{ "cells": [ { "cell_type": "markdown", "id": "7ceca7f5", "metadata": {}, "source": [ "# Unsupervised Learning\n", "\n", "\n", "\"Open\n", "\n", "\n", "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/intro-stat-learning/ISLP_labs/v2.2?labpath=Ch12-unsup-lab.ipynb)" ] }, { "cell_type": "markdown", "id": "7c613d6b", "metadata": {}, "source": [ "In this lab we demonstrate PCA and clustering on several datasets.\n", "As in other labs, we import some of our libraries at this top\n", "level. This makes the code more readable, as scanning the first few\n", "lines of the notebook tell us what libraries are used in this\n", "notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "1f7a6c07", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:58.245147Z", "iopub.status.busy": "2024-06-04T23:19:58.244639Z", "iopub.status.idle": "2024-06-04T23:19:58.980175Z", "shell.execute_reply": "2024-06-04T23:19:58.979888Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from statsmodels.datasets import get_rdataset\n", "from sklearn.decomposition import PCA\n", "from sklearn.preprocessing import StandardScaler\n", "from ISLP import load_data" ] }, { "cell_type": "markdown", "id": "19645c0e", "metadata": {}, "source": [ "We also collect the new imports\n", "needed for this lab." ] }, { "cell_type": "code", "execution_count": 2, "id": "1e14c3f7", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:58.981864Z", "iopub.status.busy": "2024-06-04T23:19:58.981743Z", "iopub.status.idle": "2024-06-04T23:19:59.038480Z", "shell.execute_reply": "2024-06-04T23:19:59.038262Z" } }, "outputs": [], "source": [ "from sklearn.cluster import \\\n", " (KMeans,\n", " AgglomerativeClustering)\n", "from scipy.cluster.hierarchy import \\\n", " (dendrogram,\n", " cut_tree)\n", "from ISLP.cluster import compute_linkage" ] }, { "cell_type": "markdown", "id": "a66c0f59", "metadata": {}, "source": [ "## Principal Components Analysis\n", "In this lab, we perform PCA on `USArrests`, a data set in the\n", "`R` computing environment.\n", "We retrieve the data using `get_rdataset()`, which can fetch data from\n", "many standard `R` packages.\n", "\n", "The rows of the data set contain the 50 states, in alphabetical order." ] }, { "cell_type": "code", "execution_count": 3, "id": "9d155861", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:59.039866Z", "iopub.status.busy": "2024-06-04T23:19:59.039756Z", "iopub.status.idle": "2024-06-04T23:20:00.015887Z", "shell.execute_reply": "2024-06-04T23:20:00.015393Z" } }, "outputs": [ { "data": { "text/html": [ "
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MurderAssaultUrbanPopRape
rownames
Alabama13.22365821.2
Alaska10.02634844.5
Arizona8.12948031.0
Arkansas8.81905019.5
California9.02769140.6
Colorado7.92047838.7
Connecticut3.31107711.1
Delaware5.92387215.8
Florida15.43358031.9
Georgia17.42116025.8
Hawaii5.3468320.2
Idaho2.61205414.2
Illinois10.42498324.0
Indiana7.21136521.0
Iowa2.2565711.3
Kansas6.01156618.0
Kentucky9.71095216.3
Louisiana15.42496622.2
Maine2.183517.8
Maryland11.33006727.8
Massachusetts4.41498516.3
Michigan12.12557435.1
Minnesota2.7726614.9
Mississippi16.12594417.1
Missouri9.01787028.2
Montana6.01095316.4
Nebraska4.31026216.5
Nevada12.22528146.0
New Hampshire2.157569.5
New Jersey7.41598918.8
New Mexico11.42857032.1
New York11.12548626.1
North Carolina13.03374516.1
North Dakota0.845447.3
Ohio7.31207521.4
Oklahoma6.61516820.0
Oregon4.91596729.3
Pennsylvania6.31067214.9
Rhode Island3.4174878.3
South Carolina14.42794822.5
South Dakota3.8864512.8
Tennessee13.21885926.9
Texas12.72018025.5
Utah3.21208022.9
Vermont2.2483211.2
Virginia8.51566320.7
Washington4.01457326.2
West Virginia5.781399.3
Wisconsin2.6536610.8
Wyoming6.81616015.6
\n", "
" ], "text/plain": [ " Murder Assault UrbanPop Rape\n", "rownames \n", "Alabama 13.2 236 58 21.2\n", "Alaska 10.0 263 48 44.5\n", "Arizona 8.1 294 80 31.0\n", "Arkansas 8.8 190 50 19.5\n", "California 9.0 276 91 40.6\n", "Colorado 7.9 204 78 38.7\n", "Connecticut 3.3 110 77 11.1\n", "Delaware 5.9 238 72 15.8\n", "Florida 15.4 335 80 31.9\n", "Georgia 17.4 211 60 25.8\n", "Hawaii 5.3 46 83 20.2\n", "Idaho 2.6 120 54 14.2\n", "Illinois 10.4 249 83 24.0\n", "Indiana 7.2 113 65 21.0\n", "Iowa 2.2 56 57 11.3\n", "Kansas 6.0 115 66 18.0\n", "Kentucky 9.7 109 52 16.3\n", "Louisiana 15.4 249 66 22.2\n", "Maine 2.1 83 51 7.8\n", "Maryland 11.3 300 67 27.8\n", "Massachusetts 4.4 149 85 16.3\n", "Michigan 12.1 255 74 35.1\n", "Minnesota 2.7 72 66 14.9\n", "Mississippi 16.1 259 44 17.1\n", "Missouri 9.0 178 70 28.2\n", "Montana 6.0 109 53 16.4\n", "Nebraska 4.3 102 62 16.5\n", "Nevada 12.2 252 81 46.0\n", "New Hampshire 2.1 57 56 9.5\n", "New Jersey 7.4 159 89 18.8\n", "New Mexico 11.4 285 70 32.1\n", "New York 11.1 254 86 26.1\n", "North Carolina 13.0 337 45 16.1\n", "North Dakota 0.8 45 44 7.3\n", "Ohio 7.3 120 75 21.4\n", "Oklahoma 6.6 151 68 20.0\n", "Oregon 4.9 159 67 29.3\n", "Pennsylvania 6.3 106 72 14.9\n", "Rhode Island 3.4 174 87 8.3\n", "South Carolina 14.4 279 48 22.5\n", "South Dakota 3.8 86 45 12.8\n", "Tennessee 13.2 188 59 26.9\n", "Texas 12.7 201 80 25.5\n", "Utah 3.2 120 80 22.9\n", "Vermont 2.2 48 32 11.2\n", "Virginia 8.5 156 63 20.7\n", "Washington 4.0 145 73 26.2\n", "West Virginia 5.7 81 39 9.3\n", "Wisconsin 2.6 53 66 10.8\n", "Wyoming 6.8 161 60 15.6" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "USArrests = get_rdataset('USArrests').data\n", "USArrests" ] }, { "cell_type": "markdown", "id": "498fa729", "metadata": {}, "source": [ "The columns of the data set contain the four variables." ] }, { "cell_type": "code", "execution_count": 4, "id": "98cd6d32", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.019290Z", "iopub.status.busy": "2024-06-04T23:20:00.018842Z", "iopub.status.idle": "2024-06-04T23:20:00.022851Z", "shell.execute_reply": "2024-06-04T23:20:00.022397Z" } }, "outputs": [ { "data": { "text/plain": [ "Index(['Murder', 'Assault', 'UrbanPop', 'Rape'], dtype='object')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "USArrests.columns" ] }, { "cell_type": "markdown", "id": "80001d60", "metadata": {}, "source": [ "We first briefly examine the data. We notice that the variables have vastly different means." ] }, { "cell_type": "code", "execution_count": 5, "id": "93783538", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.025039Z", "iopub.status.busy": "2024-06-04T23:20:00.024890Z", "iopub.status.idle": "2024-06-04T23:20:00.029072Z", "shell.execute_reply": "2024-06-04T23:20:00.028691Z" } }, "outputs": [ { "data": { "text/plain": [ "Murder 7.788\n", "Assault 170.760\n", "UrbanPop 65.540\n", "Rape 21.232\n", "dtype: float64" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "USArrests.mean()" ] }, { "cell_type": "markdown", "id": "f8157f37", "metadata": {}, "source": [ "Dataframes have several useful methods for computing\n", "column-wise summaries. We can also examine the\n", "variance of the four variables using the `var()` method." ] }, { "cell_type": "code", "execution_count": 6, "id": "1f89db32", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.031071Z", "iopub.status.busy": "2024-06-04T23:20:00.030915Z", "iopub.status.idle": "2024-06-04T23:20:00.034379Z", "shell.execute_reply": "2024-06-04T23:20:00.034033Z" } }, "outputs": [ { "data": { "text/plain": [ "Murder 18.970465\n", "Assault 6945.165714\n", "UrbanPop 209.518776\n", "Rape 87.729159\n", "dtype: float64" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "USArrests.var()" ] }, { "cell_type": "markdown", "id": "ee99bf4e", "metadata": {}, "source": [ "Not surprisingly, the variables also have vastly different variances.\n", "The `UrbanPop` variable measures the percentage of the population\n", "in each state living in an urban area, which is not a comparable\n", "number to the number of rapes in each state per 100,000 individuals.\n", "PCA looks for derived variables that account for most of the variance in the data set.\n", "If we do not scale the variables before performing PCA, then the principal components\n", "would mostly be driven by the\n", "`Assault` variable, since it has by far the largest\n", "variance. So if the variables are measured in different units or vary widely in scale, it is recommended to standardize the variables to have standard deviation one before performing PCA.\n", "Typically we set the means to zero as well.\n", "\n", "This scaling can be done via the `StandardScaler()` transform imported above. We first `fit` the\n", "scaler, which computes the necessary means and standard\n", "deviations and then apply it to our data using the\n", "`transform` method. As before, we combine these steps using the `fit_transform()` method." ] }, { "cell_type": "code", "execution_count": 7, "id": "dc04eed1", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.036290Z", "iopub.status.busy": "2024-06-04T23:20:00.036153Z", "iopub.status.idle": "2024-06-04T23:20:00.039673Z", "shell.execute_reply": "2024-06-04T23:20:00.039402Z" } }, "outputs": [], "source": [ "scaler = StandardScaler(with_std=True,\n", " with_mean=True)\n", "USArrests_scaled = scaler.fit_transform(USArrests)" ] }, { "cell_type": "markdown", "id": "40e431d0", "metadata": {}, "source": [ "Having scaled the data, we can then\n", "perform principal components analysis using the `PCA()` transform\n", "from the `sklearn.decomposition` package." ] }, { "cell_type": "code", "execution_count": 8, "id": "a350773d", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.041302Z", "iopub.status.busy": "2024-06-04T23:20:00.041187Z", "iopub.status.idle": "2024-06-04T23:20:00.042988Z", "shell.execute_reply": "2024-06-04T23:20:00.042688Z" } }, "outputs": [], "source": [ "pcaUS = PCA()" ] }, { "cell_type": "markdown", "id": "6fa0064e", "metadata": {}, "source": [ "(By default, the `PCA()` transform centers the variables to have\n", "mean zero though it does not scale them.) The transform `pcaUS`\n", "can be used to find the PCA\n", "`scores` returned by `fit()`. Once the `fit` method has been called, the `pcaUS` object also contains a number of useful quantities." ] }, { "cell_type": "code", "execution_count": 9, "id": "f4fe8410", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.044752Z", "iopub.status.busy": "2024-06-04T23:20:00.044629Z", "iopub.status.idle": "2024-06-04T23:20:00.048289Z", "shell.execute_reply": "2024-06-04T23:20:00.048020Z" } }, "outputs": [ { "data": { "text/html": [ "
PCA()
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On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" ], "text/plain": [ "PCA()" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.fit(USArrests_scaled)" ] }, { "cell_type": "markdown", "id": "1a1af009", "metadata": {}, "source": [ "After fitting, the `mean_` attribute corresponds to the means\n", "of the variables. In this case, since we centered and scaled the data with\n", "`scaler()` the means will all be 0." ] }, { "cell_type": "code", "execution_count": 10, "id": "605a0ca8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.049772Z", "iopub.status.busy": "2024-06-04T23:20:00.049682Z", "iopub.status.idle": "2024-06-04T23:20:00.051822Z", "shell.execute_reply": "2024-06-04T23:20:00.051552Z" } }, "outputs": [ { "data": { "text/plain": [ "array([-7.10542736e-17, 1.38777878e-16, -4.39648318e-16, 8.59312621e-16])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.mean_" ] }, { "cell_type": "markdown", "id": "b4f438b3", "metadata": {}, "source": [ "The scores can be computed using the `transform()` method\n", "of `pcaUS` after it has been fit." ] }, { "cell_type": "code", "execution_count": 11, "id": "963374b1", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.053341Z", "iopub.status.busy": "2024-06-04T23:20:00.053256Z", "iopub.status.idle": "2024-06-04T23:20:00.055003Z", "shell.execute_reply": "2024-06-04T23:20:00.054717Z" } }, "outputs": [], "source": [ "scores = pcaUS.transform(USArrests_scaled)" ] }, { "cell_type": "markdown", "id": "99df27b7", "metadata": {}, "source": [ "We will plot these scores a bit further down.\n", "The `components_` attribute provides the principal component loadings:\n", "each row of `pcaUS.components_` contains the corresponding\n", "principal component loading vector." ] }, { "cell_type": "code", "execution_count": 12, "id": "8d158f66", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.056542Z", "iopub.status.busy": "2024-06-04T23:20:00.056453Z", "iopub.status.idle": "2024-06-04T23:20:00.058672Z", "shell.execute_reply": "2024-06-04T23:20:00.058391Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.53589947, 0.58318363, 0.27819087, 0.54343209],\n", " [-0.41818087, -0.1879856 , 0.87280619, 0.16731864],\n", " [-0.34123273, -0.26814843, -0.37801579, 0.81777791],\n", " [-0.6492278 , 0.74340748, -0.13387773, -0.08902432]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.components_ " ] }, { "cell_type": "markdown", "id": "1ebfe5a4", "metadata": {}, "source": [ "The `biplot` is a common visualization method used with\n", "PCA. It is not built in as a standard\n", "part of `sklearn`, though there are python\n", "packages that do produce such plots. Here we\n", "make a simple biplot manually." ] }, { "cell_type": "code", "execution_count": 13, "id": "0ca1c80b", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.060083Z", "iopub.status.busy": "2024-06-04T23:20:00.059998Z", "iopub.status.idle": "2024-06-04T23:20:00.163601Z", "shell.execute_reply": "2024-06-04T23:20:00.163039Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "i, j = 0, 1 # which components\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "ax.scatter(scores[:,0], scores[:,1])\n", "ax.set_xlabel('PC%d' % (i+1))\n", "ax.set_ylabel('PC%d' % (j+1))\n", "for k in range(pcaUS.components_.shape[1]):\n", " ax.arrow(0, 0, pcaUS.components_[i,k], pcaUS.components_[j,k])\n", " ax.text(pcaUS.components_[i,k],\n", " pcaUS.components_[j,k],\n", " USArrests.columns[k])" ] }, { "cell_type": "markdown", "id": "3d0fbebc", "metadata": {}, "source": [ "Notice that this figure is a reflection of Figure~\\ref{Ch10:fig:USArrests:obs} through the $y$-axis. Recall that the\n", "principal components are only unique up to a sign change, so we can\n", "reproduce that figure by flipping the\n", "signs of the second set of scores and loadings.\n", "We also increase the length of the arrows to emphasize the loadings." ] }, { "cell_type": "code", "execution_count": 14, "id": "4266c73b", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.168170Z", "iopub.status.busy": "2024-06-04T23:20:00.167869Z", "iopub.status.idle": "2024-06-04T23:20:00.278302Z", "shell.execute_reply": "2024-06-04T23:20:00.277775Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scale_arrow = s_ = 2\n", "scores[:,1] *= -1\n", "pcaUS.components_[1] *= -1 # flip the y-axis\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "ax.scatter(scores[:,0], scores[:,1])\n", "ax.set_xlabel('PC%d' % (i+1))\n", "ax.set_ylabel('PC%d' % (j+1))\n", "for k in range(pcaUS.components_.shape[1]):\n", " ax.arrow(0, 0, s_*pcaUS.components_[i,k], s_*pcaUS.components_[j,k])\n", " ax.text(s_*pcaUS.components_[i,k],\n", " s_*pcaUS.components_[j,k],\n", " USArrests.columns[k])" ] }, { "cell_type": "markdown", "id": "f61d0295", "metadata": {}, "source": [ "The standard deviations of the principal component scores are as follows:" ] }, { "cell_type": "code", "execution_count": 15, "id": "abf3dd55", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.281501Z", "iopub.status.busy": "2024-06-04T23:20:00.281202Z", "iopub.status.idle": "2024-06-04T23:20:00.286262Z", "shell.execute_reply": "2024-06-04T23:20:00.285205Z" } }, "outputs": [ { "data": { "text/plain": [ "array([1.5908673 , 1.00496987, 0.6031915 , 0.4206774 ])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scores.std(0, ddof=1)" ] }, { "cell_type": "markdown", "id": "70497cc6", "metadata": {}, "source": [ "The variance of each score can be extracted directly from the `pcaUS` object via\n", "the `explained_variance_` attribute." ] }, { "cell_type": "code", "execution_count": 16, "id": "2b86e577", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.289493Z", "iopub.status.busy": "2024-06-04T23:20:00.288828Z", "iopub.status.idle": "2024-06-04T23:20:00.294507Z", "shell.execute_reply": "2024-06-04T23:20:00.294014Z" } }, "outputs": [ { "data": { "text/plain": [ "array([2.53085875, 1.00996444, 0.36383998, 0.17696948])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.explained_variance_" ] }, { "cell_type": "markdown", "id": "b03146b4", "metadata": {}, "source": [ "The proportion of variance explained by each principal \n", "component (PVE) is stored as `explained_variance_ratio_`:" ] }, { "cell_type": "code", "execution_count": 17, "id": "5ffec7f8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.297422Z", "iopub.status.busy": "2024-06-04T23:20:00.297193Z", "iopub.status.idle": "2024-06-04T23:20:00.304441Z", "shell.execute_reply": "2024-06-04T23:20:00.303923Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.62006039, 0.24744129, 0.0891408 , 0.04335752])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.explained_variance_ratio_" ] }, { "cell_type": "markdown", "id": "358f8407", "metadata": {}, "source": [ "We see that the first principal component explains 62.0% of the\n", "variance in the data, the next principal component explains 24.7%\n", "of the variance, and so forth.\n", "We can plot the PVE explained by each component, as well as the cumulative PVE. We first\n", "plot the proportion of variance explained." ] }, { "cell_type": "code", "execution_count": 18, "id": "427cf5d8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.307404Z", "iopub.status.busy": "2024-06-04T23:20:00.307167Z", "iopub.status.idle": "2024-06-04T23:20:00.417318Z", "shell.execute_reply": "2024-06-04T23:20:00.417075Z" } }, "outputs": [], "source": [ "%%capture\n", "fig, axes = plt.subplots(1, 2, figsize=(15, 6))\n", "ticks = np.arange(pcaUS.n_components_)+1\n", "ax = axes[0]\n", "ax.plot(ticks,\n", " pcaUS.explained_variance_ratio_,\n", " marker='o')\n", "ax.set_xlabel('Principal Component');\n", "ax.set_ylabel('Proportion of Variance Explained')\n", "ax.set_ylim([0,1])\n", "ax.set_xticks(ticks)" ] }, { "cell_type": "markdown", "id": "4b392ae6", "metadata": {}, "source": [ "Notice the use of `%%capture`, which suppresses the displaying of the partially completed figure." ] }, { "cell_type": "code", "execution_count": 19, "id": "4336fd05", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.418792Z", "iopub.status.busy": "2024-06-04T23:20:00.418713Z", "iopub.status.idle": "2024-06-04T23:20:00.490050Z", "shell.execute_reply": "2024-06-04T23:20:00.489809Z" } }, "outputs": [ { "data": { "image/png": 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q5mH+ivxjtdkNFX1kucYjnwAA+9BEAwAAAAAHtDE2Mc8jnFfzcNMQdWsaorqVrXJ1sRRDMgBwTjTRAAAAAMABnTp3/QaaJEVGBKhh1XJFnAYAwMcUAAAAAOBgsnNsWnfwTL6uDfJhqiYAFAdWogEAAACAAzl6NlVDF+3QxkOJ17zOkFTR6qlmYf7FEwwAnBwr0QAAAADAQXy147junrxGGw8lqqyHqx5rWU2GLjXM/u7Pn8d0rC0XhgcAQLFgJRoAAAAAmOx8epZGf7lbS7cekyQ1rOqnyd0aqmqAt1qEB2js13vyDBmoaPXUmI611b5OsFmRAcDp0EQDAAAAABNtizurwQu3Ky4xVRZDeub26nq2bQ25/TFps32dYN1Ru6I2xibq1Lk0BflceoSTFWgAULxoogEAAACACbJzbHp/xUFNWv67snNsquznpUkPN1DT0Mv3OHOxGIqMCDAhJQDgTzTRAAAAAKCYHT2bqiGLtmvTobOSpE71K+nVznVk9XIzORkA4GpoogEAAABAMfpqx3G99PkunUvLUlkPV73a+SZ1blBZhsHjmQDgyGiiAQAAAEAxOJeWqTFf/XbF4QEAAMdHEw0AAAAAitjWuLN67u/DA9rU0KA21eX6x/AAAIDjo4kGAAAAAEUkO8emqSsOanI+hgcAABwbTTQAAAAAKAIMDwCA0oUmGgAAAAAUsisND+jSsIrZsQAA/wJNNAAAAAAoJOfSMjXmy9+0dNul4QGNqvppEsMDAKBUoIkGAAAAAIVgy+Gzem7RNh1JvCiLIT3bpoaeZXgAAJQaNNEAAAAA4F/Iys7R1BXRmvLLX8MDJj/cQE0YHgAApQpNNAAAACc2ZcqUfF87aNCgIkwClExHEi8ND9h8+NLwgPsaXBoe4OvJ8AAAKG1oogEAADixiRMn5vn59OnTSk1NlZ+fnyQpKSlJ3t7eCgoKookG/MOX24/p5c9361w6wwMAwBnQRAMAAHBisbGxud9/8sknev/99zVz5kzVqlVLkrR//349/vjjevLJJ82KCDicc2mZGv3lb/r8b8MDJj/cUCH+DA8AgNLMsNlsNrNDFKeUlBRZrVYlJyfL19fX7DgAAKCEcIYaIiIiQkuWLFHDhg3zHN+yZYsefPDBPA03R+QM9wjm++fwgEFta+iZ2xkeAAAlWX5rCFaiAQAAQJIUHx+vrKysy45nZ2fr5MmTJiQCHMc/hwdUKXdpeEDjagwPAABnwcclAAAAkCS1bdtWTz75pLZu3Zp7bMuWLRo4cKDatWtnYjLAXEcSU/XwRxs08ecDys6xqXODSvpu8C000ADAybASDQAAAJKkWbNmqXfv3mrSpInc3C5NFszKytJdd92lGTNmmJwOMMc/hwf8t3MddW5Y2exYAAAT0EQDAACAJKl8+fL67rvvdODAAe3bt0+SdMMNN6hmzZomJwOK3z+HBzSuVk6TujVgeAAAODGaaAAAAMgjNDRUNptNERERcnWlXITz2XI4Uc8t2s7wAABAHvwtAAAAAElSamqq+vXrJ29vb910002Ki4uTJD377LMaP368yemAopeVnaNJPx/QQx9u0JHEi6pSzkv/GxCp59rVpIEGADC/iTZ16lSFhobK09NTzZs318aNG695/aRJk1SrVi15eXkpJCREQ4YMUVpaWjGlBQAAKL1GjhypHTt2aOXKlfL09Mw93q5dOy1atKhA70mth5LiSGKqun20QZN+vjR9s0vDygwPAADkYer6/EWLFmno0KH64IMP1Lx5c02aNEl33XWX9u/fr6CgoMuu/+STT/Tiiy9q1qxZatmypQ4cOKDHHntMhmFowoQJJvwJAAAASo8vvvhCixYtUosWLWQYRu7xm266SdHR0Xa/H7UeSoovth3TqC8uDQ/w8XDVf7vU0X0NGB4AAMjL1JVoEyZM0OOPP64+ffqodu3a+uCDD+Tt7a1Zs2Zd8fr169erVatW6tGjh0JDQ3XnnXeqe/fu1/1EEwAAANd3+vTpKza3Lly4kKepll/UenB0KWmZem7hNj23aLvOpWepcbVy+m7wLTTQAABXZFoTLSMjQ1u2bFG7du3+CmOxqF27doqKirria1q2bKktW7bkFlIxMTH67rvv1KFDh6v+nvT0dKWkpOT5AgAAwOWaNGmib7/9NvfnPxtnM2bMUGRkpF3vVRy1HnUe/o0thxPVYfIafbH9uCyG9Fy7Glr0RAumbwIArsq0xznPnDmj7OxsVahQIc/xChUq5I5U/6cePXrozJkzuvnmm2Wz2ZSVlaUBAwbo//7v/676e8aNG6exY8cWanYAAIDS6PXXX9fdd9+tPXv2KCsrS5MnT9aePXu0fv16rVq1yq73Ko5ajzoPBZGVnaN3fzmod3/5XTk2KcTfS5O6NWDvMwDAdZk+WMAeK1eu1Ouvv673339fW7du1dKlS/Xtt9/q1VdfveprRo4cqeTk5NyvI0eOFGNiAACAkuPmm2/W9u3blZWVpbp16+rHH39UUFCQoqKi1Lhx4yL//fbWetR5sNefwwMmL7/UQOvSsLK+G8TwAABA/pi2Ei0wMFAuLi46efJknuMnT55UxYoVr/iaUaNGqWfPnurfv78kqW7durpw4YKeeOIJvfTSS7JYLu8Jenh4yMPDo/D/AAAAAKVQRESEpk+f/q/fpzhqPeo82IPhAQCAf8u0Jpq7u7saN26s5cuXq3PnzpKknJwcLV++XM8888wVX5OamnpZ8eTi4iJJstlsRZoXAADAGeTk5OjgwYM6deqUcnJy8pxr3bp1vt+HWg+OIiUtU6O+2K0vtx+XJDWpVk4TuzVg7zMAgN1Ma6JJ0tChQ9W7d281adJEzZo106RJk3ThwgX16dNHktSrVy9VrlxZ48aNkyR17NhREyZMUMOGDdW8eXMdPHhQo0aNUseOHXMLLAAAABTMhg0b1KNHDx0+fPiyppVhGMrOzrbr/aj1YLbNhxL13KLtOnr2olwshga1qaGnb4+Qq0uJ2tUGAOAgTG2idevWTadPn9bo0aN14sQJNWjQQMuWLcvdgDYuLi7Pp5Evv/yyDMPQyy+/rGPHjql8+fLq2LGjXnvtNbP+CAAAAKXGgAEDcid0BgcH507nLChqPZjlysMDGqpxtXJmRwMAlGCGzcnWxqekpMhqtSo5OVm+vr5mxwEAACWEM9QQZcqU0Y4dO1S9enWzoxSIM9wjXN+RxFQNXrhNW+OSJEn3N6yssffdJB9PN3ODAQAcVn5rCFNXogEAAMBx/PkIZUltogGfbzuqUV/8pvMMDwAAFAGaaAAAAJAkPfvssxo2bJhOnDihunXrys0t78qdevXqmZQMuLZ/Dg9oGlpOEx5ieAAAoHDRRAMAAIAk6YEHHpAk9e3bN/eYYRiy2WwFGiwAFIfNhxI1eOF2HUu6NDxgcNsaeuo2hgcAAAofTTQAAABIkmJjY82OAORbVnaOpvxyUO8xPAAAUExoogEAAECSVK1aNbMjAPkSl5Cq5xYxPAAAULxoogEAADixr776Snfffbfc3Nz01VdfXfPaTp06FVMq4MpsNps+33ZMo7/8Y3iAp6v+25nhAQCA4kETDQAAwIl17txZJ06cUFBQkDp37nzV69gTDWZLScvUy5/v1lc7/hoeMLFbA1Upx/AAAEDxoIkGAADgxHJycq74PeBINh1K1HMMDwAAmIwmGgAAAACHlJWdoynLf9d7Kw4qxyZV9ffWpIcbqFFVhgcAAIofTTQAAADkunDhglatWqW4uDhlZGTkOTdo0CCTUsEZxSWkavCibdr25/CARpU1thPDAwAA5qGJBgAAAEnStm3b1KFDB6WmpurChQvy9/fXmTNn5O3traCgIJpoKBZXGh7wWpe66lS/ktnRAABOjk0EAAAAIEkaMmSIOnbsqLNnz8rLy0sbNmzQ4cOH1bhxY7399ttmx4MTSL6YqcELt2vo4h06n56lpqHl9P3gW2igAQAcAivRAAAAIEnavn27PvzwQ1ksFrm4uCg9PV3h4eF688031bt3b91///1mR0Qp9s/hAc+1raGnbq8uF4thdjQAACTRRAMAAMAf3NzcZLFcelAhKChIcXFxuvHGG2W1WnXkyBGT06G0YngAAKCkoIkGAAAASVLDhg21adMm1ahRQ7feeqtGjx6tM2fOaP78+apTp47Z8VAKHU64oOcWbc8dHvBAoyr6T6faDA8AADgk9kQDAACAJOn1119XcHCwJOm1115TuXLlNHDgQJ0+fVofffSRyelQmthsNn225ag6TF6jbXFJ8vF01bvdG+qdh+rTQAMAOCxWogEAAECS1KRJk9zvg4KCtGzZMhPToLRKvpipl7/Yra93HJckNQv114Ru9VWlnLfJyQAAuDaaaAAAAACKxcbYRA1Z9NfwgCHtamjgbQwPAACUDDTRAAAAnFjDhg1lGPlrYGzdurWI06C0yvxjeMDUvw0PmPxwAzVkeAAAoAShiQYAAODEOnfubHYElHKHEy5o8MLt2n4kSdKl4QFj77tJZT34TxEAQMnC31wAAABObMyYMWZHQClls9n02dZjGvPlbl3IyJaPp6te71JXHetXMjsaAAAFkq8m2v3335/vN1y6dGmBwwAAAMB8mzdv1t69eyVJtWvXVuPGjU1OhJIm+WKmXvp8l77ZGS/p0vCAiQ83UGU/L5OTAQBQcPlqolmt1tzvbTabPv/8c1mt1twJTlu2bFFSUpJdzTYAAAA4lqNHj6p79+5at26d/Pz8JElJSUlq2bKlFi5cqCpVqpgbECXCP4cHDL2jpgbcGsHwAABAiZevJtrs2bNzvx8xYoQeeughffDBB3