Lec072-075.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 線形回帰（教師有り学習）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "ここから始まるレクチャーでは、線形回帰について学びます。\n",
    "scikit-learnを使って、線形回帰のモデルを作り、新しいデータを使った予測を試みます。\n",
    "サンプルデータは、アメリカ大都市の住宅価格です。初めは、1つだけの変数を使った単回帰をやってみます。\n",
    "\n",
    "線形回帰の数学的な背景に興味がある場合は、以下のサイトが参考になります。\n",
    "- [wikipedia（日本語）](https://ja.wikipedia.org/wiki/%E7%B7%9A%E5%BD%A2%E5%9B%9E%E5%B8%B0)\n",
    "- [wikipedia（英語）](http://en.wikipedia.org/wiki/Linear_regression) \n",
    "- Andrew Ngの動画（英語）もあります [youtube](https://www.youtube.com/watch?v=5u4G23_OohI).\n",
    "\n",
    "4回に分かれているレクチャーの概要です。\n",
    "\n",
    "    Step 1: データの準備\n",
    "    Step 2: ひとまず可視化\n",
    "    Step 3: 最小二乗法の数学的な背景\n",
    "    Step 4: NumPyを使った単回帰\n",
    "    Step 5: 誤差について\n",
    "    Step 6: scikit-learnを使った重回帰分析\n",
    "    Step 7: 学習（Training）と検証（Validation）\n",
    "    Step 8: 価格の予測\n",
    "    Step 9: 残差プロット"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 1: データの準備"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "scikit-learnに用意されているサンプルデータを使います。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import Series, DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_california_housing\n",
    "\n",
    "# 住宅価格サンプルデータのロード\n",
    "housing = fetch_california_housing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _california_housing_dataset:\n",
      "\n",
      "California Housing dataset\n",
      "--------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 20640\n",
      "\n",
      "    :Number of Attributes: 8 numeric, predictive attributes and the target\n",
      "\n",
      "    :Attribute Information:\n",
      "        - MedInc        median income in block group\n",
      "        - HouseAge      median house age in block group\n",
      "        - AveRooms      average number of rooms per household\n",
      "        - AveBedrms     average number of bedrooms per household\n",
      "        - Population    block group population\n",
      "        - AveOccup      average number of household members\n",
      "        - Latitude      block group latitude\n",
      "        - Longitude     block group longitude\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "This dataset was obtained from the StatLib repository.\n",
      "https://www.dcc.fc.up.pt/~ltorgo/Regression/cal_housing.html\n",
      "\n",
      "The target variable is the median house value for California districts,\n",
      "expressed in hundreds of thousands of dollars ($100,000).\n",
      "\n",
      "This dataset was derived from the 1990 U.S. census, using one row per census\n",
      "block group. A block group is the smallest geographical unit for which the U.S.\n",
      "Census Bureau publishes sample data (a block group typically has a population\n",
      "of 600 to 3,000 people).\n",
      "\n",
      "A household is a group of people residing within a home. Since the average\n",
      "number of rooms and bedrooms in this dataset are provided per household, these\n",
      "columns may take surprisingly large values for block groups with few households\n",
      "and many empty houses, such as vacation resorts.\n",
      "\n",
      "It can be downloaded/loaded using the\n",
      ":func:`sklearn.datasets.fetch_california_housing` function.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "    - Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions,\n",
      "      Statistics and Probability Letters, 33 (1997) 291-297\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Descriptionは説明です。\n",
    "print(housing.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 2: ひとまず可視化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of houses')"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 価格のヒストグラムです。 (これがモデルを作って、最終的に予測したい値です。）\n",
    "\n",
    "plt.hist(housing.target, bins=50)\n",
    "\n",
    "plt.xlabel('Price in $100,000s')\n",
    "plt.ylabel('Number of houses')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "tags": []
   },
   "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>MedInc</th>\n",
       "      <th>HouseAge</th>\n",
       "      <th>AveRooms</th>\n",
       "      <th>AveBedrms</th>\n",
       "      <th>Population</th>\n",
       "      <th>AveOccup</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.3252</td>\n",
       "      <td>41.0</td>\n",
       "      <td>6.984127</td>\n",
       "      <td>1.023810</td>\n",
       "      <td>322.0</td>\n",
       "      <td>2.555556</td>\n",
       "      <td>37.88</td>\n",
       "      <td>-122.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.3014</td>\n",
       "      <td>21.0</td>\n",
       "      <td>6.238137</td>\n",
       "      <td>0.971880</td>\n",
       "      <td>2401.0</td>\n",
       "      <td>2.109842</td>\n",
       "      <td>37.86</td>\n",
       "      <td>-122.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.2574</td>\n",
       "      <td>52.0</td>\n",
       "      <td>8.288136</td>\n",
       "      <td>1.073446</td>\n",
       "      <td>496.0</td>\n",
       "      <td>2.802260</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.6431</td>\n",
       "      <td>52.0</td>\n",
       "      <td>5.817352</td>\n",
       "      <td>1.073059</td>\n",
       "      <td>558.0</td>\n",
       "      <td>2.547945</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.8462</td>\n",
       "      <td>52.0</td>\n",
       "      <td>6.281853</td>\n",
       "      <td>1.081081</td>\n",
       "      <td>565.0</td>\n",
       "      <td>2.181467</td>\n",
       "      <td>37.85</td>\n",
       "      <td>-122.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   MedInc  HouseAge  AveRooms  AveBedrms  Population  AveOccup  Latitude   \n",
       "0  8.3252      41.0  6.984127   1.023810       322.0  2.555556     37.88  \\\n",
       "1  8.3014      21.0  6.238137   0.971880      2401.0  2.109842     37.86   \n",
       "2  7.2574      52.0  8.288136   1.073446       496.0  2.802260     37.85   \n",
       "3  5.6431      52.0  5.817352   1.073059       558.0  2.547945     37.85   \n",
       "4  3.8462      52.0  6.281853   1.081081       565.0  2.181467     37.85   \n",
       "\n",
       "   Longitude  \n",
       "0    -122.23  \n",
       "1    -122.22  \n",
       "2    -122.24  \n",
       "3    -122.25  \n",
       "4    -122.25  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DataFrameを作ります。\n",
    "housing_df = DataFrame(housing.data)\n",
    "\n",
    "# 列名をつけます。\n",
    "housing_df.columns = housing.feature_names\n",
    "\n",
    "housing_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20640, 8)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "housing_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# DataFrameに新しい列を作って、目的変数（価格）を格納しておきます。\n",
    "\n",
    "housing_df['Price'] = housing.target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "今度は散布図を描いてみます。年収と価格の関係を見てみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Median Income')"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(housing_df['MedInc'], housing_df['Price'])\n",
