{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " CS411 - Autumn 2019-2020
\n", " Patrick Jermann

\n", " How to use this notebook?\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The MOOC dataset\n", "The data we use in this document to demonstrate the use of basic statistics is about students' performance in academic exams (e.g. the algebra course taken at the university) and their activitiy online in a related Massive Open Online Course (e.g. the algebra MOOC). The general question we try to answer is: what is the relation between the use of the MOOC by students and their academic achievement. \n", "\n", "**Question**: Does the use of MOOCs help succeed in courses ? Do only good students use the MOOCs ? Are MOOCs more helpful for better students ?\n", "\n", "As a general remark, we should note that because we did not conduct a controlled experiment with random assignment of subjects to experimental groups, we cannot establish any causal relationships between MOOC use and academic performance. Rather, we use statistical tools to \"explore\" data.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loading libraries\n", "Some extra libraries are needed to perform some operations. We collect the commands to load the libraries in this cell. Executing this cell first ensures that all the necessary libraries are loaded. If one library is missing it can be installed via the install.packages() command. Simply add the line to the cell and re-execute." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "# Uncomment and run once if these packages are not installed yet.\n", "# install.packages(\"gdata\")\n", "# install.packages(\"gplots\")\n", "# install.packages(\"plyr\")\n", "# install.packages(\"dplyr\")\n", "# install.packages(\"ggplot2\")\n", "# install.packages(\"ggpubr\")\n", "# install.packages(\"car\")\n", "\n", "library(gdata) # reorder\n", "library(gplots) # plotmeans\n", "library(plyr) # ddply\n", "library(dplyr) # summarySE\n", "library(ggplot2) # plotting library\n", "library(ggpubr) # plotting\n", "library(car) # Anova\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Loading Data\n", "Let's load data. The first step is to read a CSV file into a dataframe, which is the data structure used by R to store data." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "\n", "# TODO: Adapt the path to your own installation.\n", "# Set the working directory\n", "setwd(\"./\")\n", "\n", "# Read a csv file (header = T signals that the first line of the file contains the names of the variables).\n", "# The <- operator assigns the result of read.csv to the variable moocs.\n", "# moocs is a dataframe, similar to an excel worksheet or a DataFrame in pandas.\n", "moocs <- read.csv(file=\"moocs.basic.csv\", header = T)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our dataset contains variables which name starts with *EPFL* and other variables starting with *MOOC*. The variables with EPFL come from the academic database and describe student's performance in their EPFL exams. The variables starting with MOOC conern their online activity in the MOOC." ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "\t
  1. 'EPFL_AcademicYear'
  2. \n", "\t
  3. 'EPFL_IsRepeating'
  4. \n", "\t
  5. 'EPFL_PropaedeuticGPA'
  6. \n", "\t
  7. 'EPFL_CourseGrade'
  8. \n", "\t
  9. 'EPFL_StudentSection'
  10. \n", "\t
  11. 'MOOC_NVideosWatched'
  12. \n", "\t
  13. 'MOOC_AverageMaxVideosWatched'
  14. \n", "\t
  15. 'MOOC_PercentageVideosWatched'
  16. \n", "\t
  17. 'MOOC_NProblemsSolved'
  18. \n", "\t
  19. 'MOOC_AverageMaxProblemsSolved'
  20. \n", "\t
  21. 'MOOC_PercentageProblemsSolved'
  22. \n", "\t
  23. 'MOOC_Grade'
  24. \n", "\t
  25. 'EPFL_Topic'
  26. \n", "\t
  27. 'EPFL_BacGrade'
  28. \n", "\t
  29. 'EPFL_BacLevel'
  30. \n", "\t
  31. 'EPFL_CourseType'
  32. \n", "\t
  33. 'EPFL_UniqueTopicID_Anonymous'
  34. \n", "\t
  35. 'EPFL_AnonymousUserID'
  36. \n", "
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'EPFL\\_AcademicYear'\n", "\\item 'EPFL\\_IsRepeating'\n", "\\item 'EPFL\\_PropaedeuticGPA'\n", "\\item 'EPFL\\_CourseGrade'\n", "\\item 'EPFL\\_StudentSection'\n", "\\item 'MOOC\\_NVideosWatched'\n", "\\item 'MOOC\\_AverageMaxVideosWatched'\n", "\\item 'MOOC\\_PercentageVideosWatched'\n", "\\item 'MOOC\\_NProblemsSolved'\n", "\\item 'MOOC\\_AverageMaxProblemsSolved'\n", "\\item 'MOOC\\_PercentageProblemsSolved'\n", "\\item 'MOOC\\_Grade'\n", "\\item 'EPFL\\_Topic'\n", "\\item 'EPFL\\_BacGrade'\n", "\\item 'EPFL\\_BacLevel'\n", "\\item 'EPFL\\_CourseType'\n", "\\item 'EPFL\\_UniqueTopicID\\_Anonymous'\n", "\\item 'EPFL\\_AnonymousUserID'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'EPFL_AcademicYear'\n", "2. 'EPFL_IsRepeating'\n", "3. 'EPFL_PropaedeuticGPA'\n", "4. 'EPFL_CourseGrade'\n", "5. 'EPFL_StudentSection'\n", "6. 'MOOC_NVideosWatched'\n", "7. 'MOOC_AverageMaxVideosWatched'\n", "8. 'MOOC_PercentageVideosWatched'\n", "9. 'MOOC_NProblemsSolved'\n", "10. 'MOOC_AverageMaxProblemsSolved'\n", "11. 'MOOC_PercentageProblemsSolved'\n", "12. 'MOOC_Grade'\n", "13. 'EPFL_Topic'\n", "14. 'EPFL_BacGrade'\n", "15. 'EPFL_BacLevel'\n", "16. 'EPFL_CourseType'\n", "17. 'EPFL_UniqueTopicID_Anonymous'\n", "18. 'EPFL_AnonymousUserID'\n", "\n", "\n" ], "text/plain": [ " [1] \"EPFL_AcademicYear\" \"EPFL_IsRepeating\" \n", " [3] \"EPFL_PropaedeuticGPA\" \"EPFL_CourseGrade\" \n", " [5] \"EPFL_StudentSection\" \"MOOC_NVideosWatched\" \n", " [7] \"MOOC_AverageMaxVideosWatched\" \"MOOC_PercentageVideosWatched\" \n", " [9] \"MOOC_NProblemsSolved\" \"MOOC_AverageMaxProblemsSolved\"\n", "[11] \"MOOC_PercentageProblemsSolved\" \"MOOC_Grade\" \n", "[13] \"EPFL_Topic\" \"EPFL_BacGrade\" \n", "[15] \"EPFL_BacLevel\" \"EPFL_CourseType\" \n", "[17] \"EPFL_UniqueTopicID_Anonymous\" \"EPFL_AnonymousUserID\" " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# List the names of the variables\n", "names(moocs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Descriptive Statistics\n", "\n", "## Summary for variables" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " EPFL_AcademicYear EPFL_IsRepeating EPFL_PropaedeuticGPA EPFL_CourseGrade\n", " 2013-2014:2749 Min. :0.0000 Min. :1.690 Min. :0.000 \n", " 2014-2015:2694 1st Qu.:0.0000 1st Qu.:3.680 1st Qu.:3.000 \n", " 2015-2016:3871 Median :0.0000 Median :4.250 Median :4.000 \n", " Mean :0.1846 Mean :4.133 Mean :3.719 \n", " 3rd Qu.:0.0000 3rd Qu.:4.630 3rd Qu.:5.000 \n", " Max. :1.0000 Max. :5.890 Max. :6.000 \n", " NA's :1833 \n", " EPFL_StudentSection MOOC_NVideosWatched MOOC_AverageMaxVideosWatched\n", " SV :2199 Min. : 1.00 Min. :14.00 \n", " GM :1157 1st Qu.: 7.50 1st Qu.:44.00 \n", " MT :1128 Median :28.00 Median :45.00 \n", " MA :1040 Mean :24.46 Mean :48.95 \n", " GC : 970 3rd Qu.:39.00 3rd Qu.:58.00 \n", " PH : 649 Max. :85.00 Max. :85.00 \n", " (Other):2171 NA's :6339 NA's :6339 \n", " MOOC_PercentageVideosWatched MOOC_NProblemsSolved\n", " Min. : 0.00 Min. : 1.00 \n", " 1st Qu.: 20.00 1st Qu.: 3.00 \n", " Median : 60.00 Median : 7.00 \n", " Mean : 54.28 Mean : 10.67 \n", " 3rd Qu.: 80.00 3rd Qu.: 14.00 \n", " Max. :100.00 Max. :144.00 \n", " NA's :6339 NA's :7440 \n", " MOOC_AverageMaxProblemsSolved MOOC_PercentageProblemsSolved MOOC_Grade \n", " Min. : 17.00 Min. : 0.00 Min. :-Inf \n", " 1st Qu.: 17.00 1st Qu.: 10.00 1st Qu.:-Inf \n", " Median : 20.00 Median : 30.00 Median :-Inf \n", " Mean : 36.44 Mean : 37.27 Mean :-Inf \n", " 3rd Qu.: 25.00 3rd Qu.: 60.00 3rd Qu.: 0 \n", " Max. :142.00 Max. :100.00 Max. : 100 \n", " NA's :7440 NA's :7440 \n", " EPFL_Topic EPFL_BacGrade EPFL_BacLevel EPFL_CourseType\n", " CS-111 :1631 Min. :0.1260 HI :4346 CS :2947 \n", " CS-112 :1316 1st Qu.:0.7500 LO :4249 EE : 797 \n", " EE-102 : 797 Median :0.8083 NA's: 719 MATH:1404 \n", " MATH-111:1404 Mean :0.8062 PHYS:4166 \n", " PHYS-101:4166 3rd Qu.:0.8536 \n", " Max. :1.0000 \n", " NA's :719 \n", " EPFL_UniqueTopicID_Anonymous\n", " PHYS-101 2014-2015 T63: 336 \n", " EE-102 2015-2016 T29 : 300 \n", " MATH-111 2015-2016 T18: 295 \n", " PHYS-101 2015-2016 T46: 295 \n", " PHYS-101 2013-2014 T15: 288 \n", " EE-102 2014-2015 T29 : 281 \n", " (Other) :7519 \n", " EPFL_AnonymousUserID\n", " e2e988bc1a66ae2f50330fd60a0c2367: 8 \n", " 16af0f5438b6f7983392ab058a7e4eeb: 7 \n", " 29e1b05939960835d785c0aaa20ae388: 7 \n", " 35ad976f794b6523fe4dd3388b02ff5b: 7 \n", " 4abf1bcbc3198f4f3c2feba5bca4f6e6: 7 \n", " 4c46db8f7de7dd9b3521efad9efe0aa9: 7 \n", " (Other) :9271 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# For each variable, print some information about the distribution (if the variable is quantitative) \n", "# or about the distinct values taken by the variable (if the variable is categorical). \n", "\n", "summary(moocs)" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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AUDIT
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\n", " TODO : What is the mean and the standard deviation of the EPFL_CourseGrade ?\n", "
" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " Min. 1st Qu. Median Mean 3rd Qu. Max. \n", " 0.000 3.000 4.000 3.719 5.000 6.000 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "################\n", "# Begin solution\n", "\n", "summary(moocs$EPFL_CourseGrade)\n", "\n", "# End solution\n", "###############" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining new categorical variables\n", "It is sometimes useful to transform a quantitative variable into a categorical variable. \n", "\n", "For example, below we create a variable that reflects whether students used the MOOC or not based on the number of videos they watched and the number of problems they attempted in the MOOC. In R, categorical variables are created with the function `factor`. The variable `didMOOC` is given the value `NO.MOOC` whenever the values for the number of videos watched and the number of problems attempted is missin. In other cases, the value is `MOOC`. \n" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\t
MOOC
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3004
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NO.MOOC
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6310
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\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[MOOC] 3004\n", "\\item[NO.MOOC] 6310\n", "\\end{description*}\n" ], "text/markdown": [ "MOOC\n", ": 3004NO.MOOC\n", ": 6310\n", "\n" ], "text/plain": [ " MOOC NO.MOOC \n", " 3004 6310 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "moocs$didMOOC = factor(\n", " ifelse(\n", " is.na(moocs$MOOC_NVideosWatched) & \n", " is.na(moocs$MOOC_NProblemsSolved), \n", " \"NO.MOOC\", \n", " \"MOOC\")\n", ")\n", "\n", "summary(moocs$didMOOC)" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\t
NO.VIDEO
\n", "\t\t
6591
\n", "\t
SOME.VIDEO
\n", "\t\t
2723
\n", "
\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[NO.VIDEO] 6591\n", "\\item[SOME.VIDEO] 2723\n", "\\end{description*}\n" ], "text/markdown": [ "NO.VIDEO\n", ": 6591SOME.VIDEO\n", ": 2723\n", "\n" ], "text/plain": [ " NO.VIDEO SOME.VIDEO \n", " 6591 2723 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We consider that not taking the MOOC is like not watching videos\n", "moocs$watched_videos = factor(\n", " ifelse(\n", " moocs$MOOC_PercentageVideosWatched == 0 |\n", " is.na(moocs$MOOC_PercentageVideosWatched),\n", " \"NO.VIDEO\",\n", " \"SOME.VIDEO\")\n", " )\n", "\n", "summary(moocs$watched_videos)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\t
NO.PROBLEM
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7621
\n", "\t
SOME.PROBLEM
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1693
\n", "
\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[NO.PROBLEM] 7621\n", "\\item[SOME.PROBLEM] 1693\n", "\\end{description*}\n" ], "text/markdown": [ "NO.PROBLEM\n", ": 7621SOME.PROBLEM\n", ": 1693\n", "\n" ], "text/plain": [ " NO.PROBLEM SOME.PROBLEM \n", " 7621 1693 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We consider that not taking the MOOC is like not solving any problems\n", "moocs$solved_problems = factor(\n", " ifelse(\n", " moocs$MOOC_PercentageProblemsSolved == 0 |\n", " is.na(moocs$MOOC_PercentageProblemsSolved),\n", " \"NO.PROBLEM\",\n", " \"SOME.PROBLEM\")\n", " )\n", "\n", "summary(moocs$solved_problems)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Checking activity types\n", "Do people who solve problems also watch videos ? When using a MOOC, some students only watch videos and don't do exercices. But most of the students who do exercices also watch videos. It appears that almost nobody is *only* solving problems. \n", "> **Problem**: If we use these variables as two factors to analyse our data set we'll have very uneven groups. \n" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ " \n", " NO.PROBLEM SOME.PROBLEM\n", " NO.VIDEO 6555 36\n", " SOME.VIDEO 1066 1657" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# With two arguments, the table command cross-tabulates the number of observations per category.\n", "table(moocs$watched_videos, moocs$solved_problems)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " TODO : To fix this problem we qualify MOOC usage with three categories: \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* `NONE` corresponds to no use of MOOCs, \n", "* `WATCH` corresponds to students mainly watching videos and \n", "* `DO` corresponds to students doing some exercices." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\t
DO
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1693
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NONE
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6555
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\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[DO] 1693\n", "\\item[NONE] 6555\n", "\\item[WATCH] 1066\n", "\\end{description*}\n" ], "text/markdown": [ "DO\n", ": 1693NONE\n", ": 6555WATCH\n", ": 1066\n", "\n" ], "text/plain": [ " DO NONE WATCH \n", " 1693 6555 1066 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "#################\n", "# Begin Solution:\n", "moocs$MOOC <- factor(\n", " ifelse(moocs$watched_videos == \"NO.VIDEO\" & moocs$solved_problems == \"NO.PROBLEM\",\n", " \"NONE\",\n", " ifelse(moocs$solved_problems == \"SOME.PROBLEM\",\n", " \"DO\",\n", " \"WATCH\")\n", " )\n", ")\n", "# End Solution \n", "###############\n", "\n", "summary(moocs$MOOC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The order of the categories is a bit 'unlogical'. We'd like to have them appear in outputs and graphs sorted by increasing level of involvement: NONE, WATCH and DO. Let's fix this problem by reordering the levels of the factor." ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", " NONE WATCH DO \n", " 6555 1066 1693 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "library(gdata)\n", "# put the levels into a convenient order (for graphing, etc.)\n", "moocs$MOOC <- reorder(moocs$MOOC, new.order=c(\"NONE\", \"WATCH\", \"DO\"))\n", "table(moocs$MOOC)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Do people who use the MOOC get better grades ?\n", "\n", "## Looking at the means.\n", "Let's start by looking at the mean grade for the three groups of our variable `MOOC`. The `ddply` function allows to apply a function to a subset of the data defined by a categorical variable (`MOOC` in our case). The ddply returns a new data frame with the category and the result." ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 3 × 2
MOOCgrp.mean
<fct><dbl>
NONE 3.513959
WATCH3.828799
DO 4.445363
\n" ], "text/latex": [ "A data.frame: 3 × 2\n", "\\begin{tabular}{r|ll}\n", " MOOC & grp.mean\\\\\n", " & \\\\\n", "\\hline\n", "\t NONE & 3.513959\\\\\n", "\t WATCH & 3.828799\\\\\n", "\t DO & 4.445363\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 3 × 2\n", "\n", "| MOOC <fct> | grp.mean <dbl> |\n", "|---|---|\n", "| NONE | 3.513959 |\n", "| WATCH | 3.828799 |\n", "| DO | 4.445363 |\n", "\n" ], "text/plain": [ " MOOC grp.mean\n", "1 NONE 3.513959\n", "2 WATCH 3.828799\n", "3 DO 4.445363" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "mu <- ddply(moocs, \"MOOC\", summarise, grp.mean=mean(EPFL_CourseGrade))\n", "mu\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Looking at the variance ?\n" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 3 × 3
MOOCgrp.sdgrp.mean
<fct><dbl><dbl>
DO 1.1970954.445363
NONE 1.4909693.513959
WATCH1.3258023.828799
\n" ], "text/latex": [ "A data.frame: 3 × 3\n", "\\begin{tabular}{r|lll}\n", " MOOC & grp.sd & grp.mean\\\\\n", " & & \\\\\n", "\\hline\n", "\t DO & 1.197095 & 4.445363\\\\\n", "\t NONE & 1.490969 & 3.513959\\\\\n", "\t WATCH & 1.325802 & 3.828799\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 3 × 3\n", "\n", "| MOOC <fct> | grp.sd <dbl> | grp.mean <dbl> |\n", "|---|---|---|\n", "| DO | 1.197095 | 4.445363 |\n", "| NONE | 1.490969 | 3.513959 |\n", "| WATCH | 1.325802 | 3.828799 |\n", "\n" ], "text/plain": [ " MOOC grp.sd grp.mean\n", "1 DO 1.197095 4.445363\n", "2 NONE 1.490969 3.513959\n", "3 WATCH 1.325802 3.828799" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "sigma <- ddply(moocs, \"MOOC\", summarise, grp.sd=sd(EPFL_CourseGrade))\n", "#head(sigma)\n", "\n", "info <- merge(sigma, mu)\n", "info\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting\n", "To further investigate the difference between the ghree groups, let's plot the grade of the students `EPFL_CourseGrade` against the categorical variable `MOOC` that we just defined. We'll use three different plots: \n", "\n", "* boxplot, \n", "* histogram and \n", "* mean plots.\n", "\n", "### Boxplots\n", "\n", "Boxplots allow to visualise the distribution of the variable. The central line in the box shows the median and the edges of the boxes show the interquartiles. A simple tutorial for variations of this type of plot is available here: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization.\n", "\n", "From the plot below, it seems that the distribution of grades for people who did not use the MOOC (`NONE`) tends to be lower in the grade scale than the grades of people who `WATCH` videos or people who `DO` assignments. From the shape of the boxesm we also see that the distributions for `NONE` and `WATCH` are more symmetric than for `DO`." ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Plot with title “Grade by Activity Level”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Setting the size of plots generated with ggplot below. \n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "\n", "# Quick and simple boxplot\n", "boxplot(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade by Activity Level\", xlab=\"Activity Level\", ylab=\"Grade\")\n" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "image/png": 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HkHDhx455136ow7HI533303MzPTnZ4VTz31lCRJK1asaMxJmpKnFWiF0WicNm3a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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Setting the size of plots generated with ggplot below. \n", "options(repr.plot.width = 8, repr.plot.height = 5)\n", "\n", "# More sophisticated plots with GGPLOT.\n", "# Tutorial: http://www.sthda.com/english/wiki/ggplot2-box-plot-quick-start-guide-r-software-and-data-visualization\n", "ggplot(moocs, aes(x=MOOC, y=EPFL_CourseGrade, fill=MOOC)) +\n", " geom_boxplot(notch=TRUE) + coord_flip() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Histograms\n", "\n", "Histograms give a more precise representation of the actual grade distribution. Below, we define bins of 0.5 to represent the frequency of the different grades. The vertical dashed lines represent the means of the distributions. Notice that we reuse the dataframe `mu` that we defined above. We see indeed that the `DO` group is less symmetric than the others." ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "image/png": 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vV6ze4l8xQWFtbV1ZndReax2+25ubnNzc0+n8/sXrqCVrkuibUCEyfFnZ7yUZdE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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Tutorial about generating such a figure\n", "# http://www.sthda.com/english/wiki/ggplot2-histogram-plot-quick-start-guide-r-software-and-data-visualization\n", "options(repr.plot.width = 8, repr.plot.height = 5)\n", "\n", "ggplot(moocs, aes(x=EPFL_CourseGrade, fill=MOOC)) +\n", " geom_histogram(binwidth=.5, alpha=.5, position=\"dodge\") + \n", " geom_vline(data=mu, aes(xintercept=grp.mean, color=MOOC), linetype=\"dashed\") \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean plots\n", "Mean plots represent the mean along with the confidence interval for the mean. There is a 95% chance that the confidence interval contains the true mean of `EPFL_CourseGrade` for the population. " ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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CBWKIQAAIQQ8ujRo82bNx86dKhr1660s4BYYWgUAIDU1ta6uLhYWlo6ODjQzgLi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\n3/3ud9a78Tz/7rvv/vnPf+Y4bvjw4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"text/plain": [ "Plot with title “Grade given MOOC activity”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "\n", "# plotmeans is defined in the gplots library \n", "# make sure to load the library by executing > library(gplots) before. \n", "plotmeans(moocs$EPFL_CourseGrade ~ moocs$MOOC, main=\"Grade given MOOC activity\", ylab=\"Grade\", xlab=\"Activity Level\")\n" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "\n", "# Alternate form using the package ggpubr\n", "# See examples here: http://www.sthda.com/english/articles/24-ggpubr-publication-ready-plots/79-plot-meansmedians-and-error-bars/\n", "\n", "ggline(moocs, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n", " add = c(\"mean_ci\"))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# ANOVA - Analysis of Variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Does the grade of students (EPFL_CourseGrade) depend on students' type of MOOC interaction (MOOC, a categorical variable).\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: ANOVA a.k.a. ANalysis Of VAriance \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ANOVA allows comparing whether one variable has the same mean in different groups ? The formula to specify the test is done in tow steps. First we define a linear model with `m <- lm(quantitative ~  categorical)` and then we do the Anova of the model `Anova(m)`.\n", "\n", "* H0: mean_1 = mean_2 = ...= Mean_n\n", "* H1: mean_1 != mean_2 != ... != mean_n\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the Analysis of Variance (ANOVA) to compare the mean of a variable across several modalities of a categorical variable. In the example below, we compare the course grade (`EPFL_CourseGrade`) across different modalities of MOOC usage (the `MOOC` variable takes three possible values: `NONE`, `WATCH` and `DO`). " ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A anova: 2 × 4
Sum SqDfF valuePr(>F)
<dbl><dbl><dbl><dbl>
moocs$MOOC 1181.668 2291.59361.479869e-123
Residuals18866.1759311 NA NA
