life-expectancy-final-report-1.ipynb

{
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    "tags": []
   },
   "source": [
    " \n",
    "# An Analysis Of The Impact Of Various Factors On Life Expectancy"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    " #  <font color='black'>1. Introduction</font>\n",
    " \n",
    "\n",
    "Life expectancy is an estimate of how long a person would live on average. Throughout the years, there have been lot of studies on factors affecting life expectancy. However, these studies have not taken into account the possibility that human development index could have a significant effect. Additionally, past studies were conducted using multiple linear regressions based on world data for only one year. Therefore, there is reason to consider global data from 2000 to 2015 instead. This project relies heavily on the accuracy of the data which is provided by the Global Health Observatory (GHO) data repository under World Health Organization (WHO)$^{(1)}$. Our goal is to determine the most significant variables to create an optimal linear regression model for predicting life expectancy. For instance, if current mortality rates in every age group remained constant throughout, then it would be an easily understood measure to which any person could directly relate $^{(2)}$. In reality, life expectancy is affected by a variety of socioeconomic, genetic and environmental factors. Therefore, it makes for a good area of study to investigate via statistical methods to better understand the measure of life expectancy.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "## 1.1 Loading necessary packages for the Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
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    "_uuid": "051d70d956493feee0c6d64651c6a088724dca2a",
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     "status": "completed"
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    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Updating HTML index of packages in '.Library'\n",
      "\n",
      "Making 'packages.html' ...\n",
      " done\n",
      "\n",
      "Updating HTML index of packages in '.Library'\n",
      "\n",
      "Making 'packages.html' ...\n",
      " done\n",
      "\n",
      "Updating HTML index of packages in '.Library'\n",
      "\n",
      "Making 'packages.html' ...\n",
      " done\n",
      "\n",
      "Updating HTML index of packages in '.Library'\n",
      "\n",
      "Making 'packages.html' ...\n",
      " done\n",
      "\n",
      "Updating HTML index of packages in '.Library'\n",
      "\n",
      "Making 'packages.html' ...\n",
      " done\n",
      "\n"
     ]
    }
   ],
   "source": [
    "install.packages(\"gganimate\")\n",
    "install.packages(\"corrr\")\n",
    "install.packages(\"plotly\")\n",
    "install.packages(\"tidygeocoder\")\n",
    "install.packages(\"elasticnet\")\n",
    "library(leaps)\n",
    "library(gganimate)\n",
    "library(tidyverse)\n",
    "library(tidymodels)\n",
    "library(corrr)\n",
    "library(mltools)\n",
    "library(ggplot2)\n",
    "library(elasticnet)\n",
    "library(plotly)\n",
    "library(caret)\n",
    "library(tidygeocoder)\n",
    "library(glmnet)\n",
    "library(GGally)\n",
    "options(repr.plot.width = 8, repr.plot.height = 8)\n",
    "library(knitr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Loading dataset from Github"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "data <- read.csv(\"https://raw.githubusercontent.com/zackhamza01/Life-Expectancy/main/Life%20Expectancy%20Data.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
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    "tags": []
   },
   "source": [
    "# 2. Methods and Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To begin with, we first performed some data cleaning and exploration. The exploration was very necessary for us to have a deeper understanding of the dataset before the process of gaining insights from it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1.1 Data Preview and Cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 1"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 22</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Country</th><th scope=col>Year</th><th scope=col>Status</th><th scope=col>Life.expectancy</th><th scope=col>Adult.Mortality</th><th scope=col>infant.deaths</th><th scope=col>Alcohol</th><th scope=col>percentage.expenditure</th><th scope=col>Hepatitis.B</th><th scope=col>Measles</th><th scope=col>⋯</th><th scope=col>Polio</th><th scope=col>Total.expenditure</th><th scope=col>Diphtheria</th><th scope=col>HIV.AIDS</th><th scope=col>GDP</th><th scope=col>Population</th><th scope=col>thinness..1.19.years</th><th scope=col>thinness.5.9.years</th><th scope=col>Income.composition.of.resources</th><th scope=col>Schooling</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>⋯</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Afghanistan</td><td>2015</td><td>Developing</td><td>65.0</td><td>263</td><td>62</td><td>0.01</td><td>71.27962</td><td>65</td><td>1154</td><td>⋯</td><td> 6</td><td>8.16</td><td>65</td><td>0.1</td><td>584.2592</td><td>33736494</td><td>17.2</td><td>17.3</td><td>0.479</td><td>10.1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Afghanistan</td><td>2014</td><td>Developing</td><td>59.9</td><td>271</td><td>64</td><td>0.01</td><td>73.52358</td><td>62</td><td> 492</td><td>⋯</td><td>58</td><td>8.18</td><td>62</td><td>0.1</td><td>612.6965</td><td>  327582</td><td>17.5</td><td>17.5</td><td>0.476</td><td>10.0</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>Afghanistan</td><td>2013</td><td>Developing</td><td>59.9</td><td>268</td><td>66</td><td>0.01</td><td>73.21924</td><td>64</td><td> 430</td><td>⋯</td><td>62</td><td>8.13</td><td>64</td><td>0.1</td><td>631.7450</td><td>31731688</td><td>17.7</td><td>17.7</td><td>0.470</td><td> 9.9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 22\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & Country & Year & Status & Life.expectancy & Adult.Mortality & infant.deaths & Alcohol & percentage.expenditure & Hepatitis.B & Measles & ⋯ & Polio & Total.expenditure & Diphtheria & HIV.AIDS & GDP & Population & thinness..1.19.years & thinness.5.9.years & Income.composition.of.resources & Schooling\\\\\n",
       "  & <chr> & <int> & <chr> & <dbl> & <int> & <int> & <dbl> & <dbl> & <int> & <int> & ⋯ & <int> & <dbl> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Afghanistan & 2015 & Developing & 65.0 & 263 & 62 & 0.01 & 71.27962 & 65 & 1154 & ⋯ &  6 & 8.16 & 65 & 0.1 & 584.2592 & 33736494 & 17.2 & 17.3 & 0.479 & 10.1\\\\\n",
       "\t2 & Afghanistan & 2014 & Developing & 59.9 & 271 & 64 & 0.01 & 73.52358 & 62 &  492 & ⋯ & 58 & 8.18 & 62 & 0.1 & 612.6965 &   327582 & 17.5 & 17.5 & 0.476 & 10.0\\\\\n",
       "\t3 & Afghanistan & 2013 & Developing & 59.9 & 268 & 66 & 0.01 & 73.21924 & 64 &  430 & ⋯ & 62 & 8.13 & 64 & 0.1 & 631.7450 & 31731688 & 17.7 & 17.7 & 0.470 &  9.9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 22\n",
       "\n",
       "| <!--/--> | Country &lt;chr&gt; | Year &lt;int&gt; | Status &lt;chr&gt; | Life.expectancy &lt;dbl&gt; | Adult.Mortality &lt;int&gt; | infant.deaths &lt;int&gt; | Alcohol &lt;dbl&gt; | percentage.expenditure &lt;dbl&gt; | Hepatitis.B &lt;int&gt; | Measles &lt;int&gt; | ⋯ ⋯ | Polio &lt;int&gt; | Total.expenditure &lt;dbl&gt; | Diphtheria &lt;int&gt; | HIV.AIDS &lt;dbl&gt; | GDP &lt;dbl&gt; | Population &lt;dbl&gt; | thinness..1.19.years &lt;dbl&gt; | thinness.5.9.years &lt;dbl&gt; | Income.composition.of.resources &lt;dbl&gt; | Schooling &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | Afghanistan | 2015 | Developing | 65.0 | 263 | 62 | 0.01 | 71.27962 | 65 | 1154 | ⋯ |  6 | 8.16 | 65 | 0.1 | 584.2592 | 33736494 | 17.2 | 17.3 | 0.479 | 10.1 |\n",
       "| 2 | Afghanistan | 2014 | Developing | 59.9 | 271 | 64 | 0.01 | 73.52358 | 62 |  492 | ⋯ | 58 | 8.18 | 62 | 0.1 | 612.6965 |   327582 | 17.5 | 17.5 | 0.476 | 10.0 |\n",
       "| 3 | Afghanistan | 2013 | Developing | 59.9 | 268 | 66 | 0.01 | 73.21924 | 64 |  430 | ⋯ | 62 | 8.13 | 64 | 0.1 | 631.7450 | 31731688 | 17.7 | 17.7 | 0.470 |  9.9 |\n",
       "\n"
      ],
      "text/plain": [
       "  Country     Year Status     Life.expectancy Adult.Mortality infant.deaths\n",
       "1 Afghanistan 2015 Developing 65.0            263             62           \n",
       "2 Afghanistan 2014 Developing 59.9            271             64           \n",
       "3 Afghanistan 2013 Developing 59.9            268             66           \n",
       "  Alcohol percentage.expenditure Hepatitis.B Measles ⋯ Polio Total.expenditure\n",
       "1 0.01    71.27962               65          1154    ⋯  6    8.16             \n",
       "2 0.01    73.52358               62           492    ⋯ 58    8.18             \n",
       "3 0.01    73.21924               64           430    ⋯ 62    8.13             \n",
       "  Diphtheria HIV.AIDS GDP      Population thinness..1.19.years\n",
       "1 65         0.1      584.2592 33736494   17.2                \n",
       "2 62         0.1      612.6965   327582   17.5                \n",
       "3 64         0.1      631.7450 31731688   17.7                \n",
       "  thinness.5.9.years Income.composition.of.resources Schooling\n",
       "1 17.3               0.479                           10.1     \n",
       "2 17.5               0.476                           10.0     \n",
       "3 17.7               0.470                            9.9     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Table 1\")\n",
    "data %>% head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset contains variables such as country, year, status, life expectancy, etc. The `Adult.Mortality` column represents the adult mortality rates of both genders, which is the probability of dying between 15 and 60 years per 1000 population. `Infant.deaths` showcases the number of infant deaths per 1000 population. The `Alcohol` column describes the total litres of consumption for pure alcohol, which is recorded per capita for ages 15 and older. The `Hepatitis.B`, `Polio`, and `Diphteria` variables demonstrate the percentage of immunization coverage among 1-year-olds for each of those diseases. The `Measles` column signifies the number of reported cases of the measles per 1000 population. thinness..1.19.years` represents the percentage of thinness present in children ranging from the age of 10 to 19 years old. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We looked at the range of life expectancy in the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Life expectancy ranges from 44 to 89. This means that the people in the country with the highest life expectancy lived almost twice as long as the ones in the country with the lowest life expectancy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataframe has 1649 rows and 20 attributes."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "### 2.1.2 Variable Correlation"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "#### Categorical Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  Comparison of mean life expectancy rate between developed and developing countries\n",
    "To get an understanding of how the development status of a country is correlated with life expectancy, we compared the mean life expectancy of developed and developing countries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 2"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 2 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Status</th><th scope=col>mean_expectancy</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Developed </td><td>79.19785</td></tr>\n",
       "\t<tr><td>Developing</td><td>67.11147</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 2 × 2\n",
       "\\begin{tabular}{ll}\n",
       " Status & mean\\_expectancy\\\\\n",
       " <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Developed  & 79.19785\\\\\n",
       "\t Developing & 67.11147\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 2 × 2\n",
       "\n",
       "| Status &lt;chr&gt; | mean_expectancy &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| Developed  | 79.19785 |\n",
       "| Developing | 67.11147 |\n",
       "\n"
      ],
      "text/plain": [
       "  Status     mean_expectancy\n",
       "1 Developed  79.19785       \n",
       "2 Developing 67.11147       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Table 2\")\n",
    "data %>%\n",
    "    filter(Life.expectancy>0)%>%\n",
    "    group_by(Status) %>%\n",
    "    summarize(mean_expectancy=mean(Life.expectancy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the table above, we saw that on average, people in developed countries lived almost a decade longer than people in developing countries."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    },
    "tags": []
   },
   "source": [
    "To better vizualize the correlation between the development status of a country and Life expectancy, we created a boxplot as shown below. "
   ]
  },
  {
   "cell_type": "code",
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 10 rows containing non-finite values (stat_boxplot).”\n",
      "Warning message:\n",
      "“Removed 10 rows containing non-finite values (stat_summary).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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547d66SG6yCCNDVlvQYeonZvXdlOnHihLKfo+o4d+6cPPlGp06dXn/9dWl5zpw5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\ntra23bp127lzZ9u2bZ8/f85NI9m3b195ebmOjs7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51FxGwgEAAACav4KCgkmTJrGX3lauXMllR24U71GxJwYAACAASURBVMSJEzXeGBwc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\nnGbPgZZKpVVVVUQkFot///336Ojo1NRUdsnc3HzgwIHu7u7Gx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n78+NKWwwcAqFjptqpkZGQYDAZrV4FKMV0HOj09nZ8O2Ij58+cfO3bM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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot showing life expectancy in different country status\n",
    "initial_plot <- data %>%\n",
    "    ggplot()+ \n",
    "    geom_boxplot(aes(Status, Life.expectancy, fill= Status)) +\n",
    "    ggtitle(\"Life Expectancy VS Development Status\") +\n",
    "    stat_summary(aes(x = Status, Life.expectancy),\n",
    "     fun = mean, colour = \"yellow\", geom = \"point\",\n",
    "     shape = 18, size = 5\n",
    "   )+\n",
    "    theme_grey(base_size = 22)+\n",
    "    labs(x=\"Status\", y=\"Life Expectancy\", caption = \"Figure 1\")\n",
    "initial_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.095925,
     "end_time": "2021-11-06T00:53:46.325587",
     "exception": false,
     "start_time": "2021-11-06T00:53:46.229662",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "As we can see here, there is a stark difference in the life expectancy in developing and developed countries. To begin with, the interquartile range of life expectancy is lower in developed than developing countries.The mean and median are both much higher in developed countries. The minimum life expectancy is also much lower in developing countries. Thus, we can see that the status of the country could affect life expectancy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.092586,
     "end_time": "2021-11-06T00:53:46.513153",
     "exception": false,
     "start_time": "2021-11-06T00:53:46.420567",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The next categorical variable is Country. To show this, we created a map depicting the average life expectancy in each country."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "papermill": {
     "duration": 0.145128,
     "end_time": "2021-11-06T00:53:46.750398",
     "exception": false,
     "start_time": "2021-11-06T00:53:46.60527",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 2"
     ]
    }
   ],
   "source": [
    "cat(\"Figure 2\")\n",
    "new_data <- data %>% na.omit()\n",
    "summary_data <- new_data %>% \n",
    "    group_by(Country) %>% \n",
    "    summarize(mean=mean(Life.expectancy))\n",
    "\n",
    "g <- list(\n",
    "showframe = TRUE,\n",
    "showcoastlines = TRUE,\n",
    "projection = list(type = 'Mercator')\n",
    ")\n",
    "\n",
    "plot <- plot_geo(summary_data, locationmode=\"country names\")%>%\n",
    "    add_trace(locations=~Country,\n",
    "             z=~mean,\n",
    "             color=~mean) %>%\n",
    "    layout(\n",
    "  title = with(summary_data, paste('Mean Life Expectancy')),\n",
    "  geo = g\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.092413,
     "end_time": "2021-11-06T00:53:46.935126",
     "exception": false,
     "start_time": "2021-11-06T00:53:46.842713",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Due to a bug in htmlwidgets, rendering the interractive plotly object in the code cell above fails to show in an html file. Therefore, we took a screenshot of the plot as shown below for a quick look. However, you can uncomment the plot object and hover over the countries to see the mean life expectancy in different countries.\n",
    "Here we see that sub-saharan african countries are amongst the lowest life expectancy regions while Canada, Europe and Australia amongst the highest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.091301,
     "end_time": "2021-11-06T00:53:47.119984",
     "exception": false,
     "start_time": "2021-11-06T00:53:47.028683",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<img src=\"https://github.com/Blaise143/test_repo/raw/main/Screen%20Shot%202021-11-01%20at%2011.53.44%20PM.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.110993,
     "end_time": "2021-11-06T00:53:47.322787",
     "exception": false,
     "start_time": "2021-11-06T00:53:47.211794",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "#### Continuous Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.092234,
     "end_time": "2021-11-06T00:53:47.528098",
     "exception": false,
     "start_time": "2021-11-06T00:53:47.435864",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "To demonstrate the correlation between continuous variables and life expectancy, we created a correlation map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "papermill": {
     "duration": 0.457035,
     "end_time": "2021-11-06T00:53:48.078331",
     "exception": false,
     "start_time": "2021-11-06T00:53:47.621296",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 3"
     ]
    },
    {
     "data": {
      "image/png": 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0tEOnTo4OTkNG7cuI0bN/bo0SMvL+/7778fPHjwCy+8oJzt8ccfnz59ulartbKr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\n7Z9F8IN/osVgA90bSR+DE7PqWPXZ5T8OPk0Ie/95z1Rr+75Nl9N6+bmw1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f4tidKqcd/l4GoK9f0tfzOj7gCwwHEKmUw6eyvs7xmOPfX1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\n0iNQFJVL+BVL3hciCGKMppjxMgFBkKuef1/15NuyfdeS+QCAsHSh6w7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G0pLibevdbYb0tzQ3njt1os/Z01SqeC0r+/x585rVIwf1H9C3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\n6gAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Removing non-numeric variables for analysis of multicollinearity\n",
    "cat(\"Figure 3\")\n",
    "data_num <- data %>% select(-Country, -Year, -Status)\n",
    "\n",
    "ggcorr(\n",
    "  data_num,\n",
    "  cor_matrix = cor(data_num, use = \"pairwise\"),\n",
    "    label = T, \n",
    "    hjust = 0.95,\n",
    "    angle = 0,\n",
    "    size = 4,\n",
    "    layout.exp = 3\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.097724,
     "end_time": "2021-11-06T00:53:48.272839",
     "exception": false,
     "start_time": "2021-11-06T00:53:48.175115",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "##### Observations\n",
    "- The variables that life expectancy is most positively related are: schooling, and income composition of resources. \n",
    "- The variables most negatively associated with life expectancy are: adult mortality and HIV/AIDS. \n",
    "- Life expectancy has a negligible relationship with Population, Total expenditure, under-five deaths and Measles.\n",
    "- From the above observations, we would expect to see schooling, income composition of resources, adult mortality, and HIV/AIDS to have the largest impact in our linear model while Population, Total expenditure, under-five deaths and Measles are expected to have a smaller impact in the linear model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-11-02T06:02:49.349672Z",
     "iopub.status.busy": "2021-11-02T06:02:49.347935Z",
     "iopub.status.idle": "2021-11-02T06:02:49.361728Z"
    },
    "papermill": {
     "duration": 0.102164,
     "end_time": "2021-11-06T00:53:48.472493",
     "exception": false,
     "start_time": "2021-11-06T00:53:48.370329",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 2.2 Variable Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 Preparing the data\n",
    "Our first step is to ensure all of our variables can be used in the regression and then splitting the dataset into testing and training sets. For this study, we will be using a proportion of 0.75. We will not be using the Country and Year categories in this model as our aim is to predict the life expectancy based on factors that are more general and not specific to a place or time. Furthermore, the Country variable has over 150 levels, which will make our model extremely large. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 3"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 2 × 20</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Status</th><th scope=col>Life.expectancy</th><th scope=col>Adult.Mortality</th><th scope=col>infant.deaths</th><th scope=col>Alcohol</th><th scope=col>percentage.expenditure</th><th scope=col>Hepatitis.B</th><th scope=col>Measles</th><th scope=col>BMI</th><th scope=col>under.five.deaths</th><th scope=col>Polio</th><th scope=col>Total.expenditure</th><th scope=col>Diphtheria</th><th scope=col>HIV.AIDS</th><th scope=col>GDP</th><th scope=col>Population</th><th scope=col>thinness..1.19.years</th><th scope=col>thinness.5.9.years</th><th scope=col>Income.composition.of.resources</th><th scope=col>Schooling</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>676</th><td>1</td><td>81.0</td><td> 54</td><td>0</td><td>9.04</td><td>212.08593</td><td>96</td><td>0</td><td>59.2</td><td> 0</td><td>99</td><td>7.46</td><td>99</td><td>0.1</td><td>2797.967</td><td>1143896</td><td>0.9</td><td>1.0</td><td>0.850</td><td>13.8</td></tr>\n",
       "\t<tr><th scope=row>799</th><td>0</td><td>74.4</td><td>151</td><td>8</td><td>3.69</td><td> 18.26183</td><td>82</td><td>0</td><td>45.8</td><td>10</td><td>97</td><td>6.46</td><td>87</td><td>0.3</td><td> 244.469</td><td>1328961</td><td>1.5</td><td>1.4</td><td>0.679</td><td>12.6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 20\n",
       "\\begin{tabular}{r|llllllllllllllllllll}\n",
       "  & Status & Life.expectancy & Adult.Mortality & infant.deaths & Alcohol & percentage.expenditure & Hepatitis.B & Measles & BMI & under.five.deaths & Polio & Total.expenditure & Diphtheria & HIV.AIDS & GDP & Population & thinness..1.19.years & thinness.5.9.years & Income.composition.of.resources & Schooling\\\\\n",
       "  & <fct> & <dbl> & <int> & <int> & <dbl> & <dbl> & <int> & <int> & <dbl> & <int> & <int> & <dbl> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t676 & 1 & 81.0 &  54 & 0 & 9.04 & 212.08593 & 96 & 0 & 59.2 &  0 & 99 & 7.46 & 99 & 0.1 & 2797.967 & 1143896 & 0.9 & 1.0 & 0.850 & 13.8\\\\\n",
       "\t799 & 0 & 74.4 & 151 & 8 & 3.69 &  18.26183 & 82 & 0 & 45.8 & 10 & 97 & 6.46 & 87 & 0.3 &  244.469 & 1328961 & 1.5 & 1.4 & 0.679 & 12.6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 20\n",
       "\n",
       "| <!--/--> | Status &lt;fct&gt; | Life.expectancy &lt;dbl&gt; | Adult.Mortality &lt;int&gt; | infant.deaths &lt;int&gt; | Alcohol &lt;dbl&gt; | percentage.expenditure &lt;dbl&gt; | Hepatitis.B &lt;int&gt; | Measles &lt;int&gt; | BMI &lt;dbl&gt; | under.five.deaths &lt;int&gt; | Polio &lt;int&gt; | Total.expenditure &lt;dbl&gt; | Diphtheria &lt;int&gt; | HIV.AIDS &lt;dbl&gt; | GDP &lt;dbl&gt; | Population &lt;dbl&gt; | thinness..1.19.years &lt;dbl&gt; | thinness.5.9.years &lt;dbl&gt; | Income.composition.of.resources &lt;dbl&gt; | Schooling &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 676 | 1 | 81.0 |  54 | 0 | 9.04 | 212.08593 | 96 | 0 | 59.2 |  0 | 99 | 7.46 | 99 | 0.1 | 2797.967 | 1143896 | 0.9 | 1.0 | 0.850 | 13.8 |\n",
       "| 799 | 0 | 74.4 | 151 | 8 | 3.69 |  18.26183 | 82 | 0 | 45.8 | 10 | 97 | 6.46 | 87 | 0.3 |  244.469 | 1328961 | 1.5 | 1.4 | 0.679 | 12.6 |\n",
       "\n"
      ],
      "text/plain": [
       "    Status Life.expectancy Adult.Mortality infant.deaths Alcohol\n",
       "676 1      81.0             54             0             9.04   \n",
       "799 0      74.4            151             8             3.69   \n",
       "    percentage.expenditure Hepatitis.B Measles BMI  under.five.deaths Polio\n",
       "676 212.08593              96          0       59.2  0                99   \n",
       "799  18.26183              82          0       45.8 10                97   \n",
       "    Total.expenditure Diphtheria HIV.AIDS GDP      Population\n",
       "676 7.46              99         0.1      2797.967 1143896   \n",
       "799 6.46              87         0.3       244.469 1328961   \n",
       "    thinness..1.19.years thinness.5.9.years Income.composition.of.resources\n",
       "676 0.9                  1.0                0.850                          \n",
       "799 1.5                  1.4                0.679                          \n",
       "    Schooling\n",
       "676 13.8     \n",
       "799 12.6     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 4"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 2 × 20</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Status</th><th scope=col>Life.expectancy</th><th scope=col>Adult.Mortality</th><th scope=col>infant.deaths</th><th scope=col>Alcohol</th><th scope=col>percentage.expenditure</th><th scope=col>Hepatitis.B</th><th scope=col>Measles</th><th scope=col>BMI</th><th scope=col>under.five.deaths</th><th scope=col>Polio</th><th scope=col>Total.expenditure</th><th scope=col>Diphtheria</th><th scope=col>HIV.AIDS</th><th scope=col>GDP</th><th scope=col>Population</th><th scope=col>thinness..1.19.years</th><th scope=col>thinness.5.9.years</th><th scope=col>Income.composition.of.resources</th><th scope=col>Schooling</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3</th><td>0</td><td>59.9</td><td>268</td><td>66</td><td>0.01</td><td>73.21924</td><td>64</td><td> 430</td><td>18.1</td><td> 89</td><td>62</td><td>8.13</td><td>64</td><td>0.1</td><td>631.7450</td><td>31731688</td><td>17.7</td><td>17.7</td><td>0.470</td><td>9.9</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>0</td><td>58.6</td><td>281</td><td>77</td><td>0.01</td><td>56.76222</td><td>63</td><td>2861</td><td>16.2</td><td>106</td><td>63</td><td>9.42</td><td>63</td><td>0.1</td><td>445.8933</td><td>  284331</td><td>18.6</td><td>18.7</td><td>0.434</td><td>8.9</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 20\n",
       "\\begin{tabular}{r|llllllllllllllllllll}\n",
       "  & Status & Life.expectancy & Adult.Mortality & infant.deaths & Alcohol & percentage.expenditure & Hepatitis.B & Measles & BMI & under.five.deaths & Polio & Total.expenditure & Diphtheria & HIV.AIDS & GDP & Population & thinness..1.19.years & thinness.5.9.years & Income.composition.of.resources & Schooling\\\\\n",
       "  & <fct> & <dbl> & <int> & <int> & <dbl> & <dbl> & <int> & <int> & <dbl> & <int> & <int> & <dbl> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t3 & 0 & 59.9 & 268 & 66 & 0.01 & 73.21924 & 64 &  430 & 18.1 &  89 & 62 & 8.13 & 64 & 0.1 & 631.7450 & 31731688 & 17.7 & 17.7 & 0.470 & 9.9\\\\\n",
       "\t7 & 0 & 58.6 & 281 & 77 & 0.01 & 56.76222 & 63 & 2861 & 16.2 & 106 & 63 & 9.42 & 63 & 0.1 & 445.8933 &   284331 & 18.6 & 18.7 & 0.434 & 8.9\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 20\n",
       "\n",
       "| <!--/--> | Status &lt;fct&gt; | Life.expectancy &lt;dbl&gt; | Adult.Mortality &lt;int&gt; | infant.deaths &lt;int&gt; | Alcohol &lt;dbl&gt; | percentage.expenditure &lt;dbl&gt; | Hepatitis.B &lt;int&gt; | Measles &lt;int&gt; | BMI &lt;dbl&gt; | under.five.deaths &lt;int&gt; | Polio &lt;int&gt; | Total.expenditure &lt;dbl&gt; | Diphtheria &lt;int&gt; | HIV.AIDS &lt;dbl&gt; | GDP &lt;dbl&gt; | Population &lt;dbl&gt; | thinness..1.19.years &lt;dbl&gt; | thinness.5.9.years &lt;dbl&gt; | Income.composition.of.resources &lt;dbl&gt; | Schooling &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 3 | 0 | 59.9 | 268 | 66 | 0.01 | 73.21924 | 64 |  430 | 18.1 |  89 | 62 | 8.13 | 64 | 0.1 | 631.7450 | 31731688 | 17.7 | 17.7 | 0.470 | 9.9 |\n",
       "| 7 | 0 | 58.6 | 281 | 77 | 0.01 | 56.76222 | 63 | 2861 | 16.2 | 106 | 63 | 9.42 | 63 | 0.1 | 445.8933 |   284331 | 18.6 | 18.7 | 0.434 | 8.9 |\n",
       "\n"
      ],
      "text/plain": [
       "  Status Life.expectancy Adult.Mortality infant.deaths Alcohol\n",
       "3 0      59.9            268             66            0.01   \n",
       "7 0      58.6            281             77            0.01   \n",
       "  percentage.expenditure Hepatitis.B Measles BMI  under.five.deaths Polio\n",
       "3 73.21924               64           430    18.1  89               62   \n",
       "7 56.76222               63          2861    16.2 106               63   \n",
       "  Total.expenditure Diphtheria HIV.AIDS GDP      Population\n",
       "3 8.13              64         0.1      631.7450 31731688  \n",
       "7 9.42              63         0.1      445.8933   284331  \n",
       "  thinness..1.19.years thinness.5.9.years Income.composition.of.resources\n",
       "3 17.7                 17.7               0.470                          \n",
       "7 18.6                 18.7               0.434                          \n",
       "  Schooling\n",
       "3 9.9      \n",
       "7 8.9      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Making status a factor to be used in regression\n",
    "data <- data %>% \n",
    "    select(-Country) %>%\n",
    "    select(-Year) %>%\n",
    "    mutate(Status = if_else(Status == \"Developing\", 0, 1)) %>%\n",
    "    na.omit()\n",
    "data$Status <- as.factor(data$Status)\n",
    "\n",
    "#splitting data into testing and training sets\n",
    "set.seed(123)\n",
    "initial_split <- initial_split(data, prop = 0.75)\n",
    "expectancy_train <- training(initial_split)\n",
    "expectancy_test <- testing(initial_split)\n",
    "\n",
    "cat(\"Table 3\")\n",
    "expectancy_train %>% head(2)\n",
    "cat(\"Table 4\")\n",
    "expectancy_test %>% head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.2 Backward Selection\n",
    "We will now be performing variable selection using regsubsets. Our nvmax is 19 as there are 19 remaining variables in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 5"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>RSQ</th><th scope=col>RSS</th><th scope=col>ADJ.R2</th><th scope=col>BIC</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0.5177821</td><td>46475.58</td><td>0.5173913</td><td> -887.2486</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>0.7279422</td><td>26220.60</td><td>0.7275009</td><td>-1587.5926</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>0.7898490</td><td>20254.10</td><td>0.7893372</td><td>-1899.5934</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>0.8105975</td><td>18254.38</td><td>0.8099821</td><td>-2020.9589</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0.8145800</td><td>17870.55</td><td>0.8138263</td><td>-2040.1052</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0.8249509</td><td>16871.02</td><td>0.8240963</td><td>-2104.1260</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & RSQ & RSS & ADJ.R2 & BIC\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 0.5177821 & 46475.58 & 0.5173913 &  -887.2486\\\\\n",
       "\t2 & 0.7279422 & 26220.60 & 0.7275009 & -1587.5926\\\\\n",
       "\t3 & 0.7898490 & 20254.10 & 0.7893372 & -1899.5934\\\\\n",
       "\t4 & 0.8105975 & 18254.38 & 0.8099821 & -2020.9589\\\\\n",
       "\t5 & 0.8145800 & 17870.55 & 0.8138263 & -2040.1052\\\\\n",
       "\t6 & 0.8249509 & 16871.02 & 0.8240963 & -2104.1260\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 4\n",
       "\n",
       "| <!--/--> | RSQ &lt;dbl&gt; | RSS &lt;dbl&gt; | ADJ.R2 &lt;dbl&gt; | BIC &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | 0.5177821 | 46475.58 | 0.5173913 |  -887.2486 |\n",
       "| 2 | 0.7279422 | 26220.60 | 0.7275009 | -1587.5926 |\n",
       "| 3 | 0.7898490 | 20254.10 | 0.7893372 | -1899.5934 |\n",
       "| 4 | 0.8105975 | 18254.38 | 0.8099821 | -2020.9589 |\n",
       "| 5 | 0.8145800 | 17870.55 | 0.8138263 | -2040.1052 |\n",
       "| 6 | 0.8249509 | 16871.02 | 0.8240963 | -2104.1260 |\n",
       "\n"
      ],
      "text/plain": [
       "  RSQ       RSS      ADJ.R2    BIC       \n",
       "1 0.5177821 46475.58 0.5173913  -887.2486\n",
       "2 0.7279422 26220.60 0.7275009 -1587.5926\n",
       "3 0.7898490 20254.10 0.7893372 -1899.5934\n",
       "4 0.8105975 18254.38 0.8099821 -2020.9589\n",
       "5 0.8145800 17870.55 0.8138263 -2040.1052\n",
       "6 0.8249509 16871.02 0.8240963 -2104.1260"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Variable selection \n",
    "cat(\"Table 5\")\n",
    "backward_sel <- regsubsets(x=Life.expectancy ~.,data= expectancy_train, nvmax=19, method=\"backward\")\n",
    "\n",
    "#backward_sel\n",
    "back_summary <- summary(backward_sel)\n",
    "\n",
    "back_summary_df <- data.frame( \n",
    "   RSQ = back_summary$rsq,\n",
    "   RSS = back_summary$rss,\n",
    "   ADJ.R2 = back_summary$adjr2,\n",
    "   BIC = back_summary$bic\n",
    ")\n",
    "back_summary_df %>% head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best number of predictors to be selected is  12\n",
      "Table 6"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 19 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>n_input_variables</th><th scope=col>C_p</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>2404.139354</td></tr>\n",
       "\t<tr><td> 2</td><td> 821.437844</td></tr>\n",
       "\t<tr><td> 3</td><td> 356.633125</td></tr>\n",
       "\t<tr><td> 4</td><td> 202.179469</td></tr>\n",
       "\t<tr><td> 5</td><td> 174.149690</td></tr>\n",
       "\t<tr><td> 6</td><td>  97.948598</td></tr>\n",
       "\t<tr><td> 7</td><td>  50.986642</td></tr>\n",
       "\t<tr><td> 8</td><td>  19.934640</td></tr>\n",
       "\t<tr><td> 9</td><td>  13.454595</td></tr>\n",
       "\t<tr><td>10</td><td>  11.985773</td></tr>\n",
       "\t<tr><td>11</td><td>  11.468809</td></tr>\n",
       "\t<tr><td>12</td><td>   9.988715</td></tr>\n",
       "\t<tr><td>13</td><td>  10.121462</td></tr>\n",
       "\t<tr><td>14</td><td>  11.148805</td></tr>\n",
       "\t<tr><td>15</td><td>  12.691486</td></tr>\n",
       "\t<tr><td>16</td><td>  14.287013</td></tr>\n",
       "\t<tr><td>17</td><td>  16.079369</td></tr>\n",
       "\t<tr><td>18</td><td>  18.017771</td></tr>\n",
       "\t<tr><td>19</td><td>  20.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 19 × 2\n",
       "\\begin{tabular}{ll}\n",
       " n\\_input\\_variables & C\\_p\\\\\n",
       " <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t  1 & 2404.139354\\\\\n",
       "\t  2 &  821.437844\\\\\n",
       "\t  3 &  356.633125\\\\\n",
       "\t  4 &  202.179469\\\\\n",
       "\t  5 &  174.149690\\\\\n",
       "\t  6 &   97.948598\\\\\n",
       "\t  7 &   50.986642\\\\\n",
       "\t  8 &   19.934640\\\\\n",
       "\t  9 &   13.454595\\\\\n",
       "\t 10 &   11.985773\\\\\n",
       "\t 11 &   11.468809\\\\\n",
       "\t 12 &    9.988715\\\\\n",
       "\t 13 &   10.121462\\\\\n",
       "\t 14 &   11.148805\\\\\n",
       "\t 15 &   12.691486\\\\\n",
       "\t 16 &   14.287013\\\\\n",
       "\t 17 &   16.079369\\\\\n",
       "\t 18 &   18.017771\\\\\n",
       "\t 19 &   20.000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 19 × 2\n",
       "\n",
       "| n_input_variables &lt;int&gt; | C_p &lt;dbl&gt; |\n",
       "|---|---|\n",
       "|  1 | 2404.139354 |\n",
       "|  2 |  821.437844 |\n",
       "|  3 |  356.633125 |\n",
       "|  4 |  202.179469 |\n",
       "|  5 |  174.149690 |\n",
       "|  6 |   97.948598 |\n",
       "|  7 |   50.986642 |\n",
       "|  8 |   19.934640 |\n",
       "|  9 |   13.454595 |\n",
       "| 10 |   11.985773 |\n",
       "| 11 |   11.468809 |\n",
       "| 12 |    9.988715 |\n",
       "| 13 |   10.121462 |\n",
       "| 14 |   11.148805 |\n",
       "| 15 |   12.691486 |\n",
       "| 16 |   14.287013 |\n",
       "| 17 |   16.079369 |\n",
       "| 18 |   18.017771 |\n",
       "| 19 |   20.000000 |\n",
       "\n"
      ],
      "text/plain": [
       "   n_input_variables C_p        \n",
       "1   1                2404.139354\n",
       "2   2                 821.437844\n",
       "3   3                 356.633125\n",
       "4   4                 202.179469\n",
       "5   5                 174.149690\n",
       "6   6                  97.948598\n",
       "7   7                  50.986642\n",
       "8   8                  19.934640\n",
       "9   9                  13.454595\n",
       "10 10                  11.985773\n",
       "11 11                  11.468809\n",
       "12 12                   9.988715\n",
       "13 13                  10.121462\n",
       "14 14                  11.148805\n",
       "15 15                  12.691486\n",
       "16 16                  14.287013\n",
       "17 17                  16.079369\n",
       "18 18                  18.017771\n",
       "19 19                  20.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Using Mallow's C_P to find the right number of inputs\n",
    "backward_sel_candidate_models <- tibble(\n",
    "  n_input_variables = rep(1:19),\n",
    "  C_p =back_summary$cp\n",
    ")\n",
    "cat(\"The best number of predictors to be selected is \", backward_sel_candidate_models %>% filter(C_p==min(C_p)) %>% pull(n_input_variables))\n",
    "cat(\"\\nTable 6\")\n",
    "backward_sel_candidate_models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 4"
     ]
    },
    {
     "data": {
      "image/png": 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cLGjRsrKiqiGFZs9EADAEAeBGgAAMiDAA0AAHkQoAEAIA8CNAAA5EGABgCAPAjQ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\ngg==",
      "text/plain": [
       "Plot with title “Cp for Backward Method using a Training Set”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Figure 4\")\n",
    "plot(back_summary$cp,\n",
    "    main = \"Cp for Backward Method using a Training Set\",\n",
    "  xlab = \"Number of Input Variables\", ylab = \"Cp\", type = \"b\", pch = 19,\n",
    "  col = \"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of our backward selection tell us that the model with 12 variables is the best model, as it has the lowest $C_p$ of 9.988715. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Subset selection object\n",
       "Call: regsubsets.formula(x = Life.expectancy ~ ., data = expectancy_train, \n",
       "    nvmax = 19, method = \"backward\")\n",
       "19 Variables  (and intercept)\n",
       "                                Forced in Forced out\n",
       "Status1                             FALSE      FALSE\n",
       "Adult.Mortality                     FALSE      FALSE\n",
       "infant.deaths                       FALSE      FALSE\n",
       "Alcohol                             FALSE      FALSE\n",
       "percentage.expenditure              FALSE      FALSE\n",
       "Hepatitis.B                         FALSE      FALSE\n",
       "Measles                             FALSE      FALSE\n",
       "BMI                                 FALSE      FALSE\n",
       "under.five.deaths                   FALSE      FALSE\n",
       "Polio                               FALSE      FALSE\n",
       "Total.expenditure                   FALSE      FALSE\n",
       "Diphtheria                          FALSE      FALSE\n",
       "HIV.AIDS                            FALSE      FALSE\n",
       "GDP                                 FALSE      FALSE\n",
       "Population                          FALSE      FALSE\n",
       "thinness..1.19.years                FALSE      FALSE\n",
       "thinness.5.9.years                  FALSE      FALSE\n",
       "Income.composition.of.resources     FALSE      FALSE\n",
       "Schooling                           FALSE      FALSE\n",
       "1 subsets of each size up to 19\n",
       "Selection Algorithm: backward\n",
       "          Status1 Adult.Mortality infant.deaths Alcohol percentage.expenditure\n",
       "1  ( 1 )  \" \"     \" \"             \" \"           \" \"     \" \"                   \n",
       "2  ( 1 )  \" \"     \" \"             \" \"           \" \"     \" \"                   \n",
       "3  ( 1 )  \" \"     \"*\"             \" \"           \" \"     \" \"                   \n",
       "4  ( 1 )  \" \"     \"*\"             \" \"           \" \"     \" \"                   \n",
       "5  ( 1 )  \" \"     \"*\"             \" \"           \" \"     \" \"                   \n",
       "6  ( 1 )  \" \"     \"*\"             \"*\"           \" \"     \" \"                   \n",
       "7  ( 1 )  \" \"     \"*\"             \"*\"           \" \"     \"*\"                   \n",
       "8  ( 1 )  \" \"     \"*\"             \"*\"           \" \"     \"*\"                   \n",
       "9  ( 1 )  \" \"     \"*\"             \"*\"           \" \"     \"*\"                   \n",
       "10  ( 1 ) \" \"     \"*\"             \"*\"           \" \"     \"*\"                   \n",
       "11  ( 1 ) \" \"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "12  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "13  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "14  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "15  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "16  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "17  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "18  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "19  ( 1 ) \"*\"     \"*\"             \"*\"           \"*\"     \"*\"                   \n",
       "          Hepatitis.B Measles BMI under.five.deaths Polio Total.expenditure\n",
       "1  ( 1 )  \" \"         \" \"     \" \" \" \"               \" \"   \" \"              \n",
       "2  ( 1 )  \" \"         \" \"     \" \" \" \"               \" \"   \" \"              \n",
       "3  ( 1 )  \" \"         \" \"     \" \" \" \"               \" \"   \" \"              \n",
       "4  ( 1 )  \" \"         \" \"     \" \" \" \"               \" \"   \" \"              \n",
       "5  ( 1 )  \" \"         \" \"     \" \" \"*\"               \" \"   \" \"              \n",
       "6  ( 1 )  \" \"         \" \"     \" \" \"*\"               \" \"   \" \"              \n",
       "7  ( 1 )  \" \"         \" \"     \" \" \"*\"               \" \"   \" \"              \n",
       "8  ( 1 )  \" \"         \" \"     \"*\" \"*\"               \" \"   \" \"              \n",
       "9  ( 1 )  \" \"         \" \"     \"*\" \"*\"               \"*\"   \" \"              \n",
       "10  ( 1 ) \" \"         \" \"     \"*\" \"*\"               \"*\"   \" \"              \n",
       "11  ( 1 ) \" \"         \" \"     \"*\" \"*\"               \"*\"   \" \"              \n",
       "12  ( 1 ) \" \"         \" \"     \"*\" \"*\"               \"*\"   \" \"              \n",
       "13  ( 1 ) \" \"         \" \"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "14  ( 1 ) \" \"         \" \"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "15  ( 1 ) \" \"         \"*\"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "16  ( 1 ) \"*\"         \"*\"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "17  ( 1 ) \"*\"         \"*\"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "18  ( 1 ) \"*\"         \"*\"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "19  ( 1 ) \"*\"         \"*\"     \"*\" \"*\"               \"*\"   \"*\"              \n",
       "          Diphtheria HIV.AIDS GDP Population thinness..1.19.years\n",
       "1  ( 1 )  \" \"        \" \"      \" \" \" \"        \" \"                 \n",
       "2  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "3  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "4  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "5  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "6  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "7  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "8  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "9  ( 1 )  \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "10  ( 1 ) \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "11  ( 1 ) \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "12  ( 1 ) \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "13  ( 1 ) \" \"        \"*\"      \" \" \" \"        \" \"                 \n",
       "14  ( 1 ) \"*\"        \"*\"      \" \" \" \"        \" \"                 \n",
       "15  ( 1 ) \"*\"        \"*\"      \" \" \" \"        \" \"                 \n",
       "16  ( 1 ) \"*\"        \"*\"      \" \" \" \"        \" \"                 \n",
       "17  ( 1 ) \"*\"        \"*\"      \"*\" \" \"        \" \"                 \n",
       "18  ( 1 ) \"*\"        \"*\"      \"*\" \"*\"        \" \"                 \n",
       "19  ( 1 ) \"*\"        \"*\"      \"*\" \"*\"        \"*\"                 \n",
       "          thinness.5.9.years Income.composition.of.resources Schooling\n",
       "1  ( 1 )  \" \"                \" \"                             \"*\"      \n",
       "2  ( 1 )  \" \"                \" \"                             \"*\"      \n",
       "3  ( 1 )  \" \"                \" \"                             \"*\"      \n",
       "4  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "5  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "6  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "7  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "8  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "9  ( 1 )  \" \"                \"*\"                             \"*\"      \n",