JxcZEkZWdn66mnnpKvr2/RpAQAAECR69+/vzIzM7V3717VqlVLkrR//3716dNH/fv317Jly0xOCEf2z+EB1QK8NfnhhmoQ4md2NAAACoVhs9ls9rygfPnyWrt2bW5h9af9+/erZcuWSkhIKNSAhS0lJUVWq1XJyck0/QAAQL45Qw3h5eWl9evXq2HDhnmOb9myRbfccotSU1NNSpY/znCPHNU/hwc82LiK/tOJ4QEAgJIhvzWE3X+rZWVlad++fZc10fbt26ecnBz7kwIAAMAhhISEKDMz87Lj2dnZqlSJzeBxuSsNDxh3f13dW4//vQAASh+7m2h9+vRRv379FB0drWbNmkmSfv31V40fP159+vQp9IAAAAAoHm+99ZaeffZZTZ06NXfv282bN2vw4MF6++23TU4HR5OcmqmXvvjb8IAwf03sxvAAAEDpZffjnDk5OXr77bc1efJkxcdf+gszODhYgwcP1rBhw3L3SXNULPMHAAAF4Qw1RLly5ZSamqqsrCy5ul76rPXP78uUKZPn2sTERDMiXpMz3CNH8WtMgoYs2q7jyWlytRgawvAAAEAJVmSPc1osFg0fPlzDhw9XSkqKJFGkAAAAlAKTJk0yOwIcXGZ2jib//LveX8nwAACA8ynQTp9ZWVlauXKloqOj1aNHD0nS8ePH5evrq7JlyxZqQAAAABSP3r17mx0BDuxwwgUNWrhdO/4YHtC1cRWNYXgAAMCJWOx9weHDh1W3bl3dd999evrpp3X69GlJ0htvvKHnn3++0AMCAACgeMyZM+eKx7OysjRy5MjiDQOHYbPZ9L/NR9Rh8hrtOJIkX09XTe3RSG91rU8DDQDgVOxuog0ePFhNmjTR2bNn5eX116ahXbp00fLlyws1HAAAAIrPoEGD1LVrV509ezb32P79+9W8eXN9+umnJiaDWZJTM/XMp9v0wpKdupCRrWZh/vr+uda6p16w2dEAACh2djfR1qxZo5dfflnu7u55joeGhurYsWOFFgwAAADFa9u2bTp69Kjq1q2rn376SVOnTlWjRo10ww03aMeOHWbHQzH7NSZBd09erW93xsvVYuiFu2rp08dbMH0TAOC07F5/nZOTo+zs7MuOHz16VD4+PoUSCgAAAMUvIiJC69at03PPPaf27dvLxcVFc+fOVffu3c2OhmKUmZ2jST8f0Psro2WzSaEB3prE8AAAAOxfiXbnnXfmmdxkGIbOnz+vMWPGqEOHDoWZDQAAAMXs22+/1cKFCxUZGSk/Pz/NnDlTx48fNzsWismhMxf04AdRmrriUgPtoSZV9O2gW2igAQCgAjTR3nnnHa1bt061a9dWWlqaevTokfso5xtvvFEUGQEAAFAMnnzySXXt2lUjRozQmjVrtHPnTrm7u6tu3bpavHix2fFQhP4cHnDPlLzDA958sL7KMDwAAABJkmGz2Wz2vigrK0sLFy7Uzp07df78eTVq1EiPPPJInkEDjiolJUVWq1XJycny9fU1Ow4AACghnKGGqFOnjj7++GPVr18/z/GpU6dqxIgROn/+vEnJ8scZ7lFRSE7N1P99vkvf7oqXJDUP89fEbg1Uib3PAABOIr81RIGaaCUZxRUAACgIZ6gh0tPT5eHhccVz+/fvV61atYo5kX2c4R4Vtg0xCRq6aLuOJ6fJ1WJoyB01NeDWCLlYDLOjAQBQbPJbQxRobfbvv/+uFStW6NSpU8rJyclzbvTo0QV5SwAAAJjk1KlTCgoKumoDLSsrS8nJycWcCkXpSsMDJj/cUPXZ+wwAgKuyu4k2ffp0DRw4UIGBgapYsaIM469PqQzDoIkGAABQwgQHBys+Pl5BQUGSpLp16+q7775TSEiIJCkhIUGRkZFXnNCOkufQmQsavHCbdhy91Bh9qEkVjel4E3ufAQBwHXb/Tfnf//5Xr732mkaMGFEUeQAAAFDM/rm7x6FDh5SZmXnNa1Dy2Gw2/W/LUf3nq9+UmpEtX09XjX+gnjrUDTY7GgAAJYLdTbSzZ8+qa9euRZEFAAAADurvTx+g5Pnn8IAW4f6a8BDDAwAAsIfF3hd07dpVP/74Y1FkAQAAAFDINsQkqP3k1fp2V7xcLYaGt6+lj/u3oIEGAICd7F6JVr16dY0aNUobNmxQ3bp15ebmluf8oEGDCi0cAAAAip5hGDp37pw8PT1ls9lkGIbOnz+vlJQUScr9J0qWzOwcTfzpgKatujQ8ICywjCZ1a8DwAAAACsiw2bnBRVhY2NXfzDAUExPzr0MVJUafAwCAgijNNYTFYsnzuOafjbR//uzogwVK8z2yV+wfwwN2MjwAAIDrym8NYffforGxsf8qGAAAABzLihUrzI6AQmKz2fS/zUf1n68vDQ+werlp3P11GR4AAEAh4KMoAAAAJ3frrbeaHQGFIDk1UyM/36nvdp2QxPAAAAAKW76aaEOHDtWrr76qMmXKaOjQode8dsKECYUSDAAAAED+REUnaOji7YpPTpOrxdCwO2vpidbhcrEwVRUAgMKSrybatm3blJmZmfv91TD6HAAAACg+GVk5mvjzAX3wt+EBkx9uoHpV/MyOBgBAqZOvJtrf98lgzwwAAADAfP8cHtCtSYhGd6zN8AAAAIoIf8MCAAAAJciVhgeMv7+u7mZ4AAAARapATbTNmzdr8eLFiouLU0ZGRp5zS5cuLZRgAAAAMMfBgwcVHR2t1q1by8vLSzabjW07HERSaoZGLt2l73dfGh4QGR6gCd3qK9jK8AAAAIqaxd4XLFy4UC1bttTevXv1+eefKzMzU7/99pt++eUXWa3WosgIAACAYpCQkKB27dqpZs2a6tChg+Lj4yVJ/fr107Bhw0xOh6joBN09eY2+331CrhZDI9rfoAX9m9NAAwCgmNjdRHv99dc1ceJEff3113J3d9fkyZO1b98+PfTQQ6patWpRZAQAAEAxGDJkiFxdXRUXFydvb+/c4926ddOyZctMTObcMrJy9MayfeoxY4Pik9MUHlhGnz/VSgNvi2D6JgAAxcjuxzmjo6N1zz33SJLc3d114cIFGYahIUOGqE2bNho7dmyhhwQAAEDR+/HHH/XDDz+oSpUqeY7XqFFDhw8fNimVc4s5fV7PLdqeOzzg4aaXhgd4u7O1MQAAxc3uv33LlSunc+fOSZIqV66s3bt3q27dukpKSlJqamqhBwQAAEDxuHDhQp4VaH9KTEyUh4eHCYmcl81m0+LNR/Sfr/boYibDAwAAcAR2P87ZunVr/fTTT5Kkrl27avDgwXr88cfVvXt3tW3bttADAgAAoHjccsstmjdvXu7PhmEoJydHb775pm6//XYTkzmXpNQMPfXxVo34bJcuZmYrMjxAy567hQYaAAAms3sl2nvvvae0tDRJ0ksvvSQ3NzetX79eDzzwgF5++eVCDwgAAIDi8eabb6pt27bavHmzMjIyNHz4cP32229KTEzUunXrzI7nFNZHn9HQRTt0IiVNrhZDz99VS4/fEs7eZwAAOAC7m2j+/v6531ssFr344ouFGggAAADmqFOnjg4cOKD33ntPPj4+On/+vO6//349/fTTCg5mFVRRysjK0YSfDujD1dGy2aTwwDKa/HBD1a1iNTsaAAD4Q76aaCkpKfl+Q19f3wKHAQAAgLmsVqteeukls2M4lZjT5zV44XbtOnZpeED3ZiEadS/DAwAAcDT5+pvZz89PhnHtJeQ2m02GYSg7O7tQggEAAKB4zZ49W2XLllXXrl3zHP/f//6n1NRU9e7d26RkpZPNZtOiTUc09utLwwP8vC8ND2hfh1V/AAA4onw10VasWFHUOQAAAGCycePG6cMPP7zseFBQkJ544gmaaIUoKTVDL362S8t+OyFJahkRoAkPNVBFq6fJyQAAwNXkq4l26623FnUOAAAAmCwuLk5hYWGXHa9WrZri4uJMSFQ6rT94RkMXXxoe4OZi6Pk7Lw0PsDA8AAAAh1agjRbOnj2rmTNnau/evZKk2rVrq0+fPnmGDgAAAKBkCQoK0s6dOxUaGprn+I4dOxQQEGBOqFIkIytH7/y0Xx+tjmF4AAAAJZDF3hesXr1aoaGhmjJlis6ePauzZ89qypQpCgsL0+rVq4siIwAAAIpB9+7dNWjQIK1YsULZ2dnKzs7WL7/8osGDB+vhhx82O16JFn36vB6Ytl4frrrUQOveLETfDLqZBhoAACWI3SvRnn76aXXr1k3Tpk2Ti4uLJCk7O1tPPfWUnn76ae3atavQQwIAAKDovfrqqzp06JDatm0rV9dLZWJOTo569eql119/3eR0JdOVhwfUU/s6Fc2OBgAA7GTYbDabPS/w8vLS9u3bVatWrTzH9+/frwYNGujixYuFGrCwpaSkyGq1Kjk5Wb6+vmbHAQAAJYQz1RAHDhzQjh075OXlpbp166patWpmR8oXR7tHZy9kaORShgcAAODo8ltD2L0SrVGjRtq7d+9lTbS9e/eqfv369icFAACAQ6lZs6Zq1qxpdowSjeEBAACUPnY30QYNGqTBgwfr4MGDatGihSRpw4YNmjp1qsaPH6+dO3fmXluvXr3CSwoAAIAilZ2drTlz5mj58uU6deqUcnJy8pz/5ZdfTEpWcmRk5eidH/frozV/DQ+Y0r2h6lRm7zMAAEo6u5to3bt3lyQNHz78iucMw5DNZpNhGMrOzv73CQEAAFAsBg8erDlz5uiee+5RnTp1ZBismrJH9OnzGrxwm3YfS5EkdW9WVaPuvVHe7naX3AAAwAHZ/Td6bGxsUeQAAACAyRYuXKjFixerQ4cOZkcpUWw2mxZuOqJXGB4AAECpZncT7Voby/65As1ZZefYtDE2UafOpSnIx1PNwvzlwr4XAACghHB3d1f16tXNjuGQrlbnnb2QoReX7tQPv52UJLWqHqB3ujI8AACA0sjuJtpjjz2mqVOnqkyZMnmOHzp0SD179tSaNWsKLVxJsmx3vMZ+vUfxyWm5x4KtnhrTsbba1wk2MRkAAED+DBs2TJMnT9Z7773n1B+M/tPV6rxuTUL06aY4nUxJl5uLoRfuqqX+NzM8AACA0sruJtqOHTtUr149LViwQJGRkZKkuXPnatCgQWrTpk2hBywJlu2O18AFW2X7x/ETyWkauGCrpj3aiEYaAABweGvXrtWKFSv0/fff66abbpKbm1ue80uXLjUpmXmuVufFJ6dp0vLfJUnh5ctoysMMDwAAoLSzu4m2ceNG/d///Z9uu+02DRs2TAcPHtT333+vCRMm6PHHHy+KjA4tO8emsV/vuaywkiSbJEPS2K/36I7aFXm0EwAAODQ/Pz916dLF7BgO41p13p+83V305dOt5OPpdo2rAABAaWB3E83NzU1vvfWWvL299eqrr8rV1VWrVq3KXZXmbDbGJuZZ2v9PNl36pHJjbKIiIwKKLxgAAICdZs+ebXYEh3K9Ok+SUjOytftYCnUeAABOwGLvCzIzMzVs2DC98cYbGjlypCIjI3X//ffru+++K4p8Du/UuWsXVvZeBwAAAMdAnQcAAP7O7pVoTZo0UWpqqlauXKkWLVrIZrPpzTff1P3336++ffvq/fffL4qcDivIJ3+Tl/J7HQAAgJmWLFmixYsXKy4uThkZGXnObd261aRU5qDOAwAAf2f3SrQmTZpo+/btatGihSTJMAyNGDFCUVFRWr16daEHdHTNwvwVbPXUtXY7q+h7aQw6AACAI5syZYr69OmjChUqaNu2bWrWrJkCAgIUExOju+++2+x4xe56dZ6hS1M6qfMAAHAOdjfRZs6cqTJlylx2vGHDhtqyZUuhhCpJXCyGxnSsLUlXLbD8y7grO+daW9ICAACY7/3339dHH32kd999V+7u7ho+fLh++uknDRo0SMnJyWbHK3bXqvP+/HlMx9oMjwIAwEnku4m2ePHiPEv6jx49qpycnNyfU1NTNXny5MJNV0K0rxOsaY82UkVr3qX8AWXd5e5i0Z74FA1ZvJ1GGgAAcGhxcXFq2bKlJMnLy0vnzp2TJPXs2VOffvqpmdFMc7U6r6LVU9MebaT2dYJNSgYAAIpbvvdE6969u+Lj4xUUFCRJql27trZv367w8HBJ0rlz5zRy5EgNHz68aJI6uPZ1gnVH7YraGJuoU+fSFORzaWn/uoNn1G/uJn27M16+nm56vUsdGQafVgIAAMdTsWJFJSYmqlq1aqpatao2bNig+vXrKzY2Vjab834YeLU6jxVoAAA4l3yvRPtn4VRYhdTUqVMVGhoqT09PNW/eXBs3brzm9UlJSXr66acVHBwsDw8P1axZ02Emg7pYDEVGBOi+BpUVGREgF4uh1jXLa/LDDWUxpE83xumNZfvNjgkAAHBFbdq00VdffSVJ6tOnj4YMGaI77rhD3bp1U5cuXQr0nqWl1rtSnQcAAJyL3dM5C9OiRYs0dOhQffDBB2revLkmTZqku+66S/v3789d8fZ3GRkZuuOOOxQUFKQlS5aocuXKOnz4sPz8/Io/vB061A3W613q6sWlu/TBqmhZvdw08LYIs2MBAADk8dFHH+Vu1/H0008rICBA69evV6dOnfTkk0/a/X7OUusBAADnYNjyuaTMYrHoxIkTuQWPj4+PduzYkfs458mTJ1WpUiVlZ2fn+5c3b95cTZs21XvvvSdJysnJUUhIiJ599lm9+OKLl13/wQcf6K233tK+ffvk5uaW79/zdykpKbJarUpOTpavr2+B3qOgPlwVrXHf75Mkjbu/rro3q1qsvx8AABScmTVESVXctR73CAAAFER+awi7VqL98MMPslqtki4VQcuXL9fu3bslXVp6b4+MjAxt2bJFI0eOzD1msVjUrl07RUVFXfE1X331lSIjI/X000/ryy+/VPny5dWjRw+NGDFCLi4uV3xNenq60tPTc39OSUmxK2dhevLWCCVdzNS0ldH6v893ycfTVffWq2RaHgAAgJ07d6pOnTqyWCzauXPnNa+tV69evt+3OGo9R6rzAABA6WdXE6137955fv7nsn57Nsw/c+aMsrOzVaFChTzHK1SooH379l3xNTExMfrll1/0yCOP6LvvvtPBgwf11FNPKTMzU2PGjLnia8aNG6exY8fmO1dRG35XLSWlZurTjXEasmi7fDzddGvN8mbHAgAATqpBgwa5Txs0aNBAhmFcce9bwzDseuKgOGo9R6vzAABA6ZbvJtqf+2OYKScnR0FBQfroo4/k4uKixo0b69ixY3rrrbeu2kQbOXKkhg4dmvtzSkqKQkJCiivyZQzD0H8711FKWqa+3RmvAfO3aEH/Zmpczd+0TAAAwHnFxsaqfPnyud+byd5az9HqPAAAULqZNlggMDBQLi4uOnnyZJ7jJ0+eVMWKFa/4muDgYLm5ueVZzn/jjTfqxIkTysjIkLu7+2Wv8fDwkIeHR+GG/5dcLIYmPtRA59OytOrAafWZvUmLnozUjcHs3QEAAIpXtWrVJEmZmZkaO3asRo0apbCwsH/9vsVR6zlinQcAAEovi1m/2N3dXY0bN9by5ctzj/25z1pkZOQVX9OqVSsdPHgwz6q4AwcOKDg4+IoNNEfm7mrRB482VpNq5ZSSlqWeMzfq0JkLZscCAABOys3NTZ999lmhvZ+z13oAAKD0Ma2JJklDhw7V9OnTNXfuXO3du1cDBw7UhQsX1KdPH0lSr1698mxGO3DgQCUmJmrw4ME6cOCAvv32W73++ut6+umnzfoj/Cte7i6a+VhT3RjsqzPn0/XozF91IjnN7FgAAMBJde7cWV988UWhvZ+z13oAAKB0Me1xTknq1q2bTp8+rdGjR+vEiRNq0KCBli1blrsBbVxcnCyWv/p8ISEh+uGHHzRkyBDVq1dPlStX1uDBgzVixAiz/gj/mtXLTfP6NlPXD9brUEKqes78VYufjFS5MnzaCgAAileNGjX0yiuvaN26dWrcuLHKlCmT5/ygQYPsej9qPQAAUJoYtiuNXyrFUlJSZLValZycLF9fx9mD7Ehiqh78YL1OpqSrfoifPu7fXGU9TO1xAgCAv3HUGqIwXWsvNMMwFBMTU4xp7OcM9wgAABS+/NYQBerSJCUlacmSJYqOjtYLL7wgf39/bd26VRUqVFDlypULHNqZhfh7a0G/5ur6YZR2HEnSE/M2a9ZjTeXp5nL9FwMAABQCs6dzAgAAODK790TbuXOnatasqTfeeENvv/22kpKSJElLly7Ns6cF7Fejgo/m9GmmMu4uWh+doEGfblNWds71XwgAAAAAAIAiZfdKtKFDh+qxxx7Tm2++KR8fn9zjHTp0UI8ePQo1nDNqEOKn6b2a6LHZm/TjnpN6cekuvflAPVkshtnRAACAEzh69Ki++uorxcXFKSMjI8+5CRMmmJQKAADAfHY30TZt2qQPP/zwsuOVK1fWiRMnCiWUs2tZPVDv9miogQu2aMmWo7J6uenle26UYdBIAwAARWf58uXq1KmTwsPDtW/fPtWpU0eHDh2SzWZTo0aNzI4HAABgKrsf5/Tw8FBKSsplxw8cOKDy5csXSihId91UUW8+WF+SNHNtrKauOGhyIgAAUNqNHDlSzz//vHbt2iVPT0999tlnOnLkiG699VZ17drV7HgAAACmsruJ1qlTJ73yyivKzMyUdGlSU1xcnEaMGKEHHnig0AM6swcbV9Hoe2tLkt7+8YDmRx0yNxAAACjV9u7dq169ekmSXF1ddfHiRZUtW1avvPKK3njjDZPTAQAAmMvuJto777yj8+fPKygoSBcvXtStt96q6tWry8fHR6+99lpRZHRqfW8O06C2NSRJo7/6TV9uP2ZyIgAAUFqVKVMmdx+04OBgRUdH5547c+aMWbEAAAAcgt17olmtVv30009at26dduzYofPnz6tRo0Zq165dUeSDpCHtaig5NUNzow5r2OId8vF0VZsbKpgdCwAAlDItWrTQ2rVrdeONN6pDhw4aNmyYdu3apaVLl6pFixZmxwMAADCVYbPZbGaHKE4pKSmyWq1KTk6Wr6+v2XHyLSfHpqGLt+uL7cfl4WrRvL7N1Dw8wOxYAAA4jZJaQ+RHYmKi/P39FRMTo/Pnz6tevXq6cOGChg0bpvXr16tGjRqaMGGCqlWrZnbUayrN9wgAABSd/NYQdj/OOWjQIE2ZMuWy4++9956ee+45e98O+WSxGHqra321vSFI6Vk56j93s3YfSzY7FgAAKAUqVaqkhx9+WNHR0apXr56kS492fvDBB9q5c6c+++wzh2+gAQAAFDW7m2ifffaZWrVqddnxli1basmSJYUSClfm5mLR1EcaqVmYv86lZ6n3rI2KPn3e7FgAAKCEmz59uk6fPq327dsrNDRU//nPf3To0CGzYwEAADgUu5toCQkJslqtlx339fVlw9li4Onmohm9m6hOZV8lXMhQzxm/6njSRbNjAQCAEqxnz55avny5Dh48qN69e2vu3LmqXr267rjjDi1atCh32AAAAIAzs7uJVr16dS1btuyy499//73Cw8MLJRSuzdfTTXP7NFN4+TI6npymR2f+qoTz6WbHAgAAJVxYWJjGjh2r2NhYLVu2TEFBQerbt6+Cg4M1aNAgs+MBAACYyu4m2tChQzV8+HCNGTNGq1at0qpVqzR69Gi9+OKLGjJkSFFkxBUElPXQ/H7NVcnqqZjTF9R79kadS8s0OxYAACgl2rVrp48//ljz5s2TJE2dOtXkRAAAAOZytfcFffv2VXp6ul577TW9+uqrkqTQ0FBNmzZNvXr1KvSAuLrKfl6a37+5HvogSruPpaj/3M2a27eZPN1czI4GAABKsMOHD2v27NmaO3eujhw5ottvv139+vUzOxYAAICpDJvNZivoi0+fPi0vLy+VLVu2MDMVqdI4+nz3sWR1/2iDzqVnqd2NQZr2aGO5udi9yBAAAFxDaawh/i49PV2fffaZZs2apZUrV6py5cp67LHH1KdPH4WGhpodL19K+z0CAABFI781xL/qtJQvX75ENdBKqzqVrZrRu4k8XC36ee8pDV+yUzk5Be6NAgAAJ/PUU08pODhYffv2VUBAgL777jsdOnRIY8eOLTENNAAAgKJmdxPt5MmT6tmzpypVqiRXV1e5uLjk+YI5mocHaNqjjeRqMfT5tmMa+/Vv+heLDAEAgBNZu3atxowZo2PHjmnRokW68847ZRiG2bEAAAAcit17oj322GOKi4vTqFGjFBwcTIHlQNrcUEHvPFRfzy3arrlRh2X1dtfQO2qaHQsAADi4nTt3mh0BAADA4dndRFu7dq3WrFmjBg0aFEEc/Fv3Nais5IuZGv3lb5qy/HdZvdzU7+Yws2MBAAAAAACUaHY/zhkSEsJjgg6uV2Sohv2xAu3Vb/ZoyZajJicCAAAAAAAo2exuok2aNEkvvviiDh06VARxUFieaVM9dwXaiM926offTpicCAAAAAAAoOSyu4nWrVs3rVy5UhEREfLx8ZG/v3+eLzgGwzD0Uocb9WDjKsrOsenZT7Zp/cEzZscCAAAO5v7771dKSookad68eUpPTzc5EQAAgGOye0+0SZMmFUEMFAWLxdD4++vqXFqmfvjtpB6ft1mfPN5C9UP8zI4GAAAcxDfffKMLFy7I19dXffr0Ufv27RUUFGR2LAAAAIdjdxOtd+/eRZEDRcTVxaLJDzdUv7mbtO5ggh6bvVGLn4xUjQo+ZkcDAAAO4IYbbtDIkSN1++23y2azafHixfL19b3itb169SrmdAAAAI7DsP2LKQFpaWnKyMjIc+xqRZejSElJkdVqVXJyssNnLUzn07P0yIxfteNIkir6eup/AyIV4u9tdiwAAEqM0lpDrF+/XkOHDlV0dLQSExPl4+MjwzAuu84wDCUmJpqQMP9K6z0CAABFK781hN17ol24cEHPPPOMgoKCVKZMGZUrVy7PFxxTWQ9XzXmsqWoEldWJlDT1nPmrTp1LMzsWAAAwWcuWLbVhwwadPn1aNptNBw4c0NmzZy/7cvQGGgAAQFGzu4k2fPhw/fLLL5o2bZo8PDw0Y8YMjR07VpUqVdK8efOKIiMKSbky7prfr7mqlPPSoYRU9Zq5UckXM82OBQAAHERsbKzKly9vdgwAAACHZPfjnFWrVtW8efN02223ydfXV1u3blX16tU1f/58ffrpp/ruu++KKmuhYJm/dOjMBT34QZTOnE9X42rlNL9fM3m72709HgAATsVZaoikpCTNnDlTe/fulSTVrl1b/fr1k9VqNTnZ9TnLPQIAAIWryB7nTExMVHh4uKRL+5/9ubT/5ptv1urVqwsYF8UpNLCM5vdrJl9PV205fFYDF2xVRlaO2bEAAIDJNm/erIiICE2cOFGJiYlKTEzUxIkTFRERoa1bt5odDwAAwFR2N9HCw8MVGxsr6dI0p8WLF0uSvv76a/n5+RVqOBSdG4N9NbtPU3m6WbTqwGkNXbxd2TkFnjEBAABKgSFDhqhTp046dOiQli5dqqVLlyo2Nlb33nuvnnvuObPjAQAAmMruJlqfPn20Y8cOSdKLL76oqVOnytPTU0OGDNELL7xQ6AFRdBpX89eHPZvIzcXQNzvjNerL3foXw1oBAEAJt3nzZo0YMUKurn9t8+Dq6qrhw4dr8+bNJiYDAAAwn90bYQ0ZMiT3+3bt2mnfvn3asmWLqlevrnr16hVqOBS9W2uW16RuDfXMp1v1ya9x8vNy0/D2N5gdCwAAmMDX11dxcXG64Ya8tcCRI0fk4+NjUioAAADH8K93k69WrZqqVatWGFlgknvqBSslra5GLt2l91dGy+rlpidvjTA7FgAAKGbdunVTv3799Pbbb6tly5aSpHXr1umFF15Q9+7dTU4HAABgrnw10aZMmaInnnhCnp6emjJlyjWvHTRoUKEEQ/Hq3qyqki9mavz3+zTu+33y9XJT92ZVzY4FAACK0dtvvy3DMNSrVy9lZWVJktzc3DRw4ECNHz/e5HQAAADmMmz52AQrLCxMmzdvVkBAgMLCwq7+ZoahmJiYQg1Y2Bh9fm3jv9+nD1ZFyzCk97o30j31gs2OBACAQ3CmGiI1NVXR0dGSpIiICHl7e5ucKH+c6R4BAIDCk98aIl8r0f6cxvnP71H6jGhfS8kXM/TpxiN6btE2+Xi6qnXN8mbHAgAAxcjb21t169Y1OwYAAIBDsWs6Z2ZmpiIiIrR3796iygOTGYah/3auq3vqBisz26Yn52/RlsNnzY4FAAAAAABgKruaaG5ubkpLSyuqLHAQLhZDE7s10C01AnUxM1t9Zm/U3vgUs2MBAAAAAACYxq4mmiQ9/fTTeuONN3I3m0Xp5O5q0Yc9G6tRVT+lpGWp16yNOpxwwexYAAAAAAAApsjXnmh/t2nTJi1fvlw//vij6tatqzJlyuQ5v3Tp0kILB3N5u7tq9mPN1O2jKO07cU6PzvxVSwa0VAVfT7OjAQAAAAAAFCu7m2h+fn564IEHiiILHJDV203z+jVT1w+idDghVT1n/qrFT0bKz9vd7GgAAKAI/P7771qxYoVOnTqlnJycPOdGjx5tUioAAADzGTabzWZ2iOLE6POCOZKYqgc/WK+TKelqEOKnj/s3VxkPu3uwAACUWM5QQ0yfPl0DBw5UYGCgKlasKMMwcs8ZhqGtW7eamO76nOEeAQCAwpffGoImGvLtwMlzeujDKCWlZqpV9QDNeqypPFxdzI4FAECxcIYaolq1anrqqac0YsQIs6MUiDPcIwAAUPjyW0MUaCnRkiVLtHjxYsXFxSkjIyPPOUf/hBIFV7OCj+b0aaYe0zdo3cEEDf50u97r0VCuLnbPpwAAAA7o7Nmz6tq1q9kxAAAAHJLd3Y8pU6aoT58+qlChgrZt26ZmzZopICBAMTExuvvuu4siIxxIgxA/Te/VRO4uFi377YRGLt0lJ1vMCABAqdW1a1f9+OOPZscAAABwSHavRHv//ff10UcfqXv37pozZ46GDx+u8PBwjR49WomJiUWREQ6mVfVATeneUE99vEX/23JUVi83vXTPjXn2TQEAACVP9erVNWrUKG3YsEF169aVm5tbnvODBg0yKRkAAID57N4TzdvbW3v37lW1atUUFBSkn376SfXr19fvv/+uFi1aKCEhoaiyFgr2yig8izcf0fAlOyVJL9xVS0/fXt3kRAAAFB1nqCHCwsKues4wDMXExBRjGvs5wz0CAACFr8j2RKtYsaISExNVrVo1Va1aVRs2bFD9+vUVGxvLY31O5qEmIUq5mKn/frtXb/2wX75eburZoprZsQAAQAHFxsaaHQEAAMBh2b0nWps2bfTVV19Jkvr06aMhQ4bojjvuULdu3dSlS5dCDwjH1v+WcD3b5tIKtNFf7taX24+ZnAgAABQGm83GB6QAAAB/k+8m2jfffKOcnBx99NFHeumllyRJTz/9tGbNmqUbb7xRr7zyiqZNm1ZkQeG4ht5RU70iq8lmk4Yt3qEV+06ZHQkAABTQvHnzVLduXXl5ecnLy0v16tXT/PnzzY4FAABgunw/ztm5c2dVqFBBjz32mPr27auIiAhJ0sMPP6yHH364yALC8RmGof90vEnJFzP15fbjGrBgi+b3a65mYf5mRwMAAHaYMGGCRo0apWeeeUatWrWSJK1du1YDBgzQmTNnNGTIEJMTAgAAmCffK9FiY2P15JNPauHChapZs6ZuvfVWzZ8/XxcvXizKfCghLBZDb3etrzY3BCk9K0f95mzS7mPJZscCAAB2ePfddzVt2jS98cYb6tSpkzp16qQ333xT77//vqZMmWJ2PAAAAFPlu4kWEhKi0aNHKzo6Wj///LNCQ0M1cOBABQcHa8CAAdq0aVNR5kQJ4OZi0fuPNFKzMH+dS89S71kbFXP6vNmxAABAPsXHx6tly5aXHW/ZsqXi4+NNSAQAAOA47B4sIEm333675s6dq/j4eL311lvatWuXWrRoofr16xd2PpQwnm4umtG7iW6q5KuECxnqOXOjjiexWhEAgJKgevXqWrx48WXHFy1apBo1apiQCAAAwHHke0+0K/Hx8VHbtm11+PBh7du3T3v27CmsXCjBfD3dNLdvMz30QZRizlxQz5m/avGTkQoo62F2NAAAcA1jx45Vt27dtHr16tw90datW6fly5dfsbkGAADgTAq0Eu3ixYuaN2+ebrvtNtWoUUMLFy7U0KFDdejQoUKOh5IqsKyH5vdvrmCrp6JPX9BjszfpXFqm2bEAAMA1PPDAA/r1118VGBioL774Ql988YUCAwO1ceNGdenSxex4AAAApjJsNpstvxdv2LBBs2bN0uLFi5WRkaH7779f/fr10+23316UGQtVSkqKrFarkpOT5evra3acUu/gqfN66MMoJV7IUPMwf83t20yebi5mxwIAwG7UEI6PewQAAAoivzVEvh/nrF27tvbv36+GDRtq3Lhx6tGjh6xWa6GERelVPais5vVtpoc/2qBfYxP1zCdbNe3RxnJzKdAiSAAAUMhSUlJyi8WUlJRrXktjCgAAOLN8N9HatWunTz/9lOEBsFudylbN6N1EvWdt1M97T2nEkp16u2t9WSyG2dEAAHB65cqVU3x8vIKCguTn5yfDuPzvZ5vNJsMwlJ2dbUJCAAAAx5DvJtqUKVOKMgdKuRbhAXr/kUZ6Yv4WLd12TL5ebhrTsfYVC3UAAFB8fvnlF/n7+0uSVqxYYXIaAAAAx/WvpnMC9mh7YwW907W+nlu0XXPWH5LVy01D7qhpdiwAAJzarbfemvt9WFiYQkJCLvuQy2az6ciRI8UdDQAAwKGwMRWKVeeGlTW2002SpMnLf9estbEmJwIAAH8KCwvT6dOnLzuemJiosLAwExIBAAA4DppoKHa9W4Zq6B8r0F75Zo8+23LU5EQAAED6a++zfzp//rw8PT1NSAQAAOA48vU4p7+/vw4cOKDAwED17dtXkydPlo+PT1FnQyn2bJvqSkrN1Kx1sRr+2U75eLrqzpsqmh0LAACnNHToUEmSYRgaNWqUvL29c89lZ2fr119/VYMGDUxKBwAA4BjytRItIyMjd+T53LlzlZaWVqShUPoZhqGX77lRDzSqouwcm575dJvWR58xOxYAAE5p27Zt2rZtm2w2m3bt2pX787Zt27Rv3z7Vr19fc+bMMTsmAACAqfK1Ei0yMlKdO3dW48aNZbPZNGjQIHl5eV3x2lmzZhVqQJReFouhNx6oq3Npmfpxz0k9PnezPn2ihepV8TM7GgAATuXPqZx9+vTRlClTeOIAAADgCvK1Em3BggXq0KGDzp8/L8MwlJycrLNnz17xC7CHq4tFU7o3VMuIAF3IyFbvWRt18NQ5s2MBAOB0MjMzNX/+fB0+fNjsKAAAAA4pXyvRKlSooPHjx0u6NLVp/vz5CggIKNJgcB6ebi76qFcTPTJ9g3YcTdajMzbqfwMiFeLvff0XAwCAQuHm5qaqVasqOzvb7CgAAAAOye7pnLGxsTTQUOjKerhqTp9mqhFUVidS0tRz5q86fS7d7FgAADiVl156Sf/3f/+nxMREs6MAAAA4HLubaJK0atUqdezYUdWrV1f16tXVqVMnrVmzprCzwcmUK+Ou+f2aq7Kflw4lpKrXrI1KvphpdiwAAJzGe++9p9WrV6tSpUqqVauWGjVqlOcLAADAmeXrcc6/W7Bggfr06aP7779fgwYNkiStW7dObdu21Zw5c9SjR49CDwnnUdHqqY/7N9eDH0Rpb3yK+s3ZpPn9msvL3cXsaAAAlHqdO3c2OwIAAIDDMmw2m82eF9x444164oknNGTIkDzHJ0yYoOnTp2vv3r2FGrCwpaSkyGq1Kjk5Wb6+vmbHwVXsOZ6ibh9F6Vxalm6rVV4f9Wwid9cCLZwEAKBQUEM4Pu4RAAAoiPzWEHZ3JWJiYtSxY8fLjnfq1EmxsbH2vh1wRbUr+Wr2Y03l6WbRyv2nNXTxdmXn2NXvBQAABbRlyxYtWLBACxYs0LZt28yOAwAA4BDsbqKFhIRo+fLllx3/+eefFRISUiihAElqEuqvDx5tLDcXQ9/sjNfoL3fLzoWTAADADqdOnVKbNm3UtGlTDRo0SIMGDVLjxo3Vtm1bnT592ux4AAAAprK7iTZs2DANGjRIAwcO1Pz58zV//nwNGDBAzz33nJ5//vmiyAgndlutIE14qIEMQ/r41zi9/eN+syMBAFBqPfvsszp37px+++03JSYmKjExUbt371ZKSkruXrgAAADOyu7BAgMHDlTFihX1zjvvaPHixZIu7ZO2aNEi3XfffYUeEOhYv5LOpWXp/z7fpakromX1ctMTrSPMjgUAQKmzbNky/fzzz7rxxhtzj9WuXVtTp07VnXfeaWIyAAAA89ndRJOkLl26qEuXLoWdBbiqHs2rKvlipt5Ytk+vf7dPVi83dWta1exYAACUKjk5OXJzc7vsuJubm3JyckxIBAAA4DgYd4gSY+BtEXry1nBJ0silu/TdrniTEwEAULq0adNGgwcP1vHjx3OPHTt2TEOGDFHbtm1NTAYAAGA+mmgoUV5sf4MebhqiHJs0eOE2rfmdTY4BACgs7733nlJSUhQaGqqIiAhFREQoLCxMKSkpevfdd82OBwAAYKoCPc4JmMUwDL3Wpa7OpWXp213xemLeFi3o31yNq5UzOxoAACVeSEiItm7dqp9//ln79u2TdGnv23bt2pmcDAAAwHwOsRJt6tSpCg0Nlaenp5o3b66NGzfm63ULFy6UYRjq3Llz0QaEQ3GxGJrQrb5uqRGoi5nZ6jtnk/adSDE7FgAApYJhGLrjjjv07LPP6tlnn/3XDTTqPAAAUFqY3kRbtGiRhg4dqjFjxmjr1q2qX7++7rrrLp06deqarzt06JCef/553XLLLcWUFI7Ew9VFH/ZsrEZV/ZR8MVM9Z25UXEKq2bEAACjxli9frnvvvTf3cc57771XP//8c4HeizoPAACUJnY30bKzszVz5kz16NFD7dq1U5s2bfJ82WvChAl6/PHH1adPH9WuXVsffPCBvL29NWvWrGtmeOSRRzR27FiFh4fb/TtROni7u2r2Y810Q0UfnT6XrkdmbtDJlDSzYwEAUGK9//77at++vXx8fDR48GANHjxYvr6+6tChg6ZOnWr3+1HnAQCA0sTuJtqfBVV2drbq1Kmj+vXr5/myR0ZGhrZs2ZLnMQGLxaJ27dopKirqqq975ZVXFBQUpH79+l33d6SnpyslJSXPF0oPq7eb5vVtpmoB3jqSeFG9Zm5UUmqG2bEAACiRXn/9dU2cOFGffvqpBg0apEGDBumTTz7RxIkT9frrr9v1XtR5AACgtLF7sMDChQu1ePFidejQ4V//8jNnzig7O1sVKlTIc7xChQq5m9n+09q1azVz5kxt3749X79j3LhxGjt27L+NCgcW5OupBf2a64Fp67X/5Dn1mbNJC/o1VxkP5mYAAGCPpKQktW/f/rLjd955p0aMGGHXe1HnAQCA0sbulWju7u6qXr16UWS5rnPnzqlnz56aPn26AgMD8/WakSNHKjk5OffryJEjRZwSZgjx99aC/s3l5+2mbXFJGrBgi9Kzss2OBQBAidKpUyd9/vnnlx3/8ssvde+99xbp76bOAwAAjs7upTrDhg3T5MmT9d5778kwjH/1ywMDA+Xi4qKTJ0/mOX7y5ElVrFjxsuujo6N16NAhdezYMfdYTk6OJMnV1VX79+9XREREntd4eHjIw8PjX+VEyVCzgo9mP9ZUj8z4VWt+P6PBn27Xez0aytXF9PkZAACUCLVr19Zrr72mlStXKjIyUpK0YcMGrVu3TsOGDdOUKVNyrx00aNA134s6DwAAlDaGzWaz2fOCLl26aMWKFfL399dNN90kNze3POeXLl1qV4DmzZurWbNmevfddyVdKpaqVq2qZ555Ri+++GKea9PS0nTw4ME8x15++WWdO3dOkydPVs2aNeXu7n7N35eSkiKr1ark5GT5+vralRUlw9rfz6jvnE3KyM7RQ02q6I0H6v3rhi8AAM5QQ4SFheXrOsMwFBMTc93rqPMAAEBJkN8awu6VaH5+furSpcu/Cvd3Q4cOVe/evdWkSRM1a9ZMkyZN0oULF9SnTx9JUq9evVS5cmWNGzdOnp6eqlOnzmV5JF12HM7r5hqBmtK9gZ76eKsWbz4qq5eb/q/DjTTSAAC4jtjY2EJ9P+o8AABQmtjdRJs9e3ahBujWrZtOnz6t0aNH68SJE2rQoIGWLVuWuwltXFycLBYex4N92tcJ1vj762n4Zzs1fU2s/Lzd9fTt5uzlBwBASfTnwwr/5kMo6jwAAFCa2P04559Onz6t/fv3S5Jq1aql8uXLF2qwosIyf+cyY02M/vvtXknSfzvX0aMtqpmcCABQUjlLDTFv3jy99dZb+v333yVJNWvW1AsvvKCePXuanOz6nOUeAQCAwpXfGsLuj/4uXLigvn37Kjg4WK1bt1br1q1VqVIl9evXT6mpqf8qNFDY+t8Srmf+WIE26svd+mrHcZMTAQDguCZMmKCBAweqQ4cOWrx4sRYvXqz27dtrwIABmjhxotnxAAAATGV3E23o0KFatWqVvv76ayUlJSkpKUlffvmlVq1apWHDhhVFRuBfGXZnTfVsUU02mzR00Xat2HfK7EgAADikd999V9OmTdMbb7yhTp06qVOnTnrzzTf1/vvv55nMCQAA4IzsbqJ99tlnmjlzpu6++275+vrK19dXHTp00PTp07VkyZKiyAj8K4ZhaGynm3Rfg0rKyrFp4MdbtOlQotmxAABwOPHx8WrZsuVlx1u2bKn4+HgTEgEAADgOu5toqampuZvB/l1QUBCPc8JhWSyG3u5aX21uCFJaZo76ztmk344nmx0LAACHUr16dS1evPiy44sWLVKNGjVMSAQAAOA47J7OGRkZqTFjxmjevHny9PSUJF28eFFjx45VZGRkoQcECoubi0VTezRS71kbtfFQonrN3Kj/DYhUePmyZkcDAMAhjB07Vt26ddPq1avVqlUrSdK6deu0fPnyKzbXAAAAnInd0zl3796tu+66S+np6apfv74kaceOHfL09NQPP/ygm266qUiCFhamNiElLVMPf7hBe+JTVNnPS0sGRirY6mV2LACAg3OWGmLr1q2aMGGC9u69NN36xhtv1LBhw9SwYUOTk12fs9wjAABQuPJbQ9jdRJMuPdL58ccfa9++fZIuFVePPPKIvLwcvxFBcQVJOnM+XQ99EKWYMxcUUb6M/jegpfzLuJsdCwDgwEp7DZGZmaknn3xSo0aNUlhYmNlxCqS03yMAAFA0irSJVpJRXOFPR8+mqusHUYpPTlO9KlZ93L+5fDzdzI4FAHBQzlBDWK1Wbd++nSYaAABwKvmtIfK1J9pXX32lu+++W25ubvrqq6+ueW2nTp3sSwqYpEo5b83v11wPfRilnUeT9fi8zZrTp5k83VzMjgYAgCk6d+6sL774QkOGDDE7CgAAgMPJVxOtc+fOOnHihIKCgtS5c+erXmcYhrKzswsrG1DkqgeV1dw+zdR9+gZtiEnUM59s0wePNpKri92DawEAKPFq1KihV155RevWrVPjxo1VpkyZPOcHDRpkUjIAAADz8TgnICkqOkG9Z29URlaO7m9UWW8/WF8Wi2F2LACAA3GGGuJaj3EahqGYmJhiTGM/Z7hHAACg8OW3hrB7uc28efOUnp5+2fGMjAzNmzfP3rcDHEJkRIDe79FILhZDS7ce0yvf7JGT9ZcBAFBsbOxVvxy9gQYAAFDU7G6i9enTR8nJyZcdP3funPr06VMooQAztKtdQW93rSdJmrP+kCYv/93kRAAAFJ8NGzbopZde0gsvvKBly5aZHQcAAMDh2N1Es9lsMozLH3M7evSorFZroYQCzNKlYRX9p2NtSdKkn3/X7HWxJicCAKDoLVmyRK1atdLkyZM1Y8YM3XPPPXr77bfNjgUAAOBQ8jVYQJIaNmwowzBkGIbatm0rV9e/Xpqdna3Y2Fi1b9++SEICxemxVmFKvpiliT8f0Niv98jq5ab7G1UxOxYAAEVm3LhxevzxxzV16lS5uLho3Lhxev311/X888+bHQ0AAMBh5LuJ9udUzu3bt+uuu+5S2bJlc8+5u7srNDRUDzzwQKEHBMwwqG11JV3M0Ox1h/TCkp3y8XTTHbUrmB0LAIAisX//fi1atEguLi6SpGHDhmn06NE6deqUgoKCTE4HAADgGPLdRBszZoyys7MVGhqqO++8U8HBwUWZCzCVYRgadU9tJV/M1NKtx/T0J1s1t08zRUYEmB0NAIBCl5qammcSlbu7uzw9PXX+/HmaaAAAAH/IdxNNklxcXPTkk09q7969RZUHcBgWi6E3H6inlItZ+nnvST0+b7M+eby56lXxMzsaAACFbsaMGXmeNMjKytKcOXMUGBiYe2zQoEFmRAMAAHAIhs1ms9nzgiZNmuiNN95Q27ZtiypTkUpJSZHValVycnKeT1yBq0nLzFaf2ZsUFZOgct5u+t+ASFUP8jE7FgCgmJXmGiI0NPSKg6P+zjAMxcTEFFOiginN9wgAABSd/NYQdq1Ek6T//ve/ev755/Xqq6+qcePGKlOmTJ7zFCwobTzdXDS9dxP1mL5BO48mq+fMjfrfgEhVKedtdjQAAArFoUOHzI4AAADg8OxeiWaxWP568d8+sbTZbDIMQ9nZ2YWXrgjwCSUKKvFChh76MEoHT51XWGAZLX4yUuV9PMyOBQAoJtQQjo97BAAACqLIVqKtWLHiXwUDSir/Mu6a36+ZHpwWpdgzF9R71kZ9+kQLWb3czI4GAAAAAACKmN1NtFtvvbUocgAlQrDVSwv6N1fXD9ZrT3yK+s/dpHl9m8vL3cXsaAAAAAAAoAhZrn/J5ZKSkvTOO++of//+6t+/vyZOnKjk5OTCzgY4pLDAMprbt5l8PF216dBZDfx4izKycsyOBQAAAAAAipDdTbTNmzcrIiJCEydOVGJiohITEzVhwgRFRERo69atRZERcDg3VbJq1mNN5elm0cr9pzXsfzuUnWPX9oIAAAAAAKAEsbuJNmTIEHXq1EmHDh3S0qVLtXTpUsXGxuree+/Vc889VwQRAcfUNNRf0x5tLFeLoa93HNeYr3bLzjkdAAA4nOjoaL388svq3r27Tp06JUn6/vvv9dtvv5mcDAAAwFwFWok2YsQIubr+tZ2aq6urhg8frs2bNxdqOMDR3V4rSBO6NZBhSAs2xOmdHw+YHQkAgAJbtWqV6tatq19//VVLly7V+fPnJUk7duzQmDFjTE4HAABgLrubaL6+voqLi7vs+JEjR+Tj41MooYCSpFP9Snr1vjqSpPdWHNT01TEmJwIAoGBefPFF/fe//9VPP/0kd3f33ONt2rTRhg0bTEwGAABgPrubaN26dVO/fv20aNEiHTlyREeOHNHChQvVv39/de/evSgyAg7v0RbV9MJdtSRJr323V4s3HTE5EQAA9tu1a5e6dOly2fGgoCCdOXPGhEQAAACOw/X6l+T19ttvyzAM9erVS1lZWZIkNzc3DRw4UOPHjy/0gEBJ8dRtEUq5mKkPV8foxaU75ePpqrvrBpsdCwCAfPPz81N8fLzCwsLyHN+2bZsqV65sUioAAADHYPdKNHd3d02ePFlnz57V9u3btX37diUmJmrixIny8PAoioxAiWAYhl68+wZ1axKiHJs0eOF2rfn9tNmxAADIt4cfflgjRozQiRMnZBiGcnJytG7dOj3//PPq1auX2fEAAABMZXcT7U/e3t7y8/OTn5+fvL29CzMTUGIZhqHX76+rDnUrKiM7R0/O36KtcWfNjgUAQL68/vrruuGGGxQSEqLz58+rdu3aat26tVq2bKmXX37Z7HgAAACmsruJlpWVpVGjRslqtSo0NFShoaGyWq16+eWXlZmZWRQZgRLFxWJoYrcGuqVGoFIzstVn9ibtP3HO7FgAAFyXu7u7pk+frujoaH3zzTdasGCB9u3bp/nz58vFxcXseAAAAKaye0+0Z599VkuXLtWbb76pyMhISVJUVJT+85//KCEhQdOmTSv0kEBJ4+Hqog8ebaxHZ/6qbXFJ6jnzVy0Z0FJVA1i1CQBwXGvXrtXNN9+sqlWrqmrVqmbHAQAAcCiGzWaz2fMCq9WqhQsX6u67785z/LvvvlP37t2VnJxcqAELW0pKiqxWq5KTk+Xr62t2HJRySakZ6vbhBu0/eU5V/b21ZECkgnw9zY4FACgAZ6gh3N3dVblyZXXv3l2PPvqoateubXYkuzjDPQIAAIUvvzWE3Y9zenh4KDQ09LLjYWFhcnd3t/ftgFLNz9td8/s1U1V/b8UlpqrnzI1KSs0wOxYAAFd0/PhxDRs2TKtWrVKdOnXUoEEDvfXWWzp69KjZ0QAAAExndxPtmWee0auvvqr09PTcY+np6Xrttdf0zDPPFGo4oDQI8vXUgn7NFeTjof0nz6nPnE1KzcgyOxYAAJcJDAzUM888o3Xr1ik6Olpdu3bV3LlzFRoaqjZt2pgdDwAAwFR2P87ZpUsXLV++XB4eHqpfv74kaceOHcrIyFDbtm3zXLt06dLCS1pIWOYPs+w/cU4PfRil5IuZuqVGoGb0biIPVzZpBoCSwhlriOzsbH3//fcaNWqUdu7cqezsbLMjXZMz3iMAAPDv5beGsHuwgJ+fnx544IE8x0JCQuxPCDiZWhV9NLtPUz0641et+f2Mhizarne7N5KLxTA7GgAAeaxbt04ff/yxlixZorS0NN13330aN26c2bEAAABMZXcTbfbs2UWRA3AKjaqW00c9m6jvnE36btcJ+Xjs0vgH6sowaKQBAMw3cuRILVy4UMePH9cdd9yhyZMn67777pO3N9OlAQAA7G6i/en06dPav3+/JKlWrVoqX758oYUCSrObawRqSvcGeurjrVq0+Yis3m4aefcNNNIAAKZbvXq1XnjhBT300EMKDAw0Ow4AAIBDsXuwwIULF9S3b18FBwerdevWat26tSpVqqR+/fopNTW1KDICpU77OsEaf389SdJHq2M0bVW0yYkAALj0GOdTTz1FAw0AAOAK7F6JNnToUK1atUpff/21WrVqJUlau3atBg0apGHDhmnatGmFHhIojR5qGqLki5l67bu9enPZflm93PRI82pmxwIAOJmvvvpKd999t9zc3PTVV19d89pOnToVUyoAAADHY/d0zsDAQC1ZskS33XZbnuMrVqzQQw89pNOnTxdmvkLH1CY4mrd+2KepK6JlGNKUhxuqY/1KZkcCAFxBaa0hLBaLTpw4oaCgIFksV39IwTAMpnMCAIBSqcimc6ampqpChQqXHQ8KCuJxTqAAnr+zlpJSM/Xxr3Easmi7fDxddVutILNjAQCcRE5OzhW/BwAAQF5274kWGRmpMWPGKC0tLffYxYsXNXbsWEVGRhZqOMAZGIahV+6ro471Kykrx6YBC7Zo86FEs2MBAJzQvHnzlJ6eftnxjIwMzZs3z4REAAAAjsPuxzl37dql9u3bKz09XfXr15ck7dixQ56envrhhx900003FUnQwsIyfziqzOwcPTFvs1bsPy0fT1ctfKKFbqpkNTsWAOAPzlBDuLi4KD4+XkFBeVdEJyQkKCgoiMc5AQBAqZTfGsLulWh169bV77//rnHjxqlBgwZq0KCBxo8fr99//93hG2iAI3Nzsej9RxqraWg5nUvLUu9ZGxV75oLZsQAATsRms8kwjMuOHz16VFYrH+wAAADnZteeaJmZmbrhhhv0zTff6PHHHy+qTIDT8nJ30YzeTdX9ow3aE5+iR2f8qiUDIxVs9TI7GgCgFGvYsKEMw5BhGGrbtq1cXf8qEbOzsxUbG6v27dubmBAAAMB8djXR3Nzc8uyFBqDwWb3cNLdvMz30YZRiz1xQz5kbtfjJSPmXcTc7GgCglOrcubMkafv27brrrrtUtmzZ3HPu7u4KDQ3VAw88YFI6AAAAx2D3nmivv/66Dhw4oBkzZuT5lLKkYK8MlBRHz6bqwWlROpGSpnpVrPrk8RYq61Hy/p0DgNLCGWqIuXPnqlu3bvL09DQ7SoE4wz0CAACFL781hN1NtC5dumj58uUqW7as6tatqzJlyuQ5v3Tp0oIlLiYUVyhJDp46p64fROlsaqYiwwM0u09Tebq5mB0LAJwSNYTj4x4BAICCyG8NYfeyFj8/P5bzA8WkepCP5vZtpu4fbVBUTIKe/XSbpj3SSK4uds8EAQDgurKzszVx4kQtXrxYcXFxysjIyHM+MTHRpGQAAADms7uJNnv27KLIAeAq6lXx0/TeTfTY7E36ac9Jjfhsl956sJ4slsunpwEA8G+MHTtWM2bM0LBhw/Tyyy/rpZde0qFDh/TFF19o9OjRZscDAAAwVb6Xs+Tk5OiNN95Qq1at1LRpU7344ou6ePFiUWYD8IeWEYGa2qORXCyGPtt6VK9+u0d2PokNAMB1ffzxx5o+fbqGDRsmV1dXde/eXTNmzNDo0aO1YcMGs+MBAACYKt9NtNdee03/93//p7Jly6py5cqaPHmynn766aLMBuBv7qhdQW89WE+SNHvdIU1ZftDkRACA0ubEiROqW7euJKls2bJKTk6WJN1777369ttvzYwGAABgunw30ebNm6f3339fP/zwg7744gt9/fXX+vjjj5WTk1OU+QD8zf2NqmhMx9qSpIk/H9CcdbEmJwIAlCZVqlRRfHy8JCkiIkI//vijJGnTpk3y8PAwMxoAAIDp8t1Ei4uLU4cOHXJ/bteunQzD0PHjx4skGIAr69MqTM+1qyFJ+s/Xe/T5tqMmJwIAlBZ/TmGXpGeffVajRo1SjRo11KtXL/Xt29fkdAAAAObK92CBrKwseXp65jnm5uamzMzMQg8F4NoGt62hpNRMzVl/SM//b6d8PNx0+w1B2hibqFPn0hTk46lmYf5yYfgAAMAO48ePz/2+W7duqlq1qqKiolSjRg117NjRxGQAAADmy3cTzWaz6bHHHsuzlD8tLU0DBgxQmTJlco8tXbq0cBMCuIxhGBp9b22lXMzU0m3HNGDBFvl6uSnxQkbuNcFWT43pWFvt6wSbmBQAUJJFRkYqMjLS7BgAAAAOId9NtN69e1927NFHHy3UMADyz2Ix9MaD9XTw1HntPJacp4EmSSeS0zRwwVZNe7QRjTQAwFV99dVX+b62U6dORZgEAADAseW7iTZ79uyizAGgACyGoVPn0q54zibJkDT26z26o3ZFHu0EAFxR586d83WdYRjKzs4u2jAAAAAOLN+DBQA4no2xiTqRkn7V8zZJ8clp2hibWHyhAAAlSk5OTr6+aKABAABnRxMNKMGutgqtoNcBAAAAAIAry/fjnAAcT5CP5/UvkrT18FndUbuCvN35Vx4AcHWvvPLKNc+PHj26mJIAAAA4Hv6LGijBmoX5K9jqqRPJabJd47q5UYf15Y7j6tmimnq3DFVgWY9rXA0AcFaff/55np8zMzMVGxsrV1dXRURE0EQDAABOjSYaUIK5WAyN6VhbAxdslSHlaaT9OUagW9MQRcUk6HBCqt795aA+XB2jBxpV0eO3hCm8fFkTUgMAHNW2bdsuO5aSkqLHHntMXbp0MSERAACA4zBsNtu1FrCUOikpKbJarUpOTpavr6/ZcYBCsWx3vMZ+vUfxyX/tfRZs9dSYjrXVvk6wsnNs+uG3E/pwdYx2HEmSJBmGdMeNFfTkreFqXM3fpOQAUHI4cw2xa9cudezYUYcOHTI7yjU58z0CAAAFl98agpVoQCnQvk6w7qhdURtjE3XqXJqCfDzVLMxfLpZL69FcLIY61A3W3XUuXTN9TYx+3ntKP+45qR/3nFTjauX0ROtw3XFjBVksxnV+GwDA2SQnJys5OdnsGAAAAKaiiQaUEi4WQ5ERAde8xjAMNQ8PUPPwAB08dU7TV8fq823HtOXwWT05f4vCA8uo/y3hur9RZXm6uRRTcgCAo5gyZUqen202m+Lj4zV//nzdfffdJqUCAABwDDzOCTi5UylpmrP+kBZsOKyUtCxJUmBZd/WKDFXPFtVUroy7yQkBwDE4Qw0RFhaW52eLxaLy5curTZs2GjlypHx8fExKlj/OcI8AAEDhy28NQRMNgCTpfHqWFm06ollrY3Us6aIkycvNRQ81qaL+t4QrxN/b5IQAYC5qCMfHPQIAAAWR3xrCUoyZADiwsh6u6ndzmFa+cJsmP9xAtYN9dTEzW3OjDuvWt1bo6U+2aufRJLNjAgAAAABgCvZEA5CHm4tF9zWorE71K2ndwQR9uDpaa34/o293xuvbnfFqEe6vJ1tH6LZa5WUYDCEAgNIkLS1N7777rlasWKFTp04pJycnz/mtW7ealAwAAMB8NNEAXJFhGLq5RqBurhGoPcdTNGNNjL7acVwbYhK1ISZRNSuU1eO3hOu+BpXl7sqiVgAoDfr166cff/xRDz74oJo1a8aHJQAAAH/DnmgA8u140kXNXherTzce0fn0S0MIKvh6qE+rMPVoXlW+nm4mJwSAouMMNYTVatV3332nVq1amR2lQJzhHgEAgMLHnmgACl0lPy+9dE9trXuxjV68+wZV8PXQyZR0jf9+n1qO+0X//WaPjv8xlAAAUPJUrlzZ4SdwAgAAmIUmGgC7Wb3cNODWCK0Z3kZvPVhPNSuU1fn0LM1YG6vWb67QkEXbtTc+xeyYAAA7vfPOOxoxYoQOHz5sdhQAAACHw55oAArM3dWirk1C9GDjKlq5/7Q+XB2tDTGJ+nzbMX2+7ZhuqRGoJ1tHqFX1APbVAYASoEmTJkpLS1N4eLi8vb3l5pb3Mf3ExESTkgEAAJiPJhqAf80wDN1+Q5BuvyFIO48m6cPVMfp+V7zW/H5Ga34/o5sq+eqJ1uHqUDdYbi4sgAUAR9W9e3cdO3ZMr7/+uipUqMAHIAAAAH/DYAEARSIuIVWz1sVq0aYjupiZLUmq7OelvjeH6eGmISrjQQ8fQMniDDWEt7e3oqKiVL9+fbOjFIgz3CMAAFD4GCwAwFRVA7z1n043af2LbTTsjpoKLOuuY0kX9eo3exQ5brneXLZPp1LSzI4JAPibG264QRcvMiAGAADgShyiiTZ16lSFhobK09NTzZs318aNG6967fTp03XLLbeoXLlyKleunNq1a3fN6wGYq1wZdz3btobWjmij17vUVXhgGaWkZen9ldG6+Y0VGrFkpw6eOmd2TACApPHjx2vYsGFauXKlEhISlJKSkuerIKjzAABAaWF6E23RokUaOnSoxowZo61bt6p+/fq66667dOrUqStev3LlSnXv3l0rVqxQVFSUQkJCdOedd+rYsWPFnByAPTzdXNSjeVX9PPRWfdizsRpXK6eM7Bwt2nxE7SasVv+5m/RrTIKc7AlzAHAo7du3V1RUlNq2baugoKDcZpafn5/KlStn9/tR5wEAgNLE9D3RmjdvrqZNm+q9996TJOXk5CgkJETPPvusXnzxxeu+Pjs7W+XKldN7772nXr16XXY+PT1d6enpuT+npKQoJCSEvTIAB7DlcKI+XBWjn/ae1J//T1Q/xE9Ptg7XXTdVlIuFDa0BOA5n2G9r1apV1zx/66232vV+1HkAAKAkyG+dZ+rO3hkZGdqyZYtGjhyZe8xisahdu3aKiorK13ukpqYqMzNT/v7+Vzw/btw4jR07tlDyAihcjav566Ne/oo5fV7T18Tqs61HteNIkp76eKuqBXir/81herBxiLzcXcyOCgBOwd4m2bVQ5wEAgNLG1CbamTNnlJ2drQoVKuQ5XqFCBe3bty9f7zFixAhVqlRJ7dq1u+L5kSNHaujQobk///kJJQDHEV6+rMbdX1dD76ip+VGHNG/DYR1OSNWoL3/TxJ9/V88W1dQrspoCynqYHRUASrXVq1df83zr1q3z/V7UeQAAoLQxtYn2b40fP14LFy7UypUr5enpecVrPDw85OHBf3gDJUF5Hw8NvbOWBtwWof9tPqoZa2N0JPGiJi//XR+silbXJlXU/+ZwhQaWMTsqAJRKt91222XHDOOvR+uzs7OLLQt1HgAAcDSmDhYIDAyUi4uLTp48mef4yZMnVbFixWu+9u2339b48eP1448/ql69ekUZE0Ax83Z3Ve+WoVox7Da916Oh6lWxKj0rRws2xOn2d1Zq4IIt2hZ31uyYAFDqnD17Ns/XqVOntGzZMjVt2lQ//vijXe9FnQcAAEobU5to7u7uaty4sZYvX557LCcnR8uXL1dkZORVX/fmm2/q1Vdf1bJly9SkSZPiiArABK4uFt1br5K+fLqVPn28hW6vVV42m/T97hPq8v56PfRBlH7ac1I5OUz0BIDCYLVa83wFBgbqjjvu0BtvvKHhw4fb9V7UeQAAoLQx/XHOoUOHqnfv3mrSpImaNWumSZMm6cKFC+rTp48kqVevXqpcubLGjRsnSXrjjTc0evRoffLJJwoNDdWJEyckSWXLllXZsmVN+3MAKDqGYSgyIkCREQE6cPKcPlodoy+3H9PGQ4naeChREeXL6PFbwtW5YWV5ujGEAAAKW4UKFbR//367X0edBwAAShPTm2jdunXT6dOnNXr0aJ04cUINGjTQsmXLcjehjYuLk8Xy14K5adOmKSMjQw8++GCe9xkzZoz+85//FGd0ACaoWcFHb3etr+fvrKXZ62P1yYY4RZ++oBeX7tLbPx5Qn1aherR5NVm93cyOCgAlzs6dO/P8bLPZFB8fr/Hjx6tBgwZ2vx91HgAAKE0Mm83mVM9BpaSkyGq1Kjk5Wb6+vmbHAfAvnUvL1KJNRzRzbazik9MkSd7uLurWNET9bg5TlXLeJicEUFo4Qw1hsVhkGIb+WR62aNFCs2bN0g033GBSsvxxhnsEAAAKX35rCJpoAEqFzOwcfbPzuD5cFaN9J85Jklwshu6pG6wnWoerTmWryQkBlHTOUEMcPnw4z88Wi0Xly5e/6nRMR+MM9wgAABQ+mmhXQXEFlG42m01rfj+jj1bHaO3BM7nHW1UP0BOtI9S6RqAMwzAxIYCSihrC8XGPAABAQeS3hjB1OicAFDbDMNS6Znkt6N9c3zx7s+5rUEkuFkPrDiao96yNunvyGn225agysnLMjgoADuOXX35R7dq1lZKSctm55ORk3XTTTVqzZo0JyQAAABwHTTQApVadylZNfrihVr1wm/q2CpO3u4v2nTinYf/bodZvrtBHq6N1Li3T7JgAYLpJkybp8ccfv+Inr1arVU8++aQmTJhgQjIAAADHQRMNQKlXpZy3RnesragX2+qFu2qpvI+HTqSk6fXv9qnluF807ru9OvHHUAIAcEY7duxQ+/btr3r+zjvv1JYtW4oxEQAAgOOhiQbAaVi93fT07dW1dsTteuOBuoooX0bn0rP04eoY3fLmLxq2eIf2/zGUAACcycmTJ+Xm5nbV866urjp9+nQxJgIAAHA8NNEAOB0PVxd1a1pVPw25VTN6NVGzMH9lZtv02dajumvSaj02e6PWR5+Rk81dAeDEKleurN27d1/1/M6dOxUcHFyMiQAAABwPTTQATstiMdSudgUtfjJSnz/VUh3qVpTFkFbuP60e039Vp/fW6esdx5WVzRACAKVbhw4dNGrUKKWlXf5o+8WLFzVmzBjde++9JiQDAABwHIbNyZZaMPocwLUcTrigGWti9b8tR5SWeal5VqWcl/rdHKZuTUPk7e5qckIAZinNNcTJkyfVqFEjubi46JlnnlGtWrUkSfv27dPUqVOVnZ2trVu3qkKFCiYnvbbSfI8AAEDRyW8NQRMNAK4g8UKG5kUd0ryow0q8kCFJsnq5qWeLaurdMlTlfTxMTgiguJX2GuLw4cMaOHCgfvjhh9zH2Q3D0F133aWpU6cqLCzM5ITXV9rvEQAAKBo00a6C4gqAPS5mZGvJ1qOasSZGhxNSJUnurhY90Kiy+t8SrojyZU1OCKC4OEsNcfbsWR08eFA2m001atRQuXLlzI6Ub85yjwAAQOGiiXYVFFcACiI7x6YffzuhD1fHaPuRJEmSYUjtbqygJ1uHq0mov7kBARQ5agjHxz0CAAAFkd8ags19ACAfXCyG7q4brPZ1KmrTobP6aHWMft57Uj/tufTVqKqfnmgdoTtqV5CLxTA7LgAAAACgkNFEAwA7GIahZmH+ahbmr4OnzmvGmhgt3XpMW+OSNGDBFoUFllH/W8L0QKMq8nRzMTsuAAAAAKCQ8DgnAPxLp86lae76Q5ofdVgpaVmSpIAy7urdMlQ9W1RTuTLuJicEUBioIRwf9wgAABQEe6JdBcUVgKJyIT1LizY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"text/plain": [ "
" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax = axes[1]\n", "ax.plot(ticks,\n", " pcaUS.explained_variance_ratio_.cumsum(),\n", " marker='o')\n", "ax.set_xlabel('Principal Component')\n", "ax.set_ylabel('Cumulative Proportion of Variance Explained')\n", "ax.set_ylim([0, 1])\n", "ax.set_xticks(ticks)\n", "fig" ] }, { "cell_type": "markdown", "id": "02eb9713", "metadata": {}, "source": [ "The result is similar to that shown in Figure~\\ref{Ch10:fig:USArrests:scree}. Note\n", "that the method `cumsum()` computes the cumulative sum of\n", "the elements of a numeric vector. For instance:" ] }, { "cell_type": "code", "execution_count": 20, "id": "505827c8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.491458Z", "iopub.status.busy": "2024-06-04T23:20:00.491361Z", "iopub.status.idle": "2024-06-04T23:20:00.493334Z", "shell.execute_reply": "2024-06-04T23:20:00.493123Z" } }, "outputs": [ { "data": { "text/plain": [ "array([ 1, 3, 11, 8])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.array([1,2,8,-3])\n", "np.cumsum(a)" ] }, { "cell_type": "markdown", "id": "380c2ad3", "metadata": {}, "source": [ "## Matrix Completion\n", "\n", "We now re-create the analysis carried out on the `USArrests` data in\n", "Section~\\ref{Ch10:sec:princ-comp-with}.\n", "\n", "We saw in Section~\\ref{ch10:sec2.2} that solving the optimization\n", "problem~(\\ref{Ch10:eq:mc2}) on a centered data matrix $\\bf X$ is\n", "equivalent to computing the first $M$ principal\n", "components of the data. We use our scaled\n", "and centered `USArrests` data as $\\bf X$ below. The *singular value decomposition* \n", "(SVD) is a general algorithm for solving\n", "(\\ref{Ch10:eq:mc2})." ] }, { "cell_type": "code", "execution_count": 21, "id": "9902f1be", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.494542Z", "iopub.status.busy": "2024-06-04T23:20:00.494449Z", "iopub.status.idle": "2024-06-04T23:20:00.496446Z", "shell.execute_reply": "2024-06-04T23:20:00.496239Z" } }, "outputs": [ { "data": { "text/plain": [ "((50, 4), (4,), (4, 4))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = USArrests_scaled\n", "U, D, V = np.linalg.svd(X, full_matrices=False)\n", "U.shape, D.shape, V.shape" ] }, { "cell_type": "markdown", "id": "028297b8", "metadata": {}, "source": [ "The `np.linalg.svd()` function returns three components, `U`, `D` and `V`. The matrix `V` is equivalent to the\n", "loading matrix from principal components (up to an unimportant sign flip). Using the `full_matrices=False` option ensures that\n", "for a tall matrix the shape of `U` is the same as the shape of `X`." ] }, { "cell_type": "code", "execution_count": 22, "id": "2f56e336", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.497684Z", "iopub.status.busy": "2024-06-04T23:20:00.497595Z", "iopub.status.idle": "2024-06-04T23:20:00.499525Z", "shell.execute_reply": "2024-06-04T23:20:00.499269Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[-0.53589947, -0.58318363, -0.27819087, -0.54343209],\n", " [-0.41818087, -0.1879856 , 0.87280619, 0.16731864],\n", " [ 0.34123273, 0.26814843, 0.37801579, -0.81777791],\n", " [ 0.6492278 , -0.74340748, 0.13387773, 0.08902432]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V" ] }, { "cell_type": "code", "execution_count": 23, "id": "720e92a9", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.500875Z", "iopub.status.busy": "2024-06-04T23:20:00.500774Z", "iopub.status.idle": "2024-06-04T23:20:00.502897Z", "shell.execute_reply": "2024-06-04T23:20:00.502626Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.53589947, 0.58318363, 0.27819087, 0.54343209],\n", " [ 0.41818087, 0.1879856 , -0.87280619, -0.16731864],\n", " [-0.34123273, -0.26814843, -0.37801579, 0.81777791],\n", " [-0.6492278 , 0.74340748, -0.13387773, -0.08902432]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pcaUS.components_" ] }, { "cell_type": "markdown", "id": "d361e2ae", "metadata": {}, "source": [ "The matrix `U` corresponds to a *standardized* version of the PCA score matrix (each column standardized to have sum-of-squares one). If we multiply each column of `U` by the corresponding element of `D`, we recover the PCA scores exactly (up to a meaningless sign flip)." ] }, { "cell_type": "code", "execution_count": 24, "id": "08ad9e05", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.504280Z", "iopub.status.busy": "2024-06-04T23:20:00.504187Z", "iopub.status.idle": "2024-06-04T23:20:00.506272Z", "shell.execute_reply": "2024-06-04T23:20:00.505977Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[-0.98556588, -1.13339238, 0.44426879, 0.15626714],\n", " [-1.95013775, -1.07321326, -2.04000333, -0.43858344],\n", " [-1.76316354, 0.74595678, -0.05478082, -0.83465292]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(U * D[None,:])[:3]" ] }, { "cell_type": "code", "execution_count": 25, "id": "7ec6643a", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.507544Z", "iopub.status.busy": "2024-06-04T23:20:00.507437Z", "iopub.status.idle": "2024-06-04T23:20:00.509358Z", "shell.execute_reply": "2024-06-04T23:20:00.509140Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.98556588, 1.13339238, -0.44426879, -0.15626714],\n", " [ 1.95013775, 1.07321326, 2.04000333, 0.43858344],\n", " [ 1.76316354, -0.74595678, 0.05478082, 0.83465292]])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scores[:3]" ] }, { "cell_type": "markdown", "id": "82a7beb2", "metadata": {}, "source": [ "While it would be possible to carry out this lab using the `PCA()` estimator,\n", "here we use the `np.linalg.svd()` function in order to illustrate its use.\n", "\n", "We now omit 20 entries in the $50\\times 4$ data matrix at random. We do so\n", "by first selecting 20 rows (states) at random, and then selecting one\n", "of the four entries in each row at random. This ensures that every row has\n", "at least three observed values." ] }, { "cell_type": "code", "execution_count": 26, "id": "897e5bbb", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.510666Z", "iopub.status.busy": "2024-06-04T23:20:00.510571Z", "iopub.status.idle": "2024-06-04T23:20:00.512527Z", "shell.execute_reply": "2024-06-04T23:20:00.512309Z" } }, "outputs": [], "source": [ "n_omit = 20\n", "np.random.seed(15)\n", "r_idx = np.random.choice(np.arange(X.shape[0]),\n", " n_omit,\n", " replace=False)\n", "c_idx = np.random.choice(np.arange(X.shape[1]),\n", " n_omit,\n", " replace=True)\n", "Xna = X.copy()\n", "Xna[r_idx, c_idx] = np.nan" ] }, { "cell_type": "markdown", "id": "d1e56611", "metadata": {}, "source": [ "Here the array `r_idx`\n", "contains 20 integers from 0 to 49; this represents the states (rows of `X`) that are selected to contain missing values. And `c_idx` contains\n", "20 integers from 0 to 3, representing the features (columns in `X`) that contain the missing values for each of the selected states.\n", "\n", "We now write some code to implement Algorithm~\\ref{Ch10:alg:hardimpute}. \n", "We first write a function that takes in a matrix, and returns an approximation to the matrix using the `svd()` function.\n", "This will be needed in Step 2 of Algorithm~\\ref{Ch10:alg:hardimpute}." ] }, { "cell_type": "code", "execution_count": 27, "id": "2fd5410d", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.513710Z", "iopub.status.busy": "2024-06-04T23:20:00.513635Z", "iopub.status.idle": "2024-06-04T23:20:00.515194Z", "shell.execute_reply": "2024-06-04T23:20:00.514994Z" } }, "outputs": [], "source": [ "def low_rank(X, M=1):\n", " U, D, V = np.linalg.svd(X)\n", " L = U[:,:M] * D[None,:M]\n", " return L.dot(V[:M])" ] }, { "cell_type": "markdown", "id": "bc4a6793", "metadata": {}, "source": [ "To conduct Step 1 of the algorithm, we initialize `Xhat` --- this is $\\tilde{\\bf X}$ in Algorithm~\\ref{Ch10:alg:hardimpute} --- by replacing\n", "the missing values with the column means of the non-missing entries. These are stored in\n", "`Xbar` below after running `np.nanmean()` over the row axis.\n", "We make a copy so that when we assign values to `Xhat` below we do not also overwrite the\n", "values in `Xna`." ] }, { "cell_type": "code", "execution_count": 28, "id": "46c135c3", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.516282Z", "iopub.status.busy": "2024-06-04T23:20:00.516215Z", "iopub.status.idle": "2024-06-04T23:20:00.517899Z", "shell.execute_reply": "2024-06-04T23:20:00.517702Z" } }, "outputs": [], "source": [ "Xhat = Xna.copy()\n", "Xbar = np.nanmean(Xhat, axis=0)\n", "Xhat[r_idx, c_idx] = Xbar[c_idx]" ] }, { "cell_type": "markdown", "id": "1732122e", "metadata": {}, "source": [ "Before we begin Step 2, we set ourselves up to measure the progress of our\n", "iterations:" ] }, { "cell_type": "code", "execution_count": 29, "id": "0fd401ba", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.519024Z", "iopub.status.busy": "2024-06-04T23:20:00.518963Z", "iopub.status.idle": "2024-06-04T23:20:00.520581Z", "shell.execute_reply": "2024-06-04T23:20:00.520375Z" } }, "outputs": [], "source": [ "thresh = 1e-7\n", "rel_err = 1\n", "count = 0\n", "ismiss = np.isnan(Xna)\n", "mssold = np.mean(Xhat[~ismiss]**2)\n", "mss0 = np.mean(Xna[~ismiss]**2)" ] }, { "cell_type": "markdown", "id": "0b74b489", "metadata": {}, "source": [ "Here `ismiss` is a logical matrix with the same dimensions as `Xna`;\n", "a given element is `True` if the corresponding matrix element is missing. The notation `~ismiss` negates this boolean vector. This is useful\n", "because it allows us to access both the missing and non-missing entries. We store the mean of the squared non-missing elements in `mss0`.\n", "We store the mean squared error of the non-missing elements of the old version of `Xhat` in `mssold` (which currently\n", "agrees with `mss0`). We plan to store the mean squared error of the non-missing elements of the current version of `Xhat` in `mss`, and will then\n", "iterate Step 2 of Algorithm~\\ref{Ch10:alg:hardimpute} until the *relative error*, defined as\n", "`(mssold - mss) / mss0`, falls below `thresh = 1e-7`.\n", " {Algorithm~\\ref{Ch10:alg:hardimpute} tells us to iterate Step 2 until \\eqref{Ch10:eq:mc6} is no longer decreasing. Determining whether \\eqref{Ch10:eq:mc6} is decreasing requires us only to keep track of `mssold - mss`. However, in practice, we keep track of `(mssold - mss) / mss0` instead: this makes it so that the number of iterations required for Algorithm~\\ref{Ch10:alg:hardimpute} to converge does not depend on whether we multiplied the raw data $\\bf X$ by a constant factor.}\n", "\n", "In Step 2(a) of Algorithm~\\ref{Ch10:alg:hardimpute}, we approximate `Xhat` using `low_rank()`; we call this `Xapp`. In Step 2(b), we use `Xapp` to update the estimates for elements in `Xhat` that are missing in `Xna`. Finally, in Step 2(c), we compute the relative error. These three steps are contained in the following `while` loop:" ] }, { "cell_type": "code", "execution_count": 30, "id": "bcbe5405", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.521714Z", "iopub.status.busy": "2024-06-04T23:20:00.521647Z", "iopub.status.idle": "2024-06-04T23:20:00.524162Z", "shell.execute_reply": "2024-06-04T23:20:00.523946Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 1, MSS:0.395, Rel.Err 5.99e-01\n", "Iteration: 2, MSS:0.382, Rel.Err 1.33e-02\n", "Iteration: 3, MSS:0.381, Rel.Err 1.44e-03\n", "Iteration: 4, MSS:0.381, Rel.Err 1.79e-04\n", "Iteration: 5, MSS:0.381, Rel.Err 2.58e-05\n", "Iteration: 6, MSS:0.381, Rel.Err 4.22e-06\n", "Iteration: 7, MSS:0.381, Rel.Err 7.65e-07\n", "Iteration: 8, MSS:0.381, Rel.Err 1.48e-07\n", "Iteration: 9, MSS:0.381, Rel.Err 2.95e-08\n" ] } ], "source": [ "while rel_err > thresh:\n", " count += 1\n", " # Step 2(a)\n", " Xapp = low_rank(Xhat, M=1)\n", " # Step 2(b)\n", " Xhat[ismiss] = Xapp[ismiss]\n", " # Step 2(c)\n", " mss = np.mean(((Xna - Xapp)[~ismiss])**2)\n", " rel_err = (mssold - mss) / mss0\n", " mssold = mss\n", " print(\"Iteration: {0}, MSS:{1:.3f}, Rel.Err {2:.2e}\"\n", " .format(count, mss, rel_err))" ] }, { "cell_type": "markdown", "id": "a3e19a6e", "metadata": {}, "source": [ "We see that after eight iterations, the relative error has fallen below `thresh = 1e-7`, and so the algorithm terminates. When this happens, the mean squared error of the non-missing elements equals 0.381.\n", "\n", "Finally, we compute the correlation between the 20 imputed values\n", "and the actual values:" ] }, { "cell_type": "code", "execution_count": 31, "id": "e85cd692", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.525418Z", "iopub.status.busy": "2024-06-04T23:20:00.525349Z", "iopub.status.idle": "2024-06-04T23:20:00.527505Z", "shell.execute_reply": "2024-06-04T23:20:00.527286Z" } }, "outputs": [ { "data": { "text/plain": [ "0.711356743429736" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.corrcoef(Xapp[ismiss], X[ismiss])[0,1]" ] }, { "cell_type": "markdown", "id": "d78f16f4", "metadata": {}, "source": [ "In this lab, we implemented Algorithm~\\ref{Ch10:alg:hardimpute} ourselves for didactic purposes. However, a reader who wishes to apply matrix completion to their data might look to more specialized `Python`{} implementations." ] }, { "cell_type": "markdown", "id": "1f700d77", "metadata": {}, "source": [ "## Clustering" ] }, { "cell_type": "markdown", "id": "a042a391", "metadata": {}, "source": [ "### $K$-Means Clustering\n", "\n", "The estimator `sklearn.cluster.KMeans()` performs $K$-means clustering in\n", "`Python`. We begin with a simple simulated example in which there\n", "truly are two clusters in the data: the first 25 observations have a\n", "mean shift relative to the next 25 observations." ] }, { "cell_type": "code", "execution_count": 32, "id": "f6e58256", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.528820Z", "iopub.status.busy": "2024-06-04T23:20:00.528749Z", "iopub.status.idle": "2024-06-04T23:20:00.530487Z", "shell.execute_reply": "2024-06-04T23:20:00.530226Z" } }, "outputs": [], "source": [ "np.random.seed(0);\n", "X = np.random.standard_normal((50,2));\n", "X[:25,0] += 3;\n", "X[:25,1] -= 4;" ] }, { "cell_type": "markdown", "id": "4f0ff8a0", "metadata": {}, "source": [ "We now perform $K$-means clustering with $K=2$." ] }, { "cell_type": "code", "execution_count": 33, "id": "6d739b86", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.531627Z", "iopub.status.busy": "2024-06-04T23:20:00.531561Z", "iopub.status.idle": "2024-06-04T23:20:00.824303Z", "shell.execute_reply": "2024-06-04T23:20:00.823941Z" } }, "outputs": [], "source": [ "kmeans = KMeans(n_clusters=2,\n", " random_state=2,\n", " n_init=20).fit(X)" ] }, { "cell_type": "markdown", "id": "c5eeb7a8", "metadata": {}, "source": [ "We specify `random_state` to make the results reproducible. The cluster assignments of the 50 observations are contained in `kmeans.labels_`." ] }, { "cell_type": "code", "execution_count": 34, "id": "701ef903", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.826191Z", "iopub.status.busy": "2024-06-04T23:20:00.826070Z", "iopub.status.idle": "2024-06-04T23:20:00.828818Z", "shell.execute_reply": "2024-06-04T23:20:00.828538Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,\n", " 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", " 1, 1, 1, 1, 1, 1], dtype=int32)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kmeans.labels_" ] }, { "cell_type": "markdown", "id": "b6edb148", "metadata": {}, "source": [ "The $K$-means clustering perfectly separated the observations into two\n", "clusters even though we did not supply any group information to\n", "`KMeans()`. We can plot the data, with each observation\n", "colored according to its cluster assignment." ] }, { "cell_type": "code", "execution_count": 35, "id": "b00fbcc9", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.830418Z", "iopub.status.busy": "2024-06-04T23:20:00.830277Z", "iopub.status.idle": "2024-06-04T23:20:00.904250Z", "shell.execute_reply": "2024-06-04T23:20:00.903956Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8,8))\n", "ax.scatter(X[:,0], X[:,1], c=kmeans.labels_)\n", "ax.set_title(\"K-Means Clustering Results with K=2\");" ] }, { "cell_type": "markdown", "id": "7f0c844e", "metadata": {}, "source": [ "Here the observations can be easily plotted because they are\n", "two-dimensional. If there were more than two variables then we could\n", "instead perform PCA and plot the first two principal component score\n", "vectors to represent the clusters.\n", "\n", "In this example, we knew that there really\n", "were two clusters because we generated the data. However, for real\n", "data, we do not know the true number of clusters, nor whether they exist in any precise way. We could\n", "instead have performed $K$-means clustering on this example with\n", "$K=3$." ] }, { "cell_type": "code", "execution_count": 36, "id": "f2cad047", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.905738Z", "iopub.status.busy": "2024-06-04T23:20:00.905623Z", "iopub.status.idle": "2024-06-04T23:20:00.982351Z", "shell.execute_reply": "2024-06-04T23:20:00.982085Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=3,\n", " random_state=3,\n", " n_init=20).fit(X)\n", "fig, ax = plt.subplots(figsize=(8,8))\n", "ax.scatter(X[:,0], X[:,1], c=kmeans.labels_)\n", "ax.set_title(\"K-Means Clustering Results with K=3\");" ] }, { "cell_type": "markdown", "id": "1a939178", "metadata": {}, "source": [ "When $K=3$, $K$-means clustering splits up the two clusters.\n", "We have used the `n_init` argument to run the $K$-means with 20 \n", "initial cluster assignments (the default is 10). If a\n", "value of `n_init` greater than one is used, then $K$-means\n", "clustering will be performed using multiple random assignments in\n", "Step 1 of Algorithm~\\ref{Ch10:alg:km}, and the `KMeans()` \n", "function will report only the best results. Here we compare using\n", "`n_init=1` to `n_init=20`." ] }, { "cell_type": "code", "execution_count": 37, "id": "f1436671", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.984089Z", "iopub.status.busy": "2024-06-04T23:20:00.983822Z", "iopub.status.idle": "2024-06-04T23:20:00.992694Z", "shell.execute_reply": "2024-06-04T23:20:00.992450Z" } }, "outputs": [ { "data": { "text/plain": [ "(76.85131986999252, 75.06261242745384)" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kmeans1 = KMeans(n_clusters=3,\n", " random_state=3,\n", " n_init=1).fit(X)\n", "kmeans20 = KMeans(n_clusters=3,\n", " random_state=3,\n", " n_init=20).fit(X);\n", "kmeans1.inertia_, kmeans20.inertia_" ] }, { "cell_type": "markdown", "id": "d64b1013", "metadata": {}, "source": [ "Note that `kmeans.inertia_` is the total within-cluster sum\n", "of squares, which we seek to minimize by performing $K$-means\n", "clustering \\eqref{Ch10:eq:kmeans}. \n", "\n", "We *strongly* recommend always running $K$-means clustering with\n", "a large value of `n_init`, such as 20 or 50, since otherwise an\n", "undesirable local optimum may be obtained.\n", "\n", "When performing $K$-means clustering, in addition to using multiple\n", "initial cluster assignments, it is also important to set a random seed\n", "using the `random_state` argument to `KMeans()`. This way, the initial\n", "cluster assignments in Step 1 can be replicated, and the $K$-means\n", "output will be fully reproducible." ] }, { "cell_type": "markdown", "id": "3d49b1de", "metadata": {}, "source": [ "### Hierarchical Clustering\n", "\n", "The `AgglomerativeClustering()` class from\n", "the `sklearn.clustering` package implements hierarchical clustering.\n", "As its\n", "name is long, we use the short hand `HClust` for *hierarchical clustering*. Note that this will not change the return type\n", "when using this method, so instances will still be of class `AgglomerativeClustering`.\n", "In the following example we use the data from the previous lab to plot the hierarchical clustering\n", "dendrogram using complete, single, and average linkage clustering\n", "with Euclidean distance as the dissimilarity measure. We begin by\n", "clustering observations using complete linkage." ] }, { "cell_type": "code", "execution_count": 38, "id": "3a2d2b24", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.994226Z", "iopub.status.busy": "2024-06-04T23:20:00.994147Z", "iopub.status.idle": "2024-06-04T23:20:00.997621Z", "shell.execute_reply": "2024-06-04T23:20:00.997244Z" } }, "outputs": [ { "data": { "text/html": [ "
AgglomerativeClustering(distance_threshold=0, linkage='complete',\n",
       "                        n_clusters=None)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" ], "text/plain": [ "AgglomerativeClustering(distance_threshold=0, linkage='complete',\n", " n_clusters=None)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "HClust = AgglomerativeClustering\n", "hc_comp = HClust(distance_threshold=0,\n", " n_clusters=None,\n", " linkage='complete')\n", "hc_comp.fit(X)" ] }, { "cell_type": "markdown", "id": "a86162f3", "metadata": {}, "source": [ "This computes the entire dendrogram.\n", "We could just as easily perform hierarchical clustering with average or single linkage instead:" ] }, { "cell_type": "code", "execution_count": 39, "id": "dc8c9fa7", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:00.999073Z", "iopub.status.busy": "2024-06-04T23:20:00.998978Z", "iopub.status.idle": "2024-06-04T23:20:01.001611Z", "shell.execute_reply": "2024-06-04T23:20:01.001348Z" } }, "outputs": [], "source": [ "hc_avg = HClust(distance_threshold=0,\n", " n_clusters=None,\n", " linkage='average');\n", "hc_avg.fit(X)\n", "hc_sing = HClust(distance_threshold=0,\n", " n_clusters=None,\n", " linkage='single');\n", "hc_sing.fit(X);" ] }, { "cell_type": "markdown", "id": "c367b799", "metadata": {}, "source": [ "To use a precomputed distance matrix, we provide an additional\n", "argument `metric=\"precomputed\"`. In the code below, the first four lines computes the $50\\times 50$ pairwise-distance matrix." ] }, { "cell_type": "code", "execution_count": 40, "id": "17af050a", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.003143Z", "iopub.status.busy": "2024-06-04T23:20:01.003055Z", "iopub.status.idle": "2024-06-04T23:20:01.007137Z", "shell.execute_reply": "2024-06-04T23:20:01.006871Z" } }, "outputs": [ { "data": { "text/html": [ "
AgglomerativeClustering(distance_threshold=0, linkage='single',\n",
       "                        metric='precomputed', n_clusters=None)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" ], "text/plain": [ "AgglomerativeClustering(distance_threshold=0, linkage='single',\n", " metric='precomputed', n_clusters=None)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = np.zeros((X.shape[0], X.shape[0]));\n", "for i in range(X.shape[0]):\n", " x_ = np.multiply.outer(np.ones(X.shape[0]), X[i])\n", " D[i] = np.sqrt(np.sum((X - x_)**2, 1));\n", "hc_sing_pre = HClust(distance_threshold=0,\n", " n_clusters=None,\n", " metric='precomputed',\n", " linkage='single')\n", "hc_sing_pre.fit(D)" ] }, { "cell_type": "markdown", "id": "cd51d288", "metadata": {}, "source": [ "We use\n", "`dendrogram()` from `scipy.cluster.hierarchy` to plot the dendrogram. However,\n", "`dendrogram()` expects a so-called *linkage-matrix representation*\n", "of the clustering, which is not provided by `AgglomerativeClustering()`,\n", "but can be computed. The function `compute_linkage()` in the\n", "`ISLP.cluster` package is provided for this purpose.\n", "\n", "We can now plot the dendrograms. The numbers at the bottom of the plot\n", "identify each observation. The `dendrogram()` function has a default method to\n", "color different branches of the tree that suggests a pre-defined cut of the tree at a particular depth.\n", "We prefer to overwrite this default by setting this threshold to be infinite. Since we want this behavior for many dendrograms, we store these values in a dictionary `cargs` and pass this as keyword arguments using the notation `**cargs`." ] }, { "cell_type": "code", "execution_count": 41, "id": "b2902747", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.008552Z", "iopub.status.busy": "2024-06-04T23:20:01.008452Z", "iopub.status.idle": "2024-06-04T23:20:01.157711Z", "shell.execute_reply": "2024-06-04T23:20:01.157301Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cargs = {'color_threshold':-np.inf,\n", " 'above_threshold_color':'black'}\n", "linkage_comp = compute_linkage(hc_comp)\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "dendrogram(linkage_comp,\n", " ax=ax,\n", " **cargs);" ] }, { "cell_type": "markdown", "id": "6933178d", "metadata": {}, "source": [ "We may want to color branches of the tree above\n", "and below a cut-threshold differently. This can be achieved\n", "by changing the `color_threshold`. Let’s cut the tree at a height of 4,\n", "coloring links that merge above 4 in black." ] }, { "cell_type": "code", "execution_count": 42, "id": "81bc1753", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.159274Z", "iopub.status.busy": "2024-06-04T23:20:01.159152Z", "iopub.status.idle": "2024-06-04T23:20:01.340885Z", "shell.execute_reply": "2024-06-04T23:20:01.340610Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "dendrogram(linkage_comp,\n", " ax=ax,\n", " color_threshold=4,\n", " above_threshold_color='black');" ] }, { "cell_type": "markdown", "id": "5e4cd4ee", "metadata": {}, "source": [ "To determine the cluster labels for each observation associated with a\n", "given cut of the dendrogram, we can use the `cut_tree()` \n", "function from `scipy.cluster.hierarchy`:" ] }, { "cell_type": "code", "execution_count": 43, "id": "12fa137c", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.342467Z", "iopub.status.busy": "2024-06-04T23:20:01.342352Z", "iopub.status.idle": "2024-06-04T23:20:01.345327Z", "shell.execute_reply": "2024-06-04T23:20:01.345090Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2,\n", " 0, 2, 2, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3,\n", " 3, 3, 3, 3, 3, 3]])" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cut_tree(linkage_comp, n_clusters=4).T" ] }, { "cell_type": "markdown", "id": "404ae519", "metadata": {}, "source": [ "This can also be achieved by providing an argument `n_clusters`\n", "to `HClust()`; however each cut would require recomputing\n", "the clustering. Similarly, trees may be cut by distance threshold\n", "with an argument of `distance_threshold` to `HClust()`\n", "or `height` to `cut_tree()`." ] }, { "cell_type": "code", "execution_count": 44, "id": "bfbbb0bc", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.346645Z", "iopub.status.busy": "2024-06-04T23:20:01.346551Z", "iopub.status.idle": "2024-06-04T23:20:01.349500Z", "shell.execute_reply": "2024-06-04T23:20:01.349288Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [1],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [0],\n", " [1],\n", " [0],\n", " [1],\n", " [1],\n", " [2],\n", " [1],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [1],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [1],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [1],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [2],\n", " [2]])" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cut_tree(linkage_comp, height=5)" ] }, { "cell_type": "markdown", "id": "b5fcdb74", "metadata": {}, "source": [ "To scale the variables before performing hierarchical clustering of\n", "the observations, we use `StandardScaler()` as in our PCA example:" ] }, { "cell_type": "code", "execution_count": 45, "id": "4a183e53", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.350672Z", "iopub.status.busy": "2024-06-04T23:20:01.350588Z", "iopub.status.idle": "2024-06-04T23:20:01.504539Z", "shell.execute_reply": "2024-06-04T23:20:01.504262Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scaler = StandardScaler()\n", "X_scale = scaler.fit_transform(X)\n", "hc_comp_scale = HClust(distance_threshold=0,\n", " n_clusters=None,\n", " linkage='complete').fit(X_scale)\n", "linkage_comp_scale = compute_linkage(hc_comp_scale)\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "dendrogram(linkage_comp_scale, ax=ax, **cargs)\n", "ax.set_title(\"Hierarchical Clustering with Scaled Features\");" ] }, { "cell_type": "markdown", "id": "42cd318f", "metadata": {}, "source": [ "Correlation-based distances between observations can be used for\n", "clustering. The correlation between two observations measures the\n", "similarity of their feature values. {Suppose each observation has\n", " $p$ features, each a single numerical value. We measure the\n", " similarity of two such observations by computing the\n", " correlation of these $p$ pairs of numbers.}\n", "With $n$ observations, the $n\\times n$ correlation matrix can then be used as a similarity (or affinity) matrix, i.e. so that one minus the correlation matrix is the dissimilarity matrix used for clustering.\n", "\n", "Note that using correlation only makes sense for\n", "data with at least three features since the absolute correlation\n", "between any two observations with measurements on two features is\n", "always one. Hence, we will cluster a three-dimensional data set." ] }, { "cell_type": "code", "execution_count": 46, "id": "fca5af66", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.505992Z", "iopub.status.busy": "2024-06-04T23:20:01.505912Z", "iopub.status.idle": "2024-06-04T23:20:01.626714Z", "shell.execute_reply": "2024-06-04T23:20:01.626470Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.random.standard_normal((30, 3))\n", "corD = 1 - np.corrcoef(X)\n", "hc_cor = HClust(linkage='complete',\n", " distance_threshold=0,\n", " n_clusters=None,\n", " metric='precomputed')\n", "hc_cor.fit(corD)\n", "linkage_cor = compute_linkage(hc_cor)\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n", "dendrogram(linkage_cor, ax=ax, **cargs)\n", "ax.set_title(\"Complete Linkage with Correlation-Based Dissimilarity\");" ] }, { "cell_type": "markdown", "id": "5ed5d4bf", "metadata": {}, "source": [ "## NCI60 Data Example\n", "Unsupervised techniques are often used in the analysis of genomic\n", "data. In particular, PCA and hierarchical clustering are popular\n", "tools. We illustrate these techniques on the `NCI60` cancer cell line\n", "microarray data, which consists of 6830 gene expression\n", "measurements on 64 cancer cell lines." ] }, { "cell_type": "code", "execution_count": 47, "id": "64352331", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.628099Z", "iopub.status.busy": "2024-06-04T23:20:01.628029Z", "iopub.status.idle": "2024-06-04T23:20:01.633228Z", "shell.execute_reply": "2024-06-04T23:20:01.633002Z" } }, "outputs": [], "source": [ "NCI60 = load_data('NCI60')\n", "nci_labs = NCI60['labels']\n", "nci_data = NCI60['data']" ] }, { "cell_type": "markdown", "id": "02384331", "metadata": {}, "source": [ "Each cell line is labeled with a cancer type. We do not make use of\n", "the cancer types in performing PCA and clustering, as these are\n", "unsupervised techniques. But after performing PCA and clustering, we\n", "will check to see the extent to which these cancer types agree with\n", "the results of these unsupervised techniques.\n", "\n", "The data has 64 rows and 6830 columns." ] }, { "cell_type": "code", "execution_count": 48, "id": "224f03e9", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.634598Z", "iopub.status.busy": "2024-06-04T23:20:01.634524Z", "iopub.status.idle": "2024-06-04T23:20:01.636446Z", "shell.execute_reply": "2024-06-04T23:20:01.636188Z" } }, "outputs": [ { "data": { "text/plain": [ "(64, 6830)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nci_data.shape" ] }, { "cell_type": "markdown", "id": "a9fcff33", "metadata": {}, "source": [ "We begin by examining the cancer types for the cell lines." ] }, { "cell_type": "code", "execution_count": 49, "id": "7b5e3fe5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.637751Z", "iopub.status.busy": "2024-06-04T23:20:01.637686Z", "iopub.status.idle": "2024-06-04T23:20:01.640873Z", "shell.execute_reply": "2024-06-04T23:20:01.640636Z" } }, "outputs": [ { "data": { "text/plain": [ "label \n", "NSCLC 9\n", "RENAL 9\n", "MELANOMA 8\n", "BREAST 7\n", "COLON 7\n", "LEUKEMIA 6\n", "OVARIAN 6\n", "CNS 5\n", "PROSTATE 2\n", "K562A-repro 1\n", "K562B-repro 1\n", "MCF7A-repro 1\n", "MCF7D-repro 1\n", "UNKNOWN 1\n", "Name: count, dtype: int64" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nci_labs.value_counts()" ] }, { "cell_type": "markdown", "id": "2c2b6659", "metadata": {}, "source": [ "### PCA on the NCI60 Data\n", "\n", "We first perform PCA on the data after scaling the variables (genes)\n", "to have standard deviation one, although here one could reasonably argue\n", "that it is better not to scale the genes as they are measured in the same units." ] }, { "cell_type": "code", "execution_count": 50, "id": "8e1d2d85", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.642205Z", "iopub.status.busy": "2024-06-04T23:20:01.642130Z", "iopub.status.idle": "2024-06-04T23:20:01.835589Z", "shell.execute_reply": "2024-06-04T23:20:01.834884Z" } }, "outputs": [], "source": [ "scaler = StandardScaler()\n", "nci_scaled = scaler.fit_transform(nci_data)\n", "nci_pca = PCA()\n", "nci_scores = nci_pca.fit_transform(nci_scaled)" ] }, { "cell_type": "markdown", "id": "19ac96ab", "metadata": {}, "source": [ "We now plot the first few principal component score vectors, in order\n", "to visualize the data. The observations (cell lines) corresponding to\n", "a given cancer type will be plotted in the same color, so that we can\n", "see to what extent the observations within a cancer type are similar\n", "to each other." ] }, { "cell_type": "code", "execution_count": 51, "id": "5b76ee22", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:01.838692Z", "iopub.status.busy": "2024-06-04T23:20:01.838473Z", "iopub.status.idle": "2024-06-04T23:20:02.097401Z", "shell.execute_reply": "2024-06-04T23:20:02.097122Z" } }, "outputs": [ { "data": { "image/png": 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AwE+cwQ4AAEAgWbatnYXZKvFUKDU8RgmhEcGOBAAAAKAZodgGADghuC1Lb2xdrNe2LNbe4jxJkilDp7fsolu6n6K+Ca2CnBAAAABAc0CxDQDQ7FVYHv1u/nv6IXOL7COOW7I1O2OL5mRs0dPDfqXRrboGLSMAAACA5oE92wAAzd5zG+YeVWg7zGNb8tiWblv0gfaXFAQ8GwAAAIDmhWIbAKBZK/e49caWJTUW2g6zVbnM9P0dKwIVCwAAAEAzxTJSAECDsGxb8zK3aWNepkzDVP/E1hqQ0EaGYQQ0x7KDu5RXUeJ1nCVbn+9aq0k9RgUgFQAAAIDmimIbAMDvZu7ZoEd++lr7SvJlGoZkVxazusYk6eGB52hAYpuAZSmsKPN5bIHb97EAAAAAUBOWkQIA/OrzXWs1eeH7yijJl1Q5w806tIhzS/4BXfXD61p+cFfA8iSHR/s0zpCUHObbWAAAAACoDcU2AIDfFLnLdf+yzySpxj3SLNnyWJbuXvKpbLuuXdT8p098K6VFxnkdZ0u6uH3/ho4DAAAAoJmj2AYA8JvP0teoxFNRZzMCS7bSi3K0MGtHQDKZhqFbup/idUyL0Eidm9Y7IJkAAAAANF8U2wAAfrP0YLocPjRAcBimlgVwKenEdv10S/eRVfc+kilDcSHhevWUqxQVEhqwTAAAAACaJ4ptAAC/cVse+bI61Dg0NlAMw9AdvU7XW6Ou0RmtuinM4ZQhQy3DY/T7Xqfqi3E3q2tscsDyAKhu6tSpGjJkiKKjo5WcnKwLLrhAGzdurDamtLRUkyZNUmJioqKiojRx4kRlZmYGKTEAAEDt6EYKAPCbLjFJ+krrvY5z25Y6xyQFIFF1Q5LaaUhSO0mSbdsyfJiFB6DhzZkzR5MmTdKQIUPkdrt1//33a9y4cVq3bp0iIyMlSXfccYc+//xzvf/++4qNjdXkyZN10UUXad68eUFOD5y4Mvbm6tsvflJWZr7Cwl06aWQX9R/cQaZpyLJs7dy2X0WFZUpoEaVWbRKCHRcAAsawA7VDdROQn5+v2NhY5eXlKSYmJthxAKDJySjJ12lfPFnVfbQ2MSFhmj/hDrkcvOeD5oFnCP/KyspScnKy5syZo1GjRikvL09JSUmaNm2aLr74YknShg0b1KNHDy1YsEDDhg3zek3+jAD/KS9z6z9TZ2jml6tkGkbVm1cej6WWreM1akwPff/NWu3PyKv6nO69WuvyG0Zq+CndghUbAI7JsTxDsIwUAOA3qeExuqGr9xe9f+gzhkIbgFrl5VW+QE9IqJwJs2zZMlVUVGjs2LFVY7p37662bdtqwYIFQckInKgsy9bD972vb79cLdmVH3s8ljweS5K0b0+O3n19frVCmyRtXL9XD975rj5+d1EwYgNAQFFsAwD41V29x+j6LsNkSNWaJZgy5DBM/bHvOF3aYWDwAgJo1CzL0u23366TTz5ZvXtXdgjOyMiQy+VSXFxctbEpKSnKyMio8TplZWXKz8+v9gvA8Vu6YIsWzd2s+i6Qsq3K8c89+rU2rd/bENEAoNFgWgEAwK9Mw9B9fc/QVZ0G673tK7QhL1MOw1T/hNb6VfsBSgyLDHZEAI3YpEmTtGbNGs2dO/e4rjN16lQ99NBDfkoF4LBP318i02HI8hzbbkQOh6lP31uiPzx4vp+TAUDjQbENANAg0iLjdWfv0cGOAaAJmTx5smbMmKEffvhBbdq0qTqempqq8vJy5ebmVpvdlpmZqdTU1Bqvdd9992nKlClVH+fn5ystLa3BsgMngj27srVmRfoxF9qkyn3d5s1eT7ENQLNGsQ0AAABBZdu2br31Vn388ceaPXu2OnToUO38oEGDFBISolmzZmnixImSpI0bNyo9PV3Dhw+v8ZqhoaEKDQ1t8OzAieDA/nw9+vB0LVu0zS/XKy2p8Mt1AKCxotgGAACAoJo0aZKmTZumTz/9VNHR0VX7sMXGxio8PFyxsbG68cYbNWXKFCUkJCgmJka33nqrhg8f7lMnUgDHLvtAoW674WVlHyz02zXjE6P8di3gsPW5GXpz6xJ9vWeDit3lahEWpV+176/LOg5SUhh/5xBYFNsAAAAQVM8995wk6bTTTqt2/JVXXtF1110nSXr88cdlmqYmTpyosrIyjR8/Xs8++2yAkwInnpefnaXsg4WyDnUbPV6maeis8wf45VrAYdO2LtVDK7+UaZjy2JV/VzNK8vXM+h/16uZFevmUK9UvoXWQU+JEQrENAAAAQeVLV8OwsDA988wzeuaZZwKQCIAk5eeV6Luv1/i10BYe7tKEiwb55XqAJP2QsUV/WfmlJFUV2g6zZKvIXa4bfnxLX43/HTPcEDBmsAMAAAAAABqfzRv2yl3hqdfntEiOlmEYMh1GteOGaSg8wqW/PXWlEltE+zNms1TmcWtdboZWZe9VXnlJsOM0as9tmCtTRq3nDxfc3tu+PICpcKJjZhsAAAAA4CieesxoCwsP0dSnrlLPPm20a+dBffbBUs35dq1KissVnxCpM88boLMuGKj4hMgGTNz05ZeX6vmNc/Xu9uUqqCiTJDkNU2e36anf9ThFHaNbBDlh47KnKFfLDu7yOs6SrQ92rNSkHqMCkAqg2AYAAAAAqEFaO98KO6ZpqGffNPXqmyZJatu+hSbddaYm3XVmQ8ZrdrLLinX57FeVXpQtzxHL6922pc93r9W3+zbpjVFXq098qyCmbFz2l/reuCOrHmOB48UyUgAAAADAUVq2jtfAoR1kmrUv0ZMky7J13sVDApSq+frT8hlHFdoO89i2Sj0Vunn+uyq36re0tzmLCnH5PDbC6ftY4HhRbAMAAAAA1Oj6342W6TBlGDUX3EzTUO9+aTrp5C4BTta87CnK1ay9G2sstB1m2baySgs1c8+GACZr3DpFJ6lNRFwdO7ZVchimzmrdMyCZAIliGwAAAACgFt16ttZfn7hCEZGhklRVdHM4Kl9K9h/SQQ8/frkcTl5aHo/v9m32aZxpGPp278YGTtN0mIah67sMk7ee1pZt6YpOdMFF4LBnGwAAAACgVgOGdNDbX9yhOTPXavG8zSopKVdqyziNP6+/uvVsHex4zUKRu0ymYcpj192UwrJtFR5qnIBKV3YarBXZuzVj1xoZUrXCm2kYsm1b/zdwgrrFpgQrIk5AFNsAAAAAAHUKCwvR+HP7a/y5/YMdpVlKDov2WmiTKpdDJodHS5IySvdqc8EGeWyPUsNaqWt0D5nGiTfD0DQM/XvIBRqUmKZXNi9UelFO1bkhiW11c/eROjmlYxAT4kREsQ0AAAAAgCAa17q7Hlzxhcosd53jPLal01q21qMb/6rNhYf3bqucz5XgaqGJbS7XoPihDZ63sTENQ1d2GqwrOg7S1oIDKnKXKzksSi0jYoMdDSeoE6/sDQAAAABAIxIVEqpruwytc6N/h2GoV1yyPs98XlsLNx1xpnLhZHb5Ab247SnNOzCnQbM2ZoZhqHNMkvoltKbQhqCi2AYAAAAAQJDd3vN0nZPWW1JlYe2ww7/rHJ2kQan7VW6VylLtS06npb+igor8howKwAuKbQAAAAAABJnTNPXvIRfohRGXaURyR4U7QuQyHeoem6JHBp6jJ4efqd2lm+ostEmVnTfnH/whQKkB1IQ92wAAAAAAaAQMw9DpLbvo9JZdjjo3J+tbn65hy9bGgnUan3qOv+MB8BHFNgAAAAAAGjmP7ZEhQ/ahPdrq4vbSaOF4WLalNXk/aUn2AuW78xTljNag+JPUL26AHAYlBkCi2AYAAAAAQKOXEtrSp0KbKVMtw1s1SIassv16avO/tL8sQ6ZMWbJkyNSynEVKcCVqcue71Cq8TYPcG2hK2LMNAAAAAIBGrkdMb8WFxHsdZ8nSyBan+/3+he4CPbrxrzpQtr/qPpJkH/r/3PIcPbbpb8opz/b7vYGmhmIbAAAAAACNnGmYuqjNZXWOMWRoUPxJSoto5/f7z8mapbyKnFobNFiyVOwu0reZX/rtnqWecn25d7GmrntbD699U69vn6ms0ly/XR9oKCwjBQAAAACgCRiaMEKlnlK9k/6a7EP/k1S1pHNg/FBd1/4mv9/Xtm3N2f+t12WslizNPTBbF7a+VE7z+MoNP2at1t/Xva1iT5lMmdKhe7+6/WtdnDZKv+18jhwG84fQOFFsAwAAAACgiRiVNFr94wZp7oHZ2lSwXm7brVZhrTUy6XS1jWjfIPcss0qV786r19gEV+Ix32/RwfV6cPVrVcW9X86me3/XHLktj27rduEx3wNoSBTbAAAAAKCZKSkpV3FRmSKjwhQWFhLsOPCzmJBYnd3yfJ3d8vyA3M9hOBp0/JFs29aTmz6WvMyi+3jPXF2UNlJtIpKO+V5AQ6HYBgAAAADNxE/LduiDtxZo8bwtsm1bpmlo+Khuuviq4erVNy3Y8dBEhZgupYW30+6SdK9LSRNdSYpxxh7zvX7K3aq9JQe9jjNl6rM9C3RLl/OO+V5AQ2GBMwAAAAA0Ax+/s0h/uOV1LVmwVbZ9aPmdZWvhj5t0x69f0RefLA9yQjRlo1PGey20GTI0OnmcDMM45vtsLdwnQ94/35KlLYV7j/k+QEOi2AYAAAAATdzKpdv13GNfS5IsT/X9rTyHPv7P1Blav2Z3wLOheRiaMEK9Y/rVWggzZKhjZBeNShpzXPcx61GoM30oygHBQLENAAAAAJq4D95aKNNRd+HBNE199PbCACVCc+MwHLq50+06LekMOY3KHanMQyUFh+HQiMRR+n3XuxViHt8egT1j2nmdQVd5b0O9Ytsf172AhsKebQAAAADQhBUXlWnx/M3e9pOXx2Np7ncb5HZ75HQe+wb2OHE5TacubXu1zm11kX7KW66CinxFOqPUL26gopzRfrlHt5g0dY5qrW2Fe2V5+Us9ofUwv9wT8DeKbQAAAADQhBUWlnottB3m8VgqLipXTGx4w4Zq5jy2W4ZMmcaJuVgswhmp4YmnNNj17+x+sX6//Bm5LU+tBbdfdzpbSaHH3ogBaEgU2wAAAACgCYuODpdhGFVNEericJiKiHQFIFXzU+Ip1twDszV7/7c6WJ4lSeoQ2Vmjk8dpUPxJJ2zhrSF0j2mrxwf8TlPXTdPukgNyGKYMGXLbHkU4QvXrTmfrwjYjgx0TqBXFNgAAAABowsIjXBp6cmctWbD1qOYIR3I4TJ0yugdLSI9BTnm2Htv0Vx0oy6q2n9iOoq16afuzWpK9QDd1vE1Ok5fY/tIztp1eH3avfsrdqp9yt8ptWWobmaxRSX0V6ji+feGAhsZ3AgAAAABo4n511XAtmru5zjGWZemiK9jjqr4s29LTW/6tg2UHjtq4//DHq/NW6qM97+iStKuCEbHZMgxD/eM7q39852BHAeqFea4AAAAA0MT1Hdhek/9wlqTKGWxHcjhMGYZ0xx/PVfderYMRr0nbULBWe0p2yVLtswZt2foha5aK3EUBTAagsWJmGwAAAAA0A+f9aog6dknRh9MWasEPG2VZthwOUyNHd9dFlw9Tj95tgh2xSVqcPV+mzDqLbZLktt1ambtUJ7c4NUDJADRWFNsAAAAAoJno3b+tevdvq/Iyt4qKyhQZFSqXi5d9xyO/Is9roU2STJkqcOcHIBGAxo7vugAAAADQzLhCnXKF8nLPHyIckT7NbLNkKcIREaBUABoz9mwDAAAAAKAWg+KH+jyzrV/coAAkAtDYUWwDAAAAAKAWfeMGKj4kQWYdL59NmRqUcJJiQ+ICFwxAo0WxDQAAAACAWjgMhyZ3uUthjvAaC26GDLWJaKsr2l4fhHQAGiOKbQAAAAAA1KF1eJr+2OMRnZJ0ukIMV9Xx2JA4ndfqYt3Z9Y8Kd4QHMSGAxoQdMwEAAAAA8CIxtIUub3udJra5XDnl2XIYDiW4Wsg0mMMCoDqKbQAAAAAA+MhlhiolrGWwYwBoxCjBAwAAAAAAAH7CzDYAAAAAABAUHttSZkmBLNtWcni0XKYj2JGA40axDQAAAAAABFSRu1yvb1mkN7cuVVZpoSQpyhmqSzsM1A1dhykpLCrICYFjR7ENAAAAAIAmwGNb+iFjqxbs364Ky6MO0Yk6N6234kMjgh2tXvLKS3TVnNe1OT9Lluyq44XuMr26ZaGm71qtt0+9Vm2jEoKYEjh2FNsAAAAAAGjklh5I152LP9a+knw5D3VA9di2/rH6W93UdYRu7XmqTMMIckrf3L/sM20pqF5oO8xj28ouK9Jv57+rL864WUYT+ZqAI1FsAwAAAACgAWwp2KvP9s7X+rx0SVLP2HY6r/UIdYyqXzfTn7L36Lof35TbsiRJbtuqOldhefTMhh9V7KnQfX3P8F/4BrKrKEff7t1YQ5ntZx7b1taCA1qQtUMjkjsELBvgLxTbAAAAAADwI49t6cmNH2n63gVyGKY8h4pj24r26dM983VRm5Ga1OV8mYdmqHnzfyu/lNuyapwJdtgrmxfqkvYD1CmmhV++hobyzZ4NMmTIrrPcJjkMU1/uXtdkim22XSHLLpdpRDAbD/LtXzYAAAAAAPDJi1s/1/S9CySpqtB25O8/2j1XL2/7yqdrrcvN0OqcfXUW2iTJYRh6d/vyY0wcOPkVpT4td7VsW3nlJQFIdOxs21ZO8efamHmxVuzqpJ9299CqPf21N/dfqvDsD3Y8BBHFNgAAAAAA/CS7vEAf7PrB67h302crr6LI67i1Oft8uq/HtrUye7dPY4MpwRUhj1134VCSTMNQQmhkABIdG9u2tPPgFG0/cIuKypZWHfdYOcrIf0br9o1TSfnGICZEMFFsAwAAAIB62L3zoKa9/KNeeOIbvfPaXO3bkxPsSGhEvtm3VLYPxSSPbWlmxrIAJGpczmzTU76ssvTYls5r27vhAx2jzPxnlV380aGPrF+cteSx8rRl/5WyrNJAR0MjwJ5tAAAAAOCD/LwS/fPBj7V4/haZpiHTNGRZtl5+5judfFp33fXAeYqMCgt2TATZnpIDlXt2eSm4OQxTe0sOeL1er/hUn+7rMAz1jW/t09hgSgmP1gVt++iTnatrXRrrMAz1jmulAQltApzON5ZdpsyCF6S62zyowtqvnOLPlBj1q0BFQyPBzDYAAAAA8KKkuFx33fyali7cKkmyLFtutyXLqnyxveCHjbpn0hsqK60IZkw0AiGmb3NabNkKMbyP7RCVoMgQQ3UXdiqXkV7ecZBP9w62B/ufrcEt2kqSfjnJzZDUNjJBz464pNE2GigonS+PlefDSFPZRR95H4Zmh2IbAAAAAHjx6fuLtXNbVlVx7Zcsy9bmDfv05acrApwMjc2g+C7VmiLUxmNbGpTQ1eu4z/ctUkRYwaGPaiu42RrYIqnRdyI9LNwZopdPuVJ/HXiOusWmVB1vHRGre/qcoQ9H36iksKggJqyb2+N9RmIli0YJJyiWkQIAAABAHSzL1qfvLfG6D5dtS5++t1jnXzKk0c7Iaawsy9ZPy3Zoz65suVwO9RnQTi1bxwc71jEZ1qKnWoTGKrssv9ZlkqYMJYfFabAPxbaPd8+Vy+lWi6hCZRdFyrKPnuUWFVamAu1SheX2eWZdsLlMh37VYYB+1WGAyi2PLNtSmCMk2LF84jDjfBxpyOlIaMgoaKSaxr9CAAAAAAiS3OwiHcwq8D5Q0p5d2SopLldEZGgDp2o+5sxcq/89/a0y91VfljdkRGfdds/ZSmkZF5xgx8hhmHqg19W6c8Xzku05quBmypDTdOjPva6WadS92KzcU6G9JQclSaEhHqXG5qu0wqkyd4hkSw6HpQhXuRymrWKPdKAsTy3DExvsa2soLtMhyRHsGD6LCRsp04iUZXvrJmsrPuK8gGRC48IyUgAAAACogy+dJauPb6AgzdDnHy/TX//44VGFNklatmirbr3uJWXuyw18sOPUJ66Dnhw0ST1i2h11rldsez016Fb1jD363C/9coakYUjhLrfiIkoUF1mi6LAyOYo80s4KKdPtbVu3E55te5RX8q325j6qvbmPKrf4G9m2u97XMc1wJUVfq6N3nKs2Sg4jVgmRFx5zXjRdzGwDAAAAgDrEJUQqNj5CeTnFXscmpcQoItIVgFRN38EDBXr6n1/Wet7y2MrPL9FT//xSjzx+eQCT+Uf3mLZ6evCt2l64T5sL9kiSusa0UftI37qLSpXNFjpGttT2on1H19E2lsl8J1/GvBIZh7aI+1OPhzXx9nN05o2jZZrMrTlSXskspWffqwpPpn4uhbjlNFsoLeGvio84q17Xaxk7RSXl65VfOvvQkSP/hBwyjVB1Sn5VDrPx7j2HhsO/PgAAAACog8Nh6tyJg2Wade/DZhiGzr9kKPu1+ejLT5Z7nTVoeSwtnr9ZGXtzAxOqAXSIaqlxLQdrXMvB9Sq0HXZhm5FHFdqMecVy3JYpY/7PhTZJ2rVhrx7/7Qv6+1VPyrK8N2k4UeQWz9TWrBuOaFbgPvRLclsHtf3Azcop+qxe1zQNlzolvaS0+EcU6uxQddxQqFpEXaruqV8pKrRpdIeF/1FsAwAAAAAvLrj0JCWnxsrhqLmQZjoMtW6boAkX8uLaV8sXbau1u2s1trRq+c6GD+QD27aVXrxDy3IW6afc5Sp0+7aX3/EY33Kw+sR2kHl4yWKmW+bDByRLMjxH55Ok79+dp4+e+LzBszUFtl2h9Oy7D39U0whJUnr2fbLs0npd2zCcSoq+Wj1bfq8+rZeoV6t56tdmtdom/F1hIe2PKzeatiZTbJs6daqGDBmi6OhoJScn64ILLtDGjRurjSktLdWkSZOUmJioqKgoTZw4UZmZmUFKDAAAAKC5iIkN12P/vU6du7WUVDnbzeEw5HBUvqTq2SdNjz5/rSKjaIzgq/IKj/dBh7jdvo9tKKvzVuqR9X/U39b/WS9ue1rPbX1c96y6Ta/t+G+DFt1CTKf+0f83Oj1lgAwZcnxeKMOSjLrqlLb04eMz5PEE/79bXWzb1pKsnfrX6ln6v5Vf6aVNC7S/xL//LXNLvpbbOqi6N7Sz5bHzlVM045juYRiGQhwpCnWmyTTDjukaaF6azJ5tc+bM0aRJkzRkyBC53W7df//9GjdunNatW6fIyEhJ0h133KHPP/9c77//vmJjYzV58mRddNFFmjdvXpDTAwAAAGjqWiTH6MlXbtSGNXs0e+ZaFeSVKDY+QqeP662uPVsFO16T07Z9C23dmCGPx/tyx9ZpCQFIVLuFB+fq1R0vyPjFhvge261FB+dpS+FG3dP9L4pyRjfI/cMdofpTryt1U6ezdfP1d6rAhxWiB/Zka/Oybeo+tEuDZDpem/P36/cLP9SWggNyHurKatm2/rVmli7rMEh/7DdOIebxdygtKlshQ07Z8tYIwami8uVK1MXHfU+gyRTbvvrqq2ofv/rqq0pOTtayZcs0atQo5eXl6aWXXtK0adM0evRoSdIrr7yiHj16aOHChRo2bFgwYgMAAABoRgzDUI8+bdSjT5tgR2nyJlw4UN9+scrruJat49VngPfOnQ0ltzxHr+/8nyTJrmF2lCVLB8sO6L1db+qGDrc0aJbksHip0PeWo4W53pt6BMPOwmxdNvtVFbvLJUlu+4jqoS29vW2pcsuL9fjQi/ywB2J99q5jnzv4R5NZRvpLeXmVraETEirf4Vi2bJkqKio0duzYqjHdu3dX27ZttWDBghqvUVZWpvz8/Gq/AAAAAAANr2ffNA0Z0dlr44kbJ4/xOqYhzTswW7ZddxHGkqWl2YtUUNHwrynjUmJ9Hhtfj7GB9O8136nYXS5PLQ0ybElf7F6nhVk7jvteYSHdfZjVJkkehYV0P+77AVITLbZZlqXbb79dJ598snr37i1JysjIkMvlUlxcXLWxKSkpysjIqPE6U6dOVWxsbNWvtLS0ho4OAAAAAFDlLME/Tb1Yg4Z1kqSq/e8kyTAr98O74/5zNGpMz2BFlCStyltZ44y2X7Lk0caC9Q2eZ/x1p8vw2hlXSuveWh37Bm9GYG2ySgs1c++GWgtthzkMQ9O2LTvu+8VHnCvTiPQ6zpBLiZEXHff9AKkJLSM90qRJk7RmzRrNnTv3uK5z3333acqUKVUf5+fnU3ADAAAAgAAJD3fpkccv17rVu/XFx8uVviNLLpdTA4d21FnnD1RCi6gGvf/Bsnxll+crwhGmVuGJNS5ZrLDKfb5ehe372GN15g2n6+2pH6q4oES1Tbizbeny+y70wxJM/9uQmynLS6FNkjy2rZUHdx/3/RxmhFrH3a9dOX+sc1yruLvlMGOO+36AdAzFtn379mnWrFlKSEjQ2LFj5XK5qs4VFRXp0Ucf1QMPPODXkEeaPHmyZsyYoR9++EFt2vy8T0JqaqrKy8uVm5tbbXZbZmamUlNTa7xWaGioQkPpFgQAACBJM2fO1Ny5c3Xqqadq9OjR+uGHHzR16lSVlZXp6quv1vXXXx/siACaIcMw1Ktvmnr1DdzEh+XZm/XWzllanrO56li7iBT9qu2pOrvl0GpFquSwFGWU7pXlw35eLVzJDZL3SNGJkTrjFUMzrrHkKTZkWz9nNRy2bI+hHrcUKWnC3gbP0tAOlBXpbz99o8s7DlKH6MRjvk5S9NWy5dGenEdkq0KVi/xsSbYMOdUq7g9Kjv61v2ID9VtGumTJEvXs2VOTJk3SxRdfrF69emnt2rVV5wsLC/XQQw/5PaRU2RJ48uTJ+vjjj/Xdd9+pQ4cO1c4PGjRIISEhmjVrVtWxjRs3Kj09XcOHD2+QTAAAAM3Fm2++qbPPPlszZszQ+eefr1dffVXnn3++2rRpow4dOujmm2/WBx98EOyYAHDcPt+7UHeufF4rc7ZUO55enKl/b3hP/97wnuwjZl6d3OI0nwttnaIavvPn7qIlcvbYoXGfZavrr4vliq/MZjhttTytTKNezVGv24q08uBb8tRjVl6gdI1NlinfZtx5bEtvbF2sM795Vv/dOO+47pscfZ36tFmqNnF/VnzEuYqPOFet4+5Xn9ZLlRJzc6OcBYimq14z2+6//35deOGF+t///qeioiLdc889OvXUUzVz5kwNGDCgoTJKqlw6Om3aNH366aeKjo6u2octNjZW4eHhio2N1Y033qgpU6YoISFBMTExuvXWWzV8+HA6kQIAAHjx6KOP6tFHH9Vtt92mWbNm6dxzz9Vf//pX3XHHHZKknj176oknntDFF18c5KQAcOy2Fu7Voxsq3ziwfrEP2+GPvti3WD1j22lCq8rXkb1i+qp9REelF++os+h2fuuLZRoNvy36xrwvZchURKqlPncUqc8dRbIqJMNZuVfbYWVWgXYVLVb76JENnqk+UsKjNbpVV32/b5PXfdskVY3595rvlBAaqYvb9z/mezvNOCXHMIMNDa9e3wmWLVume++9V6ZpKjo6Ws8++6zuuusujRkzRkuWLGmojJKk5557Tnl5eTrttNPUsmXLql/vvvtu1ZjHH39c55xzjiZOnKhRo0YpNTVVH330UYPmAgAAaA42b96sc889V5I0ZswYud1ujRkzpur8hAkTtGHDhmDFAwC/+GT3PJleZjAZkt5Ln1M1u800TE3ucpfSIiqbDZhHvIw2ZcqQoUvSrtKQhMCsqCp075f9i6KfGVK90FbJUJE7q8Fy2Lat3PIS5ZQV+7QH25Hu7DVaYY4QOeo5m+zxtd/L46UzLNAY1HvPttLS0mof33vvvXI6nRo3bpxefvllvwX7JduHf7xhYWF65pln9MwzzzRYDqA5KCwt02fL1mv6svU6WFisuIgwTRjQXRcM6aXYiLBgxwMABEFISIjKy39ebhQaGqqoqKhqH5eUlAQjGgD4zff7V3ot1tiS0ov3a3fJAaVFJEmSopzRurv7g1qT95N+zPpOGaX7FGKGqHdsP41KGq2k0JQApK/kMiNVWRL09hrZVogZ4ff7F7nL9c62ZXp9y2LtK8mXJKWERevKToN1Vachigrxvi96p5gWmnbqtbp14QdKL8rx6auRKjuZzsvcplGpnY/viwAaWL2Kbb1799b8+fPVt2/fasfvuusuWZalyy+/3K/hAPjf2t2ZuunFj5RfXFk4tyXtzcnX+j379ezMBXrmhgs0uGObui8CAGh2OnfurA0bNqhbt26SpD179ig6Orrq/NatW6s1pwKApqjU4/seZsXu6hNNHIZD/eIGql/cQH/HqpcO0adod7H3lWWGHEqLHOrXe+eUFeuaH97Qpvws2UeUxzJLC/TE2tn6eOcqTTv1WiWGRXq9Vo+4VH0zfpIW7N+uPyz5RAfKinzKsLsoV5JUWrFNBwrfUG7xV7LsErkcrZUYdbkSIi+Uw/R+f6Ah1WsZ6TXXXKO5c+fWeO7uu+/WQw89pLZt2/olGAD/25dboF+/8KEKSsoO9d75mS2ppNytm//3sbbvzw5SQgBAsNx///3VOrrHxMRU2yx66dKluuSSS4KQDAD8Jy4kyvugQ+Jdvo8NpM4xZyjEjJBRR5MBQ6Y6x4xRuDPer/f+w5JPtKWgeqHtMEu20ouyddsi35vpmIahk1M6qnNMks+fE+YI0YHCaVq373TtL3hV5Z49clvZKq5Yo10592vdvjEqrdju8/WAhlCvYtuvf/1rvfnmm7Wev+eee7R9O3+pgcbqrbkrVFxeXuueCpZtq8Lj0atzlgU4GQAg2C688EKdeuqptZ6/99579fDDDwcwEQD431kth3rthGnKUN/YjkoO82+hyl9cZoTGt/6rTCNERg0v6Q2Zig9tr5OTf+/X+27Jz9IPmVvrbGrgsW0tOZCudbn76nXtU1M711k8PMyQ1Ctmj9Kz71XldAHPEWcrc1V4MrV5/+XyWL7NlAMaQr2KbaWlpZo+fboKCgqOOpefn6/p06errKzMb+EA+I9t2/pw0Rp5rLp3Q/BYtj5bvl6lFe4AJQMANAY85wE4EZzXerhCHSF1FnYs2bqy/ZhazzcGrSMG6oK2z6pd1MnVvhaXGaV+CZfp/LbPKNTh35l5X+5e51NDA4dh6vNda+t17Yva9VOIWXcZ1GEYGtOyq+zyZ1V3KcOjCs9eZRfRLBHBU69i2wsvvKD//Oc/1fbvOCwmJkZPPvmkXnzxRb+FA+A/RWXlKij17UVSuduj7MLiBk4EAGhMeM4DcCJICovT1L6/VqgZctQMN4dR+fL4tq4Xamhi92DEq5cWYV00vvUjuqrTRzq/7TO6qN0LurrTRzop6bdyNUBjhNzyEp9nn+WU16+hTnxohP455Pyqz/8lh2EoKSxa9/XpqeLyVZK8dSQ1dKBwWr0yAP5Ur2LbW2+9pdtvv73W87fffrtef/31480EoAG4nI56jQ8NqXezYgBAE8ZzHoATRb/4Tnpt2N26rN1oxYdEyZAU7nDpjJRBemHIHbqwzchgR6yXCGeCUsN7Kymsu5ym906gxyrOFV7jXm2/ZEuKd4XX+/pnt+mll0ZeoZ5xqdWOOw1TE9r00oejb1SsM8fHq9kq9+ytdwbAX+r1anrz5s3q169fref79u2rzZs3H3coAP7ncjo1uGMbLd++p9Y92yTJMKQuqS2UEFn/H5AAgKaL5zwAJ5LksHj9ptPZ+k2ns2XbdrWGMKjZWW166qn1P3gd57Etnd2m1zHdY2RKJ41M6aT1uRnaUZitENOhAQltqrqbFpaG+Xwt0+D1DIKnXjPb3G63srKyaj2flZUlt5t9noDG6sqR/esstEmSbUtXjRzAAwcAnGB4zgNwouK51zedY5J0SkqnOvdtcxiGBiemqVd8y+O6V4+4VJ3VpqfGtupWVWiTpIjQfnKYsT5cwaG48PHHlQE4HvUqtvXq1Uvffvttree/+eYb9ep1bBVsAA1vbO/Ounho71rPG5LG9e2iCwbz7xgATjQ85wEA6uKxPXpo4Fh1jE6ssaOrKUNpkfF6ctjFDZbBNEKVFHWtvJcyLCVFX91gOQBv6rWM9IYbbtCUKVPUq1cvnXPOOdXOffbZZ/rrX/+qxx57zK8BAfiPYRh68OKx6piSqJdnL9GBgp+bIMRFhOnqUQP169OHyDR5dw8ATjQ85wEAarKvZI++2/+1Fh6cqwq7Qi3jDCVFdNemHJcOlFU2QkgKi9JVnYboqk6DFR3i+1LPY5EaO1mFZYtUWLZERzdKMCVZSot/RGEhnRs0B1AXw7a9rCn7hauuukrTpk1T9+7d1a1bN0nShg0btGnTJl1yySV6++23GyRoIOTn5ys2NlZ5eXmKiYkJdhygQbk9lpbv2KOcwhLFhIdqcMc2CqlnEwUAQKXm8gzBcx4ANH8H9hzUjBdm6ptXZyvvQL4iYiJ02qUjdP6kM9Wma6tqY9fmrdJzWx+XZVuyjihsmTLlsS2NanG2zmp5vuJc4TIDuBzXskuVkfeUsgpfl8fKqzoe4eqj1JjbFRdxRsCyoPk7lmeIehfbJOn999/XW2+9pc2bN8u2bXXt2lVXXHGFLrnkknqHbkx4CAMAAMeiOT1D8JwHAM3XT7PX6k/nTlV5aYUszxHFM2flwtC7X7tVoy+v7MaaXX5AD6y5Wx7bXWcX0hs63KKhCSMaOnqNLLtMxWUr5bFL5HK2UnhI16DkQPN2LM8Q9VpG6vF49O9//1vTp09XeXm5zjnnHP3lL39ReDhdPgAAAJoynvMAoHnbtz1TfzxnqspLy2Vb1Ytnlruy8Pb3q59Uavsk9RzeTXOyZsmyPXUW2gwZ+jpjhobEDw9KownTCFVU2EkBvy/gTb0aJPztb3/T/fffr6ioKLVu3VpPPvmkJk2a1FDZAAAAECA85wFA8/bp01+poqziqELbkQzD0Lv//FSStPDgvGpLR2tiy9aekl3aX5bh16xAU1evYtvrr7+uZ599Vl9//bU++eQTffbZZ3rrrbdkWXX/AwQAAEDjxnMeADRvX73yXbWlozWxPJYWTF+qgpxCFbsLfb52gbvgeOMBzUq9lpGmp6fr7LPPrvp47NixMgxDe/fuVZs2bfweDgAAAIHBcx4ANF8V5RUqyi32aaxt28rJzFOEM1J5Fbk+fU6UM+o40p1YbNvW+vx0fbZngXYUZ8plODQwoYsmtBqmFqGxwY4HP6lXsc3tdissrHob35CQEFVUVPg1FAAAAAKL5zwAaL6cIU45QhzyVHh8Gh8RHaah9gjNyvyqzqWkhgylhrVSSmhLf0Vt1ko95Xp47Zuaf2CtHEZlR1dJWpO3Q69vn6nbul6k89sEp9kE/KtexTbbtnXdddcpNDS06lhpaaluvvlmRUZGVh376KOP/JcQAAAADa6pPOc988wz+te//qWMjAz169dPTz31lIYOHRrUTADQ2BmGoRHnDdH8TxfL466jeGYa6ti3nVq0TtSpZWP03f5vJLv28bZsjUudEJTmCE3RI2vf1MID6ySpqtAmSdahJhRPbPpQkc4wjU0dGJR88J96Fduuvfbao45dddVVfgsDAACA4GgKz3nvvvuupkyZoueff14nnXSSnnjiCY0fP14bN25UcnJysOMBQKN24W1n68cPF9Y5xrZsTbz9HElSi9Bk/abjZP1361OS7Goz3AyZsmVpTPKZGpYwsiFjNyol5RtVXL5KkhTh6qNwV3efP3dDfrrmHVjrddx/t36u01P6y2HUa4t9NDKGbdu1tyI5weTn5ys2NlZ5eXmKiYkJdhwAANBE8AwRGCeddJKGDBmip59+WpJkWZbS0tJ066236t57763zc/kzAgDpnb9/rJfunybDNKp3JTUk2dLZvxmj25//bbWZaruLd+qbzC+0NGeRLLtyGWrnqG4ak3ym+scNOiFmtRWXr9Ku7AdVVL6s2vEIV3+lxf+fIkP7e73Gvze8r6/2LpbHS4dXSfpnv5s0JLHbscatl7KKHXJbOXKYsQp1djgh/jzr61ieIeo1sw0AAAAIhvLyci1btkz33Xdf1THTNDV27FgtWLDgqPFlZWUqKyur+jg/Pz8gOQGgMbvs3gvVumsrvT31I21etq3qeOvOLXXJXefprF+POarY0iainW7ocIuuanejityFCnOEKdwREejoQVNUtlybMi+VraP3MC0uX6VNmRPVJXmaosJOqvM66UWZPhXaDEm7S7I0RA1bbMsp/lwZec+opGJN1bGwkK5Kib5ZCZETKbodJ4ptAAAAaPQOHDggj8ejlJSUasdTUlK0YcOGo8ZPnTpVDz30UKDiAUCTccpFJ+mUi07Sni37lLs/X1FxEWrbo43X4orLdMnlSghQysbBti1tPzD5UKGtpkJZ5W5r2w9OVu9WC2QYtZdYQkzfyi+2pJA6ruMP+/Ke0L68xyRVX6paWrFZO7OnqLh8rdrEP0DB7TiwCBhHsW1by7fv0YeL12j6snXak50X7EgAAAD1ct999ykvL6/q165du4IdCQAaldadW6rXiG5q1zONokot8kt/ULlnt2outB1mqcKTqbySWXVea1B8Fxny7b9z//hOvoesp/zSuYcKbdLRX1fl0uKswpeUW/Jlg2U4ETCzDdV8t2arHv38B+08kFt1zJA0snt7/enC0WqdEBu0bAAA4MTVokULORwOZWZmVjuemZmp1NTUo8aHhoZW66wKAMfKtm3tK1mldbkfK7NkvSQpJbynesVdoNTwvhSqmrGC0rmqLJu4vYx0qqB0nuIixtc64uxWJ+mV7V/LfWjfu5qYMtU/vpPaRCQdU15f7M//nySHpNpzSKb25/9P8RFnN1iO5o6Zbajy6dJ1uu216Uo/otAmVda252/aqcuffFu7meUGAACCwOVyadCgQZo16+eZA5ZladasWRo+fHgQkwFozjy2W7P2PazPdt2mbQU/qNCdoUJ3hrYVzNH0Xbfpu32PyGN7K8SgqbLtcp9no9kqr/N8nCtKd3a/uNbzpkxFhYRpSrfaxxwv265Qfun3qrvQJkmWisqXyu3JbbAszR3FNkiSsguL9eAHMyUdnjhanceylVdSqoc/rHtqLAAAQEOZMmWKXnzxRb322mtav369brnlFhUVFen6668PdjQAzdT8zCe1teA7SZJ9RIHi8O+3FMzSgv1PByUbGl5oSHvZXme1SZKlUGd7r6PObDlUD/W+Vq3CE486Nyihi54bfLtaR7Sof1AfWXaJan7FXzOPXdhgWZo7lpFCkvTR4jXyWHV3RvFYtuZv2qn0A7lq2yIuMMEAAAAOufTSS5WVlaUHHnhAGRkZ6t+/v7766qujmiYAgD8UVWRpfd501V2csLUu91MNSLxakc6jCyho2hIiLtSenL/W2Im0OkMJkRN9uuao5L46JamPVuVuU3rxfjkNh/rFd6qxAOdvphEpwwiTbZf6MNohp3liNcTwJ2a2QZK0cHO6bB8K3LakxVvZYBgAAATH5MmTtXPnTpWVlWnRokU66aSTgh0JQDO1Kf8bycclhJvzvm7YMAgKpyNeKTG3eB2XHP1rhTh832fNMAz1i++kc1sP11mthgak0FZ5X4cSIy9W5Z5tdXEoPmKCHGZEIGI1SxTbIEkqc3tbs13JkFTh41gAAAAAaKoKKjLkS7HNkKkCd6bXcWiaWsZOUXL0jYc+OrJIVfn7FlFXq3XcvQHPdaySo2+QIYdq/7tdeTwl5qaAZWqOWEYKSVKH5AStSt8nj1X39DZbUtsW8YEJBQAAAABB4jR962hsy5bToPtxc2UYptrEP6jEqMt1oOBNFZUtl2QrInSAkqKuUrire7Aj1ktYSGd1TPqftmX95tB+dEdOpqkswnVo8ZQiXH2DlLB5oNgGSdLFJ/XWR4vXeB2XGhulYV3SApAIAAAAAIKnbeRJWp3zvtdxtjxqGzksAIkQTOEhXZWW8H/BjuEXseGnqWer73Wg8A0dLPxQHitHDjNaCZEXqkXUNQoL6RDsiE0exTZIkvqkpeq0nh30w/odsurYvO32s0fKYbL6GAAAAEDz1jpikGJCWqmgIkO2am4mZ8hUTEgrtYoYEOB0wPEJdbZR67j71DruvmBHaZaomkBS5QaN/7xygk7p3l6S5DB/Xr9tGoZMw9AfLzhd5wzsEaSEAAAAABA4hmHqjFYPyWmEyqjhpbMhh5xmmM5o9X8yDN8aKaDxKyoo1awPl+iD52fpi7fmKzszL9iR0AQZtu1LD8oTQ35+vmJjY5WXl6eYmJhgxwkK27a1cuc+vb9wlbZkHJTL6dCwLm118Ul9lBoXHex4AAA0SjxDNH78GQE4VjllO7Qw63mlFy1U5S7WkmSoXeRwnZR0s+JD2wUzHvzE4/botX99rk9f/kHlpRUyHaYsy5JpGDrl3AG69W+XKDImPNgxEQTH8gzBMlJUYxiGBrRvpQHtWwU7CgAAAAAEXXxoe53V5u8qrNivA2WbJUktQrsoKiQ5yMngL5Zl6Z+3vaEfZqyoqqdansqlw5Zt68cZK5S+KUOPfny7wiNphgHvKLYBAAAAAOBFVEgyBbYjWHaZ8ktmq9yzVw4jSjHhoxTiSAl2rGOy4OvV+uGzFbWetzy2dm7cpw9f+E5XTTkrgMnQVFFswzErKi3Xq7OW6L0Fq5VXXiqnYWpQ+9aaPGGE+rRtGex4AAAAAAA/s21b+wv+q4z8p+Wx8iQZqpwOZio+4lylxT8spyMuuCHr6bNXf6xcNuqpuRGGJFmWrRmvz9Vlt46TM8QRwHRoiii24Zhs3pOlK/7zjkqsisoDhiG37dG8rTs176l0XTWsv+6deHpwQwIAjovbk6uDRe8rp3i6PFaunGayEqMmKj7iAjnMiGDHAwAAQbAn9/+0v+ClI44c3sfOUk7xDBWXr1W31I/lNGODEa/ebNvWmsVb6yy0HZZ3sFB7d2SpbZfUACRDU0axDfVWVFKmy594W6W2W/pl151DH7+5cKVaxkfr2tGDg5AQAHC8Ckrna2vWjbLsYh1+iC5Tuoqyl2hv7qPqnPymIlx0qAaAxmhvTr5mLN+grPxCRYS6NKZ3J/VJS6VjJo5bYdmSXxTafsmjMvd2ZeT9R23iHwhYruNleXzvG+lxey/KARTbUG9PfvijSuU5utB2JNvWszMX6urTBsk0+aEOAE1JScUmbcm6VrZdoZ/frVbV791Wtjbvv0w9W85UiIO9awCgsSgpr9BfPvhWX6zYIMMwZBqGbNl66fsl6tkmWY9dfY7aJDSN2UZonLIKXpPkkOSpY5RHBwrfVqvYP8g0G3/3TsMw1LpDkvZs3y/bS83NGeJQcpuEwARDk2YGOwCanhk/bZDX70KGoSJ3hRZs3BmYUAAAv8nMe0627ZZU2zu3HnmsPGUVvBHIWACAOrg9lm59dbq+XLlRtio7KLotSx6r8rl9494sXf30u8rKLwxuUDRpBaVzVXehrZJlF6m4Yl3DB/KTc64d6XWMw2Fq9EWDFRkdFoBEaOootqHeCisq6p7VdoQNOzMbOA0AwJ88VpFyiqfL+4O0pQOFbwYiEgDAB9+u2ayFm9Nl1fKmuMeylV1UrOe/XRTgZGhOLLvC57F2PcYG2xmXnKSW7ZPkcNRcIjEdhkLDXbp00hkBToamimIb6s2w5H1m2yFhrpCGDQMA8KsKT6Zs+fZw7LYOyrLLGjgRAMAX0+b9JNPLG+Iey9anS9epuKw8QKnQ3ISFdJJvZQRDoc72DZzGfyKiwvTP925Vu+4tJUnmoaKbcWhLpNjEaP3jvclq1SEpaBnRtLBnG+otLTxK2z0FXscZlnTmoK4BSAQA8BfTqM/SCEOGeFMFABqDtbsyap3VdqTSCre2Z+WoV5uUAKRCc5MUdbV2Zt/pZZRDMWGnyuVsWh07E1Nj9fSXf9DKeZs068MlOpiRp+i4CJ18Vj+NOLOvQlzVyyfF7lKVeMoV7QyXy8HzEKqj2IZ6+824k3T/F99KsmtfTmrb6pWQpMTYqFpO21q+abe2782W02Gqf5fWat+SjSYBINhCHC0V6uygMvcOVW+O8EsORYeNkGEwSR4AgBNFfOS5yiz4r0ortqjmLScMGXKoVdyUQEfzC8MwNGBkNw0Y2a3WMQsOrNP7u+ZoRc4WSZLDMHV6cn9d2vY0dY5uHaioaOQotqHeJpzWW+/PXqkVJQcql5P+suBm2wpzm3rsN+fV+PlzVmzRE+/M0e6svGrHB3Vro3uvGUvRDQCCyDAMJUffoF05D3gZ6VFy9PUByQQA8K5H62StSvc+uy3U6VD7FvEBSoXmxjTC1CX5bW3NulbF5av1c2dSQ5It04hUx6T/KsLVN7hBG8j/tn6ht3bOkqmfXwN7bEvf71+p7/ev1AO9rtao5Ob5taN+eDsa9eZwmPrfn6/QuJR2Cimufs7w2GprROrje65Vq+Sj24p/uWC97npq+lGFNklasXmPrn9kmnbsy26o6AAAH7SIulIxYadLqn3vnxaRVykmbEzgQgEA6nTFyf29FtocpqHzBvdUZJgrQKnQHIU4WqhbymfqnPSm4iPOUaRrsGLCRikt/m/q03qJYsK8d/Zsir7LXKG3ds6SJFm/mP3vsS15bEv/t/YN7S7OCkY8NDLMbMMxCXU59dgfJirrYIE+mrlSO7NyFBUWqgtO66OeXVrV+Dn5RaV6+JVvar2mZdkqLqvQwy9/rZf+eHlDRQcAeGEYTnVKelH78v6jrIJX5bHzq845zSSlxNyi5OgbZfjYmRoA0PDO6NtFgxeu1vLte2osujlMQ7ERYfrtmJOCkA7NjWGYigkfpZjwUcGOEjDv7PxehgzZdW2zYUuf7pmvSV3OD1wwNEoU23BckhKj9dvLTvFp7Ix5a+X21LSu/2eWZWvV1n3asjtLndvQ6QUAgsUwQtQq7i6lxk5WQelCeax8hTgSFRV6kgyDxwcAaGxCHA49e+MF+tO7X+ubVZvlMI1DhQHJY1nqlJKoJ645V6lx0cGOCjQ5+0oOanPhHq/jPLI0M2OZT8W2MvdOHSh4S7klM2XZRXI526pF1OWKj5hQz4ZVaIx4WkbALF2/Sz40SJJhSMs27KbYBgCNgGmEKTb8tGDHAAD4IMIVoseuPkfpB3L12fL1ysovVGRoqMb07qQB7VsxIxk4RvkVxd4HHVLgw9gDhe8oPfteVW7ZUTkhpcKzX0Vli5WR96S6JE+Ty0mzhaaMYhsCptxd96y2wwzDUIWPYwEAAABU17ZFnCaNGx7sGECzERMS4fPYaC9j80pmKT377hrOWJKkMne6Nu+/Qj1afs0MtyaMBgkImPap8XKY3t9NsyxbbVPpkBRo2/Zn64VZi/TvGT/oldlLlZFbEOxIAAAAABB0LcMT1S26TbUupDUxDVNnpA6qc8ze3EdVdynGozL3duUUfVb/oGg0mNmGgLng1D56d9ZKr+MSYiI0ok+Hhg8ESdLBwmLd9/ZXmr9pp0zDkGkasixbj38xV2cP6K4HJ45RuCsk2DEBAAAAIGguazdaD615vc4xpgxd0PrkWs+XlG9UScUaH+5m6kDhNCVG/aqeKdFYMLMNAdO5TZLOHNbd614Rt/7qFDkd/NUMhPySUl3zzLtatCVdkmTZttweS5Zty7JtfbFig2556RNVeGlsAQAAAADN2WnJ/XRN+zMkVc5gO5LDMOU0HHqw9zVqHdGi1muUe3b5eDdLZW5fx6IxoqKBgPrz9eM0dkhXSaq2pPTwjKq7rjhd55zcK1jxTjivzlmmXQfz5LFq7lxh2baWbtutz5dvCHAyAAAAAGhcru94pv7R7zcaHN+lakGp03DojJRBemHIHRqZ1LvOzzeNcJ/vZZrs19aUsYwUAeUKcepvN0/QNWcN1sdzVmvL7gNyOkwN7p6mC0b1UVJ8VLAjnjAqPB69u2CVLC8tYk3D0LR5K3XBEIqgAAAAAE5sQxO7a2hid5V5KlTiKVOUM1xO0+HT50a6Bso0ImTZ3jqWOhQXPu74wyJoKLYhKLq3S9F916QEO8YJbV9OgfKKS72Os2xb6/fsl2XZMn1ocAEAAAAAzV2oI0ShjvrtbW2a4WoRdaX2F7ykw91Ha2apRdRVx5UPwcUyUuAE5W1G25Hseo4HAAAAABytZewURbh6q+ZyTOXkhrT4hxUW0jGgueBfFNuAE1TLuGhFhHp/J8aQ1CEpnqYVAAAAAHCcHGakuiS/q+To62UaEdXOhYV0VccW/1VS9DVBSgd/YRkpcIIKDXFq4tDemjZvZa0NEg67cuSAAKUCAP/atGyrvnhxlnZv2itXuEuDxvbVuOtOUzR7hAIAgCBxmJFqE/+gWsb+QUVlS2XZJXI5Wys8pJcMg617mgOKbcAJ7MbThujLlRuVU1RSY8HNYRrqnJKo8wf3DEI6ADh2pcVlmnrlfzT/0yVyOE153JX7oiz9aqVe/uM03fXyJJ1+2clBTgkAAE5kDjNCMeGjgh0DDYB1YcAJrEVMpF7/3aXqmJwgSXKYpkzDkONQI4RBHVrrpd9erHBX/Tb+BIBgsm1bj1z2uBZ+tlSSqgpth8+Vl1Vo6pX/0aIvlgcrIgAAAJoxZrYBJ7i2LeL00ZSrtWTbbs1ctVn5JWVqER2hCQO6q2cbOsYCaHrWztugRTOW1T7AlmRIL979hoaeNYDlGgAABJBt2yqt2KgKT6ZMM0qRrn4yjNpLE9n781VSVKq4xGhFxoQHMClw7Ci2AZBhGBraKU1DO6UFOwoAHLcZ/51ZbeloTWzb1s51u7V+0Wb1HNY1gOkAALXZXpihL/ctVkZptlymU0MTuuu05H5yOVhl0VxkF01XRv6TKq3YVHXMabZQcvQNSom5uaroZtu2Zn+yTB//b7Y2r9olSTJMQ8PH9dElvxurbgPaBSU/4CuKbQAAoFnZsWZXnYW2I+3asIdiGwAEWZmnQn9f97ZmZ/0kh2HKY1syZWhW5go9vflTPdj7ag1K4Ht1U5eR94z25v1DUvUZ5W7rgPbm/UtF5SvUscULkhx6+v739cWb82SYP4+1LVuLZq7Rwm9W656nr9Woc2nihsaLPdsAAECz4gxx1GMs7zsCQDDZtq2/rHlNP2StkiR57Mo3SyxVNu8qdJfo3p/+p3V5O4OWEcevqGzFoUKbJB3dmE2ylVfyrbIKXtXX7yzUF2/Oqzz6iyZuHo8ly7b1z9te157t+xs2NHAcKLYBAIBmZcDoPjIdPjziGFLvkd0bPhAAoFYrcrZo4cH1VcW1X7Jly7ItvbDlswAngz/tL3hVkrc3w2ztL3hZH7zwrercTtWWbFv6/PV5/gsI+BnFNgAA0KxM+O0Zsu2aX7QdZjpMDT17oFLaJQUoFQCgJp/umS+HUffLUku2VuVtV3oRM5maqrySbyR5vI4r9+xWuXubvPwYl+WxNPvTOpohAUFGsQ0AADQrqe2TddM/r671vOkwFRUXqclP3hDAVACAmmwp3FO1dNSb7UUZDZwGDcWyS30e6wr3XpSTpML8kmONAzQ4im0AAKDZuXjKubrzf7coPjVOkmSaRtV+zH1P7amnF01Vyw4pwQsIAJAkOerxktRR59pCNGYhDh9/5tqG8rPCfRoamxB1HImAhsWuwAAAoFk684bROuOaU7Xkq5XauyVDIaFO9R/dW2ndWgc7GgDgkH7xnbS39KDX2W2GDHWPaRugVPC3FlFXaF/eY5Lq+nN2KCZ8pJJbdlZhzp6jmiMcyTQNnfGroX7PCfgLxTYAANBsOZwODTtnULBjAABqcX7rkzVj78I6xzhkakSLXmoRGhugVPC3FlFXaH/BS/JY+ap97zZbqTG36tLJLv3t5ldqvZZhGAoJDdFZV53cIFkBf2AZKQAAAAAgKDpHt9KlbU+r9bxpmIoMCdMtXc4NXCj4XYijhbokT5PDjFXlvg5HLgl2SHKqfeKTigobqlMm9Nc1f5hQeeYX3cVNhylXqFN/eeU3SmoZF6D0QP0xsw0AAAAAEDS/7XSOYpwRenPntyrxlMthmLJtW5ZsdY9O0/09r1DL8MRgx8RxinD1Uq9Wc5Rd+IEOFL2jCk+mHEa04iPPUYuoqxTqTKsae/lt49RrSEd9+vIcLZy5RpbHUkRUmM649CSdd90otWrfIohfCeCdYdvemuqeOPLz8xUbG6u8vDzFxMQEOw4AAGgieIZo/PgzAhq/Ek+Zfty/WvtKD8plhmhoYnd1imoV7FgIMsuyVFHmlissRAZNMhAEx/IMwcw2AAAAAEDQhTtCNa7l4GDHQCNjmqZCw13BjgHUC3u2AQAAAAAAAH5CsQ0AAAAAAADwE5aRBkB2YbE+XrJWX67cqPySMiVFR+qCIT01YUB3RYQyHRYAAAAAAKC5oNjWwOZt3KHfv/aZytxuHW5FsS8nXz+l79PTXy/QizdNVNeWdFIBAAAAAABoDii2NaANe7M0+ZVP5bYsHdnz9fBvc4tKdOMLH+iTu65RYlREUDICAAAAABqXXUU5envbMk1PX6PCilLFh0bownb9dGmHgUoJjw52vEbL47G0bM567dm6X84Qp/oM66T23eloi8Cj2NaA/vfdYlm2Xa3QdiSPbSuvuFTvLVilW84YFthwAAAAAIBG55s9G3T7og9ly5bn0IvJ4uI8Pbv+R720aYH+e/JlOimpfXBDNkLffbxUL/31U2Vn5ss0DdmHXov3HNxBt//rcqV1Tgl2RJxAaJDQQPJLSjVz9WZ5rFoqbYdYtq33Fq4KUCoAAAAAQGO1Jmeffr/oQ3lsq6rQdpglW6Uet26a947SC3OClLBx+vyNufrXbW8oOzNfkmRZP0962bBip24/7zHt2pIZxIQ40VBsayD78wq9FtoOy8ovkseyGjgRAAAAAKAxe3HjfEm2anslactWueXWG1sXyK5YJ7tijWwrP5ARG53s/fl67s8f1nre8lgqLS7Xk/e+G8BUONFRbGsgoSG+r9B1mqZMw2jANAAAAACAxqywokxf711/1Iy2X/LYtj7YvlDWgQtkH7xI9v5hsnLvke3eGaCkjcvX7yyU5eW/meWxtGbRVqVvzghQKpzoKLY1kNbxsWqTECtvJTSHaejkbu1kUGwDAAAAgBNWdlmR16LRYUWeEJVYhyd4uKXS6bIPXii7Yl3DBWykVs3fLNvHVWVrFm1t4DRApWZZbHvmmWfUvn17hYWF6aSTTtLixYsDnsE0DV11ygCv4zyWrStO9j4OAAAAANB8RThdPo81ZSnU9BxxxCPZJbJzbpZtu/0frhFzV/j29RqGIbfb430g4AfNrtj27rvvasqUKXrwwQe1fPly9evXT+PHj9f+/fsDnuWy4f10SvcOqmvS2jWnDNTJ3doFLtQRtu3P1tRPv9eEf7yiM/76P/32fx/p29Vb5PawfxwAAAAABFKLsCj1ikuV6WV9lEOWTo3fI4fxy9lcHsnKkMq+b7iQjVC7bi3lcHgvbdi2TUdSBEyzK7Y99thj+s1vfqPrr79ePXv21PPPP6+IiAi9/PLLAc/idJj6z3Xn6rdjTlJ0eGi1c6mxUfrThaP1h3NHBTyXJL30/RKd96/X9M78n7TzQK725RZo4aZ03f76Z7rq6XeUW1QSlFwAAAAAcKK6vsswWbW2R6jkkalrWm2o5axDduk3/g/WiJ115Qh5fJgwktImQf1GdAlAIkDyfRf/JqC8vFzLli3TfffdV3XMNE2NHTtWCxYsOGp8WVmZysrKqj7Oz/d/F5cQh0OTx4/QTWOGaum2PSooKVOL6Aj1b99KDjM4tc6Pl6zV41/MlaRqHVMPb8S5fu9+TXrlU73xu0tlmuwlBwAAAACBcG5aby3O2qn3dqyQIVUruxmyZcvQ79J+0vC42jb690h2UQCSNh6derXRaecP1JzPVtS5d9uv/3y+zCC9BseJp1n9TTtw4IA8Ho9SUqpPDU1JSVFGxtHfjKZOnarY2NiqX2lpaQ2WzeV0akTXdhrfr6sGdWwTtEKbx7L01FfzvYyx9dPOfVq4JT1AqQAAAAAAhmHo4YET9H8DzlZaZHy1c10icvXvrj/qtrar6riCQ3IkN2zIRuiOR6/UaecNlKRqS0oNw5AzxKEpj16hkWf3D1I6nIia1cy2+rrvvvs0ZcqUqo/z8/MbtODWGCzeskv78wu9jnOYhj5ctEYjugZnPzkAAAAAOBEZhqHLOg7SpR0GalP+fuWVlyohxFKHknNlGOVePtsjI+zCgORsTFyhTt391DX61e/G6MtpC7Rrc6acLof6jeiicZcOU0x8ZLAj4gTTrIptLVq0kMPhUGZmZrXjmZmZSk1NPWp8aGioQkNDjzrenO3J8W2prMeytetgbsOGAQAAAADUyDAMdYv9edWWZV4hFb8m1bqnm0MKGSCF9A1IvsaoQ4/W+t3DFwc7BtC8lpG6XC4NGjRIs2bNqjpmWZZmzZql4cOHBzFZ4xEW4nt9NdwV0oBJgMDxuD0qKSyRbde92SwAAADQWBnRf5BCxx/6yHHEmUMv651dZcQ/I8Ng320g2JrVzDZJmjJliq699loNHjxYQ4cO1RNPPKGioiJdf/31wY7WKJzUOU2mYcjyUnQwDOnUHh0ClApoGEu+XqmPn/xCS79eKduyFRETrrNuGK3zbz1LLTvQ9hsAAABNh2GESHFPSGXfyy5+QypfLsmSnJ1lRFwlhZ8rwzixVm4BjVWzK7ZdeumlysrK0gMPPKCMjAz1799fX3311VFNE05USTFRGte3i2au3lytE+mRDElO09SFQ3sHNhzgJ7Zt63/3vqX3/vWpTIdZ1ZWoOL9EHz/1pT5/8VtN/fKP6j2yh1/v67HKtb1wrnLKt8uQqdTw3modMUiG0awmEQMAACBIDMOUwsbICBsT7CgA6mDYrKuqkp+fr9jYWOXl5SkmJibYcRrMwcJiXfnUO9qXm39Uwc00KncA+NeVZ+vMft2CExA4Tl+/+r3+fcOztZ43TUOhkaF6bfPTik+O9cs9N+Z9qQX7n1WZlS9TTtmyZcuj6JCWOi31XrWK6O+X+yD4bNvWqgVbNGf6cuVnFyo6PlKnnjdQ/UZ0YdnGCexEeYZoyvgzAgAAx+JYniGa3cw2eJcYFaFpt16mx7+YqxnL16vCY1Wd69kmRb8/82QNpwspmijbtvX21I8rp2jW8laCZdkqLSrTVy99p8vvq7tbU7nl1oqczcotL1JMSIQGxndRqKP6fobrcj/Vj5mP/Xx9uat+X1CRoRm7puictMfVKqLfMX9daBz278nWX65/UdvX75XDYcqyLJmmqa+mLVCHHq304Mu/UUqbhGDHBAAAABBEzGw7won4jmdecal+2rlP5W6P2iXFqUtqi2BHAo7LlpXbdcvAu30a26ZrK72y4T81nvPYlqbtmKX3d81Rgbuk6nikI0wXpY3UNe3HyWk6VOrJ0xtbJspSRR13MhQT0kqXdXjLrzOfPLalHzK26Nu9m1TkLlNKeIwuaNtHPeKO7r6M45efU6TJZ/1LBzPyZB3xJsVhpsNUYmqsnv7yD7SXPwGdiM8QTQ1/RgAA4Fgwsw31FhsRplE0QkATUm65tfjgBmWV5SrCEaYhid2U4IquOp+Xle/ztXKz8mo8btmWpq6dpln7Vxx1rshTqjd3fKtthfv0UJ/rtCnvq2oz2WpmK79ij/aWrFDriIE+56vLhrxM3TL/Xe0pzpPDMGXbtgzD0CubF2pUSic9ftJFig4J88u9UOmzV3/QwX25smrZ79LyWDq4L1fTX/lBV005K8DpAAAAADQWFNsANAm2beu9XbP11o7vVOAurlol6jBMnZ7cX7/vepGiQsIVFR/l8zWjaxk7e/9PNRbaqrJImndgrb7at1gurfPpXoYc2l+yzi/FtvTCbF055zUVu8slVc5wqwxWWQSat3+bbpz7tt489Rq5TEdtl0E9WJalGa/NrbXQ9vM4WzNen6vLfz9eDgeNMQAAAIATEa8EADQJz26Zrue3zFCBu1jSz9uxeWxL32Wu0K3Ln1ahu0RdBnZQUlqi1+uZDlOjrxhZ47kPd/0oU3Uv9zRk6MNdP8qyPD5/DXZtm8jV01Prf1Cxu1yeWnYB8Ni2Vmbv1te7fSsENnXZmXma9eESffHWfC2bs0GeGpZ4Hq+C3GLlHiz0aWzewUIV5Bb7PQMAAACApoGZbQAavVW52/TBrh9qPW/JVnpRpt7c8a1u7nyuLrnrfD3z+5drHW8YksPp0ISbzjjqXJmnQuvyd3rNZMvW9qIMhTl7yNA8r4U0Wx4lhHb0el1vcstL9PmutbUW2g4zZeiNrUt0bts+x33Pxir3QIGe/fMHmvfFT9VmnCWkxOiau87W+MuG++1eplm/96YcJl1JAQAAgBMVM9sANHqf7J4nh1H3tytLtmbsWagyT4XOmzRe4647TZJk/KLo4XCacjgdevCDO5XU5ugZcBWWt/3XqmsXdZpP4yIciWobeVKdYzy2Jcuue1bWjoKDcnsZI1X+99iYt9+nbE1R7sFC3XH+45r35aqjlnZmZ+briT+8o3efnum3+0XFhqtV+xby1t/CMKSW7VooKi6ixvPlZW5999ES3XnhE7q07/26ctCf9didb2nTT+l+ywoAAAAguJjZBqDRW5q96ed9yepQ5CnV1sK96hnbTne99Dv1P723Pv7PF9q8fJukytlsp106Qr+66zx16te+xmtEOEMV5QxTobvU6/1CzRC1imiv/glXaEX2m3WOHZFyq0zj6G+5xe5SfbFvsT7ZPU97Sg7IkKEeMW11YZuROj2l/1FFxvp0MzX92Pm0sXnl759p/56cGruCHvbqP2Zo+Pg+atvl+LuzGoah8244VS88+KHXseddf0qNf045Wfm6//JntWPjPhmmIftQkfC7D5dq5nuLdenkM3Tt3RP82rEWAAAAQOBRbAPQ6Llt3/dFOzzWMAydcfWpOuPqU5WzP0+lRaWKS45VeGTdHTpNw9Q5rYbrvfTZsupYGuowTJ3VcqhcplNDWvxahmFqxcHqBTdblpxGmE5JuVOdok8/6hoHy/J1+4pntac4q+pOtmxtyE/XX9e9pVmZy/VQn+vkMn/+Vt05JklhjhCVeirq/DochqH+CW3qHNNUFeQW67sPl9RZaJMq9+Wb8fpc/e7hi/1y37MuH67ZnyzTppU7a2yUYJqGuvZvp7OvPPmoc5Zl6c/XvKD0LZmSVFVok1S1x9y7T89UYkqszr3uFL/kBQAAABAcFNsANHppEUnaXLDH675ohgy1Cj96aWh8cqykWJ/vd1HaKfp870IVuUtrLLiZMuQyQ/SrtqdW3tcwNKTFjeoZd4E25n2hnLLtMgxTKWG91SV2nFzm0UsKbdvWH1e9rH0lB4+6w+F7Ljq4Qc9tnq7fd7uo6lyk06WJ7frpne3L6ty3zWPburrTEJ+/5qZk/fLtcld4L8BaHkvL5mzw231dYSH627Tf6al739Xs6cslVe7lZlmVxbJTzxuoW/9+qVxhIUd97rI5G7R1zW6v95j2n6901pUj5AxxaHdxlr7ct0QZpdlymU4NTeiukUm9FWLyoxsAAECSKsorNPvd+Zr+zFfatmqnDNNUz+Fddf6kMzX8vMH13ncX8Bee2AE0eue1HqF/b3ivzjGmDJ2U2EMtQn0vqtUmKTRWjw24RXev/K9yKgplyJAtW4Yqu6BGOsP1936/PqqwF+lM1MDEq326x6rcbdpYsKvOMbZszdi7UNd1HK/YkMiq45N7jNL3+zYps7SwxuW1hqQzWnXXaS27+JSlqXGX12OmY3n99uDzJjwyVHc/dY1uuP88zfvyJ+VlFykmPkIjz+6vFi3jav28b95dKNNhep2Nl3ugUIt/XKvZKWs0M3OZTMOUbFuGDH21b4niQ6L0YO9r1C++k1+/LgAAgKamMLdI9531iDYs2iLTNKpWHvw0e61WzFqtky8Yqj++c7tCXEe/EQo0NIptABq9sSkD9X76HO0uyaqluGTIYZi6ruN4v92zc3RrvTXifn2XuVIzM5Yqp7xQcSGRGpM6UGNTBirCWfdyVG9mZi6XwzC97kXnsT36Yf8qndv6586aiWGReuf063XX4k+0+MBOOQxDhgx5bFsOw9BlHQfpvr5nNNs921p3SKr2sW1IVn9DVidDMiQz3Za5zJbDNtWmU0qDZGjRMk7n33Cqz+Mzd2V7LbRJlcXcV0tmakvmPkk6omFG5cNjXkWR/rDyv3pq0GR1i0mrb2wAAIBm45HLHtempZV7Mx+5xcfhZ67505fo+Ttf061P/Too+XBio9gGoNELdYTo0QE3696fXtSWwr0yZcqSVTXTLNzh0v/1uU5do/27R1m4I1QTWp2kCa3q7iJ6LHLKC3xq+mAaprLLC446nhoeozdPvUab8/dr1t5NKnKXKyU8Wme36aWE0Jo7YTYltm3LVrkMuY5qGNCuW0t1699Om1aly91bqrjBlOINyV35kOVxmlKhrZBpliZcffT+acEQHhnq0zi7m7Q5fG+t5y3Zku3R81s+0+MDf+eveAAAAE3KlhXbteybn+ocY1u2Pn/hW139wK8Ul3T8q1+A+qDYBqBJSAyN0QtD7tDS7E36ct9i7S/NVYQjVCOT+uiM1OOfaRZokc4wOWTKo7oLbpZtK8oZXuv5LjHJ6hKT7O94QVNQukhZBS8pt2SmJI8cRowSoy5VUvS1CnW2rRp37T0TdO/fn1PF7Ufsw+E8oigXKVXc5FB2l6LAha/DsHF9tHrhVtl17LMnSZ4xjqpicm0s2VqZu1W7i7PUJiKp1nEAAACB5LEtHSzLk2XbSgyNadB9Zr99Y44cTlMet5dnacvS7Hfn64LJZzVYFqAmFNsANBmmYWpoYncNTewe7CjH7dSkvpqZscynsack9W7gNI3DvryntC/vX5Ickir3ZfPY+dpf8LIOFL6pTkmvKTpsmCSp78ldFHpHlMrtEqmmfW8PzYZ7euunOr3lAEUGuRg79uKheu2fM1ReWqHa6m2mw1Ror1AVq9yna24t3EexDQAABF2Ju0wf7v5Rn+yep4Pl+ZKkSEeYzmk9TJe0PU0Jrmi/3/Pgvpxq3d1r43CYOrg3x+/3B7yhNQcABMGwFj2VGhYvs45vw6ZMnZLUW8lh8QFMFhw5xZ8fKrRJhwttP/PIssu0Nes6lbszJEmLDq5XgVFLoe0IZVaFz0XNhhQdF6H7n7tepsOUaR69l57pMNW6Q5LiEn1/GG2ue/IBAICmo6CiWJOXP6VXtn1VVWiTpCJPqd5P/0E3LX5Me4oP+P2+4VHhMnzoNGpZtiKia18lAjQUim0AEAQOw9Tf+v5aUYeWk/6SKUPtIpN1V/dLgpAu8DLynlFlH9XaWLLsUh0ofEuStCE/XQ7D+48wU4bW56f7J+RxGjqml/75/m3qO6J6l9iwCJfOvXakHvvkdvVP6OzT12XIUPdoGiSgedixY4duvPFGdejQQeHh4erUqZMefPBBlZdXn+W5atUqnXLKKQoLC1NaWpr++c9/BikxAOCwf65/VzsKMyv3lf0FS5ZyKwp1/6qXvG6lUV8nXzBEHrf3DvWWx9KIC4b49d6AL1hGCgRIUX6xvnl1tj57/mvt25opp8upAWP66ILJZ2nAmD5HbQKP5q9DVKr+O3SK3tn5vb7ct1hlVoUkKS4kShe0GaFfpZ3a5PaiOxalFdtVUrHGh5GWDha9r1Zxd8qybRl1Fud+5u+Hu+PRc3AHTX17kjJ3HdTeHQfkDHGoS980hUVUNlA43xyhL/YtqvMapkwNb9FDSWFxAUgMNLwNGzbIsiy98MIL6ty5s9asWaPf/OY3Kioq0r///W9JUn5+vsaNG6exY8fq+eef1+rVq3XDDTcoLi5ON910U5C/AgA4Me0rOai5B+p+hvPYltKL92t5zmYNSujqt3sPPrO/Ujska3/6gVo7vjucpvqM6ql2PfzbRA3wBcU2IAAyd2bprtF/UeaOLEmVL/7dFR4t/mK5FkxfqvN+N16Tn7qRgtsJKCUsXr/vdpF+2/kc7S/NlcMwlRoWL4fpCHa0gHF7snwfa2VLkjpFtZLb9v5upi2pU3TLascqyt1a+v16ZaQfkCssRANO6a5W7VvUK/PxSklLVEpa4lHHu0a30YWtR+rjPXNr/DzTMBXhCNUtnc9r6IhAwJx55pk688wzqz7u2LGjNm7cqOeee66q2PbWW2+pvLxcL7/8slwul3r16qWVK1fqscceo9jWQErKK/TZsvV6Z8FP2pGVI6dpamjnNF0+or9GdG3LMwsA/Zi1RqaMGme1HclhmJq9/ye/FtscDof+75O7NeW0B1VSUHJUowTTYapF60Td8/qtfrsnUB8U24AG5nF7dO+Zjyhr14GjZtgc/qEw/dmvldIuSZf84fxgREQjEOZwqW1k8+kqWh8O0/dW7A6jck+zkUm9FRMSofyKYi/jTZ2ZWrl0wLZtff76XL3x2JfKzy6SaRqyDv2bHDSqu37/z8uU1Cr4++NN7nq+YkIi9Hb6dyq33HIaDtmy5bEtdYpsqT/1ulKtIwJbHAQCLS8vTwkJCVUfL1iwQKNGjZLL5ao6Nn78eP3jH/9QTk6O4uOD/2+3OcnKL9QNL3yo7fuzZajyjYtyefTjhu2avW6bJg7trQcnjq1xD0oAJ46CimKZhinLyxuglm2rwMsz27Ho0Kednl3yD731yAeaNW2u3OVuSVJ4VJjGX3+6rvzTRMUl+f6cCfgTxTaggc2fvlS7N+71Ou6df3yiC39/tkJcIQFIBTQs27a1tWiTlucsUbGnSNHOGJ2UMEJtItodNTYspKtCne1V5t4p1fnOqEMJkZUF6RDTqVu7XKi/rnurzhzXdxivWFeUJGnaf77Wm49+WXXOOqKD1Yq5m3T7uY/pPzPuVIuWcbVer6igVN9/tERzPluhgtxiJSTHaMzEITplQn+5wvzzb9c0TF3XcbwubjtKszN/0r7SbIWaIRqa2E3dY9r65R5AY7ZlyxY99dRTVbPaJCkjI0MdOnSoNi4lJaXqXE3FtrKyMpWVlVV9nJ+ff9QYHM2ybN3y0idKP1DZve/I78qeQ983P1y8Rq3iY/TbsScFISGAxiLOFSWPXfMSziOZhqG4Q89j/tayY4ruenmSbn7sOu3ZkvH/7d13fBRl/gfwz8xsdrPpvSeEUAIYei9SFCnqgRyHBVFzIkXxTpRTQc52FizcqT9UFBVU9ATLCQooIIiC0nsNvSUkgfS+ZZ7fHyELMWU3YXcn5fO+V87szLMz333Y7Dz7nadAliXEtou2TdFBTVvm2YtY9eE6nD18HopOwXX92+GmewbC299b69CYbCNytbWfboCsyDXOJVChILsQu9buQ+9burspMiLXyCq7hPdOvIlzJWcgQ0HFV7W1GauQ6NsBkxIeho/uyqqbkiQhzHcyzuU8ZffYIT732H4fGtENFmHFWynfoFQ1ly8sIAAVAook4/6EEbgzbggA4Oyx9EqJtj9SrSpyswrx4YvLMfOd+6otc2DbCTz31w9QVFBS3tNDlB9398YUfPLaCrz42YOIaxPhQA05xkdnxK3RfZx2PCJ3mzlzJl599dVayxw+fBjt2rWzPU5NTcWIESMwbtw4TJo06ZrOP2fOHDz//PPXdIzmaPOxMziSZn94/8INO3DfoO7w9ODXCaLmalBYJ7x7bLmdQaTl87YNjejm0lh8AryR2KOVS89BDYfVasWHT36Ob95YAUmWIFQBSMCGL3/HB09+hkffn4KhEwZqGiOvjkQudvFclt1EW4WstBwXR0PkWvnmPLye8gLyzbkAABWVhxUcKziCN4/OwRPtnoVevnLHMcTnbhSb9iOr6AuUL5R99d9MecIuPvgteHpU7tkyIrInBoV2wtqMXTicdwYqBFr5RGF4ZA/4e1y5o7Vy8W92k96qVcXGlXsw5bkxCAz1q7Tv3PEM/HPCezCVmQFxpaeHuNzLIysjHzPveBvvrp2JgGDX3LklamxmzJiB5OTkWsskJCTYfk9LS8OQIUPQr18/LFiwoFK5iIgIZGRkVNpW8Tgiovok96xZs/DYY4/ZHufn5yM2lqv42vPdzsNQZMnWi60mRWUm/HLoJIZ3dt4cTETUuIQY/HFTRHesTd9Z47xtiiSjrW8MrvOLd29w1KR98PhifPPWyvJ2ufXye+/yf0wlJrx67zzoPT0w8C99NYuRyTYiF/MJ8IYklfeCscfLz+j6gIhcaG3GKuSbc6Gi+qSWChXnS87h90u/YnDYTbbtkiQhLugV+Hj2Qmb+BygxH7q8R0aA8SaE+z0Ib0PXao9p1BkwKrovRkXXfDHdvfGIQ0lv1ari8M7T6DeiU6XtX83/CRaTxZZcq+55eVmFWLX4N4yfPtzueYiag9DQUISGhjpUNjU1FUOGDEH37t2xaNEiyLJcaX/fvn0xe/ZsmM1meHiUD9leu3YtEhMTa5yvzWAwwGDgMKK6Ss8tsJtoA8qHhWXmF7ohIiJqyKYnjkV6aTb25p6EBAniqqSbBAlRxmC80PGvjWpRlfSzWcjLKoRvgBci40MaVezNwYVTGbZEW23mP/ox+o/pBUXRZuE5JtuIXOz6sX2wZ0PtS2IDgIdBh+7DOtfp2AcvZWDDuVMos1oQ4+OPmxMSoZZYsfr73fhx+W5kXSqEl5ce19/YAaP+0gPRcVVXPyTnKrQU4LdLv2DTpZ+RY8qBXtajs383DA67CS28W9o/QCNmUS3YdGlDjYm2q/2cubZSsg0oT7gFe49FsPdYmCzpUEURdEoIdHVYQKHG2MyO9S4FAOsfknIlRWX4+dudVbb/kaoKrPxsE5NtRHWUmpqKwYMHo0WLFpg7dy4uXrwyhLGi19r48ePx/PPPY+LEiXjyySdx4MABvPXWW3jjjTe0CrvJ8jUaHLpJqAoBb4O+9kJE1OR5Knq83mUK1qTvwP/ObcLJogsAgHBDIP4cOwC3RPWBt85T4ygds3HlHnz17k84tu+cbVt8u0iMe/BGDBnTg0m3BmLVB+sgy/anabqUmo0dq/ei982uHcJcEybbiFzsxgnX46OnPkdJYWmNvWJkRcaw+wbDN9Cx4Wen83Lw6M8rsTvzAhRJgiRJsKgqnt60FkH7rPDdWmprJRcXlWH5V9uw/MttmPH0KNx0S90SeuS41JJzeOPoHBRZCm139SxWM7Zm/4bN2Rvx5+g7MSziFo2jdJ0ccxZKrI6tNJVRdgFWYYEiVX8Z0uucN/cZALRIjETG+WyHerfFtqq8KmxWei4s5tpX2aqQnZEPs8kCDz0vr0SOWrt2LY4fP47jx48jJiam0r6KVbz9/f2xZs0aTJs2Dd27d0dISAieeeYZTJ48WYuQm7Qbk1pjw6GTdsspsoSB7Zr2TSQicoyHrMMtUX1wS1QfmFQLhBAwKI1r0bfP3/wRn/37B0h/WGX5zNF0vP7IZzh5KA0P/HO0RtHR1U4fOOtQm15WZJzaf1azZJtsvwgRXQtvPy88/+0T0Ol1kJWqf3KyLKFNt5aYMvdeh453riAPf17+OfZdTAcAWIWARS3/sClTrbhwnUBGn8pf9FWrgKoKzP3XcuzdefraXhBVq8RajDePvoJiS1Gl7vMAbD29/pe6BDtztmoRnltIaLh3+26Z0N/uRVmSJSR2aYH4dlGVtnsYHG8sSpIERcdLK1FdJCcnQwhR7c/VOnXqhI0bN6K0tBTnz5/Hk08+qVHETduIzm3hb/SEXEsPDkWSMKJzIkL8tF/tjYgaFr2sa3SJtt0bU2wLaf2xc0TF42/eX4/fftjr9tioKlmR4dDXDiGgVPP92134jYDIDboMScLbW+ZgwJhelRJu/qF+uPuff8Hcn5+H0cex+drmbNmAvLJSWGsa3yFJyLtOh9KQqp9AkiThvws31us1UO22ZG1CgaWg1iGUEiSsTFtW5QtkUxGoD6q0ymhNJEiINsbW2KvNFboNSkTnfm0gK9VfmSWp/Jp9/1N/qrIvNCoA4bFBdi/qsiKjU7/WVeaaIiJqTIx6D8z76yjodQoUueoHnyxJSAgPwuwxQzSIjojI+b79cEO1nSKuJisSln24wT0BUa2u65fo0JBeVRW4rn+iGyKqHr8RELlJQqcWePrLGfjywgd4e9srWLB3Lpacfx/3Pnc7PL0cm8A5s7gQP54+VnOirYIqkNu+aiJDVQV2bz+FS5n59XkJVIvfLv0Ce7N0CgiklZ5HWul59wTlZoqkw8CQGyDZubQICAwOvanWMs4myzKe+egBdB1QfsG13eWSyn/0nno8/cFEdOrbptrnjr5/kN2ee6pVxei/DnJ26EREbtetZTSW/P0u3NSxTaUebn5GA/46uAc+m3Yn/IyNYw4mIqLamE0W7Pj5sN0REKpV4MC2kyjIdWzKFHKd4X8dYrfHmixLiE+KRfs+2q2YzUlliNzMP8QP/iF+9Xru/osZUB3pFSVLKIms+QPo0sUChITVLwaqXq45x/GyphxEG2NdGI12hoaPxI6crbhUllltLz8JMhK8W6NP8AC3x+bl44kXFk9Fyp4zWP3FFqSdvgiDlx49B3fADWN7wtu35i+Ot947ANvWHcTe34/VOPfisDt6o8+wJFeFT0TkVq0jQjB3wi3IKSrB+aw86BQZrcKDoNfx6wMRNR2lxaY6jTopKSqFb4CXCyMie/xD/PDQW/fj/x76oNr9sixB8VDw2AcParqoBa+WRI2IVTi+oqKo5XPFaOTqYc7mKXuiEAUOlTUoTbc3gJfOG/9I/CcWnpqPIwUHIUOGJElQhYCAim4BPXFP/APwkLWZy0OSJLTrGo92XePr9DwPvQ7PfzwFn76+EisXb0Jpscm2zy/QG2OnDMFfHryRq1QRUZMT6G1EoLdjU10QETU2Xr6e0Ht6wFRqtltWUWT4BXKuyobgT1OHQe/pgQ+eWIy8SwVQdAqEEFCtKqLbRuIfC6ehfe+qI1bcick2okYkMSjEsYKqgOFS9XdowiP9ERvv4HEaGLPZih2bjyP9Qi48DR7o3qcVwiL8tQ4LANAtsBfWZqyqsjjCH/nofNHSO8FNUWnDz8Mf09vORFpJKnbnbEOxtRi+Hn7oEdgHIYZQrcOrN71Bhwf+ORp3PzoCuzemoDCvGAGhvug6IJGrjxIREVGjJYTAyaJjOFF4DAICUcYYXOfXCbLU9GedUhQZN47tiTVLtsBay1BSRZEx4JYuDk//Q643PHkIbhg/AFu+34nTB89B0SlIGtAOHa9v3yBugPPbAVEj0sIvEP2i4rDlwrnah5PKEgKOWKpsliTgz3f1gVzNhMcNmRAC3321HYs/+AX5eSWQJAlCCEgS0Of6tnhk5q0ICvHRNMbeQf2xJmOl3XIRnlFuXRhAS1HGaEQZx2gdhtMZvQ3oN6KT1mEQERERXbOThcex+MyHuFCaCgkyJAAqVAR4BGJc7AR0D+yldYgud9vEQVj75VZIKlDtVyypfGbmsVNucHdoZIeH3gPXj+2D68f20TqUKpp+qpqoiZnZexB0klxpwuJKVAGvc1Z4pVa+MyNJQL9B7TBqXE83ROmYkmITtm8+jo3rD+PoobQa50v4dMEGvDP3R+TnlQCArZwQwNbfjuHv93+EnKxCt8VdnZNFxxwqd7boNExqmYujISIiIiKq3cnC4/jP0ZeQXpoGABBQbXPu5ppz8MHJedia9ZuWIbpFXJsIPP3hROg8dFVWJZUVGYoiY+Y796FNp6Y55zK5RvPoXkHUhHQKjcDiW8bhwbXLkV1aAuXyfFiyJMEqBHr5RSFoSzFOIt32nOAQX4y5qzfGju9jd+UWdygpNmHR/PX4YflulF01P0JsfDDumzIEA2/sYNt28lgGPv9oY43HUq0CWRcL8NE76/CPZ0a7NO7abM/eAgmS3WGkJlGGw/kH0Tmgm5sio8au2HQYBaW/QcAEgy4e/sahkCXOu0hERET1J4TAJ6cXwCqstbZfPzvzEToFdINRadpzN/a64Tos+PkprFy8CT99vR0FuUXw8TNi8JgeuPXeAYhJCNM6RGpkmGwjaoR6R8Ziy90P4sdTR7Hh3EmUWiyI8fXHuMQktAkMAcYDZ09fQtbFAnh7G9AqMaJBJNmA8kTbP6Z+ghNH06H+YVXH82ey8OKsr/HQjBG47Y7yLuvff70DiiLXOoeC1api/eoDmPzIMPj5a9MQKLQU2E20VSiyaNsLj9yvzHwaFws/R2Hp7xCwwNOjHUJ97oa3oWeNc0qUmk/gTNY/UGTaifKO6BIAKxQ5EFH+jyPUd4I7XwIRERE1IccLU5BRdsFuObMwY0vWJgwJu8kNUWkrIi4YE2ePxsTZ2t3Ap6aDyTYiF1NV4ZI50vSKglGt22NU6/bV7o+LD0FcA1wI4dMFG6pNtAFX5kh49z8/olvvBMTFh2Dn1hO1JtoqWMxWpBxKRc++rZ0dskP8PPxxoTTVoYSbj87XDRFRQ5Ge9w7S8l5DecLMCgAoMR9FTvG38DfehJbB70CWK69QW2o+hZT022AVFYnZK38DVjUH53KeglXkI8LvIfe8CCIiImpSjhcehQzZNmy0JhIknCg82iySbUTOxGQbkQscPZSGZV9uw8Z1h1BWZoFfgBeG39oZo8b1RHhkgNbhaaa01IxVy3ZVm2i7mixLWPHNDjw0YwSsFvuJtgoWs/VaQ6y3XkH9cKTgoN1yRsUL7f2uc0NE9Ednj6TifEoaFA8F7Xu3gV+w65OeFwsWIy3v1cuPrn5/lv+eV7IOp7OmIyH0vUrPO5fzz8uJtprf02m5ryLQ61YYdHHODZqIiJocq6pi39l05BSWwN/LgM4toqBrIKMeSBtWYUF5r3lHyjq3jW1Vi2BVC6CT/SHLTXt4KjVfTLYROdmypdvw7r9/rDT0MT+3GN/8dwu++3oHXnzjLnTuHq9tkBo5cuA8SopNdsupVoEtG4/ioRkj0CIhFFlZBVCt9nuMxbQIdkaY9dIjqA+WpX6JQktBrXcIh4aNgIfM+bbcad+vh/DRU//Fod9TbNt0HgoG39kfk16dgKCIQJecVxUmpOXNtVcKuSWrUGw6BC99+VyFZebTKCiteZ7CK2RcKvwvogNmXnOsRETUNAkh8N/f9mDhhh3IyLsyjUWorzfuG9Qd917frdGtUk/OEWmMgVrLTb0rJEQZo51yzvzSjcjMX4D80l9Rvr6nggDjcIT7TYa3gfMZU9PC2xlETrTt92N4998/AkCVoY+qKmAqs+Cfj36BzIw8LcLTnKnM4nDZioUTbh3bw26iTZYlJHWORWwL7YbN6mU9Hmn7JIyKF+Q/fLRKlx/3COyDkZGcA8Kdfv9uOx6/8Xkc2XK00naL2Yr1X2zCw71nIetCjkvOnV+yHlbVkWMryCpcYntUaNrp4BmsKCjdXK/YiIio6RNC4IX/rcOc5RsqJdoA4GJBEeau+BX//HJ1javBU9PW2b8bvBUfB0oK9A8ZdM3nS89/F8cz70Z+6SbANu2KFdmFP+LIhdvw0pRb8Y8bn8OGpb/BbDLXdiiiRoHJNiInWrJoU613B4UQMJssWPmNo1+mm5aIqACHykmShMjo8t5GvQe0QYdOMTXWqySV/99fH7rBSVHWX7QxFk93eBk3RdwML8Xbtj3euyUmtnwI97d8ELLEj113Kcorwpzxb0GoarVDl1WLiuwLOXhz6vsuOX+Z5TQAxYGSVpRaTtkeCeF4UrouZYmIqHn56cBxfLllf61lvtt5GCt2HXFTRNSQ6GQdxsbcZbfcjeEjEKS/thvaeSUbkJb7yuVHlXvTyYoKSMDwmfuQlbUdL931Jqb1nImcjNxrOieR1vitj8hJMjPycGDvObvzkamqwOrv97gnqAYmrmUo2raPqnH1xQpCCNw8pjsAQFFkvPjGeCR1ibM9tpEAg8EDz712Ozp2beGyuOsiQB+IMdF3YG7nd/FGl/fxf10/wpPtnkPPoL5MtLnZ2sW/orSkDLXdsLdaVGxdsQsZZy46/fySpAfsTDp8uSRkyWB7ZPRo6+AZFBj17eoTGhERNQOfbdoN2U6bS5YkfLZpl5siooamX8hAjI9LhiIpkK6av61ilMaNYSPw5+g7r/k8GfnvobYbkJJUvlBa33vLV0c9c+g8Zo18CVardvMxE10rztlG5CS5WUUOl83LLXZhJA3bfVMHY/Yj/61xv6xIiIwKxKChHWzbfHw98fr8e3Fw7zn8+N1upJ3PgdGoR+8BbXDjyE7w9jHUeDytyJIMo+KldRjN2rZVjn15EEJg55q9uHnSUKee39fQH3BgdVoA8PUcYPvdS98Fnh5tUWo+Zuf5VoT6TLimGImIqGkqM1uw82Sq3XKqEDh4PhN5xaXw9/K0W56anoGhN6JbYC/8fulXnCg6BlWoiDbGYEDIYIQYwq75+BZrDgrLfrdbTtEBXUZl4evHE6BaVZzYcxpbV+5Cv1E9rzkGIi0w2UbkJHVJ+Bi9mu8E+T37tsY/nhmN/7z4HQDYegLKsgRVFYiKDsIr70yAwdOj0vMkSUJSlzhbDzcie0qLyhzKdUmyhLIS+wt31JVRnwhvQy8Ule1EzauKSpAkA4K9x17ZIkmICXgaxy/ei/JVwqp7ETICjCPgpe/i9LiJqGlISbuIJb/vxfqDJ1BmtiAy0Bfj+nTCqO7t4ePZ8G5SkXOVmus2zUCJycxkWzPmo/PFsIhbXHJsi+r4XNU6vYDOU4W5RIGsyPjhw3VMtlGjxWQbkZNExQYhLj4E585cqnXYmqLIGDT0OvcF1gANu7UzOndvgVXf7sLvvxxBSYkZEVEBuPm2bhhwQ3vo9fxoomsX2SochzanwGqpfSinUAXC40NdEkOLoLlIyRgFq1qAqgk3CYCE+OA3oci+lfb4GQehZch8nMl6FKoorYgU5UMwrAj0+hNaBL9ud0g2ETVPn/yyE6+v+BWKLMF6+abW8fQszFn2Mz76eTsWTvkLWoS6ZiVmahh8PPXwNnigqMz+RPN6nYJAb6MboqLmSCcHOFzWXCbBXFI+hFW1qkg7ke6iqIhcjxMIETmJJEkYe3ffWhNtQHl3/VHjergnqAYsPDIAf33oBnyw9CF89t0jmPvefbhhREcm2pxECAGr2rznuRh5/w12E20A4B/ii14ju7okBk+PeLSL+B5+noMASH/Yl4jWoZ8i0Ovmap8b6HUzOkbvQGzgv+BvHA4/zxsQ6nsf2kesRcuQeZAl9kAgoqp+3JuC11f8CgC2RBtQnq4XAC4VFGHigm9QwtX+mjRFljGmZxKUWhbuKi8nYXT3DjB4sP1FrqFTAuBruB72Fo2yWoA9y4JxdXvJ05ttHWq8+KlK5EQjRnXBkYOp+GHZLttEnxVkWYIQAo8+dStatg7XLkhq0o4XpOKbcxvxc+YelKlmGBUDhkV0x59jBiDOu3m9767r3w6dB1+H/RsPQ7XWnHS759nboXPhlwyDrgVah32MMst5FJXtgBAWeHq0gZe+k92eaYrsi1Df+xDqe5/L4iOipkMIgXfXbKlxADpQnoBLzy3Aqj0pGNsryZ3hkZtNuL4r/rftAErNFqjV3A2WJQkeioJ7B3bTIDpqTsL9pqDg4sYa9wtRvkjCbx9H2LbJsoS+f2IHBWq82LONyIkkScL0WbfgH8+MQouEqyYUlYCuvRLw2rv3YsQo1/SgIfohbRsmb38DazN2okwt77FQYi3DirQtmLjt39h0cb/GEbqXJEl47n+Po32fNgAA+aqVbBVd+e8Tnv4LRj003C3xGHQxCPK+DcE+f4G3oTOHgBKR0x1OzcTJzGy701VKEvDN1uZ1TWiOYoL8sWDSn+Fl8Lg8ccEVkgR4eujw7sTb0DIsSKsQqZnwMw5EdMAzlx9V7uFmtQBCBZY+1goXDnvbtkuKjJEP3OjGKImciz3biJxMkiQMu7ULbrqlMzLT81BUWIbAYB8EBnnbfzJRPe3PPYXXj3wJAQHrH+5eW0V5r67nDyzGB70eQ7x3RHWHaJJ8Arzx7w3PY9uq3fh+/mqcOXgeOr0O3W/qhD89OAwtO7bQOkQiIqfJyCt0qJwQwIXcAhdHQw1Bl/gorJ41Ecu2H8R3Ow8hu6gEAV6euLVbe4zpeR2CfLhyOrlHuN8D8NInIbPgQ+SV/ARAhdUsYe+KIGz6KBKpB8q/K0myBAjg8YXTEBzJuSWp8WKyjegaFZSV4buDR7DjfCpUVaBNaDDGdUpCuK8PwiMDtA6PmomlZ3+GJJUPVa6JgMD/zm3CY+3+4sbItKcoCvr+qQeHIhBRk+dl8LBf6DJvQ/NdGb258ffyxH2DuuO+Qd21DoWaOV/PPvD17ANVlCEvOwOfPbsKPy78FabSK3NItu7aEn998S70HN5Fu0CJnIDJNqJrsOzAITz94zqUWSy2IWE/phzDvE1bMLlPDzw6sD9kDhUjFyuylOL3S4cg7AwcsgoVq9N3YHrinyFLnEWAiKip6dIiCj6eehSWmmotJ0sShnZs7aaoiIgqkyUDAoPj8Le3p+L+l+7BoS3HYC41I7JVOFomxWkdHpFTMNlGVE+rDqfg8RWrbY//2KPovc3bIQTwj8ED3B0aNTN55iK7ibYKJtWMUqsJXjqu7kRE1NQYPHS4o29nLNqwo9oJ8StIEnB7n05ujIyIqHre/t7sxUZNErs2ENWDRVXxwk8b7Jb7YOsOXMjnnCjkWt51SJwpkgyDwqFDRERN1UM39UHX+Khqe9bLkgRJAl66YziiAv00iI6IiKh5YLKNqB5+OXEKl4qKHSr71d4DLo6Gmjt/D2908m8JGbUPWVYkGQNCO0LhEFIioibL4KHDgkl/xpShvRHgVflmTNf4KHwwaSxu7dZeo+iIiIiaBw4jJaqHlIuXoJNlWFS11nJCCKRcvOSmqKg5Gxc3GPv2L6q1jFWo+Evs9W6KiIiItGLw0GHasL6YfEMvHE7LRKnZgsgAX8QGB2gdGhERUbPA7g1E9SDbWfXRRgIXSCC3GBCahAkthgJAlR5uFY+ntRmNJP+Wbo+NiIi04aFT0CkuEr1axTLRRkRE5Ebs2UZUD12jImF1JNkmgG7RUa4PiAjAxFYj0cY3GkvPbsCh/DO27Z0DW+HOuCHoFdxOw+iujdlkhtWiwmDU21b+JSIiIiIiaoiYbCOqh15xMYgPDMDZ3LxaV/vSKTL+3KmDGyOj5m5gWCcMDOuErLJ85JuLEaD3RqDeV+uw6sVqtWL9fzdh2bwfcHTHCQBAcHQQRj04HLdOvQl+QY3zdRERERERUdPGYaRE9SBJEubcPAyyJNU6TPTpoUPg7+n4SpFEzhJs8ENLn4hGm2gzm8x4dszreO2+t3F810nb9qzUbHz8zBI82O0JpJ/O1DBCIiIiIiKi6jHZRlRPPWKj8eldYxHj7wcAUGQJOrn8TyrA6IlXbxmGu7p20jJEIpsi80WklxzApdKjsAqL1uHY9cETi7Ft1S4AgKpW7j0qVIFLadl46uaXodpZpISIiIiIiMjdOIyU6Br0jI3BT1P+ii1nzmHH+TSoQkXb0BDc2KYV9IqidXhESC/ej51ZH+N88Q7bNqMSiKTAP6Nz4J1QZL2G0VUlhMCZ8wvx/fs/QKg19xpVLSrOHUnF9h/3oPfN3dwYIRERERERUe2YbCO6RpIkoW98HPrGx2kdClElJwt+xU9pz1bZXmLNwY5LC3G+aCdujnkNOtmgQXRVCSFwLudprP1qFSxlCXbLy4qM9f/dyGQbERERERE1KBxGSkTUBBVZLmFd2vMQUCFQdailgEB6yV7syFqkQXTVyytZg0uFn6IwWwfJgY6hqlVFdnquy+MiIiIiIiKqCybbiIiaGCEEvj33it252QQEDuUuh0Utc1NktcssWAhAgdHPCmG1X15WZPiHNM4FIIiIiIiIqOniMFKiZignqxA/LN+NX9cdQmFBKUJCfTH8T10wZERHeHp6aB0eXaPVGStwqWQPjA70DjOrxbhQsg+x3j1dH1gtVFGKwrLNAIAOQ3PwrS4eqqXmOduA8p5tg8b1c0d4REREREREDmOyjaiZ2bwxBS/N+gZmixXi8iqPFzPycGj/eXz6wS949e0JiGsZqnGUVF8llhKsSvsKrY2Or9JpVotdGNEV2WX5WHVhG44VpAIAEn1jMDKqFwL1vlBFqa2cT4gF3cZcws5vQmtcJEFWZARHBaLvqB5uiZ2IiIiIqDZlJSas/3YHvv9kI84dy4AkS+jQoyVGJQ9En2FJkGUOLGxOmGwjakZSDqXiX098BVVVIcSV7RW/52QX4vGHFuODJQ/Cz9+oTZB0TXZlvAKTUGEWCvTCCqn2zmEAAG9diEtjEkLg8zPrsOjkjyh/qwkAEjZe3I+Fp37EpFY3Y1zM9ZAlb6iiCAAw6rkzyDxhxLndPpffn1deiKwIePt74aWVT0HnwcsYEREREWkrL7sQs+58B6cOp0GSJVunhv1bjmPvb8fQ/+bOmPn2fdB5ODD0hJoEplaJmpH/LtwIAVEp0XY11SqQm12EH5fvcm9g5BRCzUNm4e9QIJBl9nHoOX4eUQjz7ODSuJac/RkfnfwBavm7DwKw/WYVKt47vgL/S/0dwd63AyhvgBi8VUz+72GMnHUWAdEm27H0XlYMud8P7+1+HS2TuAIwEREREWlLCIF/PfARzhxNL3+sXvmypVrLf//9h3346OXlmsRH2mCXAKJmIie7CFs2Hq0x0VZBCIEV/9uJ2+/t757AyHlKlkORrBCQkGPxQqQ+Dx6ovXdbt+D7IDnS/a2eCszFWHRytd1yH55YhZv6PICsoqWXh5Sq8PAUGDQ5Hdc/kI78DD1UiwT/MAlJ8Sth9HB1bzwrLGoOJChQ5ACX1hERERERNV6Hd57Goe0nay0jhMDKT3/D+EdGwDfAy02RkZaYbCNqJi5m5NlNtF0pm+/aYMglhPUU2hsKsKpAAiDheEkYWhsz4YHypT0r8kVClP8e4TUUif4jXBrT2vSdsDiwtGiZasbGrEsYHLYYxzPvuzyctPwNK8tAQKQFsmRAQuhHMHq0cVm8FmsOMgsW4VLhYljULACAXolFqO9fEeozAbLs6bJzE1HjZLGq+PXwKazacwTZhcUI9PHCiM5tMaRDK+gUDiIhImrq1n2zHYpOhtVS+5zJZrMFm1btwcjxXOCrOWCyjaiZMBgcX2XUQ8+5BBonDyToixCpK0aGxYgy4YHDxZEI9ihEsEchDLBCBZBvMaLQ6o/728x0eUSnitIhSxKsdjK9OknBqaJ03Bp9G5KiNiGr6EtkFX0DizULOiUQQV5jEOxzJzwU1/VoM1lScTTjLzBZLwC40lgyWc8jNfcF5BQvR5uw/0KRfV0WAxE1Lmcu5mDqR9/iXFYeZEmCKgRkScLqvUcRFeiH9x4Yg4SwIK3DJCIiF8rJzLebaAMARZGRnZHnhoioIeDtNqJmIqZFMEJC7ScJFEVGr/6u6zlEriPpe0KSLEgOPAGdpEKGgAoZF81+OFIchb1FsThQFINzZUEYHz0CHrLjCdj6kiXHLjMC5V9QAUCnBCHcbyo6RK5Fp5hd6BC5DhH+D7s00SaEwImLE2GypuPqRFtFdIBAsekAzmQ/6bIYiKhxySosRvL8r5CWU94bXL18U6Hivxl5BUie/yUu5hdqFiMREbmel68nZAd6MquqgJcvF6FrLphsI2omFEXGbXf2tjv3lNWqYvS4nm6Kiq4mhMCBvFNYdPJHvHf8e3yX+jsKzSWOH8AwBJBDEasvxROhB9FaX3U4cKxHMaaHXUCH4AlOjLxmSf7xsAr7d/qsQkVH/5ZuiKh6hWVbUWI+BKC2Ia9W5BavhMmS6q6wiKgB+3zTbmQVFsOqVt9z16oK5BWVYvHG3W6OjIiI3Knv8I5Qrfbbu0II9B3W0Q0RUUPAYaREzciYO3tj59YT2LP9NEQNw/ruSh6Ajl1buDkyOlV4AS8c/AynitKhSDIkSLAKK94+thx3xg1BcsthdnuJSZIO8P83RM79iPIow/TQI8gwe+K02QdCANEepYjVl0IK/LC8rBsMCuuMeUe/RYGl5qShBCDAwwf9Q65zS0zVySn+DuWXRIudkhJyilch3G+SG6IiooZKVQW+3LzP1outJlYh8NWW/fj7iP6cv42IqInqc1MSQqMCkJWRX2PSTVZk9BzSHhFxwW6OjrTCqz5RM+LhoeCF/9yFO+7rBy9vQ6V94ZH+eHT2n5D84BCnnU9VBbb9fgxz/vk/zJjyMZ57fCl+WrUPpjJ7CY3m5WxRJh7eOQ9nijIBlPfysggrBACzasHi02sx7+gyh44lGfpACvoE0LUGAIR7lKG3Vxb6eF9CrFcUpKBPIBncNymrXtbhifZ3QIKE6vpUSpf/90T7O6HI2s0VaFFzUHuvtgry5bJE1JwVlJYht7jU8bJFdeilTEREjYqiU/Dcosnw9NJDqebGiqzIiGwRjOlzx2sQHWmFPduImhm9Xof7H7oRd98/EPv3nEVxURmCQ3zQvmMsZLn2IaZ1cTEjH7Onf47TJy5CliWoqoAkSfj9lxS8/9YavPjGXUjsEO208zVm7x7/DqVWM9Qqc4VdsSz1N9wc1QttfGPsHk/S9wSCvwfM+wDLgfKNuiTAo5PdYcSuMCC0I17qdD/eSPkGF8tyoVzuoWcVKsI9A/Bo4l/QK7id2+O6mk4OAqDAfs82FTo5sMa9JksaLhUuQak5BYAEb0N3BHuPg04JcF6wRKQ5pY7Xy+q+fBERUdOR0CEa81Y9jiXzVuPnb3fCYi6/ievtZ8TI8X1x+7Sb4BvgpXGU5E6SqGksWTOUn58Pf39/5OXlwc/PT+twiBqt4qIyPHTPAmRcyIO1mq7UsizBYPDAO59OQkyL5t2VOr0kG3dtfsluOUWSMSKiJ/7R/nY3ROUaqlCxI/sojhacBwAk+saie1AbhxdRcKWC0q04ljnOgZISkqI2Q6+LqrRVCBVpea8hI38+ygfGiqueoUNM4PMI9XXPPHmkDbYhGj5n/xuN+fenOJ6ehdoa0hKAuJAArHgiWZObHURE5H5F+SW4cDYLiiIhumUY9J6uX5SMXKs+bQjtv+EQUZOz+vs9uJCaU22iDSgfXmoyWbDkk01ujqzhSbmceLLHKlTszzvl4mhcS5Zk9ApuhwnxQzEhfih6Bic2iEQbAPgYesHokYTy3m01kRHodWuVRBsApOW9joz8d1GeZFNRsYJp+TqrZpzLeQpZhV+5InQi0sjdA7rWmmircM/13ZhoIyJqRrz9jGidFIOW7aOZaGvGGsa3HCJqUr77arvdLyBWq4r1qw+gqLDMLTE1VMKhr2qXy7IjsstIkoRWoR9Cr0Si6qVRAiDBS98JcUGvVnmuyZJ+uUdb7c7nvgBVmJwSLxFpb3SPDujXNg5yDYk0WZLQo1UMxvZKcnNkREREpDUm24jIqYQQSDufA0dySBazFZnpuS6PqSFL8I50qJwiyWjrZ3++Nqo/vS4K7SJWIdL/UejkkKu2xyEm8Fm0Df8SiuxT5XlZRV86dHyrmou8kjVOi5eItOWhKHj7r6NxR99O8FDKe8VWJN48FBnj+nTE/Ilj4KHTbvEXIiIi0gYXSCAip5MVCVaLY72wlGb+JSTOOwydAhJwIPcU1FoylFahYnR0fzdG1jzplABE+j+CCL+/warmAZIMRfKrdQhY+WIIDh0dJaYUBHrd6pxgiUhzep0Os8fcgIeH98OGQyeQU1QKfy9PDOmQgABvo9bhERERkUaYbCMip5IkCZ26tsDenaehqrUn3AICvREVU/PKjs3FQ61H4W8734YQ1mqHlUqQMCi0E5L8490fXDMlSTJ0iqPvTUcTxgKS1LyTy0RNlb+XJ0b3uE7rMIiIiKiB4DBSInK60bf3sptok2UJo8b1gK6Z92wDgES/WMztOgUB+vIhiookQ4YEGeW9qUZE9sRT143nBNsNlI+hBxwaNw0rfAw9XR0OERERERFpjD3biMjp+g5sixtGJOHn1QdQ3Zz+siwhoU04xt7d1/3BNVCdAhLwZb+n8dulg9ienQKT1YxIYxBGRvZChDFI6/CoFkHeY3A+90UIUVpLKRl6XSx8DP3cFhcREREREWmDyTYicjpJkvD4s7chIioQ//tiK0pLTJBlCaoqoCgyhgxPwrR/jITRqNc61AZFJysYFNYJg8I6aR0K1YEi+yIu8GWcyX6shhIyJCiID5rL3olERERERM1Ao0i2nT59Gi+88ALWr1+P9PR0REVFYcKECZg9ezb0+itf1vft24dp06Zh+/btCA0Nxd/+9jc88cQTGkZO1HwpiozkqUNwx339sWXjUWRfKoSPryd69W+DwCBvrcMjcqpgn79Algw4l/McLOpFlF9eBQArDLoWaBH0Gnw8e2scJRERERERuUOjSLYdOXIEqqri/fffR+vWrXHgwAFMmjQJRUVFmDt3LgAgPz8fw4YNw9ChQ/Hee+9h//79uP/++xEQEIDJkydr/AqImi+jUY8hw5K0DoPI5QK9/4QAr5HIK1mPEnMKJMjwNnSHj6E3e7QRERERETUjkhDVzajU8L3++uuYP38+Tp48CQCYP38+Zs+ejfT0dFtvt5kzZ2LZsmU4cuSIQ8fMz8+Hv78/8vLy4Ofn57LYiYiIqGlhG6Lh478RERER1Ud92hCNdjXSvLw8BAVdmTR88+bNGDhwYKVhpcOHD0dKSgpycnK0CJGIiIiIiIiIiJqZRplsO378OObNm4cpU6bYtqWnpyM8PLxSuYrH6enp1R6nrKwM+fn5lX6IiIiIiIiIiIjqS9Nk28yZMyFJUq0/fxwCmpqaihEjRmDcuHGYNGnSNZ1/zpw58Pf3t/3ExsZe0/GICCgtNePAnrPYvf0UMi7kah0OERERERERkVtpukDCjBkzkJycXGuZhIQE2+9paWkYMmQI+vXrhwULFlQqFxERgYyMjErbKh5HRERUe+xZs2bhsccesz3Oz89nwo2onooKy/DZh79g1bJdKCk22bZ37dkS904ZjOs68W+LiIioOVHV8qmhZZmLxBARUfOiabItNDQUoaGhDpVNTU3FkCFD0L17dyxatAiyXLlTXt++fTF79myYzWZ4eHgAANauXYvExEQEBgZWe0yDwQCDwXBtL4KIUFRYiscmf4wzJy/aGtYV9u48jRlTPsGzr41D3+sTNYqQiIiI3KHUZMbK3w7hy3V7cCotC5CAdi3CcfuNXTCidzvodIrWIRIREblco5izLTU1FYMHD0ZcXBzmzp2LixcvIj09vdJcbOPHj4der8fEiRNx8OBBLF26FG+99ValnmtE5BrvvbGm2kQbUH5XW6gqXnrqG+TnFmsQHREREblDXmEJHnh5CV5ZvA6nLmRBABACOHImE89/tBoP//sblJaZtQ6TiIjI5RpFsm3t2rU4fvw41q1bh5iYGERGRtp+Kvj7+2PNmjU4deoUunfvjhkzZuCZZ57B5MmTNYycqOnLzy3Guh/2VZtoqyAEYDZZsWblXjdGRkRERO701Hsrcez8JQDl1/4K4vKD3UdT8dIna7UIjYiIyK0aRbItOTkZQohqf67WqVMnbNy4EaWlpTh//jyefPJJjSImaj52bT8Fi0W1W04Igd83HLFbjoiIiBqflLOZ2HbobK0331QhsHrrEWRkF7gxMiIiIvfTdM42Imr8rl4MwZ7iOpQlIiIibZ0+ewmr1h1ARmY+9Hod+vZMwPW928DDo+q8az9uOQxFlmFVa78BJ0HCmq1HcM/Inq4Km4iISHNMthHRNQkN93OonCxLCI/0d3E0REREdK1Ky8x46T+r8Mvmo1BkCaoAZAlY/fNBBPp74cVZo9GxQ0yl52TnFQOouVdbBVmWcCmPc7gSEVHT1iiGkRJRw9W1R0sEBfvYLaeqAiNGdXVDRERERFRfqiow++Vl2Lj1GADAqpZP3WK9PDw0r6AEjz7zFY6dzKj0PB8vAwDJ/vGFgK+XwelxExERNSRMthHRNVF0MiY8MLD2MoqMlq3D0Kt/GzdFRURERPWxffdpbN99usa511RVwGKx4v1PN1bafkP3NnaHkFY8/4bubA8QEVHTxmQbEV2zW/7cHePvvx5AeWKtgiSV3+GOjg3Cy2/dXWkfERERNTzfrtoNRa69h5qqCmzbdQoXMvJs27olxqBVdHCtz1VkCT3axyIhOthp8RIRETVE/OZLRNdMkiQkTx2Ctz9+ADeM6IjAIG/4+HmibYdI/OOZUXjn00kIDvXVOkwiIiKy49jJDNuQUXtOn71k+12SJMz922gE+BqrTbjJsoTIYD+8MPlmp8VKRETUUHGBBCJymrYdovD4s6O1DoOoCqtaCFWUQSf7Q5J46SMiqoksO34v/o9lY8IC8NmzE/DpDzuw7Nf9KCkzAwD8vAwYM7gT7hnRA/4+RqfGS0RE1BDxGwcRETVJQqjILv4WFwsWoti0HwAgSz4I8bkLYb4ToddFufDcAgfzT2PLpcMoU80I9wzEjeFdEahnD08iatg6XxeDdb8esTv/miJLaNsqrMr2kAAfPHbXYDw0tj/SswoAANGh/vDQKS6Jl4iIqCFiso2IiJocIaw4lfU35BavwNUzJqiiEJkFC5FVuBRtwr+Al76j0899tigDzx9YjJNFF6BIMiRIsAoV7x3/HqOj++Oh1n+CIvNLJxE1TGNu7oo1Gw7VWkaRJQzun4jAAO8ay3jqPRAfGeTs8IiIiBoFztlGREQuI4QF+aUbkV30LfJK1kFVS9xy3vT8ecgtXnn50R97Z1hhFYU4nnkPrGqxU8+bVpKFh3fOw+nijPIzCRUWYYWAgFWo+Pb8Rsw5/AWEcGw+JCIid7uuXRRGjehc435FluDr64mpyYPcGBUREVHjwp5tRETkdEIIZBZ8hIz8d2BRs2zbZckbob73IdL/MciS3iXnVkUpMvM/BFBbQkuFRc1GTvFyhPjc5bRzf3BiJYotZVCrJPjKCQDrMnbj1qg+6BLY2mnnJSJypsem3oRAfy988e12mE0WKIoMVQioqkC7tpF4+rFbEB7qp3WYREREDRaTbUREdM2KLUXYnLUJW7I2It+SBw8UoqXHMbQz5sN4VR9qVRQhI38+ik0H0Dp0ESTJw+mxFJT+DqvId6CkhOyib52WbMs2FeDXzH1Qa03yAYokY9n535hsI6IGS5YlTLx7AO4c0xM/b0pBemY+PA069OmRgNYtq87TRkRERJUx2UZERNfkdNFJ/N+x11BsLbpqq8Alczx2F8dhmP9BxOhzKu0rKN2Ii4WLEeZ7v9PjsVizHSwpYLFectp5jxek2k20AeVDSw/mnXHaeYmIXMXby4Bbh3XSOgwiIqJGh3O2ERFRvWWbsvDWsVdQYv3j3GcSAAkWyPgxLwnZFq8qz83MXwghal/trj50SqCDJSXolBCnn98RwoGkHBERERERNU5MthERUb1tyFyLMmtZLckjCQLA3uLYP2wXMFnPwmRNdXpMvp79oUiOzCUkEOQ92mnnbekTCQmS3XIKZCT6/bE+iIiIiIioqWCyjYiI6kUIgU2Xfq5xMQBbOcg4URYGs6h6yRGizOlxyZInQn3vB2pNfClQ5EAEet3mtPOGGvzRL+Q6yFLtl1YrVIyJ6e+08xIRERERUcPCOduIiKhWQggcKzyCXy7+hFNFJwAACd6t0S94EIqrDB+tngoZJaoeHkqpbZsED3go4S6JOdL/7yg1pyC35AeU31e6OiGoQJa80Dr0Uyiyt1PPO6nVzdiVcxRlVnO187dJkNAnuD26BbZx6nmJiByhqgKbj53F0s17cSg1E4okoXtCNO7q1wUd4yK0Do+IiKjJYM82IiKqkVVY8NGpd/Gfoy9jd84OZJuykG3Kwq6c7fi/46/V6Vi6PyS8Ar3+BEX2dW7Al0mSDi1D3kWLoH/D6NHOtl2WvBHqex/aR66Gt6Gz08/bwjscb3WbhjDP8nnjFEmGIsmQL19uh0V0x3NJ99rt/UbUXJWVlaFLly6QJAl79uyptG/fvn24/vrr4enpidjYWLz2Wt0+g5q7EpMZDy1chikf/g+/HD6J9NwCpObkY+XuI7hr3hd48dv1UFXOJ0lEROQM7NlGREQ1Wnr2M+zM2QoAlYaL2hs6WplAoFIEo2y6/FiGJOkQ7veg8wKthiQpCPYZh2CfcbCoeRDCBJ0cAEnycOl52/jG4PO+s7A9OwVbsw6jxGpChGcghkX0QKQx2KXnJmrsnnjiCURFRWHv3r2Vtufn52PYsGEYOnQo3nvvPezfvx/3338/AgICMHnyZI2ibVxmL12N34+Wr4RsvSqpVvH7kt/3IsDLEw8P76dJfERERE0Jk21ERFStXFMONl5a75SVMzsaUyFJACBBloxoFboQRn3iNR/XUTrZ323nAgBZktE7uD16B7d363mJGrMffvgBa9aswTfffIMffvih0r7PP/8cJpMJCxcuhF6vx3XXXYc9e/bgP//5D5NtDjiRkYU1+47ZLbdoww4kD+oOH0+DG6IiIiJqujiOhYiIqrU1+zfUvsiAY9oaVXTyMcJb3w0xAc8gKXoLfD37XnuARNRkZGRkYNKkSVi8eDG8vLyq7N+8eTMGDhwIvV5v2zZ8+HCkpKQgJyen2mOWlZUhPz+/0k9ztWz7QSiy/c9zk8WK1Q4k5YiIiKh27NlGRETVyiq7CAmS3X5tMmQk+LRBVtkl5JizbNt9dX4YGj4SN4XfzDnKiKhGQggkJydj6tSp6NGjB06fPl2lTHp6Olq2bFlpW3h4uG1fYGBglefMmTMHzz//vEtibmzScvKhCvu9lBVZRlp2801KEhEROQuTbUREVC297OgwIgnx3gl4rO1TOF10AvmWfHgr3kjwaQ1F4mWGqLmaOXMmXn311VrLHD58GGvWrEFBQQFmzZrl1PPPmjULjz32mO1xfn4+YmNjnXqOxsLTwwOyJMFqJ+EmhICnnp/bRERE14pXUyIiqtZ1/p3wU+YPdsupsCLJrzNkqbyHGxERAMyYMQPJycm1lklISMD69euxefNmGAyVE/w9evTA3XffjU8++QQRERHIyMiotL/icURERLXHNhgMVY7ZXPVvF4/lOw/ZLWcVAtcnxrs+ICIioiaOyTYiIqpWom8HhBrCkVV2scbVR2XICDaEItG3g5ujI6KGLjQ0FKGhoXbL/d///R9efPFF2+O0tDQMHz4cS5cuRe/evQEAffv2xezZs2E2m+HhUb6i8Nq1a5GYmFjtEFKq7Kak1gjyNiK3uLTG4aSKLKFDdDjaRYe5OToiIqKmh5PoEBFRtWRJxuSEv0Ev6yFXc7mQIUMv6zEl4W+QpGtfSIGImqe4uDgkJSXZftq2bQsAaNWqFWJiYgAA48ePh16vx8SJE3Hw4EEsXboUb731VqVholQzD52CN+69FTpFhlzN57UiS/AzeuLV8SM1iI6IiKjpYbKNiIhqFOvVAjPbP48k/86QrlqZVIKEjv5dMLP984jxaqFhhETUHPj7+2PNmjU4deoUunfvjhkzZuCZZ57B5MmTtQ6t0eieEIPPpt2B3q0rz1snSxKGJrXB0kfGIy4kQJvgiIiImhhJCAeWJmom8vPz4e/vj7y8PPj5+WkdDhFRg5JtysL54rMAypNwgfogjSMiajjYhmj4+G90xbmsXJzIyIIsyegQHYYQP2+tQyIiImqw6tOG4JxtRETkkCB9MIL0wVqHQURE1yg2OACxwQFah0FERNRkcRgpERERERERERGRkzDZRkRERERERERE5CRMthERERERERERETkJk21EREREREREREROwmQbERERERERERGRkzDZRkRERERERERE5CRMthERERERERERETkJk21EREREREREREROwmQbERERERERERGRkzDZRkRERERERERE5CRMthERERERERERETkJk21EREREREREREROwmQbERERERERERGRk+i0DqAhEUIAAPLz8zWOhIiIiBqTirZDRVuCGh6284iIiKg+6tPOY7LtKgUFBQCA2NhYjSMhIiKixqigoAD+/v5ah0HVYDuPiIiIrkVd2nmS4C1YG1VVkZaWBl9fX0iSpHU4bpOfn4/Y2FicO3cOfn5+WofTKLDO6ob1VXess7pjndUd66xuaqsvIQQKCgoQFRUFWeYsHQ0R23n8O3cU66zuWGd1w/qqO9ZZ3bHO6sbZ7Tz2bLuKLMuIiYnROgzN+Pn58Y+wjlhndcP6qjvWWd2xzuqOdVY3NdUXe7Q1bGzn8e+8rlhndcc6qxvWV92xzuqOdVY3zmrn8dYrERERERERERGRkzDZRkRERERERERE5CRMthEMBgOeffZZGAwGrUNpNFhndcP6qjvWWd2xzuqOdVY3rC9qjPi+rTvWWd2xzuqG9VV3rLO6Y53VjbPriwskEBEREREREREROQl7thERERERERERETkJk21EREREREREREROwmQbERERERERERGRkzDZRkRERERERERE5CRMthFWrlyJ3r17w2g0IjAwELfddlul/WfPnsUtt9wCLy8vhIWF4fHHH4fFYtEm2AakrKwMXbp0gSRJ2LNnT6V9+/btw/XXXw9PT0/Exsbitdde0yZIjZ0+fRoTJ05Ey5YtYTQa0apVKzz77LMwmUyVyrG+qnrnnXcQHx8PT09P9O7dG9u2bdM6pAZhzpw56NmzJ3x9fREWFobbbrsNKSkplcqUlpZi2rRpCA4Oho+PD8aOHYuMjAyNIm54XnnlFUiShOnTp9u2sc6qSk1NxYQJExAcHAyj0YiOHTtix44dtv1CCDzzzDOIjIyE0WjE0KFDcezYMQ0jJqoe23n1w3aefWzn1R/bedVjO+/asZ3nGLe08wQ1a19//bUIDAwU8+fPFykpKeLgwYNi6dKltv0Wi0UkJSWJoUOHit27d4tVq1aJkJAQMWvWLA2jbhj+/ve/i5EjRwoAYvfu3bbteXl5Ijw8XNx9993iwIED4osvvhBGo1G8//772gWrkR9++EEkJyeL1atXixMnTojly5eLsLAwMWPGDFsZ1ldVS5YsEXq9XixcuFAcPHhQTJo0SQQEBIiMjAytQ9Pc8OHDxaJFi8SBAwfEnj17xM033yzi4uJEYWGhrczUqVNFbGysWLdundixY4fo06eP6Nevn4ZRNxzbtm0T8fHxolOnTuKRRx6xbWedVZadnS1atGghkpOTxdatW8XJkyfF6tWrxfHjx21lXnnlFeHv7y+WLVsm9u7dK0aNGiVatmwpSkpKNIycqDK28+qP7Tz72M6rH7bzasZ23rVhO88x7mrnMdnWjJnNZhEdHS0+/PDDGsusWrVKyLIs0tPTbdvmz58v/Pz8RFlZmTvCbJBWrVol2rVrJw4ePFilEfbuu++KwMDASvXz5JNPisTERA0ibXhee+010bJlS9tj1ldVvXr1EtOmTbM9tlqtIioqSsyZM0fDqBqmzMxMAUD88ssvQgghcnNzhYeHh/jqq69sZQ4fPiwAiM2bN2sVZoNQUFAg2rRpI9auXSsGDRpka4Sxzqp68sknxYABA2rcr6qqiIiIEK+//rptW25urjAYDOKLL75wR4hEdrGdV39s59Uf23n2sZ3nOLbzHMd2nuPc1c7jMNJmbNeuXUhNTYUsy+jatSsiIyMxcuRIHDhwwFZm8+bN6NixI8LDw23bhg8fjvz8fBw8eFCLsDWXkZGBSZMmYfHixfDy8qqyf/PmzRg4cCD0er1t2/Dhw5GSkoKcnBx3htog5eXlISgoyPaY9VWZyWTCzp07MXToUNs2WZYxdOhQbN68WcPIGqa8vDwAsL2ndu7cCbPZXKn+2rVrh7i4uGZff9OmTcMtt9xSqW4A1ll1vvvuO/To0QPjxo1DWFgYunbtig8++MC2/9SpU0hPT69UZ/7+/ujdu3ezrTNqeNjOqx+2864N23m1YzuvbtjOcxzbeY5zVzuPybZm7OTJkwCA5557Dv/85z+xYsUKBAYGYvDgwcjOzgYApKenV2qAAbA9Tk9Pd2/ADYAQAsnJyZg6dSp69OhRbRnWWc2OHz+OefPmYcqUKbZtrK/KLl26BKvVWm2dNMf6qI2qqpg+fTr69++PpKQkAOXvGb1ej4CAgEplm3v9LVmyBLt27cKcOXOq7GOdVXXy5EnMnz8fbdq0werVq/Hggw/i73//Oz755BMAVz6b+HdKDRnbeXXHdt61YTvPPrbzHMd2nuPYzqsbd7XzmGxrgmbOnAlJkmr9OXLkCFRVBQDMnj0bY8eORffu3bFo0SJIkoSvvvpK41fhXo7W2bx581BQUIBZs2ZpHbKmHK2vq6WmpmLEiBEYN24cJk2apFHk1JRMmzYNBw4cwJIlS7QOpUE7d+4cHnnkEXz++efw9PTUOpxGQVVVdOvWDS+//DK6du2KyZMnY9KkSXjvvfe0Do2I7bx6YDuvbtjOo4aA7TzHsJ1Xd+5q5+mcejRqEGbMmIHk5ORayyQkJODChQsAgA4dOti2GwwGJCQk4OzZswCAiIiIKqvjVKxcEhER4cSoteVona1fvx6bN2+GwWCotK9Hjx64++678cknnyAiIqLK6i5Nrc4cra8KaWlpGDJkCPr164cFCxZUKtcc6qsuQkJCoChKtXXSHOujJg8//DBWrFiBX3/9FTExMbbtERERMJlMyM3NrXQHrznX386dO5GZmYlu3brZtlmtVvz66694++23sXr1atbZH0RGRla6NgJA+/bt8c033wC48tmUkZGByMhIW5mMjAx06dLFbXFS88R2Xt2xnVc3bOe5Dtt5jmE7z3Fs59Wd29p51zCvHDVyeXl5wmAwVJo412QyibCwMNsKQRUT5169Os77778v/Pz8RGlpqdtj1tqZM2fE/v37bT+rV68WAMTXX38tzp07J4S4MhGsyWSyPW/WrFnNdiLY8+fPizZt2og777xTWCyWKvtZX1X16tVLPPzww7bHVqtVREdHc+JcUT5h6bRp00RUVJQ4evRolf0Vk8B+/fXXtm1Hjhxp1pPA5ufnV/rc2r9/v+jRo4eYMGGC2L9/P+usGnfddVeViXOnT58u+vbtK4S4MnHu3LlzbfsrrqlcIIEaCrbz6o7tvLpjO6/u2M6rGdt5dcd2Xt25q53HZFsz98gjj4jo6GixevVqceTIETFx4kQRFhYmsrOzhRBXloQfNmyY2LNnj/jxxx9FaGgol4S/7NSpU1VWqcrNzRXh4eHinnvuEQcOHBBLliwRXl5ezXKJ8/Pnz4vWrVuLG2+8UZw/f15cuHDB9lOB9VXVkiVLhMFgEB9//LE4dOiQmDx5sggICKi0Wlxz9eCDDwp/f3+xYcOGSu+n4uJiW5mpU6eKuLg4sX79erFjxw7Rt29f28WTyl29SpUQrLM/2rZtm9DpdOKll14Sx44dE59//rnw8vISn332ma3MK6+8IgICAsTy5cvFvn37xOjRo+u8JDyRq7Gdd23Yzqsd23n1w3ZezdjOcw6282rnrnYek23NnMlkEjNmzBBhYWHC19dXDB06VBw4cKBSmdOnT4uRI0cKo9EoQkJCxIwZM4TZbNYo4oalukaYEELs3btXDBgwQBgMBhEdHS1eeeUVbQLU2KJFiwSAan+uxvqqat68eSIuLk7o9XrRq1cvsWXLFq1DahBqej8tWrTIVqakpEQ89NBDIjAwUHh5eYkxY8ZUavhT1UYY66yq77//XiQlJQmDwSDatWsnFixYUGm/qqri6aefFuHh4cJgMIgbb7xRpKSkaBQtUfXYzrs2bOfVju28+mM7r3ps5zkH23n2uaOdJwkhhOODTomIiIiIiIiIiKgmXI2UiIiIiIiIiIjISZhsIyIiIiIiIiIichIm24iIiIiIiIiIiJyEyTYiIiIiIiIiIiInYbKNiIiIiIiIiIjISZhsIyIiIiIiIiIichIm24iIiIiIiIiIiJyEyTYiIiIiIiIiIiInYbKNiJqt5ORkSJIESZKg1+vRunVr/Otf/4LFYgEACCGwYMEC9O7dGz4+PggICECPHj3w5ptvori4GABw8OBBjB07FvHx8ZAkCW+++aaGr4iIiIiIKrCtR0RaYbKNiJq1ESNG4MKFCzh27BhmzJiB5557Dq+//joA4J577sH06dMxevRo/Pzzz9izZw+efvppLF++HGvWrAEAFBcXIyEhAa+88goiIiK0fClERERE9Ads6xGRFiQhhNA6CCIiLSQnJyM3NxfLli2zbRs2bBgKCgrw6KOP4o477sCyZcswevToSs8TQiA/Px/+/v6VtsfHx2P69OmYPn26G6InIiIiotqwrUdEWmHPNiKiqxiNRphMJnz++edITEys0vgCAEmSqjS+iIiIiKjhY1uPiNyByTYiIpTfwfzpp5+wevVq3HDDDTh27BgSExO1DouIiIiInIBtPSJyJybbiKhZW7FiBXx8fODp6YmRI0fijjvuwHPPPQeOsCciIiJq/NjWIyIt6LQOgIhIS0OGDMH8+fOh1+sRFRUFna78Y7Ft27Y4cuSIxtERERER0bVgW4+ItMCebUTUrHl7e6N169aIi4uzNb4AYPz48Th69CiWL19e5TlCCOTl5bkzTCIiIiKqB7b1iEgLTLYREVXj9ttvxx133IG77roLL7/8Mnbs2IEzZ85gxYoVGDp0KH7++WcAgMlkwp49e7Bnzx6YTCakpqZiz549OH78uMavgIiIiIhqwrYeEbmSJDhYnYiaqeqWg7+aqqpYsGABFi5ciIMHD0Kn06FNmza49957MWnSJBiNRpw+fRotW7as8txBgwZhw4YNrn0BRERERFQjtvWISCtMthERERERERERETkJh5ESERERERERERE5CZNtRERERERERERETsJkGxERERERERERkZMw2UZEREREREREROQkTLYRERERERERERE5CZNtRERERERERERETsJkGxERERERERERkZMw2UZEREREREREROQkTLYRERERERERERE5CZNtRERERERERERETsJkGxERERERERERkZMw2UZEREREREREROQk/w/X9IO2yc9n+QAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cancer_types = list(np.unique(nci_labs))\n", "nci_groups = np.array([cancer_types.index(lab)\n", " for lab in nci_labs.values])\n", "fig, axes = plt.subplots(1, 2, figsize=(15,6))\n", "ax = axes[0]\n", "ax.scatter(nci_scores[:,0],\n", " nci_scores[:,1],\n", " c=nci_groups,\n", " marker='o',\n", " s=50)\n", "ax.set_xlabel('PC1'); ax.set_ylabel('PC2')\n", "ax = axes[1]\n", "ax.scatter(nci_scores[:,0],\n", " nci_scores[:,2],\n", " c=nci_groups,\n", " marker='o',\n", " s=50)\n", "ax.set_xlabel('PC1'); ax.set_ylabel('PC3');" ] }, { "cell_type": "markdown", "id": "d41c234d", "metadata": {}, "source": [ "On the whole, cell lines corresponding to a single cancer type do tend to\n", "have similar values on the first few principal component score\n", "vectors. This indicates that cell lines from the same cancer type tend\n", "to have pretty similar gene expression levels." ] }, { "cell_type": "markdown", "id": "ed8042b5", "metadata": {}, "source": [ "We can also plot the percent variance\n", "explained by the principal components as well as the cumulative percent variance explained.\n", "This is similar to the plots we made earlier for the `USArrests` data." ] }, { "cell_type": "code", "execution_count": 52, "id": "9b1b74c2", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:02.098796Z", "iopub.status.busy": "2024-06-04T23:20:02.098709Z", "iopub.status.idle": "2024-06-04T23:20:02.211186Z", "shell.execute_reply": "2024-06-04T23:20:02.210897Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(15,6))\n", "ax = axes[0]\n", "ticks = np.arange(nci_pca.n_components_)+1\n", "ax.plot(ticks,\n", " nci_pca.explained_variance_ratio_,\n", " marker='o')\n", "ax.set_xlabel('Principal Component');\n", "ax.set_ylabel('PVE')\n", "ax = axes[1]\n", "ax.plot(ticks,\n", " nci_pca.explained_variance_ratio_.cumsum(),\n", " marker='o');\n", "ax.set_xlabel('Principal Component')\n", "ax.set_ylabel('Cumulative PVE');" ] }, { "cell_type": "markdown", "id": "632a2c2c", "metadata": {}, "source": [ "We see that together, the first seven principal components explain\n", "around 40% of the variance in the data. This is not a huge amount\n", "of the variance. However, looking at the scree plot, we see that while\n", "each of the first seven principal components explain a substantial\n", "amount of variance, there is a marked decrease in the variance\n", "explained by further principal components. That is, there is an\n", "*elbow* in the plot after approximately the seventh\n", "principal component. This suggests that there may be little benefit\n", "to examining more than seven or so principal components (though even\n", "examining seven principal components may be difficult)." ] }, { "cell_type": "markdown", "id": "affa23a9", "metadata": {}, "source": [ "### Clustering the Observations of the NCI60 Data\n", "\n", "We now perform hierarchical clustering of the cell lines in the `NCI60` data using\n", "complete, single, and average linkage. Once again, the goal is to find out whether or not the observations cluster into distinct types of cancer. Euclidean\n", "distance is used as the dissimilarity measure. We first write a short\n", "function to produce\n", "the three dendrograms." ] }, { "cell_type": "code", "execution_count": 53, "id": "9b95fed9", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:02.213627Z", "iopub.status.busy": "2024-06-04T23:20:02.213362Z", "iopub.status.idle": "2024-06-04T23:20:02.216618Z", "shell.execute_reply": "2024-06-04T23:20:02.216339Z" } }, "outputs": [], "source": [ "def plot_nci(linkage, ax, cut=-np.inf):\n", " cargs = {'above_threshold_color':'black',\n", " 'color_threshold':cut}\n", " hc = HClust(n_clusters=None,\n", " distance_threshold=0,\n", " linkage=linkage.lower()).fit(nci_scaled)\n", " linkage_ = compute_linkage(hc)\n", " dendrogram(linkage_,\n", " ax=ax,\n", " labels=np.asarray(nci_labs),\n", " leaf_font_size=10,\n", " **cargs)\n", " ax.set_title('%s Linkage' % linkage)\n", " return hc" ] }, { "cell_type": "markdown", "id": "55c3a79d", "metadata": {}, "source": [ "Let’s plot our results." ] }, { "cell_type": "code", "execution_count": 54, "id": "6c58d281", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:02.218730Z", "iopub.status.busy": "2024-06-04T23:20:02.218629Z", "iopub.status.idle": "2024-06-04T23:20:03.019903Z", "shell.execute_reply": "2024-06-04T23:20:03.019670Z" } }, "outputs": [ { "data": { "image/png": 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MYzX21u+hUKyR0+a95XGjVY2sPlc57VgmybJly7Rnz56aK1curVq1qkZEROjSpUt9fr31Z5j7779fy5Ytq1999ZUePXpUjx49ql9++aVeddVV2qdPH5/jqKpWrFgxxSbdqFGjtGLFij7HyWiNrOJYf8a3Wi+LWE7c56va1uhSIXOx/L1790rlypU9v8+fP1/uvPNOz0X/+vfvL61bt85ycRA8+/fvl8jIyFSXZ8uWTQ4ePBjEjGxYrpdVrBo1alzx2LfffiuPPvqobNu2TYYMGSIPP/xw0OLEx8cn+z0xMVEmTZokzz77rLjdbnn99delW7duQcvHklVOVmPvtFq3adNGli5dKrfccouMHTtWWrZsKRERETJhwgSvrw0Uq1pbxenfv/8Vj/3zzz/y3HPPyZtvvim1a9eWl156yWscq7FPsmTJElm+fLnkzZvX81i+fPlk5MiRUq9ePZ9iDBs2TGJiYtJ8zujRo32K9ddff6V4vYsbb7zR59P2nbZNE7GtUUZZzlerWKEaR8Ru7K3ihGqNnDbvrY+HLWpk9bnKaccyo0aNkkmTJsnRo0fl7rvvlqVLl0qNGjUkMjJS8uXL5/X1SazH7NNPP5VPPvlEGjVq5HmsdevWEh0dLR07dpQ333zT51i7du2SNm3aXPF427Zt5fHHH/f6eqsaWcWxei9a5WMdy0n7fMv1SknINMLcbrfn4rQiIsuXL5dhw4Z5fs+dO7ccPnw4y8WZPXt2mst9vSOHVRwn5mQVp1ixYrJx40a5+uqrU1y+fv16z/V+gpGP09bLOlaS1atXy9ChQ+W7776TXr16yVdffZWu76ZbxZk5c6Y8/vjjcvDgQXnsscekX79+EhUVFdR8XC5XsotsX/57emUkp0CMvRNq/fXXX8t///tfeeCBBzJ0TQfLMbOqdSDG7PTp0zJ69Gh55ZVXpFSpUjJz5sx0/aOOxdhHRUXJ8ePHr3j8xIkTkj17dp9ibNiwIc3n+jOGV199tXz00UdXHNjPmDEjXe8tp2zTLGpktT+zmq+WsUI1jojd/LCKE8o1SuKEeW+977CokdXnKqcdywwdOlSGDh0qw4cPz9BF0a3X69SpU1KoUKErHi9YsKCcOnXKr9xKlCghCxYsuCK3b7/9VkqUKOH19VY1sopj9V60ysc6lpP2+ZbrlaIMn1PmEHXq1NFRo0apqurGjRvV7Xbrrl27PMsXL16spUqVynJx0voO+qU/wYrjxJys4vTt21erVq2qp0+fvmLZqVOntGrVqtqvX7+wXS/rWDt27NCOHTtqRESE3n333cm+RuYPqziLFy/W2rVra0xMjD722GN65MiRTMvH5XJp7ty5NU+ePJonTx51uVwaHx/v+T137tx+nVJskZPl2Dup1suWLdNevXppXFyc1qpVS1999VU9ePBgur4iYzVmVrW2HLMLFy7om2++qYULF9bSpUvr1KlTNTEx0afXXspq7FVVu3TpolWqVNHly5drYmKiJiYm6rJly7Rq1ararVs3r6+3vhbGJ598ohEREdqiRQsdPny4Dh8+XFu0aKHZsmXTmTNn+hzHSds0y2sgWezPrOarZaxQjWM59lbzLFRrpOqseW+577CqkdXnKqcdy7z44otarlw5LVGihA4ZMkQ3bNigqur3e9FyvVRVmzRpoh06dEgW79SpU9qhQwdt2rSpz3FUVd944w3Nnj279unTR6dOnapTp07V3r17a1RUlE6YMMHr661qZBXH6r1olY9lLKft8y1rlJKQaYTNnDlTs2fPrk2aNNFChQrprbfemmz5kCFDtEOHDlkuDoJn3759WrRoUS1RooS+9NJL+tlnn+lnn32mI0eO1BIlSmjRokV13759mZ2m3yzXyyrWAw88oNmzZ9cWLVromjVr0r1uVnFatWqlkZGR2rt3b/3rr78yPZ8pU6b49BPMnKzG3mm1TnLixAlNSEjQevXqaWRkpLrdbh07dqweO3bMp9dbjplVra3izJgxQ8uVK6cFChTQsWPH6tmzZ31aj8tZjX2Sw4cPa9u2bdXlcmn27Nk1e/bs6na7tV27dj59IHG73eYXhV21apV27txZr732Wr322mu1c+fOunr1ap9f77RtWiBqZCGj8zUQsUItjtXYB+I9FGo1ctq8tzxutKqR1ecqpx3LJFm8eLF27dpVY2JitHr16hoREaHff/+9z6+3/gyzfv16LVq0qObLl0+bNGmiTZo00Xz58mmxYsV048aNfq/fzJkztV69epo3b17Nmzev1qtXTz/77DO/YmS0RlZxrD/jW62XRSyn7vMta3SpkGmEqap+++23OmDAAB05cuQVd7R45plndNGiRVkyTlouXryoc+bMcUwcy1iZEWfPnj3aqlUrz916XP//7i+tWrVK1u0PVj5WcSzXyyKWy+XS6Ohoz53eUvsJZpzIyMhkZ/Sk9BOsfJYsWaLnz5/3+jxfWOWkajf2Tqp1Sn755RcdPHiwFi5cWHPkyKFt2rTx+hrLMVO1m7NWYxYTE6M9e/bUgQMHpvrjSxyLsVdVTUxM1F9//VVPnTql27dv19mzZ+vs2bN1+/btPr0+KR+rA75z585pjx49MryfcOI2LRgHxRnZL6ZnvgY6VijEceIZYSkJlRo5ad6r2u2DLMff6nOVk45lLnfs2DGdMGGC1qpVSyMiIrRu3bqes4+CsV6XOnnypL799ts6aNAgHTRokL7zzjt66tQpv2KcP39en332Wf3tt9/8/vupyUiNrOIE4jO+1XplJJbT9/mWNVJVdale8iVXZBk7duyQSZMmyZQpU+TgwYNy/vz5TI3jxJwyEufw4cOyY8cOUVUpV66c5MmTJ105WOVjFcdyvTIS69lnn/XpeU8//XRQ4rz77rs+xfF24VOrfCIiIuSvv/5K13VBApXTpTIy9k6rdVouXrwoc+bMkUmTJnm93oHlmF3Kas5mJE6jRo28XhPC5XLJwoUL03yO1diL/Hth4hw5csimTZvSfY2fd999Vzp16pSu69KlJD4+XtauXStlypRJdwynbdOsa3Q5y2MQf+ZrsGJl5ThWYx/o91CSrFwjp837S2V0HxSs8U8PJxzLpGXDhg2SkJAg06ZNkwMHDvj8uoyO2fnz56VixYryxRdfSKVKlfxN+wqxsbGyceNGKV26dIZjXS69NQpUHCuW+fgTKyvt801qlO4WmsP8+uuvPv1ktTiXOnXqlL777rtav359dbvd2rBhQ33zzTf9/rqeVRwn5mS5bpfbsmWLlitXLlPycdp6BSOW01y4cCFofytY/yJjyXLsg1lrK8EcM6taO3G++jP2lStX1mXLlqX7b23dulV/+umnZI99++232qhRI73hhhv0hRde8Cte165dU7xFvFP5UmvrGqkGdn8GO1ZjH4j3kFNkxXWz2L/6s++wqlEgPlelxInHMufOnctwDH/Xq2jRorp58+YM/11V1bZt2/p8aYj0sqiRr3GC9V70NR/LWFlxn5+RGoXMXSNLly6d4r9Yq6rncZfLJRcuXMhScUREfv75Z5k4caJ8+OGHctVVV0nnzp3lxx9/lDfeeCPZ7VuDFceJOVmuW2rOnj0rO3fuDGo+TluvQMRav369bNu2TUREypcvL9WrV0/X37aKc7lt27ZJQkKCTJ06Vf7666+g5ePtDJz0CFSNRGzeR5lR6/vuu8/rc1wulyQkJPj0vGCwmrO+xlm0aJHUq1fP5zsxpkd6xn7kyJEyePBgefPNN6Vq1ap+/82hQ4dKtWrVpFatWiLy712M2rRpI/Xr15fq1avLiBEjJCYmRgYMGOBTvHLlysnw4cPlhx9+kOuuu05y5syZbPl///tfv/JzwjbNskYW+zPL+WoVK1TjWI295XsoVGt0KSfMe2/82QdZ1cjyc1Vagn0sM378eK/xXC6X9OvXL0M5+bteDz30kLz00ksyceJEyZYtY+2CVq1ayaOPPiobNmxIcd/Ytm3bNF9vVSOrOFbvRcuxt4rltH1+oOdHyDTC1qxZk+LjqioffvihjB8/XmJjY7NcnOrVq8uxY8fknnvukR9//FGqVKkiIiKPPvqo19cGIo4Tc7JcNwuhul7WVqxYIT179pTNmzd7bkPscrmkSpUqkpCQIDfccENQ41zq1KlTMmPGDJk0aZIsW7ZMrr/+ehk0aFBQ8+nevbvXU5NnzpwZ1JwCIbNrPWXKFClVqpTUrFkz2e2w08NyzJykadOmkiNHDqlTp440btxYGjduLHXq1MnwwXFGxl5EpGvXrnLq1CmpUaOGZM+eXaKjo5Mt/+eff9J8/cqVK2XIkCGe3z/44AMpX768zJs3T0T+3Qa/+uqrPn+ITUhIkNy5c8uqVatk1apVyZa5XC6fG2FO2qZZ1chqf2Y5X61ihWocq7G3nGehWiMRZ817S1Y1svpcFSjprfWYMWO8PseiEeavn3/+WRYsWCDz58+XatWqXdG88udY5sEHHxQRkdGjR1+xzOVyycWLF9N8vVWNrOJYvRctx94qltP2+QGfH+k+lywL+Oabb/S6667TuLg4ffrpp9N1N6HMjpM9e3bt0qWLzp8/P9mt6v29bahVHCfmZLluaVm7dq263e6g5eO09bKMtWnTJo2NjdUbbrhBp02bpmvWrNE1a9boBx98oNdff73GxcX5tI5WcZIsW7ZMe/bsqbly5dKqVatqRESELl261OfXW+Xjcrn0rrvu0u7du6f5E8ycvPH3feSUWj/44IOaJ08eveaaa3TcuHF66NAhn3O4lOWYeWM1Z32Ns2fPHp00aZJ269ZNS5UqpS6XS3PmzKk333yzjhgxQpcvX64XL170+e9mdOyTZPQOnTly5NC9e/d6fm/SpIk++eSTnt937Nih8fHxfueVEU7bplnVyGp/ZjVfLWOFahyrsbecZ6FaI6fNe2/82QcFcjtr9fnsUsE+lgkWf9crGMcyoSQQ78XM4LR9fqCFZCNs1apV2qxZM42KitKHHnoo3ddtcUKc33//XZ9//nm96qqrtGjRovrwww/r6tWrNTIy0q83klUcJ+ZkuW5p8XUnEqrrZRmrQ4cO2r59+2QbxySJiYnarl07n249bBXnlVde0cqVK2uxYsX0kUce0bVr16qq/xtsq3wsrzdllZM3vo6902qtqnrmzBmdNm2aNmvWTGNiYrRDhw46d+7cFGOnJpjXCAt2I+xyO3fu1ISEBO3SpYuWLFlS3W63TwdGVmNvpWjRop5rYVy8eFFz5cqlX3zxhWf55s2bNVeuXOmKnZiY6Nf7J4nTtmlWNbLcn1nMV+tYoRjHauyt51ko1shp894bf/YdgdjOWn0+S0mwj2WCxfJYH/8nkO/FzODEfX4ghVQjbMeOHdqxY0eNiIjQu+++W3fu3BkScZIsWLBAO3furNHR0epyuXTw4MG6devWTIvjxJwyEsfbLZDj4uL83omE2npZxcqfP7/+/PPPqS5fsWKF5s+fP2hxIiIi9PHHH7/iwqb+HtBY5eN2u812plY5WY2902p9uT179ugzzzyjZcuW1ZIlS+rx48d9ep3lmFnVOhDbtCRJZ4l17dpVc+XKpdHR0V5fYzX2l7pw4YJ+/PHHOnz4cB0+fLh+8sknev78eZ9ee8899+itt96qe/fu1VGjRmlsbKyeOHHCs/yTTz7R6tWr+5XPxIkTtUqVKpo9e3bNnj27VqlSRd955x2fX++0bVogamR5DJLe+RrIWKESx2rsA/EeShIqNXLavLfcd1iOv8XnKqcdy7z77rs+/QRrvS63f/9+Xbp0qS5dujRDxzjffvut3nLLLVq2bFktW7as3nLLLfrNN9/49FqrGlnFUbV5L1rmYxXLaft8yxqlJGSuEfbggw9KQkKCNG7cWFauXCnXXHNNSMS5VJMmTaRJkyZy9OhR+eCDD2TSpEnyyiuvSNWqVWX9+vVBj+PEnDISZ+zYsT7/nWDkYxXHcr2sYh0/flwKFSqU6vLChQvL8ePHgxbnueeek8mTJ8t7770nd999t3Tp0iVdF9+2yke9XLNky5YtkpCQIK+88krQcrIae6fV+nJut1tcLpeoqtfrVlzKcsysam059/fu3SuLFy+WRYsWyeLFi+Xvv/+WG2+8UerXry9ffPGF1K5d22sMq7FPsmnTJmnbtq3s27dPKlSoICIiL730khQoUEDmzJnjNfYLL7wgzZs3l1KlSklERISMHz8+2XVQ3nvvPWnSpInP+Tz11FMyevRo6devn9StW1dERJYtWyYDBw6UvXv3yvDhw73GcNo2zbpGIrbHIOmdr4GMFSpxrMY+EO+hJKFSI6fNe8t9h1WNrD5XOe1Ypnv37hIbGyvZsmVL9TjC5XJJ165d04xj/Rnm2LFj8tBDD8mHH37omRMRERFy1113yeuvvy7x8fE+x3rjjTekf//+cuedd0r//v1FRGT58uXSunVrGTNmjDz00ENpvt6qRlZxrN6LVvlYxnLaPt+yRilKdwvNYVwul0ZHR2vNmjXT/MlqcbxZs2aN9uvXzzFxLGM5LY6VUF0vf5QvX14/+eSTVJd//PHHWr58+aDFSbJ48WLt2rWrxsTEaPXq1TUiIkK///57n19vlc/ixYuvOKvlxIkTOnHiRK1bt666XC6tUqVKUHOy5pRaqyb/ikyOHDn0zjvv1C+//NKv615ZjpnTlClTRnPnzq233HKLvvTSS7ps2TKfz7pKSUbHPkmdOnW0TZs2+s8//3ge++eff7Rt27Zat25dn2KcP39e165dq3/88ccVy9auXevXtYPy58+v06ZNu+LxadOmab58+XyK4bRtmqptjVLjz/7MYr5axwrVOFZjb/keCsUaOXHeW7KoUbA+V/kro7WuXLmy5suXT/v376/r1q0LYKb+6dixo5YrV07nzp2rR48e1aNHj+rcuXO1QoUKetddd/kVq1ixYvrqq69e8fhrr72mRYsW9fp6qxpZxbF6L1qOvWUsJ+3zAz0/QqYR9swzz/j0k9XiIHj++ecfHT9+vB49evSKZUeOHEl1mdNZrpdVrKeeekpLliypGzZsuGLZ+vXrtVSpUjps2LCgxbncsWPHdMKECVqrVi2NiIjQunXr6qhRozIln++//1579OihOXPmVLfbrQ8//LBu2bLF59db5RSo+ZHZtX7ggQc0T548Wr16dR07dqwePHjQ73W4XEbHzKrWVnEKFy6suXPn1jZt2uioUaN05cqV6boe0+XSO/ZJcuTIoRs3brzi8Q0bNmiOHDkynN/mzZv14Ycf9vn58fHxum3btise37p1q88Xg3baNs0bf2uUUZbz1SpWqMbxxmrs/YkTqjVy2rwP5vGwrzWy+lzltGMZVdXly5fr/fffr/Hx8XrdddfpG2+84XcO1usVExOj33333RWPL126VGNiYvzKLWfOnLp9+/YrHt+2bZvmzJnTpxgWNbKKY/kZ32q9rGOlJtj7fNXArpdLNYP3n0ZANW7cWFwuV5rPcblcsmDBgqDEcWJOVnGee+45Wb9+vXz88ccpLu/YsaPUqFFDnnjiiaDk47T1sox15swZadq0qfz000/SvHlzqVSpkqiqbNmyRb799lupVauWLFy4UHLkyBGUOGnZsGGDJCQkyLRp0+TAgQNByefAgQMyZcoUmTRpkhw9elTuvvtuueeee6Ru3bqybt06qVy5ss/5W+Vk+T5KTWbU2u12S8mSJaVmzZppzjdvtwq3HDOrWluO2S+//OL5auSSJUvkzJkzctNNN0mjRo2kYcOGct1114nb7fa+cqnwZ+yT1KhRQ8aMGXPFafoLFy6U/v37y4YNG/zO4+TJk/Lhhx9KQkKCLF++XCpXriwbN2706bX9+vWTyMjIK24R/8gjj8jp06fl9ddf9xrDadu0lKSnRlb7M6v5ahkrVOOkJCPzwyJOqNbIafM+0Pt7q/dRejjtWOZSp0+flo8//lgmT54sK1askHbt2smkSZMkKirK62ut16tkyZLy5ZdfSrVq1ZI9vn79emndurX8/vvvPsUREbnnnnukZs2aMnjw4GSPv/LKK7Jy5Ur58MMPfY6VkRoFIo4Vy3ys1y0z9/mXCsSYhUwj7MyZMzJ//nxp3LixxMXFJVt27NgxWbx4sbRo0cJrsZwWZ+DAgakuO378uEybNk3Onj3r9ZoGVnGcmJNVnGuuuUZGjRolTZs2TXH5ggUL5JFHHpE1a9YEJR+nrZd1rHPnzsmYMWNk+vTpsm3bNhERKV++vHTq1EkGDhzo84bNKo4358+fl8jIyKDkEx0dLXfeeafce++90rx5c0+DITIy0u+milVOlmPvTTBr3b17d687axGRyZMnp7nccsysah3IMduyZYvnemHz588XEZEjR474Hedyvo69iMhXX30lQ4YMkWeeeUbq1KkjIv9ed2T48OEycuRIuemmmzzPzZUrV5qxfvjhB0lISJCPPvpITp8+LQMHDpRevXpJxYoVfc69X79+MnXqVClRooQnn59++kn27t0rXbt2TbZelzfLLuW0bVqSjNTIan9mNV8tY4VqnEtZzA+LOKFcIyfN+0DtOzJSI6vPVU48lrnc0qVL5emnn5alS5fK33//LXny5PH6Guv1evvtt+Xjjz+W9957TwoXLiwiIvv27ZNu3brJ7bffLr179/Z5fZ5//nl55ZVXpF69ep7rZy5fvlx++OEHefjhh5Ptn//73//6FDM9NbKKY/VetMonULGcsM9PiWWNQqYRNm7cOJk9e3aqncVmzZpJu3btpG/fvlkqTkouXLggr7/+urzwwgsSHx8vzz33nHTq1CnT4jgxp/TEiYuLk02bNknJkiVTXL53716pWrWqHDt2LCj5WMWxXK9A1uhSv//+uwwfPlzefvvtoMQZP36811gul0v69esXlHwqVqwoZ8+elXvuuUe6dOni2emktxFmkZPV2Dut1lYsx8yq1oGar/v37/ecHbZo0SLZvn27REVFyenTp9N8nfXYX3oGWtKH2qRDmkt/d7lcKR5sWZ7FJ/Lvv4D6wuVyycKFC/2KnSTY2zTrGl3K8hgE9qzGPpDvocwWrHUL9ry33HdY1cjqc5VTj2X++OMPeffdd2Xy5Mly8uRJuffee+W+++7zuZFqvb+vWbOm7NixQ86ePeuJuXfvXomKipJy5cole+7q1avTjFWmTBmf/qbL5ZJdu3alujyjNbKKY/0Z32q9LGI5dZ9vWaNkTL5g6QA33HCDzp49O9Xlc+bM0RtuuCHLxbnc+++/r2XLltUiRYro66+/nu4LFlvFcWJO6Y0THx+vy5YtS3X5smXLfL7Oi0U+VnEs1ytQNbrc2rVr03Wb5/TGKV26tNefMmXKBC0f1f+7zlRsbKxee+21Onr0aM2WLZtu3rw5w3mkJyersXdirZMcPnxYf/75Z/3555/18OHDfv9NqzGzqrVVnP379+uMGTP0gQce0IoVK6rb7daoqCitX7++PvXUU7po0SI9c+aM1zjWY7948WKff1KSI0cOvffee3Xu3LnJLpCdLVs23bRpk895BFOwt2mBqpHFfjGj8zUQsUIpjtXYB+o9FEo18ibY897yWM+qRlafq5x2LDNjxgxt2bKlRkdHa7t27fTzzz/XCxcueH3d5ayPz329DlYwrndtVSOrOFbvRat8LGM5bZ9vWaOUZMtYG805tm/fLjVq1Eh1efXq1WX79u1ZLk6SuXPnyqOPPiq7d++WRx55RAYNGpTsdqbBjuPEnDIap2bNmvLZZ595vtJyuVmzZknNmjWDlo9VHMv1sq6RU+zevTuzU7hCvXr1pF69ejJ+/HiZPn26TJ48WS5evCgPPvig3HPPPdKuXTspUKBA0PKxGnsn1nrPnj3y0EMPybx585KdUdSyZUt57bXXpHTp0j7FsRozq1pbxSlcuLBERkbK9ddfL3fccYc0btxYbrzxRomOjvb62ktZj33Dhg0z9PpSpUrJ999/LyVLlpRSpUpl/F8W/78dO3bIzp07pUGDBhIdHe05Ky2YrGptXSOL/aLVfLWMFYpxrMbe+j0UijWyYjXvLY/1rGpk9bnKaccynTp1kpIlS8rAgQOlUKFCsmfPnhSvJ+ntK4PWx+dPP/20z8/11blz52T37t1y1VVXSbZsvrcgrGpkFcfqvWiVj2Usp+3zLWuUIrOWWiaLjY3VlStXprp85cqVGhsbm+Xi/PTTT9qoUSPNkSOHDhgwIN13trGK48ScrOJ88sknmi1bNn311VeTdZsvXLig48eP18jISP3444+Dlo/T1ss6VlqCfUaYL37//fcMx/A1n2effVZPnjx5xeNJd2spWLCgZsuWLcP5+JNTsMZeNbi13rt3rxYqVEiLFy+uL774os6aNUtnzZqlL7zwghYvXlwLFy6sv/32m9c4lmNmVWurOHPnztUTJ074lHtG+Tv2S5cu1c6dO2vdunU9r506dWqKd7tKieWZl3///bc2adJEXS6Xut1u3blzp6qq9ujRQwcNGuR3vJRkxjbNokZW+zOr+WoZK1TjqNrND6s4oVyjtAR73lvv7y1qZPW5ymnHMqVKlTI5sywQ63X48GF955139NFHH9VDhw6pquqqVav83k+fPHlS77vvPo2IiNCIiAjPvrFv3746YsQIr6+3qpFVHKv3olU+1rGctM+3XK+UhMw1wurUqSPt27eXoUOHprh8xIgR8vnnn8vy5cuzVBy32y3R0dFy//33p/kda2+dUKs4TszJct2eeOIJGTFihMTFxUnZsmVFRGTXrl1y4sQJGTx4sIwcOdJrjFBdr0DESs26devk2muvTddFFK3j7Nu3T1544QVJSEiQU6dOBSWfiIgI+euvv6RgwYIpLr9w4YLMnj1bbr/99gzl409OIoEf+8yodc+ePWXHjh0yb968K+7Idfr0aWnZsqWUK1dOJk6cmGYc6zGzqrX1mK1fvz7ZhZyrV6/u1+tTk56x//TTT6VLly7SuXNnee+992Tz5s1StmxZee211+Srr76Sr776yue/f+LECc9ZfMuXL5eGDRv6feZl165d5cCBAzJx4kSpVKmSrFu3TsqWLSvz5s2TQYMGyaZNm3zOJzWZuU3LSI2s9mdW89UyVqjGuZTF/LCIEw41SklmzPtA7O8zUiOrz1WBWrdLWR7L+MNyvdavXy/NmjWT+Ph42bNnj2zdulXKli0rTz75pOzdu1emTp3qc6z+/fvLDz/8IGPHjpWWLVvK+vXrpWzZsvL555/LM888Y3JjgmCyfC86mRP2+YEWMo2wt99+WwYNGiQffvih3HrrrcmWzZkzR+6++24ZPXq03H///VkqTunSpX26/WhaFxe0jOPEnCzXTURkxYoV8sEHH8iOHTtEVaV8+fJyzz33SK1atXx6faiul2Usb82AI0eOyJIlS7we9FnFOXz4sDz44IPyzTffSPbs2eXRRx+Vvn37yjPPPCOvvPKKVK9eXQYOHCh33XVXUPJxu92yb9++VJsq/rDKKUlGx95ptS5WrJjMmDEj2R0GL7V06VLp1KmT/Pnnn2nGsRyzJFZz1iLOihUrpGfPnrJ58+ZkXyOqUqWKJCQkyA033OA1htXYJ6lZs6YMHDhQunbtKnFxcZ7G05o1a6RVq1ayb98+n9fvUlu2bJGEhAR577335J9//pHz58/79LrChQvLvHnzpEaNGsny2bVrl1SvXl1OnDjhNYbTtmmp8bdGVvszq/lqGStU46QmvfPDIk6o1sip897yuPFy/tbI6nNVEqccy1izGrNmzZrJtddeK//73/+S7c9+/PFHueeee2TPnj0+xypVqpTMmDFD6tSpkyzWjh075Nprr83wDbaCzfq9mBVk1j4/0EKmESYicu+998q0adOkYsWKUqFCBRER+eWXX2Tbtm3SsWNHmT59epaMA4SaHj16+PQ8b7cut4rTu3dvmTt3rnTo0EHmzZsnmzdvlhYtWojb7ZYnn3wy1WsuBCoft9st+/fvN7kGmFVOVpxW66ioKNm5c6cUL148xeW///67XH311XLmzJk041iOmdNs3rxZateuLZUqVZKBAwdKpUqVPI+PGTNGtm7dKsuXL/d6NyGrsU8SExMjmzdvltKlS1/ReKpcubLXMfPG37P44uLiZPXq1VKuXLlk+axcuVJatGghhw4d8hrDads0byzPTvWF1Xy1jBWqcbyxGnt/4oRqjbLavLfkz/g76XOVVa1bt24t06dPl/j4eBERGTlypPTp00dy584tIiKHDh2S+vXry+bNmwO1KimKj4+X1atXy1VXXZVsf/brr79KhQoV/JobMTExsnHjRilbtmyyWOvWrZMGDRrI0aNH03y9VY0sa23xXrTMJ1jvo2Dv8wO+Xun+UqVDzZgxQ2+77TatXLmyVqpUSW+77TadMWNGlo+DwDt48KDu2bMn2WMbN27U7t27a4cOHfSDDz7IpMwyxnK9QrVGJUqU0AULFqiq6u7du9Xlculjjz2Wafm4XC7NnTu35smTJ82fYLIae6fVulSpUjpv3rxUl3/99ddaqlQpr3Esx8yq1lZxOnTooO3bt9fExMQrliUmJmq7du20Q4cOXuNYj32ZMmX0m2++UdV/r9mRdN2Rd999VytVquT19TNmzNCzZ896fv/tt9+S3SXp5MmT+tJLL/mcT6tWrfTJJ5/05LNr1y69ePGidujQQe+44w6f41iwqrV1jTLKar5axgrVOFZjb/keCtUaWbGa95bHetY1yujnKqcdy7jdbt2/f7/n97i4OM++TFV13759Pl0fzvr4vECBArp69WpVTb5/nT9/vhYvXtyvWPXr19fx48d7Yu3atUtV/71GWIsWLby+3qpGVnGSZPS9aJmPVSynbdOsx+xyIdcICzWtWrXSI0eOeH4fMWJEsts7//333z4d8FvFcWJOVnE6deqU7ILG+/fv1zx58miVKlW0bdu2GhkZqVOnTg1aPk5bL+tYSZxwC/SIiAj9888/Pb9HR0dn+NbnGcnH5XLpuHHjdMqUKWn+BDMnq7F3Wq379++v1apV0wMHDlyxbP/+/Vq9enXt37+/1ziWY2ZVa6s4+fPn159//jnV5StWrND8+fN7jWM99i+++KJWrlxZly9frnFxcfrdd9/p+++/rwUKFPAcdKfF+gBrw4YNWrBgQW3ZsqVmz55d77zzTq1UqZIWKlRId+zY4d/KqTO2aVY1stqfWc1Xy1ihGseJHz5DtUaXcsK8tzzWC/QHWX857VjG5XIlq8+lTSdV3+tjfXzes2dPbdeunZ47d87TvPr111+1Zs2aPm9jk3z33XcaGxurffr00Rw5cmj//v21efPmmjNnzjQvOp/EqkZWcaxY5mMVy2n7/ECPGY0wh3PigYjTcrKKU7p0aV28eLHn95dfflmvuuoqPX/+vOf32rVrBy0fp62Xdazdu3dr69atNSIiQt1ut7rdbo2IiNBbbrlFd+/e7VMMqzhutzvZAfGl/2LlL4t8Lt/wZ5RFTpbzw0m1/ueff7RcuXIaFxenDzzwgI4bN07Hjh2rvXv31ri4OC1XrpznbklpsRwzq1pbxYmKitK9e/emunzv3r0aFRXlNY7l2Kv+ezba888/rzlz5lSXy6Uul0tz5MjhOSvLm0AcYB05ckSff/557dChg7Zq1UqfeOKJZB+WfOGkbZrTDq6t5qtlrFCN48QPn6FaI1VnzXvLYz2nNR+cdixjVR/LMVP9d1/WrFkzzZ07t0ZERGiJEiU0MjJSGzRokK67SO/cuVN79eqlN9xwg1aqVEk7d+6s69ev9+m1TtwWWXBiI8xp+/xAj1k2o69wZjq32y0ul0tUVVwuV7rvrOK0OHrZJdwu/z3YcZyYk1Wcffv2SenSpT2/L1y4UG6//XbJlu3fadK2bVsZMWJE0PJx2npZxvrtt9+kTp06EhkZKc8991yyaw69+eabUrduXfn5559TvX6HdRxVlaZNm3rW4/Tp09KmTRvJnj17suetXr06KPl4u8CkP6xyspwfTqp1njx55KeffpLHH39cPvzwQzly5IiIiOTOnVvuueceefHFFyVv3rxe18tyzKxqbRWnVKlSsmLFCilRokSKy3/66ScpVaqU1zhWYy8icvHiRfnhhx/koYceksGDB8uOHTvkxIkTUrlyZYmNjfX6emvnz5+Xli1byoQJE+SJJ55IdxynbdOsWO3PrOarZaxQjeNEoVojp817y+NGK1afq5x2LONyua44fkjP8YT1mMXHx8s333wjP/zwg6xbt05OnDgh1157rTRr1syvvM6fPy+9e/eWYcOGyTvvvOPXa5NY1cgqjtV70Sof61gWrPb5gV6vkGmE7d69OyTjIHhy5colR44c8XygS7pLWhKXyyVnz57NrPTSzXK9rGI988wzUqFChStuXd6uXTsZOHCgtGzZUp555hmvty63ivP0008n+/22227zug6BzCcjjepA5WQ19k6rtci/H4refPNNeeONN+TgwYMiIlKgQAG/draWY2ZVa6s4nTp1kkGDBkmFChWkatWqyZZt2LBBHnnkEenatavXOFZjLyISEREhN998s2zZskVy587t9UL9gRYZGSnr16/PcBynbdOcyGK+WscK1ThOFIo1ctq8d+LxsNXnKqcdy6iqdO/eXaKiokRE5MyZM9KnTx/JmTOniEjQj89F/m1eRUdHy9q1a6VevXpSr149f1YpmcjISPn0009l2LBh6Y5hVSOrOFbvRat8rGM5SaDXKyQaYevXr5eqVauK2+326fmbNm2SChUqeLrkTo0j4rwuuBNzsopTp04dGT9+vLzzzjsyc+ZMOX78uDRp0sSzfNu2bameERGIfJy2Xpax5s6dKzNmzEh2wJckOjpannvuOenUqVPQ4lx+QJNeVvkkJiam+Pivv/4qJ0+elIoVK/q8fbHKyWrsnVbrS7lcLilYsGC68rEcM6taW8V57LHH5Ntvv5VrrrlGmjdvLpUqVRJVlS1btsi3334rtWrVkscff9xrHKuxT1K1alXZtWuXlClTJt0x5s2b57kbUWJioixYsEA2btwoIuI5S8RX9957ryQkJMjIkSPTnY/TtmkiNjUKxL/qZmS+BipWqMWxmh+W8yxJKNXIafPe8rhRJOM1svxc5bRjma5duybbFt57770pPscbyzGLjIyUkiVLpvtMp8u1a9dOPvvsMxk4cGC6Xm9VI4s4lu9Fq/WyjuWkfb7leqXEpZb/jJ1JIiIiZN++fT7ftj5Xrlyydu1aKVu2rKPjiPx7+mWrVq08ndA5c+ZIkyZNknVC586d63VjZRXHiTlZxVm/fr00bdpUjh07JhcuXJDHH39cnnvuOc/yLl26SM6cOWXChAlhuV6WsbLSLdCPHTsmH3zwgSQkJMjKlSuDks+kSZPkyJEjMmjQIM9j999/vyQkJIiIeP7l2JeDGqucLN9HqcmMWjdu3NjrztnlcsmCBQvSfI7lmFnV2nLMzp07J2PGjJHp06fLtm3bRESkfPny0qlTJxk4cKBnO5Ve/ox9krlz58pjjz0mzz33nFx33XWebWOSXLlypfl6Xw5k/fnaQ79+/WTq1KlSrly5FPMZPXq01xhO26ZZ1chqf2Y1Xy1jhWocy7G3iCMSujVy2ry33HdY1Mjyc5XTjmV8ceLECa9f+bder4SEBJk5c6a89957Gf6a8PPPPy+jRo2Spk2bprhv/O9//5uh+CK+1cgijuV70SIf61hO2+f7IiM1CokzwlRVhg0bJjExMT49/9y5c1kijohIt27dkv2e3k6oVRwn5mQVp3r16rJlyxb54YcfpHDhwlK7du1kyzt16uTT129Cdb0sYxUpUkQ2b96c6kHfxo0bpXDhwkGLk5JFixbJpEmTZObMmRIfHy/t27cPWj5vv/229O7d2/P73LlzZfLkyTJ16lSpVKmS9O3bV5599lmfvvZnlZPl++hymVnra665JtVlx48fl2nTpvl06rXlmFnV2nLMsmfPLkOHDpWhQ4f69HxfpWfsk7Ru3VpE/r32yaUfan29bkdqZ/Gl18aNG+Xaa68VEfE0C5P4+i+hTtumWdXIan9mNV8tY4VqHKuxt5xnoVojp817y32HRY0sP1c57VhmzJgxaZ4pdfz4cWnZsqX88MMPacaxXq/XXntNduzYIUWLFpVSpUpd0bzy5/qSCQkJkjt3blm1apWsWrUq2TKXy+W1EWZVI4s4lu9Fq/WyjOW0fb5ljVISEmeENWrUyO/T7aZNmyZFihRxdBwgVA0YMEAWLlwoCxYsuOJfVQ4cOCDNmzeXxo0by9ixY4MSJ8kff/whU6ZMkcmTJ8uRI0fk8OHDMm3aNOnYsaNPc9oqn3z58snixYulWrVqIiLywAMPyMGDB+WTTz4REZHFixdLjx49fLpOgXWNrDil1im5cOGCvP766/LCCy9IfHy8T19LsRyzUJfRsU+yZMmSNJc3bNgwo6nK6dOnJTo6OsNxfOW0bZovgl2jy6VnvgY6VqjGuZzV2GckTijUKCvOe0veauTkz1UZrXV0dLS89dZbKTYFTpw4IS1atJBDhw7JL7/8Eoj0U/Xss8+mudz6UgdpsaqRRRzL96Ll2AfzfRTMfX6g1yskGmHh7pNPPpE777zTMXEsYwUzztSpU32KlZHvIvuTj1Ucy/WyinX48GGpXbu27Nu3T+69916pWLGi55pD06ZNk8KFC8vy5cu9no5tFefTTz+VhIQEWbp0qbRq1UruvfdeadWqleTMmVPWrVvn87+iWeUTExMjW7Zs8Vz0tEaNGtKzZ0/Pv5rt3btXKlSoIKdPnw5aTlZj77RaX+6DDz6Qp556Sk6fPi1PPvmk3H///Sle2+FylmNmVWurOGXKlPHpa0Q7d+5M8zlWYx8MZ8+elddee01efvll2bdvn9+vnz59urRt2/aKf0X3xmnbtLRktEaXS89+Mb3zNZCxQjXOpazGPqNxQqVGTpv3wToett6G+MJpxzKffPKJdOnSRWbMmCFt27b1PH7y5Elp0aKFHDhwQJYsWeK1qRfMzzAZ8cMPP8j111/v1+UUrGpkFceKZT7BWLfM2OcHfL0Ujnf+/HndsGGDbt26Ndnjn332mVavXl2zZ88e1DhOzMkiTu7cuVP9yZMnj2bPnl3dbndYr5dlrH/++Uf79OmjefLkUZfLpS6XS/PkyaO9e/fWQ4cO+RTDKk5ERIQ+/vjjeuzYsWSPZ8uWTTdt2uRzLlb5VKxYUT/99FNVVT148KBGREToypUrPct/+uknLVSoUFBzshp7p9U6yddff601atTQXLly6fDhw/XEiRN+vd5yzKxqbRVn7Nixqf4MGDBAo6Ojgz72l6tataru3bvXr9ecOXNGH330Ub3uuuu0bt26OmvWLFVVnTRpkhYpUkSLFy+uI0eOTFc+cXFxunPnznS91knbNMsaWR6DZHS+BiJWqMWxGvtAzLNQq5Gqs+a95bFeILez6eHEY5l33nlHY2JidNGiRaqqeuLECb3pppv06quv1j/++COo65WSBx54QA8ePJiu114uvftGixpZxrFimY9FLCfu8wM5ZjTCHG7Dhg1aqlQpdbvd6na7tX379rpv3z5t0KCB5s2bV4cOHaq//fZb0OI4MSfLdUvJn3/+qb1799bIyEht0aJF2K5XoGIlJibq/v37df/+/ZqYmJjuHDIS5/7779f4+Hi98cYb9c0339R//vlHVTP2AT0j+YwYMUILFy6sw4cP10aNGmmVKlWSLR8zZow2bdo0qDmlxt+xd1qtf/rpJ23UqJHmyJFDBwwYkO6DvUCN2aWs5qxFnEOHDumAAQM0KipKGzRooMuWLfP6mkCMfZLY2Fi/D66HDBmi8fHxescdd2iRIkU0W7Zs+p///EerVaum06dP1wsXLgQ1n8s5YZtmVSOr/ZnVfLWMFapxrMbecp6Fao0u5YR5n5r07DsCuZ21lNnHMi+99JLmypVLFy1apPXr19eyZctm6Bg/icX+PiP/sHO5jOwbrWoUqFqnl2U+GY3ltH2+1XqlhkaYw7Vu3VqbNm2qc+bM0XvuuUddLpdWrFhRX375ZT116lTQ4zgxJ8t1u9SxY8f0iSee0NjYWK1du7YuXLgwqPk4bb0sY506dUo///zzK/4lTVX16NGj+vnnn+uZM2eCFicp1pQpU7RBgwYaFRWlbdu21YiICN2wYYNPr7fM5+LFizps2DC95pprtGXLlrp58+Zky++8806dOHFiUHO6XEbeR06qtcvl0piYGB0wYICOGzcu1R9vLMfsclZz1iLOqVOn9Pnnn9fcuXNrjRo19Msvv/T79Rkd+5Sk5+C6TJky+vnnn6vqvwdtLpdLe/ToYdIkTu/BvtO2aVY1stqfWc1Xy1ihGsdq7C3nWajWyGnz/nIZ2XcEcjtrIbOPZS41dOhQdbvdWrZsWb/PcL6c5bG+xT/sWMWyqpFlrS1Y5pORWE7b518qEGNGI8zhChQooGvWrFFV1SNHjqjL5dKpU6dmWhwn5mS5bqqq586d01GjRmm+fPm0fPny+vHHH2dKPk5bL8tYY8eO1SZNmqS6vGnTpvraa68FLc7ltm3bpo899pgWLVpUc+XKpXfffbfna2+ZkU9GWOdk+T5SzfxalypVSkuXLp3mT5kyZfxaJytWtbaIc+HCBX3zzTe1cOHCWrp0aZ06dWqGP8ikd+xT0qpVK/3zzz/9ek1kZKT+/vvvnt9z5Mih69evT9ffv9x3332np0+f9vzu61ebnLZNs6qR1f7Mcr5axQrVOFZjbznPQrVGTpv3SSz2HYHczmaEU45l2rdvn+wnKipKa9WqdcXjvrJeL1XbRtgHH3yQ7CvIvpxhZFUj61pnlGU+VrGcts8P9JhxsXyHc7vdsm/fPilYsKCIiMTFxcnq1aulXLlymRLHiTlZxVFVmTp1qjz11FNy4cIFefrpp6Vnz54SERGRKfk4bb0sY9WqVUuGDRsmbdq0SXH5F198IcOHD5cVK1YEJc7GjRulatWqVzyemJgoX375pSQkJMjXX3/t9XbqVvkkOX36tHzzzTeybds2EREpX768NG/e3K+7tVjlZDX2Tq21FYsxs6q1VZyPPvpInnzySTly5Ig88cQT8sADD0j27Nn9iiFiN/ZWIiIiZN++fZ67tMXFxcn69eulTJkyZn9j/vz5MnHiRJkzZ45PN0pw2jbNqkaWxyAIDquxD8Y8yyxW6+a0eW953Oi08XfasUyPHj18+nuTJ09Oc7nlmAXDtm3bZOLEifLee+/JX3/9leZzrWpkFceKZT5WsZy2zw/0mNEIc7iIiAjZtm2bFChQQFRVSpQoId9//72ULl062fNy5coVlDhOzMkqTrVq1WTXrl3Sr18/GTBggMTExKT4vHBdL8tYefLkkXXr1knJkiVTXL53716pUaOGHD58OChx3G633HDDDdKrVy/p1KmTxMXFXfGcAwcOeDbogc5HRGT27NnSq1cv+fvvv5M9nj9/fklISEj1gDlQOVmNvRNrnZYjR47I+++/L3379vX6XKsxs6q15ZhFR0fL3XffneZzR48e7TWOxdgnWbhwocycOVP27NkjLpdLypQpI3feeac0aNDAp9e73W5p1aqV5+5Vc+bMkSZNmlxxp8eZM2f6FC/Jr7/+KpMmTZJ3331XDh8+LK1atZI77rhDOnTo4PW1TtumWdXI8hgkLf7M12DFyqpxrMY+UPMsJVm1Rk6b95bHjcEcf1847VjGiuWYXU5VZdGiRXL69Gm58cYbJU+ePOnK8dSpUzJjxgyZNGmSLFu2TK6//nq54447ZPDgwemKB3tZbZ+fUTTCHM7tdie7bb2qpvj7xYsXgxLHiTlZxkly6eszMx8nrZdlrLi4OFm8eLFcd911KS5ftWqVNGrUSI4fPx6UON99951MnjxZPvnkE0lMTJQ77rhDevXqJfXr10/zdYHK58cff5RGjRpJ27Zt5eGHH5ZKlSqJiMjmzZtl1KhR8sUXX8iSJUukTp06QcvJauydVuvULFiwQBISEmTWrFkSExMjhw4dSvP5lmNmuS2yiNOoUaMUX3+5RYsWpbncauxFRPr06SNvv/225MmTR8qXLy+qKtu3b5cjR47Igw8+KK+++qrXGJb/0nju3DmZOXOmTJw4UX744Qdp1qyZfP3117JmzRqpVq2aT39HxHnbNKsaWR6DpMTf+RqMWFk9TlY6CyOr18hp897yuNFpZ+E47VjGitV6HTlyRPr37y+rV6+WOnXqyKhRo6R169by448/iohIwYIFZf78+VK9enWfc1u+fLlMnDhRPv74YylZsqRs2bJFFi1alGm1Quqyyj7fSrZM/evwytsHi2DHsYxFnKwVxzJWlSpV5Ntvv031oG/+/PlSpUqVoMWpX7++1K9fX1599VX56KOPZMqUKdKwYUO5+uqrpWfPntKtWzcpXLhw0PJ5/vnnpUePHvLWW28le/zGG2+UG2+8UXr37i3Dhw+Xr776Kmg5WY2902p9qd9++00mT54skydPlr1790qnTp1k1qxZ0rRpU6+vtRwzp839xYsXe33O+fPnvT7HauxnzZolkydPlkmTJkm3bt08B1eJiYkyZcoUeeCBB6R58+bStm3bNONYffDq16+fTJ8+XcqVKyf33nuvzJgxQ/LlyyeRkZF+fy3Fads0qxpZ7oeSZGS+BipWKMWxGvtANThCqUZOm/eW8zVYDS5fOe1YpmbNmik2ruLj46V8+fLSv39/qVy5stc4Vuv1yCOPyLJly6Rbt24yZ84cadmypaiqLFu2TNxutwwZMkSeeOIJmTNnjtdYo0aNkkmTJsnRo0fl7rvvlqVLl0qNGjUkMjJS8uXL53NOVjWyimPFMh+rWE7b5wd8zNJ9dTEASKe33npLc+bMqXPmzLli2ezZszVnzpz61ltvBS1OSrZv366PP/64lihRQiMjI7VNmzZByydPnjxpXpxy3bp1mjt3bq9xLHMKpMys9blz5/Sjjz7Sm2++WaOjo7V9+/b68ccf+30LdMsxc5oZM2akufz8+fPpvlhpesa+TZs2+uijj6a6fMiQIdq2bdt05ZMeERER+vjjj19xxzd/30OqztumOY3VfLWMFapxnChUa8S8Dw3pqfUzzzyT4s+AAQO0QYMGmj17dv3++++DkP2/ihYtqosXL1ZV1d9//11dLpcuWrTIs/ynn37SQoUK+RQrad94+QXx/Z1nVjVyWq0t83HaulkJ9HrRCAOQKTp37qwul0srVaqk7dq103bt2mnFihXV7XZrp06dgh4nJSdOnNC33npL8+bNq263O2j55MiRQ/fs2ZPq8j179miOHDl8imWVU6BlVq0LFCig9evX17feekv/+ecfz+P+HqhZj5mTREVF6fz581NcltQEK1y4cLrj+zv2xYoV059++inV5cuXL9dixYr59LcXLlyor7zyiudAasKECVqiRAnNnz+/9urVy6fbfE+bNk2bNWumOXPm1I4dO+qcOXP0woUL6f5Q7bRtmkWNrFjNV8tYoRpH1W7sreKEco2cNu8tOWkbEmjWtX788cfTvKOotYiIiGR3YI6OjtYdO3Z4fv/rr798Xq8XX3xRy5UrpyVKlNAhQ4bohg0bVDV98ywtVjUKdq29sczHn1hZab5mtEY0whzO5XKp2+32/Dez4zgxJ+IEJ451LNV/zzS57bbbtHLlylqpUiW97bbbvJ59Esg4SZYsWaLdunXT2NhYzZUrl/bq1UuXLVsWtHyqVaumkyZNSnV5QkKCVqtWzed4FjlZj32SzK51njx5tEGDBvr222/r0aNHPY/7e6BmOWZOm/tjx47V2NhYXb58ebLHL168qLfffrsWLFhQN27c6Hfc9I59VFSU/vHHH6ku//33331qOr799tsaERGhV199tUZFRemLL76oOXPm1D59+uiDDz6ouXLl0qFDh/q8Prt27dKnnnpKS5Ysqfnz51e3253uW9c7ZZtmVSOr96LVfLWMFapxrMbecp6Fao2SOGXeW+7vrWuUUU49lknNxo0btUCBAl6fZ3ncsH//fs/vsbGxunPnTs/v+/bt8zv+4sWLtWvXrhoTE6PVq1fXiIgI07OTfK1RsOJYsczH11hO2+d7k9Ea0QhzuD179iT7yew4TsyJOMGJYx3Laf744w994YUXtFy5cupyubRevXo6adIkPXHiRNBzGT16tObNm1e//PLLK5Z98cUXmi9fPh01alRQc7IceyfV+vTp0/r+++9r48aNNTo6Wm+//XadOXOmRkZG+vWByHLMnDj3n3rqKc2bN6+n4XXhwgW94447tECBAp5/5fWFxdi7XC49cOBAqst9PVCvUqWKjh8/XlVVv/76a82WLZtOmTLFs/yjjz7Sq666yue8kiQmJurcuXO1Q4cOGhUVpcWKFdN+/fr5HSejLGptVSOr96LVfLWMFapxrMbecp6Fao0sWcx7y32H02qU1Y5ltmzZovny5fP6PKv1crlc+sILL+i4ceN03LhxmiNHDh02bJjn9+effz7djY1jx47phAkTtFatWhoREaF169Y1OZb1tUbBimPFMh9fYzltn+9NRmtEI8zB1q1bpxcvXvT5+Rs3btTz588HLI4TcyJOcOJYx3Kali1barZs2bRw4cI6ZMgQ/eWXXzI1n4sXL+qdd96pLpdLK1asqO3bt9d27dpphQoV1O126+233+7XWGSU5dg7rdaX2rFjhz7xxBNavHhxdblces899+j8+fOvuL5FSqzGzIlzP0nfvn21aNGiunXrVu3QoYPmz59f161b5/PfsBp7l8ulvXv31oEDB6b407t3b58O1KOjo5MdoEVGRurmzZs9v//666+aPXv2dOWY5NChQzpmzBitXr16huL4y6rWFjUK1L4jI/M1ULFCKY7V/AjUPAulGlmxmPfW89VJNcqKxzIvvPCC1q9fP83nWK5XqVKltHTp0l5/Mmr9+vXav39/kzOefKlRMONYsczH11hO3uenJKM1cqmqZuBi/gigiIgI2bdvnxQoUMCn5+fKlUvWrl0rZcuWDUgcJ+ZEnODEsY6VdFtdzeDtc63itG3bVnr27Cm33nqr33d5C0Q+SWbMmCHTp0+Xbdu2iYhI+fLlpVOnTtKpU6eg5mQ59k6t9aUSExNl3rx5kpCQIHPmzJHY2Fg5dOiQT6/N6Jg5ce5f6t5775VPP/1UYmNjZcGCBX7dQt1q7Bs1apTiXYQu5+2uRW63W/bt2ycFCxYUEZG4uDhZt26dpwb79++XokWLBvX23k7cpmW0RoF6LybJyHwNVKxQiGM1PwI9z0KlRk6Z99bz1UnbWScey4wfPz7Fx48ePSqrVq2SL7/8Ur7++mtp1qxZqjECvY0NpPPnz0tkZGSaz7GokWUcK5b5WMVy2j4/0GOWLV2vQlCoqgwbNkxiYmJ8ev65c+cCGseJOREnOHGsY+3evdunGN5YxZk9e7aIiJw+fVq++eabZE2M5s2bS3R0dFDzSXLXXXfJXXfdlaEYFjlZjr1Ta30pt9strVq1klatWsnBgwflvffe8/m1GR0zJ879QYMGef4/T548oqpyzTXXyJQpU5I9b/To0Wn+DauxX7x4sU/P88blcsnx48clR44cng+gJ06ckGPHjomIeP7rTZs2baRjx45y5513+rwOqXHaNs2iRpbvxZRkZL4GKlYoxLGaH1ZxUhMKNXLSvLeer4Eef3848VhmzJgxKT6eK1cuqVChgixdulTq1q2bZoxAb2Mz4vTp07Jq1SrJmzevVK5cOdmyM2fOyEcffSRdu3ZNM4ZFjSzjWLHMxyqW0/b5gR4zzghzMF//1ftS06ZNkyJFigQkjhNzIk5w4ljGWr9+vVStWlXcbrdPMTZt2iQVKlSQbNmS9+2t4iSZPXu29OrVS/7+++9kj+fPn18SEhKkTZs2aca3zictq1evlqeeekq++OKLoORk+T4SyVq13rVrl/Tp00fmz5/v92sv5euYOXHuN27c2OtrXS6XLFy40OvzMjr2lpLOwkiSdNB3+e++nM0REREhOXPmlLvvvlt69eol1113nd/5OG2bJmJTI+vtR1qs5qtlrKwax3J+WMTxRVaskdPmvfV8Deb4e+O0Yxkr1utl0bwSEdm2bZvcfPPNsnfvXnG5XHLTTTfJhx9+6Pm7mXHWNdKW1fb5GUUjDEBQOfGrXz/++KM0atRI2rZtKw8//LBUqlRJREQ2b94so0aNki+++EKWLFkiderUCfh6JZk3b5588803kj17dunVq5eULVtWfvnlF3n00Udlzpw50qJFC/nqq6/S/BtOPF3eibVOy7p16+Taa6/16UDNYsxCmcXYi9idgbVkyRKfntewYcM0l7vdbtm4caPMnz9fJk2aJJs2bZJq1apJr169pHPnzpInTx6f/o7TtmkidjUKFn/ma7BiZdU4VmMfzPdQVqyRE+e9pay2DfGVE2ttwbJ51b59ezl//rxMmTJFjhw5IgMGDJDNmzfL4sWLpWTJkjTCHChU52tqaIQBCCq32y3333+/z6fMvvHGG7J58+YrDvqs4oiItG7dWkqUKCFvvfVWiq/t3bu3/Pbbb2k2MSzzSUhIkP/85z+SN29eOXz4sOTLl09Gjx4t/fr1k7vuukv69+/vOehKi2VOVpxWa298/UBkNWahzGLsRezOwLJy+TU1VqxYIQkJCTJjxgw5d+6ctGvXTnr16iVNmjTxGsdJ27SsiEZY8OI4UVasEfM+a7KqdeXKleX777+XvHnziojIgw8+KMOHD5f8+fOLiMiBAwekdOnScurUKdsVSIVl86pQoULy7bffSrVq1UTk37OJHnzwQfnqq69k0aJFkjNnTp9iWdXIabW2zMdp62Yl0OtFIwxAUDnxq1958+aVJUuWeHbWl1u/fr00bNhQDh8+nGpsy3yqV68uXbp0kcGDB8unn34qHTp0kDp16shHH30kxYsX9zm+E09PdlqtvfH1A5HVmDnR8OHDfXreU089leZyi7EXsTsDy8rljbAkp06dko8++kgSEhLkxx9/9Poecto2LSuiERa8OE6UFWvEvM+aLPdnl+4/Lj/jb//+/VKkSBFJTEy0XYFUWDWvRP5dl59++umKfwTs27evfP755zJt2jRp1KiR3zfcSG+NnFZry3yctm5WAr1eXCwfQFBZXejaKo7Iv9dDyJUrV6rL4+Pj5cyZM0HLZ+fOndKhQwcREbn99tslW7Zs8vLLL/vdULHMyYrTam3FasycaNasWakuc7lcsnXrVjlz5ozXRpjF2CfJnz+/DBgwQAYMGOA5A+vJJ5+UIUOG+HUGVqDuPCoiEhMTI927d5fu3bt7LqScFqdt00QCXyM4l9Pu7uxEFuvmxHlvKVTHP1C1Tun8FH8bpRlx+vTpZNefc7lc8uabb0rfvn2lYcOGMm3aNJ9jVaxYUVauXHlFI+y1114TkX/vvJkeVjXK7FpfzjKf9MZy+ny1HjMaYQDCXrly5WThwoXSo0ePFJcvWLBAypUrF7R8Tp8+7fmahMvlkqioqEy5iGQgOK3WNWvWTHMn6uvp1qE8ZmvWrEnx8bVr18qjjz4qGzdulP/85z9e4wRq7GvVqiW1atWSMWPGeM7Aat68udcDOKs7tTVs2FCyZ8+e5nPKly9v8rd8ZVXrQN6dNT2s5qtlrFCN47S7O4uEbo2sOG3/KuK8GllxYq0tWDav2rdvL9OnT5cuXbpcsey1116TxMREmTBhQsYShqlQna+poREGIOz16NFDHnnkESlUqJC0bt062bIvv/xShgwZIo8//nhQc5o4caLExsaKiMiFCxdkypQpnu/EJ/nvf/8b1JwsOK3W7dq1M4sVqmN2ud27d8uwYcNkxowZcvvtt8umTZt8OuAP9Nj7cwaW5Z3aFi1alK58A8mi1sG8O6uvLOerVaxQjOPUuzuHYo0sOW3/6sQaWbGqtcvluqIpm5lnJVk2rx577DF57LHHUl3+xhtvyBtvvOE1jlWNnFZry3wsYjlxvgZ6zLhGGICwl5iYKHfddZd8+umnUqFCBalUqZKoqmzZskW2b98u7dq1k48//tjnnUNGlS5d2uuG3uVyya5du4KSjyWn1dpKKI9Zkr///lueffZZefvtt+Wmm26SkSNHyg033ODz663GvnHjxjJr1izJnTt3utfF8k5tCxculAYNGjjqw5tFrZ1411kEhxPv7uw0Tlw3p+1fnVgjK1a1drvdUrVqVc/+Y/369VKxYkXPWcYXLlyQTZs2Oe4rahlx4cIFv/aXVjVyWq0t87GI5cT5GugxoxEGAP/fjBkzZPr06Z6zScqXLy+dOnWSTp06ZXJmoccptT5w4MAVFzm/1IULF2T16tVSq1atIGblLCdPnpRXXnlFRo8eLVdffbWMGDFCbr755nTHc8LYW96pLSIiQv766y/P+6hOnTry6aefSrFixUxzTo+M1NqJd521nK9WsUIxjhPv7iwSmjUKBCdsY0WcXSMrGa31s88+69Pznn766XTnaMHf5pWIyNy5c6VYsWJSrVo1SUxMlBdeeEEmTJgg+/btkyJFikjfvn1l6NChXv8R0apGTqu1ZT4WsZw4XwM9ZjTCAMCBVFV27Ngh586dyzJfFciKLm9iVKtWTb766ispUaKEiIhftwoP1TErXLiwHD9+XPr16yd33313qget1atXD0o+FmdgWd6p7fK7GsXFxcm6deuy1Ie5lDjxrrOW89UqVijGceLdnUVCs0ahjBplPVbNK5F/rzf2zjvvSP369WXEiBEyatQoeeKJJ6RSpUqydetWGTFihAwcOFCGDh0ahDWDN2E5XxUA4Ci7du3SqlWrqtvtVrfbrSVKlNAVK1ZkdlohyeVy6f79+z2/x8bG6s6dOz2/79u3T10ul9c4oTxmLpfL8+N2u1P83e12By0ft9udbMxq166tv//+e9D+/uW8vYdgx2q+WsYK1ThORI0QbtatW6eRkZFB+3sVKlTQpUuXqqrqiy++qPny5dPRo0fr119/rWPHjtVChQrpyJEjfYoVFRWlv/76q6qqVq1aVT/66KNky7/44gu9+uqrM5yzVY2CXWtvLPNx2rpZyeh6hcY/VwNABjjtdsGDBw+WCxcuyPvvvy85cuSQV155Rfr06SOrVq3K1LwsOK3WvvDlX8hCecys7iJkNfZ62YnsmzZtkrNnz1qkmC6XX8w1pYu7BltWnGdWTC+kaxQrVOM4UTjXKJznfbAFq9aqKhcuXAhI7JTs2bNHSpUqJSL/nu3z5ptvSocOHUREpGXLlnL11VfLgAEDfDqLK2/evPLnn39KyZIl5eDBg3L11VcnW16+fHn5448/MpyzVY2CXWtvLPNx2rpZyeh60QgDEPacdrvg77//Xj755BO56aabROTfaw4VL15cTp48KTlz5szk7DLGabW2EspjlnRQnFGhOvaqKk2bNvV8VfPUqVPSpk0bz8Vck6xevTpoOYVqrQGkjnkfPMGsdTCbspbNq/bt28sLL7wgn332mdx2223yxhtvyNtvv+1Zn1dffVWuueYak7xDtQHuxH/YcZqMrBeNMABhzYm3Cz5w4ICUK1fO83uRIkUkOjpaDhw4IGXKlAnY3w00J9ba5XLJ8ePHJUeOHJ5/2T1x4oQcO3ZMRMTzX29CdcxERGbPnp3i4/Hx8VK+fHmfrg9hOfZOOwPr8ou03nbbbZmUyb+cOM+sWM1Xy1ihGseJqFHqQnneO00o19qyefXiiy9Ks2bNpGLFilK3bl35+OOP5ZtvvpHy5cvLjh075J9//pF58+YFcG2AtHGxfABhzYm3C46IiJBt27Yly6l48eLy/fffS+nSpZPlkpU4sdZJX29IkvSh6PLffbn4ciiOmYikebDvcrmkU6dO8s4776R5pyHLsfd2O+0kwTwDy0mcOM+sWM1Xy1ihGseJqFHqQnneO41lrb01XdevXy8NGzYM2nvx6NGj0qxZMzly5IineVWoUKErmle1a9f2Kd758+clISFB5syZI7t27ZLExEQpUqSI1KtXTx544AEpXry41xhWNXJarS3zcdq6WQn0ejm/NQ0AAaSqMmzYMJ9vF3zu3LkAZ/RvTuXLl7/isZo1a3r+P6sdpIs4s9aLFi0yiROqYyYikpiYmOLjR48elVWrVslDDz0kzz//vLz44oupxrAce6edgXXmzBmZP3++NG7cWOLi4pItO3bsmCxevFhatGghUVFRQcnHifPMitV8tYwVqnGciBqlLpTnvdNY1jp37txpntF8eZM20OLj4+XHH3/0NK9Kly4tiYmJcu7cObn77rt9bl4liYyMlD59+kifPn3SnZNVjZxWa8t8nLZuVgK9XpwRBiCsOfF2wUuWLPHpeQ0bNgxYDoHgxFpbCdUx88XcuXNlwIAB8ssvv6T6nFAe+3Hjxsns2bNlwYIFKS5v1qyZtGvXTvr27RuUfEK51gBSxrwPHstah/Oxg6+sauS0Wlvm47R1sxLo9aIRBgAA0m3Pnj1StWpVOXHiRFD+ntPOwKpVq5YMGzZM2rRpk+LyL774QoYPHy4rVqwISj4AAGS2FStWyHXXXScREREi8u++8OWXX5YdO3ZIkSJF5L///a907do1k7NEOPPtKn8AAISgiIgIn36Qul27dknRokWD9vfeeustGTdu3BVNMJF/r8Uyfvx4eeedd4KWz/bt26VGjRqpLq9evbps3749aPmEMsv5ahUrVOM4ETUCAmvFihXJLuHwxRdfSMOGDaVYsWJy/fXXy9SpU32OVbduXTl06JCIiMyZM0duu+02KV26tDzxxBNSs2ZN6dmzp8yaNct8HQBfcY0wAHCYpAv5ZuXrSmUVqiqlSpWSbt26ea7nlR7hOmZr166VRx55RG655Zag/c0PPvhAhg0bluryAQMGyPDhw4P2VcQLFy7IwYMHpWTJkikuP3jwoFy4cCEouYQ6q/lqGStU4zgRNUKocdqxQ926deWvv/6SggULypw5c6Rdu3Zy7733yl133SVr1qyRnj17SlxcnLRv395rrEu/dPa///1PhgwZIiNGjPA8VqZMGfnf//7nNZZVjZxWa8t8nLZuVgK9XjTCAMBhdu/endkphI0VK1ZIQkKCjBs3TsqUKSP33XefdO7cWfLkyeNXnFAeszx58qR4PZSTJ0/KhQsXpHnz5vLss88GLR+nnYFVpUoV+fbbb+W6665Lcfn8+fOlSpUqQcsnlFnNV8tYoRrHiagRQo3Tjh2smleX27Ztm4wdOzbZY3fccYe8/PLLXl9rVSOn1doyH6etm5WAr5cCABxj3bp1evHiRZ+fv3HjRj1//nwAMwoPp0+f1vfee0+bNGmiMTExetddd+n8+fN9em2oj9mUKVNS/Jk5c6Zu2rQp6PnExsbqypUrU12+cuVKjY2NDVo+b731lubMmVPnzJlzxbLZs2drzpw59a233gpaPuEgI/M1ULFCNY4TUSOEAiceO7hcLt2/f7+qqhYsWPCKfe0vv/yiuXPn9jnWokWLdN26dVqqVCldsWLFFbG87autauS0Wlvm47R1sxKM9aIRBgAO4na79cCBAz4/Py4uTnfu3BnAjMLPrl27tHHjxup2u/XQoUNen8+YBVft2rV15MiRqS5/8cUXtXbt2kHMSLVz587qcrm0UqVK2q5dO23Xrp1WrFhR3W63durUKai5hBt/52swYoVqHCeiRsiqnHjsYNG8ujSW2+1Wl8ulLpdLx4wZk2z59OnTtXLlymnGsKqR02ptmY/T1s1KMNaLr0YCgIOoqgwbNkxiYmJ8ev65c+cCnFH4+P3332XKlCkyZcoUOXXqlAwePFhy5crl9XWMWXDdd999MmjQIKlSpYrceuutyZbNmTNHXnjhBRk9enRQc3r//felbdu2Mm3aNNm2bZuoqlSoUEGeffZZ6dixY1BzCRfpna+BjBWqcZyIGiGrc+qxQ9OmTT1fkfzhhx/khhtu8Cxbs2ZNqtfDvNzlX2uLjY1N9vu5c+dk6NChacawqpHTam2Zj9PWzUow1sulesmXgQEAmapRo0YpXo8pLdOmTZMiRYoEKKPQdu7cOZk1a5YkJCTId999J61atZL77rtPWrVq5fNdw0J9zJx4EdZ7771Xpk2bJhU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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(3, 1, figsize=(15,30)) \n", "ax = axes[0]; hc_comp = plot_nci('Complete', ax)\n", "ax = axes[1]; hc_avg = plot_nci('Average', ax)\n", "ax = axes[2]; hc_sing = plot_nci('Single', ax)" ] }, { "cell_type": "markdown", "id": "4d2ce0f1", "metadata": {}, "source": [ "We see that the\n", "choice of linkage certainly does affect the results\n", "obtained. Typically, single linkage will tend to yield *trailing*\n", "clusters: very large clusters onto which individual observations\n", "attach one-by-one. On the other hand, complete and average linkage\n", "tend to yield more balanced, attractive clusters. For this reason,\n", "complete and average linkage are generally preferred to single\n", "linkage. Clearly cell lines within a single cancer type do tend to\n", "cluster together, although the clustering is not perfect. We will use\n", "complete linkage hierarchical clustering for the analysis that\n", "follows.\n", " \n", "We can cut the dendrogram at the height that will yield a particular\n", "number of clusters, say four:" ] }, { "cell_type": "code", "execution_count": 55, "id": "ed965079", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:03.021337Z", "iopub.status.busy": "2024-06-04T23:20:03.021228Z", "iopub.status.idle": "2024-06-04T23:20:03.030000Z", "shell.execute_reply": "2024-06-04T23:20:03.029729Z" } }, "outputs": [ { "data": { "text/html": [ "
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Complete0123
label
BREAST2302
CNS3200
COLON2005
K562A-repro0010
K562B-repro0010
LEUKEMIA0060
MCF7A-repro0001
MCF7D-repro0001
MELANOMA8000
NSCLC8100
OVARIAN6000
PROSTATE2000
RENAL8100
UNKNOWN1000
\n", "
" ], "text/plain": [ "Complete 0 1 2 3\n", "label \n", "BREAST 2 3 0 2\n", "CNS 3 2 0 0\n", "COLON 2 0 0 5\n", "K562A-repro 0 0 1 0\n", "K562B-repro 0 0 1 0\n", "LEUKEMIA 0 0 6 0\n", "MCF7A-repro 0 0 0 1\n", "MCF7D-repro 0 0 0 1\n", "MELANOMA 8 0 0 0\n", "NSCLC 8 1 0 0\n", "OVARIAN 6 0 0 0\n", "PROSTATE 2 0 0 0\n", "RENAL 8 1 0 0\n", "UNKNOWN 1 0 0 0" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "linkage_comp = compute_linkage(hc_comp)\n", "comp_cut = cut_tree(linkage_comp, n_clusters=4).reshape(-1)\n", "pd.crosstab(nci_labs['label'],\n", " pd.Series(comp_cut.reshape(-1), name='Complete'))" ] }, { "cell_type": "markdown", "id": "4bc69aff", "metadata": {}, "source": [ "There are some clear patterns. All the leukemia cell lines fall in\n", "one cluster, while the breast cancer cell lines are spread out over\n", "three different clusters.\n", "\n", "We can plot a cut on the dendrogram that produces these four clusters:" ] }, { "cell_type": "code", "execution_count": 56, "id": "c487bbc7", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:03.031335Z", "iopub.status.busy": "2024-06-04T23:20:03.031249Z", "iopub.status.idle": "2024-06-04T23:20:03.418631Z", "shell.execute_reply": "2024-06-04T23:20:03.417729Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10,10))\n", "plot_nci('Complete', ax, cut=140)\n", "ax.axhline(140, c='r', linewidth=4);" ] }, { "cell_type": "markdown", "id": "7976c47b", "metadata": {}, "source": [ "The `axhline()` function draws a horizontal line line on top of any\n", "existing set of axes. The argument `140` plots a horizontal\n", "line at height 140 on the dendrogram; this is a height that\n", "results in four distinct clusters. It is easy to verify that the\n", "resulting clusters are the same as the ones we obtained in\n", "`comp_cut`.\n", "\n", "We claimed earlier in Section~\\ref{Ch10:subsec:hc} that\n", "$K$-means clustering and hierarchical clustering with the dendrogram\n", "cut to obtain the same number of clusters can yield very different\n", "results. How do these `NCI60` hierarchical clustering results compare\n", "to what we get if we perform $K$-means clustering with $K=4$?" ] }, { "cell_type": "code", "execution_count": 57, "id": "345edc5f", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:03.421007Z", "iopub.status.busy": "2024-06-04T23:20:03.420875Z", "iopub.status.idle": "2024-06-04T23:20:04.678569Z", "shell.execute_reply": "2024-06-04T23:20:04.678043Z" } }, "outputs": [ { "data": { "text/html": [ "
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K-means0123
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" ], "text/plain": [ "K-means 0 1 2 3\n", "HClust \n", "0 1 20 10 9\n", "1 0 7 0 0\n", "2 8 0 0 0\n", "3 0 0 9 0" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nci_kmeans = KMeans(n_clusters=4, \n", " random_state=0,\n", " n_init=20).fit(nci_scaled)\n", "pd.crosstab(pd.Series(comp_cut, name='HClust'),\n", " pd.Series(nci_kmeans.labels_, name='K-means'))" ] }, { "cell_type": "markdown", "id": "f4d97be5", "metadata": {}, "source": [ "We see that the four clusters obtained using hierarchical clustering\n", "and $K$-means clustering are somewhat different. First we note\n", "that the labels in the two clusterings are arbitrary. That is, swapping\n", "the identifier of the cluster does not\n", "change the clustering. We see here Cluster 3 in\n", "$K$-means clustering is identical to cluster 2 in hierarchical\n", "clustering. However, the other clusters differ: for instance,\n", "cluster 0 in $K$-means clustering contains a portion of the\n", "observations assigned to cluster 0 by hierarchical clustering, as well\n", "as all of the observations assigned to cluster 1 by hierarchical\n", "clustering.\n", "\n", "Rather than performing hierarchical clustering on the entire data\n", "matrix, we can also perform hierarchical clustering on the first few\n", "principal component score vectors, regarding these first few components\n", "as a less noisy version of the data." ] }, { "cell_type": "code", "execution_count": 58, "id": "90d617e0", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:20:04.684581Z", "iopub.status.busy": "2024-06-04T23:20:04.684302Z", "iopub.status.idle": "2024-06-04T23:20:05.125639Z", "shell.execute_reply": "2024-06-04T23:20:05.125298Z" } }, "outputs": [ { "data": { "text/html": [ "
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Complete-PCA0123
label
BREAST0502
CNS2300
COLON7000
K562A-repro0010
K562B-repro0010
LEUKEMIA2040
MCF7A-repro0001
MCF7D-repro0001
MELANOMA1700
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OVARIAN5100
PROSTATE2000
RENAL7200
UNKNOWN0100
\n", "
" ], "text/plain": [ "Complete-PCA 0 1 2 3\n", "label \n", "BREAST 0 5 0 2\n", "CNS 2 3 0 0\n", "COLON 7 0 0 0\n", "K562A-repro 0 0 1 0\n", "K562B-repro 0 0 1 0\n", "LEUKEMIA 2 0 4 0\n", "MCF7A-repro 0 0 0 1\n", "MCF7D-repro 0 0 0 1\n", "MELANOMA 1 7 0 0\n", "NSCLC 8 1 0 0\n", "OVARIAN 5 1 0 0\n", "PROSTATE 2 0 0 0\n", "RENAL 7 2 0 0\n", "UNKNOWN 0 1 0 0" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hc_pca = HClust(n_clusters=None,\n", " distance_threshold=0,\n", " linkage='complete'\n", " ).fit(nci_scores[:,:5])\n", "linkage_pca = compute_linkage(hc_pca)\n", "fig, ax = plt.subplots(figsize=(8,8))\n", "dendrogram(linkage_pca,\n", " labels=np.asarray(nci_labs),\n", " leaf_font_size=10,\n", " ax=ax,\n", " **cargs)\n", "ax.set_title(\"Hier. Clust. on First Five Score Vectors\")\n", "pca_labels = pd.Series(cut_tree(linkage_pca,\n", " n_clusters=4).reshape(-1),\n", " name='Complete-PCA')\n", "pd.crosstab(nci_labs['label'], pca_labels)" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "formats": "Rmd,ipynb", "main_language": "python" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }