final_draft.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "756fdff0",
   "metadata": {},
   "source": [
    "# Classifying Cardiovascular Diseases in a Simple Way!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f627560",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Cardiovascular diseases (CVDs) collectively describe a group of disorders involving the heart and the blood vessels surrounding it. Research around cariovascular diseases have been a subject of great interest as it is estimated that 17.9 million lives are claimed by CVDs each year worldwide (1). The presence of CVDs correlate with age, cardiovasular related hereditary diseases (type 2 diabetes, thalassemisa, Etc.), and with some behavioral risk factors such as smoking, unhealthy diet, lack of physical exercise, and excessive alcohol consumption (1). It is also noted that individuals with these behavioral risk factors may also present symptoms such as high blood pressure, high blood glucose, high blood lipids, and obesity (1).\n",
    "\n",
    "Common tests to diagnose CVDs include blood work, electrocardiogram, ambulatory monitoring, echocardiogram, cardiac CT's and MRI's, stress tests, and cardiac catheterization (1). However, an accurate diagnosis still require much manual analysis integrating laboratory data and patient information (1). Thus, manual diagnosis can be complex and time consuming while depending on the examining physician's knowledge and experience. Moreover, in facilities with limited resources, the accuracy for diagnosis and treatment of CVDs would suffer. One can imagine that with a lack of diagnostic apparatuses, low physician-to-patient ratios, and shortage of medical expertise can result in poor prediction and treatment of heart patients. Here we explore whether a model that consumes several simple predictors (gathered without advanced machinaries and high quality expertise) could accurately predict the presence of CVDs in patients. The model which we will develop in this report will be a classifier which uses K-Nearest Neighbors (KNN). We opted for a classification model rather than a regression model as the predicted vector is a categorical type and not a numerical type. All the columns in our tidied data set (except for the predicted vector) will be used as predictors.\n",
    "\n",
    "The datasets which we will use to develop our classifier are taken from UCI Machine Learning Repository (https://archive.ics.uci.edu/ml/datasets/Heart+Disease). The data was collected from patients in the following locations:\n",
    "\n",
    "1. Cleveland Clinic Foundation\n",
    "2. Hungarian Institute of Cardiology, Budapest\n",
    "3. V.A. Medical Center, Long Beach, CA\n",
    "4. University Hospital, Zurich, Switzerland\n",
    "\n",
    "Each location compiled a separate database that contain 76 recorded attributes for each patient in their list of heart patients. For our purposes, we are going to focus on a subset of 7 attributes from a combined dataset from all four locations. These variables The 7 attributes are as follows:\n",
    "\n",
    "1. `age` - age of patients\n",
    "2. `sex` - sex of patients\n",
    "3. `exang` - exercised induced angina. Angina is a type of chest pain caused by reduced blood flow to the heart.\n",
    "4. `oldpeak` - ST depression induced by exercise relative to rest. A measurement taken from a patient's electrocardiogram.\n",
    "5. `slope` - Slope of the peak exercise ST segment. A measurement taken from a patient's electrocardiogram.\n",
    "6. `num` - catoregorization of the severity of CVD in 0 to 4, with \"0\" being free of CVD.\n",
    "\n",
    "The reasoning behind the choices of these variables to serve as our predictors came down to several factors: relevance to CVD's, high convenience in acquiring measurement for each predictors, and significant differences of relative incidences of CVD within each predictor's subcategories. For example, one could intuitively generalize that older individuals would be more sickly than younger individuals as their physique and immunity decreases with age and so this might be the case of prevalence of CVD's. There are different biological markers between biological sexes which may lead to higher risk factors for CVD's (2). Angina is a type of chest pain caused by reduced blood flow to the heart, which shouldn't be frequently induced in healthy individuals (3). Electrocardiogram is one of the cheapest, simplest, non-invasive, and fastest tests to evaluate the heart by its electrical activities (4). Individually, none of these predictors would reliably detect the presence of CVD's. However, concatenating these predictors in a classifier, we might be able to isolate a \"finger print pattern\" which could reliably detect CVD's."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bea5c65-9507-46fe-a290-8c31722f82d8",
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   "source": [
    "## Wrangling and Tidying Data\n",
    "\n",
    "To tidy our data we:\n",
    "- Added an origin category for each observation.\n",
    "- Combined four datasets into one mega data set.\n",
    "- Renamed each column so they are more readible and select the columns of interest.\n",
    "- Removed all observations which doesn't contain the a value for every predictor.\n",
    "- Converted the vector type for each column so they could be pass to the `recipe` function.\n",
    "\n",
    "The code for each manipulation is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cb96d65f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.1 ──\n",
      "\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.3.6     \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.4\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.1.7     \u001b[32m✔\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.9\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtidyr  \u001b[39m 1.2.0     \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mreadr  \u001b[39m 2.1.2     \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.5.1\n",
      "\n",
      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\n",
      "── \u001b[1mAttaching packages\u001b[22m ────────────────────────────────────── tidymodels 1.0.0 ──\n",
      "\n",
      "\u001b[32m✔\u001b[39m \u001b[34mbroom       \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mrsample     \u001b[39m 1.0.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mdials       \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mtune        \u001b[39m 1.0.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34minfer       \u001b[39m 1.0.2     \u001b[32m✔\u001b[39m \u001b[34mworkflows   \u001b[39m 1.0.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mmodeldata   \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mworkflowsets\u001b[39m 1.0.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mparsnip     \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34myardstick   \u001b[39m 1.0.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mrecipes     \u001b[39m 1.0.1     \n",
      "\n",
      "── \u001b[1mConflicts\u001b[22m ───────────────────────────────────────── tidymodels_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mscales\u001b[39m::\u001b[32mdiscard()\u001b[39m masks \u001b[34mpurrr\u001b[39m::discard()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m   masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mrecipes\u001b[39m::\u001b[32mfixed()\u001b[39m  masks \u001b[34mstringr\u001b[39m::fixed()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m      masks \u001b[34mstats\u001b[39m::lag()\n",
      "\u001b[31m✖\u001b[39m \u001b[34myardstick\u001b[39m::\u001b[32mspec()\u001b[39m masks \u001b[34mreadr\u001b[39m::spec()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mrecipes\u001b[39m::\u001b[32mstep()\u001b[39m   masks \u001b[34mstats\u001b[39m::step()\n",
      "\u001b[34m•\u001b[39m Use \u001b[32mtidymodels_prefer()\u001b[39m to resolve common conflicts.\n",
      "\n",
      "\u001b[1mRows: \u001b[22m\u001b[34m303\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m14\u001b[39m\n",
      "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n",
      "\u001b[1mDelimiter:\u001b[22m \",\"\n",
      "\u001b[31mchr\u001b[39m  (2): X12, X13\n",
      "\u001b[32mdbl\u001b[39m (12): X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X14\n",
      "\n",
      "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n",
      "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n",
      "\u001b[1mRows: \u001b[22m\u001b[34m294\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m14\u001b[39m\n",
      "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n",
      "\u001b[1mDelimiter:\u001b[22m \",\"\n",
      "\u001b[31mchr\u001b[39m (9): X4, X5, X6, X7, X8, X9, X11, X12, X13\n",
      "\u001b[32mdbl\u001b[39m (5): X1, X2, X3, X10, X14\n",
      "\n",
      "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n",
      "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n",
      "\u001b[1mRows: \u001b[22m\u001b[34m123\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m14\u001b[39m\n",
      "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n",
      "\u001b[1mDelimiter:\u001b[22m \",\"\n",
      "\u001b[31mchr\u001b[39m (9): X4, X6, X7, X8, X9, X10, X11, X12, X13\n",
      "\u001b[32mdbl\u001b[39m (5): X1, X2, X3, X5, X14\n",
      "\n",
      "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n",
      "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n",
      "\u001b[1mRows: \u001b[22m\u001b[34m200\u001b[39m \u001b[1mColumns: \u001b[22m\u001b[34m14\u001b[39m\n",
      "\u001b[36m──\u001b[39m \u001b[1mColumn specification\u001b[22m \u001b[36m────────────────────────────────────────────────────────\u001b[39m\n",
      "\u001b[1mDelimiter:\u001b[22m \",\"\n",
      "\u001b[31mchr\u001b[39m (9): X4, X5, X6, X8, X9, X10, X11, X12, X13\n",
      "\u001b[32mdbl\u001b[39m (5): X1, X2, X3, X7, X14\n",
      "\n",
      "\u001b[36mℹ\u001b[39m Use `spec()` to retrieve the full column specification for this data.\n",
      "\u001b[36mℹ\u001b[39m Specify the column types or set `show_col_types = FALSE` to quiet this message.\n"
     ]
    }
   ],
   "source": [
    "#Loading Packages\n",
    "library(tidyverse)\n",
    "library(tidymodels)\n",
    "library(RColorBrewer)\n",
    "library(knitr)\n",
    "\n",
    "#Loading the Data\n",
    "cleveland <- read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.cleveland.data\", col_names = FALSE)\n",
    "hungarian <- read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.hungarian.data\", col_names = FALSE)\n",
    "switzerland <- read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.switzerland.data\", col_names = FALSE)\n",
    "va <- read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.va.data\", col_names = FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c88925e7-a8e2-465e-a1d4-7f75f29f82bc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 6 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>age</th><th scope=col>sex</th><th scope=col>exercise_induced_angina</th><th scope=col>st_depression</th><th scope=col>st_segment_slope</th><th scope=col>presence_of_cvd</th><th scope=col>origin</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;fct&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>63</td><td>1</td><td>0</td><td>2.3</td><td>3</td><td>No</td><td>cleveland</td></tr>\n",
       "\t<tr><td>37</td><td>1</td><td>0</td><td>3.5</td><td>3</td><td>No</td><td>cleveland</td></tr>\n",
       "\t<tr><td>41</td><td>0</td><td>0</td><td>1.4</td><td>1</td><td>No</td><td>cleveland</td></tr>\n",
       "\t<tr><td>56</td><td>1</td><td>0</td><td>0.8</td><td>1</td><td>No</td><td>cleveland</td></tr>\n",
       "\t<tr><td>57</td><td>0</td><td>1</td><td>0.6</td><td>1</td><td>No</td><td>cleveland</td></tr>\n",
       "\t<tr><td>57</td><td>1</td><td>0</td><td>0.4</td><td>2</td><td>No</td><td>cleveland</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 7\n",
       "\\begin{tabular}{lllllll}\n",
       " age & sex & exercise\\_induced\\_angina & st\\_depression & st\\_segment\\_slope & presence\\_of\\_cvd & origin\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct> & <chr>\\\\\n",
       "\\hline\n",
       "\t 63 & 1 & 0 & 2.3 & 3 & No & cleveland\\\\\n",
       "\t 37 & 1 & 0 & 3.5 & 3 & No & cleveland\\\\\n",
       "\t 41 & 0 & 0 & 1.4 & 1 & No & cleveland\\\\\n",
       "\t 56 & 1 & 0 & 0.8 & 1 & No & cleveland\\\\\n",
       "\t 57 & 0 & 1 & 0.6 & 1 & No & cleveland\\\\\n",
       "\t 57 & 1 & 0 & 0.4 & 2 & No & cleveland\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 7\n",
       "\n",
       "| age &lt;dbl&gt; | sex &lt;dbl&gt; | exercise_induced_angina &lt;dbl&gt; | st_depression &lt;dbl&gt; | st_segment_slope &lt;dbl&gt; | presence_of_cvd &lt;fct&gt; | origin &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 63 | 1 | 0 | 2.3 | 3 | No | cleveland |\n",
       "| 37 | 1 | 0 | 3.5 | 3 | No | cleveland |\n",
       "| 41 | 0 | 0 | 1.4 | 1 | No | cleveland |\n",
       "| 56 | 1 | 0 | 0.8 | 1 | No | cleveland |\n",
       "| 57 | 0 | 1 | 0.6 | 1 | No | cleveland |\n",
       "| 57 | 1 | 0 | 0.4 | 2 | No | cleveland |\n",
       "\n"
      ],
      "text/plain": [
       "  age sex exercise_induced_angina st_depression st_segment_slope\n",
       "1 63  1   0                       2.3           3               \n",
       "2 37  1   0                       3.5           3               \n",
       "3 41  0   0                       1.4           1               \n",
       "4 56  1   0                       0.8           1               \n",
       "5 57  0   1                       0.6           1               \n",
       "6 57  1   0                       0.4           2               \n",
       "  presence_of_cvd origin   \n",
       "1 No              cleveland\n",
       "2 No              cleveland\n",
       "3 No              cleveland\n",
       "4 No              cleveland\n",
       "5 No              cleveland\n",
       "6 No              cleveland"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Adding an origin category for each row/combining dataset into one\n",
    "cleveland_data <- mutate(cleveland, Origin = \"cleveland\")\n",
    "hungarian_data <- mutate(hungarian, Origin = \"hungarian\")\n",
    "switzerland_data <- mutate(switzerland, Origin = \"switzerland\")\n",
    "va_data <- mutate(va, Origin = \"longbeach\")\n",
    "mega <- rbind(cleveland_data, hungarian_data, switzerland_data, va_data)\n",
    "\n",
    "#Adding names to each column & selecting columns of interest\n",
    "column_names = c(\"age\", \"sex\", \"X3\", \"X4\", \"X5\", \"X6\", \"X7\", \"X8\", \"exercise_induced_angina\", \"st_depression\", \"st_segment_slope\", \"X12\", \"X13\", \"presence_of_cvd\", \"origin\")\n",
    "colnames(mega) <- column_names\n",
    "mega_data <- mega |> select(age, sex, exercise_induced_angina, st_depression, st_segment_slope, presence_of_cvd, origin)\n",
    "\n",
    "#Removing all rows that with at least one missing variable in any column.\n",
    "tidy_data <- mega_data |> filter(exercise_induced_angina != \"?\" & st_depression != \"?\" & st_segment_slope != \"?\")\n",
    "\n",
    "#Combining heart severity levels 1 to 4 into one measurement and vari in presence_of_cvd into \"Yes\" or \"No\"\n",
    "severity_1_to_4 <- tidy_data |> filter(presence_of_cvd != 0) |> mutate(presence_of_cvd = \"Yes\")\n",
    "tidy_data_final <- tidy_data |> filter(presence_of_cvd == 0) |> mutate(presence_of_cvd = \"No\") |> rbind(severity_1_to_4)\n",
    "\n",
    "#Converting column into workable vectors\n",
    "tidy_data_final <- tidy_data_final |> \n",
    "    mutate(presence_of_cvd = as_factor(presence_of_cvd)) |>\n",
    "    mutate(exercise_induced_angina = as.double(exercise_induced_angina)) |>\n",
    "    mutate(st_depression = as.double(st_depression)) |>\n",
    "    mutate(st_segment_slope = as.double(st_segment_slope))\n",
    "head(tidy_data_final)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48ff06ac-ba8a-4197-a106-4b6dd7ff8a2f",
   "metadata": {},
   "source": [
    "*Table 1: First 6 rows of tidied dataset*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "052a52e7-6a1b-4f7e-bde9-d6239510927c",
   "metadata": {},
   "source": [
    "From Table 1, we see our data set is now tidy as it meets the three criteria for tidy data:\n",
    "- Each row is a single observation.\n",
    "- Each column is a single variable.\n",
    "- Each value is a single cell."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cb8f95a-b4aa-4c26-b894-9f2b3b96f2c9",
   "metadata": {},
   "source": [
    "## Summary of Dataset\n",
    "\n",
    "We decided on a 75-25 split of the tidied data, and used the larger set as the training set to maximize the accuracy of our classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "924f9866-2966-4b16-8ce9-6e9720332393",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating training and testing data set. \n",
    "set.seed(1)\n",
    "split_data <- initial_split(tidy_data_final, prop = 0.80, strata = presence_of_cvd)\n",
    "training_data <- training(split_data)\n",
    "testing_data <- testing(split_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1abcac7b-34dd-4d26-a777-99a0924090d6",
   "metadata": {},
   "source": [
    "Here we generated a table to see how many rows were removed during the tidying process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "47f7bd81-b9eb-4767-bfbe-8991321392dc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>nrows_in_raw_data</th><th scope=col>nrows_with_missing_data</th><th scope=col>nrows_in_tidy_data</th><th scope=col>nrows_in_training</th><th scope=col>nrows_in_testing</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>920</td><td>310</td><td>610</td><td>487</td><td>123</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " nrows\\_in\\_raw\\_data & nrows\\_with\\_missing\\_data & nrows\\_in\\_tidy\\_data & nrows\\_in\\_training & nrows\\_in\\_testing\\\\\n",
       " <int> & <int> & <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 920 & 310 & 610 & 487 & 123\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 5\n",
       "\n",
       "| nrows_in_raw_data &lt;int&gt; | nrows_with_missing_data &lt;int&gt; | nrows_in_tidy_data &lt;int&gt; | nrows_in_training &lt;int&gt; | nrows_in_testing &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 920 | 310 | 610 | 487 | 123 |\n",
       "\n"
      ],
      "text/plain": [
       "  nrows_in_raw_data nrows_with_missing_data nrows_in_tidy_data\n",
       "1 920               310                     610               \n",
       "  nrows_in_training nrows_in_testing\n",
       "1 487               123             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Summary of number of rows in the mega data set, tidied data set, deleted rows from mega data set to create tidied data set, and training data set.\n",
    "nrows_in_raw_data <- nrow(mega_data)\n",
    "nrows_in_tidy_data <- nrow(tidy_data_final)\n",
    "nrows_in_training <- nrow(training_data)\n",
    "nrows_in_testing <- nrow(testing_data)\n",
    "raw_stats <- data.frame(nrows_in_raw_data, nrows_in_tidy_data, nrows_in_training, nrows_in_testing) |> \n",
    "    mutate(nrows_with_missing_data = nrows_in_raw_data - nrows_in_tidy_data) |>\n",
    "    select(nrows_in_raw_data, nrows_with_missing_data, nrows_in_tidy_data, nrows_in_training, nrows_in_testing)\n",
    "raw_stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f33a87c8-79a2-4597-9031-eace953df91b",
   "metadata": {},
   "source": [
    "*Table 2: Summary of number of rows in raw data, tidy Data, training Set, and testing Set*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd2a6fe7-7ddb-4f63-af14-5242ae819df4",
   "metadata": {},
   "source": [
    "From Table 2, we can see that a significant number of rows were removed from the initial mega dataset we created. However, we still ended up with tidied 610 observations with 487 observation in our training set. This quantity should be an adequate number of data points to carry forward with creating the classifier. \n",
    "\n",
    "Another potential issue in a data set for a classifier could be class imbalance. To check class balance in our training set we generated another table:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "53e006d6-2e5d-4a77-b687-54f74b587611",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>CVD_false</th><th scope=col>CVD_true</th><th scope=col>total_count</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>173</td><td>314</td><td>487</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " CVD\\_false & CVD\\_true & total\\_count\\\\\n",
       " <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 173 & 314 & 487\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| CVD_false &lt;int&gt; | CVD_true &lt;int&gt; | total_count &lt;int&gt; |\n",
       "|---|---|---|\n",
       "| 173 | 314 | 487 |\n",
       "\n"
      ],
      "text/plain": [
       "  CVD_false CVD_true total_count\n",
       "1 173       314      487        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Summary of patients with CVD in training data set\n",
    "training_stats <- training_data |> \n",
    "    group_by(presence_of_cvd) |> \n",
    "    count() |> \n",
    "    pivot_wider(names_from = presence_of_cvd, values_from = n) |> \n",
    "    rename(CVD_true = Yes, CVD_false = No) |> \n",
    "    mutate(total_count = nrows_in_training)\n",
    "training_stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99515624-ef04-4318-bedf-ce5637ca6af4",
   "metadata": {},
   "source": [
    "*Table 3: Class distribution in training set*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62d47753-e546-40f1-adc3-f34084b8192a",
   "metadata": {},
   "source": [
    "In Table 3, we see higher counts for `CVD_false` (0.64) than counts for `CVD_true` (0.36). However, we are going assume that class of `CVD_true` is abundant enough that there shouldn't be significant bias toward the other class. Some bias could be mitigated by using higher K-neighbor values in our classifier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2318e54a-08d3-4b2d-bd81-e20616f68fd6",
   "metadata": {},
   "source": [
    "## Visualing the Relationship of Predictors with the Predicted Variable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c17f1d0-71bc-428c-9d31-53f7272cd812",
   "metadata": {},
   "source": [
    "We chose to visualize the relationship between our predictors and the predicted variable using histograms and bar graphs. The main decision to use histograms for `age`, and `ST_depression` was because their values were quite spread. Using histograms, we wanted to visualize the distribution of these predictors. The main decision to use bar graphs for `sex`, `ST_segment_Slopes`, and `exercise_induced_angina` was because the values of these predictors could be counted in selective groups. By setting our predicted variable to `fill`, we could visualize the relative distribution our predicted variable in each of those groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "66b6d5dc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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ESrVq2GDBky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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Age vs. presence of CVD.\n",
    "options(repr.plot.width = 10, repr.plot.height = 7)\n",
    "age_vs_pred <- training_data |>\n",
    "    ggplot(aes(x = age, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_histogram(bins = 25) + \n",
    "    labs(x = \"Age (Years)\", y = \"Count (n)\", fill = \"CVD Present\") + theme(text = element_text(size = 15)) +\n",
    "    ggtitle(\"Figure 1: Count of Age Groups Separated by the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired') +\n",
    "    facet_grid(rows = vars(presence_of_cvd))\n",
    "age_vs_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f265cbba-e2e1-4a8f-b0c0-d87064b1581b",
   "metadata": {},
   "source": [
    "In Figure 1, by using the `facet_grid` function to separate the distributions of age by the `presence_of_cvd`, we see that the distribution of the `Yes` group for CVD present is skewed to the left, and the distribution of the `no` group for CVD present is roughly bell-shaped."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "41bad580-ef98-42ea-8efc-342705726006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SDF0HRL9q/7qlChwvDhwxcuXLhx48a1a9fOnDlTvZvGYDDMnDnT+aqmTZsmhAgO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\n3Yo/WgAAAAC4W2mQEN57770zZsxYtWrVjh07MjMzq1Sp8sorrzz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nYmJiXn755YiIiJs3b65YsaJx48ZTpkzxbIXFxtWEcNeuXQcOHFB/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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ST depression vs. presence of CVD.\n",
    "options(repr.plot.width = 10, repr.plot.height = 5)\n",
    "st_depression_plot <- ggplot(training_data, aes(x = st_depression, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_histogram(binwidth = 1, position = \"dodge\") + \n",
    "    labs(x = \"ST Depression\", y = \"Count (n)\", fill = \"CVD Present\") + theme(text = element_text(size = 15)) +\n",
    "    ggtitle(\"Figure 2: Distribution of ST Depression with the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "st_depression_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34779fdd-8e87-4487-bd23-3a24f45df73c",
   "metadata": {},
   "source": [
    "We decided to the separate the distribution by setting `position = \"dodge\"` in the `geom_histogram` function instead of using the `facet_grid` function as there were gaps between certain ranges. This way we can better see from Figure 2 that there is a certain range of ST depression (approximately 0 to 1) that has the least relative presence of CVD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1f3549ea-e962-419d-b28d-1f351678ccba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qZ6Z8NoF63CiVdoH45UtwtYWxsSp6ur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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Converting the values into intuitive names.\n",
    "males <- training_data |> filter(sex != 0) |> mutate(sex = \"M\")\n",
    "sex_data <- training_data |> filter(sex == 0) |> mutate(sex = \"F\") |> rbind(males)\n",
    "\n",
    "#Sex vs. presence of CVD.\n",
    "options(repr.plot.width = 5, repr.plot.height = 5)\n",
    "sex_plot <- ggplot(sex_data, aes(x = sex, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_bar(position = \"fill\") + \n",
    "    labs(x = \"Sex\", y = \"Relative Distribution\", fill = \"CVD Present\") + theme(text = element_text(size = 13)) +\n",
    "    ggtitle(\"Figure 3: Distribution of Sex with the  \\nPresence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "sex_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ed7baba-6700-4a1c-a230-5e2ea45fd1a9",
   "metadata": {},
   "source": [
    "In Figure 3, by setting `position = \"fill\"`, we see that the relative presence of CVD is higher in males."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "404c5b39-5ab0-4924-9b13-a91583f05e65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ISQR48eEUKY04cMkUjk4uJSkUXLoufzXF1dFSfRw7+EkMePH9va2pY6e6noMVV6\niakaRo0aNXv27MzMzP3799O9UkJIRkbGgQMHiMJdE+zRjpW7xRCgWtCvRPjbb78xx3/Onz9P\nCKG/bh06dLh///7169e9vb3T09Pv3r0rEonosUc1KO46VFyZbdK9hDdv3qi4hD0tLa3MBeXk\n5OTk5MiWiMXixo0b+/r6TpkyhblIRJalpaXawbRq1erMmTOTJ0++d+9eaGhoaGioQCDo2LHj\n0KFDhw4dytxIoMank9vPU0TbpP8nyqymdsfSGxVKDYYealY9e6ksLCwIIe/fvy/XXAyJRPLD\nDz/s2LFjy5YtTCLcu3dvTk6ORCJR7yntmZmZdLVRXBkAqj59OTRKCGnXrp1YLL5//z793aFX\nDXTs2JEQ0qFDB0IIPToaHR1dXFzs5eVlZGRUmeGWE91LCA4OVnEcnDnSqILiqaDMzMzY2NiV\nK1eWmgVJaTsB5QrGy8srJibm6tWrc+bM8fT0LC4uPnfunL+/v4eHB72zW4OfTjFI1ePHVnzR\n9MyZtLRRzZhCugj2nJ2dCSHJycnPnz8v14wMutt39erVJ0+e0BJ6XHTkyJFs7uVXdPnyZfqi\nWbNm6oUEUIn0KBEKBAJvb++SkpLLly9nZ2ffunXLycmJjlAlmwgreFy0stC9hLdv31Z2IISo\nFUybNm0WLVp069atd+/erVq1SiwWx8bGBgUFqd0gyyDLPG9awUXTfUG6WymHuau9zJ1XOfTf\nGyFk27Ztqmtev36duUxUVps2beiJQJr/Hj58SC8yUjwVzRIdHdDS0lLxODlA1adHiZAQ0rVr\nV0JIdHR0dHR0YWEhc/CzVq1aDg4O169fz8/Pr6aJkP6uPXjwoLIDIaRiwdSuXXvatGk7duwg\nhJw5c6akpKSCDSrTtGlTQojiiHGFhYW7du3atWsXPfZYwUXT0410bBc59OwjU4c9e3v7zp07\nE0LWrl2bkJCgrFpmZuaQIUM6d+48d+5cxak05+3fv18qle7atYsQ4u3tTS8oLa+rV68ePHiQ\nEDJp0qTy7t0CVAX6tdbSC+gvX75M/ybLXv7QoUOH/Pz88+fPP3jwoG7duvRXUhlm0NGioiJN\nxVbBNvv06UMIefz4sezlr9TRo0ebN28eGhpasQA1H8z79+9//PHHXr16KX5kupOUl5dHLwnR\nxqejxzNjYmKY+9OpyMjI4cOHjxgxQiOL7t27NyHk6tWrihmL3qfh4eFRp06d8q885/AAACAA\nSURBVAa/bNkygUCQlZXVo0ePxMRExQopKSk+Pj70QRZ0SCA5w4YNE4vFr1+/vnbtGk1j6l0m\nc/fu3QEDBhQXF9evX3/q1KlqtABQ6fQrETZu3Lh+/foxMTEXL17kcDjMISby36OjK1euLCkp\nKXN3kMfj0Yssbt68qanYKthmt27d6OCQw4cPj4mJYcojIiJGjx4dExMjd3+CVrEMxtzc/MiR\nI6dOnRo3bpzsBSOpqanMWAf0ehltfLo+ffrQvztDhgxhnjD14MGDiRMnEkK+//57Ov5LBRfd\np08fV1fXkpKSYcOGyd5asHXrVpoI58yZU97ICSGenp5r167lcDjPnj1zcXGZNWtWTExMdnZ2\ncXFxYmLismXLHB0db9y4YWxsvG/fPjqujRwTE5MhQ4YQQmbNmvXixYtatWrRq6lZKiwsvHnz\n5pQpU9q2bfv+/XuJRHLs2DFtXCYGoAsqLgH4KtFxh4nCKDNJSUlMnxw8eFB2kuIN9VKZ6yMa\nNWpkY2OTl5en4pFJM2bMIIS0a9dOdWwVbPPVq1fMXRYuLi7e3t7MvWu+vr6K42fKYXPftCzV\nj4hiGUxkZCRN/0Kh0NXVtWPHju7u7jT51apVS/bhPiwbLFePPX36lI5qxuVyHRwc6tevT/fL\nHR0dP378qKmOffbsGR3IzdDQsEWLFp06daILJYQsWLBAtibLG+oZR44cYZpSVL9+/Vu3bqmY\nXTavz5w5U1k1xccwmZiYyD6JpXXr1i9evGAZM0AVpHeJkB4FKvXnhv668Xi8tLQ02fJSE+HL\nly+7dOliZGQkFovd3NwKCgoqnggr3mZWVhYdG9rMzIzH41laWvr4+OzcubO4uLjMntFsImQf\nzPPnz6dPn+7s7GxhYcHj8UxNTT08PObMmSM7BhD7BsvbY6mpqb/++quTk5OxsbGhoaGLi8ui\nRYvoQHFqfBZlUlNT582b16xZM7FYLBQK69atO3jw4CtXrshVK28ilEqlOTk5f/75Z58+ferX\nr29kZEQHBO/Vq9fff//NDMinAt3Z5XA4KgaFpyuGHBMTEwcHh4CAgPDwcPbRAlRNHGlZj6sG\nAAD4iunXOUIAAAA5SIQAAKDXkAgBAECvIRECAIBeQyIEAAC9hkQIAAB6DYkQAAD0GhIhAADo\nNSRCAADQa0iEAACg15AIAQBAryERAgCAXkMiBAAAvcav7AB0JDMzU9kkDocjFArz8/N1GU95\nCQQCPp+fn59fUlJS2bEohZ7UFA6HIxAICgoKKjsQVYRCIY/How97quxYlOJyuXw+X0VP8vl8\nQ0NDXYYEVZC+JEIVv85cLtfAwKCK/3zz+Xw+n5+dnV1YWFjZsSjF4/FEIlEV70maCLOysoqK\niio7FqV4PF7V/0shFAr5fH5hYWFxcXFlx6IU3XCqeE9CpcOhUQAA0GtIhAAAoNeQCAEAQK8h\nEQIAgF5DIgQAAL2GRAgAAHoNiRAAAPQaEiEAAOg1JEIAANBrSIQAAKDXkAgBAECvIRECAIBe\nQyIEAAC9hkQIAAB6TdePYbp+/fr69esFAsE///yjuuaNGzfCwsJevXolFArd3d1Hjx5taWnJ\ncioAAABLutsjzM3NXbNmzerVq42NjcusfOfOnaVLl9rZ2YWEhAQFBSUlJc2ZM4d5uqbqqQAA\nAOzpLhHevXv31atXoaGhDg4OZVbevXu3g4NDUFCQm5tbu3btZs2a9f79+/Pnz7OZCgAAwJ7u\nEqGTk9OKFSusrKzKrJmenh4fH9+uXTumxNra2tbW9vbt22VOBQAAKBfdJUKJRMLj8djUfPPm\nDSHExsZGttDGxub169dlTgUAACgXXV8sw0Z2djYhxMjISLbQ0NCQlqueypgzZ054eDh9LZFI\nzp49q3qh1eJaGzMzs8oOoWzVoidr1KhR2SGUrVr0pEQiqewQyiYSiZRNKioq0mUkUDVVxURI\ncTgctd8SQho2bNiyZUv6WiwWFxYWqlgWn8+X2x4OPvxY3oD10wDn2rJv0ZNqk+tJHo9XXFws\nW4KeZEm2JzkcDpfLletJWSUlJXx+1f0ZBN2oimsAvaxUbg8vKytLLBaXOZXh7+/v7+/PvE1O\nTla2OC6Xa2pqmp6eronY9Y5sv/F4PLFYjJ5Uj1xPGhsbZ2RkVGI81ZdsT/L5fENDw8zMTGWV\nRSKRiv1F0BNV8Yb6evXqEULkzvklJSXZ2tqWORUAAKBcqmIiNDU1bdKkyZUrV6RSKS1JSEh4\n+/YtPdSpeioAAEC58ObPn6+bJb169er169efPn26c+dOSkpKo0aNPn36lJmZaW5uTgi5cuXK\n2rVrGzduTK9iqFOnzqFDhz5+/GhoaBgXF7dp0yYLC4uJEydyudwyp5YqJydH2SQOhyMSifLy\n8mQLEzJwCp2Vhmb//+g6l8sVCoX5+fmyFdCTLKEnNUWuJwUCgYrRNvh8Pg6Ngu7OEe7atevG\njRvM29mzZxNC7O3t//jjD0JIWlpaXFwck65cXFxCQkJ27969cOFCAwMDT0/P0aNHM3dfqJ4K\nAADAHoc5wPh1K/NimbS0NNnCs6/zlNUHWT71DJjXpV4sg55kSa4nFS+WQU+yJNuTbC6WMTEx\n0UlcUHVVxXOEAAAAOoNECAAAeg2JEAAA9BoSIQAA6DUkQgAA0GtIhAAAoNeQCAEAQK8hEQIA\ngF5DIgQAAL2GRAgAAHoNiRAAAPQaEiEAAOg1JEIAANBrSIQAAKDXkAgBAECvIRECAIBeQyIE\nAAC9hkQIAAB6DYkQAAD0GhIhAADoNSRCAADQa0iEAACg15AIAQBAryERAgCAXkMiBAAAvYZE\nCAAAeg2JEAAA9BoSIQAA6DUkQgAA0GtIhAAAoNeQCAEAQK8hEQIAgF5DIgQAAL2GRAgAAHoN\niRAAAPQaEiEAAOg1JEIAANBrSIQAAKDXkAgBAECvIRECAIBeQyIEAAC9hkQIAAB6DYkQAAD0\nGhIhAADoNSRCAADQa0iEAACg1/iVHYCO1KhRQ8VUHo8nX+H1B+0G9LWQ7TcOh8PlctGT6kFP\nakrZPSmjpKREJ0FBlaYviTAzM1PZJA6HY2JioqICqCDbb1wu19jYGD2pHtl+4/F4hoaGWVlZ\nlRhP9SXbk3w+XyQSZWdnK6ssEAiEQqFO4oKqS18SYXFxsbJJXC5XKpWqqAAqyPUbelJt6ElN\nke03Doejuif5fH35DQQVcI4QAAD0GhIhAADoNSRCAADQa0iEAACg15AIAQBAryERAgCAXkMi\nBAAAvYZECAAAeg2JEAAA9BoSIQAA6DUkQgAA0GtIhAAAoNeQCAEAQK8hEQIAgF5DIgQAAL2G\nRAgAAHoNiRAAAPQaEiEAAOg1JEIAANBrSIQAAKDXkAgBAECvIRECAIBeQyIEAAC9hkQIAAB6\nDYkQAAD0GhIhAADoNSRCAADQa0iEAACg15AIAQBAryERAgCAXkMiBAAAvYZECAAAeg2JEAAA\n9BoSIQAA6DUkQgAA0GtIhAAAoNeQCAEAQK8hEQIAgF5DIgQAAL2GRAgAAHoNiRAAAPQaEiEA\nAOg1JEIAANBrSIQAAKDXkAgBAECv8XW5sBs3boSFhb169UooFLq7u48ePdrS0lKxWnJy8ujR\noxXLHR0dly9fTgjZuHFjeHi43NQVK1Y4ODhoI2yAquDX/fcrO4TqwSe4VWWHANWM7hLhnTt3\nli5d6uPjM3LkyKysrL17986ZM2ft2rVCoVCuppmZ2ZIlS2RLioqKVqxY0ahRI/o2JyfH2to6\nMDBQtk69evW0Gj8AAHyVdJcId+/e7eDgEBQURN82aNBg4sSJ58+f7969u1xNgUDg4uIiW7J3\n716hUDhkyBD6NicnRyKRyNWBqgn7MSxhPwagsujoHGF6enp8fHy7du2YEmtra1tb29u3b5c5\n7+vXrw8cODB27FgjIyNakpOTY2hoqK1YAQBAn+goEb5584YQYmNjI1toY2Pz+vXrMufduXOn\nnZ2dbBJFIgQAAE3R0aHR7OxsQgizS0cZGhrSchUSEhKuX78+f/582cKcnJzU1NTFixc/e/as\nuLi4QYMGAwcOdHNzk60THR2dmJhIXxsYGPTq1UvZIjgcDpfLVciseWV9JiCEENl+43K5pfUk\nsCLXkzweDz2pnnL1JJeLK+dBt1eNcjgcFW9LdeDAATs7u+bNm8vNmJKS4uXlNXDgwNTU1OPH\nj4eEhMyfP9/d3Z2pExERwVxZKpFI/Pz8VC/I2Nj4fwu+lBkbkFL6rZQSYAM9qSmK/cbnK/2h\nKyoq0nI4UA3oKBHSVVNu/y8rK0ssFquYKzc399atW4MGDZIr/+uvv2TfNm/efMKECXv27JFN\nhIMGDfL29qavhUJhZmamsqVwOBxDQ8OcnBxWnwT+l2zHcrlcAwMD9KR65HpSJBLl5uZWYjzV\nl1xPCoXCvDylB3h4PJ6KNAl6QkdrAL234fXr156enkxhUlKSra2tirlu3LhRUFDQpk0b1Y0L\nhcJ69erR05AMZ2dnZ2dn5m1ycrKy2enPd35+vuqlQKlk+43H4wmFQvSkeuR6UiAQoCfVI9tv\nfD6fz+er6EmRSKSToKBK09HxcVNT0yZNmly5ckUqldKShISEt2/ftmzZUsVcMTExEolE7hKb\nz58/L1++/ObNm0xJbm5uQkKCtbW1NiIHAICvm+5OFA8fPjw+Pn7NmjX379+Pjo5evny5ra1t\np06d6NQrV65Mnz795cuXsrMkJSUppjdLS8tPnz6tWbPm9OnTz549u3Hjxrx587KysgYOHKib\nDwIAAF8T3R0cd3FxCQkJ2b1798KFCw0MDDw9PUePHs3j8ejUtLS0uLg4udNLGRkZFhYWcu1w\nOJz58+fv27fv8OHDqampQqGwSZMmS5cudXR01NEnAQCArwiHOVb5dVN9jtDU1DQtLU228Oxr\n3D7Bik89A+Y1j8cTi8Xp6emyFTxX3dB5UNXSbZmRZXg8nrGxcUZGhmwF9CRLsj3J5/MNDQ1V\nXCsnEolMTEx0EhdUXbiHBgAA9BoSIQAA6DUkQgAA0GtIhAAAoNeQCAEAQK+xvX3ixYsXBw4c\nePHiRV5eXqkXmu7atUujgQEAAOgCq0QYERHRu3dv1QM+IRECAEB1xCoRzp07Nz8/f+DAgf37\n95dIJGyeGgEAAFAtsEqEDx486NKlS1hYmLajAQAA0DFWF8uIRCJXV1dthwIAAKB7rBKhp6dn\nQkKCtkMBAADQPVaJcPHixefOnTtz5oy2owEAANAxVucIc3Jypk+f3qdPH19fX09Pz5o1ayrW\nmTBhgqZjAwAA0DpWibBz5870xfHjx48fP15qHSRCAACojlglwp9//lkgEAgEAm1HAwAAoGOs\nEuHvv/+u7TgAAAAqRbmfUJ+dnZ2amsrlci0sLAwMDMqeAQAAoApjO+h2VlbW3LlzGzVqZGJi\n8s0339StW9fY2NjNzS00NLSoqEirIQIAAGgPqz3CL1++eHl5PXr0iBAiFovNzc2lUmlKSsqD\nBw9++umnEydOnD59WigUajlUAAAAzWO1R/jbb789evRo5MiRT58+zczMfPXqVVJSUlZW1r17\n9/r16xcZGblmzRptBwoAAKANrBLhsWPHOnXqtG3bNgcHB6aQw+G4ubkdPHiwZcuWe/bs0VqE\nAAAAWsQqESYlJXl5eZU6icPheHt7x8XFaTQqAAAAHWGVCDkcjuqHEZb6qF4AAICqj1UibNSo\n0dmzZ4uLixUnFRUVRURENG7cWNOBAQAA6AKrRDhkyJC7d+/26tXr6tWrBQUFtDA/P//ixYu+\nvr737t0bNmyYNoMEAADQFla3T0ydOvXMmTPh4eHh4eE8Hs/MzEwqlWZkZNB9xG7duk2ePFnL\ncQIAAGgF2wfzRkRErFu3rmXLljweLzU19cuXL3w+v127dlu2bDl16hRuIgQAgGqK7RBrfD4/\nKCgoKCiouLg4IyODw+GYmppyuWwHpgEAAKiayj3WKI/Hk0gk2ggFAABA95Qmwl27donF4r59\n+9LXZTaE62UAAKA6UpoIhw8fbmtrSxPh8OHDy2wIiRAAAKojpYkwODjY3Nycea2reAAAAHRK\naSJcuXJlqa8BAAC+Jqwu+xwwYEB4eLiyqcHBwT179tRcSAAAALrDKhEeOnQoPj5e2dQvX75c\nvHhRcyEBAADojqrbJ+hQMvS1slyYkpJy4MABsVislegAAAC0TFUifPv27fbt29PS0gghUVFR\nUVFRymrOmjVL45EBAADogKpEGBAQMHr06EePHrm4uPj7+3ft2lWxjoGBgaOjo+wDewEAAKqR\nMkaW4XA4zs7O/fv3HzhwYLdu3XQTEwAAgM6wGmLt4MGD2o4DAACgUrBKhNOnT1cxVSqV5uXl\nbdiwQUMhAQAA6A6rRLhq1aoy6yARAgBAdcQqEe7cuVOx8P379zdv3jx16tTs2bM7d+6s6cAA\nAAB0gVUiVDGg9oULF7777ruOHTtqLiQAAADdqeiTdTt16uTj4zNnzhyNRAMAAKBjGnjEfP36\n9WNiYireDgAAgO6V+wn1im7fvl1UVFTxdrSKz1f6STkcDofDUVEBVJDtNy6Xi55Um2y/8Xg8\n9KTaZPuNz+dzuVwVPcnlamBnAKo79e8jlEqlGRkZR48evXz5speXl6YD0zBDQ0NlkzgcDpfL\nVaiQpe2Qvg6y/aakJ4EVuZ7k8XjoSfXI9huXy0VPQplYJcIffvhBxVRjY+MlS5ZoKB5tyczM\nVDaJy+WampqqqAAqyPYbj8cTi8XoSfXI9aSxsTF6Uj2y/cbn8w0NDVX0pEgkEolEOokLqi5W\niXD8+PGKhRwOx8DAwM7Orl+/fjY2NpoODAAAQBdYJcLNmzdrOw4AAIBKUe6z8RkZGWlpaRwO\nx9zc3NjYWBsxAQAA6AzbK6bi4+PHjBljbW1tZmZma2v7zTffiMXi+vXrT548+c2bN1oNEQAA\nQHtY7RHGxMR07NiRnnA2MTGRSCQcDiclJeXVq1fr1q3bu3dvdHS0o6OjlkMFAADQPFZ7hDNm\nzMjMzJw0adKLFy8yMjJevXr18uXLzMzM+Pj4KVOmJCcn//LLL9oOFAAAQBtY7RFeu3atQ4cO\na9eulStv2LBhaGjo8+fPo6OjtRAbAACA1rHaI5RKpe7u7sqmenp6FhcXay4kAAAA3WGVCF1c\nXJKSkpRNTUpKcnFx0VxIAAAAusMqEc6ZM+f06dMXL15UnPTgwYMjR47g6RMAAFBNKT1HuGvX\nLtm3Q4cO7dy5c9euXdu3b1+nTh0ul5ucnHzz5s1jx44NHz4cowMDAChKSkrasGHD2bNnX758\nmZOTU6dOHXt7+8GDBw8aNIi5D7tnz57//vvvxo0bJ06cWGoj+fn5VlZWX758efLkSVpaWps2\nbWSnmpiY1KlTp0WLFj/88EOvXr3K/DW+fv26XAuEEJFIZG1t3alTp59//rlJkybqftxKsHXr\nVhsbm27dulWkEY5UKi19AodTroaUtVNFJCcnK5tExxpNS0uTLTz7Ok/7QX0NfOoZMK/pWKPp\n6emyFTxX3dB5UNXS7eBWzGs61mhGRoZsBfQkS7I9yWasURMTEy1FsnHjxp9++qmgoMDAwMDN\nzU0sFiclJb148aKkpKRRo0bHjx+nKefEiRO9e/du3rz5nTt3Sm1nz549Q4cO7dixY1RUFE1j\nEomka9eudGpGRsbTp08TExMJIa6urnv27GnatKmKqBRbIIR8/vz54cOHnz59MjAwOH78uI+P\nj8Z6QZukUqm5ufnIkSNDQ0Mr0o7S/w7BwcHsQ8nLQ9oAAPj//v7778DAQD6fv2zZssmTJzNP\nwIiPj//ll1+OHDni7e399OnTGjVq9OzZ85tvvrl7925MTEyplyVu3bqVEDJhwgSmxM7Obt++\nfbJ1Hj58OHPmzFOnTn377bdXr15t2LCh6vAUW8jPz585c2ZoaGhAQEBiYiKPx1Pvg+vS48eP\n5fZh1KM0Ea5cubLirQMA6KEvX75MmTKFELJjx47BgwfLTrK3tz948GDv3r3PnDmzf//+cePG\ncbncMWPGhISEbNmyZcOGDXJNJSQkXLhwoWbNmv369VOxRGdn55MnT44cOXLHjh2TJk36999/\nyxuzSCRatWpVWFjY69ev796926JFi+Dg4D/++OP8+fPXrl0LDQ2tXbv2w4cPCSElJSWbNm3a\ntm3b48ePORxOw4YNR4wYMXnyZIFAwLR27NixdevWPXnyJDk5uWbNmq1atZo+fbrsIdkyG/nl\nl19WrFhx/vx5ExOT2bNn37p1Ky8vz9XVddGiRXRfdsCAAYcOHSKErFmzZs2aNf379y/1iYFs\n4KGUAAAatm3btqysrG+//VYuC1JcLnfbtm2fPn0aN24cLRkzZgyfz9+zZ09ubq5c5b///lsq\nlfr7+wuFwjKXu3btWjMzs9OnTz9//lyNsLlcLt2V/Pz5MyGELvHYsWPLly/v3r17z549CSFS\nqXTQoEFBQUEpKSlTpkyZMmUKl8udPn16nz59SkpKaDvr16/v27fvs2fPvv/++5kzZ3bp0uXs\n2bPe3t5RUVG0AptGaEa8cuXKt99+KxKJ/P3927Vrd/Pmzd69e7948YJ2mr+/PyHE29t73bp1\nY8aMUeMjU6oulhGLxX379iUKF86UatiwYWoHAQDwNTl//jwhpNQsSFlaWsq+tbKy6t279+HD\nhw8ePDh8+HCmvLi4eNu2bRwOh0mZqpmZmXXv3n3fvn0RERGNGjUqb9jFxcXx8fGEkHr16pH/\nJsKdO3dGRES0bt2a1tm5c+eBAwe8vb3Dw8PpoxwXLFjQt2/fU6dO7dixY9SoUYSQ9evX83i8\n27dv165dm841bdo0Dw+PrVu3ent7s2yEJsIlS5YcPny4R48etB0/P7/9+/cfOHBg5syZ3bp1\nS0tL++eff9zc3IKCgsr7YWUpTYTDhw+3tbWliVD2i1EGiRAAgEpISCCEODs7s59lwoQJhw8f\n3rJli+zv7enTp9++fdu1a9cyz/kxnJycCCEq7vxWprCwcPbs2R8+fHB0dKSR00smPT09mSxI\nCNmyZQshZPny5cwDjfl8/sKFC0+dOrV9+3aaw9LT07lcLnNalBDi6uqam5vLXNHKphGqa9eu\nTBYkhPTv33///v10j1CDVF0sY25uzrzW7FIBAL5i9DpVsVjMfpYuXbrY29tHR0fHxcU1btyY\nFipeJlMmulAVF8pSiYmJsnsvKSkpsbGxb9++NTEx+eeff2TvGpDNgoSQW7du8fl8T09P2UI3\nNzcjI6NHjx7Rtz179ty6dWv79u2nTZvWo0ePWrVqEUJk7+tg0wjVokUL2bcSiYQQovHLM1ld\nLIMLZwAA2DM1NSWEfPnyhf0s9PjnL7/8snXr1uXLlxNCPn78ePLkSWtr6++++459OykpKYQQ\nZjdGmdTU1N27dzNvhUKhtbX1uHHjZs6c2aBBA9maNWvWZF5nZmbSJFTqNaW5ubmFhYUCgWDD\nhg1SqXT79u30HJ6bm1u/fv0mTJhAMyLLRhSXTv67k6rxu/VY3Qjv7Oz83Xff/fbbb5pdNgDA\nV8nBweHx48e3b9/28vJiP5e/v//cuXO3b9++ZMkSPp+/ffv2oqKigICAco1YcuPGDUJImc/F\n8/DwuH37NpsGZa8FpXlIKBT++uuvpVYuKCgQCAQikWjr1q3z588/fvx4eHj4hQsX5s2b98cf\nf5w8ebJ9+/YsG2ETm6aw6t+PHz++fftW26EAAHwdunTpcuTIkX/++Wfq1KmlDk6Slpa2atWq\nwMDAOnXqMIWWlpb9+/ffs2fPyZMn+/bt+/fff/N4vLFjx7Jf7suXL6Oiovh8vpbuiBeLxcbG\nxtnZ2TNmzJA9BViqevXqBQYGBgYGZmdnr169eu7cuT/++OODBw/K1YhusLp9YurUqUePHr1+\n/bq2owEA+AoMHz68Ro0asbGxK1asUJxaUlIyceLExYsXK06lpwP37dt37969Z8+e9ejRg17A\nyUZRUdHYsWOLiopGjhxJD0JqQ8uWLQkhly5dkitPTU1lXickJHz48IF5a2xsPGfOnG+++ebh\nw4dFRUUsG9ElVomwTZs2/v7+PXr08PX1DQkJWbdu3WYF2g4UAKC6MDEx2bRpEyFkxowZ9Onl\nzKS4uLg+ffrs27evSZMmCxculJvRy8uradOmJ06c+Oeffwgh48ePZ7nEx48f+/j4nDt3rn79\n+vQUo5aMHj2aEBISEiI7mOLu3bstLS3nzp1LCImJiWnYsGFAQADNedS7d+8+ffpUu3Ztepi3\nzEZYMjAwIP89LVoRrA6Ndu7cmb6IiIiIiIgotU65rmsCAPi6DRo0KC8vLzAwcO3atRs2bHB2\ndjY3N3/79m18fHxJSUnbtm2PHTvGjLsta/z48ZMnT964caOtrW337t1LbTwhIWHAgAH0dX5+\n/osXL548eUIIadas2eHDhy0sLLT3uYYOHXrkyJHDhw83b958wIABIpHozp07p0+frlu3bkBA\nACHE3d39hx9+OHDgQNOmTbt06SKRSD59+nTs2LG8vLx58+axbIQleir04MGDQqFQIpGofV0n\nq0QYHBwsEAiEQmF5R+IGANBbo0aN6tq168aNG8PDwxMSEh49eiSRSHx9fSdMmPDdd98p+zkd\nMWLEr7/+mp2dPXbsWC639IN2X758oaOLEUL4fL6lpeV3333n5+c3aNAgbY8RyuFw9u/fv3nz\n5u3bt2/YsKGgoKBu3bqBgYGzZs2ysrKidfbu3du2bdu9e/eGhYVlZmbWqVPH3d09KCioV69e\n7Bthw8HBYcGCBWvWrNmzZw+9VV/ND1XFnxqhKXj6hJbg6ROagqdPaErVefoEVBeszhEOGDAg\nPDxc2dTg4GA6Bh0AAEC1wyoRHjp0iA5AV6ovX76U+vB6AACAqk/VOcLw8HBmR1BZLkxJSTlw\n4EC5RhICAACoOlQlwrdv327fvp2ePIuKimKeoKFo1qxZGo8MAABAB1QlayvcYAAAIABJREFU\nwoCAgNGjRz969MjFxcXf358+C1GOgYGBo6Ojg4OD1iIEAADQojJun+BwOM7Ozv379x84cGC3\nbt10ExMAAIDOsLqP8ODBg6WWFxUVlWs0WAAAgKqG1VWjhJALFy6MGDGCeXv58mVXV1ehUGhl\nZfXnn39qJzYAAACtY5UIL1++3K1bt3379tGx4z59+tSrV6/Y2Nh69ep9+fJl/Pjxp06d0nKc\nAAAAWsEqEa5cudLQ0DAmJoYeCN24cWN6evqiRYtevXr14sWLmjVr0uFlAQAAqh1WifDWrVv9\n+vVr2rQpfXv48GFjY+Np06YRQmxsbHr16vX48WMtxggAAKA1rBJhcnIy80ysjx8/xsbGfvvt\nt0ZGRrTEysrq3bt32goQAABAm1glQgsLC+Z5iadPnyaEyN5K8eXLF4xaCwAA1RSrmx+cnJyO\nHj06Z84ckUi0atUqPp/ft29fOqmoqCgiIqJhw4baDBIAoNpQ8bCLisD+hvawSoRBQUHff/+9\njY0Nl8stLCwcN26ctbU1IeTDhw+jR49+8eLFpEmTtBwnAEC1cTI+vexK5dHL3kyzDYIsVodG\n+/btu27dOnt7ewsLi4CAgHXr1tHy7Ozs06dPDxo0KCgoSJtBAgAAaAvbcWGCgoIUs13Dhg1j\nYmKaNWum6agAAAB0hO3IMsogCwIAQLWmdI9w165dYrGYXhSza9euMhsaNmyYJuMCAADQCaWJ\ncPjw4ba2tjQRDh8+vMyGkAgBAKA6UpoIg4ODzc3NmdcaWdiNGzfCwsJevXolFArd3d1Hjx5t\naWlZas2NGzeGh4fLFa5YsYJ58CH7pgAAAFRQmghXrlxZ6mu13blzZ+nSpT4+PiNHjszKytq7\nd++cOXPWrl0rFAoVK+fk5FhbWwcGBsoWMqPblKspAAA9ERQUtGHDhjFjxvz111+y5bt27Ro+\nfPj79+/r1KlTWbFVZbp7muDu3bsdHByYS08bNGgwceLE8+fPd+/eXbFyTk6ORCJxcXGpeFMA\nAPqDx+Nt3bp1xIgRXl5elR1LtcE2EcbFxUVERLx+/TozM9Pc3NzR0dHHx6dWrVosZ09PT4+P\njw8ICGBKrK2tbW1tb9++rSwRMmOZVrApAAD94ezsLBaLx48ff+/ePRwkY6nsRBgfHx8UFHTm\nzBn5Ofn8kSNHLl++3MLCosxG3rx5QwixsbGRLbSxsXnx4kWp9XNycpQ1W96mAAD0R15e3u7d\nu93d3ZctWxYSElJqHalUum7duv/85z/x8fEikcjDw2PevHne3t66jbQKKSMR0gdNJCcnm5mZ\nde/e3cnJSSwWp6Sk3LhxIyoqauvWrZGRkRcuXLC1tVXdTnZ2NiFEbifP0NCQlivKyclJTU1d\nvHjxs2fPiouLGzRoMHDgQDc3N/ZN/fHHHxcvXqSvzczM/vnnH2WxcTgcDocjkUj+p/T1e9Wf\nCCjZfiu9J4Ed9KSmlKsnS0pKdBKU7hQXFzdt2nT69OlLly4dNGhQ48aNFessXLhw4cKFixYt\n6t+/f3Z29rx587p27Xrt2jUPDw/dB1wVqEqERUVFQ4YMSU5OHjVqVGhoqJnZ/wx29/Lly7Fj\nx547d65fv343b97k8XhlLozD4ah4KzcpJSXFy8tr4MCBqampx48fDwkJmT9/vru7O8umcnNz\nmaFveTwel6tq6AAOh6O6Aigj12/oSbWhJzWlXD359SVCqVRKCJk7d25YWNiECRMiIyPlKuTn\n569atWrIkCGzZs2iJfv3769Tp05oaOjOnTt1HW7VoCoRHjly5OHDh999912pu1P169c/ffq0\nj49PVFRUWFjYkCFDVDRlbGxM/rszx8jKyhKLxaXWl7vkqXnz5hMmTNizZ4+7uzvLpmbPnj17\n9mzmbXJysrLYuFyuqalpWlqaivhBmZSUFOY1j8cTi8Xp6RoeblhPyPWksbFxRkZGJcZTfcn2\nJJ/PNzQ0VPE4CJFIJBAIdBKXThkaGm7cuLFbt27btm0bNWqU7KTHjx9nZmZ26NBBtnKzZs3u\n3Lmj6yirDFV/OQ8dOkQI+e2335RV4PP5a9euJYSEhYWpXgy98+H169eyhUlJSWUeU6WEQmG9\nevXoMxEr2BQAgD7w9fUdNGjQ9OnT5XYD6F9VU1NT2UJTU1MtPT2qWlCVCO/cuWNnZ9e0aVMV\ndVxcXBwcHG7duqV6Maampk2aNLly5QrdbSeEJCQkvH37tmXLloqVP3/+vHz58ps3bzIlubm5\nCQkJ9NlP5WoKAEBvhYaGFhcXBwcH8/n//+AfPckld+QmPT29Ro0auo6vylCVCD98+NCkSZMy\nm7C3t//8+XOZ1YYPHx4fH79mzZr79+9HR0cvX77c1ta2U6dOdOqVK1emT5/+8uVLQoilpeWn\nT5/WrFlz+vTpZ8+e3bhxY968eVlZWQMHDmTTFAAAEEJq167922+/7dixQ3a/wsnJycTEhLmW\nkBCSlZV19+7d1q1bV0aMVYKqc4RZWVlsnolsYGBQVFRUZjUXF5eQkJDdu3cvXLjQwMDA09Nz\n9OjRzCU2aWlpcXFxOTk5hBAOhzN//vx9+/YdPnw4NTVVKBQ2adJk6dKljo6ObJoCAABq/Pjx\nO3bsWL9+PVMiEolmzJgxb948Dw+Pfv36paamzp49WyqVamoozepIdyPLEEKaN2/evHnzUif1\n7NmzZ8+ezFsTE5OxY8eOHTtWjaYAAIDicDj/+c9/5H4tZ8+eLRaLN2/ePHPmTENDw7Zt20ZH\nR7M5/ve10mkiBAAA7ZHd82O4uLgUFhbKFU6ZMmXKlCk6CaoaKCMRRkREeHp6qq6TkJCguXgA\nAAB0qoxE+OXLF32+uQQAAL56qhLhtWvXdBYHAABApVCVCPX5aloAANATGMwQAAD0GhIhAADo\nNdw+AQCgYb3szcquBFUG9ggBAECvIRECAIBew6FRAAANc1kardkGY2d1KLsSqEudPcLCwkK5\n5+ICAABUU2wTYUlJybZt2zp16lSrVi2RSLRixQpaPnfu3KSkJK2FBwAAoF2sEmFhYWHPnj39\n/f2joqKys7OZJ+KmpqYuWbLEy8vr/fv32gwSAABAW1glwj/++CM8PLxnz5537tzJyMhgys3N\nzXfs2PH69eulS5dqLUIAAAAtYpUId+3a1axZs6NHjzZv3lzu+bfDhg3r2rXrv//+q53wAAAA\ntItVIkxISOjRowefX/olpi1atHjz5o1GowIAANARthfLcDgcZZPy8/NFIpGG4gEAAHWcOHGC\nw+EsW7ZMrjwnJ8fOzs7V1VXx8bxAsUqEjo6OYWFhBQUFipPS0tIOHjzo6Oio6cAAAKAcvvvu\nuyFDhixYsCA+Pl62PCQkJCkp6e+//xYIBJUVWxXHKhGOGjUqPj6+e/fuN2/eLCkpoYW5ubln\nzpzp2rVrYmKiv7+/NoMEAICyrVmzxsTEZMKECUxJTExMaGhocHCwp6dnJQZWxbFKhD/++GO/\nfv0iIyNbtWpFj4L+9ttvRkZG3bp1u3Xr1g8//DB27FgtxwkAAGWwtLRct27d+fPnt2/fTggp\nLi4eO3Zsw4YNFyxYQCts2bKlRYsWpqamEonk+++/j4uLY+aNjY3t3bt37dq1RSJR/fr1p02b\nlpubWzkfQ+dYJUIul3vw4MHt27d7eXnRS2YKCgqMjY07deq0a9eu/fv3y11KCgAAlcLPz69v\n377BwcGfP38ODQ29e/fu1q1bDQwMCCGrVq0aO3Zsx44d79y58++//yYnJ3t5eX369IkQUlJS\n0q1bt7y8vJMnTz558mT16tV79uyZOnVqZX8aHWE71iiHwxkxYsSIESMIIZmZmRwORywWazMw\nAABQx8aNG52cnEaMGHHp0qXAwMD27dsTQgoKChYuXOjr67ty5UpCSKNGjcLCwho0aLBx48b5\n8+e/efPm3bt3s2fPbtGiBSHEzs7OwcGBGTvlq8f20OjVq1eZtyYmJsiCAABVk5WVFR0FxdLS\n8rfffqOFjx49ysjI6N27N1PN2tq6adOmt2/fJoTUrVu3devWM2bMmDZt2unTp7OyspycnJo2\nbVo5H0DnWCXCTZs2tWvXzs7Obu7cuU+fPtV2TAAAUBGDBw8mhPTq1YvZaUlPTyeETJ061UDG\n/fv33759Swjhcrnnzp2bM2fOxYsXe/bsaWFhMWDAADpJH7BKhGvWrGnfvv3Lly8XL17s6Ojo\n4eGxevVqjC8KAFBdSCQSQsj8+fPvyXj06NGhQ4doBWNj4xkzZty5cyc5OXnz5s2XLl3q379/\npYasO6wS4eTJky9duvTmzZu1a9d6eXndu3dv2rRpdevW9fHx2b59e2ZmprajBACAinBycpJI\nJImJiU1kcDicevXqEUKSkpJ2795Na5qbm/v7+48bNy4mJkZPThOW43mE1tbWkyZNio6Ofvv2\n7fr16728vCIjI0eNGlW7dm0/Pz/thQgAABUkEAhmz569bdu2pUuXPnny5NmzZ4sXL3Zycjp8\n+DAh5PPnzyNGjJgyZcq9e/cSExPPnz+/f//+b7/9VsWYYl8TdR7MW6dOncDAwKioqLdv3y5Y\nsIDH4+3fv1/jkQEAgAYFBwdv2rRp//797u7uzZo1O3ny5L59++hujIeHx4kTJ2JiYry9vR0d\nHceMGePj48PsI3712N4+Ief27duHDh06efLkw4cPCSGWlpYajQoAANRnYGBQ6lHNMWPGjBkz\nptRZevTo0aNHDy3HVUWVIxGWlJRcvXr10KFDhw8fpk+lNzExGT58+ODBg318fLQWYeX4df/9\nyg6hevAJblXZIQAAVAirRHj27NnDhw8fOXLk48ePhBADA4P+/fsPHjy4Z8+edMACAACAaopV\nIuzatSshhM/nd+/effDgwX379jUxMdFyYAAAALrAKhF27Nhx8ODBAwYMsLCw0HZAAAAAusQq\nEUZFRWk5DAAAgMqhNBHu2rVLLBb37dv3/7V353FRlvv/x6/ZZxh2QQ1ywTgBoSGIZouZRpyI\nOmWiZUklZUWZlZY+7KgPT8c1j+WaVpppUFK48WjR0hPlMZcDZrnml0xRUmNHGPaZ3x/37zu/\n+SEzDAgz4P16/jX3dV/3fX/megBv7l363OKKxo8f3551AQDgEnaDMDk5uU+fPlIQJicnt7gi\nghAAJEfeuNPdJaAV7Abh1KlT/f39rZ9dVQ8AdG1cS9jl2A1C6Z1VV34GAOBa4tQj1pKSknbs\n2GFv7tSpUxMTE9uvJAAAXMepINy8eXNeXp69uaWlpd9//337lQQAgOs4un1ix44d1h1Be1lY\nXFz8+eef88J6AEAX5SgICwoKNmzYUFZWJoTIzs52cDfhG2+80e6VAQDgAo6C8Omnn05JSTl2\n7NiAAQMmTJggPWitCb1eHxERERYW1mEVAgDQgVp4soxCoejfv//o0aPHjh177733Ntunvr6+\npqaGp28DALoipy6WyczMtJeCQoilS5f279+//UoCAMB1WvE+wpMnTx49erSmpsa2saysbO3a\ntRcuXGjvwtqZg8t5FAqFUqnkep+2sR03hUKhUqkYybZpMpJqtZqRbBvbcVMqlfxMokVOBWFt\nbe348eMzMzPtdbj//vvbr6QOUVtba2+W9EfHQQc4YDtu0h8dRrJtbMdNpVIxkm3WZCR1Op2D\nkVSrW7EzgGuVUz8EixYtyszMDAwMHDlypJeX19q1ax966CFvb+9///vfDQ0NixcvHjNmTEcX\nepXq6+vtzVIqlRaLxUEHOGA7biqVipFsM9txM5vNWq2WkWwb23GzWCwajcbxr79LikKn5lQQ\nfvrpp3379v3555+9vb0vXry4du3a55577t57762urp48efLatWtHjx7d0YUCANARnPpv6PTp\n06NGjfL29m7SbjAY3n333aKionnz5nVAbQAAdDhnDwsYDAbpg3SbRGVlpTSp0WiSkpIyMjI6\nojgAADqaU0HYu3fv7Oxsi8UihPD19dVqtYcOHbLO1el0BQUFHVUgAAAdyakgfOCBB3788cd7\n7rnnyJEjQojbb799zZo1OTk5QojCwsL09PSePXt2bJkAAHQMp4Jw5syZsbGxu3fvPnPmjBDi\nueeeKy0tHTJkyHXXXRcUFHTs2LGkpKSOLRMAgI7h1FWj/v7+e/bs2bx584ABA4QQjzzySEFB\nwcKFCy9evOjt7f3EE0/84x//6OA6AQDoEM7eTKrX6x9//HHr5JQpU6ZMmVJZWckjGwAAXdpV\n3UxKCgIAujq7e4RpaWmtWtH48eOvuhgAAFzNbhAmJye3akUEIQCgK7IbhFOnTnVlHQAAuIXd\nIPzXv/7lyjoAAHCLtlwsU19fX1VV1e6lAADges4Godls/uijj0aMGNG9e3edTrd48WKpfdas\nWfn5+R1WHgAAHcupIKyvr09MTJwwYUJ2dnZVVZX00FEhRElJybx584YNG9b531APAECznArC\nt99+e8eOHYmJibm5uRUVFdZ2f3//jRs3njt3bv78+R1WIQAAHcipIExLSxs4cOC2bdtiYmJU\nKpXtrPHjx8fHx3/11VcdUx4AAB3L2Rfz3nfffWp185eYDh48+Pz58+1aFQAALuLsxTIKhcLe\nrNraWp1O1071AADgUk4FYUREREZGRl1d3ZWzysrKMjMzIyIi2rswAABcwakgfOqpp/Ly8hIS\nEg4ePGg2m6XG6urqnTt3xsfH//777xMmTOjIIgEA6ChOvYbphRde+O6777Zs2XLLLbdIZwoX\nLFhgfQfhmDFjJk6c2IE1AgDQYZzaI1QqlZmZmRs2bBg2bJgUhHV1dUajccSIEWlpaZ999lmT\nS0kBAOgqnH0xr0KheOKJJ5544gkhxOXLlxUKBS8jBABcA5wNQlteXl7tXgcAAG7h7O0TjY2N\nDuZu3bq1PYoBAMDVWgjCvLy8Bx980GAw6PX6AQMGXPna+gsXLowePfrhhx/usAoBAOhAjg6N\nFhYWDhs27OLFi9Lk0aNHk5OTi4uLX375ZSGExWJZt27d66+/XlZWFhAQ4IpiAQBob472CJcs\nWXLx4sWEhIS8vLzKysrMzEx/f/9p06ZdvHgxLy9v5MiREydOLC8vnzhx4q+//uqyigEAaEeO\n9gi/+OILo9GYnp7u5+cnhBg9enRhYWFqampKSkp2dnZ1dXV0dPTq1atvueUWV1ULAEA7c7RH\n+Pvvvw8aNEhKQUlCQoIQ4uuvv9ZoNMuWLfvvf/9LCgIAujRHe4Qmk6lHjx62Lb169RJCxMTE\nfPnllz179uzY0gAA6HgtXDWqVCqvnIyIiCAFAQDXBmfvIwQA4JpEEAIAZI0gBADIWgvPGv3m\nm29iY2ObNH799ddXNubk5LRnXQAAuEQLQVhaWpqbm9uksaSkpKSkpMNKAgDAdRwF4b59+1xW\nBwAAbuEoCIcOHeqyOgAAcAsulgEAyBpBCACQNYIQACBrBCEAQNYIQgCArLVwH2H7OnDgQEZG\nxtmzZ7VabXR0dEpKioNX2+/du3f79u35+flarTY0NPSxxx4LDQ2VZr377rs7duxo0n/x4sVh\nYWEdWD0A4FrkuiDMzc2dP3/+Pffc8+STT1ZWVn766aczZ85cvny5Vqu9svPOnTtXrVoVFxf3\n+OOPm0ymTZs2SZ27d+8uhDCZTEFBQS+++KLtItIrogAAaBXXBWF6enpYWNikSZOkyZCQkNTU\n1N27d0sv+20iIyMjKipq8uTJ0mTv3r1TU1P37dv34IMPCiFMJpOfn9+AAQNcVjwA4FrlonOE\n5eXleXl5t99+u7UlKCioT58+zT6h1GKxLFiw4NVXX7W2SO8Hvnz5sjRpMpkMBkMHlwwAkAUX\n7RGeP39eCBEcHGzbGBwc/Ntvv13ZWaFQSMlndeDAASFEZGSkNGkymbp16+Z4i7/99ltxcbH0\nWa1W33DDDfZ6KpVKhUKh0Wha/hq4gu24qVQqRrLNmoykUqlkJNumVSPZ5N3jkCcXBWFVVZUQ\nwsPDw7bRYDBI7Y4VFBSsWrVq6NCh0dHRUovJZCopKZk7d+6vv/7a2NgYEhIyduzYqKgo26XW\nr19vvaDGz8/v22+/dbwVHx8f578OrK4cN0aybRjJ9tKqkWxoaOjgctAFuPSqUYVC4WCyWSdO\nnJg7d26/fv2mTp1qu2BxcfGwYcPGjh1bUlKSlZU1e/bsOXPmWJNSCHHnnXdadysNBkN1dbWD\nqrRabW1tbau/D4SwHVhG8mo0GUmNRlNXV+fGerou25FUKpVqtdrBSCoUCrXapX8G0Qm56CfA\naDSK/90vtKqsrPT09HSwVHZ29ooVK+64446XXnrJ9of1gw8+sO0WExPz/PPPf/LJJ7ZBGB8f\nHx8fb50sKiqytxXpV8WZfVNcyXbcVCqVSqViJNumyUgqlUpGsm1sx02tVjs+8qTT6fR6vUvq\nQuflouPj0r0N586ds23Mz8/v06ePvUV27dr1zjvvjBs37tVXX3X8L5tWq+3VqxevSAQAtIGL\ngtDb2zs8PHzv3r0Wi0VqOX36dEFBwZAhQ5rtf+zYsRUrVjz77LNJSUlNZhUWFi5atOjgwYPW\nlurq6tOnTwcFBXVQ8QCAa5jrDo4nJyfPmjVr2bJlI0aMKC8vT09P79Onz4gRI6S5e/fu3bp1\n66RJk/r27dvY2LhmzZpevXr17t37yJEj1jUYjcZ+/foFBAT8+eefy5YtGz9+fL9+/crKyjZv\n3lxZWTl27FiXfRcAwDXDdUE4YMCA2bNnp6env/nmm3q9PjY2NiUlRaVSSXPLyspOnTplMpmE\nEMXFxWfPnhVC/P3vf7ddQ0RExKJFixQKxZw5czZt2rRly5aSkhKtVhseHj5//vyIiAiXfRcA\nwDXDpZdLxcTExMTENDsrMTExMTFR+ty9e/esrCwH6/Hy8po4ceLEiRPbv0QAgMxwMykAQNYI\nQgCArBGEAABZIwgBALJGEAIAZI0gBADIGkEIAJA1ghAAIGsEIQBA1ghCAICsEYQAAFkjCAEA\nskYQAgBkjSAEAMgaQQgAkDWCEAAgawQhAEDWCEIAgKwRhAAAWSMIAQCyRhACAGSNIAQAyBpB\nCACQNYIQACBrBCEAQNYIQgCArBGEAABZIwgBALJGEAIAZI0gBADIGkEIAJA1ghAAIGsEIQBA\n1ghCAICsEYQAAFkjCAEAskYQAgBkjSAEAMgaQQgAkDWCEAAgawQhAEDWCEIAgKwRhAAAWSMI\nAQCyRhACAGSNIAQAyJra3QW4iJ+fn4O5SqXScQfY02TcGMk2sx03hUKhUCgYybZp1UiazWaX\nFIVOTS5BWFpaam+WUqn09vYuKytzZT3XDNuBValUnp6e5eXlbqyn62oykkajsaKiwo31dF22\nI6lWqw0Gw+XLl+111ul0Go3GJXWh8+LQKABA1ghCAICsEYQAAFkjCAEAskYQAgBkjSAEAMga\nQQgAkDWCEAAgawQhAEDWCEIAgKwRhAAAWSMIAQCyRhACAGSNIAQAyBpBCACQNYIQACBrBCEA\nQNYIQgCArBGEAABZIwgBALJGEAIAZI0gBADIGkEIAJA1ghAAIGsEIQBA1ghCAICsEYQAAFkj\nCAEAskYQAgBkjSAEAMgaQQgAkDWCEAAgawQhAEDWCEIAgKwRhAAAWSMIAQCyRhACAGSNIAQA\nyBpBCACQNYIQACBrBCEAQNYIQgCArBGEAABZIwgBALJGEAIAZI0gBADImtqVGztw4EBGRsbZ\ns2e1Wm10dHRKSkpAQEDbOrdqVQAA2OO6PcLc3Nz58+f369dv9uzZkyZNys/PnzlzZl1dXRs6\nt2pVAAA44Lo9wvT09LCwsEmTJkmTISEhqampu3fvTkhIaG3nVq0KAAAHXLRHWF5enpeXd/vt\nt1tbgoKC+vTpk5OT09rOrVoVAACOuSgIz58/L4QIDg62bQwODj537lxrO7dqVQAAOOaiQ6NV\nVVVCCA8PD9tGg8Egtbeqs5Or2rRp0+HDh6XPRqNx2rRp9mpTKBQqlcrLy6s1Xwj/l+24MZJX\no8lIqtVqRrJtbMdNqVTyM4kWufSqUYVC4WCyVZ1bXNXRo0d37dolffbz85s1a5bj2nQ6ne3k\nmQWJjvvDHkayvTCS7aXJSNpqaGhwZSXonFwUhEajUfzvzpxVZWWlp6dnazs7uaopU6akpqZK\nn5VKZWlpqb3aFAqFl5dXRUVFa76QqxkMBr1ef/ny5c78e6tUKo1G4+XLl91diCMeHh46na6i\noqKxsdHdtdilVCo9PDwqKyvdXYgjRqNRq9WWl5ebzWZ312KXSqXS6/XNHnmSaDSaZv8KQVZc\nFIS9evUSQpw7dy42NtbamJ+f36dPn9Z2dnJV/v7+tpNFRUX2alMqlRaLpTP/WRRCWCwWIYTZ\nbO78dXb+CgUj2R66xEgqFArHI6lWu/SoGDonF10s4+3tHR4evnfvXumXRwhx+vTpgoKCIUOG\ntLZzq1YFAIBjqjlz5rhmSz179ty8efOlS5cMBsOpU6dWr17drVu31NRUpVIphNi7d+/y5ctv\nvPFGX1/fFjs7ntssk8lkb5ZCodDpdDU1NR3wpduNVqvVaDS1tbWd+TCUUqnUarW1tbXuLsQR\nrVarVqtramoYyauk0+mkkbT+S9oJKZVKjUbj4GkbarXawRlEyITClT/Ehw4dSk9PP3PmjF6v\nj42NTUlJ8fHxkWZ9+eWX77333sKFC2+66aYWO7c490qOD416e3uXlZW1x1fsKEaj0WAwlJeX\n19fXu7sWu1QqlaenZ3l5ubsLccTT01Ov15eVlXXms60qlcpoNHby89ZeXl46na60tLQzHxpV\nq9UGg8HBeWudTsc1pXBpELoRQegCBGF7IQjbC0EIZ/D2CQCArBGEAABZIwgBALJGEAIAZI0g\nBADIGkEIAJA1ghAAIGsEIQBA1ghCAICsEYQAAFkjCAEAskYQAgBkjSAEAMgaQQgAkDW1uwtw\nEY1GY2+WQqEwm80OOnQG586dKy4uDgkJMRgM7q7Fri4xkmfOnCnjJONBAAANzklEQVQtLb3h\nhhs68+tYlUqlxWLp5CP522+/lZeX/+Uvf+nMdbY4kiqVypX1oHOSSxA6fm2vEEKr1bqmkrZZ\nv359WlraunXroqKi3F1LCzpzwAghVq1atWXLlk8++eTGG290dy0t6OQjuWTJkq+++mrr1q0B\nAQHurqUFer3e3SWgU+PQKABA1ghCAICsEYQAAFlTWCwWd9eAlp06dSo/Pz82NtbX19fdtXRt\nJ06cKCgouOWWW7y8vNxdS9d27NixCxcu3HbbbR4eHu6uBbgqBCEAQNY4NAoAkDWCEAAga3K5\nj7BL279//8qVKzUazfr1691dSxe2d+/e7du35+fna7Xa0NDQxx57LDQ01N1FdT0WiyUrK2vX\nrl0XLlxQqVQ33njjo48+GhkZ6e66gLbjHGGnVl1d/f777//444++vr51dXUEYZvt3Llz1apV\ncXFxw4cPN5lMmzZtunTp0vLly7t37+7u0rqYdevWffHFF48++mj//v0rKioyMjIKCgqWLVsW\nFBTk7tKANuLQaKd26NChs2fPLl26NCwszN21dG0ZGRlRUVGTJ0+Oioq69dZbp02bZjKZ9u3b\n5+66upj6+voffvjhgQceeOSRRyIjI2+99dbXX3+9trZ2//797i4NaDsOjXZqN91009ChQ3kc\n4lWyWCwLFiywfeBkjx49hBCXL192X1Fdkkaj2bBhQ5MWIYRCoXBTRUA7IAg7NT8/P3eXcC1Q\nKBRS8lkdOHBACMGZrTYzm811dXXnz59fv3599+7dR44c6e6KgLYjCCE7BQUFq1atGjp0aHR0\ntLtr6ao+//zz9PR0IcTgwYMXL17c4kPtgc6Mc4SQlxMnTkybNq1fv35Tp051dy1dWFxc3IIF\nCyZPnlxcXDxt2rQ//vjD3RUBbUcQQkays7NnzpwZGxs7Z86cTv6So06uW7dukZGRcXFxCxcu\nbGho2Lhxo7srAtqOQ6OQi127dq1YsSI5OTkpKcndtXRVpaWlP/30U//+/a23nej1+uDg4LNn\nz7q3MOBqsEcIWTh27NiKFSueffZZUvBq1NXVLV269IsvvrC21NbWnj17NjAw0I1VAVeJPcJO\n7ezZsxUVFUKI0tLS+vr6I0eOCCEMBgOPRGmVxsbGNWvW9OrVq3fv3tIYSoxGY79+/dxYWJfT\no0ePu+++OysrS61WR0dHV1dXZ2VlVVRUPPLII+4uDWg7nizTqc2bN0+60N9WaGjo22+/7ZZ6\nuqg///zzmWeeubI9IiJi0aJFrq+nS2toaMjMzPz+++8vXbpkNBr79u07duzYAQMGuLsuoO0I\nQgCArHGOEAAgawQhAEDWCEIAgKwRhAAAWSMIAQCyRhACAGSNIERHee211xQKRVpamrsLaYWD\nBw9GR0drtVofHx+TyeTucgC4AkGItvjpp5+eeeaZqKio7t27azQaHx+fmJiYGTNmXLp0yd2l\nXZVx48YdPnz47rvvTklJafZ9yPv371e05OLFi7aL5OfnT58+PSYmxt/fX6/X9+3bNy4ubt26\ndVVVVc3WkJ+fP2PGjMGDBwcEBGg0Gi8vr/79+6empv70008d8p0B2eMRa2i1Dz/88Nlnn21s\nbBw8ePDf/vY3rVZ74cKF7OzshQsXfvjhhz/88ENYWJi7a2yLysrK06dPBwcHf/XVV45fue7r\n6zt8+HB7c/V6vfXzu+++++qrr9bV1en1+qioKE9Pz/z8/O+++2737t2LFi3KysoKDw+3XXbl\nypVTp06tq6szGAw333yzt7d3UVHRqVOnjh079v777y9YsGDatGlX/00B/H8sQGsUFxfr9XqN\nRrNjxw7b9urq6scee0wIkZiYKLVIL/z7+OOP3VFmWxQWFgohoqKiHPTZt2+fEGLQoEHOrHDd\nunVCCLVavXDhQpPJZG3/n//5n1GjRgkhevToUVpaam1fs2aNEEKn073zzjvV1dXW9qqqqtWr\nVxuNRiHExo0bW//NADjCoVG0Tm5ubk1NzV133fXXv/7Vtl2v169evXrUqFHR0dGNjY3NLltb\nW/vWW29FR0cbjUYPD4+IiIgZM2aUlZVZO0yaNEmhUHzzzTc7d+687bbbPD09fXx87rvvvl9+\n+cV2PWazedWqVYMHDzYajZ6enlFRUUuWLKmvr3dcueOtP/TQQ9IrFH7++WfpCGdlZWUbxseq\ntLT05ZdfFkJs3Lhx+vTpBoPBOis0NDQzMzMxMbG4uPizzz6TGouKiqZMmSKE+Oyzz1555RXb\n3UoPD4/nn3/+888/T0hIaGhouJqqADTD3UmMLkZ6CLgzu0RN9gjr6+tHjBghhIiJiZk2bdrM\nmTPvvPNOIURkZOTly5elPlISvPTSSx4eHqNHj546dWpcXJwQwtvbOy8vT+pjNpvHjBkjhAgJ\nCZkxY8Ybb7wxcOBAIURCQkJjY6O9Ylrc+pdffrlw4UIhRHBw8IoVK1asWFFXV3flepzfI5Qe\njD5y5Eh7HQoLC0tKSqyTb731lhDi/vvvb3HNANoXQYjWqa2tlV5dNGbMmJMnTzro2SQIV65c\nKYS49957GxoarH2Sk5OFEDNnzrRdRKVSff/999Y+L7zwghBiwoQJ0uSGDRuEEHfddVdNTY3U\nUl9fn5iYKIRYv369vWKc2Xr7HhqVSvrggw9a7Cm57777BEc+AXcgCNFqv/zyyw033CAdUQgP\nD09JSfnwww/PnDnTpFuTIBwyZIgQ4j//+Y9tnxMnTgghQkNDbReJj4+37SO9QTAoKEiaHDZs\nmBDiwIEDtn1yc3OldLRXszNbdz4I/fz8RtuRlZUl9YyIiBBC7Nu3z8HabElXzeTk5DjZH0B7\nIQjRFnV1dZ988smoUaO6detmPcx+88032+6T2QZhQ0ODVqtVqVS1tbVNVuXp6SmdkLMu8s9/\n/rNJHw8PD4VCUV9fb7FY9Hq9Wq1uchS0oaHBw8MjMDCw2Wqd3LrzQejA4sWLpZ7XX3+9EOLI\nkSMO1mZL6n/ixAnbRqmkJvbs2ePkOgE4g9sn0BYajWbcuHHjxo0TQpw8eXLPnj3btm379ttv\nJ0yYsH//funqR1sVFRV1dXX+/v5arbbJLH9//8rKypKSEumqSCHEdddd16SPn5+fyWQqLCz0\n9PSsqakRQjR7k191dXV9fb1Go7marTtj0KBBOTk5jvt4e3sLIUpLS51cp4+Pz/nz520vHRJC\naDQa2/s0Tp482dXv1AQ6IYIQVys8PDw8PHzixInHjx8fPnz4e++999xzz0VHR9v2kW7LszT3\nFmipUan8fxcwq9VNfyylPiqVSlqPVqudMWNGs8XU1dVdGYSt2np7CQsLO378eE5OjnQst0Xh\n4eHHjh07dOjQ0KFDrY0+Pj7Z2dnWyaeeeko6RQqgHRGEaLXS0lI/P78r22+66abRo0e/9957\nOTk5TYLQ29tbp9NVVFTU1tbqdDpru8ViKS4uViqVtodYi4qKmqy5rKxMqVQGBAQolUqj0VhV\nVdXkhgTHWrX19hIXF7d169b169e/8sorzd6eX1ZWtmTJkhdffLFnz55CiPj4+M2bN2/YsEG6\nOAiAy3AfIVpn6NCh/v7+9k6VSee0bMNGolQqBw0a1NjYuH//ftv2o0ePmkymyMhI29vmDh48\naNvn+PHjJpOpV69e0n6bdNnLnj17mmyipKTEXs2t2np7SU5O9vX1PXLkyOLFi6+cazabU1NT\n586da537+OOPBwQEHDx4cPny5c2u0Gw2X7hwod3rBEAQonXi4+OFEI8++miTuGpoaFi6dOnW\nrVuNRmOTe+0lEyZMEELMnTvXeru9xWJ58803rbOstm/ffvToUevk2rVrhRDS3QhCiJSUFCHE\n7Nmzy8vLrX3S09MDAgJmzZplr2znt95evLy8Vq9eLYSYPn36yy+/bLube+rUqQcffHDTpk3h\n4eFSDUIIo9G4du1ahULxyiuvTJ8+3fbbmc3m7OzskSNHfvPNN0FBQX379u2IggHZUjR74gSw\np76+fuzYsdu2bRNCREZGRkRE6HS6oqKi3NzcoqIig8GQlpb28MMPCyFee+21JUuWfPzxx+PH\njxdCmM3mxMTEHTt2DBo06J577rFYLNnZ2QcOHBg+fPi3334rndiTFnnqqae2bduWlJTUt2/f\nQ4cObdmyxd/f//Dhw7169RJCWCyWpKSkLVu29OvXLykpSafT5ebmfv3119dff/0PP/xgLySc\n2XpRUVFgYGBUVNThw4ftff39+/ffeuutPj4+d9xxh70+Y8aMefLJJ6XPH3300YsvvmgymVQq\nVf/+/f39/QsKCvLy8sxm82233bZ9+/aAgADbZTMzM59++umKigqNRjNw4MDAwMCysrJff/21\nuLhYCHH//fevXr1aur4UQLtxy7Wq6NLMZvO2bdvGjBkTEhKi1+tVKpWvr+/gwYNnzJiRn59v\n7Xbls0alh5xFRUUZDAbpodILFy603hdvXSQtLW379u1Dhw41Go3e3t6JiYnHjx+3LaChoWHl\nypXSI9Y0Gk1ISMikSZP++OMPx2W3uPV2uX1CCDF9+nTbRQoKCv7+978PGjTIz89PrVYHBgYm\nJCRs377dbDY3u4ni4uJ58+bdcccdgYGBGo0mMDBw4MCBU6ZMaXLrJID2wh4hOpEmO5EA4AKc\nIwQAyBpBCACQNYIQACBrBCEAQNa4WAYAIGvsEQIAZI0gBADIGkEIAJA1ghAAIGsEIQBA1ghC\nAICsEYQAAFkjCAEAsvZ/AGY/c/U3YBLpAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ST slope versus presence of CVD.\n",
    "st_segment_slope_plot <- ggplot(training_data, aes(x = st_segment_slope, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_bar(position = \"fill\") + \n",
    "    labs(x = \"Slope of ECG\", y = \"Relative Distribution\", fill = \"CVD Present\") + theme(text = element_text(size = 13)) +\n",
    "    ggtitle(\"Figure 4: Distribution of ST Segment Slopes  \\nwith the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "st_segment_slope_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5683ba87-e6e2-4aea-adfc-395a1edd9ff2",
   "metadata": {},
   "source": [
    "In Figure 4, by setting `position = \"fill\"`, we can see that slopes >1 have increased relative presence of CVD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2b33a221-4ce2-494d-bbbe-f9197b6b8c4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aXRf69fv04I+fbbb8Un7CWEjBw5sn79+hxjq3QpjRs3Pnz48OXLlyVmujA2Nm7Y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bNm2aM2fOtm3bampqlixZoqrffQHUTs3X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\nAADAaAhCAABgNAQhAAAwGoIQAAAY7f8BWC9M3k1JIfsAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 300
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Converting the values into intuitive names.\n",
    "not_induced <- training_data |> filter(exercise_induced_angina == 0) |> mutate(exercise_induced_angina = \"No\")\n",
    "exercise_data <- training_data |> filter(exercise_induced_angina == 1) |> mutate(exercise_induced_angina = \"Yes\") |> rbind(not_induced)\n",
    "\n",
    "#Exercise induced angina vs. presence of CVD.\n",
    "exercise_induced_angina_plot <- ggplot(exercise_data, aes(x = exercise_induced_angina, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_bar(position = \"fill\") + \n",
    "    labs(x = \"Exercise Induced Angina\", y = \"Relative Distribution\", fill = \"CVD Present\") + theme(text = element_text(size = 13)) +\n",
    "    ggtitle(\"Figure 5: Distribution of Exercise Induced \\nAngina with the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "exercise_induced_angina_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6561f801-b3d5-41d9-bd3d-158e04e67bf6",
   "metadata": {},
   "source": [
    "In Figure 5, by setting `position = \"fill\"`, we can see that presence of exercise induced angina has a significantly higher relative presence of CVD.\n",
    "\n",
    "From these visualizations, we can confirm that these vectors contain ranges or groups with significantly higher relative presence of CVD. This ultimately implies that these vectors could be used as predictors in our classifier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "096af8e2-9f19-49bb-b618-da4ba032caf9",
   "metadata": {},
   "source": [
    "## Coding the Classifier\n",
    "\n",
    "We initially conducted a 5-fold cross validation to determine the optimal number of `K-neighbours` to use. In our recipe we also standardized our predictors. Some of our predictors contained values which could be categorized into binary values (0 and 1 for no and yes, respectively) while other predictor's values ranged from 0 to 80 or -2.5 to 7. Thus standarization was deemed necessary to prevent any single predictor from having a larger influence than other predictors in determining the outcome of the prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "12190538-6733-4e10-87a8-c4e432347d2b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xtbt2xZ5CmL5y9btta0cX34v5IPwgMqxbz/bFed8IiZiXY9Op8BB0bKKUXv6C+a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\npXAEzFgKR8CMpXD/D781SfnMCSJYAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(2)\n",
    "\n",
    "#5-fold Cross Validation\n",
    "knn_spec <- nearest_neighbor(weight_func = \"rectangular\", neighbors = tune()) |> \n",
    "    set_engine(\"kknn\") |>\n",
    "    set_mode(\"classification\")\n",
    "\n",
    "cvd_recipe <- recipe(presence_of_cvd ~ age + sex + exercise_induced_angina +st_depression + st_segment_slope, data = training_data) |>\n",
    "    step_scale(all_predictors()) |>\n",
    "    step_center(all_predictors())\n",
    "\n",
    "cvd_vfold <- vfold_cv(training_data, v = 5, strata = presence_of_cvd)\n",
    "k_vals <- tibble(neighbors = seq(from = 1, to = 50, by = 2))\n",
    "\n",
    "knn_results <- workflow() |>\n",
    "    add_recipe(cvd_recipe) |>\n",
    "    add_model(knn_spec) |>\n",
    "    tune_grid(resamples = cvd_vfold, grid = k_vals) |>\n",
    "    collect_metrics() |>\n",
    "    filter(.metric == \"accuracy\")\n",
    "\n",
    "options(repr.plot.width = 8, repr.plot.height = 8)\n",
    "accuracy_vs_k <- ggplot(knn_results, aes(x = neighbors, y = mean)) +\n",
    "    geom_point() +\n",
    "    geom_line() +\n",
    "    labs(x = \"Neighbors\", y = \"Accuracy Estimate\") +\n",
    "    theme(text = element_text(size = 12)) +\n",
    "    ggtitle(\"Figure 6: Plot of Estimated Accuracy vs. Number of Neighbors\")\n",
    "accuracy_vs_k"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9351b92a-87e2-4a56-9f4d-8d12ac1b9ed4",
   "metadata": {},
   "source": [
    "From Figure 6, we decided to use K = 24 as changing the number of neighbors by 1 or 2 didn't cause the accuracy to fluctuate greatly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b3e18b93-446f-49dc-bc2f-e9dfa84b5d84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>.metric</th><th scope=col>.estimator</th><th scope=col>.estimate</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>accuracy</td><td>binary</td><td>0.8211382</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " .metric & .estimator & .estimate\\\\\n",
       " <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t accuracy & binary & 0.8211382\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| .metric &lt;chr&gt; | .estimator &lt;chr&gt; | .estimate &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| accuracy | binary | 0.8211382 |\n",
       "\n"
      ],
      "text/plain": [
       "  .metric  .estimator .estimate\n",
       "1 accuracy binary     0.8211382"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Predict of Test Set and Summary of Test Set\n",
    "knn_spec_2 <- nearest_neighbor(weight_func = \"rectangular\", neighbors = 24) |> \n",
    "    set_engine(\"kknn\") |>\n",
    "    set_mode(\"classification\")\n",
    "\n",
    "knn_fit_2 <- workflow() |>\n",
    "    add_recipe(cvd_recipe) |>\n",
    "    add_model(knn_spec_2) |>\n",
    "    fit(data = training_data) \n",
    "\n",
    "cvd_test_predictions <- predict(knn_fit_2, testing_data) |>\n",
    "    bind_cols(testing_data)\n",
    "\n",
    "accuracy_results <- cvd_test_predictions |>\n",
    "    metrics(truth = presence_of_cvd, estimate = .pred_class) |>\n",
    "    filter(.metric == \"accuracy\")\n",
    "accuracy_results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b257490-7a77-48e9-99db-486a5a07caa1",
   "metadata": {},
   "source": [
    "*Table 4: Accuracy of Predicting Test Set*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be03524a-a1d6-42ac-bcec-635d68241311",
   "metadata": {},
   "source": [
    "To see the number of the false negative and positive predictions, here we produce the confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5cd5537f-f53f-48a0-9f10-0239206476da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Truth\n",
       "Prediction No Yes\n",
       "       No  28   6\n",
       "       Yes 16  73"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "confusion <- cvd_test_predictions |>\n",
    "    conf_mat(truth = presence_of_cvd, estimate = .pred_class)\n",
    "confusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffe13737-9c78-4f1b-b7be-73e5887ae4a0",
   "metadata": {},
   "source": [
    "*Table 5: Confusion Matrix of Prediction Results*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5e461ff-ce63-44e6-a1fa-632a9dd51738",
   "metadata": {
    "tags": []
   },
   "source": [
    "Since we used 5 predictors to build our classifier, we weren't able to generate a single plot that is able to show us whether our classifier is overfitting or underfitting the data. However, by plotting the errors in our prediction results of the test set, we could gain some intuition on if our classifier was overfitting or underfitting the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "597c81b5-a8b2-475f-8865-98cecbf99c70",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 26 rows containing missing values (geom_bar).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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HHZ9KhbrNpF/fTTT06Zs7Ozw8LCIiMj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\nlvbiHUk6luYLd3ZuqTGnluNU3Xc3fVeH0HuN6F493ek7v9q3Fl8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tPXr0aLt27ZyegpWYmHjhwoXTp0+7nEpeIQwNDbXb7dnZ2RcvXqx5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kW2+9lZmZ2adPH52mBwAAAJTM1dU1MDDw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\nNCksLLTtaTQalcm0b7/99gFV/fzzz8oOrVmuqK5du4rICy+8YDAYlAnDL77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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Age vs. presence of CVD.\n",
    "options(repr.plot.width = 10, repr.plot.height = 7)\n",
    "age_vs_pred <- cvd_test_predictions |>\n",
    "    ggplot(aes(x = age, fill = as_factor(.pred_class))) +\n",
    "    geom_histogram(bins = 25, position = \"fill\") + \n",
    "    labs(x = \"Age (Years)\", y = \"Relative Distribution\", fill = \"Predicted Presence of CVD\") + theme(text = element_text(size = 15)) +\n",
    "    ggtitle(\"Figure 7: Predicted vs True Count of Age Groups Separated by the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired') +\n",
    "    facet_grid(rows = vars(presence_of_cvd))\n",
    "age_vs_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ba6d63a-35b2-4d11-8d78-4688bf211a41",
   "metadata": {},
   "source": [
    "In Figure 7, the true class vector was passed to the `vars` function in `facet_grid` while, the predicted class vector was set to the `fill`. If we had 100% prediction accuracy, each histogram should only contain one `fill` color. However, we see otherwise. Most of the false positives were located between the ages 50 to 65 years old while there weren't nearly as many false positivies in the same age range. Our classifier could be underfitting for age in this range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cc6c3287-3403-40a1-bbae-7296dd010474",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rRokZWVZa4dy+d4WbduXXBwMM3eGjduHBwcHBwcHBcXZ3CBNDElhKxevdr0qvPz\n83VK6MfM09PTYP3ly5fTJtbe/GI/GCzLzpgxg27g27dvTYcEUJ1Vr4Rj5syZ9FQ1e/bsV69e\nFVtfP+HIzc2lJ18fH59///2Xq7ljxw56sv71119pyalTp+i8tWrV+uabbwoKCmj54cOHZTKZ\n9sm6qKioVatWhJCgoKCnT59yy9y6dSutuXPnTlqycOFCQoiLi8vjx4+5ag8ePHBzcyOEfP31\n18Y2ZOfOnYSQ5s2baxd+/fXXhBBfX19CSHR0NFeelZVFby3Fx8ezegkHy7IFBQVcHsDNxSUH\nLi4uM2bMyM3N5fYD3TPLly83savLuEz++9CYYr9Xhg8fTgihjzlwscnl8k6dOo0dO/bWrVtP\nnjzJzs4uUTA8G5T/AmlUYrG4UaNGS5cu5b5xDx48SO9BrFy5kpbk5+d7e3vTZb5+/ZoWXr9+\n3dnZmRAycuRIs+xY/scLy/uWytq1a+mnohQ32rij8p9//tGfSkOdOHGidiGfhIPmeYSQI0eO\nlDQkgOqjeiUcmZmZ9M4uIUQikfj7+y9ZsuTEiRP0e0KffsJBv7nFYrH2NwQVEhJCf5/pzNur\nVy+dml988QUhxM7OTqPRsCxLfyI7ODhkZGTo1Jw7dy4hpGXLlvTPPn360GxJp9qFCxcWLlz4\n559/Gtvw169fi0QihmG4rxaWZf39/RmG2bVrFyFk0aJFXPmxY8e0v1lLmnD07t1bZ+30ls3w\n4cONhVf2ZfLfh8aY/l55+fIlvXQ/YcIEndg6dOigU9nsDcp/gVxUgwcP1qkZFBRECBk0aBD9\nMzw8nBBiZWWlc+WJfh7kcjm9vlLGHcv/eGF5JxyTJ08mhDg7O5uuZkzTpk0JIePHj9cpP3v2\nLN11XJ8Pik/CUVBQQK9L0YuCAGBQ9erDoVKpoqOjaSd2jUZz8uTJRYsWde/e3dbW1tfXd8WK\nFSkpKaaXQG/xduzYsX79+jqTgoODCSEPHz5MTEzULqe3M7T17duXEJKamnrv3j1CCL2Z3bNn\nT2tra52atN/AtWvX3rx5QwhRq9WEkFOnTmVkZGhXa9++/ZIlS+i3l0EODg7e3t4sy/7999+0\nJC8vLyYmpnnz5kFBQSKR6PTp01xlmir16NHD+G4wZcKECTol9IdjWQbvKnaZ/PdhSRUWFv79\n9999+vRJT0+3sLCgF8+1jRo1SqfE7A1aiq0bNmyYTk26x7hqf/31FyHEz8/PztSRhuQAACAA\nSURBVM5Ou9rHH3988+bNhIQElUpVulVrK8XxUizaJ4P2jioF2kNr165db9++1S7ftGkTIaR9\n+/ZeXl4lXaZEIrGxsSGE6Az+AQDaJBUdQHmTyWSzZs2aOXPmxYsXo6OjY2JiLly4kJaWdu7c\nuXPnzi1atOi7776bMmWKsdnp/WP6tIsOehmcEHLnzp169epx5S1bttSpyfVCePz4cfPmzePi\n4ggh0dHRfn5+OjW53/337t3r1KnTpEmT9u3bd/nyZVdX16FDhwYGBvr6+iqVSj4bHhgYePXq\n1TNnznz88ceEkAsXLrx7965z585qtdrDw+PixYu5ubkKhYKUOeGgX2za6Ln43bt3pVsgn2Xy\n34emV7Rhw4bdu3dzfxYVFWVkZNBOlEqlcteuXfoDUtE7DtrM3qCl2LpGjRrp1KTPmnIdQm/f\nvk0I4bp3cORyuYeHR1lWra0Ux0ux6L2YwsJC/rNoGz169Lx587Kysvbs2UOvshBCMjMz9+7d\nS0rSXVQH3bE6Q3QAgLZql3BQIpGoQ4cO9PYKy7JxcXFHjhxZv359UlLS1KlTFQqFsQdV6OCD\nOj8KKa63fHp6una5vb29Tk36ZUkIoc+q0F9sz549e/bsmbGA6TLbtWt3/PjxKVOmXL9+PSws\nLCwsTCqVdunSZdiwYcOGDZNKpSY2OTAw8Ntvv+WuG588eZIQQr9FOnfufOPGjYsXL/r5+WVk\nZFy7dk0ul+s/usKT/k/hsit2mfz3oWk5OTk5OTnaJUqlskmTJkFBQVOnTuU6S2pzcHAodTA8\nG7QUW2fwI6ofJPdRNF2t1Du2FMdLsegB9fLlyxLNxVGr1YMGDdq6devGjRu5hGPXrl05OTlq\ntZrrvFwiWVlZ9GOj/2EAAE71uqViEMMwnp6ec+fOvXv3brt27QghCxYsKCoqMlaZEMIaGh2Z\nK6S/wDj6eQBXky6N1p8xY4aJW1/c1XVfX9/Y2NiYmJj58+e3bt26sLDwxIkTISEhrVq1ogMW\nGdOxY0elUnnjxg16fqe957p06UII6dy5MyGE3lU5e/ZsYWGhr6+vpaWliaVVNiXahybo36rP\nysqKi4tbuXKlwWyDGPpRa/YGNdfW6QdZ7EuCyrjqUhwvxaLjtbx58+bhw4clmpFDL2PExMTc\nvXuXltD7KaNGjeIz5pi+c+fO0f/oPM4NANqQcPw/VlZW9DGW5ORkY7/n6G81g0OR0h9zRO/3\nnM7tefK/Cxvkfz/y6C+258+f8w/Vx8fnq6++unz58osXL1atWqVUKuPi4kJDQ03MIpVK/fz8\nioqKzp079/bt28uXL7u5udHBrLQTjjLeT6kopdiHwjF7gwqxdXSZxfZrKeOqS3G8FItmyYSQ\nzZs3m6558eJF7rEUbT4+PrSjBs0zbt26RTvb6ncV4omOyu/g4KB/fw0AONUo4Vi/fn1gYODQ\noUNN1KGPgxJC6CN/+ujt7Rs3buhPone7uTqcO3fu6NSMj4+n/6EdAui57+bNm8VtgQG1atWa\nPn361q1bCSHHjx83dmGGCgwMJIScPXv27NmzBQUF3E2TmjVrurq6Xrx4MS8v7z1NOMqyD83O\n7A0qxNY1b96cEKI/UntBQcH27du3b99O71mUcdWlOF6K1ahRI39/f0LImjVr6FB+BmVlZX3y\nySf+/v4LFizQn0pziz179rAsS8cB8/Pzow+wlFRMTMy+ffsIIZMnTy7p1RqAaqUaHR5paWlR\nUVHh4eG057xB9D0LDRo0oGM16qMPmMTExOif6ejzhK1atdKZl5Zro++RcnR0pD376GjKd+7c\n0X5UhDp48GDLli3DwsIIIS9fvvz888/79Omj0Wh0qtHfiLm5uaZ70tEHI8+dO0d/9ml3A+zc\nuXNeXt7Jkydv3rxZp04d+m1kDPdSFf1ISq2My+S5D8uH2RtUiK2j90FiY2O5cbSoU6dOjRgx\nYuTIkWZZdSmOFz6+++47qVSanZ3dq1cvg4PYpqSkBAQE0BfPfv755/oVhg8frlQqk5KSLly4\nQNOF0nUXvXbt2sCBAwsLC+vXrz9t2rRSLAGgGjFxa7aKycrKol/wUql03rx5d+/e5V5/mpOT\nc+rUKfp9TAjhXgqqPw5HQUEB7XLv4+OTnJzMLXzjxo30K/PAgQM689rb22u/ZfTs2bP0PvH8\n+fNpSWFhIe07UqdOnWvXrnE1jx8/Th+bXLx4Mcuyubm59NQcEhKiPQYlPbcSQrp06VLsTqAj\ncLdp04ZhGO34t23bRgih1zzGjRunPYv+OBwsy9LOhkuWLOFKTLz3ZPbs2YSQjh07mo6tLMvk\nuQ9N4DPcgjYTsZm9QflvHf89VlBQQNNKDw8POsIby7I3btygbzjr379/SVdtEP/jhS3Ju1RY\nll2/fj1dgpWV1dy5c69du5adna3RaBISEr799lv60KyVlVVERISxJdCO4fQGTc2aNfPy8gxW\nM/jByM/Pv3Tp0pQpU2gPHrVafePGDT5hA1Rn1SjhYFn2yZMnbdq04ZIthUJRq1YtOt4AZWlp\nuXbtWq6+waHN79+/TweEtrCwaNOmTdeuXemQzDpflty8mzdvZhimcePGvXr1at26NT1Lent7\na4+CnJiYyD356eHh4efnx41bEBQUxJ0KT506Rb+VZTKZp6dnly5dvL29aafUmjVr8nlH9qef\nfkoXqzPq6NOnT7mdsG/fPu1JBhMOrp9g48aNnZ2dc3Nzy55wlHGZPPehMWZMOPgHw79BeS6w\nRHvs3r179KMrEolcXV3r169PP5zNmjXTHoe3jDuW5/HCljDhYFn2wIED3KL01a9f//LlyyZm\nj42N5SrPmTPHWDX919OrVCrtNye3b9/+0aNHPGMGqM6qV8LBsmxRUdGhQ4dGjRrl7u5ubW0t\nFostLCycnJwCAgK+++67Fy9eaFc29rZY+jKqFi1aKJVKmUxWp06doUOHnj9/3uC8ubm5UVFR\nPXr0sLe3l8lkDRs2nDNnjv7YptnZ2d9//3379u1tbGzEYrGDg0NAQMC2bdsKCwu1qz18+HDm\nzJnu7u729vZisdja2rpVq1bz58/XHkLUBHr12OBpnX6LiMXi9PR07XKDCceTJ0+6d+9uaWmp\nVCq9vLzy8/PLnnCUfZk896FB5k04+AfDv0H5LLCkeyw1NXXu3Llubm5WVlYWFhYeHh5fffVV\nqT+cxvA5XtiSJxwsy+bk5Pz6668fffRR/fr1LS0tZTKZs7Nznz59fvvtN24gfBPoxRuGYRIS\nEozVoR8MHSqVytXVdezYsSauoACADoY19MQalN3p06fpHYp3797RAbUAAACqrWrUaRQAAAAq\nChIOAAAAEBwSDgAAABAcEg4AAAAQHDqNAgAAgOBwhQMAAAAEh4QDAAAABIeEAwAAAASHhAMA\nAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABCep6ADKSVZWFp9qEomEZdnCwkKh4yl/\nDMMoFAqNRlNQUFDRsQhCoVDk5uZWdBSCkEqlEokkLy+vqKioomMxP7FYLBKJqurH0sLCoqio\nKC8vr6IDEYRcLs/Pz+czeqREIrGwsCiHkKAyqy4JB88DXiwWV9Wzg1gsViqVGo2mSm4dIcTK\nyqqqbhpNOLKzszUaTUXHYn5yuZxhmKradiqVqqCgoKpunYWFRX5+fpXMg0EIuKUCAAAAgkPC\nAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIJDwgEAAACC\nQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAA\nAIJDwgEAAACCQ8IBAAAAgpOU8/ouXrz4888/S6XS33//3XTNS5cuhYeHJyYmymQyb2/vMWPG\nODg48JwKAAAAlUr5XeF49+7d6tWrf/zxRysrq2IrX7169ZtvvnFxcVm4cGFoaOjTp0/nz5+f\nn5/PZyoAAABUNuWXcFy7di0xMTEsLMzV1bXYyjt27HB1dQ0NDfXy8urYseOXX3758uXLkydP\n8pkKAAAAlU35JRxubm4rVqxwdHQstmZGRkZ8fHzHjh25Eicnp3r16l25cqXYqQAAAFAJlV/C\noVarxWIxn5rPnj0jhDg7O2sXOjs7JyUlFTsVAAAAKqHy7jTKx9u3bwkhlpaW2oUWFha03PRU\nzqFDh27fvk3/b2lpOXHiRD6rlkgkLMtKJJVxt5QRwzCEEKlUqlQqKzoWQTAMU1U3TSqVEkIs\nLCxYlq3oWMxPLBZX4bYjhIjF4qq6dSKRyMrKqkp+LEEIlfeblX5Blu5PQsjly5cjIiLo/9Vq\n9bRp0/ivmp7fte2KfcZ/dhDaUO86BssVCoV+IdquUjHWdvpZPhquUjHWcHK5nM/sGo3GrOHA\ne6kyJhz0MRadKxbZ2dn0V4LpqZzPP/982LBh9P9isTg9PZ3PqhUKRVFRER54qeQMtqa1tXVm\nZmb5BwMlot92MplMLBa/e/euQuIBngwedCqV6u3bt0VFRcXOLpVKq+SVYyiRyvgJqFu3LiEk\nKSmpdevWXOHTp0/r1atX7FSOk5OTk5MT9+ebN2/4rLqoqKioqAjJeCVnrIHQcJWffhvRWypo\nu0rOYAOxLKvRaPgkHDw78EHVVhlHGrW2tm7atOn58+e5W4MJCQnPnz9v27ZtsVMBAACgEhIv\nXry4fNaUmJiYlJSUnJx89erVlJSUxo0bJycnZ2Vl2dnZEULOnz+/Zs2aJk2a2NraEkJq1679\nxx9/vHr1ysLC4sGDB+vXr7e3t//ss89EIlGxUw3KycnhE6RUKqU5u055QiZ+flUiDW0MXJmz\nsLAweFkebVep6LedRCIRiUQFBQU65Wi4SsXgQadQKPLy8vh0GpVIJDx7e0AVVn63VLZv337p\n0iXuz3nz5hFCGjVq9MMPPxBC0tPTHzx4wKUFHh4eCxcu3LFjx9KlSxUKRevWrceMGcNdlDM9\nFQAAACobppo80cSzD4elpWVRUVFubq5OeVSSbglUoIC6Bp5GsbOzS01N1S9H21Uq+m0nl8sl\nEolON3CChqtkDB50tra2mZmZfPpwyOVylUolQFzwPqmMfTgAAACgikHCAQAAAIJDwgEAAACC\nQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAA\nAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIJDwgEAAACCQ8IBAAAAgkPCAQAAAIKTVHQAAMKau+dG\nRYcA/0/AjHYVHQIAVAxc4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAA\nAMEh4QAAAADBIeEAAAAAwSHhAAAAAMFhpFEAqIwwRGylgiFioexwhQMAAAAEh4QDAAAABIeE\nAwAAAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAE\nh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABIeEAwAA\nAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QD\nAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABIeEAwAAAASHhAMAAAAEh4QDAAAABCep6ADKiUql\n4lNNIpGwLCuVSvWm5Jo9JCg1g63JMAzPVoYKpN9GYrGYYRiRCD9+KjWDB5dYLFYqlSzLln88\n8D6qLgnHu3fv+FRTKBRFRUX5+flCxwNlYbA1pVIpz1aGCqTfRjKZTCQS5eYip6/UDB5cEokk\nNze3qKio2NmlUqlcLhcgLnifVJeEQ6PR8KlWVFRUVFTEszJUFGMNhIar/PTbiF7hQNtVcgYb\niGVZjUbDJ+EQi8UCBAXvGVzGBAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEA\nAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh\n4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAA\nwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAA\nAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHh\nAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADB\nIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAA\nAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBIeEAAAAAwSHhAAAAAMEh4QAAAADBScpz\nZZcuXQoPD09MTJTJZN7e3mPGjHFwcNCv9ubNmzFjxuiXN2vWbPny5YSQdevWRURE6ExdsWKF\nq6urEGEDAABAGZVfwnH16tVvvvkmICBg1KhR2dnZu3btmj9//po1a2QymU5NGxubr7/+WrtE\no9GsWLGicePG9M+cnBwnJ6dJkyZp16lbt66g8QMAAECplV/CsWPHDldX19DQUPpngwYNPvvs\ns5MnT/bs2VOnplQq9fDw0C7ZtWuXTCb75JNP6J85OTlqtVqnDgAAAFRa5dSHIyMjIz4+vmPH\njlyJk5NTvXr1rly5Uuy8SUlJe/fu/fTTTy0tLWlJTk6OhYWFULECAACAuZVTwvHs2TNCiLOz\ns3ahs7NzUlJSsfNu27bNxcVFO1lBwgEAAPB+KadbKm/fviWEcJcoKAsLC1puQkJCwsWLFxcv\nXqxdmJOTk5qaumzZsvv37xcWFjZo0GDw4MFeXl7adX7//ffLly/T/yuVSp1OIcaIRCJCiFwu\n152QlMtndigfNjY2+oUMwxgsh0pFv41EIhHDMBJJuXZgh5IyeHCJxWKVSsVn9qKiInNHBO+f\ncj3IGYYx8adBe/fudXFxadmypc6MKSkpvr6+gwcPTk1NPXz48MKFCxcvXuzt7c3VefTo0T//\n/EP/r1arpVIp/zjFYjH/ylD+jLVmiVoZKoSxNqK5PlRaZTzoNBqNWcOB91I5JRxWVlbkf9c5\nONnZ2Uql0sRc7969u3z58pAhQ3TKN2zYoP1ny5YtJ06cuHPnTu2EY968ebNmzaL/pwkKnzgt\nLS2Liopyc3E9o1Iz2JpqtTotLa38g4ES0W87uVwukUiKvdgJFcvgQWdjY5OVlcXn6oVcLjd9\ntofqoJwSDvrMalJSUuvWrbnCp0+f1qtXz8Rcly5dys/P9/HxMb1wmUxWt25d2k2EY2Fhod3P\n482bN3ziZP+HT2WoKMYaCA1X+em3EQ6694KJg45P26F9gZRbp1Fra+umTZueP3+e+9glJCQ8\nf/68bdu2JuaKjY1Vq9U6XU1fv369fPly7nYJIeTdu3cJCQlOTk5CRA4AAABlV373TUeMGBEf\nH7969eobN26cPXt2+fLl9erV69q1K516/vz5mTNnPnnyRHuWp0+f6qcRDg4OycnJq1evPnbs\n2P379y9durRo0aLs7OzBgweXz4YAAABASZVfp1EPD4+FCxfu2LFj6dKlCoWidevWY8aM4bpn\npqenP3jwICcnR3uWzMxMe3t7neUwDLN48eLdu3fv378/NTVVJpM1bdr0m2++adasWTltCQAA\nAJQQU01urfHsw2Gs02gUHoutTALqKvQL7ezsUlNT9ctbr7okfETA15UZ7XRKjHUaRcNVKvoN\nRwixtbXNzMzk2WmU5wO0UIXhUTQAAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEBwS\nDgAAABAcEg4AAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQ\nHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEBwSDgAA\nABAcEg4AAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEBwSDgAAABAcEg4AAAAQHBIO\nAAAAEBwSDgAAABAcEg4AAAAQHBIOAAAAEJyEZ71Hjx7t3bv30aNHubm5LMvqV9i+fbtZAwMA\nAICqg1fCERkZ2bdv37y8PBN1kHAAAACAMbwSjgULFuTl5Q0ePHjAgAFqtZphGKHDAgAAgKqE\nV8Jx8+bN7t27h4eHCx0NAAAAVEm8Oo3K5XJPT0+hQwEAAICqilfC0bp164SEBKFDAQAAgKqK\nV8KxbNmyEydOHD9+XOhoAAAAoEri1YcjJydn5syZH330UVBQUOvWrWvUqKFfZ+LEieaODQAA\nAKoIXgmHv78//c/hw4cPHz5ssA4SDgAAADCGV8Lxn//8RyqVSqVSoaMBAACAKolXwvH9998L\nHQcAAABUYXyHNue8ffs2NTVVJBLZ29srFAohYgIAAIAqhu/L27KzsxcsWNC4cWOVSvXBBx/U\nqVPHysrKy8srLCxMo9EIGiIAAAC873hd4UhLS/P19b19+zYhRKlU2tnZsSybkpJy8+bNL774\n4s8//zx27JhMJhM4VAAAAHhf8brC8e23396+fXvUqFH37t3LyspKTEx8+vRpdnb29evX+/fv\nf+rUqdWrVwsdKAAAALy/eCUchw4d6tq16+bNm11dXblChmG8vLz27dvXtm3bnTt3ChYhAAAA\nvPd4JRxPnz719fU1OIlhGD8/vwcPHpg1KgAAAKhSeCUcDMPk5eWZqMCyrJniAQAAgCqIV8LR\nuHHjqKiowsJC/UkajSYyMrJJkybmDgwAAACqDl4JxyeffHLt2rU+ffrExMTk5+fTwry8vDNn\nzgQFBV2/fn348OFCBgkAAADvN16PxU6bNu348eMRERERERFisdjGxoZl2czMTHrNo0ePHlOm\nTBE4TgAAAHiP8brCIZfLIyMjf/rpp7Zt24rF4tTU1LS0NIlE0rFjx40bNx45cgSDcAAAAIAJ\nfIc2l0gkoaGhoaGhhYWFmZmZDMNYW1uLRHwHKgUAAIDqrMTvUhGLxWq1WohQAAAAoKoymnBs\n375dqVT269eP/r/YBaHfKAAAABhjNOEYMWJEvXr1aMIxYsSIYheEhAMAAACMMZpwzJgxw87O\njvt/ecUDAAAAVZDRhGPlypUG/w8AAABQUrw6jQ4cOHDcuHE9evQwOHXGjBn37t07cuSIWQMz\nM1tbWz7V6HM3CoVCd0LSv2YPCUrNYGuKRCKerQwVSL+NGIZhGEYqlVZIPMCTwYNLLBZbW1vz\nmb2oqMjcEcH7h1fC8ccff/j5+RmbmpaWdubMGbNFJIyMjAw+1SwtLQsLC02/OAYqnMHWVKvV\nPFsZKpB+G8nlcrFYnJOTUyHxAE8GDy4bG5usrCw+yYRcLsdwTWAq4aBDi9L///HHH/Hx8fp1\nUlJS9u7dq1QqBYnOfHi+Xo5Ww7voKjljDYSGq/z02wgH3XvBxEHHp+3QvkBMJxzPnz/fsmVL\neno6IeT06dOnT582VvPLL780e2QAAABQZZhKOMaOHTtmzJjbt297eHiEhIQEBgbq11EoFM2a\nNXN1dRUsQgAAAHjvFdOHg2EYd3f3AQMGDB482FinUQAAAADTeHUa3bdvn9BxAAAAQBXGK+GY\nOXOmiaksy+bm5q5du9ZMIQEAAEBVwyvhWLVqVbF1kHAAAACAMbwSjm3btukXvnz58p9//jly\n5Mi8efP8/f3NHRgAAABUHbwSDhMvZouOjv7www+7dOlivpAAAACgqhGVcf6uXbsGBATMnz/f\nLNEAAABAlVTWhIMQUr9+/djY2LIvBwAAAKoqMyQcV65c0Wg0ZV8OAAAAVFWlH4eDZdnMzMyD\nBw+eO3fO19fX3IEBAABA1cEr4Rg0aJCJqVZWVl9//bWZ4gEAAIAqiFfCMWHCBP1ChmEUCoWL\ni0v//v2dnZ3NHRgAAABUHbwSjl9++UXoOAAAAKAK45VwaMvMzExPT2cYxs7OzsrKSoiYAAAA\noIrh+5RKfHz8uHHjnJycbGxs6tWr98EHHyiVyvr160+ZMuXZs2eChggAAADvO15XOGJjY7t0\n6ZKVlUUIUalUarWaYZiUlJTExMSffvpp165dZ8+ebdasmcChAgAAwPuK1xWO2bNnZ2VlTZ48\n+dGjR5mZmYmJiU+ePMnKyoqPj586deqbN29mzZoldKAAAADw/uJ1hePChQudO3des2aNTnnD\nhg3DwsIePnx49uxZAWIDAACAKoLXFQ6WZb29vY1Nbd26dWFhoflCAgAAgKqGV8Lh4eHx9OlT\nY1OfPn3q4eFhvpAAAACgquGVcMyfP//YsWNnzpzRn3Tz5s0DBw7gbbEAAABggtE+HNu3b9f+\nc9iwYf7+/oGBgZ06dapdu7ZIJHrz5s0///xz6NChESNGSCQlHs8DAADALJ4+fbp27dqoqKgn\nT57k5OTUrl27UaNGQ4cOHTJkCDdeVO/evY8ePbpu3brPPvvM4ELy8vIcHR3T0tLu3r2bnp7u\n4+OjPVWlUtWuXbtNmzaDBg3q06dPsd96Fy9e1FkCIUQulzs5OXXt2vU///lP06ZNS7u5FWDT\npk3Ozs49evQoy0IYlmUNT2CYEi3I2HIqiTdv3vCpZmlpWVRUlJubq1MelaRbAhUooK5Cv9DO\nzi41NVW/vPWqS8JHBHxdmdFOp0Qul0skkrdv3+qUo+EqFf2GI4TY2tpmZmYWFRUVO7tcLlep\nVALERQgh69at++KLL/Lz8xUKhZeXl1KpfPr06aNHj4qKiho3bnz48GH61f7nn3/27du3ZcuW\nV69eNbicnTt3Dhs2rEuXLqdPn6bpglqtDgwMpFMzMzPv3bv3+PFjQoinU4cdIwAAIABJREFU\np+fOnTubN29uIir9JRBCXr9+fevWreTkZIVCcfjw4YCAALPtBSGxLGtnZzdq1KiwsLCyLMdo\njjZjxgz+oeh/QwMAAAjtt99+mzRpkkQi+e6776ZMmWJhYUHL4+PjZ82adeDAAT8/v3v37tna\n2vbu3fuDDz64du1abGyswccgNm3aRAiZOHEiV+Li4rJ7927tOrdu3ZozZ86RI0e6desWExPT\nsGFD0+HpLyEvL2/OnDlhYWFjx459/PixWCwu3YaXpzt37qSnp5d9OUYTjpUrV5Z96QAAAAJJ\nS0ubOnUqIWTr1q1Dhw7VntSoUaN9+/b17dv3+PHje/bsGT9+vEgkGjdu3MKFCzdu3Lh27Vqd\nRSUkJERHR9eoUaN///4m1uju7v7XX3+NGjVq69atkydPPnr0aEljlsvlq1atCg8PT0pKunbt\nWps2bWbMmPHDDz+cPHnywoULYWFhtWrVunXrFiGkqKho/fr1mzdvvnPnDsMwDRs2HDly5JQp\nU6RSKbe0Q4cO/fTTT3fv3n3z5k2NGjXatWs3c+ZM7Vs5xS5k1qxZK1asOHnypEqlmjdv3uXL\nl3Nzcz09Pb/66it6bWbgwIF//PEHIWT16tWrV68eMGDAvn37SrrVFN+hzQEAACqVzZs3Z2dn\nd+vWTSfboEQi0ebNm5OTk8ePH09Lxo0bJ5FIdu7c+e7dO53Kv/32G8uyISEhMpms2PWuWbPG\nxsbm2LFjDx8+LEXYIpGIXhp5/fo1IYSu8dChQ8uXL+/Zs2fv3r0JISzLDhkyJDQ0NCUlZerU\nqVOnThWJRDNnzvzoo4+4e1g///xzv3797t+///HHH8+ZM6d79+5RUVF+fn6nT5+mFfgshGYe\n58+f79atm1wuDwkJ6dix4z///NO3b99Hjx7RnRYSEkII8fPz++mnn8aNG1eKTaZMdRpVKpX9\n+vUjeh1IDRo+fHipgwAAACipkydPEkIMZhuUg4OD9p+Ojo59+/bdv3//vn37RowYwZUXFhZu\n3ryZYRguNTHNxsamZ8+eu3fvjoyMbNy4cUnDLiwsjI+PJ4TUrVuX/C/h2LZtW2RkZPv27Wmd\nbdu27d2718/PLyIiQi6XE0KWLFnSr1+/I0eObN26dfTo0YSQn3/+WSwWX7lypVatWnSu6dOn\nt2rVatOmTX5+fjwXQhOOr7/+ev/+/b169aLLCQ4O3rNnz969e+fMmdOjR4/09PTff//dy8sr\nNDS0pBurzWjCMWLEiHr16tGEQ7thjEHCAQAA5SkhIYEQ4u7uzn+WiRMn7t+/f+PGjdrfa8eO\nHXv+/HlgYGCxfTI4bm5uhBATI1QZU1BQMG/evH///bdZs2Y0cvqIRuvWrblsgxCyceNGQsjy\n5ctpokAIkUgkS5cuPXLkyJYtW2iukJGRIRKJuG4rhBBPT893795xT9DwWQgVGBjIZRuEkAED\nBuzZs4de4TAjU51G7ezsuP+bd60AAABlRF8pqlQq+c/SvXv3Ro0anT179sGDB02aNKGF+t1F\ni0VXSgMw4fHjx9q/xlNSUuLi4p4/f65SqX7//Xftp0G1sw1CyOXLlyUSSevWrbULvby8LC0t\nb9++Tf/s3bv3pk2bOnXqNH369F69etWsWZMQov28Lp+FUG3atNH+U61WE0LM/jgIr06j6EAK\nAACVjbW1NSEkLS2N/yz0vsmsWbM2bdq0fPlyQsirV6/++usvJyenDz/8kP9yUlJSCCHcz3Jj\nUlNTd+zYwf0pk8mcnJzGjx8/Z86cBg0aaNesUaMG9/+srCz6ZW/wGZZ3794VFBRIpdK1a9ey\nLLtlyxbax8LLy6t///4TJ06kmQfPheivnfzvoovZR7vgNWCXu7v7hx9++O2335p33QAAAKXm\n6up6586dK1eu+Pr68p8rJCRkwYIFW7Zs+frrryUSyZYtWzQazdixY0s0guWlS5cIIc2aNTNd\nrVWrVleuXOGzQO1nT+j3vUwmmzt3rsHK+fn5UqlULpdv2rRp8eLFhw8fjoiIiI6OXrRo0Q8/\n/PDXX3916tSJ50L4xGYuvPbvq1evnj9/LnQoAAAA/HXv3v3AgQO///77tGnTDA5WmZ6evmrV\nqkmTJtWuXZsrdHBwGDBgwM6dO//6669+/fr99ttvYrH4008/5b/eJ0+enD59WiKRCDRyl1Kp\ntLKyevv27ezZs7W7aBhUt27dSZMmTZo06e3btz/++OOCBQs+//zzmzdvlmgh5YPXY7HTpk07\nePDgxYsXhY4GAACApxEjRtja2sbFxa1YsUJ/alFR0WeffbZs2TL9qbS7xu7du69fv37//v1e\nvXrRB0b40Gg0n376qUajGTVqFL15IYS2bdsSQv7++2+dcu3xlBMSEv7991/uTysrq/nz53/w\nwQe3bt3SaDQ8F1KeeCUcPj4+ISEhvXr1CgoKWrhw4U8//fSLHqEDBQAA0KZSqdavX08ImT17\n9tSpU7VfYfHgwYOPPvpo9+7dTZs2Xbp0qc6Mvr6+zZs3//PPP3///XdCyIQJE3iu8c6dOwEB\nASdOnKhfvz7tAiKQMWPGEEIWLlyYkZHBFe7YscPBwWHBggWEkNjY2IYNG44dO5bmFtSLFy+S\nk5Nr1apFbw8VuxCeFAoF+V+3lbLgdUvF39+f/icyMjIyMtJgnRL17wUAACi7IUOG5ObmTpo0\nac2aNWvXrnV3d7ezs3v+/Hl8fHxRUVGHDh0OHTrEvb9N24QJE6ZMmbJu3bp69er17NnT4MIT\nEhIGDhxI/5+Xl/fo0aO7d+8SQlq0aLF//357e3vhtmvYsGEHDhzYv39/y5YtBw4cKJfLr169\neuzYsTp16owdO5YQ4u3tPWjQoL179zZv3rx79+5qtTo5OfnQoUO5ubmLFi3iuRCeaFeVffv2\nyWQytVpd6udIeCUcM2bMkEqlMpmspG90AwAAENTo0aMDAwPXrVsXERGRkJBw+/ZttVodFBQ0\nceLEDz/80NjX1siRI+fOnfv27dtPP/1UJDJ8sT8tLY2O6k0IkUgkDg4OH374YXBw8JAhQ4R+\nBwrDMHv27Pnll1+2bNmydu3a/Pz8OnXqTJo06csvv3R0dKR1du3a1aFDh127doWHh2dlZdWu\nXdvb2zs0NLRPnz78F8KHq6vrkiVLVq9evXPnTjqkWCk3qpK/5dVc8LbYqgRvi31/4W2x76nK\n/LZYeF/w6sMxcODAiIgIY1NnzJhBx34HAAAAMIhXwvHHH3/Qgd8NSktLO3PmjPlCAgAAgKrG\nVB+OiIgI7sKGsZwjJSVl7969JRpZFgAAAKobUwnH8+fPt2zZkp6eTgg5ffo098ZbfV9++aXZ\nIwMAAIAqw1TCMXbs2DFjxty+fdvDwyMkJCQwMFC/jkKhaNasmaurq2ARAgAAwHuvmMdiGYZx\nd3cfMGDA4MGDe/ToUT4xAQAAQBXDaxyOffv2GSzXaDQletsNAAAAVE+8nlIhhERHR48cOZL7\n89y5c56enjKZzNHR8ddffxUmNgAAAKgieCUc586d69Gjx+7du+mY7cnJyX369ImLi6tbt25a\nWtqECROOHDkicJwAAADwHuOVcKxcudLCwiI2NpbeQFm3bl1GRsZXX32VmJj46NGjGjVq0Nfn\nAAAAABjEK+G4fPly//79mzdvTv/cv3+/lZXV9OnTCSHOzs59+vS5c+eOgDECAADAe45XwvHm\nzZu6devS/7969SouLq5bt26Wlpa0xNHR8cWLF0IFCAAAAO8/XgmHvb0991qsY8eOEUK0H5FN\nS0vDW3kAAADABF4Ptbq5uR08eHD+/PlyuXzVqlUSiaRfv350kkajiYyMbNiwoZBBAgAA/H+y\nsrKEWCx+PwuHV8IRGhr68ccfOzs7i0SigoKC8ePHOzk5EUL+/fffMWPGPHr0aPLkyQLHCQAA\n8P/5Kz7DvAvs08jGvAsEbbxuqfTr1++nn35q1KiRvb392LFjf/rpJ1r+9u3bY8eODRkyJDQ0\nVMggAQAA4P3Gd5zQ0NBQ/ayiYcOGsbGxLVq0MHdUAAAAUKXwHWnUGGQbAAAAUCyjVzi2b9+u\nVCpp59Dt27cXu6Dhw4ebMy4AAACoQowmHCNGjKhXrx5NOEaMGFHsgpBwAAAAgDFGE44ZM2bY\n2dlx/zfLyi5duhQeHp6YmCiTyby9vceMGePg4GCw5rp16yIiInQKV6xY4erqWtJFAQAAQIUz\nmnCsXLnS4P9L7erVq998801AQMCoUaOys7N37do1f/78NWvWyGQy/co5OTlOTk6TJk3SLuRG\nOy3RogAAAMwoNDR07dq148aN27Bhg3b59u3bR4wY8fLly9q1a1dUbJUZ36dUym7Hjh2urq7c\noy4NGjT47LPPTp482bNnT/3KOTk5arXaw8Oj7IsCAAAwL7FYvGnTppEjR/r6+lZ0LO8NvgnH\ngwcPIiMjk5KSsrKy7OzsmjVrFhAQULNmTZ6zZ/yf9u48Lqqy///4NQszw76ISxip5DcBJQS0\nbCHT1ESyTTQ1NbWsLO8s8c7MJfNrLl+z3HLp1lySblFc807NNNKHuQQuXzXTL5GipCWbCMM+\n8/tjHvfc82M9JNcMjK/nX8x1rnPmgxeDb65znXNu3kxLS3v55ZetLQEBAW3atElJSakpcFif\n1XKbhwIAoGF16tTJw8PjtddeO3XqFJPrCtUdONLS0saNG7d3797Ke2q1L7300rx585o1a1bn\nQa5evSqEaN26tW1j69atf/3112r7G43Gmg5b30MBANCwiouLExISIiIi5s6dO3369Gr7mM3m\nJUuWrFy5Mi0tTa/XR0VFffDBB48//rh9K21E6ggclgfDZmVleXt7x8TEhIaGenh4ZGdnHzt2\nLDk5efXq1QcOHPj+++/btGlT+3EKCwuFEJUmLVxdXS3tVRmNxpycnFmzZl24cKGioqJdu3aD\nBg0KDw9XfqhPPvnkhx9+sHzt7e29Zs2a2iu0UKvVZrPZ1dW18oYr15TsDvvw9fWt2qhWq6tt\nR6NSdYxUKpVKpeJvxEaupg+dj4+P2Wyuc3eTySShKEeqqKjo2LHjxIkTZ8+ePXjw4Pvuu69q\nn5kzZ86cOfO///u/BwwYUFhY+MEHH/Tp0+fIkSNRUVH2L7gxqC1wlJeXDx06NCsra+TIkQsX\nLvT2/v9uMn/p0qUxY8Z89913zz///PHjxzUaTZ1vplKpanlZaVN2dnZ0dPSgQYNycnJ27tw5\nffr0GTNmREREKDxUUVGR9dE+Go1GrVZ6izPLrz+FneEQNY2m8lGGozB2TVS1A2T5VankF6bz\nBQ5LzJo2bVpiYuLrr79+4MCBSh1KSkoWLFgwdOjQ999/39KyadOmVq1aLVy48Msvv7R3uY1D\nbYFj27ZtZ8+e7d+/f7XTA23btt29e3fv3r2Tk5MTExOHDh1ay6Hc3d3FvycnrAoKCjw8PKrt\nX2npb2Rk5Ouvv/7VV19FREQoPNSUKVOmTJlifZmVlVVLeVZubm4mk6m4uFhJZzhKdnZ21UY/\nP7+cnBz7F4N6qTp2er1eq9XWNNmJRqLaD52Pj09+fr6SMKHX611cXCTU5WCurq7Lli3r27fv\n2rVrR44cabvp559/vnXr1mOPPWbbuXPnzqmpqfaustGo7a+KLVu2CCHmzJlTUwetVrt48WIh\nRGJiYu1vY7mi9cqVK7aNGRkZdZ6LsdDpdIGBgZb/Tm7zUAAANJQnn3xy8ODBEydOrPRn7c2b\nN4UQXl5eto1eXl7Wqfc7UG2BIzU1NSgoqGPHjrX0CQsL69Chw08//VT723h5eQUHBx8+fNh6\nti89PT0zM/OBBx6o2vnGjRvz5s07fvy4taWoqCg9PT0gIKC+hwIAQKqFCxdWVFTEx8drtf85\naWBZhGCJHVY3b9708fGxd32NRm2B4/r168HBwXUeon379jdu3Kiz2/Dhw9PS0hYtWnT69OmD\nBw/OmzevTZs2PXr0sGw9fPjwxIkTL126JITw9/f/888/Fy1atHv37gsXLhw7duyDDz4oKCgY\nNGiQkkMBAGA3LVu2nDNnzvr1623/Tg4NDfX09LReuyCEKCgoOHHiRLdu3RxRY6NQ2xqOgoIC\nT0/POg9hMBjKy8vr7BYWFjZ9+vSEhISZM2caDIYuXbqMHj3autQ0Ly/v4sWLRqNRCKFSqWbM\nmLFx48atW7fm5OTodLrg4ODZs2eHhIQoORQAAPb02muvrV+/funSpdYWvV4/adKkDz74ICoq\n6vnnn8/JyZkyZYrZbG6oR4U0Rfa706gQIjIyMjIystpNsbGxsbGx1peenp5jxowZM2bMXzgU\nAAD2pFKpVq5cWel/pSlTpnh4eKxYseK9995zdXV9+OGHDx48qOS8gbOya+AAAKCps53JsAoL\nCysrK6vUOH78+PHjx9ulqCagjsDx7bffdunSpfY+6enpDVcPAABwQnUEjtzc3Dv5omEAANAg\nagscR44csVsdAADAidUWOO7kq3cAAEAD4vkFAABAOgIHAACQjstiAQBN0lPtvevuhEaDGQ4A\nACAdgQMAAEjHKRUAQJMUNvtgwx7wzPuPNewBYeuvzHCUlZUVFhY2eCkAAMBZKQ0cJpNp7dq1\nPXr0aNGihV6vnz9/vqV92rRpGRkZ0soDAADOQFHgKCsri42NHTVqVHJycmFhodlstrTn5OR8\n9NFH0dHR165dk1kkAABo2hQFjk8++WTPnj2xsbGpqan5+fnWdj8/v/Xr11+5cmX27NnSKgQA\nAE2eosCxYcOGzp07b9++PTIyUqPR2G4aNmxYnz59vvnmGznlAQAAZ6AocKSnp/fr10+rrf6S\nlq5du169erVBqwIAAE5F6aJRlUpV06aSkhK9Xt9A9QAA0Hh9/fXXKpVq7ty5ldqNRmNQUND9\n999fVlbmkMIaP0WBIyQkJDExsbS0tOqmvLy8pKSkkJCQhi4MAIBGp3///kOHDv3www/T0tJs\n26dPn56RkfHFF1+4uLg4qrZGTlHgGDlyZFpaWkxMzPHjx00mk6WxqKho7969ffr0+e2330aN\nGiWzSAAAGotFixZ5enq+/vrr1paTJ08uXLgwPj6+S5cuDiyskVMUON54443nn3/+wIEDDz74\noOXsyZw5c9zc3Pr27fvTTz8NHDhwzJgxkusEAKBR8Pf3X7Jkyf79+9etWyeEqKioGDNmzL33\n3vvhhx9aOqxatapr165eXl6+vr7PPffcxYsXrfueOXPm6aefbtmypV6vb9u27YQJE4qKihzz\nbdidosChVquTkpLWrVsXHR1tWTpaWlrq7u7eo0ePDRs2bNq0qdKlKwAAOLEXXnjh2WefjY+P\nv3HjxsKFC0+cOLF69WqDwSCEWLBgwZgxY7p3756amvrNN99kZWVFR0f/+eefQgiTydS3b9/i\n4uJdu3adP3/+008//eqrr95++21Hfzd2ovRZKiqVasSIESNGjBBC3Lp1S6VSeXh4yCwMAIDG\na9myZaGhoSNGjDh06NCbb7756KOPCiFKS0tnzpz55JNPfvzxx0KI//qv/0pMTGzXrt2yZctm\nzJhx9erV33//fcqUKV27dhVCBAUFdejQwXovTaen9JTKjz/+aH3p6elJ2gAA3Mnuuusuy10x\n/f3958yZY2k8d+5cfn7+008/be0WEBDQsWPHlJQUIcTdd9/drVu3SZMmTZgwYffu3QUFBaGh\noR07dnTMN2B3igLH8uXLH3nkkaCgoGnTpv3yyy+yawIAoPEbMmSIEOKpp56y/hF+8+ZNIcTb\nb79tsHH69OnMzEwhhFqt/u6776ZOnfrDDz/ExsY2a9YsLi7OsulOoChwLFq06NFHH7106dKs\nWbNCQkKioqI+/fRTnp8CAIAtX19fIcSMGTNO2Th37tyWLVssHdzd3SdNmpSampqVlbVixYpD\nhw4NGDDAoSXbj6LA8dZbbx06dOjq1auLFy+Ojo4+derUhAkT7r777t69e69bt+7WrVuyqwQA\noPELDQ319fX97bffgm2oVKrAwEAhREZGRkJCgqWnn5/fqFGjXn311ZMnT94hyziU3mlUCBEQ\nEPC3v/3t4MGDmZmZS5cujY6OPnDgwMiRI1u2bPnCCy/IKxEAgCbBxcVlypQpa9eunT179vnz\n5y9cuDBr1qzQ0NCtW7cKIW7cuDFixIjx48efOnXqt99+279//6ZNm3r27FnLvbydST0Ch1Wr\nVq3efPPN5OTkzMzMDz/8UKPRbNq0qcErAwCgyYmPj1++fPmmTZsiIiI6d+68a9eujRs3Wv4s\nj4qK+vrrr0+ePPn444+HhIS88sorvXv3ts55OD2ll8VWkpKSsmXLll27dp09e1YI4e/v36BV\nAQDQ2BkMhmrPhrzyyiuvvPJKtbv069evX79+kutqpOoROEwm048//rhly5atW7dmZGQIITw9\nPYcPHz5kyJDevXtLqxAAADR5igLHvn37tm7dum3btj/++EMIYTAYBgwYMGTIkNjYWMuN1QAA\nAGqhKHD06dNHCKHVamNiYoYMGfLss896enpKLgwAADgPRYGje/fuQ4YMiYuLa9asmeyCAACA\n81EUOJKTkyWXAQAAnFmNgWPDhg0eHh7PPvus5es6DzRs2LCGrAsAADiRGgPH8OHD27RpYwkc\nw4cPr/NABA4AgD2def8xR5eAeqgxcMTHx/v5+Vm/tlc9AADUjWsXmpwaA8fHH39c7dcAAAD1\npejW5nFxcXv27Klpa3x8fGxsbMOVBAAAnI2iwLFly5a0tLSatubm5v7www8NVxIAAHA2tV0W\nu2fPHuvERk2ZIzs7e/PmzR4eHlKqAwAATqG2wJGZmblu3bq8vDwhRHJyci1343j//fcbvDIA\nAOA0agscL7/88ujRo8+dOxcWFjZq1CjLDc4rMRgMISEhHTp0kFYhAABo8uq406hKperUqdOA\nAQMGDRrUt2/favuUlZUVFxfzFDcAAFATRYtGk5KSakobQoiFCxd26tSp4UoCAADORtGzVCx+\n+eWXs2fPFhcX2zbm5eWtWrXq2rVrDV0YAABwHooCR0lJybBhw5KSkmrq8NRTTzVcSQAAwNko\nChzz5s1LSkpq3rx5z549PT09V61a9eyzz3p5eR04cKC8vHz+/PkDBw6UXSgAAGi6FAWOf/7z\nn23btj19+rSXl9f169dXrVr12muv9e3bt6io6K233lq1atWAAQNkFwoAAJouRYtG09PTn3vu\nOS8vr0rtrq6uy5Yty8rK+uijjyTUBgAAnISiwCGEcHV1tXxhufy1oKDA8tLFxSUuLi4xMVFG\ncQAAwDkoChz33HNPcnKy2WwWQvj4+Oh0uhMnTli36vX6zMxMWQUCAICmT1Hg6N+//48//ti7\nd+8zZ84IIR555JEVK1akpKQIIW7cuJGQkNCqVSu5ZQIAgKZMUeCYOnVqly5d9u/ff+nSJSHE\na6+9lpub+8ADD9x1110BAQHnzp2Li4uTWyYAAGjKFF2l4ufnd+jQoS1btoSFhQkhXnjhhczM\nzLlz516/ft3Ly2vEiBEffvih5DoBAEATpvROowaD4cUXX7S+nDBhwoQJEwoKCngwPQAAqJPS\nq1SqRdoAAABK1DjDsWHDhnodaNiwYbddDAAAcE41Bo7hw4fX60AEDgAAUJMaA0d8fLw965DN\n19dXSTe1Wm02m613OfuPKzwOtxGpdjTVarXCUYYDVR0jlUqlUql0Op1D6oFCNX3ovL29lexu\nMpkauiI0PTUGjo8//tiedciWm5urpJubm5vJZCouLpZdD25HtaPp5+encJThQFXHSK/Xa7Xa\nwsJCh9QDhar9cPn4+OTn5ysJE3q93sXFRUJdaEr+yqLRsrIyfjsAAADllAYOk8m0du3aHj16\ntGjRQq/Xz58/39I+bdq0jIwMaeUBAABnoChwlJWVxcbGjho1Kjk5ubCw0PJQFSFETk7ORx99\nFB0dfe0aSxwAAECNFAWOTz75ZM+ePbGxsampqfn5+dZ2Pz+/9evXX7lyZfbs2dIqBAAATZ6i\nwLFhw4bOnTtv3749MjJSo9HYbho2bFifPn2++eYbOeUBAABnoChwpKen9+vXT6ut/pKWrl27\nXr16tUGrAgAATkXpolGVSlXTppKSEr1e30D1AAAAJ6QocISEhCQmJpaWllbdlJeXl5SUFBIS\n0tCFAQAA56EocIwcOTItLS0mJub48ePWe7wUFRXt3bu3T58+v/3226hRo2QWCQAAmjZFj6d/\n4403vv/++61btz744IOWlRxz5sz58MMPLVsHDhw4ZswYiTUCAIAmTtEMh1qtTkpKWrduXXR0\ntCVwlJaWuru79+jRY8OGDZs2bap06QoAAIAtRTMcQgiVSjVixIgRI0YIIW7duqVSqTw8PGQW\nBgAAnIfSwGHL09OzwesAAABOTOllsRUVFbVs3bZtW0MUAwAAnFMdgSMtLe2ZZ55xdXU1GAxh\nYWEbNmyo1OHatWsDBgx4/vnnpVUIAACavNpOqdy4cSM6Ovr69euWl2fPnh0+fHh2dvb48eOF\nEGazefXq1X//+9/z8vL8/f3tUSwAAGiaapvhWLBgwfXr12NiYtLS0goKCpKSkvz8/N59993r\n16+npaX17NlzzJgxN2/eHDNmzIULF+xWMQAAaHJqm+HYtWuXu7t7QkKCr6+vEGLAgAE3btwY\nO3bs6NGjk5OTi4qKIiIili9f/uCDD9qrWgAA0CTVNsPx22+/RUVFWdKGRUxMjBBi9+7dLi4u\nixYt+umnn0gbAACgTrXNcBiNxpYtW9q2BAYGCiEiIyP/9a9/tWrVSm5pAADAWdRxlYpara76\nMiQkhLQBAACUU3ofDgAAgL+MwAEAAKQjcAAAAOnqeJbKt99+26VLl0qNu3fvrtqYkpLSkHUB\nAAAnUkfgyM3NTU1NrdSYk5OTk5MjrSQAAOBsagscR44csVsdAADAidUWOLp162a3OgAAgBNj\n0SgAAJCOwAEAAKQjcAAAAOkIHAAAQDoCBwAAkI7AAQAApCNwAAAI9PRxAAAaxklEQVQA6Qgc\nAABAOgIHAACQjsABAACkI3AAAADpCBwAAEA6AgcAAJCOwAEAAKQjcAAAAOkIHAAAQDoCBwAA\nkI7AAQAApCNwAAAA6QgcAABAOgIHAACQjsABAACkI3AAAADpCBwAAEA6AgcAAJCOwAEAAKQj\ncAAAAOkIHAAAQDoCBwAAkI7AAQAApCNwAAAA6QgcAABAOq093+zYsWOJiYmXL1/W6XQRERGj\nR4/29/evqfPhw4d37NiRkZGh0+nat28/dOjQ9u3bWzYtW7Zsz549lfrPnz+/Q4cOEqsHAAB/\nlf0CR2pq6uzZs3v37v3SSy8VFBT885//nDp16uLFi3U6XdXOe/fu/eyzz3r16vXiiy8ajcaN\nGzdaOrdo0UIIYTQaAwIC3nzzTdtdAgMD7fSdAACAerJf4EhISOjQocO4ceMsL9u1azd27Nj9\n+/fHxMRU7ZyYmBgeHv7WW29ZXt5zzz1jx449cuTIM888I4QwGo2+vr5hYWF2Kx4AANwOO63h\nuHnzZlpa2iOPPGJtCQgIaNOmTUpKStXOZrN5zpw577zzjrWlZcuWQohbt25ZXhqNRldXV8kl\nAwCABmOnGY6rV68KIVq3bm3b2Lp1619//bVqZ5VKZUkYVseOHRNCdOzY0fLSaDQ2a9ZMVq0A\nAKCh2SlwFBYWCiHc3NxsG11dXS3ttcvMzPzss8+6desWERFhaTEajTk5ObNmzbpw4UJFRUW7\ndu0GDRoUHh5uu9fUqVOtC0t9fX337dunvFoPD4/KTVeuKt8dstW01riWNchoJGoaI+YsG7ma\nBs7Pz0/J7uXl5Q1aDpoku16lolKpanlZrfPnz8+aNSsoKCg+Pt52x+zs7Ojo6EGDBuXk5Ozc\nuXP69OkzZsywJhIhREBAQEhIiOVrT09PhT/uarVaCGEymZR0hqNUO5parZZfao1f1TFSqVQq\nlYoPXSNX7YdLo9FUVFQo2Z3xhbBb4HB3dxf/nuewKigoqGYuwUZycvKSJUseffTRv/3tb1rt\nf0r9xz/+YdstMjLy9ddf/+qrr2wDxxtvvPHGG29YX2ZlZSmp083NzWQyFRcXK+kMR8nLy6va\n6OfnV207GpWqY6TX67VarZLJTjhQtR8uHx+f/Px8JWFCr9dXe0Ei7ih2WjRquWb1ypUrto0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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 360
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NyYD4pPwlFYWEjPS9GTggCgV/Uaw2FpaRkTE0MHsatUqhMnTixYsKBr1642NjZ+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      "text/plain": [
       "plot without title"
      ]
     },
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   ],
   "source": [
    "#Predicted and True Class Distribution of ST segment slopes vs. presence of CVD.\n",
    "options(repr.plot.width = 6, repr.plot.height = 6)\n",
    "st_segment_slope_plot <- ggplot(cvd_test_predictions, aes(x = st_segment_slope, fill = as_factor(.pred_class))) +\n",
    "    geom_bar(position = \"fill\") + \n",
    "    labs(x = \"Slope of ECG\", y = \"Relative Distribution\", fill = \"CVD Present\") + theme(text = element_text(size = 13)) +\n",
    "    ggtitle(\"Figure 8: Predicted Distribution of ST Segment \\nSlopes with the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "st_segment_slope_plot\n",
    "\n",
    "st_segment_slope_plot <- ggplot(cvd_test_predictions, aes(x = st_segment_slope, fill = as_factor(presence_of_cvd))) +\n",
    "    geom_bar(position = \"fill\") + \n",
    "    labs(x = \"Slope of ECG\", y = \"Relative Distribution\", fill = \"CVD Present\") + theme(text = element_text(size = 13)) +\n",
    "    ggtitle(\"Figure 9: True Distribution of ST Segment \\nSlopes with the Presence of CVD\") +\n",
    "    scale_fill_brewer(palette = 'Paired')\n",
    "st_segment_slope_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2120fab9-be22-46f0-9a99-ac11f0449ca0",
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   "source": [
    "Comparing Figure 8 and Figure 9, we can see that our classifier is over predicting the presence of CVD in individuals with ST segment slopes >1 and under predicting the presence of CVD in individuals with ST segment slopes equal to 1. This could imply that our classifier is undefitting the data when it comes to using ST segment slope as a predictor."
   ]
  },
  {
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   "source": [
    "### Conclusion\n",
    "In our report, we began by tidying the data to our desired format. Then, we split our data into training and testing sets. To tune our classifier, we performed a 5-fold cross validation to determine the optimal value of k-neighbors. We set our K to 15, and then performed KNN classification on this recipe to yield a result of 82.1% accuracy (Table 4). To be more precise, we had 101 accurate predictions and 22 false predictions (Table 5). The classifier had falsely predicted 16 patients to be positive with CVD, while 6 patients were falsely predicted to be negative (Table 5). \n",
    "\n",
    "### Expectations\n",
    "We expected our classifier to have significantly higher accuracy than our majority classifier (>55%). The results above indicate that our classifier has a higher accuracy by 27%. Thus our expectations were met as we found our classifier to have significantly higher accuracy than our majority classifier. In building our classifier, we had expected it to have a higher accuracy than 82.1% as we were hoping that it could be a method to be used in a practical setting. This means it should have an accuracy of no less than that of legitimate diagnostic methods so an 82.1% accuracy would not suffice. In retrospect, we could have made some alternations to our classifiier that would have improved its accuracy. For example, altering the proportion of our training sets and trying to find the optimal proportion to split our data into training and testing. Additionally, we could have also included more predictors, which could have yielded results with higher accuracy. \n",
    "\n",
    "### Impact\n",
    "Our findings show a potential new way for doctors to initially diagnose CVDs using our classifier. Looking at our data in practical settings, a false negative prediction (falsely diagnosing a patient as healthy) would have far more negative consequences than a false positive prediction (falsely diagnosing a patient to have CVD). Looking at our findings, the probability of a false negative is around 7.6%, while a false positive is 36.6%. Although we had a lower probability of getting a false negative, it is still important to recognize that even one false negative prediction could result in serious consequences. Moreover, while our classifier does indicate a new method of diagnosing CVDs for medical facilities, based on its accuracy, it is still best to use the proper equipment and knowledge instead of our classifier.\n",
    "\n",
    "### Future Questions\n",
    "Based on our results from the classifier, this could lead to future questions, such as:\n",
    "- Could medical facilities that lack the proper equipment use the KNN classification method and other methods to diagnose patients with CVD? \n",
    "- Could including and testing more columns increase the chances of having a classifier with a higher accuracy? In other words,  is there a CVD condition that will yield a higher accuracy classifier than thalassemia, which we didn’t include in our chosen columns?"
   ]
  },
  {
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   "id": "b8f74662-d364-4a47-a11a-540a75aa7141",
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   "source": [
    "### Citations\n",
    "\n",
    "1. Simegn, G. L., Gebeyehu, W. B., &amp; Degu, M. Z. (2022). Computer-aided decision support system for diagnosis of heart diseases. Research Reports in Clinical Cardiology, Volume 13, 39–54. https://doi.org/10.2147/rrcc.s366380 \n",
    " \n",
    "2. Bots, S. H., Peters, S. A., &amp; Woodward, M. (2017). Sex differences in coronary heart disease and stroke mortality: A global assessment of the effect of ageing between 1980 and 2010. BMJ Global Health, 2(2). https://doi.org/10.1136/bmjgh-2017-000298 \n",
    "\n",
    "3. Mayo Foundation for Medical Education and Research. (2022, March 30). Angina. Mayo Clinic. Retrieved December 6, 2022, from https://www.mayoclinic.org/diseases-conditions/angina/symptoms-causes/syc-20369373 \n",
    "\n",
    "4. Electrocardiogram. Electrocardiogram | Johns Hopkins Medicine. (2021, August 8). Retrieved December 6, 2022, from https://www.hopkinsmedicine.org/health/treatment-tests-and-therapies/electrocardiogram "
   ]
  }
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