04-evaluation/homework.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Homework 4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparation \n",
    "\n",
    "We'll use the same dataset and same preprocessing as last week:\n",
    "\n",
    "https://raw.githubusercontent.com/alexeygrigorev/mlbookcamp-code/master/chapter-02-car-price/data.csv\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the rest of the homework, you'll need to use only these columns:\n",
    "\n",
    "* `Make`,\n",
    "* `Model`,\n",
    "* `Year`,\n",
    "* `Engine HP`,\n",
    "* `Engine Cylinders`,\n",
    "* `Transmission Type`,\n",
    "* `Vehicle Style`,\n",
    "* `highway MPG`,\n",
    "* `city mpg`,\n",
    "* `MSRP`\n",
    "\n",
    "Preprocessing:\n",
    "\n",
    "\n",
    "* Keep only the columns above\n",
    "* Lowercase the column names and replace spaces with underscores\n",
    "* Fill the missing values with 0 \n",
    "* Make the price binary (1 if above the mean, 0 otherwise) - this will be our target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "url = 'https://raw.githubusercontent.com/alexeygrigorev/mlbookcamp-code/master/chapter-02-car-price/data.csv'\n",
    "df = pd.read_csv(url)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "features = [\n",
    "    'Make', 'Model', 'Year', 'Engine HP', 'Engine Cylinders',\n",
    "    'Transmission Type', 'Vehicle Style', 'highway MPG', 'city mpg', 'MSRP'\n",
    "]\n",
    "\n",
    "df = df[features].copy()\n",
    "\n",
    "df.columns = df.columns.str.replace(' ', '_').str.lower()\n",
    "df = df.fillna(0)\n",
    "\n",
    "mean_price = df.msrp.mean()\n",
    "df['above_average'] = (df.msrp >= mean_price).astype(int)\n",
    "\n",
    "del df['msrp']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `above_average` variable will be our target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split the data into 3 parts: train/validation/test with 60%/20%/20% distribution. Use `train_test_split` funciton for that with `random_state=1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_full_train, df_test = train_test_split(df, test_size=0.2, random_state=1)\n",
    "df_train, df_val = train_test_split(df_full_train, test_size=0.25, random_state=1)\n",
    "\n",
    "df_train = df_train.reset_index(drop=True)\n",
    "df_val = df_val.reset_index(drop=True)\n",
    "df_test = df_test.reset_index(drop=True)\n",
    "\n",
    "y_train = df_train.above_average.values\n",
    "y_val = df_val.above_average.values\n",
    "y_test = df_test.above_average.values\n",
    "\n",
    "del df_train['above_average']\n",
    "del df_val['above_average']\n",
    "del df_test['above_average']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1: ROC AUC feature importance\n",
    "\n",
    "ROC AUC could also be used to evaluate feature importance of numerical variables. \n",
    "\n",
    "Let's do that\n",
    "\n",
    "* For each numerical variable, use it as score and compute AUC with the `above_average` variable\n",
    "* Use the training dataset for that\n",
    "\n",
    "\n",
    "If your AUC is < 0.5, invert this variable by putting \"-\" in front\n",
    "\n",
    "(e.g. `-df_train['engine_hp']`)\n",
    "\n",
    "AUC can go below 0.5 if the variable is negatively correlated with the target varialble. You can change the direction of the correlation by negating this variable - then negative correlation becomes positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_auc_score, roc_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            year, 0.688\n",
      "       engine_hp, 0.917\n",
      "engine_cylinders, 0.766\n",
      "     highway_mpg, 0.633\n",
      "        city_mpg, 0.673\n"
     ]
    }
   ],
   "source": [
    "numerical = ['year', 'engine_hp', 'engine_cylinders', 'highway_mpg', 'city_mpg']\n",
    "\n",
    "for c in numerical:\n",
    "    auc = roc_auc_score(y_train, df_train[c])\n",
    "    if auc < 0.5:\n",
    "        auc = roc_auc_score(y_train, -df_train[c])\n",
    "    print('%16s, %.3f' % (c, auc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which numerical variable (among the following 4) has the highest AUC?\n",
    "\n",
    "- **`engine_hp`**\n",
    "- `engine_cylinders`\n",
    "- `highway_mpg`\n",
    "- `city_mpg`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "\n",
    "fpr, tpr, _ = roc_curve(y_train, df_train.engine_hp)\n",
    "plt.plot(fpr, tpr, label='engine_hp')\n",
    "\n",
    "fpr, tpr, _ = roc_curve(y_train, df_train.engine_cylinders)\n",
    "plt.plot(fpr, tpr, label='engine_cylinders')\n",
    "\n",
    "plt.plot([0, 1], [0, 1], color='grey', linestyle='--')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(df_train.engine_hp[y_train == 1],\n",
    "             stat='density', bins=50,\n",
    "             color='orange', alpha=0.5,\n",
    "             label='positive')\n",
    "sns.histplot(df_train.engine_hp[y_train == 0],\n",
    "             stat='density', bins=50,\n",
    "             color='blue', alpha=0.5,\n",
    "             label='negative')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2: Training the model\n",
    "\n",
    "\n",
    "Apply one-hot-encoding using `DictVectorizer` and train the logistic regression with these parameters:\n",
    "\n",
    "```\n",