    "\n",
    "plt.ylabel('Price in $100,000s')\n",
    "plt.xlabel('Median Income')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x14ead1f10>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lmplotを使って、回帰直線を引きます。\n",
    "\n",
    "sns.lmplot(housing_df, x='MedInc', y='Price')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここまでLec72"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 3: 最小二乗法の数学的な背景"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "回帰直線の係数を求めるのに使われる、「最小二乗法」について、すこし数学的になりますが、その背景を説明します。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "回帰直線は、データ全体にうまく適合するように、描かれています。各点から、回帰直線への距離をDとしてみましょう。このDを最小にすれば良いわけです。このイメージを図にしてみます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# wikipediaから拝借します。\n",
    "from IPython.display import Image\n",
    "url = 'http://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Linear_least_squares_example2.svg/220px-Linear_least_squares_example2.svg.png'\n",
    "Image(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "各点（赤）の座標は、(x, y)です。ここから、回帰直線（青線）への距離をDとすると、以下の値を最小にする直線が一番よさそうです。\n",
    "\n",
    "$$ d = D_{1}^2 + D_{2}^2 + D_{3}^2 + D_{4}^2 + ....+ D_{N}^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "直線の式は、\n",
    "\n",
    "$$y=ax+b$$\n",
    "\n",
    "で表現されます。いま、$a$と$b$を求めたいのですが、これはdを最小にする$a$と$b$を見つけ出すという問題と同じです。\n",
    "\n",
    "この問題はもちろん、手で計算することで解くことができますが、ここではこの計算をNumpyやscikit-leranにお任せします。\n",
    "もし数学的な計算方法に興味がある方は、[こちら](http://mathtrain.jp/seikiequ)が大変参考になります。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 4: Numpyを使った単回帰"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Numpyは線形代数のライブラリの一部に、最小二乗法を解く関数を持っています。\n",
    "まずはこれを使って、単回帰(説明変数が1つ）をやってみます。その後、scikit-learnを使って、重回帰（説明変数が複数）に進んで行きましょう。\n",
    "\n",
    "入力として、2つのarray（XとY）を用意します。\n",
    "\n",
    "Yは目的変数なので1次元のarrayですが、Xは2次元のarrayで、行がサンプル、列が説明変数です。単回帰の場合は、列が1つになりますですので、そのshapeは、(20640,1)です。これを作るには、いくつか方法がありますが、ここでは、vstackを使ってみます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20640,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0        8.3252\n",
       "1        8.3014\n",
       "2        7.2574\n",
       "3        5.6431\n",
       "4        3.8462\n",
       "          ...  \n",
       "20635    1.5603\n",
       "20636    2.5568\n",
       "20637    1.7000\n",
       "20638    1.8672\n",
       "20639    2.3886\n",
       "Name: MedInc, Length: 20640, dtype: float64"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 年収\n",
    "X = housing_df['MedInc']\n",
    "print(X.shape)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20640, 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[8.3252],\n",
       "       [8.3014],\n",
       "       [7.2574],\n",
       "       ...,\n",
       "       [1.7   ],\n",
       "       [1.8672],\n",
       "       [2.3886]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# これを2次元のarrayにします。\n",
    "X = np.vstack(X)\n",
    "print(X.shape)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        4.526\n",
       "1        3.585\n",
       "2        3.521\n",
       "3        3.413\n",
       "4        3.422\n",
       "         ...  \n",
       "20635    0.781\n",
       "20636    0.771\n",
       "20637    0.923\n",
       "20638    0.847\n",
       "20639    0.894\n",
       "Name: Price, Length: 20640, dtype: float64"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = housing_df['Price']\n",
    "Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "numpyで単回帰をするには、ここから、少しだけ工夫が必要です。\n",
    "\n",
    "直線の式は、\n",
    "$$y=ax+b$$\n",
    "これは、次のように書き直すことができます。\n",
    "$$y=Ap$$\n",
    "ただし:\n",
    "$$A = \\begin{bmatrix}x & 1\\end{bmatrix}$$\n",
    "\n",
    "$$p= \\begin{bmatrix}a \\\\b\\end{bmatrix}$$\n",
    "\n",
    "Aとpはベクトルで、これらの内積で直線の式を表現しただけです。\n",
    "データをこの形式に変更する必要があるので、次のようなコードを実行します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.3252, 1.    ],\n",
       "       [8.3014, 1.    ],\n",
       "       [7.2574, 1.    ],\n",
       "       ...,\n",
       "       [1.7   , 1.    ],\n",
       "       [1.8672, 1.    ],\n",
       "       [2.3886, 1.    ]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Xを[X 1]の形にします。\n",
    "X = np.array([[value[0], 1] for value in X])\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/k5/g89wjxz9235346v2wbtwbqdm0000gn/T/ipykernel_50116/1563434560.py:3: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  a, b = np.linalg.lstsq(X, Y)[0]\n"
     ]
    }
   ],
   "source": [
    "# 最小二乗法の計算を実行します。\n",
    "\n",
    "a, b = np.linalg.lstsq(X, Y)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x14ec92250>]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zQ/MgX5y4WojqOgYMc/v3X6ODQgmoVAoooYASDPzUXvDzUaKwog61dVpodfrzZ3+3ai8lvFVKlNdoUadjoFQoEBHgjQCNN6pqdaioqYPGW4Umvt5oHe6P5iF+CPXzQeGtGqRdLcDpayUor2uoX5BGhbhmgegdG4xdqbnI/H6X0fmy/14KJaBQ6OtZ0WgfCgBqFdBE4wWFQgEGDOrqdKipY1BZp7/mGtOogGA/b9yqqkV5LaBUAH4+SgzwvoXls//N2Xbe2P9ge4cBCPhwP3y9VSiqqkWQxhsPdmmOuOZBOHq5EDoGCNR44VxuGcqrtQj190J23i38nVcBBYB2kf6ICfdHwa0a5JZWo2mQGkmxYXgiKQbHsgux5fgVnLuWjzvPp6FTsyCUVNbhWlEFLuXfQnlVHQI03ujTNhQhvj44eLEARRU1qNXqEBGgRmyEP+6Li0JhRS3yy6pRWFGN3OIqRAX5ItTfG6H+ahRX1CDY1xt5ZdU4cDEfJZW1iAzwhr/GB1W1WjQN1KBryxBEBWmg0zJIycrH9eIqNA/xRdc7QrD5yGVcLaqEv1qFbi1DkV9WDR3DoKC8Gr4+XugZE4K46CDk36pG/q0aFFfWQAGgT+tw9IwNxdHswvpnSe/YMCgVCuSXVyPc3xvejOHdrIHhM+vRni3xzdErnGeYSqkwen6Zeu40fub8diobP2UU1382bUBzvDo80Ww9HEXBMBbO3oSVK1fi5MmTSE5Ori9Tq9UIDAy0+D2tVou0tDQkJiZCpVLx/sySBT9n4LMDWfU3bkB/Id3bMRLp/5Qip6SqvjzYzxs1dTpU1HDveMF+3lg4JgHD4qPN7tPS9qxd6TmYvz2Dc0yhOrcIxLap/UXZFyGEvPX7WrxwZCunrOP0Laj00UhUI/dg6iWosTBfJZIf7IzhnZtzyq09XwD9C5Svt4rzrIoO0mDu/XGc5w7f50T2whEWP+dDyDNacFDx+uuvo1mzZnj11VdFq5QtQcWCnzPw6f4sQXWwZNUT3XDiShHvfa56olv9P/Cu9BxMXp9q8Y+Mr1ZhvrhSUCnKvgghnim0ogSp/3ucUzb/3on4osdoiWrkeRQAVjZ6TtjzzGLbKNj9CX3m2BtYCHlGCx5TkZmZiZiYGFvrJoqaOh0+OyBeQAEA87adwWoB/+Dzt2dAq2Og1TGYvz1DtCDgMgUUhBA7TDj6k1FA0fWlDRRQSIB9Ttj7zGKfCfO3Z6CmTif4mfPhz2k2H1soQWMqGIZBVlYW/vzzT3z66afQarUYNmwYpk2bBh8fH1770GoNe3cbykx9ZspXf1luPrJFbmm1oO1zSqpwKDOv/v8TQoiUfGuqcHbpw5yyVb0fwsKBz0hUI8/GoOE5kZFTavczi93fV39dEvzM+WT/P3h5aILNx+b7bAYEBhXXr19HZWUlfHx88NFHH+HatWt45513UFVVhbfffpvXPk6fPm3TZ40dP1/CaztHO5r+t9RVIIQQ3J+xD//bvphT1u/5NbgWHCVRjQjraPrfOJdfI9r+jp+/YtP30tLSRKuDJYKCiubNm+Pw4cMICgqCQqFAx44dodPp8MYbb2DmzJm8xkMkJCSYHFNx+vRpk5+Z0r08C7syzwupukP0jL9T/38OH5W2IoQQj+SlrUPKyqcRUV5cX7at4wBMG/WmdJUiHD3j74R/Tqloz6zu7VvatK9EOzKlss9oPgSPqQgODoaiUda1Nm3aoLq6GiUl/FoPVCqVyf8sfWb431N3tYaZWZ02iwpUQ8guo4M0SGoTgaQ2EYgO0gj6LiGE2Ouu7DRcXPIAJ6AY/vQnFFC4CAUanhNiPLPY/T11V2vBz5xpA5rzfr5aekbzISioOHDgAHr37o3Kysr6srNnzyI4OBihoaFCdmUXHy8lJvYXd/W8eaM6YdIA/vuce38cVEoFVEoF5t4fBwCiBBatwnwpQCGEmMcw+OHr17Dxm4Yu5+PNOiDmze3IaNpawooRQ+xzwt5nFvtMmHt/HHy8lIKfOc7MVyEoqOjatSvUajXefvttXLp0Cfv27cP777+P5557zlH1M2vm8Dg8PyDWKPpTKoAhcZGIDuLOww7x84afj3G0FeznXT891Nw+DffTeDopAAyLj8bKJ7ohKsi+ud+dWwRi3xuD9PsKVNu1L0KI+4m7cQnZ79+PrjkNzd9jH3sXD41fQut2OJG133SYrxLLxyVynhN8ni+A/p/R8FkVFaThTE8V8swRI0+FEILzVFy4cAHvvfce0tLS4O/vj8ceewxTpkzhdImY4ojkV4AbZdR89m4E+TcEEgcv5uPxNYdNHqexmf/qgOz8cmw6etXqtvd2iIC/jxe2ncqxui0hQlhLBuRoSuhfKMTOqKkfcV/DyV6p9lJg4J0R6N4qlGdGzSxklpjPIKpSAN4q44yahpb9tAgjzx2o//lGQCj6vrAWdSr90Dg2o2bhrVrUCPjHuCNYjRod47iMms3DnZ5Rs6JWi78u5qPS3C8dgI9KgZgwPwRovMTPqFlyBd27djX5PJNjRk2HJr9yRKXsCSrkzty5/5T2D17enGb1+x8/lggAom8rV8/c1Qo/ncxBYbnl0dYK6KP/sqpa3KrmP13K0VQKffptuWmiUaGsSvzfI/vv9OeMQdiTkWsy4Q8b0Ewf3A4x4f4Wb8JCmEswZJiIyBL2+r7hHYUpG9PMBl7PD4jFzOFxDd/TMVj22wUs3XsBdxTn4sCn3NbgqaNmYOS7L5vM7PvC+lQeZ6cXfft3a+/vyhQp7+spmQUY+9khq9ttmpiEPm3CRD22Oz7PhJwTrVLqoiKb8OtK4bud0G2FUDZa40JqX/x1mdd27JxvVyPHgAKAQwIKoPFc/wKzCX/YsqV7L9SXmUprLISlpHYM9IHF/O0ZGBIXZfWBrGUY/HfHWYstOZ/uz4KvtxdiI/RBUfdWIdh89Cpm/r4Wz5tIs13lo8Fxg+OzdRaC7fN3NzfL+F3bfLcj/FFQ4QSmumKsXci9YkMRHaRBbkmV2ZtRmL8PEu8IRurlIgT7eqO4stbkduzbXvdWITiaXWhxW1u4SkBB3FfKpXxBQWBuSRUmr0/l1ZpgypGsQovHY4OdI1mFVt90z+bV8Equ99GvDUFRa1QgZZHBImD3TsKXPUbV/2x4fGt1NjR9cDubgy5X54iXMsIPBRUOZmrRFz5vUeysksnrU832VxeU16DT3F2WF6e5/b+jukTj7sW/u+TbOSHWCXubFtqaYEjMN92j14Vl63326I+Y/dsaTlnXlzagyC/I4vGFvHVHB2kwdVA7QfWSE2svZeyLFjvWjohHcJ4Kwh/bJ2v4IGffonalWx4wyWeEr7VWgqggDSYNiMXq/VlWA4roIA2eHxCLUH9+Kdc9WbCvt9RV8BgKBXAxr0zw9xq3JrC0OgYpmQX4Ke0fpGQWQGvmAhLrTVerY7D/cqXFbVh+NZXIXjSSE1Cs7P0wYmbsMBlQGB4/O7+c13EA9+32YFma6t94eqY7/w6kQi0VDsK3T3ZQ+wiL+xkWH41BHZoiacFeFJbz77II9vXG8se7oWdMKO5e/LvF/txgP28sH9utfibMa/d1EHw8T/NM31h8tFefpp16fxyLYYBd6Tds/j77Bi+k1ZBP92M0jzfdo9mFKOUxFWNUxj58Yphm+4XPcS2oqcntDd+0tToGm45YT9+sVADLxtrWJSQ37EuZ4b95lJ3jbYhlFFQ4CN8+2aPZhbD2TnT8cpHgB3xxZS2UCgWOXy6y2kJRXFEL5e1EXlodg+OXi/BgYnN8fjBb0DHF1u2OIKRedY11XljszXzqoLZoHxWAedsykFtKXUquLLKJxuxMDnNjL/h0P1bWarEnI9fiw+lmmeWuDy9tHQ6teArhFQ1/5z/G3Y1X7n/D7HdMvWkfySrkNW7jpUHtMLyz5zxMh8RFoYnaGymX8gEorKYFIPajoMJB+PfJVqOlSPuy53s3y6pMvslJyRUDCqDhZj4sPhrncso4A+yI62g8QNlca525sRdaHYMgXx9M6BuDzceuotzEtOOSilqrg0Ejm5hPYtc3Ow0bvuEuxPivZz7B2UhuVsxQf2/OS4WpN22+13rrCH9e27kDU/ez71OvUSuFg1FQ4SD8+2TVQKk4+7Lnewf+zsOW1H9sOo6nMLyZa3UMvvwrW9pKebD74iIRqPHG97f/bhsHDY0DQGutdYYzOfgG13wGg/aMCUWYrxIFlY2SMDEMflz3KhJzGoLRo83j8MjjizhZMdmgaN8b9+D45SKLs8dotgOX0JYpIh4KKhyE7+jjnjGhOH3KcjZMPv27pvbN9rda+64CoIDCis4tAvHDi/04b7JfHswSdWouEeb/Mm4C0I8JAvTdeKxQfx8kj47HsPho/JTG72/74MU8FJXXYMpG44eROdamlqqUCkxIDMTilGIAQKcbmdj55cucbcY+9h5SWnXmlBmu9WBt2irNdmggZo4RIhzN/nAQMUcfC1m0zHDf7Hct3STlPNBwUIcIbHi2N6YNauvQ45y6Voo9GbkA9G9B/Rb9huSdZx16TMJPSUUtiitq4a9uyPRXUF6D5J0Z2JWew/vtfNnvmZi6iX9A0Zil7oekFhqsGJeI1TsWcQKKnIAwtHnjJ6OAAtA3WEwaEMtpFbM0a4VmOzQQkmOEiI9aKhyIz+hjrVbfV6vVMTiSXWC2idPcvgyzWXrayOZDlwqRcb2U1yA1e7219TTO5pThk18vCHrwdG4eiFP/WOnjIjZj/y0Mxz2wTd3Lx3Xj3dJnayK3xoELdw0gbwRcvYrhD/bgbP/i6Lfwc4d+Fuuxen8WurYMAQBes1ZotoMeZdOUFgUVDjYsPhpD4qIsZtQ8dK0KU3b/wXkwmrtpGO6re6sQi/2ttqTulZOKGi0qapyzdkdxRS0+FjgoU6EABRQSYZu6k3dmYPaIjpiy8YToC58ZdisYjseY9dvnmHT0B853Ory6BVXe/FpP3tp6GiUVtbzHBvC537g7Gl8iLQoqnEClVJjtE919Jre+v7UxS1PdDPdlqb9VaOpeIi7nLNcnH15KoM78wpGiY5u6Q/zVJt/i7WHYrdB4cGBYeTGOL3uCs/0vE2dicmhfQXVvPE7E8DNzYwMs3W88AY0vkRaNqZCQVqdfaMgU9mKYvz3DbNY/PqiJTxoe9GIoiDMDisZullVhWHw0Zo/oyBl7YY+oIE190N94cOCzR34wCii6vrQBLwoIKPigsQGm0fgSaXlcS4XhWvbj+8TAx0t4bKXVMTiUWYC/LuXjelElmgX74q424fVZKdnPzSVdYWcPWBoLwN40Xlh3DMPio9Es2JdXdwdbr3+KKpFHQYXT+XkrUVEr0dOTmBTZRIOfT+XgxY0nbPo+e4W9MvhOxIT7GV17R7IKUZJXhOylj3C+tyLpYbx/99N21Nw6enEwRuNLpONRQcWCnzPw2YEszmCsd38+i4n9YzFzeBzv/exKz8FbW08bNU0u/yMTwX7eeLRHC3xz7Brn82W/X0SwnzcWjkkAYDzwypI9Z29iz1n99DnDgZmNx16YqxdxLjkEFAFqFW6ZSOjkjvzVKhSUVWHaN2m8vyN0ALT3t5uQsfQlTpmlNNtiorEBptH4Eml4TFCx4OcMfLo/y6hcx6C+nE9gsSs9By+sTzX7eXFFrcnjsJ9Z+i4fhj0h7NiLSQNizR6XEEP3to+EQqlARY0WJRU1OJxdJHWVHKa8Woupm9N4b68AsGxsV4T4q60/jGprgWbN0CM/v77oh7iBmH7/6/ZXnEc9aWyAZZ4+vkQKHhFU1NTp8NkByw/czw5k4bX7OljsCtHqGMzbdkbs6tmFjTFWU0BBBPjplOUVcj0V25rIq3l8715gyBBO0b+e+R/ORsYKPq6vlxKVAgac0NgA4qo8YqDmupRsq/PPdYx+O0v4LtojBZpkQDxVVKB4zf/L+azgqdMBPXpwA4p+/bDr1D84FxlrNUGdKa/e117Q9o0HiZrDd5l3QsTkES0VlwsrRNmOBkQR4nrEWiU2OkiDJGtN5ampQPfu3LLffwcGDsQwACufUBgnqANgrg2C7cJ46q4YrD2YZXEaZKi/D94e0RFRQb5WxwYIWeadEDF5RFDRKtRPlO1oQBQh7stcVwKbIbPlC0+h+d6dDR+0aAFkZQFeDbdRw8GB4f7eSD3zNz48pF9x19yiZz5eSrNLrbPbvftgPK+AgBbTIlLyiO6P8X1irOYNUCr021nSKzYUUYHmlzKWkq29qgrqjiUeTgHglXvbobpOZ9RNsCs9B4++uR592oZzAooTH6wGrl7lBBQsdnDg6MTmSGodhrvu8MXycYmICuK+lBh2YbDTIK1tZ4m1xbQA+3PfEGKJR7RU+HgpMbG/5dkRE/vHWs1XoVIqMG9UJ7tncAAQLV0wGxPc0yECv53LE/x9yvhIHClA7QVvlQJFLjDN2dw1F+TnjY8apV9nuwkA4Nozk7Hl2E+c7Tu+ugVVNzVYmZ7D+41/aKcoDI1vZnV6o73TIIUspkWzIogjeERQATRMFzXMU6FUQFCeimHx0Vj1RDez+SDM5akAgBA/bywwk6ciOkiDkspawetYsPPng3x9bAoqCHGkJY90xpC4KPx1MQ8vrDuKcglii6TWoXgyqRWSd57lXHPBft4ovr3CaWO5JVV4+9PfcMwgK+acwc/j6+73A7Bt+Wy+0xvtmQbpbotpNV6cjfJMyIPHBBWAPrB47b4OdmfUZN8mLGXUfHNYR4sZNdm3kdySCpTeuIrWrdtg/BfHeB0/1N8bs0d2QlRgw0Wm1TGIDtLQOh/EZQT7edc/dMuqaqFQiL2cFz+HLhXickEFZo+IQ4i/z+2xDmq89t1JAMZRzrNHtuLt39dyyhKnbUSxb2D9z676xu9Oi2nRYFN58qigAtB3hTzbv7Xd+1EpFejbLhx924Xb/HmfNmHQaoORlnYTV8preB/7vQeN59Gz+e5NDdAiRArFFbX69NWVNZiyMU3Sv8uckiq8uDEV0wffiamD2t6eHs4NwP1qKpFhkGZ7edIjWHz3U2b3K+SN3963bj7fd5fFtGiwqXx5XFDhqiKb8BsAOn3wnWYvJnP57gmRSm5pFRb+bHrgoBSW7v0bm45cxr/iozjlozL+wCfbl3DK+r6wFv8ERVrcH983/t1ncpG88xy3+8XXG8/0jcHUQe3qWxvNBQ1839obv1yYm0Xi6gmzrA02taXriTgPBRV2ELO/r2eM5TcMAAjy9UKPmBBodYzZ4zQe6LUnIxc/pl1HoYBWEELEtHp/Jm6UifP35+etBBRARY19a6vkllbji78uAwC8tbU4vPwphFaW1n++tdM9eHXkaxb3weaNyC2pREpmgcVr/9C1KixJMW6pKa6sxdK9F/DFX9l4tEcLbDuZYzJoACDorV3ui2nRYFN5o6DCRmL391l6w2CVVNbh8TWHrR6H7Vrp0yYMPVqFYMbWUyir8ozFo4g42oT7IzO/3O79nM0pE6E2ep891RNlVfavn8Pql3UC67+dzSkb9sz/cM4gzbap65EBUFBeg+nfngRg/trX6hisTSu12FJjbr2g3JIqvLA+FcF+3oLf2uW8mJa7DTb1NB6Rp0JsbH+fYTTNvjnsSrdtXYVh8dFYPq4rQvy9LW7H9zi70nMwZeMJCihu81erbM7n4Sn81SoE+3mLElCIRYHb2S5bh2FYfDRWjOtqNe+Mxf0xOmz76hVOQHG4RSfEvLndKKCYPvhOo7wRppi7Jo9mF6Kg0raWFTaQsLTqcOO3dkON82X0aRMmi4ACcK/Bpp6IggqBHJlcZld6DpJ3nkWhlXl3jY9Tczthj2F+f0v19ETBft5Y/FBnj/19ePN8oJRXay0+xKTAABger3/r1uoYhPirra7lY0587kVkvT8KnXMv1pc9OnYBHn18kVEmuOggDaYOaos/ZwzCpolJWPpoIkLNBPzmrv2bZc5ZK8id3trZwabm/mLZINPVB5t6Kur+EMhR/X27z+QKGiHPHidpwa+cMRPRjfJW0GDNBgoAQ+OjMaFvEdYezJa6Ok5XK/MMip8fzMbnB7MRHaTBcINBlnyt/OE9/Ovvv+p/vhYYgbufXwOtUmW0rQLcAY192oQhJbPAYsDPXpOHMgvqZ33xHYBtL7m+tZsblyb3waaejIIKgRzR36dlGMz68YxNb9GGgzDZZthn+sbYsDf3VVRRi0OXCtA82FfqqhA75JZU4XOBQWHLohzsXz2RUzZ59Fv4pUM/k9ubGx+RW1LJ63hTNqZi4UP6ad89Y0IR5qu0uQvEGrlMETXF2rg0OQ829WQUVAjE940gv6waP6X9w2uA1PcZt0RrcmYDk2+PXRNlf+7kxQ3HUVJZJ3U1iB2EBt6zf/0Mzxqk2e7w6hZUeRtfx8G+3lj+eDdOkjoW2zXJR3Flbf2sjCEdIzEhMRCLU4oF1lxPAX0a8ZLb9wd3eWvnm4dCroNNPRkFFQJZSy4D6FN/N74BWZqtUVOnw7bz4g+Ku1VND09DFFB4jvDyIhxbNp5TNnvIC1jXbaTZ7xRX1kKpUJgMKGxJKjd/ewYGtY9AUgsNVoxLxKwfzwh6eWBrsdBMan+5vrULzUNB00blhYIKgfhM/TTsvjY3n3xXeg5mbj2NSpqcQYhoJh7eiv/8YTnNtjl7MnI5DzGtjsFbW08LDijY8RVHswuhQcOCYst+u4gvDmahuNJ6cGEYNLjLWzvloXBvNPvDBuaWKDZ3fZsaGc6+/bjC6o2EuAP/6gpkLxrJCSiW9fk3Ymbs4BVQAMBPadc5szeW/XbBrq7JxrM/VEoFXh7cDsdnD8H0wXda/N70wXfizxmDjLJlynGKqCHKQ+HeqKXCRob9ffll1Rb7XBtH371iQ2m6JyEiGn3md3y84wNO2V2T1+J6oOU024YKymvq35C1OgZf2DlTKLKJGig1Lt989IrZ7yhufz51UFu7ju2qKA+Fe6Ogwg6N+/t+SvuH13dullVZbf4jhPDjra3F0WXjEVx1q77s+0734DUrabYtYd+Qj2QV8uqmMIWdldEzJhSnT13lfObpzf/usugZMc3m7o9JkybhrbfeErMusiYk+qZmPULs1z8rFReWPMgJKIZOWGZXQAE0XMuGq5gKwcD8rAxPb/5nx6UBMEpwJecZLUTPpqBi586d2Ldvn9h1cRlaHWMyS6UlQrLAUbMeIbZTMDrs+PJlrPt2Tn3ZoTviEfPmdpyPiLH43QC1F+9MjYW3+GXD9FYZ7zHYz3yqfWr+Nz8uLSpIQ8ua28iW55YjCO7+KC4uxvvvv4+EhARH1Edyti4UJiQLHJ9pqY0pFABjYUNzs1AIcTcJORew/evpnLJ/j1uII3fEW/2uAsDYXndgzYEsXpkaQ/19eNWpVmt89ZVU6HNVLB+XiKa4nTkyuwA3y6oQ7q9GVKAGN0rNX/8hft5u3/xPeSjEI/YCl/YQ3FKxaNEijB49Gm3but8gInsXCuMbfTdu/uPDUkABAJMGxNJCWcTtrfrhXU5AcS0wEm3e+IlXQAHog4g1B7IwaUAsrzfkqCDbs