       "10  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "11  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "12  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "13  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "14  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "15  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "16  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "17  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "18  ( 1 ) \"*\"                \"*\"                             \"*\"      \n",
       "19  ( 1 ) \"*\"                \"*\"                             \"*\"      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "back_summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 12 variables include: `Status`, `Adult.Mortality`, `infant.deaths`, `percentage.expenditure`, `BMI`, `under.five.deaths`, `Diphtheria`, `HIV.AIDS`, `thinness.5.9.years`, `Income.composition.of.resources`, `Schooling` and `Alcohol`. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Observations\n",
    "- Polio and Hepatitis B are not included in this model while Diphtheria is. This suggests that Diphtheria affects life expectancy more than the other two diseases, which could be due to the fact that Diphtheria is more fatal in children (fatality rate is 5-10%, while Polio's is 2-5% and Hepatitis B' s is around 0.42 per 100000 population). \n",
    "- Thinness 5-9 years is selected, but not thinness 10-19 years. This could be due to the fact that thinness and malnutrition during childhood may lead to people dying earlier, and so it has a larger impact on life expectancy and was thus included in the model. \n",
    "- While Status and percentage expenditure both impact life expectancy, GDP and total expenditure do not. This makes sense as GDP and total expenditure are both absolute measures, and do not consider population of a country, while percentage expenditure takes into account the differences between population and cost of living in different areas. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.3 Forward Selection\n",
    "Using the same methods, we will now be performing forward selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 7"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>RSQ</th><th scope=col>RSS</th><th scope=col>ADJ.R2</th><th scope=col>BIC</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0.5177821</td><td>46475.58</td><td>0.5173913</td><td> -887.2486</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>0.7279422</td><td>26220.60</td><td>0.7275009</td><td>-1587.5926</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>0.7898490</td><td>20254.10</td><td>0.7893372</td><td>-1899.5934</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>0.8105975</td><td>18254.38</td><td>0.8099821</td><td>-2020.9589</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>0.8161367</td><td>17720.52</td><td>0.8153893</td><td>-2050.5256</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>0.8216015</td><td>17193.83</td><td>0.8207306</td><td>-2080.6997</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & RSQ & RSS & ADJ.R2 & BIC\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 0.5177821 & 46475.58 & 0.5173913 &  -887.2486\\\\\n",
       "\t2 & 0.7279422 & 26220.60 & 0.7275009 & -1587.5926\\\\\n",
       "\t3 & 0.7898490 & 20254.10 & 0.7893372 & -1899.5934\\\\\n",
       "\t4 & 0.8105975 & 18254.38 & 0.8099821 & -2020.9589\\\\\n",
       "\t5 & 0.8161367 & 17720.52 & 0.8153893 & -2050.5256\\\\\n",
       "\t6 & 0.8216015 & 17193.83 & 0.8207306 & -2080.6997\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 4\n",
       "\n",
       "| <!--/--> | RSQ &lt;dbl&gt; | RSS &lt;dbl&gt; | ADJ.R2 &lt;dbl&gt; | BIC &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | 0.5177821 | 46475.58 | 0.5173913 |  -887.2486 |\n",
       "| 2 | 0.7279422 | 26220.60 | 0.7275009 | -1587.5926 |\n",
       "| 3 | 0.7898490 | 20254.10 | 0.7893372 | -1899.5934 |\n",
       "| 4 | 0.8105975 | 18254.38 | 0.8099821 | -2020.9589 |\n",
       "| 5 | 0.8161367 | 17720.52 | 0.8153893 | -2050.5256 |\n",
       "| 6 | 0.8216015 | 17193.83 | 0.8207306 | -2080.6997 |\n",
       "\n"
      ],
      "text/plain": [
       "  RSQ       RSS      ADJ.R2    BIC       \n",
       "1 0.5177821 46475.58 0.5173913  -887.2486\n",
       "2 0.7279422 26220.60 0.7275009 -1587.5926\n",
       "3 0.7898490 20254.10 0.7893372 -1899.5934\n",
       "4 0.8105975 18254.38 0.8099821 -2020.9589\n",
       "5 0.8161367 17720.52 0.8153893 -2050.5256\n",
       "6 0.8216015 17193.83 0.8207306 -2080.6997"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Forward selection\n",
    "cat(\"Table 7\")\n",
    "forward_sel <- regsubsets(x=Life.expectancy ~.,data= expectancy_train, nvmax=19, method=\"forward\")\n",
    "\n",
    "forward_summary <- summary(forward_sel)\n",
    "\n",
    "forward_summary_df <- data.frame( \n",
    "   RSQ = forward_summary$rsq,\n",
    "   RSS = forward_summary$rss,\n",
    "   ADJ.R2 = forward_summary$adjr2,\n",
    "   BIC = forward_summary$bic\n",
    ")\n",
    "forward_summary_df %>% head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best number of predictors to be selected is  12\n",
      "Table 8"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 19 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>n_input_variables</th><th scope=col>C_p</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td>2404.139354</td></tr>\n",
       "\t<tr><td> 2</td><td> 821.437844</td></tr>\n",
       "\t<tr><td> 3</td><td> 356.633125</td></tr>\n",
       "\t<tr><td> 4</td><td> 202.179469</td></tr>\n",
       "\t<tr><td> 5</td><td> 162.411842</td></tr>\n",
       "\t<tr><td> 6</td><td> 123.204489</td></tr>\n",
       "\t<tr><td> 7</td><td> 106.087435</td></tr>\n",
       "\t<tr><td> 8</td><td>  19.934640</td></tr>\n",
       "\t<tr><td> 9</td><td>  13.454595</td></tr>\n",
       "\t<tr><td>10</td><td>  11.985773</td></tr>\n",
       "\t<tr><td>11</td><td>  11.468809</td></tr>\n",
       "\t<tr><td>12</td><td>   9.988715</td></tr>\n",
       "\t<tr><td>13</td><td>  10.121462</td></tr>\n",
       "\t<tr><td>14</td><td>  11.148805</td></tr>\n",
       "\t<tr><td>15</td><td>  12.691486</td></tr>\n",
       "\t<tr><td>16</td><td>  14.287013</td></tr>\n",
       "\t<tr><td>17</td><td>  16.079369</td></tr>\n",
       "\t<tr><td>18</td><td>  18.017771</td></tr>\n",
       "\t<tr><td>19</td><td>  20.000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 19 × 2\n",
       "\\begin{tabular}{ll}\n",
       " n\\_input\\_variables & C\\_p\\\\\n",
       " <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t  1 & 2404.139354\\\\\n",
       "\t  2 &  821.437844\\\\\n",
       "\t  3 &  356.633125\\\\\n",
       "\t  4 &  202.179469\\\\\n",
       "\t  5 &  162.411842\\\\\n",
       "\t  6 &  123.204489\\\\\n",
       "\t  7 &  106.087435\\\\\n",
       "\t  8 &   19.934640\\\\\n",
       "\t  9 &   13.454595\\\\\n",
       "\t 10 &   11.985773\\\\\n",
       "\t 11 &   11.468809\\\\\n",
       "\t 12 &    9.988715\\\\\n",
       "\t 13 &   10.121462\\\\\n",
       "\t 14 &   11.148805\\\\\n",
       "\t 15 &   12.691486\\\\\n",
       "\t 16 &   14.287013\\\\\n",
       "\t 17 &   16.079369\\\\\n",
       "\t 18 &   18.017771\\\\\n",
       "\t 19 &   20.000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 19 × 2\n",
       "\n",
       "| n_input_variables &lt;int&gt; | C_p &lt;dbl&gt; |\n",
       "|---|---|\n",
       "|  1 | 2404.139354 |\n",
       "|  2 |  821.437844 |\n",
       "|  3 |  356.633125 |\n",
       "|  4 |  202.179469 |\n",
       "|  5 |  162.411842 |\n",
       "|  6 |  123.204489 |\n",
       "|  7 |  106.087435 |\n",
       "|  8 |   19.934640 |\n",
       "|  9 |   13.454595 |\n",
       "| 10 |   11.985773 |\n",
       "| 11 |   11.468809 |\n",
       "| 12 |    9.988715 |\n",
       "| 13 |   10.121462 |\n",
       "| 14 |   11.148805 |\n",
       "| 15 |   12.691486 |\n",
       "| 16 |   14.287013 |\n",
       "| 17 |   16.079369 |\n",
       "| 18 |   18.017771 |\n",
       "| 19 |   20.000000 |\n",
       "\n"
      ],
      "text/plain": [
       "   n_input_variables C_p        \n",
       "1   1                2404.139354\n",
       "2   2                 821.437844\n",
       "3   3                 356.633125\n",
       "4   4                 202.179469\n",
       "5   5                 162.411842\n",
       "6   6                 123.204489\n",
       "7   7                 106.087435\n",
       "8   8                  19.934640\n",
       "9   9                  13.454595\n",
       "10 10                  11.985773\n",
       "11 11                  11.468809\n",
       "12 12                   9.988715\n",
       "13 13                  10.121462\n",
       "14 14                  11.148805\n",
       "15 15                  12.691486\n",
       "16 16                  14.287013\n",
       "17 17                  16.079369\n",
       "18 18                  18.017771\n",
       "19 19                  20.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Using Mallow's C_P to find the right number of inputs\n",
    "forward_sel_candidate_models <- tibble(\n",
    "  n_input_variables = rep(1:19),\n",
    "  C_p = forward_summary$cp\n",
    ")\n",
    "cat(\"The best number of predictors to be selected is \", forward_sel_candidate_models %>% filter(C_p==min(C_p)) %>% pull(n_input_variables))\n",
    "cat(\"\\nTable 8\")\n",
    "forward_sel_candidate_models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 5"
     ]
    },
    {
     "data": {
      "image/png": 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4xAAwDEnwAdG6aCBgBIAgE6NtJpI9AAAPEnQMeGqaABAJJAgI4NixECACSBAB0b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UrFmzTJkyysO7aj1nzuawbk4GDx6cnp6+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\niLkHkloAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Cp for Forward Method using a Training Set”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Figure 5\")\n",
    "plot(forward_summary$cp,\n",
    "    main = \"Cp for Forward Method using a Training Set\",\n",
    "  xlab = \"Number of Input Variables\", ylab = \"Cp\", type = \"b\", pch = 19,\n",
    "  col = \"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model size we get is the same for both forward and backward selection, and contains the same variables. Due to multicollinearity, we will be removing the `Schooling` and `infant.deaths` from our model. The covariates we will be using are listed below as stepwise_selection. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'Status'</li><li>'Life.expectancy'</li><li>'Adult.Mortality'</li><li>'Alcohol'</li><li>'percentage.expenditure'</li><li>'BMI'</li><li>'under.five.deaths'</li><li>'Diphtheria'</li><li>'HIV.AIDS'</li><li>'thinness.5.9.years'</li><li>'Income.composition.of.resources'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Status'\n",
       "\\item 'Life.expectancy'\n",
       "\\item 'Adult.Mortality'\n",
       "\\item 'Alcohol'\n",
       "\\item 'percentage.expenditure'\n",
       "\\item 'BMI'\n",
       "\\item 'under.five.deaths'\n",
       "\\item 'Diphtheria'\n",
       "\\item 'HIV.AIDS'\n",
       "\\item 'thinness.5.9.years'\n",
       "\\item 'Income.composition.of.resources'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Status'\n",
       "2. 'Life.expectancy'\n",
       "3. 'Adult.Mortality'\n",
       "4. 'Alcohol'\n",
       "5. 'percentage.expenditure'\n",
       "6. 'BMI'\n",
       "7. 'under.five.deaths'\n",
       "8. 'Diphtheria'\n",
       "9. 'HIV.AIDS'\n",
       "10. 'thinness.5.9.years'\n",
       "11. 'Income.composition.of.resources'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"Status\"                          \"Life.expectancy\"                \n",
       " [3] \"Adult.Mortality\"                 \"Alcohol\"                        \n",
       " [5] \"percentage.expenditure\"          \"BMI\"                            \n",
       " [7] \"under.five.deaths\"               \"Diphtheria\"                     \n",
       " [9] \"HIV.AIDS\"                        \"thinness.5.9.years\"             \n",
       "[11] \"Income.composition.of.resources\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Stepwise Selected Covariates\n",
    "stepwise_selection <- data %>%\n",
    "    select( -Hepatitis.B, -Measles, -Polio, -Total.expenditure, -GDP, \n",
    "           -Population, -thinness..1.19.years, -Schooling, -infant.deaths) %>%\n",
    "    names() \n",
    "stepwise_selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we can find our model, and the summary of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Life.expectancy ~ Status + Adult.Mortality + percentage.expenditure + \n",
       "    BMI + under.five.deaths + Diphtheria + Alcohol + HIV.AIDS + \n",
       "    thinness.5.9.years + Income.composition.of.resources, data = expectancy_train)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-13.8030  -2.3470   0.1408   2.2385  14.0714 \n",
       "\n",
       "Coefficients:\n",
       "                                  Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)                      5.851e+01  7.554e-01  77.455  < 2e-16 ***\n",
       "Status1                          1.241e+00  4.297e-01   2.888 0.003940 ** \n",
       "Adult.Mortality                 -2.061e-02  1.175e-03 -17.539  < 2e-16 ***\n",
       "percentage.expenditure           4.885e-04  7.714e-05   6.332 3.38e-10 ***\n",
       "BMI                              5.700e-02  7.478e-03   7.623 4.95e-14 ***\n",
       "under.five.deaths               -2.710e-03  7.291e-04  -3.717 0.000211 ***\n",
       "Diphtheria                       2.744e-02  5.499e-03   4.989 6.93e-07 ***\n",
       "Alcohol                         -1.193e-02  3.958e-02  -0.301 0.763124    \n",
       "HIV.AIDS                        -4.122e-01  2.114e-02 -19.498  < 2e-16 ***\n",
       "thinness.5.9.years              -3.404e-02  3.304e-02  -1.030 0.303131    \n",
       "Income.composition.of.resources  1.659e+01  8.901e-01  18.643  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 3.94 on 1225 degrees of freedom\n",
       "Multiple R-squared:  0.8027,\tAdjusted R-squared:  0.8011 \n",
       "F-statistic: 498.4 on 10 and 1225 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MLR_expectancy <- lm(Life.expectancy ~ Status + Adult.Mortality + percentage.expenditure\n",
    "                     + BMI + under.five.deaths + Diphtheria + Alcohol + \n",
    "                     HIV.AIDS + thinness.5.9.years + Income.composition.of.resources, data = expectancy_train)\n",
    "summary(MLR_expectancy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Life.expectancy ~ Status + Adult.Mortality + percentage.expenditure + \n",
       "    BMI + under.five.deaths + Diphtheria + Alcohol + HIV.AIDS + \n",
       "    thinness.5.9.years + Income.composition.of.resources + infant.deaths + \n",
       "    Schooling, data = expectancy_train)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-12.784  -2.029   0.058   2.246  11.748 \n",
       "\n",
       "Coefficients:\n",
       "                                  Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)                      5.467e+01  7.912e-01  69.102  < 2e-16 ***\n",
       "Status1                          7.343e-01  3.917e-01   1.875   0.0611 .  \n",
       "Adult.Mortality                 -1.775e-02  1.081e-03 -16.416  < 2e-16 ***\n",
       "percentage.expenditure           4.507e-04  7.008e-05   6.432 1.81e-10 ***\n",
       "BMI                              3.397e-02  6.963e-03   4.879 1.21e-06 ***\n",
       "under.five.deaths               -7.494e-02  8.406e-03  -8.915  < 2e-16 ***\n",
       "Diphtheria                       1.281e-02  5.079e-03   2.521   0.0118 *  \n",
       "Alcohol                         -8.146e-02  3.756e-02  -2.169   0.0303 *  \n",
       "HIV.AIDS                        -4.153e-01  1.919e-02 -21.646  < 2e-16 ***\n",
       "thinness.5.9.years              -6.260e-02  3.014e-02  -2.077   0.0380 *  \n",
       "Income.composition.of.resources  9.280e+00  9.432e-01   9.839  < 2e-16 ***\n",
       "infant.deaths                    9.869e-02  1.131e-02   8.724  < 2e-16 ***\n",
       "Schooling                        8.771e-01  6.674e-02  13.141  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 3.575 on 1223 degrees of freedom\n",
       "Multiple R-squared:  0.8378,\tAdjusted R-squared:  0.8363 \n",
       "F-statistic: 526.6 on 12 and 1223 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MLR_expectancy_2 <- lm(Life.expectancy ~ Status + Adult.Mortality + percentage.expenditure\n",
    "                    + BMI + under.five.deaths + Diphtheria + Alcohol + \n",
    "                    HIV.AIDS + thinness.5.9.years + Income.composition.of.resources + \n",
    "                      infant.deaths + Schooling, data = expectancy_train)\n",
    "summary(MLR_expectancy_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analysing The Effect Of Multicollinearity\n",
    "From the correlation matrix above, we know that the pair of `Schooling` and `Income.composition.of.resources` as well as the pair `under.five.deaths` and `infant.deaths` are highly correlated. The first model `MLR_expectancy` adjusts for this by removing one variable each from both correlated pairs while `MLR_expectancy_2` does not. The impact of not adjusting the model is a decrease in the magnitude of the coefficient estimate which is caused by the newly added correlated variable taking away some of its significance. In our models: $\\\\\\\\$\n",
    " `Income.composition.of.resources` :  16.6 (without) <br><br/>\n",
    " `Income.composition.of.resources`:  9.28 (with)<br><br/>\n",
    " `under.five.deaths`:              -2.710e-03 (without)<br><br/>\n",
    " `under.five.deaths`:               -7.494e-02 (with)<br><br/>\n",
    " Therefore, it is not ideal to include correlated covariates `Schooling` and `infant.deaths` in the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we also do forward selection for interactive models, which we put a nvmax of 189 as those are the maximum number of interactions we can get. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax, force.in = force.in, :\n",
      "“1  linear dependencies found”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reordering variables and trying again:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in rval$lopt[] <- rval$vorder[rval$lopt]:\n",
      "“number of items to replace is not a multiple of replacement length”\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "105.695986302215"
      ],
      "text/latex": [
       "105.695986302215"
      ],
      "text/markdown": [
       "105.695986302215"
      ],
      "text/plain": [
       "[1] 105.696"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forward_int_sel <- regsubsets(x=Life.expectancy ~. ^2,data= expectancy_train, nvmax = 189, method=\"forward\")\n",
    "forward_int_summary <- summary(forward_int_sel)\n",
    "\n",
    "forward_int_sel_candidate_models <- tibble(\n",
    "  n_input_variables = rep(1:length(forward_int_summary$cp)),\n",
    "  C_p = forward_int_summary$cp\n",
    ")\n",
    "min(forward_int_summary$cp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown, the lowest $C_p$ for the forward selection models with interaction are much higher than the ones for the additive models. This suggests that the models with interaction may not be as good as that without, and as there are an incredibly large number of variables, we will not be doing any interactive models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 LASSO Model Selection\n",
    "We will now be using LASSO to further see what model is the best when all the covariates are included. Below, we use `cv.glmnet` to find the smallest lambda to further create a model and do analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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ka6erk9OLS2UEC7ld3/W5955hkhxJEjR5SWy5cve3l59e7d29VD23j//feFEFu2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\nQIAGAAAAZCBAAwAAADIQoAEAAAAZ/gcMqqpuYMIJfAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Lambda selection by CV with LASSO\n",
       "\n",
       "”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 7"
     ]
    },
    {
     "data": {
      "image/png": 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Y7zUSL5UTK1Jpl8KlYbdZzjNO0U0zjFNEoNnYcEATgyFGiImOvaX9dKW4io803F\nrHOd1NcfWcKt/fqSK8T+UxRirmt/fVvEdepfLCH2tVXXFRF3381xx03ue2U36bquEPV7riVc\nN+G6Qogax3WFSLru4gceOE4IIcSuv8wbfenl+weuH/0VQhTIkhAiLMuyEHmyrAoRlmVdEvmy\nFJQUVRIFkqxKIijJpiTpkgjLsiaJ+hJsSlJAkphbDLRubWT5tIB5WsAUQthC/CeZWhFPrEgk\nHo/GXCFO0LWhpnGKafTXdaZ5ADh8FGgvxV33rzXRpOs29MtGYo5rf+dk0nXrvjOMGnGc/U/Z\nrojt95opV9Tu90cOOBB7+Br6a72wLDV84wlKsioJIYQqpKC8b2gnT5JkSRJC6JIwZckUQhFS\nF1kSQgQlSROSJIk8SRZCmLKkCyEJkS/Lxfa+/+sdrdQrR3dQJRGSJFlIYZkRIwBHQhGiv671\n17VfiHDcdT9IJFfEE/+qi99fHQnJ8omGfoppnGIYx2p8ZwTQBP6a8FLKdb+wLOtAl0KSpEgi\n9J2y+N0RU1OSDPGt2zRJBCR5/xv0/a4HZUnb7/764dsD/sGQLDV8fqiS1NK7rn79r1MlqSsP\nywPQrExJGmYaw0xDCLHXcd6LJ5bHEw9HondWVndUlKGmMTJgDjcNdpsGcEAUaC/lyfLMtkVe\npwCAnNZGlscEA2OCASHE55a1Ip54J564fk+lJcRJhn56wDw9YHZkw3UA+6FAAwCwT7GqFofV\ni8OhhOt+mEi+Ho//tSZ6e2V1D009PWCeZpqDDJ1BaQAUaAAAGjMkqX6zjhsKCz5LWW/UxV+P\nxx+sibaR5WEB43TTHBkw2cQDyFkUaAAADqWnpvbUwlfkh3fY9ht18dfr4tftrZKFGG4aIwLm\nYF1n3SGQa/iaBwDgsHRUlEvCoUvCoVrXfSeeeL0uPqc68pVtt1Xkwbo+xDBKTb1E48GHQOtH\ngQYAID1BSRodMEcHTCHETtv+MJFckUgsjsVmVFUHJOkEQx+k64MNfZChG0zzAFojCjQAAEeu\nvaKcHQycHQwIIXbZ9qpE8oNE8l918QdqIrokHa/rpYY+xND7GzpPMAVaDQo0AADNo52iNOyI\nV+M4HySSqxLJt+OJv9REXCG6a+oPdK2/rvfTtd6aZtKngaxFgQYAoPnly3L9HtJCiLjrrkum\n1iVTa5PJxyKxLZYlC1Giaf10rb+u99e1Ek1V6dNA9qBAAwCQWaYkDTb0wYYuRLFa5acAACAA\nSURBVEgIEXGcdcnU2mTq42RyXiTypWUbktRb0/rp2mBDPzMYYBki4HMUaAAAWlSeLJ9sGieb\nRv2He2xnXSq5Npn6OJl6trLqLzXR6wvzG64C8CEKNAAAXmqryKcq5qmmKYSocpy5NZErdu0Z\nETCvL8wvVvk2DfiR7HUA4CAUpfEBALR2hbJ8Q2HB3zu0izrOuB277q6qjjqu16EANEaBhl+N\nHt34AAByQx9dW9T+qNlti16vi4/dsXNJtNb2OhKA/fG7IfjVrFmitFTYtpg40esoAOCB0wPm\nKabxt0jsj1XVS2Kx6wsLBhu616EACEGBhn+pqpg0yesQAOAlU5KuyA//Vyjwp+qay3buPjMY\nmF6Q30llYhvgMaZwAADgax0U5Q9tip7s0G6HZY/bsfP+6kjcZWI04CUKNAAAWaC/rj3W4aib\nigoWx2I/2rHzjbq414mA3EWBBgAgO8hCXBAKvtixw5mBwDW79/5vdQ2LCwFPUKABAMgmYVn6\nbWH+3HZtF0dr/3vn7j2243UiIOdQoAEAyD6nmsYzHdvFXXfCV7s+Sia9jgPkFgo0AABZ6WhF\nWdT+qGGmcenOPX+P1XodB8ghbGMHAEC2MiTpzjaFx+v6HZXVqxKJ24oKTUnyOhTQ+jECDQBA\ndrsoHHy8/VGrEsmf7Ny9zWJhIZBxFGgAALJeP137e4d2+bI84atdy+MJr+MArRwFGj5WXi7W\nrvU6BABkhzayvKBd2wnh4C927bm/OsLeHEDmUKDhV7Nni759Rf/+YsYMr6MAQHZQhPhNQf59\nR7V5NBq9ZvfeiEOLBjKCAg2/WrBg38H8+Z7mAIAsMypgLunQ7nPLuuir3RtSltdxgFaIAg2/\nSiQaHwAADk93VX2i/VHHaurEr3atYZdooLlRoAEAaIXyZPn+o9qcEQxct6cq7rpexwFaFQo0\nAACtkyTEjYX5cde9vzridRagVaFAAwDQauXJ8q1FBQ9HomUJJnIAzYYCDQBAazYyYI4NBm6u\nrEowkQNoJhRoAABauRuLCqoc5681Ua+DAK0EBRoAgFauUJZvLCyYVxP5TzLldRagNaBAAwDQ\n+o0JBkYFzBv3VllM5AC+Nwo0AAA54eaiwu22/VAk5nUQIOtRoAEAyAlHKfL1hflzaiKf8XhC\n4PuhQAMAkCvODQWHm8aNe6tsr5MAWY0CDQBADvl9UUGFZf0two4cwJGjQAMAkEPaK8pvCvLu\nrY58bjGRAzhCFGgAAHLLReHQIEO/eW81+3EAR4YCDb9SlMYHAIDmIAlxe1Hh2mRycZQdOYAj\nQYGGX40e3fgAANBMOqvKtQX5s6prttusJwTSpnodADiIWbNEaamwbTFxotdRAKAVmpQXeqWu\n7oa9VQ+1ayt5HQbILhRo+JWqikmTvA4BAK2WLMQdbQrP37HrH7Ha80JBr+MA2YQpHAAA5Kju\nqjolP29GVc1XTOQA0kGBBgAgd03ODx+jKrdWVnsdBMgmFGgAAHKXIsSdbQrfiSderK3zOguQ\nNSjQAADktOM07Rd54bsqqyOO43UWIDtQoAEAyHVX5oeDsvRQhG2hgcNCgQYAINdpknRNfv4j\nkegOVhMCh4ECDQAAxI9Cge6aOq8m6nUQIAtQoAEAgJCF+HVB3t+jsY0py+ssgN9RoAEAgBBC\nnGqapabx55qI10EAv6NAw8fKy8XatV6HAIAc8j8F+a/U1q1OJr0OAvgaBRp+NXu26NtX9O8v\nZszwOgoA5Ir+unZmMDCrqsbrIICvUaDhVwsW7DuYP9/THACQW35dkLc6mXozHvc6COBfFGj4\nVSLR+AAAkHnHqOqEUHBWVYSnqgAHQ4EGAADfck1+3jbL+mes1usggE9RoAEAwLe0VeTL8sKz\nayJJ1/U6C+BHFGgAANDYz/LDCcd9IsrDvYEDoEADAIDGQpL0i/y8uTXRGoe50EBjFGgAAHAA\nE8PBAll6OMIgNNAYBRoAAByAJknX5Oc/EonusG2vswD+QoEGAAAH9qNQoLum/oWHewPfRoEG\nAAAHJgvx64L8p6K1G1OW11kAH6FAAwCAgzrVNEpNY3Y1D/cGvkGBBgAAh/I/Bfmv1sXLEkmv\ngwB+QYEGAACH0l/XzgwGZjEIDXyNAg0AAJrw64K8NcnUsrq410EAX6BAAwCAJnRT1QtDwT9V\nR3iqCiAo0PAvRWl8AADwztX5edss65+xWq+DAN6jQMOvRo9ufAAA8E5bRb4sLzy7JpJ0Xa+z\nAB5TvQ4AHMSsWaK0VNi2mDjR6ygAACGEmJwXfjIaeyIa+2le2OssgJco0PArVRWTJnkdAgDw\njbAsXZ4XfiwauywvLHkdBvAQUzgAAMDhOj8U3G47KxMJr4MAXqJAAwCAw3WUIo8wjaVRlhIi\np1GgAQBAGi4IBV+pi9c47GiH3EWBBgAAaTgtYObJ8vO1dV4HATxDgQYAAGlQhDgnGFjKhtDI\nYRRoAACQngvCwXXJ1PpUyusggDco0AAAID3dVXWAoTMIjZxFgQYAAGm7IBT8f7E6nkqI3ESB\nBgAAaRsbDFiu+1pd3OsggAco0PCx8nKxdq3XIQAABxCQpLODgaeZxYGcRIGGX82eLfr2Ff37\nixkzvI4CADiAC0LBFfHEl5btdRCgpVGg4VcLFuw7mD/f0xwAgAMbaOjdNfUftQxCI+dQoOFX\niUTjAwCAz5wXCi6N1fJMQuQaCjQAADhC44PBr2znvTgjHcgtFGgAAHCE2irySNNgKSFyDQUa\nAAAcuQtCwVfr4tUO8ziQQyjQAADgyJ0aMAtk+bnaOq+DAC2HAg0AAI6cIsS5ocDfo8ziQA6h\nQAMAgO/l/FDw01SqPJnyOgjQQijQAADgezlGVQcZOksJkTso0AAA4Pu6IBT8f7V1cdf1OgjQ\nEijQAADg+zo7GHCF+1pd3OsgQEugQAMAgO8rIEljAgFmcSBHUKABAEAzuCAcfDee+NyyvA4C\nZBwFGgAANIMTdP04TXs2xobQaP0o0AAAoHmMDwWWxmptr2MAmUaBhl8pSuMDAIC/jQ8F9zrO\nu/GE10GAzKJAw69Gj258AADwt0JZHmkaLCVEq6d6HQA4iFmzRGmpsG0xcaLXUQAAh2tCOHjN\n7spKxymSGaRDq0WBhl+pqpg0yesQAID0DDfNtrL8XKzu0ryQ11mATOGnQwAA0GxkIc4NBZ5i\nFgdaNQo0AABoThNCoQ2p1NpkyusgQKZQoAEAQHPqoiqlhrGUQWi0XhRoAADQzC4IBZ+rrYu7\nrtdBgIygQAMAgGZ2ZtB0hbusLu51ECAjKNAAAKCZmZJ0kmG8wxNV0EpRoAEAQPMbZhpvUaDR\nSlGgAQBA8xthmjtse1PK8joI0Pwo0AAAoPl1UZViVWUWB1olCjR8rLxcrF3rdQgAwBEaZhrv\nJCjQaIUo0PCr2bNF376if38xY4bXUQAAR2KYaayMJ5JsZodWhwINv1qwYN/B/Pme5gAAHKGT\nTSMlRFky6XUQoJlRoOFXDb/149d/AJCdQpJ0gq4xDRqtDwUaAABkyjCT3aDRClGgAQBApgwz\njfJkao/teB0EaE4UaAAAkCk/0PV8WV7BZDy0LhRoAACQKYoQpzCLA60OBRoAAGTQMNN4Ox5n\nKzu0JhRoAACQQcNNY7ftbEilvA4CNBsKNAAAyKCOinKsxjO90apQoAEAQGYNZxo0WhcKNAAA\nyKyhhrEqkYzzTG+0FhRoAACQWSeahivEBwme6Y1WggINAAAyKyBJA3WdWRxoNSjQAAAg43im\nN1oTCjQAAMi4YaaxIZXaadteBwGaAQUafqUojQ8AAFmrj661keXlDEKjVaBAw69Gj258AADI\nWpIQQ5nFgdZC9ToAcBCzZonSUmHbYuJEr6MAAJrBUNP4Y1WNw+gdsh8FGn6lqmLSJK9DAACa\nzXDTvMGpWp9M9dU1r7MA3ws/BAIAgJZwlCKXaNrbzOJA9qNAAwCAFjLcNFhHiFaAAg0AAFrI\nUNP4MJms5ZneyHIUaAAA0EKGGLoixPsMQiPLUaABAEALMSRpiKG/k6BAI7tRoAEAQMthN2i0\nAhRoAADQcoab5qaUtdXimd7IYhRoAADQcko0taOirGAWB7IZBRoAALSoU9jMDlmOAg0fKy8X\na9d6HQIA0MyGmsbyeII5HMheFGj41ezZom9f0b+/mDHD6ygAgOY0zDSijrMumfQ6CHCEKNDw\nqwUL9h3Mn+9pDgBAMyuS5T46z/RGFqNAw68a1pew0AQAWp1hTINGNqNAAwCAljbMNFYnkhHH\n8ToIcCQo0AAAoKUN1HVDkt5LMA0aWYkCDQAAWpomSScyiwNZiwINAAA8MNQw3orHvU4BHAkK\nNAAA8MDwgLHVsj+3LK+DAGmjQAMAAA90V9UuqvIOsziQhSjQAADAG6cYBgUa2YgCDQAAvDHM\nNN6NJyzX9ToIkB4KNAAA8MZQ04i77ppkyusgQHoo0AAAwBt5stxP15nFgayjeh0gba7rVlRU\nbNq0KRKJCCEKCgpKSkq6du3qdS4AAJC2YabxdjzxfwryvA4CpCGbCnRlZeVdd921aNGinTt3\nNrpUXFx8xRVXTJs2LRAIeJINAAAcgVNMY15NJOq4YVnyOgtwuLKmQG/fvn3YsGEVFRUlJSVj\nx47t1q1bKBQSQtTU1GzcuHHZsmW33HLL008//frrrxcVFXkdFgAAHJZ+uiZL0sfJ5Cmm4XUW\n4HBlTYG++eabt27dumTJkgsvvPC7V23bnjdv3jXXXHPbbbfde++9LR8PzU9RGh8AAFodU5L6\naFoZBRpZJWsWET7//POXXnrpAduzEEJRlClTplx00UVLly5t4WDIlNGjGx8AAFqjAYa2OpH0\nOgWQhqwZgd6zZ0+PHj0OfU+fPn2eeeaZlsmDjJs1S5SWCtsWEyd6HQUAkEEDdP2ZWJ2TRaN6\nyHlZU6A7deq0Zs2aQ99TVlbWqVOnlsmDjFNVMWmS1yEAABk3yNAjjrMpZfXUsqaWIMdlzQ97\n48eP//vf/37PPfckEgfYLTIWi/3+979/9tlnL7744pbPBgAAjlgHRemoKKuTzOJA1siaH/Vu\nvfXWt956a/r06bfffvuJJ57YtWvXcDjsum40Gt2yZcvKlStra2tHjBhx0003eZ0UAACkZ6Ch\nr04kJ4SCXgcBDkvWFOjCwsIVK1bMmTNn4cKFb7zxhm3bDZc0TRs8ePDkyZMnT56ssGMDAADZ\nZoCuL47FvE4BHK6sKdBCCF3Xp06dOnXq1Hg8/sUXX9Q/iTA/P7+4uFjXda/TAQCAIzTA0P5v\nlVXpOEVy1kwuRS7LpgLdwDTNkpKS757fs2dPZWVlz549Wz4SAAA4Yn01zZCkjxLJkQHT6yxA\n01rVz3kzZ848YLEGAAB+pkrSD3RtdTLldRDgsLSqAg0AALLUAF1nIw5kCwo0AADw3kBDX5NI\n2k3fCHgva+ZADxkypMl7tm3b1gJJAABAsxug63Wu+2ky1UfXvM4CNCFrCnRZWZkQQtMO9UVl\nWVZLxUGLKC8Xti369fM6BwAg49oqcrGqliWTFGj4X9ZM4Zg+fXooFFq7dm384KZNm+Z1TDSf\n2bNF376if38xY4bXUQAALWGAoa1OMA0aWSBrCvQdd9zRs2fPiRMnplIs0c0NCxbsO5g/39Mc\nAIAWMkDXy1hHiGyQNVM4NE177LHHBg8efMMNN8ycObO5XraiouKkk0469NyPRCLRXP86pKHh\nPzv//QEgNww09K2V9i7bbsdzheFvWVOghRB9+vTZsWPHIcrumDFjCgsL03rNbt26Pfzww7W1\ntYe451//+td8BkEBAMiwEk0Ly9KaZOqMAAUavpZNBVoIkZ+ff4irI0eOHDlyZFovKMvyuHHj\nDn3P3r17KdAAAGSaIkQ/XV+dSJ7B8wjhb1kzBxoAALR6A5kGjWxAgQYAAH4xwNDXJlNJ1/U6\nCHAoradAb9y48YwzzjjjjDO8DgIAAI7QQF2zXLecHbfgb1k2B/oQIpHIa6+95nUKAABw5PJk\nubumliWSJ+i611mAg2o9Bbp3794ff/yx1ykAAMD3MlDXVycZgYavtZ4CbZpmP575DABAlhtg\n6LOrI16nAA4l+wq067oVFRWbNm2KRCJCiIKCgpKSkq5du3qdCwAANIMBur7Ttr+07E4qu0HD\np7KpQFdWVt51112LFi3auXNno0vFxcVXXHHFtGnTAoGAJ9kAAECzOFZTC2R5dTLZSeV7Onwq\nawr09u3bhw0bVlFRUVJSMnbs2G7duoVCISFETU3Nxo0bly1bdssttzz99NOvv/56UVGR12EB\nAMARkoQ4QddXJ5NjgxRo+FTWFOibb75569atS5YsufDCC7971bbtefPmXXPNNbfddtu9997b\n8vEAAEBzGWBo/66Le50COKis2Qf6+eefv/TSSw/YnoUQiqJMmTLloosuWrp0aQsHAwAAzWug\nrpcnU3U8TgV+lTUFes+ePT169Dj0PX369Pnqq69aJg8yTlEaHwAAcsMJhi6EWMtmdvCrrCnQ\nnTp1WrNmzaHvKSsr69SpU8vkQcaNHt34AACQGwKSdJyurU4kvQ4CHFjWzIEeP3787NmzS0tL\nf/WrXxmG0ehqLBb74x//+Oyzz/7ud7/zJB6a36xZorRU2LaYONHrKACAljZA11cnKdDwqawp\n0Lfeeutbb701ffr022+//cQTT+zatWs4HHZdNxqNbtmyZeXKlbW1tSNGjLjpppu8Topmoqpi\n0iSvQwAAvDHA0P9vZbUrhOR1EuC7sqZAFxYWrlixYs6cOQsXLnzjjTds2264pGna4MGDJ0+e\nPHnyZIX5sgAAZL+Bul7pOJ9bVjc1a7oKckc2fVLquj516tSpU6fG4/Evvvii/kmE+fn5xcXF\nuq57nQ4AADSbrqpylCKXJZIUaPhQVn5SmqZZUlLidQoAAJBB9dOgx4eCXgcBGsuaXTgAAEBO\nGWDoZQl2soMfUaABAIAfDdD1z1KpiON4HQRojAINAAD8qL+uqZL0MY9Tgf9QoAEAgB/pktRb\n08rYDRr+Q4EGAAA+NdDQeR4hfIgCDQAAfGqArq1OJpkEDb+hQMPHysvF2rVehwAAeGaQoUcd\nd2PK8joI8C0UaPjV7Nmib1/Rv7+YMcPrKAAAb7RXlKMVpYxZHPAZCjT8asGCfQfz53uaAwDg\npQGGvpp1hPAZCjT8KpFofAAAyD0DdNYRwnco0AAAwL8GGvpmy6rkcSrwEwo0AADwrz6aakjS\nGgah4ScUaAAA4F+qJPXTNaZBw1co0AAAwNcGGnpZggd6w0co0AAAwNcG6PrHyaTtdQygAQUa\nAAD42kBDj7vu+iSD0PALCjQAAPC1IlkuVlWmQcM/KNAAAMDvBhjsBg0foUADAAC/G6BrZYxA\nwzco0AAAwO8GGvo2y/7KZiUhfIECDQAA/K5E0/JkeQ3rCOEPFGgAAOB3shD9dY1p0PAJCjQA\nAMgC/XStPMUINHyBAg2/UpTGBwCAHNZb08qZwgF/oEDDr0aPbnwAAMhhvTSt2nF2sI4QPqB6\nHQA4iFmzRGmpsG0xcaLXUQAA3uumqaYkrU+mOgb4zSQ8RoGGX6mqmDTJ6xAAAL9QhDhO09an\nUqcFTK+zINcxhQMAAGSH3rr6ScryOgVAgQYAAFmit6atZx0hfIACDQAAskMvTfvcsmpd1+sg\nyHUUaAAAkB166ZoQYgO7QcNrFGgAAJAdQpLURVXZDRqeo0ADAICs0UtjHSG8R4EGAABZo7fO\nOkJ4jwINAACyRm9N+ySVcryOgRxHgQYAAFmjt6bVue4XFrM44CUKNHysvFysXet1CACAjxyt\nKvmyzCwOeIsCDb+aPVv07Sv69xczZngdBQDgFxLrCOEDFGj41YIF+w7mz/c0BwDAX3rrWjlb\nQcNTFGj4VSLR+AAAACF68UBveI0CDQAAskkfTdth25UOW3HAMxRoAACQTXpqqipJnzKLA96h\nQAMAgGyiS1J3VfkkyTpCeIYCDQAAskxvTVvPCDS8Q4EGAABZppeulbOOEN6hQAMAgCzTW9M2\nWlbKdb0OghxFgQYAAFmmj66lXHcTD/SGRyjQAAAgy7SR5aMUmXWE8AoFGgAAZJ8+rCOEdyjQ\nAAAg+/TSKdDwDAUaAABkn94aG3HAMxRoAACQfXprWpXj7LRtr4MgF1GgAQBA9jlGU01JYhYH\nPHG4Bdre7ye8RCLx3nvvlZWVuey/iMxRlMYHAAB8TRGip6auZyMOeKHpAm3b9tVXX33JJZfU\nf7h58+a+ffuefPLJgwYNOvXUU6PRaIYTIleNHt34AACA/fRiIw54pOkCPXPmzLlz5xYXF9d/\nePXVV1dUVPzyl7+cMmXK8uXL77///gwnRK6aNUssWiQeeUQ88IDXUQAAftRb1z6hQMMLapN3\nPPbYY+eff/6sWbOEENu2bXvxxRcnT548d+5cIUQ8Hl+8ePF1112X8ZjIQaoqJk3yOgQAwL/6\naNqWlBV3XVOSvM6C3NL0CPTmzZvPPPPM+uOXX37Zdd2JEyfWfzh48ODNmzdnLhwAAMDB9NI0\nR4hPGYRGi2u6QEv7/VT36quvhkKhESNG1H/oum6Kz1oAAOCFsCx1VhXWEaLlNV2gu3Xr9uab\nbwohvvrqq3/+859nnnmmruv1l9asWdOlS5fMBgQAADgI1hHCE00X6B//+MePP/740KFDBw0a\nFI1Gr7322vrzCxcufPTRR88555wMJwQAADiw3hrrCOGBpgv01KlTL7/88tWrV8disdmzZ48c\nObL+/HXXXderV6/rr78+wwkBAAAOrLeufZJMOV7HQK5pehcO0zQffvjhhx9+uNH5pUuXDhky\nRFWbfgUAAIBM6K1pMdfdalnFFBK0oKZHoN9+++29e/d+9/zJJ5/84YcfPv300xlIBQAA0LTO\nqpIny5+kWEeIFtV0gR4xYkT9IsLveuutt37+8583dyQAAIDDIglxnKauTzINGi3qoL/v+Oyz\nzz777LP647KyMtM0G91QV1e3ZMmSRCKRwXQAAACHxDpCtLyDFuinnnqqYYHg7bfffrDbJkyY\n0PyhgHrl5cK2Rb9+XucAAPhXb117vSbudQrkloMW6Ouuu+6nP/3p+++/f+6551566aV9+/Zt\ndIOiKMceeyzb2CFTZs8W9Xsm3n23YLMXAMBB9NK07ZZd4zj5ctMTU4Fmcaglq0cfffQ555wz\nbty4KVOmnHzyyS2WCRBCiAUL9h3Mn0+BBgAcTImmykJ8krJKDd3rLMgVTe/58txzz7VADqCx\nhun1zLMHABycKUnHaOr6ZIoCjRbTdIF2Xfepp55auHDh1q1bUweapL927doMBAMAADgsrCNE\nC2u6QM+aNWv69OlCiGAwqGla5iMBAACkobemvVRX53UK5JCmp9vfd999Z5111saNG2OxWNWB\ntEBKAACAg+mlaxtSluW6XgdBrmh6BPqrr7566qmnjj322BZIAwAAkK7empp03c2W3VPjgd5o\nCU2PQHfo0MHlRzoAAOBX7RSlrSKXMw0aLaXpAj1x4sRFixa1QBQAAIAj00vTPuGB3mgpTf+m\n45ZbbpkwYcJPfvKTyy67rLi4+LvrCHv27JmZbAAAAIelj6atZwQaLaXpAp2Xl1d/8Pjjjx/w\nBiZ4AAAAb/XStX/Ear1OgVzRdIGeOHGiruuqyqx8AADgU701bY/j7LadoxQe6I2Ma7oWH2zg\nGQAAwCeO1VRDktanUsMVw+ssaP3S+CktEomsW7eOjZ8BAIDfKEL00NT1rCNEizisAr1s2bIh\nQ4bk5+f369fv3XffrT95zjnnvPbaa5nMBgAAcLh6s44QLaXpAr1y5cozzzzz008/PeussxpO\n7tq16/333x87duwHH3yQyXgAAACHpRcFGi2l6QJ9++23d+zY8T//+c8jjzzScLJdu3Zr1qzp\n2LHjHXfckcF0yGWK0vgAAICD66Nrm1NWnM3BkHlNF+h33333l7/8ZZcuXRqdb9++/VVXXfXm\nm29mJhhy3ujRjQ8AADi43prqCPFZyvI6CFq/pnfhqK6u7tq16wEvHX300dFotLkjAUIIIWbN\nEqWlwrbFxIleRwEAZIE8WT5aVT5JpfrpjR/6BjSvpgt0x44dy8vLD3jpzTff7NSpU3NHAoQQ\nQqiqmDTJ6xAAgGzSW9PWJ1Mi5HUOtHZNT+EYO3bs3LlzP/zww/1PVlZW3njjjQ8//PC4ceMy\nlg0AACANvTStnHWEyLymC/Rtt90WDodPOumk+q58/fXXDxw48Oijj7777ruLi4tvueWWzIcE\nAABoWm9d+ySVYhUhMq3pAt2xY8dVq1b9/Oc/37JlixBi9erVq1evzsvL++Uvf/n+++936NAh\n8yEBAACa1ltTo467zbK9DoJWruk50EKI9u3bz507d86cOTt37oxEInl5efRmAADgN11VNSxL\nn6RSXVS2QEUGHbhA79ixwzCMoqKi+uP9L4XDYdd19z/ZsWPHjEYEAAA4HJIQx2na+lRqVMD0\nOgtaswMX6KOPPvqss8566aWX6o8P/RIuO5YDAAB/6FW/EQeQSQcu0BdffPGAAQMajlswDwAA\nwJHrrWlvxeNep0Ard+AC/eSTTx7wGAAAwM966+o2y444Tp7c9E4JwJE53M+tdevW7d69e/8P\ny8rKMhMJAADgCB2nabIQn/JAb2RS0wU6lUr97Gc/69ev39q1axtOvv7664MGDfrv//5v22an\nGGRMebnY77MOAIAmmZJ0tKpUWBRoZFDTBfrPf/7zQw89NG7cuG7dujWcHD169MUXX/zII4/c\nf//9mYyHHDZ7tujbV/TvL2bM8DoKACCbdFfVCkagkUlNF+hHHnnkRz/60XPPPde9e/eGk716\n9XryySfHjh1LgUamLFiw72D+fE9zAACyzDGaygg0MqrpAv3ZZ5+dfvrpB7x02mmn1T+eEGh+\niUTjAwAADkN3Vd3MCDQyqekCnZ+fv3nz5gNe2rx5c5s2bZo5EQAAwPfQPhZtDAAAIABJREFU\nXVW/sG2L51QgY5ou0OPGjXvwwQdfeOGF/U+mUqn58+f/9a9/PfPMMzOWDQAAIG3HaKrlulvZ\n5wAZc+B9oPd35513vvjii+PGjSsuLu7Vq9f/Z+/O4+yq6nzv/9awz1xD5hpSlRQhkoQEQQgi\nMd22EpFo26gNdGxoNQ+0SMPtG8Xry1bGFml5pJubvnAvT7BVeFptbKDpbnBqZiQahhAZokgS\nMs+ppIYz773uH6fm1JhU1alT5/N+8dJd++yzz6+GVH33Or+9VjgcPnr06JtvvnnkyJHa2tpv\nfOMb41AlAADAMM0yJqbUtlx+rh065wAnYOgR6Nra2o0bN1599dXt7e2/+MUv/vM///P55583\nxlx11VUvvvhiY2PjOFQJAAAwTEpkDvcRYiwN68ps1qxZ//t//+977rln7969qVSqpqYmHo+P\ndWUAAAAnZi4z2WEs9R+g9+3bFw6Hp0yZUtju2q+1jsfjra2tra2tXTtramrGukoAAIDha7J2\nA5M4Ycz0H6Bra2svvPDCn/70p4XtwU/huMsVAABMJE2e/Zf29mJXgUmr/wB92WWXnXnmmV3b\n41gPAADAyWqy9rAftAZBhR76di9gpPoP0D/60Y/63QYAAJj45npWiWzL588IhYpdCyah/i/L\nvvSlLz355JOF7auvvnrTpk3jWBIAAMBJiSs1w5h3ckwFjTHRf4C+6667NmzYUNi+9957t23b\nNo4lAQAAnKy5lpnsMFb6b+GYNWvWt771rZ07d1ZUVIjIAw888Ktf/WqgU/zd3/3dWFUHAABw\nQpo88w4BGmOj/wB9xx13XHXVVffcc0/hw4cffniQUxCgAQDARNNk7SPtqWJXgcmp/wB9+eWX\nf+xjH3v77bfT6fTy5cu/+c1vLl++fJwrQ7kzpu8GAADD1uTZ7fl8MJxVl4ER6j9Af+lLX/ro\nRz/6wQ9+sPDhlClT3v/+949jVYDIihWyeXPHBgAAIzTX2rRz+/J+nWUgBqOs/wB91113zZgx\noytAs9YgiuDOO2XpUvF9WbWq2KUAAEpPvbUhpbbl8wRojDpuIsREZa1cfnmxiwAAlCoj0mDN\ntnx+mYSLXQsmG24iBAAAk9Nca9/JMREHRh83EQIAgMmpybNvZnPFrgKTUP8BWkSqq6vPOecc\nEbnwwgs/8IEPvO997xvHqgAAAE5Wk7WPMZMdxsCAAbrLT3/608JGa2vrjh076uvrq6urx7gq\nAACAk9Vk7T7fTzsXUarYtWBSGdbciM8888w555xTWVm5ePHirrsJP/7xjz/xxBNjWRsAAMCJ\nm+tZJ8J6hBh1QwfoDRs2fPjDH37rrbcuvPDCrp0HDx588cUXV65c+fLLL49leQAAACdoitbV\nWm/jPkKMtqED9K233lpTU/Pmm29+73vf69o5Y8aMTZs21dTU/O3f/u0YVgcAAHAS5lrLCDRG\n3dAB+le/+tUXvvCF2bNn99k/c+bMq6+++tlnnx2bwgAAAE5Wk8dMdhh9QwfoY8eONTQ09PtQ\nbW1tW1vbaJcEAAAwOpqs3cYINEbb0AG6pqZm8+bN/T707LPP1tXVjXZJQKfNm+X114tdBACg\nhDV5BGiMvqED9MqVK++5555XXnml587m5uavfe1r3/3udz/60Y+OWW0ob2vXyqJFsmSJ3H57\nsUsBAJSquda2Be6QHxS7EEwqQwfoW265JZFIvPe97y1k5a9+9atnnXVWbW3tN7/5zcbGxhtv\nvHHsi0RZuu++jo1164paBwCghM2xxogwCI3RNawWjpdeeumqq67avn27iLz66quvvvpqRUXF\nF77whRdffHHWrFljXyTKUibTdwMAgBHylKqzhok4MLqGXolQRGbOnHnPPffcfffdBw4caG1t\nraioIDcDAICS0GQtU0FjdA0rQBccPnx469at7e3tFRUV4XCYBb0BAMDEN5f7CDHahrWU9/PP\nP3/eeefNmDHj/PPPX7FixXnnnTd16tQLLrjgdWZIAAAAExsj0Bh1Q49Ab9iw4YILLsjn8+9/\n//tPO+20aDTa3t7+5ptvPvnkk8uWLduwYcNpp502DoUCAACcgLnW7srnc855ShW7FkwSQwfo\nb3zjGzNmzPjFL36xYMGCnvs3btz4kY985JZbbvnBD34wZuUBAACclCbP+iI78/4p3gg6V4FB\nDN3C8cILL1xzzTV90rOInHXWWddcc82TTz45NoUBAACMgpnGxJViIg6MomEt5T179ux+H5o7\nd+6RI0dGuyQAAIBRo0TmcB8hRtXQAXrmzJkDLeX95ptvzpw5c7RLAgAAGE3cR4jRNXSA/vCH\nP/yP//iPjz76qHOua6dz7pFHHrn77rsvuuiisSwPAADgZM21lhYOjKKhu+lvvvnmxx9//OKL\nL66pqVm0aFE8Hi/MwrFv377a2tqbbrppHKoEAAA4YU2e/WFbe7GrwOQx9Aj0nDlzXnrppc98\n5jOpVOrJJ5/8j//4jyeffDKbzV555ZUvv/zyQO3RAAAAE0STtUeC4FgQFLsQTBLDms+loaHh\ne9/7nnNu37597e3tiUSipqZmrCsDAAAYFU2eVSLb8/kzQqFi14LJYIgR6AMHDqxfv76wrZSq\nra099dRTa2pq7r777qNHj459eQAAACcrqtRMY7iPEKNlsAD97LPPnnbaaTfeeGOf/b/5zW+u\nvfbaxYsXb926dSxrQ3kzpu8GAAAnqomZ7DB6BgzQe/fu/dSnPtXW1vbBD36wz0NLlixZu3bt\n3r17P/KRj6TT6TGuEOVqxYq+GwAAnChmssMoGrAHet26dYcOHVq3bt2VV17Z5yGl1HXXXef7\n/po1a77//e9//vOfH+MiUZbuvFOWLhXfl1Wril0KAKDkzbX2pUym2FVgkhhwBPrRRx+dN2/e\n6tWrBzrg2muvnT179ve+970xqQuwVi6/XD7zGeGGDwDASZvr2e153y92GZgcBgzQO3bseO97\n36v1gAdYa88777w33nhjbAoDAAAYNU3WZp3blydCYxQMmI9bWlqmTZs2+JOnTZuW4d0QAAAw\n4dVbE1aK+wgxKgYM0NOmTduxY8fgT37rrbdmzJgx2iUBAACMMi3SYJnJDqNjwAC9dOnSJ554\n4vDhwwMd8Pbbbz/33HPnnXfe2BQGAAAwmposM9lhdAwYoK+44oq2trarrroq39+PWktLy5//\n+Z/n8/nPfvazY1gdAADAKJnLVNAYJQMG6E996lMXXHDBI488ct555z3yyCOtra2F/QcPHvzO\nd75zxhlnbNiw4ROf+MTHPvax8SoVAADgxDVZ+w4tHBgNA84DrZT68Y9//OlPf/onP/nJJz/5\nSaVUVVWV7/tdSfqyyy777ne/O151AgAAnJQmz+73/aRzMaWKXQtK22BLeVdXVz/++OOPP/74\nqlWrmpqacrmciJx22mmf+9znnn322R/96EfRaHS86gQAADgpTdY6kR10ceCkDTgC3eWiiy66\n6KKLxqEUAACAsVOl9RStt+XyCzyv2LWgtA02Ag0U2ebN8vrrxS4CADB5NHEfIUYDARoT1dq1\nsmiRLFkit99e7FIAAJPEXGuZChonjwCNieq++zo21q0rah0AgMmjydp3GIHGSSNAY6LqWiWe\n5eIBAKOkybPbcnlX7DJQ6gjQAACgXMy1tt25Q75f7EJQ2gjQAACgXDRaY0S4jxAniQANAADK\nhadUPfcR4qQRoAEAQBmZa+22PC0cOCkEaAAAUEaaPCbiwMkiQAMAgDLSZA0tHDhJBGgAAFBG\nmjy7O5/POuayw4kjQAMAgDLSZK0vspM2aJwEAjQAACgjM4xJaEUbNE4GARoAAJSXOcxkh5ND\ngAYAAOWlyTIRB04KARoAAJSXJs+yGCFOBgEaAACUlyZaOHByCNCYqIzpuwEAwGho8mxzEBwN\ngmIXglJFgMZEtWJF3w0AAEbDHGuVCG3QOGG22AUAA7jzTlm6VHxfVq0qdikAgEklqtQsY7bl\n8meGQsWuBSWJAI2Jylq5/PJiFwEAmJzmekzEgRNX2gE6m81u2rSpra1t7ty5TU1NxS4HAACU\nBu4jxMkomR7ob3zjG0899VTPPffee29NTc255577wQ9+8JRTTjnnnHNeffXVYpUHAABKSJNl\nJjucuJIJ0DfccMPPfvazrg8fe+yxq6++OplMfuITn/j85z+/bNmyl19++QMf+MCWLVuKWCQA\nACgJTZ7dkff9YpeBElWqLRxr1qypqqpav379woULC3sefvjhP/3TP73tttv+6Z/+qbi1AQCA\nCW6utVnn9uT9BstkqRixkhmB7ungwYO///3v/+qv/qorPYvIJz/5yT/5kz/5+c9/XsTCAABA\nSaizJqwUXRw4MSUZoNPptIj0TM8FixcvPnDgQDEqAgAApUSLNFrzDvcR4oSUZICuq6urqqra\ntWtXn/179uypqKgoSkkAAKC0NFlmssMJKqUAvWPHjpdeeuntt99ubm6+5pprvvOd7ySTya5H\nf/vb3/7Lv/zLsmXLilghAAAoFU0eE3HgBJXSTYQ//OEPf/jDH/bc85Of/ORTn/qUiPzgBz/4\ny7/8y1QqdcMNNxSpOgAAUEqarP239lSxq0BJKpkA/d3vfvdoD8eOHTt69OiUKVMKjx49erS6\nuvpHP/rR0qVLi1snRtPmzeL7snhxsesAAExC9dYe9P2cc55Sxa4FJaZkAvRnP/vZQR79i7/4\ni6uvvlrrUupIwRDWrpW//msRkW9+U7761WJXAwCYbGqNCUT2+QEz2WGkSiZAd3HObdu2bevW\nra2trSJSVVU1f/78hoaGYteF0XbffR0b69YRoAEAo26W0UZkn89U0BixUgrQzc3Nt9122wMP\nPHD8XHWNjY1XXnnl9ddfH41Gi1IbRl8m03cDAIDRY5WaZszevC/hYpeCUlMyAXrv3r3Lli3b\ntm3b/PnzV65cOWfOnHg8LiItLS1btmx55plnbrzxxoceeuipp57qaowGAAAYRK0xe1nPGyNX\nMgH6hhtu2LVr14MPPnjJJZcc/6jv+/fee++11157yy233HXXXeNfHgAAKDm11uwjQGPkSuau\nu8cee+yKK67oNz2LiDHmmmuuufTSSx9++OFxLgwAAJSoWmP25AnQGLGSCdCHDx+eN2/e4Mcs\nXLhw//7941MPAAAodTWGEWiciJIJ0HV1dZs2bRr8mI0bN9bV1Y1PPQAAoNTVWnqgcSJKpgf6\n4osvXrt27dKlS6+77rpwuO/tsu3t7Xfcccejjz76la98ZUSnbW5uvuGGG3K53CDHbN68ecTl\nAgCACa/WmNYgaAtcQrOWCkagZAL0zTff/Nxzz335y1++9dZbzz333IaGhkQi4Zxra2vbvn37\nhg0bksnk8uXLv/71r4/otM651tbWVGqwlTyTyeTJ1Q4AACaiWmNEZJ/vn6pLJhFhIiiZH5fq\n6ur169fffffd999//9NPP+33eMPF87yzzz579erVq1evNmZkc6FPnTr1+9///uDH3HvvvS+/\n/PKJFA0AACawqUaHldrr+6d6JZOIMBGU0o9LKBRas2bNmjVr0un0zp07CysRVlZWNjY2hkKh\nYlcHAABKjBKZVVhLBRiJUgrQXSKRyPz584tdBQAAKHm1TMSBkSuZWTgAAABGHRNx4ARMngC9\nZcuWCy644IILLih2IQAAoGTU0sKBkSvJFo5+tba2PvHEE8WuAgAAlJIawwg0RmzyBOgFCxa8\n9tprxa4Co6drQpURzqwCAMDw1Vqzz/edCBNBY/gmT4CORCKLFy8udhUYPStWSGEJmxUril0K\nAGDSqjUm69wRP5hmJk9fK8Za6QVo59y2bdu2bt1amMauqqpq/vz5DQ0Nxa4Lo+3OO2XpUvF9\nWbWq2KUAACatWmtEZK/vE6AxfKUUoJubm2+77bYHHnjgwIEDfR5qbGy88sorr7/++mg0WpTa\nMPqslcsvL3YRAIBJLq5UhdZ7fX+xeMWuBSWjZAL03r17ly1btm3btvnz569cuXLOnDnxeFxE\nWlpatmzZ8swzz9x4440PPfTQU089NWXKlGIXCwAASgYTcWCkSiZA33DDDbt27XrwwQcvueSS\n4x/1ff/ee++99tprb7nllrvuumv8ywMAACWqcB9hsatAKSmZdp/HHnvsiiuu6Dc9i4gx5ppr\nrrn00ksffvjhcS4MAACUtFpmssMIlUyAPnz48Lx58wY/ZuHChfv37x+fegAAwORQQwsHRqhk\nAnRdXd2mTZsGP2bjxo11dXXjUw8AAJgcWM0bI1UyAfriiy/+8Y9//O1vfzuTyRz/aHt7+003\n3fToo49edtll418bAAAoXbXGHPL9nHPFLgQlo2RuIrz55pufe+65L3/5y7feeuu5557b0NCQ\nSCScc21tbdu3b9+wYUMymVy+fPnXv/71YlcKAABKSa0xgcgBP6i3rH2LYSmZAF1dXb1+/fq7\n7777/vvvf/rpp/0eb7V4nnf22WevXr169erVhmWfAQDASMwyWovs9X0CNIapZAK0iIRCoTVr\n1qxZsyadTu/cubOwEmFlZWVjY2MoFCp2dQAAoCR5Sk1jIg6MRCkF6C6RSGT+/PnFrgJjb/Nm\n8X1ZvLjYdQAAJjnWUsGIlMxNhCg7a9fKokWyZIncfnuxSwEATHKspYIRIUBjorrvvo6NdeuK\nWgcAYPJjLRWMCAEaE1XXfIX9TVwIAMAoooUDI0KABgAA5a6GtVQwEgRoAABQ7mqNaQmCdtZS\nwfAQoAEAQLmrNUZE9tHFgeEhQAMAgHI3zeiQUnRxYJgI0AAAoNwpkVlGE6AxTARoAAAAqTWW\niTgwTARoAAAAqbGatVQwTARoAAAAqTOWFg4MEwEaAABAaoymhQPDRIAGAACQWmv2+T4TQWM4\nCNAAAABSa2zGuSN+UOxCUAII0AAAAJ1rqdAGjWEgQAMAAEhCq4RmLRUMCwEaE5UxfTcAABhL\ntcZwHyGGgwCNiWrFir4bAACMpVpjaOHAcNhiFwAM4M47ZelS8X1ZtarYpQAAykKtNbRwYDgI\n0JiorJXLLy92EQCAMlJjzO+ymWJXgRJACwcAAIAILRwYNgI0AACAiEitNQd9P+9YTQVDIEAD\nAACIiNQY44scYC0VDIUADQAAICJSY4wS4T5CDIkADQAAICISUmqa0QRoDIkADQAA0KHWmH2s\npYKhEKABAAA61BqmgsbQCNAAAAAdalhLBcNAgAYAAOhQa8xeWjgwFAI0JrDNm+X114tdBACg\njNDCgeEgQGOiWrtWFi2SJUvk9tuLXQoAoFzUWnMsCJKspYJBEaAxUd13X8fGunVFrQMAUEZq\njRERJuLA4AjQmKgymb4bAACMsWnGeErRxYHBEaABAAA6aJFZRu8jQGNQBGgAAIBuTMSBIRGg\nAQAAujERB4ZEgAYAAOhWy1oqGAoBGgAAoFsNLRwYCgEaAACgW60x+3yfiaAxCAI0AABAt1pr\n0s4dDYJiF4KJiwANAADQrbCWCl0cGAQBGgAAoFuF1gnNWioYDAEaAACgl1nMZIdBEaABAAB6\nqTNmHy0cGBgBGgAAoJcaRqAxKAI0AABAL6ylgsERoDFRGdN3AwCAcVHLWioYFAEaE9WKFX03\nAAAYFzXGHPQZgsaAbLELAAZw552ydKn4vqxaVexSAADlpc4aX+SA79fyLij6Q4DGRGWtXH55\nsYsAAJSjGmOUyN48ARr9o4UDAACgl5BSU7XmPkIMhAANAADQV601+wjQGAABGgAAoK8aJuLA\nwAjQAAAAfdUxFTQGRoAGAADoi8UIMQgCNAAAQF81xuyjhQMDIEADAAD0VWdNcxCknSt2IZiI\nCNAAAAB91RgjInRxoF8EaAAAgL5mGOMpRRcH+kWAxgS2ebO8/nqxiwAAlCMtMtPoPYxAoz8E\naExUa9fKokWyZIncfnuxSwEAlKMaw1oq6B8BGhPVffd1bKxbV9Q6AABlqo61VDAAAjQmqkym\n7wYAAOOohrVUMAACNAAAQD9qaeHAAAjQAAAA/ag1Zg8tHOgPARoAAKAfNdaknTsaBMUuBBMO\nARoAAKAfdcaICF0cOB4BGgAAoB+VWseVoosDxyNAAwAA9K/Gch8h+kGABgAA6F+tYSY79IMA\nDQAA0L8a1lJBfwjQAAAA/aulhQP9IUADAAD0j6mg0S8CNAAAQP9qjTngMwSNvgjQAAAA/au1\nxhc5SIRGbwRoAACA/tUYo0S4jxB9EKAxURnTdwMAgPEVVmqK1txHiD4I0JioVqzouwEAwLir\ntWYPARq92WIXAAzgzjtl6VLxfVm1qtilAADKV40x+2jhQG8EaExU1srllxe7CABAuauzzGSH\nvmjhAAAAGFANq3njOARoAACAAdXSwoHjEKABAAAGVGPMkSBIO1fsQjCBEKABAAAGVGuNiDCT\nHXoiQAMAAAxohjFWKbo40BMBGgAAYEBGZIbWTAWNngjQAAAAg6mzhhYO9ESABgAAGEytYSpo\n9EKABgAAGEydNbsZgUYPBGhMYJs3y+uvF7sIAEC5qzeWEWj0RIDGRLV2rSxaJEuWyO23F7sU\nAEBZq7dmj88QNLoRoDFR3Xdfx8a6dUWtAwBQ7mZbk3fuIBEanQjQmKgymb4bAAAUQ50xWmQX\nXRzoRIAGAAAYjKfUDGN25/PFLgQTBQEaAABgCLOt2UULBzoRoAEAAIZQz1TQ6IEADQAAMIR6\na+mBRhcCNAAAwBDqrdnt0wONDgRoAACAIdQbsy9PEzQ6EKABAACGUG+tL7KPLg6ICAEaAABg\nSLVGG5FddHFARAjQAAAAQ7JKzTRmNyPQEBECNAAAwHDUWwI0OhCgAQAAhjbb2t3cRggRIUAD\nAAAMR70xu1jNGyJCgAYAABgOWjjQhQCNicqYvhsAABRPvTUHfD/nXLELQfERoDFRrVjRdwMA\ngOKZbWwgspc2aIjYYhcADODOO2XpUvF9WbWq2KUAACCzrLFK7c77jZb4VO74CcBEZa1cfnmx\niwAAoIMRqTGaiTggtHAAAAAMU72x3EcIIUADAAAM02xrdjOTHQjQAAAAw1RvzS5aOECABgAA\nGCZaOFBAgAYAABiWemsO+n6GqaDLHgEaAABgWOqtcUwFDQI0AADAMM00JqTULro4yh4BGgAA\nYFi0SI1hIg4QoAEAAIat3hrWUgEBGhPY5s3y+uvFLgIAgG6zjWEiDhCgMVGtXSuLFsmSJXL7\n7cUuBQCADnXW0AMNAjQmqvvu69hYt66odQAA0G22tbt9eqDLHQEaE1Um03cDAIBiqzfmiB+k\nmQq6vBGgAQAAhmu2NU6ENugyR4AGAAAYrunGhJWii6PMEaABAACGS4nUMRFH2SNAAwAAjEC9\nJUCXOwI0AADACMy2lrVUyhwBGgAAYATqWM277BGgAQAARmA2a6mUPQI0AADACNRb0xwE7UwF\nXcYI0AAAACNQb6yI7GEQuowRoAEAAEZgmtFRpXbRBl3GCNAAAAAjU2cNE3GUMwI0AADAyNQb\ny1TQ5YwADQAAMDKzLTPZlTUCNCYqY/puAAAwMdDCUeYI0JioVqzouwEAwMQw2zAVdFmzxS4A\nGMCdd8rSpeL7smpVsUsBAKCXemtbgqA1CCo0Y5HliACNicpaufzyYhcBAEA/6q0Rkd2+v4AA\nXZYI0ADKVJAOXDoY0VN0TKsQfywxNOe7oNV3ucBv8102CJKBywZB0hcR/1jeOXEpP0gHEojf\nkhcRv913ucDlXNDum0orWnRE64gRJabKioiOGRXWyoipsCKiE1ZZZaqsCimTsDpulKeK+ymX\nmylax5XanfcXeF6xa0EREKCB8uDEPzbEDeP+0Vz/C9MO/FyXC4L2AbsAC0Ghn/3NueN39omz\nQToI0t1ndpkgSPV4tN132Y4Pg2wQJDsf8p3f2llqZzQRkSDVfTb/6JjcOK9CWsf6ydY6rHWs\n742wytM63utgZZVO9PqFrKNah3scY1UhORWYKiuq60jTdaQKqa6XK0SujuMrjDJKRESJqer4\ne2+qbccL9Qhq5cPlXdDmi4jfkne+K8Rcca7w0+63+s53QWve5V3Q7rucK2TcoM3v2JMNgqQf\nZAuPBn6LL4Hzj+Zd4Ab5t6YjWkW00qojFseN8pTytI4bETGVVmnJH8z6nYVJ4Lr+aeSbcyIS\npAKX6e/CTytTaXTU6Ig2VVaFtY4ZU2FUWHszQl5N2KsJ2VlhrzbkzQjZGaGx+JKWm3rLTHbl\nq7x+XU40fpu/60u/K4xJlK0gHQQjHAUcCy7ngvZRzlWFP7Qn9ly/1Xf54X5ZTuaFxoLyVCEN\nHM9UWaWPGyc7LrrpuO05nKbjRvf8MGF03EjciIgOaxXtzI5WmR4ZtJAORUT1iLCFgCIdefcE\nJ3jpGkrsV76/gN4z8XfvPC4J+a155/f4Vva4BpDCoGbnh35zzm/Ju85nu5QfdJ6q56WI3+a7\nXOf2sbwM48dEx4wKqT4Jz1R5yipTYVRE66gxCaM8XRj+1DGj40aFtKmyqsf31lT3Gpbr+nb0\n+nx7fK2C9rzLddQXZF3XV9ilgyDVefHTkpdARMTlAr/zyq3r57/ri+x37en8ehZeyDnxj+ZE\npDAePMgXQVmlE0ZZbSpMIZgqo3SFVUZ17KmyUmFCTVGllam0YpVJGBXSOm50WOuo1lGjwlon\njLLKVFpllKk0cvwP/4kqjHAHKT9IB/6xvMsEQdL3W32XDfyWfOFHK3805zJB0O5ntqfaXzyW\n3ZPJH8wVPnEV0naGF6oN25khrzbszQp5M8NebTjUEPZmR+xUhlSHpd6a3T4z2ZUpAnQxKSWm\n0qrwJHlHWEf1xP9cdMzosXkLXvUZLxzp0z2tEyPIc2rY44V9cszxCn/jB6iqVyTt9axS+Haj\nX4XsJYXB+/aOpgJxEmR8lwqk8xogSPouE3QEtbQfpIOgxXf5wG/O5fZngmQQJH2XDfyjeZfv\nGPgPWv1eFwAnRIW17rwo0iHddTHW9YNayLIdO2O68C+6EF4lbnS65UvtAAAgAElEQVRYh6Ja\nRHTE6IiWHo03OmGUpztCsEghEKuw0lEjInaKJ6Xzg62MMtW238uSweUPZXMHsrl92fz+bG5f\nJrcvkzuQTf+2PX8wl92dLvw86LgJNUQ6/psdCTVEQo2R0OyIVxemUaSn2dYwAl22CNDFpONm\n9v/7rmJXAaC8FLKXiIz1FOt+my893hvx27rHmJXqdWk3yFUcRpedHrLTQ9FF/T+ab87ldmWy\nO9PZHansrkx2Z/rYG4eyO9K5/VkJnGjl1YTCjZHwvFj0jIrokkTsjIoTCPGTRp0xL6azxa4C\nxVG+P/cAgDFler+pUs5Jq1TYKZ6d4kWXJPrsd9kguzuT253O7khndqQzv08e/v6e9FvtLu9C\njZFCko4uSUSXVITnRqVsLoVmW7uTxQjLFb/OAADAYFRIh5ui4aZoz51BOkhvbk9uak291tr6\nTPOB/7XTb82bSltI0rElieiZFdHFiY67VyejemPanTsWBFXMZFd+CNAAAGDEdETHzqqInVXR\n8bGTzDup1G9aU6+1JX/Teuyxg9mdaTvFq/jQ1KoLp1eumGqnT7apPzqmgs77VcxuWX4I0AAA\n4KQpKYxSV//JzMKO/KFsyxNHjv300K6vvJX/fD7+norKD0+vunBa7KyKUZyQpIgqta7Qerfv\nLxLmLSk7BGhMYJs3i+/L4sXFrgMAMGJ2emjqZTVTL6uRwCU3tbU+deTY4wf33r7VTvUq/mBK\n1UXTq1bOKPXO+HpjdtEGXZZ40wET1dq1smiRLFkit99e7FIAACdBq9hZFbO+OOdd/3XOkt+/\nv/5vT3WB7PzSW7+Z++xbH355353vpN5sK3aJJ6iemezKFQEaE9V993VsrFtX1DoAAKPGqwlP\n+4u6U/55yRk7/uDUfz8rfm7VkR/t23zurzef++t9d76T3ZkudoEjU2/Nbp8AXY5K+60TTGaZ\nTN8NAMBkoTxV8QdTKv5gSv03Ts3uSDf/6/5D9+/Zc9OW2FkVU1fVTr10VkncdFhv7Po0f6TK\nESPQAACgmEKNkVlfnHP6q+9b9OJ5FX80df+d77z2rl9uuWTTkR/sDdon9PjubGt20cJRlgjQ\nAABgQogsjNffeurit94//7GzvNrwzi/+7rX5z79z1RvHHj/k8ie7SvxYqLcm5dyRICh2IRh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lhveOcNEdPXr0Qx/60CuvvFJRUTHIUt6P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\nUwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(123)\n",
    "cv_lambda_LASSO <- cv.glmnet(\n",
    "  x = as.matrix(expectancy_train[,-c(1,2)]), y = as.matrix(expectancy_train[,2]),\n",
    "  alpha = 1,\n",
    "  lambda = exp(seq(-8, 3, 0.2)),\n",
    "  family = 'poisson'\n",
    ")\n",
    "lambda_min_MSE_LASSO <- round(cv_lambda_LASSO$lambda.min, 5)\n",
    "cat(\"Figure 6\\n\")\n",
    "plot(cv_lambda_LASSO, main = \"Lambda selection by CV with LASSO\\n\\n\")\n",
    "plot(cv_lambda_LASSO$glmnet.fit, \"lambda\")\n",
    "cat(\"Figure 7\")\n",
    "abline(v = log(lambda_min_MSE_LASSO), col = \"red\", lwd = 3, lty = 2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00136"
      ],
      "text/latex": [
       "0.00136"
      ],
      "text/markdown": [
       "0.00136"
      ],
      "text/plain": [
