IBM4 Model Development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Development\n",
    "관련된 데이터, 많은 데이터, 그에 맞는 모델이 중요\n",
    "\n",
    "# 1. Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (Simple) Linear Regression (=SLR) - Scikit-learn\n",
    "One predictor/independent variable(X) & One target/response/dependent variable(Y)\n",
    "\n",
    "y = ax + b \n",
    "* Parameter) a : slope, weight, coefficient / b : intercept, bias  -->  data fitting으로 얻어짐\n",
    "* Noise) fitted line에서 벗어난 정도, 보통 0일 확률이 가장 높음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Linear regression model 만들기\n",
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 변수 설정\n",
    "X = df[['highway-mpg']]\n",
    "Y = df[['price']]\n",
    "# Fit the linear model with data\n",
    "lm.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16236.50464347],\n",
       "       [16236.50464347],\n",
       "       [17058.23802179],\n",
       "       [13771.3045085 ],\n",
       "       [20345.17153508]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 예측해보기\n",
    "Yhat = lm.predict(X)\n",
    "Yhat[0:5]          # .head() 기능 없음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    13495.0\n",
       "1    16500.0\n",
       "2    16500.0\n",
       "3    13950.0\n",
       "4    17450.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 실제값과 대조\n",
    "df.loc[0:4,'price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38423.30585816])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Intercept b 구하기\n",
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-821.73337832]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slope a (coefficient) 구하기\n",
    "lm.coef_\n",
    "# lm : yhat = -821.73 * x + 38423.31"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple Linear Regression (MLR)\n",
    "Multiple independent variables\n",
    "\n",
    "y = b + a1x1 + a2x2 + ... + anxn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# same with simple linear model\n",
    "lm1 = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 4개의 변수 도입 (price와 관계있던 변수)\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "y = df[['price']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model fitting\n",
    "lm1.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-15806.62462633]),\n",
       " array([[53.49574423,  4.70770099, 81.53026382, 36.05748882]]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# intercept, coefficient 구하기\n",
    "lm1.intercept_, lm1.coef_\n",
    "# lm1 : price = -15806 + 53*(horsepower) + 5*(curb-weight) + 82*(engine-size) + 36*(highway-mpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Evaluation using Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) Visualization of Simplie Linear Regression\n",
    "## Regression Plot - seaborn\n",
    "Simple linear regression 시각화에 좋음\n",
    "\n",
    "얻어지는 fitted line이 linear regression model과 같음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14.094578853046595, 50)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9LOkpSTeU7narpMdLH28pfa7S15+01trS9Q3GmGBpostSSTskPSNpqTHmfGNMQMUNolvK9XoAAACAcirbuERJ8yXdV5qe4pH0qLX2p8aYlyQ9bIz5b5Kek3Rv6f73SnrAGLNXxUr5Bkmy1u42xjwq6SVJOUn/0VqblyRjzOcl/ULFcYnfs9buLuPrAQAAAMrGFIvSs8eKFStsZ2en08sAAABAFTPG7LTWrpjMYzj5EwAAAHABgjkAAADgAgRzAAAAwAUI5gAAAIALEMwBAAAAFyCYAwAAAC5AMAcAAABcgGAOAAAAuADBHAAAAHABgjkAAADgAgRzAAAAwAUI5gAAAIAL+JxeAAB36eiKafPWbvXEk2prjGjTunatX9bi9LIAAKh6VMwBjOroiunLj+3Scz1xHR5I67meuL782C51dMWcXhoAAFWPYO6gRDrr9BKAcb72xMs6nszKFiSvMbIF6Xgyq6898bLTSwMAoOoRzB0UH8rqwPGUhnN5p5cCSJJeP5aUx0gej5ExRh6PkccUrwMAgPIimDtsOJvXweNpxYcystY6vRwAAAA4hGDuAtZaxZMZ9cZTSmepnsM57XOiKlipYK2srArWqmCL1wEAQHkRzF0kmy/o4PGUjg4Oq1Cgeo6Z95Vrl6kx4peRlMsXZCQ1Rvz6yrXLnF4aAABVj2DuQgOprHrjKQ0N55xeCmaZ9cta9PUbLtXlixo1vz6syxc16us3XMq4RAAAZgBzzF0qVyjo8EBa0aBPzdGAfF5+h8LMWL+shSAOAIADCOYuNzScUyqTV2M0oPqw3+nlAAAAoEwow1aAgrU6NjjMaEUAAIAqRjCvICOjFfuGMmwOBQAAqDIE8wpjrdXx0mjFQTaHAgAAVA2CeYXKFQqKDaR1qD+lTK7g9HIAAABwjgjmFS6VyevA8ZSOMfscAACgohHMq4C1Vv2prHriSSXSWaeXAwAAgCkgmFeRfMHqSGJYB5neAgAAUHEI5lUonc3rQDylo7S3AAAAVAwOGKpiA6msksN5NUb9qg1xOBEAAICbUTGvcrlCgfYWAACACkAwnyXSpcOJmN4CAADgTgTzWWRkektvPKVkhsOJAAAA3IRgPgvlCgW92Z/W4YG0cnkOJwIAAHADNn/OYkPDOaUyeTVGAqqPsDkUAADASVTMZ7mCtTo2NKzeeFLpLJtDAQAAnEIwhyQpkyvo4HFmnwMAADiFYI5xBkqbQweH2RwKAAAwkwjmeItcoaDYQFpv9qeVZXMoAADAjCCY47SSmZx64ykdT2ZkLe0tAAAA5UQwxxlZa9U3lFFvPMXmUAAAgDJiXCImJJsvbg6tCfnUFAnI5+V3umrV0RXT5q3d6okn1dYY0aZ17Vq/rMXpZQEAUPVIV5iUwXSxvaU/lXV6KSiDjq6Y7tyyW7FEWg1hv2KJtO7cslsdXTGnlwYAQNUjmGPSCtbq2CCzz6vR5q3d8nuNIgGfjCne+r1Gm7d2O700AACqHsEcUzYy+zyWSCvH9Jaq0BNPKuz3jrsW9nvVG086tCIAAGYPgjnO2WA6p554Sn1DGQ4nqnBtjRGlTnoXJJXNq7Ux4tCKAACYPQjmDvnv//KS7n/6DQ1VyUE+1lodT2bUE0+qP5llvGKF2rSuXdm8VTKTk7XF22zeatO6dqeXBgBA1WMqiwP2H0vqH37zhnIFq0c6e3TDFa36gysWqiZY+f848gWrY0PDGkhn1RgNVMVrmk3WL2vRXSr2mvfGk2plKgsAADPGzLbK5ooVK2xnZ6eja4gPZbR5a7fu++0bo20DNUGfrr9ioa6/olU1oeoJsyG/V801AQV93rPfGQAAoEoYY3Zaa1dM6jEEc+e80HNcP3hmv3783AGls8XNk9GgV9df0aobqiigG2NUF/KpMRKQx2OcXg4AAEDZlTWYG2MWS1pqrf2VMSYsyWetTUxhnY5yUzDffyypXKGg/mRW/7SzRz9+7uBoBT0a8OpjVyzUDVe2qjbkd3il08Pn8ai5JqAo7S0AAKDKlS2YG2M+J+kOSU3W2guMMUsl/S9r7XumtlTnuDGYj+hPZfXYzl796NkD4wL6H1yxUDdc0aq6cHUE9GjQp+Yop4cCAIDqVc5g/rykVZK2W2svL1170Vr7jimt1EFuDuYj+lNZ/fDZYkBPZooBPRLw6g8uL1bQ66sgoHuMUWMkoLpw8SAbAACAajKVYD7RnoJha21mJEAZY3ySZldz+gyqD/v12avO1w1XtI4G9KFMXg9u368fPXtAf3D5An38yjbVRyo3oBdscXpLYjirOTVBhfxsDnWLjq6YNm/tVk88qTamsgAAMGMmWjH/fyUdl3SLpD+W9EeSXrLW/ufyLm/6VULF/GSJdFY/3HlAP3yuV0PDxQp62O/VRy9foE9UeEAfURvyqykakJfNoY7q6Irpzi275fcahf1epbJ5ZfNWd113CeEcAIBJKGcri0fSbZLeJ8lI+oWk79oKHOlSicF8xGA6px8+26vHnj0R0EN+jz562UJ9YkWrGiKBci11Rng9Rk3RQNVsdq1EG+/ZplgirUjgxJtpyUxOLbUh/eCONQ6uDACAylLOYB6VlLbW5kufeyUFrbXJKa3UQZUczEcMpnP60XO9emznAQ2WTg4N+Ty67rIF+uTKNjVWeEAPB7xqjgYV8LE5dKZdffeTagj7x/X9W2vVn8rq11+5xsGVAQBQWaYSzCeafP63pPCYz8OSfjWZb4TpUxPy6Za1S/TQ51brM1ctUW3Ip3SuoEc7e/Wp72zX/+x4TX1DGaeXOWWpTF4HjqfUN5RRoVBxb8pUtLbGyOhEoBGpbF6tjRGHVgQAwOwx0WAestYOjnxS+pj/UzusJujTzWsW66HbV+uzVy1RXSmg/9POXn3qu5Ud0K21Op7MqDeeUiKddXo5s8amde3K5q2SmZysLd5m81ab1rU7vTQAAKreRIP5kDHmipFPjDFXSkqVZ0mYrGjQp5vWLNZDn1ut268+X3Uhn4bHBPS/79hbsQE9VyjoSGJYB4+nNJzLn/0BOCfrl7XorusuUUttSP2prFpqQ2z8BABghky0x3ylpIclHSxdmi/pk9banWVcW1lUQ4/52SQzOf3zcwf1aGePBtLFHvSAz6Pff+d8bVjZpuaa4LR/z3LZ0d2nh5/p0aGBlObXhfWZq5bow5cuYHoLAABwtbJt/iw9uV/SRSpOZemy1lZkf8FsCOYjUpm8Hn/+gB7p7FV/qviPK+Dz6MPvmK8Nq9o0x+UBfUd3n7715B75PEYhv0fpbEG5gtWfvGeprn3nfNUxvQUAALjUtAdzY8w11tonjTEfO9XXrbU/muQaHTebgvmIVCavx3cd1KPP9Oh4KaD7vUYffucCbVjZprm17gzoX3pkl44NDSs85vChVDav5mhQf/3JSxXyezWnhuktAADAfcpx8ue7JT0p6fdP8TUrqeKC+WwUDni1YWWbPnLZAv1k10E98kyP4smsfvzcAf30hYP64Dvm68ZVi1wX0A8NpFQXGv+vaMjv0ZsDxe0N6WxxektD2K+GyPgRfwAAAJXmjMHcWvsXpcOFnrDWPjpDa0KZhP1efWJFm667tBjQHy4F9MefP6ifvXhIH3z7fG1c1aaWupDTS5Ukza8Lv6Vins4WNK/uxOROa63iyYwGh3OaUxNUOOA91VMBAAC43ll7AKy1BUmfn4G1YIaE/F59fEWbHrx9tf5o/QVqigaUzVs9vuugbv7eDn3zV3t0eCDt9DK1YWWbcgWrVDYvq+JtrmC1YWXbW+6bzRd0qD+lWCKtPLPPAQBABZroVJb/ouJ4xEckDY1ct9b2lW9p5TEbe8zPZjib109fPKSHd/ToWGmsos9j9IG3z9PG1Ys0z8EK+shUljcHUppXF9aGlW1a1d50xsd4jFFjNKD6MJtDAQCAM8o2lcUY87qKPeXjWGsr7tQRgvnpDWfz+pcXD+kHJwX0a98+TzeuWqR59e5ocZmogM+jOTVBhfy0twAAgJlVzmAelvRHkq5WMaD/WtL/stZW3CFDBPOzy+QK+pcXD+mhHft1bLAY0L0eo/dfcp4+tXqR5teHz/IM7lIT9KkpGpDPy/QWAAAwM8oZzB+VNCDpwdKljZIarLWfmPQqHUYwn7hMrqCflQL60TEB/X3LiwF9QUPlBHSPMWqI+FUfZnoLAAAov3IG813W2kvPdq0SEMwnL5Mr6Il/P6SHtvfoyOCwJMljpPctn6dPrVmkhRUU0P1ej+bW0t4CAADKayrBfKLv7T9njFkz5hutlvSbyXwjVK6Az6OPXLZQD9y2Sl9871K11AZVsNLPd7+pW7+3Q3f/vEsH4pXR1ZTNF3TweEpHB4dVYHoLAABwkYlWzF+WdJGk/aVLiyS9LKkgyVpr31m2FU4zKubnLpMr6Be739SD2/crljhRQX/vxefppjWL1NoYcXiFE+P3etRcE1AkcLZztgAAACannK0si8/0dWvtvsl8UycRzKdPNn8ioB8eOBHQ33Pxebpp9SK1NVVGQK8J+dQcDcrrofccAABMj7IF82pCMJ9+2XxB/7r7sB7cvl9vlg4m8hjpmmUtumnNYi2qgIDu9Rg11wRVE6R63tEV0+at3eqJJ9XWGNGmde1av6zF6WUBAFBRCOYTQDAvn1y+oH99qRjQD/WfCOi/e1GLbl6zWIua3R/QIwGf5tTM3tGKHV0x3bllt/xeo7Dfq1Q2r2ze6q7rLiGcAwAwCQTzCXBTMO/pSyqbr55gPiKXL+iXL8f0/W37RgO6kfS7y1p085pFWtwcdXaBZ+ExRk01AdWFZt/JoRvv2aZYIj2u7z6ZyamlNqQf3LHmDI8sL6r4AIBKU86pLCiD1sZwVY7u83k9+sDb5+n+z67SV669SAsaQrKSnuyK6bP/2Kn/+tOX9PrRIaeXeVoFa3U0MayDx1PK5KrvF6cz6YknFT7p38ew36veeNKhFZ2o4scSaTWE/Yol0rpzy251dMUcWxMAAOVAMHeQMUa1Ib8WNITV2hhRfdhfVRsQi6eFztN9n1mlr157kRY2hGUlPfXKEd1+X6fu+om7A3o6m9eB4ykdT2acXsqMaWuMKJXNj7uWyuYdnbSzeWu3/F6jSMAnY4q3fq/R5q3djq0JAIByIJi7RMDnUXNNUIuaImqpCykcqJ4qutdj9L5L5ukfP7NSX/3AMrU2FgN6x6tHdNt9nfrLn+xW95FBp5d5StZa9Q1l1BtPKn1SYK1Gm9a1K5u3SmZysrZ4m81bbVrX7tia3FjFBwCgHBhB4TLGGNUEfaoJ+pTNFzSQympwOKd8FRyG4/UYvW/5eXrPshY99UpMDzy9Tz3xlLa+elRbXz2qdUvn6Oa1i3XB3Bqnl/oWmVzxYKK6sF9NkYA8VfTOxljrl7XoLhWr1L3xpFpd0M/d1hh5S9+701V8AADKgc2fFcBaq8HhnBLpXFVVbfMFq45XYnpg237t7ztR/fydpXN0y5rFuqDFfQFdknwej5pqAoxWnCEdXTH96WO7lEjnlCsU5PN4VBvy6es3XMoGUACAa01l8yfJogKM9KLXhvwazuWVSOc0mM6pUOG/VHk9Ru+5+Dytv6hFHa8c0fe37dO+vqR+veeofr3nqK66sFm3rl2iC10W0HOFgmIDaQ0GfGquCcg/S0crziQrSab4d0Gm9DkAAFWGinmFKhSsEsM5DaSyVTNyMV+w2vrqEd2/bZ/2HTtRQb/qgmbdsnaxlp5X6+DqTs0Yo8aIX/VhfzE0Ytq5dYQjAABnQsV8FvF4jOrDxUCYyuQ1kM5qaDjn9LLOiddj9LvLWvTui+YWA/rT+/TGsaR+89ox/ea1Y3pXKaC/zUUBfWRzaCKdU1M0oCjtLdOuJ55UQ3j8THk2fwIAqhEpogqEA16FA17l8gUNpHNKpLMVvVnUY4zWX9SidW+bq1/vOar7n96n148O6bevHdNvXzumNe1NunXtEl00zz0BPZsv6PBAWuGAV03RgIK+6pmq4zQ2fwIAZgtaWarQyGbRgXROw1WwWbRgrf5tz1Hdv22fuo+cmHu++vwm3bJ2sS6eX+fg6k6tNuRXUzRQVXPpnTJywJDfaxT2e5XK5pXNW9113SVs/gQAuNZUWlkI5lUunR1pc8mr0rkJdEEAACAASURBVP9ZF6zVv+09qgee3qfXxgT0Vec36VYXBnSPMWqMBFQX9p22/5yj5idm5OfklhGOAACcDcF8AmZbMB+RL1gl0lkNpIoj5ypZwVr9du8x3f/0Pu0dczDRqiWNumXtEi1f4K6A7vd6NKcm+JZDo6gEAwBQvQjmEzBbg/lYQ8M5DaSzSmUqu83FWqvfvnZM9z29T3tjJwL6isWNuvVdi3XJgnoHV/dW0aBPTdET4xWZNgIAQPViKgsmJBr0KRr0KZMraCCdrdiZ6MYYXXXhHL3rgmY93V2soL96eFCd++Lq3BfXlYsbdevaxXr7QncE9KHhnJKZvOrDfjVG/EwbAQAA4xDMZ7GAr9hi0RQJVPRMdGOM3nXBHK1tb9a27j7d//Q+vXI4oZ374tq5L64rFzXolrVL9I5W5wO6tVbHkxkNpnNaUB/WsaFhpo0AAABJBHOoemaiG2O09oJmrWlv0vbX+3Tf0/v0ypsJ7dx/XDv3P6/LFzXolrWLdWlrg9NLVa5Q0McuX6hvP7lH1lpFAr7RHvNN69qdXl5VY8MtAMCt6DHHKVXDTHRrrXa8Uaygv3woMXr9srZ63bp2iS5tcz6g7+ju08PP9CiWSGtRU0T/4d0XEBLLqKMrpj99bJcS6eImaJ/Ho9qQT1+/4VJ+7gCAacXmzwkgmE9ONcxEt9aqc19c9/32Db00JqBf2lqvW9+1RJe5IKBLxfGKDZHiOxenG6+Ic/OBb27VntigvB4jYyRrixOLlrbU6IkvrnN6eQCAKsLmT0w7Y4xqQ37VhvwVOxPdGKOVS5q0YnGjOvfFdf/T+7T74IB29fbrS4/u0jtb63XL2sW6vK3B0UBcsFZ9Qxkl0jk1RgOqCfLXc7p1Hx2SxxR/CZJUDOfGqvvo0FkeCQBA+fF/fkxYyO9VyO9VPlqciZ5I5ypqs+jYgP7s/uO677dv6N8PDuiF3n59+Z9e0DsW1unWtUt0+SJnA3o2X1BsIK1EwKvmaFABn8extQAAgJlDMMekeT1GDZGAGiIBJTM59acqaya6MUZXLm7UFYsa9Nz+47rv6Tf04oEBvXhgQF9+7AW9fUGdblm7WFcubnQ0oKcyeR3IptQQ9qshQnvLdDi/OaK9R4ZkCna0laVgpQvnMAkHAOA8eswxLTK5wmgVvdJmoltr9XzPcd339D690Ns/en35/Drd+q7FWuFwQJdOf3ooJqejK6YvP7ZLg8M55QtWXo9RTdCnv2LzJwBgmrH5cwII5uVVKFgNZooz0TO5ymlzGfF8T7HFZde4gF6rW9Yu0colzgf0mqBPzTVBeT1Uz6dqZFxibzypVsYlAgDKhGA+AQTzmZPO5jWQymooU1mbRSVpV6mC/nzP8dFrF8+v1S1rF2vVkiZHA7rHGDVGA6o/6dRQAADgHgTzCSCYz7xcvqBEOjc6O7qS7Oo9rvuf3qfn9p8I6BfNq9Wtaxdr9fnOBvSg36s5NQEFfbS3AADgNgTzCSCYO8daq6FMsYqerrCZ6C+UAvqzYwP6ecUK+pp2ZwN6fdivxkhAHtpbAABwjakE87LNYTPGtBljnjLGvGyM2W2M+ULpepMx5pfGmD2l28bSdWOM+bYxZq8x5gVjzBVjnuvW0v33GGNuHXP9SmPMi6XHfNs43QCMMzKmuNFuQUNYCxvDqg1VzqSRd7Y26K8+fqm+veEyXbm4UZL0yuGE/vM//7v+8MFn9dvXjjrWrtOfyqo3ntLQcM6R7w8AAKZH2Srmxpj5kuZba581xtRK2inpo5I+LanPWvs1Y8xXJTVaa79ijPmgpD+W9EFJqyV9y1q72hjTJKlT0gpJtvQ8V1pr48aYHZK+IGmbpJ9J+ra19okzrYuKubsUClaJdE4D6WxFzUT/9wP9uv/pfercFx+9trSlRresXax3XdDs2C8ckYBPzTUB+b3MPgcAwEmubmUxxjwu6W9Lf9Zbaw+VwnuHtfYiY8zm0sc/KN3/FUnrR/5YazeVrm+W1FH685S1dlnp+sax9zsdgrl7JTM5DaRySmYqp/K7+2C/Hnh6n3a8cSKgXzi3GNCvutCZgG6MUX3Yr4awn/YWAAAcMpVgPiMHDBljlki6XNJ2SedZaw9JUimcj8wpWyipZ8zDekvXznS99xTXUaEiAZ8iAZ+y+YIGUtnRWdNudsmCen3t+nfq5UMDuu/pfdrxep/2HhnUnVt264K5Ud2ydomuurB59Aj4mWCt1fFkRoPpnBqjftWGmN4CAEAlKPv73caYGkk/lPRFa+3Ame56imt2CtdPtYY7jDGdxpjOI0eOnG3JcJjf61FzTVCLmiKaWxtU0O/+qSMXz6/T1z72Dv3djZdrTXuTJOm1I0P6iy27dccDO7X11SMzfvBSrlDQkcSwDhxPVdxmWwAAZqOyVsyNMX4VQ/mD1toflS4fNsbMH9PKEitd75XUNubhrZIOlq6vP+l6R+l66ynu/xbW2nsk3SMVW1nO4SVhBhljVBsqVnzT2bwG0lkNDbt7JvrF8+v0P/7gHep6c0D3P71P27r71H1kSH/5k5fUPieqm9cu1u8snTNaQd/R3aeHn+nRoYGU5teFtWFlm1aVgv10Gc7mdfB4SjVBnxqj9J8DAOBW5dz8aSTdp+JGzy+Ouf51ScfGbP5sstb+mTHmQ5I+rxObP79trV1V2vy5U9LIlJZnVdz82WeMeUbFDaPbVdz8+TfW2p+daV30mFe2fMFqsII2i77yZkL3P71PT3cfG712/pyobl6zWCGfR3/z1F75PEYhv0fpbEG5gtUXrlk67eF8hDFGDWG/GiKVMxEHAIBK5KrNn8aYqyX9WtKLkkYS1H9SMUQ/KmmRpP2SPl4K2UbFjaHXSkpK+oy1trP0XJ8tPVaS/ru19h9K11dI+kdJYUlPSPpje5YXRDCvHqlMXol0ZZws+urhhB54ep9+89qJgB7yeRQNetUUCYyG5FQ2r+ZoUH/9yUvLuh6/16M5NUGFA+5vEwIAoBK5Kpi7FcG8+lRSFX3P4YTu37ZPv9l7IqAHvEZN0YBqgz7JSIl0Tg99bs2MrKcm6FNTNCAf7S0AAEwr105lAcrJ6zGqj/hVH3F/L/rS82r1Xz/ydu2NDepPH3tB/amsMnmrNweG1efNqCbkU1tDZMbWMzicUzKTV2MkoPoI01sAAHASZTJUlZDfq5bakBY1RdQcDbp2o+OFLTX682uXaU5NQGF/cY2ZvFXfUFYH+9P65UuHZ2xUZMFaHRsaVm88yfQWAAAcRCsLql4qU6yiJ13Yiz4ylaUnPqRcQepPZUe/1toY1k1rFus9y1rkncGDgmpDfjVFAzP6PQEAqDb0mE8AwXz2yuULSqRzSqRzyhXc2Yv++tEhPfD0Pv2fV4+MDuVvbQzrptWL9J6Lz5uRsLyju0+PdPbocCKtxU1RbVrXrvXLWs7+QAAAMIpgPgEEc1hrNVSa6JLKTL51YyZmj79+dEjf37ZPHa+cCOgLG8L61OpF+r3l5QvoO7r7dPcvujRUOnXV5zGqDfn0Vx+/jHAOAMAkEMwngGCOsTK5ggbSWQ2mcxM6mXNHd5++9eSeGZs9/saxIX1/23491RUbDejz60O6ac1i/d7FLdM+TeX2+zq179iQPB4jYyRrpULBqn1OVL/4k3fLQ3sLAAATMpVg7s6dccAMCfiK87wXNUXUXBNUwHfmvxIPP9Mjn8co7PfKqHjr8xg9/ExPWda3pDmq/+dDF+t7n16h9yxrkcdIh/rT+vovXtGt//CMnnjxkHLTOCKyJ56Ux0geY2Rk5DFGHiO90ZdUTzypgXT27E8CAACmhGAOSPJ4jOrDfrU2RrSgIayakO+UJ2MeGkgp5B//1ybk9+jNgVRZ17e4Oar//KGL9b1Pr9R7Lx4T0P/1Vd36D8/oX16Y3oB+KvmC1dHEsA4cTzG9BQCAMiCYAycZGbm4+BRV9Pl1YaWz4wNwOlvQvLrwjKxtUVNE/+mDF+sfPr1Sv7f8vNGA/v/98lXd/L0d+ukLh87pkKW2hrAKpfYVa60KBauCLV4fMZzN6+DxlI4khs860rGjK6aN92zT1Xc/qY33bFNHV2zKawMAoNoRzIHTOLmKXhvya+OqNuUKVqlsXlbF21zBasPKthldW1tTRH/+gWX6x8+s1PsvKQb0wwPD+utfvqqb792hn+w6OKWAfse6C1QX9st4ivPNjUeqC/t1x7oL3nLfRDqrnr7kuBGPY3V0xXTnlt2KJdJqCPsVS6R155bdhHMAAE6DYA5MQMjv1dzaoD6+ok0fu3yB4smMXjsypL6hjK5dfl5ZNn5ORGtjRF+5dpnu+8yq0YAeSwzrG7/ao5vv3aEtuw4qk5t4QF/V3qSPXrpAfo9HBSv5PR599NIFp319BWt1bPDUhxNt3totv9coEii2BUUCPvm9Rpu3dp/TawYAoFr5nF4AUEm2vnpEP3nhTZ1XF1LQ51Eyk9fPXzqsi+bVORbOJWlhY1hfuXaZblqzWA9t369f7H5TscSwvvmrPXpo+35tXLVIH3j7vLNubt3R3aefv3RYTdHA6NSZiby+TK6gg8dTqgn61BQNyOf1qCeeVEPYP+5+Yb9XvfHktLxmADOjoyumzVu71RNPqq0xwtkGQBlRMQcmYWwV2OvxqDbkV9jv0Q+f61XQ73V6eVrYENafvv8i3f/ZVfrg2+fJ6zGKJYb1rf9drKD/83MHzlhBP9epM4PDOfXGUzqezKi1IazUSVX0VDav1sbIpF8XveqAM2hJA2YWwRyYhJ54UuGTAngk4NOb/WktbAgXJ7oETz3RpZx2dPfpS4/s0sbvbNOXHtml3r6Uvvz+i3T/Z1fqQ++YL6/H6MjgsL795F7ddO92/fg0AX06ps4UrFXfUEbXX9Gq/mRGew4n9PKhfu05nNBAKqtN69on9doIBoBzaEkDZhbBHJiEtsbIGavAIb9XLXUhtTWG1RgJlO2EzrFGDj06NjSsupBPx4aG9a0n92hHd5/m14f1f7/vbXrgs6v04XfOl89jdHQwo795cq8+de92/ejZXg2PeT3TOXUmX7DKW8mOHI1kpKkcZ0YwAJxzqmIELWlA+RDMgUnYtK5d2bxVMpOTtcXbbN6+pQrs83rUGA1oUVNELXUhhQPla3OZSPvJvPqQvvR7b9P9t63S719aDOjHBjP626de00337tAPSwF9w8rpmzrz8DM9qgn6tLgpqva5NTq/Oaq6kG/SgZpgUPloRapcZytGAJheBHNgEtYva9Fd112iltqQ+lNZtdSGdNd1l5x2I5QxRjVBn+bXh9XWFFFDGarok2k/mVcX0p+892164LZVuu7SBcWAPpTR3z31mj517w7tiyf1h+suUHM0qEQ6p+ZoUF+4ZumUNraOW5ctVtB9Ho/29w1N6nkIBpWNVqTKNtFiBIDpwVQWYJLWL2uZ0kQCv9ejpmhAjRG/hjJ5JdJZpTLnfoLm/Lqwjg0Nj6sqn6395Ly6kL743qW6cVWbfrCjRz/790PqG8rof3a8psaIXxtWtun3L12g0DlsaD3VulLZvObWhHSoP6XmaPCsU2KkYjC4c8tuJTM5hf1epbJ5gkEFGduKJBX3ZCQzOW3e2s1kjwqwflmL7lLxn2NvPKlWprIAZWWsnUrXZ+VasWKF7ezsdHoZgCQpmy9oIJXV4HDurKdons5Ij7nPY0ZHHOYKdlKV7iOJYT20Y79+9uIhZfPFdXhMscL+H9ZdoKvfNmfa12WMUV3Ip8ZIQJ6zvIswMq6tWoNBNY+ju/ruJ9UQ9o/bEG2tVX8qq19/5RoHVwYA5WWM2WmtXTGpxxDMAedZa5UYzimRzo3bjDlRO7r79PAzPXpzIKV5dWFtWNk2pfaTX+4+rG89uUfJMZV8j5Hev3yePv+eC9/S6z0d6/J6jBqjAdWF/Kd5luo20urh95px7wicqUWqkmy8Z5tiifRoxVySkpmcWmpD+sEdaxxcGQCUF8F8AgjmcLt0Nq+BdFZDw3nN9N/PLz2yS8eGhuX3GPUls+pPZUcnqdSH/frkilZ95LKFZdnMGvB51BwNlnWjrBtVe3Ct9l88AOB0phLM6TEHJqncbQchv1chv1f5qNXgcE6JdPaMhwJNp0MDKdWFfDIyaqkNqiniV18yo+OpnPpTWd3z69f1SGevPn5lqz56+YJxYfJcZXIFHepPKVo6PdTvnR1706v9hFR6lAFg4gjmwCSMrf6NnTBxlzTtQcPrMaoP+1Uf9iudzSuRzmloOKdCGavoJ2/Y9HmLp5subIjo4gW12rLrkPpTWX33317Xo509+sSKtmkP6EPDOSUzedWH/WoI+8/af17p2hojb6mYV9vUmalumAaA2WZ2lKSAaeLUYTchv1dza4Na1BTR3NqggucwLeVMTjfH/OY1i/VH6y/UQ7ev1sevbFXQ59FAOqfv/tvruvE72/X9bfs0NJybtnVYa3U8mVFvPKVEOjttz+tGjKMDAIwgmAOT4PRhNx6PKVWww1rYGFZtaPy0i3O1qr1J1y4/T31DGb12ZEh9Qxldu/y80Q2bTdGA/nD9BXrw9tX6xIpWhUoB/Xu/eUM3fne7Hti2T4PTGNBzhYKOJIZ18HhK6Slsiq0Ek52NDwCoXmz+BCbBjRv1CgWrRDqngXRW2fy59aLv6O7T3b/o0lAmp0LByuMxigZ8+sr7l51yyks8mdGjz/To8ecPKl3qg68J+nTDlQv1sStaVROc3m65mpBPzdHgtB/SBADAdJvK5k8q5sAkuLHtwOMxqo/41dYU0fz6sKLnEIbv2fqaBlJZ2YLkMUa2IA2ksrpn62unvH9jJKBN775AD31utTasbFPI79HgcE7/+Nt9uvE723Xfb9/QYHr6KuiD6Zx6+pLqT2ZnfGINAADlRsUcmKRKOOwmly9oIJ3TYDqnXGHiVfT3f3OrZK08nhO/sxcKBckY/eKL6876+P5kVo/u7NE/P3dQqVLrSTTo1fWXt+r6KxeqdhpnlY+cpHouv4icq2o+GGg68XMCMBsxx3wCCOaYTay1GsrkNZDKTqhH+1yD+Yj+VFaP7ezVj549cCKgB7z62BULdf0VraoLT19ADwe8aooGFPRNbEPsdIVE5nNPDD8nALMVrSzALNXRFdPGe7bp6ruf1MZ7tqmjKyZJMsaoJujTgoawWhsjqgv75TnDZtG2xogKVipYKyurgrUq2OL1yagP+3Xb1efroc+t1qdWL1Ik4NVQJq8Htu3Xjd/drnv/7XUNpKZn2koqk9eBeEpHEsPKF85caBgJibFEety4y5Gf12Q4NaGn0vBzAoCJI5gDFa6jK6YvP7ZLz/XEdXggred64vryY7veEjYDPo/m1AS1uDmiOacZuXjH77SrLuyXkZTPWxlJdWG/7vidqfXQjwb021fr5jWLFA14lczk9eD2/dr4nWJA75+mgJ5IZ8/afz6dIdHpCT2Vgp8TAEwcwRyocF974mX1DWY0nC0om7cazhbUN5jR1554+ZT3N8ao7qSRiyNV9FXtTfrK+5dp+fx6za0Navn8+tNOZJmMurBfn7mqWEG/Zc1iRQPFloYHt+/Xjd/Zru/8ulv9yXMP6AVrdWxoWL3x1CnnqvfEk8rlC+o+MqiuNwfUfWRQuXxhSiGxrTEy2qYzotoOBpoO/JwAYOI4+ROocHuPDGrs9k5b+rP3yOBZHxv0eTW31qvmaECDmZwGUlmtam865yA+Ykd3nx5+pkeHBlKaXxfWhpVt+vRVS3T9lQv1w2cP6IfP9mpoOK8f7OjRj587oI9etlCfWNGqhkjgrM9zpjVm8wUdHki/pf+8NujTntigvB4jr8coV7A6cDytpS01k35tm9a1608f26UD8ZRyhYJ8Ho9qQz79lw8tn/RzVbNN69p155bdSmZy43rMOUAJAN6KijlQ4U43unwyI809nmIVvbXx3EcujtjR3advPblHx4aGVRfy6djQsL715B7t6O5TbcivT79riX5w+xrdunaxaoI+pbMFPfxMj2787nZt/j+vKZ7MnPV5zubk/vPRFhc75o805dGLVpJM8V0ImdGnwxgcoAQAE0fFHMA44YBX4YBX2XxBA6msEumcClMIrg8/0yOfx4z2F49USx9+pme02l0T8unWdy3R9Ve26sfPHtBjz/Yqkc7pkc5ePf78QV132QLtPjBw1uc5m0Q6q6HhnAbSOS2oD+rYUFaZfEEBr0fzaoIaykz+VNHNW7tVH/Zrfn149Foyk9Pmrd2EzpOsX9bCzwQAJoBgDlS4kZaMk/nO8XRMv9ej5pqgGiMBJYaLbS6TOVn00EBKdaHx/4kJ+T16cyD1lvvWBH26ee1ifeyKhfrxcwf02M5eDaRzerSzV5LUEC5u0vSVxjie7nnOpGCtWmpD6ksOa3FzdPT00JGTWyerJ55Uw0ljH9nUCAA4F7SyABXuwrlReYudFJKKt14jXTA3Oi3P7/EY1YeLJ4vOqw8pEpjY7/Pz68JKZ8cH+XS2oHl14dM8QooGfbppzWI9ePtq3Xb1ktFgfzyV0+tHkzqSGFYuXzjr85zOhpVtyuatEumshrN5DQ5np9zvzKZGAMB0I5gDFe6rH7hYkYBXI+PJjZEiAa+++oGLp/17RQI+zasPqa0povqzzETfsLJNuYJVKpuXVfE2V7DasLLtrN8nGvTpU6sX66HPrda1y8+TKfVvx1NZvX4sqb6hjD74jnmTXv+q9iZdu/w89Q1ltPfIoGIDw3r/8hatvbB50s+1aV27snmrZCYna4u3bGoEAJwLgjlQBUJ+rwJej3weKeD1KHSKGeXTaaTNZVFTcSa63/vW/5Ssam/SF65ZquZoUIl0Ts3RoL5wzdJJTXyJBHz6sw8s019+aLnm14VGA/pQJq+/+uWr+tun9urY4PCEn29Hd59+/tJhNUUDumBuVE3RgH764pv68c4Dig2kJ9Wqw6ZGAMB0M1OdRlCpVqxYYTs7O51eBjBtNt6zTbFEelyLyUjf9A/uWDNj60hl8sVNlpn8lKecTOR7PP78AT3S2Tt6MJHfa/Thdy7QhpVtmlsbPOPjv/TILh0bGh534E0qm1dzNKi//uSlMqbYttMQ9stzjj36AIDZzRiz01q7YjKPYfMnUOF64kl5jdR9ZHB00sicmsCMb0IcmeaSyxeUSOc0kM4qf4pNqef6PTasWqSPXL5QW54/qEc7exRPZvXj5w7opy8c1IfeMV8bVy06bUA/24ZUa62OJzMaTOfUGPWrNuQ/1dMAAFAWBHPAQR1dMW3e2q2eeFJtjRFtWtc+6VaImoBXe2KDKthim0cun1dvPDWlQ3Omg8/rUWM0oIaIX0OZvAZSWaWzkx9HeCZhv1efXNmm6y5boJ/sOqhHnikG9H9+/qD+5cVD+uA75uvGUwT0+XXht1TMT7WRNFco6EhiWAPpnJqjgbK3BgEAINFjDjimoyumO7fsViyRVkPYr1girTu37FZHV2xSzzOUyStvTxxuYyXlraY0m3s6GWNUE/RpQUNYCxvDqgn5igfxTKOw36tPrGjTg7ev1h++u12NEb+yeavHnz+om+7drm/+ao9iA+nR+092Q+pwNq+Dx1OKJdLKTebEJgAApoBgDjhk89Zu+b1GkUAxsEYCxVndm7d2T+p53uxPT+q6E4I+r1pqQ1rUFFFTNDA6j3y6hPxefXwkoK+/QE3RgLJ5qy27Duqme3foG796VYcH0uOmsrx2ZEh9Qxldu/y8s25IHUzn1BNPqW8oM+3tOQAAjKCVBXDIdB1QkytttBxbjLb2xHU38XqMGiIB1YfL0+YS8nv18Stbdd075+unLx7Swzt6dGwoo5/sOqQnXnxTVyxq1OvHhtQUDSjk9yidLejnLx3WRfPqzhrOR/rPB1JZNUT8qg/7p/0dAADA7EbFHHDIdB1Q4y1lQ2tP/Bl73Y1ObnOpDU1vyA36vbr+ilZ9/7ZV+vzvXqDmaEC5gtWON/qKveOprHJ5q7DfK5/H6OFneib83AVr1TeUUU9fSv2pbNkm0AAAZh+COeCQ6Tqg5sK5NfJo/MmfntL1qejoimnjPdt09d1PauM92ybd8z5ZQZ9Xc2uDo20up5qJPuXn9nv1sSta9eDtq/XH11yokQmI/emcXj+W1JsDaXk9+v/Zu/MoOerz3v/vby29zXTPImk0WkYjCSTEJjatGGOCjZfEC3YwRhiEYxNz7z1JnJs41zm5ub6+ZLn28f05P0h+uQHjxEhsxnjDiQkBZCxjtAMCyxKSGGkWbSPN1jO9VXVV/f6o7tGMFtTd6lF3zzyvc+Y0FOqamkEafepbz/d5RruyFCPruvSNZOgZSDGSyZbtmoUQQkxdEsyFqJByDaj5849cSnN9gKCpYeqKoKnRXB8oafJnuTakliJf5tLWHGFmLEQ4UL5OKAFD45PXzOGK2Q00hk2MXEKPp7Mc7EthZT0ODxYfzgFsx6U3nubQYKrs3WeEEEJMLTJgSIhJIN92sWcgydwS2y5C9QwrykvbDoNJm6RVnhXprR39fOP5PYykbbLuyU42AJqCD17WymdXzWNOY/is5ziX+qDhb3At48q/EEKI2iMDhoSYom5a0lKWUfDl2pBaLiFTp7VBJ5N1GEraZSsZUZpCx0MpMDUN09AZStn8+66j/MdvjnLLZTO5a2U7c5qKD+gjmSwJy6Ex7G8QlQmiQgghCiXBXIhJoByDisDfkHrqinkpG1LLLWjotMR0mhyXwVxAL+Vp31PbuqkPGsyoPzl4KGU7NEUCfOCyFh7b3EXvcIbndx3jhd8c4wOXzuSuVfOK/vo9z2MgaTEsE0SFEEIUQZ61ClHjylkXXq4NqRPF1DVmRIO0NYVpihTfD/1IPEXIHP+ekKnRO5zmo0tns/4LK/iTWxbTGgvhevAfvznG5/5lG3/7s9109Rf/1CA/QbRnIFm2chwhhBCTlwRzIWpcuQYVQfk2pE40Q9doqgswb1qE1oYQdcHCporOjLBlrwAAIABJREFUioVJ2+MneKZtl9aYX7Ji6hofXTqLdZ9fzpc/uJhZDX5Af3F3L5//7jb+5t9209VXfEC3si5Hh9IcGUqRycoGUSGEEGcmpSxC1Lhy14WXq179QokEDCIBA8f1GE7bDKez2I57xl97x/I2Htiwj5TtjA4YyroedyxvG/frDF3jt6+cxQcvm8kLu3t5bHMnR4bSvLSnlw17evmtJS3cvWoe7dPqirrWlOVwyEpRHzJoipS3NaQQQojaJ8FciBrX1hThwIkRhtNZLMcloGtEQwYLppfWx7xW5dstNkYCJK0sQymblDV+dXrFwma+xCKe2tbN0XiK1liYO5a3nXXqp6FrfOSKVm65tIUXd/fy2JZODg+m2bCnl5/v6eWmS2Zw9+p25hcZ0EfSWRIZh1jIoDESQJcNokIIIZBgLkTRyrXRslxWL2xm68F+NOW3/LMcl+MjFneuePcR85NZfhU9k3WIp7LjNouuWNh81iB+Noau8eErWrnlspm8uPsYj23u4tBgip+/fZyX3z7O+xb7AX3B9MIDuud5DKX8Ff7GiN/BpZzTT4UQQtQe6WMuRBHyGy1NXRE2dVK2g+14Fa3DXvPwZg72jRBPnVwxj4UN5k+rr0jv8WrkuB7xlE08beO45/8zz3E9Xtrjl7j0DJwcTPS+xTNYW2RAzzM0jcY6k5h0cBFCiElB+pgLMcHGbrQEf2U2aWV5aGNHxYJ590CSaXVBpteHRo95nlex3uPVSNcUTXUBGiMmIxm/zMXKnrkOvdDzffCymbx/SQsb9vSyPhfQf7H3OL/Ye5wbF09n7ap2Fs4ovJwo67qcGM4wlLRprgtQF5Qfz0IIMdXIT34hilBtA3igenuPVyOlFNGQ31c8bTvEUzYJyympJzr4Af2Wy2Zy85IWXn67l3WbOukeSLFx7wk27j3Bexf5Af2ilsIDuu24HIunCZk6zXUBQqZe0rUJIYSoPdISQIgitDVFSNnjNxRWOgRXe+/xahUydVpiIdqawue9AVPXFO+/dCb//Lnl/PffvpR5zf7vh1/uO8Hvr9/BV3+yi/29I0WdM207HB5McXQoLS0WhRBiipAacyGKUI015vnremhjBz0DSeZWwYbUWuR5HiOZLPF0lox9fkHYcT1+sfc46zd30jmm7/l7LprG2tXtLJoZHffrt3b089S2bo7EU8w6S6cYabEohBC1pZQacwnmQhRpsofgaus6Uwlp2yGetklkSi9zAXA9j417j7NuUycHxwT063MBffHMKFs7+nlgwz4MTY3rrf6lmxedFs79Uhw/oEuLRSGEqG4SzAsgwVyIs6vWJwKV4rgeI+ks8bR91qFFhfAD+gnWb+7kwInE6PFVC5vpH7FI2Q7hMbXkKdthWl2Qb33mqjOeT1OKhrDfYlGTgC7OQG6whai8UoK5PBMVQowa23VGKf/V1BUPbeyo9KVVhK4pGiImbc0RWhtChAOlbcTUlOKmS2bw7bXX8bWPXcbCXDvFzR397O0doS9hkR5TPhMyNY7GU2c7Ha7nMZC06B5IMpS0z2tVX0w++Rvs3uE0jWGT3uE0X312Fy/v6a30pQkhzkG6sghRQdW2qlWNXWeqxdihRUOp0spcNKW4cfEMblg0nVf2n2Ddpk46jidIWg5dVopIQGdaXQCA1lj4nOdzXI++RIahlE1jnUk0aMiQIlGVbV2FEIWRYC5EkcoVpseWjYxd1bofKvaXZ1tT5KzDioQvaOi0RHWyEZd4OstwCUOLNKW4cdEMbrh4Ot/91UGe2tZN1vVIWg5JK0XQ0PjY0tkFn29sD/SmugD10gN9SpMbbCFql/z0FqII5QzT1biqtXphM1sP9qMp0BRYjkvvsMWa5cWNsC+3cj5ZKNe5DF2juS5AU8RkOJNlKFl8HbqmFJ+/YQGXz4rx8C8P0D2QJOt6ZLIu//iLd9jW2c/a1e1cPruhoPPZjktvPM2g4V/b2N72YuqQ2QZC1C6pMReiCOWswe4eSI7b8AeVX9Xa1NHPjPoAAV3D9SCga8yoD7Cpo79i11TOetmJqL1VShEL+XXosxrCJU3sXHnRNL7zuWU8/8fv5a8+cTmLcgOJth0c4A+ffIP/9syb/PrQUMHns7IuR4fSHB5MjatdF1ODzDYQonbJcooQRSjnI+JyrmqVaxW4eyDJ9PogM6Kh0WOe51X0ZqGcTxYm+ilFOKATDujYjks8ZTOczuIWUYeulOI9F0/n+oumsbmjn0c3HWTvsRG2dw6wvXOA6+Y1cs/187liTmEr6PkhRXVBv8ViwJC1mKngpiUt3A+Tuq2rEJOVBHMhilDOMH3fjQv56rO7SFrZca0Ji13VKmd5TTU+Ai/nzdCFqr01dY1p9UGaIgFGrOLLXJRSrL5oGqsWNrPlQD+Pburk7aPD7OgaZEfXG1w7r5G1q9tZOrexoPMlMlkSmSzRkElTxMS4wEOKqm2T81Rw05IW+R4LUYNk+USIIpTzEfFNS1q4/+OX0xINMZSyaYmGSuoXXs7ymmp8BN7WFCF1SjlGqTcL5TxXITTtZJlLKe0WlVKsWjiNf7zzGv72k1ewpNWfGPpa1yB//L2d/On3d7KzZ7Dg8w2nbboHUvSNZIresFoqad0nhBCFkxVzIYpQ7kfE5VjVKucqcDU+Ai/Xk4Vyn6tY59NuMR/QVy5oZtvBAR7ddJDdR4Z5vWuQ17sGubqtgXtWz+eqtnOvoHuex1CuzOZCDCmqxk3OQghRrSSYC1GkantEXO4Wh9X29ZXzZuGmJS1c90YPz755FMf10DXFx5e2XtCv93zaLSqlWLGgmeXzm9jeOcCjr3bymyNx3uge4o3unVw1t4G1q9u5uq3xnP3M80OK4mmbxnCAWHhieqBL6z4hhCicBHMhaly1tjgsp3LdLDz44l6effMomgLDULgePPvmURZM38sffWBxGa60cPl2i43hk+0Ws25hdehKKZbPb2ZZexM7Ogd4dFMnuw7H2dkzxJ9+/02unNPAPde3c00BAX3skKKGiEksVN6AXo37FoQQolpJjbkQNW5TRz/RoI7jemSyHo7rEQ3qFW1xWK0eeeWAH8o1DU1puVf/eKVomqIhbNLWHGZGNFhU5xSlFMvmN/PgHVfzzduWcuWcGABvHRriy99/kz/+3hvs6BwoqGQm67r0jWTo7k8xlLKLnmp6NtW4b0EIIaqVrJgLUeP2HosznMmSz1GeB8OZLPuOxSt7YVUoYTmcmns15R+vNKUU0ZBJNGSStLIMJu2Ce5ArpbiuvYlr5zXyevcgj77ayVuHhnjrUJw/e+ZNLp8d457V7VzX3nTO1fB8QB9KlmcFvRr3LQghRLWSYC5EjUtZLo4LCv8DwHEhaRU3hXIqqAv4Gz7H7nV0Pf94NclvFE3bDoNJm6SVLeh9SimundfENW2NvNE9yKObOnmzZ4hdh+P8tx+8xWWzYtxzfTvLig3oYfO8atCrbd+CEEJUKyllEaLG5ftje2M+xh4XJ917wwJczw+drufmXv3j1Shk6rQ2hJjTFKa+iImiSimumdfE//uZq/l/Pr2Uq+b6A4l+cyTOV37wFn/w5OtsPdBfeIlLIkNXf5LBpIV7gdosCiHEVCQr5kLUOIlJhctv8HzklQMkLIe6gM69Nyy44Bs/ixU0dFpiOk2Oy2DSZiSTLbgG/Jp5TVwzr4mduRX0N7oH2X1kmD//4VssaY1yz/XtrJjfXNAm0f6E5W8SDZvEQhPbZlEIIaYiVa4NPrVi2bJl3vbt2yt9GUKUzaX/4zlS9umr42FTY/dffaQCVyQmWtZxGUrZxNOnB/StHf08ta2bI/EUs2Jh7ljexoqFJzv07OwZZN2mTl7vOjmY6JLWKPesbmflgnMH9DxNqVyJi4kuAV0IIU6jlNrhed6yot4jwVyI2rbsr1+gf8TCU/7GT6VAedBcH2D7X95S6curOpNpPLzjesRTNvFcL/StHf08sGEfhqYImRpp2yXrenzp5kXjwjnAWz1DrNt0kB1jA/rMKGtXt7NqYXEBPZYbVCQBXQghTiolmEuNuRA1blFLlJkNQSKm7k9YNHVmNgRZ1BKt9KVVnck2Hl7XFE11AdqaIkyrC/K97d0YmiJs6ij8V0NTPLWt+7T3Xjm3gW9++ioevONqrmtvAuDtY8P89x//mv/8+Gv8av+JgsplXM9jMGnR1Z+kbyRDVvY2CCFEySSYC1Hj7rtxIabubxK8ZGaU1oYQpq5Ln+gzGDseXin/1dQVD23sqPSlnRdNUzRE/BuN+uD47ikhU+NoPHXW914xp4Fv3raUv19zNcvn+wF977ER/sdPdnHfY4UHdM/zGErZdA+kOCEBXQghSiLBXIgad9OSFu7/+OW0REMMpWxaoiHu//jlNVueMZG6B5KEzfGtESfTePh5zXVYjkvA0DB0DaUUadulNRY+53svn93AN353Kf+w5hpW5AL6/t5cQF//Gq/sKzygx3MB/fhwRroDCSFEEaQrixAVVO5656m1Y6R4bU0RDvaNEE9l/QCra8TCBvOn1Vf60srivhsX8tVnd5G0soRNnYzr4gFrV7cXfI7LZsf4+u8uZfeROOs2dbLlQD/7j4/w1Wd3cdGMOu5e3c4NF09HO0cNuud5DKdthtM29SGDxnCgqKmmQggxFcnmTyEqJF/vbOp+LXDKdrAdr+jV7nKdZyp48MW9PLBhP5ryJ366nv/xpZsvrvqWiYXK3+ydOmUzbTvEU36rxWLsPhJn/eZONnf0jx5bOKOOtavauWHRuQP6WPVBg4aISdCoroFOQggxEaQrSwEkmItqsebhzRw4McJw+uTqbTRksGB6PU9+cVVR5+kdThMJnHwAlrSytERDRZ1nKijX97yWWVmXwZRFIuMU3Asd4O2jwzy66eC4gL5geh13r2rnxsXFBfRIwKAxYhIyJaALISavUoK5lLIIUSF7j8WJp7NoKHSlyDoefQmLrBMv6jzdA0kaw+a4Y5OpbrqcugeSTK8PMiMaGj3meV7J36tylSJdyBaOAUOjJRrCjhQ3rOiS1ih/+8kr2XtsmHWbOnn1nT4OnEhw/7/+hvnTIrmAPqOglolJK+uX2wR0miIBCehCCJEjBX9CVIjt+GFI0xRKqdEpipZT3FOstqYIKdsZdyxlO8xtipTnQieRcn6vytV6sVItHE1dY0Y0yNymMNGQWXDf8sUzo/z1rVfwT3ddy3sumgbAwb4kf/Vvu7l33XY27OnFcQv7PZyyHA4PpjgylCJ9yv8XIYSYiiSYC1EhAUMDz+8D7eHheh54FL1B7r4bF2I7HknLX/lMWllsx5N2iWdQzu9VuVovVrqFYz6gtzWFiYWLC+h/desVPHz3dbznYj+gd/Yl+et/2829j27npd3FB/TDgylSlgR0IcTUJcFciApZ1BJlejSAoSkc18PQFNOjgaIHA0m7xMKV83tVrtaL1dLC0dA1ptf7Ab2YFfSLW+r5q09cwbfvvo73LpoOQGd/kr/52W6+8Oh2Xtx9rOCAnrYdjgxJQBdCTF1SYy5EheRb27U2GOO6qZSyenvTkhYJ4gUq1/eqXK0Xq62Fo5FbQX9s00G+86sDJC2HsKlz+3Vzufv6+Wd930Ut9fyvj1/OO8dHWL+5k417T9DVn+Rvf7aHdZs6uXtVOzcvaSmoBj0f0IOmTmPYpC4of1UJIaYGWTEXokJkpbu2rV7YTO+wheW4aAosx6V32GL1wuaKnKecHnxxL//w8jtksi6GBpmsw6ObO1n/6sFzvveiGfV87WOX88ja63jf4hkooGcgxf9+bg+/991t/MeuowWvoGdsh2PxNN39SYZSdlFdZIQQohZJu0QhhCjBmoc3s+foEEOpLK7n90VvCBssaW0out1ltbVwXPq150nZDoZ2cu3GdhxCps6zf3BDUec6cCLBY5s7efnt46MDsOY0hrlr1Tw+cOnMglbQ83RNEQuZxMJmUe8TQohKkHaJQtSYC9kmT5TXvt5hRtIOpq6hFHgejKQd9vUOF3WecrdwLIeE5XDqHmRdU6Rsl9mNYQaTNkmrsEFFC6bX8T8+ehl3r06wfpMf0A8NpvjGv7/N+s2dfHZlO7dc2oKhn/sBruN6DCQtBlM20ZBBY9gs6H1CCFEr5CeaEBVSqTZ5ojysrAsKNKVQKH/AjsodL0I1trusC+hkHY9M1iFtO2SyDlnHoy6gEzJ1WhtCzG4MF9V/fP40P6D/8+eWcfOSFhRweDDNN59/m3v+ZRvPvXWErFPY987zPOIpm+6BFMeHMwW/Twghqp0EcyEqpNJt8sT5MXW/lMJ1PTzPw83VTQf04kosqrHd5fuXzMDxwPU7eOJ64Hj+8byQqTO7MUxrQ6ioFp/t0+r4y9+5lH/53HI+cGkLmoIjQ2m++R97uedftvGzIgP6cFoCujg/L+/pZc3Dm7nhGxtY8/BmWRwRFSWlLEJUiEzsrG2LZ8bOUBtusmB6cd1UblrSwv34N2o9A0nmVkFJ09G4RVPEOK1+/mjcOu3XRgIGkYDBSCbLYNI64xODrR39PLWtmyPxFLNiYe5Y3saKhc38xW9fyl2r2nlscycb9vRyZCjN//mPvTy2uYs7V87jQ5fPxCygVCUf0EcyWeqDBk0RKXERhck/uTR1Ne7J5f0gZYWiIiSYC1EhbU0ReofTRAIn/xhWuoRBFG4yt7vsHkgSC5lYWe9kC8eQ+a43jfVBg/qgH9AHEhZ2bvV6a0c/D2zYh6EpYiGDvkSGBzbs40ssYsXCZuY1R/iL376Uu1e18/iWLl7cfYyj8TTfemEvj2/p5LMr5/Ghy1tLCuiNEbOg94mpa+yTS/BvNJNWloc2dlTVn0kxdchPLCEqpBpLGEThJnO7y2jQ4NBgmqzroWuKrOtxaDBNfQH9xOuDBm3NEVpiIUxd46lt3RiaImzqKPxXQ1M8ta173PvamiP8+UeW8N3fW86HLp+JpuBYPMO3XtjH3d/Zyk93Hh4N++cyWuLSn6Q3niaTlWFF4syqZcCXEHmyYi5EhVRjCYMoTrWtdJfLaBvdfH9D75TjBcivoPeOpKkPjP+rJmRqHI2nzvi+uU0RvvLhJdy1sp3HtnTywm+O0Tuc4e9e3MfjW7pYs2IeH7miteC69pFMlpFMlkjAX0EvZsOqmPzkyaWoNhLMhaigyRrsROWUowXniOUwpzHEiRFrtJSltT5Iwip+5bm9uY7e4TRBQ8fJbZRN2y6tsfC7vm9OU9gP6KvaeWJLF8/vOkrvcIYHXtrHE1u6uHNlGx+5YlbBAT1pZUlaWcIBnYawOS6IiakrX5KWtLLnXZImRDlIKYsQQkwS5WrB2dYUIXPKJs5M1i1pFfG+GxcST9l0HB9hf+8wnX0JEpksdyxvK+j9cxrD/NmHLmHd51fw21e0omuK4yMZHnhpP3d9Zws/ev1QUS0qU5bD0SF/mmg8LdNEp7rJXJImapMsGQghxCTx0MYOrKxD38j4KaLFbmRbvbCZrQf70ZTfkcVyXI6PWNy5ormk6/LA7/muKZSmUAqiIQNdUzhuYcF4dmOYL3/oEj67ah5PbOnm33cd5cSIxd9v2M8TW7tYs3weH11a+Aq67bicGM4wkLCIhkxiIUM6uUxR8uRSVJMJ+ymklPpnpVSvUurXY441K6VeUErty7025Y4rpdSDSqn9Sqk3lVLXjnnPPblfv08pdc+Y49cppd7KvedBpZTMZxZCTGl7j8XpS1hkHQ9dKbKOR1/CYt+xeFHn2dTRT0s0QEDXcD0I6Bot0QCbOvqLvqaHNnbQEDZZ1BJlSWuMRS1RGiMBHtvSRVtThKZIwB/OVKBZDWH+9IOLWf/5FXx06SwMTdE3YvEPP9/PZx/Zwg9f6yFjF15y47geg0mL7oEUvcOyUVQIUVkTuTzwXeDDpxz7c+Alz/MWAS/l/h3gI8Ci3McXgf8LfpAH/iewElgB/M98mM/9mi+Oed+pn0sIISZUuQaTPPjiXpZ+7Xku+oufsfRrz/Pgi3tLOo/t+KvPmqZQSqFpfuC1nOLKNboHkiTSNgnLr7dNWA6JtF1Sp4p363qhaYqmugBzm8JEQ+ZZznBmrQ0h/uSWxaz7wgo+lg/oCYt/+Pk7fPY7W3lmR3EB3fM8RtJZDg2kODKUImlli7oeIYQohwkL5p7nbQROXV75BPBo7p8fBW4dc3yd59sMNCqlZgEfAl7wPK/f87wB4AXgw7n/FvM8b5PnFwiuG3MuIYSYcOWq537wxb08sGE/KdvB0PyOEA9s2F9SOA8YGq7rkc46pG2HdNbBdb2iJnMCpDI28cz4uu14xiWZsYu+pramCKlTAvKpXS8MXWNGNMicpjDhQHFdU1pjIf7rLYtZ/4UVfPyq2Riaoj9h8Y8v+wH9+zt6SBcR0EHq0IUQlXOhC+pmep53BCD3mi/qmgOMbWrbkzv2bsd7znBcCCEuiLGDSZTyX01d8dDGjqLO88grB9AUGJqGprTcq3+8WDPqg/4/eLm6bu+U4wUaSJ15tfhsx99NMf36g4bOrIYwrQ2hogcDzYyF+OMPLOKxL6zgE1fNxtT9gP5/X36Hzz6yhae3d592g3Au+Tr0rv4k/Qmr4Hp4IYQoVbXsdDlTgaFXwvEzn1ypLyqltiulth8/frzESxRCiJPKNZgkYTlop/xE0xQltSb0PA+lFAFdI2RoBHQNpVTRK75ny5+l5NJSul5EAv6QounRIIZW3F9TLbEQX/rAIh77wko+cbUf0AeSNv/0iw7uemQLT20rPqDn69C7+pOcGMkUPOhICCGKdaG7shxTSs3yPO9Irhwl/8y3BxjbO2sucDh3/KZTjr+cOz73DL/+jDzPexh4GGDZsmWy5CGEOG/lGkxSF9BJZLJ4OHgeKOWvPNQVMGXzVOXqP57vljJ2T6bn+cdLUWrXi1jIJBo0GErZDCZt3CJuMGZEg3zp/Yu4c8U8ntrWzb++eZiBpM3DGzt4els3ty+byyeunlNU6YznecRTNsPpLHVBvx960JCBRUKI8rnQK+bPAvnOKvcAPxlzfG2uO8sqYChX6vI88EGlVFNu0+cHgedz/21YKbUq141l7ZhzCSHEhMv35953bJjdR4bYd2yYeMouejDJ+5fMwPH81WgP/9Xx/OPFamuKYOgaC2fUs6Q1xsIZ9Ri6VvTNwseXtgJ+GM9/jD1+ISmlaIwEaGuO0BA22Xqgnz/53k7WfHszf/K9nWw9R6eYGdEgf3jzxTx+70o+dc0cAobGYMrm4V8e4M5HtvDk1i5SRd64jN0oenQoXXQNuxBCnM1Etkt8EtgEXKKU6lFKfQH4OnCLUmofcEvu3wF+BnQA+4FvA/8FwPO8fuCvgG25j/tzxwD+M/BI7j3vAM9N1NcihBBnku/PrXLL3KU8jjsat2iKGKPlLJqCpojB0bhV9LmKqed+N393x7V88upZoyvkuqb45NWz+Ls7rj3HOyeOrine6hni//v5fgZSGWIhg75Ehgc27DtnOAeYXh/kD26+mMe/sILfvdYP6EMpm2//8gBrvr2ZJ7Z0ldSJJWllOTyY4vCgdHKpVeXqriREOaipttt82bJl3vbt2yt9GUKIGrfm4c2nlbIkrSwt0RBPfnFVwee54RsbaAybjB3F4HkeQymbX37l5qKv6+U9vTy0sYOegSRzmyLcd+PCSTM8Zez33PU8HNcjkckyrS7Itz5zVVHn6k9YPLWti5/uPDI65TQWMvj0srncevWckkqJAExdozFiUh80kPEa1S/fXcnUFWFTJ2X7LUJl+qcoB6XUDs/zlhXzHpn8KYQQJegeSKIr6Dg+MlrPPb0+UPTmz7amCG8fjTOYsnE9f8W8MWxySWvsvK5vMi65nOl73lxnciyeKvpczXUB/stNF3PH8nl8b1s3z+48TDyd5TuvHOTp7T3cdt1cPnVN8QHddlyOD2cYSNg0hE2iIWO0n7yoPmO7K4G/8ThpZYuelitEuVRLVxYhRJWQx7qFiQYNDg2myboeuqbIuh6HBtPUFxnkWmMB+pP2aMcT14P+pE1rLFD0NZWrt3q1qg/o/vd8zGTTI0MZGsImM0ro4AJ+QP/PN13E4/eu5PZlcwkZGsPpLP/yq4Pc+cgW1m/qZCRTfIlK1nXpS5xstZiVTi5VqVzdlYQoFwnmQohRkz3YldNoGaA35mPs8QK9tOc4mvJXyhWM/vNLe4pv7Vqu3urlVq6bvdHSEDXmI3c8GjJpaw7TXBdAK6GEpLkuwH9630U8/vsruWN5GyEzF9BfPcid397Co68eZCRdfEB3Pb/VYvdAit64bBStNoUMwBLiQpJgLoQYVa3BrhrlWxMausLxPAxdMacxVHRrwoTlYOqKoKETMnWCho6pq5L6mFfj6l85b/aGM1n/e55r52ho/vc8v6I9toNLNGSWdL1NkQBfvHEhT9x7MqCPZLI8uqmTNY9s5rslBnTP8xjJ+BtFDw2mGMlkZaJoFSjXhmkhykWCuRBiVDUGu2pVrtaEdQEdK+uRsp3RDyvrUVfkaPr8NVXb6l85b/bamiLE0/boBr2U7RBP26d9fbqmmBENMqcpXFSf8rEacwH9yXtXceeKNsKmTiLjsG5TJ2u+vZl/+dUBhtN2SefO2A698TTd/SkGkzJRtJJKGYAlxESSzZ9CiFHlGpozFdx340K++uwuklZ2XDeHYlfaLp8VZdOBgXHHvNzxSl0TnOzu0j2QpO08uruUa5Ms+PX4mzpOrla7Hgwks2etxw8aOrMawiStLH0jVkkTOxsiJve+dyGfXtbGMzt6+NHrh0hYDus3d/HD1w7xyWvncNu1c4mFi1+hz7ou/QmLgaQtA4sqqNQBWEJMBFkxF0KMkse6hSvXStuuI8On/SDWcscrdU0v7+nly8/s5PXuAY7F07zePcCXn9lZUvnJmTZsHhpMl/RE4KU9x9FPqcfXC6jHjwQM5jaFmVYfLHl6aUPY5As3LOCJe1dy16ojDkRwAAAgAElEQVR5RAI6Ccvhsc1d3PnIFr7zygGGUqWtoI8dWHRYylyEmNJkxVwIMeqmJS3cD5O2D3a5lWOlLWE5mIZCUyfjueu5JdWYl+uavv7cbgaTNrpS6ErhuTCYtPn6c7uLPvdpGzYBPErq8Z2wHAy9tO+VUoqGsN9ffDBpEU+XFn5jYZPPv2cBt107lx+81sMPX/NX0B/fkltBv2Y2n76ujYZIaTXuadshbTsYmkYsbBANmSXfTAghao8EcyHEOPJY98KqC+gkrCye5+B5oJT/UReo3I/nA31JvztMLhAqBZ7rcaCv+PKT/IbNEyPWaClLayxYUgvCuoBfnjM2p7oeRa2+65piWn2QaMhkIGmRKOE6wA/ov/eeBdx23Vx+8NohfvBaD4mMwxNbu/nR64e59ZrZ3H4eAX1smUt90KAhbBIw5CG3EJOd/CkXQogKev+SGTiuHzA9/FfH9Y9XUtYZvyE165RWWlGuTbIA996wgKzjkc5dUzp3XffesKDocwUMjZmxELMbw+cVeKMhk89dP58n713FPavbqQv6Nw9Pbu1mzSObeXhjB4NJq+Tze57HcNqmZyDJ0aE0Sau0GwkhRG2QYC6EEBW0+yw15rtLqDEvl2jI4NRtkm7ueLHKuW9h6dxGwgF9dKqpB4QDOkvnNhZ9rryQqTO3KVLygKK8+pDBPbmA/rnr26kPGqRtl6e2dXPnt7fw0C/eYeA8AjpA0spydChNd3+SeNqWOnQhJiEJ5kIIUUEH+pIYuiJs6qMfhq5KKhspl7OVd5RS9lHOdnTf+Pc9WFmXoKERMjWChoaVdfnGv+8p+lynyg8oaooESqp/z6sPGaxdPZ8nfn8lv/ee+URDBumsy/e29/DZb2/hn8oQ0G3H5cSwTBUVYjKSGnMhhBDjWI6HBuNWzbXc8VKUa99Cx4kEruuRHdP3W8sdLwelFE11AepDBn0j1nmVjdQHDe5e1c6nrpnDj984xPe39xBPZ3l6ew8/eeMwH79qNp9Z3kZz3fhWj1s7+nlqWzdH4ilmxcLcsbyNFQubz/g5HNefKjqUsqkL6MTCJiFT2i0KUctkxVwIISpo4fQ6XM8f3e7h4Xoerucfr5SArs5YyhLQK9sdJOu4Z7yucq8Ym7pGa0OImbHQeZW3ANQFDT67sp0nfn8l996wgFjIIJN1+f6OHj77yBb+8eX99Cf8FfStHf08sGEffYkMsZBBXyLDAxv2sbWj/10/x9ipoj0DSYalzEWImiUr5kIIUaJyDOH5yoeX8GfP7GQ4nSXruBiaRlPE5CsfXjJBV31u0+uDdA+kGBvDvdzxSjrbgMyJGpxZFzSIBHQGkjZDqfMLu5GAwZ0r53HrNbP58euHeXp7N/F0lmd2HOLZnUf46NJZvH1kGENTo9N380OintrWfdZV81NZWZfjwxn6ExbRkEksZGDosgYnRK2QYC6EECV4eU8vX312F6auaAyb9A6n+eqzu7gfigrnNy1p4YaLp/Hsm0dxXPDwuOHiaRVtWekBLfUBTiQsXM8f5DOj7szTNSc7pRTNdQHqg/4KdqrE/vJ5+YD+yVyJy9PbexhK2fzwtUOA3/rRcV2yroep+zdpR+Opoj+PlLmIiVCuicDi7CSYCyFECR7a2IGpKyK5fuORgEHSyvLQxo6i/qJ68MW9PPvmUTQFhqFwPXj2zaMsmL6XP/rA4om6/HfV1hThwIkRwqY+2ntc01RJLQ6hfH+ZKwVnWrQ+j72aBQsYGrMawiQyWfoTFvaY8pli6sLzwgGdNSvmcevVc/jJzsM8va2bwZQ9OixJU/4mz2PxDO3TSi9rype5jGSyBE2dWMigPmic1wZXMTWVazFCvDt5viWEECXoHkiOlhzkhU2dnoHiuqk88soBP5RrGprScq/+8UpZvbCZ47mBQJoCy3E5PmKxusByirFe3tPLl5/ZyevdAxyLp3m9e4AvP7OTl/f0Fn9hZ6skuYDl1HVBg7lNJ7u3lFoXnhcO6NyxvI3Hf38lzWOGEbkeZF1wPMhmz2+VPi9jOxzPdXMZkG4uokgPbezAdhyODqV5+9gwR4fS2I7DQxs7ij7Xgy/uZenXnueiv/gZS7/2PA++uHcCrrg2STAXQogStDVFSNnjA1PKdopeVU5YDngemaw/MCeT9f+9kDHzE2VTRz8t0QABXcP1IKBrtEQDbCowbI719ed2M5i08VzQlcJzYTBp8/Xndhd9LtPQOHWdV+WOX0j57i1tTWG+v6NntC5c4b8amuKpbd1FnTNs6me9v+gaTPPAi/vojafP/+Lxy1wGkhbdAyl6h9Ok7cr9XhO1Y1/vMCeGLbKuh64psq7HiWGLfb3FzVx48MW9PLBhPynbwdD8n5sPbNgv4TxHSlmEEKIE9924kK8+u4uklR3dpFfK4JygrpG0ndHA6XlgexAxSwub5Sgb6R5IMq0uyPT60Ogxz/OKfhoAfp92TYGm+V+hUuC5Xkl92hdOr2Nf7wi6pkbLWhzXq1gHG0PXODacJhY0cDxGN4eGTK2kunAr62JooGsanufh5L4+gJ/sPMzPfn2Ej1wxizUr2pgZC73ruda/epCnd/SQsh3Cps7t183l7uvnj/s1nucxks4ykvbLXBrCJnUBXcpcxBlZWRcUaOrkn2VXef7xIox9Sgh+2VbWdXnklQMVK9+rJrJiLoQQJSjX4JzmOr98wRvzMfZ4MfI1oL3D6XE1oMWWjZTraUC5feXDS2iKmCj8FokKKt7Bpq0pQsZxMXWFritQkLZdWmPhos9l6v4eg0zWxXI8HNdDAWFTo7kugO14PLvzMHd/Zyt/98Jejp5lBX39qwd5dHMnmayDrkEm6/Do5k7Wv3rwrJ87Yzv0xtN096ekzEWckZlrl+q6Hp7n4eZuGotto5qwHLRT3qIpKvqUsJpIMBdCiBLdtKSFJ7+4il9+5Wae/OKq0jZAKcWMenP0LypNwYx6s6RVy7EbUpXyX01dFV0Det+NC4mnbPYdG2b3kSH2HRsmnrKLfhoA5e3TftOSFr5521VcM6+JWQ1hrpnXxDdvu6qiG8/uu3EhtuORsh10pcg6Lo7nccfytqLP1RwJnHFz66xYiMe/sII/+K2LmFYXIOt6/PTNI6z9zla+9cJejg6ND+hP7+gBDxwXbMd/xcsdP4es646WuRyLp8+7C42YPBbPjDGtLoChKxzPw9AV0+oCLJoZK+o8dQH9tBanrucfFxLMhRCiotqaIsTCAS6f3cCVcxq4fHYDsXCgpNXpcm1IhdzKvfLrqVGl768s9yr3mz2D7Do8xOGhNLsOD/Fmz2CJV1Yepz45mRkL87e3XsnHrp5d/HCis92MKUXQ1PnUtXN5/N6V/MFvXcy0ej+g/+ubR7j7n7fyf/7jbY4M+eUzScshl8Uh9+rmjhfK8zwSmSxHhlJ09ycZStqjK6RiarrvxoUEDJ3WhhCXzIzS2hAiYOhF37Dfe8OC3OZmF9dzc6/+cSE15kIIUVHlqlUHP+T3DqdHWzhCaSUoD23soCFsMqvhZDlGKa0g4eQq90MbO+gZSDL3PNol5jeN+fWpJzeNARWtTb1pScsZv56wqTOQ6yVeiGPx9Gk3QF7ueF7A0PjUtXP46NJZ/OytIzyxtYsTIxY/e+soz+86xocum3nW85daOm47Ln2JDP1Ji7qgTiwkPdGnopuWtHA/nPef5fyf1UdeOUDCcqgL6Nx7wwKpL89RU21s77Jly7zt27dX+jKEEGJUfsPm+QbXsX2Gx4b8Ymvfb/jGBhrD48tpPM9jKGXzy6/cXPR1lcvSrz1Pwsrief7GT6X8j7qAwZtf+1DFrutcMlmHvhHrnN1PPvCtX5xxiqmm4MU/ed8Z32NlXZ779RGe2NLN8ZHMu56/ztT46R+9t+DrfjemrhHN9USXyaJCnJlSaofnecuKeY+smAshRIWdbcW1lPPc1jN42kpUsecu18p7uY1ksrie3yKRXFcW1/OPV7OgoTO7McxIJkv/iEXWPfPGyrNVirxbBUnA0PjE1XP4yBWzeO7XR3lyaxe9w6cH9FhIZ+H0aCmXf0a249KfsOhPWEQCBtGQQUQ6uggBnFxsMWfMv7LY98ptrhBCTBIv7+nlmdcOMSMa5NLWKDOiQZ557VDRXVnKufmznEZDXz77qVOOV7n6oEFb88nhROXkB/TZrPv8Cj559WxObZRhOx4fuHRiNskmrSzHch1dBpPWaItHIaaisd2x8NyiVw0kmAshxCRRrq4sUL7Nn+UUNv20mS9lyVdiRszaCOYwfjhRfbD8D60DhsYfvn8Rn10xb1wbu5Tt8q0X9/K/n9tDd3/xm4ELkXX9VfSu/iS9w2l/WJYQU8zYn8OlkFIWIYQoUTmG+ZRT90CSxvD4/ueldGUp5+bPcrpyThO7jwwRT/slLZqCWMjg0lkNFbumUhm6RkssRMx2ODGSwcq6mBrYZ6hyKXbW1NaOfn761hFQ+CvnY8p+XvjNMV7afYybl7Rw16p25jWXvzxp7OCiUH5w0QTchAhRjc70c7gYsmIuhBAlKNcwn3Iq12CgcrZdLKf7blxILBxgwfQ6rpgdY8H0OmLhQMVLbM5HyNSZ2xRhWn2wpBrzM3l44zsMJG2sbH56qH+O6XUBZjWEcD14cXcvn//uNv7m33bTVcIU1kKlbYdj8TRdfUkpcxFTwpl+DhdDgrkQQpSgnGUj5ZIfdpO0snie/1pK68VqnfxZrmmr1aghbOKcJbOe7fjZdJwlaJ9IWDz6e8v5sw9dMhrQX9rTy+99dxt//W+76exLFHnVhRtX5hJPn7NDjRC1auzP4VLIsyUhhChBucpGyqlcfYbL2Vt9okzGdVfFxH9dhq7xkStaueXSFl7c3ctjWzo5PJhmw55efr6nl5sumcFdq9pZUMJk1kJ4nsdIJstIJkvA0IiFTeoDBtqpM9prVLWVt4kLb+zPYZRWdM6WYC6EECWo1paC5Wi9WK6AX25j+7SPLR+6P3fNtc44S425MQGZ1dA1PnxFK7dcNpOXdh9j/eYuDg2m+Pnbx3n57eO8b/EM7l49cQEd/B7sJ4Yz9CuL+pBBLGQSMGr3Qf5k//0pCpf/OazuO/hWse+VYC6EECWohVXl81Gu3urldGq3g0jAqIpNqeUSC5v0JU6fEhoLTdxf1bqm+ODlrbz/0pm8tKeXxzZ30jOQ4uW9x3l5rx/Q105wQHc9j3jKJp6yCZk6sbBJXQ32RJ/svz/FhSHBXAghSlCtq8qTWTWWD5XT4pkxDpwYYTidxXJcArnpmgum1zOrIcyJkQy2c+bhRGOdrSTm3WKurik+eNlM3r+khZ+/3cv6TZ10D6T4xd7j/GLvcW5cPJ21q9pZOKO+1C+vIGnbIW076JoiGjKJhgzMGpks2j2QRFfQcXxk9P/f9PrApPn9KS4MCeZCCFGialxVnsyqtXyoXPJPYVobjNOewoQDOnObwgwmbQZTNp539mr0s/2XQurXdU3xgUtn8luXtPDy272s39xFV3+SjXtPsHHvCd67yA/oF7VMbEB3XI/BpMVg0p8sGgsbJfeFvlCiQYN9vSPomkLXFFnX49BgmkUT/L0Sk0tt3IYKIYSY8srVdaZanavrTH440ZzGMKFT2lmWm64p3n/pTL5zzzL+8ncupT3X7/yX+07w++t38NWf7GJ/78iEXkNe0spydChNd391t1wcvVnyxnyMPS5EAar79lMIIYTImQrlQ4U8hQkYGrMbw4xksgwkrILKW0qla4qbl7TwvsUz2Lj3OOs2d9LZl+SV/Sd4Zf8J3nPRNNaubmfRzOiEXUOe7fgtFweSNnUBvxZ9om9QijFiOcxpDHFixBotZWmtD5KwpDWkKJwEcyGEEDVDyodOqg8a1AV0hlI2g0kbdwJXZnVN8VtLWnjfJbmAvqmTg31JfvVOH796p4/VC6dxz/XtLL4AAf3UlosNYZP6oFHxzaL5UquxdfhJK0tLNFTBqxK1RkpZhBBCiBqllKIxEqCtOUIsbE54ONWU4qZLWnjknmX8z49dNtqtZVNHH//psdf4ix+9xdtHhyf0Gsaysi7HhzN09ScZSFS2zGWyl1qJC0NWzIUQQogap2uK6fVBYiGTppDBQPr0qYONZWy7qCnF+xbP4L2LpvPKvhOs29RJx4kEmzv62dzRz8oFzaxd3c6ls2Jl+5zvxnE9BpIWgymbuqBOQ9gkaFzYMpepUGolJp6aapsSli1b5m3fvr3SlyGEEEJMiJf39PKf1m8jPaa0OajD//r4laxY2Dwhn9P1PF7Zf4L1mzp553hi9PiKBc3ccwED+lhBUycWMqqizEVMTUqpHZ7nLSvqPRLMhRBCiMklPxq+qy9BSyzEZ5a1TVgoH8v1PF7d38e6TZ3sP36ya8vy+U2sXd3O5bMbyvJ51r96kKd39JCyHcKmzu3XzeXu6+ef8ddqSlEfMoiGjAu+ii6mNgnmBZBgLoQQolrlA3X3QJK2MpVC5Ms8htPZC9a6z/M8Xn2nj0c3dY5rq7is3Q/oV8wpPaCvf/Ugj27uRFOgFHgeuB7cs6r9rOE8T1bRxYUkwbwAEsyFEEJUo5f39PLVZ3dh6mrcgKGxvczPh5V16UtkSBXZvm9rRz9PbevmSDzFrFiYO5YXvvrueR6bOvp49NVO9o0J6Ne1N3FPiQH9Y3//CinLGW0VrnIf4YDOT//whoLOkV9Fj4VMXt1/ouw3Q0JAacFcurIIIYQQVeChjR2YuiIS8FdzIwEDU1c8tLGjLOcPGBqzGsLMjIUKHnO/taOfBzbsoy+RIRYy6EtkeGDDPrZ29Bf0fqUU1180nX+661r+5tYruCTXTnFH5wB/9NQbfPn7O3mzZ7CoryNpObicnGTqAW7ueKFczyOesvnhjh7+4kdvcXQoRUPIoHc4zVef3cXLe3qLuiYhykW6sgghxCQyEaUQ4sLoHkjSGDbHHQubOj0DybJ+nrqgQSSgM5i0GUzZ71re8tS2bgzNX8HPX0/KdnhqW3dRNetKKVZfNI1VC5vZcqCfdZs62XN0mNe6Bnmta5Br5jWydnU7V81tLOBcfvnKmY4X66lt3eiawtQ1bNcjoGt4nsNDGzvkz42oCAnmQggxSYwthWgMm6Orf/eDhIwJVK6bofyAmkjg5F/NKdthblOknJcL+EG5qS5Afcigb8QiaZ3eXhHgSDxF7JQ2iyFT42g8VfLnXbVwGisXNLP1oB/Qdx8Z5vWuQV7vGuTqtgbWrp7P1W1nD+hhQyNhnz7tNGwUXwQw7uvzwPE8dE3R2ZcgZTmEA7JZVFxYUsoihBCTxESXQojT5W+GeofT426GSimFqMSAGlPXaG0I0dpw5vKWWbEw6VNCcNp2aY2Fz+vzKqVYuWAa/7DmGr7xu1dy2Sy/xOWN7iH+5Omd/NfvvcEb3WcucVk0M0YspJNfIFdALKSzaGbxLRnP9vW1REMcGUrRM5AknrZxKzi4SEwtEsyFEGKS6B5IjpYc5E1EKYQ4qZw3QzctaeH+j19OSzTEUMqmJRoq28bPc4kEDOY2hWmuC4zrVnLH8jayrkfKdvDwX7Ouxx3L28ryeZVSLJ/fzN+PBnQ/XO/s8QP6H3/vDV7rGhhXbnPH8jbqgiZzm8IsaqljblOYuqBZ0jWd6+uzsi4ncpNF+0Yy2M7pK/VClJN0ZRFCiElizcObTyuFSFpZWqIhnvziqgpe2eR1wzc20Bg2x4VZz/MYStn88is3V/DKSpd1XPoSFomMX96S78pyNJ6itciuLMXyPI8dnQOs29TJrw/HR49fOSfGPavnc828RpRSZb2mYs8VCRjEwsa4P2dCnIm0SyyABHMhxGQ10e32xOkm881Q0srSN2JVZJXY8zxe7xrk0U0HeevQyYB+xewYa1e3c117U8X7kJu6RjRkEA2Z6Jr0RBenk2BeAAnmQojJLL8RsWcgyVzpyjLhJvvNUH71fyD57t1bJvLzv949yLpNnbzZMzR6/PJcQF9WBQFdKUVdUCcWMgmZsllUnCTBvAASzIUQQpTTVLgZOrW8pRLe6B7k0VcPsnNMQL9sVpR7rp9fFQEd/MmiDWGTuoBeFdcjKkuCeQEkmAshhBClqWR5S97O7kEe3dQ5rmvLpbOirF3dzor5zVURiA1NIxaWMpepToJ5ASSYCyGEEKXzPI+BpM3QOYYTTbSdPX6Jy+tdJwP6klY/oK9cUB0BXSlFfdDfLBo0pMxlqpFgXgAJ5kIIIcT5s7IuJ0YypG2notfxZi6gvzYmoF/SGuWeKgroACFTJyZlLlOKBPMCSDAXQgghyieethlIWDgVHsLz60NDPLqpkx2dA6PHLpkZ5e7V81i9cFrVhGFDy3dzMTDOMNRJTB4SzAsgwVwIIYQoL8f16EtkGElXbnNo3q8PDbFuUyfbxwT0RS31rF3dzvUXVU9AV0pRF/BX0aWby+QkwbwAEsyFEEKIiZGyHE5UyYTMXYf9gL7t4MmAfnFLPWtXtfOei6snoIPfEz0WNokGDTTZLDppSDAvgARzIYQQYuJ4nsdg0mawwptD835zOM66zZ1sPdA/euyiGXWsXT2f91w8Da2KArqmFHWyWXTSkGBeAAnmQgghxMSrls2hebuPxFm3qZMtYwL6whl1rF3Vzg2LpldVQAe/J3osZFAfNKpqdV8UToJ5ASSYCyGEEBdOtWwOzdtz1A/omzvGBPTpddy9up33VmFA1zVFLGTKZtEaJMG8ABLMhRBCiAurmjaH5r19dJh1mzrZ1NE3emzB9DruXjWPGxfPqLqALptFa48E8wJIMBdCCCEqo5o2h+btPTbM+k2d/OqdkwG9fVqEtavauXHxjKqc3Bk0dRqkJ3rVk2BeAAnmQgghROVUy+TQU+07Nsy6zZ38av+YgN4c4a5V7dx0SXUGdOmJXt0kmBdAgrkQQghRedW2OTRvf+8I6zZ18sr+E6PH5jVHuHvVPG66pKUqA7qUuVQnCeYFkGAuhBBCVI9q2xya907vCOs3d7Jx38mA3tYU5q5V7dy8pDoDOkDAONkTXcpcKkuCeQEkmAshhBDVxXE9+hMWw2m70pdymneO5wL63pMBfW4uoL+/igO6phT1uTIX6YleGRLMCyDBXAghhKhOadvfHGplq2dzaN6BEwnWb+rkF3uPk09OcxrD3L1qHu+/dGbVBnSAkKkTlZ7oF5wE8wJIMBdCCCGql+d5xFNZBpIWbhVmlAMnEjy2uZOX3x4f0D+7ch63XFbdAV3XFPVBg2jIJGDIZtGJJsG8ABLMhRBCiOqXdVz6EhaJTPX0Ph/rYF+CxzZ38fM9vaMBfVZDiLtWtXPLpS1V3yUlZPqbRaXl4sSRYF4ACeZCCCFE7UhaWfpGrKrqfT5WZz6gv91Lfv/qrIYQd+VW0Ks9oMsq+sSRYF4ACeZCCCFEbfE8j6GUzWDSrsryFoCu/iSPbe5kw57xAf3OFfP40OXVH9ABwgGdaEhW0ctFgnkBJJgLIYQQtSnruPQnLEaqtLwFoLs/yWNbunhp97HRgN4aC3HnSj+gmzUQ0HVNEQ2ZRENGTVxvtZJgXgAJ5kIIIURtS1l+95ZqLW8B6BlI8viWLl74zcmA3hINcteqeXzo8taaCbyyil46CeYFkGAuhBBC1L5q796Sd2ggxWNbOk8L6HeunMeHL2+tmbpuWUUvngTzAkgwF0IIISYPx/XoS2QYSVdveQvAocEUT2zp4vldR8cF9DUr5vGRK2onoIOsohdKgnkBJJgLIYQQk081Dyca63A+oP/mGE4uoc+oD7JmRRu/feWsmgrosor+7iSYF0CCuRBCCDF5xdM2AwlrNPRWqyNDKZ7Y0s2/7zo6eq3T6wOsWTGP36mxgA7+KnosZFIXNCp9KVVDgnkBJJgLIYQQk5vjevQnLIbTdqUv5ZyODqV5YmsXz/36ZECfVh9gzfI2fufKWQRNvcJXWBxD04iGDKIhoyZaRE4kCeYFkGAuhBBCTA1p26EvYZGxnUpfyjkdjad5cosf0LP5gF4X4I4VbXy0BgO6UopIbhU9HKitay8XCeYFkGAuhBBCTC21Ut4CcCyeW0F/62RAb64L8JnlbXxs6SxCNRbQAUxdIxYyqQ8Z6NrU2SwqwbwAEsyFEEKIqcdxPQaSFvFU9Ze3gB/Qn9zazXO/PoLt+FmtKWJyx/I2PnbV7JoM6Eop6gI6sbBZk9dfLAnmBZBgLoQQQkxdmaxD34hFugbKWwB6cwH9Z6cE9NuXtfHxq2cTrtGAOxVW0SWYF0CCuRBCCCGG0zb9NVLeAnB8OMOTW7v4t7dOBvTGsMnty9v4RA0HdKUUdUG/Fn2yraJLMC+ABHMhhBBCALj58pZ0llrJQ8eHM3xvWzc/ffPwaEBvCJvcvmwut149p6Y3WgYMze+LHjTQJsEqugTzAkgwF0IIIcRYtVbeAnBiJMNT27r51zePjA5VioUMbl/Wxq3XzCYSqN1+4pNlFV2CeQEkmAshhBDiTEYyWfpHLLJudU8PHasvF9B/ekpA/3RuBb3WB/4EDI1Y2F9FV6q2VtElmBdAgrkQQgghzsZ1PQZTNkMpu2bKWwD6Exbf29bNszsPkxkT0G+7bi6fvKb2A7qmFPUhg1jIrJmpqBLMCyDBXAghhBDnYmVd+hIZUlbtlLfAmQN6dExAr6/xgA4QDuhEQyZ1Ab2qV9ElmBdAgrkQQgghCpXIZOlPWNhO7ZS3AAwkLZ7e1s1P3jhMOhfQ64MGt103h09dO3dSBHRD04iGDKIhA0OvvlV0CeYFkGAuhBBCiGJ4nsdAsvbKWwAGkxZPb+/hx28cIm37Ab0uqHPbtXP53WvnUh+q/YCulCIS8DeLVlNXGgnmBZBgLoQQQohS2I5L34hF0spW+lKKNpS0eXpHNz9+/TCpXPeZuqDO7147l9smSUCHk4OLoqHKt1yUYF4ACeZCCCGEOB9JK0vfSO2Vt4Af0J95rYcfvnboZEAP6Hzq2mPQ9tMAAAusSURBVDncdt1coiGzwldYHkop6oMGsbBB0KjMKroE8wJIMBdCCCHE+fI8j6GUzUCy9spbAIZSNs/s6OFHrx8iaZ0M6J+8dg63XTuXWHhyBHSAoKkTCxnUX+CWixLMCyDBXAghhBDlknVc+hIWiUztlbcAxFP+CvqPXjtEIhfQIwGdT17jr6A3TKKArmv5VXQT8wJsFpVgXgAJ5kIIIYQot5TlcGIkU5PlLQDDaZsf7DjED17rGQ3oYVPnk9fM5tPXtdEQmTwBHS5My0UJ5gWQYC6EEEKIiZAvbxlM2rg1mq+G0zY/eC0X0DMnA/qt18zm9kkY0POr6NEJGFwkwbwAEsyFEEIIMZGyjkt/wmKkRstbAEbSWX74eg/P7Dg0+nWETI1br57D7cvm0hgJVPgKyy9k6kTLWIsuwbwAEsyFEEIIcSGkbb+8xcrWZnkLwEgmy49eO8Qzr/UwnM4FdEPjE1fP5vblbTRNwoCuKUVd0B9cFDJL7+giwbwAEsyFEEIIcaF4nkc8lWUgadVseQv4E1B/9Pohvr9jfED/2FWz+czyNprrJl9ABwgYGtGgSX3IQC+yL7oE8wJIMBdCCCHEhea4Hn2JDCPp2i1vAT+g//iNQ3x/ew/x3NcSNDQ+PskDen66aDRkEAkUNoxJgnkBJJgLIYQQolImQ3kL+EOWfvz6YZ7e3j0a0AOGxseWzuKO5W1Mqw9W+AonTqHTRadkMFdKfRh4ANCBRzzP+/q7/XoJ5kIIIYSoNL97i4Xj1nYOO1tA/+jSWayZ5AE9X4t+tumiUy6YK6V0YC9wC9ADbAPWeJ73m7O9R4K5EEIIIaqB43r0JyyG03alL+W8pSyHH79xiKe39zCU8r8eU1d8dOls7ljexozo5A3o4Hd0iYXH90WfisF8Nfz/7d19sFR1Hcfx94cHgRQHDHIYwUEdJp8yNCUNMjVT0KZyMsGyqMyHMSebNI1sQpuc6o8CnRxHjQcnCaMSH8hMEwlNU0GuD4iNE5DSZSQTEFGeLt/+OL87s633XlnZs+fs8nnN7NxzfnvOnu/9znfu/e7Z357DNRFxelqfAhARP+luHzfmZmZmViZbtnfw383b2Lq9o+hQdtvb2zq4+5l25j31ChsqGvQzPzSMc8cc2PINep9evRjYP7u7aJ/evWpuzPO/H2m+DgBeqVhfk8bMzMzMmkL/vr05YNAAhgzsV/OVP8pmwF69mXTcCOZc8FEuOvFgBr+vL9s7grva2jlvxhNc/5eXWPfGlqLDzM2OnTtZ/9Y2Xn79rfe0/659rbS8uqred3wEIOlC4MK0+qakf+zGMYcAr+3G/vbeOO+N55w3nnPeeM55MZz3xitFzm9Ijz3EB2vdodkb8zXAiIr14UB79UYRcQtwSz0OKGlJrR9L2O5z3hvPOW8857zxnPNiOO+N55w3nqSa5043+1SWp4BRkg6StBcwCbin4JjMzMzMzGrW1GfMI2KHpEuBP5NdLnFmRCwvOCwzMzMzs5o1dWMOEBH3Afc18JB1mRJjNXPeG885bzznvPGc82I4743nnDdezTlv6sslmpmZmZm1imafY25mZmZm1hLcmPdA0kxJ6yQ9XzF2jaR/S2pLjzOKjLHVSBoh6WFJKyQtl3RZGt9P0oOSXko/Bxcda6voIeeu9RxJ6i/pSUnPpLxfm8YPkvREqvXfpi+2Wx30kPPZklZV1ProomNtNZJ6S1omaUFad53nrIucu85zJmm1pOdSfpeksZr6FzfmPZsNjO9ifFpEjE6PRs5v3xPsAC6PiMOA44FvSjoc+B7wUESMAh5K61Yf3eUcXOt52gqcEhEfBkYD4yUdD/yMLO+jgPXA+QXG2Gq6yznAdytqva24EFvWZcCKinXXef6qcw6u80Y4OeW389KUNfUvbsx7EBGLgdeLjmNPEhFrI+LptLyJ7I/KAcBngdvSZrcBnysmwtbTQ84tR5F5M632TY8ATgF+n8Zd63XUQ84tR5KGA2cCv0rrwnWeq+qcW6Fq6l/cmL83l0p6Nk118ZSKnEgaCRwNPAHsHxFrIWskgQ8UF1nrqso5uNZzlT5qbgPWAQ8C/wQ2RMSOtMka/CaprqpzHhGdtX5dqvVpkvoVGGIrmg5cCexM6+/HdZ636px3cp3nK4AHJC1Nd52HGvsXN+a1uwk4hOxj0LXAz4sNpzVJ2gf4A/DtiHij6Hj2BF3k3LWes4joiIjRZHctHgMc1tVmjY2qtVXnXNKRwBTgUOA4YD/gqgJDbCmSPg2si4illcNdbOo6r5Nucg6u80YYGxHHABPIpoWeWOsLuDGvUUS8mv6w7wRuJftnanUkqS9ZgzgnIu5Mw69KGpaeH0Z2tsvqpKucu9YbJyI2AIvI5vgPktR5j4nhQHtRcbWyipyPT9O5IiK2ArNwrdfTWOAzklYDd5BNYZmO6zxP78i5pNtd5/mLiPb0cx0wnyzHNfUvbsxr1Jnc5Czg+e62tdqluYczgBUR8YuKp+4BJqflycDdjY6tVXWXc9d6viQNlTQoLQ8ATiWb3/8wcHbazLVeR93k/MWKf5oim//pWq+TiJgSEcMjYiQwCVgYEV/CdZ6bbnJ+nus8X5L2ljSwcxk4jSzHNfUvTX/nzzxJmgucBAyRtAaYCpyULjEUwGrgosICbE1jgS8Dz6V5oADfB34KzJN0PvAy8IWC4mtF3eX8XNd6roYBt0nqTXaSZF5ELJD0AnCHpB8Dy8jeNFl9dJfzhZKGkk2xaAMuLjLIPcRVuM4bbY7rPFf7A/Oz9z30AX4TEfdLeooa+hff+dPMzMzMrAQ8lcXMzMzMrATcmJuZmZmZlYAbczMzMzOzEnBjbmZmZmZWAm7MzczMzMxKwI25mVmJSRop6R3XG5b0I0mnvsu+10i6Ir/ozMysnnwdczOzJhQRPyw6BjMzqy+fMTczK7/ekm6VtFzSA5IGSJot6WwASWdIelHSo5JukLSgYt/DJS2StFLSt9L2V1YsT5O0MC1/UtLtafkmSUvSMa+teH5+5wtL+pSkO6uDlfRVSXdJulfSKkmXSvqOpGWS/i5pv7TdIknTJT0m6XlJY9L4UEkPSnpa0s2S/iVpSC6ZNTMrETfmZmblNwq4MSKOADYAn+98QlJ/4GZgQkSMA4ZW7XsocDowBpgqqS+wGPh4ev5YYJ80Pg54JI1fHRHHAkcBn5B0FLAQOCzdPRDga8CsbmI+EvhiOu51wFsRcTTwOPCViu32joiPAZcAM9PYVLLbiB8DzAcOfJf8mJm1BDfmZmbltyoi2tLyUmBkxXOHAisjYlVan1u17x8jYmtEvAasI7tt9FLgI5IGAlvJmuVjyZr1zsb8HElPk90u/Qjg8MhuFf1r4DxJg4ATgD91E/PDEbEpIv4DbATuTePPVcU/FyAiFgP7ptcdB9yRxu8H1veQGzOzluE55mZm5be1YrkDGFCxrhr37RMR2yWtJjvj/RjwLHAycAiwQtJBwBXAcRGxXtJsoH96jVlkTfYW4HcRsUPSWWRnuQG+0cVxd1as7+T///dEVbyxC7+TmVlL8hlzM7Pm9iJwsKSRaX3iLu63mKz5Xkx2lvxioC2dFd8X2AxslLQ/MKFzp4hoB9qBHwCz09j8iBidHktqjH8igKRxwMaI2Ag8CpyTxk8DBtf4mmZmTclnzM3MmlhEvC3pEuB+Sa8BT+7iro8AVwOPR8RmSVvSGBHxjKRlwHJgJfC3qn3nAEMj4oU6/ArrJT1G9mbg62nsWmCupInAX4G1wKY6HMvMrNSUnRwxM7NmJWmfiHhTkoAbgZciYlqOx/slsCwiZuzm6ywCrqg+yy6pH9CRpsmcANwUEaN351hmZs3AZ8zNzJrfBZImA3uRfVnz5rwOJGkp2TSXy/M6BtlVWOZJ6gVsAy7I8VhmZqXhM+ZmZmZmZiXgL3+amZmZmZWAG3MzMzMzsxJwY25mZmZmVgJuzM3MzMzMSsCNuZmZmZlZCbgxNzMzMzMrgf8BeuclKmp+t2kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# figure design - plotting 보다 먼저 나와야 적용됨!\n",
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "sns.regplot(x='highway-mpg', y='price', data=df)\n",
    "plt.ylim(0,)     # price가 0이하가 될수 없으므로 범위 자름\n",
    "plt.xlim(right=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47414.10667770421)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# peak-rpm로 해보고 그래프 비교해보기\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot('peak-rpm', 'price', data=df)\n",
    "plt.ylim(bottom=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg  peak-rpm     price\n",
       "highway-mpg     1.000000 -0.058598 -0.704692\n",
       "peak-rpm       -0.058598  1.000000 -0.101616\n",
       "price          -0.704692 -0.101616  1.000000"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 실제 correlation 정도 수치로 비교하기\n",
