{ "cells": [ { "cell_type": "markdown", "id": "improved-explorer", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# Cancer RNA-Seq Data Clustering" ] }, { "cell_type": "markdown", "id": "christian-experience", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "In this notebook, we will learn to cluster data, i.e., to divide the data points into distinct groups, so that there is relatively small variation within a group and larger variation between groups. This task belongs to \"unsupervised learning\", because the training data is not labeled. Compared to classification where our goal is to match the known answers, here we try to find patterns in the data without additional information." ] }, { "cell_type": "markdown", "id": "conventional-parliament", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The dataset that we will use as our example is the [gene expression cancer RNA-Seq dataset](https://archive.ics.uci.edu/ml/datasets/gene+expression+cancer+RNA-Seq). It contains the expression levels of 20531 genes from 801 patients having different types of tumor. Our goal is to analyze the data and cluster them into groups, so that these groups may correspond to different tumor types. The dataset in fact comes with labels --- the patients were diagnosed with 5 types of tumor: BRCA, KIRC, COAD, LUAD and PRAD. But when we analyze the data, we will pretend that the diagnoses are not known (or not all correct?) and see how well we can figure them out." ] }, { "cell_type": "markdown", "id": "golden-combine", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Load data" ] }, { "cell_type": "markdown", "id": "delayed-porter", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The dataset can be loaded and printed using the `pandas` package, which is a popular data analysis and manipulation package. The data loaded in `pandas` are in the format of `DataFrame`s, and they can be operated by `numpy` just like a normal array (in most cases)." ] }, { "cell_type": "code", "execution_count": 1, "id": "solved-nothing", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "id": "lined-resistance", "metadata": {}, "outputs": [], "source": [ "data = pd.read_csv('data/cancer-data.csv', header=0, index_col=0) # load data, using row-0 as column names and column-0 as row names\n", "labels = pd.read_csv('data/cancer-labels.csv', header=0, index_col=0) # load labels, will use later to check results" ] }, { "cell_type": "code", "execution_count": 3, "id": "flush-demand", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
gene_0gene_1gene_2gene_3gene_4gene_5gene_6gene_7gene_8gene_9...gene_20521gene_20522gene_20523gene_20524gene_20525gene_20526gene_20527gene_20528gene_20529gene_20530
sample_00.02.0172093.2655275.47848710.4319990.07.1751750.5918710.00.0...4.9267118.2102579.7235167.2200309.11981312.0031359.6507438.9213265.2867590.000000
sample_10.00.5927321.5884217.5861579.6230110.06.8160490.0000000.00.0...4.5933727.3238659.7409316.2565868.38161212.67455210.5170599.3978542.0941680.000000
sample_20.03.5117594.3271996.8817879.8707300.06.9721300.4525950.00.0...5.1252138.12712310.9086405.4016079.9115979.0452559.78835910.0904701.6830230.000000
sample_30.03.6636184.5076496.65906810.1961840.07.8433750.4348820.00.0...6.0765668.79295910.1415208.9428059.60120811.3926829.6948149.6843653.2920010.000000
sample_40.02.6557412.8215476.5394549.7382650.06.5669670.3609820.00.0...5.9960328.89142510.3737907.1811629.84691011.9224399.2177499.4611915.1103720.000000
..................................................................
sample_7960.01.8656422.7181977.35009910.0060030.06.7647920.4969220.00.0...6.0881339.11831310.0048524.4844159.61470112.0312679.81306310.0927708.8192690.000000
sample_7970.03.9429554.4538076.34659710.0568680.07.3203310.0000000.00.0...6.3718769.6233359.8239216.5553279.06400211.63342210.3172668.7459839.6590810.000000
sample_7980.03.2495823.7074928.1859019.5040820.07.5365891.8111010.00.0...5.7193868.61070410.4855173.5897639.35063612.18094410.6811949.4667114.6774580.586693
sample_7990.02.5903392.7879767.3186249.9871360.09.2134640.0000000.00.0...5.7852378.60538711.0046774.7458889.62638311.19827910.33551310.4005815.7187510.000000
sample_8000.02.3252423.8059326.5302469.5603670.07.9570270.0000000.00.0...6.4030758.59435410.2430799.13945910.10293411.64108110.6073589.8447944.5507160.000000
\n", "

801 rows × 20531 columns

\n", "
" ], "text/plain": [ " gene_0 gene_1 gene_2 gene_3 gene_4 gene_5 gene_6 \\\n", "sample_0 0.0 2.017209 3.265527 5.478487 10.431999 0.0 7.175175 \n", "sample_1 0.0 0.592732 1.588421 7.586157 9.623011 0.0 6.816049 \n", "sample_2 0.0 3.511759 4.327199 6.881787 9.870730 0.0 6.972130 \n", "sample_3 0.0 3.663618 4.507649 6.659068 10.196184 0.0 7.843375 \n", "sample_4 0.0 2.655741 2.821547 6.539454 9.738265 0.0 6.566967 \n", "... ... ... ... ... ... ... ... \n", "sample_796 0.0 1.865642 2.718197 7.350099 10.006003 0.0 6.764792 \n", "sample_797 0.0 3.942955 4.453807 6.346597 10.056868 0.0 7.320331 \n", "sample_798 0.0 3.249582 3.707492 8.185901 9.504082 0.0 7.536589 \n", "sample_799 0.0 2.590339 2.787976 7.318624 9.987136 0.0 9.213464 \n", "sample_800 0.0 2.325242 3.805932 6.530246 9.560367 0.0 7.957027 \n", "\n", " gene_7 gene_8 gene_9 ... gene_20521 gene_20522 gene_20523 \\\n", "sample_0 0.591871 0.0 0.0 ... 4.926711 8.210257 9.723516 \n", "sample_1 0.000000 0.0 0.0 ... 4.593372 7.323865 9.740931 \n", "sample_2 0.452595 0.0 0.0 ... 5.125213 8.127123 10.908640 \n", "sample_3 0.434882 0.0 0.0 ... 6.076566 8.792959 10.141520 \n", "sample_4 0.360982 0.0 0.0 ... 5.996032 8.891425 10.373790 \n", "... ... ... ... ... ... ... ... \n", "sample_796 0.496922 0.0 0.0 ... 6.088133 9.118313 10.004852 \n", "sample_797 0.000000 0.0 0.0 ... 6.371876 9.623335 9.823921 \n", "sample_798 1.811101 0.0 0.0 ... 5.719386 8.610704 10.485517 \n", "sample_799 0.000000 0.0 0.0 ... 5.785237 8.605387 11.004677 \n", "sample_800 0.000000 0.0 0.0 ... 6.403075 8.594354 10.243079 \n", "\n", " gene_20524 gene_20525 gene_20526 gene_20527 gene_20528 \\\n", "sample_0 7.220030 9.119813 12.003135 9.650743 8.921326 \n", "sample_1 6.256586 8.381612 12.674552 10.517059 9.397854 \n", "sample_2 5.401607 9.911597 9.045255 9.788359 10.090470 \n", "sample_3 8.942805 9.601208 11.392682 9.694814 9.684365 \n", "sample_4 7.181162 9.846910 11.922439 9.217749 9.461191 \n", "... ... ... ... ... ... \n", "sample_796 4.484415 9.614701 12.031267 9.813063 10.092770 \n", "sample_797 6.555327 9.064002 11.633422 10.317266 8.745983 \n", "sample_798 3.589763 9.350636 12.180944 10.681194 9.466711 \n", "sample_799 4.745888 9.626383 11.198279 10.335513 10.400581 \n", "sample_800 9.139459 10.102934 11.641081 10.607358 9.844794 \n", "\n", " gene_20529 gene_20530 \n", "sample_0 5.286759 0.000000 \n", "sample_1 2.094168 0.000000 \n", "sample_2 1.683023 0.000000 \n", "sample_3 3.292001 0.000000 \n", "sample_4 5.110372 0.000000 \n", "... ... ... \n", "sample_796 8.819269 0.000000 \n", "sample_797 9.659081 0.000000 \n", "sample_798 4.677458 0.586693 \n", "sample_799 5.718751 0.000000 \n", "sample_800 4.550716 0.000000 \n", "\n", "[801 rows x 20531 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data # print data" ] }, { "cell_type": "code", "execution_count": 4, "id": "grave-judgment", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Class
sample_0PRAD
sample_1LUAD
sample_2PRAD
sample_3PRAD
sample_4BRCA
......
sample_796BRCA
sample_797LUAD
sample_798COAD
sample_799PRAD
sample_800PRAD
\n", "

801 rows × 1 columns

\n", "
" ], "text/plain": [ " Class\n", "sample_0 PRAD\n", "sample_1 LUAD\n", "sample_2 PRAD\n", "sample_3 PRAD\n", "sample_4 BRCA\n", "... ...\n", "sample_796 BRCA\n", "sample_797 LUAD\n", "sample_798 COAD\n", "sample_799 PRAD\n", "sample_800 PRAD\n", "\n", "[801 rows x 1 columns]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "labels # print labels" ] }, { "cell_type": "markdown", "id": "scheduled-immigration", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Our data is a (801, 20531) array, where each row corresponds to one patient, and each column represents one gene. The values of the entries are non-negative numbers that are readings from the RNA-Seq measurements. We can think of each data point as a 20531-dimensional vector, representing a particular patient that belongs to one of the tumor types. Thus, our goal is to separate the 801 data points into different categories. This may sound like the classification problem we did before, except that here we do not know what are the categories or even how many they are." ] }, { "cell_type": "markdown", "id": "spanish-capital", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Dimensionality reduction" ] }, { "cell_type": "markdown", "id": "historical-filename", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "When dealing with such high-dimensional data, it is a good idea to first reduce the dimensionality, such as by using **Principal Component Analysis (PCA)**. The goal is to find a small number of principal components that capture most of the variation among the data points. Imagine that there is one gene that is not expressed in any patient, then this gene (or the dimension it represents) is not useful at all for distinguishing the data points. Therefore we are interested in finding the directions in the data space along which the data points vary the most." ] }, { "cell_type": "markdown", "id": "imposed-blogger", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Recall that, to perform PCA, we first calculate the covariance matrix of the data. Instead of calculating this by hand, we can use the function `numpy.cov`. Since it expects a 2-d array as input, where each column is a data point, we have to transpose our data." ] }, { "cell_type": "code", "execution_count": 5, "id": "indian-shipping", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "cov = np.cov(data.T) # calculate the covariance matrix" ] }, { "cell_type": "markdown", "id": "3702a127-45d2-4bfe-aa53-aca8617a0773", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Then we need to find its eigenvectors that correspond to the largest eigenvalues. We can calculate the eigenvalues and eigenvectors using the `numpy.linalg.eigh` function as before. However, this function calculates *all* eigenvalues and eigenvectors, and there are too many (20531) of them here. Since we are interested in only the largest few eigenvalues, we can instead use the `scipy.sparse.linalg.eigs` function (or the `eigsh` function for symmetric matrices) as follows." ] }, { "cell_type": "code", "execution_count": 6, "id": "composite-parish", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "import scipy.sparse.linalg as spla\n", "\n", "w, v = spla.eigsh(cov, k=50) # calculate the largest k eigenvalues and their eigenvectors" ] }, { "cell_type": "markdown", "id": "royal-shower", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Here we calculated the largest 50 eigenvalues and their eigenvectors. Recall that each eigenvector represents a principal component (PC), and the corresponding eigenvalue represents the variance along that direction. Let us find the directions with the largest variance and see how many we need to capture most of the total variance. (Note that we need to normalize the eigenvalues by the total variance, which is the sum of all eigenvalues. But because here we did not calculate all eigenvalues, we cannot use the sum of only these eigenvalues. Instead, the total variance can be calculated as the trace of the covariance matrix.)" ] }, { "cell_type": "code", "execution_count": 7, "id": "baking-helicopter", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "order = np.argsort(w)[::-1] # argsort gives ascending order, [::-1] reverses the order\n", "w = w[order] # order the eigenvalues\n", "v = v[:,order] # each column is an eigenvector, so we order the columns\n", "\n", "wnorm = w / np.trace(cov) # normalized eigenvalue = fraction of total variance captured\n", "wsum = np.cumsum(wnorm) # cumulative sum of variance captured" ] }, { "cell_type": "code", "execution_count": 8, "id": "handy-sapphire", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(wsum, '.-')\n", "plt.ylim(0, 1)\n", "plt.xlabel('# principal components', fontsize=24)\n", "plt.ylabel('variance captured', fontsize=24)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "legitimate-ballet", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see that the captured fraction of variance increases rapidly with the first few eigenvalues, then slows down and almost plateaus (it will slowly increase to 1 when all 20531 eigenvalues are included). Let us pick, say, $K = 10$ principal components. We will project the original data onto these 10 components as follows." ] }, { "cell_type": "code", "execution_count": 9, "id": "interior-quantum", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "K = 10 # number of principal components to use\n", "\n", "projected = np.dot(data, v[:,:K]) # project data points onto principal components" ] }, { "cell_type": "markdown", "id": "outstanding-season", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We can try to visualize these principal components, although it is hard to make plots in more than 2 or 3 dimensions. Since the first few components capture the most variance, we may hope that plotting 2 or 3 of them would be enough. It turns out that the first and third PCs give a pretty good impression of the data." ] }, { "cell_type": "code", "execution_count": 10, "id": "a2815355-4354-40c4-a9a0-c930bd203969", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "plt.scatter(projected[:,0], projected[:,2], s=5)\n", "plt.xlabel('PC1')\n", "plt.ylabel('PC3')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5f434906-77aa-4eff-b1bd-315b6b2b68b7", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see that the data points are naturally separated into 5 clusters. To improve visualization, we can color the data points according to their labels (which we have pretended not to know). For that we need a bit of processing of the labels since they were given as strings but we want indices." ] }, { "cell_type": "code", "execution_count": 11, "id": "molecular-strap", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'BRCA', 'COAD', 'KIRC', 'LUAD', 'PRAD'}\n" ] } ], "source": [ "types = set(labels['Class']) # collect all tumor types\n", "nt = len(types) # number of types\n", "print(types)" ] }, { "cell_type": "markdown", "id": "19dce532-118d-4879-a618-10e67379cb63", "metadata": {}, "source": [ "These represent kidney cancer, breast cancer, prostate cancer, lung cancer, and colon cancer, respectively." ] }, { "cell_type": "code", "execution_count": 12, "id": "precious-connecticut", "metadata": {}, "outputs": [], "source": [ "type_to_index = dict(zip(types, range(nt))) # map string labels to indices\n", "indices = labels['Class'].map(type_to_index).to_numpy() # convert labels to indices for all data points" ] }, { "cell_type": "markdown", "id": "generic-graduation", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We can now plot the data points in 3D with colors." ] }, { "cell_type": "code", "execution_count": 13, "id": "greenhouse-factory", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import animation as anim\n", "plt.rcParams[\"animation.html\"] = \"jshtml\"\n", "cycle = plt.rcParams['axes.prop_cycle'].by_key()['color']\n", "colors = np.asarray(cycle)[indices]\n", "\n", "fig = plt.figure(figsize=(8,6))\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1)\n", "ax = fig.add_subplot(projection=\"3d\")\n", "ax.scatter(projected[:,0], projected[:,1], projected[:,2], s=5, c=colors)\n", "ax.set_xlabel(r'PC1')\n", "ax.set_ylabel(r'PC2')\n", "ax.set_zlabel(r'PC3')\n", "fig.set_facecolor('w')\n", "\n", "def animate(i):\n", " ax.view_init(elev=10., azim=i*10)\n", " return fig,\n", "\n", "mov = anim.FuncAnimation(fig, animate, frames=36)\n", "# mov.save('source/cancer.gif', fps=5)\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 14, "id": "218c8581-e71f-43ad-a4e3-e5bc57ff0192", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "
\n", " \n", "
\n", " \n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", "
\n", "
\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mov" ] }, { "cell_type": "markdown", "id": "backed-patient", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We see that the clusters match very well with the colors. It shows that the first few principal components successfully capture the main features of the dataset. Therefore, we will use these principal components to cluster the data points, again pretending that we do not know the labels (colors)." ] }, { "cell_type": "markdown", "id": "ancient-ontario", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "## Clustering" ] }, { "cell_type": "markdown", "id": "a4173d12-4f8a-4ead-bc88-94f041c8d54b", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Our goal is to separate the data points into multiple clusters according to their relative positions in the data space (or the reduced low-dimensional space). We would like the data points within the same cluster to be close together, and different clusters to be relatively far apart. The number of clusters needed to separate the data points is often not known beforehand, so finding the appropriate number of clusters is part of the task. In simple clustering algorithms, such as **k-means** that we will use, the number of clusters is chosen by hand and given to the algorithm. More sophisticated algorithms may select this number automatically according to certain criteria." ] }, { "cell_type": "markdown", "id": "beautiful-annotation", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The k-means algorithm aims at minimizing the mean squared distance between all pairs of data points within the same cluster, i.e.,\n", "\\begin{equation}\n", "L = \\sum_{i=1}^k \\frac{1}{2 N_i} \\sum_{\\mathbf{X}_n, \\mathbf{X}_m \\in S_i} \\big| \\mathbf{X}_n - \\mathbf{X}_m \\big|^2\n", "\\end{equation}\n", "where $S_i$ is the set of data points belonging to the $i$-th cluster for $i = 1, \\cdots, k$, and $N_i$ is the number of data points in $S_i$. Each data point $\\mathbf{X}_n$ is a vector in the data space, and $|\\mathbf{X}_n - \\mathbf{X}_m|$ is the Euclidean distrance between two such points. This cost function can be equivalently expressed as the sum of squared distance from every data point to the center of its own cluster, i.e.,\n", "\\begin{equation}\n", "L = \\sum_{i=1}^k \\sum_{\\mathbf{X}_n \\in S_i} \\big| \\mathbf{X}_n - \\mathbf{\\mu}_i \\big|^2, \\qquad \\textsf{where} \\quad \\mathbf{\\mu}_i = \\frac{1}{N_i} \\sum_{\\mathbf{X}_n \\in S_i} \\mathbf{X}_n\n", "\\end{equation}\n", "This minimization problem is not easy in the sense that the global minimum is hard to find. However, the k-means algorithm quickly converges to a local minimum, which may be good enough." ] }, { "cell_type": "markdown", "id": "79c17159-36b8-4a71-b3d2-241eb72b2904", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "The algorithm requires the number of clusters, $k$, as an input. One may also provide an initial guess for the center position of every cluster. If not given, the algorithm will use random initial positions for the cluster centers. Because of this randomness and the fact that it only finds the local minimum, running the algorithm twice may give different results. So you may have to try a few times and check if the clustering result is satisfactory." ] }, { "cell_type": "markdown", "id": "38160443-05b0-4b6f-903d-c497df620cf1", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "The heuristic idea behind the algorithm is to iterate over two simple steps. The first step starts with the current guess for the center position of every cluster, and reassigns all data points to their nearest center. The second step then collects the data points now assigned to each cluster, and recalculates their center position. The algorithm alternates between these two steps until no reassignment happens, which means the result has converged." ] }, { "cell_type": "markdown", "id": "instructional-inquiry", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Luckily, we don't have to program this algorithm ourselves, since it is already provided by the python function `scipy.cluster.vq.kmeans2`. In the following, we will use this function to cluster our data. We will use the dimensionally reduced data that we got from PCA above. Also, since we saw that the data points seem to separate nicely into 5 clusters (in agreement with the 5 diagnosed tumor types, which we pretend not to know), we will ask the algorithm to find k = 5 clusters." ] }, { "cell_type": "code", "execution_count": 15, "id": "2284786a-2c4d-4c4d-8846-5244384979a3", "metadata": {}, "outputs": [], "source": [ "import scipy.cluster.vq as vq" ] }, { "cell_type": "code", "execution_count": 16, "id": "incorrect-wages", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "k = 5 # choose number of clusters\n", "centroid, lab = vq.kmeans2(projected, k) # perform k-means clustering" ] }, { "cell_type": "markdown", "id": "sporting-prediction", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "The two outputs are: `centroid`, which is a 2-d array where each row represents the center of a cluster, and `lab`, which is a 1-d array where each entry is an index telling us which cluster each data point belongs to. We could use the `lab` indices to color our data points and plot the clustering result. (Note that the clusters are randomly ordered by `k-means`. We can reorder them to match the \"true labels\" we saw above.)" ] }, { "cell_type": "code", "execution_count": 17, "id": "looking-hours", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "colormap = []\n", "for cent in centroid:\n", " med = np.argmin(np.sum((projected - cent)**2, axis=1)) # find a point close to each center\n", " colormap.append(indices[med]) # find the true label for that point and use its index for the cluster\n", "newindices = np.asarray(colormap)[lab] # convert to new indices for all points\n", "newcolors = np.asarray(cycle)[newindices] # reorder labels" ] }, { "cell_type": "code", "execution_count": 18, "id": "74995f48-0bcf-427f-a964-165dd8221f34", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAFzCAYAAADVHcVxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAACOhElEQVR4nOzddXhUV/rA8e8djbsSBRKCE9zdSqFKhbpQ1627/Nqtbre6la23W1egpUWLU9w9Qtw9mYzf8/tjQiBNSAJxej7Pw0OYOffeMyGZd+6R91WEEEiSJEnSiTQd3QFJkiSp85HBQZIkSapHBgdJkiSpHhkcJEmSpHpkcJAkSZLqkcFBkiRJqkfX0R1oDUFBQSI2NrajuyFJktSlbN++vUgIEdzQc2dEcIiNjWXbtm0d3Q1JkqQuRVGU9JM9J4eVJEmSpHpkcJAkSZLqkcFBkiRJqkcGB0mSJKkeGRwkSZKkemRwkCRJkuqRwUGSJEmqRwYHSZIkqR4ZHCRJkqR6ZHCQJEmS6pHBQZIkSapHBocuKKu0msmvrGbuuxuptjlqHxdCIGuCS5LUGmRw6IJWHMgnq7Safdnl7MkqB8BkdTDpldX0eXIJe7LKOqxvBRUWzn97A9d/uhWL3dlh/ZAkqWVkcOiCJiWEEOhppFeoN4Oj/QBIKzaRV27B7hRsSC7usL79vi+P/TnlbEguYldmWYf1Q5KklpHBoQv6YXsmxSYrh/MqKa+2A9A33IfrxnZnZt9QLh0e1WF9m9onhEh/D/pH+DIw0rfD+iFJUsucEfUc/m56hXqjoODtpsPLzfVfqCgKD8/qXdsmt9zMt1symdonlAEneZNOLzbh72nAx03fan2L9Pdg1f2TWu18kiR1DBkcuqBzEyMYHO2Pn4ceD0PD/4X3fbebTanFfLIxjd1Pzaj3/E87snj4x714uelY/9Dkk55HkqS/Jzms1EVFBXjg3cgn/rgQL7QahZhAjwafTymsQiCotNgxWeXEsSRJdSlnwtLHYcOGia5eJrTa5mDxnlyGxPjTM9jrlI61O1VMVgd+Hobax1RVkFJYRXSgB0adtt4xJquDTzYcJSbAE4vDyfj4YMJ83Vr8OhqiqoK7v93J3qxy3r1yKH3CfdrkOpIknRpFUbYLIYY19Jy8c+gknlq4n8d+3se5b61HVRsP2EKI2v0NdqfKtFfXMOyfK1i4M7u2jUajEB/q3WBgAPA06rhjSjxfb83g8QX7mPf+n633Yv4ip9zM73vzSCuu5tutmW12HUmSWo8MDp1EdpkZm1Ol2uZscn/AZR9sot9TS/lsYxoVZjtZJdU4VcGWtJJ6bZfuz6Pvk0u47cvtDZ7LTa+t83db6ObrztkDwuke5NmhK6kkSWo+OQvZSfQO82ZTajEKkFVqpleYd4PthBBsTStFCPjjUAE7Mko5dqORGFV/VdL32zKptjn5bW8eVRYHb69KwsOg4/bJcWg0Cm9fPoSNKUUMiwlos9em0Si8edngNju/JEmtT945dBL3TO/FLRN74qbXMuet9aw+XNBgO0VR+M9lgzlnYDhPndOXg7kVCEAAP+3Iqdf+H9N6MTjaj0dm9Wb5wTw+2ZjG26uT2Zji2ijnbtAytU8ovh71J7eLq1x7KY7Zn1PO2W+u46XfD7bKa5YkqfOSdw6dhKrCeYnd+Gj9UQSCpPwqKs0ONqYWc8+0eL7anMFnf6YxtU8Ij8zqw6wB4Ty3+ABH8qsI8Tbgoddx1egYSk02/D2PT0z3j/Dl59vGAnAwtwIAvUZDj2DPRvtTYbEz6ZXV2Bwqz18wgLlDI3lvTQoHcio4mFPBbZPjGl0tJUlS1yaDQwcRQvDAD3vYlVnGxcMi+deSw3Tzc+Om8T34bV8u4b5u3P3tLoQQOJwqi/fmUm1z8sP2bHLLLXx5wyiWHcgHQKPR8PzcAVz3yVZ0GoWV901qcOVRn3Aftj8+Ha1GaXKOwWxzYnWoIATZZWYALhsezfqkIkb3DMTLKH90JOlMJn/DO0hOmZmfd2bjVAU/7chGCEF2qZlPN6ZRaXXwxMJ9xAR6cLTQxOojhXi76bA5nCiKQqCnEYBXLh7Ef9ekcP3Y7qQXVwPgUAVFVdaTLkv1bOabeqiPGx9fM5zkgkrmjYgGYExcEDufdG2o25BcxFOL9nHJsChumtCzpd8OSZI6GRkcOsjLSw6hqgI3vYYnZvdhyf48ovzceWnpYQBCvI0svms8F727kV1Z5WgUePWSQYT5ujMk2h+A4bEBDI91TSQPd6pUWuyEeLvRP6J1chqNiw9iXHxQg8/9e9lhkgtMvLL0iAwOknQGksGhA1RY7GxLL0UAfu4Gbv5iOxF+7jx4yxjWJBWxNa2Ew/lVjHnxDzSK6xiDVsO0vmEnHc7RazW1b9JVVgdL9+XRI8iT277agQAW3j6WUJ/W2+R2/djuHC3ax9whka12TkmSOg8ZHNqZqgpmvLqWEpON/t288XE3sCmlmLTiarJKzXxy3XASHl8CQEGlFQUYEevPk+f0azAwCCH497IjZJZW88y5/fH10PPgD3tYeTAfg06D3aEigG1ppcweGN5qr2POoG7MGdSt1c4nSVLn0ubBQVGUj4E5QIEQon/NY08DNwKFNc0eFUL8VvPcI8B8wAncJYRY2tZ9bE9OISittiEQ5JRbOJJfhbtBy6XDo+kd5o1Go/DMuX15ZdkRKiwOBJBfYT3pUNH+nAo+WJeKUxXEBHqybH8eeeUWADyNWob1CkYImNI7pFX6X262423UoTl2SyNJ0hmpPe4cPgX+A3z+l8dfE0K8cuIDiqL0BeYB/YBuwApFUXoJIc6YzHB6rYZvbx7N1qMlrDiYz67MMuJCvHjynL6kFlbx0I97GBLtx/mJEfxvUzoA88d3r3MOu1Nlb3Y5fcJ8iPBzQ6tRsDtVzDY7SfmufQm3Torj2rGxBHkZW63vn/+ZxtOL9tOvmy+L7hiLosgAIUlnqjYPDkKItYqixDaz+XnAN0IIK3BUUZRkYATQdol/OkBilB+JUX5cPjKazUeLGVYzqfyvpYfZmlbK1rRSjDoFg07h8dn9uGR4JPkVFgI9Dby+Ioml+/NIL6mmV4gXT8zpi1MVaDUKqw4V4qzZLT2zXyhuei3P/LKfHkGeXDk6ttE+WexOjDpNo2/4G5KLELg2wzlUgV4rg4Mknak6cs7hDkVRrga2AfcJIUqBCGDTCW2yah47I3kadUzpHVr7b1NNMj0AjQKKomFkjwBmvLaWzJJqAjwMVFod2GrmEfblVHDj51sJ8TZSZrZTaTl+/GM/72NSQgif/5mORqMwqmcQcSENZ3tdtCubf3y7iz7hPiy8bSxarVInSCTlV3LJf//EYldJjPTj5ok90Gvrb64vqLDw9ZYMJiWEMCjKr+XfIEmSOkxHpc94F+gJJAK5wL9P9QSKotykKMo2RVG2FRYWNn1AF3DH5HiCvAzM6h/GjidmsOOJ6UT4uZNZUo0qoMhkw+FUMeqOv3FXWJy8cskgZvQNpdhkQwF0GjicX4nF7kRRwMdNR4jP8eElIUSd5H6rDxcigAM5FfR5agkzX1+L1XH8+T8OFVBabcdsd7I3u5yz+jc8sf3AD3t4Y2USl3+4qcHnJUnqOjokOAgh8oUQTiGECnyAa+gIIBs4MW1nZM1jDZ3jfSHEMCHEsODg4LbtcDsZ0T2AbY9P590rh+Ju0OGm1+Jp1PHo2X1q2wyO8uOGccf3FWgV+HF7JlpFQatRCPE2EB/iTVSABzeM7862x6ez4eEpdUqB3v7VDno/sYS3ViYBcN/MBOYMCGdiryCcquBokYn8cmtt+wuGRNAjyJVuY9aAsJP2Py7EC51GQ3RAwwWGJEnqOtql2E/NnMOvJ6xWChdC5NZ8fQ8wUggxT1GUfsBXuIJFN2AlEN/UhHRnLfYjhOCd1SmkFlbxxJy+dYrxNGV7eglZpWbmDOxGUaWFkS/8UfucRgFPg5bKEyq4eRl1/G/+CG79YgfFJivvXz2MyQkNr1Aa8PRSKi0OBkb6suiOcbWPF1RYeHzhPvp38+XOKXGnPOEshCCpoIroAI82TQEuSVLraKzYT3ssZf0amAQEKYqSBTwFTFIUJRFXMtE04GYAIcR+RVG+Aw4ADuD2rrxSKamgijdWJuFUBT2Cvbh9clyD7exOleSCKuJDvNifU8GyA3l8sDYVjUahwuJgVPe66bRVAZEBHhzMPZ4xtVeoaz6h2GRFVQV/JhfhZdQR6GnAZHUyIPL4Utibxvfg9325PHNev9rHyqpt3P3NLgw6DQMifbA61FN+g1cUhV6hDacalySpa2mP1UqXNfDwR420fw54ru161H66+bkT5Gkgr9zCZxvTGNUjkKEx/vXa3fK/7axLKmJcfCAbk4txqAIhBBqNgpdRS1yIFyO7B7AvuxybU8Vdr2VyQghJeZU4am78yqttXPbBJuw1y5V+3pnNp3+m43Cq6LUaXr5oIOclRpBZUs1/ViUDsCO9lMQoV3+WH8hnR0YpNqfKhuQiRvUI5IsbRtbrqxCCLzal43AKrhkTK/c7SNIZSu6QbgVCCF5dfoSk/Cr+eUH/2r0FXkYdv/9jAon/t4yCSiufbjjaYHBIKzbhUFXSi6sJ8DRQbLJxybAozh8cwdCaIjzf3jwacNV+1moUjDoN0/uGcuE7G2vqOShY7GrtOUur7QC1hYCKq2wAeBi06DQKDlUQ6uMOuIaTys023PRaHKrrbKXVrvbrk4r4YlM6t07qyaAoP9YmFfHcb656DuF+7pzV/+RzEJIkdV0yOLSClMIq/rsmFYeq0jvMm39M71X7nK+7nnkjolh5sICoAA9sDhWDru46gA+vGc4vu3OYPTCc5xcfZE9WOZcMi2JApF+9a52YVTUxyo/Hz+7DkYJKys12UotMAOg0CtP7huDrbmBUjwBsTsGFg10rggO9jKy6fxIl1TZ0Gg2z3lhLVomZaptrN7Zeq3DZiBhuneQaArv7m50Um2wcLTKx9J4JRPi5o6AghJATz5J0BpPBoRUs2p2DooBWozC+V/0spg+f1YefdmTz0fqjaDUK981IIKu0mis/3Iyvu56vbhzFXVPjyS4zs/pIIU5VcMWHm5mYEMwblw4+6dDN99uyeP73gzgFxAV7EhvowYAIX4bFBvDPX/cjcBX7uXJUTJ3jQnzcCPFx45lf9tfOW+g0IATotVpunNCzNknfhF7B/Lwzm6l9XJPbcSFerH9oMqqAYO/W230tSVLnIoPDadiTVcY1H2+hZ7AXH187nDdXusbwZ/YLrR0GOpFOq2DQarCrKv415ThXHSogu8xMbrmF3ZlljIkLws9dh06j4FQFFRYHv+zO5fbJcSTlVfHwT3uYNSCcVy4eVHtevU7h2EBSscnGU+f0Y2a/MNYmFXBshOnd1Sn1gsMxFw6J5Pd9ecSHeHHZiGiGxPjhZdTXuTt57dJEnr9gAO6G45PTga2YkkOSpM5JBofTsHRfHmXVdnZnlVFYaeHsAWGsSyqqLYrzV55GHcvvnUhmaTXDauYczuofzoJdOfh76BlS85jJ5kQIUHAt49JpFLoHefJ/vxzAZHPy044s/nXRwNolpucnRqBBYWtaMQt35/Lwj3tYc6SQYbH+tefwMJ58xVH/CF/+fGRqvcdzyszMfXcjNodKv24+PDa7LwlhdVchVVrslJhsxAQ2Xm5UkqSuSQaH03DZyGi2ppfSO8ybHsFevHPF0CaPCfN1I8zXjUN5Fdz6xQ7CfNwoNdmY2jukdsloiLcbt0/uyXurU+gV5s1/Lh+MqsIDMxN4auF+LhgSUWfvwYKd2Sw/WMCDM3uxeG8e1aqg2GRlSkIIHgYt1TYnj87q3WTfSk021iUXMSE+CD8PA5uPFlNismF1qKxNKsLxy36+unFUbXuL3cmkV1ZTaXbw7Pn9uXR4VCNnlySpK5LB4TRE+nvwXc3qoVP17dZMjhaZOFozefzq8iPcVrP/YUdGKW+sTEIVsDurnCcW7mfN4ULum9GL8xK7kVZkotJix9tNj82hct/3uxECVCHQaTQ4VcHaI0Vc/N8/sTlVNBqFA7mVTD4hf1NDrv54C0fyK+nXzYefbhvL9L5hLN6Ty57McgqqrPVWJFXbnFSY7QgBKQVVp/V9kCSpc5PBoY3sziwjwNNA1F9W9FwyLIo/DhUQ5Gkgrbia8xOP5xXcmVGGRnGtBDpnYDdWHspHAIv35JJaZMKpCiL83Ll5Yk/0WoXB0X7szChjZHd/lu3Pqz1PXrmF2yfFkV5SzRUjGx7qAtcdwKbUYtSaXfLH7kq8jDo+vGY44Nqg99ckewGeBt6/ehj7ssu5bmzddOKSJJ0ZZHBoA7/uyeH+73ejoLDq/kmE+R4vz9kn3Ic1D0xu8LhLh0eRWlhFNz93bpvUk1WHC/h+Wxbzx3Xnli+2U2F21GY7VRSFH24ZQ06ZmZUHCzDqNKgChsb4cduk+Dq1n8uqbRSbbPQMrpuV9R/f7GLV4QKi/D147dJExsbVX2nVUPZVgMkJISdNzyFJUtcng0MbKDe7NqA5VZU7v95BRnE190zvxUVDI9FpNbz1RxLL9ufz/AUDiA70wGp3UmGxsyuznCfm9K2dg5jSO7Q2pffGh6dic6p1SoUqisKtX+7gUF4lsYEePH1OP0b3DEQI2JpWggIcya/kxd8PYXWovDx3IOcNPn6nYrI5EAKsDidnD2i9EqKSJHV9Mji0gXnDo/EwaHGq8MhPe7A7BY8t2Mfe7HKeOqcf/152BIB/LT3EjowybA4nqhA4VVi0M4vP5o+sl/Quo8TE8gMFXDA4os6diJteiwL4uOkZU/PJ/40VR3h7VRJ2FQxaDQ5VRatRSCs21R73wbpUdmeWMb1vCI/O7tv23xRJkrqUjqrncEbTahQuGBzJhYMjOGdQNzSKK5NqqcmGQafhnIHheLvpmJwQgt3p2pDgUF1LT7dnlNHvqaVM+tcqTNbjxXuu+mgLryw9zO1f7ah97L7vdrHlaAnnDurGJ9cNr328qMpau8/BoarM7BfGgzN7c/PE46m+P15/lAqLg+0ZZUT4ubftN0SSpC5H3jm0IY1G4dVLErltUhybUoqZ1tcVDNwNGrSKwjdbM3j4rN6YbA7Kqu18tSUDrQIVVifZZWaOFpnILjPzyE970dbswD5aWEWfJ5bw8bXDWbo/H4BDeZUUVdm486udTEgI5tGz+7D8QD5FVVbOHRTBK5cMQvuXXdaPzurDG38kceeUhjPFSpL09yaDQzvoGezJgz/s5slF+7h6VAw/78zB7hRUWR0EeBm4LtG14ufGCT0Y/cJKAOJDvOkb7sOzvx6gxORKgjc2LoA/U0oQAn7bm8uDMxP4cH0qQgjOf3s95WYHa44U0jfch6X3TOBQbiVPLtrH/E+38v7VwzDoNGxMKeJwXiWXjYjGoFNYsCuHvuE+xJ8k1fbiPTlsSi3hrqnxMl2GJP2NyODQDpyqYFdmGaqAFYcKsDsFCtAn3JtJvY6v+PF11zOyewAlJjv/vWooGo3C3dPimf/pVsx2lQ3JJZzdP4wys50bx/fgli+2k1lqRghzTc1pCPQ0cPXHW+gd5s3sAeGkFJpIK65mf0450QEeXPvJVhCuLK3vr03F5lQpM9v5cv5Ilu7PI8THrTZzbIXFzp1f70QIsDmcvHTRoJO8ws4vs6SaO77eQVywNy9fNLDenZQkSXXJOYd28PWWTDyNronj7DIz4Jpf+Pm2sfh6HC/f+eXmDLanl5FWbKqt8TymZxB3To0HXGk1bhjfnUuGRaHXKcQEeqDXKPi664kO8ODioZF4GXU4VUFeuYWzB4TTI8iT0T0C6NvNBze9Fne9FkWBCH93RvcMRFFgau8QHv15L7d+uYOL39tIRnE1AEWVVoRw9VWla/theyZ7sspZtDublEK5cU+SmiLvHNrBW38kUWlxogB6jQajXsNFQ1zLWk8UH+IFimsF0onJ7W6bFMdZ/cJw12t5bME+NiQXEeRlZM0DkziUV0mvUG8+3XiUl5ccRqMoXDM6lstGRBEV4MGn14/gkvc2Muv1dfx46xhW3T+J/AoLfcJ9mDc8qrbi24zX1gCu+g/HuuVu0GLUaxACxjWwB6IrOat/ON9szSQ2yJNYmQ9Kkpokg0M7uHNKPO+sTubyEVGkFZtYuj+fuJqynkIInKpAp9UwoVcw6x+cjLtBi7ebvs45etRsYDNoNSi4Mr3qtBr6R7jKf/bv5vrboaqUm221cwgbk4soqin0szOzlCm9QwnwdNWyVhSldk/FKxcN4t7vdjF7YDgR/q5d3eG+7iy+azwlJhvDY+tnm+1K+oT7sPnRaR3dDUnqMmRwaAdXjY7By03H/d/txlmTquLF3w4xKMqP6z7ZSnm1na9uHMmw2ABCfNwaPdfr8xJZe6SwTkU5IQRj4oKY0juEZQfy+WlHNs+c1x9Po44Z/cL4bW8ubnotY3qe/NP/F5vTa+YmKuo83jPYi57BLXjxkiR1STI4tJMNyUW1OYwAQryNXPjOBmwOgUaBTanFDPvLp/OyahuL9+YyLi6oNjX2xpQi7vpmJyNiA/jommFc8O5GDudV8sm1I7h5Yk8O51UyMSG4tiaDr7ueT64b0WT/dmeV41BFveAgSdLfkwwO7USnURDAwAgfZg3oxri4QC56dyNaDfTr5svlI48X5Pl9by7/+HYXnkYtlWYHqhAEeBr54dbR/LwzG4tdZV1SEZmlZg7kVKAKuPe7Xfz5yFTWPNhw3qaGCCF4Y2USOzPKeGJOX1YcyGfukMg2ePWSJHU1MjicorxyC++sTnYlnutdP/Hc73tzSS6s4oZxPXA3aBFC4FAFm1KLASiosnHrJNdO5W9rEued1S+sTinQn3ZmY3WoWB0qWo1rkrjcYufPlGLunhpPQYWVSb2C6RHsRf9uvuzJLqeg0sr29FJGdK9792G2OfkztYih0QH4eugpN9vZerSE0T0DqbDY+c8fyThVQY8gT54+t1+jr90ViETtPEdjCiutfL0lgwm9gkmsSRYoSVLXIYPDKXrm1wP8vi+XLzdncOjZs+pkLc0qrebub3YhcO1juG1SHOe9vYH9OeXcM60Xe3PKuW7M8RTXiVF+Db5xBnoZ0GsVECAQxAR6EBfixawB4fi66/n2hFoSb10+mHPeWk+l1cEdX+1gy2N1J11v/3IHG1KK6BHsxe93j+eqDzdzOL+SYTH+fHr9CPp28+FwXiXT+zVe82F3ZhmX/vdPAL68cVSdOY+GPPLTHv44VMC7q1M4+OxZjbaVJKnzkcHhFA2L8WPZ/jx6Bnuh+8tGKh93PR5GVwW2uBBvqmwO9ueUI4C0YhPvXzWsWdf4dksmAte+BoNOYXTPQK4cFcMNn21lbM8g/jG9V23bmEBPpvYJZfHeXEL/MpltsTvZn1OO3alitrnyNFkdrh0LFoerTsOiO8Y1q09mu9PVoZrzNqVnsBdrjxQR6S/zNklSV6SIEyZJu6phw4aJbdu2tdv1Ciot+HsYGqx1UGmxU2Fx1Caz+3JTOuuSi3js7D71Cv+Aa/e0Q1Ux6rSoquBgXgWvLT/CioMF6LUKN03owaSEEOb990+cNfWltz8xvXY5KoDDqbI3u5zeYT64G47XjP5+WyaPL9iHKgQvzR3IhUMiKai0sPZIEVN7h+DvaWB7einXfrKF+BAvvr159EnrNwCsPlyAKkRtGvHGCCE4kl9FdIBHnT5JktR5KIqyXQjR4KdWeedwGkK8T77c1NtNX2ePwhWjYrhiVEyDbausDqa/uobiKhtf3TiSBbuy+W5bFpF+7hh1GjSKK7vr5qPFaBQFpxD0i/BBFYI5b65DURT+N38Efh4GBkfXHebZnVnGoz/vxe4U+LjpGN0zsLbvFw09Pum8ZF8uVRYHe7LKyS2zEB1YP4AdM+kUivsoikJCWMP5miRJ6vxkcGhHKw7k8cbKZG6b1JNZA8LJLjVTYrKhCsHWtFLSi6txOlVKTDbWPjiZjJJqPlyXSmpRFTqdwsWJkTx3wQB+2ZNLUk3t5o0pxQ0W6tmVWYYCGLUKH187nHDfhod3rh4dy77scvpH+BIV4I7F7mThrhwUBc5L7IZR13Gf+oUQVNuctctyJUlqP/K3rh09/csBskrNPP3LfmYNCKdXqBd3TY0nrcjE5SOjmTskgu+3ZzE5IYRQHzfu+GoHW9NKa4+3OlQURWFifDADInzRKDAuPogft2exPrmIB2Ym0K1mOOuioZEcya8k9IREeg2JCvDg65uOT3A/8MNuftmdC8DWoyX86+KOS7Z3xYeb2ZRazOOz+3D9uB4d1g9J+juSwaEdXT4imjf/SOKy4dGAa+jl9skn1FNw13P75DgqLXYe+H43qirQKgrB3ka83XRcN9a10snXQ88Pt44BXENTD/6wB4FrM92/L0kEwNOo47kLBpxyH53O43NQTrXj5qOEEGw5WoIqYNXhQhkcJKmdyeDQjm6bHMdtk5survPTjmwW7spGoyi8f/VQJieE1O6DUFXBl1syMGgVluzLY0NyMWG+RvLKrUyIb1meC7tT5az+YcSFeBHkZeSS4VGnfa7NqcXc+91upvYJ4Znz+p/y8Yqi8Pblg/l1Ty73nLA6S5Kk9iGDQycihODdNSlsTilBURS83fUMifavs0Fuyf48nlt8ACEEVofrk33/CF+W35uIh6Fl/52vLjvMJxvT0GoUtj8+vTYpn9nmRKtRMOian+H9o/VHyS4z8/mf6Tx6dp/ac52Kmf3Dmdm//nyKJEltTwaHDpZdZuZIXiXj44PILDXz+vIknKrKzRN7cv+MhDqBAXAtkRWgUTTcNimWnZll3DcjocWBwWR10NCy5p0Zpcx7fxNeRh0r7p2I/wlLaBtzw/geHMytYGqf0NMKDJIkdSwZHFqR3alyz7e7XCk2rhjSZIZVm0PlrNfXYneqXDe2O3dPjSfcz42cMjPj44NrA0NRlRVfdz16rYZBUX6semASWo1Sb0ltudnOC78dpHuwJzeN74GiNK/a2XdbM3j4p730CffhtUsS6RPuU/uGvjuzDCEEJquDjJLqZgeHEd0DWPfQlGa1lSSp85HBoRXtySpj+YF8nKpg0e4cbhjf+CSqQNRO+tpqiu6svn8SDlXUbkb7ZksGjy/YR3SAB8vvnYhWo5x0Wer//kzjh+1ZaDQKUxJCTloX+q+WHyhAFbA/p4JQHzdig44Xw7l4WBQphSbCfN0YGNl0TiVJks4MMji0UFZpNf4eBjyNOvqG+9In3JuCSitT+xzfRbw+qYjUoiouHR5VZ9+AUadl0R3j2J9TzqyasXVFUVx5lWpsSy9FFYKMkmos9sbX/A+LDUBRIMDDQLhf02krCiut2Jwq5w3uxspD+SjAwbwKhpyw9NXTqOPZ809tQjm7zMwFb29Ar9Ww4PaxBHsbmz5IkqRORQaHFvhpRxYP/7gHX3cD6x5yVXBbcHvdXEV55Rbmf7YVgWvZ6W2T6q5WigvxIi7E66TXePCsBDwMWsb0DGxyM9ioHoHseWomCoJnfj1IicnGSxcNxNddX69tZkk1M15biyoEn88fwZ1T4ikx2bhw8Kmn7DZZHSzZl8fw2ACiAz3YcrSYcrMdRXENS03r23S6DUmSOhcZHFrgUG4lqoAys40qq6PBiVd3vRa9VoPdqRLexBxEQ0K83Zq9FNRid/L99kzsDpUfd2QhhGt466oG0ncUVFpd2WMVyCkz11suujG5iNdXJHHD+O7M6BfW6HUf/mkPy/bn42HQsvPJGczoG8ay/fkYdRrGxXft2tOS9Hclg8MJlu7PY+XBfO6aGk+k/8lzDB1z59Q43PQaBkT6EeTV8NCJr4eeVfdPothkpXeYT2t3GSEE29NLiQ3y5Is/03lndQoCQbC3EZPVyegegQ0eNzTGnxcuHEB5tZ1zB0XUe/6xBfs4WmQitaiqyeDgrtfWZJB1zZN4GnW8e+XQFr82SZI6jgwONexOldu+3IEqBOVmO/9tRnptbzc9985IaLJdsLexyXH39GITR/KrmJwQjO4kmVE3JBdx42dbCfFx48dbxxDoZeStP5J5Z3Uy7not983ohaKAm07Lsnsm4tXEMNQFJwwhOZwqm4+WkBDmTZCXkQsHR/D6yiTOayBw/NU/zx/ArP7hzSoCJElS1yCDQw2dRqFvuDf7cyoY07N9h0Isdidnv7kOpyq4YVwP7p/ZcMD5dONRqu0qacXVvLb8CP+8YAAlJitCuOotzB0SxeBof0J93JoMDH/1z8UH+WZrBl5GHVsfm8adU+O5c2p8s4416DQNVsU7FSUmGzvSSxkXHyT3RUhSJyCDQw1FUVhw+ziqLA58PepP4LaEyergnLfWk19p4b7pCcwbEVVn05oQrj+ur0+ez+i2SXGsPlSIUwhGdncNFz10Vh/iQ70ZFOmHu0FLv24Nf3pPLqjih+2ZXDA4ssFU2pUWO0KAxa4iBDRzi0SrufCdDeSWW5jSO0QOSUlSJyCL/bSDqz7cxLpkVw1prUZhfFwQn14/ok6b1MIqDudVMq1v6EmLCL26/AjdgzyYMzCiTrGf5pj+6hqSC1zFd9Y8OLne8yarg4W7stiW7kr1/cx5/ds1VfbYF1dSVGVjbFwQH187vN2uK0l/Z7LYTwfbcrQEAI0CWuV4qc4T9Qj2okfwyZe0frohjf/9mY5GUZgQH3LKwaF3mDdpxSZ6NXDXIIRg/mdb2XK0BK1GQaMoDI8NYN6I6FO6Rkt8f8sYNqUWM10ue5WkTkEGhzawLa2EpfvzuGZMLJH+Hvzr4kF8vz2LG8Z1p6jKxrQ+p/4GOCDSF0UBX3c9Qaexqez1eYNJLzYRE+hZ7zmTzVmbHluvKOg0SqM1INpCNz93Lhxy6nssJElqG3JYqQ30e3IJ1TYnY+IC+fKGUa1yznKzneyyanoGe51ydbZtaSUcya9i7tCIkx778fpU1hwp4slz+hIb6IlW086TDpIktTs5rNTO4kO92ZddzoBWWtpZVm1j4r9WY7Y7eefyIc3acSyE4P7vd7MxpZiiKisaRSGvwsy90+uvhCqotJBbbuHG8T3oecLQlsnqYG92OYOj/Tq0XKgkSe2v+Qn6z3BbjpYw9sU/eOznvS0+1/e3jOaP+yZitjmZ/toa9ueUt+h8ZdV2LHYnQghSi6pO2u7d1SnEPfob//z1AGXVdn7emU1uuQVqbg6DT7JR7+lFB/ho/VGu+3QLDufx+ZDLP9jENR9v4a6vd7ao/5IkdT0yONT4uKY4zZebMzDbnC06l16rwdtNz/82pZOUX8VH64+26HyxQZ68dmki90zrxdWjY0/a7vvtmThUwU87s/Hz0HPJsChiAz344JphfHvzaK5sII0GwMBIX7Qahai/7AovqbahCkGxyYaqusp2lphsddoUVVmZ+K9VjHvpD/IrLC16nZIkdR5yWKnGDeO7cyC3gskJwbgbWj6E4ueh5+wB4Ww5WsLlTaz62ZBchNnmZGqfkJPWYDh7QNMV0Z45tz+vLT/C/HHdURSFF+cObFZfb5nYk3AfN+77fheTXlnN8nsm4m7Q8tUNo1h5MJ/ZA7vxr6WH+WTjUbyMOrY8Oq221sS2tFLyyl1BYVNqMeclNr2jWpKkzk8GhxrDYgNY28D6/9OlKAr/uXxIk+12ZZYx/7OtKMB/Lh9SJ9X3qRoXH3Taie5Si0wIFPLLLfyyO4e5QyOJCvDggsGR7Mspp7DSiirAZHWiCoEGV3CY2CuYiQnBOJyiRX2XJKlzkcGhnSXlV/L+2lQuGBLBmJ5BGHUaECAUVwK703Uor4LUQhMz+4XVWWlksTvRKE3Xf75mTCwZxSZ+25fHk4v2kVZsotrm5PM/XTWlZ/UL48k5fRka418n95O7Qcv7zchDJUlS1yKDQzt78Ic97MwsY+n+PPY8PZM+4T78fPtYbA6VQVF+p3XOsmob57+9AYC7psbX1ozYn1PO3Hc3uhLx3TuBEG838issmG3OOtXeAAI8DbwwdyBLD+SjqgKz3ckXm9JRBQinoMrmPOmchSRJZx4ZHNrZqB4B7M4qY0j08U1mfcJblspbUVy7mlUhMJzwqX5vVrkrX5LDydFCE1a7yozX1uJUVRLCfJg1IKxO8SE3vZaFt49lX045Zw8IJ9zXjS83ZTCtbwh3TenV0KUlSTpDyU1wHaC4yoq/h6F2Urc1pBWZSC+pZnxcUO15LXYnV3+0mUN5lbx00UAi/Ty4+L2N2JwqqgCtorD18WmnnIpDkqQzQ2Ob4ORS1g4Q6GVs1cAAruWuE3sF1zmvm17LwbxKKiwOXl+exIBIX/59SSJXjY7BoNUwONoPvwZKiJ5MldXB/E+3cuPn26i2OVq1/5IkdS5tHhwURflYUZQCRVH2nfBYgKIoyxVFSar527/mcUVRlDcVRUlWFGWPoihNL/fpYrLLzCQXnHwjW2u7aXwPgrwM3DKxBwCzB4bzf+f258hzs/jh1jFNBikhBE7VdXf5x6EC1icXsfZIIWsOF7Z53yVJ6jjtcefwKXDWXx57GFgphIgHVtb8G2AWEF/z5ybg3XboX7vJKK5m2r/XMPvNdWxILmqXa945NZ5tj0/ngiGRbEwu4tlfD5BTZm7WsSargwkvr6Lvk0vYmVHKqO4BhPq4EebrxvDuAW3cc0k6bm3WWh5Y8wApZSlNts2pysHmtDXZrrOptld3dBfqaPPgIIRYC5T85eHzgM9qvv4MOP+Exz8XLpsAP0VRmt791UVUWOwIIVAUWJdUyJH8ylM6dvab65j8yuraTWenQgjBtZ9s5eMNR3l8wb4G21jsTs5+Yx0DnlrKnqwy0ourya+04lAFf6YWE+LjxtoHJ7PmgcknrZktSW3hvtX3sSRtCc/8+Uyj7T7Y8wGzf57NJb9e0mjhrM7mhc0vMOqrUTy98emO7kqtjppzCBVC5NZ8nQcc2z0VAWSe0C6r5rEzQv8IX968bDDnDOzGJxuOcu5/1jc75cT29FJSCqrILjWz9sipD+koikJ8qBdaRSHxJEtm04urSS6owmRzsOpQAX3CvblxfHdm9Q/jsuHtV9tBkv5qaOhQFBTGR45vtN3+4v2oqkp6RTqqqF83pbNal70OgWBD9oaO7kqtDl/KKoQQiqKccohXFOUmXENPREd3nTeuGf3CKKqy8cueHADUZn66GdU9kNE9AzHZnKddEGfB7WMprLQS7uvW4PO9Qr24clQMKYVVXDYiGkVReGBm7wbb/r43l2+2ZnLfjF4MjPQ7rf5IUnO9O+1dzA4zHnqPRts9OvJRoryjGBcxDq3m9DeVppSlsDFnI3N6zMHfre1rm7ww/gU+2/8ZV/S5os2v1VztspRVUZRY4FchRP+afx8GJgkhcmuGjVYLIRIURflvzddf/7VdY+fvaktZVVWw8lAB4b5u9G+ltN6nyuZQm9w13Zh+Ty7BZHOSGOXHgtvHtmLPOo7FZEdRwNjKNcSltlduLefZP58l3Cuce4fee9IcZSdanracrflbuXngzQS6B9Z5btw34zDZTYwJH8Pb095uq253uM64lHURcE3N19cAC094/OqaVUujgPKmAkNXpNEoTO8b2mGB4elF++n1+O8888t+hBCo6ql/QDhWU+LsAWGt3b0GbU8vZcHO7DopxVtTUVYlnz28gc8e2Uh5YeeaGJSa9nPSz6zMWMlXh77iQMmBJttX2ap4YO0DfHv4W97a+Va95wPdAtEqWoI9gtuiu11Cmw8rKYryNTAJCFIUJQt4CngR+E5RlPlAOnBJTfPfgLOBZKAauK6t+3cmcU12N+MT04E8AJbuz2fV4UJyysx8fdOoOru2m/LGvMG8ekliu1SMyyu3cPkHm1AUKDHZuH5c91a/RmmeKyAIVVBeaMY3uPHhC6lzGR4+HJ1GR6B7ILE+sU22d9O50c2rG7lVuSQGJyKEoMJWgY/BB0VR+PLsL0kuS6Z/UP8mz6UKFY1y5m0Za/PgIIS47CRPTW2grQBub9senXnsTpUL3t7A4fxKPr1uBGPjGs/M+srFiXy4LpVZA8J49Od9OFXB+qSiUwoOQJOB4VBeBQ/+sIfx8UEnnbtoDr1WQaNREELg7dY2P7I9BwdTXmRGp9MQ1Ucu0+1q+gX2Y/MVm1FQmvUBSafRsfC8hVTYKgh0D+SJDU+wMHkhc+Pn8tSYp/AyeJEYktjoOVShcs3v17C3aC+vTnqVKdFTWunVdA4dPiEttUyJycbhvEoO5VXiVAXLD+Q3GRxG93RNbgshSCuqJqWwiitGtv6k/rurUtiTVc6+7HJuntgTH7fTG8sP9DKy7B8TyK+wMDSmbSYHNVoNw86KbZNzS+3jVD+967X62rmGLblbEAg2521u9vFV9ir2FO1BCMHKjJXNDg4O1cH8pfM5XHqYt6e+zdDQoafU7/bytw4OFruT1EITCWHe7TI80toqLHYm/WsVVofKjL6hWB0qN03o0ezjFUXh/pn1a0q3lkuGR7H6SCEjugfgbWzZj1pUgAdRAXKoRzp9ewv34qH3oKdfz3rPvTzxZb4++PUprRbyMfjwwLAH+DP3T24ZdEuzjysyF7G7cDeqUFmWtqzTBoe/deK989/ewIGcCi4YEsFLzaya1pnkV1gY//IqEHD75J7cPU1mTpWkhqzPXs89q+5BIPjunO/o4dv8D1GtTQjBGzveYHfhbp4Z+wxR3lEd1pfGViv9re8cMkurcagqR4tMHd2V0xLq48YHVw8jKb+yXq2F4iorpdV24kK8Oqh3bSPvaDkGNx0B4Z5NN5akGmbH8ZQxHZ1aQ1EU/jH0Hx3ah+b4WweHL+aPZMWBfC4aFtnRXTltE3sFM7FX3eV2ZdU2Jr2yGptD5d+XDGLOwG4d1LvWdXRPEcs+2IcA5j0+Ar9QOcwkNc+06GloJmjw1nvTO+D0F0ecqMRSwkd7P2JY6DAmR7deieHO4m8dHPqE+7S40E5nVGV1YHWoIATZpc1LstcV2K0OUAABJbkmjJ463L1kLQqpaYqiMDW63gLJFnlzx5ssSF7AVwe/Yt28dXgZzqy79L91cDhTRfp78N8rh5JWbOLyE1YhHc6rZH1yERcOjsC/Cxb4iR8WilaroTCjkmUf7ker13D182MwussfY6n99Q/qz8KUhYR6hOKmazglTVd25u3cOEO9vOQQPR/9jX8vO9ys9pN7h3Dd2O4Ydcfzy1z83kZe/P0gD/20p6262aYURaHnkBC0eg0CgdPuxG5xtvl1hRB8sSmdN1cmYXN0nWRuZ4IN2RtYmbGyU2ZYvajXRXx21mfoNXpuXHYjFsepZ0sGSK9IZ8p3U7hg4QVU2dqv1ktTZHBooe+3ZRL36G/c9uX2Nr3OzzuzcaqCn3dmn/Y5Ar2MaBSFMO+O/5STtDWftd8ewVx16pODg2dEM/r8nsy6dSBe/m2fOnxnZhn/XHyAt1cl8/POrDa/nuSyp3AP/1j1Dx5e+zCrM1c3+7gySxlfHvyS1PLUNuvbMbsLd5NVmcWeoj0cKG46bUeRuQi7017nsQ3ZGyizlpFZmcmhkkNt1dVTJu/HW+jnndk4VMGSfXnNTl9xOp6/cADvrErh9sn112g316I7xpJUUMWgDs6iaq6yseLTA65Pg0IwYd6p7bXQ6bUkTmvdTXtCCFJ2uFKh9xwSXOf/sZuvOzqNBrtTPeNWf3Vmbjo3BK47Bk9981enPbbhMf7M+RMvvRdr5609pWvaVTu7CnbRO6A33gbvJttPj5nOLym/4GPwoU9An0bbvrfrPd7e/TZeei/WXboOnVZHYXUhy9KXEeAWwLCwYQwKGXRK/W1LMji00KNn9+G5xQc5f3C3NgsMAJMTQpicEHJax+aUmam2OYkL8TrlFBltweCmw9PPiKnMSliPjkk++FeZB0pY+Znrk5/RcyBRvY+n0AjzdWPjI1OwOVRZ5Kgd9fLvxTezv8Gm2ugb2LfZxwW6BaJRNPgZ/U75mk9teIpl6cuI8Ipg4fkLT9qu2FzM/uL9jA4fzaSoSby/530uWHQBz459luFhwxs85ve03wHXzuoJ307go5kfsT57PTsLdqJTdFzX7zr0ms6TEVgGhxbqH+HL1zeN6uhunFRmSTUzXluLKgQfXjOM8fEdn2VSq9Nwxf+NwmZxnHS1UUF6BQc25NB/QiRBkY1/Wq8ssZC+t4juicF4+p7em7fRU8+xYW23BlJ2n27qD6ll4vzjTvmYJ0c/yXlx59HLv+FNoUXmIiqsFfTwq78RrsRSgipUyqxlHCg+UC8oVdmqWJ21mn9v+zeVtkpmdZ9FTlUOTuEkuyqbG5fdyMqLV6JRNLV1IP7I+INdhbu4qvdV/N/m/3Odx17FqsxVTImewmf7PyPcK5wYn+N7lfJMruSYge6BbM/fTm//3vi5+Z3y96Il5JzDGa7cbEfgKk1aWGnt6O7U0uo0jS5DXfLffexfm8OyDxsuaXqiX97cxbrvkvjtXddEe8rOApZ9uI+y/Oan3g6N9eHSx4Yz7/ERBEc3PZwgtb6C6gJWZayqNyZ/qnQaHUNDh9YbFhJC8MWBL5j540wu/vVinlj/BFtyt9Rp8+L4F7mq71WUWEq4bPFlfHf4uzrPP7TuIZ7e+DQlZlflY4vDwtOjnybAzXWn6RROzltwHlO/n8rGnI2UW8u5b819fL7/c3YW7cSgMaBFS5R3FBfGX0jvgN58NPMjgtyDWJG+AoAjpUeY8/McZv80mwfWPMAdK+/g0l8vbdH35HTIO4dOZk9WGY/+vJez+oVxx5T4Fp+vf4Qvb84bTFm1nfMSO3fF1eLsKg5syKHPmHBCuvtQVWYltIlhp6St+ZgrbaC4PvELVbD0g/0IVWA1OzjnzsRmX98/TO667ihCCC7+5WKq7dXM6TGHp8Y81erXWJWxite2v4ZNtaFBw6LURfx29DdWXryy9lO5n5sfTtW1Ak4VKkmlSXXOcWzYJ8wrjNsTb2da9DQ89B5c2edK3tv9Hu4699rd2EdKjjA8dDhB7kEUm4sZHjqceQnzyDHlMD1mem2iwJe3vsyWvC1sytnEnJ5zOFR8CKvT9UHuaNlRhBCY7O2fxUEGh07mjRVJ7MuuYF92BTdP7Ilee3o3d+XVdrzcdGg1CjP6tU9BnpZa8r7r037aniKufHY0pjIbnn4nv7tQVcHyj/eTqXHyu6+DmeEK52gUwnr4kJdSTkz/wJMeK3U+TtWJQGBXW3bn0JCP9n7EGzveQEFBp9ExKmwUm3M34653x6irOxQ5t9dclqYtxdvgzT1D76nz3AvjX2BjzkYGhwyuvVsAuGHADQwKHoS/mz97CveQWZnJJQmXoNPo+OGcH7A4LIR6ugpkDQgeUOecM2NnsjVva2197N4BvdEprrfmeb3nodfqGRbaYPqjNvW3TrzXGa08mM8/vt3FlN4hvDFv8Gmd4/ONaTz9y376dfNl0R1j23SivDUt+2g/KdsL6J4YxFk3DThpO1O5lc2LUunWy58Da7N5L7eAIwbX/oODz5yFm16D3erE0Ea1H6S2kVWZxZ7CPUyJntLqm8ouWHgByWXJeOu9+fHcHwn3CiepNIkQjxB8jae3KMLqtPL4+sexOC3cP+x+5v06D5vTxltT3mJMxBiEEFy/9Hq252/nyr5Xctug2/AyeKEKlYfXPszuwt08P/55hoYOrVMwyKE6+OrgVxi1RubGz0WnbfjnuLC6kJe3vszA4IFc1feq03oNMvFeFzK1Tyh7n57ZonNsSClCAAdyK3CoAr22awSH6df1ZdR5PfAOaPyNYcuiVA5tzOXQn3lc9/JYIvMqeODnvUxOCMHd4Nr0Z3DTIYTg9/f2kpNUxswb+8siPp1cpHckkd5tk+fssZGP8faut7mizxWEe4UDEO/f9LBttb2a/+75L9He0ews2MmWvC28POFlEkMS2Zy7mVWZqxBC8LXn11gcFhRF4WjFUcZEjMEpnOzI34FA8OWBL9mWt43vzvmOlLIUlqQtQSC464+7+PWCX9Eomtog9dTGp1hydAlB7kE8v+V5xkeM5z9T/1Ovbx/v+5hlactYkb6CGTEzau9MWouckD4DPTGnLxcNieSdywef9rBUR1A0Cj5B7ih/qa0hhGDzolR+eWs3lSUWIhL8QVHwDXbH6K5jRFwQax6YzNPn9qtznM3i5OieIqzVDg5uPONKkUvNUGmr5JWtr5BjyuHjmR8T6hFKkbmo2cd/fehrPj/wOc9teo5FKYvINeXyzaFvABgQNIAQjxD8jH78kPQDABGeEazLWsfuwt3oNDqeH/c8/kZ/NIqGSlslADE+MfgYXDndfAw+TPpuEpO/m0xaeRoAuVW5OIWTQnMhqlBZm7WWSltlvV3iYyNcowLRPtF1hrhai7xz6CJyy8089tM++kf4cM/0Xo0OFUX6e/CvizvPZhprtR2Du+60h7cqiy3sWJqOqgr2/JHJ2IviiRkQhN6gQdNI8DO66xg6K4bMAyUMPSvmpO2kM9dn+z/jy4NfoigKmRWZfLL/E4xaIysuXoG7zr3J4+P84xBCYNAamB07mx35O7iy75UA+Lv5c9/Q+3hr51tU2ipRNAq51bmkVaZRYC7gp3N/YnbP2QwMHsgXB7/g0gTXiiOD1sCqS1axr3gfr2x9hayqLFShsrtwNxtyNnBb4m3sK9pHtE803xz6BnedO2O/HsuEyAl17iDGRYxj6xVb0WlO/3erMTI4dBEfrz/KqiMFrE0q5OJhUV2mKtq6b4+wZ3UW8cNCmTG/X9MHNMDTz0hgN09K8qqJHegqgdrcZHujzu3JqHNPf1e51LX1C+yHoih4G7z58uCXWJ1WVKFiV+2403RwKKouQqtocagO5iXM49mxz9Z5/t/b/01mZSb+Rn9eHP8iXx36ijVZa5gePb22zf1r7ye5NJnFqYvxMfrw3rT3iPaJZlnaMvYW7QUgyC2I5enLWZ+9HiEE9w2/jypbFd4GbzIrMxEItuZtrdc/vbbt9t/I4NAF/JlSzBebMgBICPUm1MeNzanF3PXNTsbFBfHKxYM67aRz5qFSEJB9uPS0z6HVabjksRGt2CvpTFZkLuJwyWGifaIZEDyAFRev4HDJYe5YeQcaRcO8hHm1wzoNSS1P5VDxIabFTCPaJxpFUdAqWoLc69dmv7LPlfxn53+4os8V7Cvax6bcTQS6BXLjwBsB15BoblUuNtWG3Wanyl7F8vTl6DQ6FqcuRiAIcAtg5SUreebPZ1CFikDwytZXXPuTUBgVPopZ3Wdxbs9z2+x71hAZHDo5pyr4ZXcOFrsTRYFPrh+OQafhf5vSya+w8tOObP7vvP54tbBGc1uZfl1fdi7PoP+Ezr3HQjozqEJl7qK5VNmqcAonBq2BH8/5keFhwzmn5zkUW4q5edDNJz3e6rQy79d5qEJlf/F+Hhj+AIsvWIxRa6yzQ9nsMGOym7i8z+Vc3udyAP5v4//hFE4qbZU4hRMdOg6XHsZkN6FBQ6xvLEatke6+3Xlw7YOoQmVA0ADuG3YfGkXD46MeJ9gtmA/2foAT114LBYXZPWZzXtx5bfp9a0jnfEeRALjuky2sPlzIPdPjGRbrz/DYAEJqMqreOL4HB3MrmNgrpNMGBoDgaO/THk6SpNNxbOgIXJ/ciyxFRPlE8fSYp5s8VoMGnaLDLuwYNK49Nn9dBVRtr+bsn86mwlbBKxNfYWDwQDZkb2D+gPnE+sYyKHgQRq1r70S4ZzieBk9MNhNPjn6SoaFDyanKQSBQhcqDwx8kMSQRcO3svn3I7fQL7sezfz7LOT3P4dbEW2vP1d4677vK35wQgjVHChHA1rRSvr9lTJ3nB0X5sfK+SR3St86gMLMSrU7TYC3pDT8msW91NqMv6MnAKR1XvF1qfxpFwzezv2FnwU6q7FX4Gf1IDE5s9vF6rZ4fz/2R5LJkxnQb02CbMmsZFbYKhBAcLDnIO7vf4WjZURICEvhq9ld12voafVlx0Qrsqr02s+z67PUIVaBVjtda+e7Qd/xn13+4vv/1XNv/WiZFTap97rXtr7ExZyPPjn221UqcNocMDp2Uoij8++JB/LInl4dntd8PRHuzWRwkby/A4K7D6KEjMsG/yfmTXSsy+PPnFBSNwsUPDyMwom5ivoMbcnHYVfavy5HB4W8o1jeWWN/Y0z4+3Cu8di9EQ4Ldg3ly9JOkladxTd9r2Ji9EUVRMGqNZFdlszFnIzNiZtTuWzBoDRi0x3f6e+o8cQgHOnSEe7qu88n+Tyi1lvLp/k+5tv+1ABwoPsCqzFV8su8TBIJP9n3CSxNeOu3XdapkcOjELhgSyQVD2mZTUGex6n+HSN1ViOoUaHQw84YB9Eg8eebY9P3F/LkgBdUp0Cpgt9avBDfu0l7s+SOT0efJVUrS6RNC4BAO9Bo9Xx38ijd2vMH5cefzS8ovOISDb2Z/g5fBi/emv8f2/O0MDxvO+QvPp9hczPK05bw/4/1657Q4LLy24zVXmhBhZ132Oi7qdRF3DbmL/+z8D/MHzK9te/3S6zHbzQS6BeIQDubGz23Ply+Dg9SxjB46VNW1uUd11H3O6VTZtCAFjUZh5Lk90Gg1KApoFAW0MObCuAbrQfQeGUbvkV0jn5TUOQkhuHbJtewq2MXz457n60NfU+2oZmHyQpzClQPqYMlBevj1wNvgzaSoSQghsDgsOFVnnXmCInMRqlAJ8Qjh+yPfU1BdALgmm/2NrrTes7rPYlb3WXX6EOYRRmZlJmd1P4uHRjzUfi++hgwOndS6pEJWHMzn5gk96ebX9HrsrsRSZWfDj0kEdPNi/Lxe5KWUU5JnwsPHSPdBx5cLHt1VxL7V2aBAWA9fug8KJrpvIHPuHIRWryGsuyswVBSZMXroMDZQh0E6NUIISq2l+BubHt47k9lUGzsLdgLwR+Yf3D/sft7c+SZX9bmK9Ip0rKqV6THT6xyTVJZUmz21X5BrEUZqeSqX/nIpAsHnsz6np29P9Bo9eo2eN6e8SZ/APry76136BfVjQuSEOuf7avZXZFRm1KlLsTh1MZmVmVzT75pmbeJrCRkcOiFVFVz/6VYcTkF2qZkPr2m4slRnYK22k32kjIgE/0Y3plVX2Nj9RyZRvf3JSS7j8OY8NBoFT18DgZFe9BgSTN+xdavpBUV6uVJpKNSZV4jo5fq0lbqzkKQd+RzdWYjOoOWqf46WAaKFnv7zaRYkL+Ds7mfzwvgXOro7HcaoNfLU6KdYk7WGu4fcTbRPNBOjJjZ6TKRXJBFeEeSZ8hjbbSwA+aZ8wHWXkFKawtSYqSyZuwQPvQeeek9e3vIyXx/6GkVR+OPiPzhQcoB7Vt1DYnAi705/l2jvaLIqs4j2iSatPI0nNzyJQOCmdaudm2grMjh0QhqNQq9Qbw7nVTIkpuPLejbml7d2U5RVRUi0Nxc+MPSk7dZ/f4Tk7QXsWp7B7NsHoigKHj5G1n13BEuVg6AoL0bMOV6ZqyC9gqKsKuY+NAS/YE+0+rppMoqzq/j9v67dpYoCDpuKtdohg0MLbc/fjipUduTvaLVz5lTl8Mq2VxgdPpqLEy5utfOCa1/DN4e+QafRcXGvi1v1bmdur7nM7dX8cX4PvQe/XPBLnVryo8JH8fCIh0mvSOfpTU/zxMYnSAxJ5O2pbwOu9ByKouBr9MVd787i1MVUO6rZlLeJEnMJly6+lFJLKQ8Of5BZ3WfhpnPD4rA0WMWutcng0EktuH0sxVU2wnxbN3Vxa1OdAoRrfqAxQZHepOwoxDvQjag+Adz42gQUrcJnD28AwMPn+GoOc5WNH/+1HdUhUDQw9eo+JIyqu3qkKKuq9uuQ7j4MmR6DT5A7pnIreanlxPQLRKvX/K2HRk7HSxNe4ptD33BJr0ta7Zxv73qbFekrWJmxklndZ+FlaLzs66lYlekq4AMQ4RXB2IixrXbu03Xiz5yiKMztNZeFyQtRVRWncLIzfydLji5hbq+5XBh/ISPCRhDgFoBRa2T+gPlkVWYxMnwk+4v3185PJJcm49vbl6Vzl2Kym1o9A2tDZHDopPRaTacPDADn3DmIjAMlRPdrPCvkkJkx9BwSgqevAUVR0Bm0OB0q5kpXYRet7vidgUajoNEoqLgCT3HO8SpY+9dlU5JjYtD0aIKjvXE6VWbfNhB3LwNCCH54cRvmKjvd4n3JTS7H08/IJY8Ol7UdmqlfYL96+YNaakLkBH5N/ZXeAb3x0LduTrAQjxAcqgONoqldFtoZnd39bI6UHuF/B/6Hisr3R76vvSuJ9I5ECIHdaaeHbw8+m/UZAA+vfbj2+OsGXAeAl8GrVYNrY+RvjNQi7t4GEpq5Msg3uO4EmlanYfwl8aTuLmTkucdvk40eei57ciSHNuehOlWGTHdlVC0vrGbdt0dQVXDz0nPJo8fnYrIOl/LLm7tqVz6VF1pwOgRVJVbKC80ER51aXWhTmZWcpDJiBgTKwNJCM2NnMiVqSptkD/0z508AVFVt1QJBOVU5OFQH0T7RLTqPEK6aDVvzt/KvCf9iV8EuDpceJtQjtE6bq3+/mt2Fu7l10K1c3e9qPPWeXNf/OlLKUxgdPpoIr/ZPPyN/6qUONXBKVO1GtapSC1qdBkWjcHBjLtt+S6PH4GAMNRPdBzbk4kppLwiJrZs4LWVHvmuIq0ZFoZmY/oEEhHsSFHnqn7R++td2TBU2ovr4M/u2zpP+vCOVW8s5WHKQoaFDa2spN9epZA91qA6u+f0aksqSeHvq2wwPO/mCjG6e3UABh3Bw9e9Xs+j8RS2+O0ktS+XSX10rjD6c8WFtegu7085PST8R5RN10t3Tf2V2mFmTtQaBYGHKQj6Y8QEHig8wMHhgbRubamN34W4Egnd2v8M3h75hzbw1JAQk8P0537fotbSEDA5ShylIr2Dnsgz6je+GRqdh0Ru7XPsYNAo2i2tzW/q+YsC1KmrH0nQQ0HNIMDH9jteHVlXB0d3F9c4/44Z+p/+pv6bg0F8LD/2dzft1HoXmQmbFzuLZcac39CSEYEnaEnwMPiedHygyF3Gg+ABO4WRlxspGg8OcnnPYV7SPbw5/Q6mllDxTXosna0ssJYBrhVGx2fVzlW/K56ZlN5FemY5W0bL4wsWEeTZ9x+yh9+D2xNtZl72O+f3nk1GZwaDgQTy07iHWZq3l/mH3k1OVw6zYWfyW9pvr+taSRs9Zbi3H6rQS4hHSotfZFBkcpA7zx+cHKc42kX24lDEXxQEgVHA4nSga8A3xYOQ53QEwuOuI7htAbnI5fcd1q3Me1alirrShaCCspy/CKRg4JapOYLCZHexakUFwtDfdB518B/Yxcx8YSm5KGdF9A5ts29U5VSf7ivfR07dno+PZJrsJIQQVtorTvtbStKW1yzH/N+t/9AnsU69NqEco8wfMZ0/hnmbVRr4o4SK+P/I9Cgo6Tcve0vYX7Wdf0T4eGfkIWkXLlOgpAHx58EuOVhxFIDBqjae0x+DmQTdz86CbuXf1vazOXM2QkCFsztsMwMtbX8auuubdFBQEotE3/YLqAs5dcC52p533pr/XaOBsKRkcOqH9OeUEexkJ8Wl6DFUIQXJBFZH+HrX1k7uK6H6BFGeb8PQzsmlBCnFDgl11nhUoyTYxfE53dDWvSVEUzrkzscHz6PRazr0rkZykMgZMisTNq/4Qxrbf09i9IhM0cM3zY+usjmqIh4+BnoPb9pPZ6SoyF/HmjjdJDEnkwvgLW3y+l7e+zA9JPxDqEcpvF/520nb/O/t/bMnbwszY069x7m3wRuAa/jvZ8I+iKNwx+I5mnzO7MhuNokEg2FO0p9nzBPmmfG5beRu+Bl/envY2Bo2Ba5dci0M4mBkzkxcnvFjbdkLkBL48+CXhnuG8P+P92rxJzXW45DCHSw7jVJ3kmHLoG9CXAyUHsKt2V9+Fq3YDQJWtiqVpS9mSu4VbE2+tU0eiyFyEQ3WAAmkVaTI4/J38sD2Tx37eh16rYcNDU/BtYt3+ayuO8N7qVLr5ubHq/kldaunmmAvjGHZ2LJ8+vAG7xUlhRhV9x0Ww6A3XxLLD7mTsRfGNlgI9JiLB31Vb+iQCu3mCxjXZbXBzBRxrtZ2yAjMhMd5d6vv2/p73WZiykEUpi5gYOZFA95bd3eRX56MKtXY45WRifGKI8WlZudWxEWP54uwvcNe5t/hcx8T7xeNv9MfL4MWUqCnNPm515mqSS5MRCBYkLWBe73n4uflRaimlm1fdu9NhYcPYduW20/o5SS5N5orfrkAIwZwec7hh4A2UWcu4YekNOIWTp0c/jZfBC4PWwO7C3YwIG8HNy29GCIHNaaszhNc3sC9PjHqCInMR5/c8/5T7cipkcOhkCiqsANicKhaHE18aDw7JBSacqkpOuQVVgLYV3+PsThWt4lpW2mg7q5ONPyfj6Wtg6Fmxp/QLZHDTMfzsWHavymLY7FiWfbgfp8O1Z2Lvmmy8A91JnHb8k6DFZCd5ez45SeUMmhpFaGz9il5pe4vQajVE9T2+vDZhVDjh8X64eerRGbSoquCr/9uMtdrB4BnRjDyn7TcVtZYRYSP47vB3RHpHNlrRrLn+b8z/sShlESPC2qfaXmunnf4h6Qfyq/MpshRRUF3QZEZWq9PK/238P8osZai4ftY25mzksj6X8dO5P5FRkUHfwL71jjvdDxA21Qa40olPjZlKd9/ulFpKcQgHQgh2FOzgmbHPAK47FKfqJMo7iszKTIaEDql3vvYq/CODQydzw/ge+Ljr6RHsSWgzhpWePa8fvcO8GRsXiLYVJ0/3ZJVx8Xt/4uehZ9k/JjZ6B3Poz1wOrM9BURQiewcQFOnFtt/S8PQ10H9iZJO/VINnxDB4hutTZPL2AlJ3FgKuyWCDu46irCoWvLoDL38jFpMdU5nrl60gvYIrnxld51wZ+4tZ+sE+EHDu3YmEx/nVPucTeHycWAiBtdqBUAVVJZZT+t50tGkx09hw2QbctG5oNS0fSvQ1+jZrbL+zmhA5gf8d+B8xPjH1PvE3ZE3mGpakLUFBYUjIENIr0rmi7xWAa9jrWF6k1tI3sC/vTnuXant1bf4kfzd/bhl4C1vzt9bJxAqg1Wj56byfqLJV4e/WcRkSZHDoZAw6DVeOav7tdqCXkbumxgOQUVzNvPf/xNddz3e3jMbb7fRTSWxLK0UVgrJqO0eLTSR6+LF9SRp712Qz/uJ4eg45Ph4fEuODoijojVq8Aoz88fkhUnYUoGgUQmJ9G/x0fzJn3difqjIrqqpSXW4nrIcPO5dlYLM4KMt3ugKNAgiI7F3/F0dn0FCzd6425YYQgoMbcwHoMybcVRNYq+HC+4eQm1xO7zGdd/PUyRwrHCNBYkgiW6/c2uz2Xxz8ArtqR6/R88L4FxoMKE7VyQd7P0AguHHAjS2e6G5obuDWxFu5lVsbbK/X6Ds0MIAMDmeUNUmFFFZZKTbZ2JtVzpi4+gXRm2tWzyBSYkMIjPZiUKRr8m377+nYrU42/3KU2AFBtW++od19mP/v8Wg0CgfW55CyowDVKdDrNXgHnNrGJEWjHD9GVPPlU5tw89QTFOmFh6+RUef1IPtIGd0HBdW5EzimW7w/F9w/BEWj1G58y9hfwrpvjwCuiebYAa7vS0iMDyExLR+WkbqWEksJWkVLT7+eJ73TWJu1lo/2fgRAL79eTI2Z2m79E0IgEGiUpufa2pIMDmeQ2QPCWbI3Fz8PA8NiG09n0RhrtZ1fXtxBtCoY2yusdlho6KwYdi7LoDTPxJdPb+LKZ0bVThbra1YVefoaUTQKOq3CJY8Od6XBUEWT8xYnyjpUwqaFqTgdKhWFZiqLXcM+pXnVVJVYGdRAdbfCjEpK803EDQmp94bv6WesvZvw8u+YerzSqRNCsD1/OyEeIS3eqXyid6e+y4qMFY2uuurh16P25749ktwdU2QuYu6iuVidVr6a/RU9fDtuLkwGhzNIgKeBL28c1eLzOB0C1akiBJir7LWPDz0rlooiCwc35mAqs+KwqRjc63668Qow0nt0GH3HdiN9bzEbfkgiONqbix+pe1stVEHqrkJ8gtwJjnZ9wnfYnfz+3j6yj5TitNck8lMgONKLouyq2n//VXWFlR9e2oaiQEWRhWGzYus8H9jNk4HTolBtaoM1p6XOaUHyAp7f/DyKovDbhb/VWdLZlP/u/i+LUhbx+KjHGd2t7rxUlE8U1/W/rtHjY3xiWH3JagSiXYfwjpQeodpejUCwu2C3DA5S53JsqafAVZjnRKPO74HBTUt4nG9tWotjzHv3suDtbOwYKMuvRm/UIoDCzKp6dw97V2fx588pCOCqf47G09dIfmoF2UdKUR1qbRDQG7XMvn0QVaUW7FZnbS2HE238KaU2dYZOX/9WPOtQKXtWZoKAkFgf4oe3fUZLqeXMDjPgSsvt+GuZwCa8t/s9HMLBu7vfrRccmqu1kwQ2x4iwEcztNZfcqlxXKVGn/ZRSj7QmGRykehRFQad3ZU39awBw9zIw9qL4Bo/LeehhjP4X4/CKwC/Eg8EzonHz0mN015GTVEbkCfsQclPKcDhUNBooSK8kdoCBkFgfQqK9MVfZOffuRIQQGIw63Lz0jW5ac9hVNFoFrU7DoKlR5CaXUZJroveocLR6Db4h7iiKgsPuZM03h3Hz1NdZ5trZFJuL+fzA54wMG8mYiObl8DkTXZpwKQFuAUR4RTQrVcWJruh7Bb+m/Mq1fa9tm861EZ1Gx12D72LSd5PYkLOBtPI07h12b4f0RRFCNN2qkxs2bJjYtm1bR3fjjFJVaqE0t5rI3v7Nzi+U+9wL/JKcgN3oA7j2GcQNCWHdt0cQwLzHR+AX6oHqVHn39tWAq1CPVqdh0hUJ9Wo2nKgkx8SC13bg4Wtk7gND0RuPL+G0mR0kby+gW7wfRg8dnz26EXClCR8xx5V+w1xp4+MH1gMQOzCwUyfTe2TdI/x29Dc0iobNl2/GoG18N7fUdrKrstmcu5mp0VNPeVf06bI6rUz6dhIO1cH1/a/n1sSGVzS1BkVRtgshhjX0nLxzkBrk5e+Gl3/TK41sFgcLX9uJxWTnnDvvRv3nFnCoIFzDOX3Hut7wFaVmmSmg0WronhhE+t4ijo0fWc0NDxsIVbB9aRqZB0sxV9mxmZ0U51TV1o8GV96lY/mWbGYHWq2C0ylw9z5+O+7ubWDIzBhSdxcw9KzY0/mWtJs+AX1YmraUcM/wFi+hlFrmmt+vodRSyvL05bw77d12uaZRa+Snc3/iaPlRRnVr+Rzi6ZI/eVKLFKZXUpxjQqiCjAMlzH1gKCk7CijKriRhRDhxQ0PxCXKvLes5eFo0ccNCOfsWV8rivNRyKorN9EhsOBledlIZ239LRwjwD/MgtLtvo8tPDe46Lv+/UVSVWAmJrVvDwc1TR1memb1rsgjr0T6fAk/H1f2uZlrMNALdAzt8OePfnYfOgzKlrN33lYR7hRPu1bH7b2RwkFokrIcv0f0CsFTa6TkkGE9fY+3qo2NCYnxY/tF+ygrMrPnmCHHDQuscv31JGss/OsCEeb0YMCmyzrF+Ie5odBpUh8qES3sR2TsAU5mVPasziekXRLd4v3p98vQ14ulbf8lq0jZXycWju4ta4ZW3rebs9D2T5VblYtAaWpw3qqX+d/b/2F+0n2FhDY68nNHknIPUZuw2J398dpDc5DJ8Q9zJT6tk4JRIxlwQV6fdu7evQnUKInr5cf69Q0jbW8TqLw8RkeDPkJkx+AS68cNL2ynNq2bs3DiyDpeQtrcYrU7DzW9ObHbOm/yjFWz5JZW+47t12oyrZzohBFvytuBt8G4wfxHAtrxt3LziZnSKjgXnLejwT9BnMjnnILU5m8XB8o/3AzD9eleRnSOb80jZUYAQYCq3cf2/xuHuXX9ydeo1fTiyJZ9R5/cEYPuSdExlNo5szidlRyHznhhBaV41CEFuchlBkd5k7C/Br2YVUnOFdvfhnLsSW+X1SqdnZcZKHln3CALB9+d8T3df14KBfUX7cKgOEkMSyarKQkHBKZwUW4plcOggTQYHRVHCAIQQeYqiBAPjgcNCiP1t3Tmp68jYX0LmwVLAVb0tflgood190Wg1OB0qEQmujKgN6TUijF4jji9VHHpWDCs+PYDd7KoGpygKZ986gPS9xQydFYOnn2ujnZdf69UMltqHUzhrvz5W12Ff0T6uW+LalPbOtHeY02MOVbYq/Nz86B/Uv0P6KTURHBRFuRl42PWl8hJwLbAPeEFRlJeFEB+1fReltiBUwZIP9pGfVsGsmwecUnK8hoTH+dakqRC18wBBkV5c/vRIDm/Oo/ug4GYtiS3JMRHW3Zf5r4zn6O4iKorMCFUQOyCoNicSgG9w+29QklpuRswMPPWe+Bp8a3f/nrjBzaE60Gl0XNn3yo7q4ikzO8x8d/g7evj2YHzk+I7uTqtpdM5BUZS9wEjAHUgH4mruIPyBVUKIxHbpZRPknMOpKy8y8+UTfyIE9JvQjUmXt26O/WMWvLqDnKQy3Dz1XP9K4784BzfmsOarI+gMGq5+fgx7V2ex7bc0AK57aVzthry13x4hZXsBU67pU1tL2m5zotNpZM3nLmpr3lacwsmo8I5bunm63tn1Dh/u/RCAJXOXtHlt59bU2JxDU+vk7EKIaiFEMZAihMgDEEKUAi2eyVYUJU1RlL2KouxSFGVbzWMBiqIsVxQlqebvjs1be4ba/vtRABQN9J8Q0WbX8Q1xR6NV8DohO6vd6iR1V2G91BwVxRaEEDhsTuxWJ8Ipan/Kjv2wCVWwd1UW1RU2dq/IAODIljw++Mcavn1+K0Lt+gss/i6KzEXM+3UeNy67kf5B/btkYACI9o5GQcFD54GH7sy5o21qzkEoiqIXQtiB2cceVBTFjaYDS3NNFkKcuLbwYWClEOJFRVEervn3Q610LamG0y7Q6DToDBoCI05eVL6lJl7em/4TI/EPPf5Ls/SDfWQdLsU3yJ3LnhoJuLKqWk12Bk2NIqp3AJ6+RoacFYN/uCf+YZ4Ya+4aFI3CsLNjSdqWT1SfABa+vhMUEAJKcqqwW531Un5IndMfGX9wpPQIGkXDzoKdjOnWNVOFzOk5h35B/QhwC8DL0Ha/S+2tqd+iC6j50CaEyDrh8UDgvjbq03nApJqvPwNWI4NDq5t0RW+i+wUS1sO3Tesna06oq3CMzeKqwOZ0qrWP/fbuHqpKrQRGeDLmQtdSV41WU6eo0DEjz+3ByHN78OkjGzCVWvHyN9JreCiRvf1PGhhUVZC2uwjfUHcCu505v8Cdxcr0lTiEgxkxM5r98zQxciLfHPoGL4MXicGJbdvBNnZs1dWZpKngYMA157DhL493B462wvUFsExRFAH8VwjxPhAqhMiteT4PaDCFpqIoNwE3AURHt16u978LvVFLwshTS2bWGpK255N/tAKtTsPs2127pDMPlGD00FFdYSM4uvkT43FDQti9MpNeI0IZ/Ze9E3+1c1k62xangQLXvDD2pCunpFO3NW8rD697GAB3nXttKcymhHqG8tN5P7Vl16QWaCo4vA480sDj5TXPndPC648TQmQrihICLFcU5dCJTwohRE3gqKcmkLwPrgnpFvZDageOmk1xqlMghIpGo1BRZGbxO3sQCFeivHOa/wls3MXxjJ0b16xJaEWj1KYBb8Mbpb8lb4N37bLU9kpOJ7W9poJDqBBi718fFELsVRQltqUXF0Jk1/xdoCjKz8AIIF9RlHAhRK6iKOFAQUuvI3UOdqsTp8M1lBTV1x/fYA+qK2xotAqqCoERXqc8xNXc1UmDp0UTEO6JX4gHRg9519Caegf05vtzvkcI0a5V06S21dRS1iQhRIPJ+xVFSRZCNH4v39iFFcUT0AghKmu+Xg48A0wFik+YkA4QQjzY2LnkUtauI21PEQUZFSROja6dHzCVWTFX2QmM8GTdd0nkp5Yz7bq++Ie5kp05HSpaXesmoBNCUJBeiW+wuxxikv62WpI+Y5uiKDcKIT74ywlvALa3sF+hwM81nxR1wFdCiCWKomwFvlMUZT6uvRWXtPA6UicSOzCI2IF1yz16+hnx9DNSVWpl35pshCrY80cWEy9PYPuSNDYtSCVuaAgzb2y93bJbF6exY2k6Rncd17w49pRqXEvS30FTweEfuN7Ar+B4MBiGa6L6gpZcWAiRCtSruFKzp2JqS84ttb2/lv1sTFFWFeu+PULPIcEMnBx10nYevgaievtTkFFJwijXZHnqrkIA0vcXt7zTJzCVWhCqwGp2uPZTyOAg1Si3lvPy1peJ9o7mpoE3telqvs6s0eAghMgHxiiKMhk49rFtsRDijzbvmdShrMnJ5D39f3hOnEDQjTfWeW7n8nQ2/phC/LAQZtzQ9Kf5TQtSyEkqIyepjP4TItBoXUNEBekVbFqQSu/RrtxKGo1SLzHepMt7s+XXVLrF+bFjaTp9x3bDzavlw0BjL4onoJsXYT190TZQd1r6+/rhyA8sTl2MVqNlcvRkevn36ugudYimciu5AbcAccBe4CMhxKlV+pa6pKJ336V62zaqt2/H/7LL0XodL3aSssP1aT5tb/M+zSeMCiPzUAkx/QJRNApbfkmlvNBMeaGZ/KMV5CSV1Um8d6LgaG9m3TKQ9+9eg+oUFGZUtsrwksFdx6CpJ7+Lkf6+hoYORatoa+tX/101Naz0GWAH1gGzgD64hpqkM5zPOedQufIPPIYNQ+NZNyXAhHm92PxLKn3HNq8gTfywUOJrCvwUZVWxY2kGqiqIGRAICnQfFNTo8YoCnj4GTOU2fIPdT+8FSVIzJYYksunyTWg12r91Jb4mE+8JIQbUfK0DtgghhrRX55pLrlZqOZvFgc3sxMu/fgW1kxFCsHNZBiW5JsZdFN+s4R6bxcE3z2yhqtSCh5+Rked2p8/opoOMzeKgosh8WstdJUlqWIsS7x37Qg4nnblsZgdfPP4n/3tiY+0EcHOU5VezaWEKhzflsWNperOOMbjpuOq50Xj4GjGVWtm8qO5Ge6dDZdeKDJK3u7a35B+toCC9AoObjqBIbxkYJKmdNDWsNEhRlIqarxXAvebfCq4NzC0rAiB1CpZqO1aLAwQUZ1XSIzG4Wce5exsQNemRCjMrm3VMdYWN71/cit3iwOCuxc1Dx+ovDzFhXi80Wg0H1uewaUEqKOCwO1jz5REAzr9vSL2aE9UVNrR6TW1SPkmSWk9Tq5W07dURqeP4BLoz7dq+lOSYGDSt+XmqjO46fIPdqSyx1NZVaEpeajnVFTYQED88hKRtBZQVmIkfHkpEL398glxzChqtglanrfkYAqqz7vBnbnIZC1/fhUancMXTo1yFhiRJajXyI5cEUDthfCoUjcK8J0dQXW6rfVNvSmh3b9fdhhB4+BnRG7QY3HW1acNj+gdy+dMj0btpcfcyYPTQodEohPesm7OnNK8aFFfQqCq1yuAgSa1MBgepRXR6bbMDA4CiaNBoFUDB6KbjhlfrZ/A88XzRfRu+I0kYFYapwoqHl4GQWO8G20iSdPpkcJDalYePgfPvHUxZfjXxw0/9buUYrU7D8LPPvBz6ktRZyOAgtbuw7r6EdZepnSWpM5PBQWo3JTkmfn51B+7eBi56aCg6vYZNC1NxOlTGXBDXZBoLIQQOu4reINdJSFJbk8FBajcZB4qxmR3YrU5KckxYTHb2rs4C4bqbiB8eihCCgxtzsVTZGTQtCq32eMBY9MYusg6XMu6ieJn6QpLa2N93b7jU7hJGhhHZO4CEkaGExHgTGOGFRqtB0SgER7smlQvSKln3zRG2/HqUI5vzao8VQpCTVAYC0vcVnfwieXvhh/mQsqqNX03n8Pzm5xn8+WA+2fdJR3dFOsPIOwepVRxLpWEx2QmJ9SYowhu/0Lo5mdy9DZxz5/Es7d4Bblz/r3EgqB1S8vQzoGgUhCrwDTl+vKIoTJ/fjy2/pGKpdlCaZ6otBlTHwjsgdxekrISH0tripXYqi1MX4xAOFqYs5Lr+13V0d6QziAwOUqvITS5ny69HUZ0CRXFtYrvupXG11d5O5q8V3rz83bj6+TE4HSqevnX3LkQm+LPsg2qEgO1L0pl2bd/6J+w5FXJ3Q+z4uo9Xl0DKH9BjMng2b8NeV/DU6Kf48uCX3DH4jo7uinSGkcFBahU+Qe5odRpUp5OWpj86WdlOo7uOiAR/8lLL6XWyZbDTnoRx/wDjX/Y+fHUJ5O2B4D5w85qWdbATmRE7gxmxMzq6G9IZSAaHLsaamkrxRx/je845eI4a2WAbR2EhFb/9htfEiRhiY9ulX17+Rq59aSxOu0pOUhn+YR5N3jWcKkWjcN4/Bjfd0K2BlF8aLaDU/C1JUlMaTdndVfydUnanzbsM865daLy9Sdi6peE2V16FedcudMHBxK9qu6J9anU1ec+/gNbXl5B770HRtt8br83iYPfKTIIiveg+qBmJAi3lkLoauk8Ad/82758kdQUtSdktdTIeI0aARoP7oHrlt2vpgoNRtBp0gW07tl7+669U/PILpV9+SfW27U0f0JAjS+G/E2HfT6d02I4l6Wz7LY0lH+zDVG5t+gA3X+h7ngwMktRMclipiwm59x4Crr0GrZ/fSdtEvPwS5r17cevdu0374p6YCFotGnd3jPFxp3eSJQ9DSSr8/iD0v7DhNkJA1lbwCgH/WAACunmCAkY3HQY3+WMsSa1N/lZ1QbqAgEafV/R6PIa0fcE+t169SNiyGTQaFM1p3oQOvQ5WPw9Drz15mz3fwi93g6KBu3eDVwi9RoQR1sMXN089eqOcR5Ck1iaDg9Qiiq6FP0Jj73L9aYyl3PW3UMFpq334VLLBSpJ0amRw+Bsq/fobSr//ntCHHsJz5IiO7k7Tht8Abn7gHwO+kR3dG0n6W5AT0n9D+S+9hPXAAQpeeaXj+pBWQVFWFQDmSlfp0J//vQObpYFS5RotDLoUoke1cy8l6e9LBoczjOXwEbLuvJOKFStO2sZv7lwUDw/8581rx54dl3WohAX/3sEPL22jKKuK9H3FFGdVkZ9WQc6Rsg7pkyRJdclhpTNM3rPPYN62nap16/HZtbPBNmFPPE7YE4+3c8+Oc9hUUEAR4HSoRPcLxD/cE61eQ7d4vw7rlyRJx8ng0IUImw17Tg76mBiUk+So8J4yFfP2HXiOHt3OvWu+mAGBzLyhPzqDhtBY127mSx/rAnMfkvQ3IndIdyFpl12Ged9+/OddSthjj520nWq1ohgMJw0gkiRJIHdInzGsqUfB4cB66FCj7TRGY4cEBqG6ai5UV9iabixJUqcmh5W6kOgPP6By2XL8513a0V1p0JbFR9m1LAOdQcu1L4+tU8VNkqSuRQaHLsR9wADcBwxo1XNak5IQDgduffq0+FyWKjtCgMPuRKgC5MZlSeqyZHD4G7McOkTapa7lrNEffYjHsAaHHpttzNw4giK9CIn1QaeXkUGSujIZHP7G1GozxyrzOKuqWnw+vUFLv/ERp318dYUNp0PFO8CtxX2RJKllZHD4m3BWVZF93/2Yt20j6O67Cbz6KjyGDCbyzTcQNhteEyd2aP8qSyx8/X+bUVXBOXcOIqKXTK0tSR1Jzhh2Yea9+yh4403sublNti149VVMa9agmkwUvvYaSVOmUr17N14TJuA9bVqHL3s1V9pQVdey6ooic4f2RZIkeefQpWXccANqRQXmnTuI+fTTRtsaIqNAqwUhEGYzDrOZrDvuJH7N6tNOt21NScG0YQM+c+Y0mUa8KSExPky+sjeWKjsJI8NadC5JklpO3jl0YbrgYBACW1oawtFAwroTBFx3Ld1/+hH/+fNrH3MWFlL84Uenff30q64m/+V/kfPQw6d9jhMljAxj0NQoNHIJrCR1OPlb2IV5TRgPioKjqBhbZmajbRVFwS0hAdPy5ccfMxgQ1maU2DwJbUAAilaLLqQZNZwlSepS5LBSF+Z38cWUL1yExtsbXUhIs44JuvMOCv79Kt6zzsK9b198Zsw47evHfvMN1iNHcB/YunsvJEnqePLOoQuzZ2Whmkw4cnOpPOGOoDHCbsetTx/8516E7+zZKHr9aV9f6+WJx5DBLa8GJ0lSpyODQxdmTEhwDQ3ZbBR/9DGqrfGcRsLhIPeRR6lauZL8F15op15KktQVyeDQgYTNhj0v77SP14eE4DNnjmtSOimJzFtuBaBi+XKK3n8f1WKpe4BWi8bHlSLbkpR02tdtT0IVHNmaR8b+4o7uiiT9rcjxgA4ihCD1gguxpacTct+9BF533amfQ1VRtMfTVFRv344tK5uc++7nWCr2oJtuqn1eURSMCQmYd+5E62Zs+YtoKw4bfH4ulKSQPvgDVi0EBMx9aChBkd4d3TtJ+luQwaGjOBzY0tJACMy795zaoUVF5D37LGq1GdOff4JOh9bbm8CbbkLr443i5gYWC4bY2HrHRr35BpV/rMJz7JhGr5Hz8COUL15M2BOP43/JJafUvxYrSYHs7eB04Fe0EiGmogB6o8zXJEntRRb76UBV69Zj2rCegOuvR3/CaiO1Znmpxnj8070QAhwOFL2egtdfp/j9D0BVXU8qCj2X/I4hJgYAZ0UFzooKDJGRp923QwMHIWw23BMTif3m69M+z2lRVfjlbig6DHM/pLDSH71Ri1+IR/v2Q5LOcI0V+5HBoZOxZWVx9PzzEU6VwPnz8Zo6BUdBAYWvv471SBIRb76BzseHjPk3gKIgnE48x44l+r/vtWo/yn78ibKffiL0gftxT0ys97zD7mTTglSM7jqGnR2LopFV5ySpq2ksOMhhpXbgrKqi6o8/8BgxAn3Y8dQQQlXrpa6wHklCOJwIi4Wid96h6N13QaeDmrsJ0+o1hD/7DAk7d6BarVgPHcZ9QP9W77Pf3Avxm3vhSZ9P2lrAvjVZKAqEx/sRmdAGifLMpWC3gE94659bkqRGydVK7SDngQfJfeJJ0i6/AnANEaVffTWH+g+g/Pff67T1mjCegKuuQhMQ4MqF5DrA9bVWi8+c2QAoWi1aDw/XPoMT9ioIIbDn5dHWd4TBXkUoTgtaRxX+2pzWv0BlHrw+AN4YBEfXtv75JUlqlLxzaAeKwfXmfWyzmLBaqd6yFYD8F15AVFejj4jAlpmJ5/gJVO/Zjfess/CdNg2Nvz8VCxdR+rVr3N9ZXHdJp2q1ouj1tXcgOfc/QMWSJfjMmU3ESy812i/hdNZZ7XQqgozZXN/tZjSoaJ0fAP1O6zwnVVUATjsoQFESdJ/QuueXJKlRMji0IntODmmXXY6i1xP73be1mUq7vfQSpo0ba8furYcPu4aKHA6cBYXkPvY4isEAioIu9EPsGRmYN29BVFYR8fJLuMXFoWg0qA473tOm1V6vYvlysv9xD4YePejx80+Ytmyl4vffQVUx79rdaF9zHn6E8gULCL7nHoJuvqnRtg2Kn4F+Wk3CvfiZTbdPWw+b34cxd0LU8Kbbhw+EOa9BRS4MvvLU+ydJUovIYaVWVL11K86yMhyFhZh3H39z1ri54T1lSm2wsOfkuO4iaoaD3AYNcgULwNC9e+1xFYsWIex2FJ2OkAfuJ+yRR1xBpIZp/QZQVWypqTgrK8l9+OHaFUxh/3y20b5WrlzpusaSJaf3YjUaGH2b609zUn7/eCMcXAgLbmn+NRIvhwn3Qf4++GIuHFh0en2VJOmUyTuHVuQ1dRqey5ejMbrhOebk+wi8Z84ktKwMxc0dn9lno+j1OAoKsGVmYktOwZiQQOn33+M7fVqjuY+CbrsVtaoSj+HD0fn74zlmDOULFqB4eeHZRD3o8BdfoOzrbwi+847Tfr2nJG4a7Pwc4k8j0d/i+yFnB2Rsgr7ntn7fJEmqRy5lbUNCCCp++QW1uhq/Sy5psqhOxk03Y9qwHo2bOwnbm/d67Dk5WNPS0Pr44Na7N87SUrT+/p0zGZ6tGgynsVdh41uw7HHofzFc9GHr90uS/qbkUtYOYt6xg9wnnwJA6+ODz9lno5pMlP3wA279++MxdGid9pZ9+8CpopqbLpNZ+uOPlH7+P6xHj4LdDhoNPrPPJuLll9vktbTI4SXw232QeCVMfuTUjx9zJ4y6DTRyh7QktZdOO+egKMpZiqIcVhQlWVGU1ik11s50QUGuL4RAF+5aq1/w+hvkv/JvMq67HmeVqU57zwkTQKutnbhWrVbs2dn1zms5fJi8x59wTWzbbK6lrqqKPat+205h5f9BeRasf/X0zyEDgyS1q05556AoihZ4G5gOZAFbFUVZJIQ40LE9OzWGmBh6LlsKdjv6iAgA9OHh4HQihMC8fRteEyfWtu/2/HME3TAfQ0wMQlVJPfc87NnZhDxwP4HXXFPbTj0WEGr4nHsOxu498L3g/HZ7bc3msLqWogKE9OnYvkiS1Gyd9c5hBJAshEgVQtiAb4DzOrhPp0UfElIbGAB8L77ItaJICMoX1l19o2g0GOPiUPR6hN3uumsQAsv+/QCUfv0NR+deRNWqVbUrndBqMcb3IujWW+rsvu40FC24+4HODXrNqv+8tRL+eA4O/tLw8Xl7IWVVnWAoSVLb65R3DkAEcGJR5Cxg5IkNFEW5CbgJIDo6uv161kI6b28Cb7mFqjVr8L/icgAsBw9iTU7B56yZtauTNEYjUe+9h2nTJgKvuxYhBPkvvoiwWhFOJxqjEaHT4X/5ZQRc1Yn3AWh1cPsWKE6ByJp5r+IU1/LUhLNh3auw8U1QNHD3nrqpMkqOwofTQFHg3P/AgIs65jVI0t9QZw0OTRJCvA+8D67VSh3cnWYr+d8XWI+mYk1NJf2664n+/DMyr3XVcrClpxN8x+21bb3GjcVjxHDSLr4Y29E0PMeNw7RpEwFXX43vuecA1FuVZM/Pp+i/7+M9cUKdIasO5RHg+gNgN8N/x7vunkbcBOGDXIHBzRfcfOoeJ9QTvu4y/8WSdEborMEhG4g64d+RNY+1OdViIe+559C4uRH64IMtqrH8V7bMTApefhnhcNS+2RX86xVQVYSioHF3r3dMwauvYT18BABD91ii3nm7bn+tVqpWrcJ9wAD0ERHkP/8ClcuWUfbtt/TetbNV+986FNcfBdck84C5EDUC3P3B4Fm3aWBPuH4JmIpc+yQkSWo3nTU4bAXiFUXpjisozAMub48LVy5bRsWiX0BR8Bo3rlU/feuCgtAGB+HIPV4a1HboEABaTw8Crq9fDa6sJqeSxtubgKuvqfd83j//ScUvv6IYjfTa9CfuQwZTuWIFhh49andddyp6N7hlPRQcPL4hzjcSVr8I+Xth9mvgHXq8fbfBHdNPSfqb64TvHiCEcCiKcgewFNACHwsh9rfHtd0HDnQlstPpMPZu3dU1Gnd34pYtw3o0jey778ZZWYnGwx17RiYoGhSlfk2EwJtvouy77wl94nH0oSH1nj92zLG/A6+5Bt+zz0br51f7mHA6Kf7oIxS9noBrrmlyM16bC+ju+nPMwV9g7csggOA+MPWJDuuaJEkucod0A4TTCYpS7020Ytlyyr7/nuC77mpxDYXyRYvIeexx1wY2XHcGCVu3NOtYZ0UFafMuQzWZiPrkY2zJyRh79cIQE9NggKlYspSch11bRSLfehOv8eNb1PeTSl3j2sk87HoYdgo1sV8fAGUZgALX/QYxjZcwlSSpdTS2Q7qzLmXtUIpW2+Cn69yHH8a0bh15zzzT4mtovL1rAwMaDQHX1B0ycpSWkjx9BkfGjsOWkVHnuYrfl2DPysJZWop52zbUKhOpZ88m/bLLG6zjUJvMT1EwREXVe/6UOWxQ0UANh+VPQt4eWProqZ0verRryevAeTIwSFInIYPDKfCaOgUAn7POOmkbIQTV27djLyho9FzekyfjMXYsACH33VdnlRKAZf8BHAUFqJWVVG85fkdRvngxec89h3A6cR8yBJ8ZM6hasxqEwLxnD+JYwDmBW0Iv4levIn7Nagyxsc18tSd9gfD+BNen/Q1v1n1u+A1g8IIhV5/aOS/4L9x7EC54t2V9kySp1XTKOYfOKuJf/6Lbiy82WiCn5KOPKPzP2ygGAz1+W0zWbbejVlcT/dFH9eYMYj76EOFwNJgkz3PEcLzPOgu1qhLvmcfrJTgKClAAtFq6PfdPtH5+hNx/PygavCZPQnNCSu8Taf38TuMVN0B1unY8CxWy/zKUN+Qq159TpSh1J6ElSepwMjicoqYqpzlKy0AIhNWKeedOV/4jIahauwa/iy4i+667qN66lYjX38Bz1EiE3U761dfgLCkh+qMPa3dTO0pKCLnvXvQhdQNKwBVXoHFzQx8dXdvWEBVF5OuvtcnrrUerg8u/haQVMPYu136FjW/A0XUw+AroP9fVTlWbV+dBkqROSQaHVhZ8150YYmNw690HY1xPPIYNxVllwnvKFNTKSipXrAQhKPvxRzxHjcSybx+W/fsRTieVf6wi4KorMe/dR/qVV4KiEPP1V5R8/AkAoY89isbDA42fH1l33oX31KlE/KsDsrDGTTu+7yBpuSv9hWqHo2tcS0/3/Qh//BOGXAPnvtn4uSRJ6pRkcGhlGqMR/4svxpqURPmvvxL51ltoPDwQQlD2ww94jhuHLTOzdv7CbdAgPEePxlFcjPcM17p/e06Oa6gFqFq+gsplyxCqSuXSpSgGA4ZevRDV1VT8+ivdXnoRRaPBcuQIlStW4Hf++ei7dWu/F+zf3bXDGUDv4drMtsu1N4P9C2DO6/IOQpK6IBkc2oBqt3P00kvB6cS8ew/d/vksprVryX/uedduaCHIfehhjN2745aQQNR7dSdivadPI7T0IRS9AY8xoyn9/ntUiwVsNoTDgc9ZM8HhcFWRq3njzbzhRhxFRVStWUv3b79pvxcbFAf3H4ayLPCPBrsFymvSYlkrYOHtzZtotpRDaTqEDagNjJIkdRwZHFqZarGQet55iGozil6P1seVL0h3LGOqEKBREICjsAgSEuqdQ9Fo8J83r/bfvdatxbxnD9kPPIhbv74EXHEFgVfXXRGkj4rCWVaK8YQa1H8lhKD0f1+gmqsJnD+/9arFufu7/oArd5JybF5GQOHBpo9XnfD2SDCXwvj7YOKDrdMvSZJOmwwOp0m12cj/5z8RQhD2+ONojEYAHHl5OHJyQaPB+6yzCLnvXgDcEhLouXQJQgisBw+S98yzZN58M2FPP4V55y4qV6wg/IXn8Zk6tcHr5f3zOezp6TiLixucFI/+5GNsR49ijIs7aZ+rN2+m4FVXwR19RCS+c2bXbeB0wN7vXTmNokY0/5shhOsNXqsD7zC4YTmkrYeqwuatXlIdYC5xTWKXpjX/upIktRkZHE5T1arVlC9y1SDwGjvONdQD6GNiCLztNqyHDxP68EN13sj1oa7lmjofHxwFBSAE1dt3ULFgAQBlX3190uDgPXkylr178RxTf5OYcDopfP0NnJUVhD36KEoDCfwA9JGRrvF/1Ymhe2z9BpvegVXPub6+a1fd9Nkn43TAB5NcuZLmfQW9ZrqGhsIGNH3sMTojXLMYMjed+h4JSZLahAwOp8l9QH+UmrsF9wH9sWVmkvPQw7j170foI480