FinalProject_group047.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COGS 108 - Final Project "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We were curious about the rating system in the Google Play Store works, since smartphones take up a big chunk of most people’s time. We decided to see if more downloads of an app correlates with the rating that the app gets. After cleaning and analyzing our dataset, we concluded that there is not necessarily a positive correlation between the popularity(number of installs) of an application and its rating. This project did lead to the fact that more downloads leads to a more accurate rating of an application, since more people have rated it.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Names\n",
    "\n",
    "- Akshay Rao\n",
    "- David Zheng\n",
    "- Hao Luo\n",
    "- Kevin Wu\n",
    "- Nikita Hegde\n",
    "- Tianhui hu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Research Question"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does popularity of Android applications have a positive correlation to higher ratings in Google Play Store? Popularity of apps is measured by the total amount of downloads since the app was released."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Background and Prior Work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why is this question of interest to your group?\n",
    "If we step back from our daily routine and take time to audit where we spend most of our attention, it’s arguably on our smartphones. The medium of the smartphone is applications. Due to this increasing demand, app creators are pressured to preserve high ratings, as higher ratings means more downloads, which in turn leads to more money in their pockets. As we were discussing it and seeing as how most of us were intrigued by it, we decided to do a data science project exploring the correlation between number of downloads and the rating of the application.\n",
    "What background information led to your hypothesis?\n",
    "Mostly common sense went into our hypothesis. To break it down in graphic specificity we thought that since more people install the application, it is an application that benefits many people. The fact that it benefits people means that they regard it in a positive light, since it offers some sort of value to them. Since they perceive value in the application they are more likely to rate it higher on the Google Play Store.\n",
    "Why is this important?\n",
    "This question is important because people who are app developers are going to want to know certain data on ratings of apps and the correlation of that with downloads.\n",
    "How do references relate to our project?\n",
    "The first reference is an article that explains how App Store ratings impact downloads. This would be an important study to do after we do our project because it explores the opposite of our project. In addition, there is causality involved in this article, and that is different than ours. We chose to focus on correlation, which doesn’t imply causation.\n",
    "\n",
    "References (include links):\n",
    "1) How App Store Ratings Impact Downloads (Infographic)\n",
    "https://www.adweek.com/digital/how-app-store-ratings-impact-downloads-infographic/\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We hypothesize that there is a positive correlation between average rating and the total number of installations for Android Applications. We predict that the more downloads there are, the higher the ratings would be because people may have a biased attitude toward already popular apps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dataset(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Link to the dataset: https://www.kaggle.com/lava18/google-play-store-apps?fbclid=IwAR0ynkTjJl92etJH3FiytTpChyziBCN92xNtqqyDeq2LD7cPNh-KC6a1fWg\n",
    "Number of observations: 10.8k\n",
    "\n",
    "Description: \n",
    "The data set is Web scraped data of 10k Play Store apps for analysing the Android market. The data set contains 10.8k observations, and each entry contains the following 13 features of a particular app:\n",
    "\n",
    "App: Application name\n",
    "\n",
    "Category: Category the app belongs to\n",
    "\n",
    "Rating: Overall user rating of the app (as when scraped)\n",
    "\n",
    "Reviews: Number of user reviews for the app (as when scraped)\n",
    "\n",
    "Size: Size of the app (as when scraped)\n",
    "\n",
    "Installs: Number of user downloads/installs for the app (as when scraped)\n",
    "\n",
    "Type: Paid or Free\n",
    "\n",
    "Price: Price of the app (as when scraped)\n",
    "\n",
    "Content Rating: Age group the app is targeted at - Children / Mature 21+ / Adult\n",
    "\n",
    "Genres: An app can belong to multiple genres (apart from its main category). For eg, a musical family game will belong to Music, Game, Family genres.\n",
    "\n",
    "Last Updated: Date when the app was last updated on Play Store (as when scraped)\n",
    "\n",
    "Current Ver: Current version of the app available on Play Store (as when scraped)\n",
    "\n",
    "Android Ver: Min required Android version (as when scraped)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imports \n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import patsy\n",
    "import statsmodels.api as sm\n",
    "import scipy.stats as stats\n",
    "import warnings\n",
    "from scipy.stats import ttest_ind, chisquare, normaltest\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.impute import SimpleImputer\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.metrics import mean_absolute_error \n",
    "from sklearn.metrics import accuracy_score, mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Cleaning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Describe your data cleaning steps here:\n",
    "\n",
    "We first read data from cvs file to data frame. Then we drop unrelevent info and null values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>App</th>\n",
       "      <th>Category</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Reviews</th>\n",
       "      <th>Size</th>\n",
       "      <th>Installs</th>\n",
       "      <th>Type</th>\n",
       "      <th>Price</th>\n",
       "      <th>Content Rating</th>\n",
       "      <th>Genres</th>\n",
       "      <th>Last Updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Photo Editor &amp; Candy Camera &amp; Grid &amp; ScrapBook</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.1</td>\n",
       "      <td>159</td>\n",
       "      <td>19M</td>\n",
       "      <td>10,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>January 7, 2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Coloring book moana</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>3.9</td>\n",
       "      <td>967</td>\n",
       "      <td>14M</td>\n",
       "      <td>500,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Pretend Play</td>\n",
       "      <td>January 15, 2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>U Launcher Lite – FREE Live Cool Themes, Hide ...</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.7</td>\n",
       "      <td>87510</td>\n",
       "      <td>8.7M</td>\n",
       "      <td>5,000,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>August 1, 2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sketch - Draw &amp; Paint</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.5</td>\n",
       "      <td>215644</td>\n",
       "      <td>25M</td>\n",
       "      <td>50,000,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Teen</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>June 8, 2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pixel Draw - Number Art Coloring Book</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.3</td>\n",
       "      <td>967</td>\n",
       "      <td>2.8M</td>\n",
       "      <td>100,000+</td>\n",
       "      <td>Free</td>\n",
       "      <td>0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Creativity</td>\n",
       "      <td>June 20, 2018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 App        Category  Rating  \\\n",
       "0     Photo Editor & Candy Camera & Grid & ScrapBook  ART_AND_DESIGN     4.1   \n",
       "1                                Coloring book moana  ART_AND_DESIGN     3.9   \n",
       "2  U Launcher Lite – FREE Live Cool Themes, Hide ...  ART_AND_DESIGN     4.7   \n",
       "3                              Sketch - Draw & Paint  ART_AND_DESIGN     4.5   \n",
       "4              Pixel Draw - Number Art Coloring Book  ART_AND_DESIGN     4.3   \n",
       "\n",
       "  Reviews  Size     Installs  Type Price Content Rating  \\\n",
       "0     159   19M      10,000+  Free     0       Everyone   \n",
       "1     967   14M     500,000+  Free     0       Everyone   \n",
       "2   87510  8.7M   5,000,000+  Free     0       Everyone   \n",
       "3  215644   25M  50,000,000+  Free     0           Teen   \n",
       "4     967  2.8M     100,000+  Free     0       Everyone   \n",
       "\n",
       "                      Genres      Last Updated  \n",
       "0               Art & Design   January 7, 2018  \n",
       "1  Art & Design;Pretend Play  January 15, 2018  \n",
       "2               Art & Design    August 1, 2018  \n",
       "3               Art & Design      June 8, 2018  \n",
       "4    Art & Design;Creativity     June 20, 2018  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read data from the cvs file\n",
    "df = pd.read_csv( 'googleplaystore.csv' )\n",
    "\n",
    "df = df.drop(columns=\"Current Ver\")\n",
    "df = df.drop(columns=\"Android Ver\")\n",
    "df.dropna(inplace=True)\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We filter by \"Content Rating\" column and keeps applications that are available to everyone. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = df[(df['Content Rating'] == \"Everyone\")].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function to pre-process last updated date column. Convert the string to integers, which represent last updated year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standardize_last_updated_year(string):\n",
    "    \n",
    "    string = string.strip()\n",
    "    \n",
    "    if \"2018\" in string:\n",
    "        output = 2018\n",
    "    elif \"2017\" in string:\n",
    "        output = 2017\n",
    "    elif \"2016\" in string:\n",
    "        output = 2016\n",
    "    elif \"2015\" in string:\n",
    "        output = 2015\n",
    "    elif \"2014\" in string:\n",
    "        output = 2014\n",
    "    elif \"2013\" in string:\n",
    "        output = 2013\n",
    "    elif \"2012\" in string:\n",
    "        output = 2012\n",
    "    elif \"2011\" in string:\n",
    "        output = 2011\n",
    "    elif \"2010\" in string:\n",
    "        output = 2010\n",
    "    # Otherwise, if uncaught - write 0\n",
    "    else:\n",
    "        output = string\n",
    "    \n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"Last Updated\"] = df[\"Last Updated\"].apply(standardize_last_updated_year)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert review column to integers for future regression tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Reviews'] = df['Reviews'].astype(np.int64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Converts Mb and kb values to bytes and removes the unit of memory\n",
    "def standardize_size(str_in):\n",
    "    if 'k' in str_in:\n",
    "        try:\n",
    "            output = round(float(str_in[:-1]) * 1000)\n",
    "        except:\n",
    "            output = 0.0\n",
    "            \n",
    "    elif 'M' in str_in:\n",
    "        try:\n",
    "            output = round(float(str_in[:-1]) * 1000000)\n",
    "        except:\n",
    "            output =  0.0\n",
    "            \n",
    "    else:\n",
    "            output = 0.0\n",
    "            \n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Size'] = df['Size'].apply(standardize_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert install column from string to int for future regression tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove '+' and ',' symbols from Intalls and cast to int\n",
    "def standardize_installs(str_in):\n",
    "    output = int(str_in.replace('+' ,'').replace(',',''))\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Installs'] = df['Installs'].apply(standardize_installs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cast Price as a float without the '$'\n",
    "def standardize_price(str_in):\n",
    "    output = float(str_in.replace('$', ''))\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Price'] = df['Price'].apply(standardize_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display cleaned dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>App</th>\n",
       "      <th>Category</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Reviews</th>\n",
       "      <th>Size</th>\n",
       "      <th>Installs</th>\n",
       "      <th>Type</th>\n",
       "      <th>Price</th>\n",
       "      <th>Content Rating</th>\n",
       "      <th>Genres</th>\n",
       "      <th>Last Updated</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Photo Editor &amp; Candy Camera &amp; Grid &amp; ScrapBook</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.1</td>\n",
       "      <td>159</td>\n",
       "      <td>19000000.0</td>\n",
       "      <td>10000</td>\n",
       "      <td>Free</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Coloring book moana</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>3.9</td>\n",
       "      <td>967</td>\n",
       "      <td>14000000.0</td>\n",
       "      <td>500000</td>\n",
       "      <td>Free</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Pretend Play</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>U Launcher Lite – FREE Live Cool Themes, Hide ...</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.7</td>\n",
       "      <td>87510</td>\n",
       "      <td>8700000.0</td>\n",
       "      <td>5000000</td>\n",
       "      <td>Free</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pixel Draw - Number Art Coloring Book</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.3</td>\n",
       "      <td>967</td>\n",
       "      <td>2800000.0</td>\n",
       "      <td>100000</td>\n",
       "      <td>Free</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design;Creativity</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Paper flowers instructions</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.4</td>\n",
       "      <td>167</td>\n",
       "      <td>5600000.0</td>\n",
       "      <td>50000</td>\n",
       "      <td>Free</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>Art &amp; Design</td>\n",
       "      <td>2017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 App        Category  Rating  \\\n",
       "0     Photo Editor & Candy Camera & Grid & ScrapBook  ART_AND_DESIGN     4.1   \n",
       "1                                Coloring book moana  ART_AND_DESIGN     3.9   \n",
       "2  U Launcher Lite – FREE Live Cool Themes, Hide ...  ART_AND_DESIGN     4.7   \n",
       "4              Pixel Draw - Number Art Coloring Book  ART_AND_DESIGN     4.3   \n",
       "5                         Paper flowers instructions  ART_AND_DESIGN     4.4   \n",
       "\n",
       "   Reviews        Size  Installs  Type  Price Content Rating  \\\n",
       "0      159  19000000.0     10000  Free    0.0       Everyone   \n",
       "1      967  14000000.0    500000  Free    0.0       Everyone   \n",
       "2    87510   8700000.0   5000000  Free    0.0       Everyone   \n",
       "4      967   2800000.0    100000  Free    0.0       Everyone   \n",
       "5      167   5600000.0     50000  Free    0.0       Everyone   \n",
       "\n",
       "                      Genres  Last Updated  \n",
       "0               Art & Design          2018  \n",
       "1  Art & Design;Pretend Play          2018  \n",
       "2               Art & Design          2018  \n",
       "4    Art & Design;Creativity          2018  \n",
       "5               Art & Design          2017  "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Analysis & Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a general over view the data set, we get the max, min, average, and media of the rating. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Overview of the data \n",
    "df[\"Rating\"].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Rating\"].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.186374663072782"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Rating\"].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.3"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Rating\"].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check for normality of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_p_val(p_val, alpha):\n",
    "    if p_val < alpha:\n",
    "        print('We have evidence to reject the null hypothesis.')\n",
    "        print('The data is not normally distributed.')\n",
    "    else:\n",
    "        print('We do not have evidence to reject the null hypothesis.')\n",
    "        print('The data is normally distributed.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test statistic: 2871.7869107159167 p-value: 0.0\n",
      "We have evidence to reject the null hypothesis.\n",
      "The data is not normally distributed.\n"
     ]
    }
   ],
   "source": [
    "ratings = df['Rating'].values\n",
    "st_ratings, p_ratings = normaltest(ratings)\n",
    "print(\"test statistic:\", st_ratings, \"p-value:\", p_ratings)\n",
    "check_p_val(p_ratings, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(ratings.min(), ratings.max(), 0.1)\n",
    "fit = stats.norm.pdf(xs, np.mean(ratings), np.std(ratings))\n",
    "plt.plot(xs, fit, label='Normal Dist.', lw=4)\n",
    "plt.hist(ratings, 30,  density=True, label='Actual Data');\n",
    "plt.title('Rating Data')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test statistic: 15584.97433551716 p-value: 0.0\n",
      "We have evidence to reject the null hypothesis.\n",
      "The data is not normally distributed.\n"
     ]
    }
   ],
   "source": [
    "reviews = df['Reviews'].values\n",
    "st_reviews, p_reviews = normaltest(reviews)\n",
    "print(\"test statistic:\", st_reviews, \"p-value:\", p_reviews)\n",
    "check_p_val(p_reviews, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DgynLj1fV6cD/MpgSmXZdg40N5rrfAfzjSkOX6RvH/nUccCFwMvCLwCsYvJ6H2vZY6lrPQT/UWy1M2BNJNgG0532tf6K1JjmSQch/tqq+OEu1AVTV08BdDOZGNyY5cD/H0m0/V1dbfyzw5BjKOQt4R5K9wOcZTN98dAbqoqoea8/7gH9icHCc9uu4CCxW1d1t+QYGwT/tug44D/haVT3Rlqdd11uB71bV/qr6CfBF4NeY8P61noN+Ft9q4SZge2tvZzA/fqD/Pe0v/duAZw78OrnWkgS4BthdVR+ZldqSzCXZ2NovY/ADsBu4E7joEHUdqPci4I5qE5drqaour6otVTXPYB+6o6rePe26krwiyasOtBnMOz/AlF/Hqvoe8GiS17euc4BvTLuuJd7F89M2B7Y/zboeAbYleXn72Tzw/Zrs/jXOP4qM+8HgL+ffYjDX+8cT3vbnGMy5/YTBUfhSBnNptwMPt+fj29gw+Gcs3wa+DmwdY12/zuBXvfuBe9vj/GnXBvwycE+r6wHgT1r/KcBXgD0Mft0+uvUf05b3tPWnTOA1fQvPX3Uz1bra9u9rjwcP7N/Tfh3btk4DFtpr+c/AcTNS18uB/waOXdI3C3V9GPhm2+8/Axw96f3LO2MlqXPreepGkjQEg16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM79PwsajVmiVFNTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(df['Reviews'].values, bins=100, range=(0, 800))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test statistic: 2871.7869107159167 p-value: 0.0\n",
      "We have evidence to reject the null hypothesis.\n",
      "The data is not normally distributed.\n"
     ]
    }
   ],
   "source": [
    "intalls = df['Installs'].values\n",
    "st_installs, p_installs = normaltest(ratings)\n",
    "print(\"test statistic:\", st_installs, \"p-value:\", p_installs)\n",
    "check_p_val(p_installs, 0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is clear that the data for ratings, reviews and installs are all not normal so tests that assume normally distributed data will not be accurate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First by using the scatter_matrx method, we plotting the whole dataframe.\n",
    "Since every attributes have multiple valules, we choose the scatter plot to show the relations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V1GXpFjUtybmBFKUBN6d646P3eqH/9XRPnN/+3kt85bEz/O4PDue1X7emnKsaSriqoYRr1pRP+b6qmFkYVNki9IcuWneoEMIDLM6wxDngle4EXpeSl3jaWGr/3TaQmpELp8yn8p7rGnjr3iYqw34Mw0IRtnK7pipUF11+2sNccqQ9wh//6GX8bo2/fdsOyoIzW3NYDEwVwdlYFqS53E/WtLgwkKRtMI0q7KT7gUSarAG6afHardWcG0iQ1U0MC3wuhbKAm1TOwDDtZ32x38WayhC6ZdE+lB7N7VoImquK+dD1TVyIprlt4+TrTXNBMp0hnTOR2JHNE/G7FfavrUJVFQJu9bKFHxYzpiV54nQf3ZEMuxpLKPK5+NCNLfgKyCT2J7PEMwamlPRE8z+vypCHiuH77lLrrfHMzNaCVZW8HNqFZjHPBN8P/PtCd2K+ONUbZ21lCGVCSPKI4WsbmFlliJwFvzgxSGXYNqKapvAbN66mqTzAx27NTyheLPzbU+foiWVo7U/wnYNLM+JTUnhtSgHCPg2XplAd9qGqCtVFXjRNpcTnRqIAEoFgKKXz+u11rK60jebG2jA7m0q4Y0s1IZ9dpy1rSM70JmgfTHGkI8qBs5O7+e7ZVUfArXLPrrpJ97kSinwufm33Ku7etYpbZyjzd6U8PSbndSRVYiwBj4t9q8vxuFSCXjfPnB0goy9Gx9zlk84ZRFI6COgeHgj43VpBkfWmsiCrKwKU+t3sX5s/03vw5W46Imk6ImkefLk7r32sWd1cP3U6xkR6F1+u/OI0gkIIF3CjlPLhSdo/KIQ4KIQ42NfXN8+9mxtO9sRZW5XvuqgMeXCpgs4CI7bJ8Kq2+2xf8/gL9OO3reOh37qJD9+0eOuqXdNShiIEbk3l2papXTGLEbdqu5sLzQQlcLY/yVBK52RvnHjGIKNbuFQFEzvCU1EEQsBgMssL520d0bfuWcXVLeVsrC7i83fv4FN3bKCuxIdhWcQyOh2RDJoq8gqUjuBzKTx1ZgBFwFOXWZ5rOmyoDnPLhqp5d8vevqVqtBhxfUm+h0NTFW5eX8mtG6pQFUFdsW/UXbhcCHk11leFKPG72dEwdU6xpkDI56Yy7MVTYKa4tb4IlypwqYKtBeICfGPc3Y1lM/MoLcZwpMXqDn0X8K3JGqWUXwW+CrB79+7FIkF32UTTOj2xbF5QDNhpElVh74zWBJ/49C0MJXXWVS+9Gmp3717FtWvK8WmLN+BlpBRModelFFiTiDVLbFHy+lIfmlDoimTQFDsYalWpn2TW4HBHhJBb42xfksFkjkTW5MJAis+8YTM3rK1AUxXevLOenliW/36hHY+msKkmwEdvWcOWApXkX7u1io/ftp63/NPTANMKn19qNFWEefrTt/L8+QHu2FKL5wvj269fXW4bwg2V7G4qITDJDGmhiaRyPHisB59L5fbN1bhnYKgVRcHnUoildUp8Uw9CTEsST+eIpg2SBcQb1laFeM2WmtHtiYS8GomsiQDcM5RCXIwP6zk3gkKIvyvwchQ4KKX8n0kOWw/sEEL8BrBZCPGbUsovzVknF5jJgmJGqC320RWZ/kzQpaisq16ca37T4Upk2uaDQhKdI9GeuTGNfpeClLYLVDclQoGN1SG21RWjWxbHu2NkdYv11SHu3FrD1584S3nATV8iR9CjkTEsTCmJpnW+/3wHG2tsIzeUynGsM4rPpWABr91Ww67Gwm6pgaTOz45286H9LXzv+XbumUEVkaVERdjDHVtq814XwD17VlE6XMYrtIjrCh66EKFjyB7srqlMsHEGer29sTS/PGEnyX/r2QtT7tsTz5LSLRB2OsREjnXGODKclrW+OsTuCdqhI2ZPANmJdcYuQTDoIrXI8iTmwyfgBXYAp4Z/tgGlwPuEEH9T6AAp5aeklLdLKe8AXl7OBhDglVEjWDgxvbbIS2d0+jPBP//ZCZLZxaXkv5wodNsHvSpCUUZTGlyKYFtdETsbS3BpKkGvi5vWVVJT5KdtIMUzZwbJ6rY7M54xePxkH5qq4He7aCoLUB700FQWwO9W8bpV6kp9fPvZ83z72fNkcia6KUnmTMqDHl69uXrSElXPtw1x/3PnOd4dpzzo4Xh3YVmx5YpbhdVLJBp0VakfRQg8LoXqMdVcpkNZwE1lyD5mssH0CA2lfuqKfZT43VzVmJ9D2DaQ5MnT/Tx5ur9gLMKoso6AyqKZBa4VuxefG3o+3KFrgFuklAaAEOLLwIPAq4AjlzpYSnn93HZv4TnVkyDgVqmbZAZUU+yj+3AXpiWnVY8vmTVI62ZBXUCHuUE3LFyKQkWxj4qQi211xbznuhb+6fEz5AwLr1tlR0Mxz5wZoG0gSU8sQyStD69/CuIZg9UVAcqCHt6442LwSl88TTRt8IvjPbT2J+2SQALu2lbD9w7qDMQz/P5/HybgdfG+6/KLxpqWJJUzGUrZUXyR1OIahc81ugkHWvu5af38ButcDqsrgrz/hmZURcyo+PVgMscvj/dw47pyDEvyxqvqeeqvJ9+/yOfiTTvraBtIcfP6/DzAnClHjbBRwO3RXBEgrRtoQqDOcB5lyMUXmTsfZrmO8euhAaBWSmkCCyczsYg42RNnTVVo0nWK2iIvhiXpT0zv43rHvgbKl2BqwVJgsiFIxpAYloUQkvXVYW7ZVEXIp/HWPfVsrAmxp7GEk90JUjmTgWSOaEpHSoklJSGvi7t317Oxpoi7ttZwojtGNKUT9rnwuV0c74qjKgqKsPO+ttQVsaUuzFDKwLDgQOsQ5wdS/NcL7eP6pAIel0p9sY/3X9dCc7m/oKFczigCvvF0G8mMnTi+kGkk0yHg0WZkAMGe7Z8bSPLk6QHah9KX1A7tiWU53hUnlTML1it9w45a9jSVsKephNdtz3cx/86r1lIe8HD9mopL5hFOZE31zNRrpmK2VnXnY6rweeCQEOJR7H7vBz4rhAgAv5iH91/0nOxJcPP6yRPXR9bIOiPpcUVvJ+Oa1UsvqnKxMXKDyQmvTRwXjw2SEUJBABnd4sGXe3ihLYIQ9hrMM2cHEQJKA25iwxUhJFBf7OPVm6rYXFvE5toi/uXJVn7+cjcuVfCea5s50hGlO5oh5NXYUlfE7ZurcakKzWUB1lUF6YxkRgdPG6vHu9NDHlhfW8SeplI6ommqwj46ZuBWXw6oil3c9SPfepGMbhLwqPzt265a1GuDM6W+xMeR9giJrMGFwdSoW3Qyiv0uQl6NeMZgVWm+96k7mhmNGu2OZvIS7v/qwVN0RNJ0x7Mc7YiwpW58NKpLtcUJXGq+maornr3B+WwF2cy5EZRS/rMQ4ifAXuznyO9LKTuHmz851++/2BlM5uhPZFlfPblQdU3RiBHMcFXDpLs5zCJeTaAogpxhYVp2crqmCAxTjko/1Ra5AYXBZBafS2NzbQi3S6VjKE1NsQ+3qnCiO040nSOtG7hUhcqQm6zuQwgIez187p4tVIV8JLIG33ymjf85ZAsXh7yu0fWY6iIvN66rYEtd0WjEoNet8Zf3bKcvnqU04CaS1vOEFsqCbj73pq00lvn5yuNnAUbdoiuFEp+LkEfjQOsgmiqoL/GTyBjLyghurAlTEXJjWhaGBbXFUxtBr0vl3muaSOfMgukskbTOSIBzobzLs/1JkjkTRZi09ibyjKBn2Ah6ChhBy7roDl0sq4PztWikAH3D77dGCLFGSvn4PL33ouZEt10maSojOHJRd62wUfxC49EUpJRoiiTkc1Nb5CWjW5ztT6IqgqwhUYXEpaqUB93Ul/jpT+UI+zRayv0YFrSU++mOqVSGPJgWVBf52VJfTE8sy5uuqqMqZA9wDl+I8OSpftyaQla3uHNrNW/d08CTp/rxuVV2rCoeJ6QgpWQwmaMs6CHo0Qo+1D2aRvPwKP7OLTUc64qxaQYRh8uBnCXpiKYJ+1xkdJOGUj81izz6+HIoD3p5/Y56zvQluKqhmEtFEmYNk3hWJ+zLTxfZWlfEgWE36dYCaTchj4YQoApBuID2cCJnjfs9Fpd28Tq90plcYJbGMfORIvEXwFuBl2FU+lACjhHEriEIsH6SyFCwF7J9LpXOGaRJOFwZqqKQylnoph2MVBpws74mjJTg92jkTIuBRJaMbiGRRNI6B84NksyaNJT42L6qhCK/i8de6aOxPMC+5jIeeaUXl6pw985VlATGPzxqin2EfS4My+KurbW8+1p77e62TYUDOh4/1c8LbUP43CrvvqYJnzt/HalkzLpwU3mApvLFmKo8t2R0i/VVYc4PplCE4O5lmiIC9kB6qsH0CMmswTeeaSOrW+xpKuX6CaoxP3yxY7Q+Z0XIw927Vo1rD3hVVCFQVIXy4MwskTZGa7SQEVS5KLJ9qZXR2dJkmI+Z4BuB9VJKJwimAK90xynxu6iYQqNPCEFt8cwS5h2mhwpUFXtQhSCZtRVcwj47GVhiiy6blqR9KM1QMseGmiL+39duosTv5rFTvfzq9ADtQymSWRMFQcijUeR38WzrIPde28j/ua4Jr0vF61LRTYuTPXF64pk8I9hcHuDPfm0L8YxBTdGl130Hk/btlM6ZpHJGQSNYFpxZmP1ypDjg5u17G6gv8WFaclnOAmdKMmuQ1e35yEAy/7F8pjeBHPaHnu5J5LU3lwXpGMrgdysIke/U9KqQMe3fExlMX0zdKhTYsr4myLGuxOj2VJhydszXfBjBs9i1FB0jWIAT3XHWV08eGTpCbbHPcYfOEhrAcMGBgFulyOumLOimK5phVYkftwovdcRIZQ1Spj0uTWZNdNPi3ECCX5zo5R37Grhray1hr5vuWIaMbtoFTbOGbRRzOk+c7OMtey4u4h5oHSSe0bkwlGbDHfluyWK/m+JJSluNJWdYrK0MoQqFuhLfpCLjH7iumY5Imuqwd1qpNcuRm9dVsK2+CG2GyibLmcqwl91NJbQNpNhfoJLMh/av5mx/cnR7IuuqghzrilEWcBe89srDXvpiWcoLFNy9a1st333eXveuLRAkM/YZd6nn3b7Vs1M6bD6MYAo7OvSXjDGEUsqPzcN7L2osS3KyJ85bdq+65L61RT6Od62sROe5wgCEhLBXw5KSrmiajG7i1lS6omlK/S6ktOWhhBB2hQIpMUxJOmfxzJkBVCHY11LKG6+6mNP34vkhPvuT45zqidMbz+VF8gbcKk+e6iPkdXG0I1pQ5mw6fP+FdrqjGVaV+tlVINl5hO8+f57SoI91VSHu2lZzWe+11PG4VFK6SdgxgqMkswZHO2JkdJPjXTGunZDmEMvqbKoNj25PlC9UhCDo0VAUMarZOhaXouDWFFxKoc9cogxXTREF5oIeVWHEIeq5xHcWcs3OwG4+jOCPhn8cJtA+lCaVM6flx68t9tGfyJI1TDza/NZrW45IIJo2ULHD6HOGRUtFgFjGROJGFYKsYYK0KPJpBL0uuqNpfG4VfXh22J+wIy3P9Sd54fwQ7YNJBhM5DNPOGZz4PV3dUkb7kH2OqXI+c4bFI6/0YlqSm9dX5rk6T3TH6IpkLqkK1DaYpjTom3Z+6XIkksgQS+uEl1E06JViu/3ta7ivwLXRn8iNRof2J3J5JdxypkUsnUMRHswCyfRel4KmCryufCMWyxi4FFtft5B4t8+jQVy/uD0FQ5nZ0cGdjxSJFVMOaaZMJzJ0hJEI0e5oZkZ1BR0uYhcqGr8gbwKmBQiLeMbg6uYysobB+cEUkZSOImzVjIBHw6UqZHUTNeBiTWWQbfVFDCSy/PJEL7G0Tnc0Q9inEkkrFPvcTBwkr6sKccO6ClJZgz3Deoy6adGfyFIR9Iy67I53xXihbQgp7bzCq1vGu32EtEfjl3Kh37CmjMqiqWeLy53nz0dnJES91EjnbDd8VdgzbVHwyrCXa1eX0RvPcl2BZPctdWEGk7nR7Ym09iXRTUkklaM3nqVygsdDAMpwzuxE9jaXUR7yEEnp3LYxP+hrrKB3IXHvsTxzpn/K9ukyZ0ZQCPFdKeVbhBBHKBAIJKXcNlfvvVQ40R1HiMk1Q8cyIqnWEUk7RvAy8WgKCIYjOseTMyGeMUBANG2iDOcFMlzRvSLkJa3bWp37msvZ11LKd569MGwg7RFtQ1mAyrCHly5EaSwLsKZc6V5eAAAgAElEQVRy/PeqKIIb141fg/newXZ6YhmaywOjrlXTkhxujyKRXLsmf91jU20RRf40jWX+vLax3L6lhoaypaGbOVekDZNvPnOeG9dXsLNheQ0GMrrJfz7TRiJrsKuxhP3rJhfcmMi+lsnX0zyayqsmiUoGe9DeNpjC71apLqAdGvC68GYMgr789e1z/Ql6YlksKXnkRC+/d+fGce3+MV6PQIFgr7HUFlhzvBzmcib48eHfr53D91jSHG6P0lIeIDgNjc+RqLaZVJNwGE/OtPC7FRrLfPTH06Ryds6OADyq/VA5eG6IyrCH1ZVBaoq9ZHImqeGk4rvqa7lhTTk9sQxffvQMQ8kcDaV+1lWF2FgTpsTvJmOYJDMG7UNpOqNpXhkOfCpENJ3jV6f7calinMtTVQTbVxUhJQUltN60s46BZI6ywNRBNCvdAIJdWBYKV5xf6qRzJolhl/h8ysG974YWrllTRnXIR2mBcmfXrS6nJ56hqoByzYnuOJYlsWB0tjmWyqCXcwN2QEzFJaKba2fp+p4zIyil7Bre/IiU8lNj24ZzBz+Vf9TK4khHhOumKXE2EjbvpElMzqWcQaYcKf0iaK4Ic7InjmFKhLDVYaSUWJaFtCBnSLqGMiRyBiBwqSles6WGjkia584N0h2zXZhBr0ZTmZ/KkO2OcmsKYa+L/z3cSTJr0jaQYl1VsKCr6tnWITyaQjSdG1c2Z2NNmN54FsO02LGq2A5pN6zRckCaqkxLPs8Brm4uY3VlMM+lvBwoCbi5fm05nZE018zz/7epZvKgrtu3VHGgdTCvqDfAnqZSfG6FrCFZX51vxMJereD2CGPzCPcWOP/lMB/O8lcVeO018/C+i5qeWIaeWLZg5eZCeF22KslMSio52LgU8LtUXKq9IJ/M6vhcKkU+N36PRsir2QVxhcDv0di/voKNNSECXhduTcHjUlAUwYmuGOmcScCt4XOprKkMoBsWP3ixk0df6Rv3niN5n+XByddqYmmdjkianClpHuPadGsKr9pUxWu21pDOmfzbU+f496fOcXS4xpvD9NlQE+L122unlXqyFNnTVMobdtTlrcstJC93xhlK6rzcmR/NHva6qAr7qAp78jRJAdZVh/BoCh5NYV0BD8pYDRqjgCLN5TCXa4IfBj4CtAghDo9pCgG/mqv3XSocbrcfaNumaQTBjhB1VGMmp5Ct0YRda21TbRGRVI7ueAavquJSBBuqglQVeWks9fJvT53H0k08msLG6hDrq2t573VN9MaztA+lOdYZw+NSaa4I8NrttZjSQhGC7z5nV27onuCOet22WnrjWfriWX70Uic7G4qpn6DtGfJqbK0vwqWIgpXqAQaSOXKGfbP3xDKXnVaxUjnYNsQ7r2508gTnkRHXbCEXrUtT8LkU0jmDskD+mt7e5hJ+8FLn6PZExt4mrUP5BYEvh7lcE/wW8FPgz4FPj3k9LqUcnMP3XRIcujCEqogp3QoTqSnycrYvv8ilw+QYEuJZgxPdcaqLPPg0lZBXAwEuTaWxLEBNkRfdsqNAu6IZDrQO4nGp7Gosob40wPZVkuCw6v7e5jKKfC4iqRxuTeGGteW0DaS4ekzibn8iS8irURZ0892DF5AShpI53n1t07i+7WsuI62bhL0uGksLB7k0lwfYvqqIeMbIq/CdM+yivGUB97QjA1caPdE0J7rjzuBhlhlIZCct+3TbxqpJ82BP9cTpjmWwJDx9doD/Z0L7k6cHyAyvcz55eoCbNlSPax/rDp2OstJ0mMs1wSgQBd4OIISoxK4yHxRCBKWU5+fqvZcCz5wdZGtdUUG5q8moLfbx5Kl+pJTOQ68AcpLZVEa3kNIWtg773OQMg7aBNJVhDw2lAZrK/VQXeegYsjAsybHOGLppcaQjyjuvbiTo0bhlw8VouWOdMX7+cjduTeEd+xrGGafHT/bxfNsQxX4Xv763gWKfi6GUTlmBAIIiv4s3jCmgWwhVEePeewTdtPjWgTaGUjpXNRRzU4HiqA7gcWl5EnUOV8azrYP86nQ/QY/GO69uzHuGTaVhWl/iG74HTVoKaNlWhr2jXpFCLl5FheE0XcpmSTx0PgS0Xwd8AagFeoFG4Diwea7fe7GSzBq8dCHCB/a3zOi4umIfyZxJLG0ULIGy0hHiYs0/hYvb2nCl7mtXlxNJ5TjVm8DjkhT7XOxtKqG62Mfn37SNf3mqlWKfm2TWLrWTzpkMJXN50but/QnO9CVwqwp98SyJrMFLF6KsqQyOSj1FUjoZ3eJtexvoT2RHy2GN5blzgwwkslzTUj7j7zOtmwwNV4l3XOST87a99aPpRQ6zw8g1nsgaxDJ6nhFs7U/ycmeUzbVFNE8wdE3lQT5x21pe7ozyGzeuyTv3tvpittYVIYS9PRGfpqCb9vKAOkuiIfOhGPOnwNXAL6SUVwkhbmZ4drhSOdg2hGHJGUd0jRbXjaYdI1gATVEQwp4RjltAtyRFPg3dtLi6pZyhlJ3YvrkujNulYpgW2xtKeLthcWEwxcbaMCe745QE3NSX5D9ApYRUzsDSVISAh471EEnpnO5N8Maranm2dZBVpf7R72jiWiBAZyTFQ8d68GgKloQ7t04taxZJ5fC51VEVmrDXxXVrymkbSC7LyMfZQiso3eVwJVzTUoZuSqrCHioLCP//5Egn0ZRB20CS+25eO66tN57hTF8Sr0vjidP9vH5C5XqJtPN5h7cn4nO7iGVtlZtiz9IxgrqUckAIoQghFCnlI8MpEiuWXxzrwetSRlVDpsuID7xjKD0upN7BptjvGtUlHIuqCAZTOofboyjDcmhhn4ucIfn3p85RFfby9r2ruLqlbNSgbKmdfA3JsCTJrEnOkCjCLrMUSekU+TQaSv3TEjN47twQRzuiwzPUqY3Y822DPH6yn5BX4x37Lrqf9jaXzlqY+HLFmQXOPpVh75Qlqc4PpDg3kKKpgJhDwK3hcdk1M0sLROz2x7Kc6rWrSPTH8/MIs8ZFFRnXEpoJRoQQQez6gd8UQvRiaxivSExL8tOj3dyyIV8T8lI0DT9czw04wTGF8LpUVEVgTLCClpQYpoWmCLqiGdZVhVGErRDjdan0xDJkDQuvS6V9KMWR9ihrq0IYpsU/PXaG0qCbj968dnRtKejR2FwbxqUqWFJy19YaOiMZKmcgXTWYzLGtroisYXHVJZRM2ods91M8YxBJ5/C5nQf7dFmJNRQXmppiHz63RnEBb1VgeB0xmtILelmiaZ3y4coU0VS+ERRjfnfHZ0cTdz6M4BuANPAJ4B1AEfB/5+F9FyXPnB2gP5HlNVtmrupfEnBTHnRzqkCNLwf7BmuoCnGkIzbqSBHY7kvDlOim5G17V5EzJKmcweryICd6YqypDOIddov+8IUOBpI5DrYN0h3NcOhCBEtCddjLB4bLyuxuKiGa1gl6NZrLg6iKoOESEmYT2b+ugoPnBkffeyquaSkja1hUhDxUL6J8sKVAyBHOnndu21jFy52TV0kJe12TCprfubWW48OFxu/cWpvXXhrwEEkbqAJWly/y6NARpJQj0xYL+HchhAq8DfjmZMcIIfYBX8SOhj0opfzEXPdzvvjG020U+11TavNNxeqKIKd6nZJKhdAUwas3V9MTyzKQzKEqtoJLOmegqQqv2VKVF2m5vcFefNdNi28/e54fH+ni/FAKr6aypTaMaUkyusXLnTEGkzlKA3bNvzdfYYXy1RVBVhdIFi5EZdg7rXJbDg6LgS11RZedkpIxzNGBXsbIF9BuKPPTG8+gqQqVRbMzy5/LZPkwcB9Qh11K6aHhvz8JHGIKIwi0AbdIKTNCiG8KIbZKKY/MVV/ni65omoeO9/D+G5ovOfqfjLVVQX50qHPSNAmftnJTJ1I5k2zOpDzgJpXTKfK7WVcRwkLid6vEsyaPvdLLQDJHVrfYXBcejUBLZg0GEjk7sMaSSClpKAuwoSbEE6f6GUjk6IqkRqXLHJYGGd287HvNYf4515/k6bN2dYhdjSWjwYAjrC73c+DsAGGvQok/PyhnJCJ8Jk/BuQyd+gawHjgCvB94ELgHeIOU8g1THSil7JZSjsR9G1zMj1zSfO3xVgDeua/xss+xripELGPQMYmGaNqYJFluBRDP6LzSG6czmkYfrgqhS8nWuiIUoWBYki8/dpYfH+7igcOd/PJ472itPZ9bZVt9EbsaSyj2uwn7XKyuCOBzaWR0i65YhguDV6ZQIaUkltGRkyU0zjLZAiPplcZz51a8Lse8cyXX+Zm+BJ2RDJ2RDGf68pd9/vdINxnDojuW5dHjPXntyoTf02Eu3aEtUsqtAEKIrwP9QIOUctq+PCHENqBcSnlswusfBD4I0NDQMHs9nkO6oxn+80Abb7qqjlWTqINMh92NdjTgs62DBUPvV+480J4J/up0PxndQlEEihCcH0jSH7dLt8QyOfoTWaKKoDzkwa0p+FwqA4ks3zl4AcOUvHlnPZUhL4Yl2VgTpn0oRUXIgxAXK3lcLg8c7uJ0b4I1lUFetz1/vWO2cdIDcIrpLgBXcp3nDHO0ukSuwCDONK3hqvRQEsz/boUCWMO/p8lcGkF9ZENKaQohWmdoAEuBvwfeMrFNSvlV4KsAu3fvXhJTn8//7ASWJfnYrWsvvfMUbKgOUex38egrfbxpZ/661EqWSHSp9mzPkqAiqQm7Kfa56YxlqQx5kFKwpiKAJSW/dlUd16wuJ+DRaO1PktXtzMJ41uDX9zWQyBo0lPrZ11JGfYmfkE+bkcRdIdqGo3rb5im6V51Y1XcFsn1VfsK1w9xyqev8SHuU3niGPc2leYMUIZTRivSigCWrL/ESSet4VIG7QIqEHbFt4ZrBg3AuH5nbhRCx4Z84sG1kWwgRm+pAIYQG/CfwSSll9xz2cV742dEu/vvFDj5y0+ormgWCXZj1jTvq+OnRLo6051cVcK/gB58iQCCQgGFBNGMHxOxtKqWlIsh1a+woS1VRaKkIUux3Y5gWdcVe6oq91BZ72VZfTFnQQ2NZYHTNdV9L2RUbQIAb1lZQHvJww9rpFz91uDIyuuMSnm+uX1NOyKtxfYGq9X3xLL843sPh9iiPTai8AmBJCymHBS9kfpWI0oAPTdgDvEKJ+mGfC0UIwr7pewDmzAhKKVUpZXj4JySl1MZsXyrT+x5gD/AXQohHhRDXzFU/55pnWwf5+P2H2L6qmPtuyZcJuhw+ctNqKkNe3v61Z3i+bcKax8q1gQQ9GmGf7dyQ0r7hjncnuGVDJZ95w2b6Elm7QK7PRZHPTUY3+fen2/i9HxzhxQsRiv1uimZw88yU7auKedfVjc7sZB453eukE803HZEM8YxBRwE5P69LwaXaD6lggXqBzeVBWirsn+by/OjpnnianGXHPmT0fCMppT0Ynsly5HzkCc4YKeW3gW8vdD+ulBPdMd73789RV+LjX9+zZ1Ty6kqpDHv5rw9fwz1feZo/+uHL/Phj14+2KSt4Jhj2uWguC2LJBJnhtAhVgf9+sZ2Qz0XQ42JDdYjm8gCJrMHjp3rpjqQZSuoIBK39hd03XdE0x7tirKsKFVyHdVi8tA+lnQoS80xrf2Lc77GEvC52NZbS2p9gVwGRiFs3Vo0ORCdWTQFI50y04fX+toEkuybsI6WFoti/p8uiNILLgQuDKe7952cJuDX+4717Zz20vqbIx9//+s68MjqFXAQrBcOS1JX4GErlKCkPYAHRlE5lyMtzrYM0lflJhDxc01LKjw93YVoWad1kW30RYZ+LnQ3FpLIG/gmC2Q+81EViuBzTR26andn8XON3rdzB0AgqsLPRmXXPN9etKedIR5StBQYf/Yksz5wdAODxU328dlt+4Ewh4zfCnsZSeuPdBD1qwcr1Hk0hnmFUf3Q6LBsj+N73vpcHHniAyspKjh49OuW+n/jEJ3jkkUcASKVS9Pb2EolEZq0vA4ks7/6XZ8noJt/7jWvnbPawY4JbTWArKqxUFAHVRV56Yhmqwl5+69XrON4V52hHFJem8OrN1QQ8GjnDwuNSSOcke1vKeP32Wp5tHeArj55FIvng/hauWX1xPcPvUUlkDQLupXO7BDwrNypyxPz7PSqVIUdhZ765qqFkUilAt2a7Q3VTXtb9dMfWGqqLfbhUQaiA9mjOtLWDczNYCl46d/UleM973sNHP/pR7r333kvu+8UvfnF0+0tf+hIvvvjirPWjP5Hl3n9+lo5Imv98/75J62rNNgI7MrQ6vHJ1JRUhuLqlzC7cGU3zyIle3r63gcYyP+VBDxeGUvTEsuxqLOHtexrojmVGS7283BEjmbMlbV/ujI0zgm+6qp7zg6mCWoeLDUWAKqAksIKNoBCoAsIF1pwcFpaw18Xb9jYwlMzRUkAxybQkz7cNAXay/MQI512NJXRHMzSV+wumvyjYhnYmq0LL5irZv38/586dG/famTNnuO++++jr68Pv9/O1r32NDRs2jNvn29/+Np/5zGcu+33PD6R4+EQP7UNpBpI5njzdTzyj87V7d8+4SsSVIhDkjOn7wpcj5UEP3bEsiYzOM2cHuHNrDeuqQgwmc/z0iB1oHM/ovHZb7bhyVDeur+BUbwJLSm5aPz560+dW520wMxsIITBX9GVgqymZSyJ5auVRHvSMimRP5GhHlF+dthVjPJqSF0T2xKl+umMZumMZ1lWFKJtwnsZyP6d7kzSWBTgwzf4sGyNYiA9+8IN85StfYe3atRw4cICPfOQjPPzww6PtbW1ttLa2csstt8z43EPJHF96+DTfeOYcuinxuVTKQ242VIf41B0b5n0xXlMVKsMeVldNT49yuVIScNFcHqAnliHkdeEeXhtwqWLUDeMrIKPVUhHks2/aOt/dnXU0RaEq7KGlYuVWT3Cp9mewygliWnKMraxTqMqOz23fz5oicBVY97trWy0DiRxlQTffneZ7LlsjmEgkeOqpp7jnnntGX8tmx5feuP/++7n77rtR1elHbfbFs3znufP80+NnSWYN3rpnFR+5ac0V5/9dKWUBN6/ZUsPHb1m9oP1YaGqKfPzOq9dxoifOjvri0SoCIa+Lt+5pYCCZZW1l4VmdYVo83zaES1O4alXxtMsiLSaqwh72r63gY7cujQCeuaCmyMv1a8p53/VNC90VhxmyriqE+yrbuBUqg3Xjukpqi32UBTwF3aE3rCnnV6cHuG7N9AtNL1sjaFkWxcXFHDp0aNJ97r//fv7hH/5h9G8pJcmcyWAiR18iQ38ix2AyR188yys9cY53xWjtTyIl3Ly+gk+/ZuOicZNZUhLwaLxwIcq1q/OTVFcSDWUBGgoUtq0IeaiYInr2xQsRnjpjR64F3Nqi+W5nQtawqAx7OdA6xBuvWpkzobRuUV3k47m2COuqnfSIpcZUNSBVRbChevI084eO95DMmjxUQFd0MpaFEfz6E2fpi2fRUv0kswYvXYhgSkl5zSr+6ItfY8f+1xBL5zhx7Cih2jXEMjrnz57m1IVu/uygQfzJR4hldOIZA3NiWfJhVpX62FQT5o076rhzaw1rKhen23G2chFXImPDqt0zCLFeTIzMXmcSIr7cGJm/O/fCysOjqSSz5oy++2VhBJ85O8h3Pv87pNsOY6Zj7Nq0hqLr34F374f4qy/9I+affxYsE//G/dTd/E7CPhe9jz5A3a7bqAr7WFupEfbZhR5DXo3SgJuKkL14WxpwUxpwL/pyLH3xLH/3y1Ncu3pl50W90h3j4eO95EyTdM6kO5qhusjH+29oIZLW6Y1ncKsKloSrGopp7U8ykMhh3zOCa1aX0hnJ4HUpxDI6R9qj1Jf4aByeWUZTOkc7ozSU+hfcBV6I/niWv/3lKe7dV89rts68cPNyYDBpfwZ7G8LcfYV1H1ciliU51G6njO2oL56xAEdvLMPJngTrqoJUzrAIdC5n8sWHTwHwiVvW4p6wLnimN8Fnf3KMTbVF/Par1+cdP5jM8l/Pt8/oe18WRvDr797N1+59hIFkjvahNP3xLKoq8KgKoT+8m7BPGzVw2oiw6u/durCdnmXk8M/bvvocrZ+7a6G7s2B84aGTtPYl6Y5lsKQkZ1oE3BrxjE5F2MvQsHt7bVWIvrh9sw4mswyldFZXBIlndEJeF13RDJUhD+1DaZ5vE7z/hmb8bo2fHu2iK5rhhbYhPnhjy6KbbZjDelH/caCd//tr2xe4NwtDbjgs9NnzMU71xFlbtfTc2gvJ0c6Lup4uRWFr/cxcyj881EEya3K8K8YH9rfM6Nh/fOw0PzrUAYBPU/nYbeMLDnz8/hdpG0jy3LkhdjWUcNOGyvHHP3oG05L846Nnpv2ey8IIgu0Gmir0dqWwglXTgIs5QooApEAAQoDXpaIIgaqI0ZHtuNeG3YgjyvQuVeAeHjCNbR9Rp9dUZfQ1h8WLx7Vy3cKXy9gKDJo682vcPt68rGP9YxLovQW+O88Yj5zfmz8AFRN+TwcxXwU+54ry8nLZ1NS00N2YVXKGRX8ii9+tUlxAFaEQ586dY7l9DjPlldNnCVfUUBHyoq3Q0cBKvQ4iqRypnEl50ENb2zn8ZTWULYFljLlipV4HyaxBJK1T7HNx4uhLUkp5yVHQkp8JNjU1cfDgwYXuxqzyrn8+wNm+BEII/u09e1gzDXfO7t27l93nMFOC9etpet/fsbOhhC/9+s6F7s6CsBKvg9M9cd7zb88hpaSlIkjrH99Ly/v/joqQlx/ed91Cd29BWInXAcCrvvAYpTkDv1vjxG/f9MJ0jnF8BYuQkVmMIqbvjtBNmV9WaYWireTKwisQ211tb7tUZdQXdjnuOIeljTq8RDGTgtLO02IR8pd3b+PNO+v5k9dvpqlATa1CnOiO8eYvPz3HPVvc1BR5ecvuBv6/129a6K44zCPNFUH+5PWbefPOej7/5q3UF/t4w446/urubQvdNYd55gtv2c4bdtTxhXumHxS25N2hy5HykJffKhD+OxUl01w7XM4U+Vx8fEI0mcPK4JYNVdyyoQqAgEfjd+/YcIkjHJYjm+qK2DRDyUpnJrhM0JSL0YwODg4ODtPDeWouE4SAnGmx1KN9HRwcHOYTxwguE0bksnIru4aOg4ODw4xwjOAyYSQWynCKqDk4ODhMG8cILhNGxEuMSQTAHRwcHBzycYzgMkEMzwUnq4Lh4ODg4JCPYwQXkJ8c6eQj33yBnxzpvOJzXZwJrtw1wZ5Yho/f/yLn+hML3RWHeearj53ho996gZc7ogwmc9z3zRd48nTfQnfLYZ65nGeqkye4gPzlz0+SM0xOdMW4c2vtrJxzJc8Eh1I6B88N8rmfvsJX3rVrobvjME8c64jyH8+0IaXkT398jL54lkMXhmgbTPLAb1YsdPcc5pGxz9Tp4swEF5Cgxxb3DXiuXOR3dCa4ggNjRoKDygKuBe2Hw/xS5HePSqQV+92j90LY61wHK43LeabOykxQCHEP8DMpZVwI8YfATuBPpZTTEjBdqXzlnbv55fFubt1YfcXnGlkTXMmBMfUlPj56yxre4hRSXVHUlfj40tuu4qX2CG/euYon/zLAh/a38LptdQvdNYd5Zuwztf5j0ztmttyhfySl/J4Q4nrgduCvgC8D+2bp/MuSuhIf917bPCvnGhn9mit4TTDg0Xj73saF7obDArC1vpit9cWAXUNwtu4rh6XF5TxTZ8sdag7/vgv4spTyf4BJxSyFEE1CiB4hxKNCiAcntNUKIR4WQjwlhLhtlvq3YljJM0EHBweHmTJbM8EOIcQ/AbcBfyGE8HBpA/uQlPKdBV7/NPCHwGHgAeAXs9THZY2TLO/g4OAwc2ZrJvgW4OfAHVLKCFAKfPISx9wshHhCCPGJCa9vA56WUiaAuBDi0hVlHZxkeQcHB4fLYLaM4KeBONAJIKXsklI+OMX+XcA64GbgNiHE2MJfqryoAh0FSiYeLIT4oBDioBDiYF+fkwsEY5PlV+6aoIODg8NMmS0jeA54O3BQCPGsEOKvhRBvmGxnKWVWSpmUUhrYLs8tY5rNMdthIFLg+K9KKXdLKXdXVDh5QMCoP9Rxhzo4ODhMn1kxglLKf5FSvhd7ZvefwD3DvwsywcV5HXBmzN+HhRDXCCECQFhKOf2sxxXM6Jqg4w51cHBwmDazYgSFEF8XQjyFnRahAXdTwI05hhuEEM8PH9MppTwghPjScNvngT/DDoj57Gz0byXgrAk6ODg4zJzZig4tA1Rs1+Ug0D/s6iyIlPInwE8mvPabw7/bgVtmqV/LhpM9cdoGUuxsKKYs6Mlrd9YEIZUzefhED/uaywh4HEXA+eZYZ4zOSJrdTSUU+yfNkJpzsobFQ8d62L6qiMqQd8H64TD/XBhMcaI7zobq6cdTzsqTQkr5awBCiI3YyfKPCCFUKaUj3TELpHIGPznShZQwmMzy1j0N+Ts5a4LEMzovXYiim5LbN1+5Co/D9ImmdB481o2UEMvovGnnwt360bTO0Y4o3dE077qmacH64TD/PHC4i4xucrp3+iL6syWb9lrgBmA/thv0YeCJ2Ti3A2iKgs+lksqZBD2F9RBH1gRXsoC2GPYJh5xZ4Lzj1hTcmkJWtwgu8OevDN8MIUc7dMUR9GpkdJOQd/rX4Gxdra8BHgf+Vkp55XWBHMbh1hTevq+B3liGprJAwX1GDIC+go1gacDNG3bU0lxe+DNymDt8bpV37G2kL5Fd8M+/NODmddtraCh1roOVxt076+mIpKgr9vOuaR4zW+7Q+4QQjcAmoFMI4QM0KWV8Ns7vYCviT0cVfyWvCWqKoKUiuNDdWLEU+V0U+Rd+9qUIwZpKR2NjJeJzqzP+7mcrOvQDwH8B/zT8Uj3ww9k4t8P0cGTTHBwcHGbObCXL34ed7xcDkFKeAipn6dwO0+BiFQnHCDo4ODhMl9kyglkpZW7kDyGEBjhP43nEWRN0cHBwmDmzZQQfE0L8PuATQrwK+B7wv7N0bocZYJord0GqKgIAACAASURBVE3QwcHBYabMpoB2H3AE+BB2IvwfztK5HaaBoxjj4ODgMHNmKzrUAr42/OOwADh5gg4ODg4z54qMoBDiu1LKtwghjlBgDVBKua3AYQ5zwIhsmjMTdHBwcJg+VzoT/Pjw79deaUccrgzhyKY5ODg4zJgrMoJSyq7hzTcB35VSdlx5lxyuhJWcLO/g4OAwU2YrMCYMPCiEeEIIcZ8QomqWzuswA1yqcNyhDg4ODjNgtorqfkZKuRk7ab4WO2XiF5PtL4TYJ4R4athofnFC258IIV4SQjwqhPit2ejfSkFVhBMY4+Dg4DADZmsmOEIv0A0MMLViTBtwi5TyBqBSCLF1QvtvSylvklJ+YZb7t2R55EQv//qrVk72TC7HqikK+gpeE4ymdf7j6XN0RtIL3ZUVh5SSB1/u5l9/1crZvumXsZkLElmDf3mylZc7owvaD4f55+C5Qf7lyVYOnhuc9jGzpR36YSHEo8AvgXLgA1NFhkopu6WUmeE/DcCcsMtfCCF+IYTYMRv9W+rEMjqHLkSIpHSebZ38y7Vngit3TTCjmwwkcrx4PrLQXVlxDCZzvNwZI5LSOXhu6P9n77zj47rKvP89d3qRNOpdttx7iR0njlOcYgKBtIUEWAKEliUQFnZZWNjdF7IQlgVeykvZZCGhQyAkBEhCEtKbHTu2415lq/cyvd5y3j9mNJY0I1m2Vazy/Xz8meu5c+eeGd25zzlP+T2TOpZwXMMfVdl+cvQ3wlmmB9tO9OKPqmw70TvqY8aqldIc4DNSyj1ncpAQYhVQJKU8NODp70sp7xZCLAR+SrJP4dDj7gDuAKipydJgdorzracP87NXGynLs/H8v1yJ22qmwmOnzRdjQcnwXRJmekzQpAgUIZhfMnVa6LR4g9zww22ouuRHf7+GyxdNzXB6nsPCb15vwBfVuHFNObdeWD1pY/FFVH70wnE2zi/gw5fWTto4Zpl4njrQwdHOAItLc0d9zFjFBL8AuIUQHwIQQhQLIUa8+oQQBcAPgY8Mea++1OPxEc73Yynleinl+uLi4nMe//nG/S/XE1F1TvZE+OmrJ1EUwa3rq7lz83wunlc47HEzPSZY5Lbx8c3zWFI2+h/AZPOZ3+2jL6wSjGn868MHJns4Z80vtzXQE1bRDMnje9tP+/rxJKEbaAZsOzG5K9JZJp7DHQE0I/k4WsbKHfpl4F+BL6aesgC/HuH15tT+z0kpO4bsy009FjF2K9UpRY4j2ZNNEXBBjQdICmTbLaYRjzMryoxeCQLYzCN/R+cb6+bkp2s8J7sZ7blwQY0n3dE91zG5PQX71ZNO93uZZfphTl2E/Y+jOmaMzn0zsBbYDSClbBNCjNTZ8BbgQpKxP0gaz7+XUn4K+JYQYgVJA/2FMRrflOK1z13ON/52nKuXlLKmpmDUx5kUgTYroD2l+OJ1y5hb4KInkuBTVy2c7OGcNWtqCvjVhzfw3JFO/vUtk/s55he7eedFNXz2mkWTOo5ZJp6/feZSfvpqIx++dA61/zW6Y8bKCCaklFIIIQGEECNOaaWUDwIPDnl6W2rfP4zRmKYsNpuNL12/4oyPMyszOyY4VXnvxXMmewhjwqaFxWxaOPnhCYfVxFduHppwPstMYG5x7hn/7ceqROIhIcT/Ap5Ul/lngfvH6L1nND2hOI/sauGFI11IObKBM5tmdkwwGNN4ZFcLvaH4ZA/lvONQW4CH3mjmUNvoYyVTlUhC56E3mie9VGOWiedsrvOx6iLxf1N9BAPAYuBLUspnxuK9ZzL+aILH9rbhi6g09UVYUOKmusA57OtNMzwmGI5r7Gvx4bCauG5l+WQP57zi+SOdqLqkOxRnWcX4JA6Fogk6AnEWlI4UCRl/AjGVfS0+IgmNecXDZ1PPMv149lAHncE4nYHR1wqPWeJJyug9AyCEMAkh3iel/M1Yvf9MoysQ5cpvvUhENVhU4uLmddXku6wjHmOe4TFBbyTBH99sRTOMSTGC9zx+kL/u7+DDm+by0cvnT/j5R2Jvs5dtJ/u4ZP7oY8xngjec4H0PvI4/orJlWSl333Dm7vyxojcU59fbm5hT4OD2TbMlEjOJn29toC+iUuAcfXLWOblDhRC5QogvCiF+KIR4i0hyF3ASuPVc3numcqjNzyvHu/nGk4cJqwYSONoV5vZL5uK2jTxnMc3GBDEpgtZhFGO6gjF+8vJJvvHkYXqDY+syDYTi/PS1Btr8Mf77qaNj+t5jwTOHuwnFdf52qHtc3v9EVxB/RAXgQOvkulz7fwKNfbPKQTONvtQ12P84Gs51JfgrwEsyqeWjwOcAK3DjmRbOzwKH2v189fHDqJqO3XIqxdckRpfubZnhMUEJJFSdsjx71v0HWv08sruFYEzlWGeIB26/cMzObRsw8Rx9cvb0Yd3cAjbUFnK8I8AHNk6PRJ9ZZgbnagTnSSlXAggh7gd6gBop5fACl7Nk8NjeVo60Bdh2spfdzUm9wyWlLswKaAasrsob1fvM9JWgbkgiqsHW49klk+YXu4mqOiZFEElog/Y9d6gDf1Tl79adndKJzWbjP96+lD/sauHTVy04q/fIRl1nEIfNRKVn+FjwaLCaBAldYjWNj4kORDWe3N9KXIPfvd7ADWsqx+U8w/H5h/eyu9HL3dcvm9DzzjL1OVcjmF5zSil1IUT9rAE8M37w3DF++MIJ4trgWN7xznBaUHVPs5/PPrSHb75zJSbT8CtCs6IQVYfKsM48mrzZ3WBzCl18+R3LeOlYN1ctOaXv/oedTXz18cNIKdnf6ufLZxnP+vCl8/jwpfPO6JhANMHnH95PRNX5yg3LmFt0KpHjyQPt/Py1BsyK4P+8YxlLypMJLQ+8cpJtJ3vZvKgYf0zlkV2tXFSbz9ffuXrY8/RnFp8uw/hs+eHzR4ml5hVbGyZWu/XJ/W08tLMFgI/9ateEnnuWqc+5lkisFkIEUv+CwKr+bSHE9M/FHgMOtQez3pgGmjKDpDDsg280j3gTmy2WPz1XLS3l7huWM6/YTTCWnMMdHfA3aOqLjPk5+wIR1n/1Gdb851P86PnBaoC/3t7I/lYfJ7qC3PfiyUH7TnQlU/w1Q1LfG04//+zhLoIxjacPdfLz1xroDsZ4Yn8HPaEYw6Eagx/HmnlFp1aq47TYHJZjHae6RUTH6wPOMm05JyMopTRJKXNT/3KklOYB2xMq4PjhD3+YkpISVqw4/Sy+qamJK6+8krVr17Jq1Sr++te/TsAIs/OfNyyltshFjcdBiWv4VV6HP8bBZj/PH+ka9jWzxfKj494X6/jAT7fzwZ/uwBdJ8Jkti1lbk8/islz+zzvG3p125XdeoSecwBfV+f3OZgB+8OwxNnztWR7d1QokZfGWVw7+ydy6vprlFXlcNK+Aq5ecEtZeVZV83ZpqD6W5yfhnjt2Mxz55KoNrak5p2josY92hbWSqC06tns0zMSA7yzkxbbQ5b7/9du666y4+8IEPnPa199xzD7feeit33nknhw4d4rrrrqOhoWH8B5mFklwnT//TFQDc9dudPL6vM+vrDOD3u1roiya4emn2TgMzvVh+NPzk5Tp+9MIJzCZBQjPY3+rnsoXF/PIjF435uY50BAhENaID4o81+Q7+/dF9/OnNVlRd4osk+IfLa9myvJxVVZ5Bx5fk2vlSlhjX59+6lKcPtmNI+ODGOWyr72XjvELM5sn7OT9z6JQEcDgxsauxVVUe8hxmogmd1dUemif07LNMJDFVZ0+zj+IcG/PHqAZ02hjByy+/PMOQnThxgk9+8pN0d3fjdDr5yU9+wpIlSxBCEAgkvbV+v5+KiopJGPFg/vMvB3hxhFUeJA3h80e7UXUDiylztp1sqjvrDhpKhz/GQ280okv44fN19Pcdri1wsW5Ofvp1B9v8tHijrJ+TT6HblvW9vOEE+1r9zC10MqfwlDpgIqHzs631bK/voyjHxrsvrOblYz1A0gX72okeagudWC1mXjzaTVw1UqLoCpctLM4wgCNxvCvIIzubeP5oMgHo6iVFXL8qeyKKlBIhxn95tLLiVPLWeCXfDMeC0hxuu6iGQ+1BPn7FfP7ynxN6+lkmkHseP8gju1tx2808/ZkrKDhN7fRomDZGMBt33HEH9913HwsXLmT79u184hOf4Pnnn+fuu+/mLW95Cz/4wQ8Ih8M8++yzkzI+TdM40hliSambX21rRBvNIk5KHni1nvdcWI3HOfgC8Dgt9IUT4zPYKUpM1fncw3vYXu9FSpk2gAB5LgtOa/InEIipPHOoEykhEFW5ZX01fzvYQUIzuG5lGYqSnHQ8dbCDvc0+4qrOf7xjWdpYfukvB3h8Xzsx3WBhsQurImjyRgnHNWwWE9+9dQ3XLCvjzl/vQkpJkdvCRy6t5cqlZZTlOnh0dyuLSl30hFV8kQRluXacVjPLK3JRhijiF7psvNkcoP+jbBumeewnfrOL3Y1e3rth/HtuhlTt9C8aJ7yhBM8e7sQbVnli/+S2cZrl9Gyt66ErGGfTgiKKc7JPNofj0TfbiKoGMTXBz1+r55/fsvicxzNtjWAoFGLr1q3ccsst6efi8WSB9IMPPsjtt9/OZz/7WbZt28b73/9+Dhw4kL7RTRQ3/c82GnvDzCl0MVov5vLKHDr9Mdr9sQwjWJnvwBtRCcc1XKcprJ/uSCl5ra6Hn2+tZ1+LH00zMCuQa1MIxA0EyVUdgGFI3mz0UdcVxG42saDEzbOHOnjg1XoA4prOO1OlEwlNp74njNkkeOpAO8e6giwpzeHJgx2EEsl0piMdITRdYjMrNPRGWFru5tevN1KW5+DuG5bx748ewGU1sbjcw4KSHO554hD7W/z4wnESuqQk10ZzXxSXzcw/XbOQ61YN9lQU59h4x8pSfrU9mRF50YAekwnN4I5fvIGUBs8cSa5E731x2NacY0ahy4ZZJAvVC4ZZRY8Xu5p6OdqZTBx6dPesM/R8pjMQY3t9ctImBNx4hqU0JTk2GnojKApsqB0b9aNpe6c0DAOPx8OePZk1+w888ABPPfUUABs3biQWi9HT00NJSUnGa8eKQEzlqf0d5LssXL2kFEURNPWFUXWDox0BRuvEPNgaJN9px2bONNirUy61+146wS3rqinLsyMEWV2n051/e2Qff97bSkKT9LcYNJsEt15YxR93t2NWBDetreJPb7bySl03bouJ/S0+nFYzSytyyXNY6A7GaPNF0HWdrXU99IYTfOiSucwtdOK2mfnJKyfpDsaJJAyGzmHafFGsZgXNMDjUHsBiMvOHnc2sqs6jtsiFphscbPOzcX4h8VRG44meMIYBjX0R8h1mhIAdjX0ZRhDgKzev5l3r5+CNJNg0vyj9fIs3wt8OD3arxyZgkbamwpP2ZJgzvo3xpa7jlFB2KD4bDjifybVbcFpNRBJ6OqlrIIYheb0+OXnbOK8ow5X/uWtq+dTvD1KRa+XSMepYMmlGUAjxXWA9sFtK+ekBz68A7iMpvHGnlHLf6d7rN9uSqeWbyhUkEE3o5ObmUjNnLvf+7Fe87fqbsZkEW3fupqBqIZ6iUr79s4d568230lp3mF5/iLreBMf8nbxytIfKfDMtXjUpwOtxUu+L0uqLUOI00RPRaOqLIOJxOuLgH+B9NAMOBYLj+DtUDXjhaDcvHH0p/VzDf78dgIvnFXLZwiJ+8HwdP3i+Lr2/0GXFZlawpgynSRE4reZ0M1chBCYByhjEjrLd/rKVdQx9JlvlR9ZbaZYXVngc3HvbukHPPZiqGwPQUkYgokruf7Up/fxXHj+U7Qx89fHDg/6/s8nPzqZkGv6LqTjfSEggrBqEB6Xrq/xiWyO2bTBQsO0b2STWJAQjGv6IxvP7GnnlSAe6prOy2sPWE33E4gZ2K4RiYLdAVIM1Nbn84iOXEE7oTGhadoq7Hzv1M232T2wXj6r8UzfTofHITXc/wdvXVbGi0kO+287cQjeV+c4MF3NPKIbTak67xyeLaCIp5mDNMsnNhm7IpACEEPQFIzz6Zht3XZN0EQZjKm6bOWtM+M3GXl4+1sWntyzN+r7feCL59/zXt6/K2NcTirP+nmcpBban7j0D2fKFJzgOLAL+NmS/w2ri608eAeCGVZkJfve/XMd/PXUMgH976yLu2Dy4N+Unfn8QgGZfgjt/+Rr3fmBT1vGfCZPyFxdCXAC4pJSXCSHuFUJcKKV8I7X7q8B7SeaB/A9w40jvdawzyL//+TDdf/kmWssBtEiA8spK7vznL2C9+tN8/mv/l3/6wpcxdA3n0svxbHoviYW3sOvHP+B/fvh9EIL8az7F3/9i7zl/Lo3xNYDDMfcLT1BE0rj94kMbONDm52BbgJ5gHF1KOgNxVN0gkSrI1wyDaMp1J0m6sAxDIs9wBi8lZLObIotw2Gjsa7Yfa7bDhr4sb5I7mZ8JozUP/XOrpuCpoxr8pwxwOFUSGE/JVexoDLD5G5MT2waYWzxiC9Fx5S0rK7l4ezMnesN8cvN8/uGnp/a1xuDHr7UAyUmR3aLwgYvn8MXrlqavtz/vaeXBHU3k2Mx8/Z0rKXJnl90bb052h3hsbztWs8J7N2TG/Iei6gYP7mjiWEeQUDTGn/YlPQDfe74OEVW5/5V6Fpa6eccQT8KjOxv5p4cPAPA/L9Zz9GvXDdq/7itP0xtJzhwf2tXOri9dO2j/+nuS11knyXtPwxBD1+98P5ZlzHO/8ER6++rvvppxbL8B7N8eagQH8uShsRFlmKxpz0aSPQdJPV4M9BvBAillM4AQIqtemBDiDuAOAFNuMQVA8Q2fRwD/eHXyS4urOsa+Nsrf/RWklIOKhK1FNZTd9q0x/1DnA4oiWFXlOaNsw1mmB73hyUtOuXp5Od9/vp64Zoxbq6bhsJoVfvfxS9L/H6krd0JNuqfjmpHW493X4k8mRMU0TnSFJ80INvVFMKQkpupZY/5DCURVekMJfFGVxt5TIg+aAUZqwtvQE8447pevn/KGxPXMiW+/ARy6PV2ZrGCRBzALIXaT7DBfOGCfIoRYIYR4FVgrhMhYj0spfyylXC+lXF9Wcsov/JFNNcwrdlHhsfOBS+ayrCKXCo+DCo+dAqcFh2VmihvPMjP452sXTdq5F5fm8ZP3r+Mz1yzkFx/eMGnjOB0V+XZuWVc9SJD+5rWVlOc5WFOdx9qa/BGOHl9WV3mo8NiZV+xi3ihW1gUuK2uqPayozOOtyyvp96CW59lw28wUubPHze67bU16e2lZZq3dey4oz7qdje9fMuLuKYEYLy3BEU8qxCcBH/BX4BXgfinl91L7XgL6gH8Efg90SymHdYkWFRXJuXPnjvuYzxZDSlq8UTRd4nFaBtW1eMMJwgkdl9VErtNCJK4RSejohiSmGUQTGoYEq0nBYhI4bWbcqX9DefPQccx5JZgVwdLyzJm4lJJWXwxFQHmefUJqxyaahoYGzudrYSLovw4AFpW4saVu9sGYSl9YpcBlIcc+ddzHZ8PA76A0144gaTBMyvS75odjuv4WpISIqmFRlKxx0/2tpyT0Eh11Ukp52oXeZLlDtwH/IKX8jRAiH9g+YF8fUEZSPrMbyHCJDnSH1tTUsHPnznEbaCCm4o+oVOU7zspw1HUG+dzDe4mpBsvKc/n2u9fgiyT47fYmHt7VTIErOWtbWZXHthO9eMMJuoIxgvHBCQ4WRTCn0Mm1K8r43LVLMs5jK19I+Qe/B8Cz/3ENHreNP+1upjuU4GOXz+df/rCXpw8ka6jeeVEN/3bd9FPbX79+/bheC1OBgddBnsfKN9+1lgtqPGz8+nMYcQ2nzczOL197mneZ2gz8Dj6dCo9ct7KcxWWT2/F+IpnKv4VDbUlDtqwiMxr2xN5WHt/XTmGOjc9uWZzRaHxgzLHxG+/YPZrzTYoRlFLuFkLEhBCvpJ5qEkL8u5Tya8CXSa4O/wB8Evh+luN/DPwYYP369eO2lA3FNX79eiNx1WD93HwuG0VKbmcgxs4GL3MKnayozKPAZaE3nCAY08ixm3lweyNvNvs41hkkktCxmVTyXRZeP9lLOK7S4g0Tz9IIQjUk3kgiq49/KPdvrceuKHznueNICW809JE/IL5gnuB6yImkwx/jlv/dynUry/ni27Jnvs0UfBGV//fccZaU5+KNJmM7/Y8zhZLc5CSztmjyEndmGT0vHe3i3pdOAHDnFfO5YvHgsrWfb2tgX7MfkyJ41wWV5LvOvVZw0vKB+8sihBAvAp0pA4iUcp8QYo+U8orU/kkr/IkktHQNlzdLp2IpJYfaAwRjGiYBtcVunj/SRYc/xvGuILVFLoJxnfI8B3ZLgkBM5f5X69OZmk6rGV2CqhlImQyMZzOA/ei6kV6N9p8bYNkQ92dvMMGOhr50Af7Wuh5e+fxmukIxpCH4zDWTFzsab373RhPNfVH+96WTfOKKBeQ5p7frbyTKUnVYPcHhu0tMd9w28xkXZM8yebT6ooRSha2tvsyWaI09YRK6ROiSus4ga2rO3Qier0uCPiFElRCiAvCf9tXjREmOncsXFbO0PIfLFxZl7D/YFuBvBzu576UTPPpmKw/vasGTStd328xYzQpzCl3csq6KpWU5rK32oBuSApeV2iI3LpsZq1mwq8nH4fYA0dMID1vMCqW5tkHn/tvBzrQx7Ocjl9by3g3VKCL5B15dnc9zR7qJxA2iqs6vXm8cmy/oPGRXoze9vb0+e3PdmcLSylxWVuVxx+Xz6A+HTXSbo8lmT5NvVlR+ClFV4CCS0IkkdKoLHBn7JQJJsrRLGSMRkMkslrcATwKrgaeFEF8BLh3gEv0dyWTOT07WGIFBAssj0f8ze8uyUlZU5lHotqaVWt61vpp3ra+mqS/MhlovJ7vDbFleyiO7WnjucCehmDaqCr1AVMuqDTo0t2lBaQ4LSnMozbWzp9nHiso8ily24Q+YRuxv9fOudVX8ZU8buxq9vGV52WQPadLoDcX5wXvXA7CyMo8Wb4Sq/HPrUD/VWFWVN6MSYqY67b5YWk+03ZdZVVuZbycQUzErCpWeTCN5NkymO1QFrhny9EupffuASyd8UGfI8lQ91MZ5hSgK1Ba5MZkUqgsybzQnu0M8vq8dl83MxzfPx2UzU5XvpLE3TGcwjqpLBMOopAxgZ4OXuq5Q+twDx9FPdyBKca6D61dXcv3qU66gmKrjjarcNE3dQ7oh8UVUFpfmML/EzdHO4GQPaVIJDajx+s671/BaXQ+bFmR6NKYzN19QNdlDmOUMuGJRMQfbkp6tyxdlXqufv3Yp9796kup8J2vGqJxl2mqHni2qbvDUgQ6CMY0ty0oHqZzHVJ3ecILyXDuKIhBCsKIyaz1/Giklzx/p4rnDnVhMCrohaffHWFDipqE3zLqafI50BPFFEpgUCCeSZtAsSGsxWpTkkthhVYhrOve9WMc/Xr1o2HO7hkmB3zLNV0WJVBupqnwHi0vd7KjP3l1hpnDbRXPT2/OL3WPWf22WWcaLsjxHurF1Ns3jmkInq6s8zCl0YRmjBL/zNSY4aTT2RqjrCtEZiLGn+ZQsj6ob/GZ7Ew+90cxzp+n7N5DuYJx9LX6cVjPeSAKbWeFAq5/OQIytdT0c6wphVgQOqwljQEhQCFAE5NhMLC5z85MPrKPC46A7mOBPe1p55vDwLWNG0j/sl06bjqhavxF0srgslzZ/jEAsM6FpprC3bXA4fTr/7WeZPlhMyrCi/7/d3sRrdT38YVczjX2nz5QfDbMrwSGU5tpw2UxEEwZzC0+5NeOaQSCavKF2B0enAHmwzc/TBzqp7wkxp9DFu9dX8V9/PUpXMMb8YjdblpfSG4rT5o9hSOjXsBCQKpJPBoG9EZWHdrWm9T51Aw60BIY77bCNVPtb9ly2sIi7rhpek2+qMnAlOD+luNHQE56xEnI7G0+thL/19FF2NvSxfm4Bn7v23HuwzTLLZBCIqbT6ojit5qzC/GfDrBEcQo7dwoc21aIbcpC0kttm5qolJTT0htlQW0BCM+gLJ7CYBCZFZNX5O9YZRAiYW+Ti5rWVuKwmWrwR4prBnmYvuQ4ziiJQUn3YDEjHBXUJuiYx60nDd7AtQJXHQYc/htlsYvOSEh7ZlRQFfuuKwW7Ow20BYqrBiqq8tKqCqhnsb0muDAZmUE4nEppBvtWEx2lJd31v6I3MWCM4v8hFhz9GSY6N3Q19hOIquxtmlou4MxDL2rJnlvOTXQ193PnrXQDce9s61s0dXAKxuDSHzkCMXJsZxxh1/Jh1h2bBYlIGGcB+Vld7uHFNUmfw4V0t3PfSCf7jTwf4xdZGmgYI2Pazpjofly3ZpHVOoQuP00q+y4IhJSZF4I9qzC1y4bCYMStQ4LKQ5xj8h9UkhOI6bb4oXcEEK6o8fPrqBRS5bDT1RWjqi3B4SInEp373Jv/4uzf59jOn2vRYzAqbF5fgspnYsiyzhcl0oCTXzu//YSNCCGpSyUmNoxAXmK4IRfDgjiaePthBVNNp8UaJaiMUok5DHtndcvoXzXLe8J1njuGLqviiKt95JrMPxZqafDx2C7XFbkpyxmZyM7sSPAsMQ6aaqWqEYhqGlHSHYtQUDs4KPdwW4MWj3ZTk2NmyrBRFpDJIhUJCN8i1mynNsfH3F1WzvzWAqhv4IirBWIih4u66ITErgkqPk49eNp92f5Q3m5Mrusr8wanCMVUnoRkcag1gGDLdO+3OzfO5k/nj98VMMmblVKKSw2qiLNdOY1/m5GSm0K8S1BmI4bCYqMp34sgyuZvOjFUa/SxjR4c/Rk8ozuKynIzY3+bFxexI1fduXpyp0PWHN5p49kgXuXYzN66poLrg3JWAZo3gWaAogi3LSjnQ5iea6pA8MFPTMCRP7G/nZ6/VI4F2f5TjnUEWl+WiCIEhJbkOM4fagxxo82NIKHbbAElDT6YBhKR7NBBLkGMz8fi+Nt6yrIyPXjYPIGPV2u6L4bSZKPfY6Q0nBmW4GKREaQAAIABJREFUziRqCpMlKDOVV4/3Ykh417pKuoNxGnsjzCmcWXWCsxmx5xe+SIL/fvIwwZjGtcvLuPXC6kH7i3NtlOXZ09tD+duhDryRpJ7zrobeWSM4mSyryB22b9qRjgC/29FEKKahGgab5hdRW+TmlePdxFUdl81ETDXwRxKAJJGyekIag/oeZqPFF8XU4KUnGOdtK8uzxjsMkvGx8jwHqj5zMwLnFjp54Wj3ZA9j0mjxRijNs/PXAx20eKMIAS3eTCmq6Ux8NiP2vKLDH6Pdn5TxG6p0BXCsI0QkpZx1rCOUsV9N1Y1JQB8jz/5sTHAcMCkCRQjyXVbevb6Ge25eya4mLwda/dgsJirynZTm2dNtlUxK8g9R6LaTpTtImhZfnO31vRxs89Pmj/HLbQ2c7M68UPrxhuNUDHAH/fb1Rh7e1Tyqz3DPYwe59d6tdAdG2wv9/GNOoSvttp6JmFMJwgtL3FhNgoQusY6jbtr3/naUv/ufV2noHj5zeaJZWz0zk6LOV+YWubhgjodKj4O3ZMlNWFWVR57DTJ7DzKqqzDroOUUuLArYLQrVYySKPrsSPAMSmpGU7BGCI51BGnrCrK3Jz2jRsqg0h9s3zaU7GE/LdrmsZmKqwZKyHFZV5fFms5em3jCFbhs9wTgJTSeh6RS6rXQGMqXR+okkDGwmhTZfhPqeCCe6wty5eXCcz2YSrKzMpX5Ass4Pnz/OgzuSHaXjmsH7Lpoz7Dl++upJHtjagJTwtu+/zM7/2HLG39X5QL/rr7E3krXH4nTHZhEsLsvh5jXlPHuoA5Ng3DwDLx3t5Psv1GFIuP5H29h/9/nRrqkvHKdojBIoZjl37BYT/3TNYmKaTm4WUY/5xW7etqI8vT2UmgIHh1p92M2C8rzZxJhxJRBT2d3opdLjYGFpDppu8OCOJuq6gvijKj2hBMsrcgnE1AwjKITg6qWnZjnHO4McavPjjyZQFEGzN8qxzjCRhI6mG+hS4o9peKPaaWU97WaFlVUewgmVTn8cbyTB4Y7BM++L5hUgEVy6oAhVN3ijoY/jnaF0/WB/veNw9Ibi6XGoU9idNDdVJtHYG56RRtBiVgjHdR7a1YrNYkI19HST3bHGG06kJf+088gF//OtDfxLlv6bs0weVnP2hrgAC0tzeM+GGoCs8pPb6/uI66DGdHY1eGdjguNBTNV5eFcLr5/spdhtI89p4UO5dhQBfam+gKGYjtNqIpLQTytI3B2M888P7aHFG8Wa6g5/pD1IZyCGIpL1hR2BONoolO5r8u0sLsvl2hVlFDqt/PdTRwDYNH+wxt6/vnUpy1OJOt995ig/fvkkAlg/N59l5Xl87NLaEc/zubcu5Y16L03eKN+5ZdVpx3W+0r8SrO+ZmRmiDktypj2/JIdtJ3tHdY2dLdevqeLHL9fT2BfhU1cuGLfznCnWMeo0MMvEkc349ROKa+k66tgYhTlmjeAQWrwRuoPJlVB3KE5Rjg2LSeC0mtm0oIhCtxU1lXSyfm4+Re7hMy8Ptfn5zjNHaeyNAJKoAfkuK1aTgqonSxfsFoWyXDtt/gi6ASPdpwIxlVZvlMf2tvG25aVp15YvMth9+outJ7loXjGbFxfz5IF2NF0iBHgcNr5w3egazT505yWjet35TI7dQpHbRn3P8HHT6YzLauK//m4ltYVO7n2xDoBAbHzio95IIq1NWzDCb2KiScrSw86GPn6/s5ll5bl8aNPIk8BZJpeuQDJxpiRL0t9Az1RvaGz6ZM4awSFU5TspzrFhNSksr8xlZWVeWotzQ20BG2ozmzh2B+Mcag+woMQ9qC7pt9ub8IYTaIbEJAR5TjPleQ4uW1DMyZ4Qh9oDzCt20+qLEoyp+LI07h1IQpPU94bpiyY42hEgktCxmJSMLKsTXRHKPRE++dvddAXi6IYk32XhI5fOPfcvaIoxr8hF/QwtmDekQas3Sr7TikIya3i81kX5Titzi5y0+WKnFZWfSPY0JxVyfrO9iTZflKbeCNcsK6V6hrWUmirsqO/lK48dAuDLNyznwiGKMQO9GWMl+zBjjWBPKM6f97RhVgQ3X1CZDtLaLSZuu3j4pJFsPL6vja5AnF9ta2DD3AJuXFuZcnVa0A2Jy2rC47RS6LayuCyHXIcZA4nDYkLTdYpdVvZpetY2SlYFVIOUooyVUFwjmtCxKBCIqlQXOLmotnDQMTmpbuq9oQQumxmXzcxPb7+QxWUzLy5WW+Q6I8Hz6UQ4obGr0UuzN0Ke00JCM4aNxZwrJkVw89rzr22ROdVpYH6xizZflAKXlUJXpsThLOcHf9zdyvGuZAu0P+5qyTCCA3ObzWKKN9WdbI51BNMJIvXdYVafQyq1zWzCH1WJawbhhMYb9X2c7AkTUw2qPE6sZhN2i4kcu4WeYIITXe3sbvIhDUm8xI0/ojJc30+X1URE1SlwWvnuu1axu8XPK3U99IRUekNxDCkzVoI1+XYuX1TEvCIXv9jWQGW+lY//chc2q4lv/N1KVo9RH66pQG2xi56dcQIxNWs22nTGbU8mwdjMJmoLnext8bO4dPyKx1v6Quxt8fP2VedPv8oqj52EZnDXVQt56/IyyvIcI3ZZmWVyiSY01FTddLbSJrOioKba7ZTnj0126IyNGi8oceO0msixm9NZhGfLTWsruGltBRvnF2K3mKnMd6Abkv2tPo50JrNJ5xW52DivAE0a7G8L4A2reKMabzb6ON4dJhQ3sq4EvTGduA6dwQTfe6EOhKAs14EmjWRni5jG/hbfoGNePtbDzgYvN66t5JcfvJC/7uuivi/CkY4g3/zb0Sxnmb7UFp3qJjHTaO6Ls2VZKe9YVU5ddwS7xURd9/gkCTV0h9j8rZf45G/3sPmbL4zLOc6GZw93c7QjubJYUJqD2z5rAM9ninPsmBWBWREUZyltiQ6ICT57cGw8POd8RQghSoH/AiqklG8TQiwDNkopHzjn0Y0jJbl2/uGK0eloNvVGePpgB/kuKzesrshwKTmtZjbUFrJhgFsyGFN5/WQPUVXHZTNTmmvnyYMdNPVGkEZS8UByyq99urw9A/BHVV440oVZEeTbLdSTrF3sbxvUT6s3yu92NHO4PciNq8sGybCtrDh/4jUTQb8RrJ+BLZVcFgW7RUERAkWBYEwnzzk+895HdjWlm0A3ec+fbNySXNuMlQ2ciqyu9jD/hDu9PRKJMZKMGYtfxM+Bp4GK1P+PAZ8Zg/c9b9jf6icU12jui9DhjxFN6MRHUOP3hhPsbfZjt5gocFpZWOKmLxxPZzaZlNMbvWz0BGNEVZ2EISnNc+BxWHBZTXQO6W9oSDApkpPdQV481kNNgQObWbCxtmDU2aHThZoCJ0LAye6ZtxL0RXS+9OeD/GpbA2UuC26bQplrfFzC71xfgynl06/wnD/F6TeuLU9rUc5y/rOhNp9it41it40NtSOHbUpyxia2Oxa+gSIp5UNCiC8CSCk1IcS06teyuCyHk90hPC4r4YTGoy+3YjUrvOfCavKzBNmjqo5mSMpy7ai6ZHFZLm9bXkpMT/Yo3NN8dv38ClxWVlTmYTEJFpa40x0Slg9Z3UmgMxBHURKsm5PPzWuruOPyebhsM88VZLeYqPQ4ZmSGqApsO9HLsZRLXtUlEXV8tEPnFrn5xYcu5M0mH7eNoEY00Rj6+MnEzTL2PHu4K633+uzhrhGVrYQ8fxJjwkKIQlKLGyHExYB/DN73vMAXSWBSBJ/YPB+TSeHFo10YUhJTdeq6QxzZH6SpN4zdohBJGFTnO7huVTmbFxfzzKFO8p1WDCkpzLHz/otq+OxDe9OBXzjVRHc02KxmvOEE1QVOrl9VkW4ce/G8wdmhBrCoxE0wrmO3mPE4LdjGKStwKrCgxM2xzuBkD2NSkCQ9E0IkmzePUTPurFy6sJhLF2a2v5lMLpqXWdI0y/lLjt3MkZQC1vvsNSO+1jCPzVprLIzgZ4G/APOFEK8BxcAtY/C+k04orvGb7U0kNIML5uRzxaJi1lR76ArEsVtNROIaO072sqfZhyElTquJSxcU88ArJ6nKdxKMqrT5YxS6rexv8fPC0U4OdwTPSrnDLCAW1zjRHcJiVqjrCaULn/Usd7ajXSEWl7pIaDp/t6YCcxbljB113ZR47MwtysnYN51YVp7Lq8d7iGs6NvPM6qcH4LaZEELii0py7TNrZdQTHl6Hd5bzj5ePdhOMauntG1YPn2nc1H2eFMtLKXcJIa4AFpNc2ByVUo5c9Q0IIb4LrAd2Syk/PeD5nwNLgSjwYynlb891jGdLNJFsTgukyyk8Tmu6B9ZzhzvpCyfwRhJYTIKEZlDfHUQi2H6yj0K3jZiqE4xp/GpbA52BGHrKAAqStVWjNYhCgDeioSiCvnCC7Sf6eLmuB0g2kx1KKK6zryVANGGwqtrDjWsGX0zv+8k2tp7sQwD3vm8t166oyHiP6cKyilw0Q3K8M3ReFXKPN2YFSnLsLC7LSbeU8kXPH13PiaCuM8hl59nqdJbhqe8JYQzYHomFY9RF4px9ZEKIE8BHpZQHpZQHpJSqEOLx0xxzAeCSUl4GWIUQFw55yfuklJsn0wAahiSS0LiotoDlFblcvijzh7SgxM2S8hyqPA6q811snF9IntPGiZ4Q7f4YDouC1SzY2+zjaGeAnlA83SrJpAjEGaTHqAbENZ2KPBvLynOwWhRa+sK09IXxDyOIrRpQ3xtmbpZGqvtbA0iZTKJ5ZFfbqMcxFVmWEs/O1r9sOqMZSb3bs0vDmh54wwnuf+Uk+1umTYTmvCem6tT3hImpZ+6uHNgftSyLbNpAXPax8eqMRaBIBa4UQvxMCNGfJXK6atmNwLOp7WeBiwfsk8AvhRCPCSEmLcL+wtEu/ri7lX2tfi5fVEyew4JMxQL70Q2JSVG4ZEERH7t8Hv918ypU3cCU0gS1mhQCEY2uYIw2X4xQXEMIsAgwpDxtA92heKMaRztD+KMq+1t86BIUoWAME+ixmgSVHierqzOzrD64sQaLInBZTXzphsVnNpApxpxCF06riUNtM8sIAsQ0g9dP9k32MCaNn75Wz9YTvexomLnfwVizp8nLB3+6g688diDr/v9+8jB3/XYX33jySNb9P3vtJP/xp/3UZ+mFum9AzfPeIfXPQ9lRP/L+0TIWMcGIlPLdQojPA68IIW7l9FNPD3Aite0Hlg/Y91kpZZ8Q4lLg28C7hh4shLgDuAOgpmbk4OnZ4k3peEYTOjE1qdH58K5m2nwxNs4v5OJ5hfiiKg6LCSwmKvMduO1mCt1WdD3ZLX57fS/+qEZ/fWckrmO1KETPodVMVNXZ1+LHahLouqTIbaHQnZmhajXBlqWlfPLq7Ir+n712KZ+9dmaUS5gUwbLy3NP+qKYrMdXALECTpxrtzhRCCYOjHQGuzdLAdZaz4+7HDnKiO8yeZi+XLSzmyiWDv9s/7m4lpuo090X58g3LB+3b0dDD9545jmpI6rpC/O6OjYP2LyvPocUXT2+PRF9kbOK9Y2EEBYCU8ptCiF0kawZPl5LlA/qFLHNT/yf1Pn2px1eFEP+d7WAp5Y+BHwOsX79+XHw9Vy4u5o2GPio8DjxOK4GYSpsvGYit6wohJRxo9eNxWKgtdrEyFWsyKQoep5WTPeFkNt6A+YAORM90+TcEj91MTyhBrs2ExSyYW+jK2ski12bmR7etO6dzTSfWzy3g/ldOEk3oOKwzKznGZhbJ7iSpziUzCQHML3GzZVnZZA9l+iAhoemYFAVnlt+SlBJdJh+H0u6LEU5oGAa09GWKKlTmu7GZetPbI7GwxDHi/tEyFu7QL/VvSCmfA64FfniaY7YBV6e2rwFe798hhMhNPS5mgHGcKKSUbDvRy4tHu4gmdA63B3jqQDuGIVlT48FlNaHqBg/tbCYYU0noBpsXl6Rdkisqc5lT6MRuVsi1manOdzKW1Qm+mIYhJcW5NjxOK4LBorKQ/KNaLKasF+FM5aLaAjRD8mbT2dVoTlU8Dgvv31iDhNSkbGbhsgq+9a7VFGTxlsxydly3sowFJTlcOCc/az/VCo8Dh1mhwpNppAqcFoQQIMhqQA2po0uJLiVSjrxg6PBP8kpQCLFESnkEaE0lugxkxMQYKeVuIURMCPEKsBdoEkL8u5Tya8BvhBD5JH+vd45mLP2xnqXlOckv+Bxo6I3w+sleDrUHEAL8EZU11R4SuuSG1RUoAp7c30F3MI7LZmJ1tYcXjnSxp9nHghI3160sR0rJm00+AjEVXzTBWDZn14zkzazK40SS7NKsD8kwrfDYWD+3kG88dZTbLq45bePfmcC6ufkoAl6v7+OSBUWnP2AakGOFD14yl0J3UrXoWGeQhSXjJ6B9PqLpyWSLpw90ENN0rl9VjqJMz5rZrmCM5r7IuHeL2Ti/mIhqUOCyUpRFks5lM2O3mrKKc9gtZhSRrGV2OzL3N3WH0vfLxu6Ra3s7/JNfIvHPJONy3079f+gk86qRDh5YFpHia6nnrz+TQURVnacPdqQGIDPUU86UXLsZsyJwWBRMikJc1ZNanan2RO2+WFp95O0ryyl223hwRxOGhD3NXjbMLWBxWS5um5muYGxMDWA/CV3iDcU52RfFblW4ae3g8oZ1cwqIqjpvNnlRBHzqqoUzzgU4lFy7hZVVHl461s0/b1k02cOZEISEJ/a3cfmCYuKaQbHbllbjmCksK3fzb3/cx55mPzl2M3HN4Nb11ZM9rDFH1Q0e3tVCXDWo6xrfJtIrq/JYVObGoihZ3ettvij+SIK2LPta/VESWjJI1NyXqV50tDuadTsbtWNUInEuRvB+IUSZlPJKACHEB4F3Ag3A3ec+tDNnLLx/hW4bt108h1BcQ0owmwS6IanKTy7tawqcLK/IxawIWr1RvvfsMVr6orjtZnRD0hWIs2VpCdUFTlq8ETQj86YjAJsJYmcpeOCLqOxq9qEogjyHk2Mdgy963ZA4rCYsJgW7WRkUl5zJXLu8lG8+dZQ2XzSrq2a6EVDBEk5wsN1PvtNKXNXJd84st+Dx7gjl+S4CMZWc1G90utJ//xvvj+iPqLxyvIsKj4ML5mSmfwRiGjL1OJRY/NRzup45UJPIvp2NUGLyFWPuIxnPQwhxOfB14FPAGpJJKxlZneOBw2LimqXJ7KTlFcO7ATr8MToCMZaW55xWNSTfZc3QBDUMycO7mmnqi7CgxM2CYjeP72+nxRslEEugGTrBmE5PKE6zN0JNgYuqfDv1PRE0I2n4+s2h5OwNYD/hhAYIvBE1LZ/Wz8vHu9j2xS0cbAtQ4bHP9k9Lce3yMr751FGePtjBhzbVTvZwJoTesIraHqTS46ArGCdnhvVUNGEwp9BFSa6d5eW53LTm/Ol1OJZYTArvvKCKxt4wSyty0+658eA7zx7luUNdOG0mfnzbeuYO6WJTkmOjMxCjJIur9II5BTitJuKawaqqzPu1WTllGE8n7iTE2Fj7c7k7mvozOYF3k1R3eQR4RAix59yHNnpWVo3sAg3HNf6wsxnNkLR6o7x9VXl630M7m3nhSBd5DgtrazxcUJNPTaEzw1CGEhot3ihxzeDlY928erwn1fdKQVEUoqpBTDNIaAZdgTiVHieqkZzK9LdNGktMQuC0magtdiGHzJjCcQOXzcyG2lndxIHML3aztDyXh3a2cPslc885fjwVECRrUk/2hFH15ONMosht466rFuCwmKb937sszz4hHTOaepMernBc0h6IZhjBq5eUsLvJy7o5mfXJUVWnusBBQjModGd6Y3rCp4Q/ekIjJ74YeuZK82w4lwixSQjRb0SvBp4fsG/Clh4SePV4D68e70Ebpv7OkDLtIhjqnvzLnlaa+iK8VtfDY3vb+ORvdvOVxw5hDPEp5NjMrKjMo6EnxKE2Pzsb+0hoOoaUCAS5juQMW5NJlYrt9b10BqLjEhMEsFsEihD0hRLpFk2nPi9oMyz2M1o+sHEOh9sD7GycOVmibqsZTUs2bZ5p14XZrOC0mk9rAGfa93IuXFxbgFlJTjCWlmeu5pr6IugSGnszSyCWludR6LYhJVy2sDBj/5m4QzsDp1XnHBXnYgQfBF4SQvyZpM7nKwBCiAVMYBeJaELnjYY+3mjoY39r9tPm2C3pzu9bhhTNLirNwWZWKMm1cawzhD+a4OVj3fiHFGIKIdiyrJQClw1fVCOm6jT5IvSG4sRUFVUzcFlNmASohoEvoqJrRkb5wlhgFmCzWNJu1qGlEBJ43wPb+eZT2RUbZjI3rqkg127mvhdPnP7F0wCTItCkkW7ePK16nI2CDn+cSGLkFcNzhzv5wM92cNdvd2f87mfJRAeq8l0Uum2E45nfrd1qwmExYc+SjHeyO0QkruGymdndlFkBNzBjNFv26EByx6g35lkbwVQ5w2dJNtW9VJ66EyskY4MTgmlABtJI8Y45hS4unleYER/7wlsXc/f1y/j6TStYXp6L226h3GPHZU/KpD13uJMHdzTR5ktmKpXm2rCZFRwWBYsQxFSDuAY2kwIIUiUwyfIFiymjC/1YUJxjpdhtxdANuoJxosMEiN9s8mFkScyZyTitZj6+eT7PHeli+8neyR7OBCBxWWdWHHAgihA8vrd9xNe8VteDbki6g3EOt8/MlltnQo4t2Z4t32nJmh36qSsXcNPaSj51ZaZalQCavVGa+iJ0+DOzP69bXpGufb5u+cii/tWn0RYdLefktpRSvp7luWPn8p5nitWssCDlk+4XipZSjtr//5d9Hew42ctrJ3qwW0wsLcvhA5fMxWpW6PDH2JcS3t1+spebL6hiXrGb2iIXfeEEiqLgspnQDYkU4LKZMAmJZkjMZgWzEAgMEvrYZmyFEwbRvgj+uI4/rvPCsc5B+8tyLDitJi6eVzhta6LOhQ9dUsuvtzXyxUf38/inLp3WiUNFbjuVHgc1BXZ2NflYV+OZ7CFNKAtK3SROI1N47fIymvoiFLttrKqeOV1GzpZNC4qIqQYluTZKcjIN0aKyXBYNU6sYVXWklBhSZg1f5TgsWFJ+0BzHyJO3A+1jUwoy5X/90YROXXcy2L+joY8j7UFims6Nayqp9DjQdIOjnUGK3LZBCuX9dAZiNHuj+CIqQqi4rCZeP9nHmup8PE4LQkBdV5DOQJRwQueCGg+Ly3LY3+qnNNeeVDfQJQ6LiVBCI24xEYgm8Ea0dDLMWCfFDE093lo3WBx4ZUUO37x1NW3+GJ2BWNbPPZNxWE3831tX8777t/O5P+zj++9dO8ijMJ1YWp7D21eV09QXoSrfRXFuZsbedMZpM/H2leUjvuaieYVcNC8zPjXV8IYTtPqiLBhnQYSaAieXLCikyG0789+NALOioCkya4/TV+t6SKRKJ16t6+FTVw9f0yv1yS+ROC8wKYK4lvwygjE13VboeGcyLfzRN1t5+mAHOXYLd1+/jLwBdVL+qMrGeQX0BGMc7wqiagZFbhsOiwmTIojGdaSEQFSjritMdzBOXyhOc1+YvnACq0nhsgXFHGwP0NgTpjDHRkWema0nokykE9IYIi+0ozHA1/56mEqPE5Mi+OAlc8lzWAjFNF451s1li4px26f8n/6cuGR+Ef9+3VLueeIwCd3g27euJncalg/sbfbhcSQnc3uafaypHr+VYLsvyv42P285j3Q6d5zs46YfvkJPWOWqJcV8/Z2rcWdRMpnqaLrB73c2p6Uex5NH32zlqYMd5NotfPn6ZXiG1J7qhqQ3HKfQlWkkk4Yz6e4sdGVOyPYOiBPuzRIzHMhYJftO+atBAAnNQAhBbaGb7mCCmKqns5YOtgUIxjSCMY2G3jCBVj85dgt5Dgt/2dOGIuCqpaUIIUjoButq8rlmWWkyoUA3ECJZY9jUF+FEd4i9zV4MCXEtuZxXUkbYleo03xuMYzebiGljk747GoYWnfpjGofbg5TlOhCCdIHwTT96NVW/Y+e5f9k8YeM7X/noZfMwK4J7njjMTT98jZ98cD3zi6eXrJgvqvL0oQ5cNguhmEowPj5x0HZflBt++CoxVWfdnAJ+/uEN43KeMyWiShq9MRTgucPd7Gvxccn86SebZ0jS7sXTuX/PlYNtAUIxjVBMo90XzTCC9zx+iK0neti0oIgvXT+4i0RLX4SuYBzdIKuOrzrgXqZmKaYfSDB+Dh9iAFPeCGqGkbrJS4JxldsuHtyCcMuyEvxRlZIcGx3+GK/W9WAxKaysykuXTuTazbxjdQW6IbmgJj89eyl027huZTk76vvwRVX8kQSCZGsaVTfoC0s6/H3YLQKP00qR24bLZqYvNDaadqMlNqQzhQ1YPyefVZV51Ba7KEgV/vfX3fSGx+jqmQbcvqmWZRV53PnrXdz0o9f4+YcuZF0WFYypiiGTqeb9N8jhyojOlaMdwXSvzYbe86sW0SSSaioFLiuV01QpyGpWyHVY2DvOq31I3lMDUZXiXBu1WSaNf9rTiqYbPPpma4YRfPFoR7ps7FhnZkzPGGY7G2OV7jDljaBA0J2aEliz+Jg3LShmRYUHh9XEb7Y3cqwzhBDwjlXlmBUFi0mwtDwvncWpG5JnDnUSjKlctaSERaU5fOWG5dz30gl6Q3F6gzEavVFiGun6vKgqMcVUIqrBohI3OQ4z/vjEpVoPdYearQrXrSzPiHPcur6KZw51cvWSkgkb21RgQ20Bf75rE+9/YAe3/+wNfn/HRpaNoD401ZDAlqUl7G3xj9sNcvOSEi6eV0hdd5hPbJ43Luc4GwRw7dIyrlhSyNtXV01LVygku7n3hhJU5TvT2sbjxaYFxVR5nBS4rdgtmWUQLpuZ3lAcjzPzu06cZnUnh9nOxhiFBKe+EQRYWJpsvjhcBmae00JdV5BQTGVukRO31UKR255V966hN8yBVL3hzgYv1ywrpTLfyU1rq4ioGr/c2gDe2CCdUkmyIN8kJQ3dIfrCY1PEOVqGqrULZNZA/7+9fRn/9vZlEzWsKUX1OlglAAAgAElEQVRVvpNffWQD77p3Gx/82Q7+eOclVBdM/e4bZgWsZhNfvmEFzd4I1ePYUeQnH7xw3N77bJHArhYvq+Z4pq0BBJKZ7eW51HUFWT3OK8E3Gvp49XgPOXYzt108J8MQXlDjYU+zn7U1mZm2C0tONcq1nmOHZ2WMegJM+avCYTWls6FWVGZPb/ZHVR7f146qGxS6bLx1RRk1qXKKV453s7fZx+pqD5ctLKbIZUPVDQIxlWhC5UfPH+fNZh9FLisNvRFimo6WRak7pkqcVoXecGLCC5LzhqQSf2jTHH7zeiMnuoMsLs3h4V0t9IVVPnb5PN6zoWaCRzd1SBvC+7bx/ge28/Cdl2RtWDyVyHVY2LKklN9ub+R3bzTzngur+djl88f8PAnN4KuPH6KhN8x7L6zhulUjZ2ROJH2hBM8cbOfjV4z95z6feOuKMmD8k5Javcn6vmBMwxdRKcsbbI2SrnGNI1lqLnc2nMpkj2nnljcfnV0JJhnYOuRkdyi9KhyIxSSwmBSkTKaML6/IwxdJYFYETx5opzsQpysY57KFxcR1HUUIugJxHtvXwZH2ADaLQqc/htNmpshtxWnN43hnEF9EpT8cp0vwRhJj0sniTImog5Nw3mjwcbCtmVBcR5KMiZTl2XnyQAfv2VDDc4c7+ev+di6cWzBrFIewsDSHn95+Ie+7/3Xe/b/buPe2dSzKck1NFSIxjT3NXn6/qwWAr/31yLgYwabeMMc6kze9F452nVdG0GoW5MzwbOgzpV9lJ1sN7cb5hSR0g9JcO6VZSm6C0QTecIJsC712b6aU2mQz5a8MXcq0mktwiITP4fYA3kiCC2ryefeF1bSm+lx995ljhOIq3ohKXWcIu0Uhz5FMHoklDEyKSKu+mE0KFkXBpCSbVnYFJIqi4LRZ0HWDvgHTEc2Ayeja1xsa7H490OrHQKR96roETZdcsywZC/zF1nrqeyJsP9nHktIc1mQRup3JrJuTz89u38Bdv93Ndf/vFW5ZX81HL6udkpmjMV1ysmf8bzw1hS7mF7to7I1w2aLzK/uyKt/Jv/5/9t47PI7qXPz/nNmu3m1Zki333rCMMWA6CYkhtBQSci8hhYQkNz33Qr4khMsvXNJJSCAhlU4oSQglIXRs3G2Mbdxlq9rq0vY2M+f3x65kda2kVbF0Ps+zz87OmXPm7OzsvOd9z3ve9zI1DZAotW1B/hofNF2zqriHM9GUDGe/ORnrPBHM+Ht3Llg4hU0VoxZVMyFOeyEIsfm4l+7/Pn+4+W2mTZ3Cvn37qHOH+Ne+WLLdQNjgkkVTeO+Eh23HWnhz137eefT/CHjasLrSWPHJ75JbGpsfLMhw4A5GkcB5c/MozHRxqM6Dy2ahzhPGNCVtwRACSLFbcFgF4U5q/VjEZuzmF4OuS1ZMz2JLRcwF2abBs18+m6mZMRNwbrqT8kY/GU4bJz0hVox2h08D1s7O5V9fO49fvnqEv2yv5vFtVVwwP58bz5nJeXPzTquMBPoo5NCzWzUuX1bI5mMtXDR/ysAVRpHPnDOThRPI0WmkOdkWpCUeQ/VkW7CHEHzjUAN/3lRBUZaL765fiLObtmh2e+/MxqONI9Dj4XHaC0FNxEZ6F1z+ES689Rvc/o0vAjETqCYEppTYrVoslBoxze7Ic/dz3gevJWfFpezeupH61/6Ef+ldvHGogc3lTeyqbMVp09hd00ZOip2cVDvljT6yU2w0+sIYpsSQYIka2C1dheBY0N3hKmTCnlp3zCnCovHnG8/sEIAAP7xqKY9sr8Rh0Vit0i31SX66gzuvWsJXLp7LY1ureGRrJTf8cRuz81P51DkzuXhBAYWZznEvEO0WQXgAr7zhUt7g44uPvYNhmLx9tIm/fvGcET3fYCjMVhGTBoPDplEVzwDhtPX0uP/nvpPUuUM0+8IcqveyvCRxS5I2to/KXjnthaDDaiGs6xQvWsmSmafs07lpDlbnRvjvb3yVh92t+E0LV335DtacsRRaa7nooot5tSpCWulytv/uO1wQ0vne3/fR7AsTNSXpLhtN3hBh3SQQjWWDyEq1M78gnS3HYpO7AV3GcieNMb2NuEJRE6tFoGkaq0q7Cjq73cKnzxk/buzjnfx0B1+9ZC43XzCbF/ae4E9vV/Ddv+/ju0Buqp0zZmRz1qxczp+Xz+z81HEnFLtnGRkJmrzhjvRjnuDoekcPxOLCyREP9KV9dRyo83DevPxhtXO80d+x1vNYo58lRV29TdMdVtoCETJcNnK7JR8fiGo1J5h8mv1hnt5ZC4Dwdf1Bvvutr/CnB35DTuF07vzjP3j63jvwfvvXTCmdx1v/fp7mkouo2/MW0VCATBGi2R8hbJgYJvhDUfyhKFFDYrWI2PILEdvfMWE4jnFYweWw8r6FUyZsXMzRxm7VuHplMVetKOK9Ex52VbXybrWb7RUtvLy/njuB4mwXF84v4MIF+Zw5M3dcuOVHTXBYNcK6iWMEspoArJmdy0dXFbOn1s03L50/IucYKntPuDl/3sReGxuM6Dy1sxpvSKfBM7xgHXXuEP6w0bHdnVSHldxUO6kO66AD9J9sG3+BOsb+HzpMwrqJNxQbeVY2n3KM8fl8bNq0iWuu/TAWTeAN6TS6feysaiW8/Do2vPJb3I2PkzpjKa6sfCpaQ2S5rNS5Yx6VYV0Sl3voRsz82eqPYtN6mh/HI9kpDj69blaPCDqK4SOEYElRZmxJztrYvprWAG8ebuT1g408vbOGh7dUIgSU5qayqDCD5SWZnD07j0WFGb2mnxlJJLGlRFZNYBshIQhwW7foIOOF7/19L2/+98Vj3Y0Rwx/WefNQI03eMKGogZTDWws6NdNJRtybdmpWT1OyOxDFE4pimLIjSlCiDPLwUeG0F4I2i8AaH43kpZ9aL+cJRrC60rjw1j+xsiSb8+fnc98bR3njUCMBazr513yHRekOGpraaNjzFgea9S4xODtngGj3K5BA5DRJz5eeYuMTa6b3GtFBkXyKs1O4fs0Mrl8zg7BusP14K+9UtfLeCQ97att4YW8sp112io2zZ+cxOz+VDJeNrBQ7WS4bWSntr9jn3iLsD4cPn1HMywfqef/i8eW0MhpUtYR4Zmc158/PJy9tfM8P1ntC2C0a2QmaGU+6gzz/7gla/BEafGF0wySkD/yQak82UJTl6mG+XzMrtyPqzJqZPYNuvFPVTHVrCKsWt4wNgvFlKI8xZkJQCPFzoAzYJaX8aqf9S4DfEFPCbpZS7umvHU0ILPH8Uym2U1+nLiBwZE/ljX/9g9o1l7L/pJuqw/sxzFxCXjdRI51Wf4SWNx8lc/ml+EI6EonQ6DHJdhoofl1wWAR3X7NsQufJG884rBbOnZvHuXNPLRVo8IR4u7yJt482s+loEy/uO9nvmtIMp5XsVDtZKXYyXbEEz4Yp8UcM/GG94zU100lZaQ6XLpzCurm9L02wa7CgMINUh3VCRMEZLBL40b8O8sBbx5g/NZ3PrpvFsuLxl1dxX62bl/fXY9EE160uoWCAFGi+sM7TO2qobg3Q4outzZOSjohXfeEP69z3+lGa/REuXzatxxxiKGrwdtyL86qVRT3qv1sbW5etm/DUziqWDsIxZjwyJk9JIcQZQKqUcp0Q4n4hxGop5fZ48Z3Ax4mJovuAK/ttCyhIc7DvkTu5+969+N2tFBcX861bb+OKr/4fL/zmTmpff5RXojpFqy4m79yPU1u1l9a3HgQEKdOXMOWDXyI71Y7LZqG2LYh+mmdjDxuSq+/b1GVfd9l+9qxsCrNcNHjDLCzMYGVJdizFUrc5rEN1Xg7Ve1lRnNURZWcw1LQG2FXVxpz8tITicda2BrnjufdIdVi56+qluOx9a7LBiMFtf9+LN6TzvSsWDrpvo0lBhpOrVxZz9cpiAExT4g3puINR2oIR2gJRWgOn3lv9EVrj2+5gFE2AVRNkumwUZTlJtVtx2S1UtwT4x+4TPPfuCXbedmmv546Y8K2n3u34/OFVxSPyHUtveQEApwUO/mD9iJxjoHP39UDzBiOEdZNg1OD+N8r55cdXYkuytj1cWvyxZQmGKWkNRAcUgjKeAKAw00VJtpONR5s66gYjBo9sqWRZcWYPgV9e7+b+N48BsPFwI5u+c0mX8q88tpN3a70d28/+13l99uHvO2r436uWD/q7jifGSlVYC7wS334FOAtoF4I5UspqACHEgG5daU4bc6akM+ebP+K/L5vPrLxTC5rr3CG+ee06/JEoGw434wlGqWjyEznzYvzLzyesm1gEzJ+awcz8VFaUZHGk3stze07iD+lYNIgYp58m2BvdxfqmY604rG4yHBb21Xpw2aw4bBoXLThlLjNMyb/21WFKSYMnxGfXDd6j9NUDDbT4Ixxr9DG7IBWHtX/z7L2vHuG9E7GR7KNbK/s95+Nbq9hyLJYa6BevHh1038YSTRNkptjITLExneFpZ2HdoLzB3xEEfixY8f0XO7ZDozzvs+i2Fzq2+0pglp/pQspYDrtMl43x6CpWVppNMGrgslmYm0Bi3HSnjatXFnHSHWRWXipP7TyBLxxlRk4K28M6jd4wbx1u7CEE737pUMf2CU9PR5UDdd5et3vDM3oZ40aMsRKCWUCrEGIXsAS4q1OZ1skkulQIsay7SVQIcRNwE8D06dO57xNnxCp2cziYmulkamZsNLWsKBt3MMqUDAfvVrfx2sEGGryxzOsz89KYPzWdj62ejpSSK5YXxXMHxuZydENi1WJzg5qICZSwHvMiHQ8sL0rj5CDr2LSYx6AQgrS4ttU9yaUmICfVRpMvQn760GJo5qbZafFHyHLZsCXgSTYrP5UNRxvRhBjwQTB3SmrHWtA5eWm8PqQenv44rJYxz3qxbnYez703Nguh18zI5vXynrnp2pmW6eCxz52Fy2rh3Zo2Fk/LTPqcazJIsVt5/+LBxf6cnpvSYaH58YeXseVYCx9aMZVLf63Fy1N71LludQmb4tcrtZd1gBfPn8I/99d3bPfHmpLBpaYqToGacbZKQozGGqIeJxXiS0Ab8CKwAfi9lPKeeNmbQAvwFeAvQKOUsk+TaF5eniwtLR3xPo8Elc0BfKEoFovAYbFgswjaQtGOuSJBLDr81AzngJngKyoqmD5jBpXNAfxhHQSk2CxMy3IRjBo0ecOEdRMJOK0acwrSxt16NoCoYXLSHUITIj5p3/exUsZCPJlSUpjpZN+hcqyZBVg1WDhJ1oZ1p6KigtP1/5As3tl/BGtmbEnE0j6C6k90Jut9sLfTfGik7qiUUg442hkrTXAz8Hkp5aNCiGxga6eyFmKh0A2gEej3Li4tLWXHjh0j1tGRZNatL5AaF3hOm0bUMHF20y5tGpQWpPOvr/VtlwcoKyvj2/f/lVv/upf0eJsWAYtLs4noJrur3V3Mup/7wHy+cP6c5H2ZJHHL03vYEJ+Uv/Gcmf2aQ/+48Th/2Bib2zhnTh4H/+vDFN5wDwA77h7dOanxQllZ2Wn7f0gWjsK56j6YpPdB+9wwQOUPL9+VSJ0xsQlIKXcBISHEhviuKiHE/4tv3w4sAp6Kb/fooxDiJiHEDiHEjsbG8ReLLlGsncy3FiFw9WKasAiYOsAEeTtFWa4uC+NtFo2S7BTSnTY6W4o1AQunjs9YijPyYuYVIQSz83uacjozq1N0lhlDcNqZiBim5Ddvlo9YBnmFYqIxZj707csihBBvAPVSyh/E9+8RQuyWUp4fL+/xb5ZSPgA8AFBWVnba+q387eZz+N3GY6ydlU1umos0h5XXD9RzuK4VHQuLp6VTmOXi+gTTHZ07N5+Hbyzj4a1V5KXZWT0zlw8snkqTP8q28ibeOtxISyDCR8tKOH/++IygcfMFc1kwNYNMVywcWX9cML+AX163krZAmIsWTuXbcUFfMUlH/wAn3SHu/udB5k9N58Jx+huPNO2DyW9fOLHzByp6cvmifJ7f38jli/L5dYJ1xutCshYhRDExH5TxlXcjiSwuzuSe61Z22XfW7J6LUwfDWXMKOGtO14fflAwLV6ws5oqVI+Man2wuXJD4gu7OgnLRtMxJa/5qJ8NpJUJsLdhkZU5B+qS/DyYrv/rPM/lVfPvXNyRWZ8xcpIQQNiHEK8By4CUhxPndTKJPcMokqlAoEsAVD5DgCU5eIahQDIaxNIdGgUu67X4zXrYHOHfUO6VQnOa0e/57BhnOSqGYrIy/xTIKhWLIaHFHoUBkHEYqVijGIUoIKhQTDLtVI6wrIahQJIISggrFBMNh1QhH1RIJhSIRlBBUKCYYTpuFcALpdBQKhRKCCsWEw6HMoQpFwighqFBMMJQ5VKFIHCUEFYoJhsNqUZqgQpEgSggqFBMMh01Tc4IKRYIoIahQTDCcVosyhyoUCaKEoEIxwYhpgsocqlAkQlKEoBDiR0KIjHg80FeFEE1CiE8mo22FQjE4HFaNkNIEFYqESJYm+D4ppQe4HKgB5gHfTlLbCoViECjHGIUicZIlBG3x9w8Cj0spW5LUrkKhGCQOq0ZEOcYoFAmRrCwSzwkhDgJB4ItCiHwglKS2FQrFIIjFDlVCUKFIhKRoglLKW4C1QFk8RZIfuDIZbSsUisHhsFqUJqhQJMiwNEEhxDW97Ov88a/DaV+hUAwepQkqFIkzXHPoFf2USZQQVChGHYdVI2KYSCm7D0oVCkU3hiUEpZQ3JqsjCoUiOditsVmOsG7itFnGuDcKxfhmuObQb/RXLqX82XDaVygUg8cRF4IRQwlBhWIghmsOTU9KLxQKRdJoF4LhqAnOMe6MQjHOGa459I5kdUShUCQHhzWm/UUM5RyjUAxEUtYJCiGcwGeAxXQae0opP52M9hUKReJ0zAlGVdQYhWIgkhUx5mFgKvB+4E2gGPD2V0EI8XMhxAYhxC+67f+zEGKrEOINIcQnktQ/hWLS0HlOUKFQ9E+yIsbMkVJ+RAhxpZTyQSHEY8BLfR0shDgDSJVSrhNC3C+EWC2l3N7pkOullEeT1Ldxz4GTHp59p4a/bK+mNah37E+xxdLiLCrKZGZeOvOnpPG+xVMpyOg50ROI6Fz7qw3sOeFhWpaLr186j0e3VGCa4I/oeEM6Vy4t5LEd1aTYLTz02TU0+6P8+706rl1ZzKKizC7tfenRHRyu8/GDq5YgLBrzpqST6bL1OO9AeENRDtZ5mZGT0mu/k8neWjelt7zAZ9cWc9uVyzv267rOnS8ewDDg+1csxB8xeX7vSWbnpXHW7FwA7n7xAO5ghNvXL8bpTNbfAgzD4Na/7uONQ418eFUh//2BxUDX6/K1J3bjDkV4/NNryEhzDPuc9s5zgpOQ9vsAoOLu9WPcG8Vo0v67D4Zk/duj8fc2IcQSoA4o7ef4tcAr8e1XgLOAdiEogYeEEM3Al6WUlUnq47jkSL2Xf+2r4zdvHe9RFohCIGqw8WgLm4+1MjM3hf0nPdx1zbIex1a1BAnUeACobAny9b+8i+x2zH0bKwBoCxlc99vNZLgchHWDLcdaeOEr6zqOu/e1I7y4rx4p4YY/b+em82ZzqM7LJ8+aMejv98Kek5x0h9hm1fj8ebOwWkY+e9fvN9d0EYJ3//MQf91ZC4CUkOa0sLvajSYERVkunt1dy6NbY7eZL2xw7yfOSFpf/rCxgid31gBw/5sVXL68iEXTsjquy617TnC00Q/AVfdv4rVvXzjsc7bPCaoF8wrFwCTrifSAECIbuA34B7Af+GE/x2cBnvi2G8juVPZNKeXZ8fo/7a2yEOImIcQOIcSOxsbGYXde0RWVZPL0pl0TVKHTFIqBSZYm+KqUshV4C5gFIISY2c/xbUBGfDsj/hmA9gwUUsqNQoi7e6sspXwAeACgrKysu8JzWjF3SjqXLZGEo3oXc6gAXH2YQ3tjeo6LhcUZXcyhj22twDBiplJPyODKpVP7NId25ksXzWX/SQ+H67xdzKFDYf2ywg6z32hogQCfXdv1+9zygflEpdnDHDonP42S3BS+fPFcfGG9wxyaTD5zbilHG3wd5tBF07KAU9fl+jXTu5hDk0HHEgmVTkmhGBgp5bBfwK5e9u3s5/gzgN/Gt+8DzuxUlhF/nw88P9C5V61aJRVSquugroGUsWuw/4Rbzvif5+WLe06MdXfGBHUfqGsgpZTADpmA/BpuxJgFxJZFZHYLpp1BP8t0pZS7hBAhIcQG4F2gSgjx/6SUPwAejZtWJXDzcPqnUExGHJ3CpikUiv4Zrjl0PrFs8ll0DabtBT7XX0Up5Ve77fpBfH9/QbkVCsUAqDlBhSJxhhsx5lngWSHEWinl5iT1SaFQDINT3qFqTlChGIhkeSpcLYTIEELYhBCvCiGahBCfTFLbCoViENiVOVShSJhkCcH3SSk9xEyjNcA84NtJaluhUAwCNSeoUCROsoRgeyiRDwKPy/gyB4VCMfrYLWpOUKFIlGStE3xOCHEQCAJfFELkA6Ekta1QKAaBpgnsFk1pggpFAiRFE5RS3kIsFFqZlDIK+IErk9G2QqEYPHarpjRBhSIBkhcpGBYCpUKIzm0+lMT2FQpFgjismvIOVSgSIFn5BB8GZgO7gfZ/nkQJQYViTFCaoEKRGMnSBMuARfFQNQqFYoyJaYJKCCoUA5Es79B9xJLqKhSKcYDSBBWKxEiWJpgH7BdCbAPC7TullB9KUvsKhWIQOKwWNSeoUCRAsoTg95PUjkKhSAJOm0YwqoSgQjEQSRGCUso3k9GOQqFIDulOGw1etVRXoRiI4aZS8hLzAu1RBEgpZUYvZQqFYoRJc1gpb9THuhsKxbhnuFkkhpZuXKFQjCjpTivekBKCCsVAJMs7VKFQjCPSnTZ8SggqFAOihKBCMQFJd1qJGCYh5RyjUPRLMsOmKbphmpLKlgDZKTayUuxsKW8mJ83OvCnpPLK5gjSnlatWFnPva4d5+d0q9tSH+21vZm4Kt69fyKKSLArSnV3KjtR5KL3lhV7rOTUozHKiaYLsVAc/unYZT2yvZndlM+vmT+G6M2cQjBhMz01J1lcfE/bWuim95QXOBu773qWk2C08urWSbJeNVw/W0+AJU5TtZGt5C7Py07j3+lVkpdgJRgzeOFRPozfC8ulZFGY4CUYNyuvd/HlzFXOnpJFqt5LpsvPxNdN59UADUzMdWBE8saOaSxYWsO1YM28dbaKy0c9Zs3O548ql3P/GEVaX5pCb7sQ0DQ7W+fnk6hKe3XsSiybZXe3mvLn5pNgs7Kxq5eIFU/j3gTrOmplLdqod3QTdMEl3WVlUmNnxPVt8EV47WMfGw434ojpzctP50BlFLJp26pgMVyyxiycYxWmzjPZPMaa03wcAFXevH+PeKLrTFojQGogyIycFTRM9yt+pakUTsLwku0dZTbOHa+7bwpqZOdz7ybIe5X09A/tDCcERZMPRJnZVtmK3arhsGi+9V49FE0zJcPDK/nqEEDy8uZLdNW4Mc+BgO8ebA3zqoZ187ZK5fGx1CYWZro6ykNF3/ZAJx1vinoJNQS762VsdZduqPGw91sKq0hzOm5fHqhk5Q//C44RNwKNbq9hT08bbR5sIRAw6Lm9F7K3W08L6X27g318/n5+9fJi/7aohEDEoynKxcFoGdovGs7trMSS8daQZiC07eHhzBboEw5S0BSKEdZO/7Kjpcv43jjRz0U/eQAr4y45aSnNTqG0L4rBq/GHjMaKGxBPSEcAzO2uxWTRMKfnNm8fQhOBPb1dSmuMiaoJFg9w0B7d+YEHHQ+HbT7/LxiMNhONK3is08czuWjZ868KOPhRmxAZJJ9whCjK6DpgUirHCG4ry6NYqIrrJGTOyOX9efpfy1w428Ns3ywH4/PmzuWhBQZfydT/egASe21fPtBf2cev6JcPukzKHjiCeYBSI5XWrc8e0PMOUVLcEAZBSUtsWZLDR5qQkqfM9jb5wvL8TZw4popvUe2KCv6/xhS+kE4joNHpDGKZEAoGogS+k44/odB9XSFPiDulIKYlEDaJG3xFZOgfQ9YcjmPHfOBA2OtypZbxvhjQ79VNimBLdMIkaJlFDIiU0ek9ZCdqCEbqfOqybhIxTv19xTmyAVNMa6LOPCsVoE4qaHZGM2p+PnWnstKynsZclPp3/ku9Uu5PSJ6UJJoGIblLbFqQw09nF9HTevHycNgtCSKK6ycGTbqZlu7h2VTH3vHwYb1BHYtDg6d8M2pkF+U4WFmYwpyBtSH21ANetLuL1Q000+MIUZTm586ql+MJRzpqVO6Q2xyMNniBZTgspNoHTaqXFr9NZbgjgixfO5mi9j3S7lXn5Lqrbwpw1K4f1Swqpbg1yoiXAwXovFiDFYcVp07h6RTEH6r0UZjoJhHU2lDehEftDh+KSzwKcOSubd6pamZrhZN28Auo9IZr9US5fNoUX99bjj+g0eyPMzHOhm4JWf4R5U1PZVdnG0qIs5hSkEYwYpDos5KY5uoyIv3HpPB54s5wdFS1EDUl+uoOPnTmdrNRTGl9xdsy0faTeB0DUMHn9YAPnzs0jxa7+9oqhI6WkqiVAVoqdTJetR7k7EGFPrZtlRZlkpti7lOWnx+7lBm+YM2f2tDpduXwaz+yo7tjuzmVz0/jXkdg9/eQXzknG11FCMBn8490TVLcEyEm1c8PZpR37M102Vpdm87W/7GZvTRuekI6lQuAL6Xx09XS+9sTuXhdZ9sehxhCH6rysKMliamb/Zi67RfDrT5zBpYsnX1jXx7fX9Ftuswpe3l/Pz14+gmGaGCYIAS+9V09BmoN3qt3UuEMIIUCAO6TjDsHv3j7O9NwUMlw2CrNSMAxJU1yDtggoznZhSMmWY61I4IQ7jGHCTz66glDE4PFt1Zw9O4+LFhSwvCSLLz26kyZfhDNKs6luDmC1aBxv9rN4WgYOm4X1ywqZN6XrSqRz5uSzvDibrzyxC3/YYEVJFl+5eF6XY9IcVs4szeHhLZWsX1bIHzce54nt1TDbgocAACAASURBVJw3L58/f2p1r3MxCkUibDjSxM74NM8NZ5eS5ugqRm7/x35OuoMUZrq457oVPeovL8nqs+2vPP4O2yrbOrYfuGF1l/J2AQjwX49u497rzxzOVwHG0BwqhPi5EGKDEOIX3fYvEUJsFEK8LYRYNlb9GwxtgQgQ0wbMbrY3dzBKMGIQ1k2klJhS0hKI4A5GBy0Aod2EJvGEepoSumNKyfFm/xDOMvExTEmLP4JhmkgZN7PImCNKdWuQQFRHN2K/l2FKTHnq2kd0E2/cZBrqFKQ6ZvrUiUTNjt/WMCXeUAR/WMcT0jvMom3BKKZp0haI/Y4tvgit8fvIF9LR4/dRe3l3/BGdQCSmejb5erck3HXNUqya4H0/f4sntleT6bLx1uFG/rSpYjiX7tT3jV+baNwL9XC9l3/uPcmuqtYR9UptP2+7ybjd9L31WPOInVNxirZO0zyBSM8plJZAuMv7YKhoDvS63Ru7azyDbr83xkQTFEKcAaRKKdcJIe4XQqyWUm6PF98JfBwwgftIIEP9h+6NOXr847/Oo8UfIawbFGa62F/r5lijFzQBEho9Yd6pbiHVZsEflbT5QwR1g2avzsw8F5omOFTvwzANfMEoNpsNuyYJ6dAS1HEA0gKRfv7fP3358AC9lWwqb2FTecuA16kvfvHqEX7x6pGOz315wK0uzeY/15YO+TwTGcOEY01d/2QmEDEkL+6r67WOlLF5u6qWIFXxed0u9SU0+bsKLUPCc3vqeG5P7232xa/fiDkHdP6d+2LrcXhmVy1/vnFVl/1zCtJ45uazuevFA8wpSOPrl8zjMw9u587n9/Pzlw9jiWuDopNSaJqyY1BgxgdtUrZ/d9mxf6BpbKsmSO2kIXQ+R6y9U+eR8XY7nwMJEtllXyJT53u//74un0tveYFsO8wvzKAkJ5WLFxVy3rx8UrppLzsqWpiS6aQke2w9pE+6gzisFnJS7QMfDPjCOq3+CAJ4dX8dT+2q4UcfWYqUUNnsZ2qmE4e1p3fw157YxbZjzTz9udVMy++qmXlDUc67+1UA3rrlYtKdXU2em99+h8erYttfvXhuj7bfOtzUZ39rmj2c++MNHZ+7P7sqG3y9bvfGRbMGL2R7Y6zMoWuBV+LbrwBnAe1CMEdKWQ0ghMjspW4X9p/w0FTrBWDF91/ixnNnYUrJnPxUfvLyYRo9ISQxx4H+HDCPtfQy6oh0faCF4ZTHwziiN7dgp1XwqbNnTTr3+MnMFx7aSfeZ4pKcFO7/5Cnh+Ovrz+CpHTVUNPs7hFE7EtCEQIjYuyZAdPosOLWf+HvHfk0wLcvJ7Pw0TrSF2FfrxheOaQndzxGrHmtX0N5+fB+xA9rbbT+m/Zzt+7qUC0GG08qs/DTs1p7GrdYIbKn0sKXSw9/31HHliiJ+dO2yDpPwn94+zr/21WG3atx1zdIxE4T7at28vL8eTQiuO7OEKQN49YaiBo9uqaS80UezN8Srh2LCZ/0vNiECEf66q5apmU4+fub0LvV+/M/3+PvukwCc+9O3OdZNEK26898dA/1Vd/6bwz/oWt4uAAFmfefFQS1D6SwAeyPcx3ZvPLgT7vhIwqfuk7ESguuB6cCTwCeAMiHEHCnlVwFNCPFzYol6Z/VWWQhxE3ATgDXjlIutN3zK3HSkwYdumHFTluxXAE5ECtIdLClWoVsnE44EBjwpdmuXeeuRYFkxXLZkfM5DG6ak0Rsiapo4tNj1qnPHtPqIbtLgCY+ZEGw3h5tS4g5GExKCgYhBMGrQHK8LcS0+/sBr7bS/nb013o7t3vybO1u6+rN6TRRGXQgKIRxADmCNm0XTgZ8CC4UQq4EUTplKa7uZSgGQUj4APAAwd9Ey2a6v/fKjS8hISyEYMVg3Nx9PKMr+Ex40EfO+80WiNHri7uoyptS1y8Z2a81EkJWvfuNcSnLSex0VKyYmTgF//NRqPv/8WPdk/GLXYHlxFjdfMLuLifA/zy6FTRVMzXSxakbPBdqjRdmMHIIRA5fdwpz8gb2/s1LsXLiggBmNKZhSUtm0n7agzprSbN5z2Zg3JZ3F03oOhB/63FksuO1FQrrkE2VFPcp/+bHFfOUv7wHwq48t7rcPgw1GUHH3+iEtaE/GuftCDHaN2rBPKMSXAJ1YDsL/D/gQ8F2gBJgGfAb4DfAP4O/Aw1LKe/tqLy8vT5aWlo5sp4eIL6zjC+uEIgZOm4UUu4V6bxjDlDitGlaLIBR3oshwWkmxW2jyRdANE7tVI8VhJS/V0WU+pS/e2X8Ea2YBVk2wsHByaoBHyo9hpOShmxJNCGxWDWvc5JXutJKX5uhRJxAx8MadjASxQVCK3dJjHqQddzBKKGpg0USv7Y017feBAJYUDTibMCGpqKhgvD4TRouJeg0qmvz4IwZCwKy81B7TPftq3R0m93DdUSmlHFATGFUhKISwAY9KKT8qhKgFosAeYqbNu4jF88gDLgLcwEPAFCnl/3Zrp8McOn369FWVlZWj9h0Gw7O7a9l/wsNbhxspyHCwqiSLJ3fVIqUk02UjN81Bqz+CJ6Rz9coiUuwWXjvYQKM3TF66nbWz8rjxnFKyUgaeJHcUzqXwhnuwanD0rskZKmrG/KXkffKnHdFY0pw2CtLsZKbYWV6SxbfeN7+HdvzK/nr21roJ6wbBiEFWip2iLBcfXV3S6zke3lJJkzeMEPCF82ePuznX9vsAJm/IsFVlZTz47KssnpYRW+IyCSkrK2PHjh1j3Y2k8/573uJEPADEXdcs5YrlXTXZmbe+gJSxueKKuy/fKaXsGVutG6NtDv0P4LH49nHgcaBRSlknhHgeKAaagY1SyieFENcAPYbbnc2hZWVlY2LBjOgmTb4wBekOrJbeBxvr5uYTjMRcx502C2kuO59cM51Nx5r5+OrpuOwWXj3YQF6qnYWFGaybk4uUsSgf86ems7goMyEB2JlPrun94T0ZyEm1s25uPntqWokaUJTlYmqWk5m5qVy6aGqv5uE1s3KIGiYZLhspdgs1rUHW9LKIt52LFxSwo7K111HoeKD9kb+0aPJmOWvzR7j83o28/q0LmJmXOtbdUSSRWy9bwI9eOkhpbmoPAQix+MpVzQGm56a0R0gckNEWgvOBFUKILwCLiWl9y4g5yFwC/JmYqfTz3faNO57aWU2DJ8zMvFSuWtnzx4DYQ/nqM4rwhXW8IZ25U9JYNzefL1wwp+OYC+Z3jY33hQtmD6k/aQ4ra2bmsGZW/sAHT1AsmuDrl87jyR3V7Kl2M7sgjQ8uLew1MkU76U4bH1ha2PF55fT+54SmZbn4UJar32PGknRn7D44b97kvQ9sVg0DaPaFlRCcYFywoIALusUT7UxZaQ756U5m5KbweoJtjqoQlFL+T/u2EGKjlPIOIcQvhBAbgHellNviZaHu+8YTpilp8sa8rjrHdOwNh9XCJ8+agScU7ZH5IZm4bBaWl2R1WZs1GWnyhbFqGkuLM1k1I7tfATgRcdgsLC3KpCB9/M1Xjhbt2nAo2ndsV8XEpCQ7hQynrddwbn0xZk9MKeW58fev9lLWY994QtME718yhYMnvf2GAGrHabOMuOks1WFlRUnWmHq3jQeWFGXS5IstHj53bt5Yd2fUyXBaWVqcydoJFAd2sGjxeUCVS3Hy8YGlU9lX62FJUeLOgZNbbRgGC6ZmsGDq+PHCTHda+WAns95kxWG18P5JGCu1nRS7lStX9G6enyy0O8OEdaUJTjbmFKQzp2Bw8+FqIZlCoZhQtDuE6qYSgoqBUUJQoVBMKNrnBBNJVK1QKCGoUCgmFh2aoBKCioFRQlChUEwo4mG4lSaoSAglBBUKxYRCKE1QMQiUEFQoFBOKjjlBQznGKAZGCUGFQjGxiEtBQymCigRQQnCUMUxJWyBCsgOXS0lHEtPJjicUJaxPzoXSEnAHogMeN5E55R2qNMHJhmlKWv2RjnyKiaAWy48iUkqe3FFNnTvE0qJMLlk0JWltN/rC/GHDcdYvK2ROwcC5yCYq7dm5U+wWrj9rBmmTLIxciy/MH98+zlmzclk7e3JGjWl3jFFzgpOP5/ac4Fijn1n5iceMVZrgKBLWTercIQCq4+lAkoWUElNKapLc7ulGdUvs+wciBs2+/uO6TkTaH/zJvr9OK9rNocoeOulo//+3vyfC5BomjzFOm4V1c/M40uBjdWlyAzs7bRam56QMmAVhorN6Zg7esE52ip2S7JSx7s6ok+qwUpjp5OxJqgXCKXOo0gQnHxfML2BvrZulg0gorYTgKFNWmkNZkgUgQKbLxrWripPe7ulGXpqDj5ZN3pyKaQ4r1505fay7MeZYNKHWCU5ClhRlsmQQAhCUOVShUExALJpQmqAiIZQQVCgUEw6rJjCT7IGtmJgMWwgKIVTqZoVCMa6waAJdOcYoEmDIQlAIcbYQYj9wIP55uRDivqT1TKFQKIaIVRNqnaAiIYajCf4ceD/QDCClfBc4LxmdUigUiuFg0TQ1J6hIiGGZQ6WU1d12Tc4wHQqFYlxh0VQWCUViDGeJRLUQ4mxACiHswFeIm0YVCoViLLEqTVCRIMPRBL8AfAkoAmqAFfHPCoVCMaZYNDGo+JGKycuQNUEpZRNwfRL7olAoFEnBqgmiSggqEmA43qEPCiGyOn3OFkL8MTndUigUiqFjtSjvUEViDMccukxK2db+QUrZCqzsr4IQYo0QYpMQYoMQ4ufxfd8WQmwUQjwqhLD1tU+hUCgSxaJpRNU6QUUCDEcIakKIjmjNQogcBjavVgIXSSnXAQVCiHXAhVLKc4E9wFVCiPzu+4bRR4VCMQmxWVTsUEViDMc79KfAJiHE0/HPHwF+0F8FKWVdp486sAx4I/75FeATQKCXfU91bkcIcRNwE8D06SpYsEKh6IpFE0QNZQ5VDMyQNUEp5UPAtUA90ABcI6V8OJG6QohlQB7QBnjiu91ANpDVy77u535ASlkmpSzLz88f6ldQKBQTFJumqbBpioQYtCYohMiQUnri5s864LFOZTlSypYB6ucAvwI+CqwitsQCIIOYUGzrZZ9CoVAkjEqlpEiUoWiC7UJvJ7Cj06v9c58IIazAI8C346bR7cD58eJLgC197FMoFIqEsVoEUeUdqkiAQWuCUsrLhRACOF9KWTXI6h8BVgM/jDXBrcBbQoiNQBVwj5QyIoTosm+wfVQoFJMbq9IEFQkyJMcYKaUUQvyNmDlzMPUeBx7vtnsz8MNux/2w+z6FQqFIFKtFLZFQJMZwlkhsEUKsTlpPFAqFIkmoVEqKRBnOEokLgS8IISoAPyCIKYnLktExhUKhGCpWi/IOVSTGcITgB5LWC4VCoUgiVk2oLBKKhBjKEgknsQwSc4C9wB+klHqyO6ZQKBRDxaoJdLVYXpEAQ5kTfBAoIyYAP0AscoxCoVCMG2JLJJQmqBiYoZhDF0kplwIIIf4AbEtulxQKhWJ4WDVNLZFQJMRQNMFo+4YygyoUivGIih2qSJShaILLhRDtsT0F4Ip/bvcOzUha7xQKhWIIqCwSikQZSsQYy0h0RKFQKJKFRQXQViTIcBbLKxQKxbjEZhHoarG8IgGUEFQoFBMOiyYwJZjKJKoYACUExzlbypv5zJ+38z/P7MEX6tsPqbolwE0P7WD/Cfco9m7iUtsW4L8e38XNj+ykvNE31t1JmBNtQW780zb+/V7dwAdPYGyW2KNNLZifXPzurXJu+OM2fvdWecJ1lBAc57x8oB5fWKeiyc++2r4FXNSQuINRXjnQMIq9m7hsPNJEgydMiz/Cawfrx7o7CROKmgQiBi/vP336PBJYNAGgTKKTjDcONRKKGrxxqDHhOkoIjnPOmZOHVRMUZDhYWJje53EWTWC3apw9O3cUezdxObM0hzSHFafNwjmz88a6Owljt2poQnD2adTnkcDaIQSVJjiZKCvNRojYe6IMJ3aoYhS4aEEB583Jw2rtf7wyIzeFB29cjaapcU0ymJmfxu/+M5Yp7HS6psXZLh7+9JkD3i8TnXYhGNWVJjiZ+Pql89F1E6tV4xsJ1lFC8DQg0Qfa6fSwPh04Xa/nZBeAACn22KMtGDXGuCeK0Waw97/6tygUiglHqiMmBP1hJQQV/aOE4Biy7XgLv99wjG3HW2jyhXntYD0VTf4htVXnCXH7s/s46Q4muZenD4aU/Pzlw9z+7D6qWwJj3Z0xockX5pZn9rC7qm2suzKmpDpiMT18YRXZcSLhC+u8fqiB9/rwgu/8TE0UZQ4dIfbUtPHC3pPsq3EzLcvFHVcu7jDRtLP1WDO6KXlp30msFo3KFj/FWSn892ULsA9SpW/yhnlsaxURXef/rl2RzK9y2hAMG2wqb6LVHyFqmNx1TeL5naOGyZF6HwUZDvLSHH0e5w5EePNII8uLs5iRmzroPpqmyR3PH+BIvZcrV0zjY6unD7qN/qj3hHl6RzVH6j0888Vzk9r26cQpTVAJwdGm3hNi6/Fm1szMZUqGs0f5/pNuKhoDXLQgH6d9cCLol68c5p/76kh3Wvntf6yiJKfrf3DD4Uaa/RHcgWgfLfREaYIjQHmjj/978SB/21lLVYufqpYAR+q9PY6bNzWd1kCEem+Yv+2q4c1DjTy/52RHzMN7Xj7Elx7dxf6TA6/9k0DUlPxr3+RdH2a3apxoC9LgDbO9opUWXyThuj996SDX/34L1/9+C4FI3w/OH710iEe3VHH7P97r97i+qPeEOXjSg2FKNhxpGnT9gTClRJewu2pyrxdNtSshOFbc8dx7PLqlijuee69HWXVrgB88f4AHN1dw3xuJr+VrZ0+Nm9ZAhJPuUK/Wnh2VLfxz30l2VCpNcMSpaQ1wtMHHomkZFKR3He34wzpRw8Rh0/CGdSyaYG5+WpdjQlGD8+bkYtVg27EWfGEdU0p84QjHGr387Z0TPLu7Fqsm+MaTPtYvLaTBHaK2LciUDCdfvmhOx0N0/bLCjnbdwck7B6JpAqdVw4vEF4qwvbKJ9y+e1uO4iG7yk38f5HCdl6XFWXxkVQmPbKkiEDFwB6O8+l49V6ws6lHPG4qy/4SHtmCEgnRHx2ClxR9m45EmwrrJhQsK+tUkp2Q4WFqcyaE6LxfMy0/K93YHo/jCOkVZro59k/cuiJEW1wS9SgiOCA2eEBlOa6+a3InWIM2+COFenJLCEYOIbmJIiT/Ss9wbivLCnpNA7LmW7rR1KW/xhfCFDQQGdpvoUX9vjZuQbrC3JvFBoBKCCWCakvJGH5kuGwUZTkxT8uzuE0R0k+NNfv5zbSlNvjA5qXakjJnW8tLtuINRVs3IxhOMcOvf93HjOaUsLMygwRPm8a1VbCxvJBwxaPZHsQiQpiRqwNX3bUI3JO3O3e5glF+/dhSQaEJQmpfK0ztraF8CdbDulJY5mR3Cyxt8tDXFRoeekMHND7/DzPxD3HnVEs4oyeZIgw9PMMpDmyvZVN5M1DR5p6qViiYfFovABCzArIIUtle0cLjeS9mMHOZPja3PPHDSw+JpGZQ3+rh00VTSnTa2HW/mh/88SKMvzLlz80h1WPng0sIefWvyxRbez85P47b1i5L2nd3BKI9sqSSim5wzZ3KvDexMQYYDTUDNJJ0bHkke31bJY1uryE118IvrVpCZYu9Snuq00uQLk+rsKV6KslOYkumkpjXA6l7W8u0/4eGhzRUAzMpP5cyZXdc9H4v/vyXwyr56ymZ0ved9ccHq60XA9sW4FYJCiJ8Ty2C/S0r51f6OrW7xIxAU56T022YoarDlWDPpDiuLizJx2izUe0Icrvcyf0o6BXH7tWFKfKEo79a04bBobDrWzM7KVnRTcu6cPIqznGwpb6KmNUjUMHhmRw1nzswm3WWj3h1iw9EmPIEITruVHRXNNPnCgODFd0/gsGkEoyamjP2QPem5NxA1u5TvP+klHI7Q6Atjt1m5ctnUfr/3ZCHSLX+cCZQ3BvjE7/rO+xyKwnN76jrmBaSEu144gKZpeAJh/u/F/UzPTiHVYaHZF6LBEyEv3clT2yv48UsHSLdpNAYMJPD24UbmFaTx+LZKFk/LwGmxsKuqDadN44ntVdR5wly1vJCKlgBh3WBlSQ52q6AlEOVjZcUUZadyvNGHO6Rj0+DNI02cOyePZcVZXfrc6A3x4KYKnDYLZ8/JJRJfC9fiDyfxap7eOG0W5k1J55GtVZxwh0hzWDsCCQgRy/sm4oqE4NS+dtr/hVK2f5bdPnc6ttsx3d6Qsve6slMj3ds/1bZMqD+dj/n6JfMYiD01bZxoDXDO3Pwe2hb0/0z9684a9tZ6cGiw/6SHtd0CM7xb2YwvCm3+UI+6lS0+no9renc+u5fLlnQdMN7x13fY3xS7j7//13d48ZuXdCnXO33fiN77E3SwjEshKIQ4A0iVUq4TQtwvhFgtpdze27HVLQHW/egNAD60rIALFxYSjJhcMC+f257dF5uLkxJPSCcY0YkMU1XacqynrbmmLcy+k54e+72RznNSsR8sOtwOxClviT/wIjoX/XxDl7LSW14YsL7g1J9m3dwcLlsyjfctmkp+uoNGT5iLfvoGwajBxQvyOXtOPqtmZLOkKHPQ/Txw0sO24y3MLUjj7AQ0ld1VrXz/uf2k2C3c87HlFGS4+jy2yRviK0/sJhAx+N4Vw9OuzE7vbx9r7VK2v65r7FBfyykP3M7r0CpbQ3z/uQP9nuee107Ng/xz36kQd7989Wivx/+IQ/22x79PbX5iTXGXor7ug4q71/ff5hDYvHkzH3/21H9jJM7RF8eOHeOiB05d9/a77AdXL+XHLx1k45EmAhGdqCExTIlEdhFIUsouQuaUcIy/x3ec+txe3kls9qjT9ZiB2uy9jcTqim6NfP68WQQiBn9++zjLSrI4Y3pXjWtXZSPX3B8bGBak2dh22/u6lN/4h828fiT2W144N4c/fWZtl/LtlTHP47AJtz+4lX//b9ff2hft+t6Zy+7Z2LFd6+15QLsABNjf2P+g7o+bK/nelUv6PSYRxqUQBNYCr8S3XwHOAnoVgm3BKO2Pyef2NDAzP/agfmhzBYfqPDR6w0gpiU5mO2EvdB5DbS5v4YzpueyubuPSRVP48Uv7O+ZSXjvYyILCTDaXNw9JCG4ub8YdjLL1eAtnzMjGaes/HeXDWypp9MZGkE/vquGLF8zt89ind9ZQ2RxbUvLI5spB922i8dT2mjE7d2cBONp88Pe9DzxWzcjmiZvW9lo20fGFdVoDUTYdbeohBO987mDHdkMvkqpdAHbf7o3DifuejVvGq3doFtCuWrmBLr+iEOImIcQOIcQOS/jUfNjiwjRcdgsWTXDhggLSHFYcVg2nzYJVE11HXYoOCtIdaEIwMy9m+vjIqmIsIjbCLMyOmYhn5Q9+OUDneiU5KTgSWPZx7pw8LJrAYbWwbk7/jiPr5uTjsFrQNME5c1TM1OUlWQMfNEKsmW4f+KAR4j/OLBmzc49X2v9rs7o55AF8rZO5NN3ec1A6PcvR63Zv5I9XNWoQCNndCD0OEEJ8CWiUUj4phLgGKJZS/rK3Y7NycmXYGXsATs9xYZgx80a6y0YgrOMN6wTCOpJYPMH2gLpWTRDWY3NzAtnPHN3pge5uwJpZMKS66Q4rGS4bGS4bVk1gmJJDdV5MKclw2Uh1WEm1WwbU4nojFDXxR3ScVq1j7VZ/BCMGJ9xBNCEoyUnpiAHZG7opqW4JYErJtEwXB48eG/I1mAjkpNppOFEz4DVYOgSNfiD8fj/H2k55Yo7EOfoiHA5zuOnU/FNv/wWrJkh1WEmxW3DZLF3uxWDUoMkbxmbRmJLh7GZeHD0MU+IJRhFCkOmyJdQPb0gnFI3NSTf5wpimJNVuRfgbKS0tHekuj2t27twppZQDjrz7fCoJIfqNPyql/NlQOpYgm4HPA08ClwB/7vPItHwKr/8pACV5qaxfFnOJL852UdMa5JldNXiCUUJRA5tVwzBigk/TBFHdxDidJV8nTj74NQpvuGdIda0afOnCuSwpyuTSRVO45endtO6oBcCmCb544RzSHFY+d96sQbf9x43HcQdjJpebL5g9oCD95pO72XKsGYDrz5rerzn0t2+Wd3iSrZmZy9GvfWTI12AioAHWBO6DHSMwX1d6ywt0dnEYiXP0xYLvvEBhp+mO3v4LFhFbNnHxwimU5KR0uRfvfH5/R5qyb1w6jzWzxsaq8MahBt6JR/q5bMlUFhZm9Ht8sy/MQ5srKW/0Ud8WZHu8rkVA9su3s2PHjhHv83hESokQAiHErkSO709KpsdfZcDNQFH89QUgeT7evSCl3AWEhBAbAFNK2ad7X7rTiiYEmhBcuCAfpy1mDl1clEG600phphO7VeCwamQ5bTisGnabhRyXFatFQxPj1yY8WuSlxcyhpbkxc+iHlhd1mEOnZsbMoaV5QzOHzozXK8p2JWQOXTsrF00I7FYLZ8/q35Fm7exc7FYLmhCsVSmkmDOlp+lrtBjv5tD2dGSZLhtFWV3vxWXFmQgBGU4rswuGdp8ng+k5KVg0gdNmoTCzZ6SV7mS4bOSm2cly2SjJcWKJa45ZqT29PScLJ9qCXPGrjf3mXu3OgOZQIcS/gWullN7453TgKSnlZcPpbLIoKyuTD/0j5kOzaFpWbCGmKXHZLUQNk6hhdizsjJqgGxKnTRDRJWHdwIKkJaBj1yAqJVuPtTBvigt3UBKI6hRluKhuCxDWTQpSbHh1k9cP1JPjhJYgNLc24/NLGgxYVgCmNZvqFj8ZWoSmqEatZ2Q8ciycWhBdcfd6HIVzu4x+NcAFOKywbkEWUV0j22XhWEuQa1ZOY/bUXCpbPOS4HJw5Kw+EhqvT/EBNq5fyhgDr5hbgj+ikOawdXmmDxRuKkmq3ovVj2uzMibYgLquF7LSBH6ytvgiBqBETst2uwUiRa4doBAKADqRyypRuA1wuyLdDTQCsUQhpUJSjkeNy8ZG1M9lcXk8gLGn1RvdrTgAAIABJREFUhMhM0QjpGoFgmOXF6dQFBdOyLDhtTgKBKN5IGJfDCVJnUVEuOyua0MwQVW0GdiGZW5jNwToPFyzO54a187pcAycQInZ/dPYUHSnPzdue2cxj21s4NopaYDtPbjzGrzce5c1b3tflGly9NJfPXjAPm8XK9NxUoobZ673Y5AuRYrf2CG042gQjRkdu0EQwTEkwamARgkAwwubjLVy+ooiysrJJqQk+uKmC2//xHq9983xmF6TvlFKWDVQnESF4EFgupQzHPzuAd6WUC5LS62FSVlYmJ+OP3Z3JetN3Rl0DdQ1AXQOYvNfgjufe4y/bq3nvjvejaVpCQjCRYc/DwDYhxN+IDXivBh4aZl8VCoVCoUgqta1BirNdg7JaDSgEpZQ/EEL8E1gX33WjlPKdIfZRoVAoFIoRwRfWyeglAk5/JGoATwE8Uso/CSHyhRAzpZTHB93DEeK5d2OejFcs7xr02B2I4glFKclJwRuK0uqP8taRRrJTbGSn2PGGogSiOgdPevnAkkLSnVb21LjxhXVafGHSnDaQ4A5FqGn2o1k0altDzMl3EdZN9p3wUt7gQ9NgZl4aWS4r3kCIg40hNBNGMojVoqlpHZFMKu5ez95ad8e8z2OfWc3aOfnc8dxepmen8bEzpye0POF0p/M1GCoWwC7AkJCbbiUrxUZFUxC7BTJcdkxDx263E4hG8YUMirJcaAJaAlGynTbOmptHZbOfE20hZmfbiAobppQ0ecM4bRYump9HvVdHN2PzOAUZToQQnDM3D29I50idD28kwurpeayamU2jN0wgrNMajDJvSjqZLhsH6zxsPtpEVDdIcVgpK81lRm4qLrulyzX49NoSnthRw68+sRJfSOeuFw/ynQ8u4EMrJ/a6us7X4NIFOThtdj64rBCLJshLc7KiJCvh+enTifIGH68drOcjq3oGf58s+MM6WSmDc9JKZE7wdmIeovOllPOEENOIOcacM+SeJpHp85fKrI//BICb1s3iyxfHXOrdgSgPb6kgakhWzchm/0kPf3+nloomP7opyXJZCURNghEDIcBu0SjIcNDqj+ALG6fdmsHubuGluSlUNseCzV61cho/+vBybJaJ7Qc7Wo4xycYiIMWuIYQWzyYCWS4bH15VjBCw8UgTTpuFxdMy+ODSQm55Zg8n3CF0U2LVoDg7hRvOLuVTZ5finDZvwGswmiHNxoK+7oMMp5WcVDvffv/8jqVUEwVfSOfCn7xOKGpQlJ1C0yPfmJRzgpf87E3mTUnjvutXIYRIaE4wkafi1cCHAD+AlPIEsaUT44KwbsRi/0lJeaes7N5wlGh8EWCjN0QwYuAJRZFITCkJRgzMeMxAKWO5+IIRg6ghTzsB2BvtwZQlUN0cIGqouHHjFVNCWDeJxIM3QCwTSXWLn7Ae83DWTRNvSKfeEyIQiaXdaq8bCOt4gnpHIAhF7+imJGqY1Ht6BnY+3fGGooTjgdTbghMgltkQ8Yf1jlySiZLI0REppRRCSAAhxNgtpOmFwkwXC+PRKf7f+lMOq8XZKZw7N49mX4Sz5+Ty/7d33mGSVWXifr+K3dU5d0/OmWFggCENAgKiiKBgAgPK6roGEDPrb1dcA7IG1hV1F13BgKCgCIiiSJoBhsxkJufpmemcKofv98e51V3T091T3dM91dN93ue5T918vvvVvffcc84XdjUFKfC7eWTNAVwo82oLqe+IcrDddDedPLmU2dUFvLanlZ1NIWLJFEV+j5Mb0LhLpKOWe91CPKGjJmfb0kke/pyxPKnYzb+9YzH/+uAGAl43X79yUc5Nv8cLXhckUz0BudOdbunqqSzfQyyRJIXgcZlsB/k+D2fPKCMUV9buayWWML0XN108l+2NXVQU+ghFE7xpTjVLppSyvbGTxzYcIhxLUJLv46IF1bztpNp+W/pVBV7cLuFgZ4zaotz58+UKv0eYW1tMdaGfyeUBrjxl0tEPOsGoK83nmjOm8Oy2Jj589lRu+0OuJcoNwWhi0EM/2XSHfgGYDVwM3Ap8FLi3vzBmxxvrImEYrybRmVgdWB2A1QGMTx2oKrO++lc+8aYZfPEt87LuDs3GOvR7InIxJqD1XODfVfXxYZDZYrFYLJZhIeoEShlsr9dR9xaR21T1y8DjfayzWCwWiyXnhJxs8oWD7A7NxjDm4j7WvXVQpVgsFovFMoIEnRyogT7SQw3EQFkk/gX4JDBDRNZmbCoCnhu8iCNDIpniY78y+Xa/deWi7kzkqsqz25poCcY4b3YVZQU9BgF/eHUvz21rJppIklKjtJpiP4smlrJ8ZiW/WLWTfa1h5tYW4ULojMR5blszhXluFk0o5q/rD3anLUm7U7i0J5anC0bUaMZFj+EFwKeWTznMN+qu607jgnk1IyjB6GQ4/ATBZNWYVlHAnOpCntvRTHu4J0WQ12UsMt0uk6mk0O/F6xY2H+winkxSFvARiqeYUpbHyVPKcLtcXH7yBB5bf5BXdzXTFk6Q53Xz9sW1fPrCnrxur+xq4eWdzby4s4XCPC+TSvJ4cE09c2uK+NX1y7r364jE+e2Lu2nqilHgddMUjHH10kmc4iROzdRBiQuibuHShXW87aQ6nt7cwPlzq7lkYe0x62g00/s+uPmtc7lgXg1zakaNUbtlBAjGzHM62JbgQHv/FvgrxhjmKxnrO1U1d2mke9HYFWNjvcm/+/Nnd/Gvb5sPwL7WMK/sagWMD+BbTzKJXjojce5/dR/1bWE6IwmSKTWZKFyC1+1md3OQ57c109gZZcvBTvK8bg60h+kIJ0imUqze00Z7KH5EJZdZKY201WhvZ4cfr9xz2PJ3H9vE+XOrhxzweryTSMGOpiC7moMkeik77iwnk7CjKYzfHSGe0m7XhoOdxjx944Eu9rdHmVNTxJZDm2kNxtjRFCSZUtwu4ZE1B7hwfg0L6kpoD8VZubWJJ944xL7WEAV+D3/vioLCCzuaWbWtkbOcBMMv72zhmc2NhONJDrZHmFpRwK9W7e6uBDNpTwEp5c9rD9AcjBFLpNjbunvMV4K9ueu5XSRS2EpwjNPdEhyu7lBVbVfVXar6flXdDYQxlt6FIjLlGGQdVvK97nTuKE6a0JN/qzTg7c4XVl3ck5Yk3+OmstBPvtckic3zmmSv6SSWiyYU4/O48LpdVBb6KfR7qCj04XYJXo+L6uI8fENILjuS5Pf6z2dWF9kK8BgxDuwD/88uwON24evlmiCA1yMUOQ/j7OpCAj4PXpfgFsHjEorzvdQWmV6LfJ+b4nwv5YU+vM69l4564fO4mF7V45VUU5xHgd+D3+OmLGDCQ00pzx9QzoCvJzXPhNKB9x2LTCzNo6b46KmJLCc2wWh6THCYukPTiMjlwA+ACUADMBV4A1g4WCFHgtKAlzs/sBSABRnZrIvyvHz47KkEo0mqivzd6z0eF99512J2NQfxewRxCZFYiqpiHz6Xm7ICH3Nqi+kMxynO9+J1u4inUmw/1EVVkZ+ifC8b97ejJNnbGqUrHDeOyy5BU0k6QnEmVxbx9KaDbKzvpLzQR8DtoikUZ2JZgGQizramMM0h89UiDJzR3gsU5bspzYdYysMHl9bgCwRYt6+DN/Y24ff7+dNnzsP/f58F4KuXzuC65XOHW80nPG6gxA95XqgpLaa5K8KsqgISKaW+LUJNST61RT4au6JcOLea6dXFzK4p5MVdzWzY304iAeKCObVFNLRFwCW8eX4tTV0Raor8bKzvYFdziAvmVbFhfwdzaouYXllIWzjO7OpC9jSHaO6K0BFN4EJYNLGU8sKeiu7aZVN426JaWoJRRITZVQF++/I+zplVQW1JoPs6Fk0s4VvvXEQwmqQk38OB9igL6vpu4Tz+2eU88No+PnXeTHw+N9sag8yqGlVuviPO99+9iHNn11BRMP78I8cbPWOCw+8nuAa4EPiHqp4iIhcA71fVjw9N1OHF+gkaxqNfUG+sDqwOwOoAxqcOHnh1H1+4fw0rv3QBk8sDwxo2La6qzYBLRFyq+hSw5JgltlgsFotlmBiqdWg2lWCbiBQCK4B7ROSHmITaAyIiy0TkeRFZKSK3O+u+KCLPisg9IuJ1plUi0iUiszKObReRp52pfFBXZLFYLJZxR9o6dLBh07LZ+wogAtwEXAuUAP+RxXG7gQtVNeJUesuBC1T1XBH5MnAl8IDze1uvY9ep6vlZXkNWRBNJOiMJKgv9xJMp2kJxKgt9AxqQNHVFKcozRgiv7W6lqshHvs9DKJIgFI+zZk8HF8ypwiXCy3tamVSWRywW4+H1jcyryScYg85wjKJ8N1sawtS3BHFJgj2tcSQeAYU9XbCoykMymmBDB1T7wZ/vJxRLUpafojUsLKgrYWZVPinxsGxyEcWF+bhdLnY1d+JxuXn36T0uEhtvuZhAno/WYMyJSzm6jHhGkm2HjnSRKHZDwA81pQHm15XQGUlyxSkTefKNBlKqvGVBFTubwnQlUyydVMr06iJUoSsSI+DzEI6nmFQWIJJI0BaKQyrFq3vbOHlCCeGEgkBrMMb8uiLqSgP9SJYdqZSyvy1MntdFVdHQDDnS98GpJfDHm3uyRSRTSkswRnmBMfIay2S6SDz9hfOpLcmjPRwnlkwxuezY/iPL6CUYTeB2CX7P4LLlZBM2LZix+MtsT6yqBzMWE8Bi4Gln+R/ANap6P3Coj4povoisxPgj3qxHG7g8CtFEkt+8sIeOcJzTppaxuyVEY2eUBROKeUs/5uLPbWvipZ0tFOd7aewI8/CaeqIJZfGkYurbo2xv6EJTSiDPQ57HRUckRiIlJIcQyX9NY0/D+lAUiJoMEE0mExIrtrewYruZ/+UqY0yT6Yv45OZD3ccvuOVxHv70OTzxRgN5XjfXnjll0EkmT1TCCSjtta4jCR0hOBgKsabeKPTRDQ3d23//Wn33vAB1pXl4XEIwmsTjFgp9biaVB0gkUuxqCdHUFTMZORQK/C4icVMR1hT7+cm1S1k8qbcE2fPH1/fx4Gv7yfO6ufGi2cd0rtfa4Yrbn+Shmy4E4KHV+9ndHGJqRYB3nTr2Akj3x/nfe5r3nDaR3c1hXCJ88oKZLJ9dlWuxLCNAMJqkwOcetGV8v1WmiHSKSEd/U7YFiMhioBJow8QfBWgHjnRs6mE2cJ6zz+V9nPPjIvKKiLzS2Nh4VBmC0SQd4TgAe1pNBQhwoC3c7zH7nW0d4Tgb6jtRIJZIsq81TDgaJ5kyKZfCsSRd0YTJHHCcUtkoh/sirt17+N9R32ZSxUTiSVqD4zetymBRoDMcJxhNEEukCEYThOMpDrRH6Iwmu9MdqRpfzVgiRSJl0ngFo0m2HOw8pvJ3NJpcl13RBPta+r83s2XdoZ5zHGiPHPY7ntjdHCIaN6nTjvU/soxehpJBAgZoCapqEYCI/AdwEPg15mP5WrLMJ+iM590BvAdYCqRTHhdjKsX+ym5xjv8TcArwcK/tdwJ3grEOPZoc5QU+ls0op74twjmzKjjQHmFbQxenT+t/uPHcWZU8v72ZCaV5LJ9Vwfcf34LHLZw7q4JNB7twu9poC0VZMKGUwjwPG+rbwIku0x42VZQL82IdzqrR64YCn4fSgIe9LRE8LuG2qxfx5oycHmdMLycUS1Aa8Nrun6PgdRnneAVK8z2cO6sSlwsaOmIU5blxu1ycPr2clmCcTQc6ONgeZk9LiNKAh7KCPNrDMaKJFKdNLecti47NCf3KJRMJx5OU5ns5c2bFMV/br647pXv+wnnVrNvfzkkZbkTjgWI/fGDZVNbsayOegitOGVvJdC09hGLJIVWC2bhIvKiqy462ro/jPJjK6+uq+qKIVAN3qeplIvIlYJeq/t7Z927gm6q6zclXGFHVpIh8EzM++Lv+yrEuEobxaBLdG6sDqwOwOoDxqYMP/+Il2kIxHvr0uQDD6iKRFJFrRcQtIi4RuZbsIoO9GzgduE1EngZmAitE5FmMi8WfHEF/D1wC/FJErsB0hb7sjAlOxhjPWCwWi8XSL6HYMHeHZnAN8ENnAnjWWTcgqnovcG+v1avoZQmqqu/p4/BTs5DLYrFYLBYAuqJJJpYOPjJQNtahuzBuEhaLxWKxjEpMS3DwLmHZxA6dgWkFnomxH1gF3KSqOwZd2gigwMqtxkL0rBkVeNz99/CGY0lW7WiiKM/LyZNKWbWjGY9LOHNGRbfvlKryyu5WDrSFERGmVxawyDEm2HSwg93NIZZOLaMzkmDD/jbW13fQGUmQ73ERiifpiMTZ3RxiT3MIBc6ZUc62piDNnRG8HjctwRjxlIllqRyZEaI36f3yvC6WTiujuTNOWYGXdy6p4+ktzQT8bv79svmH+Ubt+s5lA55zrNJXKiU3pu/ehTEqUqAk38dZM8oozPMxq7qQcCzB01uaWDa9gs+8eRZ+T8+D9OruFp7e3Mis6kJElftf20dbKM45M8pxe9w0d0bZeKCD6mI/X7hkHvPqisklmTq484NLeX1PG5ctruu+h8cDmTq4fHE1CyaU0xGOUeD3cN3Z0ynMG3yXmWX0E4wOzTAmmyN+C/wYeKez/D5MN+eAhjHHi3As2Z0yqdDv6TOlTJoXdjSzZm87APWtYXY0GRfIknxv90tid3OIZ7c28caBDvK8bqZXFjC5LIDHLTy2/iCq0NwVpbkrxpp9bWw51EVHJI7P7SISTxKJJ4kle4yNHtvYkGEdmuxjbmDS+4XiKVZubcYl4HEJOxo7CcZSFOV5+OmKUfE9MipJ6y8FOEHmaeyK8ei6Q1QU+nllVwv1jtvA9oYuzp5VwdkzKwFoCcb4zQt7qG8L88yWRpIpZeuhTlTNvlVFfg51REmmUmxtcOF1b+VH7z9lwA+x48m3H91ATUmAva0h7rhmfI4wPLK2gY0HgoRjSSaXB5zA+tNyLZZlBAhGExQMIThINk+rqOqvVTXhTL9heK3+j4nM6BdFR3EKL3ZyDrld0p1ZQoTDnMkL/J7uqAN+j4s8rxu/16S3yXdSKJUGfBTleQj4PHhcJjVOntf8etxC5t/gFuNXMizXiuMoL0Jxvo/0pU8oGX/pcY4Vtwu8bqHA7yXP40YQ/F73YfdCntdFkdNqKPC5Kcn34hJzz/g9brweFx63IGL+k8pCH65RlMKq1Em1VBYY3xkU8rxuvB7zv1QX+4+yt+VEJJlSwvGRawk+JSJfAe7DVH7vBR5Nx/TMdYJdv8fFe0+fjAjUHaUyWDq1nKrCPAJ+k1NwSkUAr9t1WK6xqiI/1yybQmckgapSUejvzkt4zbIpNHRGmVoeIJZMsXxOFc1dURKpFLGEkucRgrEkG+o7aAlGOdQe4epTJ7C3LcK6fZ2UBLwcaA2ytr6T2dX5JGKwsbGLfJcSiSZoj0OhDzwuF7GUUFXoo9DvwuWC2TWlnDK1jPZQnOpiPydPLmPzgXb8Xjdvnl/LRx35N//HJSOl6lFP7y+6sjxh6bRyDrRH8Lpd1JbkE0ukmFIW4Pz51SSSysTSfLxuF09sOsTZMysP6zYM+Dx8/uK5rK9vZ0ZVgEhceXV3My1dcZZOKyOZUhLJFGv3t1NXnM9FC2pwjaKQZHd+6Aw2HujgjOnjN/zu/R9fhtfrdiI5CUunDhSjw3KiEkrHDR1kGiXIzk9w5wCbVVVnDLrUYcT6CRrGo19Qb6wOrA7A6gDGnw4OdURY9u0n+PY7T+KaZSbne7Z+gtlYh04fBhktFovFYhkRuqLpDBLDaB0qIu/qtUqBJmC1qtoAfBaLxWIZFaRzCQ6lO3SgI44IXA2UA4tF5HpVfXLQpZ2ApFJKLJnqHhfsTbovWhA8LmOFGI4lcSOEEwmiiSRVgTzy8jw0d0XxuaChK06R30MyGaO+I0E0EiIpHoKxFLPK82iNKs3BCIsnFuPxmL8o3+MhiVKaYeSQLjvg87DtYDvzvvIob9z6tkFHUR8rdIZjLL/1UT5wxjROn1HFzJoy3G7wulwoJqB4cZ4Hl8uMHsYSKUTA61hzhtJJOZ3B9XgyRTJpskSgJrB1WYG/2xgrkUyZtFzBOIE8NyX5uTdAOdBm3AO2fOMteD1uIvHUuEqnBdDV1cW0rzzKHz62lCnVpZTl+/AMMr2O5cQi3RIcivvLQAG0P9LXehGZCvyeUeIiMZJEE0nue2kvraEYF86rPiK1zfr97dz22CZaumLMrS0ikVI6wnEOtoepb4+QSKZIKpQFvFy7bDL3vbSXhs4YoKSAVOroZrZ5LvB4XLhcLmZUFnD5yRO4fvmM7rIBvnzpPMJJk/Rx+s1/Yec4rQh3tYSJtsOtj+8CduF3w9zaEkoCHhJJpTOSYG5tEbe9azGNwSh/fG0/AO8+bRK7GoP8z4rtqMLHz5vB7Joi7n1xD6v3tlFZ6GPtvna6ogmWz6ni39++gGg8xW9f2sNf1x9gR0MXhfkefvi+U1g2/dgDXx8LTUGoA+b829+45e3zaQ0nWDq1jPPmjJ/0QTvbk9QBV/3sVfLdcO7cam5/zynWP3AM0xVxKsEhWIcO+vNIVXcD4yJBXUswRkswhqpJc9Ob1/a0Ekuk6IjE2dsS4lBHhPq2MG3hGJG4Sb2TSJqUPH/f0EAipcRTSiIFySwqQIBICiKJFJF4ks5ogjX72g8rO5ZIsXpP6+HHxI/mgj8+iCahNRSjuSvGvrYwkbhJhdUcirGnOdStv70tYTYc6CAYTRJyrHv3toRoj8TpiibY0xKiuStGSo2fYEswxv62MO3hGAfbwyRVicSSrNzalOtLPox19eZe2d7YlWNJckc4aVKL7Wk98vm1jB3SWeWHUgkO+ggRmQtEB13SCUhNUR7z64o41BHt07T64vk1rNnbRoHfw8K6QpJqUintbgqypzVEJJYkklCmVOTz2Ytmcfvj24gmlFQq1Z2PLtOxvi+qC1z4vD48bmFGZQHvOLnusLIB3jy/5rBjxlv3V3/UFntZOKGIsgI/yWSKhs4Yp04to6Y4j3yfm51NQVwuYV5tEWUBL1sPdZFS5fy5VUwozWdbQxfReMpxVXFzoCPKWxbUUlucR3mBjzk1RZwxvYJXd7VSUejjvaeNrmS1l500kd0twZy3TnPJhCIPZ82oYF5NVtnfLCco6ZbgsKZSEpFHOLKxUo7pbfmAqq4adGkjgHWRMIw3k+i+sDqwOgCrAxh/Ovjp09u57bFNbPrGpd32G8PhIvG9XssKNANbVdWmK7dYLBbLqKArGu+O9DVYBjKMeeaYpLJYLBaL5TgQjCYp8LmHZBBo7YYtFovFckLTGUkcNXZ0f4wJm+HXHOvIJZNKcxK7sbkryqaDncysKqQ9HOPu53Zx5owKLllYy+t7W6ku8lNbnM/9r+7FLcLM6kIWTiimvi3Mii1NnDenkgK/h8fWH2Tl1gZiCeX29yxhYnmASDzJ63vaKC/wMbe2/8H9dPqYn75vCW9dMvE4Xv3oYUdjFzNvfpRp5QF+/IGllBX4WLW9iZ1NQcoLfMyrLUbV+BKN1dRCG+rNfbB8Zhm//tjZuRYnJ2w80MG0rzzKvJoCHrvp/FyLYxlGYokU//3EVs6ZVclZM3sMvoLRoeUShOzyCd6oqj882rpcEY4leWazySfodbk4adLxf7k9sqae1lCcNfvaeOqNBurbwzy7rYnOSILGrigi5s97eVcLB9ojnDmjnN3N5fzjjYMEo0le3tVCYZ7HpPVpi+AW+PhvXuXRG5bz7NYm1u03pu6lAe9hwb774l/uW82ucVoJBmNJihW2N4f41wfXcfGCGh5ZU09LMIbP42J+bTGlBT5qi/Mo9HuYVlmQa5GHnZRjyrZyeyvbGjqZVT3+rCKTjhI2HQqy9VAns61l6JjhodX7ueOpbfxy1S7Wfu2S7u7PrmhiSO4RkF136If7WHfdkEobATK7gD3u3DiIe53BWK/Lhd9r5t0uIc9n5l0i5PvcThokkyXC4xZ8TqQSr1vweVwmEolzCT7nWtLndokcljbKMjB5Xjc+jxu3S3CJmTxuF+lbxDsOIoh4R0lew1ySfh4tY4NV25sB0/25taHH/7UtHDssmtZgGCh26PuBa4DpIvJwxqZijJXoqCDP6+Zyx3cuV1+9VyyZyI7GLqaWF3DFkjrue2kfy2aWc+qUMjYf7KSi0EdVgZ/pFQX4vSZ10+zqIs6ZVcEL25s5c2YF+R4PT20+xOo9rXREEtx6xUkAnDurkooCH2UFPioL+8+F5hKTu/DZm8Z8IJ9+KQ/4KPS5OGNaOd++ajH5Pg9zawvZ3xqmLOBjakWAlJr4ghNLx2YORp/bhQCfPn8qUyvGXks3G9J5P69eUsOU8vGpg7HKhvoOZlQWsKMpyKu7W5njtPJbg/Hu+cEyUPvxeeAAUAl8P2N9J7B2SKWNELnu8in0ezJCqnm54aLZ3dsyx57efvKEw46b6Atw1dJA9/JVSydz1dLJh+3jdklW41cLJ5Twyq2XDUH6scPEsnxe+Y+3Hrbu3FnjJ1wYwNzaIl75zvi+D2ZVF457HYxFIvEk2xq7+OfzZnD387vYfLAnj0NrKDbk5NEDuUjsBnaLyEVAWFVTIjIHmAesG1JpFovFYrEMgS2HOkmmlEUTS5hbW8Smgx2AifEciiUpLxhaJZhNh/kKIE9EJgJPAB8B7h5SaRaLxWKxDIGN9abSWzihmHm1RWw62Imq0haKA8ZwcChkUwmKqoaAdwE/UtV3AguGVJrFYrFYLENgQ30HhX4Pk8sCzK0poi0U51BHlKYuE8q6fLi7QzMQETkLuBa4fhDHjRue39bEK7tbWVBXTGWRn5VbGplaWcDli+tIqTHr3d8a5sL51fzp9f28vsek5ykv8JNIpXh+WzN5Xhe3XLGwewwrFEvwtYc2sL2xiykVAZZNr+Bdp07E7+nbFybtJ7iwrohHbzzveF7+qCGtA48L/vVtC7hm2ZR+80COVdI6yPe42PiNS8dlSq20DlwCT37+TUyrLMy1SJZBsKspSCIYeD91AAAYCUlEQVSlzKo+/H/beKCD+XVFuFzCQsdOYoOTKQWgtmRg97H+yKYleCNwM/Cgqm4QkRnAU0MqbYyybn87yZSybn87a/a1kUgp2xu66IwmaAvF2N0cIpFSXt7Z0p2XbuuhLnY2BVm/v532cJxwPMlf1x7oPufWQ53saQnREY6zvaGLg+0RDrUfPXnHGwc6j7rPWCeRgjcOdHCwPZJrUXJGOJEa9ym1Ugqv7W49+o6WUcOmgx1cfPszvPWHK7qz5IDx/dxY39FtJDi/rhgR0zqsd57zCUO0+D5qJaiqK1T1Hap6m7O8Q1VvGFJpY5STJ5fi87g4eXIJpzjzs2sKKfJ7KAv4mFFVgM/jYtmMCpZMLqUk38vcumJmVRewZHIpZQVeCnwe3r64x3p0bk0R0yoLKHNS9kwozcvqS2fRpOKRvNQTAq8LFk0spq50aF+GY4ECn2vcp9RyCSydWp5rMSyD4M5ndpBIKYLw3b9t7l6/vbGLcDzJSU4lWOj3ML2igPX729nfGsbjkgFdyAYim4gxVcCXgIVA91tFVS8cUoljkDNnVHDmjJ4QPpkZ6EWMH2Ga+XXZVVJ5Pg+3XbU4axlOmlgy7s3CrQ6sDsDqYDSjqtzx5DbW7W/nc5fMYV5tz/vwYHuEh9fU8+GzplFbksd3/rqJ9fvbWTSxhLVOMvGTMtzFFk4s4eWdLSRSysyqwiEHE8mmO/QeYBMwHfg6sAt4eUilWSwWi2Xc8vOVO/n+41t4YlMDH/q/l2jo7BmyuOv5naRUuf7c6VyzbApFfg//u2IHAM9ubaS8wMeMqp5xwnNnVXCwI8KTmxpYMGHoPWDZVIIVqvp/QFxVn1HVjwJnDrlEi8VisYxJgtEE3/vbZs741j/41D2vsb8t3L3ttT2t3PbYJi5dWMujN5xLRyTOjfeuJplS2kIx7nlhD287qY7J5QGK87xcc+YUHl1bz+aDnTy5qYHz51Qd1tq7aH5N9/z5c4ceFCMbK8+483tARC4D6oFJRztIRJYBtwNJ4BVVvUlEvghcAeymJ/7oCuAkYImqbnOOPWw/VY1jsVgslqxQhYbOCMmUkkiq+U2lf1OkHJspERNj1udx4XULIkLK2S+pSiql3fu0heK8sruVv60/yOq9bZQGvLx5fjUXzK2mtiSP1Xvb+PFT2zjUEeXMGeU8uamBpzc3cONFs6kq8vPtv2yipjiP265eTEm+l29csYgvPrCWG+57nabOKJF4ks9c2BNt66PnTOeuZ3fxjjueJZpIce2ZUw+7xopCP3dddzrr97dz2Ul1Q9ZVNpXgN0WkBPg88CNM7NDPZnHcbuBCVY2IyD0ishy4QFXPFZEvA1cCDzi/t6UPcsYge+93/6Cu6gQkGE2w5VAnk8sDQxrgjSZSbKhvZ35tcU7SSY0GEkll9d425tUWjTvXiDRxqwMSKeX1PSauZMEQMwuc6ARjCc741hMjcu55tUV84MypHOqM8PDqeu59aW/3tiWTS/nJtaeydGo5e1tC3PzHdXz7L5sAmFoR4OcfOo2SfOPU/u7TJrO3NcyPn9qGxyXc+q6TDksXV1Ocxx3XnMKdK3bw9sV1LJ1adoQsF8yr5oJ51cd0PUe9Q1T1z85sO3ABgIgctRJU1YMZiwlgMfC0s/wP4BpVvR841MuX6Yze+zEOKsFH1x5gf1uYPK+bjy2fjmeQGQDaQjH+vuEQ4ViS06aNT4u4llCMpzY1sKclxDt6xWkdL7Q6OtjfGuayxUP/Oj6RaQ3GeHpzI1sbunjPaZOPfsAYxO9x89UrF+F1mewzHrfgdrnwOMsuEQRIqRJPKrFkkljCNA/TGWvS+ykmFVyh38O82qLDUpBFE0nW7G2nNRRjaoVxYk+/zyeXB/j19WewoylIMJpgQV3xEe+1z108h0+8aQYukT4/2i5ZWMslC2tHTE8wdKf3zwH/lc2OIrIYE4S7DdM1CqZCPbJaN5QCHQPtJyIfBz4OMGXKlKyFHs0knBxoKVV0GM4znkkkx7F/nPP3J1LjVwfpJyCRHL/PgtctfLBX9+FI4Pe4OWN6/x/dIsLMqoGDFQR8uW2tD7X0rPrbRKQcuAN4D7AUSPsKFGMqxb5oO9p+qnoncCfAaaedNibu9MtOqmPDgXamVRQMKQ9ccb6X8+ZUcnKGe8Z4ozTfy5kzKnKSWHm0UBowOlg8jnVQFvCybEY5C+vGrw4s2SOqg69DRGSPqg7YBBMRD/Aw8HVVfVFEqoG7VPUyEfkSsEtVf+/sezfwTVXdNtB+/ZTTiBl/HEkqgaYRLmOopGU7FdjD6JWzP4ZTtyeqDoaDE/0+GA5OFB0cj/fJqcBrx6msoXA85Jqqqkc1Gx0oqW4n9NkzJ0A28WneDZwO3Ob0Ed8MrBCRZzE36H855fweOBeYLSL/qaoPicgR+/VHNhd5rIjIK6p62kiXMxQyZRvNcvbHcMt8IupgODjR74Ph4ETRwfGUbbTqYTTJNVA+wWPKVKuq9wL39lq9igxLUGe/9/Rx7G2997NYLBaLZbgZ/OCTxWKxWCxjBFsJZseduRZgAO7sZ/5EYbhlPhF1MByc6PfBcHCi6OB4yjZa9TBq5BqSYYzFYrFYLGMB2xK0WCwWy7jFVoIWi8ViGbeMz8B6ljGDiCzFZDUpwwRWeEFVX8mtVMeXXjooBn5vdTD+dGAZGnZM8ARERApwXvqq2pVreXKFiNwO+DExZtsxL7+LgKSq3pBL2UYaEUn34nwfo4MnMOEGvws8h9XBqNCBiBQCn8BU0KU4H2rA/6pq5zCX5cYkHDjsoxD4k6omhrOsQcpVqqptzvzbgUXAduABHQUVkK0EeyEin1XV/xKRkzFZMxTTYv6Kqq7MsWwXAv+GedAFE4zAD+wFWjA3/ddUdW3OhBwAEXmfqt4nIlMwL65aoBWj241DON8KVT0v2/VjCREJYV5w6cggYO6JxapaYXUwOnQgIg8Dv8ZU0Jkfah9S1cuHuaxfA2v7KOtkVf3AcJY1SLmeVNULReRWzIfAQ8A5wCRV/Uiu5EpjK8FeZPxhfwc+6YRyqwQeUtVzcizbs8AlqhoSkZWYmKwdwN9V9RwRmQD8TlWX51LO/sjQ7UPAf6rqcyIyF7hTVd80hPP9AAhgWoIdmIf+zUBUVbNJ93XCIiKvAhcCX+NwHXwXeB6rg1GhAxF5DliuqqmMdS5g5XC/T0RkZV/Pfn/rjxcZz/0zmc957+VcYccEj6TcaXGVp5P8qmqTiIyGr4UoJgHxi86yOMuRjOXRTL6IzAAqVfU5AFXdnNGtNShU9XMicgpwFjAH0xK+U1VfHzaJRy9vB8J96OBnwHNWB6NGBz8GnhaRtZgKugRYCPxkBMp6SET+jElFl/4ofBPwyAiUNRhOFZEVwIJ016jzzA+cXuI4YVuCvRCRr2Us/tD5w4qA76rqJ3IlF4CI1AFfweRmLASmYirGfc5vM3CLqq7LmZADICJ3ObMKfC5Dt/eo6jtyKJrFMmI4yQTm0DMmuGWkxuicXqszMsp6WVUbR6KsY0FEAsBsVV2Tc1lsJWixWCwjw2gwChGRy1U1163BIxgtclk/wSwRkR/mWob+EJH/zpi/OZeyDIUTUebhRkR+ISINIrI+i32niMhTIvK6iKwVkbcdDxlHmkHqYKqIPOFc/9MiMul4yDgE/gjgGIVcBqzG9OT8YrgLEpEZfUwzgS8Nd1ljQa40tiXYByKyEGNevSlj3Zmq+kIOxToMEVkEXI7p9uikxxx6j6o25FK2gejLr49RLnMaEfkqcA2QBFLAPwMfA34wFOvWXuc+D+gCfqWqi46y753A66r6UxFZAPxFVacdS/kZ5+5S1UGP1YjIlZhuvgH1ICK3AF2q+j0xeUT/rKoPONsGo4P7nWN/6Yzhf0RVPzhYuUea42kUIiIdwAMcaRtwsarm7CNhtMqVxhrG9EJEvg/UAAkRqQA+6vSpfxtjiZZL2R5T1UtF5LPADRjXCAXqgfuBj2Be0KPSP6yXX98mzMD9qJY5jYichTHEOFVVo87Yi09V/2k4zq+qK0RkWq8yZ2IMK6qAEPAx58NMMboDY2hRPxwyHCNXAn8GhvwxMEgdLABucnZ7CvjTUMsdYY6nUch64Mu9xwBF5HcjUNZgGK1yGVTVThkT8EzG/GKMpdXpwJOjQLYn0zICKzLWP5sxv+J4yjRI+fuUbTTLnCHju4BH+lj/NHAa8A5MV9dqYDOw09m+1Pm/XgX+BtQNUMY0YH3G8hMY4wGAZRn/fx2wDmMQ1QosHcbr7HJ+z3eu7QHMB8s99PQcfQdT2a0FvgecjfFT3elc/0xMC/llYA3wByDgHHsL8AVn/m7g6l7nfANoykIHvwVuzPhvFKjI9X3Sj04XAfMzlgPAmSNQjifX13oiyZWebEvwSDwi4lPVmKquFZF3Ar/BmDXnmgUi8ivMS+aPIvI/mFZVtYhcjfGRe22gE+SYVzJkzvTrG80yp/k78O8isgUj/+9U9Zn0RlV9GHgYQER+DzwjIl5MwIUrVLVRRN4LfAv46NEKExNp5GzgfpHuXiS/8/t+4G5V/b7TQv21iCzSDF+0YeIUzH1fj4nAco6IbATeCcxTVc1o3TzM4V2bbar6M2f+m8D1GF30da3l6XNiLJ7/4qwfSAdfAO4QkeuAFcB+IGdRUfrD6VmqBpKZPUsiMhI9SyoiVzHKIsaMYrkA2x3aFzdhxtkaAFS1VUTeAbw7p1IZljm//4Z5MS3CfLE/j3nQRrWPnJ7Afn2q2uWMZy4HLgB+JyJf6b2fiHwJ47v2Y2fcdhHwuPMSdwMHsizShQmLt6SPbdcDlzpyrRKRPKAS554dRl5S1X0AIrIa01J9AeOX+nMReRTTBdoXi5zKrxTT9fe3AcrpSJ8TeAnTqoMBdKCq9ZgWYLqyvEpV2wd1dceH09QZ+xORxZgK/YsjVNbdmNb5vRweMeZuIGcRYxi9cgG2EjwCVX2pj3VJ4L4ciNNbjt29Vr3uTCcMToV3QsmcxrkPnsY4P68DPpy5XUTejPlYSofqEmCDqp41hLI6RGSniLxbVe8XU4suVuNXtQfTgr5bROYDecBI+IJFM+aTmG6thIic4ZT/PuDT9N2iuRu4UlXXOK218/srpNc5r8e0BgfUgTMm2+K0fm9mBKwth4nj2bM0TY80DnpdTHSpXDJa5QJsJWixZIWY8G4pVd3qrFoC7Ma09BCRqZgoIJeqatjZZzNQJSJnOS02LzBHVTf0cf57MRVFpYjsw4QCuxb4qYj8P8CL+RBbA3we+JmI3IRpNV2nzuDLSOO0ugKq+hcReQHY5mzqBIoydi0CDjjXfC2mu3LAcwIfxMSULMhCB+cDt4qJ5LQC+NSwXeTwcjx7lh6WviPGPDwCZQ2G0SoXYCtByyhARH6Bsbxs0KObxk8Bfol5sbgxwbf/MvJSUgj8SERKMWNP24CPYwxHAK4DKoAHna7PelV9mzNW+98iUoJ53v4LOKISVNX391PupX3suxFTWeSCIkx4rjxMSzdtoXkfpmK+Abga02X/IuZDYR2HV5B9npOeFu2XVfWXGdv70sED9Oh+1HI8e5ZU9bsisgoTSrETYzj1S2DGcJc1FuRKY/0EHUQkiXlYPRgrtw+qE+mhn/1LgWtU9SfO8gTgv1X16uMh77Ey2Osd4DzHfN2jxUfOYjmRyTTCwXyQpY1wnlTVnLl3jVa50tiIMT2EVXWJ8xJu4ejdK6XAJ9MLqlp/olSADoO93j4ZjutW1RWODN2IyEwReUxEXhWRlSIyL707o89HzmIZDZymqh9U1euAr2KMcE7PsUwweuUCbCXYH6uAiWDGK8SEZ3pNRNaJyBXOPt8BZorIahH5rohMEyfck4hcJyJ/dF7iW0XkP9MnFpHrRWSLmFBPPxORO4771R1J9/UCiMgXReRlMSGpvu6su01EPpmxzy0i8vle1+12dJE+9p+d9T9xxkEQkQed7s+0Lr4pJknwLzD6XC/GleBO4DOquhRjDp+Oun8L8AFnzOgvwGdGUjEWC5ieE+dZXy8i94sJAN3Xfn9xeolygUdEfABqcoq+E/O85Nq9a7TKZci1o+JomehxEnZjoq9c6ix7gGJnvhIzFiQc6djcvYwZH9qBaankYcZFJgMTgF1AOWaQfyVwxyi73kswFZBgPpL+jLF2PIXDAwlsBKb0uu6PA//PmfcDrwDTMVaE33XWvwS84MzfBbwFuApjPp0+zwQgTI/z+WrgDWfb54DPO/NnOXK4cn3/2GlsT+nnxZm/B5MFJXO75Po+xGSPqO61zg28z8rV/2Rbgj3kO75QzZhK6nFnvQDfFpMP7B+YFlNNFud7QlXbVTWCeVFPxdwMz6hqi6rGMZVPrujvei9xptcxTuzzMBE7Xsc45U8QkZOBVlXd0+uclwAfcs77Iqb/fzamsl/ujOFtBA6JSQt1FsbHcR1wLlAjIssx44Ntarpr09N8p4zrgd+D8ZHDfGRUDqtmLJaBWQnMcnpB3hCRn2Celckisstx30BEPuT0iKwRk/UdEakSkT84vSUvi8iwGTip6kvaKwavqiZVNafuXaNVrjS2EuwhrMYpdyrgo2eM7FpM3MKlzvZDmBfv0TjCx4rRlfS2v+sV4NaMymeWqv6fs+0BjOXfe+nbuk0wXZjpY6er6t9VdT8mUsSlGHP2lcB7MF/Xnaq6BWMdGgFuBT4L7BSRdwOI4WSnjLSPHDKyPnIWyxGIyQ34VsyHG8BcjEHXKZrhxysmCP9XgQtV9WTgRmfTD4HbVfV0TA/Iz4+b8JY+sZVgL9REnbgB+ILj41SCMd2Pi8gFOI68HOkXlQ0vAW8SkTLnYbpquOQeKn1c79+Ajzq+W4jIRBGpdna/D9O1eTV9m6f/DfgX5zyIyBxnvA/MuONn6akEv+D8IiJ/Ah4DajEtzysxHx/Xi8gajEtBeiz288DHnPX3chx95CzjmnTPySuYD7H0h+Fu7Tu7zIWYnIFNAKqaNvy6CBPubTXGT65YTGJpS46wfoJ9oKqvOy/Z92H6/x8RkVcwY1ObnH2aReQ5xyjkr5hI90c7734xMQNfxFg1bsSEEcopmderqr92WlirxPi7dWFCGzWo6gbngd2vqn2F//o5ZozwNTEHN2IqNDAV3iWquk1EdmO6YNMRI36K8Rk6BMSBf1HVnYw+HznL+CXdc9KN83wE+9lf6An/lokLOEt7AiqMCDLElFgZx08DzlbV3/ax7XxMEPS3Z6y7m4zYscMho/RyQxvEeW/BSdeV1f72I/r4IiKFauJQeoAHgV+o6oO5lstisfRPXy9sp6L4s2b4torILkxWkRrM832W88FcrqotIvJbjJ/rd539l6jq6uMh7yCPP59eFd1A20aoEpxGL/1med5bGEQlaLtDjz+3OF0h6zFO6qM1D5rFYhkiakLjfQuTTWQN8ANn0w3AaY7BzEbgE8dLJhG5XEReFJHXReQfIlLjrH+T4/6x2tlWhHEBW+6su2ngMx9Rzi4xLlUvOdMsZ/10EVnlGAR9I2P/rNzQnH2PcN9y1n9VRDaLyD8w47TZk2vzVDvZyU52stPwTmS4dGSsK6On9++fgO87848A5zjzhZhhsvMxrbC+zn3ENg7PDbkL+Koz/6H0vpgx0A8585+ix00rWze0/ty3lmIMlQKYQBrbcHJWZjPZMUGLxWIZH0zCpACrw1iE73TWPwf8QETuAf6oqvtEBjRk728MLXP9vRm/tzvz59BjDPhr4DZnPu2Gdh6Qon83tEz3LTAV9myMgeKDqhoCEJPbMmtsd6jFYrGMD36ECc5xEvDPOK5eqvodTMswH3hBekIU9kczplWZSTnQlLGsWcynydYNbSD3rSEbt9hK0GKxWMYHJfSktOrOhSkiM1V1narehnEBmcfALmBbgQmOFXk6jdjJGOv5NO/N+F3lzD+HsbgHU/FlypWNG1p/7lsrgHeKSL4znnn5wGo4HNsdarFYLGOPgJj4uml+gInXeb+I7AdewIQ0BPisU/kkMW5bf8V0SyYco567VTXdpYmqRkXkA8BdYlJqxYF/UuNznMYvIi9iGlrpNGE3Ar8VkRuBP2Tsm5Ubmqp+sS/3LVV9TUR+5xy7mx7Xq6ywLhIWi8ViGTbSbiLqBAoY7djuUIvFYrGMW2xL0GKxWCzjFtsStFgsFsu4xVaCFovFYhm32ErQYrFYLOMWWwlaLBaLZdxiK0GLxWKxjFtsJWixWCyWccv/BxOovRTZGGMvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x504 with 36 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig =  pd.plotting.scatter_matrix(df, figsize = (7,7), diagonal='kde')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot above, we can see there is a positive correlation between rating and installs. According to it the more installs the higher the rating will be .\n",
    "We can get a feel from the plot, last updated time, size and reviews have impacts on ratings. A larger app can often get a higher rating while apps that haven't been updated for a while are unlikely to get a lower ratings.\n",
    "\n",
    "And there are also some other correlations, such as, the later the apps updated the bigger size of the apps will be."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Installs(1000000)')"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df['Rating'], df['Installs'])\n",
    "plt.xlabel('Rating')\n",
    "plt.ylabel('Installs(1000000)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Last Updated(year)')"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TM91aWURmZtbxmkkeZ0bEn5B0lJPeZbedc5CYmVmbNZM8XpPUQzrXuqQzSa5EzMxsnGpmtNXHgEeAWZJWkUwEdVVRJUmzgM8Ap5HMDHhXRHxC0mSSmyzOAbYB74uIlyWdTfIR2XnATRFxR01b24CDQD/werOTlYwXrczY164ZDFvVStytzCSYN8Nh0UyCrcxSWDTLZd4sc2ff9GX+rf/I0hO7xHO3vWfged4Mh506695YnUkw73Uqev/kvQeKZqmsQuE0tACSfgo4n2Rfn4qIf22iznRgekQ8LWkCyWyEi0kSz76IWCFpOXBKRFwvaSrJN9cXk3whcXDymN/MdjPjZSbBtZt2csOazfQdPjJ9ZU93F7dfdm7hybSVuu3UStyD/wAzC8+czOXzZ+e2e/Pazdz31NC5z648fzbrn/3BUX/4mewEUBTz4MSROWvqSUydcELDmFd98IIhJ6SMgBO6dFTiyGQJZPBJJ3OcqFue2bbikronymaX5+nUuq22nfc6TZ1wfO77J+99u+Ff9jV8DcsmkDIzCTYz2uoLwALgKxHxpWZP4BGxO7tte0QcBLYAM0nmB7k3Xe1ekmRBROyJiG+R9q1Yc1au23rUCQmg73A/K9dtrbRuO7USd70/wKy8qN3VG3bUrbt6w466f/jAQHlR2/USR1aeFzNQ94SUlddLHNSUN0oQeYnDhifvdSp6/+S9B9r1GjbT5/EXwBXA85JWpB8vlSJpDjAP2ABMi4jdkCQYYGoTTQTwd5I2Sro6ZztXS+qV1Lt3796yYY5Ju/bXnSW4YflI1W2nquIuare/wVV6o/IybZuNNYXJIyK+GhFXkPRFbAPWS/pfkj4gqbuovqSTgQeAayPiwDDjXBgR5wHvBn5f0i82iPWuiJgfEfOnTJkyzE2NLTMm9ZQqH6m67VRV3EXtdqn+IMNG5WXaNhtrmrnyyPo8rgJ+B9gEfIIkmawvqNdNkjhWRcSatPiltD8k6xfZU7T9iNiV/t4DfBF4ezNxjwfLFs2lp7vrqLKe7i6WLZpbad12aiXuhWdOblhe1O6SBfXvB7pkwSymTTi+7rKsvKjts6aeVLf+WVNPyo0ZGo+bF0nfRj1Z+XENKjcqt+HLe52K3j9574F2vYbN9HmsAb4BvAn41Yh4b0R8LiL+C3ByTj0B9wBbIuLOmkUPAUvTx0uBBwu2f1La4Y6kk4D/CDxTFPd4sXjeTG6/7FxmTupBwMxJPU13eLdSt51aiXvVBy8Y8oeYdTwXtXvr4nO58vzZA1caXRJXnj+bWxefy4abLh5yAqgdLVPU9vrrLhySQLLRVnkxQzJaZ/B5IhvF89xt7xmSQGpHW3339kuGnGSyjtbaUUK1svJWlo/Fuq22nfc6Fb1/8t4Dea9hlQpHW0l6Z0R8rXTD0jtIks5mkqG6ADeS9HvcD8wGtgOXR8Q+SacBvcDEdP1XgXOAU0muNiAZWvzZiLitaPvjZbSVmdlIKTPaquH3PCS9IyK+2ShxSJoIzI6IulcBEfFNGl+pXVRn/R8Ap9dZ9wDwc43iNDOz0Zf3JcFfl/QnJF8Q3AjsJZmG9t8Bv0TynYwPVx6hmZl1nIbJIyL+QNIpwG+QTD07nWRiqC3A/0yvLMzMbBzKvT1JRLwM3J3+mJmZAfl9HtflVRw0gsrMzMaRvCuPCenvucC/JxliC/CrwNerDMrMzDpbXp/HLQCS/g44L70/FZI+Bnx+VKIzM7OO1Mw3zGcDtXfteo3kdupmZjZONTOfx18D/yDpiyQ3KPw1knk6zMxsnCpMHhFxm6SvAP8hLfpARGyqNiwzM+tkTd0YkeS+Vgci4hPAi5LOqDAmMzPrcM3cGPGjwPXADWlRN3BflUGZmVlna+bK49eA9wI/goHbo0/IrWFmZse0ZpLHa5Hcejdg4LboZmY2jjWTPO6X9D+BSZI+CHwV+FS1YZmZWSdrZrTVHZIuJrk1+lzgjyMidwZBMzM7tjXTYf7fImJ9RCyLiI9ExHpJ/62JerMkPSZpi6RnJV2Tlk+WtF7S8+nvU9LysyU9KemQpI/Uaa9L0iZJXxrOjpqZ2chp5kuCF5OMtqr17jplg70OfDgink6nkd0oaT3JXOiPRsQKScuB5Wlb+4APAYsbtHcNye3gJzYR87Cs3bSTleu2smt/HzMm9bBs0dyOn5K1SKv71K5jUrTdquJqpd2iujev3czqDTvoj6BLYsmCWdy6+NymlhfVvfjOx3l+z48GnmdT2AKcfdOX+bf+IzOG1k5DW9T2Wz/6CAcO9Q+sO/GELr5zy7sGni+4bT0vHTxyA4raqVMB5ix/eMhxyqZlLYorr27esirrApyx/GFq51/NppItWgZwxd1P8sT39g08r51OOO81hPz3V167VWk4Da2k3wV+D3gL8L2aRROAJyLiylIbkh4EPpn+XBgRuyVNBx6PiLk1630MeDUi7qgpOx24F7gNuC4ifqVoe2WnoV27aSc3rNlM3+Ejfyg93V1jYk7vRlrdp3Ydk6LtVhVXK+0W1b157Wbue2r7kHrZHOh5y4HcuoNPOpmzpp7Ejh/++KgTdCY7Uedt96FNO49KHJksgQxOHJksgdQ7CdduPy+uvLp5tq24pLK621ZcMiQ5ZLIpUxste2HFJUNO8JmFZ05mz8FDDV/D9dddmPv++nzv9obtlk0gZaahzfvY6rMkd9B9KP2d/fz8MBLHHGAeyfzl0yJiN0D6e2oTTfwp8IccmQt9xK1ct/WoFwag73A/K9dtrWqTlWt1n9p1TIq2W1VcrbRbVHf1hh1162XlecuL6tY76WTl9U7QwEB5Xtv1EgcwUF4vceSV19t+s+WdolF0UbAMqHuCz8rzXkPIf3/ltVulhskjIl6JiG0RsSQivk8yi2AAJ0ua3ewGJJ0MPABcGxEHygYo6VeAPRGxsYl1r5bUK6l37969pbaza39fqfKxoNV9atcxKdpuVXG10m5R3f4GV/hZed7yorqtqLJtGzmdeH5qpsP8VyU9D7wA/D2wDfhKM41L6iZJHKsiYk1a/FL6cRXp7z0FzSwE3itpG/A3wDsl1f2Ge0TcFRHzI2L+lClTmglxwIxJPaXKx4JW96ldx6Rou1XF1Uq7RXW7pLrLs/K85UV1W1Fl2zZyOvH81Mz3PG4Fzgf+OSLOAC4CniiqJEnAPcCWQbMOPgQsTR8vBR7MayciboiI0yNiDvB+4GtlPzZrxrJFc+np7jqqrKe7i2WL5jao0fla3ad2HZOi7VYVVyvtFtVdsmBW3XpZed7yorpnTa3/vd2zpp7EiV31k0BWntf2xBO66i7LyqdNOL7u8kbl9bbfbHmnaBSdCpZB0gdRz8IzJ+e+hpD//sprt0rNJI/DEfFD4Cck/UREPAa8rYl6C4HfIrlS+Hb68x5gBXBxejVzcfocSadJehG4DrhZ0ouSKhtZNdjieTO5/bJzmTmpBwEzJ/WM6c5yaH2f2nVMirZbVVyttFtU99bF53Ll+bOPutLIOryLlhfVXX/dhUNOPllH63O3vWfICbl2VFNe29+55V1DEkjtaKsNN108JFHUjraqHaFUa9uKSwrjyqubt6zKupB0fA9OElmHeN4ygFUfvGDICT3r1M57DSH//ZXXbpUajrYaWEH6Ksnw2duBU0k+Zvr3EfELlUbWorKjrczMxruRGm2VuZSks/wPgEdIhu3+6vDDMzOzsa6Z25PUjiG7t8JYzMxsjGiYPCQdpPHQZSJi1PojzMysszRMHhExAUDSx4EfkMxlLuAKPJ+Hmdm41kyfx6KI+P8i4mBEHIiI/wH8etWBmZlZ52omefRLuiK9q+1PSLoCqH/fAjMzGxeaSR7/B/A+4CWSYbqXp2VmZjZONTPaahvJcF0zMzOguXtbvUXS30raK2mPpAclvWU0gjMzs87UzMdWnwXuB6YDM4DPA6urDMrMzDpbM8lDEfHXEfF6+nMfOd//MDOzY18z09A+lk4X+zckSeM3gYclTQaIiGpnHDEzs47TTPL4zfT3/zmo/D+TJBP3f5iZjTPNjLY6YzQCMTOzsSPv3laXDSoK4F+Bb0fEwUqjMjOzjpZ35VHvtuuTgbdK+u2I+FpFMZmZWYfLuzHiB+qVS3ozydDdBXkNS5oFfAY4DXgDuCsiPpF2tH8OmEMyH/r7IuJlSWcDnwbOA26KiDvSdk4Evg6ckMb7hYj4aIl9NDOzEdZMh/lRIuL7krqbWPV14MMR8bSkCcBGSeuBq4BHI2JFOoprOXA9sA/4EMmshbUOAe+MiFfT7X5T0lci4qmysdv4sHbTTlau28qu/X3MmNTDskVzO2I64ZvXbmb1hh30R9AlsWTBrIGpZCE/7qJ9ymv7iruf5InvHRkUOXiK0ovvfJzn9xyZtqd2+tMirbRdtN23fvQRDhw6chu92ilw5yx/eEgstVPInrH84aO+T1A7HWzesmbaztvnouNR9B4YrqrazVM4De2QCtJc4K8iotQEuZIeBD6Z/lwYEbslTQcej4i5Net9DHg1u/IY1MabgG8CvxsRG/K252lox6e1m3Zyw5rN9B0+ctLp6e5q+3z0N6/dzH1PbR9Sns0Xnhc3kLtPeW2/sPfVo05mmeykNvgEnmkmgQw+UZZpG8jd7uDEkZl4Qlfd8sy2FZcMSQ6ZbH7xRsteWHFJ3cRR23bePgO5x6PoPTBcI9nuiExDm96S5KFBP98EvgxcVzKgOcA8YAMwLSJ2A6S/pzZRv0vSt0luzLi+KHHY+LVy3dajTrIAfYf7Wblua5siSqzesCO3PC/uon3Ka7veyQyOnOTqncDzyuu1MZy2i7bbKEHkJY5Mo3+Ho2BZM/L2ueh4FL0HhquqdovkfWw1+D//AH4IPB8RrzW7AUknAw8A10bEAUlFVYaIiH7gbZImAV+U9LMR8UydbV0NXA0we/bs0tuxsW/X/r5S5aOlv8EVflY+nLizZUVtW2eo6nVq1+uf12H+9602nvZRPACsiog1afFLkqbXfGy1p9n2ImK/pMeBdwFDkkdE3AXcBcnHVq3Gb2PPjEk97Kxzwp0xqacN0RzRJdX9Y+5K/5kqijtvWV7bTiCdo+g90GntFmnm3lbDouQS4x5gS0TcWbPoIWBp+ngp8GBBO1PSKw4k9QC/DDw38hHbsWDZorn0dHcdVdbT3cWyRXMb1BgdSxbMyi3Pi7ton/Lazj6LHywrz/ofBmtUXq+N4bRdtN2JJ3TVXd6ovFajU6YKljUjb5+LjkfRe2C4qmq3SOkO86Yblt4BfAPYTDJUF+BGkn6P+4HZwHbg8ojYJ+k0oBeYmK7/KnAOyZDee4EukmR3f0R8vGj77jAfvzzayqOtPNpqeO2W6TAvTB6SromITxSVdRonDzOzckZktFWNpXXKrioVkZmZHVPy7m21hGSu8jMkPVSzaCLJqCszMxun8obq/i9gN3Aq8P/WlB8EvlNlUGZm1tnyhup+H/i+pF8G+iLiDUk/DZxN0gluZmbjVDN9Hl8HTpQ0E3gU+ADwV1UGZWZmna3ZOcx/DFwG/FlE/BrJEFozMxunmkoeki4ArgCyAdCl78ZrZmbHjmaSxzXADcAXI+JZSW8BHqs2LDMz62TNzGH+dZJ+j+z5v5DMu2FmZuNUYfKQNAX4Q+BngBOz8oh4Z4VxmZlZB2vmY6tVJDciPAO4hWTq2G9VGJOZmXW4ZpLHT0XEPcDhiPj7iPjPwPkVx2VmZh2smVFTh9PfuyVdAuwCTq8uJDMz63TNJI9bJf0k8GHgz0jubXVtpVGZmVlHa2a01ZfSh68AvwQgycnDzGwcG+5MgteNaBRmZjamDPeb4oWzNkqaBXwGOI1kZsC7IuITkiYDnyOZIXAb8L6IeFnS2cCngfOAmyLijrx2hhl3rk6dgc7Gh1bef0Uz2FW13VZmR2y17eHWXXDbel46+NrAutMmHM+Gmy5uqt0i4+kcMqxpaCVtj4jZBetMB6ZHxNOSJgAbgcUkE0nti4gVkpYDp0TE9ZKmAm9O13m5JnnUbSci/ilv+2VnEly7aSc3rNlM3+Ej0172dHdx+2XnHrMvvnWOVt5/gxNHppkE0sp2b167mfue2j6k/MrzZ3Pr4nMrbXu4ddc/+4OjEkdmJBLIsXAOGZGZBCWUkyHHAAANkklEQVQdlHSgzs9BYEZRwxGxOyKeTh8fBLYAM4FLSeYkJ/29OF1nT0R8iyOju4raGVEr12096kUH6Dvcz8p1W0d6U2ZDtPL+q5c48spHarurN+zILa+y7eHWrZc4gIblZYy3c0jefB4TRmojkuYA84ANwLSI2J1uY3d6xTGcduotvxq4GmD27NwLoyF27e8rVW42ktr1/mtlu/0NPrXIyqtsu6q6rRhv55Dhdpg3TdLJwAPAtRFxoMp2IuKuiJgfEfOnTJlSqv0Zk3pKlZuNpHa9/1rZbpfqd31m5VW2XVXdVoy3c0ilyUNSN8kJf1VErEmLX0r7MbL+jD3DbGdELVs0l57urqPKerq7WLZobhWbMztKK++/hWdOLlU+UttdsmBWbnmVbQ+37rQJx9dd1qi8jPF2DqkseUgScA+wJSLurFn0ELA0fbwUeHCY7YyoxfNmcvtl5zJzUg8CZk7qGVMdXTa2tfL+W/XBC4YkimZHW7Wy3VsXn8uV588e+I++SzqqQ7vKtodbd8NNFw9JFCM12mq8nUOGNdqqqYaldwDfIJnv/I20+EaS/or7gdnAduDyiNgn6TSgl+Qb7G8Ar5LMWPjWeu1ExJfztl92tJWZ2XhXZrRVZTMCRsQ3afx9kIvqrP8D6t8zK68dMzNrg8o7zM3M7Njj5GFmZqU5eZiZWWlOHmZmVpqTh5mZlebkYWZmpTl5mJlZaU4eZmZWmpOHmZmV5uRhZmalOXmYmVlpTh5mZlaak4eZmZXm5GFmZqU5eZiZWWlVziQ4S9JjkrZIelbSNWn5ZEnrJT2f/j4lLT9b0pOSDkn6yKC2/lLSHknPVBWvmZk1r7LJoIDXgQ9HxNOSJgAbJa0HrgIejYgVkpYDy4HrgX3Ah4DFddr6K+CTwGcqjNesrdZu2snKdVvZtb+PGZN6WLZobtNTmLZSt8p2b167mdUbdtAfQZfEkgWzBqaSLWo7b/kVdz/JE9/bN7Bus9PujoRW9ulYUuVMgruB3enjg5K2ADOBS4EL09XuBR4Hro+IPcAeSZfUaevrkuZUFatZu63dtJMb1mym73A/ADv393HDms0AhSefVupW2e7Nazdz31PbB573Rww8n//myblt5237873bj0ocAE98bx9X3P1k5QmklX061oxKn0d64p9HMn/5tDSxZAlm6mjEYNbJVq7bOnDSyfQd7mfluq2V1q2y3dUbdjQsL2o7b/ngxJFpVD6SWtmnY03lyUPSycADwLURcaDibV0tqVdS7969e6vclNmI2rW/r1T5SNWtst3+iIblRW1XtU+tamWfjjWVJg9J3SSJY1VErEmLX5I0PV0+HdgzUtuLiLsiYn5EzJ8yZcpINWtWuRmTekqVj1TdKtvtkhqWF7Vd1T61qpV9OtZUOdpKwD3Aloi4s2bRQ8DS9PFS4MGqYjAbK5YtmktPd9dRZT3dXSxbNLfSulW2u2TBrIblRW3nLV945uS67TYqH0mt7NOxpsrRVguB3wI2S/p2WnYjsAK4X9JvA9uBywEknQb0AhOBNyRdC5wTEQckrSbpZD9V0ovARyPingpjNxtVWYfqcEbqtFK3ynazEUiNRibltZ237cXzZrZttFUr+3SsUTT4DG+smz9/fvT29rY7DDOzMUPSxoiY38y6/oa5mZmV5uRhZmalOXmYmVlpTh5mZlaak4eZmZXm5GFmZqU5eZiZWWlOHmZmVpqTh5mZlebkYWZmpTl5mJlZaU4eZmZWmpOHmZmV5uRhZmalOXmYmVlpTh5mZlZaldPQzpL0mKQtkp6VdE1aPlnSeknPp79PScvPlvSkpEOSPjKorXdJ2irpu5KWVxWzmZk1p8orj9eBD0fE/wacD/y+pHOA5cCjEXEW8Gj6HGAf8CHgjtpGJHUBfw68GzgHWJK2Y2ZW19pNO1m44mucsfxhFq74Gms37Wx3SMecypJHROyOiKfTxweBLcBM4FLg3nS1e4HF6Tp7IuJbwOFBTb0d+G5E/EtEvAb8TdqGmdkQazft5IY1m9m5v48Adu7v44Y1m51ARtio9HlImgPMAzYA0yJiNyQJBphaUH0msKPm+YtpmZnZECvXbaXvcP9RZX2H+1m5bmubIjo2VZ48JJ0MPABcGxEHhtNEnbJosK2rJfVK6t27d+8wNmVmY92u/X2lym14Kk0ekrpJEseqiFiTFr8kaXq6fDqwp6CZF4FZNc9PB3bVWzEi7oqI+RExf8qUKa0Fb2Zj0oxJPaXKbXiqHG0l4B5gS0TcWbPoIWBp+ngp8GBBU98CzpJ0hqTjgfenbZiZDbFs0Vx6uruOKuvp7mLZorltiujYdFyFbS8EfgvYLOnbadmNwArgfkm/DWwHLgeQdBrQC0wE3pB0LXBORByQ9H8D64Au4C8j4tkK4zazMWzxvKRLdOW6reza38eMST0sWzR3oNxGhiLqdh+MefPnz4/e3t52h2FmNmZI2hgR85tZ198wNzOz0pw8zMysNCcPMzMrzcnDzMxKc/IwM7PSjtnRVpL2At8fZvVTgX8dwXBGiuMqx3GV47jK6cS4Wo3pzRHR1Desj9nk0QpJvc0OVxtNjqscx1WO4yqnE+MazZj8sZWZmZXm5GFmZqU5edR3V7sDaMBxleO4ynFc5XRiXKMWk/s8zMysNF95mJlZaeM6eUj6S0l7JD3TYLkk/XdJ35X0HUnndUBMF0p6RdK3058/rjqmdLuzJD0maYukZyVdU2eddhyvZuIa9WMm6URJ/yDpH9O4bqmzzgmSPpcerw3pjJudENdVkvbWHK/fqTqudLtdkjZJ+lKdZaN+rJqMq13Hapukzek2h9wBdlT+FiNi3P4AvwicBzzTYPl7gK+QzGZ4PrChA2K6EPhSG47VdOC89PEE4J9Jbpnf7uPVTFyjfszSY3By+ribZArm8wet83vAX6SP3w98rkPiugr4ZBveY9cBn633WrXjWDUZV7uO1Tbg1Jzllf8tjusrj4j4OrAvZ5VLgc9E4ilgUjYLYhtjaouI2B0RT6ePDwJbGDqXfDuOVzNxjbr0GLyaPu1OfwZ3MF4K3Js+/gJwUTqJWrvjGnWSTgcuAT7VYJVRP1ZNxtWpKv9bHNfJowkzgR01z1+kA05MwAXpxw5fkfQzo73x9CODeST/tdZq6/HKiQvacMzSjzu+TTLV8vqIaHi8IuJ14BXgpzogLoBfTz/u+IKkWXWWj7Q/Bf4QeKPB8rYcqybigtE/VpAk/L+TtFHS1XWWV/636OSRr95/Nu3+L+1pklsI/BzwZ8Da0dy4pJNJ5qW/NiIODF5cp8qoHK+CuNpyzCKiPyLeBpwOvF3Szw5apS3Hq4m4/haYExFvBb7Kkf/4KyHpV4A9EbExb7U6ZZUeqybjGtVjVWNhRJwHvBv4fUm/OGh55cfLySPfi0DtfxKnA7vaFAsAEXEg+9ghIr4MdEs6dTS2Lamb5AS9KiLW1FmlLcerKK52HrN0m/uBx4F3DVo0cLwkHQf8JKP4kWWjuCLihxFxKH16N/DzFYeyEHivpG3A3wDvlHTfoHXacawK42rDscq2uyv9vQf4IvD2QatU/rfo5JHvIeA/pSMXzgdeiYjd7QxI0mnZZ72S3k7yGv5wFLYr4B5gS0Tc2WC1UT9ezcTVjmMmaYqkSenjHuCXgecGrfYQsDR9/BvA1yLt7WxnXIM+G38vST9SZSLihog4PSLmkHSGfy0irhy02qgfq2biGu1jlW7zJEkTssfAfwQGj86s/G/xuJFsbKyRtJpkJM6pkl4EPkrSgUhE/AXwZZJRC98Ffgx8oANi+g3gdyW9DvQB76/6jyi1EPgtYHP6eTnAjcDsmthG/Xg1GVc7jtl04F5JXSTJ6v6I+JKkjwO9EfEQSdL7a0nfJfkv+v0Vx9RsXB+S9F7g9TSuq0YhriE64Fg1E1c7jtU04Ivp/0PHAZ+NiEck/V8wen+L/oa5mZmV5o+tzMysNCcPMzMrzcnDzMxKc/IwM7PSnDzMzKw0Jw+zYZDUn97R9BlJf5t9dyJn/UmSfq/m+QxJX6g+UrNqeKiu2TBIejUiTk4f3wv8c0TclrP+HJK7sg6+FYjZmOQrD7PWPUl60zlJJ0t6VNLTSuZbuDRdZwVwZnq1slLSHKVztiiZE2KNpEckPS/pT7KGJf22pH+W9LikuyV9ctT3zqyOcf0Nc7NWpd/UvojkG9AA/wb8WkQcSO+f9ZSkh4DlwM+mNyTMrkRqvY3kjsCHgK2S/gzoB/6IZH6Xg8DXgH+sdIfMmuTkYTY8PentUOYAG4H1abmA/5re5fQNkiuSaU2092hEvAIg6Z+ANwOnAn8fEfvS8s8DPz2SO2E2XP7Yymx4+tKriDcDxwO/n5ZfAUwBfj5d/hJwYhPtHap53E/yj13lkx2ZDZeTh1kL0quFDwEfSW8N/5Mkc0AclvRLJMkFko+dJpRs/h+A/13SKeltyH99pOI2a5WTh1mLImITSV/E+4FVwHxJvSRXIc+l6/wQeCId2ruyyXZ3Av+VZGbErwL/RDKDnlnbeaiuWQeTdHJEvJpeeXwR+MuI+GK74zLzlYdZZ/tY2jH/DPACozztsFkjvvIwM7PSfOVhZmalOXmYmVlpTh5mZlaak4eZmZXm5GFmZqU5eZiZWWn/Pz8tbCQYtIdQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df['Rating'], df['Last Updated'])\n",
    "plt.xlabel('Rating')\n",
    "plt.ylabel('Last Updated(year)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown in the plot, the higher the rating is the higher the installations will be. However the positive correlation seems not clear enough when comparing to other factors. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 Rating   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                  0.002\n",
      "Method:                 Least Squares   F-statistic:                     19.53\n",
      "Date:                Wed, 12 Jun 2019   Prob (F-statistic):           1.00e-05\n",
      "Time:                        17:20:50   Log-Likelihood:                -5910.0\n",
      "No. Observations:                7420   AIC:                         1.182e+04\n",
      "Df Residuals:                    7418   BIC:                         1.184e+04\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.1812      0.006    659.570      0.000       4.169       4.194\n",
      "Installs    3.357e-10    7.6e-11      4.419      0.000    1.87e-10    4.85e-10\n",
      "==============================================================================\n",
      "Omnibus:                     2848.285   Durbin-Watson:                   1.748\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            13299.863\n",
      "Skew:                          -1.826   Prob(JB):                         0.00\n",
      "Kurtosis:                       8.448   Cond. No.                     8.49e+07\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.49e+07. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "\n",
    "outcome_1, predictors_1 = patsy.dmatrices(\"Rating ~ Installs\", df)\n",
    "mod_1 = sm.OLS(outcome_1, predictors_1)\n",
    "res_1 = mod_1.fit()\n",
    "print(res_1.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we have created a linear model to predict rating from installs (using df as data).\n",
    "We used patsy.dmatrices to create the design matrices, calling the outputs outcome_1, predictors_1.\n",
    "We then created an OLS model (sm.OLS) using outcome_1 and predictors_1. Call it mod_1.\n",
    "Finally we fitted the model, assigning it to res_1.\n",
    "Based on the R-squared (using alpha value of 0.01), we can safely conclude that installs do have a positive correlation to the rating of the phone apps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "                       Rating\n",
       "Installs   Reviews           \n",
       "1          2         5.000000\n",
       "           4         5.000000\n",
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       "50         1         3.125000\n",
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       "           3         4.740000\n",
       "           4         4.900000\n",
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       "           8         5.000000\n",
       "           9         4.700000\n",
       "           12        4.600000\n",
       "           14        5.000000\n",
       "           15        4.800000\n",
       "...                       ...\n",
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       "1000000000 2129689   4.200000\n",
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       "           3419249   4.000000\n",
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       "           4604324   4.300000\n",
       "           4604483   4.300000\n",
       "           8021623   4.400000\n",
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       "           9231613   4.300000\n",
       "           9235155   4.300000\n",
       "           9235373   4.300000\n",
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       "           69109672  4.400000\n",
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       "\n",
       "[5359 rows x 1 columns]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pv = pd.pivot_table(df, values='Rating', index=['Installs', 'Reviews'])\n",
    "pv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multivariate regression: \n",
    "\n",
    "In order to eliminate the impact of number of reviews, we use Multivariable regression with three variables Installs, Reviews, and Ratings. \n",
    "\n",
    "We create a linear model to predict ratings from both Installs and Reviews: \n",
    "\n",
    "We use `patsy.dmatrices` to create the design matrices, calling the outputs `outcome_2`, `predictors_2`\n",
    "\n",
    "We create an OLS model (`sm.OLS`) using `outcome_2` and `predictors_2`, and call it as `mod_2`.\n",
    "\n",
    "We fit the model, by assigning it to `res_2`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "outcome_2, predictors_2 = patsy.dmatrices( 'Rating ~ Installs+ Reviews', df )\n",
    "mod_2 = sm.OLS(outcome_2, predictors_2)\n",
    "res_2 = mod_2.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assertion statement to make sure the model is built successfully. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert isinstance(outcome_2, patsy.design_info.DesignMatrix)\n",
    "assert isinstance(predictors_2, patsy.design_info.DesignMatrix)\n",
    "assert isinstance(mod_2, sm.regression.linear_model.OLS)\n",
    "assert isinstance(res_2, sm.regression.linear_model.RegressionResultsWrapper)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the result from regression tests. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 Rating   R-squared:                       0.004\n",
      "Model:                            OLS   Adj. R-squared:                  0.004\n",
      "Method:                 Least Squares   F-statistic:                     15.11\n",
      "Date:                Wed, 12 Jun 2019   Prob (F-statistic):           2.82e-07\n",
      "Time:                        17:20:57   Log-Likelihood:                -5904.7\n",
      "No. Observations:                7420   AIC:                         1.182e+04\n",
      "Df Residuals:                    7417   BIC:                         1.184e+04\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      4.1802      0.006    658.970      0.000       4.168       4.193\n",
      "Installs    1.303e-10   9.86e-11      1.321      0.186    -6.3e-11    3.23e-10\n",
      "Reviews     1.117e-08   3.42e-09      3.266      0.001    4.47e-09    1.79e-08\n",
      "==============================================================================\n",
      "Omnibus:                     2852.043   Durbin-Watson:                   1.750\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            13347.137\n",
      "Skew:                          -1.828   Prob(JB):                         0.00\n",
      "Kurtosis:                       8.460   Cond. No.                     8.50e+07\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.5e+07. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "# Print out the results \n",
    "print(res_2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the model you we above (using alpha value of 0.01), we exame the p-values. \n",
    "\n",
    "According the OLS Regression Results above. The p-value associated with Installs is 0.186, while the p-value associtaed with Reviews is 0.001. \n",
    "\n",
    "We can safely conclude that Reviews do have a positive correlation to the rating of the phone apps, while Installs do not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- A Random Forest is an ensemble technique capable of performing both regression and classification tasks with the use of multiple decision trees and a technique called Bootstrap Aggregation\n",
    "- We used Skit-Learn's RandomForestRegressor as our model because of its high accuracy \n",
    "- Before using the model we must ensure all the data is in numerical format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "#before using regression model convert strings to numbers\n",
    "warnings.filterwarnings('ignore')\n",
    "encoder = LabelEncoder()\n",
    "df[\"Content RatingNum\"] = encoder.fit_transform(df[\"Content Rating\"])\n",
    "df['App'] = encoder.fit_transform(df['App'])\n",
    "df['Genres'] = encoder.fit_transform(df['Genres'])\n",
    "df['Type'] = pd.get_dummies(df['Type'])\n",
    "df[\"CategoryNum\"] = encoder.fit_transform(df[\"Category\"])\n",
    "df['Reviews'] = pd.to_numeric(df['Reviews'])\n",
    "df['Price'] = pd.to_numeric(df['Price'])\n",
    "df['Installs'] = pd.to_numeric(df['Installs'])\n",