    "df[['highway-mpg', 'peak-rpm', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residual Plot - seaborn\n",
    "(Actual value) - (Predicted value)를 plotting 한 그래프 - variance를 확인하기 쉬움!\n",
    "* x축 : predictor variable\n",
    "* y축 : residual\n",
    "\n",
    "--> x축(y=0) 기준으로 위아래로 고르게 퍼져있으면(+_similar variance), linear model이 적합하다고 할 수 있음(<b>linear model is  good fit for the data</b>)!\n",
    "\n",
    "--> 고르게 퍼져있지 않거나, curvature(곡선)이 생기면 non-linear model이 추천됨"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# residual plot\n",
    "width=12\n",
    "height=10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.residplot(df[['highway-mpg']], df[['price']])   # residual이지 price가 아니기 때문에 y>0 지정할 필요 X\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<결론> regression plot에서 peak-rpm보다 highway-mpg가 더 line에 더 가까이 퍼져있어서 적합해 보였지만, residual plot으로부터 highway-mpg도 linear model이 적합하지 않은 것으로 판단됨"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Visualization of Multiple Linear Regression - Distribution Plot\n",
    "하나의 변수에 대한 관찰값 범위를 histogram이나 확률분포로 나타낸 것(<b>predictor variable 고려 안함!</b>)  -->  예를 들어 price는 다변수에 의해 관찰된 값이기 때문에 multiple variables를 가질 수록 정확해짐!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[13699.11161184],\n",
       "       [13699.11161184],\n",
       "       [19051.65470233],\n",
       "       [10620.36193015],\n",
       "       [15521.31420211]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 위에서 한 MLR 가져옴\n",
    "lm1 = LinearRegression()\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "y = df[['price']]\n",
    "lm1.fit(x, y)\n",
    "yhat = lm1.predict(x)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZWVm11nvEEUfw8ccfExcXx3vvvcfdd9/NG2+8UeP+I0eO5Morr2TLli2kpqYybdo0brzxxkbVFeq7777jtdde47PPPiM+Pp7rrruOV155hQkTJtTr+JpEa5LRHVgb8nM+cHxN+6hqhYgUA6mu/Mtqx3Z3j8PVmQpsVdWKMPvfD/xHRG4E2gE/DResiFwNXA3Qs2fPel2gaeEqKuCGG+Bvf4PTToMFC2DQILjqKu/NKinJ7wiNMU1o6tSp3HLLLQCMGzeOqVOncswxx/Dee+9x2WWX0bZtWwA6duzYoHqLi4u55JJLWLFiBSJCeXl5rfsnJCQwatQoZsyYwdixY1m4cCEjRoxoVF2h3n//febNm8dxxx0HwI4dOzj44IMbdC3hRGuSEa4La/X26Jr2qak83K2h2vYHGA+8qKp/EZETgJdEZICqVu21s+oUYApAVlaWtZu3dpWVcO658NZbcNdd8NBDUFwMv/89PPEE9OrllRtjml4dLQ6RsGXLFubMmcO3336LiFBZWYmI8Oijj6Kq9Rp1ERcXR1WV99EROgz0t7/9LaeccgozZ84kLy9vz22U2owfP56HHnoIVWX06NF7JseqT12hcYTGoqpccskl/PGPf6zz/A0RlX0y8FoTeoT8nMa+tyr27CMicXi3MwprObam8s1AB1dH9XNdAUwHUNUvgCSg035cl2kN3nrL+3rsMfjDHyAmBg46yHvzO+cc+NOfvH4axphWYcaMGUyYMIHVq1eTl5fH2rVrycjI4NNPP2XEiBG88MILbN++HYDCwkIAkpOTKSkp2VNHeno68+bNA9jrFkZxcTHdu3uN5y+++GK94jnllFNYsWIFkydPZvz48Q2qKz09nfnz5wMwf/58cnNzATjttNOYMWMGmzZt2nMdq1fXuLhqvUVrkvE10NeN+kjA63Q5u9o+s4FL3OPzgDmqqq58nBt9kgH0BebWVKc75gNXB67ON93jNcBpACJyJF6SUdDkV2talsmTIS0Nbr55321//COUlsLDDzd/XMaYiJg6dSrnnnvuXmVjx47l1VdfZeTIkYwaNYqsrCwyMzP3dKq89NJLufbaa/d0/Lzvvvu4+eabGTZsGLGxsXvquf3227nrrrsYOnRovTtaxsTEMHbsWLZs2cJJJ53UoLrGjh1LYWEhmZmZPPPMMxx22GEA9OvXj4ceeogRI0Zw9NFHc/rpp7N+/foGPU/hiEZpr3g3XPRxIBZ4QVUfFpEHgGxVnS0iScBLwCC8FoxxIZ067wEuByqAW1T17ZrqdOW9gWlAR2AB8AtV3eVGn/wdCODdQrldVf9TW9xZWVmanZ3dlE+FiSbffw+HHw4PPgj33ht+nyuugJdfhuXLIT29WcMzpjX67rvvOPLII/0OwxD+dyEi81Q1bA/XqE0yWipLMlq5W2/1WjLWrIEuXcLvk58PffvCeefBSy81b3zGtEKWZESPhiYZ0Xq7xJjoU1YG//gHjB1bc4IBP95KeeUVWLGi+eIzxpgoY0mGMfX16qveKJLrr697XzdunVdfjWxMxhgTxSzJMKY+VOHpp73JtoYOrXv/7t3hpJNg2jSbDdQYc8CyJMOY+sjN9WYZvPxyqO9KhOPHw7JlsGhRZGMzxpgoZUmGMfUxZ473/fTT63/M2LEQFwdTp0YmJmOMiXKWZBhTHx98AIccAg3p4d6pk5eU2C0TY1q82NhYMjMz93zl5eWRnZ3NTTfdBHjLqX/++ed79p81axZLly6tqboaBQKBfcqGDx/Ou+++u1fZ448/znXXXdfgupqbJRnG1EXVa8k49dT63yoJGj/eG+76xReRic0Y0yzatGnDwoUL93ylp6eTlZXFk08+CTRdkhFO9ZVXAaZNm7bXbJ/RypIMY+qybBls2OAlGQ01erS3WJrdMjGm1fnwww85++yzycvL49lnn2XSpElkZmby0UcfMXv2bH7zm9+QmZnJqlWrWLVqFSNHjuTYY49l2LBhLFu2DIDc3FxOOOEEjjvuOH7729+GPc95553HW2+9xa5duwDIy8tj3bp1nHjiiZSWlnLaaadxzDHHcNRRR/Hmm2/uc3wwzqAbbrhhz7Tj8+bN4+STT+bYY4/ljDPOaJJZPkNF6wJpxkSPDz7wvp9ySsOPTUmBs86C6dO9tU1CphM2xjTcihW3UFratEu9BwKZ9O1b+8JrO3bsIDMzE4CMjAxmzpy5Z1t6ejrXXnstgUCA2267DYBRo0Zx9tlnc9553ooVp512Gs8++yx9+/blq6++4rrrrmPOnDncfPPN/OpXv2LChAlMnjw57LlTU1MZPHgw77zzDqNHj2batGlceOGFiAhJSUnMnDmTlJQUNm/ezE9+8hNGjRpVr0XbysvLufHGG3nzzTfp3Lkzr732Gvfccw8vvPBCvZ63+rAkw5i6zJkDPXtC796NO/788+GNNyA7G44/vmljM8Y0i+DtksYoLS3l888/5/zzz99TFmyV+Oyzz/YsmPbLX/6SO+64I2wdwVsmwSQjmAioKnfffTcff/wxMTEx/PDDD2zcuJEutU0Y6Cxfvpxvv/2W012H9srKSrp27dqoa6yJJRnG1KaqymvJGDWq4f0xgn76U+/Y//zHkgxj9lNdLQ7RqKqqig4dOtSYpNSn1WHMmDFMnDiR+fPns2PHDo455hgAXnnlFQoKCpg3bx7x8fGkp6fvtZQ81L68e//+/fkign3GrE+GMbX55hsoLGxcf4yg1FQ49lgvyTDGtErVl3YP/TklJYWMjAxef/11wPtwX+Tmzxk6dOieTp2vvPJKjfUHAgGGDx/O5Zdfvs/y7gcffDDx8fF88MEHYZdn79WrF0uXLmXXrl0UFxfz/vvvA3D44YdTUFCwJ8koLy9nyZIl+/M07MOSDGNqE5wfozH9MUKNGOGNMNm2bf9jMsZEnXPOOYeZM2eSmZnJJ598wrhx4/jzn//MoEGDWLVqFa+88grPP/88AwcOpH///ns6aD7xxBNMnjyZ4447juLi4lrPMX78eBYtWsS4ceP2lF188cVkZ2eTlZXFK6+8whFHHLHPcT169OCCCy7g6KOP5uKLL2bQoEEAJCQkMGPGDO644w4GDhxIZmbmXiNkmoKtwtrEbBXWVuacc7wl27//fv/q+egjGD4cZs3yRpwYY+rNVmGNHrYKqzFNpaoKPvnESw721wknQLt2dsvEGHNAsSTDmJrk5Xmrrh533P7XlZDg3XKxJMMYcwCxJMOYmixY4H139y/324gRsHIl5OQ0TX3GGBPlLMkwpiYLFniTZw0Y0DT1jRjhff/vf5umPmMOINZ/0H+N+R1YkmFMTRYu9BZES0pqmvoOO8yb1MtumRjTIElJSWzZssUSDR+pKlu2bCGpge+HNhmXMTVZsGD/5seoTsRrzXj9daistCnGjamntLQ08vPzKSgo8DuUA1pSUhJpaWkNOsaSDGPC2bQJ1q1ruv4YQaecAs89B4sXN33dxrRS8fHxZGRk+B2GaQS7XWJMOMHpf5s6ERg2zPv+8cdNW68xxkQhSzKMCSeYZAwc2LT19ugB6emWZBhjDghRm2SIyEgRWS4iK0XkzjDbE0XkNbf9KxFJD9l2lytfLiJn1FWniGS4Ola4OhNc+SQRWei+vheRrZG9ahM1FiyAXr2gY8emr/ukk7xJvqwTmzGmlYvKJENEYoHJwJlAP2C8iPSrttsVQJGqHgpMAh5xx/YDxgH9gZHA0yISW0edjwCTVLUvUOTqRlVvVdVMVc0E/gr8O1LXbKLMggWR6zNx0klQUOBNV26MMa1YVCYZwGBgparmqOpuYBpQfcGH0cA/3eMZwGnirZc7GpimqrtUNRdY6eoLW6c75lRXB67OMWFiGg9MbbIrNNGrrMxbqyQzMzL1W78MY8wBIlqTjO7A2pCf811Z2H1UtQIoBlJrObam8lRgq6sj7LlEpBeQAcxp9BWZlmPxYu9WRqRaMvr2hUMO8W6ZGGNMKxatSYaEKat+A7umfZqqPNQ4YIaqVobZFxG5WkSyRSTbxnG3AsFOn5FqyRDxbplYS4YxppWL1iQjH+gR8nMasK6mfUQkDmgPFNZybE3lm4EOro6azjWOWm6VqOoUVc1S1azOnTvXeXEmyi1Y4HX47NGj7n0ba9gwWLMGVq+O3DmMMcZn0ZpkfA30daM+EvA+5GdX22c2cIl7fB4wR705Z2cD49zokwygLzC3pjrdMR+4OnB1vhk8iYgcDhwEfBGB6zTRaOFCrxVDwjVyNZGTTvK+2y0TY0wrFpVJhusfcQPwLvAdMF1Vl4jIAyIyyu32PJAqIiuBicCd7tglwHRgKfAOcL2qVtZUp6vrDmCiqyvV1R00Hq8jqY03PBCowtKlcNRRkT3PgAHQoYPdMjHGtGpin51NKysrS7Ozs/0OwzRWfr53m+SZZ+DaayN7rrPP9pZ+X7YssucxxpgIEpF5qpoVbltUtmQY45vgB/4RR0T+XCee6M2VsXlz5M9ljDE+sCTDmFDNmWQMHep9/8K6+xhjWidLMowJtWwZtG/vzWMRaVlZEB8Pn30W+XMZY4wPLMkwJtSyZV4rRiRHlgS1aQPHHGNJhjGm1bIkw5hQy5bB4Yc33/mGDoWvv4bdu5vvnMYY00wsyTAmqKQEfvihefpjBA0ZArt2wfz5zXdOY4xpJpZkGBMUXBW1OZOMYOfPzz9vvnMaY0wzsSTDmCA/kowuXaB3b+uXYYxplSzJMCZo2TKIjYU+fZr3vEOGeEmGTYxnjGll4urexZgDxLJlXoKRkNDgQ7dvX8mGDS8QG5tCmzZ9aNPmUAKBoxGJrfvgoUPh5ZchN9dr1TDGmFbCkgxjgoLDVxtgx448Vq9+kA0b/ulKKvdsS0kZwpFHvkKbNum1VxLsl/HZZ5ZkGGNaFbtdYgxAZSV8/32DkozNm99k7tzD2LjxZbp3v4ETTsjnxBO3kZW1kL59J1NW9g3Z2Zls2jS99or69YOUFOuXYYxpdawlwxiAvDxvrop6Jhmlpd+wdOnFBAKZ9O//BklJPfZsCwQGEggMpGPHkSxdehFLl15IScl8+vT5U/jKYmPhhBNshIkxptWxlgxjoEFrluzevZlvvx1NXFwKAwbM2ivBCNWmTW8GDfqErl2vZu3aR1i//sWaKx06FL79FrZubUTwxhgTnSzJMAZ+TDLqmO2zqqqcpUsvYNeudQwYMIvExG617h8TE0/fvpPp0OFUvv/+GrZt+yr8jkOGeKNLvqphuzHGtECWZBgDXpLRuTN07FjrbmvWPMLWrR9w+OF/JyVlcL2qjomJo3//6SQmdufbb89l1651++50/PHebRPrl2GMaUUsyTAGvIm46mjFKC/fytq1j9Gp0xi6dPllg6qPj09lwIBZVFQUs3TpeLT6nBiBAAwcaEmGMaZVsSTDGICcnDon4crPn0RlZTHp6fc36hSBwNH07fskxcUfs3HjS/vuMGSId7ukoqJR9RtjTLSxJMOYnTu9hdFqmaOivLyI/PzH6dTp5wQCAxt9qi5dLiM5+XhWrfoN5eXVOnkOHQplZbB4caPrN8aYaGJJhjGrV3vfMzJq3CU//3+orNxGevp9+3UqkRgOO+xpyssLyMurVteQId53G8pqjGklLMkwJjfX+15DS0Z5eSH5+U/QufN5BAJH7/fpkpOPoVu3a/nhh6coLQ1ptejZE9LSrF+GMabVsCTDmJwc73sNLRn5+Y9TWVlKr17714oRKiPjIeLiDmLFihv27gQ6dKglGcaYVsOSDGNycyEpyVt2vRrVStavf56OHX9GIDCgyU4ZH9+RjIyHKC7+hKKi//y4YcgQWLvW+zLGmBYuapMMERkpIstFZKWI3Blme6KIvOa2fyUi6SHb7nLly0XkjLrqFJEMV8cKV2dCyLYLRGSpiCwRkVcjd8XGNzk5kJ4OMfv+ORQVfcDu3evo0mVCk5+2a9fLSUzsSV7e739szQgulmb9MowxrUBUJhnirY89GTgT6AeMF5F+1Xa7AihS1UOBScAj7th+wDigPzASeFpEYuuo8xFgkqr2BYpc3YhIX+AuYKiq9gduidAlGz/VssT6xo0vERubQmrqOU1+2piYBHr2vItt276gqOh9r3DgQGjb1pIMY0yrEJVJBndxi7oAACAASURBVDAYWKmqOaq6G5gGjK62z2gguL72DOA0ERFXPk1Vd6lqLrDS1Re2TnfMqa4OXJ1j3OOrgMmqWgSgqpsicK3Gbzk5YftjVFaWUVDwBp07n09sbJuInLpr18tITExj9WrXmhEXBz/5CXzySUTOZ4wxzSlak4zuQOhN6XxXFnYfVa0AioHUWo6tqTwV2OrqqH6uw4DDROQzEflSREbu53WZaFNUBMXFYVsyNm9+k6qqsgbP7tkQMTGJ9Ox5J8XFn7J164de4bBhsGgRbNsWsfMaY0xziNYkQ8KUaT33aapygDigLzAcGA88JyId9glW5GoRyRaR7IKCgjDVmahVy8iSjRtfIjGxJ+3bD4toCF26XEFCQjfy8n7vFQwbBlVVdsvEGNPiRWuSkQ+Erp+dBlRfVWrPPiISB7QHCms5tqbyzUAHV0f1c+UDb6pqubv1shwv6diLqk5R1SxVzercuXMDL9X4qoY5Mnbt2kBh4X845JBfIBLZP5PY2CR69ryd4uKPKC7+3LtdEhcHH38c0fMaY0ykRWuS8TXQ1436SMDryDm72j6zgUvc4/OAOep10Z8NjHOjTzLwkoK5NdXpjvnA1YGr8033eBZwCoCIdMK7fZLT5Fdr/FNDS8amTVOBKg455BfNEkaXLlcQF9eB/PwnoF07OPZY65dhjGnxojLJcP0jbgDeBb4DpqvqEhF5QERGud2eB1JFZCUwEbjTHbsEmA4sBd4BrlfVyprqdHXdAUx0daW6unH7bhGRpXiJyG9UdUskr900s9xcSE2FlJS9ijdtmkogcCzt2h3ZLGHExQXo2vUqCgreYOfOtXDSSTB3rreuijHGtFCyz5LTZr9kZWVpdna232GY+jrjDCgshK+/3lO0e/dGPv+8CxkZD9Gr1z3NFsrOnav58sve9OjxG/osHQqjRsFHH3kJhzHGRCkRmaeqWeG2RWVLhjHNJjd3n1slhYXvAtCx45nNGkpSUi86d/4569dPofKEQSBit0yMMS2aJRnmwFVZCXl5+3T6LCx8m/j4gwkEMps9pLS0W6ioKGLDrrdgwADr/GmMadEsyTAHrnXroLx8r5YM1UoKC/9Dx44jIz6qJJyUlCEkJ2fxww9PoMNO9IaxVlTUfaAxxkQhSzLMgSs4siSkJWPbtrlUVBQ2+62SIBGhe/eb2b59GUU/7QClpbBwoS+xGGPM/rIkwxy4gnNkhLRkFBa+DcTQseMIf2ICDj74fOLjO/ND2nyvwPplGGNaKEsyzIErJ8dbebVnzz1FhYVvk5JyPPHxHX0LKyYmka5dr2BL2X/ZmdULPvzQt1iMMWZ/WJJhDly5uZCWBgkJAOzevYmSkmzfbpWE6tr1akBZPyHVG8Zq/TKMMS2QJRnmwJWTs1d/DL+GrobTpk0GHTuOZH2/XKpKi2H+fL9DMsaYBrMkwxy4qs2RERy6mpx8jI9B/ahbt2vZHVvEliHA++/7HY4xxjRY1CUZIiLueycRmSgi8SHb4mo+0pgG2LED1q/f05KhWuWGrp7hy9DVcFJTzyIxsQfrLgpYkmGMaZGi4910b8GYLgeOVtVyETlVRJ4ExvgYl2lN8vK8764lo6xsKRUVW+jQ4VT/YqpGJJauXa+i6IhStud+YuuYGGNanKhLMlS10j08H3hcRE4GfgF0ACaIyIm+BWdaj2pLvBcXe8NEO3QY5ldEYXXteiWisaw/fbc3MZcxxrQgUZdkwJ7bIi8DI4BHgFdUdQJeolHo9hH/IjQtXrUl3ouLPyEhoStJSb1rOaj5JSZ2pdNBZ7P+TKj84F2/wzHGmAaJqiRDfrwZfgGwDS+peEBV3xeRU4A4VV0KoLZ8rNkfubnQpg0ccgiqSnHxJ7RvP4xozF279bqRivZQUPCG36EYY0yDRFVHSlWtcg8vVdUR4CUermWjL/CEK4sNua1iTMPl5HitGCLs3JHHrl35tG8fXbdKgjp0OJU2ZR1ZN2AVXYqLoX17v0Myxph6iZqWjJBRJRnAJhE5R0TaqGqVqlao6hRgOuzVb8OYxgkZvvpjf4yT/IyoRiJCt3YXsm0AlH7yT7/DMcaYeouaJCPk9sdwoBdwFTBWRAaLSDcRibFbJKZJqO41EVdx8SfExXWgXbsBPgdWsy5Zv0V2w7qNf/c7FGOMqbeoSTKCVPUfwIXA68DJwHXA7UCan3GZVqSwEEpK9mrJSEkZGjXzY4QTH+jKwSu6s7H7EirKt/kdjjHG1EtUvKsGO3yKSAcRORQYALyrqlcBfwbygB/8i9C0KiFLvO/eXcD27cuibuhqON3aXkRlkrLpm0l+h2KMMfUSFUlGiMeBG4HfAVNEZBJwKDDF+mGYJhOyxHtx8acAUdvpM1TKqdfTbiX8sGEKdufQGNMS+J5kiIioapWIdMNrwbgb6AT8E+gP/BrIqKUKYxomZI6M4uJPiIlJIjk5y9+Y6kF69aJ7djfK2q5j27av/A7HGGPq5HuSUa3D5xtAH2CNqs7Em4hrgaou8Sk80xrl5kKnTpCcTHHxJyQnH09MTILfUdXLwZ0uJHY7rFv9hN+hGGNMnXxPMkQk0T2cB8wA4oF8EWkDnISLUaK5V55pWdzIkoqKUkpKFrSI/hhBcSN/ziH/hU1b3qC8vNDvcIwxpla+fnCLyPHA70XkNFVdrqorgKV4k4RtAI4EnvQzRtMKuTkySkqygUpSUob4HVH9/eQndPsoBZVyNmx40e9ojDGmVn63DtwNrAA+gD0zee5w65SMBzKBt0XkzpDZQHH7JorIayKyUkS+EpH0kG13ufLlInJGSPlIV7ZSRO4MKc9wdaxwdSa48ktFpEBEFrqvKyP4XJjmUFkJq1dD796UlMwFICVlsM9BNUBcHIEjzyZlWRzr1j1rHUCNMVHNtyRDRJKBw4CXgglEcASJiJwK/AsYB/QDxotIv2pVXAEUqeqhwCS8/hu4/cbhdRodCTwtIrEiEgtMBs4MU+cjwCRV7QsUubqDXlPVTPf1XJM+Cab55edDRQVkZLBt21ySkvoQH5/qd1QNc9ZZdPt3BTt2rGDr1jl+R2OMMTXysyXjaGCZqu4Os20H3i2TXLd9GjC62j6j8UaggNeX4zQ3NfloYJqq7lLVXGAlMNh9rVTVnNA63TGnujpwdY5pqos0USZkjoySkq9JSTnO33gaY+RIOn8SQ9zuJNate9bvaIwxpkZ+JhnfAIkiclWwIKRz5xigRFWLXFk+0L3a8d2BtQCqWgEUA6mh5U7w2JrKU4Gtro7Q8qCxIrJYRGaISI9wFyIiV4tItohkFxQU1O/qjT/cHBm7egbYtWsNyckt6FZJUMeOxA47jS4fJLJ58yx27Vrvd0TGGBOWb0mGqm4D/ghcICL3uw/wdiLyM+CngPuXk+Da29VvPodbk1ubsBzgf4F0VT0aeI8fW06qX8sUVc1S1azOnTuH28VEi9xciI2lJGUd0ML6Y4S68EK6vVSMagXr1z/vdzTGGBOWL0lGcMVVVf0EL9EYDHwNvAxcD7wF7HT7VOKtW7KuWjX5QA9XXxzQHigMLXeCx9ZUvhno4OoILUdVt6jqLlf+d+DY/bhsEw1ycqBHD0q2zwdiCQQG+R1R45x7Lm03xXNQQS/Wr5+CTYhrjIlGviQZoaupquocVf0Z0BO4FzgXeBDo60Z9JOB15JxdrZrZwCXu8XnAHFfvbGCcG32SAfQF5uIlMfvU6Y75wNWBq/NNABHpGnK+UcB3TfIEGP+44avbts0lEDiK2Ni2fkfUOB07wogRdJtaxq5da9my5f/5HZExxuyj2ZMMEUkTkcEhP8e6oau7VfUb970CuAF4F++DfbqqLhGRB0RklDv0eSBVRFYCE4E7AdzsoNPx5tt4B7heVStrqtPVdQcw0dWV6uoGuElElojIIuAm4NLIPCum2eTkoL0zKCn5muTkFtjpM9S4caTO3kwCqaxb94zf0RhjzD6kucfZi8gzwKvAKiARyNPmDiKCsrKyNDs72+8wTDjbt0O7dmx/7FbmHjuJww77O926teCpT7Ztg4MPJnfSQFYf+TXHH7+KNm1smR9jTPMSkXmqGnYBKD9ul3QDzsAbMirBBENEYtxcFsZEhhtZUtLbGzXdYjt9BqWkwFln0fWpXEBYv36K3xEZY8xe/EgybgKG4M2TMcnNqtlGVatsOXcTUS7J2NapgJiYtrRtW31+txbowgtJWlpAqp7A+vXPUVm5w++IjDFmj2ZPMlR1NfA08DjerJ7nAl+IyOsicmJzx2MOIG4irpKEHJKTjyEmJq6OA1qAs8+GlBR6/L+2lJdvtvVMjDFRxa/RJTNU9V5VfQNvVMd4vHkx0sBWXDURkptLVXIbSnd92zIn4QqnbVuYMIH2T35ISpss1q79M1VVFXUfZ4wxzaDZPsyDiYOI9BORR0UkX0T+BoxR1e9U9Q5VnQZQfTE0Y5pETg5lQ7tRVbWz5ffHCHXNNcjucnp+05+dO3MpKHjd74iMMQbwpyXjIWA9cDKQDdwpIi8GJ+gyJmJycyk5ph0AyclhO0K3TAMGwIknkvrop7RteyRr1vzJVmc1xkSFZksyVLXKzap5MPC6qq5S1b+r6rFAB7wVWY2JDFXIyaG0jxIb256kpN5+R9S0fvUrZMUqepacTVnZYgoL3/E7ImOM8aUl4z28ia+6i0h7EemEtyx7Th3HGdN4mzdDWRklh2wjOXkQra7hbOxY6NSJg/+2ksTEHqxZ8ye/IzLGmOZNMtysm6/itVz8EW/68H/iLc1ebvNkmIjJyaEqBsrarm+565XUJjERLruMmH/PpkfKlRQXf0xR0Qd+R2WMOcD5MYT1e+Aa4DW8Phk34iUcANbh00RGbi47ekKV7CYQOMbvaCLjmmtAla4vFZGYmEZOzl3WN8MY46tmTTLEE6uq5ar6f6r6L1XNUdXtsPfCacY0qZwcSvp6D5OTW2FLBkCfPjB+PLF/nUJ66q8pKfmKzZvf9DsqY8wBrLlvl6iqVrpF0eKb89zmAJebS+nRbYiJaUObNof7HU3k3Hsv7NjBIS/8QJs2h5Obe7ctA2+M8U1Ek4zgsFQRiReRXiJytoh0cKuilkfy3MbsJSeHkn5xBAIDW8dMnzU54ggYP56Yp56hd6c72L79OzZseMnvqIwxB6hIt2QE638QmARcBPxbRJ4RkVE2N4ZpLpqXQ2naztbZ6bO6e++F7dvp9NxykpOPIy/vd1RW7vQ7KmPMASiiSUbIgmcn403CdT3wG2AFcBvelOLGRFZFBTt3r6Eyobz1dvoMdeSRcOGFyFOT6Z16F7t2rWXt2j/7HZUx5gAUsSQjZBrxI4GPgPWqWqSq84CngAuBWZE6vzF7rF1LSR9v4FJy8gGQZAD87newcycHPfz/6Nz5Alavfpjt21f6HZUx5gATsSQjZP2RC4FbgH+IyMkiIqq6W1XXW78M0yxycyntC6KxtGvX3+9omseRR8Ktt8Jzz3Fo8cXExCSyYsV1NqTVGNOsIj66RFXvBzKAd4D/ARa6PhntI31uY4A9w1fbJR5OTEyi39E0n9/9DtLSSLzud2T0eoCiov+yadM0v6MyxhxAIpJkhNwqSRWRLOB04Eu3TsnlQDxQGolzG1Od5uZQ2hcCHY7zO5TmFQjAE0/AokV0n1lFcnIWK1feSnn5Vr8jM8YcICLVkhFsk/0DcB9wNPArEZkCLFXVK9UG75tmsnvDEsoPgkBKK1p5tb7OPRfOPBP57X0clnw/5eUFdtvEGNNsmjzJcH0uVETSgJNU9RzgAeC3wG7gNzYRl2lOJVXLgAOo02coEZg8GYDkSx4ivefv2LRpKhs2vOhvXMaYA0KTJxkhU4MfAix2ZdtUdQ3wd2CYdfg0zak0KR8U2rU72u9Q/JGRAX//O3z5Jb2mlNGhwymsWHEDZWXf+R2ZMaaVi0RLRhKAG6oqIvK1iNwkIgOBCcAyt5+tuGoir7SU0q7babOzE3FxAb+j8c+FF8LVVyOP/JkjN15JbGxbli4dR2XlDr8jM8a0Yk2aZIhIJjDETSPeTVUvwOuTkQ68DmzAm5QLfuy3UVNdI0VkuYisFJE7w2xPFJHX3PavRCQ9ZNtdrny5iJxRV50ikuHqWOHqTKh2rvNERF0nVtOS5OZS2gcCcqjfkfjv8cdhwAASf3EzRxz0Z8rKFlv/DGNMRDV1S0Z7YA1wJvCgiEwAioA/qOphqvpnVd0Ie82jsQ/XyjHZ1dMPGC8i/artdgVQpKqH4k1Z/og7th8wDugPjASedguy1VbnI8AkVe3r4r0iJJZk4Cbgq0Y+J8ZHFbnfsrM7BFrryqsN0aYNzJgBFRWknv9nenW5nQ0bXmTNmj/4HZkxppVq0iRDVT9S1ZXAauBbYBhwJXCDiPxSRDrVs6rBwEq3DPxuYBowuto+o4F/usczgNPcWiijgWmquktVc4GVrr6wdbpjTnV14OocE3KeB4FHAVv8oQUq3fg5AIFuw3yOJEocfji88QZ8/z3pN83nkM4XkZt7Lxs3vup3ZMaYVqjJkgwRaee+jwBGquok4FrgRaASrwWhvh/U3YG1IT/nu7Kw+6hqBVAMpNZybE3lqcBWV8de5xKRQUAPVX2rtmBF5GoRyRaR7IKCgnpeomkOpdu/ASDQ1ZKMPU49FaZMQf77Hoc/mUj79iezbNllbN36sd+RGWNamaZsyTjK3R65G2gH3gJpqvoJ3u2I21W1tJ4rr4bbp/qN45r2aZJyN6HYJODXtcTp7aw6RVWzVDWrc+fOde1umlFpTA7xpbEkJFbPUQ9wl10G99xDzJR/MOCdIbRp05tvvjmHbdvm+h2ZMaYVacokoxBv0q1jgS4i8isROV1EOuJNKT4Q9hriWpt8oEfIz2nAupr2EZE4vP4ghbUcW1P5ZqCDqyO0PBkYAHwoInnAT4DZ1vmzZSlLKSCwpSP1y20PMA8+CBMmEH/3Hzl6yWXEx3di0aIRlJTM8zsyY0wr0SRJhpuA63u8fg73AG/jda6cAPwOSATebUCVXwN93aiPBLyOnLOr7TMbuMQ9Pg+Y4xKY2cA4N/okA+gLzK2pTnfMB/y47PwlwJuqWqyqnVQ1XVXTgS+BUaqa3YDrMD6qqiqntOtO2pX3qHvnA5EIPPccjBxJ0pV3kVlwF3FxHVi06HRKShb6HZ0xphVo6tEltwAfqepMVb0Rb1rxWcDPVbUiuKZJXVz/iBvwEpPvgOmqukREHhCRUW6354FUEVkJTATudMcuAaYDS/FaUK53t23C1unqugOY6OpKdXWbFm5H/udoAgQSD5CVVxsjPh5efx2OPZakC24ks+oxYmMDLFp0GiUl8/2OzhjTwsn+jpEPmUa8Pd6cGEuBV1V1e1ME2NJkZWVpdrY1dkSDjZ/+nu8q7idr+1MEfna93+FEt4ICGDIECgvZ8eFUFpZeTUXFVgYOfJeUlOP9js4YE8VEZJ6qhu1KsN8tGSF9LAYDZ+DNMXGpiBwlIu3r2dHTmCZXuvVrZDe07XWi36FEv86d4d13IT6eNmdfxaCur7k+Gj9l69ZP/Y7OGNNCNWWfjP8Cg4Df4HUAfRx4zj02ptmVli+jXR7EZPT1O5SWoXdvePttKCoiacw1DDriHRISurN48RkUFc3xOzpjTAu0X0lGSCtFioicjNfJsz9e/4ixeB0uN+9XhMY0gqpS2uYHAj+0gbZt/Q6n5Rg0CF57DRYvJvGG+xmU+aEb3noWhYUN6bttjDH735IRPP424FZgK5AJvAVkuWnEf9jPcxjTYLt3b6A8aSeB0kP8DqXlOfNMeOABeOUVEqa8zsCBH9C27RF8880oNm/+X7+jM8a0IPuVZKhqpXv4c+BXqvqYqv4KbxKrX4pIl/0N0JjGKC31hmDawmiNdPfdcM45MHEiCV99x8CBcwgEBrJkyc/ZvLnWCXCNMWaP/e6TISIHAQuAjiHF/8bri7Frf+s3pjFKt3nDLwOBTJ8jaaFiYuCllyAjAy66iPjtMQwc+F8CgUyWLj2frVs/8jtCY0wL0BSjS4qAj4H3ReQlERkL3AWsU9Wi+s6NYUxTKt30BUnrIa5X9cV7Tb21bw8vvwzr1sGttxIX156jjnqbpKQMvvnmHJsZ1BhTp6ZKAP6BNwX3x8CNQClws9tmQ1hNsyvbvpjASrz/xE3jDR4Md9wB//gH/N//kZDQiaOP/g9xcR1ZvHgk27cv9ztCY0wUa1SSISKx7vtwEXkMbyrvGcAuVR0O/NUt+R7ab8OYZlFZWcZ28mm3CksymsJ998FRR8FVV0FhIUlJaQwc+B4gfPPNOZSXF/kdoTEmSjW2JaPKfb8bb0TJROAB4CwRubKei6AZExFlZd+CKIG8WEhL8zucli8xEV580ZsV9LbbAGjb9lAGDJjJzp15LF16AVVVFf7GaIyJSg1OMkKmEe8ALFbVh1T1O1WdAzwMXCUi6U0cpzH1Vlq6CIBAeS+IjfU5mlbimGNg4kTvtombNr99+6EcdtizFBW9x6pVE30O0BgTjRqcZIS0UlyOt6jYkyGbi4EqVc2zDp/GL6WlC4ndEUNSh8P9DqV1ueceOPhguOUWcG8DXbteTlraRH744a+sW/eczwEaY6JNY/tkCPAkcDVwvIjsEpFvgcfwlnpHVatqqcKYiCktXUhgFcihNp14k0pJgYcfhs8+g+nT9xT36fMoBx30U1auvJGysiW1VGCMOdA0KslQTwXeaqvHA12BV/FGmLwkIi+KSKAJ4zSmXlSrKC1ZRGB5FfTp43c4rc9ll0FmJtx+O+zYAYBILEcc8RKxsSksXTqOysodPgdpjIkWDUoyQkaVjBORfwPPi8jzwNmq+gdVPRIYA5SpamnTh2tM7XbsWEWVbiewCjjUZvtscrGx8PjjsGYNTJq0pzgxsQtHHPFPysq+ZdWqX/sYoDEmmjQoyQgZjvpb4GngKeB1YKyITHD7fK2q1zdplMbU057pxFdiLRmRcvLJ3pTjjz0G27btKU5NHUla2q9Zt+4ZCgpm+higMSZaNGZ0ySC82TzfU9XPVPUd4C/AeSKS1OQRGtMApaWLkKoY2q4G0tP9Dqf1uu8+KCqCp57aq7h37z8QCBzL999fze7dBT4FZ4yJFo3pk7ESqBKRv4nIQFfWDmirqjttVInxU2npQtpuTSa2ay9vfgcTGcceC2edBX/5C5SU7CmOiUngiCNepKKimJUrb66lAmPMgaChfTKSgJOBa4EC4HoR+R64DPhzcLcmjdCYBigrW0QgL85ulTSH++6DwkKYPHmv4kBgAL163cumTVNtaXhjDnD1SjJCWid+BoxT1VzgReAZ4DzgFlV9F2waceOf3bs3s2tXPoFvdlinz+Zw3HFw5ple34zSvft59+x5J+3aHcX3319LeflWnwI0xvitobc2fgqsAlDVlaq6QFUXq+q6pg/NmIYpK/Nm+my3eLu1ZDSX++6DLVvg2Wf3Ko6JSeDww19g9+4NrFp1m0/BGWP8Vq8kI2RirVK8WT4/FZGrRCQlcqEZ0zB7phO34avN5/jjYfhwePJJqNh7/ZKUlCx69JjIhg3PU1z8uT/xGWN8VWeSISK9ReRMEbkOeBk4FG9p9xHAPBF5JsIxGlMvpaULSag8iIRirCWjOd16K6xdC2+8sc+mXr3uIyGhOytWXG+LqBlzAKpPS8a/8NYpyQBuBWJV9XlVPR8YhTfT556JupqKiIwUkeUislJE7gyzPVFEXnPbvwpdlE1E7nLly0XkjLrqFJEMV8cKV2eCK79WRL4RkYWu9aZfU16jaVqlpQsJbDvY+8GSjOZz9tley9Hjj++zKS4uwKGHTqK0dCHr1j0b5mBjTGtWa5IhImOBVS6h+BtQDlwT3O5WX/3EPW6yDp8uYZkMnAn0A8aH+YC/AihS1UOBScAj7th+wDigPzASeFpEYuuo8xFgkqr2BYpc3eBNm36UqmYCjwL/01TXaJpWZeUOysqWEshPgkMOgYDNat9sYmLg5pvhyy+9r2o6dz6Pgw76Kbm597J79yYfAjTG+KWuloxbgfXgdfQEPgc6AohIXATjGgysVNUcVd0NTANGV9tnNPBP93gGcJpbuG00ME1Vd7lRMCtdfWHrdMec6urA1TkGQFV/nM7QmwtEMVGprOxboJLkpeXWiuGHSy+FDh32mmo8SEQ49NC/UlW1nZycO5o/NmOMb+pKMt4DfiEi+SLyJ+AG4K8AqlrhPqAjoTuwNuTnfFcWdh+3WFsxkFrLsTWVpwJbXR37nEtErheRVXgtGTft11WZiCktnQ9A4KtC6/Tph0AArrrK65exZs0+m9u1O4K0tIls2PAi27Z95UOAxhg/1JpkqOr9qpoGnI/3wZsBvC4ivxaRZFWN1H/24ZKX6ueqaZ+mKvceqE5W1T7AHcC9YYMVuVpEskUku6DAplL2Q0nJAuJiO5C0YIO1ZPjlxhtBFZ4J3xe8V697iI8/hJUrbyVybx3GmGhS3yGsX6jqL1U1FXgQuAhvpEmk5AM9Qn5OA6rPxbFnH3frpj1QWMuxNZVvBjqE3P4Jdy7wbq+MCResqk5R1SxVzercuXOdF2eaXmnpfAIxh3kZo7Vk+KNHD2/htBdegN2799kcF5dM794Ps23bF2za9JoPARpjmluD1xlR1Rmqeizwc2j6USXO10BfN+ojAa8j5+xq+8wGLnGPzwPmuJaV2cA4N/okA+gLzK2pTnfMB64OXJ1vumvrG3K+s4AVTXydpglUVVVQVvYNgbKuXoG1ZPjn2mth0yaYGX4V1i5dLiUQyCQn53YqK3c0c3DGmObW6MXMgqNJIjGNuOsfcQPwLvAdMF1Vl4jIAyIyyu32PJAqIiuBicCd7tglwHRgKfAOcL2qVtZUp6vrDrxJxlbi9dF43pXfICJLRGShO0cwqTFRZPv2ZVRV7SQ5v61X0Ldv7QeYyBkxwlv99tnww1VFYunTZxK7dq0lP98GaxnT2ondZYUTiwAAIABJREFUG21aWVlZmp2d7XcYB5QNG/7FsmWXcNz/jqXdSx97/0kb//zpT3DXXfDdd/D/27vz8Kqqc/Hj3/ckJwkZISGQBJCEIYRRQZzHOqK2om1xrlSlaqv1qm2vevWxVdve2ttqJ6uieK3trYpTtbbiAFj7c2IQJIkQCJMgQ8g8J2dYvz/WjhnICGdM3s/z7Oecs/baa6+zwzm8Z+01FBR0m6Wo6OtUVr7FccdtJj4+J8QVVEoFkoisNcbM7W6fLsuuol59/TpcrmEkrtkPU6aEuzrqmmvA7YbHH+8xy8SJ/4MxrWzf3m1faqXUIKFBhop6dXWfkJx8JLJpswYZkWD0aPj61+Hpp6Gp+34Xw4ZNZOzY/2Dfvqepq/sktPVTSoWMBhkqqhnjt9OJu6fZ2yQaZESGG2+E6mp44YUes4wffw9u90gd0qrUIKZBhopqTU3b8PlqSa4ZbRN66AOgQuy00+xQ4iVLeswSG5tGbu791NS8R3n5yyGsnFIqVDTIUFGtvn4dACm74m2CtmREBhG49lp47z3Y0vPI7+zsRSQlzWDr1h/h8zWHsIJKqVDQIENFtfr6dYjEklTUALGxkJcX7iqpNgsX2sXT/vd/e8zicsUyceJDNDdv54svfhfCyimlQkGDDBXV6uo+ITFxOq5NW+0kXG53uKuk2uTkwPnn2w6gXm+P2dLTzyYj46vs3PlTWlv3h65+Sqmg0yBDRS1jDPX160hJmQ2bNumtkkh07bWwdy8sW9ZrtokTf4Xf38T27feGqGJKqVDQIENFrZaWXXg8ZaQkzYHSUg0yItFXvwqjRvXaARQgMXEKOTk3sXfvk9TXbwhR5ZRSwaZBhopatbWrAEipG2MX5NKRJZHH7Yarr4bXX4f9vd8Kyc29l9jY4ZSW3q5DWpUaJDTIUFGrrm41Im6Sdzhr9GlLRmS67jrbJ+OZZ3rN5nank5v7E6qrl1NR8fcQVU4pFUwaZKioVVe3mqSkWbhKttkEDTIiU0EBnHiiXQK+jxaKnJwbSUwsYOvWH+D3H7xcvFIqumiQoaKSMX7q6taSmnoslJRAejqMHBnuaqmeXHed7Zz74Ye9ZnO53Eyc+Guamkr54otHQlQ5pVSwaJCholJj42Z8vlpSUo7RkSXRYMECSErqswMoQHr6eYwYcS47dtxHa2t5CCqnlAoWDTJUVKqrWw1gg4ySEu30GelSUuDSS+H556GurtesIsKkSb/G56tnx46fhKZ+Sqmg0CBDRaW6utW4XEkk+cbAvn3akhENrrsOGhpg6dI+syYlTScn5wb27HmMhobPQlA5pVQwaJCholJd3WpSUuYgm0ttggYZke+EE2yL01NP9St7bu59xMQkU1r6HzqkVakopUGGijp+v4e6unX2VklRkU2cNi28lVJ9E7GtGR98ABs39pk9Lm4kEyb8jKqqdygrez4EFVRKBZoGGSrqNDQUYkxLe5AxbJhdt0RFvm99yy5k18/WjJycG0lJmcvWrbfh8VQHuXJKqUDTIENFnbZOn6mpx0JhoW3FiIkJc61Uv4webacaf+YZ8Hj6zC4SQ37+Y7S2lrF9+z0hqKBSKpA0yFBRp7Z2NbGxGSQk5NkgY+bMcFdJDcR110FZmZ1qvB9SUo5mzJib2bPnj9TWrgly5ZRSgaRBhoo6ttPnXKSiwo4smTEj3FVSAzFvHmRn92vOjDZ5eQ8QF5fF5s3X4/f33QKilIoMGmSoqOLzNdLQUExq6jG2FQO0JSPaxMbCt78Nb7wBe/b085BUJk9+hPr6deza9T/BrZ9SKmAiNsgQkXkiUiIipSJyZzf740XkeWf/xyKS22HfXU56iYic21eZIpLnlLHFKTPOSb9dRD4TkQ0islxExgf3Xau+2JVXfaSmHq9BRjS79lrw++FPf+r3IZmZF5OZeQk7dtxHQ0NxECunlAqUiAwyRCQGeAQ4D5gGXC4iXccoXgdUGWMmAQ8DDzrHTgMuA6YD84A/ikhMH2U+CDxsjJkMVDllA6wD5hpjZgEvAr8MxvtV/Vdb+z4Aqakn2CAjIwOyssJcKzVgkybBqafaWyYDmANj8uQ/EBubyqZN1+L3e4NYQaVUIERkkAEcC5QaY7YZY1qB54D5XfLMB9p+Br0InCki4qQ/Z4xpMcZsB0qd8rot0znmDKcMnDIvAjDGrDTGNDrpHwFjg/Be1QDU1LxPYuI03O709k6fIuGuljoUixbB1q2wYkW/D4mLy2Ty5D9QV7eK3bsfCmLllFKBEKlBxhhgV4fXu520bvMYY7xADZDRy7E9pWcA1U4ZPZ0LbOvGG4fwXlSAGOOnpuYD0tJOsk3tRUV6qySaLVhgV8997LEBHZaZeQkjR17M9u33Ul9fGKTKKaUCIVKDjO5+mnZtU+0pT6DS208kchUwF+i2x5mIXC8ia0RkzYEDB7rLogKgoaEYn6/GBhk7d9p1MDTIiF4JCXDNNfC3v8Hevf0+TETIz3+M2Ng0Nm68Ep+vOYiVVEodjkgNMnYD4zq8Hgt07Yb+ZR4RiQXSgMpeju0pvRwY7pRx0LlE5CzgbuBCY0xLd5U1xiw2xsw1xszNzMwcwNtUA1FTY/tjpKWdrJ0+B4sbbgCvF558ckCHxcWNoqDgaRoaCtm+/a4gVU4pdbgiNchYDUx2Rn3EYTtyvtYlz2vAQuf5N4EVxq6i9BpwmTP6JA+YDKzqqUznmJVOGThlvgogIrOBx7EBRlmQ3qvqp9ra93G7R5OQMKE9yJg+PbyVUodn8mQ4+2xYvNgGGwOQkXEeY8Z8n927f0Nl5ZtBqqBS6nBEZJDh9I+4GXgT2AgsNcYUi8j9InKhk20JkCEipcDtwJ3OscXAUuAzYBlwkzHG11OZTll3ALc7ZWU4ZYO9PZIMvCAi60Wka6CjQqim5n3S0k5CRGyQkZcHKSnhrpY6XN/9LuzeDf/4x4APnTDhQRITp7Nx40JaW/cHoXJKqcMhuoRyYM2dO9esWaNTHwdaS8sePvxwDBMn/ppx4263LRiTJsGrr4a7aupweb2Qm2tnbl22bMCH19cX8sknx5KaeiJHHvkWdrS6UipURGStMWZud/sisiVDqa7a+2OcBC0tUFKi04kPFrGxcP318Oab9u86QMnJM5k8+RGqq1ewY8d9QaigUupQaZChokJNzfu4XMNITp4NGzeCz6edPgeTG2+E+Hj47W8P6fDs7GvJyrqGnTsfoKJi4K0hSqng0CBDRYXa2vdJSTkWlysOVtul3pnbbeucikajRsGVV8LTT0NFxSEVMXnyH0hKmsnGjVfR3Px5YOunlDokGmSoiOfzNVBXt87eKgEbZIwYARMnhrdiKrBuvRWamuxIk0MQE5PI9OkvYoyHoqKL8Pka+z5IKRVUGmSoiFdb+xHg6xxkzJ2r04kPNjNn2uGsf/gDtLYeUhGJiflMnfp/1Nevp6RkEdqxXanw0iBDRbyqquVADGlpp9hfuoWFcMwx4a6WCobbbrPLvy9deshFjBz5VfLyfkZZ2bO6LLxSYaZBhop4VVXvkJp6PLGxKbB+ve30eeyx4a6WCoZzz4WCAnjooQGtztrVEUfcSWbmJWzbdicVFf8MYAWVUgOhQYaKaB5PJXV1a0hPP9smtHX61JaMwcnlgh/+ENatgzcOfT1CEaGg4CmSk4+iuPgS6urWBbCSSqn+0iBDRbTq6pWAYcSIs2zCqlWQk2M3NTh961swfjzcf/9htWbExCQxc+bruN0jKCz8Ks3Nu/o+SCkVUBpkqIhWVfUOMTHJpKQ4t0dWr9ZWjMEuLg7uvBM+/hjeeeewioqPz2HmzH/i89VRWHgBXm9tgCqplOoPDTJURKuqeofhw0/H5XJDdTVs3qxBxlBwzTUwZgw88MBhF5WcPJPp01+isXEjxcUL8Ps9AaigUqo/NMhQEaupaQdNTaXtt0rWrrWPGmQMfvHxcMcd8O9/w7/+ddjFpaefTX7+41RVvcWWLd/Toa1KhYgGGSpiVVXZpvIRI7p0+tSZPoeGRYtg9Gj48Y8Pq29Gm+zsaxk//h727n2Szz//RQAqqJTqiwYZKmJVVb1DXFw2iYlTbcLq1XaWz/T08FZMhcawYXD33bYl45+BGYaam3s/o0Zdwfbt/8X+/c8GpEylVM80yFARyRg/1dXLGTHiLKRtZk/t9Dn03HADTJ4M//mfdkn4w9Q2tDUt7TQ2bVpIZeVbAaikUqonGmSoiFRfvwGPp7y9P8aePbBrlwYZQ01cHPziF/DZZ/DUUwEp0uWKZ8aMv5GYOI2iooupqfkoIOUqpQ6mQYaKSJWVdrnuESPOtAnvvmsfTz01PBVS4XPxxXDSSXDvvVBfH5Ai3e7hzJq1jLi4bAoLz6e+vigg5SqlOtMgQ0Wk8vJXSEmZS3z8GJuwciWkpcHs2eGtmAo9EfjVr2D/fvjlLwNWbHx8Fkce+TYuVwIbNpxDU9P2gJWtlLI0yFARp7l5N3V1qxg58uvtiStX2laMmJjwVUyFz/HHw2WXwYMPQklJwIodNiyPWbPewu9vZsOGc2ht3R+wspVSGmSoCFRe/jcARo682Cbs2gVbt8JXvhLGWqmwe/hhO+LkxhsDMqS1TXLyDGbO/ActLXv49NNz8XiqA1a2UkOdBhkq4pSXv0JiYgFJSQU2oa0/hgYZQ1tWlr1d8u678PTTAS06Le0EZsx4mcbGzygq+ho+X0NAy1dqqNIgQ0UUj6eC6up/tbdigL1Vkp