6+yl2zyznP462olBiz+A2M/O4SXN6fh8c8Po6pOa/FFoKiiFnsycm0+vly4y4wWKTlqgUtbCWqpSElJwbFjx7B9+3bMmzfPQVWShtCELObwjb7ZAOTNLSdRymMV0WfuaoVf0nORW9rQJBsVqMa8UZ0wLD4aXVuGGEWqAWoVblVTEgwib62KrmPf6kmcshcemIld7ftyyqKDNBjZORqf/5llccGxbSdzsO+Ne3D8cpHFa5RtUbR1UDU74PKDQ8bftzZNle/9xhnMrc9BpCfWc0tMvIOK6upqzJ07F3PmzIFGY3tfn1Zr/JBjy0x95iyHLhXwGpF9KDMPSa2tj8juFRPc6Ms6mDq1IR0j8eLdrbFw9wWr+2sWrMH+NwbiaHYhbpZVI7KJGj1j9Be3VqvFkI6RGNQ+wujzFX9cxEe/ZlrdPyGuaM7e1ZhwfBunzDDNtlqlxGtD2mJc71bYdPSKxYCiPilVVj73OjZzjc4e0UHQQn9iEXq/cZTdZ3Lx3x1njV5m5ozsiKGdLC/s5gr3dSk487zFfm6ZI+RceAcVy5YtQ3x8PPr3729TpVinT5+26TNHO3qF32JBR9P/hqZUvEWpKooqeG1Xlp+D06dKoAHQEgBKYTRVDYDx57f4nRchrsRUmu23h0zG+m4jjLat1urw3q6/sXDX3+C7bBff67gpgNf7BGPl8RLcquGGFr5eClTWOTbcEPt+I8Sha1Um1yzJLa3GixvT8EafYCS1sP6CKeV9XUrOOG+pnluW8A4qdu7cifz8fHTt2hUAUFOjXx1z9+7dOHHiBO8DJiQkQKXiLjWs1Wpx+vRpk585S1VgAXD4qNXtesbfiUQR3xwqAvKAI8etbtc7ob3J42p1jMnWCxbf8yLEVUw6/D1m/fEFp6zLtE0o8W1i8XtC1gEVch3f8M5FeUqaUXmVgwMKQPz7DV9aHYMpu/8w+7kCwPqMKkwc3ttss7or3Nel4MzzdtZziz0nPngHFevWrUNdXcOCTEuWLAEAvP7664Iqp1KpzP6iLX3maEltInglZElqEyFq31Tv1uFWl0aONnNcPiN+rZ0XIa4iuLIUaZ+M45T9r8+j+GDAeDPfEE7odazVMUjeec5sn7Wl49h7vQX7egMKJaBQOn0Mw5HsAk6XhyG2Wf34lRKrCbqkvK9LyRnnLdVzyxLesz+aN2+OVq1a1f/n7+8Pf39/tGrVypH1cxqpErKolApMSAy0OHfe1HHNjfjNKanCC+tT8fOp6/X7FzLThBApvPX7WqOA4q7Ja0UNKFhCrmO+2W9D/bl5KaKCNFgxrhuiAtVWv2uuJsWVtXh8zWH0W/Sb00fwe3qCLrlwxURitKBYI1IlZElqocHycYmINjhutJnjWhrxy5q66QR+PqW/EbHnxXfePSHOoq6tRvaikXjhyNb6slIfP8TM2CF43Q5rQv29BV/HfB+as0d2wqaJSfj4sURsmpiEP2cMwvDO0ZgzsqPF7z0/IBZNrQQefKYGip34iBJ0yYerJRKzee2PhQsXilkPl+HMhCxaHYNDlwpw9EolesZ785rmBvB7e9IxwIsbU7FKqf+jGhYfjUEdmiJpwV4UltPKqER6T6TuxDt7VnLKxj72LlJadXHI8WaP7CT4Bsv3oRkVqLFjnQ7L9xZrUwMdkfiI1ueQF1dKJEYLipnQeKEwRzG6ERw+Wn8jGJ3Y3OJ3hTQ5Nr4R+Xgp8Uj3Fvh0f5Y9VSfELkqdFpcWjzYqj3lzuz59rINEBQp/q7bn4arVMfjvDvMrFwPgfS2aW2SM7QY1rBvbumHrm6qQDMHENTjjucWHW3R/SJHz3NQx+dRDq2Pw8d6/8YKF8RDJ289YPA8hTY45JVVYc+ASluw+h8nrj1NAQSQ1+MJho4Bi+ohXETNjh0MDijB/H+SWVAq+P9jTZ30kq9DiYEdbNH6hsJb4CNC/VNh6P3S1ZnUiD7JvqZAi57mpY7ILCDXOlGdYj13pOZi3LcPq6oefH8zG5wezzZ5Hr9hQBPt5W83Kx1rwyzle2xHiSNmLRhqVtX39R9SpHH8bKiivwfRvTwIQfn9gH66G13yUlf04YhBj4xcKZyyh7krN6kQeZB1UOKrpz5ZjmnrAN64HAJPfs8TceezJyOUdUBAitcTr5/HjOu5y5Iv7j8fyux6VpD623B9sebiGB1if+cGXqW4WZ83QcJVmdSIPsg0qpMh5zmfWhal6zNt2BoBC8Lx1U+fB1oEQOfht9SS0LrrOKYt/5VvcUvs59LjBvt5QKBgUVdQZfWbr/UHww1WkXlhz3Sw0Q4O4ItmOqRDS9OesY5qrR25ptdUuD0vfb3wettSBEGdrWZSD7EUjOQHFNwlDEDNjh8MDCkCf48FUQMFyxP3BUH65OOMpzI1hYAeRWspxE00zNIiTybalQorkLFImemGPTclmiKv77PtkDLl4mFPW+8UvcaNJuEQ1Ms+R15OtLQTsbIsJfWMwJC7KbDcLzdAgrki2QYUUTX9SNiPml1Xjp7R/kF8m7mhyQsQSUlGCE/97nFN2tHkcHnnifdGOoQAQ6u+DgvIaUfaXnc9vQT9b9IoNRVSg2uwMEAWAID9vaLxUnJZMawNAG7N1ECkhjiLboEKK5CzWjmmKAridMU+BG6W2rb+hVADJOxvmu4uxrgAhYpr12+eYdPQHTtl9E5bh74gY0Y+VPDoeyTszrHYDBmm8UFJlvgsEADYfvYKpg9o65G1epVRgzsiOeHFjmtmWhIVjEuyeXUEzNIgrke2YCilynls6pinsNvNGdcK8UXE2BwKG08wpoCCugk2z3TigKFH7I2bGDtEDCgWAofFNEeTnjf/8q4PV7bU8LhRHj6sY2ikKb/QJNkrF3XicBDsAdHRic/RpE2bTPUuMfRAiBtm2VADSNP2ZO2aInzcYcKeWGtZjQt8YrD2YzftYSoVxQEGIqxifugPJe1ZxyhyZZpsBsCv9Bnal34C/2vrqj7eqLbdSsGwZV6HVMbxbBpJaaDBxeG8cv1JCLQnE7ck6qACkafozd0wAFusxJC6Kd1AxoF049l/Id0T1CbGLVGm2Gyuv1oq2L6FjpWxJuEe5HoinkH1QAUhzwZo7pqV69IoNRbCvN4orrSeuOna5yK76EeII9/2dgtU/vMspe3nka/ip0z0S1cgyNsQRa9yVFAn3CJETtwgq5EKlVOCZvjFYuveC1W0rasR7EyNEDFKm2bYV+/AXY8qlFAn3CJEb170bCGCqfxO4vaBPSSUKy2sQGqBGZBM1dFoGh7MLwAAI9vVBeIAPooJ8jboqGu8z3F8NKID8W9XG+y+tQuGtagT7+aC4ogbBvt64UVqFn9NzUFxRh8gmPni05x1oGRaAXrGhmDqoHVbvv4RyChqITJhKs/3+gCexos+/JaqRMBP6xuCX9Fy7x10dyiwQba0NIWMyCOHDVf6mZB9U8F3cy5rGfaKm9tmYkP1fK65E6tUSzjEmDWiDpXv/5l03QqTy++qJiC3K4ZQ5I822mIbEReE/I+LsuuHuSs/BW9+f5rWttYGfUiyCSNybK/1NyTqoELK4lzU5t/tEJw2Ixer9WRanbdq6mBd7jOXjusLHS4maOp1N+yHE0VoVXce+1ZM4ZZs734e3/jVNohrZhk1Tbc+4K3P3GXMsDfwUMibDVd48iWtztXE+sg0qhC7uxQcD4LMDlgMKMY4xf/sZ1GopoCCu6bPv/4shF49wynq9+BVuNpHf7IXZIzra9SAWcp+xNvBTyJiMPRm5LvPmSVyXK47zkW3yK0ctrOWMvBA3ymrAUP4J4mJCK0qQvWgkJ6A43KITYmbskGVAAQAh/vYtPy70PmNp4CffRRCX/XYBk9enGm3LvnnuSs8xvQPicaRYWNMa2bZU0MJahIjnP7+twcSjP3LKhkxYjgsRraSpkEjsvU/w/X6wrzcWPpRgsRWB776+OJjtUm+exHVJsbCmNbINKqRc3IsQd6GprcK5Dx/mlBVrApD48maJaiQue+8TfL+//PFu6NvW8iqsfPdlKY+NkBkmxP1JsbCmNbLt/mAX9xI7Vlcq+K3rQYjcPXV8u1FAMfax99wmoIgWYUFBa/cZxe3jJLW2/oDnsy92Zpk11FJLAP5/n2IurGmNbIMKoYt78aEAMLF/rKj7JMTVKHVaZC8aifl7P+WUx7y5HSmtOktUK/HNHmH/goJiLlzIZ1/P3BXLq17UUksAaRbWtEa2QQXQsLhXVBD3Agvx8+Yd8bOib68aOHN4nMl9NhZsw/4JcQX3/Z1itG7HtPtfR8yMHU5bt8NZQvx9RNmPuftM45VGxdrX1EFtXe7Nk7g2Mf8+xSDbMRUsa4t72ZJRs/E+92bkYuuJayiqaFjxUOOlxJyRcQjxVxtl1Az09cbcH0+jos726R2GKYX5uCNYg4gmatwR6o8xXZsDCmDyhuOoqKGpqwQAwyD7/fuNil09zbY9xOwiEHPhQmv7mnt/HCavTxUltTjxDFIsrGmOW9xNhC7u1b99BK99llTWYK2Jkdg3SqsxZeMJrHyiGx7s2pzzWUpmgV0BBSA8oACAq8VVqGOA5/q3gY+3Cgcv5lNAQQAAXf85hx/Wv84pW3T3U1iZ9IhENXKO7PwKUfcn5sKFlvbFvnka5qmwJbU48RyushKuWwQVjiA0qQib/e4XCeeQ55RU4cWNqZIdn7iefZ8+h1bFuZyyTq98i3IZpdm21eajVzB1UFtZvtW70psnIUJ4TFAhNOUt36Qihy4V4Fh2Eb44mMVrSXNCnCGm8B/88dnznLKNXYZi1rCXJKqR88l96qWrvHkSIoRHBBW2LLayJyPXZLmhiV8fo2XKiUv5fMt83Jt5lFMm1zTb9qKpl4Q4l6xnf/DBLrYiJOXtrvQcrD2YzWv/FFAQV8Gm2W4cUBy+I17WabZZ0UEaTB98p+Dv0dRLQpzLrVsqbFlshf0OIXIy+9fP8Oyxnzhl7pBmG9AvCvZ0X33+BiHdjDT1khDnc+ugQshiK2zfpaMWKiPEEUyl2S7wDUT3aRslqpF42FU/n+4bWx/092sXjh2n+A2GpqmXhDifWwcVtiy2Qn2wRC6ePrYN835dzSl7bOx7ONTSfbJisoGBVsfgUGYBDlzIt/odpQJYNtb5SX8IIW4eVNiy2Ar1wRJXp9RpjbJiAvo02+6SFbPxQGpTA60teTCxGWp1OqRkFnjsNEyhs90IEYtbBxXsYiu5JVUmx1WwzauN+12tfcfZbMmuSdzX0PN/4dMf3+OUTbv/DWyLu1uiGolv+uB2mDqoHVRKRf1AayHXwPcnruP7E9cBWJ/l5Y5sme1GiFjcevaHLYutNP6OK2BvpvSO4eEYBtmLRhoFFG1f/9FtAopQf2+seqIbXh58Z32Xh7mB1nxZmuXljmyZ7UaImNw6qABsW2yF/U60hUXFnOmZu2IsLnBG3Fu3f84ardux8O6nETNjh2zW7QjhsQCft0HzvBiDptmAZP72DGh17t3mZ222G+AZvwciLXnckexkS8pb9jsztpzEltR/nFhbY1tSr2HBAwkIa6LGwYt5WPZ7pqT1Ic5zYNWzuKPkBqdMbmm2g/28kTwqDlM3n7S43Y2yGkxen1of7Is1aNrULC93ZMtsN0LE5vYtFSw25e3oxObo0yaM96ClvWdvOrhm1pVV1WHq5hP44/wNTB/SHsG+tOy6u4sp/AfZi0ZyAoqNXYYhZsYOWQUUgL7r7t6OTRHgY/2aYwDM+uE0aup0og+adveZXbbMdiNEbB7RUmGrI1mFLrWex6f7s9ClRbCgufpEfr74bi7uuXScU9ZzytfIC5BnIqeiilqsP3wZt2r4NbsXltciacGveGd0J1EHTbv7zC5bZrsRIjbBLRWXL1/Gs88+i65du2LgwIFYs2aNI+rlNFodg4MX87Fk93ks2X0OBy/k1/c5umJE/58f03E0q1DqahAHCCsvRvaikZyA4tDtNNtyDShYQpchLyyvwZSNJzCqS7TdAYUCnpFdk525Zq49yFN+D0RagloqdDodJk2ahISEBPzwww+4fPkyXn31VTRt2hT333+/9R24mF3pOXhr62kUVzS0Riz7PRPBft5YOCbBJSP6ogrXaTkh4pmzdzUmHN/GKRv87ApcDG8pUY3EZWv6jG0nc/DMXa3wxV+X+R0H3CnY5mZ5uSN25trk9ake/Xsg0hLUUpGfn4+OHTti3rx5iImJwd13340+ffrg+PHj1r/sYnal5+CF9amcgIJVXFGLF9anoqi8xmLkT4i9NLVVyF40khNQ5PsFIWbGDrcJKAAgQO2FUI1C0LXEDixsEcJvDMn0we0EzfJyR7bMdiNETIJaKiIjI/HRRx8BABiGQWpqKo4ePYq5c+c6om4Oo9UxmLfN+qJh/91xBnNGxmHKxhOUhIqI7pljP2Hur59xyh4duwCHWyZIVCPHWbU/CwE+CpuuodAANa8kdlMH6ZNm2ZJJ0p0yUNoy240Qsdg8UHPQoEG4fv067rnnHgwdOpT397Ra46XC2TJTnznCoUsFyC21Pl4it7QaQb5eWD4uEf/dcRa5pdX1nykVAE33JrbwhDTbprADNYN9vVBcWcf7e5EB3pg9ogOmbEwz26w/e0QHgNEBAHrFBDdswOhg7bay+0yu0fUdFajGnJEdMbRTFO96muLse1tjQn8PYpPy3KXkjuct5FwUDMPY9Gg8ffo08vPzMW/ePAwZMgRvv/221UqlpaXZcijRHbhSiY8Ol/Da9pXeQejf0hdahsHZvBoUVekQolGifbg3zufXIuVaFXZlVjq4xsRdDDt/EKt+XMApe+n+N7DdTbJi8hHmq8TUnoEoqNRibdotVNSavwWF+SqxckQEVAoFDl2rwtq0UhRU6jifT0gMRFIL28Y/HbpWhcUpxWY/f6NPsM37JsTdJCYmQqVSWdzG5paKhAR9E211dTVef/11vPnmm/Dx8eH1PcNKabVanD592uRnjlAVWAAcPspr257xdyKxtT5RTHfDzwC0vVSAXZn89kU8GMMYZcUEgDZv/ASt0vF/866koFKHO9u1Q1LrMMS1y8WUjWkAjFsgGACjut6B2qBIJMaEIjFRgYnDGRzNLsTNsmpENlGjZ4ztzfpaHYMpu