    "df = df[pd.notnull(df['Last Updated'])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>App</th>\n",
       "      <th>Category</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Reviews</th>\n",
       "      <th>Size</th>\n",
       "      <th>Installs</th>\n",
       "      <th>Type</th>\n",
       "      <th>Price</th>\n",
       "      <th>Content Rating</th>\n",
       "      <th>Genres</th>\n",
       "      <th>Last Updated</th>\n",
       "      <th>Content RatingNum</th>\n",
       "      <th>CategoryNum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4720</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.1</td>\n",
       "      <td>159</td>\n",
       "      <td>19000000.0</td>\n",
       "      <td>10000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>9</td>\n",
       "      <td>2018</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1799</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>3.9</td>\n",
       "      <td>967</td>\n",
       "      <td>14000000.0</td>\n",
       "      <td>500000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>11</td>\n",
       "      <td>2018</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5916</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.7</td>\n",
       "      <td>87510</td>\n",
       "      <td>8700000.0</td>\n",
       "      <td>5000000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>9</td>\n",
       "      <td>2018</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4773</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.3</td>\n",
       "      <td>967</td>\n",
       "      <td>2800000.0</td>\n",
       "      <td>100000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>10</td>\n",
       "      <td>2018</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4658</td>\n",
       "      <td>ART_AND_DESIGN</td>\n",
       "      <td>4.4</td>\n",
       "      <td>167</td>\n",
       "      <td>5600000.0</td>\n",
       "      <td>50000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Everyone</td>\n",
       "      <td>9</td>\n",
       "      <td>2017</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    App        Category  Rating  Reviews        Size  Installs  Type  Price  \\\n",
       "0  4720  ART_AND_DESIGN     4.1      159  19000000.0     10000     1    0.0   \n",
       "1  1799  ART_AND_DESIGN     3.9      967  14000000.0    500000     1    0.0   \n",
       "2  5916  ART_AND_DESIGN     4.7    87510   8700000.0   5000000     1    0.0   \n",
       "4  4773  ART_AND_DESIGN     4.3      967   2800000.0    100000     1    0.0   \n",
       "5  4658  ART_AND_DESIGN     4.4      167   5600000.0     50000     1    0.0   \n",
       "\n",
       "  Content Rating  Genres  Last Updated  Content RatingNum  CategoryNum  \n",
       "0       Everyone       9          2018                  0            0  \n",
       "1       Everyone      11          2018                  0            0  \n",
       "2       Everyone       9          2018                  0            0  \n",
       "4       Everyone      10          2018                  0            0  \n",
       "5       Everyone       9          2017                  0            0  "
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We will select the depedent variables that will predict the variable Rating\n",
    "- Following the 80/20 rule split the data into a training set(80% of the data) and test set(20% of the data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "#select features used in model \n",
    "features = ['CategoryNum','Reviews', 'Size', 'Installs', 'Type', 'Price', 'Content RatingNum']\n",
    "X = df[features]\n",
    "Y = df['Rating']\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The most important parameter of the RandomForestRegressor class is the n_estimators parameter. This parameter defines the number of trees in the random forest.\n",
    "- We create many RandomForestRegressors and evaluate their performance using mean squared error between the predicted and actual values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create model using a range of different estimators \n",
    "model = RandomForestRegressor(n_jobs=-1)\n",
    "num = [300,320,330,350,370,390,410,430,450,470,490]\n",
    "trainScore= []\n",
    "testScore = []\n",
    "for i in num:\n",
    "    model.set_params(n_estimators = i)\n",
    "    model.fit(X_train, Y_train)\n",
    "    y_train_pred= model.predict(X_train)\n",
    "    y_test_pred = model.predict(X_test)\n",
    "    trainScore.append(mean_squared_error(Y_train, y_train_pred))\n",
    "    testScore.append(mean_squared_error(Y_test, y_test_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c3e1934a8>]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the effect of the estimators based on the model mean squared error\n",
    "plt.title(\"Effect of Estimators\")\n",
    "plt.xlabel(\"no. estimator\")\n",
    "plt.ylabel(\"Mean Squared Error\")\n",
    "plt.plot(num, testScore)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Given the above graph the mean squared error ranges from about 0.2550 to 0.2580\n",
    "- The mean squared error measures how close the predicted values are to the actual values \n",
    "- The smaller the means squared error, the closer we are to finding the line of best fit. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We now create a final RandomForestRegressor with the n_estimators set to 415"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = RandomForestRegressor(n_jobs=-1,n_estimators = 415, oob_score=True)\n",
    "model2.fit(X_train, Y_train)\n",
    "y_pred = model2.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The out of bag score, which measures the prediction error, is quite low indicating that the features chosen may not be the best features to predict the rating of an app "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0907201219114585"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.oob_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Even though our model may not be the most accurate we can use the feature importance of the model to discover which variables are the most relevant in predicting the target variable 'Rating'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16950663, 0.38627276, 0.29155913, 0.11191764, 0.00584621,\n",
       "       0.03489764, 0.        ])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_importances = model2.feature_importances_\n",
    "feature_importances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 7 artists>"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the feature importance\n",
    "featureName = ['Category','Reviews', 'Size', 'Installs', 'Type', 'Price', 'Content Rating']\n",
    "plt.bar(featureName, feature_importances,.15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Given the graph above we can see that 'Reviews' and not 'Installs' is the most relevant variable out of the ones we have in predicting the app Rating. This is consistent with our earlier results from the multivaritate regression that Reviews are more important than Installs to determine the Rating."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>actual</th>\n",
       "      <th>predicted</th>\n",
       "      <th>difference</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.7</td>\n",
       "      <td>4.430816</td>\n",
       "      <td>0.269184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.3</td>\n",
       "      <td>4.409796</td>\n",
       "      <td>-0.109796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.8</td>\n",
       "      <td>4.064490</td>\n",
       "      <td>-0.264490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.4</td>\n",
       "      <td>4.667347</td>\n",
       "      <td>-0.267347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.5</td>\n",
       "      <td>4.478163</td>\n",
       "      <td>0.021837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.4</td>\n",
       "      <td>4.147143</td>\n",
       "      <td>0.252857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.3</td>\n",
       "      <td>4.199898</td>\n",
       "      <td>0.100102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.2</td>\n",
       "      <td>4.048776</td>\n",
       "      <td>0.151224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.5</td>\n",
       "      <td>4.460000</td>\n",
       "      <td>-0.960000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3.7</td>\n",
       "      <td>3.952245</td>\n",
       "      <td>-0.252245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>4.1</td>\n",
       "      <td>4.002653</td>\n",
       "      <td>0.097347</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.0</td>\n",
       "      <td>4.033878</td>\n",
       "      <td>-0.033878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.3</td>\n",
       "      <td>4.457755</td>\n",
       "      <td>-0.157755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.1</td>\n",
       "      <td>3.983265</td>\n",
       "      <td>-0.883265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.4</td>\n",
       "      <td>4.369184</td>\n",
       "      <td>0.030816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.2</td>\n",
       "      <td>4.384490</td>\n",
       "      <td>-0.184490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.2</td>\n",
       "      <td>4.018776</td>\n",
       "      <td>0.181224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.0</td>\n",
       "      <td>3.825306</td>\n",
       "      <td>0.174694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.5</td>\n",
       "      <td>4.195714</td>\n",
       "      <td>0.304286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.3</td>\n",
       "      <td>4.206735</td>\n",
       "      <td>0.093265</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    actual  predicted  difference\n",
       "0      4.7   4.430816    0.269184\n",
       "1      4.3   4.409796   -0.109796\n",
       "2      3.8   4.064490   -0.264490\n",
       "3      4.4   4.667347   -0.267347\n",
       "4      4.5   4.478163    0.021837\n",
       "5      4.4   4.147143    0.252857\n",
       "6      4.3   4.199898    0.100102\n",
       "7      4.2   4.048776    0.151224\n",
       "8      3.5   4.460000   -0.960000\n",
       "9      3.7   3.952245   -0.252245\n",
       "10     4.1   4.002653    0.097347\n",
       "11     4.0   4.033878   -0.033878\n",
       "12     4.3   4.457755   -0.157755\n",
       "13     3.1   3.983265   -0.883265\n",
       "14     4.4   4.369184    0.030816\n",
       "15     4.2   4.384490   -0.184490\n",
       "16     4.2   4.018776    0.181224\n",
       "17     4.0   3.825306    0.174694\n",
       "18     4.5   4.195714    0.304286\n",
       "19     4.3   4.206735    0.093265"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff = Y_test - y_test_pred\n",
    "predicted = pd.DataFrame(np.c_[ Y_test, y_test_pred,diff])\n",
    "predicted.columns = ['actual','predicted','difference']\n",
    "predicted[0:20]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- As expected given our low model score, our predicted values differ significantly from the actual values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ethics & Privacy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We found this data set on Kaggle https://www.kaggle.com/datasets, a open source data set website. We read through the terms and condition and made sure that we have permission to use this data for this purpose.Since this data does not involve individuals’ data, there is not much concern regarding the privacy of the datasets we are dealing with. One privacy concern is that app creators may not want others knowing the amount of downloads or ratings their app has. We will not release all name of app that have a low average rating, in order to avoid potential negative impacts on those applications. \n",
    "\n",
    "There are biases in our Dataset. For example, there are 10k apps used in our dataset. There may be a host of other apps that if we chose to analyze would give us a different conclusion. Maybe in another dataset of 10k apps, more downloads correlates with a higher rating.The issue with our data set is that it only contain 10k entries. It does not contain all the apps in Google Play Store. \n",
    "\n",
    "We handle this issue by acknowledge the facts that it does not contain every app in Google Play Store. Those sample we have may not represent all the application. With the potential bias in mind, we are more careful about drawing a conclusion. All the analysis and conclusion we have might not suitable for the all the apps. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion & Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to perform data analysis on the data set, some preprocessing and data cleaning was required. However, some of this preprocessing could have affected our findings and results of our analysis. Dropping NaN values from the dataset could have skewed the dataset. In addition, while the number of reviews in the data was simply an integer value, the number of installs was an estimate with different cutoff thresholds which meant that it was not as specific in comparison to app ratings or number of reviews. \n",
    "In terms of normality, it is clear for our analysis that both the distribution of ratings as well as the distribution of reviews and installs were non normal and could therefore affect the accuracy of inference as a result. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset we got is all paired numerical data. And the dependent variable has multiple values for each value of an independent variable. Therefore we chose the scatter plot to show the relations among all the attributes. After showing the scatter plots, it turns out that, there is a positive correlation between rating and installs. However, a positive correlation is not very clear. Additionally, according to the plots between rating and other attributes, we can tell size, last updated time and reviews all have impacts on ratings. Although the number of installation alone is not enough to determine the rating, consider other factors together can lead to a better prediction.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we have also created a linear OLS model to predict rating from installs (using df as data). We have a total sample of 7420 different apps so it’s sufficient. We used patsy.dmatrices to create the design matrices, calling the outputs outcome_1, predictors_1. We then created an OLS model (sm.OLS) using outcome_1 and predictors_1. Call it mod_1. Finally, we fitted the model, assigning it to res_1.  Based on the model, F-statistic is 24.69, Prob (F-statistic) is 1.78e-80 and Log-Likelihood is -5703.4. Based on the R-squared value 0.057 (using alpha value of 0.01) and adjusted R-squared value 0.054, we can safely conclude that installs do have a positive correlation to the rating of the phone apps.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though, from the Linear Model Based on the R-squared (using alpha value of 0.01), we can safely conclude that installs do have a positive correlation to the rating of the phone apps. The conclusion is somewhat biased because we only consider the two factors \"Installs\" and \"Rating\". However, the correlation might come from some other factors like \"Reviews\". Therefore, we conducted Multivariable Regression Test to verify. From the Multivariable Regression Tests Results, and analyzing the p-values, we safely arrived the conclusion that Reviews do have a positive correlation to the rating of the phone apps, while Installs do not. From the different test results from different regression tests, we learned that to arrive a more well-rounded conclusion, we should take multiple factors into consideration. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the pitfalls of our hypothesis that was evident after looking at the dataset was that even though more downloads may not lead to a higher rating, it leads to a more impactful rating. For example, if an app has 1 download and that person gives it a 5 star rating, it is less trustworthy than if 500,000 people have downloaded it and given it a 4.5 rating. Even though the rating is less for the more downloaded app, it is more trustworthy. Also, we probably should have focused more on causality than correlation, since we cannot derive causation from correlation. For example, if we asked “does more downloads lead to higher ratings on the Google Play Store,” we may have gotten more relevant information out of this project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are still some potential improvements to be made.  Given the low out of the bag score after applying the Random Forest algorithm, it is likely we do not have a complete picture of what contributes to the average rating of an app. In the future to accurately predict the rating of an app, additional steps such as feature engineering to gather more relevant features is necessary."
   ]
  }
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