4Os2aFr2IqMixaBCefDD/4AZSVBbTo9PRzmTr1L9TUfEBh4YX4fI0BLV+poUiDDBVRKipeB3wHBxmnnWaXAVdDm8sFixfbUSY33RTQ2yYAo0ZdQkHBn6iuXklR0Xx8vqaAlq/UUKPf2iqiHDjwCvHxY0lJcaYO37HDbnqrRLWZOtUunPbii7BkScCLz8q6ioKCp6mqWk5R0UX4fM0BP4dSQ0XEBhkiMk9ESkSkVETu7GZ/vIg87+z/WERyO+y7y0kvEZFz+ypTRPKcMrY4ZcY56aeKyCci4hWRbwb3HSufr4GqqjcZOfLi9lk+V660jxpkqI5+9CM46yy45RY7UVeAZWVdzZQpT1FV9TbFxRdroKHUIYrIIENEYoBHgPOAacDlIjKtS7brgCpjzCTgYeBB59hpwGXAdGAe8EcRiemjzAeBh40xk4Eqp2yAz4FvA38NxvtUnVVWLsPvbz74VklmJkyfHr6KqcjjcsEzz0Bysh3a2hz4ICA7+9tMmfIklZXLKC7+Bn5/S8DPodRgF5FBBnAsUGqM2WaMaQWeA+Z3yTMf+JPz/EXgTLE/f+cDzxljWowx24FSp7xuy3SOOcMpA6fMiwCMMTuMMRsAf7DeqGpXVvY8bvdI0tJOsQnG2CDj9NPthExKdZSdbUeZFBbCzTcHvH+GPcW15OcvprLynxQVaaCh1EBFapAxBtjV4fVuJ63bPMYYL1ADZPRybE/pGUC1U0ZP5+qViFwvImtEZM2BAwcGcqhytLYeoLz8b4wefRUuV6xN3LABdu+Gc84Jb+VU5Dr/fLtS65Ildh6NIMjJ+Q75+Y9RWfkPp4+GjjpRqr8iNcjo7mdr158pPeUJVHq/GWMWG2PmGmPmZmZmDuRQ5di//y8Y4yEr67r2xJdfts3iF14YvoqpyHf//fCNb8APfwh//3tQTpGTc4Nz6+RNNmyYh9dbE5TzKDXYRGqQsRsY1+H1WGBPT3lEJBZIAyp7Oban9HJguFNGT+dSQWSMYe/eJ0lNPZ7k5BntO15+GU45BUaNCl/lVORr658xZw5cfjmsXx+U02RnX8e0ac9RW/sh69efQWurtloq1ZdIDTJWA5OdUR9x2I6cr3XJ8xqw0Hn+TWCFMcY46Zc5o0/ygMnAqp7KdI5Z6ZSBU+arQXxvqova2o9obPyscyvG5s1QVARf/3rPByrVJjERXnsNRoyAs88OyogTsPNozJjxKo2Nn7Fu3ck0NW0LynmUGiwiMshw+kfcDLwJbASWGmOKReR+EWlrO18CZIhIKXA7cKdzbDGwFPgMWAbcZIzx9VSmU9YdwO1OWRlO2YjIMSKyG1gAPC4ibflVAO3duwSXK4lRoy5tT3zlFft48cXdH6RUVzk5sGIFxMbCmWfaQDUIMjLO58gj38HjKeeTT06gtnZNUM6j1GAgJgg9soeyuXPnmjVr9Eunv7zeOj74IJtRoy6loKDDxErHHWdHC6xaFb7Kqei0caOdITYuzo5Omjw5KKdpbCxhw4Z5tLaWMX36UjIyLgjKeZSKdCKy1hgzt7t9EdmSoYaOsrLn8fsbyM5e1J64a5cNLvRWiToUU6fC8uXQ0gInnhi0QDUxcQqzZ39IYuJUCgu/xuef/wr90aZUZxpkqLAxxrBnzyMkJk4jNfX49h1/s0u9a5ChDtnMmfD++5CSYmeL/ec/g3Ka+PgsZs/+F5mZ32Tbth+xadNCnR1UqQ40yFBhU1HxD+rr1zNu3I/apxEHeOklmDED8vPDVzkV/fLz4cMPoaDADoP+7W+DMmFXTEwS06Y9T27uA+zf/2fWrz+V5uadAT+PUtFIgwwVFsYYdu68n4SEPEaPvrJ9x9at8N57sGBB+CqnBo/Ro+Hdd+GCC+DWW+GKK+wKrgEmIuTm3sP06a/Q2FjCmjWzKS8PzpwdSkWT2L6zKBV4lZVvUle3mvz8J3C53O07Hn0UYmJg0aKeD1ZqIFJS7GilBx+Ee+6xM8n+9a9w5JEBP1Vm5kUkJ39CcfECioouZNy4H5KX9zNcrriAn6vfmprg00/tsN6NG+2om337oKwMKirA57MtPC4XZGTYeWmys2HaNHvb6cgj7XOX/iZVA6ejSwJMR5f0zRjDunUn0tKyh+OO29L+BdzYCGPH2nkOnn8+vJVUg9Py5XDllVBZCT/+Mdxxhx3yGmA+XzNbt97Onj2Pkpx8FAUFf+480VwwVVfb1psVK+CDD2yA4XVWTYiPh0mTYMwYG0xkZIDb3VZpG3SUldnp/EtKwOOx+zIz7bDgc86B+fMhPT0070VFhd5Gl2hLhgq5qqrl1NZ+xOTJj3b+hffcc1BVBTfdFL7KqcHtzDOhuNj+G7vnHnj1VfjjH2Fut9+PhywmJoH8/D+Snn4uJSXfYe3ao5kw4eeMHXsrdkHoACspsR2mX30VPv4Y/H47Qdlxx9np1o87DmbNgvHjbUthf3g8ttVj9WobnC1fbj+jbrf9IXDFFXY694SEwL8fNWhoS0aAaUtG72wrxsm0tHzOcceV4nLFt+2Ao4+2X2wbNuiqqyr4li6FW26xv9yvuQZ+/nPbhyPAWlvLKCm5noqKV0lJOYb8/MWkpBx1eIX6/XZobltgsWmTTT/6aLto3FlnwfHH27lCAsUY+OQT28q4dCns3GlbNBYuhBtugClTAncuFVV6a8nQICPANMjo3d69SygpWUR+/hPk5HTod/Hhh3ZOg0cfhRtvDF8F1dBSWwsPPAC/+Y39Rf7978Ptt8PIkQE9jTGGsrJnKS29DY+ngrFjbyU39yfExib3v5CWFju5WFtgsW+fvdVz+ulw0UV2BM24cX0WExDG2Lo8/rjt7+Lx2ODm1lttgKM/EoYUDTJCSIOMnrW07GP16qkkJc3iqKNWItKhI9lVV9kVNL/4ApIH8MWrVCCUlMC998ILL0BSEnz3u3bLywvoaTyeSrZtu5O9e58gLi6LvLyfkZW1sOdbKFVVsGyZDSzeeAPq6mz9zjvPBhbnn2/Xawmn/fttsPHII7ZVaPp0G2xceSUMGxbeuqmQ0CAjhDTI6Flx8SWUl7/GMcd8SmJih6bVoiLbg/3WW+HXvw5fBZUqLoaf/tTeDjAG5s2D73zHPgbwP8yamo/YuvV2ams/JClpFhMmPEh6+rmI32/7QLz5pt3a+leMGmU7XF50EZxxRmT2g2hpsX02Hn7YdjYdOdK2Sn7ve3a0ihq0NMgIIQ0yulde/hpFRfPJy/sp48ff3XnnvHn2y7S01PZ2Vyrcdu+GJ56w2969tvXgggvsLYnTTrOjoA6TMYYD+55l2+Yf0Wz2kLI/ndwnWklfXm8np5s713425s2zHTf722Ez3IyBf/3LBht//7u9pXPZZXDbbTB7drhrp4JAg4wQ0iDjYK2tZaxZMwe3ewRHH72284iSZcts0+9DD9kvIaUiicdjh4O+9JLte1BWZtPz8uDYY+38EdOmQW6ubW0YNapzK4Pfbyf/qqmxtwI//9x2mCwuti14xcX4vc3sOxd2LoyhJdNHsmc8Y3JvZ9SE64mJicAWi4EoLYXf/Q6eegoaGuDUU+3n/Gtfi56gSfVJg4wQ0iCjM5+vmU8/PYP6+vXMnv1vUlKObt/p9drbJK2t9ks3kD3hlQo0n8+OfHrvPftLff162LHj4KnKXS77H2hMDDT3sI5JdradOn/GDNtKccIJ+MeMZn/ZX9i162EaG4txu0eSnb2I0aOvJilpatDfXlBVV8OSJfD739sga8IEO7LnmmsgNTXctVOHSYOMENIgo50xho0br6Ss7FmmTXuBUaO+2TnDY4/ZznUvvwwXXxyeSip1OBobbafR3bttK8f+/Taw8HrtlphoZxxNTYWcHDv644gjYPjwHos0xlBdvYLdu39HRcXrgJ/k5DmMHn0lGRlfIzExOEvXh4TXazux/uY37QvYLVhgb6d85StBmRhNBZ8GGSGkQUa7HTvuY8eOn5CX93PGj7+r885Nm2xz85w5diicDnlT6iAtLfsoK3uW/fv/TH39OgCGDZtMevr5pKWdTFraCcTHjwlzLQ/RqlV2IrSXX7ajZjIz7WiZCy6wM4umpYW7hqqfNMgIIQ0y7C+xzz//Bdu3/xdZWd9mypSnOq+yWl9vA4wDB+zkPqEa269UFGtq2kpFxRtUVv6D6up38fvtrZj4+HEkJc0gMbGAxMQC4uOPID4+m7i4LGJj0zuvDRSJmpvt8NwXXrB9tKqq7K2mOXNsH45TTrHPx47VHyMRSoOMEBrqQYbf72XLlu+xd+8TjBp1BQUF/9u5o6cxcPnl9gvlrbfsNM9KqQHx+1upr19HTc2H1NWtorFxI42NJfj9TQflFYkjJibZmV23u/+kDcb4MMYH+L58bowPkVhcrvgvNxH7GBubits9mri40cTFZXV4zGbYsMm43T3fDuqV12tHmi1bZvu+fPyxHRoLduTZUUfZbfZsO036pEk6F0cE0CAjhIZykOHxVLNx4+VUVi7jiCPuJi/vgc4tGAC/+AXcdZedwvmuu7ovSCk1YMb4aWnZRUvLF7S27qWlZS9ebzU+Xz0+Xz3GtPRydAwi7Vvba2O8+P0tGNOC39/iPG/F662mtXU/ra378XorDyrN7R5NYuKUDlsBiYnTSUgYf/B3Qm+am2HdOrutX28fCwvbAw8R28clP//gbSDrtKjDokFGCA3FIMMYw4EDL1JaegutrQfIz3+s85ThNpMNKh58EC691C61rUtHKxX1/P5WWlvL8Hj209y8i6amzTQ2ltDYWEJTUwkeT/mXeWNiUklKmkFS0kySk2eRlDSTpKSZA2v58HptZ9vCQtiyxT7fvNk+1ta254uLs0ONJ060o1k6Publ2U65KiA0yAihoRZkNDaWsnXrbVRUvE5y8hymTFnceZgq2LkGFi2CZ56xo0l+/3v9haHUEOHxVNDYuImGhiLq6wtpaCikoWEDXm/1l3lsv5KZnYKPxMQpnW+19sUY289r8+b2oGPrVti2zT52DEDADiOeMOHgAGTCBLtQnvb/6DcNMkJoqAQZNTUfsWvXrygvfxmXaxh5eQ8wZswtuFxdhqCtWWMDizVr7HTN//Vf+uFVaogzxtDS8gUNDRtoaCh0go8NNDZuwhgPACJuEhMLnOBjBgkJucTHjyMhYRxxcTkD69BqDFRWdg46Oj7u3t15vpPERHu7peOWm9v+PDtbW2I70CAjhAZzkNHYWEp5+UuUlb1Aff1aYmOHk5PzXcaM+T7x8V3WJigrg/vus6uqjh5tZ/1bsCA8FVdKRQW/v5XGxs0HBR8tLbu65HQRF5dFfPw44uIyiYlJIzZ2OLGxac42nJiYFFyuYcTEDMPlSsDlGvbl1jktAWlptZOEdQw+du5s3yoqOp/e7baj4roGH23buHE2zxARlUGGiMwDfgvEAE8aY37RZX888AxwNFABXGqM2eHsuwu4DvABtxhj3uytTBHJA54D0oFPgG8ZY1p7O0dPBkuQYYyf5uYd1NZ+SE3N/6O6+j0aGz8DICXlWEaPvpKsrGuIjU1pP8jns1MwL15sp2D2+eDmm+H++3XMu1LqkHm9dU6n1l00N+/68nlLyy48nkq83mpnq8F+7Q+MSHyvwUiMGYa7OQ53nYvYSi/ushbcX9Th3lGFe0sZ7q1lxNaCmC8LhDFjDg4+Om6DqE9I1AUZYrs3bwbOBnYDq4HLjTGfdcjzPWCWMeZGEbkMuNgYc6mITAOeBY4FcoB3gHznsG7LFJGlwMvGmOdE5DHgU2PMoz2do7e6R0uQ4fd78Xqr8HjK8XjKaG7e6WzbaGj4jMbGz/D56gHbWSst7URGjDibzMxvkJAw3jYt7t1rJ9X69FM7odZ779k1GtLTYeFCuP56KCgI8ztVSg0Vxhh8vgZ8vhq83lr8/mb8/ib8/iZ8vqZOr3tP65zu9dbi8VTg9VZgjLeHs7twmxTcnkTcjbHE1oK73IN7XxPuXXW4q/y4a2jf3BnEZuYi43PbA4+sLDspWduWkREVs6D2FmREau2PBUqNMdsAROQ5YD7wWYc884GfOM9fBP4gdmzUfOA5Y8drbReRUqc8uitTRDYCZwBXOHn+5JT7aE/nMCGKzGprV9HUtNUZs+6l6xj2nl77/c34fI34/Y2dHn2+GjyeCjyecrzeqm7PGReXTWLiVLKyriUpaTopKceSnDwT2fE5/OAO2Pc3O3Xynj12Uq02kybBJZfAWWfZlSojcSlE8CPNAAALMElEQVRqpdSgJiLExiYTG5sclJlQbRBT5/w4q+jwfVrRIa0cj6ecZk85dZ4KPJ5GjPF3U1oFmApimtcR0+gnphFiaiBmH8Q0tW8uE4/LFYfEJOCKjUdiExB3AhKbYNPFjbjciCsOccVATCzEupGYWBAX+PyMqBpPXHNi+3T3+flw9dUBvz7didQgYwzQ8SbcbuC4nvIYY7wiUgNkOOkfdTm27V9bd2VmANWmPTztmL+nc5R3KAcRuR643nlZLyIVXfNEj73OtmJgh5WW2u2JJ7rbO5KovR5BodejM70enen16GyQX4/uApCOWpytri0hMNdj4cLDLqKD8T3tiNQgo/tp6fqXp6f07roC95a/v/XAGLMYWPxlxUTW9NR0NBTp9ehMr0dnej060+vRmV6PzqLtekTqGJzdQMcFLcYCe3rKIyKxQBpQ2cuxPaWXA8OdMrqeq6dzKKWUUqoPkRpkrAYmi0ieiMQBlwGvdcnzGtDW3vNNYIXTV+I14DIRiXdGjUwGVvVUpnPMSqcMnDJf7eMcSimllOpDRN4ucfo/3Ay8iR1u+pQxplhE7gfWGGNeA5YAf3Y6dlZigwacfEuxnUS9wE3G9oqkuzKdU94BPCciPwXWOWXT0zn6YXHfWYYUvR6d6fXoTK9HZ3o9OtPr0VlUXY+IHMKqlFJKqegXqbdLlFJKKRXlNMhQSimlVFBokNEPIrJARIpFxC8ic7vsu0tESkWkRETO7ZA+z0krFZE7O6TnicjHIrJFRJ53OqHidFR93sn/sYjkhur9BVNP12EwEJGnRKRMRIo6pKWLyNvO3/dtERnhpIuI/M65DhtEZE6HYxY6+beIyMIO6UeLSKFzzO+cyeYikoiME5GVIrLR+az8h5M+VK9HgoisEpFPnetxn5M+4M//QL9jIpmIxIjIOhF53Xk9ZK+HiOxw/j2vF5E1Ttrg+7wYY3TrYwOmAlOAd4G5HdKnAZ8C8UAesBXbqTTGeT4BiHPyTHOOWQpc5jx/DPiu8/x7wGPO88uA58P9vgNw3Xq8DoNhA04F5gBFHdJ+CdzpPL8TeNB5fj7wBnbuleOBj530dGCb8zjCeT7C2bcKOME55g3gvHC/516uRTYwx3megp3Cf9oQvh4CJDvP3cDHzvsc0Of/UL5jInkDbgf+CrzuvB6y1wPYAYzskjboPi/aktEPxpiNxpiSbnZ9OYW5MWY70DaF+ZfTohtjWrGLr813IskzsFOUg53C/KIOZf3Jef4icGYk/1Lrp26vQ5jrFDDGmPc4eN6Ujn/Hrn/fZ4z1EXZulmzgXOBtY0ylMaYKeBuY5+xLNcZ8aOw3xjMdyoo4xpi9xphPnOd1wEbsjLlD9XoYY0zbvPtuZzMM/PM/oO+YIL+twyIiY4ELgCed14fyfThorkcPBt3nRYOMw9Pd9Odjeknv9xTmQNsU5tGsp+swmI02xuwF+x8vMMpJH+i/lTHO867pEc9p2p6N/fU+ZK+Hc2tgPVCG/fLfysA//wO9TpHsN8B/0j6P9qF8Hw6m62GAt0RkrdilKWAQfl4icp6McBCRd4CsbnbdbYx5tZt0CMMU5lFmML6nQzXQafCj8tqJSDLwEnCrMaa2l8a4QX89jJ2f5ygRGQ68gr3telA25zFQyyREJBH5KlBmjFkrIqe3JXeTdUhcD8dJxpg9IjIKeFtENvWSN2o/LxpkOIwxZx3CYb1Nf97rFOZOdN7dFOa7ZfBMYd6f6eEHm/0ikm2M2es0WZY56b1Nd396l/R3nfSx3eSPWCLixgYY/2eMedlJHrLXo40xplpE3sXeSx/o53+g3zGR6iTgQhE5H0gAUrEtG0P1emCM2eM8lonIK9hbPoPu86K3Sw6PTmHeu/5MDz/YdPw7dv37Xu30Ej8eqHGaQ98EzhGREU5P8nOAN519dSJyvHMv+uoOZUUcp45LgI3GmIc67Bqq1yPTacFARIYBZ2H7qQz08z+g75jgv7NDY4y5yxgz1hiTi63rCmPMlQzR6yEiSSKS0vYc+++8iMH4eQlVD9No3oCLsZFhC7Df+SO27bsbe6+1hA69d7G9gTc7++7ukD4B+6EoBV4A4p30BOd1qbN/Qrjfd4CuXbfXYTBswLPAXsDj/Pu4DnvfeDmwxXlMd/IK8IhzHQrpPErpWufvXgpc0yF9LvaLZyvwB5wZeiNxA07GNsduANY72/lD+HrMwi5RsMGp871O+oA//wP9jon0DfvLu210yZC8Hs77/tTZitvqOxg/LzqtuFJKKaWCQm+XKKWUUiooNMhQSimlVFBokKGUUkqpoNAgQymllFJBoUGGUkoppYJCgwyllOpARPR7UakA0Q+TUmrIa1uM0Jlt0d9XfqVU/+g8GUop5RCRJUASdobFF41d0VMpdYi0JUMpNeSJiFtEfoxdY2MY8AGQGN5aKRX9dIE0pdSQISJium++zQTOA04AvmmM2RHSiik1SOntEqXUoNbWkbOvvhYisg/4CXA24AP+D1hrjNkd7DoqNVjp7RKl1KAjIhkicjnY4KItwBCR00XkPBFJdl6LiMQ4h80D4rCLcyUCpwAPhr72Sg0e2pKhlBp0RCQfOAK7kmUScBqwAJgINACfG2Ou7+n2iYjcAFQAJ2JXUK0PWeWVGkS0T4ZSatAxxmwWkUTs8t9rgZuAOmPMKSKSBfxbRLKMMfs6Hici44As7C2TE4A7NMBQ6tDp7RKlVFTqcJuju32xwDHAjU4g8f+AMhFJdV6XYAOQrvKw/TK2AH82xvwl4BVXagjRIEMpFZWMMT4AEZktIsO67PNiAwuviEwBVgFeoMDJ8hLw9W7KfM8Yc4Ex5i5gpYgkBfM9KDXYaZChlIpoTufMg76rRGSRiPwb+G/g1yJynJPe1sKxB9gEzAc+Agww1dn3AjBeRMb2cuq3jTENAXobSg1JGmQopSKOiMxvm+rbWH4RGSEiV4jIEU62EcBVxph5wFzgB05+n7O/Fvg3tm9FA1AFTBWREU4/i6N7G56q04srdfi046dSKmKISKxzq2MasAKoExE3cBdwFfAe8J6InARcDpzkdNZ8H3ikY1nGGCMiW7AzeM4GngSajDHVIuIyxrQ6jxpMKBUkOoRVKRV2Xf+zF5HhwHnGmGdFZBrwO+DsjsNNRWQ/8H1jzNIOaZnGmAMiEmOM8TkBSroxZn8I345SyqG3S5RSISUiWSLyAxF5XUS+IyLDndshR4jINSLyV+wcF0+KSBp2cqxWINU5vq2T5zLgNBGZKSKnishSnM6cbbdMjDEeDTCUCh8NMpRSISMi52M7ZCYBzwBnAreJSA52UbIpwH8bYzYAHwPnAPFAETAdwBjT5BT3Q2AD8BBwD/A28KeQvRmlVJ+0T4ZSKpT+BdQbY+4HEBE/cAEgQCm2K0Whk/c54EpnOxn4pYh8Cztz5yTgFmPM4yLynDGmJsTvQynVD9qSoZQKGWdI6FoRuclJSrDJ5gvsgmRzOmT/C7YD6EjgV8DLwGPYAOMRY0yz0/eipqdhrkqp8NKOn0qpkBKRS7BBwxPAhcBiY8wTIjIa+Cd2qfXtTt4VwDvGmJ/3sky7UipCaZChlAo5EakEngZ+Zoyp6JD+Z2CPMeYO5/U4oLxDP4y2pduNBhxKRT7tk6GUCoe3gApjTIWIxAOtTtDwFHb9EACMMbu6HqjzWigVPbQlQykVciJyIrDcGDOsz8xKqailHaWUUiFnjPkAeF5ERnTd1zaduFIq+mlLhlJKKaWCQlsylFJho60WSg1u2pKhlFJKqaDQlgyllFJKBYUGGUoppZQKCg0ylFJKKRUUGmQopZRSKig0yFBKKaVUUPx/+zUyBj+JmsUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution plot\n",
    "plt.figure(figsize=(8, 5))\n",
    "\n",
    "ax1 = sns.distplot(df['price'], hist=False, color='r', label='Actual Value')\n",
    "ax2 = sns.distplot(yhat, hist=False, color='y', label=\"Fitted Value\", ax=ax1)\n",
    "\n",
    "plt.title('Comparison of Actual and Fitted Value for Price')\n",
    "plt.xlabel('Price in $', rotation=20)\n",
    "plt.ylabel('Proportion of Cars', rotation=70)\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<결론> 상당히 유사한 결과가 얻어졌지만 아직 더 개선될 가능성이 있음 -->  non-linear 방법으로 넘어가보기!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Polynomial Regression - numpy\n",
    "General linear regression의 special case (<b>non-linear</b>) - Linear regression이 정확하지 않는 경우 고려  -->  Curvilinear relationship에서 유용함\n",
    "* Quadratic-2nd order : y = b + a1x1 + a2x1^2\n",
    "* Cubic-3rd order : y = b + a1x1 + a2x1^2 + a3x1^3\n",
    "* Higher order : y = b + a1x1 + a2x1^2 + ... + anx1^n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<색깔 참고>\n",
    "``'b'``          blue\n",
    "``'g'``          green\n",
    "``'r'``          red\n",
    "``'c'``          cyan\n",
    "``'m'``          magenta\n",
    "``'y'``          yellow\n",
    "``'k'``          black\n",
    "``'w'``          white"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data plotting을 위한 function 정의\n",
    "def PlotPolly(model, independent_variable, dependent_variable, Name) :\n",
    "   # 예측값 설정\n",
    "#     x_new = np.linspace(15, 55, 100)    # 15~55까지 99조각으로 나눔\n",
    "    y_new = model(independent_variable)\n",
    "    \n",
    "    # line graph & Marker plot\n",
    "    # 아래 plot argument 중 line 속성을 지정하는 format=[marker][line][color]\n",
    "    # 실제값은 dot marker로, 예측값은 기본 line으로 설정\n",
    "    plt.plot(independent_variable, dependent_variable, '*r', independent_variable, y_new, ':b')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Highway-mpg')\n",
    "    ax = plt.gca()    # Get the Current Axes\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()   # Get the Current Figure\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "    \n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 변수 설정 - 1차원으로 설정해야\n",
    "x = df['highway-mpg']   \n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    }
   ],
   "source": [
    "# fit the model (cubic-3rd order)\n",
    "f = np.polyfit(x, y, 3)  # x^3, x^2, x, intercept 순으로 반환함\n",
    "p = np.poly1d(f)     \n",
    "print(p)       # 공식으로 바꿔줌! print 꼭 붙여야 함"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 정의한 PlotPolly를 이용해서 그래프 그리기\n",
    "PlotPolly(p, x, y, 'Highway-mpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<결론> linear model 보다 더 정확한 것을 볼 수 있다. 3차 이상으로 degree를 높일수록 더 정확해지는 것을 확인할 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial Regression with Multi-demension - scikit-learn\n",
    "x1, x2,... multivariable이 들어간 고차 방정식  -->  numpy로는 계산 안됨!\n",
    "\n",
    "Dimension이 커질수록, 각 variable을 standardization하는 것이 필요  -->  skikit-learn의 preprocessing 이용!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-06T00:35:07.296276Z",
     "start_time": "2021-07-06T00:34:59.088343Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'df' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-968692d91fa0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# StandardScaler 사용해보기\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'horsepower'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'curb-weight'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'engine-size'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'highway-mpg'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mscaler\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mStandardScaler\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m   \u001b[1;31m# 아래 순서 맞춰서 진행해야 함!\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mscaler\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mscaler\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmean_\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'df' is not defined"
     ]
    }
   ],
   "source": [
    "# StandardScaler 사용해보기 - feature(컬럼)별로 정규화\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "scaler = StandardScaler()   # 아래 순서 맞춰서 진행해야 함!\n",
    "scaler.fit(x)\n",
    "scaler.mean_\n",
    "scaler.transform(x)         # fit_transform(x)로 한번에 가능"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-06T00:35:08.302583Z",
     "start_time": "2021-07-06T00:35:07.300264Z"
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'df' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-f6864df45ae8>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# 2nd order인 polynomial regression 모델 만들기\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mpr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mPolynomialFeatures\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdegree\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m   \u001b[1;31m# 변수 개수는 지정 안함\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'horsepower'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'curb-weight'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'engine-size'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'highway-mpg'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[0mpr_t\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit_transform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m     \u001b[1;31m# 변수 개수에 맞게 fit, transformation 한번에\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mpr_t\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m         \u001b[1;31m# 계수가 구해지는 것이 아니라 [a,b]의 [1, a, b, a^2, ab, b^2]가 얻어짐\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'df' is not defined"
     ]
    }
   ],
   "source": [
    "# 2nd order인 polynomial regression 모델 만들기 \n",
    "pr = PolynomialFeatures(degree=2)   # 변수 개수는 지정 안함\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "pr_t = pr.fit_transform(x)     # 변수 개수에 맞게 fit, transformation 한번에\n",
    "pr_t.shape         # 계수가 구해지는 것이 아니라 [x1, x2]의 [1, x1, x2, x1^2, x1x2, x2^2]가 얻어짐 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b><중요></b> y = p + bx1 + cx2 + dx1^2 + ex1x2 + fx2^2의 polynomial regression에서 실제 [x1, x2] 값에 대한 [1, x1, x2, x1^2, x1x2, x2^2] 값을 안다면, y = k + bx1 + cx2 + dx3 + ex4 + fx5의 multiple linear regression의 식에 대입하는 것과 같음!! \n",
    "    \n",
    "다만, [1, a, b, a^2, ab, b^2]에서 1을 버리고<b> (include_bias=False)</b> linear regression에 대입하면 됨!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'x' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-5c417a9352a2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Polynomial regression의 fit, transformation 따로 해보기\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mfit\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m   \u001b[1;31m# 4개 변수 인식\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mtrs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtransform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mtrs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m     \u001b[1;31m# fit_transform과 같은 결과\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'x' is not defined"
     ]
    }
   ],
   "source": [
    "# Polynomial regression의 fit, transformation 따로 해보기\n",
    "fit = pr.fit(x)   # 4개 변수 인식\n",
    "trs = pr.transform(x)\n",
    "trs.shape         # fit_transform과 같은 결과"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((201, 4), (201, 15))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# x -> pr_t으로 transformation 이후 형태변화\n",
    "x.shape, pr_t.shape      # 열마다 별개의 결과를 만들어냄 --> 총 201개 생성"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pipeline - Scikit-learn\n",
    "Standardization(Z-score 변환) & Polynomial transformation & Linear regression을 더 쉽게 할 수 있음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pipeline은 list of tuple로 만들어짐 - bias 포함 안하도록 설정 \n",
    "Input = [('scaler', StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model', LinearRegression())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pl = Pipeline(Input)\n",
    "pl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 각 단계를 fit and transform한다\n",
    "pl.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 예측하기\n",
    "y_pl = pl.predict(x)\n",
    "y_pl[0:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    13495.0\n",
       "1    16500.0\n",
       "2    16500.0\n",
       "3    13950.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 예측값을 실제 데이터와 비교\n",
    "y[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Measures for In-sample Evaluation\n",
    "시각화가 아닌 숫자로 모델을 평가하는 법"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mean Squared Error (MSE) - scikit-learn\n",
    "* 공식) MSE = (실제값 - 예측값)^2 / 개수"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## R-squared ; Coefficient of Determination - scikit-learn\n",
    "* 공식) R^2 = 1 - (MSE of regression line)/(MSE of the average of the data)  -->  보통 0~1 사이, (-)이면 overfitting 때문\n",
    "\n",
    "    ==> <b> R^2는 클수록 좋고, 0.1이상이면 괜찮음! </b>\n",
    "* 의미 : 실제 data가 얼마나 regression line에 가까운가?\n",
    "      \"Target variable의 R^2%의 variance가 해당 simple linear regression으로 설명된다\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4965911884339176"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1. Simple Linear Regression의 R^2 - score\n",
    "lm.fit(df[['highway-mpg']], df[['price']])\n",
    "lm.score(df[['highway-mpg']], df[['price']])   # fit해야 구해짐\n",
    "# 49.6% of variation of price는 해당 simple linear model로 설명이 된다.\n",
    "\n",
    "r2_score(y, lm.predict(df[['highway-mpg']]))  # 아래서 배울 식으로도 구해짐"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2. SLR의 MSE \n",
    "yhat = lm.predict(df[['highway-mpg']])\n",
    "mse = mean_squared_error(df['price'], yhat)\n",
    "print('Mean squared error of real price and predicted value is:', mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3. MLR의 R^2\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "lm.fit(x, df[['price']])\n",
    "lm.score(x, df[['price']])\n",
    "\n",
    "r2_score(y, lm.predict(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 4. MLR의 MSE\n",
    "y_ml = lm.predict(x)\n",
    "mse = mean_squared_error(df['price'], y_ml)\n",
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 5. Polynomial의 R^2\n",
    "from sklearn.metrics import r2_score\n",
    "x = df['highway-mpg']\n",
    "y = df['price']\n",
    "f = np.polyfit(x, y, 3)    # 계수 구해짐\n",
    "p = np.poly1d(f)           # 3차식 모델로 만듦\n",
    "r2 = r2_score(y, p(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 6. Polynomial의 MSE\n",
    "mean_squared_error(y, p(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8463341969864728"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 7. Multivariate Polynomial Regression의 R^2\n",
    "x = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "r2 = r2_score(y, pl.predict(x))\n",
    "# 또는 linear regression이라는 점을 이용\n",
    "lm1.fit(pr_t, y)\n",
    "lm1.score(pr_t, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 8. Mutivariate Polynomial Regression\n",
    "mse = mean_squared_error(y, pl.predict(x))\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction and Decision Making\n",
    "## Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 만들어진 모델로 예측할 값\n",
    "new_input = np.arange(1, 100, 1).reshape(-1, 1)\n",
    "new_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df[['highway-mpg']]\n",
    "y = df[['price']]\n",
    "lm.fit(x, y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 아예 새로운 x값을 넣어서 y를 구함\n",
    "yhat = lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 예측하는 그래프를 그리기\n",
    "plt.plot(new_input, yhat, '-.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Making : Determining a Good Model Fit\n",
    "R_squred 값이 크고, MSE 값이 작게 나오는 model이 better fit for the data\n",
    "\n",
    "<b>Simple Linear Regression</b> : Using Highway-mpg as a Predictor Variable of Price.\n",
    "* R-squared: 0.49659118843391759\n",
    "* MSE: 3.16 x10^7\n",
    "\n",
    "<b>Multiple Linear Regression</b> : Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "* R-squared: 0.80896354913783497\n",
    "* MSE: 1.2 x10^7\n",
    "\n",
    "<b>Polynomial Regression</b> : Using Highway-mpg as a Predictor Variable of Price.\n",
    "* R-squared: 0.6741946663906514\n",
    "* MSE: 2.05 x 10^7\n",
    "\n",
    "<b>Multivariate Polynomial Regression</b> : Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "* R-squared: 0.8463341969864728\n",
    "* MSE: 9.7 x 10^6 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>1) Simple Linear Regression vs Multiple Linear Regression</b>\n",
    "\n",
    "MSE가 작고 R squared가 큰 MLR가 더 적합한 모델\n",
    "\n",
    "highway-mpg 하나보다 다른 variable을 추가할 때 더 정확하게 예측함\n",
    "\n",
    "<b>2) SLR vs Polynomial Regression</b>\n",
    "    \n",
    "MSE가 작고 R squared가 큰 Polynomial Fit이 더 적합한 모델\n",
    "\n",
    "highway-mpg 한 변수 기준으로는, SLR보다 polynomial이 더 정확하게 예측함\n",
    "\n",
    "<b>3) MLR vs Polynomial Regression</b>\n",
    "    \n",
    "MSE가 작고 R squared가 큰 MLR이 더 적합한 모델\n",
    "\n",
    "highway-mpg 기준으로 polynomial을 만드는 것보다 다른 variable을 추가하는 것이 더 정확하게 예측함\n",
    "\n",
    "<b><결론> MLR이 가장 적합한 모델, 그러나 multivariate polynomial까지 고려하면 후자가 가장 적합함!</b>\n"
   ]
  }
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