/8w+7kCwPqMKkwc3tv2Yzj53uZKPPXc3fG82XPiQ1BQkZ+fj7S0NAwePLi+rG3btqitrcWtW7cQGmp9qpJKpTL7i7b0mZiS2kQgKlBjtQskKlCNpDYRFm8oJZXu08RFHKPbtbPYuuENTtl7A5/B6t4PSVQj6d28VQuVSoXhnZtjpVJptACWQgEwDPDFX5fxxV+XOQti9W0XKUodjmQXcLo8DLEDRY9fKbE7A6Wz7m2uyFPP3VPPW9Dsj2vXrmHq1Km4caMhy196ejpCQ0N5BRSuQqVUYN4o64uGzRvVyWJAodUxSN5pfcAn8Vx/rnzGKKCIm/6dRwcUAJC840z94lbD4qPx54xB2DQxCc/2jQFgPF7JEQtiUQZKQsQnKKhISEhAp06dMGvWLFy8eBH79u3D4sWL8cILLziqfg4zLD4aq57ohmATCx0F++lXS7Q2/UqMBY+Ie4q9nWa7RWlefdn6xH8hZsYOVPj4Slgz11BYXssJElRKBXrFhuLn9FyT2ztiQSzKQOmatDoGKZkF+CntH6RkFtACaDIjqPtDpVJhxYoVSE5OxqOPPgpfX1+MHz8eTz75pKPq51Ds1KtDlwqQklkAgEGf1uFI4rk2iD1vMD1aBcNLqcChrCKb90Fc05ffzsXALMM02+uQFxAiUY1c1/ztGRgSFwWVUuH0BbHYDJTWpqpSBkrn2ZWeY9QV1rjri7g+wQM1mzZtimXLljmiLpJQKRXo2zYcfduGC/6uPW8wY3u1whtbLK/aSOQlrLwYx5c9wSn7q2VnjBv7nkQ1cm2GQYKzuyMoA6Vr2ZWeg8nrU40CPLbri5J3yYPHrFLqCOybji3SrhZRngs3Mnfvp0YBxb3PrqSAggc2SJCiO4IyULoGrY7B/O0ZJluMHNH1RRzHLVYp5ZMNr6ZOh3Up2bhcWIFWoX4Y17sV0q4Wm/2OqX0CqC8LD1BDp2OQeEcwckpM9wObExWotv+kiUvwranC2aUPc8ry/IPRc+p6iWokP2yQYK07AtAnnSsqrxH1+JSBUnrO7voijiP7oIJPH9yCnzPw2YEsTstA8s6znP00/o6pfbIDOk2tFSJUVZ0OlTU66xsSl/bs0R8x+zfuKr3/HrcQR+6Il6hG8mI4ZqFxd4Q5OgaYsjEVK5XitiKolAp6WEmIZuK4D1kHFXz64E5cKcKn+7Os7ov9zqQBsVi9P8ton2IEE6ySilpsSb0m2v6Ic3lqmm2xMTAeszAsPhrLx3XF1E0nLHYPNh7gSeSPZuK4D9mOqeDTBzdv2xl8dsB6QMF+hwHw2QHjgEJs1CsoX/8696dRQDF11JuImbGDAgqBQvy8MSTOeG2NEH+1xYCicVM4cQ9s15e5K0gBfWsyzcRxfbJtqeDTB2cpW545NA6ImERptkVXVFFrso+cmsI9D83EcR+ybamgGwpxlu7XMowCincHTkDMjB0UUNjJ1HVMTeGeiWbiuAfZtlTQDYU4w18rnkazsnxOWdz07ygrpkhMXceUlMpz0Uwc+ZNtSwWfPrioQDWE/i0qFTC7T+I5WhdcQ/aikZyAYl3X4ZRmWySW+sjZpnB2O8PvAdQU7s7YmTijE5ujD8/sxsR1yDao4HPjmTeqEyb2jxW032f7xZjcJ/EcX38zG7+t4a5n03PKOsy+70WJauRe+AQG1BROiDzJtvsDaLjxGOaUiGqUc4K9+RjmqTBnx6lcTBoQi20nczj79PNRobJWC4YGcrqt8PIiHFs2nlP2Z6sueOKxdyWqkXuK4rmWAzWFEyI/sg4qAH43npnD4/DafR04GTXDA9R4+Zs0o/3lllRh9f4s/O+xrrhRVoWsgnJcLazAvr/zjbYl7mP+npV4KnUnp+ze51YiM+wOiWrknl65tw1eurc978CAklIRIi+yDyoAfjceHy8lnu3fGoA+x0W/Rb+Z3I5tiJj2jeXkO8Q9mEqzfSMgFL2nfC1RjdzbN8f+wUv3tpe6GoQQB3GLoEIoazkuAMpX4QmePfIDZv/+OafskXELcZTSbDsMm7SqV2wodWsQ4oY8MqigHBeeTaXTIpPSbEtmT0YuXv02zeJ6PYQQeZLt7A97UI4LzzX83J9GAcWUUTMozbYTrT2YbdRSyK69sys9R6JauTatjkFKZgF+SvsHKZkFtAQ4cVke2VLBZ4ll4mYozbZLUCpMdy0y0E81pYXCjPFZiZkQV+GRLRWWclwQ99Pj2hmjgOKdeyjNthQ8baEwrY5B+s1qbDt53aYWBnYlZmrZIXLhkS0VgPkcF8S9HFr+JKJucR9SlGZbOMNFnlhqLyWq63RWvx/s641+Lbyx40KF1W3dZczTrvQczNt25vbChkUAhLUwWFuJmVp2iCvyyJYK1rD4aPw5YxBmj+godVWIyNoUXEX2opGcgOLrriMozbYNpg9uZ5TZMtjXG9MHt8OaJ3vw2sfHj3ZBz2ZqXts6YsyTs8cksC0MhislC2lh4LMSs7u17BD589iWCpZKqcDTfWOx5s8sarFwE+s2v43+l9M4ZT2mrkO+f4g0FZKxUH9vtAzzx5JHugAMkF9ezZkCevACv6RwSgXQMcIHUYFq3CitdupCYc4ekyBWCwMtAU/kyKNbKlgqpQKzR8Tx3p4aGl1TeHkRsheN5AQU+2O6ImbGDgoobFRYXovp36Th8TWH8fqWk1B7KTmLPP167gav/eSX10ClUGDOSH2roKlriAHwWE9xM5hKMSZBrBYGWgKeyBEFFbeF+Pvw3tbXhwb3uZr//t9Ko3U77n1uJZ58NFmiGrkfwwfxrvQcrD2Yzeu7kU30XR9DO0WZXCiMtXTvBfRb9JsoD3trLQaAvsVA7K4QsVoY+KzEbG6lV0KkQkHFbXsycnlt98Ldsaiq1Tq4NoQv35oqZC8aiSdPNKzbkRsQipgZO2jdDhs8kdQSoWYC7MYP4po6HeZvz+C1z+ggDXrGNDz42LFM0wffaXJ7sVoRpBqTIFYLAy0BT+SIggoIe+Mqr9ZSCm8X8dyRrUbrdjz8+CIk0bodNosN80dheY3Zz9kH8boU4wRW5ph78G0+esXsMQD+rQjmBmFKNSZBzBYGWgKeyI3HD9Rkm0j5iA7SgEZUSI/SbDtGdJAGoQH8ZmhcLrQ+NRQAnu0bg2Hx0dBqua17QloRLC0WaGkQplRjEtgWhsnrU42m4trSwkBLwBM58eiWCq2OwZcH+c/6CNR44XeeA9OIY4w4e8AooJg8+i1Ksy2CUV2iERXI7wFbUV3Ha7vBcVEmy8VoRbA2CLOovFqyMQlsC0PTQG6QxrYwDImLEjTFlV2JeXRic85AWUJcjce2VJh6w7Hm/I1bDqwRsYjSbDvctpM5eGVwe7OptFkKAH9etD6VNCpQjV6xodDqGBy6VICjVypRFViApDYRglsRtDqG86bevVWI1WmbyTvPYvaIOEzZKE6LgVDD4qMxqH0ENu09gsCmdyAqyA+9YkOxJyMX/Rb9Rmm3iVvyyKCCfcOhoRHy0PNqOr7b+BanLHnQc/i85wPSVMhN5ZRUYePhy1bHDDGAUVInU3rE6B+gnOD98FFEB2kwe0ScxfV3GuesMPUCEOrvw2vsR4i/j8nMuVFOeoirlArER6qR2KUZVCqV2XsP27pC4ySI3HlcUGFpmhlxPUeWjUdkeRGnrOP0Laj0obn5jsB3rAQfv5+7iR2njGdw5JZUYcrGVEwaEIvV+7MstiLsycg1+RC2FFA0drOsCqMTm7vEmARKu008gceNqbA2QIy4BjbNduOA4stuIxEzYwcFFA5UWlkr2r7Ka0xPvWYfqttO5mD5uK5mZzYMiYuy+wWA7T5xhTEJlHabeAKPa6mglLaub/3m/6Df5ZOcMkqz7Rw/pl23+LkCQNNANSprdSixIwBp6J5Q488Zg0y2IqRkFtj8AuColN/2oLTbxBN4XFBBKW1dV8StIhxdzs2KuT+mK2XFdBHsu/28UZ1wPrcMS/desHufN8uq6lsRTH1mC7aes0fESd7l0Ril3SaewOOCCjYxjbkBYkQayf+3AuNP/MwpG/TcKlwKayFRjeRP461Eda1OtL/zID9vLByTUJ834Yu/slFcYV93iaUHKN+Ha6i/NwrLG+oRFaTBqC7RSN7pvEXE+LB273HF1hVChPK4MRWWUt8S5/OrqUT2opGcgOJ6k3DEzNhBAYWd7rkzHID5v/N/xZvOIWFOSaMAQqVUYOGYBJP7Vtz+L9jP264cEXwzUx6aORibJibh48cSsWliEmaP6IjV+43zzzhyETE+KO028QQeF1QA5lPf0qXsXBMPb0XG0kc4ZQ89/j7uevFLaSrkZsb1ijH5dx4dpMGqJ7phmMCgAuCmzmavo2gzAy0XjkkAYPsDlO9D2Of2yqmjE5ujV2wokneedfoiYnxR2m3i7jyu+4NlKvXtlYJbmLE1XeqquT1Ks+0cb3x/CvNGxVkcCCmEYepsrY5BkK8P3hzaHoXlNQgNUCMqkDt2wd4cEexDmO8+xEr/7UiUdpu4M48NKgBwBojtSs/Bot1/S1wj9zfy7H4s2/Y+p2zy6LfwS4d+EtXIfd0otZxQydbxRTfLqiyuudH44cg+QA9l5uFo+t/oGX8nktpECHqACnkIy2WGhbnBqYTInUcHFSzKsOkElGbb6awlVLK08JUl2fnl+GjvBd5ZIVVKBZJah0FT6ovE1rbliOD7EKYZFoRIS9CYihs3bmDatGno1asX+vfvjwULFqC62nq6XimYWw7Z1HaUYdOxel85bRRQJA96DjEzdlBA4WDWEiqZ6+M3hR0YuenIFZcdsyDmsuNi0OoYpN+sxraT13ktHEaI3PFuqWAYBtOmTUNgYCA2bNiAkpISzJo1C0qlEjNmzHBkHQWz1DQrtA+W2Ofo/55AREUxp4zSbIuHbwuDpeb+xt0LezJysfZgttnU2Y/1bImle813E0o9ZkHsZcftsSs9B/O2nbm9Too+M6zU01oJcTTeLRWXLl1CWloaFixYgHbt2qFHjx6YNm0aduzY4cj6CWZtOWTD6WRS9626qzb5+jTbjQOKL7rfT2m2Rcb3vTc8QG3xc7Z7Yc79nbDKwuyEmHA/XseT8rpyhRkW7H3IcOE1qae1EuJovFsqIiIisGbNGoSHh3PKb91yneXAbVmwh/pWxbdx0yzcdeUUp6z71PUo8A+WpkIEr32bhnmjOvGecWFuYCTfGSPWghhDhkub2zsbQsoZFrRwGPFkvIOKwMBA9O/fv/5nnU6H9evXIykpSdABtVrjRYbYMlOfCXHokuW1Atim2UOZeUhqrW+a7d4yCFGBatworaZxFXYylWb7j9juePrf8yWqEWHdKK3G5PWpWD4uEUM78ctP0SsmuOEHRgetlv/18uL641gwJr7+WJau8d1ncvHfHWc5b/VRgWrMGdmRd12FnIOj2XIfckdi3dflxh3PW8i5KBiGselZumjRImzYsAFbtmzBnXfeyatSaWlpthyKtwNXKvHR4RKr273SOwj9W/rW/3zoWhUWpxQ7sGbu793dy/B42i5O2T0TP0VWaHOJakRMCfNVYuWICKjsyAci5Hp5o08wklqYbw20ti9r33dFtt6HCHF1iYmJUKksD663aUrp4sWL8dVXX2Hp0qW8AorGEhISjCql1Wpx+vRpk58JURVYABw+anU7TXBTHC0Fjl8phq+3Eh2bReDJpED8cOIflFU3RGRRgWo81rMFKmu0+PRAts31cmd+NZVGWTGvBUag3+QvJKqR+/D3UZldPtxWBZU61Aa1RHcrb8haHYOj2YW4WVaNyCZq9Ixp6DpITARatcrBtG9OwtpkhnVnKjFxeG+A0Rld41odgym7/7D4/fUZVZg4vLesugn43od6xt+JRDdvqRDjvi437nje7DnxITioSE5OxqZNm7B48WIMHTpUcOVUKpXZX7Slz/hIahOB6CCN1dkcCw2SXG07lWtyu6paLTpEB2Hj4cs218mdPX94C2b+8SWnbMzji5HaoqM0FXIzz/VvjY9/tX8lUEP55bUWrzM+s6fCmvhaDSgAILe0GsevlNR3QzS+xo9kFxgNZDSUU1KFlfsu4eXBwl5epMTeh6wtHCY0CZhc2XtflytPPW9BeSqWLVuGzZs348MPP8SIESMcVSebqZQKjOoi3sju4so6vLA+FfsvCEtn7O5UOi2yF400Cihi3txOAYWI2jcNQLCft+j7tTQ4me/sqb0ZpgNxU8zNBOE7Q2Tp3guymi1BC4cRT8Y7qMjMzMSKFSswceJEdO/eHXl5efX/uQqtjsG2k/K5+cjR/Rn7jNbteP6BWYiZsYPW7RCRAkDyzrN474EEUfcb6u+N7q1CTH5mbdYCoJ+1UFOnww9p//A+prkgRsjMKykTapliLbkeO621aSB3FgwtHEbcHe/uj19//RVarRYrV67EypUrOZ+dP39e9IrZghJZOZCZNNut3/gJOsqKKTp2hkCIvw+eHxCLT/dnibLfwvJa3L34d7sW41qXko3C8lqz2zUWFajWZ69kdEafsdkv+VyzUi8C1hjf5HrD4qMxqH0ENu09gsCmdyAqyI8WDiNuj3dLxaRJk3D+/HmT/7kKSmTlGKbSbP930ETEzNhBAYWDfXYgE6tFCihY9iaCu1xYwftY80Z1MvsQbdxNwIcrXN9Ck+uplArER6oxqksz9Glj27onhMiJWy0oRomsxHf8k3EIqyzllHV4dQuqvOl37Qy/nbO9ezFArcKtauPZI40TMA3q0BTHLxfhZlkV8sv4rePTKpRfVs3pg++02sw/LD4a0wffaTH1N0vq65uSWhFinVsFFbYu5UyMtc2/gr2fv8gp+6L7/Zg/+HmJakSEMhVQsNiujKQFezldGUoFzM7qYGctjO8TgzV/Zlm8zqIC1Zg6qC2vek4d1Babjlw2OxOEPa6zFgEzh2/3kKt00xAiBUGzP1yd0OZUYtrmjW8ZBRTdp66ngEImFACCffnNGjEcG2FtLOTc++Pg46U0O7uBZanbw5BKqcC8UZ2gMLE/V5otwbf7xRW6aQiRilsFFUDDqOtoHks5E66IW4XIXjQSSVfT68t+b90dMTN20LodMsIAGNyxqaj7VCqASQNi67sz2OssyMSUV1umwbrCImDW8O1+kbqbhhApuVX3B4tdTOjQpQJMXncMpRaagYnee7uWYdxJbprtgRM/RTal2XZp5rortqRes9iVIRTDAKv3Z6FryxDOA76kwngWSElFLSavTxUcDEi5CBgf1rpXXaWbhhApuV1LBUulVKCsqhYUTljmX12B7EUjOQHF1aCmiJmxgwIKF8Z2FSwb2w3TB7czuY2YaR0a56nQ6hjeOS2E5pZgl2Afndjc5WZLUFIrQqxz26CCnfpVTq0UZk0+9B3OfPRvTtmYJxaj/wufS1QjwpfidnfE0PgobD561eK2hs+4MH8fm47ZeCCikEGL7kQO3TSESEn23R81dTp8+WcW/u9sLgAFhsQ1xZN9Ysy+RRHAS1uHi0seMCqPeXM7ZcWUCd3t7gg/Hy+ryaMaNxaE+ntj/v1xePunMyiu5JfAypCQgYjuOGjR1btpCJGSrIOKBT9nYPX+LE7wcOxyERb8ck6yOrm6URl/4JPtSzhlzz8wC7vb3yVRjYg9vjiYLWj7ovJavLQ5DSM6R2PHKdtS2gsZiOiugxbZbhpCCJdsg4oFP2eIlrrYI1CabbfDAIJbG9gkTccvFyFIo0JJFf/uQcOBiDRokRBiSJZjKmrqdPjsAAUUfCVdOWUUUMy7dxKl2fZQ7HiHCf1a8/6O4UBEGrRICDFFlkHFupRsUUe2u7MTH4/F5k2zOGUdXt2CL3uMkqhGxFXEhPtj1RPdTOaVMAwFTA1EpEGLhBBDsuz+ELKgkadql3cZe9ZO4ZR93mM0ku+dKFGNiKuJbKJBnzZhGBIXhU9+vYA1By6hvEbfHcJAP6jzwcTmGBwXZXYgIg1aJIQ0Jsuggu+CRp7qmw0z0PvaGU5Zt5c2oNAvSKIaEVdiON5hT0YuPvn1gtHYiKLyWqw9mI2eVoIEGrRICGHJsvtjfJ8Yo7n3BIgsK0D2opGcgOLXNj0RM2MHBRRuponGtrEwhuMdHJXEihDimWQZVPh4KTGxf6zU1XApC375BEdWPMUpu3vSajz78FyJakQcJczfB0dmDUF0kMbsgl4K6NfgiAq0PN7BU5NYEUIcQ5bdHwAwc7h+5LlhngpP419dYZQV83JwFO5+fo1ENSKOwgYQ7z4YD18fFebeH4fJ61OhADjXALvdwjEJVsc70MqbhBAxyTaoAPSBxWv3dTDKqBnu74PXtpySunoO92LKt3hz/9ecsgefWIITzTtIVCPiSFFBGsy9P85opdD52zM4rQ2G21ka70ArbxJCxCTroALQd4VMGtgGkwa2qS9LySyQsEaOR2m2PU+ovw9mj4gzmqbJd/aFVseY3IZW3iSEiEn2QYUp7I3S2poIcjT6zO/4eMcHnLLnH5yF3XdSmm13VlhegykbU7FSaZz/wdrsi13pOUatGdGNWjOsdaNQEitCCF+yHKhpjUqpwOwRHaWuhrgYBr9+9oJRQNH6jZ8ooPAgQmdisKv1GgbYuSVVmLw+FbvScyiJlQS0OgYpmQX4Ke0fpGQW0Owa4jbcsqViV3oO/rvjrNTVEM2dedn4v7VTOWVzBz+Pr7obr+VB3FfjmRh88kJYmy6qgD5IGRIXRUmsnMhayxEhcuZ2QcWu9By8sD5V6mqIZsnOpXg4/df6nyu91Ojy8mbUeBmnViaege9MDCHTRfu0CaMkVk7AthwZBnpsyxG1DBG5c6ugQqtj8NbW01JXQxTRpXlIWfkMp+y14dPxfcK9EtWICBXi542RnZth3aHLou6X70wMmi7qWoS0HFELERHK3GBsZ3OroOLQpQIUVwhbCtoVTT+wHi//tZlTFv/Kt7ilpvTkclJUUYuYMHH/zYJ9vXnPxKDpoq5FaMsRIXy5UpeaWwUVcp9KGlRZhpOfjOWULbr7KaxMekSiGhF7hfr7WJyyKdQzfWMsvn00flsJ91cjKlCDG6U0XdQVUMsRcQRX61Jzq6ACMs6t+cSJn/HO/63glPWcsg55ASES1YiIISrI1+KUTQbAhL4xCNR445PfLsDSJIAQP29MHdTO7Oem3laC/bzrm9atTRd1leZTd0UtR0Rsrtil5lZBRZ/W4Vj2e6bU1RBEXVuN8x8+xCn7qtsIzB0yWaIaEbGE+nnXP5hXPtEN87ZlILfUfObLO5sG4MWNJ0zuSwFgwZgEszcGc28rJbe7A4P8vDldg4bHdqXmU3dFicaI2FyxS82tgoqkNmEINrh5urKh5//Cpz++xykbOPFTZIc2l6hGRExP9jHsquA+ShiG+/Pwzs2wSqkQ/HDn87ai8VJiw3O9kX+r2qgVwtWaT92VSqmgRGNEVK7YpeZWQYVKqcDCMQkuP6VUpdNi36cT0aL0Zn3Z/7VLwqQxb0tYKyK22Ah/ABYe2qXVeGF9Kp7tG4PBcVHoFRtqU74IPm8ruaXVUCoUGJ3IDVhdsfnUnfFdr4UQPlyxS82tggpAf9GueqIb5m07g9zS6vryqEA17gjxxdHLxdJVDkCvq+n4duNbnLJRT36IU9F3SlQj4iiRTTQWH9qszw9m4/OD2ZwWCSFNlfa8rbhi86m7o0RjRCyu2KXmdkEFYP6iPXSpAI+vOSxNpRgGmzfNRNLV9PqijMhYjHj6YzAKt8yW7tGib1/I1h7ajeWUVOGF9alYMa4rhnduxvtY9rytuGLzqSegRGNEDK7YpeaWQQVg+qItqaiRpC6m0mw/9ch87GvdXZL6EMdSoOFCtuVhPHXTCSyDAsM782sKt+dtxRWbTwkh/Llal5rsgwqtjsGhzAKkXMoHoEDv2FAoFQrkl+sHpHVvFYKj2YVYf+gyfknPdXr9Ptj5IR5K/63+51K1P7q/tB61Kkqz7Y7C/H3w7oPx9ReyLQ9jHQO8uDEVq0ysSGqKPW8rrth86glo+q5l9PsRxpW61GQdVOxKz8FbW09zZnss+527jUIBMBKkr2hWehN/rZzAKXt1xHRsjac02+5s1r86IMjXBz+l/YNwfzV0DINgX28UVwqfkSRkgKStbyuu2Hzq7mj6rmX0+7GNq3SpyTao4LtwmBQBxWv71+GllG84ZZRm2zO8+8s5FJaL080mdICkrW8rrtZ86s5o+q5l9PuRP1kGFVodg3nbzkhdDSOm0mwvvPtprEp6WKIaEWcTK6BgCR2TYevbiis1n7ormr5rGf1+3IMsg4ojWYWc6aKu4InUnXhnz0pOGaXZJvZy5gBJV2k+dVc0fdcy+v24B1kGFa40vU1TW4VzH3JbIr7ofj/mD35eohoRd1IkcssHkQ5N37WMfj/uweYECTU1NRg5ciQOH3Z+3gdXmd427PxBo4Bi4MRPKaAgoknemQGtpVXGiGzQ9F3L6PfjHmwKKqqrq/Hqq6/iwoULYteHl16xoYgKVEtybECfZvvgimew6scF9WX/1y4JMTN20LodRFRscy+RP3b6rrnRAAo0JE3zRPT7cQ+Cg4qLFy/i3//+N65cueKI+vCiUiowOpF/xkEx9b5yGpmLR6N5WV592agnP6R1OzyEFOPDqLnXPbDTdwEYPThp+i79ftyF4KDiyJEj6N27N7755hvrGzuIVsdg28kc5x6UYfDNhhn4ZtPM+qIzka0R++Y2WrfDzfVpHYKPH0vEpolJWDa2KxQwvuk5UnZ+uROPRhyJnb4bFcRtwo8K0tB0SdDvxx0IHqg5btw4uw6o1WrNlpn6zJRDlwp4r6cghvZ52dhtkGb7yUfmYz+l2fYIZ3Nu4V+dmta/IS0fl4j/7jjLmYEUHaTByM5R2H4yR/SZSZuOXMHku1vL+g1N6DXuLkyd95COkRjUPgJHswtxs6wakU3U6Bmjn77rTr8fW//N5f77cce/dSHnomAY29NDtW/fHl9//TV69+7Nq1JpaWm2HorjwJVKfHS4RJR9WfPBjg/w0JmGNJ0lan/0oDTbHmf+3SGIj2wYx6NlGJzNq0FRlQ4hGiU6RvhApVBwyoPU+jaNkmodiqu0+PLkLdGOTwghzpaYmAiVSmVxG6dPKU1ISDCqlFarxenTp01+ZkpVYAFw+KijqgjAdJrt6SNexQ/xgxx6XOKaApvegcQuDeN4tDoGtY3epBJjGhJFmWq/0uoY7Mr6w+ZWDMPjy43Qa9xdeOp5A5577u543uw58eH0oEKlUpn9RVv6rLGkNhEI9vPmrPkhptf3f42pKd9yyijNtmeLCvKr/9u0ZW0ClQqYN6qTyRTEQo8vZ3yvcXfjqecNeO65e+p525ynwh0FV5Yie9FITkDx3sBnEDNjBwUUHizM36d+Ghu7NoHhmB52bYJd6eYHEA+Lj8bycYkI8+VedpaGStA0OkKInMgyo+aRrELRWynGp+5A8p5VnLIeU9ch35/SbHu65NHx+kFiIqxNMLRTFMJrclAb1BL55bWIbKJBUXk1pmw8Ub8fFk2jI4TIjSyDCjHn7VOabWLJ8wNiMbyzvktDrLUJVAoFurcO4zSNrlQqaJVQQojs2RVUnD9/Xqx6CCJWmtZ/nfsTK39ayCm7e9JqXA6R74A4Io5Qf2+8Mzoewzs3/C04cm0CWiWUEOIOZNlS0b1VCBSATQPeAH2a7f2rnuNkxdzdLgnPU1ZMjzZ7REeEN1GbfaA7em0CWiWUECJ3sgwqjl8usjmgSLpyCps3zeKU3f/kUpyObmd/xYhsRQdp8HTfWIstA+zaBLklVSb//hTQd1nwHVSp1THUMkEIcSuyDCpsGlPBMPh24wz0upZRX5TetA3uf2opGAVNgvF05gZDGj74Z4/oiCkbTxi1lAkdVLn7TC6Sd54TNC2VEEJcnSyDCqHNyx1uZmHXFy9xyijNNgGAED9vLBiTYPJBbi4fxaQBsdh2MsfmQZWHrlVhSUqaUWsHOy2V1jgghMiVLIOKXrGhvJNfLd2+BA9m/FH/c7EmAD2nrqM0227s+QGx6NoyxGRA8O8ed0Cr0wHQj19Iah1msmWBzUdh6sG/en8Wlo/rhhB/H8FdF1odg7VppXZNSyWEEFcly6CCj+YlN3FwFTfN9isjX8OPne6RqEbE0RQK4Ll+sZg5XL98sq2zKazlowCAWT+exvKx3TCyczNBD/+j2YUoqNSZ/ZzvtFSp0DgQQoglsgwqrCW/enPfl3jx0BZOWadXvkU5ZcV0awwDrDmQhe6tQjAsPtrm2RTW8lEAQHFFLR7//LDgcRA3y/it/SFmLhax2JKenBDiWWQ5QtHcDZdNs904oGDTbFNA4Tnmb8+AVmfz4ruCHuh80nM3FtmE30qjYuViEYs96ckJIZ5DlkFFeIDxjfnJ49uR9sk4TlmPqeuwuvdDzqoWcQGNuw9sJeSBzoYufAOZnjGhCPNVwlyHgSuu9cGnO8jeQI4Q4h5kGVQY3t02b3wL/937af3Pn/cYjZgZO2jdDg9mT/cBm4+C70gBIYGMSqnAhMRAADDav6uu9SEkPTkhxLPJMqjIL2/UL80w6P7P2fof7560Gsn3TpSgVsSV2NN9oFIqMPd+/WBPIY92voFMUgsNlo9LRFQQt45RQRqXnE7qyPTkhBD3IsuBmpwHhkKBRx5/H9GlefilQz/pKkUESYoNwaGsItH3KzSrpTnD4qOx8oluRgMTLRESyAztFIWh8c1kMZPC0enJCSHuQ5ZBhWGeirRm7ZHWrL3EtSJ83dshAsvGdkXvd/egtMb2fnh7s1pawy7ydehSAaZsSEVxpekZR7YGMnJZ60Ps9OSEEPcly+4PAKitMz/XHwC8Va73xkf0OrcIwT0f7LMroHh+QKxTug9USgX6tg3HwocSoIB8xkGIyVJ3kCecPyGEP1m2VBy6VIDyGq3FbWq1NBLd1SgABPl546O9f9u8IFxUoBrzRnXCsPhovDmso9O6D8x1hwhJzy1nnn7+hBB+ZBlUpGQWSF0FYgPG4H9NUSj0SaxY0UEaPNazJWLC/YwCB0d2H5jKHMl2h8hhHIQjePr5E0Ksk2VQYfmxRFyRPji4A0v3XrC4HcMAs0d0RHgTtWQPLWuZI+UwDsJR5DIOhBAiDVmOqejTOlzqKhCepgxsg00Tk/DnjEGICffn9Z3wJmqMTmyOPm1ML/blSJQ5khBCbCfLoCKpTRiC/WiVUVcXHaTBq/e1rw8OXH1qImWOJIQQ+8gyqFApFVg4JkHqahArZo/oyGlpsJapUuoU1ZQ5khBC7CPLoALQL2tNrRWuLXnnWU53gatPTaTMkYQQYh/ZBhXWlj8nzqPxMv1nZGocAjs1sWkgd1E4V0hR7erdM4QQ4upkOvuD3hadReOtRFWt5URjVWYSkTHQt0DM356BIXFR9S0Qw+KjMah9BDbtPYLApncgKsjPJaYmUuZIQgixj2xbKuht0TmUCvse9HIah+Dq3TOEEOLqZNtSYe2tkoijwkrmUr4atyztSs/BvG1nkFtaDUC/qFi0i2RmpMyRhBBiO9kGFexb5eT1qUYLSxF++P7egn29UVJZa9fvmG1ZYvNAGO6LHX8h9bgKgDJHEkKIrWTb/QE0vFUaLiwV7OdtNDPEzlZ8t/Tyve14bfdM31gA5rsEgv28eU0TlVMeCDZzpFRJuAghRI5k21LBMvdWCYBTlldShZe/S+OsK+Gp2K6GIXFR+ObYVasDE6cOaov2UQFmuwQAmGwxMhyHkJJZwDsPBKWCJoQQ+ZF9UAGYX4+ALfv51HVM+zZN1GMqAEzo1wo/n75h8UHpakL9vbHvjXvgc3saqLkuJMOAwFqXAJ9xCJQHghBC3JtbBBWW/HwqB1M3nRB9vwyAwR2jMWt4J3x5MAvJO8/avK8Ab+CWk1JuFJbX4vjlovqAS8jAREuLSfEZh0B5IAghxL25dVCxKz0HL25Mddj+b5ZVQaVU4Om+sVjzZ5ZNM1GigzQY11GNDw6VCD5+mL8PnuwTg6V7/xb0PcOWALEGJlpbwZLyQBBCiHuT9UBNllbHICWzAD+l/YOUzAJodUz9oEBHYt+oLeU3sGb2iA646w5fTLunjeDj398lGlMHtUVUoLA3e1MtAc4YmGgtDwQD4LGed2DHqev1/46EEELkQ/YtFbvSc4ya7qODNHisZ0uHjXUw9UY9LD4akwbE4rMDWZzBoAroH6Z1Bg/IED9vLBiTgCEdI7FqRza+SReeHOrLvy4jqXUYxvZqybu1IszfR9KWALa7pSFPhV7Q7dk6S/deqC9zldwVhBBC+JF1UGEp54HQLgG+zGVW3JWeg9X7s4zqwgCo0zF4+d62t9+89S0CSa31rQE/n/oHi1OKba7L/O0ZeHNoe97fGZ3YTPLpkYZpuq8UVuGjvX+7dO4KQggh1sk2qOCT88ARTA1gtFQXQP/w//bYNfw5YxDnga7VMfjvDtsHeLJTMAvLa3h/Z0hclM3HE5NKqUB8pBoJCdG4e8k+s/+OptYOIYQQ4ppkG1QcySq0u3tDqQCaaLxQWllnceDgkoe7IL+82uwARmt1MZd/4UhWIacLwFahAWpEBaqt7ivaBQdBHs227XdHCCHE9cg2qBCSy8BcOuplY7tBqbSeuKlvu3BR6mK4nVj5GKICNZg3qhNeWG95posrLoZ1s4xfUEW5KwghxPXJdvYH31wG0we3M0rjHR2kwaonumF452izqb6jgjS8+/Jtzb9gbz6Gximwh8VHY9UT3YzSkwP6QaGrXHRcQmQTNc/tKHcFIYS4Otm2VPDNeTB1UDtMHdTOYg4Ge/M02Jp/oVdsqMVuCwX0syJKKvSZsSxlvGx8HocyC5ByKR+Gg0JdUc8Yyl1BCCHuQnBLRXV1NWbNmoUePXqgX79+WLt2rSPqZZW1nAdAwwOXTw4Ge/I0CKmL4ffmjOxo8XsLxyQIaklRKRXo2y4crw/tgNeHtkfftuEuG1AAtv/uCCGEuB7BLRXvv/8+0tPT8dVXX+H69euYMWMGmjVrhmHDhjmifhYJSTHtqnUZ2ikKb/QJxrozlZwWC8PvufNS3K7070gIIcR2goKKiooKfPfdd/jss8/QqVMndOrUCRcuXMCGDRskCSoA8VJMS1mXpBYaTBzeG8evlJj9nrUU2HLnSv+OhBBCbCMoqDh37hzq6urQtWvX+rLu3btj1apV0Ol0UCqlGffpSg9cW+viSucgFfodEEKIvAkKKvLy8hASEgIfH5/6svDwcFRXV6O4uBihodYH02m1WrNlpj5zd5567nTedN6ewFPPG/Dcc3fH8xZyLoKCisrKSk5AAaD+55oaflkdT58+bdNn7s5Tz53O27PQeXseTz13Tz1vQUGFWq02Ch7YnzUafnkEEhISoFKpOGVarRanT582+Zm789Rzp/Om8/YEnnregOeeuzueN3tOfAgKKpo2bYqioiLU1dXBy0v/1by8PGg0GgQGBvLah0qlMvuLtvSZu/PUc6fz9ix03p7HU8/dU89b0MjKjh07wsvLC2lpafVlx48fR0JCgmSDNAkhhBDiGgRFAr6+vnjggQcwb948nDp1Cnv37sXatWvx5JNPOqp+hBBCCJEJwcmvZs6ciXnz5uGpp55CQEAAXnrpJdx3332OqBshhBBCZERwUOHr64tFixZh0aJFjqgPIYQQQmSKBkIQQgghRBROW6WUYfRrUFLyKy5PPXc6bzpvT+Cp5w147rm743mz58I+xy1RMHy2EkFNTY3HJgMhhBBC5C4hIcEoAaYhpwUVOp0OdXV1UCqVUChokShCCCFEDhiGgU6ng5eXl9X0EU4LKgghhBDi3migJiGEEEJEQUEFIYQQQkRBQQUhhBBCREFBBSGEEEJEQUEFIYQQQkRBQQUhhBBCREFBBSGEEEJEIXlQUV1djVmzZqFHjx7o168f1q5dK3WVnOLGjRuYNm0aevXqhf79+2PBggWorq6WulpONWnSJLz11ltSV8NpampqMH/+fPTs2RN33XUXPvzwQ15pb+UuJycHzz//PLp164ZBgwbhyy+/lLpKDlVTU4ORI0fi8OHD9WVXr17F008/jcTERAwfPhx//vmnhDV0DFPnnZaWhsceewxdu3bF0KFD8d1330lYQ8cxde6ssrIy9O/fH1u3bpWgZs4neVDx/vvvIz09HV999RXmzp2LZcuWYdeuXVJXy6EYhsG0adNQWVmJDRs2YOnSpfj999/x0UcfSV01p9m5cyf27dsndTWc6p133sFff/2Fzz//HB988AG+/fZbfPPNN1JXy+FeeeUV+Pn5YevWrZg1axY++ugj7NmzR+pqOUR1dTVeffVVXLhwob6MYRhMmTIF4eHh+P777zF69GhMnToV169fl7Cm4jJ13nl5eZg4cSJ69eqFH374AdOmTUNycjL++OMP6SrqAKbOvbHFixfj5s2bTq6VdJy2oJgpFRUV+O677/DZZ5+hU6dO6NSpEy5cuIANGzZg2LBhUlbNoS5duoS0tDQcPHgQ4eHhAIBp06Zh0aJFmDFjhsS1c7zi4mK8//77SEhIkLoqTlNcXIzvv/8eX3zxBTp37gwAmDBhAk6ePInHHntM4to5TklJCdLS0pCcnIyYmBjExMSgf//+SElJwZAhQ6SunqguXryI1157zaj16dChQ7h69So2b94MPz8/tGnTBikpKfj+++/x0ksvSVRb8Zg777179yI8PByvvvoqACAmJgaHDx/G9u3bMXDgQAlqKj5z5846duwYDh06hIiICCfXTDqStlScO3cOdXV16Nq1a31Z9+7dcfLkSeh0Oglr5lgRERFYs2ZNfUDBunXrlkQ1cq5FixZh9OjRaNu2rdRVcZrjx48jICAAvXr1qi+bNGkSFixYIGGtHE+j0cDX1xdbt25FbW0tLl26hNTUVHTs2FHqqonuyJEj6N27t1Hr08mTJxEXFwc/P7/6su7duyMtLc3JNXQMc+fNdusacqf7nLlzB/RdIrNnz8acOXOsLsLlTiRtqcjLy0NISAjnFx4eHo7q6moUFxcjNDRUwto5TmBgIPr371//s06nw/r165GUlCRhrZwjJSUFx44dw/bt2zFv3jypq+M0V69eRfPmzfHjjz9i1apVqK2txZgxYzB58mSrC/TImVqtxpw5c5CcnIyvv/4aWq0WY8aMwSOPPCJ11UQ3btw4k+V5eXmIjIzklIWFhSE3N9cZ1XI4c+fdokULtGjRov7ngoIC7Ny50y1aZ1jmzh0AVq1ahbi4OPTr18+JNZKepEFFZWWlUQTH/lxTUyNFlSSxePFiZGRkYMuWLVJXxaGqq6sxd+5czJkzBxqNRurqOFVFRQUuX76MzZs3Y8GCBcjLy8OcOXPg6+uLCRMmSF09h8rMzMQ999yDZ555BhcuXEBycjL69OmDUaNGSV01pzB3n/Oke1xVVRVeeuklhIeH49FHH5W6Og538eJFbN68Gdu2bZO6Kk4naVChVquNLiz2Z0956CxevBhfffUVli5dijvvvFPq6jjUsmXLEB8fz2ml8RReXl64desWPvjgAzRv3hwAcP36dWzatMmtg4qUlBRs2bIF+/btg0ajQUJCAm7cuIGVK1d6TFChVqtRXFzMKaupqfGYe1x5eTlefPFFZGdnY+PGjfD19ZW6Sg7FMAzefvttTJs2zaiL2xNIGlQ0bdoURUVFqKurg5eXvip5eXnQaDQIDAyUsmpOkZycjE2bNmHx4sUYOnSo1NVxuJ07dyI/P79+DA0bQO7evRsnTpyQsmoOFxERAbVaXR9QAEBsbCxycnIkrJXjpaeno1WrVpwHaFxcHFatWiVhrZyradOmuHjxIqcsPz/fqEvEHd26dQvPPfccrly5gq+++goxMTFSV8nhrl+/jhMnTuD8+fNYtGgRAH1r1dy5c/Hzzz9jzZo1EtfQsSQNKjp27AgvLy+kpaWhR48eAPQD2hISEty6nxnQv7Vv3rwZH374oVvPdGls3bp1qKurq/95yZIlAIDXX39dqio5TZcuXVBdXY2srCzExsYC0M8CahxkuKPIyEhcvnwZNTU19V0Aly5d4vS1u7suXbpg9erVqKqqqg+ujh8/ju7du0tcM8fS6XSYOnUqrl27hnXr1qFNmzZSV8kpmjZtiv/7v//jlI0fPx7jx4/3iNY5SZ/cvr6+eOCBBzBv3jycOnUKe/fuxdq1a/Hkk09KWS2Hy8zMxIoVKzBx4kR0794deXl59f+5s+bNm6NVq1b1//n7+8Pf3x+tWrWSumoO17p1awwcOBAzZ87EuXPncODAAaxevRpjx46VumoONWjQIHh7e+Ptt99GVlYWfvvtN6xatQrjx4+XumpO06tXL0RHR2PmzJm4cOECVq9ejVOnTuHhhx+WumoOtWXLFhw+fBjvvPMOAgMD6+9xhl1B7sbLy4tzn2vVqhW8vLwQFhaGpk2bSl09h5O0pQIAZs6ciXnz5uGpp55CQEAAXnrpJdx3331SV8uhfv31V2i1WqxcuRIrV67kfHb+/HmJakUcbcmSJUhOTsbYsWPh6+uLxx9/3O0frk2aNMGXX36Jd999Fw8//DBCQ0MxefJkjxisx1KpVFixYgX+85//YMyYMWjVqhWWL1+OZs2aSV01h9q9ezd0Oh2ef/55TnmvXr2wbt06iWpFHE3BeEKeYEIIIYQ4nHsPXCCEEEKI01BQQQghhBBRUFBBCCGEEFFQUEEIIYQQUVBQQQghhBBRUFBBCCGEEFFQUEEIIYQQUVBQQQghhBBRUFBBCCGEEFFQUEEIIYQQUVBQQQghhBBRUFBBCCGEEFH8P2CO6o3Cmt+NAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# まずは元のデータをプロットします。\n",
    "plt.plot(housing_df['MedInc'], housing_df['Price'], 'o')\n",
    "\n",
    "# 求めた回帰直線を描きます。\n",
    "x = housing_df['MedInc']\n",
    "plt.plot(x, a*x + b, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここまでLec73"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 5: 誤差について"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "すべてのデータが完全に乗る直線を描くことは出来ませんので、どうしても誤差が出ます。\n",
    "\n",
    "最小化しているのは誤差の2乗和でした。全体の誤差が分かれば、それをサンプルの数で割って平方根をとることで、ちょうど標準偏差のようなイメージで、平均誤差を計算できます。\n",
    "\n",
    "[numpy.linalg.lstsqのドキュメント（英語）](https://numpy.org/doc/stable/reference/generated/numpy.linalg.lstsq.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/k5/g89wjxz9235346v2wbtwbqdm0000gn/T/ipykernel_50116/1641407615.py:3: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  result = np.linalg.lstsq(X, Y)\n"
     ]
    }
   ],
   "source": [
    "# 結果をすべて取得します。\n",
    "\n",
    "result = np.linalg.lstsq(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "平均二乗誤差の平方根は、0.84\n"
     ]
    }
   ],
   "source": [
    "# 2つ目の要素に、誤差の合計が入っています。\n",
    "error_total = result[1]\n",
    "\n",
    "# 誤差の平均値の平方根を計算します。\n",
    "rmse = np.sqrt(error_total/len(X))\n",
    "\n",
    "print(f'平均二乗誤差の平方根は、{rmse[0]:0.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "平均二乗誤差は、標準偏差に対応するので、95%の確率でこの値の2倍以上誤差が広がることは無いと結論付けあれます。\n",
    "正規分布の性質を思い出したい方は、[こちらを参照](http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 6:  scikit-learnを使った重回帰分析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "説明変数が1つだけだと単回帰ですが、重回帰は複数の説明変数を同時に扱うことができます。\n",
    "\n",
    "scikit-learnの線形回帰ライブラリを利用します。\n",
    "[linear regression library](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html)\n",
    "\n",
    "sklearn.linear_model.LinearRegressionクラスは、データを元にモデルを作り、予測値を返すことができます。\n",
    "\n",
    "モデルを作る時には、fit()メソッドを呼び、予測をするときは、predict()メソッドを使います。\n",
    "\n",
    "今回は重回帰モデルを使いますが、他のモデルも同じように、fitとpredictメソッドを実装しているところが、scikit-learnの便利なところです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import sklearn\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# まず、LinearRegressionクラスのインスタンスを作ります。\n",
    "lreg = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "lreg.fit() はデータを元にモデルを作ります。\n",
    "\n",
    "lreg.predict() は作られたモデルを元に、予測値を返します。\n",
    "\n",
    "lreg.score()は、決定係数を返します。\n",
    "決定係数は、説明変数でどれくらいうまく目的変数の値を説明出来ているかの指標になります。[Wikipediaへのリンク](https://ja.wikipedia.org/wiki/%E6%B1%BA%E5%AE%9A%E4%BF%82%E6%95%B0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "カリフォルニアの住宅価格を、目的変数と説明変数に分けます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 説明変数\n",
    "X_multi = housing_df.drop('Price', axis=1)\n",
    "\n",
    "# 目的変数\n",
    "Y_target = housing_df['Price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# モデルを作ります。\n",
    "lreg.fit(X_multi, Y_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "切片の値は-36.94\n"
     ]
    }
   ],
   "source": [
    "print(f'切片の値は{lreg.intercept_:0.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "係数の数は8個\n"
     ]
    }
   ],
   "source": [
    "print(f'係数の数は{len(lreg.coef_)}個')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "単回帰の時は、直線だったので係数aと切片bはともに1つでした。今は、切片は1つですが、係数が8個あります。これは8個変数がある式になっている事を意味しています。\n",
    "\n",
    "$$ y = b + a_1 x_1 + a_2 x_2 + \\dots + a_{8} x_{8} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "実際に求められた係数を見ていきましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "tags": []
   },
   "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>Features</th>\n",
       "      <th>Coefficient Estimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>MedInc</td>\n",
       "      <td>0.436693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>HouseAge</td>\n",
       "      <td>0.009436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AveRooms</td>\n",
       "      <td>-0.107322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AveBedrms</td>\n",
       "      <td>0.645066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Population</td>\n",
       "      <td>-0.000004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>AveOccup</td>\n",
       "      <td>-0.003787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Latitude</td>\n",
       "      <td>-0.421314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Longitude</td>\n",
       "      <td>-0.434514</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Features  Coefficient Estimate\n",
       "0      MedInc              0.436693\n",
       "1    HouseAge              0.009436\n",
       "2    AveRooms             -0.107322\n",
       "3   AveBedrms              0.645066\n",
       "4  Population             -0.000004\n",
       "5    AveOccup             -0.003787\n",
       "6    Latitude             -0.421314\n",
       "7   Longitude             -0.434514"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 新しいDataFrameを作ります。\n",
    "coeff_df = DataFrame(housing.feature_names,\n",
    "                     columns = ['Features'])\n",
    "\n",
    "#求められた係数を代入します。\n",
    "coeff_df[\"Coefficient Estimate\"] = lreg.coef_\n",
    "\n",
    "coeff_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ここまでLec74"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 7: 学習（Training）と検証（Validation）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "ここまではすべてのデータを使って来ましたが、機械学習では一部のデータを使ってモデルを作り、残りのデータを使ってモデルを検証するという作業をします。\n",
    "\n",
    "サンプルをどのように分けるかが問題ですが、scikit-learnに便利な関数train_test_splitを使ってみましょう。\n",
    "\n",
    "サンプルを学習用のtrainと検証用のtestに分けてくれます。追加のパラメータを渡せば、割合も調整できます。\n",
    "[詳しくはこちら](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 説明変数をX、目的変数をYとして受け取ります。\n",
    "\n",
    "X_train, X_test, Y_train, Y_test = sklearn.model_selection.train_test_split(X_multi, housing_df['Price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(15480, 8) (5160, 8) (15480,) (5160,)\n"
     ]
    }
   ],
   "source": [
    "# どんな感じに分かれたか、確認してみます。\n",
    "print(X_train.shape, X_test.shape, Y_train.shape, Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 8: 価格の予測"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-6 {color: black;background-color: white;}#sk-container-id-6 pre{padding: 0;}#sk-container-id-6 div.sk-toggleable {background-color: white;}#sk-container-id-6 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-6 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-6 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-6 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-6 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-6 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-6 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-6 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-6 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-6 div.sk-item {position: relative;z-index: 1;}#sk-container-id-6 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-6 div.sk-item::before, #sk-container-id-6 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-6 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-6 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-6 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-6 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-6 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-6 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-6 div.sk-label-container {text-align: center;}#sk-container-id-6 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-6 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# まずはインスタンスを作ります。\n",
    "lreg = LinearRegression()\n",
    "\n",
    "# fitでモデルを作りますが、使うのは学習用のデータだけです。\n",
    "lreg.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "予測を、学習用のデータとテスト用のデータ、両方でやってみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "pred_train = lreg.predict(X_train)\n",
    "\n",
    "pred_test = lreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "それぞれの平均二乗誤差を計算できます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_trainを使ったモデルの平均二乗誤差＝0.52\n",
      "X_testを使ったモデルの平均二乗誤差＝0.53\n"
     ]
    }
   ],
   "source": [
    "print('X_trainを使ったモデルの平均二乗誤差＝{:0.2f}'.format(np.mean((Y_train - pred_train) ** 2)))\n",
    "    \n",
    "print('X_testを使ったモデルの平均二乗誤差＝{:0.2f}'.format(np.mean((Y_test - pred_test) ** 2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Step 9 : 残差プロット"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "回帰分析では、実際に観測された値と、モデルが予測した値の差を、残差と呼びます。\n",
    "\n",
    "$$ 残差 = 観測された値 - 予測された値 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "横軸に予測値、縦軸に実際の値との差をプロットしたものを、残差プロットと呼びます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "残差プロットを描いて、多くのデータがy=0の直線に近いところに集まれば、よいモデルが出来たことがわかります。\n",
    "また、均一に点がプロットされている場合、線形回帰が適切だったことが分かります。そうでは無い場合は、非線形なモデルを使うことを検討しましょう。（これは後のレクチャーで解説します。）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Plots')"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 学習用のデータの残差プロットです。\n",
    "train = plt.scatter(pred_train,\n",
    "                    (pred_train-Y_train),\n",
    "                    c='b', alpha=0.5)\n",
    "\n",
    "# テスト用のデータの残差プロットです。\n",
    "test = plt.scatter(pred_test,\n",
    "                   (pred_test-Y_test),\n",
    "                   c='r', alpha=0.5)\n",
    "\n",
    "# y=0の水平な線を描いておきます。\n",
    "plt.hlines(y=0, xmin=-5, xmax=15)\n",
    "\n",
    "plt.legend((train, test), ('Training', 'Test'), loc='lower left')\n",
    "plt.title('Residual Plots')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "英語になってしまいますが、scikit-learnのドキュメントには有用な情報が沢山あります。是非チェックしてみてください。\n",
    "http://scikit-learn.org/stable/modules/linear_model.html#linear-model"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}