    "LogisticRegression(solver='liblinear', C=1.0, max_iter=1000)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction import DictVectorizer\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dicts = df_train.to_dict(orient='records')\n",
    "dv = DictVectorizer()\n",
    "X_train = dv.fit_transform(train_dicts)\n",
    "\n",
    "model = LogisticRegression(solver='liblinear', C=1.0, max_iter=1000)\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "val_dicts = df_val.to_dict(orient='records')\n",
    "X_val = dv.transform(val_dicts)\n",
    "\n",
    "y_pred = model.predict_proba(X_val)[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9790257223864177"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "roc_auc_score(y_val, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "What's the AUC of this model on the validation dataset? (round to 3 digits)\n",
    "\n",
    "- 0.678\n",
    "- 0.779\n",
    "- 0.878\n",
    "- **0.979**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3: Precision and Recall\n",
    "\n",
    "Now let's compute precision and recall for our model.\n",
    "\n",
    "* Evaluate the model on all thresholds from 0.0 to 1.0 with step 0.01\n",
    "* For each threshold, compute precision and recall\n",
    "* Plot them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def confusion_matrix_dataframe(y_val, y_pred):\n",
    "    scores = []\n",
    "\n",
    "    thresholds = np.linspace(0, 1, 101)\n",
    "\n",
    "    for t in thresholds:\n",
    "        actual_positive = (y_val == 1)\n",
    "        actual_negative = (y_val == 0)\n",
    "\n",
    "        predict_positive = (y_pred >= t)\n",
    "        predict_negative = (y_pred < t)\n",
    "\n",
    "        tp = (predict_positive & actual_positive).sum()\n",
    "        tn = (predict_negative & actual_negative).sum()\n",
    "\n",
    "        fp = (predict_positive & actual_negative).sum()\n",
    "        fn = (predict_negative & actual_positive).sum()\n",
    "\n",
    "        scores.append((t, tp, fp, fn, tn))\n",
    "\n",
    "    columns = ['threshold', 'tp', 'fp', 'fn', 'tn']\n",
    "    df_scores = pd.DataFrame(scores, columns=columns)\n",
    "\n",
    "    return df_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_scores = confusion_matrix_dataframe(y_val, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>threshold</th>\n",
       "      <th>tp</th>\n",
       "      <th>fp</th>\n",
       "      <th>fn</th>\n",
       "      <th>tn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>654</td>\n",
       "      <td>1729</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.1</td>\n",
       "      <td>644</td>\n",
       "      <td>332</td>\n",
       "      <td>10</td>\n",
       "      <td>1397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.2</td>\n",
       "      <td>623</td>\n",
       "      <td>201</td>\n",
       "      <td>31</td>\n",
       "      <td>1528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.3</td>\n",
       "      <td>606</td>\n",
       "      <td>143</td>\n",
       "      <td>48</td>\n",
       "      <td>1586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.4</td>\n",
       "      <td>590</td>\n",
       "      <td>106</td>\n",
       "      <td>64</td>\n",
       "      <td>1623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.5</td>\n",
       "      <td>569</td>\n",
       "      <td>75</td>\n",
       "      <td>85</td>\n",
       "      <td>1654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.6</td>\n",
       "      <td>550</td>\n",
       "      <td>51</td>\n",
       "      <td>104</td>\n",
       "      <td>1678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.7</td>\n",
       "      <td>506</td>\n",
       "      <td>30</td>\n",
       "      <td>148</td>\n",
       "      <td>1699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.8</td>\n",
       "      <td>464</td>\n",
       "      <td>21</td>\n",
       "      <td>190</td>\n",
       "      <td>1708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.9</td>\n",
       "      <td>376</td>\n",
       "      <td>3</td>\n",
       "      <td>278</td>\n",
       "      <td>1726</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>654</td>\n",
       "      <td>1729</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     threshold   tp    fp   fn    tn\n",
       "0          0.0  654  1729    0     0\n",
       "10         0.1  644   332   10  1397\n",
       "20         0.2  623   201   31  1528\n",
       "30         0.3  606   143   48  1586\n",
       "40         0.4  590   106   64  1623\n",
       "50         0.5  569    75   85  1654\n",
       "60         0.6  550    51  104  1678\n",
       "70         0.7  506    30  148  1699\n",
       "80         0.8  464    21  190  1708\n",
       "90         0.9  376     3  278  1726\n",
       "100        1.0    0     0  654  1729"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scores[::10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_scores['p'] = df_scores.tp / (df_scores.tp + df_scores.fp)\n",
    "df_scores['r'] = df_scores.tp / (df_scores.tp + df_scores.fn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ymN5xEQxIjKR9hJIMkSqqMyLSGIYBxXnmzJ7MVHOmT8Zqc72ek4XFQq/LYMRtEJnU4qFK0yurdLJsWy7/25DNorT9HCk7vvRBXEQQF/WN5aJ+sQxIiMRu981EVARU9EzEGgWZsG+1mZhk/ADZPx1fo8fmgN6Xwcg7IW6AlVFKI+UUlPLvVXt454d0DhcfH3MUeywBuVgJiEgNSkZE3EFFCexeBqteNmf6VIlPgehuNVczjultDooVt2IYBhsyC5j7/W7+7+dsKo8NPI0JD+SivrFc0i+OgYlKQETqomRExN1k/wwrXjQHxxqnGNgYkQSJQyFpuJmc2E8c1mUzx7R4yHRjp9NJamoqACkpKW5fDt4wDIrLneQeKWPb/iNs2JfPhswCNmQWknvk+DIFQztEceNZHbigV3scSkBETkvl4EXcTWw/uOJ1OP9R2LO85mDY/HQ4uMUcc1KQDhs/rPs5HIHm1OXel0P3CW5fWba4uLjFXqu80sXBI2UcLCrjQGEpB4rKKCipwGG3VS8U5++wc7Sskryj5eQdKSPvSDm5R8rIPVJO3tEySitcdT63v8PGJf3iuHFUR/omRLTYexLxFUpGRFpaRAL0n1T7eFnRscGwqyF9lTmb50SVpWZ9lC3/Z27+IZA8snYl2eDWx2uhRMRDmy4eP3A241AxW3OKOHikjAOFZRwoKiX3WDKRd9RMKIpKK8/8RPUQ5G+nQ5tQ+sRH0Dc+gj7xEfSKDdd6LiLNSMmIiLsIDINOY82tLoYB+zcdWzjwI7PK7I6v6/fc7fuaCwn2vhxad2iaeFuA02Xw8nc7mPH1tlqVSOvi77DRtlUgbcODaBcWSOsQf1wGVDhd5mJxlQbBAQ7ahAYQ3SqANq0Czf2wQKJDA2nTKoDQQH0sirQ0/a8T8RQ2G7TvY27nPgxZ6yDnZzNJqWK4zCnHBRnHu4DydkDOBnP7+jFz8GzX8ebYlITBblukLaeglCnz17Fq1yEAerQPIz4ymHbhgWbCERZIdKtA2rQKJCo0gDahAUQE+2sgqYgHUjIi4olsNogfZG5nUnzIXERw48ewZ5nZFZSZeux57OZA2aSR0OtSSBoBduu7I75O28+9H/7E4eIKQgIc/O1XfbgiJcHqsESkmSgZEfF2IVGQcr25Fe03x5vsXXG8SFtVq8nqV6FVe7Mrp8+vIWFIi1eOzSko5Z9fbeXD1H0A9I4L58XfDaRT21YtGoeItCxN7RXxZYVZZnG27V/Dls/NRQWrRCSZRdr6XAGx/RucmDidTn788UcAhgwZctqpvUfLKnl16S5eX7qLkgpz2vONozpy/4TuBPpZ31IjIo2jOiMi0jCVZbDzW7M7Z+sCKD9y/L6oTtDjEnNmTkQ8hCeYt79wvEl5pYsPU/fx3KJt1bU8UpJb8+BFPUlJbv2LnltErKdkREQar6IEtn9lJibbFkJlSd3nnVikLXEotOsNjjP3/pZWOHlvdTqvLd1FVkEpAMltQnjgwh5c2Kc9Nh9dWFDE2ygZEZGmUXYEtn4Be5ebs3MKjhVrKyuodaoRGI4x6Frsw28zW06OcboM8o6Usb+wjGU7DjL3+93kHikHoG1YIH8a05k/DE8mwM/eYm9LRJqfkhERaV6lBRze8QPZGxdjz/iRhKMbaYVZcbXCcPCl/Sy+9ruAfa7WrC+OwGnUTDQSWgczeUxnfpOSQJC/xoWIeCOVgxeRJrW/sJTN2YVszi5iS04hm7IK2XGgAhgFjMKOizH2n7jV7/8Ybt/MRcYywirKKSGAwQHrcODCbrNRaQ+krF1/2vc+G0dcCBADKBkR8WVKRkTklMorXXyxMZu53+/mp321u2UA+sSHM6pLNKO7tGVA0gQqKu8jZ+8aAn6chbEnj2CjnCjbERwcW/fFVQQ535gbgCPAXGfn/MfMgbIi4nPUTSMitRw+Ws47q9N5e+Ue9heas1zsNujUthU92ofRMzacnrFh9E+IpE2rwDqfw+l0suybhVBRzOiUXsen9pYchn0/muvvZPwARw+ax+3+MPxPcPY9EKTF6ES8gbppRKTe8ovL+XHPYX7cc4gfdh9iY2YBzmOLwbQNC+Ta4clcPSzplInHKQWEmFvb7nBinZGk4TDyz2Yp+5wN8PWj5rTiFTNh/Tsw5j6z6FpEAoREg10DW0W8mZIRER+UX1zOql2HWLUrj1W78tiSU1TrnD7x4dw4qiOX9ItrvlkuNhvE9oM/fAzbF8HCByFvO3xx3/FzHAEQHne8tknVasSRHcxy+CFRzRObiLQYJSMiPmL7/iK+2JjDwk05pGUXcnIHbee2oQztGMXQjlEM6RBFQuuQlgvOZoNu46DzObBmLmz40FzsrygHnOXmCsWH99T92DZdIXEYJA0z65xExENoO7WmiHgQJSMiXmzXwSN8vDaTLzZms/Pg0Rr3dWnXiuGdohjRKZqhHaNoG9bALph68Pf3b9gDHP4w7FZzA3BWQFH28domhfuOr0acu91sRana1v/n+PPY/c3WlMgks/Uk8VhRttDopntzItJkNIBVxMsYhsGKnXnM+X433245UH3c32HjrC7RTOgTy9gebWkXFmRhlE2k+NDxwbD7foRDu8zkxXDVfX6bLmYrSuJQM0GJ7qYWFJFmpKJnIj7mSFklC37OZu7y3dVjQGw2OKd7Oy7tH8e5PdsRHtTAlgpP5Kw0E5LCTMjbYc7YyVgNB7fUPjcoAhKGml08icMgPgUCQls+ZhEvpWRExAdUOl0s25HLp+syWbgph9IKs0Ug2N/BbwcncMOojnSM1pcrYE4pzvgRMlaZyUlmKlQU1zzH5oD2fY536yQNN2f0iEijKBkR8RIul8Hh4nIOHikj83AJGYeKyThcwr7DxaTuPVy9xgtAp+hQrhySyO+GJBERYm0riNPpZMOGDQD07dv3eJ0Rd+GsgP0bIf2HY60nP5itKScLj4eEwdC6w7EZPcdm9bTtCX4BLR62iCdRnRERD5FxqJj/rs9kf2EZR8oqKSqt5EhZBfnFFeQeKefQ0TJcp/mToU1oABP7x3HZwHj6J0S41Yq3+fn5Vodwag5/iBtobsMnm8cK9h0ff5LxA2T/bCYoaXUkKW17wo1fQnBki4Yt4o2UjIhYwOUy+H5HLm+v3MM3Ww7UmmZbl9Yh/sRGBJMYFUxi6xASWgfTpV0YwzpF4e/QIMwmEZEAfX9jbgDlRyFzLWSvPzajZ9/xmTwHN8P/TYHfvGEOzhGRRlMyItKCcgpK+eynTN5dncHu3ONTbUd3jWZgUmvCAv1oFeRHq0A/woL8iG4VSNuwQKJCA5RwWCEgFDqONrcT7UuFueNg0yfQ6RxIuc6a+ES8hJIRkWZWVFrBlxtz+HR9Jit25lW3goQF+nFFSgLXjEimc9tW1gYpDZOQAuc+bJax/+J+cyZOux5WRyXisZSMiDQTwzB478cM/vZ/aRSXO6uPD+nQmssHJvCrAXGEBuq/oMcaeSfsXmKuqfPhDXDLt+AfbHVUIh5Jn4QizSC/uJwHPtrAl5tyAHOWy+UD47lsYDyJUS1YZl2aj90Ol78Ks0fBgTRY+BBc8pzVUYl4JCUjIk3sh115TJm/nuyCUvwdNu4d352bz+qE3e57gxzt3l7dtFU7uPwV+M+vYc0cOLD5eAG1hKEQ2sbqCEU8guqMiPxCpRVO0rIL+Skjn9S9h1mwIRuXAR2jQ5l51UD6JkRYHaI0t8X/DxZPr308/IRVhsPjzVolXc6DqE4tHqKIFVT0TKSZGIbBpqxCFqXtZ/HWA2zKKqTypEIgv01J4LFLe2tMiC/J3QHpK4+Xn8/deupz4wZCnyug9+Wq8CpeTcmISBPKO1LG2vR8lm0/yNdp+8kqKK1xf3SrAAYkRtI/IZIRndswuEOURZGK2yg+BId2H19puGCfWfF1z7KaC/l1GA0j7oCu47Ron3gdVWAV+QUOFJXyddoB1uw5xNr0w+zJq7mGSbC/g9Fdo7mgVwwjOrchPjLYrSqfugOXy8XGjRsB6NOnj/ePHzlZSJS5kVLz+JGDsPm/sPFj2LvCTE72LIPo7jDyz9DvSvALtCRkEas0qmVk1qxZPPPMM2RnZ9O7d29mzJjB6NGjT3n+vHnzePrpp9m+fTsRERFceOGF/POf/6RNm/oN7lLLiLSEw0fL+XJTDp//lMWqXXm1SrB3adeKIR2iOL9nO0Z1iSbI383WWnEzTqeTZcuWATB69Gj3W5vGHRTsgx9egTVvQrm50jKtYsyEpPevze4cJbniwZqtm2b+/Plcc801zJo1i1GjRvHqq6/yr3/9i7S0NJKSkmqd//333zNmzBief/55Jk6cSGZmJpMnT6Zr16588sknTfpmRBqiqLSCden5/LjnEKt3HyJ17+EaYz/6J0Yypms0A5NbMyixteULz3kaJSMNUFoAqW/BqtlQlHX8eOuO0OfX0ONiaN/PXE9HxIM0WzIybNgwBg0axOzZs6uP9ezZk8suu4zp02uPJv/nP//J7Nmz2blzZ/WxF198kaeffpqMjIx6vaaSEWkqpRVOPlmXyXur09mQWVCr9aNXbDiX9I/lkr5xJLVRPZBfQslII1SWw7YvYdPHsPVLqCw5fp9/CMSnQOJQSBoJncaCQz3t4t6aZcxIeXk5qampPPDAAzWOjxs3jhUrVtT5mJEjR/LQQw+xYMECJkyYwIEDB/jwww+5+OKLT/k6ZWVllJWV1XgzIr9E7pEy/r1yL/9ZtZe8o+XVxxOjghnSIYohHaIY3qkNHaNDLYxSfJ5fAPS61NzKjhxLTD4xx5SUFhwfX8Kz5sDX374JodFWRy3yizUoGcnNzcXpdBITE1PjeExMDDk5OXU+ZuTIkcybN49JkyZRWlpKZWUll156KS+++OIpX2f69Ok8/vjjDQlNBID9haXM/zGDg0VlFJVWUFRaSVFpJev35VNeac5giI8M5oZRHbikXxztI4IsjljkFAJbHV9B2OWC3G3Hpw2nfWomJa+Ogav+Y44tEfFgjWrjO3nWgGEYp5xJkJaWxp133skjjzzC+PHjyc7O5t5772Xy5MnMmTOnzsdMmzaNqVOnVv9cWFhIYmJiY0IVH1FUWsFrS3fx+rJdlFa46jynf2Ikt4zuyIW92+OnFXDFk9jt5kJ87XqYKwSP/DO8dzUc2glzL4SJL0D/q6yOUqTRGpSMREdH43A4arWCHDhwoFZrSZXp06czatQo7r33XgD69etHaGgoo0eP5sknnyQ2NrbWYwIDAwkM1NQ2ObMKp4v3Vqcz4+vt1d0vKcmtGdUlmrBAP8KC/AgL8icpKoQ+8eGafiveoV0Pc2G+T241u3I+uRWy1sG4JzXIVTxSg5KRgIAAUlJSWLRoEZdffnn18UWLFvGrX/2qzscUFxfj51fzZaoGsnlAvTVxU5VOF5+uz+LFb7ez91gNkI7Rodx/YQ/G945R0uEGHA4HY8eOtToM7xUcCVe9C0v+Hyx5ypwinLMBfvsWtGprdXQiDdLgbpqpU6dyzTXXMHjwYEaMGMFrr71Geno6kydPBswulszMTN5++20AJk6cyC233MLs2bOru2mmTJnC0KFDiYuLa9p3I16v0univ8eSkKpCZG1CA5hyfleuGpqEv7pfxJfY7XDOgxDbHz6+FfYuh9fGwKR/mzNvRDxEg5ORSZMmkZeXxxNPPEF2djZ9+vRhwYIFJCcnA5CdnU16enr1+ddffz1FRUW89NJL/OUvfyEyMpJzzz2Xp556qunehXi90gonH63dx+tLd1UnIVGhAdx6dif+MDxZa8CIb+txsdlt897VkLcd5k6AS56Hgb+3OjKRetHaNOLWDhaV8e+Ve/jPD+kcOjYmJCo0gD+e3YlrlIS4NZfLxebNmwGzFpHPlYO3QmkBfDIZti4wf44dcHxBvkhNApCWp7VpxGPlHSlj6faDfLvlIAs35dSYknvjWR25akiikhAPYBgGBw8eBKBHjx4WR+MjgiJg0jxY+gwsfRqy15vboochYajZUjLgDyqWJm5Hv5HiFopKK3hz+R6+3nKAn/flc2J73YDESG4Z3YnxvWM0JVfkTOx2GHs/DLkJ0qoW5FsO+1ab26rZMP7v0OV8qyMVqaZkRCy3N+8oN7+1hu0HjlQf6xkbzjnd23JBrxgGJEZqdoxIQ4VGmwnJkJugMBs2fADfPw8Ht8B/roCu42Dc36FtN6sjFVEyItZauTOPP81LJb+4gpjwQO4+vxtju7dTZVSRphQeC6PuhEHXwNJ/mtOAt38FO76BUXfB2GlmKXoRi6jNWyzzzg/pXDPnB/KLK+ifEMFnd5zFVUOTlIiINJfg1mYXzW0/QLcJYDjh++fg9XMgZ6PV0YkPU8uItKiMQ8Ws3JXHt5sP8OUms5Lvpf3jePo3/Qjy16quIi0iugtc/Z45puT/7ob9G+G1sXDONBh5lwa4SovTb5w0u6z8EmZ+s53vd+Sy73BJjfvuHd+d28Z21pgQESv0+hUkjYDPp8DW/8E3T5gDXgdcDb0ug4h4qyMUH6E6I9KsfsrI56a31pB7pAwAP7uNfgkRjOjchgt6tWdAYqS1AUqzMQwDl8uclm2325VwujPDgJ/ehS/uh7LC48eTRpoJS6t2Nc9v2x1ierdsjOKR6vv9rWREms2XG7OZMn89pRUuerQP44EJPRjSIUo1QkTc1dFcs2Vk08eQvvI0J9rg3IfgrL+YU4lFTkHJiFjGMAxeXbqL//fFFgDGdm/Li78bSFiQVhMV8RgF+2DTp7DzG6gsP368ohiy1pr7PS6By1+BwDBLQhT3p2REWoRhGOw8eJQ9uUdJP1RM+qFituQUsmrXIQCuG5HMw5f0UrEyH+Ryudi2bRsA3bp1Uzl4b5L6Fiy4B5zlEN0drpoH0V2tjkrckMrBS7Patr+Iz9Zn8fnPWew9tnDdiew2eOSSXlw/qqMF0Yk7MAyDnBxzxlTXrvqi8iop15ljRuZfA7lb4fVzYeAfIHGYuYXHWh2heBglI1IvhmGQll3IN5sP8L+fs9m6v6j6vkA/O13atSIpKoSkqBASo0IY3KE1PdqrFUvEayUMhj8uhg+uM8eXrJplbgCRSWaF13MegpAoS8MUz6BkRE7J6TJYuv0gX6ft59stB8guKK2+z99hY0y3dlw6II7ze7YjJEC/SiI+JywGrvvcrFeSvhIyfoD9myA/HX78F2z5H1z6EnTVOjhyevoGkTptzSni/o9+Zn1GfvWxYH8HZ3WN5oKeMYzv3Z6IEA1IFfF5Dn/o+xtzAygrgr0rYOFDkLcd5l0BKTfAuCchsJW1sYrbUjIiNZRVOnn52x3MXrKTCqdBq0A/fjUgjvN7xjCicxtVSRWR0wsMg27joePZ8PXj8MNsSH0Ddn5rzrxJHml1hOKGlIxItdS9h7nvw5/YefAoAOf3jOFvl/UmNiLY4shExOP4B8OE/wc9LoJPb4P8vfDGRTDyDjjnr+CvNajkOM21EwA2Zhbwu9dXsfPgUdqGBTLr94N4/doUJSIi8st0PBv+tMKcbYMBK16E18ZA1jqrIxM3ojojwuGj5Vzy4vdk5pdwdre2vHjVQI0HkV/MMAwqKioA8Pf3Vzl4ga1fwGd3wtEDYPeDwTeaU4TDE8x1cCISVEDNy6jomdSL02Vw/RurWbY9lw5tQvjvHWcREaxERESaydE8+N9USPu07vv7XgkTntKUYC+homdSL89+tZVl23MJ9nfw6jWDlYiISPMKbQO/fdOc9rvzGyjIhMJMKMiA0gLY8D7sWaYpwT5GyYgP+3JjDrMW7wTgqd/0o3t7NY9K03G5XOzYsQOALl26qBy8HGezQc9LzO1E+9bAJ7dC3g5NCfYx+nTwUVtzirjng58AuOmsjlzaP87iiMTbGIZBVlYWWVlZeEBvsLiDhMFw6zIYNtn8OfUNeOUsyNlgbVzS7JSM+KCVO/P47SsrOFJWybCOUTwwoYfVIYmImAJCzDEj130OEYlweDf86wLY8KHVkUkzUjLiYz5dl8m1c3+gsLSSlOTWvPKHFPy1oq6IuJuOZ8OtS6HzeVBZAh/dBF/9FZyVVkcmzUDfQj7CMAxe/m4HU+avp8JpcFHf9sy7eRitQwOsDk1EpG4hUfD7D+CsqebPK16E//wadn4HuTugosTa+KTJaACrDyirdPLIp5uYvyYDgD+e3YkHLuyB3a66DyLi5uwOOP9RiO1vVnLdvcTcqgRHQcfR8KuXVaPEgykZ8XLpecXc/s5aNmQWYLfBoxN7c93IDlaHJSLSML0vg+hu8N3fIXe7OR24/AiUHDJXDQ6OgokzrI5SGknJiBf7alMOf/ngJ4pKK2kd4s/zkwYwtns7q8MSEWmcmF5w1Txz3zDMuiS7l8D715ozb3pOhC7nWRujNIoqsHqhCqeLZxZu5bWluwAYmBTJy1cPIi5S68xIyzEMg7KyMgACAwNVDl6az4L7YPWrEB5vroMTHGl1RHJMfb+/NYDVy1Q4XdzxztrqROTGUR2Z/8cRSkSkxdlsNoKCgggKClIiIs3r/EchqpPZdbPwQaujkUZQMuJFKp0upry3noWb9hPgsDPr94N4ZGIvAvz0zywiXiwgFC6bDdhg/TzY+qXVEUkD6VvKSzhdBlPf/4n/bcjG32Hj1WtSuKhvrNVhiQ9zuVzs3LmTnTt34nK5rA5HvF3ScBhxu7n/+Z1QfMjaeKRBlIx4AafL4N4PfuKzn7Lws9uY/fsUzumhgapiLcMwyMjIICMjQ+XgpWWc+1dzxs2R/fDBdVBWZHVEUk9KRjycy2XwwEc/8/G6TBx2Gy9dPZDze8VYHZaISMvzD4bLXwX/UNi9FN6aCEdzrY5K6kHJiAdzugzu+fAnPkjdh90GL1w1gAv7qGtGRHxY/CBzXZvgKMhaB3PHw+G9VkclZ6BkxENVOl3cPX89H681W0ReuGogl/TTyrsiIiSkwE1fmQvt5e0wE5L9m6yOSk5DyYgHqnC6uPO9ddVjRF6+eiAT+ysRERGpFt3VTEja9oSibHhjAuxPszoqOQUlIx6mrNLJbfPWsmBDDgEOO6/8IUVdMyIidQmPgxsWQMIQs1rrvN9AYZbVUUkdlIx4kIxDxUx6dRWL0vYT4Gfn1WtTNFhVROR0QqLg6vfNWTaFmTDvSigttDoqOYmSEQ/xxYZsLpq5jPUZ+YQH+TH3uiGco3VmxI3Z7XaGDBnCkCFDsNv1USMWComC338Ioe1g/wZzLRtnhdVRyQn0CeHmSiucPPLfjfxp3lqKSisZmBTJ/+4czVldo60OTeS0bDYboaGhhIaGqhy8WK91Mvz+fXPa767v4PO7zMX2xC0oGXFjBcUVXPnqSt5eaU5Lu3VMJ96/dQSJUSEWRyYi4oHiBsJv3wSb3Swb/+2TVkckxygZcVNHyyq5/s3V/LyvgKjQAN68YQjTJvTE36F/MvEMLpeLPXv2sGfPHpWDF/fRbRxc/Jy5v+yfsOQZa+MRAPysDkBqK6t0cuu/U1mXnk9EsD/v3jKc7u3DrA5LpEEMw2DPnj0AJCYmWhuMyIkG32CWil/0MHz3JPgFwKi7rI7Kp+nPbDdT6XRx57vr+H5HLiEBDt68YYgSERGRpjbqTjj3YXN/0SOwara18fg4JSNuxOUyeODjDSzctJ8Ah53Xrx3MwKTWVoclIuKdzr4Hxtxv7n/5AKx+3dp4fJiSETcy89vtfJi6D4fdxotXD2RUF82YERFpVmOnwVl3m/sL7oGcDdbG46OUjLiJ9Rn5vPjtDgCm/7ov43u3tzgiEREfYLPBeY9C94vNn9e+bW08PkrJiBsorXAy9f31OF0GE/vHceVgDfYTEWkxNhsMudHc//l9qCi1Nh4fpGTEDTz15RZ2HTxKu7BA/var3laHIyLiezqdA+HxUJoPWxdYHY3PUTJisRU7c3lj+R4AnvpNPyJDAqwNSKSJ2O12Bg0axKBBg1QOXtyf3QEDrjb31/3H2lh8kD4hLFRUWsG9H/wMwO+GJmmtGfEqNpuN8PBwwsPDVQ5ePENVMrLzWyjYZ20sPkbJiEUMw+Dxz9PIzC8hMSqYhy7uaXVIIiK+LaoTJJ8FGPDTu1ZH41OUjFjA6TJ4+L8b+TB1HzYbPPvbAbQKVDFc8S4ul4v09HTS09NVDl48x8A/mLfr/gP6vW0xSkZaWGmFk9vnreU/q9Kx2eCJS3sztGOU1WGJNDnDMNi1axe7du3C0Oqo4il6XQoBYXB4D6SvsDoan9GoZGTWrFl07NiRoKAgUlJSWLZs2WnPLysr46GHHiI5OZnAwEA6d+7M3LlzGxWwJysoruDaOav5clMOAQ47L189iGtGdLA6LBERqRIQCn0uN/fXzbM2Fh/S4GRk/vz5TJkyhYceeoh169YxevRoJkyYQHp6+ikfc+WVV/LNN98wZ84ctm7dyrvvvkuPHj1+UeCeZn9hKVe+upLVew4RFujHWzcO5aK+sVaHJSIiJxt4jXmb9imUFloaiq9o8ECF5557jptuuombb74ZgBkzZrBw4UJmz57N9OnTa53/5ZdfsmTJEnbt2kVUlNkd0aFDh18WtYepdLqY/J9Utu4vol1YIG/dOJSeseFWhyUiInVJGALR3SB3G2x4H4bcbHVEXq9BLSPl5eWkpqYybty4GsfHjRvHihV196199tlnDB48mKeffpr4+Hi6devGPffcQ0lJySlfp6ysjMLCwhqbJ3vx2x2sS88nLNCPDyaPUCIiIuLObLbjA1kX3Auf3wVHDlobk5drUDKSm5uL0+kkJiamxvGYmBhycnLqfMyuXbv4/vvv2bhxI5988gkzZszgww8/5Pbbbz/l60yfPp2IiIjqLTHRc8ujr9lziBe/3Q7Ak5f3IblNqMURiYjIGQ39I/T+NRguSH0TXhwEy1+AyjKrI/NKjRrAenIBI8MwTlnUyOVyYbPZmDdvHkOHDuWiiy7iueee48033zxl68i0adMoKCio3jIyMhoTpuUKSyuYMn89LgMuHxjPrwbEWx2SiIjUh38w/PYNuOELiB0AZYWw6BF4eRhs/hw0Q6xJNSgZiY6OxuFw1GoFOXDgQK3WkiqxsbHEx8cTERFRfaxnz54YhsG+fXVXuAsMDKyu3Fi1eaJH/7uJfYfNomZPaM0Z8TF2u50BAwYwYMAAlYMXz5U8Em75Di6bDa3aw+HdMP8P8NZEyP7Z6ui8RoM+IQICAkhJSWHRokU1ji9atIiRI0fW+ZhRo0aRlZXFkSNHqo9t27YNu91OQkJCI0L2DP9dn8kn6zKx22DGpAGEBflbHZJIi7LZbERGRhIZGaly8OLZ7HazVPyfU+Hse8EvCPYsg1fPhv/eofEkTaDBf65MnTqVf/3rX8ydO5fNmzdz9913k56ezuTJkwGzi+Xaa6+tPv/qq6+mTZs23HDDDaSlpbF06VLuvfdebrzxRoKDg5vunbiRrTlF/PWTjQD8+dyupCSrqJmIiMcLbAXn/hXuWAN9fgMYsO7f8OpoyPjR6ug8WoOTkUmTJjFjxgyeeOIJBgwYwNKlS1mwYAHJyckAZGdn16g50qpVKxYtWkR+fj6DBw/m97//PRMnTmTmzJlN9y7cSGZ+CdfNXU1RWSVDO0bx53O7WB2SiCVcLheZmZlkZmaqHLx4l8hE+M0cuGkRtO0BRdnwxgRzoKs0is3wgDrNhYWFREREUFBQ4NbjRw4fLec3r6xg58GjdItpxQe3jiQiRN0z4pucTmd1debRo0fjcDgsjkikGZQVwae3webPzJ9TrocJT4NfoKVhuYv6fn9rVFkTKSl3cuNbP7Lz4FHiIoJ468ahSkRERLxdYBhc+Tac9whgM1tH3rgI9m+yOjKPomSkCVQ6XdzxzlrWpecTEezP2zcNJTbCO8fDiIjISWw2GP0X+P2HEBQBmWvglbPg8yka3FpPSkaawMxvtvPNlgME+duZe/1gurQLszokERFpaV3Ph8nfQ6/LjhVLe+NYsbSZKpZ2BkpGfqGi0greWL4HgKeu6KeZMyIiviwyCa58C65fALH9jxVLexg+/ZPVkbk1JSO/0HurMygqq6Rz21Am9ouzOhwREXEHHUbBLYvh0pcAG2z8CA5ssToqt6Vk5BeocLqYu3w3AH88uxN2uwo7iYjIMXY7DLoGelxs/rziRWvjcWNKRn6B//s5i+yCUqJbBWrdGZGT2O12+vbtS9++fVUOXnzbWXebtz/Ph8Isa2NxU/qEaCTDMHhtqdkqcsOoDgT5q4aCyIlsNhtt2rShTZs2Kgcvvi1hMCSPAlcFrJpldTRuSclII32/I5fN2YWEBDj4/bAkq8MRERF3Nuou83bNm1CSb2UkbknJSCO9tnQXAFcOTiQyJMDiaETcj8vlIicnh5ycHJWDF+lyAbTtCeVF5pRfqUHJSCOkZRWybHsudhvcdFZHq8MRcUuGYbBlyxa2bNmCB6w6IdK87PbjrSOrZkNFqbXxuBklI43w+jKzVeSivrEkRoVYHI2IiHiEPldAeDwc2W8OZpVqSkYaaH9hKZ//ZI6G/uPZnSyORkREPIZfAAy/zdxfMRPUfVlNyUgDfbAmg0qXweDk1vRLiLQ6HBER8SQp15nr1+TtgC2fWx2N21Ay0gAul8G7qzMAuFozaEREpKECw2DoH839pc+AxlMBSkYaZNmOXDLzSwgP8uOivrFWhyMiIp5o+G0Q0ApyNsC2hVZH4xaUjDTAuz+kA/DrQQkqciYiIo0TEgVDbjL3lz6t1hGUjNTbgcJSvt68H4DfDVUXjciZ2O12evXqRa9evVQOXuRkI/4MfsGQmQo7v7U6GsvpE6KePkjdR6XLICW5Nd3bh1kdjojbs9lstGvXjnbt2qkcvMjJWrWFlOvNfY0dUTJSHy6XwXs/ml00ahUREZEmMepOcARA+krYu9zqaCylZKQelu/MJeNQCWFBflysgasi9WIYBgcOHODAgQOqwCpSl/A4GHiNub/kaWtjsZiSkXp4d/WxgasD4wkO0MBVkfpwuVykpaWRlpamtWlETuWsKWD3g91LIGO11dFYRsnIGRwsKuOrTccGrqq2iIiINKXIJOh/lbn/7d98duyIkpEz+PDYwNWBSZH0aB9udTgiIuJtRt8DjkDYvRQ2fGh1NJZQMnIGX27MBuC3KYkWRyIiIl4pqiOMudfc//IBKD5kbTwWUDJyGgeLyvhpXwEA5/dsZ3E0IiLitUbeBW17QHEufP2o1dG0OCUjp7F46wEA+sSH0y48yOJoRETEa/kFwCUzzP21b8PeFZaG09KUjJzG4q0HATi3u1pFRESkmSWPOF4I7fO7oLLM0nBakpKRU6hwuli6zUxGxvZQMiLSUDabjR49etCjRw9VYBWpr/Mfg9B2kLsNlr9gdTQtRsnIKazZc5iiskqiQgPonxBpdTgiHsdut9O+fXvat2+vtWlE6iu4NVw43dxf+gwc2m1tPC1EnxCn8N2x8SJju7XFYddfdSIi0kL6XAEdx4CzHFbNtjqaFqFk5BS+3WImI+eoi0akUQzDIC8vj7y8PJWDF2kImw3OutvcX/cfKMm3NJyWoGSkDhmHitlx4AgOu42zu7W1OhwRj+RyudiwYQMbNmxQOXiRhuo0Ftr2hIqjZkLi5ZSM1KGqiyYluTURwf4WRyMiIj7HZoPhfzL3f3gVnJXWxtPMlIzUobqLRlN6RUTEKv2uhJA2UJAOW/9ndTTNSsnISUrKnazcmQfAuRovIiIiVvEPhsE3mvsrZ1kbSzNTMnKSFTtzKat0ER8ZTLeYVlaHIyIivmzwTWD3h4xVkJlqdTTNRsnISY7PommrQk0iImKt8Fjo82tzf9Ur1sbSjJSMnMAwDL47loyoi0ZERNxC1UDWTR9DYZa1sTQTJSMn2He4hKyCUgIcdkZ0irY6HBGPZrPZ6Nq1K127dlUro8gvETcQkkaCqxJWv251NM1CycgJco+YixK1DQskOMBhcTQins1utxMfH098fLzKwYv8UlWtI2vmQtkRa2NpBvqEOEF+SQUAkSGqLSIiIm6kx8UQ1QlK82Hdv62OpskpGTlBQbGSEZGmYhgG+fn55Ofnqxy8yC9ld8DIP5v7K18GZ4W18TQxJSMnOFxcDkBkSIDFkYh4PpfLxfr161m/fr3KwYs0hf6/g9C2UJABGz+2OpompWTkBPlVLSMqAS8iIu7GPxiGTTb3l78AXtTiqGTkBPnVLSNKRkRExA0NuQn8Q+HAJtjxjdXRNBklIyeoGsDaWt00IiLijoJbQ8r15v7yGVZG0qSUjJzg8LFuGq3UKyIibmvEbWD3gz3LvKZEvJKRExQc66ZRy4iIiLitiATo+1tzf/kL1sbSRJSMnEB1RkRExCOMvNO8TfsMcndYG0sTUDJygsNHNbVXpKnYbDY6depEp06dVA5epKnF9IJuEwADvv2b1dH8YkpGjnG6DApLKwG1jIg0BbvdTlJSEklJSSoHL9IcznsYbHZI+xQyfrQ6ml9EnxDHFJQcr2anAawiIuL2YnrDgKvN/UUPe3TdESUjx1TVGAkL9MPfocsi8ksZhkFhYSGFhYUqBy/SXMY+CH7BkL4StvzP6mgaTd+6x1QNXo1QF41Ik3C5XKxdu5a1a9eqHLxIc4mIN6f6Anz9qMeuWaNk5Jh8TesVERFPNGoKhLSBvB2w9i2ro2mURiUjs2bNomPHjgQFBZGSksKyZcvq9bjly5fj5+fHgAEDGvOyzSpfK/aKiIgnCgqHMQ+Y+4v/H5QVWRtPIzQ4GZk/fz5TpkzhoYceYt26dYwePZoJEyaQnp5+2scVFBRw7bXXct555zU62Oak6qsiIuKxUq6HqE5w9CAsn2l1NA3W4GTkueee46abbuLmm2+mZ8+ezJgxg8TERGbPnn3ax916661cffXVjBgxotHBNidVXxUREY/lFwDnPWLur5kLLqe18TRQg5KR8vJyUlNTGTduXI3j48aNY8WKFad83BtvvMHOnTt59NFH6/U6ZWVl1aPwq7bmpuqrIiLi0XpcAkGRUJwLe0/9neyOGpSM5Obm4nQ6iYmJqXE8JiaGnJycOh+zfft2HnjgAebNm4efn1+9Xmf69OlERERUb4mJiQ0Js1EOV48ZUcuIiIh4IIc/9LjY3N/8mbWxNFCjBrCeXNrZMIw6yz07nU6uvvpqHn/8cbp161bv5582bRoFBQXVW0ZGRmPCbJCq2TSRGjMi0iRsNhsdOnSgQ4cOKgcv0lJ6Xmrebv4cPGhKff2aKo6Jjo7G4XDUagU5cOBArdYSgKKiItasWcO6deu44447ALP2gGEY+Pn58dVXX3HuuefWelxgYCCBgYENCe0Xq5pN0zpUyYhIU7Db7XTo0MHqMER8S+dzICAMirJh34+QNMzqiOqlQS0jAQEBpKSksGjRohrHFy1axMiRI2udHx4ezoYNG1i/fn31NnnyZLp378769esZNsx9LlJ+idkyEhGsbhoREfFQfoHQ/UJz34O6ahrUMgIwdepUrrnmGgYPHsyIESN47bXXSE9PZ/LkyYDZxZKZmcnbb7+N3W6nT58+NR7frl07goKCah23Wv5RDWAVaUqGYVBcXAxASEiIumpEWkrPS2HDB5D2GYx7Ejzg/16Dk5FJkyaRl5fHE088QXZ2Nn369GHBggUkJycDkJ2dfcaaI+6mwumiqMxcsVdTe0Wahsvl4scfzZVER48ejcPhsDgiER/R5XzwD4GCdMheD3EDrY7ojGyGB6xgVVhYSEREBAUFBYSHhzf58+cdKSPlya8B2PH3CfhpoTyRX8zpdFZXZ1YyItLC3r8W0v4LZ02F8+tXVqM51Pf7W9+6HJ/WGx7kp0REREQ8X9WsmrT/gvu3OSgZASg4NnhVNUZERMQrdBsPjkA4tBMOpFkdzRkpGQEOa/CqiIh4k8Aw6HysdEaa+8+qUTLCiaXg1TIiIiJeotevzFsPmOKrZARVXxURES/U/UKw+5ndNLk7rI7mtJSMcEL1VXXTiDQZm81GYmIiiYmJqjEiYoXg1tDhLHN/5zfWxnIGSkY4ofqqumlEmozdbqdz58507twZu10fNSKW6DDavN273No4zkCfEJywYq+6aURExJtUtYzsXeHWU3yVjAAFWiRPpMkZhkFpaSmlpaV4QG1FEe8UNxD8guDoQcjdbnU0p6RkBDhcPYBV3TQiTcXlcrFq1SpWrVqFy4OWMhfxKn6BkDDE3N/7vbWxnIaSEY4PYFWdERER8TrJo8zbvSusjeM0lIwABaozIiIi3qrDsWRkz3K3HTfi88lIeaWLI9Ur9qplREREvEz8YLD7Q1EWHN5jdTR18vlkpKpVxGaDsCAlIyIi4mUCQiB+kLnvpl01Pp+MVFVfDQ/yx2FXYSYREfFC1eNG3LPeiJKRElVfFRERL+fmyYif1QFYrWomjaqvijQtm81GXFxc9b6IWChpGNjs5piRgkyIiLc6ohp8vmWkqsaIWkZEmpbdbqdbt25069ZN5eBFrBYYBrH9zX03HDfi858QBSoFLyIivqC6q8b9ip/5fDJSXX1V3TQiTcowDMrLyykvL1c5eBF34MbFz3w+GckvUfVVkebgcrlYsWIFK1asUDl4EXeQPAKwQe42OHLQ6mhq8PlkRN00IiLiE4JbQ0xvc9/NZtX4fDJSPYA1VN00IiLi5ZJHmrdu1lXj88lI9dRetYyIiIi3q0pGMn6wNo6TKBmpntqrlhEREfFy4Qnmbclha+M4iZIRDWAVERFfERBi3lYUWxvHSXw6GSmrdFJc7gQgMlgtIyIi4uUCQs3b8qPWxnESny4HXzWTxm6DsCCfvhQiTc5ms9G+ffvqfRFxA/7HkpGKYnC5wE2qI/v0N3BVF01EsD92rdgr0qTsdjs9evSwOgwROVFVNw1AZcnxlhKLuUdKZJHDRzV4VUREfIhf8PH9cvcZN+LTyUh1y4gGr4o0OcMwcDqdOJ1OlYMXcRd2O/hXDWJ1n3Ejvp2MVK1LoxojIk3O5XKxbNkyli1bpnLwIu6kKhlRy4h7qCp4pm4aERHxGW44vde3kxF104iIiK/xd7/pvb6djKj6qoiI+Bo3rDXi48mIqq+KiIiPccNuGp+uM/Lnc7vyqwHx9IwNszoUERGRluGG3TQ+nYz0igunV1y41WGIiIi0HLWMiIivsNlstG3btnpfRNxE9dRetYyIiJez2+307t3b6jBE5GQBJ6xP4yZ8egCriIiIz1HRMxEREbFUgPuVg1c3jYg0C6fTybJlywAYPXo0DofD4ohEBHDL2TRqGREREfEl1UXP1E0jIiIiVqgewKqWEREREbGCBrCKiIiIpdyw6JmSEREREV+iAawiIiJiKTdsGdHUXhFpFjabjaioqOp9EXETbjhmRMmIiDQLu91Ov379rA5DRE524mwalwvs1neSWB+BiIiItJyqlhGAyhLr4jiBkhERERFfcmIy4iZdNUpGRKRZOJ1Oli5dytKlS3E6nVaHIyJV7PbjCYmbFD5TMiIizcblcuFyuawOQ0RO5maDWJWMiIiI+Bo3m97bqGRk1qxZdOzYkaCgIFJSUqpX5qzLxx9/zAUXXEDbtm0JDw9nxIgRLFy4sNEBi4iIyC/kZoXPGpyMzJ8/nylTpvDQQw+xbt06Ro8ezYQJE0hPT6/z/KVLl3LBBRewYMECUlNTOeecc5g4cSLr1q37xcGLiIhII7hZy4jNMAyjIQ8YNmwYgwYNYvbs2dXHevbsyWWXXcb06dPr9Ry9e/dm0qRJPPLII/U6v7CwkIiICAoKCggPD29IuCJiEafTWd1qOnr0aBwOh8URiUi1Ny+BPcvgijnQ9zfN9jL1/f5uUMtIeXk5qampjBs3rsbxcePGsWLFino9h8vloqioqLoyY13KysooLCyssYmIiEgTCfDgbprc3FycTicxMTE1jsfExJCTk1Ov53j22Wc5evQoV1555SnPmT59OhEREdVbYmJiQ8IUETcRGRlJZGSk1WGIyMmqq7C6RzdNowawnrzOhGEY9Vp74t133+Wxxx5j/vz5tGvX7pTnTZs2jYKCguotIyOjMWGKiIUcDgcDBgxgwIAB6qIRcTfVU3vdo2WkQWvTREdH43A4arWCHDhwoFZrycnmz5/PTTfdxAcffMD5559/2nMDAwMJDAxsSGgiIiJSX57cMhIQEEBKSgqLFi2qcXzRokWMHDnylI979913uf7663nnnXe4+OKLGxepiIiINA03K3rW4FV7p06dyjXXXMPgwYMZMWIEr732Gunp6UyePBkwu1gyMzN5++23ATMRufbaa3nhhRcYPnx4datKcHAwERERTfhWRMSdOJ1OVq1aBcDw4cPVVSPiTgLcqxx8g5ORSZMmkZeXxxNPPEF2djZ9+vRhwYIFJCcnA5CdnV2j5sirr75KZWUlt99+O7fffnv18euuu44333zzl78DEXFbFRUVVocgInWpLnrmoS0jALfddhu33XZbnfednGAsXry4MS8hIiIizSXAvQawam0aERERX1PVMuIm3TRKRkRERHxNgHsNYFUyIiIi4ms8eWqviIiIeAE3W7W3UQNYRUTqIywszOoQRKQubrZqr5IREWkWDoeDlJQUq8MQkbq4WdEzddOIiIj4mhPHjLhc1saCkhERERHfU9UyggGVJZaGAuqmEZFm4nQ6+fHHHwEYMmSIysGLuJPqZASzq6aqpcQiahkRkWZTWlpKaWmp1WGIyMnsdvALNvfdoPCZkhERERFf5EaFz5SMiIiI+CI3KnymZERERMQXuVHhMyUjIiIivsiNCp8pGREREfFF1YXPrG8Z0dReEWk2ISEhZz5JRKwR4D7dNEpGRKRZOBwOhg4danUYInIq/uqmERERESsFuE83jZIRERERX+TvPlN71U0jIs3C6XSSmpoKQEpKisrBi7ib6jEjSkZExIsVF1v/IScip1A9tVfdNCIiImIFf/dpGVEyIiIi4ovcqOiZV3XTOJ1OKioqrA5DGiAgIAC7XTmxiEiLq24ZOWJtHHhJMmIYBjk5OeTn51sdijSQ3W6nY8eOBAQEWB2KiIhvcaNVe70iGalKRNq1a0dISAg2m83qkKQeXC4XWVlZZGdnk5SUpH83EZGW5EZFzzw+GXE6ndWJSJs2bawORxqobdu2ZGVlUVlZib+/v9XhSBMLCgqyOgQRORWVg286VWNEtAaGZ6rqnnE6nUpGvIzD4WD48OFWhyEip+JGLSNeM3JQTfyeSf9uIiIWcaOiZ16TjIiIiEgDBJxQDt4wLA1FyYgPWbx4MTabrV6zjhpyrkhdqsrBp6am4nQ6rQ5HRE5W1U2DARUllobi8WNGpP5GjhxJdnY2ERERTXquyKkUFRVZHYKInIr/CWMty48en+prAbWMeIjy8vJf/BwBAQG0b9++XuM0GnKuiIh4ILsd/ILNfYvXp1EyYpGxY8dyxx13cMcddxAZGUmbNm3461//inGs365Dhw48+eSTXH/99URERHDLLbcAsGLFCs4++2yCg4NJTEzkzjvv5OjR479EZWVl3HfffSQmJhIYGEjXrl2ZM2cOULvrZe/evUycOJHWrVsTGhpK7969WbBgQZ3nAnz00Uf07t2bwMBAOnTowLPPPlvjPXXo0IF//OMf3HjjjYSFhZGUlMRrr73WXJdQRER+KTcpfOZ1yYhhGBSXV1qyGQ0cAPTWW2/h5+fHDz/8wMyZM3n++ef517/+VX3/M888Q58+fUhNTeXhhx9mw4YNjB8/nl//+tf8/PPPzJ8/n++//5477rij+jHXXnst7733HjNnzmTz5s288sortGrVqs7Xv/322ykrK2Pp0qVs2LCBp5566pTnpqamcuWVV3LVVVexYcMGHnvsMR5++GHefPPNGuc9++yzDB48mHXr1nHbbbfxpz/9iS1btjTouoiISAvxP2EQq4W8bsxISYWTXo8stOS1054YT0hA/S9pYmIizz//PDabje7du7Nhwwaef/756laQc889l3vuuaf6/GuvvZarr76aKVOmANC1a1dmzpzJmDFjmD17Nunp6bz//vssWrSI888/H4BOnTqd8vXT09O54oor6Nu37xnPfe655zjvvPN4+OGHAejWrRtpaWk888wzXH/99dXnXXTRRdx2220A3H///Tz//PMsXryYHj161Pu6iIhIC6luGVE3jc8aPnx4jTEZI0aMYPv27dUzDwYPHlzj/NTUVN58801atWpVvY0fPx6Xy8Xu3btZv349DoeDMWPG1Ov177zzTp588klGjRrFo48+ys8//3zKczdv3syoUaNqHBs1alSNeAH69etXvW+z2Wjfvj0HDhyoVzwiItLC3KTwmde1jAT7O0h7Yrxlr92UQkNDa/zscrm49dZbufPOO2udm5SUxI4dOxr0/DfffDPjx4/nf//7H1999RXTp0/n2Wef5c9//nOtcw3DqDWYta5uqZOrqNpsNlwuV4PiEu+hqroibs5NSsJ7XTJis9ka1FVipVWrVtX6uWvXrjgcdSc1gwYNYtOmTXTp0qXO+/v27YvL5WLJkiXV3TRnkpiYyOTJk5k8eTLTpk3j9ddfrzMZ6dWrF99//32NYytWrKBbt26njFd8m8PhqNWaJiJuJsA9xoyom8ZCGRkZTJ06la1bt/Luu+/y4osvctddd53y/Pvvv5+VK1dy++23s379erZv385nn31WnTx06NCB6667jhtvvJFPP/2U3bt3s3jxYt5///06n2/KlCksXLiQ3bt3s3btWr799lt69uxZ57l/+ctf+Oabb/jb3/7Gtm3beOutt3jppZdqjGkREREP4+8eY0Y8ownBS1177bWUlJQwdOhQHA4Hf/7zn/njH/94yvP79evHkiVLeOihhxg9ejSGYdC5c2cmTZpUfc7s2bN58MEHue2228jLyyMpKYkHH3ywzudzOp3cfvvt7Nu3j/DwcC688EKef/75Os8dNGgQ77//Po888gh/+9vfiI2N5YknnqgxeFVERDyMmwxgtRkNnY9qgcLCQiIiIigoKCA8PLzGfaWlpezevZuOHTt61HLlY8eOZcCAAcyYMcPqUCzlqf9+cmZOp5MNGzYAZheiuvNE3NCC+2D1qzD6L3DeI03+9Kf7/j6RWkZEpNlobSMRN6eiZyIiImKp6qJnGjPikxYvXmx1CCIi4uvUMiIiIiKW0tReERERsZS/exQ9UzIiIiLiq9xkaq/GjIhIs7Hb9feOiFvT2jQi4s0cDgdnn3221WGIyOm4ydo0+rNFRETEV7lJy4iSER/y2GOPMWDAgOqfr7/+ei677DLL4hEREYu5ydReddOISLNwuVxs3LgRgD59+mj8iIg78j9haq9hgM1mSRhKRtxEeXk5AQEBVoch0mQMw+DQoUPV+yLihqpaRjCgouSEn1uW/lSxyNixY7njjjuYOnUq0dHRXHDBBaSlpXHRRRfRqlUrYmJiuOaaa8jNza1+jMvl4qmnnqJLly4EBgaSlJTE3//+9+r777//frp160ZISAidOnXi4YcfpqKiwoq3JyIinsD/hOTDwnEj3tcyYhjWXVD/kAY1cb311lv86U9/Yvny5Rw6dIgxY8Zwyy238Nxzz1FSUsL999/PlVdeybfffgvAtGnTeP3113n++ec566yzyM7OZsuWLdXPFxYWxptvvklcXBwbNmzglltuISwsjPvuu6/J36qIiHgBuwP8gqGyxJxRExptSRiNSkZmzZrFM888Q3Z2Nr1792bGjBmMHj36lOcvWbKEqVOnsmnTJuLi4rjvvvuYPHlyo4M+rYpi+Edc8zz3mTyYdXyaVD106dKFp59+GoBHHnmEQYMG8Y9//KP6/rlz55KYmMi2bduIjY3lhRde4KWXXuK6664DoHPnzpx11lnV5//1r3+t3u/QoQN/+ctfmD9/vpIRERE5tYCQ48mIRRqcjMyfP58pU6Ywa9YsRo0axauvvsqECRNIS0sjKSmp1vm7d+/moosu4pZbbuE///kPy5cv57bbbqNt27ZcccUVTfImPNXgwYOr91NTU/nuu+9o1apVrfN27txJfn4+ZWVlnHfeead8vg8//JAZM2awY8cOjhw5QmVlJeHh4c0Su4iIeAn/UCDPs7ppnnvuOW666SZuvvlmAGbMmMHChQuZPXs206dPr3X+K6+8QlJSEjNmzACgZ8+erFmzhn/+85/Nk4z4h5gtFFbwb9jAn9DQ460oLpeLiRMn8tRTT9U6LzY2ll27dp32uVatWsVVV13F448/zvjx44mIiOC9997j2WefbVBMIiLiY9ygJHyDkpHy8nJSU1N54IEHahwfN24cK1asqPMxK1euZNy4cTWOjR8/njlz5lBRUYG/v3+tx5SVlVFWVlb9c2FhYf2DtNka1FXiLgYNGsRHH31Ehw4d8POr/c/StWtXgoOD+eabb6oTwRMtX76c5ORkHnrooepje/fubdaYRUTEC7hB4bMGzabJzc3F6XQSExNT43hMTAw5OTl1PiYnJ6fO8ysrK2vMFDnR9OnTiYiIqN4SExMbEqZHuv322zl06BC/+93vWL16Nbt27eKrr77ixhtvxOl0EhQUxP333899993H22+/zc6dO1m1ahVz5swBzPEn6enpvPfee+zcuZOZM2fyySefWPyuxJc5HA7Gjh3L2LFjcTgcVocjIqfiBiXhGzW113bSjBHDMGodO9P5dR2vMm3aNAoKCqq3jIyMxoTpUeLi4li+fDlOp5Px48fTp08f7rrrLiIiIqqLRT388MP85S9/4ZFHHqFnz55MmjSJAwcOAPCrX/2Ku+++mzvuuIMBAwawYsUKHn74YSvfkoiIeIK+v4Wz74W23S0LwWY0oBpReXk5ISEhfPDBB1x++eXVx++66y7Wr1/PkiVLaj3m7LPPZuDAgbzwwgvVxz755BOuvPJKiouL6+ymOVlhYSEREREUFBTUGpBZWlrK7t276dixI0FBQfV9K+Im9O8nIuK9Tvf9faIGtYwEBASQkpLCokWLahxftGgRI0eOrPMxI0aMqHX+V199xeDBg+uViIiIiIh3a3A3zdSpU/nXv/7F3Llz2bx5M3fffTfp6enVdUOmTZvGtddeW33+5MmT2bt3L1OnTmXz5s3MnTuXOXPmcM899zTduxARERGP1eCpvZMmTSIvL48nnniC7Oxs+vTpw4IFC0hOTgYgOzub9PT06vM7duzIggULuPvuu3n55ZeJi4tj5syZPl9jREREREwNGjNiFY0Z8V769xMR8V7NMmZEREREpKl5TTLicrmsDkEawQMa5kREpJl5/Kq9AQEB2O12srKyaNu2LQEBAaeteSLuwzAMDh48iM1m08wqEREf5vHJiN1up2PHjmRnZ5OVZdGaNNJoNpuNhIQEVegUEfFhHp+MgNk6kpSURGVlJU6n0+pwpAH8/f2ViIiI+DivSEaA6qZ+NfeLiIh4Fq8ZwCoiIiKeScmIiIiIWErJiIiIiFjKI8aMVNWiKCwstDgSERERqa+q7+0z1ZTyiGSkqKgIgMTERIsjERERkYYqKioiIiLilPd7xNo0LpeLrKwswsLCmrSgWWFhIYmJiWRkZJy2Zr78crrWLUPXuWXoOrcMXeeW0ZzX2TAMioqKiIuLw24/9cgQj2gZsdvtJCQkNNvzh4eH6xe9hehatwxd55ah69wydJ1bRnNd59O1iFTRAFYRERGxlJIRERERsZRPJyOBgYE8+uijBAYGWh2K19O1bhm6zi1D17ll6Dq3DHe4zh4xgFVERES8l0+3jIiIiIj1lIyIiIiIpZSMiIiIiKWUjIiIiIilvD4ZmTVrFh07diQoKIiUlBSWLVt22vOXLFlCSkoKQUFBdOrUiVdeeaWFIvVsDbnOH3/8MRdccAFt27YlPDycESNGsHDhwhaM1rM19He6yvLly/Hz82PAgAHNG6CXaOh1Lisr46GHHiI5OZnAwEA6d+7M3LlzWyhaz9XQ6zxv3jz69+9PSEgIsbGx3HDDDeTl5bVQtJ5p6dKlTJw4kbi4OGw2G59++ukZH9Pi34WGF3vvvfcMf39/4/XXXzfS0tKMu+66ywgNDTX27t1b5/m7du0yQkJCjLvuustIS0szXn/9dcPf39/48MMPWzhyz9LQ63zXXXcZTz31lLF69Wpj27ZtxrRp0wx/f39j7dq1LRy552nota6Sn59vdOrUyRg3bpzRv3//lgnWgzXmOl966aXGsGHDjEWLFhm7d+82fvjhB2P58uUtGLXnaeh1XrZsmWG3240XXnjB2LVrl7Fs2TKjd+/exmWXXdbCkXuWBQsWGA899JDx0UcfGYDxySefnPZ8K74LvToZGTp0qDF58uQax3r06GE88MADdZ5/3333GT169Khx7NZbbzWGDx/ebDF6g4Ze57r06tXLePzxx5s6NK/T2Gs9adIk469//avx6KOPKhmph4Ze5y+++MKIiIgw8vLyWiI8r9HQ6/zMM88YnTp1qnFs5syZRkJCQrPF6G3qk4xY8V3otd005eXlpKamMm7cuBrHx40bx4oVK+p8zMqVK2udP378eNasWUNFRUWzxerJGnOdT+ZyuSgqKiIqKqo5QvQajb3Wb7zxBjt37uTRRx9t7hC9QmOu82effcbgwYN5+umniY+Pp1u3btxzzz2UlJS0RMgeqTHXeeTIkezbt48FCxZgGAb79+/nww8/5OKLL26JkH2GFd+FHrFQXmPk5ubidDqJiYmpcTwmJoacnJw6H5OTk1Pn+ZWVleTm5hIbG9ts8Xqqxlznkz377LMcPXqUK6+8sjlC9BqNudbbt2/ngQceYNmyZfj5ee1/9ybVmOu8a9cuvv/+e4KCgvjkk0/Izc3ltttu49ChQxo3cgqNuc4jR45k3rx5TJo0idLSUiorK7n00kt58cUXWyJkn2HFd6HXtoxUsdlsNX42DKPWsTOdX9dxqamh17nKu+++y2OPPcb8+fNp165dc4XnVep7rZ1OJ1dffTWPP/443bp1a6nwvEZDfqddLhc2m4158+YxdOhQLrroIp577jnefPNNtY6cQUOuc1paGnfeeSePPPIIqampfPnll+zevZvJkye3RKg+paW/C732T6Xo6GgcDketDPvAgQO1Mr4q7du3r/N8Pz8/2rRp02yxerLGXOcq8+fP56abbuKDDz7g/PPPb84wvUJDr3VRURFr1qxh3bp13HHHHYD5pWkYBn5+fnz11Vece+65LRK7J2nM73RsbCzx8fE1lkrv2bMnhmGwb98+unbt2qwxe6LGXOfp06czatQo7r33XgD69etHaGgoo0eP5sknn1TrdROx4rvQa1tGAgICSElJYdGiRTWOL1q0iJEjR9b5mBEjRtQ6/6uvvmLw4MH4+/s3W6yerDHXGcwWkeuvv5533nlH/b311NBrHR4ezoYNG1i/fn31NnnyZLp378769esZNmxYS4XuURrzOz1q1CiysrI4cuRI9bFt27Zht9tJSEho1ng9VWOuc3FxMXZ7za8th8MBHP/LXX45S74Lm21orBuomjY2Z84cIy0tzZgyZYoRGhpq7NmzxzAMw3jggQeMa665pvr8qulMd999t5GWlmbMmTNHU3vroaHX+Z133jH8/PyMl19+2cjOzq7e8vPzrXoLHqOh1/pkmk1TPw29zkVFRUZCQoLxm9/8xti0aZOxZMkSo2vXrsbNN99s1VvwCA29zm+88Ybh5+dnzJo1y9i5c6fx/fffG4MHDzaGDh1q1VvwCEVFRca6deuMdevWGYDx3HPPGevWraueQu0O34VenYwYhmG8/PLLRnJyshEQEGAMGjTIWLJkSfV91113nTFmzJga5y9evNgYOHCgERAQYHTo0MGYPXt2C0fsmRpynceMGWMAtbbrrruu5QP3QA39nT6RkpH6a+h13rx5s3H++ecbwcHBRkJCgjF16lSjuLi4haP2PA29zjNnzjR69eplBAcHG7Gxscbvf/97Y9++fS0ctWf57rvvTvuZ6w7fhTbDUNuWiIiIWMdrx4yIiIiIZ1AyIiIiIpZSMiIiIiKWUjIiIiIillIyIiIiIpZSMiIiIiKWUjIiIiIillIyIiIiIpZSMiIiIiKWUjIiIiIillIyIiIiIpZSMiIiIiKW+v+9fTIwDhrmrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df_scores.threshold, df_scores.p, label='precision')\n",
    "plt.plot(df_scores.threshold, df_scores.r, label='recall')\n",
    "\n",
    "plt.vlines(0.48, 0, 1, color='grey', linestyle='--', alpha=0.5)\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At which threshold precision and recall curves intersect?\n",
    "\n",
    "* 0.28\n",
    "* **0.48**\n",
    "* 0.68\n",
    "* 0.88"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4: F1 score\n",
    "\n",
    "Precision and recall are conflicting - when one grows, the other goes down. That's why they are often combined into the F1 score - a metrics that takes into account both\n",
    "\n",
    "This is the formula for computing F1:\n",
    "\n",
    "$$F_1 = 2 \\cdot \\cfrac{P \\cdot R}{P + R}$$\n",
    "\n",
    "Where $P$ is precision and $R$ is recall.\n",
    "\n",
    "Let's compute F1 for all thresholds from 0.0 to 1.0 with increment 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_scores['f1'] = 2 * df_scores.p * df_scores.r / (df_scores.p + df_scores.r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "threshold       0.520000\n",
       "tp            563.000000\n",
       "fp             62.000000\n",
       "fn             91.000000\n",
       "tn           1667.000000\n",
       "p               0.900800\n",
       "r               0.860856\n",
       "f1              0.880375\n",
       "Name: 52, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scores.loc[df_scores.f1.argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "plt.plot(df_scores.threshold, df_scores.f1)\n",
    "plt.vlines(0.52, 0.45, 0.9, color='grey', linestyle='--', alpha=0.5)\n",
    "\n",
    "plt.xticks(np.linspace(0, 1, 11))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At which threshold F1 is maximal?\n",
    "\n",
    "- 0.12\n",
    "- 0.32\n",
    "- **0.52**\n",
    "- 0.72"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5: 5-Fold CV\n",
    "\n",
    "\n",
    "Use the `KFold` class from Scikit-Learn to evaluate our model on 5 different folds:\n",
    "\n",
    "```\n",
    "KFold(n_splits=5, shuffle=True, random_state=1)\n",
    "```\n",
    "\n",
    "* Iterate over different folds of `df_full_train`\n",
    "* Split the data into train and validation\n",
    "* Train the model on train with these parameters: `LogisticRegression(solver='liblinear', C=1.0, max_iter=1000)`\n",
    "* Use AUC to evaluate the model on validation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['make',\n",
       " 'model',\n",
       " 'year',\n",
       " 'engine_hp',\n",
       " 'engine_cylinders',\n",
       " 'transmission_type',\n",
       " 'vehicle_style',\n",
       " 'highway_mpg',\n",
       " 'city_mpg']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns = list(df.columns)\n",
    "columns.remove('above_average')\n",
    "columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(df_train, y_train, C=1.0):\n",
    "    dicts = df_train[columns].to_dict(orient='records')\n",
    "\n",
    "    dv = DictVectorizer()\n",
    "    X_train = dv.fit_transform(dicts)\n",
    "\n",
    "    model = LogisticRegression(solver='liblinear', C=C, max_iter=1000)\n",
    "    model.fit(X_train, y_train)\n",
    "\n",
    "    return dv, model\n",
    "\n",
    "def predict(df, dv, model):\n",
    "    dicts = df[columns].to_dict(orient='records')\n",
    "\n",
    "    X = dv.transform(dicts)\n",
    "    y_pred = model.predict_proba(X)[:, 1]\n",
    "\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.981 +- 0.003\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "\n",
    "kfold = KFold(n_splits=5, shuffle=True, random_state=1)\n",
    "\n",
    "for train_idx, val_idx in kfold.split(df_full_train):\n",
    "    df_train = df_full_train.iloc[train_idx]\n",
    "    df_val = df_full_train.iloc[val_idx]\n",
    "\n",
    "    y_train = df_train.above_average.values\n",
    "    y_val = df_val.above_average.values\n",
    "\n",
    "    dv, model = train(df_train, y_train, C=1.0)\n",
    "    y_pred = predict(df_val, dv, model)\n",
    "\n",
    "    auc = roc_auc_score(y_val, y_pred)\n",
    "    scores.append(auc)\n",
    "\n",
    "print('%.3f +- %.3f' % (np.mean(scores), np.std(scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How large is standard devidation of the scores across different folds?\n",
    "\n",
    "- **0.003**\n",
    "- 0.030\n",
    "- 0.090\n",
    "- 0.140"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 6: Hyperparemeter Tuning\n",
    "\n",
    "Now let's use 5-Fold cross-validation to find the best parameter C\n",
    "\n",
    "* Iterate over the following C values: `[0.01, 0.1, 0.5, 10]`\n",
    "* Initialize `KFold` with the same parameters as previously\n",
    "* Use these parametes for the model: `LogisticRegression(solver='liblinear', C=C, max_iter=1000)`\n",
    "* Compute the mean score as well as the std (round the mean and std to 3 decimal digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C=0.01, 0.952 +- 0.002\n",
      "C= 0.1, 0.972 +- 0.002\n",
      "C= 0.5, 0.979 +- 0.004\n",
      "C=  10, 0.984 +- 0.003\n"
     ]
    }
   ],
   "source": [
    "kfold = KFold(n_splits=5, shuffle=True, random_state=1)\n",
    "\n",
    "for C in [0.01, 0.1, 0.5, 10]:\n",
    "    scores = []\n",
    "\n",
    "    for train_idx, val_idx in kfold.split(df_full_train):\n",
    "        df_train = df_full_train.iloc[train_idx]\n",
    "        df_val = df_full_train.iloc[val_idx]\n",
    "\n",
    "        y_train = df_train.above_average.values\n",
    "        y_val = df_val.above_average.values\n",
    "\n",
    "        dv, model = train(df_train, y_train, C=C)\n",
    "        y_pred = predict(df_val, dv, model)\n",
    "\n",
    "        auc = roc_auc_score(y_val, y_pred)\n",
    "        scores.append(auc)\n",
    "\n",
    "    print('C=%4s, %.3f +- %.3f' % (C, np.mean(scores), np.std(scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which C leads to the best mean score?\n",
    "\n",
    "- 0.01\n",
    "- 0.1\n",
    "- 0.5\n",
    "- **10**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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