\n" ], "text/latex": [ "A anova: 2 × 4\n", "\\begin{tabular}{r|llll}\n", " & Sum Sq & Df & F value & Pr(>F)\\\\\n", " & & & & \\\\\n", "\\hline\n", "\tmoocs\\$MOOC & 1181.668 & 2 & 291.5936 & 1.479869e-123\\\\\n", "\tResiduals & 18866.175 & 9311 & NA & NA\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A anova: 2 × 4\n", "\n", "| | Sum Sq <dbl> | Df <dbl> | F value <dbl> | Pr(>F) <dbl> |\n", "|---|---|---|---|---|\n", "| moocs$MOOC | 1181.668 | 2 | 291.5936 | 1.479869e-123 |\n", "| Residuals | 18866.175 | 9311 | NA | NA |\n", "\n" ], "text/plain": [ " Sum Sq Df F value Pr(>F) \n", "moocs$MOOC 1181.668 2 291.5936 1.479869e-123\n", "Residuals 18866.175 9311 NA NA" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# needs library(car)\n", "\n", "m <- lm(moocs$EPFL_CourseGrade ~ moocs$MOOC) \n", "Anova(m)\n", "\n", "r <- residuals(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "This is the way you report the ANOVA in an article.\n", "\n", "> We conducted a one-way ANOVA to test whether the course grades differ for different categories of MOOC usage. There is a significant difference of course grades across different types of MOOC use (F[2,9311]=291.6, p<.001). \n", "\n", "Beware, that since we did not randomly assign subjects to experimental groups, but rather students chose whether they use the MOOC or not, we can't conclude about any causal effect. It is possible that better students are inclided to use MOOCs more than weaker students. Hence, the \"effect of\" the MOOC would be due to this hidden variable which actually explains the difference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Advanced topic : There are different ways to run anovas in R. They differ with regards to the type of Sum of Square that they report. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following http://goanna.cs.rmit.edu.au/~fscholer/anova.php the Type III Sum of Square is more adapted to interpret the contributions of the differnt variables. R and anova report Type I sums of square.\n", "\n", "Here is an explanation about how to obtain Type III sums of squares: https://www.r-bloggers.com/anova-%E2%80%93-type-iiiiii-ss-explained/\n", "And some explanations here: http://prometheus.scp.rochester.edu/zlab/sites/default/files/InteractionsAndTypesOfSS.pdf\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Which groups differ among each other ? Now that the ANOVA tells us that the three types of MOOC useage do not lead to the same grade, we want to know more precisely which categories are different from others.\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: Pair-wise t-test\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A pairwise test allows to know which groups differ from each other. Because of repeated testing, we have to adjust the p-value by dividing the .05 value by the number of tests. In our case, the tests show that all groups differ from each other when taken 2" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tPairwise comparisons using t tests with pooled SD \n", "\n", "data: moocs$EPFL_CourseGrade and moocs$MOOC \n", "\n", " NONE WATCH \n", "WATCH 6.7e-11 - \n", "DO < 2e-16 < 2e-16\n", "\n", "P value adjustment method: bonferroni " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Checks which group is different from what other group in doing 2 by 2 tests.\n", "pairwise.t.test(moocs$EPFL_CourseGrade, moocs$MOOC, p.adj = \"bonf\") \n" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Means" ] }, { "data": { "text/html": [ "
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\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[NONE] 3.51395881006865\n", "\\item[WATCH] 3.82879924953096\n", "\\item[DO] 4.44536326048435\n", "\\end{description*}\n" ], "text/markdown": [ "NONE\n", ": 3.51395881006865WATCH\n", ": 3.82879924953096DO\n", ": 4.44536326048435\n", "\n" ], "text/plain": [ " NONE WATCH DO \n", "3.513959 3.828799 4.445363 " ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Standard Deviations" ] }, { "data": { "text/html": [ "
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\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[NONE] 1.49096929439005\n", "\\item[WATCH] 1.32580239254368\n", "\\item[DO] 1.19709461657678\n", "\\end{description*}\n" ], "text/markdown": [ "NONE\n", ": 1.49096929439005WATCH\n", ": 1.32580239254368DO\n", ": 1.19709461657678\n", "\n" ], "text/plain": [ " NONE WATCH DO \n", "1.490969 1.325802 1.197095 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "cat(\"Means\")\n", "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, mean)\n", "\n", "cat(\"Standard Deviations\")\n", "tapply(moocs$EPFL_CourseGrade, moocs$MOOC, sd)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here is the wording for the article. \n", "\n", "> A series of pair-wise t-tests with bonferonni adjusment for repeated testing, shows that the average grade for students who did not use the MOOC (m=3.5, sd=2.5) is smaller than the average grade of students who watched videos (m=3.8, sd=1.3) and smaller than the average grade of students who did the assignments (m=4.4, sd=1.2)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Assumptions\n", "Is it ok to run an ANOVA blindly as we did just before ? \n", "\n", "Not really, we should have checked the assumptions for ANOVA first.\n", "\n", "* Normality of the residuals\n", "* Homoscedasticity of the residuals = the error distribution should be the same regardless of the category.\n", "\n", "### Visually inspecting normality Assumption\n", "Testing normality visually with quantile plots. If the variable is normally distributed, the observations would follow the line drawn by qqline. We see from the plots below that the distribution of the residuals of our model used for the Anova departs very strongly from a normal distribution.\n" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "image/png": 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El4poKDsXoxtjoGjk8YH5CQCrOi0JgVNQnfECuISE/L2QLjxieUAUhod2hJeEqs\nYDadWuiFceMTygAktDuUJDwtOhZ12aYzGQJqJDzZ6n/6FA4SUqN8zcThE9dqHqqIjoRnRQ5e\nTKMKuqJqTxjQqekHSEiLYwUIpbJ/v/9ozIeOhCIHSR0Y2QhVEvZ4XZ/CQUJaDKvzTjE++qxv\nuMZ8aEhYYuun6KVQJeE3jRf/oUfhBkn4y4D+0lyLthBWSTQJMz7kJ09pfeKDhoSeaAdlPldu\nbYwbqVcGBkm4xjNRmmHofcIqiSZhcvAZmHWp8pIT+0agIGF6tIPTTC/eCFRJWCigsXCjJEwi\nLNgBEoboEuwe/WGZPeQSm+CbL+EV0Q62NLt0YzCuG3wZgIS0+KLBv38t2VfYcI+85NaR8K9o\nBweZXLhRKJfwzm0Ylx/VZdQ3kJAW0X/KxEQy+kYwW8JyV1TFx5pbtnEolxAtw/go+lCPwkFC\nWhRGQUwkw1STJdwffWF0qKlFGwlIyJNoEspCRt8I5kr4d/TPwvVmlmwsICEPSCgBsW+En8Lj\napn7AFGNKAdrmVmwwYCEPAkn4YcjLy/giJWG2DdCfsQFrXf7lXAsykF7jfgSBxUSTt6w4V00\nkz9M0Vg4SEiLeSjrorgSEvtGOBsea9nMw9GN0Qej/zWvXONRIaGcC2vyAAlp0aBfiS75mCjh\nTdF/eO1MK9YMlEv4ShQaCwcJaZGyQnbSsh2nyAvNk3BetINOaDAaBdys50k0CbvNlJ30KPqE\nvNA0Cf+MdnCNSYWaBUjIk2gSbq2/UW5SS0j4dbSDGeaUaR4gIU+iSVh+LwrU44if1BISip5e\nOmpOmeYBEvIkmoST0PkDh3LET2oBCQ9GN1ZzTmu1MCAhT6JJWE3+8+il206SF5oi4cfRCqLH\nTSjRZEBCnkSTMPVdffIxQ8LvoxVkNHeLY0FAQp5Ek/CKR/XJxwQJHxXtB1caXh4FQEKeRJNw\n//kvH9YjH8MlLM8VOfiEwcXRASTkSTQJ9WrzZLSEy8Sd3X9hbGm0AAl5Ek1CvTooMVjCbSIF\n0ShDC6MHSMiTaBLqhcESekUOPmZoWRQBCXlAQnUYKmFZNZGDSwwsii4gIU/CSXhk1u0DODRm\nY6iE3UUO3mVgSZQxVMLtS+fOWbqdvBwkpMWualWZBqkooLXPQCMl3B+toPt34wqijoESrmgU\n3H5NiPd2QEJa9L7krH8nfr/ueo35GClhlSgHmxpXjAUwTsIiptWMtZs3r52ex5AeXgMJaVHr\nTZz0PcbrOmrMx0AJJ/ANZIIOrjWsFEtgnIT5fUuDM6W9SAMGgIS0SNqEcz7DuDhFYz6GSXim\nZtR+8P8MKsQqGCehf7Uwt9JPSAIS0qLhW7jDkxh/WV1jPkZJODL6fJDWkNymYZyE2XOFuWdy\nCElAQloMnYDnuW+9J/sWjfkYI+FH7mgHndWfjBTGSTg6bRHfmVDxwgDpuRmQkBZ7NuFz4zIz\nBx3RmI8REs4VKYiYGF3cOATjJDzaCSXldS/I86OuxwhJQEK7o7+Ev9RAYu7RuwTrYeAtirJl\ng/Jzc/MHF1V4BKwk3GtlaoJJuP2INFoHraaH7hKezazgoFfnAqwIhRYzrSJb+BmdshRjUQm3\nICIfElYxkjMvjn1a8x1wvSVcl1Rx06yOv5LtoSDhwfBIBimrdMpSjEUl/Aj9e6s0afJ7AdWD\nmXlnMT7Xkf0LzzmgMSudJexbUUHvx7rmb1EMl/AI6YQQJ9o54UfoM8KSDHMlLOCuib6Exux5\nPWW0xqz0lXAafyEmoqDPoc8PVsQ4Cb/4m31Z3hihFsT2Dtok3DZqpDRXeghrgIQ8Oc+zL1fV\nOofx+IYas9JVwvI0zkFGsJBJhCNRHuMk5EZvWsPk3Dokw/MVIYk2CZ+q2l+a80k1BQl5vFwv\nTxlD2JfXSM0o5KKnhOWTgvKF+jfsXaZf1hbHWAk7NjyE8U9ZvQlJNErYibDgCZAwJjWfw3gn\n4tpSvJ2mMSsdJZwp6lxUaysCW2GohKVuvtXMJFLjKJAwiMkSXtH+NJ6I9rBzj2sdWUU/CceJ\nLsjo1BmcTTBUwlPBoTsWks7RQMIgJkv4AarZFl3JzXWwTLO1rfyFmNDpILNIp1xtgoESPvDe\ne1Ve5+amVSMkAQmDmCwhfrN9o5vZ8wS8u7HWgvWS8G/+4cHatYMXRYv1ydQ2GCghxwhu7oaL\nCElAwiBmS6gfOkm42cvfm2DS05GLQVfpkqeNME7CLRzfsTNne80jJAEJgyS6hMWp3K0J1kJP\nde7q6Nd65GknbNzRE0hoNNU4qX0AACAASURBVB9d227YXm5mdW1CCl0kPJrHqucWbg9639Eh\nS3sBEvKAhBJs9XqbeFKXs3PLSFtUDwk3BYLNZHgLvfeUaM/RboCEPCChBNfl/oAPXOFeaqyE\nR9NY/5IucrlcqY4bjF4mICEPSChBrRnsS9ko92tGSvhpevCuxBVcczVXjP4xHQxIyAMSSpD0\nCvdaPsq12DgJH2HV82cxwYNRz1sac7MpICEPSChBk0n8pHy4q49BEu6tx+8Gq/j588HkE5oy\nsy8gIQ9IKMGw1sFp+bAKQ6hd11AA3a6lgFXcJVEPYpjcJAYx7vla8rIzICEPSCjBR1fvDc6U\nj+8gWrDxBQH0oIb83+GbbLubsC9+F2J6ntOQl60BCXlAQnVoORw9lBp8fLAt4+Fm5jhxNHp5\ngIQ8ICGRsh0x+hzUIuFcj4tBl1VLQUkBj8v1ovqMbA9IyAMSEjmKPiEv1CDhrzl+j98/4iJ+\nINDUN1Xn4wBAQh6QkIhBEv43w83fl2h2I0KuQWpzcQYgIQ9ISMQYCZe4WAW9jI/rbbvKy4nT\nk4UkICEPSEjEEAnfZpLrX/y4p2oVxs28pi4LBwES8oCEREq3nSQvVCnhsy5Xcrv78foLUUqt\ngMp6OQiQkAckVIcqCcvv899eh6nX9TeMk6+6kPSUVAIBEvKAhOpQI2HJgMz/G854s12Bl0+6\nGtVNqH7VpAEJeUBCdaiQ8Ei3Wv9d73H3rtKsqmuAz1X1ZwOqZTNAQh6QUB3KJfzpvPN/KW7q\nRsjrymAQU/CLEdWyGSAhD0ioDsUSflvn4mN4oOe2f16ugZi0ajEGKkkgQEIekFAdSiXclN6v\nGL+BGKbRS2Wz0x8hRTDBAAl5QEJ1KJRwsW9cGV7vTuvX5Mkqo4+i+g8bVC2bARLygITqUCbh\ns26uw4zzup//R+1O/3LNQjX/NqhaNgMk5AEJ1aFEwtI7/Vz3FQfQYs+BAwN9yO3abVi97AVI\nyAMSqkOBhCU3ZPLD7n6Pfruow258rmXaOMOqZTNAQh6QUB3yJfy7S/3vuemp1a66OVWZxrVR\nzzPG1ctegIQ8IKE6ZEv4Y/O8A9z0hUyE0AUjfAXdqidqt06VAQl5QEJ1yJXw29o9+FuC85Pa\ndP6zI5PRDeV8aWS97AVIyAMSqkOmhBuqDDnLTQ8EznffeQ6/7r6++d2G1stegIQ8IKE65En4\nqncc/9juO6loCEpv/Qfu/PjNtxpbMVsBEvKAhOqQJeGzHr5H0R/6uQJoecYLF/TD3R69ILEG\nxI6N9SU8vpXAHRcS1rCdhFVmEr7iN1YfokiGhKW3+9/mph+nNM9c7Hd1bbbMsy/5Ls9Ow+tm\nH6wv4RBEIp2whu0kdBG/4tOENaxCfAmL+2UFu8c4b+QjPfD0JG/7NJSd5nvO8KrZCOtL2P+2\nI9JcnEZYw3YSMuMJX7GrTkPCG0ZcCf/uXD+4z9uD9j97Hi5/mvGlomrDdxlfNRthAwlJflzq\nHAknEhZcYncJf2jW6iA/c3AA6nmnmz33bT28Q1sTKmYrQEIekFAdcSTcktPzH35mdaANGtY8\n1T1ySXLT9P+aUTM7YRkJF08k0LwfYW2QkD6xJVyfdjN3e/D0nIH+i4/3uPhw/0Y9Ut1DfzWp\nbvbBMhI2Pq+nNEl5hLVBQvrElPAV7zhukJedDWpf6q1f+/2mNW9ETTI3mFU1G2EdCV8iJKoD\nElqXWBJO9SzgJuVtrjv5XPOSm5qcnDvQNeQvs2pmJ0BCHpBQHWQJS0enrOJnvkU/4XeqnD3s\n+RgfRDtMq5mdAAl5QEJ1ECU8eU3Wp+zk3Bv39U0uw/9kPI3rvlp2a/PEHYMwFiAhD0ioDpKE\nhzs14G4F7muVeXUH1PYgftt3me+2C6t8YWrlbANIyAMSqoMg4f6mbd9asOpIWZvL/8Znqtct\nwHhXe3f+nb+ZWznbYKiE25fOnbN0O3k5SBiEKOH5bUcSeJewhgEc3krujyki4fZhHa+cGWrq\nujm7XYOkFlWqFrq4O/Ur3OiZtwe5XzW6nvbFQAlXNAq2f2yykpQCJAxClDCzen9pml5LWENX\npjRoshBP9yL3JFKKsISzPddMua9Wc35fty6tb8qYE/jcv9zV+GXbPZnVr/zK+OraFuMkLGJa\nzVi7efPa6XkM6UkdkDAIWcJuhAX3mCHhUtS4i2s+6jetAL1OSCJIuNuzhH09fsFA9nWhZ+KE\nDvynPT2l3OS09wPjK2tnjJMwv29pcKa0l7ix4Olw++TUaAlnExox12pBasAdICyYhAgLPkNv\nEpa4hhMWVG9LWNAxg7BgHENY8D5aS1hCbMCd0Ymw4E4zJOzY7Rx+ysd6Vdr2YkISQcIprfnJ\n6qQzeKrnedwzuOt8mVnMTeaknzK8rrbGOAn9q4W5lX7RgrzIkzoLIp+2Ij7OA0gwQFkwVJH5\nHMY/oSJ2blomIYkg4dg+/GQ3+mUk98t65b3821fTffd/9vE4z8vG19XWGCdh9lxh7pkc0YLD\n+wW2RX16ZD+BHd8TFuzZTlrla9KCb4hr7COVvpOwYPe3hAX7iIWQF5BK/3Y3aRUzuipLeg3j\nE/xg2Ys8hCSChE8FD3bW+q6syh1zP9GE787w6gHv5rk97dYZX1V7Y5yEo9MW8RfLihcG7lC2\nJmAN6s3AuGQQ1032dPHP6Evh1vUouMvD37u5HebpCzMb8r1q/13n4i0lu4ek7GDDD72LxsU4\nCY92Qkl53Qvy/KgrDIBlS3r1EeZu7C5aMD7cup6ZEvpoinvgvMfreFv/GXz7wzXsIXP7zWbV\n1OYYeIuibNmg/Nzc/MFF0FbJnmwtCs2UXruQkCRyffvzG1rmp/Q4Hl7y12cwBK9cqLaYAexO\n9E2mlSm3nqNXEzsDEgKxKdsR4wZDlIT/9hYaXxlnAhICsTmKPiEvDEtYXuh5wZTqOBGQEIiN\nLAnPjUhdTU4FxMYyEm7+ktTJL4nP1ildY+sqxWts/FjpGpvfV1zI+5uVrvGxeeNrxpZwVrA6\nnbKWiCu4fv4SBbz4nJLUz7+gJPWCl5SknrdQSeo5ryhK/TkhmndZRcIU2m1Q7EVDQ4MRTUwJ\n69PeDs7gStnRMFZCYgNuIsSxKIj8gb5Xuso19ypdo4jUsptM5jtK1zClAXeQ0m0nVaz1cE8l\nqceQetSTZPBwJamVRbDzk0pSt5ynJHXt15SklgYklIXTJFQHSFgZkJADJDQNkLAyICEHSGga\nIGFlQEIOkNA0QMLKgIQcIKFpgISVAQk5QELTAAkrAxJygISmARJWBiTkAAlNAySsjPUl7C5n\nrEIRCxVFjuNETcXdz474l9I1PmmtdA3c6lOla8wcqbgQc5k/REnqp8YqSX3fI0pSK4tg/38r\nSX3ZciWpO+gwIhU04AYAyoCEAEAZkBAAKAMSAgBlQEIAoAxICACUAQkBgDIgIQBQBiQEAMqA\nhABAGZAQACgDEgIAZUBCAKCMoRJu7V0vKavjUiWrfDyyeUrt3tviJwxzeEK3NLREfvpjt+f4\n2xTFT6e+BDXfQs22Mh1ldVS0EZRsY0URVBY8ZYHTK2aGSlh0/fQlC7qgKfFThrk6b/Jr02r7\nYnRNW5EdWT37KFCkrHPanNV9mBUK6qSwBKzmW6jZVqajrI6KNoKCbawsgsqCpyxwesXM+MPR\ns40bKEi9l3vZ71XweGsZxhsUKLIMLcK4tFUjBXVSWAJW8y2CKNtWdJBdR0UbQcE2VhZBZcFT\nETgdYmbCOWGXpopXadJOUXIligxK4sb7noG2G1ZCGIXfgkPFtjIdZXWUvxHkbmPFEVQcPGWB\n0x4zgyUsOfHzVJfiPi4OeocpSq9kK+fnca9rkbIjeTUSKv0W6raVuSiuo4KNIHcbK46g0uAp\nqLM+MTNYwkEI+eYrXansytS9ilZQspVzC7jXzWiOYSWEUPwtVG0rk1FaRyUbQe42VhxBhcFT\nUmd9YmaMhKVHWdijcbz7k+UD0QxFq+DyUW5ZvXxE1lAj4VzZaygtIYjcbxFB/rYyHWXxVBRK\n5VFUHEFlwVMUOH1iZoyE27ihoXaE3vTzHlayCrsR5B1oRAqx4OGo7G8hRt62Mh1l8VQUSuVR\nNPZwVHngtMfMGAlPfsIijIo+DW1VsEr5cJfMTRYpRNGFGX8x+zrd4Asz8r+FGHnbynSUxVNR\nKJVHUXEElQRPReC0x8zQc8JS/qXA/bf8VcqHuV5VXI6SrbwcLWTrlKfkFoXCErCqb6FiW5mO\nsjoq3Qhyt7HiCCoInrI66xUzQyW8bsi/Xp3WDj2oYJXxqM8yFiVjpa9cNhmNW7asTF7qsk6B\nWSt7KbpZr7AErOpbqNhWpqOsjso2gvxtrDCCioKnrM56xcxQCRd2z/Zkdld0iN0hONRwbQWr\npAdXKZaZ/OjobH++omZrSktQ9S1UbCvTUVZHZRtBwTZWFkFFwVNWZ71iBg24AYAyICEAUAYk\nBADKgIQAQBmQEAAoAxICAGVAQgCgDEgIAJQBCQGAMiAhAFAGJAQAyoCEAEAZkBAAKAMSAgBl\nQEIAoAxICACUAQkBgDIgIQBQBiQEAMqAhABAGZAQACgDEgIAZUBCAKAMSAgAlAEJAYAyICEA\nUAYkBADKgIQAQBmQEDCMEyjMtkKFf2mfFZ7jJrPQCcnF0Z9vHVDTm9PvK6W5krI2H5AQMIxS\nbpixFlnc6zGlEs4IjqO0pOVpycVRBr3sbv7syvmtXS8ozBUkBBKFguA4Y3IkPBU1PyP2YGYR\ng7Z5unCenr3CvTl+CdG5goTUWIE2cpNn0D7aNUkQwhL+0jtQY8Rxbn7fTdV9zZ/n5r68NC25\nwyp+8Tc9A60ii+7hD2IPhEzZN6SGr86gk3jPsKbJdfrswdEG3cTs4qcHPddjPCqHm30CsQed\nkbSF6H+Xp/BFi3INZS3U5fdbavuyu39t4pYJk3ASnq0+mJu07kq7IolCWMKWE1cUekazs3uz\nGr+0ZjwzlXXQl7+0qCezlFvceOnPOyKLjkxCu378sTRoyq7MOnPWLe5/CG+6+61Nb16S8Vu0\nhNl5oZmuaWXREkbSFqIW7/z+n3S2aFGu/EukLgX1F330zv0bzd9ACSghHp/C/iR+w417DphB\nWMIF7OuwVPalT8bv7OuYwAnco+o/7Jnj+bXL2cWLsWhR6MCRN+W6tN+iMjxbdWqUhGdQ79Dn\nQ9GhaAkjaQvRO+zs3VzR0bnyL+ECy71TDdsE8Ug8CbejlzEem2qV8wHHE5bwEPs6Fx3GZSn8\nscgm9FGpbxg3Nw3tZBf/wc5FFkXrUpZ0cyiv0ucuqpHkZ26JkrAkLOHNbN5REkbSFqJj7IcL\n2MWVJIwqsFONGVtLjd4Y0iSehLhNF3ym6i20a5EwiC7MvMSekB1Dbj+LDxUdRQ9xHy5Bn4YW\nRxZF63IMTQrldZf7iU+/29lggOhwtFVopmuy6JwwkjZSdCUJowr8887aKGvMceM3SGUSUMLZ\naO9y9pcPMIdKEpb6B+/kOS7aE3JzkUXSe8LMW7nXVJGEg5g9/PRX79WseVW52fs4CSNpY0gY\nVSDL/hm+UcZuDGkSUMLDvoevaVROuxYJQyUJ8XV1j4aW9Yw6J+Q/iCyag45wE/E5YeY97Mv7\naID4FkUBJ9a5q9E69mOGXav8Al7CcNqooqNzDWYdLpCnSycjNkE8ElBC3KeG5wnadUgcKku4\np1qz+etXTOsqXB1FS8O3ESOLPkQPfbHlbOjqaEadueuXDjyEB2V/Wby+bmBAhZv1581ZtaAN\nmszOH0wadHD/6AxOwkjaqKKjc+VfwgX+ceEzqz98gs4fRiJK+B5y/Uy7DolDZQnxz7fV8Vbv\nMp2d+6JnIKnDShy5lx9ZNLGGK3yfcO/Aat7cIafwkaHVkjusaymWEG+5gU3qe5+f39g2uU7h\no5yEkbTRRUflGsxCKPDkyJaB1PP/ReUIKRElBJzHm8xY2lVQD0gIOIJn0cO0q6AakBAAKAMS\nAgBlQEIAoAxICACUAQkBgDIgIQBQBiQEAMqAhABAGZAQACgDEgIAZUBCAKAMSAgAlAEJAYAy\nICEAUAYkBADKgIQAQBmQEAAoAxICAGVAQgCgDEgIAJQBCQGAMiAhAFAGJAQAyoCEAEAZkBAA\nKAMSAgBlQEIAoAxICACUAQkBgDIgIQBQBiQEAMqAhABAGZAQACgDEgIAZUBCAKAMSAgAlAEJ\nAYAyICEAUAYkBADKgIQAQBmQEAAoAxICAGVAQgCgDEgIAJQBCQGAMiAhAFAGJAQAyoCEAEAZ\nkBAAKAMSAgBlQEIAoAxICACUAQkBgDIgIQBQBiQEAMqAhABAGZAQAChjeQmXIYR2Rt5WRWiU\nkvQi5uYnI9RMv7oBcoAIxoOWhDsQB5PadMgXsRPqGMIX+TLVh/BKrsb7+Vm++v/h5q4O57jr\n7raZnqwL7v+Bnb8CIf/fwY+HsivtE6/tCCCCukFXQg7X6zETbmrXrt1PkbdaQtgVoUYrP/xK\naVUFDrq56j7Mz/PVP78UR0JY9iAT+kKep4O1mMenPBlAqHuFtR0BRFA3aErYqO9VNdlJHSXr\naQlhLkIjo98fV1Iwxk/yAapTxs0H/wJfxpEQjud+Jttc24r7/DF8phpCF/Brvcq+X1xhbUcA\nEdQNmhLeiXFxI3Z6jPvgs0H1/KmtC4/yS5dfnu1Jze1x36FISEoea+hr+GhJMISz2A+5lH6E\nHsL4zzFd6wQ8WZ2mn8aR9FFZBBka+pm7i0/y3bMt/QXspx8OqOtPbTme/6V+g/t8ZuOklotw\nycP1fM3mi2pczla1KZtijVB9hGqdCodwM/s28xN25j8pCLl38RH9jkt5MULppyus7QgggrpB\nWUJuC3i5Y4JHQocCdfewb54VDnS2hUNSdjn/Qc+McAi5wAdDuE1I3vZkOH10FkHEIezB/u+G\n8T2hDwPc2QEXwu7829nBybPRNf6Q/WBFfYT6CdVn9wFPhEN4K/vBM3y6h9i5CXyC+9h3PzPB\nH37R2o4AIqgbdCUs3piG0EAc3Hq3Lnu5WfAwvQFCNy5f9sxNmZEQzuPCO26gC4VDyB2KhELY\n9P4X3n3zdnZjzQinj84iyPtTqiDUYcqUjXwSlDvyjmF4ETvT6IE7ktkY/hqsBGo7wMdN2gzw\nskGKrvEQ9ofyzAMI+Q6Fqj8zHaX9KYSwYeiPCuMf2bn2GF/Ars5+lSfYd5srru0IIIK6Qf/C\nzJXcUUnrYCS/Y9+vxbg6Quu5ROfOhENyPrsJ2G8/OxJC9kAiFELuKL305InLELoknD46C4Ha\nobMRLkkev73ZXKuyxa9iP3gkGMKryvgfwsvKcCE7+SWy8jE2ziP4as8KVf+VqQjdLoSQXVo1\nmLCMjX0tjJ9D/MW3JmxRldZ2BBBB3aAuYTvumu9xFOFJjK9hJ/WvGL+Mi1IwJKfZH8lb2Hcn\nIyEsxkII8duXVwuu2zQcwugsBKJD+Co38w87M5ybYVfvEQzhKoyXsJPlGBexk+2RlbmQ/B8f\n9LxQ9V8pzkWeXZEQVgsmDIWQC9oN+NNQ0MRrOwKIoG7QlDD/7qvZyOQcxPinqBDey75tEZzN\n2SWE5Hf29QFuvUA4hOy5cqmbD+Fj4XXrhUMYnYVAdAi3cDNcsfwlZ3bTtgmGcHtw8dcYv4ui\nTkf4g5M65Rg/jfiDEz6E3HWz3pIHM+0wf/jiPzoidPgiXtsRQAR1g/KFGe5EoX/wd3TMj0GO\nsEvLP585sisbn2sIv6PcMc3fGO9FXAhLUhDqursU94kOYXQWAtEh5K+BS/yO7gwu3oHxClEI\nIwdffCbBEJbl8yf3lU/r78bBE/lZ6cET+QprOwKIoG5QlrD8ouCPVit2Q3CXp/HZF85iHDz1\nfTI6JOIzCu7Wzfu4/FY+hD+zr7PZo4ec6PTRWQhUCqHEGQUphOOjgpB+OhRCvIF/z4XwK3aa\n+Sk7s4a7wM3/DTVCiJ3nL2lXWNsRQAR1g/YtijXstBfGS9lJ6wUrF46qzp0ptG//yMur/t2M\nv1sa2t5z2Endu4RrazvZSVq/NogP4ekk9uRh0avcu3rh9NFZCFQO4SJ2rtGD0dfWCCHkbt3W\nHMDRDXG3bkMhxJcLIcR3sTNM2+v4W72P8utEbu5WXNsRQAR1g7aE+EJ25huMHxaaDHEhbBea\ndb8b3t6lPflPOlQJhqEX/+5SL39GMZF/U/Wi6BBGZyFQOYR4QihZ+C4TIYTcZ//i544mc42Y\nhBBudwkhLJsofAP3U8F1Is2cKq7tCCCCukFdwveDP6T4y6GNklMadCv8kp1fNrxtDZ+//k1c\nI0FhexcXNvDWvf9kqNHTqXE1fU2nnA1d4H6hVXLVfnsHRYcwOgsBiRDiD26o40tpcdeP3HyM\nEF4RuT80hGvOK4SQP5MINf/dOT4/w5PZ/r5wE9+rUKjBb8W1ddyO9IAI6oblH2UCAKcDEgIA\nZUBCAKAMSAgAlAEJAYAyICEAUAYkBADKgIQAQBmQEAAoAxICAGVAQgCgDEgIAJQBCQGAMiAh\nAFAGJAQAyiiXcPvSuXOWbo+fDgAAWSiVcEWj4MPHTVYaUh0ASDwUSljEtJqxdvPmtdPzmBXG\nVAgAEg2FEub3LQ3OlPZqq39lACARUSihf7Uwt9Kvd1UAIDFRKGH2XGHumRy9qwIAiYlCCUen\nLSrhpsULA3cYUR0ASDwUSni0E0rK616Q50ddjxlTIQBINJTeoihbNig/Nzd/cFG5IdUBgMQD\nWswAAGVAQgCgDDRbAwDKQLM1AKAMNFsDAMpAszUAoAw0WwMAykCzNQCgDDRbAwDKQLM1oCJt\nMxOIjNR0g3IeKHuDQ7M1oCKBJzYkDOvbN3zfmJxHXiB7g+vVYubAVoENZTplCVAi8B7tGphH\nYcb++IlUMd18CVuhMPN1yhKgRAJJuNHzjlFZGy7hkUonhCVHBFITJ4QOJXEkPFD9fsPyNk7C\nL/5mX5Y3RqjFWlKSxAmhU0mYCJ7t3PGsYZkbJyFahvEaJufWIRmerwhJEiaEjiVhInhX9kH8\nhxfJgWFxub1+f0p6ZtXadRu1uLB9pxtuurTnA78t6NN5xDY+u2OPXn7JhF+FzI2VsGPDQxj/\nlNWbkCRhQuhYEiWC77rX47dkKVgBF0piXP7qPqbtpPPd6eMev8Y9k81ue41mEx++IE04RDRU\nwlI332pmUnVCkkQJoXNJkAjuTX8KY0aJfAxi3MiLAqhaenLqbF/zz/wrRmTWO4fxm+5vMc7v\ndwbj8nuzTwazN1TCU2gNN7fQQ0jirBCWH5HC2Q0VnBVBEsVtrirDPynaAzJe5HJ5MuumurOr\njuvgysBDb0j/t+cTNrOOD+Od6Ac+28CqYP4GSvjAe+9VeZ2bm1aNkMRZIZwuHY6NtOtlJM6K\nIIlbc9mzqncUSYi8Ll+Kt15Ock7APy83HZ14qgP6uuYbbGZDb8EbQ3ulFguCUwMl5BjBzd1w\nESGJs0L4UIetEqQvp10vI3FWBAm87P2Mfd2jdE/odnuq5Qa81bPua+cOlI+8PvV13wdsPt0n\n4m/RQS7fs+lFwQKMk3ALx3dcWb3mEZI4K4QPXSr1aVWQ0OZ8mxL8+1V4Tojc7L8MlJUVyPyX\nr+XOwNJBtWqUYLzRtRmXNx3ONeWckhE6V6HQYiaCs0IIEjqS480HBGdmKtoVBlVkGJTscqdn\neNz5czozNZ566TbPRDarTwMdZy24yvtmqAiQUDdAQidS3rfpP6HZzxXsC7lbhW6vP6lKWtXs\n+vUbdClodf4tOyZf1OSaDXxWB0fltxj0vVCGGRKWFRMWOCuEIKETmZn6P8PLMEPCZaQ1nRVC\nkNCBfOFbZHwhIKFugITO46/ao4XZFS7uMDPjjAGlGCfhkjDjElnCjMlSj3F+Z3blDMJZEaxE\n2eWtT4dmc4SzvcX6F2PwfcIQhCTOCqG0hC7J8/aaZlfOIJwVwUpMDj/H+yAXtVfrc6+luhdj\nnISBvsLP/uRElpC5V+LDt0mtae2GsyJYkajneD2sfbMx5p6jKNS9HOMk7Br+m0zoc0KQ0Lb8\nUm1ieJ67O1HG/lGzkza6F2SchOOzhLmV6YQkzgohSOgsznYuOBd+w0n4F8bc8ehlupdknISH\nd8TtZc1ZIQQJncW4nF8jb6rzJ/KnuHPCbbqXBC1mdMN5En50bbthe7mZ1bUJKZwVwQi7yI1j\nAvqXBhLqhuMk3Or1NvGkcvc5E+SsPsxucnu0bAN60QUJdcNxEl6X+wM+cIV7aeJJKH1fiYP0\naKwmQELdcJyEtWawL2Wj3K9VlPCOngLMk3SqZjDkHaEhY8aDhLrhOAmTXuFey0e5FleQ8PWp\nAug+GhUzHJDQrjhOwiaT+En5cFcfUuyZyeZVx0TIDjJGFAcS6objJBzWOjgtH0bcAThTwuPk\nc8ICI8oDCXXDcRJ+dPXe4Ez5+A6EJI6UsLxvU9IdCrchBYKEuuE4CWXgSAlnpP6PvzlfmV7G\nFAgS6gZI6Ay+8L1qcokgoW6AhI7gz9q3m10kSKgbIKETKLus9elA8OCzilllgoS6ARI6gUcy\n90WuyphUJkioGyChA9joXpHO6XdRG+7VkEZqlQEJdQMktD+/VHsAh/aBjHm7QpBQN0BC23O2\nc7fQfXqmQypIaENAQtszNiWqgRpIaENAQrvyssfNU6m1mt+c8kFC3QAJ7UlNYkNRVGJODUBC\n3QAJbUkPooKMEb1tSwES6gZIaEvI+0HTqgAS6gZIaEtAQt2zpAhIaEuIDn5gWhVAQt0ACW0J\nycG55lUBJNQNkNCWeKQMHGhqFUBC3QAJ7YnEU/RzzK0BSKgbIKFNuUCsIWNIZ06xAAl1AyS0\nK3/WvoNq+SChboCENqXs0vzT8VMZCEioGyChHbkpdAxaTLEOIKFugIQ2pHn4VPBc/MRGARLq\nBkhoQzj9+mMfMqhvbXmAhLoBEtqP30L7QFNbqVUCJNQNkNBubBfuTWSChA4BJLQZN1Jqr10J\nkFA3HCxhGenaoR0lg+GhKwAAIABJREFU9DEhxA6m0qsRSKgbDpaQOFKv/SRsQWqwTbFOIKFu\n2EnCrzdi/M+oTk/KHIDdORJ+b0EHQUL9sJOEXR/E+A5fF8/sWImWhBknjv2R/QK2k5A08iDF\nGxQgoSqK+/aUoEFzqbTWlDBzJS7NfAY/1ipWIuKOIi/y+XBDq6k/pIEHu9OsFEiogl/QqImV\nqV1VKq01JfR+jLeiH/AHgViJAn03hJjsmD0hQUKqO0KQUA2/oH0Sn3a2kYS1luDpdTB+Ly1W\noq7h42vnnBNKH4666FYKJFSB/SUc2mBqjbFs9FvGSjQ+S5hbmU5IYjsJ90ooeJJ2pQyVcPvS\nuXOWbicvBwlp8VuBt/NfGLcbFSvR4R1xL57aTkLcqpKD5nZlIYWBEq5oFPySTVaSUoCE9OD9\n+kPrTsB+EmLsD92pD96xT6JdHWykhEVMqxlrN29eOz2PWUFIAhLS48RHRce152JHCTnKLr3A\npC7u5WCchPl9S4Mzpb3aEpKAhNSYGkBoJ+48Q2M2NpSwusfzEp6U+QPtekRhnIT+1cLcStLg\nNgkr4XPJIyUYtUXfasbgOdfYTb6d+KkCjfnYTcLdwi2Kd2nXJBrjJMwO9576TA4hScJKeDfT\nX4LsR/StZgyaT2B/JXfi5TU05mM3Cfl7gtyLl3ZNojFOwtFpi/jD7uKFAVJfVokroeSNqR7m\nSehdw0u43qcxH5tJWIXVrwU+W6kJEGWMk/BoJ5SU170gz4+6HiMkAQlFmChhtZd4CeflaszH\nZhIyvH13etnJIdp1icLAWxRlywbl5+bmDy4i3m0CCUWYKOGNjX9nJTzabITGfGwlYUC4M8gN\nR/857dpEAS1mVGB/CfdlZQx2D65b/YDGfOwkoXjQCZkPcZkCSKgC+0uI9/RJRv5eUl9DETaQ\nMFWyzTbdFtsVgGZrKnCAhOzZwrEy7ZlYXsJywmMTR2lXLBpotqYCR0ioC5aXkODgbbTrJQKa\nranA5hKeiEJjVpaXUNpBtJ92vURAszUV2FzC6L9GjVlZXcJygoS06yUGmq2pwOYSzopCY1ZW\nl5CwJ5xIu1pioNmaCmwuoY7YUkKG7kBolYFmayoACQUsL2Ga1Q9FOaDZmgpsLuGJ0zhhLsxg\nf8XdoKVuTgSBZmsqsLmEqCXWa7dgfQkxfsjj5mEYt9sKz9FXhkKLmTemCvje0ClLk7G5hLOW\n4IS5MBPhQUs9xyuCgoR3hLvLdb+oU5YmY3MJdcT6EnLDv7jZ6WqXpZ7jFQHN1lRgfwkPBO/h\nnnV6A+7U0FF31Z+rPUy7LmRUSfijrPTQbI3DmhKiH/nJFoefE07i/v74SzNNLy6lXRkyqiR0\nXbs2/pMgzmi2Nj5TgnQk1RuMDSX8QmvX0xaXMPgQL38Z6jfadYmBKgmnNUBNZsW71OuMZmvX\nXPt2ZZ5GmySS2kbCc8XFaFcxy5GHamrMyuIScrck3JP4vu9pVyUW6s4Jy967gkkdGeNsDzul\n2do1Ug59ZW8JCyN3zR7QmJWlJbxE+JZuR0rIsndCJuryVowDbWc0W3OihJ/NmIEmzWCZ86HW\nrKws4VrRPXratYmFaglLFrdFmajZNmJyZzRbc6KELPcckZcu3vVtS0rYUeIhwvm0KxULlRL+\nOLEac+Wa8g/z2hCTO6PZmkMllEf869tWlFBq9DNrtpQRUCXhf65xVRm7h5vb5CGnd0SzNedK\nePgAR6wUMq5vW1DCpyUctPQZoUoJUdPZocFE9vXSUjhIKMJECY+PTo3/10m8vh1peIjuM6yK\napEcBpR2pWKjbk+oU39xIKEIEyUckTFhwUscsRIRr29HGh6iMQZVUD1SvcpY+rKMSglPBrsv\nPnRK3oplxYQFIKEIEyXMWSsjkYzr2xY8HJWQ0OIOqpPwpuDgpv1vlrciccRzkFCEiRKm/CEj\nkYzr2xaUsH0lBzNoVykeqiSsvZSfLJY5kgFIWBHqEl5GutISjYzr2xaUsNKusJB2heKiSkLv\nen6yLuaYPkvCjAMJK0Bdwv+1eIfkVRTxr29bUcIKl2b+Rbs68VElYc48fjInO2by+BenQEIR\nZjbg1umyoSUlDPOAdZ/jFaFKwsF1f2dff61zY6zkgb4bQkwGCStAXcJCAY35WFrC993/oV0F\neaiScF9mlZsn3ZyWsTdW8q6XCnNwTlgR6hLqhRUlvINhYTfwz1Xtsj3VNVvbdV0SSuq1O2by\n8VnC3Mp0QhKQUARIqAfCGeGu9lZ+jleE2gbc8cf0Obwj7i19kFCEmRIemXX7AA6N2VhPwnTW\nv4KT3BXSGlZ+jlcEjE8YG4dKuKtaVaZBKgq01JiP9SRk7VsZnBTRrops1EoYv/mvDEBCESZK\n2PuSs/6d+P266zXmY0kJ2TPC/7IHpZqaNZuKKgllNf+VAUgowkQJa72Jk77HeF1HjflYTsKo\nO/X3066LbFRJKKv5rwxAQhEmSpi0Ced8hnFxisZ8rCYh76DbDk9ORKPuZr2c5r8yAAlFmChh\nw7dwhycx/rK6xnwsI6GolQxjh1bbUaiSUFbzXxmAhCJMlHDoBDzPfes92bdozMcqElZ+csJG\nO0J1Espq/isDkFCEiRLu2YTPjcvMHCSzqxkiFpHQm4ASymv+Gx+QUATcrFeLhIOOl1CvLwoS\nigAJ1SLhYFb8tSyDKgn1av4LEoowUcJzAhrzsYiElZ+mt9FlGWgxEw+HSqjXsYxFJEyp6OAw\n2jVShEoJT3xUdFx74SChCBMlfILjvvYZj2rMxyISVtwV2mo/qFbCqQGEduLOMzQWDhKKMP2c\nsHz04xpzsIqE4uujdjof5FAl4XOusZt8O/FTBRoLBwlFmH9hZl9djRlYRsIQtnmOV4QqCZtP\nwNi/Ey+vobFwkFCE+RIedFiztZ+rWqs+MlHX0dMaXsL1MTt6kgFIKMJ0Cf++qb3GHCwi4clg\nQ7US+zzHK0KVhNVe4iWcJ7PLQyIgoQgzO//lqIqSP9CYjzUkvE04Gcz+nXZVVKFKwhsb/85K\neLTZCI2Fg4QiTJRwFMddsw5qzccaEvLXQ39ibHdVVEBdR09ZGYPdg+tWh4d6o7GThAohDmRg\nCQnfC97v3GivtmpRqLtFsadPMvL32qe1cJBQhJkSlh06rCA1sb88S0jYgT8hZJonmIRyOnqS\nAUgowjwJv+wdQCj56g1y01tawk/s2Wo7Cmi2FhtHSjjf7el689CuHm6YhofJyWQMZEBZwj+q\nBQIB3r6MhJNQr+a/IKGIi8fsl+BPBbWVx+euq3/lpr9ehVaPifF3K+PBIKoSplZqtj2IYm00\nAI8yxcZMCatX+qPi8PytoLqy6NMm9Ot5Nt/HPEtOJ2MgA5oSVmq1bdeLo+ok1Kv5r6Uk/OPO\nkRLUvUkiqUESZl0gsSPchDTfR6hI9gJhbj56K0Y6GQMZ0JSw8u9VQkkYRHvzX0tJ+J6nvwR+\nqe1jlIRdJT7co7+E3lXC3Ep3rHTEgQx6NxRAt+tdOdl8WVnC1tQqow0tF2Y0N/+1loQBqU9z\nHChhjTnC3OyasdIRBzJY/4IAelDfqilgQWUJqdVFI1ok1Nz8FyQUYZaEN5wXuvdefN5AjVlR\nPBw9UelgVKc+AM1Hg4Tam/+ChCLMknCLu4AfUGt3N8/X8VOX7ThFXkjznLBinxb76VVFI+o6\n/9Wp+S9IKMIsCfHLHiavd+9WjHeRjMRH0SfkhTQl/EbsYBq9mmhFlYR6Nf8FCUWYJiHedlM2\nQtmDtstJa1kJMXZHdoaMjH26ZYEWMwKJJCFLyRmZCS0sIcdPVQtpV0EzIKFAgkkoG2tLWNLu\nEls+xytClYTFUWgpHCQUYU0JS7edJC+kKWFy8DjUns/xitDWbE3jvRmQUIQ1JYwJRQm580HG\nxs1kolAl4dO5OaMKR2bXfXrKlClaCgcJRYCEChjB+rdvF9eGezCtKuiGurajHblbRyc7PK2x\ncJBQBEioABdCdU60uK6RE3aFqiSsU8RPlkOztWjsJaE+fajTkzB4d4JZYePWamFUSeh7h58U\n+TUWDhKKMFNCnfpQpyZhH/s/OxFBlYRtupawr8Wd22osHCQUYaKEevWhTkPCei4WXr9W/O7w\nLvOroDOqJFznqT3myTG1vLL7KCEAEoowUUK9+lA3X8IWTnmIMAp1N+s/7eFDvh6fay0cJBRh\nooR69aFuuoSzKz2/9JTJNTAAtS1mSo/q0FABJBRhooR69aFuuoSVhwP9xuQaGACMTyiQUBLq\n1Ye66RJWctD+10ZhfMIICSWhXn2o05dQ677cCsD4hAIJJaFefahTPxxNNrl8Q4DxCQUSS0Kd\n+lA3XcIBFSQk9IJjL2B8QoFEk1AXzL9FkSRyUGt/f9bA0PEJty+dO2dpjMe3QUIRZkl4IgqN\nWVG4Wb/LxY2BxuMxvXBjMHB8whWNgr9WTVaSUoCEIsySUMdrizRazDjiOV4Rxo1PWMS0mrF2\n8+a10/OYFYQkIKEIsyScFYXGrGhImF/lL/MLNRTjxifM7xv6vSrtRWpjChKKgHPC+NwR3IHP\nNblYYzFufEL/amFuJelpC5BQBEgYlwe4xqLcbYpV8dPaBzUSnmz1PxnJs8O/Vs/kEJKAhCLM\nlLB8zcThE9dqvsBvtoSsfxeW40ec0VAmjKo9YeBnGclHpy3iHnjCxQsDdxCSgIQiTJTwWAFC\nqQhd/I/GfMyWkLXvGOZdNLdcY1ElYY/XZSQ/2gkl5XUvyPOjrscISUBCESZKOKzOO8X46LO+\n4TFTfXRtu2F7uZnVtQkpKEgYOiA1t1xjUSXhN40Xyxh8o2zZoPzc3PzBRcSDHpBQhIkSZnzI\nT57KipVoq9fbxJO6HFtnfEI3CvawBoejDh2pN6EkTA4+A7MuNVai63J/wAeucC+1hIRJ3N15\nfjdYg5to7VnFUqiSsFBAY+EgoQgTJewSvHT98BWxEtXinpIpG+V+jb6Ekxz4AFMEQ7vBh2Zr\nVpXwiwb//rVkX2HDPbESJb3CvZaPci2mLWGJE58ijKBcwju3sYE5ei5+eus2W/vqbQkmSj4V\n41AJZf09N5nET8qHu/qIE/24VQA9YkDlKtMcJAwR+uJoGTdIyIdxk1u42Vq91MzKJEn2GORQ\nCQujICYaFhoDvnxYhT/6NhEZtD6aLw93RQcbmlKsWRgnoYWbrdVZIvHh5ESSUBYfXb03OFM+\nvgMhiUmHox5H7wgNlJDYbG1oOwH387IL1xWQUC9MkrBPBQf/NKVU0zBOQmKztWVTBfxvyS5c\nV0BC/OHIyws44qe0xJj1Ygcd0NWoCBUSTt6w4V00cwNHrOQWbrYGEs5DWRfJlNASg4R+5GQH\n1Ugo89Dcws3WQMIG/UrkJrWChMVte3zlcwVJ+tuUIs1EuYSvRBEzvXWbrYGEKaQL1pWxgoQj\n6jjtOV4RCTlmPUjYbabspBaQcKn3021JrlpnzCiLBiChQEJJuLX+RrlJ6Y9ZvyPliWCrbbcJ\nhdHAcAmPkE4IMUhYARMlLL8XBepxaMzHDAlPnNeL61+tBeOwZtsRjJPwC+4EenljhFqsJSWJ\nK+HZFVINzN7+VVlNKgESTkLnDxzKoTEfMyQc1HgMQvewMz6H9PVbCeMk5O4nrmFybh2S4fmK\nkCSuhB8gifZlmT6tw0KChNVId40UYoKEs5O+SUao6OJDeD9C7xheHA2MlbBjw0MY/5TVm5Ak\nroQbJLt37TdGWU0qARKmvqtPPsZL+JVvIbcL5MhB6EWji6OCoRKWuvlWM5OqE5KAhCJMlPCK\nR/XJx3AJ/64/nO9ShgkOkB2j8Y6NMVTCU2gNN7eQ1F05SCjCRAn3n//yYT3yMVrCsivzVof6\ns/Azjmu4LWCghA+8914VvkeoadUISUBCETSeJ9SYj9ESPpZWM7qF