240309-AIML-Lecture-preprocessing_featureEngineering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Data Preprocessing and Feature Engineering "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Advantages of data preprocessing and feature engineering \n",
    "- it is the magic touch for AI and ML. Essential steps to the DS pipeline before deploying ML\n",
    "- Features (cols) are teh building blocks of ML prediction. Refining them will help improve the model performance and accuracy. \n",
    "- Feature engineering care create additional features that could help the model find hidden patterns in the data (feature extraction)\n",
    "- To perform good FE and DP: \n",
    "    - Technical expertise\n",
    "    - Domain knowledge\n",
    "    - Emperical process is stats and ML "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Techniques\n",
    "- Imputations: handling missing values\n",
    "- Outlier treatment: removing/replacing outliers\n",
    "- Binning: feature extraction by converting continuous values to ranges \n",
    "- Grouping: feature extraction using aggregation \n",
    "- Scaling: normalizastion of numerical ranes\n",
    "- Encoding: converting categorical variables into numerical \n",
    "- Dimensionality reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\chand\\AppData\\Local\\Temp\\ipykernel_64928\\555797462.py:1: DeprecationWarning: \n",
      "Pyarrow will become a required dependency of pandas in the next major release of pandas (pandas 3.0),\n",
      "(to allow more performant data types, such as the Arrow string type, and better interoperability with other libraries)\n",
      "but was not found to be installed on your system.\n",
      "If this would cause problems for you,\n",
      "please provide us feedback at https://github.com/pandas-dev/pandas/issues/54466\n",
      "        \n",
      "  import pandas as pd\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imputation\n",
    "use this when: \n",
    "- data is missing at random \n",
    "- missing would look like most of the observations\n",
    "\n",
    "Pros: \n",
    "- easy to implement \n",
    "- fast\n",
    "- can e applied in a production pipeline\n",
    "\n",
    "Cons: \n",
    "- Possibility of distorting the data distribution. the more missing values, the worse it gets \n",
    "    - when data is normally distributed, use the mean \n",
    "    - otherwise use median for skewed distributions \n",
    "\n",
    "Dropping Missing Values: \n",
    "- pros\n",
    "    - quick and easy\n",
    "    - preserves distributions \n",
    "- cons: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>Name</th>\n",
       "      <th>Score</th>\n",
       "      <th>University</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mark</td>\n",
       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>NaN</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>NaN</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex    NaN        NaN\n",
       "2   John   44.0        MSU\n",
       "3    Amy    NaN        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd    NaN        MSU"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "students = {\n",
    "    'Name' : ['Mark', 'Alex', 'John', 'Amy', 'Steve', 'Ally', 'Kelly', 'Todd'],\n",
    "    'Score' : [40, np.NaN, 44, np.NaN, 26, 39, 42, np.NaN],\n",
    "    'University' : ['UTC', np.NaN, 'MSU', 'MIT', 'CalTech', 'CalTech', 'CalTech', 'MSU'],\n",
    "}\n",
    "  \n",
    "# creating a Dataframe object\n",
    " \n",
    "df = pd.DataFrame(students)\n",
    "df\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38.2\n"
     ]
    }
   ],
   "source": [
    "#for numerical, use median or mean to replace missing values \n",
    "print(df['Score'].mean(skipna=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.0\n"
     ]
    }
   ],
   "source": [
    "print(df['Score'].median(skipna=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pip install scikit-learn as sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Score</th>\n",
       "      <th>University</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mark</td>\n",
       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>38.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex   38.2        NaN\n",
       "2   John   44.0        MSU\n",
       "3    Amy   38.2        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd   38.2        MSU"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#method 1: sklearn \n",
    "from sklearn.impute import SimpleImputer\n",
    "\n",
    "imputer = SimpleImputer(strategy='mean') #define the engine for using average for missing values \n",
    "\n",
    "df['Score'] = imputer.fit_transform(df['Score'].values.reshape(-1,1)) #values converts into numpy and reshape adjusts the orientation (it takes the vertical col rather than horizontal)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\chand\\AppData\\Local\\Temp\\ipykernel_64928\\1260901243.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.\n",
      "The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.\n",
      "\n",
      "For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.\n",
      "\n",
      "\n",
      "  df['Score'].fillna(df['Score'].mean(skipna=True),inplace=True)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Score</th>\n",
       "      <th>University</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mark</td>\n",
       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>38.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex   38.2        NaN\n",
       "2   John   44.0        MSU\n",
       "3    Amy   38.2        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd   38.2        MSU"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#method 2: using pandas - easier\n",
    "df['Score'].fillna(df['Score'].mean(skipna=True),inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\chand\\AppData\\Local\\Temp\\ipykernel_64928\\210662795.py:1: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.\n",
      "The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.\n",
      "\n",
      "For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.\n",
      "\n",
      "\n",
      "  df['Score'].fillna(df['Score'].median(skipna=True),inplace=True)\n"
     ]
    },
    {
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       "    <tr style=\"text-align: right;\">\n",
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       "      <th>Name</th>\n",
       "      <th>Score</th>\n",
       "      <th>University</th>\n",
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       "      <th>0</th>\n",
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       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>38.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex   38.2        NaN\n",
       "2   John   44.0        MSU\n",
       "3    Amy   38.2        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd   38.2        MSU"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Score'].fillna(df['Score'].median(skipna=True),inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\chand\\AppData\\Local\\Temp\\ipykernel_64928\\2106343497.py:2: FutureWarning: A value is trying to be set on a copy of a DataFrame or Series through chained assignment using an inplace method.\n",
      "The behavior will change in pandas 3.0. This inplace method will never work because the intermediate object on which we are setting values always behaves as a copy.\n",
      "\n",
      "For example, when doing 'df[col].method(value, inplace=True)', try using 'df.method({col: value}, inplace=True)' or df[col] = df[col].method(value) instead, to perform the operation inplace on the original object.\n",
      "\n",
      "\n",
      "  df['University'].fillna(df['University'].value_counts().index[0],inplace=True)\n"
     ]
    },
    {
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       "      <th></th>\n",
       "      <th>Name</th>\n",
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       "      <th>University</th>\n",
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       "      <td>Mark</td>\n",
       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>38.2</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex   38.2    CalTech\n",
       "2   John   44.0        MSU\n",
       "3    Amy   38.2        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd   38.2        MSU"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#For categorical values: can either fill with your manual entry or use the value with the highest frequency/count\n",
    "df['University'].fillna(df['University'].value_counts().index[0],inplace=True)\n",
    "df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Score</th>\n",
       "      <th>University</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Mark</td>\n",
       "      <td>40.0</td>\n",
       "      <td>UTC</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alex</td>\n",
       "      <td>38.2</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John</td>\n",
       "      <td>44.0</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Amy</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MIT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Steve</td>\n",
       "      <td>26.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Ally</td>\n",
       "      <td>39.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Kelly</td>\n",
       "      <td>42.0</td>\n",
       "      <td>CalTech</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Todd</td>\n",
       "      <td>38.2</td>\n",
       "      <td>MSU</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Name  Score University\n",
       "0   Mark   40.0        UTC\n",
       "1   Alex   38.2    CalTech\n",
       "2   John   44.0        MSU\n",
       "3    Amy   38.2        MIT\n",
       "4  Steve   26.0    CalTech\n",
       "5   Ally   39.0    CalTech\n",
       "6  Kelly   42.0    CalTech\n",
       "7   Todd   38.2        MSU"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#dropping missing values \n",
    "df.dropna(axis=0,inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## outlier treatment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Dictionary: Boston house prices dataset\n",
    "---------------------------\n",
    "**Data Set Characteristics:**\n",
    "Number of Instances: 506\n",
    "Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
    "    :Attribute Information (in order):\n",
    "        - CRIM     per capita crime rate by town\n",
    "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
    "        - INDUS    proportion of non-retail business acres per town\n",
    "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
    "        - NOX      nitric oxides concentration (parts per 10 million)\n",
    "        - RM       average number of rooms per dwelling\n",
    "        - AGE      proportion of owner-occupied units built prior to 1940\n",
    "        - DIS      weighted distances to five Boston employment centres\n",
    "        - RAD      index of accessibility to radial highways\n",
    "        - TAX      full-value property-tax rate per $10,000\n",
    "        - PTRATIO  pupil-teacher ratio by town\n",
    "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of black people by town\n",
    "        - LSTAT    % lower status of the population\n",
    "        - MEDV     Median value of owner-occupied homes in $1000's"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 14)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD  TAX  PTRATIO  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "        B  LSTAT  MEDV  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston_df = pd.read_csv('boston_sklearn.csv')\n",
    "print(boston_df.shape)\n",
    "boston_df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ugkg9b3WWoS9SygWQVj5SygWQVj7MpWxSyseQuagvpatUqjLXV5l8KrMcfZDScQKklU9tzKUq88sEQRAqG7xnzx5kZmaiRYsWSE5Oxty5c/H333/jwoUL2LFjB8aMGaNRUADASy+9hF69euGLL77A+PHjcevWLezbt0+cnp2dDVtbW+zevRuBgYFa1ztnzhzMnTu31Pj169fDxsamsukTEdV6dzKB8AQFprVWwcPO+MshKi47Oxuvv/460tPT4eDgUKl5dGpRKV5IvPDCC+jUqRM8PT3x66+/wtraWrdsdTBz5kyEhYWJwxkZGfDw8EC/fv0qvaHaKJVKREdHw9/fH+bm5vpItVbkIrV8pJSL1PJhLs9GPobM5eK9DIQnxKFr1654voH278fK5FOZ5eiDlI6T1PKpjbmor4joQudLP8U5OTmhefPmuH79Ovz9/ZGfn48nT57AyclJjElNTRXvaXF3d8fp06c1lqF+KkjbfS9qlpaWsLS0LDXe3NxcLwdPX8vRBynlAkgrHynlAkgrH+ZSNinlY4hc1A84KBSKCtdVXj66LEcfpHScAGnlU5tyqcq81epHJTMzEzdu3ED9+vXRvn17mJub4+DBg+L0xMRE3L59G35+fgAAPz8/JCQkIC0tTYyJjo6Gg4MDfH19q5MKERER1UI6tahMmzYNgwYNgqenJ+7du4dPPvkEZmZmeO211+Do6Ihx48YhLCwMzs7OcHBwwLvvvgs/Pz907twZANCvXz/4+vrijTfewKJFi5CSkoJZs2Zh4sSJWltMiIiIyLTpVKjcvXsXr732Gh4+fIh69eqha9euiIuLQ7169QAAERERkMvlCA0NRV5eHgICAvDNN9+I85uZmWHnzp2YMGEC/Pz8YGtri9GjR2PevHn63SoiIiKqFXQqVDZu3FjudCsrK0RGRiIyMrLMGE9PT+zevVuX1RIREZGJ4rt+iIiISLJYqBAREZFksVAhIiIiyWKhQkRERJLFQoWIiIgki4UKERERSRYLFSIiIpIsFipEREQkWSxUiIiISLJYqBAREZFksVAhIiIiyWKhQkRERJLFQoWIiIgki4UKERERSRYLFSIiIpIsFipEREQkWSxUiIiISLJYqBAREZFksVAhIiIiyWKhQkRERJLFQoWIiIgki4UKERERSRYLFSIiIpIsFipEREQkWSxUiIiISLJYqBAREZFksVAhIiIiyWKhQkRERJLFQoWIiIgki4UKERERSRYLFSIiIpIsFipEREQkWSxUiIiISLJYqBAREZFksVAhIiIiyWKhQkRERJJVrULl888/h0wmw+TJk8Vxubm5mDhxIlxcXGBnZ4fQ0FCkpqZqzHf79m0EBQXBxsYGrq6umD59OlQqVXVSISIiolqoyoXKmTNn8O233+KFF17QGD9lyhTs2LEDmzZtwtGjR3Hv3j2EhISI0wsKChAUFIT8/HycPHkSa9euxZo1azB79uyqbwURERHVSlUqVDIzMzFixAh8//33qFOnjjg+PT0dUVFRWLp0KXr37o327dtj9erVOHnyJOLi4gAA+/fvx6VLl/Dzzz+jbdu2CAwMxPz58xEZGYn8/Hz9bBURERHVCoqqzDRx4kQEBQWhb9+++PTTT8Xx8fHxUCqV6Nu3rzjOx8cHjRs3RmxsLDp37ozY2Fi0bt0abm5uYkxAQAAmTJiAixcvol27dqXWl5eXh7y8PHE4IyMDAKBUKqFUKquyCeL8xf83JinlAkgrHynlAkgrH+ZSNinlY8hc1JfRVSpVmeurTD6VWY4+SOk4AdLKpzbmUpX5dS5UNm7ciHPnzuHMmTOlpqWkpMDCwgJOTk4a493c3JCSkiLGFC9S1NPV07RZuHAh5s6dW2r8/v37YWNjo+smlBIdHV3tZeiLlHIBpJWPlHIBpJUPcymblPIxRC53MgFAgePHj+OWXdXz0WU5+iCl4wRIK5/alEt2drbO8+hUqNy5cwfvv/8+oqOjYWVlpfPKqmrmzJkICwsThzMyMuDh4YF+/frBwcGhystVKpWIjo6Gv78/zM3N9ZFqrchFavlIKRep5cNcno18DJnLxXsZCE+IQ9euXfF8A+3fj5XJpzLL0QdDH6ebD7OQlVcAAMjJycbNG9c0pheoCpCQkIDWrVvDTGEmjm/i3QzW1kV/GNtamqGJi22N51obz2H1FRFd6FSoxMfHIy0tDS+++KI4rqCgAMeOHcPXX3+Nffv2IT8/H0+ePNFoVUlNTYW7uzsAwN3dHadPn9ZYrvqpIHVMSZaWlrC0tCw13tzcXC8HT1/L0Qcp5QJIKx8p5QJIKx/mUjYp5WOIXBQKhfh/ResqLx9dlqMPhtg3SQ+y4L/shDicl3IdKWsnV2pe99HLYOneVBw+PK0nvOrWfLEC1K5zuCrz6lSo9OnTBwkJCRrjxowZAx8fH3zwwQfw8PCAubk5Dh48iNDQUABAYmIibt++DT8/PwCAn58fPvvsM6SlpcHV1RVAUVOSg4MDfH19dd4AIiKiysjKU0GmyMD0wPrwcLZBXp49/g79SSOmsLAAiVcS0cKnBeTyf1pUGno0hqWlFe48ysbiPcnIymOXGoaiU6Fib2+PVq1aaYyztbWFi4uLOH7cuHEICwuDs7MzHBwc8O6778LPzw+dO3cGAPTr1w++vr544403sGjRIqSkpGDWrFmYOHGi1lYTIiIifTF3OoUV1w+WH+QOnHiyQ3Pco+LL6ANggN5zI+2q9NRPeSIiIiCXyxEaGoq8vDwEBATgm2++EaebmZlh586dmDBhAvz8/GBra4vRo0dj3rx5+k6FiIhIg/JJJywJeh3ertrvEFapVDhx/ARe7vqyePmruBtpmXhv3Y2aTpOKqXahcuTIEY1hKysrREZGIjIyssx5PD09sXv37uqumoiISCeCygFeDi3g6+KodbpSqUSSIgktnVtqvZ+iMDcdgup+TadJxfBdP0RERCRZLFSIiIhIslioEBERkWSxUCEiIiLJ0vtTP0RERFKUoyzqkfbC3+llxmTl5OHsfcD91mPYWpfuMuN6WmaN5UfasVAhIiKTcOP/i4wPtyZUEKnAT9dLv8+uOFtL/vo0FO5pIiIyCf2eL3pNi7erHazNzbTGJCanY+rmBCwZ0hot6mt/hNnWUmGw7vOJhQoREZkIZ1sLDH+pcbkxKlVR1/je9WzRqqH2QoUMizfTEhERkWSxUCEiIiLJYqFCREREksVChYiIiCSLhQoRERFJFgsVIiIikiwWKkRERCRZLFSIiIgA5OfnY13UCjyKXol1USuQn59v7JQILFSIiIgwY8YM2NjYIHz+x3h6bifC538MGxsbzJgxw9ipmTz2TEtERCZtxowZWLx4canxBQUF4vhFixYZOi36f2xRISIik5SdnY24uDiEh4eXGxceHo4nT54YJikqhYUKERGZpCtXrsDPzw+CIJQbJwgC5syZY5ikqBQWKkREZJJ8fHzwwgsviMOWlpYa04sPnzp1ymB5kSbeo0JERCbJxsYGGRkZ4nCfPn3w3HPP4erVq2jevDn++usv7N69GwCQkpJirDRNHgsVIiIyWTY2NgAAmUyGvXv3orCwEACwf/9+yOVyyGQyCIIgxpHh8dIPERGZLHd3dwBF96GoixS1wsJC8f4VdRwZHgsVIiIyWe3bt9drHOkfCxUiIjJZ6enpeo0j/eM9KkREtYxMkYGkjETIrey0TlepVLinuofLjy5DodD+ayApIxMyRYbWabXJxYsX9RpH+sdChYioljF3OoWPTi+oMO6bvd9UsJw+AAboKSuiqmGhQkRUyyifdMKSoNfh7Vp2i8qJ4yfwcteXy2xRuZGWiffW3ajJNCUhODgYJ06cqFQcGQcLFSKiWkZQOcDLoQV8XRy1TlcqlUhSJKGlc0uYm5trjSnMTYegul+TaUrCO++8g+nTp1cqjoyDN9MSEZHJioyM1Gsc6R8LFSIiMlk///yzXuNI/1ioEBGRyVK/Fblx48bIyclBeHg4BgwYgPDwcOTk5MDDw0MjjgyPhQoREZmsevXqAQBSU1Mhk8nQpk0b+Pj4oE2bNpDJZEhLS9OII8PjzbRERGSy/P398fvvvyMvLw9WVlbi+KVLl5aKI+NgiwoREZmsfv366TWO9I+FChERmaxu3brpNY70T6dCZcWKFXjhhRfg4OAABwcH+Pn5Yc+ePeL03NxcTJw4ES4uLrCzs0NoaChSU1M1lnH79m0EBQXBxsYGrq6umD59OlQqlX62hoiISAcHDx4Ufy7Z+V3xPmaKx5Fh6VSoNGrUCJ9//jni4+Nx9uxZ9O7dG4MHDxbfgTBlyhTs2LEDmzZtwtGjR3Hv3j2EhISI8xcUFCAoKAj5+fk4efIk1q5dizVr1mD27Nn63SoiIqJKUN+L0qFDBwiCoDFNEATxrckl71khw9HpZtpBgwZpDH/22WdYsWIF4uLi0KhRI0RFRWH9+vXo3bs3AGD16tVo2bIl4uLi0LlzZ+zfvx+XLl3CgQMH4ObmhrZt22L+/Pn44IMPMGfOHFhYWOhvy4iIiCqgfuz47NmzCAoKwnPPPYfExES0aNECf/31F3bt2qURR4ZX5ad+CgoKsGnTJmRlZcHPzw/x8fFQKpXo27evGOPj44PGjRsjNjYWnTt3RmxsLFq3bg03NzcxJiAgABMmTMDFixfRrl07revKy8tDXl6eOJyRUfRGT6VSCaVSWdVNEOetzjL0RUq5ANLKR0q5ANLKh7mUTUr5GDIX9aV0lUpV5voqk09llqMPxj5O7dq1w9mzZ2FhYYGEhASxMNm/fz8aN24MCwsL5Ofno127dgbP0dj7pjh95VKV+XUuVBISEuDn54fc3FzY2dlh27Zt8PX1xfnz52FhYQEnJyeNeDc3N6SkpAAAUlJSNIoU9XT1tLIsXLgQc+fOLTV+//79sLGx0XUTSomOjq72MvRFSrkA0spHSrkA0sqHuZRNSvkYIpc7mQCgwPHjx3FL+zsJK5WPLsvRB2MdJ3d3dwBAfn4+bt++rTGt+LC7uzt2795t0NzUatM5nJ2drfM8OhcqLVq0wPnz55Geno7Nmzdj9OjROHr0qM4r1sXMmTMRFhYmDmdkZMDDwwP9+vWDg4NDlZerVCoRHR0Nf3//Ml/MZShSykVq+UgpF6nlw1yejXwMmcvFexkIT4hD165d8XwD7d+PlcmnMsvRB2Mfp8pe0vH29saAAQNqNpkSjL1vaiIX9RURXehcqFhYWKBp06YAgPbt2+PMmTP48ssvMWzYMOTn5+PJkycarSqpqalixeru7o7Tp09rLE/9VJA6RhtLS0tYWlqWGm9ubq6Xg6ev5eiDlHIBpJWPlHIBpJUPcymblPIxRC7qJ1cUCkWF6yovH12Wow/GOk4PHz6sdJyxzqPadA5XZd5q96NSWFiIvLw8tG/fHubm5hqPcCUmJuL27dvw8/MDAPj5+SEhIUHskhgoakZycHCAr69vdVMhIiLSyYMHD8SfAwMDERwcjNatWyM4OBiBgYFa48iwdGpRmTlzJgIDA9G4cWM8ffoU69evx5EjR7Bv3z44Ojpi3LhxCAsLg7OzMxwcHPDuu+/Cz88PnTt3BlDUs5+vry/eeOMNLFq0CCkpKZg1axYmTpyotcWEiIioJhW/D8XMzAxhYWH4+++/0bBhQyxatEhrHBmWToVKWloaRo0aheTkZDg6OuKFF17Avn37xHcgREREQC6XIzQ0FHl5eQgICMA333wjzm9mZoadO3diwoQJ8PPzg62tLUaPHo158+bpd6uIiIh04OHhgYSEBHTv3l0c16RJE3h4eODOnTtGzIx0KlSioqLKnW5lZYXIyEhERkaWGePp6Wm0O6eJiIiK8/T0BADcuXMHQUFBCAsLw7Vr19CsWTPs379ffFxZHUeGx7cnExGRyerduzcWLFgAADh06JBYmADQ6P5C3ZEpGR5fSkhERCarZ8+ecHV1BYBSXegXFhYCAFxdXdGzZ09Dp0b/jy0qRES1SI6yAABw4e/0MmOycvJw9j7gfusxbK21P8hwPS2zRvKTGjMzM6xYsUK8t7I49fCKFStgZmZmjPQILFSIiGqVG/9fYHy4NaGCSAV+un6mwuXZWprGrwmZTAYrKyvk5OSI46ytrTWGyThM4wwkIjIR/Z4v6jzT29UO1ubaWwESk9MxdXMClgxpjRb1Hctclq2lAl51bWskT6koKCjA1KlTMXDgQGzZsgVHjx7Fnj17EBgYiB49eiA0NBTTpk3D4MGD2apiJCxUiIhqEWdbCwx/qXG5MeoXDnrXs0WrhmUXKqYgJiYGN2/exIYNGyCXa962KZfLMXPmTHTp0gUxMTG8T8VIeDMtERGZrOTkZADAjRs34O3tDX9/fyxduhT+/v7w9vbGX3/9pRFHhscWFSIiMln169cHAIwcORLW1tYa09LS0jBy5EiNODI8tqgQEZHJ6tKli3jJp3fv3oiJicGGDRsQExMj9p0il8vRpUsXY6Zp0lioEBGRyYqJiRH7SwGAc+fO4cSJEzh37pw4rrCwEDExMcZIj8BLP0REZMKOHDkCABg6dCi2bt2q0TOtQqHAq6++ik2bNuHIkSPo06ePkbI0bSxUiIjI5G3atAlBQUHw9/cX3/UTHR2NzZs3Gzs1k8dLP0REZLK6desGAKhTpw42b94MX19fWFhYwNfXF5s3b4aTk5NGHBkeW1SIiMhkqTtxe/ToEZycnJCbmwsAWLp0KaysrMRhdvZmPGxRISIik5WWlib+nJ+frzFNqVRqjSPDYqFCREQmS/3mZB8fHzRurNmjb+PGjeHj46MRR4bHQoWIiExe3bp1ceHCBbzzzjto27Yt3nnnHSQkJKBu3brGTs3k8R4VIiIyWepLOsePH4e9vT0EQQAAnD9/Ht9++604zEs/xsMWFSIiMlnFu8aXyWQa04q/pJBd6BsPCxUiIjJZnTp1AgBYWFggMzMT0dHRCAsLQ3R0NJ4+fQoLCwuNODI8FipERGSyvv32WwBFT/wMHToUly5dQn5+Pi5duoShQ4eKTwKp48jweI8KERGZrBs3bgAAJkyYgO+//x47d+4UpykUCkyYMAErVqwQ48jwWKgQEZHJ8vb2BgCsWLECQUFBeO6555CYmIgWLVrgr7/+wooVKzTiyPBYqBARkcn697//jSlTpkChUODChQviSwn3798PT09PKBQKqFQq/Pvf/zZypqaLhQoREZmsU6dOAQBUKhWSk5Mxffp0eHl5ISkpCV9++SVUKpUY17NnTyNmarpYqBARkcn6+++/AQBeXl64ffs2Fi9eLE5TKBRi0aKOI8PjUz9ERGSy7t+/DwD46KOPkJ2djfDwcAwYMADh4eHIysrChx9+qBFHhscWFSIiMln16tUDAGzduhVjx47Fe++9h6ZNm2LAgAEwMzPD9u3bNeLI8NiiQkREJqthw4YAgD179iA4OBhxcXHIyclBXFwcgoODsWfPHo04Mjy2qBARkcnq1q0bmjRpgrp16+LPP/9E9+7dxWlNmjRBhw4d8PDhQ3Tr1s2IWZo2FipERGSyzMzMsGTJEgwZMgQDBgzAoEGDcPXqVTRv3hxJSUnYvXs3Nm/eDDMzM2OnarJYqBARkUkLCQnBtGnTEBERIT6OvH//figUCkybNg0hISFGztC0sVAhIiKTtnXrVoSHhyMoKAj+/v64du0amjVrhujoaISHh6Nz584sVoyIhQoREZmsgoICTJ06FQMHDsT27dtRUFCA3bt3Y8CAAZg0aRKCg4Mxbdo0DB48mJd/jIRP/RARkcmKiYnBzZs38dFHH0Eu1/yVKJfLMXPmTCQlJSEmJsZIGRILFSIiMlnJyckAgFatWmmdrh6vjiPD06lQWbhwITp27Ah7e3u4uroiODgYiYmJGjG5ubmYOHEiXFxcYGdnh9DQUKSmpmrE3L59G0FBQbCxsYGrqyumT58u3sBERERkKPXr1wcAXLhwQet09Xh1HBmeToXK0aNHMXHiRMTFxSE6OhpKpRL9+vVDVlaWGDNlyhTs2LEDmzZtwtGjR3Hv3j2Nm5AKCgoQFBSE/Px8nDx5EmvXrsWaNWswe/Zs/W0VERFRJaj7UVmwYAEKCws1phUWFmLhwoXw8vJiPypGpNPNtHv37tUYXrNmDVxdXREfH4/u3bsjPT0dUVFRWL9+PXr37g0AWL16NVq2bIm4uDh07twZ+/fvx6VLl3DgwAG4ubmhbdu2mD9/Pj744APMmTMHFhYW+ts6IiKichTvRyU4OBjTp08Xe6ZdvHgxdu7cyX5UjKxaT/2kp6cDAJydnQEA8fHxUCqV6Nu3rxjj4+ODxo0bIzY2Fp07d0ZsbCxat24NNzc3MSYgIAATJkzAxYsX0a5du1LrycvLQ15enjickZEBAFAqlVAqlVXOXz1vdZahL1LKBZBWPlLKBZBWPsylbFLKR0q5ABAvtatUKqPnJIV9M2jQIGzcuBEffPCBRs+0Xl5e2LhxIwYNGmSU/KSwb9T0lUtV5pcJgiBUZWWFhYX417/+hSdPnuD48eMAgPXr12PMmDEaRQUAvPTSS+jVqxe++OILjB8/Hrdu3cK+ffvE6dnZ2bC1tcXu3bsRGBhYal1z5szB3LlzS41fv349bGxsqpI+EZHJupMJhCcoMK21Ch52xs5GOgoKCnDp0iU8fvwYderUga+vL1tS9Cw7Oxuvv/460tPT4eDgUKl5qtyiMnHiRFy4cEEsUmrSzJkzERYWJg5nZGTAw8MD/fr1q/SGaqNUKhEdHQ1/f3+Ym5vrI9VakYvU8pFSLlLLh7k8G/lIKRcA+OP2IyDhLDp37ow2jZ2NmovU9k3//v0lk4+U9o2+clFfEdFFlQqVSZMmYefOnTh27BgaNWokjnd3d0d+fj6ePHkCJycncXxqairc3d3FmNOnT2ssT/1UkDqmJEtLS1haWpYab25urpeDp6/l6IOUcgGklY+UcgGklQ9zKZuU8pFKLgqFQvxfCvkA0tk3alLKpzblUpV5dXrqRxAETJo0Cdu2bcOhQ4fg5eWlMb19+/YwNzfHwYMHxXGJiYm4ffs2/Pz8AAB+fn5ISEhAWlqaGBMdHQ0HBwf4+vrqvAFERERUe+nUojJx4kSsX78ev/32G+zt7ZGSkgIAcHR0hLW1NRwdHTFu3DiEhYXB2dkZDg4OePfdd+Hn54fOnTsDAPr16wdfX1+88cYbWLRoEVJSUjBr1ixMnDhRa6sJERERmS6dCpUVK1YAAHr27KkxfvXq1XjzzTcBABEREZDL5QgNDUVeXh4CAgLwzTffiLFmZmbYuXMnJkyYAD8/P9ja2mL06NGYN29e9baEiIhKyc7OxpUrVzTGJSY/QV7KdVy+YI3Ch07ieB8fH5N+QKGgoABHjx7FsWPHYGtri169evFmWgnQqVCpzANCVlZWiIyMRGRkZJkxnp6e2L17ty6rJiKiKrhy5Qrat2+vddrrazWH4+Pj8eKLLxogK+nZunUrpk6dips3bwIAli5diiZNmmDJkiV8c7KR8e3JRES1mI+PD+Lj4zXGZebkYdfhWAT18oOdtaVGrCnaunUrhgwZgoEDB+Knn37C3bt30ahRIyxatAhDhgzB5s2bWawYEQsVIqJazMbGplQriVKpxOMHafB7qYNkniYxloKCAkydOhUDBw7Eli1bcPToUZw5cwZ169bFli1bEBoaimnTpmHw4MG8DGQkfHsyERGZrJiYGNy8eRNdunRBs2bN4O/vj6VLl8Lf3x/NmjWDn58fkpKSEBMTY+xUTRZbVIiIyGQlJycDKOpY1NraWmNaWloaPvroI404Mjy2qBARkclydXUVf+7Tpw9iYmKwYcMGxMTEoE+fPlrjyLDYokJERCaroKAAQNHLdbdt2wZBEPDw4UN06tQJ27Ztg5ubGx49eiTGkeGxRYWIiEyW+t6Tx48fIyQkBHFxccjJyUFcXBxCQkLw+PFjjTgyPBYqRERk8j755BMkJCSge/fueO2119C9e3dcuHABH3/8sbFTM3ksVIiIyGSpe1o/cOAArl69iujoaISFhSE6OhqJiYniu+tK9shOhsNChYiITFbPnj3h6uqK48ePIyQkBJaWlujYsSMsLS0REhKCEydOwNXVlYWKEfFmWiIiMllmZmZYsWIFhgwZgoMHD2Lnzp3iNBsbG8hkMqxYsYKdvRkRW1SIiMikhYSEYPPmzXBzc9MY7+bmxu7zJYAtKkREZPJCQkIwePBgHD58GHv27EFgYCDfniwRLFSIiIhQdBmoR48eyMrKQo8ePVikSAQv/RAREZFksVAhIiIiyWKhQkRERJLFQoWIiIgki4UKERERSRYLFSIiIpIsFipEREQACgoKcPToURw7dgxHjx5FQUGBsVMisFAhIiLC1q1b0bRpU/j7+2Pp0qXw9/dH06ZNsXXrVmOnZvJYqBARkUnbunUrhgwZglatWmH58uWYNGkSli9fjlatWmHIkCEsVoyMPdMSEZHJKigowNSpU9G+fXtcuHBB46WETZo0Qfv27TFt2jQMHjyYPdUaCVtUiIjIZMXExODmzZuIj49H69atERMTgw0bNiAmJgatW7dGfHw8kpKSEBMTY+xUTRYLFSIiMll///03AKB///7Yvn07OnXqBGtra3Tq1Anbt29H//79NeLI8FioEBGRybp//z6Aorcny+WavxLlcjmCg4M14sjwWKgQEZHJqlevHoCiG2oLCws1phUWFmL79u0acWR4LFSIiMhkNWzYEACwZ88eBAcHIy4uDjk5OYiLi0NwcDD27NmjEUeGx6d+iIjIZHXr1g1NmjRB3bp18eeff6J79+7itCZNmqBDhw54+PAhunXrZsQsTRsLFSIiMllmZmZYsmQJhgwZgqCgIISFheHatWto1qwZoqOjsWvXLmzevJmPJhsRCxUiIjJpISEh2Lx5M8LCwkr1o7J582aEhIQYMTviPSpEREQAZDKZsVMgLVioEBGRSVN3oa+twzd2oW98LFSIiMhkqbvQHzhwoNYO3wYOHIhp06bxTcpGxEJFAvhqcSIi41B3of/RRx9BpVJh+fLl+O6777B8+XKoVCrMnDmTXegbmc6FyrFjxzBo0CA0aNAAMplM7AxHTRAEzJ49G/Xr14e1tTX69u2La9euacQ8evQII0aMgIODA5ycnDBu3DhkZmZWa0OeVXy1OBGR8SQnJwMANm7cCFtbW0ybNg27d+/GtGnTYGtri19++UUjjgxP50IlKysLbdq0QWRkpNbpixYtwvLly7Fy5UqcOnUKtra2CAgIQG5urhgzYsQIXLx4EdHR0di5cyeOHTuG8ePHV30rnlG8LkpEZFz169cHAHz55Zdae6b98ssvNeLI8HR+PDkwMBCBgYFapwmCgGXLlmHWrFkYPHgwAODHH3+Em5sbtm/fjuHDh+Py5cvYu3cvzpw5gw4dOgAAvvrqKwwYMADh4eFo0KBBNTbn2VH8uujPP/+MkSNH4s8//8QLL7wgDvPV4kRENatTp07izwqFAvn5+VqHi8eRYem1H5WkpCSkpKSgb9++4jhHR0d06tQJsbGxGD58OGJjY+Hk5CQWKQDQt29fyOVynDp1Cq+88kqp5ebl5SEvL08czsjIAAAolUoolcoq56uetzrLqKqjR4/i5s2bsLKygqOjozj+1q1bcHR0hI+PD5KSknD48GH06NHD4PkZc9+UJKVcAGnlY8xcsrOzkZiYKA5n5uThZMIN2DvFwc7aUiO2RYsWsLGxMWh+PE5lk1I+xs7l66+/Fn92cnLC7NmzYWNjg+zsbMybNw9paWli3OTJkw2am7H3TXH6yqUq8+u1UElJSQEAuLm5aYx3c3MTp6WkpMDV1VUzCYUCzs7OYkxJCxcuxNy5c0uN379/f5W//AoKCnDp0iU8fvwYCQkJ8PX1NWjLxbFjxwAAV65cAQA4ODhAJpNBEARkZGSI4/fs2YOsrCyD5VVSdHS00dZdkpRyAaSVjzFyuXHjBqZOnVpq/CItsUuWLIG3t3fNJ6WFqR+n8kgpH2PlsnnzZgBFl3YKCgowadIkcZqbmxvc3d2RkpKCzZs3o3nz5kbJsTYdp+zsbJ3neSZ6pp05cybCwsLE4YyMDHh4eKBfv35wcHDQeXnbtm3DBx98gJs3b4rjmjRpgi+++EJri05NEAQBS5cuFYfVrUQldevWDQMGDDBITsUplUpER0fD398f5ubmBl+/VHORWj7GzCU7Oxtdu3YVh68mp2P6tktY/Iovmtd31Ig1VosKj5P08zF2Ll999RUAYNiwYZg9ezZGjRqFhIQEtG7dGj/++CPmzJmD5cuXw97e3uDfxcbeNzWRS1m/68qj10LF3d0dAJCamqpx41Fqairatm0rxqib0tRUKhUePXokzl+SpaUlLC0tS403NzfXeYdt3boVw4cPx8CBA/HTTz/h7t27aNSoERYtWoThw4cbrLvkVatWaQy3aNECderUwePHjzWa01etWoXg4OAaz6csVdnHNUVKuQDSysdQuSQ9yEJWnkoctmnYQvzZWp4OS/d8WDdsAZsShcqdTACZRX9J2Voq4FXXtsZzVTPF41RZUsrHWLl07NgRBw8eRGRkJJYtWyaOv3XrFpydncWcOnbsaLR9VZuOU1Xm1Wuh4uXlBXd3dxw8eFAsTDIyMnDq1ClMmDABAODn54cnT54gPj4e7du3BwAcOnQIhYWFNX6zUsmOfQoKCvDw4UOxY5/g4GCD3cBa8pHt4sVJeXFExpL0IAu9wo9UGDd1c0KFMYen9TRosUJUlr59++Lzzz8X753o0KEDmjZtiuvXr+Ps2bPi+OL3XpJh6VyoZGZm4vr16+JwUlISzp8/D2dnZzRu3BiTJ0/Gp59+imbNmsHLywsff/wxGjRoILYKtGzZEv3798fbb7+NlStXQqlUYtKkSRg+fHiNP/Gj7thnw4YNkMvlGh2ryeVyzJw5E126dEFMTAx69uxZo7mkpqbqNY6opqlbUpYNa4umrnalp+fkYeeRWAzs6Qdb69ItoABwPS0Tk385r9EqQ2RMJf9APnv2LM6ePVthHBmOzoXK2bNn0atXL3FYfe/I6NGjsWbNGsyYMQNZWVkYP348njx5gq5du2Lv3r2wsrIS51m3bh0mTZqEPn36QC6XIzQ0FMuXL9fD5pRP3WFPq1attE5XjzdExz7W1tZ4/PgxAMDKykqjn5niw9bW1jWeC5EumrraoVVDx1LjlUolUuoBL3rWkUwzNVFFPvzww0rHFX9CiAxH50KlZ8+eEAShzOkymQzz5s3DvHnzyoxxdnbG+vXrdV11tanvm7lw4QI6d+5cavqFCxc04mpS8S/y4kVKyWF+4RMR1ZyrV6+KP5f3R2PxODIsk3rXT7du3dCkSRMsWLBAaw+ECxcuhJeXF7p161bjuZR8hLu6cUREpDv102iNGjVCRkYGoqOjERYWhujoaGRkZKBhw4YacWR4z8TjyfpiZmaGJUuWYMiQIRg8eDD8/f1x7do13Lp1C9HR0di1axc2b95skP5USraiVDeOiIh05+Pjg99++w3JyckQBAE9evRAVlYWevToAUEQxP69fHx8jJyp6TKpQgUAQkJCMG3aNERERGDnzp3ieIVCgWnTphnk0WQA+PPPP/UaR0REulNfXi8oKIC9vT2Cg4NhY2OD9evXi0+HFo8jwzO5QmXr1q0IDw/HgAED8NxzzyExMREtWrTAX3/9hfDwcHTu3NlgxQrRs0amyEBSRiLkVqWf+lGpVLinuofLjy5DodD+1ZKUkQmZQvcOn4hqSs+ePfHpp5/Czs4OmZmZ+PXXXzWmq8fX9JOgVDaTKlTU/ai0b98eFy5cwK5duwAUdcXv6emJ9u3b80WAROUwdzqFj04vKDfmm73fVLCMPgAM39sykTY9e/aEo6Mj0tPTIZfLNe5flMvlyMzMhKOjIwsVIzKpQkXdj8rNmzcxaNAg/Pzzzxo90+7YsUOMq+mTskOHDlqf1dcWRyQVyiedsCTodXhr6UdFpVLhxPETeLnry2W2qNxIy8R7627UdJpEOinrSVaZTFbudDIMkypU/v77bwBAYGCg1p5pBw4ciD179ohxNankTbIymQweHh64c+eOxoeCN9OSlAgqB3g5tICvi/Z+VJIUSWjp3LLM6/mFuekQVPdrOk2iSjty5AgyMjLQsmVLZGdn49atW+I0Dw8PWFlZ4cqVKzhy5Aj69OljxExNl0k9nnz/ftEXZEhICORyzU2Xy+Vi77nquJpU8rFjQRBw+/btUpU7H08mIqo5R44cAQB8/fXXuHr1qngPY3h4OBITE8WXFqrjyPBMqlCpV68egKIbarX1o7J9+3aNuJpU2Ufd+EgcEVHNi4mJQYsWLTBt2jTs3r0b06ZNQ4sWLXD8+HFjp2byTKpQUXfcs3fvXgQHByMuLg45OTmIi4tDcHAw9u7dqxFXkxYvXqzXOCIi0p36fsQ5c+agVatWiImJwYYNGxATE4NWrVph7ty5GnFkeCZ1j4q6Z9q6desiISEB3bt3F6d5eXmhffv2ePjwoUF6pi3+QkR9xBERke66desmPu0jCIJ4+b34z3K53CC/F0g7kypUivdMO2DAAAwcOBBXr15F8+bNkZSUhN27dxusZ9o33nij0nHbtm2r4WyIiEzTyZMnUVhYCJlMhoMHD4rdVgBFL4WVyWQoLCzEyZMn2apiJCZVqACaPdOqVEWvmt+/f7/Be6at7Auu+CIsIqKak5ycDAB47733EBkZqTFNqVTivffew5dffinGmaL4+HiNrjLOnj2L9u3bG2z9JleoqHumDQoKEt/106xZM0RHRxu0Z9rs7GzxZwsLC0yePBleXl5ISkrCsmXLkJ+fXyqOiIj0q379+gCA5cuXa+2xfPny5Rpxpkbdl0xx6qLFUP3LmFShou6ZduDAgdiyZQuOHj2KW7duwdfXFxMmTEBoaKjBeqb19PTEzZs3AQCJiYkICgrCnTt34OHhgcTERHh5eYlxRERUM7p06QKFQgFbW1skJCRo9FjeuHFjODg4ICsrC126dDFypoanrUgpOd0QxYpJPfWj7pm2S5cuaN68Ofz9/bF06VL4+/ujefPm8PPzQ1JSEmJiYmo8l4cPH4o/e3l54dKlS3j69CkuXbokFikl44iISL9OnjwJlUqF9PR05ObmYsqUKRg/fjymTJmC3NxcpKenQ6VS4eTJk8ZO1aDi4+P1GlcdJtWior7G+NFHHyEoKAhTpkzRuPTz3//+VyOuJrm5ueHChQuViiMiopqh7oncy8sLd+7cQUREhDhNoVCIl+QN0WO5lFT29S0dOnSo8VYVkypUXF1dARR1opaQkICdO3eK0zw9PdGiRQtcuXJFjKtJxS/pqHvJLSws1Pi5ZBwREemXuifypKQkDBw4sNS9i+rfE4bosZy0M6lCRe3y5cuwtLTUGJeSkoK8vDyD5RAbGyv+XLyX3JI95haPIzKmHGVRnz4X/k7XOj0rJw9n7wPutx7D1tpSa8z1tMway4+oKlxcXAAU/SG7bds2CIKA3bt3Y8CAAfjPf/6Dhg0bIi0tTYwzlPz8fHz11Vc4dOgQrl+/jnfffRcWFhYGzUEqTKpQSUlJEX9WKpUa04oPF4+rKampqXqNI6ppN/6/yPhwa0I5UQr8dP1MhcuytTSprx6SMPV9gPfv38crr7witqjcunUL0dHRYkuKIe8XnDFjBpYsWSL+4bp7927MmDEDU6dOxaJFiwyWh1SY1LdF8QLE0tISOTk54rCVlZX4KLAhChUXFxc8evSoUnFEUtDveXcAgLerHazNSz8Vl5icjqmbE7BkSGu0qF/67cpqtpYKeNW1rbE8iXShfrdbkyZNsGfPHo1bAhQKBZo0aYKkpCSDvAMOKCpStL06pbCwUBxviGJF3VtvcS+++CLOnTtXKq6mmVSh8uDBAwBAnTp1kJycjJiYGOzZsweBgYHo1q0b6tevj8ePH4txNSk3N1evcUQ1zdnWAsNfalzmdHUHit71bNGqYdmFCpGUqN/tlpSUBFdXV4wYMQJZWVmwtbXFunXrkJSUpBFXk/Lz8yt8v9vixYvx6aef1vhlIDMzs1KFSskiRR1X00zq8eS7d+8CAB4/fowhQ4bg0qVLyM/Px6VLlzBkyBA8fvxYI64mlSyGnJ2dMX78eDg7O5cbR0RE+qPuR8XR0RFWVlaIiIjAd999h4iICFhbW8PR0REKhcIg/agsXbpU/HnAgAEaL0gcMGCA1riaUtkCRCaT1XjHpCbVotK4cdFfg/Xr1y/VxGdmZob69esjOTlZjKtJ6p5n1R49eoTvvvuuwjgiItKf4v2opKdr3ih+69YtjbiaftfPt99+CwBwd3fHjh07UFBQgIcPH6JTp07YsWMHGjZsiJSUFHz77bf48MMPazSXyhYq+fn5uHLlCl588cUay8WkWlR69+4NoKiflJLPfQuCIPafoo6rScXXn5SUBF9fX9jb28PX11dsaiwZR0RE+lXZfrMM0b9WRkYGgKLWlJL3fsjlcvTr108jria1atWqUnEvvPACfHx8ajQXkypUunXrJnYJXPLam3pYJpMZ5HXexatVLy8vZGVloVfQK8jKytLomdbMzIzv+yEiqiHFH1goed9H8WFDPNjg4eEBAPj5559x+vRpxJ4+i5MJNxB7+ixOnz6NjRs3asTVpH379lUq7tixY7CxsanRXEzq0k9MTEyFLRSCICAmJgZ9+vSp0Vw6dOig0UfKrVu3cOvWj6XilEpljTerZWdn48qVKxrjMnPycDLhBurUPQu7Yn1i+Pj41PhJSURkKH/88Yf4c3ndVvzxxx9ii0ZNGTt2LN5//33k5+ejU6dO4viSz/iMHTu2RvMAAEdHR3h7e+PGjRtlxnh7e8PRseZvnDepQmX//v2VjqvpQmX79u0a3ePLzcxQWAjI5UBhQYE4/ujRozXerHblypUyX9ld8gMSHx9fo0UTEZEhnThxQvzZ3NwcISEhsLGxQXZ2NrZu3SreJ3jixAlMnz69RnMZM2YMpk2bVqpgKs7c3Bxjxoyp0TzUrl+/jqZNm2otVry9vXH9+nWD5GFShcrWrVsrHffFF1/UaC6urq7o2LEjzpwp6hxLXZwU/lOjoGPHjujevXuN5gEUtZKUfLFUYvIThG1KwNJXW6NFfSeNWCLSlPQgC1l5KnE4JycbSdevisMFBQU4n3AD2YqYUjcpejVtDmvrolZK9jFjeJmZRR0ZKhQKqFQq8fIKUHRfiHq8Oq4m2dvbY+PGjQgNDS0zZuPGjbC3t6+R9Zc8jwFg+9F4pKenY9xrIbiedAtNvTwRtWErHB0dtfZSXRPnsEkVKpV91NdQjwSfPn0aL730klisFNexY0ecPn3aIHnY2NiUaiWR33oIy5gctGzVBm092ekcUVmSHmShV/gRjXF5KdeRsnZypeZ3H70Mlu5NxeHD03rW6mKl+KXm69ev4/XXX0dBQQHMzMywfv16NG36z74wxKVm9e0AKpUKVlZWGn1XWVhYiMOGerAhJCQEW7ZsweTJk3Hnzh1xfOPGjREREYGQkJAaWW/Sgyz0XvY/yBRPtQe8Mh6NAeQDeOPXvWUuR1DZ49Dkf+n1HDapQqW85rSqxOnD6dOnkZmZiUEhQ3Hi90t4uZ0vdmz9FXZ2dgbLgai2SU9PR2BgoPhyuT179tTYtXT1X6DLhrVFU9eiz21OzotIGt5WjCkoKMD538+jbbu2ZbaoXE/LxORfzpf6i/ZZF3/3Fu49/edVIH9dv4oP331bHDZvZA5zmAMARs8YrTHv5199j+eaNgcANLB3Q/tG+n9Ja/Hv2sLCQkyfPl18Y/KXX36pNa6mhYSEYPDgwVi9aSdmrj+Bha+/jDGvDqzRztWy8lQwdzoFy3oHq7WcvPt9kJU3oOJAHZhUoVLZPkkM3XeJnZ0dIr7/CcEr4hAxobNBPhDamviKu3E/S/xfoSj7NGFTtfHk5OQgLCwMcXFx2Lt3L5YuXQpra2tjp2V0Ja+pP3jwAE5OTjV+Tb2pq12xHnkd0bFpfXGaUqmEjeopBvTrBnNz8xrLQWou3cvAaxsjSv3yazq3aRlzaPrh0RfA/zcs593vg31vfqb375v69f85TuX1DFs8Tl8q+h6u07QdbH0VqNO0NS6nlH3pSR/fwznKAiifdMKEjv8SC26N6Xn5iDmbgG4dWsPaUnuvuHceZWPxNf0/xm1ShYoUW1SMQVtTdVmmbi7vBXRFantTtRQFBwfjt99+E4fPnz+PlStXYvDgwdi+fbvxEjOy4kVKQEAAevXqhcOHD2Pfvn24ceMGmjZtarAbAAn48+4TKJ90girTVxyX/SAV6TsXiMO2rfrCulln5FyLQ9aFA+J4x4EfwabuPw8cCKqauS+jTp06eo2rLKl9D99Iy4SgcsCXe3IA5JQR1Rg7rmt/e/o/HPT+0lGTKlSoiLam6lIxOXnYeSQWA3v6wbbY48nF1damaqkrWaQU99tvvyE4ONgki5X09HSxSMnKyoK5uTl2796NsLAwKJVK2Nra4saNG0hPTzfII5WkfpHlyxovsmzrVQ8F///H4E+/7UdyRj6WHriOD4a/g/oO7+GNwUWPACtXzkXslTs1fqNxeS3GVYmrLKl9D5f30tH8/Hws/+orbD36O0J6tMN7775b5ruGeDPtM0yKl1o0m6o1KZVKpNQDXvSsY1JN1VKXk5NTZpGi9ttvvyEnJ8fkLgMFBQUBAPr37w8bGxuNllEbGxv069cP+/fvR1BQEI4fP26sNE2KthdZFhQ7LuqiBABmrNWct6CgAGYZyWjVtGa7Q6jsO3xq4l0/MkUGzKz+htxKe6FirVChQZ17sLZPgbyM3wtmVpmQKarfU21ZLx2dMWMGIiIixJeOrj23E+u+WogpU6YY5C3OgAkVKsbs3VVqTXxA0QckKSOxzA+ISqXCPdU9XH50uczCKSlDPx+Q8kRFReGtt94Sh3/44QeMGzeuRtcpZSNHjqx03JYtW2o4G+nIzs4WL+kMGzYM586dK9Vp4dChQ7F//36N97eQ8VhaWuLkyZPIzMnDrsOxCOrlBztrS/j5+Yn3CRqiO4SEhIq/c9VxgYGBel23udMpfHR6QYVx3+z9poLl9AGg3xtYgaIiZfHixXBzc8P4yR9i1V0XjG30EN8t+1y8l8cQxYpRC5XIyEgsXrwYKSkpaNOmDb766iu89NJLNbKukj2vGpLUmvgA6X9AAIivOyjurbfewltvvWUy70Aq2RJXsi+grr37oqlPG1y/8geOHzqgEVe8j4PaftPzlStXkJpa9GRJyc6wSn6NGqIrdCrbkCFDsHnzZuTl5aFBgwZwcXHB4wdp8HupAx4+fCgWKUOGDDFIL9j/+9//Kh03Y8YMva23optXAePewJqfn4+IiAi4ubnh7t27uPB3On5cEYeQ1wZg9rRJaNSoESIiIvDpp5+WeRlIX4xWqPzyyy8ICwvDypUr0alTJyxbtgwBAQFITEyEq6ur3tenS2Wu7RekPkjlUovUPyBA6WPg7u6OlJQUjem1vVi5dC8DQd/s0ujXwMrTSiPm7I3jOHvjuNZp//r+F/HnmujbwNiKF3EFDvWxeuNvGDN8MABg9ZbduJ9diKUHriOsb1PUs5FjTGhRQR0etVHvRdyz0kIpBT/++CM2b94MoOhJGhsbGwwePBivv/66Rsv3jz+WfqVITSgo1hO4paUl8vLyxOHi/aoUj9OHyt28ChjrBtZly5ZBpVLh7bffxp9//onE5CfIS7mOyxesUfjQCW+99RY+++wzzJw5E/Pnz6/RotJohcrSpUvx9ttvi3/9rFy5Ert27cKqVav09vrqkn+N/rL/JIb1q/g648Z9J2r1X6NS/4BERUWJP+/btw+9evXC7t27MWDAABw+fBgBAQFiXG2+DPTn3Sel+jWo7GOdRb4Sf8q73wfAv/SXHEq/I6rkF1lx+u64S1sRBwC2rRqh4OkDTAgLgUUDH9i29sen36xB/r0rsPK0gpl9XYzfcUxjnuoWcTnKgmeihVIqrK2tMXjwYPFeq+zsbGzYsEEjZvDgwQa7x6r4m4gfP36MEydOYM+ePQgMDMTLL78snrf6fmNxeTevqiUmp2Pq5gQsGdIaLeqXfQN4TfyOUvdW/umnn+LTTz8Vx79e4l6ipUuXYsSIETX6ahWjFCr5+fmIj4/HzJkzxXFyuRx9+/bVeFGfWl5enkaVqz5hlEplmY8SX05+isHf7RO/yApVeVA9SSv1V6c2M46ehfzEP9ctBZU99k8KRBOXqp0IT3PyIFNkYN/VM7j+uGgZuXm5SL57W4wpUBXi+vVruKZ6BDOF5kut6zdqDCtLK9x5nAOZIgMqlapaj1D3au6Czwb74rl6trA2N0NOTjZu3rimEXPrQSa+PJyE93t5wbPuP38lNvFuJt6FDwC2lmZo5GhR5XweZeVje8IVZKoei+NmzZ8kHqefzx7Dj6ePIO3+fWxKOAW5XC5OmzR/Ev6u5wRb+6IPcDOX+ghs2bxKeZSVT9bTdFy/8LtGTGFhoUY+ak1btdNrLr2au2Bq3htwtB8CK0XRF9lrA3uL0+UyObr07IO67g3xIOVvnDxyEIXCP28F37DzkPhzfft61TpO2ly4cEHjxWlqJb/IAODUqVNo166d3tb9+62HWjun8prmBMDp/4dUAPbApQsAFC/wvtKYJ+9+H6hUgVXeN1eT00s9gqv+vqkMhZMr5Iqiy72Cyh6WZkKNd5GgXr6xumLYtGkTQkNDsWPHjlLTBg0ahE2bNhkst6ysLPHnJk2a4OOPP0arVq1w5coVjBgxQiNOnznZW8gQ2k6zb5bs7GwkJiaKwznJ6chLuY6cvy2QXfhPodKiRYtShb++91fbtm3x66+/YubMmQgODkZmTh72xZxBQLeOsLO2xPbt27Fw4UJMnjwZ3t7eNdr9h0wwQvv5vXv30LBhQ5w8eRJ+fn7i+BkzZuDo0aM4deqURvycOXMwd+7cUstZv359mX+lxabKsDXjULV72QOKvsimN+oF1yoW+FLKRZsbN25g6tSplYpdsmQJvL299bZufe+baY16wa0a+0Zf+egjF23mz59f6r1M2rRv3x4ff/yxfldeQl5eHu7evSsOKwuBR7mAsxVgrllro1GjRrC01H7vVVVkKoEzj57CxuopzOVA6t93sHZFRKXmHT1hCtwaeojDdczs4WVT9T46MpVAwiMZXK0FWPz/dt9JuoFFH1fuMzVj/hJ4eBV9pizNoNfPttTl5uZi7dq1SE5ORv369TF69GhYWVX8x6Q+TZ06tdw3BKt5e3tjyZIlNZpLZb+L9f09rE1+fj6GDx8OBwcH/PDDDxqXLFUqFd566y08ffoUGzZs0OkelezsbLz++utIT0+Hg4NDpeZ5JgoVbS0qHh4eePDgQZkbqv7L2NE+B1YKs1ItGKn37mL5os8gCAJkMhnem/FfuDVoBOCfFgy1+vb18GKDqnfdXDIXoOwWlaZNm5XZoqKPXLQpWcUDKFU9q2mr5KtDa4vKmEHiz6+Onyq2YLjWqwe5XI5N3/3zZTFz+c9Ga1FR56Om7xYVbTIzM+Hs7Fxh3KNHjwz+GgalUono6Gj4+/sb/JF2Y57DlcmnrFwMlU9JxjxWUstlz549GDy46N6mkve+yeVyFBYWtVL+9ttven/qp6TKnjeGOmc+/PBDLF26FK6urvj4449ha2uLrKwszJ8/H2lpaQgLC8Pnn3+u0zIzMjJQt25dnQoVCEaQl5cnmJmZCdu2bdMYP2rUKOFf//pXhfOnp6cLAIT09PRq5ZGfny9s375dyM/Pr9Zy9EFKuQiCcfP54YcfBAACAGHfvn0auezbt0+c9sMPPxg8N0Ew/rHq2LGjuA+0/evYsaNR8jL2filJSvlIKRdBkFY+xs5FpVIJFhYW4uenXbt2wssvvyy0a9dOHGdhYSGoVCqD52bsfSMIgjB9+nRBoVBofMcoFAph+vTpVVpeVX5/l2igNQwLCwu0b98eBw/+07xeWFiIgwcParSwkGkqfoNsQEAALCwsMG7cOFhYWIg30paMMyWnT59Gx44dtU4z5Fu3iWoDMzMzjZt5f//9d5w4cQK///5PS+qGDRtq9IWAUrZo0SJkZWUhPDwcAwYMQHh4OLKysgzW2RsAGKVQAYCwsDB8//33WLt2LS5fvowJEyYgKyurVB8IZJqEElckHz58WO50U3P69Gk8ffoUgwYNgqenJwYNGoSnT5+ySCGqgpCQEGzZsgWNG2v2zOrp6YktW7YgJCTESJlJg4WFBd577z2MHz8e7733Xo33m1KS0R5PHjZsGO7fv4/Zs2cjJSUFbdu2xd69e+Hm5lbxzGQSBEFgz7TlsLOzw5YtW8RHt419rwHRsywkJASDBw/G4cOHxceTe/XqZbItKVJi1J5pJ02ahEmTJhkzBZK4cePGYdSoUfxlTEQ1zszMDD169EBWVhZ69OjBIkUijHbph4iIiKgiLFSIiIhIslioEBERkWSxUCEiIiLJYqFCREREksVChYiIiCSLhQoRERFJFgsVIiIikiwWKkRERCRZRu2ZtqrU73nJyMio1nKUSiWys7ORkZFh9B5PpZSL1PKRUi5Sy4e5PBv5SCkXqeUjpVyklk9tzEX9e1uX97U9k4XK06dPAQAeHh5GzoSIiIh09fTpUzg6OlYqViY8g6+hLSwsxL1792Bvbw+ZTFbl5WRkZMDDwwN37tyBg4ODHjN8tnORWj5SykVq+TCXZyMfKeUitXyklIvU8qmNuQiCgKdPn6JBgwaQyyt398kz2aIil8vRqFEjvS3PwcHB6CeBmpRyAaSVj5RyAaSVD3Mpm5TykVIugLTykVIugLTyqW25VLYlRY030xIREZFksVAhIiIiyTLpQsXS0hKffPIJLC0tjZ2KpHIBpJWPlHIBpJUPcymblPKRUi6AtPKRUi6AtPJhLkWeyZtpiYiIyDSYdIsKERERSRsLFSIiIpIsFipEREQkWSxUiIiISLJqRaGSkpKCd999F8899xwsLS3h4eGBQYMG4eDBgwCAJk2aQCaTQSaTwcbGBq1bt8YPP/ygsYwjR45AJpPhyZMnGsN16tRBbm6uRuyZM2fE5VWWenll/evVqxdu3rwJmUwGV1dX8TUBam3btsWcOXPKXP6bb76J4OBg8WeZTIbPP/9cI2b79u0aORfPSS6Xw9HREe3atcOMGTOQnJxc5vK1bZd6vxUUFODzzz+Hj48PrK2t4ezsjE6dOmHJkiUVHqNly5aVWv6cOXPQtm3bUuPv3r0LCwsLtGrVSuv+OHr0KHr37g1nZ2fY2NigWbNmGD16NPLz80ttV2X2VUFBASIiItC6dWtYWVmhTp06CAwMxIkTJ8SYFStWwMnJCXfu3NFY1rvvvovmzZsjOztba67lUecnk8lgbm4OLy8vzJgxQ+OcVE+Pi4vTmDcvLw8uLi6QyWQ4cuSIzutWi42NhZmZGYKCgkpNy8/Px+LFi/Hiiy/C1tYWjo6OaNOmDWbNmoV79+5p3Y7i//r3769zPiX3iZubG/z9/bFq1SoUFhaKcSXPqT/++AP/+te/4OrqCisrKzRp0gTDhg1DWlpatXPQdlyAis/T4vvC1tYWzZo1w5tvvon4+PhK51Le94pMJtP43vDx8YGlpSVSUlI0lpGVlQVvb2+EhYVp3UaFQoGmTZti3rx5GDlyZLnra9KkCQCgZ8+e4jgrKys0b94cCxcu1PqOF23nWFnnjLb1TJ48WWN5Fy9exNChQ1GvXj1YWlqiefPmmD17dpmfwZLrcnFxQf/+/fHnn39W+jiUXJ6270ug/PNwzpw5FR5PtQ0bNsDMzAwTJ04UxxXf59r+9ezZUyOXiRMnQiaT4c0339S6H7R9Tov/PrW2tkaTJk0wdOhQHDp0SIxZsmSJ1t+dAJCdnQ0HBwcsX7680vvzmS9Ubt68ifbt2+PQoUNYvHgxEhISsHfvXvTq1UvjAM6bNw/Jycm4cOECRo4cibfffht79uypcPn29vbYtm2bxrioqCg0btxYpzy7dOmC5OTkUv++/fZbyGQy/Oc//xFjnz59ivDwcJ2WX5KVlRW++OILPH78uMLYxMRE3Lt3D2fOnMEHH3yAAwcOoFWrVkhISNB5vXPnzkVERATmz5+PS5cu4fDhwwgJCcG8efMqPEa6WLNmDYYOHYqMjAycOnVKY9qlS5fQv39/dOjQAceOHUNCQgK++uorWFhYoKCgoNSyKtpXgiBg+PDhmDdvHt5//31cvnwZR44cgYeHB3r27Int27cDAN555x289NJLGDdunDjvwYMHsWLFCqxZswY2NjZV2tb+/fsjOTkZf/31FyIiIvDtt9/ik08+0Yjx8PDA6tWrNcZt27YNdnZ2VVpncVFRUXj33Xdx7NgxjeIjLy8P/v7+WLBgAd58801xXy9fvhwPHjzAV199pXU7iv/bsGFDlXJSL+vmzZvYs2cPevXqhffffx8DBw6ESqUqFX///n306dMHzs7O2LdvHy5fvozVq1ejQYMGyMrKqlYO5R2X8s5TtdWrVyM5ORkXL15EZGQkMjMz0alTJ/z444+VyqP4/ly2bBkcHBw0xk2bNg0AcPz4ceTk5GDIkCFYu3atxjJsbW2xevVqfPXVV4iJiRHHOzs7o1evXrhx4wamTp2KOXPmoFmzZhrLL74NycnJOHPmjDj/22+/jeTkZCQmJmLmzJmYPXs2Vq5cWWobtJ1jX375ZaXXU1xcXBw6deqE/Px87Nq1C1evXsVnn32GNWvWwN/fv9QfK2rFz8+DBw9CoVBg4MCBlToGlVXReTht2jSNbW7UqJH4u6v4flDvsxkzZmDDhg1iQbB161Yx7vTp0wCAfv36oUGDBnBwcMC6devE+XNzc7F+/fpSv8sq8zlV55SYmIgff/wRTk5O6Nu3Lz777DMAwBtvvIGsrCxs3bq11D7YvHkz8vPzMXLkyMrvOOEZFxgYKDRs2FDIzMwsNe3x48eCIAiCp6enEBERoTHN2dlZmDJlijh8+PBhAYA4j3p41qxZQt++fcW47OxswdHRUfj444+F6u6+S5cuCfb29sJ///tfQRAEISkpSQAgTJ8+XbCzsxNSU1PF2DZt2giffPJJmcsaPXq0MHjwYPHngQMHCj4+PsL06dPFmG3btmnkXHKbi29jixYthJdfflnr8osruYw2bdoIc+bM0Yip6jESBEH45JNPhDZt2miMKywsFJ577jlh7969wgcffCC8/fbbGtMjIiKEJk2alFqWNpXZVxs3bhQACP/73/9KzR8SEiK4uLiI23b79m3BwcFBWLFihZCeni40btxYY7m60rbfQ0JChHbt2onD6vPUwcFByM7OFsf7+/uL5+nhw4ertP6nT58KdnZ2wpUrV4Rhw4YJn332mTht4cKFglwuF86dO6d13sLCwnK3o6rKWtbBgwcFAML3338vCILmObVt2zZBoVAISqWyxnIoeVwqOk8FoejYbdu2rdT4UaNGCfb29sKjR490ymv16tWCo6Oj1mlvvvmm8OGHHwp79uwRmjdvrjVmypQpgre3t5CZmSl07NhRUCgUwt27d8Xp/v7+QufOnSu1DT169BDef/99jXEvvvii8Morr2iMK+8c03U9hYWFgq+vr9ChQwehoKBAI+78+fOCTCYTPv/881LL0HY8Y2JiBABCWlqa1nzKU9Y5qut5WNb34l9//SVYW1sLT548ETp16iSsW7euVIz698mgQYOEwYMHC61atRJ+/vlncfq6deuEF154QRg8eLAwevTocvOuTE6zZ88W5HK5cOXKFUEQij4Pffr0KRXXo0cPYdiwYeWuo6RnukXl0aNH2Lt3LyZOnAhbW9tS052cnEqNKywsxJYtW/D48WNYWFhUuI433ngDMTExuH37NgBgy5YtaNKkCV588cVq5f7kyRMMHjwYPXv2xPz58zWmvfbaa2Iza1WZmZlhwYIF+Oqrr3D37l2d5rW2tsY777yDEydO6Nws7u7ujkOHDuH+/fsAqnaMKnL48GFkZ2ejb9++GDlyJDZu3KjxV7G7uzuSk5Nx7NixSi2von21fv16NG/eHIMGDSo1berUqXj48CGio6MBFLVsLFu2DNOnT8fIkSNhZ2dX6vhWx4ULF3Dy5MlS52779u3RpEkTbNmyBQBw+/ZtHDt2DG+88Ua11vfrr7/Cx8cHLVq0wMiRI7Fq1Sqx6X7Dhg3w9/dHu3bttM5bnReGVkXv3r3Rpk0brX/Fubu7Q6VSYdu2bTq9Xr6ytB2Xis7T8kyZMgVPnz4Vz6vqevr0KTZt2oSRI0fC398f6enpGi0nap999hkUCgVGjhyJc+fO4YUXXkDDhg3F6dbW1mW2SJRHEATExMTgypUrpc7d8s4xXZ0/fx6XLl1CWFhYqRfetWnTBn379q1UK15mZiZ+/vlnNG3aFC4uLlXKRRt9nYerV69GUFAQHB0dMXLkSERFRVU4z9ixYzVaXVetWoUxY8ZUOYeS3n//fQiCgN9++w0AMG7cOBw6dAi3bt0SY/766y8cO3ZMo9W5Mp7pQuX69esQBAE+Pj4Vxn7wwQews7ODpaUlhgwZgjp16uCtt96qcD5XV1cEBgZizZo1AIoO7tixY6uVd2FhIV5//XUoFAqsW7eu1Be6+p6J7777Djdu3Kjyel555RW0bdu2VHN0Zaj36c2bN3Wab+nSpbh//z7c3d3xwgsv4K233tL5GBX/t2DBglJxUVFRGD58OMzMzNCqVSs899xz2LRpkzj91VdfxWuvvYYePXqgfv36eOWVV/D1118jIyOjzHWXt6+uXr2Kli1bap1PPf7q1aviuDFjxqBVq1bYsWMHVq9eXe2eHHfu3Ak7OztYWVmhdevWSEtLw/Tp00vFjR07FqtWrQJQdMlhwIABqFevXrXWHRUVJTbR9u/fH+np6Th69CiAom1u0aKFRvwrr7wiHrsuXbpo3Y6Kjm91+Pj4aD1nO3fujI8++givv/466tati8DAQCxevBipqalVXldFx6Wi87Si7QB0//yVZePGjWjWrBmef/55mJmZYfjw4Vp/uVlbW+PLL7/E9u3b4e7uDg8PDwBFhcaBAwewb98+9O7du9Lr/eabb8Tv3e7du6OwsBDvvfeeRkx555iu1J/D8j6vxT+rxRU/P+3t7fG///0Pv/zyS6Xf8FsZ+jgPCwsLsWbNGnGfDR8+HMePH0dSUlK5840cORLHjx/HrVu3cOvWLZw4cULr5Zeqfk6dnZ3h6uoqnrMBAQFo0KCBRnG0Zs0aeHh4oE+fPpXeXuAZL1R0qUinT5+O8+fP49ChQ+jUqRMiIiLQtGnTSs07duxYrFmzBn/99RdiY2MxYsSIqqYMAPjoo48QGxuL3377Dfb29lpjAgIC0LVrV3z88cfVWtcXX3yBtWvX4vLlyzrNp963uv5V7OvriwsXLiAuLg5jx47Fo0ePAACRkZEVzqs+RsX/vfPOOxoxT548wdatWzU+YCX/ojAzM8Pq1atx9+5dLFq0CA0bNsSCBQvw/PPPl7pJuLjy9pUu59off/yBc+fOwcbGRutfrbrq1asXzp8/j1OnTmH06NEYM2YMQkNDS8WNHDkSsbGx+Ouvv7BmzZpqF9SJiYk4ffo0XnvtNQCAQqHAsGHDyv3r7ZtvvsH58+cxduzYUjcuqrejvONbXYIglHnOfvbZZ0hJScHKlSvx/PPPY+XKlfDx8anSvVhA+celMudpRdsB6K9VatWqVaVy2bRpU6mb9oGiwsHGxgaPHz/WKMYCAwMxbNiwcm/qL2nEiBE4f/48Tpw4gcDAQPz3v//VKGCrco5VRlVaK4qfn6dPn0ZAQAACAwM1WgT0obrnYXR0NLKysjBgwAAAQN26dcWbyctTr149BAUFYc2aNWKLTN26dUvFVedzWvzzZ2ZmhtGjR2PNmjUQBAGFhYVYu3YtxowZo3Px90wXKs2aNYNMJsOVK1cqjK1bty6aNm2Kbt26YdOmTXjvvfdw6dKlSq0nMDAQOTk5GDduHAYNGlStpsCNGzciPDxc/AunPJ9//jl++eUX/P7771VeX/fu3REQEICZM2fqNJ/6l7X6znoHBwekp6eXinvy5AnMzMw0LuvI5XJ07NgRkydPxtatWyGTyXDw4MEKK371MSr+z9nZWSNm/fr1yM3NRadOnaBQKKBQKPDBBx/g+PHjpf5SatiwId544w18/fXXuHjxInJzc7XeyKdW1r5q3rx5mYWeenzz5s0BFD0FM2rUKIwYMQLffPMNZs2ahcTExHK3uyK2trZo2rQp2rRpg1WrVuHUqVNav8hdXFwwcOBAjBs3Drm5uQgMDKzWeqOioqBSqdCgQQNxX69YsQJbtmxBeno6mjVrVmrb6tevr/W4Fd+O8o5vdV2+fBleXl5lTndxccGrr76K8PBwXL58GQ0aNKjyjevlHRddztOytgNAudtSWZcuXUJcXBxmzJgh5tK5c2dkZ2dj48aNGrG//PILdu7ciZMnT4pPVJ0/fx7Xrl1DTk4O1q5dq/USblkcHR3RtGlTdOzYEb/++iu+/vprHDhwQJxe0TmmK/XnsLzPqzqmpOLnZ8eOHfHDDz8gKysL33//vc55VKQ652FUVBQePXoEa2trcZ/t3r0ba9eu1XjqTRv1H91r164t8w+Zqn5OHz58iPv372ucs2PHjsXt27dx6NAhHDx4EHfu3KnS5aZnulBxdnZGQEAAIiMjtV77VT8yW5KHhweGDRtW6V/eCoUCo0aNwpEjR6r1V+r58+cxbtw4fP755wgICKgw/qWXXkJISAg+/PDDKq8TKCp4duzYgdjY2ErF5+Tk4LvvvkP37t3FSwctWrTAxYsXkZeXpxF77tw5eHl5wdzcXOuynJ2d4efnBwDifSvFlXWMyhIVFYWpU6dqVPt//PEHunXrVu5fFHXq1EH9+vUrvEdA274aPnw4rl27hh07dpSKX7JkCVxcXODv7w+g6G74R48eISIiAqNHj4a/vz/GjBlT4RdIZcnlcnz00UeYNWsWcnJySk0fO3Ysjhw5glGjRsHMzKzK61GpVPjxxx+xZMmSUvu6QYMG2LBhA1577TVER0dXq5DWp0OHDiEhIUFra5M2FhYW8Pb2rvJTP8WVPC5VPU/V1E/v9O3bt9q5RUVFoXv37vjjjz808gkLC9MoeFNTUzFx4kR8+umnaNOmDbp27Yp79+7h2rVraNy4MRQKRbXysLOzw/vvv49p06ZBEIRKnWO6atu2LXx8fBAREVHqM/fHH3/gwIEDYutNRdTdNmj7nOmTLufhw4cP8dtvv2Hjxo0a++z333/H48ePsX///nLn79+/P/Lz86FUKiv1O0gXX375JeRyucZj2d7e3ujRowdWrVqF1atXo2/fvvD09NR52dU78yQgMjISL7/8Ml566SXMmzcPL7zwAlQqFaKjo7FixYoyK+v3338frVq1wtmzZ9GhQ4cK1zN//nxMnz69yq0pDx48QHBwMHr27ImRI0eW6segrF8qn332GZ5//vlqfUm0bt0aI0aMKPO59bS0NOTm5uLp06eIj4/HokWL8ODBA42bEkeMGIF58+Zh1KhRmDFjBhwdHXHs2DEsW7YMixYtEuOGDBmCl19+GV26dIG7uzuSkpKQnZ0NMzMzjBkzRqdjVNL58+dx7tw5rFu3rtQ9L6+99hrmzZuHTz/9FFFRUTh//jxeeeUVeHt7Izc3Fz/++CMuXrxY6pHZyuyr4cOHY9OmTRg9ejQWL16MPn36ICMjA5GRkfjf//6HTZs2wdbWFmfOnMEXX3yBXbt2wdHREQDw7bffolWrVoiIiMDUqVMrtZ0VefXVVzF9+nRERkaKj56q9e/fH/fv34eDg0O11rFz5048fvwY48aNE7dFLTQ0FFFRUYiJicGuXbvQp08ffPLJJ+jWrRvq1KmDq1evYs+ePaXO6by8vFLnvUKh0Nr8XBH1sgoKCpCamoq9e/di4cKFGDhwIEaNGqV1ezZu3Ijhw4ejefPmEAQBO3bswO7du0s91l1VxY9LZc5T9Wf6yZMnSElJQV5eHq5evYpvv/0W27dvFx/7rA6lUomffvoJ8+bNK9WXy1tvvYWlS5fi4sWLeP755zF+/Hi0bNlS7JOkbt26aNasGcaPH48LFy6UOg+q4t///jfmz5+PLVu2QKFQVHiO6XppUCaTISoqCv7+/ggNDcXMmTPh7u6OU6dOYerUqfDz8yvV54pa8fPz8ePH+Prrr5GZman1JvrKSE9Px/nz5zXGJSQkYN++fVU+D3/66Se4uLhg6NChpS4LDhgwAFFRUeX2TWRmZiZ+35b1O6cyn9OnT58iJSUFSqUSSUlJ+Pnnn/HDDz9g4cKFpW6pGDduHN5++20AEO/11JlOzwhJ1L1794SJEycKnp6egoWFhdCwYUPhX//6l/hIZlmPUwUEBAiBgYGCIJT9eHLJR3fVSj7qW5E1a9YIAMr85+npKT5O9vvvv2vMO378eAGATo8nl3zELCkpSbCwsND6eDIAQSaTCfb29kKbNm2E6dOnC8nJyaXWkZiYKLzyyitCgwYNBFtbW6FNmzbC999/r/EY6nfffSf06tVLqFevnmBhYSE0btxYePPNN4XTp09X6RgVfzx50qRJgq+vr9btT05OFuRyufDbb78J586dE0aOHCl4eXkJlpaWgouLi9C9e3etjxdXdl8plUph8eLFwvPPPy9YWFgIDg4OQkBAgHD8+HFBEAQhNzdXaNmypdZHUNetWydYWVmJj+3poqzHBRcuXCjUq1dPyMzMLPOxTUEoevwbVXg8eeDAgcKAAQO0Tjt16pQAQPjjjz+E3Nxc4fPPPxfatGkjWFtbC5aWloKPj48wZcoU4fbt2xrboe28b9GihU55lVyWQqEQ6tWrJ/Tt21dYtWqVxiOpxc+pGzduCG+//bbQvHlzwdraWnBychI6duworF69Wuf1q3Mo67goFIoyH48vfp4KgqCxL6ysrARvb29h9OjRQnx8fJXyKvl48ubNmwW5XC6kpKRojW/ZsqUwZcoUYe3atYKNjY1w7do1jW0cNGiQ0KpVK2HMmDFlrrOs80/b48mCIAj//ve/heeff77S51hV1vPnn38KoaGhgrOzs2Bubi54e3sLs2bNErKysrSur+T5aW9vL3Ts2FHYvHlzmdtdnrLO9169eul0Hpb8XmzdurXwn//8R2vsL7/8IlhYWAj3798XBKH048llKfl4ckWfU09PT3G8+jt+6NChwqFDh7QuX92lh7Ozs5Cbm1v2TiuHTBBq4Fk9IiIiIj14pu9RISIiotqNhQoRERFJFgsVIiIikiwWKkRERCRZLFSIiIhIslioEBERkWSxUCEiIiLJYqFCREREksVChYiIiCSLhQoRERFJFgsVIiIikiwWKkRERCRZ/wdDWzM/Ek3y2QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#using default pandas lib \n",
    "boston_df.boxplot() #hard to interpret because the scale for each variable is different. better to do this one-by-one so each can have own y-axix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use loops to automate process above\n",
    "fig, axs = plt.subplots(nrows=2,ncols=7, figsize=(12,6))\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "index =0 # resetting the index to iteration\n",
    "axs = axs.flatten() \n",
    "\n",
    "for col in boston_df.columns:\n",
    "    sns.boxplot(data=boston_df,y=col, ax=axs[index], color='lightblue')\n",
    "    index +=1 #add 1 to index to move on to next cell\n",
    "\n",
    "plt.tight_layout(pad=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#IQR functin \n",
    "\n",
    "def outlier_treat(col): \n",
    "    #calc Q1 & Q3 (the 25th and 75th percentile)\n",
    "    Q1,Q3 = np.percentile(col,[25,75])\n",
    "\n",
    "    #calc IQR\n",
    "    IQR = Q3-Q1 \n",
    "\n",
    "    #calc the lower and upper ranges (the whisker values)\n",
    "    lower_range = Q1 - 1.5*IQR \n",
    "    upper_range = Q3 + 1.5*IQR\n",
    "\n",
    "    return lower_range,upper_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.0624999999999964 36.962500000000006\n"
     ]
    }
   ],
   "source": [
    "lower_range,upper_range = outlier_treat(boston_df['MEDV'])\n",
    "print(lower_range,upper_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get rid of outliers \n",
    "mask = boston_df['MEDV']>lower_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.boxplot(boston_df_no,x='MEDV')"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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