter.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8u95fy/5Pv6HPC+MA8AoNouPwgXw2cQYXo44Ru+8Q68a+TKcRg/AI8q+O5pSL\npFZTZ9Qwzry9jLQ/DpIdfYY/p76Cd2RbPNu0KlHfkp2DKS3dvoUO6Y8hLIQ/p7wMioLKRU+9MaOI\nWfA2yTt3k3fxMidnvo7NaMS9RTMntNAxq8XCnz9vodvD/0d487b4123I/RNf4crZk1w9F+3wmILc\nLDo/OIqI7v/Cwy+QFj374htWj7hThVf954/uJy3+Ev2emUFQo2b4121I36f/Q9ypP4k/faI6m3dL\nNquFC3u307TvY/g1aoVnSH3aPTaVtAsxpF88U+qxuSkJnP5+A951mxYrtxjzSY09SYNeQ/AIrodH\ncD0a9X6QjLhYzPm5Vdmc21KVz4Izm82sW7eO5557jq5du9KsWTMWL17MoUOHOHr06C2Pu3jxIu+8\n8w7t2rWr1LZWSgek0Wiq9TsszucZKbDaaOHhYi8L0GkI0Gk45aADOpqZRxtPAwZ10dVBb39PFrYs\nTKA4nVOALEk0dS86X4S7C7IE0Q7O5ywNu0WSfukKc1v1JfVCXKl1G93VgbO7DxQrO7PrDxp2j7Sf\ny2a1ErvvkH1/7N4obFYrje7qWPnB3yb3Zk1QGwykHyiKs+BKAvnxV/DuUPofg9bXhwYTx3Dm7WWY\n0zMA8O7QHlmrIfGHoqlla24ee/41iIyoI1XTiNuQcikWc0EBoRGt7WUefoF4+AVy5YzjzqJlr35E\n9ivMTLXZrJw9sJv0hDjCW7YHIDPpCgZPbzwDgu3HuHn7oXf34MrpY1XYmvLLunIBi7EA3wYt7GUG\n7wBcvP1JO3/qlscpNht/fr6UhvcMwS0grNg+Wa1FrdMTf2gnloJ8LMZ84g7twtUvCI2La5W15XZV\nZQcUHR1NXl4enTp1spddn9WKiopyeIzNZuOll15i3LhxNGzYsFLbWilfSLdjx45KD6w0qSYzAD7a\n4uF7a1SkOhixXMk30drTwIa4FHanZAPQxceNx8J80cgyqSYLnhoVqmtrBQAqScJTrSalBo2ADmzY\nwoENW8pV1zssmEuHi39QZV5JRGtwweDtiVdoENlJqSg2m32/YrORnZSKd3jwzadzGn1Q4f1lBYlJ\nxcqNScnog0u/96z+uCcwpqQR9/lX9jJDvXBMaRl4tm1F42efxiUshKzo05xesJjc2OobxZclJ71w\netjVu/i8vKuXD9lpyaUem3ThLJvmTkGxKTS/+37qte547VhfCnKzsZiMqLU6AEz5eRhzs8nLyqiC\nVvx9BZm5/wRMAAAgAElEQVSpAOg9fYqV6z187PscObfza5BkGvYcxLEvVxTbJ6tUtBn6DMe/WskP\ns0YhSaBz96LrhLmV34BKUJVJCImJhcsKN9+3GRAQwNWrVx0es3LlSmRZZsyYMcyYMaNS47ntNGyb\nzUZOTg6HDx/mk08+Yf78+ZUaWGmMNgVJoliHAaCRJUy2ktl6+VYbPydl0t7LlRcbB5NmsrDqQhJZ\nZiuTGwZhtNnQ3nQuALUsYb7hA/pOojXosRQYi5VZjCagMPnA0f7rdTR6XbXEWB4qvb6wk7zpfbCZ\nzMi6W8epMrgQ+tBATi98p1i52tUNtZsrzWZM4/TCdzClpFF//BN0Wv8hv/V9EHNGZpW04++yGI1I\nsoQsF5/TV6m1WM3mUo/18A/i0deWknwxlt3rV2Dw8KLLQ6Op27oDWr0LOz56l54jnwFg19plIMnY\nLDXjQstqMiJJEtJN7ZbVGqxmk8NjMuNiOb/nW+6a/OYtz5uTFId7cF2a9HkUJIkzP3xG1CcL6fbM\nAtTamrX2V5Vp2Pn5+ciyjOqmtSKtVovRWPLz4MSJE3zyySd8+eWXVRJPhdKwARo0aMDMmTN54IEH\nKj24W9HKEopSmAkn39BxmG0KelXJjkQlSbirVUxpGIQkSTR0BYui8NbZBJ68lglndtA+i01BV0Oz\n4Mpiyi9ArdMWK7v+2pib73D/9Tqm3Joz7Wg1GguvCCWpMKPtGlmrwVpKtl7Av+5BkmUS/vddsXKb\nxYJKr+PUzPmkRxVeXB17fjo9d39HyKAHuPjJhqppSBmitm4kauvn115JRD4wFMWmoNhsxa6IrRZT\nmRlreld39K7u+IU3IC8rg4Nb1tP5wVHoXd3pP2U2P61+i9WTHkGt09H6XwPxC6+P1uCcqahzO77m\n3I7CEaokSTS8ZwiKUrLdNovZYUdhtZg5+vkSmt4/HIOP4xFx2vlTnPlxI/dOX43OvTCDMHLUNHYs\nmEBc1E7qdft3FbSsZtLr9dhsNmw2W7FlE5PJhIuLS7G6JpOJl156iWeffdb+dTyV7bbTsNVqNZ6e\nnuj11X/14KctfBRQutmC77V/F762lpiWA/DVqtHKEtINnVWYS+GHb5LRjJ9WTabZiqIo9jpWRSHT\nYsH3FmndNV365QQ8gwOKlXmGBGLMyaUgK5v0ywm4BxR/grkky7gH+JIR73go7gwFCYWx6AL8MCYW\nTT3pAvwx3jQtd6OA3neTvGsPtpuu6q4fk3P2nL1MMZvJj4vHJSykMkP/W1rd05/GnXraXxfkZLH/\n67XkZqbh5l30PuVmpJWYlrsu/vRxtC6u+NdpYC/zDauHxWSiIDcbFzcPghpGMPKND8nPzkSrd0Gl\n0bJ613d49uxbdY0rRd2u9xPSpuhBxqa8HE7/sBFjdnqxFOmCrDR0N03LAWRcOkNO0hVitn9K9LbC\nTFyb1QKKjR9efZy7n3+P9Etn0Xn42DsfAI2LK67+IeSl1Jzf9euqcgQUFBQEFH7Nzo3TcElJSSWm\n5f7880/++usv3nrrLRYtKswYNJvN2Gw22rdvz/bt2+3nu11lfrqGhoZW6AdUhXoGHXqVzMmsfO72\nK+yAkoxmkoxmmru7lKjfzN2Fn5MzsSqKfdruUp4JWSpMXvDSqLEqCqdzCoi4dnx0dj4K2F/fac79\nFkXX/3uoWFlE727E7i1czI/dG4WsVtGga3v++r1wJNC4RyckSeLcXseLkc6QHXMGS14ePh0jSdj6\nPQD60GBcQkPsIxhHvDu049ySlSXK06/dB+TRqgWpv/0OgKzTYagTRsL/tldBC8pH5+qGztXN/trN\nxw+NXk98zHGadr0HgKzkq2SlJBLStGT2H8ChbV8gSTIDphalVSfGxuDi4YmLmwcZiVf4ec3bDHh2\nNi7uhffUxJ8+jik/l/DmlZvdVF4aF9diiQB6TzNqnZ7Uv04R2q4HAHlpSeSnJ+Nbv3mJ473qNOGe\naUuLlcV8t578jBTajZiC3sMbF09fTNkZmHKz0Lp6AIVTfXmpiYR3uKcKW3d7qnINKCIiAoPBwIED\nBxgwYAAAcXFxxMfH07Fj8eSjNm3a8OOPPxYre/vtt0lISOCtt94iIKD4Be7tKNflvcVi4auvvmLb\ntm2cOXOGnJwcPDw8aNasGQMHDmTgwIHFRhdVTSNL9A3w5ONLybirVXhoVKy6kERLDxeauLlgsSnk\nWK24qVSoZYn7Az3ZnpjBktirDA31JcVk5pNLyfTy88DtWmZcN193lv2VyDMNArEBy88n0svPw+GI\nqiaS1WpcfbzITcvAZrGwb83n3PfiOIYvn8eO9z6iWZ+76DBsAEvuHwVAZkIShzdtZ+SaN1k3ZhqS\nLPPYqvn8sfZrsq6WvshdnRSzhcsbNtHkpamYMjIxpaXTfNbLpO2PIvPYSSS1Go2nB+bMLJRr6xha\nP1+0fr5knz5X4nwFVxK48u13NJ/9CidnzMOYmETDZ8ahWKwlpuucSaXW0Kp3f/Z+vhq9mzsu7p78\nuu59wiLaENSgMM3YarFgzM1G5+qOSq2m7X1D+N/iGRz+7isaRnYlLvoYR77/iruGjwcKs+hy01P5\n9dPldB7yONmpyfy0ehHN7+5bLDPOmWS1hrpd7yd66ydoDW5oXT058c1qfBu2xKtOY6BwhGPOy0Fj\ncEOl1mDwLX4VrtYbUGm09im5gOYd0Hv5cXj9Ypr1G4WkUnHmx42otDpC2/csEYOz3bz+VZm0Wi0j\nRoxg4cKFeHl54ePjw5w5c+jcuTOtW7fGbDaTmZmJp6cnWq22xNSbm5sbOp2u0qbkyvx0zc3N5amn\nnuLIkSNERkbSr18/PDw8yMnJ4dSpU7z88st8/fXXrFq1Cl0pi8KVbUS4H1bg3dirWBWF9l6uPFWv\nsEeOyclnVnQcc5qF0cLDgJdGzevNw/nvxSReOHERvUqmp58Hj4cVTW08Uz+Q1ReTmHc6HpUk0c3H\njSfr1pz7YW5285pcw26RTN2xgcX3DOfcngNkJ6eytO9ohi55jemHt5J6MZ6PRk7l7O799mPWjpnG\nsKWzmbTtI2wWC4c3bWfT1JqXGXT2neVIKjWtFs1FVqtJ2b2X6DkLAfBq15qOaz/g4Mjx9hGRzt8P\nFAVzpuOEgpP/mUPjqZNo9eZc1G6uZBw9xsFR4zFnZlVbm8qjy0OjsVmt/LRqETarlbqtO9Dz8Un2\n/VfPnWLzwpcZ8vJCQpu2ok7L9vx70gwOfPMp+zevxc3Hn56PP21/EoKsUjFg6hx+/XQ5n818Br2r\nG8163E/nQY85q4kONb1/OIrVytGNS7DZrAQ0bUeLwWPt+9MvnOaPVa/RZfxrxdK1b0Wt1dNl/Gyi\nt63l4Eevo9hseNdvRteJc1HrauAMRxV2QABTpkzBYrEwbdo0LBYLd999N6+++ioAR44cYfTo0axd\nu7bEiKgqSMqtsguuWbhwIdu3b2fFihU0b15yCBwTE8PTTz/NsGHDGDduXJk/8NSoAbcf7R1qybrj\nzg6h2g1pXHK+vjY4+8lXZVf6h/krqebdzFkdFg9qWSXnzfvqrQodb3johUqKpOqVOdn4008/8fLL\nLzvsfKBwTvH5559n69atlR6cIAiC8M9V5hRcYmIiLVuW3tO3bt2aK1euVFpQgiAItZVUjue5/VOU\n2QGZzWYMBkOpdVxcXMjNrZ3DcEEQhEpVxWtANcmdkeIlCIJQW4gOqLi1a9eWuEv2Rnl5eZUWkCAI\nQm0mvpDuBiEhIXz77bdlnig4uGbcRyAIgnBHEyOgIjt27KiOOARBEASoVR1Q7RnrCYIgCDVKmSOg\nJ598slwnkiSJNWvWVDggQRCE2kysAd3g5iek3iwqKorLly/j4eFRaUEJgiDUWrVoCq7MDmjBggUO\ny7OysliwYAGXL1+mV69ezJ4922E9QRAE4W8QHVDpduzYwWuvvYbJZGLhwoUMGjSosuMSBEGolcST\nEG4hPT2defPmsW3bNu677z5mzZqFr6/jL8cSBEEQboNYAypp+/btzJ07F1mWeffdd+nb1znfoCgI\ngiD8M5TZAaWkpDB79mx+/vln+vfvz4wZM/D09KyO2ARBEGofsQZU5IEHHiArK4uwsDD0ej1vvXXr\n76qYO7fmfZmZIAjCnaQqvxG1pimzA2rSpIn93xcuXKjKWARBEASxBlRk3bp11RGHIAiCgBgBFSOe\nhCAIglCNRAdUpKwnIQiCIAjC7bjtJyEIgiAIVUCsAQmCIAjOIJ6EIAiCIDiHWAMSBEEQnEJ0QIIg\nCIIz1KbvA6o9LRUEQRBqlGofAcna2jO8vG5IYx9nh1DtNp9Nc3YITtHP08XZIVS7nAKLs0P4ZxFT\ncIIgCIJTSLVnYkp0QIIgCDWJ6IAEQRAEZ1BEByQIgiA4RS3qgGpPSwVBEIQaRYyABEEQahJJcnYE\n1UZ0QIIgCDVJLboRVXRAgiAINYhIQhAEQRCcQ3RAgiAIglPUog6o9rRUEARBqFHECEgQBKEmqUUj\nINEBCYIg1CAiCUEQBEFwDtEBCYIgCE4hbkQVBEEQnKIWjYAqpaVXr16tjNMIgiAItUipHdDo0aNJ\nTk4u9QTffvstAwcOrNSgBEEQaitFkiu03UlKjdZoNDJw4EB+/fXXEvuys7N5/vnnefHFF+nYsWOV\nBSgIglCryHLFtjtIqdGuX7+ewYMHM2HCBObPn4/ZbAbgjz/+sHdM8+fP5/3336+WYAVBEP7xJLli\n2x2k1CQElUrFSy+9ROfOnZk+fToHDx6kXbt2bNy4kcjISBYuXEhISEh1xSoIgvDPd4d1IhVRriy4\nXr16sXjxYsaMGUNMTAzdunXjww8/RKpF6YKCIAjVohZ1QGW2VFEUVq5cydixY4mIiGDSpEkcOHCA\nsWPHlpmgIAiCIAi3UuoI6PLly0ybNo1jx44xfvx4Jk2ahEqlolevXjz//PMMGDCAOXPmcN9991VX\nvHY2ReHTC8nsSMok32qjvbcr4xsG4aV13KQ3o+PYl5KNBCjXytp4uTK7VR0AMkwWVscmcjwzFxno\n5u/B6HoB6FQ16GpEkmj83CRCBg9A7WogZc8+ome/gSktvUTVjms/wLtTZFGBothvcDvw2FgyDh0F\noP74Jwh/9CE03l5knYwmZt6bZMecrZbm3I4RK15HkiXWj//PLevUiWzF0HdnEt6uBelxCXw3bxn7\nP91s36/R6xj63izaDrkfWa3m8KZtbJo6F1NefnU0odxsNhvfr/+QQzu/x5ifR9N2nRgybipuXt63\nPObAz9v4dcvnpCUl4BsYSs/Bj9Kx97/t+81GI1vWLOHE/j3YrFZad+vFwCefQat3qY4mlYtis3Fo\ny1rO/bEDc0E+YS3a02XYRFw8vMp1/E/vz8ZiMvLvqfPtZRlXLnHgqzUkxUaj0mip264rHYY8gdbF\nUFXNuG1Vnclms9l455132Lx5M7m5ufTo0YNZs2bh6+vrsP7x48eZP38+0dHRBAYGMnHiRAYPHlwp\nsZTa0oEDB5KWlsZnn33G5MmTUalUALRs2ZLNmzfTq1cvJk+ezCuvvFIpwfwdn11MZldSJs81DWFB\n67qkGi0sjI67Zf2LuUZG1w/go86N+fjaNq1ZKABWRWHm8UvE5xuZ3jycmS3r8FdOAa+fuvX5nKHR\n5AmEDHqA4y/O4MBjY9AHBdJm6SKHdY9Mep5d3foUbT36knXqNGn7o8g4/CcADZ8ZR/0xo4ie+ya/\nDx6OMTGJ9quXonLRV2ezym3A7KncNW54qXVcfb2Z/P0nXIw6zuvtHmDX0k8YuWYhEfd2t9d5bNUC\nGnSLZFm/J1je/0ma9OrCiJWvV3X4f9uPGz/i8K8/MnzKDCbOX0pGajJrF828Zf1jv//K5lXv0vuh\nx5i2dB13D3yEL5cv4tTBffY6X65YxIWYk4yZsZAnpr9B7ImjfLXy7epoTrkd2bqe2P07ufuJ5+n3\nwkJy01PYuWpBuY6N2f0dcSeiipWZjQX88N4M9G4eDHjlHf719KsknjvJb2vfrYrwK66KkxCWLFnC\nli1bWLRoERs2bCAxMZHJkyc7rJuWlsbYsWPtn/kjR45kxowZ7Nu3z2H9v6vUaAcNGsQ333xD69at\nS+wzGAy88cYbvPXWW/z000+VEkx5WWwKW6+kM7JeAK29XGngpueFiFCis/I5nVXyKtZsU7haYKKx\nmx4vrdq+uaoLO9SDqTlczjPycrMwmnq40MBNz4sRoRzPyOVkZl61tu1WJLWaOqOGcebtZaT9cZDs\n6DP8OfUVvCPb4tmmVYn6luwcTGnp9i10SH8MYSH8OeVlUBRULnrqjRlFzIK3Sd65m7yLlzk583Vs\nRiPuLZo5oYW35lsvjCm/bKDH+BGkXYwvte5dTw0nLyOLTVPnkHT2PLveX8v+T7+hzwvjAPAKDaLj\n8IF8NnEGF6OOEbvvEOvGvkynEYPwCPKvjuaUi9ViYe+2r/j340/RqHV7Qus35vHnZ3Eh+jgXT590\neExedib3DX+CyF734x0QRKd/PUBw3QacO34YgIyUJI7u2cGDE6YS3rgZ9Zu14pFJ0ziy5xey0lKr\ns3m3ZLNaOLXjWyIHjyYkog2+4Q3oNfYlEmNPkfRXTKnHZiVd4fCWdQQ0KP77m5uaRGDjFnR77Bk8\nA0Pxr9+Upnf1JeH0n1XZlNsnSRXbSmE2m1m3bh3PPfccXbt2pVmzZixevJhDhw5x9OjREvU3bdqE\nh4cH06dPp379+jz++OMMGDCANWvWVEpTS+2AXnvtNVxcSh+a9+/fn2+++aZSgimv87kFFFhttPQs\nGj4H6DUE6DWczCrZYcTnG7EpEGbQOTxfQoEJL62aIBetvcxXp8Fdo6oxHZB7syaoDQbSDxyylxVc\nSSA//greHdqVeqzW14cGE8dw5u1lmNMzAPDu0B5ZqyHxh1/s9ay5eez51yAyoo5UTSNuU8NukaRf\nusLcVn1JvVD6qLTRXR04u/tAsbIzu/6gYfdI+7lsViux+4r+H2P3RmGzWml0V825n+3K+bMYC/Jp\n0KKtvcw7IAjvgCDOnzrm8Jgu9w3kniEjALBZrfy5dydJcZdo0qYDABdPn0CSZeo1bWk/pl5ES2RZ\n5ny043NWt9TLf2ExFhDUpChGN98A3HwDSDznuOOFwmm7PR+/Q6v7H8YrKKzYPq+QOvQa+xJqbeHf\nf2ZiPLH7dxLavH3VNKKiqnAEFB0dTV5eHp06dbKXhYaGEhoaSlRUVIn6hw4dokOHDsXKOnfuzOHD\nhyulqeXKgrt06RJffPEFR44cIS0tDR8fH9q1a8cjjzxC3bp1CQsLK/sklSjFWHg/ko+uePg+WrV9\n340u5hpRSRIbLiZzOD0HrSzT3c+doXX80MgyPlo1ORYrRqvNvuaTZ7GSY7GSYbZUfYPKQR8UCEBB\nYlKxcmNSMvrgwFKPrT/uCYwpacR9/pW9zFAvHFNaBp5tW9H42adxCQshK/o0pxcsJjf2fOU3oAIO\nbNjCgQ1bylXXOyyYS4dPFCvLvJKI1uCCwdsTr9AgspNSUWw2+37FZiM7KRXv8OBKjbsiMlILE3w8\nffyKlXt4+5GRmuToELu42NMsfWkiiqLQ6d5+RER2ASAzNQU3Ty/ka1PpALJKhZunNxkppZ+zuuSl\npwBg8Cq+HmHw9CX32j5H/vz+CyRZotV9D7J33ZJb1tvy+mTS4s7j5htA7wnTKyfoSlaVa0CJiYkA\nBAYW/8wICAhw+Ei1q1ev0rx58xJ1CwoKyMjIwMurfOtyt1JmSzdv3syAAQPYuHEjLi4utGjRAjc3\nN7788ksGDhzI5s2byzpFpTPaFCQJVDcNNzWShNmmlKh/Kc8IQLhBx8wWdRhWx4+frmaw/Fzhf3ik\ntxsuKpn3zyaQa7GSa7Gy4txVJCQsDs7nDCq9vvBD84YPTgCbyYysczyyA1AZXAh9aCDnV39crFzt\n6obazZVmM6YRu3w1h8c9izUvn07rP0Tj5VkVTagWWoMeS4GxWJnFaAIKkw8c7b9eR6O/9f9jdTMb\njUiSVKyzAFBrNFhMplKP9QkM4dm3VjN00kv8uXcn329YYz+nRqstUV+l1mAxl37O6mIxGUGSkOXi\n7Vap1VhvEWPKxXOc+mULPf7vuTLPf9eoKfR7fiEGDx++f+c/Nabd1SU/Px9Zlu3r+ddptVqMxpJ/\nFwUFBehu+nzRXvsdclT/7yp1BHT06FFeffVVnnrqKSZOnGj/wVA4l/jhhx8yc+ZMGjZs6HCdqKro\nZAlFKcyEk2/ohMyKgs7BoyhG1gtgSJgvbtfWfOq46pAlibdj4hlTPxA3jYrpzcN578wVHv/9DFqV\nTP8Qb+q76uzrRM5mNRqRZLlwjlcp6hRlrQZrKdlbAf+6B0mWSfjfd8XKbRYLKr2OUzPnkx5VOJw+\n9vx0eu7+jpBBD3Dxkw1V05AqZsovQK0r/iF7/bUxN9/h/ut1TLnOy4Lb8dWn7Pjy08IXksQ9D45A\nURRsNhvyDb/TFrO5zIw1g5s7Bjd3Quo1JDszjZ+/WMv9w59ErdViMZecIbBazGh1zsmCO/b9F/z5\n3Sag8Fe71f2PgKKg2GyFv+/2GC2otSWTY6xmM3s+Xkz7gSNx9wsq8+f5hjcA4J7x/+GLV0Zz6ejv\nNOjYs5JaU0mqcASk1+ux2Wwlfq9MJpPD5RadTofppgue668NhopnEJbaAa1Zs4YhQ4bw7LPPltin\n0WiYOHEiqamprFmzhvfee6/CwZSXn04DQLrJgu+1fwOkmSz46hw3ye2mjqSua2GvnmIy46ZR0dTD\nheUdGpJltuCiktHIMj8knKGPXuPodNWuIKFwtKYL8MOYWHT/lS7AH2PiradPAnrfTfKuPdhuulq5\nfkzO2XP2MsVsJj8uHpewO/fpFumXE/AMDihW5hkSiDEnl4KsbNIvJ+AeUHxaS5Jl3AN8yYh33lPd\nu/YdRJvuve2v87Iz+eGz/5Kdnoqnb1FyRFZ6Ch43Tctd99fJP9EbXAmp38heFlynAWaTkbzsLLz8\nAsjJzEBRFPtN5DarlZzMdDx9HZ+zqjW9ux/1I++2vy7IzeLI/z4lLzMNV++imPIyUzF4dSlxfPKF\n02RejSNq80cc/PojAGwWM4pi49MpjzBk1goUm420uPPUadPZfpzB0xudqwd5GTUj+eJGShXe4B8U\nVNhJJycnF5uGS0pKKjEtBxAcHFzifs+kpCQMBgPu7u4VjqfUrvbIkSM8+uijpZ7g4Ycf5tChQ6XW\nqWz1XPXoVTInbkgQSCwwkVRgpoVnyV75zeg4FtyUUn02Ox+1LBGs15KQb+KVPy+QY7HioVGjkWVO\nZuaRZ7XSxsu1yttTHtkxZ7Dk5eHTsejeHn1oMC6hIfYRjCPeHdqR9sfBEuXp1+4D8mjVwl4m63QY\n6oSRd+lyJUZevc79FkWjuzsVK4vo3Y3YvYW/o7F7o5DVKhp0LVqAbtyjE5IkcW5vyUXY6uLi6o5v\nUIh9C67XCJ3ehb9OFmUmpSUlkJ50lQbN2zg8x87NG/h+w4fFyi6djcbN0wtXD0/qNWuFzWotlkV3\nPvoYiqJQL6JkJmV10BnccPcPsm8+YfVR6/RcPVu0jpedkkhOahJBjVuUON6/XlMemrOKQdOXMnhG\n4VanbVf86jZm0IylGDx9SL5whh0fzKcgO/OGc16lICcTr5C61dLOv0NRKraVJiIiAoPBwIEDRYk6\ncXFxxMfHO3yodGRkJAcPFv/8+OOPP2jfvnISOErtgLKysvDx8Sn1BB4eHuTm5lZKMOWlkSX+HezN\nR+eTOJyeQ2xOPm/HXKGVp4Em7i5YbAoZJot9/aa7nwcHUrPZEp/K1XwTe5Oz+Ph8EkPCfNGpZAL0\nGlJNFlbHXiUh38SxjFzejomnT6BXscw4Z1LMFi5v2ESTl6bie1dX3JtH0GbxAtL2R5F57CSSWo3W\n1wdJXTQC1Pr5ovXzJfv0uRLnK7iSwJVvv6P57Ffw6doJ1wb1aLlgForFWmK6riaT1WrcA/yQr7V7\n35rPcff3ZfjyeQQ2bUivZ0bTYdgAfli4EoDMhCQOb9rOyDVv0qBrexp278Bjq+bzx9qvybpac57s\nodZo6Np3MFs/XsHpIweIiz3D+rfn0LBlO+o0KUwztlosZGekYbUUJsr06P8wpw8f4Nctn5OSEG+/\nKfX+YU8ChQkNrbv1ZNOyhVyIOcH5U8f4cvlbRPa6Hw8fxzchVjeVWkNEz34c/Oq/xJ88RMqlc/y6\n5k2Cm7TCv35ToDBVOz8rHZvVgkqjKdaBufsHodW7oNLqcPcLQpJlwlt1xMM/mF//+xbp8RdIjI1m\n56o3CGzYjLAWkWVEVP1silKhrTRarZYRI0awcOFC9uzZw8mTJ3n++efp3LkzrVu3xmw2k5KSYn/w\n9MMPP0x6ejqzZs0iNjaWdevWsW3bNp566qlKaWupU3ChoaEcO3as1AeOHjt2jPDw8EoJ5u94rJ4/\nVkXh3dNXsCgKkd5ujGtYOLyMycrj1eOXmNe6Li08DXT398CsKGyOS2X9hWQ8NWoGhvrwcHjhEF8l\nSbzaIpxVsVeZeuQ8bmqZfwV5MayOc6YlbuXsO8uRVGpaLZqLrFaTsnsv0XMWAuDVrjUd137AwZHj\n7SMinb8fKArmzEyH5zv5nzk0njqJVm/ORe3mSsbRYxwcNR5zZla1tenvUm76A2vYLZKpOzaw+J7h\nnNtzgOzkVJb2Hc3QJa8x/fBWUi/G89HIqZzdvd9+zNox0xi2dDaTtn2EzWLh8KbtbJo6t7qbUqa+\nI8Zgs1r57N3XsVktNG3fmSFPTbHvvxBzgg9mTWXCnHdp0KINTdp2ZOS02fy48WN++Oy/ePkFMPip\nZ4s9CeGRZ17im9Xv8d95LyGrVPYnIdQk7QeNRLHZ2P3xYmxWC2EtOtBl2AT7/qTYaL5/Zzp9n5tP\nUOOWpZypkFqr475n53Bg04d8t/gVQKJuu650enhMFbbi9lV12tOUKVOwWCxMmzYNi8XC3Xffzauv\nvh9BHxUAACAASURBVAoUznqNHj2atWvX0rFjR3x9ffnwww+ZN28eDz74ICEhIbz55pvF0rgrQlJu\n/ou+wXvvvcd3333Hpk2bHM73ZWRkMGzYMB555BHGjCnfmxkztnIe4XAnubj7krNDqHabz6Y5OwSn\n6HfyD2eHUO1OJWY7OwSnePmexlVy3uwKPhLK3VBzHqtUllJHQGPHjuWnn35i0KBBPPHEE7Rt2xYv\nLy9yc3M5dOgQa9asISAggJEjR1ZXvIIgCP9oNeTOj2pRagfk6urK+vXrmTNnDm+88Qa2a/egKIqC\nRqNhyJAhTJs2rVh6tiAIgnD7SpmU+scp80kInp6evP3228yYMYPjx4+TlZWFl5cXrVu3xsPDozpi\nFARBqDXECOia6wtTjvzwww/2f0uSxJw5cyovKkEQhFqqFvU/pXdAFy5cKPXguLg4EhISUKvVogMS\nBEGoBGIEdM26descllssFlauXMmRI0eIiIhgwYLyfVeHIAiCIFxXrqdh3+jUqVO88sornD9/nqef\nfppx48ahVv/t0wiCIAgOiCQEB0wmE8uWLWPNmjW0aNGCr7/+mkaNGpV9oCAIglButrKr/GOUqwM6\nevQo06dPJy4ujueee44nnnii2JNUBUEQhMpRiwZApXdARqORxYsX8+mnn9KuXTuWL19O3bo17+F9\ngiAI/xQiCeGaAQMGcPnyZcLDw+nevTvffXfrh1ROmPD/27vz+Jiu//HjrztLJvsuIvaliBAi9q2W\nIqK0KLX3oz5VLT+lLS3Vb6P4oIuW0mpV6xNLLW3tBKVqq31fYonaCdn3ZZbfH2EYWZFk4pP38/GY\nxyNz7jl3zklm8r7n3Pe9MzzXbUIIIQpGzgHdo9frKVeuHHq9npUrV+ZaT1EUCUBCCCEeS54BaPv2\n7cXVDyGEEEgSghBCCCspRStwEoCEEKIkye9L5f6XSAASQogSpPSEHwlAQghRopSmNGy5mlQIIYRV\nyAxICCFKkFJ0CkgCkBBClCTGUnQWSAKQEEKUIDIDEkIIYRWlKQlBApAQQpQgpWkGJFlwQgghrEJm\nQEIIUYJIEoIQQgirKE1LcMUegN6q+25xv6TV9Rpa0dpdKHbBLnbW7oJVbPRrZu0uFLtBLUvf+xuA\n3buKZLdyLzghhBBWYShF38cgAUgIIUqQ0jQDkiw4IYQQViEzICGEKEEMpWgGJAFICCFKkNK0BCcB\nSAghShBJQhBCCGEVMgMSQghhFaXpHJBkwQkhhLAKmQEJIUQJIl/HIIQQwioMpSgCSQASQogSRJIQ\nhBBCWIWh9MQfCUBCCFGSlKYZkGTBCSGEsAqZAQkhRAkiSQhCCCGsojQtwUkAEkKIEkSSEIQQQliF\nzICEEEJYhbEUnQOSLDghhBBWkecM6MiRIwXeUcOGDZ+6M0IIUdrJOaB7+vfvj6Io5uemXNYmFUXh\n7NmzhduzAjCZjCTuX03Kub2YMtPQVayLS+v+qO2dc21jSIolfs8y0q+dQdFosa0WiEuLPigabba6\n0RtmYeNdA6fArkU5jMdmMhr5+7eFhO/5g4y0VCrXDeT5wSOxd3bNtc2ZnZs5EvYbCXdv4+JVjoZB\nvfBt3cm8PSU+lp1L5nH97DEUlYoajVvTovfraHW2xTGkfBmNRsKW/MjhP8NIT02hVkATegwbg6Or\nW65tDvyxgb/WLCfmzi08ypbn+ZdfpXH7LubtmenprFkwm1P7d2E0GPBv0Zbur4/ExtauOIZUYP2/\nm4qiUljy5oRc61QKrEefr/+PigF+xF6/xaYpc9i/eJV5u9ZWR59Zn9CgR2dUGg1HVm5g5ZjJZKSk\nFscQCkZRqDxsGF5dglDb2xO7fz+XvpxJZlxctqp1Z8/CuUGDBwUmE9z7X3Vy5EgST5xEZWND1dHv\n4NG6DYpGTdSff/LP7G8wpqUV14ieSEk4BxQTE8OkSZPYu3cvWq2Wnj178u6776JS5b9olpCQQPfu\n3XnllVcYOXJknnXzDEBVq1bl8uXLBAYGEhwcTKtWrVCr1Y83kiKUeHAtKef/xq3DUFS2DsTtXELs\nlnl4vjwux/omg57odTNRObjh2fNDjGlJxG37iQSVCpdW/Szqxe9cTPq109h41yiu4RTY/lWLCN+7\nnY7DxmHr4MSO0G/YNGcKvSZ8kWP9iwd3syN0Du2HvINPrXpcO32U7QtnYevkQtUGTTEaDKz+fDyK\nSs2L74Sg1trw1+K5bJg9iZfHTivm0eVsy7KfOfLXFvqNnoidkxO/z5tJ6Of/x9tTv8mx/om//2LV\nD1/zytvvU61OfS6cOMyv336Og5MLdRq3AODX7z7nxqWLDJ04A71ez4pvpvPbvC/pN3picQ4tT90m\njaHVsH7s+XFZrnUcPNwYFfZf9i9eTejr46jTqTWDFswg/tYdwrftAWDAD9OoGODHnOAhaGy0DP75\nc/rPm8rCwe8W11DyVWno65Tp3Inzn05Gn5BAtfffo9aUyZwa+f+y1T074SNUmof+falU1Pn8M/SJ\nSSSePAVA9XHjcKj5HGfGjkXRanluwniqv/8+F6ZMKa4hPZGS8H1AI0eORK1Ws2TJEm7fvs2HH36I\nRqNh9OjR+bYNCQkhMjKyQK+TZzjbtGkTq1evplGjRoSGhtK7d2++++47rl69Srly5Shfvrz5UdxM\nBj3JJ7fj3LQnugq+aD0r4dZxGBm3LpJxOyLHNqkX9mNITcA96C207uXR+dTCqfFLZET+Y66Tefcq\nUb9PI/3meRQb++IaToEZ9HqO/7GGFq/8i4p1GlCmcnU6vzWemxdOc/tizrPQtOQEmvYcTO2WL+Ds\nWRa/54PwqFCF62eOAfDPsf3E3LhK8MiJeNfwpUzl6gS9PYHrZ45z49yp4hxejgx6PXs2/EaXgW9Q\nw78h5as+x8D3PuHy2ZNcOXc6xzYpifF06jeEwLadcfPypskLXSlXuRoXT2YtK8dF3eHYru30HD6G\nis/5UtW3Hr1HjOPorm0kxEQX5/By5FGlAqO3LaX1m/2JuXIjz7qt3uhHSlwCK8d8yp0L/7Bjbij7\nF6+m4/vDAHAt703jft355a2JXDl0goi9h1n07w9p0v8lnL3LFMdw8qWo1ZR75RWufP8D8UeOkHzx\nIuc/CcHZ3x9HvzrZ6huSksiMizM/vLoEoStXjnMhIWAyYePpSZkXOnDpiy9JCg8n8eRJLk6fQZmO\nL6D18Cj+AT4Go9H0VI+ndfToUY4ePcqMGTOoWbMmbdq0Ydy4cSxevJjMzMw8265fv57Tp09TtmzZ\nAr1WvvOpWrVqMXr0aMLCwli4cCHu7u588skntGrVipCQEA4cOFCwURWyzOhrmDLTsPGpaS7TOHmg\ndvIg49bFHNukXzuNrkIdVDYPlljsa7egTK8HSxtp189g41OTMn3+D5VNyVh+eljU1Qgy09IoX9vf\nXObsWRZnz7LcPJ9zsKjbNpjA4N4AGI0GLhzYSeyt61Ssm3XeLv7OTexd3HDxKmdu4+jmia2TMzfP\nnSjC0RTMzX8ukJ6WSjW/B0subl7euHl588+ZnPvXrFN32vXoD4DRYOD4nj+5c/0qNes3AuDKuVMo\nKhVVatU1t6lSuy4qlYp/zlp/zNVbBBJ79SaT6wURffl6nnVrtGrEhZ2Wn8PzO/ZRvWWgeV9Gg4GI\nvYfN2yP2HMJoMFCjVePC7/wTcHjuOdR2dsQfO2ouS4+MJP32bVz86+fZVuvmRoXBg7ny/ffo7y3X\nOdWri8loJOHUg89EwsmTmIxGnP3rFc0gConB9HSPp3X48GF8fHzw8fExlzVp0oSkpKQ8T7VERkYy\ndepUPvvsM2xsbAr0Wo+Vhu3r64uvry/vvvsuZ86cISwsjLfffhs7Ozt27dr1OLt6aoakWADUDpbn\nANQOrhiSY3Jso4+LxKaCLwkH1pB6fh8oCrZVA3Bu+jKKOusckFNAUNF2/CklxUYB4OBmeRTn4OpO\nYszdPNveuXyBlZNHYzKaqNOmM1X8G99r60FaciL6jHQ0NjoAMlJTSE9OJCUh+/p7cYuLzhqXi7un\nRbmzmydx0XfybHs94hzffPAWJpOJJh2CqR3YDID46CgcXVxRPbSkrFKrcXRxIy4q730WhwNL13Bg\n6ZoC1XWrUI6rRywPPuJvRmJjb4e9mwuu5b1JvBONyWg0bzcZjSTeicatYrlHd2cVNl5ZM7GMu1EW\n5RlRUdh4eeXZtsLAgWTGxBC5Zq25TFfGi8zYWHhozBiNZMbGovMq2NF5aXX79u1sMxive3+D27dv\n4+/vn1MzJkyYQJ8+fahfP+8Dhoc90XVABw8eZPPmzWzZsoX09HQaNWr0JLt5KiZ9BigqlEdPiqk1\nmPQ5TxONmWmknN2FbaV6uHUejjE5jvhdSzGmJeLW/vVi6PXT06eno6gUVCrLc3FqjQ2GfKbHzmW8\neTXkG+5eiWDnku+wd3alWa/XqOzfCBtbO7b//DXPD8o6abgjdA4oKox6fZGNpaAy09NRFMUiWABo\ntFr0GRl5tnUv68M7X8zn5qULrFkwG0dXd4L6DyUzPR1tDkdpao0WfWbe+yxpbOxt0aelW5Tp07PG\noLXV5bj9fh2tra5Y+pgftc42K8np4YABGDMyUelyP5pW2dnhFdyFy3O/tSy31WHM4b1hzMxEVcCj\nc2sp6iSEGzdu0KFDBxRFyZZYptPp6N69Ozqd5ftCo9GgKArp6dnfRwChoaFERUUxatSox+pLgQKQ\n0Whk//79bN68ma1bt5KYmEjLli1577336NChA46Ojo/1ok8i8chGko5svPdMwTEgCExGTCYjivJQ\nEDLoUbQ5f6gUlRqVrSOuHYZmZfeVqYzJoCd26/e4tHwVlc6hyMfxuA6tX8ah9cvvPVMI7NoHk9GE\nyWi0CL4GfUa+GWu2Dk7YOjjhWbEaKQlxHFyzhKY9B2Pr4MSLoyexdf4XzB/RG41Oh/8L3fGsWBUb\n++L/nWz/bTHbf12c9URRaNezPyaTCaPRaJGFo8/MzDdjzd7RCXtHJ3yqVCcxPoY/VoTSud/raGxs\n0OcQsA36TGx0JSsLLj8ZqWloHvknff95enJqjtvv18lILhlZcIZ7BxkoSlZG2z0qGy3G1Nyz1jxa\nt0ZRq7m7ZYtFuTE9I8dAo9JqMaSVjDHnpqiTEMqWLcumTZty3KZSqVi0aBEZjwRvvV6PyWTCzi77\nZyMiIoLZs2ezePHix05SyzMA7dq1i82bN7Nt2zZSUlJo1aoVH3zwAe3bty+WoPMwB7+22NV4sF5t\nTEsi8eAajMnxqB0fLMMZkuOwdcg5HVnl4IqitrFILde4+4AJDAnRqMqUvABUr92LPNfkefPztKQE\n9v8eSnJ8DI5uD5akkuNisi3L3Xfj3Els7BwoU6maucyjQhX0GRmkJSdi5+iMd/XaDJr+I6mJ8djY\n2qHW2jB/xyZcni/+JcnmQS9Rv2V78/OUxHg2//ITibHRuHg8OGmeEBuF8yPLcvddOn0cW3sHfKo+\nyGIsV6kamRnppCQm4OrpRVJ8HCaTyfx+MBoMJMXH4uKR8z5Lqthrt3ApZ7lM5eJTlvSkZNISEom9\ndgsnL8sxKSoVTl4exN24XZxdzVXGnaxlTxsPDzKiHizD2Xh6kh6V+9Kye6uWxOzdm222k34nEq3r\nI/8HVCq0bm7ZlvlKmqK+G7ZGo6Fq1aq5bvf29mbnzp0WZXfu/X1ySi7YtGkTqamp9O/f3zyjSktL\nY968eWzevJl169bl3pe8OvrGG2+g1Wpp3rw57dq1MwedP//8M1vdbt265bWrp6bS2aPSPchKMzm4\noWhtSb95HvuaTQHQJ0RhSIzGplzNHPehK/ccKWd3W8we9NHXQaVC7VwyM2N0Do7oHB4Ee0d3T7S2\nttwIP0mt5u0ASLh7m4SoSHxq5Xxy9fCGFSiKim5jJpnLIiPCsXN2wc7RmbjIm/yx4Eu6vTMJOycX\nICtoZaQmU7FOQBGOLmd2Dk7YOTiZn7t4lEFna8el08cIaNMRgJg7t4i9c5tqdXJeb/5z1VIUReH1\nj6aby65eOIujiysOzi5U8a2H0WDgyrnTVKmdlYjwz9kTmEwmqtQu2SepH3Vx9yGa/6uXRVnt9i2I\n2JOVdBCx5xAqjZpqzRty6e+sLMDnWjdBURQu7jlU7P3NSfLFixhSU3EOaEDU1j8A0Hl7o/P2JuHY\n8VzbOfvX5+qCBdnKE0+cRFGrcapbl8R7iQjO9f1BUUg4ebJoBlFIrP11DIGBgXz55ZdERkaaA86+\nfftwdHTE19c3W/3Bgwfz0ksvWZS99tprdOjQgddfz/vURr5LcJmZmezcuTNbRHyYoihFHoCyvaZa\ng4NfWxL+XonK1gGVnRPxu5ZiU74WNmWzorvJoMeYnoJKZ4+i1mBf53mST/5J3PYFOAV2w5AcQ8K+\n37Cv1aJELr/lRK3RUq/9i+xZPh9bRyfsnFz4a9FcKtSuj3e1WkBW2nJ6ciI6ByfUGg0NOvVg7cyJ\nHNn0G9UDm3P97AmOhv1Gq35vAllZdMmx0fy1+Fua9hhIYvRdts7/nDptgiwy46xFo9XSPOhl1i/8\nDnsnFxycXVn1w1dUrxtApZpZHwiDXk9KUgL2js6oNRpav/gKCyZ/wF9rluPXpBWXTh/jrzXL6T5k\nBJCV0ODf4nlWzplB75EfYDIa+fXbLwhs2xln95J5MHKfSqPBwd2V5Jg4jHo9excsp9PYYfT7dgrb\nZ/2Mb8dWNOrbjdmdBwMQf+sOR1ZuZNCCz1g0dByKSsWAH/7DvtDfSbidd+JKcTHp9dxetZqqI0ag\nj08gMy6Oau+OIf7IUZLOnkVRq9E4O6NPSMBkMACgdXdH6+5G8qXsl11kREcTtWMHNT78gIvTZ4BK\noca4cdwNCyMz2vpp9nmxdgAKCAigfv36jB49mo8//pi7d+/yxRdfMGTIEDT3rr1KSUkhJSUFT09P\nnJ2dcXa2vPhfo9Hg4uJCuXJ5///IMwCFh4cXqMM5zYiKg1OTlzEZDcRt+wmT0YBtpaw7IdyXERlB\n9Nov8ej+PjqfmqjtnfF4eSwJe1Zw99cpKFoddjWb4dy0Ry6voORSbl3Ner2G0WBg6w+fYzQYqOzf\niOcHjjBvv33xDKtmfEiPD2dQvlY9KtVtSJcREzmwejH7V4Xi6F6G5we+bb4TgkqtptuYT/lr8bf8\n8n8jsXVwxLd1Z5q+NMBaQ8wmqP9QjAYDv3w9FaNBT62GTenxxoOL4i6Hn+L7T8Yw/NOvqeZXn5oN\nGjNo3CS2LFvI5l9+wtXTi5ffeMfiTgi9R37A6vmz+GnKB6jUavOdEEqaR08UV28RyJjtS5nZrh8X\ndx0g8W403wS9Rp/ZIXx0ZD3RV27w86AxXNi539wmdOg4+n4ziREbfsao13Nk5UZWjplc3EPJ05X5\n81HUap77eCIqjYbYffu4NPMrAJzq1aPurK85NeodEo5nzYhsPDzAZEKfkJjj/i5Om061MaOp8/ln\nmPQGonZk3QlB5G/u3LmEhIQwYMAAHBwc6NOnDyNGPPgf89NPPzF37txc07IfPs2RF8WU2/117tm0\naRObNm1Co9HQvXt32rZta94WHR3NlClTCAsLK/CteNp9nftM6n9Vr6YVrd2FYlfJ5dk6kV9YNvo1\ns3YXit2glqXv/Q3QcnfRXHoy/c8LT9X+w3bPFVJPil6eF6IuXLiQMWPGEB4ezrlz53jrrbfM2RMb\nN24kODiYbdu25Xu/HyGEEAVjMJqe6vEsyXMJbsWKFQwcOJCJE7PujfXjjz8yf/5888wnMDCQyZMn\nU61atbx2I4QQooCetSDyNPKcAd28eZN+/R7cpHPgwIGEh4fz1Vdfme8NJMFHCCEKj8yA7klLS8P1\noVx6W1tbdDodb7/9dr7pdUIIIR7fsxZEnsYTfSNqhw4dCrsfQgghSpknuhdcSfpOICGE+F9SmmZA\n+Qag0NBQi/v/GAwGli5diouLi0W94cOHF37vhBCilJEAdI+Pj0+2+/h4enqyefNmizJFUSQACSFE\nIdBLAMqyffv24uqHEEIIZAYkhBDCSkpTAHqiLDghhBDiackMSAghSpCi/kK6kkQCkBBClCClaQlO\nApAQQpQgEoCEEEJYhQQgIYQQVmEwGq3dhWIjWXBCCCGsQmZAQghRgsgSnBBCCKuQACSEEMIq5F5w\nQgghrEJmQEIIIayiNAUgyYITQghhFTIDEkKIEqQ0zYAkAAkhRAkiAUgIIYRVSAAqQnevJxT3S1rd\nparJ1u5CsUtK01u7C1YxqGVFa3eh2C3ac83aXbCKlkW0X5MEICGEENZgLEUBSLLghBBCWIXMgIQQ\nogQxyTeiCiGEsAY5BySEEMIqStM5IAlAQghRgphKz/fRSQASQoiSpDSdA5IsOCGEEFYhMyAhhChB\n5ByQEEIIq5AsOCGEEFZRmgJQnueAunfvTmhoKLGxscXVHyGEKNWMJtNTPZ4leQYgPz8/Zs+eTZs2\nbRg1ahQ7d+4sVRkaQghR3ExG01M9niV5BqBp06axZ88epk+fTnp6Om+//TbPP/88X331FVeuXCmu\nPgohhPgflO85IJ1OR9euXenatSsxMTGsW7eOtWvX8sMPP9CwYUN69epFly5dsLOzK47+CiHE/7Rn\nbRbzNB7rOiB3d3dee+01fvvtN9avX0+zZs2YP38+rVq1Kqr+CSFEqWI0mp7q8Sx5oiy49PR0zp8/\nz4ULF4iMjKR8+fKF3S8hhCiVStN59gIHIIPBwO7du1m/fj3btm1Do9EQHBzMwoUL8ff3L8o+CiFE\nqSH3gnvIgQMHWL9+PVu2bCEhIYHmzZszefJkOnbsiI2NTXH0UQghSo1nbRntaeQZgNq0acPdu3ep\nWLEir732Gj169MDb27u4+iaEEOJ/WJ4BqGXLlvTq1YtGjRoVV3+EEKJUK01ZcHkGoGnTppl/vnXr\nFufOnSMpKQknJyd8fX3x8vIq8g4KIURpIgHoIadOnWLKlCkcP37cIjtDURSaNm3KhAkTqFmzZpF2\nMjeKAu8E1aZ7owo46DTsPneHqatOEZOUkWP9n4Y3o1E1D/NzE6Dc+/m1b/dy9LLlLYc6+pfjy4EN\n6fSfbdyOSyuiUTw+k9HIuc1LuX5oB/r0VMrUCqBujzfQOboUqP3Bn/6DITOdZm9OMpdlJCdwZt3P\n3D13DACP6nWp0+1f2Lp45LabYmUyGjm8JpSL+7aTmZZKBb+GNOv7FnbOrgVqv3XuJPQZ6XQZ8x9z\nWdzNqxz4bQF3Is6i1tpQOaA5jXoMwcbOvqiGUXCKQuVhw/DqEoTa3p7Y/fu59OVMMuPislWtO3sW\nzg0aPCgwmbI+HMDJkSNJPHESlY0NVUe/g0frNigaNVF//sk/s7/BmFZy3tcP6//dVBSVwpI3J+Ra\np1JgPfp8/X9UDPAj9votNk2Zw/7Fq8zbtbY6+sz6hAY9OqPSaDiycgMrx0wmIyW1OIbwxErC7XRi\nYmKYNGkSe/fuRavV0rNnT959911Uqtyv3Fm8eDGLFi3izp07VK1alVGjRtG2bds8XyfP64BOnz7N\nwIEDyczMZMqUKaxcuZItW7bw+++/8+mnn5KYmEjfvn2JiIh4okE+rRGdavJiYHk+/OUog7/dS1kX\nO2YODsy1/jsLD9H2063mR/vJf3D2ZjwHIqI5dsUy+Hg46fi/XvWw/lshu/Nbl3PjyF806PcOzd+e\nQlp8NEcWfV6gtlf2beHOuSPZyo8smUlq7F2aDvuEpsM+IS0hlsOhBdtncTi6fgkR+/+kzZD3CH5/\nBsmxUfz5w7T8GwLhOzdx/dQhi7LM9DQ2z5qIraMz3cZ/xQtvf0zkxdPsDv26KLr/2CoNfZ0ynTtx\n/tPJnHx7BDZlylBryuQc656d8BEHu7/04NGjJ8kXLhB/5CiJJ08BUH3cOJzq1uXM2LGcGfcBLgEB\nVH///eIcUoF1mzSGVsP65VnHwcONUWH/5cqhk0wN6MqOb/7LoAUzqN2hpbnOgB+mUa1FIHOCh/Dt\ni69Ts20z+s+bWtTdf2ol4VY8I0eOJCYmhiVLljB9+nR+//13Zs+enWv9NWvW8OWXX/L++++zbt06\nOnTowMiRIwkPD8/zdfIMQN988w3NmzdnxYoV9OrVi3r16lGpUiXq1KlD7969+fXXX2nZsiU//PDD\nk43yKWhUCgNaVWXWxnAOXIzm3M0Exi45QsMq7vhXyvmoODFNT0xShvnxUqMKVHC3Z+ziIzx60DG5\nT33O3UwohpE8HqNBz+U9G6kVNADPGvVw8alKwIAxxFwOJ/bK+TzbJkfd4lzYUtwq17Io16enEh1x\nmmpte+BcrgrO5apQo31P4q5HkJmaXJTDKRCjQc+Z7esIfPk1fGrXx6NiNdr++wMiI85w51Leb/CE\nOzc5smYRXtV8LcqTo+9Q9jk/WgwYiUvZ8pSpWotarYK4de54UQ6lQBS1mnKvvMKV738g/sgRki9e\n5PwnITj7++PoVydbfUNSEplxceaHV5cgdOXKcS4kBEwmbDw9KfNCBy598SVJ4eEknjzJxekzKNPx\nBbQeJWOGC+BRpQKjty2l9Zv9iblyI8+6rd7oR0pcAivHfMqdC/+wY24o+xevpuP7wwBwLe9N437d\n+eWtiVw5dIKIvYdZ9O8PadL/JZy9yxTHcJ6YtQPQ0aNHOXr0KDNmzKBmzZq0adOGcePGsXjxYjIz\nM3Nss23bNlq3bk3Hjh2pUKECI0aMwNnZmX379uX5WnkGoKNHjzJ8+HDUanWO2xVFYciQIRw8eLCA\nQys8tcs7Y6/TcPBStLnsVmwqN2JTCKzmnm97D0cbhnWowdcbw4lNtlyye7VFZTyddHz/x4VC7/fT\nSrh5GX16Gh7V/Mxl9m5e2LmVIeafM7m2MxmNHF/+DdXb9cDRq4LFNpXGBo3OlhuH/0Sfloo+PZXr\nh3fg4OmN1s6hyMZSUNHXLqFPT8O7Zl1zmaOHF44eXkRePJ1rO5PRyK6FX1Gv8yu4eluO2dWnloRh\nPAAAHBxJREFUEm3//QEaGx0A8ZE3iNj/J+XrNCyaQTwGh+eeQ21nR/yxo+ay9MhI0m/fxsW/fp5t\ntW5uVBg8mCvff4/+3nKdU726mIxGEk6dMtdLOHkSk9GIs3+9ohnEE6jeIpDYqzeZXC+I6MvX86xb\no1UjLuw8YFF2fsc+qrcMNO/LaDAQsfeweXvEnkMYDQZqtGpc+J3/H3L48GF8fHzw8fExlzVp0oSk\npCTOnj2bYxt3d3cOHTpknvGEhYURHx9P3bp1c6x/X57ngJKSkvJNuy5fvjx3797Ns05RKOuSde+5\nO/GWa9h3E9Lxdsn/vnRD29cgOjGDlfuuWpRX9nRgVFAtBs/di7OdtvA6XEjS4rMCrq2LZZC1dXY3\nb8vJxT9/B0VF9edf4sSv31lsU6nV1O8zkpO/zWPzJ4NRFNA5udJ8eM5LPsUtJTYKAHtXy6N1excP\nku9ty8nxsBUoKoV6nXqyZ1EeywdTRxFz/R8cPbxoP/yjwun0U7DxyjpCz7hrObaMqChs8kn8qTBw\nIJkxMUSuWWsu05XxIjM2FowPXeFoNJIZG4vOq2zhdfwpHVi6hgNL1xSorluFclw9csqiLP5mJDb2\ndti7ueBa3pvEO9GYHhqzyWgk8U40bhXLFWq/C5u1rwO6ffs2Zctavi/uJ5zdvn07xxsPjBgxgnPn\nzvHyyy+jVqsxGo1MnDgx3wzqPAOQwWBAo8k7T0GtVqPX6/OsUxRstep7339hWZ6hN2KjzfsWd3Y2\nal5uXJEv11nOGFQK/KdfA37cHkFEZBIBVdwKu9tPzZCRjqIoKCrLWalKo8WQmXPyRfz1CP7ZtY5W\noz7Ldb9Jd67jVK4yNTu+CorC+c2/cOi/M2gxchoaG9tCHcPj0mekg6KgemTMao0m1zFHXbnImW1r\n6Db+q3z332rwaPTpaRz6/WfCvprASx/PQaO13kXWap1tVsKP0fKSeGNGJipd7v1S2dnhFdyFy3O/\ntSy31WHMyP57MmZmonpGLya3sbdFn5ZuUaZPzxqj1laX4/b7dbS2umLp45Mq6lvx3Lhxgw4dOqAo\nSrbX0ul0dO/eHZ3O8nek0WhQFIX09Oy/U8jKkk5PT2fq1Kn4+fmxbds2ZsyYQZUqVWjZsmWObSCf\nAKQoCoqi5FWl2Py7fXXeaP8cACZMLNgegUpRUBQszt/YaFSkZhjy3FeHut6oFYX1RyzXmd984TmM\nRhM/77BOUkVOLm7/nYvbfwOy/h7V2/XAZDJhMhpRHspIMeozcwwUBn0mx5bPplbnfti753y0G/PP\nGc5vWUaHj+ajc8o6fxY4eBzbpw3n+qE/qdKiSxGMLHcnwlZwfNNKICuZq17n3pDDmA16fc5jzsxk\n18KZNOw+CCfP/C+c9qhYDYB2b05gxfjXuHrsb6o1fr6QRvP4DOlZBxmPvrlVNlqMqblnrXm0bo2i\nVnN3yxaLcmN6Ro6BRqXVYkgr2RlhuclITUPzSDC+/zw9OTXH7ffrZCSX7DEXdRp22bJl2bRpU47b\nVCoVixYtIuORAxa9Xo/JZMr1Ww/ef/99+vTpQ69evQCoXbs2V69eZebMmU8egEwmE3369Mn1HBBk\nzZKKw/K9Vwg7dsv83NVBy8igWpRxsuVOwoMPZRlnXbZluUe19SvLX2cjSddbHmF2b1SBMs627J8S\nBICiykrTXvN+W37YdoEFfxZ/YKrcvDM+9VuYn2ekJHFu8zLSE2MtUqTTEmLQuWQ/9xV39TxJd24S\nvnExZzcsArJO6mMysvnjgbR5bxaxVy+gc3Y3Bx8ArZ0DDmV8SIm6XYSjy1mtNsFUDWxjfp6WnMDR\ntYtJiY/Bwc3TXJ4SH429a7Ns7e9ePkf87escWvUzB3//GcgK0CaTkcWje9Pjk+8wGY3EXP+HSvWb\nmtvZu7ihc3AmJS73pczikHHnDgA2Hh5kRD1YhrPx9CQ9KvflbvdWLYnZuzfbbCf9TiRa10cSc1Qq\ntG5u2Zb5nhWx127hUs5yOdLFpyzpScmkJSQSe+0WTl6eFtsVlQonLw/ibhT/e/pxFPUSnEajoWrV\nqrlu9/b2ZufOnRZld+69Jx9dmoOslO2rV6/i5+dnUe7v78/27dvz7kteG0eOHJln4+KUmKYnMe3B\nUt/teIWUdD2Nqruz8ehNAHzc7CjvZs+hSzF57iuwqjtzNmfPGBvy7d9o1A+OsP0quvDZgIYM/3E/\nF28nFtJIHo/WzsEiEcDWJRONzpboS2coH9AagJSYO6TG3sWjavYMKddKNWk37huLsvBNS0iNiyKg\n/2hsnd2wc/EgIzGOjOQEbBycgaylvpToSCo2aleEo8uZzt4Rnb2j+bm9mwcanS23L5yiepO2ACRG\nRZIUfQfv5/yytS9TpRa9PrXMzDy0+r8kx9zh+aFjsXdx5/LRvfy14HP6zgjF1snl3j5vk5YUj6tP\n5aIbXAEkX7yIITUV54AGRG39AwCdtzc6b28SjuWepefsX5+rCxZkK088cRJFrcapbl0S7yUiONf3\nB0Uh4eTJohlEEbu4+xDN/9XLoqx2+xZE7MlKOojYcwiVRk215g259HfWZQfPtW6Coihc3HMo2/5K\nEpOxeA7qcxMYGMiXX35JZGSkOeDs27cPR0dHfH19s9V3dXXF1taWc+fO0bx5c3P5+fPnqVw578/S\nMxOAHqU3mFi+9wrvv1iHuORMYpPT+ahHPQ5ERHPqWlb2j0al4GKvJT4lE/29owoPJx0ejjou3Mqe\nYn37kZlTGWcdCnArLtUi+FmTSqOlcvPOnF3/X2zsHbFxcOHU6vl4VK+La6WsJUqjQU9mShJae0fU\nGi32HpbLUBpbe9RaG/OSnFedRti6enJkyUx8gwejqNWc37IMtY2O8g2ttxR1n1qjpfbzwRz87Sds\nHZzQObmw75fvKFezHmWqZqWUGw160pMT0Tk4odZqcSpjOWYbWzvSbHTmJbmK9RrjXKYcf/30BU1e\nGUpGWir7l39P2eq+VPDL/Vqy4mDS67m9ajVVR4xAH59AZlwc1d4dQ/yRoySdPYuiVqNxdkafkIDp\n3gqE1t0drbsbyZeyz9IzoqOJ2rGDGh9+wMXpM0ClUGPcOO6GhZEZbd3ZXkGpNBoc3F1JjonDqNez\nd8FyOo0dRr9vp7B91s/4dmxFo77dmN15MADxt+5wZOVGBi34jEVDx6GoVAz44T/sC/2dhNvFnzT1\nLAkICKB+/fqMHj2ajz/+mLt37/LFF18wZMgQc05ASkoKKSkpeHp6olKpGDBgAN999x1ly5albt26\n7Ny5k99++42vv877uro8A9CWLVto164dWm3u2WDJycl89dVXTJw48QmG+nRmh4WjVitM698AjUph\nd/hdpq56kBnToIobC4Y35/V5f3P43qyojJMOExCfknM++6NK4oWotTr3w2QwcGzZbIxGA161AvB7\n+d/m7bGXz7HvhxCavRlika6dG42NLc3enMTZDaEc/HkqJqMRt6q+NH9rMhpdyfim24YvDcJkNLJz\n4UyMBj0V/BrRrO9w8/Y7EWcJ++ojgt79D97P5Z36CaCx0dHpnU85sPJHNs0cDyhUDmhOk1eGFuEo\nCu7K/PkoajXPfTwRlUZD7L59XJqZlVDhVK8edWd9zalR75BwPGtGZOPhASYT+oScZ+oXp02n2pjR\n1Pn8M0x6A1E7su6EUFI9enK8eotAxmxfysx2/bi46wCJd6P5Jug1+swO4aMj64m+coOfB43hws79\n5jahQ8fR95tJjNjwM0a9niMrN7JyTMnI7MyLtWdAAHPnziUkJIQBAwbg4OBAnz59GDFihHn7Tz/9\nxNy5c81p2e+99x5ubm7Mnj2b27dvU7VqVWbOnMkLL7yQ5+sopjxSLnx9fdm9ezceD12s1qFDB0JD\nQ81fQhcVFUXr1q1zzQ9/VN331xeo3v+STq2rWLsLxc7LuWRnGhWV1h+/bu0uFLtFe65ZuwtWMc90\nuUj2W+lfi56q/dWFgwqpJ0Uv3ySER8XExGA0lqJvTBJCiGJkKqbErpLgib6SWwghRNEoCUtwxUUC\nkBBClCClKQDlfcsAIYQQoog89p0QSsqdEYQQ4n9RaZoB5ZuE0KZNG4syvV5Ply7Fe2sWIYQoLSQA\n3fPwV3ILIYQoehKA7m/M507YQgghCpdRAlCWsWPHWpzzye2aVUVR6NatW+H2TAghSiGZAd3TqlUr\n9u/fT/369QkODiYoKAh39/y/bVQIIYTIT54B6McffyQ+Pp4tW7YQFhbGjBkzaNiwIcHBwXTq1AkX\nF5fi6qcQQpQKMgN6iIuLC71796Z3797ExMSwdetWNmzYwOTJk2natCnBwcF07NgRR0fH/HYlhBAi\nH6XpVjyPdSGqu7s7r776KgsXLmTHjh20aNGCKVOm0KJFi/wbCyGEyJfJaHiqx7PksdPcEhMT2bZt\nG2FhYezduxcXFxc6d+5cFH0TQohS51kLIk+jQAEoLi6OrVu3smXLFv7++2/c3d3p1KkTP/30E4GB\ngXJ3BCGEKCQSgO5ZtmwZmzdv5uDBg3h6etKpUyeGDx9OYKB1vzFSCCHEsy/PABQSEoJWq6VFixYE\nBASgKAoHDx7k4MGD2eoOHz48hz0IIYR4HKZS9H1reQYgHx8fAC5evMjFixdzracoigQgIYQoBLIE\nd8/27duLqx9CCCGQACSEEMJK5F5wQgghrEIuRBVCCCGKmMyAhBCiBJFzQEIIIaxCApAQQgirkAAk\nhBDCKkpTAFJMuX3NqRBCCFGEJAtOCCGEVUgAEkIIYRUSgIQQQliFBCAhhBBWIQFICCGEVUgAEkII\nYRUlMgC1b9+eefPm5br92LFjDBs2jMaNG+Pv78+LL77IvHnzyMzMBGDVqlXUrl0bX19fateune3h\n6+vLzZs3LfY5dOhQateuzZkzZyzKd+3ale++Tpw48dRjHj9+PK+//joAgwYNomnTpkRFReVZD7J+\nVw/3p169erzwwgvMmDGD5ORkc70bN25Qu3Ztjhw5km2fOW2LjIxkwoQJtG7dmrp169KuXTs++eST\nHPtUVNq3b0+nTp1IT0/Ptm3QoEF8/PHH5ufJycnMmjWLLl264O/vT6tWrfh//+//cezYMYt2ISEh\nBAQEcO3aNYtyg8FA3759ee2114pmME/o0b9v7dq1adCgAcHBwSxcuNBc7/62Xbt25bifLl265Pr3\nL073x7Ns2bIct//73/+mdu3arFu3Ls/Psa+vL1u2bAFgzpw5FvX8/Pxo2rQpw4cP5/Tp0+Z9jx8/\nnjZt2uTat/Hjx9O9e/fCHbDI0zN3IWp4eDivvfYar7/+Oh988AE6nY5jx44xdepUrly5wrRp0+ja\ntavFG61Xr1689NJLDB482Fzm7u5u/jkyMpJ9+/ZRtWpVli9fzqRJk8zbmjdvzp49e8zP33jjDXx9\nfXnvvfe4fwmVq6troY8zISGBSZMm8c033+Rb98033zSPLSUlhVOnTjF9+nSOHz9OaGgoGk3Wn1lR\nlFz38fC2jIwMBg4cSM2aNZk7dy5lypTh8uXLfP755wwaNIh169aZ91nUrl27xsyZMxk/fnyudeLj\n4xkwYAB6vZ7Ro0fj7+9PTEwMy5cvZ+DAgUyePJkePXoA8MEHH/D3338zbtw4li5dah73F198wZUr\nV1i7dm2xjOtxPPz3BYiLi+OXX35h+vTplC1bli5dugCg1WrZvHkzrVu3tmh/7tw5Ll++nOffvzjd\n72ffvn0tyuPj49m/f79FPzUaDTt37iSnyxWdnZ3NP1eoUIEVK1ZgMpnQ6/Xcvn2befPmMWDAABYv\nXkzdunXp1asXq1ev5sCBAzRp0sRiX+np6WzdupVRo0YV8mhFXkrkDCgva9asoUaNGrzzzjtUr16d\nChUq8OKLLzJ27FjWrl1LUlISNjY2eHh4mB8qlQo7OzuLsoff5GvWrMHHx4dXX32V9evXk5qaat6m\n0Wgs2mm1Wuzs7HB3dzeXqdXqQh9nhQoV+OOPP9i4cWO+dR8eW8WKFenSpQvfffcdR48e5bfffjPX\ny+ua44e37d69m+vXr/P555/j7+9PuXLlaN68ObNmzeLy5cu5HmUXhYoVK7J48eJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "\n", "cm = np.corrcoef(df[cols].values.T)\n", "sns.set(font_scale=1.5)\n", "hm = sns.heatmap(cm,\n", " cbar=True,\n", " annot=True,\n", " square=True,\n", " fmt='.2f',\n", " annot_kws={'size': 15},\n", " yticklabels=cols,\n", " xticklabels=cols)\n", "\n", "# plt.tight_layout()\n", "# plt.savefig('./figures/corr_mat.