mMbiGI2HBxGvvYZp0yaCb70FY/fuVPz+O0F/2QhnTUqi5Isv8bvgfIJuvYWA666tvaY1NZX0q69BFxhI8D/upvSrr0AIPBIT8Zs7t8HrGiIjiV+9CuF0ovP3b+BF+QGKK4DojM37RphLIf8AIODIUldwOB1Rw11/JEnqFGRwOE36bt2IW70KW0oKurAwCl75N+adOzHv2UPA1VdjiIxs9HifGdPxmTEdgIBrrsZRVEjV2nW4DxpUO8mc/cCDWA8donLlSnqtX4fGza32+Kq1a3GWlaFWVkJNum/VasV94MBGr3tsDqRBg6+CoATXHcOx+gtN8QqGGf+E9I0w/t6G26hO15LXoHjXkJUkSZ2eDA4tkDn/Biz79uF91kwCrriC8p9/RhcRQca112HsnUDkG280uWkOoGLxb5R99z0oCp4jR+A5ahQA7oMHY01Kwn1g/SEa3zlzqFqzFn1oCF7jxhG/fh2oasvqNygKRI9suh3AkWXwy10w8FKY/n8w+raTt/3hejiwEDQ6eOgoGL1Pv4+SJLULuQC9Bew52QiHA3tGJu6DBtFr0594jhyBPSuLqtVrsGdlAeAsK8OWlUXavMvIvP12VJsNa1KSa4mqyYRb//6g0aAYja46DDXCnnyC6M8/R9jsFH/yaZ1r64KCiPnkY1c6D53OlSywPQv7bHgdKnNh41tNtz26BhCujXKv9oEf5rd17yRJaiF559AC0R9+SOWKlfied27tY35z51K1di1uCb3RR0Vh2riRzFtuBa0WYbejaLVU79hB1m23g8OBeecugu+6k57LlqLz9UU5ITeSoiiUff89pg0bMG3ciN/cCxsfFmpP4++D8iwYNK/ptqNuhVUvuOYxrJWw7we44D3QdrYqdZIkHSODQwsY4+LqLR019uxJz19/rf235eBBhKqCEOiCg9GFBOPWty8aoxFVVXFWVZEyYyaK0UjPJb+jCwyscz6fGTOo+PVX3AcNROPl1S6vq1nipsI/9jSvrdPh+lt1uIr5DLxEBgZJ6uRkcGhjfnPnYjmShPugQQRcfhkAGTfcgLO8HO/p03EfOgTT6tUImw1nSUm94OA9ZTK99+5pdPVTm1Gd4LSBvuGlsZRlwo7PoffZ4BEIP90Ewb1h9qt1U2YkXgY7vwBTIfSeffKJa0mSOg0ZHFqRPSeHkq+/oeK3xTgKiwi6/Xaq16/HvHuXK8V1TXCw7NsPqoo9L5du8+YhLFb03bphjI9v8LwdEhjsFnhnlGvo6PJvXXcKf/XTTZCxCbZ9BEOvd32dvd01jBR8ws7vgB5g9ILKHFdbWQZUkjo9GRxaUfaDD2Hevt21YxgoevNNtH5+CIcTW1pabbvId96mfNEv+F54Ifb0dIJuurGDetyAnJ1QlAwRw6AiyxXUjq5rODiE9HHVdAjoCX3mwI5PXUtV/RtI4TH9WVj5NIy6vf5zkiR1OrKGdCvKeeJJyn/4wTWk4nSiGI1Ef/gBFX/8gbOsDL9zzqnd4azabCRPdqXxDnngfgKuajjNhFBV7Dk56Lt1a7B0aasyFcFr/QDFld9I7w65u137GDyDjrdTVVcQCewJVQXgHwu6E4oMOR2uoKJruPCQJEmdg6wh3V6ODf84nQAIhwOP4cOxp6dTsWAhGTfcSMqcOZR+/wPCakWtqECoKraMzJOeMvuuu0k5axY5jzzS9v3XaF1/FCB1tasmdEjfuoEBYOkj8OkseH+ya2L5xMnlqgL4dy94KaZm57QkSV2RDA6tRDgclH/3Xe2QEoCupiyo+6BE0GpRdDpsySnkPfMM6ddcS9jTTxNyzz8Ivvvuk57XcvAgOBxY9u9v65fgyqx660a4/HvI3+eajN75ef125dmuu4eydPjPcPj9hCyqhYfAVg3CWb+MqCRJXYYMDidhz8mh6P0PsB492qz2ik6Hz+zZULMjWhsaSswnrgpuQTffRNyK5YQ8/BCKlxc4HFgPHMC8ZzeB8+ej9fI86Xkj//MW/ldfTeRr7VQG1D8Wuo+Hs/8NkcNhVgOV5s59E6Y9DUZP1/LUnF3Hn4sZCyNvgYTZsO7f8Nl54LC1T98lSWo1cs7hJI7OvQjLwYNoAwPxOXsWgdfPRx8a0uRxKXPmYEtJRR8VRdyypfWeF6pK1u13YN6zh8j/vIXH4MGt2u92lbUN9v8Mw+e7ViQBOKxQkgoHf4XVL7hSZsxfBt0SXc9nb4e9P7qOkXmWJKlD/X979x5dVXnmcfz7JIRAgCIIBAwpcldQishFrThjh8qlKjK6rDMUnNEur3Qclx0VWV3jdOp0jdV26SzFW7VKO0XtCFK8IQojUxUE5a7cBJSYGJRLiOYGeeePd8cc2DmQnJxkn3Py+6x1Fjt775PzvGuvw5O93/d93uP1OWi0Uhw5BQVUbt3KkS++YP+833O4pIS+Dzxwwvf1ffBBDi5YSNdLL2nwuGVlUTj34WSH27pKNsJLt/n5DRPvOfrYU5OhZAMMuwzyh/mRS/nD64//91V+vsMn78B1y1o1bBFpPCWHOAruv4+KDz+iePZsqnfvpsMJqp3WyR0w4JsFfjLW8v/way98uhLGXg859dVi2bfTP2o6VAw3/F/4vfnD/UJAfUa2Wrgi0nRKDnFYTg55I85kwIIXOLxvHzl1y3wKjJwOO5bBgAvD6z7MXAhbXvHlvxsy/U9+/sRJ/Vo8TBFJnJLDCVj79koMxetg6b/5InsjrvQlMOYUH31OxX54ZipYFsxcBB3iFAjMbuc7vUUkpWm0UjMcWLiQojvuoKakpFU+70j5Vxx6cxlHDh1qlc/7xqt3wo434MVZ8c9Z9YRPIp99AKse9/uqDkHpR0cN7xWR9KDkkKAj5eUU3zWHsj8vZu8DD7bKZ+65+WaKbr2VT65NcD2Ekg2+T6ApyvfCoIv8HcHQyfHP63U6fvacQY9BvmjfQ+Pg0QvgL8fpyP/oZZj7XVj/XNPiEpEWpcdKCcrq2JHcQYOo2r6dTt89r1U+s7aqCpzDVSUwb2DbUnj2R377pnegewP1j471+SZ4IqipdMNf/OijeE6/2Bfoc7U+idRU+FFJrha+3Bb/fUvm+KGvr832j6xEJCUoOSTIsrPpv3ABrqKCrE7xJ7ElU+Hchylf/r90Hn9+099csc//Ye+A6vLGvWf/7vrtg3uOnxwAhkys387pCDMW+lFNo6+J/54x18Gye2BMChUfFBFNgmszamv9Cmwdu8PgCSc+v6oc3n3ED1ft8x248K6j12gQkbSnSXDi/2M/0WObIzXw8k+hsgw694GVc4Fa2PUWnHE57FgKgydCzyGtErKIREd/CraQmtJSypYsobayMupQGm/XClj3LGx5CarK/GMoAAwW3wJL74ZnGp753Sh7t/p6SwfiV6EVkdSgO4cWUFtRwccXX4KrrKTzhAn0/fX9UYfUOL1HQF53qP4Kxt8K59/ih6b2GgZv/5cvsNc5P/Hf//vLoazI111S6QyRlKbk0AJK77uf2rIyAFxNClUkrSyD138GXb/t13H+fJMfTdQnKA3SqQfcGpQGr1ubokewdOnUh2DMj0/cKX08JxVC+eeaBCeSBpQcWkB2t26Qm4tlZ3PKL34RdTj1PpgHa/8Alg1dC+DPwToSMxfBt8f5bTPY/obfjl0aNLsdFI5p3ufPWAClmyH/zOb9HhFpcUoOLaDHTTfS6dxzaN+vH9ldu0YdTr2+Y/1ktg5doeNJflgrR3yRvDo7V8Cz0/329D/BqQkMm42nXS6cksYlykXaECWHFmBZWeSdfXbUYYQVjoE7dkNWjr8T6H4qfLnDdxK36wDlJdBjaJA0HGTHFNU7XAVv/jvk5MFf3alhrSIZTskhU+3f5YvlDZkE3/lh/f6cjvXbHbtD1i6/HOjzV/t9k++Fa14BrH6BHoBNC33NJDMoHHf0IycRyTj68y8BlZs38+mNN1G2dGnUocT3+r/6VdoW3gA1cYbT/v18+NvH4Ion/eMmgC59/KOf2MQA0PtMf05WDvQc2qKhi0j0dOeQgJKf/5yKtev4auVKvvX+mqjDadjgi+DDRf4/+mPXXKjToSsMm+q3Z632VVR7ndbwufnD4F92+AQRu7iPiGQkJYcEdJ7wfSrWrkusxlFrOWs6DJ/mHyOZnfj8rgUnPqd9XvPjEpG00OZrKznnqN61i5z8fLLyGv+fn6uuxtq3T+gzRURSwfFqK7X5Pocvn3yKnZdO5eNLLsUdOdLo97X5xLBnjS+HISIZqc0nh+rt23C1tdSUluIOH446nNThHKybD+/PC6/ktuVV+N0P4NHxfihsrCM18TvARSRttPk+h163305OQQF5o8eQlRun4zbTOecnwnXu7ecvVJbBI+PhwG7fmZ13Mpw2pf786nLfj+Gcn/9Qp3wvPDwOar6Ga5bUl+UQkbTT5pNDu27d6DnrOGsjtwUvzoL1f4TTLoErn4bitXDoM8D55T679D76/DMuh6x2vkhfbK2lL7dB9de+XlPRGiUHkTTW5pODAEXv+SRQFHTqF46DoVN8gpj8q/CcBzMYfln49xSeA+f9BL7+Ekb8MHxcRNKGkoPAFU/Be0/AWTP8z+1y/R1EU2VlwffmJDc2EYlEm++QFiB/OFz8GygYdfT+igNQXprY71z5KDz/D1D2WXOjE5EI6M5BGnZwDzw0Dmpr4OrFUDi28e8t3wuv3eXXrc47GX6QJosdicg3dOcgDSv7zPdDYPBFE+czlJf6kU9mMOj7LRKeiLSsSJKDmd1tZkVmtjZ4TYk5NtvMtpvZFjObGEV8AvQdA5N+CRfc3rTO5apD8NsJvlN6/G0wdFLLxSgiLSbKx0q/cc7dF7vDzIYBVwHDgVOApWY2xDnX+KnLkhxmMPofE38vDtq18VnkImks1focpgLznXNVwE4z2w6MBd6JNqw09tFL8PFy/1f8sfMVWkJuF7h+BXyxDQbrkZJIuooyOcwys5nAauA259x+oAB4N+acPcE+SURNBTw3009Kqzzo125oDScP9C8RSVst1udgZkvNbGMDr6nAXGAgMBIoBpo8nMXMrjOz1Wa2eu/evckNPlNk50L3AX4NhsJxUUcjImmkxe4cnHMTGnOemT0OLA5+LAIKYw73DfY19PsfAx4DX7I78UgzWFYW3Pg2VOyHzr2ijkZE0khUo5X6xPw4DdgYbC8CrjKzXDPrDwwGVrV2fBklO6fxicE5mD8d7h0AO1eEj1eVw7xp8NQU+HpfcuMUkZQSVZ/DvWY2EnDALuB6AOfcJjN7DtgMHAZu1kilVlR5ALa87PsoPpgH/ccffXznW7D7bZ9Etr4GI/8ukjBFpOVFkhycczOOc+we4J5WDCdzbX3Nz1QefS2ce9OJz+/YDc79CexcDuf9U/h4v3Ohx2A4XA0Dv5f0cEUkdbT5ZUIz2iMXQMk6yOkEcxqocXS4GtY8Bd36w5CLWj8+EYmUlgltq86bBXk94JwbGz6+6lFY8jN47kewb2frxiYiKS3VJsFJMo240r/i6VroZzNn50Dut1ovLhFJeUoObdnwy6DX6dCxO3Q6OepoRCSFKDm0dT2HRh2BiKQg9TmIiEiIkoOIiIQoOYiISIiSg4iIhCg5iIhIiJKDiIiEKDmIiEiIkoOIiIQoOYiISIiSgzRfbS18uBg++yDqSEQkSZQcpPne/x288GN4chIcbHBVVxFJM0oO0nzZ7f2/ZpCVHW0sIpIUKrwnzTdyOnTtC11OgS69o45GRJJAyUGazwwG/HXUUYhIEumxkoiIhCg5iIhIiJKDiIiEKDmIiEiIkoOIiIQoOYiISIiSg4iIhCg5iIhIiJKDiIiEKDmIiEiIkoOIiIQoOYiISIg556KOodnMbC+wO4KP7gF8EcHntoZMbhuofeksk9sGrdu+fs65ng0dyIjkEBUzW+2cGx11HC0hk9sGal86y+S2Qeq0T4+VREQkRMlBRERClBya57GoA2hBmdw2UPvSWSa3DVKkfepzEBGREN05iIhIiJJDAszsbjMrMrO1wWtKzLHZZrbdzLaY2cQo40yUmU0K4t9uZndGHU8ymNkuM9sQXK/Vwb7uZva6mW0L/u0WdZyNYWZPmlmpmW2M2ddgW8x7MLiW681sVHSRN06c9mXEd87MCs1smZltNrNNZnZLsD/1rp9zTq8mvoC7gZ82sH8YsA7IBfoDO4DsqONtYtuyg7gHAO2D9gyLOq4ktGsX0OOYffcCdwbbdwL/GXWcjWzLBcAoYOOJ2gJMAV4BDDgHWBl1/Am2LyO+c0AfYFSw3QXYGrQh5a6f7hySayow3zlX5ZzbCWwHxkYcU1ONBbY75z52zlUD8/HtykRTgaeD7aeBy6ILpfGcc28B+47ZHa8tU4FnnPcucJKZ9WmVQBMUp33xpNV3zjlX7Jx7P9g+BHwIFJCC10/JIXGzgtu8J2MeRxQAn8acsyfYl04yoQ0NccASM1tjZtcF+/Kdc8XBdgmQH01oSRGvLZl0PTPqO2dmpwJnAStJweun5BCHmS01s40NvKYCc4GBwEigGLg/ylilUc53zo0CJgM3m9kFsQedv4fPiKF7mdSWGBn1nTOzzsD/AP/snCuLPZYq169d1AGkKufchMacZ2aPA4uDH4uAwpjDfYN96SQT2hDinCsK/i01swX4Rw+fm1kf51xxcKteGmmQzROvLRlxPZ1zn9dtp/t3zsxy8InhD865F4LdKXf9dOeQgGOe+U0D6kZVLAKuMrNcM+sPDAZWtXZ8zfQeMNjM+ptZe+AqfLvSlpl1MrMuddvARfhrtgi4OjjtauDFaCJMinhtWQTMDEa9nAMcjHl8kTYy5TtnZgb8FvjQOffrmEOpd/2i7r1PxxcwD9gArA8uXp+YY3PwIya2AJOjjjXB9k3Bj6LYAcyJOp4ktGcAfkTLOmBTXZuAk4E3gG3AUqB71LE2sj1/xD9aqcE/g742Xlvwo1weCq7lBmB01PEn2L6M+M4B5+MfGa0H1gavKal4/TRDWkREQvRYSUREQpQcREQkRMlBRERClBxERCREyUFEREKUHESawcyOBFVCN5rZ82aWF+zvbWbzzWxHULLjZTMbEhx71cwOmNni4/92kegoOYg0T4VzbqRz7gygGrghmOi0AFjunBvonDsbmE19vZxfATOiCVekcZQcRJJnBTAIuBCocc49UnfAObfOObci2H4DOBRNiCKNo+QgkgRm1g5f1G8DcAawJtqIRJpHyUGkeTqa2VpgNfAJvm6OSNpTVVaR5qlwzo2M3WFmm4AroglHJDl05yCSfG8CuTGLCmFmI8xsfIQxiTSJkoNIkjlfzXIaMCEYyroJ+CV+hS/MbAXwPPA3ZrbHzCZGF61Iw1SVVUREQnTnICIiIUoOIiISouQgIiIhSg4iIhKi5CAiIiFKDiIiEqLkICIiIUoOIiIS8v+SRUoXa8Uk9AAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "plt.scatter(projected[:,0], projected[:,2], s=3, c=newcolors)\n", "plt.xlabel('PC1')\n", "plt.ylabel('PC3')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "administrative-morning", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "We see that the colors match very well with the clusters. You may notice some points that seem to wander into another cluster --- that is because we are only plotting two dimensions, and the points that look overlapping may very well be separated in some other dimensions. Try plotting some other principal components yourself." ] }, { "cell_type": "markdown", "id": "million-protein", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Finally, let us see how well we have clustered the data compared to the true labels. Let us highlight the points that are wrongly labeled." ] }, { "cell_type": "code", "execution_count": 19, "id": "4d6155aa-93cb-43a1-afe7-529dc9f73ae1", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "wrong = (newindices != indices)\n", "\n", "plt.figure(figsize=(6,6))\n", "plt.scatter(projected[:,0], projected[:,2], s=3, c=newcolors)\n", "plt.scatter(projected[wrong,0], projected[wrong,2], s=100, c='k', marker='X')\n", "plt.xlabel('PC1')\n", "plt.ylabel('PC3')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "metropolitan-recorder", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "It turns out that we only made 4 mistakes out of 801 data points. Also, it can be seen that the wrongly labeled data points lie near the boundary of the clusters, which makes the mistakes quite understandable." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }