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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/skilfoy/759c503298a9dc433e59df5312a9148c/predictive-modeling-of-health-insurance-charges-using-advanced-machine-learning-techniques-r.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Predictive Modeling of Health Insurance Charges Using Advanced Machine Learning Techniques" | |
| ], | |
| "metadata": { | |
| "id": "wlojYNg3oG9A" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "ecrM7jnQQtyI" | |
| }, | |
| "source": [ | |
| "Author: Sean Kilfoy" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "4K1EIIp1Gy5w" | |
| }, | |
| "source": [ | |
| "# Introduction\n", | |
| "This project involves a detailed analysis of health insurance data to develop predictive models that estimate insurance charges based on demographic and health-related attributes. The goal is to identify key factors affecting insurance costs and to compare several predictive modeling techniques. This analysis will provide insights that could help insurance companies in risk assessment and premium setting." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "qeSIxr2qG00F" | |
| }, | |
| "source": [ | |
| "# Methodology\n", | |
| "The analysis employs various statistical and machine learning models to handle data irregularities and to predict outcomes effectively. Each model is chosen based on its strengths in dealing with specific types of data characteristics, including linearity, non-linearity, and interaction effects." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Part 0: Environment Setup" | |
| ], | |
| "metadata": { | |
| "id": "a75q2itfoTNw" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "kBbtZ5iVYSBW" | |
| }, | |
| "source": [ | |
| "***Note:*** This project notebook requires a few libraries. If your environment doesn't yet have them installed, the following cell may take many minutes. Go grab some coffee! ☕️" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "fg0MYL6lGxdg" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "invisible(suppressMessages(suppressWarnings({\n", | |
| " library(stats)\n", | |
| " library(MASS)\n", | |
| " install.packages(\"caret\")\n", | |
| " library(caret)\n", | |
| " install.packages(\"tree\")\n", | |
| " library(tree)\n", | |
| " install.packages(\"randomForest\")\n", | |
| " library(randomForest)\n", | |
| " library(e1071)\n", | |
| " library(ggplot2)\n", | |
| " install.packages(\"factoextra\")\n", | |
| " library(factoextra)\n", | |
| " install.packages(\"neuralnet\")\n", | |
| " library(neuralnet)\n", | |
| " install.packages(\"doParallel\")\n", | |
| " library(doParallel)\n", | |
| " install.packages(\"googledrive\")\n", | |
| " library(googledrive)\n", | |
| "})))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "I already uploaded the dataset to my Google Drive, so I must authenticate to GDrive and download the dataset file to this notebook environment." | |
| ], | |
| "metadata": { | |
| "id": "d5PNZkLIoe0Q" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "TPSYwr_Ngm0_" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "drive_auth()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "*--- Output redacted ---*" | |
| ], | |
| "metadata": { | |
| "id": "oE492-_1t_dA" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "fPHSyTzVYgAN", | |
| "outputId": "d6895c31-3dad-42f6-9e8c-7e29505785bc" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stderr", | |
| "text": [ | |
| "Auto-refreshing stale OAuth token.\n", | |
| "\n", | |
| "File downloaded:\n", | |
| "\n", | |
| "• \u001b[36minsurance.csv\u001b[39m \u001b[90m<id: 1yCFDM_5QATaZWVhmi_kAcSNjg9d0Vdsg>\u001b[39m\n", | |
| "\n", | |
| "Saved locally as:\n", | |
| "\n", | |
| "• \u001b[34m./insurance.csv\u001b[39m\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"File downloaded successfully.\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "file_info <- drive_find(pattern = \"insurance.csv\")\n", | |
| "\n", | |
| "if (nrow(file_info) > 0) {\n", | |
| " drive_download(as_id(file_info$id[1]),\n", | |
| " path = \"./insurance.csv\", overwrite = TRUE)\n", | |
| " print(\"File downloaded successfully.\")\n", | |
| "} else {\n", | |
| " print(\"File not found.\")\n", | |
| "}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "-a3gLWiGG3gx" | |
| }, | |
| "source": [ | |
| "# Part 1: Data Preparation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "TPXw5uV7G45m" | |
| }, | |
| "source": [ | |
| "### Load the dataset into memory\n", | |
| "\n", | |
| "Now that the dataset is loaded into our notebook environment, let's load it into memory so we can start our analysis." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 536 | |
| }, | |
| "id": "NmJ4EyAXgrTn", | |
| "outputId": "ec597051-deec-4b7c-8d9c-a5161470ee12" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| " age sex bmi children \n", | |
| " Min. :18.00 Length:1338 Min. :15.96 Min. :0.000 \n", | |
| " 1st Qu.:27.00 Class :character 1st Qu.:26.30 1st Qu.:0.000 \n", | |
| " Median :39.00 Mode :character Median :30.40 Median :1.000 \n", | |
| " Mean :39.21 Mean :30.66 Mean :1.095 \n", | |
| " 3rd Qu.:51.00 3rd Qu.:34.69 3rd Qu.:2.000 \n", | |
| " Max. :64.00 Max. :53.13 Max. :5.000 \n", | |
| " smoker region charges \n", | |
| " Length:1338 Length:1338 Min. : 1122 \n", | |
| " Class :character Class :character 1st Qu.: 4740 \n", | |
| " Mode :character Mode :character Median : 9382 \n", | |
| " Mean :13270 \n", | |
| " 3rd Qu.:16640 \n", | |
| " Max. :63770 " | |
| ] | |
| }, | |
| "metadata": {} | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A data.frame: 6 × 7</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th></th><th scope=col>age</th><th scope=col>sex</th><th scope=col>bmi</th><th scope=col>children</th><th scope=col>smoker</th><th scope=col>region</th><th scope=col>charges</th></tr>\n", | |
| "\t<tr><th></th><th scope=col><int></th><th scope=col><chr></th><th scope=col><dbl></th><th scope=col><int></th><th scope=col><chr></th><th scope=col><chr></th><th scope=col><dbl></th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>1</th><td>19</td><td>female</td><td>27.900</td><td>0</td><td>yes</td><td>southwest</td><td>16884.924</td></tr>\n", | |
| "\t<tr><th scope=row>2</th><td>18</td><td>male </td><td>33.770</td><td>1</td><td>no </td><td>southeast</td><td> 1725.552</td></tr>\n", | |
| "\t<tr><th scope=row>3</th><td>28</td><td>male </td><td>33.000</td><td>3</td><td>no </td><td>southeast</td><td> 4449.462</td></tr>\n", | |
| "\t<tr><th scope=row>4</th><td>33</td><td>male </td><td>22.705</td><td>0</td><td>no </td><td>northwest</td><td>21984.471</td></tr>\n", | |
| "\t<tr><th scope=row>5</th><td>32</td><td>male </td><td>28.880</td><td>0</td><td>no </td><td>northwest</td><td> 3866.855</td></tr>\n", | |
| "\t<tr><th scope=row>6</th><td>31</td><td>female</td><td>25.740</td><td>0</td><td>no </td><td>southeast</td><td> 3756.622</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/markdown": "\nA data.frame: 6 × 7\n\n| <!--/--> | age <int> | sex <chr> | bmi <dbl> | children <int> | smoker <chr> | region <chr> | charges <dbl> |\n|---|---|---|---|---|---|---|---|\n| 1 | 19 | female | 27.900 | 0 | yes | southwest | 16884.924 |\n| 2 | 18 | male | 33.770 | 1 | no | southeast | 1725.552 |\n| 3 | 28 | male | 33.000 | 3 | no | southeast | 4449.462 |\n| 4 | 33 | male | 22.705 | 0 | no | northwest | 21984.471 |\n| 5 | 32 | male | 28.880 | 0 | no | northwest | 3866.855 |\n| 6 | 31 | female | 25.740 | 0 | no | southeast | 3756.622 |\n\n", | |
| "text/latex": "A data.frame: 6 × 7\n\\begin{tabular}{r|lllllll}\n & age & sex & bmi & children & smoker & region & charges\\\\\n & <int> & <chr> & <dbl> & <int> & <chr> & <chr> & <dbl>\\\\\n\\hline\n\t1 & 19 & female & 27.900 & 0 & yes & southwest & 16884.924\\\\\n\t2 & 18 & male & 33.770 & 1 & no & southeast & 1725.552\\\\\n\t3 & 28 & male & 33.000 & 3 & no & southeast & 4449.462\\\\\n\t4 & 33 & male & 22.705 & 0 & no & northwest & 21984.471\\\\\n\t5 & 32 & male & 28.880 & 0 & no & northwest & 3866.855\\\\\n\t6 & 31 & female & 25.740 & 0 & no & southeast & 3756.622\\\\\n\\end{tabular}\n", | |
| "text/plain": [ | |
| " age sex bmi children smoker region charges \n", | |
| "1 19 female 27.900 0 yes southwest 16884.924\n", | |
| "2 18 male 33.770 1 no southeast 1725.552\n", | |
| "3 28 male 33.000 3 no southeast 4449.462\n", | |
| "4 33 male 22.705 0 no northwest 21984.471\n", | |
| "5 32 male 28.880 0 no northwest 3866.855\n", | |
| "6 31 female 25.740 0 no southeast 3756.622" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "insurance_data <- read.csv(\"./insurance.csv\")\n", | |
| "summary(insurance_data)\n", | |
| "head(insurance_data)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "D5r_D8BkG9o7" | |
| }, | |
| "source": [ | |
| "### Transform Response Variable" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "Hul_eGGAG3Hy" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "insurance_data$charges <- log(insurance_data$charges)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Pj6f9QXLHA-_" | |
| }, | |
| "source": [ | |
| "### Dummy Encoding of Categorical Variables" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 52 | |
| }, | |
| "id": "Q9m7cV1eG0UO", | |
| "outputId": "7f20a15f-88bb-4e3a-ee6c-208da7972526" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Intercept column verified as all ones and removed.\"\n" | |
| ] | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<style>\n", | |
| ".list-inline {list-style: none; margin:0; padding: 0}\n", | |
| ".list-inline>li {display: inline-block}\n", | |
| ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n", | |
| "</style>\n", | |
| "<ol class=list-inline><li>'age'</li><li>'sexmale'</li><li>'bmi'</li><li>'children'</li><li>'smokeryes'</li><li>'regionnorthwest'</li><li>'regionsoutheast'</li><li>'regionsouthwest'</li></ol>\n" | |
| ], | |
| "text/markdown": "1. 'age'\n2. 'sexmale'\n3. 'bmi'\n4. 'children'\n5. 'smokeryes'\n6. 'regionnorthwest'\n7. 'regionsoutheast'\n8. 'regionsouthwest'\n\n\n", | |
| "text/latex": "\\begin{enumerate*}\n\\item 'age'\n\\item 'sexmale'\n\\item 'bmi'\n\\item 'children'\n\\item 'smokeryes'\n\\item 'regionnorthwest'\n\\item 'regionsoutheast'\n\\item 'regionsouthwest'\n\\end{enumerate*}\n", | |
| "text/plain": [ | |
| "[1] \"age\" \"sexmale\" \"bmi\" \"children\" \n", | |
| "[5] \"smokeryes\" \"regionnorthwest\" \"regionsoutheast\" \"regionsouthwest\"" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "model_data <- model.matrix(~ age + sex + bmi + children + smoker + region, insurance_data)\n", | |
| "all_ones <- all(model_data[,1] == 1)\n", | |
| "if (all_ones) {\n", | |
| " model_data <- model_data[,-1]\n", | |
| " print(\"Intercept column verified as all ones and removed.\")\n", | |
| "}\n", | |
| "colnames(model_data)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "jFx8gMv0HD--" | |
| }, | |
| "source": [ | |
| "### Split Data into Training and Testing Sets" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "I5A8XuyjHFBl" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "set.seed(1)\n", | |
| "index <- sample(1:nrow(insurance_data), (2/3) * nrow(insurance_data))\n", | |
| "train <- insurance_data[index, ]\n", | |
| "test <- insurance_data[-index, ]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "nvAWgJ_qHHZT" | |
| }, | |
| "source": [ | |
| "### Prepare Model Data for Training and Testing" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "ELhgYr_0HI1p" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "train_model_data <- model_data[index, ]\n", | |
| "test_model_data <- model_data[-index, ]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "n299YVW0HKRA" | |
| }, | |
| "source": [ | |
| "# Part 2: Regression Analysis\n", | |
| "\n", | |
| "Regression analysis is fundamental in exploring the linear relationships among variables. Here, we delve into multiple linear regression techniques, serving as a basis for understanding the significance and contributions of different predictors in the dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "wu_gSiuHHN1v" | |
| }, | |
| "source": [ | |
| "### Multiple Linear Regression" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 481 | |
| }, | |
| "id": "MVzQuG_jHPga", | |
| "outputId": "7315af4d-81dd-4e4f-a9f1-45312de7273e" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "Call:\n", | |
| "lm(formula = charges ~ age + sex + bmi + children + smoker + \n", | |
| " region, data = train)\n", | |
| "\n", | |
| "Residuals:\n", | |
| " Min 1Q Median 3Q Max \n", | |
| "-1.03533 -0.17138 -0.03868 0.06382 2.12159 \n", | |
| "\n", | |
| "Coefficients:\n", | |
| " Estimate Std. Error t value Pr(>|t|) \n", | |
| "(Intercept) 7.042076 0.082891 84.956 < 2e-16 ***\n", | |
| "age 0.034915 0.001030 33.911 < 2e-16 ***\n", | |
| "sexmale -0.063228 0.028700 -2.203 0.027847 * \n", | |
| "bmi 0.011805 0.002441 4.836 1.56e-06 ***\n", | |
| "children 0.100152 0.011894 8.420 < 2e-16 ***\n", | |
| "smokeryes 1.533561 0.035475 43.229 < 2e-16 ***\n", | |
| "regionnorthwest -0.082398 0.041040 -2.008 0.044972 * \n", | |
| "regionsoutheast -0.140025 0.040180 -3.485 0.000516 ***\n", | |
| "regionsouthwest -0.107718 0.041108 -2.620 0.008934 ** \n", | |
| "---\n", | |
| "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", | |
| "\n", | |
| "Residual standard error: 0.4259 on 883 degrees of freedom\n", | |
| "Multiple R-squared: 0.7839,\tAdjusted R-squared: 0.7819 \n", | |
| "F-statistic: 400.4 on 8 and 883 DF, p-value: < 2.2e-16\n" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "model_lr <- lm(charges ~ age + sex + bmi + children + smoker + region, data = train)\n", | |
| "summary(model_lr)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "3L_ZvwagHRYY" | |
| }, | |
| "source": [ | |
| "### Evaluate Predictor Significance\n", | |
| "\n", | |
| "Significant relationship confirmed by the F-statistic, with a p-value < 2.2e-16, indicating robust predictors.\n", | |
| "\n", | |
| "`sex` shows statistical significance with p-value 0.027847, males having slightly lower charges compared to females." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "EHpbcaMIHqeu" | |
| }, | |
| "source": [ | |
| "### Model Optimization with AIC" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 678 | |
| }, | |
| "id": "lhXna6-lHqA5", | |
| "outputId": "118f4fd7-18ef-410f-8945-46151b234a40" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "Start: AIC=-1513.99\n", | |
| "charges ~ age + sex + bmi + children + smoker + region\n", | |
| "\n", | |
| " Df Sum of Sq RSS AIC\n", | |
| "<none> 160.13 -1513.99\n", | |
| "- sex 1 0.88 161.01 -1511.10\n", | |
| "- region 3 2.39 162.52 -1506.80\n", | |
| "- bmi 1 4.24 164.37 -1492.67\n", | |
| "- children 1 12.86 172.99 -1447.09\n", | |
| "- age 1 208.54 368.67 -772.14\n", | |
| "- smoker 1 338.89 499.02 -502.09\n" | |
| ] | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "Call:\n", | |
| "lm(formula = charges ~ age + sex + bmi + children + smoker + \n", | |
| " region, data = train)\n", | |
| "\n", | |
| "Residuals:\n", | |
| " Min 1Q Median 3Q Max \n", | |
| "-1.03533 -0.17138 -0.03868 0.06382 2.12159 \n", | |
| "\n", | |
| "Coefficients:\n", | |
| " Estimate Std. Error t value Pr(>|t|) \n", | |
| "(Intercept) 7.042076 0.082891 84.956 < 2e-16 ***\n", | |
| "age 0.034915 0.001030 33.911 < 2e-16 ***\n", | |
| "sexmale -0.063228 0.028700 -2.203 0.027847 * \n", | |
| "bmi 0.011805 0.002441 4.836 1.56e-06 ***\n", | |
| "children 0.100152 0.011894 8.420 < 2e-16 ***\n", | |
| "smokeryes 1.533561 0.035475 43.229 < 2e-16 ***\n", | |
| "regionnorthwest -0.082398 0.041040 -2.008 0.044972 * \n", | |
| "regionsoutheast -0.140025 0.040180 -3.485 0.000516 ***\n", | |
| "regionsouthwest -0.107718 0.041108 -2.620 0.008934 ** \n", | |
| "---\n", | |
| "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", | |
| "\n", | |
| "Residual standard error: 0.4259 on 883 degrees of freedom\n", | |
| "Multiple R-squared: 0.7839,\tAdjusted R-squared: 0.7819 \n", | |
| "F-statistic: 400.4 on 8 and 883 DF, p-value: < 2.2e-16\n" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "model_best <- stepAIC(model_lr, direction = \"backward\")\n", | |
| "summary(model_best)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "5JPRJorbH3QE" | |
| }, | |
| "source": [ | |
| "The results indicate that removing any variable increases the AIC, hence the full model remains the best choice." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "gjDR8mpiH5pD" | |
| }, | |
| "source": [ | |
| "## Model Evaluation and Validation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "DpD2qxUAH8Ep" | |
| }, | |
| "source": [ | |
| "### Leave-One-Out Cross Validation (LOOCV)\n", | |
| "\n", | |
| "To assess the stability and performance of our linear regression model, we employ Leave-One-Out Cross Validation (LOOCV). This method is particularly useful for understanding model behavior on a smaller dataset by using each data point as a test set once while the remainder form the training set." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "iKNZJY3dH4BR", | |
| "outputId": "f8b19f71-942d-4f1f-f725-174b5364841f" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"LOOCV MSE: 0.183368385186224\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "train_control_loocv <- trainControl(method = \"LOOCV\")\n", | |
| "model_loocv <- train(form = formula(model_best), data = train, method = \"lm\", trControl = train_control_loocv)\n", | |
| "mse_loocv <- model_loocv$results$RMSE^2\n", | |
| "print(paste(\"LOOCV MSE:\", mse_loocv))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "YDL5uUmaH-mm" | |
| }, | |
| "source": [ | |
| "This approach provides a robust estimate of the model's prediction error, helping us ensure that our model performs reliably across different subsets of the dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "FKOt2d-nIBqR" | |
| }, | |
| "source": [ | |
| "### 10-fold Cross-Validation\n", | |
| "\n", | |
| "Cross-validation is a cornerstone of model validation, and performing 10-fold cross-validation allows us to understand how the model's performance generalizes to an independent data set. This method splits the data into ten parts, training on nine and testing on the remaining one, iteratively." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "yLNRVlPPICWy", | |
| "outputId": "7d66c55e-0496-4a80-c4c0-63139e676182" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"10-fold CV MSE: 0.179237202596322\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "train_control_10cv <- trainControl(method = \"cv\", number = 10)\n", | |
| "model_10cv <- train(form = formula(model_best), data = train, method = \"lm\", trControl = train_control_10cv)\n", | |
| "mse_10cv <- model_10cv$results$RMSE^2\n", | |
| "print(paste(\"10-fold CV MSE:\", mse_10cv))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "8sCxL9PnIEh3" | |
| }, | |
| "source": [ | |
| "This metric is crucial for confirming that the model does not overfit and maintains a high level of accuracy when exposed to new, unseen data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "6kCvtRXsIFzE" | |
| }, | |
| "source": [ | |
| "### Model Testing with Test Dataset\n", | |
| "\n", | |
| "To evaluate the practical applicability of our optimized model, we calculate the Mean Squared Error (MSE) on the withheld test dataset. This gives us a clear measure of how well our model predicts new data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "8SaaWviFIHgY", | |
| "outputId": "dbf5f568-bc2e-4586-dc83-973a3ee600f4" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Best Model MSE: 0.231290999067122\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "predictions <- predict(model_best, newdata = test)\n", | |
| "mse_test <- mean((test$charges - predictions)^2)\n", | |
| "print(paste(\"Best Model MSE:\", mse_test))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "NLmNSUj9IKDQ" | |
| }, | |
| "source": [ | |
| "This step is essential for verifying the model's accuracy and reliability before it can be recommended for real-world applications." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "CDpfMSF2ILof" | |
| }, | |
| "source": [ | |
| "### Comparison of MSEs\n", | |
| "\n", | |
| "Finally, we compare the MSE from the 10-fold cross-validation with the MSE obtained on the test set. This comparison helps illustrate the consistency of the model's predictive power." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 129 | |
| }, | |
| "id": "q6h9OVtgIKk4", | |
| "outputId": "7779c660-6074-4049-e9c7-e3f93c60c2cf" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A data.frame: 1 × 2</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th scope=col>MSE_10CV</th><th scope=col>MSE_Test</th></tr>\n", | |
| "\t<tr><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><td>0.1792372</td><td>0.231291</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/markdown": "\nA data.frame: 1 × 2\n\n| MSE_10CV <dbl> | MSE_Test <dbl> |\n|---|---|\n| 0.1792372 | 0.231291 |\n\n", | |
| "text/latex": "A data.frame: 1 × 2\n\\begin{tabular}{ll}\n MSE\\_10CV & MSE\\_Test\\\\\n <dbl> & <dbl>\\\\\n\\hline\n\t 0.1792372 & 0.231291\\\\\n\\end{tabular}\n", | |
| "text/plain": [ | |
| " MSE_10CV MSE_Test\n", | |
| "1 0.1792372 0.231291" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "data.frame(MSE_10CV = mse_10cv, MSE_Test = mse_test)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "_E7n73rNIOIg" | |
| }, | |
| "source": [ | |
| "As we can see above, the close proximity of the MSE values from 10-fold cross-validation and the test set shows the model's ability to predict consistently across different data segments, affirming its robustness for practical applications." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "O11TL2wwIPzM" | |
| }, | |
| "source": [ | |
| "# Part 3: Advanced Decision Tree Modeling\n", | |
| "\n", | |
| "Decision tree modeling provides a graphical approach to decision-making processes in insurance cost estimation. Here, we show the non-linear and complex interactions between variables, and present a more intuitive method of understanding how different factors affect insurance charges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "7MgofSEiIS4S" | |
| }, | |
| "source": [ | |
| "### Constructing the Regression Tree\n", | |
| "\n", | |
| "To explore non-linear relationships and interactions between variables, we build a regression tree model using demographic and health-related factors." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 213 | |
| }, | |
| "id": "jahX00X3IQKg", | |
| "outputId": "f3137e3b-f957-4678-cbe0-b77eebb77eb0" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "Regression tree:\n", | |
| "tree(formula = charges ~ age + sex + bmi + children + smoker + \n", | |
| " region, data = train)\n", | |
| "Variables actually used in tree construction:\n", | |
| "[1] \"smoker\" \"age\" \"children\" \"bmi\" \n", | |
| "Number of terminal nodes: 8 \n", | |
| "Residual mean deviance: 0.1372 = 121.3 / 884 \n", | |
| "Distribution of residuals:\n", | |
| " Min. 1st Qu. Median Mean 3rd Qu. Max. \n", | |
| "-0.84080 -0.19220 -0.05068 0.00000 0.08704 2.40300 " | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "train$sex <- as.factor(train$sex)\n", | |
| "train$smoker <- as.factor(train$smoker)\n", | |
| "train$region <- as.factor(train$region)\n", | |
| "\n", | |
| "tree_model <- tree(charges ~ age + sex + bmi + children + smoker + region, data = train)\n", | |
| "summary(tree_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "eJz09Y1_IWqv" | |
| }, | |
| "source": [ | |
| "This model allows us to visually inspect how different predictors split the data, offering intuitive insights into how various factors impact insurance charges:\n", | |
| "\n", | |
| "1. **Smoking Status as a Primary Factor**: Smoking status significantly influences insurance charges, indicating that smokers may face higher premiums due to associated health risks.\n", | |
| "\n", | |
| "2. **Influence of Age**: Age is a critical predictor, with insurance costs generally increasing as individuals grow older due to higher healthcare needs.\n", | |
| "\n", | |
| "3. **Impact of Family Size**: The inclusion of \"children\" in the tree highlights that the number of dependents affects insurance costs, likely due to increased medical expenses or coverage needs for larger families.\n", | |
| "\n", | |
| "4. **Role of BMI**: BMI is used as a predictor, underscoring the relationship between body mass index and increased health risks, which can lead to higher premiums.\n", | |
| "\n", | |
| "5. **Visual Insights and Interactions**: The tree structure visually demonstrates how different factors like smoking, age, BMI, and family size interact to influence insurance charges. This helps in easily understanding complex relationships.\n", | |
| "\n", | |
| "6. **Model Fit**: The low residual mean deviance indicates a good model fit, suggesting it effectively captures variations in insurance charges across different groups." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "viNa_G2YIYOj" | |
| }, | |
| "source": [ | |
| "### Cross-Validation for Optimal Tree Size\n", | |
| "\n", | |
| "To determine the most effective complexity of the tree model, we perform cross-validation. This process helps in identifying the tree size that best generalizes the data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "BNU5GeClIXG-", | |
| "outputId": "9d69a126-0f96-4df2-c9f2-22a2cc2e9d10" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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NoomvMAGHN4SNjgHNRweEi/sK9pTgRg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\nSa7glVu36Z4jQlhzozGEROJEXmYb1jZzo+45IgFCcrh1mWfjapM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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "cv_tree <- cv.tree(tree_model, FUN=prune.tree)\n", | |
| "plot(cv_tree$size, cv_tree$dev, type='b', xlab=\"Size of the Tree\", ylab=\"Cross-Validated Deviation\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "HVqaPUwNIabH" | |
| }, | |
| "source": [ | |
| "We select a size that minimizes overfitting while preserving the tree's ability to capture essential patterns in the data. The optimal tree size of 3 offers a balance between model complexity and predictive accuracy, minimizing the risk of overfitting while maintaining sufficient flexibility to capture underlying patterns in the data." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "ScKb5yGAIqJ_", | |
| "outputId": "2408e673-4936-423b-e54d-90358448aaab" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Optimal Size: 3\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "opt_size <- 3\n", | |
| "print(paste(\"Optimal Size:\", opt_size))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "grzjAHWQcGxH" | |
| }, | |
| "source": [ | |
| "### Pruning the Tree Model\n", | |
| "\n", | |
| "Next, we prune the tree to this size to enhance its predictive efficiency and interpretability." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "zGPgXNPfcKU7" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "pruned_tree <- prune.tree(tree_model, best=opt_size)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "CWku5o-_I4_Q" | |
| }, | |
| "source": [ | |
| "### Visualizing the Pruned Tree" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "pWA0ZgNPI5v1", | |
| "outputId": "9ab14658-2a35-4038-d34d-af70d6cf476c" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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0L+Su24cHbxb7a8Wjyh+GekeE6YuODjfRr5y3bbeLTvwHkLJofzY5f7/Sh8sXha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\nBwgpsCYAHjqLAAAAAElFTkSuQmCC" | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "plot(pruned_tree)\n", | |
| "text(pruned_tree, pretty=0)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "avdYHKQ6I7Nj" | |
| }, | |
| "source": [ | |
| "### Evaluating Model Performance\n", | |
| "\n", | |
| "The final step in this part of the analysis is to calculate the Mean Squared Error (MSE) on the test dataset to assess the model's accuracy." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "qbVQ6fSiI8ax", | |
| "outputId": "1c6ac0ba-3d19-4761-db78-3c5222015af6" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Best tree MSE: 0.289093540232673\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "test$sex <- as.factor(test$sex)\n", | |
| "test$smoker <- as.factor(test$smoker)\n", | |
| "test$region <- as.factor(test$region)\n", | |
| "\n", | |
| "tree_predictions <- predict(pruned_tree, newdata = test)\n", | |
| "tree_mse <- mean((test$charges - tree_predictions)^2)\n", | |
| "print(paste(\"Best tree MSE:\", tree_mse))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Uwb3xyOOJA8C" | |
| }, | |
| "source": [ | |
| "The MSE of 0.289 for the regression tree model indicates a moderate level of prediction accuracy when assessing insurance charges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "fCTeBUv4JDg2" | |
| }, | |
| "source": [ | |
| "# Part 4: Ensemble Learning with Random Forest\n", | |
| "\n", | |
| "In this section, we explore ensemble learning with Random Forest, a technique that combines predictions from multiple decision trees to improve accuracy. By training each tree on different data subsets and features, Random Forest captures complex interactions and reduces overfitting. This approach aims to predict insurance charges accurately and highlight the most influential predictors driving health insurance costs." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "WvBjaQsqJErx" | |
| }, | |
| "source": [ | |
| "### Building the Random Forest Model\n", | |
| "\n", | |
| "The Random Forest model is built with 500 decision trees to capture patterns in insurance charges, considering key features like age, sex, BMI, children, smoking status, and region." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "OFxQObnWLVEz", | |
| "outputId": "19009b10-5afc-495c-e5bc-a30b229fc7b5" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "\n", | |
| "Call:\n", | |
| " randomForest(formula = charges ~ age + sex + bmi + children + smoker + region, data = train, ntree = 500) \n", | |
| " Type of random forest: regression\n", | |
| " Number of trees: 500\n", | |
| "No. of variables tried at each split: 2\n", | |
| "\n", | |
| " Mean of squared residuals: 0.1348921\n", | |
| " % Var explained: 83.76\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "rf_model <- randomForest(charges ~ age + sex + bmi + children + smoker + region, data = train, ntree=500)\n", | |
| "print(rf_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "qfmuRGi4LWTk" | |
| }, | |
| "source": [ | |
| "### Computing the Test Error\n", | |
| "\n", | |
| "The effectiveness of the Random Forest model is evaluated by computing the mean squared error on the test dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "SxVQqnKlLXwF", | |
| "outputId": "21cf6c8b-989e-460e-f658-31111e5e0a12" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Random Forest MSE: 0.178165779907903\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "rf_predictions <- predict(rf_model, newdata=test)\n", | |
| "rf_mse <- mean((test$charges - rf_predictions)^2)\n", | |
| "print(paste(\"Random Forest MSE:\", rf_mse))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "dG_1ieW7LZYI" | |
| }, | |
| "source": [ | |
| "### Analyzing Variable Importance\n", | |
| "\n", | |
| "Understanding which variables most significantly impact the model helps in focusing analytical efforts and interpreting the model's decisions." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 255 | |
| }, | |
| "id": "OCrR5-dgLa3K", | |
| "outputId": "978a4023-d83e-42cc-db7a-d8aa91fe59f5" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A matrix: 6 × 1 of type dbl</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th></th><th scope=col>IncNodePurity</th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>age</th><td>235.15334</td></tr>\n", | |
| "\t<tr><th scope=row>sex</th><td> 6.49339</td></tr>\n", | |
| "\t<tr><th scope=row>bmi</th><td> 56.93295</td></tr>\n", | |
| "\t<tr><th scope=row>children</th><td> 32.77906</td></tr>\n", | |
| "\t<tr><th scope=row>smoker</th><td>317.18361</td></tr>\n", | |
| "\t<tr><th scope=row>region</th><td> 15.79779</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/markdown": "\nA matrix: 6 × 1 of type dbl\n\n| <!--/--> | IncNodePurity |\n|---|---|\n| age | 235.15334 |\n| sex | 6.49339 |\n| bmi | 56.93295 |\n| children | 32.77906 |\n| smoker | 317.18361 |\n| region | 15.79779 |\n\n", | |
| "text/latex": "A matrix: 6 × 1 of type dbl\n\\begin{tabular}{r|l}\n & IncNodePurity\\\\\n\\hline\n\tage & 235.15334\\\\\n\tsex & 6.49339\\\\\n\tbmi & 56.93295\\\\\n\tchildren & 32.77906\\\\\n\tsmoker & 317.18361\\\\\n\tregion & 15.79779\\\\\n\\end{tabular}\n", | |
| "text/plain": [ | |
| " IncNodePurity\n", | |
| "age 235.15334 \n", | |
| "sex 6.49339 \n", | |
| "bmi 56.93295 \n", | |
| "children 32.77906 \n", | |
| "smoker 317.18361 \n", | |
| "region 15.79779 " | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "importance(rf_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "G6aPW1DGLc9n" | |
| }, | |
| "source": [ | |
| "### Visualizing Variable Importance" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "FR2spECbLfrL", | |
| "outputId": "3a8cb841-0c90-457f-f82f-487ae8a9617c" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "Plot with title “Variable Importance in Random Forest Model”" | |
| ], | |
| "image/png": 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EABIQEKCAlQQEiAAkICFBASoICQAAWE\nBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWE\nBCggJEABIQEKCAlQQEiAgsYXUvEKIFgf1v+0bXwhPSJAwJbX+7RtfCHN2S3oGWAnt03eqfdt\nCAmIQkiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEK\nCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEBBow1p\nrKyt+5UJCQEjJEABIQH18POS/5bEupyQgDr78HARaXPNtqp7Aghp66w+bVrtP6vUmHFSdG52\ni4FLN13SpeUh7zn7vj6rS0qHkUtNKKTSExPmGVMwNScla/Qy98L1x6S/WHVIQkJDWNrylKWb\nv/1r5+GlVXYFENIkGX/PvSfIBcZMlGNmvD83PWfEtBXPtN2l2Jg12a0un3tD17RFoZAuk5uN\nKeyROW1eXre0hcZMkPHD8j6uOiQhoSH0neCuVrX6a5VdAYSUcYizvOykEpMrU+zWqXKyXV7i\nTGSiPGc3VyYd7IV0p1xuv5ySvNwu17QeYMxkGVL1Z4EhJDSIf8vX3saFx1XZF0BImV3Wh7Zy\nZb5dXiP25Zu5W54xZZm7lDmXD5IfnJBeSjrTflmW1T/fMVQ22hs8GnPIOTkflJqfV7Bg4efi\nb+1C59sDPavs3dLwId0ubSY89K2zlSsr7XK6LHBakMfNd3KU8S5/14b0QsvDttsvCiTsU7tj\nRcwh5/RcW2a2fsOChZ+LF1qWeefbnXtX2bs1gE/t3hjTUhKO/9oJZpVxQlpkvJBWyUj3Chfa\nZ6qx0loyv7JfrJJ+r3iKQjeoipd2aADfJb7tbYw5o8q+YD7+3jp/YsJu26qElB96RpokS2xI\nx76QeGiJ84zUr/x2hIQgndxvg7N6MnFxlV2B/R5piiytEpJp39l97hyYUOR+2HClXGu/ykov\nci4sNISEYP3Qp9v0Z+8/LWl21V0NH9LiLo84qwvk/aohnS3P280PEo72PrUrHpD0lpPc1fbC\nwk4jCAkB23zjoA67nbIoxp6GD2n7fqnn3HX35MRBZVVDWtep1dWPzMhu/VHo90ift+xeZNbn\nyKS5eTkprxMSGq0AXtr9eGnvjMy+eRurfthgzJpJnZOzT3M+y/P+ROgB53dM+VO6J7cd5fy5\nAyGhkWq0f2tXL4SEgBESoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEAB\nIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEAB\nIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEAB\nIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEAB\nIQEKCAlQQEiAAkICFBASoICQAAWEBCggJEABIQEKCAlQQEiAAkICFBASoICQAAWEBCggJDQ6\npU+dPeikPxUEPY16CSKkpWM6pPQ44ytn8+8Htdjl4s3dDrCbBVNzUrJGL4trREJqTn49puVp\nMy/aq/0bQU+kPgIIaUV6l5n3X9k6+wdj/pXUacZdR4zKHGhMYY/MafPyuqUtjGdIQmpOztz9\nK7ssuazNd0HPpB4CCOnu/m/a5R1yhzHHynL7iB0pNqQpyXbTrGk9IJ4hCakZWZPwlrsu7XN1\nwDOpj4DeIxVveUN+Z0z6Xs4Xr9qQyrL65zuGysY4hpvT60cbZCGL5rC4P6vM+67+4dDA51L3\nRRAh/fXwtmJdYopkhPP1LzakAgn7NI4R5+S8U2I2LGLRHBbTwi8vZu8R+Fzqvtjc8CFdJQMe\nXrj4ARvSF3Kqe0nSQLNK+r3iKYpjSF7aNSOvttjkbZw/OtiJ1EvDPyNtadHdefX2qg3pGxnl\nXLLJfUbqtwNjElIzsrnDze56Xdu5Ac+kPho+pK/kBGd1lQ1pW2JfZ3OB82FDVrr7VFQY15iE\n1JzMTZlln5Pe3vuwkqBnUg8NH9LmBOe3Rh90lfOM+U3CZ/ad2lD3UztxPqMp7DQinjEJqVl5\nJCupd5vE8fG8yA9MAB82jJDzHr+23cvJ3R779WnpedN9gyem2ZDW58ikuXk5Ka/HMyQhNS+b\n337wpbVBT6J+AgipcHzHzKMWmRmtOuWbB/dM7XFNceqh9uL8Kd2T245aGteQhISANYa/tfvZ\n+8xhBxASAhZsSA/9doVd3i6zdnAcQkLAgg1pSVqnGXOmJufs6NtKQkLAAn5p9/aw7JSuk9ft\n6DCEhIA1hvdIO46QEDBCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAQQAhjZW1NezLj2dIQkLAGllINw7dEM+Q\nhISANbKQ4hR8SOten/9d0HNAgAhJwxdHSXqaDPkq2FkgQIGEtPp/uqTueZfdHCdF52a3GLh0\n0yVdWh7ynmmq75G+6TTk/ZKSFUd1XRfoNBCgQEIaPjjvul4yx5iJcsyM9+em54yYtuKZtrsU\nN9WQTj+02FltO2hSoNNAgAIJaXCpMV+n9jQmV6bYC06Vk+3yEmcmTTKk4owXvI2n2pQGOQ8E\nKJCQHnVWR8oaG9J8u3WNzLPLu+WZ+EPKWVZiihYHtHhJVnnT+EReC3AaLIJcbA4ipI+dVa4s\nsv+stFvTZYETgzwef0g9C+wTw3cBLT6TD7xpLJEvA5wGiyAXgTwjfeOsLrLPRrnuz/LpNqkd\nDCnY90h7/MlbX7tfoNNAgAIJ6T/OKtceuZmEdG+rd53VWxkPBzoNBCiQkJ53VkfYZppJSGVT\nU8bdesvY5EsDnQWCFEhII+1ybeo+prmEZMyrZxxwwIR/BjwJBCiQkIaMue/WvZ1umk1I2NkF\nENJo2XBp59S9HzaEhGaDfx8JUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQ\nEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQ\nEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQ\nEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQ\nEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUBBoSLmyKrw5\nVvLtP2vDXyYNrNdAhISANZaQbhy6gZDQdDWWkByEhCaLkKrx6+zhex55xdrarwiYYELKz+2S\n0ee27U5Iq/+3Z2r3mWUR75H+0T+9Y26RE9JYWX9M+ovGFEzNSckavczecJxsvKJHardbyqJH\n1A/p2726/s+91/XPfEN7YDRPAYRU2DXzoptHSK4T0qQDbpzVXR6rCOntpC55c84YnGJDmiDj\nh+V9bAp7ZE6bl9ctbaExE2Xo+YvfGSIPRQ+pHlLZoMN/tqvSy9p9rzwymqcAQpoir9nlcPnE\nhjSo2Jj3ZFRFSMPEeeqZKjakyTKk1Ll68nK7XNN6gBPeOLu5WkZED6ke0pLEL9319t3+rDwy\nmqeGD6msQ3fnpdnqBd/bMJ53LkgaUB5SaYveznU+cELKlUedvVn98x1DZaO95FVnb0a/6DHn\n9Cwwpvg7vcX1+4VGvuB45ZFZNM9Fw4e0To4Nb+baZyUrc9/ykL71dm7xQlphNwsk7FN7ycrw\n9Subk7OsxBQt1ltMOTg08pUHK4/MonkuNjd4SF9UvDILfWoXEdJ/ZaS7J2FgeO8q6feKpyjy\n+pWpv7R7ov12b2PkFOWR0Tw1/DPSrzIovFk1pLXeM9JGKQ+pQCpeyDVcSEVt/uKu309eoDwy\nmqcAPmzo2KHYLv9zxycxQtqe6ibxTkVIJiu9yFkVmoYMyTyQMrPAbHys4wTtgdE8BRDS2TLH\nLk+T92KEZI5wP7UbHxHSFLnaLgs7jWjQkMxjXSUzoeUfitUHRrMUQEhrOyVfeNMIOTPWSzvz\nckL2lTeNOCqzIqT1OTJpbl5OyusNG5LZ/ukLy3/VHxbNUxB/2fD1GdkpvWaXxAzJPLF/asfJ\nRd0PqPgDovwp3ZPbjlpqGjgkoB7495EABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQE\nKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQE\nKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQE\nKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQE\nKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQE\nKGhsIY2V/DhuRUgIWGML6cahG+K4FSEhYI0tpPjEE9Lmdx564Rv9qWDntNOG9Fh2Uq/MhLE/\n+jAb7IQCCGmsrD8m/UVjCqbmpGSNXuZc9PeDWuxy8eZuB4TeI319VpeUDiOX2h3jZOMVPVK7\n3VJW85D1D+mx5Bs3GrN4v4HFcd0HoLIAQpog44flfWwKe2ROm5fXLW2hMf9K6jTjriNGZQ70\nQlqT3eryuTd0TVtkzEQZev7id4bIQzUPWe+QtmXnueuC9vfHdyeASgIIabIMKbWrKcnL7XJN\n6wHGHCt2s+RICYU0UZ6ze1YmHWxMroyzm6tlRM1D1jukBam/eBsXD6v3/IGqAggpVx61y7Ks\n/vmOobLRpO/lXP5qKKSyzF3cV3KD5Ad73VedzYx+NQ85J+edErNhUd0Xj+SEbnnHfvW5GQsW\n1Sw2BxHSCrsskLBPi7wnnF9CIX0nR4Wu9679Z6WzmblvzUPO6fWjfUorrPviuczQu66Zh9Tn\nZixYVLMI5BlplV2ukn6veIq+kFPdHUleSKtkpPvlhTI/dN3aQ6rvS7uCxH+667IDL6/nLYFY\nAgupQMpfrn0jo5zVptAzUn7oGWmSLPEtJJPba7Vdll7Rak19bwnEEFhIJiu9yFkV2jkk9nW2\nFoQ/bGjf2X3dNTChyL+QNh2XMXbmxfu0fa2+NwRiCS6kKXK1XRZ2su+PfpPwmX2dOTQc0tny\nvN3zQcLRxr+QTNmz5ww6ceZ39b4dEEtwIa3PkUlz83JSXjfmael5032DJ6aFQlrXqdXVj8zI\nbv2RnyEBmoILyeRP6Z7cdpTz9wvmwT1Te1xTnHpo6C8b1kzqnJx92kpDSGgqGtHf2v3sfeYQ\nD0JCwBpFSA/91vnN0u0yK94BCAkBaxQhLUnrNGPO1OScongHICQErFGEZN4elp3SdfK6uG9P\nSAhY4whpRxESAkZIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQo\nICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCnaWkBaftnuHw/70a0NMBjujAELa\nOqtPm1b7zyq1mwVTc1KyRi8zZn7COGfXsMRFcQ1Za0h3Jp1y37MzcvZZH9fwQG0CCGmSjL/n\n3hPkAmMKe2ROm5fXLW2hMefLfGOekcviG7K2kN5Pmuesfj5oZHzjA7UIIKSMQ5zlZSeVmCnJ\ny+3WmtYDjNm46+5bf+2+x+b4hqwtpNzjvPVy+Sq+AwA1CyCkzC6hF1hlWf3zHUNlozELEqb/\nPvHdOIec03Ntmdn6TbWL/WaHrtju/hqvx4JFnIutDR/S7dJmwkPf2o0CCfvUfjU1LeXyeIec\nk/NBqfl5RbWL3neFrtj5f2u8HgsWcS62BPCp3RtjWkrC8V+bVdLvFU+RvfQ9kY/jHbG2l3aj\nz/HW3yUuj/cQQE2C+fh76/yJCbttK5B+FReVHrJLh8FlcY5XW0hPtfjMXZ+9V7xHAGoU2O+R\npshSk5XuPBWZQmdxkzzxsNwW52C1hVR2QvbDa7csH5f+dpwHAGrW8CEt7vKIs7pA3rcxXW23\nCjuNMObzFscbc2TGf+Mbs9bfIxX/MdO+FTt0RXzDA7Vp+JC275d6zl13T04cVGbW58ikuXk5\nKa/bF3Ytv7Y1pR1WGteYdfgTodIvFv8U19hAHQTw0u7HS3tnZPbN22g386d0T247aqkxN8st\nzq6ZMruWG8fG39ohYDvL39oBviIkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoI\nCVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoI\nCVBASIACQgIUEBKggJAABZ+cvQkAAAocSURBVIQEKCAkQAEhAQoICVBASIACQgIUEBKggJAA\nBYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAA\nBYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAA\nBYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKGgeIT0iQMCW1/u0bXwhFa+I7ZQD5/no\n4KP8HH3vE/0cvcskP0fPuNTHwR+S6T6Ofou8VM3JVIsP63/aNr6QqnPpGD9HP+18P0c/Yrqf\no+91j5+jt33ex8G3yGIfR/9KvvJx9MoIyUNI1SGkOiEkDyFVh5DqhJA8hFQdQqoTQvIQUnUI\nqU4IyUNI1SGkOiEkDyFVh5DqhJA8hFQdQqoTQvIQUnUIqU4IyUNI1SGkOmk6IV1xqp+jn3mx\nn6MPucHP0fs86Ofo2f/wcfDipPd8HH2drPNx9MqaTkg/f+/n6D/85OfoBb/6OfrabX6O/lWJ\nn6Ov9nNwn0evpOmEBDRihAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJ\nUEBIgAJCAhQQEqCgqYRUdEmPlM6532kP+3Do/z5wvfohiq9MPNDbihhX7RDlo/txBzb8Lid1\n19HuvwPuw9wrRvdj7qvP6ZWaNXqpMf487tVrIiFt6y8n3TA5pecG5XFvlXHTHAu0D7Gyf+vQ\nqR4xrtohKkb34Q78uKsMv/b05PR/+zL3iNF9mPt/OqSeMf30lJR3/Xnca9BEQrpF/myXT8rv\nlMedXvF/wlE9xM8tBqxKOzB6XK1DRIzuwx24QO6wy2fleF/mHjG6D3M/NuFfdvmcnOrL3GvS\nRELq13qrs9otu0x33EtklS+H+PF3xSZ0qkeMq3WIiNF9uAOXHl1sl2Utevgy94jRfZj7H65y\nliUpfX2Ze02aRkhbko5212eJ8n/OYqJ8X7L2e38O4Z3qEeOqHiIUkm93YGvKYb7N3Rvdv7l/\nK2N8nHtsTSOk/8pZ7nq6zNcdeIxc005kj0f9OIR3qkeMq3qIUEi+3YHb7Uswv+buje7X3De9\n2af1ch/nHlvTCOk9ucBd3yTP6Q58hPS68a9XtZF7fTiEd6pHjKt6iFBIft2BhamDtvs2d290\nn+aeKXLGav8e9+o0lZAudNezRPk/+/nGM85/ce7TtPbb9A8RDql8XNVDhELy6Q48ltb/R//m\n7o3u09yvPPfQxEGrfZt7dZpGSKtkorv+g/zTl/FPkGX6h/BO9YhxVQ8RCilE9w6UXSfH/WL8\nmnt49DD9B//Nln1K/Xrcq9M0QtqWfIS7Hiff+DL+ebJA/xDeqR4xruohKoekegfKJstF7n9e\n1Ze5l48e5sODP15W+vW4V6dphGQGZmyyy9Iu3XWH3Xj3Y+56kKzWP0ToVI8YV/MQ3ui+3IFL\nJC+05cfcy0f3Ye7f9pngrk+U5X497tVpIiHdL3+0y3tkhu6wpV1bfWZXL8gBPhwiFFLEuJqH\n8Eb34w48K5eEN32Ye8Xofsy9W+oSu/y8Vastfj3u1WkiIZUMltEzTkvYf5PyuC8mtMy99oSE\nNu8pH2LhtGnTkjrZxQ+R42odImJ0H+5Ab7nI/cudaRv8mHvE6D7M/fmklNOuOaul3Gn8mHtN\nmkhIZuPve6R0veBH9XHfHdY2ucuZq7QPcWPo7zGd391HjKt0iMjR9e9AeHDnfy6kP/fI0X14\n8JeM6ZjU9piXoob06+yJ0FRCAho1QgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKg\ngJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKggJAABYQEKCAkQAEhAQoICVBASIACQgIUEBKg\ngJAABYQEKCAkQAEhAQoICVBASIACQmpukgbW59pjJd+viexcCKlR+kyGVrdrnqR97m317htr\nf1RI89z/z2Ri9gmLYo5249ANdrEq3nkijJAapRpDkqO9rTqGdNi0adMuHpqY8Eh1I34nr8Q1\nSUQgpEapxpAGyzx3q44hTXfXbyW321rNiC8S0o4jpEbJC2mcbLyiR2q3W8rsdn5ul4w+t213\nynihR/YG50puSF+f1SWlw8ilztf/6J/eMbfIDalgak5K1uhlpiIkM1SWmuFSZLe2O09pY2X9\nMekvOu+Rhjuv/RYNSlzjXOuH5IMb/M42C4TUKHkhTZSh5y9+Z4g8ZExh18yLbh4huU4Z/3hJ\nznWu5IS0JrvV5XNv6Jpm3wG9ndQlb84Zg1NsSIU9MqfNy+uWtjAipPHyZmRIE2T8sLyPnZAW\nT5Drnv9xrvzJudZ9cm9Ad7mJI6RGyQspV8bZ5WoZYcwUec1uDpdPbBn/Z0YnvGu8kCbKc3Zr\nZZJ9HhkmzjPQVLEhTUlebjfXtB5QEVJxr4T8yJAmy5BS431qd6Pz0m5T5u7O1Y5O/ymAu9sM\nEFKjFA7pVeeLjH6mrEN35/Xd6gXfuyGtabn/djekssxdnMvNIPmhtEVvZ+sDG1JZVv98x1DZ\nGAppy79PdKKMCClXHnWuXh6SOV/etk9lSeOCuLvNACE1SuGQVjpfZO5r1smx4V1OSOYmmeWG\n9J0c5V6YK+9+611liw2pQMI+DX38bY36JSqkFc7VK0JaIWcbc4+83tB3tZkgpEYpHJL7Cx4b\n0hfOyzuPG9L2PhlfOyGtkpHuhRfK/P+GNhMG2kv7veIpslf/7fTp02fc+aGzr1JI7tgVIZkD\n2mw2R3Yvbci72YwQUqMUHdKvMii8yw3JvJsw0uze1+SHnpEmyZK13jPSRvcZqZ+puPr0imG9\nkDbFDulOeTo/8Rp/71fzRUiNUnRIpmOHYrv1nzs+CYVkzpHn9u1rTPvO7nukgQlF21N3c7be\ncT5syEp3gjGFJiqkMeJc9EnskIpanHyb8DcOcSKkRqlKSGfLHLt1mrwXDmlDx2779HUuf95+\n8UGCTeMI91O78e6ndnK13SzsNCIqpCnyL7u8IiqkWe4nf8acntFvkEF8CKlRqhLS2k7JF940\nQs4Mv7Qz5hERG9K6Tq2ufmRGduuPjHk5IfvKm0YclWlDWp8jk+bm5aS8HhXSYjlwwZKrBreu\nHNIz8pvZToNvijzQ0He02SCkRqlKSObrM7JTes0uqQjJHOmEZNZM6pycfZr76d4T+6d2nFzU\n/QC7mT+le3LbUc7fO1QKyczdp8Uu5/7UZVClkIpPatHuaeeLnIxfGuj+NT+EhLA1KecHPYWm\ni5AQdkrK50FPoekiJLhW3TWk0otA1A8hwfVsQse8sqAn0YQREqCAkAAFhAQoICRAASEBCggJ\nUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJUEBIgAJCAhQQEqCAkAAFhAQoICRAASEBCggJ\nUEBIgAJCAhQQEqCAkAAFhAQo+H9hg0D2CxJRoQAAAABJRU5ErkJggg==" | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "varImpPlot(rf_model, main=\"Variable Importance in Random Forest Model\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "zlcMjDvpLemP" | |
| }, | |
| "source": [ | |
| "This plot not only highlights the most critical predictors ('smoker', 'age', and 'bmi') but also quantifies their impact, providing deeper insights into the factors driving insurance charges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "2EMMkhY2LlNX" | |
| }, | |
| "source": [ | |
| "# Part 5: Support Vector Machine (SVM) Modeling\n", | |
| "\n", | |
| "In this part of our analysis, we employ Support Vector Machines (SVM) to explore and model the non-linear relationships within the insurance charges data. SVMs are particularly useful for this purpose due to their flexibility in handling various types of data and their ability to model complex interactions between features using different kernels." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "ClLYHlgzMAbq" | |
| }, | |
| "source": [ | |
| "### Building the SVM Model\n", | |
| "\n", | |
| "To begin, we construct an SVM model using the radial basis function kernel, which is well-suited for our dataset containing multiple continuous and categorical variables." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 356 | |
| }, | |
| "id": "1DFAt4t9LhKR", | |
| "outputId": "31c94260-1b27-4c10-b7b1-c354c062e2d3" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "Call:\n", | |
| "svm(formula = charges ~ age + sex + bmi + children + smoker + region, \n", | |
| " data = train, kernel = \"radial\", gamma = 5, cost = 50)\n", | |
| "\n", | |
| "\n", | |
| "Parameters:\n", | |
| " SVM-Type: eps-regression \n", | |
| " SVM-Kernel: radial \n", | |
| " cost: 50 \n", | |
| " gamma: 5 \n", | |
| " epsilon: 0.1 \n", | |
| "\n", | |
| "\n", | |
| "Number of Support Vectors: 715\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "\n" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "svm_model <- svm(charges ~ age + sex + bmi + children + smoker + region,\n", | |
| " data = train,\n", | |
| " kernel = \"radial\",\n", | |
| " gamma = 5,\n", | |
| " cost = 50)\n", | |
| "summary(svm_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "uTL0E_aCMELJ" | |
| }, | |
| "source": [ | |
| "### Grid Search for Optimal Parameters\n", | |
| "\n", | |
| "To optimize the model's performance, we conduct a grid search over multiple kernel types and parameter values. This rigorous approach ensures we identify the most effective model settings. For notebook efficiency, I implemented a concise parameter grid." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "iJ5s_Df9MFTc" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "registerDoParallel(cl <- makeCluster(detectCores() - 1))\n", | |
| "\n", | |
| "tune_grid <- expand.grid(\n", | |
| " cost = c(1, 10),\n", | |
| " gamma = c(0.1, 1),\n", | |
| " kernel = c(\"linear\", \"radial\"))\n", | |
| "\n", | |
| "tune_result <- tune(\n", | |
| " svm, charges ~ age + sex + bmi + children + smoker + region,\n", | |
| " data = train,\n", | |
| " ranges = tune_grid,\n", | |
| " best.model = TRUE,\n", | |
| " na.action = na.omit,\n", | |
| " cores = detectCores() - 1)\n", | |
| "\n", | |
| "stopCluster(cl)\n", | |
| "\n", | |
| "best_parameters <- tune_result$best.parameters" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "r7nQWtaYMH-c" | |
| }, | |
| "source": [ | |
| "### Evaluating the Best Model Parameters\n", | |
| "\n", | |
| "Next, we review the best model parameters, which guide us in refining our predictive model." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 428 | |
| }, | |
| "id": "NgjcVzvRMJN8", | |
| "outputId": "00ef09a6-3968-482b-bfc0-c3bf41be7931" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "\n", | |
| "Call:\n", | |
| "best.tune(METHOD = svm, train.x = charges ~ age + sex + bmi + children + \n", | |
| " smoker + region, data = train, ranges = tune_grid, best.model = TRUE, \n", | |
| " na.action = na.omit, cores = detectCores() - 1)\n", | |
| "\n", | |
| "\n", | |
| "Parameters:\n", | |
| " SVM-Type: eps-regression \n", | |
| " SVM-Kernel: radial \n", | |
| " cost: 10 \n", | |
| " gamma: 0.1 \n", | |
| " epsilon: 0.1 \n", | |
| "\n", | |
| "\n", | |
| "Number of Support Vectors: 292\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "\n" | |
| ] | |
| }, | |
| "metadata": {} | |
| }, | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"The best cost is: 10\"\n", | |
| "[1] \"The best gamma is: 0.1\"\n", | |
| "[1] \"The best kernel is: radial\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "best_svm_model <- tune_result$best.model\n", | |
| "summary(best_svm_model)\n", | |
| "print(paste(\"The best cost is:\", best_parameters$cost))\n", | |
| "print(paste(\"The best gamma is:\", best_parameters$gamma))\n", | |
| "print(paste(\"The best kernel is:\", best_parameters$kernel))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "t9VrFdMDMK9r" | |
| }, | |
| "source": [ | |
| "### Model Prediction and Validation\n", | |
| "\n", | |
| "We utilize the optimized SVM model to predict insurance charges on the test dataset. This step is critical for assessing the practical applicability of our model." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "7Zia-o2dMM4-" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "svm_predictions <- predict(best_svm_model, newdata = test)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "nwY81NeXMOHx" | |
| }, | |
| "source": [ | |
| "### Calculating the Mean Squared Error (MSE)\n", | |
| "\n", | |
| "Finally, we compute the Mean Squared Error on the test data to quantify the model's accuracy and reliability in real-world applications." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "1Fyy8_zGMRp3", | |
| "outputId": "ced85d09-0064-41e7-9625-ea5dc5f5b6ff" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"SVM MSE: 0.174901041474651\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "svm_mse <- mean((test$charges - svm_predictions)^2)\n", | |
| "print(paste(\"SVM MSE:\", svm_mse))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "MZ_oop9pMROd" | |
| }, | |
| "source": [ | |
| "The SVM model achieves an MSE of 0.174899627136402, indicating a slightly improved prediction accuracy compared to earlier models like the random forest (MSE: 0.178165779907903) and regression tree (MSE: 0.289093540232673), showcasing its effectiveness in handling the complexities of the dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "q4g2r7u8MUQV" | |
| }, | |
| "source": [ | |
| "# Part 6: Perform K-Means Clustering Analysis\n", | |
| "\n", | |
| "This section delves into the k-means clustering technique to segment the insurance dataset into meaningful groups based on demographic and health attributes. K-means clustering helps in identifying patterns and structures within the data that might not be immediately apparent." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "kEKz71X2MWUV" | |
| }, | |
| "source": [ | |
| "### Data Preparation\n", | |
| "\n", | |
| "Before clustering, we remove the categorical variables 'sex', 'smoker', and 'region' to focus solely on the numerical attributes 'age', 'bmi', 'children', and 'charges'." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "F2Aw-ffXMX97" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "clustering_data <- insurance_data[, !(names(insurance_data) %in% c(\"sex\", \"smoker\", \"region\"))]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "L1apwCodMYws" | |
| }, | |
| "source": [ | |
| "### Determining the Optimal Number of Clusters\n", | |
| "\n", | |
| "To decide on the number of clusters, we employ three different methods: the Elbow method, the Silhouette method, and the Gap Statistic. Each provides insights into the optimal clustering arrangement by evaluating within-cluster sum of squares, silhouette width, and statistical significance respectively." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "WFGWYsEoMb8u" | |
| }, | |
| "source": [ | |
| "* Elbow Method Visualization" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "Gesm2n9oMZ6R", | |
| "outputId": "5993721e-abf4-4a49-c5c3-1a097980c6b0" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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lpYWHi2ShITE0N6ZE3mdrsrKyvj4+MtFovc0tViE2JfUVVA/liiWmlpqdfrtdvt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\nTCAQGI3GDh1tBwiFwu3bt/N4vPT09IiIiD/+8Y8bNmxwu90t9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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "wss_plot <- fviz_nbclust(clustering_data, kmeans, method = \"wss\") +\n", | |
| " theme_minimal() +\n", | |
| " ggtitle(\"Elbow Method for Optimal Clusters\") +\n", | |
| " xlab(\"Number of Clusters\") +\n", | |
| " ylab(\"Total Within-Cluster Sum of Squares\") +\n", | |
| " theme(plot.title = element_text(hjust = 0.5))\n", | |
| "wss_plot" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Ek5ezYKzMeMN" | |
| }, | |
| "source": [ | |
| "* Silhouette Method Visualization" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "VxT9avL3MfKP", | |
| "outputId": "eb854fea-7a62-4568-ded4-1137ce3a8b7f" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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zh4OLo7cZCv+GJZ/c5TpcVVDXZWpgh5ZEy8hZAtx664q0AAAACwx7UTESQSyZIl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\nthWTYIdzqKysXLRo0cUXXzxnzhylZ5GFVqtdt27dk08+mZCQ8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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "silhouette_plot <- fviz_nbclust(clustering_data, kmeans, method = \"silhouette\") +\n", | |
| " theme_minimal() +\n", | |
| " ggtitle(\"Silhouette Method for Optimal Clusters\") +\n", | |
| " xlab(\"Number of Clusters\") +\n", | |
| " ylab(\"Average Silhouette Width\") +\n", | |
| " theme(plot.title = element_text(hjust = 0.5))\n", | |
| "silhouette_plot" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "ncwXoljuMheM" | |
| }, | |
| "source": [ | |
| "* Gap Statistic Visualization" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "1h93zcu1Mh45", | |
| "outputId": "9f155c5d-a3cc-462e-d38e-f6f46e614562" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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BgEgh0y3bPv7u658Y1PazujHgAAI4Ve6QKAYRKKxLyBsNcfcftDXn/EGwh7/WGP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\nRUWZyeFL5XqW5GICIQ8uVVfB7quvv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AAFwmCdcFQMIsif3dtFKfz6dVJnFdCAAA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\nr9fL3KQoSmCngTZv3ux0OufPnz9r1qxZs2ZZrdbXXnvthRde4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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "gap_stat_plot <- fviz_nbclust(clustering_data, kmeans, method = \"gap_stat\") +\n", | |
| " theme_minimal() +\n", | |
| " ggtitle(\"Gap Statistic for Optimal Clusters\") +\n", | |
| " xlab(\"Number of Clusters\") +\n", | |
| " ylab(\"Gap Statistic\") +\n", | |
| " theme(plot.title = element_text(hjust = 0.5))\n", | |
| "gap_stat_plot" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "x3nlOPKhMkp2" | |
| }, | |
| "source": [ | |
| "#### Optimal Cluster Analysis\n", | |
| "\n", | |
| "The elbow method graph shows a sharp bend at 2 clusters, indicating a significant drop in within-cluster variation, suggesting 2 as the optimal number of clusters. Additionally, the gap statistic and silhouette method both show reference lines at 2, further supporting this conclusion for the optimal number of clusters." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "F6mZt5S0MnOw" | |
| }, | |
| "source": [ | |
| "### Performing K-Means Clustering\n", | |
| "\n", | |
| "We have a recommendation for two clusters, and the project's scope demands exploring both two and three cluster solutions:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Za6ZfhIYMo76" | |
| }, | |
| "source": [ | |
| "* Clustering with Three Centers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 161 | |
| }, | |
| "id": "UgLuidPJMlMl", | |
| "outputId": "6cab23a3-8420-4a82-f94e-eee25394152e" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A matrix: 3 × 4 of type dbl</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>children</th><th scope=col>charges</th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>1</th><td>23.42251</td><td>29.89235</td><td>0.8726115</td><td>8.524738</td></tr>\n", | |
| "\t<tr><th scope=row>2</th><td>39.70353</td><td>30.41379</td><td>1.4588235</td><td>9.202735</td></tr>\n", | |
| "\t<tr><th scope=row>3</th><td>55.54977</td><td>31.72505</td><td>0.9819005</td><td>9.610162</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/markdown": "\nA matrix: 3 × 4 of type dbl\n\n| <!--/--> | age | bmi | children | charges |\n|---|---|---|---|---|\n| 1 | 23.42251 | 29.89235 | 0.8726115 | 8.524738 |\n| 2 | 39.70353 | 30.41379 | 1.4588235 | 9.202735 |\n| 3 | 55.54977 | 31.72505 | 0.9819005 | 9.610162 |\n\n", | |
| "text/latex": "A matrix: 3 × 4 of type dbl\n\\begin{tabular}{r|llll}\n & age & bmi & children & charges\\\\\n\\hline\n\t1 & 23.42251 & 29.89235 & 0.8726115 & 8.524738\\\\\n\t2 & 39.70353 & 30.41379 & 1.4588235 & 9.202735\\\\\n\t3 & 55.54977 & 31.72505 & 0.9819005 & 9.610162\\\\\n\\end{tabular}\n", | |
| "text/plain": [ | |
| " age bmi children charges \n", | |
| "1 23.42251 29.89235 0.8726115 8.524738\n", | |
| "2 39.70353 30.41379 1.4588235 9.202735\n", | |
| "3 55.54977 31.72505 0.9819005 9.610162" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "# The project task states to use 3 clusters.\n", | |
| "km <- kmeans(clustering_data, centers = 3, nstart = 420)\n", | |
| "km$centers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "FNAplh3hMrrr" | |
| }, | |
| "source": [ | |
| "* Clustering with Two Centers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 129 | |
| }, | |
| "id": "i-zsWf8rMsol", | |
| "outputId": "a5177c5f-5245-4007-92d6-bb54f210f0f6" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A matrix: 2 × 4 of type dbl</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th></th><th scope=col>age</th><th scope=col>bmi</th><th scope=col>children</th><th scope=col>charges</th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>1</th><td>26.92354</td><td>29.98921</td><td>1.053973</td><td>8.678490</td></tr>\n", | |
| "\t<tr><th scope=row>2</th><td>51.41729</td><td>31.33356</td><td>1.135618</td><td>9.516323</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/markdown": "\nA matrix: 2 × 4 of type dbl\n\n| <!--/--> | age | bmi | children | charges |\n|---|---|---|---|---|\n| 1 | 26.92354 | 29.98921 | 1.053973 | 8.678490 |\n| 2 | 51.41729 | 31.33356 | 1.135618 | 9.516323 |\n\n", | |
| "text/latex": "A matrix: 2 × 4 of type dbl\n\\begin{tabular}{r|llll}\n & age & bmi & children & charges\\\\\n\\hline\n\t1 & 26.92354 & 29.98921 & 1.053973 & 8.678490\\\\\n\t2 & 51.41729 & 31.33356 & 1.135618 & 9.516323\\\\\n\\end{tabular}\n", | |
| "text/plain": [ | |
| " age bmi children charges \n", | |
| "1 26.92354 29.98921 1.053973 8.678490\n", | |
| "2 51.41729 31.33356 1.135618 9.516323" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "# Additionally, based on my optimal cluster analysis, I perform the task using 2 clusters.\n", | |
| "km2 <- kmeans(clustering_data, centers = 2, nstart = 420)\n", | |
| "km2$centers" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "hZOcpQS-Mvs8" | |
| }, | |
| "source": [ | |
| "### Task 6d: Visualize the clusters" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "rJDhIx65MymN", | |
| "outputId": "979b584b-24c8-4ec3-ed62-fe074da86e7f" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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rrdTLo6E+1Jr0eEZlHWJI+ZRUPLF/Wcpuc1r8eFag+DHWqEp9NHAGCbgtviAuyY\n7seMHrL0Hts4ZOrlbVOw+3FToZS90zN2+J1xxli0Jda6ukMQ8T3F7wghclSRowosA8bYy88d\nFokjcZQnzOuhodrAb0JUd4Na/mBuYqUgrRNxZ1ZIRMhU92N1svvxQVMv737cHU9tiKdWRRM8\nrrIKqYlx7c196WLB5EWhfXVHpCXm9YhQ1QghFiUWCITYPHG8Hg6qDQx2qO7+NITlutAqdT9+\nr5IodT8+bBp7Rwf3jg6KHNcVTXbHU+vjLdj9ODSwm0n4UIa/gIUHBjtUX33F3OF8ZpUgdQn4\nvh5yM7sfH7D0ntx4T24cALD7cTiMDBf270sbBnYzCYkzt6wBgNxIZuRIetOJy1aswt/AAw+D\nHaqvpyfLddgCrYnM2v24b7bux1EBN+UFBnYzCTFeFADANG2vB4JqAIMdqqN38hO9hexaQVkt\n4Oq6JlXqfqwzesQyDjtGj6lPdj8eIJ1KpDue6o6nsG2KnzEGA32Zt98acbCbSUi5k+mmicvs\nwgCDHaqjXUO9ALBVxVXVCBTCbZTUjaCeo0LasY5YRo+tD2iFIa2wK90bEcR1sWR3PLU21iLz\nuGDLR47pZrK6I97egnW68OFFDHbhgcEO1cuB3PiAlu8WlRU8/nKPjiIAbtuUMyGmUafXNnts\nvccyXp8YeX1ihCNkOXY/9gdK2aGDY4ffGaeUqclox+pOXsK3jHDiBAEALJyKDQX8LkX18sxQ\nL+DqOjQvleM3SupGSZ21+3FSktdi92OPlHczWbYWu5mEHMcRwnGmgRW7MMBgh+pif2Z0WC9s\nlNQOHlfHo4WVdz/OUueQZRx2jEPWMd2Pu+Op4xKpBHZDrDPbpgfeGunvzQBAvD3ZurKd4zmv\nB4XqThB4nIoNBwx2qPYYwO7hPkLINhnLdahqCbdtCkRsYAOWecgxeqa6H//fwDvl3Y9xrVfN\nlXcz6VizTIlhN5NmwYu8XrAYY7jZOegw2KHae2NiZEQvbpbUVh6/wNDiCTDZNmWu7serI4ll\nnLSeS2LrraXDbiZNbqrjiSPL+HM72PDzh2qMMeaW687Gch2qnVm7Hx/MTxwE2J1Nt432didS\n3fHUykgcw0i1pnUzaV/TKWI3k+bjdjyxMNgFH37+UI29NjE8bmgnSZEUlutQHZR3Px6xzX35\nzCDHBqa6H6u80BVLdsdbuuMpBb8CK1AsmK+9PIzdTBCHrezCAn/woVqijD073BuPeR4AACAA\nSURBVMcDnIWbYVH9tXLCySCezot8XJ3W/ZgQ7H68AErZ0IA2kp4IQTeT5549PO0a96QsVLnJ\nqVgDO54EXlC/jZE/vTKezpjGKVIkic0pUAPN2v24f0b343XxFqkpvzL/9/dvzbxSjYha0eIE\nvnNdZzSJ3UwA4CmA93k9Bs/g4ROhgcEO1YzN6J+H+wQgZ2K5DnlkWvfjd2yjxzYOW/q07sfd\niVSb3Oz7PbWiJSfU1pXtiqp4PRY/eMrrAXgMD58IDQx2qGZeGR/OWebpcizelEUR5Dcqx2+W\nIpulCGOsn1oHLf2IZbjdj58aOux2P+6Op9bGkjxpuj5tDiPLNixzmIM96o7VvEU7QXB3xeJU\nbOBhsEO1YTP2/NigSMiZCs7pIH8hhKzipVW8BAq4bVMOO8Y7ljGt+/HGRCreBN2PGYBmCxrl\n16hysVj0ejh+YAPsKvuwSbPd5OYJPHwi+DDYodrYV5go2tZZSjzSfMUPFCDJUvdjxgZs85Bj\nHLBm6X68Oprgwrg71GEkZ4sOC/ZTm7lVohzHgSA4AEUAe44/zrEfIgAAjucIITgVGwIY7FAN\n2Iy+XpyQCTlDxu2HKBhKbVPc7sc9lt5j6/1Hux/zXdFEdzzVnWiJCcFu6kYpcy84jGRtkQYv\n1dFpmayzM8/zDi8wXnB4gQk85QUajXJTt3Gfb+8898iAOIyjjHNAoqzgMMYREjt6/mGTFu14\nUbBwKjb4MNihGnhxYtigztlSVMFyHQqgJMefJkdPk6MWY7220WPrBy2jJzfekxsn/dCpRtfE\nkgHtfuw49NWXBgDAZlzWEpnX45lC5y6nTf4hxI7FDACYWVRbs37WeySUcZQJNnCUcQ7jpqIb\ncRjvMOJeyYBQIDYrrQPe6/5PJPxxkVSdnm1Q8CJvFvFUscBraLAbGxu7//77X3rpJdM0u7u7\nr7jiiuOPP76RA0D1YDj2q9lRCcipUsTrsSC0JCIh60VlvaiACqPUPmjqhxyjTy8OaYU9w/2q\nIHZFE93xlg3xlByE7seW5by8tz+b0SOJaGf3imnv1qZp1u6h5glqDgAr+9ACsKaKavPfI3GA\n2JS3QS4PahTI4EDOtMF0wLLBtIllg26Tze9avqiRn+b+z2Jg0X6R4wC2Lup+woAXeMbAsqgk\n4Qa4AGvoz6bbbrtNkqRvfOMbqqo+9NBDt95663333acouNM+2PaMDBjUOR0kGct1KETaOKFN\niZ0JMZ1Rt/vxgUB1P9Z1+6UX+ooFM5aKd6xdBtXVYMqDGp03t1UR1OhkMhPdy3MV1RzgHMZT\nxorFYjQ6y8v79mChmudSKY3KIlcEKAI06e+o/NTGWAx2gda4YJfL5To6Oi699NKuri4AuOyy\ny5588skjR45s3LixYWNANac59oujgwqQzYA/CFA4He1+rLA0tQ9a+kFLH5rqfpwQ5XXx5Jpo\n0lfdj4sF88UX+gzdTnS0tK7qAAIzwxnP64qiCwKZUVFzw9zCKpz9dGByDrTOT3qpdColoAiQ\na95gJ05tjMXeBkHWuGAXj8dvuumm0oejo6Mcx7W3tzdsAKge/jzcZ1JnG6+Kjt9/aiO0RIQQ\nt/vxViVepPSQrbvdjyfbphBuZTS+NprckEi1NqL7sTNVLZv+J5elL+2VLZMkl5mtK3sA3p51\n7yfPA39sEJ0KarwNYjXL1EKi6LjNbrIAyzweikfcwycs3BgbcIQxD1bT5nK5G2+88ayzzvrc\n5z43122y2axlWQ0cFLgvhW8XjfpwQatGnd+kD0oMPkEinP+GV86Hr14JfuEtheevHgUYBnoE\n7AHmjEwVumK8sFKOdCmxFZJaYfdjQightvuH45zyCwAOIazseovj7LlmPyfGI6+8uMq2udZV\nuXhHwWGcTYlDic04hxKHgc04yghlYDNiO0AZZzPiUGJRzjdbKyY1+GuPEDi9YwKYlMudsOCN\nPf/CW9AiXj2zYOSHMitXR9o767tEqtpXLx6PS1KwN6c3kgfrf3t7e7/5zW+eeuqpl19++Tw3\n4ziO5xv3GyFjzHEcjuM4zqcLxWzbbuQLUolXssMOY6dxigCEMkYI8eePOfeHiG8/s47jgI+H\n5/M3MMdxCCEevnocwArgVoAAADnG+ph9BOx+x+nRM/3mRERgKxR5uawsV2SVZ6Xoduyf+YJa\nOcrAppxFOerwlHE2JTblLErsqcuFcSXbkwRG9DbrAFHY8HxvzwwYpZTjOAIEAAjx3VwpBco1\nduVuweLjksHzjC1Uj6SUMn//0FvE2NyKneNAvd9rbNsGqOJR/Pki+1ajg91LL7307W9/+9Of\n/vQFF1ww/y1jsYZO8pummc1mFUWJRHy6umJsbKylpcXrURyVs4z9fdk4x5+RSJmabhhGNBr1\nW/R02bZtmqZvP7PZbJYxFo/79IBdXdc5jvPnr8uU0mw2KwjCrEvsa49Q4Bz3DyFO6XLpT5Jz\nVhNnC2cD5wCpqP5FgTiMM6loM95hnM04p+yCPTkfytuMsxk/3zI1AtY40Xo4IGCu5CEqLjgZ\nbFmWruuSJImiuNBtPcAYKxaLkWhDv21NsACysRgFWOCHbbFYNE0zFov581cyy7Js21bV6pYE\nWKKZ6RsjINT7vWZsbAwAfPWOFiYNDXavv/76P//zP//DP/zDGWec0cjHRfWwO93nMLpVbeF9\n93s+QpVZKKgRzgHiQFVBjYHjENsiDuVshximYwE/ZtNh2x427YIDRYfZlItJkTY51qkm1Rq1\nTTEHiX6IYxxYqwSq4rfkIhWp1AYAkANo9XosHuBFPC42DBoX7EzTvPvuuz/2sY+tXbt2ZGTE\nvTIWi2G7kyDKmsbrE8MtnLAZe9ch/5g/qBEKhB3NarxT4exneVBzKLEdcCixKaGUMAY2hcnr\nKbFsgGN/zykWiqoqEY5LAEQYSztWn20M2taRYhYgS6A/JavLI7FVkUSnsvhvJaOXGH0c48Fa\nLVAZU93iadTdP5HxeBwewVPFwqFxwW7fvn2Dg4MPPfTQQw89VLryqquuOv/88xs2BlQrz6R7\nHca2qnE/TkKgGvDHkUrTghph5dcA5/DETrSbnMA4nlYX1BziWBylQNkxWc1xSHlQsx1Sw91l\nAiErBWmlIJ0FkKFOv2X0OeaIoY0Z2uvjwzIvrIzEVkcSyyNxqfLZPQb6Qc4cJkwk1iqB+nHC\nPEjcaXGJywMwaMq5CE7kTQMrdsHWuGB3yimn7Ny5s2EPh+pn3NDfyIykeOF4EautIVafbFfr\n2U8BgDKwHGKbsxTV6hrUliLJ8Uk5shkiBqNp2+pzjD7bOpibOJibIIS0y5HVkfjySGz+timM\ngn6As8YIk4i5mmcBOAsjADQqSVwBIA/g02WvdcULgqXpjFXZ0Br5Cf4kQFV7Jn2EMrZdjnP4\nrR9OT1Vx2/ovU5snqFGHZrJFQRCUKheJ+4dMuC5R7hJlYGyMOv222Wcbw3phWC/AGMREaYUa\nW67GVkbiwrFlPEZB28/ZGcIUYqzigcdvxtooOnJSKADkmjPYCQJvMrAtR8TDJwILgx2qzohe\n3J8ZbefF46SgvpWihfEcETjgdgN3gqDoHE+JCMDRY9MbBVLRWhyHEtshjs3ZFBxKnMlYBqXE\nNnkDOnm58mGyam7sd4S08kIrL5wkR3RGB22z1zEHLfMta+yt7BhPuA4lskKNrY4mEpLMbKK9\nSew8oRHOXMkDLomoHc1x57OzACs9HooXJg+fMDHYBRgGO1SdZ9K9DGC7Gg/ROyoq9xQIPLcs\nOjUTc2Tmqi3qxjKL2A4/GcsoHI1rZbnNcYgdpuzVKArh1onKOlFxFDZiWwOO1W8Zg1p+UMvv\nHRts4yJnTKyXTdGJE2sFvvsCAOx7dXDaNZtPWr64uzKYSBnHkeySBxVIpY2xUcAFm0GFwQ5V\nYUgrvJ0dW8aL3QKurgulpwCAJGQgZCSb1S3TdqhhrHQYASK4Bxg41C/L1JoBD2SZIC0TpFPl\naJ7SQdscNtmGkS6ZigeF3KtOpnVE6VSjHUpEqVHbFAQARSrFeB3AAJC9HkujuT2KcWNsoOHP\nAlSFZ9JHAGC72oxLT5qFyJOIqJnGwfTQ1FUZ2zpJELEy5LEYx61niRVjrYzyOUUblwqCw9J6\nIa0XACAmSJ1qtF1WW2W1MW36ZxbJYAl1Ml/RHDnG6wBZgA6vx9Jok8HOwGAXYBjsUKX6i7mD\nuYmVgrQWy3Wh9T6SfAcg2zvaAtDmXmUapi9b6zcdR5f1oVZGOSuqC6q1GSKbAYqMpm1rmFpj\nttmTM3ty4yLh2pRIuxLpVKKyL0+C8b+pbna5Jgx2nIA9igMPgx2q1DNDRwBgu5LweiCobqQi\nUbIFg58oYCDwF7uo6OlWYGDGdEcxS9dHCLdOlNeBbDE66tij1Bp2bHc1HiEkIUgdSnSZGk1I\nTTeluDhuGZLnYPWZoBeHX39VOHPLGq8H1VClzRNeDwQtHgY7VJG+Qu5wIdslyqsFXFEbWiQ5\nCAC9I/gp9hc7H9GHU0DATBQdafZSiki45YK0HCQAyFBnzLHSjjVhGRnLeDs3JnO8W8NrUyIi\nFmAX4lDIFElLxOS4pltP6k7FWhjsggyDHarI0+kjALBVxtV1oUXkPJHzOY3LakEp1+0lHAAc\n5/Uw6svKRs2xJBAwEgUqVvR2m+T4JMevFxWT0THHHqbWkGP3FXN9xRwhpEVUlimRNiWiEkx4\ncxrLk1SURaOG1wNpNF7ggRCcig00DHZoYe/kJ3oL2XWivArLdeE1Wa4bxTk7H7EycWMswThq\nJopUqLqIIk2V8U5mLMPosGMN2+a4qY2bGmRHVV5I8uJywpYJPBfwkFfzTRujObJhGcTi5sI3\nDR1B4HHzRKBhsEML2zXUCwBbFSzXhRZRsyAVJwpCXg9Muc79Xyz+tq5t8nYodcGIMZq0clHG\nUSNZZDxd9D0dPDDqXuABlgO0cVBUCLTJI7Y16NiDpsZnRlKS0qFGl6sRhRcrvNtwbICdy2iO\nAEAsrns9EA9wAm/qzZhoQwODHVrAgez4gJbfICrLeSzXhRUjiUEA6BvDT7EvMEaMkZSdVylP\nzcSSUt1MIoVkka1fETU4a9Q0sjwZofaIURwxivsmICKInUqkU4k2rG1KbdWqU7FmEs2EWMwE\nYADBex2Wghd4kzHLckRschRMGOzQAp5Ju+U63AwbWiQyAaI+lheKRlDm4/aWf6CobwCc5tVQ\nao4xog+1OprCBMdMFlllB+wuAg+kBUgnL2+So0VGR20rTe1R23onn3knnxEI1yqrFXY/ruHB\nD94qH7bFjalCAUADiHg4pMbjJQEALBODXVBhsEPz2Z8ZHdYLx4tqB/a1Dy1GEmkW+HLd3pBk\nO4fT062OLlPJNmNa/VLdNBHCRUS5C2SHsTFqpx1z2LGndT/uVKItstI8xSuNigkAgGzTBbup\nwyciUa+HghYF363RnBhjz6R7CSG4ui7ESHQcBGMkK+pmIMt1YcIcXhtso6boyLYZ1wA86LXB\nE9LBix28CAB55gzb1gi1S92PJcK1KpFOJdKpxkLfNkVz3I1EWYBAVh8XberwCdwYG1QY7NCc\n9mVGxwxtsxRpxXJdWBFG4mnGYGC80iXzPnC0MscoLRQKgiAoqurhgGqC2bw22E4twVYsK6Z5\nPRwAgBjhYyK/HmCW7scTw6HvfqxTiTLCkZzXA2k0fvLwCdwYG1T4ho1mxxh7driPA9iixLwe\nC6oXEh0FwUxPiIYViOpLqVYXilnXMtQU9cE26vCWati17p22fkPbEu9h1u7H42Xdj8UIp1q8\nagthaujLAHQmRUgRwAII0G8+SyXg4RMBh8EOzeKuV3e7F06WIy0cfpGEFKEknqYUBsYDsbou\nPDOwT/S+Xbp87urjHEPSB9sY5ayIbkf83mZi7OAEAHQCtHGQV6AgkaJsGxLJSxYBkG1OtYSI\ndcwPjcennu95q6voJv3Ga0MAAHBMwWzBPRm13bSh2XJEMgByAK01vNsaeu7ZwzOvXOIxaFOn\niuFUbFDhezY6RinSAQAB1j/YB+tbPBwPqh8SGwHeHhqXLCdwC+IDvFWiPNUBwJ+PjJ3onAQM\nrJhmK5ZXo5qp1P2uXHnxj6eQLEKyyACgZX0i7VhjtpURHF0wx1VzfPBQu6x2qtHnRgZK/+Tx\n3rerynbVqvnm3CKV2gAAsr4NdvXA4VRswGGwQ7NiAETRDY7WsoEW8hHOIfFhh8LgREDLdQHO\ndiUdrPN4exMQYsY1R158qpsZwpY+/VqVFCekOAFEtcjoiG2lHXvctg7b2cOFbCOHUXMaLe2f\naCIczwMhFh4+EViBWFiDGo8QYBHNFyu4UT2Q+DBwzuCEZONPb4+soCtPsDdRYEa8uJRU5ysR\nwq0R5TOV6Dlq8gw5JpkW5xyz7O7xYwuWPucwzqQiQB6giX7FJQR4nsOp2ODCih2anaLrWK4L\nLc4msRHbIUMTgVgSPtfqur0ApzR0ILWzmq5Z56y3wXmRHX6X1NDqWmO4bVMU0wAwDEkypMnC\ncD2mYmfOwNZQkUoSVwAoADRR1ydeEEzT78s90VywYoeO8Xcnng0AhLFIEct1vvPzA6+U/izl\nfkgiDYT2j4sODdzqusA7d/Vx3XTDOme9DtYe2pNhRa9HVEfbO7sAoFFdlmex79XBJca+qW52\nzdX0hJd4Splt4+/2gYQVO3SMvaMDAKDqOsfYZzac7PVw0FHTwtzPD7yyyE8Qb5HomGWT4Uwg\nynUw71q64L3x6MOplU6E8hSSxqncMq+HU52DB0arXb23vbPr/8Yno1Vdd07Uiea4tcYswEqP\nhzKbJW6AnQs3efiELQiBWIOLjoHBDh1lOM5zIwMyIZctX68QrOaGE0kMAaF9YwplWK5rKEY5\nYzhlFxUqOGaiyMLU821ex8dTL5vFk1KdS7wfT86fNZjoMJ4nzbV/QnA3xhpOpLlOUwsJDHbo\nqBdGB3TH3qbEA5HqShUsrCxWQTBIZMywuJEcfu/X3dQkYBYAOCK0yxtkXnFE20xoXk5PzmvW\nLidLxAEBADuwa3Y1KsZ4HcAACOcZGzO5p4pZ2PEkmPCHO5pkOPYLo4MK4U4LwlET5fOS7mWM\nd5UgiTQQ6BuTmE9zRThxROxQjpO4iCNZZkKv+SGwDW5uUi2eEACgjEIdWs01QNGRY7wOkAXo\n8Hoss3QkrsdsLPYoDjQMdmjSnpF+w7HfqyQkwBk6P/rMhpPL4+xigqz4DInENZMbzfG1HBma\nl0CkdmWjyCkZMy+1B7VqtRRuxY4ulGYXvcuhPBrWY4esfrSbnffBrjF4EXsUBxgGOwQAoDn2\ni6NDKsefIuOSCv9aWlXyKZKIALC+URnCkN2D0aCYAOlQjhc4edTIDOlj68HXpbU64YEAgMMa\nEWrrUf/THJEBkGZqU8wLeFxsgGGwQwAAf073mdT5gJoQg7C6DlXvKZB4oooFQx8vBGCqfSGB\nOTc2KnQInDxu5ob0Ma/Hskjzz/NWcugFTwAAnMBO/1PgDCopXAHAAWiKavdksDNwKjaQ8F0c\nQcG2XhofihLuZCnq9VgWCRfYLYgkFQDoHR0NUCqaw94ZFxrzoFU/HAGSkJYxxoaN8XqMKSi4\ngAc7ACg6MgADyHs9kAbhBJ4QrNgFFVbsEOxO99qUvj+SFEhgZujcJLf4Xm7N5SmQBSILOU3L\nFn3VDjcY06mLFhU7eCKNGlmbBuYNsh77MJYyFeuTrRUaddu5ZQCSHg+lIQghhOMx2AUUBrtm\nl7OMV8eHExz/rgCW6zDVVYhLKgDQN1aaNQtuojqmbEa4lwAa0PO2vEZY8evGSKu6kjosshzW\n875bWlc2haq7/6vf1lp38pLOEewWt91h1n9VvxRY9M35E3XqSDyTIPGWGZIjjJsNTsU2u13p\nPofRLUq8KVaONKOniCKAxE8UCjnNV8fE7S37r+dqPwwzF2UOb4g645pxJ2w5jrgVOwYAm09a\n7pMiXFVsxluUB8jWvFWNb/GC4DjMcZr9qzeIsGLX1O56dTdHSAsnbBZVr8eC6uR9JLkfQO8b\nawfw5wFWlZfBZolfsfjburZpyQOYZxh7Z3xYwWgZsSdiDJguFqSm/zHLAyGEOAv1O5kW+Bhj\nxdlWDtSjoUklNCqLXBFAA2iK1gGljbGqigWggGn2nzhN665Xd7sXKGNOdoJLLPW0H+RPJDIB\noj6WF4qGr2qyi6uQTU9UjNJCoSA0+sfYwtnOykapwzuqyUjdCx7PpI+ULm/v7Kr3w01T4QQu\nD0ADeLBvOY1KCSgCZJsr2BmOqgblUGk0CZN4MyqlOgAQHEcxTQ8Hg+qJkcQQA+gf89VJ3jNT\nnYcTsnvnuDzXNRVgxMrEgIClGosdVaXKU93MDz138MCo+wdsVtTtfa8OelVvW7qpZXbN0s2O\nm+xRjB1Pggcrds0uomkADLeXhhKJjoNgjGZFzcRf4RZnMVtMzGyUOrytGsA1y3qsZmBQiTKO\nI97vn2iMqVPFcGNs8GCwa2qC48iGCbi9NJQII/E0Y9A/7vNyXen6xm/UnbVEt6RhsKPlOh8V\nwme2EV76PVS1i5ZnYNftl4vG7MZgADoVI3wRwAII/+ykOxVrYbALIAx2zejvT9rqzsZGi8Xm\n2eTVbEh0FARzOCMalq/aE/q/zcqSsp2djTGHtyOm/8t1XWuTpmlIkizUf5UiYYySoy9IEDfG\nAkDRUSK8AZADaPV6LHXHCwLg4RPBhMGuGQ1pBQAQbFsysVwXUoSSeJoyMuCvcp0Hnuh9271w\n7uqZHe9qnDIZI2YmCgRspe6r61zbO7u83TxRIUKBkWOS7szFdv5Pe1NtirPNEOwEPC42sDDY\nNaOnh44AwMdalq1pb1Cvy8oFfbXfzw+84l7w9lmQ2Ajw9tC4aNq+Ktc1WinVlS7PFu9qxspE\nmcNbqsEaWK7zbZgr507DUlKDOqaH+U+jEgBpkv0THAa7wMJg13T6i7l38hMrBWmNIDfg4UpB\nxzVP3Cnd0r0QxHhX/mS9TKgcJfFhh8LgRLOX6+qtvBzIGLGycSDM9tPqOp9wq3UMGECAf9Nw\nGGdSQeLyEPDWLZUgHOEEDnfFBhEGu6bjluu2KYkGPNa0VFftvw1Wtpv5ZL16CiSWBs4ZHJNs\nJ8Bvov43rRz44dhpzOHsSLNshp22nWLWvRSlK7NGIe+YGza1q3ywtx0UqSRxBYDC1ElpHnvu\n2cMzr6zVsWO8IGCwCyIMds3lcD5zpJDtEuUuoWa1HDfQnN9W0XzQXFlnKREQHYOzSXzEdsgQ\nluvqqTzVAQAPvJmJAWGW4sdy3aypy7areM+edg/VbrPlCQAApcwfcWjxNEduEQoAWYCU12Op\nO17gLd10HMbz+CtikGCway67hnsBYLscr8m9laexx0aPfCp+Yk3uNqA+s+FkP8RTkhgGQgfG\nZTzjcaZFLbBzW6IssM1iFV3NaBOV66rFwdHjYucxW/vinK82VWhOaf9EUwQ7ALBMm8fDJwIF\ng10TOZib6Cvk1ovyitqV68o9/M7r06pxM7NO5eW6YM3DzsqDp8BbJDpq2SSdwR/EAFNJbgnb\nJvaWXZgz2/EgrKSrgDDbl+W6Rpq1krd+QxtfWbBbnFlPs6hTHDSY6DCeb442xZMdT0xHwWAX\nKBjsmsiudC8AbFFqU66rUHm2qzzo1C8S1XXdm+dhlCSGgNC+cXmh89abSz12wp67+rjSbOwq\nZ5XARCvS0M2wwcITN9gdLSNXGbw86V89O41KMV4jxAj0RpBK8BJujA0kDHbN4u3s2KCWP05U\nlvONXno1M+54MmUZgl23CxBMEhk3LG4ki79e18TeGR8eky3cvPj73nfWkDWMMKc+m2GXeOSD\nT7gr6+pUsWuwoiPFeI3nCwAxr8dSX1Ot7HD/RMBgsGsWu9K9BGBLjTbDzprMPrWuojV2fliI\nBgHcdbsgkhgEwvrG5FC8e1YqFn9b1zZ5OIAPRN9tTnBO1JjWgNcn5pobbfAw3DV2lC5u4efe\nqf/6ominOQpAhpB86IMdN3n4BFbsAgaDXVN4MzM6rBdPECMdfL0+4xXuiq2QT9r8Bomok0hG\nM7mxXNN9UyvqG3V4y5/1TNvp2YJRzspGmV83w9ZPtdHQ3VXpwAKHTyzEF9lOpwIDwvMFrwcC\nULvOJrPC42IDquneA5oQY2xXupcQskWpze+XjSy5ha+uVickMQTA+kZlP1aN6oZwL9XtvisK\nEFYmxihnRw3wZbnOPyaDXfXF5M0nDdR+NGUWcbIZBU6nkspphIR85zkv4lRsIGGwC799mZEx\nQztRirTWqFznk74e6CipSNRMweDGC037He1BLYdRzszGGGGOXHW5ziczpJWoyVAXPRW779UV\npcubTxqY9RPd+H4omiOqnMHzRYCWBj90I/Hi5K5YrweCqtO0bwPNgjK2O93H1Xkz7F+vPM4w\nKj31fFouLC/I1TUvzvO4QUcSQwDQN9qIM+L8ZNbZ0saxJmJAiR0N3mZYN6t1rU3W/J7nCnxu\nuxM7LMs/NSoD5AWh6PVA6osQwvEcBrvAwWAXcq+OD0+Y+slyNMnVrOO7Oz1avgxO07Sq7mGu\nUFVh37tFC1OYO0ouECWX1/lM0W9N/RtcRWvowzHKmblFluvmEo4NsLNy251QqEmw836lXdGR\nAcAny+zqihN408Cp2IDBYBdmDmN/HunjgZwt13h1Xf06huA8b7W4xCAA9I767QCxeu9krGhz\nQ/2Yk+U6nXGsrvOqS7wf959XewJYtbdf8F/pIkA7NzxSoEesJcycer9zwmUz3qS8KGgsLDXI\nufCCYBgWpYzjQt60L0ww2IXZy2NDWdM4VY7Ga1euK1ennQ3hrKvVB1FyIBcyRT6n8TDjANN6\nNOb1B48nYRnlrFyMcYs5auKZ9BEAWAGROoxrqRaX5yrBUQCoTb1uisd1u4ItpiSdMS3cTU8E\ngTcALNORFUwLgYGfqtCyGd0z0i8Qcmaty3XIP0hyEAD6RiWYkeo8tffYszJ32QAAIABJREFU\nyzV/A568Q0ZpoVAQBEFR1Vo/xHzMibi7uq7aowfcVNeE3NdpWqu/eUp31XdCWaRFlw8LlpCS\nACAb7mA3dfiEjcEuQPBTFVovjg7lLfMMORarT7muqfhz1wVRJ0DUxvJCwfDVp9jjclq9MYe3\ncxFGKJ4MWzl3e0ntejh737K4YIsAQEjeqwE0Rum4WK8HgqqAwS6cLEqfG+kXCXdGjcp1UP+d\nDb417Vn7prUeI4khBtA/5rfVdTN5v9q9hqZ61+lu77rFTV8OxI9uqNzeOdncu34zobMu1LPt\no4viK3no9RtGAE5Y3ADcRFf55onNJy1njBWLxWg0OuMv610ProhmC5QRjmQ9efSGcXsU4+ET\nwYLBLpxeGB0o2tbZcizCcTW822mbYWt4z6haJDoOojGaFTWzlp/iJZurXBeSbMcc3spFGMcc\n1Zr/lmVRqQBT0Wp7Z9e02dhSqvO59RtGlvLPJ0t1S6jYlU3OTna2q3fv4vkxgLwlJCQNwATw\n/y9Xi8TjcbEBhMEuhAzHeX5kQCbk9BodNVEO85wvEEbiacagf/zoO8q5q48rX2bn0c6JMKS3\neZgTMUY5O6azWuwEmJbqfNvcpCzVvbm4oh0BIAxoXTZWevY7Q97kE5IFkAPw6Sdu6TjsURxA\nGOxC6PnRAd2xt6sJhdSsluOb+UcEAECiYyCYwxnRsI55qwzvNlhfYA5n5aKMY46yQLluHkEp\n0cExQbO8XDdntps/mPZoGUkUNq9t9CkR9ZO33LWt2UUHu+eePTzzyroe/1otYfJUMQx2QYLB\nLmx0x35hZEAh3KnyzLUpi9GA3nU+57sjKwgl8TRlMDAe2gkgf7ImEsCIHalNuS4QDh4YnTkJ\nu7i+ffyizoqdl8fl4bwlABCAnLfDqCtOEADAwqnYQMFgFzZ7RvpN6rxPTUjVdmKYDbY4cXkf\n5sqQ2Cjw1tC4aNrYMrRxmMOZuQjjJjfDVr/RYZGTmKHBA1is6rNi/cymxKCCzOUAKICvlrrW\nDMcRwnG4eSJYwvm12LQ023pxdChKuFOk2pTrZsKo5zGOkvgwpWRwol7luid633b/1On+A8qc\niAMjVsSc6zem9Rva3D9z38eb9RlaHS1xz0Q5HggN3TkNRUcCoABhbnoiCDxOxQYLVuxC5dnh\nfos629WkQLCWE04klgbOHhiTbKf2n+JpYe6J3rdDvWivikX3zObtXJRxdMknw/q0bjdXHj14\noL1WD8EBcdgx+WBmF+J52gUv4SCyOtIcKSUWAHIACa/HUi+8yOsFizFG8G0lIDDYhUfBtl4e\nH4oR/mSpjqcV+WpSsulwNomN2A4Zqlu5rlHcriiB2UJrTsQZI3ZUr2SBQ3lI0jVdViRC3qrj\n4GqhrsfdujgCjAFllKvdpi7PFR33OzELsKpW9+m3HRX81MZYWcbAEAzh+QZDu9O9NqVblBiW\n68KKxIeBowPjohOSpUoenlGxt+y/C6C2YOcjjKO2vJjNsDNSXfAmZGuCJwQAnHBNxppUcBgP\nEOY2xW4rOwtnY4MDA3hIZC3j1fF0guNPrNFmWJfvNoQ2M94isVHLJulMOMp1gWFNluuqPhkW\nlePBDXZUDFdBoUilOK8B6ABKtf921jrcrBU7D3ECdjwJGAx2gXfXq7tLl7eq8ZofGophzidI\nIg2E9o/LtG41j2ktjhvCk+6yVZxJRW3ezquMo/aiVtcp6qHZrvbpSruZajgbyxOARXY88fXE\nvebIcV4DyC4i2AXC5FSsgR1PAgODXbCVpzrBcV44cuBE/+Ww5jxhtsYEk0TGDIsbzop1fZz6\n75bwqlw3T4CbL9u5q+us2PTVdRUmHl1bKysS8euqsqEBHUBvzGNxQAAgfBtjNUcGAIAcQKfH\nQ6kPHit2QYPBLjwixSLOFIUVSQwCYf1jcsDfFmdNdQ0o2u2d4/ICqM07+QjjqLOo1XWNNHP3\ng98OKJuciqVH14dWttF1b9kFPxbtdCowIAQyXg+kXng8fCJoMNiFBG/bslnf957FFd5m9r3D\n08mqJuokktFNbjTf6G/YJ3rfPqfDRwccLc08kW720GCNJybLdWjJJoOd7w/tmNmEBebNoBQ4\nnYoqVwRwAGq+FsZ7guDuisWp2MDAYBcSUV2Dxv7ExHzWMCQxCMB6Ky3X1aawUVps94fhw1Cz\nKVpPKi7lea6KAVBbsPIRxgegXFdDVdX5qioTcgQAgFZz+EQ0uv/YK3xatNMcWeVMgBxAy9Lv\nzVdnxUJpKhYPnwgOn678QBW67Lh3A4BgO7JhQj2Xry3uwIlZ/xXGwepIGlGzBYMbr6Jct9R1\nbCE6dmLvvB/OxxyPA4AdMZby8HNsnmhGbi3LWereHz9uqdZoqZtdCBGe4ziCU7EBghW7YPvT\n0BEAOD/Zsb69a+n3hrscfIgkBgGgb1Su7Ob1etsL+ykU01FLsPMRyi+yd90U71vWNaDzcIVK\n7U4qvD0hL9ZzOLVUnNw/Ec5gBwCcIFg4FRscWLELsCGt0JMbX8aL68W6bLOfv4Pd4mIfhsXq\nyAWi5PI6nylWsnZnkVsEwmuuvRoLMydqUK5z+f/YiUU4eGB01sg4j8l2Jwvc6uhnh7FTC4Xj\nAU6b8cd3bMZbVADINng9TMPwIm9ZDgv41q3mgRW7APvT0GEAeI/aoDMKy5sVYz5rDC4xBAC9\no4vrSLz4BUkzG9oFs1y3yKfPLMGeXF23lCrF0XKdf8pm0yxboUiS7K6Orzf3JLHyXbFz8OlC\nuvlpVBa5AoAGsKQTHf12npiLF3jGwLKoJIVwd0j4YLALqv5i7lA+s1KQ1ggVTtLVQOV5DlfX\nLR1RciDnM0U+p1VbrquB8mz3F8vW1vbOPVd6arMGVmM8AQBWRF9CAeZNADh4oH2x/7w61RbP\n6meukazf0Oa+2cy7ecLvnU3mUaRSAgoAmSUGO3/ipzbGYrALBAx2QfX00BEA2KY0qFxXlZmp\nbsFIh7XAmUhiCAD6xpYS3Jf0BumGHtNYzIkLflZejJy5dpBZglNUGE8dKcyLisoS2NFmLnUt\nIk41KAaYraVIZT3tGmFxI9Ect6yeA1hR2/H4wWQrO8OBmNdDQRXAYBdIh/OZI4XsGkHuEmp5\nbGj9ToadpzfKtBQY0C4qNQ+mRM2AVBzPCwW9woWwAatweGXBDb/GRIIxYkWmHzVRDe/3TPiQ\n2+7EnrNiN3P/8ql1HlEtGVSkjONIOPdPuB1PLNwYGxAY7ALp6XQv1Kdc1+BQNeuMbeCyXfmz\nqNHgGUkMMoC+sVoGd//xxYxbedGOWqJTUJjgONJSNsOWzoH1fobUDyv5XHxIjxRzMSA6FSO8\nBmAC+OjbtiaL9iaPi8WNsQGBwS54enITA8XcelFZIdT32NBFm1b5gzny4uJ641V4P3WKhpVU\nNJee7Uh0HERjNCdoZoj3rftl3275VKw5HmeMWBFzCeU6//J2Kd7krtjZKnabTxqYeSUhLwIc\nX+9R1VDRUSK8AZAD8EuYrhU8LjZYMNgFz+50LwBsUQKz2KGu5bdapcNFPJYb4Go/AAIknmYM\n+pe0ui4oGl20m7nht4SaolNUqOA4YhMdNbE40wqBlURGbrKP3SwVu32vrpi5so0xBlBcwhgb\nrXi0TfHig53nG2BnhYdPBAsGu4B5Kzs2qOWPE5XlfH2r/UtsVryUMFeTINiw+dyaZzsSHQXB\nHM6IhlVt1citgXk/uVmBpZTrlpoFS9lu2rYJt1xnq0bgynX+mW+dh/tmU3mD4pqo9uDXpdCp\nBEAAcvW4c2/hVGywYLALEgawO91LALYoca/HUgNLj0SNLNdVbkmBkjAST1MGA+M+WqZTZ1UF\ntdpM4M7sckJN0dEUKjhL6113jPUb2nRNlxWJEG5mTevggdEF616BSGyzmjlyjoR5jR0AOIwz\n6P9n792D5LjKs/HndPf0XHZnV9LqtrpYWq+MkS0HSzbGljHmIzEIm48EQ5EQh4DjmHsBZa4G\n6sMQHCBOBTA4pCBASDAEV2KgAKNfCBTEIGzjsMYWyGtblmWttNLed+c+fTm/P3q2t6fv9+5Z\n9VNbW7Mzp8853bs7/czzvu/zcnmmAsirzPyfYRlCsq5iPYOM2PUSxhdnppv18/niBtY8uy5g\nTasNT4pIAAvI7WwOj7P8IkTrZtI/A1aYWuDboj+5DimpSLCFkZx53XP456gUw4ql1ebt4h5R\nk0gGhBCi9IpNj7mJilAcWOpSPs9UgSqQRiOqIGBybEbsegUZsesZUEofmDpJCHlB3lyuC+gb\nkh71K7VVsTZ2MOFsmEikPC3L5PS817KYtBQiRIyoTlNu56RaQQ5aDBsJUtu1wgdYEAmxhmJj\nRkPOr0UVWEoPsQsraY/lOKHRpBSk1xIVzkJkxK5ncLRRmWs1LuBL69gEfms2xGWF68w6jAy+\nlungOM2NI12ClGfAiKfneEHSvXd6TZ5Lv2ing4/dBjpHnS9xe74M4OTiTGW2K1s/cf6UnpYS\nRvjYG7tsULxasWxTnGo3O6MBihvyx3Fsm0IUpFzWfCL1yIhdb0Cm9LfVWaYXsuu86m3BM+0S\nkfcCFpeYgBFJ/7QokdMLuuw6xxirVav7ZLmdFRn1vdtw5Dq1JFatn5BavFgvypxUESOpwfzV\n9EkAwynoNKXyVFtONq7x4QsZDCDJqzmc16acSFmOrMr6iY7jSUbs0o+M2PUGDs9PVUThonzf\nIBPfP1VshClm1S04jEw0BO+68jQYeXKWl1ZzqAqh0s0x4HluxqkcztToRJHrhFIrCjvh31Sm\nw580MBSGJ4piu93i+TzHhX8jMJaGAGCB5uotnlDQkPky2wCaQCHpvYQJtTC2L032yxlMkRG7\nHoBE5QenT7Igl+XtvOsCNgQL0bZDmcerbhdwuYCTJAuGk0j/rCCSKUu5Tv3RSIxSGHUNvZLD\nXK4jzG+BXZoB+rV0bWGNM/zixJmLxa0yJ8t+OsNaiVud5w9NnfA03cjoUNKx1/Hl75GIdiyI\nHG+OXfxVGg0pX2YbwJJK7PyFPtOGzKO4h5ARux7Ao3NTFaF9IcmVneS6gMwmXGLkg975XkV9\n3KPcrrBhAUQ+NZ9fFRlIUZQ4mLNDKstALci8l/IXiiLEvqb3Q+05kP75yXIdwP6N23XjdOQv\n1IitskN/FC0SbscQIsuUUkrSl4EfFgXUpNltDGXClCDzKO4hZMQu7RBl+dczpzhCLiIpbSCW\nKphyu28fP6I+DoX5ueyZ5hJMTsyvrbVFMr2k+xU7pKOZuuymD5Fn+xWKj/tbq5/2i/W8zElS\nLkTn1fHwpooZke+cBQNAopRLH7HzimNPLQDQfq5QqGFD5ikISXf9hA8wXOZR3DPIiF3a8cjc\n6arQvjTfX0qdD0PycBM7DugCY4UQ8wILGxdA6MnZgiH7yJKj6CKMaeJ2cRuv9Jd1AVYHbqfN\ntLskd6EkQii1lB+Xc8LcCF3j3Y/PN31+/8bz7aOxPmK1rseOax640d6MrG782NH13te1g9Iu\ndhV7FAOgIE2ZLzJ1QALSWGfgLxCsFk+EvZ0M4SMjdunFPxx+QHmQI8y+fL8oVE2HrYIMM9+I\npFWrl9VDmIVr8QPVeguzVf//jCnjdkboyJY994pQ4VOukvJdavGNUwU5J3Zn13nlQw6D95U3\nKPUTxiCsKSbLdWWkj2S77kNUTjYTUVzVR0YgQ4BOV7EUMZ5QrIm1mDgjnDdMn3j86NLi6qmf\nUEKxQkbsegEZsUspVFYHIFevlgY3myr7acgwS5Zd6dBz7JYMngbB05MwVTFSz9iMCOha4k3w\nI8xvLSbpbEOrz+k7w84NACtynT20DGZkdMZilInoBey4YsNWQkwaTNnLdfFa6JkHYUdGZ1TR\nLhQobE5a1YodgLkKwTD6y63VRuwIyUKxPYGM2KURWlZHKC02mncffez/btihGxaF6YY/XL9l\n172nTEoOY0DPWaV0gW+Q4mK1gZkF9HVXPBvt1uLfXQRwWS0bpmhneumkZl5q5uWcJOe0CoSO\n33gV7UxQKB6n9DzXk7gV9lS41szsz2XlpbDKck2JKYtV3i5WwUyVAOjvX/nM0ItlsEZwHJsV\nT/QE0kvsKpWKKMb34YBSCqDRaLRarj7Bx4ZSo8FQCkCW5aUl54RcN2OiwHVD2384q1cg/u+G\nHQH38/3p47oJjWOUJ78/fVxleKbDwtpSiOg75wwDPH2KUopa1a668+DEU1etGbZ69ao1w/aH\nB0er1QbQ1/8EgFr1Of4m6SavY7p5lMkVuD6d51AqgxACXTK+w+F0cR2AGrckNDrNYccqM/tN\nqhjHGw39LVkVsTZvca5gpVQmxPwtZW95/VhlRvdMo9FwnNMf1JlPn9L5MDcdT0Rle25OWbec\nimLxWSoNA6g2aqwgAnj2mImR7zkjKx7ssizXatH+YZvC36LqUS2B1Fqkr79FSEeJT+o9RxDC\nTM2mBO22ND8/H3wqWZYBuJ+qr6+P5zP/PLdIL7Erl2NtsdBut5eWlorFYqmUsEG8Vq5jZLnY\n7BgxMAwzMLDSf9A0+pmUZKUQ4j/becG/P/P7EDdjPEftFbAZ+f3p4+rqNwxcJIrit48fSZ2e\nl68x/Y1qk52ryCC0r7+v69UF/XDtgAP9uxCXmNdutRmGcLmVil39Vt1CH2btnmes+6Un3Ih2\nVJZrtRrHsoVi0f0+pCbfaBdlTuL6WA5FAIemTuzfaN52otiZ2eTVootFm41mvsBrQ7FaSUw1\nN1FT67zDsVtGR43TbFZ/SPeJ2E1oIIWWML04PMdDaOTyhb6CcuImxK6vr/NXQSmt1+vqj1FC\nvw13i9ocVZmtkHPWy8WiUK/nYP3GFR0EQRBF0c2fqHvU85VGu97fP5DLBU2RnJubA7B27dow\n9pVBj/QSuwwAis0moRTADaMXJagzubf2SB15WsarhkeT3oIeZOA0gIlZHvBhogYkEJ+NwnY4\nHnflroXa8wMAhL6OkKbkuh2aWvlE55dj+UcMK7qMsWpDqO7DsmaBV13wdxwAh2mgf3WEYkd2\nrREEob+vjzAmCZRzVXLOevT3txRitzrA8hwAoS0FJ3YZIkVG7NILRpZLjSZcs6WISFV6CiOi\nRvjtX61BChWSry3W2UrD1VtkCnLs3PTAcH+4m1cjoX1SQ82us8z0ODR1wg3T0vGeeMsdLGGo\n7ZiJrverNczdmxlQAJK8yrvmAZitEAB95Ram7NoF9RbU5hOlGFTUDAGQEbv0otRoAKvho21P\nIGb+SgbOADg5l7caYFPO2Zuwp2iR6nZjy9/3AmgvKJ1h7VTS+BU7hSOGRA3jp3E2ULhdp7KE\nIRSAlLK3tdDbju3esxmgMj01tF4cWr8ayiYULDefyApj046M2KUI2uw6VpYLzRasdaOAnWF7\nAu7PMYqrEV2JMSkugq/PV9la0ySIoyI9fI7LHTZ7OrZAamjoyHW8qC2G3b9xu6NRsI5yuY9R\n/qYyreZixc8XE4JlBwuuY1B8Argwvu0kA9KQ+T62CbSBVZL1z3aaT2SFsWlHRuxSimK9QUDt\niYX9q/G0ao0aNvvXuZwEOdN4K1GoItedspbrMoQHbZB3rL1wDQChqC9TVSiXywisFYxsT+kP\nqyLg/KaINP7rw4LYDCs8bzkU2ylhDl0qSxUaUr6PbQIVIBUx+uDgsuYTPQI7wSBDUmBkuRDA\ndeXuo4+pTCV4hFHHb1LCFHXOzAnuxCtIaQG55mwlV2/3zH+fKOwB9pp99RLExgapmZdyYrd3\n3QriUdRGRoeUr0hXOTR1wn2/srC86wDYN5ztEDuK+FvPxY+6rAh1aTFXCo7lrmJZKDbtyBS7\ntEAbh+2v10l4aShBQorp9P6NgclFdb4EZOAMpTg5t0qiMwlC2zDXImzdxR6EhfMAiH3pMqq0\nhv8+YCqlUx4EIazhEdDzAXAQgYqETatGxLJBU+YpCFlFxI7JQrE9gozYpQJaVsdJEt+yy66L\nDWnoV+YSKd+eCtI3C649vZhrCcR5dK8ijtw7LavDcu+17nKTLlYnNTZKzXUyvyhzTwQvLzCl\nOyFFLc9ffuAA0+VGRoeshDp1z6Hqc8Zd6VuQaa8Vo3SeiLcqNvRWsC4hUaYt5/JMFZBXR3CM\nYVkQImTNJ1KPjNilDqVGIw33/N6Kb4aLyOQ6SspTMsXk/CqW6xILsWmp3sGJpw5s6yKX7fkN\nAI7P1RrT6wFt49cIpaPhSkmbZueonB07qu5t/cjojA/R7tjRWa3psadjjVPpngl+rRgCWPSK\nNdIvdHehCBGxUb26xOeZNlAF4jYojgKEgGWZLBSbfqyGjxGrCawo5lttpECuSzNML04QJnrD\n6EUrnSoiu/KkfwasMLWYa4tpoO6RYszicXzQ8jyxXpBavMSLDSnuOOy+8oYrNmzdv3G7kdUt\nJ9vNGJzntHCW7rwiQb89jhAAEl39PnYKGrJSILV6orEsx2Wh2PQjU+xSgVv2XK5EY/vD8K7T\nen/YV5VavWpKkrTjV6XTSrQnQiRSnpZlcjqT62KH0PGuSyC7bvJUTdu4NiUmxklBERJWR+cJ\nN2hIq65+gmfbTSqKMsdlqlB6kRG7VGCqUQPASSLfDkeuc+OEAu+WKAq309G+u48+dv2W5B3X\nUs4vSXkGjHh6jhekUOQ6hUK5SmWLp6WsRWuKLnPgEKHNqLOH1JHrBMpFqzT48rpzI8j5r6KA\nRfxX2aooiu12i+fzHBfTjUDJsTMNxa5KtCknUpYjJi1xexRMp/mEyHGr+ANqzyMjdqmAku/8\nioFNO4cSsCnvlcoDLYz8MtVgRNI/LcnkzEKgxpGa4gDPh8RF77TQBWTD53ZUlmu1GsdxP5s9\naXxVedBeGAAgJiHXGaFle1Grd/6KYSMtrVgOxZ4txA5AQ+bLbANoAMWk9xIClM8A7ZZUKjmO\nzZAYMmKXPE43qk9XFjaz/M5cDzjWpodO9RAZJeVpMPLkbF6U/ct1GlanCgAObMmlphUGEg7C\nWgl4Yr0otXISL8pcCvO67OW68DuDGUnbpuFC6KvYgwU5e3LsADQkhdhVVgexU7qKCVmaXbqR\nEbvk8YszJwBcWYik/it09JhUlgawIumfFaSgcl3vI1obFEWiU3xP1CeVzrBiqYmItSgfMDqD\neILvLmeRwlGGZAgxVeyMdamU0nrdbWGvaVGtMmey/S0aUgFYBJaAjQluIyxkHsU9gYzYJYyT\n9cqz1cWtLL89TXKdVgwz0jhjY9ZGo2E6uIdEtehAylMg8qm5vBxGAEoj1ylIQ8PWFNVMaFmd\nWCvIrZzEC6mU67pgbN517Oisp1ht1L3FwpqKPZuqYgE05JwMwqyW+gk2l3kU9wCywpaE8csz\nJwBcUYxVrtPyLa3Th/1gK0+Qu48+du8p85Bfpu2BFUjfbFsk00shyHUGVuc43jKj7uDEU8pX\n4E15QqwUMFXZdRkUsLEbFCcLCtKUeaAOrAYyxHJZu9geQKbYJYnj1cWJ2tIOrrCNi1uu86Sl\nuRn8w9kTf1a+IMCOVifI4GkQenIuHzxf3NhNYRlq/amJdGfoxwCYePkGqaiw52qJqYlirSi3\nk5TrFJWr2WjmCzwhTEpCpYlAe+7SeiJwzJHDp5ONkMaJppQvMS1gCVib9F6CokPsWlkoNtXI\niF2SUIphLy/2J72RcPDvz/w+6S2kDFyLlBaaApmthJVdZ8WT7FxFHHlbYG5nROLRYbQXyiDO\nnWGj6K9ging6egWH4+kHvWKUUEKRXKev+FGX+HU5AJVVQOwYjiUkU+zSjozYJYanK/OT9eq5\nXGGYTaMhUJYtFxxk8DRAT84WYrR3cE65CzX8aiXXJZz5J9ZKcjsn5gWZjUiu63jLxcYLPcGK\nO+r2pvjYxbKjFbCUAmSVNE91h7qsvMMvJryPMEAIIQybEbuUIyN2ieHQmQnEnl0XCqwy5/5s\n5wU60e6spoO5BikuNdrMXJWNeCVviWvurX1dwJ69JUPvKO3IdVKxHc0Kgdp8BWd+prwtimmj\nIKlE+ZBDgnfY6UKiap/D37lE2bbM8UwFoEDPtxPkeFZoC0nvIoMdMmKXDJ5Ymptq1s7jixvY\nNFpgGKmbamJsxequG9p+loRiXbbrUOS6idnCwYmj6pOx+AN7plPR7CrkOgktGTXdsBraK3Fr\nh/LcYrt68vi0lpoYaYqvqOi45kGYVnMBWVTKI7wqFGIngzJ+KY6Ns0n8IMxv3QxryHmeqQF1\noC/qLUUNluPajbYkySx79qiuPYaM2CUACjw4NUGAF+RTl13no45VsTtptVZ/7aH24ph2zl1h\ne3yNFCrVJvPv48ei28/Biae81skqMLV8CwvLLS6Un8IR7XQSo+3OyUBuC0BnWgvB1z3LoSOL\noQh4CrFbda0nHP7OGzI/iBqwqCN2Dz/4rG7kpS9IoPmQJ6iFscViRuxSiozYJYDHF2amm/Xn\n8sX16ZDr3JC5NARVTfhTojB2zlXZHhk8DeA7j8/oDgmLS2kahZXh19wuSlaXWHPMErc2xxQW\nhGpLtowWKUVLAIbhtS/SuOFHzybDEQVS0wzt2TXa9SWxRRmKcJomJ4ly2W1KQ11S0uxWQ9PY\n5cJYqVhMxf0rgxEZsYsblNIHpk8SQl6QjyO7zrEPbE9Yzek26am5rc5L2fi8y6lML5RpzPov\nLtxJ8rWlOvfMQkQ5XnocnCjH2wTWDvFYKCsM8mVbztU9X2TXAChuOI7j5qRNZXXpRPojqgE5\nqCLy7Dh33eSTq0xStfs7b8k5mTIMWQ02xUzHozhzPEkvMmIXN363MD3falzIl9ayoV1806wv\nlXPY5IT50OqMbSfUx7riiTToalaM0CqoagOXvdRuGF0gA08C3Mm5XKhlChlM8P+devqFg5vU\nHwlIgRukTEvm6iOjdceeXZPlOoD9G7e7W81VzYTXjhG6Y/0d6AbG5haIsVesunSlTNBPjh2b\n3btnazxLR4RC4YiX4aQh831sE2gDabRBcI/lrmJZYWx6kRG7WCG6AZfXAAAgAElEQVRT+uD0\nSQa4LKTOsO4JiieVyx4286SBzDnCpjTEE0ypHinmwHPztVq1aZJAGbGuptQrhCiP+ajDMA02\nBRXtXFLkAjfAgJH4iHwlTEslUiqw+SCX2kOio5idHLueD8PaWIWboy7l+9gmsOQjfJ8qKKFY\nISN2KUZG7GLFY/NTi+3WH/B9g0wkFhiOtau9hbSdhZbJKdfZoF8ukIEygFNzs8AmhMDkfFCi\ncEOfY8CFXsbvdSxf9QdHbrd7z+bWrCAsQeQ7Mb6R0RlgNeeu9SIYWfGxsy+fUGjTxerPppWw\nqYTlf1+j42a3Cogdh6z5RLqREbv4IFL5oemTHMjzC+EUwwbnPS7Di4kguo0FOWujsKd55n5S\nyiHHzFYq9VYrUhe3A9sqStkEVshT6G1YfU4YnSpp5HYv23JurVZTf2wuDBNCnz7B05V7pz4w\nun/jdm2ancs47KGpE64jtj4RRCTrodoLxeUklKrYpCxOjhw+DQx73UlT5ikICVw/kXghLZe1\ni009MmIXHx6dO1MR2vvy/eVo5DotjNzFKtSoKnymUl8ioVUr1qWclNcut1YZgbphnnZoDkLI\nQIFSemo+rDCWVaOwMThUngbnlCusjs//ThT2BJstNOha31JNO3m5/TTLbF0SatSJNniiaCoL\nVB4EpnfjI6PKg67ArhtWNzI645g1GBYiZIpKKJax+R11/vYIeQR4TlTbiB0SZdpyLs9UgJW+\nG+k3NzGCyYhd6pERu5ggyPJD06dyhFwaklxnCi1BMcYN3RyopXcpTJjzlwknimK73S6VSton\nwzZPuZ+UeHDMzNJic8WWXSFYodAsmxlC1+pSDdWET2V4Lx7aCkCsXwygIjZCXMuxhHZkdAaA\nL77l1t9Yw7H07jm9CLZjUGyFrj/mvr4n0tB3OCzUJT7PtIEqMBDuzEYZT0EUxJEwhOGYrCo2\nzciIXUx4ZPZ0XRSeX+gvkQhNHXWClm/KkiqhLiKEfI7khWTgcZkKp+aGgVDK/WzasLo83Pcd\nUb8ElzucqvurLiD7s9mTB7btEusFgFbFmtVRocA0JqvTt1Q6aBhptMFz37siUB+zFEGmAHFU\nVVclGnJ+LarAUujELmawHJcRuzQjI3ZxQJClh2cnc4TZx5v3kwkxABqb2BZimS3SVyfhFaR/\nFqwwvcC3RR1xtwqn2sPI3pLpu9orkCVWbuXqUlOSrcUgd7CmZUaYtBfTinyHpk7sK28Ispll\nyji+/KPbaKxjbHdkdEgUxXY7poYxKvedlcSTrcrQRtPAhedSU5jVVSTaN9YODUmtn+htsBwr\nNNuSRFm258ubVyUyYhcH/ndmsiEKlxfKxVCz65IqgHXjkGdzlPtDfI+PG0Qi5SlZJpPzMVix\nG29yprfDICyw69h2q80whEveZN7uBi/VCwAqQj3gGsuJdPVDUyVFnNNFYzVsz0RCsw3dmkpu\n4TScDWKe53Uh3TNe11WYgES9ZWhZcbXeqZYFgDblRMpyvW9TvOx4IrJZ84lUIiN2kaMlib+Z\nPZ0nzMV5V3IdPIphwStbPVEu091ev8WhENJ364i0UzoAACnPgBFPz/GCvkvSWPdjl2TLJgjr\nktV5Wi4ERGRxgpUmbA7Cp1gLgdiprE77jJbb2Wp45hTtN5Xp/cWAdLOLEQbI6ksFWBAAkmwa\niu365VJK6/V6X5/522aCUFhms9kUBKG/r48wHrJrGhJf5hpAAyhGtsHI0XE8aUuFjNilEhmx\nixD/cPgB9XGpXi8MpjFAEKRbV6RIyTacwUikf0aSyZmFsN7jPBGyiNibB69jXcZbBP1wnwLK\n2ipgne/Ji4e2S1M8ZeWtI6GlLimi3fJjI5+zkt/0fcyGK6VjlZUnFVpmOOp8W91LzxfT33bM\nBiwhAJx87FYtGnK+jAZQ8U3s0lBIy/JZYWyqkRG7qKBldYwsl5pNq5HurUlCR2oz23qG1QGk\nPAVGmpzlRdlGrlOf8c/DolPFUgijF/HBCYXbda6hcgWoLNdqNdoqUZmRim0YgqGe3En2b9we\nsEbBGLrNoIOSjCJRO2LXHWDtEPrUZs55Ql3KAwAWgY2RLvS8fcOiGFV9w7KVXVY/kVJkxC4O\nlBpNQml0Ypgu2c7NKkEceo00tNEI5DGRWn7pDFYk/VOixEwt6uS6kCOkEalixiU0cU8kFc/1\nempyqwRA4k1uM0GMhfdvrFsnwFkmxinLKetaSGvekup6Wp8zQgnFioFrXHoUTTkngzCBbYp1\nMMp4giCYjgwFTKf5RKbYpRQZsYscjCwXm01E32I1NpUruAmcm0w+7ZjEffUszvd+Uj4XhJya\n4yW9XNdLFaxa1nhw4qkD27Qvem0pFs4ebMd2001KaLMEhso50VQtc2csrGTIhWYpYp+Np82Q\ni61phPuFgldI2CB4KNa+YMJJ2Eu4upyCNGW+xNQAsXfvv1m72JSjV/+w0o9b9lyuRGNLjUZI\nHXQcYKyBsKqKsFHIIqppCG7gguTonfZyaRjn/WAZ0jfTFqWppae0fS17HctBT7dw7OIaCrq3\npLk9SwXInFRw0CdcSHehV62OJ9gVNFy+qFbdBp+WAIQQ2bx4IgQotC/NcduGxJeYFlAB1ia9\nF59gc1koNtXIiF1UqAhtKHJdy0GuCwXGGgirAb7bagXxK7GHTZZh4lFamw2QgTwIOTk3S20T\nhhxx/8IkACwAqUyec9NSLOC2TXmhrnsY9FmGy49a/QCknAD/KW72Qp0/bmc3Z5zNwVIIlkKk\niYRi/ZlKhoyGlEeuAiz1MrHrVMUmvZEM5siIXVR4cHoCwEv61+1Zt81xcJzwR5XiLJ7thcqJ\n+8GxpI9vCsJsRVGSok2ei0cVSwpWZ6dV6SwvVLufAjLfuccELl8IwVVOM08npmkshg3I7WIL\n4EYBlpCkq2KT5HZ1Wamf6GE3O0IIwzIZsUstMmIXCZbard/NTw8w7G5eb3+QTiTOpRLfgBfc\nD4CU8wBOzmrlumjvFrGJebqF2q22F6MuR7i6SoaTHQPKxmFUYiHlRVagZIUoqOUL7vYTpM2X\nK5hZnASFLg0uCM87cXwx8Ha8gQVk78UTRw6fDhZgTUtLZYkybZnjmQpAgV7t3MBwbLuVhWJT\niozYRYJDUxMSpVcUy2E2mjgrEdx+OZINEJAiJ4jiXDXk6rZEoA10RkwfLWNh6h40G3C+E4v1\nIgCRM+mLpZPutLbDGsTRgNW3Mqdlb70YvbWynmGANqU2rcB279kcaksJP53KIkVDzvNMDagB\npq3VegAsx7VagixThulVbrqKkRG78DHfbj6+OLOW5c7PxectbpqmZl8kkXipqUsEL8INawM3\njF7UkesKOTBkbqlqGNvDHV3jTe8zv1Be9yA1igAErp0DBwMT2u/TKSx80S4gFM1P4XYjo0NB\nDFCiN09RuLLdBWRBJJyldicKGjI/iBqw1LvEjuPYFiC0pXwhYxGpQ/YrCR+HzpyQKb2iUGZI\nrB9ljKTHpgTBK6vT0cSYCZbNcvFwPs3kVwFA8VlgYa46DARNoNSll6WweCI8eIiFKd0mlMdK\npt2BbZWDEyvR2APbdlGZkZt5iRFkRjJ9K1NbR6Cj2BkZm/rjuNmTkaCn0+OcoF7Gce3FV6AW\nJrOEobLkOwzpMSBr81eX2MewupgHD4TtZhcnlptPiBmxSyGyX0nImG01nlicXc/mzotRrnOE\n0f1EgWMNhMr/YtbMXLbisDAiiRiEksJSWyTVZjipZ1etGaag/f2ePrtb3ZN6qEWs5VYNdRJl\nZXKlElZ59eDEU+vlDc+lw22zOOzI6IyOWByaKllEY+Eyzc5U64qBpWlT9EZGZwAPK/rW5yI9\nLwYEACUgZhUUoQZhdUiLmt6inEwZhvRw/YTaLjbpjWQwQZhJ0RkA/PLMCQpcUei3+TAabtLY\n3UcfczmhG0MTdTbttDr+5Hen/mG6aFK5d6RQASPPV3PpS3yONT3cWKZqGDJm8bjrKOXLx6Lr\n6BCANmtC7CzS0dIVYDXi2NFZ7ReiKbyIDF382Eij1Rw7lgAxtYtNS8GEAaQh80ATaCe9E59Q\nPIqz5hPpRKbYhYmpRu2ppblNbG7UQq4L12vXyLdC8QGGE2eKTxvrXhQpyQgsLgCYq3oqjFFu\nMGEJBvZ2XCnJ89Nu0pLVaR971PzIWnmdAPHh+plLBjcE2GfovsQrGBkdajaa+QJPSIgfoUP2\nPd6+Y5Dj/NwIDJW5+gHa+hWtOzTr8QOR32LYkJs1h4qxujTaxzaBpQRdrIOAzdrFphgZsQsT\nv5w6AeCKwoDpqz4iobEhcR/gngGRSbHSFplqM6mKZ5sutNrHAW9gAWfQbdJkqoC2fAN0IIfc\nKcwHbuuSXhnPUa5zEzANu5zWnPJabHV8/0aTwQrJpQyFlDbNOx6MAWisuNn1JLFjMo/iFCMj\ndqHhdKN6rLKwheN35vJJ78USobiHJNuz1SpfMOoVFZBCBUSaq+a8zDGmeRCuYKBOGDTkpKNZ\nB7YhvN2OqUlyjntYzqWzLChRXxqS1wOYkSsX969TX9VWjA5XSpPllWjgcKUEn0WygTB5SnG1\nWIGXnq3rdYTJK0ULO5I7vvxdT9fUjbk5OxYEwI7RdYN8IdTtaWHz+ScVol1DPkIxRHrWpni5\nq1hG7NKIjNiFhl+csZPr0oOeMDqxJ6DGl6I4F/O4eWkRgBdiF26Wj/vZ/N/AXDaKtaZfJpt0\nE2nVETj7wevokAx63vrBetOqJAL7N9a9MKHUuZxoEaxNxYwp8RJFsd02yVC0gB/PPyUUq+vS\nyxICQA7WiM8JqWBvZuj8d8iUtmS+wFQBOcRk94cffNb45KUvOCes+VUooVghC8WmEhmxCwcn\n65Vnq4tbOX47x1uNsemI6ojOgdNdR/mW30yNURynSsTixPcVs4GbOc2vBpFJYaktMjX/9bBR\niHZB0c3PtKzOYbcus+J0TiUBcWDbLlng6hNFmRepaV2lH8ThVOwDwaKo5idlKJVtOspsx47O\ndkcMZ90oc2qCnY7eKVWxx47NrX3u1JHDw8qTWndi5QGltF6v9/X1OS7UO+j6b21ISwWmAFSB\ncOQAU1YXERiGYRgmK55IJzJiFw5+2ZHrHO5e/nxDbPq0hii/2ZjeeUWIjncxOK243O3dRx/7\ni4u2g8hzFUvubkC4lvc2HC49+oR/oum+fkKsFwCIvJ1aoDX1tZ1svPuxpWgXlgPIsaOuWFG4\nGBmdiVmPtGnpxoEA2LJjLsbtpBENWViLArAYFrGLGSzHZqHYdCIjdiHgmerCRG1pB1fYxjln\n14XOTsKdMFxWFwriPEGHcpaiEoeNuWxCJYJRsTc1qGoWhB0DLvQyWWeThqS9MI2XpXoBgJwz\nIXYKZ0p5My7VqlcHLeEL2F7CmF0Xds8J/8W5Sg8qWSYAdu+ZVEW71Q79Z56GpPwB96pNMZtj\nmzWBUkriteLP4IiM2IWAX52ZAHB5sVebw6iwIj0uqdW/P/N70zkj4rKRZgqaxM13XUgKv28J\nTK3lntilR0hzgC5hLuzJw7x1UZmRmnmZkyhraYXmumjAGKwMnmnn3FNLiyh8j01PPwDBNedw\nvjep/P9IyzaQZw23078btClEeorrWZtitTA2n8+IRLqQ/T6C4mhlfrJRPTdXGGbdR+hiQvCQ\nqMuj7j1lxwlC5HbasKzvM3Lv56xdjhTnQeS5asy/ZXvLujBhLapZeaiam/MZtDpzVuebSnbk\nOrs4rJ6ueQxEhlBFEX1LVj/wy+3OB4yn43CJtCZ2OrDkNDAgxeBPnHrUpfwAVwcaQIo6FbnE\ncv1ERuxSh+z3ERSHzkzARXadb/iuALXJzIsfoawefwOxriU6cdg4/2UCWdOptCma/rPOnsOG\n8Q77d51glwcgWRC7Y0dnjU65FoiiYKIzZ7Lx32RDzyuOM1jp6qaV91jIAGR55ZDdeyYB1YU4\nLY4kMaAp8wOoA0sREbso6mFVLHsUZ2l2qUNG7ALhicXZ6WbtPL64gTX3vwhY1BmPr4d28tQ6\nFYdo76w7ypWuSWRSqLYEUm/1Rhe+YE0dPCGIr8rKrtTGYo5blRo5yggy93svTrkw6HChsDrt\nnB50PtMEOx3iL7CwQaibGWeQAyBRm8Qsl39UPU8B65JqU7wp4a14R6ddbCtzPEkdMmLnHxR4\nYPokIeSKvLlcl1qSZIMYqlDTBjenSYpLILI7+7qwuof5b4hklM3C5nZjhh8D3Ybd01CpeYLK\nW+XCFABgHDhPN8BGrHKt5LnEuOFxF1nUiXaeuJGhW1fIJG95wvF6fRvPx2yofj4LEahI2GiW\nuue1qrq3uV1T5mVKGBJOEqpWnxMEQRSjpVwsnyl2KUVG7Pzj8YWZmWZ9N19cx7q9jOnpIWaD\nUJxTepHU2qHo0pfYZ5OJ/v4ne/r+ZAuH8/JEQ8XaJgAiv6D8+MzT88uvVL1sKaBcZ6R00cKY\nsWdP9dwRwXEApdLEoamSGwUxRCgGxZJsn2Q3BlzsNEB90Kv/OxRoUr5EaoDYc7djLgvFphU9\n9peUHlBKFbnuMgu5zhRxsjodu7KyqQtlS9dv2dVqtX44e8JqwijIov2cusGvGraUa5wVSiKT\nwlIzsjhsX/8TZk+HfK9yKdq5sCmxM+dTxjul9/l38hPrLwGRZT6gwmEVMx3XPAjB9S2FTium\nsLJfWUbIPTmU/yKzzhPhtmnpDTREvsS3gCVgnfNoa8TWc0JFJxSbNZ9IHzJi5xO/W5iebzX2\n8KW11nJdcOHKipy5P1z3jOl+woq9/tnOC1iWDWUqU7h3OXF/2d0UZJDiIgh14UvsL0Dpe/wK\ndEQqUu8SN7BlkPo6X/e7ldtlKpYkfh6QnUd7xrjhR1M24yjRdR01vKWZL/CEWH4k0KlrUZTT\nmgl+K5mI+zfWD02VrLld+JKkotiJVPdL1LM6Qh4BnmMxR8D/tRShIStvLJWAxC5+MIpilzWf\nSB8yYucHMqUPTp9kgedH02pCN4PyYGnJ0u4oyBKhlJree+qp64ZiiuaESBndFmSUFgHMB6uH\ntVbCApW+ItQ6CdOo6Es2aD/0W2kqYd5WrXQ+sb4LgJRfCHEtj3JUSjuPeYJrkz8tuq6Svfee\nYyBY+fDnpldsX98TZn9aq0rYq8sFAEDvudkxLMMwJAvFphAZsfODx+anFtut5/GlQcbZqzbq\n8Gu4JiBeZ1BX/+HsCcyuxnoLRiL5SrPN1Nv2cVi7AKVH/cwDvTOlYqYjoymMVfbp/kZrzmJd\n7G0MgFjfBEJlflF56tBUyWhra+w8YQuToofuV32EIEMOXMYARbQzeyUSIqv0ijUQO/3f/HKv\nWJez9qpoJ1GmLXM8UwEo0GMtHBiOE7JQbPqQETvPEKn80PRJDuTSyLzr3MOrCUjUZQ09UR2i\nws3V6MRhncsmPJvMHdi2y6L0FWHdpZQop3tKZ4yKHti2q92yMihWEJN8QqU8ba+R2RolguPg\nkdEhFx0gvLIWb0FYf4g6Mmsl15nFYV3Gpj1jORTr26G4JwmcDRpynmdqQA3osfZFbI5t17Ou\nYqlDRuw847ezZypCe1++v+xCrkscxoIDXXQ4CM9Lbemr7rz+dMfudtuenawcqH8qAV/i0BCx\ny4n2GTdM1L+BC7BXqvdRSiSe09CLE5PlOoD9G+uakTNmfnVuGIlv1tJL+pxVMYepF4xh8GxY\nxissIbI+x+7sRV3OD6IGLPUeseNYSiEIMs/3wN3w7EFP3q4ShCDLv545lSPk0kKP/QcqUBQ1\ne0nP/WyeeGHw/maeoF3Cxs9JLcgw3xIjkXy12WYaDnFYB5gqYU4HuSI96swHtlUOTuglZB9N\nWpd1xJWlfzr9rLup7DccVNhbbjixktCjNK3qZnUK3HSA7YzRcJeONuaduyQQe9UqeTYbdi/4\nqSNVizvfe3MDBkRaVuyOHD5tHLB7z2bjk6sVDZEHDyDMlsrxQC2MzYhdqpARO28Ymz1dF4Xn\nF8ol6zI3TwhId+xNQNywLgdm430/ps8n0t9MXfRPd+y2H2m1GVJcAqGzrnyJHaDldq5VNG8B\nWR23W6ZiNpOYvtQVC1b3rM68vHmvRC1Q+IxSIjUKlKWU68rUvmLDVuDJIDN7QQLK3MjoUEJt\nZ5WTnb1gcKTr6RkAuGBwQPvc7xePeZ2dBaRMsVtGi+YkyrBkMcgkOmeTGAyKAbC55cLYnhQ6\nVi0yYucBgiz97+xknpBL8m4Teu0RCt0JpVdEkAPV1f9s5wXq876jtF7PxYoZa5//9vEjOh87\nt6sUFxC4HlaFGZ/bC6BWrVHQ/n4/BEWV6wxruRHYHAd4ZWNRJbDLzTylROL18XRC3F80Xfsv\nB3j1BPZ3iJtJ0g8fp8kCbTkjditoyPl+tgG0AUdbpRRBaRcrZIWxKUNG7Dzg4ZnJhihcXigX\nQpLrwoIVO4mnA8QNoxc1Go1WqxV8Kq8Vvu6Z8Xcmj5paNNutwkgkX20EjsMGgzlVsi59NQnI\nmk1ilRvXxfasi3mjK5gwP1+xVgAg8fqyCUrPazQaLMvl82pfLDcxRK325olIpbri1dSvLp0O\nySyIDN/FE6sQDYnvZxvAIrAh6b14AJvLPIrTiIzYuUVLEsdmT+cJszckuS4eBLQ49oew2KRx\nnuD7d19HbKyH1XWp9x5atYdPixOdOGdRbOsGQehaiEKdCbcTGwUQKnMBhYGAtEz1RtFPErXM\npkpinhay96tLLsgLACwhkiylzd4jwWw/jU1xTxG7rKtYKpERO7f49cxkUxKvLAzkUybXOcJN\n3ptjj4pwGaHv2WK1Uymu+BIbTYB1zyAqozhnKBKdht7ZOeqZDfAQP7VmjaEEYc2ZpdziqchK\nedEdC7CPtyq0LLjw5mqGZeZUU58Jq6rUPYKIdiOjQ/BhZuwCDCEAqCwTJu1vp0cOn46B2zXk\nPAVIr9kUs1nziVQiI3au0JDER2ZPFwnzvFDlurDkNJuMMTcpaAibMHnt6xoD1Bw7t+FpRiSF\nar1lHodNtmGXKQz0zoiwqlZjcBHr2mqnHjbnbF/XDXvi1WFmvphWwIpR9w4serjfrZv2Ett3\nDLbbLZ7Pc1zcNwLFo1gCmLOsANYKMiUtmS8wVUBe7qbbA8hCselEz/wBJYuHpk+2Zen5+X4+\nbBtGHdnyEcTUZYxZvaT90XEV03ilp11pzyu2kg6b8d+ZPOrpKFJcAmhYZRMBcXDiKeVL+dGd\nNLjX7Au2epvp+KgxZnigh1gvAlTOh3XzCMvII73txXSsTv1xZHRI/XI3U1TnqHhjPH7kzJHD\np9WviNbqFdQlHqC9ZXrCsAwhWVex1CEV962UoyYKv50700eYP4glu86TeBacgUUHfxW+WD4F\nN4cHab/rcJ1LC0iHL7FpK1ijMd4yHNmYJ/+UXcBYtxYYbt2rDavrLEQlVm7npJxISaBc+0NT\nJ6C3MrYLp3ZTnxD5zbjmgcnq8cdqrREhc2UJAFBCQVOVZZckmnIeqAJLwGDSe/EAJsdmxC5t\nyBQ7Zzw4NSHK8guKZW61dE1x5EPGAXHGUrUWyjrlL9x4seVrjEjytXqLbQrm/yBGzSy2BLuw\nKzaccWBbxYfRsRdYaXVKf9gCAJkXgXHfVENhdWYwds1yHOPypQSwrMaZBGHdRGbjBKu0i10l\nb6ieodUp1a+6pFR295JiB4DlOKEt+e8PlyECJC9IpBwVofXY/HSZYS/kTZtkrxIENI2LFPHn\n55HiIkDnqite6kZ7YeV71GUTSSfzRVcnYZzcfE6pXgQg8Woc1n/dg1mPCi2sWJp5ywot3FeY\nHju6XsOxPJyL6fwW8p75nKZNw2wRobGL8q8VhVpnDOn2Sg6fQFlBZnNMj9VPcBzbplQUpFzW\nfCI1yIidAx6YOilR+fLiGjaawvyAkVNPTnWe8t4c62TjLFD1QSh1V0ZnUOwAszisKXuLWjaz\nDrmurB4ludwLoN1qMwzhciG03/AKSonY4GVWpuyRgFMNV0rHKvrPZiOjMwZ2ZU+2LJuVaTlW\nL5oMxwy24y2QLp0ncQrYkPM5pg7UgZ7RETrNJ9oZsUsRMmJnh6V26/cL02sYbnc0cp0pJ/NX\nMaDSrJSUo4ao7fkmlOowURTbbX3TAkuwIsnXay2mZRGHTRYJRoFDhWVSnRZSowBKZH3DiRBd\ngj30orAeMx7ABDhcx+NU+ydrofxrnbWhWCs05PwA6kClp4hdpzC2r6d6ZqxuZMTODoemTkiU\nXl4sR3GHD7fKwdGsLk6Gl6C2FxxKHHa+yi+Tj3iKQy2hynL2BE4r7KWe6rm1Vuk0nMg/HXC9\n/Ru3H6uYqmiqrZ3xSSNMnvQlzkXEvSJJ+Gust48M+qSSit3Jlu2Dw6WsyegKGpLCjZaATQlv\nxTUyj+IUIiN2lphvNR9fnF3Lcs/JFZLeiweYNs5Cr7GrBEGKi0hHPawW7lkdXLDApOGKK1MK\nqZEHI8lc1fBi1NJUz0hfBsS5c8tWHI7gCADItAfaxcaZtNeUeZkShvRSml3mUZxCpDHYlBL8\ncuqETOn+fJmJoBjWSq5LM/fS7S3NW/UPVkS+VmsyLeGR5aei64t6NsP5qsqtPJVYKbdg8frq\nt6M7dnRW/XIam96zMMWyQXG6cuwMiPt/nwJNygN1wKsdd2JguMyjOHVIlyyRHsw0608uzq5n\nc7v4YmyLpp8qBeyN4dt2LrZq3OV6WF2hQLjmbc4wdIONSH5LRazZ6vJKSsMJvmRdlzoOnBfG\nBnpUnFPhMpQc8qKazMIO73RvwscSAkCSw1fswpPTImR1NptsiPkS3wIqwLroNhAi1OKJpDeS\nYQUZsTPHL6dOUGB/sZzO7N6Ux1WtanV9bzu2kyXFBQDztST1j6QtTmLA2PL3vXYNJxoFEK3R\nSXSIKXwZlvmwi3nGjx1dH6XXcdB/EKV+UpJTrtgBGAOG41yvLvNDALDUM8SOYwEIGbFLEzJi\nZ4IzjdrRpflNbO5cLqrsOk82JVro2oLZMJ44hS7T1ZGmNt31B1sAACAASURBVBiuwIrI16vN\nZkswkokuVSnmSgXHnDmdK4q7LWm7PkQn2hknHzN7rB8mi5zczsm8CH3DiS5KQciTwDY3+3Dq\nJGHO7YwxUB1bSoHLSY8FYRV0qmK9hGJNe45Flu6WWAJGQ1ZsinsmzY7lWBCShWJThYzYmeCX\nZ04A2F8sx7yuo6Bl2kDMntu5X9rHUasMpLgA0PmqMVW/C+msVPC4hzjvWx6Io3rz7s9tWsvj\nzNLi/PSSlfK0HApsAgA6vzU3apbLzfQIzkfcnNLuAjpSYQVK4rKU0uKJrv+O3XsmjxyOT7ST\nKNOWczxTBSiiMU8NHRzHZsUTqUJG7PQ4Va88U13YwvE7IpPrFJhqWonEWOPcQ5oZJCkp9bA7\ngJ3ejw4tX81oSqz0bI1XVwtrWsdnzPdQYgcBVAVdr4hQOFlaMuq8NJNIFdQL6J9Ncp0cu8RC\nsZ5qXXfvmYwzFbUh8zxTA6pA3OKCPzAc2266NgrNED0yYqdHR64rDCS1gRB5VaQsyo1Dnu+I\ncwJgBfD1apNpi0E+JYfPkCKQA0NsFObyKG+TM4TNs/1NuS3IuviOjpMFl6nGzabNEDmUqlhP\nodi4kHwVfF3KD3I1oNIrxI7l2DalgiDlclnziVQgI3ZdmGzUTtSWtufy27g0mmgbeZINqYpU\nh9NOfvfRx67fYkk+rHz11C2lRMNT4rBzVX+/95BvBgYyp6028IRI617tdzVm+6PVhMMA8kwZ\nIFWhEXB/aYMq0fmW5XpBz3OFTvFEGlvHJ14krrUp3pLwVtyB5TkAQjsjdmlBRuy68OuFMwAu\nzyf5Ocme3GiZkHtWFzXuPfXUdUPbfRyYhki0AiUOO+/Cl9isUkFXEJD8vQGANZcy52HqSYWh\nEZou7eaynAbAMjkALTkUKy+bitdxF2M8QMe6osx70284EcLnZVG9MqrYnYgGuxOzCGmfv+31\nLlo0J1GG7R2bYrX5ROms+12lFBmxW8HJVv1Uo7ozl98ao1znI1gZOvVJSjZLUaCWbYOvV5us\nyzhsN/VxK9f5ZU7BWaPDUQcnnjqwTfejY1af6a4cD3G1eQYcAIkmn44dhDApxzYbzclTNfdH\nrT4vYg1W+ChLgZSGYlOBhsz3s02gBeST3oszlptPZIWxaUFG7Fbw2+ocgMsLcct1URApl5zJ\nfWA3ONITdTWiUzZR8fHv4DZfTSvyKY89mpLYTe7iQLujDmyrKN8PTuj++F2GWY2HBNIsGYaF\ni5LJkdEhSuVGo8GyXD5vev+z6XmViKmvf4yMzmgMgZHaDZtRYRMmSgghHg2Ko2vkFQrCdWNp\nSPl+tgksARuC7SsOsJ3mE8l/EsugICN2HTxdXZgRmiMsv5lNY3ZdcBiJlGnSm+lIR1y/ZVer\n1fKxh5Sg0x+2FuK/Q3oCso6w4qbBJ/EM5UbYnC6LVQxvLVNOF9pxqHU4NHVCebB/oy4xwA0N\n8kOVglS2mg6zsAsZ1z5YhtWGU8X5LAk0S0iCOXYpp4nLbnaVniB2XNZ8ImXIiF0HD81OAriU\ni6+BWKQIoo25SXRTvVqUB41GOHnuyTA/VgBfrzRYwU89rH/2ptXwXrjG9DZjxZYcWaPPuldF\ntFMEPM1RF7rblYeF7EFlBgAYb3d9ldUpj/dvrFuP7a1o5rjhgZvBaQcHkoVirdCQeQoQLCa9\nEVdY7iqWhWLTgozYAcD44uxMqzECdohEVdSTYFlAFEs7xnldBnnToOGR0gKAORdlE9HhFwun\nD/QbI7MxaH7JmzuYQCYAqJ7YGWsdVnrFalnd8jOlbm6n1bHcC1qpUr+McCvamSqL23cMulkj\ngCppyjI7e2Oi6RW7OiBT0pL5AlMDpOUa4pTi4QefJcA6HpMnlyZPLgH4P9eE0sE5g39kxA6U\n0l9NTRBCLqY559He4b4JWOgrap+JzuukJ1z3bLDcHzaE/wUzY+FEYGSEbg1TuuU6AODzvxOF\nPbaTw1NKnyOoxOo6iR2aOrF/o25Uz0hTO89dSwjj79iR0Rkvw3vmmgBgQdpptDtJC+pSvsC0\ngSrgin8nCAoABJn+mhr4fLtZTTiyODPXajyHzQ/GcjXuPvpYSkpBw1LRrHL17J+xH2A1PvxL\nx7XBN5Z8xmEdoHNFUXlePO1l1S/rUW7lOi532Pb1ULL0VkBlQjXEziyu2mEwhDypPDAk1ZnC\nJe/RhT5jZUsjo0Pql/Wo8zVfKozZbInDuM+VxyyIZKACu/dsVr+ee+Gmc0Z6w6E3CjRlJdu7\nN6KxcsbR04SzWrH7h8MPKA8Y4Pl8CWIz9CVsCEqcopQjh3PjjacbGTMiEj47cl1ccVjflM5L\nIa1pN1v1J62W5lJUGxOFPZylnO2jzMJhXSqxlOskYhtjrDqUShOt1k7j8+6onhFp4EMdeJTr\n0F02C6UzR8o8jVdixAwhVKaUUkJ6oyNqzKhLav1ED4CCAbLAeloQK7GrVqtf+tKXHn30UUEQ\nzj///Le85S0bN+rjK7FBZXUA8q3mYB/rwWwqDETH7Xz7w7nZj5vJPXXIcIPogsuktEhjJHYq\ndC7HFsUTgMEnJfbwriNvC9lXz1g5YVsGsQKFyR2aOuGX0mnh1gwlStpkRTGtkurSDJPtMQQA\nREpzPUvsJo7XAP19I6x6W4GygszmmCWAAmm/RAzJFLsUIdb72Wc/+9lqtfrRj340n89/85vf\n/PjHP37nnXcyTALhYC2rI6CleuOe6uP+eifYIykPXk+kJ6AYdsPoRWFVxcYNro1co9JgBSmB\n902VotWqNeo6PSUMbufZRpjLHXa0OFYeOO1tTPPAYkKZAJC7QrEl7etGnpfPP6PSnWCszoYe\npbyKQtlbdL0uQkTnSnJKu9gshGeNhpzPMXWgAZScR5vh4QefNT556QvOCbYvE5AswS5NiI/Y\nzczM/PrXv/7MZz4zMjIC4C1vecvrX//6xx577HnPe15sezBFvtlioizOSlF/BTP42JtLYc/r\nnPFfJSUO66Me9v5mQffMVYUmzLuN+UAMHnj6JTTMTPuqqzBruJqiLLHAimK3f+N2bTTWpXq3\nKpAWHhlYlTTS5XHgfJYAHRvqaKs+w7UOjhMNmR9AHVjyTeziAZN2PfGsQ3zE7sknn8zlcgqr\nA9Df379t27bx8fHEiV1OiMR9xxiLjLPNQ+LwcbI2YyK6eqS0QIEFj8TOyOqUJ1VuF3xjAbmd\nV37ZzczKxsJYT1uy4HZuW2hQmQDQVsV2c7suuqPpPOFma/ZwjGaOq0lsFv0VPLmoQB1vYUoc\nJkwnFEWHt74wNmZ5VZVITYIexelHo5NmtwSkl4Ze+oJzhEZ74vHjw1sHnnvBpqS3kwGIk9gt\nLS2Vy2Vtnuzg4ODiomXJT61Wc3zf8Y2btu/+yokjymOGygBeuXGnJEntdjuiRe8++tgfbxoB\n8L0zx5QH1WrV0wyyLHs9xBHfO3PM+KSPVWRZBlCv163yoNXT940/3jSi7vaPN4142iSllFKq\nO4Thhf5cc6FKlioe4sgPM+usXrq/WbhUnnM/1cr2QEFpo14HUCx1boTKj0ZcvW6L1Uu6Yepj\nN+O1ODhRPrDNvNC1Uddzl5/PnTKOM65YNFMctMOKpXFlctpkALRFodVsApg8WQMwvKxYHKvM\nAhje2tWRQpKlZjNQ5VOhcNz0+WZzh7IBw/NdyymHm+5BhtxqtrUpUupaNnsOeDpup6IAIAiC\n+zc97xvbYTUTpRRAvdHgrD9ay7Ls9a/XJdRplf844x+2I6xM+ELccAM4p8CALtbrPt+TTRH6\nfaRdbwOgsmhzQ9dB2Z778aVSKZeLxI9sVSLWHDtP1U+iKAqCEN1m/nLzrn89/RQAVpavG9ou\nSRIAWZZt/h/c44ezJqV8yrvndUPbfXPH6JhuKKso1xC2px8EahKkv6l0v9niugqAM3Oy5KkR\njm1G6MPMur3CtI+9AZAkqb+8opwVS+PVyi4ALxzcBOAXi2eUx5K37TpDmdn9JnXPvHBwk3EG\n3TDteWmhnqMyoPOjxADI8dMN2UQZVSDL3dugVKaBLku9vs3iFfNp1Q2UShPqsYXCcdN5ZBht\nPfTjda1g9ScYAI5TUeohz00325lJPc/bNGz5W9OBQAYgSJJoa/Inhv0Hr522vPyXWSyNVyrh\nlCWFu+GqwAzwTVluyXJoAevQ7yOiIAAgDPV6y3Y/PpT78tmD+IjdmjVrlpaWtMXti4uLa9eu\ntRo/MDAQ9ZZ2VKePVxdfe85z84QIglCv1/P5fKHg9o3JDmbMZnAwkM9kpVIpl8N2dTLs88/P\n3WM60B7NZrPVavX397MsazotAp9+ECgfEorFrn5xzNopStEQ+/r73X7euL/l3HGuv7/f6/Zq\ntToF7e/T9UVFf/kp0IuVxwc0j8PFgf7+gyePmr9GLwbQbgsMQziOA2B+ct3E7sDW0a5XySPG\nOVXoJuwvPyVIV7UAmRFLeUWlM5GISssCIAXthGL56Fo8W2yAPNF5XJpYeb40AfqcroObrXyB\nJ6pkt3zUyjzAyOgEulEyVTidMHJu6djTes3YZipRktrtFp/jlV+uGfTnbpjNcYAl8kILYiNf\nyPcXLA6htN5olErB08tMNFfl//TI4WHdsOde6DaYaNUd28c7gA3akIBKuQyvNsWCIFh9CAz9\nrbgiLNSAwTUDQ0Nu71Dz8/MAbAiADpknjifER+zOO+88QRCOHj26a9cuAEtLSydOnNi9e7fV\n+Bh+kTVR4AgpMIy6HCEkonXDyQmL/poEWUK5elY1EHH+Z+ps+dRf7soIrkVyzcU6K8qMmZNA\ngBQ336epI0DG2aK5gEYH45UcO/LIynWwXl2b0uecYmgyT1fYt6NMEBHkCcusNXUSVWuK+X3f\nZjnTl6zGa86xS7QL8XQMUxky55roSp6zTRZ03JjrnXOEAJCs3xloZ75IfrOEEGAMGDZ73i22\n7ejr7+sjURo7NOQ8UCGkAnjLbrQ5kdAvqSTKAPJ5zuvMGV2LCPERu3Xr1l1xxRV33XXXO9/5\nTp7n//mf/3l0dPSCCy6IbQNGVIV2n99WPzYIXt3p3i64VxDniZh2PPvO5IoodcPoRcv9YU2T\nNlLVPlWhmG4bgoUEx1X0O7Hmc25rJlYgzQP9YFLeUNyfMYpV79Qeg2n3WK/oVMVmITZbNGS1\nfsIPonA2MUIWJQC5XKp72p5ViDXH7p3vfOeXvvSl2267TZKkCy+88CMf+UiChF2itCmJ67jo\nIjg+EVEnVlMok0fdxDYpVmfzzOv35ynFQnd/2IMTT2kKQk34x1WFpmlJrGESf8k68ZA2/4jG\nHlnP/KicA0CJEkUaB9YbDlm10GXaGWHKqEItoVW7qEVutqJ8pJaj9z+zcDZJ1ec3S0iUacs5\nnqkCcmpbgIoKseMzYpcWxErsSqXSu9/97jhXtEFdbAOIQrELYskWXYsFG6waXdAlBktArrlU\nZ0VNCoptT1W3qM0chqFFbOBZx7ofJ8D//vtMp5BTw31tdmLsWubhJkplHgAlYseXuFxf9hxW\nla1YDd4snE26oLNQBqy6Xxh3rp9qZHRGGRaDB4otxoHzI12RBUHHxy4RKH+ZJhZ3aUNd5nlG\naXGR0s65mWKXNpy9vWKrogCgj4njbzER5qTliAlStxSyxp0bATNfYoN/m0/RTovAKlfkuoKj\n6d1Pp03M6wEEYJlW/WrHAFApJ0I+NL1Sp3Jo6kQYvsRhqVAhRk6tpvK/1W4qpszvnpwFOjWv\nLJBVcuyyUKwTGlJ+DVcDKmkmdizLsGyWMJcWnL3EriZEpdghAJsJqwGDbhJT2S+iTL54wrs2\nqztaQ+/YAEqxUFtJsPMk11lxO0WuM8KR292/MAkAC4ArhS980c5x0QPbKgcnyjDhvkYY0wEd\nuak6eC8AKpdEap9g54P3xBdhHK6UsOy3p2DnuVb5HjYCXogxaJdnbd4fIrLllkOxifoT90b/\nCUn5+1kCtjgMTQiiKPFZHDZNOIuJXYyKXRBExI2izuTTThhzyw0tk1PW+tMdu799vONHvaYP\ngyW6UOPEbisAT+0WlCYT0DSc8B3J1R3YzQKtKFGY3E63AY/64phRcrN4yepAwznKjEDaTplX\nCXZuNV3XxN/HO+wEs8lyfXKqrkg2CncMMltk8LBoJxSLTLFzQIvmJMqyxGf9RNSgFFSS+FLm\nHpwiuCJ2tVrtBz/4wX/913/95je/mZmZWVhYGBwc3LBhw759+1760pe+4hWv6DNYcKUfNSXH\nLrxK9bDoSwwqV5yZfCnJGnzV8KhiiEUGTgNT85o4rMJsFEVKhUt+ozI8XUAzCDTcLsFyihVa\nplBeF1qdFayYn8lylBJKiRBy3tV49+OwArIr8+ga2vqd0BKT5bruR3fcTjv5ym7VmKkoiu12\ni+fzHGdhZBilaLccis1aijmjIfP9bANoASH0zgsXVJYoXYWVEy984QtnZmYef/zxpDfiBw7E\nrtVqfeELX/j0pz89PT3N8/xzn/vc5zznOWvWrFlYWJiZmfnGN77x1a9+dcOGDR/4wAfe8Y53\n5MPo1xgbaoIAoESi+nOMgb5kcIRCK/90x4pdIikuUor5mt1fvr+sOCtuF0ElaQiwoqEaWql1\nWrGBtfbmLNrpQSUWwGCeNxjfJqXP2WBcW8E6jJJCmLRB2OTgVa7zdnkt0um8LZr1inWPuqQQ\nu0VgY9J70UMSspJYSzzyyCN79+6lsf+R293ennnmmde85jVjY2Ovec1r3vCGN7z4xS/WmYDX\n6/Wf/exnX//619///vd/61vf+o//+I+dO3dGu9/woCh2/SHl2IWSGBcidIlljhRzVXJQ9Qp8\n+/iRVw2PAkCuiVxrscZKy5JQWDKbAoUSeXDrtZ4kOrg4ZRsyF0REtOeIY8BeyAQAGKpUlR6a\nsiovdY+wUsfs5wwIzxN6r1cdtyq2BZoRVL86X+SOYpdYVawRyZScu0Gz42ZXSSOxEyUAWY6d\nKe6///5E1rWjNfv27RsYGDh8+PC3v/3ta6+91tjapVQqXXvttd/+9rcPHz48MDBwySWXRLnV\nkFEVBQYopD7HzjduGL1I/TK+FOc2ElldR7W/M3kUuJ+UHkW3L3HoLEpLm9ywxrTped37MRXh\nrLDX7MvNgStjqMQAoMtvSxGwujAxMjoT0kznG79GRofUL4+zpSS7zmEbyjuvhz61cSCl5nYN\nKUdBfNsURwqlcVnvep38+Mc/vvrqq8vl8ubNm1/72tc+9ZTJm/bFF1988cVdvRD/5E/+ZP36\njmA/OTl5880379ixo1AobN68+dWvfrUSwD1w4MA73/lOAISQSy+9VBn885///JprrhkYGCiV\nSvv27fvqV7+qzvnCF77wRS960Q9+8IPt27fv378/yEnZKXZvf/vbb7vttk73T1vs3r37xz/+\n8Uc/+tEgW4kZNaHdx4RQn22l1aVWA4u5lAFm1QxJgRR52eBLrEMQpmVkckpkU+cnovvxqjXD\nFNRdi8kYRAU/9zYXIqWbqC6ozACgxEbFUeiCnRqkprvtN1E3nLU6JxNgB77SCchqJnnm6XnD\nJN6gy+Hbv3G7rctdID3SlweyHyqp9PKT06LYjWkepE63k8E0Zb7I1ABpmRKnBUootkcVux//\n+Mcve9nLrrnmmn/6p39qtVq33377i170ot/85jebN3sol77++uufeeaZT3ziE+eee+7k5OSn\nPvWpq6+++tixY5///Off9773fe973/v1r3+t1CH85Cc/ednLXnbllVd+85vfzOfz99577003\n3TQ/P/+e97wHQD6fn5mZed/73nfrrbfu2LEjyHnZ3eH+5m/+RvfM2NjY9773vYmJCQA7d+68\n/vrr1Z5gLMt+4hOfCLKVOEEprUviJuasK+RJpJQBLvhc1HTzhtEF5FhwzGKtKsldFEqNn0Yk\nnhnrXnU/XrVG37DSFlHbnbhPqutAJ1IGuYxUPgmso86ftywjfRpWF9z6zhnaXhEKJYrI1Dew\neBkUuuqQ7v34oZIsIQQQU6HYpU6oO3JY75y8aV+hyLSACrAmkS1ZQe7lthMf+tCHdu7c+cMf\n/pDjOAB79uy56qqr7rnnHkVpc4OlpaUHHnjggx/84E033aQ884IXvOCee+5ZWFg477zzFFVP\nleve9773jYyM/OhHP1Lin9dcc82pU6c+9rGPvf3tby8UCoSQRx999N57733Vq14V8Lw8ZJh9\n/vOfv+SSS+69997Tp09PTk7efffdf/AHf/C1r30t4A4SQV0SKaWlyEzs0inXpS0R0AZRbJWU\ncgDmqubVnYFZ3ZjvSTo+du6WCA7bTXpewlSk9DJzV+iWSucAAGN1sw8eZBzXfNfj2NFZpy6o\nJgeGF5BNLwLX/JqDIUSm8pHDp3VfUazlBanjeQAasupmly50iid6MBQ7Ozv78MMPv/zlL1dY\nHYDLLrus1Wq5Z3UAisXi0NDQt771rZ/85CeyLAMYHR299dZbt2zRmw5OTU2NjY1dd911DMM0\nl3HttddWKpXHHuvc73ief8UrXhH81Dz42N1xxx333XffgQMH1Ge+853vvPe9773xxhuD7yNm\ndNyJXUSZM/Qoun2SFwCAZwEs1RuRRVtiC+IEXUgNBxtInsm07Vabz//O9cwVnXGMN8gs9KFY\nK3HOIT1fbfNl0Lp8s8MoaiZSWO0bFYykmWwkUvLvwWmkcUY0JLV+Il1Qcux6MRQ7OTkJYOPG\nQPUouVzue9/73utf//o/+qM/GhoaevGLX3z99de/9rWvVcmiilOnTgH43Oc+97nPfU730sTE\nxPOf/3wA69evz+VCCCTaEbvXvva1d955pxpsXlxc3Ldvn3bAlVdeOTubhtp+z+j0EyOMVhm6\nbijhYEeG0LEsnd4PAKKMPAo5viqFzu0C3RuUHDuP5iAhcDuXI81YndblTm/yYuF452q3skwA\naEKx2o4R4fKq0EiV1vTE4waSgTZ8nDRImqpitUhdpp1AWUFmc8wSQIEUNe/q3VAswzAA5MBN\n7a688sonn3zy5z//+Y9+9KP77rvvhhtu+MxnPvM///M/xWLROPiv/uqvbr75Zt2Tu3Z13o1D\nYXWwJ3Zzc3O7d+++4447brrpJkLI1Vdf/fKXv/ymm24655xzADz77LNf/vKXr7nmmlD2ETMU\nr5PDM6e1F/6HsydevfU8x2N1SWlejUUShGm/sjRvOCQsF5y3JfShr1CoNhuRrTWm6+eoM0CJ\nZkUkcRMyufN1Uzpft0aZBQDG+FZrSoPGAf0/rLHOwMU8LqEngk5xWxtoW4fFKtqNjA4BMyOj\nM8D5qkFxnBvQgqWuesWaBmfD6waWLgJng4aczzF1oAF4sqeOFqIgMQxh2UjymiLF9u3bAZw4\n0ZVmcPz48VKptGHDBu2TDMMIgqB95vTprr9JlmVf8pKXvOQlL7njjju++MUvvu1tb7vnnnve\n8IY3aMcoxEmSpMsvvzzcEzHCjtj993//97/8y7+8973v/cY3vvGlL33pa1/72q233vrxj3/8\nzJkzADZv3vya17zm9ttvj3qLUUBxJ2ap5DhSC5UV6Rqh9hA3UgOUadtzlPz4KlEU2+12KccQ\nPNGX3wzsDG9y6LQ001IM9bEVw+vvf3J5KtPbjKkiGFMIqd26kGEIZ/1R0qwHmrFjrCtQSVHs\nlBy7cVjoYWpaGyFPAtvy+WcAqAzJdZ2BW1Llox5iZHTIjERGUlfhEVpOOap9wYan7t9YV0Pb\nCK+Sg6SmJjb9OHL4dHuz/LwdAJZSRexkUexFuQ5AuVy+6KKLfvCDH1QqlXK5DODxxx/fvXv3\nbbfdprP4WLt27aOPPkopJYQAmJqaevTRR5UCiP/93/+944477rzzTjWk+9KXvhTA9PQ0AGW8\nKIocx61bt+6yyy777ne/u7CwsGZNpwLmX//1X5944onbbrvNGLoNAoe53vjGN1533XXvfve7\nn/e85334wx++6667vvSlLynUNSzNMBEoih3jpZuNYzp/r+h2SOv2It+VkIfM9BfCvZWYt1uw\nCnT67Ty218JPJBGPBiuNMASiSWUWRAk02UtrHUJGqQy41187c167d+C+saXlZ+y4nYHSmffm\nslnLxUt+RDu/tbc+nJA7HFpTZexttzZ8kaTLoDjtmK0oEdglICy1MgRIklwq8Unvwic++clP\nvvKVr7zmmmve9a53VavVv//7v9+4ceOb3/xm3bBXvvKVP/3pTz/96U/feOONp06des973nPu\nuecqot3WrVvvu+++I0eOvOtd7zrnnHNmZ2fvvPPOgYEBpbJVKaH427/92wsvvPDVr3713/3d\n311zzTVXX331e97zns2bN99///2f/vSnb7jhhnBZHdxUxW7YsOHuu+/+zne+85WvfGXfvn0P\nPPBALpfraVYHoCYKAEiw4PrdRx9TvmCgfT1Uf5o41GsYPQgVivmczLHhOCxYUzQPFOfAtl19\n/U/YH2themzMuosTLlf3uCuJ2JrYmaBUmlh+aM9anDmN1hPY2hk4SDDX6tho8+2Ual8jwbJu\nEWuP0HarVD/LKUoYCwpjha+/It/dezYbY82LdSLK6bIplkUZlPZiSayC66677vvf/z4h5K//\n+q8/8pGPXHjhhb/4xS+MJnZvfetbb7nlli984Qs7duy48cYbb7nllhe/+MXtdhvA5s2bf/GL\nXyiVsNdee+0tt9yyadOmn/3sZ6OjowBuvvnmvXv3fuITn/jwhz8M4Oqrr/7pT3+6adOmd7zj\nHa94xSvuueee22+//ctf/nLo50XcdzGr1+v/7//9vzvvvPNNb3rTJz/5SUW67FH8w+EHALp+\ndk77lnLd0PZCoVAoFEwP8Uo+QteflpaWBgYGbAb4MwEOxUCu0Wi0Wq1yuezGzjr01R3RCcWW\nSmRwkpSnnzhVXKz7eSdyFNt82Z0YqY+lS1z3Qg4HhoV2q60JxWoXddlYwnlX6s1vW2lvi4p0\n42/VlyxCsR3KRalMyJOaV5zFpGv3dsxl7hvzZB8I8KyshQAAIABJREFUDaHxIFk1G818gScr\nzkpWrCjCTLtlgz0TW5Z6fRvP5xXBwMKa2NTMxcNubRS7k2tJtUD+aHgkZ/a+QSmt1+t9fX0R\n59j5RLPZFAShv6+PMCv6SLhbNc521W5xwwAFLgcctBVBEERRNM3fDxFCqz3x++ObhssXeDzH\nubk5AOvWrYtmX2c7HARAWZYfffTRiYkJSumOHTvuuOOOP//zP7/55psvuOCCu+6665WvfGU8\nu4wCjNxlg/rac55bq9VsxptWHqQH2r25T6HzfUa6A6/f4se/LYHr2S4B6CtIPoid1xCqrr2E\nl0PdxFWtsu4iDcjaVObutRgD97siYAhhZFl65uh6rLA3uwKFblan6y1rEuJUWZ13jHc/9s3D\n0uVvUipNiOKo87iwt638chdbtarUFiHnUtZNIbWYrTIbBiSgAqSCEi03ig05kpghIOx+Hw8+\n+ODrXve6Y8eOEdIR9s4999yvf/3rDz300Gc+85nXve5111577ec//3lPzTfSA+IlwU5Barld\nzP0korsIUVd10HaRAH15b0UzPmBsL2HB7WwimD1TrKdBoHAwQzgAoocEiRWypab2KyWxbtpO\nXLt3clm0c25TpoNtR6+UQqt9Krtdrop1c7QDl/XViAwcAQBZpva8LnFxLj2Y69SdL6WE2MlC\nr3qdrG7YEbs3velNb3rTm/7iL/5i69atAI4dO3bXXXfdcMMNx48ff+973/vqV7/6rW996+7d\nu+fn5+PabTj4h8MPAGB9Je1qbW91z/dQ8UTouPfUU6G4AEZ+3SQeUq6/IEYxt6847F4AtWrN\npldsuEZxAeBGI9zbPdK0wMJ6nwQA2O5+MG4Ik7ZgsxtddMQo12m4nT1X08dP02QFFxvCd2ZR\nftNSKrqKxQRjdNUTbZ2pKLVFaUmzkxV34lzveZ2sbjj42H3wgx9Ufzz33HPvuOOOL3zhC0qy\n18jIyMGDB+++++7oNxkmFFYHgNEIAzeMXqRzqbHH2WoIFzISUUBpu8QVF/M5uSWE9mYUUZNZ\n3fzLsl/vinwOHiiS3G5J1T6uv8Dmm1LLxYTnG3LsAM9dYjukzStXW33cbpnIxueczILBWUbs\nPMGU87Xl0zxTAWRPHUEjgthxJ85CsemC3e9j3bp1d9xxxxvf+EbFrG9ycvKLX/zixo0btSn8\nN9xwQ+R7DA8qq4OG2PkjZKmicUaG5HJ7/oRG43LXb9nVarm5E9tNFdMlFQooLvblQyN2AVnd\nihq34DCb7UIxUDqbLDotxrofe9vYkjC5gT1vQ37NifoZN+ONrM6Ajs5klV2nsT7pcDWlXKCb\ntOmUKkuDvYjQnTsYNbpOtrtLrJ9t2GiuLCEwdzxJ/6cUc8QQNa7LPM/UgJrOCz0RZKHYdMKO\n2P3jP/7j6173uve///0cx1FKJUnaunXrv/3bv8W2uUjhI8cuzfDtPBycTt0welGj4b+XQ9wU\nudUHoK8gzVW9fco0dR62GeyveMLl/AZEeCNcbimmC7O6XHrM7EDLQ0Z2j9dPbShjTZ7hTWN/\nKs/QMgytfa5Huc4/4lHs1PNdzh105FUmF82KWp04vggAaFqN7GZ14UOhA7JesQvfuCeddbX+\nUJfya7gasJQGYtdpFNuzdierFXb3tiuvvPLYsWNjY2MnTpyglG7fvn3fvn1e/SzSi1VknqQi\nNpIU6UKRllBQoURAfNsUu2ddupEBimS1sHIbSRZd7O3ghK6pmv0hALB7z4qcxg8ebU5dsmN9\nwZgboeUZh6ZOaDmcwu0sWN34tXvtfIJ0op3mQeg+dt7gl1fF0aYsQDu1FTAwKnZaz+2Lgy8R\nLowE8bkX9MW8h6akVLssAVtjXtoIqWcbxa5uOIgWLMteeuml559//uOPPz49Pf2DH/ygXC6P\njo7u2LEjnv2Fi1v2XK5GY5UPiamKqGbQNm2L6lcjMxD5Ur5FCGLL7XFdJOsJCjeKzeLEp45y\ncOIpi2oPc7Cl0wxf4VrrxNIpynrgKFZanT2rU8eo3M4WXawu/jQ7U8ESXTRL2Y9iXBd3oa7X\nFVkCeMyxC1h8YJyq53S7Fs1JlGXJDHA/cFWym5EEiWEIxyWf7ZdBCwdiNzY29uEPf/jHP/6x\nKHYVEm7duvUv//IvP/CBDwwODka5vfCxwu0IyVhdqmDs3hHRL4i2S0ypVeTleit170e2hM80\nDIoouZ1uRUezur1Gtz9rVmcapQUhlB842py5mGtsFvqfUfUno3x1aKp0xYatjUaDZbl83qqT\nvVuBTc2u6z7WgVYm5XLiOjIL+PUi8YFjR2c9TcuCoCsUq/tLeAR4TmibW0VoyHw/6z/7JURI\nktS7bSdWMeyI3a9+9as//MM/LBaLb37zm7dv3/7AAw/86le/+tjHPrawsPCTn/zkU5/61H/+\n53/ef//9au/bXoGSsH/emlVV0ZbBA9ollOb78qkgdtpsPNPo7fKTMXcMM4UzgzSasxycKHtS\n7ABw5ZNk4Tlca71YOkWZtudtauBGrlPw9te073O4xqYc0ZL8aejUivO5J96zf+P2qLPcHDcA\na5kwOBjL4okO+vqeSFPKQQgIRSCsS7P9rJJUmrBoJwtSrr9XG8WuYtgRuw996EPbt28/dOjQ\n0FDnzeg973nPj370o+9+97sf+MAHHnrooQMHDtx6661f+cpXYtlqaMgxDAAhq7E/W9GxKS5I\n00upqNK/as2wzsdO1xzWRdzWSLkUkhLkphioS5gKF5s36naUH3y6NbuHa2wW+p5VyJOR5ezf\nuJ06uFGOA26JnfUMKm9LoGmEPbeLp1o21CW6eLAi9YidOrZkProkHpD1Xtgx1pBSwaVkSaa9\n3Cj2vhNPyb7sbG1wxabtQ/lo27i5gd2N7aGHHrr99ttVVgfgbW9723nnnTc5OTk8PHzZZZe9\n733v++xnPxv9JkNGjmEBiBmxO2shFEFJfyHy/hMqfBfJKjg48dSBbaZmv/HDRrTrvGSmQTpK\nffpz4crPCgu7uOYGsXiKMp08EC3Lcck2NJlzbmiZ1+6xcUA9Uy3D0xYCWyOOKoog6IRiOwnP\n+r+Q5V6xsW8r9aDQ3rwSE+06JbE9Wznx5NJs6B6KFw9tRsqJHQC+u92MLMuU0pMnTw4PDwPY\nsmVLtVqNcHfRoKPYISN26UJ83TsogVAs8HWGobIcU3W0J8cTF6PsbUfGzJ70ir2KWNhutRmG\ncDmHpuNadJ+sGwKqF+0IeR432GrPFbjmBUJpxSLRi3o0bvgx1SzHESqvVctEnK6Gw/lu3zHY\nbrd4Ps9xXCzXZ3z5e2chJRQbumpihCqAmcpjPuYB0Gw2Pdnah4QxAOtyhdjXNcEqMLEbYrg/\n6Q8n2fTXzeqjbbt283HCjthdcsklX/7yl2+88cZiscNAP/vZz7Is+/+z9+ZBktRl/v/zybvu\nrqq+j+kZema62x2EUQQZuUQGRkcFhsVbYcUIwg1gcXXDI3YDjPgirhEososa4cbuhoiIG26I\nIIw48BM5RBZpjxlmmpnuuXru6aPOrDw/vz+qu6a6jqzMqszKo/IVHZBTlceTdeU7n3PdunUA\nIIrij370o8nJyXaYaSoUQQCAbP2viY9R2lbOgsUAYvIhFmd4x7W9qU5Tq8JyX13JgOLCNX0N\nq+DrlXHol5gVJzVFR98hLUUonpEDIkZGb8Pa15Sknaz2WbbYsW8aYKxsuRJt52gxWbDZpifL\n2q5YFSt7q6Wo1TCIjFAVpUINnHav/+FI9YMXXbKmRUuWe524NhQLAARCEcIc+xnkoEuJlrC7\n7777rrzyyo0bN37wgx8MBoO//e1v33jjja985SvF4Oz555+/f//+xx57rF2mmgaFCISQ7P+Y\ndDJiEGA+xMkZ3vxsldVFDyZQtStjCqn19PNdpw4bLNc1AYTeoGNXiosRssDIgWbmmlSh0ynl\naN/eaj23bGpzJa4UNSOK5W0Gz514VcvA2q5BI8ddpR2LilAiAPqIxSV+7/GTOrPcWkyGm9zU\n36LTzm42J+hFBFmAcQCbyxaLws69oVgPoyXsLr/88ieffPLuu+/+wQ9+AADxePyb3/zmF7/4\nxeKzW7Zs+dd//dcbbrihHWaaDYWI5kKx7Z5/5WMNWAwigBBrste2ougBmpV3GqWybUBfLLge\nNSPC1U9Vb1UDOpoVU2GaZ2ROBGNOO+cqs/ZTJb9WaSyKmmm4h5arNGo7UFeK0v2bbL2QSInR\neQB2pWGhnah+d2Kn0iDHbvv27du3bz916pQkSYODgwRxrj3Ef/3Xf1lsm4XQBCGphi/q5Rlg\nlk5H8LEcmQWVbGf9RBH9JRTNDq6oqZAsbWJsdMhYTTbX7JmHCJWJ5MRUmBJomWup74luKvPA\nmqYopwp8geUYhKob6zR3iGWFVNYYeb78cEYJBueqrWpfjxUMAKAYjrO3hOs6EpeToHIEqABD\n51SxffgeO8eiq91DX1+f1Xa0GZogJKXVi7qv7WrSpgKIlsFikOEyNIUlWSs3wkTPmcH5E+fk\nkZENTRBw1Ul+OnLsqjEkMeuqQzqWFdMhimdkVmzvGMCi8CoKKYv8f7bEfFvKPmyq13HdI5JF\nRddeYec0qoXm3t0naw7YIBCO01kACsBybaonLc8DOXZepaU+Xt/73vdUVb3jjjvMsqZt0ATJ\ngzEHQMVcBJ+atG16hAmIQeAyIVZZkut+C4z3kzMXCz1t2qdTru2u7tFIsq6XXWea5YhU6Ehe\nSocogbHeade2kovpsoUG2m61lmpDAG56S2+l0661OGzlCZafEcKALdbrxhvFOZQ4lSWRArBm\npQOgzfihWMfSkrC76667FEVxo7CjEGG0Tr2iGYdLaX+OYBu0XZOHkAIAEGLVpTol6tWpZm3U\ndhbWvVZUvNY7o9LjoqAhp0xRbw3UIRPLyJkglbda2FWrOgPyq4UDtdNvp1O5rtJ2lvZAJjD4\n7Qn0gADiVAaAaKLbYusFsDWRZQUhoCjPCrsHl45XPHJ312Dru52enr7llltef/31ikmtJtKS\nsPvZz36mGs9UcwI0QWCMZcBUC9Ed5/qi6uC9HMHSGTVxOsv1E6am2RXFUMtVsVOrl8102tmq\nVuvR4AQRpZAhHmeDlEDLbPs7hxVxdKmsTsoy82pTHlRtw0wLKHrs2nAYY7Q+tcV8olSeJhSA\nAYBmCvmrQ6utqz1VlmmadFKXDzOpVnWlB1uRd48//vgXvvCFrVu3vv76680b14iWhN2OHTvM\nsqPN0Mut7DBl5FPpASVUTnu0nXWHaDXsq1Cg0GHOwD2TTgGk4QNrquB0atvw5lYGV5RordxV\nG0vrM4Dpysi5AMUzMiNZk2nX/iBsxYPOVI2WGFYuH+f4lIyQGwOjbSZJpwEQwJDdhpxDlRU2\naKBvuYuoqepMQRCEV1999Y033nj00UctOgQ0J+wEQbjlllu+/vWvj48788eoMRRBAoCEMafv\nIlHUEK4Wdu2JI7dveoQZYDFIBlIcjQtSjc9BszpMC31TX5vbsAFWqjrLIWiZChbkXICQKJUp\nafFphABgWGPD4mor6kRDpoyXrdxwP+VrmvUb2KqEOjgz31xhbCOsFZ0EoOqxTquz4jLQ1pQ4\nU6a2VNJinl9/XGUJBaAHwP5xVUVUFasq7syS2AeXjjfttPvMZz4DAG+88YapFlXSjLCTJOnx\nxx+/44473CvsSh67hmt6JnxpS46g018xMQiBVIhTClLtL4LdMcoSldcYUxx4pc1Nih23w2lH\n86zArHKyBoNzgrC2/nbTqxe0ZUob/HYliel8ahhpunYkASnYWDqEZ4oh6lF9LqOB0wCKw9x1\nMni0JNY6d13b0BJ2w8O1b4UxxgCwY8eO4iTZubm5mqs5GRoRACAZHwDsdKViBCtOxF31JStt\nipX5TEs5CabSWBsZbJuid2/NyjvL55sVIRiJChbkPEdIpEor5bKDZQ/VkWvTVQtN0HDPRu9v\n6xlTe1c1tVT9WV5WONga7rP5gxIIMAaM1Vqt/tqP+VNbWidAiEFCAOgCiLTtoA0z8JZ7nTDO\n+eX0OYfWu3LmzBlRFK+++uqBgVVlOLIsP/7445s3b+7p6bHYPKugi6HYWv2TPDxbotxp1+LZ\n6Y+3WieFTQj7ihwACnHNFwC1cz5Ei7HU6shyy7FmU1oTG4Dpysh5js5zQqyVYdv1VIh+8ddi\nWat1gQ4THYFNvxrGIBACABkDbVkOvm5nXptuUYySZDIAoCPloK343YmdjJaw+9Of/vS5z33u\n97///de+9rUvf/nLNL2cJpnNZh9//PF/+Zd/ueyyy9pipPlQy6HYyiv6z4/tLy17yTlXouYZ\nVbjZGp51ddXCjkF7QpatvkGYBIkNsQWEwLj31vYud3WNgTpCs4moa/3dWt7BrhqCFUlOgAJL\nSMfUyqTtanVlVHC4NbGkirpCs9z5V9/nZ2yfuleoTbEvgYJV2gGjFGphs9OORVKE5AFCAPFW\n9mN6xxNV8mx34ru7Bt0ejdX6Lk1OTr744ovf+ta3vvWtb73jHe949dVX22aW1azk2K168Ffz\nlYN03BVYbI7qc2zlrKuVlsPFMRaDCEGQMaHpiWXVCVMAU9o713/obcPrHZM42Ax0VwYAaF67\nldd0I1XXipOpXlmry1g3lhwZjfUNcCOjsXVjyeLfypP6z3G60QraTJMoDQBqE/dV5rO5zp+d\nJJkMAAZoR+sZQyhK53YnbqXdycmTJ+fm5ubn5wFgbm5ubm4um82aZ9oyDW6SCIK444479uzZ\nMzo6+p73vOfOO+/MZDKmG9F+6JWq2IZrfnLs/JI0KV/20YMLXi4xAACtRGNdTYXI0xhQu/oR\n7aCVhSEtKiCQ7CIhdhFysOpJ96mrKsw6BdOVq1UQgAGgujDWBwAopESpPADXlokjxvB2KFZD\nurXYo/jd7373yMjI5z73OUVRRkZGRkZG/uM//qOVHdZEV+bjyMjIU0899dhjj/3DP/zDE088\n8d3vftd0O9oMtVw8sepyvj05Uu20K+ICgeIY3PVanWtTnHJmQ6ZlkbRtOLNzblXqdLkIa8VZ\naEZVLLTTscHEVP40kPyAGpmp9Xy5LrEiurq8z/KhW8VevtWPGMSAoqqqqKjcthRpNV7Hqv9F\nqzmrw9jm5LKwW/VTXMyKwxjn8/lQKKR7h86luaLdJJ1FgAGGoL1jkvWwHIr1qLCDOgHZ1idP\nHDp0qMU96MFAScvHP/7xa6+99u67777pppusM6g9FEOxDT127tIozVHdBqXhWVdXLfA8b4lx\nbUDiABMh1gSPnQUhzlWuLyv66pX2bGTNmg659qUikaECwUiUEJeDkyoh8zxPkhTLsgDQtmld\nFaNUXzl9tELJVT+iG3PKbNeNnW04Z6LI0cOpqm31aMEWHXvLm5MIAEDFbwG8XeeWXupsogGJ\n1C4qC0ADOPF8ZUUBAMaLOXYlTBkgZgvGapWTyeQjjzzyqU996sknnxwcdOs5w0qDYrnqLuim\noQ0cx9lgkK00US3rIcmLQAoEmBxJYEU1dlts0gAx/UxtG64tnio0X01nXhMWWiclW4SJZQtn\n4hTPiCGrhi0apULqgWFtZ0JDFj31EAZrJhoftEVWQrGO80jZTheVJZAKMNIwY8oW1OKgWE8L\nO/fSWNhV+8Ovu+666667DgCOHz/+5ptvXnPNNRYaaA06PXadg4eEmmGwGERMLsSqaX7Vj5Se\nOlONx1vGWKZaTTNar9vdNrxeFESCQBRdClXb39mLCvFoKUIVGClQ7iqund1f03FlzZAGs7B5\nwli1+DP75Tr3TpHnhJ0jmsY5BAQ4QWcBSADtOiHbUCWFojw7KNbtaN0KYIwfeOCBZDIZDofX\nrl378MMP49VK6Omnn966davFFloCXafdiQfohEpek1mun2hQGOsM31UDtbdz7kD5X/WzlhnW\nXhBmolkAoHnn+tdbc9e5vhDk4Mx89d/Kk+OlPxJ6AUBR1/iqrpwYnaeQAtAP4MzcX5AVxcMJ\ndm5Hy2P3wx/+8Etf+tLk5OQNN9ywf//+O+6447e//e1PfvITmnboR00/+qtiXURJ0nlgsm07\nWamfcJrKt+Q618bAsbXQ0ZyUClMFhgiU7k7rebmaDj7WnQa7pXdkdalEHgBeOV1dqOvTgOUc\nO7vNcBg4SaUBkKNmiJWDMcaK6tWSWA+gJey+//3vv/e973322WcpigKARx555Pbbb7/11lt/\n/OMfI5d7YJdHioF3hJ3VjjoPD+QAmQGVCrMmtLKzF/0OOdvbKZsCFc2JCzFODgtUvv1H39I7\nUuFX29KbbzaE6pneyIYhAAGArPrS7hxRimcIGaAPgLXbltp4uDuxN9ASdgcOHHjggQeKqg4A\nPv3pT0ej0R07dmzYsOHee+9th3WWQXVAjp2JkzPKVaMnB3JgMUBzGYbCYnVBjY9ToSN5KRXh\n5KCICxbsvuE02HoNe+uqND25a630THF24mBtillaqhezYpomQRc71jrUXQcr3Yk94LGTMT4u\ni6bsKosd5BpoUDxR0RP5+uuvf/DBB++6665169bdcsstVhpmLcVQrOxpYWeFqis94jVtJwaB\ny4Q4Vcye+6nSKDV1IDXddY4tazUFRKh0JCMuxRiRg7opktNmNHc12p6tSQ9cwy4qrVMu/mRZ\nFkWBYdji3bt5BbMGKHrsVKf+Eu/dfbLiEaubrYRIIUAIAAkA5zbwK3Yn9kCO3aIq/yx71m4r\nzEdL2G3ZsuUHP/jBZz7zme7uc7+Md9555+zs7G233cbzfMmZ5zqWZ8V6KBRb3Y7OxwBiEABC\nrLKYXfVT5XAxp4fyniwVDzqMZooiqUhWTIU5KVjAGVN7uDasXahYYXy1KpoHd/rPqrH6LMiV\nWbGWHsVFJOk0AAAM22yHJt7oTvyO5IBqtgaI0I6Inmsps/vuu+/SSy8dHx9/+OGHP/axj5Ue\n/853vsNx3Oc///menh7rLbQEBEARhOStX5Mm2tH5FMFiAOkojHUs9dx15cutNLRrF4a1HSJU\nCCyhfJIqsHJAqHp+GgDWjRXvyFsZqACN/HAm+AWrO+GBNU679qBTERaLJ/yRYkVYQgyRBYAI\nQMxuW7SQZS90J768f9aCup2YEzIjtYTdRRdd9MILL3z1q1/N5XIVT91///1XXHHF3XfffebM\nGSvNsxBZVRcVyWNRxepzqRgRYdFRXI9KgcyEWAmBh7y4q3GwnoPVbVwMyrvAAvAJKk/LAVHH\nu7esz2qGHcu1SK3ud/MrK1jSi6Si0raEe7WdHnxhV043nQWAmbcCi4tHSg9edMka+yyqjap4\nwWMHkMegKticwCMBCoEwgCO8Aw1OacuWLS+88ELNp97//vdv3bp1aWnJAqus5du7Xy0uYITA\nkxljK1QEZ5s7U+cHeU0Rr1gMkcFFjlF50Yl93rWpzqVztoyrYKrmst4zQgoRTKu5GFWgZE4q\ne6J6vFhpQdt7N26SdDOtz7CHtR3hh2JXoJESoXKFArW0FLDblgbIngjFAgCvMHtz5ujmIe5s\nP+MUOaR1DfvsZz+rPQOUoqhS+h3P87fddpuZplkPdnnTlrZRUkufHDvfaSK4Wrzq2aTGaiIH\nbo7GVgRebbTEDKYM1XwQwUWEMJU3MQKyLMhWwrjVz1b/mcCW3hGvCrh6FKWBL+wAIEGnEcDJ\n4zHnuy9VWQYAhnFrkr3n0Xpjnn/++Xe/+90PPfTQlVdeqb2XF1544a677kqlKodJOxwVIZ7l\nAoIVvRK8htP0nAbajsl6bZyX2xSzqntLpNyp5/ROTivrvVcVqyVlMszjTJASaJktOu20XW4G\nUuLWjZ2tOZRMH9MAo8WlV04fhcjyo85Ub7ZUe6y0O3G8lrEYEqldVB6AWTgbttuWxqjFqlja\nfcGNDkFL2P3xj3/8xCc+cdVVV11xxRW33nrrtddeOzS0qrPOsWPHnn322f/+7//+3e9+d+21\n1z7//PMWW2s+2XCI8G8WOwYtf54UAGx4sJg7tVRNigLLKWOdtg1nds5FGq+3wtHTswOBTeoS\ndTB7CgAXddtqpVJb6p2InGtuvA5WKZuSu06PtqulioqPFMBgH5PqZDtnCkFTIAAhhBSn9jux\nurlJiQSVJZAKMOSKln6yrFA04fY5BR5GS9glk8lnnnnmJz/5yde//vXPfvazANDX19fd3R2L\nxVKp1NmzZ0+dOgUAGzZseOSRRz7xiU8QhDv0+z9uencpzQ4AMuHwaUWK22iQZVSkx7nI69Yi\nzWQTYgLkQJDhCYRVXPsHy8094Rw7Yb1kVQPXXZm7DqpPR1aFvLwQpBIROpCRqgdRVKq6olYr\nV3XVK2jbYylWK7nVtSMFsLU5CwlI6eyhYgTCcToLQAL0Axy325zGqLLCsZ0Sh31n9AAA/DHt\npnv4Bu8NQRCf+tSnPv7xj7/00ku7du2ampo6c+bMwsJCNBpdu3bt5s2br7nmmssuu4wkXZZE\nWdJ220c2/Oro/iey8zcFupwmS03RZJ4XczVrO5o7aywGEc0HWTVb0Pt5bm42V9s7j9QWQ1Ur\naK9jKTVUXbnTrtYLVWlqSjoRpOLdbLyWsKtBtarTcKS1FpD10YJY1aDYsXcgFtJF5UikAAw3\nvCI7AoxVRfVA5YQh3hk94CJtp+tjRJLklVde2TDTzl3846Z3FxeWxMLLp44+VUhtA4az16Yy\nqmsCPtQzapcxnqFBha8YhNB8iDMg7Jpg59yBkmTxxszW1iheyDdXe0O3Da/fVtmlVcurJ6sF\nXk4FqK4wFczKFaKtWNwwXbYMADV6i6xQI27rjYbDjqLoOFR7CUGWizMeJjdBp2k7BDhOZQCI\n4gwxBzY3qUDppAS7orvOdXTEe6PNJT1DFyT6FlTleRAUz3Yx8ybV9a0N63Y1KnyxGACAEGug\nMLYJWbZtOFP+T+vDu7WbidR/UG81gxlMlf23mc0R8efyf6el4wC4L5CoFUqv7H6ypVeXY6/+\nHgxQ4Qj0cM5cExAYqwQAwOSmE3bbYgNRime0/AY4AAAgAElEQVQIGaAXgLHbFl2sDIp1g3PR\nVEwRecePH//EJz7R19cXjUavvPLK1157rfV9VtNx701Nrh5YmxIKh3Kp34r57ZzTewj5FGm6\nu15d5SexoBJhrm66T+vTY3fOHSh6oYwWB1hGO2Vci9Q2NRw5UOAnisuiyufkxRCViNHhJSlb\nc32N9nJlesv8ybADmWBp+WBmOcXN615AXS8OgQFX3lF3kNMuQRfv9IYarFeH1/9wpOIRq31+\nilea2DXECnfd9ddfz3Hczp07I5HIPffcs3379kOHDoVCJs8F9oUdAABC6NqBtf9zaN9+WXi1\nkHk354Qrrk/7QVgKsGyOIrGs1K6faDFyWuGus55qMaTnktmGy2qlm3Db8GZN0axXgKbFY0Eq\n3sN1paTyeTm1mxVv6c2b0YLOtEbErqB6aEeL8hSpgBGe+Btj7rpi6LYcgxWsjtCOIbLAESJA\nEiDYeG1nsNzrxOvCrqaqazHTbmFhYc2aNf/v//2/yclJALj//vt/8pOfvPnmm+9617uaN7QW\nvrBbhiHI9yUGdi4cf7WQiRLk2xibv2bVBa3pdNpGe2ykrYW9YhDYXIhVU3nLf7aKTrttw+tz\n2cqRfRZTfknb7JhGJ1PbhjdD3bzDavPOST0usG9y07kVhPk8SofWDw7IUD09tpp6skyPXNM/\nzcJZFKWYLMuiKDAMS1FWXAiKL850ddFJhRAs5gOpGJGo3G83BXChBVaVdu4Iuunir3plMqmT\nUTwxKNYWEonEz3/+89I/jx07RpLkyIj5iRm+sDtHkKC2D6z7xfGZXfmlMEGuoWwe5ev5glY9\naExFq66EMOEVE4MAEOIUa4Rd5eXEegee7XKtJlqX1darSZiutJwNUHlG5kRAuIXcuOmyqotq\n3WbJxFivYODFKco5BSNydUAWoT8BbDTXLABwQA34MgFCDJICQAwgqn+r6tir9gqmR2aVDvDY\naQRhzSqPXVhYuO222774xS/295vfK7Fx8QTGOJer7VE4fvz4rl27zDbJTuI0++E1GxFCT2UX\nziiy3eaYTO1RWm6mXMmZooNX6idWpdntnDtQ+mth305xEqxmqmqhbUc09FTDNc89gkiVjmYR\nRjTP6FMY1evoecToCj41OBHJC6QCAM+dCD0zF9m7e6BYJQ2wGWPrPHaOYCW7zk3uOih57Dwt\n7LRpPfdu3759l1xyyVVXXfXNb37TFJMq0BJ2GOMHHnggmUyGw+G1a9c+/PDDePXgl6effnrr\n1q1WmGUjI6HodUNjIuAncvMZ1a2TQysol3Te03ZmTrBVGFDocNn8iQox14K221znz8cszmk7\nuiuLSIXiWYQnjU90nV69XFOx+TJOA70vTnUrwfI8uX17Th05mNm7+2TpzwzbbKwBXwWD5AjF\nAwQBEnbZ0Bwr88Q8K+ysbnHy3HPPXXbZZXfdddf3vvc9i6Z3aAm7H/7wh1/60pf6+/v/7u/+\nbmRk5I477vjIRz4iSZIVdjiKia7ud/cOZ1Xll7kF0YtDDD2m7cwFi0GKxCxtSSt8Mzx/JtL+\ni1zDQ+i0YcWpo16Qzawv8BMVKhkhzHRlAQOVr2ghMV7nTw++084ayn5jn7Hhq2GPtkvSaQQY\nwH2NbzohFNuQpsXfSy+9dPPNNz/yyCN33nmnuSaVo5Vj9/3vf/+9733vs88+W0ytfeSRR26/\n/fZbb731xz/+seeHxG3pHU6LwptLZ57OL3w4mCC8fr6OxYapaBIHgVSIVQXJ5C6P5XrOAa2J\n6/W0s92JaI4NVCQnpUIUz8iciEn9Ml2nODNcKuH1ziYljKlbDEimm0n1bmqKq1PSISikRmke\ngC0ONW6RUhZdw/Q7U1BkhaIIgvDmNdFSdx3P87fccsvdd999/vnnz83NFR+Mx+NtbXdy4MCB\nBx54oFQw9elPfzoaje7YsWPDhg333nuvuXY4kGuHzsvJ4qFs6jk+tTXYZbc5WphfQ+Ak2n06\nK/UTC1kzS4sc46WzlwrFVvdCW3y5WtG+CGEmnimciVN5VorwDdd/5fRRANjSq72Wy6pfraCR\nQq1+fSrbo5Qj0TQuu21+v7V3O7bftCyToDIEqADDbpwRoMqKV0tiDam6JqooXnnlldnZ2Xvu\nueeee+4pPfhv//Zvd9xxh6H9NKTBpSubXdXk8/rrr3/wwQfvuuuudevW3XLLLeaa4jQIhD60\nZuPjs3v2FPJdBPkupza38+Oq5oLFEAJUqp9ovSlxPex22jnhIlfDhp1zBwAOlJabeomWG7iQ\noTyRClMCrQRElaqbL1uUdCvLwbI2xfWy6zpd2xlCQwhe3Dv8XG6x9E+LVZ1TIJEap7MAFECf\n3bYYBmNQFYUO0XYbYglWT4N93/veh9uS3KUl7LZs2fKDH/zgM5/5THf3OXfxnXfeOTs7e9tt\nt/E8b033IwfBEOSNoxOPze5+uZAJE9Qk446hFOU9QYqUBzQ95s8zH5UAmQlxAkLLyT8WyS+7\nQ7HuoAX5O4XQZiaeLpxK0nlWiOodIPbK6aNNjaDwMcwhScAIbYgk1sdcVkDQCl1UlkBFd10z\nfi+N9iXlT0mSJMtyIGDyNUtVFIw7uiTWFWgps/vuu+/SSy8dHx9/+OGHP/axj5Ue/853vsNx\n3Oc///menh7rLbSZMM1cv2b88YNv7sovhhExQtvc3K5pfD2nHywGiaAQYNS8YFqgpMLzp4fS\n+h0gAZfz6swIWK8K71LBAhkQgGcJiVRpQ0XufiWEtcgYH5YFChGjEUcnupgLAohTWQACYMBu\nW5qhc+aJuRqt69ZFF130wgsvbNq0qbqP3f333//000/H43ErbXMKvYHQB0c2YISeyi+cVVxQ\nFOxruFYpptmxJje7KemzbcPrK7TaS0snK6pl6y17lykwX8JOAQATTwMAnWvOdTFdteBjDodk\nQcLqeZEumqh9GZr4m7416yKTm/pLf2220AqiVI4mFIB+AKbx2s5DVTze68QbNIilbtmy5YUX\nXqj51Pvf//6tW7cuLS1ZYJXjWBfpet/gut8cm/1lbuFjkZ4gclDGqw11o14HiwEEEOLUM2ZP\ncaspXF5cOjclsxh5rFZydifkVVJhYWu2mTiIosauSFYkQwXIcaRAK+zyjVl5Xl0t/Ow6aym5\n69aEO8hdBwBJOgOAAAbtNqRJ/O7ErsBYklwmk1GUVW4Mz6fZlTg/3rskFv7vzPEnsvN/G+6m\nndQAxRdzJiMFAKMQ14721E1542xuSmLEZkOmTgFsLte1rau64j7ZeCqf4+g8WxR21apuS+/I\nSlVsMbuuokdx+bKv7Uyg6K7bGE3Uc9d5kgiZZwkJoAfAHena1fihWFeg60s1Ozv7wQ9+MBwO\nR6PReBVWm+gcLu9bM9nVfUqRns4vtKe2xcceMAIpEGBUgrDhXa4pm8okzlTZf52CQXk6VWcZ\nSgHZ6mh1KxC0TEdySCGowkK9dbb0jtRSdT7lmPPKyFg9JAs0IkY7zF2XYIpdJlw2Q6wcPxTr\nCnT522677bapqakbbrhhYGCAJDv6Hb12aCwniQdz6ecL6fcFYnab42MVWAwgJh9icYZvt2u2\nKGiarrQAO4ot6hyxpEGrnXbNOx3Lz/S6wfPKnqm5w2XhyMQzci5A5Ydk9q8AGiVQesZL2O+0\nOzhT2RzORQ2QD0qCjNXxaILqJHddkBCChAAQBwjbbUvzeCwUSxNqL2NOOlmIEEzZjynoEnb/\n93//9+yzz27ZssVqa5wPidAH12x8bHbPX4VcnCDfwbr4K2oLrumlLAYB5kOsnOGtzXGuVy2r\nKZVKy8tSpnqgraXaTl+Fb21TNd111StXUnHcXx+fvSym0QzsnLJEpEJHDomp86hCL0BK03Kf\nmkyv/LclXStj9bAi0h2YXcdkAMDV7joAUCQZPBSKpZE8wp212wrz0SXsQqHQ2rVrLbbENXAk\ntWN04rHZ3S/y6ShBrac5uy1yDS7qpYzFYLF+og3HurxrAAN+aemko8ojtGkhE65EScBVyDsr\n0genAICJMVJmhMr3v6fnzMtnzun1sq51UKVajFZROMKf52QOSqKM1Ylostpdt3f3yer1JzeZ\nPG3JIKtuM6otnHibLvNYJIXJAkAIwN1ydnlQbFNT4JyGLF2IweRfeIoKOyH9Xtfb8+lPf/o/\n//M///mf/9lqa9xCjGFvHJ342cE9O3OLO8LJQcp8p06HFLpW91J2CjILKhluS/1EER3yqNq/\nZWcVhabB9Uyt+XjNNZugYsOqPZMiHZsRFycofmBL71F9CsyJKq06Dms95lSQSFg9LBcYRIyE\nOyuPJclkADDASONVnY2qKCSJSNIB4qVlXv5dXlVNzqLefJHa5YC6A13C7hvf+Mb27dt37tx5\n6aWXJpOVmRxf+cpXLDDM6fQFQttHNjxx5K1f5hY+Gu6Ok2bewVR4tpyrflrGyeeFxSDDZWgS\nS4oXfsUcgB5VZ+LOa8DEDkqZtVS+V+ZOYTPzu4pax5xgpfOodls2eY4HZVEGPOGa7DqNJFED\nUEiJUnkADqC78drORpEUmvGCu64IQRJcyJwKZakgSqJT2tzqeoe+/e1v79q1CwBefvnl6mc7\nU9gBwHmR+PsG1u46fvAXufmPhnuC7vip8tGNGAQuM52de2t+OSvW7lDp5lqZbQeKBaT2Fk+s\npnW5VvdSWnGm1w2et7p9er3w7gpIYbr2C2fPp/KDUth7CszRSFg9UnTXhTrMXUdnEGCAYQDX\n3yIqihoKemdQLMXQfWPm9BRcOH42dWqx8XptQZewe+ihh2666aYvfOEL/f39HV4VW8HbE30L\nQuGN+RO/zC38bThJOSG67mBc1ktZ4gBgMEqXhJ3TugSXY7zlm3UxXK3qVN1oabvSMlZVAOAC\n+3QfazMdRmJKpgrdciCASVMybKbL/lt6xB2S8dSJAkCh4sHVBbb1yoQNn+OsLMgYT8Qqs+tq\nptY5gHrVP8YgkdpF5QAYAI0qH3egyApg7JnKCQ+jS9gtLCw89NBDg4NubZZtKVcOjGYkYX96\n4df5xQ+EEr6y08bpYq4MLIYQwGDEQben1eWojhWaVVilI8ORCi9mo2swwmw8XTidoHOcGM1b\nZJU2NZPk2tOvxHh+njkKVcLqUVlgELEmFDVlh22nSW0Xp7IEUgEGdHaNdTKq7Hcndge6hN3b\n3va2M2fO+MKuJgjg/cPrc4f27s9nXuJTl5vR3M5lni2volA5wVnCDjTLUXVHY83JHHIwDU6N\nCvEEK4LAEBKl0nJrxzLNoeVtZqVldx2pL2VlclM/xjift0d513P6ls+rLRQKktQgpwoBjtNZ\nABJgwEzrbGK5iZ3fndjx6BJ2Dz744D/+4z9+5zvfefvb3261QW6EIojrR8d/OrP7j0IuQlAX\nsibU53eImCvpV2ee73warekhEgFqgW/x8m8mNUVbU63sXK/tEPHn5jZkE2n+RDedZ4VYK++s\ndjfjVrSd1rYu6kVcRMTqUUVgCXLUJndddbS3XKJVUS+Ub/j70kXnKKQADAE46/6wORTfY+cS\ndAm7r33ta4cPH77gggvC4XB1VeyhQ4fMt8ttBEjqxrUTj83ueYFPRQhijHbrKMB2Uu6VdGbl\n7wjTD3BiKEoXhZ174p4aOGsWWYtg9YJcLkdRFBcw9o0jOYEKCDLPEiKlMuaq9qIga2X6ltdm\nmh2UCjLG66Nxwh0VZsvqrZYcNLAXBDhBZQAQwJBZltmLH4p1C7qEHUEQ4+Pj4+N+ZEGLLoa7\ncXT8ZwfffCa/dFOIGqC8cItmHdXNih2o7Yptii8d6B6iNYZQuQhndcKzFyaRUo730DlOoLNN\nVSvqCcJOA4w2u1uPBHNFrB5VJM4+d51dRCieIWSAPs0Rdlbx5zdOVDxy0SVrWtxnh4RiD07t\nb7jOus0b2mBJ0+gSdr/73e+stsMb9AfC24bGfnV0/y/zCx8NJ7sI7/T76VBEDgC1Z/6ET3OE\nIwcK/EQTGxKMRIYKOBsgBVrhmmhApaG6zmk+LnAY43ZeA4qH1hiMUdlKbWQ0RlEW/lLNSgUZ\nqxtiPfXcdZpRUReToL0wQ6wcPxTbOnv37v3yl7/88ssvY4wvvPDC++6779JLLzX9KK5wjLuJ\njbHk5f1reFX5ZXahgH1B4HIwCRIbYhXn97GpCBPXihprZA7ZTpM2NJ1jV4SNpxDCNM+Bmf3n\nTQzCGt2V42K4AlaPKiJHkGuCEbttaSshUggQIkASIGi3Labhh2JbRBTFa665pqur65VXXnnt\ntddGRkY+8IEPZDIZ0w+kdaM2MTFxyy23fPWrX52Y0Loh3rdvn8azHchF3YNpSfzT/Mmncos3\nhhOk+5tSWkFF5S84tX4CiwFEF4KMkhOc/nPWKAXQ4SFXo0Hhc+tzgX3NnR2iFCqclzIhSmBk\nTmxiD7qOgvZXuNCsr36oGcadBoB1Y6WR5+OyLIui0HBfrTRnOSgJCsbjsYRF2XUGqyLaR5JO\nA4CX3HUAIHdGKNY6UqnUF77whdtvvz0SiQDA1772tR/96EczMzMXXnihuQfS+rJ1dXUFAoHi\nggbmGuQN3ts/OhaNz8nCr3NLdtviXMqVnDNVHQCAGASAEHfYbjs8zFTVgtENm9scAICJZ4DA\nVJ4F3PAGbLrOcr11jFJzW/07dJx7T8DqUUXgCHKkw9x1LCGGyAJABMBTaYWqrBAEIik/0Nck\nPT09X/rSl4qqbmFh4bvf/e7ExMTk5KTpB9Ly2L366qsVCz46QQhtH97wPwfffIvPdvHUlkBn\n/a7px7l6boVi/USI5Uzfc3mDksu6HOFmcA+mjZ1FpEJHs9JShOYZKajhvqpWdTW9YpWPFPgC\nyzH6QvnmlkpUmNekjDPe0LhsW6mgYDxhmbtOP8258Zp2/nUvZ9eNNLe5Y1FkxY/Dto6iKKFQ\nSBCEK6+8cteuXSxrfm2N3pzZmZmZt956K5PJJBKJCy+8sLvb8mHG+XxeURSrj1JCVVUAEATB\nxINenRx64sTsa0KGUZS3EUyLe7O1XWcDZFkGgEKhgByZjKaqqqqqTb56CMK9OMRxAFOFgmm3\nVr89O1f+z5eWTl5FOTRqoyoqQiBb82XkuL2rH2j8IldtYmzzGrAiIoJknsmRWYxq5MWyzKGV\nxWlBXMuufJUFHXFMFVRRlKxOxyiz8Bwl82o+CwAUNSOKw7IkK6rhN7fhuYsARxWRRUSSoAuF\nyqllOsEYG922uP7BAzVCJevWmxlfKl4pCoJQ8aPHEkoklFdVrlDgABz0i9365UOVFYImTckJ\nwxhjjPXvKhAIWFri005IkvzTn/508uTJf//3f7/qqqtee+21eDxu7iEav1I7d+788pe//Je/\n/KX0CELo6quv/sY3vnHxxReba005LMtibGZKszaSJEmSRNM0x5nmmwkA3Dg6/j+H972s8HGa\nWUu1JMxlWbZC2puFKIo0TTtzlLCiKJIkNffqkeQrIIUDDEMSBMftVZULTDevCEO3Kv0tQgSR\nQETbflVbfB2ae4/kaEZc6gpKYTHIa69ZLpJY5pCqNqh4VRWVpCjCyhsegqjdnaFkXj0jFUUB\nEEmKrP7aHj7YYJw5XaudU/lWp6NICaEYzwT6m/xFxYAVRSn/PEzvPd1wK43Pj7lfMQELqqrS\nNE2gVf7Ifm4JAWAYZi1w8+vn/Av7FEUx8ZKhKirGmOPogMGekTWRJAkhpH9XzryyNM3ExMTE\nxMTll1+eTCYfffTRO+64w9z9N/ix/uEPf3j77bcHg8Fbbrnlne98ZzgcPnv27Isvvvj0009f\ndtllP/rRjz72sY+Za1CJNr+RRY8dQZh8Aeuhwh9es/Hnh/b9upC6OdzdQ7bU3M6xH+7iPStJ\n1rhCOAGMMUKoaduwqCCGjAaCi7ksQWoElVrqCae5ZzshZIIgkDXm1YifEuSfNV/GxiHXClP1\nTFpjun4vZ7fSAqsEJUxUOO20gpgNg4wIEEkghCx9c+vGcLWtK/7oIYSaCJUSBKERpZUJWAoi\nSiHCAt30J6d4Y290cw3xZ+5nePlHjyBQ2atHIrWLzgOwBNFnb9OJYpjCxB9kLKsAwLCUiZdI\nzzjhdPLss8/+/d///V/+8pdgMAgABEHQNG1FmEvrZZ2Zmbnzzjvf+c53Pvnkk/3957IN/umf\n/mnfvn033njjrbfeetFFF61f74F2/BYyHIpuGx771dH9T2QXPhrpjhBOlD4+dXgRAHBOQGFm\nMJFYzGUr1FvV2NbG2q5i9ldnY1Gh7rl3Qd+ktSlAwMQzhTNxKsdKkQZOu9V4pI2wucyHEUYQ\nE2ii2cLVsq0y+reynQSVJRAGGPReK7Hlklg/x64F3vWud2Wz2VtvvfXee+/lOO6hhx7K5XLb\ntm0z/UBaH77vfe97BEH84he/KFd1RSYmJp555hmE0Le//W3TbfIe47Hke/pGslj5RXZe8Jvb\nuYYXl/8vqZiXgiybCIfLny4XDXrk2s65A/VWs6h4onhEjeO6kM3lf1htPTK+7AKkQq8QjESJ\nNCGXX7oc1xnOCWj3OpEJSBXddZLl03cmN/WX/qw+VkMIhON0FoAEGLDbFvNZbmLn9zppgXg8\nvmvXrkwmc/HFF1944YV/+MMfnnzyybGxMdMPpOWxe+6552644Yahodpz7tauXfuRj3zk2Wef\nNd0mT3JJz1BWEv+8cOrJ3MKN4W7/y+EGLi8t4ZSAAm8NJQcXc6F6mZ875yLbhjOGArJF71Eu\nm8MrHXL1xA11os9Z5W7qNyg2HhZHmIlnCqcSdJ4VoqU0c7O8cV5w7OnsXVdy16H25Ug7gi4q\nSyIFYATAgz/wqiyD77FrmU2bNj3zzDNWH0VL2M3Ozn7qU5/SWOEd73jH448/brZJnuW9A2tT\nonAou/RcfunaoN//z1XILM53ccHFZEQ6m7bKD9EJUsw8pooeu1wuR1EU12RC96qMPSr4Csld\nCwWGECmVkU2xsgwvaDto1AClne66hrTTjYcAElQGgAAYbNtB24ksFcdOeD8rzuFzYPWg9SZl\nMplYLKaxQrEXi9kmeRYCoQ+u2fD47JtvFnIxgrqECzfexscx4FQ/CiwNJcT5DN2oXLulKgpP\nY+4rMwXQIBS7bXi9IScoE0/xJ3ponhV0CTtdWg2hxjPFnUZzszHWjSXfFPNYFia6u0dGl3vz\nVufYNY0T4q31iFJ5mlAA+gEcWt7eIqrih2JdQwP17cy2ZO6FIcgb144/NrP794V0lCAmGe+M\nEfQ+Co1zSSZ8ticqnU7V8EZsGzbW3qkJb1yFS8+d/jxTtJ2BdsT1X6UaOyG5P5DBayDPkQKl\nsKZpu6ZWtooql1vBlBFn68aSBazOySJH0sMdNmoCABJ0GgAB1M5c8gB+8YSLaCDsZmdnNcZO\nzM7Omm2P9wlTzI61kz+d3fOb/FKIINe01tzOp53gTC8KLQzGxbNpWsVFxTC1cy4CNVRdDflS\nVBhFcda6qmuIUWeV9TQ5HEIDRPwZoOnzqq0v2Xg6z7M0zylsVnNzXXUVXKCDhtHNSAUV8Ppo\n3BaPgI3+vDBZ4AgJoBvAs/fq6nIo1hd2LqCBsLv//vvvv//+9pjSOSTZwIfXbPzfQ3ufyi7c\nHGm1uZ1P+1AonE3SkTN9XdKJxeK7tnmbwYERGgLLdCnmADFXYmr1citOu1UCMRw5UOAnWthb\nJQQjUSFezgbJAqNwoo4tyv1wDX1yjnDaWUEBq8dkMVDlrtOht2p8HiY39Rdn7YRCIVPNtIQk\nkwYAD7vrAEBVFIQQ5Q+KdQNawu6ee+5pmx2dxkgo+r7Bdc8em30it/DRsN/czjXgTA8KzffH\nxdMpSlHNd0s4SYpZStPazny3XzVMPK3kAnSeVVgJatd2Tlf9s6a2a75bSnWNwonIuZFQW3od\nN4d0RuJbcNe5OC01QIhBQgCIAUTttsVCZH9QrHvQEnb33ntvu8zoRDbFe1Oi8Iczx57ML9wc\nStLW9qa3lv89fgAAYB4+OXa+3bZYjErhbA8VPdXfJR1b8GaWtAU0ocYMXOm5wD4dKxvYIUEp\ndCQnpsNUgZYDepx2RarVXr3VDDvtylUdALxy+qhztN2JSF5FRE5GAZIZMpxdN1W24CBtV7Pm\no6b3ccVd55S3wyJUSQmEvPaLJ0vSmcPmFPeIvIMKSb1fuuxk3tM3kpHEN5fO/Cq/+OFgwtKB\nktbx6Mxfy5c9r+1wphuF5/u7pNMpWlLa95Y5L2euIcVrdr2r9dTOuUids9AQgqv2hlV1pd1J\naUNzxAEdz0jZIMWzMisBUeG0q6nYplcvjxfVW4EvsBxj8UixtlJRafHK6aMAINIMBsQrUqfV\n2zGEHCELACEAk+e4OwqsqBhj73nsVFnNLhgrenMFvrCzmWuHzsvK4qFs6nk+dY0Lm9uVq7rS\nIx7XdpjEmR4idqI/Lh0929ZbWDeIuWoqxVbFxI6qk2rRhVNzqymjO0SESsey4mKULrBSsLD6\nyZr+tlVq7+DMvCmlpg6nqOpUREhNXvKnqv7pIKedHpJMFgADGMy0bS+v/+FIxSMXXbLG0B5k\nxYOVExdfOlrqDG8WHOeIjHlf2NkMgdCHRjb8dHbPbiHfRVAX+c3tjFCSlW2WkjjbjcJne2Pi\nqSValDvHRWHoulvb61Zd22teH+Z6fj6jdRvL69CxrJQOkXlaZkVMak8CrPThrRs7C9CKsJte\nNwYHZ7pb2ENdSopTlmVRFBim1cJ8gWEwLH8Lnpk78H5X3n40A03gGJUHYAF67LbFWoolsR7r\ndRIIOkKEWYF3AgTuhSWpHWsnIzTzUiG9TzQ0gNwcHp35a/Gv/YduhYoQcFuPjRHO9BIIBuL6\nE7Dag3W1BYb2XO2JsXrD1req3BYhzHRlECCKb84v23TlRI0Nt/TmV//TKRldKiJk+pyDwIiq\nq/k2taM4xiz6QwUCFd11Hr+78wfFugvfY+cIIjRz/Zrxxw+++Zv8YoggR6j2BfhazJD75Nj5\nFaKqPc4z20PAOJdE4TM9UfHkEiNIDuNi+/YAACAASURBVPlZNxxwLEdfAl+rwbKKTEHz0OOu\nKz1SN+2vYh06mpPSYapAKwFR1XLajVcXsbYeil03dnYl7DsNVdrOCWzpHXkufabZaFabo64m\nxHn37j5Zqp8gEe4NiAAUQF/LttlDdYgW6kRpi6FYj3nsPIzvsXMKvYHQB0c2YIR+lVtYVFqa\nU1nywDX0w9WUR0YPVy6nPJ5dVw4GnOlFCAYTDimGasnVUT2mtvyfFL27ZUvqmlcmIk104bTu\n+FneAx1PAyAq37ZG4jr9fM03UjGRLFZk6px3YO1SeO/ukxV/NppXxlTZf82hm+NJAmM8COB9\nueN3J3YXvsfOQayLdL1vcN1vjs3+Ijf/0UhPsKlKOlsiqjsG1wuCEIl01hwhnIuj8JlkRDi5\nqPKio+6RLE1Cb7jzBoeu7w5s0mYusK/OMxpuvHoFFpXQIV5mRRAYIiCqlFJ8sNo/ZxkaAs7+\nXscHxAIG2Jwc6A+EAGDvkkNknAlMburXUKUIcA9XwJjAuL8T6oAVPxTrKnxh5yzOj/cuCoXX\nzx5/Ijv/t+Fu2ozfDE+WqdoVAl4Nwuk+lDwylBAPnOT0bFDyhJld32phZhLD7rFu560TjtQL\n7Fa/JkaF47L+Y+IZ/mSSzrFCzOpgaD0ZZ7KAWy1MC9BU4DijKqcUMUqzRVXnYEycerJMjMrT\nhCKKSYoyMwFff2y0zSh+KNZV+MLOcVzRvyYni3uXzj6dX/xw0ISpixqKxxnyqEnKjbfLbMx3\nIelMPMyHWCUnNPjVa9Tmw1zsddq1j2xmPUVRXCBQ9Uwr1R6rIAMFMiAAzxIipTK10yQ6oblJ\nBW9JBQywMdZxJw4ASToDgAqF7rAb2hi0Lg39UKy78IWdE9k6dF5aFA7mM88X0u8LxAxtW63V\n9K/vIlVXxAkG41Q/6j44lBTfOl6tLc5hTcVAEUMBx9rU735sws4dg4bNDc6Fiad4vpfOcwKd\ntbIC0jVjZFOqckYRu2iuh3P42HtD1TO6iJA8Q0iynFBVr01iqIciKwgBRfnCzh34ws6JUIi4\nfnT8sdk9fxVyCYLazDYf6dAjfZwgj9wLLkSQEIoFc5GAkuFb+uFrNlBrgsCqrzs3i4JIEIii\n3dXzyeTYNMlKVJCX8wFSpBS2pdqmptCVTmdFZW499os8AGyMJSzav8Xo0nY1B4gBQILJAIAs\nu7UYtoR+T54iKzRNdkI2oTfwhZ1D4Uhqx+jEY7O7f8enIgS5ntaVwlVEv1Bzr6/OUajpfqJn\nZjgp7p3Tctpp095AbWNj3DnlooT53kQmkZbzASrPKUzW9J3rwP5SiRKLqnxWleJMIOl0dx2Y\n/kkIEmKQEADiqhoEcFobS6tQZYUN+mrBNfhvlXOJMewNo+P/c/DNnfnFHaGk6bkcnTbj1UKE\nEBbCYS4bCyqpfG2nnXb/tpeqygmdKq20x796GYKW6UheygRJgWlvRp0jOpuUU3TXjVe56+q5\nuLxEkkkBgIkzxGoWTDgKjLGqqn5JrItwVI8Gn0r6A+HtIxsUgCdzCynQHmpkDFM62PmUwKl+\nABhKavW02za8vqjVSgtuw01TAayAjqcRoTJ5FqltC0pN11luiXVjyXVjyZHRWN8ANzIaM6RT\nzyrSgip3s8E427x/2qWwSAqTAkAYwH1zvZtGkWTwS2Jdhe+xczrnReJX9K154eTh3+DCx1Ul\nQPjfLkciBjEfCwVS8ZC8mNP6WrlC0jUy0o2VEyZAkAoVyUmpCCUwUsCWxtT2B2QPSDwAbIi6\nNLuuJZJMBgAD6J3nVu2N05nW5oQWJyWW54n5ws49+MLOBbyzeyAjCW/Mn3wit/i34SRlTQqr\nH4ptSLlTs/rlwuk+FEgPJcXFHFmaHamzHuKyrv7qaGwbmdo2DACwcy6iOUysyZ17SQUyXVk5\nEyLzjMSKQDQ7TEsvjgvCnlGkJVXp40JdrIGsXwDwwMeARkqUygNwAJ3V4UX2uxO7DT8U6w6u\nHFg7yoVPKuKv+SVTLia+jDNKRai6RuRa4nA+FmDUZEQBgJ1zByrqIbT3X62orOyQUs45xbZt\nOFNTwO06dXjnXKT0V7GVoUO0TvGFLf79+vhsG45YDiJUpiuLMKL5tg0Zq8BOtVfMrttguBjW\nC0H8BJ1GgAGGwcqGNw6k6LHzQ7EuwvfYuQMEcEV8YFfq5P585mVEXhaItr7PTtZ22r63psHp\nPhRYGkqIC1kvf7N2zkW2DWf0rWv5Ff2l1KmrkkN1Dm2Ji4iOZsV0iCowCieqpJmZr1WUoq7T\ntR6sxOqSjpOKlMZKfyAcoQ2J2qmyBbc67UikdlF5AAbA9V1OjLI8T4zx8m+ax/DfKtdAInTD\n6PhPZ3a/LmQjBHlBC83tOpxq35tp2k5mcT7Bhha6I+1vddYcNYXXqgvw82fqVe0Zuk6386Ju\nsZJAmO1KF87GSZ5Vw7z5+69kuuqf9qTZzYo8Aljfkdl1cSpLIBVg0PQwl6PS6Wqi+B47t+GH\nYt1EgKRuXDsRoOjfFtKzUsFuc3xqgNN9gImhhEARro7XNPS0bdahmbwQgKsJFeYJWqIEmpBr\n/oROOzA9rkWOy2IaK4PBSIQ2NG5hSvOf7oAAHKezACTAgN222IDq59i5DV/YuYwuhvvwyEYS\n0NP5xROKN9tjPjrzVwf2Xqnw6tV18ik0ziVoCn/ybYZvxCvS7NpSP7u5/t8yV/dUnkhNw8pT\n3+ocy5KL+mWxitBYW5QEwkwiAxiovEZQ0hRtV3MnbVeNGM9IPEJoLBJv96GtwsAHI0bnKKQA\n9HdmjEvxq2LdRid+TN3OUCiybXjsV0f3P5Vd+GikJ+qtBiglSVdccFQioE5jcLoXhRYG4+L2\nNWO/OjIDRiSaM5uhXNM3uuvUYY0VKsTczrkDdZLwTIiNbhvOrBRwwLbhTDZTLuza5xCigjzJ\niiAwhCSqtFL2jNd8dQAwp4g5rA4Ho6GW3HWlB23PtDPwOUGAE1QGAAHUTOXUwvlhVj0sCzva\ndwO5Bl/YuZKNseSSKLx06sgvsvMfiXRzyCNfufY46j45dr5FxRPLqBTOdlOR030xyZlCrQkq\nTqSo5DTPzqKL9xQsV+8a2mRzo0eagUmk+RPddI4TunJ1VpkGGK14qHqiK2jVPYyv7Mc2MMCs\nVEAIrY8addeZ/hkwVxTq2luU4hlCBugDsKsO2mZUqTgo1tW5JZ2FL+zcysU9g1lJ+NPCqady\nizeGE6RHK/AtmnVmtSMQZ3pQaL4/Lp5OM7LSeH0XYetM2xqOlnDkQIGfWPmXnqv+1Mp/W5UI\nJCeQgQLwHClSClMsl7FCgdnsApyThTxWR0OxAEVbfCjtN8Usd6yx/STo4l2EaTPEXIeiKBzn\nSwU34RFPT2fy3oG1Y9H4nCz8Ordkty1W4ahQrAFUEme7SQL6u7yZB1nClIy6Rsl5FmGCUGAT\naYQwlWcBUE0FxgW0Qtgt0Ca1pwCekQokIs4z7K5rjnpvylSjFZrbf4O9hcgCR4gASYBga8d1\nK1jFqqL6JbHuwhd2LgYhtH14Q38g/JbE/76QttucuhSLIfSEWd0q42qBMz2gUH0xkSatnk9g\nP1VlH0Unh65rsJE2zpUVHli9IJsx5DKsl/XVpFwgGIkMHidkkhSsc2mM1/lrB0cloYDVNeEo\nR1rts7GrYFbruEm6+Lva0e468Eti3YbvX3U3FEFcPzr+2MzuPxSyYUSe77zmduV6Tk9ctTwB\nzt06DxM400t0HR+Ii0fOej47Z3koWQXlQq1eLW31I20M75oQkGUT+5T8AJ1jFWa8OiGiwBcM\nD9+yj4r8PwXBoR6Coojzwu0shq2ZE6m9gv49G4AlxBApAEQATGgI71L8QbFuxBd2ridE0Teu\nnXh8ds//x6eiJDlKOfoyolPbtceYFmlYgYFzSRQ52xsTT6VoQfK2d7zGhbZWqay9pST13HWl\nhSbkwhSigI4cEdNrSYFROE9F3peCSCZhLNzFkFZf182SbtoY22c3nQUAAC9UtjaNIvndid2H\nL+y8QJINfHjNxp8f2ver3OLN4e4e0uocZ704sB2dWegaX4ERTvei+NxAXDp02iNOu6I4a1gV\nqzNhbtvweo01Gzr8HALd9ZaYHaZzlMJKgBpE3s0d/GWwxtYAKoKlECIwWhfpan1vLWBPzxQG\nyREqBxAE8EzrvmZQ/O7ELsTbXoQOYjgUvW74PBHjJ7ILGdUpdZhu8b1ZB87FQWa7oxLHWDpU\ntN1sG15vkdIq7bba4dfyvus2YV7BaJrX8vqIFJnoLMIUzRtq8+ZoFkNIJiFaoGnC6stEbem2\nb8+pIwczDRtoW0SCziAAgGHwaMMBnSzn2PkeO1fhe+y8w0Sse1Eo/P70XLG5HevI5nadJ/UQ\nTvehxJHBuDR7ylqnXYX0sdfFpe2Kq1gT7AnUmukKortmpMwoxdNyQMLI9SJeQbAYRAQmomIb\n3P/LL/je3SetP5YuSKTE6DwAC9Bjty02o/qhWBfiCztPcWnvcFoS9iyeeTK3cGO42wnfxaKS\ns6gdnSvA+RiKcMlI4eQSnResUttt7xViGG3d5uRIax1W6UKEFKbrgDD/N1SOlcJ863t/5fTR\n0vKW3pHWd2iIhTBSSIjzFIHR3t0nJzf1t9kAe0lQOQJUgCE/qOXPE3MjvrDzGlsHz8tK4uFs\n6vn80tagvckx5/CeqjMyvgLhdB9KHh5KiPtPOLq0xVyfn+O1WovhvM1l2m4zAFARJKVkqkDL\nAQGTLTntylVd8Z/t1HYKAUtBRKooInonsqwfAuE4nQUgATpLztakGIpl/Bw7V+ELO69BIPSh\nNRsfn92zp5CPkeTFbMRuizyLfrWK+RgSg12hfJhTsgUTfiLbE7hsy1Hqhj4rgrnOk4lTq5c3\nI4TpeEY4E6fzrBgxwWnXNDUrKkBHUcW6seTBmfn5MFIJiPM04f0OjDWIU1kSKQAjAL6aWQ7F\nUr6wcxW+sPMgDEHeuHbisZndr/CZCCInmQ7tme4ocLoPdR8cSojTxwP6tyopm+qSAh3TWo1h\nRzC3wXQvO7LuWnLjUaG8lAqDQBMBUaWcUsNkCJmApSCiFBQROtFdhwDiVAaAABi02xZHoMgK\nRREE0dEVJK6j0xMIvEqYYm4cnWBJ8jf5paOSYLc5PoALESyEokElGtB7va8eyaChvSrKVJ3n\n3zKFNgwn0HmI6tWmAAAhYBNpAKBybepus24sWfHX4g7nwwgjiAlMZ14bolSeJhSAPoBO1LXV\nKIrsJ9i5Dt9j51m6ueD2kQ2/ODz9ZG7hI5Hubsc0t3MLulPo9IJT/ah3ZjgpvDnX2Ieq039W\nES1tRc9V17FarA4rQ5lG1tdYp2mXW4P9V3tPa0IGCmRAAJ4lJFKlm3TabekdsaV4ooDVVBBR\nChGWbPi5qCjRwBjn8/k225Ck0wAIYKjNx3UmGGNVVpmwr3Fdhi/svMzacNc1g+uePTb7RG7h\nI+HuCOHfeOlFV/9ho4ghXIiEuExXSFnKOfG9KNd2jvH5VWg1izrTaqnMWiM0tGxg4mme72Fy\nXKEr17RB7a+EBYADEo8RTHZ3D4924hCtMMmzhATQDWAgX8LDqIoKfndiF+ILO4+zKd67JAqv\nnTn2ZH7h5lCSdlhzuwr95L3i2Qpwqh9x2eGksJQLNNH4tA1OtXbpuZqhTA21pNNd13A/7YBk\nRSrIy/kAKdIABY01S245W2RcBXmsHJPFEMUMBa2uuLL/PapJkskAgO+uK6HKMgDQjK8TXIb/\nhnmfy/pGspLw5tLZX+UXPxxMEMgpabAeHjhWFymA+WggkEqElYWs1revXoNfRzrVrGOq7L/l\nD2rLAqO6wajKbAyTSMv5AJ1jgcvUW6c82GpiQ5Niml29wlgNDkgFDLA+Ekdm/ETU7DY8uam/\npv6uXrn9nfMChBgkBIAugE70VtZE9rsTuxNf2HUE1w6NZWXpUDb1PJ+6xjHN7ToTnOpHgfRQ\nUljMUViznUS9kQwdoOcaUi28TK+raEnbEbRMh/NSNsjIHECNnnYVnepMx2gVRU5VTihSmGIG\nQh3aIGnFXTdssx1OQvUHxboTZwXmfCyCQOhDIxu7ueBuMf9Hofm8n86hIihsZoxYZnG+i6Nx\nMiLpWb2DZZxercYF9jW9LQA0nEaq+y2YKl9gEmlAOCiGAetygFkt9bTZLxcwxhtiSYv9+VN1\nlm2GRVKE5AFCAHG7bXEQxbETvsfOdfgeu06BJckb1ow/Nrv7RT4VQsQE42cHN8C6hD+c6keB\npaGEOJ+htZ123qU5Z5htiVk6BtpOrV6YQuRmOpqTUmG6wMpBseEhbEyzy6jKKVmM0ExfIGTd\nUSY3nbBu5y2SYDIA2HfXVeDPE3Mpvseug4gy7A2jEzRB7MovHVMaX2msxkKvmMNRaJxLMhTu\niepy2tnHlH1uFb3HDUfq9YUx33IdrrtVB2VjGSAUimdBrXSEOaFaosRbUgEDjFvurqvGEU47\nCqlRKg/AAfTYbYuz8EOxLsX32HUWfYHQ9pGNvzwy/WR24aPh7jhp8wegg8TcanCmF4UWBuPi\n2bRj+wvaeNGtd+gaeW/ZzHqKosqise3x6lU3Yam1DrkZBRYh103zjBSq7BNe3qzOTncdVs4o\nYoxme7gOddcl6QwBGGCoiUJ1b6P4xRPuxBd2Hcd5ka6rB9btOj77i9z8RyM9QYc1QOkUFApn\nk3TkTF+XlKlbN+kIGHaPLG1q7zF1irMpgAugMseu+aIH3a1k9EveKRSaBCFO8YwckDBRWUXh\nBL/dAVkAgI2xVkdWGMFBvU5IpHZRWQAaoN11uM5HUfxQrCvxhV0n8vZE76LI//HsiV9mF24K\nJ2nHNEDpKHCmB4Xm++PioeMgOWisaFEYOSJG1hBE/DlsWRFnnYy68ly6zasfqYlKR9PiQpzK\ns1KYN9nElkkDzGMlzgS6OZMnSq/uV9Lg49T+5iYluqgsgVSAET8xqRpFVkh/UKwL8T/KHcqV\n/aMTXd0nFfHp/CLu1AR+m1EpnO2hCDzs+MQeit5t2b6bTuPT2KptqrSx8cHQNB3JErRMFSik\nOO739hDIALAxlmjvYZ1y24AAJ+gsAAkwYLctTkSRFMZPsHMhvseuc7l26Ly0KBzMZ14sZK4I\n+D05m6SV4Rk4043C8yO98v/Ons4tnQT7m5vUbAhceqqdEbSiDa0MfrV68liRhpl2AABMPFM4\nHadznBht9/BTDRZUZQnUJBNIsJbWyDtFxlUTo/MUUgCGAByb6mobGANWFZrxXxn34bg7SJ+2\nQSHihtHxOMu9IWT/5De3a4pWh2dgEmd6SAIuHQkXH6g5bcK7TFUt1Fuh4eN1u9BZTLklNZrh\n5XPjAECF8iQrkiJFyA7yf8woAgCcF7KlY7kT1B5OUhkA5M8QqwlWFIz9BDtX4nvsOhqOpHaM\nTj42u/sFPhUhyDGas9uijuOxv5y84WJ411DgtblcWlCgQbM0S6m41i5rI1EQCQJRdDtv3LWv\n+lZpgooxblXvgq7jVkjzK+KDxQUmkeZPdNM5Tog54ibqjCKlsJKg2BjDWHwoB5VKlBOleIaQ\nAHoBWLttcSJysTuxH4p1Ib6w63RiDHvD6PjPDr75TH7xplBygGrwK99K5NGnGkWF3Ufg4g3o\nstHQ02+l7TOk/R6UehNgjU6GNbRaAzQldeP9Vztcf7d4/LrAeQBAcgLJCVBgSYlSaLklK81g\nRiwAwKiVHYnNov7Y2ZY2TNBZAPDddfVQ/e7ErsUPxfpAfyC8bXi9gvEvcwuLqrFLTquxyI7n\nk2Pn7z+BsgXYPBCIBxz1G2qp1KuXxqeHc4FOrF6Qzawv8BOOdQuVwyZTCGE6y4Hd1UqnFGkJ\ny/1sMER0aAZViBQChACQAAjbbYtD8YWde/GFnQ8AwMZo4or+UR6rT2QXeNVBvTccjinDM1QM\nfzkMBEKXj4bBnvoJoylu1tGK4HM6BCORQR4pBCnaLKdmRB4BrA3bkl3nCBJ0sXukP0OsLn4o\n1r34oVifZd7ZPZCWhKn5k0/lF28MJym/Cbs+Wg9Gf6hnFCs4lT/89v4AKSZ5G4a9td/dVe+I\n7tZwFVl6UJZjV4SNZ+RckM5zCiPZ9Q07IYtprAwFI2GKLsideBfHIilM8gARgJjdtjiR1/9w\nBACCpBIgYe+eU3v3nHrv1g12G+VjAF/Y+ZzjqoG1GUk8kF74dX7pA8G4r+zaB4YoP4qCh4cS\n4oGTnVzC4oKIqjbl2m7b8Pp8blV/E0TLdCQnZUKUwMicHfOaMZ6ReITQWCSuc4vqTLUm+gmb\nshOz6GaK7jr7x344GWR7xoBPs/ihWJ9zIIAPDK8fCIb3i/wrhdqJ/KYEH32qwXwMpEA8LIe4\nysFTPu5i2/D64l9NByQTTyOE6Txry3XzmCJmsToUiIRoq4thHQqNlAiVAwgAtLkts8vwBxK5\nF99j57MKiiBuGJ14bGb3/xWyYYK8gKlRNOeLOYvAqX7UfXAoIb51vJOddi5Fb1kuIlU6lhWX\nIjTPSkHBarPKwQAzUgEhtD6q113namo6BRP0EgIAGAY/26Q+NKHSyL/DdCu+sPOpJEBSN4yO\n/3R2z2/5dIQgz6N8kdEmcCGChFAsmIsElAzv5yy7nSkACIamsXpBxRN0LCulQyTPyJyIifY5\n7uYkIY/VNaFYgHJTMayJQVsSqV1UDoAB6DVrnx4DK2qIkjmiE5MvPYMfivWpQYINXL9mnAD0\ndG7xpGJHJlCnoqb7AWA4Wfma75w7UPqzwy4fbapHsWlVgSBCZboyCCOKb19rXAXwjFwgETHW\nJndd01OALSROZQmkAgz5176aFHL83PQRX9W5Hf/D7VOboVBk2/CYjPGT2YW03wClbQghXIiE\nOSUWPPeaV4g5T2s7J6oBI9QwHhF/rn6QjuYISqYKDFKN/ghPN2UYHJWEAlbXhKIc2YZAjRPf\nRALhBJ0FIAFsq9twLBjjheNnT+6fkwXJblt8WsUPxfrUZTyWXBILL586+kR2/uZIN4f824B2\ngNN9iMsMJYVUPmi3LXZhzhiJdlEtYmo+svqMEKbjGeFMnMqxUoTXfawmVZ2M8UFZoBBxnu5i\n2BKtRUJNeyubnj9RoovKkUgBGPYvfBUIucKZI6ekgsgF6Mm/6euKB+y2yKcl/M+3jxaX9Axl\nJfHPC6eeyi3eGE6QfrpxGxCDmI+FAql4SF7MddQ31IluHuPoPQs6xEupMCXSiiyqlCGn+DTA\nuCGbjsqCgNWxSJwhV+Vuzh3OAayaXWtGQluNoXA2NjcpggDHqQwAAhhsvHbngHHq9NLCiXnA\neHA4tn5jN0n6N/Cux38LfRpw9cDasUh8ThaezaXstsXdPDrz1+JfwzVxug8ADSVF6KBWUtVq\nwBXot7NqTYSZeAYw0HmdmXbTdZYbIGO16K5b18GjJqIUzxAyQB9A+/IaHY7Ei8ffOrpw/CzD\nkG+/cHB8stdXdd7Afxd9GoAQev/I+l4uNC3lXy1k7DbHrZTrucbaTuJwPhZg1GREgaohY3bM\nHPOpiYaqW55mm8+NY/WClX9WQgV5khMJkSJEC12zh2RRxOracBdNtqHU2qFD4VZmiA3ZbIcz\nwBhSpxaPTR8R8kJvX/jiS9cke2p0tvJxKR0V6PFpEoYgb1w78ZOZ3a8WMlGCfBvTsblfTVKt\n5B6d+at2O0Cc7kOBpaGEuJClMPa8mKunBhyeaWfCYDQmnuJP9NA8KzCy5orVLjpdAVkZq4dl\ngULE2kjnuutCZIEjRIAkgP/bBZIonT18qpDlGYbcONnb0xu22yIfk/GFnY8uQhS9Y+3ET2f3\n7MovhQlyDeWHMyxGZnE+wYYWuiPymXQz39Ni8axLFOEqheQqy+uhV5WSnEgGCsBzpEApbD1t\n12TNBAAclEUJq+PRBE20Jz7jRC3eveyuG7bZDgeQOZtaOHZWVdWe3vD4ZC/N+P0yPYgv7Hz0\nkmQDH16z8X8P7X0qu3BzpKenHU0TOhqc7kPBpaGEMJ8hVWygbKW8H8rOuQMuUkgVloMr5Z3h\nsCObSPHHWZrnFDZbZxVjpRIlRKwelgsMItZ0cHYdR4hBsgAQA4jabYudyKJ09shpPpOnKGLD\neO/gcMxui3yswr82+xhgJBS9bmjs6bkDT2TnPxrpjhD+3Z4uPjl2fkU0VtdYNoXGuQQdPtsT\nk04tNT/Z013azkPoddoRjEyFeCkbJAuMwpnZD3xWKsgYT8SSVJvcdRbSdF1t0nfXAeSWsmeP\nnlJlNZEMTrytj+X8S7+X8d9dH2NMdHUviIVXT889kVu4OdzN+pOi9VFUcg1T6yrA6V4UWhiM\nS2fTtKL6L7XzabJKgI6n5VyAzrMKKwEypxRawOpRReQIcjRU11M1PBriOI6m3TRhzAhTDCIj\nVAIgCNAR43GrUWTl7JFT+VSOJNGG8Z7hNZ3ru+0cfGHnY5gtvcNpUXhz6czTucXrQ3HC13a6\nMaTqAABUCme7qcjpvi7p+ELzTjs3FCJ4gJp9iXVFUQlKoSI5KR2mCrQcMMdpNyMVFIwnuhKE\nU911rfccbkiCDiDAACPQkT04c0vZs0dOq4oS6+Im/6Y/EPSqgvdZhS/sfJrh2qHzcrJ4OJt6\njk9tDfq3gBaCMz0oNN/fJZ5OMfL/z959BTl2XveiX9+3E7CRc2g0OnfPkBySwyxKFCXLkihR\nojg8lnl15bLLT344b/aTHx2qXHa5TsnHD7fq3lt+uHUlSo5MkinTx5I4lEVKtEYSwww5iTPT\nudHIO4fvPPSoOaEDuhvA3gDWr6ZYmCZ67zXoBvDH2l84+NZuT5QGeIWakbqCLCZadlvmNcmW\nLKBHbdrpzF20zQAnjMuRrpQ3gM5whMaErWleaY9r6TvXdRvLVa2pUkpm5tLjEwn8AD46fPpJ\nDvkcJeTL5flMQH7XVH+Gi9v1lMuxVoajkI932sjZJQ95v5bYvp4ozW4XP4Cp7uROfzpFqCvE\nFOISQe/ClPMLluYCm4smyAjv37KG4gAAIABJREFUBJjig/R6o+7HHpfSX1pLXftgSWuq0Wjg\nwUfK5UlMdaMFO3bokETKnZo49tyld36st0Q+NOF1PUOMtdMkXMnFzLW6YDkdvUL7uVG3PfV1\nt+g2gJGuO4RYy2rKnCrYksk499DH0Zi7bJshXhwb7XZdQgh4XUa/uY5bXa60Kg1CSGEsvHA8\nTzDTjZ7R/TCHji4siKcmjkkc95qtrMDBLxOiDjHKWllKoZA44uirwzftXlm8sPXnaAXssKDJ\noOjWI7AHQpgQbxEgvHaU8ZRb7TqYjSRG9U39DADE+cDNw39Pe1VN3xiKtnzuaqvSCIXFu0/m\nxyeio/oLMOow2KEjSQfkL5bmGCE/AGPT2XvpfHR4TEmBI2ZjliR02MjZ8SLgIedP/Pvale3b\nR0k2t3/voGS7vuVRMapQ3uZ1gTq7vTjvs1ix4jrLjhXixYI8ujsKUCDJUWrXMcaqy5WV84u2\nZZXK8QceLocjR/psgAYaBjt0VFOR+CdSRRPgJb2usMNfP0J7YYQ1s4RAIWF19g0Hbs7t1pH6\nj42rt9/zoAcfBGd2e9D6nEfFZAuA8OqOI+3234LivK0zxuajyRHu1pyMC7M8oQBjAI/d8Gc4\nGYq+dO5qY60mBYR77y/NLWQoHdkfPQLAMXaoK45HklVdfadde7G9+VvhtDC67yg9xJQEiWyk\no8ZqXdDNw30k23XRE6+2fBjZ4XR74EMqJ4XAEGnQdPkbRzi8f8ONnVdRabnOmm1GBDH363bd\n7UuKdHc9kR1P0eFZul7JFgKQ5FsAdPgXJWastlptrFUZg2IpNjuf5jhs1iAMdqhL7gunbI6e\na2x+T61+WU7i4nY9QFgzR5JXiwnr0tq+Eyd7uGrdodPYE6VZv3b7ztxwY/+Hrtd5VEy0tNWU\noEhGTD3QN563dAYwH0uN8tMvyisCtQEKAMN8OdLSjfUP10zNCAT4Y3fmEknZ64qQX2CwQ13z\nmfykaluXleYP9MZngri4XfcxNUYigVREX60LqtGnj+a/kSnffjX20AaxRdf/PMoFdS5ogCZR\nk3fFraGrt1yE3aFp13CddceMCVI2EOpPnb7EUkILgACMeV1JrzDGmuv12uomc1k2F144nuMF\nbNShj2CwQ13DEfKl8vy3L737tqEmKH+fNLpjt3uGsGaOpK6MJY3zK8G+nfU3cxO8IAzvnrNn\nbvvrrU27/v/DxURD07KCGjCEdoebJpw3dQCYj6V6W5m/RXlNohZAFqB/T5B+skxr48M1Q9FE\nkVs4nk1n8WUW3QpjPuqmAMefmjgm88JrWvN9U/O6nCHEtBiYcjzkhAM9XF9mxxwzpKluR94v\n5sxJFi9r1Kacye8yZ+KmL9Ydu+KaCTGYDoz0JbmUsLWC47jHdfRGq9JYPnvVULRsLvzQoxOY\n6tCOsGOHuiwmSqcmjv395XdfVesRyhX5YR7m4gnWzJH05bGk+f5y13oSW6Gtn9MmfKPLGW7f\n5Zc7Jyabthrk1YAjLuzbtPvA0gBgPpY84kkHWojTA9QESAEMW7q1TatydU1raTxP5xayxVLM\n64qQf2GwQ92XC4aeHJ9/4er7LyrVZ8PpBIe/Zt3E9AgYoaisRINOU+O6eORBjnQdTXrYSTdn\nmdwyufiIjycVbD6i2i2ZM0QnsNfa1JuOVXXttCQnpeG8/tihtNgEgOGbDNuuNiuLG8xxkyn5\n2J05ScJXVLQX/P1APTEdiX+mMPnvy5efVzafDWdkihf9u4k1CiR7oZQy3lvstDNxY+YY5AC3\nh0Nnu+7Ycbm7TyaKRzmmmGg6SkBUJV20GGW73e2CpQPAXHSHdl2PlhTp8yk6EaSmTA2AOEDU\n61q6xrGdytU1taHwPJ05jo061BEMdqhX7k7mqob+882VF5Xqb4VTPC6A0kWmzPRIKNCKh+y6\nsv+z2K+LjBzC1pXTmwJcIHjOk1L6gHIOH1GsRoQ3RCto7HifimPVXDsbkOPSYOy1cOh17/aW\nFhsAMEyj65R6e/PaumM7sXjw+J25oCx4XREaDNhHQT30eGFiLppcdczvq7Vduw3oUFgjD0BK\nKRNgn4d2cDfyOjjvJz3cqCudUTHeJtTlVBHcnT8aXTB1AJjdqV03OiRqhjkdIAIwDAstuba7\ncWV1/fIKc92ZufTJB0qY6lDnMNihHiIAXyjNFuXIeUs/rTW8Lscb37z49vafbh7XCjItGhTd\nZLiH02N95sxtNyAcubDLffptpxjXhWIIdcV4mzAiaDusSr3mWHVm54PhmDgY7boeSQ/RZFi1\nqSydu9KutqKxwIOPlMuTCbzagQ6kr5diq9Xq3/3d3/3yl780TXN6evr3f//35+fn+1kA6j+e\n0qcnFp679M7PDSVK+Xul0Vo69ZYw982Lb3995kS3Ds4aeRJsjqWMmsKz3dt2Pt7vwWPdngV8\n5om9Ru3vcBG5Q0K0bTZDvCbYQZPRm7ZjvmiqZOTbdSKxI7wGIAMM9uPgOm51udKqNAgh5cnE\n9GxqhDf8RYfX147dn//5n1cqlT/5kz/5xje+kU6n//RP/1TX9X4WgDyxvbjdj7TGRQsXt+se\nW2JKIiCwVMQ60PcN5uSJ25cRBkJ/2cE9d/DK4oXtsNul1LvzSeXQ+x2WtBfCxHgTgPDqTU27\nFcdoMrcgRyLCSC8qlBKbBBjAOHS4lLMv6S118dyVVqURCov3PzQ+M5fGVIcOp38du1arlclk\nfud3fmd8fBwAfvd3f/dHP/rRtWvX5ubm+lYD8kpcDDw9sfD3l9/7V7X+30J8gR/+8SJdvvC6\nC9bMEbk2ljQ3W8LeTbs+FNNLOwajM8y9R1EUnucDwSMt89GNTTV2bsWpinpzaYecuiuENbMR\n4XXeDnCMdwAAGLto6oSQ2UjiEAccGgJxYrwKEADIeF3LITHGaiubzfUaAJQnE1MzKUox0qHD\n61+wi0Qif/zHf7z9183NTUppOp3uWwHIW/lg+Imxme9eO/+iWn02nIrTYZ6R3Z9UBwDgCExJ\nieFKJmqtN/wflz1ekWRLny9M79JWPOhRmJRs6mtJQRXNqAYAS47ZZm5JjoZubtf1aM6pbyWF\nFgEGUBrQdp2h6BtX1izDDAaFY3fm4omRXokQdYU3b66tVutv//Zvn3766URi18+auq47Tv9G\nhW+dyzRNtkffw1OMMUVRvK5iZ5ZlAYCmaXTP9erG+MDDyfwb1dXnW5tPixGpXy/EjDHbtjXN\n+6vAzxRnby+DMcYYO3R5xIrKoc1CwljacF13//sflOM4lBLHOeqhpcB7AGDoO6/Zsd/3fnTb\n0O/Yvs3ABADHcQ902E+nx39QuXbLFw9X2L52ej05c+M/4QCoQQUZzICrKRZnX3B0Qsi4FDKM\n/Svf8T5bvy62bffk92Z303M7vOzvWCFjbO9/HUfcuKwwJuh6FKCvT3DbtgFA1/UjXDBl7UpL\n2WwyBtl8aHwiwnFut17kHcdx3a4dreu2nhedlydJEs8Pcy+gu3r4SL3++ut//dd/vXX7L/7i\nL44fP751e3Fx8c/+7M/uvffe3/u939vj2w3D2IoL/WTb9tbT1Z/8EE320MkbzLwYrofi55T6\nvxrNz4HE9fFDdifl9c6TqfG9azh8eQbQzUgg3czFratrPflY0pX3/a1wJgXea7cOdtHzlnmv\ntx+BMdey9tqYYV+fiOWOeITd3DZpF+BQD8J18jo0yqImXwpsaODmRZlzXdPcv/I97uPnVzzY\ns3IAKEV0SlxNyxpGv98stnTy4O/IMW1lo+WYtijSsbIcjgim2f0XKJ//cDt/R+N5HoNd53r4\nSN13331/8zd/s3U7n79+IeCXv/zlX/3VX33ta1/70pe+tPe3h0KhfjbPbNtWFEWSpEDAp6sG\ntFqtSCTidRU703XdMIxwOMxx++9w9ZvRqLF88XK78Qbvfj7Qj4XUHcexLKuvP9nNW78QDu+6\nXbeqqoyxUOgI84XVILjtiRyrKQHb6XJWtmyLEtrJT3YPHP+r7dvB4FH38dw+AgOmaxqlnCRd\nn1Xw6urlrRufzU/tcYTPBqe27vlEqeXYdx+xnt3c+K++xSEfhCAYhiboQdORON6dj6cDO/xc\nduiCyPIOp3NsxzANURT9+Za51a7b42lLwc3LTQBeEMqC0M299Tqh67pt27Is732ZYgeMtSrN\n1lqdMZbOyLPzaV7o/izGrSaFb9/Oms0mAESjne4RcsTXn1HTw+ezLMsTExM3fuW99977y7/8\nyz/6oz+6//779/32Pr/WbIVIjuMEwb8DlXxb29bH1s4/VH25vPAPH753Xm0nbO3RQD/SquM4\n/fyN+vrMiRuH2XWyxMnRyuNZO8NH14opd6na5QmSW5diOb5rL6wc/6uDjLTbYdrE9hGY6wLA\ndnk3Dp57dfXyvvMhnii1AKCL/7TbnFQVNRgMkNve+w+9f3Ig1VKXA3NWlMbEkNjpz3rH90X3\n+qN31NTeI9uvybvdISUolLjLS9HlxbUbv/7Aw+WeFwewled4nj9QsDN1c+PKmqnqosgt3JFL\nZ3q1/BNjzHVd375lbF2/9m15g65/b3WmaX7jG9946qmnJiYmKpXK1hfD4bBvP1Kg3uEpfbq8\n8Nyld3+qt8KU3i0O4eJ2XVyvrhOslSbhzXzcWm8IVrebdkd2lMU+Oo2AO26wsWO2u2GhkwgA\nPFHyxZSODjHBXBMbOSN+jOywXvHooMCSQhuAW1/16XWM27UqjerShuuybC48fzzb/y4jGhH9\nC3Znz55dXV391re+9a1vfWv7i3/wB3/w5JNP9q0G5B9BXnh6YuHbl979gdaMEG5KwHx/NIxj\nrQyNreQT5rWKf97yd4t0nmWpQV+r+QNL+0Bu5sxYYBOM6IDOBO2CuKDwxAEYs+0B2D/JNq2N\nK2t6W+N5euyOXK4wMGEUDaL+Bbt77rnnxRdf7NvpkP8lpeBT5fl/+vDcv6q1r4bTGQ7b8kfC\n2mkSrmRj1lpdNG3/vOF71gzrcGm6VxYjg9K0s5l7ztRsnnAZ5qwTruE68VtjzRCvbLKNACT5\nJgAFKAHssLyLr7Qqjc2lCnPdZEo+dmdOkvw4ohENkwH4rIOGWCkUfaI0YzL2Qrvackdnz9Pe\nYIS1MpRAIdGTCZ4Hd+aG//bckVcYPlCd3uxIe87UdeYej6flEgMO+E0H+rpQiV9EeUWgDkAO\nwNdbbji2s3ppuXJtnaOwcDx7z31jmOpQH+AvGfLYQixVN/Ufr117vr3525G0RPDDxq62J2Ts\nNoCPKWkSrmSi5mpdNCxvm3YeRJ9Ost3tO+duTaHwP4u571uaQLlj8RShIOVdY4nyNcdOjdpQ\nLZYSWgAEYMzrSvai1Nub19Yd24nFg8fvygWDeEUC9Qm+iSLvPZwZuyeZ23Ttl5Qqdu12c+M0\n2113tmDAmjlCoJj0ctG+23jT39rNjfnvidIswMlf/+lQXzuR284ausncO+JpkXIAIBYZFYCv\nMTJiz5kor0nUAsgA+HSTBtd21i+vrF9eYa47M5c++UAJUx3qJ+zYIV/4dGGyYRoftuv/pta+\nII/03pe32zHGffPi2zv27ZgaJ5H1VMRYrbma6dUnN38ludsN3Oa5BnM/sFWJcgux69swEgpC\nkRlXgNt07ewIfURPCVsd1vGtv/ZncZPOqU2lcnXdsexoLHD8zpwc8vXFYjSURujlAPkZJeRL\n5blMIPS+qb2pD8alsf44+LazhDXzBGAs6ZORdlv8HvU6dmaX27111lAtxu5MZIUbVk0Tsy6V\ngK87xFc/6l4KcXqAmgApgKMuc911ruNWrq2vXVx2bWdyOnnfg+OY6pAnMNghvxApd2pyISJI\nP9FbZ03V63J84eCpDgCAaTGwgomwHQp4MrR+jyVOhk8//lE6cz+w9SDHz0eTN36dUJBKLgAI\nm6NyOTYtNgEAoORxHbfRmuriuSutSiMUlh54eHxqJnX4LWQROhoMdshHwrz4zOQxieNfVetX\nbV+NEvOdvRdAZo08eNa0u3G82smb/ww6b7Lpu4bqMHZXIsvdtskBn2JUZrTlEr1/GzB6JUhN\nmRoAcYBOt6LqA9dlm4sbqxeXXMspTyYeeHg8HPHPQpJoFGGwQ/6SkoJPlecJIS+3qxuONxt7\n+8du6W3fbS2YHgEjHJPtSHBoejndClWHPo43nUjVdS9YusyLs9Edxp4SAoESAwChsscP+swN\nNwa4b5oWGwCwPbrODwxVXzp3pblRDwaFkw+MzcylKcVOHfIYTp5AvjMein6mOPVvS5deUKrP\nhtMROmqrOeyl853K3GaOZtqllHl2sf+TB29MEl1s1Hl7NG86ju+aigvsRCJDd1kJiE8wLsKg\nBVR1XbmTz+qDsRrzLSRqhjkdIAIQ97oWAADGmFZV6s0NxqBYis3OpzkOGyXIFzDYIT+6K5Ft\nmMabG0svqdWvhlLCCC9ud/g9Z40Q0yPhQCsmOw21n+G4Fz2h7rbrBibZKK57ydJDgjgd2Wuq\neKDMlHeJUHGN8u3PFG8WZ+m6tNAGAJ+060zdqF7ZsA0rEBSO3ZFLJH268AoaTaP7fol87uO5\n8TvimXXb+q5ac9nwjx/qBdbMAcBYytvRikePFL2YiDoYcedtU3EB7k7k6J5D8bkw4xOM6Ixr\ndzhdxu//8FuIxI7wKoAMkNz/3r3EGGus1Zbfv2YbViIp3v/gGKY65DfYsUP+9bmx6bZtfthu\n/IfW+E3ZF9dfBowpMy0WCjYSIbum9OfJvmNi8MkF2T7U1k0tx/nQNiKCNBmO7XvnwLjbrnP8\nhuuECHyUAncNcGff2d5iVQHf7zCbEpsEGMA4gJcj2EzdrFxZNVRDFLnyVDQoA8djcwT5Dv5S\nIv+ihDxVns8E5HdM9S297XU5A4k1cwBkLGUO7Ihuz+dMeOZXpsIYuze5T7tuCw2CkGbEYlxz\nu7291z/5+F0r3aixHwTixHgVIACQ8aoGxqC5UV8+d9VQjWwu/NCjE/EETn1FPoUdO+RrIuVO\nTRx77tI7r+vNMOWOiXjV44CsAFNjQbmejNibrT483/vT/fJJC7CH6o59zTbiYmC8g3bdFqnk\nWpucsOk6Ebr7Z/aTN/TqBkNSaBFgACWv2nW2aW1cWdPbmiByC8ezmWwYAHTdk1oQ2h8GO+R3\nYUH8SnnhO5ffe1WthSg3zuNi7gfDmjkSrI8lzWqbH8DBil2JXIPXrnvbVBnAPclc51mGiiDm\nmLkCfN21k7/c5V5nAArdKbEvOOLGeQVABMh5UkCr0thcqjDXTaVDC3dkJQnfNJHf4e8oGgDZ\nYOhL43MvXH3/u0r12XA6weHv7UHYElOTUqiajlobjdHcjHw7He6xFp2PmnZVx160jaQULIUO\nthKvVGTWBnBVx47dC9xumXCQOnZJvk2JCzDW/4FDjmVXrq6rTYXn6cxCtljqtHWKkLfwDRIN\nhqlI/DPFqVeXLj2vbD4bycgjvADKIbBmjsj1sYS52eRdNrDD7brAR+ltD78yFQC4J3ngHhXh\nmVQA/Rrha66dHvgFIDnCkkILgO9/l1GptzevrTu2k0jKx+/MSQF8r0QDA98d0cA4kcg+kC42\nXOeF9qY1gNcUveQITEkKPMvERn0zD/+r2NaKbWYCoaIcOcS3i3lGReBrLrG7Xlq/ZYPGr9t1\n/Qupju2sX15Zv7zCXHdmLn3PfWOY6tBgwd9XNEg+mS8rtnm2XvmeWn1KTpLu7bP9zYtvb904\n/ILA/saaWRKqFhNWpSk47ig37fzul4dt111HQRxz9cuU23Ts3A55aHtlE8uydF0PBAKC4McL\n9BRYVtYBuH6269R6e+Pquus40Vjg+F05WcYRvWjwYMcODZjPjc2Mh6KXLeM/9Ga3jrmd6m65\nPVRcnrUyPMdycWza+deGba07Vj4YzgVDhz6ImGE0CHzTJeYAN7bjgipQF6AA0I/c6Tpu5dr6\n2uUVYO7MXPq+B8cx1aEBhcEODRiOkC+X5xNS8G1DOWP0ZHG7Yc12rJ0Bl8vHTX7gB18NoVcW\nL7yyeOGH7U0AOJE42gxQAtKYCwyESocbUfgOAUgJTQAKMNaH02ktdfHclValEQ5L9z80Xp5M\ndO9iAEL9hsEODZ4Axz8zcUzmhde05gULl5PqmEtZK8NRyMdNr0tBN3ll8QIAWDxvcxwAvLp8\n8YgHFFKMCzPadok+kE27KK8I1DHNBEBv22auyzYXN1YvLLmWU55M3P/weDiCKw+jwYbBDg2k\nmCh9pbzAUfqKWlux8dpip1g7DQ6fi5kCN5Dv90OMAdECgS4eUCoxABA2nC4es19YWmgBENPs\n7VYTuqIvnbvS3KiHQuL9D5Vm5tKUYqcODTycPIEGVUEOf7E0+9LVD15Uq8+GU3HatV/mYZ0/\nAQDAKGtlaXy5kDCvVnrYmdhqQW15ojTbuxMNDSUYdLhuXiPnY4yLMmgCpzJHHqS8EuU1kVoA\nWdft1a8oY6y2stlcrzEGxVJsdj7D7brsH0IDBjt2aIDNRpOPFyY013m+XdXcw3cmvj5zYjvM\n+TzVHX38H1NSYIvZmCUJvRqAdWOqu/2v6HZ6IGCJ3Z8iECi7AMCvOzBQ/dmU0AIAxko9Or6h\n6EvnrjbWalJAOPlAaeF4FlMdGibYsUOD7b5UoWkaP99cfUGp/VY4xR9hzPOgRLqtG4evlhHW\nypLEYiFhfbiOw4m8d802NemmH0S3fhW5EAhJZlWBa7tOZDA+xoc5LUBNgBSADNDq7sEZY831\nenVlExgrlmKz82mOG4yHBaHOYbBDA+/xwmTLMs83q9/X6l+UE0P50fv2Rt03L7596Ld/piRI\nZCMdNVbrgm7iG5uXqo79E73JE+5zpemE2MkYu9MAj3V+fGmcWTXCV1wnTGEQnhspcSvMdb9d\nZ2pm5eqqoRqiyB27I5fKHH5BGYT8DF/T0cAjAF8ozRbkyHlTe13r2uJ2Q42wZo4AFBM478RL\nGnNf05ouYx/PlTpOdQdDA0zIMGIxrjEAS58EqSlTAyAOcLBNcvfGGDQ36svvXzVUI5sLP/To\nBKY6NMQw2KFhwFP69MRCQgz8l9H+f5fOf/Pi28O6Fl23MDUGViAVsWSp++/3t8yWwMkTO7KZ\n+yO1rjHn3lShFDpQjjlYvAuMuYQCv+kQ30e7tNgAAIDxLh7TMq3VC4ubixuCQO+6p3Dn3QVB\nwIUc0TDDYIeGRJDjT00eA4B2KGSKIgzXOsO3X3U98jAswpo5ABhLGgBnjnaoHTxRmt3+0/WD\nD4f/1Ns115mOJO6Ipzv7jtO73N4HEUHMM+IAV/N1spOoGeZ0gAhAvFvHbFUaS2ev6m0tlQ49\n+Eg5kw1368gI+RYGOzQ84r++mNUMh22eh19nu+9cOfsvKxcHvY13Y5LryuB6psXAlOMhJxwI\n9CLboT38QleWbCMbDD2c6cfOCmLRJTzwNYf4eFW7tLC1kUx32nW2aa9eWKpcW+coLBzP3n2y\nKEo4phyNBAx2aHj8j3fe2LrBCGlEIg7l4La+3aBnuxtXZjm66027VAoAMNv1zSVLP2upEUF6\nPD9BO53HfXuL7iBNOw7EogsucFWfJjuR2BFeBZABkkc/mlJvL71/RWupyZT80McmiqXY0Y+J\n0KDATzBoePzhXY9sZzuX0kY0kmg0CBuoJbz6i+kRMOxoUI4Gg01N69t5b1nZbqQu12441s/0\ntkC4x/MTIu1wsNeBBtVt3fnWmbNSjlmrjK+7TpwywXfzY1NikwADGIejzd11bKdybV2ttzmO\nzC1kSuWuXdVFaFBgsENDy+E4PpN31ldhsJZn7avTrMGTLD+ZzZ1dvGY5ZwBO9r+IVxYvjEi2\na7vuaa3FCHwiPx4TO19EsPP1TU7fcOPm76IgjTHtMuE3HSvvr1d+gTgxXgUIABxpDzGl3q5c\nXXcdJxYLHL8rH5S7v+YzQv6Hl2LRUPnDux75w7se2bo9H02uOmYjgsOld3MaAMC0WcuQBGG+\nOMZ12kA6kpHdiMIG9ppaN5jzQLpYlCP9L0DIMCozrsWo4a+POkmhRYABlA7drnMdt3Jtff3y\nCjB3Zi598sFxTHVoZPnrcxtCXbGV7WzmKpfPLkGrFQ5H2m2vi/Iv1tCBEjkkzReL7y//0nXv\n8bqiYcTY63qzwZyFWGo+2oVhZDs5fdtfb27aEQiMMfU84SuuOeaXJT844sb5NoAIkDvcEbSW\nWrmyZlt2OCwdvysXjuB+KmikYbBDQ4sn9OmJY9+5/G4F4F459kikR++m1904LcPnu5P92kfv\n+qzGgF4NB2Emt3BhFXo6LvGJ0uwINu3eMpQV2ywEI/elCh6WwScZF2HQcqlKwR8trRTfooQB\njB3iCpLruNXlSqvSIISUJxNTMylKfTd8EKE+w0uxaJhJHHdq4liYF95w9LOm2rsTDf7cW8Kq\nZaZH4iF7Kqv3elTiqK1g/IGpnbe0qCB9Ij/e8TTYg9pxgsUOX5RKDACEii+mx3LETQhtAB7g\nwHlXV7Sl96+2Ko1QWLz/ofGZuTSmOoQAO3Zo6EUE8anS3D9ePfeqWg9RrszjZZpdMMI2J0jm\nYiqiOS65stHbB2row9y2Fcf6uamIlPtUYbLjabCH0OkECz7K+Diz68Cr3n+0j/NtSlyAcYAD\nPDKMsdrKZnO9BgClchwjHUI38vppjVDvpaTgZzNlQsjL7eqGY3tdjo8x6lamwJKyMauYNL2u\nZhi0wP1Pow0An8xPRATR63KuC4y7hIBU9bgMCiwptAG4A7XrDEVfOne1sVaTAsK995fmFjKY\n6hC6EXbs0EgoBkKfH5v53uKFF9qbz0bSkb5M//TQLdeCDzDmz+XdyjTNXhhLmo5L1ur+GIc1\nmEzmvukaFrgPZ8ZyQR/tOk9l4FOMVUhA4yDgWRlxQeGJA1CCDof7MdZYr1dXNoGxYik2O5/m\nOOxNIHQrfFagUXEsnv54brzNnOfbmzrr8qaZvpotcdQRfo7gbkyDy5fTRjKMDc5DYgCntaYC\n7h3xzGyvpsEe3geVRQYvy5PjAAAgAElEQVQsUOMufVA9+87q1p9+FkAAknwTgAJ0tKmapZlL\n71+rLldEkbv7ZHHheBZTHUI7wo4dGiEPZ8YUy/xFde1lpXYqnOSOtsb9LXyV7W7xzYtvH6w8\nW3IrkzRzaTqnGwbfUIe8wdkLP9Nb645VkEL3JLJe17IDC+wGtOIkmqbSuqP3v4AorwjUASgA\n7HOFmjHWXK/XVjYZY9lceP54VhDwFxKhXeEnHjRaPl2YnI0mF23j+0rdX4u0+o0ps8okAXJs\n3I7IXW5wDr33DPWipSfE4H3RtNe17GoT6i64BU6e4MN5LpigEtEZOP15WrC00AIg+7brLN1c\nOb9YXa4IAj1xb/HOuwuY6hDaGwY7NFoIIV8szRbkyAeW9rrW9Lqcnri9OXe4biIzwqxapgSO\nj1uyhNlu2xmAM3v870Xb/JWpBDn+U4UJrleLm3SBA04F6hQgSaUCJ0/yYemqHbhoSxct6aot\nrDj8psM1Xaox0u2lUaK8JlILIAMQ3O0+jIHeUJfOXTUUPZMLP/ToRDrjo3GKCPkWXopFI4en\n9OmJhW9feue/jHaYcielIXy3+PrMie2Rdke5Rsy0mLWeF3Or8wXt7FLQsPCj4F6RDgBqjv0T\nvUkJ/WRhQuaFFnhwlbNzdWjUoSkAJ4AgAD9eSDKDuAY4GnD6za07AownTAAmEiYQVyJMAMaT\nww1nSAktAAAY3+0OtmlVrq5pLY3n6cxcpliKHeY0CI0kDHZoFAU5/pmJ489deuc1rRGh3Kzg\n3czAnunWmD+7FaWCIyQ3Fora2UXZcvzbguqvMwAnb/mSztzXtKbN2Cdy42lJ9qSsg2MW2BbY\nADBXTlxfm5qBawIziKODq8NW2nM1YBaAekPguzHt8cQVCAjAJML2/B0Jc1qAmgApgJ0fona1\nWVncYI4biQon7ilJAXyfQugA8AmDRlRMlE5NHPv7y+++otRORVJjnF/WGPMhu576QKncMc4K\nmcb/94vqp/LTXlfklb3adQ5jp9Wmypx7krmJsN87TA88XDZNU1VVWZZF8bZffgJUApAYF936\n+/Uwx2ziGuAa4KrgasQ1wNWBqfunPVck2wN/UuJWu64EAG+9efXG01ICIc4SqctxZGo+HY4C\npjqEDgqfM2h05YKhJ8fnX7z6/kvt6m+H00kOnw47+4dr7wOAKJDZPP+1uxP//y8vfqYw43VR\nfnBT0+5NvV1xrXI4dpcvp8F2BeEZxwMXAkjC7WmPGcTVwdGBGeDekvYAGAdMIJzgGiGBBcO8\nKAk3D9wUqRvmbEJYLB44fmc+EOTr9Xrf/mkIDQ18J0MjbToS/0xx6tWlS88rm89GMiGCY8h2\n9cYHIHKknBGeuSPerAMbuUnFe7XrfqWrV2w9Ewg9mi31rSCf+Cjt3bDFMLPBNcDViauDaxBX\nJ67OmA5MJ/VWGAAArgJAQgAXqMMIBSbQ6znv5APjhAAbvd8whLoCgx0adScS2aZpvLmx9C/t\nza+G05KPpzF6izE4fRZ+gyfzKWlT1C+tSdDVhQAH0xmAk9cs411LCfHiJ/NlDj8bAAAA4YHj\ngQtthbPrES1AjAlY17SEps5oqqVpVq2qUnD5m3+P8CmI0FFgsEMIPp4bb9vmu7WNl5XNp8Np\nXCZrNy6DH70Ln70HUhHbccmVDcnrivrp1qkSW6qO/ROjJRDu8cJEAK/m76kYqIUFIxwpASS2\nvvKDV897WxJCwwc/XCIEAPDZ4vRkOH7NNl9Va17X4jtfHV/Yvm05kGjdAbaUjVmFhOVhVX6g\nuO6PtIbL2MfzpYQ4hHOru0iiVlxQAMIAOa9rQWiY4edLhAAAKCFfKs/9/aX3zulKjPIfC0S8\nrshfblo8xQV3Y5pmL5RShstgrd7ZDu5Dx2bstNbQmXt/ujAmR70ux+8KUo0AA5jDK/gI9RQG\nO4SuEyl3avLYc5feeVNvyZTeIw7hwsVd4wjuxjTNXiynDcsm1fYovpL8WG/VXHsmkjwW8+++\nYT4hUjsptABkgOKNX//0Z+e8KgmhYYWXYhH6SIgXnpk4FuD4H2rNi5bmdTn+ZktuZRIYN53T\nY3K395zyvZ/ryrJtZIOhhzLF/e898nJinQADmMF2HUK9hsEOoZskpeBXygsckH9V6yu26XU5\n/mbKrDJBgMwWtHBghLLdJUt/31LDgvjJ/ATFOZz74YmTFhoA0h57iCGEugWDHUK3GgtFnizP\nOQAvKtWaY3tdjq8xI8yqZUrIXEEPiu7+3zD41m3zZ3pLpNyn81MSxSnU+8uJdUq22nX4joNQ\nz+HTDKEdzEQSv1GY1Jj7glJV3ZHIK4fGtBirFXmOzRc1SRjyx6rtuq/rLUbIY7ly9PaduNBt\nOOJmxAaAAFD2uhaERgIGO4R2dk8yd3+6UHftF5WqhYvg74kpKdbMiTxbKOoC19fH6vXG2g83\nl15ZvNCHc5nM/aFWN5j7YLqYl8N9OOMQyIgNjrgAUzhXD6H+wGCH0K4ez08cj6dXHfN7atXF\nbLcn1syxVloS3PkxjaN9eqy+v3xp+3avsx0DeF1vtVzneDw9F0329FxDgwLLinUADmDS61oQ\nGhUY7BDay+fGZsrh2GXL+A+t4XUtfscaRaYkZNGdK+i09zMKbk9yPc12b+ntNdssBCMnk/ne\nnWXIpMWGQByASQC8bI1Qn2CwQ2gvHCFPleczAfkdU/2Z3vK6HL9jtRLTopGgM5PXhmm26DlD\nvWBpMUH6RL5Mhukf1ksEICfWASjAlNe1IDRCMNghtA+RcqcmjkUE8cd66z1T9bocnyOsWgYj\nHA85U1m9p2d6ojTb0+NvW7XNX1iqRLnHC5MixdfMTqWEpkhtgHEA3GwNof7BFymE9hcWxFMT\nxySO/3e1ftU2vC7H3xh1NyfBCqYidjnT18eqF1Gv4Tqv600K5FOFyYiA1xM7x3JSHYAATHtd\nCUKjBacpIdSRdEB+qjz/zx+ee1mp/lY4neVGdIPUjrjU3Zii2Yu5mGHZZKXWqzz0+eK0oig8\nzweCwV4c32DuabVhMfZotpQOyL04xbBKCO0ANQHGAHBrPoT6Cjt2CHVqPBR9ojRjMvZCe7Pp\njtBGC4fh8u7GFDhCKWVmopbX1RyGA+w1rdlizolEdioS97qcAZMX6wAA0KfL5QihbRjsEDqA\nhVjqE7mywtwX2ps6G/LFeI/KEd3KFLjcRNZIhgdvA4+f6q2KY42HYieSOa9rGTAxXpE5AyAP\nEPG6FoRGDgY7hA7moUzxZCq/6dovKVUbcHG7PVkBtzJFGDed02PyIPU43zHUDy0jIQUfzZZw\nEuxB5aUaAADMeFwHQiMJgx1CB/apwuRcNLlkm99X65js9mHKrDJBgMwWtHBgMHqci7b5jqkE\nOeFT+Qkep8EeUIjTw5wOkAZIeF0LQqMIX7MQOjAC8IXSbFGOnDe1H6i4cPE+mBFm1QlKyFxB\nC4p+z3Y12/6J3qSEPl4oyzxOkTmwwvV2HY6uQ8gbGOwQOgye0qcnFhJS8Fem8nO97XU5fse0\nKKsVeY7NFzVJ8G+205j7mt60GXs0W0pJOA32wIKcEeMVgDhA2utaEBpRGOwQOqQAxz8zcSzE\nC6/pzXOm5nU5fseUFGvmRZ4tFHWB8+MVbIex02pTZc7JZL4cjnldTodOe13ATQriVrtuzuM6\nEBphGOwQOryYKD09cUyg3Ktq7ZqFCxfvgzWzrJWRBHe+qHHUd9nuDb216VpTkcQdiYzXtQwk\niVpxQQGIAGS9rgWh0YXBDqEjyQVDXxqfY4S8rFY3nIFcsK2fWKPAlKQsubMFnfppuukvDOWq\nbWQCoUcyRa9r6dzpG/7rvYJUI8AAZgH89KNFaMRgsEPoqKYi8d8sThmMvaBUW7hw8X5YbYxp\n0WjQmclrxB8B4ENLP2uqIUH8ZL5MCb4qHoZI7aTQApABBigZIzSE8CUMoS64K5H9WLbUdp0X\nlKqBCxfvg7BqGYxQPORMZb2/fl2xrTf1tkC4T+UnAtwA7bJ4epfb3siJW+26GWzXIeQtDHYI\ndcfHsqW7EtmKY72kVB1cuHhvjLqbU2AFUxGrnPYy2ymue1pvMgIfz5fiYsDDSo7My2zHEzst\nNAEkgHEPy0AIAQY7hLros8WpmUhi0Tb/TcHF7fbjUndjCmwpF7cKCW/GJtqMvaY1dOY+kCqM\nyVFPajgs71t0N8qJDUq22nX4noKQx/BJiFDXEEKeHJ8ryOH3LfU/9ZbX5fiey7sbU+CIpZSR\nifY92zH2Y71Vd+2ZSHI+lur32Y9kt1TnTdrjiJsRGwACQNmTAhBCNxqgASUIDQCe0qfLC9++\n9O5P9ZZM6L1SyOuK/M0R3cokzVycyBqOS6rt/r0ivWUoy7ZRCIYfGqRpsFse87qAm2TEBkdc\ngFl8Q0HID7Bjh1CXBXnh1OQxmRd+pDcvWLrX5fieFXArU4Rx0zk9JvdpTvElSz9vaVFB+kS+\nTH0yNXcwUcJyYgOAA5j0uhaEEAAGO4R6IS4Gnp5Y4Al5Ra0t26bX5fieKbPKBAEyk9dDUs+z\n3apt/tRoi5R7vDApUq7XpxtuaaHBExtgEkD0uhaEEAAGO4R6JB8MPzk+5wC8qFRrju11OX7H\njDCrjXMU5ot6UOzhejFNx/mx3gKAT+YnogJmkSMhADmxDkABpryuBSF0HQY7hHplOpL4TGFS\nZ+7zyqaKi9vth6lxVi/yHJsvaiLfk/ViTOa+pjVM5j6YLuaCOPzxqFJCU6Q2wDjAQK8Ug9BQ\nwWCHUA/dncw9mC42XOeF9qaF2W4/rJ1izZzIs4UxTeC6nO0YwGmt2WLO8XhmLprs7sFHEstJ\ndQACMO11JQihj+AkJoR667F8WbGt9+ob31VrT8lJXw3V/+bFt7dufH3mhLeVbGPNHFA3EN6Y\nK+rvLwUct2sP11t6a92xinLkZDLXrWOOsoTQDlAToASAvU+EfAQ7dgj13OfGpifCsQ8t439p\nPlq4eDvV3XLbc6xeYEoyJDmzBZ12KdedM9ULlh4TpE/kysRP2Xpw5cU6AADMeFwHQuhmGOwQ\n6jlKyJfL85lA6F1TfVNve10OwE5JzmfZrsT0SDTozOT1o8ewFdv8hakGOf43ipMCxRe9Lojx\nqswZAHmAiNe1IIRugq9xCPWDSLlTkwsRQfqJ3nzPVL0ux/cYsM0JMELxkD2ZPdJagA3X+bHW\npEA+mZ+QeZwG2x15qQYA2K5DyIcw2CHUJ2FefGbyWIDj/12tX7Fx4eL9MOpuToEVTEfsUuqQ\nawHqzP2h2rCAPZIZSwfk7hY4ssKcHuY0gDRAwutaEEK3wmCHUP+kpOBT5XlC6EtKbcXxcuHi\n22dL+Gf+xEdc6m5MgS0VEmY+ceCHywF2WmuozDmRyE1G4r0ocDQVpCoAAMx6XAdCaCc4Kxah\nviqFok+UZr537fyLSu3ZcCpOPXsObiW5b15824+RbpvLu5UpmrkwnjIdh2w0hU6+6ZXFCwAQ\nTWcrjl0Ox+5OZntc5QiROTPKqwBxgLTXtSCEdoAdO4T6bSGWeiw/obnO8+2q5vZpd9Td+DrV\nbbFFtzINLjeRNRLhffbweGXxwlaq0wOBK5aRlIKPZkp9qXJU5MWtdt2cx3UghHaBwQ4hDzyQ\nLpxM5euu/ZJac3qyycJwsQJuZYowOpPTY/L+UdgURE2SAKBqaBxOg+2eADUTggIQAcAmKEI+\nhS95CHnjU4XJuWhy2TZ/xHSMdvszZVaZJEBm8npI2msPD10UVRl3uOqJvFQHYACzALgWIEI+\nhcEOIW8QgC+UZoty5EOwfwpeTqQYFMwIs1qJozBf1ALiDtmOMaYGglowyDB29IBI7aTQApAB\nil7XghDaFQY7hDzDU/r0xEKMF99j1n8Zvli42OeYmmD1As+xhaIm8jc1Om1gr+ktQ8KV6nol\nJ9YItusQ8j0Mdgh5KcDxn0+Phzj+tNY8a2pelzMAWDvNmjmRZwtjmsBdz3Zt1/l+u7ZsG4Vg\nePueX585MQBTQwYET+y00ASQAHAyCkK+5t/lTgzDcN29RtJ0l+M4AGBZlqb59M2VMebb2mzb\nBgDDMCzL8rqWHTiO4ziObx89mXKfSRRfqS6+qtYE2xnnOlrRo28cx3FdlzE/jQPciAvMDMRq\nc0X9521Yday3VNVi7lQodjKepb/eg8wwDG/LBADGmGma/tyddutFz7btTn64uVCDEmZZZdvu\n06PKGPPzi97Wo6frOvXl7Byfv+ht/cp1Xp4oihzH9bKioeLH30iERk1CkD6fnyKE/JvZ2vR6\nAZSBYFWyTisaDrK5aXgLDBvYyUT2/kSO+jJCDTqOsHywzRhv2zi6DiG/82/HTpKkfp7ONE1d\n1wVBCAaD/Txv5zRN821trutaliVJEs/78TfKsizGmG8fPV3XGWNzycznKfne4oXvma1nI+kI\nPczH029efHv7dreuQjLGKKWi6Luxa25jokIvFCLa705JV/WxbDDkdUU7ME1TFEV/NnVM0zRN\nk+f5fX+4BanKExdgNhiM9Kc2AGCMGYbh26etbdu2bQcCAX92kkzTtCzLt4/eVq/Ot+UNOj++\n3CA0mo7F049mx9vMeb69qbMDj0O4MdXd/tchozP3n9ub37oir6ninTH6UBKnnvQKJSwrNgE4\ngEmva0EI7Q+DHUI+8kh27N5kbtO1X1ZqDvhpWJufVBzrudbGom2W5DhTTjhOKCW0xqRNr+sa\nTmmhwRMbYBLAd11bhNDtMNgh5C+fLkzORpOLtvF9pY7J7nYfWsY/tCsN1zmZyn+lvMATQVVP\nAITyUi0n1ryuzs9OH+J7CEBOrANQgKmuF4QQ6gUMdgj5CyHki6XZghz5wNJ+rDW9LsdfzhjK\nC8qmDeSJ0synC5NbEyUYEwEeBpBKgc20gI/Yjg6T6gAgJTRFagOMA+BmHggNBgx2CPnO1sLF\nCSnwltE+YygdftctsyWGbAk3B9j31fqPtIbMC789fccd8czN/18GeARAKAc3EgKOt7vF6dtu\ndIQAy0k1AAIw3fWaEEI94sc5jAihIMc/M3H8uUvvvKY1IpSbFTrqlwxZmNumMPfldnXFMTOB\n0NMT8xFhxynzEYCHCLwxFVxzGG3acr+rHDpxoR2gFkAJwI8zjhFCO8KOHUI+FROlpycWeEpf\nUWpLzuhuJrvhWN9ubaw45nws9bXpO3dJdVsSAA8QINPBVZnzfnVifzi951/3khfrAAAw08Vq\nEEK9hsEOIf/KB8NPjs+7BF5qV6uO7XU5Hjhvat9pV1qu82Cm+KXxOX7/BeEyAPdwhM3JywE6\numl4Tx1luxivypwBkAfo39p1CKGjw2CHkK9NR+KfKU7pzH1e2VQOvrjdQHtLb39PrRFCvlye\nfyxX7vj7xgDu5IkzJy+LdBTT8A0OOWcCAPLS1hRjbNchNGBwjB1CfncikW2axpsbSy8om18N\npQQy/J/HLMa+r9YuWHpEEJ8qL+QOvKvEJIAh0vOz8vIHypjN/Lg3QF88dsD7n976ljCnhzkN\nIAOQ6EVZCKHeGf53CISGwMdz43cmMuu29aJSHfqtZNuu84/tygVLL8qRr8+cOHiq27IAMBWk\n5qy8QslodToP66P2XkGqAgDArFelIIQODYMdQoPhs8XpyXD8mm2+qg7zMrwrtvlca2PNsY7F\n0781dVzmhSMc7A6AYojTZ4OrBLfx6NRpmTOjvAoQB0h5XQxC6MAw2CE0GCghXyrPZQOhc6b2\nE73ldTk98b6l/lN7UwX2WK78xdIsf9SLzgTgJEA2wqvTMma7vX3UrsuLW+26Oa9KQQgdBQY7\nhAaGSLlTk8eigvSm3vqV2enCxQOBMfa63vxXpU4p/Up5/sFMsUsHJgD3AyTjvDIeqHTpmMMs\nQLmE0AaIAGS9rgUhdBgY7BAaJCFeeGbyWIDjf6A1L1m61+V0h8nYS0rtLb0dFwNfm7lrOtLd\nAfscwEMA0YzYKF4fOoZucUO7Ttpa3KQFQLyqBiF0FBjsEBowSSn4lfICB+R7am3FHvil2uqu\n/Z3WxiVbHwtFvjZ9Z0oK9uAkPMBDAHJBquauL7qLrhPFNz+6TWlS6MXjjxDqHwx2CA2esVDk\nyfKcA/CiUq25A7xU25Jtfqe9uenadyezX528I3ikqRJ7CwA8AiCVApW00OzZWQaPaT4M8NjW\nn5w4TwAA7gb4ktd1IYQOCYMdQgNpJpL4jcKkxtwX2lXVHcjlPN421H9qVwzmfrow+ZvFaUp6\nfe1PBngEQCgHN+L8cIxQPH2UJYhvwRM7LbYAJIBSt46JEOo/DHYIDap7krn704W6a7+oVC02\nSFM+XcZ+qDX+l1YXOf6ZyeMnU/l+nTkC8BABOiWvhbkhGaHYLTmxQcEFmMH3BYQGGj6BERpg\nj+cnjsfTq475PbXmDki205n7L2r1F4aSkAJfm76zHIr29/wJgPsosFl5WeaM/p66u07fduPw\nOOJmxAaAAND51m0IIT/CYIfQYPvc2Ew5HLts6T/QG17Xsr+aY3+nXblmGZPh+P85fSLRk6kS\n+8oB3MsRNicvB+iAzj45vedfDywr1jniAkzhPpMIDToMdggNNo6QL4/PZwLy24b6M38vXHzF\n1r/drtQc+2Qqf2piQeI83MJ1DOBOnjhz8rJIB3j2SVdQwrJiE4ADmPS6FoTQUWGwQ2jgSRx3\nauJYRBB/rLfOmqrX5ezsjKE8r9RsgM+PzXy6MEl6PlViX5MAcyK1Z+VlvpubyXZtNsMBT3H4\n86aFBk9sgEkA8dAHQQj5BAY7hIZBWBBPTRyTOP5VtX7V9tfQMQfYv6n1H2mNAOX+2+SxOxMZ\nryvatgAwFaTmrLxEu5ntBgkByIl1AAow5XUtCKEuwOEUCA2JdEB+qjz/zx+ee1mpfjWcznC9\nWxPuADTmflepLdpGJiB/ZWIhKkheV3SLOwCMELc8G1w5rxbZUbdbOP3r/z7WhdJ21c2DZwJt\nkW616wJdPCxCyCvYsUNoeIyHok+UZkzGXmhXm67jdTmw4VjPtTYWbWM+mvw/pu/yX6oDAAJw\nEiAb4bVpeZXAIWYW7zg7tQ8XZLuAAIwFmwAEYNrrWhBC3YHBDqGhshBLfSI33mbOC+1NnXl5\nefGCpf99u9J0nQczxSfL8wL17asNAbgfIBnnlfFAxeti+iorGwHOBhgDkL2uBSHUHb59qUUI\nHdJDmbGTqfyma7+s1OzDtKC64C29/V2lyoB8oTT7WK7s+USJ/XAADwJEM2KjKFUP8o3b115v\nb9ENQNNuIqoBAMCMx3UghLoHgx1CQ+hThcm5aHLRNr6v1vuc7Gxgr6i11/VmSBCfnb7zeDzd\n3/MfmgDwEIBckKo5sd7ZtwxAdNtDQtQjou04GYCI17UghLoGgx1CQ4gAfKE0W5Qj503ttNa/\nPe/bzPnH1uY5UyvI4a/PnMgFQ307dTcEAB4GkEqBSkroyoPm6+Q3FmwAgONMel0IQqibcFYs\nQsOJp/TpiYXnLr37c6MdJvS+QLjXZ1yxrZeVTYW5C7HU58dmeP8OqttDCOBhgJ9MBDccxtXt\nPYLpjqHt9vmqPl0yOsJpEcGwrLjrxryuBSHUTRjsEBpaAY5/ZuLYc5feeU1vypQ7JnZ//65v\nXnx764YhSWokYjP2sWzpY9lS10/UR1GAhwi8MSWvnVeKbWc4FwHJSzUAUNWi5MOZygihIxjE\nj9QIoU7FROnUxDGBcq+qtWtWlxcu3k51qiw3w2Gbsa+UFwY81W1JANxHgc3KyzK344O22zVW\nX1973SZzZpRXXTdqWVGva0EIdRl27BAacrlg6MnxuRevvv9dtfbVSDpFu/Osd4BZgmDxvCmK\nFn/9mDPRRFcO7gM5gHs58os5efl9ZUx3b9lrq6frD/dcXqwCgOPg2nUIDSHs2CE0/KYj8c8U\np3TmvtDebLPDL1xsM7Zom2/orX9sV/6vxmo9GlVkeTvVDZ0xgDt54szKKwLxfrXnbglQMyEo\nABHXHZQJywihAxjWV2SE0E1OJLIty3xjffH5dvWr4ZREOv1QZwFUXWtDN684xoplbi+MFxOl\nhumvTWl7YBJAl+iFudDSB0rJZsPwSTgv1QEYwCwcdf80hJAfYbBDaFQ8mi21LfOd2vpLSvVU\nOMXt/r5uMXfVtpYcc8kxly1ju1sVE6WJcKwoR8ZDsYggAsD/eOeN7e/6w7se6e0/wBvHAMwg\nvTorL32gjrkDnu1EaieFFoAMUAQwvS4HIdR9GOwQGiGfLU5ptnWxVft/1q5E2tdX4vj6zAkA\nMIGtWeYVx1i2zVXb3NqMjBASF6SiHJ6KJsvhWIC79RVjSMPcLU4A2CFueSa4ckEtskFudOXE\nGsF2HUJDDYMdQiOEEPLk+Nz/fO+nuiRyrhzQNFsQ/u/Vi5FQdN2x2K/vkw2GinJkTI6UwzHX\nMDmOk0Z6VQwCcC+AFeU3JoPrl7XsgKYinthpsQUgAQzBzGWE0M4w2CE0Wv7nez/duqEEg0rw\n+sp2husUQ5GSHC2FokU5ItywtrCKF+wAACjAAwBvJIWaw+hVPeN1PYeRExsUXIAZnDaH0BDD\nYIcQgv9+xwN8x9MpRhUH8CDATzJiw2bcspH0up6D4YibERsAIkDZ61oQQj2EL+UIjZYdR8Vh\nquuMCPAwgFyQqjmx7nUxB5MV6xxxAabw8zxCww1fzREadaMxAaJbAgAPA0ilQCUlNL0uplOU\nsKzYAOAAJryuBSHUW/jRDaGRg0nuaEIADwP8ZCK4bjO+Ycte17O/tNDkiQMwAyDuf2+E0CDD\njh1CCB1UFOABAnRaXg1zutfF7IMA5MQaAAWY8roWhFDPYbBDCKFDSAHcT4HNyssy5+sdOFJC\nU6Q2QBkg4HUtCKGew2CHEEKHkwO4hyPunLwSoJbXxeyMAMtJNQACMO11LQihfsBghxBCh1YC\nuIsn9qy8LBBn/7v3XVxQAtQCGAMYgLGACKGjw2CHEEJHMQkwI1FrLrTEE9frYm6VF2sAADDj\ncR0IoX7BYIcQQg/59VMAABZlSURBVEd0HKAcpOasvEwJ87qYj8R4VeYMgDxAxOtaEEJ9gsEO\nIYSO7gRAIcTpM8EVAn7Jdnlpq10363EdCKE+wmCHEEJHRwBOAmSivDoZXAcfZLsIp4U5DSAD\nEPe6FoRQ/2CwQwihrqAADwAkkkKrHKh4XQy26xAaURjsEEKoWziABwHCGbFRkKoe1iFzZpRX\nAeIAKQ/LQAj1HwY7hBDqIhHgEYBgUapmxYZXReTFrVg551UBCCGvYLBDCKHuCgA8AiCNBzby\nsgcbjgWomRAUgChArv9nRwh5C4MdQgh1XQjgYQBhId6ICWqfz52XagAM165DaDRhsEMIoV6I\nAjwAQGbl9TCn9e2sIrWTQhtABij27aQIIf/AYIcQQj2SUtXjlLBZeUXmzP6cMi/WCDCAWQDS\nnzMihHwFgx1CCPWKZSUZu5sj7qy8LFGr16fjiZ0SWwABgFKvz4UQ8icMdggh1EOMjQEcF4g9\nJy8LxOnpuXJig4ILMI2v7QiNLHzyI4RQr80AzEjUmgstccTt0Tk44mbEBoAIUO7RKRBC/ofB\nDiGE+uA4QDlIzTl5mZKebDiWFesccQGmAPheHB8hNBAw2CGEUH+cACiEOH06uNr1eQ2UsKzY\nAOABJrt9bITQIMFghxBC/UEATgJkYrwyGVwD6GbfLi00eeIATAAIXTwsQmjgYLBDCKG+oQD3\nA8SSQqscqHTroAQgJ9YAKMB0t46JEBpQGOwQQqifeICHAcIZsVGQql05YkpoitQGKANIXTkg\nQmhwYbBDCKE+EwEeAQgWpWpWrB/xWARYTqoBEGzXIYQAgx1CCHkhAPAIgDQe2EwK7aMcKCEo\nAWoBjAHI3SoOITS4MNghhJAnQgAPAnCTwdUYrxz6KDmxBgAAM90qCyE00DDYIYSQV+IADxKg\n08HVMKcd4vtjvCJzBkAeINL14hBCgwiDHUIIeSgFcB8lMCuvBDnjoN+cl7aG6M12vSyE0IDC\nYIcQQt7KA9zDEXdOXpGo1fm3RTgtzGkAGYB474pDCA0WDHYIIeS5EsAxgdhz8rJAnA6/Jy9t\nja7Ddh1C6CMY7BBCyA9mAWYkas2Fljji7ntvmTOjvAoQB0j1oTiE0KDAYIcQQj5xHKAcpOac\nvEzJPhuO5cWtxY3n+lAWQmiAYLBDCCH/OAFQCHH6dHCV7H6nADUTggIQBcj1rzSE0CDAYIcQ\nQv5BAE4CZGK8MhlcA9i5b5eXagAMR9chhG6HwQ4hhHyFAtwPEEsKrfFA5fb/LVI7KbQBZIBC\n/4tDCPkcBjuEEPIbHuDh/93enUdFVf5/AH9mX2CAhEFxBghUUnGLMUQrUfNomWImmnBMIj02\n6jm4VJAcxC01UQNx40AuWGpZmuGSphzxQK5HcCnXUBFcIFR2Z7+/P27NbxpBEb/MvXN5v/7w\nzH3unXs/88z43Dd3mSHE1Vtc/e+tr/+vg/gR75/DdU85WwsAbRSCHQAAC4kJCSNEppI88BZX\n/duYL+KZPcW1hEgJUTNZHQCwFYIdAAA7SQkJI0TiK33wkqiObvIWP+ITCyGdMHoDQKMwNAAA\nsJYLIa8RIgiQ3XcTnhHw+ErxQ0LEhPgyXRgAsBSCHQAAm3kQouERfieZh5/UTcDjE2IgRMh0\nVQDAUgh2AAAspyTEwufx2olkTFcCAGyHYAcA4HT2MV0AALAUgh0AAMshxgFAcyHYAQCwWVOp\nDmkPABqBK3ABANhsJNMFAIAzwRE7AAAAAI5AsAMAAADgCAQ7AAAAAI5AsAMAAADgCAQ7AAAA\nAI5AsAMAAADgCAQ7AAAAAI5AsAMAAADgCAQ7AAAAAI5AsAMAAADgCGaCXW5ubkRExMmTJxnZ\nOgAAAAAnMRDsqqqqsrOzxWKx4zcNAAAAwGEMBLuMjIxBgwbJ5XLHbxoAAACAw4QO3t6JEyeK\ni4tnzZqVl5f39CVNJhNFUQ4pihBCzGYz/a/RaHTYRp8Xa2uzWCzE4W9Z85lMJovFwtreozuN\nteXRby47y6O7juVvrslk4vF4TBfSCJYPek7x/4IeW5iupRFms5nl/y/I87y5AoGAz8ctAc3l\n0GBXV1eXkZExe/ZsqVT6zIXr6+sd/6HU6/V6vd7BG22+6upqpkt4mrq6OqZLeBqW9x7Ly2Mz\nk8nE5t6rqalhuoSnefz48ePHj5muoklsfmcJIbW1tUyX8DRs3p2R53lzFQqFRCJp1WK4pBWD\nXUFBwcqVK+nHy5Yt69at28aNG0NCQvr06dOcp0skEqHQcbnTbDYbDAahUCgSiRy20eei0+ma\nE4gZYTQaTSaTRCJh5x9VFovFZDKx9rJOnU5HUZRMJmO6kMYZjUY+ny8QCJgupBEURel0Oj6f\nz9pBX6/Xi8Vi1h6xMxgMYrGYnW8uYfegZzAYzGazVCpl7ZtrsVjYvDsjhDT/zWXtR5SdWjE5\nhYSErF69mn7coUOHc+fOFRYWrl27tplPd/D/Z4PBQI9xrL34T6/Xu7i4MF1F4+rr600mk0wm\nc2QWbz6j0ajT6VjbewaDwWKxsLa8hoYGgUDAzuRksVh0Op1QKGRt7xmNRrlczs4/ePR6PT3o\nsTM8URRlMBhY+85aLBaz2SyTydiZOQwGg9FoZG3v0YcSWVues2vF3bBcLvf397dOHj58uL6+\nXqvV0pN1dXWpqal9+vSZO3du69UAAAAA0HY47viKVquNjY21Ts6ePXvSpEn9+vVzWAEAAAAA\n3Oa4YKdQKBQKhXWSx+MpFAo3NzeHFQAAAADAbYxdEbV161amNg0AAADASWy8pBcAAAAAWgDB\nDgAAAIAjEOwAAAAAOALBDgAAAIAjEOwAAAAAOALBDgAAAIAjEOwAAAAAOALBDgAAAIAjEOwA\nAAAAOIKxX55gG6FQ6OrqKhSyt0NcXFyYLqFJYrFYIBDw+Sz9O0EgEEilUqaraJJcLqcoiukq\nmiQWi3k8HtNVNI7H47m6ugoEAqYLaZJcLmdt79GDnkgkYrqQxvF4PLlcznQVTZJKpSKRiM2D\nHms/eITduzMO4LF5jwIAAAAAzcfSvzYAAAAA4Hkh2AEAAABwBIIdAAAAAEcg2AEAAABwBIId\nAAAAAEcg2AEAAABwBIIdAAAAAEew9/t4Ha+0tDQ7O/vy5csURQUEBHz44Yddu3Zluiin8fDh\nw02bNp0/f95gMAQGBsbGxgYFBTFdlDO5c+dOamrqX3/9tWfPHqZrcQ51dXWZmZkXLlwwGo2v\nvPKKVqv19vZmuihngo9cy2CsexHYzzoAjtj9w2QyzZs3z8XFJSUlZdWqVUqlcuHChY8fP2a6\nLqfx5ZdfVlZWLly4MC0tzcvLa9GiRTqdjuminEZ+fn5iYqJarWa6EGeSlpZWUVExf/78FStW\nyOXyRYsWWSwWpotyGvjItRjGuhbDftYxEOz+UV9fP3r0aK1Wq1KpfHx8xo0bV19ff+/ePabr\ncg61tbVKpXLGjBmBgYE+Pj6TJk2qqakpLS1lui6nYTQaV65cGRYWxnQhTqOysvLMmTNTp04N\nCAjo2LGjVqu9c+fOxYsXma7LaeAj1zIY614E9rOOgVOx/3B3dx8zZgz9uLa2NicnR61W+/r6\nMluVs1AoFHPnzrVOPnjwgM/ne3l5MViScxkyZAghpLi4mOlCnMb169dFIlFAQAA96erqqlar\nr1692rt3b2YLcxb4yLUMxroXgf2sYyDY/YfFYhk3bpzRaOzRo8fixYtZ+/PYbFZbW7tmzZr3\n3nvvpZdeYroW4KyamhqFQmH7M+fu7u7V1dUMlgRtDca6lsF+trW13VOxBQUF7/3r8uXLdCOf\nz1+9evWSJUvc3NwSExPr6uqYLZK1Gu09QkhZWdlnn33Wo0ePmJgYBstjuaZ6D56LbaoDcDCM\ndS2G/Wxra7tH7EJCQlavXk0/7tChg7VdrVar1erg4ODo6Ohjx469++67DBXIao323vnz51NS\nUqKiokaOHMlcaU6gqc8eNJ+Hh0dNTQ1FUdZ4V11djQMn4BgY614Q9rOtqu0esZPL5f7/kkgk\nRUVFU6dO1ev19FwejycUtt3U+0x2vUcIuXTp0vLly+fMmYOR7pme7D14Xl26dDEajdZLxOgL\n2Lt168ZsVdAWYKxrMexnHQN9+o8uXbrodLq0tLTo6GiRSLR3716dTqfRaJiuyzkYDIa0tLSI\niAh/f//Kykq60dXVVSqVMluYs3j06JHZbK6trSWE0B2I3nu6du3a9e/ff926dXFxcWKx+Jtv\nvunUqVP37t2Zrstp4CPXMhjrXgT2s47BoyiK6RrYoqSkZPPmzZcuXeLxeH5+fhMnTsQdds10\n/vz5efPm2TV+8sknOMDeTFOmTKmoqLBriYiIYKoep9DQ0JCZmVlUVGQ2m4ODg7VaLU7FNh8+\nci2Dse4FYT/rAAh2AAAAABzRdq+xAwAAAOAYBDsAAAAAjkCwAwAAAOAIBDsAAAAAjkCwAwAA\nAOAIBDsAAAAAjkCwAwAAAOAIBDuAtmvBggU8G+7u7hqNJiEh4ebNm7aLhYWFde3atcVbuXLl\nikaj4fF4BQUFz1z4wYMHL7/88uTJk+3aL1++LJFI1Gq1bWNhYeHbb7/t7u4uk8nCwsIOHDjw\nlDXn5ua+9dZbnp6eMplMo9Fs2bLFOuv48eMajUatVoeEhJw+fdruiUOHDh0/frx1MikpydPT\n89atW898LQAAjodgB9DWzZ07NysrKzMzMykpqXPnzunp6d27d9+8ebN1gQkTJsTExLRs5RkZ\nGRqNxu5HDppisViio6Pd3d3Xrl1r205R1JQpUwwGg23jtWvXwsPDS0pKkpKSVq1aJZFIRo0a\ndfDgwUbXvG/fvmHDhlVVVS1cuJBeODY29uuvvyaEmM3mCRMmjBs3rqysLDIyMioqymKxWJ+4\nZcuWs2fPpqenW1sWLlzYu3fvyMhI609eAgCwCAUAbdX8+fMJISdOnLBtLC0t7du3L5/PP3jw\n4Auu//jx41KpdP369VlZWYSQ/Pz8py//7bffEkLy8vLs2tesWSOTyQYPHqxSqayN0dHRrq6u\n9+/fpycNBkO3bt2Cg4MbXXOvXr06d+7c0NBAT+p0uoCAgE6dOlEUdebMGUJIeXk5RVGlpaWE\nkKKiInqxiooKT0/PrKwsu7VdunSJz+evXLmyOZ0AAOBIOGIHAP+hVqtzcnKkUml8fDzdYnsq\nduDAgW+++WZ+fn5oaKhMJlOpVCtWrDAajV988YVKpVIoFEOHDr1x4wa9sFKpPHXq1LRp05qz\nXbPZvHjx4oEDB4aHh9u2l5aWJiYmJiYmduzY0XbhX375JSIion379nSLSCSKiYn5888/r1y5\n8uSaP/7449TUVJlMRrdIJJKwsLBbt25RFFVaWioUCr29vQkhKpWKEFJWVkYvNmvWrB49ejx5\nXrhbt26RkZEpKSn19fXNeWkAAA6DYAcA9nx8fCIjIy9cuFBcXGw3SywW37p1a/78+RkZGdev\nX+/Xr198fPyIESPkcvnp06f3799/5syZuLg4euHOnTv36tWrmRv9/fffr1279tFHH9m1T5s2\nzd/fPyEhwbaxuLi4vr6+T58+to30ts6dO2e3BoFAMHPmzJEjR1pbKIq6fv16UFAQj9fI72XT\nLYcOHdq1a1dmZiaPx3uy2piYmIqKiv379zfz1QEAOAaCHQA0om/fvoSQa9euPTmrrKwsNTU1\nJCRErVbPmTOHENLQ0JCcnKxSqQYOHDhq1Ki8vLwWbPHIkSOEkGHDhtk27tix49dff83KyhKJ\nRLbt9EV7SqXStrFDhw6EkPLy8qY2odfrb9++feLEiaioqIsXL6akpBBCfH19TSbT/fv3CSH0\nLRF+fn4NDQ1arTYpKUmpVI4ePdrDw8Pf33/dunXWVQ0aNEgsFv/2228teKUAAK0HwQ4AGuHq\n6koIqa2tfXKWi4tL79696cc+Pj6EkAEDBljn+vj41NfXN/rEpyssLGzfvj19MpT24MGDmTNn\nTp8+PSwszG7hx48fE0LEYrFto0Qisc5q1NGjR/39/QcMGHDq1KmcnBz6GN6rr76qUqk2bNhA\nUdT69esDAgJ69eqVnJzs4uKSkJAwd+7csrKya9eubdiwIS4uzno4UC6Xd+3a9ezZs8/7MgEA\nWhWCHQA0orKykhDSrl27J2d5eXlZHwsEAkKIp6enXYvZbH7eLf7999+2ayaEzJo1SyqVLl26\n9MmF6avl7O5L1el0hBC5XN7UJjQaTU5OzqZNmzQazTvvvLNkyRJCiFAo3Lp1a1ZWllQq/f77\n77Ozs4uKitLT0+nDhHv27Jk8ebK3t/eIESOCg4P37NljXZuXlxfdSwAA7CFkugAAYKOCggIe\nj2d3EVurqqmpsc2Rhw4d2rZt248//sjj8erq6gghJpOJoqi6ujqRSESfdaXPn1rdvXuX/HsD\nRKOUSuWoUaMIIbGxsZ9//vm8efMiIiJ69uw5ZMiQu3fvVlVVeXh4mM3m0NDQqVOn9u/f32g0\nlpeX+/n50U/38/Oz3ldBCPHw8KiqqvpfdgEAwAtDsAMAe1euXDlw4MCQIUPsDqG1Kjc3t+rq\nauvk3r17KYqKjIy0W0yhUHzwwQfbt293c3OzOxNKf3EJfXWgrfLy8p9++ik0NPS1116zNoaF\nhVEUdeHChZ49e9ItHh4ehJDU1NSKioply5Y9s+Cqqip3d/fneIUAAK0PwQ4A/qOkpOT999/n\n8Xj0mUqHUSqVJSUl1sk5c+ZMmDDBdoHFixcXFRXt3r1bqVTy+fxx48Zt3769rKyM/jmKhoaG\n7OzsAQMG+Pv7261ZIBDExcWFh4fn5uZab3E9fPgwIcRuYfqG3+3btysUCkIIfWjw9u3b9Nwb\nN27YXu1XWVlpd/cGAADjEOwA2rqcnJw//viDENLQ0HDu3LkffvjBbDZv3ry5X79+L7jmgoIC\n+lvl6B8T27dvHz05fPhwX19fu4X79Omzf//+O3fu0OdSAwMDAwMDbRdQKpVisfiNN96gJ5OT\nk3/++efBgwdPnjxZLpdv27bt3r17O3bsoOfu3r17/Pjx6enp06dP9/Lyio+P/+qrrwYOHDh2\n7FiJRJKXl7dz587w8PDXX3/ddhNarXbEiBGjR4+2towdOzYrKysyMvL48eNXr14dM2YM3d7Q\n0HD16tXo6OgX7CIAgP8tBDuAts562lEsFqtUqokTJ3766adBQUEvvuYtW7Zs3LjROrl8+XL6\nwd69e58MdkOHDl2yZMnhw4ef/Cq7Rvn5+RUUFCQkJCxbtsxkMoWGhubm5vbv35+ea7FYzGaz\n9cfBli5d6ufnl5WVlZiYKBAIAgICli5dOnPmTNvvqNu2b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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "# 3 clusters\n", | |
| "fviz_cluster(km, data = clustering_data, geom = \"point\") +\n", | |
| " scale_color_brewer(palette = \"Set3\") +\n", | |
| " theme_minimal() +\n", | |
| " labs(title = \"Three Cluster Visualization\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "WE0EVldIM0gs", | |
| "outputId": "c05e72f1-c027-4fd5-fecc-38f2973629e7" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "plot without title" | |
| ], | |
| "image/png": 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3Q/7jQbD2ob9mnrdrXadj8uTMq5LipegGAkADDm2sKInhPbSBwjZQq+L4xg2qBN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VzZHqzCSVT9c5qQrdUiu67wyNILrpZdmm70k7p7THW3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L7D2DzpNNlaJb1ZYujvfLOOhuoZONPqt+\nfEy8pfnDZ1l/OH4ulrtO5yNQrNjkpqLerEJ2Dxn+WQRo3WxHN/UB3/OHpv6Z6cb5MrU227V/\nnjJHTSIGAPnZJMLuwPwRtM2RoWrBqIL7Ko2bn+sqlnY8drbECcVS48v6g/89+M3wrsVj8vtY\nbYsimdWUVopsdNicFamcTnc2xISi403vP5Nua46PvFnJXSetTEH8iJUqNkwNp+TdEX4rFQqi\nPXa82aIddfrzbYlvSM2TNxm9BD7CiHD+LU/nXr8cPze2euVUUdxcaDD1Gy67is5TaN3huvaY\n2+Xu7iPPxzJB3tUtLjVucjZcCAApx2NnSxyPHTUWfvYGC+w9A8+z2hAVMqLQCbpWi/QtI67F\n8h61ehBay8Rbmz9czWaHhLXrECglGYjQ1IALJ9KKFnCyLL3g6mg0qvTucReiT2dQqdxLvV6J\nahIG+qz6Z6bnXr8cc7l5lRXlAOX7Ni0cXMZ9mtL5lRqEKH2aUkfmcVfEstFoLCeXxCtm9H7K\nmni0W3bAoz0f1gQ9Z45HkAlxyROOsLMjjrCjwyc1P71X9d15XXuen1eiNAbREVUV2XAeWv0g\nkK6LM5XJykY2yEjFBpw5MyU2zRmP/viaPlydbmuOj74D4a7jXwvFkKp0MLP0neyiLMMI39Lp\nZURcDrFQEHWeQGe8ap0cXykWz1wjGqxpuXmVFThyX7QE/3OlKu9sUp0OkxTDNCXjg3MKtZ4o\nklwm7LQzcAlfEHzBVLOTFWtHnFAsHR7evgUA7hmk8l8loYYgU3WgLPJ0ih5uBlrKSZhgq9Mq\n2dcUwbTWDlIPcQeUbhQTb21+/xk2O5QYcaOxxh2FWO3R3XW3cHAZ98V9i3C5caqlfN8mig0S\nECgtIcqcpat1lFpNKGXFIuAUnmqsU/VOZsp2Oim1iSgAm0+jSyx175o57joOJlToeOzsieOx\no0DloW8+qv6htHuf87r1VB1MXZ3QnVC/fKEugMy8QOrpLCJfmv7JMbUdT/OHz6bbmhKlc9mA\nYp08Pqgq9cpUr5yad9NTWo0URWnBLN8eL4aEqyMq2HHw73JxRor2yGqX8n2b5ilkiWryqOmM\nw2pCegN16k5NtQPtRm17GwAUaBR2VgVhjXPaseHC9E/72XTS5dFbvdyBLo6wo8BfdmwFgN8O\nPNdqQ/Sis0HF5ZtWyM5pkJY1dOubnri5dCoaFpHAxKNNH65ms0Pxc1VUglSKUaR83yadW9w0\nIb0QTtup9q2iAi/R8CdHdNZCn0UW1RW9S5AVi/mBUhfKNqE2EQXtws7C+iYGaTs2VAAsm26p\n83ZV92g4mIkj7PSy5cBXO+p+vrig/9ldiqy2RYx+XxHmWRO3opw6FLWdsIQb8RXh13O2tket\nfmXZ/NHqdLQhMXoOwl3Hs6x0suzTOhFPaFpUpKuUvGV6pCSBgwdzvMkaVAlMUUhwH2hlmOLs\nv6zGa/WBOaF9qE3EAKAwYK/qxLLuOkPVJF/KzhF2dsMRdrpggf3rjjdd4PqNYe464gxQ6c48\na8uUGFTCzVBslQmr9ZJ//erf/vjl0x5vdnLENOrGVK+cyjtjhFFFJa2G89imFa7FlIzGuetU\nJxfKR6Xdb7IYJH3Qn46e+sC80w7/w7W/wqvl+ollQtsJY/MzOppP1GYbtYADIY6w08Wmn3bv\naTh8WfGg00P5sgN0Ol3MqeshnNwOKQKyUCzvLDqL7h44WuiveHdxzfbcVGx9nzGvfPIG3S1u\nwsoXoKNphEgRqqamcqh2a5V2QZDOie58gF92WFgVGa2N8EvDcPMYGjjmZk4lk+3t7X6/X0/n\nCVUwe06I9hdill+2RALWcv3EArmQZlQHm4ZIwCWTyVQqFQgEjFuxo12sU8rOfjjCjhyGZZd+\n8ZbH5f5Nf3l3nW1FEgLL44/m0/kuc/z6R31Mckz1jjZv9n96/QJ0aC9ZyLINEI9h/N5ioqZe\nRTOeBYCmNTNBoIdAGv81ILoqsgTUxKJs+w1041cy4YKj/4yWRIjeawQ5H+jx5mu7ung0nB3w\ne7yJtLZdCp2NsNMu1qY4wo6cf//wxb7G6qt6nHJSbjfMU+zTQwwBlczNTBS1+qHo/NOZvVFa\nsyM3FVvfpzTqNfC/7DioPndlO1UQyFC0D4+4hJvsbLSmwllLmIeBo2MwhQ6+B1ErVJq0Vq+c\nWnzbczirmKztGJapT7T17yIforEDpjWiZZyuYnbFEXaEpFlm2Zdve1zuO/qfg3+WmapOqdCG\nESV//zXu1ng8fv07zytNaIRYRM8pGvzy2OmqI3UaSX1TI7E+9jHJMdXb4x7f1pJf8Acx1ZJq\nmRLRY1vktOPGKzUH04lUMYi6dWHKLNVkUopaIXzDE4GA36XQokB2FdWcVj2b3rhzRZ8ysUOX\nei8NWlMZR0OiPc0yhYGQ1YbIY2odu7ATirUpjrAjZN23n3/fXHdtyakDc7oqjdHvuNJZBU06\nXtYeWspmQ9lsj8dDZSpZ8Kuc4N928xMyEAaA5Lq0Jspw41fnBY8kY+v7lLZkkfeyxEeqCTS1\nFzO00gqP1gZcSuO1lpeLRWPYNsrPT0XuCCeRvdu0tB1x7zWZC181LTTlcZzBZjrtahNtAFAY\ntKmw4zgwf0SP379v+DIhJxRrUxxhR0KKST+6879ZLvdcNXed/i1r/FmRSERpjJ4lqCibiVuf\nWjvapMYGFLUXxYQMrWvJNkzTP/P49Y9u/NX0pg+eint8W0tGap1KNiq6ZOSvjxsg8M/xTQi0\nhv/QeRKyx/G9cVT6uirNoOd0Wui5EGlmCQK0+1b2btAVWC0vzsqRTGjtp1AXjwJAUUC+O5+1\nCN11VQtGFdxXaehyrD/EZgXTTlcx++EIOxJe/OaTAy0N03qf0Qfj19toJxBdn5PWGfjVEXFY\nB00eRLL7z/PI6tuvaD2ytffolqzjuqfrj4pKZZ+mpzhiLx1mJiwOmkQPb5JssT3i3AVdqssA\nyKYVdRAWZckg0iPIkJmBZaPY/k7TnHZcrZMC+3nszAzCHiOU73jsbIgj7DQTT6ce27kt2+2Z\n3W+Y1bZo9jkZndaQEdkhPHTvhqa4OeJG6emo4WOSF1V/Hvf4uGRYLsqJL+lkW4EhChQbtwHf\nBLTGf3X2+MJBOoN0UaViKPhIVVr5vk2I2dAN2SiCeVHWVrmrSbQBQJFd99gJqVtcanQWBRMu\nTO/fzqZTLo+jJWyE82FoZs2+j6qizTP6nNWDRhNoo5FGAEXRYT3Kxrapr6LrWj9+ViKBVZhA\nf7qDntOFkEnkC2q/DCVjm3pfwLnr6FY5ESHSB4auJfssV1RmktYX0tNlzyVTDMbpDCodGpT6\n1fKfHWY8HVFUmcAqTDttCOexKwyEIGWjInbWuOs6uooxTPSIJ2y7xksnMo6w00YslVixa1vQ\nk3V7/7OttoUETi5obSSPGEyWpmBy04hUKoUeZrSjkax2CY5V/MxPbH/+zrOuvajqs7jH95+S\n84lNlYqzez96VWmwpjp2su5AreahJ5Rl4eCyciML3hoUBBRVPxa9pX9dTD8cvruOyn2wf9uJ\nunjM780K+fyxlLa0GEOReua4AsVGr8ty+RPNNY6wsxWOsNPG6q8+qGtrndP/nAIfnfJgOuUO\nWjHgqC66ygYdXhR+a4K24xddP34WeqQ5QlOa40I3Frx0++oUE9vc+4KI79juOoQjTfYhKqpU\noqScZGsUqzrthFKMintv6QVX3/XuP3VOgtAuwhIh+O0o8AejJ5G+poJSfono52FZ6WSl5FPq\n2itT3HUAUJeIFQbVOy+fIHRUPIk4+RP2Qr66koMs0WRi1Z53Q17fzL5nUplQKncIJhGKEmKB\nQuXEDWWz+dfj1z8q/MKfUOspSqsIv52wWVw0gcAw/XC+UrKCJkrw7joANs3G4h7fGxJ3naw4\nk32UijpAyK64rHSypmxW2dMpBm0XDBuPY4PoejGHIQ7in06M6mxK1qJb1tpcRdnBPCUbIsl4\nezpVGMyATTgmcdRjZ7UdDsfhCDsNrNzzzpH26K19z+ya5bfaluOQVQxgVo7q5gl3/GvcrVTK\nnYgyfDWNR58y6c2niVcxmn+MmfZS6VRNH59UmKaZdpZlotndhe46JWQf/LJZq+jTOShurid7\nqC8eMYFAL3LjVd11ZObpUSeic4tnruG/iCchOMs0UWgHJSdF1qraRAzsWuvEEpgQ57FzhJ29\ncIQdLpFE29N73g97s6f3GWq1LRqg6x/ChJZaErn9qFd9UzqCtkdqnn6rODCdr6IVn9j+PAAw\nTIx1uRuDPWTFjQkVgGk54fQ/5kWW8NINU6jJNn7l3WDohrCyx0XtMTSh1WmHH8NVbb/BScmF\ng8v4L15cmtBIzdD5iVevi8cAoDDoCLuj5OaD47GzH84eO1xW7HqnOdF2/6CRYW+21bZoA2ff\nm2qPCrqKkHg2q8qpSIsFSt1+hm5SRHD7sBs9LPPIp8sSnkDKnSVbgVaodZQ2TuHkIkj3XXEI\nUyaJofg4V7KTb72qsxU9zh5/UfaDpi16svNQL7ycf8vT7e3tfr/fm5UlOwDReYxWlgPqopC9\nYk1Aeo01XBG7gBOK7eDoHjtH2NkLR9hh0dAefXbvB3m+wNTeQyhOq7NjGA+i84TS/IZmM+hs\nYG8EfK9YKvkKdgjgCkm73Ptzi3tHa1wsw7rcmpJVtWJC0qJRBW8lS6h6rfDfVT0o0mcE/cpw\npCR6gGhw/i1Pq49TXoViBqv8PCxLZXJNoO9hLeexy4QidubAhovAEXb2wxF2WDy2c1trMv6/\nJ4/K9cr/15YYoc4gc/wgOk8oqTdVXaK/15b+XmqgXYQhFpr05tNK71ouOlUR3UnZ2/JzTmHf\n1ip/KtqWFQJBTitOGyih0054HNErgjqmRd9oLYQoR0KM0buWJWwAACAASURBVKJZNH8qmdQ6\ngz33wxmHSLxywq6IXij2wPwRRtcQNhQ20AW82Smnq5jNcISdOrWxlue//qgwOzil1+kmLKdJ\nQunZMWY0ZNVbQIvA1dN+N1OaZMgKd6m2O5BTBACFI66KjziWxSIVYZqkA2ahOD1wStGIgrfS\nheD4PA/EEqLjFLUgzur6J0eMob6ongmNcP4JJ9c6p+o9rEtGvW5Pt+ygDrs6G0yowPHY2Q0n\neUKdv+98uy2VvHPAOYHO0jUFp+yt1lMoIszwFeUT0I0XUzzXtPuj5Ac9ECwCAM/hXeaYoZ95\nlRWc2MLMvRVW8SBYC3MJ1TGYbxmH0qIEmbOqKKWhGIHJlWLwTxEer2lvyw/kul0ucssEcO0i\nrGoaQY1QYbqlDlgb9eFw6CRKxTgORZvWfvNpiT/32p6nWW2LgWDqEpO7R5i8ENoGaTwUqKZN\nyILvf60O5CfcWZ6q3QZZQheR0lo4uAwzwqvHtYPWJQjBpDpMmpBhkP+Mz8xFnGictquWu4HE\nn4gJsliTbUp1m/l52lOp1lR8QNcCegZ2BphQvjudSrc2eEL5Vtvi0IEj7FRY+sVbiXRq3inn\n+tweI+bXGTnVtAtNUylj1TxZM0OZBIJSdGf45AliZNc1+g6gP1+huNx4xZ2Hat9tO7DdFW9l\ns6ll7YmiscZ1g0Xv3jNOBEgFGUIKYIaMO+tGNIqSEb3X04jJcUCvXpvkap3QyZwQOuoyeqcd\ne7SUnSPs7IMj7FD83Nr48nfb+wW7TOp5ihHzyz6ztWoF0Y4xm6SjUvTtEQtKflgqlUokEnps\nsA+IKHB2yZC2/Z95qr9K9aUZ3Fky8tdut0upIob5ED/+Fw4u4512BLvoVEN1ZB44/FMM3aLX\nWaEoFmsnPwxOdWIJbLgQAFKRWl+JGXvQHXBwhB2Kv2zfmmTSvxlwrtdFfzMi3SwH1WJ1Zio8\nC317nQ/MVI/x6x8990j1jQAb3nvhUqrCzgikaRmGuuu45ZQyJ5QK+4nAqY0irKKiFLTVbr59\nZRyxYcZdjnHu0u/eXAG9hlApYifdV5e5TruO5hNOjWI74SRPKPJDpP61H78YEOx6edEgq23R\ngFJ7Mftky2YEdNtd6EdV1QHAz8FCAOjfctiEPhP6ESo5raqO4OEtXcLQrAicnfg6JxQe4TJR\n+C+yJchMslXcmdZPi+wM9b4A0Kh1opQtkalZFFy7WCcx1k44HjtFlmzfkmKYewed53Wb566z\ns2eLVjll+5OhHseaQF67x9ev9bDVhuCiZ8eeVl+R7NO9QwMJQrQEZuAsJBpAq+srN5XlOt62\nDkUeMgtFZzX4gkBjj12GeuaUcDx2NsQRdvJ83Viz6addg3O7X1o4wLRF7a8edPbGIC47d4II\nSh6yjZIsuA7mFA1sOZiTasMZj2iBYCZaczyFe9qKZjyrZ2m+RYcJN4FW6qjWebr86ZTm//ma\nYGk0Fjrq8AsQ6lxF9OKIL+ACtm3JJfDHj2it0glgwwXgeOxshiPs5Hl4+38Ylr130AhaJYvo\nYnMfklIuJ7HZdr5Y6ugJ/h4IFg6K/NyvpYqiPXQR5dhS0QdNa2aqPtGFA7S6uBAKGD8l1kK3\nFnVtp5odbH8fHibCKz3iC4RT7V6nYNvxsI7Hzn44e+xk2Hnk0JYDe4eGCsYW9DNoCT2uL+7B\nr7r9S7SEydqIbjFhu2HyDjzVVfhbfSC3GADuKOiuOqfUIWE+CBsw96jVPHmTAXaRg7iZmqqo\nII5r+ry6/MmQdH5ZcKo901rF6B9a6fxpt7vZm9093gqZuxnOGNhgN/BkpSNOVzEb4Qg7GR7+\n/D8ssL876TwXmOquI2vhihjPJ1Koaiy75QpYC1oTS3fgmWGTGtyn/MfL7wEAr1qZYqvEHKar\nTNPDu3XtHPzBHJr29tlBAaOR9ofgTBWqOooKD2cTIa21jEa2nYls+Ntz43IWXL1PHtVn/ied\nbJOcXlwuNjffCcXaCkfYifmsdv+2Q9+c27V4dPc+hi5kn9xVM5VKpihIfE1sxNKqR5TIyuvr\nCXR1a+w/YcSTWDVPU5SvoKeSHP4MPGQ5uXoMQLvlNCVhSN8q37eJ/0LYQAVE7zKjnXaiyjIU\nZ1MdWRePAkBBgE514k4GEypMR2qBZa02xKEDZ4+dmIe3bwGAewaeZ5UBFPfPGZpzgFMhT1Nj\njMzF0PusbUKXy1dyevq7993RI0yOfEDW0KL/SqAbS4gsEb4WWkW3x8OxHX402mlgClN0QFZ6\nscJpNX1AUhcd3Z12mOFjQ3+uKBYfVipqyFOTiAFAEaW2E52NUAF78Mt0rMmT081qUxwAHGEn\n4tO6/R9UfT8qr9cv8kqstkUGqU5CPPUNrdkhnHz8+kf/Ne5WpZH8orJx5M6X8UrlPisFf3Fm\n9vcc2vbd++6qPcyg0TrNQEPwWOXrEss6lvTXAaErIzQpYIJWFuhhmvxJmCMpajuccs3EdGSr\n3PYc9ZlVZ1O6rrcPfgUAhbqL2HVKmHChh+sq5gg7e+AIu+NYunsbANw1cLiFNqAf3tJu9LKY\n7CebuPWptaNvJDgxEyvGmeyGFGlo1fvjLxkKAJ6q3XMOHcuNFXrLZB9d8yor4GjAFMe1Nq+y\nAgaXaTrluJEK46lrNcTpws1z1L1K/ISxaCwQ8PNJHmjnEP8uWlOqOjLNzJkQgs720Pk5Kh2n\n7rSTpTYeA4AijFBs5vaQIIYNFQCXGNtjsNW2OAA4wk7I+7U/flq7/8L8Pud17WnaogQqwYhg\nnyVus8wN1ApvEf4lELR3U3JzIk7xlQwBgL27/wOnXc8fREdCRXvg8MOmek7BR/aha0JVEa3u\nQxMKfOj3WhlU1o4DraExb9Exwb1qWmjK4+iZySDYjVCbiAJAPo1+Yp0PtqP5hJMYaxccYXeM\nx7/5AAB+M+Bck9c1QkhhaiayQrhkdL6oqyZEjjcw7A5kdS3x5Hbv16K3/wRCq+Ektwq7weJr\nPvznNzeSZZhoNOr1ev2BgHQMQk8YsRVMaRJRTRZuGOYeNaF7T+jMQxhslbtOiQxKkkVQG4/l\n+vxBrw89jKuEcqI57ZhwIQCkncRY2+AIuw62HNy7u7FqXH7fs7oUWW2LIeBk4BILjn+NuzUe\njxPY0AkwVLCSOTWze57R7ZvKLomWZp965EhWpXEHuX+XjPw1zqKiysOgr2OYLIhCwSIbREvj\n6DY92k6rdsEJEAtHypZckZ0ER9URO+0IbpFWAS0a3/LirBwD/KBar4Jl2fpEW99wHnVLOgm5\nhQCQcmoU2wan3AkAAAvssp3/dYHrjj5nW20LHURSQ5PawFES/Jx0C4JkqPIjq43Cl325dttz\n6qMFa6mO8fccCgADMJrG4vje7v3oVeG31SunqtbUsKR7qXDReZUVVPIStCKdOfLC7bTmpGi2\n3bx6Nqcx2Z5i0oV+lcwJYeHiE6qIMRMuAICGDX+22hCHDhyPHQDAhh937W2svjSv7+Aco/5P\nZmFagBFLa62lrGRAhio56lxXuYbiLcouGQIA/VoO7cjreH5Td57xXVZFr41DmutQLegVK5WS\nCweXCQWo0FeE77DBdPUh3g3f8EQg4He5sf4LLZ1KdBVo8wyVa5r2yQlPkR7UlFFrzuZFNLXx\nNgAoDKI22EmV3IkTkOX22DnYB0fYQZplHvniTY/LPbPnGUbMz0scQ3dWya4oPGJcrZOMqLpn\nDmbuWUTACbuyLHbMUT1HsN1NCf4pu4w/VDoZDHbRzausKD/+iE12btFN4xWdqMnxOa+yAkY/\nKDwi/ayJE1RVQ8BUEE/LstFoLCc3x4i1NFGbaAWAAqeInQIH/lp2mssFLPvNTZ6Tn01bbY6D\nE4oFePX7L75tqr2iaNCAQBcTlrNP0wVaLiKcRmdaPXxK421y6zBRCogbLfi84eLmrNy2/Z9J\nGz+ItIL02S89grnHzjjmVVYotang8xJwBKvW2nJKPSHMRNZdx/d+UBJYSmUCZV8bh9ROhM12\nhvPYFSmHYpUCrydIQJYFSIHHaiscjnFCe+x6rb6fe+F1ue/odzYY8D8NhEAx052jquHwK3FY\nJa3Md3waAbHZmq56/PpHZ+QUDmn6oXu86Uh2V9G7onRX7rXwoCihtXrl1PxbnkavKDwF1Jp0\naXq0q3qtWtfO6Tp1paxJBC0lNCkeE0quEFO+bxOVjhpA1StphztDQG08CgCFSI/dCRJ1lcKJ\nV8bt5h6gjtPODpgq7FpbW1etWrVz585kMnnKKafcfvvthYWWxeZ5VQcAoVSqjz8cjUbNNMA4\nbUdcHw7HHpzJNXXIwMHo4LL5iG7RS6WKeoIs8P1zTvGQph/6t1ZJhZ0sIinGf4svdPCDvFqf\n7pj9T6UKlRjMXE5DNUr1yqkwuEy0ebF83yalRaVdPVSLIavqdVrYJ25O9pGhhV1GlDgxyDze\nJelhjok5R9tZjqmh2KVLl9bW1v7xj39csmRJMBh88MEHGYYx0wAeoapzARQk2Stef8KIhawS\nH8I8TXwnHFmYOKMFloXwn84/xkzDPwvzAzqQWwQAfVsOERp3PPXPTEcPkMZ8ZSFL8Fw4uEz4\nJR3QtGYm/1qPqrMkkVaJ4plrpGobrUuWlU5WDcJqBbPenv4JjUbPurXxtmyvN+zzo4fZNvDK\nS0+D5ncBuFlHydkI8zx29fX1n3766SOPPNK/f38AuP3222+88cZdu3adeeaZptkgS16K9bEG\nzm/z/goGKTmtas/mdwkT+xRhPpBTBAD9IzLCTlb6yO69w3wWivbw0c3AFQV5Mb13RqBaRc+I\n+XXeTM5HpWRzKplUnUG2iZlWG2StIptNJ2RL1yWjBf6QC1zStw4+OJKGXZkK5wV0t9S6Hjgp\n9+zLe877t9UWOQCYKey+/fbbrKwsTtUBQG5ubq9evb7++mvLhV2QMUTWSWORNkmZNAeCi0WM\nyaC7p98w/VFm7nY1ZIcHtB52sezSMdeCxk4S0sH4T0TZhfQ83YXaTnQK33kCZx40Oj1JBHVA\nqIsbg5xhRjj8TEaPGa2pRFsqVRhUKWLHYcOArKi6niHmtdQDgCdUQH9mByLME3aRSCQUCrlc\nx/7T06VLl+bmZqXx0Wg0lUoZZMyeq8pPf2Uh99rLAgBUXHhTOp1OJBIGLTp+/aPrLroZAK55\nezX3orW1VdMMDMNoPUWVa95eLT1IsAoXUo/FYsLPVwh/+cSsu+hm3tp1F92syUiWZVmWpX73\naMGbx18gp2Jl7xjmta+76ObGpi/j37y15OSz22IxAFh07uXcC0xkpViXG8U7Fu7/dIP0XMyF\n8O3hHXVt514ufTeVTmu6NCnNz8uXEeavlx8gexO4d2VtYFimra1d+GvBTyUcj55fD4gJWRYA\nIB5PJJVddziGcWNk31U6BfPzYllG5ycrRXQhCOM5DrRFACAvyy/6vUun05GlF0vH2+TvDPc3\nOZ0WR0iNMM9XdzAHIOULIx7oIjjz8McHg8GsrCxC+048TE2eUHrqy5JKpRB/bvTzxeX3nLXh\nLwDgBVg7+kbuF4BhGCrb/q5/53npQU4yrh19I7F2NE7pUlmF/yOCuHw9rB19o56prNrQiYn0\noq55e/Xa0TdyV83dUk0/PN6i0+LfvOU+vCcd6okY9vvtm/GNlD4nFgwbL51BNKx17RzZ2Zqf\nvz33+uVCGxYMG8+fwr0lOp0/5ThYVmqYJmTmBICjFyKyX7iW0E552wAYhe1H/HjE/JoQzcYb\ng56QZRnMBZUuEGcVYvRPK/3x4+fk30JcWk28FQC6+4KiXz1ZVQcADX+5KHzXFj0GU6Tpb2NF\nR4wwz9dSCwBsoJvWRzb+eJv/9bYb5gm7rl27RiIRlmV5edfc3NytWzel8eEwlutbD6N7nvTO\n4W9fvWRGyOtLJpOxWCw7O9vvV9khS0yXLrrq5LW0tIRChlfI3HT5XIKz2tvb4/F4bm6ux6NY\nzUjn5euB+09CQK5PvB1oaWlhWfa6SpnAHH/TCD4X38Bzo+9CTuN3nlxUIbplo6+Z98466fGF\ng8uWjb4GABKJpNvtwg93cmfxVK86LjWk+DZx/zTh6r/fvnnZ6Gu4U3JzOwr9izwM/HEAYFmW\nC8Ua92srNaB17Zzi257jr0uoG7i3hINjsbZAwM//0RPdDe5aZOfXb63qPNWrpuVevzw7O1vJ\nFyKyFo6/+aIxOs2WwrJsLNaWkxPUOY/UQ8WbKnxLemkckWgVAPTumi/6C+b73bZEIhEKhdx4\nbUVMJplMKmli6n+KfUwMAELFfcPdu2Oe0tjYCAAIASBCk1fIwTxhd9JJJyWTye+//37QoEEA\nEIlEfv7551NPPVVpvAkfZE1bxO/2hrOy+eVcLpdB61LZE2bCPdGzBHf3lHIgzPzNFJXl4z9c\n0wwgQDZ9RI/N2SVDweXyVO8G5CRKqazifXLKk4jq3qmYpXZF895ZxzWZqF41rXjmGpmI8Kpp\nx3ansUc3yBr24cpvz0IsJ/uWwvjqVdMWDi4DQXM29fmRiK1Vm6d17Rz/LU/jL3fczZfWhTn+\nXZ102KTvk1XM6pVoViXj67jqxDlh2V9G4x4ZOuGsMmfDnzt6BAC84UKtt8Ket64TYJ6wy8vL\n+8UvfrF8+fI777zT5/M99dRTAwcOPO2000wzQEptrKUwW+9/B6Xoz+7ELxecKZh5IbKF3ya9\neaxkV6bcVYLy0UI8gS5Z3fqwh3cDy4BLm1NBazKm0njVnAmprBQ1eNVkhmmgC6Pg90IVVW/h\nO8OqpmJg5mpobcyqaUBGgLhLmBdYwxWxCxgeQcpcXC11AOAJ5VttiEMHpu6xu/POO1etWjV/\n/vx0On366af/4Q9/sFCwJ5l0U7xtUNciqwxQwqBOrLJwkxvdy8EqVYc4ImuS/sRbnXdS6LST\nqjrQ/vOQXTIkuWuju2E/070//lmI5Fm6pUwAo5qJtY0KLBE3okuWijO+15nscRGy2k44sv6Z\n6fwAoedV9c7jL2dD8I2vi8c8bneeAS6AToOrtR4AvE5WrG0wVdgFg8G77rrLzBUR1La1sMAW\nZNPvMK2nJJslLRYyxYNlKPrvvKjpGQdBPT+KVvlLhrTu2ug5vEuTsJNy9wevcC8w+4bx8FXQ\nCBbt8GZVVojEH+bSVJDVKKqON85mqUqQmQ27pLMJaKpHmOn+PNkoP8hpu7pELN+f67HlRjq7\n0HoEnHInduLE7RVbG2sBgEKfGf8Ps0Q52aRS7gmiGm3SFFiEr2QoAHirdieHTFAao9rm9d6P\nXpU9kdiBJ3p28q3AeHedSCepNrQgWFTPPBSHKZ0rEsRKzcFEF4V5gbLxcWlLD02fb0Z46QiI\np9PNyUTvLk6QEYW7pd7tz3X5bJqddgJy4gq7mrYIABQZ42CnEozTg2gSWXlh0E4+c8K7iNVV\nS0NLMbTphaq2u3bbsVxCfmSfrSsAAALHsozPaNNc98Hfcwi43J6qPehhqs/v8n2bZHt5iZ79\nZO0rOHWyrHTysab1akpOq6ZUil0aTfXKqeEbUEXplCLRsmFWTcZr9a1qArF1MlNCsYAnRusS\nMQC2KGB4OYKMxtVa77jrbMWJK+w6PHYGhGLpYpA2Mnonn3BCk5tGSHeqrR8/a8Lmx00zQBOy\nErxD1R3P7oAHAA6Mm40/uTs7x5ffP161B5g0uOUr0RgX5UTIL6lTShOmhWKlyKuB4++hpr5n\n/LWIM0yP/3bh4LKOVY4mWPDDpCaJPlPRB8GPTyWT7e3tfr/fm5W1TLdnNNODs7LUcZkTeG0n\nTlBYBmKNnsIBVtvhcAwsYReNRjdu3Lhly5bt27fX19c3NTV16dKloKBg2LBhF1988WWXXZaT\nY3d5JKW2rQWoeuxoyRcTZIeZO/lssmvw5bHTg0H5z1rJXafJSIq9bmVVHTHZJUMSdd+7679n\nCk8mm4GTEUpOOx4lWYCojiE8bnQPVroLcfPwncGEjjeRqou8cHtgxrOajJSilDxrKAj1jM60\nzSCnnSo18RgAFDoeO2Vc0UYXk3ZSYm2FirCLx+OPPfbY4sWL6+rqfD7f4MGDTz755K5duzY1\nNdXX17/wwgvPPPNMQUHBfffdN3fu3OzsbHOMpkJNLAIABYbtsbN2c5UDBye21o+fpekssg9O\nSdvR/THos3WFJqddds8hLV/821u1J3G8sFPSYSLvDlpw6PGcIWaWZkvQWpQiog1wxxxvxksu\noLGnrXrl1PxbnhYe0XljO6XHrjbhCDsVuJRYJxRrK1DC7qeffpo0adKOHTsmTZo0bdq0MWPG\niHwesVhs27Ztzz333O9+97uXXnrp5Zdf7tevn7H20oPz2NEKxRq6SYsAkchQ1RadUoPyd2DC\n5sdfHjsdPYYKwv2FYI+7ml0yBAA8h3fBmR39J1Qjbsft+hIcL9+3CaEnVHNX0Q9+pYwK6moD\n35+kNBJdxE56sObJm1SL0im91XEijfQRKfXPTEe0CNNDJjrtZG2ujccAoCjoCDtFHGFnQ1Ap\n3MOGDQuHw7t3766oqBg/frw0khUMBsePH19RUbF79+5wOHzOOecYaSplamMtXpe7W5aBnYis\nZfOEO/gv6VtmmmHJ6iLFJixQbKgxos2LquNFBuwOKPZkI8Pf8wyXx+up2k12uigISOzAw3Hn\nSMdY7kPSmgNbPHON8Is7WDTjWfTporOkMyDWlbVQ9b7xZym18QWNd09WQOOfbhOkNtfFowCu\n/IB8tzEHAHC3cm0nHGFnI1Aeuzlz5syfPx/R/ZPn1FNP3bp16x//+Ed6hhlOdSxSkB10666Q\nTGWHlpmYnMoACnV3zQczUVePhUobCkXeU9G3/xgzjWVZvoEj3T12rqyAL38QU7MPmBS4dSVL\nIbZ2qbYUUyobphV+WxtizLHtbnJmaFoI/zgCVY+dKqolaWRPUXoL/xLw+1tgTmhbZCvLAEBN\nItbVH/Tp+8Uh5sD8Eeb0BNOF47GzH6if1z/96U+iIzt27HjttdcOHjwIAP369bvqqqv4nmAe\nj+ehhx4yyErqpFmmoT16xom339OSVAbAUEumyU2pvOPjp+akj0i//ccYcdtKuvhKhsRr9nlq\nv0kXy3fwQ5Qs4eD9dlxupkg0aCpsi0Z/pyylJAZNNlAxia7ckd5VJS2iFWHnCenkPIg4O8V8\nFP3zkC0tezzNMg2J9pO6WiNZDswfAZmg7ZxQrA3RUE370UcfPeecc1555ZXq6uqqqqoXX3xx\n6NChq1evNs444zjSFk2zjEG1TmSjn3bAbhsBEZhvKpWPjGwSYR07Vc5oS2u9OX5um93RaKxW\n4ZV301OiIyIlh3iXR+nZqSn4aFpolex0rXvvLEFrTJx7TaVGtKoNNrlLvBn1iXaGZSyvdcIp\nPNviauGE3QnnJbEzGoTdkiVLNm/evHPnzo0bN27atGnv3r3//Oc/M8hLJ4SrTlzotP/rvNhW\nXquCk/SqSdtl9zwDBMIOBNpuWelkkc6TfqvUeUIWE8pwcKiKgIWDy7gvrbvWlA7q3HNGNgbz\nXKsEK60Vhd5Hay0RUhdvBQBLqhPbXMwJcUUdj53tQIVir7nmmr///e/FxcXct83NzcOGDRMO\nGDVq1JEjRwy0zjCOVicOCh+Qa0ffaJ1FDoYgSlM1Av2Tc3vshEcOjJstu9OOoPkEAGT3OM3l\n9noOHZc/gfDbaXLpSZNhy/dtAskMZFE24dY9Kg914mrM+FkUiBpvOCX9jIbb7MhZIixQbJph\nNnHLoeFuUW28DQDybVDrxM4BWXdLHTjCzmagPHYNDQ2nnnrqU089xT11SktLL7300hUrVmzc\nuHHjxo0rVqy45JJLxo0bZ5apNOFqnazbe9yvyvXvPI9zLno3mJ29RLK22dlgWmitY0cRYsfh\ngXGzhV9ntKXJVB0AuLzZvuJTPLVfu1JxgtOXjPy16IiSHqLrrkMHfEFBIiAckKrxRHTZEf0h\nY6lfikzlINyKemZAQOuTlQZ5pcag7x51XYjIR66NR8GKWicZ5K4DAFfrEVeW3+13EodtBMpj\n9+abbz777LP33HPPCy+8sGrVqtWrV5eXlz/44IM1NTUAUFxcPGnSpAULFphlKk246sReYDSd\nxUs60Qb8DNJGRicKEKO18J5WXh47nat4YloWsDQ/A5Tde9dVrhGNxAH/jmX3HBI/vMdd83W6\nZCj+/Dx/Pf+quz94hXstVXXS2rx8U3niRAoZL6AcNU/elHv98qY1M0HgFKRbwVhJwyG0XfHM\nNbIikpZhepIMhHJKVKBYuoqwwYYQsgvRo0ct8fPpqU5M3cdmW6edq7XeEy602gqH41DJ4r7p\nppvKysruuuuuM8888/e///3y5ctXrVqVTCYBIEvgvc84OI+dl3UBsKqDOTQ1krebbBJhT/PM\n7zOmH63FbmS7UwiTJzA1t3Qe9In+kqGRz/7hqdpNJuxAS2k0IforDEsRyhqWYaLRKJVpqSex\nKjkIybJu9aPTO8hrazJrNak69D0x7Y5xwq4oYHbyhEjA2dqBx7KuaIO3N+FfFQeDUC/PU1BQ\n8OKLL77xxhuzZs2qqKh48sknR44caYJlhsLtscticVWdLMLabJqesg5CMMvL2RCDtu5Jf3j0\n14Lh+k94q3Yn9NmmVE1N+oRW7S0ri+wzGx0H5Evs6nze45yrR6eiC8tZUulD2nlCNlQqgrq1\nBBkt5tyx2vZY0OsLZvm0nkixUolQ1dnRadfWDOmkkxJrN3DrLv7qV7/as2fP//7v/44ePfq2\n225buHBhKGT9llJi3jiwxwXgOV7XESdP2KSMCFkRYPPrFcuunhHyjqCThOoATZ5gfDNE+IoH\nu7zZ7qo9Wk8UInJBqaocTtvhiyF+ExXXepVbTqrqiB/qBGV+efgTuReYJYKldZutSh2wNmVB\nuHrmtBpj6xKxktxuWk+j6GCzta8OAADcThE7W6Ii7BiG2blz58GDB1mW7du375IlS66//voZ\nM2acdtppy5cvnzBhgjlWGoGHZYVNJ1679HZ0TEepGQeCtwAAIABJREFUxbtNEHWywlRIxFck\nOvFf427VP4nN0arqbBWad7m92cWnMod3QbINsgLU5+ef1tL4I4GLS6TtENQ8eZPwW1URSSsu\nzC2kKjGXlU6ORWOBwLG+hXaTNa1r5/iP7rRTb1mLgbQ1iM7Qs2mOQxFNyXiSSevMnOj0O+06\nqhN3xn5iv/zlL+vr6/ft22e1ISSgsmI//vjjQYMGnX322RMmTJgwYcKZZ545aNCgWCz2ySef\nzJs377rrrrv66qurq6tNs5UWLLDQscFOG5Y/npWg4tTRs5z9ZzYZdLcJIbR66aqelV0yxMWk\nPdVfEUyOD7Fykn1+KwVhpQmSXMk6AJhXWaGzmq5q0wUlG2yL1Egu8TP/lqf5UCyVAnJGZEIQ\nN9LVSU2cy5zQtsEO08d2YP4I1ZH2d9cBgKv1CDgeO2W++OILl+62pQSgPHa33XbbbbfddsMN\nN5SUlADAjz/+uHz58ilTpuzfv/+ee+6ZOHHirFmzTj311MbGRrOspUPv1eUA4MVOmxCiVBfN\n6KROmzNx61NUqgBm9H0jNp6rY3dd5RqlejRU9C63zc5zeE+69zn6Z8NBtgsW5vOYG4k5WLqZ\nT7V3rXQk0KuWZyswr0i1xp4mDxk/OHPvZ117FAAKg3qreBD72GzlmVPC6SeG5t1337VkXZU6\ndvfff3+vXr1cLpfL5RowYMCSJUuqq6sjkQgA9O/f/4033njsscfMMpUOvVbfz73IEpQ60fpI\nVnoA8186DDyB6DQ3isqHjpiBnx+RbKs6P58/QWqgjEhC9xMTvYtwcZE9/otnruEddUqgvXfS\nXYOy9kgvXOhKzETtYkT3M9kTLXG2IcC/uppEG2j02Cn52ETH+W8zwieH5mg/sQwWdlu3bi0t\nLQ2FQsXFxddcc813330nHXPWWWedddZZwiNXXnllfn5HykhVVdWMGTP69u3r9/uLi4snTpzI\nBXB/9atf3XnnnQDgcrmGDx/ODa6srBw3blw4HA4Gg8OGDXvmmWf4OX/5y1+OHj1648aNvXv3\nPv/88/VcFMpjl5eXt2TJkptuuqmgoICz/vHHHy8sLAyHj/2sT5kyRc/yJsOrOhBcuUGRLzOR\nOnUwzSNzNEqX+9e4W+NxkuK3wqlsdUvx0Wk2/genc6HsgpPcvqBbh7CTBb2tTU8aqYVd4aWI\nMiGqzeqcxqHnNuLcQ+GtFo0/TvtqMUPPx2eHj74uodhPTMkJh+Nj6wRiTgiXPOHN2KzYrVu3\ncn0WnnjiiXg8vmDBgtGjR2/fvp1vuIXDVVdd9dNPPz300EMDBgyoqqpatGhRaWnpjz/++Oij\nj957772vvfbap59+mpOTAwBvvfXWJZdcMmrUqLVr12ZnZ7/yyivTp09vbGy8++67ASA7O7u+\nvv7ee+8tLy/v27evnutCCbsVK1Zcd911v/vd77xeL8uy6XS6pKTk+eex2jPYH6+uUie2g7jy\nMBVXU1tbm57TdRpgDpruMHFoHj2/bEwWd3K3J7vHacyB7a54K5ttSJl4hHtMVEdD9NgWed04\n9aBUGE84xjikRnIrduzhG1wGAr+dcUJEazYugSX1z0xXXV11RYpuS+M8oMK0a9XBXD+xAoXk\niQPzR+T/bpt+k+yWDKGVTA/FPvDAA/369du0aZPX6wWAM84444ILLli3bh3nacMhEol89NFH\n999///TpHb9H55133rp165qamk466STOq8e76+69997+/fu//vrrwWAQAMaNG3f48OH/+7//\nmzNnjt/vd7lcO3fufOWVV379a3GzH62gQrGjRo368ccfP/3003Xr1q1bt+6TTz7Zv3//hRde\nqHNJm8AS7bGzOaaJJEPjznZOocC/XtEtGr/+Uf6LbGldqg4AuGgsy2jKn5hXWXHvR6/ybSek\nlO/bxD+JabVenVdZgVZ1gKc5qCNalKBQn57lMNEUZhVWASReS7WFmtYJcc7Vo/9wzq2Nx7I8\nnq7Z4hRyPS63TuauAwDI5KzYI0eOfPbZZ5deeimn6gBgxIgR8XgcX9UBQCAQ6N69+0svvfTW\nW28xDAMAAwcOLC8v79mzp2hkbW3tjh07ysrK3G53+1HGjx/f0tKya9cubozP57vsssv0XxpK\n2AGAx+MZPnz42LFje/fuXVdXt3Hjxrfffnv//v36F7aEgzcv4l8zLoDMcRedIPC6x87ajgD8\nJFlNaP3pze45BAA82NFYqZAi8JMpqTQcVPWf6Miy0smIXrFSRO+KknBxzDZ50xjnL8TsaaEV\nnaebuZdOj2TEnKE2ES0MhFygmNJY//AYrTbIQqb2cPJqTcDVesTl9bn9ZjfnoEJVVRUAFBbq\n6oeWlZX12muvud3usWPHFhYWTpo0ae3atalUSjry8OHDALBs2bKAgNtvvx0ADh48yI3Jz8+n\n0tNLpY7djh07fv/732/dulVkaElJydSpU++7774uXbroN8JMDt68iNtpx4Jr84S5VpvjcAyn\newcQFZfGP6VD2B0m3GbH7fSSTR1FhLcQJUtwTuGHyaqZpRdcfde7/+Re8ypNk/o8rn+GMTvn\nap68ibrEkepsdLAb5AKRiCAsDtR7o4knXDUtNOVx9HidbXOVTo+lU7FU8hRJ5oROLZXRUVdZ\nXNF6T24+WFHRQz9utxsAODebHkaNGvXtt99WVla+/vrrmzdvnjJlyiOPPPLOO+8EAjIVQ2+5\n5ZYZM2aIDg4aNIh7QatTK8pj9+GHH44aNerjjz+eOXPmokWLrrzyyqKioieeeGLRokWnnXba\nokWLRowYUVtbS8UOM+EehGX9nfZ2DtYjlGXSphQ4vj388K6vYIA7OxffY0eAVFRpjVeiG4hJ\nWTBs/OIRE5TEHH5ZO4O2dkVeuJ14cqP3EUqRpgMLbTDfnpYXZ0kP6nfXqR6vbW8FgEK16sSR\npRdrtQQBvmq0T16tu6U+czfY9e7dGwB+/vln4cH9+/fX1dWJRrrd7nQ6LTwiquDr8Xguuuii\nJUuW7NmzZ8WKFZ999tm6detEk/Tp0wcA0un0SAl8gi0tUMLugQce6N279zfffPPYY4/dd999\nr7766pQpU15//fX77rtvy5YtH330UV1dXXl5OV2DTCDo9QFALC3jLHVwMJ9/jJn2UulUUdcK\nUbM1oLJtwOXO7nm6u/GAq61ZzzSagm7LSier1rzgFYOsquOevlJVgdYZQklHvCEPXffEBKGj\neo3cC1kfqtK3Wksrc/JOZAnFsjWaztUaUcWfWUhtgqtOfJywk1VRBx+k0zmdQNVZjqu9BVJx\nTzhTU2JDodCQIUM2btzY0tLCHdm3b1+/fv1WrFghGtmtW7fq6mr2aHP52tranTt3cq8///zz\na6+9VujhuvjiiwGAU4dcdWIu4JmXlzdixIh///vfTU1N/OA1a9b84Q9/kA3d6gEViv3kk08W\nLFjQvXt3/sjs2bNPOumkqqqqHj16jBgx4t577126dCldg0yAE3Zt6aTVhjicKOisX81HpfkT\nZXuNSBuaSRfKLhna9uPHnqqvUgN+ockGUBMZfGBL2iMVJ2SG00BMtvsqJqoVQzCDeprWVQ2P\nalpReH+4PryqqyutyL2VSibb29v9fr9XYwDICO+mjKksG43GcIxB31j+XfzCy7XxGACI+omJ\nAqmxWCyRSAiLf+mHIElW0yl0k3CPpsTq2qNmLQsXLpwwYcK4cePmzZvX2tr6l7/8pbCwcObM\nmaJhEyZMePvttxcvXnzzzTcfPnz47rvvHjBgAOe0Kykp2bx58969e+fNm9enT58jR478/e9/\nD4fDXGYrl0Lx5z//+fTTT584ceLDDz88bty40tLSu+++u7i4+N133128ePGUKVP47A1aqEzn\n8/mE3zIMw7LsoUOHevTowRnd2tpK1yATCHizACDGOB47e9G5u3doqniiZyFR12DR0n6u/0TV\nLkxhx2sp8o1r2CJA6K5TelSbHw20D/xnwd8ozLuB6dbC150IqaQ0j0i185ZrbWiBOVIntUT9\nxIgROuHQ2ss+7jo4Kuy8mZkSy1FWVrZhw4Y//elPt956a25u7qhRoxYvXiwtYjdr1qwDBw48\n9thj8+fPHzx48EMPPfTGG2+sWbMGAIqLi99777358+eXl5c3NjYWFBScd955jz322MCBAwFg\nxowZGzZs4ErcTZw4sbS09O23337wwQfnzp3b3t7ev3//BQsW/OY3v6F+XS7euyhl9OjRLS0t\nH3zwAb8HcM6cOStXrqypqenevXsikbj00kubm5s/++wz6mYZSjydGrjmD+fnlfzjnCv4g8lk\nMhqN+v1+v9+PONdCIpEI3f8dUqStrS0ej4dCIY/HY7UtMqRSqUQiwZUOsiGRSIRlWWEekmzP\nOtERpcrG6HOTR37a/8iFyVMvjk1CyUfRY/iv51+FdurwT1zRQ1r4JEY/v2X7mSLGc7AME41G\nvV6vX7JPWTZnVnVCiih1YtA57bzKCl7YYRYfVnor/5anOY8dl0WhVJpY6b4hZpYaJivsuBkU\nr4Jlo9FYTm6O0ipk4Hwui7798L0jB58dO60wqPgnl/fYcXvwiZFqNQJhJz0lmUymUinh/n3+\nXFpOO+/uNwIrJ+dP/FPe5Q9oPbehoQEA8vLyqFjiIALlsVuwYEFpaenJJ5982WWXBYPBbdu2\nbd++/f777+eCs0OGDPn2229feukls0ylRrbH63G525w9dg7GoDVZVRXVHrL4a2Xl9fUEurKH\n92gy4O4PXkGoIoP8KFa1H6CyLmK3vs7JZVOGEcgO4Myrf2Z67vXLZWcTVbqR/fTxL0S29ZwJ\n5Z2JqY23uV3u7n5D6nirgnDaEWsyfKcgPplenbgTgxJ2F1xwwYYNG+66664nnngCALp167Zo\n0SKu9wUAnH/++YsXL77yyivNMJM2fq+XTNhlev8rB0NBh0HxwRRtJJO7XL6S09Pfve+OHmFy\nussO0VP7V/iQxi+HYYQ05BtFgBUBXP5KY9FYIOB36XPqICBQRaK7jVP0RKrtbKjGMMFrO9Ha\n3Z/jMexT40GHVm3el6ITNIrtrKjssSsrKysrK6upqUkmkz179hT6nFevXm2wbQYS9Ppi2pMn\nRI9tR9s5aAV/E6G09Anmiar4ew5t++59d9UeZtBoPfNwaKppp4S0JxUt0aBV0mnqOqUH/YKM\nCnznCX6J4plrVJW9VkukmTHSWtD2kYlJhmlKJs4wJdnTnO100qnwJSNi5FGPXaZmxXZisP5H\nUlRU1KtXL507CWxFwOvTnxXbyboj0EJ/7yxbQfFaiPtPaDpR2OdNtuebv2QoIPtPSMXQX8+/\nCtNUHk3lMFSrdZgPr/CMbl2qfzCtebRC986Y8IljLlGbiAKwBQFr4rAirM2W4FZXssGVyf3E\nOje6kmxXrFjBMMzcuZnXvyHgzWpoa9F0SueQKUbTybpHWOij1blRD3Gir2QIAOzd/Z8BF8xW\nGiN0sSwZqdiR2ridZJZgmpoUdkQl8G6CxFSKN7x65dRlEqcdWZoz3RmogHOj6uIyRexMhq6e\nMyie6+yxsy26nHB33nnnHXdk5GM74PW1HV9IWpWMFig85vvSTFjLoCVka8UZsZB0FWl1Yopc\n8c4rLVnBfi2H0V0ZZMvSilCqPKxJZFBsIa8HhNfQUNeUQSV29cxTvXIqZsMJik0gjAZ/3Y5a\nJ8r5sEYjUnV0Y7JklZBlz3K3HgG3xxPsSsc4B3ro8titW7dOf581Swh6fWmWiTPpbDd5eY6M\nk3qdb4+gUADZ4XI4G+hmxdLVdtxsP+cUntb0U9dES5MvpFq512js5tvjC/9qzT81Bz1eUpG3\nL/+Wp/nMCem5sj8V+rdUWpXpLHyNtqE2HgWAIks9diLoZlFQy4pt4RrFdp49Wp0GXR/JVVdd\nNWnSJFqmmAlXo1jrNjtuxxL/ZYxp5mGO/8m4G0W8ZY0YzGtR+vHAOV32KkQnEt9SfvKfg8UA\n0L/lMNk8nQ/+wS9s56C1y62mhVQPot8VekYJvKQcqvmwBM5Fusj2ijWajQe+AoACtUaxZKg6\nzIzbVKdpZtl8C/Gg1vqMrk7ciSHx2MXj8WnTpv3f//3fKaecQt0gc+DbxXbFa6VDvTKZ+Zgm\n4zpN9wjRtdCak2xR/XdSOO3+nGIA6Nd6aEf3TP0Vxof30CBcNdxxdDao6HSV4rqkRmo9S+u5\nWh1+wuMmO9uqV01TGYB34VrbY6R8LgCY+fYL1P988bkICIeZOfVN9Pe3cCVjrmTMSYm1JyTC\nLplMVlRUzJ07N9OFHU4pu04TvjRCpqiS0XcM7CFMZW3QqZ735xYBQP+WQ0DaNEwIcf9WnfD9\ntbpOXak0RrRPzvKIqmzqA84pVLAqf5YA1fwSnR8o4sSUy8W9yPQ/X0I0ueuwxKVTxM7GoIRd\nr169ZI9zXciuuuoqrpPswYMHjbDMUDraxRKVsus0v+pGXIiTO6wf1erE+lOPW7JymrNyuVAs\nL8vI5B1OiwLqCBddOLisfM1MxLMfdGgU1YrKFMvRaZ1Kdt+YHuWK47SzBJ0GaDqXBTCoJZER\nvR/0oNMGd2sdZLiwe6/qO0a5pSoZZ+X3CvvE7Q3NByXs6urqEonERRdd1KNHD+HxVCpVUVFx\n9tlnFxRk6ofa4bFjZH6FO3FvCbImVLLge4yMk8J2CPsa9NOCo+cI5hTO8HNu4RmNP3SPNx3J\nJkxq6xAWx29EsyQVY+HgsmXYgxEqQVpHV2kGzAllMU4kEezVozKY+oeuurqmZAhNpFy0ZrIR\nRuzbc7UegQwXdjduWZ1ktBXHUOXlS28bWTyA7pwEoITdF198ceutt3744YcPPPDAfffdl3W0\nC3hra2tFRcX//M///PKXvzTFSPr4vVkA0C7x2F215Un+dWdyzvHgKAbVq5Z6jP417lb9thFg\n7QdkqzA9zofIa7vNE+5o+C/b8NYj/Vur0MJOqZ6Z5QWERUif7sTl1qzqQqYJdHEWWaEjPZhK\nJtvb2/1+vzdLZa8xelMaGN+6zTSvoVDYUfyN1tP7QT9GLNQ5+okV+ALXlZxGZaoPGg991lRN\nZSr9oITdqaee+u67765YseKBBx6oqKh48sknR44caZplhhLwcHvsjlPr17/zvGjYiRBYlK3W\npqcurlaZ2GkwVNuhfxTxf1B5C7n+E/0ihz7rfqoew8r3bRJmj9pcD3GgVQL6EpTSWs0MVhqt\nqjGvUU9PYeFCWhU5lS52siwrnfx23f6/ff8JmPKHyw4BWWKOtp0otNoQXRRm59wz6DwqUy38\n9sPMEHYA4Ha7586de8UVV8yaNWvUqFGzZ8/+85//7HJlvLc6mIW7x86IymQnDs4d04lx/7XI\nLhkCAL/KSr0sOCjSNNInNxd0s5u7jkPc53Rwmaghqf3BFCjSMRQbUej5cMlisiJrj71m2Wg0\nlpObQ2wPATXxKAD88bzL6E6buQJOCU7YeZ2sWFuClRXbu3fvjRs3vvTSS/PmzXvttdeWLcPf\n0GJTOI+dSNitHX2j1GnH4QgUfJx7RQvVnrCYI2Xx5HT3du3JVu1Zdv0z895ZBzqcbeX7Npm8\nuZ4Tl5ynUKjeREp04eAy6h5E/kqFa3GrSI9ognp/C/SHUr1yav4tT0vHm/ZRUs9oocLR6sSW\ntZ3IFJxGsXZGQ4Hi6667bu/evaWlpRMnTjTOIHMIZmGVOzkRNIr0GnFqrWkaf4KQcfchu2So\nq63Z3fSzauswHiV3nfk+vOKZa5aVTl56wdW51y/vOnUlWYVeYkQKUta1STazOU26cD5E1Wml\nPzP4ctby0sdK1CS4fmI2ajthT5xGsXZGWx277t27P//88zfccMOGDRt69uxpkE0mEPBkAUBM\nkhX7ysUz/H6/FRZZCUG2bMaJGCMwP0yvtAoiQRjxyfp7DonuecNzeDfTrY/stJhZopmCoTvh\nlMLWmKfrUTbSssn8a/T11j8zPff65cKztN4i4U+I0sVaXi1FE7XxWK7Pz5VNcEDgaj0CLrcn\nJ89qQxxkUBd2LMvGYrGcnGMbHS655JJLLrkEAA4fPvzVV1+NHTvWQAONAdNjd+LgCDUpmFkg\nNrl1qvnO0twOf6+hAOCp2p08fbzStMtKJyfiCbfbxSdOZtBDWohNChTjQNFI2alEIlK2sRj+\n7aIVdLbDR8OybH081q+Ls29MHVdLvSc3D3Q0W3cwDpSwY1n2b3/724IFCxobG/v27XvvvffO\nnj1bmDmxefPmGTNmsLRL/JnA0c4TmgsU2x/L6250Viy/scStZoXvCifx9RwCLpf38C4KxtkD\nkYvR2hRdPe46PR3GNNG6dg6VpZWQFYiWCzgljiTaUixTEHDisOq4Wus93XtbbYXh9Nm6Qvjt\ngXGzrbJEE6g9dk8++eQ999xTXFx888039+7de+7cuddcc00y2RnEEHHnCTszfv2j3HOdf+GQ\n0WyecAevw2hpSuHPhifQJatbH3fVHmAZKpPbAW6/oGjXoChAiTlV9cqpSoNFoq183ybbZuAS\n7GYju13GzWMa3Aa7ImeDnSqpuCve2rk32PXZukKk6kCi88j4+uuvR44c6fWSNHTFBDX1448/\nfuGFF27ZsoWz4Pnnn585c+ZNN930wgsvZHrFkwB2r9hMwWgl14kbctgc/BuO/zPAu+6yS4Yk\nd210H/mJybe+WnpmIc0jwcwOlrrEaHmwVOchU1d2CJKaQ1089v/ZO8/4KKq2jZ+Z2b6bTS+k\n0EvoSEmoBqSo1NBEEVIogiD2hvoK+jwY9FEBlRIVpAiKBRFJ6EgEEZReQws1IZ2QbG/zfhhc\nli2zs7tTd8//lw+b2Zlzrp1Nslfuc+77BjAllgLoverEQbtmTWLgGu9aFkjcbuPGjS+99NLg\nwYOPHDni9yBeITN2ly9f/uSTT+y+cvLkyWq1esyYMa1atZo/fz5zmliAiNgFk7FzhcalQ161\nWIDQiCypk+b0Vuz2mSA2dv4tdFJsQu/HyOSnMbqU7DSp284TdIXWmCsjzBwVRg0AINYlYkf0\njQi+WnR+E+IpsYF4O6PReOjQoWPHjq1fv55eVY54KXei0Wgcvx01atTixYvfe++9NWvWMKeJ\nBRRBF7FzhQlX5+lIUCKsqi5u3xSvmiVJHQEAottnGNHEAzzZFOYapwbSsNVrFRWmoeV2CZdK\nox4AkPCgsWOi0arguVedODiNHS3rrZ7Iyspq3Nh9FQIaIYvY9e7de8WKFVlZWTEx9yOuc+bM\nKSkpmTp1ql6vZ3SRmFFkmBgBiN4WPHvsXHt5QQKH52aOCo41WZwOAgBkiR0BgmK3z3KgjEV8\nDRT52tWKGN+noiH8D1+BANaISQwin191BWl1YkF3AKMXWJ2Y55BF7BYsWHD16tU2bdp8//33\njscXLVr02muvPfvss2+99RbD8pgCRRApJgqy5AlHFxIEjgRCHa/hOk+PUalSEtMMvX0W2B7o\nm8w+LxRtpD1A5ei0vJ5DcoR8BL8HcfrW7ctnM2hH8VVQgagX7fYrYJkMUmXUKUQSpVhqP8JV\nuI7nYUI0tJdi+Q+ZsevevXtRUVGHDh20Wq3TU3l5eYWFhZGRkUxqYxaD1Xy5vibIolxEHqVT\nfVr7F42z0DUUhDVcfzYIpEkdEbMerb7CiSrwoKXjpB6yr/bFv94bfjRyIAimGtH8Bq806eKV\nZJkTbPotPnu7EN9jx3+87LHr3bt3UVHR1KluKlg+/vjjZ8+eraqqYkYYgyR/82byN28CAIga\nD0Hm7Rxxemn+vVL+2zgmzKuw8KMvnB1pYkcAgKiML9vsHE2e45ev47gNjzmN49ZseYoq0eL/\n/BuTBW8X4rvrAAB3TEazzeq4Dst5uI633u5fYxecWbFeEyP4X82ObJPclClTli5dKpfLPV4s\nEtm33+n1+ueee27lypWeTuYhNmHXbGEP+wY+Hpo8V/PqVSRvX0sg+NEXjkCadK//BOgyhhFl\nvsOQjynPzwKpw4jBnYqVuK2g63YjHXDn/Ki4HyqrkETQjpMQHc8XSVmAKGLntTox3GkH7u+x\ni+NaiPAoLy+3WCw1NTUAgFu3bgEAIiIiVCoVvbOQGbu9e/f27Nnzs88+y8jIIB+lqKjo+eef\nv3v3Lq3aGMcGwB0MjbQGT3VW5hCQDSL3dnb3E3z2zr/XIktsj2AijPeJsfbWq+Qb8IlnvTqt\nF4o2znV3oeO31LV5mrE8P0s9aYV9RvtxbltiOKLZMFs2RUj/jTNHpVEDAIhX3jd2nBg4pygd\nP30k0lADEARTRXMthCmImJzb9NgAw3U9e/a8fv068TglJQUAsGjRohdffDGQMV0hM3ZHjx6d\nOHFi//79H3744ZycnCFDhiQlJTmeUFpaunPnztWrV//xxx9DhgzZu3cvveJYoEyCYEYYuAsV\nAl+rpdhAVkAgYrkkpqWt7HRF/uT4Geu4lhMQdnfl5PxIYmB5qcPsj5d4G5zEUHp6SqfVuQqw\nm1S3ODVGA4wZQbddYkOWSoMOAJDAaXVi3q69OoFqqjFFBIKJvZ8qZG4MnuXo7WhZgb127Vrg\ng3iFbI9ddHT0tm3b1q1bV1ZWNmXKlOTk5ISEhA4dOvTp06dDhw4JCQnJyclTpky5ffv2unXr\ntm3bFh0tDP9+K3eh/TEOwC0pcqa+mkM9zCGsSmw0wtBmu2DdwydJ6ojgNqlFx8nsFF2LPVwH\nvKUvUA+2Obo6KiOwtuHMsTEa0+E9aO8IKsw64K46Mefw0e1pqkMkc+LG4Fn2L661+ICXQnQo\nik6aNOmpp546cODA7t27jx8/XlVVVVtbq1armzZt+tBDDw0aNKhv374YhrEjly5u5S4k8ieW\n9Z84e993OSe2/vTQyAhvqSQs42gj/PZkQW/m3BbwY+1V+9eHg+X+bF6n053YBgCQWrRclRlz\njVE5HXQ1N1QWZEnGX5Ix4QWXq/JShxFBO7dLq0G2C41XWRH294vDQncVBrIiduzAw1VXN1jN\niKEeS+7AtQ6IRyhVGMYwLCMjw+tOO2Fhj9vGjVpSAAAgAElEQVRdb6j58OiOqae3r24zSAZk\n3Kqy45oT8H3/bK7EBA18KOPMcn82KtOhiMgKgMysvcuXH/97OPk5n8rRuQ5FnJOXOsxrDIxX\npocJXFOGObetnHu7KqNOJhKrJTz7HeAfiKYG4HiwpsQGB/yKUXHCnE4DslN7XdLWvXDpDxPX\nZVohPuFa4sRtqTanEyieSYXAR2DUaFJpB3djfhqCiABAlKZ6BOBsehq/S5kQlOdnVXyVQ/Ks\n22/trs7XJc5A7ozjXHOLC/iTPGGHQy/rxxq628sDpMqki1dwGa4LhBvz01hbsQ3uWifBgVB7\ngtHL+z1H3Gqo3VN6Ye7F/V90eRQBMJ1CAPhtiQJZ1w5wfZzzeKET/34YICgiEVsNKmNdg5Sl\nquOOfo6Kt/P0+a3ZMNunecvzs5y21tmx+y3qESPq4SX74OXFBdxGyGhxQnS1TfO0XZLi/aHL\n1dWZjQarRbjGjk0QTQ2AtU74DTR2AACAIeiiPuPGb//qt6qSlleOvNSiB9eKIDwlkBAd31yd\nIximsFmMkbrbDdJIFmwH+Y464MsiLAAgIitf5rncptfLA4yf+XS7+LDIa1drMZsNBoNMJhOJ\n/Ulv9OOFM/RzFfhPbKVRCwCI81bEjp84FjRmYZce7CfGf6Cxu4dKLP0ifUz2n98tLjmSLA8b\nn5jKrR7X4FB9fT2HejiEliQS3sLoO+u6p9DpBjp+DJR+MxlcOZA87CVL8kMM6SHw1BTVXp7X\n1WmR1wSuWzvDp8/1ucUFnoJ2juNTjzZRNBYkJZGFBZUXbs9fJs9xIXkq4Zk1FGX4gdOPWaVB\nYMaO3MPdmJ/W6O0/GZoa0VSBYDF2l7V3Bh38jpahqkx6WsahBbjH7j6xMtXXGRPDJLI3zu3b\nX3uTazn3m3sGn5uhDklXtED6aPEEFgQ7TuE6nWM3tsi+0wEAkkOrGNXjddWV9v1nbj/+5xYX\nUL/Qv+aw/gkLDjxtcPTpJZd/6UO6GPWR7ds6Hfd3Vpj0AABhLcUSgTrXgsbEkdsL+jA1saYa\nACASvrFTiaUiDCs1aWn5MgGbUizBUF5UCPEescNxXKfTKZVK16fKysrOnTs3aNAgBoRxQ0t1\n7MqBkyfuWDnzxPYfe4xpFyaMynwUCcpeCyyUDhF6yNCTZifTPO78yfyEtviFPeidG7bIxqxI\newB7sy+vZ7p+inuKDNG1H99rgI3KCX4o4SG+ZtSSvPCEGWvJSjHjuFar87SG69/99PR/RZVJ\nAwCIF0jEjttmskGTPPFHpBK3WegdUy3iRbCMzNjhOP7pp58uWLDgzp07TZo0ee2112bNmoUg\n9xMLCgsLp0+fjuM48zrZo1dC80X9xs8p2phzfOvmtLGJMpqbuHECyyU22ITNciEgsLsXeO4F\n00T0zq3Y9Lrk8FrDY+8wMT6jXVDdOgy3noO8u5fTgqmnufxU6TKOcBdkPUF+cxxfciAJ0eQj\n+zygUQcAiFMKw9hRpOrDDCa23KENQbLHrvrnd3CLid4x5S16iqJS6B3TD8iM3VdfffXqq6+2\nbds2MzPz0qVLzz333L59+zZs2CD2a6etgMhs3uXK3apFJ/ZkH9+6qceYMJGEa0U0E2TeTojw\n8/6rOmfW7PoYP/GTMeM5XB5B+/huCxH7gf3zG7fZtFqtSCQiT55wleHHpAEG7YLDwNHiqEjO\nd9r61rD+WZ+m8NvbVRp0EkwULvHhp4grXKN0dvfGTgDvXlas8CN2AABbdBPjmDxahhL/vUF0\ncistQwUOmbFbvnz5gAEDdu7cKRKJAADr1q2bMWNGTk7Ot99+6xi3C0pefmjQLU3dj5ePzjq1\n85suQ0UoL+KrIQj/o1zU4X/cFMHE4elZNbs/lhzbaOwzg2s5HEAxFBccLs0P/Ctfwr4MX6ky\na+MVav4XuvLVujGRJ4toqlG5GhEHQyVnXB5u6eQlj4oi2NXDtIxDC2TG7vLly5988gnh6gAA\nkydPVqvVY8aMadWq1fz589lQxx0IQP7XZ0yFrr6o7NJbxUUftRvAtSIygq8zvSPB8XJ4WOvE\nrWlWp0+6s3+55PBaU3oOLpLSPqlTozBPATzq++3ogphxLuk5QblySi8B3h/Hd9wpeYKWm2/P\nvHb8tt5s1Fss8fzrEksRwr2xWaA4CNZhgxsvyRMajcbx21GjRi1evPj5559v1qxZdnaQd7gS\noVj+I5PGFKz4vvR8E7l6drNuXCtyDw8dQzDBXMiQD0E7+6uzK8Hk4WEPjb17aK34bKGp82gm\nJnX88HYtX+dUuJgFb+c4o2PDMdo3ckGcICleyGjkz+mHqtKkAwKpdUISfnN6ymw2WywWuS9b\nFKiA2KyIrg5LaE3vsBB6ITN2vXv3XrFiRVZWVkzM/dX0OXPmlJSUTJ06Va/X24N5wUqYWLpu\nSO6IrUs/uvx3I5lqTKM2XCuihKtjYCd7NFhh6I7x5I1wlRHRZ9rdv9dLD60ydcoEzG+6ILdu\nvno78sQIiiP40YIC4h8+vUcMuepKA2HshFTrhDO0tQC3BccGO+qEzQlv+Pwu1yp8gMyZLViw\noFevXm3atFm6dOmTTz5pP75o0SKZTPbss8/GxgZ/PDZBoV41MGvctvzXzv4eL1X2iUrmWpGf\n8MRGhCyutYK9wpUXF0emKNsO1p7dLir509KiLwsz2j+wA0ytcLo8kIBf0FQnESgJM9YS5U6U\nKjeVtuilwqQFAMQHV0osQ6DBUsSOOmFzwrmW4DNkOQHdu3cvKirq0KGDVqt1eiovL6+wsDAy\nkqW2ktzSMTppRf+ncQQ8c3L7BU0t13K8Az0cP7G/L65Fp58qWktUCbYf8fSYHSIfngkAkB5a\nydqMhJFic1MdFQLsTw8RBBVGLQAgHkbsqEAUsVOHirGzuzph2Tsva6m9e/cuKipy+9Tjjz8+\nePDguro6BlTxjgHJbfJ6jX7tz5+nHC/YnD4ulk9Z8cGUNxr0uH13ntx3v3USsYzu6uRY3pAn\nS+osa9zVUHIQqzgPIlq4nkBWV9ZHGG3k6gny0CDcXRdSVBn1AC7FUuPfWiehYuwEim9VPBoa\nGuoc0Gg0Qb/Nzs5TrXvM6phx09CQe2yrzmrmWs4DwOZjwoW3uS+RfaYDACSH3fTrZKjOsGvQ\njjVXZ59oScYEp0nL87Ng3C64qTBqxRgWKePRv+u8BQmW6sRUcIrS0RK0KysrmzhxYnx8vFqt\nzsjI+Ptv+itIA4rGrqSkZPjw4SqVSq1WR7rAhCx+Mrf7Y2NaPHSqoWrW6Z1W3Ma1HEhw4tbq\nsW/Zle2GiKObSk7/hjZUeD2ZrhYCdm/narCo4HQJeVcJ12uJ8wXk3hxNJzvTsTYXm1SatHHy\nMP4XseMD//YTCwlj50rg3m7UqFE3b97cvn37sWPHkpOThw0b5rrVLXAoxdumTp16/PjxzMzM\nRo0aYRgvetxyAgKQT/qOq9DV77195Z3i/XltM7hWBAlCCA/n1t6RFCykfzkeQSN65VZtnSc/\n9p1+wEvk57paKBrXaklGXtxvvFclTpTnZ4FUjyVJvXoXuCDLAmzeZI3FpLOYUxU+rMMyUfVX\nKKDaIGkU6xUmNtXV1tY2btz4v//9b9u2bQEAeXl5GzZsOHfuXI8ePeidiJKx++eff3bu3Nm7\nd2965xYiYhTLH/D0qILl62+dba4Mn964C9eKBEZw11L2A0/Zsq53hmTRlsaGto6ou42v3btY\nfvJHQ58ZQHz/z1wgncEcL5xbXOD0bF7qsLmkH+pO8764/8cFXYd6PVlwoTgqOC4Qs2CDiOlY\nmIvlt6mS6BLrY3XiG/PTYl7fx4ggfoM0VIEQSJ4gcXWBlD6Jior6+eef7d+WlpZiGJaSQn9v\nWUpLsUqlsmnTprTPLVAipIp1g3Nj5aoFF//aVlHCtRwhwdv9ZNzyff/s7zKygLtsWXKYvp+I\nWK5Om4gY6mWnfnF6inwnnKvtI444Hc9LHebqEvI8h9N8wqnQsaNdcDKUjvoTZqx1/HI7Monz\nCDLvyCGs3clKE1lKrGs7B9YaPPATJPTKnTBEbW3t1KlTX3nllYSEBNoHp2TsJk+evGrVKtrn\nFi6Nw6LWDMqRYeLnz+w6UlfOxBRE8QunEhjBR3C/Op/gZ/AyolcOIpLK/lkLbFanp3zdCec2\nyOf0+U1YLv/CgY5DuY7g5BfnFhdQ0e/k88gNH5u43ZvIznSMzvXARF+y0dyowqAFfrWdqP6o\nP/1q+I+mBpEoEImCax0M4nURNvBV2uLi4vT09P79+y9cuDDAodxCydh98MEHRUVFffv2fe21\n1xa6wIQs/tMpJnlZ/6csOD71RGGJjuaaL64ra/SOzx/46Wb4CSf3ClPGyNsPQ++Wii7spn6V\nq1ty659cl2L9httQmX2Zkh0lTEzhUxiSodfIyZtYadIDAOLd7bEjgnOOIboQD9cBAFBNNQzX\ngcC83Z49e/r27fv8888vW7YMYaa1DyVj9+mnn+7evfvPP//8+OOP57rAhCxBMCil7YJeo+6Y\nDVnHtlab9FzLgdCPY9yUn/baqdMrAb0WMCw9ByCI7ODXAY5DMbZH7vacBnFKnrA7Aypz8WHZ\nlEYNfHg5tNOw/lmmpyCqE/vXKLZ+8RC65fAbHEd0d4J7gx3ThYgPHDgwfvz4devWzZnD4D/q\nlJInPvvss7Fjx7700ksJCQmhnBXryqQ26ZfvVn199sCUE4Ubu42SY6FS1c8/hF5LmeUqwT7B\nnDBxXCt5iz76ywewm0etKd0oXkXFWtnXNH1KoXV8FrfZAAB1a2dQ0sNMVTzXQB37mbO+Tuek\nkCQxwpNfpP01cmVMq0xaEYpFyZwblzkF6hrP/9ttuO7W+z1DJ0MW0d0BVkvI1jpxwo8sCr1e\nn52d/eKLL3bs2PHWrVvEwcjISKWS5r55lIxIbW3tZ599lpiYSO/cwcG7PYaVauq2XT/z0tk9\nyzoOQZlvmi5oeGuMBIFrCi079zOs51T95QPSQ9/oKBs7t3hybI5ptr4WRtFsmO34rd1w8K07\nmSs05pn6MUh5flbMFOeWca7jcLKh8N6kOK7V6pieq8Kgi5GrvP7dhouwwF7ELqgjdn5nvFLh\n4MGDJSUl8+bNmzdvnv3g559//txzz9E7ESVj165du6qqKmjs3IIiyOcZE57c3lBYcSVP9tfb\nrWkoCiP0yBaEORx/Npx+MCj+zPjxoyVr3lvaqB24sAetvWaLauqTYIrQ6MPYDJj5HdDyO0AV\neAjNPkL1qqmqiUurV031TwmNsBOuI2ZxvEt6i0VjMbWMiHc6062Nc4rM6XQ6k8mkVodQI7IQ\nr04cOAMHDsRxnIWJKBm7xYsXv/zyy4sWLerUqRPTgoSIDBOvGpg1qmB5/vUTSfKwnJSOgY8Z\nImbOk0eBkOD2XlEsZef3TsGI3lMrfn5FeniN/vF53s9mi4qvcjicndyO+OS0nM4kuZaFMnIs\nR+ncJmewo6HCqAEAxCsfMGeegnOhXJeYADaKFQqUjN1bb711/fr1zp07q1Sq6Ohop2evXbtG\nvy6hESVTfjskd+TWZfMvHGgkUz4a25xrRQLA0WTwc/takIVOXV0d9duu6jyyZvcn+MlfDBnP\n4wq+NBKMn75aq9WKRCKZnC+NPh03Di7xcI5XR0i3KI+DOy1kBzFu6zlXmnQAgFi5yvFMR/fm\naPKE6OoI/XQpRxtgETthQCkrFkXRNm3aDBw4MD09vaULTEsUCk3CotcMypFiojmndh+76729\nZojj1mRwooQcomiwr6WDgw8EFYWnT0bMeunR77nWwgtIlkRfKNpoL8g898hvPo3m+oBGKI7J\nh/6z7Ggg2k54qk4McQIuxQoFShG7P/74g2kdwUGX2JRF/Z6YtW/D1BOFv/QY01TBbOI0BOIT\nntqXUSQ8beKdoi/E/6wz9pqCi6Q0CgsEzYbZEVn57M/raa3Qa3VlRvNMXbeRUYHDkstkU9O3\nG8m1njMxL1HrxG0RO+CyJiu4pdiqD+91M6dNuSZUGsUKHVieg2aGN+14s9vjC44UTj1RuClt\nTDhvPv8gwY1/q8Y+hSFRmVrd7Ym6g9+Izmw1dxnrs0QG4HaPHUVe3P+jU9cyT2d68h8UoR7l\nIoa1mM0Gg0Emk1Efnw9dN1whF+b2thCXEEuxbhvFut1pJzhvRy+hkBUbHJAZu9TU1Ozs7Llz\n56amppKcVlxcTLcqYfNsx4fLtHXfnD847cS29V1HSFBY+c8NXFXuCGKo3MAAb3J47yl3D6+T\n/fW1ufNogFDayEEFIsrld2Js3doZ/DQcBE5VlFnAa0U6/8qj+HchO/gnrMKow1A0WkpzFTE+\ncHtBH8dvabGkiDbYlmIRHEfMBnrGstnoGYcOyIxdRESEXC4nHrClJ0iYnz68TFu348a5l87s\n+aLTYATA4nZuIKncAeEn4ohkZdshmjOFoisHLC0fpmVM+9rlC0UbKXo7+yVs9r1xtA4kNsKx\nJp+v45NP6sfl5Oe71rGjMjjfvF0gucmVRm2sPAxD3fyLEnyRucC9HdpQg4ikqMyfLh38BC09\nrXrZudhNEEBm7A4dOuT0AEIRDEG/yHjqie1f/lZxuenliNdawuKW7hGKn2MiadcxYPldhmD6\nQUX0e0ZzplB6aBUtxs7JA1Hxdo6X5KUOI1qQMe02nJwN+YyO3i6v+wiKU9DeyMG1t0Tg4zB6\nVYDj+zqpwWqpNxubhAfhjjGGyikjmqpgWoeVt3kYt5rpHRNV8iIKhlAsl3flypWLFy82NDRE\nRUV16dIlJobxXwadTme1WpmexY7NZjObzRiGiUS07TusNmgm7F1dprv7boueExPIlrOpYDab\nxWIxLcJox2Kx2Gw2sVjMUEvjALHZbDabzb93dtzuB6IaPw2ip5qr07A0jkw7VqsVQRDUIapR\nvS7LdPNobdb35vi2AQ7+xuFfnY58mD7K10t8HcFX6tY8Y38ckf2l/duI7C+9XmuxWEQYBhj+\nvXBUaMcuz+2zBKqJS1EUQzGPq+qernV87XVrnnG6Fa5H/MNisbj+2hKSiPFd5TkJcz1o55ah\n4cXiff0TWz3Xzp9/UYL4j557cDz+7SaiRm1j36AhmdJkMuE4LpVS3YMul8vpfC3Bjvc7tX37\n9jfeeOPUqVP2IwiCPPLIIx988EFaGoOBKKlUyk6NZgKz2Uw4J+pbib2SIpevHZQzdvuXC0r+\nbqyMGBjTJJDRLBYL9V8D9jGZTGKxmJ+thK1Wq9ls9uPujShY5nSEubeAt2+u0WhEUdTxn4rI\nvtMqvjuqOrZeO/Ij2qeTiCWcj0CCo5OoW/NM3LTV5OdbLVaRWIzStx/Rlcqvc9wet8vzJNJi\nsZhMRpFI5Okj09PIwOEmE+c43nPiCJWbQw6O41aL1dO76clxup3X7SC1OjMAoJEywr9fPRzH\nbTabRCJB3a3kco7FYrFarTT+VUH0d4HVLA6Pk9NRM9JsNiMIQn0ofn6y8BYvxu6rr76aMWOG\nQqHIzs7u1q2bSqWqrq7ev39/YWFh3759165d++STTzKkjOU30mazAQBQFKX334LU6EarBmY9\ntXPli+f2/Nh9dPvAEsV5+8NN/M+KYRg/FeI4jiAILdpGFCxjaPmYn7cOAICiKIqijvLC2g25\nE9sCnNtmHPiKTd2I5uk8R48o8tKBB7JQHZduPa3zkqzikS9ielWLIAiGogiTn/1+L3qiNgQA\ngKKIH/e88uscx3nt3zreLsdh/VmcxfGG9c82PPgCqawpE2Icz3RSS1Bl1gEAEpTh/v3q2f/o\n8dPYERE7Gv+qIPo7AACxOo7Gj0gYhGMIsp/IK1euzJkzp1u3bpcvX169evWcOXNyc3Nfe+21\nLVu2nDlzpkWLFjk5OZcvX2ZNq0BJT2i2qN94rcWSc7yg1KDhWg6EToZu+Zz48vUS5iSxAYKG\n98oBNovkn28DHMnJadHYMZbAdQ+f6zmB1MJls5Yvy5C8tIQZa11tnNcRAr9XriMQSuxfJGe6\nHqkiqhO7q3UCcQWF1YmFA5lfXrZsGYqimzdvTkhIcHoqNTV127Ztbdu2/fTTT5ctc16ugjgx\nqlnna/U1/zu2M/vY1k1po9WwuJ1AIK/J4tQSze05jpD4OYaSJ5jrh6Z+aGztnkWSo98b+87E\npQF9NPpq5ojzCYu2uN94rVb79rFCvwd022nK9dlQw+0Ld21o6/USp6d8ituVf5ntx1XUKb9X\nxA62naAE0gAbxQoGMmO3Z8+ezMzMpKQkt882bdr0iSee2LlzJzPCgo0XOj9SoatfW3xo2olt\n67uNFDO55wZCI37UZKGeQkucVl9fb99OSqMVc/KR9Cb2ImK5usfEO/u+EJ/YZErPpmtY6hDu\nDWe4dhRdfoJvJUL8w6ngi6+XBD57gJKcxFQZdCiCxspUJJdA7PxbnTiOayEQ75AZu5KSkkmT\nJpGc0LVr140b/anYFJq8nz7iekNtUenFueeKPm4/gGs5EKqwVpOFUStGOxE9c+oOfCU7vMbU\nYxJgvQq344f0h2kjZX5t6A6w04OvcwnI29Eo1b+bTMtbQ35JhVETLVO6LWIHcQU2ihUQZD/T\nDQ0N4eFk3U6VSqXRaKRbUtAiQrH8AU+3j0r8oez8kpIjXMuBQAICU0WHdR6F3C0Vn99B8RJ6\nVzapjMboHj6KL4effc/K87OqV/lZYcfphTttdHO76S2Q8UkO+n2JyWatM5s8dYmFuPJvxC4I\ny/4FH15yUvhZoUe4qMTStYNzRmxd+umVf5JkqnGJgRa3gwgXP6JxfGvCFtFvRv2xn6SHVpnb\nD6V4CY2t7ilCkgnr9qCv7Vl92DQmqKAddRi9aRTxdcBKow4APE4OMyeoApMnBIQXY1dSUkLS\ndqKkpIRuPcFPvEL97ZApmQUrXj+3L16m7BeVwrUiiJ8Qvso1JcKT33I8P3BXR0Uec8kTBJKY\n5opWD+su7hPd+MfSuAf5yUwkIlR8laOauNS/awP0FhRfTv23MwOZBTBjg+ziNRtmyyg3FnO6\nlgr+Kb93FY5rtTqlipFGrpVGLQAgXgkjdlQhInYiaOyEgBdjl5eXl5eXx46U0KF1RPzXj0x6\neueqmSe2/9RjdNvAittBuMVXw0RyPu1WjIWQXmTfZ3QX90n/WkVu7GhsNupkLDQbZkdk5fs9\nWuBQ7CFL8QTX8wMSRzee9AguGFlp1AEAYMTOBxpqEEyMysl2Z0F4ApmxmzdvHms6Qo3ejVrk\n9R796oGfso8X/Jo2thHMzIIAAHiwuuor8ua9pIntwaXfseor1pgWFK/y2wfwxOiQbO33I3WU\nynQJM9ZSqbRMcTTHb6tXTaXFk/n9nhKvi/YShuRUmKgauxvz0xrP/5t5RXwH0VZjYTFMN8eD\n0AKZsZs/fz5bMkKRJ1t1v9lQu+Tk3mknt/3QLVMp4mkfWCqM3fU18UBwvgQSOBG9p1X89JL4\n77XWoe+5PYFpN1a3doZXS8FCSIliXTfqShxHcK20TKMToi7JbV3ivNRhxIMlPs7r+KLofUVe\nubcU6y154sb8NAC9HQAAAERbg8W34loFhBKwoQeXvNp1cKm27qfLx549vWNV56EiYSbeO9Xp\nhd6OIVjYM+cfqk7Da3b/Dz/5iyljjk1JdV9BeX5WXuowT5/lnj7mnfwHbrNptVp7YyJ2FgS9\nJmASMgglOq1OLpf50VKMITdMy7CON5lGc8amt6s0ahEEiZWH1lKJ3w4VMWoQkx6Du4YEAjR2\nXIIA5OM+Yyt09fvKLr9VXPRRO+EVt3Pd0Q+9HXPw88YiqCiiZ3b19jzx0Y3Gh2cTBx9YN3zQ\nbJFbAfuz/n3MkzSQoMv2uR2EJ2vEXnEUbzGbDQaDTCYTif1cLnDbok0QVBh1UVKFmLT+IhGu\nsz8WetDO8eX4CixiJywEGSIKJkQo9uUjk1MjE74vPb/82nGu5QgMP1q1QphA3WMiKg2THFmP\nmA2AtEOrqxUgedYn30Cy9On1nACh0pk0wAGFgiCsngW33TEbfC1iF4gx4hy7eLevwutLQxqg\nsRMS0NhxT5hYum5wbiNl+MJLh365fZF9AQK1R55atULYB5Wq1N2fQLU14jNbuNYSkCt6oWgj\n8cWhDPuFjpV+5xYXOJ7DcqoBdXgrzJFKoxbHcfIusYK2cbSDaGoAAJgaGjthAI0dL2ikDF81\nMEshFr96du/B2lI2pw7QHrkuDrKzXOh2CZiFeflMgAbdfrnrCJnb870OHtF7KoKKpH+tAjhZ\n/1aGPviphOvIzwTeIoskuF2cpbEOM/FgbnGB/SvAkenCp+LP5JcvyZjAqCl0lETUOon3vdaJ\nQN2ek2y335K/NLgUKyygseMLHaOTlvd/GkfAzFM7rmjrAhnK8ROa/GOeFnvk6OT4uQksFAjQ\noLu2qbU/HrPzK5Iz7YjCGynbP47WXBVf3u/T1Ex8nPsRLfMjSleen0X7minFAemaV7NhdoAj\nOJkz4HtfEKYtHXDYZEl8e6+IHWnErvH8v4kvp4OMaXwAThwkyaSwOrGwgMaORzyS3OaDXpl1\nZkP28a1VJr1/g3ASuPp58LQND0/+bdgs9qeGANbjl54Gj+g3HQAgObSSvEOr/bPc9RPdv9au\ndWtnuD1OPYznFnKr53XrHi3ei8Q7Bj6+371inXB8K52ijPzkXq0TakXsmJfDLOSb6ii+wH8j\ndjArVhjArFh+MbF12tX66uWn/8g9XvBD91EKjIbidkGZpupU+wMIJFho1ywItb4iS+wob5qu\nv3YYKz3ldwzG1ws9xZxcjYWva6MUldBYY8WTGWK0hgtdBYpd4Uk7CtdKNOX3Inb+LMWyELSj\nt3ieT4N4mvSesVPHBa4HwgIwYsc73ur++OgWD52qr5x9epeVdLsSRch7WFE/mW8IbgmYzWwP\nRm8IyeARfacBACR/r2FudidUE5dGZOU75hnYa8j5hE+GkmItYj7DhGah3IcqoxYAxKuxC4Jw\nHTnUXyDMihUW0NjxDqK4XVp80z1V1xuE9pgAACAASURBVP7vgm/blUBgrUsFYY8cKRw5h/ji\nWoh3GHVytHeVdfx205Dp1MdRthkoiW0pObcNvVsWoCTa8Wo7XLeLsYyrPfXDpPqx8485Q8a5\n1XObPVNh0kXIFBKUbMHKk+lh2u05Fc9jZyKvxxFNDUAxTBnJnB4IjcClWD4ixUQrB2ZlFiz/\n9ubZlorIKY07+T0UlY98QRijUCCQhVriEr+X3cl95+bHZkgkEkoDIUhEr9zKLW9L/l5nGPyG\nH0powW8/QcXPedpRx9yyI+2Dh3K4zoagtUZt68hG5KexX47Y7TIoc4u/Pg2LaqowVTRAYCRI\nGEBjx1MipYp1g3NHFSx7/+KfiTLVY3HNqV9L/aM9uLd8CQtaOrPR9T4Gsi8zrOvYmj2LJMc2\nGh+ehUt93sZEC3zY2kUvFL2dY+6Cp/MZMqb8vOdu2pAYtLYThX5ssGMUKjVHOATRVGOxzbhW\nAaEKNHb8pXFY1OpBOeO3ffn86d0buo1sjSroHR/2eGUT12wPR54qcv74Ee47goik4elP1+5d\nIjn+o7HnFK7l0A/LDiaQQsfkBfYCbykmRIiU2Di5b20nOITzbmaISQ9MOhFMiRUO0Njxms4x\nyUv7PzVtz7ppJ7etazu4o5q2P0awxyv7BLhayjmOPzPkLyE8ffKd/fmSw2uMaVmAdCcThBzX\njE6KJ0M8UWnSAgDi2Y3YkZszx0AdHzvSaqsAzJwQFHDJnO8MTmn7To+htSb9zOLfa/wtbgfh\nDzx0da4u31UkSQVjVzBldFiX0Wh9ufjcDloUQgj4kxUhXCqNegCAr41iA8GnBVYersbeS4mF\n/cSEAzR2AmB6+75T2/W5aWzIPVGot1oYmoWHhoNvUOzn4fYS8tO+y+DsA5iKq/ODiD7TAIJK\nD62C3sJvfLp18D5TpOLeUixLETuvpYBdj/PN26FEo1gYsRMOcJVEGMxLG37tTtWe2xdfPrtn\nacchKIIEOCD5li+IK64hK3ID5Ov5ru8IfxZtM7fn+3qJJKa5ok1/XfFeeWRbepM6nRpCLOg6\nlK6RBYHXnXMQcir8rU4cOK4LsnzzcG6BjWIFBzR2wgBFkIXdh888/FNBxZXG8kNzW/UKfEye\nmAZOoL5dDOI3EX2m64r3Rulul4YzuOz19rHCD9NGOh0kzB8ntehoxO7VHKNxgjNwjkacD+9I\nlVEbLpXL6Gjq4xWvvo2PO+pcgMZOcMClWMEgRUXfDMxupo5Zfu346punuZYjYHzaLgYZs/Mr\n14NU3LCiWU8EEauMdVKrnrWFwheKNtqdBHmzV6Eg6C4XTm8B5++I1WarNus5TIkVRIjOCWjs\nBAc0dkIiSqb8dkhutEz53oU/d1Zd5VoOJBgg6TkRIDfmp2GIHAAQqbtN15i+womT8KP3A4Qd\nakwGq83GTkqsED2cW5B7e+yiuRYCoQpcihUYTcKiv3xk0sQdK+ec3vV9t1EPhcdzrYh+iBAa\n31ZInfbAeZXnxy5GX6egC/KJNg2Z7hS0c3u+W+UIIkUApjZUVyuTGOrNwNs9dlSqk3i9Iex3\nuQhuKk0aAEC8Qs1CcThBLLNSAUbsBAeM2AmP9Phmi/s9YbRZp53YdkvfwLUcmrH7A5+ST9nB\n3pqWouWyn+bTJTxsgLv5sRnkJ7iubhPhCgQBKKZAcDxaWwZoWkacW1zg9jFPoPgaidNgYI9l\niMwJ0b4VXAsREkhDNUAQTAULFAsGGLETJCOadbrRUJt3dHv28a2b0saEi6RcK6IHdpwcm4Ex\nXvmzQHB6IV6jqjO7TiaexW2WG4sGRtwtw6Z9Z4tIDlAG4YR46OfcUp6fpZ4UkIcgInPC9X9L\nMibQmDwReKiy0qgDAEQbNYAHHR2EAqKpxpRRCAbdgmCAb5VQmd2p/23d3dXn/5p2Ytv6riMk\nKMa1IkZgqORH0Pgt9vG1Ex2CiiIHPFe56XXpn1/qh70fyNRu/Y1mw+yIrPvVWAjrQJIVa/cZ\nTGRo+hSusz8O7n4S1O8z+a2g5T4Q/cRiTNrAhwodEE01FpnEtQqID8ClWAHzXvqIRxu3O3yn\n7OUze3GAcy2HEaAD4zlUgqzqLmMk0c0kJ35G6265PYFIZaUx0WFJxgRyVwcYyKtw6zzqv51J\n7ywkcwlofF/ntR8PUNjNq0cAAFFGDfFt0OQ3MIjFhBg1cIOdsIAROwGDIegXGU+N3/7llopL\nza6Ev9KCp3+k7J/9TCQcQPiAlzcOxSIynq3c9Lr0QL5++H+cnnQyWyQBHtdwDm6zabX+R1/I\np6MIYTWoLxG6WhPySFWI5EmwYyWrJQqF1SSz3e/fAxdkyUE01QDHsTC4wU5IwIidsJGLxKse\nyUpWRS4pOfLtzbNcy3GD08qd1/MdzR8M1wkIT6myxNfEm7clMc0lJzc5Be1cw2bsFyihK1iY\nMGOt61eAe+w4gdvEDrfGl/wEitzOz74jlseYNH4qC0lQDWwUKzxgxE7wxCnC1g7OHV2w/N0L\n+xsrwh6Obsy1IjKo7MoSip+D7SuccIzbOcXwbAiyOqzVxOoSt0E7DnGqZuxrAM9xiZBiaI2h\nCJyga6C4tW4Jz6yhdxZxznLr8YLk5j0aT5hH78hBDKKFjWKFB4zYBQOtI+JWDpyMoujMUzvO\nNlRzLec+QbyuGrLtKxxLsbiWZbHXanG9IX/HtPs3aHfTfpDcSNn33nHesYAKHGY50Di1U2IH\nXcP6jadKfn4MVWHirEusgGmoAgCIoLETFNDYBQk9E5p/2ne81mLJOV5QZuDLWgOMYwUrflTa\nsyFIZMazwGaRHsgnOc1u9ZjoRmVPqvCUXeETfPA9jgSux+syKBN4TJj4Mht4WOD2LzZZZdQB\nAOK56ycmRGB1YiECl2KDh8zmnUvqqz49vjvr2NZNaaPVvCxuB60eczgFybi91W6DdmGdR98p\nWg5O/mLsO8MWkUIctBcoYa1DPHMTcbIe6lPxFB7iJJg5K1lh1AAYsfMRFBo7AQIjdkHFS10G\nTmjV/aK2dvrJ7WbcxrUcABxCO3zrphBk8H8tuHDkHIBikQ/PAjaLdL9zSgFrro4EnzQwHcqi\nuAztVQZ1nV5LjbCA01wN65+lcfBKox4AEK+AETsfQBqI5AmYFSskYMQuqEAA8mHv0eW6u0Wl\nl946t+9/7R/hWtE9gs/ScdXXlVHojfm5vTysS+adP5aBU5uN/Wbag3Zc4bWaMQl5qcNch6IL\n12VoX8v8+lqExelku8ESXPyPhAqjFgAQL4cROx+AS7FCBEbsgg0RiuUPmNQuqtHGsuLPrx7h\nWk4ww2FfV3bic4zM8m/QTrZ/OfmJTlaGuZCeH/vteJLMQbGcr68hN67yJ2jMk3BLpVGnEEuV\nYj7uUeEtiKYGAAAbxQoLGLELQlRi6brBuSO2Lv348j+J0rCxiW24VgTxE9fazvYjXru1+j0X\n0xBBO/zUZrTPM3NOHyYxVSyvzwayQY3NPYJ2PKkNxAz5Wj+ZaeibGq8y6ZLDImkaLVRANNWo\nPBwRSbgWAvEBGLELTuIV6nWDp6gk0tfO/X6gxn0fJwjPca3tTOK9nAKHvF4aRrHIjNmIzXri\np7mAvvrAtMC3RFc/YDruxRzOqa/PrAl72ktYlzq1JoPZZoUpsb6CaqphdWLBAY1d0NImMn55\n/4kAATNObivW1HAtR3jYuyZwkpdAcVLXXXF+Lw27XsWcO3zqxq1KWVSfyhMJ+ntlF2nxdvRG\nqpxwTGVwDc7RG65jbRnaCT7kTzDEv5kTcIOdL1gtQH9XFBbHtQ6Ib8Cl2GCmf1LrvF6jX/vz\n5+zjBZt7jGkkU3GtSDC41h/mdQyMJpxaRzA3kQ1BdiSlT76ybdjN/Stbj/Z6vpPto93okFcM\ncZvKsCRjgv04E8bLvzFJHBiVFdVgSpVw4t9aJzBi5wOItgbgOEyJFRzQ2AU5T7Xucb2h9otT\nv087ue2HbplKkZhrRQ/Aq9Jr/Me1OBztd4y1t+BoVOqjpYf7VJwsSOlXLif75KAYzLMnCrDm\nTgL3c7RbQ+K1kwTeWLZubrNrPcnwI5OXOpUwJdZ3YEqsQIFLscHPG92GjG3R9XR91azTOyw2\nXhS3I+B/6TUO8WSwBLORzhtE0A7FbcNu7Pd0jn/b7wJJAvVvBP9wfGn07jL01K2Bw4BcgIm6\ngVNh0gNYndhH7qXEQmMnNKCxC34QgHzSd2zfRi1/r77xdvEfXMuBUMVTbWeuaqzQztGo1ApZ\nVJ/Kk/addo745HVoNwos1B9mdHw+4NM9dHJ+tPNvxA4uxfrAverE0NgJDWjsQgIRin31yKTU\nyITvSs/lXz/BtRwB4NrbnidKggPiRdkQZEfivaCd01qkT76nbu0MpyM+mQOvwS2K66QBWpOg\nt3rl+VlcVcgDAFQatXKRJEwiY3NSoYNqobETJHCPXagQJpF9Myh75NZlH1z8K16iyGzUmmtF\nfCcoHRXfOBad+mjZ4b5VpzQ1V23RzahcwknzMa8NbV2XGn1d9+RDUzUa8S9cZ/+W7lVjvMqk\nS1BG0Dpm8AP32AkUGLELIVJUkWsG58hF4tfO/f533W2u5fAoKgZhH2I1eeuo5zuNeBexWaV/\n5js+69bluG0RodkwGwCQlzqM+LIfZyIg5NV7UZ80yGycf7AWtKszm4xWK+wS6zMNVQAAEcyK\nFRowYhdadIpOWt5/4tS9a6ef2Lapx5gWXP8LC80cb3FMbdn8mPNaJ42EdRx+Z9/n+Oktxj4z\nSIJ2npyQauLSt48V2r/NSx3GgmdyCil5qglMHnZiumAKhwQSrrMfTHhmDV164AY7/4ARO4EC\njV3IMTAldUHPzDcObso+vvWXtLGxEjnXiiC8wylhOXN7PoMWHMUi+8+p+PFF6YEV+lEf2g97\nXf0kcHR1BH5396JYLY+6aynPz1JPWkFyQpD5OTuujtbxpjk969H+4jhdeioNWgBAnAIW8vQN\nFDaKFSZwKTYUebpN2jPt+93Q1085XqCzmrmWAwl1wjoOl8S2FJ/5Da256vQUh9bHbTaDa4ZE\nEHRlYBrOb1G5SQcAiIMROx9BNNWoTIXAf/6FBjR2Icr/pQ3NbN7lZH3l7NO7rDiPittBQhEU\nixowB7FZpQfI4lt27N29Xtz/o+uzbDbg8mpZ6r+dyY4YAcG+z6sy6gAAcI+dryCaargOK0Tg\nUmyIggDkk77jSjV39lReW3Dpr3db9+FakVChpRXEU0VrA7mcLlguGe04XeGI2dKiZfiZ34x9\nZ1JMj2UfV0fidacdhA+3pcKkBbBRrI8gNivQ1WFxLbgWAvEZaOxCFykmWjUoe9TWZV9fP5ki\nC8tt3IlrRcKDFif05L77m8Q5bEpL8lqYSJ5w7sb729IfMmaV//CCbP/y6ZHd7Mcpht+IRAT2\n120dMyTc7hXTaXXsKhIGLDc3K7t9UaqKVMMidj6hu4PYrFgY3GAnPKCxC2kipYpvh0wZuXXZ\nexf/TJSFPRrH00hJEONqpzjxdm5dHSHDYDCwo0HVcbi0aJntzG8J3ZvYu8dSt2uBuzrHNFXX\nASlGnpx25uV1HxGgKqFDo4Hz2w7WSuTxcjUCELqUhAIwJVa4QGMX6jQOi1ozOGfctvw5p3d9\n121Ut4h48vOZbkIPCV0QNDJjlvGHF0bdKMpvM5YTCSTukIqlcM23mHvkt8X9xgcqCxJA5efL\nX08zdHg0rPQMM7qCFrShGgAgUsdxLQTiMzB5AgI6xyQv7veECbdOPVl4VVfn07Us78oKPqAz\ndkTVcfhteUx65elGuiqS0xzt14KuQz9MG8m8NIggKc/PqpEqAADRJs2N+WlcyxEURK0TGLET\nINDYQQAAYFjTjm93H1pr0mcdK6gx6bmWIxiYaJ7BidVznZRpGe5vHYLuSEpHcdvIm3+QX050\noYDBMNbgNgcikCaz1WLC2Glp1hTswKVY4QKNHeQeMzr0y23b+7r+7syTO4w2K9dyBAPRGov4\n8m+E7/tnf5eRZR+KVnU+YJ+dNRn2WRyn+2/2Z45BO2GV8HVVG0x77AL3dlQKxNAIMVe15F7E\nDgAAg3bUqd/6AQAAU0NjJzygsYPc5730EY81aX+4ruyls3ts9JV9h1CBJ2uyLMtwYyIR9KGR\n81Dc9r7xmrBcHYGjZiHqdwt/wnWejpBQI5EBAKKMGjo1BTs35qeJbBYAQOmnw7nWAvEZaOwg\n90ER5IuMJ7vGNt5afvmjK4fdnsPE4iME4oiqw1BpfKrobCFaXcK1Fn8glomXZEzgQwk3egnk\nFdHbq8PrIPYTaiQKAECM6Z6xg0E7imA4XLcRKjArFvIAMky8elD2yIJly64eayRVZad0cD0H\nmjkIsyBoZP/nyjc+J92/VD/6E67VUILlwmxswrk99e/G2q+6e2qX2NjQ/u0iWO6EIjfmp0ms\nJoX53mbrizlY69XQ5AkJGLGDOBMlU64elBMhVcy/cGBXlXPvTgiEBVQdHpfGtxGf24ZVX+Fa\ni58Qfij4Wor55/OcrmLTLFaatLCInU/ILfpmd2+IbRb7kYs5GId6IL4CjR3EDS3DY1cOnIyh\n6HOnd524W8G1HAgYuuVz+xfXWlgBQSP7z0FsVsn+pVxL8Y69xJrTkSDA7Quh8uoc8yQ4vBsa\ni0lnMcfBZmKUqX27Q9P6WyK4Ditk4FIsxD3p8c0W93ti9r7vpp3ctrnH2GQ5/MvIGc7dt7hr\nO8Ymqg5DpUVtwdltxj4zbXGtuZZDCbcLshVf5Qh3ldY/5RSdn9+DU7+wwqADAEBjRxHx4Q1N\ntOUIJkqYvjosPUhSf0IQaOwgHhnZrNP1hpoPj+7IOb7157Qx4SIp14ogwYyjfy0cOQcgSGT/\n58q/ny39c4V+9KccCiOHSs4mz3fgMSePGJnermLAF8FVZi0AIF6upktAECPZtVj623xUqkp8\n7kdFh8Fcy4H4D1yKhZAxp9OA7NReF7V3pp/YboLF7SCM4RqVBACo2j8uTWgrObsNrbzAkS6f\nYW7Z8YWijY5f9A5Oo2wOt9O5UmHQAgDiFdDYkYHYrLIfXpZumScKT0h5ax90dUIHGjuIF97v\nOWJI43aH7pS+cnYvDmBxO/8JrU1ytIAgkf3nANwmO5DPtRT3UHctAfob2p2cnepVU4kH/N8X\n6McuxkqTHgAQB3eSkGAxylZPEe9fKUls2/j/Dkobd+FaECRQoLGDeAFD0M8entAhOvHX8kuL\nrxzhWo5QcfRzvnq7UK4dqGr/mDShrfgcH4N2JN6CWH9MmLFWPWlF/PTV9C5HEjBn9QLB72QL\nhoAROy/o6hRfZIqOb5a16Jkyd58oujHXgiA0APfYQbyjEkvXDsodsXXp4pIjyfKw8YmpXCsS\nGK5OztcEiJAycw+AIJH955R/P0t2YIVuzCKu1TyAJ6/G/9CXHc2G2Y7f8nkvoH87F6vMWhGK\nRUoVjOkSMEhdmWL5OLTsrKrryEYzNyASOdeKIPQAjR2EEnGKsHVDpmQWLH/j3L4EmbJfVArX\niiBeINykUBxh4cg5ngKZRNAOnNuO9p1pi2vDsjD/oN0hLcmY4BSi42e/MuaSMPy7sMKgi1Wo\nUAQWsXMGLTsnXzEOvVMa3i83LmcFgkEzEDzApVgIVVpHxK0cOBlBkJkntp9rqOFaDsQjjjv5\nBLSlz8mD3n8VCBI14HmA22QHVnCjzBeYC9fR3oXWvrvOEX6GG+1L205f5FfprBaNxQRTYl3B\nLu5XLHoUrSuLznw3furX0NUFGfDthPhAr4Tmi/qNn1O0Mfv41l/TxibKVFwrEgau4Sg2A2lB\nUPdO2e5RImiH9ZlhjRfGTgAmljXpjdLFTFlpMBhkMplILKZxWP5QadAAuMHOBfGJLdK10xGr\nOT5nRXjGNK7lQOgHRuwgvpHZvMuLXR6pMGqzj29tsJi4liMYCkfOIdyV/QHEBxAk6pEXAG6T\n8jtox89wF/9h6L5VmHQAgFg5/P/zPuJ9y2WrsjEUS3phM3R1wQo0dhCfefmhQeNbdrugqZ11\naqfFZuNajpDgytIFQZkVZdsh0oS24vPbsYpirrW4h0qlYogrrg3ZaOGFoo3Lzx4AAHxbfJje\nkYUKjku35cl+fhNTRia/tkPZeSjXgiBMAY0dxGcQgPyvz5iHE1sV1dx4q7iIazmQoOUBH3wv\naIdL9y/nThFEGBCJJpZ/UyaE/l8NDVhMsjXTJYULxbHNUt45IGvZi2tBEAaBe+wg/iBCsfwB\nT2cWLv++9HxjuXpqQjuuFUHuQ5JhynMIJ+cpn1fZdoi0UTtQvAOrKObhTju3O+p0Wh37SgSE\nU81henclmmEuLIFRq1g5GTu/R9ase9JLv2HqOK4FQZgFRuwgfhImka0dnBuvUP/v8t9bq0q4\nlgN5AD5v4/PagcPjNkQEiRoAg3YQSlgRRIdCZweQ+grF4sex83sU7Qcmv74LurpQABo7iP8k\nKSPWD5mikkjfvLj/cEM513IgDEJXP7RAOnAAAJRtB8uSOomLd7C/046hJq2hDKO7EhtQ2AAR\noNVXFYsfw26dVPeZnPRyAQorv4QG0NhBAiI1MmFZxlM4Al66tP+CppZrORBGyNx+v1VrIN7O\nbQcO34ZAkMj+swGOy/Yv81uGHzj6OejtaMGTh6PF233cb3ydwz4jPgewmUN845jik0FoVUnE\n4DkJ075BsOAsagNxBe6xgwTKgOQ287sOfefI1mmntv+aPjZWArv3CBK7x3L6FByz8yvXMzn8\npFSmDpYldTIU78Qqii2xrVmY0dXJvVC0kavGD/5NTbglptuF+bRJjlExOypLrAAZ0/Khae36\nMjcLnxGf3a5aOx2xmuImfxEx8Fmu5UBYBUbsIDQwvvlDuS3Tbhkaco8V6KxmruVA3EBuxZxW\nSFnLvfDHIP4btJPuX0qjEv4vs9oV8lMqf2q7WHHbL7cvijBsdPOHuNbCDeJD68NW56C4rdHM\n9dDVhSDQ2EHo4fm2/UY373KqoWrWaVjcjhc4eiZ6A2x+j0aXDGXqYFlSZ3HxLqyShp12jj6J\nomdiP1wXiJOzWy4WvBcf7N3v1TcqjNrBKW2jZUqutXCAZNdi2fpZmCws5vlfw9LGcy0HwgFw\nKRZCDwhAPuo1ulLfsPf2lXcu/LGwbX+uFUHoMVKbhkx3XY31G3q8HYJE9p99e/0z0v3LwWMf\n0DAgKUsyJvAwQuYfTDQ6AwxXLfEJHMc3lV1EEXRsi5AL1yE2q+THVyQHvhFFJMY9vxnhX0kg\nCDtAYwehDTFR3K5g+YZb51ooI6Y37sK1Igg9bH5shkQi4VXPWWXbwbKkzuDCLnH3HJz5Mopc\n7agLnBCJ0tk5WFt6Q3+3f3KbRGUE11pYBTHrZKtyRGd2SJLaJ79SYFPFm81wV0yIApdiIXQS\nIVWsHZwbK1f998Jfv5Zf4loOxE/cGjj+uDqCyAHPARwPO0RbNDH4cGu5gtvq/Xj7AgDIEy27\ncSWAExDdHfkXo0VndihSMxq//YcoKoVrRRAugcYOQjONw6LWDMqRi8Svnt17pA4WtxMGjjWB\n+WbgPKFMHSRN6iS/sk9UdSGQceiNxjFU7m5JxgRHnfyJIPIqXHesrvyyprZnQrOm6miutbAH\nWnNd8clgrOSQqltm0ssFqCK0QpUQVxAch0UcAQDAZDLV19crFAqFgqfVOmpra6OiorhW4R6t\nVqvX6yMiIkSie4v7e24WT9mzVi2S/JI2pjnXf2gsFovJZOLtO1tfX4/jeHh4ONdC3GMwGFAU\nlUgkXAtxg+b87vL1042tHrl2Vxvgvi7CigVomJz83JKMCTqtTi6XISgf/4W2mM0Gg0Emk4nE\n3FQ487IbD8e1Wp1S5UMCxJvn9p2pr/q477h2UY1o0EeKTqczmUxqtRrl9M1Fy84qlo9D6soi\nBj0X9/QigNwTYzKZzGazUsnT9JHa2loAAG8/0YQOH//cQIKAgSmpC3qNumM2ZB3bWm3Scy0H\ncr91hEDbyLpF0eYRUUJ76eXfZWZNgKEjp5CYH7gtdxfIgBCfKNbUnqmv6hyTzIKr4wnYhSLF\nokeRu7ejM9+Nm7TE7uogIQ78OYAwxaQ26dPa972hr889XqC3WriWE9IEk5lzQtHrGYDj0boy\nroVAfIMw4jSu5H5/6ywA4IlW3ekakOeI/tmoWD4WtRgTnlkbnTmPazkQHgGNHYRB3u0x7PEm\nHU7WV750do8NLvpzBA2NvHiDa8RR0uJhBBGrjHcCD9pBhMtV7d0jdRWtIuIfig2JvAHxvuXy\ndTNRsTTxhc3qXhO5lgPhF7DcCYRBUAT5PGPCk9sbCiuufCA7+E7rPlwr4gBHIyKUvAQe4tQb\nA/x7M+sXDxEhCjN+N1pbWhrRhtsiahCK0F737oey8wDgE1qHQLgOt0l/elPyR74oPCHp5a3S\nJiFXrg/iFVYjdrW1tR9//PHkyZMnTJgwd+7cixcvsjk7hBNkmPibQdnN1TFfXj+5+uZpruWw\njVN4iZNQWdC7SQSVIIhYZapTmu76dCG96avkW/TK87NgQJEhyg2aP2tLU8KiesY341oLw1iM\n8m9yJH/kSxLapLxzALo6iFtYNXb//e9/q6ur33vvvcWLF8fExLz//vsGg4FNARBOiJQq1g3J\njZGp5l84sKOqhGs5kOCxerfe70k8EGFKAECc5hoCbFT8k1MbMYbk2a0etHSOuN6NAO/PD2XF\nNtw2oVV3FEECGYfnIPq78mVjRMd/lTVPS3m7SBwb7C4W4i/sLcU2NDTExsZOmjQpJSUFAJCV\nlVVUVHTz5s1WrVqxpgHCFU3ColcPyh6//cs5p3Z/331U1/B4rhUxDq/2sQWNk3Mi+d1D9fX1\nYrFYqVRWbnq9/tiPjTsPNPbM9XWcF4o20lIZzusgbK4U83NV2pOH81tttVG3t+p6gjI8IzGY\nP0qQu7flK57Abp1SdhmeOOs7RMLT4k0QPsCesQsLC5s7d67925qaGhRFY2JiWBMA4ZYusSmL\n+j0xa9+GqScKf+kxpqmCp2XbxbAzfwAAIABJREFUaIFXrk7oULyZ0UPe0JzdLi363NR+OB4W\nS3Imy1VIKr7KYXM6AnvOKd+8He16Nt2+aMFt41p0xXhZLJAW0PJi+bJx6J2b6r7Z8blfIhjc\nHA8hg5ufj4aGhs8//zwzMzMyMtLTOQaDwWq1siaJmMtkMvG2YjOO41qtlmsV7iGaEur1evJa\nnQNim7/SceD/Tu3OObb1+87DwkVSduThOG6xWPR67svp/Tx4mqsMHMdxHOeDPLdYLBYURdn8\nZfTKz4OnAQD0ej3x22q1WvV6PcAUYf2evbv7I8meT+ofe4/k8o/SM18/vNnpoNFgZEKq69+T\n8vysyGz22qCRvC4ctwEALBaL1WpjTY9P4AAnf18arKadVSURUkWf2CYs/wZZLBYAgMFgQBhe\n/xXfOBr+zWRUWxs25KWwUe/pDEYAvP+sWq1Wm83G248M4veCujypVGqvfg/xCoN36sCBAx9/\n/DHxOC8vr23btsTjW7du/ec//+nSpUt2djbJ5Uajkf0exhaLhfh15Se8/ewnMBq9/7l5ukmX\nWw2131099uyZ3fltBkhQjAVhBFTkMceGhyeTa+BWHjmBu7qJf6yzPyZuRSA43SubzUYcEXUa\njx39QXrmV6T9KFNCB+oDLug61Gw2BajKLZoNs10P3lkzXTVxKRPTuU7qdS4+/8UDAJC/L5sr\nLxms1jFN2uJmqxFw8L+HycTIj40d+fmdET/OQaxmxdiPxL2yff0I4PmbS/3liEQiaOyow+Cd\n6tq165IlS4jHCQkJxIOTJ09+9NFHTz311PDhw8kvVyqVbAbPLBaLVquVSqUymYy1SX2ioaEh\nLCyMaxXuMRgMRqNRpVJhmHej9p/eo6rNul23iuff/GdJ+4EIYHy/s9VqNZvN3L6zKpXK01M6\nnQ7Hcd42/zGZTCiKBvJXdWThcsdvJ/6xbsvQZwORZL+ZRBgbwzC5XE4c+U9891l3rt0tfDdq\n1jbgOZTyaZ9xL//5EwBgbnFB7NRvAhFDQtVKj7v95HKm9ki5TuppLqvVajIZxWIJPz8yiXAd\nya+tzmbZdeemSiIb2bJL3cL+AIDEdw6yJs9gMFgsFoVCwVxLMen+rxW/zEVEkthnvlV2G+3T\ntUSQgrcfZ/X19QAAtVpN8XwqnywQOwz+PisUiiZNmjgeOXfu3IcffvjKK69069bN6+Us/60h\nTCSGYWKO2iZSgbfaiH9bKf5TJQZg2YCnJ2z/amtlSVNl5Ost05kXCKxWK5s/UYUj5/havo6f\nH67g36VYeuUFOJr9cpvNBgCwyxu65XOgbnwmonmHupL8X9598okPyMeZW1wAAMBETH1mJMxY\ny4desVUrc93ubCOWYjEMZe4OBASOG0nfne2lF7UW09Nt0tUyRR0AgN1fIsLPiUQiRowdjku3\nL5QULsSUUYkvbpa38rkCKI7jNpuNtx8ZxPo1b+UJHfZ+DUwm0+LFi0eOHNmkSZPq6mrioEql\n4u2/FBDmkIvE3wzKHlWw7IurRxNkiqzkjlwrop9gTURlH4ou2X7Opib9U+9ef/Lqjjf3pC4c\n6CYH0548kZc6DAAwl38ZBn4TOnVVzDbblorLMpF4RLOON+anEQdvzE9rPP9vboXRgNUi++El\n8cG14pimSa8USBqlci0IIjDYM3bnz58vLy/fsGHDhg0b7AdnzJgxbNgw1jRA+EO0TPnNwOzM\nguXziv9MlIYNim3KtSIIf/HJJVdLI4oSug68/c+wm/sBcDY6LKfEskzQOFSv7KgsuWMyjGn5\nkFoir+NaDJ2YdPKVWaJzu6TJHZNeKRBFJnEtCCI82DN2nTt33rJlC2vTQfhPq4i4VQOzntq5\n8vkzu37sPrp9GKx9E5z4sTAdINsT07tXnx9e9ldD7TVbVFPyk/NShwVT0C4UsOK2TeUXRRg2\nuvlD9nAdgaCDdmhDpXz5E+jN44q2AxKf/xmVB3NNKAhzBG3hH4ggSE9otqjfeK3FknO8oNSg\n4VoOhE6Gbvmc+AIAFI6cY/9iaDrHkY2YZGtyX2A1y3d/RPHy0FnEDAJ+r75RadAOTmkbLXOT\ncuRk9YQCWnNNsegx9ObxsB5jk17eCl0dxG94ul8bEjqMatb5Wn3N/47tzD62dVPaaDVbxe2E\niD3uxf8NfI4huqFbPmdH8AOz4PitL8caLuwRXdlvadHPfnhJxgSn1VgihQIiFHAc31R2EUXQ\nsS2cw3XCBbtxVL5iAtJQFTF4TtzETwECYy4Q/0F4W4+XZUwmU319vUKhUCh42qqltrY2KiqK\naxXu0Wq1er0+IiLC76y0t/7avLb4UM/IxPXdRorp/qNmsVhMJhNv39n6+nocx8PDvfyD7tSA\ngTVvZzAYUBSVSCTUL3HbK4IJwTabzd5SzPVZQ9npW8szrdHNNDO2APSBn0y7t/Ojk5hP1/Ih\nK9YTFrPZYDDIZDIRP5MTcVyr1SlVzu/snzW38i791T+5zetdh3Cii0Cn05lMJrVaHXhWrOjC\n77KvJiEmbewTCyMff5UWeSaTyWw287aIUm1tLQCAt59oQoePf24gIcj76SMyklofulP28pk9\nOID/bDyAfUHT6SAnYgSELLFjWJcxWPUVyT8bnJ5akjGB+PJ1TMdoX3DnYfCWH29fAAB5oqX3\nmlmCQHx4g3z5eNRqajRzPV2uDhLiQGMH4QUiFMsf8HT7qMRfyy8tKTnKtRweERwGjqu145jH\n3kClYbKiJYimKvDRXJ0c9HYsc6yu/LKmtmdCs6bqaK610IBk12LZ+lmoWJb04pawdJ//zYBA\n3AKNHYQvqMTStYNzkpQRi67881NZMddyeIFAXR1/tgBiypioAc8hRo1s32dca4HQwA9lxQCA\ncS27ci0kUBCbVfbDy9It80ThCSlv7VN0GMy1IkjwAJMnIDwiXqFeNyQ3s2DF6+f2xcuU/aJS\nuFbEX/hjntzCH3nhvXLrj2wEJ34ydR1vTewUyFCuiRcQNinW1J6pr+oSk9IuqhHXWgLDYpSt\nfUZ0fLMksW3yK4Wi6MZcC4IEFTBiB+EXrSPiv35kEoIgM09sP99QzbUcjvFkj/hjm9xiL3TC\nh4gjgoljHn8H4Db5jjyA4/SWNfFjlx772F9yeX6WoKu6fH/rLADgidYC312nq1N8kSk6vlnW\nomfK3H3Q1UFoBxo7CO/o3ahFXu/RDVZz9vGC27C43YMwWgqOFpzMHF3eLhCbqGgzQNG6P3br\nmPhsYYAy7CkX/uVe8AGBerur2rtH6ipaR8Z3iRFwIB+pK1N+Ngy7clDVdWTKG7sxWJUdwgBw\nKRbCR55s1f1mQ+2Sk3unndz2Q7dMpYiX5RhYgec2jgVoKYkXO2zejSsHJb++iUR3Lg+4z4SA\nLB1h49yauepVU1UTl7KuyE823j4PAD6hVXeuhfgPWnZOvmIceqc0vF9uXM4KBIOfvxBGgBE7\nCE95tevgcS27nq6vevb0DovNxrUcCF/wL24njm4a3jNLZDNF68oAAC8UbbR/0S1QAAguaFdu\n0BysKU0Ji0qPb8a1Fj/BLu5XLHoUrSuLznw3furX0NVBmAMaOwhPQQDycZ+x/RJb7qu+8VZx\nEddyINxA4y493eHNAKBRuttiqzFEuk2QGDjiKc2G2SzK8Z+NpedtuO3JVt1RBOFaiz+Ijm5S\nLB+LmvUJU1dGZ87jWg4kyIHGDsJfRCj25SOT20Y2+r70/PJrx7mWA6GE01JpgEvJdK1E35if\nBgAiQpUIbotruAYcOokFa9BOcGE5T1Qbdb9X30hQhj+c2IprLf4g+X2pfM1UVCROfGGzum82\n13IgwQ+MBkN4TZhYum5I7oitSxdeOpQgVY5u1JprRRDvMLovMJDBUVSG4gaVqS7MeKdBGkmj\nKqFAbC509HzVq6YGuOOQaX6+fdGC28a16IrxsjMbGTgu3b5QUrgQU0UnvfirrGUvrgVBQgKh\n/Z5AQo8EhXrVwCyFWPzq2b0Ha0u5lgNhG0cn55+rc2wVj6EqAEBcwzUMtwbxgqyncJ3biid8\nju01WEy7qq9GyJSDGqdyrcVHLCbZmumSwoXi2GYp7xyArg7CGjBiBxEAHaOTVvR/OnfPmpmn\ndvzSY0wLZQTXiiCsEmAIsPH8vx2/zV/6xMDb/1yRir9r/jgQVIordUiCcHy2ca5svn3JYLE8\n3SZdggrq08qoVaycjJ3fI2vWPeml3zB1HNeCICEEjNhBhMGA5DYf9MqsMxuyj2+tMum5lgMR\nMM88s0YcmTKk7O8v2nQMSldHAkkkj2UlVNDbLFsrLqskssebdOBaiw8g9RWKxY9j5/co2g9M\nfn0XdHUQlhHU/0CQ0GZi67Sr9dXLT/+Re7zgh+6jFFjoFreDBAIilseO+E/Z2hx5wTxt7vc4\ninGtiD0cI3kWs9lgMMhkMpGYp79KO2qvay2mp9ukK0QSrrVQBa2+Kl82Bq0qUfeZHD/lKwT+\nmYKwDozYQYTEW90fH93ioVP1lbNO77TidBa3408LLAgLKFpnKNsNwcpOiY/9wLUWiHtMNtu2\nmmsykXhEs45ca6EKdu2I4pNBaFVJxOA5CdO+ga4OwgnQ2EGEBAKQT/uO692oxd6q6+8U76dr\nWKfeBnQNC+EzscPmoVKlbO/HiKaSay0QN+yoKqkzG4c17aiWyLnWQgnR6W3yz0Ygujtxk7+I\ne3oxEGbJPUgQAI0dRGCIUSx/wNMtwmPX3zq78vpJJqaA3i4UEIUnRj3yImLUyHd/xLUWAEK+\nGYYTVtz2y+1LIgwb3bwL11ooIT60Xr5yEopbG81cHzHwWa7lQEIaaOwgwiNSqlg3ODdWrvrP\npYPbK0u4lgMRKuE9c6SJ7cWnfxOV/MWtEiczB73d79XXK43a/gkto2RKr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e75coSb3+asK1/dOkM7DgiU2KOxW9fxbHmh9NB/aWcRCgNv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" | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "# 2 clusters\n", | |
| "fviz_cluster(km2, data = clustering_data, geom = \"point\") +\n", | |
| " scale_color_brewer(palette = \"Dark2\") +\n", | |
| " theme_minimal() +\n", | |
| " labs(title = \"Two Cluster Visualization\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "NKnBowzWNBBp" | |
| }, | |
| "source": [ | |
| "**Two-Cluster Visualization Analysis:**\n", | |
| "* The two-cluster model clearly separates two distinct groups, likely representing different age or cost demographics. This simple division provides a straightforward categorization for broad strategies.\n", | |
| "\n", | |
| "**Three-Cluster Visualization Analysis:**\n", | |
| "* Adding a third cluster introduces more nuanced segmentation, revealing subtler variations potentially related to specific health or demographic factors. This model is likely more suitable for more detailed analyses and targeted interventions.\n", | |
| "\n", | |
| "**Conclusion:**\n", | |
| "While both offer advantages, the choice between two or three clusters should be guided by the need for simplicity versus detail in addressing insurance strategies and policy development." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "fgPv0HhKNDzv" | |
| }, | |
| "source": [ | |
| "# Part 7: Neural Network Modeling for Insurance Charges\n", | |
| "\n", | |
| "This section explores the construction of a neural network to model insurance charges based on numerical attributes such as age, BMI, and number of children. Neural networks are advantageous for capturing non-linear interactions between variables." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Zaey0vaDNFg-" | |
| }, | |
| "source": [ | |
| "### Data Preparation\n", | |
| "\n", | |
| "First, we prepare our dataset by isolating numerical variables, which are more suitable for neural network processing." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "pfzJG9zpNBbR" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "insurance_data_numeric <- insurance_data[\n", | |
| " , !(names(insurance_data) %in% c(\"sex\", \"smoker\", \"region\"))]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "rggqmQDTNH5M" | |
| }, | |
| "source": [ | |
| "### Standardization of Input Data\n", | |
| "\n", | |
| "To ensure that our neural network model performs optimally, we standardize the input data by scaling the data to have zero mean and unit variance, which helps accelerate the learning process. Then, we convert the standardized inputs to a data frame" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "vK2iZYiXNJGm" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "insurance_data_scaled <- scale(insurance_data_numeric)\n", | |
| "insurance_data_scaled <- as.data.frame(insurance_data_scaled)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Q90ETrgtNLVE" | |
| }, | |
| "source": [ | |
| "### Splitting the Data\n", | |
| "\n", | |
| "We then split the standardized data into training and testing sets to validate the model effectively. Approximately 80% of the data is used for training." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "Kq8Xsf2ONLoF" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "index <- sample(\n", | |
| " 1:nrow(insurance_data_scaled), 0.8 * nrow(insurance_data_scaled))\n", | |
| "train_data <- insurance_data_scaled[index, ]\n", | |
| "test_data <- insurance_data_scaled[-index, ]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "-dC4-IsWNOCC" | |
| }, | |
| "source": [ | |
| "### Building the Neural Network\n", | |
| "\n", | |
| "With the data prepared, we construct a neural network using the 'neuralnet' package. The network includes one hidden layer, a common architecture for regression problems." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "2-VjJhq6NPOB" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "nn_model <- neuralnet(charges ~ age + bmi + children,\n", | |
| " data = train_data,\n", | |
| " hidden = 1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "tds-b14XNQZv" | |
| }, | |
| "source": [ | |
| "### Visualization of the Neural Network\n", | |
| "\n", | |
| "After training, we visualize the structure of the neural network to provide insights into the learned weights and structure." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "id": "Nv2kk69rNRgF" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "plot(nn_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "a5QV1BO5NSkV" | |
| }, | |
| "source": [ | |
| "We see that age, BMI, and number of children have varying weights influencing the charges, suggesting complex and significant impacts on the prediction of insurance charges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "-l9bTyONNX3W" | |
| }, | |
| "source": [ | |
| "### Model Testing and Evaluation\n", | |
| "\n", | |
| "To assess the model's performance, we predict charges using the test dataset and then calculate the mean squared error (MSE) between the predicted and actual charges." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "_9oiyqzoNULa", | |
| "outputId": "1efdedeb-d043-4abb-d487-2eadf6bca6e3" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"Neural Net MSE: 0.673733886634395\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# Forecast charges in the test dataset\n", | |
| "test_predictions <- compute(\n", | |
| " nn_model, test_data[, c(\"age\", \"bmi\", \"children\")])\n", | |
| "# Get the observed charges of the test dataset\n", | |
| "observed_charges <- test_data$charges\n", | |
| "# Compute test error (MSE)\n", | |
| "nn_mse <- mean((observed_charges - test_predictions$net.result)^2)\n", | |
| "print(paste(\"Neural Net MSE:\", nn_mse))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Z8xwdAFENtHx" | |
| }, | |
| "source": [ | |
| "The neural network's MSE of 0.6737 indicates the error magnitude in the model's predictions. This value provides a discouraging benchmark for assessing the neural network's accuracy in estimating insurance charges based on demographic and health-related factors." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "g1S1xhgRNulI" | |
| }, | |
| "source": [ | |
| "# Part 8: Model Comparison and Recommendations\n", | |
| "\n", | |
| "### Real World Applicability\n", | |
| "\n", | |
| "The real-world applicability of our models is demonstrated through rigorous validation techniques and comparative analysis. This section evaluates each model's performance to ensure reliability and accuracy, discussing their potential implementation in practical insurance settings where predictive insights can significantly impact risk assessment and policy pricing strategies." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "DavrSaUsNvrA" | |
| }, | |
| "source": [ | |
| "### Model Evaluation and Selection\n", | |
| "\n", | |
| "To determine the most effective model for predicting insurance charges, we conduct an extensive comparison of several models, including Multiple Linear Regression, Regression Tree, Random Forest, Support Vector Machine, and Neural Network. We focus on the MSEs of these models to identify the best performance in terms of prediction accuracy." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 142 | |
| }, | |
| "id": "Alh36ReqNu7Z", | |
| "outputId": "b79a6410-1a9c-4d97-8412-296d24db587e" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| " Model.Type Test.MSE\n", | |
| "1 Multiple Linear Regression 0.2313\n", | |
| "2 Regression Tree 0.2891\n", | |
| "3 Random Forest 0.1782\n", | |
| "4 Support Vector Machine 0.1749\n", | |
| "5 Neural Network 0.6737\n" | |
| ] | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/html": [ | |
| "'The best model based on the lowest Test MSE is: Support Vector Machine'" | |
| ], | |
| "text/markdown": "'The best model based on the lowest Test MSE is: Support Vector Machine'", | |
| "text/latex": "'The best model based on the lowest Test MSE is: Support Vector Machine'", | |
| "text/plain": [ | |
| "[1] \"The best model based on the lowest Test MSE is: Support Vector Machine\"" | |
| ] | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "model_comparisons <- data.frame(\n", | |
| " Model.Type = c(\"Multiple Linear Regression\", \"Regression Tree\", \"Random Forest\", \"Support Vector Machine\", \"Neural Network\"),\n", | |
| " Test.MSE = c(mse_test, tree_mse, rf_mse, svm_mse, nn_mse))\n", | |
| "model_comparisons$Test.MSE <- round(model_comparisons$Test.MSE, 4)\n", | |
| "print(model_comparisons)\n", | |
| "best_model <- model_comparisons[which.min(model_comparisons$Test.MSE), \"Model.Type\"]\n", | |
| "paste(\"The best model based on the lowest Test MSE is:\", best_model)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "MdtcgsCON0vB" | |
| }, | |
| "source": [ | |
| "After reviewing the MSEs, the Support Vector Machine emerged as the superior model due to its lowest test MSE, indicating its high accuracy and superior performance in handling the given dataset." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "_8jkY0pFN3kq" | |
| }, | |
| "source": [ | |
| "### Recommendation for Sales Department\n", | |
| "\n", | |
| "Another supervisor from the sales department has requested your help to create a predictive model that his sales representatives can use to explain to clients what the potential costs could be for different kinds of customers, and they need an easy and visual way of explaining it. What model would you recommend, and what are the benefits and disadvantages of your recommended model compared to other models?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "y0DRIj9JODwb", | |
| "outputId": "0d5611dd-03f6-4591-e21f-af2b1248ddbb" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1] \"The Regression Tree model is recommended for sales representatives as it provides an easy-to-understand decision process. This model visually displays how different factors contribute to the final insurance charges, which can be effectively communicated to clients. However, it may not capture complex nonlinear relationships as effectively as more sophisticated models like Random Forest or Neural Networks.\"\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "recommendation <- \"The Regression Tree model is recommended for sales representatives as it provides an easy-to-understand decision process. This model visually displays how different factors contribute to the final insurance charges, which can be effectively communicated to clients. However, it may not capture complex nonlinear relationships as effectively as more sophisticated models like Random Forest or Neural Networks.\"\n", | |
| "print(recommendation)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Pxqq8xrZOGJR" | |
| }, | |
| "source": [ | |
| "### Adjusting for Log Transformation\n", | |
| "\n", | |
| "The regression tree model, initially favored for its interpretability, used log-transformed values for charges, leading to underestimation when communicated by sales representatives. Upon realizing this, we reverse the log transformation to reflect the actual charges more accurately." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 437 | |
| }, | |
| "id": "UbfqHrs3OII0", | |
| "outputId": "43efb915-8ddb-4622-b508-c182fef58cca" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "Plot with title “Revised Regression Tree”" | |
| ], | |
| "image/png": 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SkhJNsISQkh2UZISgjJNkJSQki2EZIS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\nIQEe/C+W4K3z6jlVAwAAAABJRU5ErkJggg==" | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 420, | |
| "height": 420 | |
| } | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "# Copy the Pruned Tree Model\n", | |
| "copy_pruned_tree <- pruned_tree\n", | |
| "# Reverse Log Transformation\n", | |
| "copy_pruned_tree$frame$yval <- exp(copy_pruned_tree$frame$yval)\n", | |
| "# Replot the Tree with Labels\n", | |
| "plot(copy_pruned_tree)\n", | |
| "text(copy_pruned_tree, pretty = 0)\n", | |
| "title(\"Revised Regression Tree\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "AcQ5trQaOOWB" | |
| }, | |
| "source": [ | |
| "This adjustment ensures the model's outputs are practical and relevant for real-world applications." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "OqVgE68jOP1r" | |
| }, | |
| "source": [ | |
| "# Project Conclusion\n", | |
| "\n", | |
| "This comprehensive study on predicting insurance charges using various modeling techniques has illuminated the intricate relationships between demographic and health-related factors and insurance costs. The comparative analysis of models ranging from regression to machine learning approaches like random forests and SVMs demonstrates the potential of advanced analytics in refining risk assessment and premium setting in the insurance industry." | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "provenance": [], | |
| "authorship_tag": "ABX9TyOooxTFzHiFf7JCcrE806NT", | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "display_name": "R", | |
| "name": "ir" | |
| }, | |
| "language_info": { | |
| "name": "R" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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