       "[1] 0.00136"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_min_MSE_LASSO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The smallest lambda we found from LASSO is 0.00136."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Ridge Model Selection\n",
    "We will also be using ridge as a model selection method. Below, we perform ridge and find the smallest lambda for our models. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 8"
     ]
    },
    {
     "data": {
      "image/png": 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KABAAAAB9BAAwAAAA6ggQYAAAAc4KV1Aa7hwIEDZWVlWlcBAACgI15eXu3bt9e6\nCjtooKu3e/furl27al0FAACA7uzatatLly5aV2GNBrp6JpNJCFFSUuLt7a11LQAAALpgMpl8\nfHyUNkw2rIEGINLS0rQuAb8ymUxHjx7VugoAQKVooAG9u3DhQvv27U+dOqV1IbgpJSVl4MCB\nWlcBAKgUDTSgdx4eHup/IQMPDw/eDgCQGWugAb0LCwvLyMiIjIzUuhDclJSURHAZAGTGSQ4A\n4o477tC6BPzKy8uLv2cAQGY00AAIEcqFECEASM6tGuirV68ShAIcRYhQNoQIAUByrtRAp6Wl\nDRkyJCoqqmfPngsXLiwvL7c64K233oqOjtakNsB1ESKUDSFCAJCcy4QIt2zZ0r9//5KSEj8/\nv19++eXnn39eunTpihUrQkJCtC4NcG2ECGVDiBAAJOcyJzlmzZpVUVGxYsWKgoKC/Pz8f/zj\nH1u3bk1MTLxx44bWpQEujxChVAgRAoDkXKaBTktLGzVq1PDhww0Gg4+Pz+TJk7///vsDBw48\n/PDDtms5ADiEEKFUCBECgORcpoG+cOGC1Umyfv36LVq06Lvvvvvzn/+sVVWAGyBEKBtChAAg\nOZdZA924ceP9+/dbDY4ZM+bIkSOzZs1q1qzZtGnTNCkMcHWECGVDiBAAJOcyDfSIESPee++9\n+fPn/+EPfzAajer4m2+++csvvzz//PO//PILazmAW0CIUDaECAFAcgaz2ax1DTWSm5vbqVOn\n7OzsAQMG/PTTT5Z3mc3mP/3pT++++676Ze1OvXXr1h49epSUlHh7e9fuMwMAAMAuk8nk4+Oz\nZcuW7t27a12LNZf5lLBhw4Z79ux55pln4uPjre4yGAzz5s1LTk6OiYnRpDbA1REilAohQgCQ\nnMucgdYQZ6Dh3i5cuBAREZGVlRUVFaV1LRBCiGXLlk2ZMiU7O1vrQgBAS5yBBiAvQoSyIUQI\nAJJzmRAhgDpCiFA2hAgBQHLuc5IjIyNjwIABAwYMcOhRmZmZ3t7ehir16NFDCFFWVlY3hQPa\nYydCqbATIQBIzn3OQOfn569bt87RR0VHR69fv764uLiKY1atWjVv3ryKiorbqA6QWlpaWkJC\ngtZV4CaTyZSZmRkbG6t1IQAA+9yngY6NjT148KCjjzIYDL/73e+qPiYjI+NWiwJcgLITISFC\neaSkpBAiBACZuU8D7evra3uFOwDVIkQoG0KEACA5t/odnZube/LkSa2rAFwMIUKxYCsAACAA\nSURBVELZJCUlpaamal0FAKBSbtVAz549u1WrVlpXAbgeQoRSIUQIAJJznyUcAG4ZIUKpECIE\nIKesrKz09HTb8aKiIl9fX4PBYDUeHR3dpk0bp5TmbDTQgN4RIpQNIUIAcgoNDY2Li7MaLCsr\n279/f1RUlJ+fn9VdDRo0cFZpzuYyDXSXLl2qPebcuXNOqARwM4QIZUOIEICcAgICAgICrAZN\nJtP+/fubNWsWHBysSVWacJkGet++fUIIo9FYxTHsdQLcAkKEsmEnQgCQnMuc5Jg2bZq/v/+h\nQ4eKKzd16lStywRcEiFCqRAiBADJuUwDPXPmzJYtW44ePbq0tFTrWgB3k5aWpnUJ+JXJZDp6\n9KjWVQAAKuUySziMRuPnn3/euXPnF198cfbs2VqXA7gPQoSyIUQIQCtHjhzJy8uzGiwrKyss\nLAwKCrI9vk2bNvXq1XNKaXJxmQZaCBEXF3fhwoUqFjoPGjRIVwvYgVpBiFA2hAgBaMVoNNrm\nzUpKSgoKCho2bGg1bjAYdPvLypUaaCGE3b9+VL179+7du7fTigHcAyFC2RAiBKCVli1b2g6e\nPn06Pz+/suuhmUymOi5KRjr9uwGAJUKEUiFECACSo4EGQIhQLoQIAUByNNCA3ikhwlOnTmld\nCG5KSUkZOHCg1lUAACpFAw3oHSFC2RAiBADJuViIEECtI0QoG0KEACA5GmgAhAjlQogQQB2p\nqKjIyMgoLy+3Gi8sLDQYDLZXdPby8oqJiXFWda6EBhqASEtLS0hI0LoK3GQymTIzM2NjY7Uu\nBIC7KS8vP3v2rO2WGjdu3DAYDH5+flbjRqMxOjraWdW5EhpoQO/YiVA27EQIoI4Yjca+ffva\njm/fvt3Ly6uyKz3DFjkVQO8IEcqGECEASI4z0IDeESKUDSFCAJAcJzkAECKUCyFCAJAcDTQA\ndiKUCzsRAoDkaKABvWMnQtmwEyEASI4GGtA7QoSyIUQIAJIjRAjoHSFC2RAiBADJcZIDACFC\nuRAiBADJcQYaADsRyoWdCAHcssuXL6enp5vNZqvx/Px8Pz8/T09Pq/HQ0NA2bdo4qzr3QQMN\n6B07EcqGnQgB3DIfH5/g4GDb8ZycnJCQkMDAQKvxgIAAp9TlbmigAb0jRCgbQoQAbllgYKDd\nTxQzMjKioqKaNm3q/JLcEr+jAb0jRCibpKSk1NRUrasAgJq5di341CnD1ata1+FUNNAACBHK\nhRAhANdQVib++EfvJk0G/uUv9WNixJgxIj9f65qchAYaADsRyoWdCAG4hldfFe+9J8rKhBDC\nbBaffSb++Eeta3ISGmhA79iJUDbsRAjANSxebD3yxReipESDSpyOBhrQO0KEsiFECMAFmEzi\n/Hk7g7/8okU1zsbvaEDvCBHKhhAhABfg7S1atrQeDAgQLVpoUY2z0UADIEQoF0KEAKTikZcX\ncO6cKC21vuOll6xHXnxR6OMDNF18kwCqRohQKoQIAcji7FkxeHDzDh36Pv20CAsTCxf+5t4x\nY8Rnn5nj4yuMxoqWLcV774m//EWjQp2NBhrQO0KEsiFECEAK5eVi1CixZs3NL/PyxMSJYsWK\n3xzz2GOle/Z8/dln13ftEpMm6eT0s6CBBkCIUDaECAFIIT1dbN1qPbhokRalSIetvAG9I0Qo\nm6SkpK5du2pdBQDdy8y0M5iV5fQ6ZEQDDYAQoVwIEQKowokTJ36xuVRcRUVFQUFBUFCQ7fF3\n3nlnRETErczUpo2dwbi4W3kqt0MDDUCkpaUlJCRoXQVuMplMmZmZsbGxWhcCQEb+/v4hISFW\ng0VFRTk5OZGRkQaDweouX1/fW5ypVSvx4IMiOfnXEaNRTJ16i8/mXmigAb1TQoRZWVlRUVFa\n1wIhhEhJSZkyZUp2drbWhQCQUZMmTZo0aWI1ePny5dOnT7dr166WExT/+Y+IjKz45BPDtWuG\nDh3E3/4m7rmnNp/fZZFTAfSOEKFsCBECcKryct+zZ33OnhUVFdZ3BQaKf/zjzN69q5OTxe7d\nggsE/Q9noAG9I0QoG0KEAJznp5/EU091UK5k2qqVWLRI9Ople5SZv+p/i5cDACFCuRAiBOAk\nGRlixAih7gNw4oQYPlycPatlSS6CBhoAOxHKhZ0IATjJsmWioOA3I1evipUrNarGldBAA3rH\nToSyYSdCAE5i9zc//zuoARpoQO8IEcqGECEAJ7F7pWe7g/gtfkcDekeIUDZJSUmpqalaVwFA\nB8aMEVa//Fu1Eg8/rFE1roQGGgAhQrkQIgTgJCEhYv168cAD5QEB5UFBYtQosXatCAjQuiwX\nwGXsALAToVzYiRCA88TEiOXLd23f7uXl1aVLF62rcRmcgQb0jhChbAgRAoDkaKABvSNEKBtC\nhAAgOZZwAHpHiFA27EQIoDZdvizmzr3n++8D77xTPPOM+N3vtC7IHdBAAyBEKBdChABqzdmz\nolMnkZMTLoTYs0f897/igw/EH/6gdVkuj08JAbAToVzYiRBArZk+XeTk/GZk8mSRn69RNe6D\nBhrQO0KEsiFECKDWbN9uPVJUJA4c0KIUt8ISDkDvCBHKhhAhoHM7duwoLi62GjSZTGVlZX5+\nflbjnp6eVV1+zt/fziBXer5tNNCA3hEilA0hQkDngoODS0pKrAZzcnIqKipCQkKsxg0Gg6en\nZ6XPdd991uebmzcXbdvWTqE6RgMNgBChXAgRAjrXunVr28FDhw7l5uY6vOnVq6+KnTvFhg03\nvwwNFf/9rzAab7tGveNTQgCECOVCiBBArfH1FevWiZ9+Ovj441fffVccOyZ69NC6JndAAw3o\nHSFC2RAiBFCbDAYxYMDJYcMKR4wQNitAcGtooAG9I0QoG0KEACA51kADekeIUDaECAHI6eLF\ni2fOnLEarKioEEKkp6d7e3tb3dW4cePmzZs7qTjn4iQHAEKEciFECMCFeHh4BAcHe3np65ys\nvr5bAHalpaU5nOxGnTGZTJmZmbGxsVoXAgC/0bhx48aNG2tdhRQ4Aw3oHSFC2RAiBOCwigpv\nNuh2IhpoQO8IEcqGECEABxQVialTG0ZHDx8/3iMiQsyfr3VBusASDkDvCBHKhhAhAAf8+c/i\ngw8Myu1Ll8SzzwpfXzF+vLZFuT0aaACECOVCiBBATRUWio8+sh58991bbqAPHDiQl5dnNVhc\nXFxSUrJp0ybb49u1a9egQYNbm8ul0UADIEQoF0KEAGoqI0OUl1sPHj8uzGZhMNzC84WEhBhs\nHlhWVubv7x8UFGQ1bjAYfH19b2EWN0ADDeidEiLMysqKiorSuhYIIURKSsqUKVOys7O1LgSA\n9O64Q3h6WvfQrVrdWvcshIiMjOQTsJogpwLoHSFC2RAiBFBT/v5i3DjrwWef1aIUfeEMNKB3\nhAhlQ4gQgAPmzhV+fuYPPjCUlIiGDcVf/yqeekrrmtwfJzkAECKUCyFCAA7w8xNz5+aePv3N\nv/5VcemSmDxZ64J0gQYagEhLS9O6BPzKZDIdPXpU6yoAuBRPz+L69bUuQkdooAG9YydC2bAT\nIQBIjjXQgN4RIpQNIUIAdaSkpGT16tVlZWV2783MzLQaMRqNQ4cO9fKiXbTGKwLoHSFC2RAi\nBFBHfHx8evXqVW5z6WiTyWQwGIxGo9W4l5cX3bNdvCgACBHKhRAhgLrTqFEjrUtwBzTQANiJ\nUC7sRAi4t7y8vK1bt5rNZqvxkpISLy8vT09Pq/GAgIDevXs7qzrUCA00oHfsRCgbdiIE3Ftg\nYGBCQoJtA52WlhYaGhoREWE1rtvtsmVGAw3oHSFC2RAiBNybp6dns2bNbMePHj0aHBzcvHlz\n55cER9FAA3pHiFA2hAgBQHI00AAIEcqFECEAa/v3hy5eHHTliigpEVwnXgJ8SgiAnQjlwk6E\nAH5jzhzRpUvjefMilywRiYnikUeEzfppOBkNNKB37EQoG3YiBPCr9HTxwgvC8srNX30llizR\nriAIwRIOAIQIZUOIEMCvUlOF7caB69eLsWPtHn7p0qW0tDTbS3yUlZUdOHAgPT3dajw0NLRD\nhw61VKuO0EADekeIUDaECAH8yu6225XsxS2ECAgIsHuJj6CgoICAANuLTNevX//26tMpGmgA\nhAjlQogQwK969LAz2LNnZYf7+fmxDZMT8CkhAEKEciFECOBXHTuKF174zUj//mL8eI2qwU00\n0IDeESKUDSFCAL8xa5ZYuzb3978/P3SoWLJE/PijsFmJASdjCQegd4QIZUOIEIC1/v3PN26c\nm5sb0bu31qVACBpoAIQIZUOIEAAkx0kOAIQI5UKIEAAkRwMNgBChXAgRAoDkaKABvSNEKBtC\nhAAgORpoQO8IEcqGECEASI4QIaB3hAhlQ4gQACTHSQ4AhAjlQogQACTHGWgAIi0tLSEhQesq\ncJPJZMrMzGQzXgB2nT9/Picnx2qwqKhICHHw4EGDwWB1V2RkZHBwsJOK0w0aaEDvlBBhVlZW\nVFSU1rVACCFSUlKmTJmSnZ2tdSEAZJSfn3/16lWrwYqKinr16uXl5dkeHxoaSgNd62igAb0j\nRCgbQoQAqnDnnXfeeeedWlehdzTQgN4RIpQNIUIAkBwnOQAQIpQLIUIAkBwNNAB2IpQLOxEC\ngORooAG9YydC2bATIaBH2dlhW7b4bdsmbtzQuhRUjwYa0DtChLIhRAjozksviZiY9q+91uzx\nx0Xr1mLTJq0LQjUIEQJ6R4hQNoQIAVd3+fLlX375xXb8ypUrISEhVpdqDv7xx8g33/z163Pn\nxKhR4sgRERJS13XiltFAAyBEKBdChICrKyoqsnup5pycnIqKCk9PT8vxiDVrrB9/8aLYskXc\nf3+dFonbQQMNgJ0I5cJOhICra968efPmza0Gi4uLv/nmm65duwYGBlb/FJcu1UllqCUsswP0\njhChbAgRAvrSsaOdwU6dnF4HHEADDegdIULZECIE9OX550V4+G9GxowRHTpoVA1qhCUcgN4R\nIpQNIUJAX8LCxO7dYubM/LVrvRo2rPfYY+KZZ7SuCdWggQZAiFAuhAgB3WnaVHzwwfaffmrR\nosWdd96pdTWoHp8SAmAnQrmwEyEASI4GGtA7QoSyIUQIAJJzvSUcZrM5KysrMzMzPz9fCFG/\nfv1WrVrZXiwGQA0RIpQNIUJA57KyskpKSqwGc3Nzb9y4YfvxlIeHR0xMjNW1pVHXXKmBvnr1\n6ptvvrlkyZJLNhdHjIyMHD9+/NSpU+vVq6dJbYDrIkQoG0KEgM6dPXu2uLjYarC0tLS8vPzM\nmTNW4x4eHs2aNfPz83NWdRDChRro8+fP9+jRIysrq1WrVoMHD27RooW/v78Q4vr16xkZGZs2\nbXrllVeSk5M3bNgQwtaXgIMIEUqFECGgcz179tS6BFTDZRrol19++ezZs0uXLh05cqTtveXl\n5R9++OGkSZNee+21uXPnOr88wKWxE6FU2IkQACTnMsvsVq9ePWbMGLvdsxDC09PzmWeeefjh\nh5cvX+7kwgBXR4hQNoQIAUByLtNA5+bmxsTEVH1MXFzcxYsXnVMP4DYIEcqGECEASM5llnA0\nadLkwIEDVR+zb9++Jk2aOKcewG0QIpQNIUIAkJzLnOQYPnz4smXL3nnnHdsLuwghbty4MWPG\njJSUlFGjRjm/NsDVESKUCiFCAJCcy5yBfvXVVzdv3jxt2rTXX3/9rrvuat68eUBAgNlsLigo\nOH369M6dOwsLC3v27PnSSy9pXSngeggRSoUQIQBIzmUa6ODg4G3bti1YsODTTz/duHFjeXm5\nepfRaOzcufO4cePGjRvHhcQBRykhwqysrKioKK1rgRBCpKSkTJkyJTs7W+tCAAD2uUwDLYTw\n9vaePHny5MmTi4uLz5w5o+xEGBQUFBkZ6e3trXV1gKsiRCgbQoQAIDlXaqBVvr6+rVq10roK\nwE0QIpQNIUIAkBwnOQAQIpQLIUIAkJz7NNAZGRkDBgwYMGCAQ4/KzMz09vY2VGnChAlCCLPZ\nXDeFA9pLS0vTugT8ymQyHT16VOsqAACVcsklHHbl5+evW7fO0UdFR0dv2LChqKioimNWrVo1\nb948g8FwG9UB8iJEKBtChAAgOfdpoGNjYw8ePOjoowwGQ48ePao+JiMj41aLAlwAIULZECIE\nAMm5TwPt6+sbHx+vdRWA6yFEKBtChAAgObc6yZGbm3vy5EmtqwBcDyFCqRAiBNzQ4cPGp5/u\n++qrvhMmiD17tK4Gt8utGujZs2dzeTvgFhAilAohQsDdbN4sOnb0XLw49MgR4xdfiG7dxOrV\nWteE2+JWDTSAW6CECE+dOqV1IbgpJSVl4MCBWlcBoPb88Y+itPTXL8vLxaRJ2lWDWkADDegd\nIULZECIE3EpRkbC9yMGpU+LSJS2qQe1wmRBhly5dqj3m3LlzTqgEcDOECGVDiBBwKz4+ol49\nUVDwm0EvLxEQoFFBqAUu00Dv27dPCGE0Gqs4pqyszFnlAG6FEKFUCBECbsXDQwwaJJYtsxy7\n3K7djg0brA4sKipKT08/ceKE1XhgYGCvXr3qtkg4yGUa6GnTpi1cuHDv3r0tW7as7JgXXnjh\nrbfecmZVgHtIS0tLSEjQugrcZDKZMjMzY2NjtS4EQC1ZsEBkZqoX3zC3bVs0f35ceLjVUTdu\n3PDx8fHysu7N6tWr54wi4QiXaaBnzpz5448/jh49euvWrVWfhwbgEHYilA07EQLuJjRU7Nxp\n+v77Q8uXxw0ZUm/o0OY2XTJci8u8f0aj8fPPP+/cufOLL744e/ZsrcsB3AchQtkQIgTkZzKZ\nSi0vrCGEEMJsNpeXl9ueQhZC+Pn5VfTrd7KgoNWAAYLu2fW50lsYFxd34cKFKhY6Dxo0KDg4\n2JklAW6AEKFsCBEC8tu0adPVq1drfnzPnj1DQkLqrh44mSs10EKIoKCgKu7t3bt37969nVYM\n4DYIEUqFECEgvz59+phMJqvBM2fOnDx5sm/fvlbjBoPBz8+vuLjYWdWhzrlYAw2gLhAilAoh\nQkB+RqPRNpHl4+NjMBj8/f01KQnOxDI7QO/YiVA27EQIAJKjgQb0jhChbAgRAoDkWMIB6B0h\nQtkQIgQAyXGSAwAhQrkQIgQAydFAAxBpaWlal4BfmUymo0ePal0FAKBSNNCA3hEilA0hQgCQ\nHA00oHeECGVDiBAAJEeIENA7QoSyIUQIAJLjJAcAQoRyIUQIAJKjgQZAiFAuhAgBQHI00IDe\nESKUDSFCAJAcDTSgd4QIZUOIEAAkR4gQ0DtChLIhRAgAkuMkBwBChHIhRAgAkqOBBkCIUC6E\nCAFAcjTQgN4RIpQNIUIAkBwNNKB3hAhlQ4gQACRHiBDQO0KEsiFECACS4yQHAEKEciFECACS\no4EGQIhQLoQIATdgslFaWiqEKC0ttb3LbDZrXS8cwxIOQO+UEGFWVlZUVJTWtUAIIVJSUqZM\nmZKdna11IQBu0aFDh9LT0+3etXbtWtvBVq1adezYsY6LQm2igQb0jhChbAgRAi6ppMR3+/bw\nw4dFmzaxsbFNmza1d0iJj4+P7XhAQEDd14faRAMN6B0hQtkQIgRcz+7dYtSoiMzMCCHErFle\nzz4b8s9/CoNB67JQVzjJAYAQoVwIEQIupqhIjBwpMjNvfllRIebNE4sWaVoT6hYNNABChHIh\nRAi4mD17hO1eVMuXa1AJnIUGGtA7diKUDTsRAi7m0qWaDsJd0EADekeIUDaECAEXY/cCGlxV\nw63xOxrQO0KEsklKSkpNTdW6CgA1Fh0tJk36zUhwsHj5ZY2qgTPQQAMgRCgXQoSA65k3T3z4\nYfE99+RHRYknnhB794oWLbSuCXWIBhoAIUK5ECIEXI+Hh3jqqfOff546f774979FdLTWBaFu\n0UADekeIUDaECAFAcjTQgN4RIpQNIUIAkBw7EQJ6R4hQNuxECACS4yQHAEKEciFECACSo4EG\nQIhQLoQIAUByNNCA3hEilA0hQgCQHA00oHeECGVDiBAAJEeIENA7QoSyIUQIaK6srGzv3r3l\n5eVW44WFhR4eHr6+vlbjRqOxc+fOzqoO2qOBBkCIUC6ECAEZGI1G28+CiouLPT09AwMDbQ92\nVl2QAg00AJGWlpaQkKB1FbjJZDJlZmbGxsZqXQigX15eXh07drQd37p1q6+vb6dOnZxfEqTC\nMjtA7wgRyoYQIQBIjgYa0DtChLIhRAgAkmMJB6B3hAhlQ4gQACTHSQ4AhAjlQogQACRHAw2A\nnQjlwk6EACA5GmhA7wgRyoYQIQBIjgYa0DtChLIhRAgAkiNECOgdIULZECIEAMlxkgMAIUK5\nECIEAMnRQAMgRCgXQoQAIDkaaEDvCBHKhhAhAEiOBhrQO0KEsiFECACSI0QI6B0hQtkQIgTk\nd/z48evXr1sN5ufnl5SU7N6922rcYDC0bt06ICDAWdWhztFAAyBEKBdChID8ysrKSktLrQY9\nPT0DAgJsxw0Gg9lsdlZpcAYaaAAiLS0tISFB6ypwk8lkyszMjI2N1boQAJVq06aN1iVASyyz\nA/SOEKFsCBECgORooAG9I0QoG0KEACA5lnAAekeIUDaECAFAcpzkAECIUC6ECAFAcjTQANiJ\nUC7sRAgAkqOBBvSOEKFsCBEC0jJUVAguSAcaaACECGVDiBCQUXq6uO++bv37d+jZU4wYITjp\noG+ECAG9I0QoG0KEgHQuXRL9+4sLF27+abtihTh0SOzdK9hcUK84yQGAEKFcCBEC0vnkE3Hh\nwm9GTpwQy5drVA20RwMNgBChXAgRAtJJT7czeOSI0+uALGigAb0jRCgbQoSAdOx+TMdndzpG\nAw3oHSFC2RAiBKQzerT1cufGjUVSkkbVQHv8jgb0jhChbJKSklJTU7WuAoCFli3FypUiJubm\nlwkJ4ttvRViYpjVBS1yFAwAhQrkQIgRk1L+/OHlyz/Ll3v7+7RITta4GGuMMNABChHIhRAhI\nqyQ8vDQ0VOsqoD0aaEDvCBHKhhAhAEiOBhrQO0KEsiFECACSYw00oHeECGXDToQAIDlOcgAg\nRCgXQoQAIDkaaACECOVCiBAAJEcDDegdIULZECIEAMnRQAN6R4hQNoQIAUByhAgBvSNEKBtC\nhAAgOU5yACBEKBdChAAgORpoAIQI5UKIEAAkRwMN6B0hQtkQIgQAydFAA3pHiFA2hAgBQHKE\nCAG9I0QoG0KEACA5GmgAhAjlQogQcIJr166dPHnSbDbbjgcEBHh6elqNh4aGtmjRwlnVQXZ8\nSgiAEKFcCBECTlBaWmoymUptXLlypbCw0Ha8pKRE65IhEc5AA3qnhAizsrKioqK0rgVCCJGS\nkjJlypTs7GytCwHcWaNGjRo1amQ7npycHBsbGxER4fyS4EI4Aw3oHSFC2RAiBADJcQYa0DtC\nhLIhRAgAkuMkBwBChHIhRAgAkqOBBkCIUC6ECAFAcizhAPSOEKFsCBECmquoqMjIyCgvL7ca\nz8/PLyoqsv0T12g0xsTEOKs6aI8GGtA7QoSyIUQIaK6srOzs2bNlZWVW46WlpWVlZWfOnLEa\n9/b2jo6O5l+uftBAA3pHiFA2hAgBzXl7e/ft21frKiAv/lQCQIhQLoQIAUByNNAACBHKhRAh\nAEiOBhrQOyVEeOrUKa0LwU0pKSkDBw7UugoAQKVooAG9I0QoG0KEACA5QoSA3hEilA0hQgCQ\nHCc5ABAilAshQgCQHA00AEKEciFECACSo4EG9I4QoWwIEQKA5GigAb0jRCgbQoQAIDlChIDe\nESKUDSFCAJAcJzkAECKUCyFCAJAcDTQAQoRyIUQIAJKjgQb0jhChbAgRAprZv7/Fxo0+qami\npETrUiA1GmhA7wgRyoYQIaABk0k8+KDo2LHL/PkNHnlExMeLQ4e0rgnycvnf0aWlpYcPH96z\nZ08JfywCt4QQoWySkpJSU1O1rgLQmZkzxfLlv3558qQYNUpUVGhXEKTmSg30+vXr+/btGx0d\nPXjw4B07dgghfvjhh6ioqPj4+C5duoSFhS1cuFDrGgGXRIhQKoQIAQ188431SHq6OHlSi1Lg\nAlymgd62bVtiYuLGjRuvXLnyww8/9O/ff9u2bQ8//LCnp+fYsWOVGxMnTvz++++1rhRwPYQI\npUKIENBAbm5NBwEXaqBnzZrVqFGjAwcOXLt27cKFC3fdddcjjzwSHR197NixTz755KuvvsrI\nyIiKipo3b57WlQIuhhChbAgRAhro3Nl6xNtbJCRoUQpcgMs00Fu3bp04cWJCQoIQIjQ09O23\n387Ozp48eXK9evWUA0JCQsaPH79z505NywRcDyFC2RAiBDQwa5bw9//NyN/+Zj0C/I/L7ER4\n7dq1Fi1aqF82bdpUCBEaGmp5TERExPXr151dGeDiCBHKhp0IAQ20aSP27xd///uV1FS/6Gjf\niRPFsGFa1wR5uUwD3bBhw4yMDPXL48ePCyFO/nZ1f0ZGRsOGDZ1dGeD6CBFKhRAhoI2WLcWi\nRRuSk7t37x4REaF1NZCay3xK2Ldv3/fee2/Dhg0mk+ngwYPPPvtsXFzcnDlzzp07pxxw5MiR\n999/v2fPntrWCbgiQoRSIUQIAJJzmQZ6xowZpaWl/fr18/HxSUhIOHfuXHJyssFguPPOO/v1\n69e9e/eEhITr169PmzZN60oBF0OIUDaECAFAci7TQMfGxm7dunX06NHdunV7/PHHt27dGhcX\nt2rVqvj4+I0bN27bti0yMjI5Ofmuu+7SulLAxRAilA0hQgCQnMusgRZCxMfHf/HFF1YjO3bs\nKCgoKCoqsgoUAqghQoSyIUQIAJJz4CRHfn7+4cOH8/Ly6q6aWxMQEED3DNwOQoRSIUQIAJKr\nUQO9adOmLl26BAUFxcfHb9++XRkcNmzYunXr6rI2AE5CiFAqhAgBQHLVN9A7d+4cOHDg8ePH\nExMT1cGcnJxdu3YNHjx4z549dVmeAzIyMgYMGDBgwACHHpWZmWk0Gg1VpDJ5tAAAIABJREFU\nmjBhQh3VDMiAEKFsCBECgOSqXwP9+uuvh4eHb9myxcvLS70sYmho6IEDB7p27Tpz5syVK1fW\ncZE1kp+ffwtnxKOjozdt2lRYWFjFMatWrWKHcLgxQoSyIUQIAJKrvoHevn371KlTmzVrduHC\nBcvxsLCwCRMmzJ49u85qc0xsbOzBgwcdfZTBYOjevXvVx1hu4AK4H0KEsiFECACSq76Bvnbt\nWvPmze3eFRERUVBQUNsl3SJfX9/4+HitqwBcEiFCqRAiBADJVd9Ah4eHHzlyxO5dqampTZo0\nqe2SqmE2m7OysjIzM/Pz84UQ9evXb9WqVWUtPoCaSEtLS0hI0LoK3GQymTIzM2NjY7UuBABg\nX/XL7AYPHrxw4cK9e/daDl69evWvf/3rf/7znyFDhtRZbdauXr06derU8PDwmJiYe++9d8SI\nESNGjOjfv39kZGSLFi1mzpxZVFTktGIAt0GIUDaECAFActWfgX7ttdfWrFnTrVs35QTV9OnT\np0+ffuTIkZKSksjIyFdeeaXuixRCiPPnz/fo0SMrK6tVq1aDBw9u0aKFv7+/EOL69esZGRmb\nNm165ZVXkpOTN2zYEBIS4pySAPdAiFA2hAgBQHI1WsKxe/fuV199denSpUKI/fv3CyEaNWo0\nbty4V199NSwsrM5rFEII8fLLL589e3bp0qUjR460vbe8vPzDDz+cNGnSa6+9NnfuXOeUBLgH\nQoSyIUQIAJIzmM3mGh5qNpsvXbqUn58fGBjYuHHjOi3LVkRExODBgz/++OMqjnnkkUe2bt2a\nnZ1du1N/+OGHEyZMyM/PDwgIqN1nBgAAUklOTu7evbt63V5oyGQy+fj4bNmypdoLpjlfTT8l\nPHz4cG5ubuPGjVu2bNm4cePDhw/v27evTiuzkpubGxMTU/UxcXFxFy9edE49gDthJ0KpsBMh\nAEiu+ga6tLT0//7v/+Lj4w8dOqQObtiwoVOnTk888UR5eXldlverJk2aHDhwoOpj9u3b5/yr\nggCujhChbAgRAoDkqm+g33vvvX//+99Dhgxp0aKFOnjvvfeOGjVq8eLF8+fPr8vyfjV8+PBl\ny5a98847JSUltvfeuHFjxowZKSkpo0aNck49gNsgRCgbQoQAILnq10AnJCS0aNHi22+/tb1r\nyJAhx48fP3HiRN3U9ht5eXn9+/ffu3dvYGDgXXfd1bx584CAALPZXFBQcPr06Z07dxYWFvbs\n2fO7776r9ZXKrIGG28vMzGQvFXmUlZX98ssvxDoBTbAGWh4yr4Gu/iocJ0+efPzxx+3e1adP\nn59++qmWK6pEcHDwtm3bFixY8Omnn27cuNFy6YjRaOzcufO4cePGjRvn6enpnHoAd0L3LBV2\nIgRqRUlJSWFhod1xHx+f8vLyvLw8g8Ggjvv5+Xl4eJjN5ry8PNtPgQICApTr5wKiJg10UFBQ\nZYsjT5061aBBg1quqHLe3t6TJ0+ePHlycXHxmTNnlJ0Ig4KCIiMjvb29nVYG4H7YiVAq7EQI\n1Iq9e/eeOXPmFh548OBB28FmzZpJeB4UWqm+gR4yZMjHH3983333DR48WB0sLS1dvHjxv/71\nr9GjR9dlefb5+vq2atXK+fMCbkkJEWZlZUVFRWldC4QQIiUlZcqUKbV+RU5Ab+6+++7OnTtb\nDebk5GzZsmX48OFW4waDwWg0Oqs0uLzqG+g33nhjzZo1Q4YMiYyMbN26tY+PT15eXnp6+pUr\nVyIiIt544w0nVAmg7hAilA0hQqBWGAwG2w+olS6ZD65xm6r/HR0REbFv374JEybcuHHjp59+\nWrVq1c8//+zp6fnkk0/u2rWLhXqAq2MnQtkkJSWlpqZqXQUAoFLVn4EWQjRu3Pj9999fuHDh\n+fPni4qKwsPDWUcPuBNChFIhRAgAknPgU0KDwdCkSZOYmBi6Z8DNsBOhVNiJEAAkV/0ZaLPZ\n/PXXX3/66adnz54tLS21PcByh0IALocQoWwIEQKA5KpvoOfMmTNt2jQhhJ+fHwFVwP0QIpQN\nIUIAkFz1DfS8efMSExMXLlzIKknALREilE1SUlLXrl21rgIAUKnqG+iLFy9+/fXXdM+AG+Mf\nuFQIEQKA5Kr/lLBx48Zms9kJpQDQCiFCqRAiBADJVd9Ajx49esmSJU4oBYAmlBDhqVOntC4E\nN6WkpAwcOFDrKgAAlap+Cccrr7zy0EMPPfbYY2PHjo2MjLTNEbZs2bJuagPgDIQIZUOIEAAk\nV30DHRgYqNz44osv7B7AAg/ApREilA0hQgCQXPUN9OjRo729vb28arRnIQBXRIhQKoQIAUBy\n1bfFlZ14FkLcuHEjPz+/VusBoIG0tLSEhAStq8BNJpMpMzMzNjZW60IAAPbd1jK7lJSUTp06\n1VYpADRBiFA2hAgBQHI1Wphx+fLlL7/88tSpU2VlZepgcXHxqlWrCgoK6qw2AM5AiFA2hAgB\nQHLVN9CnTp266667cnJy7DzYy+vll1+ug6oAOA8hQtkQIgQAyVXfQL/00kvFxcXz58+Pi4vr\n37//okWLmjVrtnHjxiVLlnz88ceJiYlOqBJAnSJEKBVChAAgueo/Jdy8efPEiRMnTpzYvXt3\nIUTbtm0TExNnzZq1atWqRx99dMuWLXVfJIC6xU6EUmEnQqCu7NkT+Pzzv3vrLTF9ujh/Xutq\n4MKqb6DPnz+vnJ1S1uSZTCZlvEOHDhMnTpwxY0ad1gegrhEilA0hQqBOfPWV6Nat3iefNNm7\nV/z976JNG3HihNY1wVVV30AHBgZevHhRCOHt7R0QEJCZmane1aZNm927d9dhdQDqHiFC2RAi\nBGpfWZl4+mlRXv7rSF6emDJFu4Lg2qr/Hd2zZ88PPvhg48aNQoh27dotWLBAvfLG+vXrfXx8\n6rQ+AHWNEKFskpKSUlNTta4CcC9Hj4qrV60Ht23TohS4g+ob6BdffDE3N3fq1KlCiCeffHL3\n7t1t2rQZMWJEx44dP/roo3vvvbfuiwRQtwgRSoUQIVD7/P1rOgjUQPUN9F133fXzzz//3//9\nnxDi8ccfnz59+uXLl1esWHHgwIFhw4bNnTu37osEULcIEUqFECFQ+6KiROvW1oNcSQy3qkbL\n7Dp37vz0008LIQwGw9/+9rcrV65kZWXduHEjJSWlUaNGdVwhgLpFiFA2hAiB2mcwiC++EBER\nv4507Sreflu7guDa7F8H+sKFCz4+PiEhIcpt2wN8fX2vXbt27do1IUR4eHidlgigThEilA0h\nQqBOdOokjh27/tlnWVu2tH/kETF4sOAfGm6V/QY6IiIiMTHx+++/V25X/RRms7n26wLgLIQI\nZcNOhEBdCQwsfvDBYw0btr//fq1LgWuz30CPGjWqQ4cO6m0n1gNAA4QIpUKIEAAkZ7+B/vLL\nL+3eBuCW0tLSEhIStK4CN5lMpszMzNjYWK0LAQDYV/3qn969e3/00Ud5eXlOqAaA8xEilA0h\nQgCQXPUN9ObNm5966qnw8PAHH3xwxYoV6lbeANwDIULZECIEAMlV/zs6Ozv7n//8Z6dOnVas\nWDFixIjw8PA//OEPmzdvJjsIuAdChLJhJ0IAkFz1DXSzZs3+9Kc/bd26VemkY2NjP/roo169\nekVHR//1r389cuSIE6oEUKcIEUqFECEASM6BTwmtOukWLVq8/fbbbdq0qbviADgHOxFKhZ0I\nAUByt7LMzt/fv2HDhs2aNQsKCqr1ggA4GSFC2RAiBADJ2b+MnV2XLl1auXJlcnLy+vXry8rK\n6tevP2LEiNGjR9ddcQCcgBChbAgRAoDkqm+gz507t2LFiuTk5M2bN5eXl9erV2/48OGPPvro\n4MGDfXx8nFAigDpFiFA27EQIAJKrvoFu3ry52Wz28vK69957R48e/cADDwQGBjqhMgBOQ4hQ\nKoQIAUBy1TfQPXr0GD169MiRI0NDQ51QEADnYydCqbATIQBIrvoGevPmzcqN/Pz87Ozspk2b\nBgcH13FVAJxHCRFmZWVFRUVpXQuEECIlJWXKlCnZ2dlaFwIAsK9GOZVNmzZ16dIlKCgoPj5+\n+/btyuCwYcPWrVtXl7UBcAZChLIhRAgAkqv+d/TOnTsHDhx4/PjxxMREdTAnJ2fXrl2DBw/e\ns2dPXZYHoM4RIpQNOxECgOSqb6Bff/318PDw9PT0xYsXq4OhoaEHDhwIDw+fOXNmHVYHwCkI\nEUqFECEASK76Bnr79u1PP/10s2bNrMbDwsImTJjAaRLADbAToVTYiRAAJFd9iPDatWvNmze3\ne1dERERBQUFtlwTAqQgRyoYQIVArbty4Ydul5OXlCSEuXrxoe3xISIi3t7czKoPrq76BDg8P\nP3LkiN27UlNTmzRpUtslAXAqQoSyIUQI1Ir09PRz585ZDZrNZoPBsG3bNtvj27dvHx0d7ZTS\n4PKqb6AHDx68cOH/s3en8U1WaR/HrzRNum8spQUKxVJbFgEBQURcEFHUoaCA44I6DG64jIjr\nuCCM+6Cjgjwyo6PCKJsClW1ERUA2ERRaZJO2UPYCLXRvmuR+XiSTrYEC0uSk+X0/vkjOSdIr\n0uXq3fM/Z+rNN9/s2iuXlJRMmjTp448/HjNmTEOWB6DBESJUDScRAufFJZdcwpcSGohO07TT\nP+Lw4cO9evU6dOhQly5dfv75527duonI9u3ba2pq2rRps2HDhhYtWvikVL+ZNm3aAw88UFZW\nFh0d7e9aAAAAgoLJZAoLC1uzZs1ll13m71o81f9XwqSkpI0bN95777179+4Vkc2bN2/evDkm\nJubBBx/86aefGn33DAQDQoRKIUQIAIo7o2V2iYmJU6dOPXr06OHDh3/77bfDhw8fPXp06tSp\niYmJDV0fgIZmCxHu2bPH34XALjs7e+DAgf6uAgBwSvWvgRaR3377bf369UVFRaGhoa1atbri\niisauiwAPkOIUDWECIEzlJ+fbzKZPAZramrMZnNUVJTHeEhISFpaml6v91V1aMzqaaA3bNjw\nl7/8xXF8t41Opxs8ePCkSZPat2/fkLUB8AVChKohRAicCU3T9u/fX1NT4zFeVVVlsVjqxpb0\nen2bNm1ooHFenK6B/vrrr4cMGVJdXd29e/frrruuVatWtbW1u3fvXrx4cXZ29ooVK5YuXdqn\nTx+f1QqggXASoVI4iRA4EzqdzuufxHNyck6ePNmvXz/fl4TgccoG+sSJE3fddVdISMjcuXOH\nDRvmOvXuu+9+8MEHY8eOHTp06M6dO+Pi4hq+TgANKCcnp0uXLv6uAnYmkyk/Pz8zM9PfhQAA\nvDvlMrtPPvmkqKhoypQpHt2ziOj1+oceeugf//jHkSNHpk6d2sAVAmhYhAhVQ4gQABR3ygZ6\n8eLFrVu3vvvuu0/1gAcffLBNmzbZ2dkNUxgAHyFEqBpChACguFN+j87Nze3Xr99pvomHhIRc\nffXVbFYKBDpChKrJyspatWqVv6sAAJzSKfvj4uLi5OTk0z85MTHx5MmT57skAL5GiFAphAgB\nQHGnbKBra2sNBkM9T+aPjECjwEmESuEkQgBQHB0wEOwIEaqGECEAKO50+0CvXr36pZdeOv0D\nznM5AHyOEKFqCBECgOJO10CvWbNmzZo1PisFgF8QIlQNJxECgOJO2UDPmDHDl3UA8CNChEoh\nRAgAijtlA33nnXf6sg4AfsRJhErhJEIAUBzL7IBgR4hQNYQIAUBxNNBAsCNEqBpChACguNOF\nCAEEA0KEqiFECACK4yIHAEKEaiFECACKo4EGwEmEauEkQgBQHA00EOwIEaqGECFwjoqL5dFH\nM2+4ofctt8jtt0tBgb8LQqPFGmgg2BEiVA0hQuBc1NbKjTfK+vVG292ZM2XVKtm8WZo1829d\naJTqb6A1Tfviiy+mT5++f//+2traug/YunVrAxQGwEcIEaqGECFwLpYskfXr3UYOHJBp0+S5\n5/xUEBqz+hvot95668knnxSRyMhIg8HQ8CUB8DVChEohRAici9xcL4Nc40PDqP+vhO++++51\n112Xl5dXUVFxwhsfVAmgQREiVAohQuBcpKR4GWzd2ud1ICjU30AfOXJkwoQJXKACGitChKoh\nRAici+uv91zubDDIrbf6qRo0cvU30C1atNA0zQelAPALQoSqIUQInIsWLeTLL8Vxva9pU/nk\nE+nZ0681odGqfw30bbfdNmPGjEsvvdQH1QDwPUKEqiFECJyjK66QHTt2LVhQeeJEtzvukMhI\nfxeERqv+BvrFF18cNmzYHXfccdddd7Vp06ZujrB9+/YNUxsAH2GNllIIEQLnzmCozsgoO3mS\n7hkNqv4GOiYmxnbj888/9/oAFngAgS4nJ6dLly7+rgJ2JpMpPz8/MzPT34UAALw7oyUcRqMx\nNJQjV4DGyRYiLCgoSE1N9XctEBHJzs4eN25cYWGhvwsBAHhXf1t8qgvPABoHQoSqIUQIAIo7\ni+vKx44d++233yoqKmJiYjIyMuLj4xuuLAA+Q4hQNYQIAUBxZ3SRY/Xq1Zdeemnz5s0vu+yy\na6+99tJLL23SpMmAAQM4xBtoHAgRKoUQIQAorv4r0Bs2bBgwYIDZbL788sszMjIiIiIqKiq2\nbdu2fPnyvn37btiwISMjwweFAmg4hAiVQogQABRXfwP98ssvN2/e/JtvvvH4bv7LL79cf/31\nEyZMYJE0ENAIEaqGECEAKK7+JRxr164dM2ZM3WshF1988ZgxY5YvX94whQHwEUKEqiFECACK\nq/8K9MmTJ1u3bu11KjU1tbi4+HyXBMCnCBGqhhAhACiu/osciYmJ27dv9zq1bdu2xMTE810S\nAF8jRKgUQoQAoLj6G+iBAwdOnjw5Ozvb9cRBTdPmz5///vvvDxo0qCHLA+ALOTk5/i4BTiaT\naceOHf6uAgBwSvUv4XjppZeWLFkyZMiQpKSkjh07RkVF2XbhOHz4cHJy8vjx431QJYCGQ4hQ\nNYQIAUBx9V+Bbtu27caNG+++++6qqqrly5cvXLhw+fLlJpNp9OjRmzZtOtXyaACBghChaggR\nAoDizugkwpSUlE8++UTTtMOHD1dUVERHRyclJTV0ZQB8gxChaggRAoDizvQob4vFotfrk5OT\nRaSmpubHH380Go3dunXT6XQNWR4AXyBEqBRChACguPobaIvF8uijjxYVFc2dO1dE9uzZc801\n1+Tn54vI5ZdfvnTp0ujo6AYvE0BD4iRCpXASIXCG8vLyamtrPQaPHz9eXV1dN4kbEhKSlpam\n1+t9VR0as/ob6L///e9Tp059/PHHbXcfeuihgoKCBx98UKfTffDBB1OmTHnmmWcauEgADYgQ\noWoIEQJnQtO0gwcPVldXe4ybTCar1bpv3z6PcdvfdmigcV7U30B/9tlnN99881tvvSUiBw4c\nWLp06ahRo6ZOnSoi1dXVs2fPpoEGAhohQtUQIgTOhE6n69evn7+rQJCq/3v0nj17Bg4caLv9\n9ddfa5p222232e726NFjz549DVccAB8gRKiarKysVatW+bsKAMAp1d9Au8YEv/3226ioKMcv\nfJqm1V17BCDgECJUCiFCAFDcGe0DbbsWcuTIkYULFw4cONBoNNqmtmzZwj7QQCPASYRK4SRC\nAFBc/Q307bff/vnnn1922WXdu3cvLy//y1/+YhufPn36p59+Onjw4AauEEDDsoUIWY6ljuzs\nbMfCOQCAguoPEY4dO3bXrl2zZ882Go3vvffelVdeaRt/5plnMjIynn322QauEEDDIkSoGkKE\nAKC4+hvo8PDwjz/++OOPP/YYnzdvXs+ePUNDz/QoFgBqIkSoGk4iBADFnd1JhLbbNTU1mzdv\nDgsLYzNFoHEgRKgUQoQAoDhOIgTASYRq4SRCwKa8vHzr1q2apnmMl5WVhYeHGwwGj/Ho6OiL\nLrrIV9UhqNW/zM52EqHjcojjJMIxY8asXbt2ypQpDVwhgIZFiFA1hAgBm5CQEIM3lZWVZrO5\n7rhjlzCgoXESIRDsCBGqhhAhYBMZGdmjR4+648ePH2/Tpk379u19XxJgw0mEQLAjRKgaTiIE\nAMXVfwVa5ZMILRbLtm3bysrKUlJSUlJS/FgJENAIESqFECEAKC6QTiJcu3btww8/7Lj7n//8\np1WrVl26dOnbt2+bNm26devGNRvg3HASoVI4iRAAFBcwJxGuWLHi6quv/vTTT21p3C+++GLk\nyJEVFRXDhw8fM2bMtddem5ubO3DgwE2bNvmmHqDRIESoGkKEAKC4gDmJcMKECfHx8WvWrLEt\nKXnqqafatm27bt265ORk2wN+/PHHq6++esKECV999ZVvSgIaB0KEqiFECACKC5iTCH/++ef7\n7rvPFrk9efJkQUHBu+++6+ieRaR379533nmnbbNqAGeOEKFqOIkQABTnvf09fPhwWFhYQkKC\n7bbXx6Smph47dkxEkpKSGq4+B4vFEhERYbsdHh6u0+nqLr9u3bp1dXW1D4oBGhlChEohRAgA\nivP+V8Lk5GTHXnXJ9fFNod26dZs1a1ZlZaWIhIWF9enTZ926da4PqKmpmTdvXkZGhm/qARoT\nQoRKIUQIAIrzfgX61ltv7datm+O2D+s5pWeeeeYPf/hDv379Xnvttf79+0+ePPmmm2666KKL\nhg0bZjAYfv7557/+9a9btmyZNm2avysFAowtRFhQUJCamurvWiAikp2dPW7cuMLCQn8XAgDw\nznsDPWvWLK+3/eimm27617/+9dhjj1133XURERHt2rUzGo133333qFGjRMRiseh0uscff/ze\ne+/1d6VAgCFEqBpChACguLOIAB47duy3336rqKiIiYnJyMiIj49vuLK8Gj169B/+8IcZM2Z8\n++23O3bsKC4uDgsLi46OTk1N7du379133929e3cflwQ0AoQIVUOIEAAUd0YN9OrVq5944okf\nf/zRMaLT6fr37//OO+907ty5wWrzokWLFk888cQTTzzhyw8KNHqECJVCiBAAFFd/A71hw4YB\nAwaYzebLL788IyMjIiKioqJi27Zty5cv79u374YNG8jtAYEuJyenS5cu/q4CdiaTKT8/PzMz\n09+FAAC8q7+Bfvnll5s3b/7NN994fDf/5Zdfrr/++gkTJnz++ecNVh6ABkeIUDWECIHTKSho\n8cMPkUeOSHKyREX5uxoEqfpzKmvXrh0zZkzdayEXX3zxmDFjli9f3jCFnbW8vLwBAwYMGDDg\nbJ9lMBh0p/XAAw+IiO0IcaDxIUSoGkKEwCk9+aSkp3d75ZWWd98tmZmyerW/C0KQqv8K9MmT\nJ+seWWKTmppaXFx8vks6R2VlZd99993ZPistLW3jxo1ms/k0j5k3b96rr75qO0IcaHwIEaqG\nECHg3YwZMmmS8+7+/TJihOzYIbGx/qsJQar+BjoxMXH79u1ep7Zt25aYmHi+SzpHmZmZubm5\n5/DErl27nv4BGzduPKeKgIBBiFAphAgB7+bP9xw5dEjWr5eBA/1RDYJa/X8lHDhw4OTJk7Oz\ns13XMGiaNn/+/Pfff3/QoEENWd5ZCA8P79y5s493BQEaB04iVAonEQLeHT3qZbCoyOd1AGdw\nBfqll15asmTJkCFDkpKSOnbsGBUVZduF4/Dhw8nJyePHj/dBla40TSsoKMjPzy8rKxORuLi4\n9PT0lJQUH5cBNBqECFVDiBDwrnt3L4ueOQIC/lB/A922bduNGze+8MILCxYscEQGmzRpMnr0\n6IkTJyYnJzdwhU4lJSWvvPLKjBkziur8utmmTZvRo0c/8cQTERERPqsHaBwIEaqGECHg3TPP\nyKxZbpec771XOnb0X0EIXroz31xC07TDhw9XVFRER0cnJSU1aFl1HTp0qG/fvgUFBenp6X37\n9m3btm1UVJSIlJaW5uXlrVy58uDBg127dv3+++8TEhLO74eeNm3aAw88UFZWFh0dfX5fGVBE\nfn4+y6DVYTabDx48yDJowIsDB+Rvfyv99ltDYmLEyJFy332i1/u7JjQUk8kUFha2Zs2ayy67\nzN+1eKrnCnRNTc2WLVsqKyszMzOTkpJ8eb3ZwwsvvLB///45c+YMHz687qzFYpk2bdrDDz88\nYcKEd955x/flAQGN7lkphAiBU2rVSj74YN3XX6elpbVv397f1SB4ne6vhJ9++mlSUlLv3r2v\nvvrqli1b3n777bZlx36xePHikSNHeu2eRUSv148ZM2bEiBHz5s3zcWFAI0CIUCmECAFAcads\noFetWvWnP/2pvLz8uuuuu/3229u1azdz5sy77rrLl8W5On78eFpa2ukf06FDhyNHjvimHqDR\nsIUI9+zZ4+9CYJednT2QbbkAQGGnXMIxadIknU63fPnyfv36iYjJZPrjH/84f/78rVu3+mWr\nuJYtW27ZsuX0j/nll19atmzpm3qARoMQoWoIEQKA4k75PXr9+vUDBw60dc8iYjQaX3rpJRFZ\ntWqVbyrzMGTIkLlz506aNKmmpqbubEVFxfjx47Ozs2+99Vbf1wYENE4iVE1WVpa/vtMCAM7E\nKa9AHz9+/MILL3Qdsd09fvx4gxflzUsvvfTDDz88+eSTEydO7NWrV0pKSnR0tKZp5eXle/fu\n3bBhQ2VlZb9+/Z5//nm/lAcENEKESiFECACKO2UDbbVaPfZUDg8PFxGLxdLgRXkTHx+/bt26\n999/f/r06StWrHAtw2Aw9OjRY9SoUaNGjdKznQ1w9nJycrp06eLvKmBnMpny8/MzMzP9XQgA\nwLv6D1JRh9FoHDt27NixY6urq/ft22fbEiQ2NrZNmzZGo9Hf1QGBipMIVcNJhACguEBqoB3C\nw8PT09P9XQXQSBAiVA0hQgBQ3Oka6NWrV9uCg65WrFjhMVj3MQACCCFC1WRlZV1yySX+rgIA\ncEqna6DXrFmzZs0aj8GVK1euXLnSdYQGGgh0hAiVQogQABR3ygZ6xowZvqwDgB8RIlQKIUIA\nUNwpG+g777zTl3UA8BdChKohRAgAiiOnAgQ7QoSqIUQIAIoLyF3KXlqMAAAgAElEQVQ4AJxH\nhAhVQ4gQcKisrNQ0zWPQarWaTKaKigqPcaPRaDAYfFUaghoNNABChGohRAjYFBUVrVixwuvU\n1q1bt27d6jEYExMzaNCgBi8LoIEGIIQIFUOIELBJTEy88cYb646bzWa9Xq/T6TzGufwMn6GB\nBoIdIULVECIEHKKiovxdAuAFORUg2BEiVA0hQgBQHFeggWBHiFA1hAgBQHFc5ABAiFAthAgB\nQHE00AAkJyfH3yXAyWQy7dixw99VAABOiQYaCHa2EOGePXv8XQjssrOzBw4c6O8qAACnRAMN\nBDtChKohRAgAiiNECAQ7QoSqIUQIAIrjIgcAQoRqIUQIAIqjgQZAiFAthAgRPDRNM3lTXV3t\ndVzTNH+XDIiwhAMAJxGqhpMIETxyc3PP6tfFCy+8sFu3bg1XD3CGaKCBYEeIUDWECBE8Onbs\nmJKS4jFYXV39ww8/XH755RERER5TMTExvioNOB0aaCDYESJUDSFCBI/Q0NCEhASPwcrKShGJ\ni4uLioryR1FA/bjIAYAQoVoIEQKA4migARAiVAshQgBQHA00EOw4iVA1nEQIAIqjgQaCHSFC\n1RAiBADFESIEgh0hQtUQIgQAxXGRAwAhQrUQIgQAxdFAAyBEqBZChACgOBpoINgRIlQNIUIA\nUBwNNBDsCBGqhhAhACiOECEQ7AgRqoYQIQAojoscAAgRqoUQIYJdRUXs/v1SUeHvOoBTooEG\nQIhQLYQIEbxMJnnkkciWLa8fNy6qZUt56CGpqfF3TYAXNNBAsCNEqBpChAhezz0nU6aI2Swi\nYrHI1KnyzDP+rgnwggYaCHaECFVDiBBBStPko488B//9b7Fa/VENcDp8jwaCHSFC1WRlZa1a\ntcrfVQA+d+KElJR4DpaWyvHj/qgGOB0aaACECNVCiBBBKiFBkpM9B5s3l+bN/VENcDo00AAI\nEaqFECGCV90Vz6yBhpJooIFgR4hQNYQIEbweeUSmTtUuuEDT6bR27WTKFBk71t81AV7QQAPB\njhChaggRInjpdPLgg1W5uV/MnFmZmysPPSQ6nb9rArzgJEIg2BEiVA0nEQIafTPUxkUOAIQI\n1UKIEAAURwMNgBChWggRAoDiaKCBYEeIUDWECAFAcTTQQLAjRKgaQoQAoDhChECwI0SoGkKE\nAKA4LnIAIESoFkKEAKA4GmgAhAjVQogQABRHAw0EO0KEqiFECACKo4EGgh0hQtUQIgQAxREi\nBIIdIULVECIEAMXRQAMgRKgWQoQIHhUVFcXFxR6DNTU1InLo0KGwsDCPqSZNmkRFRfmoOODU\naKABSE5OTpcuXfxdBexMJlN+fn5mZqa/CwEa3L59+7xGZnU63datW+uOZ2RkdOjQoeHrAupB\nAw0EO1uIsKCgIDU11d+1QEQkOzt73LhxhYWF/i4EaHCZmZn8rohARE4FCHaECFVDiBAAFMcV\naCDYESJUDSFCAFAcFzkAECJUCyFCAFAcDTQATiJUCycRAoDiaKCBYMdJhKrhJEIAUBwNNBDs\nCBGqhhAhACiOECEQ7AgRqoYQIQAojoscAAgRqoUQIQAojgYaACFCtRAiBADF0UADwY4QoWoI\nEQKA4lgDDQQ7QoSqIUSIxiQvL6+iosJj0GQyVVVVxcXF1X18+/btIyMjfVIacO5ooIFgR4hQ\nNYQI0ZhUVlbWbaDLy8vLy8tDQ700IRaLxSd1Ab8LDTQAQoRqIUSIxuSiiy6qO5iXl7dr164+\nffr4vh7gvOCvhAAIEaqFECEAKI4GGgh2hAhVQ4gQABRHAw0EO0KEqiFECACKYw00EOwIEaqG\nECEAKI6LHAAIEaqFECEAKI4GGgAhQrUQIgQAxdFAA8GOEKFqCBECgOJooIFgR4hQNYQIAUBx\nhAiBYEeIUDWECNHohZw8GXn4sFitwu+KCEx84gIgRKgWQoRozPbuleuua9ejx5WjRklSksyY\n4e+CgHNBAw2AEKFaCBGi0aqtlVtukWXL7HePHpW77pJvv/VrTcC5oIEGgh0hQtUQIkSjtWmT\nbNrkOfjhh/4oBfhdaKCBYEeIUDWECNFo5eV5GczP93kdwO9FiBAIdoQIVUOIEI1Whw5eBjMz\nfV4H8HtxkQMAIUK1ECJEo9Wtm1x7rduI0SiPPeanaoBzRwMNgBChWggRotEKCZHZs+W++6yx\nsZpeLz16yNKl0r27v8sCzhoNNBDsCBGqhhAhGrOEBJk2reDnn5fNny8bN0r//v4uCDgXNNBA\nsCNEqBpChAgG1lBSWAhgfPoCwY4QoWoIEQKA4rjIAYAQoVoIEQKA4migARAiVAshQgBQHA00\nEOwIEaqGECEAKI4GGgh2hAhVQ4gQABRHiBAIdoQIVUOIEAAUx0UOAIQI1UKIEAAURwMNgBCh\nWggRAoDiWMIBBDtbiLCgoCA1NdXftUBEJDs7e9y4cYWFhf4uBDgPfvzxx9LSUo/Bmpqampqa\nb775xmNcp9P16NEjISHBV9UB54gGGgh2hAhVQ4gQjUnr1q3Lyso8Bs1mc3V1dXR0tMe4TqeL\nioryVWnAuaOBBoIdIULVECJEY9KqVSt/lwCcf1zkAECIUC2ECAFAcTTQAAgRqoUQIQAojgYa\nCHacRKgaTiIEAMXRQAPBjhChaggRAoDiCBECwY4QoWoIEQKA4rjIAYAQoVoIEQKA4migARAi\nVAshQgBQHA00EOwIEaqGECEAKI4GGgh2hAhVQ4gQABRHiBAIdoQIVUOIEAFE07TCwkKLxeIx\nXlVVpdfrjUajx3hYWBhnE6IRoIEGQIhQLYQIEUCqq6u3bdtmtVrrjoeEhNRtoA0GQ8uWLXU6\nna8KBBpEY2igS0tLX3311XvuuSczM9PftQABKScnp0uXLv6uAnYmkyk/P59vaAgIERERgwYN\nqju+evXq6Ojobt26+b4kwAcawzK70tLSN954Y/fu3f4uBAhIhAhVQ4gQABQXMFegR48efaqp\nyspKEZk8efKCBQtE5MMPP/RdWUDgI0SoGkKEAKC4gGmgP/roo9M/YNmyZbYbNNDAWSFEqBpC\nhACguIC5yDF27Fi9Xt+tW7f//ve/Je5+/fVXEZk1a5btrr8rBQIPIUKlECIEAMUFTAP99ttv\nr1+/XkQGDRr017/+VafTxf9PbGysiERFRdnu+rtSIPBwEqFSOIkQABQXMA20iPTs2fOnn356\n7bXXPvnkk44dO3755Zf+rghoDAgRqoYQIQAoLpAaaBEJDQ19+umnc3NzO3ToMGzYsMGDB+/b\nt8/fRQGBjRChaggRIuDl5ycuWxa/bJkcOuTvUoAGEZDfo9PS0r799tuPP/54zZo1HTt2JDUI\n/B6ECFWTlZW1atUqf1cBnKtXXpHMzAv/9rfUp5+W9HSZMcPfBQHnX0A20Db33HPP9u3bb7rp\npgkTJvi7FiCwESJUCiFCBLDvvpPnn5faWvvdigq57z7ZtcuvNQHnXwA30CKSmJg4c+bMJUuW\njBs3Li0tzd/lAIGKEKFSCBEigC1a5DlSXS3ffOOPUoAGFNgNtM2gQYMmTZrUoUMHfxcCBCRC\nhKohRIgA5nUzWXaYRaPTGBpoAL8HIULVECJEAPN6BhAHA6HRaTzfo/Py8gYMGDBgwICzfZbB\nYNCd1gMPPCAimqY1TOGAnxEiVA0hQgSw0aPl4ovdRgYPFv6igkYnYI7yrldZWdl33313ts9K\nS0vbuHGj2Ww+zWPmzZv36quv6nS631EdoDRChEohRIgAFhYmP/wgb799Ijs7JCws9rbb5P77\nhR+gaHQaTwOdmZmZm5t7Dk/s2rXr6R+wcePGc6oICBg5OTldunTxdxWwM5lM+fn5mZmZ/i4E\nOCdRUfLCC1uvvjo6Orpbt27+rgZoEI1nCUd4eHjnzp07d+7s70KAAEOIUDWECAFAcYF3BVrT\ntIKCgvz8/LKyMhGJi4tLT09PSUnxd11AoCJEqBpChACguEBqoEtKSl555ZUZM2YUFRV5TLVp\n02b06NFPPPFERESEX2oDAhchQtVkZWVdwq4FAKCwgGmgDx061Ldv34KCgvT09BtuuKFt27ZR\nUVEiUlpampeXt3LlyhdffPHLL7/8/vvvExIS/F0sEGAIESqFECEAKC5gGugXXnhh//79c+bM\nGT58eN1Zi8Uybdq0hx9+eMKECe+8847vywMCGiFCpRAiBADFBcwyu8WLF48cOdJr9ywier1+\nzJgxI0aMmDdvno8LAwIdIULVECIEAMUFzBXo48ePp6Wlnf4xHTp0mD9/vm/qARoNQoSqIUSI\nAGKxWHbu3Fn3OIXS0tLq6uqcnByP8bCwsIyMDF9VBzSUgGmgW7ZsuWXLltM/5pdffmnZsqVv\n6gEaDUKEqiFEiABiNpuPHz9utVo9xnU6ndVqLSkp8Rg3GAyapnE2GQJdwDTQQ4YMee+99y65\n5JJHHnkkLCzMY7aiouLNN9/Mzs5++umn/VIeENAIESqFECECSFhYWL9+/fxdBeBrAdNAv/TS\nSz/88MOTTz45ceLEXr16paSkREdHa5pWXl6+d+/eDRs2VFZW9uvX7/nnn/d3pUDgIUSoFEKE\nAKC4gGmg4+Pj161b9/7770+fPn3FihUWi8UxZTAYevToMWrUqFGjRun1ej8WCQQiW4iwoKAg\nNTXV37VARCQ7O3vcuHGFhYX+LgQA4F3ANNAiYjQax44dO3bs2Orq6n379tlOIoyNjW3Tpo3R\naPR3dUCgIkSoGkKEAKC4QGqgHcLDw9PT0/1dBdBIECJUDSFCAFAcFzkAECJUCyFCAFAcDTQA\nqbtXK/zIZDLt2LHD31UAAE6JBhoIdpxEqBpOIgQAxdFAA8GOEKFqCBECgOICMkQI4DwiRKga\nQoRQiqZplZWVdcfNZnNoqJcuIiwszOs40JjwKQ6AEKFaCBFCKfn5+Zs2bTrzx7dq1apv374N\nVw+gAhpoAJxEqBZOIoRSLrjggqSkpLrjS5Ys6dWrV7NmzTzGw8LCfFIX4E800ECw4yRC1XAS\nIZSi0+mioqK8ToWHh59qCmjcyKkAwY4QoWoIEQKA4rgCDQQ7QoSqIUQIAIrjIgcAQoRqIUQI\nAIqjgQbASYRq4SRCBID169t9/33Y8uVSU+PvUgA/oIEGgh0nEaqGkwihtOpqueEG6dOn5//9\nX/ztt0unTvLrr/6uCfA1Gmgg2BEiVA0hQijthRdk6VLn3bw8ue020TT/FQT4Ad+jgWBHiFA1\nWVlZq1at8ncVwCksXOg5kpsr/AkLQYYGGgAhQrUQIoTSiou9DJaU+LwOwJ9ooAEQIlQLIUIo\nre4eixER0qmTP0oB/IYGGgh2hAhVQ4gQSnvzTYmMdBt56y3h+G4EGRpoINgRIlQNIUIorVMn\nycmR++47npFRfdNNsmyZPPigv2sCfI2TCIFgR4hQNZxECNWlpcm0acvnzr3iiivCW7TwdzWA\nH3CRAwAhQrUQIgQAxdFAAyBEqBZChACgOBpoINgRIlQNIUIAUBwNNBDsCBGqhhAhACiOECEQ\n7AgRqoYQIZRy5MgRr2uKNE3LyckxGo0e4y1atMjMzPRJaYDf0EADIESoFkKEUEpERERCQkLd\ncZ1OFxsbW/evJTExMT6pC/AnGmgAkpOT06VLF39XATuTyZSfn881PCgiNjaW7w+AB5bZAcGO\nEKFqCBECgOJooIFgR4hQNYQIAUBxLOEAgh0hQtUQIgQAxXGRAwAhQrUQIgQAxdFAA+AkQrVw\nEiEAKI4GGgh2hAhVQ4gQABRHAw0EO0KEqiFECACKI0QIBDtChKohRAgfW7t27f79+8/88b16\n9UpNTW2wcoAAQAMNgBChWggRwscuvvjiDh06eAweP3588+bN11xzTd3Hx8bG+qQuQF000AA4\niVAtnEQIH4uIiIiIiPAYrKmpERGvh3gDYJkdEOwIEaqGECEAKI4GGgh2hAhVQ4gQKtBVVkYf\nOSJms78LAVTE92gg2BEiVE1WVtaqVav8XQWCWEmJ3Hlni/btr3/4YUlIkL//3d8FAcqhgQZA\niFAthAjhZ6NGyWefiaaJiJSXy1NPyUcf+bsmQC000AA4iVAtnEQIfyoqkgULPAenTfNHKYC6\naKCBYEeIUDWECOFPeXleBvPzfV4HoDQaaCDYESJUDSFC+FNmpuh0XgYBuOB7NBDsCBGqhhAh\n/CkhQUaP9hx88kl/lAKoiwYaACFCtRAihJ+9+64884y1SRPR6SQjQ2bOlKwsf9cEqIUGGgAh\nQrUQIoSfRUTIa68V/frrvM8+kx075I9/9HdBgHJooIFgR4hQNYQIoQirweDvEgBF0UADwY4Q\noWoIEQKA4kL9XQAAPyNEqJqsrKxLLrnE31UgiJw4caKsrKzuoKZp+/btq/v4xMTEsLAwn5QG\nKIoGGgAhQrUQIoSP7d69e//+/R6DmqbpdLpNmzbVfXyPHj1SUlJ8UhqgKBpoAJKTk9OlSxd/\nVwE7k8mUn5+fyc678JWePXv27NnT31UAgYRldkCwI0SoGkKEAKA4Gmgg2BEiVA0hQgBQHEs4\ngGBHiFA1hAgBQHFc5ABAiFAthAgBQHE00AA4iVAtnEQIAIpjCQcQ7GwhwoKCgtTUVH/XAhGR\n7OzscePGFRYW+rsQNBJWq3XVqlW1tbUe4yaTyWq1hoeHe4zr9fq+ffuy0zNwGjTQQLAjRKga\nQoQ4v0JCQtq0aWMymTzGDx48WFtbW3dHZ71eb+AQb+C0aKCBYEeIUDWECHHeec05VFdXV1RU\nsOM4cA5ooAEQIlQLIUL4QnFx7OrV4eXlcsEFkpzs72qAAMNfCQEQIlQLIUI0uLlzpX37Cx55\nJPPZZyUtTSZP9ndBQIChgQaCHScRqoaTCNGw8vLknnukpMR+t6pKHn9c1qzxa01AgKGBBoId\nIULVECJEw/r6a6msdBsxmyU720/VAAGJNdBAsCNEqBpChGhYRUVeBo8e9XkdQADjIgcAQoRq\nIUSIhtWjh5fB7t19XgcQwGigARAiVAshQjSsG2+Ua65xG+nUSf78Zz9VAwQkGmgg2BEiVA0h\nQjSskBBZuFBefrmiW7fyDh3kqadk9WqJjPR3WUAgYQ00EOwIEaqGECEaXESEPPfcbzfeWFFR\n0bdvX39XAwQeGmgg2BEiVA0hQgBQHA00AEKEaiFEiPPLarUuWbLEbDZ7jFssFk3TFixY4DGu\n0+kGDhwYERHhqwKBwEMDDUBycnK6dOni7ypgZzKZ8vPzMzMz/V0IGomQkJA+ffrUbaBra2ut\nVmtYWFjdx9M9A6dHAw0EO1uIsKCgIDU11d+1QEQkOzt73LhxhYWF/i4EjUfTpk39XQLQqJBT\nAYIdIULVECIEAMVxBRoIdoQIVUOIEAAURwMNgBChWggR4mwVFRWtXLlS07QzfHyTJk0GDBjQ\noCUBjRsNNABChGohRIiz1axZsyuvvLJuA71hw4aUlJTk5GSP8UiOTQF+HxpoINgRIlQNIUKc\nrZCQkMTERM/Rb7+9cN68punpze6+W1q18kddQKNFAw0EO0KEqiFEiN/LbJahQ2XRogzb3dde\nk//8R7Ky/FsU0JjwPRoIdoQIVZOVlbVq1Sp/V4FA9o9/yKJFzrvl5XLPPVJS4r+CgMaGBhoA\nIUK1ECLE77VsmefIiROyYYM/SgEaJxpoAJKTk+PvEuBkMpl27Njh7yoQyCorz3QQwDmhgQaC\nnS1EuGfPHn8XArvs7OyBAwf6uwoEsssu8xwJDRU2FwfOHxpoINgRIlQNIUL8Xs89J+3bu428\n/LK0bu2naoBGiF04gGBHiFA1nESI3ys+Xn75RaZMObxoUVRKSszo0XLNNf6uCWhUaKABECJU\nCyFCnIPa2lq3g1SMRnn88Z+7dGnfvn1YaqqYTK4PDg0N5a8cwO9BAw2AkwjVwkmEOFtHjhxZ\nuXKl16nNmzdv3rzZYzA+Pp519sDvQQMNBDtOIlQNJxHibCUmJl577bV1x00mk9eLzWFhYT6p\nC2i0aKCBYEeIUDWECFHXzp07d+/e7TGoaVp1dXV4eLhOp/OYuvDCC9PT031VHRB0aKCBYEeI\nUDWECFFXcnKywWDwGKypqcnNzU1PT6871bx5c1+VBgQjGmgAhAjVQogQdcXGxsbGxroNffml\nZdKk1J07wzp2DHnqKRk82E+lAcGIvxIC4CRCtXASIer38ccybJh+/fqIkpKQNWskK0tmzvR3\nTUAQoYEGgh0nEaqGkwhRv+eeq38EQIOhgQaCHSFC1RAiRD2KiuTQIc/BggIpLfVHNUAwYg00\nEOwIEaqGECHq0aSJRERIVZXbYFycxMT4qSAg6HCRAwAhQrUQIkQ9QkNl+HDPwVtvlTqb2QFo\nIDTQAAgRqoUQIeo3ebJkZTnvDhsmb7/tv2qAoMMSDiDYcRKhajiJMDjl5eVVVFR4DJpMpurq\nas8N7ER0Ol36rFnW3bt/mj279+23h3fo4KsyAYjQQAMgRKgaQoTB6eTJk2VlZR6DlZWVVVVV\nFoulrKyssrLSdWr79u0iIhdd9FVuruTmejyxY8eOnTt3bsh6gaBGAw0EO0KEqiFEGJy6d+/u\ndr+2ViZPrp4+3VxSEt2/f+1f/1rerFndZ1VVVUVERNQdj4qKaqA6AQgNNAAhRKgYQoQQEfnT\nn+Szz8Jttz/5xLBoUcLmzdKqlcejEhISfF4ZAEKEAAgRKoYQIWTLFvnsM7eRY8fkzTf9VA0A\nTzTQQLDjJELVcBIhZPPmMx0E4A8s4QCCHSFC1RAibKwqKys1TfMYtFgsOp3O419cHxcXXvf5\nSUkNWByAs0EDDQQ7QoSqIUTYKJWXly9ZsuQMH2yoqrq+SZOI4mK30WHDzn9ZAM4JDTQAQoRq\nIUTYKEVHRw8dOtTtCrSmhcybd2TuXENsbMKdd2pXXOH6eH1amowcKba1VUajPPusl9MHAfgJ\nDTQAycnJ6dKli7+rgJ3JZMrPz8/MzPR3ITjPDAaD847VKoMHy+LF9m01Pv205oknTjzxhPMB\n6em6lStPfPtt6b59bYcMsSYlyZEjjkmdTtesWTOW+gD+0qga6JKSkpMnT3KaGnBWOIlQNZxE\nGBQ++UQWL3YdCJs0Kad58xKPL8PoaOnQIX/nTtm503VYp9P179+/adOmDV8oAC8CqYHOycl5\n9tlnf/3115SUlNtuu+3+++/X6/WuD3jjjTfeeOONuhENAKdBiFA1hAgDVEFBwZYtW+qO19bW\nhoaG6nQ618Hu//lP3WU614aHy4gRDVYggPMmYBroNWvWXHPNNTU1NZGRkQcPHly9evWcOXPm\nz5/PHvLA70SIUDWECANUq1atIiMj3YasVuOqVXuXLm3Rvbt+8GDN5cjA2NmzvbwEvzgBASJg\nGujXXnvNarXOnz8/KyvLZDJNnTr16aefvu66677//nsOLAV+J0KESiFEqKzy8vKKigqPQU3T\nKisr6/4k0pWVNb/zTt2PPyaIyKefyqRJsnixXHSRfXrQIJk1y+0JoaHiniMEoKyAaaBzcnJu\nvfXWIUOGiEhYWNjYsWO7du06aNCgESNGfPXVVx5rOQCcFUKESiFEqKzc3NwjLkk+G6vVarFY\n3AKCIiLS7f/+T/fjj877+/bJ7bdLbq797siRsnChfPGF8wHjxwtfhkCACJgG+vDhwx4Xyfr3\n7//hhx/eddddjz/++LvvvuuvwoBAR4hQNYQI/cVqtf7888+1tbUe49XV1Var1bY8o0WLFo5x\nvV7f48gR04cfVublNe3fX556Stq2dT7t0Uc9P8DWrZW7dmmt7BtvyCef6P/4x6IvvjDExMTf\ncYe1Z09xubwdGhoaFhZ2Ht8dgPMoYBroFi1abK5ziunIkSO3b9/+2muvtW7d+sknn/RLYUCg\nI0SoGkKEv4emaXU7YBGxWq0hISGlpaU762xnodPpSktLIyIiDAbDiRMnXJPoRqMxPj6+8uBB\nS22toX17j9dMnjVL/9ZbESIRIrJjh8yYIZs2SXq6fbqsrG4ZqxYtKm3d2m1o6FARkSNHPDbl\nMBgMQ21TANQTMA30zTffPHny5ClTptx///2ufyl75ZVXDh48+NRTTx08eNBisfixQiBAESJU\nTaMPEVqt1qqqqrrjZrM5NDTUYrEcPHjQdVyv1+v1+oqKCoPBYDQa9+7dW1NT45jV6XTh4eG1\ntbW1tbWRkZGlpaVeX/xUEhISEhISzAcOaCkphsjI5s2bu862OHQo5YUXZP16EZGuXeX//k/6\n9LHPlZXJ5Mlur1VWJs8+61yV0bu3fP2167wWH99v9GhxX3NosVhCQkI89ugQkdDQgPkBDQSh\ngPn6fPHFFxcsWPDII49kZ2d/8803jnGdTvfxxx/HxcW98847fiwPCGiECJUSECHCwsJCs9ns\nMVhTU6NpWnh4+L59+8rLy12njEajxWKprq6Oioqqrq4+qx7XtpihqqpKr9cbjcba2lrXi8QG\ngyE5OflEUVFtSUlCq1ZxcXEmk8kxq9Pp2jZvrv/qq4Nr17a55hrr4MFiNLq+eNySJSGjRsn+\n/Zperxs2TN57TxIT7XNHj8rgwXLokP3uli1y442yebPY/nVycsTlA9n99JPz9ttvS+/e4vj/\noNfrpk6Nio098zcOQFkB00A3bdp006ZN48ePN7p/7xMRnU737rvvXnnllU899VReXp5fygMC\nGiFCpfgmRFhTU1NZWVl3vKqqKiIiori4ePv27a59qm2pQ3V1tdFotN1wndXr9WFhYbYLw2Fh\nYRaLxWq1OmZDQkJatWpVtW9fcUFBm2uusRoMrqssdDpdy+bNI5cty1u0qNWll4bdfrsWE+Na\nUnhNjf6tt04sXhwaExN9xx1y771uF3H37ZNHHtEWLdJZLJKZKf/4h1x/vXN21y658kopLGwq\nIrNny1tvyfLl0rKlffabb+TOO+1lWCwye7YUFcm339q3k1uwwNk925SUyMyZ8vTTIiJeN1Ft\n0sR5u2NH2bZN3n778IoV8Z06hT/6qPTq5eUpAAKQjmNH6lfA+IoAACAASURBVDVt2rQHHnig\nrKwsOjra37UA59/hw4eTk5MJEapj7ty55yVEuGfPnurqao9Bk8lUU1MTExNz4MCB48ePn/mr\ntW7durXVenDJkvj09LC+fTX3BQaxBkOz//yndN480bTYIUPk8cfFdUfkQ4dk9GhZskREJCpK\nXnpJXM+sPnpUrr5afv3VfjcpSZYulW7d7HfLy6VnT7dz+G67TT7/3PF+pE8f+fln52xYmKxb\nJxdfbL972WWybp3bO8nKkgUL7LeHDnXedsjJsW8299RT8ve/e87++c/y4YciIhaLdOggv/3m\nOrnt5pu33nqr51NOoW3btr179z7DBwNByGQyhYWFrVmz5rLLLvN3LZ4C5go0gAZCiFA1Zxgi\nrKqq2rJlS92LIOXl5Uaj0Wg0Hj9+3HWVhU6ni4yMNJWXWyorTyQmiojrQVR6vb6PwaCfNq1k\ny5bmffuGPPGEuGbmNE0efVSmTm1ju67coYPMmSOdO9tnLRbp319WrbKvTti0SZYskZUrxZZX\n0TS57TZZudL+4IoKefJJSUpyXPqVxx5zds8icviwjBzp3O5t8mSPU6xl5kx56CHp21dEZPVq\nt+5ZRGpqZNo0+eADEZHSUnHdSM7mu+/EarVfY3Zvf+1++83eQGdkeJl1DOr1MmeODBkie/fa\n/ycNHtz8vfeurLN22XZRv+4rxbKcAwhYNNBAsCNEqBpHiLCwsNBjywib8vJy27EdHiuJo6Oj\nm5lM+jVrQuPi5NJLk5KSXGdjT5y4cMoUbfFindksXbrIO+/I1Vc7pxcskGHDxGJpISJbt8qn\nn8oPP0jPnvbZqVNlyhTng7dvl2HDJDfX3iLPnSurVrmVuG6dzJwpd90lIrJ7t7N7dvj3v50N\ntEusxW7rVjl0SJKTRUQ2bvTy/2jjRnsDvWuXl1nHYHW1uKwksTOZxGy2r4TOyHDr3W0cLfIt\nt8jf/uboj0VEa9bsUP/+ln377PebNtV9843566+PbduWMmiQqVs3sVpdF0a3aNGi7rJDAI1A\n42mg8/Ly7r//fhH59ttvz+pZGRkZZ7J9B9fn0IgRImw4ZrPZWqeHs1021ul0GzZsOHr0qGPc\nthWDpmkWi+Xnn3/WNM31ubY8XPLy5WUbN0Z16FB1880W9197UmbMiJo0yd7AJSfL9OkyYIB9\nrqZGeveWLVvsez3k5MiNN8pPP0mnTvYHjBkjrt8Jq6vlL3+RNWvsd13P+7DZuVNyc6V7d5FT\n9LibNtkb6IICL7OOQU2TOutMREQcvxu4rip2cAxeeKGXWcdgYqKkpYlHNqZHD2eO8JFH5Kuv\nxDUNOXCgdOhgvx0fL//9rzz6qLZ8uWiarm/frffem7dvnzgaaNs7aNXKkpS032KRTZs8Crnk\nkktaOXZ9BtCINJ4Guqys7LvvvjvbZ6WlpW3atKlultxVTk7OqFGj2FEIjRghwnNWU1Nz4MCB\nuuNlZWVRUVFWq9XrKouQ2loRsdY5u06n0115/LjMmpW/b1/nK68sffBBi8tV5NBDh5KGDdPZ\nurdFi+Sjj2TZMunRwz69aJG8+qrztQ4dkj/+UbZvF9u+bN9/L1u2uH2wqir55z/FdgpVYaFn\nWk5Efv5ZzGaxfes7fNjLm3ecyde0qZdZR4/bsaOXWcegTid9+siyZW6zycnSrp399h/+YF9z\n7BAd7bx2fvnl0r275xro++933v3nP2XQIOdV4agoef995+xVV8ns2fL007J7t2Y0ym23bRk5\nsspj1ceECScffthqsSQkJYlIC5cZvV7fvXt3fjoAQajxfNlnZmbmOtbMnY2uXbue/gGuG44C\njQ8nERYVFdX9MnfsK+wRttPpdKGhoZqmVVZWRkdH19bWeuxlYTAYEnfsCN++/UTz5scvuSTC\nNUsnklJS0vmf/wxZu1Z0Omvfvqa33rI6rneKGF9/3fDyy3NFxokU5udHZ2fLL7+I4zLzQw+5\nXfssLpZ77nGuFZ43z/ONHT8uK1bI8OEip1jq4FgfEhMjOp14NPpRUeJoDS++WHbscJvV6cTx\nzfOGG2T8eHE9viQ0VG680X67dWu56y6ZPt1t1raRhc1778mll8qJE/a7BoP861/i2Bd58GB5\n7jl5/XX7BfL4ePnoI3GcRWI0yoIFnrtwOBKEItK/v+Tm1rzzzrGNG5OuuKLqz3/eWVmpuV4y\nb9NGZs48uGNHbHJydFzc8ePHrY5KRIxGY1xcXFRCgqZpdQ/r1uv1dfdvBhAMGk8DHR4e3tmR\naFFPWVnZCZdvyjaappWWlsbFxVksFo/ZmJgYo9FYVlYWGRmp1+tLSkpc/5JrNBpjYmIcW65W\nVFS4Zu1DQkLi4+M1TauoqIiJiTGZTGXuB2LFxcWFhoaePHnSFmEpLi52nY2IiIiMjKysrDQY\nDAaDobS01HXDqdDQ0Li4OLPZXFNTExUVVVVV5dE9JCQk2I718vq+oqOjw8LCysvLIyIiTvO+\nrFZrRESEx/vS6XQJCQmappWXl8fGxtbW1paWlrq+eGxsrK3gmJgYESkpKXG98hceHm4r2LaV\nbFlZmetmsXq9Pj4+3vG+qqurK1zO1NXpdHFxcXq9/uTJk17fV1RUVHh4uON9nThxwnVd0Jm8\nLxEpKyv7Pe8rJCQkLCzs5MmTri+u1+ttBdv2362pqfH4ZGjSpElJSYmI7N+/32w2e3wyREdH\n2z7BwsLCQkNDS0pKXN+XwWCw7blrNpsjIyMrKipcl+TqdLomTZrYPsnj4+NNJlPdFzcajSdP\nnoyOjg4JCSkqKnL9ZLC9r8rKSp1OZ9tVzfXfKyQkxPZ5WFlZGRcXV15e7vEvEhERodfpzPv2\n6Vu2NIuU1TkTLqy0NH7PntrIyBNt23pcCdbpdM337Uv86Sd9dfWBTp0O9ejhtiObSNctW5rM\nmqU/eNCSnn78gQfKr7zS+VyTKW3cuFDHQrIWLeTLL+2rdUWkqEi6dnVczdWvWhUxZIhs2WK/\ngltUJK+9ZvsQ9hVjxcXy4ovyySciIlarl5XEW7dKUZF932LH9WBXRUX2G47j8Vw5ljokJEif\nPrJ2rdvsoEHO2+PHy1dfuR40LWPHOjeD69pV3n9fHntMbN8NIiJk0iTn+mkR+eADad3a8u9/\n644eDbn4Yvnb3+SKK5yzGRmyfbs2ZcqB775r1q1b+KOPliQlSUmJ8wHjxoUMHbrviy8imzRp\nMnTo3oqKmg0bHJN6vd4wceKJhx+uKCpq1blzUVFR8Zw5nu/0qqvkqqtEROpcZ2nSpEl8fHxk\nUlJYZKSINHW/mh4TE5PhNUoIILgF3jZ2mqYVFBTk5+fbfiLGxcWlp6enpKQ03Edcu3Zt3759\na2pqfk8WZOvWrXtdkigikrRuXduvvoooKqps3fq3oUMPuK/ka3L4cMc5c2Ly8mpjYg7077/j\nyis1l31Pw6urO82f3/Tnn3WaVtyt29abb65yucql07SM1atbffON8cSJ8nbtdtx661HHzznb\nh87Pz/jyy8jCwppmzfbecEOe+5ln0aWlnebOTdi61RIWdrR376033mh2eeN6s7njsmVJq1fr\nKypOdujw6/DhpS4/b3Q6XZstWy5YuDDi8OHKli13Dx26330v2yZHj3aYPTv2t99qo6MPXn31\njv79rS6Ly8NqajotWNBs0yad2VzSrdvWW26pjIpyzIaItF+zJmXZMmNJSUVq6vbhw4+6/7u3\n2LMn84svIvfurWnatHDQoN29eonLxaHo8vJOc+cm5OZaDIZjvXr9+oc/mFzfl8XS4Ztvklat\nCq2oKM3M3DZixAn395WSm5v21VcRhw5VJifnDRmyz/2v0gnHjnWcMydm505zVNThq67aPmCA\nxeV9GU2mTl991eynn0LM5pIuXbbeckuly5aIOpG09evb/Pe/YcXFFampO4YNK3Jf2Jq4b1/m\n3LlRe/fWJCTsu+663y691PV9RVZUdPryy4ScHC009FjPnr8OHuz6vkKs1szly1uuXBlaXl56\n4YXbhg8/0ayZ6/tqvWNH2vz5R/bvb9GyZX5WVqFjRayIiMQVF3ecOzduxw5zZOThK67YPmCA\nxeXzMMxs7rBwYfMffwwxmU5cdNGvw4ZVuOwqoBNJ37gxZdEi47FjVampvw0fftD9CnfSvn0Z\ns2ZF7t5d26TJweuv33nllVaX9xVbWnrRrFmxmzZpISEne/fedtttrv/TjDU1XefPb7J0aWhZ\nWVVm5p777z/k8pmm07RO8+cnfvppSGWl1WgsueOOvffe69olp86d2/S993TV1SJiadv25Pvv\n17p0e3H/+lf4Sy85FwQPHSpffCGOf9BXXpHnn3d9I/LVV/KHP9hvv/ii/O1vbrMpKbJ7t33R\n7bvvymOPiYepU+XBB0VEvv7atoGxWeSgiP2ToGNHe8rNYpG4OLcW1ubgQXvY7oUX5OWXPWfX\nrBHb9k9VVdKrl2zd6pwKD5cffxTH0p3du+WGG5y7Ulxyifz3v27rj3fskIkTy3/4wdCyZdif\n/3xsyBCL+4+PkCNHji1YoGla86ysQovF9fdAnU5nOwmluLi4VatW5eXlJ0+edH2u7VKuyWSy\nXeX1ehb3qYSEhDRv3tzxFwOr1eqx90h6errt91uvW5HGx8eHhYWd+YcD4DMqb2MnWuAoLi4e\nN25couOMKBdt2rSZOHFiZWVlQ3zcNWvWyP9O2Dpv/vlPTcTtv8WLnbM7dmhRUW6zDz/snK2p\n0Xr2dJvt1Elzfe/PPOM2Gx6ubd7snP3+ey001O0Bb7/tnC0u1tq0cZsdOFCzWJwPGDHCbbZZ\nM+3AAefsJ594vq/5852zu3drsbFus/fd55ytrdX69HGbzcjQysudD3jxRbdZo1HbuNE5u3q1\nZjC4PeD1152zJ05o7dq5zV51ldv7uvNOt9kmTbTCQufs5597vq85c5yzBQVafLzb7D33OGfN\nZu2KK9xm27fXSkudD3j5ZbdZg0Fbv945++OPnu9r4kTnbFmZduGFbrP9+mlms/MBf/6z22x8\nvFZQ4Jz98kvP9/XZZ87Z/fu1Zs3cZm+/3TlrsWgDBrjNpqZqJSXOB7z5pttsaKi2cqVz9qef\nNKPR7QFPP+2cPXlSu+ACt9kuXbSqKucDbr7Z85Nhwwbn7Guveb6vsWOdswsXes62bOmsfNs2\nzy8QEe3DD+2zJpMWHu45e/HFzhfv0cNzVkTbtMk+++CDXmb/8hfnv3Xd2csvd774wIGes+3b\nO2ePHdNat3abveUWzVV+vjZokBYSYvviqpw/v9Ddvt27902Z8vOf/nR4+vTcLVuys7MXuFi4\ncOGiRYvmzJljuz37bMydO/fHH39ct27dN99889NPP61fv37FihXfu9ixY0dhYeG2bdv27t1b\nWEdZWZkGIPjYFtetWbPG34V4ETAN9MGDB9u1ayci6enp99xzz/jx4998880333zz+eefv+22\n21q2bCkiXbt2LS4uPu8f+vw30Far1qSJ5w/Ciy5yPuCOOzxndTpnP/ef/3j5KfvBB/bZY8fs\nPyBd/8vKcr64R5MqokVGaiaTfXbiRC8vvmyZfXbjRi+zrq1JixaesxkZztk//cnL03fvts/O\nmeNl9r337LMnT2p6vefsoEHOF7/ySs/ZsDBny/X6615efNEi+2xOjpfZhx5yvnhKiudsu3bO\n2fvv9/L0bdvss9nZXmbfess+W1Hh2R+LaNdc43zxa6/1nA0Ndf5e8Y9/eHlxxy8tO3d6mb33\nXueLp6XZBrc4Zlu1cs4++qiXpzt+GVu61Mvsq6/aZ2tqvDSaffs6X/yGGzxnQ0I0x9fvu+96\nefEZM+yz27d7mR0xwvniHn2kiBYZ6fy9YuRIL09fuNA+O22al9k77rDPbtvmZdZodP4y5vH7\njO2/77+3z779tpfZKVPss9XVWtu2mkiNyHbH7BtvON/Xrl1uv9JERdUuX17jwrR3r+X++0sv\nuKDi4ovNr7++buXK5S6+//77FStW/Hf+/EWffrpixYpFixbNdTdv3rx58+bNmTNn/vz58+fP\n/9Ld+vXr8/LyNm/evGvXrrw6jhw5ogHAeaVyAx0wa6BfeOGF/fv3z5kzZ7gtEOPOYrFMmzbt\n4YcfnjBhwjvvvOP78s5OYaG4LwYVEdm2TUwm+995N2/2nNU02bxZbCsW6s6KOPP1OTle9j11\nPEXTPJP4IlJZKbt22Xezqjtre/q1157yQzsGDx3ysgpz1y6prLSfSXaqp6elnXLWUU9urtTd\nbdD1KXWfXlMj27fb40Snel+2nNPp39fx4x67VomIFBTIyZMSF3e6p9vCYad/8V9/lbp/rT79\n+zKbZetWsR1gdqoXHzJEROSXX073ocvKJD9fRA6LdBUpEEkVkQMH5OhR+74Np3pxW3TsVP9L\nbXbs8LI3metT6j7dapXcXPvSWK+BYMfgtm1eZh2DVVWyf7/nbGWlHDhgT+MdPOjl6Y5Br5ta\nOr6mWrWSkBDPL7HWrZ0LPHr39ozrhYU5M2233iqvvirHjjlnW7SQYcOcj5w9W265JfvAgXEi\nhSLm4cMLhw61/TOJiOj1IV9/HT1zpm0bu5Kbb95y9KjnQXr9+0v//vbb7ltnhIaGtm/f3hQV\nZTKZoqOjE9xPog4JCcnIyKibkwMA1BUwDfTixYtHjhzptXsWEb1eP2bMmFWrVs2bNy8AGujm\nzSU0VDz2zmva1Lk1aVKSl739bcscXW+4cux1dfpZnU6Skpw/j+s+wP3khbP70La34JL0EhGJ\njxfHEVy/58VPP2t7gPuqSrdn/Z4PHRcnERHifmKFREdLTMwZvbjX2TN/X0lJ4rJP8Pl88ago\niY6WsjJb62dvAMPDJT7+jF78HD6062CrVlJ39zfHYn2vqQbHoGODM1eOwYgIadtW3CMHEhUl\nju14u3WTulteOjaUuPxyLy/er5/9RmysDB7s2bM6DgQRkVdekaVLXVvk2ldeMYWG2tcux8WF\nfPFF2NixIb/8IiLWnj13PvbYoV9/dXy963Q6w0cf7fn3v81Ll256++2jrVtX5OS4fiij0Rhy\n1VVVvXuHh4framoi3bf4aN26dXp6utls9nqWoV6vDw8P9/LuAABnKWAa6OPHj6fZrlOeWocO\nHebPn++ben6XyEi58UbJznYbdP3dYMQIzx/wGRnOrM9NN8nzz7v1c0aj/YqjiFx4oXTr5nnt\ncMQItw/0xhtus9dc49zGddgwt01SRaRJE+dZDH37SsuWnhfwHC9uNEpWlsyd6zY7bJgz8TZi\nhCxd6jbbvr39IAYRueEGeeYZt4yUwSBDh9pvt2snPXt6ntfg8b48wlv9+jn7uVtukcmT3X5p\niYuTgQPtty+9VNq0kcJC7y8eGio33yyffeY2e8stzouOI0Z4/mumpkqvXvbb118vMTHiuguE\n7QVtWreWPn1k3Tq3p7t+Mgwf7nk5tndv575mQ4fKW2+5va/oaFsQTUSkZ09JTZU9e7y/eEiI\n3HKLfPJJokieI7I2ZIg4rkEOHy4euxm0aiV9+thvX3utxMeL694XoaFyyy32282by9VXy/ff\nuz3d9d/rj38Ul40UREQuuUQcX+PDhslrr7ldw46NdQb1LrpIevXyfPqoUc7bjz0mY8e6zT76\nqDjij48/LtOnu/1aMnSo/Yq+7cVffFEmTnRMatdcU3nHHY7PTN1774XV1Ohtn8l6fdXIkbnX\nXWddv97x+PDPPkv6/HPZskWXmFgyeHBO8+ayeLFbMc88Y6yo0ERqbRlZl27blni76okn2g0f\nbrjwQrfwr4hOp7vggguiXJK1AAC/CJhdOFJTU3v37j179uzTPGbIkCFbtmwp8Hrq1e9wXnbh\nOHbs2DGXH5P64uJWjz8e+b/t+ksHDMh96imr4+KQpmV8+GHzzz/XWSwiUpOWtm38+HKXHQyS\n165t9/rr+hMnRMQSE7P3iScOuBzJG7l/f6eJE8Ntm7aGhBwbNmz7mDGObk9XW9v5rbfilyyx\n3a28+OKtL7xQ47IzQ9uFC1tPmRJSVSUi5hYtfnvuuWPdujlm47dvz/zb3wz794uIZjQeuvfe\nvFtvdcyGlpZ2eeWVqP+1g2VXX537zDMWxxVokYyPP24+fbrtfZkuuGDbiy+WuZyB12L9+rTX\nX9cXF4uINTp67+OP73f07iIRhw51njgx3HatLiSkeOjQbY88ojnel9nc6R//SFi40Ha3qmvX\nrS++WG1biiAiIm2WLk15992QykoRMTdvnvfcc0WO3l0kbteuzIkTjYWFIqIZDIdHjdp9xx3O\n91VeftGrr0avXm1/X/365f71rxaXPiZ9xowWH3+sM5tFxNS27Y7x40+2b++YTdywIe2110KP\nHxcRa1TUvsceK7zuOuf7OnKk04QJEf/bHqEkK+vXxx5zbLqis1g6vvNOk/816NWdO2998cUq\nl6u/KV9/3eadd0IqKkTE0rRp3rPPHnH07iJxu3dnTphg3LtXRLTQ0KK77sr7858ds/qKis6v\nvBL1v83RKvv23TFhgtlxZV0kdfr05v/8p662VkTMKSm7J04sddl+pMlPP7WbOFFfVCQiWmTk\nocce25+V5Zg1FhVljh8f/r8TLkqzsnY+9ZTm2FfYak1///2EmTNtSyZqunbdOWFCtcsl6hZr\n1rR+9VX9sWMiYk5O3vP880Uun4cRR49e+MYbts80a0zMgYce2u34dej/27vz4Cbq/4/jn23S\nTXOVUFrsXShlAq1+GQtUUJBrcNTxa0FHBRWdIqLgOSiKB16DFyjDOAMqHkA9q+NRvB1HBBVq\nFQW0h1QK5SotFNOkF2nT/P7Iz05IW/wuNN1t9/n4Sz677L63zWfzYv18PiuEJETGJ5/Eb9hg\nPH68zW4/Onv2rv/+tz1o/ZAYlyt9wwbLzp3tNptrypQd06e3Bm2VJCl+9+7Ybdsimpvd//nP\nvnHjWjuN67AcO2apq/MkJJwIWngkwOFw2O32+vp6q9VqNBp9Pl/wbXbAgAHDhg0LrAZoCDrp\n//9GeEgMAP/Q8iocfSZA33333S+88MLy5cvvuOOOzksONTY2Ll++/Iknnrj//vufeeaZnj11\njwTo3bt3hyxjJ4SwVlZK+/e3Z2S44+NDVlOOioqyu91yWZk/NrYhI8PT0hL8mzIajdGSZC4p\nEX5/c2amW5JClm2yWyzWioqI2trWESPcDkfIqsNms9leW2vYvdufnOwZOrSxqSn44LIs273e\nqNJSf1RU88iR7ra24KV/IyIiok0mS3m55HafyMz0WCzBb6CQJMlisUTv3y9VVbUPG+ZOSOji\nujweubS0PSamyel0NzeHXJddkiylpcLna87M9BgMwatZSZJkt1ptFRVSTU2r0+mJiQlZdTgq\nKiq6rs5QXi6Sktzp6V1cV2trVEmJX5abMzPdPl8X1/Xnn5LLdSIz02O1dnFdBw9Ke/e2Dx3q\nSU5uPHk1MZPJFN3YKJeW+gcObHI660++LoPBEG0wWEpKRGtrS1aW22gMuS6bxWLfs0ccOuQb\nOdI9aFDzycNFzGZz9PHjhtJSkZjYMHy4p7Ex+OCRkZHRbW1RJSXCaGzKynK3twdflyRJ0VFR\n1vJy6e+/vZmZbrs95LrMZvOAgwf3FBUNy8lxp6V1fV0lJf7o6KaRI+tPnDhpReSICIsQtvJy\n6cSJppEjG0ymkJd6mqOiovftM1RXezMyPLGxIaeOjIy0ud3yX3+1x8U1pKU1nzgR8kMzS5K5\nstIvSS3DhjX7fCGnttlshro6qa7OP2xYS3t7yMHtdrvRaGw6csQSH+/3+xsaGoILs9lsdrvd\n4/GYTCZZlhsbG4N/aCaTKSEhobW11ev1Wq1Wv98f8iNNTk42GAw+n69zAg78Rs7w5Rper7ey\nsnLEyUtAAoDeEKB7gMvlmjZt2q+//mq323NyclJSUmw2W+B7saqqqri4uKmpaeLEiZ9//nmX\nK32eiR4J0IBmHTlyJCEhQc9vItSa999//5577tkfMqYIAHRGywG6z4yBdjgc27ZtW716dX5+\n/nfffRfyOrTRo0fPnTt37ty5XT4QAnAKgdlmneecQS1dTgEEAGhHn3kCHaylpeXAgQOBNxFG\nR0enpqaG9dkwT6DR71VWVqYHDUaHutra2g4fPpx68gspAUBveALdw6KiooYPH652FUD/QXrW\nFKPRSHoGAC3j/xICELtOXmwY6vJ6veWBVXQAAJpEgAb07siRI6NGjdoXslw01FNYWHhR0Kp8\nAACtIUADesckQq1hEiEAaFyfHAMNoAcNHjx4z549DLrVjtzc3LFjx6pdBQCgWzzkAMAkQm1h\nEiEAaBwBGgCTCLWFSYQAoHEEaEDvmESoNUwiBACNI0ADesckQq1hEiEAaByTCAG9YxKh1jCJ\nEAA0joccAJhEqC1MIgQAjSNAA2ASobYwiRAANI4ADegdkwi1hkmEAKBxBGhA75hEqDVMIgQA\njWMSIaB3TCLUGiYRAoDG8ZADAJMItYVJhACgcQRoAEwi1BYmEQKAxhGgAb1jEqHWMIkQADSO\nAA3oHZMItYZJhACgcUwiBPSOSYRawyRCANA4HnIAYBKhtjCJEAA0jgANgEmE2sIkQgDQOAI0\noHdMItQaJhECgMYxBvrfybIshDCZTGoXAoTR0KFD1S4BJ5EkSe0SAEB9gRimNZLf71e7hj5g\n586dbW1talehdcuWLauurr799tvVLgTqcLlcd9xxx/LlyxMSEtSuBep49dVX29rabr31VrUL\ngTqOHj26aNGilStXxsXFqV0L1PHSSy85HI7HH3+8pw5oNBpHjRrVU0frQQRo9Jjbbrvt2LFj\nBQUFahcCdVRXVycmJpaXlzudTrVrgTrmzZvn9Xrz8/PVLgTq2Ldv39ChQ/fu3TtkyBC1a4E6\n5syZExUV9corr6hdSNgxBhoAAABQgAANAAAAKECABgAAABQgQAMAAAAKEKABAAAABQjQAAAA\ngAIEaAAAAEABAjQAAACgAAEaAAAAUMCodgHoP2RZD2BidQAADVNJREFU1uYL69E7IiMjJUni\nM6Bn/PZ1LvAB4GOgZ/pJArzKGz2mvr6+ra1t0KBBahcC1VRWVqanp6tdBVTjcrna29tjYmLU\nLgSq4Sagc8ePH4+IiHA4HGoXEnYEaAAAAEABxkADAAAAChCgAQAAAAUI0AAAAIACBGgAAABA\nAQI0AAAAoAABGgAAAFCAAA0AAAAoQIAGAAAAFCBAAwAAAAoQoAEAAAAFCNAAAACAAgRoAAAA\nQAECNAAAAKAAARoAAABQgAANAAAAKECAxplqbW194IEHDAbDmDFjOm91uVx33333kCFDZFlO\nTEycN29edXV17xeJ3rF+/XqpK8uWLVO7NIQXPV3P6Pj6pPNvf6PaBaBvKysru/766ysqKrrc\n6vV6p02b9uuvv1555ZXZ2dl79uzJz8//9ttvt2/fPnDgwF4uFb3A5XIJIWbPnp2amhrcfsEF\nF6hUEXoDPV3n6Pg6xLe/8AOnq76+3mw2jxkzpqKiwmQyjR49OmSHlStXCiGeffbZjpaCggIh\nxD333NO7laKXPProo0KIn3/+We1C0Kvo6TpHx9cbvv39fj9DOHD62traFi5cuHXr1oyMjC53\nyM/Pt9vtd911V0fL1VdfnZGR8cYbb/j9/t4qE70n8CDK4XCoXQh6FT1d5+j4esO3v2AMNM5E\nTEzMc889FxkZ2eXWlpaW33//PScnx2QyBbdPmDChtrZ27969vVIjelXH96jP5zt48OCxY8fU\nrghhR08HHV9v+PYXBGiEz4EDB3w+X0pKSkh7WlqaEKKyslKNohBe9fX1QohVq1bFxcWlpKTE\nxcU5nc63335b7boQRvR00PERTCf3BCYRIlw8Ho8Qwmq1hrTbbLaOrehnAg+i3nnnnfvuuy8p\nKamsrGz16tXXXXedx+O55ZZb1K4OYUFPBx0fwXRyTyBA49+5XK4lS5Z0/DEjI+Pee+/9H/+u\nJEkhLYHxT53b0Yd095FYunTp7bfffvHFF3fcOq+//vrs7OwHH3wwLy9PlmV1ykX40dP1jI6P\nzvr9PYEAjX/X0NDw8ssvd/zxggsu+F8CdHR0tOjq35put1sIYbfbe7RG9KruPhJTp04N2TMz\nM/PSSy/96KOPdu7cOXbs2F6tEr2Cng46PoLp5J5AgMa/S05OPo1ps6mpqUajsaqqKqR9z549\nQojhw4f3THFQg6KPxODBg4UQDQ0N4awIqqGno0t0fN3SyT2BSYQIF1mWR48eXVxc3NTU1NHY\n3t6+efPmlJSUkPX20Q80NDS8+OKL77zzTkh7SUmJ+Gf6CPoferrO0fERQif3BAI0wuimm25q\nampasWJFR8vatWsPHz48b948FatCmFgslieffHL+/Pnl5eUdjYWFhT/88MO5556bnp6uYm0I\nK3q6ntHx0Zke7glSv1nRGr1v8+bNX3zxReC/n3vuubi4uBtvvDHwx8WLFw8aNMjn802ZMuX7\n77/Pzc3Nzs4uKysrKCg4++yzi4qKLBaLeoUjXDZu3DhjxgyLxTJr1qzExMQ//vjj448/ttvt\nmzZtys7OVrs6hAs9Xefo+HrDt78QvMobZ+Dpp5/u7nNVUVER2Mfj8dx7771paWmRkZFJSUm3\n3XZbXV2dumUjrLZu3XrJJZc4HA6j0ZiYmHjDDTd0fBjQj9HTdY6Oryt8+/v9fp5AAwAAAAow\nBhoAAABQgAANAAAAKECABgAAABQgQAMAAAAKEKABAAAABQjQAAAAgAIEaAAAAEABAjQAAACg\nAAEaAAAAUIAADQAAAChAgAYAAAAUIEADAAAAChCgAQAAAAUI0AAAAIACBGgAAABAAQI0AAAA\noAABGgAAAFCAAA0AAAAoQIAGAAAAFCBAAwAAAAoQoAEAAAAFCNAAAACAAgRoAAAAQAECNAAA\nAKAAARoAdGfZsmWSJD3xxBNK/+LkyZMlSfrxxx/DURUA9BWS3+9XuwYAQO+pqanJyMiIjIzc\nu3fvgAEDFP3dzZs3T548+bzzzisqKgpTeQCgfTyBBgB9eeSRRxoaGhYtWqQ0PQshJk2aNGnS\npJ9++um9994LR20A0CfwBBoAdKS2tjYlJcXn8x06dOiss846jSO8++67s2fPHj169C+//NLj\n5QFAn8ATaADQkddff93r9U6fPr1zep4wYYIsy+ecc05hYeEpjpCbm2u327dv3759+/ZwVgoA\n2kWABgD1vfnmm5IkPfbYY+E+0SuvvCKEuPbaaztvmj9//sKFC//6669rrrlm//793R3BbDbP\nmDFDCLF27drw1QkAWkaABgC9qKioqKysFEJMnDix89Ybbrhh1apVTz311IkTJ1577bVTHOfC\nCy8UQnzxxRdhqhMANI4ADQB6sWXLFiFEXFzckCFDutsnLy8vKipqw4YNp5ghc9555wkhDhw4\nEIjjAKA3BGgA6Buqqqry8vKSkpJkWY6Njb388suLi4uDd/jss89ycnIsFkt8fPxdd93V3Nyc\nkpKSnZ3dscNPP/0khBg1atQpzuJwOCZPnlxVVbVp06bu9snKypJlWQixdevWM70qAOiDjGoX\nAAD4dwcOHMjJyWlqalqwYEFWVtahQ4fWrFlz4YUXfvPNNxMmTBBCbNmyJTc3Ny4ubsmSJbGx\nse+///6sWbM8Hk9SUlLHQQ4fPiyEiIuLO8WJXC7XDz/8IIRYt27d1KlTu9wnIiJi4MCBNTU1\ngQMCgN4QoAGgD1i6dGltbe2HH344c+bMQMvMmTPPOeecxYsXb9u2TQixbNkyn8/3ySefjBkz\nRghxyy23TJ8+vb6+PvggR48eFULExMSc4kRr1qxpaGgQQnzwwQerV6+Ojo7ucreYmJiamprA\nAQFAbxjCAQBa5/f7P/7447POOiuw/EXAyJEjx48fX1RUVFdXJ4T4/vvvR4wYEUjPQgiDwXD/\n/feHHKelpUUIYTKZujtRS0vLCy+8YLVa8/LympubCwoKutvTbDYLIZqbm8/gsgCgryJAA4DW\nHTlypL6+PisrS5Kk4Han0ymE2L17t8vlamlpycjICN56/vnnhxxn0KBBQoi///67uxNt2LCh\npqZm/vz59913nxBi3bp13e15/PhxIURsbKziiwGAvo8ADQBa19jYKISwWq0h7YHHwI2NjYGH\n0BaLJXir3W43GAzBLYHRz4Hs21l7e/vzzz8fGRm5aNGiESNGjB8/ftu2bX/++WeXOwcOcurh\n1ADQXxGgAUDrbDab+CdGBwu02O32yMhI8c8IjQ5NTU0+ny+4JTMzUwjR3dpzH374YUVFxZw5\nc5KTk4UQc+fOFUKsX7++8551dXVut7vjgACgNwRoANC6+Pj4mJiYsrKykLWZS0tLJUlyOp3x\n8fERERFVVVXBWwOL1gULvACltLS0cxYXQqxYsSIiIiIweEMIMWvWLKvVmp+fH5LChRCB5fNk\nWR43btyZXRkA9EkEaADoA6644orq6urCwsKOlh07dhQXF0+dOtXhcMiyPGbMmF27dpWXlwe2\n+ny+Z599NuQg48aNM5lMPp/vl19+Cdn03XffFRcXz5w5MzCuWghhs9muuuqqw4cPf/311yE7\nB6L5uHHjAmNIAEBvWMYOALTiyy+/dLlcIY25ublTpkx5/PHHP/300zlz5tx5551Op3Pfvn2r\nV6+22WwrV64M7LZ48eKrrrrq0ksvXbhwYXR09Jtvvpmenh6y4IbZbJ4xY0ZBQcHGjRsnTZoU\nvCmQtpcsWRLceNNNN61fv37dunWXXHJJcPvGjRuFENdee20PXTcA9DV+AIDa3njjje7u0itW\nrAjss3///ry8vISEBKPROHjw4FmzZpWWlgYf5LXXXnM6nbIsp6WlPfTQQ16vV5bl888/P3if\nb7/9VgiRmJjo8/k6Gnft2iWEmDZtWufCnE6nyWSqq6vraCktLRVC2Gw2t9vdkz8CAOg7JP/J\nI+oAAP2D2+0eMGDA5ZdfHjzwQwiRmZlZVlb21VdfXXTRRadx2AcffPDpp59esGDBmjVreqhS\nAOhjGAMNAP3BunXrJk+evH379o6WwAIagRd9B3vyySeFEM8888xpnKW+vv7FF1+0WCwPP/zw\n6dcKAH0cY6ABoD/IzMwsKiq67LLLFixYkJiY+Ntvv61duzY1NfXmm28O2XPmzJkTJ07ctGnT\nli1bAuty/O9WrVrlcrmWLl2amJjYc7UDQB9jeOyxx9SuAQBwppKTk6dMmVJRUVFYWPjBBx8c\nPHjwyiuvfOutt7p818nYsWMHDx7scDhGjBih6Cw7duwYP3784sWLZVnuocIBoO9hDDQAAACg\nAGOgAQAAAAUI0AAAAIACBGgAAABAAQI0AAAAoAABGgAAAFCAAA0AAAAoQIAGAAAAFCBAAwAA\nAAoQoAEAAAAFCNAAAACAAgRoAAAAQAECNAAAAKAAARoAAABQgAANAAAAKECABgAAABQgQAMA\nAAAKEKABAAAABQjQAAAAgAIEaAAAAEABAjQAAACgAAEaAAAAUIAADQAAAChAgAYAAAAUIEAD\nAAAAChCgAQAAAAUI0AAAAIACBGgAAABAAQI0AAAAoAABGgAAAFCAAA0AAAAo8H+uk0BWJ0nZ\ndAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Lambda selection by CV with RIDGE\n",
       "\n",
       "”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 9"
     ]
    },
    {
     "data": {
      "image/png": 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6Gw3UEAHBUFGgCALFKqqlPyfE/wKCGQxSjQAABkl+sK8leGI1ticbuDAOgcBRpw\nvVBIli+X1la7cwD43FDdO0z3PhVkEhrIUhRowN2CQRk+XGpqpLJSduywOw2Az11TkP9CW3vQ\nsuwOAqATFGjA3errpalJRKS5Werq7E4D4HNT83ymorzEfnZAVqJAA+4Wifz9OsxT/0C20BXl\nkoK8P7QFmYIGshAFGgCAbHRNQf62WHxNJGp3EABHokADAJCNyjTtHJ/JfnZAFqJAAwCQpa7M\nz3sjFD6YTNodBMA/oEADAJClzvaZharyOqcSAlmGAg0AQJbSRL7q87EXB5BtKNAAAGSvr+f7\nVkeiO+IJu4MA+DsKNAAA2etMXR/o8bzSHrI7CIC/o0ADAJDVpuX5XmxnFQeQRSjQAABktYvy\nfVti8Y9iMbuDAPgcBRoAgKxW7vFU6fpLQVZxANmCAg0AQLb7er6vrj3Eg4RAlqBAAwCQ7abm\n+fYnk43hiN1BAIhQoAEAyH49VHWCabzEXhxAdqBAA+7m8XR+DSDLfD3P95dQKGxZdgcBQIEG\nXK66WoqLRUR0XWpr7U4D4Kgu8JmWJUs41hvIAhRowN38fmlslHnzZNUqqaqyOw2AozIVZWKe\nj1UcQDbgN7aA61VUyKxZdocA0LWv5/lm7N3fkkyWqsx/AXbiXyAAAM4wzjR6quprTEIDdqNA\nAwDgDKrIFFZxAFmAAg0AgGN8Pc+3NhLdHo/bHQRwNQo0AACOMVT3DvJ6XmYSGrAVBRoAACeZ\nlud7MRhiO2jARhRoAACc5KK8vE/j8feiUbuDAO5FgQYAwEn6ebSRhl7HKg7APhRoAAAc5ut5\nvleCoYTdMQDXokADAOAwU/J8Act6KxyxOwjgUhRowPVCIVm+XFpb7c4B4HgVqWqNadQF2+0O\nArgUBRpwt2BQhg+XmhqprJQdO+xOA+B4fT3P99dQuN1iNw7ABhRowN3q66WpSUSkuVnq6uxO\nA+B4neszvYqyqD1sdxDAjSjQgLtFDltDGeY7MeAYhqJM9pkvtbOKA7ABBRoAAEf6er5vZTiy\nL5G0OwjgOhRoAAAcabRh9NC0xfzuCMg4CjQAAI6kipznMxZxogqQcRRoAACcaqLPtyISDSRZ\nxQFkFAUaAACnGmfoPkVZxokqQGZRoAEAcCqPotSaxqIQy6CBjKJAAwDgYBN9Zn0oHOFEFSCD\nKNAAADhYrc9MiKxiFQeQQRRoAAAcLE9RxpnGX1nFAWQQBRoAAGeb6DMXh8IJuwxvCucAACAA\nSURBVGMA7kGBBgDA2S7wmQeTybWRqN1BALegQAMA4GwlqjrS0P8a4kQVIEMo0AAAON5En29R\nKMxOHEBmUKABd/N4Or8G4CgTfebOeOKjaMzuIIArUKABd6uuluJiERFdl9pau9MAOEH9PNoQ\n3cteHEBmUKABd/P7pbFR5s2TVaukqsruNABO3ESfuYhl0EBGUKAB16uokFmzZMQIu3MAOCkX\n+nwbY/Ft8bjdQYDcR4EGACAXDPJ6TvN43mAVB5B+FGgAAHLE+T5zUTsFGkg7CjQAADniwjxz\nfTTanOBQQiC9KNAAAOSIr+h6X01bwioOIM0o0AAA5AhF5DyfuYgCDaQZBRoAgNwx0Wc2RKIH\nk0m7gwC5jAINAEDuGGPoeYryZjhidxAgl1GgAQDIHR5FOdc0FrVzogqQRhRoAAByysQ837Jw\nJGxZdgcBchYFGnC9UEiWL5fWVrtzAOgeNaYhIm+xigNIGwo04G7BoAwfLjU1UlkpO3bYnQZA\nNzAVZYJpsBcHkD4UaMDd6uulqUlEpLlZ6ursTgOge0z0mUtCYc5TAdKEAg24W+SwX/KGma8C\ncsR5PrMtmWxkFQeQHhRoAAByTbGqVrOKA0gbCjQAADloos9cFAqzEweQDhRoAABy0ESfuTuR\n2BCN2R0EyEEUaAAAclBfTfuy7l3CKg4gDSjQAADkplrTXMbDwUAaUKABAMhNtT7jg2hsXyJp\ndxAg11CgAQDITVW6Xqqqy5mEBrobBRoAgNykiowzjaXsBg10Nwo0AAA5q8ZnLg9HOJIQ6F4U\naAAAclaNabQlk+9GonYHAXIKBRoAgJxVqqrDdH0ZqziAbkWBBgAgl9X6jHqeIwS6FQUaAIBc\nVmMaH0ZjuxMshAa6DQUacDePp/NrALlimK73UNW3WMUBdB8KNOBu1dVSXCwioutSW2t3GgDd\nTxWZYBosgwa6EQUacDe/XxobZd48WbVKqqrsTgMgLTo2s4tblt1BgBzBb2wB16uokFmz7A4B\nII1qTKM9mVwfjY0ydLuzALmAGWgAAHJcsapW6fpS9uIAugkFGgCA3FfrM5aGWAYNdA8KNAAA\nua/GND+OxXaxmR3QHSjQAADkvi/r3h6aupy9OIDuQIEGACD3KSI1pslmdkC3oEADAOAKtabx\nVjjMZnbAyaNAAwDgChNMI5S01kZjdgcBHI8CDQCAKxSp6pkGm9kB3YACDQCAW9SYxjI2swNO\nGgUacL1QSJYvl9ZWu3MASLta0/w4FtvJZnbAyaFAA+4WDMrw4VJTI5WVsmOH3WkApNcQ3dtH\n09jMDjhJFGjA3errpalJRKS5Werq7E4DIL0UkbNNY2mIZdDASaFAA+4WOWwiikeLABeoMY2V\n4UiMzeyAk0CBBgDARSaYRkTknWjU7iCAg1GgAQBwkUJVPVP3shcHcDIo0AAAuEutabIbNHAy\nKNAAALhLrc/YGIv/Lc5mdsAJokADAOAug73evpq2jElo4ERRoAEAcJeOzeyWsRs0cKIo0AAA\nuE6tz1wRjkTZzA44IRRoAABcZ7xhxETeibCZHXAiPHYHSJllWVu3bt2yZUsgEBCR4uLiioqK\nAQMG2J0LAADHKFCVkbpeH46cZRp2ZwGcx0kFuqWl5YEHHnjsscd27959xEvl5eXXX3/9rbfe\n6vP5bMkGAICznG0aL7W3ixTZHQRwHscU6J07d06YMGHr1q0VFRVTp04dOHBgfn6+iBw8eHDz\n5s319fVz5sx5/vnnlyxZUlpaandYAACy3TjT+I/Wg3sSid6aZncWwGEcU6Dvuuuuzz777Jln\nnrniiiu++GoikVi4cOEtt9wyd+7cefPmZT4eAADOMlT3lqjqykj0ojx+eQukxjEPEb788svX\nXXddp+1ZRDRNmzlz5pVXXvnCCy9kOBgAAE6kiow1jZVsZgekzjEFet++fWecccax3zNkyJBd\nu3ZlJg+QIzyezq8BuMA4w1gRjrCVHZAqxxTofv36rV+//tjvWbt2bb9+/TKTB8gR1dVSXCwi\noutSW2t3GgAZNcE0dicSW2Jxu4MADuOYAn3xxRc/++yzP//5zyORTn7ZFAwG77777hdffPGq\nq67KfDbAwfx+aWyUefNk1SqpqrI7DYCMOsWjDfBoK1jFAaRIsRxyCtGBAwcuuOCCd955p7Cw\ncMyYMQMGDCgoKLAsq62tbfv27Q0NDe3t7TU1Na+88kpBQUH3/tULFy6cMWNGIBDo9s8MAIC9\n7mk5sDuRXNCrh91BgCNFo1HDMN56663x48fbneVIjlnyWFJSsnLlyvnz5z/66KNvvvlmIpE4\n9JLX6x01atT06dOnT5+usRcPAADHbZxh/HD/gbhleRTF7iyAYzimQIuIruuzZ8+ePXt2OBz+\n9NNPO04iLCoqKi8v13Xd7nQAADjPONMIW9b6aGyUwXdS4Hg5qUAfYppmRUXFF+/v27evpaVl\n0KBBmY8EAIATFanqEN27MhyhQAPHzzEPER6PBx98sNNiDQAAjma8aazs7AF9AEeTUwUaAACk\napxhrI9EA8mk3UEAx6BAAwDgaqMMXVeUxkjU7iCAYzhmDfTo0aO7fM+OHTsykAQAgFziVZRR\nhr4yHDnfZ9qdBXAGxxTotWvXiojX6z3Ge+JxzlICACBl40zj+WC73SkAx3DMEo7bbrstPz9/\nw4YN4aO79dZb7Y4JAIDzjDeNLbF482FnLAA4BsfMQN93331/+ctfrr766hUrVhx7HjollmUt\nW7YsGj3Wwq8PP/ywu/46IBuFQrJmjVRVSXGx3VEA2GOw19tLU1eGI5fk59mdBXAAxxRor9f7\n+OOPjxo16s4773zwwQe769Nu3bp10qRJkePYvscpZ54DqQkGZeRIaWoSv19Wr5ZTTrE7EAAb\nKCJjDYMCDRwnxxRoERkyZEhzc/MxFjpPmTKlpKQkpc95+umnh8PhY79n4cKFM2bMUDjjFDmp\nvl6amkREmpulrk5uvNHuQADsMc40/qP1oCXCdzugS04q0CJSVFR0jFfPOeecc845J2NhgFxw\n+K9fuvphEkAOm2AaP9qfbIrFBnffOkkgVznmIUIAAJA+fk071eNZGeZIQqBrFGgAACDScaY3\nBRo4DrlToDdv3jxx4sSJEyfaHQQAAEcabxoNkWiUh+aBrjhsDfQxBAKBN954w+4UAAA41RhD\nj1nWumh0jGHYnQXIarlToCsrK9977z27UwAA4FSFqjpM11eGKdBAF3JnCYdpmsOGDRs2bJjd\nQQAAcKrxprGCZdBAV5w3A21Z1tatW7ds2RIIBESkuLi4oqJiwIABducCAMDxxpvGrw8GWpPJ\nYjV3ptiAbuekAt3S0vLAAw889thju3fvPuKl8vLy66+//tZbb/X5fLZkAwAgB5ypew1FaYhE\nL/SZdmcBspdjCvTOnTsnTJiwdevWioqKqVOnDhw4MD8/X0QOHjy4efPm+vr6OXPmPP/880uW\nLCktLbU7LAAAjuRVlNGGsTIcoUADx+CYAn3XXXd99tlnzzzzzBVXXPHFVxOJxMKFC2+55Za5\nc+fOmzcv8/EAAMgN4039ybZ2u1MAWc0xK5xefvnl6667rtP2LCKaps2cOfPKK6984YUXMhwM\nAIBcMt40t8fjn8UTdgcBspdjCvS+ffvOOOOMY79nyJAhu3btykweAABy0iCvp7emrYqwFwdw\nVI4p0P369Vu/fv2x37N27dp+/fplJg8AADlJERln6GxmBxyDYwr0xRdf/Oyzz/785z+PdPYz\ncTAYvPvuu1988cWrrroq89kAB/N4Or8G4GLjTGNlOJK0OwaQtRzz/fKee+5ZtmzZbbfddu+9\n944ZM2bAgAEFBQWWZbW1tW3fvr2hoaG9vb2mpuZHP/qR3UkBR6muluJiaW0VXZfaWrvTAMgK\n402jNZn8OBobonvtzgJkI8cU6JKSkpUrV86fP//RRx998803E4m/P9zg9XpHjRo1ffr06dOn\na5pmY0jAefx+aWyUV16R2lqpqrI7DYCs0EfTTvd6VkQiFGigU44p0CKi6/rs2bNnz54dDoc/\n/fTTjpMIi4qKysvLdV23Ox3gWBUVMmuW3SEAZJeOM73/ubDA7iBANnJSgT7ENM2Kigq7UwAA\nkLPGG8azbe0RyzIUxe4sQNZxzEOEAAAgY6pNI2ZZ70ZjdgcBshEFGgAAHClfUb6s62+zmR3Q\nGQo0AADoxFhT5zgVoFMUaAAA0ImxhvFuNBayLLuDAFmHAg0AADoxytBFZF0kancQIOtQoAEA\nQCdMRanSvW+zigP4Ago0AADo3FjDWBVmBho4EgUaAAB0bqypb4hG25Isgwb+AQUacL1QSJYv\nl9ZWu3MAyDrDdd2jKO9EWcUB/AMKNOBuwaAMHy41NVJZKTt22J0GQHYxFOVMXX+bVRzAP6JA\nA+5WXy9NTSIizc1SV2d3GgBZZ6yp8xwhcAQKNOBuh39fDIftywEgS401jI+isYPJpN1BgCxC\ngQYAAEf1Fd2rK0oju0EDh6FAAwCAo/IqykhDb2AVB3AYCjQAADiWsYbBc4TA4SjQAADgWMaa\nelMstp9l0MD/okADAIBj+bKu56tKY5hVHMDnKNAAAOBYNJFRhvE2zxEC/4sCDQAAujCW5wiB\nw1CgAQBAF8YaxuZYfHciYXcQICtQoAEAQBcqdW+JqrIbNNCBAg0AALqgiowy9Ld5jhAQEQo0\nAAA4HmN5jhD4XxRoAADQtbGm/kk8/rc4y6ABCjQAADgOFV5vT01tZC8OgAINuJ3H0/k1APwj\nRaSaVRyAiFCgAberrpbiYhERXZfaWrvTAMhqYwx9Fc8RAhRowO38fmlslHnzZNUqqaqyOw2A\nrDbWMHYmEp+yDBqux29sAderqJBZs+wOAcABTvd6+mpaQyQywJNndxbATsxAAwCA41XNbtAA\nBRoAABy/saaxiucI4XoUaAAAcLzGGPqeRGJrPG53EMBOFGgAAHC8yj2efh6NVRxwOQo0AABI\nwRjDaGAVB9yNAg0AAFIw1tAbwhHL7hiAjSjQAAAgBWeZxr5kclOMZdBwLwo0AABIgV/Tyj2e\ntyMsg4Z7UaABAEBqxrAbNNyNAg24Xigky5dLa6vdOQA4xljTaIxEk3bHAOxCgQbcLRiU4cOl\npkYqK2XHDrvTAHCGsYZ+MJn8KBqzOwhgDwo04G719dLUJCLS3Cx1dXanAeAMvTXtVI+nkWXQ\ncCsKNOBuh3//C4ftywHAYcaYeiO7QcOtKNAAACBl1YaxmmXQcCsKNAAASNkYQ29NJptiLIOG\nG1GgAQBAynpr2kCPpyHMKg64EQUaAACciDGGznOEcCcKNAAAOBHV7AYNt6JAAwCAEzHW0FuT\nyU0sg4b7UKABAMCJ6KNp5R5PA5vZwX0o0AAA4ARVG3pjmGXQcB0KNAAAOEFjDGN1JGrZHQPI\nMAo0AAA4QWNMfX8yuTkWtzsIkFEUaAAAcIL8mtbfozWwmR1chgINAABO3BjDaOQ5QrgMBRoA\nAJy4jucIWQYNVzneAp1IJA5dRyKRt99+e+3atZbFvxfA4Tyezq8B4PiMNY19yeQWlkHDTbou\n0IlE4uabb/7mN7/Z8eG2bduGDh161llnjRw5sra2tq2tLc0JAaRTdbUUF4uI6LrU1tqdBoDz\nlGlaP5ZBw2W6LtAPPvjgggULysvLOz68+eabt27detNNN82cOXPFihW/+tWv0pwQQDr5/dLY\nKPPmyapVUlVldxoAjsQyaLhN17+xffzxxy+99NKHHnpIRHbs2PHqq69Onz59wYIFIhIOh59+\n+unbb7897TEBpE9FhcyaZXcIAA5Wbej/0XrQElHsTgJkRtcz0Nu2bZs0aVLH9euvv25Z1tVX\nX93x4ahRo7Zt25a+cAAAIPtVG8beRHJbnGXQcIuuC7Si/P3nyUWLFuXn59fU1HR8aFlWLBZL\nVzQAAOAEAzxamaY1cKY3XKPrAj1w4MClS5eKyK5du1566aVJkybput7x0vr16/v375/egAAA\nIOtVmzrLoOEeXRfoa6655oknnhg/fvzIkSPb2tpm/e9ayUcfffT3v//9RRddlOaEAAAg240x\njAYKNFyj64cIZ8+e3dTU9PTTT+u6/otf/OKcc87puH/77bcPHjz4jjvuSHNCAACQ7aoNfU8i\nsT0eH8iO8nCBrke5aZoPP/zwww8/fMT9F154YfTo0R7+nQAA4HrlHo9f0xoiUQo03KDrJRzL\nly/fv3//F++fddZZ77zzzvPPP5+GVAAAwGE6zvS2OwWQCV0X6Jqamo6HCL9o2bJlN9xwQ3dH\nAgAAzlNtcpwK3OKov2fZtGnTpk2bOq7Xrl1rmuYRbwiFQs8880yEozsBAIBItaE3JxKfxOPl\nrOJArjvqEH/uuecOPSB47733Hu1tl19+efeHApBJoZCsWSNVVVJcbHcUAA52qsfTR9MaI1EK\nNHLeUYf47bff/p3vfKexsfEb3/jGddddN3To0CPeoGna6aefzjZ2gLMFgzJypDQ1id8vq1fL\nKafYHQiAg1UbekMkcll+nt1BgPQ61s+IZWVlF1100bRp02bOnHnWWWdlLBOAzKmvl6YmEZHm\nZqmrkxtvtDsQAAerNvT/Pthmdwog7br+JUtdXV0GcgCwx+GPMYTD9uUAkAuqDeOeROtn8UR/\nj2Z3FiCNui7QlmU999xzjz766GeffRaLxb74hg0bNqQhGAAAcJjTvZ4+mtYQifT3sIoDuazr\nAv3QQw/ddtttIpKXl+f1etMfCQAAONUoQ2+MRC9lGTRyWtf7QP/nf/7n5MmTN2/eHAwGD3Qm\nAykBAIAjVBv62xynglzXdYHetWvX3LlzTz/99AykAQAAjjbGMHYmEn+LJ+wOAqRR1wW6b9++\nlmVlIAoAAHC6072enprawDlryGldF+irr776sccey0AUAADgdIpItcGZ3shxXT9EOGfOnMsv\nv/xb3/rWt7/97fLy8i8+Rzho0KD0ZAMAAM5TbeiPBNgNGrms6wJdWFjYcfHEE090+gYWeAAA\ngEOqDeO+ltadiUSZxm7QyE1dF+irr75a13UP59oDAIDjMMjr6amqjeHoRfk+u7MAadF1LT7a\nxDMAAMAXKSKjDL0hEqFAI1d1/RDhIYFA4P3332fjZwAAcGzVJs8RIpcdV4Gur68fPXp0UVHR\nsGHDVq1a1XHzoosueuONN9KZDQAAOFK1oX8Sj+9KsBs0clPXBbqhoWHSpElNTU2TJ08+dHPP\nnj2NjY1Tp05ds2ZNOuMBAADn+ZLXW6Kqq5mERo7qukDfe++9fr//gw8+eOSRRw7d7N279/r1\n6/1+/3333ZfGdADS7fDng3lWGEA36VgG3chxKshRXRfoVatW3XTTTf379z/ifp8+fWbMmLF0\n6dL0BAOQEdXVUlwsIqLrUltrdxoAuWMMx6kgd3VdoFtbWwcMGNDpS2VlZW1t7JQOOJnfL42N\nMm+erFolVVV2pwGQO6oNfUssvptl0MhFXf/G1u/3f/jhh52+tHTp0n79+nV3JACZVVEhs2bZ\nHQJArhmsewtVdU0kOiWPzeyQa7qegZ46deqCBQveeeedw2+2tLT88Ic/fPjhh6dNm5a2bAAA\nwKnUz5dBs4oDOajrAj137tyCgoKxY8d2dOU77rhjxIgRZWVlP/7xj8vLy+fMmZP+kAAAwHmq\neY4QOarrAu33+1evXn3DDTds375dRNatW7du3brCwsKbbrqpsbGxb9++6Q8JAACcZ4xhbI7F\n9yWSdgcButlx7VrVp0+fBQsWzJ8/f/fu3YFAoLCwkN4MAACObYjuLVDVNdHoJJ9pdxagO3Ve\noJubmw3DKC0t7bg+/KWCggLLsg6/6ff70xoRAAA4kSYyQvc2hiMUaOSYzgt0WVnZ5MmTX3vt\ntY7rY38Ky7K6PxcAAHC+asOoaw/ZnQLoZp0X6Kuuumr48OGHrjOYBwAA5I5qU/9/rQcPJJMl\natePXQFO0XmBfuqppzq9BgAAOH7DdD1PUdZEohewigM55Hh/HHz//ff37t17+Idr165NTyQA\nAJAjNJHhht7AZnbILV0X6Fgs9s///M/Dhg3bsGHDoZtLliwZOXLkd7/73QRHdAJOFwrJ8uXS\n2mp3DgC5qdowOE4FOabrAv3LX/7yd7/73bRp0wYOHHjo5oUXXnjVVVc98sgjv/rVr9IZD0Ca\nBYMyfLjU1EhlpezYYXcaADmo2tA/jsYCSXaDRu7oukA/8sgjX/va1+rq6k477bRDNwcPHvzU\nU09NnTqVAg04W329NDWJiDQ3S12d3WkA5KAq3WsoyhomoZFDui7QmzZtOu+88zp96dxzz+04\nnhCAUx2+MDEcti8HgJzlVZQzDZ1VHMglXRfooqKibdu2dfrStm3bevTo0c2JAABAbhnDc4TI\nLV0X6GnTpv32t7995ZVXDr8Zi8V+85vf/PrXv540aVLasgEAgFxQbRgfsgwaOaTzfaAPd//9\n97/66qvTpk0rLy8fPHiwYRgHDhz44IMP9u/fX1ZWdv/992cgJQAAcK6v6F6PoqyNxmpNw+4s\nQDfoega6rKxs7dq1M2bMCAaDf/3rX+vq6pYvX65p2g033NDY2FheXp6BlAAAwLl0RTlT1xtZ\nxYFc0fUMtIj07dv3v/7rvxYsWLBz585QKOT3+/Pz89OdDAAA5IxqQ18ejkix3TmA7tB5gW5u\nbjYMo7S0tOP60H1VVfPz8wOBQCAQOHTT7/enOyUAAHC0alP/74OBoGXlK4rdWYCT1XmBLisr\nmzx58muvvdZxfexPYVlW9+cCAAA5ZLiuexRlXSQ6gWXQcL7OC/RVV101fPjwQ9cZzAMAAHKQ\noSjDdG9jJEKBRg7ovEA/9dRTnV4DAACcmDGG8TbPESIndL4Lx/e///3Fixd3XM+YMWP9+vUZ\njAQAAHJQtaG/F42FWfkJ5+u8QM+bN6+hoaHjeuHChVu3bs1gJAAAkINGGLqIrONMbzhf50s4\n+vbt+9Of/vTTTz8tLCwUkccee2zVqlVH+xT//u//nq50AAAgV5iK8mWvtyESPYtl0HC4zgv0\nz372sxtuuGHBggUdH77wwgvH+BQUaAAAcDyqzY7jVArtDgKclM4L9LXXXvu1r31t06ZN4XC4\npqbmxz/+cU1NTYaTAcgEj6fzawBIg2rD+H0gGLYsk92g4WSdf7/8/ve/P23atPPPP7/jw9LS\n0rPPPjuDqQBkSnW1FBdLa6voutTW2p0GQI4bZehJkfeisWpDtzsLcOK6fohQOGsQyGF+vzQ2\nyrx5smqVVFXZnQZAjstTlKFebwOb2cHheIgQcL2KCpk1y+4QANyi2tAbw1EpsjsHcBJ4iBAA\nAGROtaH/oS0YsSyDZdBwLB4iBAAAmTPS0OOWtSEaG8UyaDjWUR+6LykpGT16tIhMnjz53HPP\nHTduXAZTAQCA3FSoqpW6tzESoUDDubreteq1117ruAgEAp988skpp5xSUlKS5lQAACBnVRtG\nQyQ6w+4YwAnrfBeOI9TX148ePbqoqGjYsGGHnia86KKL3njjjXRmAwAAOWiMoa+NRGOWZXcQ\n4AR1XaAbGhomTZrU1NQ0efLkQzf37NnT2Ng4derUNWvWpDMeAADINaMNPWZZ70VjdgcBTlDX\nBfree+/1+/0ffPDBI488cuhm7969169f7/f777vvvjSmAwAAOadQVQfr3rfZDRqO1XWBXrVq\n1U033dS/f/8j7vfp02fGjBlLly5NTzAAAJCzxhpGQyRqdwrgBHVdoFtbWwcMGNDpS2VlZW1t\nbd0dCQAA5Lgxhr4uEo2yDBrO1HWB9vv9H374YacvLV26tF+/ft0dCUBmhUKyfLm0ttqdA4CL\njGIZNJys6wI9derUBQsWvPPOO4ffbGlp+eEPf/jwww9PmzYtbdkApF8wKMOHS02NVFbKjh12\npwHgFoWqOoRl0HCsrgv03LlzCwoKxo4d29GV77jjjhEjRpSVlf34xz8uLy+fM2dO+kMCSJv6\nemlqEhFpbpa6OrvTAHCRMYbRyDJoONNxLeFYvXr1DTfcsH37dhFZt27dunXrCgsLb7rppsbG\nxr59+6Y/JIC0OXz6Jxy2LwcA1+nYDTrCMmg4UNcnEYpInz59FixYMH/+/N27dwcCgcLCQnoz\nAAA4GaNNI25Z70Zj1ZzpDac5rgLdYd++fVu2bAkGg4WFhYZhcKA3AAA4YfmK8mVdb4hEKNBw\nnOM6ynv58uVnnXVW7969x48ff+GFF5511lk9evSYOHHihg0b0p0PAADkqmpDbwizDBrO0/UM\ndENDw8SJE+Px+Nlnnz148GCfzxcMBj/44IPFixdPmDChoaFh8ODBGQgKAAByzBjTeKwtGLYs\nU1HszgKkoOsCff/99/fu3fuvf/1rZWXl4ffXrl371a9+de7cuU888UTa4gEAgJw12tCTIuuj\n0bGGYXcWIAVdL+FYsWLFzJkzj2jPIjJixIiZM2cuXrw4PcEAAECOy1OUoV5vI6s44DTHdZR3\n//79O33p1FNP3b9/f3dHAgAAbjHW1DlOBY7TdYHu06fP0Y7y/uCDD/r06dPdkQAAgFuMMYz1\n0ViY3aDhKF0X6EmTJv3yl7988cUXrcMGt2VZf/zjH+fPnz9lypR0xgMAALlspKFbIus4khCO\n0vVDhPfcc88rr7xy8cUX+/3+oUOH5ufnd+zC0dzcXFZWdvfdd2cgJQAAyEl5ijLM622IRM8y\neY4QjtH1DPTAgQNXr179ne98JxQKLV68+KWXXlq8eHE0Gr3++uvXrFlztOXRAAAAx2OsqTew\nDBqOclwnEQ4YMOCRRx6xLKu5uTkYDBYUFPj9/nQnAwAAblBtGL8LBEOW5WM3aDhEFzPQu3fv\nXrlyZce1oihlZWWDBg3y+/3z588/cOBA+uMBAIAcN8rQhWXQcJRjFeilS5cOHjx4zpw5R9x/\n9913b7nllmHDhm3ZsiWd2QCkn8fT+TUAZIqpKFW6t4ECDec4aoHeuXPnXOgHDQAAIABJREFU\nZZdd1tbWdv755x/xUlVV1S9+8YudO3d+9atfDYfDaU4IIJ2qq6W4WERE16W21u40+P/s3Xuc\nXVV9N/7vuuz7uc1MEoaEBBBGQIlcYkJiSLiIVfGGF0RbsZqiIKI0LdraclEf6fM8Vp+mtlRp\na21B1EoB0YC/KhBCgMQERESsBkJICBCSzPXc9m2t9fvjTDKTyeRGZmbPmfN5v3iFPfvss893\nzpzLZ6+99loALWqB46AbNDSR/Qbof/mXf9m1a9c3v/nNL3zhCyNuYox95jOf+frXv/7MM8/8\nx3/8xzhXCADjqbOTNmygFSto3TqaOzfragCgRS1w7F/HSR2jQUOT2G+Avvvuu0844YRly5bt\nb4OrrrrqmGOO+fd///dxqQsAJkxXF119NZ1xRtZ1AEDrOsOxOdEv0YsDmsR+A/TWrVvPOuss\nzve7gZRy4cKFTz/99PgUBgAAAK1idzdo9OKA5rDffDwwMNDR0XHgO3d0dER4rQMAAMARW+A4\n60O0QENz2G+A7ujo2Lp164HvvHHjxunTp491SQAAANByFjj2U3FcRTdoaAb7DdDz58+///77\nu7u797fBs88+u2bNmoULF45PYQAAANBCznBsydgT6AYNzWC/AfrSSy+tVCqf+MQn0jTd99aB\ngYE/+qM/StP0Yx/72DhWBwAAAK3BQTdoaB77DdDvf//7L7jggrvuumvhwoV33XVXuVxurN+5\nc+e3v/3tN7zhDevXr3/ve9/7zne+c6JKBQAAgKnsLMf5BbpBQzPY78RjjLHbb7/9D//wD3/6\n05++733vY4wVi0Wl1J4kfckll3znO9+ZqDoBAABgilvg2t8aKFe0yXGWdS0AB3KgqbxLpdK9\n99577733fvjDHz7++OOTJCGik0466eMf//hDDz30gx/8wPO8iaoTAAAAprjTbVsy9ssYjdAw\n2e23BXqPt7/97W9/+9snoBQAAABoZTZjp9n2+jBa6jpZ1wJwIAdqgQaAllCv08MPU39/1nUA\nANAC196AgThg0kOABmht1SqdfjotWUInn0wvvph1NQDQ6hY4ztNxXNY660IADgQBGqC1rV5N\nGzcSEW3fTitXZl0NALS602zLYuyXaISGyQ0BGqC1DR9yNQyzqwMAgIjIZux0x16PAA2TGwI0\nAAAATCILHBvTqcAkhwANAAAAk8gCx/mfOEE3aJjMEKABAABgEnmDbdmMoRcHTGYI0AAAADCJ\nWIzNc+x1IXpxwOSFAA0AAACTy0LXWYtu0DCJIUADAADA5PImx9mUpNuVyroQgNEhQAMAAMDk\ncpJttXO+PkQ3aJikEKABAABgcuFEC9CLAyYxBGgAAACYdBY69qO4jhAmKwRoAAAAmHQWuc4O\npZ5L0qwLARgFAjQAAABMOnOkPEaKdejFAZMSAjQAAABMRmc5zlr04oBJCQEaAAAAJqNFrvOL\nKMZQdjAJIUADtDYpR18GAMjaQsepaP10jMHsYNJBgAZobfPnU7FIRGTbtHRp1tUAAAzpELzL\nstZhNGiYfJq7wSmO4yeffLJSqRx33HHHH3981uUANKHOTtqwge69l5Yupblzs64GAGAvi1xn\nbRR9knJZFwKwl6Zpgf7KV76yatWq4Wtuvvnmzs7OBQsWnH/++a95zWve+MY3/upXv8qqPIAm\n1tVFV19NZ5yRdR0AACMtcuwnojg0JutCAPbSNAH6uuuu++///u89P95zzz1XXHFFrVZ773vf\ne/nlly9evPjxxx8/99xzN23alGGRAAAAMIbe6DqK6FcRenHA5NKsXTiWL19eLBbXrl17yimn\nNNbceeedH/jAB2688cZ/+7d/y7Y2AAAAGBMBY2+wrbVRtNB1sq4FYEjTtEAPt3PnzmeeeebT\nn/70nvRMRO973/ve8573/OxnP8uwMAAAABhbizAaNEw+TRmgwzAkouHpueHUU0/dsWNHFhUB\nAADAuFjkOr+Nk36tsy4EYEhTBuiZM2cWi8Vt27aNWP/SSy/l8/lMSgIAAIDx8AbbchjbgG7Q\nMJk0U4DeunXrY4899uyzz/b29l555ZXf/va3a7Xanlt/97vf/ed//ufixYszrBAAAADGlsXY\nGx0bvThgUmmmiwi///3vf//73x++5qc//en73/9+Ivre9773yU9+sl6vX3fddRlVBwAAAONi\noevcXqkdfDuAidI0Afo73/lO3zD9/f19fX1tbW2NW/v6+kql0g9+8IP58+dnWycAAACMrUWu\n89W+ge1KdQqRdS0ARE0UoD/2sY8d4NaPfvSjV1xxBefN1CMFAAAADsVJltUh+Lowuijws64F\ngKiJAvQexpjNmzc/99xz5XKZiIrFYldX1+zZs7OuC6Bp1ev0+OM0dy4Vi1mXAgAwCka0wHHW\nRgjQMFk0U4Du7e298cYbb7311n3HqpszZ85ll112zTXXeJ6XSW0AzapapTPPpI0bqbOTHnuM\nZs3KuiAAgFEscp1/6C8bIpZ1JQDURAH65ZdfXrx48ebNm7u6ui688MJjjz02CAIiGhgY2LRp\n0+rVq6+//vo77rhj1apVezpGA8DBrV5NGzcSEW3fTitX0uWXZ10QAMAoFjvO9arvuSQ9wWqa\n6AJTWNO8Cq+77rpt27b98Ic/vPjii/e9VSl18803X3XVVV/60pdWrFgx8eUBNKto2MhQYZhd\nHQAABzJTimOkWBtFCNAwGTTNVXf33HPPpZdeOmp6JiIhxJVXXvnBD37wzjvvnODCAAAAYAIs\ncpx1GA0aJoemCdDd3d0nnHDCgbc55ZRTXnnllYmpBwAAACbSItdZF0Yq6zIAqIkC9MyZM598\n8skDb/PEE0/MnDlzYuoBAACAibTQderGPB1jTm/IXtME6Isuuuj222//2te+FkWjnL6pVqs3\n3HDD3Xfffckll0x8bQAAADDe2jh/rWU9il4cMAk0TU/8L37xi2vWrPnc5z735S9/ecGCBbNn\nz87lcsaYSqWyZcuW9evX12q1JUuWXHvttYe12xdeeOGtb33rqKF8j4GBASIyxhzRLwAAAABH\nZpHrrAvjKwpZ1wEtr2kCdKlUWrt27U033XTLLbc8+OCDSg11grIsa968ecuWLVu2bJk4zEk+\njzrqqM9//vPxAc8HPfTQQ7fddhtjGHoSAAAgSwtd57uVat0YD1/KkKmmCdBEZNv28uXLly9f\nHobhCy+80JiJsFAozJkzx7btV73PA08STkTGmNtuu+3V7R8AAADGynzHZkRPRPGbXCfrWqCl\nNVOA3sN13a6urqyrAAAAgAnlMTbXttZGEQI0ZKtpLiIEAAAAWOQ6a3EdIWRt6gToTZs2XXDB\nBRdccEHWhQAAAMB4WeQ4/xMnvVpnXQi0tKbswjGqcrl8//33Z10FAAAAjKM32JbH2Poweqvv\nZV0LtK6pE6BPPvnkp556KusqAAAAYBxJxs5ynYcRoCFTUydAu6576qmnZl0FAAAAjK+zXeef\nByqGCEPZQVaaL0AbYzZv3vzcc881hrErFotdXV2zZ8/Oui6A5iTl6MsAAJPVUtf9cm//s0na\nZeFTC7LRTK+83t7eG2+88dZbb92xY8eIm+bMmXPZZZddc801nocTOgCHY/58Khapv59sm5Yu\nzboaAICDmyXF8VKuCcMuK5d1LdCimiZAv/zyy4sXL968eXNXV9eFF1547LHHBkFARAMDA5s2\nbVq9evX1119/xx13rFq1qq2tLetiAZpHZydt2ED33ktLl9LcuVlXAwBwSJZ4zpowWpZHgIZs\nNE2Avu6667Zt2/bDH/7w4osv3vdWpdTNN9981VVXfelLX1qxYsXElwfQxLq66Oqrsy4CAOAw\nLHXd71d6qsYEmNMbstA040Dfc889l1566ajpmYiEEFdeeeUHP/jBO++8c4ILAwAAgAk237El\n0TrMqAIZaZoA3d3dfcIJJxx4m1NOOeWVV16ZmHoAAAAgKzZj8x3nYQRoyEjTBOiZM2c++eST\nB97miSeemDlz5sTUAwAAABla6jkP1sOsq4AW1TQB+qKLLrr99tu/9rWvRdEoh5vVavWGG264\n++67L7nkkomvDQAAACbYOa67XalNSZp1IdCKmuYiwi9+8Ytr1qz53Oc+9+Uvf3nBggWzZ8/O\n5XLGmEqlsmXLlvXr19dqtSVLllx77bVZVwoAAADj7hgpjpVyTRiegMHsYMI1TYAulUpr1669\n6aabbrnllgcffFAptecmy7LmzZu3bNmyZcuWCSEyLBIAAAAmzBLXWRNGH8NgdjDhmiZAE5Ft\n28uXL1++fHkYhi+88EJjJsJCoTBnzhzbtrOuDgAAACbUEs/94a6emjE+BrODidVMAXoP13W7\nurqyrgIAAACytMCxOdH6MDrXc7OuBVpL01xECAAAADCcy9h8x16DwexgwiFAA7S8ep0efpj6\n+7OuAwDgsJ3tug+FGMwOJhoCNEBrq1bp9NNpyRI6+WR68cWsqwEAODxLPWdbqp5PMZgdTCgE\naIDWtno1bdxIRLR9O61cmXU1AACH5zgp50j5UB29OGBCIUADtLbhMxPhNCgANKHFrvMwPr5g\nYiFAAwAAQBNb6jrrozg0JutCoIUgQAMAAEATO8t1iGh9FGddCLQQBGgAAABoYh5j8xwbvThg\nIiFAAwAAQHNb4jq4jhAmEgI0AAAANLclrrslTbdiMDuYKAjQAAAA0NxOsORsKTAlIUwYBGgA\nAABoeotdFwEaJgwCNAAAADS9s13nF2GEwexgYiBAAwAAQNN7k+tooscxmB1MCARoAAAAaHoe\nY2c69kMYzA4mBAI0AAAATAVnu87D6AYNEwIBGgAAAKaCpa77XJK+kKqsC4GpDwEaAAAApoIu\nSx4tBKYkhAmAAA3Q2qQcfRkAoAmhFwdMDARogNY2fz4Vi0REtk1Ll2ZdDQDAEVniuWvDKMZg\ndjDOEKABWltnJ23YQCtW0Lp1NHdu1tUAAByRRY6TEP0Sg9nBOMMZW4CW19VFV1+ddREAAGMg\nx9kZtvVQGC10naxrgakMLdAAAAAwdZzjuavquI4QxhcCNAAAAEwdb/Hc59N0U5JmXQhMZQjQ\nAAAAMHXMkfJES/68Xs+6EJjKEKABAABgSnmL592HXhwwnhCgAQAAYEp5s+c+HSfbMCUhjBsE\naAAAAJhSXm9bx0iBSwlh/CBAAwAAwFRznufejwAN4wYBGgAAAKaaCzz3sSjq1TrrQmBqQoAG\nAACAqWae4xQ5fxCN0DA+EKABWl69Tg8/TP39WdcBADBmBNG5nouxOGCcIEADtLZqlU4/nZYs\noZNPphdfzLoaAIAxc4HnPhJGVWOyLgSmIARogNa2ejVt3EhEtH07rVyZdTUAAGNmsetIokfC\nKOtCYApCgAZobdGwr5YQ5zoBYOqwGVvsOvfVMCUhjD0EaAAAAJiaLvC9B8MoQS8OGGsI0AAA\nADA1nes6oTEbojjrQmCqQYAGAACAqSnP+QLHxlgcMOYQoAEAAGDKusBzf16vYz4VGFsI0AAA\nADBlvcXzepR+KkYvDhhLCNAAAAAwZXUI/gbb/nkNvThgLCFAAwAAwFR2ge/+HN2gYUwhQAMA\nAMBU9hbP3ZqmzyZp1oXA1IEADQAAAFPZHClPtOR9dcyoAmMGARoAAACmuLd4HgazgzGEAA0A\nAABT3AWe+3ScbEtV1oXAFIEADQAAAFPc62zrGClWoREaxggCNAAAAEx953suenHAWEGABmht\nUo6+DAAwtbzZcx+Poh6NSQlhDCBAA7S2+fOpWCQism1aujTragAAxss8xyly/iAaoWEsIEAD\ntLbOTtqwgVasoHXraO7crKsBABgvguhcz70fARrGAs7YArS8ri66+uqsiwAAGHcXeO7y7t6q\nMQFjWdcCzQ0t0AAAANASFruOJHokjLIuBJoeAjQAAAC0BJuxsz33vhqmJIQjhQANAAAAreLN\nnvtgGCXGZF0INDcEaAAAAGgVF3huasxD6MUBRwYBGgAAAFqFx9j5nvvjai3rQqC5IUADAABA\nC3l34K0Koz7MqAJHAAEaAAAAWshi1y1y9rMaBoSGVw8BGgAAAFqIILrQ935cQy8OePUQoAEA\nAKC1vMv3fxnF21KVdSHQrBCgAVpevU4PP0z9/VnXAQAwQU61rRMsuRKN0PBqIUADtLZqlU4/\nnZYsoZNPphdfzLoaAIAJ8k7f/1EVM6rAq4QADdDaVq+mjRuJiLZvp5Urs64GAGCCvDvwXkjT\np+Ik60KgKSFAA7S2aNhsAiGuSQeAVnG0EGc69k/QiwNeFQRoAAAAaEXvCfx7qvUU03rD4UOA\nBgAAgFb0Ns+rGfMIpvWGw4cADQAAAK0ox9k5nvvjGi4lhMOGAA0AAAAt6l2+d389LGNabzhM\nCNAAAADQos5xHZ+xn9dxCTUcHgRoAAAAaFGSsbf53k/QiwMOEwI0AAAAtK53B976MNquMK03\nHAYEaAAAAGhdp9v2HCnvQSM0HA4EaAAAAGhp7wy8u6qYUQUOAwI0AAAAtLR3+d5zSfq7BNN6\nw6FCgAYAAICWNkfK02z7x1X04oBDhQANAAAAre7dgbeyVseFhHCIEKABAACg1V3oe/1ar8O0\n3nBoEKABWpuUoy8DALSSIudLXOfHNVxKCIcEARqgtc2fT8UiEZFt09KlWVcDAJCZd/nez2th\nzZisC4EmgAAN0No6O2nDBlqxgtato7lzs64GACAz53uuzdh9mNYbDgHO2AK0vK4uuvrqrIsA\nAMiYxdgfeO5PqrV3+17WtcBkhxZoAAAAACKi9wT+2jDaiWm94WAQoAEAAACIiM507FlS/hdm\nJYSDQYAGAAAAICJiRB/O+T+o1FJcSggHhAANAAAAMOj9gV/R+ue4lBAOCAEaAAAAYFCe83cH\n/m2VataFwKSGAA0AAAAw5CO54JdR/Js4yboQmLwQoAEAAACGnGDJs1zn+2iEhv1DgAYAAADY\ny0dywcpavVvprAuBSQoBGgAAAGAv53nuDMHvwHh2sB8I0AAtr16nhx+m/v6s6wAAmCw40Ydy\nwfcqVYxnB6NCgAZobdUqnX46LVlCJ59ML76YdTUAAJPFxYE/oPUDYZR1ITAZIUADtLbVq2nj\nRiKi7dtp5cqsqwEAmCwKnL/T975brmRdCExGCNAArS0a1rgSYuIAAIAhH83nHovi3yUYzw5G\nQoAGAAAAGMWJlnyjY99Wxnh2MBICNAAAAMDoPpLPrazV+zTGs4O9IEADAAAAjO7NntuB8exg\nHwjQAAAAAKMTRJcEwfcqVZV1JTCpIEADAAAA7NcHcn6P0g/WcZk1DEGABgAAANivNs4v9L3v\nVnApIQxBgAYAAAA4kEvzwS/CaCPGs4PdEKABAAAADuRkyzrTsb9fwaWEMAgBGgAAAOAg/igX\n/Kha68d4dkBECNAAAAAAB/UHvlfi/C6MZwdEhAANAAAAcFCC6IM5/7sYzw6ICAEaAAAA4FBc\nkgt2Kf0QxrMDBGgAAACAQ9HO+Tt871/LlawLgewhQAO0NilHXwYAgH1cWcg/FScPhVHWhUDG\nEKABWtv8+VQsEhHZNi1dmnU1AACT2iwp3ht43+gfMFlXAtlCgAZobZ2dtGEDrVhB69bR3LlZ\nVwMAMNl9upDflKT3oyd0a8MZW4CW19VFV1+ddREAAM1hhhAX5/y/7x8433PRDNmy8KcHAAAA\nOAxXFPIvpereWj3rQiAzCNAAAAAAh6Gd8w/ngn/sL2NM6JaFAA0AAABweC4r5Lq1+hEmJmxV\nCNAAAAAAh6fE+R/ncv80UI4NBuRoRQjQAAAAAIftj/NBVZs70AjdkhCgAQAAAA5bnvM/yee+\nOVAJ0QjdehCgAQAAAF6Nj+QDTeb7lWrWhcBEQ4AGAAAAeDU8xj6Zz//LQKWKRugWgwANAAAA\n8CpdkvMdxm4tV7IuBCYUAjRAy6vX6eGHqb8/6zoAAJqPw9jlhdy/lav9WmddC0wcBGiA1lat\n0umn05IldPLJ9OKLWVcDANB8PhD4bZz/Rxk9oVsIAjRAa1u9mjZuJCLavp1Wrsy6GgCA5iMZ\n+1Qh9x/lSrdCI3SrQIAGaG1RNLQchtnVAQDQxN4V+EdL8W/oCd0yEKABAAAAjogg+nQhf1ul\nul2prGuBiYAADQAAAHCk3up7x0v5zwNohG4JCNAAAAAAR4oTLS/lf1ip/k+cZF0LjDsEaAAA\nAIAxsNR1L/C9v+rpSzGvylSHAA0AAAAwNq4tFV9S6hZM7j3VIUADAAAAjI1pgn+uVPiH/vLW\nNM26FhhHCNAAAAAAY+b9gX+6Y1/f049uHFMYAjQAAADAmGFEX2wrPhnHd1drWdcC4wUBGgAA\nAGAsHSvlpwr5/9M3gLkJpyoEaAAAAIAx9ieF3Cwp/ndff9aFwLhAgAYAAAAYY4LoxvbS/1er\nP1APs64Fxh4CNAAAAMDYO9myLs3nvtLbX8Ww0FMOAjQAAADAuLi6mLcY+/v+gawLgTGGAA3Q\n2qQcfRkAAI6Yy9iX2orfK1efiOKsa4GxhAAN0Nrmz6dikYjItmnp0qyrAQCYaha6zjsC74be\nvgQdOaYQBGiA1tbZSRs20IoVtG4dzZ2bdTUAAFPQF0rFHqX/tVzJuhAYMwjQAC2vq4uuvprO\nOCPrOgAApqYS53/RVvzWQGVTgvm9pwh0eQQAmKR0TZn44Od81UBq1ME3477gzn4bTbjH2f5v\nBYAj9C7fW1mt3dDbd8uMaXinTQEI0Bk7xC9IgAmjY62ramz3qfpTOpyXua6mJjnIHVQ5Nfsp\nU9eUiUaZ/UvX9b7rjTKqPLJNyIRah3ttaVKj997MKBpxRxNrXVN7rzEj1xhSfcnIh0vMmD/n\nR4qRKA59QYiSxdieZUlEzObcF0Qk8oIJRpw1tue+YDYTeckEEyXJBOMFyS3GA8E8zh0hSpL7\nggdC5EQGvxdAdm5oK73nlR039Zc/U8xnXQscKQToLCXbo9+c/IhJEaABDtWBG0pFQTLB9l3P\nHM69Ue4lCpL4XtszTqIw8oOR5wSzuGizhtb4gtl73VHkJJN7rynIEb3keCCYvdcqtndOHbpv\nydp35bA9ixFlHy5dVyYa5ZNH15SJB48cjCHVP3SEoPqSxlGQibWuaSJSldSkhjSpgXRwn6FO\nd8WqrEykdV3pmjaxVmVlUj3qQZQoSh4I7guRF6IgeSBEUcqSJdqkKFnDlqUsWqIkeYDMDU1s\nphR/19F+xc7uLku+zfeyLgeOCAJ0lqxO5+RHF4z6NQYwTpjNGg2H4/gQkon8YX+2MIshHk1x\n2qgBpatK1ZSuKNWXDC33p7qqVEWp/iTeFqZPpaovUf2p6k1UZahtnntcTrPlDNuaZslptuyw\nZKcjOyw5zbamWVanI2fYzDqiQwuAcXW263y6mP/rnr4TLKvLQgZrYvjjZcx7XS7rEgAAJgRn\noiRFSR6odX0fJjWNMJ32pml3orrjZFeSvhKlu5JwYy19tC95JU67k8GuMoysoxzraNs62rFn\nurLTto9xrU7bnuVaM51RG/sBJtgVhfwzSfqpXd23HzW9jaM7dLPCpwkAAExeTDI5zZbTbOeA\nm+mqSl6Jk+1RvC1MtsfJi2HyUlT/TTl+KUq2x41+KaIg7eM85zjXnuM5x7n2sZ5znGfPcXHq\nAyYSI/pKe+nDr+y6prv3n6d34MXXpBCgAQCg6fFAOK/xnNeM3q802REnL0Xx1nr0fBhvqUfP\n1gbu64631HVdE5GcbjvHus4Jvvta3+ny3RN950R/vHs6QSvzGfunae0Xv7Lz7/oGrikVsi4H\nXg0EaAAAmOKsGbY1w/ZPHzn0QbIjjp+vx1vCaEs92lTr/1l3dNMLaU9CjOxjXOdE3z3Rd17r\nu12+2xXYx7qZFA9T0iwpvt7R9omd3afY1jtwQWETQoAGAIAW1QjWwYLi8JVpTxI9Uws31qJn\na+EztfLDvdFzdRNpUZDuKYF3as57fc57XeCdmm+M6Afw6ixynT8rFf66p+9YKU+1D+vSAMge\n3vwALa9ep8cfp7lzqVg8+MYAU51st+RZxeCsobeDUSbeXK//plL/baX+dHXHTS/Ez9eNMtZM\nx3tdzjs1552a80/PO13+qKMoAuzPsnzu2ST97K6e24+a3iFwQWEzQYAGaG3VKp15Jm3cSJ2d\n9NhjNGtW1gUBTDpMMOdE3znRL100o7FG11T4u2r96Wr9t5X6r8vdt72c7ox5IPw35P3T8/4Z\nef+MgvNa5Gk4uBvaipfu2HV1d893pncMzVcEkx4CNEBrW72aNm4kItq+nVaupMsvz7oggCbA\nfeGfWfDPHLr8K3kxqj0xUPtVufbEQO+drySvxDwQ/tycf0bBPyPvv7HgdgWEdAT7cBj7+2nt\nF2/f+dW+gb9uw2nApoEADdDaomhoOQyzqwOguVmznOKs6cV3Tm/8mLwU1Z4o1341UHui3MjT\noiSDBcXgjcVgQSGYX8Sg1LDH0UJ8Y1r7x3Z2n2RbHwj8rMuBQ4I3MAAAwBizZjrFmU7xHdMa\nP8Zbw+r6/uqG/oH7urd//XkTa/e1QSNJBwuK7ikBOnu0uDMd+y9Lha/09r9GyjMdO+ty4OAQ\noAEAAMaXPce157htHziKiEyka0+WqxsGqhv6t3/t+XhrKPIyWFjMLSzmFpf8eUXu4WKyVvSH\nuWBTkn5yZ/e3pne8ERl60kOABgAAmDjM4cGCYrCgSDSbiJLtUXVdf+WRvr6f7Hz5bzaTYP4Z\n+dyiUm5RKVhUlO0Y3ayFXNtWlIw+sbP7pmntb3IPPPkmZAwBGgAAIDNWp1O6aEZjfA9VUdVf\n9FfX9lUe6dv5z9t0XbknBbmzS/mz23Jnl6xOJKopjhF9oVQMGP/Urp7/19H2Zg9z90xeCNAA\nAACTgsiJwpvbC29uJyKTmNoTA5V1/ZVHerf+6e9UX+p2+bmlbYNh+miE6Snrs8W8z9jy7t6v\nd7S9BRl6skKABgAAmHSYxRo9PY767BzSpv6bSnlNX3lN7wt/9vsprEu2AAAgAElEQVS0N3FO\n9PNL2nJLSvklbQjTU89lhRxjtHxXz9+0t707wETfkxECNAAAwOTGmfeGvPeG/IxPzyZt6k9X\ny2t6K2t6t12zMe1J3C4/d05b/pz2/JKSnIaLz6aIP8nnfMb+qqc3JfM+jG03+SBAAwAANA/O\nvLk5b25uxpW7w/TqnvLq3q1X/o+qpN7rc/lz2vLntOeWlEQeX/HN7cO5QBC7vqevbswf5YKs\ny4G94N0FAADQnPaE6avmmNTUnig3wvSu77xkIu2fmc+f054/py1YWMLQeE3qgznf5+wvu3uV\noY/mkaEnEQRoAACApsckC+YXgvmFzmuOM5Gubugvr+4tP9j7yt9vYYIFZxXz57bnz2v3z8hj\n0pbm8k7fE0Sf7+mrGv2pQj7rcmAQAjQAAMCUwhyeO7std3bb0X9Nuqaqv+gfWNXT9+MdL/2v\n57jHgwXFwnnt+fPa/dPzhCzdDN7ue4Kxa7p7Y0OfKeZxNmEyQIAGAACYsrgv8ue1589rJ6J0\nZ1xe3Tuwqmfnt7e9eP2z1kynkaTz57VbR+Hqw0ntDzz3H6e1XdPd92Qc/217W4dAis4YAjQA\nAEBLkNPttg8c1ZhRPNpcL6/qKa/q2fb5jWlv4r0ulz+/vXBee25xiQci60phFEtd9+7O6X+2\nq/c923f8n462szFVYaYQoAFam5SjLwPAlOYc7znHz5q2bBZpU3uyUl7VM7CqZ9e/bDOp8ebm\n8ue1F85rz53dxix08phEjhbiu0dNW9E/cPnO7mWF3J8WCzjWyQq+LwFa2/z5VCxSfz/ZNi1d\nmnU1ADDhOPPPyPtn5I/6s2N1TVUe7Ss/0DPw8+5X/m6LKMr8ue2F89sL57fbx2E6j0lBEP15\nsXCGbf9VT9+TUfy1jrYZAik6AwjQAK2ts5M2bKB776WlS2nu3KyrAYAscV8ULugoXNAxq9Fh\n+sHegQe6X/6/m7d+9nfOa7zC+R3589vy57SLIsJDxs733B91Tv/z7t73bt/5vzvalqI7x4TD\newCg5XV10dVXZ10EAEwucrrddvFRbRcfRUTh76sDD/SUH+h5/hO/NaH25xUK57fnz28P5hfR\nxyMrnULcMmPaN/vLV+7s/sN88PliQTL8LSYOAjQAAAAciHtS4J4UzPjUbJOY6vr+gQd6Bu7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fJhoBGjJj7xjYs/zckz96uHfNWO2ZCybc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\nobkAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(123)\n",
    "cat(\"Figure 8\")\n",
    "cv_lambda_RIDGE <- cv.glmnet(\n",
    "  x = as.matrix(expectancy_train[,-c(1,2)]), y = as.matrix(expectancy_train[,2]),\n",
    "  alpha = 0,\n",
    "  lambda = exp(seq(-12, 10, 0.3)),\n",
    "  family = 'poisson'\n",
    ")\n",
    "lambda_min_MSE_RIDGE <- round(cv_lambda_RIDGE$lambda.min, 5)\n",
    "plot(cv_lambda_RIDGE, main = \"Lambda selection by CV with RIDGE\\n\\n\")\n",
    "plot(cv_lambda_RIDGE$glmnet.fit, \"lambda\")\n",
    "cat(\"Figure 9\")\n",
    "abline(v = log(lambda_min_MSE_RIDGE), col = \"red\", lwd = 3, lty = 2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.00335"
      ],
      "text/latex": [
       "0.00335"
      ],
      "text/markdown": [
       "0.00335"
      ],
      "text/plain": [
       "[1] 0.00335"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_min_MSE_RIDGE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.5 Cross-Validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now be performing cross-validation to test our predictive model. Below, we have a few different models. \n",
    "- `model_5CV` and `model_holdout` are the cross-validation with 5 folds and holdout models respectively built using the stepwise covariates found through the variable selection methods.\n",
    "- `model_lasso_cv` and `model_lasso_holdout` are the cross validation with 5 fold and holdout models built using lasso for the cross validation and the lambda found from LASSO for the holdout model. \n",
    "- `model_ridge_cv` and `model_ridge_holdout` are the cross validation with 5 fold and holdout models built using ridge for the cross validation and the lambda found from ridge for the holdout model. \n",
    "- Lastly, `model_elastic` is the cross validation done for 5-fold using the elastic method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :\n",
      "“There were missing values in resampled performance measures.”\n"
     ]
    }
   ],
   "source": [
    "set.seed(123)\n",
    "lambda <- 10^seq(-3, 3, length = 100)\n",
    "# define training control\n",
    "train_control <- trainControl(method=\"cv\", number = 5)\n",
    "\n",
    "# train the models\n",
    "#5 fold CV using stepwise covariates\n",
    "model_5CV <- train(Life.expectancy~., data = expectancy_train[,stepwise_selection], \n",
    "               trControl=train_control, method=\"lm\", preProcess = c(\"center\", \"scale\"))\n",
    "\n",
    "#stepwise covariates lm holdout\n",
    "model_holdout <- lm(Life.expectancy~., data = expectancy_train[,stepwise_selection]) \n",
    "\n",
    "#lasso with CV\n",
    "model_lasso_cv <- train(Life.expectancy~., data = expectancy_train[,-1], \n",
    "               trControl=train_control, method=\"glmnet\", preProcess = c(\"center\", \"scale\"),tuneGrid = expand.grid(alpha = 1, lambda = lambda))\n",
    "\n",
    "#ridge with CV\n",
    "model_ridge_cv <- train(Life.expectancy~., data = expectancy_train[,-1], \n",
    "               trControl=train_control, method=\"glmnet\", preProcess = c(\"center\", \"scale\"),tuneGrid = expand.grid(alpha = 0, lambda = lambda))\n",
    "\n",
    "#lasso holdout\n",
    "model_lasso_holdout <- glmnet( \n",
    "  x = as.matrix(expectancy_train[,-c(1,2)]), y = as.matrix(expectancy_train[,2]),\n",
    "  alpha = 1,\n",
    "  lambda = lambda_min_MSE_LASSO\n",
    ")\n",
    "\n",
    "#ridge holdout\n",
    "model_ridge_holdout <- glmnet( \n",
    "  x = as.matrix(expectancy_train[,-c(1,2)]), y = as.matrix(expectancy_train[,2]),\n",
    "  alpha = 0,\n",
    "  lambda = lambda_min_MSE_RIDGE\n",
    ")\n",
    "\n",
    "#elastic cv\n",
    "model_elastic <- train(\n",
    "  Life.expectancy ~., data = expectancy_train[,-1], method = \"glmnet\",\n",
    "  preProcess = c(\"center\", \"scale\"),\n",
    "  trControl = train_control,\n",
    "  tuneLength = 10\n",
    "  )\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to test which model is the best, we will be finding the RMSE's of the models and comparing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 9"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 7 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Method</th><th scope=col>RMSE</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>LM Hold-out   </td><td>3.919471</td></tr>\n",
       "\t<tr><td>5 fold LM CV  </td><td>3.919471</td></tr>\n",
       "\t<tr><td>LASSO CV      </td><td>3.664511</td></tr>\n",
       "\t<tr><td>RIDGE CV      </td><td>3.720796</td></tr>\n",
       "\t<tr><td>Elastic CV    </td><td>3.663029</td></tr>\n",
       "\t<tr><td>LASSO Hold-out</td><td>3.667097</td></tr>\n",
       "\t<tr><td>RIDGE Hold-out</td><td>3.663632</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 7 × 2\n",
       "\\begin{tabular}{ll}\n",
       " Method & RMSE\\\\\n",
       " <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t LM Hold-out    & 3.919471\\\\\n",
       "\t 5 fold LM CV   & 3.919471\\\\\n",
       "\t LASSO CV       & 3.664511\\\\\n",
       "\t RIDGE CV       & 3.720796\\\\\n",
       "\t Elastic CV     & 3.663029\\\\\n",
       "\t LASSO Hold-out & 3.667097\\\\\n",
       "\t RIDGE Hold-out & 3.663632\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 7 × 2\n",
       "\n",
       "| Method &lt;chr&gt; | RMSE &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| LM Hold-out    | 3.919471 |\n",
       "| 5 fold LM CV   | 3.919471 |\n",
       "| LASSO CV       | 3.664511 |\n",
       "| RIDGE CV       | 3.720796 |\n",
       "| Elastic CV     | 3.663029 |\n",
       "| LASSO Hold-out | 3.667097 |\n",
       "| RIDGE Hold-out | 3.663632 |\n",
       "\n"
      ],
      "text/plain": [
       "  Method         RMSE    \n",
       "1 LM Hold-out    3.919471\n",
       "2 5 fold LM CV   3.919471\n",
       "3 LASSO CV       3.664511\n",
       "4 RIDGE CV       3.720796\n",
       "5 Elastic CV     3.663029\n",
       "6 LASSO Hold-out 3.667097\n",
       "7 RIDGE Hold-out 3.663632"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Table 9\")\n",
    "holdout.prediction <- predict(model_holdout, newdata = expectancy_test[,-2])\n",
    "\n",
    "holdout.rmse <- rmse(\n",
    "    preds = holdout.prediction,\n",
    "    actuals = expectancy_test$Life.expectancy)\n",
    "\n",
    "model.5CV.pred <- predict(model_5CV, newdata = expectancy_test[,-2])\n",
    "\n",
    "model.5CV.rmse <- rmse(\n",
    "    preds = model.5CV.pred,\n",
    "    actuals = expectancy_test$Life.expectancy)\n",
    "\n",
    "lasso.holdout.pred <- predict(model_lasso_holdout, newx = as.matrix(expectancy_test[,-c(1,2)]))\n",
    "\n",
    "lasso.cv.pred <- predict(model_lasso_cv, newx = as.matrix(expectancy_test[,-c(1,2)]))\n",
    "\n",
    "ridge.holdout.pred <- predict(model_ridge_holdout, newx = as.matrix(expectancy_test[,-c(1,2)]))\n",
    "\n",
    "lasso.cv.pred <- predict(model_lasso_cv, model.matrix(Life.expectancy ~., expectancy_test)[,-c(1,2)])\n",
    "lasso.cv.rmse <- rmse(lasso.cv.pred,expectancy_test$Life.expectancy)\n",
    "\n",
    "ridge.cv.pred <- predict(model_ridge_cv, model.matrix(Life.expectancy ~., expectancy_test)[,-c(1,2)])\n",
    "ridge.cv.rmse <- rmse(ridge.cv.pred,expectancy_test$Life.expectancy)\n",
    "\n",
    "elastic.cv.pred <- predict(model_elastic, model.matrix(Life.expectancy ~., expectancy_test)[,-c(1,2)])\n",
    "elastic.cv.rmse <- rmse(elastic.cv.pred,expectancy_test$Life.expectancy)\n",
    "\n",
    "holdout.lasso.rmse <- rmse(\n",
    "    preds = lasso.holdout.pred,\n",
    "    actuals = expectancy_test$Life.expectancy)\n",
    "\n",
    "holdout.ridge.rmse <- rmse(\n",
    "    preds = ridge.holdout.pred,\n",
    "    actuals = expectancy_test$Life.expectancy)\n",
    "\n",
    "RMSE <- tibble(\n",
    "    Method = \"LM Hold-out\",\n",
    "    RMSE = holdout.rmse)\n",
    "\n",
    "RMSE <- rbind(RMSE,tibble(\n",
    "               Method = \"5 fold LM CV\",\n",
    "               RMSE = model.5CV.rmse))\n",
    "\n",
    "RMSE <- rbind(RMSE,tibble(\n",
    "               Method = \"LASSO CV\",\n",
    "               RMSE = lasso.cv.rmse))\n",
    "\n",
    "RMSE <- rbind(RMSE,tibble(\n",
    "               Method = \"RIDGE CV\",\n",
    "               RMSE = ridge.cv.rmse))\n",
    "\n",
    "RMSE <- rbind(RMSE,tibble(\n",
    "               Method = \"Elastic CV\",\n",
    "               RMSE = elastic.cv.rmse))\n",
    "\n",
    "RMSE <- rbind(RMSE, tibble(\n",
    "               Method = \"LASSO Hold-out\",\n",
    "               RMSE = holdout.lasso.rmse))\n",
    "\n",
    "RMSE <- rbind(RMSE, tibble(\n",
    "               Method = \"RIDGE Hold-out\",\n",
    "               RMSE = holdout.ridge.rmse))\n",
    "RMSE "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the model with the lowest RMSE is the elastic model with an RMSE of 3.663029. The coefficients for this model can be found below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Table 10"
     ]
    },
    {
     "data": {
      "text/plain": [
       "19 x 1 sparse Matrix of class \"dgCMatrix\"\n",
       "                                          s1\n",
       "(Intercept)                      69.10258900\n",
       "Adult.Mortality                  -2.30326426\n",
       "infant.deaths                    10.27596986\n",
       "Alcohol                          -0.28613317\n",
       "percentage.expenditure            0.62442166\n",
       "Hepatitis.B                      -0.06411130\n",
       "Measles                          -0.04012417\n",
       "BMI                               0.66222164\n",
       "under.five.deaths               -10.55426961\n",
       "Polio                             0.27901943\n",
       "Total.expenditure                 0.14502042\n",
       "Diphtheria                        0.18339641\n",
       "HIV.AIDS                         -2.68744580\n",
       "GDP                               0.19137946\n",
       "Population                        0.02274985\n",
       "thinness..1.19.years             -0.02926623\n",
       "thinness.5.9.years               -0.24398017\n",
       "Income.composition.of.resources   1.74121425\n",
       "Schooling                         2.42970613"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat(\"Table 10\")\n",
    "coef(model_elastic$finalModel, model_elastic$bestTune$lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>alpha</th><th scope=col>lambda</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>11</th><td>0.2</td><td>0.002935766</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & alpha & lambda\\\\\n",
       "  & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t11 & 0.2 & 0.002935766\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 2\n",
       "\n",
       "| <!--/--> | alpha &lt;dbl&gt; | lambda &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 11 | 0.2 | 0.002935766 |\n",
       "\n"
      ],
      "text/plain": [
       "   alpha lambda     \n",
       "11 0.2   0.002935766"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_elastic$bestTune"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is a convex combination of Ridge and LASSO. The equation to understand the alpha for this elastic model is $\\alpha \\times LASSO + (1-\\alpha) \\times RIDGE$, which combines the L1 and L2 norms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cXg2FQxLq/sMIX014uXGNuV+bLzG/Xd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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(varImp(model_elastic)) + ggtitle(\"Most important variables from elastic CV\") + labs(caption = \"Figure 10\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Observations\n",
    "- The most important variables we get from this are under five deaths, infant deaths, HIV/AIDS, Adult mortality, Income composition of variables, BMI and percentage expenditure. \n",
    "- Population, thinness, Measles, Hepatitis B and total expenditure are less important.\n",
    "- Alcohol and Polio are right in the middle of the variable importance graph. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.098506,
     "end_time": "2021-11-06T00:53:49.060642",
     "exception": false,
     "start_time": "2021-11-06T00:53:48.962136",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n"
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    "# 3. Discussion\n",
    "### 3.1 Results and impacts\n",
    "In our study we used variable selection methods (both forward and backward) to find that the best model is the one with 12 covariates. From there, we used those covariates to create cross-validation models with 5-fold and holdout models. Additionally, we performed LASSO and ridge and created 5-fold cross validation and hold-out models for the two. The last type of model we did was an elastic cross-validation model.\n",
    "We discovered by comparing RMSE that the best model is the elastic cross-validation, and thus found the coefficients for the specific model. Our findings help us see the best model in predicting life expectancy, thus also allowing us to see which factors affect life expectancy the most. Our analysis showed us that Under-five deaths, infant deaths, HIV/AIDS, Adult Mortality, Schooling and income composition of resources are the factors that affect life expectancy the most.   \n",
    "\n",
    "### 3.2 Are the results what we expected?\n",
    "- It is unsurprising that a disease such as HIV/AIDS affect life expectancy. One could question why Measles was not equally as important, but a reason for this could be that there is a vaccine which is quite widespread, and so the disease is not as impactful anymore.\n",
    "- Similarly, infant deaths, under five deaths and adult mortality being the most important are also what we expected, as they directly involve life expectancy. \n",
    "- Our variable selection methods suggest that Alcohol is an important aspect of our model, but the Important variables for our best model seem to suggest otherwise. We would expect Alcohol to be higher up on the important variables graph.\n",
    "\n",
    "### 3.3 Improvements that could be made\n",
    "- This study only takes into account additive models, and so, we are not able to explore the relationship between variables in the model. While we showed that the $C_p$ is much higher with interactions, our model could be improved using interactions, so there is further room for improvement here.\n",
    "\n",
    "### 3.4 Future questions/research\n",
    "Our results with this study hae allowed us to see the factors affecting life expectancy and the best way to predict life expectancy in any random country. In the future, this study could lead to questions about:\n",
    "- How can governments help in increasing life expectancy and what areas should they be focusing on specifically?\n",
    "- The data in this study predates Covid-19. How much does Covid-19 affect life expectancy and how much would it change our model?\n",
    "- As mentioned above, the data in this study is from 2000 - 2015. There have been multiple advancements in the medical field since then. Further, 15 years is also a long period of time. It would be interesting to explore how for different and shorter periods of time how life expectancy changes and how its changed over time. "
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   "source": [
    "# 4. References"
   ]
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   "source": [
    "$^{(1)}$ World Health Organisation (WHO). (2018, February 10). Life expectancy (WHO). Kaggle. Retrieved November 6, 2021, from https://www.kaggle.com/kumarajarshi/life-expectancy-who. \n",
    "\n",
    "$^{(2)}$ Tier 1-life expectancy and wellbeing-1.19 life expectancy at birth. Department of Health | Tier 1-Life expectancy and wellbeing-1.19 Life expectancy at birth. (n.d.). Retrieved November 6, 2021, from https://www1.health.gov.au/internet/publications/publishing.nsf/Content/oatsih-hpf-2012-toc~tier1~life-exp-wellb~119. \n",
    "\n",
    "National Progress Report 2025 Goal: Reduce HBV Deaths. (2021, June 03). Retrieved from https://www.cdc.gov/hepatitis/policy/NPR/2021/NationalProgressReport-HepB-ReduceDeaths.htm\n",
    "\n",
    "Clinical Features of Diphtheria. (2020, May 26). Retrieved from https://www.cdc.gov/diphtheria/clinicians.html"
   ]
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