poc-r-lasso-pima-indians-diabetes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Gerardo de Miguel González"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** The aim of this notebook is to find a basic workflow for doing machine learning classification of an imbalanced dataset using best practices taken from other people's examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Classification Proof of Concept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** These ones:\n",
    "\n",
    "  - [STHDA](http://www.sthda.com/english/articles/36-classification-methods-essentials/149-penalized-logistic-regression-essentials-in-r-ridge-lasso-and-elastic-net/) Penalized Logistic Regression Essentials in R: Ridge, Lasso and Elastic Net by kassambara -- 11/03/2018 from  [Articles](http://www.sthda.com/english/articles/36-classification-methods-essentials/) - Classification Methods Essentials\n",
    "  - [Stanford](https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html#log) Glmnet Vignette: Logistic Regression by [Trevor Hastie](https://web.stanford.edu/~hastie/) and Junyang Qian, Stanford June 26, 2014\n",
    "  - [Lab Notebook](http://homepages.uc.edu/~lis6/Teaching/DM18Spring/Lab/lab5_logit.html) in [Data Mining I (BANA7046) 2018 Spring](http://homepages.uc.edu/~lis6/DM-18Spring.html) by [Shaobo Li](http://homepages.uc.edu/~lis6/), see [Variable Selection section](http://homepages.uc.edu/~lis6/Teaching/DM18Spring/Lab/lab5_logit.html#variable-selection).\n",
    "  \n",
    "**::NOTE::** The LASSO is not very good at handling variables which show correlation between them and thus can sometimes show very wild behaviors. (From [rstatisticsblog](https://www.rstatisticsblog.com/data-science-in-action/lasso-regression/))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Helper function to install missing libraries before loading them\n",
    "# https://stackoverflow.com/questions/4090169/elegant-way-to-check-for-missing-packages-and-install-them\n",
    "using<-function(...) {\n",
    "    libs<-unlist(list(...))\n",
    "    req<-unlist(lapply(libs,require,character.only=TRUE))\n",
    "    need<-libs[req==FALSE]\n",
    "    if(length(need)>0){ \n",
    "        install.packages(need)\n",
    "        lapply(need,require,character.only=TRUE)\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: repr\n",
      "Loading required package: mlbench\n",
      "Loading required package: caTools\n",
      "Loading required package: glmnet\n",
      "Loading required package: Matrix\n",
      "Loading required package: foreach\n",
      "Loaded glmnet 2.0-18\n",
      "\n",
      "Loading required package: plotmo\n",
      "Loading required package: Formula\n",
      "Loading required package: plotrix\n",
      "Loading required package: TeachingDemos\n",
      "Loading required package: MLmetrics\n",
      "\n",
      "Attaching package: ‘MLmetrics’\n",
      "\n",
      "The following object is masked from ‘package:base’:\n",
      "\n",
      "    Recall\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#::NOTE::Downsizing to simpler packages\n",
    "#using('tidyverse','caret','glmnet', 'mlbench')\n",
    "# ... repr to fix size of graphics within jupyter noteboook  ...\n",
    "# https://blog.revolutionanalytics.com/2015/09/resizing-plots-in-the-r-kernel-for-jupyter-notebooks.html\n",
    "# ... [NO] crossval: Generic Functions for Cross Validation ...\n",
    "#     Contains generic functions for performing cross validation and for computing diagnostic errors ...\n",
    "# https://cran.r-project.org/web/packages/crossval/\n",
    "# https://cran.r-project.org/web/packages/crossval/crossval.pdf\n",
    "# ... plotmo: Plot a Model's Residuals, Response, and Partial Dependence Plots ...\n",
    "#       Plot model surfaces for a wide variety of models using partial dependence plots and other techniques. \n",
    "#       Also plot model residuals and other information on the model.\n",
    "# https://cran.r-project.org/web/packages/plotmo/index.html\n",
    "# https://cran.r-project.org/web/packages/plotmo/plotmo.pdf\n",
    "# ... MLmetrics: Machine Learning Evaluation Metrics\n",
    "#     A collection of evaluation metrics, including loss, score and utility functions, that measure regression, \n",
    "#     classification and ranking performance.\n",
    "using('repr', 'mlbench', 'caTools', 'glmnet', 'plotmo', 'MLmetrics')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** `crossval` package first install output here:\n",
    "\n",
    "```R\n",
    "Loading required package: mlbench\n",
    "Loading required package: caTools\n",
    "Loading required package: glmnet\n",
    "Loading required package: Matrix\n",
    "Loading required package: foreach\n",
    "Loaded glmnet 2.0-18\n",
    "\n",
    "Loading required package: crossval\n",
    "Warning message in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, :\n",
    "“there is no package called ‘crossval’”Installing package into ‘/home/jovyan/R/x86_64-pc-linux-gnu-library/3.6’\n",
    "(as ‘lib’ is unspecified)\n",
    "Loading required package: crossval\n",
    "  1. TRUE\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** `tidyverse` output first install here:\n",
    "\n",
    "```R\n",
    "Loading required package: tidyverse\n",
    "Warning message in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, :\n",
    "“there is no package called ‘tidyverse’”Loading required package: caret\n",
    "Loading required package: lattice\n",
    "Loading required package: ggplot2\n",
    "Loading required package: glmnet\n",
    "Loading required package: Matrix\n",
    "Loading required package: foreach\n",
    "Loaded glmnet 2.0-18\n",
    "\n",
    "Installing package into ‘/home/jovyan/R/x86_64-pc-linux-gnu-library/3.6’\n",
    "(as ‘lib’ is unspecified)\n",
    "also installing the dependencies ‘tinytex’, ‘rmarkdown’, ‘selectr’, ‘broom’, ‘dbplyr’, ‘modelr’, ‘reprex’, ‘rvest’\n",
    "\n",
    "Loading required package: tidyverse\n",
    "── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──\n",
    "✔ tibble  2.1.3     ✔ purrr   0.3.2\n",
    "✔ tidyr   0.8.3     ✔ dplyr   0.8.3\n",
    "✔ readr   1.3.1     ✔ stringr 1.4.0\n",
    "✔ tibble  2.1.3     ✔ forcats 0.4.0\n",
    "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n",
    "✖ purrr::accumulate() masks foreach::accumulate()\n",
    "✖ tidyr::expand()     masks Matrix::expand()\n",
    "✖ dplyr::filter()     masks stats::filter()\n",
    "✖ dplyr::lag()        masks stats::lag()\n",
    "✖ purrr::lift()       masks caret::lift()\n",
    "✖ purrr::when()       masks foreach::when()\n",
    "                           \n",
    "    1. TRUE\n",
    "``` "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** First installation of plotmo:\n",
    "\n",
    "```R\n",
    "Loading required package: plotmo\n",
    "Warning message in library(package, lib.loc = lib.loc, character.only = TRUE, logical.return = TRUE, :\n",
    "“there is no package called ‘plotmo’”Installing package into ‘/home/jovyan/R/x86_64-pc-linux-gnu-library/3.6’\n",
    "(as ‘lib’ is unspecified)\n",
    "also installing the dependencies ‘plotrix’, ‘TeachingDemos’\n",
    "\n",
    "Loading required package: plotmo\n",
    "Loading required package: Formula\n",
    "Loading required package: plotrix\n",
    "Loading required package: TeachingDemos\n",
    "\n",
    "    1. TRUE\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::There are two versions in mlbench\n",
    "# https://www.rdocumentation.org/packages/utils/versions/3.6.1/topics/data\n",
    "#::NOTE::2nd version comes with zero outliers as NAs\n",
    "utils::data(PimaIndiansDiabetes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>pregnant</th><th scope=col>glucose</th><th scope=col>pressure</th><th scope=col>triceps</th><th scope=col>insulin</th><th scope=col>mass</th><th scope=col>pedigree</th><th scope=col>age</th><th scope=col>diabetes</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>6</td><td>148</td><td>72</td><td>35</td><td> NA</td><td>33.6</td><td>0.627</td><td>50</td><td>pos</td></tr>\n",
       "\t<tr><td>1</td><td> 85</td><td>66</td><td>29</td><td> NA</td><td>26.6</td><td>0.351</td><td>31</td><td>neg</td></tr>\n",
       "\t<tr><td>8</td><td>183</td><td>64</td><td>NA</td><td> NA</td><td>23.3</td><td>0.672</td><td>32</td><td>pos</td></tr>\n",
       "\t<tr><td>1</td><td> 89</td><td>66</td><td>23</td><td> 94</td><td>28.1</td><td>0.167</td><td>21</td><td>neg</td></tr>\n",
       "\t<tr><td>0</td><td>137</td><td>40</td><td>35</td><td>168</td><td>43.1</td><td>2.288</td><td>33</td><td>pos</td></tr>\n",
       "\t<tr><td>5</td><td>116</td><td>74</td><td>NA</td><td> NA</td><td>25.6</td><td>0.201</td><td>30</td><td>neg</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       " pregnant & glucose & pressure & triceps & insulin & mass & pedigree & age & diabetes\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t 6 & 148 & 72 & 35 &  NA & 33.6 & 0.627 & 50 & pos\\\\\n",
       "\t 1 &  85 & 66 & 29 &  NA & 26.6 & 0.351 & 31 & neg\\\\\n",
       "\t 8 & 183 & 64 & NA &  NA & 23.3 & 0.672 & 32 & pos\\\\\n",
       "\t 1 &  89 & 66 & 23 &  94 & 28.1 & 0.167 & 21 & neg\\\\\n",
       "\t 0 & 137 & 40 & 35 & 168 & 43.1 & 2.288 & 33 & pos\\\\\n",
       "\t 5 & 116 & 74 & NA &  NA & 25.6 & 0.201 & 30 & neg\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 9\n",
       "\n",
       "| pregnant &lt;dbl&gt; | glucose &lt;dbl&gt; | pressure &lt;dbl&gt; | triceps &lt;dbl&gt; | insulin &lt;dbl&gt; | mass &lt;dbl&gt; | pedigree &lt;dbl&gt; | age &lt;dbl&gt; | diabetes &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 6 | 148 | 72 | 35 |  NA | 33.6 | 0.627 | 50 | pos |\n",
       "| 1 |  85 | 66 | 29 |  NA | 26.6 | 0.351 | 31 | neg |\n",
       "| 8 | 183 | 64 | NA |  NA | 23.3 | 0.672 | 32 | pos |\n",
       "| 1 |  89 | 66 | 23 |  94 | 28.1 | 0.167 | 21 | neg |\n",
       "| 0 | 137 | 40 | 35 | 168 | 43.1 | 2.288 | 33 | pos |\n",
       "| 5 | 116 | 74 | NA |  NA | 25.6 | 0.201 | 30 | neg |\n",
       "\n"
      ],
      "text/plain": [
       "  pregnant glucose pressure triceps insulin mass pedigree age diabetes\n",
       "1 6        148     72       35       NA     33.6 0.627    50  pos     \n",
       "2 1         85     66       29       NA     26.6 0.351    31  neg     \n",
       "3 8        183     64       NA       NA     23.3 0.672    32  pos     \n",
       "4 1         89     66       23       94     28.1 0.167    21  neg     \n",
       "5 0        137     40       35      168     43.1 2.288    33  pos     \n",
       "6 5        116     74       NA       NA     25.6 0.201    30  neg     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::See first rows\n",
    "# https://www.rdocumentation.org/packages/utils/versions/3.6.1/topics/head\n",
    "#::NOTE::Some NAs show up!\n",
    "utils::head(PimaIndiansDiabetes2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::GMG::** The goal of this stage of our study is to get to know the data, their flaws and perhaps some clues to improve them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t768 obs. of  9 variables:\n",
      " $ pregnant: num  6 1 8 1 0 5 3 10 2 8 ...\n",
      " $ glucose : num  148 85 183 89 137 116 78 115 197 125 ...\n",
      " $ pressure: num  72 66 64 66 40 74 50 NA 70 96 ...\n",
      " $ triceps : num  35 29 NA 23 35 NA 32 NA 45 NA ...\n",
      " $ insulin : num  NA NA NA 94 168 NA 88 NA 543 NA ...\n",
      " $ mass    : num  33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 NA ...\n",
      " $ pedigree: num  0.627 0.351 0.672 0.167 2.288 ...\n",
      " $ age     : num  50 31 32 21 33 30 26 29 53 54 ...\n",
      " $ diabetes: Factor w/ 2 levels \"neg\",\"pos\": 2 1 2 1 2 1 2 1 2 2 ...\n"
     ]
    }
   ],
   "source": [
    "#::GMG::PimaIndiansDiabetes2 (say, v2) has the outliers from \n",
    "#       glucose, pressure, triceps, insulin and mass as NAs\n",
    "str(PimaIndiansDiabetes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    pregnant         glucose         pressure         triceps     \n",
       " Min.   : 0.000   Min.   : 44.0   Min.   : 24.00   Min.   : 7.00  \n",
       " 1st Qu.: 1.000   1st Qu.: 99.0   1st Qu.: 64.00   1st Qu.:22.00  \n",
       " Median : 3.000   Median :117.0   Median : 72.00   Median :29.00  \n",
       " Mean   : 3.845   Mean   :121.7   Mean   : 72.41   Mean   :29.15  \n",
       " 3rd Qu.: 6.000   3rd Qu.:141.0   3rd Qu.: 80.00   3rd Qu.:36.00  \n",
       " Max.   :17.000   Max.   :199.0   Max.   :122.00   Max.   :99.00  \n",
       "                  NA's   :5       NA's   :35       NA's   :227    \n",
       "    insulin            mass          pedigree           age        diabetes \n",
       " Min.   : 14.00   Min.   :18.20   Min.   :0.0780   Min.   :21.00   neg:500  \n",
       " 1st Qu.: 76.25   1st Qu.:27.50   1st Qu.:0.2437   1st Qu.:24.00   pos:268  \n",
       " Median :125.00   Median :32.30   Median :0.3725   Median :29.00            \n",
       " Mean   :155.55   Mean   :32.46   Mean   :0.4719   Mean   :33.24            \n",
       " 3rd Qu.:190.00   3rd Qu.:36.60   3rd Qu.:0.6262   3rd Qu.:41.00            \n",
       " Max.   :846.00   Max.   :67.10   Max.   :2.4200   Max.   :81.00            \n",
       " NA's   :374      NA's   :11                                                "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::NA counts yield the outliers (!)\n",
    "#::NOTE::Should I standardize some of the features ('glucose', 'pressure', 'triceps', 'insuline', 'mass')?\n",
    "#::NOTE::Should I do feature engineering on some of the features \n",
    "#        (i.e. age, p.e breaking it into intervals with labels)?\n",
    "summary(PimaIndiansDiabetes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>pregnant</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>glucose</dt>\n",
       "\t\t<dd>5</dd>\n",
       "\t<dt>pressure</dt>\n",
       "\t\t<dd>35</dd>\n",
       "\t<dt>triceps</dt>\n",
       "\t\t<dd>227</dd>\n",
       "\t<dt>insulin</dt>\n",
       "\t\t<dd>374</dd>\n",
       "\t<dt>mass</dt>\n",
       "\t\t<dd>11</dd>\n",
       "\t<dt>pedigree</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>age</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>diabetes</dt>\n",
       "\t\t<dd>0</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[pregnant] 0\n",
       "\\item[glucose] 5\n",
       "\\item[pressure] 35\n",
       "\\item[triceps] 227\n",
       "\\item[insulin] 374\n",
       "\\item[mass] 11\n",
       "\\item[pedigree] 0\n",
       "\\item[age] 0\n",
       "\\item[diabetes] 0\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "pregnant\n",
       ":   0glucose\n",
       ":   5pressure\n",
       ":   35triceps\n",
       ":   227insulin\n",
       ":   374mass\n",
       ":   11pedigree\n",
       ":   0age\n",
       ":   0diabetes\n",
       ":   0\n",
       "\n"
      ],
      "text/plain": [
       "pregnant  glucose pressure  triceps  insulin     mass pedigree      age \n",
       "       0        5       35      227      374       11        0        0 \n",
       "diabetes \n",
       "       0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Check for missing values ... I know they are marked witn 'NA' in mlbench 2nd dataset\n",
    "sapply(PimaIndiansDiabetes2, function(x) sum(is.na(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "neg pos \n",
       "500 268 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Now I test the imbalance of the dataset\n",
    "# http://metadatascience.com/2013/07/03/plotting-the-frequency-distribution-using-r/\n",
    "table(PimaIndiansDiabetes2$diabetes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "      neg       pos \n",
       "0.6510417 0.3489583 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prop.table(table(PimaIndiansDiabetes2$diabetes))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GHDqVOnampqtHZ7e/shQ4ZERkZGRkbq9XorVggAFmRLAa2pqKjIzs5WnyR0c3Pz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\nNABIioAGAEkR0AAgKQIaACT1/wB+Dz8P+HgeEgAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Outcome Imbalance”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Plot the imbalance\n",
    "# https://www.statmethods.net/advgraphs/parameters.html\n",
    "# http://www.programmingr.com/content/positioning-charts-fig-and-fin/\n",
    "#::NOTE::I don't know how to make the fig smaller and the margins tight (!?)\n",
