Module_1f_Exercise_LinearRegression-Completed.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise - Linear Regression\n",
    "\n",
    "Over 370,000 used cars were scraped from Ebay-Kleinanzeigen. The content of the data is in German, so one has to translate it first to English. The data is available [here](https://www.kaggle.com/orgesleka/used-cars-database) The fields included in the file data/autos.csv are:\n",
    "\n",
    "- seller : private or dealer\n",
    "- offerType\n",
    "- vehicleType\n",
    "- yearOfRegistration : at which year the car was first registered\n",
    "- gearbox\n",
    "- powerPS : power of the car in PS\n",
    "- model\n",
    "- kilometer : how many kilometers the car has driven\n",
    "- monthOfRegistration : at which month the car was first registered\n",
    "- fuelType\n",
    "- brand\n",
    "- notRepairedDamage : if the car has a damage which is not repaired yet\n",
    "- price : the price on the ad to sell the car. \n",
    "\n",
    "**Goal**  \n",
    "Given the characteristics/features of the car, the sale price of the car is to be predicted. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#import the required libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('fivethirtyeight')\n",
    "plt.rcParams['figure.figsize'] = (10, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Load the data\n",
    "cars = pd.read_csv(\"data/autos.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>seller</th>\n",
       "      <th>offerType</th>\n",
       "      <th>vehicleType</th>\n",
       "      <th>yearOfRegistration</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>powerPS</th>\n",
       "      <th>model</th>\n",
       "      <th>kilometer</th>\n",
       "      <th>monthOfRegistration</th>\n",
       "      <th>fuelType</th>\n",
       "      <th>brand</th>\n",
       "      <th>notRepairedDamage</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>privat</td>\n",
       "      <td>Angebot</td>\n",
       "      <td>kleinwagen</td>\n",
       "      <td>2001</td>\n",
       "      <td>manuell</td>\n",
       "      <td>75</td>\n",
       "      <td>golf</td>\n",
       "      <td>150000</td>\n",
       "      <td>6</td>\n",
       "      <td>benzin</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>nein</td>\n",
       "      <td>1500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>privat</td>\n",
       "      <td>Angebot</td>\n",
       "      <td>kleinwagen</td>\n",
       "      <td>2008</td>\n",
       "      <td>manuell</td>\n",
       "      <td>69</td>\n",
       "      <td>fabia</td>\n",
       "      <td>90000</td>\n",
       "      <td>7</td>\n",
       "      <td>diesel</td>\n",
       "      <td>skoda</td>\n",
       "      <td>nein</td>\n",
       "      <td>3600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>privat</td>\n",
       "      <td>Angebot</td>\n",
       "      <td>limousine</td>\n",
       "      <td>1995</td>\n",
       "      <td>manuell</td>\n",
       "      <td>102</td>\n",
       "      <td>3er</td>\n",
       "      <td>150000</td>\n",
       "      <td>10</td>\n",
       "      <td>benzin</td>\n",
       "      <td>bmw</td>\n",
       "      <td>ja</td>\n",
       "      <td>650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>privat</td>\n",
       "      <td>Angebot</td>\n",
       "      <td>cabrio</td>\n",
       "      <td>2004</td>\n",
       "      <td>manuell</td>\n",
       "      <td>109</td>\n",
       "      <td>2_reihe</td>\n",
       "      <td>150000</td>\n",
       "      <td>8</td>\n",
       "      <td>benzin</td>\n",
       "      <td>peugeot</td>\n",
       "      <td>nein</td>\n",
       "      <td>2200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>privat</td>\n",
       "      <td>Angebot</td>\n",
       "      <td>limousine</td>\n",
       "      <td>1980</td>\n",
       "      <td>manuell</td>\n",
       "      <td>50</td>\n",
       "      <td>andere</td>\n",
       "      <td>40000</td>\n",
       "      <td>7</td>\n",
       "      <td>benzin</td>\n",
       "      <td>volkswagen</td>\n",
       "      <td>nein</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   seller offerType vehicleType  yearOfRegistration  gearbox  powerPS  \\\n",
       "0  privat   Angebot  kleinwagen                2001  manuell       75   \n",
       "1  privat   Angebot  kleinwagen                2008  manuell       69   \n",
       "2  privat   Angebot   limousine                1995  manuell      102   \n",
       "3  privat   Angebot      cabrio                2004  manuell      109   \n",
       "4  privat   Angebot   limousine                1980  manuell       50   \n",
       "\n",
       "     model  kilometer  monthOfRegistration fuelType       brand  \\\n",
       "0     golf     150000                    6   benzin  volkswagen   \n",
       "1    fabia      90000                    7   diesel       skoda   \n",
       "2      3er     150000                   10   benzin         bmw   \n",
       "3  2_reihe     150000                    8   benzin     peugeot   \n",
       "4   andere      40000                    7   benzin  volkswagen   \n",
       "\n",
       "  notRepairedDamage  price  \n",
       "0              nein   1500  \n",
       "1              nein   3600  \n",
       "2                ja    650  \n",
       "3              nein   2200  \n",
       "4              nein      0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Do basic sanity check.\n",
    "#1. Look into the first few records\n",
    "cars.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['seller', 'offerType', 'vehicleType', 'yearOfRegistration', 'gearbox',\n",
       "       'powerPS', 'model', 'kilometer', 'monthOfRegistration', 'fuelType',\n",
       "       'brand', 'notRepairedDamage', 'price'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#2. What are the column names?\n",
    "cars.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "seller                 object\n",
       "offerType              object\n",
       "vehicleType            object\n",
       "yearOfRegistration      int64\n",
       "gearbox                object\n",
       "powerPS                 int64\n",
       "model                  object\n",
       "kilometer               int64\n",
       "monthOfRegistration     int64\n",
       "fuelType               object\n",
       "brand                  object\n",
       "notRepairedDamage      object\n",
       "price                   int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#3. What are the column types?\n",
    "cars.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#4. Do label encoding\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['seller', 'offerType', 'vehicleType', 'yearOfRegistration', 'gearbox',\n",
       "       'powerPS', 'model', 'kilometer', 'monthOfRegistration', 'fuelType',\n",
       "       'brand', 'notRepairedDamage', 'price'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['seller',\n",
       " 'offerType',\n",
       " 'vehicleType',\n",
       " 'gearbox',\n",
       " 'model',\n",
       " 'fuelType',\n",
       " 'brand',\n",
       " 'notRepairedDamage']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_object = [x for x in cars.columns if cars[x].dtype == \"object\"]\n",
    "col_object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['yearOfRegistration', 'powerPS', 'kilometer', 'monthOfRegistration', 'price']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_others = [x for x in cars.columns if cars[x].dtype != \"object\"]\n",
    "col_others"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "le = preprocessing.LabelEncoder()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cars_encoded_object = cars[col_object].apply(le.fit_transform)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "seller               int64\n",
       "offerType            int64\n",
       "vehicleType          int64\n",
       "gearbox              int64\n",
       "model                int64\n",
       "fuelType             int64\n",
       "brand                int64\n",
       "notRepairedDamage    int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars_encoded_object.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cars_encoded = pd.concat([cars_encoded_object, cars[col_others]],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>seller</th>\n",
       "      <th>offerType</th>\n",
       "      <th>vehicleType</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>model</th>\n",
       "      <th>fuelType</th>\n",
       "      <th>brand</th>\n",
       "      <th>notRepairedDamage</th>\n",
       "      <th>yearOfRegistration</th>\n",
       "      <th>powerPS</th>\n",
       "      <th>kilometer</th>\n",
       "      <th>monthOfRegistration</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>118</td>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>2001</td>\n",
       "      <td>75</td>\n",
       "      <td>150000</td>\n",
       "      <td>6</td>\n",
       "      <td>1500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>103</td>\n",
       "      <td>3</td>\n",
       "      <td>31</td>\n",
       "      <td>1</td>\n",
       "      <td>2008</td>\n",
       "      <td>69</td>\n",
       "      <td>90000</td>\n",
       "      <td>7</td>\n",
       "      <td>3600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1995</td>\n",
       "      <td>102</td>\n",
       "      <td>150000</td>\n",
       "      <td>10</td>\n",
       "      <td>650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>2004</td>\n",
       "      <td>109</td>\n",
       "      <td>150000</td>\n",
       "      <td>8</td>\n",
       "      <td>2200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>1980</td>\n",
       "      <td>50</td>\n",
       "      <td>40000</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   seller  offerType  vehicleType  gearbox  model  fuelType  brand  \\\n",
       "0       1          0            4        1    118         1     37   \n",
       "1       1          0            4        1    103         3     31   \n",
       "2       1          0            6        1     11         1      2   \n",
       "3       1          0            2        1      8         1     25   \n",
       "4       1          0            6        1     40         1     37   \n",
       "\n",
       "   notRepairedDamage  yearOfRegistration  powerPS  kilometer  \\\n",
       "0                  1                2001       75     150000   \n",
       "1                  1                2008       69      90000   \n",
       "2                  0                1995      102     150000   \n",
       "3                  1                2004      109     150000   \n",
       "4                  1                1980       50      40000   \n",
       "\n",
       "   monthOfRegistration  price  \n",
       "0                    6   1500  \n",
       "1                    7   3600  \n",
       "2                   10    650  \n",
       "3                    8   2200  \n",
       "4                    7      0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars_encoded.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['seller', 'offerType', 'vehicleType', 'gearbox', 'model', 'fuelType',\n",
       "       'brand', 'notRepairedDamage', 'yearOfRegistration', 'powerPS',\n",
       "       'kilometer', 'monthOfRegistration', 'price'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars_encoded.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#5. Ideally, we would do some exploratory analysis. \n",
    "#For practice, plot: year of registration vs price\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f0c7a90>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2Nta1/5133qnmzZsrLi5O3333nbZt26b4+HiNHDmy1FlbAAAA1C5eXQM7evRoZWZmauHC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\nAAAARvl/qKb9DjM6bdsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c582978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars_encoded.yearOfRegistration, \n",
    "           cars_encoded.price,\n",
    "           s=20, alpha = 0.05)\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('price')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cars_encoded['log10price'] = np.log10(cars_encoded.price + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10d8dc2e8>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oEaZm6t93WHBIxWIDuSGbnkTbT76AC4XsnKK2YeCO+RtTgKbZy1Koo46dbqCg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\niIiItJj/AQDJATqjxR91AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f09c4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars_encoded.yearOfRegistration, cars_encoded.log10price,\n",
    "           s=20, alpha = 0.05)\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('log10price')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Plot of month of registration with price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10d939198>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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964w/50tf+tJBBTzXyq7HYMljbwkyOYeOlE1reBtVNay3DLE4Y+u39Rq00squ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\nMUbNqIiIiIgYo2ZURERERIz5X6r3rxzpIW/pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d8dc898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cars_encoded.monthOfRegistration, cars_encoded.log10price,\n",
    "           s=20, alpha = 0.05)\n",
    "plt.xlabel('monthOfRegistration')\n",
    "plt.ylabel('log10price')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>seller</th>\n",
       "      <th>offerType</th>\n",
       "      <th>vehicleType</th>\n",
       "      <th>gearbox</th>\n",
       "      <th>model</th>\n",
       "      <th>fuelType</th>\n",
       "      <th>brand</th>\n",
       "      <th>notRepairedDamage</th>\n",
       "      <th>yearOfRegistration</th>\n",
       "      <th>powerPS</th>\n",
       "      <th>kilometer</th>\n",
       "      <th>monthOfRegistration</th>\n",
       "      <th>price</th>\n",
       "      <th>log10price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>118</td>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>2001</td>\n",
       "      <td>75</td>\n",
       "      <td>150000</td>\n",
       "      <td>6</td>\n",
       "      <td>1500</td>\n",
       "      <td>3.176381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>103</td>\n",
       "      <td>3</td>\n",
       "      <td>31</td>\n",
       "      <td>1</td>\n",
       "      <td>2008</td>\n",
       "      <td>69</td>\n",
       "      <td>90000</td>\n",
       "      <td>7</td>\n",
       "      <td>3600</td>\n",
       "      <td>3.556423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1995</td>\n",
       "      <td>102</td>\n",
       "      <td>150000</td>\n",
       "      <td>10</td>\n",
       "      <td>650</td>\n",
       "      <td>2.813581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>2004</td>\n",
       "      <td>109</td>\n",
       "      <td>150000</td>\n",
       "      <td>8</td>\n",
       "      <td>2200</td>\n",
       "      <td>3.342620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>1980</td>\n",
       "      <td>50</td>\n",
       "      <td>40000</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   seller  offerType  vehicleType  gearbox  model  fuelType  brand  \\\n",
       "0       1          0            4        1    118         1     37   \n",
       "1       1          0            4        1    103         3     31   \n",
       "2       1          0            6        1     11         1      2   \n",
       "3       1          0            2        1      8         1     25   \n",
       "4       1          0            6        1     40         1     37   \n",
       "\n",
       "   notRepairedDamage  yearOfRegistration  powerPS  kilometer  \\\n",
       "0                  1                2001       75     150000   \n",
       "1                  1                2008       69      90000   \n",
       "2                  0                1995      102     150000   \n",
       "3                  1                2004      109     150000   \n",
       "4                  1                1980       50      40000   \n",
       "\n",
       "   monthOfRegistration  price  log10price  \n",
       "0                    6   1500    3.176381  \n",
       "1                    7   3600    3.556423  \n",
       "2                   10    650    2.813581  \n",
       "3                    8   2200    3.342620  \n",
       "4                    7      0    0.000000  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cars_encoded.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = cars_encoded.iloc[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = cars_encoded.iloc[:,0:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# From sklearn import the linear models\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_ols = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ols.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -3.44100506e-01,  -2.48931559e+00,  -1.45016778e-02,\n",
       "        -2.15433457e-01,  -1.72855546e-04,   7.75851320e-02,\n",
       "        -2.21562066e-03,   4.63360547e-01,   3.18689809e-02,\n",
       "         5.22540972e-04,  -3.43232660e-06,   5.24214376e-03])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ols.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-59.912081033556944"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ols.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_ols = model_ols.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.26061808366881362"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#7. Report the diagnostics. And discuss the results\n",
    "metrics.mean_squared_error(y_ols,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#8. Build L2 Regression using sklearn - linear_model.Ridge \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_ridge = Ridge(alpha=10e10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=100000000000.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ridge.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3.12292970e-12,  -1.02760799e-10,   6.50003153e-09,\n",
       "        -1.54680630e-07,  -2.87347351e-06,   4.69374603e-07,\n",
       "        -2.25296042e-06,   1.33893300e-07,   3.76199402e-06,\n",
       "         4.33738513e-05,  -5.73678960e-06,   3.34487916e-07])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ridge.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.7062097352428309e-05"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(model_ridge.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_ridge = model_ridge.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.26071136846619347"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.mean_squared_error(y_ridge,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#9. Try with different values of alpha (0.001, 0.01, 0.05, 0.1, 0,5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10.\n",
    "The following code is from sklearn [official documentation](http://scikit-learn.org/stable/auto_examples/linear_model/plot_ridge_path.html#sphx-glr-auto-examples-linear-model-plot-ridge-path-py)\n",
    "\n",
    "```\n",
    "# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>\n",
    "# License: BSD 3 clause\n",
    "\n",
    "print(__doc__)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "\n",
    "# X is the 10x10 Hilbert matrix\n",
    "X = 1. / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])\n",
    "y = np.ones(10)\n",
    "\n",
    "#compute paths\n",
    "n_alphas = 200\n",
    "alphas = np.logspace(-10, -2, n_alphas)\n",
    "clf = linear_model.Ridge(fit_intercept=False)\n",
    "\n",
    "coefs = []\n",
    "for a in alphas:\n",
    "    clf.set_params(alpha=a)\n",
    "    clf.fit(X, y)\n",
    "    coefs.append(clf.coef_)\n",
    "\n",
    "#Display results\n",
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.axis('tight')\n",
    "plt.show()\n",
    "```\n",
    "\n",
    "Can you modify this code to plot for 10 values of alpha and see how weights get changed ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_std = preprocessing.StandardScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kSTx48ADvv/++1k+eDRs2xJw5c5Cfn48//vij1DjLIyUlBeHh4XB2dsaXX37JS5wBVb9T\nBweHEtdRkX09c+ZMrQRr6tSpAIC4uLgyPx91cldUvXr1DD4LoqufIsuyCA4OBqD6MDVkmwKBwOCR\nQTw9PbU+IAHgnXfega2trc5tVrU1a9bwnqeTkxOGDh2KrKwsxMfHa8p37NgBuVyORYsWaf1fAVT4\nYqXY2Fjcv38fHTt25CXOANCnTx+8+eabeP36NY4fP67V1t/fXyupmDJlCoRCocGvtV27doHjOCxY\nsECTOAMAwzBYuXIlLC0tsXfv3iobfcjQ56RUKrF161Y4OTkhJCSE93pjWRYrV64EwzA6k6SSTJs2\nTecvSlu3bgXHcfj222+13gcTJkyAr68vjh8/rvmCGRsbi0ePHqFbt268xBkA3n33XTRv3rxMcZWV\nm5ubzmNE37590apVK73vQWdnZ71nkw1x7NgxLFmyBM2bN8e+fftgYWGhWVYVx4X9+/dDKpXi/fff\n5yXOAPDxxx/D1dUVJ06c0PTbL6qyj92EzjzXaup+VUV99tlnWLRokUHt1f3B/P39df482KNHD60+\nWeo2us5s29jYoF27drh48SKvXN3n79KlS7h165ZWu5SUFACqM+etWrUqMeZr164BgN4uJUWpt6Xr\nS0Dbtm3h5OSEBw8eICcnBzY2Npo4ExISdPbtVPcX/ueff0rddnlcv34dSqUS/v7+sLGxKdc6KrKv\ndX3hUidYGRkZBscwevRobN26FZMnT8Zbb72FXr16oUuXLmW+4CwtLQ0bNmzAyZMn8fTpU+Tm5vKW\nF/0Q6dGjB9zc3LB+/XrcuHEDAwcORNeuXdG+ffsy/fQtk8nw448/Ijw8HPfv30dWVhaUSqXObZqC\nra0tmjZtqlWu6/9UlvdKeahfX/p+xu/Tpw+OHDmCW7duYezYsbxlul5rZmZmcHZ2Nvi1VtL21ddB\nxMXF4cGDB1rJiDEY+pwePHiA1NRUNGnSBKGhoTrXZWlpiX///bdM2/fz89NZHhsbC6FQiCNHjuDI\nkSNay6VSKRQKBR4+fIgOHTqUeIxnWRZdunTBgwcPyhRbWXAchwMHDmDv3r24e/cuMjIyeNc46Pvl\nqm3btuXunhAXF4cPPvgAjo6O+PXXX1G/fn3e8qo4LpT0ejY3N4e/vz9+++033L59m/dlEai8Yzcp\nRMlzLaZ+U+Tl5eH69euYP38+Vq9eDS8vL60PK12ysrIAqM5c6aLrivTytElLSwOg6pNXkuLJkS6Z\nmZmwtbU1KLnMysqCra2tzrORgGoEjJSUFGRlZcHGxkYT5+HDh0sc2siQOMtDfSFd8QNjWVRkX+v6\n1UB9tkXXBXr6+Pn5ITIyEuvWrcPRo0dx4MABAKqzN/PmzcN7771X6joyMjIQGBiIp0+fws/PDxMm\nTICDgwMEAgEyMzOxdetWXhcWW1tbnD59GmvWrEFERATOnTuneU5TpkzB0qVL9fZ/LGr69Ok4evQo\nvLy8MHToULi4uGg+rLds2VJqtxlj09dnUtf/Sf16MtZQhupjgb6RK9QjzOi6QLSk52Hoa60i2zcG\nQ5+T+j36+PFjnSdAykvffkhLS4NcLi91W+oLLMtzjK9Mn376KbZs2YKGDRuiX79+cHV11ZwF3rt3\nr86LBisS15MnTzBhwgQAqrO/Xl5eWnWq4rhQ2e+n8hy7SSFKnusAKysr9OzZE7/++iu6deuGefPm\noWfPnqUOY6buyqA+G1ncq1evtMrUF0WUpY16O48fPy6120Fp7OzskJqaqjlbXBJbW1ukp6cjPz9f\nZwKtvspcHZ96GhYWhrfeeqtCcZaH+gBYkbMYlbmvK6Jz586anyFv376NqKgo/O9//8OCBQtgZWWl\n+bDSZ9euXXj69CkWL16s1Tfx6tWr2Lp1q1YbNzc3fPfdd1i/fj3i4+Nx8eJF7Ny5E5s2bUJmZmap\nXyhu3LiBo0ePok+fPjh48CBv6EGlUokNGzaUYQ+UjGEYvR9qlZXsqV9PiYmJRrmhjfq1pus9D2i/\nv4y5fV3Pz9jbLy91PIMHD8b+/fsrbb0Mw+jdnkwm05t0FleeY7y6i1lFX9MpKSnYtm0bfHx8cOLE\nCa2Lcw8dOqS3rb7nX5K0tDSMHTsWqamp2LVrl86z91V1XDD1+4nwUZ/nOqRx48aYO3cucnJyNH16\nS6LuHxcbGwu5XK61XH3xoa42ly9f1lqWk5Ojc0gw9UVdly5dKjWm0nTq1AkAcPr06VLrtm/fHgC0\nupEAwF9//YWUlBQ0b95ck4Sr49T13KqCn58fWJbFlStXeMNslUVl7uuSGHpWQyQSoVOnTvj44481\nCe/Ro0dLXb+6i4yuLzG6XpdFMQyDFi1a4L333kNERATMzc3LtM0hQ4ZojdkdFxeH/Pz8UtdhKHt7\ne80Fe8UVH2ayvMryXinPWSr1+0vfLYbVF6Uacv1FeZS0/devX+Pvv/+GtbW1wSN36FPZZ/BatGgB\nOzs7xMXFlWlIuvLq3LkzsrOzDR6usaRjvFKpxNWrV7XK1V9edL2m5XK5pitIaZ48eQKlUonAwECt\nxPnFixd48uSJQesxhFgsxqRJk/DgwQN89dVXeoeOLM9xobLfTxKJRNMlT12PGBclz3XMrFmz4Ojo\niD179pTaL61Ro0YIDAzE8+fPsWXLFt6yEydO6HwTDx06FLa2tggPD8fNmzd5y9auXavzDMOMGTMg\nEonw2Wef6ezHp1Ao9H4AF6e+AnrZsmU6D9RFx7VUDym3cuVKXjIqk8mwdOlSAIUXVaifW9OmTfHj\njz/qvMgJUPVLU//sWtkaNGiAMWPG4NWrV1i6dCmvTx2gGv+5tLGGK3Nfl0TdJ1DX2azY2FidHyjq\nMyf6utEUpR4GrPgXn1u3bum80v7vv//WOV5tWloaZDJZhbaZkpJi8HUEhurUqRMSEhJw8uRJXvnP\nP/9crrGOdXn//fchFAqxdu1a/PXXX1rLi45Mo/5/6kvodenatStatmyJuLg4rYvbzp8/jyNHjsDR\n0RFDhw4t5zMo2ZQpUwAA33zzDe9/z3Ecli9fjry8PEycOFHnzYvKojz7piRCoRDBwcGa11VeXp5W\nndTUVIMTztKox6meN28e73+uJhaLeYmyv78/mjRpgsuXL2uNm//TTz/p/FypV68eWrZsidjYWNy7\nd09TznEcvvrqK4P3nfo9eOXKFV7imZOTg7lz5+o8yVMeHMdh5syZuHLlCj766CPMmDGj1JjKclwo\nz2tm/PjxEIlE2LFjh9ax+5tvvkFiYiIGDhxYoW59xHDUbaOOqVevHubNm4dly5Zh9erV+PHHH0us\nv3btWgwYMADLli3D+fPn4evriydPnuDw4cMYPHgwIiMjefVtbW2xbt06zJgxA0OGDOGN83znzh30\n6NEDMTExvJEivL29sXnzZsyePRvdunVD//790axZMygUCrx48QKxsbGQSCR49uxZqc+vb9+++Pjj\njxEaGgp/f38MHToUHh4eSElJwbVr1+Dl5aW5+cOYMWMQGRmJgwcPwt/fH8OGDdOM86y+G2PRUUbM\nzMywe/dujB49GpMmTUKnTp3Qvn17WFtb48WLF7h9+zbi4+Nx4cIFrQtKKktoaCj+/vtv/Pzzz4iJ\niUG/fv1gYWGB58+f48yZM9i0aZPW8G9FVea+LklgYCCuX7+Od955BwMHDoSFhQU8PDwwYcIEfPfd\nd7hw4QK6deuGxo0bo169enjw4AFOnDgBS0tLvTdSKGrChAnYsGEDPvnkE0RHR6NZs2Z4+PAhTpw4\ngeHDhyM8PJxXPyoqCsuWLUOXLl00N1ZITk7G8ePHNcN/laZjx47w9/fHkSNHMHDgQPj7++PVq1c4\nffo0vL29K/VDa86cOThz5gymTJmCkSNHwsnJCTdv3sTNmzcxaNCgUm9SZIhWrVph3bp1mD9/Pvr0\n6aMZ5zk9PR23b9+GRCLRfJHy9vaGu7s7Ll++jA8++ADNmjWDQCDAkCFD9I7dzjAMtmzZgpEjRyI4\nOBi//fabZpznw4cPQyQSYevWrQb1NS+PLl26YMGCBfjmm2/QrVs3jBw5Era2toiKisKtW7fg4+OD\nZcuWVcp2rKysEB4eDpFIBHd3dzAMg7fffltrrGdDffzxx/jrr78QFhaGkydPolevXmjUqBFev36N\nx48f48qVK5qbDFVUr1698MUXX+Dzzz+Hn58fBgwYAC8vL4jFYjx//hyXLl2Cp6enJjlkWRYbNmzA\n2LFjMWXKFLz11luacZ6joqIwYMAAnDp1Sms0oLlz52LWrFmazwUrKyvExsbixYsX6Nmzp85fAItz\ncXHBmDFjcOjQIQQEBCAwMBBZWVmIioqChYUF2rVrZ/AZ9JL8/vvv+OOPP2BrawsrKyudF4j37NkT\nAQEB5Tou9OrVCyzLYuvWrUhPT9f0Y54xY4bevvGenp5Ys2YNFixYgMDAQIwcORIuLi6IjY1FTEwM\nGjVqZNAQjqRyUPJcBwUFBWHz5s34/fffMW/evBJ/5mnWrBlOnz6NFStW4Ny5c7h06RLatGmDPXv2\n4PXr11rJMwCMGzcO9vb2CA0Nxe+//w6RSITu3bvj1KlTmg+r4j+5jR07Fm3btsWmTZtw/vx5zcGw\nYcOG6N+/P0aMGGHw81u6dCm6du2Kbdu24dSpU8jJyYGTkxPatWuHadOm8epu27YN3bt3x65du7Br\n1y4olUo0a9YMK1euRHBwsNZZKR8fH8TExGDLli04fvw49u3bB47j4OLiglatWmHOnDkV/hm4JPb2\n9jh58iS2bt2K8PBwhIWFgWVZuLm5Ydy4cQb9BF6Z+1qfhQsXIisrCxEREfjuu+8gl8vRo0cPTJgw\nAUFBQXBwcEBcXBxiY2Mhk8ng6uqKCRMm4KOPPjJo1A1XV1dERERgxYoVuHLlCs6ePQtvb2+sW7cO\nvXv31kqe+/Xrh4SEBFy+fBmRkZHIysqCs7MzunTpguDgYAQGBpa6TYFAgH379mHVqlU4efIktm3b\nBldXV0ydOhWLFi1C165dy72/iuvVqxf27duHr7/+WpNoqt9Df/zxR6Ukz4Bq+DIfHx9s3LgRV65c\nQUREBBwcHNCqVSsEBQVp6gkEAuzevRsrVqzAiRMnkJ2dDY7j4Obmpjd5BlRfOM6dO4fQ0FCcO3cO\nZ86cgZ2dHYYNG4aFCxdWSvJXkuXLl8PX1xc//PADDh48CIlEgsaNG2PRokWYO3duqTe0MYT6LoRr\n1qxBeHi45lcsf3//cifPQqEQYWFhOHToEPbs2aM5jtWvXx8eHh6YP39+qdcFlMWcOXPg7++PrVu3\nat4jNjY2cHV1xbhx4zB69Ghe/YCAABw7dgyrVq3CqVOnAKi6lR05cgQHDx4EoH2MVw9X+P3332P/\n/v2wsbFB3759sWvXLqxevdrgWDdu3AgvLy+Eh4dj+/btaNCgAYYMGYJPP/1U82tiRanP9mdlZeHr\nr7/WWy8gIKBcx4UWLVrghx9+wMaNG7F7927NL3Hjx48v8UYp06dPR9OmTbFx40YcO3YMubm5cHV1\nxYwZM7Bo0SK6rXwVYjIyMnTfs7WWiIyMxGeffQalUol58+bxfoYnVUuhUKB9+/aQSqVlHmaJEEJI\n9Tdo0CBcu3YNz549g7W1tanDIcQoanWfZ7lcjqVLl+Lw4cO4cOECNmzYUGqfUFJxmZmZWv30OI5D\naGgoEhISMHz4cBNFRgghpKLy8/N1jg+8Z88exMbGom/fvpQ4k1qtVnfbiIuLQ6tWrTTjmPbv3x9n\nzpwxaIxjUn43btzA1KlTERgYCE9PT+Tm5uLPP//EnTt34O7ujiVLlpg6REIIIeWUlJSE7t27o0+f\nPmjatCnkcjnu3LmDy5cvw87ODqtWrTJ1iIQYVbU+8xwTE4MJEyagdevWmn5lxW3fvh2+vr5wcXFB\n7969eUNwvXz5kncDADc3N5PfAawuaNq0KQYPHowbN25gx44d2L17N7KzszFz5kycPXtW7+D6hBBC\nqj9HR0eMHz8e8fHxCAsLw48//ojnz59j8uTJOHfuHFq2bGnqEAkxqmp95jk3Nxc+Pj6YOHEigoOD\ntZaHh4djyZIlWLduHfz9/bF9+3aMGzcOV65cgYeHBziuVnfnrrY8PT3xww8/mDoMQgghRmBnZ1ep\nNwUipKZAVRjGAAAgAElEQVSp1meeBw4ciOXLl2PEiBFaw94AwKZNmzBp0iRMmzYNLVu2RGhoKFxc\nXLBz504Aqivyi47rm5iYWOpd9QghhBBCCNGnWifPJZFKpbh58yb69u3LK+/bt6/mJgJ+fn74+++/\nkZiYiJycHJw+fRr9+vUzRbiEEEIIIaQWqNbdNkqSmpoKhUKh1X/WyclJc+93oVCIVatWYfjw4VAq\nlZg7d67Rbl5BCCGEEEJqvxp75lmNYRjePMdxvLKhQ4ciLi4ON27cwLvvvlvF0ZUsPj7e1CHUOrRP\njYP2a+WjfWoctF8rH+3Tykf7tGarscmzo6MjBAKB5iyz2uvXr2k0B0IIIYQQYhQ1NnkWiUTo0KED\noqKieOVRUVGVeptcQgghhBBC1Kp1n+ecnBw8evQIAKBUKpGQkIDbt2/DwcEBHh4emD17NmbOnAk/\nPz907doVO3fuxMuXLzF9+nQTR04IIYQQQmqjap0837hxg3cr55CQEISEhGDixInYsmULRo8ejbS0\nNISGhiI5ORmtW7fGgQMH4OnpacKoCSGEEEJIbVWtk+eAgABkZGSUWCcoKAhBQUFVFBEhhBBCCKnL\namyfZ0IIIYQQQqoaJc+EEEIIIYQYiJJnQgghhBBCDETJMyGEEEIIIQai5JkQQgghhBADVevRNggh\npERKBSCXAxwHKJUAp1RNlUow6seaKaeqX1CXUepZXvCYKVIXxdel5ACWBQQCgBUAAgG4gilYASAU\nAqwAXJHlxeuxEjEglRQuYxhT701CCCEGoOSZEFJ9cRyQnQk2JRHsqyQwKYlgXyWCTUkE8yoJTHoK\nGI4zdZTl0r7YPFcsGecn30IdZQXTgnZcsSS9tOSdvw4D6qpze4aBZqZows8wOpYXrcOAY4qUqx8U\nWc7fRvHlhrFNTIQgJ6XYdsqDvsyo2SYmQpD72tRh1Cp1YZ8qPZuDq+9k6jCMgpJnQohpyaRgXr8E\n+ypJlRSnJIF9VTBNSQQjzjd1hFVCcyYcssIy04VTYzUzdQC1EO3TylcX9ql45lLIuw8wdRhGQckz\nIcS4OA5MdgaYV4lgU5JUU/XjlEQw6a9r7NljQgghdQ8lz4SQipNKVGePi581Vp9NloiNtmnOzAxg\nWFX3Bc2UUXU5YJhi5QVTlgHHCABWz3KGARhW1ZVCU84U9k1mWFX/Z4VC1U9aoVD1kS4yD4Vcu0yp\nAFMwVcrkYKEsaKs02v4hhBBSuSh5JoSUn1QC0cEfYBZ1BIxMapRNcOYWUDq5gXN2LZi6QenkBqWz\nKzhHF0BkbpTtGlt8fDy8vb1VM+qLFRUKAxJyJS8Z59VTlymLJOp6kne921EqddSVF8RZEKt6pvgv\nBhxXbHlhOaOeKdqGK1rGaZpplZVBbm4urK2ttWMj5abZp6TS1IV9yjk0MHUIRkPJMyGkXJi0V7DY\n+DkEj/6u0Ho4hgHn0KAwKXZyLXismnL17Gv/SBQMU3BRIP+QrCv9o5SwZI+KfikhlYL2aeWjfVqz\nUfJMCCkz9p/bsPj+c7BZ6QbV58wtoHRuBM7JFUpnN9W0Fpw9JoQQUvdQ8kwIMRzHwezM7xDt/V71\nk37RRTa2ULo30Tp7rHRuBNSzq/1njwkhhNQJlDwTQgwjlcD8529hdjFSa5G8vT/EM5cC1vVMEBgh\nhBBSdSh5JoSUyiwzDZZfroXg8T9ay6QjpkI68l3VqBSEEEJILUfJMyGkROz9m2i5YxUEedm8cs7C\nEuIPPoWiU4CJIiOEEEKqHiXPhBDdOA5mp3+DaN8mrf7NyoYeyJ+7CpxbYxMFRwghhJgGJc+EEG1S\nCcx/+gZmMSe0Fsk7dFP1b7ayMUFghBBCiGlR8kwI4WFSk2GxYRkET/7VWiYdOQ3SEdOofzMhhJA6\ni5JnQoiG4O8bsNi0Akx2Jq9cIbKA9MPPoOjY00SREUIIIdUDJc+EEFX/5lOHINq3WXX75yKUrh74\nZ8QH8KTEmRBCCKHkmZA6TyqB+Y/rYHbppNYi+Rs9IJ7xCSQvkkwQGCGEEFL9UPJMSB3GvH6p6t/8\nNF5rmWTUdMjeeof6NxNCCCFFUPJMSB0l+Ou6qn9zThavnLO0hnjmUije6G6iyAghhJDqi5JnQuoa\njoPZiV8h+mWLjv7Nnqrxm109TRQcIYQQUr1R8kxIXSIRw/zHtTC7fFprkbxjD4hnfApYWpsgMEII\nIaRmoOSZkDqCSUlS9W9+9oBXzjEMpKOmQzZ8CvVvJoQQQkpByTMhdYDg3jVYbF6pu39z8FIoOlD/\nZkIIIcQQlDwTUptxHMwiD0D0yzYwXLH+zW6NVf2bG3qYKDhCCCGk5qHkmZDaSiKG+c5QmF05o7VI\n7hcA8QefAJZWJgiMEEIIqbkoeSakFlL1b/4MgmcPeeUcw0A6+j3I3pxM/ZsJIYSQcqDkmZBaRnC3\noH9zbrH+zVbWEM/8DIoO3UwUGSGEEFLzUfJMSG3BcTCL+AWiAz9o9W9WuHlBPHcVuIbuJgqOEEII\nqR0oeSakNuA4Vf/mC8e1Fsk79YI4aAn1byaEEEIqASXPhNQCwqvntBJnjmEgHfO+qn8zw5goMkII\nIaR2oeSZkJouPw+ivZt4RZyVDcTBy6Bo39VEQRFCCCG1EyXPhNRwot9/ApvxWjPPCYTI/3QDlB5N\nTRgVIYQQUjtR8kxIDcYmPILZyV95ZbLB442WOMvFcogzxRCn50OcUWSaKQan4FSVCnqI8HqKFMww\nxecZ/nxh2yKNdZUVbSJgwQgYsLwpC1bAlDIt1k7IgmGL1SkoY4UsWPUyoWoqMBNUaF8SQgipmSh5\nJqSm4jiYh30HRlk4sobS0QXSEe+U2lQhVRQmwZliiNPFEGfkq6bFk+NMMXJSsnEy5xjk+XJjPqMa\nRWAuhKWDBSwcLGFhZwEL9WN7C1jYW8LCwQKWDpYwt7eAZcG8uZ0FJd2EEFLDUfJMSA0lvHQKgn9u\n8cqSOk9A4tFHyE/PhyRDrJpmipGfLlbNZ6jKpTlSE0VdeygkcuS8zEHOy5wytRPVE8HC3hKMJYO7\nDW/Bwr5Ikq1OvotMLe0tIKpnDoaliz4JIaQ6qDPJ8+TJk3Hx4kX07t0bYWFhpg6HkIrJzYboly28\nomfiRti15AGAh7rbkGpBmi2FNFv15SXz3wyD2jACpuDstuost7m9RWGSbVfwuODPXH3m294C5pR0\nE0JIpaszyfPMmTMxZcoU7Nu3z9ShEFJhot9+BJuZrpmXK1kcvdUCRXoVGwUrZAu6IVjA3N4Slg4F\nyZqdBQQiATiuSGX1jHpS2nzRDZWhrVLJgVMowSk4KHlTJTglB6VcCaVCVUd7ym+nrs+ro+TAyYtM\nFRyUckVhH+8qwCk45KflIz8tv2wNGfCTbbsiiXVBmaW9ZeFydQJuawFWSLdvJ4QQXepM8tyrVy9E\nR0ebOgxCKox9Gg+z07/zyi4/a4b0fGuD18GwDMzV/XTt+N0ENP13C/rpWthb4GVGMlp1aAWRjUjr\nwr26iOM4yPJkhX3DC/qHa7rLZOi4qLKg/ziqLucGOGjiyyxjU5GtueastnnBlyNWwIBh1RdaFn2s\nmjIC9YWVRR4LdZQVv1izSBnDqi7YVC8reuWp1kuv6HWlBQuTkpKAf5XF6ulZh56LUHVvrGpUx7dX\ncmISBE+qYWA1WF3Yp05tXVDPtZ6pwzAKkyfPMTEx2LhxI27duoWkpCRs2rQJkydP5tXZvn07NmzY\ngOTkZLRq1QohISHo3r27iSImxISUSpiHrefdfjs93wqXnjXXzHv28oJDU4ciibA6MVYlxOXpQ5sV\nnw3zeuaV+lRqMoZhILIWQWQtgq27ncHtOCUHSZaqD3r87X/hVM+p8ELNItOifdTF6fmQ5cqM+Gx0\nk2ZJIM2SIOt5WdNu07th6gBqoThTB1AL1fZ9Omj9ULQa5WPqMIzC5Mlzbm4ufHx8MHHiRAQHB2st\nDw8Px5IlS7Bu3Tr4+/tj+/btGDduHK5cuQIPDw8AQM+ePaFQKHS2dXV1NfpzIKSqCKIjIHhwj1d2\nMr4N5EoBhJZCBK7qD5+xbU0UHSkNwzIF3SYs4SCvjybehg0pqJAqCs4gFznTXXDxp3qoQHW5RF0v\nU6zpW00IIaTymDx5HjhwIAYOHAgAmDVrltbyTZs2YdKkSZg2bRoAIDQ0FGfOnMHOnTvx+eefAwAu\nXrxYdQETYiLSxBRY7fyeV/bPaxc8SHOBY6sGGPr9cNT3djRRdMSYBCIBrJ2tYe1seNccAFDIFJAU\nSazFmeLChLtIIq6pU9DFRJIlMdIzIYSQms/kyXNJpFIpbt68iTlz5vDK+/bti9jYWKNsMz4+3ijr\nrS7bqwtq4z7NuJ+O+v/bivYOhReMyRQsTj1oA49hjeEzqx1SkYbU+DSjxVAb96upVek+tVP9CT1F\nsIEINrDVW5VTcJDlyCDLlhb8yVQXUCo51YWSysLHnK7HReeL1texrLAcgI71FQbF7yzO6es7Xs56\n0L8pQkg5ZMgzq/QY5+3tXWXbqtbJc2pqKhQKBZycnHjlTk5OePXqVZnWNWLECNy9exd5eXnw8fHB\nTz/9hC5dumjVq8qdHx8fX6Xbqwtq2z7lOA43tsfh6fdH0Kf9I96yKy9boVvoeLR8q5XR46ht+7U6\noH1qHLRfKx/t08pH+7Rmq9bJs1rxq/s5jivzFf9//PFHZYZEiNHlp+fj1MIIPDnzEO92vM27Cj9D\nbocmW1fAvrmz6QIkhBBC6qBqnTw7OjpCIBBonWV+/fq11tloQmqTF38mIHLOMeQkZaOj2zO42fJH\nPBAu+pQSZ0IIIcQEqvUo+CKRCB06dEBUVBSvPCoqCl27djVRVIQYD6fk8OemWBx6+xfkJGXDykyC\nPk3u8+rIOvcB3qDXPyGEEGIKJj/znJOTg0ePVH05lUolEhIScPv2bTg4OMDDwwOzZ8/GzJkz4efn\nh65du2Lnzp14+fIlpk+fbuLICalcuSm5ODn/OJ5FP9WU9W16H5ZmhWP8cuYWkE7SHpWGEEIIIVXD\n5MnzjRs3MHz4cM18SEgIQkJCMHHiRGzZsgWjR49GWloaQkNDkZycjNatW+PAgQPw9PQ0YdSEVK5n\nF5/ixLzjyEvJ1ZS526ahvetzXj3pyHfB1afuGoQQQoipmDx5DggIQEZGRol1goKCEBQUVEUREVJ1\nlHIlYr+7hKsbr/CGymIYJYa05t8MReHmBdnAsVUcISGEEEKKMnnyTEhdlfMyG5H/dwwvYhO0lvXr\nlglnEf8iQenUuYCQ3rKEEEKIKVXrCwYJqa0en32EvUPCtBNnBuj5YRt0sbvJK5Z16w9F6zeqMEJC\nCCGE6EKnsQipQgqZApdDLyJu259ay6ycrDBo/TB4390FJr+w7zNnaQ3phA+rMkxCCCGE6EHJMyFV\nJCshExEfHcXLG0layzx6Nsag9UNh+/pfmF0+zVsmHT0dnL1jVYVJCCGEkBJQ8kxIFXh4Ih6nFkVC\nkiXhlTMsA/+FPdB5VlcwSgVE33zHW67wbAZZv5FVGSohhBBCSkDJMyFGJJfIERNyATd/vK61zKah\nDQZvfBONurgDAMwif4Ug8QmvjmTqfEBAb1NCCCGkuqBPZUKMJONJOiJmH8Wru8lay7z6NsXAdYNh\nWd8KAMCkvYLo9594dWQBQ6D0blsVoRJCCCHEQJQ8E2IE/xy+j7OfnIQ0R8orZ4UseiwOwBtBncCw\njKZctHczGIlYM89Z2UA6fkaVxUsIIYQQw1DyTEglu/jVBcRtuapVbutuiyHfD0fDN1x55YI7f8Ls\nz3O8MsnYD8DZOhgzTEIIIYSUAyXPhFSiJ1GPdCbOzQZ7Y8DXg2BuZ8FfIJPCfPcGXpGiSUvIA980\nZpiEEEIIKSdKngmpJHKxDOeWn+GVCUQCBHzWB75TO4BhGK02ZpEHwL58rpnnGEZ1kSArMHq8hBBC\nCCk7Sp4JqSTXtlxF5rPCW2ozLIPRe8fDrXMjnfWZlCSIDu/ilcn7vAll01ZGjZMQQggh5Ue35yak\nEmQ8Sce1Yt01fN/poDdxBgDzvd+DkRaO+8zZ2EIyNshoMRJCCCGk4ih5JqSCOI7DueVnoJAoNGVW\nTlbotrCH3jaCm5chvB7DK5OMnwnY2BktTkIIIYRUHCXPhFTQw8h4PD3/hFcW8Gkf7YsD1aQS7YsE\nm7eBPGCIkSIkhBBCSGWh5JmQCpDmSnF+ZRSvrJG/O1qOaq23jejYXrApSZp5jmEhmToPYOntSAgh\nhFR39GlNSAVc3XAZOYnZmnlWyCLwi/46R9YAACb5BcyO7eWVyfqPhLKxt1HjJIQQQkjloOSZkHJK\n/fc1bmyP45W98b4fHFs00N2A42C+ewMYmUxTpLRzgHTUdGOGSQghhJBKRMkzIeXAcRyilp2GUq7U\nlNm41kOXud30thHEXYTwdiyvTPr2h4B1PaPFSQghhJDKRckzIeXwz+9/48WVBF5Zr+WBEFmLdDeQ\n5MN87/e8IkXL9pB3H2CsEAkhhBBiBJQ8E1JGkiwJolef45U17u2F5kP091sWHd4NNjVZM8+xLCRT\n5wJ6+kYTQgghpHqi5JmQMrq87iLyUvI08wJzAfqs7Kf/IsHEpzCL+IVXJhs4Fkr3pkaNkxBCCCGV\nj5JnQsrg1d1k3A67ySvzC+4Cey8H3Q04Dua7vgOjkGuKlPYNIB35rhGjJIQQQoixUPJMiIE4JYeo\nz06DU3KaMlsPO3Se1UVvG+HVKAj/us4rk06aBVhaGS1OQgghhBgPJc+EGOjeL3fw8kYSr6zPyn4Q\nWpjpbpCfB9HezbwieRs/yLsEGitEQgghhBgZJc+EGCA/LQ8xX13glTUb1BxN+urvtyz6/SewGa81\n85xACMk7dJEgIYQQUpNR8kyIAWLWREOcIdbMCy2E6LVc/xlkNuERzE7+yiuTDXkbnKun0WIkhBBC\niPFR8kxIKZKuJ+Le/ju8si5zu8HW3U53A46Dedh3YJSFN1BROrpA+tYUY4ZJCCGEkCpAyTMhJVDK\nlYhaeppX5tCsPjoGddLbRnjpFAT/3OKVSSZ9BJhbGiVGQgghhFQdSp4JKcHtXTeR8tcrXlngF/0h\nEAl0N8jPg+iXLbwiuW9XKPx6GitEQgghhFQhSp4J0SP3VS4ur7vIK2vxVit49NDfb9nsxEGwmema\nec7MDJIp/0cXCRJCCCG1BCXPhOgRvfocpNlSzbzIRoRen/XR3yA7A6LidxIcMgGcSyMjRUgIIYSQ\nqiY0dQCEVEcJl5/hn9//5pX5L+wBaxcbvW1ER/eCERfetpuzsYV06ASjxUhITcIp5YBCDE6RDyjy\nC6YF8/J8cAqxdrlCDI5TAlDfmIgDOK5gXv0YReYBh9xsiPOti9UFr52qWfFlymL1DHpW5d8hOldX\nyeurJA3EYuRnWpg6jFqlLuxTsyaTIXTUf31QTUbJMyHFKKQKRC07wytr4OOE9lPf0NuGSU2G2Znf\neGXS4VMAS2ujxEhIVeGUMihznwCynGIJbj64kpJeTZKsWg6lrEritYRqc6TyiAAopaVWI2VQJ/ap\nLMvUERgNJc+EFHNjZxzS4lN5ZYFf9Acr1N/LSfT7z2BkhcmBsr4TZH1HGC1GQoyJ4zgos+Mhf3ka\n8uRztfpDkBBCyoqSZ0KKyE7MQuz6S7wyn/Ft4dZJf79lJvEphNGRvDLpyHcBkbkxQiTEaJSS15C/\njIL85Slwuc9MHQ4hhFRLlDwTUsT5/0ZBni/XzJvbWaDHkl4ltjE/tAMMV+SGKK4ekPccZLQYCalM\nnEIMRcplyF+egiLtJjR9fysdCwgswAgsAWHBVGAJRmABCKwKppaFU6ElwJoDjGpYSIZhABT88R6j\n8DGApKSXcHVzK1YPOucZzSg4bJERcYpuozIZuL5qODLP8+fP4eHhYeowapW6sE9ZSzdTh2A0lDwT\nUuDJucd4GBnPK+uxJABWjlZ627CP7kN47QKvTDLmfUBAby1SfXEcB2XGXVW3jFfRgCKv5AZCG7A2\nTVUJrcCyIPG1ACOwKkyIBRZghEWXWfKSYbCiIsmq8Ygz4yF08jb6duoS2SszCOxon1Ym2qc1G33C\nEwJALpbj3HL+RYIuHRqi7QTfEtuJfv0fb17h1QKKTr0rPT5CKoMyPwnypNOQvzwDTvyy5MoMC4Fj\nZwgb9oegQVcwrKhqgiSEkGqOkmdCAFzbehWZTzMKCxggcFV/MKz+M2WCe3EQ3ovjlUnHzaiWP7uS\nuouT50L+KhrypNNQZt4ttT5r0wxC1/4QugSCEdlXQYSEEFKzUPJM6ryMpxm4tjmWV+b7Tge4tGuo\nvxHHQfTrdl6R3KcjFG38jBEiIWXCcQoo0m5A/vI0FCmXSh0TixE5QODSF2au/cDaNK2iKAkhpGaq\nE8lzQkICZs6cidevX0MgEOA///kPRo4caeqwSDXAcRzOLT8DhUShKbNsYIXui3qW2E4QdxGCR/yb\nqEjHBtFZZ2JSypwnqn7ML8+Ck6aVXJk1g6BBN1W3jPp+YFhB1QRJCCE1XJ1InoVCIUJCQuDr64vk\n5GT06dMHAwYMgLU13cCirnt44gGennvMKwv4tDfM7Uq485NSAfNDxc46+wVA2czHGCESUiJOmgl5\n8jnIX56GMju+1PqsnQ+EDftD6BwAxqxeFURICCG1S51Inhs2bIiGDVU/wbu4uKB+/fpIT0+n5LmO\nk+VJcf6/Z3llbl3c0Wp0yUmwMOYk2MSnmnmOYVUjbBBSRTilDIrUq5AnnYEi9SrAyUusz5g7Q+ja\nD8KG/cFa6R+znBBCSOn03zKtisTExGDChAlo3bo17O3tsWfPHq0627dvh6+vL1xcXNC7d29cunRJ\nx5oMc/PmTSiVSri7u1ckbFILxG64gpzEbM08I2AQuKpfycNpSSUQ/fYTr0jeYyC4Rl7GCZKQAhzH\nQZH1LyT/bkZezGRI7nwBxetL+hNngSWEDQfA4o01sOz+E0RNp1HiTAghlcDkZ55zc3Ph4+ODiRMn\nIjg4WGt5eHg4lixZgnXr1sHf3x/bt2/HuHHjcOXKFc0A4z179oRCodDZ1tXVVTOfnp6O4OBgfPfd\nd8Z7QqRGSP33NW787xqv7I33/dCgpVOJ7cyiDoNNTdbMc0IzSEe9a4wQCdHgZNmQ3FsDRdq1Umoy\nYB06QNiwH4TOPVVjLBNCCKlUTEZGBmfqINQaNWqEr7/+GpMnT9aU9evXD23atMGGDRs0ZR07dsSI\nESPw+eefG7xuiUSCkSNHYtq0aZgwYYLeevHxpfcZJDUbx3GIXXQJabdea8osGlig14/9ILTU/32S\nlYjhs+kTmOXlaMpedemHFwP1v54IqSiBPA31U7bATK5/XGaZ0Bn51l2RZ9UZSqFDFUZHCCHVg7d3\n1d10xuRnnksilUpx8+ZNzJkzh1fet29fxMbG6mmljeM4zJo1C7169SoxcQaqdufHx8dX6fbqAkP2\n6f3f/+YlzgDQd+UAePu2LLGd2W8/8RJnzsIS1u98BG/b2p+s0Gu18hmyTxXZDyG59R04uY6RM4Q2\nELr0gdB1AKzqtYA9jfQCgF6rxkD7tPLRPq3ZqnXynJqaCoVCAScn/k/pTk5OePXqlcHruXLlCsLD\nw9GmTRscO3YMALBt2za0adOmUuMl1Z8kS4LoVed4ZZ69vNB8aIuSG2ZlQBR5gFckGzQeXB1InIlp\nyFPjILm7ClDk88pZ25Yw8xwHQYMudNc/QggxgWqdPKsVv4CL47iSL+oqplu3bkhPT6/ssEgNdOWb\nGOSl5GrmBSIB+qws5SJBAKKje8CI8zTznI0tpEPGGy1OUrfJkk5Ben89wPGv5RA49YS5z3/ACChp\nJoQQU6nWybOjoyMEAoHWWebXr19rnY0mpDQp917h1s83eGV+wZ3h0KTks8dMajLMzv7OK5MOnwJY\n6h7qkOM4pMWnIvdVLgTmAgjNhRCIBBCop6KiZYIyfREktRvHcZA92QfZ4zCtZUKPURA1/wAMY/JB\nkgghpE6r1smzSCRChw4dEBUVxbsjYFRUFN566y0TRkZqGk7J4ezSU+CUhdfH2nrYofPsrqW2Ff3+\nMxiZTDOvrO8EWd8ROutmPstA5P8dw8sbSQbHpk6oBeYCCETCguS68LGqXJV8C4s81krEC8qtXWxQ\nv3l92Hs5QCCiu8bVFJxSAem/30OeGFFsCQNR8w9g5jnaJHERQgjhM3nynJOTg0ePHgEAlEolEhIS\ncPv2bTg4OMDDwwOzZ8/GzJkz4efnh65du2Lnzp14+fIlpk+fbuLISU1y78BdrYS293/7QmhhVmI7\nJvEphNGRvDLpyHcBkblW3fjj/+L0fyIhzZaWKTaFVAGFVAHklF63LBgBA3svB9RvXh8OzR1Rv3l9\n1G/uCIdm9SGypp/9qxNOIYbk7peqG54UxZrB3OdjCJ17mSYwQgghWkyePN+4cQPDhw/XzIeEhCAk\nJAQTJ07Eli1bMHr0aKSlpSE0NBTJyclo3bo1Dhw4AE9PTxNGTWqS/PR8xHx1gVfWdGBzNO3XrNS2\n5od2gOGUmnmlqwfkPQfx6sglclz88jxu/XSjeHOT4hQc0h+mIf1hGnDiAW+ZjVs91C+SUKsTbCtH\nKxNFW3dx0nSIby3XvrW20AYWvisgsG9rmsAIIYToZPLkOSAgABkZGSXWCQoKQlBQUBVFRGqbS2ui\nIU4vHLFAaCFE788DS23HProP4TV+0i0Z8z4gKHzbZD7LwPFZR/DqTnLx5nDycYbQUqg5syyXyFWP\n1VOpAgqJ9s19qkJOYjZyErPx7MITXrllfUveWWp1Us1x1WY4+FpFmZcA8c1l4MT8X0UYC2dYtF8F\n1ppOEhBCSHVj8uSZEGNKup6Iu/tv88o6z/GHrbtdqW1Fv/6PN6/wagFFp96aeX3dNFgzFgFL+6D9\nu2+UejEgx3GaJFohlRck2YWPFeJiiXex5FsukavaFpTJ8mXIfJqBtAdpyEnKLnHbuuSn5SP/agIS\nrzNUZDQAACAASURBVCbwygUWAsR5x6q6fRRJrO0a20NgRv2qy8NM8hj5cdsBWRavnLVpBvP2K8Ga\nO5ooMkIIISWh5JnUWkqFElGfnQaKnDR1aFYfHT/oVGpbwb04CO/F8cqk42YADKPqprH6vNbIHYDq\nIsQhm95Ew/auWst0YRgGQnMhhOZCANr9qCtCmiNF2sNUpD9IQ9qDVKQ9SENafCoyn2bwLpw0hEKs\nwKs7yVpn2FkzFvaN7eHQ3BHWztYwsxZBZC2CmbUZzKxEEFmbwczKDGYFZaplIlWZlRlYQd0cOUKe\nchkNUjYCnIxXLqjfEeZtPwMjpO4zhBBSXVHyTGqtO7tuIuUef5jDPiv7FSSqJeA4iA7yzzrLfTpC\n0cYPGU8zEDFbdzeNZoO9MeDrQTC3s6hw7JVBZCNCw/auWom8XCJHxpN0flL9IBXpD9OhkMjLtA2l\nTFnQXscd8AwgtBAWJto2osJE28qsIPHWkXSrE/GCx6yQBcMyqj+GASNgePNgi8wX/2PUjwGGZXnL\nwGiPMV8ZZAmHIf13KxgoeeXChgMgajUXDEuHZUIIqc7oKE1qpfz0fFxaF8Mra/FWK3j2bFxqW0Fc\nNASP7/PKpGODVN00Fp+oUDeN6kBoLkSDlk5o0JI/VrpSoUT2iyykxRdJqAumkiyJUWKRi+WQi+XI\nT80vvbIpMCiSULMFSbZqnhWwYIQsBELVlBWyYAUsWDPdU0bAgJEmAtIXYAVtwLIcWIESjICD0L45\nhA4twZpFgxUwYM0EqqlQoFqvZv2qZYyABSssiEFQUK6OQ1BYlz/PgiloUzjPgmUZfvxCpmD9bI14\nPRNCSFWj5JnUStc2xUJaJOET2YgQ8Fmf0hsq5DA/tINXJG4fgLM/J1VKN43qjBWwsPO0h52nPZoU\nGYmE4zjcu3oXdgo7XkKtvhFMrcapRi3hFBxQ7Exx+TnrKMsHcLOS1l95GLYgKRcwhYl00TPyDICC\nx5o0m2Ggybl5j4vULaysp27RbZUtZplMjmizs/z1lAN9bSgkk8txURhl6jBqlbqwT3stD0SzQd6m\nDsMoKHkmtU52YhZuhfET3c5z/GHjYlNqW2HMKbCJTzXzaWIbHIpsjFf/aCfO1a2bhrEwDAPz+hbw\n8PaER3f+6A+SLAnSHqQi43E6JFkSyPJkkOVKIc2VQpYrgyxPCmmuTGe5LFemZ4ukuuCUqgtaaxqx\nqQOoharpb0M1Wm3fp7K82nuMp+SZ1Dqx313mDQFn09AGHd59o/SGUglEv/+kmf37lSuOPuwIqYQ/\nlCJrxqLXZ33gO61mdNMwJnNbc7h2dINrR7cyt+WUHORimSq5LkiqpQVJtSxXClmeDNIcqSbxluXJ\nVMl3sXJOyYFTKFVTTrVezR9XMFUUzqP4ckWxugV/oNH5CCGE6EDJM6lVcp5l468Dd3llXed1L/VO\nggBgFnUYbGoy5AoWpx/6IC7RS6uOrYcdhm4eDhffhpUVcp3FsIzqgkArEeBkbepwtHCcKoFWFiTm\n0CTXAKdQQqlQQinnoJQroJQroVRwUMoUqqlcAUX2C4j//gEKSRaUCgacglFNhQ0gcH8bL1Py4ezo\nrGqr/lMoefOcXAlFwVQpV0IhU4BTcqpl6u0XtOHUbRUcL77C8oL1KLhi84Xr4Yq2l1dWNxVCCKld\nKHkmtcq/P93nDcNm39QBPuMMuENbfh5ER3YjPd8K4fc64mWOvVaV5kO80X9N7e+mQVQYRjXihoAt\n+zjWirSbEN9ZDbsmebxy1rY1LHxXgBHZQRAfD2/v6tsfUH0mXp3IqwpReMMcDkDBY66wETT309H7\nuEiZnnaaSTluzvPkyRN4eXlV6JcDuikQn2afkkpTF/apZS2+Yy0lz6TWeHkrCS8vJPLKui/qCVZY\n+ljCZpEHcP+hFY794wuJgn+WWiASIGBpb+qmQQwifxkFyd/rAI4/7J/AqTvMfRaDEVTueN7Goh72\njxWwlT0EuVFZ5lsZdBMkYjgriTXsPLVPKJDyo31as1HyTGqNS19f5M07t3NB8yEtSm0nT3mN6G9u\n4vozP61ldp52GLJ5OFzaUTcNUjKO4yB7dhCyhzu1lgnd34LIeyYYhu7GSAghNR0lz6RWeHbxKZ5f\nfMor6744QHWzixJkPElHxMSf8SrRXWtZ8yHe6P/1YJjb1qDTbsQkOE4B6b9bIH9xVGuZWbP3YeY5\nln61IISQWoKSZ1LjcRyHS19H88rcu3uWekOUf4/ex5n/nIA0l9+/USAEApb3g+/UDpTwkFJxCjEk\n99ZA8foyfwEjhHnrhRA2DDRNYIQQQoyCkmdS4z2MjEfyrZe8sh7/CdCb+MrFckSvOofbu7RvSmFv\nLcbg3f/P3p3HR1Xe+wP/nHNmy76RhLBvQSCGJSGEhH1HBQIoKuJSBdSr9bpVq9VKW3tLlWt767VX\nfy2ldW2hCLIoi2wCCfsW2QOEnSSQkG2SzHLO+f2RZCYnMwkJzGSyfN6vV14z5/s858w3Q1q/88xz\nnucJRCd09kqu1Lqo1iJUZC6AUqzdkRK6AJji34EUNsA3iRERkdeweKYWTbEryFiknevcc1Is2g9y\nv+Nf4fmb+O65Nbh+LM+lrU/kVYx/dzQkFs7UAErZVVQc+SXU8iuauGBsB9OA30IM7OabxIiIyKtY\nPFOLduLrY7h5tsAZEIGUnw1z2/f0mpPY/MZGWEutmrgkyBjf6zgGJSoon3ivN9OlVkIuPoWKI+8A\ntiJNXAjoBtOAdyGaIn2UGREReRuLZ2qx7BV27P5jhibWaUIXRPRu59Jv+7tb8eMXR1yuEWoyY2bc\nAcQEFaP8gV9VTngmqoOqWGHP3QbrqT8DikXTJoYNhCn+lxB0zW/DFyIi8hxWCtRiZX5+GKXXShzH\nkkFC7ON3afrczL6Jdc+twfXjrtM0+kZexb13ZcKks0Pu1hvy4FFez5laJqX0HGxXN8CeswWwl7i0\nS9FjYOz7CgTx1jtZEhFRy8bimVokS4kF+/68RxPr/9hA+EU7dzQ6t+ksNrz4res0DZ2A8d0zkdjh\nAqrvKbTOehrgyhpUg2o3w567Dfar66GUZNXZT9/1Ieh7/IQrsxARtREsnqlFOvjX/ai4We441gfo\nMfj5ZFwpqLx562b2TXz33GrIFllzXkjXUMzo/yM6ljjXhLb3S4Ac57pBCrU9qqpCKfwR9msbYM/b\n6TI1Q0MQYYh9DvpOU5ouQSIi8jkWz9TilN0w49Bf92tiCU8nwT/CHyioLIB+WLDZpXCOva83Jj4U\niNAlX2ji1gfmc9S5jVMs+bBf+x72axuhll+tv7MuCLr2Y6HveB/EgC5NkyARETUbLJ6pxdn30R7Y\nymyOY79wPyTMG+w4PvPdaVz44bzmnGFvjkTivEEI+OU8TdyeOAJKz75ezZeaJ1WxQ87fC/vVDZDz\n9wFQ6uktQAwbBH2HSZDapUCQDE2VJhERNTMsnqlFKb5UhMwvtJubJL0wFIbAymLGXm5Hxm9+0LR3\nSumMxGeSoN+xHuJV53QNVRBhuX+u95OmZkUxX6qclpGzGar1Zr19BWMUdDEToIuZCNEvuokyJCKi\n5ozFM7Uou/+YDsXmHCEM6hiE+DnOXdzOfH4KpTmljmNRJ2L0b8ZBsFlh+OYfmmvZh02E2rGbt1Om\nZkC1l8OetwP2a+uhFB2vv7OghxSZAl3MJEjhAyEIUtMkSURELQKLZ2oxbpy6jhMrtIXP0FeGQWes\n/DPOP30D2V+f1bQPmj8YEb3bQb/h3xDzcx1xVaeHdcZPvJ4z+Y6qqlCKT8B+dQPsedsBubze/kJA\nN+g7TIau/VgI+uAmypKIiFoaFs/UYuz673RAdR6Hx0agz4x+ACoLpa1vb4IqOzsEdghC8n8OBcrL\nYFijvUnQNnYa1HbtmyRvalqqtRD2nM2wXdsA1Xyx/s6SP3TRo6HrMAliUG8uN0dERLfE4plahGsH\nruLcxjOaWOprwyFKIgDg1MoTuLLnsqZ91DtjoPc3QL/yKwglzm2UVZMfbFMf9X7S1GRUVYacfwD2\naxsg39gNqHK9/cXQeOhiJkEXNRyCZGqiLImIqDXwSPG8d+9eFBUVITU1FQEB3JrWF1RVBRQLVHsp\nYCuFaq/6sZUCtZ8rNgAqoCoAFEBVnY9VMVVVnX00/ar71O6rPd/dNR151hw+hlrVFzXiavUv5Tj2\nL7fhiY9VQFAhABBEAZJxO8zbVFjMErYvGALAuQJCp/h8tDe8BPMWFQhSgUeNQOXpgE4H9fDTgCBC\nEERAkACIgFDrB2LlfFdBqNXu7C9o+kua8wVBB4j6yh9BV7n7XFVMqBGHqNf0rdkPog6CoHe9jqgH\nBH3V67TN0VJVkaFW5MJ+bSPsOZugWm7U218whDtv/vPv2ERZEhFRa9Oo4nnRokXYs2cPli9f7ojN\nnj0bGzZsAADExMRg3bp16NKFa5/eDlVVALkcqq0Eqt1cWejaSioLYrvZ8dzl2FZ5DNV26xdpoXTu\nVgZTKkcXD6zojvJiZwdJJyNlzkkIQtWNhSIAVBaYleW4DbDbahzX7Vbtvidoi/Dqwlo0QBANQNWP\nIBoAyU2s+rlU/VwPQTRqn0sG6KzXoJT5AaKx6jUMVc9db6ZTFXvlBznZUrnJiGyBqlgAuaIqZoUq\nV9Rqcz7WPFfzWP28up9qb8DbI0GKSIauwyRI4YPd5ktERNQYjSqely9fjvHjxzuO161bh/Xr1+Ol\nl15CfHw8fv7zn+P999/HRx995PFEWxul7Aoi8j5CeaEC1eYsiOtfa5Zqu3E+CCc2d9bE+t93ASHR\n9d8c1nqogGIFYAVklzF9j4kCUJ7rpkEQHQU4qormW02ZaAqCfyfoYiZBHzMegiHM1+kQEVEr0qji\n+erVq4iNjXUcr169Gj179sSCBQsAAFlZWfjiiy/qOp1qUhUYLafq3f2X6qcqQPrnfaCqzmkLQZFl\nGHDved8l1daoCiBXVP74mmiELnoUdDGTIIb0a7PTWYiIyLsaVTwLggBZdo4q/fDDD5g6darjuEOH\nDrh+/brnsmvFBH2gNy5aeV1dAARdIAR9EKALhKA5Dqj8Kl4Qa8zlrTGnF4Lj0TGftzpWq73yPKmq\nSKkZr54nLLieAzj7OxOvsT2281G2y/hX2lcovuC82a/HpFhM+uN9AICjS4/h+rmtmrfgrhdHIXji\nLyBcuwj/t+dBUBXHZSueeAn24RM087jV6ueqXGO+duWPqiqoHM5VtD+o2V6zTdaer9grp9IoNkC1\nV841V+yAYoNaHa/qo1bFK58741Cqzqvqr9aIQ7GhbX9TIQKSEWJgD+hixkMXNQqCzt/XSRERUSvX\nqOK5V69e+PbbbzF37lxs2rQJOTk5mDBhgqP9ypUrCA0N9XiSrZKujhsrJRMEXWBV0RsIQR/oPHbz\nXNAFAtVx0diqRttOLDuC/FNmVP+ZCpKA5JfGQJBMKC8oQ8Z7uzT9e07qhaihHSCIOhhXfgZRcRaW\nSvvOkEdMgSBp/+Rb+rulqnKtIry6KLdUPpetUBVr5dQOpdZzuY64m3ZLRSkMOlQV8Naq+cdWuJ8c\nUlnUQjRCkIyAZKyaO22qmntd3WaqejRojiFVnSdWn1d9bKqat10Zg6BvVX/vRETUMjSqeH7hhRcw\nd+5cdOvWDWazGX369MHo0aMd7T/88APi4+M9nWOrJIgG5Ld7Dh279q4cGXaMCut9nVqzYCu3Yc//\nZGhicQ/FI6xHOAAg/b0dqCh0ThXQ+ekw8p0xyC3Pg3ghC/p92zTnWmbOBaTWtzKjIEiAJAFV98F5\nq5S8nJWlmbIFVK2cosqOAhuCrqqo1bGoJSKiVqtR1cSMGTMQFhaGjRs3Ijg4GPPmzYNOV3mJmzdv\nIiIiAg8++KBXEm2NLH59IYXE3rpjG3TkHwdhzjM7jiWjDskvpgAArh28imP/+lHTf8h/piC4Uwhy\ns/Jg+Ppvmja5ayzkwSO9n3QbIwhC1SofOgCcLkFERG1Do4fiRo8erRltrhYWFsabBckjKooqsP//\n9mpiA58chMD2QVDsCra+vUnTFtYzHAnzBgMAAi6dge7Ibk279f65gCh6N2kiIiJqExpVUYSHh+Pf\n//53ne0rVqxAeHj4HSdFbduB/7cPlmLnMiSGYCMG/8cQAEDm54dx/Viepv+Yd8dDMkiAqiJm60pN\nmxx7N+T+yd5PmoiIiNqERo08q2r9K8cqisK5jnRHzLmlOPy3A5pY4jNJMIX6wZxnxq4Pdmraek/r\ng87DKjflkY4dgN/F05p2ywPzaqzkQURERHRnGv1ddn3F8f79+7naBt2RPR/ugr3CuXOcf6Q/Bj2V\nAADY+bsfYC2xOtoMgQaMfHt05YGqwrB8seZa9rjBUPoM9HrORERE1HbccuT5448/xieffOI4fvPN\nN/Huu++69CsqKkJxcTEefvhhz2ZIbUbh+ZtubwTU+xtwefclnFx5XNM29JVhCIiuXC9bOrgTUvZJ\nTbv1gXneTZiIiIjanFsWz5GRkejTpw8A4OLFi4iJiUFMTIymjyAICAgIwMCBAzFvHgsWuj27PkiH\nYneuzRzSJQR3P9wfsk12uUmwXd9IDHhiUOWBIsOwYomm3Z4wHEqPPl7PmYiIiNqWWxbPDzzwAB54\n4AEAwJQpU/Daa69h1KhRXk/MUwoLCzF9+nTY7XbIsoxnn30WTzzxhK/TolquH8vD6dXakeOhrw6H\nZJBw4JO9KMjK17SNeXc8RF3lrCPdnq2QLmc72lRBgPX+p7yfNBEREbU5jbphcO3atd7Kw2uCgoLw\n3Xffwd/fH2azGSkpKZg6dSpXBWlmMhbt0By36xuJu6b1Qcm1Euz5k3YnwX6z7kaHpI6VB3a766jz\n0HFQOvXwar5ERETUNt3WlmsnT57E+fPnUVhY6HYFjtmzZ99xYp4iSRL8/Ss3cLBarVBV9ZarhlDT\nurLnEs5vzdbEUl8bDkEUsP03W2ErsznixhAThr3p3PBEt3M9xLyrjmNVlGCd8ROv50xERERtU6OK\n5+zsbDz99NM4cOBAnQWoIAgNLp7T09Pxv//7vzhy5AiuXbuGP//5z5gzZ46mz+LFi/Hhhx8iNzcX\nffr0wcKFC5GamtqYtFFYWIj77rsP586dw29+8xtEREQ06nzyHlVVkf6edtS5Q1JHdBvbAxd+yMaZ\n77RLz6W+Phz+EVW72VktMKz6VNOeP2AYTNGdvJozERERtV2NKp5feuklHD9+HAsXLkRKSsodL0tn\nNpvRr18/zJ49G88++6xL+4oVK/DGG2/ggw8+wNChQ7F48WLMmjULu3fvRufOnQEAw4cPhyzLbs+t\nvrExNDQU6enpyMvLw2OPPYa0tDRERUXdUe7kGdmbz+HagauaWOrPR0C2yNj6zmZNPHpAe9w9u7/j\nWL91NcSC645jVa9Hzoj70M2rGRMREVFbJhQWFjZ4DkP79u3xyiuv4PXXX/d4Ih07dsT777+vGXke\nN24c4uLi8OGHHzpiCQkJSEtLw4IFC27rdV555RWMGjUKaWlpbtuzsrJu67rUeKqsYsczW1F6vsQR\nixoajcG/HYqsL04h6x81biAUgNSPRiL0rjAAgGitQL+PfgF9mfPcvOTxuDLhoSbLn4iIiJqH2NjY\nJnutRo08R0REIDg42Fu5aFitVhw+fBgvvPCCJj527Fjs2bOnwdfJzc2Fv78/goKCUFRUhF27dmHu\n3Ll19m/KNz8rK6tJX89XZEVGucUMRZUhiRJEQYIk6nB69SmUnC+GgKqNdwRg/K8mw2DUY8M/v9Vc\nI37OACRNGeI41q/+XFM4q0YTAh59Hsi90Sbe06bWVv5WmxLfU+/g++p5fE89j+9py9ao4vmpp57C\nsmXLMH/+fEiS5K2cAAD5+fmQZRmRkZGaeGRkJPLy8hp8ncuXL+PFF1903Cj49NNPIy4uztPptimK\noqDMUgpzRTHMFSVVjzWfOx/LKkpQbjFDRR1fcPwagAJAFiCKEv56cAFMn7WHZPF39glUcPzu7Ti9\nJh2iKEJUAUP2CUj9oyCqKiQVEGK6AoeXwlxqxvHrYRAFCaIoQRIl6CQ99Doj9JIBel3Vj6R91OkM\nMEgG6HVGR39JlLjdPBEREWnUWzyvXLlSc9y9e3fY7XYMGzYMs2fPRseOHd0W0TNmzPBYgrWLF1VV\nG1XQJCYmYufOnR7LpzVyVwyXVZSgtOqxdlFcbzF8O0QAogoFdsg/+kE66a9pLplwBRZLIWCpEQwx\naK9hvw6cq5r/3PDPVvWnJYjQ1Sqyaz/XSQYYdDWLbgMMVc/9jYEI9g9DkH8YgvxCYdAbPZMYERER\n+Uy9xfNTTz0FQRAcK2vUfP6rX/3K7TmCIHikeI6IiIAkSS6jzDdu3HAZjaaGuVGUg4NntqOgOE9T\nEJdbSj1bDN8uq4CAdR00IVsXMywDCn2SjqIqsNorYLVXeOR6Jr0/gvxDHT/BfmGVj1UFdrB/KAL9\nQqCT9B55PSIiIvK8eovnNWvWNFUeLgwGAwYOHIitW7di+vTpjvjWrVsxbdo0n+XVEpVVlGLrkW+w\n9+QWKKrryiRNwc8YAEnUQVFkWCussNtslSPOOmfR7r89ClKhc0RZFVWUTrkCtJKZExW2MlQUleF6\n0dV6+/kbg6qK6lDHqHVlge18DDAFQxK9O3WKiIiIXNVbPA8fPtyrL15aWopz584BqJw6cPnyZWRm\nZiIsLAydO3fG888/j2eeeQaJiYlITk7GkiVLkJOTgyeffNKrebUWdtmOvSc3YeuRVaiwlnn02n7G\nAAQYgxFgCkKAXzACjFWPpiD4G4MQ6BcMf1MQAk3B8DMGOgq98oIy/GPkYlhLrAAAFSoG/zQZvaf1\nxtLffgUFiuM1+j3aDwnPPgZZsUNRZCiF16H/33egqDJkQYAiABVjpsI6IBmKIkNW7Lh27SraRbar\nOpahqDJssg02uwV2uw022QKr3Qp7Vcxmt8ImWysfaz331QeNMksJyiwlyL15qc4+giAg0BRSxyh2\nKIL8Kgtvf1MgREFswuyJiIhat9vaYdBTDh06hKlTpzqOFy5ciIULF2L27Nn4+OOPMXPmTBQUFGDR\nokXIzc1F3759sWzZMnTp0sWHWTd/qqrixMUD2LB/GQpKcht0jp8hwFHs+puCKotiU3Ctx8rn/qZA\nSOLt/ens/7+9jsIZAEwhfhg8PwnfPbcGis1ZOAdEBWDU6+NhDHLOEzauWgb9TeeHACU8CmX3zAf0\nztHqAMVzdzDLih02e1XhLdtgtVtgk62wVxXX1urnLsW3BVa7BeaKEpSU3URxWSFKywshK54rxlVV\nRUl5IUrKC4H8uvuJgoRAv5CqUezqorqysA72C0Vg1Qi3n5FFNhERUUM0qgKqWei6IwgCTCYTOnTo\ngBEjRiAtLQ06Xd0vMWLECBQW1j+fdd68eZg3b15j0mzTrtzIxvp9/8T53FNu20MD22Fk/BSEB0V5\npBhujJJrJTjy2SFNLOm5Ibi44wIupV/UxEe+M0ZTOAs5l6HbsU7Txzr9CU3h7GmSqINk0MFk8Lvj\naymqgnJLKYrLCqsK6psoKStESVkhisudz0srijy6fbyiyiguK0BxWUG9/SRRQqCfs7iunH/tnDpy\n01wMc0V7+BsDuQIJERG1aY2qmBRFwbVr15CdnY3Q0FDHCPDFixdRWFiIHj16IDg4GPv378enn36K\nP/7xj1i1ahW3w24CReYCbDq4HIfPprttN+r9MKr/VAztOwF6nfcKzvrs+Z8MyBbn6GtAdCD6PtAP\nX93zuaZf5+FdETvlLk3MsPLvEBTnyLQS3Qn24ZO8m7AHiYJYNYIfjJjwur85kRUZ5oriGsV15ch1\nSXmN52WFKLOU1HmN2yErMorM+Sgy1z2MveZw5QeKygI7xDEfu3pE26g3QZJ0lR86RB0kUao8FiT3\n8arnoihx1JuIiFqMRhXPb731FubMmYOPP/4Ys2bNcixTJ8syli5dirfffhuffPIJBg8ejK+++gov\nvvgifv3rX2t2CCTPstos2HH0W6QfXQebbHVpFwQBSb3HYMzAGQj0a5oNbtwpOJOP48uOamJDX07F\n/v/bB3Oe2RET9SLG/GacZnRTvHgW+t3arbqtM58EJJ/OOvIKSZQQ7B+GYP+wevvZZVtlcV1e6BjN\nLikrrCy6ywsdbZ6e6y4rdhSab6DQfMOj1xUFCZIk1Siwq4psUecadxxXPgqCCEEQIEDQPlb9wHEs\nQgCqHgVAcD6vfR5qXkNzvgAIAkRBqMq5Rp6iDpKkg06Te+3fxfl7VK7kYoEk6iBW/Q5ERNT8Nar6\neOedd/DYY4/h4Ycf1sQlScIjjzyCkydP4he/+AW+//57zJkzB/v27cP69es9mjBVUlQFh8+kY9PB\n5ZXzXt2I7dgfkwY/hOiwTk2cnatdH6RDVZzTEUJ7hCGqfzS2vPW9pl/C00kI6xmuiRlWLNEcy517\nwj5kjPeSbQF0kh5hQZEIC6p/2Uar3YLSskIUVxfUjoL7JkrLixwj3BZbeRNl7p6iylDsMmxw/QDY\nqlVtlipAuMUHBdcPDqKo/RDhLqY9do1p2qu+JRBdvjGo3BW08kNKdbZVqj5cVD6t/tBR3UeAc/PQ\n+vvUuKL7Po2gqAqU6m+p7uDzSGNf11P4IYqo+WtU8Xzs2DE89NBDdbZ36tQJR486RxcHDhyIf/7z\nn7efHbl17toJrN/3T1wruOC2PSq0IyYnzUZsx/gmzsy9nCPXcOa705pYyivDsO2dLVBlZ0Ed1CkY\nQ14Yquknnj0O3SHtVBTr/XMBkV/zN4RBZ0R4cDTCg6Pr7We1WTRTQ0qrR7Sriu78ojxY7GZYbJ5Z\n85q0VKiwKzbYFZuvU2kdMnydQCvkfkYg3YlW/p4+MOIZDOiZ6us0vKJRxXN0dDS++eYbPPXUUy47\nC8qyjJUrVyIqKsoRKygoQFhY/V8/U8PdKMrBhv1LcfLSQbftAaZgjBs0EwmxI5vVGsAZ72t3RCaJ\n+AAAIABJREFUeIy6Oxq2chuu7b+iiY9aMBZ6P+0GIYblizXHcs++kAemeCfRNsygNyJCH42IOors\nrKzKVUwstgpnYV12EyXlRY5Hm90KWbE7lhaUFTtkWYa9KlZ97Ghz/PhmSUAiIqLb0aji+fnnn8fr\nr7+O8ePH44knnkD37t0BAOfOncOnn36KzMxMvPfee47+q1atQkJCgmczboPKLKXYdngV9pzc7Hbt\nYZ2oR0rcRIyMn+qRlSE86VL6RVzaqR0hH/zTZGytNV2j29ge6DGhpyYmHT8I3XHtBwXrA/MBfq3p\nM0a9CUZ9e0QEt/fYNVVVrVyTu3ZRLdthr4o5i3FnwW2vOlahQlUVx7VUVal8hFp1rALVz2vEap6n\nqDWv4Xq+ChWodZ7syFeukZe7Yzvscu3fTYbNboUKxfE7EBFRy9Co4nn+/PkQRRG/+93v8PLLLzvm\nZqmqivDwcLz33nuYP38+AMBqteK//uu/uCbzHajc5GQzth1ZhXKr2W2f+O7JmJAw65ZzX31BVVWk\nv79dE+s0tDMu7byA8nznHFvJqMPoX4/VzvVTVZdRZ3u/BMj9+GGstREEATpJV3UDqPGW/VuL6tF8\noHIlo9ofHBwfEGocy7INsio7NgGqWawrqqx5bperPnSoVbEa/ZWqa9eMOT+kuI85PoRUF/oqqj5U\nVD1CReUqi6ojXn1UXx+X69Xu01gqKuc638HnEX6YIaL6NHq5grlz5+Lxxx/HoUOHcOlS5Q5onTt3\nxqBBg6DXO79yNxgMXt+hsLVSVRUnLx3Chv3/Qn6x+01OOkf2xOSkR9AlqlcTZ9dw5zaeQe7hHE2s\nz/39sOn1DZpY0vPJCOkSqolJR3ZBOntcE7PeP9c7iRL5mCiKEEUD9PDNMpKtSc0PJeQZfE89j+9p\ny3Zba33p9XoMGTIEQ4YM8XQ+bd7V/PNYv++fyM456bY9JCACExMfRHz35GZ9V7YiK8hYpJ3r3H1C\nT2R+flgzIhTSLRSJzyTVOlmBYfnfNCH7wFQoveK8lS4RERFRg9RbPNccWa55fCvV/anhis0F2HTo\naxw+k+72K0Oj3oSR8VOR0m+izzY5aYxT35xAQVaNDTcEoF3fSGR/f1bTb8xvxkFn0v4Z6vZtg3RJ\n2896/1Ney5WIiIiooeotnvv37w9BEJCTkwODweA4vpWCgvq3AiYnq82Cnce+w86j38Fmd7/JyeDY\n0Rg7aAYC/UJ8kGHjyVYZu/+gXYOn1729kfnpYW3snlh0HdW91sl2GFb8XROyJY+F0qX5Tk8hIiKi\ntqPe4vmjjz6CIAiOuczVx3TnFFXB2bwjWHnoI5SUud/kpFeHuzE5aXaz2OSkMY5+dQTFl4sdx6Je\nBFTAUuRcI1jvr8fId1w3OtGlb4SY4/yGQxXFyt0EiYiIiJqBeovnOXPm1HtMt0dRFPxt/X/hYt4Z\nt+2RIR0wOelhxHZs2Eh/c2Irs2LvR7s1se7jerhskpL8YgqCOtTaLtxmheGbTzUh+/DJUNtzGhAR\nERE1D7d1wyAAVFRUoKCgAO3atYPB0Pzn4DYnoiiiS1Rvl+LZ3xiEcYNmILH36Ga1yUljHFpyEGXX\nyxzHkknCzbM3NX3CYyMwcG6iy7n6bWsh5jtXF1F1elinP+G9ZImIiIgaqdF7HKenp2Py5Mno1KkT\n7r77buzatQsAkJ+fj2nTpmHLli0eT7I1GtV/Kkx6fwCAJOow/O578fL972NIn3EttnCuKCzHgf+3\nTxPrNLSL9sZBAGPeHQdJX+t3tJRDv+ZzTcg2ZirUiPq3lSYiIiJqSo0qnnfs2IHp06ejqKgI8+fP\nr1o0v1JERAQA4LPPPvNshq2UyeCPAZ1H4e5uQ/DijN9j0uCHYDL4+zqtO7L/k32wFlscx4YgA/Iy\ntes835XWF51SXDfO0W9aCbHIOUKtGkywTeE0ISIiImpeGlU8/+53v0P//v2xY8cO/OxnP3NpHzZs\nGA4ePOjmTHKnd/sEPDT6+Wa5O2BjmXNLceTv2n/7yLgolBc4dxLUmXQY9uZINyeXwPDtPzUh24SZ\nUEMjvJIrERER0e1qVPF85MgRPPTQQ9DpdG5vZIuJiUFeXp7HkmvtWtrNgPXZ8+Eu2CvsjmNTuAk5\nB69p+iQ8k4SgmCCXcw0b/g3BXOI4Vv0DYL33Ye8lS0RERHSbGlU863Q62Gy2OtuvXLmCoCDX4oha\nt8ILhTj2rx81saAOwZCtsuM4ICrAdSdBACguhH7DvzUh6+SHgMBg175EREREPtao4jk5ORmrVq1y\n21ZaWoovv/wSw4cP90hi1HLs/kM6FLviOPaPCsD1o9pvIFJfHwFDgOuqLIZvv4JQ4ZzaoQaFwDbx\nAe8lS0RERHQHGlU8v/nmm8jMzMTMmTOxbt06AEBmZiaWLFmCUaNG4ebNm3jttde8kig1TzdOXsep\nVSc0Mb2fdgXEyLgo9L0/zuVcoSAP+s0rNTHrlEcBv5Z94yQRERG1Xo0qnhMSErB8+XJcunQJP/3p\nTwEA77zzDl599VUAwL///W/069fP81lSs5WxaCfgXHQFge0DUXShSNNn5C9HQxBd53cbVn8OocY0\nICWsHWxjp3ktVyIiIqI71ehNUoYPH459+/bhxx9/xNmzZ6EoCrp3746BAwe2qhvg6Nau7r+C7E1n\nNbGa85wBoOekXm6XphNyr0C3/TtNzJr2BGAwej5RIiIiIg9pVPE8YMAApKamIjU1FSkpKZg+fbq3\n8qJmTlVVZCzaoYkFxgSh9Jpz1QxRL2LYm6Pcnm/45h8QZGehrUR1gH3EPd5JloiIiMhDGlU8Jycn\nIz09Hf/6178gCAIiIyORkpKClJQUpKamIj4+3lt5UjNzcft5XNl9WROruFmuOR7w+CCEdQ9zOVe8\nnA3drk2amHXGk4DutneLJyIiImoSjapW/vKXvwCoXJIuIyMDu3btwu7du7F69WoAQFBQEIYOHYql\nS5d6PlNqNlRFRcb7OzWxgPaBMOeUOo5NoSYMeTHF7fmGFUsg1NidUu7YDfahY72TLBEREZEH3dZQ\nX8eOHTFr1izMmjULhYWF+Pbbb/GnP/0JWVlZ+P777z2dIzUzZ9adRt7RXE3MnFuqOU5+KRWmEJPL\nuWL2SegOaKd7WGfOBUTJ84kSEREReViji+e8vDxkZGQgPT0dGRkZOHnyJPR6PQYMGICXXnoJKSnu\nRxupdVDsCnZ9kK6J+UX4oTzfOWUjtEcY4h8d4PZ8w9d/0xzL3e+CnMi1wYmIiKhlaFTxnJSUhLNn\nzyIgIACDBw9GWloafv/73yMpKQkmk+soI7U+J74+hptnC5wBAZrCGQBGvDUakt51JFk8eQS6H/dp\nYtb75wFcpYWIiIhaiEYVz2fOnIEoihg2bBhGjhyJ1NRUDBgwgEvUtRH2Cjt2/0+GJmYINMBaYnUc\ndx7WBd3H9XA9WVVh/HqxJiT3GQD57sFeyZWIiIjIGxpVPO/btw8ZGRnIyMjAJ598grfeegtBQUFI\nTk52LGGXkJAAvV7vrXzJh3788ghKrzqXohMkQVM4QwBGvD3a7YcpKXMvpNM/amIWjjoTERFRC9Oo\n4rlXr17o1asXHn/8cQDaVTc+//xzvPvuu/Dz88OVK1e8kiz5jrXUin0f7dbERJ0IucZazXEPxSOy\nX5TryYoCQ61RZ3v/ZCi9vbu04cmTJ3Hw4EFUVFRU5iuKmkdBEG7751bni6KI8PBwDBgwgB8miYiI\nWpHbXli3pKQEx48fx/Hjx3H06FFcvnwZqqrCarXe+mRqcQ79bT/KC5xzm0WdCNniLJz1AXqkvOr+\nxj/pwHZIF7I0Mev9c72TaBWLxYKdO3dCrbkknizXc4bnXbhwARcvXsSkSZMQEBDQpK9NRERE3tGo\n4nnt2rWOVTaOHTsGWZbh7++PxMREvPzyy0hNTUVSUpK3ciUfKS8ow8G/7NfEVEXVHA9+LhkBUW4K\nREWGccXfNSF70igo3Xp7PM+aSktLNYWzr+Tn52PVqlWYPHkywsPDfZ0OERER3aFGFc+PPfYYQkND\nkZycjPvvvx8pKSkYNGgQdNwZrlXb/397YS11fqMg6kUoNsVxHNghCAnzEt2eq9u5EeLVC45jVRBh\nmfmU95JthsxmM1avXo0JEyagY8eOvk6HiIiI7kCjqt6dO3ciLi7OW7lQM1RyrQRHPjukidUsnAFg\n2M9HQmdyM6/XaoFhZa1R52EToHbo6vE8a6s96hweHo6pU6dCVVXNDwAoiuI4p7E/Nc+veZ3jx4/j\n0qVLjte32WxYv349RowYgd69vTvqTkRERN7TqOKZhXPbs/dPuzRzm0WdCMXuLJ7bD4rBXWl93J6r\n37IKYkGe41jV6WGd8aT3kq2HIAgwGAxN9nqdOnVCRkYGTpw44YgpioIffvgBpaWlGDRoEJd4JCIi\naoFEXydAzdfNcwU4tky7vFzNwhmoe2k6lJXCsOYLTcg2Ng1qu/Yez7M5ql4PfciQIS5tBw4cwPbt\n2x0j1URERNRysHimOu3+QzpU2Tn9QZC0RXLvqXehw2D3c3gN65dBKC12HKsmf1inPuqdRJspQRAw\nYMAAjB071rE8XrXTp09j/fr1XJ2GiIiohWHxTG7lHc3F6TWnNLGahbRklDDs5yPdnisUFUC/fpkm\nZr3nISA41POJ1qE5rLRRrWfPnrjvvvtgNBo18StXrmDNmjUoLS31UWZERETUWCyeya2MRTu1gVoz\nMwY+lYjgziFuz9Wv/hyCpcJxrASFwjZplqdTbBRfzy9u3749pk2bhqCgIE28oKAAq1atQn5+vo8y\nIyIiosZoM8VzWVkZ7r77brz99tu+TqXZu7L3Mi5sy9YGawzk+kX4Ien5ZLfnCnlXod+6RhOzTXsM\n8PP3dJotTmhoKNLS0hAZGamJl5WVYc2aNZrVOYiIiKh5ajPF8wcffIDBgwf7Oo1mT1VVpL+3o94+\nKa8OhzHI6LbNsGIJBNnuOFbatYdtzFSP5tiS+fn5YcqUKejaVbtcn81mw4YNG3Dy5EkfZUZEREQN\n0SaK57Nnz+L06dOYMGGCr1Np9s5vOYdr+6/U2R5xVzvEPRTvtk28eAa63Zs1MevMpwB90y0R1xLo\ndDqMHz/eZelHVVWxY8cO7N+/v1nN2SYiIiInnxbP6enpePjhh9G3b1+Ehobiyy+/dOmzePFi9O/f\nH9HR0Rg1ahQyMjIa/Tpvv/02FixY4ImUWzVVUZHx3zvr7TPi7dEQde7/bAzLF0OoUfTJnXrAnjLO\nozm2FqIoIjU1FUOHDnVpO3ToELZt2wZZlt2cSURERL7k0+LZbDajX79++P3vfw8/Pz+X9hUrVuCN\nN97Aq6++iu3bt2PIkCGYNWuWZm7o8OHDkZKS4vJz7do1AMC3336LXr16oVevXk32e7VUp9ecxI3j\n1+ts7zamO7qO7Oa2TTx5BLojuzUx66x5gCh5MsUGaykjt/Hx8Rg/fjwkSfs+nTlzBuvWrYPFYvFR\nZkREROSOUFhY2CyqjI4dO+L999/HnDlzHLFx48YhLi4OH374oSOWkJCAtLS0Bo8k//rXv8ayZcsg\niiLMZjPsdjuef/55/PznP3fbPysr685+kRZKsSvY/tQWlF01u20XRAHD/zoaQV2DXRtVFbGfvofA\ny2cdodJOvZD1xOuAj1a5KC4uxsGDBx3HQUFBSExM9EkuDVFUVISjR4/CZrNp4v7+/ujfvz9MJpOP\nMiMiImr+YmNjm+y1GrU9d1OyWq04fPgwXnjhBU187Nix2LNnT4Ovs2DBAkeh/eWXX+LEiRN1Fs5A\n0775WVlZTfp69fnxyyN1Fs4AED9nABLGuy8+pYPp8KtROAOA+MR/IrZ3b4/m2BDV72leXp6meDaZ\nTM3mva5LbGws1q9fj+Ji5+YyZWVlOHLkCCZNmuSySkdTak5/q60F31Pv4PvqeXxPPY/vacvWbG8Y\nzM/PhyzLLgVDZGQk8vLyfJRV62SvsGHPn3bV2W4INiL55VT3jYoMw/K/aq83MAVK7/6eTLFNCAkJ\nQVpaGqKjozXx8vJyrF27FhcvXvRRZkRERFSt2Y48V6u9uYWqqre94UXNKSHkdOQfh2DOrXuXuyE/\nHQr/CPfrNOsyvod05bzjWBUEWB+Y7+kUG62lzHmuzWQy4d5778W2bduQne1ca9tut2Pjxo1ITU1F\nv379fJghERFR29ZsR54jIiIgSZLLKPONGzd8+vV1a2MptmD/x3vrbA/pEoIBPxnkvtFmhWHF3zUh\ne8oEKJ17eDJFj/D1DoONodPpMG7cOPTvrx29V1UV6enp2LNnT4v9cEBERNTSNdvi2WAwYODAgdi6\ndasmvnXrViQnu9/djhrv4F/2oaKwos72YW+Ogs7o/gsK/dbVEPNzHceqpIN15pMez7EtEgQBycnJ\nSE1NdSn8MzMzsWXLFtjt9jrOJiIiIm/x6bSN0tJSnDt3DgCgKAouX76MzMxMhIWFoXPnznj++efx\nzDPPIDExEcnJyViyZAlycnLw5JMs0Dyh7IYZh/52oM72DkM6odc9ddzQUG6GYfXnmpBtbBrUyBhP\nptjmxcXFITAw0KVYPnfuHMxmMyZOnMiVOIiIiJqQT0eeDx06hJEjR2LkyJEoLy/HwoULMXLkSPzu\nd78DAMycORMLFy7EokWLMGLECOzevRvLli1Dly5dfJl2q7Hvz3tgK7PV2T7yl6PrnO5gWL8MQkmR\n41g1+cE27VGP50hA165dMWXKFJe10HNzc7F69WrN6hxERETkXT4deR4xYgQKCwvr7TNv3jzMmzev\niTJqO4ovF+HHL47U2d5nZj9E92/vtk0ovgn9+mWamG3yg1CDwzyaIzlFRkZi2rRp2LBhg+Z/M0VF\nRVi1ahUmTZqEqKgoH2ZIRETUNjTbOc/kXXv+Zxdkq/vtn3UmHVJfH1HnufrVX0CoKHccq0EhsE5+\n0OM5klZwcDCmTZuG9u21H2oqKiqwdu1anD9/3jeJERERtSEsnpuYqqouP02tICsfJ74+Vmd7wjNJ\nCIoJctsmXL8G/ZZVmph16qOAX4BHc7xTrXU1CqPRiHvvvRc9e/bUxGVZxvfff4+jR4/6KDMiIqK2\nodmv89zalJeX48svv3Qc7927F48+2rRzhXd9sBOq4r64DIgKwOBnk+o817Di7xBk541rSkQ0bGPT\nPJ6jp7WkpepuRZIkjBkzBkFBQTh8+LCmbdeuXSgpKUFycjJEkZ+NiYiIPI3/dW1jcjNzcGZdVp3t\nqa+PgN7f4LZNvHQOul3fa2LWmU8Cevf9yXsEQUBSUhKGDx/u8sHg6NGj2LBhAyoq6l6CkIiIiG4P\ni+c2JuP9HXW2RcZFoe/9cXW2G5YvhlBjOoTcsRvsqRM8mh81Tt++fTFp0iTo9XpN/PLly1i5ciVu\n3Ljho8yIiIhaJxbPbciljIu4uONCne0jfzkaguh+eoN4OhO6wxmamPWB+YAoeTRHT2mtc57d6dy5\nM6ZMmQJ/f+0W6qWlpVi9ejVOnz7to8yIiIhaHxbPbYSqqvWOOvec1AudUupYP1tVYVz2F01I7nU3\n5EGpnkyR7kC7du0wffp0l+XqZFnGDz/8gJ07d0KW3a+uQkRERA3H4rmNOL36JHIOXXPbJupFDHtz\nVJ3nSkd2QcrSruJgefBpoBXdhNcaBAQEYMqUKejXr59L24kTJ7B27VqUlpb6IDMiIqLWg8WzjzXF\n9AJbmRU7F26vs33A44MQ1r2ODU4UGYZ//1UTsg8YCuWu/p5M0eta02ob9ZEkCcOGDcPo0aMhSdop\nNXl5eVi5ciWuXr3qo+yIiIhaPhbPTcwXRdz+T/ah9FqJ2zZTqAlDXkyp81zdrs2QLmc7jlVBqJzr\nTM1abGws0tLSEBSkXa+7oqIC3333HTIzM9vUvHAiIiJPYfHcyhVfLsKBT/bV2Z78UipMISb3jTYr\nDCuWaEL2oeOgdOnpvj81KxEREZgxYwY6d+6siauqij179mDz5s2wWq0+yo6IiKhlYvHcyqX/fjtk\ni91tW1jPcMQ/OqDOc/Xb1kK8keM4ViUdrDOf8niO3sBR1UpGoxGTJk1CQkKCS1t2djZWrVqFwsJC\nH2RGRETUMrF49jFvFnlX9l7G6TWn6mwf/tYoSPo6lporL4N+1WeakG3MVKhRHTyZYpNpK3Oe3REE\nAYmJiZg0aRIMBu2GNoWFhfjmm2+QnZ1dx9lERERUE4vnJtZURZwiK/jhV1vqbO88vCu6j+1RZ7t+\nw78hljhHJFWjCbZpj3k0R2paXbp0wYwZMxAeHq6J22w2bNq0CXv27IGiKD7KjoiIqGVg8dxKHV92\nFNeP5bltC4gKwMQPJtddyBcXwrBuqSZkm/wg1JBw9/2pxQgODkZaWhp69erl0paZmYl169ahvLzc\nB5kRERG1DCyeWyFLsQUZi9xviCIZdZjy1+kIbB/kth0ADGu+gFBR5jhWA4Nhnfygx/Mk39DpdBg9\nejSGDRsGUdT+X8DVq1excuVK5OW5/+BFRETU1rF4boX2frgL5fnuRw8nLJqE9gNj6jxXuJED/ZZV\nmph16qOAf6BHc/Q23jBYP0EQ0K9fP7fbepvNZqxZswYnTpzg+0hERFQLi+dW5ua5AhxacsBt25AX\nhuKutL71nm9Y+Q8IdpvjWAmPgm1smkdzpOYjOjoaM2bMQEyM9gOVoijYuXMntm/fDrvd/WotRERE\nbRGL51Zmx2+3QZVdRwt7To7F0FeG1XuueDkbuvSNmph1xpOAwejRHKl58ff3x7333ov4+HiXttOn\nT2PNmjWcB01ERFRF5+sE2jpPfi1+fls2sjefc4lH9ovCpD/eA0Gsf6UPw9eLIajO1RbkDt1gHz7R\nY/n5Ulteqq4hRFHE0KFDERkZ6TLafOPGDRQWFiIsLMxlwxUiIqK2hiPPTcxbRZxsk7HlF9+7xP3b\n+WPq36ZD729wc5aTmHUUuoPpmpj1gbmAWMc60NQq9ezZE9OnT0dISIgmbrfbsX79ehw8eJDzoImI\nqE1j8dxK7P1oN0quFGtiol7ElL9OR1CH4PpPVlUYl/1FE5J79oOcMNzTaVILEBYWhunTp6Nbt24u\nbQcOHMDGjRthsViaPjEiIqJmgMVzK1B0uQj7PtztEp/w/mTEJNx6R0Apcy+k05mamOXBp4EWPNWB\no6N3xmAwYPz48UhKSnL5tuTixYv45ptvUFBQ4KPsiIiIfIfFs4/daZGnKipWzF4GVdFeZ8BPBqHP\nzH63voCiwLBcO+psjx8Cpc/AO8qrueGc58YTBAEDBw7EPffcA71er2krLi7GqlWrcObMGR9lR0RE\n5BssnpuYp4u4LW99j+KLRZpYeGwERi0Y26DzdXu2QLp4VhOzzprvsfyo5evYsSMSExPRrl07Tdxu\nt2Pr1q3IyMjgtt5ERNRmsHhuwU6tPoGjX2mnW4h6EfcvfeiWK2sAAOw2GL5eognZho6D0jXWk2lS\nK2AymTB16lT06dPHpe3YsWNYu3YtysrK3JxJRETUunCpuhYq58g1bHxlnUt8zG8nwD/C380ZrvTb\n1kK8ftVxrEoSrDOf9FiOvsQ5z56n0+kwYsQIREZGIiMjA7IsO9pyc3OxdOlSREREIDw8HOHh4Y7n\ntad8EBERtWQsnlug0pwSrJn7DRSb9qvy6AHtEffQ3Q27SEUZ9Ks/04Rso6dCje7kqTSplerTpw8i\nIiKwadMmlJaWOuJ2ux25ubnIzc3V9A8ODnYU0tWPgYGBnIdOREQtEovnFsZWbsOa+d+g7LpZ2yAA\nE/57coMLEv2G5RCLbjqOVYMJtmmPeTJVasUiIyMxY8YMbNmyBVeuXKm3b3FxMYqLi5Gdne2IGQwG\nTTEdERGBsLAw6HT8vyQiImre+F8qH2vM9AJVVbHptfXIy8x1aRv4kwRE9G7n5iw3SgphWLdUE7JN\negBqaESDc2lpOMrpeSaTCZMnT8aRI0dw9OhRVFRUNPhcq9WKnJwc5OTkOGKCICAkJMRllNrf35//\nfkRE1GyweG5id1IE7P1wF06vOeUSN4YYkfxSSoOvY1j7FYRy58i1GhAM670P33Ze1HaJoohBgwZh\n4MCBMJvNyM/PR35+PgoKCpCfn4/i4uJbX6SKqqooLCxEYWEhzp51rgBjMplcRqlDQ0MhSdz9koiI\nmh6L5xYi69tT2P2HDLdtKT8bDlOoX4OuI+TnQr95pSZmnfII4B94xzlS2yUIAgIDAxEYGIiuXbs6\n4jabDQUFBY5iuvq5zWZr8LUrKipw9epVXL3qvLlVFEWEhoYiPDwcnTp1Qs+ePSGKXDyIiIi8j8Vz\nC5D3Y67blTUAIOKudoh/ZECDr2X45lMINQoXJTwStvEz7jhHInf0ej2io6MRHR3tiKmqipKSEs0I\ndX5+vubmw1tRFMVRiJ85cwaHDh3CkCFD0LVrV07xICIir2Lx3MyZc0uxZt5K2CvsbttHvjMGoq5h\nI27ClfPQ7ViviVmn/wQwGO80zWaHS9U1X4IgIDg4GMHBwejevbsjbrVaNQV1dXFcc0m8uhQVFeH7\n779HdHQ0kpOTNcU6ERGRJ7F49rH6ijx7hQ1rnv4GpTnuR+R6TopFl+Fd3ba5Y1y+GILqXN5OiekC\n+/BJDU+2BeNoZPNnMBgQExODmJgYR0xRFBQXF7sU1Waz2e01cnNzsXr1anTr1g1JSUkIDQ1tqvSJ\niKiNYPHcxBpaxKmqik2vb0Tu4Ry37ZJBwoi3RzX4daXDu6A7uFMTszwwD5D4J0DNV/Xc5tDQUPTs\n2dMRr6ioQEFBAbKyspCVleXyIfT8+fO4cOEC+vTpg4SEBPj7N2zjICIiolth5dRM7fvzHpxadaLO\n9kHzByOkSwNH1crNMH76B01I7tEXcuKIO0mRyGdMJhM6dOiADh06ID4+Hnv37sWlS5c0fVRVxYkT\nJ5CVlYX+/fsjPj4eBoPBRxkTEVFrwdvTm6Ez67Owa9HOOtv9IwOQ9Fxyg69nXPYXiAUrph6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v2MJWKSwjNekyl0tMO4remvav/gRdmuX/ZQZO7FWlQAAOAKFM9+yDx8gsIy18p0R4LDuK3lVM+H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\nlB0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fbd3c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>\n",
    "# License: BSD 3 clause\n",
    "\n",
    "#compute paths\n",
    "n_alphas = 20\n",
    "alphas = np.logspace(-10, 10, n_alphas)\n",
    "clf = linear_model.Ridge(fit_intercept=False)\n",
    "\n",
    "coefs = []\n",
    "for a in alphas:\n",
    "    clf.set_params(alpha=a)\n",
    "    clf.fit(X, y)\n",
    "    coefs.append(clf.coef_)\n",
    "\n",
    "#Display results\n",
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#11. Build a L1 Linear Model\n",
    "from sklearn.linear_model import Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_lasso = Lasso(alpha=0.1, fit_intercept = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.1, copy_X=True, fit_intercept=False, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_lasso.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.00000000e+00,  -0.00000000e+00,  -0.00000000e+00,\n",
       "        -0.00000000e+00,   9.06125056e-05,   6.15534174e-02,\n",
       "        -3.52407975e-03,   0.00000000e+00,   2.04062618e-03,\n",
       "         8.09221369e-04,  -5.82902308e-06,   8.85392698e-04])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_lasso.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.061849361425333364"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(model_lasso.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#12. Feature selection from L1 Linear Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import SelectFromModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Lasso(alpha=0.1, copy_X=True, fit_intercept=False, max_iter=10000000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Lasso(alpha=0.1, fit_intercept = False, max_iter=10000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sfm = SelectFromModel(model_lasso, threshold=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SelectFromModel(estimator=Lasso(alpha=0.1, copy_X=True, fit_intercept=False, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False),\n",
       "        prefit=False, threshold=0.1)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SelectFromModel(estimator=Lasso(alpha=0.1, copy_X=True, fit_intercept=False, max_iter=1000,\n",
       "   normalize=False, positive=False, precompute=False, random_state=None,\n",
       "   selection='cyclic', tol=0.0001, warm_start=False),\n",
       "        prefit=False, threshold=0.1)"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfm.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/amitkaps/miniconda3/lib/python3.5/site-packages/sklearn/feature_selection/base.py:80: UserWarning: No features were selected: either the data is too noisy or the selection test too strict.\n",
      "  UserWarning)\n"
     ]
    }
   ],
   "source": [
    "featureSel = sfm.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(249176, 0)"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "featureSel.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([], shape=(249176, 0), dtype=float64)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "featureSel[:,:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#13. Find the generalization error.\n",
    "#Split dataset into two: Train and Test : 80% and 20%\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(X, y,test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((199340, 12), (199340,))"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#14. Build L2 Regularization model on train and predict on test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model_ridge = Ridge(alpha=1.0, fit_intercept=True, normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=True, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_ridge.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ridge_output = model_ridge.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14217.47449793072"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#15. Report the RMSE\n",
    "np.sum((y_test - ridge_output)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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