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sns.reset_orig()\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Implementing an ordinary least squares linear regression model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Solving regression for regression parameters with gradient descent" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class LinearRegressionGD(object):\n", "\n", " def __init__(self, eta=0.001, n_iter=20):\n", " self.eta = eta\n", " self.n_iter = n_iter\n", "\n", " def fit(self, X, y):\n", " self.w_ = np.zeros(1 + X.shape[1])\n", " self.cost_ = []\n", "\n", " for i in range(self.n_iter):\n", " output = self.net_input(X)\n", " errors = (y - output)\n", " self.w_[1:] += self.eta * X.T.dot(errors)\n", " self.w_[0] += self.eta * errors.sum()\n", " cost = (errors**2).sum() / 2.0\n", " self.cost_.append(cost)\n", " return self\n", "\n", " def net_input(self, X):\n", " return np.dot(X, self.w_[1:]) + self.w_[0]\n", "\n", " def predict(self, X):\n", " return self.net_input(X)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X = df[['RM']].values\n", "y = df['MEDV'].values" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "\n", "sc_x = StandardScaler()\n", "sc_y = StandardScaler()\n", "X_std = sc_x.fit_transform(X)\n", "y_std = sc_y.fit_transform(y[:, np.newaxis]).flatten()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "<__main__.LinearRegressionGD at 0x118f523c8>" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lr = LinearRegressionGD()\n", "lr.fit(X_std, y_std)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(range(1, lr.n_iter+1), lr.cost_)\n", "plt.ylabel('SSE')\n", "plt.xlabel('Epoch')\n", "plt.tight_layout()\n", "# plt.savefig('./figures/cost.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def lin_regplot(X, y, model):\n", " plt.scatter(X, y, c='lightblue')\n", " plt.plot(X, model.predict(X), color='red', linewidth=2) \n", " return " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rN9hNWcEInbZH0n388ceY+cQTjkTZj997E5ufK/Iww5WVlUmWK3q4YBwUCgUS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\n+/jriotROGY4DMYE1FYflpyjI5bJYjopcpZZAP4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lin_regplot(X_std, y_std, lr)\n", "plt.xlabel('Average number of rooms [RM] (standardized)')\n", "plt.ylabel('Price in $1000\\'s [MEDV] (standardized)')\n", "plt.tight_layout()\n", "# plt.savefig('./figures/gradient_fit.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: 0.695\n", "Intercept: -0.000\n" ] } ], "source": [ "print('Slope: %.3f' % lr.w_[1])\n", "print('Intercept: %.3f' % lr.w_[0])" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Price in $1000's: 10.840\n" ] } ], "source": [ "num_rooms_std = sc_x.transform(np.array([[5.0]]))\n", "price_std = lr.predict(num_rooms_std)\n", "print(\"Price in $1000's: %.3f\" % sc_y.inverse_transform(price_std))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating the coefficient of a regression model via scikit-learn" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: 9.102\n", "Intercept: -34.671\n" ] } ], "source": [ "slr = LinearRegression()\n", "slr.fit(X, y)\n", "y_pred = slr.predict(X)\n", "print('Slope: %.3f' % slr.coef_[0])\n", "print('Intercept: %.3f' % slr.intercept_)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LvbtRfcR+fZvNhvETJkAIC4dSo8Vttccw5r77POy48POfw/T995hz6iQscQmo\nOFAOW1UVBlx7I1eBYEKLtrhZAJQAspo/ZwNQ+uKm+WtBJw/x+TuFmAkcjtTnzP4DQjKOIjckqDWI\nlDt/CWmb07/FKLvdVquV1q1bRykZmZIYV2xyCk3Of+XScKBaTRqtjjRaLVmtViopKSGlWk3z1m/y\nOpznoKioiMQoo2fauQ/DlAzjK/BnDArAhwBeB9DTl5MGaulMgQr1Fx5ziY7Gg/xx/da+yMglVcSZ\nLWRO60V6UaS8vDzn8Q6xcZ/vpNbpKFKhpDizhRQqFRljYkmrFyk+2UylpaVUUlLSqjC5252Xl0d6\nUaTe2Vfw/3Mm4PhboG4EkOnLCQO5dJZABfuFx/iGPzLq2ovcFxk5wZL9PxVlpJKSEsl+rudTazSk\nUKkpNSubdKKRpixbSYmpaRQeEUHz1m9ynkehUtG53r1lhemOyEjS6vUt/t/lkQKms/BVoFrrqLtb\nEIThgiA8Dvvk2ZMAPgawqfli3ZK2No1jQgO5GnadUbBUbi7U+N/ehciISMQlSyfvyiZVrFyBoUOH\ntni+GaN+g5tHjcXVQ3+DelstfjhxHIkpqc7ae1lavb154H89W2G89U01vrjjVxAbfkJxcTEyMzMx\ncOBAj//DPKeJCVVaa1i4HEAYgO2wV3jQA7gNwC0AHgm4dUEiWC88pn04X/4u3WJXrQx8wVL3LzJG\nUywuXryI5/76juzk3ZaSKmw2G7Zt24bouATJF6O4JDPWLpyDd18rxPHaaowbOxYbN2/Gl6V7MWfc\nvbJ2Lduyw3l9W81RNF64gIX5y1Bvq3X2l+pIxQuG6Sxay+LLJqIb3db9TRCETwJlUCjQ3hRiJrg0\nURMuNDSgiZo65XruX2S+2LsbRlNsi563nLfiyO6LSUhC5aHv8Paa5c7mf7VVlZiybCV6xsbj/Lmz\nWDZ5gj1tXEacXn5zK2Y+PArC2BHQG3ui3laLi42NWLRpu6Slu3tldIYJVVoTqDBBEH5BRB87VgiC\ncAMAmVr83QuuN9Z1cNawW7+5w2WHfMH9i0xN5WEQkU+et9yw3szRw7D3vbdhq6lCdEwsrrrpNgBA\n9qJ5mFNf73GO/1UoYdj1f0jq0RPxZgtWvLQMAHDgwAG8tGKVRDBjkpJx8fx5Hq5mugStCdRDAJYJ\nglAEe0uMJgCfA5gQYLtCAh6b7xoEM2Y4ZswYDBgwAKWlpRg8eDC++OILnzxvOdtT0nvhmWlTMXjw\nYFxz3XWCBIOiAAAgAElEQVSo/PLfmHzv7bLHv/VNNV4cfhMmNjcLrKupdsaZBg4ciNlznpUIpvVo\nJcIE8HA10yVoLUniOwDDAUAQhHAiutgpVjGMD3R2zNB1QvDOnTuRk5sLY3QMjluPYebTT2Pru+/i\n22+/xeDBg9G3b1/Z48vKygAAycnJHrZbq6pw++23w2Qy2YfzZMTJNc5UU/E9lj75e5w9fQqrCwok\nw4mrVq7AhAfuhi6qhzMGVbhmjXOfzp7czDA+0VKKH4A0AO8AqARQAeAIgK0AevuSKuivBVyLj/GC\nIz3bX/N5vKVeS9LKo4ykVKlIa7hUO09rEEmhUlFqZl8SjUYqKCiQnKegoIC0Oj3FmS2kVKtJrdHQ\nI488QjqDwblOo9V6nc+0dfFipw2pmX1JoVKRKT6BtDq9pI6eq/2OeVUtpbTzHCimM4Cf50F9AOAq\nt3VXA/jEl4v4a2GBYlrCH/N5XCevur+4y8vLSavXO+cgzVu/iRRKlXNu07z1m0ihUknmOilUKopL\nNpNGq6Xf/va3Hts1ej1FKBSkVKlo9KRptOEp70VdXQvDutviOlevLcLDc/2YYOCrQLUWg1IR0Wdu\nHtc/BUHwj/vGMH6kozHD4uJi5D46EWqDiCYCfjlyLJQaNXJyc/HDDz9g6rTpEHuasOSJCRj71ExE\nRCoQZYpxxo9Uao1HmrjRFIvj1mPoGRuPDW9uRFxyimS72CMadceq0XihEcUvL5G1S6lSITG1F2xP\nTIDeoEdFRQUAIMmS5pwP5Yi7lZWVtalPFc/1Y7oCrQnUF4IgrIW9UOwp2OdB3Q7gP4E2jGE6C0dM\nKPfRiZjzZ2k2Xbw5FQ0NDZg0+Uks3PAujKZYbFyxDGsXzkHPuHicqD2GopcX475J03H+3FnUHZM2\nGay31eKPq/+K7MHX4svSvVgwYaxk++mTJ9Hw00+ydll690HNkQqMevwpZ9r5zNHD0NDQgB9//BHV\nRyo84m4AvAoPAGe8ief6MV2Cltwr2DP3RgBYCqAQQD6Au+GlX1OgF/AQ32VJIEvxOIbDzOkZFGe2\nSMolpWRm0aKN25x9mnLnLyGt3t7DaezUZ0gnGsnSpx8plCrqGRtPCqWK9FFGUihVlJjWixQqNcUm\nmSXnFHuaSKFUUVxKKh0WwmSH8iZFREiG3nSikdbu3U+bv6mm5PQM0ur1lNl/AGl1OlKqVJTWJ0tS\nZklu6M7RF8oRO8tbsMC5juvwMZ0F/N2wEIAJwL0AxjeLU7wvF/DnwgJ1+RHIQL7ry/ylrbtJo9d7\nFQZTQhKptVoaPWkaJaVlODvUOmNJOj31iIklg2ikHjGxNHtNEak0GtIapAVfwyMjKTEi0mucKWfu\nCy0KpUKlonnrN9GUZSudVdD1BlGSIOGeMOIQIkljRLXa2dCQ6/AxnYVfBQr2ckalzR7UPADLAOwD\nkOvLRfy1dDWB4iKcHaOtgXxvxVnbWmF8yrKVpBONFJtkJoVSRcnpvUihUtHYqc9IhEWpUlNq32xS\nKFVkSkyWiEhSegZFKBRk7tWbIhVKuvW3D9PdOU9QRGQkRSqVFJOYTOoWsvPCIyJI7NGTBCGMFCpp\nl12FUkWmhCRSqFQUm5hMa/fu9xBI9+fiev9yxXRTs7Jpcv4rnBjBdCq+ClRrMaiHAVxHRM7KEYIg\nKGBvzb6qQ2OL3RxH+Zq4JGnRUKbttCWQX1xc7JyHVF9nReEq+3/Ltjx7i8WCo4e+x6pnp+O519+G\nJTMLX5buRd6E30IQBLz5ylLsePOv+OHEcSiVKjz317cvxadGDcM7r66AJbMfIhSRsB6txOw1b+BU\nnQ0Fc2fg3x9/iBPWYwAAU0ISqg59J3uP735WjoPHqhE+ehiUag0UZ8+i8UID/vjbuxBntsB6tBJC\nmIDrfnMn3l23GufOnMYXe3cjJjHJp5JK7vEmblDIdAVaE6hIAGpISxtpAHTbSub+QK58TWeU3ulu\ntBbId+0gG6FUoYmA340fD4VCKUl2cH32jompOp0O8+bNw/nz52FyedlnD74W8eZUXHPbHXi/6M8I\nCw/HUy8V4q/LFnq0Zt+2/lWcOXUSFy82Qqs3ILlXJpY8MQHz/3Kp5JJ15O14QUactusNOLfvG/v5\nxCjEp6RhYl4+IhQKzHngHvx07hxOWGvR2PATIIThP598jIiICNx26y1YM3cGGhsvtjnBwbWYrtog\n4vTJevx+7guot9VyYgQT0rQmUM8B+JcgCAdhz+IzAOgFYEqgDevKcAqvf2itaG9ZWRkuXryIhS7V\nw2eM+g3i4+Jln/3OnTuRO3EitHoRddZj6BETB6VSiRPHaiQv+2OVFeh/9fV4u/BPOH/urN1Dcm/N\nfuok/vT3Pai31WLOA/fg7I9n8M/3t17ybC5exJThN8ne1/9u3Y0/3n8X5rmc7/ixGpgSkyH26ImY\npGTUVVXh3OnT6BEbh9Mn63HXIxORmJ6BeePuBQQBv7p3DJ4ddy96xiWg5vD3WJiX58zUk6sS4agt\nWVhYiEVLluC9tSu5CDIT+rQ2Bgi7iPUHcF3zvxG+jCH6c0EXiUFdbpMgAx1r83b+kpISj4SCmMRk\n0rslJuhFkfbs2UN6UaScuS+QVi/dHqlQkE6McjYGjElKpgem/ZEiIiMpLDycVFotRccnkkKpotjk\nFFKq1DRl2UpJPCcmMZkUKjUpVWqvcSadaKTo+ESavaaIbhv7sPN8CqU03qXR6SUTgF0TNtL79iNz\negZt/qaa1u7dT4s2bqPYxGSPicUtJZdwbLTz4WduB/7O4gulpasIFJH/S++EKsEsl2O1WklnMEhf\n5AaDM2vNUQoowZxCWp2eIhUKsvTJIqVaKjBxZgtNmPs8Ldq4jeat30ThkZEUEalwpoQn98okjU5P\naq22WeCk19QaRIpUqrwK0+v5rzj3jYhUkEKlpjizxZlMkTt/Mal1Orv4qdWkVKo8hNeZ1BBllLSC\nl6te4b5Pd/+CFOpwSalL+FWgACz0tvhyEX8tXUmgiLr/t6ZQ8BSLiopIjDJSet9+JEZ5L0vkEJK1\ne/dLPs9bv4kiFAqKiFRQYlovu4A0i5Ljxb927366a8JEMppiaO3e/TRl2UrS6PVOQbkmPMKrOMUk\nJtOijdto7d79tHbvflK6Zeg5PKO1e/eTMSaWnnrqKdqwYQMp1dL9lCo1afV6iXfUO/sK0ur1lJrZ\nVyJmrl6WY+mdfQWVlpZ22u+FsRMKfyOhhK8C1VoMygrgUQALYJ+0y/hAd2/XEchYW1urbMv17bLZ\nbCgtLUWC2SIpBRSTlAxbVSV69f8ZdGIUptzxK5w9cxqxiWbU22qR2q8/bFVH8fyb76GxoQErZ09D\n1XcHMXvsCBiMPXH29Gk8+uur8NiCpXh6+WtY+PtxOH/unKxdy7bswKz7hoOO27By9jTU1VTjF3fc\nBWOMtKFhz7h42KoqEaFQ4McfTmH8+PGIjo5GeFgY5jxwD2KSkmGtPAIIQMn27VAoFLBYLDh44IAz\n2eOa666TxMfqaqrRRE1cJSIE4Hh0B2lNwQC8DuAmX1QvUAu6mAfV3QnUt8OODIk4jk3v289j6MvV\ng9KLImm0WqeHNDn/FYqIVJBKq6Xxz+RR3htbSKsXPYbz7MVdlV49ps1fVTrjQ+5ekEKpokil0mNd\nTJKZFCoVTZo0SXIfelEkc1ov0osiTZo0yeszkRtOvlyGmEMd9qCkIACVJFQAonw5aSvniwCwHsBH\nAP4J4A4A6QA+BrAbwPIWjg3MU2PaTSDaXHj7g25tyNT92LFTnyGFSkUZ/bJJZzCQRqu12xllpIce\neohiEpMvTdJNtk/SjTNbSKlSU0RkJMWmpHrEgraqNbLCNDU8QlI1YnL+Kx7Hmnv1pgcffJAUKhUl\nZ2SSToyiOx7+Pak0GtqzZ4/H/Tl+Li8vb/Ul197Jykzg4S8Ll/C7QJFUINIBpPpyjMw5HgKwrPlz\nFIDDALYA+EXzupUAhns5NiAPjekY/nwRlpaWUka//h7xk7y8vFa9KrmKCWl9sujll1+mkpIS2rNn\nD+Xm5pJWpydL7z4UqVCSWqejees3eVRm0BpEZzxq6ZYd9LfSr716TUqVmq649gZ7tQm1mmKTUyhS\nofTIxFOoVFReXm7vCaXXS2roteQ1yt0Xx5S6FvxlwY6vAtViDEoQhGcAJBLRREEQJsFeWaJBEIS3\niGhRO0cV3wSwsflzOIBGAFcS0cfN67YDuLlZtJgugD9jbWVlZTj83UFn/OTL0r04eug7LHz+eTz3\nxpYWJz7LTew9dvQIZs95Fj1i41B1+BA0Oj1IAG4dOx5KjRobXs6HSq3xqMygFUU0NjRAZzR6nc/0\n1jfVAICom69B1fffIjw8HBcaLqCupgrG6BicOl6H2WNHIDY5BbaqKvQ0mXDmzBnk5ORgxIgRzrhZ\nXV0drrrmGsxdv1n2/rjyeNenu8ejA0WYtw2CIMQAGAngRUEQUgA8BmBM8zJcEARzey5IRGeJ6EdB\nEPSwC9UzkCZgnAYgtufcTNfGZrNh+owZGPX4U3h23Ejk/voqLJgwFmLPGDQ2XsQHm4oAeLaQcGXa\n1KmY/+BIzLz3Vsx94B4IEDDnzxuRv2Unnt/wHhovNOLp5a9h7cLZOGmzot5ai/Pnzjon4gLAl6V7\ncdJmxfnz51BXU+1xjXS9iGVbdgCAc9LukrdKMOrxpxAREYGk9N44f+4cRk+eBhAwYsLjuO8P01Fn\ntTpbvZtMJgwaNAg7d+7EoKuugt7Y02uLDMeE5fkP2e9r/kMjeYItc1nQkgdlAaAAcA2ADNjbvV/V\nvE0HYAjssSSfEQQhGcBbAF4homJBEBa7bNYDOOnt2Llz5zo/DxkyBEOGDGmPCUwI4sh4GvHIY/if\nXw7FzFG/wfNvviepf3fzmHG42HjBw4NwrX3YRE0Y2K8vjh76DmJ0jOTFb0pMhEqtQXxKGja8shQN\nFxqwYMJYaAwGzBw1DMaYWNxdfRQ/XbzoYd+XERH475dHcNe2LXh23L3QiVGot9bisYXLAADvrF4h\nsffZcSMRrlBg+cw/wBgTi4jISPxhyhSMGDHCmW2Yk5uL+5+ahaIXF7XoIcllKzJMqLNr1y7s2rWr\n3cd7FSgiKhUE4TCAXwD4HwATYW9UuBjA10TUXnGKBVAC4DEi+rB5dZkgCDcQ0UcAboO91bwsrgLF\ndC9ch7JO2mwQe0Z71L9bMP4+NPx0TuJByNU+nDl6GHKefQGF82Z4FEk9f+4sjh+rgUarQ1PjRTyz\n+nWo1Brs2fo2/rZutaxtSqUKQlgYFjZ7WU0XL+LCTz+hiZpgrT4KW1UlouOl3XR7xMah+tB3WLRp\nm/P6s8bcgbKyMgwdOhSFq1ejoaEBO998A40XLmD22BEQe0TjzMkTKFy1ykOEeJiI6Wq4OxHz5s3z\n7QQtBagAKGHPsstu/jkSwAOwt4Jvb5LESwCqYRehD5v/7Q9gF+xV0tfAS0NEcJJEt8eRLJCQkuIx\nqVWpUtOCBQs8As2OJAJH6Z+1e/dTfEoaPf78S9QzLp60BpGSe/V2tq3QiUYaO/UZilSqKN6SRpu/\nqfaaAGHu3de5v0anJ41W72GXQnWpYaFHCrlbW444s4U2bNhAJSUlZBCjPHpKabRaKi8vD9LTZ5jA\nAh+TJAT7MV0DQRCoK9nLtA9HC/Y777oLEZEK+2TVo5W4eKEBRw4f9vAibDYbLGlpEMLCEZtkRu3R\nIzh/9kdce+sd+Oc/tiEu2YK6mmr0/Z/B+M+nH0M09sSpE8ehNRhw8nidrA2frP4r7p43E6Mem4Ir\nb/w1xB49MWX4rzHwhl/hnyVbsfz9vc59J958DWxVlRDCwxERHoEoUwzqbbW42NgIhUKJvKJLyR2z\n778L4RHhMEbHoOHCBY/znLTVYt1rr3FrFqZbIggCiKjNRR+8Jkkwlwc2mw379u2DzWYLtilOTCYT\nhg4dinVr1yIMQMPZswgD8NratV6HuMLCwjD/L5ux5K0SjMh5HOHhETj4nzIolCqMnPgk8t54G1/+\n8xNQUxNOn6zHrxKTvIrTW99U47OYWJyss8KUmASxR09UHChHzeEKvLduNX44cdyZUFFxoBz11lqo\nNRos3rQdKz8oxZjJ0xAZqcSctcUQBGDeuHsx7a6b8OwDd4OoCXPXb8bcv7yF0/UnJOf58YdTmFX4\nOnInTgyp3wfDBA1f3K1gL+AhPr8SrCKWvswJaWtnXMfcKblus456d4lpGaTW6rwO57nX2ItUKp1F\nXBUqFYWFh1N4RASNnfoM6UQjpWRmkUKporvuustj7lZqVjYt2riNemdfQTNnzSKtXk+WDHt9v/uf\nfJpy5y8mlUZLSpV93pRGr3cWsO1qc5x4jg/TVuDjEF+bPChBEH4mCMIKQRDWOpaAqiYTcFwTCxZu\n3I456zZ2yjf34uJiZGRm4oHxE5CRmYni4uIW93ekY7eUHPDRRx/h0MED+LJ0r2yygikxEV/s3Y2j\n3x/E2R/PeByvjYjEsi07cN3tw/H08tfstewuNsEYHYPGhgs4dbwOjRcuYOjNNyM2IRHvrF6BHrGx\nqDl8CADw76++ds7dAuzeUG3lYZw/dxY1lYexYsVKzH/9bdz96JOIVCjxwVsbsHbhHNw78UmnxwUC\nsq++vsvNcfL198kwPtEWFQPwbwCPALjFsfiigv5awB6U3whGdYJA1CUrKCiwlw5qrj5uNMVSRKRC\nUsV8qZdq4/935z2kUKpICAuzlzlKSSWFSkXXDxtBCpWKwiMiSS8aSaFSkaV3HxKjjKTRamne+k00\ne00RabQ6mpz/Cr20dTcp1RrSGkRKzcq2t99QKEgvipSXl+dM4PD07KLopa27adHGbRSTmEzmtF5e\nPdlQ9FK4zhzjKwhEqSMAf/flpIFaWKD8RzBeLv4WRavV6tGcUKFSNTcPVFFyfILX4bzUzL6kUKpI\nqVbbmweqVBSfkkpavYGmLFtJqVnZNGHu86RQqWje+k3OXlE6g4H0okjRsfGkVKkpLas/qbV6Mvfu\nI8kiTO/bj0pKSpzPeXL+K5SWJR0GjE1OoUilkpJ7ZVKEQkGTJ0+Wff6h2k+ISzAxvuKrQLXWbsNB\nhSAIMwCUAXAoxft+dOSYTqa1duqBwN8leyoqKmBKSJQM58WnpGFiXj6mj7wdkKkCUVhQgKnTp0N/\n/jwAwBDVAx+/+zae33Bpgu2cB+4BCIhLskBrELHkiQmISUyCteoo9GIUXspfgkcm5GDhhned5ZgW\n5IxFva0Wvfr/zN7y4lg1Bg4c6HzOObm5aGho8Ggb39TUhOPHqpGUloGVBQVINptxwy9+IWkd4j7H\nK2fcPejRo4fz/MGCSzAxAactKgbgNbdlrS8q6K8F7EH5HX8NHbXlPFarlfLy8kgvin6p7Gy1WkmM\nknqB3jym7Ts+o7Q+WR6dZh3NCd3nKt3/5NM0/ZVXZQu+btiwwcNziIo2kVan97gv14rkjz76KCnV\namdr+dz5iz1bcqhU9uaLzedw91KmLFtJSrVask8w4UrdjC/Az8ViI4ioEcDvAyuTTLDwR3UC1zJD\nx44ewaoVKzzm8bjuEyaEYdx9o5EzYUKHrm0ymbBq5QpMeOBu3KDSYKv1mMc+//3Zz/Fl8buoOFCO\nqopDSE5L96hOUXP4kMQLOGE9ho//thk1lUcQHR8vrQ5higUAD8+BGhuxr/QznDlzxun9uD+XxS+8\ngIiICNz5u1wMuPZGfLF3N4ymWA8PMGf+EkQoFMh9aCQ+/eQT57WMplgUzJ2BhcXvtlg0tzPhEkxM\nQGlJvQC80fzvIQDfNy+HAHzviwr6awF7UCFHW2JZ/ox3yXpqXrym8PBwSeJCeEQEaXV6j0SFqJ7R\npNXrKaNfNolRRhp+112k1ekpKTXNw4NSqtVUUlLi9BzS+mSRVq+ngoKCNj2XufPmkUKpopTMLNLq\nRVLrdLIp8a7xHMe1zGm9PHpMccyH6UrAnx4UEd3f/G9qADWS6cLItbSOjktw1pvztk972l4XFhZi\nytSpiEsyo+5YNU7W18vu18MUgzM/nIIpLgELi/4GW1UlTInJmDl6GBrOn8PMUcMQk2zGSZsNd014\nDO++ugL7PvsMb731Fp5ftAh/Lylxeilvr1mOmaOHIcGSDlv1UYSHhTljP1XV1Zg7dx7ik1MwfcYM\nGAwGp+fo7Z4tKSmIS0rGxLx8mBKT8eU/92DW6DsQl5yMmsojGPX4U86JwY54zqBBgzBgwADs2LED\nf5w9h2M+zOWDL2oW7AXsQYUccp6CUq0mvShK4jAd9aAc6eSWPv1ouZeW69crFGTp0490opHunfik\n0/txtHRXa7U0e00RTX/lVYpQKCilV29n3KSlbLuYxGSKTUiS3JPDHm/35DifawagXhTp3XfflcTB\n7DUBlZSclk5ane5S11+XeI5rFp9GqyWdwUAZ/bJJL4oenltnEIop70zXAIHsqBvshQUqtHC8qAoK\nCkiMMlKc2UJag0hTlq30eGF3JJhutVpJL4q0Yv0mWWE6GxvrUcBVJxqpZ0wsRSgUpFSpKcoUQwqV\nisy9+5BONFJ8cjKtW7fOaZ9rwVn3+UpilNFZ4NXRel6r15OlTz+niK3du5+S09KopKTEafekSZNI\noVJRgsU+VCgae9jnakWb7LakZ3iKXJTReR3HvbuLu1qrJa1OH5REiVBNeWe6BgETKNh7Qt0OIAle\nqo0HemGBCh3cX1QzZ84kc3qGM34iFx9pzzdvq9VK69atkxUmAshqtVJJSYlHbCYlM4s0Gi3pRVG2\npbsjG09OCKYsW0lag0hxZguJUUaaNGmS8171oki5jz5KloxM5znd93f1yNxF02HL9FdeJaVKRamZ\nfVuMKbln8a3du98j86+zJsfyxFymo/gqUG2aByUIwuMARgDoAeDPAHoBeNyvY41Ml0Fubs7ccfeg\nqakJ9bZaZwyl+kiFJD7ia8ZgcXExsseOxYMyzQMNSiXyX34ZOSYTBg4ciDMnT0hiMzUV30MAITbZ\nLNvSvYcpFtNm/RGnTtQ5sw5d54WFCcDjOY9gyJAhuOW22zB9+Ws4VWdDwdwZeGfrdpywHsPgm27D\nnLH3oLGxwSOz7s3iYo8YlKNZYo+YWBz99r8gANVHKqR2Vx5GfX09bDabbLt3ucw/13iezWYLWEad\nv2KJDNNm2qJiAPbAXvn8w+af9/migv5acBl5UKE8zl9aWkrpffs5qyZs/qaaMvplk1KtlmTNabTa\ndtt/4h//kPWYHm2OBbnHXoqKikgvihTXXHg1d/4Smrd+k7MShLsHpTWItHbvftnYkeO5O86ZYEkj\nnRhFKo1Wco5IpZJ0oujhvaVm9qWSkhKvHpRCpSKNVufhfWm0OtIZDB7DZ0VFRSRGGSm9bz/SG0TS\nGQyyXkygh9/Yg2I6CgJU6mgvAAHAB80/7/HlIv5aLheBCvVxfteEBUczP70oUnrffpJyP+1Kgb54\nUVaYGgB71W+tVjalO2/BAtJotRQdnyAZZoxPNpNeFCk+2UwKlYpSMnqTUq12Vg53H1ZznVirF0Wa\nnP+KU8iUajWt3bufXtq6m24ZM44UShVFxyXITuYtLy+/JJrNNf5ikpJJJxpJ3xyvcx22S0xJ9Sjb\n5Hj5FxQUkEarpURLGulF0Tnk6Joo0VniwRNzmY4QKIF6HMDHAI4A2AZgqi8X8ddyOQhUqH9LlbNP\noVJRfn5+h+y2Wq2ywkRAizEXhwgo1WpZT8k1waG8vJxKSkokWXTz1m8irV7vFBT7i78/qdQaZ609\nnWikKctWUmxyCv3s+iGkUKmcCSG/GfcI6UUj6cQoZ4WIqGiTM1mivLyctHo9TX/lVWc2n1ar86ho\nodFqqVdWtkc8aubMmR5fBkSjkfLz80mrv5QoMXPmTErv28/j+EDMkQpl754JbQIiUPbzIgvASAD9\nfbmAP5fLQaBCvQCnnH0Z/bIlE0p9/XZddt99ssKUrNfLpn07nodcanju/MWk1uopJslM2uYW6rJD\nZkYjxZvtfZ5SM/uSXrw0dLZ2737SunkzWoNIKo1G4i2NnfqMU6w0Oj3d/+TTNG/9JudkXgeO66Vm\n9rVn9ZlTSK3RkFqrdWbyxSYmyWb0afXuE4uNlNKrt2fJJpWqxbR3hgkFAuVBTQCwpPnz+wAe8OUi\n/louB4Hqih6UtxhOq1RVyQrTExoNlZSUeE/7br6ee2q4eyNBtVrj8cJ32OUYwnNsz5n7gnPYbdHG\nbR6iGGe20N333EMJljTnsJy7XUq1mjQ6Pamb7Xd9Bg5Pat76TZQ7fwlp9HqKM1tIoVLRyIl/kAhe\nRr9sEo1GyluwwKMRYkpmFqk0Gtn19z/5tEc2IcOEEoESqM8BRDR/jgTwqS8X8ddyOQgUUeiP8/vF\nPhlhuhgR4fSQXJMM5NK4idxf+os9PAhHzMhVZPLy8ohI6glOWbaStHrROZdK1oPS62nPnj3Oayza\nuE0yD2rzN9UUn5JKSpVKNtHBcT05O13LG6X1yXLOz/JlONVxjrV795M5rZfEg2OYUCFQArXP7ee9\nvlzEX8vlIlBE9pfvunXrqLy8PNimyNLuOER2tqw4LX3nH86KD3pRlGSl9c6+wtn8z33ir2PYrGdM\nrEc2XZzZQpPzX5EM0znO7VrpwWM+U3IKRURGklqno9SsbNLo9KRsTnxwTL6NSTJ7JEfoDaLXRAfH\nZGOVVkspmVkSO829+9KijdtkveVLcTFp5QjX9QqVisZOfSYkPW6GcSVQAvXH5iSJpQA+BDDDl4v4\na7lcBCrUs/iI2iFQ774rK0zUnJyg0elIqVZTnNlCOoPBo11FS8Vn563fRGqNxiMuo9Xp7TGm5uSF\nKctWSuJ5RUVFpNXrncN2jqE7sUdPikky09q9++n+J58mnRhFCc0ZdEVFRc4vD/lLl0o8ydYSFfLy\n8sjQM9rDg1IoVZKyS2191pJKHiHscTOMg0AmSfwMwGgAA3y5gD+Xy0GgQj0GReSjgJ49Ky9Mjz3m\n3BFVTW0AABY8SURBVEWur5Or5+H+cnYfntOJRkqwpJFaoyGdweB8URcUFHikirs/S/dYlKsnJJsV\nKFOp3SESjmxCb/uXl5c7vR2daKSkXr1JoVRRbGJyh+vqcWYd0xXwq0ABeKT53+cBLHRdfLmIv5bL\nQaBCPYvPJwH1kjbujrd7zsvLkxVCq9VKOoNBVkD0oihJUGhLvExuHznvytvvwlVgvcXLHPfpKG30\n0tbdpNba42eh+kWEYfyNrwLVWqmjyuZ/DwLwrDfD+J1Qb6PdpnI3OTnA6tWeB587B6hUHqtl7/lo\nJRYtWYK56zd7NOcDgKaLF/H8ow+ih3vDv+QUGI1Gpy2tNdSz2WxIT0/Hp598Imk2CAADBgzAVddc\n0+rvorCwEGqDCEtmFiyZWci++nrMHTsCf95Q7Gw54rjPE9ZjqDhQjsaGBsQmm5E9+FqP5+h4ztwA\nkLnsaYuKAXjfF9UL1ILLwIMi6vwsPl+Gh1r0oPbvl/eYtm9v9byu5XzEKHuKtTdP0uFxvbR1t0e2\nXVu9EEf1CTGq5aHK1n4XjuQHuaw/OTtcGx3KzVtyxJMCEX/kYUAm2CBASRIbANwJoA+A3gB6+3IR\nL+e8Cpdq+6XDnoSxG8DyFo4JyEMLRTrrZdKehIyCggLS6vWU1ifLfswbb8gL05VX+mSHXhTJnJ7h\njMd4E8KWKo+3xX7X6hNtEbeWfhelpaWU0a+/MxaWmmWvSahUqb3+7rwlN7R0zx2lKyTeMN2fQAnU\nh27LB75cROZ80wD8B83p6gC2APhF8+eVAIZ7OS5Aj+3ypD0JGa7lgPSiSN9deaW8OPnBjpay01pK\nQW/LtVqqUOGr7Y4kC0eavFYvUkxisnPOVWvHO8QvUPHHrpB4w1we+CpQrbbbEATBAOA3RHS2/QOJ\nHnwLe/uOvzT//HMi+rj583YANzeLFhNAfG2f4NpmY7DNiusfuR/4/HPpTjU1sIWHo2LfvjbHULzZ\nMXDgQBw8cEA2HtNabKmla8UkJGHAtTfi1edme8S9fI31mUwm5C9ejCdGD0N8ShqOH6vBiN8/jrcL\nX8GiJUuQk5Mjsa2ldhiBij9ymwymy9KSesFeJPYQ7EkSt/iifK0tAFJwyYOqcln/SwDrvRzjf0m/\njPH1m3VpaSll9+tPJzMyPT2m994jovYNJXXmN3xXj8d1eFCpVlPeggXtPu/MWbMoUql0dux1n3NF\n5PlsXBshumYP+jv+yB4UEyrAz2nmewEoAEQD2O7LiVu9sFSgKl3W3wngZS/H0LPPPutcPvzwwwA8\nwssLX16IZ6ZM8RCm7ZGRLbYnb+uLsDMTQxztQlIys0irF+nW3z7srDDRXhzC523OldzkYm/FXQMR\nfwz18llM9+TDDz+UvLP9LVAfuHze6cuJW72wVKC2ALih+fNKACO9HBOAR9g96MhLrdVjd+70EKZ3\nxCgSo6I85vl0JIbSmVlmHokeMtl5bbHFvcGhNxFwfzaLNm5r0xwrf8JZfEyw8VWg2tTyvRnBh319\nZSqA1YIgRAL4GsCmAF6r21FcXIzciRMRl2TGsaNHnC3M24rXVuy1tUBcnHSdVou6f/8bCfX1OOgW\nR+loDMXVjra0Lve1vbnr/jk5ORgxYoTzZwDYt28fdDod3nrrLSxasgQJZkuLz1PuuXuLmbk/m/Pn\nzqLuWLVf402tPQ+vv2eGCVVaUi8AtQDeAFDk8vkNAG/4ooL+WsAelAcBiS9cvEh0220eXhN99lmr\nh7p7EQUFBT5/a29LHMvXWFdL+zu2JZgtkmaEU5at9Po8O5IB6Xg2jhiUP4bdOI2c6QrAz0N8N3pb\nfLmIvxYWKE/8npq8cqWnMOXn+3QK93k+/k6Y8FUcWtpfrqq5ewsLuefZ3ufuPszmj2E3ToJgugq+\nClSLQ3xEtNv/PhvjT/yWmvzFF8DPfiZdd8MNwM6dQETbRoJdh5gsFgtuvuUWzFm30aNUUUvDTG1J\nifY1bbql/QEgLskMlVqDmMQkyT6mxER8sXe37PNs73N3H2bzx7BbWVkZouMSOI2c6Xb4EoNiQhCT\nyYRVK1Yg96GRiE1MRm1VJVatWNH2F9Pp00B6OmCzSddXVgJJSW22wz0eM+2pp3yeY1VRUQGdTtfq\ni99XcWht/2NHj+D8ubOwVh2V7FN96Dusfe4ZFK5a5WGzr89dLj7kawxNjuLiYuTk5qKhoSFk6zcy\nTLvxxd0K9gIe4vNKa0NFHtubmohycjyH87Zubde13YeY9KLotYWGO97mB7UUx/I1bbql/R3b4pPN\n9v5RmX2d9QB9yeJr7dpy8506EjPqaMknhulsEKh+UKGwsEC1D/eX4Ucy85noySfbfX6v7TIWLGhV\nRLzFT8rLy1uNY/kav2lpf8c2x3X9Fb/pqHi3hPt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lin_regplot(X, y, slr)\n", "plt.xlabel('Average number of rooms [RM]')\n", "plt.ylabel('Price in $1000\\'s [MEDV]')\n", "plt.tight_layout()\n", "# plt.savefig('./figures/scikit_lr_fit.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Normal Equations** alternative:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: 9.102\n", "Intercept: -34.671\n" ] } ], "source": [ "# adding a column vector of \"ones\"\n", "Xb = np.hstack((np.ones((X.shape[0], 1)), X))\n", "w = np.zeros(X.shape[1])\n", "z = np.linalg.inv(np.dot(Xb.T, Xb))\n", "w = np.dot(z, np.dot(Xb.T, y))\n", "\n", "print('Slope: %.3f' % w[1])\n", "print('Intercept: %.3f' % w[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Fitting a robust regression model using RANSAC" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7nMf1PE45G2nDJL5kl1fc25Pk5Dgcjp9xuSpITu6F07kzpIavQssh3K2OjgPO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\ndSIFES8IsUSoEdRi4HGMllcQok5Iwwc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import RANSACRegressor\n", "\n", "if Version(sklearn_version) < '0.18':\n", " ransac = RANSACRegressor(LinearRegression(), \n", " max_trials=100, \n", " min_samples=50, \n", " residual_metric=lambda x: np.sum(np.abs(x), axis=1), \n", " residual_threshold=5.0, \n", " random_state=0)\n", "else:\n", " ransac = RANSACRegressor(LinearRegression(), \n", " max_trials=100, \n", " min_samples=50, \n", " loss='absolute_loss', \n", " residual_threshold=5.0, \n", " random_state=0)\n", "\n", "\n", "ransac.fit(X, y)\n", "inlier_mask = ransac.inlier_mask_\n", "outlier_mask = np.logical_not(inlier_mask)\n", "\n", "line_X = np.arange(3, 10, 1)\n", "line_y_ransac = ransac.predict(line_X[:, np.newaxis])\n", "plt.scatter(X[inlier_mask], y[inlier_mask],\n", " c='blue', marker='o', label='Inliers')\n", "plt.scatter(X[outlier_mask], y[outlier_mask],\n", " c='lightgreen', marker='s', label='Outliers')\n", "plt.plot(line_X, line_y_ransac, color='red') \n", "plt.xlabel('Average number of rooms [RM]')\n", "plt.ylabel('Price in $1000\\'s [MEDV]')\n", "plt.legend(loc='upper left')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/ransac_fit.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: 9.621\n", "Intercept: -37.137\n" ] } ], "source": [ "print('Slope: %.3f' % ransac.estimator_.coef_[0])\n", "print('Intercept: %.3f' % ransac.estimator_.intercept_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Evaluating the performance of linear regression models" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "if Version(sklearn_version) < '0.18':\n", " from sklearn.cross_validation import train_test_split\n", "else:\n", " from sklearn.model_selection import train_test_split\n", "\n", "X = df.iloc[:, :-1].values\n", "y = df['MEDV'].values\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(\n", " X, y, test_size=0.3, random_state=0)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "slr = LinearRegression()\n", "\n", "slr.fit(X_train, y_train)\n", "y_train_pred = slr.predict(X_train)\n", "y_test_pred = slr.predict(X_test)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gMm68cRbFxROi5h9iE/YdfsTh7Ni+I3xcaVVpWKxiJ9P7gjviBOL++6+is7OT\nadMOiQhIeyUu9wLbcnGF9w2VD4TnoJqaLqCrp4fOznX9dY+zjF6lL+g8UhIqN3Qea+iyI4FTRPw8\nVW/wOZzm0awhv5MBK/9TskSE6UYK7xfxT9HZ+SZeby1dXQHg5bBXXXHx0ZSURN+/8//93Lihy/LS\n6Y4OJE4kG3pUh4jhRwVKGTSZdkaxQhL7xFrk9kR51Q1Uh0RuwpEWiTEurrjiG5x77jlRdY21mEqr\nSsOCEKpT5ER8vyUWzznn/DuWV9uVnHrq13C7PwX8LCIPkokTBX+VnzPOmEtra6stgOsGNUEfe2xo\nzik1xjl6APYF+/D5aujsNER6+bncnqh9y8rLqKubHHV/k1kjkfcuJHpdXbOAiVHnKSmZyPLlN1Nd\nXR3+rsV+LyKtsHfffZdnnnmGhoaGqHsd+X3VrLz5jQqUMigGslpiSSYkoSE0ywlhFb3BQ+gMDrwe\nJRAI8Lvf/c4WgoiO07Ufq1atijvfTTc1cu6550SVMVBHFf/ZbCwRcqIMeAJYz/LlTRQXu4H9SSRo\nAIvuvo+qmip27NgRdqi4pOYSR6G0nBL6RSPSYnK53fQFg3Hl9wV/hWX9pMKvE2bmfeKJezjxxNPZ\nsyfS7bsC+DU+3ym8+uoaZsw4yiF54xsJ71+sVWolP+zAcnk3dnt/Gx6STSQ2oeG5FSue5dvfPoee\nnl5gX4qLAzz00L2cccbc8Pe1u2cHvcGeFK+HMlyoQCkZk0xsUu2MYiezB/o8lkjPth073gR+DvwA\n2MCuXW8yb14TRUUTcEqSN7gFmC8Cj+Nyb4ixNCrpC1YBn8OyAFwcfvgMXnhhLcmsLus6WhZcYqF8\nDTiaviDAuAQi4gXiBQrmOaRcdwO+uPf6gs5WRGV1JccddxyLF9/Dd75zNN3de2O5nfspLj6J5uZ7\n2blzZ1r3D6z5wR27XsNyX4e+oJMFezxNTec4et0VF9fT1bWZ73zndM4665ucffZ59PS4gTXAIXR3\nbwiv/eq31A5l4daFajHlOSpQSsakKyYwcJbaVLPYgvPQkOVZdg+WC/hiurvHAsc7lhf59O1E7FxO\nNJ8DgrbTwCmAVYe+4Gr7fC+Hz9faOptrrrmKm276Am73p+nqifWeq8TjqUs44W8N0VXaXoYTgauw\nsvE6cW14rqu/fDd9QRd9QQ/wKv2WzxHAb3G5T7QTIkJfMIjLjS2C0YTmZCIz627bto2qqirGjx/P\nzp07KS86K4v0AAAgAElEQVQvT/n+haitrU3gNRjJyzQ3N/LVr36FhoYGID7yw6JFR7Jo0YMUFVUS\nG+3D5dqPtWvXxnxfLSFMlKlYyQPSiYs0nBsai29YcYpzlmkg14FSXAz0eQin2HSlpVOlpOTTEpnO\noaSkXrzeqqjyYuOulZWXRcWtK60qDcfLi899VCnRaSNCwV0n2Qn9ouPT+XyflaKiUoESgTEO5VXY\n17H/3LGf98ehqxL4uX0Op7xLVjw8j2esHbPuULtuP4tINvjZAeMDWueMjuOXLGFj5LXMJH+VUx2c\n2lVWdpD4fDVy1VULpKzs0Jg4gA1iBZH1CYTuUf/3cuPGjRHf1/jzaU6o3IMGi1WyTbIgmqmKSSwh\nwUsUNDSVqNJOAun1VkUEPo3unELlrVmzxk4HsSpOWJ0y95ZXlEtLS4tD6ozItBGrxOv1y5o1a6Sk\nJDrYq9VhlokVeHWiY+d46qlzxeUuCgtHvGC47XLG2ULncxARv30NKsXjsV47BYy1EhjiKAbRgjDJ\n3vexhJ13ooeUVIPBhnCuQ6RAr7KvX7t9rhKJz3VVY39+gLhcoc/3l+LiyvD3MvR9LXJ7HB8SEuXJ\n0gjn2UEFSskqqVhJmf6AB5MKI3S+UBk+32cFfOLzTRCPp1yKiyulomKaeL1VURlk58+/2NEiiu2A\nY9O4FxX57P/7r0MoL1GsOEeKttdbZVszpXYnGy0O/Z3xBLsDfixhZ+1ylzuIzSTbWii3LYhS+frX\nT5Hy8ml2PZ3KirYgEu8TysPknKJDJHnU92QPILE4RZafP/9iW5QPtP9eJP0R0g8Q+KFYFmUoR9Vj\n4QeCNWvWSEtLi7S0tDg+/Fx//Y3idpfZ96Ve3O4yx0zDGuE8uxSkQGHNjt6DtQLwWWCiwz5Zv1jK\nwGSSMDBZGosQgx0ejOww+pMH9ltEbneZeL1+qaiYGs4XZKUsL3HskCPP7ZzHySfGeOOsxVhxjrUM\n16xZI263z+5QW+y/ToKw1j5PpePnsZZV/DBgkcCj4nK74gQ4criy3zpKVpbbFqfHJGQphnJSxeJ0\n7T2eCvuhYaL90DA17c7d+R5UC9xn/z3AruN9UlQ0xr6vkwR8Mn/+RWmUfZ99zQ+Iq6Nm3s0+hSpQ\nJwOL7deHA0847JPta6WkQCY/UqcONpZMhC9RXULDb/HDWdbcjcvti3rfqX6LFt0XlVPI55saVTcr\nl5FXli1bljQFfGS69rPP/p74fDVSUjLFtgDuESh1nN/pnzPbPy4ZYGlVqYPV53IQuZKE7XMeOost\ns0is3E+hITXrGpeUVCdtr3WtfFJSUi8lJVW2pblKEmUaTgXnbMT7i5VbKj4B45o1a+Shhx6SjRs3\nDlh2S0uLlJUdJFZOqSqxhmnb4+qYjWzOSjTpClS+ePEdhRWFEhH5szHmX4a5PopNKikeMiEdb70Q\nibwGwYpE7ZT/CDbRF4xPYRFLZEidM888xSGlxnvAOKqqqhIGkQ1FjICfAeNZvLg/JJLl/m4FMu0L\nerFi97UBu+gLzgdqCeVTCi2oTTXwaz9O3obR+7vcLm5vvz1JmV7gNvpj7v2NH/3oR44BV2M9KEVm\n8cgj9/K97/2M7u4yrHViqXl4xkZ08Ff52blrFyHXc6vuRXg9B0Xdf6jBuD7gqKOOCu+XLBBtyDW9\ns7MGmGGXfxtwIXB3VB0z+Y4q2SUvopkbY+4HfiUiLfb/bVjDfH0R++RBTRVFUZRMMYAUYDTz7UBF\nxP+uSHEKcW3E69n2piiKouQnq+0tY9IZD8zVBnyd/jmoI4CnHfbJ3kCokheQwlyVE05eg2vXrnVw\nHXYLtMTN6Vju3P6Y98rseYZV9lxOaF7Cch/fuHGjtLe3i8dTYU/Sx9f9mmuus+eaIudIQu7OqwT8\nKc2HOc03Oc1LJTo+8vxObY8sN/Yzj6c8Zc+72CUGixbdZ88RroqY29ko8KiUlFSFP3fyiHNuRyL3\n93aBFvH5JkpLS8uA36NQPS3PRp/Az+wyopcDlJRUJ1yioM4S2YECnYN6HJhjjHnR/j/RMnlllOIU\nkLatrQ0gPF9Q7KmgM9g/J2JFSnibvuChWBEULPqCBwBvOcy/HIqV08kN/AdwDh6PiwcffIApU6bw\nzDPP2PHd1uAUwfvmm2/D46mnpydy3mUsLlcRXV3twBj6gm+mOJfUF/V/X7AIGCjagoXPZ80X7ty9\nISpAbGlVqZ076j7gSjvqxSbgXKAcT9FOfvzjH7D33nszZcoUx7Ijic2f1D9HOBtYBFwA7IXXG2Dh\nwp9z6aVXJQyLlSiYbHySxQ12nc+ns3MvTjrpDMrKy9IKRAtHUFLyIL29PRhzNCUlE+np2cKCBZdz\n662/jsoZ5vHUOUSgyFa4LGVA0lGz4dxQC2rEQYoWVHykgosdn8Tnz7/IfkK23I2PO+7L9hNx7IJO\nZwvIcgNP/KRsPa0fIJZnYKzHYGjhr08SL5AtjbN+nOrhdlfE1LdK4PE4a6jI7XY8PmRhOrfRipgQ\nWivm9zdISUmVnHrqXCkpqRrUep94L8t+6zMbHnFLljzmeD+TWTNr166VioqGqPPCVPF4ysJWccha\nTLboWC2o7ECaFlSq4nAIVo7nw4GVwBfTOUk2NhWokUdm66X6RcC5E1kl1pqiVeH3zzvvfLtTa5D+\n9T1Onfej4ooZJixye6IWnbpc5THiUWkPJcYPo8WXXxwnSrFi5a/yy7e+9Z0IoQ3Vt10sN+ufhyNW\nrF27VvxV0UOVoWvY3t6eUKAiO+RQu7LVASeKLJKtNUWWi3h0iKNkQtfe3i5eb/SwHdRIeflnHY9J\nVP9MI6Yo0eRKoF4CpgNPYs0RPZ/OSbKxqUDlJ7kOAxP/5L1WrMgC0R3UQw89lPAJvb293X7y7l/v\nEmuNlJWX2fvEd+per1/Kyg4Sr9dvx7OrFmiIKiO1+ZPxCUMZtbS0RKyjahBrvU+ZLbiP2efcR8An\nHs+UpJ1kqByn8zg9BGR7vU+i70Q2OvlMhG7RovtswT9EQnEJkx2TqP4a8mjw5EqgnsVaINFi/78q\nnZNkY1OByj+GIgxM+haUc8eVSueY2OqoFpguVsSBfWyR6x9CS12gagTGO35WUlJtxweMfNIvttsa\ncrIYuGOOvF6xw4xO4uR8jXM3hJWsk09VADIRukWL7hOv1y/l5Z9VC2gYyZVArQSWARcDpwHPpHOS\nbGwqUPlFLjq1REN+sR1SomjZyTquVIYTRSSBsMQGfl1l/59YoGIDzlrW1s/EGhKMDS0UGx3d+mVW\nVEyTyy67zI7UsNYWSYn6PNbKydQaGu4hrND5y8oOjbNuEw39pmvNqAU0/ORKoPYGjrdfNwI16Zwk\nG5sK1NAyUIeeizAwTh19iEQx7wYahknmMODU5njXa3dUG2F/8Xr94vc3hMssinPldkUI+NViBYg9\n2Ba3++xyWsSaY4ouuz86uhWZfc2aNfYcSrwF5fXGB3BN9OCQaK4q2bUbKtrb22MC8Wa2/EDJf9IV\nqKRu5saY7yX4fxKWr6oyQhkoBfpQh4EJpfNO9L/T+5EZV1PBqc1FppS+iDYWF3/M+vUv8+677/Ll\nrxwfvi6xx40ZMwYAl/smSku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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(y_train_pred, y_train_pred - y_train,\n", " c='blue', marker='o', label='Training data')\n", "plt.scatter(y_test_pred, y_test_pred - y_test,\n", " c='lightgreen', marker='s', label='Test data')\n", "plt.xlabel('Predicted values')\n", "plt.ylabel('Residuals')\n", "plt.legend(loc='upper left')\n", "plt.hlines(y=0, xmin=-10, xmax=50, lw=2, color='red')\n", "plt.xlim([-10, 50])\n", "plt.tight_layout()\n", "\n", "# plt.savefig('./figures/slr_residuals.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE train: 19.958, test: 27.196\n", "R^2 train: 0.765, test: 0.673\n" ] } ], "source": [ "from sklearn.metrics import r2_score\n", "from sklearn.metrics import mean_squared_error\n", "\n", "print('MSE train: %.3f, test: %.3f' % (\n", " mean_squared_error(y_train, y_train_pred),\n", " mean_squared_error(y_test, y_test_pred)))\n", "print('R^2 train: %.3f, test: %.3f' % (\n", " r2_score(y_train, y_train_pred),\n", " r2_score(y_test, y_test_pred)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Using regularized methods for regression" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.11311792 0.04725111 -0.03992527 0.96478874 -0. 3.72289616\n", " -0.02143106 -1.23370405 0.20469 -0.0129439 -0.85269025 0.00795847\n", " -0.52392362]\n" ] } ], "source": [ "from sklearn.linear_model import Lasso\n", "\n", "lasso = Lasso(alpha=0.1)\n", "lasso.fit(X_train, y_train)\n", "y_train_pred = lasso.predict(X_train)\n", "y_test_pred = lasso.predict(X_test)\n", "print(lasso.coef_)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE train: 20.926, test: 28.876\n", "R^2 train: 0.753, test: 0.653\n" ] } ], "source": [ "print('MSE train: %.3f, test: %.3f' % (\n", " mean_squared_error(y_train, y_train_pred),\n", " mean_squared_error(y_test, y_test_pred)))\n", "print('R^2 train: %.3f, test: %.3f' % (\n", " r2_score(y_train, y_train_pred),\n", " r2_score(y_test, y_test_pred)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Turning a linear regression model into a curve - polynomial regression" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "X = np.array([258.0, 270.0, 294.0, \n", " 320.0, 342.0, 368.0, \n", " 396.0, 446.0, 480.0, 586.0])[:, np.newaxis]\n", "\n", "y = np.array([236.4, 234.4, 252.8, \n", " 298.6, 314.2, 342.2, \n", " 360.8, 368.0, 391.2,\n", " 390.8])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from sklearn.preprocessing import PolynomialFeatures\n", "\n", "lr = LinearRegression()\n", "pr = LinearRegression()\n", "quadratic = PolynomialFeatures(degree=2)\n", "X_quad = quadratic.fit_transform(X)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Gp7WW2TaEWWkt9zHlRYa/UXfFilX4+LxNvnxuaH2L5ct/onXr1knPv/ZaF7ZsqUR8/H+B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\nTvy+NbAL0829jZRSdkopZ55yc68lPCH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fit linear features\n", "lr.fit(X, y)\n", "X_fit = np.arange(250, 600, 10)[:, np.newaxis]\n", "y_lin_fit = lr.predict(X_fit)\n", "\n", "# fit quadratic features\n", "pr.fit(X_quad, y)\n", "y_quad_fit = pr.predict(quadratic.fit_transform(X_fit))\n", "\n", "# plot results\n", "plt.scatter(X, y, label='training points')\n", "plt.plot(X_fit, y_lin_fit, label='linear fit', linestyle='--')\n", "plt.plot(X_fit, y_quad_fit, label='quadratic fit')\n", "plt.legend(loc='upper left')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/poly_example.