1gvGlkYLAyUMP252w0WE\nJCChCBrPE2rMx2AJP/A8JWq5PcHQ0qhhnIRbOL5jZ872mkdIAhKKgEeZKvB7jXvSgvbVCU52\nG1kaPazdYgYkTGQJz3W96IzLwc/yhgEJBRJLwiOzbh/AoTEbQyW8J/uguGOL1fHXsSUgoUBC\nSbirWlWmQSoKtNSYj5ESrnKvw3gob9+FjJN3hCBhmISSsPclZ/078ft112vMx0AJ96Y/xpcQ\n2RFebFhZlAEJBRJKwlpv4qTvMV7XUWM+xklY3LYH31FYafiA9EqjiqIOSCiQUBImbcI5n7F/\n6Ska8zFOwttyDwmz394/YWyhUeVYAZBQIKEkbPgW7vAkxl+SGhTKxTAJl3o/NShnCwISCiSU\nhEMn4HnuW+/JvkVjPkZJuCNltjB7m4thphpTilUACQUSSsI9m/C5cZmZg45ozMcgCU+c1z80\nV8I4s4M1ESChQEJJqBcGSdi/idAfgwuhGfhGhCQHCnEKIKEASKgCYyR8Numb0NzRYG/ba5x7\nj5DD4RJ+3F+K5GkSSRNNwjMvjn36dzkJD28l9/RpiIRf+V4RZmcjdKs/YwVG6DcDCrIKDpfw\niToTJWBGSyRNHAln5p3F+FxH7ln1AzETTmnQZCGe7kXuSaQURkj4d/3IUE//Dt+pd16XvxGc\nLmEXqU/diS1hAXdN9CU0Zs/rKVIbIsxS1LiLaz7qN60AvU5IYoCEZVe0Oh1+sxohZm5P5z7O\nGwQkFEgcCXO4wbCuqnUO4/Exx/nr2O0cfso3EOPStqQWYwZI+Gjarsgb7iGKzA1+hDJ0L8dC\ngIQCiSOhl+vlKWMI+/JazI48M5/D+CdUxM5NyyQk0V/CTZ7lUe8QCg1NCBIGAQkFbC5hTVau\nnYjrg+vttFjpkl7D+ATfCf4iUi9Bukv4ew3R9kLo+C+13U1roZgVtTsgoUDiSHhF+9N4ItrD\nzj3eIla6ejMwLhnEPc0+XTzC5MyRAnp3OME9xxv9nkEtg5Oh+pZjLUBCgcSR8ANUs23wmYQO\nMZut9eojzN3YXbRgcvhmDxqvb9UmZIu/7VSEauBDLqd2vR0CJBRIHAnxm+0b3cw9o7C7ccwR\n0rYWhWZKr11ISKLz4ehK7jleEfWDp4Tv61qM1QAJBRJIQv3QV8K96U9U+uz3ZIbR+vy/1QEJ\nBUBCacwbs154jjfhAAkFLCrhFlS3oQSFUhkYgnmDhA6LPMebWICEAhaVcD2a9EJlLr1WKgND\nME3C1xLpOV4RIKGAZSXcKvHpPc6T8NuUObrlZTNAQgGQUBqTJDzR/Aa9srIdIKEASCiNSWPW\n92vyj15Z2Q6QUAAkVIFuEj6TtE2nnGwISCgAEqpALwm/jDzHm4CAhAIgoQp0kvDv+iNJi5ox\njOcLXQqxLiChAEioAn0kFD3HK+LjYKs1Rz9DARJGAAlVoI+EhRn7CEsQ19FTO4T66VGMZQEJ\nBUBCFWiRsPTmqMFeYpLt7N4tQMIwIKEKNEhY3kCmgo4eFY0HJBQACVWgQcJXlTgIEoYACQVA\nQgENEhaAhAIgoQBIqAINEuYpcfAiHetsPUBCAZBQBRok7K9EwjU61tl6gIQCIKEKNEi4DY5G\nBUBCAZBQBVpuUdwv38F/61djKwISCoCEKtB0s/67RvJuFLpi9K/hCEBCAZBQBdpazHybMlev\nitgakFAAJFSBJgmPJ/BzvCKcI+G6tyUY0FYqKUioF8olLJ9XyxU50kwvir+G83GMhEdQlczK\neNOlMgAJ9UKxhKdaVzjhu86QetkLx0h4CO2Q+LRHFakMQEK9UCzhJBdT4WqMs28BygIkFAAJ\nCZwaupO4TLGEtVkFxRb21FY7JwASCoCEBI6iD4nLFEvoc1fcEzbRVDlHABIKgIQVyQmSjTJz\ncghJFEuY7WIq7AmlvnSCARIKgIQVQTV6cBSgtj16EJIolvDOSueEb2qtpv0BCQVAwoo8mTT6\nGNb5cPRIboWro+211NAhgIQCIGElvu9Yq0hnCXHJ3SlRCnorj4WWgICEAiBhZcpmpfQ+qK+E\nHOMrjMeb6ICEAiChFPsvqfJ0JQm7hhtDoNtV5Pmue70ONXMQIKEASCjNi+mVJNyxQcCvotnZ\n3vSn9KiXgwAJBUBCAoe2nSAuixvByhS3uapMS3UcCEgoABJKE3O4bBUS3pqo4/GSAQkFQEJp\nYo5PqFzCl72faamNIwEJBUBCafSV8NuUeZpq40hAQgGQUBpdJTzefIC22jgSkFAAJJRGTwnL\n+zZN3PF4yYCEAiChNDGHy1Yo4czU/2msjSMBCQVAQhUok/AL3yKjKmJrQEIBkFAFiiT8q7bU\ndgdAwjAgoQqUSFh2eWvCeLyJjqESbl86d87S7eTl0SGc0l+CbpJ/rCChBSXcPqzjlTNL+Nn3\nB3Tou3TnyM6X9e3VPq9t4/q1srPSAkk+F3K5GIZBrqr3FVOrsCUxUMIVjUL9F6wkpYiWsHG3\nkZXpIFnmRY0lfL0OfSWRFCQ0lnAEZ3uumXJfrea/YVw+1HfL9NF+V4/H6rkCaQHk8aCKD9Oj\nHHiKIhrjJCxiWs1Yu3nz2ul5zApCEpGEL0kkmCZZZp0sCV8HIKlSQEJjESK427OEfT1+wUCM\n30z5BuNfkwLPPFZnb3r1u3JdTb3u7IiFfh/jdrmuplprq2GchPl9S4Mzpb3EPfCePiKQGi3h\n7COVeRRJfHikVguJDzejJRKfFqRJZeC+VeLD+xippNXbSHy4Eb0r8WmHTKkMmLESH97hkkqa\n0VHiw3fQBxKf3mkxCae05ierk87g60ewM8/Vn9yhxcyDyFVzvuu8ukyjKlUY9miUU9GTnOlD\nXg+cHUZhnIT+1cLcSr9oQdTokAsin7ZCgAIs0vBEkHBsH36yG/2KL5rKzjxyyZI6mSu2IOR6\nA9XpjGpm+5hU4ag0kI786Cd6dbYexkmYHR7s4xlxX12H9wtsi/r0yH4pvpb6cMf3spPu3i71\n6Tf7JD+VLGun7LJ2fSu7rH2SZX27W3ZZ+8lPF5mKIOFTwYOdtb4S3Is71p/f6PELms/6Bbly\nnmOa12capSB3cnBP6E7K9COv2+kDLSnCOAlHpy3iL5YVLwzcoWxNwDYIEn7v5p7uPd25H8ZL\n0r7H+Bdf+rSH6x/MyL6zoau5x1U9uA/kXpKTGLebuZxqra2GcRIe7YSS8roX5PlR12MKKwXY\nhfCltSnugfMeb1D/F4zL+iePfe7eZOa6GbnulJRMxuOpfDCdBUej0Rh4i6Js2aD83Nz8wUXl\nClcEbEPk+vbnN7TsWhhsZfrmVc0ve3HrTXkdL+vepFHTmjkZPsbv97r5m4Tc/jBtxHFqFbYk\nVFvMAHZHVouZF72fG14RWwMSAhqQI+H25PnGV8TWgISABmRIeLyZRW6nWBeQENBAfAnhOd74\nWFvCstVbZbNKftLVX8lOuvFj2Uk/WS876eb3ZSfdaumOcgOz+DouXbiExI3+qcRlBOb/W+ka\nsVjwkp65Pf+inrm9GPyjvcvSEr5qYhsUy/Kz+dtdNvVpbxxncKXsDU5BQunnCSWRfpRJmjpL\nZCe9Rqr9tTQPXSo76dvVZSfdg2zwxEHbf+mZW8GjeuamIIIyGKjrc8kjBildAySMDUioEyAh\nGZAwNiChToCEZEDC2ICEOgESkgEJYwMS6gRISAYkjA1IqBMgIRmQMDYgoU6AhGRAwtiAhDoB\nEpIBCWMDEuoESEiGgoT/bSQ76amaB2SnvUh+U7AR8v+85t0sO+lHbeOnCfFnTRs8En3t63rm\nduOLeuamIIIyuPsxPXObrPgHAhpwAwBlQEIAoAxICACUAQkBgDIgIQBQBiQEAMqAhABAGZAQ\nACgDEgIAZUBCAKAMSAgAlAEJAYAyICEAUIaShE+gnPiJMN7au15SVselcpJ+PLJ5Su3e2+In\nxPjwhG5pSNaDT8duz/G3KdI3TyU1pY3MMMlAzy8tPyoyMCAaircaHQm/T8qRVc+i66cvWdAF\nTZGR9Oq8ya9Nq+37REbSHVk9+8gSpqxz2pzVfZgVeuapqKaUkRsmGej4pRVERQb6R0P5VqMi\nYVnH0T3k1/Ns4wYyUu3lXvZ7r5VTPMYbZAmzDC3CuLSVnOcfZeepqKZ0URam2Oj4pRVERQa6\nR0PFVqMi4axax5TUs0tT2UmbtJOXTp4wg5K4scFnoO065ikgt6YUURgmGejypZVFRR46RkPF\nVqMh4f6UIiy3niUnfp7qekluzge9w+QllCdMfh73uhbJOilVJqHsmtJDSZjkoc+XVhYVWegY\nDTVbjYaEl/TGsus5CCGf7OEoy65M3SsvpTxhcgu4181ojo55BpFfU3ooCZMsdPrSyqIiBz2j\noWarmSlh6VGWMvxilYNx6xlKivHuT5YPRDNkJcXlo9zL5eWqUMK5MtIqkjBuTWmiIEzyc8P6\nfWllUZGBntFQtdXMlHAbN2DUjkPpT7NhKcg+eipu0tCbft7DcpKy2zLOEUokV7qHo/FrShMF\nYZKdG9bxS+t9OKpnNNRtNTMlPPkJy6ltwvhtQ+MmDb2ZhrbKSFo+3BVPgkiuMi/M+IvZ1+l6\nX5iRUVOaKAiT7Nz0/NLKohIXXaOhbquZf0544kOOtpkf7oyftpR/KXD/HT9p+TDXq/IrIU+Y\n5WghW3yezIvhciVUVlNaKAmTDHT80sqiEg99o6Fuq9FqtibvsPm6If96dVo79KCMpONRn2Us\nq+Vku3LZZDRu2bKyeOnKOgVmrewl77aw3DyV1ZQ2ul2Y0fFLK4lKfIyIhpXPCaORV8+F3bM9\nmd1lHbF3CB4G1JaTNj2YtjhuwqOjs/358hpIyc5TUU1po5uEen5pBVGJjxHRsIuEAACEAAkB\ngDIgIQBQBiQEAMqAhABAGZAQACgDEgIAZUBCAKAMSAgAlAEJAYAyICEAUAYkBADKgIQAQBmQ\nEAAoAxICAGVAQgCgDEgIAJQBCQGAMiAhAFAGJAQAyoCEAEAZkBAAKAMSAgBlQEIAoAxICACU\nAQkBgDIgIQBQBiQEAMqAhIBhnEBhthUq/Ev7rPAcN5mFTkgujv5864Ca3px+XynNlZS1+YCE\ngGGUcoOOtcgWrk4SAAAELElEQVTiXo8plXBGcICrJS1PSy6OMuhld/NnV85v7XpBYa4gIW00\nDgINyKYgOOqYHAmjgzIj9ihzEYO2ebpwnp69wr05fgnRuYKEFClE3/QMtKJdi4QhLOEvvQM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"text/plain": [ "Plot with title “Residuals from ANOVA”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# split the plotting area into 2 lines and 2 columns\n", "par(mfrow=c(2,2))\n", "\n", "# Setting the size of plots below. \n", "options(repr.plot.width = 7.5, repr.plot.height = 7.5)\n", "\n", "# we generate 1000 data points from a normally distributed variable (by default average = 0 and standard deviation = 1)\n", "v <- rnorm(1000) \n", "hist(v, main=\"Normal variable (generated)\")\n", "qqnorm(v, main=\"Normal variable (generated)\");\n", "qqline(v);\n", "\n", "# The residuals of the model we used to run the Anova\n", "# r <- residuals(m)\n", "hist(r, main=\"Residuals from ANOVA\")\n", "qqnorm(r, main=\"Residuals from ANOVA\");\n", "qqline(r)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Are the residuals normally distributed ?\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: Shapiro-Wilks Test\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Normality can also be tested statistically, however the normality tests are rather sensitive to small deviations, especially when sample sizes are large. For example, the Shapiro-Wilks test, is testing the null hypothesis that the variable is normally distributed. In this case the adequate p.value is .1. Hence, with p <<.1 we have to reject the null hypothesis and conclude that the variable is not normally distributed. This test work with samples smaller than 5000 observations. \n", "\n", "* H0: variable is normally distributed\n", "* H1: variable is not normally distributed\n", "\n", "We see below that for our variable `v` that we generated to be normally distributed, p = 0.47, far greater than 0.1, hence we cannot reject H0.\n" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: v\n", "W = 0.99838, p-value = 0.4792\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "shapiro.test(v)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "However, for the residuals of our Anova, we have to reject H0, and conclude that they are not normally distributed.\n" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: sample(r, 1500)\n", "W = 0.9573, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# taking a sample of 1500 residuals for illustrating the output of the shapiro test\n", "shapiro.test(sample(r,1500)) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Are the residuals homoscedastic ? In other terms, is the variance of the residuals the same for the different groups ?\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: Bartlett test\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* H0: variances are the same\n", "* H1: variances are different\n", "\n", "We see below, that the p-value is much smaller than .05 and therefore we reject H0 (and conclude that variances are different). \n" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tBartlett test of homogeneity of variances\n", "\n", "data: r by moocs$MOOC\n", "Bartlett's K-squared = 130, df = 2, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "bartlett.test(r ~ moocs$MOOC)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "The difference in variuance is also appararent in a boxplot, where we see that the variance for the DO group is smaller. We also see that the residuals for WATCH tend to be slightly more positive than negative (their median is above 0) " ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "boxplot(r ~ moocs$MOOC)\n", "abline(h=0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## If variances are unequal or residuals are not normally distributed\n", "\n", "If variances are unequal we can either \n", "\n", "* adapt the oneway test by stating that `var.equal = F` \n", "* or use a non parametric alternative to ANOVA like the Kruskal Wallis test. " ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tOne-way analysis of means (not assuming equal variances)\n", "\n", "data: moocs$EPFL_CourseGrade and moocs$MOOC\n", "F = 366.38, num df = 2.0, denom df = 2495.4, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# adapt the caluclations to take unequal variances into account \n", "oneway.test(moocs$EPFL_CourseGrade ~ moocs$MOOC, var.equal = F)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Are samples from the different groups stemming from the same distribution ?\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: Kruskal test, a non-parametric alternative to ANOVA which does not pressupose normally distributed residuals.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tests the null hypothesis that the location parameters are the same in each of the groups. This test does not make assumptions about the distribution of the residuals, nor about the variances.\n", "\n", "* H0: the mean ranks of observations are the same in all groups\n", "* H1: the mean ranks of observations are different." ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tKruskal-Wallis rank sum test\n", "\n", "data: moocs$EPFL_CourseGrade by moocs$MOOC\n", "Kruskal-Wallis chi-squared = 608.7, df = 2, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "kruskal.test(moocs$EPFL_CourseGrade ~ moocs$MOOC)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Because the assumption of normality of residuals was not respected (W = 0.94655, p-value < .001) in our sample, we conducted a non-parametric Kruskal-Wallis test that showed that the mean rank of course grades differs significantly across groups (X2[2]=608.7, p < .001). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise : analyse the effect of prior knowlege on the grades.\n", "Students' baccalaureat grade is given by the variable `EPFL_BacGrade`. In the plot below we see the distribution of the grades at the baccalaureat and display the median and quartiles as vertical bars.\n" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "image/png": 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ADWIXAAAAAA6xA4AAAAgHUIHAAAAMA6BA4AAABgHQIHAAAAsA6BAwAAAFiHwAEA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"text/plain": [ "Plot with title “Histogram of moocs.bac$EPFL_BacGrade”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 6, repr.plot.height = 4)\n", "\n", "# Remove observations for which we do not have a EPFL_BacGrade\n", "moocs.bac <- subset(moocs, ! is.na(moocs$EPFL_BacGrade))\n", "\n", "# Draw a histogram with 50 bins\n", "hist(moocs.bac$EPFL_BacGrade, breaks=50)\n", "\n", "# Draw a vertical line at the median\n", "abline(v=median(moocs.bac$EPFL_BacGrade, na.rm=T), col=\"red\", lwd=3) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Task 1 : Define two categorical variables named prior and prior4 that distinguish students given their baccalaureat grade. \n", "
    \n", "
  • prior : The values of the variable are HI for strong students and LO for weakers students. use median() to define high and low levels of ability
  • \n", "
\n", "
" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", " LO HI \n", "4318 4277 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# TODO: Define two categorical variables named moocs$prior and moocs$prior4 that distinguishstudents given at their baccalaureat grade.\n", "\n", "# 1) moocs$prior. \n", "# The values of the variable are \"HI\"\" for strong students and \"LO\"\" for weakers students.\n", "# => use median() to define high and low levels of ability\n", "\n", "################\n", "# Begin solution\n", "moocs.bac$prior <- factor(\n", " ifelse(moocs.bac$EPFL_BacGrade > median(moocs.bac$EPFL_BacGrade, na.rm=T),\n", " \"HI\",\n", " \"LO\"\n", " )\n", ")\n", "\n", "# reorder the levels of prior so that low comes before hi in the graphs\n", "moocs.bac$prior <- reorder(moocs.bac$prior, new.order=c(\"LO\", \"HI\"))\n", "\n", "\n", "# end solution\n", "##############\n", "\n", "\n", "# count the number of observations in LO and HI \n", "table(moocs.bac$prior)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Task 2 : Plot the means for the EPFL_CourseGrade given the prior grade level. \n", "
" ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "image/png": 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XmkgwD0M85FuHv37i63y8jIuLq67tixo78jAQDfKSoqcnd39/f3HzVqFOksAP2M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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "################\n", "# Begin Solution\n", "\n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "plotmeans(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n", "\n", "# end Solution\n", "################\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Task 3 : Compare the means of EPFL_CourseGrade. \n", "
    \n", "
  • Check assumptions to run an ANOVA
  • \n", "
  • Run an ANOVA or a replacement if the assumptions are not set
  • \n", "
\n", "
" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tShapiro-Wilk normality test\n", "\n", "data: sample(r2, 2000)\n", "W = 0.95358, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tBartlett test of homogeneity of variances\n", "\n", "data: r2 by moocs.bac$prior\n", "Bartlett's K-squared = 114.6, df = 1, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tKruskal-Wallis rank sum test\n", "\n", "data: moocs.bac$EPFL_CourseGrade by moocs.bac$prior\n", "Kruskal-Wallis chi-squared = 867.09, df = 1, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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IWmn2eOZwqtkPye1ZujNyAdh3+EPlF1Bm4VRGEpNP088ztsZwnT96wm0LfrIA9w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\nvdC7e1XOuPpD5enVd+QFq/f+QS6/0Ton44qn/lQ22t6jqm+NZv1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"text/plain": [ "Plot with title “Normal Q-Q Plot”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "################\n", "# Begin Solution\n", "\n", "# Build model\n", "m2 <- lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n", "r2 <- residuals(m2)\n", "\n", "# Check normality of residuals\n", "shapiro.test(sample(r2, 2000))\n", "\n", "# Check homoscedasticity \n", "bartlett.test(r2 ~ moocs.bac$prior)\n", "\n", "# Plots\n", "options(repr.plot.width = 6, repr.plot.height = 4)\n", "par(mfrow=c(1,2))\n", "qqnorm(r2)\n", "qqline(r2)\n", "\n", "boxplot(r2 ~ moocs.bac$prior)\n", "\n", "# The variances appear to be different across the levels of prior experience\n", "# => Kruskal test instead\n", "\n", "kruskal.test(moocs.bac$EPFL_CourseGrade ~ moocs.bac$prior)\n", "\n", "# end Solution\n", "################\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Two factor ANOVA" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can add more than one categorical predictor and also model the interaction of two factors. When there is an interaction, the effect of one variable is conditional on the effect of another variable \n", "\n", "Interaction between two terms is represented by a `:`. A syntaxic equivalent for the model that contains single and interaction effects is `A * B == A + B + A:B`" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Anova Table (Type III tests)\n", "\n", "Response: moocs.bac$EPFL_CourseGrade\n", " Sum Sq Df F value Pr(>F) \n", "(Intercept) 31721 1 17373.5762 < 2.2e-16 ***\n", "moocs.bac$MOOC 374 2 102.4039 < 2.2e-16 ***\n", "moocs.bac$prior 1179 1 645.7809 < 2.2e-16 ***\n", "moocs.bac$MOOC:moocs.bac$prior 20 2 5.3793 0.004626 ** \n", "Residuals 15682 8589 \n", "---\n", "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n" ] } ], "source": [ "\n", "m3 <- lm(moocs.bac$EPFL_CourseGrade ~ moocs.bac$MOOC + moocs.bac$prior + moocs.bac$MOOC:moocs.bac$prior)\n", "print(Anova(m3, type=3))\n", "\n", "r3 <- residuals(m3)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> We conducted a 3 x 2 factorial ANOVA with prior performance and MOOC useage as factors. The results indicate a main effect of MOOC usage (F[2,374]=102.40, p<.001), as well as a main effect of prior knowledge (F[1,1179]=645.78, p<.001). There is also an interaction effect between the two factors (F[20,2]=5.3, p<.01). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting\n", "\n", "The ggline package comes in handy to plot interactions between variables. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> In our case here, we see that the relation between the different types of MOOC activity is not the same from strong or weaker students. It seems that for strong students, watching videos does not increase the score compared to doing nothing. However, doing exercices is beneficial for both strong and weak students. " ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "image/png": 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VM+XKVrGyp0fUkWul7g1MHaRUEDg8AB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\n", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggline(moocs.bac, x = \"MOOC\", y = \"EPFL_CourseGrade\", \n", " add = c(\"mean_ci\"),\n", " color = \"prior\", palette = \"jco\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Testing Assumptions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Advanced topic : With relatively large samples, normality and variance tests tend to produce small p-values and force us to reject the null hypotheses for normality and homoscedasticity. Instead of systematically (and somewhat blindly) using normality and homoscedasticity tests, we suggest that you explore visually the distribution of residuals to judge whether there are strong deviations from normality and whether there are large variance disparities.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tBartlett test of homogeneity of variances\n", "\n", "data: r3 by moocs.bac$MOOC\n", "Bartlett's K-squared = 116.22, df = 2, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tBartlett test of homogeneity of variances\n", "\n", "data: r3 by moocs.bac$prior\n", "Bartlett's K-squared = 131.29, df = 1, p-value < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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gIqIzD/SiwG1BdYyphYeVuNV5uFXk3jhurDjjRrN7REV3AEUSkBlRGYAJXiZyOJ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\nOatrs0btwgKvQF+bz30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"text/plain": [ "Plot with title “Normal Q-Q Plot”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 8, repr.plot.height = 4)\n", "par(mfrow=c(1,3))\n", "qqnorm(r3)\n", "qqline(r3)\n", "\n", "boxplot(r3 ~ moocs.bac$MOOC)\n", "boxplot(r3 ~ moocs.bac$prior)\n", "\n", "bartlett.test(r3 ~ moocs.bac$MOOC)\n", "bartlett.test(r3 ~ moocs.bac$prior)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear regression\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: In our example data set, we want to know whether the EPFL course grade can be predicted by the percentage of videos that were watched by students.\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Linear Model: The null model\n", "
The resulting model indicates that the average EPFL_Course_Grade is 3.74. \n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Test: t-test on Estimate\n", "
The resulting model indicates that the average EPFL_Course_Grade is 3.74. The t-test in addition tests whether this value can be considered larger than zero. From observing the statistics reported for the residuals, it appears that the median is larger than zerp (we would expext a median of zero if the residuals were normally distributed and if there were as many positive as negative error terms). \n", "
" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = EPFL_CourseGrade ~ 1, data = moocs.bac)\n", "\n", "Residuals:\n", " Min 1Q Median 3Q Max \n", "-3.7433 -0.7433 0.2567 1.2567 2.2567 \n", "\n", "Coefficients:\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 3.74328 0.01572 238.1 <2e-16 ***\n", "---\n", "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", "\n", "Residual standard error: 1.457 on 8594 degrees of freedom\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# lm estimates the parameters of y = ax + b so as to minimise the Error. \n", "# In this model, we use a = 0 and estimate only b (represented as the constant term ~1)\n", "m0 <- lm(EPFL_CourseGrade ~ 1, data=moocs.bac)\n", "\n", "summary(m0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Linear Model: The model with one predictor\n", "
The resulting model indicates that the average EPFL_Course_Grade is 3.62 + 0,01 for each percentage of videos watched. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Tests: Again, the t-tests check whether the Estimates can be considered larger than zero. Additionally, a F-statistic is computed to compare the new model with the null model. This test checker whether we have reduced the residuals, and augmented the variance explained by the model by adding a term (in our case MOOC_PercentageVideosWatched. This indicates that this model m1 is better (accounts for more variance of the response variable) than model m0. \n", "
" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = EPFL_CourseGrade ~ MOOC_PercentageVideosWatched, \n", " data = moocs.bac)\n", "\n", "Residuals:\n", " Min 1Q Median 3Q Max \n", "-4.6502 -0.7257 0.2607 0.8770 2.3770 \n", "\n", "Coefficients:\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 3.6230215 0.0433419 83.59 <2e-16 ***\n", "MOOC_PercentageVideosWatched 0.0102719 0.0006735 15.25 <2e-16 ***\n", "---\n", "Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n", "\n", "Residual standard error: 1.23 on 2766 degrees of freedom\n", " (5827 observations deleted due to missingness)\n", "Multiple R-squared: 0.07756,\tAdjusted R-squared: 0.07723 \n", "F-statistic: 232.6 on 1 and 2766 DF, p-value: < 2.2e-16\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# lm estimates the parameters of y = ax + b so as to minimise the Error. \n", "m1 <- lm(EPFL_CourseGrade ~ MOOC_PercentageVideosWatched, data=moocs.bac)\n", "\n", "# The adjusted R^2 is interpreted as the proportion of variance explained.# \n", "# The F-statistic indicates whereh this model is better than the null model that would include only one parameter (the mean).\n", "summary(m1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Question: Is the model satisfying the assumptions for regression ? \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assumptions for linear regression :\n", " * Linearity: The relationship between X and the mean of Y is linear.\n", " * Homoscedasticity: The variance of residual is the same for any value of X.\n", " * Independence: Observations are independent of each other.\n", " * Normality: For any fixed value of X, Y, and the residuals are normally distributed.\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Linear Model: Checking linearity\n", "
A simple way to check whether the relation between the dependent variable and predictors is linear consists of plotting one against he other. \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the plot below, we see there is clearly a problem. because the cloud of points does not seem to be well summarised by a line." ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "image/png": 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8e7Istx48aNOXPm1FWVoaFhXQWZTGZERASeaGJiIvbcqpmZWUJCwuDBg/GK01sS\nSaB3nWtKdHQ0iaimD+uytGvXDrusra3t3r178coaGxtj65aXl2OXbTqAEWoZV1dXpa9Taq/k\ntLe311S0srKSfKYde3EBQojH4w0dOvT48eMlJSWatgTvwS4lJWXz5s0YBRFCeXl5eAVpHj58\n2L17d40eK42NjWfOnHno0CHF0QL1Wbp0qYp3VZxg+vr66mzuVIrS3dxqov4Ts1JIxutoSktL\nMUqRjMpSFEWy1oZkFNrOzg7P+FHdVy118Pb2xi7bdAAj1DKTJ09WsdumXgYNGoRhSCSXVykk\nP8JLly7hzdghhPDGka5fv479ENyiRQu8gjQLFizQ9IBnZGQcPHhwxowZ/fv3x1tSKBKJEhMT\nVXxAxdHg8XjY488uLi6dO3fGKysWi0m2bcyZM4dwdDQ/Px+jFEmbJRKJv78/Xg3v379fsmQJ\ntvTLly+xPRj7qR0hFBUVhTGb09QAI9QyHz58wF4u369fv2PHjmEUtLS0lF2oiYednR12WU2n\nrGTp378/RqnCwkJsRZJNkyKRCO8RliY6OnrXrl0YBdPT00ke+svKyvAKMhiMM2fO4N0kOTs7\n6+vr4+kihPr37y8XU01T8O6xSG5kEUJxcXG3bt3CKLh48WLCO9pr167hFSTZ/PDy5csnT55g\nF28igBFqE4qipk6dyuPxNCrl6up669atpKSkqKgojHFRmk2bNuEVlNKmTRvsstgjb0wmE2+L\nG8mATElJCfYCEDabXVc8KjV59OgRRikHBwfFPcvqb9RRGkBZTdzd3ZOSkjAeo1euXIktSjNq\n1CiMzfhS8CLLk2+JwxsdwbNPWbBvd/r16zdt2jRs3Xfv3mGXbSKAEWqTrKys9+/f1/Wu0iVh\nbDb7+PHjQ4YM8fDwwNuASKPONnYVWFhYDB06FLu4v79/y5Yt1RSS/s1kMv/73//iGfDo0aNJ\n9ntxOBzssiNHjsQuixDCe8QxNjYeM2aM3ItqLjKcOnVqr169MESl6OnpqXl7Z2Jiwmaz3d3d\njx49SnJtlUJyWqpYQKSC7du3Ew6e4615IQ/4YGlpiV328OHDJ06cwBueURHKuNnQuLs3mgXq\n7yNUugqZzWb3799/1apVVVVVwcHBsm+xWCwtBrxW/fNTMfLp4OBA3ozHjx9Lfw91xVtis9kl\nJSW//vrrjBkzFi9eTBgDs6qqasWKFd27d+/SpYuKkWFF43F3dyfRraioIMk7s1ptmk4AACAA\nSURBVGfPHjzdsrKysWPHSjs1b948xeWvZmZmERERZ86cWbFixcCBAwMCAg4cOKCVPCfdu3ev\nt2v29vZaT2ai/oprOTgcTkZGBp5oYmIi9l2pnp4e3j5Cwk2EDAZDK+H7Nb3P8/PzU3PzYlPe\nRwhGWD/qG6FEIlFMAie7g1sgEPz444+dO3e2tbUdNmwYoRPI8eDBA9npDVNT04iIiOXLl8+e\nPfvQoUM8Hk8uUxqTyTxw4MCzZ894PJ5WGiAWi9+9e5eSkpKQkKB0cmjFihVaEVIkNTXV39/f\nyMhIcTTs119/tbW1lf7X2to6Li6OXDEmJubIkSP37t3bvXu31IbrHYsLCAggtKWCgoLnz59L\nL3nLli2TOr2trS1JgALV3L9/X/GWQl9fv3fv3j169PD09Jw1a9aHDx8aQlrN1Tqyz0NsNnvf\nvn0kothzDf7+/niKW7ZswVOkCQgIIOmvFB6P5+LiolTCyMioZcuW1tbWxsbGDAbDyMho8uTJ\nBQUFatYMRti80SiyzP3792XdyMHBIScnp6FbKCU3N3fTpk2zZ8/+6aefFBNKFBYWTpkyxdDQ\nkMFgdOnS5fbt2w3XksOHD8seByaTuXDhQrywF+ojkUieP38uzcTL4XDWr19PURSfzz927NiK\nFSt+/fVX7KgfKigvL4+Kinr+/DmPx/vll1+CgoJGjx69adMm2TUmbDabbozWyczMPHPmzM2b\nN7UeyE2O+Pj48ePHd+vWLTAw8MSJE0+fPi0vL29QRZr8/Hy5sUpPT0+5xdVmZmYvX768c+fO\n+vXrd+zYkZKSQq6bkZExYcIExfFGNpvt7e2tdDr/s88+w77RkUgkffr0ka1NbhTH0tKyrrGW\nIUOGaPHbz8rK+uqrr2itTp06Xbx48a+//oqOjq6pqZF+hsfjadrTpmyEDErDTAU6yL59+0JC\nQqqqqtRcTpaXl/f777/n5uZ27Nhx+vTphIvQtI5EIhEIBHjTJxrx8ePHR48e8Xg8BwcHX19f\ndbJSaAWhUJiQkFBWVta1a1cbG5tPI6oUgUBw/PjxxMREOzu7iRMn1pulEqiL2tra7du3R0dH\nOzo6zpo1i35GzM7OPnToUFZWlqur63fffSf73K9FKIo6d+7c7du3i4qK7OzsZs6c6e3tzWQy\nhULhy5cvS0tLO3Xq9OrVq6ysrKFDh0pvwrC1zp8/f+XKFTabPXHixIEDB544cYJ+Fh82bFhg\nYCCfzz9z5kxpaWnnzp29vb0fP35cWVn5+eefN8SpJRAIuFwuybyjHEKhkMPhPH78WM7vmwJg\nhPWjqRECAAAAcjRlI4RVowAAAIBOA0YIAAAA6DRghAAAAIBOA0YIAAAA6DRghAAAAIBOA0YI\nAAAA6DSaGWF1dbVWMv4AAAAAQBOhnvi/fD7/8uXLkZGRDx48yM7OFggEDAbDwsKia9euAwYM\nGDVqFEk6ZgAAAABodOo0wuLi4i1bthw6dKikpAQhxGazraysLC0teTxeSUnJ3bt37969u3Ll\nyv79+y9atMjf3/8Ttrn58fLly4SEBDs7uz59+nC53OTk5FatWrm5uZGkm1CT6urqrKwsBwcH\nwoD6gKakpKTEx8dbWVn5+fkZGxt/SmmhUMhmsz/B2fUpqaioSEtLq6ys9PT0bNmyZU5OTnR0\ntEQisbe39/LyMjc317piQUHBxYsXKyoqEEKZmZnW1tYuLi6enp65ubkPHjzg8/k9e/a0srIq\nLy/PzMy0srIaOXKk1iO88Hg8Q0PDiooKOhqUgYEBm83OzMx8+PAhk8l0d3f38vLCyzalJlwu\nNyMjo3Xr1mw2m44h7Onp+QniUn1qlAZe27p1K33d7NWr186dO58/fy4UCmU/kJ+ff/HixZCQ\nEDqrzqBBg5KTkxs8HlwjoVGsUTmEQuHo0aOVHnk/P7/Xr1/v2rVr3Lhxs2bN0kokaJrXr1/f\nvn07PT19xIgR0quhn5+fbBeSkpJ27tx57Nix/Px8belyuVz6Dz6fv3379hEjRowZM+bgwYMV\nFRUNGpRSIpHcvXt3586dZ8+eraqqSkpKmjhxopeX19ChQ7/55puAgICgoKC9e/c2dKRTKSKR\nKDg4WHp5YrFYXl5ee/fura2tbWjpR48e9ezZk8VimZqafv3115cuXYqPj9dKxxMTE9evX79w\n4cKzZ8/SQSbfvHmzc+fOLVu2aDd2vBwvX7709fWVjbGpr68/fPhwuURaY8eOPX/+/M6dO3/7\n7be8vDxy3ZkzZ2p6J2FsbPzHH3+QS1MUVV1dPWTIEDrKuazP6enpyd1U6evrL168WCAQECpG\nR0ePGzfOx8dn+vTpV65cOX/+/NWrV7/99ls6ej6DwZCG0bexsenVq5eFhYWBgUGHDh1++eWX\nf232CSaTOX369Ldv39Zbng5n7Orqunr1ai03rclAYoQrVqxQ8cuRC+c/YsQIwtQE+fn5n3/+\neV1yrVq1oq/FY8eOlf7ImUzmL7/8QiIqFArXrl1LB0F2cHD4+eeflWa/69atW0xMDImQUrhc\nrmxSJBsbm7qyoo8YMUIikWi9AbLk5eWNGzeOzWYrbcDcuXMbVP3NmzdGRkaKuh07doyNjSWp\ned++fbLnKofDGTBggOwrc+bMyczMTE1Nra2tPX/+fEBAQM+ePb/77jvsREg0SUlJeOkbx4wZ\ng/eDpTl06BCGKELIyMiIPKp7dna2psmfGQzGgAEDsG83161bh9dfGjVP7OZnhKmpqRrVIhKJ\nCM/4pgyGEYrF4q1bt2Kkm9+4cSN2OwUCQb0xf+fPnz9s2DC5FxkMBkm0/vDwcDV7x2Aw+vXr\npy07LCkpmT17tkaXjKCgoNzcXK2oUxSVk5MTFhY2aNCgL7/8MiIiIjU1VXXSPgaDkZWVRSjK\n5XKXLFni4OBgYGDQp0+fe/fuSd8KDQ2tS7pt27aK2UjUJDc3V/2A6XJfh6mpqaYXEymE0X2/\n/fZbPF1KveSLdTF69GhsXYqi+Hy+s7MznrSHhweGYnp6OvkoelFRUb1Czc8IAVkwjHDjxo14\n55OjoyN2O0mS1M+aNQtPVCgUYqSV6NWrV1paGnZPKYoSiUTYGep79uz56tUrEnWKolJSUuQu\n+upcTQiHzoqKiuSu0Uwm89q1a/S7gwYNUiF969YtPNHz58/jHWear7/+Gk93ypQpJLqGhobY\nY8Jt2rTB1iW83QkJCSHpNcYd7dGjR0kUadRJN92UjVCDWdb379/HxMTQU8dNgYcPH3755ZfW\n1tampqZdu3bdvn17E9naQVHUtm3b8MrSS5MwePTo0ZUrV/DKIoTi4+PxCr5//57P52ta6smT\nJ6NHjxYKhXiiCKGbN2/GxMTglX369Km/v395eTm2OkLoP//5T2VlpewrlBqJXEhSBcXExLi6\nusbGxsq+KBaLR4wY8dtvvyGEVD9J5OXl4elKJBK8gjRxcXF4Bf/44w8SXR6PV1xcjFcWbzyW\nhqKo6OhovLLJyckHDhzAlkYI3bt3T9MiJD9DKR8+fCCvpDFRxy1jYmK6dOlCf16aAvvUqVMe\nHh5RUVENZtL/wNbWdt68edL/njx5UjFH5ciRIxtiEkjTJ0KSc8LFxQWvkUOGDMEWRQgFBQXh\n6fL5/Lrm5OrlyZMneKIURUVERJD0FyF04sQJbHWKouSSpqqDi4sLj8fDk5NIJCp8jl7RFxMT\nU9f0JEIIe5owOzsb+ytGCPn6+mKICgQC8sWQ2A/BhIs/x48fj6c7YcIEwi5jfMtZWVmEogih\nP//8s16h5v1EmJycPHjw4IyMjJEjR8q+7u/vn5WVde7cOfKDqA6FhYXSh9GSkpLg4GCKolas\nWJGRkVFaWnrx4kU7O7vLly+fPHny07RHBatXr8Yuq/58mxyJiYnYogihuXPn4hXkcDjffvst\nXlnsG2eEkKOjI3ZZmvT0dLyCRUVFixYtKisrU+fD0vHSDh06nD9/Hjs7cVZWVkZGRl3vikSi\nXbt29erV69SpU0pnpkeNGuXj44Mn7eDgMHXqVLyyCCG8EXt9fX2MWw05rl27hlewurqaRPfm\nzZsYpZ4+fXrmzBkSXX19fW9vb01LtW3bll7phg2Lxfrss89Iamh86rXKiRMn6uvrv3r1qqio\nCMk8EVIU5e/v7+Xl1YA2LQNCaNq0afTf9CPa/PnzZT/w5MkThNAXX3yhdWmNngjpZmCgp6cn\n+8irKSTLCr766itsXYqiampq6F00mjJgwABs0aKiIsKM5GfPnsXQLSws1OgC/eTJk8uXLz96\n9IhwgXtKSkq9WsuXL9+7d+/8+fNXrlx569atsWPHOjo6enp6rl27tqamhkT9v//9L95BHj9+\nPPZE3Z49e/BEpUyZMgVDNyMjg/BhVE9PD0N32bJlhP0NDAzE0KUoKikpiUSXwWCUlJTUq9KU\nnwjrHwq/c+dOUFCQp6en4oB7x44dsedpSHj16hVC6LvvvpN9sWfPnl27dn358qVGVWVnZ3/x\nxReqJxfpqSBKjRkghBC2ET5+/FjprgM1MTQ0xL6NHThwILYuQqi8vFzNxyM56O8RD2tr60uX\nLk2dOvXdu3cqPsZgMJR+ce7u7l999RWG7saNG/Pz89X/fGVl5YcPH7Zv315SUtK9e/dVq1bh\nrQlUx/Vll2hZWFjcvn2bZPWjLB4eHhilmEzm+vXrsefbvv/++8uXL9+6dQuvOELI19cXo9Sv\nv/5KOC2q5rVCDvpJg4Rp06bhFfTw8GjVqlVBQQFecYqiioqKLC0t8Yo3Beo/R0tKSpycnJS+\nxWQyq6qqtNwiNeDxeAihdu3ayb3u7Oz8+vVrjaqyt7ffvHmzaiOMjIw8cOCAmiuMsWOIiMVi\nvIIIoXfv3pH8ivbu3btgwQLs4iKRCK9gSUnJ77//jr04sHfv3snJyfv371exbaB9+/apqaly\nL5qYmFy/fl3plrt6ef78uUafP378+LFjx+i/X79+ffny5RcvXtT1g1KBpquoysrKpk+fTnin\nTyMSiZ49e8bhcOg7evURi8XXrl0LCwvDlv748SN2WTabPWPGDIyChw8fxhalwdg3hRDq1q0b\noS7ewAxN3759SZYHK16Nmxn1PjO2bNmS3pGjODQ6ZMiQtm3bNsyjqjxIZmiUvvMtKCiQ+8yA\nAQOsra21Lq3R0GhcXBzeppw1a9Zgt/Dy5cuEp8GQIUNIxu4UFy6pScuWLUnWN3G53LoC9xgb\nG+/cufPRo0dK38KOp6PRc6TSiZOZM2di6IrFYowoYoWFhXjdlOWHH37QVFeKiYkJ9vqgkpIS\nwv1tDx48wNAlWRlE4+/vj6HL4/FcXV1JdIcOHYqhS0M4LPTu3bt6JZry0Gj9RhgYGGhra8vn\n8+WM8M6dOwwGQ2pODQ1CSE9Pj8PhcDgcemncX3/9JfcZJycnb29vrUtrZITffPMN3pmE9+Oh\nIRljlLJu3To89ejoaJIL1vv377E7ruKWn97YJBaLlYbawd71vHTpUvW75uLiovhit27d8KQx\nFtaTBxurqqoinDALDw/Hky4sLCTRRQiFhIRg6OINFcji5uaGocvn81WEhVIHAwMDvNtKsVhM\nssgAIfTo0aN6VZqyEdZ/ii9atKioqCgoKOjNmzcIIR6P9/z584ULFw4bNozFYpEMqWmEm5tb\n+/btnZycnJycnJ2d3dzcnj17JvuB+Pj4rKysnj17fpr21MX169fxCpKciO7u7ti7y6VgT8Yc\nOHCAwpoUQQgxmUwrKyu8slwu98iRI3W9e/fuXYSQnp7evn37FN+l76IwRNVfX2dkZKR0YSr2\nGp+ZM2devXq1f//+KvZIyKH0gVgjkpOTCSfMoqKi8Ara2Ni4ubmRSNNzKJpSb3imeqmpqcEo\ntWHDBuxjRYM9vSKRSLAnOBBCDAbD09MTu3iTQB233Lt3r+KMN5vNPnr0aMPatCY8e/Zs69at\n8fHxWq9Z/SdCsViMfTt55MgRkkbm5OTgrWiQgv0w3bdvX2zR4cOHY3dZ9Y4R6fphpRvJDQwM\n8FYzbtmyRc2uDR06VOnrv/32G3aXpbx69erUqVP17mpYsGABoRDJLB3N559/jq3+8OFDkufR\ngwcPYohqOg2sSK9evTB0yVc2kcSlIpnkGzNmjDoSTfmJUN0Qa0lJSXPmzPHx8XFycvLy8po1\na1ZSUlKDtqzpoNHQKN5+mm+//ZY8FACfzyfxwtDQUDzdmTNn4im6uLh8+PABu781NTUqViQu\nX75c+knFxSmfffYZnqg6y6StrKzWr1+vdIutdrcbZWRkqM6utXbtWnKVVq1a1dtlFezatYtE\nHfuh0MLCAjsIdVBQEEmXV61a9Sl7KuX48eN4/aUIokK6u7uree36NxihLqPpYhkVm6aZTGar\nVq1kZ9T09PR++uknbTW1vLw8PDxc/aEzKa1atVInbK5S4uPjMdYXsNlswlQbVN1hpl1cXGQv\ngrdv35ZtoYmJSUJCAraoisUjTCZTGs2kvLxcLkAJi8VSZypFI2JjY/v376+vr29iYiI3U8ti\nsbSSIIkkiE/Pnj0Jk0/VFa6h3pP86tWr2KJVVVWTJ0/G7jXet4y9+QEhxOFwtm3bht1fiqIE\nAgHGdWPRokXq/4rBCJs3moZYS0tLCwkJ8fPz8/DwcHd3ly728/LyooOKPX/+fNKkSb179540\naRJhfhylREdHa7R5a/jw4RUVFSSKkZGRctvM5Ua0GAyG3CtaGVfn8/nh4eF08GsLCwtvb+8v\nvvhi5cqVio8Cb9++nT9/flBQ0JIlS8gTUNy6deubb76Rs39vb2+5WN5xcXHSuRNLS8uGm0qg\nzWbbtm3SaxmbzSa8MspWLhsdhsPhHD58+ObNm7KRqVksluzYGoPB6Nq168GDB8lTMObm5rZs\n2VLxpD18+PCzZ8+mTp3q7+8/c+bM9u3by76rlaxwePnG6aBX2uqp0pFh2VSXY8aMefjwoVby\nfZ46dUp2+be1tfWzZ89UTIprGk69KRuh8u3GgCz79u0LCQkhSQpDxyIgjGOkEZmZmevWrXvx\n4oWNjY2Hh8f9+/cLCwudnJyGDRtmb2//8OHDuLg4Ho/n4eGxbt06Ly8vrYjeuHHjwoULpaWl\nPj4+s2fPLi4uNjY2Tk5OLi0t7dq1a0VFxZYtW1JTU9u2bTtv3jzVqRI0pbKyUtMUbuTU1NTs\n2bPn2bNn5ubmY8eO/eKLLxQ/IxaLMzIyqqurO3XqhB1fTX0yMjLosMsDBgzAzuajlNu3bz99\n+tTMzCwgIICuWSgUnjx5MjEx0c7Obvz48ba2tr///jt9NEaPHt2jRw9tSRcWFm7ZsuXhw4cF\nBQVMJrNz585z586VC64rkUhOnz798OFDExOTgICAfv36keuKxeINGzYcOHCgsrLSwsLCyclJ\nJBI5OTl16NCBy+U+e/bs7du3tAPp6+vb29v36NFj1KhRde3nUYfi4uINGzZcvHixuLiYxWIN\nHDhw7dq1p0+fvnDhAp/PHzRo0JIlSywsLGxsbCoqKgoKCtq1a0e+2UOWtLS0I0eO5Obmdu7c\nOTg4uEWLFoWFhREREU+fPpVIJHw+Pz8/XygUOjo6Tp48OSwsTC49smqEQiGHw3n8+HGfPn20\n2GatoNwINdrwq5WYrU0ZciMEAADQcZqyESofQJML1iUWi6U5a4yNjblcLv23ubk59k5qAAAA\nAGgKKF+aXCxDVlZW586du3Xrdu3ataqqqurq6qqqqmvXrnl7e3fu3Plf/zgIAAAA/Lupf4/O\nypUrP3z4QGfBpccGTUxMvvzyy0ePHn348GHlypUN30gAAAAAaCjqN8Jz586NGjVKcZ+4kZHR\nqFGjSOK0AgAAAECjU/8ie3p7mdK3qP+PxA0AAAAA/6C6GqWlobQ09O4dSktjp6RsauwW1UX9\nRujk5HThwoW1a9fKJRjicrnnz59v9tk3AAAAAEJ4PKnh/e+P1FT0z8ydDISabMbC+o0wJCRk\nwYIFfn5+a9as6devn6WlZWlp6YMHD9asWfP+/Xvs1NUAAABA80MgQOnp/zM8qfnl5qLmvCW9\nfiMMCwtLTk4+cOAAHX+PxWJJ09gGBwfPmzevYRsIAAAANAoiEcrMRGlpKDX176e97GyEl5BE\nT6+SLJNJw1G/Eerp6e3fv3/ChAlHjx598eJFRUVFixYtvL29p0+fTpg9C/jEiMViet8nl8uV\nG+gGgOaIQCDQKLgJHh8/fiwoKHB1dZVdMygSiZhMJmGyRhVUVVVlZ2c7OTlJf6p8Pr+goMDB\nwUFu97bWDsKHD+jNG5SRIUpJYefkoIwMKimJIRBg1mZhgZydkbs78vBAzs7I2Vno7PwfS8vH\nWmio9lE3IuWAAQMGDBjQoE3515CQkHDkyJHCwkIPD4/Q0FDFxOKRkZGXLl3i8Xh9+vT55ptv\nNIoLWi8URZWWll68eDExMTE/P5/BYNA/kqioqLy8PFNT09ra2pqaGn19fUNDw9atW4eGhs6e\nPVuLDXjz5s327dulodR8fX0piiJMNa6UyMjI1atXJyYmtmrVasaMGQsWLNDX14+Pj//pp5/e\nvn0rEokcHR179uzZvXv3X375JTExkcvlenp6rlq1ijD+llgs/u23365evcrj8T777LOFCxea\nmpoihCQSSURExO7du4uKilxcXFauXDlp0iQt9VWeJ0+erF+//s2bN3Z2dsHBwdOmTZMeYYlE\ncvbs2adPn5qYmAQFBXXr1k3r6uXl5UlJSZaWlh07dmw4J6iL4uLiTZs2Xbp0qaCggM/n29jY\nzJ07Fy/WfF3k5ORMmTIlPj6+trbW1NSUzkVlYGCwZMmS1atXv3jx4ocffqAj+np5eZmbm3/4\n8IEOQuLp6bl69Wpvb28SdR6PFxYWdvDgQYlEwmKx6F/omDFj6IQ/bDZ70KBBnp6eVVVVlZWV\nT58+zcjIsLKyCg4OXrlypbph/MrK0OvXtO3979+bN+j/0zdKj6O6P1ra82Rtz80NKcbhEgrV\nrK8RaLwwp80GjYJunzx5UvZ+rUWLFlOnTg0JCblw4QJFURUVFb6+vrLHv3379gMHDnRxcfHx\n8Vm3bl1NTQ12O8vLy2fNmoXxqKdp8FwVPHr0SO56xGQyGQyGo6OjVvLwSbl3757cDcScOXOu\nX79eb6gjNpv98OFDEunx48fLVuju7s7lcillMZqPHTtGUVRycvLcuXMDAgIWLlyYlZVF3nfF\ng7x+/Xr6LaFQKDtOw2QytZjbhGbTpk2GhoZ0/d7e3q9fv6Zfr6ysDAsL69ev3/jx458/f64t\nuerq6hcvXkjjpFdUVLi4uCh+reHh4dpSTE9PVxHA09/f39JS1ZoPDodDmBU1JCRErk417yNn\nzZqlpLrSUio2ljp6lAoPp8aOpXx8KGNjCiG8f6UIxSJ0FqHTTk6SI0eo2FhK7Xj9TTnotrpG\nWFJScvny5T179vxXgQZtX1NAfSPk8/kqfEh16jiaIUOG4CUmlEgksikCNCUzMxNDVEp1dfWj\nR4+ioqJU3wvv37+fREWWwYMHy1Uuffatl8GDB2PrPnjwQLHCjRs3hoWFKb5uZWUlF/nayMiI\nPN+I4tgMm82mzXjbtm2KbxF+ubKsX79erv6OHTvy+fxjx47J3oIwGIyIiAhyuY0bN0pNd/Dg\nwTk5OZs2KV+Bz+Fwnj9/Hh8fz+fzCUXJw4UHBARgqycmJmI/ZFsyGJX37lFnz1KrV//P80xN\nyT1vM0LBCPVFSO76lZqaqlHXmr0Rbtq0ScUTd0M3sdFR3wifPn2KdwbLcvv2bYxGpqamkoiS\npOy5dOmS4vCvUiwsLHr06OHu7h4QEHD9+nWSaxZJtlhbW1ts3e3btytWqFE0drz05bIofSKh\nH8ICAgIU3zpx4gShIk1dK+OWLFmi+KKenl56ejqJ3OHDh+Xq9PPzGzlypOrDa2dnd/nyZWxR\nsVhMns8BL1O8SCSaOnWqmhIWCPkgNBahcISOIRSLUAWu4VEIiVis1zKeNxghdRKXuLq6CoVC\n9TvYvI3w1KlTCKEePXrQKYwXLly4YcOGgQMHIoTGjh37+++/f4JWNi7qG+GVK1cwfzoyTJgw\nAaORV69eJRGVjq1pSnR0NPYNrJOTU0xMDJ5uz549sTvbtm1bPFGKog4dOoStS6Ovry8QCLAb\nQFGUh4eHYrX04GHDGSF9HVBKXScA4cWhf//+So9evUfY0NAwOTkZT7S2tpbcCF1dXTGk68oR\nL+t5+xCKRCifwPMoDodydqb8/anwcGrfPioykkpPP6Jwz6EmGl2smrcR9u3b19bWtqamJj8/\nHyF048YN+vXjx48zmcw7d+40cAsbH/WNMC4uDve38zfDhw/HaGRycjKJ6Llz5zBEKYqSJp7F\no3Xr1ng5gffs2YMtymQyN2/ejJczNisrSzHcoEaYmJion9Rbjuzs7A0bNnTt2lWuTgaDQRth\nww2NapSajebHH3/8xIpSNmzYgK0rl+MXgxYtWmDo+vj4GCDk8U/PSyfxPH19ytmZGjyYmjdP\n6nmUsnMvOzsbb92pnp6e+vcczdsITU1NZ8yYQVFUQUEBQujatWvSt/z9/QcOHNiArWsaqG+E\nQqGQPC/VypUrMRopFovVmYOsC7xrlkgkIl/yev36dQxpiUSydOlSEt21a9di6FIUdfr0aXqZ\nKEIIYwF9UFAQnu69e/dUzECPGjVq7dq13t7esj6trcUyOTk5GEfYzc1No6EzOYYNG4YhSoOd\nJp6iqO+++w5bV0pBQUE9Mnw+lZ5OXblCbd5MBQdTgwe/Z7EkuJ4nRCgdoUiEikaNonbuVOF5\ndaF0klsd1J8Mbt5GyOFwli5dSlFUaWkpQujkyZPSt1asWIF379O80GjVKIkbIQ3vsGTh8/kk\nHmxqaopxzeJyueT7Ig4ePIjRX6qOdSvqY2ZmhrcuiaKogoKCM2fOHDlyJDg4WCNRIyMj6QJI\njZBIJI6Ojqprlv2vnp6el5fXzZs38TooB/ahJlk+umXLFjxRhNCuXbuwLKiBAgAAIABJREFU\ndY8ePYqtS6Ovr/+P+W+BgEpPpyIjqZ07ac+jnJ0pPT3M+bz/97x9CIUjFICQM0LSXz72suQd\nO3bgdXbOnDlqSjRvI2zbtu13331HUZREIjExMaFNkWby5MlghHJInxXwMDc3x2sk+fTky5cv\nMXTt7e0JdePi4jB0uVxuhw4d6q1c9eManidJSU1NVXOVkCzr1q3D0MrIyNBUCCFkZ2dXWFhI\n0keawsJCDHVEMOROUdSRI0fwRJ2dnfHG22mqq6vNzMzwpNkIOSO0zNeX2rePCg+n/P0pZ2eK\nycQe3vwg43ljEfJBSMU+QT09PZFIhNHld+/eYc+Mqj/C0byNcMSIEX5+fvTf9B6av/76q6qq\n6sKFC/r6+p999lkDt7Dx+ZRGiBDCm0Dq3bs3oS6eIf34448komw2G6+/dS2jVx9jY2O8aUKK\nompqambNmoX3NIy3ZjUzMxOvm4sWLcLroyx1reOol8WLF2OLJiQkaCrHZrMnTpyYnZ1N2F91\n1iSzEHJGaDBCwQhtRugsQq8RqiWZ0rOwKGzfXtbzNJ2Lxl6H9dVXX2l6qKUwGAw1va15G+G+\nffsYDEZOTg5FUc+fP5fdR8FkMu/du9fgbWxsNDJCej0tCSkpKZq2sKqqijDAB5PJxPsJ8fl8\npYsY1ScvLw9Dt95l9PXyzTffYOjSfP/99yTSlZWVGKJ4i0e0MouPvX7E2toae/yZoiiM5DbP\nnj0j7Oy7d+8Uq7X/p+fFIsQj8zzKx4eaMoXavJk6e5aKjaWqq2lpkrkG7McSwoCL7du3V0el\neRuhHLGxsZMmTfLz85syZQr5Odcs0MgISbYT0GAYA8a9sxwsFkvzA/M/8vPzp02bZmFhYWBg\ngHHFxNv1NXnyZMIuYy945vP5JCvs7e3t8XQfPHiAMd4wbtw4PDkpEomEJJTlu3fvsKWV7lBU\nDclgLM2GhQv7/tPzuOSeN3YstXr1/zyv7tugzZs3Yx9nBoOBF6uBPKcsnYmhXqHmbYQxMTEv\nXrz4BE1psmhkhBRFnTt3DvuU8vT0xGhhdXU1+aIVOgMzIVlZWZrqzp8/H0MIewKJhsFglJaW\n4vWRMHbBli1b8HQpivrw4YNcgLd6OX36NLacFJKApU+fPsXWjYmJ0XRZ8n/+8x8NBOjwY7Kh\nWExMsD1PGoplj5kZtW8f9fCh+uHHaL7++mvs44xw7+3IU+lxOBx1JjiatxEyGIzRo0d/gqY0\nWTQ1Qgp3xs7AwODVq1d4jbSysiI8m/HG6xT54osvNNJVf9WZHNLgWxiEhYVhd1AoFOI99FtZ\nWW3ZsgV7EyHNixcv1Ff88ssvSbSkXLp0CaO/CCEOh0MSPpfSfDVjly5dlFck9bzNm6kpUwjD\nj5X9M/zYYIRkJxVZLBbevhFCIzx8+DCGqKYrnxVRM2Zh8zZCa2vrKVOmfIKmNFkwjDA/P1/1\nZVrpfS72zjaKoggzSDAYDJKFdrIUFRVpdB+A/ciC3WVfX1+8xXVSrK2tVdSvOOMyYMAA8hUc\nNGKxWGnIFUXGjBlDMj8nh4+PD8ahJo9FnJeXp5GimZnZPzwvOJjy86NatMD2PD5CmoYfYzKZ\n1dXVGJ2NiIjAOMhS8DarEK53a9WqlZrndvM2wjFjxri5uWGvr/sXgGGEFEXdvXtXNiakra2t\njY2Nq6vrjBkzoqOjX7x4YWNjI3s+de/encfjYTeyqKiIZCLH3d0dW1opz549U2e+MCgoCPti\nzeVyAwMDNe3p1KlTNf0qFVGdX+nmzZtff/01/dSor68fHh6u3Z9PQUFBr1695ETnz5//9OnT\n3bt3r1ix4qeffiIZkFSKprv6zMzMyKfrKIqqra1VEcrHXCH8WLG+Pv583v+HH7vcqZPU8zCm\nHLp27YrX2Tdv3ijWpuasR0BAAN5PKTMzEztYkouLCx3tXR2atxGmpqZaWVnNmTNH/Q7/y8Az\nQoqiSkpKTpw4sXPnTqV5f0Qi0d69e/39/ceOHbt3717C+JMURR04cKCu89XAwGDixIl1vctm\nsxvo7ExISJgwYYKslrOz86lTp0JDQ2fNmnXmzBnyR5bIyEh1fsYMBqNPnz6JiYla6VdaWprS\ndSsGBgY7duygP1NdXZ2cnEyeDKEuDh065OzszGAwbG1tV69eTX7+qIbL5SodfmcwGHROKDab\nPX78+AULFsyYMUMr57MU+tGfIxN+7IK19R09Pe2EHwsOVgzFUlZW1rJly3pPKqVwOJzo6Gjs\nzi5evFi2tg4dOhQVFf3222/e3t5yjshkMu3s7CwsLJydncPDw0lu7+7cuYMRjoPBYGjU06Zs\nhAyKolT3dvr06dnZ2ffu3bO2tu7atau9vb3c90G4bKHps2/fvpCQkKqqKo2SDDQK69at27Rp\nE33CWVtb6+vrV1VV9ejRY9OmTT179oyMjDx79mxpaamtrW1aWtrLly9ZLFa/fv0iIiLksgVp\nlwcPHpw6daq0tLRbt26hoaFaP4yvX79etmzZvXv3eDyeWCymQx5nZWWJxWI2m927d++tW7d2\n6tRJu7qpqanr1q2Li4uztrYODAxs3769SCTq3bs3eYQBjRAKheRBotXk3bt3EyZMiI2NRQgZ\nGRm1a9fOx8cnLCzM09MzJyenTZs2WmuJUIhyc1FGBp08VvLuXWlsrFVlJeZ6MDYbOTj8L3Os\nNHls27ZI5aW/urp69OjRkZGRFEWxWCw/Pz8Wi6Wvr29nZxcbG/vu3buamhoWi2VhYTF8+PCw\nsLAjR45kZma6uLjMnTtXacZE9bl8+fKFCxcqKyt79eo1d+5c6Uh7TU3NhQsXoqKiysvLBw0a\n9N1332kxF3FhYaGfn196ejr9X/r+hsFg0BeTli1bDhs2LCEhISUlhX7F3Nx87969Gi3dEgqF\nHA7n8ePHffr00VaztUX9Rljvg3m9NTR3mpERIoSKiooSExPNzc27dOlCHgi02UFRFPkCWkAF\nVVVVPB5PbmAfH6nn/b/toYwMlJWFJBKc2lgs5Oj4t+fRtufmhnB/CFVVVdnZ2U5OTorzvlVV\nVeTRM5oa6enpKSkpNjY23bt3p18pKCgwMzOTHXTJycnhcrmurq6aXl6ashHW3xONVqkBjU7L\nli3JN/U3X8AFGxpTU1NMAxCJUE7O/zxPanvv3yOxGLMpdnbIw0Pe9gjWEitiampaV7yIf58L\nIoRcXFzkHmcVg+w4ODh8whZ9Iuo3QsWcLwAAAKqorUXZ2X97Hm17qamothazQguLv0c1ac/r\n1AmR5cMCACk6N3QGAICWKSv7e1ST/vfmDeLxMGujPU/W9tzcUHOYlQCaL2CEAACoTVnZPybz\nMjLQ27eIy8WsTep5Utvr0AH9G4ccgSaOKiM8evTohw8fFixYQG9QW7Vq1cmTJ2U/EBgYqJgR\nGwCAfwO058naXkoKqq7GrE3W82jb8/REZMk7AUBb1GmEqamp33777axZs6TbtD9+/ChdXEvz\n3//+Nzg4WJ20cAAANF2knie1vbQ0VFmJWZu5OXJx+YfteXggOzutthgAtEmdRnj06FGKohYt\nWiT3en5+Pv3H+/fve/XqdfToUexcZQAAfGpkPY+2vaQkVFGBWRuHg1q3/scaFmdn1K4dgrW7\nQLOiTiO8e/euu7u74j5r6WraVq1adenSJSoqquEaBwAAPnw+Sk//xxoW+h8e+vqoTRv5pZvg\necC/gjqNMCUlpd40As7Ozg8fPtR2kwAA0BCBAOXlyS/dzMxEeMEuZEOxSG3PyQmRJdoEgCZL\nnUaoGDfh+++/HzZsmOwrlpaWFdiDKrqBWCzOycmxsrJ6/Pjx1atXP378SFFUbW2tQCDo3bt3\nSEiImZmZgYGBtuTS0tKSkpJsbGx8fX3p8Etv37599OjRu3fvJBJJ27ZtR44caWlpmZaWJpFI\nDA0Na2pq7O3tFffMYvPx48cnT57cvn07Pj6eyWT26dNn4cKFslFIsrOz16xZ8/jxYxMTk8DA\nwEWLFmFnUxKJRAcPHoyOjjYyMho5cuTw4cO11AkNuHXr1vHjx+nocT/88IOlpSWfz9+5c+eN\nGzeEQuGAAQNCQkKSkpKqq6t79uzZtm1bLUgKhSg3t/jZs3u//MJKTXWSSJwRMistZZB7nsrw\nYzU1NdevX8/Ly3N3dx88eLCKwAUikejYsWPPnz83NzcfM2aMNEYJCRkZGUlJSXZ2dj4+Pnp6\neuXl5QKBwNbWFiGUmpp6584dgUDQv39/b29vci1Z3r59m5ycbG9v36NHD7ncW1wud//+/fHx\n8dbW1hMnTuzRo4cWdUUikWz4tIqKiosXL+bk5Li7uwcGBjZcxCg6NiGPx2vfvr1c/DaxWJyc\nnPzTTz+lpaW5uLiEhYV16dKlgZrRCNQVhLRFixZjxoxRHah09OjRFhYWWop62nTRNOh2ZWXl\nDz/8YGdnx2Kx6g1ly2AwrK2td+/eTdjI2trab7/9Vlotrav0aqX44siRI8mz8paVlf3888+K\npt6yZcvXr1+/fftWKBTm5ua2+OdCQeyQ+QKBQC4Dw+LFi+m3pNHha2trY2JiLl68+PbtW8Le\nyVJUVBQaGurq6iqbXQQhxOFwfv7558GDB8u+KD0B9PT0pk6dqpmSUEilp1ORkdS+fdS8edTg\nwZSzM6Wnhx9p2s7uf2GmN2+mzp6lkpIo9dJRvXr1ytHRUdqpPn36VFZWlpSUJCYmyqUbrKio\ncHNzk+3+L7/8olmv/4lIJJo+fbq0QlNT0zZt2kgrZ7FY0vOZyWQuWrSIREsWgUAgmx3QxcXl\n/PnzNTU1tbW1mZmZ+fn5shFYmEzmvn37yEXLy8snTZpEOxCTyfT19c3Ly4uLi6Mtn8bY2Pjr\nr7/etWtXSkrKzp07V69efeXKFa3k2zp58qQ0iqSenp6jo+PSpUsrKysPHTrUvn17xZDft27d\n0qj+phx0u04j9PLyateunerCTk5O2AlHmhEaGaFEIhkxYgTSnA4dOty9exe7kZs3b8YQleLv\n74+nKxQKV61aZW5uXq+EmZmZmZmZ4utKU3PUi9J8rTNnzqQzJLRp02bt2rWyQZEmTpyIlytV\nDh6P5+XlhX2cQ0NDldcrEv3teeHhlL8/5exMMZnYnicxN6f8/P72vNhYiiBBbufOneU6Il09\nwGKxhg4dOnXqVD8/P/rOWO6THA4nNzcXW3rFihUaHeFr165ha0nh8XiKia7oztK3eop3kxwO\nJysri0RUIpEMHTpUrlomk6lOWNeBAwcSpvt48eKF0nTTKoLIt2/fXiOJZmmE8+fPRwjdvHmz\nrg/cuHEDIfTDDz80TMOaEBoZYUJCQr1nrQouX76M18i6IiKqD95D4dKlSwl1d+3ahaE7evRo\nTYVWrlyJISTHsWPHSDrLYrEEAgGVl/e3540dS/n4UAYG2J5XilAsQscQCkdoLEI+CBkjxGQy\nZ8+erZU8iNnZ2SRdRghduHABW12deyxZwsLCCPsrFovVSaWpCIfDkSbhwuD169cYolLWr19P\n0muMmQUGg1FaWqq+RLM0wrdv3+rp6dnb279+/Vrx3aSkJHt7ez09vZSUlIZsnlrMmDHjyJEj\nDVe/RkZ46tQpkrO5Y8eOeI3ESCcmR1xcnKaitbW1ilH5NeX8+fMY/VWdGlcpWkk+rLihSDUW\nCPVFKBihzQidRSgWITGB51EWFtxOnS5zOGv+3/NURx5bt24deZfj4uI0PdRy/PHHH3jSOTk5\nmmrNnDmTsL+EgyvY97Lnz58n0e3Tpw9Jr5WO1qiGzWZrlG6zKRthnZOubm5uK1euXLt2rY+P\nz8SJE7/44gsHBweKonJzcyMjI0+ePMnn89esWdMUdtMfPHgQITRt2rTGbghCCAmFQpLiqamp\nNTU1miaM/vjxoxg7hD9CCCEGg4FxF5yXl8fFDq+FEEJIT0/v888/xyg4ePDgEydOaFREugWW\nhNatW9f1lgVCzgh5IOSOkDNCzgh1REjJbQKfr5aSYvix9u2fp6T07dtX/XPsxIkTs2fPtrCw\nUDrqpSanT5/GLosQYrFYPXv2xCv79u1bTYuUlZUdO3YsMDAQ48pOc/XqVbyCNMePH8ebHCHM\nCSoX7UQjSktLKzWPnyASiYKDgw8fPkxydjURVK0+Wr16NYPB2LBhw6FDhw4dOvSPYizWmjVr\nVq1a1cDN+xvVUwVxcXHSD2zYsOGTtEg5eXl5JMXNzMywV1GSQFHUrl27li1bplGp1q1bGxgY\n8NW8sitDIpHExsYqTo3Uy7Rp086dO3f9+nX1i3C53NraWsIVdwEBAStXrmRXVzv/0/Y6IIQf\nIlMu/JizM+rcGSlbyrts2TKN7rRSU1Otra2NjIxmzZq1ceNGvFPr2rVrGKWktGjRAntZMsY4\nx4ULFy5cuNCqVas///zTx8cHQ1SClwrx/8nNzcUr2KVLFy8vL+y5lbKyMolEgudJSUlJeKLH\njh3z9fUNDQ3FK96EqPeZ8d27dytWrBgwYEDHjh07deo0YMCAFStWpKenN/jD6j/RYo80RaOh\n0ZUrV5J8HSNGjMBrJPkeDEdHRwzdyZMnE+pqvJby/zl8+LCmWoGBgSL11kn+TWkpFRtLnT1L\nbd5MBQdTfn6i/2PvvOOixr6/f6dQho4gTToIKGJDkWYDG4IFxYqIZWEVQVEX29p7x7au2Nde\nV2V1xYINsKHAIk2QohSRLuDQZibPH/k9+WYnUzI3A4Kb98s/JJPcz72ZTM4t556jogI9t8lX\nVES6d0cmTUKWL0eiopAHDxBZfkqoKxAcwcHBsjX8/0MxB6+Wlhac7tu3b6lkYLexsYHzpdyw\nYQOV9s6dOxeuvQiC3Lhxg4r0hQsX4HSFXJ1lwsvLi6RKe54alZ6hvp3AYDDU1NTQrVpCHy1e\nvNjZ2XnKlCnon6ibD0kQBImPj0e/IXHcvn17//79JDPU//33397e3uQrIISJiUlmZibEwpu6\nuno9dEBkAAAAqqqqECXU1dV16dKlrq4OWnfy5MmXL1+W9ari4uJevXpVVlbKemFYWNiBAwdE\nf1ZTA3Jz/xWEJS0NlJbKKoHSBEAxABkApAOQB0AeADxT08cFBVRCsdjb22dkZMBdy2Kxampq\nyDzDQvj4+FAZFI4YMeLevXsQFxoaGpbC3nyUvLw8CwsLWa9qamoyMzP78uULhCKDwcjOzra2\ntoa4FgBgbW1NZYazV69eKSkpsl715MmToUOHQou6uromJCSQObM9Z6iXYfxUUFDw/Pnzmpqa\n1jLKEomOjtbT0zM0NLx9+7bQR4BCLyw3N1dRUZHMjaqtrSVToEAgmDBhApVvBGITBcX3BYrU\n3TLiiI+PpzJo2LNnD4QohLMMCoPBKCoqQhobkbS0/43z0C16sOO8JgByAXgAwH4AggEYBoAl\nAMQpKjc3N5mcC4hQXIxISUmBEL1//z60opKS0rt37yBEqXStMOCkEQr+MhMnToRTRKE4bw+3\nq3vr1q1URMPDw0kKtecRISlD+OLFCyyIwIMHD9CDFy9etLe3f/LkSWtW71+UlZWNHz8eADB7\n9uyvX79ixwG16QipyLqhns/nb9q0CXoWC8IDVi5uINHR0bLqYlRXVy9duhRC1NbWFtv/LhPk\ne/pKAFgCMAaA5QBEAfAAgG8GBgiDAWn2FBRqO3d+AEAUAIv+v80jv5C1atUq6JuMIEhzczP0\nXDSTyST/DOMZPXo0nKKKigp0KIOqqio4UQxFRUWZp8H/PxCz7gAAJpP5+vVrOEUEQSj62QEA\ndHR0IHT37dsHrWhsbEx+21XHNoQZGRmqqqpqamrjxo0DOENYV1enqqoqdoNwq3Hy5El1dXUT\nE5P79++jR0A7M4QvX74kOcoUCdx+ICxbFhxmZmYQonjgxg27du2Ck+vevTuxNEUALAEYBkAw\nAPsBeABALgB86L0KbDZiaSkcioXHoxLLzcHBgeJ9RhAkOzv7xo0bsjoZent7Q2jx+Xx1qEy5\nTCaTw+F4enpCbMtBoeg1NmHCBDhdgUDg5uYGJ9q3b184UQRBjh49SqW9AAAbGxsI3Xfv3kkI\nmCcOBoMRERFRWVlJXqhjG8Lp06crKiqmpqaWl5cDnCFEEMTHx6dXr16tWT3R5OfnDxo0CAAw\nb948dAqlXRlCijPgoaGhEJWEWPvBc+XKFQhRPDt37oTQhfvpIgiyJCwMs3nbAfgLgFwAeNA2\nDxDCj715gzQ0iJTu27evuOYoKSk5ODhIsBxdunShcI//hcg9CVpaWuJeanp6ejJtf0YRCATQ\n+xBQ1NXVP3z4ANHAn3/+GVoUfWVBiCIIcvXqVWhdBoPRIOaxkQo+khwcgYGBELrNzc1wU7Jv\n3ryRSag9G0LpvraxsbG+vr4ODg7Ej+zs7KB9halgbm7++PHjnTt3njp1ikq8q9ZAIBAkJydT\nKUFCTCMJSNjfJhUmkykyoJRMoN0FWcnNzZW+A5LHA3l54OFDcPQoWLECTJ4M7O33/P47uiwX\nBcByAHxkmaKsBiABgLMcjmDrVnDlCnjzBnz7BkpKwIMHICoKLF8OJk0Cjo5AjCOuBEPY1NR0\n5cqV8vJyYkwyFDmGZsZHwsT4+vWruCWfsrIykk4NeBgMxuDBg2WuHI66ujqx3kkSwcfOlZUd\nO3aIfGWRIT4+HloXQRCI0RUKlWkkFB8fH4ir3r9/z+PxIC6kGEWrXSHdEFZWVpqbm4v8iMVi\nyWVNGwImkxkREZGYmEhxJCR3mEymUFxpmWCz2XC7ccW9eckgEAiSkpKgLwcAlJeX50ElurO2\nthbeK1ZS8i+b168f0NAAVlZg+HDw889gxw5w9SrIyADkfrrVALwF4CwAq5jMyQD0A0ANgE4A\nuAMws6Eh3cfn/2yeLBEMVq9eLWEiWkNDQ0lJSeQrSUFBgWLUEjzBwcHE3QUIgvTp0ycmJkbk\nWxXOE/LQoUMUnTjggof17dsX2jYQQ56Sh6JBgrvJAAAXFxcqukwm08/PD+JC6H2TcF329ol0\nQ6itrY1OihJJTk42NDSUd5VkwMHBISUlpaWlhfr0uhyBs2QAACaTefToUbiooRRHxhQjtCkq\nKkroCA8ePHjIkCGLFi2aOXMm/rg2ANu8vf9l81RVQZcu/7J5b9+ChgYydWjkcN4CcBWAHQAE\nAtAPAA0AOgHQD4CZAPyuoXEVgLcA4APhIFB7h8zMzIKCgkR+1Lt3b/TtIJSwDADAZDKvX7+O\nz8xAETU1NZEZjoyNjUeOHBkWFkb8CC5LkampKbSPLoq4nrRk2Gw29OwoPl2DrHh6ekJfCwCA\nXtoMCAiAXpsEAEAH+cLnFSGPiYkJldq2O6ROno4fP15fX7+xsVFojTA2NpbBYMDNSncsINIw\nkdyXo6Wl5ezs7OzsbGdnN2nSpPz8fOhKJiUlQe8+VlVVRRMlUsHJyUmoWCUlJU9Pz9jYWAT5\nv23pzefP33d1/ZPNfgNAPbTfJgCItjbi6Pi/belxcUhNDYIgnz59CgkJIfboORwO6uqFp3Pn\nztBehc+ePSPeRkNDQ3xg3o0bN2LdCwUFBSrhmMVBnI7u27cvGmi7tLRUyBhMnz4dWqiiokLc\n3jip4yc2m/306VM43ebmZqkTpET3bCMjI7xXOQSLFi0SqaWpqSnZK61Pnz5UdJubmyVMvEsG\nejc9giCydqP19fUh/GPb8xqhdEMYHx/PZDK9vLyePn0KAIiOjn79+vWSJUsUFBQUFBT++eef\nNqjl90VWQ4iSkJCwZs0afF9YQ0Pjp59+Gj16tLOz89SpU589eybfekZFRWFBSpWVlZ2dnV1c\nXHr37j1gwICRI0du3749PDx88ODBnp6e+D6goqLimTNnqKunp6ej0wPaADgCEKqvX7NyJRIQ\ngDg6Iurq8DZPS+tfNu/BA+TzZ8k1+fTp0/jx47FQO8bGxrdv3/7y5Qt+x4WysjJxQ6pM4O0c\nk8mcMWMGl5DnKCMj4/fff4+KisrJyaGiJYGVK1diHSAnJye8W0phYWFQUJCDg4Obm9vevXsp\nZqHicrmHDx8OCQnBp2Pt1KlTTExMbGzs6NGjselTRUVFLAWxjo4O9afr2LFj+E6eiYnJvHnz\nwsPDDx48eOfOnYaGhrVr12InmJmZyeVVm5CQEBAQgDd7vr6+PB6Px+MdPXrU3d0dnQXBT4R0\n6dIlLS2Nom59fb3QtIGuru7KlSsjIyOdnJzQR47JZHp4eMyYMQNttZ6eHsVsiFlZWSYmJpii\npaXlihUrsC5Op06d8A5T48aNg9sO254NIanIMkeOHAkLCxNaUFVQUDh+/LjQZNcPSVRUFOqe\nCrceWVNTU1JSwmAwrK2tqYSMIsOXL18SEhIYDIarq6uE2SGBQHD9+vXExMROnTr5+vrCz9dV\nV+PjsPBTU/n//KNIbiZTBEpKwMoK2NsLB96EQiAQFBQU8Hg8S0tL9B3N5XJPnTqFGmx/f3+K\nMY4BAOnp6U+ePGEwGEOHDu3WrRvF0qCpqKjIyMjo3Lmzra1t24Q/zsjIeP36tYaGhoeHB5Ym\n6cuXL69fv1ZQUHBycurUqdPHjx+/fftmbW1N3QcEAJCTk3Pt2rXy8nJHR8cpU6YQ1yyLi4uT\nk5M1NDScnJyohxvE+PLly507d2pqavr164d6qgvR0tISHR2dlZVlamrq6+srL5eFM2fO3Lhx\ng8ViTZkyxc/PD29uS0pKdHV10bvK4/Gqq6s7d+5MXZHL5f75558fP360sbEZN26coqJieXl5\nUlKSsrJy//79m5qaYmNja2pq+vfvD70K054jy5ANsZaenn7kyJEXL15UVlZqamo6OzuHhYVR\nz4HXIaBoCH8QiOHH0tMB9EZ+RUVgbPy/vAqowbOwoBJ+jIaGpj3Tng0hWWcwe3v7gwcPtmpV\naNoLTU2guBikp4OMjP+Zvfx8ABeWFrN5eLNnbg46fuoWGhqaHwMYr+jCwsJHjx6pqKj4+Ph8\nl5xBNHKjuRkUFf3f8A4ze9A2T0EBmJgIZ9EzMwOUkwbT0NDQtB4QlQV0AAAgAElEQVTSDeHO\nnTtPnDjx8uVLdGtOXFzc6NGj0TQFDg4O8fHxFANPdBAiTUxUO/S8nSJoNhIUmfHzzAV5dvx0\nO0GGGT/PVFDABDC7iHiAXcQ0/ciyLGD+37/3rO4fWLa8ajZ4CwDVlOY0NDQ/HooA7P3edRCN\ndEP4559/GhkZYRtUIyIimpubV65cWV5efvz48cOHD69YsaKVK9keUKmp6TBmUAG0mIBCS5CH\n/rMH6d1Bhhn4yAKQWew/A8N0YJ8HLLF/GaB7g4ADZUNpaGj+s8gQuaItkW4I8/LysFR/nz9/\nfvXq1YIFC9AwTrm5uZcuXfpvGML2ixEo6Q4y8GbPBmSzAUzMJABANdBG7Rxm+TJBN257fXxp\naGhoqCPdENbU1GC5cNFYhVjklP79+x87dqz1Ktee+NSnj6BtfNMloMGvtmxIt2zM6NKUh/6z\nbMxQEkBuV6hlaRcrWRYrWeYpd8/j2BcrWX5UtuUyhT1jv9u2ABoamh8IBEGSkj4BABkDtlWR\nbgg7deqERc978uQJPkAzn8+XnNv9B2LLs2cr2nT7BLpFD+/DkpUFvn2TfqFItLWFfVi6dtXQ\n0NCg7RwNDU2b0NzcoqS0FQDv710REUg3hD169Lh169batWvZbPbly5ddXFww75j8/HwDA4NW\nruF/AGxbOmb23r8H9fWQpeFtHmr2HBwAhTjgNDQ0ND820g3hokWLxo4da2pqymKxmpubsd2E\nCIK8fPlSZFI0GpTU1NS8vDxzc/PevXv/3yF8KBbU7OXkgNpaSAFlZWBp+a9QLPb2ABcGvb6+\nnsvl6mlq1tbWAgDw/r2fPn3Kzs42Nja2s7ODbqAQtbW1nz59MjMzg0vl2kERCATR0dHJycl6\nenrjxo0zNjb+3jX6Pnz58uX69eulpaUODg6+vr4UE1YIIRAIGhsbORwOg8FoamrKy8szMTFR\nU1NraWn5/Pnzhw8funXr1toJAOrr62/fvl1cXGxvbz9ixAhsoaSkpKSxsbGhoSE3N9fc3Bwf\ngg6OrKysR48e8fn8IUOGYMmkPn78mJCQwGQy3d3dW+8ZKyoqio6OzsjIMDIyGjFiRFpaWkVF\nRa9evYYNGyYUVT8lJSU5OblTp04eHh4/wu+dTBy2U6dOubq6urq6Hjp0CDv45MkTHR2d33/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cCxcuFBUV8Xg8TU1NKyurhQsXDh8+nKJQ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\nmpqalJQUW1vbkJCQVatWtfjedtpkUYjYtPbYA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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 5, repr.plot.height = 5)\n", "\n", "# Simple plot with basic R plotting. Use the command plot(y ~ x). \n", "# pch means plotting character, 20 is a small dot, 1 is a circle, etc.\n", "# jitter allows to add a little bit of noise so that the points do not overlap in the plot.\n", "\n", "plot(jitter(EPFL_CourseGrade) ~ jitter(MOOC_PercentageVideosWatched), pch = 20, data=moocs.bac)\n", "\n", "# also plot the regression line that corresponds to model m0\n", "abline(m0, col=\"blue\", lwd=3)\n", "\n", "# also plot the regression line that corresponds to model m1\n", "abline(m1, col=\"red\", lwd=3)\n", "\n", "# See https://rpkgs.datanovia.com/ggpubr/reference/ggscatter.html for more sophisticated plotting.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Linear Model: Checking normality and homoscedasticity of the residuals.\n", "
A simple way to check these assumptions consists of plotting a QQ plot for residuals and investigating whether there is a \"trend\" in th residuals with th fitted values. \n", "
" ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [ { "data": { "image/png": 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mrVqrVq1aooHeLTTz/Nzc3Vb0lNTUVbtenBBUFwdnZev3798OHDS0vm8kk5chot\nxYyBK1euvH37dlF7c3JyHjx4IG7+/PPPo0aNwr9FVwxZGgMAjBs3bty4cXLlFHnnnXc2b97s\n8JzHjx8LgsDz/J9//imle1BQ0Pnz56OioozjrSUu68yaNYsxNnv27L59+2JLly5dli9fHh4e\n/tFHH2Figxcyfvx4/bSSp0+f5jguOjraYLWIeLkxiERVq9WBgYF9+vTRT8BMEBWFvLy8TZs2\nabVa49KvjLHw8PCff/7ZRMqlvLw8g8iU/v37v/nmm5jvy9raWq1W16hRIzAw0Dzily/KkcJR\nihkD79y5k5CQUNRenU537do1cfP9998HAA8PDzEGValU6nQ6WZm77ty5U6VKFVFHUSgUsgwD\nmzZtWrhw4ZQpUzIzMzH2yd/f3yCkygTr1q3bsmXLypUr9TUDjIaSWB95//79YBRfMHr06PDw\n8L///lvKCCkpKahtRERETJ48GQAGDhy4fv36rl27ylLd4uPja9SogX87OjqmpaVJ70uUBwws\nbQRRoXn8+HFeXl6vXr0M2hMSEmrVqiUlP6Q4F3Ac98knn6DLxatJOVI4SjFj4Pz5803s5Xne\n2dlZ3ER7hn7GCxORS4XSpk0bA99MufoKAEyePBnn6WJgbW3t6+v76NEjjuPc3Nzs7Ozu37/P\nGBOv4QtxdXUFgLt372JIMIKTvf61MkGbNm0A4JtvvhEtPevWrbt27VpsbOy3334r0fzj5OSk\nvwaEmYAPHz5cfjLlEQTxShEQEDBixIjbt2936tQpNjbWuOiJRHiev3TpknFurleKcuTDUVTG\nwOHDhw8dOhTdFMqMF3r66IPahlKpFF1jUF+R5R6ckZEh+pHwPN+5c2dZAj98+BBn5eTk5Hv3\n7jHGXF1dC3WNLhSMqjWY15s3bw4Ac+bMkTICmpQMFAs0nEhMvvT111+jthEcHCxeRniuykjn\n6tWrGFTG87x+ol/CrORKwNIyEoRUYmNjV65ciX/Xrl27SpUqZ8+e1el0xdY2fv/991dc24By\npXBgxkCDRswYOHTo0K1bt5alMHK/VQa1V9C2Id3CMWnSJExnK559z549cn1XDx8+jPP006dP\nGWPJycnS+7722msBAQF37961s7N79913hwwZ4uDgcP36dW9v71atWkkZodA8acePHwfJNpIJ\nEyYAwIgRIy5fvowtmLAVAKKioiR+ELVaHRwcLLqRX7p0yUz5pggDbCRgaRkJQlkWc4UAACAA\nSURBVBLp6el//vlno0aN0tPT/fz8rl+/XpLRHB0dnz592rt379ISr+JSjp7FQ4YM8ff3j4+P\nN2jHjIHjx483U9QDWiP0X4Wx6J9EI8cff/wh/eCiwFW9evXq4TSJ3huMMVkv9+np6WgjwRLJ\nP/74oywZ7ty507ZtW41Gs2HDhrVr12ZlZTVr1iwxMVFi9yFDhgBA7dq19RuxOIVECwfqWz//\n/LN+Y+XKlQFgzJgxUkbo3r07OpNXqlSJMXblyhW8uXJ1jqNHj6KNRKFQoADEC5n/nHnz5gUE\nBLi5uY0YMWLmzJkffPBB9erV7e3tZ82aZWkZCUIS+PrXtGlTZ2fnR48elXC0CxculKv84pak\ntOJrKxAG8fSTJk0Sr4a+3pCcnCxxQChZptHdu3cbj4A6h/GwRVFokSobGxuJ3fW5c+fOrVu3\nitER53Vra+sRI0Z069YNV5QcHBwkdseLb9Do6OgIAL6+vtJHWLZsmX6j3O+5sXYi/S6UGRaP\npzfB7NmzmzRpgin2EZ1ON2rUKMyHWHGhPBwvPWlpadu2bcvJySnFEO7Jkydb+mP9PxZ/bpDC\nwRhjhw8f1lc15E4w2GvQoEFii5hCTkr3pk2bAoBx4mdZMyUeXLt2bdwUHS9Wr14tcQTGmGgj\nQT+S9PR06X0ZY5mZmWIaf8QgX7tp8KLhu4UIjiNR+Sv0iuGws2fPljKCuDCEHjniKgCW/5XO\n9evXFQoFJg3cvXu3rL5SsPiDwwT+/v6bN282aExMTPTx8bGIPKUFKRwvMXXr1gWACRMmDBky\npISFsfSpWrVqQUGBpT/c/2Px50Y5WlKxIK1bt9ZPHicrugQAcFqKjIxER0WO42T5cLRv3x4A\njAv9geSVmrfeegsAlEolVpIDgKlTp06fPh0ARowYIekzAHTo0MHJyUm8DoIgODk5vf766xK7\nA4C9vX1WVhZjLCIiYt26dey5nUYi6OKKSk+bNm08PDzw43Mch0E0JcHb21vKYeiI8/nnn+Mf\nGo2GMQZy3HEAQKFQ1KpVC/3LdDpd586dy1d2YTPz9OlT4+8tx3GynIoIosywsrL6559/AGDT\npk2RkZGyMhqYGPPLL7+Mj48vRfXlJYAUjmfoZxqVOz1oNBr0XcCpGmRmGsXK2vn5+foRoVj+\nR2I9lwMHDgCAwRr5V199JVEABCNKxAgRDFGJjY2VnqsUALKzs+3s7KZMmfLee+9JnOP1wUQg\njLEjR45g6Q1Re5MCznNhYWH6jdh95MiR0sWYN2+e8bASUSqVeEYsiIDfJSxLLX0QxM7OriI6\nkQQHBy9ZsiQnJ0dsYYzNnj27Tp06FpSKIAzIy8uzs7PjOC44OBhNs/fv35f7tmnAH3/8gc/P\nvLy8GTNmlJKkLw+kcMDGjRsN9AMxOEI6V69e1Tccyf3WOjg4AICTkxM6KnIch2XbJJZPw+7r\n1q2TdVJ9sMiyq6urGCFy4sSJqlWrAoD0BJHt27e3t7dHqwBj7MmTJxzHSfQYRXDhY8OGDWq1\nGi3wsq7k0qVLAeDgwYMKhWLPnj3VqlUTbSTSBykhaKe5fv06vidptVp0cZceogwA+B3QaDSC\nINy/f5/juEKDgMonCxYsOH36dFBQ0NixY+fOnTthwoQ6deqsWrUqIiLC0qIRxDN27dqlVqs1\nGk23bt06d+5ssBZcDFQq1eHDh7t3714q4r20lP4qTbnHYC0WZyP9QvCyPDAMxkHw7VYWBiHa\nHMdJd6EQ03EayyOxJnihDpusCH/YQnny5AnK0KZNG2zx8fEp3ndMtDa5u7vL7WucIVjWfcTr\ngPltRWR9ikLPWNTlLRTRa5Xn+Zo1a4qbGHqDWHwt1jTHjx8PCwvDKhJWVlZhYWEnTpywtFAl\nhXw4Xg7Cw8P1HcPr16/v4eEhd960srJKSEi4e/fugwcPHj9+bOnPJBWLPzfIwvEs06i+BRhf\nRpnkNZG2bdsa2Egw06gsMS5fvqx/YwRBwAANKTg5OYmv8gqFwsrKSpTn7t27UkZAaffs2aPf\nKHqESAHNId27dz906BC2PHr0CJeEpPuRYHFF0Y8kKSmJ4zhZQfC3b99mjFWtWpXneWtr6927\nd8uykaAhYe3atfiHjY0NXtiyTOaBAjPGdDrd9evXdTpdhw4dAEC/AFA5p0WLFvv379doNKmp\nqRqNZv/+/bhCRxAWJCcnh+f5FStWYLE09L27ePHiv//+K2scV1fXjIyMoKCgypUr+/n5eXl5\nmUfelxBSOApHlhEeC8HrWzWKkWkU9PxIeJ4X64lIRBAErIwsCAI6PHIcJ70QyWeffQYABlXW\ncNG9T58+UkbIzs6G51lJRM6cOQMAGzdulDLCr7/+igKLhg28C6+99pqU7vqg2pGfny9ReJG8\nvDzULTC9PSbH5DhO1oKIsaoqXXlFDL5+f/31VzEGsTgKhcLZ2fmVcpglyieMMRsbG1tbW/wR\n1ahRY+zYsQZJg6TQrFmzhw8fJicno48dIRdSOAqnGDOEvm+z3Eyjb731lr6NhDEWFxcn9606\nJyeHMXbp0qWoqCj2PMxEYt+5c+eiABzHOTg4ODo6YiAoFqyXJYY+OFO+sEAzgqWZO3bsKL5w\noDMNY2zz5s0Sz6hUKvVtJFlZWXIvo06nO3LkCCp/mBxdlo1EXI9r0KABADRo0KDsbSQWISsr\nC82EWUVjaRmJV5FVq1bxPK+fWd/Z2fnQoUPnz5+XNU50dHRMTAy6uxHF4yV/CEqEMdaoUSNx\nEx2IJBo5MN9+Cd0SMae7WI1l7dq1KJXoBiERnCD79+/P8zxO9tIRXWWzsrIwa5OsCBFM1YpJ\nWkUwW/mmTZukjID61t69e/UbcXlV4qKMh4cHmiLQ2tS/f//iZRpt1aqVeEP9/f1l9dXpdNj3\n4sWLHMddvHgRSsNGUv5xcHBo0qQJ/lEUlpaReLVISEhwdnYePXq02IKPgtOnT8fExEgchOO4\nkJAQnU5nYAAmigGFCMM777yzefPm8+fP43dRfNaL8RqmwRruJZkhvv/+e/hvNZZBgwZ5enq+\n+eaboifmCxk+fPgvv/wibjLGOnXqZG9vj8XuJYLqRXh4eH5+vqzoEgCIjY3lOC47O5vn+Xbt\n2qWlpZ0/fx61FoM41aIoNJZYo9FAEYVajMFMD9WrV7958yYAbNiwYcOGDbJClAFAqVSKygFj\nLDo6Wm7hX0EQunbtiglkAaBz587GRYJMICpJe/fu7dChQ8uWLbEkTTlfm1i2bBlWe162bJml\nZSEIsLGx0bdq2NnZ9evX78mTJ1J+jBzH5eXlVaDQsApDCRxOKyrG3uY//fSTQaZRrH8mEew1\ncOBAsUVWnAsaVIwDW2TdIDzY09MTN4cNG4YtkZGREkdAMCATVxNkdWTPa5fof7tkDYJ9nZ2d\njRv//fdfKSMUesXwXtStW1fKCOLqD94OcbMYV0OlUvE8r1Kp5HZk/414Er+T+gdY3Nv8pSQ5\nOflW0VCUSgXCOINRo0aNhg0bJsXMJvFZURGx+HODllQAAEaOHGmQaVRWoBTmdFq3bl3xMo2K\nScOKJTsAQK9evQCA53nRIrJ69WrUOQYPHixxkI4dO6LlX7wIHMehkVwir732miAIT548adSo\nUVhYGGNM1jrC06dPASAtLY3n+YkTJ1arVk30I8FX55IgMc4ejUwhISHokZOXl8fkZxpFP5KC\nggJ04C1GKjmMURIz0XXo0KGE+YgIKbRp06Zq0TDGSl7HizAr48aNw58MWkb1OXfu3C+//GLa\n4rty5UrG2KVLl8wp4ysNLak8A+c28W9ZM2VBQYG9vX12drY4AsdxBvEaJjhz5oyxtwROURKd\nD9B6j2k6RVavXq2/yPJC9u3bBwCenp6otQQEBNy7d+/s2bPSR0CCgoLQedDf319WJKe7u/vb\nb7+9detWxhim8AL5mUYZYy4uLqmpqWIjdpe4ZIt38OTJk8bDSpRBpVLhl4fn+YCAgLt37wqC\nIAiCSqUSl8ykkJ6e7u/v//jx465du0r/LpUHzp8/n5qaiutoGRkZkydP/ueff7p06fLFF1+U\nZQa2YnD06NGUlJSi9larVo0cBsszkydP/u677wwamzdv7unp+cJfkEqlSk9PF2snEWaCLBww\nZ86ckmcaxRoi+jaSbt26Se8uLsFgplHRaUCi3oO/ky1btsiSWR8MJbe1tRVtJHfv3sWSygZ+\noCbo1KkTvlvgRXj48CHHcWvWrJEuxpYtWxhjb7/9Ns/zarX6r7/+kvVmX61aNQBIS0sTC9WK\nF1b6ICUETSOffvqpTqdLSEjQ6XQ///yz2C4RXNh6+PChTqfbsWMHx3ESI33KA+PHj8dc+wDw\n+eef//LLLzzPz5o1y3gyKG84OztXKRpLS0cUyb///svz/KJFiwzaq1Sp0q5du7i4OBN9scBk\nfn4+aRtlgflWa8othWYa1V+kF5NoyR0WLynHcWK8iXQMrO4cx8XExEjse/v2beO7iXOtxGSd\nJc80KpZcQeMz0yu1KqW7PmI+Ent7e7l9jUuWyLqP2GXJkiXGjdJHKGGmUfGbgC4g4vcqMDBQ\nPMbia7EmcHFxwYoSWq3WxcVl6dKljLEvv/yyXr16lhatRJAPR/kETbOFwnGc6bXUTz75xNLi\nlykWf26QheOZFV3fliCmepQ4AkZRMr2ZSavVyg3F1Gq1eEvmzJnDGBMEoVmzZhL7BgYGikqS\nSqWysbERbSSykugZRNLeuXNHel+0kTRu3Dg+Ph5bNBoNTv/S/UgwR6pBFg1RnZICFoNGCwHP\n83Xr1i1GptGJEyeiRQGr24AlqrFcvnxZp9Pl5+cLglCzZk2QnDTW4mRlZbm4uADAhQsXUlNT\ne/bsCQAtW7ZMSEiwtGjES8WTJ08UCgXm4dXH3d0dS3AzxjAhoTF16tRheku3RNlACgdAYdOJ\nrAkGoxZFG8mxY8dQ/5BbIBSnyWnTpvE8L7e0piAI+Gas1Wpzc3MZYxzHSZ+q33//fQB48803\n9RvRjNy6dWspI2AEGqYWFTly5AhIzjS6YsUK9HIQA3bwMmLS9OJR1OOmKPLz81HDQGfPjIwM\nJjMfCZRSplH92jqY3F3uIJbCw8MDdaODBw/6+/sHBQUBQHZ2djl34CAqFr169fL29jb+YdrZ\n2Y0cOdLV1dVE3wYNGmA9eqKMIYWjcGQ93HFOEm0koaGhsjww4HmmUfHHwxi7cuVK8WwkkZGR\nGKArCIJxJbOiWLFihZj+wd3d3cvLS/SiFWujFANZCSTGjh0LAG5ubqK7g5hpdMWKFRLPiGsQ\nGGsjCEJCQkIxMo2+//77+ss6xcs0iupanTp1XpFMoyIdOnSYMWNGRETE0qVLMX4KAK5du1a5\ncmXLCka8HMTGxvI8v3379kL35uTkbNu2rahkg6dOnWKMxcbGmlNAokhMPQTPnz8vOn9lZGSE\nh4e3aNFi7ty5FeVNSzqMMf04WLSrS3whw9iQUsk0KtpIRo4ciVKh26Z0FArF4MGD169fz/P8\nhg0bZPUVZ/fk5GRMQ8JxnH64h2kqVaoEAAbh71OmTAGA5cuXSxkBv1dJSUn6jaisfPjhh1JG\nqFq1KioraCOpUqVK8TKNrly5Ukxt/sEHH8jqK2YavX37NsdxV65cgVcj06jI/PnzK1euPH36\n9KpVq06fPh0bN27cGBoaalnBiJeA5s2bv/7668Y/ELQK41LyjRs3Cv0FHTlypGnTpmUiJlEE\nJvw7WrZs+fnnn+PfY8eOtbKyCg0NVSqV33zzjSw/kfKGgfOXmONBTHuAm6tWrZI4IBTmJ/jC\nyyvyww8/GI9QaKMJCl2CMU4mJoWGDRsGBwcXo6N4GUeMGNG6dWu5vreFelaiwiHxg+AI6HZu\nIJVEGVhhJfeKkfXL1tZW/DrZ2NjI6iteNywg3L17d+O7aXHnrxein9iGMfb48WODSK4KBzmN\nWhw0ghbKwIEDP/30U+N8X/hTqlmzpqVlLxdY/Llh6kH86nib16tXz+ALKl3bYM+ntGHDhokt\nOGlJnGvRoFIqmUbFqVFMqPfFF19IHAHRr1grqyNjbN++fQaWHlkRItjXIDUnNh44cEDKCIVe\nMTRvtGrVSsoIYhFInud79uwpeuEU42qo1Wqe562treV2ZC9FptHMzMwjR45s2bIF/WBeAkjh\nsCym7ZRt2rRBV2UDgoKCLC14OcLizw1Tt/DV8Ta/ePGi/kURBGHUqFHSu6N6gfkGELSfHz16\nVEp3LA/GSmBF9/b2hv/a7TMyMtByM3/+fImDhIWF6UeI4AoLlmSTSPv27QVB2Ldvn7u7e0BA\nwPXr12V5P9y6dQsACgoKeJ6fO3eufqbRdu3aSR+nJOTn58PzInDbtm3DmBcoVqbR3NxcQRDy\n8vIwTFqWGJgoTLSR+Pn5VaxMoxERET4+Pq1bt+7du/fDhw8BIDQ0dPHixZaWi6h45OTkeHt7\nF1XPSIwjO3z4sMH6L8dxFy9efPlmqwqNKYXjlfI2F2uIcPITUWu1WrRSiCoLx3HDhg2TuGiN\nP4mSZBrF2Ff9uAaQGRALAAcPHgQ9A4NarQaAYmT57dmzZ3Jy8r179+RqCUFBQX5+fgDAGJs2\nbdqtW7eYzAgR/GaiN4kIdsd4mReC6gUmWTcYViL6mUatra3xDup0OrmFoPLz85s1a6ZQKCZP\nniwrYavFWbFixRdffDFs2LADBw6I+cq6dOny559/WlYwosJhZWWF2QgLfR+rX7/+uHHjAgIC\njHeFhYUJgmBguiYsjqn57BXxNsdMjvqzmiAIct0M8/PzcZ4+duwYmgdkVVstYaZRnBFv3Lgh\nS2Z9HB0dUQx8xQeAnJwcXF+QnuOybdu2HMdhinfG2KNHjziO++2336SL8eDBA8aYs7MzGore\nffddWW/2qBM/ePAALQqNGjWyVKbRQYMG6XS63NxcnU6HnrOyMo2ijSQmJkar1UZERHAcJ671\nlH+++eab8ePHf/vtt+3atROvfM2aNUvy/SReQWxtbU1XA/D399+1a5dB8L9CocjKytq/f7+Z\npSOKg6lp9RXxNselIoNMo0x+aAPaSFq2bMnzvNxE1DqdDk/HnnvbcRyHfqNSiIyMBKMpTZaN\nJCsrC4z0G0ytIXGmTEtLO3z4MACI6UHx1IMGDZLS3UAYHOHixYuyOt66dQs/NYaKnD9/Xq6N\nBFm5cqX+ptzVLo7j1q5dK27Onz9flsajVCpFGwl+qQAgPz/f09NTlhiW4tatW8a5mBwdHU2U\nKSEIA5RKJZZkMkF0dPS5c+f0W77//nutViuxUiNR9piajXx8fA4fPpyXl3f8+HExajQ6OnrJ\nkiVlIlsZwUqcaXTIkCEGWTTQEUGWGJg6YvPmzc2bN0e1w4RLtgEDBgxAJQnXg5RKpWgjkfVi\nvWfPHv3Nq1evSu+L3xB/f3+xHqMYINq3b1/pg3AcJyZdxWQkskp0Yl8x06iXl5dc9wsACA8P\nxxWlKlWqWCrT6OrVq3U6nVarFQQBk8QbBAyXW5ycnIzXgG7evIm5aAnihZgon+nk5DR69Gjj\nKtYcx2VlZckNYifKmBdPigaPWi8vr5dPfyxhplE0MIg2kl9//bXYmUb79OkTExPD8/xbb70l\nq69YcE4QBNRdOI5bv369xO5t27YFgC5duug3YqitxLJV+IC4f/++fiNqMFu3bpUywoEDB3BO\nxSsZFRWFlxGdamWB6gIAjB8/XlZHUVNEZ8/bt28Xw0ZirKoWw0YybNgwcRNrbZfErbgs6dCh\nQ0RExOPHj8WWtLS07777ziCPLUEYoNFo8FXBxFe9RYsWGo3GIE9ocHCwIAgv38T08lGIwpEl\ngbIXtIyR9XBn/800OmTIELmZRkeNGiVGiOCA0dHRcn1XsXtAQIBarUYbyYABAyT2PXDggLiQ\n5Orqqp9pVKyNUgzQ4ClRe0M7vLe3N163fv36ibnIxAR0L8TBwUH0IxEE4fPPPy+GqSkoKEgM\nD1ar1cXINMrzPGpvXbp0EVtkiVFxmT17dkpKSu3atQcNGqTVaufOnVu/fv2UlJQZM2ZYWjSi\n/HLgwAE7O7sX/tZ27doVGRmJq73ImDFjLl++bGbpiNKhkIeggwTKXlCzwhjT94SVlWn0iy++\nkH5wUWAFc9FGgvYGQRDk+ueqVKp79+7l5eXxPH/z5k1ZfZ88eYKze2pqqphpFBNlSgHdTkXT\nAjJ16lQA+Oqrr6SMgPpNYmKifiM6S3bt2lXKCB999BFqwzzPnzp1CouwFMMdJyEhAaNSFQrF\nCxeSDcCFJMbY7t27OY7bvXu3gT4qhYpizCiUqlWrnjx5sl27dlu2bNHpdJs2bWrYsGFMTEwx\nLFXEK4K3tzeWWyuK1q1bv/HGG8btWq32xx9/NJtcRClTiM1/2bJlZS+HBbG1tdVoNPfv3xen\nJXzcjxkzRkr3efPmzZ8/vyQzBP5g9OekgwcPTpw4cenSpdLjIadMmRIREaHfUrNmTWdnZ+m5\nyT08PARBuHr1arNmzXQ63ZkzZ1577TXJHwLS0tI4jkNdZ/r06deuXdu8eTPOtZ9//rn0cQyQ\ndWHRzTasceP9u3dDRkb84cNgZ2fn6qqRM4hKpTIo5mJiRblQ0OsiLy8PN62srPRfyF6IaGrC\nt71BgwatW7cOJJekKQ9Ur159y5YtgiBkZmY6ODi8OtYdohiIXtJF0bhx4+bNm//+++8G7efO\nnatAPwoCClU45C57lzqXLl26fPlySkoKY8zNza1OnTpmDafOzs729fVNTEy0Z2wuAAeQDdDw\n9dc7Vq4MERHg6AgKBdjYgFoNSiWgdcfZGTgO7O1BpQJraxcAgbE1a9YMGTIEx0TvDYlmjwkT\nJoCRyX3JkiWY2lXip0BtQ6lUYiBZ9erV4+Pj09LSDh48KCsfRoMGDXC6rV+/vumYNGNWrlw5\nevRoxpho0uA47gWxCVotZGaCIEB6ejWOc2KsnZPTwa1bgTFISwOtdmh+vjXAp6NGwfTpUFAA\nqalQUABZWZCTA7m5kJEBWi2kpUF+PmRn5zJmBQBnz4JeZRwsF6u1slLa24OdHVhZgYMDKJXP\n7qyzM/A8ODuDQgGOjhFLlkzUavMBNBzH2dg8zc1NFYR0QaiuUMQlJYGTE0ibO3NycmrVqhUf\nH+/r63vv3j1ZlxGjstl/842iL62scSxCdnb2G2+8sX79+uDgYJ7nnZycLC0RUa7ZuHHjC7X5\nf/7558aNG6I3Os/zubm5chPbEOUBeV6N5mb79u2TJk3CjJP6VK9effHixWJRiVLnWRxEejqM\nGwc5OZCRATod7NwJubnPpjcAQFNBVhYYTcPPZtShQ2Ho0AwAHcBjgAwAXx8fCA4GGxsAeDbJ\ncRw4OwMAWFkBujjZ2S2zts7Iy0sXBIiI+H+dBuBdgAIA2LTp/3sBgLU1iPUCUOMBGDN2rAsA\nx3HJT5+CRgO2tnFxcSEhIadPn8bsn1IuQp8+fTZv3ixuarVajuNCQ0OPHTsGmZnPNAOT/39f\nq31/6tQjBw5cO33aiufbNW0a6OcHAwdCfj5oNJCXB7m5kJMDeXmg0fz/hX1OHP6TkQHt2zOV\nKofnU/PyJgNkAPifOgVOTs8+u50duLhAUNAzpUGtBhsbvLxd+/YtADh89uwzBREA0tObNm7s\nJAg9O3f+4L33nkmLp0YxUHHJzob8fLhzp5FW6whgrVTWDwiAggJIT4f0dAAAQQAseO3gAE5O\n4OQEzs7P/sC/8T8nJ3ByatWtW4pOlwVgA3D//n1cmpGlLgiCoFQqxQBpuTYSC2JnZ5eQkPDy\nrboS5uCvv/7q379/UXt9fHx8fX3PnTuXl5cn2gu//fbbjz76qKwEJEqZFygcqampa9asuXnz\npsF7alRUVKmLsnXr1nfeeadu3bqLFi2qW7euq6srAKSkpFy6dCkyMrJnz55bt27FnBnmQKFQ\n4MSMiajF/FeFg3OVTgcZGQAA6ekhTZpY63TWAEoABwCO4+pWqzZt0iQAeKa+CMKzqQv7wnPd\nJTV1TNOm+/fvVzEGWFI5JwdycxMSEmYDOALA6NEA8P/nKozlAMsBgLFnkyIAAJzCfxgDfFFW\nqcDevvD+1tZgaxuRkIBLMhiW8m9CghLA4fhxKMpOg7qR0f+15865CYJWEE5fvRpYrx5UqfL/\nChNahtBOgMejzmRrC9bWYGNTr2nTWw8eaABErU5WhMgBjmOMffTrr999953YeEYQAGDfH39I\nGaEDFpD7r07pxvOOjN2+cAHS0yEt7ZkWIv6dnAy3boktuU+e6Ce0zwVIBkjW6Q7xfNt+/cDN\nDdzcwN392R+ens82jYpOabXayMjIESNGvOCrWP4ICQn5+++/X7L0gESpk5+f36lTp6L2ent7\nDxs2TL+OfDES6hDlDVMKx40bN0JDQxljKSkpgYGBT58+zc7Otre3LzSVbMmZPXv222+/vXHj\nRoNluU6dOk2YMKF3796zZ8+WqHDs3bsXk7IXSkhIiKenZ25uLno4xsXFTZgwwcvLC90VQ0JC\n3N3d/fz8sAZEcnJyXl6eq6srHvz/my4uAJDMcXl5ea6+vqe0Wtw7efLkH374wfDgF212Uiia\nNm3q7u4eGxubmJjIGAtp1szd3X3Tpk1g3DcnJ/np07yCAlcHB3VuLuh0fYYMcXR2Fh4//mXF\nCgBI1mrzsrJcAbq1b89x3IZ9+/IAXAHUjAFjyRpNHs+7FhSodToASLayyuP5BZ988i+AE8fN\njYx8pFS65ud7qNV9Bgxwb9LEwcvrq2nT1CoVODgk5+fnKZWuLi5qNzfjT/TJJ5/Ex8efc3fH\nK9msVq3IBw8+6NED4yGlXI3TcXFqtdre3r5evXru7u4qlWrLli3Sr2TLli2PHj169uzZ3r17\nr1u37tixY506dWrWrJmHh4d4u00P1axZM3d3d4OD1T4+dx49gvr1pYjRuHHjlMTEVvXrb4iM\nzMvMdM3IiJw48cnVq9VDQmq+/rrr1avqy5chKSm5cuU8KyvX06fViYkAz40dNAAAIABJREFU\nkNyqVV5AgOujR2qeB3f3tXfu5Li53T53LqyggOO4Zs2a+fj4rF+/XjyRh4eHq55yWa5YtGhR\n3759tVptx44dKfcGUSjNmzc/efKkiQMyMjK2b98upgIibePlwJTCMWXKlHr16u3Zs8fBwWHX\nrl21atWKjo4eO3asmbxKr127Nnfu3EKdgBQKxfDhw6Xnj1q1atWFCxeK2jtq1KiAgID09HR8\nfG/ZsmXAgAH5+fm4sIIeJHl5eQqFQqfTPXz4EKPD8WATmwqFYu7cuWFhYT169Dh+/Hh2drb0\nvjqdLiIiolKlSnl5eajo9OjRo27duqKQ/+lrY/MwPV2j0SgcHNQBAQAwbt68+/fvr1mzBho1\nAoCHly5pGBs2c+Z+AGsrq4ceHhqNRhEUpPbyerbXaPNG1ap/3brFBOGS3t5NffosWLCgcuXK\n6ZUq/f/BaWkKBweMRTH4RF5eXk2aNNHpdHglse/SpUtR4ZB+NRhj3bt3r1y58pkzZ6CwExW1\neeTIEaVS2aNHj8qVK3fv3n3fvn14Jdu0aVP4lTTaxL5///13WFiYuDc4OBg/kRQx6tSps//x\n478uXLh06ZKG5xUNG065coXn+Xk9etxr2VIxePB/7oKXl1qng6Skh1lZGsYUDx+q4+L+t2BB\npblzrSpXbpKXN+Dx47+eSzV69Og1a9bgiby9vQMDAyX+HMqY119/HQAGDx5svMus0Tdl7PtF\nFJsTJ04UpW0olcrKlSsnJCRoNBrUNnieP3fuXIMGDcpWRsI8sKLx9fWNiorCOl5Xr17Fxr17\n92IqzFLH09Pzu+++K2rv0qVLvby8SuVEBmWmC70OL7w4+hQalyWrMrvIyJEjnZycitFRdDC0\ntbX18vISN2V1P3HihH4j1jCT+EHQh8vFxcV42D59+kgUw9fXt+SX8cGDB2IWjVq1asnqK+Zq\ns7W1ZYxNmDABP4J0MQo9GAeRPgIATJ06VWzB2GD9YS1eZtoEM4vGTGfctm0bhkAbUL169T/+\n+KO0zkLl6UsFE86eKpVqxIgRH3/8sdhSuXJlS8v7UmHx54aph6BarT5w4ABjzMvL6++//8bG\nnJwcfBaXOuHh4Q4ODr/++mtubq5+e05OzurVq+3t7ceOHVsqJzJWOEo4Q+DBYhaNmTNn4q9F\noVDIEkycJjmO+/rrr2X1Zf8NasAPtXXrVol9Q0JCjK8DDujn5yf97AaNmzZtkn4dYmJiUHKe\n52NiYgYNGiR3shcJCAjAQiS7du2S29c4hlOWAIXqebKUv0LPaDCCxR8c5YctW7ZwHFevXr1F\nixbt2bPn9OnTp0+f3rNnz8KFC+vWrctx3LZt20rlRKRwlBzToSXW1tZdunSxf+5qdufOHUvL\n+7Jh8eeGqSUVX19fTDUdGBh46NAhzLty8eJFM2WQnT9//qVLl4YOHRoeHl69enU3NzfGWEpK\nys2bN/Py8lq2bDlv3jxznLdQWAkyjc6aNWvWrFmycj39+uuv+qmsAWD8+PETJkyQm/4BAIKD\ngxMTE0+ePFmjRg3pfU+ePCmmf2jYsKFKpTp9+jRehJLURr9z5470g/EL5ujomJ6eDgDNmjVb\nu3YtqnEnT55s1qyZlEHc3Nz0HZy7dOkid/VXp9MFBASIOdpVKpXoIS8FzJ/B8/z48eOXLl26\ncuVKTOhCuSjMRCn6fm3YsMFEDDNjTG4WOEJk3Lhx+q7cBmAypLy8vF27dmHLDz/8YCZnQcKC\nmFI4WrZseerUqb59+w4aNOjjjz++deuWq6trZGSkxLSPcnF2dj527NjWrVu3b99+5coVDI51\nc3Pr06dPr169evXqZb4CWoyxMWPGLF++HDd9fHxAchYN7FVC2VDbEBNMtWvX7tChQ4IgtGvX\n7uDBg9LHsbW1xfjJ2rVry1JWAODKlSt16tRhjJ0/fx5bOI77+++/JXa3sbHRaDT44BAbJ0+e\nDADjxo2TLgZqGyKYWaRVq1ZSgjW++uor1DZ4np85c+aCBQtycnKYXhItidy9ezc0NDQmJsbF\nxUVuyTQs/MsYW7Zsmejt9EplGi1jStH36/jx46bz85LCUTxatGhx4sSJovY2b968Q4cOX3/9\ndcbzQLxVq1aNGjWqrKQjyhAT1o+bN2/ikkpBQcG4ceNcXFxcXFwGDhyIblkVFwPTqBi/hzkl\nRdVhyZIlEgcECTZwE2BVd4MRZs+eXeiwRSFqS/oUw+slKipKpVIplcqffvpJbl/xMkZHRy9a\ntEiuH0mhB6P7gkqlkjICnrFq1aovHNYExlZfcbFMOlZWVuLqmJWVlay+BgtJa9euNVizY+XA\nNFp+sJTvFyGRFyZlGTZsWHBwsLhZPO83QgoWf27IeBC/NBg/OAy82TmOCw8Plz4g9rp06ZLY\nImYaldLd3d0dAIynpWLM1uKc5OnpiS24MiKdoKAgnCZ9fX1ldWSMGacw5zju1q1bErvjtOru\n7m7cuGfPHikjFHrFcC3jyy+/lDJCtWrVRMnVarW4DiLXHYcxNn36dKVSOWrUKLkdWWHmDYPv\nksUfHOUHS/l+EVKwsrIyrW0YUAzlnpCOxZ8bpHD8h4MHDxZjQNGca2Ajkegh37Bhw0J/adIV\nDgxBNJiTsBKK9NeFb775xvj3/8UXX0jsLtK+fXvMrSlLaWOMYS178VLs2bOnGBEiRSkc7777\nrpQR8IzBwcFii5gJQKIMrDAbiVKplN4dwTrd+PGNDTwWf3CUH1JTU9H7R61W161bt02bNq1b\nt65bty7axlq2bJmWllYqJyKFQy4Y5lYoHh4e4eHhBl4aLVq0sLTILzkWf26YcmTTFo2JXhUU\nhULB83y7du14nrfBZOSS0Wq1qHMwxsR01I0aNZKYix19JgycDPDNQKJryPr16wFg0KBB+o3S\nC70iGI0mGlrwIhTDUTcwMNDZ2dnNzU1urslOnTphyVksmfbmm2/ilZReiwQv1yRM8PocxhgA\nYP2zF4IH61e7rl27tiwHHWtra6xBg1oX9tVqtTj/SUer1QqC0KhRI0EQKlyy0bIEfb82bdrU\nu3dvhUJx69athIQEhULRp0+fLVu2HDlyhOq5WITHjx+LdlZjunbtmpqa+qymBAAAODg4HD9+\nvExEIyyHCWWkeL3KP8ZvKsYfsHjriH/88UcJs2iguiPX+wEns3r16hm0S/8gaGUxWNbBcCTp\naytr1641vpKYOFUWOE9zHBcUFCSrY506dfCkzs7OjLF79+6Vio2kGFk0ateuLbY0atRI7q/G\n2EbSqFEj/QMs/qZiTI4ELC1jiSALhyxMh2UZOPlaWthXBYs/N0xFqaDfokhGRsahQ4fi4+Mt\nXk62dMEfhhg8+eDBA8w2g5lGpY8jVtvied7e3j6j6NInxgiCgMVcBEEQPeE/++wzid137doV\nFhb2zz//6DfipCWxpuLFixcB4N9//9VvzMrK4jgO85RLAVd2/Pz84uPjHz9+HBwcrNFofHx8\nmMyYi06dOv31118qlUqsOiuRf/75By9jWlqaqLSVPCmyXPk5jhMXYgDg7NmzuEgksbtKpUIj\nImpd+EM9d+7ce++999tvv8mSpCyRYheUeyWJCgo+DA0aeZ5v27bt/fv3b968KT5aOY4jA96r\ngymFY9q0aQYtjLGxY8e+ZBkF8CEo/jz8/f3RpC99ljpz5kzTpk31B8zMzJQbiikGxJ45cyYu\nLs7b21t633bt2olZNDw8PKpVqxYTE4OfS1YOiYyMDFzUEDel961fvz4AtGnT5tChQwAQGBiY\nnZ1tZ2en0WgiIyMNlnuK4r333hPXPrRa7aBBgwYPHiz3Mp44caJly5b48V1cXJKTk6V3Ry2T\n47gWLVocP3782rVr6D9vvpBsY1Db+OKLL+bOnYstDg4OWVlZ69evL88Kx/z58/EPxtjKlSuz\nsrJ69uzp7++flJT0119/JSYmGix1ES8rr732WqGvau3bt69fv76+Ln7jxg1Z6YKICo9ck0h8\nfHxFTzdrpkyj4iCdO3fGayvXVVBcSuA4zkSkn2kx9Fm+fLnEvr169QIjx1WMtWnYsKGUEdCU\nYtCIaTwCAgKkjJCamopi8zy/bdu2Pn36FDvT6LRp06ytratUqSK3IyvsMlKmUVnMnj27SZMm\nmZmZYotOpxs1atSECRMsKFXJoSUVKZh4HXV2drbXK1j9+++/W1rYVw6LPzdk2yrUarXcVEgV\nESY/06j4Ir5r167Tp0/Dc6OFFDZt2oS5ocQb89FHHxWay8gEgiAkJSW5uLhYW1tHRkYyxsLD\nwyX23bp1K47A8/yiRYu+/fZbnufxVVvMA2ZusPxptWrVdDpdz549f//9dzQ1McakZyzt2LEj\nx3Fz5szJy8tLSEjAuCFZYgiCEBwcLGp+hRqHTYCn43keMx2dOHFCXLOTJUbFZeXKlZ999pn+\n1MLz/FdffbVhwwYLSkWUAWq12vjHUqlSJax0k5aWlpWVhY2MsT59+pS1fISlkfcsTklJmTx5\nMsZbvkwwxvQdJjC8QuIM8fvvvxsf3KRJE5CjtfTr1w/03mtdXFwAQBAE9OWUTuPGjdPS0vLz\n899//31ZHQHgypUrKMDkyZM//vhjFP7IkSMSu9euXRsAWrVqpd/YoUMHAIiIiJAuRlxcnP4m\n1jdv3bq1lL47duzACrEcx3Xp0gWXh9iL/NeMuXz58sKFC3meb9WqFYacSAdXZBhjLVq0wKUZ\nA31UCrL03fLG06dPC7USyVrbIioWSUlJPM8bL+BWq1Zt6NChBgvEX3/9dRmKRpQnTFg/vP6L\nm5sbANjY2BQvWUX5wcA06uzsjJfCIIvGmDFjJA4IJcs0Kqos+o1Y0l26Mf/AgQPGN7dp06YS\nu4vMnj3b1tZWrVYXIwMHntTHxycnJ+f27duiF6Gs7gaNVapUAQBvb28pI+C9M4jmlyUDex6b\no08xsn4plUpxPUjuyprBQtLNmzcrVqbRhg0bvvHGGxqNRmwRBOGDDz54/fXXLShVyaElFRMU\nNb94eHgYvKC+9tprlhb21cXizw1TTqMGFY/UanVgYGCfPn38/PxM9KpwpKamYsUvvCLYGBYW\nVmjR+aJg//3JycqigQ6VBm/hu3fvxilHogBhYWGgV43Fy8vr6dOnp0+fvnfvnqx8GHfv3lWp\nVIIgFKNmW1RUVP/+/RMTE/UDFqQHueDn7dWr17Zt28TG27dvw/MVnxeCl8sgmh+H3bFjh5S0\nKCEhIdnZ2fA8iwbGDel0OqVSKSv9DNpFfH199TMNSAQ96dh/vUk4mdVYLMiCBQu6du0aFBT0\n9ttv+/n5JScn7927Ny4uTqzLRbxMeHt7P3nyxKDRysrKxcXlyZMn//77r0Hsm9z8QMRLhaU0\nHQti4k2la9euxRhQ1BWwJLo4T8ybN09Kd0xtXpJMo9OnTwcjcwimf5D+dl5onbadO3dK7C4y\nZswYFxcXT0/PpUuXyuq4d+9ePKmnpye2lEoWDXSFkXgv8Ix+fn5iy/Xr1+X+UozzHRnka5eC\naGwr1EZi8TcV0xw/fjwsLAzVbisrq7CwsBMnTlhaqJJCFg5jCi3kaW9vP2bMmCFDhtB0U96w\n+HPjpQpwLQkODg48z0dHR/M8X716dVl9dTodzmr4NswYAwAPDw/j2iKFgm8ABmv8YjUWKSMs\nXrwYAD788EP9xrNnzxoPa4IWLVqA3tSIJXO7desmsbuIWq3WarXiNZFOx44dsZQJOgGgnsFx\nnH65edPg5dqxY4d+I14BifcC752+dadmzZqy/D2rVKmCGZ31V+iSkpLk5l3V6XSCIERFRQmC\nINePxOK0aNFi//79Go0mNTVVo9Hs37+/efPmlhaKKGUOHDgQHR1t3K5Wqx8+fLhx40aDdv0E\nvsSrSSEKR64Eyl5Qs8LzfFZWFk42jLH4+Hi5boZarZYx1rlzZ/Fl1EQdAWP032WxZhjazw08\nKIsCtZMbN27Iklmfjz76CAB8fX1F++ejR48wRN5gZc0E69at4zhu2bJlmZmZycnJH3/8Mc/z\nsmKa4uLiGGOYa5XjuMaNGwuCIDrZvBAMSO7Ro0fHjh2xBe1GZRkhgmtA3bp1Q+1TEAT0CL5/\n/770QQICAvAK9O/fHxWXCpdtLysr6++//z548KBGo7G0LETps3Xr1vbt2xs04oMoKSlpx44d\nBtNEZGSkfklY4hXF2OhRvF4VCAPTqIHd/saNG9hSkiwabdu2LYZUBhc5JCREYl/0GDVYesCq\n0La2tlJGwEndOPk0ANjY2EgUA8W2tbW9fv363r17RQuHxO4iq1ev9vHxadKkyd27d+X2Nc6s\nWh6yaMhK64JLbGDkxbxy5UrxGIubRk2zYMECMSz22rVrjLEWLVosWrTI0nKVCFpSESn0nTMs\nLGzKlCkv33zxMmHx50Yh7/HznzNv3ryAgAA3N7cRI0bMnDnzgw8+qF69+v+xd54BTSXf35+b\nDqEXIRSlWkAUBawIgr0hdlR0QUWsu2JfsayKfZVV2bWtvYsFFdwVC4KCXVREEUGxoAjSOyS5\nz4t59v7zSzBMQgrgfF6RyZ25J5dk7rkz53yPlpbWb7/9Vue3qolC/q/SaOvWreHf6EGCUO9B\nVEUjLi5ODvkHkiS5XC6dTofz2r179xD7iiqNDhgwYOXKlTQarbS0FAAAQyARqXMeQVwegLsh\ndnZ25eXlbdq06d+/P5/Ph088Bw8eRDRg9+7dBEFMmTLly5cvDx8+bNWqFaI0O0VNTc2tW7co\nz69Vq1Yy5aNCJ4kgCCqvWPUqGnBNaPny5dQaCXRB0FVV1Mvu3buXLVsWGBh448YNqjr54MGD\no6Oj1WsYRiEkJCRwOByxRk1NTQcHh8jISLF2+NimKtMwjR4pzsgPohgIFK00SgVSSVYVlw6P\nx6PulHBzQSYkb4p//vknYl/4aGJoaCjaCNORJk+ejDICvDGLNcJwCrFhvwflG3E4nGPHjo0b\nNw5+IjmyUh8/fuzg4LBkyRJZO5JYabTBtG3blpoi2Gw2XOE4e/YsYm5zowWvcEDQnW/REoaY\nxoDa5w1pT+E/smIg2QCl0ejo6OvXrwNZ1kgyMjIIghAtrAoXk2SyWSgU3rhxQ1dXl8PhhIWF\nkSQ5a9YsxL6wEEZ+fj6Xy33x4kV6erqOjk52djYA4PDhwygj1HnFYGVwxIsJ1YF69+5dWVk5\nceJEGC8Jl47Q4wDCwsIIgnBxcXn58uWmTZsIgkAPAYEIhUJTU1PRqBqZ1kgozQyq5UdTGs3M\nzISCb6Lo6OigB/9iGi2wXAD10tzcPCgoCO7eimFsbCxaNgWDAdKVRn8cxUCSJEW1H4YOHQqQ\n7xB1Km5BVQx0rwWGZ1LPtTC6qry8HOa7onPs2LGamhqhUCj6cRCBMacVFRVOTk5t2rSBOzIw\n1QUFmNXi6uoq2gjDyhAzRKDsMaz9RtG1a1cAACz1Ui/v3r2DV4xOp1OCMcXFxdDvQefLly9C\nodDOzu769euyZohQcuzUYhX5gymN6urqSoq4pKenQ9FYTNMlIiICxkRTjB8/Pjc3V3Lf9uXL\nlzJFzWN+FKSsfvwgioFUviJBEGw2m/Iz0BfkQcOURmEqitgIsLQm+mJ+nTpdISEhiN0pdu7c\nyePxTExMZFXRIP/7yNTKOZvNRr8I5HeuGHT+unXrhjICjMAYM2ZMvcNKQdK50dfXR+8OYTKZ\n1BqJrFtCkrqiTUtpdPz48XZ2dnC5Dm6pFBYWtmnTJigoSN2mNYgffEtFU1NTcoYRlfij8PX1\nVbexmLpR+7whbSK+evUqg8EwMTGZOXNmWFhYSEiIg4MDk8m8du2ayuxTBpITh4WFhdhvRiYF\nMMlbGtwNQXQX2rZtCwDQ1taud9h6baByUjp06ABbRP1FFGbMmKGhocHhcBBDN0ShyqmLkpaW\nhtgdxoeuW7dOtBHuRzx79gxlhDqvGJwoU1NTUUbYsmULHIQgCE1NTcr7lMPnIElSviASuJMl\nhth3Se0ThxQyMjIMDAz09PT8/f3pdLq/v3/Lli2NjY0/fvyobtMaxI/scIh6GwwGo1+/fsbG\nxpLfUgDA5s2b1W0s5ruofd6o5372QykGvn79Wr7FG1GlUaqIBkCO2YSVydhstlg7usNx8eJF\n+A8SbRw7diyQReNSTBEcIofSaM+ePZlMJofDmThxokwd79+/D086aNAg2AKD4RuoNAprAMHy\nufUC/3f9+vWjWih1E0QbSJJ0d3cXu4xyFLWhvlRw4U3sXbVPHNJJT08fOXIkfPxls9nDhw/P\nyMhQt1EN5cd0OPh8vtjm8rhx4+bNmwcLTIoh+UXFNCrUPm8gTaN8Pr+wsBBqWzUD6pw4bGxs\nqDVwOQTOJZNgLS0t0btL3tLMzMzQ77VQGjUiIkJyWFnv1gwGIzU19e3bt1RCI2J3ij179rRs\n2dLe3j4uLk7Wvr169ZKcxfLy8hC7w/+g2GKGTAlHdX5kmUbw8vKiHAVRFQ13d3fEEVBQ+8SB\ngkAgKCoqEk0Xb9L8mA6HpF6wubl5ndsrAwYMULexmHpQ+7yBpBVBp9P19PRkVapuQtBotLdv\n35L/KY1CgXOZRoCzqqOjI51OhwsbHz58QO9O+TqmpqaTJk2i0Wiw6BeiTCeUuxArkiQ6cr3A\n5RAOh1NbW+vg4GBtbV1dXQ3Lu0s+r38PKIARHBz84cOHN2/eeHl50en0yspKxO4AgISEhPLy\nckNDQ5ge0r9/f1JECKtegoODAQCOjo5U/Wv4yKXKDJFbt24BAAYOHEipaMCgkDoXkL6Hv78/\nIQKNRmuKlc9oNJqurq6sPyVM4+HZs2dUyUArKyv4S8zOzpbMGiMI4t9//1W1fZgmh6QPUlpa\nCjf+S7+PCl0ixSNdafT58+ewhcvlyjSsvr4+dYeQQ1RR8qbo7++P2PfJkydAQq+iS5cuAAAr\nKyuUEeB6xtevX8XaJYeVAjSbw+FcvHhx27ZtVDooYneKJ0+euLi4jB8/XtaO5H+SqWJA3XoU\n6vxRfO+Xgj6CTGsksKgNvHQQ+PL27dvUMWp/UpECAKBz587Z2dmija9evUK/AupixIgRNt8H\nADBz5kx126g6ampqqF9Qp06dVq5c6eTkhH4fwTRC1D5v1FGeXltb29HR8cWLF3VmV1Nfr++9\n1eQg/1dp1MnJCWY2yqTRCTMIqJeLFi1asmSJTPXEhUJhQUFB27Zti4qKlixZsnbtWvS+nTp1\ngnoVdDp9//79Xbp06dq1K8wyFUtjkw6Xy0U/WNIGAICtrW1GRgZsCQkJYTKZfD4fsTQ8AODS\npUvDhw+Hfz9+/PjkyZMaGhoyFeMoLCy8cePGgAED4D/U1dX1wYMH6N3ZbHZ1dTWNRrt+/bq3\ntzeQS0WjgQsqsGzv6tWrV65cCVusra2zsrI8PDxkyq1VIxkZGV27do2JiaGCl5sEM2bMyMrK\n+t67wcHBsmq6NGlgMDukrKzs1KlT6enpdR4pWZ4eg6mTOhyO8PBwuHQWHh6ucnvUw/fEJRG7\nUxXC4P1gxIgRUVFRQqGwZcuWMm2sHDx4kMlkampqxsfH19TUUFEUKAiFQjqdLhQKAwMDqcYT\nJ04gdh86dOj58+dbtGgh6mbBuDA3NzeUEVJSUgAAlLcBOXfu3PDhw2fOnInocEBvg81mz5o1\n6+nTp3FxcZWVldAJQPwgAIA+ffqUlZXNnTt34sSJvXv3Ru8IAKiqqoL/TaikQtFAFQ1ZHXS4\nCEe9fPfunUxfSLUTFRW1aNEid3f3M2fODBw4UN3moELV/KuTGTNmyCq033RZs2bN27dv2Ww2\ni8UqLS39XhVJgiD4fD7eNcOgora1FfWBIm0u08WRPBhu2KPvJlRXV0vOZXKs3168eNHa2trI\nyGjVqlWy9oUnZbFYX79+LSsro8olIHavU9oc7vUYGxujjADdXA8PD0mr0JN7L1++LHYZ27dv\nj9iXokePHtRGm5aWlkx9xXbo6myRDsoXUu1Lo1IAALx69aqsrMzHx4dOp+/atYtsIlsq0vlx\ngkahe21gYPDLL79IeVSQY7cUo17UPm80Ls80ISHBx8fH1dV16tSpYs/KV65ckVTLUBQkScIH\ndAh8uERcGH/x4oXkwXAbnkR+JNXR0amtraVuzKGhoQCAXbt2iVqFQlZWFkwmgjGnMgHl2Gtq\nakxMTLS0tGAht7NnzyJ2h2k1AwYMEG2EWSdQxKxeoIJtfHy8aCMMWQ0ICEAZoaioaNiwYQAA\nDoczdOhQa2trAMCLFy/atGmD0p0iMTFRKBTu2rVLKBRCxVV0sNIohMvlXrhwYe7cuTNnzly0\naFEz+EQ/CK9evYIPD4aGhu/evfvnn3/qPIzFYjWVDT5MI0KKM/L48ePr16/Dv4uLi4ODg3v0\n6BEWFgbrmiqcR48eMZlMJpNpb2/PYDC4XO7Zs2epd2EdQoWcSOxJBZY5BQDQ6XQrKyvKdVix\nYgXKaHD/siFrJPCWJlYFPjY2FiCXPSNJsri4WDKNSLSgOSIjR45ksVgsFkvW3GAq0oJaUaA2\nvBFHqPPg8ePHAwC8vLxQRoB6a9OmTat3WCkcO3ZM7DIOHz4cvTuExWKJVmORqS/sKKqqQkgU\nsVP7k4oUwH8l6SERERF0Oh1K1KvRqobzI6xwFBcXIz5oqdtSjDyofd6Q9r3p1avXr7/+Cv+e\nNWsWi8Vyd3dnMBjbt29Xhik+Pj6WlpYwPfXjx48DBw6k0+nHjx+H7yrP4SBF1M0pGqg06uLi\nUqcXUie///47AGDChAmSw4qqWUsHThM6Ojq5ubmkiNJoVVUV4giQmJiY7t27d+nS5eLFizJ1\nJP9bmBHjyZMniN2hFPrBgwdFG2HGL+IgdU6FUBLx3bt3KCNQ4mM0Gs3CwoIKo6G0yFQA3IcS\nowkpjYo5HCRJxsTEQF9QXSYphGbvcIwdO5ZGow0dOnTq1KnSvY3CwkJ1G4uRB7XPG9KmAH19\nfXjX4fP5+vr6sLjG6tWrO3TooAxTzMzMRLNJBQJBcHAwnU4/duzTNnwTAAAgAElEQVQYqWSH\nA3L58uXWrVs/f/5c1gGpmCkGg9GhQwfqEQHuXtfL/v37AQDDhg0TawfIKalJSUkAALFoAxg9\n2rZtW8RP8eXLF7E4EjqdnpmZididon379gwGg8ViyXqTpsq2zZgxA7ZQaoaII9R5MAy2//ff\nf1FGgP+72bNnUy1paWky2UCSJKUCQrFp0yb07hDRQDxJ2Xu1TxxSyMvLkxQJzMjI+Oeff9Ri\nj6Jo3g7Hb7/9BgCwsLAICQmxtLSU4m2gTymYxoba5w1p0yiTyUxISCBJEpYMhWsPN2/elDWM\nDhEOhyP2dCsUCoODg2k02pEjR5TtcGzatElfX5/JZBobG8vxcC8Zp+3g4IDeXdK3WL9+PQCg\nZcuWKN179OgBANi/f7/ksEwmE9EG+BGMjIweP378/PlzWNtTjriwtLQ0T0/PMWPGwLUWmYAf\nRIw3b94gdocfAZYNE2tEHKFO30KmETZt2gQHIQiCKuEGAFi9ejXiCCiofeL4AWnGDgeU/0cB\nB4o2adQ+b0gLGjU2Nn7//j0A4ObNmxYWFjAEr7y8XEm6jZaWlmLJVwRB7Nq1a8qUKQEBASdP\nnkQf6tWrV9e/D/lfGDYFl8tdsmRJYWFhbW1tXl7e8OHDYWVzdKDSaJs2beh0+sKFC0mSTE1N\nRe9ubGwsEAhYLNZff/319u1bR0fHZcuWAQBkGqQh7NmzRygUWltb5+Xlde7c2cnJKScnx8nJ\niSTJ5cuXIw7y+vVrBoPRtm3b+Pj4yMjIFi1a1FlMUgqJiYn5+flQnpLBYEA5cCrIpl4WL14M\nAODxeFevXoUtpqamQqGwgWl7cFsHkaVLlwIAfv75Z6FQWFNTIxQKYcwsfIJEZN26dWJKo7KG\nD6uesrIyqCpb9n3UbSOmDkJDQ3V0dKC4bb0HyxGNjsH8H1KckZ9++sna2nrjxo2mpqZz586F\njZs3b3Z0dFSG7zNlypSOHTtKtguFwilTptRrrSiurq7SP/X06dOpg1u1agUA0NbWrq6uJkky\nMzMTRl+OHDlSJvtDQkI4HA6NRtPX10d/KKdo0aKFqIUEQVDxK/Xy8OFDIFIqFuLn5weQk0Kh\nkKKkhiwAwMTEBNEMaLmWltaePXuWLl0K79OyhkySJFldXR0ZGfno0SNZO5L/1aARA33Luc6v\nmUzfvToPlklpFMrMAwmlUdHNPrU/qUgCAIAzg3yzTeOnua5waGlprVixol+/ftLnTIAcu41p\ntKh93pD26LZhw4bx48evWLGiS5cuK1asgI2nT59GL64hEz/99NPXr18zMjLEnmgJgvj77791\ndHTu3r2LOBS8AX8PGo1mampKvXz//j1BECUlJfCljY0NLJB44cIFdOOh6Bb8u7Cw0N7e3tra\n+u3bt+gjfP369cOHD4sXL87MzAwJCZkwYQJ6X1dXVzqdXlFRweVynzx5wuPxXF1d4XIR4pMx\nNL5OqTHE5Deo2dWhQ4dnz57Blg0bNmhoaFRVVd29e7d79+4og+Tk5PTs2ZO6bgRBTJ06dd++\nfSh9IdnZ2VevXvX19a2qqoLJEVC4ExFra+t3797RaLTc3FyoCwKjHWVaI2ngEuCZM2cAACtW\nrFizZg1lVVZWVseOHRtzIuIPKBjYDIiMjCwrK9u5c2dRUZH0I0+fPk25whiMnNTrkoglwebk\n5KBXpmicSAp/SWafwvBJxAGpR3moTxUWFgavbWhoqEyG7dmzx9zcXEdHR44nCXh/Ffvnnjx5\nErE7VFLv1KmTaCMsfCq6GiQFuHsi1njt2jUgi/QWVBvz9PQ8d+7c77//DhNMZF1qgqxatUqs\nbCwidRYpLC8vR+xe588K8bdGHdykhb+aK81shaOysvL69euI1Qx++ukndduLUQBqnzfqnwRL\nS0vj4+PPnTtXUlKiAoNEEQgEKSkp6HM9IpIOh2QWQAMjDeHqgkwBVpKBAqK5EoicPHnS1tbW\n1NQUSi3JBHwuh3EbpMi2FGJ3mNQq1piZmQkAsLOzQxkBxjrAWrsU5ubmMl3GuLg4sQUGZ2dn\n9O6QiRMnUioaiMZTwG+OaAgw9GB+HKXR5kozczh2797966+/UoLC34MgiE+fPqnbWIxiUPu8\nUc9C8aZNm3g8nqen56hRo7KzswEA7u7uUDdCBZSUlDg5OdUpS6BACIIoLS0VjWi7f/++UChE\nrJtQUFAA/is7QgF3hUhkdUUWi8Xn8zU0NIqLi0mSHDNmDADgzz//fP36NeIIEB6PZ21tbWlp\naWtrK1NHAMCjR48IgkhJSYFxA/AlLLaOAjzjnDlzRBs9PDwAAPPmzUMZISoqikajzZo1S7QR\nTvExMTEoI1RWVsLFITqd7uzsDP8pT58+RQ87hRw7dkwoFKalpQmFwu9VkfgesGKfQCCgIjBg\nS2PeDVEIVQio20bM/+Hp6RkeHl7vP6WgoEDWCHoM5ntIczh27969bNmywMDAGzduULv7gwcP\njo6OVoltKmLGjBkAAG1t7R49emzdurVdu3bdunUDAERFRaF0h1sJtbW1chtQXV1dW1sLd2R0\ndHQAAGfOnDly5AgAAJaYR6G2tlZbW7t3797Xr19/+PDhjBkz6HT6jRs30M3o3LmzUChcvHix\nqampiYnJL7/8IhQKPT09EbtDv/DPP/8cPXo0bHF0dIRO6uzZs1FGqKmpkdzOgJIAeXl5KCPA\n7L5hw4bx+fzk5OSCggLo88GFFkQePXrEYDAIgmjbti30GNatW4feHQBA/qc2BjEyMkJ3PcF/\nyxu6urpUC1w1kSlZRvVoIKBuGzHg3bt3cOe3ffv20r0NGo1WW1v7QxXIxSgbaVPY9u3b582b\nt3XrViASB9emTZudO3eqwjRV8ddff5WWlh47duzu3btUXOqmTZsGDx6M0h1Oo2Ipf3/++ScA\noM5oAEngipFYUc1JkyZNnjwZvZCHrq5uZWWlqalpUlKSgYGBj49PQkJCv379ZH2wDgkJMTAw\nEAgEiOVLKNhs9qpVq1avXn3u3DnRTQ3pAbyitGvX7sOHD1lZWVZWVlQjjEAcMmQIyggwLfPS\npUuijbq6usXFxdnZ2SgPam/fvoXVcVkslo2NTXZ2dmlp6fLly4uLizdv3oz4QQAAubm56AeL\nce/eva5du5aUlIheRoIgGuLUqoANGzbAP0iS3LNnT1lZma+vr4WFxbdv32JjY798+YJYUgej\nPBISEm7dujVhwgQnJye48CaFgoKCRu7jYpoeUrZbmEwmJQ7IZrOhXHFsbKxolQelUlhYCAC4\nffu2Yof93l5sbGzshAkT5FAapR5n+/bt+++//8JYfQBAXFwcSvctW7bAvmLtAHnjH+68mJqa\nijbC+R1d7rO6urpdu3ai3w1bW1vJRNl66dy5M5vN1tTU9PHxkakjXA7hcDgPHjyALYsWLQIA\n8Hg8xBHq/EpD9yUyMhJlBOg+Ll++nGqRQ2n0+fPnovtxTCbz8ePH6N0honkxXC5X7F2178VK\nYe3atW5ubqLfHIFAEBQUNH/+fDVa1XCaQQzHvXv3JEsF1Ymenp66jcUoHrXPG9KmUSMjo337\n9sG/KYcjIiLC0tJSFaaRJFwYV3hSTJ0Tx+vXrxcsWODr6/vrr79+/fpV1jElpfoofW4UgITS\nKEx1MTAwQOkOK5xJCqQCAHR1dRFt4PF4AIBevXo9f/48NTW1b9++4L/tAJmoqKg4fPhwVFSU\nrB1Jkty+fTtVqAz+oaenV1RUhNgddsnPzxdtbLjSKAysQxzh3r17cBAOh2NlZUUF5SnWb1b7\nxCEFCwsL0bKLkC9fvqA7jo2TputwVFZW1tTUkCQJQ4tQHI709HR1W41RPGqfN6RNo+PHj7ez\ns4NC0dDhKCwsbNOmTVBQkKrMUwqSE0dgYCDcrdfQ0CAIgk6nr1mzRo6Rhw0bZmFhAYvOyARM\nTmMwGJGRkbm5uY6OjvBnj6gOPm7cOADA1atXxdoBADo6OigjPHjwAAAwZswY0UZYw+nKlSuI\nn6K0tFRsjURy2QZlkHHjxtnZ2bm4uMh6JWH5GABAUlISbIFeVAMzRKA3iTgCjHYSlZk/fvw4\nkEVjniTJxMRE0RUOFotVWVkpeoDaJw4psFisc+fOiTXm5OSobGVUSTRRhyM7O3vLli3Q3xXV\nH5KCKksVYlSJ2ucNadNoRkaGgYGBnp6ev78/nU739/dv2bKlsbHxx48fVWafMhCbOGBI4Jgx\nY6DSaH5+PiylHRMTI9Ow27Zt09fXZ7FYVlZWclRT1NTUFPvZb9y4EbEvVEC3sLAQbYTSGn36\n9EEZYfLkyQAAGE1GwefzAQDoOyMwvqxHjx4XL148ceIEzA2RIyuVJMkLFy7Ip6IhGmtJgZ7X\nB48Xa5RJJxTUVXIPRvMgjrB7925oBo1GE81aFP1SqX3ikEKnTp169Ogh+l0SCoWzZ8/u3Lmz\nGq1qOE3U4UhMTIyJieHz+bAkFgqwUAOm+aH2eaOeSTA9PX3kyJFwY5vNZg8fPjwjI0M1likP\nsYnDyMiodevWYsfo6urKVBRXMrrK1dVVVsMePnzo5uZmYWGxdOlSWftCGQxra2soW+Lr6wvN\ngEup9QJ10CXb0R93Dh48CAAICQkRbYQBmGLV1KSQl5cnJvE+duxYxL4Ue/bsoaQv7O3tZeoL\nDWaz2VVVVbClTZs2sAVxBACAhoaGWCNcwUIfAQCwe/duqgVub4kOq/aJQwpXr15lMBgmJiYz\nZ84MCwsLCQlxcHBgMpnXrl1T0hnj4+OHDRvm4uIyZcoUsaoCMTEx5ubmCjlLE3U4IBkZGYib\nKdHR0eo2FqMs1D5vIE2CAoGgqKio2bi9YhMHnU6fOXOm2DG9e/dGj36ADhmDwYB3Vqramaw7\nAp8+fYqIiAgNDYUV5mSivLwc+hwUBEGgl72FOcBijs7GjRsBAFQcj3R69eoleU9NT08Hsiiu\nQr+tVatWq1atmjp1KtyekK+CQ15ennzf2DqlkCj/o15AXZsyDV8jgWZQL9U+cUjnzp07ffr0\ngf8+FovVp08fapNL4Tx69IjJZDKZTHt7ewaDweVyRSNIlF1lunFSU1Nz9uzZy5cvUy2I+Sai\nbi6m+aH2eUPmn+KVK1ca80yHgtjEwWAwJk+eLHZMt27dJPXOv4fYzYD8L22ERqOhWzV+/HhK\n3RIAwOPxnjx5gt4dcuLEic6dO9vZ2a1YsULWvlwulyAIyjmABUs5HA5idzc3N8kbLUzr/fnn\nn1FGgIm4YmskcKcJ0QaSJMvLy4cNGwanV4IgeDyeHN7b7NmzqTUSWTcC4Da5g4MD1dKxY0cA\ngLGxMeIIAAAtLS3JxibkcED4fH5hYSGfz1fqWXx8fCwtLd++fUuS5MePHwcOHEin06nChz+m\nw/H48ePw8PCcnBz4cuXKlSjeBnoJAkwTRe3zRt0/xfLy8nPnzu3atevmzZtU47Vr12BwgxyZ\nC40KsYnDxsYGKk9QLYWFhUwm09vbG2U0mLvbokULsXZJL0QKkyZNAgD4+flBpdHIyEgtLS0O\nhyOrrHt2dva6desWLVqUnJwsU0eSJN+9e6etrS06AXG5XPRAivnz5wOJCFMoqpaYmIgyQp2x\nmXC56OjRoygjCAQCExMTGo02evTo/fv3r1y50sjIiCAIyRhGpULFe4r+gd69zuObisNRVlbW\noUOHFy9eqOyMZmZmW7ZsoV4KBILg4GA6nX7s2DHyR3U4SJKkJjQqr1s6Dx8+VK/BGBWg9nmj\njp/i+/fvYcV2yLBhwyoqKmAehJaW1sqVK1VfVEWxiE0c//zzD0EQ5ubmZ86c+fTp065du3R1\ndRkMBnxmqhcoNiW5HILucAgEAgaDIRYqkZ6eThDEggULUEaAuLi4iM4gxsbGmZmZ6N0he/bs\n8fb27t27944dO2TqWF1dTaPR6HQ6dXeHaySSdWq+h46OjuQayYkTJwBy/OyqVasAALGxsVSL\nQCAwNTVFX10gSbKoqMjBwYHa8DYyMpLDe/P09ITeBo1G69mzp0x9YccBAwZQLVDoRfRTqH3i\nkIKWltb79+9VdjoOh3Pw4EHRFqFQGBwcTKPRjhw58kM5HC9fvpTMKYNavdJJSUlRi8EYFaP2\neaOOn6K/vz+TyVy8eDFVsRPeyfz9/eUQqGiESE4ckZGRUFMcYmZmdvfuXfQBJX2L8+fPAwAY\nDAZKd5hjIilcYWRk1LVrV0QbYD6qq6trampqbm4uLD+GHupIUVpaunHjxrVr18qRaBMdHQ33\nMmg0Grxhc7ncd+/eIXZv3749AEDMSercuTMAICsrC2UEZ2dnExMTsUaYrQNTkOqloqICfgQH\nB4epU6e6u7vDD3Lr1i3ET9FwUlJS6rwriB6j9olDCn369Dlx4oTKTmdvb79s2TKxRqFQOG3a\nNBqNNnLkSHSHIysr69H3AQDIsVOpMrKzs1evXi22mpicnFyvt9HUV6wx6Kh93qjjp2hqair6\nYA3DCadOnapCq5TL955UXr9+feLEiQ8fPsg6oImJCfzpLliw4MuXL5QWBaLSaMMdjvz8fABA\nt27dRBuhvPqqVauQPgNJ1tbWij0MmZqayqE0OnfuXCcnJzc3t/Xr18vUEV4HBoNBre7CUnCS\nSR/fo3Xr1ra2tmKNsCoNoq/cu3dv8L8Sal++fKHRaIgKbJDy8nIfHx8ul0uj0bhc7pAhQ+S4\njFpaWtQ/wsbGRuxdtU8cUnjy5Imdnd2RI0eoGAKlMmXKlI4dO0q2C4XCKVOmSPpqUnB2dpZ+\nb542bZpCbVckfD5f8ksuFkheJ3LMeJgmitrnjTp+inQ6XVQHGtbNojTOmwHKWBoVqxYr09wk\nZUtl4cKFKCNAcXRKEZyCIAh0GQyoYGFhYXHixInIyEhra2tQl6g2Cp8/f/727ZscHakyb9SO\nBoPBQFfR6N+/P5vNFktOGTdunGTSx/fQ1NSUzE6CxfwQRygsLNTR0aHRaH379l2wYEG/fv1o\nNJqWlpaY/mkDUfvEIQUp9zZlnC4+Pn7IkCFi2bAQoVA4b9489GVC6TTOLZWysrLExEShUCjW\nzufzxUKy6gRdxhfTDFD7vFFHrpRAIBDNDIR/iz5vYSQpKCjIysoKDAyEyiUy1bej0WgTJkw4\ncuSIn5/f3r17dXR0IiMjp0yZwuFw4HZAvdTU1AAAoNiDKFRt9HpJSEgoLi52dXWlaq2NHj3a\ny8vr1q1bZ86cGTt2LMogAoFg9+7da9asgaXL7OzsNm/ePGLECJS+kIiIiOXLlw8ePDgzM5PD\n4QwbNuzvv/9G775mzZpu3br17t07NjYWfm+h84Re85bP50uWx7S0tKQEy+slICCgrKwsOTm5\nQ4cOsOXly5cdOnSYPHkyepnlDx8+tGnThirm2aJFi69fvyL2VTswkkZleHh4eHh41PkWQRCw\n+F9zpbq6et++fVwut1u3bqIyGyRJmpmZ1Vv6MSAgoE6hPAxGWUj6IACAsLCwa/9x+fJlAEB4\nePg1EVTuGCmSxvmk0pC02A8fPgAABg8eLNp48eJFAMDcuXNRRujXrx/4Xy1LkiRhedIuXbog\nmvHzzz/r6elt3749PT39+fPnoaGhLBZr7969iN1FuXPnzufPn+XouHz5coIgmEymhYUFdB1s\nbGzQk32gVqxYo7W1NXqaiZ6entjeFkmS7u7uiBrzJEnGxsbC3yadTtfW1qZSXUTDUNT+pNKY\nEQgEKSkpsmZ41UsjnDf4fP7Dhw/FxP2EQiHK2oZk6jWm2aP2eaNuh0MON6UJ0QgnDsjnz5+h\n8JdoNjIisGjIhAkT4MsdO3bAnBFEFYQ6ZbtIkgQAICquZmZm0mi0GzduiDZu375dX18fMWCT\nJMmioiIDAwPRb9rIkSMR+1JkZGSMHj26ffv2np6eu3btkqlvaGgoAEA0I3r16tVAFoF2Docj\nVpKGJMmJEyeiVxKBEiCi1ViGDx8OABCNh1X7xNGYUXGVabWQlZX1PV07xGVROVLYME0dtc8b\ndWypQI1qjOrh8XhUEIOspKent27d+sSJEzCPFADAZrOvX78O7171Mn78+Nu3b0+fPn3v3r1U\n47JlywAAPj4+KCMkJCSYmZl5e3uLNv7000+//PLLs2fPoGR4vRgYGMDns0GDBmVnZyclJZ0/\nf75r1673799H6Q6xtbWNjIysqamBSpcyERYWFh0dffPmTQaDoaOjU15eXlNTo6urm5SUhDiC\njo7Oy5cvxRpfvHghmgYlHYFAwGazqYBHAEBUVBSNRmtCuyqFhYWHDx9OT08vKCgQbT916pS6\nTGpOxMTEJCcnz549WzJ0DAAAI7qk4+HhYWNjowTTMBipqNHZUReN6klFsURHRw8fPrxv377b\nt2+XtS90TSihT6i4hb6VsGvXrnbt2ok18vl8Go2GmFMKMxh9fX1FG2GSKqINJElWV1f7+flB\nV4NGo1lZWd27dw+9O+TgwYOWlpZcLtfU1BRRJpVi7ty54H8lovfv3w8AkJTP/x4AAMlK7mLl\n39T+pCKFtLQ0IyMjQ0NDgiCsra1haJGWlpajo6NqDGj2KxxXrlz5XmoJlAUSQ+ypgyAIZcu/\nYhonap83sMOB+f88fPhQbGKi0Wjomzu3bt1iMpliddri4+PhoznKCHVWOJs6dSqQpcSDubk5\nQRCDBg0KDw+fN2+erq4uQRCyFv5tCAKBwMnJCToN3bp1MzMzAwA4ODigF3YBAEjuv4g9Hqh9\n4pCCr6+vt7d3TU0Nm81+9eoVSZLR0dEtW7YUFWRTKs3V4aiurpbMRhHj119/rfchMyEhQTUG\nYxobap83aOhrIZjmjaurK5/PnzNnjrW1tZWVVXBwsEAg8PLyQuzu7u7u6Ojo7+//5csX2PLy\n5cvg4OBx48aJFYD9Hnw+X7IRCn/BInD1sn79+uzs7IsXL165cmXevHnh4eHfvn0zMjIS3Z6o\nF4FAsGvXLldXVz09PQcHh6VLl9Yb7S8KjUZ7/vx5RESEvr5+Zmamnp5eeHh4amoqFftZL0wm\ns6amZuHChVSLq6srAKCprIE/ePBg+vTpTCYT6sYCAIYMGbJv3z6VZa9oa2snJyd36tRJNadT\nDW/fvg0PD4dFmr5HTU3Nhg0bRFtgKSJRUlNTYcAWBqMG1OjsqAu1P6k0V969e9e1a1dNTc3u\n3bu7uLgwmUxfX19YHQYFuBggpijfunVrAABiSZdOnTpJqpj/9ttvAIDa2lqUEQQCwaBBg/T1\n9VevXn3x4sWdO3fa29vb2dnl5uYifoqG8/z5c/jbJAiCCkMR29tS+5OKFDgcDowdNjExoYQv\nKysrNTU11WpXQ1HvvHH+/Plr165JX+FYsGCB9Nk+LCxMZQZjGiFqnzfwCgdGYVhZWSUlJZ09\ne3bo0KF+fn7x8fEXLlxAD5aE4a52dnbPnj2DLTNnzkxPT6fT6Q4ODigjlJWVSZ4OLgxAMdZ6\nOXXq1J07dx4/frxy5UofH585c+Y8ffpUQ0MDMfIfUlNTM2HCBH19fQaDoaen5+fnB4VSEHFy\ncqqurobaprBj+/btEfVUGgNmZmbfvn0DAFhZWcXFxcHGZ8+eSerEYNAZMWJE3759RcU2xKio\nqNi6dSv10svLS+zg1atXwyQsDEZd1JGl8mNy//79adOmZWdn29vbR0ZGtmzZUt0WNUloNNqg\nQYMGDRokR19PT89Bgwb9888/zs7O1Go8QRCPHz9GHKFVq1Z37twRa4yNjaXRaJT8vHSio6NH\njRoFVVYhmpqas2fP3rRp044dO1BGKCsra9myZVFRUY8ePRwdHV++fHnmzJmrV6++f/8e3fdi\nsViIHlIjpFevXvfv3x87duykSZN++eWXzMxMAwODo0ePDhkyRN2mNTGqqqqioqJsbW1Rkrz8\n/PxEX8bFxdFoNBqNRrmq2NvAqB3scAAAgLm5+efPn+HfDx48aNWqVZcuXWRKxcQohCtXrrx8\n+bJPnz7fvn1jMBiurq63b99G775ixQpPT88BAwbExMTA9JbLly+fPHmyR48eiCMUFBTAqBFR\nzMzM0G//gYGBxcXF9+/fp24Sjx8/7tKly+TJk2FZIhQEAsH+/fujoqI+ffpkb28fEBAwbNgw\nxL5qJzQ09OPHjwCA4ODg9PT0o0ePAgAGDx68bds2dZvWxIiPj8/Pzx8wYEC9R549exYqNELo\ndLpAIBAKhVSLkZERYoY8BqM88JYKcHV1/fz5M51Of/78OUmSp06dIgjiwYMHolF7KPz5559s\nNhsW+lKSqT8CDg4OX758qa2trayslMnbAAB4eHiEhIRcu3aNy+Xa2dkZGxv7+PjweLyYmBjE\nEVq1avXixQuxxpSUFCsrK8QRbty44ebmJvpI6uLi0q1bt1u3biGOUF5e3rt376VLlzo4OAQF\nBRkaGo4ePRpm6zQJ7O3toRwLg8HYvn17QUFBQUHBsWPH6hSNwEjB29t7xowZKNdt/Pjxoi/F\nylMAANC/fhiM8sAOB4Ar9nw+H2Yzjhs3DtawkKkKA41GmzNnDtQYLiwsJAgCMTUDo1i2bdv2\n/PlzuNtta2u7ZcuWjx8/ou9lTJ48OSYm5ty5c1RLSkrKtm3bAgICEEeorKyU3I+ztrauUyCh\nTrZs2fLhw4fU1NTff/997ty5e/fuTUpKOn78ONSqxzR7nj17BksaMZlMlGWJ0aNHi2Z4wS5U\nIR4AgKmpqaOjoxIsxWBkAzscAAAg9gzBYrHodLrogqR0YAYBQRAzZswg/yu7mpeXN3PmTJnM\nqK2tffnyZWJiYtPdv28MtG/fPiYm5s2bN/fu3ZN1mapnz57r16/38/Pz8vIKCQkZNWqUi4tL\n//79oZwXCtra2pK5iy9fvkQpbwE5e/bszz//DLXqIS4uLmPGjDlz5gziCGqhCgF129gESE1N\nvXjxIpPJRDw+Pz///Pnzoi1CodDW1la05dKlSwqzD4NpAI3d4aioqAgICEhLS1PqWdB9izqB\n4Y1CoXDXrl0AgKKiIqguvGfPHvRBzpw5Y21t7ejo6O7u3rgKeWsAACAASURBVKJFi2nTponJ\nQmNUw5IlS5KTk93c3N6+fWtqahodHX3ixAkYEYLCyJEjU1JSKIF5AMDp06efPn3q6+uLOEJO\nTo5o1CrExsaGEjhpnGggoG4bmwDW1tbTp093dnZGPP7ixYvkf7pwlHReZmYmdYCdnR1iYQEM\nRtk09qDRmpqaw4cPBwQEtG3bVnlnKS4uFn2Zk5MjEAgQY6ygrKFYBtrChQsXLVpEolXCAwCc\nOnVq8uTJK1euDA4O1tXVTUxM/Pnnn4cOHXrnzh10wShIUlJSUVFR7969JTV/MIi0b99+8+bN\n8vWNiIiIi4ubOHHismXLrK2ts7KysrKybG1td+/ejTgCj8d7+/atWGNmZibUKWm0UJJTJEnu\n2bOnrKzM19fXwsLi27dvsbGxX758kXW16YeiuLj406dPjo6OmpqaMv1yYUwuzOoqLy/39PS0\nsbE5dOgQNfkcO3ZMKRZjMHKgFvWPOjGpCxgJoa+vD18q5ERiAj4DBw4EAFCNEyZMgFcGsRwJ\nXIeAP3hRZLq8dnZ2YppC2dnZmpqaly5dQhyBJMlffvlF1Eny9vZGF93CKJb169fb2dnp6ura\n2tquWbNGpr6rV6+2tLTMzs6mWh48eMBms0W/DGoX8JHC2rVr3dzcSktLqRaBQBAUFDR//nw1\nWtVwlCf8VVhYuGXLlpMnT8rR18jICP7e65To8Pf3V7i1mKaL2ueNRuRwAABMTU37/C+enp4A\ngM6dO8OXCjmR5MTh4uIi9kMdN26cTJaL+RYRERF1eiF1kpeXBwB49uyZWHvfvn2XLl2KaIO/\nvz90MuLj4589exYcHEyj0aytrRG7ixIaGkqVcMOonvLycg8PD11d3Xnz5v3xxx+BgYFMJjMo\nKEj0GLVPHFKwsLA4e/asWOOXL18kK9I1LZTncJSVlSUlJclXUI2K9uByufb29qKPHKampgo3\nFdOkUfu80Yi2VMLCwsLCwuzt7Tdu3AjjLgEARUVF+vr6W7du7d27t/JO/ejRo4KCgpCQkPv3\n7w8cOPCPP/6QqTt0LGg02ubNmxcuXMjj8XJycgAAiKkNMMJcspY6i8Wqs7yIJFVVVSdOnPD1\n9b1w4QJs2b17t7u7+6RJk86ePTt69GjED8JkMqkzhoeH0+n0kpISvDWjYjQ1NePi4g4cOBAV\nFRUXF2dvbx8VFTV48GB124VKbm6u5NM2QRA4FFoMkiRzc3NNTEy4XG737t3lGKGmpobP51P7\nKW/evBF9Nzk5WUGWYjCKoREFjYaGhj558uTZs2cODg5icdcqwMDA4PDhw2lpabJ6GwAAoVAI\nf/OLFi0iCAJ6G3p6egcOHEDp3qJFCx6PFxsbK9pYUlJy9+5dxAJU//77r1AoXLdunWijv78/\ni8WKjIxE/BQ0Gg1OXnZ2dm3btiUIQiAQaGlpIXYX5f3791DcGiMfNBpt2rRp0dHRT58+jYyM\nbELeBgDA0dFx69atomnAJEmuXbu2ffv2arSqsSEUCiMjIw8cONAQ0fqnT5/CB0f4kiAIKuTL\nwsLC1NRUAYZiMIqjEa1wAADatWt3586dHTt2TJo06ejRoxEREfLVXygpKVHxDU8oFC5btmzz\n5s1CoVBDQ6O8vBy9L41GW7Ro0fLly01MTMaNGwcA+PDhw7Rp04yNjUeOHIkyQllZGZBI7gUA\nMBgMxFzEHTt2kCRJp9NF11Tggsf8+fMRNSL5fL6Li4to7bERI0aIalpgfgQ2btw4ZMgQa2vr\nkSNHmpub5+fnX7169c2bN1euXFG3aY0IuIEydepUuQVAb9682bdvX9EWUedj+PDhDTURg1E4\natjGQSAzM9Pb21tHR2f9+vUAgLi4OJm6QwkvKcycOVM5hsuJUCgMCwvT1NTU09OzsbGh0Wge\nHh4ZGRmI3aEu+/Lly0UbU1NTAQCbNm1CGQE6dvfv3xdtfP/+PQCAxWIhmgE3wnR1dSdPnuzr\n68tmswEAHTp0QOyOQUfte7HSuXPnTp8+feAuIYvF6tOnT1JSkrqNaiiKiuEQCATydUxKSho8\neLCBgQGbzWYwGNS+FYPBaN26tVjWcXh4eMNNxTQz1D5vNK4VDgobG5sbN27s27dv0aJFcnSP\ni4sTy3QVxcnJqbGtURMEERoaOnXq1Lt37xYVFTk6Orq5uUmpDCkGj8dr3779xo0bW7ZsGRQU\nBAC4d+/eoEGDNDQ05s2bhzJCbW0tAKBLly6ijVAxE3HJ98CBA8XFxT179hQtn2ZkZPT8+fOi\noiI9PT3Ez3L69OnNmzenpqZqaWl5enpu2LABVqjHNCF69ux5/fp1gUBQWlqqra2Nq3hQvHz5\nMioqavr06VR2CQpVVVVDhgy5efNmne/y+fz09HSCINq0aUOJziEWWMZgVIoanR0U8vLykpOT\nRVPsGo6Wltbly5cVOGBjoLi4GN6YmUwmfNaBeh6I3aE0kJ2dnWhjt27dAACIqS7t2rWT/DrB\nKRIKsKIwb948TU3NZcuWxcbGRkZGQp+pGTwcKxy1P6n8gChkheOvv/5KSEiQtdfkyZNlndjz\n8/MbaCqm+aH2eaORrnBAhEJhTk5O69atcaJEvejo6Lx+/frixYvnzp2rrKzs1avXnDlz0EXD\nHjx4QBBERkaGl5dXXFwcAGDYsGH37t0DAEiKUNVJnWErMPYeRtHWS0pKyo4dO27cuEFlJI0e\nPTowMHDu3LmPHj1C+xwAAHDmzJkdO3akp6cbGhr2799/1apVuJyeWsjPzxerIGNhYaEuY1AI\nDw+XImpMkiQMlmoIspY7AACUl5cfP35cpi46Ojr4O49phDRqh6OkpMTJyen27dvu7u7qtqVp\nMHz4cLmDxWbPnv3nn3/eunVLdCsHBrGi4Ojo+OHDh7i4OC8vL6pxzpw5AICxY8eijHD16lUn\nJyex/OdffvmlU6dOubm5iMXwgoKCjh8/PmfOnJCQkNzc3N27d0dGRiYlJaGXe8U0kNLS0sWL\nFx89elTSByWRtXfVQkFBARQO/h7y1UAoKyu7dOlS9+7dJRXrUXj+/Dnc1oSpcChdli9fLseJ\nMBhl06gdDowqiYiIiIiI0NLSqqioAABoaGjk5eWhry0dOXLE2Ni4X79+iYmJXbt2BQAcOHBg\n//79NBpNrHb29ygqKjI2NhZrNDExAQAUFhaiOBzx8fGHDh1KSkqiikdMmzatb9++ixcvbuSV\nz5oTCxYsiIyMDA4OtrOzQy9C1hhYu3atlHdpNBp62WFRLl26VF5eLnf5aCqzHdHbMDc3nz9/\nvnznwmCUCnY4MP+D3IvGRkZGy5cvDwsL69atGyyfS5IkQRDoyZA2NjYHDhzg8/mildKSk5PZ\nbDbiUvzly5e9vLxES1UxmcwFCxb4+fkJhUJZq9Jg5OPSpUunTp0aMGCAug1pLAwfPpzD4cgX\nOVtRUSFTDUgnJ6fk5GQcpYtpnOApGKMw1q5dm5eX5+DgwOFwtLS0evXqVVNTg37j8fX1raqq\nWrJkCaUF8vHjx0WLFvn5+SHKsRQUFEhWODM3N6+srITLNipj/vz55ubmmpqa5ubmiIlCzYbS\n0lL0YqfNmEePHsGqrVwuF9EDyMzMHDdunIGBAYPBoNFoNBqNy+Wif3W1tbXv3buHvQ1Mo6VR\nOxza2trJycmIapuYxoCRkVFqamp5eXlJSUlCQgJ6VXcAgIGBwZkzZ44cOdKuXbvAwMBRo0a1\na9fOyMho+/btiCO0bNkSqo+I8uLFCyMjI/kkU+WgpqbGwsIiPDxcT0+vf//++vr627dvNzMz\nQ1Rgawa4u7vfvXtX3VaomcTERKj/i97l/Pnz7dq1i4yMLCoqorQ60Lu3bt369evXOL4e05hp\n1A4HnU53dnaWT2wU0xTp27dveno6TKM1Nzc/cuTIrVu3qMI69TJ+/PinT5+KLkF//PhxzZo1\ncmQVyk1QUNDnz59jYmJSU1OjoqJevHhx9erVnJycadOmAQD8/PwIEdasWQMAEAgELi4uTCaT\nIAgGg+Hh4VFdXX3u3Dl/f38oYkEQBIvF8vX1pc5y79695ORkgiDgnpF8wYxKYtu2baGhoRcu\nXJCihdPssbe3DwoKsre3l37Yq1evwsLC+vbt26lTp7Fjx8LgUJIkaTSaqLMONcsp5XL4Vpcu\nXcLCwlatWhUZGVldXf369Wsej6fMz4TBNBh15OKqmWapw4GB7N27l81m9+zZMyQkZNKkSVwu\n18vLq6ysTGUGGBoadu7cWayxS5cu+vr6JEn26tWLw+EcPHgwKyvr2bNnjx49IkmyuroaasC/\nf/9+z549NBrN1NRUQ0Nj4sSJxsbGzs7OdDrd3d2dIIi5c+fCAR0dHdls9owZM1xcXOzs7BD1\nZFVDc51tUHQ48vPzP3z4gDjg2rVrmUymtrb296KLxHwOIFKDnkajRUdHN/gzYX4ssA4HBqNI\ngoKCvL299+7d+/LlSxMTk/37948dOxZdsxWRCxcu/Pbbb2lpaUZGRmvWrJk6dSoAoLq6es6c\nOfn5+aWlpQsWLNiyZQt1I+FwOEVFRWw2m8/nOzg4wDLCixYtOnPmTE5OjqGh4ejRo4cMGcJm\ns/39/RcsWJCXl5eWlmZnZwe737x5c8CAAYaGhgkJCQAAkiTfvn1raWlpa2ubkpIyffr0rVu3\nLl68WLGfUW5WrVqlbhPUw+fPn48cOdKxY0dLS8t6D75w4cLq1autrKwqKioqKipgHYCamhoG\ngwHLrID/FfklSZLFYhEEUV1dDQDQ0dERK6SCwTR+sMOBaW7Y2tpu2rRJeePHxMRMmTJl165d\nffv2LSoqKi0the3Lli17/Pixvr6+ubn5pUuXTExMoBMQExOTmJiooaHx6tWrVq1avXv3DiaL\n2tnZnT592tHR8fPnz5MmTRo2bNizZ88KCwtra2t79+5NeRsAAG9vbx8fn6ioKB8fHwDAp0+f\nKisrqd36Tp06vXnzpqqqisPhKO9To/Pbb7+p2wT1QBCEh4cHSqH527dvT548WSgUZmRk0Ol0\nGo3GZDIFAgFBEHB3jE6nwzAOICK/UVtbS/63gBQREQF9FAymCdGoYzgwmEbIqlWrli5d6ufn\nZ2RkZGdnB4OaSZI8ePBgaGjokCFDUlNThw4dun//fnj8/PnzhUKhj48PXPAwNTW9evXq9u3b\nMzIyAgICtLW1LS0t9fX1tbW1nzx54uXlRaPRJPXWoCDbn3/+Cf5LXaaSEfT09EhFiGBi5EMo\nFJaUlAAAeDxejx496l1Oe/fu3cCBA+l0OpTF69Spk6WlZXl5OYvFYjKZ0OEQDcphMBgaGhp0\nOp0kSTg4j8fz8/NT4kfCYJQDXuHAYGSgvLz8yZMnI0aMsLW1LS4u9vDw2Llzp7m5+adPnwoL\nC52dnYcMGXL9+vU//vgDADB69Og3b96kp6dzudz79+937NgRADBjxgxvb29vb+/nz5/v2bOn\nRYsWRUVFMK5ow4YNBQUFRkZGf/zxx4wZM+AZhUKhs7NzSUnJ4MGD4RoGzLih1tuLiooIglBZ\nGg4KhYWFhw8fTk9PLygoEG0/deqUukxSEjU1NadPny4rK0PULL9+/bqfnx/MdIXuI4fDMTc3\nLyoqsrGxefr0KZAQ+KqtrYW1FeFbbDb73LlzOPcV0xTBDgcGIwOFhYUkSZ4+ffratWsGBgZT\np06dMGFCfHw8XGDQ1dXlcDjZ2dmTJ08+fvz45cuXoTaljY1NVFSUgYGBubn5vn37Fi5cCACA\nGysJCQlZWVkXLlzYtWvX69evr127Nn78+Bs3bhQWFurr6wuFQicnJ7gLM3HiRGiDhYWFhoYG\nJc/w9OlTOzu7RrKfAgB4/fq1u7s7SZIFBQVWVla5ubnl5eVaWlqtWrVSt2mKB65tIK43REdH\njxgxgsfjjRkzRltb+/DhwwUFBS9fvqTT6YWFhW/fvjUzM2MymZmZmdQ2ClzSgGsbGhoagwYN\n+uuvv+QWLcVg1IwaAlXVDc5SwcgNrLWxb98++DIlJQUAUFRU9OHDBwBARkYGbIfF8CorK0WP\nr66uhoF+d+/ePXPmDIvFsre3J0myoqLC2tqay+W+fv366tWrlpaWhoaGPB5v9erVpqamDAZD\nU1Nz2LBhBQUF5eXlcHx3d3dYVrdz58729vbr169Xx8WoG19fX29v75qaGjab/erVK5Iko6Oj\nW7ZsGRsbq27TGkTDq8U6OjouXLiwf//+S5YsKS4udnBwgMr9GhoaMCGFw+EwmUxdXV1NTU02\nm43rJGMUi9qzVHAMBwYjA3p6ei1btpTcp7ewsNDX13/27Bl8Sa06iB5PkiSUpujRo8f48ePb\ntGlz69YtAMC3b9/evXtXXl7epk2bAQMGfPz4sWfPnr/88su5c+dycnL4fH5FRcXly5cNDAxa\nt24Nx9fW1q6oqFi/fv2TJ0/evHkTFRWlsitQLw8ePJg+fTqUFSFJEgAwZMiQffv2NarsFTFB\nlO3bt3fs2JHNZmtpaZmammpqatrZ2Xl7e7dq1YrNZpuZmTk7O5MkuX79ejs7Ow8PDysrKxaL\nZWtrO27cuC5dunA4HHd39+rq6qCgIF1dXUNDQ0lxlPz8/NTU1IkTJ3bv3v3ixYsaGhp3796d\nNGkSi8WqrKyE6rpVVVW1tbWVlZUeHh7Jycko8acYTBMCb6lgMLIxffr07du39+/fX09Pb82a\nNb1794bSZAEBAevWrevevXtVVdXvv/8Olb7EjreysuJyuXFxcVVVVRERERUVFUVFRZmZmVZW\nVgMHDty1a5foiZYsWfI9G7y8vL59+/bgwQOlflL5KCgogEX4dHV1qeKrHh4elDfWSFi9ejUs\ncnb16tVp06bt2rXLw8Nj4cKFAwYMGDZs2L1790aPHr1p06aAgID379/36dMHABASEuLu7j56\n9GhPT88DBw5UVVWNGjVq5syZnp6ed+/ehWlKr169qqqqGjBgACzf8+bNG3NzcxhKDABYunRp\nx44dCwoKhg0btmXLlk2bNj1+/Dg3N/ft27d37txxdHQEAOD0E0xzBTscGIxsLF26tKCgAD7y\nent7nzhxAravX79+zpw5bdu2pdPpAQEBCxYskHI8jUaLj4/fvHlzSUmJmZnZqFGjoOpoM8DM\nzOzbt28AACsrq7i4uB49egAAnj171tgkg1ksFoy03bBhA0w7AgBQ/83BgwcPGTLkzZs32tra\nNjY2zs7OsbGxGhoaPj4+w4cP5/F43t7eAIChQ4fy+XxYwefgwYP79u2Dfzs6Ov7xxx9aWlqV\nlZVMJnPPnj0sFovD4VRXV+/bt6+oqOjGjRsdOnSg0WhCobBly5Y3btx4//59YGCgmLiLmFjL\nli1bsDuCacKocTtHXeAYDkxTR+17sVL46aef5s+fT5JkREQEnU4PDAxcsGBBixYtAgIC1G3a\n/zFu3DgzMzNzc/MuXboQBBEWFmZjY2NoaDhixIhPnz6RJFldXW1lZTV+/PgWLVowmUx9fX0u\nl7tq1aqvX79aWVkdOHAAHmNpaRkcHDx06FBbW1vwXxBPfHw8TIE+cuRIXl6ep6dn27ZtDQ0N\n+/fvr6GhYWdnN336dH19fQsLCxsbGx6PV1JSEh0draend/Lkyby8vDdv3jx58gTaeffu3Xfv\n3pWUlKSlpbm5uYWGhqrxomGaOmqfN/AKBwaDUSShoaEfP34EAAQHB6enpx89ehQAMHjw4G3b\ntqnbtP8jICBg/vz5+vr60dHRDx482L17d3x8vGja0cyZM83NzXft2lVWVpaSknLhwgUYcLNk\nyRJzc/NJkyYBALy9vT9//hwVFcVisT5//gwAuH//vq2t7bFjx7S0tEpKSgYNGiQUCm/fvp2Y\nmBgXF3fy5EmhUPj27VsAQGlpaWlpKZ1Of/Dggba2NiXuAgAwMjKi7OzWrRv8A4q1vHnzRuWX\nCoNRHGp0dtQFXuHANHXU/qTSbIBRJg4ODvAlTDsKCgpydXWFKdCQffv20Wg0Nzc32C4UCocO\nHUoQxLZt2wQCwZYtW1xcXAAATCYzNTUVBnwQBGFtbQ3je9LS0i5dugR3cGJjY/fu3duyZcsh\nQ4bAVKaysrI6V1kg4eHh1CpLYmKiqi8Qphmh9nkDZ6lgMBhF8unTJ9EiIJDa2tpPnz6pzIaK\nioqAgIC0tLR6j9TT09PV1aUySkiSBAA8evTo2rVrenp61GFCoVAoFGZnZ1+7dk1XV3fmzJkJ\nCQmTJ08OCQmBuyccDkdfX79169Z//fUXjFZhsVjXr1+H5W8mTZr0+fNnOGCnTp2CgoIAAD16\n9CBJsqysTFTcJSMjgyCICRMmUKcOCgp68uTJpUuXxowZg1KlBYNptGCHA4PBKBJLS0u4pSLK\ns2fPVHmzrKmpOXz4cE5OjpR3P378WFhYGB0dXVNTU1JS8vHjx5KSkuHDh2tpaV25cgUAsHHj\nxrS0tKKiori4OBgC7Ofnx2azp0yZcvfuXU1Nzd69e5eXl5eWlsJya/7+/gUFBY8fP4bprF5e\nXjY2Nh06dLC3t3/48OEff/zRv39/AEBxcfHJkydzcnI6duwIJWLhysfPP/9sY2Ojp6e3evXq\nhIQEmEENAOByuebm5gMHDnRzc4ORpBhMEwXHcGAwGKXD5/O/V4S9gZiamko2woWKkSNHslgs\nAICY50GS5OHDh+fPn19RUdGqVavffvvt69evzs7OAoEA3uZ5PB48EhaiMzExgUqy27ZtE41E\nCQwMDAwMpF4mJSVpamo+evTo9evXDAYjISFh9erVzs7O3bp1e/Pmzfv372fNmsXlcmfOnHnz\n5s1NmzZ9/vwZirVwOJw6xV0kP1RmZqY81wiDaRxghwODwSgAPp8P1asAANXV1VVVVdRblZWV\n0dHRUFVT4Xz9+tXU1BQqWIgak5uba21tra+vL9mFzWbfvHlTrHHr1q3ST0Sj0VasWLF69Wr4\nMiAg4OPHj9evX6cchaqqqvbt2wcGBoaGhq5du3bPnj3nz5+HDoqZmVmvXr22bdsmFArv3bt3\n6tQpFxeXgQMH1inWQom7QLEWX19fIyOjp0+frl+/fuDAgbJfIQym0aDG+BF1gYNGMU0dtQd/\nSVKvkOjSpUuVcd6wsDAOhzNjxoyioiKqEYaCxsXFKfBEYtLm6enpurq6w4cPf/jwYX5+/q1b\nt3r06GFlZQUDMvh8/vz58w0MDPT19UeNGvX582fYq7KycurUqTo6Ovr6+iEhIXAv5nvHV1dX\nDx061NjYmM1mW1tbL1iwgNK2x2DkQO3zBl7hwGAwCqB///4wFmHRokXLli0TXVpgs9lOTk69\ne/dWxnlDQ0NHjhw5depUBweHnTt3jhw5UhlnkcTe3j4xMXHu3Llubm4AAIIgxowZc/r0aRgZ\nSqfTt27dKrlqwuFw/v7777///lusvc7jWSzW5cuXlfkhMBiVgh0ODAajAHr06AFFRXNychYu\nXFjnXoaSaNeu3Z07d3bs2DFp0qSjR49GRESoRtXU0dHx5s2bhYWFnz59sra2hv4WBoP5Hj+o\nw5GRkfH48WMAwP3792EBcbVQW1tbXl4umn2nYgoLC7W1tWGlSrWQl5cH626oBVgrS1tbW10G\nFBYWurm5wTr1MpGdna0MexTC77//rvqT0mi0efPm+fj4BAUFOTg4LF26VI5BvLy8pBR8IUny\n5cuXcN6Q5PXr1zKdKz09vaqqSo5/PQrK+1kJBIKSkhIleZOlpaVMJpPD4Shj8Ly8PCMjo3oj\nc+WAJMmCggJDQ0OFjwwAqKio4PF4UC+/4ah93vj/5Rx/KKytrbOystRtBQbTIAYNGgSzNxst\nMPs0JSWFx+MFBgbWmU6iDPbt27do0aLi4uK4uDiZ9nEePXr07t277707Y8aMgoICBdiHwagP\nNc8baowfUTvQ3Xv9+rW6DNi4cWPXrl3VdXaSJNu3b79z5051nf3JkycAANFYPxUzf/58Hx8f\ndZ2dJEkjI6PIyEg1GqBAfv/9dycnp5qaGviytrZWtLq6iYnJx48fVWZMXl5ecnJyaWmpys4o\nK25ubps3b1bGyFBkPS0tTRmD7969u02bNsoYmSTJoUOHLly4UBkjQyW6+Ph4ZQx+4cIFPT09\nZYxMkuSUKVMmT56spMFVDxb+wmAwCuDy5csuLi7UHsGhQ4fu3r07Z86c9PT0EydOlJaWrlu3\nTjWWCIXCnJyc1q1b46AKDKZR8YPGcGAwGMWSlpY2fvx46uWFCxfMzMzCw8MZDIa9vf2DBw8u\nXbqkGktKSkqcnJxu377t7u6umjNiMBgU8AoHBoNRAAUFBaJRGklJSX369KHikV1dXdUesIbB\nYNQLdjgwGIwCMDIy+vLlC/wbliDp0qUL9S6LxYIq4xgM5ocFOxwYDEYBdOzYcf/+/ZWVlQCA\nQ4cOAQAGDBhAvZuWloYrnWIwPzg4hgODwSiAxYsXe3t729ra8ni8J0+eDBo0yN7enno3JiZG\ndMFDqWhraycnJ4ueHYPBNAbwCgcGg1EAXl5ep06dMjc3Ly4unjx58pEjR6i30tPT8/Pzhw8f\nrhpL6HS6s7OzasRGMRgMOniFA4PBKIZx48aNGzdOsr1169Zv3rxRvT0YDKZR8UM7HFpaWjwe\nT1dXV10GKFCzVj7Mzc1Vpv8oib6+vpmZmZKUjFHg8Xjl5eXqOjsAwNLSUklF2zGNHHNzcx6P\np4yRuVyu8qY1U1NTCwsLZYwMAODxeEq6JgRBtGzZ0sjISBmDt2jRQnnxSTwej8/nK2lw1fMj\nSptjMBgMBoNRMTiGA4PBYDAYjNLBDgcGg8FgMBilgx0ODAaDwWAwSgc7HBgMBoPBYJQOdjgw\nGAwGg8EoHexwYDAYDAaDUTrY4cBgMBgMBqN0sMOBwWAwGAxG6WCHA4PBYDAYjNLBDgcGg8Fg\nMBilgx0ODAaDwWAwSgc7HBgMBoPBYJROc3Y4Hj9+PGLECCsrKw0NDUNDwx49epw4caLeXomJ\niYMHD9bX19fU1HRwcNi6dasKTFU2YWFhBEHUWxi22t6aPwAAIABJREFUuLh41qxZpqamHA6n\nc+fO58+fV415KgDxCsh9PAaDjnxTU2MgPz9/wYIFnp6eOjo6BEEcO3as4WMqb9pRhrUUt2/f\nDg4ObteuHZfLtbCwGDFixNOnTxU1eNP9hkinOTsc79+/Jwhi9uzZ+/btCwsLo9PpEydO3Lhx\no5Qup0+f9vT0LC0tXbdu3Z49e8aNG5ebm6syg5XEq1ev1q1bV28ZdKFQOGTIkGPHjoWGhp4/\nf97a2nr06NFRUVGqMVKpIF4BuY/HYGRCjqmpkfDly5dDhw6xWKx+/fopZEClTjsKt1aUTZs2\n3b17d+zYsXv37v35558fPnzYtWvXO3fuKGTwpvsNqQfyh6GmpsbOzs7a2vp7B3z58kVLS2vU\nqFECgUCVhikVgUDQvXv3GTNm9OnTx8TERMqRkZGRAIBDhw7Bl3w+v0OHDra2tioxU4mgXwH5\njsdgGki9U1PjgZobr127BgA4evRoAwdU6rSjcGtFefPmjejLzMxMJpM5bNgwBZ6Cogl9Q6TT\nnFc4xGAymaampkwm83sHHDp0qKysbMOGDTQaTSgUqtI25bFjx47379+juMZRUVEcDsfPzw++\npNPpkyZNyszMfP78uZJtVC7oV0C+4zGYBlLv1NR4oNEUfMtQ6rSjcGtFsbOzE31pY2NjZWX1\n+fNnZZyrCX1DpNP8HY7q6uqysrIPHz5s2rQpKSlp0aJF3zsyISHBwsLi6dOnbdu2ZTAYhoaG\n06dPLyoqUqW1iuXt27ehoaE7d+7U1dWt9+DU1FR7e3s2m021ODk5AQBevHihRBOVjExXQI7j\nMRi5QZ+amjHNZtrJzs7Oysrq2LGjAsdsft8QhroNUDpTp049fvw4AIDFYu3cuXPatGnfO/Lz\n589FRUWBgYErVqxwcXG5d+9eWFhYSkpKYmKiUj1l5REUFNS/f/+RI0eiHJyfn29jYyPaYmBg\nANuVYpxKkOkKyHE8BiM36FNTM6Z5TDtCoTAoKIjFYv36668KHLb5fUOav8OxcuXKGTNmfP36\n9ezZs7Nnz66oqFi4cGGdRwqFwrKysvDw8Hnz5gEA+vbtSxDE8uXLY2NjBw4cqFqrFcC+ffse\nPXr08uXLBo5DEIRC7FE9sl4BRV0xDIZCIBCUlpZSL3V0dKinF/SpSS1IsVwFNKFphyTJWbNm\nxcbGnj59WmyfpYE08m+IPKg7iESljB49mslkfvv2rc53e/fuDQB49eoV1fLkyRMAwLp161Rl\noMLIy8vT1dVdv3594X94enq2aNGisLCwvLy8zi7Ozs5OTk6iLf/++y8A4Pjx4yoxWcHIegXk\nuGIYTL0kJyeLzrcpKSl1HiZ9alIL0i1XVBimaqYdZQSNQoRCYXBwMJ1OV/Y82Qi/IXLQJHcK\n5MbNza22tjYrK6vOdzt06AAAEA0XhX83xf2UT58+FRcXL1u2TP8/4uPjc3Nz9fX1Z82aVWcX\nR0fH9PT0qqoqqgXGbbVv315FRisUWa+AHFcMg6kXe3v72yKIbR9QSJ+a1AKi5Q2kSU87JElO\nnz593759hw4dmjBhglLP1Qi/IXLQnLdUBAIBnU4XfXnlyhU6nW5tbV3n8aNGjdqxY0d0dLSD\ngwNsuXTpEgCgW7duKrBWsdjZ2cXFxYm2LFiw4N27d+fPn/+emNWIESOOHz9+8uTJwMBAAIBA\nIDh69KitrS30w5ocsl4BOa4YBlMvXC7X3d1drFHWqUkt1Gm5wmm60w5JktOmTTt06NDBgwf9\n/f0VO3iT+IbIQXN2OEaOHKmrq+vs7GxkZJSTk3PmzJnHjx//+uuvMCgJAHDv3r3u3buvXbt2\n+fLlAAAPD4/Ro0f/P/buOy6K438Y+Owd16hHrwoIKAYRVBRFASsWjCKKvWADNNg1lhjFYMca\nC/b+NbFijUFsoLHEgl0BMVFRsADS++3zxzzub7N3HHvAcod+3n/4krndubm929nPzk75+eef\n8/LyPDw8bty4sXr16h49euBHLfWLrq4uo9iGhoZv376lJzI+fr9+/by8vCZPnpyTk9OoUaNd\nu3Y9fvy4/k42quoRYLM9ALWiyqpJk506daq0tPTRo0cIodu3b4vFYoRQYGBg9VqCua52are0\ndNOnT9+1a1dgYKC2tvbRo0dxora2dq9evWqYM6rnvxBl1P1Mh0O7du3q2LGjmZmZlpaWoaFh\nx44dGY/Zbty4gRCKjIykUoqLi3/66aeGDRsKBIKGDRvOnj27qKiozgvOCflprOQ/fnZ2dlhY\nmJmZmUgkcnd3P3bsWJ0Xk0NsjoDy7QGoFVVWTZpM4YjxmtSTnFY7tV5aiqenp3zO1tbWNc+Z\nrOe/ECUIkiRrOYQBAAAAAPiv+tcdEgAAAAD1DgQcAAAAAOAcBBwAAAAA4BwEHAAAAADgHAQc\nAAAAAOAcBBwAAAAA4BwEHAAAAADgHAQcAAAAAOAcBBwAAAAA4BwEHAAAAADgHAQcAAAAAOAc\nBBwAAAAA4BwEHAAAAADgHAQcAAAAAOAcBBwAAAAA4BwEHAAAAADgHAQcAAAAAOAcBBwAAAAA\n4BwEHAAAAADgHAQcAAAAAOAcBBwAAAAA4BwEHAAAAADgHAQcAAAAAOAcBBwAAAAA4BwEHAAA\nAADgHAQcAAAAAOAcBBwAAAAA4BwEHPXSnj17CDnh4eEIoXXr1hEEkZ+fj7e8fv16REREeXk5\nfXeFiapavnw5QRDFxcU1yUQhxkcA4GuVn58vfyLT3b9/PyIigiAIdZf0/yisPWrrnGWTz927\ndwcPHmxlZSUUCi0sLIKCgv7+++8avq9K2BwBqMQU0lJ3AUD1LViwwNXVlfrT0dERIWRiYuLi\n4sLn83Hi9evXFy1aNGfOHC2t//uuFSYCAOqYRCI5cuQI9efChQszMjK2bt1Kpdjb26ujXMoo\nrD0Y1Q53du7cGRoa6uTkNHv2bHt7+7S0tG3btrVr1y46OjokJITrd8fUewTqNbje1GPe3t5d\nu3ZlJA4fPnz48OFqKQ8AQCV8Pn/AgAHUnxs3bszJyaGn1LHCwkJtbe1q7Fg31c79+/fDwsLa\ntWt3/vx5iUSCE8ePH9+nT5+JEye2aNGidevWXJehMlDxsgGPVL429Ka8mTNnzpo1CyEkkUhw\nC21aWprCRLxvamrqsGHDzMzMRCJR06ZN6XdaCKELFy60atVKLBbb2touX76cJMnKynDixAmC\nIC5evEhPXLt2LUEQqampCKGUlJSxY8c2adJEW1u7QYMG/fv3T0lJqSy3sLAwCwsLesrixYsJ\ngqA3aSopeUZGxujRo21sbEQikbm5eadOne7du1f1cQRAk7x586Zfv356enqWlpYhISF5eXn0\nV5Wfubdu3fLz89PX19fW1m7btu3p06epl/DzmsTExG7duunp6bVr1055hpXVHvJPEFJTU0eO\nHGlpaSkSiRo0aDB8+PCCggKk4rnPEBUVVVFRsWPHDiraQAgJBIIdO3YQBLFs2TKcUmWNobwM\n+Jg8efKkR48eOjo6jAPO/ggwQB2FoIWjXisoKPj8+TP1p4GBAeNZ708//SQSiZYuXfr8+XOR\nSIQQsrS0VJiIEHrx4oWnp6eRkdHSpUttbGxiY2MnTJjw+fPn2bNnI4Ru3LjRq1evVq1a/e9/\n/yNJcsWKFR8/fqysYP7+/qampnv27OnSpQuVuHfvXm9vbwcHB4TQmzdvDAwMIiMjTUxMPn78\nuG3btjZt2jx9+hSXRFXKSz548OBXr14tWbLE3t4+MzPz5s2b2dnZ1XgXANSoZ8+evXv3HjVq\n1P3795csWcLn86Ojo/FLyn//t27d8vHx+e6777Zs2SIWi6Ojo/v27XvgwIGhQ4dSmQ8cOHDR\nokU7d+7Mzc1VnmFltQdDUlJSu3btdHR05s2b16RJk/fv358+fbqoqEhHR6cm5/6FCxeaNWvW\npEkTRrq1tXW7du0uXLggk8l4vKrvotmUYeDAgYsXL96zZ09iYuKQIUOoA87yCDBAHfX/kaAe\n2r17t/xXmZ2dTZLk2rVrEUJ5eXl4y6ioKIRQUVERfXeFiYGBgVKpND09nUoJDw/X1dXFWXXp\n0sXMzKygoAC/lJuba2RkJJ8JZerUqdra2rm5ufhPHLDv2rVL4calpaXGxsa41UT+I4SGhpqb\nm9O3j4yMRAiVlZVVWXKZTCYQCKicAdBkvr6+1tbWjMSFCxcihDZv3kyljBkzRkdHh/qzyjPX\n2Ng4JycHv1ReXt6sWTNra2uZTEZlvm/fPvo7Ks9QYe3BOGf79Omjp6f37t27Kj+y8nOfrqSk\nBCEUEBCgMJ9Ro0YhhD5+/EiyqDGUlwEfk+PHj1MbTJs2jX7A2RwBxp9QR2HwSKUeW7Vq1WUa\nXV3damclk8n+/PPP3r1705si+/Xrl5+ff+/evYqKiqtXrwYGBlLPd/X09Pr166ckw9GjRxcW\nFh4+fBj/uXv3bh0dnaCgIPxnRUXFli1b2rVrZ2lpKZFI9PT0srKynj9/XuslJwiidevW69at\nW7Vq1d27dysqKqrxFgCoHXXuIIRatGhRUFCQmZmJ2J25ffv21dfXxy/x+fwRI0a8ffs2KSmJ\n2t7Pz4/6v/IM2RRVJpOdP3++X79+Cm/9q33uk5U/w6VeZTmch00ZOnfuTP3fycmJOuDVAHUU\nBQKOeszNza0jTU2GnOTl5RUWFv72229imp49eyKEPn36lJeXV1paamNjQ9+F8SdD8+bNW7Ro\nsWfPHoRQaWnpwYMHg4KCqJBoxowZ4eHh/v7+R48evXv37v379+3s7IqKimq95AihmJiY/v37\nr1u3zsPDw8zMbNKkSYzn3wBoPhMTE+r/YrEYIYTPFzZnLuPCb2VlhRCiXz7Nzc2p/1d5QlUp\nLy+vuLi4svqh2ue+SCQyMzN7+fKlwlf/+ecfiURibGzMpoRsymBgYED9XyAQoC8HvBqgjqJA\nHw6AEEK6uroikSgoKOinn35ivGRtba2trS0UChkBfpW1T3Bw8JQpU168ePHgwYPMzMzRo0dT\nL+3bt2/kyJHz58+nUj58+FBZPmKxmDHkHT9pZlNyhJCZmdnGjRs3btz48uXL48eP//TTT2Vl\nZVu2bFFeeADqBTZnbnp6Oj393bt3CKHKrs1VnlBV0tPTE4vFVFd0BpXOfYZu3bodPHgwJSXF\nycmJnv7u3bubN29S7TTKa4walqEaoI6iQAvHVw53a2LE5vKJfD6/e/fuCQkJFhYWzv+lp6fH\n5/O9vb1jY2OpVk3caqr8rYcNGyYUCvfu3btnzx4HBwdvb2/6q7gLCHb27Fncg10hOzu7rKws\nqhcVSZJXrlxhWXJ6Po0aNZo5c2abNm0ePXqkvOQA1BdVnrk+Pj4nT56krrgVFRX79++3traW\n73rJJkNUSZVCx+Px/Pz8YmJiGIEOhf25zzBz5kw+nz9+/Hj6fIPl5eUhISFlZWWTJ0/GKcpr\njBqWAbE4AgxQR1Eg4PjK4ZnBVq9effPmzTt37pSVlVWWuGrVqsLCwrZt227evDkuLu7EiRMr\nV6708fHB+SxatCg5OXnSpEkfPnzIyMgICwurrDahGBsb9+7de8eOHX/++WdwcDD98WqvXr32\n799/69at4uLiuLi4iRMnKumAEhQUJBKJJk2a9Pbt25cvX06cOJExjk5Jyd+/f+/p6bl27do/\n/vjjypUrixcvvnnzJm7MBODroPzMXbx4cV5enq+v78GDB48fP96jR4/Hjx+vXLlSSXcH5Rkq\nrD0YVq5cyefz27Rps3Hjxri4uIMHDw4ZMgS3iap07jO4u7tv2bLl2rVrLVu23LBhw+nTp6Oj\no9u0aXP27NkFCxZQLRxV1hg1KQPLI8AAddT/p9Yuq6Ca8CiVuLg4+Zfku3nPnj3bwsICjxZ7\n8+aNksRXr16NHTvWxsZGIBCYmpp26NBh5cqVVD6xsbEtWrQQCoWWlpbTpk2LiIhAlY9SwfCI\nfx6P9+rVK3p6VlbWqFGjTExMJBKJp6dnbGysi4vLoEGDKvsIFy5caNmypUQisbGxWbhwIX5r\nep/zykqen58fEhLi4uKiq6uro6PTrFmz1atX4/75AGgaJaNU6Cnbt2+nn7ZkVWfujRs3unbt\nqqurKxaLPT09T548qSRzNhnK1x7y52xKSsrgwYNNTEwEAkGDBg1GjBiBx7ipeu7Lu3379sCB\nA6kCCIXCM2fOMLZRXmMoLwObA17lEZD/IFBHkSRJkEq7/gIAAACa6dChQ0OGDAkPD//111/V\nXRZQNeg0CgAAoF4aNGhQRkbG1KlT8URe6i4OqAK0cAAAAACAc9BpFAAAAACcg4ADAAAAAJyD\ngAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAA\nnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAA\nAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4AD\nAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyD\ngAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAA\nnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAA\nAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4AD\nAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyD\ngAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAA\nnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAA\nAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOAAwAAAACcg4AD\nAAAAAJyDgAMAAAAAnIOAAwAAAACcg4ADAAAAAJyDgAMAAAAAnIOA4xuSlpZGEERAQIC6C1IX\nvqkPC74R7H/VJiYmdnZ26i0DAAwQcKhfWVnZxo0b27dvL5VKhUKhpaVl69atp0yZEh8fr+6i\nVaq4uJggCKlUqu6CoBcvXhAEMXjwYHUXBHy78OlA4fP5RkZGHTt23LNnD0mS6i7dN0FzaiSg\nhJa6C/CtKykp6dq167Vr17S1tTt16mRpafnx48fk5ORff/01NTXV19dX3QWsr8zMzK5evWps\nbKzugoBvhVAoHD16NEKorKzs5cuX8fHx8fHxd+7c2bhxY229BfyqQb0GAYeabdu27dq1a61a\ntTp//ryRkRGV/uLFi2fPnqmxYPWdUCjs0KGDuksBviESiWTLli3Un5cuXfLz89u8efOMGTPs\n7e1r5S3gVw3qNXikombXr19HCE2aNIkebSCEHB0dv//+e8bGN2/eHDhwoJWVlUgksrS09PPz\nO3z4MPXq9u3bAwIC7O3tJRKJVCr19fU9cuQImzLcuHGjf//+FhYWQqHQyspq+PDhz58/r/En\nQwih33//3dvbW19fXyKRuLq6Ll++vKSkpBY/1PLly52cnBBChw4dohq0Dxw4gCp/0qy8SPfv\n3ycIIjg4+M2bN0OHDjUxMZFIJK1bt/7jjz9q5YCAb0fnzp1btmxJkuTdu3fp6VWebufOnevW\nrRt1RnTo0CEqKgq/pPBXLZPJ1q1b17RpU7FY3KBBg2nTpuXn5zMKc+bMGYIgIiIiGOlSqdTR\n0ZGeUr1qREmZGW7cuEEQRGBgoPxLTZs2FYlEWVlZqubJnpKDz75gyvNBtGokNTV18ODBZmZm\nPB7v5s2biN3hraioWL16tbOzM/5Cp06dmp+fr7BTDndVN1dIoFaTJ09GCEVGRla5ZXR0NI/H\nE4lEQUFBc+fOHTt2rJubm6+vL7UBQRCenp6jR4+eM2fOmDFjzMzMEEIrVqygNnjz5g1CqG/f\nvvRst23bxuPxTE1NR48ePXv27IEDBwqFQh0dnZs3byopTFFREULIwMBAyTazZs1CCJmZmU2Y\nMGHmzJlNmzZFCPn6+paWltbWh3r8+PGqVasQQm3btt3/xcuXLyv7sFUWKTExESHUuXNnc3Pz\nli1bTpgwoX///nw+n8fjJSQkKPmw4FtW2eng4eGBEDpx4gSVUuXptnfvXoSQhYVFaGjozz//\nHBYW5u3t3bhxY/yqwl91SEgIQsjW1nbGjBkzZ85s1KhRhw4dpFKpra0ttc3p06cRQgsXLmSU\n0MDAwMHBgZ5SjWpEeZnlNWnSRCAQfPr0iZ5469YthFD//v2rlyebGqnKg8+mYGzyoaoRY2Pj\nJk2ajBgxIjAwMDExkc3hJUlyzJgxCCE7O7sZM2bMmjXLwcFB/gtlUwwNBAGHml2/fp3P5wuF\nwqlTp168eDE7O1vhZg8ePMA90Z4+fUpPf/PmDfX/169f018qKCjw8PCQSCRZWVnUxoya4unT\npwKBoHv37oWFhfT30tXVbd68uZJiV3l6JyQkIITs7e0/fPiAU8rKynr27IkQWrJkSS1+qJSU\nFITQoEGDGAWQ/7BsioRrCoTQ/PnzZTIZTty/fz9C6Pvvv1dyQMC3TOHpcPHiRXxqv3v3Dqew\nOd28vLz4fP7bt2/pWSk5hS9fvowQcnNzy8/PxykFBQUtWrTAIQi1GfuAoxrViPIyy1u6dClC\naMOGDfTEiRMnIoROnTpVvTyrrJHYHHw2BWOTD1WNhIeHl5eX03Or8vBeuHCB8YUWFhbiyJX+\nhVa76lav/x9wKPkiAdd+//13a2trqs3Jzs4uODj46tWr9G3CwsIQQr/++muVuclkss+fP2dk\nZKSnpy9ZsgQhdPLkSfySfE0RHh6OEIqPj//4X3379kUI/fvvv5W9S5Wnd3BwMEJo9+7d9MSn\nT58SBGFvb1+LH4p9wMGmSLimaNiwYVlZGf3dDQwMzM3Nqywn+Dbh00EoFIaGhoaGho4ZM6Zj\nx474AR/9583mdPPy8hIKhe/fv1f4RvK/6lGjRiGEYmJi6JudPXu22gEHplI1orzMCj8Fj8fz\n8PCgUkpKSoyMjMzMzKjzTtU8q6yR2Bx8NgVjkw+uRkxMTAoKChQWRsnhHTlyJKNVjCTJP//8\nk/GFVrvqVi9EkuSlS5fMzMzUXZJvWnl5+ZUrVxYvXjxgwABTU1McecyaNYvawN3dHSGUkpKi\nJJN79+716dNHT0+P8dRs8+bNeAP5mqJVq1aocjdu3KioqPjhv1JTU0kWp3fz5s0V/u6trKwQ\nQrghp1Y+FPuAg02RcE3BaLImSdLFxUUoFCopJ/iW4dOBgSCIXbt20Ter8nQjSXLDhg34WvXD\nDz8cOXIkPT2dnkNlv+rMzEz6Znl5edUOOKpRjSgvs0LdunVDCD158gT/efToUYTQtGnTqp1n\nlTUSm4PPpmBs8sHVSNeuXeWLUeXhdXV1lf9Ccacc+hfK8uNoGi2EUEFBQWFhIS7oiRMnzp07\np+STYKNGjfLy8qpyM8ASn8/39fXFg2BJkvztt99Gjx4dFRXVq1evjh07IoQ+f/6MEKI3hDDc\nu3evQ4cOYrF4woQJbm5uBgYGfD7/woULq1evlu+nScnMzEQInTp1SiKRyL/atGlTmUy2adMm\neuLgwYMbNWpU5SfKyclBCFlYWDDSLS0t3717l5OTI5VKOfpQNSkSTpEfza+lpVVRUaHqO4Jv\nioGBAf5J5+fnX716dezYsWFhYba2tp07d8YbVHm6IYTCw8MNDQ03bdoUHR2NT7127dpFRUW1\nb99e4Zvm5ORoaWkxupzr6urq6OhU4yNU74xTtcwIoeDg4Li4uL17965YsQIhhHts4Naaauep\nHJuDz6ZgLPNBCOE7GTo2hzc3N1f+C9XR0WF8oeyLoVGYw2Lz8vKys7Or3K2goICb8gBEEMTQ\noUOvXLmyffv2uLg4HHDgS+Dbt28ZXcopa9asKSoqOnXqVNeuXalERvd4eQYGBgghCwuL1q1b\nV7YNWa2Zi3DOGRkZtra29PT09HTqVY4+VE2KBEDN6erq9uzZ8/Tp056enqNGjUpKStLW1kbs\nTjeE0LBhw4YNG5abm3vjxo0TJ07s3LmzZ8+eT548adCggfzGBgYGr169ysrKol+i8vPzCwoK\nTExMqBQej4cQKi8vp+9bVlbG2KzaZ5xKZUYI9evXT19f/8CBA0uXLs3Kyjp37pybm5ubm1tN\n8lSO5cGvsmAs80EIEQTBSGFzePX19eW/0IKCAsY3xb4YGoU5LHbEiBGHWcDtToA7AoEAIUTd\nVbdt2xYhpKTx6d9//6U2o1y6dEn5u+Dtf//99xqVVRHcbe3KlSv0xKSkpPT0dHt7exxq1MqH\n4vP5iHagalgkAGpLq1atxo8fn5aWtnbtWpyi0ummr6/fvXv36OjoGTNm5OXlVXYu41817hBN\nYfyJEDI0NEQI4achlMTEREYIUr1qRNUyI4QkEsnAgQPfvXt34cKF//3vf+Xl5fRWhOrlqRzL\ng19lwWpSZ7I5vPhB87Vr1+iJjD9rWAw1UjYPx7179y5evIj/n5ubGxYW1r59e9yfv07K9k3Y\ntGlTTExMaWkpPfHOnTsHDx5ECHl7e+OUiRMn8vn8iIgIxjDrtLQ0/B/8mCMuLo566eDBg1We\nnOHh4VpaWhs2bGBsmZ+ff+jQoWp+JIQQQnhkV2RkJG76QwiVl5fPmDGDJMmxY8fW4ofCsy6+\nfv26VooEQC2aP3++WCyOiorCUziwOd3i4uIYQcCnT58QQriNRB6+HEZERFCtzoWFhT///DNj\nM1dXV7FYfPLkyYyMDJySk5Mzffp0xmbVq0Ym2GJvAAAgAElEQVRULTOGO3Hv27dv3759Wlpa\nw4YNq3meSrCv65QXrCZ1JpvDizuNRkREUP0ciouLFyxYUO2Po1GUzTQ6derUDh06dOnSBSE0\nd+7c3bt3t2nTJiIiQk9PD88ewZGHDx8+fvwYD5wxNjZu1qwZ7hj1Vbp9+/bevXv19PTatGlj\nZ2dXVlb24sUL3OVn4MCB/v7+eDNXV9cNGzaEh4e7u7v36dPHyckpMzPzzp07enp6eFxceHj4\nwYMHhwwZMmjQIFtb2/v37//xxx9BQUHKJ+1p1qzZ1q1bQ0NDu3bt6ufn16JFi4qKiufPn1+6\ndMnOzm7QoEHKC19YWIhPTobt27f7+PhMnz59zZo1Li4uAwYM0NbWPnv27NOnT729vfFkGLX1\nofT19T09PW/dujVkyBBnZ2c+nx8QENCsWTP5UrEpEgC1yNraOjQ0dP369StWrFixYgWb023I\nkCFaWlq+vr62trZ8Pv/WrVuXL192cXHp3bu3wrfo1KnT+PHjt2/f3qxZs/79+xMEcfz4cSsr\nK0aLna6u7oQJE9auXevu7v7999+XlpbGxcW1atVKX1+fvln1qhFVy4y1b9/e0dHxyJEjZWVl\n33//PZ6RooZ5KqmR2Nd1ygtWkzqTzeHt2rXrqFGj9u7dS32hMTExFhYWUqkUPxereTHUiSTJ\n06dP6+rqyncoNTQ0xGN1ysvLDQ0N16xZQ5LkokWLuBvmGxMT4+DgIF9IJycnatTQV+bt27db\nt24NDAx0dnbW09MTCARWVla9evU6ePAgNQ8E5dq1awEBAaampgKBwNLSsnv37keOHKFevXz5\nMp5DU19fv3PnzhcvXsQTSKxduxZvoHDWIJIkExMTR4wY0aBBA6FQaGho6OLiEhYWdvnyZSXF\nVtgtn1JUVIQ3O3DggJeXl66urkgkcnFxWbx4MfVSbX0okiRTUlJ69+5taGiIH5ru379fyYdV\nXiTcvXzUqFGMvdzc3Ph8vpIDAr5lSoZIZGRkaGtrSyQSakoJ5adbdHR0QEBAo0aNtLW1DQwM\nmjdvvnjxYmp6HoW/6oqKijVr1jRu3FgoFFpbW0+dOjUvL8/Y2JgxT1R5efnChQttbW0FAoGt\nre38+fNLSkrkR6lUoxpRXmYlIiMjcY1x9OhRxkuq5smyRmJZ1ykpGJt8KqtGSHYVWnl5+cqV\nK52cnPAXOnny5KysLC0tLTc3N5WKoYEIkiTPnDkzZMgQPJKKTigUXrx40dvb++7dux4eHi9f\nvrS3t798+XKfPn3kN66548ePDxgwwNXVdcSIEa6urrjLTFZW1sOHD/fv3//48ePjx4/DmsgA\nAAC+KQ8ePHB3dx88ePBvv/2m7rLUiLJHKqampq9evfL29r506ZKNjQ1ef6igoEC+822tiIyM\nDAwMPHToEO4GSOnevfv06dP79+8fGRkJAQcAGu7evXvZ2dn4UWxubu6PP/746NGjXr16zZs3\nj6OqA4CvyadPn+gDUgoLC/Ez3379+qmvULVDWcDRrVu3BQsWvH37dt26dUFBQTjx2bNnDRs2\n5KIoz549W7JkCSPawPh8/pgxYwYOHMjF+wIAapG6+n4B8HWIiIi4cuVKx44dLSws3r1798cf\nf7x69apnz57UVbj+UjZKZdmyZQ0bNvz5558dHByobs+HDh3iaH1kAwODly9fVvZqamoqDFwE\nQPM9fvwYj9mrqKj47bffli9ffvXq1Z9//nnnzp3qLhoA9UCPHj2srKyOHj0aGRm5d+9eIyOj\nqKiokydPfgUNhMpaOCwtLa9cuUKSJP1znj17VldXl4uiBAYGzps3T09Pb/DgwSKRiEovLi7+\n7bffFixYgMcLAQA0WX5+Pp714f79+9nZ2fgxqLe3d83XFgfgW9C7d2/lg3HqL2UBB8aIqszN\nzTkqyrJlyx4+fBgcHBwWFubk5GRsbEySZFZWVnJycklJibe3N17KDwCgyeq47xcAoL5QEHDg\ndWKU46KRQyqVXr169fjx4ydOnHjy5ElqaipCyNjYOCgoqF+/fv369YMKCwDNV8d9vwAA9YWC\nYbFsruskTDYKAFAkPT19yJAh169fb9OmTUxMDF792MPDw8PDY8uWLeouHQBAbRS0cFAz/3+t\nWrVq9c8//6i7FADUSPfu3TVzUH4d9/2qM5XVGwKBoEWLFn///XfdFwkAlZSWlhobG7969Upd\nBVAQcEydOrXuy1GlxYsXI4Tmz5/PZuOSkhJqInp5SUlJc+bMYaygAwB7f/311759+16/fm1g\nYDBq1KiePXsihMrKyjZs2BAfH8/n87t37x4SEkJdcRVuv23btvj4+KysLH19fR8fn5CQELxi\nHxtHjhzBsxlqrDrr+1VnkpOTZ8+eLV9vEATB4/HYLB8IgHrNnz//8ePHaixA1Z1GNQQel8sy\n4GjTps3Dhw+VbPDhwwf6AsEAsHf27Nl169ZFR0d37dr18+fPeXl5eMXOGTNmZGRkpKSkFBcX\nd+/ePTEx8ccff1Syva6u7sqVK42Njd+9ezdixIi//voLR9WU8vLyDx8+WFpayj/lTExM1LSA\nQ119v+qSu7u7fL1RVFR0584dX19f+lIXAGigdevWqbcAVQQc2dnZe/fuTU5OxqsdUup+Vdwb\nN26w3/js2bPv37+v7FUPDw+Y0gNU28KFC+fMmTN48GCEEDUhIEmSu3fv3r59u5WVFUJo1qxZ\nq1evxgEHffvw8HD6Wo6LFi1asGCBlZVVUlLS3bt38cR3Xl5e27Ztmzdv3tmzZ6llhAUCQa9e\nvU6cOIH/vHnzZmJiIkEQWlpakydPjoqKUvvVTk9Pr8ptvsq+XxKJhFrVGQCghLKAIykpqUOH\nDnhsqp2d3YcPHwoKCnR1dW1tbeusfBSVnoDY2NjY2NhU9ipBEDDgBVRPQUHBvXv3+vXr5+Dg\nkJOT4+Pjs2HDBmtr67S0tOzsbHd3d7xZ8+bNU1JSfvnlF3d3d/r2BEGIRKItW7Z06tQpJydn\n37595ubm2dnZCKHFixcPGzbszz//nDBhgpubW4cOHY4dOzZt2rSuXbtevHgxJyfn1KlTkydP\n/vXXXxFCSUlJfD5/3Lhxt2/fPnXqlLm5OQ5u1Oir7/sFAKgpsvLVYgMCAjp37lxaWioSiZ49\ne4bHszRs2PD8+fN1tLQcNwiCWLBggbpLAeolvFSmq6trampqdnZ2YGCgj48PSZJPnz5FCH38\n+JEkyf3790skEvpZZmNjg7cXCoVGRkZUbvn5+WlpaefOnQsJCXn9+jVJkgUFBRKJRCKRlJeX\nU5tlZ2dbWloaGBjg5SJlMplEInF0dIyKimrfvv3WrVsbN25c1wfi26Orq3v69Gn59IqKivT0\n9LovDwCq8vf319HRUWMBlDXD/v3337gjG0EQJEkihPz9/bdv375w4UIuQyAANBfuhTB58uRG\njRpJpdJFixYlJCTk5OTg9JycnPj4+JEjR0qlUoIgioqKYmNjEUJv3779559/BAJBaWkpXmla\nIBB4eHh8/vzZ2tq6R48erVu37tatm7m5uVQqLSoq6ty5M31RIalU2rdv39zc3FatWiGE0tLS\nioqKtLW18astWrTAHUfUcDgAQoWFhc+ePYNOowBUSVnAkZWVhcfQGxgY4FZfhJCPj8+DBw84\nKk1CQkKfPn08PDzGjh374sUL+kt//PGHkqckANQNqVTasGFD+UdyNjY2hoaGDx48CA8P19PT\ni4iIcHR0FIvFfn5+DRs2FIvFkyZNok6imJiY9evXP3jwAK9whhAiSbK0tPTevXudOnXi8Xi9\nevVi5H/48GE+n79p0yb0pXsmFZFIpVKSJNn02awz2dnZ69atmzhx4uD/Une5OMHn87W0tOAp\nLQBVUtaHw8rK6tOnTwghOzu7y5cve3l5IYQePHigo6PDRVHu3r2Le4Db2dnt27fv0KFDe/fu\n7d+/P361sLDw7du3XLwv+Mp8/vz50KFDz549MzMz69q1a5s2bWo3/5CQkPXr1/v5+Uml0l9+\n+aVjx44GBgYIoeDg4CVLlqSmprZt23b16tXjxo2jtl+5ciU1hUOTJk2+//774uLi/fv337x5\n8/Xr1y9fvly6dGmPHj2WLVuG+0utXLly4sSJeHuZTObu7p6TkzN8+HCxWIy+tLJQt9SfP38m\nCEJzBoBoVN+vOgCdRgFgSVkLh7e3961btxBCI0aMWLhw4ZgxY2bOnNmnTx9/f38uivLLL79Y\nWFgkJSUlJyf/888/3t7egwYNOnjwIBfvBb5Wf/zxR5MmTZYuXfrvv/+ePXvWy8tr3Lhx5eXl\ntfgWc+bM6datm7u7u62trUwmo36iS5cubdGiRVFR0bVr1/z9/WfMmEFtb2FhUVJS0rx5c21t\n7ZCQEIQQj8fLyMhACDVu3HjMmDH9+/cvKyu7detWXFxc586dX79+fezYMYSQTCZr1qxZUlIS\nQRAzZ87EGdrY2EgkEmqmmfv37+PWlFr8jDUxZ86c5s2bp6enC4XCP/74Iz8//8yZM0ZGRtCr\nFIBvHVl5p9Hk5OSLFy+SJFlWVjZ58mRDQ0NDQ8Nhw4ZlZWVx0Z3EysoqKiqK+rOioiI0NJTP\n5x84cIAkySNHjuDS1hx0GtVkGRkZixYtCgoKGjdu3N69eysqKtjv++bNG21t7Tlz5pSWluKU\nv//+29TUNDIykpvCKtC4cWN6t1DMxMTEwcGhpKSkf//+zs7Ojx49Onz4sFAodHJyIkmysLCw\nTZs2zs7OSUlJsbGxtra2rVu3FolETZs21dHRIQhCX19/9+7d2dnZBQUFOMMOHTpoa2vPmzev\nZcuWTk5OS5curbMPWCUrK6vff/+dJEmxWPz06VOcGBsb265dO7WWq6ag0yio79TeaVRZwFHH\nxGLx7t276SkymSw0NJTH4+3btw8Cjm/ByZMnDQwMXF1dJ06cOGzYMAMDg9atW+OhH2wsW7as\nadOmMpmMnrhhwwYbGxsOCqsYnirDzc0tLS2NJMl3797hab6OHTtWXFzcsWNHsVhMEASfz3d1\ndX379i1Jkq9fv2bcBgQEBKSkpMyZM4eRbm1tjd8Fz1VKadOmTZ19wCqJxWJ8o2Jubv7XX3/h\nRNzLVa3lqqnKAo68vLxLly7RRxUBoJnUHnBo0NR4DRo0SElJoacQBBEdHT1mzJjg4GDNXDYC\nMOzdu1dbW5vH4/F4PKlUih/JsfTx48cRI0ZMmjTp/v37mzZtOnDgQHJycllZ2aRJk1jmkJKS\n0rp1a0b3PU9Pz7S0tIKCAhU+Rg307dt31apVT58+tbGx0dLSsrKyevz48YoVKwIDA0Ui0eXL\nl4uKimQyWXl5+cOHD/EsYQ0aNGCcljExMY6OjsuWLWOkp6Wl4Xfp1KlT69atqXSVjjPXGH2/\ncCJ3fb/UDjqNAsCSsoCjvHJcFMXb2/vs2bOMRIIgtm3bFhwcfPz4cS7eFNQiX1/f4ODg4uJi\nfX19XV3dnJyctm3bsp+Q6sSJE/r6+hEREdSkmWZmZitWrDh+/DjLIRi6urrUSBBKVlaWQCCo\nyy4OM2bMyMrKio6OHj9+/KZNmz59+qT2WbnqUh33/ULqHt2GO42qfaZXADSfslEqSpaSIjmY\nonjUqFHv379/8eKFo6MjPZ0giB07dujr66s0uzmohl69ep07d47609vbOyEhgeW+9+/fT0hI\n0NPTw/NMIIQyMjJsbGyioqJWrlzJJodXr141bdqUPv8EQsjV1bW0tPTt27dNmjSpMoeuXbsO\nGjQoNTXVwcGBSty2bRtjWos6oKurGxYWVpfvqDl++uknPD1aaGhocnLy/v37EUK9evVas2YN\nF28Ho9sAwF6/fm1vby+TyfCfYrG4qKhIvUViUBZwREZG0v/Mzc29fPnyixcvOFpO1sfHx8fH\nR+FLBEFAF3eu6enp4YYE3DhMkuTVq1clEgnLn+yECRMQQs+ePcPRBkLIwsJi2bJlP/7447Jl\ny+bOnVtlDkZGRunp6YzE9PR0giCMjIzYlKF3794dO3b09vZesGBB27ZtP3z48Ouvv8bHx1+7\ndo3N7qBWODk5OTk5IYS0tLTWr1+/fv16Tt8Oj26Lj4+3t7dPS0sbP378oEGD9u3bN3ToUE7f\nlyKTyT58+GBhYVE3bweAQkeOHBk4cCD+P56rs7i4mJq0U0MoCzjkl2YlSXLixInQeKiZbt26\nNXLkyH///VcmkxkbGy9evJiaCqJKSUlJONooKCigprAkCKK4uPj8+fN+fn5V5oDvI62tremJ\n06ZN+/HHH1n2MOjZs+esWbPOnTtH9YgkSTIqKqpt27Z4AroqEQQRExOzdu3aRYsWZWRkiMXi\nLl263L5929nZmc3uoD66c+fOtGnT7O3tEUI2NjZnz56dOHHiyJEjSZIcNmyYSlmNGzfu/v37\nlb1aUFBw//793r17M9LxTKOmpqZ13IoG1IXH41FXcZFIpCGT/OJoY9iwYQcOHMApNjY2b9++\nFYlEJSUlai3a/1FteXo8GUDnzp3xYvFAc+zYsSMkJERfXz8oKEgikVy8eHH8+PFxcXH0tUmV\n6NChA0IoIiKCijYQQgcOHBg+fHj//v3z8vKqzMHc3PzNmzefP3+mr8S7Z88ehJCrqyubMjRt\n2nTOnDkBAQETJkzo2LFjTk7Orl27EhMTr1y5wmZ3TCQSzZkzZ86cOXi6cbgG1D0lfbyo1q9a\nlJWVRa3ZixDi8XjR0dEIoZEjR+JFZ9hn1a1bN9w2o9Ddu3cVngjQafTbceDAgREjRtBTSkpK\nNKcVgSAIKtpACKWlpREEQa04rRFIFYfFpqWl1ffhbZo5LDY9PT00NNTJycnMzMzX1/fUqVMq\n7S4Wix0dHemzVowePRohlJiYyGZ33F9HPh0hxOfz2eTw119/IYRMTU2plKKiIpxtWVkZmxyw\nM2fOeHt7GxgY2Nrajhgx4tWrV+z3/XasXLmSPkpFoyivbWqdk5PTvHnzGIkymWzcuHE8Hi8w\nMLC23lcz641v0/nz50UiEUKIIAhtbe3nz5/XzfvisNLBwYFKwbc0WlpadVMAJRBCAoFAPpH+\n+1f7sFjVbjiysrJ+/PHH7777TtWwBij35MkTHx8fBweHWbNmGRoaXr16dcCAAVOmTGHZ3TI+\nPr64uHjz5s30p107duzYt2/fxo0bd+zYUWUOJiYm6enpYWFhW7ZsoRJXrVqFEGI5mtHLy6t5\n8+YPHz7k8/k2NjYlJSXv379HCI0dO1al+1p/f3/uhjOAOlDHfb/w6LYlS5bQE/HoNplMtmvX\nLi7eFKhRx44d4+Pj0ZfeZoWFhc7OzmPHjmVT0dUQSZIEQdBHQpWXlxMEwdHITVVpSDGUIStv\n4TD/L2NjY4SQRCK5dOlSXcdFtYqLO5W+ffvSjypBECrNx9q1a9fvv/+e3j4RFxfH4/Hu37/P\nZndcq8pPkKWjo+Pv788mh48fP+KSUy0KVMqDBw/YfQiSJMmFCxdS4YVYLD506BD7fQF7mtzC\nIU8mk4WFhf3yyy9cZB4fH+/v75+SkqLwfadOnerp6Vkrb1RZvQEzjSqUk5Ojr6+PYwKxWHz9\n+vVayfbVq1e4gqVaNahHrrWSv3LoS39MRmLdvLtyuBiDBg2iUvA0P0KhkEpRewuHsoAj9L+m\nTJmydu1aPH9ivVbrAQc1CJMgCPqjXJa75+Xl8fn8hIQERrqHh8fixYvZ5JCYmIgQ+t///sfI\nliCIKVOmsCyGmZmZfDxqYGDAcndQuz58+HD48OG1a9eePHmSmtGcUr8CDpIkX7x40bBhQ3WX\nokYqqzdgplF5CxculK9MamVue9y+fuzYMXoiHiI3dOjQmuevnCYHHIcPH6bf8Sq8DGl0wPG1\nkq84Hj58SJ90RFdXNy8vj32GeK8jR45QKbirmvxPUyE8aYH8LVrfvn2nTp3KsgyGhoZGRkYZ\nGRn4z7KyMk9PTx6Pp1KAyJifauzYsez3BbVo69atBgYGJiYm7u7u+vr6DRs2PH/+PH2Dehdw\nfMV9vwoLCxMSElRa9Ke+SE1Nbdq0qa6urrGxMf3WuUq4Alm4cCH+My4uDqfUvLMFXplZ4Tva\n29vXMPMq4U8RGhpKpeAR+yyreq59/PiR/lRdLBYzNoCAQw0YFcfJkyfx1yMUCulj2zIzM1lm\nWMOwt6SkRCKRnDx5kp4ok8mcnJzWrVvHsgzx8fECgQCv0OHp6SmRSAiC4KgRG1QpOzt71apV\nY8eOXbVqFfsfEnbq1CmBQLB582Z8DSsoKJg+fbpEIqGHpPUr4MjMzBw6dKiHh4e6C1Ij31qn\n0eDgYFyJ8Xg8fMfM5/NTU1Or3HHWrFkIIcbXjdemsLCwqGGp8GMCxjMsvLRy+/bta5h5lUJD\nQ6kmBHorQk5ODtdvXSs0MeAoYkF9Ba4FjIoDRxj0NropU6awf5pw79499GVkNp1K7WzBwcGu\nrq5U+4RMJlu+fLm2trZK7RPZ2dkBAQE2NjampqZeXl4q9b0AtWjJkiW4Iwv1r0qRX+fOnSdM\nmMBIbNu27fTp06k/NTnggL5f9Yu3t7dEIsFrF5eUlODE27dvI4QEAsGTJ09wCl5KUCKRVJkh\nHlr84cMHRjpSNIxCVTi2YFw1cR1eNz1pjh07Rg81CILQnGgjMzOTUTbGBpoYcCAW1FfgWsCo\nOBBCIpFIfhv2H7OGLRwkSWZmZnp6ehoYGAQHB0+dOtXDw0NHRwev8Q3qnkwmS05OPnv2bGJi\nIrXSPUu4QvTw8Hj//j1Jkh8/fmzbti1CiP23aWZmJt/Zdt68eV27dqX+1OSA41vr+1V/O40q\nnOFmxowZJEniufIY3xpe97jKr9Lb2xshtHz5cnoinh2rVq52enp6uMo1NzenpgSs7z2Eao4+\nGXd96sOx7IulS5fa2toaGxuPHTt24cKFP/zwg5OTk66ubkREhPoKXAvkAw4TExPGNpXNS6EQ\n/l7Nzc3pb4EQUumhdUVFxZ49e4KDg/v06TN37tzXr1+z3xfUoqdPn+Ip9vEcaI6OjrGxsex3\nd3Jykv85mZmZNWrUiGUONjY2e/bsYSROmzaNPuBIkwOOr9XX12kUV1x9+/YVCAT0ZwSZmZl6\nenryN1E7d+5ECK1evVp5th8+fJC/B8N9L+bMmVMrJcdBPKVv3761ki1L9Mu5fNu2uuBSWVpa\nUim4Pwf9i1B7wKFgggTcdIYQWrx4sZmZ2ePHj3V1dXEKHt6Wm5srv1e9Jr/EaFlZGfvdo6Ki\nZs2a9f79e0ZzlkpLovN4vFGjRo0aNYr9LqAy+fn5ly9fbtKkSePGjVXa8dOnT3jl95SUFEdH\nx8zMzGXLlvXu3Ts+Pr5du3ZsckhLS5OfCd7Hx+fMmTMsy+Dt7f3777+PHDmS+jkVFRXFxMTg\nrvhA09TTmUbxWHodHR2qExvFyckJj6VkpD99+hQh1KhRI+U5m5qaGhkZZWVlEQRhYWEhEonw\n7ROfz1+2bFmtFF5dC3nOnTt3+fLl9BSZTMbj8aj10tSIJEmCIN69e0elVFRUaM4sqJiyVVG2\nbt06e/ZsKtpACPF4vF9++QV3//lqSCSSioqKoKAgKqVp06aIxXlFmTlzJvnfsFcqlWrCT/Ab\n9OrVKzc3Nz09vT59+jRp0kRbW3vz5s3sd4+OjjYwMIiJicFLFhsbG69atWrAgAGMeaWU4PF4\n8tFqWVkZ+wvS/Pnzr127NmjQoAcPHuTk5CQkJHTp0oUgCA1ffraYBXWXkRP1dHn6rVu3IoTw\nTRF114tbdrOysgICAhBC4eHheOORI0fyeLzVq1cjhMRicZWZZ2ZmtmzZEiGUkZGBp/YxNjau\nxWmptm/fjruyEgTB4/HYL2pdQytWrED/nXwZX9FhCQWWlJ0kHz58kK8lCYLIzMzkskh17eXL\nlwiho0ePEgSB71SeP3+O+2OrlI9MJqN+hfJNJkAleKiwqoqLi11cXJ4/fz5//vxHjx7FxMTY\n2dn98MMPmzZtYpnD7du3/f39GVOjBgQEsFx/DiHk4OCQkJBADzdlMtnly5fx6mJsfPfdd1ev\nXn337p27u7tUKvX19W3QoEFCQoK+vj7LHNRCwoK6ywj+D37GgRDS1dXFCzcihKh1Ny5cuKCl\npbVp0yYbGxsej7d//37qRrlnz55srq93794lSbK4uBgPbPn06VNtlVwqlYaEhJC0fnK+vr6q\ntmVWD44w6JETPtPh9pIlZQGHi4vL6tWr6auTkyQZGRnZrFkz7gtWd/BILTs7O4IgcBtU+/bt\n68EcsV+jsrIyKysrgiAaNmyI711CQkLY7z5nzpzCwsK7d+/iX2lAQMDTp08bN248b948ljkw\nWqow+uKQVdq0aVNBQYGtre358+cRQnFxcfb29nl5eXhFMZbc3d2vXbv28ePHxMTE3NzcQ4cO\n2djYsN9dLdj0/VJ3GTkhk8kyMjLUXQqVUROB01ekc3d3x/95/fr1x48frays3r59S37pFz92\n7FhPT0+EkEwmMzc3V55/Tk4Oj8cTi8UODg48Hs/V1ZXP5/N4PD6fv3fv3moX++7duzk5OQih\n9evX47s7PFQ1JSWl2nl+NUiSxF8QRk0Hpb4SySErn4cjNjZWS0vL3Nx8woQJixcvnjZt2nff\nfScQCOLi4mqrC4lafK3D274C+M5JIpH4+vq6uLjgU6VTp04sd2/WrJmVlRUjcc2aNQgh+ck6\nFVqwYIGLiwujA2BwcHD37t1ZloEkycOHD+OO9Jiuru7BgwfZ7065cuXK6NGjFc58oMmdRiMj\nI1u3bk2fOq+iomL8+PH0Yb310dfXaZSaXWPo0KFTpkzBqybhRKqnIf4N04fh4D6hSGmfevlu\nTAzV7muJWx+HDx9OT8STc9D7S3IEafBMo9TzL/TfIIM+D5DaO41WMfHXtWvXunTpIhQKEUJC\nobBLly61NSW+GkHAwZ2kpKTRo0e3aNHC09Nz6tSpeGgoS8OHD0cIdenShZ6IH42zzKFx48by\nsw1WttCMQunp6UZGRoMGDcI1bEFBQT12mWMAACAASURBVEREhJaW1pUrV1iWAauoqIiPj1+z\nZs2VK1eqMQfl0KFD6bUzQRDU/RymyQGHjY3N0aNHGYnp6el1cD3g1Nc306h8s5lYLMbXqoED\nB5Ikee7cOeoXSL9QVXmJxRs0bdqU/HIKYxcvXqSeV1ZvhdXKJizAheTxeDwej7spR3HJ6avz\n4HskDZlp9OTJk/VvHg555eXl2dnZ9TGEVwgCDo4cOnRIKBR27959zZo1y5cvb9mypVQq/fvv\nv1nujm+wGIkjR45ECG3fvp1NDgEBAVpaWoyJ6Xr27KnSdEP37t1r1aoVvmHS0tKytrY+fvw4\n+91rbvTo0bi+aNeu3YoVK3D3VYQQPejR5IBDKBQylrogSTIjI4O+iFR99FXWG9SVycrKqnnz\n5vTmDYXLRONvVnnA0aZNG0RbMwxvPGzYMKphY8+ePdVuFcAlpKYjw3r16iVf1B9//LEa+Stn\naWlJHTH6pf2ff/6p9ffiQv0IOL4yX2XFUSuys7ObNm0qFotFIlHjxo1Vms7o8+fPUql06dKl\nVEpFRcXw4cObNWvGMgeRSCRfB23ZsgUhxHIJuqSkJIIgHB0dqVlM5s6dSxAEvl1jr6Ki4s6d\nO7/99ltCQgLLZzF0BQUFvXv31tbW5vF42traPXv2rMbSPNScj+SXCZro09NpcsDRokULLy+v\nwsJCKkUmk/3www8tW7ZUY6lq7qusN65cucJ4xo+HBURGRtITSVr88fvvvyu/p8dtGLdu3cJ/\nUhsjuSc11SgwbgdlvDtVcmdnZzc3N+oTVSP/Kvn6+jIO1+XLl6lXtbS0eDzeyJEjuXhrNpTP\nEaKJAUdeXh6uLPIqp7by1oavsuKouXXr1uGfKZ/Pp3qhR0ZGstz96NGjUqmUMS/nv//+ixB6\n+vQpmxwsLCwQQu/evaMn4h7K9+/fZ1mMXbt2CYVC3AKMKz4fH5+6bO7Ozs7W09Pj8Xh+fn6z\nZ8/u3r07j8fT1dVVaWke+Wn1GY+WNDng+Nb6ftXfmUb3798v3zDg5+dHfrlubdu2jXogYmFh\nQb+YKQkfcWiC8yFrO+AgaddUapEX+RAEp1fvqU0NS0Vp3rx5nb07SZLbt2+X/zaR5s80ihBy\ncXEhlXbLV1t5a8NXHHDExsYOGDCge/fumzZtUnVffNLGx8fjP2/evInrGpZL52zcuBH/bOhk\nMhmfz2e5iEZsbCwOd6j2CbzItar9y/Ly8ubPn+/v7z9mzBjq46hk69atVlZWEonE1NQ0LCxM\npX379OnD4/EePXpEpTx79ozP5/fq1YtlDgghMzMzRiIOAak/NTngIL+xvl/1t9MorsxNTExw\njE5dMt+/f0+v5+WnGJFfhpTu4cOH8rEFzhy3d9bkkQrGGLiOENq3b5/8p+OoawU9tsBzclAp\nfD7f2NiY0yYW5aWiL3bD6P9LakDAoWCm0bVr15qYmOD/KIk5gEYpKipydHSkppmLjY2dMWNG\nXFxchw4d2Ow+d+5chNDatWvxrN4IIU9PzwMHDgwdOjQ8PJwaQaeElZXVmzdvSktL8WUG++ef\nfyoqKqytrdmUwc/Pr0OHDteuXcNjYhFCJEkihFSd1UdXV5fRIKwSFxeXp0+f8vl8qVSam5u7\nZcuWAwcOpKen02fAUyIhIcHT05M+dNzZ2dnLy+vatWvsy/Dx40dGSkVFRT2aWqp9+/YXLlyo\nqKjIy8vT09P7uqdFqqczjc6YMQMhpKWlJT9DBj4ByS+xQkVFxY0bNzp16oTbL319fRUuwkJx\ndXXFuxMEgYfC4jmKEEKPHj0SCoV4Zjz5oIE9+tx6+IYEdxzh2i+//ILvgij4xMSfjqTdpWtp\naeGX6myKDnzACwsLqRSZTKZpM41CHw7NUlBQ8O+//1ZjRzwwbNCgQfjP9evX4yHvLG+8vLy8\nUCV9v11dXdnkkJuba2xsPH/+fCqltLQ0KCioRYsWbHanXLlyRSqV8ng8gUDAvv8HHV6VJiQk\nJDIy8sWLFyrti+f1p7dGREVFsT8IJEmKxeKgoCBG4rBhw9h3mcRfpVQqxd04UlNT8QWb/mBY\nw1s4vkqaXG9UAzXxF6I9eqCCWtyhytDQEKc7OTlRL7FchhBPWlqZGi5BsnjxYvrDFPkMcWnp\nU4LWCvn3ordtMDZGdTt6ReHbUVd5TO0tHBBwaIqDBw8aGhpSv92+ffuy7674+vVrxmWSJEm8\nRMLkyZPZ5IBnMk5KSqIn4vvsjh07sizGyZMntbW127dvv3Tp0gULFnz33XempqYPHjxguXut\nOHPmDJ4DgxquRgVhbBgaGspHBo0aNWJfP5qZmck/WnJzc5Nf0U0J+dmjGYthamDAAX2/6hcz\nMzP802L84KnfG3U5r2wqPDYuXry4a9cukiTd3Nxwlwsejye/NqFKKmswo0pFxUY1eReFlFzU\nFQYcXJShMvUi4FDWSHvv3r2LFy/i/+fm5oaFhbVv337JkiWkRjXRfBU2bNgwdOhQPT29NWvW\nHD58ODAw8PTp03hJFzYOHDiAEML34hTcmeDy5ctscsCrJDA6YHt4eMhnq0SfPn2ePn3q7u5+\n5syZa9euBQQEJCUlNW/enOXudK9evarG0hvp6el9+/bV1ta+d+9eeXl5WVnZsGHDDh06xH4V\nkoKCAvw8ka5Vq1bs20WHDBny5MkTPLgG27Fjx4MHDwYNGsQyB4RQUVFRZGSkgYGBQCAwNTU9\ne/bsq1ev2O+uFnp6eq1bt8b/qYy6y1iF4uLi7MpVtlc9nWn04MGD+D8lJSVUInXP8+bNm3Pn\nzjH6YQgEAtxuIZPJ6E9OK8Pj8bp27TpmzBg8NwbVpaAmk/THxsZWVFQghDw8PHDZcGdz9OUJ\nAkEQ+Gxl+SS3tjCqCLwUVx0/aCNJskuXLtSf9WymUW9v77lz5+L/T5w4USgUdujQQUtLizEH\nUb3DxZ1KUVERboTEVB0BqKOj4+zsTE85duwYQmjjxo1sdscxgfyMFwRBuLm5sSyDs7MzQkgo\nFHbr1q1Hjx7449jZ2bHcvVYUFRU5ODhQh5EgiGnTprHffdCgQXw+Pzs7m57o4+NDH1CqnLa2\ntr6+PiMRzxbMMoeKigo3NzeEkIWFRZs2bXBt6OLiUrsjZTSwhWPt2rV4xY21lVN3Gavg6uqq\nvLYcN26c/F71t9MoFQG0bdu2T58+CueMwn/OmzeP2gsPi1V+RtDXwlSo2o9UcOsFXo+Cgts8\n+Hw+Djhq/UkKBVXeikB/iYrG+vXrx1FJ5PXo0YMqBv2r/PDhA7WN2ls4lAUchoaGJ0+eJEmy\nvLzc0NBwzZo1JEkuWrSojkf71LpaDziOHz9ekzMKjx2Vb2bU19f38fFhkwNeTq9du3b0RLx4\nx8KFC1kWgyTJgQMH0p+M+vv7s9+3VuAT1djYeOjQod26dcP1SGBgIMvdnZ2dbW1tGYnbtm1D\nCDGikMp07twZfZndCHv79i2PxzM2NmZZBmzTpk3NmjUzNTV1cXFhGTUqVNkQIQ0MOL4CHz9+\nTK0cQujnn3+W36v+zjRqbGzMqLWoaxV+kHr9+nUqkTGSUXnAgTfAYQG9s/P169epByIqTcdH\nYTPTKH0m0NqFS04/9ahHt/KXAO7insqsXbuWETXSow1SwwMOgUCQkJBAkuSdO3cQQi9fviRJ\n8tKlS/W9w4fCgOP9+/dRUVHjxo3Di2+plCH+didMmECl4JHoLPs84sN7/vx5RrqFhQX7lhL8\n/KV169bJycmfP38eOXIkQRDs7+zpioqKqv24PTk52cXFRU9PTyqVenl5ff78mf2+eC2AESNG\n0BMVzgZWme+++65BgwaMxI0bNyKEWH6iwsJC3GjcpEmTESNGeHp64tr2r7/+YlmGWoHXf6EH\nr3fu3KFvAAFH3fvK+nBg1JXJwMCgY8eO9PGcCodlxcbGklUFHG3btkW0jqh4427duqEvbQD+\n/v5VhiyVwSX8888/6YnUmnP0a+3QoUOrkb9yVE9Y4gv856lTp0iSpJpYCIKQr881gUYHHFZW\nVriNdOXKlTY2Njjx9OnTenp6dVnEasCdD5TAqxtTZs2ahQNVPFJLKBRGR0ezfzukKFpnf0YV\nFRURBMGY76GgoIDP5zPWKFKOcdaZmJgoXPeLO3hsLULIwMCAWgjqxIkTLHc3NTWVP2KzZs1C\nCB05coRNDmPHjiUIgprGA3N3d1fpHMvLy6MmKyQIwtzc/OHDh+x3rzk8Ugb/Di0tLak7QnqX\nXk0OOO7evXvhwgX8/5ycnNDQUC8vr8WLF+OxkfXXVxlwHDlyRP5S/ezZs6VLl9ITSdrUF5Mm\nTVJeueEtqZlXqDgDyT2pqUaB8RguopKZRoVCIZ5TpNr5V4nRLEQQxKJFi6hXRSIRn8/ftm0b\nF2/NBr2Fo37MNEoZNWqUvb398uXLLSwsJk2ahBNXrlwp3wlf0zx9+jSucggh+uhNfAfcqVOn\nnJwckiT//fdfZ2dn+hRYyqWnpyOEqICMotIv3sPDg8/nHz58GP+ZmZn53Xff8Xg83KrE3uvX\nrxctWjRp0iT2K5gwvH37dsmSJb/88ouqqwPg46Cvr0814iUmJmppabGf7E9fX1/++eihQ4cQ\nQvQZ05XIyckRiUS6uro7d+4sKSl59uwZnoYkIiKC/QepFVOmTBGJRDweTyQShYeHq7Qv/uXQ\n21Rw2w89qNXkgONb6/tVf2capXpj0OHVE/F1a+nSpfSBsvSLmZIHIniMFTVornYDDpJ2TaW3\nMRCaN9Mod092FJo8ebL8t8k4yBodcLx7987X11cgELRv3566irRq1So0NLROy1jbGBWHubk5\no2tkRUWFjo5Oq1atWGaIFE29p9IZlZOTY2dnhy/Y5ubmeAqNaswWWhOFhYVNmjSh/1IbNWrE\n/pkIXpyJ0aayatUq9N8uEUrgXquMurt9+/by2SqRmJhIXwNTS0uLuvjVGXr3YaqyZr+7woqS\n8XPS5IDjW+v7VX87jeIflVgspp4F4JTc3Fz6703VYbFUzw/6u+BMcE1LdXqrdsnli8R4gILH\nV3I0DQYVhFEdVKny8Hg8+ixwXLx7ZSqbI4TQpJlGq56Hg9EQmpGRkZ+fz3m5uMSoOPh8vnwI\n5ePjI5VKWWaIf1v0x4qNGzdGCJmbm6tUsC1btnTr1q1Vq1ZjxoxRaWH3WoHHU/j6+j579iw5\nOdnPzw8hxL6zZKtWreRP7/LycoTQxIkT2eRw8+ZNfG2mpj5buXIlkpsngI3ExMS1a9fGxMRU\nY+k1rLi4eP78+W/evFF1RycnJ4SQkZERlYIfFTVq1IhlDggh+UqhHgUc31TfL7LedhrFY8UV\n9nakLpnUxoMHD6YWLmEzlR+VrUAgoHcaJWnheM2bHzZs2PDnn38q70Zaw7dg+Omnn+QPl8Lw\nAj8JreH8ZipR+HkZBasHAUdeXl58fPyxY8dyc3PrsGAcYlQcWlpaY8aMYWzj5eVFv2YohycJ\nxj8v+t1trZWYnTt37kgkEqotccWKFez3xRd7xhxZ48aNQwidOXOGTQ44QKGvcUp+WeY0KiqK\nZTGoySrwLRc+pPR1SerAvn37GLXwsGHD2O+u8KuvrE5kn0M9Cjjqb98v5b6yPhx4kgaq4sKJ\n1C8fXy+pm66RI0dScQOj/3JllE//UMMr8aZNm+gPU+QzrPuZRuU/ERcRjxJfQ8CxfPlyqq/y\ns2fPSJJs3749++uHZmJUHA0bNjQ3Nx87diyO6wUCwYYNG0QiUYcOHdjnefr0afrpVPc3c9On\nT8dvLRQKqaCncePGLHcfOXIkQoi+pDj5pX2iT58+bHLAsQVjWlJLS0v5KES5R48e2dnZicVi\nPT09asHJOnP79m186AwMDAICAho0aKBqzIH+u34ShrvQsswB97mjP+bDXyi9jUSTA4762/dL\nua8s4KBm32JcKXGitrY2dTlX9ZEK3dKlS/G5g3to4ZGrNRxvr96ZRuWzxYlVPgblWr0POKKj\no3k83qRJky5evCgUCnHAsWTJEl9f3zouZe1iVByHDx9W+PN98uRJHRcsNTXVz8+vSZMm1Zi5\nAf/a6AMZcNctlu0TgwcPVnhuIIR69uzJsgx43iQjI6OgoCB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OMsC7YwsKYuL6KwAAIABJREFUeMv8ksxMKCj4z4WdnMDBARwdwdERHBze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\nhgz59NNPEULR0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"text/plain": [ "Plot with title “”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "options(repr.plot.width = 6, repr.plot.height = 6)\n", "par(mfrow=c(2,2))\n", "\n", "plot(m1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Part of our trouble comes from thre asymetric distribution of the variable MOOC_PercentageVideosWatched" ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "data": { "image/png": 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nsLBFbE4lK/MhA4KAIXqXGoVwgs47PAHiQYAmvxTOCCpoSQPOFf0wKGQ71CYBmf\nBfYgwRBYi2cCV/bu/kIlrXyhpHfqpyllILCMzwJ7kGAIrMUzga/vVCW+VnW63rE+IbASnwX2\nIMEQWItnArebGyvMbe9YnxBYic8Ce5BgCKzFM4Fz5sQKc3Id6xMCK/FZYA8SDIG1eCbw2R2P\nia/His5xrE8IrMRngT1IMATW4pnA95Juaw/RQ2u7kRWO9QmBlfgssAcJhsBaPBO4dgohhP3t\n/ql4mCFOmAT2IMEQWIuHd2K9UtG1qGvFqw72CIGV+H4nlusJhsBacCulVSCwIhaX+pWBwBDY\nYSCwIhb14t4tR5zeAgQOkMBu59cbILAiFuXCW10J+/+BnzzvNQe3AIEDI7D7+fUGCKyIRVHe\nmddoKEtwZd4MB7cAgYMisAf59QYIrIhFUR6b8+FBlmB6RTcHtwCBgyKwB/n1BgisiEVRLhxF\nowmea+5JpLpd69f8Yf2uOuNaEDgoAnuQX2+AwIpYFOWsebEEzzPzd6Grl7aL/g289kurjepB\n4KAI7EF+vQECK2JRlFtOjCX4J0X1NzzWg0RKRk6ZOrI4QnpWGVSEwEER2IP8egMEVsSiKA8r\n/F5M8MsZFfU3XEDG7Y+W9o0hCw0qQuCgCOxBfr0BAitiUZTfiAx6nax/58bs7G31N+xUGr/f\nsra70QyFwEER2IP8egMEVsSiXFiVJX7pyX7URMMcxUP/s40ePwyFwNs2GXF7Q8PGQRHYg/x6\nAwRWxKJa2jGztGO3aTvMNGw5VC4PKTSoGAqB8/X/Q0tGhmHjwAjsfn69AQIrYlGU33rfQsMx\nkfjv8UcyxhpUDIXAxnEvMb6jPCgCe5Bfb4DAilgU5YyrLDTcnU9K5q9eu3b1/GLSVG/YGBA4\nKAJ7kF9vgMCKWBTlFuOttNxeJh1Alm03qgeBgyKwB/n1Bg4Fbv/TZTo8pdfEHMqpN6JLjaW2\nW5dPLi+fvHyrcS0IHBSBPcivN3AocE7z0uR0bqTXxBzKqfdxwUyjK/Y2gcBBEdiD/DrJ7p/0\n16H5aJ0mARZ4nM6Kei5B1oty6lVcQlr0v7qCkVqnKiBwUAT2IL9O8nyO3lHnaT/WaZLmAiuu\ni5hqm0YPM4RCYA/y6yT6U7s5BJZjUZTflzHR0oWHGTY0MLxfYtNBE2G5QygE9iC/TgKBzWD7\nb2K58TDDUuPbJcgUu8GmTCgEtoS9/P5yqh4rLUcAgc0Qn3pP/sNaQzceZqhHhAkTzAbnOPwL\n7FF+B+r4++MuliOGwGaITz1SIfy45zLTDd14mAECa3FKYJ/z+wAETo6zAleYP6I2vNn983M7\nxWlLvpdXQGAtHgrsVH7395IvZHYxlV8IrLPCN4ENb3Y/sfrBODfjE5hHgQ3ze/w++ZrOtfgE\njsOTwG48zACBtfglsMP5hcA6K3wT2I2HGSCwFr8Edji/EFhnhW8Cu/EwAwTW4pfADucXAuus\ncE7g7Pz8/GySH8VUW8cfZoDAWhwT2N/8QmCdFc4JrCK1TlVA4GAI7G9+IbDOCscEPq4itU5V\nQOBACOxzfiGwzgrfbqU0DQQOhMC2mbTaeD0EluFK4Nonps3aFC0a3uADgfkWmEwyXg+BZXgS\nuGYw+y41/CgrG57c5EPgp/QeHo+S+XujxmEUeKEEKRZ+GFSEwDI8CbyKFC67v4yUfktDIfCE\n8+cZYSxZGAU2fdILAsvwJHCvrF3CYfQvSNnRcAhs3HcaCtzo1hUipKfww6AiBJbhSeDGfcWX\nleSiYxA4hAKvb9Ummit8B9YQCoFzy6Ovy8kl1RDYsDGXAtOvh5Fr2BkOCKwhFAJ37hUrLCYD\nx0BgI/gUmNKHG3d4CQInIRQCj8g5EivdQDIhsBG8Ckz39CHTKyGwhlAI/DhZJRWnOHCWUqQe\nEQYanyme/7W5yJMCgZNRe3duJwisIRQCf7fiWalYe/c8g4rOCdy5UbkRWYZ91wMETs6HXSGw\nhlAIbBoHBTYWwbjveoDAOtSdqjWuAIFlILBhTxA4iEBgGQhs2BMEDiKpCvz3B3WY2UCvCQRW\nxJJacxNAYAhsJPC5LTolp1mGXhMIrIglteYmgMAQ2Ehg3f/6erHuqEJgRSypNTcBBIbAEBgC\n03pFaHi74f+M9oFhYwhsFwgsA4ENe6pHhAzj/xmtiWFjCGwXCCwDgQ17clMECGwXCCwDgQ17\ngsBBBALLQGDDniBwEIHAMhDYsCcIHEQgsAwENuwJAgcRCCwDgQ17gsBBBALLQGDDniBwEIHA\nMhDYsCcIHEQgsAwENuwpNdbcvBcAAA7XSURBVBEafmrEVeNT6BsCS0BgHSAwTVGEZcb3aZFz\nUugbAktAYB04E7ju7/I9yPcFQ+AlxPATuCi1vg0bh1Dgbe/GeRgCxwmNwJ9mKz/cvpdX+Ckw\nn30HUuDdmcr8QmCJ0AisJCCH0Lz2HUiBadXhOC9C4DgQ2LCnwEqWfgIrwHdgGQhs2FNgJYPA\nEhBYBwhMAywZBJaAwDpAYBpgySCwBATWAQLTAEsGgSUgsA4QmAZYMggsAYF1gMA0wJJBYAkI\nrAMEpgGWDAJLQGAdIDANsGQQWAIC6wCBaYAlg8ASEFgHCEwDLBkEltDN79wGpTo0mKvTBAKb\nAQIHvO+QCDwuc5kOmXpTGwKbAQIHvO+wCGx9akNgM0DggPcNgbVAYEUsqTU3AQSGwBAYAtMA\nSwaBJSCwDhCYBlgyCCwBgXWAwDTAkkFgCQisAwSmAZYMAktAYB0gMA2wZBBYAgLrAIFpgCWD\nwBIQWAcITAMsGQSWgMA6QGAaYMkgsAQE1gEC0wBLBoElILAOEJgGWDIILAGBdYDANMCSQWAJ\nCKwDBKYBlgwCS0BgHSAwDbBkEFgCAusAgWmAJYPAEhBYBwhMAywZBJaAwDpAYBpgySCwBATW\nIZAC1+1av+YP63fVGdeCwLwK7GR+IbDOCv8Erl7aLvoftLdfWm1UDwLzKbCz+YXAOit8E/hY\nDxIpGTll6sjiCOlZZVARAnMpsMP5hcA6K3wTeAEZtz9a2jeGLDSoCIG5FNjh/EJgnRW+Cdyp\ntFYq1nZPHJ3DP58aZ6gqwQOnGnABMVo7tUkTw9WkNIx9D/JJYIfz2zmit4ORzjorSnVHNbe1\nzooBZLTOGt0cjCYDdNa0ztXbvm7GbOzlQL8EzrleLs/OTVipTHDFjxQrbtPbQZGfXWi4eqCh\n/VMv/FkY+556m90MpYbD+R35I701Pxqps0J/VPsN1VlxTckUnTW6OZhSco3OmqH99LavmzEb\ne5lqfm0L3HKoXB5SmFoQIHggv3xgW+AxkUel4iMZY50JBgQH5JcPbAu8O5+UzF+9du3q+cWk\nqd6pA8AtyC8f2L8OvL2MxCjb7mBAICAgv1yQyp1YW5dPLi+fvHyrY8GAQIH8coD790IDAFwD\nAgPAMRAYAI7xWOBsAiyS7W2GUgP5tUyK+fVY4NPue9c+Q4ak0Pi+hik0frehf3EH/XlgFTby\nW7TAcpOySZab2MjBpDLLTRYUWW6San49Ftj4YYZ6mDAhhcap3TTOa9xeY2OcujxguUn/RZab\n2MjBov6WmzzQxXKT4P9FDhW8isBr3F4Dga0CgU0Cgb0AAlsFApsEAnsBBLYKBDYJBPYCCGwV\nCGwSCOwFENgqENgkENgLILBVILBJILAXQGCrQGCTQGAvgMBWgcAmgcBeAIGtwpnAzV5KofHU\nqSk0fqlZCo25jdtrbIzT+Q9bbnK59T8EZyMHt11uucnD51tukmp+PRZ4T239dXQ5fDiFxrV7\nUmjMbdxeY2OcvjhRf50EvjxmuYmNHBz70nKTE19YbpJqfvE4IQAcA4EB4BgIDADHQGAAOAYC\nA8AxEBgAjoHAAHAMBAaAYyAwABwDgQHgGAgMAMdAYAA4BgIDwDEQGACOgcAAcAwEBoBjvBR4\n99jC3M4Lq6w1qnxq9DkNm1z0f7W2+1hPyEK7jTcPbZXT/spX7bSue65fuwZnjNhicdPPzvxR\nHhklLama2Ro/D7Een3pnzZAwHUxRc9vA0xs2K15yyMqGqHLimKJL9H8bLLS0DeUEs4WHAm9v\nmjFkdnfSs9pSqxUkp2d5nyxyZa3NPr4ubBTLg/XGt5DcviMvKVhop/XPSf7PZg+KZKy21riU\nNDk7PqdVzeyNn3fYiE+1s6ZQTwdzHCet+4wY2JK03WtlS4qJY44ukQrGLCvbUE4we3gocBl5\nhNLaMWSppVZ/uv+I8PNfrcgTNvsY1ubWWB4sN36Y9NonvNR+Y6P1p6TFfuFlHelgrfGrn9Rt\niM9pVTN74+cdNuJT7awp1NPBHHWiuCfGkSlWtqSYOObokmupe4ZqgtnDO4G3kmL2si/Svs5G\n67vINHt9PEyeXxHNg+XGJ1rnyX8WyWrrzUT8m2i1WQ0tN47PaVWz1MbPfWzGZ1HgGNHpYI3X\nyMVWqssTxyTWBVZNMJt4J/ByMl98LSa7bLS+n8yy1ceextfQWB4sN95Ixh1/atEdm+vstN6X\n2fIAZfNzmOXG8Tmtapba+LmPzfjsCRydDta4jsy2UFsxcUzSJfuOiTMetPJFWzXBbOKdwJOJ\n+G2QjiTrrTeu60k22emjtk+HI1IeLDf+JZl1Fjst0etLO61vJ03HXz84a/BBy43jc1rVLKXx\n8wCb8dkSODYdzDN72ujOpOvX5hsoJ45JoiexGlk4tldNMJt4J3A5WSu+TiV/sN54MRluq4+7\nyUtUyoPlxjNJZpdXKz8cIB56WQ//iSZCbro8YX3T8TmtapbS+HmAzfhsCRybDubJE1Ix0Iom\nyoljkjs3HajeMTOS+TfTLVQTzCbeCzyFrLHcdiXpftROHx/mTqcagU0HcC3J+kh4OdaW/NNG\n6yUZN++p2voT8cDSWmONwGKzVMbPC2zGZ0dgaTpYoO7AU0Wtt5qurpo4llhIBpmuq5pgNuHi\nEPoeUnrYTh913c6opNT2IfQC8kPxtYKsst76r2QMe6nukLkXh9AG2BA4Ph2ssYN0NVtVPXEs\n8RkpMF1XNcFs4v1JrBLLJ2EWk15HbPVxisSZZCOAR0lv8XU2WWG99SzykPhaTtZZbaw5iVWi\nPIllffy8wWZ81gWWp4NF2hCz3qsnjiUOk0am66ommE28vIxUwl72R9pZPOl2A7m40l4ftZNE\nepLiSattBLAvo8VJ9tqPOWi19XRyu/jah2y02lhxGUnRzPb4eYTN+CwLrJgO1vguk3xnsqp6\n4lhiLelmuq5qgtnE0xs5HhWGZpzFGxFqp5DL5Ht7bPWxIn4jh8XGw8liyqZYi2PWWz9OWrP/\nKGd9xmlHrDZW3sihaGZv/LzDXnwWBVZPB3O89QH7+c0w0sdiQ0uH0O9sYz//2ZbcY76NaoLZ\nw8tbKfMjQ68vJT2sjf/dJDJGvEXtHtt9SHmw3Hh/R9JrxhWR7HU2WtdcQvJGzRpAol9vzDd+\ntqLiUtKxomKOppm98fMOG/GpdtYU6ulgjrtIp0tH9G5I2nxkvo2IJYGXkzP7Dy/JIFeeNN9G\nNcHs4enDDGNa5nRaYPGXzTzpy8hltvuI58Fy44PXFWUX/PSftlqfuLesUWbLIS9bbLwwtrtF\n2ma2xs9DrMen3lkzJEwHU+ycU9oiM79sieUzX5YEfm/K+c2zWgxYY+kLhGqC2QKPEwLAMRAY\nAI6BwABwDAQGgGMgMAAcA4EB4BgIDADHQGAAOAYCA8AxEBgAjoHAAHAMBAaAYyAwABwDgQHg\nGAgMAMdAYAA4BgIDwDEQGACOgcAAcAwEBoBjIDAAHAOBAeAYCAwAx0BgADgGAgPAMRAYAI6B\nwABwDAQGgGMgMAAcA4EB4BgIDADHQGAAOAYCA8AxEBikIwVFfkfgEOET+DgRiBT0e9x+F5+Q\nUc7FAzzk3zcUN8tq3mvBv+urCIEDy3GSM23axD6E3GC7CwjMJ3VLIqTjVZPKu5DIo/VUhcCB\n5TjJZy8bIxl77HYBgflkCWm7USx8PO3OeqpC4MASE5heQJ6mdMvwwuw24z4SFt8nFbtHtcx4\ni9K3ytvktB7wR1ZHtfrzMQUNLnhBKN9FRNZQ+tDQjg3y+zwt9ldzT5fc9rMrY5mXW4Kg8GlW\ngx1S+XuqSLkyjbUrzsltf3140hhegUvJM/ShSMtr5o3MyfsHy2a/gi7jh79PV0Vyy+dP6tZX\nqKJeXdj92qsyI3+jdMc9pOeaNWs+ozSjxzW3TGxFfsX6m0g6zrnpzN5Ni6i6JQgKi8hE1XI8\n5co0TiVFc+Z2Ck8aQyvwXyIZe3dmX1YtFLc16sqySWbWsIXM5jvZ+i8oTVi9qI7SNWQIVRxC\nf85+VF3Q8DClm0m3Y5RWX0CKqLolCAqXkCdVy1LKlWl8VUxjVUlo0hhGgcWTWBnkBjqTvH6Q\nMZTsFbLZooqtnk5+I9VUrz79lPBWXX4hVX0Hrjvy5YE7yJ8pvZqsY8sviplXtgRB4Vzyd/by\nwTSBWymNp5wq0lhB1rLlF0KTxjAKzC4jNb/kMXYULfGWkM3+4upi8olUU716qPjeeTlUIfB7\nVzYW199P6fnkEHvnmJh5ZUsQFM4hb7CXtSwvZ1IaT7kyjV2jaawMTRrDKHC+VOxI1m+KckTI\n5tWx96qTr64Q3+uWSWWBtzZsdvPjz2+cQ1ZQWpQVbZRXlNASBAX5EPpATOBoykOdxlAL3I28\nE39bMlTxCZxstUrgcWQTe7mdZV71CaxsCYKCfBJLErhCXFKmUfUJHIY0hlrgaeTG+NtSNhXf\ngZOtFgX+jIwQFy4ileylH8v8ePYNSvoOrGwJgsLurAb/ipbUAivTqPoOHIY0hlrg7VnZL7PX\nyqfkbH6Y2Vy87PdF8tWiwEdJmbgwnjwn/HycsMxvIiVVQudlYuaVLUFgWELavigW/qESWJnG\nV6JnobuHJo2hFpj+PivjsltuGpJ3npxNen8kt3zBtNKLk68WBaY9yOglS7fTtzNzr751SGY5\ny7zwu/uMuTd17t30jISOQWCoWxwhZ4yY9NNuJMI+WqWcqtI4hXSUrwOHII3hFpi+P75DTrPz\npr+qEJi+MaxldpvLnkm+OirwJ1c0y2B3Yr364yZN+r28Rsx8zd1n5bSbdTirW0LHIEDsur5b\nflbzXvPFhxniKVemsfbes3Paxe/E4j+N4RPYXT4go/0OAQAZCGyWg+xH1QDyR78DAUAGAptl\nxnkzll5bRAbV+R0IADIQ2CwbBhTmnFay/KTfcQCgAAIDwDEQGACOgcAAcAwEBoBjIDAAHAOB\nAeAYCAwAx0BgADgGAgPAMRAYAI6BwABwDAQGgGMgMAAcA4EB4BgIDADHQGAAOAYCA8AxEBgA\njoHAAHAMBAaAYyAwABwDgQHgGAgMAMdAYAA4BgIDwDEQGACOgcAAcMz/Axwr1xT3gI1YAAAA\nAElFTkSuQmCC", "text/plain": [ "Plot with title “Course Grade”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "par(mfrow=c(1,2))\n", "options(repr.plot.width = 8, repr.plot.height = 4)\n", "hist(moocs.bac$MOOC_PercentageVideosWatched, main=\"Percentage Videos Watched\", xlab=\"Percentage\")\n", "hist(moocs.bac$EPFL_CourseGrade, main=\"Course Grade\", xlab=\"Grade\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Anscombe's dataset\n", "Anscombe, Francis J. (1973). Graphs in statistical analysis. The American Statistician, 27, 17–21. doi: 10.2307/2682899." ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 11 × 8
x1x2x3x4y1y2y3y4
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
101010 8 8.049.14 7.46 6.58
8 8 8 8 6.958.14 6.77 5.76
131313 8 7.588.7412.74 7.71
9 9 9 8 8.818.77 7.11 8.84
111111 8 8.339.26 7.81 8.47
141414 8 9.968.10 8.84 7.04
6 6 6 8 7.246.13 6.08 5.25
4 4 419 4.263.10 5.3912.50
121212 810.849.13 8.15 5.56
7 7 7 8 4.827.26 6.42 7.91
5 5 5 8 5.684.74 5.73 6.89
\n" ], "text/latex": [ "A data.frame: 11 × 8\n", "\\begin{tabular}{r|llllllll}\n", " x1 & x2 & x3 & x4 & y1 & y2 & y3 & y4\\\\\n", " & & & & & & & \\\\\n", "\\hline\n", "\t 10 & 10 & 10 & 8 & 8.04 & 9.14 & 7.46 & 6.58\\\\\n", "\t 8 & 8 & 8 & 8 & 6.95 & 8.14 & 6.77 & 5.76\\\\\n", "\t 13 & 13 & 13 & 8 & 7.58 & 8.74 & 12.74 & 7.71\\\\\n", "\t 9 & 9 & 9 & 8 & 8.81 & 8.77 & 7.11 & 8.84\\\\\n", "\t 11 & 11 & 11 & 8 & 8.33 & 9.26 & 7.81 & 8.47\\\\\n", "\t 14 & 14 & 14 & 8 & 9.96 & 8.10 & 8.84 & 7.04\\\\\n", "\t 6 & 6 & 6 & 8 & 7.24 & 6.13 & 6.08 & 5.25\\\\\n", "\t 4 & 4 & 4 & 19 & 4.26 & 3.10 & 5.39 & 12.50\\\\\n", "\t 12 & 12 & 12 & 8 & 10.84 & 9.13 & 8.15 & 5.56\\\\\n", "\t 7 & 7 & 7 & 8 & 4.82 & 7.26 & 6.42 & 7.91\\\\\n", "\t 5 & 5 & 5 & 8 & 5.68 & 4.74 & 5.73 & 6.89\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 11 × 8\n", "\n", "| x1 <dbl> | x2 <dbl> | x3 <dbl> | x4 <dbl> | y1 <dbl> | y2 <dbl> | y3 <dbl> | y4 <dbl> |\n", "|---|---|---|---|---|---|---|---|\n", "| 10 | 10 | 10 | 8 | 8.04 | 9.14 | 7.46 | 6.58 |\n", "| 8 | 8 | 8 | 8 | 6.95 | 8.14 | 6.77 | 5.76 |\n", "| 13 | 13 | 13 | 8 | 7.58 | 8.74 | 12.74 | 7.71 |\n", "| 9 | 9 | 9 | 8 | 8.81 | 8.77 | 7.11 | 8.84 |\n", "| 11 | 11 | 11 | 8 | 8.33 | 9.26 | 7.81 | 8.47 |\n", "| 14 | 14 | 14 | 8 | 9.96 | 8.10 | 8.84 | 7.04 |\n", "| 6 | 6 | 6 | 8 | 7.24 | 6.13 | 6.08 | 5.25 |\n", "| 4 | 4 | 4 | 19 | 4.26 | 3.10 | 5.39 | 12.50 |\n", "| 12 | 12 | 12 | 8 | 10.84 | 9.13 | 8.15 | 5.56 |\n", "| 7 | 7 | 7 | 8 | 4.82 | 7.26 | 6.42 | 7.91 |\n", "| 5 | 5 | 5 | 8 | 5.68 | 4.74 | 5.73 | 6.89 |\n", "\n" ], "text/plain": [ " x1 x2 x3 x4 y1 y2 y3 y4 \n", "1 10 10 10 8 8.04 9.14 7.46 6.58\n", "2 8 8 8 8 6.95 8.14 6.77 5.76\n", "3 13 13 13 8 7.58 8.74 12.74 7.71\n", "4 9 9 9 8 8.81 8.77 7.11 8.84\n", "5 11 11 11 8 8.33 9.26 7.81 8.47\n", "6 14 14 14 8 9.96 8.10 8.84 7.04\n", "7 6 6 6 8 7.24 6.13 6.08 5.25\n", "8 4 4 4 19 4.26 3.10 5.39 12.50\n", "9 12 12 12 8 10.84 9.13 8.15 5.56\n", "10 7 7 7 8 4.82 7.26 6.42 7.91\n", "11 5 5 5 8 5.68 4.74 5.73 6.89" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# library(datasets)\n", "anscombe" ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "\tPearson's product-moment correlation\n", "\n", "data: anscombe$x1 and anscombe$y1\n", "t = 4.2415, df = 9, p-value = 0.00217\n", "alternative hypothesis: true correlation is not equal to 0\n", "95 percent confidence interval:\n", " 0.4243912 0.9506933\n", "sample estimates:\n", " cor \n", "0.8164205 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tPearson's product-moment correlation\n", "\n", "data: anscombe$x2 and anscombe$y2\n", "t = 4.2386, df = 9, p-value = 0.002179\n", "alternative hypothesis: true correlation is not equal to 0\n", "95 percent confidence interval:\n", " 0.4239389 0.9506402\n", "sample estimates:\n", " cor \n", "0.8162365 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tPearson's product-moment correlation\n", "\n", "data: anscombe$x3 and anscombe$y3\n", "t = 4.2394, df = 9, p-value = 0.002176\n", "alternative hypothesis: true correlation is not equal to 0\n", "95 percent confidence interval:\n", " 0.4240623 0.9506547\n", "sample estimates:\n", " cor \n", "0.8162867 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "\tPearson's product-moment correlation\n", "\n", "data: anscombe$x4 and anscombe$y4\n", "t = 4.243, df = 9, p-value = 0.002165\n", "alternative hypothesis: true correlation is not equal to 0\n", "95 percent confidence interval:\n", " 0.4246394 0.9507224\n", "sample estimates:\n", " cor \n", "0.8165214 \n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# x and y are correlated with r = 0.81\n", "cor.test(anscombe$x1, anscombe$y1)\n", "cor.test(anscombe$x2, anscombe$y2)\n", "cor.test(anscombe$x3, anscombe$y3)\n", "cor.test(anscombe$x4, anscombe$y4)" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = anscombe$y1 ~ anscombe$x1)\n", "\n", "Coefficients:\n", "(Intercept) anscombe$x1 \n", " 3.0001 0.5001 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = anscombe$y2 ~ anscombe$x2)\n", "\n", "Coefficients:\n", "(Intercept) anscombe$x2 \n", " 3.001 0.500 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = anscombe$y3 ~ anscombe$x3)\n", "\n", "Coefficients:\n", "(Intercept) anscombe$x3 \n", " 3.0025 0.4997 \n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = anscombe$y4 ~ anscombe$x4)\n", "\n", "Coefficients:\n", "(Intercept) anscombe$x4 \n", " 3.0017 0.4999 \n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the parameters for a linear model y~x are the same\n", "m1 <- lm(anscombe$y1 ~ anscombe$x1)\n", "m1\n", "\n", "m2 <- lm(anscombe$y2 ~ anscombe$x2)\n", "m2\n", "\n", "m3 <- lm(anscombe$y3 ~ anscombe$x3)\n", "m3\n", "\n", "m4 <- lm(anscombe$y4 ~ anscombe$x4)\n", "m4" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "data": { "image/png": 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GZyL5csYkkHlUgxy7w//hdrsnKLRSpq2EydX21Zc8Wjtp9bWrU5aESyNkZuWsSS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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the relation between y and x for the four datasets (y1~x1; y2~x2; y3~x3 and y4~x4) \n", "# What do you observe ?\n", "options(repr.plot.width = 7, repr.plot.height = 7)\n", "par(mfrow=c(2,2))\n", "\n", "plot(anscombe$y1~anscombe$x1, pch=19)\n", "abline(m1)\n", "\n", "plot(anscombe$y2~anscombe$x2, pch=19)\n", "abline(m2)\n", "\n", "plot(anscombe$y3~anscombe$x3, pch=19)\n", "abline(m3)\n", "\n", "plot(anscombe$y4~anscombe$x4, pch=19)\n", "abline(m4)\n", "par(mfrow=c(1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Homoscedasticity" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [ { "data": { "image/png": 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PUIjR0AgEAtXLgwJiamsgua9O/fv1ob7YAdDEPBwTRsGM2aRaGh1bpoMGtUVenS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"text/plain": [ "Plot with title “Model 4”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linearity (there should not be huge residuals) \n", "# and homoscedasticity (there should not be a trend for residuals as we increase the fitted values)\n", "par(mfrow=c(2,2))\n", "plot(m1, which=1, main=\"Model 1\") # \n", "plot(m2, which=1, main=\"Model 2\") # Looks like there is a pattern\n", "plot(m3, which=1, main=\"Model 3\") # There is a trend downwards, the error becomes larger and more negative as we predict larger values. This means we surestimate more and more the predicted values. \n", "plot(m4, which=1, main=\"Model 4\")\n", "par(mfrow=c(1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Normality" ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“not plotting observations with leverage one:\n", " 8”" ] }, { "data": { "image/png": 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p/cEeiFxkX/Uz+4vdOVok4fcIsRUicISEK2RGMoCeN1QbFdO0eF7OOpovY/O70g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\nXRxljMt1NgI4P9Kj8Tglcen96D80d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"text/plain": [ "Plot with title “Model 4”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Assumption: normality of residuals. \n", "par(mfrow=c(2,2))\n", "plot(m1, which=2, main=\"Model 1\") # \n", "plot(m2, which=2, main=\"Model 2\") # Looks like there is a pattern\n", "plot(m3, which=2, main=\"Model 3\") # There is an outlier (observation 3) \n", "plot(m4, which=2, main=\"Model 4\")\n", "par(mfrow=c(1,1))" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“not plotting observations with leverage one:\n", " 8”" ] }, { "data": { "image/png": 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RyUpKQkqn2j6hiJECJiVOtAta5JosZO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HR+fGjRuampp0BwEAQlDrRAa1roNCY8dYe/fuvZPGsyEAACAASURBVHnzpqOj4/nz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"text/plain": [ "Plot with title “Model 4”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Fitted agains standardised residuals. there shoudl be no trend in the data \n", "par(mfrow=c(2,2))\n", "plot(m1, which=3, main=\"Model 1\") # \n", "plot(m2, which=3, main=\"Model 2\") # Looks like there is a pattern\n", "plot(m3, which=3, main=\"Model 3\") # There is an outlier (observation 3) \n", "plot(m4, which=3, main=\"Model 4\")\n", "par(mfrow=c(1,1))" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "data": { "image/png": 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VU3EGVTbO/bNBApAohEwwGRNm8Oe/nx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"text/plain": [ "Plot with title “Model 4”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Cook's distance. Measures the influence of one particular observation on the parameters of the regression. Values close and above 1 have a too large influence and should be observed. \n", "par(mfrow=c(2,2))\n", "plot(m1, which=4, main=\"Model 1\") # \n", "plot(m2, which=4, main=\"Model 2\") # Looks like observations 6 and 8 are quite large\n", "plot(m3, which=4, main=\"Model 3\") # There is an outlier (observation 3) \n", "plot(m4, which=4, main=\"Model 4\")\n", "par(mfrow=c(1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Categorical variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", " Test: Chi-square test\n", "
\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do people with higher prior ability (the `prior` variable) use the MOOC differently (the `MOOC` variable) ? This question asks about the relationship of two categorical variables (`prior` and `MOOC` both have a set of distinct nominal values). \n", "\n", "The chi-square tests whether the observations in two categorical variables can be considered independent. It does this by comparing the observed number of cases and the expected number of cases under the assumption of independence. \n", "\n", "* H0: the variables are independent.\n", "* H1: the variables are not independent.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "tt <- table( moocs.bac$MOOC, moocs.bac$prior)\n", "print(tt)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "tt.chisq <- chisq.test(tt)\n", "print(tt.chisq)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "print(tt.chisq$obs)\n", "print(tt.chisq$exp)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# pearson residuals larger than 1.96 are significantly different from 0 with p<.05\n", "# the Pearson residuals, (observed - expected) / sqrt(expected).\n", "print(tt.chisq$res)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Compute residual for cell 1,1\n", "(3235-3030.8894) / sqrt(3030.8894)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " Reporting\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> A test of independence shows that the students with high prior ability do not have the same pattern of MOOC useage compared to the students of low ability ($\\chi^2$[2]=116.57, p<.001). A closer inspection of the Pearson residuals shows that low ability students are more likely to not use the MOOC and that high ability students are more likey to do the exercices. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Setting the size of plots generated with ggplot below. \n", "options(repr.plot.width = 5, repr.plot.height = 5)\n", "\n", "mosaicplot(tt, shade = TRUE, las=2, main = \"MOOC Usage and Prior Ability\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 4 }