    "# https://blog.revolutionanalytics.com/2015/09/resizing-plots-in-the-r-kernel-for-jupyter-notebooks.html\n",
    "options(repr.plot.width=4, repr.plot.height=3)\n",
    "barplot(100*prop.table(table(PimaIndiansDiabetes2$diabetes)), \n",
    "        col = c('blue', 'red'),\n",
    "        ylim = c(0,70),\n",
    "        main = 'Outcome Imbalance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Preparing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG:: (STHDA) Load the data and remove NAs\n",
    "#::NOTE::I've already attached that dataset earlier\n",
    "# data(\"PimaIndiansDiabetes2\", package = \"mlbench\")\n",
    "# https://stat.ethz.ch/R-manual/R-devel/library/stats/html/na.fail.html\n",
    "# https://www.statmethods.net/input/missingdata.html\n",
    "pima_clean <- stats::na.omit(PimaIndiansDiabetes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>pregnant</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>glucose</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>pressure</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>triceps</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>insulin</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>mass</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>pedigree</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>age</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>diabetes</dt>\n",
       "\t\t<dd>0</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[pregnant] 0\n",
       "\\item[glucose] 0\n",
       "\\item[pressure] 0\n",
       "\\item[triceps] 0\n",
       "\\item[insulin] 0\n",
       "\\item[mass] 0\n",
       "\\item[pedigree] 0\n",
       "\\item[age] 0\n",
       "\\item[diabetes] 0\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "pregnant\n",
       ":   0glucose\n",
       ":   0pressure\n",
       ":   0triceps\n",
       ":   0insulin\n",
       ":   0mass\n",
       ":   0pedigree\n",
       ":   0age\n",
       ":   0diabetes\n",
       ":   0\n",
       "\n"
      ],
      "text/plain": [
       "pregnant  glucose pressure  triceps  insulin     mass pedigree      age \n",
       "       0        0        0        0        0        0        0        0 \n",
       "diabetes \n",
       "       0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Check for missing values ... No NAs after cleaning with na.omit()\n",
    "sapply(pima_clean, function(x) sum(is.na(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>pregnant</th><th scope=col>glucose</th><th scope=col>pressure</th><th scope=col>triceps</th><th scope=col>insulin</th><th scope=col>mass</th><th scope=col>pedigree</th><th scope=col>age</th><th scope=col>diabetes</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>4</th><td>1</td><td> 89</td><td>66</td><td>23</td><td> 94</td><td>28.1</td><td>0.167</td><td>21</td><td>neg</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0</td><td>137</td><td>40</td><td>35</td><td>168</td><td>43.1</td><td>2.288</td><td>33</td><td>pos</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>3</td><td> 78</td><td>50</td><td>32</td><td> 88</td><td>31.0</td><td>0.248</td><td>26</td><td>pos</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>2</td><td>197</td><td>70</td><td>45</td><td>543</td><td>30.5</td><td>0.158</td><td>53</td><td>pos</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>1</td><td>189</td><td>60</td><td>23</td><td>846</td><td>30.1</td><td>0.398</td><td>59</td><td>pos</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>5</td><td>166</td><td>72</td><td>19</td><td>175</td><td>25.8</td><td>0.587</td><td>51</td><td>pos</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       "  & pregnant & glucose & pressure & triceps & insulin & mass & pedigree & age & diabetes\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t4 & 1 &  89 & 66 & 23 &  94 & 28.1 & 0.167 & 21 & neg\\\\\n",
       "\t5 & 0 & 137 & 40 & 35 & 168 & 43.1 & 2.288 & 33 & pos\\\\\n",
       "\t7 & 3 &  78 & 50 & 32 &  88 & 31.0 & 0.248 & 26 & pos\\\\\n",
       "\t9 & 2 & 197 & 70 & 45 & 543 & 30.5 & 0.158 & 53 & pos\\\\\n",
       "\t14 & 1 & 189 & 60 & 23 & 846 & 30.1 & 0.398 & 59 & pos\\\\\n",
       "\t15 & 5 & 166 & 72 & 19 & 175 & 25.8 & 0.587 & 51 & pos\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 9\n",
       "\n",
       "| <!--/--> | pregnant &lt;dbl&gt; | glucose &lt;dbl&gt; | pressure &lt;dbl&gt; | triceps &lt;dbl&gt; | insulin &lt;dbl&gt; | mass &lt;dbl&gt; | pedigree &lt;dbl&gt; | age &lt;dbl&gt; | diabetes &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 4 | 1 |  89 | 66 | 23 |  94 | 28.1 | 0.167 | 21 | neg |\n",
       "| 5 | 0 | 137 | 40 | 35 | 168 | 43.1 | 2.288 | 33 | pos |\n",
       "| 7 | 3 |  78 | 50 | 32 |  88 | 31.0 | 0.248 | 26 | pos |\n",
       "| 9 | 2 | 197 | 70 | 45 | 543 | 30.5 | 0.158 | 53 | pos |\n",
       "| 14 | 1 | 189 | 60 | 23 | 846 | 30.1 | 0.398 | 59 | pos |\n",
       "| 15 | 5 | 166 | 72 | 19 | 175 | 25.8 | 0.587 | 51 | pos |\n",
       "\n"
      ],
      "text/plain": [
       "   pregnant glucose pressure triceps insulin mass pedigree age diabetes\n",
       "4  1         89     66       23       94     28.1 0.167    21  neg     \n",
       "5  0        137     40       35      168     43.1 2.288    33  pos     \n",
       "7  3         78     50       32       88     31.0 0.248    26  pos     \n",
       "9  2        197     70       45      543     30.5 0.158    53  pos     \n",
       "14 1        189     60       23      846     30.1 0.398    59  pos     \n",
       "15 5        166     72       19      175     25.8 0.587    51  pos     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Inspect the data\n",
    "# https://dplyr.tidyverse.org/reference/sample.html\n",
    "#dplyr::sample_n(pima_clean, 3)\n",
    "#::NOTE::Downsize use of tidyverse to R core functions\n",
    "# https://www.rdocumentation.org/packages/utils/versions/3.6.1/topics/head\n",
    "utils::head(pima_clean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t392 obs. of  9 variables:\n",
      " $ pregnant: num  1 0 3 2 1 5 0 1 1 3 ...\n",
      " $ glucose : num  89 137 78 197 189 166 118 103 115 126 ...\n",
      " $ pressure: num  66 40 50 70 60 72 84 30 70 88 ...\n",
      " $ triceps : num  23 35 32 45 23 19 47 38 30 41 ...\n",
      " $ insulin : num  94 168 88 543 846 175 230 83 96 235 ...\n",
      " $ mass    : num  28.1 43.1 31 30.5 30.1 25.8 45.8 43.3 34.6 39.3 ...\n",
      " $ pedigree: num  0.167 2.288 0.248 0.158 0.398 ...\n",
      " $ age     : num  21 33 26 53 59 51 31 33 32 27 ...\n",
      " $ diabetes: Factor w/ 2 levels \"neg\",\"pos\": 1 2 2 2 2 2 2 1 2 1 ...\n",
      " - attr(*, \"na.action\")= 'omit' Named int  1 2 3 6 8 10 11 12 13 16 ...\n",
      "  ..- attr(*, \"names\")= chr  \"1\" \"2\" \"3\" \"6\" ...\n"
     ]
    }
   ],
   "source": [
    "#::NOTE::Originally 768 Observations!!\n",
    "str(pima_clean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Stratified Train/Test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::NOTE::Make it reproducible\n",
    "set.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# Split the data into training and test set\n",
    "#::NOTE::STHDA uses caret to do the stratified split and dplyr %>% notation\n",
    "#        and I think It's a bit of overdoing it ...\n",
    "# https://topepo.github.io/caret/data-splitting.html\n",
    "# https://github.com/tidyverse/dplyr\n",
    "#training_samples <- pima_clean$diabetes %>% \n",
    "#  caret::createDataPartition(p = 0.8, list = FALSE)\n",
    "#::NOTE::... downsizing to caTools (that does a pretty good job, I think)\n",
    "msk <- caTools::sample.split(Y = pima_clean$diabetes, SplitRatio = 0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::NOTE::Do the actual split with the indices just computed\n",
    "#train_data  <- pima_clean[training_samples, ]\n",
    "#test_data <- pima_clean[-training_samples, ]\n",
    "#::NOTE::downsizing to caTools\n",
    "train_data <- pima_clean[msk,]  # use output of sample.split to ...\n",
    "test_data  <- pima_clean[!msk,] # create train and test subse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t274 obs. of  9 variables:\n",
      " $ pregnant: num  1 0 2 1 5 0 1 3 11 3 ...\n",
      " $ glucose : num  89 137 197 189 166 118 115 126 143 158 ...\n",
      " $ pressure: num  66 40 70 60 72 84 70 88 94 76 ...\n",
      " $ triceps : num  23 35 45 23 19 47 30 41 33 36 ...\n",
      " $ insulin : num  94 168 543 846 175 230 96 235 146 245 ...\n",
      " $ mass    : num  28.1 43.1 30.5 30.1 25.8 45.8 34.6 39.3 36.6 31.6 ...\n",
      " $ pedigree: num  0.167 2.288 0.158 0.398 0.587 ...\n",
      " $ age     : num  21 33 53 59 51 31 32 27 51 28 ...\n",
      " $ diabetes: Factor w/ 2 levels \"neg\",\"pos\": 1 2 2 2 2 2 2 1 2 2 ...\n",
      " - attr(*, \"na.action\")= 'omit' Named int  1 2 3 6 8 10 11 12 13 16 ...\n",
      "  ..- attr(*, \"names\")= chr  \"1\" \"2\" \"3\" \"6\" ...\n"
     ]
    }
   ],
   "source": [
    "#::NOTE::See the split datasets\n",
    "str(train_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "neg pos \n",
       "183  91 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Now I test the imbalance of the dataset\n",
    "# http://metadatascience.com/2013/07/03/plotting-the-frequency-distribution-using-r/\n",
    "table(train_data$diabetes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "      neg       pos \n",
       "0.6678832 0.3321168 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Just to be sure proportions are kept ...\n",
    "prop.table(table(train_data$diabetes))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t118 obs. of  9 variables:\n",
      " $ pregnant: num  3 1 10 1 13 3 5 8 7 0 ...\n",
      " $ glucose : num  78 103 125 97 145 180 88 176 187 100 ...\n",
      " $ pressure: num  50 30 70 66 82 64 66 90 68 88 ...\n",
      " $ triceps : num  32 38 26 15 19 25 21 34 39 60 ...\n",
      " $ insulin : num  88 83 115 140 110 70 23 300 304 110 ...\n",
      " $ mass    : num  31 43.3 31.1 23.2 22.2 34 24.4 33.7 37.7 46.8 ...\n",
      " $ pedigree: num  0.248 0.183 0.205 0.487 0.245 0.271 0.342 0.467 0.254 0.962 ...\n",
      " $ age     : num  26 33 41 22 57 26 30 58 41 31 ...\n",
      " $ diabetes: Factor w/ 2 levels \"neg\",\"pos\": 2 1 2 1 1 1 1 2 2 1 ...\n",
      " - attr(*, \"na.action\")= 'omit' Named int  1 2 3 6 8 10 11 12 13 16 ...\n",
      "  ..- attr(*, \"names\")= chr  \"1\" \"2\" \"3\" \"6\" ...\n"
     ]
    }
   ],
   "source": [
    "str(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "neg pos \n",
       " 79  39 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Now I test the imbalance of the dataset\n",
    "# http://metadatascience.com/2013/07/03/plotting-the-frequency-distribution-using-r/\n",
    "table(test_data$diabetes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "      neg       pos \n",
       "0.6694915 0.3305085 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Just to be sure proportions are kept ...\n",
    "prop.table(table(test_data$diabetes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Logistic regression model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::First off, I use stats:glm() to fit a baseline Logistic Regression Model\n",
    "# https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/glm\n",
    "full_model <- stats::glm(\n",
    "    formula = diabetes ~., \n",
    "    data = train_data, \n",
    "    family = binomial(link = 'logit')\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "stats::glm(formula = diabetes ~ ., family = binomial(link = \"logit\"), \n",
       "    data = train_data)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-3.0102  -0.6115  -0.3240   0.5692   2.3546  \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -1.197e+01  1.654e+00  -7.237 4.60e-13 ***\n",
       "pregnant     9.257e-02  6.656e-02   1.391  0.16428    \n",
       "glucose      3.786e-02  7.377e-03   5.132 2.86e-07 ***\n",
       "pressure     1.775e-03  1.566e-02   0.113  0.90976    \n",
       "triceps     -5.802e-03  2.176e-02  -0.267  0.78976    \n",
       "insulin      4.154e-04  1.710e-03   0.243  0.80804    \n",
       "mass         1.027e-01  3.682e-02   2.790  0.00527 ** \n",
       "pedigree     1.328e+00  5.655e-01   2.348  0.01887 *  \n",
       "age          6.135e-02  2.624e-02   2.338  0.01936 *  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 348.35  on 273  degrees of freedom\n",
       "Residual deviance: 224.03  on 265  degrees of freedom\n",
       "AIC: 242.03\n",
       "\n",
       "Number of Fisher Scoring iterations: 5\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Let's see a summary of the model I've just got\n",
    "# https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/summary.glm\n",
    "# https://www.youtube.com/watch?v=xl5dZo_BSJk\n",
    "# \n",
    "summary(full_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Relevant:  glucose mass pedigree age \n",
      "diabetes ~ glucose + mass + pedigree + age\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Selecting the statistically significant variables in an R glm model\n",
    "# https://stackoverflow.com/questions/16153497/selecting-the-statistically-significant-variables-in-an-r-glm-model\n",
    "toselect.x <- summary(full_model)$coeff[-1,4] < 0.05 # credit to kith\n",
    "# select sig. variables\n",
    "relevant.x <- names(toselect.x)[toselect.x == TRUE] \n",
    "# formula with only sig variables\n",
    "sig.formula <- as.formula(paste(\"diabetes ~\",paste(relevant.x, collapse= \"+\")))\n",
    "cat('Relevant: ', relevant.x, '\\n')\n",
    "print (sig.formula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::PENDING::** <span style=\"color:red\">Discussion here</span>\n",
    "\n",
    "**::GMG::** Help ...\n",
    "\n",
    "  - [Jeff Harmrick](https://www.youtube.com/watch?v=xl5dZo_BSJk) Understanding the Summary Output for a Logistic Regression in R, Published on Nov 14, 2012.\n",
    "  - [Cross-Validated](https://stats.stackexchange.com/questions/232548/r-how-are-the-significance-codes-determined-when-summarizing-a-logistic-regres) R - How are the significance codes determined when summarizing a logistic regression model?, Apr 13 2017 at 12:44\n",
    "  - [Cross-Validated](https://stats.stackexchange.com/questions/72258/how-to-interpret-the-significance-code) How to interpret the significance code?, Oct 9 2013 at 2:26\n",
    "  - [Cross_validated](https://stats.stackexchange.com/questions/60074/wald-test-for-logistic-regression) Wald test for logistic regression, May 26 2013 at 20:40 (Check out the [answer](https://stats.stackexchange.com/a/60083))\n",
    "  - [R Tutorial](http://www.r-tutor.com/elementary-statistics/logistic-regression/significance-test-logistic-regression) Significance Test for Logistic Regression\n",
    "  - [StatQuest](https://www.youtube.com/watch?v=yIYKR4sgzI8) Logistic Regression, by Josh Starmer Published on 5 Mar 2018\n",
    "  - [StatQuest](https://www.youtube.com/watch?v=vN5cNN2-HWE) Logistic Regression Details Pt1: Coefficients, by Josh Starmer, Published on Jun 4, 2018\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "simpler_model <- stats::glm(\n",
    "    formula = diabetes ~ glucose + mass + pedigree + age, \n",
    "    data = train_data, \n",
    "    family = binomial(link = 'logit')\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "stats::glm(formula = diabetes ~ glucose + mass + pedigree + age, \n",
       "    family = binomial(link = \"logit\"), data = train_data)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-3.2444  -0.6066  -0.3246   0.5644   2.2921  \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -12.033503   1.498942  -8.028 9.91e-16 ***\n",
       "glucose       0.038316   0.006299   6.083 1.18e-09 ***\n",
       "mass          0.094153   0.026905   3.499 0.000466 ***\n",
       "pedigree      1.204507   0.551618   2.184 0.028993 *  \n",
       "age           0.084284   0.020097   4.194 2.74e-05 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 348.35  on 273  degrees of freedom\n",
       "Residual deviance: 226.13  on 269  degrees of freedom\n",
       "AIC: 236.13\n",
       "\n",
       "Number of Fisher Scoring iterations: 5\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(simpler_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::PENDING::** <span style=\"color:red\">Discussion here</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### out-of-sample prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Named num [1:118] 0.0244 0.1991 0.4243 0.0233 0.713 ...\n",
      " - attr(*, \"names\")= chr [1:118] \"7\" \"19\" \"26\" \"28\" ...\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Make predictions (from STHDA)\n",
    "# https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/predict.glm\n",
    "probabilities_full <- predict(\n",
    "    object = full_model, \n",
    "    newdata = test_data, \n",
    "    type = \"response\"\n",
    ")\n",
    "str(probabilities_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Named num [1:118] 0.0257 0.2673 0.3513 0.0243 0.6708 ...\n",
      " - attr(*, \"names\")= chr [1:118] \"7\" \"19\" \"26\" \"28\" ...\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Check the simpler model (I don't expect mmuch ;)\n",
    "probabilities_simpler <- predict(\n",
    "    object = simpler_model, \n",
    "    newdata = test_data, \n",
    "    type = \"response\"\n",
    ")\n",
    "str(probabilities_simpler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### out-of-sample P/R Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Compute the curve\n",
    "# https://cran.r-project.org/web/packages/PRROC/PRROC.pdf pp. 7\n",
    "# Soft-labeled classification problems:\n",
    "# Each data point belongs to both of the two classes with a certain probability, where for each datapoint, these \n",
    "# two probabilities add up to 1.  In this case, the classification scores for all data points need to be provided \n",
    "# only once as scores.class0 and only the positive/foreground weights for each data point need to be provided in\n",
    "# weights.class0, while the converse probability for the negative class is automatically set to \n",
    "# weights.class1 = 1.0 - weights.class0.\n",
    "pr_curve_full <- PRROC::pr.curve(\n",
    "                scores.class0 = probabilities_full[test_data$diabetes == 'pos'], \n",
    "                scores.class1 = probabilities_full[test_data$diabetes == 'neg'],\n",
    "                min.compute = T, \n",
    "                max.compute = T,\n",
    "                rand.compute = T,\n",
    "                curve = T\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  Precision-recall curve\n",
      "\n",
      "    Area under curve (Integral):\n",
      "     0.6497258 \n",
      "\n",
      "    Relative area under curve (Integral):\n",
      "     0.5690321 \n",
      "\n",
      "    Area under curve (Davis & Goadrich):\n",
      "     0.6477119 \n",
      "\n",
      "    Relative area under curves (Davis & Goadrich):\n",
      "     0.5665622 \n",
      "\n",
      "    Curve for scores from  0.007455057  to  0.9921034 \n",
      "    ( can be plotted with plot(x) )\n",
      "\n",
      "\n",
      "\n",
      "    Maximum AUC:\n",
      "     1   1 \n",
      "\n",
      "\n",
      "    Minimum AUC:\n",
      "     0.1872383   0.1872234 \n",
      "\n",
      "\n",
      "    AUC of a random classifier:\n",
      "     0.3305085   0.3305085 \n"
     ]
    }
   ],
   "source": [
    "#::GMG::See all the computed AUCs\n",
    "print(pr_curve_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Fix figure size\n",
    "options(repr.plot.width = 8, repr.plot.height = 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eO7C+Dy3CdAd+3aNS0tzdG7PD09ly1bZr/N+vXr9+3bd5fdAgAAAHBlOv4mEdob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\n0AAAAIAbCNAAAACAGwjQAAAAgBv+P1+4LcO4Bb9DAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “PR curve\n",
       "AUC = 0.6497258”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Plot the curve\n",
    "# https://cran.r-project.org/web/packages/PRROC/PRROC.pdf pp 3-4\n",
    "plot(pr_curve_full, \n",
    "     rand.plot = T,\n",
    "     fill.area = TRUE, \n",
    "     fill.color = rgb(0.8,1,0.8),\n",
    "     maxminrand.col = \"blue\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "pr_curve_simpler <- PRROC::pr.curve(\n",
    "                scores.class0 = probabilities_simpler[test_data$diabetes == 'pos'], \n",
    "                scores.class1 = probabilities_simpler[test_data$diabetes == 'neg'],\n",
    "                min.compute = T, \n",
    "                max.compute = T,\n",
    "                rand.compute = T,\n",
    "                curve = T\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  Precision-recall curve\n",
      "\n",
      "    Area under curve (Integral):\n",
      "     0.6749048 \n",
      "\n",
      "    Relative area under curve (Integral):\n",
      "     0.6000117 \n",
      "\n",
      "    Area under curve (Davis & Goadrich):\n",
      "     0.6746313 \n",
      "\n",
      "    Relative area under curves (Davis & Goadrich):\n",
      "     0.5996825 \n",
      "\n",
      "    Curve for scores from  0.00864713  to  0.9929608 \n",
      "    ( can be plotted with plot(x) )\n",
      "\n",
      "\n",
      "\n",
      "    Maximum AUC:\n",
      "     1   1 \n",
      "\n",
      "\n",
      "    Minimum AUC:\n",
      "     0.1872383   0.1872234 \n",
      "\n",
      "\n",
      "    AUC of a random classifier:\n",
      "     0.3305085   0.3305085 \n"
     ]
    }
   ],
   "source": [
    "#::GMG::See all the computed AUCs\n",
    "print(pr_curve_simpler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ABuYBEhAAAAquXBkwhZRAgAAAD4AgI0AAAA4AYCNAAAAOAGAjQAAADgBhYRAgAA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\ncrHmQpAAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “PR curve\n",
       "AUC = 0.6749048”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Plot the curve\n",
    "# https://cran.r-project.org/web/packages/PRROC/PRROC.pdf pp 3-4\n",
    "plot(pr_curve_simpler, \n",
    "     rand.plot = T,\n",
    "     fill.area = TRUE, \n",
    "     fill.color = rgb(0.8,1,0.8),\n",
    "     maxminrand.col = \"blue\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### binary classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Factor w/ 2 levels \"neg\",\"pos\": 1 1 1 1 2 2 1 2 2 1 ...\n",
      " - attr(*, \"names\")= chr [1:118] \"7\" \"19\" \"26\" \"28\" ...\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Make class predictions (from STHDA)\n",
    "#predicted_class_full <- ifelse(probabilities_full > 0.5, \"pos\", \"neg\")\n",
    "#::NOTE::I make the result a factor with levels that match the taget variable\n",
    "#::NOTE::This is claasificatin with the default cut-off ...\n",
    "predicted_class_full <- as.factor(ifelse(probabilities_full > 0.5, 2, 1))\n",
    "levels(predicted_class_full) <- c('neg', 'pos')\n",
    "str(predicted_class_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>7</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>19</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>26</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>28</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>29</dt>\n",
       "\t\t<dd>pos</dd>\n",
       "\t<dt>41</dt>\n",
       "\t\t<dd>pos</dd>\n",
       "</dl>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'neg'</li>\n",
       "\t\t<li>'pos'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[7] neg\n",
       "\\item[19] neg\n",
       "\\item[26] neg\n",
       "\\item[28] neg\n",
       "\\item[29] pos\n",
       "\\item[41] pos\n",
       "\\end{description*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'neg'\n",
       "\\item 'pos'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "7\n",
       ":   neg19\n",
       ":   neg26\n",
       ":   neg28\n",
       ":   neg29\n",
       ":   pos41\n",
       ":   pos\n",
       "\n",
       "\n",
       "**Levels**: 1. 'neg'\n",
       "2. 'pos'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  7  19  26  28  29  41 \n",
       "neg neg neg neg pos pos \n",
       "Levels: neg pos"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(predicted_class_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Factor w/ 2 levels \"neg\",\"pos\": 1 1 1 1 2 2 1 2 2 1 ...\n",
      " - attr(*, \"names\")= chr [1:118] \"7\" \"19\" \"26\" \"28\" ...\n"
     ]
    }
   ],
   "source": [
    "# predicted_class_num <- ifelse(probabilities_full > 0.5, 1, 0)\n",
    "#::NOTE::I make the result a factor with levels that match the taget variable\n",
    "#predicted_class_simpler <- ifelse(probabilities_simpler > 0.5, \"pos\", \"neg\")\n",
    "predicted_class_simpler <- as.factor(ifelse(probabilities_simpler > 0.5, 2, 1))\n",
    "levels(predicted_class_simpler) <- c('neg', 'pos')\n",
    "str(predicted_class_simpler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>7</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>19</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>26</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>28</dt>\n",
       "\t\t<dd>neg</dd>\n",
       "\t<dt>29</dt>\n",
       "\t\t<dd>pos</dd>\n",
       "\t<dt>41</dt>\n",
       "\t\t<dd>pos</dd>\n",
       "</dl>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'neg'</li>\n",
       "\t\t<li>'pos'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[7] neg\n",
       "\\item[19] neg\n",
       "\\item[26] neg\n",
       "\\item[28] neg\n",
       "\\item[29] pos\n",
       "\\item[41] pos\n",
       "\\end{description*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'neg'\n",
       "\\item 'pos'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "7\n",
       ":   neg19\n",
       ":   neg26\n",
       ":   neg28\n",
       ":   neg29\n",
       ":   pos41\n",
       ":   pos\n",
       "\n",
       "\n",
       "**Levels**: 1. 'neg'\n",
       "2. 'pos'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  7  19  26  28  29  41 \n",
       "neg neg neg neg pos pos \n",
       "Levels: neg pos"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(predicted_class_simpler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "### evaluation: confusion matrix and metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Factor w/ 2 levels \"neg\",\"pos\": 2 1 2 1 1 1 1 2 2 1 ...\n"
     ]
    }
   ],
   "source": [
    "#::GMG::'Raw' Model accuracy\n",
    "observed_classes <- test_data$diabetes\n",
    "str(observed_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>pos</li>\n",
       "\t<li>neg</li>\n",
       "\t<li>pos</li>\n",
       "\t<li>neg</li>\n",
       "\t<li>neg</li>\n",
       "\t<li>neg</li>\n",
       "</ol>\n",
       "\n",
       "<details>\n",
       "\t<summary style=display:list-item;cursor:pointer>\n",
       "\t\t<strong>Levels</strong>:\n",
       "\t</summary>\n",
       "\t<ol class=list-inline>\n",
       "\t\t<li>'neg'</li>\n",
       "\t\t<li>'pos'</li>\n",
       "\t</ol>\n",
       "</details>"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item pos\n",
       "\\item neg\n",
       "\\item pos\n",
       "\\item neg\n",
       "\\item neg\n",
       "\\item neg\n",
       "\\end{enumerate*}\n",
       "\n",
       "\\emph{Levels}: \\begin{enumerate*}\n",
       "\\item 'neg'\n",
       "\\item 'pos'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. pos\n",
       "2. neg\n",
       "3. pos\n",
       "4. neg\n",
       "5. neg\n",
       "6. neg\n",
       "\n",
       "\n",
       "\n",
       "**Levels**: 1. 'neg'\n",
       "2. 'pos'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] pos neg pos neg neg neg\n",
       "Levels: neg pos"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(observed_classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy Full Model:  0.7288136 \n",
      "Accuracy Simpler Model:  0.7457627"
     ]
    }
   ],
   "source": [
    "cat('Accuracy Full Model: ', \n",
    "    mean(predicted_class_full == observed_classes),\n",
    "   '\\nAccuracy Simpler Model: ', \n",
    "    mean(predicted_class_simpler == observed_classes))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Confusion Matrix AND metrics\n",
    "# https://www.rdocumentation.org/packages/base/versions/3.6.1/topics/table\n",
    "# https://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/\n",
    "# https://stackoverflow.com/questions/33621592/sum-of-antidiagonal-of-a-matrix\n",
    "# https://stackoverflow.com/questions/14577412/how-to-convert-variable-object-name-into-string\n",
    "confusion_matrix <- function (true, pred, beta = 1) {\n",
    "    t <- table(true, pred)\n",
    "    p <- t[2,2]/sum(t[,2])  #::NOTE::I assume 'positive class' is class2 (whatever it is)\n",
    "    r <- t[2,2]/sum(t[2,])  #::NOTE::I assume 'positive class' is class2 (whatever it is)\n",
    "    s <- t[1,1]/sum(t[1,])\n",
    "    list(cm = t,\n",
    "         accuracy = sum(diag(t))/sum(t), \n",
    "         precision = p,     #::NOTE::Precision of 'positive class'    \n",
    "         recall = r,        #::NOTE::it's also called sensitivity ('positive class again')\n",
    "         f1 = (1 + beta^2) * p * r/((beta^2 * p) + r),  #::NOTA::beta = 1 -> equal importance (class1, class2)\n",
    "         specificity = s,   #::NOTE::proportion of actual 'negative class' that are detected as such\n",
    "         balanced_accuracy = (r + s) / 2\n",
    "        )\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pred\n",
      "true  neg pos\n",
      "  neg  63  16\n",
      "  pos  16  23\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Confusion Matrix\n",
    "cf_full <- confusion_matrix(true = test_data$diabetes, pred = predicted_class_full)\n",
    "print(cf_full$cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     pred\n",
      "true  neg pos\n",
      "  neg  63  16\n",
      "  pos  14  25\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Confusion Matrix of the 'simpler' model ... no difference!\n",
    "cf_simpler <- confusion_matrix(true = test_data$diabetes, pred = predicted_class_simpler)\n",
    "print(cf_simpler$cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              accuracy precision recall    f1 specificity balanced_accuracy\n",
      "full_model       0.729      0.59   0.59  0.59       0.797             0.694\n",
      "simpler_model    0.746      0.61  0.641 0.625       0.797             0.719\n"
     ]
    }
   ],
   "source": [
    "#::GMG:Pretty print the model metrics as a table/data frame/...\n",
    "# https://cran.r-project.org/web/packages/tibble/vignettes/tibble.html\n",
    "# tibble::tibble(metric = names(cf[-1]), pima_logit = cf[-1])\n",
    "# https://www.r-bloggers.com/converting-a-list-to-a-data-frame/\n",
    "#as.data.frame.list(x = cf[-1], row.names = c('pima_logit'))\n",
    "# https://stackoverflow.com/questions/32059798/list-of-named-lists-to-data-frame\n",
    "# https://stackoverflow.com/questions/10432993/named-list-to-from-data-frame\n",
    "# https://www.rdocumentation.org/packages/base/versions/3.6.1/topics/as.data.frame\n",
    "# https://www.rdocumentation.org/packages/base/versions/3.6.1/topics/names\n",
    "#::NOTE::sensitivity (pos class) is recall\n",
    "results <- as.data.frame(t(sapply(list(cf_full[-1], cf_simpler[-1]), rbind)),\n",
    "                         row.names = c('full_model', 'simpler_model')\n",
    ")\n",
    "colnames(results) <- names(cf_full[-1])\n",
    "# https://stackoverflow.com/questions/23217520/limiting-the-number-of-decimals-in-a-dataframe-r\n",
    "print(results, digits = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::PENDING::** <span style=\"color:red\">Thresholding here here</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model with Lasso (L1 regularization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'cf_full'</li>\n",
       "\t<li>'cf_simpler'</li>\n",
       "\t<li>'confusion_matrix'</li>\n",
       "\t<li>'full_model'</li>\n",
       "\t<li>'msk'</li>\n",
       "\t<li>'observed_classes'</li>\n",
       "\t<li>'pima_clean'</li>\n",
       "\t<li>'PimaIndiansDiabetes2'</li>\n",
       "\t<li>'pr_curve_full'</li>\n",
       "\t<li>'pr_curve_simpler'</li>\n",
       "\t<li>'predicted_class_full'</li>\n",
       "\t<li>'predicted_class_simpler'</li>\n",
       "\t<li>'probabilities_full'</li>\n",
       "\t<li>'probabilities_simpler'</li>\n",
       "\t<li>'relevant.x'</li>\n",
       "\t<li>'results'</li>\n",
       "\t<li>'sig.formula'</li>\n",
       "\t<li>'simpler_model'</li>\n",
       "\t<li>'test_data'</li>\n",
       "\t<li>'toselect.x'</li>\n",
       "\t<li>'train_data'</li>\n",
       "\t<li>'using'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'cf\\_full'\n",
       "\\item 'cf\\_simpler'\n",
       "\\item 'confusion\\_matrix'\n",
       "\\item 'full\\_model'\n",
       "\\item 'msk'\n",
       "\\item 'observed\\_classes'\n",
       "\\item 'pima\\_clean'\n",
       "\\item 'PimaIndiansDiabetes2'\n",
       "\\item 'pr\\_curve\\_full'\n",
       "\\item 'pr\\_curve\\_simpler'\n",
       "\\item 'predicted\\_class\\_full'\n",
       "\\item 'predicted\\_class\\_simpler'\n",
       "\\item 'probabilities\\_full'\n",
       "\\item 'probabilities\\_simpler'\n",
       "\\item 'relevant.x'\n",
       "\\item 'results'\n",
       "\\item 'sig.formula'\n",
       "\\item 'simpler\\_model'\n",
       "\\item 'test\\_data'\n",
       "\\item 'toselect.x'\n",
       "\\item 'train\\_data'\n",
       "\\item 'using'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'cf_full'\n",
       "2. 'cf_simpler'\n",
       "3. 'confusion_matrix'\n",
       "4. 'full_model'\n",
       "5. 'msk'\n",
       "6. 'observed_classes'\n",
       "7. 'pima_clean'\n",
       "8. 'PimaIndiansDiabetes2'\n",
       "9. 'pr_curve_full'\n",
       "10. 'pr_curve_simpler'\n",
       "11. 'predicted_class_full'\n",
       "12. 'predicted_class_simpler'\n",
       "13. 'probabilities_full'\n",
       "14. 'probabilities_simpler'\n",
       "15. 'relevant.x'\n",
       "16. 'results'\n",
       "17. 'sig.formula'\n",
       "18. 'simpler_model'\n",
       "19. 'test_data'\n",
       "20. 'toselect.x'\n",
       "21. 'train_data'\n",
       "22. 'using'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"cf_full\"                 \"cf_simpler\"             \n",
       " [3] \"confusion_matrix\"        \"full_model\"             \n",
       " [5] \"msk\"                     \"observed_classes\"       \n",
       " [7] \"pima_clean\"              \"PimaIndiansDiabetes2\"   \n",
       " [9] \"pr_curve_full\"           \"pr_curve_simpler\"       \n",
       "[11] \"predicted_class_full\"    \"predicted_class_simpler\"\n",
       "[13] \"probabilities_full\"      \"probabilities_simpler\"  \n",
       "[15] \"relevant.x\"              \"results\"                \n",
       "[17] \"sig.formula\"             \"simpler_model\"          \n",
       "[19] \"test_data\"               \"toselect.x\"             \n",
       "[21] \"train_data\"              \"using\"                  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### features/target split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::NOTE::The R function model.matrix() helps to create the matrix of predictors and also automatically \n",
    "#        converts categorical predictors to appropriate dummy variables, which is required for the glmnet() \n",
    "#        function.\n",
    "# https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/model.matrix\n",
    "# Dumy code categorical predictor variables\n",
    "X_train <- stats::model.matrix(diabetes~., train_data)[,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# Convert the outcome (class) to a numerical variable\n",
    "y_train <- ifelse(train_data$diabetes == \"pos\", 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:274, 1:8] 1 0 2 1 5 0 1 3 11 3 ...\n",
      " - attr(*, \"dimnames\")=List of 2\n",
      "  ..$ : chr [1:274] \"4\" \"5\" \"9\" \"14\" ...\n",
      "  ..$ : chr [1:8] \"pregnant\" \"glucose\" \"pressure\" \"triceps\" ...\n"
     ]
    }
   ],
   "source": [
    "#::NOTE::Check the results (a named 2D matrix of features)\n",
    "str(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:274] 0 1 1 1 1 1 1 0 1 1 ...\n"
     ]
    }
   ],
   "source": [
    "#::NOTE::Check the results (a numeric 1/0 vector)\n",
    "str(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Do the same with test, of course\n",
    "X_test <- model.matrix(diabetes ~., test_data)[,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:118, 1:8] 3 1 10 1 13 3 5 8 7 0 ...\n",
      " - attr(*, \"dimnames\")=List of 2\n",
      "  ..$ : chr [1:118] \"7\" \"19\" \"26\" \"28\" ...\n",
      "  ..$ : chr [1:8] \"pregnant\" \"glucose\" \"pressure\" \"triceps\" ...\n"
     ]
    }
   ],
   "source": [
    "str(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "y_test <- ifelse(test_data$diabetes == \"pos\", 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " num [1:118] 1 0 1 0 0 0 0 1 1 0 ...\n"
     ]
    }
   ],
   "source": [
    "str(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### computing best lambda with cv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Make it reproducible\n",
    "#::NOTE::Not sure if necessary but CV in involved ...\n",
    "set.seed(123) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::In penalized regression, you need to specify a constant lambda to adjust the amount of \n",
    "#       the coefficient shrinkage. The best lambda for your data, can be defined as the lambda \n",
    "#       that minimize the cross-validation prediction error rate. This can be determined automatically \n",
    "#       using the function cv.glmnet()\n",
    "# https://www.rdocumentation.org/packages/glmnet/versions/2.0-18/topics/cv.glmnet\n",
    "#::NOTE::compute lasso regression by specifying the option alpha = 1\n",
    "# Find the optimal value of lambda that minimizes the cross-validation error:\n",
    "cv_lasso <- glmnet::cv.glmnet(x = X_train, \n",
    "                              y = y_train, \n",
    "                              alpha = 1,\n",
    "                              type.measure = 'class', #::NOTE::misclassification error\n",
    "                              family = 'binomial')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+23padJSUmjR4/WaDQjR45s0aLF+fPn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\ngAABDQAAAb8AVweUeywH540AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::See graphically the best lambda\n",
    "plot(cv_lasso)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "The plot displays the cross-validation *misclassification error* according to the log of lambda. The *left dashed vertical line* indicates that the log of the optimal value of lambda `lambda.min` is approximately -3, which is the one that minimizes the prediction error. This lambda value will give the most accurate model. The exact value of lambda can be viewed as follow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimum lambda:  0.0660483"
     ]
    }
   ],
   "source": [
    "cat('Optimum lambda: ', cv_lasso$lambda.min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Generally, the purpose of regularization is to balance accuracy and simplicity. This means, a model with the smallest number of predictors that also gives a good accuracy. To this end, the function `cv.glmnet()` finds also the value of lambda that gives the simplest model but also lies within one standard error of the optimal value of lambda. This value is called `lambda.1se`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simplest model within one sd of lambda optimum:  0.08731196"
     ]
    }
   ],
   "source": [
    "cat('Simplest model within one sd of lambda optimum: ', cv_lasso$lambda.1se)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### shrank coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Using lambda.min as the best lambda, gives the following regression coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9 x 1 sparse Matrix of class \"dgCMatrix\"\n",
       "                      1\n",
       "(Intercept) -6.01175423\n",
       "pregnant     .         \n",
       "glucose      0.02358263\n",
       "pressure     .         \n",
       "triceps      .         \n",
       "insulin      .         \n",
       "mass         0.02949961\n",
       "pedigree     0.04111407\n",
       "age          0.04315104"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/coef (?)\n",
    "stats::coef(cv_lasso, cv_lasso$lambda.min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9 x 1 sparse Matrix of class \"dgCMatrix\"\n",
       "                      1\n",
       "(Intercept) -6.01175423\n",
       "pregnant     .         \n",
       "glucose      0.02358263\n",
       "pressure     .         \n",
       "triceps      .         \n",
       "insulin      .         \n",
       "mass         0.02949961\n",
       "pedigree     0.04111407\n",
       "age          0.04315104"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::NOTE:the \"native\" glmnet packaage coef() (same result)\n",
    "glmnet::coef.cv.glmnet(cv_lasso, cv_lasso$lambda.min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Using `lambda.1se` as the best lambda, gives the following regression coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9 x 1 sparse Matrix of class \"dgCMatrix\"\n",
       "                      1\n",
       "(Intercept) -4.85014301\n",
       "pregnant     .         \n",
       "glucose      0.02070629\n",
       "pressure     .         \n",
       "triceps      .         \n",
       "insulin      .         \n",
       "mass         0.01526296\n",
       "pedigree     .         \n",
       "age          0.03382121"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef(cv_lasso, cv_lasso$lambda.1se)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gMAAHwkCjTKkrGxsZubm5ub25uDT548\nuXnz5s2bN2/cuHHz5s3ff//91q1bubm5mpqa9vb2DRo0qFevXoMGDZydnZ2dndkGBAAAVHIU\naJQ7Y2NjDw8PDw+PNwfv378vq9RxcXFnzpz57bffMjIy1NXVa9WqVf8Nzs7OBgYGopIDAAD8\nHQUaYsh2ofb393898vjx4/j4+ISEhPj4+NjY2LCwsNTUVEmSatWq1ahRo0aNGn3yySeNGjWq\nU6dOlSr8vQUAAMJQRFBZVKtWzdfX981F1U+fPk1ISLh27drVq1dPnz69cuXKv/76S0dHp0GD\nBo0aNXJxcZG1ajMzM4GxAQCAqqFAo/KqWrWqp6enp6fn65HU1NSrV69euXLlypUra9euTUhI\nKCwstLS0bNSokdt/ODg4qKmpCYwNAACUGwUaikS2WXWHDh1kTwsKCq5fvy7r0+fPn//ll1+y\nsrKqVq3q6ur6uk/XrVtXQ0NDbGwAAKBMKNBQYFpaWi4uLi4uLq9H7ty5Exsbe/HixYsXL4aF\nhWVkZOjr63/yySeyMu3h4eHs7Kyuri4wMwAAUHQUaCiV2rVr165du2fPnrKnKSkpF/9j+/bt\nqampRkZG7u7uzZo1a9asmYeHh5WVldjAAABA4VCgocysra2tra27dOkie5qWlnb+/PkLFy5c\nuHBh5cqVWVlZVlZWTf7D19fX2NhYbGAAAFD5qRUXF4vOUNlFR0d7e3vn5+draWmJzoIyU1RU\nFB8fHxMTc/bs2bNnz8bFxampqTVo0MDLy8vLy8vHx6dWrVqiMwIAoLoKCgq0tbWjoqK8vLxE\nZ3kbM9BQURoaGrLtpT///HNJknJzcy9cuHDmzJmoqKgJEyY8evSoZs2a3t7e3t7ePj4+Li4u\nbD4NAABklKoTZGVlPX36lIlDfAR9ff0WLVq0aNFC9vTOnTunTp2KiooKDQ398ssv9fT0XF1d\nfXx8ZH3axMREbFoAACCQIm1HcOXKlU6dOtWqVcvX13f58uVFRUVvnTBv3jx7e3sh2aBkateu\nHRQUFBoaGhcXl5aWtmHDhmbNmh0/frxnz55mZmaNGzcODg5et27djRs3WAQFAICqUZgZ6Kio\nKH9///z8fD09vQcPHpw6dSo8PHz79u3MBaK8WVhYdO/evXv37pIkvXjx4ty5c6dPnz5z5kxI\nSEh6erqpqalsTw9PT89mzZpxGSIAAEpPYQr03LlzX716tX379q5duxYUFCxfvnzq1Knt27c/\nevSovr6+6HRQFbq6um+u9Lh79+7p06fPnj27f//+uXPnFhQU1KtXT1amvby8GjRowJ7TAAAo\nH4Up0FeuXOnbt2+3bt0kSdLW1p4wYcInn3zSsWPHPn367Ny5k1vNQQg7Ozs7O7t+/fpJkpSf\nnx8bG3v27NkzZ87MnTv37t27JiYmPj4+vr6+Pj4+7u7umpqaovMCAIAyoDDTY+np6bVr135z\nxM/P79dff927d+/EiRNFpQJe09bW9vT0HD9+/B9//JGcnPzgwYPQ0FB7e/vNmzf7+PgYGxv7\n+PiEhITs2rXryZMnosMCAICPpzAz0BYWFpcuXXprcNCgQQkJCXPnzrW2tp48ebKQYECJrKys\nevfu3bt3b0mS/vrrr1OnTp08efL48eM//vhjcXGxm5ubr69vy5YtW7ZsaWRkJDosAACQg8IU\n6B49eixduvTnn38eOXLkmx+Ff/vttw8ePJgyZcqDBw/+vi8HUBmYmpp26dJFdkPE3Nzcs2fP\nnjhx4uTJkytWrCgoKHB3d/f39/fz8/Py8tLR0REdFgAAlEJh7kT4+PFjNze3e/futWnT5tCh\nQ28eKi4u/vLLL5csWfL6adl+a+5EiHLy8uXLy5cvR0ZGRkZGnjhx4tWrV5988kmbNm3atGnT\nokUL/r4BAFRZZb4TocKsga5WrdqFCxeCg4MbNmz41iE1NbXFixdv3brVwcFBSDbg41SpUqVJ\nkyZTp049dOjQo0eP/vzzzxYtWuzfv79du3bm5uZdu3ZdsmRJfHy86JgAAOC/KMwMtEDMQKOC\nZWZmHj169PDhw0eOHLl9+7atrW2HDh06duzo7+9vaGgoOh0AABWhMs9AK8waaEB1mJmZ9enT\np0+fPpIkJSUlHTp0KDIycvDgwbm5ua6urp07dw4MDHRzc1NTUxOdFAAAVaQwSzgA1WRvbz9i\nxIjw8PDHjx8fO3asTZs2u3fvdnd3t7KyCgoKioiIYFM8AAAqmPLMQCcmJo4cOVKSpMjIyA9/\nVXFxcVRUVF5e3nvOiYuL+6fhgH+sSpUqPj4+Pj4+kiQlJyfv379/3759Q4cOzc/P9/b27tq1\na9euXe3t7UXHBABA+SnPGuhLly41btxYknMXjjt37jg7OxcUFJR6Zk5ODvcMR2WTn59/6tSp\nPXv27Nix486dOy4uLrImzQIPAICiq8xroJWnQOfl5d2+fVuSpL9v0/EPhYaGjho1Kjs728DA\noGy/MlCG4uLidu/evWvXrujoaDMzs/bt2/fu3bt9+/Zc/AoAUESVuUArzxpoHR2dhg0blnl7\nBhRFgwYNpk6deurUqfT09Pnz52dlZfXq1cvU1DQwMHD9+vVPnz4VHRAAACWhPAVakqTHjx/L\nJqEBVWZubh4UFLRr166HDx+uWrVKT09v3LhxFhYWXbt2DQsLy87OFh0QAADFplQFev78+XXq\n1BGdAqgsjI2N+/fvv3nz5szMzG3btpmYmIwZM8bc3Lxnz56bN2/Ozc0VHRAAAIWkVAUaQIm0\ntLQCAgLWrl378OHD8PBwfX39ESNGVK9eXba6IycnR3RAAAAUCQUaUCHa2tqy0ixr0iYmJmPH\njjU3N5cNMicNAMCHUJh9oN3d3Us9JzU1tQKSAEpAR0cnMDAwMDDw+fPne/bsCQ8PHzVq1Lhx\n43r06DFw4MDWrVurq/O/awAASqYwBTo2NlaSJE1Nzfec8/Lly4qKAygJPT293r179+7dOycn\nZ+fOnWFhYR06dLCwsBgwYMDAgQNdXFxEBwQAoNJRmEmmyZMn6+vrX7t2Le/dJk2aJDomoKgM\nDAwGDBiwZ8+ehw8fzpgxIzo62tXVtUGDBrNmzUpKShKdDgCASkRhCvScOXMcHR379+9fWFgo\nOgugzExNTUeMGHHq1KmkpKSgoKCNGzc6Ojr6+PgsXrz48ePHotMBACCewhRoTU3NsLCwuLi4\nf//736KzACrBzs5u6tSpN27cOHnypIuLy5w5c6ytrfv27btnz56ioiLR6QAAEEZh1kBLkuTs\n7Jyenv6ehc4dO3Y0NjauyEiA0lNTU/Py8vLy8lq0aNH+/fs3bNjQs2dPU1PTgQMHfvbZZ/Xr\n1xcdEACAiqYwM9AyRkZGpqam7zrasmXLkJCQiswDqA4tLa0uXbpERESkp6fPmjUrOjq6QYMG\nDRo0mDdv3qNHj0SnAwCg4ihYgQYgnLGxsWyRdHx8fGBg4KJFi6ytrQMDAyMiIrhEAQCgCijQ\nAD6Ss7Pz999/n5qaunv3bhMTk8GDB9vZ2Y0fP/7y5cuiowEAUI4o0AD+EXV19TZt2qxfv/7+\n/fv/+te/oqKiXF1dfX19w8LC8vPzRacDAKDsUaABlI1q1aqNGzfu/Pnzly9f/uSTT4KDg62t\nradMmXL79m3R0QAAKEsUaABlzMXF5eeff3748OHChQsPHz7s5OTUtm1bVkgDAJQGBRpAudDR\n0QkKCrpw4cK5c+dq1649ZMgQW1vbkJCQu3fvio4GAMA/QoEGUL6aNGkSGhqakpISEhKyc+dO\nBweHbt267d+//9WrV6KjAQDwMSjQACqCsbHx+PHj4+LiIiMjdXR0unbtWq9eveXLl+fm5oqO\nBgCAfCjQACqOmppaq1atNm3adO/evf79+8+ePdvGxiYkJCQ1NVV0NAAAPhQFGoAAFhYWs2fP\nvnfv3qJFi/bs2WNnZxcYGHj69GnRuQAAKB0FGoAw2traQUFBV69ePXbsmCRJ3t7e7u7u69ev\nf/nypehoAAC8EwUagHg+Pj67du26ceOGt7f36NGjnZyc5s2b9+TJE9G5AAAoAQUaQGVRp06d\nxYsXJycnDxkyZNGiRbVq1QoJCXn48KHoXAAA/BcKNIDKxczMbPr06cnJyT/99NOOHTvs7e2/\n+OKL+/fvi84FAMD/oUADqIy0tbWHDBkSFxe3efPmM2fOODg4BAUF3bhxQ3QuAAAo0AAqMXV1\n9cDAwJiYmCNHjqSmptavXz8wMPDChQuicwEAVBoFGoAC8PHxOXz48PHjxyVJ8vDwCAwMPHv2\nrOhQAAAVRYEGoDBkm3VcuHBBV1e3efPmsqeiQwEAVA4FGoCCcXV1DQ8Pv3TpkrW1dbdu3Vq0\naHHy5EnRoQAAKoQCDUAhubi4bNq0KSEhwcbGplWrVh07djx//rzoUAAAlUCBBqDAnJycwsLC\nrl69amho6OHh0bZt20uXLokOBQBQchRoAAqvfv364eHhZ86c0dHRadKkSZ8+fW7duiU6FABA\naVGgASgJDw+PXbt2nThxIiMjo0GDBkFBQUlJSaJDAQCUEAUagFLx9vY+duzY3r174+Pj69Wr\nN3LkyPT0dNGhAABKhQINQAm1adPm3LlzGzZsOHHihJOT08yZM3NyckSHAgAoCQo0AOWkpqbW\np0+fa9euLVmyZM2aNU5OTqtXr3716pXoXAAAhUeBBqDMNDQ0Pvvssxs3bowfP37ChAmNGjXa\nv3+/6FAAAMVGgQag/HR1dadOnXr9+nUfH5/OnTu3bds2Li5OdCgAgKKiQANQFVZWVqGhoVeu\nXNHU1GzcuPHIkSMzMzNFhwIAKB4KNADVUr9+/b179+7duzcqKqpu3brz5s3Lz88XHQoAoEgo\n0ABUUZs2bWJjY7///vuFCxc2atQoIiJCdCIAgMKgQANQUZqamiNGjLh+/XpAQMCnn37apk2b\nhIQE0aEAAAqAAg1ApZmami5atOjatWuampqurq7//ve/nz9/LjoUAKBSo0ADgOTk5LRv374t\nW7aEhYU5OTmtX79edCIAQOVFgQaA/xMYGJiQkDBs2LDhw4cHBgYmJSWJTgQAqIwo0ADw//T0\n9GbNmnXlypUXL140aNBg1qxZ7NEBAHgLBRoA3la3bt1Dhw6tXLlyxYoVjRo1OnjwoOhEAIBK\nhAINACVQU1MLCgq6fv16x44dAwICAgMDU1JSRIcCAFQKFGgAeCcTE5PFixefOnUqJSWlYcOG\ny5Yte/XqlehQAADBKNAAUApPT8/z58/Pnj373//+d4sWLW7cuCE6EQBAJAo0AJROQ0Nj/Pjx\n169fr1atmqur67x584qKikSHAgCIQYEGgA9lZWW1Y8eO9evXz58/393d/dKlS6ITAQAEoEAD\ngHx69+597do1e3t7Dw+PkJCQgoIC0YkAABWqiugAcisuLk5KSrpz5052drYkSVWrVq1Tp46N\njY3oXABUiKWl5bZt2yIiIoKDg/ft27d69eomTZqIDgUAqCCKNAOdlZU1adIkS0tLBweHtm3b\n9ujRo0ePHv7+/ra2tnZ2dnPmzHnx4oXojABUiGwq2snJydPTMyQkhFuuAICKUJgZ6LS0NG9v\n76SkpDp16gQEBNjZ2enr60uS9OzZs8TExOPHj8+YMWPr1q1Hjx41MTERHRaAqrCwsIiIiIiI\niBgzZsyePXtWr17dtGlT0aEAAOVLYQr09OnTU1JSwsPDe/fu/fejRUVFoaGhY8eOnT179qJF\niyo+HgBV1rt371atWo0bN87Ly2vy5MmzZs3S0tISHQoAUF4UZgnHnj17Bg0aVGJ7liRJQ0Mj\nODi4T58+27Ztq+BgACBJkpmZ2aZNm8LDw9esWePp6Xn9+nXRiQAA5UVhCvTjx48dHBzef46z\ns/PDhw8rJg8A/F337t2vXLliY2PTuHHjxYsXFxcXi04EACh7ClOga9Socfny5fefExsbW6NG\njYrJAwAlMjMz27FjR2ho6LRp0zp27JiWliY6EQCgjClMge7WrVtERMSCBQtKvM49Nzd35syZ\nO3bs6Nu3b8VnA4C3BAUFnT9/PjMz09XVdc+ePaLjAADKkpqifML45MkTf3//ixcvGhoaenh4\n2NjYGBgYFBcX5+Tk3L17NyYm5vnz576+vnv37jUwMCjbbx0aGjpq1Kjs7Owy/0voM0wAACAA\nSURBVMoAlFthYeG33377zTfffP755z/99JOenp7oRACgMAoKCrS1taOiory8vERneZvC7MJh\nbGx8+vTpZcuWrV+//tixY0VFRa8PaWpqNmnSZOjQoUOHDtXQ0BAYEgDepKmpOWvWrBYtWgwe\nPPjUqVNhYWGurq6iQwEA/imFKdCSJGlpaU2YMGHChAl5eXn379+X3YnQyMjI1taWHaMAVFp+\nfn5Xr14NDg5u3rz5rFmzJk+erK6uMMvnAAB/p0gF+jUdHZ06deqITgEAH8rY2Hjjxo3r168f\nM2bM4cOH165dyxXPAKC4mAUBgAoSFBR04cKFJ0+eNG7c+MCBA6LjAAA+kkLOQJcoMTFx5MiR\nkiRFRkbK9cJr166VuLPHa/fu3ftHyQDgP5ycnKKioqZNm9apU6f/+Z//mTFjBss5AEDhKE+B\nzs7OPnz4sLyvSkxMdHFx+ZCtSBRluxIAlZympuYPP/zQokWLoKCgEydO/PHHHxYWFqJDAQDk\noDwzH/Xq1bt69erVq1flepWDg8OzZ8/+eq8ff/xRkiQ1NbXyCQ5AFXXu3PnSpUu5ubnu7u7R\n0dGi4wAA5KA8M9A6OjoNGzb8iBeWurszW7cCKA+2trYnTpyYMmVKy5Ytv/nmmylTpvAfdQBQ\nCMozAy1J0uPHj2/fvi06BQB8KG1t7cWLF69Zs2bOnDk9evR48uSJ6EQAgNIpVYGeP38+29sB\nUDgDBw48d+7czZs3mzVrduXKFdFxAAClUKoCDQAKytnZ+cyZM40bN27WrNmvv/4qOg4A4H0o\n0ABQKRgaGm7atGnx4sVjxowJCgp6/vy56EQAgJIpzEWE7u7upZ6TmppaAUkAoPyMGDGiYcOG\nffv29fX13bp1a61atUQnAgC8TWEKdGxsrCRJmpqa7znn5cuXFRUHAMqLl5fXxYsX+/fv7+Hh\nsWXLlhYtWohOBAD4LwqzhGPy5Mn6+vrXrl3Le7dJkyaJjgkAZcDMzOzAgQNDhw719/f/+eef\nRccBAPwXhSnQc+bMcXR07N+/f2FhoegsAFDuNDQ0vv/++xUrVnz11VcjR47kRx8AVB4KU6A1\nNTXDwsLi4uL+/e9/i84CABVk2LBhR44c2bFjR5s2bTIzM0XHAQBIkgKtgZYkydnZOT09/T0L\nnTt27GhsbFyRkQCgvHl7e58/f75r167NmzffuXNn/fr1RScCAFWnMDPQMkZGRqampu862rJl\ny5CQkIrMAwAVwNra+vjx4y4uLp6enjt37hQdBwBUnYIVaABQTQYGBlu3bp02bVrPnj3nzZsn\nOg4AqDRFWsIBAKpMTU1t6tSp9vb2Q4YMuXz58m+//aarqys6FACoImagAUCR9OnTJyoqKioq\nyt/fPz09XXQcAFBFFGgAUDCurq5nzpx59eqVh4fHpUuXRMcBAJVDgQYAxWNlZXXs2DFfX98W\nLVocPHhQdBwAUC0UaABQSDo6Or///vvEiRM7deq0atUq0XEAQIVwESEAKCo1NbVZs2bZ2NiM\nHj06NTV11qxZohMBgEqgQAOAYvv888+rV68+YMCA+/fvh4aGVqnCD3YAKF8s4QAAhde1a9cj\nR47s2rWrZ8+ez58/Fx0HAJQcBRoAlEGzZs1Onz6dkJDQunXrjIwM0XEAQJlRoAFASTg4OJw4\ncaKoqKh58+Y3b94UHQcAlBYFGgCUh6Wl5fHjx52dnb28vKKjo0XHAQDlRIEGAKWir6+/Y8eO\nnj17tmvXbvfu3aLjAIASokADgLLR0NAIDQ2dPn169+7dV65cKToOACgbdjsCAOU0depUU1PT\n4ODgzMzM6dOni44DAMqDAg0ASmv48OGWlpZ9+vR59uzZDz/8oKamJjoRACgDCjQAKLPAwMD9\n+/cHBgY+e/ZsxYoV6uqs3AOAf4qfpACg5Fq2bHn48OGtW7cOHDjw5cuXouMAgMKjQAOA8mva\ntOmhQ4ciIyN79OiRl5cnOg4AKDYKNACohMaNG584cSI2NjYgICAnJ0d0HABQYBRoAFAV9erV\nO3ny5L179wICAp49eyY6DgAoKgo0AKiQWrVqnTx5Misry8/P79GjR6LjAIBCokADgGqxsrI6\nfPhwUVFRy5YtHzx4IDoOACgeCjQAqBxzc/OjR49WrVq1devW9+/fFx0HABQMBRoAVJGxsfGh\nQ4dsbW19fHxu3bolOg4AKBIKNACoKH19/Z07dzZs2LBVq1bx8fGi4wCAwqBAA4Dq0tXV3b59\ne/PmzVu3bn3t2jXRcQBAMVCgAUClaWlpbd682d/f38/Pjw4NAB+CAg0Aqk5DQ2PDhg3+/v7+\n/v5xcXGi4wBAZUeBBgBIGhoa69ev9/Ly8vf3Zz00ALwfBRoAIEmSpKmpGR4e7unp6efnl5CQ\nIDoOAFReFGgAwP+RdehmzZr5+fldv35ddBwAqKQo0ACA/6elpRUREeHu7t62bdvExETRcQCg\nMqJAAwD+i5aW1tatW11dXVu3bn3nzh3RcQCg0qFAAwDepqWltWXLFhcXl9atWyclJYmOAwCV\nCwUaAFACbW3tiIiIOnXqtGrVig4NAG+iQAMASqarq7tz505HR8fWrVsnJyeLjgMAlQUFGgDw\nTnp6ert27apdu3arVq3u3r0rOg4AVAoUaADA++jp6e3cudPW1rZdu3YZGRmi4wCAeBRoAEAp\nDAwM9uzZY2xs3KFDh6dPn4qOAwCCUaABAKUzNDTcu3dvfn5+x44dc3NzRccBAJEo0ACAD1Kt\nWrWDBw+mpaX169evsLBQdBwAEIYCDQD4UDVr1jx06ND58+eHDBny6tUr0XEAQAyFL9CFhYVx\ncXEXLlzIz88XnQUAlJ+jo+PBgwf37t07btw40VkAQAxFKtBHjhxp3bq1vb19QEDA2bNnJUk6\ncOBArVq1GjZs6O7ubm5uvnz5ctEZAUD5NWrUaM+ePevWrZs9e7boLAAgQBXRAT7U6dOn27dv\n//LlSyMjowMHDpw4ceLQoUN9+vSpWrVqUFBQXl7eoUOHxowZU7t27Q4dOogOCwBKrnnz5tu3\nb+/cubORkdGECRNExwGACqUwBXru3LnVq1c/cOCAi4tLZmZm3759+/XrZ29vf/r0aV1dXUmS\nsrKy3NzcFi9eTIEGgArQtm3bNWvWBAUFGRsbDxkyRHQcAKg4CrOEIzo6esyYMS4uLpIkmZmZ\n/fDDD/fu3ZswYYKsPUuSZGJiMmzYsJiYGKExAUCFDBgwYMmSJcOHD9+2bZvoLABQcRRmBvrp\n06d2dnavn9asWVOSJDMzszfPsbKyevbsWUUnAwAVFhwcnJmZOXDgwP3797do0UJ0HACoCApT\noKtVq5aYmPj66c2bNyVJun379pvnJCYmVqtWraKTAYBqmzlz5rNnzwIDA48ePerm5iY6DgCU\nO4VZwtG6deulS5cePXq0oKDg6tWr48aNc3Z2XrhwYWpqquyEhISEFStW+Pr6is0JACpowYIF\nvXr16tChw/Xr10VnAYBypzAFeubMmYWFhX5+ftra2i4uLqmpqVu3blVTU3NycvLz8/Py8nJx\ncXn27NnkyZNFJwUAlaOmprZy5cpmzZp17NgxLS1NdBwAKF8KU6Dr1asXHR3dv3//Zs2affbZ\nZ9HR0c7Ozrt3727YsOGxY8dOnz5ta2u7detWDw8P0UkBQBVpamqGh4dbWVkFBgbm5OSIjgMA\n5Uhh1kBLktSwYcONGze+NXL27NmcnJwXL168dUEhAKCC6erq7tq1y8vLq0+fPjt37qxSRZF+\nxQDAh1OYGej3MDAwoD0DQGVQrVq1vXv3nj9/Pjg4WHQWACgvylCgAQCVh4ODw+7du8PCwhYs\nWCA6CwCUC+X5fC0xMXHkyJGSJEVGRsr1wpSUlIKCgvec8OjRo3+UDABUjIeHx9q1a/v371+j\nRo0BAwaIjgMAZUx5CnR2dvbhw4flfVViYqKjo+OHnFlcXCx/KABQUb17905KSvr888/t7Oy8\nvb1FxwGAsqQ8BbpevXpXr16V91UODg4pKSn5+fnvOeePP/74n//5HzU1tX+QDgBUzpQpU+7d\nu9e1a9fo6GgnJyfRcQCgzChPgdbR0WnYsOFHvFB2V/D3qF69+kclAgBVt3jx4pSUlI4dO54+\nfdrc3Fx0HAAoGx9aoIuKijQ0NGSP8/PzL126pKWl5erqWvHzssXFxUlJSXfu3MnOzpYkqWrV\nqnXq1LGxsangGACAUmloaGzcuLF169adO3c+duyYnp6e6EQAUAZKL9BFRUVffPFFRkZGRESE\nJEnJycn+/v537tyRJMnHx2ffvn0GBgblHlOSJEnKysr69ttvN2zYkJGR8dYhW1vbYcOGTZo0\nSVdXt2LCAAA+hJ6e3p9//tm8efPBgwdv3rxZXZ3dnwAovNIL9Pz585cvXz5x4kTZ0zFjxiQl\nJY0ePVp249aff/45JCSknENKkiSlpaV5e3snJSXVqVMnICDAzs5OX19fkqRnz54lJiYeP358\nxowZW7duPXr0qImJSQXkAQB8ICsrq71793p7e0+dOnX+/Pmi4wDAP1V6gQ4LC+vRo8fChQsl\nSUpNTd23b9/QoUOXL18uSVJeXt7mzZsrpkBPnz49JSUlPDy8d+/efz9aVFQUGho6duzY2bNn\nL1q0qALyAAA+XP369bdv396hQwdbW9tx48aJjgMA/0jpH6UlJye3a9dO9vjAgQPFxcX9+/eX\nPW3SpElycnL5hXvTnj17Bg0aVGJ7liRJQ0MjODi4T58+27Ztq5g8AAC5tGrVas2aNRMnTtyx\nY4foLADwj5ReoN+8TDAyMlJfX9/X11f2tLi4uLCwsLyi/bfHjx87ODi8/xxnZ+eHDx9WTB4A\ngLz69+8/bdq0Tz/99PLly6KzAMDHK71A29nZnThxQpKkhw8f7tq1q127dlpaWrJDly9ftra2\nLt+A/1GjRo1Sf+DGxsbWqFGjYvIAAD7CzJkzu3Tp0rVr18zMTNFZAOAjlV6gBwwYsHHjRi8v\nLzc3t5ycnPHjx8vG169fv27dui5dupRzwv/TrVu3iIiIBQsWlHjTk9zc3JkzZ+7YsaNv374V\nkwcA8BHU1NRWr15tYWHRvXv3goIC0XEA4GOolXqH6ry8vNGjR2/evFlLS2vOnDmvL/6oUaNG\n9erVjx8/XjG7Xjx58sTf3//ixYuGhoYeHh42NjYGBgbFxcU5OTl3796NiYl5/vy5r6/v3r17\ny3xbvdDQ0FGjRmVnZ1fYhn0AoNzS0tKaNm3arl271atXi84CoJIqKCjQ1taOiory8vISneVt\npe/CoaOjs2bNmjVr1rw1vm3bNnd39ypVKuhehsbGxqdPn162bNn69euPHTtWVFT0+pCmpmaT\nJk2GDh06dOjQ13d7AQBUWlZWVhEREa1bt3Z3dw8ODhYdBwDkU3r9PXXqVP369U1NTd8a9/T0\njImJuX//fs+ePcsn29u0tLQmTJgwYcKEvLy8+/fvy+5EaGRkZGtr+3pZNgBAITRv3vyXX34Z\nNmxYvXr1/Pz8RMcBADmUvgba19dXdhHh3508eXL48OFlHal0Ojo6derUcXNzc3Nzc3R0pD0D\ngCIKCgoaM2ZM7969ExMTRWcBADm8cwb69u3bt2/flj2OjY3V0dF564QXL16Eh4eXeEkfAAAf\nYsGCBTdu3AgMDDxz5oyRkZHoOADwQd5ZoLds2fKvf/1L9vjrr79+12m9evUq+1AAANWgoaER\nFhbWrFmzoKCgbdu2qauX/rkoAAj3zgIdEhIyePDgc+fOde3addCgQfXr13/rBA0Njdq1a1fY\nNnYAAKVkYmKya9euZs2azZ49e/bs2aLjAEDp3ncRoZWVVZcuXTp16hQcHOzp6VlhmQAAKqVu\n3bqbN2/u3Llz/fr12c4fQOVX+i4cu3fvroAcAABV1r59+zlz5gwZMsTR0bFJkyai4wDA+5Re\noIuLi7ds2bJ+/fqUlJTCwsK/n3Dt2rVyCAYAUC1Tp069evVqz549Y2JizM3NRccBgHcqvUAv\nXLhw8uTJkiTp6elpamqWfyQAgCpSU1P77bffWrZs2aNHjyNHjrBFKYBKq/TrnRcvXty+ffvE\nxMTc3NwnJamAlAAAVaCjo/Pnn38mJyePGjVKdBYAeKfSZ6AfPny4ZcuW2rVrV0AaAICKs7Ky\nCg8P9/Pz8/T0HDFihOg4AFCC0megLSwsiouLKyAKAACSJHl5ef30009ffPHF+fPnRWcBgBKU\nXqD79++/YcOGCogCAIDM6NGj+/Xr17Nnz0ePHonOAgBvK71Az5gxIzEx8dNPPz1w4EBCQsLt\nv6mAlAAAVbNixQpTU9PBgwe/evVKdBYA+C+lr4E2NDSUPdi4cWOJJ7DAAwBQ5nR1dcPDw5s2\nbTp37txp06aJjgMA/6/0At2/f38tLa0qVUo/EwCAMlSnTp1169b17NnT3d29ffv2ouMAwP8p\nvRa/a+IZAIDy1rVr1y+++GLAgAEXL160s7MTHQcAJOlD1kC/lp2dHRcXx8bPAICK9MMPPzRo\n0KBv374FBQWiswCAJH1ggT5+/Li7u7uRkVHDhg3PnDkjG+zSpcvhw4fLMxsAAFKVKlXCw8Pv\n3bsnuy0uAAhXeoGOiYlp167dzZs331x/lpmZee7cuYCAgAsXLpRnPAAAJEtLy40bNy5fvpxt\nVQFUBqUX6K+//trS0jI+Pn7t2rWvB83MzC5fvmxpaTlnzpxyTAcAgCRJktSqVauvv/46ODg4\nPj5edBYAqq70An3mzJnRo0dbW1u/NW5ubj5q1KgTJ06UTzAAAP5LSEhI27Zte/To8ezZM9FZ\nAKi00gv006dPbWxsSjxkZWWVk5NT1pEAACiBmpra6tWrX758OWLECNFZAKi00gu0paVlQkJC\niYdOnDhRo0aNso4EAEDJjI2Nt23btmvXrp9//ll0FgCqq/QCHRAQsHz58osXL745mJWVNW3a\ntDVr1nTq1KncsgEA8DYXF5fQ0NCJEydGRUWJzgJARamVeiPu9PR0Dw+PtLQ0FxeXixcvurq6\nSpKUkJCQn59va2sbExNjYWFRIVGFCQ0NHTVqVHZ2toGBgegsAABJkqTPP//80KFDFy9erF69\nuugsAMpFQUGBtrZ2VFSUl5eX6Cxv+6AlHOfPnx8+fPjdu3clSbp06dKlS5cMDQ1Hjx597tw5\npW/PAIBK6Oeff65WrdqQIUNKnQYCgDL3QTdSMTc3X758eWZmZnp6+q1bt9LT0zMzM5cvX25u\nbl7e+QAA+DtdXd2IiIjjx48vXbpUdBYAKqdKiaPp6ena2tomJiayx28eMjAwKC4ufnPQ0tKy\nXCMCAPB3jo6OixYtCg4O9vX1bdy4seg4AFRIyQXaysqqffv2+/fvlz1+/5fg4zMAgBBDhw49\nfPhw3759L1y4YGhoKDoOAFVRcoHu27ev7GJB2eMKzAMAgBxCQ0Pd3NwmTJjw66+/is4CQFWU\nXKA3bdpU4mMAACoVAwODsLAwHx8fPz+/AQMGiI4DQCV80EWEkiTFxcU9evTozaexsbHlEwkA\nADk0bdp01qxZwcHBSUlJorMAUAmlF+jCwsLPP/+8YcOG165dez149OhRNze3IUOGFBUVlWc8\nAABKN3Xq1KZNm/bt27ewsFB0FgDKr/QCvXTp0tWrV3fq1MnOzu71YNu2bfv27bt27VpupgoA\nEE5dXf3333+/f//+zJkzRWcBoPxKL9Br167t3Lnz7t277e3tXw/WrVt306ZNAQEBFGgAQGVg\nYWGxZs2aH374ITIyUnQWAEqu9AJ9+/bt1q1bl3ioVatWstsTAgAgXIcOHcaNGzdw4MCHDx+K\nzgJAmZVeoI2MjJKTk0s8lJycbGpqWsaJAAD4WN9//33NmjW5xTeAclV6ge7UqdNvv/22d+/e\nNwcLCwtXrVr1yy+/tGvXrtyyAQAgH21t7c2bN586dWrx4sWiswBQWiXvA/2mb775Zt++fZ06\ndbK1ta1bt662tvaTJ0/i4+P/+usvKyurb775pgJSAgDwgRwdHZcsWTJq1KgWLVq4ubmJjgNA\nCZU+A21lZRUbGztq1Kjc3NxDhw7t3r371KlTGhoaw4cPP3funK2tbQWkBADgw3322We9evXq\n27dvdna26CwAlNAH3UjFwsJixYoVmZmZqampt2/fzsnJycjI+OWXX2rWrFne+QAA+AgrV65U\nV1cfP3686CAAlFDJSzjS09O1tbVNTExkj1+Pq6ur6+vrZ2dnv/l/ektLy/JOCQCAXAwMDDZs\n2ODj49O2bdv+/fuLjgNAqZRcoK2srNq3b79//37Z4/d/Ca50BgBUQh4eHrNmzRozZoyvr6+1\ntbXoOACUR8kFum/fvq6urq8fV2AeAADKTEhIyP79+4cMGXLw4EE1NTXRcQAoiZIL9KZNm0p8\nXNkUFRXFx8dnZ2fb2NjY2NiIjgMAqFzU1dXXrl3r6uq6bNmysWPHio4DQEmUfBHhV199deTI\nEdnjUaNGXb58uQIjvVN0dPSbP/5+//33mjVruri4eHt729raurq6njhxQmA8AEAlVLt27Xnz\n5k2dOvXGjRuiswBQEiUX6EWLFsXExMgeh4aGJiUlVWCkkh07dqx169br1q2TLbnesmXLoEGD\ncnNze/fuHRwc3LZt26tXr7Zr1+7ChQuikwIAKpdRo0a1atXq008/LSwsFJ0FgDIoeQmHhYXF\nvHnz7t+/b2hoKEnShg0bzpw5864v8f3335dXujfMnj3b2Ng4KipKtohtypQpdnZ2p0+ffn2N\n49mzZ1u3bj179uydO3dWQB4AgKJQU1NbtWqVi4vL999/P336dNFxACi8kgv0Dz/8MHz48OXL\nl8uebtu27T1fomIK9MWLF0eMGOHo6ChJ0tOnT5OSkhYvXvzmDiHNmjUbOHBgREREBYQBACiW\nGjVq/PLLL3379u3QoUPTpk1FxwGg2Eou0AMHDuzcufPt27fz8vJ8fX2/++47X1/fCk72lqKi\nIl1dXdljHR0dNTW1v+9JZG1tnZeXV+HRAAAKoEePHr169Ro8ePCFCxde/0IBgI9QcoGWJMnY\n2Njd3V2SpPbt27dq1ap58+YVmKoErq6umzZtCgkJ0dPT09bWbt68+enTp3v06PH6hPz8/G3b\nttWtW1dgSABAZbZixQoXF5dp06b9+OOPorMAUGCl78JRq1YtPT29CoxUspCQkFu3bvn6+h48\nePDly5dLly4NCwtbv3798+fPCwsLz549GxAQcPny5eDgYNFJAQCVlLGx8W+//bZkyZKjR4+K\nzgJAgSnMLhydO3detWrVjRs32rdvb2RkNGjQIC0trcGDBxsZGenq6np6eh49enTixInDhw8X\nnRQAUHm1bdt25MiRQUFBWVlZorMAUFQKswuHJEnDhg0LDAzcsGFDZGTk9evX//rrL21tbQMD\ng1q1anl7ew8ePNjNza1ikgAAFNf8+fMjIyMnTpy4Zs0a0VkAKCQ12bbKb/n999+HDx/+gRfk\nlfgVlEloaOioUaOys7MNDAxEZwEAlIELFy40b95848aNvXr1Ep0FQMkKCgq0tbWjoqK8vLxE\nZ3mbwuzCAQBAWWnSpMmUKVNGjx7t4+NjaWkpOg4ABaMwu3CUn5ycnPffm+r58+cVFgYAUDFm\nzZp18ODBkSNH7tixQ3QWAArmnQX6tf3798seZGdn37t3r2bNmsbGxuWc6mMkJiaOHDlSkqTI\nyEi5XlWnTp0PWYWi9CtVAEClVKlSZd26dU2aNFm9evXQoUNFxwGgSEov0JIkHT9+/Kuvvrpw\n4YIkSfv27evQoYMkSV26dBk/fry/v3/5Bvxg2dnZhw8flvdVDg4OV65cyc/Pf88527Zt++67\n72S3EAcAKA1nZ+c5c+aMHz++RYsWsjvdAsCHKL1Ax8TEtGvXTltbu3379gcOHJANZmZmnjt3\nLiAgIDo6ukmTJuUc8oPUq1fv6tWrH/HChg0bvv+E8+fPf1QiAEBlN2HChF27do0cOTIyMpKJ\nEgAfqOR9oN/09ddfW1paxsfHr1279vWgmZnZ5cuXLS0t58yZU47p5KGjo9OwYcNS2zAAAK+p\nq6uvWbMmJiZm1apVorMAUBilz0CfOXNm0qRJ1tbW6enpb46bm5uPGjVq/vz55ZatZMXFxUlJ\nSXfu3MnOzpYkqWrVqnXq1LGxsangGAAA5WBvb//1119Pnjy5Y8eO/DYB8CFKL9BPnz591w8U\nKyurnJycso70TllZWd9+++2GDRsyMjLeOmRrazts2LBJkybp6upWWB4AgHIYP378tm3bRo4c\nuXfvXtFZACiA0gu0paVlQkJCiYdOnDhRo0aNso5UsrS0NG9v76SkpDp16gQEBNjZ2enr60uS\n9OzZs8TExOPHj8+YMWPr1q1Hjx41MTGpmEgAAOWgrq7+66+/urq6btiwYdCgQaLjAKjsSi/Q\nAQEBy5cv79Gjx5tdOSsra8GCBWvWrAkODi7PeP9v+vTpKSkp4eHhvXv3/vvRoqKi0NDQsWPH\nzp49e9GiRRUTCQCgNOrWrTt9+vQvv/yyXbt2FhYWouMAqNRKvpX3m9LT0z08PNLS0lxcXC5e\nvOjq6ipJUkJCQn5+vq2tbUxMTMX8oLGysgoICPjtt9/ec06/fv2io6Pv3btXtt+aW3kDgCp4\n+fKlp6dnzZo1ubUKUBlU5lt5l74Lh6Wl5fnz54cPH3737l1Jki5dunTp0iVDQ8PRo0efO3eu\nwv6b/vjxYwcHh/ef4+zs/PDhw4rJAwBQMlWqVFm9evW+ffu2bt0qOguASu2DbqRibm6+fPny\nZcuWZWRkZGdnGxoaVvzHWzVq1Lh8+fL7z4mNja2wNdkAAOXj4uIyderU0aNHt2jRwszMTHQc\nAJVU6TPQrz1+/PjOnTvJycnJyclPnjwpv0wl6tatW0RExIIFC0q8a2Bubu7MmTN37NjRt2/f\nCg4GAFAm06dPNzc3/+qrr0QHAVB5lb4GWpKkU6dOTZo06ezZs///MjU1L2aP4QAAIABJREFU\nPz+/RYsWVdiNS548eeLv73/x4kVDQ0MPDw8bGxsDA4Pi4uKcnJy7d+/GxMQ8f/7c19d37969\nZb5SmTXQAKBSzp496+3tvXXr1q5du4rOAqiuyrwG+oNu5d2mTZuXL1/6+PjUrVtXV1c3Nzc3\nPj7+yJEj3t7eMTExdevWrYCgxsbGp0+fXrZs2fr1648dO1ZUVPT6kKamZpMmTYYOHTp06FAN\nDY0KCAMAUGLNmjUbP358cHBwy5YtjY2NRccBUOmUPgPdpUuX2NjYQ4cO1atX783x2NjYDh06\n+Pv7b9y4sTwTliAvL+/+/fuyOxEaGRnZ2tpqaWmV37djBhoAVM3z589dXV39/PxWrlwpOgug\nohR7Bjo6Ovqrr756qz1LktS4cePg4OAVK1aUT7D30dHRqVOnTsV/XwCAitDT01u1apWfn1/P\nnj3btm0rOg6AyqX0iwifPn1qbW1d4qFatWr99ddfZR0JAADxWrZsOXLkyBEjRuTk5IjOAqBy\nKb1Am5ubv+tW3vHx8ebm5mUdCQCASmH+/PlqamrTp08XHQRA5VJ6gW7Xrt3SpUt37Njx5mrp\n4uLi7du3L1u2rGPHjuUZDwAAYfT19VetWrV06dJTp06JzgKgEil9DfTMmTP37t3brVs3S0vL\n+vXr6+vry3bhSE9Pt7KymjlzZgWkBABACH9//4EDBw4bNuzSpUs6Ojqi4wCoFEqfga5Vq9b5\n8+cHDx784sWLI0eO7Nq168iRIwUFBcOGDbtw4cK7lkcDAKAcfvzxx6dPn86ZM0d0EACVxQfd\nytvGxmbt2rXFxcXp6em5ubkGBgaWlpblnQwAgMrA1NR06dKlAwYMGDBgQIMGDUTHASBeKTPQ\nGRkZp0+flj1WU1OzsrJydHS0tLRctmxZxd/NGwAAIXr16tWhQ4dRo0Z9yO17ASi99xXoEydO\n1K1bd8aMGW+NX7lyZezYsQ0bNrxz5055ZgMAoLL4+eefL1269Ntvv4kOAkC8dxbotLS0nj17\n5uTk+Pn5vXWoUaNGS5YsSUtL69ChQ15eXjknBABAPFtb2+nTp0+dOjUjI0N0FgCCvbNAr1q1\n6tGjRytWrPjXv/711iE1NbVx48YtXLjw1q1b69atK+eEAABUChMnTrS1tZ00aZLoIAAEe2eB\n3rFjh4ODw9ChQ991wtixY62trdeuXVsuuQAAqGSqVKkSGhq6cePGyMhI0VkAiPTOAn3v3r1m\nzZqpq7/zhCpVqnh6esbFxZVPMAAAKh0PD4/hw4cHBwezghFQZe/sx8+ePatWrdr7X1ytWrX8\n/PyyjgQAQOU1b9683NzcuXPnig4CQJh3Fuhq1ardu3fv/S++efOmmZlZWUcCAKDyMjIyWrBg\nwffff5+QkCA6CwAx3lmgmzZtevjw4cePH7/rhNu3b588edLT07N8ggEAUEn179+/bdu2bAsN\nqKx3FuhBgwbl5Pwve3ceF1W5/wH8O8zKMMwM+w4qICBmP5fMXG6LLVftKmZumVpmubVpruUC\nLllpuZfcm93SUtOrZSl1b5pSmkaaiiYqKiA7CDPDwLAO8/vjMMdxWAcGzgzzeb/mRWfOeWbm\nCxPyOc8853lKX3755ZqamvpHS0pKJk2aVFNT88ILL7RjdQAAADZp69at586d27lzJ9eFAAAH\nGg3QY8aMefzxx7/55psBAwZ88803Wq2W2V9YWLhjx45evXolJSWNHj366aef7qhSAQAAbEWX\nLl2WLFny1ltvFRYWcl0LAHS0RgM0j8fbv3//sGHDzp0798wzzygUCjc3N7lc7u3tPX369IyM\njPHjx3/11VcdWSsAAIDtWLBggY+Pz6JFi7guBAA6WlNLeSuVyoSEhISEhIkTJ3bt2rW6upqI\nIiIiXnzxxV9++WXv3r3Ozs4dVScAAIBtEYlE8fHxX3zxxc8//8x1LQDQoQTNthg2bNiwYcM6\noBQAAAD7Mnjw4BdffHHWrFnJyclisZjrcgCggzTVAw0AAABN++CDD9Rq9bp167guBAA6DgI0\nAABA67m7u69bt2716tXXrl3juhYA6CAI0AAAAG0yZcqUwYMHY1poAMeBAA0AANBWn3zyyZkz\nZ/bs2cN1IQDQERCgAQAA2io8PHzx4sVvvfWWRqPhuhYAaHcI0AAAAFawePFiV1fXuLg4rgsB\ngHaHAA0AAGAFYrF43bp1W7ZsuXTpEte1AED7QoAGAACwjlGjRj355JNz5szB1YQAnRsCNAAA\ngNVs2rQpKSlp//79XBcCAO0IARoAAMBqwsLC5s2b99Zbb5WWlnJdCwC0FwRoAAAAa1q6dCmf\nz1+7di3XhQBAe0GABgAAsCapVPr++++vX78eaxMCdFYI0AAAAFY2fvz4wYMHv/7661wXAgDt\nAgEaAADA+rZs2XL8+PHvvvuO60IAwPoQoAEAAKyvR48ec+bMmTt3bkVFBde1AICVIUADAAC0\ni7i4uPLy8g8++IDrQgDAyhCgAQAA2oVcLn/33Xffe++9tLQ0rmsBAGtCgAYAAGgvU6dO7dev\n3/z587kuBACsCQEaAACgvfB4vE2bNh06dOjHH3/kuhYAsBoEaAAAgHbUu3fvl19++fXXX6+s\nrOS6FgCwDgRoAACA9rVmzRqVSrV582auCwEA60CABgAAaF/u7u6rVq1atWpVdnY217UAgBV0\nhgBdUlKyePHiq1evcl0IAABAw1555ZWoqKhFixZxXQgAWEEnCdDvv//+jRs3uC4EAACgYU5O\nThs3btyzZ8+JEye4rgUA2krAdQEtNX369MYO6XQ6ItqyZcu3335LRJ9++mnHlQUAANAyDz30\n0JQpU958881z587x+XyuywGA1rObAL1jx46mG/zvf/9jNhCgAQDANq1du7Z79+6fffbZyy+/\nzHUtANB6djOEY+7cuXw+///+7/9+/PFH1b3++usvItq7dy9zl+tKAQAAGubr67tkyZKlS5dq\nNBquawGA1rObAP3RRx+dOXOGiIYNG/b222/zeDylkVwuJyIXFxfmLteVAgAANGrevHmurq7v\nvfce14UAQOvZTYAmon79+v3xxx9r1679/PPPe/ToceDAAa4rAgAAsIxYLF6zZs1HH3108+ZN\nrmsBgFaypwBNRAKBYNGiRZcuXYqKinr22WdHjhyZmZnJdVEAAAAWGD9+fP/+/d9++22uCwGA\nVrKzAM0IDQ09evTov//971OnTvXo0QNXDQIAgH3ZtGnTf/7zn19//ZXrQgCgNewyQDNeeOGF\nlJSUp59+Oi4ujutaAAAALNCnT5+JEye++eabtbW1XNcCABaz4wBNRN7e3nv27ElISHjrrbdC\nQ0O5LgcAAKCl3n///WvXru3evZvrQgDAYnYzD3QThg0bNmzYMK6rAAAAsEBAQMC8efMWL148\nevRoFxcXrssBAAvYdw80AACA/Vq8eLGTk9OHH37IdSEAYJnOE6Bv3rz5+OOPP/744xY96tat\nWyKRiNekmTNnEpHBYGifwgEAwEFJpdKVK1e+9957mFEKwL7wOk0uvHDhQu/evcnCpGswGE6d\nOlVRUdFEm8OHD2/atEmr1cpksrZWCQAAYKK2tvbBBx+Mjo7+/PPPua4FwLZUVVWJxeJTp04N\nHDiQ61rMdYYx0IzIyMhLly5Z+igejzd48OCm22CuewAAaCdOTk6bNm0aMmTInDlzHnjgAa7L\nAYAW6TxDOCQSSc+ePXv27Ml1IQAAABYYOHBgTEzMm2++2Wk+Ewbo9OyvB9pgMKSlpd26dUur\n1RKRQqEIDw8PCgriui4AAIBWWrduXY8ePQ4ePDhmzBiuawGA5tlTgFapVGvWrNm1a1dBQYHZ\noeDg4OnTp8+fP9/Z2ZmT2gAAAFqtW7dur7322oIFC55++mmxWMx1OQDQDLsJ0Lm5uYMGDUpL\nSwsPDx8+fHhISAgza2ZJScnNmzcTExOXL19+4MCB48ePu7m5cV0sAACAZZYvX75r167Nmzcv\nWLCA61oAoBl2E6CXLVuWlZW1b9++sWPH1j+q1+vj4+NfffXVuLi4jRs3dnx5AAAAbeHq6rpi\nxYpFixZNnjzZ19eX63IAoCl2cxHhkSNHJk+e3GB6JiI+nz979uxx48YdPHiwgwsDAACwilde\neaVLly5xcXFcFwIAzbCbAF1UVBQaGtp0m6ioqPz8/I6pBwAAwLr4fP6GDRv+9a9/tWJWVgDo\nSHYToP39/S9evNh0m/Pnz/v7+3dMPQAAAFY3dOjQJ598EsOgAWyc3QTomJiY/fv3r1+/vrKy\nsv7RsrKyFStWHDp0aPz48R1fGwAAgLWsX7/+2LFj//vf/7guBAAaZTdLeavV6qFDh/7555+u\nrq79+/cPCgqSyWQGg6G0tDQjIyMpKUmn0w0ZMiQhIcHqC27Hx8fPnDkTS3kDAEDHeOWVV37/\n/ffz5887OdlNPxeA1WEpbytQKpWnT5/etm3bzp07T5w4odfr2UNCobBv377Tpk2bNm0an8/n\nsEgAAIC2i42N7d69++7du59//nmuawGABthNgCYikUg0d+7cuXPnVlRUZGZmMisRyuXy4OBg\nkUjEdXUAAADW4e/v/8YbbyxdunTs2LFYVwXABtnlZ0MSiSQ8PLxPnz59+vQJCwtDegYAgE5m\n8eLF5eXl27Zt47oQAGiAXQZoAACAzs3V1fXtt99evXp1cXEx17UAgDkEaAAAAFs0a9Ysd3f3\ndevWcV0IAJhDgAYAALBFIpFo1apVGzduzMzM5LoWALgHAjQAAICNmjBhQnR0dGxsLNeFAMA9\nEKABAABsFI/HW79+/RdffHH58mWuawGAuxCgAQAAbNcjjzzy+OOPL1myhOtCAOAuBGgAAACb\n9sEHHyQkJPz8889cFwIAdRCgAQAAbFqvXr2ee+65JUuWGAwGrmsBACIEaAAAANu3evXqixcv\nHjhwgOtCAIAIARoAAMD2hYSEzJkzZ9GiRVVVVVzXAgAI0AAAAPZg6dKlarX6008/5boQAECA\nBgAAsAdubm4LFy6MjY3VarVc1wLg6BCgAQAA7MMbb7zh7Oz80UcfcV0IgKNDgAYAALAPEokk\nNjZ2/fr1eXl5XNcC4NAQoAEAAOzG1KlTw8LCVq1axXUhAA4NARoAAMBuODk5rV69+p///GdK\nSgrXtQA4LgRoAAAAezJixIi//e1vy5cv57oQAMeFAA0AAGBn3n333QMHDvzxxx9cFwLgoBCg\nAQAA7MyDDz44atSopUuXcl0IgINCgAYAALA/q1evPnr06IkTJ7guBMARIUADAADYn+jo6AkT\nJqATGoATCNAAAAB2KS4uLikp6ccff+S6EACHgwANAABgl8LCwqZOnbp06VKDwcB1LQCOBQEa\nAADAXsXGxl65cuWbb77huhAAx4IADQAAYK8CAgJefvnlt99+W6/Xc10LgANBgAYAALBjS5cu\nzcnJ2bNnD9eFADgQBGgAAAA75uXlNWfOnGXLllVVVXFdC4CjQIAGAACwb4sWLdJoNJ9//jnX\nhQA4CgRoAAAA+6ZUKufNmxcXF1deXs51LQAOAQEaAADA7r355ps1NTXbt2/nuhAAh4AADQAA\nYPdkMtmiRYveffddrVbLdS0AnR8CNAAAQGcwe/ZsiUSyefNmrgsB6PwQoAEAADoDiUTyzjvv\nrFu3rri4mOtaADo5BGgAAIBO4qWXXvL09Pzwww+5LgSgk0OABgAA6CSEQuHy5cs3bdqUn5/P\ndS0AnRkCNAAAQOcxadKkkJCQ9957j+tCADozBGgAAIDOg8/nx8XFbd++PTMzk+taADotBGgA\nAIBOZcyYMffdd9/q1au5LgSg00KABgAA6FR4PF5sbOxnn3127do1rmsB6JwQoAEAADqb4cOH\nDxo0CJ3QAO0EARoAAKATiouL27179+XLl7kuBKATQoAGAADohB5++OHHHnssNjaW60IAOqFO\nFaBVKlV6ejrXVQAAANiElStXHjx48MKFC1wXAtDZ2FOATk5OHjFiRJcuXYYMGfLxxx/r9Xqz\nBu+//37Xrl05qQ0AAMDWPPTQQ0899RQ6oQGsTsB1AS116tSpoUOHVlZWSqXSnJyckydP7tu3\n75tvvnFzc+O6NAAAABu1evXqBx54ICkpqX///lzXAtB52E0P9Nq1a2tra7/55pvS0lKtVvvR\nRx/99ttvTz31VFlZGdelAQAA2Ki+ffs+/fTTcXFxXBcC0KnYTYBOTk4eP358TEwMj8cTi8Vz\n58798ccfL168OG7cuPpjOQAAAICxZs2aH3/88ddff+W6EIDOw24CdF5eXrdu3Uz3PPbYY59+\n+mlCQsK8efO4qgoAAMDG3XfffTExMatWreK6EIDOw24CtI+PT/3riCdPnrxkyZLNmzevW7eO\nk6oAAABs38qVK48dO5aYmMh1IQCdhN0E6Geeeeb777/funVrdXW16f41a9ZMnTp14cKFc+fO\n1el0XJUHAABgs6Kjo8eOHbt06VKuCwHoJOxmFo7ly5d/++23r7322qFDh3766Sd2P4/H+/e/\n/61QKDZu3MhheQAAALZs5cqV0dHRP//882OPPcZ1LQB2z256oD08PM6dOzd79uyePXuaHeLx\neJs2bTpw4EBoaCgntQEAANi47t27T5gwYdmyZVwXAtAZ8AwGA9c12Lr4+PiZM2dqtVqZTMZ1\nLQAAAK1048aNqKiow4cPP/XUU1zXAtC8qqoqsVh86tSpgQMHcl2LObvpgQYAAIC2CAsLmzx5\n8jvvvIO+M4A2QoAGAABwFCtWrLh06dKRI0e4LgTAvtnNRYTNunnz5owZM4jo6NGjLX9UWlra\ngAEDzGb2MFNZWUlEOF8HAAB7FxIS8sILLyxfvnzEiBE8Ho/rcgDsVecJ0Fqt9tixY5Y+KiQk\nZMeOHeXl5U20+emnn/71r3/hHxoAAOgEli5dGh4e/u23344ePZrrWgDsVecJ0JGRkZcuXbL0\nUU5OTk8//XTTbYqLi//1r3+1ti4AAAAbEhQUNH369GXLlo0aNcrJCSM5AVqj8/zmSCSSnj17\n1p/kDgAAAEy98847t27d+s9//sN1IQD2yv56oA0GQ1pa2q1bt7RaLREpFIrw8PCgoCCu6wIA\nALAPfn5+M2bMWLZs2ZgxY/h8PtflANgfewrQKpVqzZo1u3btKigoMDsUHBw8ffr0+fPnOzs7\nc1IbAACAHXn77bc//fTTvXv3Tpo0ietaAOyP3QTo3NzcQYMGpaWlhYeHDx8+PCQkxMXFhYhK\nSkpu3ryZmJi4fPnyAwcOHD9+3M3NjetiAQAAbJqXl9esWbNiY2PHjx8vENhNGACwEXbzO7Ns\n2bKsrKx9+/aNHTu2/lG9Xh8fH//qq6/GxcVt3Lix48sDAACwL4sWLdq+ffuXX375wgsvcF0L\ngJ2xm4sIjxw5Mnny5AbTMxHx+fzZs2ePGzfu4MGDHVwYAACAPfLw8HjttddiY2Orqqq4rgXA\nzthNgC4qKgoNDW26TVRUVH5+fsfUAwAAYO/mz5+vVqs///xzrgsBsDN2E6D9/f0vXrzYdJvz\n58/7+/t3TD0AAAD2zs3Nbd68eXFxcU0vKAYAZuwmQMfExOzfv3/9+vXMwtpmysrKVqxYcejQ\nofHjx3d8bQAAAHZq3rx5NTU18fHxXBcCYE94BoOB6xpaRK1WDx069M8//3R1de3fv39QUJBM\nJjMYDKWlpRkZGUlJSTqdbsiQIQkJCTKZzLovHR8fP3PmTK1Wa/VnBgAA4NyHH3743nvv3bp1\ny9XVletaAO6qqqoSi8WnTp0aOHAg17WYs5tZOJRK5enTp7dt27Zz584TJ07o9Xr2kFAo7Nu3\n77Rp06ZNm4YJ4QEAACwyZ86cjRs3bt68+Z133uG6FgD7YDcBmohEItHcuXPnzp1bUVGRmZnJ\nrEQol8uDg4NFIhHX1QEAANgliUTyzjvvLF68eNasWe7u7lyXA2AH7GYMtCmJRBIeHt6nT58+\nffqEhYUhPQMAALTFSy+95Onp+eGHH3JdCIB9sMsADQAAAFYkFAqXL1++adMmzAYL0BII0AAA\nAECTJk0KCQlZu3Yt14UA2AEEaAAAACA+n79y5crt27dnZmZyXQuArUOABgAAACKiZ5555v77\n71+1ahXXhQDYOgRoAAAAICLi8XixsbGfffbZtWvXuK4FwKYhQAMAAECdYcOGDR48eOXKlVwX\nAmDTEKABAADgrtWrV+/du/fixYtcFwJguxCgAQAA4K7Bgwc/8cQTsbGxXBcCYLsQoAEAAOAe\na9asOXTo0JkzZ7guBMBGIUADAADAPfr27RsTE7N8+XKuCwGwUQjQAAAAYG7VqlU///zz8ePH\nuS4EwBYhQAMAAIC56OjoiRMnLl26lOtCAGwRAjQAAAA0YNWqVWfPnk1ISOC6EACbgwANAAAA\nDejSpcuLL764ZMmS2tparmsBsC0I0AAAANCw5cuXp6amHjhwgOtCAGwLArQ17dmzJzIyMiIi\n4ocffuC6FgAAgLby9/efOXPm0qVLa2pquK4FwIYgQFtNUVFRbGzs77//fuLEib1793JdDgAA\ngBUsWbIkJyfnq6++4roQABuCAG01x44d+8c//qFQKPz8/L744guuywEAALACLy+v119/ffXq\n1eiEBmAhQFvN7du38/PzXV1du3fvnpiYyHU5AAAA1jFv3rz8/Pzdu3dzXQiArRBwXUDnodfr\nExISJk2aFBwcPG3atBs3bvB4vGYeYyD6lajq3p1SInG9ljwiZUPPoCQyexEBkasldQMAADTJ\nw8Pj1VdfXbVq1XPPPScQIDkAIEBbj5+f38yZM52dnd3d3ZVK5Z07d7y8vJp5TD7RKCJ1+xdX\nP2cr6n384HbvXSGRrMmHmAV9FyKRyV0ZkdC4zSeSN9LSNO6bNnMiUjS0LSJyIQAA6GBvvfXW\n1q1b9+zZM3nyZK5rAeAeArTVPPnkk/Hx8U8++aRWq9VoNJ6ens0/xpdI1cihUqLqejuriUrr\n7awl0tTbWVavY7uSSNfcnnKiinv3qIkMjTeoIiozbqvqPaFpY8O95wmmh2qItPXqbwnTBC8n\n4hMRkZhIatzJnhKwkZ09K2DDumnXPnuawT4bu8GePJieRbT8YwEAADvn4eExZ86clStXTpw4\nEZ3QAPgdsBpfX98XXnghNjbWyclp+/btzY/fICKivLy82tpaZ2fnZlu6uroKBALybnOhtkxP\nVGLcNj0xMN1vGtNNzxPYrK8jqqz3qBIi/b1Hs43Pw56WsO3Zl27w5KQVzPrgGRIis7fdmUhy\n757643nMPigwPWGo/0Kmnff1j5q9HHu2YPa6ps1Ma67/IQYAdGrz58/ftm3b3r17n3/+ea5r\nAeAYArQ1vfzyy/n5+Z6eniNGjGhJ+9zc3MDAQGut8CQWi6VSaWNHeTyeUtlgfykRkVQqFYvr\nj7wmInJxcRGJRPX3CwQCV9cGRls3tl8mkwmFQrOdIpHIxcV8TEb9lnw+Xy6/J4EKhUKZTEYu\nd0d0SPwkZuchCoXCycnJ/CHN1dmwJiJ1gx8LmGZ3Vv0OfqrXx2+oN6Sn/lOx5wAs088x7tR7\nTg0R+7+Y2fObfoZADX1w0RJsqjbN667Gf13Y7n+2GTsOh/1AgN3DtmFTO/twt3tbMmOEGvsQ\nAADagYeHx+zZs1euXDlhwgR0QoODwy8Al/z8/G7fvl1ZWZeGqqurS0vrZzFzarXaYDA00aCk\npESv1zd2tKysrKqq4ZRUU1Oj1TY8nKK8vLyion76a/Qh9b8XlUpFRBqNpv4JQ2lpaXX1PQNW\nDAaDWm0+Nlyr1ZpNotT0d2oRs4xudjYil8v5/LruWbPk7ebm1mAz0xOPuk8PiIhIqVQyn044\nOTkpFAom/7EnMHU76Z6dpq9o+nLtyzSmm0b/CqJyIro3i7PJ2/R0go31bIJnByaxT55u3GAP\naYlqTB5V/4yiQUzgZvM004POBnombTPhm23DRHzmgexYfOanywzCYbrkmcc2eGkvgONZsGDB\nxx9//PXXX0+aNInrWgC4hABtNefPn588eXJhYaFAINi6devJkyeb6PFlBQQEdEBtDqJ+7K6o\nqCgvL2+iARPrWaYnJ2bnAKYpX6/Xl5SUNPgkbMpXqVSmDzE9c2Dbm55+1D89aBobyp2dnSUS\nSYMbbARn0zwT8dmYzp4nsL3+TEBnnoFt5uLiInIT1f8coEOxQ3eYhM1+FMAGeqbfnb3L/IyZ\n6M82ZkbyZBNVmGR9piWT4Bv8lIAlMQZuZ5MNiTFeM53lTOBmwrebcdgMk92ZxkwDJZGgoYE9\nALbNw8Nj1qxZcXFx48ePRyc0ODL83281vXv3vnz5MtdVODQej9dxHbTtpsFUzZ4JmB5lgzjb\njO2SZzfY4M6cG9y5c4eJ/uwTMo9lTy0qKyt1OrNrS80x2V0ikTg7O7O940zPOpPUmVzOjJlh\nYjebxZk3iGnMjLFhtt3c3JoeZURiYx9wB7zDTFhnEjZzkSsbwVXGr0zXOLNfb4zmKqJCIq3x\nGZiOdibxm42rYTEp3JVIRKQwDmpnQrab8a6cSEzkSiQjEhMpjFmcbYDrVqEDLViw4JNPPkEn\nNDg4BGgA2yIQCNjTAA7PB5jAzQzdYeO1TqerrKxkQzzThuloZ5J3bW2tRqMhY3C/ceOGXq9n\nGjBjh5gnNPtkwBQTtZnYzURwJqkzfeQKhUIgECgUCmb0PNNT7urqKhaL5XI5c1ehUIjFYplM\n1tjw/eaxYd261+wyaZsZd850dZcQVRNpjIGb6QVXGduUERUTqY3d6mqiSqIyk1Euppgg7kYk\nJXImUhj7vOVErkRSIhciJdVdNuBKJDduK0wGrAO0gKen58yZM+Pi4iZMmMAOWgNwNPhXEwAa\nwHQGt2uCZzI3E6mZaM6EbCZwM13jJSUlNTU1arWaGVFTXl6u0WgyMjKqq6vVajXTgHmexgbE\nu7m5MT3iTMJ2cXGRy+USiUQmk7Ebrq6uTEaXy+UuLi5SqVSpVLqZCd0uAAAgAElEQVS4uLi4\nuJheeNpWTtbrPmf6xcuIKonUxkReQlRKVE6kJSohKicqI9IQ5RGVEamJSo0xvX53uIjIlUhB\npDBmbiZkK4nkxj1y4x6lsaX5VcHgKBYuXMh0Qj/33HNc1wLADQRoq6murp42bVpubm55efnC\nhQtHjRrFdUUANk0sFovFYitmdGZsOpPI1Wo1k8XLysoqKyvVajWzX6VSMf3fKpWK+W1lDjEb\nOp2u/sWyCoWCSdUKhUJmpFAoTO+6ubkxG66urnK5XKFQMD3o1vrWzAmI3NoWx5kRJiVEJcbe\nbg2Rxhi+ma/FROn37jGbt15qDNxMnmaztbKRG1ZB6iyYTujY2Njx48ejExocEwK01Rw6dEgq\nlR49erSoqKh///4I0AAdjM/nu7m5tTGRMylcq9XqdLqysjKVSsVsaLXakpKSsrKy0tLSkpIS\njUaTnZ1dWlqq1WrVarVWq2U6yE2fytnZWW6kVCrl91IaMVmc2WjJlPDWISWSErVguSdzJcao\nbXZTEWmISoiyidQmN9MR9UJjknZr6OZ+790WTzIJnFi0aNH27dv37ds3ceJErmsB4AACtNV4\neHgUFxcTkVar9fDw4LocAGiNtqRwJnxrNBomgpeUlDB31Wo1uyc7OzslJUWlUpWUlKjVao1G\nYzqtpFgsNs3TbkZKpdJsg9nmoPOPGcgR1OL2VffmaeamMt7uEKUSFRvvms6RIyByb+7mQeSJ\nyUy44enpOWPGjFWrVo0fP950xn0AB4EAbTWPPvpofHx8ZGRkcXHxvn37uC4HADpa68K3TqfT\naDRMzma/qlQqZlulUmVkZDAbKpWKGQ7OPlYul7u5ubm7u7u7u3t4eLg3wsPDo5XXU7adiMi7\nxZdjGkyydXG9202iP0zusj8GIZEHkYcxUnsQeRk3PIwh24vIvb2+RYe1ePHi+Pj4ffv2TZgw\ngetaADoaArTVHD582MnJKSUl5fbt2yNGjEhOTm7+pFyno7Vr6d41RGwah5PESSTU3p9uu7pS\nB09r2gHflBkej1owPXmLWFS8TEYtHBBs/xMRWkoqlUqlUj8/vxa2Ly0tZcM0s1Fs4saNG0VF\nRcy26SJHrq6uHh4eXl5eHh4enp6eHkaenp7sTk9PT85yNoNn7FpuCS1RMVER0R2iontv54kK\njdvsZO4CIk+TPO1F5Gly8zHu5/QHYF+YTuiVK1eOGzcOndDgaBCgrebUqVNPPfUUj8cLCQkR\nCoV37tzx9m6u16W6mtLTqbKymWamSkrISmvvtZfaWtJomm9mRRoNWWk59AZUVlJz8yK3l47/\nSdoLZ2eSSJpqwOdT02u+NP0MTRxt4pmbOOTiQg0G08ZeSKGg+nFEKiWxmIhkRDJ2DIVEQoGB\nFBh4T0ulkng8ImJmKdFoNKqKimKdjsncRUVFKpWq6MqVayUlxcXFTP5mJgtXESkUCh8fH08j\nb29vLy8vZtvLy8vHx8fLy6vjBmo3jZkqJKS5ZpXGkH2HqMC4wey5arLNjqNREPkY47W3SbD2\nNt68iHDVnBEzJ/T+/fvHjx/PdS0AHQoB2mrCwsLOnj07depUpluoRcOgFQratav9SwNogbac\nKrT8vM5goHqLtDdMq6Vml2asqKBG5pNuaQOVqtFDej2ZrDdpronTNrWaDPfOEse8ik7X8Nly\nWRmZDINuprYGf9SN/PzZUcRdGy60IRoNaTR0/XpdaUKhvrbWYERE+UTk5MQ3MgiFtc7OAoFA\nKBQKhUKBQCBQKgWmCVssJqn07l0nJzIuVt/AXbOTEJGIXExm7jD9HMPsgaanKAIBuZpcgahQ\nkLMTBREFNfkpk4Yon6iQ6A5Rocn270T5xp3Mh4U8Ywe2N5GvMVL7GXf6EfkQNXl+15n4+PjM\nnDlz5cqVY8eORSc0OBQEaKt5/vnnExMThw4dWllZuWnTJszsA3ZGLGY6OFvD8cZd2LqqKior\nM99ZP9mXlpoPIbv3lMOF7p5ZVVZWajSaao2mtLBQV1ys0Wi0Wq1Wq9VoNDyNRqdSlZWVMSHb\nRSDwlEplMplUKpXJZDKp1M3JSSqVOjs7S6VS55oagU53N/EXFZmfjZjWaXYaY3YS0sT5T7NM\n47hp/jYN2UxfvjeRrxMpFFRFVEFkEFOtlMqJNETFcjrLJx2Rjk9lcmM3tpQkYlISyfnkKa+b\n489PRh5CcifyFlKgrO5vr/GzgrvFmJ1v2IOFCxdu3779P//5z7hx47iuBaDjIEBbjUgkksvl\nFy5ccHJykjf98TEAQLsSiRoYNNK28xxxc1cD6vX6goKCwsLCnJycgoKCnNzcvLy8goKC7Ozs\ngoKC3MuX1cYPH+RyeUBAgK+vb4Nfpa1LkKbZ2ix2m/bQm36yYXr+YPo5gGl7NqObPmd5OdXN\nF666G/erq6mklGqIqolKtFRVQ4VEOVVUWUYGolqiWg1RiwebmXbGs28cO7aHTfls9GcjOHtI\nLic+v+6yB+bZhEKSyequXmBGBDGPanDIUIv5+PjMmDEjLi7u2WefRSc0OA4EaKtJSEjIy8tL\nTk5OTU0dM2ZMcnIy1xUBAHQcPp/v5+fn5+fXq1evBhtUVFQUFBQw8TorKys/Pz8rK+vKlSs/\n/fQTE7WZDmwmXvv5+QUEBAQGBvr7+wcHB/v5+QUGBvr4+DQa0aTSe/puPVsxx3X7KyXKJsqq\noNvllE+Up6fMErrDjBLRUBETr3UkqSQvIkUlKXWkJFLWkFhLbkSyWuJr6haAZJM9m+CZPcXF\ndaOk2IsomFML5syhsaFHUil5eJC7O7m7k4dH3Y25y+xh9zc0BmbhwoXx8fEHDhwYO3asdX9g\nADYLAdpqHn300cGDBxORv7+/uoWjPAEAHIZEIgkODg4ODm7waHV1NROp2a+3b98+e/ZsdnZ2\nZmYmM6OIUCj09fUNCgoKCAjw9/cPCgoKDAwMCgoKCQnx9fW1g4FzMqIIogiJyShpk6BfTVRA\nlE2UT5RDlGv8+hdRLlG+cQF2OVEAkR9RAJE/UQ+iQCI/omAinxb8VWeuQ2A61KurqbSUKipI\npaLiYioqouLiuo1bt6ioqG6PyXQupFCQl1ddmPb0ZDZ8PTy2PfZYwsKFYyIjnby9ycurLV3a\nAHYBAdpq2I8dN2/ePGXKFG6LAQCwL0KhMDAwMNBsRhGj0tLSzMzM7OxsJk/n5ubeunXr119/\nzcrKKigoICKBQMBE6uDgYCZYh4SEBAUFBQUFedpmb3R9QqIAooBGjtYQ5RNlEeURZRHlE2US\nXSA6TJRjXGXdicjHGKyDiPyIAo3PGWxcSp3HqxsT0vIfS3V1XZhmb4WFdRupqXTmDBUVTSks\nfEGlIubDBx6PvLzI05O8vMjLi3x86ra9vYmJ1z4+hOXGwM4hQFvZjh07fv3110OHDrX0AadP\nN3CtT4OYAW32zka+iw676M1srgAAaBWZTBYVFRUVFVX/UEVFxe3btzMzM7OysjIyMjIzM5OT\nkw8fPnz79u3S0lIikkqlXbp0CTEKDg4OCQnp2rWrr6+vPY3ZFTQZr8uJMolyjV+zibKIzhNl\nEuUZ5w9REAUSBRrjNRus/YmaTrNCIfn6kq9vE02ciJa9887+Tz75ac+eIImECgspP5/u3KHC\nQioooMuX67bv3KkbQyISkbc3+fuTtzf5+NRt+PmRj0/dXdMJWABsj/0FaIPBkJaWduvWLeYT\nPYVCER4eHhTU8oVl29FXX3118ODBgwcPClu4ZkRuLj36qGXzQAMwrLUIi3F24dZobHrjJlhU\ndrPTOVv6tC1Zz6XZ9XTYmRMa1MTPs+lVbBp72ibOwRq79stGTlM7ikQi6d69e/fu3esfUqlU\nWVlZ6enpGUZ//vlnRkZGfn4+EYlEImb4R0hISJcuXboa+fv785p4i22TM1F3ogZ+BkS1xq7r\nbKJMomyibKJEohyiLKJy48MbDNaBRD5ELTvLiFu16kJy8pNvvnn69GllY/+r19bWReqcHMrP\np/x8ys2lggI6daru7p07dS1dXCggoC5M+/qSnx/5+ZGvL/n7k48PeXlZ/CMCsCqewWxWIxum\nUqnWrFmza9cu5gM7U8HBwdOnT58/f357zPAfHx8/c+ZMrVYrk8maaJadnT169OjExERbWWXA\nlN0tydGua6M0q/5sX+2h2SmKW6Ets3oxWl1Vg/OmNY0Zf9lCLZkWuuXP2djUy6xm56tu+vtt\n+jeuhd+LdTUWxOt/GmN2mlH/gWYnTmazNZu1Z2Z+YJmd6phmfbP5m01PRcyexLTmli9yaaKi\nooJJ1bdv32aCdVpaWlpaWk5ODhGJxWLTPM1yd++Mq4EX3RusM43BOouI+V9YSORLFGTsvQ42\nbgcR+RLde6Kh1WoHDhwYEBBw5MiRVg5Jr6qiwkLKyaG8PMrNpdxcysujnBwqKKCsLCooqPvN\nZTqwg4LI15cCA+u++vmRvz/5+2NizU6jqqpKLBafOnVq4MCBXNdizm4CdG5u7qBBg9LS0sLD\nwwcNGhQSEuLi4kJEJSUlN2/eTExMzMnJuf/++48fP+5m7d+cFgbotWvXbtiwgV198PTp066m\nfwwAAJpVf2JmRhOBvrFVbBo8C20w99dfMqZ+M7PQb9agfnmmZ6FmpxNmJzmmJzMtX2enQaaZ\n23RCZdOIb7r6o2n4VijIyUmv12t1uuKaGo1Go1arC7Xa/JKS4uLi8vLyEiKxVOrl5eXh4yMP\nCPD19fXx8fEODfXw8eHxePekf/asgD1bsNOhXKX3Bmvm622iLOOQaxFRAFEgUYhxsHUIpYnS\n+k/qP/WFqevXr2+XqpjBIUzCzs6m3FzKyqK8PMrKovz8uv+XnJ0pIID8/Oq+BgeTvz8FBNQF\nbm7XqwdLIEBbwfTp03fu3PnVV181OEuOXq+Pj49/9dVXX3/99Y0bN1r3pVsYoAEAwJruTrdM\nVFNzz1wQpgHd9KzD9CGmi2uabpvOGG16YsB+gGMa8XU6qqzU6/WVlZW1KlVNVVVNTQ1VVgqr\nq5n1zxUtHeBgxI4RYuM+m/UbnPuZHdvDbrBDd9ikzu6p35h5HvaZrbVQSxlRhrGj+jZRpnE7\njaicfqVfH6fHt4RseaXfK9SFKISoK1EXoi5E7f1XND+/Lkzn5lJ2NuXkUE4OZWZSTg4VFhIR\n8Xjk40MBAeTvT0FBdV8DAykoiIKC7p5cgW1AgLYCPz+/4cOH79ixo4k2EyZM+O23327fvm3d\nl0aABgAAM1VVVenp6Tdv3rxx48bNmzdvp6bm3LiRkZFRWVnpLRQGBwd37do1IjCwi79/cHBw\nsJ+fN5tc2aTOxnc207NBnw3x7JkD+0EBu8F27bN7zE4zmsDGdzaFM1GbHS3DdtWziZ9pwEZw\nZj8bzdn2tZ6UJ9lx5PtZ/3nnf0O/fYSeoNtOdJtfN9jag6gbURhROFE4URhR2D1T+bWjigrK\nyaHsbMrMpNxcysysS9i3b1NeXt0b4eNDgYEUGEghIXWROiiIQkLI19ehriuwHbYcoO3mIsKi\noqLQ0NCm20RFRX3zzTcdUw8AADgykUhU/+JFvV5/+/bt1NTU1NTU69evH01NTT15Mj09vaam\nRiqVhhtFRkZGRkZGREQo2mloB5uk2SDO9s2zHfZMLz6bwtlhOWyaZ0YB1dbWJf68vLpwz+R+\nNrWzz2zyscBLROeJnv1pxO9Exr/cPkQhVN6DLnelv8KpthvVdKEaHyIiQSlJs0mWR8o75JpH\nfqUkLyAvHgkEdcNg2JjO9Kwzo/CZKM8MnmEHyTRxja9EQt26UbduDRzS6yk3lzIyKDOTMjMp\nK4syMujkybpR10QkEFBgIHXtSl263P3atSv5+WHGa4dlNwHa39//4sWLTbc5f/68v79/x9QD\nAABghs/nM1ccPvnkk+zO6urqtLS069evX79+PTU1NSkpaefOndnZ2UTk5+cXFRUVERHBRurg\n4GArzAEiENwdBOLdxPrr7cAYxDcWF1+dMmVkQcFvn36qkMnqBuuzgV5ziWovkqaasqVUIKcc\nKak9qfA+yhhKvyuJiESl5JxJ0ixySiVxBhlOEV2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UW7duff311//973+TkpLuu+8+rquDNjBAZ3T27DLd1nkAAA9eSURBVFk+n7969Wqu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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Plot the shrinkage of the coefficients\n",
    "# https://stackoverflow.com/questions/36656752/plotting-cv-glmnet-in-r~\n",
    "#::NOTE::How do I put the feature names on that plot?\n",
    "# https://stats.stackexchange.com/questions/133873/lasso-plot-label-lines-with-names-using-glmnet\n",
    "# https://www.rdocumentation.org/packages/glmnet/versions/2.0-18/topics/plot.glmnet\n",
    "plot(cv_lasso$glmnet.fit, \"lambda\", label = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::PENDING::** <span style=\"color:red\">Discussion here</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### better coeff shrinkage plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Adhoc function intermediate fix\n",
    "#::NOTE::Adapted from\n",
    "# https://stackoverflow.com/a/43327018\n",
    "lbs_fun <- function(lra, ...) {\n",
    "  fit <- lra$glmnet.fit\n",
    "\n",
    "  L=which(fit$lambda==lra$lambda.min)\n",
    "\n",
    "  ystart <- sort(fit$beta[abs(fit$beta[,L])>0,L])\n",
    "  labs <- names(ystart)\n",
    "  #::NOTE:: max gap between biggest and smallest coefs at smallest lambda\n",
    "  #         i.e., 64th (more than that yields an error ... given 100th lambda\n",
    "  #         in original!)\n",
    "  r <- range(fit$beta[,63]) \n",
    "  yfin <- seq(r[1],r[2],length=length(ystart))\n",
    "\n",
    "  xstart<- log(lra$lambda.min)\n",
    "  xfin <- xstart+1\n",
    "\n",
    "  text(xfin+0.3,yfin,labels=labs,...)\n",
    "  segments(xstart,ystart,xfin,yfin)\n",
    "  # https://www.r-bloggers.com/r-add-vertical-line-to-a-plot/\n",
    "  # https://www.statmethods.net/advgraphs/parameters.html\n",
    "  abline(v = log(lra$lambda.min), col = 'darkgreen', lty = 3, lwd = 2) \n",
    "  text(log(lra$lambda.min) - 1.5, r[2], col = 'darkgreen', 'chosen lambda')\n",
    "  segments(log(lra$lambda.min), r[2] - 0.3 , log(lra$lambda.min) - 1, r[2], col = 'darkgreen')\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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t5P4Ao0vCPe5h7u7u7dD9bW1j548IBXpu/duxcXF7dz587KykpCiKamJr9Mm5qa\nDhkyxNDQkMnEr1YBoLcYsY1Svk0J+CPAab3Twc8Pdp/wAj0rqzSrvrm+vrn+ftV9O3072nHE\nTnNzc3x8/JEjR2gHESMo0NCTlJWVhw8fPnz4PxaA1tbW3rlz586dOwUFBXfu3Dl06NDdu3eb\nmpqYTKahoaGlpaWZmZmlpaW5ubm5uTm2AQGAHqTAUji+8PjPsT9P3Tn1+/Hf/+j/IyatgOiJ\ni4vr7OwcOfJdFlbBu0GBhl6nrKzs4ODw3L6PJSUlvEqdk5OTmpr6xx9/VFZWSkhIGBgYWHRj\nbm7efY4oAICgGAzG8nHLjVSN5uyfk1+Rj0krvQGTCOnicDgjR47Ef5d9Cd/oQAdvF2ofHx/+\nkerq6tzc3Ly8vNzc3Bs3bkRERJSVlRFCDAwMhg4dOnTo0GHDhg0dOnTw4MFSUvi+BQDBTLOf\nZqpuOmnHJLeNbqcWncKklZ6FSYR0nTt37quvvqKdQrzgTYRvhjcR0lJXV5eXl5ednX379u3b\nt2/funXr6dOnMjIylpaWQ4cOtba25rVqNrsHxkYAgDh40vhk2q5pBRUFJ4JPOBk50Y4D0AOy\ns7OHDh169+7dV01YE154EyHAuxgwYICTk5OT09//yZWVld2+fTsrKysrK2v//v15eXnt7e0a\nGhpDhw4d/j/GxsZY4wgAL6WqoHrhqwtLjy712uS1c/bOOa5zaCcCeF8cDsfMzEz02nM/hwIN\nwoS3WfW4ceN4n7a1teXn5/P6dGZm5u+//15TUzNgwAAbGxt+nx4yZIikpCTd2ADQf0hJSG2f\nuX2o9tD5B+enPkjd8fEOLNsFoRYdHT1+/HjaKcQO/tUAISYtLW1tbW1tbc0/8uDBgxs3bly/\nfv369esRERGVlZXy8vLDhg3jlWkHBwdzc3MJCQmKmQGgP8CkFRANdXV1KSkpYWFhtIOIHayB\nfjOsgRZepaWl17spKytTUlKyt7d3dHR0dHR0cHDQ1NSknREAqMGklR6ESYRUHD16NCgoqKqq\nSiQrCtZAA9Cho6Ojo6MzYcIE3qfl5eWZmZnXrl27du3arl27ampqNDU17f7H3d1dTAaQAgAP\nJq30FEwipIXD4YwZM0Yk23M/hwINYkRTU9Pf39/f358Q0tnZmZubm56enpaWdvLkybVr1zIY\nDEtLSxcXFxcXFzc3NwMDA9p5AaDXPTdpJWxCGO1EQgmTCKno6uqKjY3dsGED7Vq9kSIAACAA\nSURBVCDiCAUaxJSkpCRve+nPP/+cENLU1HTt2rXU1NTk5OSlS5c+efJEW1vb1dXV1dXVzc3N\n2toam08DiCr+pJXP9n1WUFHwx2d/YNIKCIX09PSqqqqxY8fSDiKORKoT1NTU1NXV4cIhvAN5\neXkPDw8PDw/epw8ePEhKSkpOTt69e/eXX34pJydnY2Pj5ubG69MDB+L9RgCiBpNW3gcmEVIR\nHR1tZ2enpaVFO4g4EqbtCLKyssaPH29gYODu7h4eHt7Z2fncCRs3bjQ0NKSSDUSMkZFRQEDA\n7t27c3JyysvLDx486OjomJCQMHXqVDabbWtrGxwc/OeffxYUFOBtuAAiY5jusIzvMwbIDnBa\n55T6IJV2HGHCm0Q4Y8QMTCLsSxwOBxvY0SI0u3AkJyf7+Pi0trbKycm1t7e3t7d7enqePHmy\n+7XA0NDQjRs39vhXhF04gK+5uTkjIyMlJSU1NTU1NbWiokJFRYW3p4eTk5OjoyPehggg7No6\n2oIjgg+lHtr1ya7PXD6jHQfg5crLy7W1tdPS0kaMGEE7S2/BLhw9YP369V1dXSdPnpw4cWJb\nW1t4ePjy5cvHjh17+fJleXlsmgN9RFZWtvtKj6KiopSUlLS0tJiYmPXr17e1tZmZmfHKtIuL\ni6WlJfacBhA60lLSez7d42DoEHQgKOV+CiatQP8UHR2tqqpqZ4e3bNIhNP8oZGVlffTRR5Mm\nTSKEsFispUuXDhs2zNfXd/r06WfOnMGoOaBCX19fX19/xowZhJDW1tYbN26kpaWlpqauX7++\nqKho4MCBbm5u7u7ubm5u9vb2TCaTdl4AeFtBHkFmGmYf7vqwqLrocNBhTFqB/iY6OtrPzw+X\naWgRmj/3iooKIyOj7ke8vb337NkTHR391Vdf0UoFwMdisZycnEJCQg4fPlxYWPjo0aPdu3cb\nGhoePXrUzc1NWVnZzc0tNDT07NmztbW1tMMCwJt5mHqkfJtSVlvm8JND7qNc2nEA/tbe3n7p\n0iUsgKZIaAq0urr6zZs3nzv4ySeffPvtt9u2bdu0aROVVACvoqmpOW3atK1bt2ZmZlZVVR0+\nfNjZ2Zn/NkRHR8evv/767Nmz9fX1tJMCwCsZs41Tvk2x0rZyWu905tYZ2nH6tbrmuqbWJtop\nxEViYmJTU9Po0aNpBxFfQrOEY8qUKdu3b//tt9/mz5/f/VfhP/3006NHj7755ptHjx69uC8H\nQH+goqIyYcIE3kDEpqamtLS0xMTEK1eu7Ny5s62tzd7e3sfHx9vb28XFRUZGhnZYAPgHBZbC\niYUnfo79eWr41LWT1y4ft5x2ov4Ikwj7GIfD4f1uk3YQ8SU0BXrlypWnTp1asmTJ6dOnL1y4\nwD/OYDD27ds3YMCALVu2UIwH8Jbk5eW9vb29vb0JIR0dHbdu3bp48eLFixc3bdrU1dU1bNiw\nUaNGjRo1ysPDA7u+APQTvEkrhqqGc/bNuVl8c++cvbJMWdqh+hdMIuxjHA4nMDCQdgqxJjRL\nOAYNGnTt2rXg4GArK6vnbmIwGFu3bj1+/LixsTGVbADvRkpKys7Obvny5RcuXHjy5MmpU6c8\nPDxiYmLGjBmjpqY2ceLEbdu25eZi5SVAvzDdfvrV0KspD1JcN7gWPy2mHQfE14MHD+7cuYMF\n0HQJTYEmhKiqqu7YsePXX3996a1Tpky5d++esGxrDfAcRUXF8ePH//LLLzdv3nz8+PHvv/+u\noaGxfft2S0tLfX39+fPnnzp1qqGhgXZMALE2THdY5veZSjJKTuuc0h6m0Y7Tj2ASYV86e/as\nnp6ehYUF7SBiTZgKNICYYLPZ06dP37179927dx88eLBixYqamppPP/104MCB9vb2YWFh165d\nw8+KAFSoKqieX3reb6if58+e+6/upx2nv8Akwr4UHR3t7+9PO4W4E5pJhBRhEiH0Bx0dHamp\nqVFRURcvXrx27Zq6uvqYMWP8/f1Hjx6N95EA9L3fE39f/J/Fc1znYNIK9KWmpiZVVdUTJ074\n+vrSztLrMImwL9y/f3/+/PmEkIsXL779vbhcbnJycktLy2vOycnJed9wAO9NSkrKzc3Nzc2N\nEFJYWBgTE3Pu3Lm5c+e2tra6urpOnDhx4sSJhoaGtGMCiIvuk1aOBB3B1hPQNy5evMhgMDw9\nPWkHEXeicwX65s2btra2hBCBvqIHDx6Ym5u3tbW98czGxkbMDIf+prW1NSkpicPhnD59+sGD\nB9bW1rwmPXz4cAaDQTsdgOi7X3V/4m8TWztazyw+Y65pTjsOiL6goKDy8vKzZ8/SDtIX+vMV\naNFZA21mZnb79u3bt28LdC8jI6PW1lbua+3atYsI2MsB+gaLxfLx8fnll1/u37+fnZ09a9as\nuLi4ESNGaGhoBAQEnD179m1+OASAd2bMNk79LtVK28pxnePZW2LRaYAiLpd77tw5Pz8/2kFA\nhAq0jIyMlZXVi5vcAYgJS0vL5cuXJyUlVVRUbNq0qaam5sMPP1RRUfH39z9w4EBdXR3tgACi\niTdp5avRX00Jn7IxZiPtONRgEmEfuHXrVmlpqTisfu7/RKdAE0Kqq6vv3btHOwUAZWpqarzL\nz48fP/73v/8tJye3ZMkSdXX1iRMnRkREYC88gB7HYDDCJoRFzItYfXb1rH/Pam5vpp2orxVV\nF+kt1zNZYVL7rJZ2FlEWHR1tZWVlYGBAOwiIVoHetGnT4MGDaacA6C+UlZVnzpx59OjRqqqq\nEydODBw4cNGiRWpqalOnTj169GhTE64VAfSk6fbTk0OTr96/6rrBteRpCe04fYo3ibCiruJ+\n1X3aWUQZh8PB/JR+QqQKNAC8lLS0tJ+f3/79+x8/fnzs2DF5efmgoCBVVVXe6o7GxkbaAQFE\nhI2uzX8nrazHpBXoYU+fPk1LS0OB7idQoAHECIvF4pVmXpMeOHDg4sWL1dTUeAdxTRrg/akq\nqMYujR1nNU6sJq1gEmEfOHfunIKCgpOTE+0gQIgQ7QNtb2//xnPKysr6IAmACJCRkfH39/f3\n93/27BmHwzl27NiCBQuWLFkyZcqU2bNnjxw5UkICP10DvCOWFOuPT/9wNHQMOhB0o/jGL9N/\nkZSQpB2qd/EmESrJKGESYe+Jjo4eN24ck8mkHQQIEaICfePGDULI679vOjo6+ioOgIiQk5Ob\nNm3atGnTGhsbz5w5ExERMW7cOHV19VmzZs2ePdva2pp2QABhxZ+0UlBRIPKTVhRYCpwvOLRT\niLLOzs7Y2Nhff/2VdhD4L6G5yLRs2TJ5efns7OyWV/v6669pxwQQVgoKCrNmzeJwOI8fP165\ncuXVq1dtbGwsLS3DwsIePnxIOx2AUPIw9Uj5NqW0ptThJ4e88jzacUCIpaam1tTUjB07lnYQ\n+C+hKdBr1qwxMTGZOXNme3s77SwAokxFRSUoKCgpKenhw4cBAQH/+c9/TExM3Nzctm7dWl1d\nTTsdgJAxZhunfJtiqW3ptN4Jk1bgnXE4HAcHBzU1NdpB4L+EpkAzmcyIiIicnJzvvvuOdhYA\nsaCvr798+fKCgoIrV65YW1uvWbNGR0fno48+4nA4nZ2dtNMBCA1FGcUTC08sHbVUzCetwPvg\ncDgYQNivCM0aaEKIubl5RUXFaxY6+/r6KiuL8iIzgL7HYDBcXFxcXFy2bNkSExNz8ODBqVOn\nqqiozJ49+7PPPrOwsKAdEEAI8CatmGuaz90/91bJrT8++0OWKUs7VA+ra66TkpCSZ8nTDiKC\nSktLb9++vW/fPtpB4G9CcwWaR0lJSUVF5VW3enp6hoaG9mUeAPEhLS09YcKEyMjIioqKsLCw\nq1evWlpaWlpabty48cmTJ7TTAQiBj0Z8xJu04rbBTcQmrWASYa/icDgaGhq2tra0g8DfhKxA\nAwB1ysrKvEXSubm5/v7+W7Zs0dHR8ff3j4yMxFsUAF7PRtcmY0WGooyi03qn9IfptOP0GEwi\n7FXR0dF+fn4MBoN2EPgbCjQAvCNzc/MNGzaUlZVFRUUNHDjw008/1dfXDwkJuXXrFu1oAP0X\nW5HNm7Ti8bPHn1f/pB0H+rvW1ta4uDgMIOxvUKAB4L1ISEiMGjXqwIEDJSUl3377bXJyso2N\njbu7e0RERGtrK+10AP0Rb9LKtpnb5h2YF3IkpLNL6N+Vi0mEvSc+Pr6trW3UqFG0g8A/oEAD\nQM8YNGjQkiVLMjMzb926NWzYsODgYB0dnW+++ebevXu0owH0R0EeQVFLog6mHPxg+wfCvnSY\nN4lwxogZmETY4zgcjoeHh6KiIu0g8A8o0ADQw6ytrX/77bfHjx9v3rz50qVLpqamo0ePxgpp\ngBeNsRyTviK9+GmxsE9a4U0iPBx0GFege9y5c+ewgV0/hAINAL1CRkYmICDg2rVrGRkZRkZG\nc+bM0dPTCw0NLSoqoh0NoB8xUTNJ/TbVQssCk1bgRfn5+ffu3cMC6H4IBRoAepednd3u3btL\nS0tDQ0PPnDljbGw8adKkmJiYrq4u2tEA+gVFGcWTwScxaQVeFB0dbWRkZGpqSjsIPA8FGgD6\ngrKyckhISE5OzsWLF2VkZCZOnGhmZhYeHt7U1EQ7GgB9vEkrhwIPrT67+uM9Hze3N9NOBP0C\nh8Px9/ennQJeAgUaAPoOg8Hw8vI6cuRIcXHxzJkzV61apaurGxoaWlZWRjsaAH28SStJd5O8\n/8+7vK6cdhzB1DXXNbXi5+GeVF9fn5SUhPUb/RMKNABQoK6uvmrVquLi4i1btnA4HH19fX9/\n/5SUFNq5ACiz0bXJ/D5TWkrafq29EE1awSTC3nDhwgUmk+nh4UE7CLwECjQAUMNisQICAm7f\nvh0fH08IcXV1tbe3P3DgQEdHB+1oANSwFdnnl54faznW42ePAykHaMd5K5hE2Bs4HM6oUaNY\nLBbtIPASKNAAQJ+bm9vZs2cLCgpcXV0XLlxoamq6cePG2lpcygIxxZJi7f1s77aZ2z7f/7lo\nTFoBQXG53NjYWKzf6LdQoAGgvxg8ePDWrVsLCwvnzJmzZcsWAwOD0NDQx48f084FQEeQRxDn\nC45QTFrBJMIed/369fLycl9fX9pB4OVQoAGgf2Gz2T/88ENhYeGvv/56+vRpQ0PDL774oqSk\nhHYuAAq6T1rJr8inHeeVMImwx3E4nGHDhuno6NAOAi+HAg0A/RGLxZozZ05OTs7Ro0dTU1ON\njY0DAgIKCgpo5wLoa/xJK47rHKOyomjHeTlMIuxxHA4H6zf6MxRoAOi/JCQk/P3909PT4+Li\nysrKLCws/P39r127RjsXQJ/iT1qZvGMyJq2Ig6qqqszMTEzw7s9QoAFACLi5uV26dCkhIYEQ\n4uDg4O/vn5aWRjsUQN/hTVo5GHgQk1bEQXR0tLKysqOjI+0g8Eoo0AAgNHibdVy7dk1WVtbZ\n2Zn3Ke1QAH1nxogZScuTku4m+Wz2EbpJK/D2oqOjfX19JSUlaQeBV0KBBgAhY2Njc+zYsZs3\nb+ro6EyaNMnDw+PKlSu0QwH0EVs929TvUrlcrv1a+4zCDNpx/oZJhD2lo6Pj/PnzWADdz6FA\nA4BQsra2PnLkSF5enq6urpeXl6+vb2ZmJu1QAH1Bc4Bm/LL4fjVpBZMIe1BycnJDQ8OYMWNo\nB4HXQYEGACFmamoaERFx+/ZtRUVFBweH0aNH37x5k3YogF7Hm7SydcZW3qSVLm4X3TyYRNiD\nOByOs7PzoEGDaAeB10GBBgChZ2FhcezYsdTUVBkZGTs7u+nTp9+9e5d2KIBe9/eklW39fdIK\nvD0Oh4P9N/o/FGgAEBEODg5nz55NTEysrKy0tLQMCAh4+PAh7VAAvYs3aaXoaZHjOkeKk1Yw\nibCnFBcX5+bmYgF0/4cCDQAixdXVNT4+Pjo6Ojc318zMbP78+RUVFbRDAfQi3qQVMw0z1w2u\nF3IvUMmASYQ9JSoqSkdHZ+jQobSDwBugQAOACBo1alRGRsbBgwcTExNNTU1//PHHxsZG2qEA\neouijOKpRaeWeC/x2+pHZdIKJhH2FN4AQgaDQTsIvAEKNACIJgaDMX369Ozs7G3btu3bt8/U\n1HTv3r1dXZTfawXQS7pPWpm9ZzYmrQij5ubm+Ph4rN8QCijQACDKJCUlP/vss4KCgpCQkKVL\nlw4dOjQmJoZ2KIDewpu0cuXuFZ/NPhV1WLwkZOLi4jo7O0eOHEk7CLwZCjQAiD5ZWdnly5fn\n5+e7ubl98MEHo0ePzsnJoR0KoFfY6tmmfJvS1dXV3yatwBtxOBwvLy8FBQXaQeDNUKABQFxo\namru3r07KyuLyWTa2trOnz+/qqqKdiiAnqelrJXwTcJoi9F9OWkFkwjf37lz57B+Q1igQAOA\neLGwsIiOjo6Ojk5OTh4yZMjGjRtbW1tphwLoYSwp1r45+/ps0gomEb6/nJycwsJCX19f2kHg\nraBAA4A4GjVq1I0bNzZs2LB58+ahQ4dGRkbSTgTQ84I8gqK+iDqQcuCDbR/UNdf13hNhEuH7\n43A4ZmZmJiYmtIPAW0GBBgAxxWQyg4KC8vPz/fz8Pv7441GjRuXl5dEOBdDDxlqOzViRUVhd\n6PCTA8VJK/BGvA3saKeAt4UCDQBiTUVFZcuWLdnZ2Uwm08bG5rvvvnv27BntUAA9yUTNJO27\nNN6klYt5F3vjKTCJ8D3V1dWlpKRggrcQQYEGACCmpqbnzp3766+/IiIiTE1NDxzoo/ddAfQN\nRRnFE8En5rnP893i2xuTVjCJ8D3FxMTIysq6ubnRDgJvCwUaAOC//P398/LyAgMD582b5+/v\n//DhQ9qJAHqMpITkhqkbDgYeXHVm1ew9s1vaW3rwwTGJ8D1FR0ePHj1aWlqadhB4WyjQAAB/\nk5OTCwsLy8rKam5utrS0DAsLwx4dIEpmjJiRHJqMSSv9SldXV2xsLBZACxcUaACA5w0ZMuTC\nhQu7du3auXPn0KFDz58/TzsRQI/hTVrp7OrEpJV+IiMjo7KycuzYsbSDgABQoAEAXoLBYAQE\nBOTn5/v6+vr5+fn7+5eWltIOBdAzuk9aOZhykHYcccfhcOzs7LS0tGgHAQGgQAMAvNLAgQO3\nbt2alJRUWlpqZWW1Y8eOrq7eHUgB0Df+nrTy5+ehx0Pff9IKJhG+Mw6Hg/03hA4KNADAGzg5\nOWVmZq5ateq7777z8PAoKCignQigZwR5BJ1dcnZ34m7/7f7vM2kFkwjfWUVFxY0bN7AAWuig\nQAMAvJmkpGRISEh+fv6gQYNsbGw2btzY2dlJOxRADxhrOTZ9RfrDJw8dfnIoqHjHHw4xifCd\nRUdHq6qq2tvb0w4CgkGBBgB4W5qamqdPnz5w4MCmTZvs7e1v3rxJOxFADxisNjjtu7QhGkNc\nNrj00qQVeBXe+g0JCfQxIYMXDABAMNOmTcvOzjY0NHRwcAgNDW1ra6OdCOB9Kcoongw++c6T\nVjCJ8N20t7dfunQJ6zeEkfB9o3O53IcPHz548KChoYEQMmDAgMGDB+vq6tLOBQBiREND48SJ\nE5GRkcHBwefOndu7d6+dnR3tUADvhTdpZZjusM/3f55dlv3vgH/LMGXe8r68SYRKMkqYRCiQ\nxMTEpqam0aNH0w4CAhOmK9A1NTVff/21hoaGsbHx6NGjp0yZMmXKFB8fHz09PX19/TVr1jQ3\nN9POCABihHcp2tTU1MnJKTQ0FCNXQATMdJiZFJqUcCdBoEkrmET4bjgcjqurq7KyMu0gIDAG\nl8ulneGtlJeXu7q6Pnz4cPDgwa6urvr6+vLy8oSQ+vr6+/fvJyQkPHr0aNiwYZcvXx44cGDP\nPvXu3bsXLFjQ0NCgoKDQs48MAKIhMjJy0aJF6urqe/fuHTFiBO04AO/rUe2jKeFTSmtKTy46\nOcIA39K9xczM7PPPP1+2bBntIP1UW1sbi8VKTk52cXGhneV5QvOT4g8//FBaWnrs2LFp06a9\neGtnZ+fu3bsXL168atWqLVu29H08ABBn06ZN8/LyWrJkiYuLy7Jly8LCwqSlpWmHAnh3vEkr\n8w/O9/jZ498B/57tNJt2IhH04MGDgoICLIAWUkKzhIPD4XzyyScvbc+EEElJyeDg4OnTp584\ncaKPgwEAEELYbPaRI0eOHTu2b98+Jyen/Px82okA3gtLirV/zv4NUzd8tu+zHpm0As+JiorS\n09OzsLCgHQTehdAU6OrqamNj49efY25u/vjx477JAwDwosmTJ2dlZenq6tra2m7dulVY1sgB\nvEqIT0jUkqi3mbSCSYSC4nA4/v7+tFPAOxKaAq2lpXXr1q3Xn3Pjxg2MkgcAuths9unTp3fv\n3r1ixQpfX9/y8nLaiQDeyzircbxJK47rHF81aQWTCAXV1NSUmJiICd7CS2gK9KRJkyIjI//v\n//7vpe9zb2pq+vHHH0+fPv3RRx/1fTYAgOcEBARkZmZWVVXZ2NhwOBzacQDey2C1wanfppqq\nm7pscLmUd+nFEzCJUFAXL15kMBheXl60g8A7Epo3EYaFhV25cmXZsmWrV692cHDQ1dVVUFDg\ncrmNjY1FRUXp6enPnj1zd3f//vvvaScFACCEEDMzs9TU1J9++mnixImff/75r7/+KicnRzsU\nwDtSklU6GXxyxckV47aMWzt57fJxy2knEm7R0dHe3t74N0F4CU2BVlZWTklJ2bFjx4EDB+Lj\n4zs7O/k3MZlMOzu7uXPnzp07V1JSkmJIAIDumExmWFiYh4fHp59+mpSUFBERYWNjQzsUwDvq\nPmnlXuW9HbN2SEv9d7cZTCIUVExMTGhoKO0U8O6EZh/o7lpaWkpKSniTCJWUlPT09Hp1xyjs\nAw0A76m2tjY4OPjkyZNhYWHLli2TkBCa5XMAL7pefH3Sjkm6A3WPLzyuMUCDENLY2vjR7o+U\nZJQOBh5Eh36jW7du2djYPHz40MDAgHaWfq0/7wMtlP+Iy8jIDB48ePjw4cOHDzcxMcF+qwDQ\nzykrK//nP//ZvXv32rVrx40b9+jRI9qJAN7dcL3hqd+mdnR12K+1zyzMJJhEKCAOh2NlZYX2\nLNSEskADAAijgICAa9eu1dbW2traxsbG0o4D8O60lLUSv0kcZTHK/Wf3Q6mHaMcRMhwOB/NT\nhJ3o/KR4//79+fPnE0IuXrwo0B2zs7NfurMHX3Fx8XslAwD4H1NT0+Tk5BUrVowfP/77779f\nuXIllnOAkOJNWrHVs/1s32fZZdnrpqyTYOCb+c2ePn2alpa2fv162kHgvYhOgW5oaLh06SV7\n67ze/fv3ra2t32YhuDAuFgeAfojJZP78888eHh4BAQGJiYmHDx9WV1enHQrgHYX4hJiwTT7e\n83F+Rf6hwEMKLLxZ6A1iYmIUFBScnZ1pB4H3Ijo/LJqZmd2+ffv27dsC3cvY2Li+vv7pa/3y\nyy+EEAaD0TvBAUAcffDBBzdv3mxqarK3t7969SrtOADvbrz1+JRvU7LLsjfFbKKdRQhwOJxx\n48YxmUzaQeC9iE6BlpGRsbKysrKyEvSOCgoKA18L2zQCQG/Q09NLTEycMmWKp6fnxo0b8Wsu\nEF5y0nJVDVW/X/kdkwhfr7OzMzY2FgugRYDoFGhCSHV19b1792inAAB4WywWa+vWrfv27Vuz\nZs2UKVNqa1E+QChllWbVt2AS4ZulpqbW1NSMHTuWdhB4XyJVoDdt2jR48GDaKQAABDN79uyM\njIw7d+44OjpmZWXRjgMAvYXD4YwYMUJNTY12EHhfIlWgAQCElLm5eWpqqq2traOj4549e2jH\nARAMJhG+pejoaKzfEA0o0AAA/YKiouKRI0e2bt26aNGigICAZ8+e0U4E8LbcB7v7DfWbMWKG\npbYl7Sz916NHj7KyslCgRYPQ/KRob2//xnPKysr6IAkAQO8JCgqysrL66KOP3N3djx8/jlll\nIBR4kwhpp+jvoqKiNDQ0bG1taQeBHiA0BfrGjRuEkNdv+9LR0dFXcQAAeouLi8v169dnzpzp\n4ODw119/eXh40E4EAD2Aw+H4+flhV1zRIDRLOJYtWyYvL5+dnd3yal9//TXtmAAAPYDNZsfG\nxs6dO9fHx+e3336jHQcA3ldra2tcXJyfnx/tINAzhKZAr1mzxsTEZObMme3t7bSzAAD0OklJ\nyQ0bNuzcufNf//rX/Pnz8U8fgFCLj49vbW318fGhHQR6htAUaCaTGRERkZOT891339HOAgDQ\nRwIDA+Pi4k6fPj1q1KiqqiracQBeqa65rqm1iXaK/is6OtrDw2PAgAG0g0DPEJo10IQQc3Pz\nioqK1yx09vX1VVZW7stIAAC9zdXVNTMzc+LEic7OzmfOnLGwsKCdCOB5RdVF1qus5aTl8lbn\nKcvhP+KXiI6ODg4Opp0CeozQXIHmUVJSUlFRedWtnp6eoaGhfZkHAKAP6OjoJCQkWFtbOzk5\nnTlzhnYcgOdllWbVN2MS4SsVFBTcu3cPG9iJEiEr0AAA4klBQeH48eMrVqyYOnXqxo0baccB\nAAFwOBwjIyNTU1PaQaDHCNMSDgAAccZgMJYvX25oaDhnzpxbt2798ccfsrKytEMBEIJJhG/C\n4XD8/f1pp4CehCvQAADCZPr06cnJycnJyT4+PhUVFbTjABCCSYSv1dDQkJSUhA3sRAwKNACA\nkLGxsUlNTe3q6nJwcLh58ybtOAD/nUR4OOgwrkC/6MKFC0wmExORRAwKNACA8NHU1IyPj3d3\nd/fw8Dh//jztOADwShwOZ9SoUTIyMrSDQE9CgQYAEEoyMjKHDh366quvxo8f/+9//5t2HAB4\nCS6XGxMTg/03RA9+1QIAIKwYDEZYWJiuru7ChQvLysrCwsJoJwKAf7h+/Xp5ebmvry/tINDD\nUKABAITb559/rqqqOmvWrJKSkt27d0tJ4R92oKCuuU5KQkqeJU87SP/C4XCsra11dHRoB4Ee\nhiUcAABCb+LEiXFxcWfPnp06deqzZ89oxwGxU1RdpLdcz2SFSe2zWtpZjoZbHAAAIABJREFU\n+pfo6Gis3xBJKNAAAKLA0dExJSUlLy9v5MiRlZWVtOOAeMEkwpeqqqrKyMhAgRZJKNAAACLC\n2Ng4MTGxs7PT2dn5zp07tOMAiLtz584pKys7OjrSDgI9DwUaAEB0aGhoJCQkmJubu7i4XL16\nlXYcEBeYRPhSHA7H19dXUlKSdhDoeSjQAAAiRV5e/vTp01OnTh0zZkxUVBTtOCAWMInwRR0d\nHefPn8cAQlGFnxQBAESNpKTk7t27jYyMJk+evH379gULFtBOBCKON4mQdor+JTk5uaGhYezY\nsbSDQK9AgQYAEE3Lly9XUVEJDg6uqqr64YcfaMcBEC/R0dFOTk6DBg2iHQR6BQo0AIDImjdv\nnoaGxvTp0+vr63/++WcGg0E7EYC44HA4H3/8Me0U0FtQoAEARJm/v39MTIy/v399ff3OnTsl\nJPDWF4BeV1xcnJOTgw3sRBj+JQUAEHGenp6XLl06fvz47NmzOzo6aMcB0VTXXNfU2kQ7RX8R\nFRWlo6MzdOhQ2kGgt6BAAwCIvhEjRly4cOHixYtTpkxpaWmhHQdEDSYRPofD4YwfPx6LpkQY\nCjQAgFiwtbVNTEy8ceOGn59fY2Mj7TggUjCJsLvm5ub4+HhsYCfaUKABAMSFmZnZlStXiouL\n/fz86uvraccBEE1xcXGdnZ3e3t60g0AvQoEGABAjBgYGV65cqamp8fb2fvLkCe04ICIwibC7\n6OhoLy8vBQUF2kGgF6FAAwCIF01NzUuXLnV2dnp6ej569Ih2HBAFmETYXXR0NPbfEHko0AAA\nYkdNTe3y5csDBgwYOXJkSUkJ7Tgg9HiTCA8HHcYV6JycnMLCQl9fX9pBoHehQAMAiCNlZeUL\nFy7o6em5ubndvXuXdhwAEcHhcMzMzExMTGgHgd6FAg0AIKbk5eXPnDljZWXl5eWVm5tLOw6A\nKIiOjhbh/TekpKScnJx4H8+YMYPBYFRUVNCNRAsKNACA+JKVlT158qSzs/PIkSOzs7NpxwEQ\nbnV1dVevXhWTBdA2NjZjx45lsVi0g9CBAg0AINakpaWPHj3q4+Pj7e2NDg3vDJMICSGxsbGy\nsrJubm60g/SF0NDQmJiYgQMH0g5CBwo0AIC4k5SUPHjwoI+Pj4+PT05ODu04IHwwiZCHw+GM\nHj1aWlqadhDodSjQAABAJCUlDxw44OLi4uPjg/XQIChMIiSEdHV1xcbG9pMF0JMnT2YwGOXl\n5YGBgerq6iwWy8zMbOfOnd3Pefz48aJFi/T19aWlpdls9qRJkzIyMrqfEB0dbWdnJysrq6am\nFhgYWFv7j5+OnlsDzeFwHBwc5OTkNDQ0QkJCmpubdXV1hw8f3v3kysrK0aNHy8rKnjlz5i0z\n9Fvivt0MAADwMJnMY8eOTZs2zdvb+/Lly+bm5rQTAQiTjIyMysrKcePG0Q5CCCG8pcmTJk0a\nOXLkyZMnu7q6Vq9eHRwczGQyAwMDCSFVVVWOjo61tbULFiywsrIqKSkJDw93d3ePjY319PQk\nhCQlJU2YMEFdXX3lypVsNjshIWHChAkSEi+/8JqYmDhx4kQ2mx0aGqqqqhoZGTljxoyGhgZt\nbW3eCbyr8kuXLmUymStXrjQyMnqbDFVVVX3yp/VOuPAmu3btIoQ0NDTQDgIA0OtaW1snTJig\noaGRl5dHOwsIjejb0SSQkEBys/gm7SzUrFy50s7OjnaK//roo48IITNnzuQfqa2tZbFYBgYG\nvE8XLlwoJSWVkZHBP6G4uFhRUdHe3p73Ke8ngfT0dP4JwcHBhBBHR8fuT1FeXs7lckePHk0I\n4T9aR0fHyJEju588d+5cQsiYMWM6Ozv5D/jGDPPnzyeEJCcn98wfSo/CEg4AAPibtLR0ZGSk\nvb396NGj798X31/Hg0AwiZAQwuFw+tv+GzNmzOB/PGDAAHd398LCQl7ljYyMtLa21tHRqfgf\nJpPp4uKSmZnZ2NjY1dWVkJBgbGw8YsQI/iPMmzfvVU905coVMzMze3t73qeSkpLLly/vfgKD\nwSCEfPrpp/xr2G/MwOVyjx8/3oN/Gj0LSzgAAOAfpKWljx8/PnXq1JEjR8bHx/N+2QrwGrxJ\nhLRT0FRRUXH9+vXw8HDaQf7B1NS0+6e8BRUVFRUSEhJPnjx58uSJpqbmi/cqLi4eMGBAc3Pz\nc3/3zczMXvostbW1LS0tz82OcXFxefHMIUOG8D+urKx8fYZBgwY9efLklV8bbSjQAADwPGlp\n6b/++ovfoQ0NDWknAujXoqOjVVVV+ZdgaUlNTc3MzFy8eDHvUzk5ue63ysvLE0Jqa2sVFRUJ\nITY2NuvXr3/xQbS0tHiLj2VkZLofl5GR4V1Ifk51dfWLz6WoqCgpKfncmQMGDOB/3NDQ8PoM\n/bk9ExRoAAB4KRaLFRkZ6e/v7+XlhQ4N8HocDsfPz+9V77HrM6Ghod2vOjc1/WNn7rq6OkLI\noEGDeAWaEPKqtzw2NjYSQlpaWp47yOVyXzyZyWS+ePKzZ886OztfE/WNGVpbW19zd+qwBhoA\nAF6Ot9uUiYnJyJEjCwsLaccB6Kfa29svXbpEfQO7a9euJSYm8i8/E0Ly8vK6n3D37l1CiKam\nprq6uqqqan5+/nM70/F3vdDQ0JCWln748GH3W7Oysl76vBoaGhISEkVFRd0PpqWlvT7tGzPw\nTnj9g1CEAg0AAK8kJyd39uxZIyMjLy+v5/6DBOhOnCcRJiYmNjU1jRkzhm6MX375ZezYsdbW\n1vwje/fu5X98586djIyMIUOGsNlsQsi0adNaWlo2bdrEP6Gqqsra2trf358QIiUl5eLicu/e\nve67Mu/YseOlzystLW1vb5+VlZWfn8870tnZuXHjxjcGfn0GQsjUqVPf4uumA0s4AADgdeTk\n5M6cOePn5zdmzJgrV66oqanRTgT9TlF1kfUqazlpubzVecpyyrTj9LXo6GhXV1dlZZpfeFlZ\nWWRkZFRUVPeDra2t/v7+H3zwQVdX188//8zlcleuXMm7KSwsjPP/7N15IFT7/z/wGYQQStkK\nLVylrivShnZr2hW5pY1Ciygtt5X2kp2iRLmlVZszTREpWohK222RpEW0WLM1ze+P+f76dLuy\nzjlnZjwffzFz5v16fr/XvZ+X433eL4LYunXru3fvhg8f/vbt27179378+HHJkiW8C1asWJGa\nmmprazt37lwlJaXU1NQvX778uIn5R97e3lOnTrWxsXF3d5eXl//777979uzJO4u6AY1mWLdu\nXURERKv+/0Ia3IEGAIBGyMnJEQShqKhoZWXF20YJ8KM2PolQEA6wCw4O1tXV5Z3H/N2ePXu0\ntbV9fX2XLl0qIyMTExPj6OjIe0tZWfnWrVtubm5JSUnOzs47d+40MDBIS0v7voK1tXVcXJyK\nioq/v//OnTuVlZVPnTolLy9fW1v73+p2dnZRUVGSkpJr1qzZunXrsGHD9u3bx+Vy//sc4Y8a\nzcC7WS6YmPXuB4cfRUREuLq6lpeXy8nJ0Z0FAIA2Hz9+HDZsmIKCQmJiIu9xfgCe8/fOjw8d\nz2Awbq+9baRlRHccSr148aJXr14PHz7U09OjK0NlZaWmpqafn9+cOXN4rzg4OBw7dqygoKBb\nt260RCorK1NQUBg/fvzZs2dbvEhtba2UlFR6enq9h+LRC3egAQCgSZSUlC5duvTu3TsHB4e6\nujq644AAkRD/vx2hEmJtbmtoQkKCpqYmjd0zg8HYv3+/hITE9OnT6QoQHR09YsSIrKys76/E\nxMQwGAxTU1O6IpGtzf2gAwBAi3Xt2jUxMdHMzGzOnDmHDh2i/dAuEBC8SYTy0vJtcBIhi8Wy\ntbWlMQCHwwkJCVm0aNFPxzZTSU9P7+bNm7a2tm5uburq6nfu3ImMjNTU1GxgeKGwE/r/9tXV\n1T18+DArK0vAzwsEABAN2traly5dYrFYixcvpjsLCAreJMK4+XFt7Q50ZWVlamoqvRugz5w5\n8+bNm/nz59OYYdCgQZcvX+7fv39YWJi7u/vZs2ednJxu3LhB74OVpBKmBjo5OXnkyJE9evSw\nsbHhnS948eLF7t279+vXb8CAAcrKyoI2QhMAQCT9/vvvBEEcPHjQx8eH7iwAdLp8+TKTyRwx\nYgSNGQICAmbNmqWiovLji0ePHuVyuVRugDYxMWGxWO/fv6+trX39+nVUVJS6ujpl1aknNL8p\n3rhxw9LS8uvXr/Ly8hcvXrx69WpiYuK0adMUFBScnJyqq6sTExMXLlzYs2fPX420AQAAfhky\nZMjp06dtbW3l5eU9PT3pjgNAD4IgRo0a9dMUayrdvn37+vXr+/btoytAmyU0d6C3bdvWuXPn\ne/fulZaWFhYWDhw40MHBoUePHk+ePDl48OCxY8dyc3O7d+8eFBREd1IAgDbB3Nw8Ojra29s7\nOjqa7iwA9GCz2fQOIPTz87OxsenTpw+NGdomobkDff369aVLl/Lm63Tp0mXnzp3Gxsa+vr7t\n27fnXdCxY0dnZ2d/f39aYwIAtCGOjo4lJSUuLi4KCgqTJ0+mOw7QqbSqVEJMQlaqDZ1veO/e\nvVevXtHYQOfn5586dYrNZtMVoC0Tmga6tLRUS0vr+7ddu3Zl/OeEbTU1tbKyMqqTAQC0Ye7u\n7sXFxTNmzGCz2cOGDaM7DtCjbU4iJAiib9++3bt3pytASEhInz59Ro0aRVeAtkxotnAoKSnl\n5v5vvtHTp08ZDMbz589/vCY3N1dJSYnqZAAAbduGDRvc3NzGjRuXnZ1NdxagR9ucRMhisWg8\nf6O8vHz//v3Lly9nMpl0ZWjLhKaBHjlyZEhISEpKSm1t7f379xcvXtynT5/du3e/efOGd8Hj\nx4/37NljZmZGb04AgDbIz8/Pzs7Oysrqn3/+oTsLABU+ffp069YtGhvo/fv3y8rKOjg40BWg\njROaBnrDhg11dXWjRo2SkpLS19d/8+bNqVOnmEzmb7/9NmrUqKFDh+rr65eVlXl7e9OdFACg\nzWEymXv37h00aJC1tfW7d+/ojgNUa4OTCNlstqys7JAhQ2ipzuFwQkNDFy5cKCkpSUsAEJoG\nunfv3tevX58+ffqgQYNmz559/fr1Pn36JCQk9OvX78qVKzdu3NDU1Dx16tTAgQPpTgoA0Ba1\na9fu+PHjampq48aNq6iooDsOUIo3idDB2KHtTCIkCMLKyqpdu3a0VD916lRhYeGCBQtoqQ4M\nBoPJ5XLpztBaFRUVVVVVPz1QyEcRERGurq7l5eVycnIklQAAEA0fP34cOnRor169zp07JyHR\nVm5GQlvD4XBUVFT8/f2dnJxoCTBkyBBDQ8OwsDBaqlOmtrZWSkoqPT196NChdGf5mdDcgW6A\nnJwced0zAAA0nZKSEovFun37tru7O91ZAMhy8+bNz58/W1pa0lL9+vXrt27dWrx4MS3VgUcU\nGmgAABAcvXr1SkhIOHz4sJ+fH91ZAEjBYrGMjY1/mp5NmYCAgHHjxvXu3ZuW6sAjOn9fy83N\n5W0GSkpKatYHX79+XVtb28AFHz58aFUyAIA2ZuDAgTExMdOnT1dXV3d0dKQ7DgCfEQQxZcoU\nWkq/fPnyzJkziYmJtFSH70SngS4vL798+XJzP5Wbm6utrd2UK0VgszgAAGWmTp2al5c3b948\nLS0tExMTuuMA6drOJMK3b9/m5OQcOHCAlupBQUH6+vojRoygpTp8JzoNdO/eve/fv9/cT/Xq\n1ev169c1NTUNXBMXF7d27VocVA4A0CwrVqx49erVhAkTrl+//ttvv9EdB0jUpiYRJiQkqKio\n9O/fn/rSZWVl0dHRoaGh1JeGn4hOAy0tLd2vX78WfJA3FbwBnTt3blEiAIC2Ligo6PXr19bW\n1jdu3FBWVqY7DpCFN4mwrKostzjXSMuI7jjkIgjCxsaGlttqkZGRcnJy06ZNo740/KSpDTSH\nwxEXF+d9XVNTc/fuXUlJSQMDA+p/gLhcbl5e3osXL8rLyxkMhoKCgo6OjoaGBsUxAACgUeLi\n4keOHBk5cqStre2VK1dkZGToTgTQKjU1NcnJyQcPHqS+9NevX0NCQhYvXozhKYKg8Qaaw+Es\nWbKkqKjoxIkTDAbj5cuXo0ePfvHiBYPBMDU1vXDhAmWnI3/+/HnLli2xsbFFRUU/vaWpqens\n7Lx8+fL27dtTEwYAAJpCRkbmzJkzQ4YMmTVr1rFjx8TEcPqTCGo7kwhTU1NrampGjx5NfekT\nJ058+PDB2dmZ+tLwX43/oO/atSs8PNzLy4v37cKFC/Py8tzc3HiDW0NDQ1etWkVySAaDwXj3\n7p2JiUleXp6Ojo6NjY2WlpasrCyDwSgrK8vNzU1NTV2/fv2pU6dSUlI6duxIQR4AAGgiNTU1\nFotlYmKycuXKXbt20R0H+I83iVBeWl7kJxESBDFs2DAFBQXqSwcFBc2bN09JSYn60lAPbmP6\n9es3efJk3tevX79mMpnz5s3jfTt37lwDA4NGV+CLefPm8ebE1vvu169fw8LCmEymh4cH30vv\n3buXwWCUl5fzfWUAgLYjJSVFSkoqODiY7iAALaetre3v70993atXr4qJiT179oz60jTinfGQ\nnp5Od5B6NP6ntJcvX1pYWPC+vnjxIpfLnT59Ou9bIyOjly9fktXa/xtBEDNnzpw6dWq974qL\ni7u7u0+bNi0+Pp6aPAAA0CwjRoyIjo728vI6e/Ys3VkAWuLJkyfPnz+3sbGhvnRAQMCECROa\nePAuUKDxLRw/PiaYlJQkKytrZmbG+5bL5dbV1ZEV7d8+fvzYq1evhq/p06fP6dOnqckDAADN\nNX369CdPnvz555/p6el//PEH3XEAmocgiJ49e+rq6lJcNy8v79y5cykpKRTXhQY0fgdaS0vr\n6tWrDAbj/fv358+ft7Cw+P74571797p160ZuwP9PXV393r17DV9z584ddXV1avIAAEALbNiw\nYfz48RMmTCguLqY7C0DzsFgsW1tb6usGBAQYGBh8v30JgqDxBtrR0fHIkSNDhw41NDSsqKjw\n8PDgvX7o0KGDBw+OHz+e5IT/Z+LEiSdOnPDz86t36EllZeWGDRvOnj1rb29PTR4AAGgBJpN5\n4MABFRWVSZMm1dbW0h0H+Ka0qrSyppLuFCSqqKhIS0sbO3YsxXVLSkqio6OXLVtGcV1oGJPb\n2ITq6upqNze3Y8eOSUpKbtq0afHixbzX1dXVO3funJqaSs2pFyUlJaNHj87Ozu7QocPAgQM1\nNDTk5OS4XG5FRUV+fn5GRsaXL1/MzMxYLBbfj9WLiIhwdXUtLy+n7MA+AADR9u7dO2NjYwsL\nC7rmIQN/tYVJhPHx8U5OTh8+fJCWlqay7o4dO0JCQvLy8tq1a0dlXUFQW1srJSWVnp4+dOhQ\nurP8rPE90NLS0tHR0dHR0T+9Hh8fP2DAAAkJik58VFRUvHHjRlhY2KFDh65cucLhcL6/1a5d\nOyMjo7lz586dO/f7tBcAABBYampqJ06cGDly5IABA9zd3emOA63VFiYREgQxZswYirvnurq6\nsLAwDw+PNtg9C7jG29+0tDQ9Pb1OnTr99PrgwYMzMjIKCgqmTJlCTrafSUpKenp6enp6VldX\nFxQU8CYRysvLa2pqYioPAIBwGTJkSGRkpLOzc+/evUeNGkV3HICGcLlcNpu9YcMGiuseP368\npKTExcWF4rrQqMb3QJuZmfEeIvyva9eu0fIPVVpaWkdHx9DQ0NDQUFtbG90zAIAwcnJyWrhw\n4dSpU3Nzc+nOAq0i8pMIs7Oz3759a2VlRXFd3vAURUXR3BUj1H75g/78+fPnz5/zvr5z585/\n/2ZRVVV1/Pjxeh/pAwAAaAo/P78nT56MGzfu5s2b8vLydMeBFhL5SYQsFuuPP/7Q1NSksuiV\nK1eys7Pj4uKoLApN9MsG+uTJk6tXr+Z97evr+6vL7Ozs+B8KAADaBnFx8cOHDw8aNMjJySk+\nPl5MrPG/i4IAkpOSI5YQdKcgEUEQ1J+/ERAQMGnSpEaHYAAtftlAr1q1atasWZmZmRMmTJg5\nc6aent5PF4iLi/fs2ZOyY+wAAEAkdezY8fz584MGDfLx8fHx8aE7DsDPiouLMzMz/f39qSz6\n7NmzhISEa9euUVkUmq6hvUpqamrjx48fO3asu7v74MGDKcsEAABtiq6u7rFjx2xtbfX09HCc\nPwiaCxcuKCoqDho0iMqigYGBRkZGAnh8G/A0vtk/ISGBghwAANCWWVpabtq0ac6cOdra2kZG\nonkOGggpgiCsrKyoPCf38+fPBw8exCnpgqzxBprL5Z48efLQoUOvX7+uq6v77wUPHjwgIRgA\nALQtK1euvH///pQpUzIyMpSVlemOA81TWlUqISYhKyVLdxA+43A4SUlJISEhVBbds2dP586d\nJ0+eTGVRaJbGG+jdu3d7e3szGAwZGRmc4w0AACRhMplRUVHDhw+fPHlycnIyjigVIiI8iTA9\nPb20tNTS0pKyinV1dXv27PH09KRsVh20QOPPOwcFBVlaWubm5lZWVpbUh4KUAADQFkhLS585\nc+bly5eurq50Z4Fm4E0iLCwtzC0WtSO9CYIYPHiwkpISZRXj4uJKS0vnzZtHWUVogcYb6Pfv\n3/v4+PTs2ZOCNAAA0MapqakdP378yJEjkZGRdGcBoOEAu8DAQBcXFwUFBSqLQnM13kCrqKhw\nuVwKogAAADAYjKFDhwYEBCxZsuT27dt0Z4EmEdVJhK9evXr48KGNjQ1lFS9fvpyTk7No0SLK\nKkLLNN5AT58+PTY2loIoAAAAPG5ubg4ODlOmTPnw4QPdWaBxvEmEDsYOIjaJMCEhQV1dXV9f\nn7KKAQEBdnZ2PXr0oKwitAyz0bvLFRUVdnZ2SkpKTk5Ompqa/32OUFtbm7R4AiEiIsLV1bW8\nvFxOTo7uLAAAbUVVVdXQoUPV1dXPnz+PCYVAC1tb265du0ZERFBT7unTp3369ElPT8fwDZ7a\n2lopKan09HQBPA+78T+1dOjQgffFkSNH6r0AGzwAAIDv2rdvf/z4cWNj423btq1Zs4buONDm\nVFVVpaSkxMXFUVbR399/yJAh6J6FQuMN9PTp0yUlJXGWCgAAUExHR+fgwYNTpkwZMGAAleeI\nATAYjJSUFA6HM2rUKGrKffr06e+//z548CA15aCVGm+Lf3XjGQAAgGwTJkxYsmSJo6Njdna2\nlpYW3XGgDSEIYsSIEZTt3gwLC+vSpcvEiROpKQet1IxdZeXl5Q8fPsTBzwAAQKWdO3f27dvX\n3t6+traW7izwS6VVpZU1lXSn4CcWi0XZ+Rs1NTV79uxZunQplQPDoTWa1ECnpqYOGDBAXl6+\nX79+N2/e5L04fvz4y5cvk5kNAACAISEhcfz48VevXvHG4oIAyv+Yr7lSU3uNdskXEbnL9vDh\nw5cvX1LWQB85cqSysnLOnDnUlIPWa7yBzsjIsLCwePr06Y/7z4qLizMzM21sbLKyssiMBwAA\nwFBVVT1y5Eh4eDiOVRVMojeJkMVi6erqUnbOWFBQ0IIFC+Tl5akpB63XeAPt6+urqqr66NGj\nmJiY7y926dLl3r17qqqqmzZtIjEdAAAAg8FgMEaMGOHr6+vu7v7o0SO6s4Doo3IAYWJi4sOH\nDzE8Rbg03kDfvHnTzc2tW7duP72urKzs6up69epVcoIBAAD8y6pVq8zNzSdPnlxWVkZ3FvgX\nEZtEWFpaev36dcoaaH9//2nTpmlqalJTDvii8Qa6tLRUQ0Oj3rfU1NQqKir4HQkAAKAeTCbz\nwIEDX79+nT9/Pt1Z4F9EbBLhxYsXpaWlTU1NKaj15MmTixcvenh4UFAL+Kjx3xRVVVUfP35c\n71tXr15VV1fndyQAAID6KSoqxsfHDxkyJDQ0FH/yFhxyUnLEEoLuFHxDEIS5ubmkpCQFtfz8\n/MzMzAYOHEhBLeCjxu9A29jYhIeHZ2dn//ji58+f16xZEx0dTdkfOAAAABgMhr6+fkREhJeX\nV3p6Ot1ZQAR9+/bt4sWL1LQ3xcXFhw8f9vT0pKAW8FfjDbSPj4+cnNygQYN4P0yrV6/u37+/\nmpra1q1bNTU1169fT35IAACA/5kxY8bMmTOnT5/+4cMHurOAqLl9+3ZRUZGVlRUFtcLCwlRV\nVceNG0dBLeCvxhtoVVXV27dvu7i45OfnMxiMu3fv3r17t0OHDm5ubpmZmSoqKuSHBAAA+JfQ\n0FAlJaU5c+ZwuVy6s4BIIQjC0NCQgh2qNTU1vL+lYHiKMGrSIBVlZeXw8PDi4uLCwsJnz54V\nFhYWFxeHh4crKyuTnQ8AAOC/2rdvf+LEidTU1JCQELqzAIMhQpMIKTvALjY2tqamZvbs2RTU\nAr6r/yHCwsJCKSmpjh078r7+8S05OTkul/vji6qqqqRGBAAA+C9tbe3AwEB3d3czM7P+/fvT\nHadNy/+Yr++jLyMp89j3saKMIt1xWq6wsDA7OzssLIyCWiEhIQsWLJCTk6OgFvBd/Q20mpqa\npaUlm83mfd3wEvjzGQAA0GLu3LmXL1+2t7fPysrq0KED3XHaLt4kwrKqstziXCMtI7rjtByL\nxercubOxsTHZhdhs9uPHjxMSEsguBCSpv4G2t7c3MDD4/jWFeQAAAJohIiLC0NDQ09Nz//79\ndGcBocdisaytrcXEmrTBtTUCAgLs7e1/NWcDBF/9DfTRo0fr/RoAAECgyMnJHT582NTUdNSo\nUY6OjnTHaaNEYxJhXV1dUlJSZGQk2YUePHiQmJh469YtsgsBeZr6O9bDhw9/PC3o4cOHd+7c\nIScSAABAMxgbG2/cuNHd3T0vL4/uLG2UaEwivHbtWmVlpYWFBdmF/P39R4wYQcFGESBP4w10\nXV3dvHnz+vXr9+DBg+8vpqSkGBoazpkzh8PhkBkPAACgcStXrjQ2Nra3t6+rq6M7S1vEm0QY\nNz9OqO9AEwRhYmKiqEjuQ5BFRUVxcXEYniLsGm+gQ0JCDhw4MHa6I0BXAAAgAElEQVTsWC0t\nre8vmpub29vbx8TEhIaGkhkPAACgcWJiYn///XdBQcGGDRvozgLCiiAIGxsbsquEhoZqaGhg\nkLOwa7yBjomJsbW1TUhI6NGjx/cXdXV1jx49amNjgwYaAAAEgYqKSnR09M6dO5OSkujOAsIn\nLy/vyZMnZPe11dXVkZGRnp6eFDynCKRq/J/f8+fPR44cWe9bI0aM4I0nBAAAoJ2VldXixYtn\nzJjx/v17urOAkElISNDU1Ozbl9w93AcPHqyrq3NyciK1ClCg8QZaXl7+5cuX9b718uXLTp06\n8TkRAABAS23fvr1r164Y8U09YZ9ESBCEra0tqSW4XG5QUJCbm5usrCyphYACjTfQY8eOjYqK\nYrFYP75YV1e3b9++yMhICh5WBQAAaCIpKaljx46lpaUFBQXRnaUNyf+Yr7lSU3uNdsmXErqz\ntERlZWVqairZ+zdYLNbz589dXV1JrQLUaPxp2c2bN1+4cGHs2LGampq6urpSUlIlJSWPHj36\n9OmTmpra5s2bKUgJAADQRNra2sHBwa6ursOGDTM0NKQ7Tpsg7JMIL1++zGQyR4wYQWqVgIAA\nR0fHbt26kVoFqNH4HWg1NbU7d+64urpWVlYmJiYmJCSkpaWJi4u7uLhkZmZqampSkBIAAKDp\nZs+ebWdnZ29vX15eTncWEAIEQYwcOVJGRoa8Evfv309OTl66dCl5JYBKTXoIVEVFZc+ePcXF\nxW/evHn+/HlFRUVRUVFkZGTXrl3JzgcAANACe/fuFRMT8/DwoDtImyDskwjZbDbZ+zf8/PxG\njx5tYGBAahWgTP0/6IWFhVJSUh07duR9/f11MTExWVnZ8vLyH3+nV1VVJTslAABAs8jJycXG\nxpqampqbm0+fPp3uOCKON4lQXlpeGCcR5uTkvHr1itQToN++fXv06NHTp0+TVwIoVn8Draam\nZmlpyWazeV83vASedAYAAAE0cODAjRs3Lly40MzMDBtPScWbREh3ihYiCKJv377du3cnr0RY\nWFiPHj2srKzIKwEUq7+Btre3//5XBnt7ewrzAAAA8M2qVavYbPacOXMuXbrEZDLpjgOCiCAI\nUvdvfPnyJSIiYuvWrRieIkrqb6CPHj1a79eChsPhPHr0qLy8XENDQ0NDg+44AAAgWMTExGJ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1yQkBAADop6mpuW7dupUrVxYVFdGdReDw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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Let's what it looks like ...\n",
    "plot(cv_lasso$glmnet.fit, label=FALSE, xvar=\"lambda\")\n",
    "lbs_fun(cv_lasso)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### better coeff shrinkage plot with plotmo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xfkfOWIUqL/+bFcTEiMEFJRXVFWVUYIEREUaTgqIijS8GeMA7cOlFaUVnGq1Duo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",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::It's weird with those numeric labels (plot.glmnet)ç\n",
    "#::NOTE::It seems there's an alternative with adhoc plotmo package\n",
    "# https://stackoverflow.com/questions/30560689/adding-labels-on-curves-in-glmnet-plot-in-r\n",
    "# https://stats.stackexchange.com/questions/133873/lasso-plot-label-lines-with-names-using-glmnet\n",
    "# https://cran.r-project.org/web/packages/plotmo/plotmo.pdf#page=17\n",
    "# plot_glmnet: Plot a glmnet model (Plot the coefficient paths of a glmnet model.)\n",
    "# http://www.milbo.org/doc/plotres-notes.pdf#page=7\n",
    "plotmo::plot_glmnet(x = cv_lasso$glmnet.fit, xvar = 'lambda', label = TRUE)\n",
    "r <- range(cv_lasso$glmnet.fit$beta[,63]) \n",
    "abline(v = log(cv_lasso$lambda.min), col = 'darkgreen', lty = 3, lwd = 2) \n",
    "text(log(cv_lasso$lambda.min) - 1.5, r[2], col = 'darkgreen', 'chosen lambda')\n",
    "segments(log(cv_lasso$lambda.min), r[2] - 0.3 , log(cv_lasso$lambda.min) - 1, r[2], col = 'darkgreen')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**::GMG::** In STHDA a new model is trained with the best lambdas found out with the CV approach. Is it really necessary to do that? Does not `cv.glmnet()` already have provided such a model?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of 13\n",
      " $ a0        : Named num [1:63] -0.699 -1.096 -1.46 -1.795 -2.164 ...\n",
      "  ..- attr(*, \"names\")= chr [1:63] \"s0\" \"s1\" \"s2\" \"s3\" ...\n",
      " $ beta      :Formal class 'dgCMatrix' [package \"Matrix\"] with 6 slots\n",
      "  .. ..@ i       : int [1:334] 1 1 1 1 7 1 7 1 7 1 ...\n",
      "  .. ..@ p       : int [1:64] 0 0 1 2 3 5 7 9 11 13 ...\n",
      "  .. ..@ Dim     : int [1:2] 8 63\n",
      "  .. ..@ Dimnames:List of 2\n",
      "  .. .. ..$ : chr [1:8] \"pregnant\" \"glucose\" \"pressure\" \"triceps\" ...\n",
      "  .. .. ..$ : chr [1:63] \"s0\" \"s1\" \"s2\" \"s3\" ...\n",
      "  .. ..@ x       : num [1:334] 0.00323 0.00616 0.00884 0.01097 0.00337 ...\n",
      "  .. ..@ factors : list()\n",
      " $ df        : int [1:63] 0 1 1 1 2 2 2 2 2 3 ...\n",
      " $ dim       : int [1:2] 8 63\n",
      " $ lambda    : num [1:63] 0.243 0.221 0.202 0.184 0.167 ...\n",
      " $ dev.ratio : num [1:63] 2.97e-15 3.53e-02 6.45e-02 8.89e-02 1.15e-01 ...\n",
      " $ nulldev   : num 348\n",
      " $ npasses   : int 380\n",
      " $ jerr      : int 0\n",
      " $ offset    : logi FALSE\n",
      " $ classnames: chr [1:2] \"0\" \"1\"\n",
      " $ call      : language glmnet(x = X_train, y = y_train, alpha = 1, family = \"binomial\")\n",
      " $ nobs      : int 274\n",
      " - attr(*, \"class\")= chr [1:2] \"lognet\" \"glmnet\"\n"
     ]
    }
   ],
   "source": [
    "#::GMG::Cross-validated model with ... lambda.min or lambda.1se?\n",
    "# https://www.rdocumentation.org/packages/glmnet/versions/2.0-18/topics/cv.glmnet\n",
    "# https://cran.r-project.org/web/packages/glmnet/glmnet.pdf pp. 6, \n",
    "# glmnet.fit: a fitted glmnet object for the full data.\n",
    "str(cv_lasso$glmnet.fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9 x 1 sparse Matrix of class \"dgCMatrix\"\n",
       "                      1\n",
       "(Intercept) -4.85014301\n",
       "pregnant     .         \n",
       "glucose      0.02070629\n",
       "pressure     .         \n",
       "triceps      .         \n",
       "insulin      .         \n",
       "mass         0.01526296\n",
       "pedigree     .         \n",
       "age          0.03382121"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#::GMG::Let's see the regression coefficients\n",
    "#::NOTE::By default it uses \"lambda.1se\" (!) perhaps because it's simpler (?)\n",
    "coef(cv_lasso)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#::GMG:: (STHDA) Fit the final model on the training data and lambda.min\n",
    "model_lambda_min <- glmnet(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    alpha = 1,                     #::NOTE:: L1 LASSO regularization\n",
    "    family = \"binomial\",\n",
    "    lambda = cv_lasso$lambda.min   #::NOTE::Lambda min for L1\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Display regression coefficients\n",
    "coef(model_lambda_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#::GMG::Final model with lambda.1se (this is the only way to get it this time)\n",
    "model_lambda_1se <- glmnet(\n",
    "    X_train, \n",
    "    y_train, \n",
    "    alpha = 1, \n",
    "    family = \"binomial\",\n",
    "    lambda = cv_lasso$lambda.1se\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Display regression coefficients\n",
    "coef(model_lambda_1se)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**::GMG::** Looking at the `coef()` from `cv_lasso` and `model_lambda_1se` I conclude that the model returned as value (`cv_lasso$glmnet.fit` reported in the documentation) is the simpler regularized L1 model indeed! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Make predictions on the test data using the new trained model (STHDA)\n",
    "probabilities_lambda_min <- predict(model_lambda_min, newx = X_test)\n",
    "predicted_classes_lambda_min <- ifelse(probabilities_lambda_min > 0.5, \"pos\", \"neg\")\n",
    "#::NOTE::For the P/R Curve function\n",
    "predicted_classes_lambda_min_num <- ifelse(probabilities_lambda_min > 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Make prediction on test data on the test data using the lambda 1se model\n",
    "probabilities_1se <- predict(model_lambda_1se, newx = X_test)\n",
    "predicted_classes_1se <- ifelse(probabilities_1se > 0.5, \"pos\", \"neg\")\n",
    "predicted_classes_1se_num <- ifelse(probabilities_1se > 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Predict using the cross-validated model\n",
    "# https://cran.r-project.org/web/packages/glmnet/glmnet.pdf pp. 18\n",
    "# https://www.rdocumentation.org/packages/glmnet/versions/2.0-18/topics/predict.cv.glmnet\n",
    "# This function makes predictions from a cross-validated glmnet model, using the stored \"glmnet.fit\" object, \n",
    "# and the optimal value chosen for lambda.\n",
    "#::NOTE::So as long as I don't want the simpler model with lambda.1se I can predict with this!\n",
    "probabilities_cv_lasso <- predict(cv_lasso, newx = X_test)\n",
    "predicted_classes_cv_lasso <- ifelse(probabilities_cv_lasso > 0.5, \"pos\", \"neg\")\n",
    "#::NOTE::For the P/R Curve function\n",
    "predicted_classes_cv_lasso_num <- ifelse(probabilities_cv_lasso > 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "probabilities_lambda_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### evaluation: confusion matrix and metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::'Raw' Model accuracy\n",
    "#::NOTE::observed_classes <- test_data$diabetes\n",
    "cat('Accuracy L1 Lambda Min Model: ', \n",
    "    mean(predicted_classes_lambda_min == observed_classes),\n",
    "   '\\nAccuracy L1 Lambda 1se (Simpler) Model: ', \n",
    "    mean(predicted_classes_1se == observed_classes),\n",
    "   '\\nAccuracy CV Lasso Model: ', \n",
    "    mean(predicted_classes_cv_lasso == observed_classes)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Confusion Matrix\n",
    "cf_lambda_min <- confusion_matrix(true = test_data$diabetes, pred = predicted_classes_lambda_min)\n",
    "#cf_lambda_min <- MLmetrics::ConfusionMatrix(y_true = test_data$diabetes, \n",
    "#                                            y_pred = predicted_classes_lambda_min)\n",
    "#print(cf_lambda_min)\n",
    "print(cf_lambda_min$cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Confusion Matrix\n",
    "cf_lambda_1se <- confusion_matrix(true = test_data$diabetes, pred = predicted_classes_1se)\n",
    "print(cf_lambda_1se$cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Confusion Matrix\n",
    "cf_cv_lasso <- confusion_matrix(true = test_data$diabetes, pred = predicted_classes_cv_lasso)\n",
    "print(cf_cv_lasso$cm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Metrics\n",
    "# https://stackoverflow.com/questions/3443687/formatting-decimal-places-in-r\n",
    "cat(sep='', \"Accuracy: \", format(round(cf_full$accuracy, 2), nsmall = 2), \n",
    "    \", Balanced Accuracy \", format(round(cf_full$balanced_accuracy, 2), nsmall = 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "cat(sep = '', \"Precision: \", format(round(cf_full$precision, 2), nsmall = 2), \n",
    "    \", Recall: \", format(round(cf_full$recall, 2), nsmall = 2),\n",
    "    \", Fl: \", format(round(cf_full$f1, 2), nsmall = 2)\n",
    "   )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "cat(sep='', \"Specificity: \", format(round(cf_full$specificity, 2), nsmall = 2), \n",
    "    \", Sensitivity \", format(round(cf_full$recall, 2), nsmall = 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Confusion Matrix of the 'simpler' model ... no difference!\n",
    "cf_simpler <- confusion_matrix(true = test_data$diabetes, pred = predicted_class_simpler)\n",
    "print(cf_simpler$cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### evaluation: P/R Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Compute the curve\n",
    "# https://cran.r-project.org/web/packages/PRROC/PRROC.pdf pp. 7\n",
    "# Soft-labeled classification problems:\n",
    "# Each data point belongs to both of the two classes with a certain probability, where for each datapoint, these \n",
    "# two probabilities add up to 1.  In this case, the classification scores for all data points need to be provided \n",
    "# only once as scores.class0 and only the positive/foreground weights for each data point need to be provided in\n",
    "# weights.class0, while the converse probability for the negative class is automatically set to \n",
    "# weights.class1 = 1.0 - weights.class0.\n",
    "pr_curve_full <- PRROC::pr.curve(\n",
    "                scores.class0 = predicted_class_num, \n",
    "                weights.class0 = probabilities_full,\n",
    "                min.compute = T, \n",
    "                max.compute = T,\n",
    "                rand.compute = T,\n",
    "                curve = T\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::See all things within the pr_1 object\n",
    "print(pr_curve_full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "#::GMG::Plot the curve\n",
    "# https://cran.r-project.org/web/packages/PRROC/PRROC.pdf pp 3-4\n",
    "options(repr.plot.width = 8, repr.plot.height = 6)\n",
    "plot(pr_curve_full, rand.plot = T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "**::PENDING::** <span style=\"color:red\">Discussion here</span>\n",
    "\n",
    "**::NOTE::** Is this right?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "ls()"
   ]
  }
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