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [], "source": [ "y_lin_pred = lr.predict(X)\n", "y_quad_pred = pr.predict(X_quad)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Training MSE linear: 569.780, quadratic: 61.330\n", "Training R^2 linear: 0.832, quadratic: 0.982\n" ] } ], "source": [ "print('Training MSE linear: %.3f, quadratic: %.3f' % (\n", " mean_squared_error(y, y_lin_pred),\n", " mean_squared_error(y, y_quad_pred)))\n", "print('Training R^2 linear: %.3f, quadratic: %.3f' % (\n", " r2_score(y, y_lin_pred),\n", " r2_score(y, y_quad_pred)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modeling nonlinear relationships in the Housing Dataset" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tLa1GawQHB1NQUKBdp6WlERERYdOnJi4pIQS9evVi+fLlvP/++zzzzDNaW0FB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\nPF4C31VRRhEPjX6ImefO5Ppjryc7LZvZG2bzi0W/SGh5saJzUIpylJK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = df[['LSTAT']].values\n", "y = df['MEDV'].values\n", "\n", "regr = LinearRegression()\n", "\n", "# create quadratic features\n", "quadratic = PolynomialFeatures(degree=2)\n", "cubic = PolynomialFeatures(degree=3)\n", "X_quad = quadratic.fit_transform(X)\n", "X_cubic = cubic.fit_transform(X)\n", "\n", "# fit features\n", "X_fit = np.arange(X.min(), X.max(), 1)[:, np.newaxis]\n", "\n", "regr = regr.fit(X, y)\n", "y_lin_fit = regr.predict(X_fit)\n", "linear_r2 = r2_score(y, regr.predict(X))\n", "\n", "regr = regr.fit(X_quad, y)\n", "y_quad_fit = regr.predict(quadratic.fit_transform(X_fit))\n", "quadratic_r2 = r2_score(y, regr.predict(X_quad))\n", "\n", "regr = regr.fit(X_cubic, y)\n", "y_cubic_fit = regr.predict(cubic.fit_transform(X_fit))\n", "cubic_r2 = r2_score(y, regr.predict(X_cubic))\n", "\n", "\n", "# plot results\n", "plt.scatter(X, y, label='training points', color='lightgray')\n", "\n", "plt.plot(X_fit, y_lin_fit, \n", " label='linear (d=1), $R^2=%.2f$' % linear_r2, \n", " color='blue', \n", " lw=2, \n", " linestyle=':')\n", "\n", "plt.plot(X_fit, y_quad_fit, \n", " label='quadratic (d=2), $R^2=%.2f$' % quadratic_r2,\n", " color='red', \n", " lw=2,\n", " linestyle='-')\n", "\n", "plt.plot(X_fit, y_cubic_fit, \n", " label='cubic (d=3), $R^2=%.2f$' % cubic_r2,\n", " color='green', \n", " lw=2, \n", " linestyle='--')\n", "\n", "plt.xlabel('% lower status of the population [LSTAT]')\n", "plt.ylabel('Price in $1000\\'s [MEDV]')\n", "plt.legend(loc='upper right')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/polyhouse_example.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Transforming the dataset:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ll4ZLbvjwg0yeXMaAAY2Wa3raQ5aWlubRfZmWlkZGRobP+/VkUQW7UkYg1TuE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\nEjY+/tg4HjUKnnwSjj46qMuEPRLjEgS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = df[['LSTAT']].values\n", "y = df['MEDV'].values\n", "\n", "# transform features\n", "X_log = np.log(X)\n", "y_sqrt = np.sqrt(y)\n", "\n", "# fit features\n", "X_fit = np.arange(X_log.min()-1, X_log.max()+1, 1)[:, np.newaxis]\n", "\n", "regr = regr.fit(X_log, y_sqrt)\n", "y_lin_fit = regr.predict(X_fit)\n", "linear_r2 = r2_score(y_sqrt, regr.predict(X_log))\n", "\n", "# plot results\n", "plt.scatter(X_log, y_sqrt, label='training points', color='lightgray')\n", "\n", "plt.plot(X_fit, y_lin_fit, \n", " label='linear (d=1), $R^2=%.2f$' % linear_r2, \n", " color='blue', \n", " lw=2)\n", "\n", "plt.xlabel('log(% lower status of the population [LSTAT])')\n", "plt.ylabel('$\\sqrt{Price \\; in \\; \\$1000\\'s [MEDV]}$')\n", "plt.legend(loc='lower left')\n", "\n", "plt.tight_layout()\n", "# plt.savefig('./figures/transform_example.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Dealing with nonlinear relationships using random forests" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Decision tree regression" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jm/JtWPXyZPTv3x/AVVPJ+XNn0Vhbo5hMvinfBrMlHgNGPIOf33onhPtuBa5c\ngbVbd1wBoNXpEZuQBGtOHk4eO4oPVixRisE5Fp9zNAVN/t8pIJBbs4xrs5j3V76BCZMmeewf4K/p\nxdFM482UlJ+fj/79+3MNIYYJIr4UwMsA/ikIwh7YooBMALoCGBvqiYULrvbtm+99CJtXL1eEqBLR\nMmokVKooTHzkXsQkJOJIXS1UUSrFL1B4xabN91d9h9ReP8H5c2dxpM5W/+fShQuITUxqUnxu6pAB\nuHTpEuaUfugUFTTziUGIT3GOntmxY4cyT1mhTFn5DuY/NzIoUUL+RPmwTZ9hgosvJ/CHgiBsBpAL\nm/A/BeA7IrrUGpMLB/xxhubn56N379647vrrMXnFH6DV6XH+3FnMLRyGdxcvwCtrP0LUoHuACz9i\n6pABiO+ajYbaGhQWFNiqiMYnorb6e6d7nDl1EpMmTMCbb//RaQWfkpGF3y2Yr7SmdFctVFYoqV1z\ncP+TBZg2bCDEaDNOHTuCiS+9FPAzCKQVZUeHK6Ey7YpA7EWtNRCGPgBf9m13YZNpmV0ps3sebdhd\nSxfVGiKAcjK70urVq5uUfpCTrrr1vIb0RiMZTSbKyu3RxLHszYYvzzOzex5FqdVkMEmUmdfLXqxO\nTSYpulnO4M6cuevo4+D6REyoQZCdwHM8jUBuEugINwVA5NsZ6i4SRpQkkqJt2b0/yHkAGo1S4sHd\nNcrKypRIn7ELl5JGpyeNtqnz2ds8y8rKyCCKylzGL36T1Br/FYk/360zRPk4CnxRkshoMnW678i0\nLwJVAL58AA0AngYwG7akMCZE+LJvO2a3xsQnor7mIBYWFQEAnhszBqs0WuDH85j51nqM+80QWK1W\n9OnTp4mDFQASUtNgtsRj2rBBmFP6J5gt8fjbJx/hj/NnoXfv3j7naTabkWLPHv5y00YsnTIeMQmJ\nzXYGd8bMXVez1l8/eg9rXy9qkcOcYYKN14YwRLQItrj/WiJ6y3G0zvQYR/Lz8/Hq3LloPFyDpDQr\nxk+YgMbGRqRnZUOItP0qD3//X1y4cAGjnh+rNFwpLS1FVnY2Bj76OB4aOBA1+/fhm/JtiEu2RfB8\n+/ftKPntq4i2xOO6669326SlsbERO3bsQGNjo+IP+LaiHMtnTMKEpb/H6RMnvDac8ee77amqwh9W\nrcSeqiqPZR7c4Ti39oKrc7/3DbfgeGN9i54RwwQdX1sEAFoA0YFsK1o6EIYmIH/wZgY6r9MTAZQo\nmpp8rjeSPAEyAAAgAElEQVQYFXu9wSSRRqMh0SSRRqejGWvWK81nPJkm3NmuS0pKyCCKlGTNpA27\na5XeBInpGSRKUqvZt9urXd3d70pvMJAUzbkMTOhAkE1AIKLzAM4DgCAIWQCuENG+0KkkxhPuSiIk\npqZj2KODcX7yZGgAiJLk9LkpuguONNRhzjsfKBE2k/Lvw8oVy7Hnv//FK6OehBRr8Wia8BShs6eq\nCju++grXXX89qqsqceOvHoAUa8GrzzyJHV99hdzc3JA/j/YcPeTOrPXmypWcy8C0K7wqAEEQJgNI\nJqJRgiCMBvAkgAuCILxHRPNaZYaMgqeQ0YKRIyHOmwecOoW7jh6FdvnvEJuYjCOHa3BHXS10RhE3\n/d9u4P92IwXAr/UGdP/Xv/DINddg+NQpmDptmtM5v9i3Fzn//CewZw9O7d2LES7nP2Uw4tSyZcjN\nykLZ0KF487EH8J/YOLx/8jhWLl/eKsIfaH6NoNbCU/Jae5gbwwD2qp5uP7CVcP4EwCAAF+yv77e/\n/iOAfCI6EJJJCQJ5mle4IydMOTpL8/Pzgfh4oKGhTed2cs0aSEOHttr9GhsbkZ2T47QDmGnfnbCQ\nZcIRQRBARH4H7HhTANfC1sxlLoBs2DqBvW3/eByAIiJa06LZepoUKwCvOCYTAbaVcM7XX+P46tWo\n2LEDGp0e58/+gNzu3WEwGlFXV4cDBw5Ao9Phx3PnkJGRga5ZWTAYjdBqNACA8z/+iOPHjgEAzF26\nKO8DwP79+1GxYwe0egPOn/0B1/bti/T0dOX9vgCsFy9i0/33o+/Kla0qfD0qRIYJQwJVAL6csZsB\nrACwE8D1AAwA3gCwNhBHQ6ADYewEDqSGfXFxMYmSRNk9ejWJM/9/d95Dao2WLEkpSoz+qvJd9Msh\nTypF4WRHZENDA82aPZukaM/OVHe9hfUGIy3Y+Cltv+FmIoBeMnchKTo0bR69wXX/GcYGgpwIpgFw\nH4Ce9p9VAIYC0AZyk0BHuCqAQCJaiouLnbJ4xxQtVprGDH5uHKk1WhoybjLpDCIlWjNp7MKlZBCl\nJmWg9UajEhHkb5JSQ0MDzZ49mxLSrLSqfBcttWch75z8slPVUdfv4E5QN1d4+5M4x0qBCTeCqgDa\naoSjAggkG9Zdd69Z72wktUZLA0c9T5GRURSXmk5GydZHQKXRkMEk0ZiixW5LSo8pWkxp3bo7lWLI\nyMl1W4pBVlIxcfGk1mhpTNFiWtUlhgigv48Z7zGk1FMoaXNCOH2d115DQxkm1ASqAHyGgTKtQyAR\nLdXV1YhLSkHj4VqlpPOSKeOgMxrx/oo3YLbE4Vj9YSSmZeDPf3wL/Qc+hq+/2IIfz55Fzb7/KlFE\ny6dPgNkSj4zcXqg7UO0UXVSzfx+MRiOAqz4Ho9GohF3++2/b8c6COVgxfSJmnz8HADh7/JhT1VH5\nO+zcuROFT4/C1LfWKSWvRxQUICoyClPfuurALRj2MLp06eKUweyKr9DP9hwayjDtDa+ZwEzr4Rji\nCXjOFG1sbMT7H3yAmv378ODIUZg65CG8MXks7nxkCH44fQoxcYk4ffI4fnbL7Ti8fx9iEhJx92PD\ncbT+MN4umo1Hnv0fTBs2CI//rBv+ufVTnD5xHPu+2wVzbBymDRuIsQ/0x7RhAxFjicOZM2dQWlqK\n7JwcDH1qJPpedx26xMWjZu8erH19PmISkzBs/FRcts/ti/fXobZ6b5PvsHXrVuhMEmr27sHoX96M\nD1cV48KFC4i2xCnKombvniYZzO7wpij9+Zxp/7THzO5Oiz/bBAA/AbAEwCp5BLLNCHQgDE1ARL6r\ngpaUlJAoSUonMK3BSFFqNUkxFlJrtYq5R6PTk8EkkcEkKWaaLnHxis3+iQnTKUqlJmv3HjR24VLS\nG0RSqTWkN4qUlJFFeqNIeoOBKisrnVpEDhz1PKnUNnPSjDXrSWcwkMEk0VcP5xMB9OEv7yONVkei\nSaLsHj2VNpSiJJHeKJLBofm8Y8eyVeW7nD7zZf7yZiqrrKxscZeylsL+h+bD5ruWgVD4AAB8DVt/\n4LvkEchNAh3hqgCIPAsPWfCNKVpMmXm9aFX5LjJK0TR+8ZsUpVYr/oDCmfNJo9OTSq0htVZLg0a9\nQHqjSGqNljQ6PemNImkMBopLSSOtwUBDxk0mg2gitdbZCWw0mWjixImKY9l2PzPd/fiTynuPPf8S\nJaRZ6bvCMUQAbbr7PtLodGTNziG9wUBjxoyh119/nbrm9VSOXVW+i+at20SryndRYmoaiZJEaZld\nlWv6Kgfd0NBAgwcPJrVWS4npmaTWamn06NFEdFV4JKWlk0qjoaQ0a9DLUvgS7izAmk9nrQrbmoRK\nAfw5kIu2dISzAvBERUUFZffopQhiWRHMW7eJkjO7klGKdlpdR6pUFG2JI6NkJktSCkVGRVGUSk16\no0hRajVFqdQUGRVFaq1WuZajAE7v2o0M9hpCCzZ+SvPWbSJr9x6K4lFW7qKJygcPJQJotlpDCzZ+\naldCOlJrdWSKiSW1Rksz1qwnrX3HINck0un1tGLFCpo9ezaZHOYv1zAqKytrUpNI3gHNWLOe5q3b\nRDPWrCfJbLbtVsxXy1wbRBMlpFnJJEUHTQj7Eu4swFpGZ+4L0VqESgEsAzDBvvq/E8Cdgdwk0MEK\noCmOYZ82s42RNFqdXbAabXX97U3lI6NUFKVWk1qrVYq9jZz+ihLxk5nXi9K6daeYhCRKy+6uKBXH\nBvJRajUl2cNHjZKZ0rp1V/IJxi5cSgaTRAlpVtIbDDRTpSICaKFJosKZr5JKoyGd0ajc290uQ76H\nPGetTkdGk6lJwxqDKFJRUZHSx8CdsurW8xpavXo15fTq3eS7+BPS6o+5xpNwr6ysVM5nAdYyWIG2\nnEAVgL9OYA2AHAD5AB61/8u0Eo2NjRg/YYLiwH17wRxcvHgReqMRs0Y+jiuXL2NO6Z8wb/2fcd2d\n90AQBFgSU5CQZoVWp0dccgoSUqwwW+LR+4Zb0FBzCPmjX8TJo0dQd7AaxxvrMeR/JmHKkAEovO1a\nvLt4AaasfAenjh+HFGvBCwuWILv3T3HlymVMyr8P7yyaB1y5jGcLRuCxRx/FRZvSxoUzZ7B63gyY\nLfGQusQq945LSsHly5cRE58Aa04evvvXDmxYuggarQ5zSj/EG5+UY3bphxAg4OUpk6GKUuHBgudQ\nX1sLrdGESZP/F8NHFkBnkpT5uzqar732WtQdOuBU5hrw7gR2dHB7czwD7p3LetGE666/Xjl/586d\nfjnyGffIBfRmDh+EiQPvxszhgzp8X4h2jzftACDK/q/adQSiZQId4B2AE44ry0Ufb3NymBZMn0sJ\naVZlpZ6UkUVxyalkECXFWWuUomngqOedVvB6o0gREZEUHWux7yB0FJecSpFRKkrr2o0WfbyNet94\nM6m1WopLSXPKJh5TtJhESaLt27eTWqulvw4bQQTQu3k9KS45lbR6g2KmcZ6HmW66bwBFqdUUk5DU\nZCWflduDVq9eTVm5PZQcBneOYscdiGPmcXFxMRlEkTRa30ltga42XY93dGI7nu/YepN9AM2DnejN\nB0HOBH7H/u8+AN/bxz4A3wdyk0AHKwBnHIWPbIuXhWbhzFeVyBxZUOqMRluUkN5AKo2GIiKjlMxg\noxRNqdk5FKlSUYo94sfg0EPg/id/Q5FRKls0kV2Qut5zVfkuSsvsSvfccw8lpmfQv1+cQgTQPwYM\nVqKRolQqMpgkMsfFKQ7eJ16aqiSryclpTnZ/k0Rr164lg1Gk1K45pDNcTXZbVb6LHnv+JdJodWTt\n1p1Ek0SzZs1SBG5Or96kNxrJIIoUn5xKaq2WMnJyPQrhsrIyysrt4be5xrFcRree15BBFCkjJ9ft\n+cEWYCwQGX8JqgJoq8EKoCmODdldV8WOkTmryneRVm9ztiZndiWVWkNag4HSc/KUz+et20RpWV1J\nlJzPLZz5quI7cLS1O9rVC2fOJ70oUlxyqnLsll8XEgG0WK2m6FhbSKrOYCCVWkNme8bwgo2f0rOv\nLFIylGUFpdHpKD41nTR2H0BOr96k0+spSq2m1K45yrFGyUwxicmkUmsoPiWNRJOkCP8FGz+lRR9v\nI71Dn+IZa9aT3mCgtWvXNhGcjs5kf3YArr19Z82aRdu3b2+VcFOOKmICgRVAJ0ZeCcqCTw6fdIzM\ncYzWefaVRZRkzaT0brlNHKOiJCkx+rK5RmcQKSYhiZKsmW4dw5EqlSLM5fvcPuhxej4ykgigf93z\nAG3YXUvPvrJIifyZsrKE+g98lNQaLaVlZFGUyibYZcUyZWUJxcYnkGg3E81bt8nWZN6uXGQz0P1P\n/qZJ43mdwUDZPXrR2IVLSWe42p1M7lCm0ekoK7eHk+B03E25mpLcCVe3nb2MRpKibeGmvnYaLf19\ns1OUCQRWAGFCQ0ODEhnjKMzi7OYPeYcgJ2DJq+j0HNsOori4WLnOrNmzyWAUKT41nbR6vVO0kcEk\nUXxqOhnsUUeySWbRx9tIY99pvCRFEwG099EnaMPuWnpq8ixKTM9Q/BKZeb1IrdHSww8/TA8//HAT\nQR6lVlN8SioZJTPFp6bZY/wzSKPTkUqjIVNMLEWqVE1yBeKSU8lg/37jF7/pZAbzlFjmGqkjm7PK\nysrcPmd3xzvuHGx+DpEqKyuD/jvmqCImUEKmAGDrCfArACmw9xEI1WAF4D+O2cMGUaTCwkIqWrBA\neU9vMJBWpyONTkexCUmk0WqpqKioyXUqKyttDlQ5iUyjpYT0DIpSqSk3N5c0Wi3FJac6hHVKSljn\nl3YfwDd33UNjFy4llVbnlDEsx+ubpGgqKyujhBSbkzopI5MMokRitFnZMTjuOmy+BDVFqdUUl5Le\nJP5frdXSvffeq+Q7xKfYlEdMfJLHxLKWOn8dq66GWijzDoAJlJAoAADPAvgMtr4AzwNY7Mc5UQDW\nAPgrgL/DVlY6C8AXALYBeMPLuSF+TJ0Ld/X8HWvyNzQ00MSJE+0lGpqWaZavUfj004pJaexvi+nG\nXz1Iao2W1FqtspO47o5fKeUl5Mqi/5w5nwigHwCqAahWEKherabaiAiqFQSqi4qiWkGgwxGRdK5L\nF6oVBKf3awCqi4yk0+YuVBcVRWct8fRDrMV2TmQkHY6MVI6rAehwZKTyus7++rQ5hn6ItdBxo0jr\nBIFEh94IjoLT8Vllds8jgygquyFPOCpZx74LjhFRoRLKvsqDMIwjoVIA22ErHLfF/vMOP84ZDmCh\n/XU0gP0ANgL4hf29pQAe8HBuKJ9Rp8PXStHX57KQycrtoZh/Cme+qjiDkzKyKDOvFxXOfJUio6Io\nIc2qfL5g46f0+bsf0wW7H6C9jJEPPEAmKZqs3bor2cCODlWdwUAGo+hRIbp7xrJCLSkpIb3RqCSx\nGU2mkArmQKOAOGoofAmVAigHIAD43P7zdj/O0QMw2F/HANgL4KDD5/cD+J2Hc0P5jDodvmzF3j53\nVQ5Dxk0mlUZDKo1GcSbLsfwjp7/itBuQ/QopWd0oRq2hl2cVUZpaTVatjjJ0OvpJcip9vO1fyrgu\nqyut/e1v6bqsrvTxtn/R9GmvUJZBpHSNhp4tHE1dRYkydXpKV2uoV2ISpas19MAdd1NqVBSlqdSU\n2yWWuooS9UlNp95JKfTxtn/RijUbKCUqitI1Glq2qpTOJKUQAZSrVpNKo6HYxCRSaTQ0YsQI5Xs6\n+gjkVbxBFJuUnvBEQ0ODU5G89mSa4aih8CZQBeBvJvA7dlNOV0EQNgH4wNcJRHSWiH4QBEEEsA7A\nZLsSkTkNQPLz/owXfJWS9va5a4brgBHPwJKQhMSUNDTUHMDxxnr8ZsZcXLp4Eb+fPQ1d4hLw4IhR\nEKPNGDDiGby++a94cMQoqJOSoc7Jw7kYC2qJMLz4bfz3zBnsPnEM5+MTsPvEMew+dhTJfftiZ80h\n/GP/9yha9CqGLf096iOj8Pt33sIRrQaHrlzB6HUfY/qWf6DviKex+a9b8fyGP6PgrXXYe/YMnv7D\nBjyxbA32nD6J3SeO4bujR1AXEYErqVZYbrgZFyXbfymRgLnvfoziLf/A3Hc/xuo1a2BJTIY1Jw+N\nNQcRn5KmlKcufe1VXLxwEQXPjkZWdjZmz57ttRRxdXU1ElLdl5wOVinj5lzHsRfCnHWbMXX1OhSO\nGsVllRmP+NUQhogWC4LwOYAeAHYT0S5/zhMEIRXAe7D5DEoFQXjV4WMRwAlP506fPl153a9fP/Tr\n18+fW4Ylcgp94fBBTs3R5RR6X5/LykFu1nLy2BFECBG4fOkypg59GHEpqYiMjMTlSxdxrL4OFy78\niGMNdUoDmbqD1Th6uBZH6w/j9KkTSEizIrVrDu5/sgDThg2EGG3GmRPHsHzZMqjVasTGxWPu00/C\nbLHg0oWLSEhLx/MLluLFAXciNilZEay5P70O2z/6ANacPPx319eIS05Fzd49WD5jInQGI14a+Ctc\nuXIZXSzxqD+0H9VVlbhoEAEAyV26OAnoLnEJqDto+54avQGH93+P4ukTMH7xm5j/3Ei88u5HqNm7\nB8XTJ2Dx8pWYX7QAy5a6bzDvqFDlpjP1NQexc+dO3HHXXUhISUPdoQPNblAvN7oP9Dr+NBWSm/tY\nrVYusdAJ2Lp1K7Zu3dr8C/izTQAwEsB8++tPAAz145x4AJUAbnV4byOAm+mqD2CQh3NDtEHq3DS3\nT647m/bgwYOblG9Oy+xKloQkUmu1TuYftUZLN903gNRaLan1eopSqZWqn3qjSBqtVgmTlE1O4xe/\nSRq9wfa5TkcF0+dSrP3acgiqzmBQQkYXfbxNKTKnRCFptKTR26KWLPYIpU+NIhFAA6JUTnkFUWo1\nTZ8xQ/meWoOBEtKstqS4bk0L4jkWeysrK3NbmVROzJML1gUjYsddyQl/w0z99fWweajzghD5AP6F\nq3WBVAD+5sc5iwDUAvgcwBb7v70AbAXwJYCV8BBOygqgdXFn0xYlyW2JZoNRpPScPCWJq9+Dg5Xw\n0PGL31SEtON5BlF0X9bZHkY6duFSilLbSk/cdO8ApQzFmKLFFJ+SZq9xlKnkOcjlsJMysii9Wy5p\ndHql8ul/bryFCKBhkZGk1mjJbLFlIqdk2jKfDaJ4tUaRaLIlnXkoiZ2Ylk46e7ayrBgdo6vkRLrs\nHr28loYIBEd/jVLfyZrpd18DT1FDHFIaHoRKAexw+bk8kJsEOlgBtC6enMSzZs9uIkyKi4spSm1b\n4ad3y7X1FrA3pHn2lUUUm5jkVEJi7G+LyRwbR2vXrnW6p1yLR1Yktp2ArZOZJSnFKcN5xpr1dM/Q\nEUqNIlfn9JBxk23lsLU6Wm0wEgE0xqEUtrwTkAvnzVu3iTLzrmYQGyTJqfbRqvJdNHL6K041lmQH\nuVqrpewevZzCQTfsrlUUSbB2AK45EYFcz91Oj5PKwoNQKYD/hS1+f4F9NT8hkJsEOlgBtC4NDQ1O\nwkxu91hZWdlEmDQ0NJDBXnNn3rpNlJieSZbEZFJrtcoOwCCabNFEWh2pNbasXsfOXXIWs97ecCYp\nI0upaGoQJYpPS1eK12n1BlJrtRSl1lBMQpLSxEbeOciCPzYhidQaDX36058SATQ/IZHmrdtE8alp\nSjayQZSUHgpy6YxZ72xUdg+PPf+SfTehI7MljmLiE93WQ3JNCJNX6mZLfFBKQ5SUlJBBdC5t0VKB\nzTuA8CAkCsB2XfwEwGAAvQO5QXMGK4DWpaGhgfT2bl1x9lIMCWnu6+M4riQdV+GDRr1g6/JlFJXu\nY64rYrVWq2QpZ+X2cCox7RqWqdXplPOnrCyxdz0z06BRL5BGa+s2Fp+aTnqDgR548EElye1lrZYI\noPdUKlpd8Cw9rFLRB5NmUPkbq+iDSTPowchIGqhW00NRUfSwSk1DJDMNiEugDZWHnGoqPVTwHKk1\n2iYd0VxLQriu1INVGiIUvY05qax5dKS8iqAqAAAj7P++AmCO4wjkJoEOVgCtiyzUXXsNuBM67vIG\nolQqpdSEnCUcm5jUZAUbl5JGRnvpaVeB6lq8beLEiZTZPc9p9e3oeI5UqWj06NFOrSA37K6lTwue\no+Ykjv1p/BSnQnoG0WTvsqZXeiXI5SrkUhR6ezJZMFfqjoRCYLe1MGvr+wdKR3OcB1sB3GX/99cA\nnnAcgdwk0MEKoHVxbTjvS5i5Cqbi4mIqKyuj119/XelbrDeITXYAUWo1dc3r6dakIjuZy8rKnKqU\nutrf07t2I4PxavkGV9v2R9u/oVK9nj6MjKTNWi39KSKCdvf5OVX+5Gf0YVQU/btHL/rEKFLNbXdS\nzW130smsbCKA5mk0SqltuUS2o0kqSq2mn/ftS2qtlpKsV5vRV1ZWkk5vcK4WajB2+F4AobhvRxOm\nHdFsFiofwCeBXLSlgxVA6xNojXx3AsLxD+aeoU9RpD0SJyEtg9QarVM2rrNTtaciEByvIfceSEiz\n2vwFRiOlZWU7RcS4/pHKBeTkMFSVxlbYLjYxycGxfPX4smfGEgF0/MEHqaKigoqKipwimWSTlE6v\nd5v9u337dqX5TUZeTzKYJIpSqZqYgJojUNtK+PsjqJtTnqKjCdOO6DgPlQJYC1vphu4AugHoFshN\nAh2sANoG165XzVmluSqSRR9vo8GjX1RCQd3tHhwFSUVFBWXk5CqOVTnSSO8SWuouvj2zex5FqlRO\n0TyyScuxYYxjH4AB9qghuu02p/vLTXVkoa7RaCi7R9Pd0dSpU5X+CXK+RGJ6Bq1evdrpmQS68m2r\n1bI/gro5c+uIwrQjKq1QKYAtLuPzQG4S6GAF0LZ4Wt37u+Lz1W7R27UqKyubtIv0pwSzXM1UiolV\njp2ysoSs3fMUZRJv722cnt1N6ex19IsvbH8G2dnKdQyiqPgCZKGekdPdrVNW7ovs6ASOVKloxYoV\nSvXRQIVIWwoeX4K6uXNryXlt6TPoaI7zoCsAACYA+kAu2tLBCqB9EeiKryUCrKKigmLjE5wEvmsT\nFk/OaVGSSK3TKSGkBlEilUMkjxKlY3SI0jl1yvZnoNVSQ329YgYKpOH76NGjSa21JZ1FqdSk0V5N\nHJs1a5bXQnzuhFtbrpZ9/e5aMrdAhWl78Rm0tRIKhGA7gZ+FrQn8Htkh3BqDFUD7obnC3J8/dnc5\nBmVlZSSaJKdG9TbHqsGraUoWTA/95jkydYlRYvttPgjn3UN2j57OAkuSiAD6mclE1+fmUZYk0QuP\nP04ZokjX5XSnDFGkWaNH05a1a6nqiy/oX3/+MzX+5z9E9fXK+OrDD8mq15PVKNKSt9bRR1/+m5a8\ntY4yjCJlmSSn97IkiZYvWeJRuLW16cHb766lc/NXmLb1M+ioBFsBlANQA4gFsDmQC7dksAJoP7Rk\nxeftj911dTd69GjlZ73BoDhvExySyLxdTxYYshM4PSeP5q3bZO+H3LSkheM1LubmUih7E7gb30VE\n0ML3ynza2dvK9ODP786TggjGarkj+gzaA8FWAJ87vP4skAu3ZLACaD+EYiXmruCZqx1dXsHLMff+\n3LO4uNipkbycpCUnqaV1y3Xqhyyz/4UXqCEqis51iaFzXWLobHQXaoyIpHMmEzUIAjUIAp0RTXTG\nJNEZ0fbe5dhYIotFGZdjY5Vjf5Ci6VyXGPpBilaOvRwbSxfMZtt5cu7B3//jVbi1Z9NDZWUlrV69\n2inaKZgmG94BNI9QKoCQOn5d7huCR8M0l2CvRl1Xd/PWbXKKpJmysqRZyVUVFRVKpE7hzPlkMElk\nkGxVQ+NTbbH8I0aMaHKerDhcI4QMRpGS0qxO5SSMkpksCUm0evVqxcnr2ClMp9eTWqOlmPhEMhiN\nbp+VrASWvrXOL+HW3hSBO0EfCoHd1rugjkiwFUA9bM1gShxevwPgnUBuEuhgBdD+CMR26+s4dzsA\nucCcXEJaLhPhTph4uofrdf0p0CafIzuNHZ3N8rwcrzFk3GRSa7SU0a07aXQ6MoiikxlLZzAoTmCD\nKLoXWklJRADlSpLSZ3jWrFl+mcraWgh6EvRlZWUhMdm0N+XX3gm2ArjF0wjkJoEOVgAdk0CElWuj\ndb3BOc5fq9O5dfr6uofjdf0p0SzH/TuGjTqWp5B7ILuWpJALyzkqC9fw1QUbPyUp2s0qOD2dCKAj\nO3YoeRft0RnsDk+2+bKysqDNlYV+8wlZMbjWHKwAOh7NjXevqKjwuHosKytTBIEcIeRPL175uq51\ngtwdX1lZqazwXYvSGUySreaP8Wr105SsbmSUzEq5CHm+U1aWOFUPlUdm97wmq+CLGRlEAP1306aQ\nhVyGCm+/52CYbPxdRLSmkuhICokVANMmtDRayJsglIVCWla2z4QwV7w1SJGVT1JaOhklM2Xk9SSt\n3mbCSbZmKqUj5Kzg2KRkilKpKbVrjlIFdfziN+nZVxbR/U8WOlUPVSKOTM4RR8XFxfRdRAQRQD/X\n673uUNrjDoAodFFA/n7f1jSLtTcTnC9YATBtQkuFlT+drBxX6IFmkzq2dXT8o5bNT47tI7V6Pa1Y\nsYKk6KsF8uRKqQNHPa80wPnpL24llVpDorkLqdQaUqnUSvXQhDQrqTXOEUeys7nBmkkE0LKX5/v0\nUTR3Ve0rZLalK9pg+oRk/FlEtKZSdHcvuWBhqJRwS383rACYNqOlJgB3//ldhYJr2ehA6+q4dvKa\nsWa9UszNtRfC6NGjlbpGjpVSn3hpmtIJTe5pLEcQ6Y0imS1xpDcYnIR/Q8PVEhPHelxDBNDn6zZR\nYmoqiXZnsLsdimukUSC/B3er1va8evZHuLemWSwY//cCIRi/G1YATJsSbHtpS1dhrue71hWSQ1Dd\n9UIQJYnWrl1LEydOJNHkHCH0kxv7KX2LHe3+q8p3UVpmVyorK3OaR0VFBWXl9iCjZKaaHFvi2Ttz\nXyODKNLatWudvo8sCLJye5DeYKCJEycGlGkrmc2KaWr84jcVIdrQ0LT3czBWz+5+581dqftaRLTV\nDls8LjEAABeaSURBVKC5u8/m3Ksl12cFwHQ6WrKzcF3FudYVkpPOXAW542pPlCR64MEHSedg3tFo\nNE7lpb0lrTk6sIeMm0zbI6OIALo1KsopjNQxnn7IuMmkNRiV+3kMKXXzfc2WOKe+BZK5C61evZom\nTpwYsA/FF55WrY45GcHMIHe8Z2vkByj+p8yuQX92jgRrZ8MKgOmUNHdn4W5l5VhXSG80Ku0n3ZWR\nls06jp/J/QFk+/09Q58itbZp72MiZwGpNxjIaDLRl3o9EUD3uilwJ1dSlZ3MPkNKXb7rihUrnHIo\n5LwFa3aO/2GqLXi2svJzTK4L1Yq5NaOA/I1Aa8k9eAfACoAJAe5WjK5/1KvKd9FN9w0gtUZLSekZ\nTqt7d53SMrvnkU6vJ519le7uD1fu6+u4OxAliRp//nMigEamZ7gNfTWIIiWmZza5Z1ZuD7crwoaG\nq30c4pNTKdF+XcfmN3K7S7k0dkZeT9LodDRr9uxmP1dfOQFyC8/0nDy3JTg6GqHeeQTj+oEqgCgw\nTCcnPz8f/fv3R3V1NaxWKywWCwDAbDYjITUN1pw8rJo9BRV/2YxoSxzqaw9BrVbjm/JtiEtOQe8b\nbsGbL09BdVUlrDl5qK6qxNH6w1j029/ihbFj0SUuAdacPACANScP8cmpWL5iBV6ZOxdqnR7znxuJ\nuOQUNNQcgmiSEKnTAQDOHGlwumZ9zUH06dMHC4uK8Ozo0VBrtE6fHzlcC6vV6vTdSktLUVBYiAsX\nLmBO6YeIjFJh/MN3obqqEpcuXEBsYhKsOXk4eewojhyuRXJWNl7f/Fd8U74Nq16ejIcGDMCOHTuc\nnou/WK1W1B060OQ7AEBCShoGjHgGtz2Uj8aagyieMg59+vRp4W+ybfH0/6ijXN8drACYsMBisTT5\ng5IF2FefbsZf1v0Rr6z9SBFkLw38Jd6cMQkXL13E8cZ6FEybg6lDH4YYbca5UyexbOkS5Ofn4xe/\n+AWuu/56JyF4+OB+zJ9fhGdeWYRF455xuu7EwfcisnsOAGD0E09g4LCBiIlPwNH6Oqz87UJYtFoU\nPPooVOfP46UJEzBn8L2Ijo3DDyePY+Vrr8Gi1QKnTwMAjhw5gnFPP42nX5yCzW+vQtfkNADA/Q8O\nwuxB90CKteDUkUbU7PwH0rO7I/+JpzD7kXuQlpGJxrrDKHz0Udxxww2IT0rB4UMH8MKYMXjyyScR\nGxvr3zPVarFywQI8/8RAxCUmo+FwDVYuXIifZmfjzMH9yn3PXLqEH+tqkREbq8y9o2LRamHp3t32\nQwi+i0WrhaVnT8C+SAg5gWwXWmuATUBtRkfKegwET9+rpKSEtHq9YjaRR2J6Br3++us0a/ZsEk0S\npWV2JYMouq3Z47p1l5vAzFu3idK6dXe6bkZOLh254w5q7fLTPDrQePTRZv8/t8tO+Dt4B8AolJaW\nonDUKCSkpKHu0AEsW2Jb5XZ0vH2v/Px8pKam4rbbb29i4rn99tvxzTffICIiAiqNBlGRUcjKymqy\nk3DdugPA/AULcP7cWRyrr3e67rGGOqieH40r//gHfjh+HBqtDkJEBOjKFfx4/hz0ej0AQBAERAiC\n1+91hQg//PADNFodrtAVXPzxRwiCACKCSqXCxYsXERERgStXrkCtVkMQBPz444/Ke4IQAY1Oi/Nn\nzzaZh8Fg8Hl/X1yxCxl/vsvFS5dw/vx5ZW5arRaqqDAVT1pt690rEG3RWsM2LaY1aa9lB1qKv99L\nbuuY6NKAprnPRN4VJNqTyzJycpuESbo6UBPT0kmUpGY1j3esKupaA2nGmvWkNxjI5NAYx1P4a1vU\nG+qs//faAvAOgGkO1dXVSEhJa+LMrK6ubhVnVDBpbGxUVuP+fq/XXnsNhYWFqKiowLXXXovc3Fzs\n2LGj2c/EcVdgNBpx5swZJ8eeqwP124pyHG2oV/wF31aUY0TBk+jduzdiY2M9OgbdOQ4d5/3lpo1Y\nPmMS9CYJUSq18l16XnsDYixxWDljIi5dutTEkevqbA4lnen/XkeDFQADwHNER2sKgmDgau55de5c\nv79Xbm4ucnNzlZ9b+kzcOZ4dP1u2ZAkKhw9CfHIqavbvQ3J6hpPQlmIs+FnfvoiMjERyeoZHs5zr\nfeR5f1tRjuUzJmHGmnWIjFJhUv69Tt/l7JnT2PHVV3jv/fcx84lBiE9JRX3NQSxbsqRVBW9n+b/X\nIQlku9CcAeA6AFvsr7MAfAFgG4A3vJwTmv0R45WO3oHJkymhuLi42d+rpKSERMnmBBYlKejPxLV0\ntdzG0lf5AX+yZQ2iSEnWTCX2Pz4ljdQaLaVndwtKFc9gntPR/++1FxCgCSjUwv9FAP8GUG7/eSOA\nX9hfLwXwgIfzQvV8GB905Cggb+n0rt/L3+9ZUlJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.tree import DecisionTreeRegressor\n", "\n", "X = df[['LSTAT']].values\n", "y = df['MEDV'].values\n", "\n", "tree = DecisionTreeRegressor(max_depth=3)\n", "tree.fit(X, y)\n", "\n", "sort_idx = X.flatten().argsort()\n", "\n", "lin_regplot(X[sort_idx], y[sort_idx], tree)\n", "plt.xlabel('% lower status of the population [LSTAT]')\n", "plt.ylabel('Price in $1000\\'s [MEDV]')\n", "# plt.savefig('./figures/tree_regression.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Random forest regression" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X = df.iloc[:, :-1].values\n", "y = df['MEDV'].values\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(\n", " X, y, test_size=0.4, random_state=1)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE train: 1.642, test: 11.052\n", "R^2 train: 0.979, test: 0.878\n" ] } ], "source": [ "from sklearn.ensemble import RandomForestRegressor\n", "\n", "forest = RandomForestRegressor(n_estimators=1000, \n", " criterion='mse', \n", " random_state=1, \n", " n_jobs=-1)\n", "forest.fit(X_train, y_train)\n", "y_train_pred = forest.predict(X_train)\n", "y_test_pred = forest.predict(X_test)\n", "\n", "print('MSE train: %.3f, test: %.3f' % (\n", " mean_squared_error(y_train, y_train_pred),\n", " mean_squared_error(y_test, y_test_pred)))\n", "print('R^2 train: %.3f, test: %.3f' % (\n", " r2_score(y_train, y_train_pred),\n", " r2_score(y_test, y_test_pred)))" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EGkMkZSfx6YZPGXvRWEKhEFVlVZx/9vmkp6ezdu1aAEaOHInNZvwpbdq0ifLy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\nt4umcBO9T+iN3WHn2WnPEolG8Pl8SCn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(y_train_pred, \n", " y_train_pred - y_train, \n", " c='black', \n", " marker='o', \n", " s=35,\n", " alpha=0.5,\n", " label='Training data')\n", "plt.scatter(y_test_pred, \n", " y_test_pred - y_test, \n", " c='lightgreen', \n", " marker='s', \n", " s=35,\n", " alpha=0.7,\n", " label='Test data')\n", "\n", "plt.xlabel('Predicted values')\n", "plt.ylabel('Residuals')\n", "plt.legend(loc='upper left')\n", "plt.hlines(y=0, xmin=-10, xmax=50, lw=2, color='red')\n", "plt.xlim([-10, 50])\n", "plt.tight_layout()\n", "\n", "# plt.savefig('./figures/slr_residuals.png', dpi=300)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..." ] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }