{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Clustering\n", "\n", "So far in this course, we've focused our attention in machine learning on two fundamental tasks. \n", "\n", "- **Regression** aims to predict the value of a quantitative variable. \n", "- **Classification** aims to predict the value of a qualitative variable. \n", "\n", "However, this isn't all there is to machine learning. In this lecture, we're going to take a quick look at another task, called *clustering*. Clustering fits into the broad set of *unsupervised* machine learning tasks. In unsupervised tasks, there's no target variable to predict, and therefore no \"right answer.\" Instead, the aim of an unsupervised algorithm is to explore the data and detect some latent structure. \n", "\n", "Clustering is the most common example of unsupervised tasks. In a clustering task, we hypothesize that the data may be naturally divided into dense clusters. The purpose of a clustering algorithm is to find these clusters. \n", "\n", "This lecture is based on the chapter [*In Depth: k-Means Clustering*](https://jakevdp.github.io/PythonDataScienceHandbook/05.11-k-means.html) of the [*Python Data Science Handbook*](https://jakevdp.github.io/PythonDataScienceHandbook/) by Jake VanderPlas. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import pandas as pd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start by generating some synthetic data. The `make_blobs()` function will create a user-specified number of \"blobs\" of data, each of which are reasonably well-separated from each other. Under the hood, it does this by assigning a true label to each data point, which it then returns as `y_true`. However, in a standard clustering task, we would not assume that the true labels exist, and we won't use them here. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "X, y_true = make_blobs(n_samples=300, centers=4,\n", " cluster_std=0.60, random_state=0)\n", "\n", "fig, ax = plt.subplots(1)\n", "ax.scatter(X[:, 0], X[:, 1], s=50);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visually, it appears that there are 4 clusters. Let's import `KMeans` and see how we do: " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(n_clusters=4)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.cluster import KMeans\n", "kmeans = KMeans(n_clusters=4)\n", "kmeans.fit(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get cluster labels, we use the `predict()` method: " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "y_kmeans = kmeans.predict(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's visualize the results. The use of the `c` and `cmap` arguments to `ax.scatter()` allow us to easily plot points of multiple colors. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fZ/5jWbCTCv+s38pXE+bww9RFlposNja1TdLmtkKIHGAkcAFQBAwHRkgpP7M6Z283t33my3GMmrIoYZoewIX9D+OeC46r0twj/5zPS8MnElIjFQEHn9vF6Ud15P4hAxKeu2jNZq4eNjxhCffu4nM7CanabsWqE+FyKKiajiIEbqeDU4/swP9dfEJKqXElgRCf/DaLD8fMNF2XQxEM7tOVBy4yPrewGmHFpnw8LgetGuUlvcbs5Ru45fXvUCNaRYaPz+2iZ/smDLt+UNIGDZXxB8Pc/tYoFq7ZjK5LHIqCLnXuPLc/5/ZLLTRmY7MnJGpum8pm4gnAainltuhk3wJHA5aGem+iRjRGT12c1Ei3b1KXu8/vX+X5zznmUNo0rsuHY2awYlM+DXIyuWRAD8tOKuUUlwW5/r8ja8RIC9it8EcqSAmD+3YhO93HyT3b065JvQRjJf8WFAOCRrmZlPhDBMKq4e2b3D80XfLH/JUVhtrtctKpeWIPuhxdl9xvUoUZCKvMWraBcXOWc9Lh7VN9mzz22e/MX/Vvpb8b47/DRk6kVaNcerRtkvJcNjbVTSqGeh1wlBAiDQgAA4C95y4nodgfRCbZXKublc6rNw3e7YKJbq0b88qNZ1XpnFFTF+3RI3kiUvWhFSGq7HG7nA66tmzEmb07Jzx30oJVPPvleApLA4BRbl6eGplIETCRHGwiFq7ZHJd6WU4gpDJi0vyUDXVhiZ+J81aa3tyD4QgfjplpG2qbvUpSQy2lnC6EGAH8DUSAOcC7Nb2w3SUr3YuSIN0rK83DiIeHkpVuvvFXUyxcs9lSg6MyLocCQsRoUjsVUWXd58p43UZ2SK+OzZk0f1WVztV0jeET5/H0F+PQNJ22Tepx2+Bj6N2pecWYaUvWcu97P8U8LaTy5OByKJzcM3WvtzIlgVDCnOodVYgvr9+WWHbAKs/bxqa2SCmIJ6V8RErZQUrZRUp5qZQyubDxXsLlcDC4TxdLqdBbzupb60YaSNwyqxI+t4vnrxnI5Sf15PC2TejUrD4dmzfY7UIPl0PhrdvOYfwLN/DKDWemLDFaTjiis3T91miFolHu/Z+3f4hR33t55KQqh3QciiAr3ctlJybfmDSjQ9N6loU6LodSJeGtetnpCUNl9XOSZ7nY2NQkB6TM6a1n9eXwtofgdTsr+gp6XA5OO7IjZ/ftGjP299nLOP+JT+h966uc+sB7fDRm5m719Fux0Shs+Xv5BopKAvwy4x++n7KQDduKACr+m4yykErbQ+oya9kGFqz+l2Ubt7Ng9ebd1l5ulJfFoS0b4fMYmiJPXnGKZRXkrrcCRQgExJWhh9QIz349Hl2XhNVIlT1Ot9PoyP7FAxeTm5VWpXPLyctK5+Se7U3fi8vpiClRT0aj3Cw6NWtg2njB53Zx6YDDd2uNNjbVRdKsj91hb2d9lLN47WamLFqL06HQv1trWuyiRvfez9P5cMyMmJCEQxG0aJDLJ/cOqTBuiSgo9nPHW6NYvnE7iiJQNR01ouF1ORFCoOk6/bu1ZuL8VSmHA9K8bkoCoT0Wxne7HAy7fhBHd2oR8/rsZRu4+70fCasRhBBENI1DWzXG43Iy4591hvKelChCWMaBfW4Xn943hGb1c+h966sJ49CVEQJuHtSHy046Yo/LwdWIxlNfjOXXmUtxuxxouiQ73cszVw3k0FaNqjTXlsISLnv+K0oDIfwh1chyid7cH7xogC0AZVPjJMr6OKANdSIKS/yc+sD7lo+8aR4X/7vrgqRZDkOe/pxV/+YnLMP2uJzoUlr2QqyMEOBUlCrnN+9KbmYaT195qqV4kabrzF62gR1lQdo3rV8hGVriD1JYGqRedjpnP/oRWwrN+xv6PC4+uedCWjeuyy2vf8eUxWtI9U/J63bSt0tLnrt6YLUYwMISP8s2bicrzUOHpvV3e86QGuH32cuYsngNWWlezjiqE51bNNzj9dnYpEIiQ31Ahj5SYfLC1TgSxI39IZUbX/02oQGev/pf1m8tSqqVEVIj6LqeUpxaEWKPjbTTIXjt5rMSKsw5FIUjOzTjxMPbxeg6Z0Z1nn1uFwO6tzU2N03wuV20bGj0Prz7/P5keD0xoYNEpjIYjvDXojXMqKZuOzmZafTq0IyOzRrskeH3uJycflQnnr7yNO678HjbSNvsMxyQ6nmpENF0kj1NhFSVvxatpnPzhnw+/m8mzF2BIgSn9erIBcd2Y9n6bSmnu7mcDtI8LorLgkkzOCzSjlMmokme/Gwsnz9wccJxUxav4ePfZrFh2w6a1c/m8pN60qvjzmyOy07qyU/Tl5jqQd99fv+K0EWz+jl8+eAlvP/zdP6YtwKEYED3NjTOzeLtH6ea3ngCIZVbXv+ONo3rcuUpRzCge1s7vGBjY8FBG/rYsK2Icx//JOFuv9vpYOiJhzN80nz8oTBqxDA4HpeD3Mw0rjntKF4aMZEyC9H9Xef65qFLufm179hgIYQkBFx7Wi8+/n12Sql8yXjhmoEMsFC5e/vHqXz6+6yYQhmv28lVp/biqlOOrHhtU34xL434gz8XrEbXJS0a5nDb4GNSKr0fNWURz389wbLLTOXrXtj/MG4dfEyK78zG5sBjTysTD0ia1MvmhB5tGTNrmWUhitOhMHnhmjiPMqRqbNtRxsI1m5N65WCEM45o35QmdbPZVGCtPyIQnHl0FwpKAvw4bUlSA5eMhz4aQ492TeP6La7fVsTHv80ktEt6WzAc4b2fpzHwyI40zM0EDHW7l64bhKbraJoe0xwgGd3bNLbURtn1ul+Mn8O5/Q6lcV58txwbm4OdgzZGDfDo0JM5P4GOg9vpYMWm7abhjYimM2bWUp69emBSQaTcrDQeufQkgISGXZeSsx75iF9m/kP/bq3p3qYxdeuk73Z2hKbr/DhtcdzrY2YutczSkFLy2+ylca87FKVKRhqMkEjvTi1Sboowfs6KKs1vY3OwcFAbaqdD4e4LjuPFa07H7XTgcRlKb2keF1lpXl649vSEm2IhNULfLi2545x+pjm4ALmZPkY9dkWFwe3aMnHaWDiiURoIM2HeCjo0bUDPtk2QFkbVSpmuHFXTWbRmc9zrJYGg5QaoGtFTCuWkyjNXncapR3bA43JYbkyCceML1oAOio3NgcBBG/qozPE92jKmfVN+nfkPmwtKaN04jxN6tDNi0VlplilqHZvVB4yWVrOXbWDG0vUVEqZupwOX08Ebt5wdk499x9n9uOG/I5MapWA4wsg/59O5RUPLjUWnQ6Fzi4bMWbHRcp6Ckviejdt2lFmO97md1SrW73E5efiSE7njnH78OG0xr38/2VRAyuNyckS71KsJbWwOJg5qj7oyddK9XND/MG6LNm71uo2ClZsH9TUVtfe6nNw0qA9ghAVeum4QT15+Ckd3bkGXFg0ZeuLhfPfo5bRvWj/mvG6tG/PazYNp0zgPl0NJ6LG7nA7qZ6dXePq7oumSI5OUSu+aSVHiDzJhrnWIId3n5sj21d84NtPn4YJjD6Np/ew4z9rtdNC+ab0qF6nY2Bws2B51EgYe1ZHSUIjXv/8LMGK4bpeTB4YcH5OnrCiC4w5rw3GHtUk65+HtmvDNQ0MpKg1wz3s/MmvZBsuxfTq3ZPLCNXEbf26ng+5tGtO9zSF4XU5TD93oRB5bsDN7+UacDkfcfOU0qZtdYw1kFUXw3h3n8eQX45g4byVOh4Km65x4eHvuv/B4Oz3PxsYC21CnwAXHHsaZvTvz8e+zGPf3coJhlT/mraRFg1zaHFJ3t+fNzvBxTt9DWbR2i2nXF03XOf6wNrQ9pC53vjOawtIADkUQjmgc1aE5T115Kj63i+wMH5sLS+LOdzkcnHdst5jXkpnCVMWjdpfMNC/PXT2QkkCI7TvKqJ+dQbrXXaPXtLHZ37ENdQrouuT+D35hxj/rKlLmNhWUMH7uCl645nT6dGm523Mf36MNn4//m+Ubt8V4uV63k9vP7kea1037pvUZ/cSVLFm3hYKSAK0b59Eod2fn9NdvGcw10c4x/pCK2+lA03Ua5GTwxqi/OK9fNw5vZ+gpH96uieVGos/tZGCv5O3EqoNMn4dMn6dWrmVjs79z0Ba8VIUJc1fwfx/9aur1ZqV5GPv89XvkiQbDET75fRYjJs2nJBCiVaNcrj+9d5X6OYbVCOPmrGDi/JVMmLsCKSGi6wjA43Zydt+u3HVefwA+GjOTd3+eFlNU43I6aFK3Dl88cHHK6XQ2NjbVh13wsoeMnLzAsiGtpkv+Xr4hoa5GMrxuJ9cOPIpr96Djttvl5MTD2/HC8D9iSrYlxo3gu8kLGNC9Ld3bHELbJvVwRCVMy2/TLern8O5/zsXjcjJv1Sa+njCXfwuK6dyiIRf2P4wm9bLNLmtjY1ML2IY6BUr8ibuFVM471nVJSSBEmseFK0mec3Uze9l6S4W+YDjC8InzSPO4uPvd0XEl6uu3F/HRmFm4XQ4+HTvbaN4rYdHaLXw7eQEvXHsGfTq3qIV3YWNjsyu2oU6Bozo0Z+n6baa6IGpEM3KdpeSzcX/z4a8zKAupCGBA97bcfX5/sncp4a4pCksDlpWPEiN/+oNfZph2RgmGI3w5YQ5CiBjd7IimE9F07n3/R8Y9f70dFrGx2QvYedQpcN6x3Uy9Y4/LyfGHtaF+dgbDRkzkrdFTKCoLokY0whGNsX8v47Lnv6wWgaVUaNeknmVpeHk637xVmywV/xJpZgsEkxeurra12tjYpI5tqFOgbp10PrjzfJo3yMHrdpLhdeN2OjjliPY8OvQkCor9DJ80P84gq5rO9mI/Y2bFa2fUBK0a5dG1ZUNczvhfq9OhcF6/bmQkyLTQdWlpxDVdpyjaYdzGxqZ2sZ9jU6Rdk3p89+jlrPo3n6LSAK0a5VWENGbONYo3zEIjgZDK77OXcubRnWtlnS9ddwZ3vfsj81f9i9MhkBK8bhcvXXcG9bIzOK9fN179/k9TLz8nw0tZULUsb++wS5WljY1N7WAb6irSqlFe3GuKIhIq6CXqJFPdZKZ5eef2c1mzuYBlG7eRk5FGj7aH4FCMNZxzTFd+m72Uf9ZvrTDWLoehjPfcNadz+1ujYJcEF6dDoVXDPLvjiY3NXsI21NXAUR2bWReReFycdmTHWl4RtGiYG9fMF4x86XfuOJdfZ/zDt38tpCwYpk/nFgw5rjv1szN4947zuOPNUZQEQkZzXk2nQ7P6vHT9oFp/DzY2NgZ2wUs18eGYGbz38/SYkILb5aB1ozw+uudCXI7aTdXbE3RdMm/VJrbvKKN14zzTp4hU58kvKSPN47bLxG1skmAXvNQCV5x8JIfUrcM7P05j7dZCMrwezjmmK1ef1mu/MtJghHL2ROpUSsmISfN556eplAXD6Lrk8HZNefCiARxS1+7gYmNTVWyP2maPmLZkLW+M+oulG7bhdbs446iOZPq8fDJ2VszThSIEWWkeRj5yGTmZaXtxxTY2+ya2R21TI/w8YwlPfj62wiCXBkKMmDTf6PC+y1hdSvwhla8mzOWGQUfX/mJtbPZj7Dxqm91C1TSe+2qCae641TNaOKIxLkHTAhsbG3NsQ22zWyxas9myOCYRifom2tjYmGOHPvZT/i0oZv7Kf/F6nPTq0Ny0XVhNomlVN9Jel5MzetdO4Y+NzYGEbaj3M9SIxiMfj2H83BU4HQpCCHQpefjiEzj5iA61to5OLRqgW+iKOB0KUsoY3RGX00GDnEzOqqUKTRubA4mUnkOFENlCiBFCiH+EEEuEEL1remE25rww/A8mzFtJOKLhD6mUBcMEQiqPffY781f9W2vr8LldXDfwqDhPXlEEmT4Pz19zOt1aNcbjcpCd7mXIcYfxyX1DSLPzqW1sqkyqHvV/gV+llOcKIdyAnV+1FygNhBg9dZFpY9pQOMIHv07nvzeeVWvrGXpSTzLTPLw1eio7/EGklPTu2Jz7hhxPo9yslBr92tjYJCepoRZCZAH9gMsBpJRhIJzoHJuaYd3WIlwWHcQl8M+6rbW+psF9u3JWny4UlQXxup343K5aX4ONzYFOKqGPVsA24EMhxBwhxPtCiPRdBwkhrhVCzBJCzNq2bVu1L9QGcjPTCGvmetEAOZm106BgV4QQ5GT4bCNtY3vAbtQAACAASURBVFNDpGKonUAP4C0pZXegDLhv10FSynellD2llD3r1atXzcu0AWiYm0nbQ+qhmEj1ed1OLjyu+15YlY2NTU2TiqHeAGyQUk6P/jwCw3Db7AWevvJUstK9eCu1xPK5XRzRvilnHNVpL67Mxsampkgao5ZSbhZCrBdCtJdSLgUGAItrfmk2ZjStl833j17OqKkLmbxgDRk+N2f26ULfzi1RlASi2DY2NvstKYkyCSEOA94H3MAq4AopZaHVeFuUycbGxqZq7LEok5RyLmA6gY2NjY1NzWJXJtrst0gpIfQrsvQ90P8FRwtE+rUI73EpnKtD6Hdk2aegF4C7ByL9KoSzZew4bTuEpwACPH0QSnzXnIMBqf0L2lZwNkco2Xt7OQcdtqG22W+RxU9AcCTIaHd0PR9ZdDsy41qUjJusz5MSWfQfCE0AoucGViODoyH7TYSnjzGm5Dnwf4bxNRFABJl+FSLjNoRJ5o3U/cjADxCeACId4TsH3Eebjt1fkNom47NSF4FwgVSR3pMRdZ5AiL2TDnowYhtqm/0SqS6FwAgguMuRAJS+jfSdg3BYNOMN/WEY03IjDYAGMoAsugPqT0X6vwT/lxi1XZXqu8o+RDqaItLOiV2P9i8y/zzQSyrmlaHx4D4asl9DiPguP7peCGUfQuBbkH5wdUFk3Ipw7xtRRqn7o+8pH9BBhowDwTFIvRCR+8FeXd/BhK05abNfIoM/krBANvib9bn+r3Z64XGoyNAMKHuTWENeTgBKX4+fs+juqEGrdI70Q+gvwxBXHqsuRt9+IWztBWVvg74VZCmEpyELrkQP/Gr9vmqT4I+glwK7Nm4OQXgGUl2+N1Z1UGIbapv9E1MDUk7EMJJWyIIEEwuQ20G3TGoCfaMR4y6fTtsG6lzArGo0gPR/tHOsugxZcBFE/raYPAjFDyFlxOJ47SFDf2J+swIQoM6uzeUc1NiG2ma/RHj6gLDQBhNucB9pfbL7aIxMUxOkCq4eJIwKinSEqPTV0fONa1qh5++cvnRYAm++fFAEGZ6beExtoGRhxOZND1p//hihKRkci1SX1cjSDjZsQ22zf+LpD0oD4g2qG5ztwWVdTi/SLrYwrB7wHIfiPAR8gzE35m7wnRf7kqMJJPKAne13/n9oMlg2KyunDAovQS+4BhnZe63LhG8w4LU4GkA647XFpbYRffsgZP75yB33IPPPRd8+GKltrtG1HujYhtpmv0QIJyLvS3D3AdwgMjAM7QmInP8lzLQQjvqI3E8NAyvSQGQac3hPRGS/YIzJvBuczYlV9E0DZxtExu2x8ykZUcNuZtR8iPQbK/2c6ldOh/Akw9AVv4wsfRMZmhwTcqlxXIeD92TM1yyg8HJkpacDKVVk/hCILAMCRtydIET+QRZctE+Ec/ZX7KwPm/0WoeQict9D6gWgbQZH45RzfIWrM9QdB5ElRjza2Q7h2CkmJpRMyPvOyHAI/gQoCO/phjEX8SqBIutBpF4YTflTMLxmHTIfQHh67Rzo6Q+h37COr1dGGrF2/zuGDy68oDSE3M8Qjropvc+qYNwEtIr3J4RApt9gbCrGrVcHvRgCoyHtfOOl0DiQJSZjNeMzDk0E74BqX/fBgO1R2+z3CCUX4epU5UIMIYRxnqdPjJHeedwN3lNRct5GyXkT4TvN1EiXjxXZL4LnOHZmozig7G1keN7OcZl3RmO7Vcmt1o1/0g/aOmTRLVU4NzlS24JedAdyS1fkli7o205BBsca61VnA1bytQFkaMLOecLzQJZZXKQMqS6o1nUfTNiG2sYGkDKCDM9Ghv5C1wrRS99D33IUcksn9C2Ho5e8jNEzI8EcOx42crTRMPK7A0aGSOFlSG0TAMLZHJE3EjwnYBhABzh7kPpXMQLqImRk7e6+1dg16wXI/MEQ/BVQAQnaKmTRf9D93xpevEiwtsrS9Eoulpu0eOyKxj3ADn3YHHRIbSNEVoPSAOFqiwyOR+64D8NQiWhqn6Ai3U6WQNn/kOo8yPnQvCpR2x4NEZgYc6kiyz5GZN0PgHC2ROS8ETNE3342RBam9gaEC7Q10Rj6nmGU0BcTn1oYhJJnkHV/S7BRmobwnb1zWb4zkKWvWl/MO3BPl3vQYhtqm4MGqe8wKg/DM42sDxlGigyQRZjnQFcmZORKq7PAfUT84cgiEB4w9bpVCE9NOLvIehBZcAXxlZZmb0QFxyHG/8owBH9E+r8HIuA9FeE7G6HENWEyJ/gT1oVDEYS+Hpn5AJQ8S2xOtQ88fcBdqc+10gDShoD/U3Z+ngrgNmL1JuElAKmXGgY+MNIInThaIjJvR3hPTu09HATYhtrmoEBKiSy4ytg8RN1ZDl3+35QmCSCDYxBmhlpkkXiDUEeqyxCudqZHhftwyP0QWXg9yB0J5lHA2RrhbIPUy5AFF4K2fmeBj7oIWfY+5I2spg1HgZI+BOlsgSx7C9Rl4MhDpF0OvrMrni6kDCELr92l8EeA0giyX0VxdzWdXcoQsuACiKyl4oahrUQW3Y3M3IySflk1vIf9HztGbXNwoM6HyHKM8EYN4OqWsACEyLpoTvFZhhKdGY6mSYphHCByIdsoYZdlbxghnJgqzADo25DFj6e2bu9ArOPKTnB2BEB4eqPkfoLSYBpK3Z8QaefF6JfIkpcg/Pcu65eGMqFqVYWJkTWibSDeqw9CyTCknqDC9CDCNtQ2NYqUOjI0Gb34GfSSYUj1n72zEHUesId5vMKH8J5k5Av7v0Hffhb61uPRi+4GbRUi+2XAB8QLMBkhjSBEllrnFEeWG+ETSzQjXl54BTI8C/zfYB62iEBoXNLNTwCRPjRagbjrmr2Q+SBCJH/oljICga8Bs6eTAJRZizfJwCjrm5NwQHi6+bGDDDv0YVNjSL0UWXApaOVen4Is+wjpG4jIerp25T+VZKGJZHjB0REp3VAwFNTFVMRsg5uMkEjO24i6o5BlHxjZH/o2k2tqoBcZ+dbeE2OOSJzRIpFEhEBbY4RxEolSgfGZJyptB4SSA3nfGZKuwTFABBytEJl3IVLNeZYlIBPE+PVtCU5OtjdQiwU++zC2R21TY8jiRwwvseLRXAeCEPw5TlGuWq4XWYsMTkCqS4yYtJRIGQ11eE4guVEoxwF4gCyMr0g6OBpCZAEUDo2KEVX2Ao33JXfcBY5mKHWeAN+ZWBoZWYZU58e+JCWUPEXy8vJygpBID1pkRuPmyRGOBijZwxANFiIaLEKp90vqRrriWgl8PqW+9THvqRhPISZINbFmy0GE7VHb1AhSL4tKjZqlqwWQZe/FaTrv/rUKkIW3gLrAMBhSi2ZgqIAfqeRA2tUYf+7Jwh8C0i5BpF+DlMLwfMveBG0jSePbMmCEWNzdEUoOEjfmXq8Tgr+jB38GfQdIAa72Rrw59Xcd9WK9xGeKOMB3TqxwVAoYTzhVNwlCOJG+C6L63buuxQvpV1mf6zvbeALRVWJ/Nz5Iv9KoELWxPWqbGkLPN2KMlse3VMtljGyOK0CdAwSjoYNANOWujIoNrdLXoiJOVuEWAXgR2W8jMh9Aln0C24+DkidA30Rqm5DKzso878AE14qAtiqarVEM7AB1BuYx3kRISL8Sw/uvjAb+T9FNdLNrCpF5J7h7YHjHAuOpxAvekxFpl1ifp6QbBUDeUzAKgFyg1IXMexAZt9bK2vcHbI/apmZQ6iaOW0bzgPcYdTZoa0nuKQeisdJyD7RyiEEB7zmIzP8gHHno/hHRXODkm3ExyDC4DEU54WiIzLwXSp6PzlMTsdagsVEnPCZphkEofRfpPgbh7lYD145FCDfkfAjqfGToD8CJ8J5omY4Yc64jD5E9zNj8lEEQmft1+7KawDbUNjWCUNKQvjOM9Ks4T9GHSL+uei6kLoiGOFIk/RJQl0QLUCQ4OyGy7kNUjoWWvYG1YL4VXvANNkIeUhqFMeoccLaLGlEZvaFU1WtORihBLngI6f8Y4R5Wzdc0RwgB7m67fWMQwp108/NgxTbUNjWGyHrI0KRQF2IYKAegQNoF4D29mi5SB+OROTVjLZQ8RO7/oulxumEcKiGljMajU8UH6JB2HiLzfiMUU/woBL5np7F3RteY6kZh3KpBZINM0HXGFAnBH9F31Edk3VPlmLXNvoNtqPdxtm8qIH9jAY1aNSArb//aWBHCB7mfGRts4SmGt+Q5CeFsVn0X8Z4IxY+kuqKouh2W+cFCCKTIjMp1JsMJ6JB+OSLjP8a5oUkQrGykwQjL7EkOt8vInNCqaqijBD5COjIQGTfvwRps9ia2od5Hyf+3kGcveZVFU5fi9rgIh1SOHtSTO9+/AV9GgrSsfQzjcfgw419NzK9kIrOeguL/w/CqreLiXkMHw9kyhVl9QCqGOmqA/Z8ghQeRcbMhcpSwulBQZc9a1DHSC/1rMA+dlMdzrebVoex9ZPq1gNP2rPdD7N/YPogaVrnt6AdZ8Odi1KBK2Q4/alBlyqhZPDjwmb29vH0OJW0QIm84eE8zyrCd3cBzSrTriwIiBzJuQdRJ/tnJyIokWhtmJwWg7D2kDBodxRMiMEq2y7MjkuFF5LyKSL/IUM2Lww2O9phXQ1ZeYwi5pSdySwf0bQPQ/aOMl7V89JLX0POHoBdeb+Shy1iDb1SXTkH6v4getzu11Da2R70PMvnbGRTnl6BFYjMF1JDK8r9XsXTmCtof0cbyfH9JgKk/zKKksJSOR7Wjfc/WNb3kvY4MT4Hg79HCi0KI/APp10L6tYaof6pZBJGVhkGsilgTgFQgsgJch0WFnywQPsh6HCFcSN1QviP8h8lAD3jPQ2RehSjPkMn9zGgaoOcb18OPkeq3juTFPNrOMdp6KH4YXZ1vhGlkmHJPXYangbsfZL+CEIpRRFRwuZHuKLVoyqUHct9HuLqk/PHY7Bm2od4Hmf3bXAKl5nKXEVVjwZ9LLA31+K8mM+zqt1AUBS2iIRSFVl2b8fQvD5KRnaL05X6GDP4KJS9j5FFXOlD2Pij1EOkXpj6Z0pDdS6ULG6JMrkMh8GWCxeoIZ1uEqwMEJyBNtSwEOJohsv5j9GMsf9XVCeqOhcgSQ9Y08BVGquHuCBcFIPAZceES6YfwJAj+gvSejCy4JPqUEB0nAcqQBZdBvYkx67OpOezQxz5IWp00FMXcA3Q6HfgyzDtDr5i7mmFXv0XIHyZQGiQcVAn5Qyyfs5qnhrxck0veq8hyIx1HAMper3iUlzJsNAnwD0eqi80ncx1q5IBXqVUWgIosujMaK7dCAWdTw0gD0v8h5mmAErTlyK1HoOefH7PW8vZhhMaQknZ1Qixi2tKP9H8GoUnRAiKTcTKCDIzew+vbpIptqPdBTrz0WFxe8z51uq7TZ7C5/sHwF0ejBuPT1CLhCPMnLmbL2kTiOPsnRjrdGusBeoGhrRGaitx6NHLHXcjiJ5H5Q9C3n2s0pK2EEAKR83Y07a9809YZ/ZckDhxZRMIQhFIXkf32zp+1zYnnQwN1rqG2F1lZ8aqUGugWUqkVpIPIA9EoyTgL9O1GN3FpdTMIQMTiZmdT7aRsqIUQDiHEHCHEjzW5oAMRNayyfulGtm8qSGl82x6tOHFof7zpsaXBnjQPVz17Mdn16piet3LuanTd3EtyeVysX7qpagvfTcp2lPHxo19zcYsbOL/R1Tx32WtsWFYz1xZCJNaBRolqgVxvlGuXl5hHDY0svCF+TmcbRL0J4DsDyMDI7lBIXdTJDA9kv45wNgGiNxhHe1L6CsogsuS1mPeU+D17EQ3+RmkwFZF5a2LxJlMUcHUHR33iy9PLcYOjcRXntdldqhKjvg1YgiEpZpMCUkq+eWEUXzz9Lbou0VSNll2bcfeHN9Gic9OE5976xtV0P74LI4aNZtv6fJp1asKF955F9+PNO2UA1G9ej7WLN5ge01SNuofk7tH7SYXSojJu7Hkv2zcWoIYM7378F5OZ/N0MXhz/aM1sbPrOBv/XxJd8Ow11Nv+XmOcxR0BdbNp5RQZGRKsqy0MTVSwnj0MglFykth1Z+iIEErXA2hUdQhORge+R/uHRdlWtjQ3TuEIft1EhWb556hsIpW+D3Eic6JGzabSzyq4bp25E+jWGIRaPW0RIBMI3OMX12+wpKXnUQogmwEDg/ZpdzoHFZ0+M4NPHR+AvDhAsDRpZG7NXcnvf/2PbhvyE5woh6Hdub16d8jRfrn+H58Y8lNBIA5x928A4L7x8roat6ie9OVQHw1/8ge0b8yuMNICu6QRLgwy75q0auabIuMNIy4uRy/SBo6HRUFadj2XlonAYj/iVkLofSoZR9TLyBDibgVLH6Pgd+AHDOEp2WkHzUNdOgsgdj4A60wg5RJZiePiV9yvSwNkCkXm38T7Cc5H5F4O+MTpWAIpRPJN5H+SOiBYAeYxu4iIdRJaRDuhqawgmZb+G8bmWV3A6jWtmPYFwNKyGD8YmFVL1qF8B7gEsS+OEENcC1wI0a1aNlWf7KYGyIF8/P4qQP9ZbkRJCgRAjho3mhmGXV+s1e57UjdOvP4nRb41BDarousSb7sGT5uGRkXdX67Ws+O3jP1BD5nm265duYvvGfOoeklet1xRKBtT9DgKjjY4h6OAdiPCdhVDSkY5GoCYoNFF26S2ozjYM+O5WfMfhRNR5Aen/1GgaYOrdO424uNxuMYdG7I0jjJEdUs/QE0FHeM8A70kI4UaqC5AFQ4nfcPRAnZdRPNG+jzmvIrVNxs1MZIC7F6JSvrbwHAP1fkP6vzE8eGcLhO+C6q0utUlKUkMthDgd2CqlnC2E6G81Tkr5LvAuQM+ePavtT3x/ZeWc1Thc5ptPkbDGjJ//rnZDDXDdC0MZcNEx/PrheIq2FtOtf2dOuOSYWqtmDAetH+cdDoWgf09DCOYI4TX0NtLOiz+WdjEy+BumWRLCZyJOX91/vopxncBPWIoyCQUyb4Pip8zXaYoEbSsi9/M471YWP2cxT9DoKO4ZufPSjsYJ483C0QCReUuKa7KpCVLxqPsAg4QQp2E8Z2UJIT6TUlqLzNrg9rmRmnU+rsdXcyphbbq35Obu1mLtNUm347ow+dvpSJNNTbfXRaOWCbp91BDC3R2ZfgWUfchOyVEvCAci+634kmpXD0i5+s4BjragLSNh/nVoAolvAALhbA95XyJLhkE4RX1q4TSaD1Qy1BXqfVZEFiFlCCE8RjWl9IOoE9Os1mbfImmMWkp5v5SyiZSyBXAhMN420slp070lXot8Z0+am1OuqkKro1pESkkoEELTdi/D4dKHzzO9CXnSPFz+xIU4nHvHGCiZdyDyvgDfueA+FjKuR9QbZyrJKZQMyLgZyxZRMYN9iDqPgOe0JANltO2U1Q1agKsTwtUZJfcDRM6bRsw4KTo4m5vPZ71opFaIXngrcsvhyK39kFuPQi99P6583GbfwM6jriEUReHu/92IJ81N5eplt9dF49YNOfWq41OaRw2rzJ2wkJlj5lK2o6yGVmsY6F8/HM9FzW9gUNZQzsi4lBeueIPi/FTEiXbSsksznvn1/zikbSM8Pje+DC8ZOelc+/wlnHH9yTW0+tQQri4odZ5EyX0PJeNGhGKdBaNkXAtZD4OSLA9ZGvog2qpEVwZPf0T6paBkYt7x+55YyVV9R2oRGO+ZRtin8tWEAE8/LI21qzsUXAihsRibrGFD36T0VWTJsylc1Ka2ETVxB+3Zs6ecNSvBo9dBxNJZK/ns8eEsmroUX7qX064ZwNm3n44v3dzbrsy4L/7k1Rvfi/4kiIRVzv3PGVz+xIXV3gHj86dG8tUz3xGstPnpdDmo17Qu78x7MaX1VkZKyebVWwkFwjRp1wina/9UK5BSIsvehNJ3MI9xp0U72ViFKYx2VEr2C8Z82mZk8dMQGgdo4GgS7fh9Sux1I2uR209PMG8U1zEoeR/ErzuyEpl/brSxcPl3XBixct9Q8H9k/n5wIupPTngTs6kZhBCzpZQ9zY7ZHnUNous6hZuLEIqgReemDLzuRE6/7qSUjN7cCQt5+dq38RcHov/8hIMqI1/5iRHDqrd0t6zYzxdPfxtjpMHQFSnYXMTYTyZWeU4hBI1aNaBF56b7jZGWUiL1IiNuG0UIgUi7DBx1iU+h84LUsd4gTIOMGxF1dnqpwtEQJedVRIN5iAZzUeqNjTPSAMLZHNy9SFrKrv5lGq4QztZGL0LPSRjhFjd4jkPkDgd1LtYblhFkcFzia1ogpYpe+gH61v7om7uhbz8TGfx9t+ayicX2qE3QIlpKsdR/V21h67rtNGpVn/rN6sXOoWk8ds6LzBm3gGCZ8UV2+9y4vS5emfwkzTs2sZ539RZu7nU/xdvNww4ZOemM2PJBtcV7p/04m2cu+S/+YvO84S59O/DypCdSmmvH9mJ+/d94lkxfTv2meZx2zYm1kr+9p+j+b6H0ZaPkHMBzDCLrYSMjAgwDXvIqBEcZZdWujkYD29LXotWOJjgPQ6n7zW6vSeplyO2nJS0XFw2WVukJS8+/KPFmo+cMlJyXUp4PolKohVdDeBYxNwHhg/QbUTKuixtP+E+k/1vD6/cch/CdiVAOTOGwVEjkUe8frk4toOs6I14azfCXRlO0dQfp2WmcedMpXPLQubjcsZ7U9o35PH7+MFbOWY3L40INqXTp25EHv7y9ogvL+M8nxxhpgHAgjBoM8/SQV3hn7oum6/h39RZuPPxeSous49FqSCV/U0HczWF3SfYdFxYCUbuyZPpy7jvpCbSIRigQxuFU+Om9cQx99HwuuPvMalhpzaCXfRRV36t0owr9gdw+F+r9jFByEUo2os7DUOfhiiEyNDlJGHnP+iMKJR2y7kcW3YZ1DngjjLzsZAUzlXB2SGyo9d0o9w9PBvVv4jx1GYDS15Bp5yOUHOMlGUEW3Whktsio8l94hhFiyhthF9KYYIc+orx45Zt88thwirYaovFlRX5GDPuRB09/JubRUg2r3Nb3/1g6YwXhqKh/OKgyf+Ii7hrwaMXY71//OcZIlyMlbFz+LxtXmHtJHz74Jf7ixLKVWkQnLSuR1kPV6NqvE5pqnuXhTfdwwsX9ks6haRoPDXoWf0mAUCBcsc5wIMynj37Dynlr0DSNKT/M5MkLX+axc19k/Bd/ooar0Ji2BpAyBKWvEF+FqBtiTmWfW5/s6pagsa4HPNWQ2eMZAEqCG7JegMwfEhOuST5nXxJ+9ZWqFyTJwA87jW4cTgj9sXOs/xsITd9lfAD0fOSOe6p87YOBfcJQF24p4qNHvubWox/g/lOf4s9vp+92etjusH7pRiYOnxpXRRgOhFkydRkL/twpBD/l+5mU5Jei75IjHVE1Nq/ayvyJhqLYjm3W2RIOl4Oxn07imkP/w1m5l3HD4fcwacRUpJRM+WGWpbASGN7vof06Vau2dFqmj8sevwBPWmz5ueJQ8GX66H2m6dNYDHPGLTRV7gNQwxG+f/0X7uz/KM9c8ioTv5nC5G+n8/L173LdYXcnfHqocdQFWH8NQoYus16K9H+LLPsAGfrLeGzHaANG2lDi0/gUEF5E2sV7vDwhXIi8UeDsbL3GyFJk6XsWx03m9PRNIOrkQ6SdX+V1Jm60IGNvaP6PMS/P1yD8N1JLLK9wMLLXDfXqBWu5osNtDH9hFEumLWfWmLk8f9lrPHLW87VmrKf/9LdlcUrIH+LPkdMqfp43abGlqH/IH2LRlKUAtDuitWXIIFgaZPhLP7Bm4XrKivysmLOaF654g/898AV6kvecmZPJ9cMuY8JXf/Hz++NYu8RchKmqnHfnIO58/wYaVipIkVISKAlwaaub+PNbM4H7neRvKkDXzT9DXdOZ/8cils9eSbDSZxcsDfLvqi28efuH1fIedo9kLaz8hjxq8ePIkpeQRTcht5+CjEqUisy7IOM6o/xapAFucHVH5I1AOKqnVF448hC5nydYayhxs4Jd5xNuRJ2XMOrXKs/pA+8AcB9T9TV6T0hg/HVw9670Y4ImvcK1G93WD3z2uqF+asgrFeGDcoJlIeb9sYjxn0+ututsWrmZ5y9/nXPqX8l5Da8ypDeXG7G4ZPuplY9n5WZYbuK5PC7S6xh/rEPuG4zbRFPa6XGCEIR2KaUOloUY+d+f6NirnWXMuE69LC599Dxu6XU/L1/3Nm/e/iE39ryXB057Ki5jY3c47sI+ZNfLqnh/UpcEy0KE/GGeG/oq65dutDw30Yahy+Ni+6bCmN9xOZFwhD++mbL3QiCuLlh/Ddygb2FnF5WI8biurUcWGptjQggjJ7v+NETe94j6k1DyvjSyNqoTWUrCLSW9avnuwnuckRXiHQSOVuA6ApH9HKLOS7uX+uk9NaqZsusavYb+iLPS34ezHZZIDRRbPnVX9qqhXr90I5vXmDcDDZaF+P71X6rlOqsXruPabnfx+ycTKd5eQtHWYsZ+Ookr2t/GQ2c+R9djOiAc5h+FJ93LMWf3qvj5hEv6WRpqTdPpe7ahG9G2Ryvu/+w20rJ8xr9MHy6Pi8atGlgvVEraHdEajy9eAc/jc3PR/YN5/77PCAXCBEqChPwhwoEw8/5YxMvXvm0yYSyB0gCj3xrD3Sc8xgOnPcWEr/7CXxrglw/GcctR9zO07c0s/3s1WiTeq4+ENb5/zfr30a5naxq3bohi8jk6nAqRRIZYQqBkT7uV7B5CuCDzYWJV6MDYnHNhXhauQWTNLp1X3Ahni5rLP1ZyQVhpQwPOqsvHCldblOznUOr9ipL3OcJ7ym7n5wvhRuR9E43Lu41sD5EOaUMRdZ6LHZtxE/GfN8ZraecjlOrbfzlQ2KtZH8X5pThdTkIWurxW6WlV5fFzX4yLP5cz46fZbFmzlb6De/HX99NjPF2310X7nq059NhOFa81adeY8+4+g5HDfozfLBRwffd7uP/z2+gxoCt9zjqSEVs/YO74hfiLAzTv3JT/3vAuumbumWoRncycDF4Y/wiv3/I/VsxdjRCC7u/meAAAIABJREFUxq0bcMPLVzDq9V8IB+I/q3BQ5c+R07npvyUVWSflLJm+nM+eGMHSGcspLSpDCEEkunFYHnuXuqzYALRCi2gs/3u15XEhBE//8iD3nfQEm9duQ2o6DqcDoQgeGXkXr970PhssGhd40tykZ++9L6eSNgjpyDU0NiL/gPCCowtEpmOZbSEUiKwGVyfz49WMEE5k+jVQ+ibx8V0vIuO2WllHIoSSi8h5DamXGk0alLqx1Zbl4zy9kVkPGgJUwoERw9bAewIi897aX/h+wF411M06HhKjW1wZRRF0OjrBI9IuSClRQyoujyvGK9i2IZ8Ny6zzUHVdsnnNVi5/4gJadm3K8JdGU1JQii/Dyxk3nMzQR8+P8zIuf+xCuvbtyEtXv2XoSke/y5FQhKKtO3j4zOd4Y+azNO/YBJfbxRGndKdgcyE3HXkfRVuLLdeiOBSkrtOyazNen/4MZcV+IqrGzF/m8P59n7Fy3hpLu+H2uti4YnOFodZ1neEvjubjh79CDZsLDJllpSTCk5ZYSCqvUQ7vzn+JRVOWsnr+WrIbZNNrYA8cDoVep3Vn08rN6Lt0VvekeTj/rkE4HHtXEEh4+hqbbIBU5yPzLyFxDbeMEUKqDUT6NUh9O/i/inZbF4Z4VObdCO9xtbqWRBgNbxM3vVXSLkB6B0L4z2he+hEV3W9s4tmrhjozJ4MThx7L2E8nxXl0Lq+LC+89K+kcWkTj86dG8t2rP+MvDuDL9DL4ltO4+P/OwelyMvWHmUnnCJQEmfXbfG59/WouuOcs1HAEl9uZ8DGw/RFt2LGt2PS7rIZUvn7ue+756OaK1968/SMKN+8wDSuUEwlH+OzJkXz9/Cge+uY/9Dz5MO475Unmjl8Yl2Vids2cBkaLrpm/zuGFK96gcMuOJO+8aoQCyQ27EIIufTrQpY/RwHXrum3c0e9hSgpLY4y00+1ACIUBlxzDBSn8nmsTWfo+SXOgRY6hsleLCKEgsh5EZtwQVddzgrv3flskIpSMqFCVTTL2esHLTa9eSSgQZtLwqTjdxnIcDoV7P72Vll2Tb8g8ft5LzP5tXoWhLyvyM/zFH1j+9yqe+OG+isf8RCiKwBv1FoUQuD3JiwfWLFyHy+My3SDTNZ2Fk/+p+FmLaPz1/YyERrqcSDhCJBzhsXNepNVhLVgydVnSc4SAVt1a0LBFfZbNXslj574Yt1lZHZQWJs7vNuOhQc+xfWOByY1G8MQP93L4ifHqdXudyHISe9PpiJx3q11vJVWEkgsmZec2By573VC73C7u/fgWrnrmYpbOWIEv08eh/TqmpA+xbPZKZv8+L84bD0U32JbOXEGHXm3/v73zDo+qzP745713WioJSQiB0Kv03kWKgIgisnZXxbKIYsHF7tpXdy27q2tdBESxsBZQ1x8qFgRFSugloZcQCGmklyl33t8fE2JCZiaTkArv53l4nszMnfeeOyRnzj3vOd9T1j3o0wabmbHXjKqW3aGRoX6/BEIjgtnxSxJuw027nvFIH6VrvrAXO0haV7WTBghuFsKjH3lylIuf+cxrHrs2qG4r+IFthzm2/4TXuwG34WblkjWN01HrrcE44ONFMzT/EGHuUq8mKc5tGtxRnyK6VXOip50+acM/65dv9tlkYS9ysParjcx49ho69G7L/i2HvDoMa7CF0VcMp8uAjtU6d7se8US3juTYvhOVXjNZTBxJTOEvl/4N8FSD2EJsFOZWMyINQIbFZNa58ckrievgqSZJWrunynLDmmANtnDVA1Or9Z7j+0+gm7xX07gNt89BvA2NCLkZ6Uig8qadBqYuaJb62UBUKE7R4HXUZ4IQwrdQhfBoVAgh+Pt3f6Hf2F6YrSZPbXPpa3GdYrnr37dy/8I7a3Tuxz6+j6CwoLKUDXg29QyXgaPEWaZ8Zy+0U1Jkr3BcbWG2WYjv+nvdqa9hBWeC0AR3/GsG3YdUL4ps2aGFz9y6pmu06dY462WFdSQE3wBYKWsIEcGgRSEiXm9I0xTnKI0moq4Jwy4ZyJK/L/Oaj7XYLAyf6hngGRYZygsrHufE4XSO7jlOdOvmdOhV/eGcG77ZwofPfUZy0jGat4zgD3MuYd72l/ny9W/Z/MN2QiNCOH4gjUwvE8YNp0FIRDC6SUc3aUi39NnhWB2sQWYGTuxT9vjiP13Ih89+5jV3XlMsVjPjrqt+t1rn/h2IbRfD0d3HKrXFm60mpt87pbZMrHW08PuRQVORxctAZiMsQ8E2uZJIv0JRHzRpR925XweGTB7Ahm82V3DW1mALAy7sTbdBFZsAWrZvQcv2NZvZ9+k/vuK9Jz8pq8cuyC7kzfsWMfTiAfzlv/chhEBKySTT1T7XKCko4aPk/3Bw+2FeveMdHMUOjCqqOarirtduq1DaNv3eKaz65DeO7Ust+0x0s+5TdCkQdLPOjtVJhEaGEN26OS3aRFf9Jjx3Hc/+72H+PPoJCnOLKC4owWz1VNPMfOlGOvfvUGOb6gNh7oowq7peRcPTpB01wGMfz+G/L33J0n99TW5mPuFRoVx+7xSuffhypJSsWPQzS174goyUTKJbNeeqBy5j8m3jq7Vjn5uZx6LHl1SKUu1FdjZ8s5mdv+6m9/nnIYTAGmzxWZ8s3ZJtP+8kNCKEnIy8M3bSAOlHMio8tgVb+fdvz/Htuyv5Zv6P2IscxLaPZucvu6tsavFFcUEJT17+ItYgC067k26DO/Pox3OIblV1F15ch1jeP/A6v32RwO6E/US0aMb460YR3bp2dDAUinOBs2pwwOmC/6/e+Q4/LF5VwXFag62MvXoEcxcEnpf+9t2VvHHvwgqCQqcQAi66ZRx/fucOAF6ZNY/v3v3Ja0WIpgmsIVacdheGy/A6qbu6DLm4P899/ajfY5a/8wNv3rfIZ3dmddF0jejWzVm099+VtLoVCkXNOGdGcZV30sm7j7HivZ8rRbf2Ijsrl6zh0M7kgNd1ljh8qutJSYVc8y3PXUt06ygsXiZxu92S4vwSXA5XrThp8EiUVkX/8b2rXR7oD7fhJv9kAb8u3VD23P4th/jitW/49t2V5J2sndZ/hULh4axy1OVZs2yDz7ys0+Fi9WdrA16rzxhfWsAeZbihUwaWPQ6PCuPtrS8x45mrie8aV6dNEbYQG5NurnqaeVzHWM6/YrjXFnAhhNcvFc+L+BzZV1xQwuYftlNcUMz9455izvl/4Z2HFvPGPQu4Nv52vv7PimpciUKh8MdZ66idDqfP0jC34cZp965/4Y1258XT/8I+aF70pV0OJ4nr9lR4LiQ8mCvnTmXEZYP9ziY9VT5YE2whVvqP78XACX0qPG8YBoV5RZW0oR9YeCfT50whOCwIa5AFs9XM6CuG8eB7dzF3/h3c9dqtWIMtBIXasNgsWIOtxHWIxWrz7sQ1XSM0MoR/3PYWiWv3Yi9y4ChxUlJox1Hi5O2571cYuKBQKGpOk99M9MXACX359OWvvG7s2UJtDL6oX7XWu3LupSQs38zpXShSwncLV3Ll3KllTScAqz75jWX/Xu4zxaHpGkMu7o/JbOLwzqNkpGRW2fYtNEF4VCjNW0Zy+T0XM3HGmDJH7yhxsODRj1j+zg84HS5swVam3T2ZG564kqL8YtKOZHD5PVO48cmryM3MJzQiuJKc6oQbL2Dd15soyC6k+9DOxLSJ5vp2d3i1xWwxMXTKAB69+HmvXZ/2IjtL/r6M3uef5/eaFApF1TRJR31oZzJrv9qIdEuGThngtcyrx/CudB3Uid3r91Wo1rDYzHTs3ZY+o6vXXbbmiw0+R2RJCWu/3Mj0OZ66YMNl8O/Z7/iN2s0WEzc9dTWd+3dg94Z9PHDhM1XaYLGZmfnijUy8acxp55c8fNFzJK3bi6tUKa8wt4j/vvAl3y1aSW5GPmarCafdRb9xvXhw0WyvmtfBYUGMu7ZiK/2fXvgjCx79qMJGpC3EyqSbx2KxWbBYzT67Qw/vOlrlNSkUiqppUo7aMAxenPEGa5aux+U0kFLy8d+XMuDCPjzx6dwK+iBCCJ5f/ihv/fk9fnh/FZTWOY+/7nzueGVGtVMOLqcLXxUy0u3G5fzdKe/fetintOgpps6eVPYFk56c6TWtcjr2Igcrl/xayVFv+3kXu9f/7qTL25yZchKgLOrd8sN25ox6nAW7/uVzAEJ5Lr/nYjr2aceSF5aRnHSMFm2iuWLupYy4bDAZRzP9aqhEt64jEX2F4hyjSTnqZa8uZ82y9RXqge1FDjZ/v53Fz3zKzc9eW+F4a5CVOW/N5I5/3kRuRh7NYsK9RpKBMGzKQFa8t8priZ5u1hk48XdxIbfh9v9FIODL17/l2P4TXPvIdL5+ewVFed6GfXp5q5d1V3+2NuCcu8tpcDI1m9++2sj504diL7bz5RvfsvrTtbjdkvOvGMbUOyYRUm7Ked8xPenrZUO1RdsYug7qROLavZX2A2whVq7486UB2aRQKPzTpDYTP335K695XHuxgy9f/9bncFVrkJUWbWNq7KQBBk7sS9vurTGfJoFqDbLQb1xvOvVtX/Zcp37t8Yv0TGXZsHwL9454jK0rdwVkgy3UyvjrR1d6Pv1IZkDvP4WnYmMbh3Ym84eYW3jnwQ/Yk3CAfZsOsvCRj7i61Uz2b/U9zaU8j340h+ZxEWUaI5omsAZbGXf9+YwqN8LsXOekvYDducfIdhQ0tCmKJkiTiaillJw8kePz9ZJCOyWF9oDqimuCpmm8/NOTvDlnET997Bm6q+kal8ycwC3PV4zkLVYztz5/HW/c+65fwf/TUxX+MJl14jrEcv4Vwyq91qF3W9Yv3xzwWpquYQuxcf+4p7x/8RXZeeSi5/jv8Xlomv/v8pj4KN7b+xqrPlnLxhVbCY0MYeKNY+g2uHPA9pzN5DqKeHrHZ2zI2o9Z03G6DYZFd+GJ3lcQbq6b31XF2UeTcdRCCCJahPscZWUJMmMLqXnEHAhBoUHMnX8Hd79+K/nZhYRHhWK2mMk8lsXJEznEdYwlLNIzgqjbkM612mTSe/R5PLX0Qa9DDSbOGMN/X/oy4CYas9VEyw4t/MquFuQUsn1VIv3G9qpyPYvNwoQbL2DCjRcEdP5zBbd0M2vDOxwpzMQlDRxuzxfz2oy93LlhPotH3NVgwwe8IaVkV24Ky49vpsjlYERMV8bG9sSsNRk3cdbSpP4Hpt87hQ+f+7xSFGgJsnDprIlVRn+1hcVmISrOQvrRTP72x1fZm3AAk8WEy+HigqtGMObqETw1/aVa04UODgvi0lmTfN4ttOnWmiGT+5Pw3dZKMwlPxxZiZfwfR6Npmt9j3YbbMw9SUWPWZ+7neHE2Llmx8copDY4WZZFw8gBDohrHnYeUkqd3fMZPaTuxGy4kkp/TdvHm3hUsGDaLKGtY1Yso6owqPZsQoo0QYqUQIkkIsUsI0WDjjq964DIGTuiLLcSK0AQIj+PpOaIbNz1zTb3aUlxYwj3DHyXxt71l2tOOEierPvmNx6e+UK2Gmqpwu90Mnty/wnOGYVSoQnni07lMvHEMZpuZ4PAgzFYzvUZ154F3Z9NrVHciWjSj68COzJ1/Bz1HdGPx05/4rGIBT665sepFNxU2njxAseG9Nr7YcLDlZGD7APXBN8e38lPaTkoMJ7K0V6DIcJBWksszOz5rYOsUgUTULmCulHKzECIM2CSE+F5KmVjHtlVCN+k8vexB9iTs59dl65FuybBLB9FzRLd6v4Vc+fEaCnOLKuWga1MHWtMEZpuZB96djS3Yk9bZtmoX7zy4mL0bD6LpgiGTB3D7P26kdec45s6/g1n/uJHUg+lEtAgvU6grX8732T//x6InllTZXNOyQwuVZz5DgnUrutAwZOU7F5PQCTbVLFUnpWRn7lH25aUSZQ1jREzXM05PfHj4F0qMyr+7hnSz6eQhsh0FRFr8TxZX1B1V/u9KKVOB1NKf84UQSUBroN4d9Sm6De7c4E4k4dstPuVMq0IIqkyLCCHo2Lc99y+8s6yiZNP323hy2otl5YmGS7Lu601s/yWRtze/RMv2LQhpFuJT57m4sIRFT/y3SifdPC6SF394slHlT5siE+L6sOjgz14dtSYE42N7V3vNLHs+92x8l5Sik0gp0YWGEIIX+1/PoKhOVS9Qilu6sRsubLoZIQSZdt9CWmahk2VXjrohqdbXsBCiPdAfWF8XxjQlQpoFB+RwyyM0wfjrz+fXZRu81mOXR0pJ1vHsMictpeTfs+dX0pSW0qPI98Ezn3L/wtl+19y1Zo/PGYYAoZEh3L/gTkZcNlg56VqgbUg0V7UbzqfJ6ypEqzbdzPXtR9EqOLLaa87Z9B4H89MxqOj8525ezKfn30cLWzO/7y8xnLy1dwWfH11ftrlp0UyEm3xXoDilQUtbRLVtVdQeAe++CSFCgc+BOVLKSqUXQoiZQoiNQoiNGRkZlRc4y5h40xiswdW7dQ0KtXHXa7dy7cPTylIZ/shOyymrDc9KzfY64gs8G39rvkyocr2qfG9811aMnDZEOela5O5uk3m2z9X0jmhLtDWMvpHteK7vtdzeZUK110rKPcaRwoxKThrAJQ2WJvuPn9zSzV0JC/jkyG9lThrA4XaR5cj3qh9m0UxMjOtDqFmNIGtIAoqohRBmPE76QynlUm/HSCnnAfPAMzig1ixspPQ+/zxGXDaY375MOG0wgYWrH5zG1//5nuKCYpx2F2arCZNJ57nljxESHsy1j0xHCMHHf1vmd25ieHTY75UsVYXuAXziPUd291nXbQ22MO66UV5fU5wZF8T24ILYM59cfiD/BMKHHKPTbbAr1/9U9/WZ+9mbl4rh5ZdFArrQkFJi0U24pURD0DeyPQ/2uOyMba8ux4pOUugqoW1IDDa98Q2n2JuXytfHNpHjKGJQVEcmxvXBpvuQC64FqnTUwhNeLQCSpJT/rDNLmhhCCB56/25WfryGz1/5mpOp2bTv1ZbrHp1On9E9uO7R6Wz8bitH9xwntl0Mwy4dWDYNRQjBtY9M5w/3XcIrd8zj5yW/VdLMsAZZKgx/jWrVnOjWURw/cKKSLZquMXyq18EQFbAFW7n1+euY/0hFkSWTWad5bAQX3Ty2ph+Hoh6Isob5dNQagrggTypFSkm6PQ+T0CqU1a1KS6TE7Xuz25BuOoe15Kq2w7EbTvo370DX8LjavYgq2J17jCe3f8rx4pOYhI4bN9e2G8XMLuPRRONopH5193I+S16P0+3CjWRVemJZGWPr4LrRtwkkoh4J3ADsEEJsLX3uUSnl8jqxqAmhaRrjrz+f8ddXntCtm3SGThlYYahAeRwlDlZ9uhYkRMY2IycjzzNJBo9D7Tu2F1c/+HskI4Tgrtdv5enpL1XIUwshCAq1ccOTVwZk87S7LyYyNoJ3H1/C8f2pmG0Wxl9/Prf97XqCQlWnXGNmcFQnrLqJIqPyJrZZM3FF26H8dGIn/9r9f+Q4CnFLSduQaB7pOY0+ke2qzn2VMq3N4CqPkVKyL/8EBa5iuoTFEVYLXZapxdnM2vAORaUljXY86ZmPjvyKId3M7jbpjM9xpqzN2MvSo+uxl/vCKzYc2A0nD235kA9G3l0n5z2rZiY2FdKOZHDvqL9QVDqZW2gCk0mnY9929LmgJ6OmD+W8oV285oq3rtzJvAcXs3/LIYQQDL6oH7P+cRPxXatf82wYBpqmqZx0E2JnzlHuSliIIQ3sbhc6ApOmc1uncbQLieHx7Z9UcCIANs3M/GG3k+Ms4v5Ni31G1RahM6PTGG7rPN6vDduzk3l8+xJyHEXoQuBwG1wWP4j7uk/BpFWtyOiLlxK/YtnRDbi8VMlYNTPfjnuUEC8ljVJKEnNTWHFiO07DxcgW3RkW3QW9DiLwuxPeZX3WPq+vWTUzH4y4i3ahMTVa29/MxCbVmXi28MyV/yD7RE5Zvli6JU6HiyOJKdz0zDX0GNbV53v7je3Fmwkv4HK6EJpA12v+h3Em71U0DL0i2rDsgrl8eXQjO3OPEmtrxuVthtApNJZpq1+u5KQB7G4nb+79nn8NvJFeEW3YcvJQpTy1AELMNq5oO9zv+Y8VneTujQsrNfIsPbqBYpeDJ/pcUeNrW5e5z6uTBjBpGnvzjtO/ecXSU7d08/i2T/glIwm74UQCy49vIT44ireH/olQU+1ugp4oyfb5mlnTSbfn1dhR+6NxJH3OIVL2pXJk11Gvm3olhXY+/+f/AlrHZDYpR3uOEmkJZUanMbw84AYe6DGVzmEtyXYUkmn3roMjgc0nDyKE4JVBM5jRaQy2cg0yGoJRMd15f/hsIizBXtc4xQeHfsHhozHm6+ObOZSfXuPrCtZ9V0JJKb02CC07uoFf0pNKOyo9FBkODhWk89Kur2psiy86h7b0uU/gcLtoGxxV6+cEFVHXO5kpWZgspkr10KdIq6ZkqeLcJdOez5LDa1iVnoQuBC4/ImB6afWQRTNxe5cJ3N5lAobbIN9Vgk23BFxZsfHkAa9VI6d4dc9yXhk0o1rXcYppbQbx6u5vvKZmBII4L7XcHx761evxTmnwY9pOHnZNI8hUe9UYN3QczZqMPZXOaRY6A5t3IDaoburNVURdz7Tq3BKHj6koQgja9YyvZ4sUTZGjhVlc8+srfHxkDUcKMzhYkF6m0XE6utC8dkHqmk6EJaRa5W8hfqJe8ETuNeXS+EF0CG2BVatsj0O6uHTViyRkHajwfJbDd0elJgQ5zsIa2+ONHs3ieaDHVKyaiSDdglnTselmuobH8de+dac3pCLqeqZFm2j6ju7B1p93VdKjtgSZueqB+q9Z9YZhGBzYehiX06Bz/w5e5VUVdYvT7UKUbhaeznM7l5LvLPHpnE8hgGDdwu1dLqwVmy6JH0hi4jGfr/uL6t2l+eeMkjwWH/qFXzN2Y9FMXNJ6AFe0HUawycoL/a/n/s2L2ZufWuG9TreBE4P7Ny/m/8Y8XNaAE2uL4HCh9wY7KaF5HbS9Xxo/kDGxPViVnkS+s5jeEW3p2Sy+TjfllaNuAB79eA4PTXyWo7uP4XK4MJlNuN1u7vjXDL8bifXFL0vX8+qseTjsDkTprMkZz17D9HumVP1mxRmzPfsIr+xeTmJpA8uA5h2477wpdAnz1DTnOYvZkZNcpZMGT37a4XaxP/8EMbbwM7btstaDeGX38gqdjeXp3qwVb+/7nk1ZB4mwBDO9zVAizMG8uucbtmYfRiLRhAApyjos39n/I/87tok3Bt/KzPXzSC/J9X09UrIidRvT2w5lX34qaSXeh4lYNROXxg/EWkfNMmHmIC5pPaBO1vaGKs9rIKSU7PptD0nr9hHSLJhRlw8hPKrhNX+3rdrFYxc/XymHbg22MvvfNzP5Fv+lW4ozY2v2Ye5JeLdSDjRIt7Bw2B10CoslrSSXK1b/02uFhy+iLKH839iHA2oaOVKYycoTO7G7nQyJ6ky/yPYVosUVx7fx1I7PKulsW4QJTQjcyDJHbtVMON0G7iq+VCyaTr+I9mzLSa7yum7ocD53dp3EpT+/4FNMqn9ke14bfAuWJjT0QJXnNUKEEPQa2Z1eI7s3tCkVePcvH3vd6LQX2Vn0+BImzRhbbwMazkX+kfS1182xEsPBG3u/458DbyTaGkaQbq6Woy42HOzOO06PZt73QPKcxSxNXs+SI2vIdhQi8DjcDw79QruQGOYNmUmw2ZOfntiqL27c/Gv3ck+1hZSE6Fbs0kWBq6Ikgt1H5H06DrfBpuxDXpUGyxOkm2kbEsPGrAMUubyrV+oIuoe3rhUn7XIb/JqxhxPF2cQHRzE8pmud1GdXhXLUigrs2+R7Myj/ZCG5mflEtvCv0KaoGUUuO/vzK0sEgCeFsT7T02ihC40/dR7Pa3u+9dsSXh4hhFe9aYATxTnMWPsGec7isjrmU2kVu9vF3vxUJv/8PC/2/yNDo7sAcFGr/kyM68v27CO8lPQ1hwvScZ4WYVeXQO7uHW6DRQd+xqqZcLm9n89AsjX7MIZ0n5FTTco9xj0b3/Xkx6ULc6mG+OuDb6FjaGyN160JKjRSVMAS5LuUSbrd2ILrTnjmXMFuOH1Gg34pzT4cLkhnXea+gKNV8GzydQ/33r36/K5l5DiKfDabABQbTu7f/EFZ3vwUz+36goP5aWfspAXQNjjaa8VHeQzp5ljxSQ4WpuPwc859+anMWPtGpQg/UIpcdmYnLCDXWUSRYcfpNigyHGTZ87lzw3yc1fjsawPlqBUVmHDDBZgslW+0hCboc0FPpQdyBhwqSGd2wgLG/PA04398lqt++Re/Zewpez3YZKVrmHcRJIFgeHRXDhekM2PtW/yasSegzUQ4pX890mvDSIGrhE1ZB6vMIYOnw/E/+74ve5yQdYCMklyvsqvVxaqZebjXNKKsoZhOi4J1Hw0m/nBJNwfz03k5MbAGstNZkbrdaxpGAiWGi9XpSTVat6YoR62owB+fuILo1s2x2H6PbMwWE6ERIdz71p8a0LKmTUpRFrese4uNWQcwpBtDujlcmMFDWz5iVdrvw5Lu73EpNi9RpVnTuaPLBP6951uKDYdXJ90rPJ5ZXSbQwhruuU3XLQTrVmZ0HONT/7rQZa+WKt26zH18c2wL4EkN2H2kUwIhSDdj1UyYhI4mNF5M/Ipr241kcqv+WDUTAmgTHEVXH3cCVeGUBj+c2EGJj7mV/tiXn+pn3qWdwwX1q7mvctSKCoQ3D+PtLS/x9dsr+P79VbicBiOnDeEP902hecvqTyRReJi//0eKXY5K7tXudvKPpP8xusV5CCHoHdGWN4fcxtzN75Pt+L1ZQxOCR7cuIbkww2ckvTMvhf0FaWW52WhrOG8OudXv1JcoSygWTQ94Y1ICf0v8gqNFWURbwzBrJoxqbGoKoH9kB+7sOpEfTuxgafIGXNLAZRgcLEjjjX3fMSqmO6sufAopPPn4a399NeD1T0cTghxHES39pPS8ERcUiUUzeS1DtOksfDGKAAAT60lEQVSWCqWOOY5CtmQfxiR0BjXvWKudkKdQjlpRiZDwYK5+cBpXPzitoU05a/g1Y4/P9EK2o4gTJTlletKHCtIrRXMlhpOUoiy/7dtA2eaiUxocLz7JX7b9l3lDZ/o8PttRSJgpiPxq5HJLDCfvH1rNhyPuCTj9Ap70TbfwOGZ0GkOb4Gg+T15fKbddYjhZk7GHbTlHygSYuobHcaAgLeDzVEBCpCWk2m+7uFX/Cmme0xnfsjdSSl7d49GmNms6SDBwM6fbxUxvO7Rm9vpApT4UinrAl5APUNoE8vuf4geHvE8Ed0rD7zqn45JuknJTSC70rh9jN5zcsu4tv4pwvjAJjaS8FB7uOQ2rZkYLwC6JZHfecR7a8iF3b1zocwOy2HDwf6XpFYCZnfx3VeoIzKJy96ZVMzE1flCNml6aW0N5qveVWDWTxwmXrmfTzbzQ/3pCTFbeO7SKpckbcLhdFLrsFBp2Sgwnr+xezppyew+1gYqoFYp6YFxsL746ttHrBlWsrRktrL/fSmf4UMEDj6iSLNdQUhUmTedIYSZtQ6IrvfZT2k5yHUU12gp0S8mhgnTOaxbP3/pdy49pOziQn0aMNYz1WQf82ldsONh3Wov46ZQfjtA6pDkDI9uzKfuw12Ml0LNZGxLzUkBK3Eh0oTOgeQfu6T65BlfnYXxcb3pFtuWrlASOFGTSMSyWqfGDiLaG4XIbLD642nvNu9vJvH0/MDKmW43PfTrKUSsU9cAtncfyU9oO8p0lFVIgVs3MQz0vq9D5Fx/cnN15x32sJHl14Aze2PcdSbkezY0g3eKzDK3Y5eDVpP9jZdpOrm8/ik5hLcteW5exL+A67NMpcTtZcuQ3NAROaTCweUfeGvInQkxW3j+4ijf2rvCbFqkqYdIhtEWFx1e1H8mu3GNe7bXoJu7pPpnmllBWpyfilAZDojrTrYabkOWJtTXjT50rR/QnHQU4fNRxAxwsqLncqzeUo1Yo6oFYWzPeH3EXb+xdwc9pu3C5DfpEtuWurhd5xmSV4+aOY3hyx6eV0h8WzcSkuL4MjOrIwqg7KDEcSAm7co9y78ZFXlMJbiTJxVkkH8ti+bEtPNbzci5tMwgpJduyj5zRNZXPo2/KOsAjWz/ilk5jmb//p2rlrr2xKesgvZq1oVt4K3bkJKPj2Rw9UZJdod7bopnoFtaqTBTpmvYjz+i8gRJispWJTHkj1Esp5JmgHLVCUU/EBUXy175XV3nc2Ja92JufyuJDvyA4pUgncbkNvjq2ifVZ+7m54xgubzOElKIsHt/2SUANJ24kf921lOEturEseQPHa5Cb9oVDGmw+eYj04twaR+nl2ZJ9iO2bjuDCjU23oCMwpJt2ITEcLcrCLHSc0mBsbE8e6Tmt3sfJhZisDI3uwtqMPZU2eK2aielth9Tq+ZQok0LRSEkvyeWnEzv54NAvZDsKKzhjm25mQss+fHt8a7W7AifH9eWHEzvPuJvwdIJ1S2mNd9UIqk5/eMOqmXii9xW0D42hpS2iVobq1pSMkjxmrH2TfGdx2ZdTkG6hfUgM/xk6s1o63+BflElVfSgUjZQWtmbEBkWQ7yrxWsb29bFNNXK2Z+Kk/VV3BJLuCNatBOlm7ut+SQ36DT3aI8/s+Ay74WpQJw0QYwvnv+fPYXbXSfSPbM+QqM480nMa84fdXm0nXRUq9aFQNGK+T93us0OupvfCgTjpcFMQDrerQhrDJDRCTTaKDIfXqo5iw+nX+XYNi+PWzuMYHt2F5EJP+sKfXocv7G4XdybMZ9HwO+tdHOl0Qk02rm4/gqvbj6jT86iIWqFoxNRFajIQpsYP5NGelxMXFIlWWqc8vmVvFo+4y+/7vFkrEATrVv7a92rGxvbEplv4LWMPxhlcm8NwMX/fjzV+f1NDRdQKRSNmfFxvfsvc6zOqrgt0BJNb96dLWBwXte5HieHErOnoQmNb9hH0AOI7gUADhNAYGdOV2V0n0b5cyZ0QouaJajwboxtOHqj6wLMEFVErFI2YMS160CY4qlLnnU0zMzSqs1cBJ4DRMefxWI/LaW4JqVY3o0XoXBI/sGzsF3g2Lk/pOhe6StC0qtcL0s082edKfpv0LC8NuKGCkwYYGdMNk5duwupgbkTTW5xuF+sz97EqLZGT9oJaX7/xXKlCoaiESdOZN3Qmb+z9jv+lbMIhXUSYQ5jR8QKubjeCL1MSeH3vdzgNFy7pKWW7/7xLmNy6PwBT2wxiR04yd25YgENWziubhEYzSwgOw0kLWzNu6DCaya36+bSne3hrnH4aPX5HlLVee6NzWEsuiD2P1WlJFfLgVs1EjC2cdsHRxAZF8OOJHeQ6iyu93yx0LvZjZ33yY+oO/rprqefuQHgG8U5pNYAHe06ttWkwqjxPoWgiuKUbh9vwSICWqxt2uQ0OFaZjEjrtQ2K81hTfuu5tknKPVZpzGKxb+Oz8PxNdjcG3z+74nBWp2/0q7lk1M9+Me4RQk83nMYZ08+GhX/nwsKf8sJk5mKvbDWdGxzFlk9d35CQzO2EBdsNVVlViFjrNraEsHnE3EZbggO2uC3bkJDN7w4JKteM2zcyV7YZxd7fAW9j9lecpR61QnAPkOoq4f/NiducdRxcCEFh1Ey/1v4E+kW2rtZbLbfBS4v/4KmWjz6EBMzqM4c5uEwNe09/YrAP5aczf/yMJWQcwazqTW/Xjxo5jGtxJA8zZuIi1mXu9ptptmpkV4x/Dpgcme6qG2yoUZwl78o7z1t4VbM4+hFnoTIjry22dxxFt9T/BvpklmHeG3c6B/DT25h0ny1FAkcvOjpwjtLCF0zIootJ7pJQk5qaw/PgWCl12hkV3YVzLXlg0E4/0msbmkwc5UlRZmU8AR4qqJ6zvL0XQKSyWv/W/rlrr1RdJecd87ofqQiOl6CSdy+mr1BTlqBWKJsKWk4e4d+Mi7G6nZyQUTr5KSWBV2i4+GHk3UVU46xxHIb9m7Objw2socJXgdLswaTpv7fueGR0v4LbO48uOlVLy7M7P+SF1B3a3J+3wc9ou3t73PfOHzcIkdI4Xe29Bl8DazL21eOWNl3BzUIUBD+VxSoPwWmrKUY5aoWgi/G3XF5VyoS7pJtdZxHsHV/Hn8y4pez4xN4Vvjm2hwChhaFQXBIK/7lyK0+2qoN53amPw/UOr6dEsnhGl0pzfpW7zjLEqd74iw4G9xMVT2z/lub7X+K2sq06lSVPmyrbDeH3Pd5X+XwSCrmFxfqfrVIeAHLUQ4iLgVUAH5ksp/14rZ1coFAGRVpLrM4J1STcrUrfz5/MuQUrJ87uW8V3qNhyGxyn/mLqzSqGkEsPJewdXlTnqDw//6nV4gSHdbM0+jEsatA+NYX/+iUrHaAhGxXSv1vUZ0s3ig6tZfGg1BS47Vt3E1NYDmdN9StnGYmNkepuhrExLJDE3pazW3TNgwMLTfa6qtfNU6aiFEDrwBjABSAEShBBfSSkT/b9ToVDUFi634Vdn41Q1xw8ndvBd6rYKTjZQNbujRVllP2eU+B5eIKUksySPB3tM5e6EdytUfwgEwSYLs3wM0/W13pyNi1iftf93mw0nnySv4+f0RJaNvr9R1UyXx6TpvDboZn5OT+SLowkUGw5GxXTj8jZDa3WzM5AivyHAfinlQSmlA1gCXFZrFigUiiqJC4ogxOy91E1DMDy6K+A7Eg6EVkG/Dy9uHxLj8zinNPjg8C/0i2zPW0Nuo19kezQEutAY3aI77w6fTZuQqIDPuz0nmQ1Z3rsM00vyeP/A6sAvogEwaToXtuzN64NvYcGwWdzcaWytV6QE8jXVGjha7nEKUGlyoxBiJjAToG3b6pX7KBQK/2hCY063yTy3c1mlCNmqm7mt0zjAI41aE2y6mRs6jC57fHOnMezYlOxTwGllWiIpRVn0imjDvKEzyzRJaqILvSx5vV/lvU+PruXWLuOqve7ZRCARtbdPvtKnKqWcJ6UcJKUcFBPj+9tYoVDUjEmt+vF47z8Qa2uGRTNhEjo9m8Uzb+hM2oV6/ub8RcK+sGomrmw7jAtie5Q9NzS6C138lJUJYG3G75UdQogai/cXlpuP6I2a3iGcTQQSUacAbco9jgd8DXRTKBR1yIS4PlzYsjdZ9nzMmolmp91iz+g0hp05RytF3ToCiUcfw+52Yi3N+U6NH8RV7UbQzsvw2y7hcSTmHfNqh6DmjtnbNa1KT/L5evfw1rVyHiklO3KSOVCQRrQ1jGHRXRpt7vt0ArEyAegihOgAHAOuARpn9blCcQ4ghPDZ8j0kqjN3dJ3IG3u/QxMCw+3p+OsREc9Tva5kdUYS6SW5dAmLY2zLnlj8OKoLW/ZmhQ89bDey2pUdvhgX24tm5v+R6yyq9JqGOKNJ4qfIKMnj7o0LSS3OQUqJJjR0ofHygD/Sv3mHM16/rgmohVwIcTHwCp7yvIVSyuf8Ha9ayBWKhiXbUcCqtCSKDDsDIjvQvVnlqNQTYR5lRepW7G6DUTHdPKp2peVwbulmdsJCduYkYy83KMCmm7m09UAe6DG11uzNcRRy67q3K1SeWITO032uYnxc7zNaW0rJtWte5UhhJsZpA2mDdAtLR8+tslmoPlBaHwqFogKGdPOXrUtYk7mnTPAoWLcQFxTJvKEzy8ZcOdwuFu5fyWdH15HnLCbW1oybOl7AH9oMrZOBsqlFOWw8eYAYaxiDojrVSg319uwj3L3xXa93BlbNxIyOY7i1c8NvViqtD4VCUYGlyetZk7GnUudhclEmLyR+yV/7XgOARTMxq+sEZnWdgJSyzqd9xwVHcGnwwFpd80BBms9JOXa3i8TclFo9X12gBgcoFOcgHx9e47URxuk2+DktkSJX5UqMunbSdUW0Ncyn6JOO8CpI1dhQjlqhOAfJcvieQqIJ4XVjr6kyLLoLmg9HbdJ0prep1BbS6FCOWqE4B2kd1Nz3ixKaW0Lrz5g6xqyZeHnAHwnSLWVliToCq2ZiVpeJdApr2EnmgaBy1ArFOcjNncbw7M7PKzWTWDUTU+MHYdW9z2KsLfKcxTjcLqIsofWSUunfvANLR8/li6MJJOam0DIogulthjYJJw3KUSsU5yQXtuzNvrxUPjqyBgG4S2uLB0V1rJW6ZV/szTvO33d9ye6842hCEGkJ4d5uk7kwrk+dnfMUUdawRlHdUROUo1YozkGEENzZbRJ/aDeM1WmJOKXB4KhOFaaP1zZHCjP50/p5v5fJSY986zM7PseQbiY1kmG1jRHlqBWKc5hYWzOubDe8Xs61YP9P2L3odpS4nbyy5xsmxPXxuel3rqM+FYVCUS+szdxbYbpMeQqdJT4HIyiUo1YoFPWEvwG2biRm0XgnuTQ0ylErFIp6YVJcH0w+nHVcUCSxTaDxpKFQjlqhUNQLN3UcQzNzcAVnLQCbZuaRntMazK6mgHLUCoWiXmhuDWXxyLu5LH4wYSYbNt3MsOguzBs6kwFNQGq0IVHqeQqFQtEI8KeepyJqhUKhaOQoR61QKBSNHOWoFQqFopGjHLVCoVA0cpSjVigUikZOnVR9CCEygCO1uGQ0kFmL69UnTdX2pmo3NF3bld31T2OyvZ2UMsbbC3XiqGsbIcRGX2UrjZ2mantTtRuaru3K7vqnqdiuUh8KhULRyFGOWqFQKBo5TcVRz2toA86Apmp7U7Ubmq7tyu76p0nY3iRy1AqFQnEu01QiaoVCoThnUY5aoVAoGjlNxlELIZ4VQmwXQmwVQqwQQrRqaJsCRQjxkhBid6n9y4QQTUIhXQhxpRBilxDCLYRo9CVMQoiLhBB7hBD7hRAPN7Q9gSKEWCiESBdC7GxoW6qDEKKNEGKlECKp9Pfk3oa2KRCEEDYhxAYhxLZSu59uaJuqosnkqIUQ4VLKvNKf7wF6SClnNbBZASGEmAj8JKV0CSFeAJBSPtTAZlWJEOI8wA38B7hfStlotWuFEDqwF5gApAAJwLVSysQGNSwAhBCjgQLgfSllr4a2J1CEEHFAnJRysxAiDNgETGvsn7kQQgAhUsoCIYQZ+BW4V0q5roFN80mTiahPOelSQsDHlMxGiJRyhZTSVfpwHRDfkPYEipQySUq5p6HtCJAhwH4p5UEppQNYAlzWwDYFhJRyNXCyoe2oLlLKVCnl5tKf84EkoHXDWlU10kNB6UNz6b9G7U+ajKMGEEI8J4Q4ClwPPNHQ9tSQW4BvGtqIs5DWwNFyj1NoAk7jbEEI0R7oD6xvWEsCQwihCyG2AunA91LKRm13o3LUQogfhBA7vfy7DEBK+ZiUsg3wIXBXw1pbkapsLz3mMcCFx/5GQSB2NxGEl+cadZR0tiCECAU+B+acdufbaJFSGlLKfnjubocIIRp1ysnU0AaUR0p5YYCHfgT8H/BkHZpTLaqyXQhxE3AJMF42oo2BanzmjZ0UoE25x/HA8Qay5ZyhNMf7OfChlHJpQ9tTXaSUOUKIn4GLgEa7mduoImp/CCG6lHs4FdjdULZUFyHERcBDwFQpZVFD23OWkgB0EUJ0EEJYgGuArxrYprOa0k25BUCSlPKfDW1PoAghYk5VXgkhgoALaeT+pClVfXwOdMNThXAEmCWlPNawVgWGEGI/YAWySp9a1xQqVoQQlwOvATFADrBVSjmpYa3yjRDiYuAVQAcWSimfa2CTAkII8TEwBo/kZhrwpJRyQYMaFQBCiFHAL8AOPH+XAI9KKZc3nFVVI4ToA7yH5/dEAz6RUj7TsFb5p8k4aoVCoThXaTKpD4VCoThXUY5aoVAoGjnKUSsUCkUjRzlqhUKhaOQoR61QKBSNHOWoFQqFopGjHLVCoVA0cv4fwOTKOVRy6FYAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "ax.scatter(X[:, 0], X[:, 1], c=y_kmeans, s=50, cmap='viridis')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like `k-means` did a pretty good job of detecting our clusters! \n", "\n", "Under the hood, `k-means` tries to identify a \"centroid\" for each cluster. The two main principles are: \n", "\n", "1. Each centroid is the mean of all the points to which it corresponds. \n", "2. Each point is closer to its centroid than to any other centroid. \n", "\n", "The `KMeans` class makes it easy to retrieve the cluster centroids and visualize them. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "centers = kmeans.cluster_centers_\n", "ax.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5)\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the cluster centroids do indeed correspond pretty nicely to the \"middle\" of each of the identified clusters. \n", "\n", "This experiment went very well, but of course, things in the real world aren't that easy. Let's take a look at the Palmer Penguins again, for example. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import urllib\n", "def retrieve_data(url):\n", " \"\"\"\n", " Retrieve a file from the specified url and save it in a local file \n", " called data.csv. The intended values of url are: \n", " \"\"\"\n", " \n", " # grab the data and parse it\n", " filedata = urllib.request.urlopen(url) \n", " to_write = filedata.read()\n", " \n", " # write to file\n", " with open(\"data.csv\", \"wb\") as f:\n", " f.write(to_write)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "retrieve_data(\"https://philchodrow.github.io/PIC16A/datasets/palmer_penguins.csv\")\n", "penguins = pd.read_csv(\"data.csv\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make a simple scatterplot of the culmen lengths and depths for the penguins. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "\n", "for s in penguins['Species'].unique():\n", " df = penguins[penguins['Species'] == s]\n", " ax.scatter(df['Culmen Length (mm)'], df['Culmen Depth (mm)'], label = s)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we include the colors, it looks like there might be some clusters of penguins here. Maybe even 3? Let's see. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(n_clusters=3)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = penguins[[\"Culmen Length (mm)\", \"Culmen Depth (mm)\"]].dropna()\n", "\n", "kmeans = KMeans(n_clusters=3)\n", "kmeans.fit(X)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1)\n", "ax.scatter(X[\"Culmen Length (mm)\"], X[\"Culmen Depth (mm)\"], c = kmeans.predict(X));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ummmm...these don't really seem like the \"right\" clusters! There's a reason that `k-means` doesn't do very well on the Penguins data set. `k-means` works best when the clusters are roughly *circular*. On the other hand, the true clusters in the penguins data set appear to be elliptical (stretched out). They also have a somewhat diagonal direction, not aligned with the horizontal or vertical axis. There are more sophisticated clustering algorithms that can handle data with this kind of structure, but we won't focus on them in this class. \n", "\n", "For a nice exposition of a more sophisticated clustering algorithm (with helpful diagrams), you might want to check out Jake VanderPlas's [chapter on Gaussian mixture models](https://jakevdp.github.io/PythonDataScienceHandbook/05.12-gaussian-mixtures.html) in the [*Python Data Science Handbook*](https://jakevdp.github.io/PythonDataScienceHandbook/). " ] } ], "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }