04LogisticRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **LAB: LOGISTIC REGRESSION**\n",
    "Packages used:\n",
    " - `statsmodels` is meant for \"conducting statistical tests, and statistical data exploration\" it is technically more similar to R in its function, syntax and general use;\n",
    " - `sklearn` is meant for prediction; knowledge of scikit-learn is a very valuable skill nowadays, so I thought it best to include it;\n",
    " - and of course, `pandas` for data wrangling and organizing, as well as `matplotlib` and `seaborn` for pictures.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **0. Preliminaries.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the necessary packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "\n",
    "sns.set_theme(style=\"darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll work with the `Smarket` dataset, which contains the percentage returns for the S&P 500 stock index over $1250$ days, from $2001$ to $2005$. For each date, the dataset contains the percentage returns for each of the five previous trading days, stored in the columns `Lag1` through `Lag5`.\n",
    "The column `Volume` corresponds to the number of shares traded on the previous day (in billions), `Today|` the percentage return on the date, and `Direction` whether the market was up or down on this date.\n",
    "\n",
    "This dataset is part of the ISLR package; a .csv version is available in the data folder. \n",
    "\n",
    "We use `df.describe()` to get a summary of our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Lag1</th>\n",
       "      <th>Lag2</th>\n",
       "      <th>Lag3</th>\n",
       "      <th>Lag4</th>\n",
       "      <th>Lag5</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Today</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.00000</td>\n",
       "      <td>1250.000000</td>\n",
       "      <td>1250.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2003.016000</td>\n",
       "      <td>0.003834</td>\n",
       "      <td>0.003919</td>\n",
       "      <td>0.001716</td>\n",
       "      <td>0.001636</td>\n",
       "      <td>0.00561</td>\n",
       "      <td>1.478305</td>\n",
       "      <td>0.003138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.409018</td>\n",
       "      <td>1.136299</td>\n",
       "      <td>1.136280</td>\n",
       "      <td>1.138703</td>\n",
       "      <td>1.138774</td>\n",
       "      <td>1.14755</td>\n",
       "      <td>0.360357</td>\n",
       "      <td>1.136334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2001.000000</td>\n",
       "      <td>-4.922000</td>\n",
       "      <td>-4.922000</td>\n",
       "      <td>-4.922000</td>\n",
       "      <td>-4.922000</td>\n",
       "      <td>-4.92200</td>\n",
       "      <td>0.356070</td>\n",
       "      <td>-4.922000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2002.000000</td>\n",
       "      <td>-0.639500</td>\n",
       "      <td>-0.639500</td>\n",
       "      <td>-0.640000</td>\n",
       "      <td>-0.640000</td>\n",
       "      <td>-0.64000</td>\n",
       "      <td>1.257400</td>\n",
       "      <td>-0.639500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2003.000000</td>\n",
       "      <td>0.039000</td>\n",
       "      <td>0.039000</td>\n",
       "      <td>0.038500</td>\n",
       "      <td>0.038500</td>\n",
       "      <td>0.03850</td>\n",
       "      <td>1.422950</td>\n",
       "      <td>0.038500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2004.000000</td>\n",
       "      <td>0.596750</td>\n",
       "      <td>0.596750</td>\n",
       "      <td>0.596750</td>\n",
       "      <td>0.596750</td>\n",
       "      <td>0.59700</td>\n",
       "      <td>1.641675</td>\n",
       "      <td>0.596750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2005.000000</td>\n",
       "      <td>5.733000</td>\n",
       "      <td>5.733000</td>\n",
       "      <td>5.733000</td>\n",
       "      <td>5.733000</td>\n",
       "      <td>5.73300</td>\n",
       "      <td>3.152470</td>\n",
       "      <td>5.733000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Year         Lag1         Lag2         Lag3         Lag4  \\\n",
       "count  1250.000000  1250.000000  1250.000000  1250.000000  1250.000000   \n",
       "mean   2003.016000     0.003834     0.003919     0.001716     0.001636   \n",
       "std       1.409018     1.136299     1.136280     1.138703     1.138774   \n",
       "min    2001.000000    -4.922000    -4.922000    -4.922000    -4.922000   \n",
       "25%    2002.000000    -0.639500    -0.639500    -0.640000    -0.640000   \n",
       "50%    2003.000000     0.039000     0.039000     0.038500     0.038500   \n",
       "75%    2004.000000     0.596750     0.596750     0.596750     0.596750   \n",
       "max    2005.000000     5.733000     5.733000     5.733000     5.733000   \n",
       "\n",
       "             Lag5       Volume        Today  \n",
       "count  1250.00000  1250.000000  1250.000000  \n",
       "mean      0.00561     1.478305     0.003138  \n",
       "std       1.14755     0.360357     1.136334  \n",
       "min      -4.92200     0.356070    -4.922000  \n",
       "25%      -0.64000     1.257400    -0.639500  \n",
       "50%       0.03850     1.422950     0.038500  \n",
       "75%       0.59700     1.641675     0.596750  \n",
       "max       5.73300     3.152470     5.733000  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('data/Smarket.csv')\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pandas DataFrames have a `.corr()` method that displays the correlation matrix. It ignores categorical variables by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Lag1</th>\n",
       "      <th>Lag2</th>\n",
       "      <th>Lag3</th>\n",
       "      <th>Lag4</th>\n",
       "      <th>Lag5</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Today</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.029700</td>\n",
       "      <td>0.030596</td>\n",
       "      <td>0.033195</td>\n",
       "      <td>0.035689</td>\n",
       "      <td>0.029788</td>\n",
       "      <td>0.539006</td>\n",
       "      <td>0.030095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lag1</th>\n",
       "      <td>0.029700</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.026294</td>\n",
       "      <td>-0.010803</td>\n",
       "      <td>-0.002986</td>\n",
       "      <td>-0.005675</td>\n",
       "      <td>0.040910</td>\n",
       "      <td>-0.026155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lag2</th>\n",
       "      <td>0.030596</td>\n",
       "      <td>-0.026294</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.025897</td>\n",
       "      <td>-0.010854</td>\n",
       "      <td>-0.003558</td>\n",
       "      <td>-0.043383</td>\n",
       "      <td>-0.010250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lag3</th>\n",
       "      <td>0.033195</td>\n",
       "      <td>-0.010803</td>\n",
       "      <td>-0.025897</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.024051</td>\n",
       "      <td>-0.018808</td>\n",
       "      <td>-0.041824</td>\n",
       "      <td>-0.002448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lag4</th>\n",
       "      <td>0.035689</td>\n",
       "      <td>-0.002986</td>\n",
       "      <td>-0.010854</td>\n",
       "      <td>-0.024051</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.027084</td>\n",
       "      <td>-0.048414</td>\n",
       "      <td>-0.006900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lag5</th>\n",
       "      <td>0.029788</td>\n",
       "      <td>-0.005675</td>\n",
       "      <td>-0.003558</td>\n",
       "      <td>-0.018808</td>\n",
       "      <td>-0.027084</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.022002</td>\n",
       "      <td>-0.034860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Volume</th>\n",
       "      <td>0.539006</td>\n",
       "      <td>0.040910</td>\n",
       "      <td>-0.043383</td>\n",
       "      <td>-0.041824</td>\n",
       "      <td>-0.048414</td>\n",
       "      <td>-0.022002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.014592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Today</th>\n",
       "      <td>0.030095</td>\n",
       "      <td>-0.026155</td>\n",
       "      <td>-0.010250</td>\n",
       "      <td>-0.002448</td>\n",
       "      <td>-0.006900</td>\n",
       "      <td>-0.034860</td>\n",
       "      <td>0.014592</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Year      Lag1      Lag2      Lag3      Lag4      Lag5    Volume  \\\n",
       "Year    1.000000  0.029700  0.030596  0.033195  0.035689  0.029788  0.539006   \n",
       "Lag1    0.029700  1.000000 -0.026294 -0.010803 -0.002986 -0.005675  0.040910   \n",
       "Lag2    0.030596 -0.026294  1.000000 -0.025897 -0.010854 -0.003558 -0.043383   \n",
       "Lag3    0.033195 -0.010803 -0.025897  1.000000 -0.024051 -0.018808 -0.041824   \n",
       "Lag4    0.035689 -0.002986 -0.010854 -0.024051  1.000000 -0.027084 -0.048414   \n",
       "Lag5    0.029788 -0.005675 -0.003558 -0.018808 -0.027084  1.000000 -0.022002   \n",
       "Volume  0.539006  0.040910 -0.043383 -0.041824 -0.048414 -0.022002  1.000000   \n",
       "Today   0.030095 -0.026155 -0.010250 -0.002448 -0.006900 -0.034860  0.014592   \n",
       "\n",
       "           Today  \n",
       "Year    0.030095  \n",
       "Lag1   -0.026155  \n",
       "Lag2   -0.010250  \n",
       "Lag3   -0.002448  \n",
       "Lag4   -0.006900  \n",
       "Lag5   -0.034860  \n",
       "Volume  0.014592  \n",
       "Today   1.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the `Today` column: the values are pretty small, which (as one would expect) means the returns of the day have little to do with the returns of the previous days. There does seem to be a substantial correlation between `Year` and `Volume`. Let's plot our data to check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Year', ylabel='Volume'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x='Year', y='Volume', data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The volume traded increased between 2001 and 2005: that's a positive correlation, which is what we got in our correlation matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **1. Logistic Regression**\n",
    "We fit a logistic regression model to try to predict `Direction` in terms of `Lag1` through `Lag5`, and `Volume`.\n",
    "\n",
    "First, we convert our categorical variable to a dummy variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.get_dummies(df, drop_first=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['Lag1', 'Lag2', 'Lag3', 'Lag4', 'Lag5', 'Volume']]\n",
    "y = df['Direction_Up']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Basic syntax.\n",
    "`statsmodels`'s Logistic Regression function is called `Logit()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.197001\n",
      "         Iterations 4\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:           Direction_Up   No. Observations:                 1250\n",
      "Model:                          Logit   Df Residuals:                     1243\n",
      "Method:                           MLE   Df Model:                            6\n",
      "Date:                Tue, 06 Oct 2020   Pseudo R-squ.:                     inf\n",
      "Time:                        13:58:11   Log-Likelihood:                -2746.3\n",
      "converged:                       True   LL-Null:                        0.0000\n",
      "Covariance Type:            nonrobust   LLR p-value:                     1.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.1260      0.241     -0.523      0.601      -0.598       0.346\n",
      "Lag1          -0.0731      0.050     -1.457      0.145      -0.171       0.025\n",
      "Lag2          -0.0423      0.050     -0.845      0.398      -0.140       0.056\n",
      "Lag3           0.0111      0.050      0.222      0.824      -0.087       0.109\n",
      "Lag4           0.0094      0.050      0.187      0.851      -0.089       0.107\n",
      "Lag5           0.0103      0.050      0.208      0.835      -0.087       0.107\n",
      "Volume         0.1354      0.158      0.855      0.392      -0.175       0.446\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/discrete/discrete_model.py:3489: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1 - self.llf/self.llnull\n"
     ]
    }
   ],
   "source": [
    "X_sm = sm.add_constant(X)\n",
    "logit_sm = sm.Logit(y, X_sm)\n",
    "logit_sm_res = logit_sm.fit()\n",
    "print(logit_sm_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(I'll just ignore the warning...)\n",
    "\n",
    "The p-values are all fairly large; the only low-ish one is for `Lag1`, and even this one is quite high. So it seems that the direction of the market can't be predicted well from the figures of the previous days.\n",
    "\n",
    "To access just the coefficients, we look at the `params` attribute of the fitted model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    -0.126000\n",
       "Lag1     -0.073074\n",
       "Lag2     -0.042301\n",
       "Lag3      0.011085\n",
       "Lag4      0.009359\n",
       "Lag5      0.010313\n",
       "Volume    0.135441\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sm_res.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-values are stored in the `pvalues` attribute (duh):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const     0.600700\n",
       "Lag1      0.145232\n",
       "Lag2      0.398352\n",
       "Lag3      0.824334\n",
       "Lag4      0.851445\n",
       "Lag5      0.834998\n",
       "Volume    0.392404\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sm_res.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method `.predict()` returns the predictions of our fitted model; by default, those predictions are done using the training data. Here, we get an array with 1250 entries (our original number of observations) corresponding to the probability that the market will go up each day. In other words, the $i$-th element in the array is $P(Y=1 \\vert X_i)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50708413, 0.48146788, 0.48113883, ..., 0.5392683 , 0.52611829,\n",
       "       0.51791656])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sm_res.predict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To check how our model did, we can use the `pred_table()` method to display a confusion matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[145., 457.],\n",
       "       [141., 507.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sm_res.pred_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diagonal entries indicate correct predictions and off-diagonal ones indicate incorrect predictions. So our model predicted the market direction in $145+507 = 652$ cases, that is, we got a training error rate of $47.8\\%$. Considering the training error is often overly optimistic, it's... not great."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we move on, let's go over the syntax for `sklearn`'s logit models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sk = LogisticRegression()\n",
    "logit_sk.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-values aren't implemented (and likely never will be) in `sklearn` so we'll skip to evaluating our model directly. \n",
    "\n",
    "We get our predictions with the `predict()` method. We can also call `predict_proba()` to get the probabilities (as we did above) and `predict_log_proba()` for the log-probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, ..., 1, 1, 1], dtype=uint8)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sk.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the proportion of correct predictions, we call the `score()` method, passing the observations (here $X$) and the true values ($y$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5208"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_sk.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2. Train/test splits.\n",
    "\n",
    "To get a better idea of the true error rate, we might want to evaluate our model on observations it hasn't seen before; so we divide our data into a _training set_, which we'll use to fit our model, and a _test set_, on which we'll make predictions.\n",
    "\n",
    "This notion is explored in detail in Chapter 5 of ISLR (Resampling methods); for now, we'll use years 2001 to 2004 as our training set and year 2005 as our test set. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = df.loc[df['Year'] < 2005]\n",
    "df_test = df.loc[df['Year'] == 2005]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We prepare our independent variables for `statsmodels` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = df_train[['Lag1', 'Lag2', 'Lag3', 'Lag4', 'Lag5', 'Volume']]\n",
    "X_test = df_test[['Lag1', 'Lag2', 'Lag3', 'Lag4', 'Lag5', 'Volume']]\n",
    "y_train = df_train['Direction_Up']\n",
    "y_test = df_test['Direction_Up']\n",
    "X_train_sm = sm.add_constant(X_train)\n",
    "X_test_sm = sm.add_constant(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 3.346650\n",
      "         Iterations 4\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:           Direction_Up   No. Observations:                  998\n",
      "Model:                          Logit   Df Residuals:                      991\n",
      "Method:                           MLE   Df Model:                            6\n",
      "Date:                Tue, 06 Oct 2020   Pseudo R-squ.:                     inf\n",
      "Time:                        13:58:14   Log-Likelihood:                -3340.0\n",
      "converged:                       True   LL-Null:                        0.0000\n",
      "Covariance Type:            nonrobust   LLR p-value:                     1.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.1912      0.334      0.573      0.567      -0.463       0.845\n",
      "Lag1          -0.0542      0.052     -1.046      0.295      -0.156       0.047\n",
      "Lag2          -0.0458      0.052     -0.884      0.377      -0.147       0.056\n",
      "Lag3           0.0072      0.052      0.139      0.889      -0.094       0.108\n",
      "Lag4           0.0064      0.052      0.125      0.901      -0.095       0.108\n",
      "Lag5          -0.0042      0.051     -0.083      0.934      -0.104       0.096\n",
      "Volume        -0.1163      0.240     -0.485      0.628      -0.586       0.353\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/discrete/discrete_model.py:3489: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1 - self.llf/self.llnull\n"
     ]
    }
   ],
   "source": [
    "logitsm_split = sm.Logit(y_train, X_train_sm) \n",
    "logitsm_split_res = logitsm_split.fit()\n",
    "print((logitsm_split_res).summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, let's just ignore the warning...\n",
    "\n",
    "As far as I've seen, there's no `statsmodels` method to evaluate our predictions directly (since `pred_table` doesn't allow to pass a test set). We can, however, do it with pandas; the following code makes a dataframe with our predictions, then returns the confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>col_0</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Direction_Up</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>77</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>97</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "col_0          0   1\n",
       "Direction_Up        \n",
       "0             77  34\n",
       "1             97  44"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_sm = pd.Series(data=logitsm_split_res.predict(X_test_sm))\n",
    "pred_sm = pred_sm.apply(lambda x : int(x > 0.5))\n",
    "pd.crosstab(y_test, pred_sm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test error rate is $52\\%$, worse than random guessing. Oh, well... \n",
    "Before we try to do something about it, let's review the `sklearn` syntax:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48412698412698413"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logitsk_split = LogisticRegression()\n",
    "logitsk_split.fit(X_train, y_train)\n",
    "logitsk_split.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Easy peasy.\n",
    "\n",
    "To try and improve our model, we look back to our original regression: the variable `Lag1` had the smallest p-value; why not try to refit our model with just `Lag1` and `Lag2`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train2 = df_train[['Lag1', 'Lag2']]\n",
    "X_test2 = df_test[['Lag1', 'Lag2']]\n",
    "X_train_sm2 = sm.add_constant(X_train2)\n",
    "X_test_sm2 = sm.add_constant(X_test2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.875695\n",
      "         Iterations 3\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:           Direction_Up   No. Observations:                  998\n",
      "Model:                          Logit   Df Residuals:                      995\n",
      "Method:                           MLE   Df Model:                            2\n",
      "Date:                Tue, 06 Oct 2020   Pseudo R-squ.:                     inf\n",
      "Time:                        13:58:14   Log-Likelihood:                -2869.9\n",
      "converged:                       True   LL-Null:                        0.0000\n",
      "Covariance Type:            nonrobust   LLR p-value:                     1.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0322      0.063      0.508      0.611      -0.092       0.156\n",
      "Lag1          -0.0556      0.052     -1.076      0.282      -0.157       0.046\n",
      "Lag2          -0.0445      0.052     -0.861      0.389      -0.146       0.057\n",
      "==============================================================================\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/base/model.py:547: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  warnings.warn('Inverting hessian failed, no bse or cov_params '\n",
      "/home/keroubino/.local/lib/python3.8/site-packages/statsmodels/discrete/discrete_model.py:3489: RuntimeWarning: divide by zero encountered in double_scalars\n",
      "  return 1 - self.llf/self.llnull\n"
     ]
    }
   ],
   "source": [
    "logitsm_split2 = sm.Logit(y_train, X_train_sm2)\n",
    "logitsm_split2_res = logitsm_split2.fit() \n",
    "print(logitsm_split2_res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>col_0</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Direction_Up</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>35</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>35</td>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "col_0          0    1\n",
       "Direction_Up         \n",
       "0             35   76\n",
       "1             35  106"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_sm2 = pd.Series(data=logitsm_split2_res.predict(X_test_sm2))\n",
    "pred_sm2 = pred_sm2.apply(lambda x : int(x > 0.5))\n",
    "pd.crosstab(y_test, pred_sm2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks a little better: we have a successful prediction in $56\\%$ of the cases. That said, predicting the market would go up in all cases would also have resulted in a $56\\%$. Not so great.\n",
    "\n",
    "Let's wrap up with `sklearn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5595238095238095"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logitsk_split2 = LogisticRegression()\n",
    "logitsk_split2.fit(X_train2, y_train)\n",
    "logitsk_split2.score(X_test2, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain the confusion matrix, we call `sklearn.metrics.confusion_matrix()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 35,  76],\n",
       "       [ 35, 106]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred2 = logitsk_split2.predict(X_test2)\n",
    "sklearn.metrics.confusion_matrix(y_test, y_pred2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the accuracy rate in case of 'Up' prediction is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5824175824175825"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "106/(106+76)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a small silver lining: when the model predicts the market will go up, it is correct in $58\\%$ of the cases. We could possibly build a trading strategy where we buy stocks on days the model predicts an increase in the market, and do nothing on other days. \n",
    "\n",
    "This small improvement, however, might just be due to random chance, so further investigation is needed..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **2. Linear discriminant analysis.**\n",
    "`statsmodels` does not support linear discriminant analysis as of yet so we'll do this bit with `sklearn` only; we'll use the same train/test split as above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis()"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "lda = LinearDiscriminantAnalysis()\n",
    "lda.fit(X_train2, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access our estimates by calling the various attributes of our `lda` object:\n",
    " - `classes_` lists the different classes (here 0 for 'Down' and 1 for 'Up');\n",
    " - `priors_` the priors $P(Y = k)$ corresponding to each class $k$ (in the order listed in `classes_`;\n",
    " - `means_` the class-wise means of each predictor (eg. `lda.means_[0][1]` is the mean of `Lag2` (the second predictor) over all observations where $Y = 0$);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classes: [0 1] \n",
      "Prior probabilities: [0.49198397 0.50801603] \n",
      "Group means:\n",
      " [[ 0.04279022  0.03389409]\n",
      " [-0.03954635 -0.03132544]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Classes:\", lda.classes_,\n",
    "     \"\\nPrior probabilities:\", lda.priors_,\n",
    "     \"\\nGroup means:\\n\", lda.means_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict what class an element will belong to with the `predict()` and `predict_proba()` methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix:\n",
      " [[ 35  76]\n",
      " [ 35 106]] \n",
      "Accuracy score: 0.5595238095238095\n"
     ]
    }
   ],
   "source": [
    "lda_pred = lda.predict(X_test2)\n",
    "print(\"Confusion matrix:\\n\", sklearn.metrics.confusion_matrix(y_test, lda_pred),\n",
    "      \"\\nAccuracy score:\", lda.score(X_test2, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance is remarkably similar to that of the logistic regression model.\n",
    "\n",
    "There is no out-of-the-box option to adjust prediction threshold (eg. to predict the market will go down only if the probability of it is greater than 90%) but we can do it manually with eg.:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([], dtype=int64),)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(lda.predict_proba(X_test2)[:,0] > .9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a bonus, let's visualize our decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "ax.grid(b=None)\n",
    "ax.set(facecolor='w', aspect=1)\n",
    "\n",
    "sns.scatterplot(x='Lag1', y='Lag2', data=df_test, hue='Direction_Up', s=75, zorder=2)\n",
    "\n",
    "\n",
    "x_min, x_max = plt.xlim()\n",
    "y_min, y_max = plt.ylim()\n",
    "\n",
    "nx, ny = 100, 100\n",
    "xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))\n",
    "Z = np.c_[xx.ravel(), yy.ravel()]\n",
    "plt.scatter(Z[np.where(lda.predict(Z) == 1)][:, 0], Z[np.where(lda.predict(Z) == 1)][:, 1], \n",
    "            s=1, c='tab:blue', alpha=0.7, zorder=1)\n",
    "plt.scatter(Z[np.where(lda.predict(Z) == 0)][:, 0], Z[np.where(lda.predict(Z) == 0)][:, 1], \n",
    "            s=1, c='tab:orange', alpha=0.7, zorder=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **3. Quadratic discriminant analysis.**\n",
    "The syntax for this is very similar to that of LDA:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classes: [0 1] \n",
      "Prior probabilities: [0.49198397 0.50801603] \n",
      "Group means:\n",
      " [[ 0.04279022  0.03389409]\n",
      " [-0.03954635 -0.03132544]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis\n",
    "qda = QuadraticDiscriminantAnalysis()\n",
    "qda.fit(X_train2, y_train)\n",
    "\n",
    "print(\"Classes:\", qda.classes_,\n",
    "     \"\\nPrior probabilities:\", qda.priors_,\n",
    "     \"\\nGroup means:\\n\", qda.means_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix:\n",
      " [[ 30  81]\n",
      " [ 20 121]] \n",
      "Accuracy score: 0.5992063492063492\n"
     ]
    }
   ],
   "source": [
    "qda_pred = qda.predict(X_test2)\n",
    "print(\"Confusion matrix:\\n\", sklearn.metrics.confusion_matrix(y_test, qda_pred),\n",
    "      \"\\nAccuracy score:\", qda.score(X_test2, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a little bit better! We have almost a 60% accuracy score. On the plot, the decision boundary now appears curved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rt0grrZRIe+TCcxdaaKGjSotc8fXTzU2DJu4FNYi0Ry48d6GFFjqa9LYNayRDpSnyPnakPfQm9NgNBpvw2AUCgUAQGQoKCvD5giQlpaBQKJHJZJEO6bhGkiRsNguBgIfOnTvXu5yyGWNq9djcPpbt1XPuyekkaFWtXuO2Vk23dR4M2kShhRZa6Bq6vX0T+uTeGI06/D4f+N2g1IJMXpWGtaU0RK7t+ugGEBOjpX379g0qIzz2RhBpT1x48EILLXQ0afm8F8i0bKR79+6cJt/Pabn3VP33tFNbVkey7froBvx17twZlUpFg2jQxL2gBpH2xIUHL7TQQgsdQkdTLKF0MyOTJOGxCwQCgUDQWhBT8Y0g0uvOI62jYt3sCaYDeUvRGezMXJ7HR79tYFruLnQGO/5AICriE1roqNDRFEso3czIW6SVVkqkPe9I62jw9E4kHSjZyB5XFg+9s4j//bmZuasL+fzfnTzw9kJ25Jvwl26Oqnhbp34R8pdGUTxCh9TRFEso3dy0yIR/KyXSnnekdcR9qhNMVxps0o3PTZeuGPNPrb/rnpkmVRhsURVva9NWi00qKamQNu3WSfuKzZLBZJOkPfOjJj6hD9PRFEso3czIJEl47ALB8cCmPZU8/9nysMdfvKc//U7NbsGIThyMFjef/LGR1dt11a9lpcby/F1n0yE7EblcrNcWRA9iKr4RRNrjjnYdcR+rlWmT1UVdGMwu2LcoauJtLdphs/P535trDOoAOqOTp/+3DIPZEVXxCm2NrlhC6WZG3iKttFIi7XFHu464j9XKdIc0NXXRJVsLc56Lmnhbi7baXazYWkYoHC4fW/aUR1W8Qi+KrlhC6eamRSb8WymR9rijXUfcx2pl2mS2SWPeXxTSY3/4nQWS0SQ89ubQuwsMIfv84N/E3zdEVbxCW6IrllC6mZFJkvDYBYLjBb3ZxUe/bWDD7srq13qdnMbjN/YhIyU2gpG1XoorbDwwfkHY43ePOI3/G3xyC0YkENSNmIpvBJH2sI93HXGf6zjU6eULeerm0/n8mWG8/9j5fP7EOTxzS++qQT0K4muNOkEjo0vbJEIhl8s4p2dWVMUrtDW6Ygmlmxl5i7TSSom0h32864j7XMejnv0M8UULaJMez8m2pbSZfCEJxQuiJ75WqJN0yxl7e18ykmM4HKVCxrM3dCXFtiOq4hV6UXTFEko3Ny0y4d9KibSHfbzriPtcQgvdAK032qS1WwqkH6Zvk2atyJPK9TbJvX9l1MQn9GE6mmIJpZsZmSQJj10gEAgEgtaCmIpvBJH2qFubjrjvJbTQQrcOHU2xhNLNjLxFWmmlRNqjbm064r6X0EIL3Tp0NMUSSjc3LTLh30qJtEfd2nTEfS+hhRa6dehoiiWUbmZkkiQ8doFAIBAIWgtiKr4RRNqTPtF0xH0xoYUW+vjQ0RRLKN3MyFuklVZKpD3pg3pTkRkp4Gd/hY2JC/ZEPB7hwQsttNAR1dEUSyjd3LTIhH8rJdKetM3llQy6Msm6ZbFUNvktSffvRMmUv1NyWU1REZ/w4IUWWuiI6GiKJZRuZmSSFD0e+/jx45k9ezYlJSVMnTqVbt261Tpn4sSJ/Pzzz2RmZgLQp08fXnrppZYONSrwmSso++lF/JbKGq8nnHkhKRfcjDIuMUKRCQQCgSBSRNVU/LBhw5g0aRJt27at87yrr76aKVOmMGXKlIgO6pH0nAMeJ4a539Ya1AFsG+bi0xdijzKPXHjuQgstdIvoaIollG5m5C3SSj3p27cvOTk5kQ6j3kTScw667Dj3rA0bm3nlVIoqTVHlkQvPXWihhW4RHU2xhNLNTYtM+DeQIUOGSLt27Qp57KOPPpLOP/986YorrpDuuusuaf369S0c3SEi6Tl79MXSvtdHhv0r/mas5LSao8ojF5670EIL3SI6mmIJpZsZmSRFj8d+kKFDh/LZZ5+F9NgrKytJTk5GpVKxbNky/vvf/zJjxgxSUlIiEGnk8NsMlHzzFAG7OeTx5POuJeW865EpFC0bmEAgEAgiSlRNxdeHjIwMVCoVAOeeey45OTns2bMnIrFE0mNWxKeQfMFNIeOSqbQknDEUuy8YVZ648OCFFlroFtHRFEso3czIW6SVJkSn01X//44dOygpKaFTp04RiSWSHrNMJseU0QvNBXcg18RWx6TKaE/qTa+gTEyPuAceaR1xH01ooYWOjI6mWELp5qZFJvzryWuvvSadf/75Uo8ePaSBAwdKl112mSRJknTvvfdKmzdvliRJkp566inp8ssvl0aMGCGNHDlSWrRoUcTijbTHbHV5pXV5FZLbVCF5dPmSq6JIKiopk2zu6PDAI60j7qMJLbTQkdHRFEso3czIJCn6PHaBQCAQCATHxnE3FR9NRNpDFlp47kILLXQIHU2xhNLNjLxFWmmlRNpDFlp47semc/H5gxiMFgxSCu7KvCiLT2ihG6mjKZZQurlpkQn/VkqkPWShhefeYL17rqQz2KSv/tki3fzCDOn6Z6dJ701aK5VU2CS/0xr5+IQWuil0NMUSSjczMkkSHrtAcKJQaXby1MQl6M3uGq/HaJRMeGwQ7TITIhSZQCBoKsRUfCOItGcstPDcG6IDbjtzV+yvNagDuDx+vp++HWfR1qiJV2ihhcd+bMhbpJVWSqQ9Y6GF594QbdXrWLShnHCs3laOw+WNmniFFlp47MdIi0z4t1Ii7RkLLTz3hmij0SrdO26OdMWYf0L+XfnEP1JFaWnUxCu00MJjPzZkkiQ8doHgRMAfCPLbvN38OmdXyONnn5rFmJvPIi5G1cKRCQSCpkRMxTeCSHvEQgsPviFa6bNzUe80UhO1HIlGreDOy3sQVzg/auIVWmjhsR8b8hZppZUSaY9YaOHBN1RnzLyLd+7vw5XndyI+RoVWreCC3m34cMxgcpybYdbYqIpXaKGPSUdTLKF0c9MiE/6tlEh7xEILD/5Ytcfnl/RGm6QvKZKcdnvE4xFa6CbV0RRLKN3MyCRJeOwCgUAgELQWxFR8I4i0Byy08NyPS+2xV2mPIzriEbr16WiKJZRuZuQt0korJdIesNDCcz+etFS8lkp1RxZt0vHx5I38saSAMu0puMt3R0V8QrciHU2xhNLNTYtM+LdSIu0BC31iee4+p02qKC2VisvNUoXRIbkdNknaPjV6fMOj6IIys3TzCzNqrZ1fsrFIcnl8EY9P6FakoymWULqZkUmS8NgFgmjHbHMzdWkeU5fsx+Xxo1EpGH52B64f3i3k8rVow2R18+ynyyiusNc6JpfB588MJzstLgKRCQStDzEV3wgi7fkKHV26uXw5u83O11O38fu83bg8fgA8vgDTl+Xx3k9rsVjszdp+U2ib0xdyUAcISrBqW7nw3IUWHnsTIW+RVlopkfZ8hY4u3Sy+3LyXsdqcLFpXTCg27zNgMNmbp/3CFdhNenQmJzqjA5u+HFZ+cgz15eI8+OUnDDqjE3Rbo8sHFfr41dEUSyjd3LTIhH8rJdKer9DRpZvFl9s1W1q+qThsfvcrxvwjTV28t8nb9/kDUkGpWXr+06XV7Tw1cbG0N69c8jisDa6vtNIujXgi/DUs31wiSW5bdPmgQh+/OppiCaWbGZkkCY9dIIhmNu2p5PnPloc9/thNZzKsb4cmbbO00s6jExbh8QZqvK5UyHn/8QvomJPYoPocLh8fT97I0k2ltY6lJGiY8NgFpCfHNCpmnz9AMFiVHlcgOJERU/GNINKertDRrZvKl2uTFoM2zGAll8vo2TGlSdtzO+z8Pn93rUEdqjaS+WH6dhxuX4Pqj4tRMerKUxnUOwe57FB9HXMSefPBgVWD+rHEu2MaZoudLXv1vDtpHW9+v5qFawvRW1zgtkWXryq08NiFxx79RNrTFTq6dVP5csnmLTxxy1k1BsSDPHB5R5LsTbsO3GE2sGa7rnZjB1i3qwKX29/g+lPLFvLgSWv5/IlzmPDYIP435hxeG2qlrXnVMcdr8sfwyZ9bePbTZSzfXMa6nRVM+GUDT3+8lAqLGxa90bDrz30renxYoYXHfqy0yIR/KyXSnq7Q0a2b0pdzeXxSQZlZmvjrOmnMB7nSu5PWSnuLjJK9YHOT+4AGo1W689VZYf3w656ZJunNzsj7lG6btHz9/rBxTvh5reQq2FiP+qySz26WPLoCyblnjeSpKJB8doskuazR5csKLTz2eiKTJOGxCwTHC15/AI83gFolR6NSNksbgUCQ3+fv5ufZofdtv/zcTtw94jTUqsh62Tanl9e/WcX2PGPI40qFjC+eGU5GSmyd9fjMFej+fAdv+f7q1zRtTiZz5BOokjKbNGaBoCUQU/GNINIertDHl24Kn069ezoJcnfVoN5MPqDCZ+fCs0+iTXrthDHpyVpGDu5cNahH2KcMeD3YneGX0fkDEgGnpc76/OW7Kf/19RqDOoCndC/lv72Jv3xX9PiyQguPvZ7IW6SVVkqkPVyhjy8dcV+vATo9OYY37u7F6Es70LltEh1zErnz0m68c0t7Mg0rIx4fQKx1N2d0iiccbdLj0FRuDF9f/jL8lgp8hpKQ5X2VhQSsBshfEhXXK3QDdDTFEko3Ny0y4d9KibSHK/TxpSPu6x2DDu5fIpnNNslsc0t+lz3i8RypS0srpGvGTg3psa/cUiJJ+xbV6dFb1kyT9r0+Muyfdf2sqvX1UXK9QtdTR1MsoXQzI5Mk4bELBILjE38gSH6ZlQ9/3UB+WdU0Z0qChnuu6knfU7KIi1HVWd65fyPlv7wW9njOLa8Q07Fnk8YsEDQ3Yiq+EUTasxW6denm9PWCXjc+cwU+3T4CNkOzt9dSWrlrGidnKHlt9EA+e2oIH//nbN7/z3mcf0Zb4mSuoz+zEJ+AXBt6Ol8em4gqRhtV1yt0PXU0xRJKNzPyFmmllRJpz1bo1qWbxddb8xU+qwH9zM8p+vQRir56ivK/3sNdupdg+bbo8h2PVe9bQHKChraGRZz09yWklS1ALpfVq7xi/otkX/ckMnXNHfJkmlhyrn0SxbznIn99QjdcR1MsoXRz0yIT/q2USHu2Qrcu3Ry+nq8iT8r/4O7a/vG4ayVX4Q5J2j0venzHCOmgyyL5zBWSdUuupJ/7rWTbukTymiukoFjHfvzqaIollG5mZJIkPHaBoDUiBQOYV/yDadHPIY+rszuTc9MLKGIblvddIBBEN2IqvhFE2pMVunXrxvp4QbsJx/ZlhMNbvp+gtSJ6fEehhRYee5Mgb5FWWimR9mSFbt260T6erRSZoq7sdDJwVESP7yi00MJjbxpaZMK/lRJpT1bo1q0b7eO57ZJl7Yywa7RLJ70q+Yvrk0tdaKGPMx1NsYTSzYxMkoTHLhC0Vvw2I+W/vYFXl1fjdZk6hrZ3vYU6vV2EIhMIBM2FmIpvBJH2YIU+sfSx+HrK0tVkXz+WtIvuQZXeHmVSJon9Lqfdve+hik+KLt9RaKGFx94kyFuklVZKpD1YoU8sfUy+3qyxKItXkNj3UnKuuJc25w4m9ZReqFKykO1fGF2+Y9TqXACC+r2wa0YUxCP0UXU0xRJKNzctMuHfSom0Byv0iaUj7gtGnbZKUsEKSfLYJUmSJJvVJlWWlUp6o03y+QJN0l4gb7nk1ZdIxsW/SWWT35KMi36WvIZSKeDzRsH1Cy089tDIJEl47AKB4PjCbzfjM5bh3L0KmSoGbfcBrCvw8N6fO9GqlVzc/yRGnN+Z9OSYY24jGPDhzt9K+e9vQjBw6IBcSc6Nz6HtcOpRVh0IBJEhqqbix48fz9ChQ+nevTu7d+8OeU4gEOCVV15h+PDhXHjhhUyePLmFozxEpD1XoYVuqVzzR2q310+Fwc7aLQWs2VaGzujAZbc3f/s7puG36tFNHk/Zj89jWTUV89LfKf96DJ30i3nwii44XD7+WrSX5z5dhqG8/JjbC9qM6P58p+agDhD0U/7H21U596PJtxVaeOwHkLdIK/Vk2LBhTJo0ibZt24Y9Z+rUqRQWFjJnzhx+++03Jk6cSHFxcQtGeYhIe64ngv51dSHbSy1RE08065byCW36EuasLGD0+AW88t1GXv1mNfe9OZ+/l+RjdXqbtf1gwXLMK/7GU1r7i79340xOS3aQceBXeqnewYZdOijdeEztecr2IPk8tdoBkLwuvBX5sOyD6PFthRYe+0FaZMK/gQwZMkTatWtXyGOjRo2SZs6cWa1feeUV6csvv2yp0GoQac+1NWuP1y+V6e3SzBX50q9zd0qb9lRIOpNDWrizPCrii0bdIj7h7rnSxl3lIfc/v2LMP9KStfvrvX+5wWiTdKVlkt5ok/z++nnivvI90v7xN4Vdm1/808vSz1M3VMcz9uMlkt16bPupW9bPqXuv9s0LJWmPyLUflTqaYgmlmxmZJEWfxz506FA+++wzunXrVuvYiBEjGDduHKeffjoAX375JTqdjueff76lwxQ0Ex5fgM17KnnjuzX4A8Hq17PTYnl99ECy0uIiGN2Jjc3h5dVvVrIz3xTyeLvMeN548FxSErQhjwNYHR7W7axg0qyd6IxO4mNUXDmoM5cM6EhKYvhyAD5TOUX/eyjscVV6O7Z3u5ePp+0HoGeXNJ6/q/9R92UPhad8PyVfPxn2eNtRE9BkntTgegWC5iaqpuKPNyLtqbZWbbC4GPft6hqDOkC5wck7k9ZhsLqjKt5o1c3hE3ot5RTr7ISjpNJOwO8PW95TuJ5ZK/KZ8PN6dEYnAHaXj59n72LCL+swl+bV2b7MY0GRkFqlZXJiTu5DxhUPk3XNk6Scfz3KDr3YX3lo+vySfjnEyT3HdL2K2EQ0bWr/uADQtD8VRUxcdPm2QguP/QDyFmmlCcnJyaG0tLRal5WVkZ2dHZFYIu2ptkY9fUsZSzeVEgiGnkjaVWDCZPM0azzrC00EnFa8FgPJkoNdZcenx98cPqGyeAVZqbEh7w1AZkoscmf49i0+Db/MCf1g7MbdeiotXshfFra8Ysl4UgaORK6NI/v6Z1Cnt8e48Cd0f7+Pq2AbSaedh5yq906nnER6Jhpg34Jjul5l6RqyhowkttvZIDvwUSmTE3vKALL+73GUJaujy7cVWnjsBzjupuL/+usvpk+fzpdffonZbObqq69m0qRJtG/fvsXjtLl9LNur59yT00nQqoRuAr23wk7u8jzmrykK2+8THhtE1/YpzdJ+SYWRDpIe04If8ZTtQxGbQGK/y0k4YyguZXzE+6chGre16oOk82DQJjaNLlnHCkc33vh+bch78/DIU7mobw4yTXzI8tsKrDz9xbqw9/bGYZ25ZXhnUMeFjSfQ/lx8Fj362V/hLd9/RA0y4q58kq3uHHp3TSNNtwROGnjs15u/hED7gQS9XoIeB3KZhDw+DUVccvP0r9BNoyF6Ygmlm5moGthff/115syZg16vJyUlheTkZKZPn86oUaN49NFH6dWrF4FAgFdffZVly6q+1Y8aNYobbrghwpELmpI5q/KZ+PumkMdkMvji6eFkpze9zy4FAzh2rqTi7wm1jmna9yBr5BMo41OavN3mwO31Y7F7sdg9qFUKEmPVpCRqkMlkja7bYvcwef4epizeV+P14f06cOcVp5IUrwlbdmeBkSc/WhL2+O2X9eC6YaGnvw/HsXsNuslvhTymTMog5443UB2cshcITjCiair++eefZ/HixWzfvp1ly5Yxffp0oOoBuV69egGgUCh45ZVXmDdvHvPmzYvooB5pD7W16jO6ZhCjCZ34o3/PHDQaRbO077Wa0M/+KmS7nqIdePUlLNypi3j/HE0bLC5+nrWT+9+axxMfLuaRdxfy34mL2V1gxL9/WaN9wiSlhxsv7M5nY4fw0P/14P7/68WnY4dy92VdSSqcA24rLo8fg8mGsSSfgNteXT5N7SFWGz6py4DuyUdtP+i2Ydu0IGwdfkslktsReR9VaOGxh9PNjLxFWmmlRNpDba16r8HJmw+eS+oRT0if2S2TC8/rzNoic7O077ZbCDrD/8OzbV5I7q6KiPdPXXr5Xj0zV+Tzd+4+/IFDk3GVJhfPfbYCvSyTg7nPG+MTxseqaOPZzSXSdC5vV067zAQSihfg3zGdYoOHjydv5OH3lvDfb3bz5+ICDBYXFCwnZeXrPHrNaYSaOBgxsAPJBVOP3r5+Dxxt4kEmi7yPKrTw2MPpZiaqpuKPNyLtobZmHa9RUml2oTM58XgCZKfFEqNVsr7YwoDOabXOj1ME8dnNuO02tDExKGMTcMljWNqA9t26fEq/eiLs/Y4/Yyilp99Ml8z4iPdPOK0zOXl24lJcHn/Ia7hxWBduHNoRhTa0B35Unb8UU/YgiipdzF9bhEIOF53dgez0BJLVXvaVOXjy0zX4/DVXNHTISuDVUWeTVrYAZ4chlJoD/DpnF/tLLaQnxXD98G50bRtHUvGCo8fTZQjOoj2U/zYu5DUqk7Noc8c4lEpFdPmqQrechuiJ5UT32AWCY8FvN2Ne9gfWDXMhUDWgadqcTOZVj6FKzal/PVYDJd8+RcBuDnk85/ZxxLQ/pSlCbjaKdDYefDv8NHWvLuk8f/fZxGobvq4bwGhx8+b3q9lZUHMd+4DTshk9shdvfr+W3YWh17g/duOZDOvXoVo73T7cngAqpZyEOHWD4vDbTej+fBdP8c6aB2Rysm96gdhOpzeoPoGgNSGm4htBtHiqJ5JeuFOHx2LAuX8j+nnfY9uzDtOS37CunVk9qAN4SvdS+uMLGCvK612/R5NA0kWjCTXPG9PlTGRJWRG//qNpbyCIvI5p6rQkLdUz9A30BQNuO7OW7601qAOs3FbOht2VBMMsUwSYvbIAe9H26vpicZFaMocEhbvB8SjjU8j6v8dJHXIzyqQMZOoYYrr0oe3tr6LN6nBM1yd0K9LRFEso3czIW6SVVko0eKonkl6dZ6Cz1o1u0kuU//Ia1lX/olAosG2cH/L+BOwmHIU72VRPT37JHgNf79eQfvubxHTujVwbjyq1DUkX3UfGFQ+zuMgdVf0RSs/eoePs08LndRjYpy2r8gxVooG+oNlkZtrywrB1T8ndx6Azw+/zEJQkpIJl4dvLWwybfobS9fWKR1m8nKSyWbS55j+0H/0hmeddjmbGg8jzFx/T9YXVRauqtG4bLHgtenxaoYXHHgYxFd8IosFTPZG0y27F9O8HuPMOLYXLuu7psMueAOJ6DSHxkvuJUSvr3d55J6cTgxe/20Wlw0dKejpxmshff330qv0GemUn8OLnKyjVO2r0xe2X9eCUrhl0PPCMQEN9wUqjnbvHzQ/b18nxGkb/Xy/G/xh6jftD15zOxdnFyNqcUat+W0CLyeZi864yFEo1Z3TLJEkLcUX18NybTdvwW3R47VYce9aiiEkgvltfFAlpKOJTI+/TCh1eQ/TEIjx2gSA8ofKEZ9/4AuW/vha2TPL515M6qOmXRHp9AWxOLzIgIU6DShldk18Gi4uCMiurt+tIildzfu+2pCRoiItpmJd9OBa7hxe/WMH+EkvI4/1Py+b2y3rw6HuLamUOzEmL442HziU9qfb+6Gabm6//3cai9TV3abx26Mn83+CTSYwLvy6+OfFb9JT98io+Q0mN11MG3Uhi30tQxCREJC6B4GhE16fRcUY0eKonkg54a2+h6TfrUKW3D3uPFN3OadJ4lu6poEzv4OupW3n0vUX8Z0Iu303fRoXJid0TPf2VlhRDt06p9DurHVcNPpl2mQkEZbJG5ZZPUvm465KTQ/azXAY3X9SNbM8e3n9sEGedkolCLiNOq+T/LujCGw8OJF3jr1V/MH85SzaW1BrUAf5YsJdd+8rBc2gdfEv5oAGPC/3872oN6gCmxb/iM+ki79MKLTz2MMhbpJVWSjR4qieSdqFCpqj5NLd55RTSht+JXBtf6/4kXTSKHzaam6z9lfsNxCsVPPFhLjOW5WN1eDHbPfy7eD///XAxepOLt2ftjJr+WrpHz+O/bWTx7sp6nX9UX3DfArpW/M0TN/QiIfbQfUhN1PLivQNo49+P+p+76WRfxZO39uXrJ/ryyS1J3HaGi/TkWNi/sFb9laoO/LFgb617d5DfFhZgrSypX3xNqIMuG86dq8LGZVk1laB+T3T5tkILj/0AYiq+EUSDp3oiaafTiW3xLzjWzahxH9RZHUkdejt+sw5X/haUSZkknDGEgDaJ3Hx7k7VvcXj4+t9tLFxbFPL9cNWgLvQ5ow1dsxOior+Opu1uH7t0NrplJTTIcw90HorJrcDmcCMLeEhIiCclKQ6519Ywn9Fjp8AY4OF3F4X9N5Ycr+GDx84lLSWhRX1Qr91G8eePho1LeyDFsKJwSfT4tkIf0hA9sQiPXSCoG7/djHHRz9g3LwQpCIAiIY2sa59Ck9URZHJk8uaZiDJYXIx+cz4eXyDk8eR4DR+MuYC0ED5ytBAIBNGbXSzdXMrOfCNtM+IZfnYH0pNi0IZJ49tcOFw+Nu2p5Ltp2ykzOEKe06tLGs/eeTbxscf+bMCx4LfqKf5yDEF36LiSBo4kddCNyBSKRrdlsXvw+YPIZTKSEjQo6lqvKBDUAzEV3wgi7TmfiHp+vouEIbfT/oGPyb7tddLueJvsO95Ek9MFu09i9vbmy+UeCEoE6/geHJQk9HZPVPVXDe3ysS3fyEPvLOS7adtZubWcPxfu5cG3F7B6ezlmh6dRHnxDdcDrYeXWMq44r1PYPr3xwm7EH+N+6o3RirhkkgZcFTImmVJNYu9hyHyORrVnt9nZsL2Il75cwd2vz+HxD3KZsnAnJoujxa+31eloiiWUbmbkLdJKKyXSHuqJqMfN2EFung1VShZLbclc9UsBC4u8yGSyZm+/zOqm36nh14ife3ob/thQElX9dbjWmZy88+PaWjMOkgTv/bwek83TOA++gTrWvJ2MOAmZXMaI8zsjP+yXqkop547LetBGbYb9C5ul/bq0TKEkoUtPkvpeAopDMxmKxHRybngaZWJ6o+r3BwKs2FrOi1+vZ1+xBUkCo9XNtzN28/4vGzHbPJH3gY9nHU2xhNLNjSQ4ZqwurzRzS6lkdXmFPkH0vhKzdN0z06QrxvxT4++m56dLpZV2afbW6Ir3cL2zwFgr7sP/Zq7Ik5buqQhbXnJZJGnblKr/NpEuL6uQrntmmvTJ5I3Sxt0V0qwVedLcVQXSup06aeveSknal9uk7TVUBwrWSl5jmeQq2SN5yvMkX9kuKeiyNrr+CpNDuv7Z2u+jg3878g2S5LK2+PW2Gh1NsYTSzYxMkoTHLhDUl0BQQmdw8MucnSzbXIZcJuP8M9tyw/BuZKXGNsl+583F+l0VvPTFirDHb7nkFG68sHsLRlTVn8U6Gx/9vpE9RSaS4zUkxmm4fnhX+nTPbHFvvaXYV2zmsfdzwx4fcX4n7rta5LsXHBtiKr4RRNwzFbrF9dzt5SQkaHjw2t589vQw3vrPIO4acSrZaXHYPf6Ix1eXzkyp+6G+UzulsaAB+803he+o2DmVk1JkvHRPfz57agjj7jmDV+7tx3lntCVe7o4uX7Qp9VG+/ynkcvA6oyfe401HUyyhdDMjb5FWWimR9kyFjpyO0ShZX2Lh7h/Xsny/MeLx1EebPf6weeTbZcYTG6vi5X+31bu+pvMdF5IYr6GNfhHt/7qEtLIFVX57pH3QZtRJcRriY8LvsHfBme2iKt7jTkdTLKF0c9MiE/6tlEh7pkK3Hh3weSW3uVLSl5dJTpul2drbX26VPvxtvXTVf6dIV4z5RxrxxD/SC58vk3RGh2RrYH0R9ymPY+33B6QlG4pC+utvfLdKMtvcURXvcaejKZZQupmRSZLw2AWCoyEFAgQ9DpDLUYTIctcY/FY9ltXTsW6ch+R1oz2pJ2nDbkOV1ha5qunzpLs8fqwOL063D61aSUKsqt5etsXuwe7y4Q8EidOqSEnQoFCIib9jwen2UaSz8dPMHewttpCSqOWaISdz1imZJCdoIx2e4DhG/ItsBJH2TIVufr1sTwVeUwWmZX9Q9sur6H5/C9uO5fjt5iap31iho2zSy1hW/YvkcYIUxJ2/mZJvxuIu28+SPZVNfn1+SSIrNZb01Fg2lVuRDiwzq6t8ICiRV2rhpS9XcP9b83n4nYX8Z8IiZq8uwGht+H7qQlftR9/ds4axt5zBx08O4Y37zmZYWj7JKm/1+cHCtQSslQTcTnDboir+qNbRFEso3czIW6SVVkqkPVOhm1evyTNyktJO6TdPYl7yO97yPNxFO6j86z0qpnyE02xsVP1bSyw49m3AZyyr/eaSghhnf4nLaop4fyzfq0dvdjL246XsKz60s5vV4eXTPzazdqcOSZIa7zsWLMOhL0ZnclJSacdotCBt/St6fNHm0DOfIr5oAWlJMSSXLoCpj8D+RQR9XrzmCgwbl1H66zgq/noXV9EOAi5bdMUfrTqaYgmlmxkxFd8IbO7oyv0tdDPs/z7lfdz5m0Pe/4xrnmKjvBO9O6Qce/1/vY27aEfY91jq3R+gSMmuX+53j499OjvdshMatP98ffann7JwD7/O2xMyxrQkLe/95wLSNN6qD65jzJ9drrfx5T9bWbuzgqAEGckx3HlpV/p0zyA+Ib5+9RUsh07ngzquwe1Hi5Y6D8Fdnk/ZL69BMFCjrxPPuoSUc0eiSEiLmnijUkP0xCJyxQsE0YPPrKPokwfDHtee1JOsa8ei0MYeU/0BtwPd5LdwF24Pe077Bz9BlRI+291B/DYjnrJ92LctRa6NI7H3cJRJGShiE44ptsOx2py88s1adheawp7z2dPDaJtx7M8e6M0unvhw8aFp/cMYc1MfLujTrkZmulCYrG7KDA427q4kIVZN3x6ZJMVriNWGf/o8GvHbjJR88xQBe+j+bjfqfdSZHVo4KsHxhJiKbwTR4AEL3Xw6GKj5a+lIJJ+b/ErrMdfvlqnR9BoWtn51ThfKnNRZ39zt5XjMlZT99CK6yW/h2L4U2/rZlHzzJMbcXygqbXzufFnAS0JM+A1i5DJQKmS1ytfXd5Q8dtZsLw85qAN8M20bJpu7zvoMFhevfLWSsR8v5Zc5u/jiny2Mfms+81buw2GzNSieSOuAwxJ2UAewbV0cVfFGpY6mWELpZkbeIq20UiLtAQvdvNrglaNMyQl7/9Vd+/PpitJjrn/JHj0lsR1RZXasXblCScLwe3lqel6d9e0uNmBa9HNIn962fjYYi1mb37h19kG3jSvOSgvbD/16ZBKnltcqX1/f0V2Rx/ItIZ4zOIDZ5sHh8oUvX5nH99O3s6/EUqOcJMGXU3dRfnDnuEj7qvXSLyJ5Q+8oV31dnuPpeiKkoymWULqZEVPxjSDSHvDxpt12K267Fa08iEITg0+dwOJ9pqiJ70jt8Pjw5W/C+Mebte69PDaRnLveZmGxv1Htrc4zcF4bFc7tS7Ctm03Q6yKm0xmknH8dvrh0lhylf/yWSkzfPA5Bf8j3qLbzmaRc+RgxcfHH3B9D2irQ79vJr9tULNpcUaP+tCQt40afQ1pSDD6oUb6+vqO34zDe+31bnYP7508Po01CMGT5iqyhjB6/AH8g9EfZ4LPa8eh1vVEFHNHls4bR/jb9Kfr8MSS/N+T15NzyMjEde0VNvFGpIXpiER67oLXiM5VTOeMz3PlbAJCptSQPuIqEPhejjEuKcHThCXpcuIt3Ypj7LT5DCcjkxJzch/Thd6JKDf9rvqFIwQABpxUkCbkmBrm6fnu6+4xlFH36cNjj6uzO5Nz0YqO89qDfiyn3F9zxbTHGdmTmRhNOt5/TT07npOxEvpqylZ4np3HzRaeQklj3+uuA2wEBPzJNLHLlIe97y149z366LGSZbh1SeOne/iTGhV7TX6yz8cDbC8K2eWqnVF64ewDxsceH1x70e7Gsmopp0c+1jqmzOpN947Mo41MiEJngeEFMxTeCSHvAx4v2WPSU/vhC9aAOIHndmBb/hnHVdJwuV1TFe7ies8eM1K4nObe+Stv7Pyblng9JvvxhVKk5TdqeTK7ApYxnXoEHR1BZ7/JGDygSUmu/OQ+gatcDj1zVqPgcfhlJ/a9CWbaVdMlI24x4MlNiWbqplJe/WklxpZ1ZKwr47K/NbC0yhazP77Dg2LUa3e9vUTrpJYwLfsRnLEXKWwJuK+2zEzi/d5ta8cdplTx6/RlVg3oY31KjkhGjCf8MQNf2yWg18sj7qvXUcr+bxDMvJP3yB6rvrUypJqHPxWRf/RBKpSKq4o1KHU2xhNLNjBjYG0GkPeDjQf+yuhBHwXYCNmPIPnSsmYrHao6aeEPpJXv0KOOTWVgGV32/k9w8e9TE9+aiMuLPvT5k38qUanynDGXJPlOj21PGJ+PsdzOm+E78Onc3M1fks6fIXKO95VvK8HoCLD+ivMVowDD7K3R/jMddtB1fZRHWNdMp/vIJvAEVFK8hOV7DfcPSeeWWrpzZPYNuHVK4aXgXPry3K+2dG6saCONbpth2cNUFnUP2gVIh47J+2SgVisj7qvXVeYtRxCaSkKSl7bCRtL/7LdrdP5G0nmei/PW6yMd3POhoiiWUbmbEVHwjiLQH3NTa6fGxt8JGl8wE4jRNU//+ShvZa7/HsX1p2H5sc/c7aHM6N97DtxhxulzEadWo4pNx+Imq/q2vPr9rBhqfnUDAT7ndT3p6Wp33Y/BJsbi3L8a0+Dckb9XshzIlm4wr/8NWTxKntE1tomcO/MxYtp8fpodfd//k7X2rtls9UH5NvpEBMQbKf3oh5PmqjPa0ufF5FInpVb9milbhyjkHv1xNrNyLYv+CevmWZp+aSbN3MmdlAcEDn2iJcWqeuqkXPU5KRh1bz3XwEdQBlw2T2YbRq8XtC5CZrCXRVUBsRoeoiO+40hA9sQiPXRAJAi47fpsB24Z5BOxGYrv2JaZjL5SJ6U1Sv37ud1hXTw17vN3oD1Gntzvm+gMuG668zRgXTsJv1iFTaUk4czjJA65CWcc0dTTid1hw7VuPedmf+C16VOntSLngRrTtuqOISQhbLhjwEbRbCLhsyBRK5DHxzeLDLlhbyPu/bAh7/K2HzuO0zoeeoJcCfir+nVjnF7t293+EOq1to2Nzun1YHV50RicxGiWpidrjJpe91xdgV4GJ8T+uwWKvemhOLoOLBnTklou7i9zxggYR/e/4KCYaPODG6r1FOixrZ1Hy5Risa2fg2LmSyqkfU/LNWDyGUhY2YH/uUHrutnLiTx8Stg9V6e0JquOOuf6N+ZXYtiym4u8J+M06oGp9uXX1NMonv4WuvPHruFtKu+0W9PN/onLqx/iMZUgBH15dHrrf38S2cT5OhyNseblChUuTxEK9Fk9CNsr4lGaJt1PbZBRhEsXEx6jQxqhqnL+91IzkC70+vZrAgSf6G+lbxuIiWzefM9pr6NYhhXStD8WuadHjq9ah9WYXL36xvHpQBwhKMGtFPtOX5eH3B6Mq3qjX0RRLKN3MyFuklVZKNHisjdEr9xvQesyYF/9S69oCDjP6qROxmBqXq/y16dsp8mpJGXRDrTbkmljkwx9kdbnvmOvX+h2Ycms/PQzgLduHV39oHff2UgvL9+rZWWaNiv4/UntsZpxbQj/dbcz9Ba/D2jy54PfpCfp9uM0G2mvc6A3h171/u7KAh6/vjeyIsV2pkPPErWcxYf7uGue/O28/qu4DQ14TVC0blEsHBrNI+56N1QXLYcvvULymQeX9up3MXJEfdrnelMX7qxL0RPr6jicdTbGE0s2MmIpvBNHiyTbGU7fN/xrHhrlhrzHtng+QJ4fPVb5in54BndLw+QIEghJFFhfdshNrnR8refCaK7CunUnQYSKm4+nEnDKAdXro1e7Ycq3b3D6ClfkYfng6bPxJg28hoecgfKZyvHYrUmIOlW4l8cnJxMaoWVVgjJr7YVo9DdPcb8NeS9aNL7DSm83ZndKarP01+UbOy1FgWzMd64a5SF4XmnankDb8DoLJbVmcZ61Vvn/HVOwOL7NW5FNcYefk9skM79eBuFgVy/cbaq+Db69C99OL1TMqh5Nx2f3E9zgHmbZhHnhAnYDFakdymIhNTiMmLpK54Yfg9/nwGUvxFO9EmZyNpl13FGoN8ryjl3e0H8qr329ge17oB0wBPh07lHaJUnT5xNGsIXpiER67oCUJ+n1U/PUuzj1rw57TdtQENJknhS4flKgwOfk7dy/LN5Uhl8sYclY7Lj+3ExkpofOnS0E/UiCATKlGduTPvmPAoyug5KsxIY/FdO5NYt/LqPz3Q4LuQ9m81B174+x7Kzsrggzr24G4mOhY32xePR3j3G/CHs+++UViO53RpG36bUbKJr1ctUa/BjKyb36hzvYCgSD+QBClUhF2ev4gPkslpkU/Y9++HIJ+lMlZpA67nZiOPRu8v73B4iJ3fTEzlufj8vjp3S2Dmy7qTlZqLKqDS8FaEJ+5gvJfXq2R/U+mVJN1/TNo2/eosV4/ZHlfgImTN7JwXXHI40qFjM+fHk5m6rHtSSA48RBT8Y0g0p5sY7UrIEPZsXfY65OpNDgkddjy5QYHj7+fy4xl+ZjtHoxWN38u3MuTE5dQaXKGbH/29kocATkyWe3c4seiLZIaRaiHxGRykgdche7Pt2sM6gDe/I3Ebf8Xo8FCYYUtYv3vsRgw7d2MccnvWDctIKZjz7D3AoUSRXJOk7bv8Piw7N8SYlAHkNDP/IKysvKw5Z2+AAt3V+L0+o/aniopg4Th95J89/u0feAT2twxDlmnvszde6j/6+NTGspLefXrlXw7bTs6oxOrw8viDSU8+t4iCkotsGdei/qmgdKtVPw9oVZKX8nvpfzXcQSMxUetTxVwcNWgLmFv/XlntCUhTh15X/h40tEUSyjdzIiBvRFE2pNtrF6ypxJLxqnIwzxtHd9vBJ+tqgxZ3u31M2nOTuwuX61yBoubmSvy2V3ePJ7w4fqlucUkXfYQyGq+lWM69sKVv/XQg1lH4Nm5jMGnJjF7RQF7dLYW7f/VeQZ8lkoqfnkF02+vYF78G/ppn+DYuZL4M4aGjDd1yK3stsAbM3awcr+BoM+DxaDHYTWz6cB68obGU6Qz4d2WG7I9AL+pHJfd1mTXn5tn5ervd7KwVEIZn8KSPZUNyy1fsp6t+/TsL6n94ejzB/nkzy1Yzebq8/2mUrzqdLymcvwOS5X33cS+acDrxlO6J3QHBv04d62Esk1HrS87LY5RI7rXenahc5sE7hjevioBT6R94eNJR1MsoXQzI6biG0GkPdmm0JuLTPRN9lA55UO8ujygahoxqf+VxJ11CQsL3CHLe9x+Rr0xD38gGLJv0pO1jH/4fNaXWJp/3XfnJFQOA6blf+Ep2YMiLom0i+7GvHQyzt1rwt4/1TWv8/USM2NuOYvEWHWL9f8FHeMw//shrryNNQOSyUm/bDQyuRLzir/xWyqrlrsNuglt2644ZRr2lBo5LcGLZcXfuAt3oIhNILH/VcR2PA2nIq5B8bicTsz/TsC1L/zytdS730eRktMi78ej+ZIOm53Xf9jI1v2GsPF+MaY/WclaPJVF6Gd+gc9YCoA6qyPpl45G7a1EntOryXxTd0UhpT++FDaehN7DybjwDlDHHrU+p92OxeZi7R4rVqeXM7tlkBPjJCUlBbQJkfeFjycN0ROL8NgFkcLvsBB025H8PuTaOBRxSciV6rDn680u7h03l0Aw9NsnNVHL+49dQGpSy62/DXrdBL3uqnXc2jiMiyZhWf536JNlchTXvcXa4iAjB5/cJH5/ffEZyyn69KGwx1MvvIf40wZCIIBMqUIRe+iDwFW4nbJJL0MwUKNMbPf+ZFw6GkUD8+47dq9GN3l8yGOqjA60ueXlBtfZFEhSkIDdXJ0/XxGTgEsZz+vfrqnzIbPPnx5Gqq+M0u+eBemIL50KJe3ufa9ROROO5Gi5+tOveIjEMLMwAkFzIabiG0GkPfKm1Mq4JDxxmSys1ODWJCNXqus8P1arpP9p2WH75rwz2qBSyVv0ehxBBfPyXThlGmQyGfG9htSaoj+Itksf1uxz0KdHFnbP0T3iptQBb93rut2FW1Fo43GpE5m731Fd3m0xUjn141qDOoBz1yo8xjIW7Dj6un2724fd5UVncmJLPYW4QbciO/JLnFxJ+mX3s7zE0+LvR6fTiWv/Jkq+fpKSr56g5Ov/UvTFY8gKNzC0T+188gc5KTuBGMmBcd4PtQd1gIAf05LfCTrNBzq68b6p3FVJTJc+IeORqWOIyekUPb7uiaSjKZZQupmJqoE9Ly+PG264gYsvvpgbbriB/Pz8WudMnDiRc845h6uuuoqrrrqKV155peUDPUCkPfJI6litiusu7I5WXfsp5MQ4NVcO6sLyPENE491lU6K97DFQ1NwgRJXVicDZt9CzRzvembe7xeNzy9QgD//0tjKnGzKFslZ5j90acsnYQWwb5rJ0T+hnIg7qBTt0FOvsvP3jOkaNm8tD7+Tye1lHtLdPJKZjLxRxScT0OJd2o95juzeZV6dtZ6/OhsHiotTgYMnuylq54Juyfz6avwe/qZzy394g4DBXX5vkdVHx17uc2TmenPS4Wtcul8t48OpTSHAV4S4Kn/LWlb+FoKW8SjSBb6r4934yht2CtsOpNdpRxCeTc+OzKBdEka97IuloiiWUbmaiair+9ttv55prruGqq65iypQp/Pnnn/zwww81zpk4cSJOp5OxY8dGKMpDRINHHlHt8lJhdDF53m5WbStDJpNxfu+23HBhN3LS4rB7/BGPd0+pkdNSZXhLduO3W1DlnIwUl4pfnYBarWDJnsNzoXtxmAwkKoMolCr8qliWFdjp37np1o0v26vngs6J2OZ/h31z7WQ0MpWGNqPeR5OSVau8W5dP6VdPhH0/xvUYiK7vXXTKTAjZvt3to6DcxvP/W1orGUpqopZ3Hj6XgMdGcnIiMbFx2N0+Kk0upi/dz8qtZSjkcgYfWM6YmRLbLPeruMJEytofce5YHvIaNe1OQT3iaaYuLWD2qgLcHj+9Tk7nzitOo32KAoW9nKIfXqnOmX8kypQc2tzyEsqkjCb1TQNBCNhN+CoLUSRloEzKRKFSIdu/MHp83RNJQ/TEciJ77AaDgYsvvphVq1ahUCgIBAL079+fOXPmkJqaWn1eNA3sgipcHj8Olw8ZEB+rQqMOv4VmtBJw2nDsXo0p92cCdjPI5MR2O5u04XegSs5s8vb8dhOG2V/h2Lmy+jVFfDJZ1z6NJrszMkXtX/R+q4Hir54g6LKFrDPrhmeJO/msqutxWAh4nFX1amJRxCVhdXgY9+3qsB717Zf1YOTgk6tzq5dU2hnzQS5Od82VBZkpMYx/+HzSk+u3Z3xD8NtNlH77DH5rZdhz2j/8GcSlYXV4kCTQqhXEx1ZZCUG/D9Oin7Gs+jdk2bQL7yax36XIwlg0AkFrIGre3WVlZWRlZaE48IGmUCjIzMykrKys1rnTp09nxIgR3H333WzYEP6J3uYmmjzySGq/JJGeHINaq2Th7sqIx9NgT9flwb5tCfrp/6sa1AGkIM5dKyn76UU8Fn2Tt6+MTyHx4tGk3/MhWTe+QJu73iL7zvGsdyZh9wVDlveoE0gcckfI96Iq4ySUGR1Zv1+Hq2gnZT+/QvGnD1P86cOU/fwK7uJdOFy+Oh88y11fzI4SCza3D6fbx3fTt9Ua1AEqTC4WrC3CfgzXP2dblccf7niR2YMiPjlsjDJNLDIkVEo5aRof6aVziZcfeGbBbUW+exZJ/S5DlVrbi9e0ORnNyX0pLLOSV2pBb7ITyF8RPb6r0MJjbyKiZmCvLzfeeCPz589n6tSp3HPPPTz44IOYTKaIxBJNnrfQx65dViOm3Nr58gH8lkocBdubpf3cfAdX/ribld5stG26srDIx9N/bw17/pK9BqaaM0m95mlUB57slqm0xPW9nJybnmOVLkA2Fsp+ehFvRUH1NXgrCij98QVkQX+tddKHI5fL2FBUtTeAw+Vj9dbysOfOW1NIYaW93tcrBQN4zHpOVerxFmzGZyyjQm/indk7a5z/4ux8YvpdGbbdxF6DUJirlmWG9jGfR6lbT86tr5Bx2f1oO/YiptMZZF7zJIkjxvDUt9t4+L1cHn1vEY+8t5iFRQnYK4vrqE/o41JHUyyhdDNz3E3FH8nIkSN5+umnOfvss1sw2ioi7nEL3SR6cLqH0q/r8K67DyBz5OPYvVJUxHt+13Q0PgcBnwebN0hsYgqxMVpcdhvmaR/h2rc+9HVc9hifrJazYbc+5PH7ru5FRptETmubhNvl455xcwn36ZCdFsu4B89lffHR8xSc3yUFhT6P8j/eJug89Isl9tSBKM+9DU1izb0CBp8Ug3XhD9i31Eyeo2nTlawr7q/airc+PqbHgd9uJBAI4ty3AafDBR37krvDxi+LiqrrffGes+l3ak7kfVehhcfeRETNwA5w2223ce2111Y/PPfHH3/w448/1jhHp9ORlZUFwI4dO7jzzjuZNm0aGRkZkQhZ0Arw6osp/vw/YY/HnzGUjMseQCaP7gkuv9VA0acPI/mrdkuTKVSoMjuAJOGtKESRkApXv8aT/1uFy1Nzir1dZjyv3z+QtKQq39xtt2PS6/G53ci0cRRZoLjSyfY8I+t3VXD9sG7ceFF3lPXY69xn1lH8+WPVcR1OQp+LSRt+B3KVpsbrAacVv6US25ZcJJ+H+J7no0pr26A95v1WA+W/v1mdeOkg6n4jWSvrxdezql7vkJXAuAcG1rnneTDgh2CgVpwCQTQSVZ9UL7/8Mj/99BMXX3wxP/30U/VStlGjRrFlyxYAJkyYwBVXXMGVV17J888/z9tvvx2xQT1aPOLjXRttboorbExdup+/Fu2lsNyKzeltsfaD6lhU6e3D3ueEMy9GJpdHTX+F034J5JoYkMnRnHcrjHyTde1uYX2HW5Ff+xaq3peR6tjPe/eexkV925CSoCErNZZbh57EK3eeQYxWybzt5XgtesxzPsf950soA252F9n4e3EeyzeX0TEnkXEPnMulAzvi8gWOGt/aPAO2LYtDDuoAtk3z8R14ruHw8orYRLwpHSjofjXxF44i5qSeuJTxNeqvy8cM+jwYc3+tNagDeNf8Rb82EknxVQ/cFepseH3BkPUFSrfhLtpB5b8T0f35Dta1M/CbK47avtAR1tEUSyjdzETVwN6lSxcmT57M7NmzmTx5Mp07dwbgyy+/pFevXgCMHz+eadOm8e+///Lnn39ywQUXRCzeaPGIj2ft8wX4edZOHhi/gC/+3sK3U7fx0DsL+W7adspNzqOWf2f2TjYUmhoVz+pyP5lXPYpMVfsXm7rnUCpIiJr+qktvNwVRnDaUmEsfZ3JRDo9+vpmvZufz5ax8HvlsM/+Wt8UZ1OCf/Awj49cybkQ8L1+o4nzLNBK8lazYb0DptVPx5zs4dyxHc+njTJhn5oN/9rAz38S+Egt/LtzL+B/W4PUFWbX/6HkKlu0ux1Oyu1a/VhPw43I6w5Z//LeN5O6uDHk8rI9ZtomA04p92+Kwzcq2zWLIGVUzfzEaJXK5rFZ9flMxhlWzKP3heRzbl+LatwH97K8p+eE5fKbyqv3Xo8m3FVp47AeIqqn4441o8YijSe8qs9ArBWR+D5JCSYFdRk5G6P3WHR4fyzeX8dGvoVc2PHbjmcSkxtKrbVLoXOc2C167GZm+AIU2FmVGB7YZJbq2SW1w/PFqOV5LJZb18/AVbkUem0hS/ysxqDNITm14fZHSuGws21LOJ1NCb0zy32u60WXblzUerlMkptP2zjdwqRIJVuzH8OOzaHK6sK3L7Uz8d1/Iegae3oYHrjmdlfl172e/V2el/a4pWNdMD/OvSEbbBz5Gk5rd4Os90reU3Db8Nj2uwl2o0ttT9tOLYf/tanK6sKrtLXw7J5+Rg7tw26WnovTba9TnyttM2c+hE2DFdOlD5hUPoihcEj2+rdDCYz+AGNgFTUbAacW+fdmBtJ3WqrXgXfuSduFdIdeCm20envt0GYW60Ouy22bE8+ZD55ISwvv0203oZ36Bc/fq6tdkSjUZVz5CbJczkauPbY21FPAfyjevbrk8902Fyepm7MdLKTM4Qh7vmJPI2HN9eBd8DoAiIY2cm1+szp9uWTMdw5xvUJ9/B++tS2JvsTlkPXK5jK+eHU5GytH3CK96huExoPZHTUzXvmRe+SgKbe1scg1BkiS85XmU/vQiktdF5v89gX7WF2HX/GtOv4jfLL0prHTxwt39q58tOEjQ66Hinwk496wN06KM9g99gio5q1FxCwTNQVRNxR9vRNpTjSYd9PuwbpyPYfZXh558loI4d6+m7KeX8FsNtcp7/QEqTM6w/aszOjHYa+cqd7lcWFZMqTGoQ9Ue2BV/TcBrrqxX/E6Pn02FJhyeQ8dn76jEKdMgV2ujqn/rq41O71H7VN35LDJGPEz2ba8Rc/2reBOqBieHx4dfHV/Vlwo1Hl8gbD3BoIQvEKxfngNtMhlXPlIrb78qoz2xQ+7CibrR1x+wmyif/GZ1xjnbloUk9r0kdPByJdreFzO0X0devLELaZranr0U9BNw2cNeP0hIPm90+bZCC4/9AGJgbwSR9lSjSQccFszL/gjZT35LBe7SPWwsMtcoX2n30i4zIWz/ts+KZ12BuVZ7LqsZ64Y5YUpJWFZPJ+j3hYz3rZk7KKq0s6fQxBd/b2ba/N0s2VCC3uxifYEpavrzWPWGQhPtMuPr6NMEDD4FCacPYYUjlWt/2M7SPQfWye/R40/vAnIlirKt9OuaHLaeLm2TsLj99Ypvcb6NuO79Sbv3Q1SD7yH+vBvIue111Fc+zW2/7Wn09a/YpydgNxGwVSXfUaXmEGjfF3X380jsfyXID2VCVMQlk3PD0yRnt6G3fDOpv18R0geVq7XEduoZ9voV8cnIA67o8m2FFh77AcRUfCOIBk81WrTaUkJJnXnMzyXx8kfIPSw3u93jY/MePW9+uzpkmefvPhuvWknv9sk11zlnBSn94tGwbWnadif7xmdxoqkVb5HeQe7qAmYsy69RJj1ZyxsPnMv2Sjtnd2ra3PAtqTcVmZG7fbz53ZrQfXpPf07rkka8JnR5h82BVLAR17zP0Fz/Jk98swOHy1ejDpkMxo3qS7e2CSzMd9Q7PrvHx5ZiM2e0SyFWo2zS61eUbaf851dR9xuJLuNsflxUQl6phWvP78DlZ6Wj9dtQaDQoZEEUSdnI6rG/uc9UTsnXTxL01J4BybjiIeJPORvZvgXR49sKLTz2A4iBXdAkHG0teOJZl5B+yahar9ucXuatLuSHGdurNyZRKmTccskpXDygIwmxtfeE91kqKf7s0bBLqBLOGEbaJaOQK1W1jm3bb+DpT5aGLHdWj0yevLUvcdqa5QIeZ9UUr0yBIi6pRfduPxasdg+zVubx8+zdBIIH+1TOnZf3YGi/DiH79CB7ikzMWrKbkWenoSzbiqd9P76ek8+G3XokqWpr1FEXn0Ta/lnEpqaTPPD/kB+55esRGK0u9GY3FSYnWalxpCVpSU1s2ucXvMYyKmZ/w852/8eH/9R+cPCMk9N44ta+IZ/XCIckBfFVFlM57WM8ZfsAkMckkDr4ZuJ6nIMiJqHJ4hcImhIxFd8IosFTjRYt18ahSmsbtq8Seg8PWX7ZfgND+rXn86eH89K9A3jmzrP5dOwwrji3M8hloT1bdTwJZ14YpiUZCf0uR65U1WrP6vTyT+7esDGu31lBudFZfb7D6cRasp/KfydS/MUYSn94DsOq6Xisxoj3dzi9aFcFakc5A73L+WT0qbxwY3deuKk7H9/XgwGqndgsxjrLBySYs66ch7/Ywb/6TiRi46G+AT4Z1Z1PRnXnmQsgdcVHeLctwLLiHywGQ9j67B4f+0osjP14KU98uJjxP6xlzAe5PPu/ZZTp7dg9TXf9ipgEFP1v4qvZ+SHv7aa9BkorbLB7dr19UJnHjtqyi+zrnqLdAxNpN2oC7W55noRTDwzqkfZphRYeexjEwN4IosFTjRatjE8h6fJHQq4FjzvrMpRJ6WHLr8wzkpkaixUYn7uXjWVWtJra+5FXe7b7zSSf839ouvSp2ZBCieaiB9nn1oaMN1/vwOoI/SsfQJKgwuapPt9fthf992Nx7l5N0G3HbyrHOv9b9P9MwG83tXh/7yyz8uuawjrPt5pNGGb8D++G6Xh+G0vWsrfJXDIez29jcSz8loC+iHUFxrDlC80uMlJi8AeCWJ0+POunY5/5Ib4/nsP/53N45n6CT1+VW13ye7FZaj8DcVCXG5yM+2YV5YaaU9kllXZe/nIlpYaj5ymor1bExONQJdeyDQ5n4bpi2DO7Yb7ojP+iKFqOOrUNav0mlL9eU7UVa33LCy089lC6mRFT8Y0gGjzVaNIOl4eAzYBvey7ugi0o4pLR9rkcbUY7tAlJTd6e22bGYzNBxX4U2jhUWZ3ZYZLoEmYdu93tY0ruPn6dsyvk/UyKV/Py6IFkpcYS47dT+v1z+M26kOdm3/gCwXansXRP8/bvpkIT/TJl+HX7cZfug+Rs4jv1RJ2Qit1XO3d9wFyO8evHwr5nY7r2I3nEf4iJiQnZ3p5yK5ogvPj5cvqcksndWZtxbZgVtr60uyYgT20TMv4te/U8++mysGXfefR8ihxeBjTRfvf7Ssw8NiE3bHuXDezIA2d7IOOU6PBZhRYeezMhBnZBkyMFAgR9LmQKVdTl1tYZHTzy7qJaudIBHrjmdC4e0BGFXHbUZwZiu/cn8+rHQ/r4TYm3spDSn16qsXmKTKkm+6YX0LbthkyhrHn+UfPeD0N53h3Y3AH8/iAJcWqS4zWoVQqgyg//aspWLh7QkfU7K7j8VBX2X58JWZcqoz05t7yCMi4p5PFZK/L55I9NYWN54pazGNynXdjjDcVgcfGfCYuw2EPPyrz76CC6n1T/XPMCwfGKmIpvBNHgqUajtvuCKLTxOALyo54/d1t51S9vXT7mtTMxbMzFY9IR9LqbJb69BidvPXQeHXMOfWuO0yq596qe9O+Zzdzt5VXnH+37rhTE4z96rvTGaI/FQPlvb9YY1KFqCrz819fx2oy1ypt8iqrNXkKg6tALY4+RjP3fch5+ZyGPvZ/Lg+MX8OfCPVgO5AuoNLtZsrGUF79YQXGlnVKXmtj+I2vVJdPEknHVYywvqZ1n4KDOSqs7eU1GcgzzDvZ3E/SXRqNk9MjTQ25NO+C0bLKTVTV8TrvNTlmpjoIyM5UmJz6XPbp8WKGFx36MiIG9EUSTxx0p/c+GEhwmAz5jGX5LJYU6I6v2G+pVfvk+PW01Xgz/fkDJV09gnP0VlukfUfLZIzh2rqBYZ2zyeJ/5ewtFDg+vjR7IhMcv4Nl7BzDu4fO4/NyOrCk8tM5ero1DkZge9t4nnDGMNYXWZu1ft9WI31IRsn3J58FeuJOfVhbUKP/q/BISh95Zu4Bcgey8u3n+y7U1PG+PL8DPs3eRu6GYnWVWDHYPUJWAZvW2cl74dhMrgj3RjHyFmNMuIKZzb9Kuepy297yLDQ0b91ewMsz9TkzQkhwfesYmPVmLWqvk1Wnbm6y/lu7Vs6zYwpsPncdZp2SSGKemfVYCD157Bg9d15uk0kVVPmfhKnRGB+/+spnRE1by8Lu5PPTOQiYvysccjIseH1Zo4bEfI2IqvhFE2tOOtHbZLLjyt2DPnVQ1AMnkxHQfQOrQW9GkZB21vNPlwrboJxzrQ3u4be55jyVGbZN5sA3R8Rolzn3r0f32JkemQlVndSb7hmdwqRKaNR773nVU/PZG2Pdf8gU3sbvNYE5rUzOX/gUd4wiW7sIw7zv8pnKQyUkcfAszTF2ZvCD0qoDEODUTHrsAp8fPmPdz8QeCNY7HxagYemYbbh3cBs+u5dg2zEHyudF0OpOU865BnZxZy/O3u30UV9h57auVNR5aTEnQ8Pr955KWomVJI59RWFdgYkAbDQq/i2BQosIjJzUtFYLgcPsw2L10yIwnTqOs9jkNOUMZ+78V6Iy116f/36BO3Dy8M9q4+Mj7sEILj/0YEQO74JiQggHs25ZQ+e/EWscUiem0veMNlIlpddZxtPXo8acPIf3S0c3uY4cj6HHhrSzEMP9HPCW7kGvjSDzrUhL7XIgyzHT3QawODz5/EIVcVuc+33XhrSyi+IvHwh7PvukFYjv3Dnvcbzched2gUOKWx/Hqd2vZmW8Ke/6nY4eSnhzDL7N38dei2l8A3r/vdLSLJ9bYQAYOeP63v4E3IYek+JrXKkkSBoubIp2N4gob7bMSaJeZQHryseXyr1F3wI+3sgj9zM/xlFatXVdndST9kvtQZ3UM+3zHqq1lvB4mKZJSIefzp4eRmXr0HPjHgtvrr35yPylOg1IpJk0FTY94VzWCaPG0I6EDdjPG+T+E7JeAVY8rfzMOj7/O+gJeT9hBHcBnKGF/Wd3rrptTOyQlKx3JpI58kg4Pf0bOPe+Rf9JQXKqEsOW3FplYt1PHK1+t4oHxC3jus+Xkri+u9rAb0n5Qm4C67Skh+0aRkIoirV2d5V3KeOaXgluTjEqjqTMpjFwuQ6GQs2h3JVde0IXbLj2FWG3Vg3lyGYwc3IUMV16tQR2qPH/D7C/ZsDmfpZtKMdrc1fHM3laOVqukVzs1w0+W0V6/HNXeXHymcpwOxzHfHykYwGeuxG8zktj3UrQdewHg1eVT+sPz+Awl2EOU31BoYtW28rD94A8EsTmq4m9KXzUQCFJaaeOzPzdWPd8wIZcfZmynUlcJHluTt3fC62iKJZRuZsTA3giiweOOlA56nAQclrB9Y9++jMKKunOvO4KKkOveD6LMOInJG3WNjndnqRm/1UBQX8hpWitusx5JCtar/ItTtpFb4ESZmMbCIi+P/b4l7Pm7y61s2lHBy1+uZHehCZfHT2G5jXcnrePn2TvJr7DXOH9TkRncNjwWA367mS3FNXPpLyt2471gNJr2p9boF1V6O3JueYVVumC9+0OrVnDJwE5h+/qcnjlUOLy8MWMHawpNjBxyMuMePo9nRw1gwpjB3DSkPfaN88KW95bson2qkvE/rGHF5jL8gar+/WDebvw2A2WTXqXsmyexLPwRw+wvKfr0EVw7lrGvRN+g+zl+1k5cVhOWVVMp/eFZdL+/gXHBD8R0OI2MEQ9XbTQjBTEs+BGdvvYzGpNWFZAQV3emPBUH1sI3la9asIwyg4PH3l/M/LUl2F0+zHYPf+fuY+wXG6g0u5u2vQM6qNuOPyYTV+leXAXb8FkNBAuWR4/P3Jw6mmIJpZsZMRXfCCLtcUdSaxyVFH/2SNi+iesxkMRLHyJ3n6kOj92Nfdnv2FdNqV2BTE6bURNYXKHknC7HHm9JhZG21t0Y5nxdvYWnIj6ZjMsfhJxTWJxnrVd9cfIAXpcdnd1PenoacSFyrZcbHDwwfkEtf/ognzw1lB16OwO7pBMbdOEs2IZ5yW/4DGWoUrJIOu86bGndSEw5tA5/dZ6Bc9tpkXsc+GxGAup41AlJaBNTG9wfBquLvxftY0ruvhpx5aTH8fr9A4mJUYUtHyu5Kf91XPWUd0iueYv/fLmdOK2Sj58cgkaroqzSROKq73HuWhmySMZd70Fq23rfT73eSOzaX3BsW1Krrvheg1HEJ2NZ8Q/I5LR96FMWFvlqlF+xT0/3tDgefmdhyHhy0uIY/+AAUpKbzmN3dhjK+5O3sXJr6JmCWy7uznXDuqHw2ZukPToPJoAc+7alGOd9Xz0rJlOqSb3gBuJ7DkIRnxp5n1l47M2GGNgFx4TfYaX8l1fx6vJCHs+57TViOpwa8liNeuxmDHO+xrFjefVrMpWGjCsfJbZz70bvie4q2ErZTy+FOCKj7T1vo8nuXGf5oM+L31KBaekfuAu3oYhJIGnAlcR06o0yPrnGuRt2VfDiFyvC1nXf1b0YcX5nAh4nlpVTMC/9o0Y8MZ3PIKHPRWjbdkMZ3zzrrW1OLwaLm/lrCrE5vAw8vQ1d2iXV2o/8SCRJwrp2JoY5X4c8rs7uxK5ud/HBP1Xe/EdPDKZTmyR8Zh1F/3sYpNBfdhLOvJCkAVej0MSgCLEeXpIkAnZT1eAkVyB53XU8dyAj++YXKf/lNWQqNe1HfxTyOQ+Hy8eM5Xn8MGNHjddjNErGPTCQru2btu8rzU7ufX0uwTCftDnpcYx/6DxSmjB/vit/C2WTXg55LPuG54g9uU+TtSWIPuo9FW+xhJ52LS8P71e1dqLJ825prYxLJP2Kh0JOpcf2OBd1Wtt61Te/wEXSRffS7v6JZPzfE6Rc9xxt7vuQ2JPPwhFU1Cseh8dHwGnDZTOzap+++rjbFv45AJAwLvqFPUW68B67x4etaDfFX47BsW0JAZsRb0UBlf9OpHLax7itNdeRB8J9ch8gKEms2KfH77BiXvZX9euqtLbk3PwimuxOmJf9ScVf72HfvgyP1XhoXX0T3b9l+w2kpcRwz5U9GX3N6bhVctQa5VHLy2QyYrqdjTIps/aFyeQoBt7Ob0vLDr0kk2Fz+3A4nGEHdQC/uQLrmmno/noPr9XAnG2H2nfbLRjXz6Pk27EU/e8hdH+8jXN/+IQ3IOHTF6FMyiDhjGF4VXEhr0eSwaAz2/LSvQMYclZ7zuyWwbVDu/LcXWejN9pw2A/sw95UvmowSF3vjOrfVk3UXsBmwLjo57DtGXN/JuC0RN5nFh57s3HUgT0vL49LL72U/v37c/755zNjxowaxy+77LJmCy7aiSbPOxJ6oz0O5Q1vEN//KtRZndCe1BPVFf8leM4tKOKS6lXfuOk7WJTvRJ3WhvWKk7lzjoOFxX7kStVRy6/NN9I51otrw2zKfn0Nw+Q3aFO2Av+BTVocTjeesv1h75+ndA96sy1s/VajAcusTyEYqFXWtW8DropiPl+8r/r8tOQYlIrwO7/16JzGxwv24ijZVz3YybVxpF8yioopH2Be/jfesn24i3ZQ8fcE9P9MIE3marb7l7u7kuf/2Vrv822eABkjHiah97ADX+hkaE7qRcy1r/LDSjtlekdVPyRpSYitun86V9UUcDjUGR3wmXW4C7dhyv2VHUWGqmc4/F7sG+djmfVZ9T7rks/DkUsPj0SmUKGITyG5/5Us2R/6GY/8SjsTf9/I2z+uRZIk2mbGs7fYzAufL+eNHzZgNB9YBtdEvmqso5CzTgnxhegAg3tnV/n+TdSe5DDgrSwM2563ohDJ74+8z9ycOppiCaWbmaNOxd9777306tWLO++8kzVr1vDqq69y6623ct999wFw5plnsmHDhhYJNtqIJs87Unr5Xj3nd0lFI3nwSjJWl7jo0yGlRdr3mispn/RSrXzuqtQccm55hYAEZd/8t1bmturz0trCiGdITguTi76yiNI6lpvFnToQXd876ZSRSIJWhdnhYebyfH6etbPWucP7deDWy3qwtcxKn+A+Kv96F4Ck/iPwGctw7lkbso2kyx9B2+PckJ5+S2tn8S50P71EXI9ziO83AqNHwerdZqasLMdorXoATC6X8dK9AzizWwZ2j598nZmc3dOxrp5a69pkChXZNzxL2S+vVX3RUShJuet9lEkZaD3mEEshD021h5wFkCtpc9dbyGMSUCelh72eXlkJ3P/W/LD39cpBnblnRE/kXlsT+apDKLTAmA9y8XhrfklMTdTy7iPnkpHadJ6+v91Ayn55rXqzniNRJmfR5o5xKJWK6PKdhcfeZBx1YO/fvz/Lly9HoajKJV1eXs4999zD8OHDefzxx0/ogV0QOYIBH6ZFv2JZ+U/I48nnXUvyuddiWTkFU+4vIc9Jv/wBEnsPD9uGt7KQ4i8eD3s8tvvZZF49psY6e5vTy/Y8Iz/N3EGRzkZmSizXD+9Kv1OzSTqQhe1w3znr+mfQTR4fdrpa06Yr2Tc8hyI2IWwcjSEQlLDY3UgSaNQK4mPC/7p27FqN7o/xVUKuRHvJf9jjSmbK6krMdg89OiRz/UWnkJ0ai0Z9KIe9327GuOBH7FtyOfiLWx6bSPol92HbOA/X/o3V57Yb/SHq9HZ4yvZT8s2TtWJI6D0cRXzyEc8nVJF2ySgSeg0+6nMZ+aUWHnlvUdjj/U/LZuztfVEpFXXW0xD8gSA6g4NJs3examsZSqWcIWe1Z+SQk8lMiSXodRP0Vu2voIiJb3R7ti25VP77Uchj6ZfdT0Lv4chC5d4VtAqOOhUvl8txOBzVOjs7mx9//JHFixfz+uuvN2tw0U40ed4nmg46bdg2hf/VZdswD6/DivrUQWja1V4LHtO5NzGdziB3lw6XzYLPWIa7spiK8nIcnqr2JFUsiiMekDuc+F5DWLrfVMvD7nlyGq/dP5Avnh3OmNv7cs4ZbUmK11TH71fFkXLedYcqqsODDvrceP3+ZunPSrOLyfN3M+aDxYx+az5v/7iObflGLA5PyPMVKdmHBebHPeM9Om/9gjFnWXnlIjWjL2pLvsWN98CzBgfLu5RxpF10N20fmEjmyP+Sdc2TpF8yCsvKKTUGdZlSjT0gr2pPEXpQtW2cB8jIuuFZYjqdjjI5i5gufWhz++vEdOyFrbIUt8WAJElhr1+rUaKqIzHMaZ3Tqgb1pvBV85bgt+rBZSEnQeKRwVq+eHoI/3tqKHdf2oV061Y8ujwqp39C6ffPUf77mzj3rCXgaJxPHNO5N/GnD651bXE9BhJ7cp+qQT3SPrPw2JuNow7sZ555JnPnzq3xWmpqKt9//z0bN27E7XY3W3DRTqQ97hNaS9IBzzU0QZ+7ar2woZLE3sPJvOox4nteQPzpQ8gc+QRx3c7Gsm05PWMdGP98i6JPH6b0i//g+v0FvLtXEXA72GiQUJ1/e8j6VRkn4UruENKjXrJHT3K8hvUlFu77eT1L9lTWOJ6bZyOx76WkjHyKoNuBOvOksNeh6HQWO4yBJu8/o9XNm9+tZtKsnRgsbjzeABt2VfDsx0vYVWgOWb7Sr0HdtnuN+HyVRXgXf4e05nfcKHhhSmjPXqGNI7cMLLE5VPw7kYq/3qu1dC72jGF8vbZqXbsiJiHsZjbmpZNRJmXhGPQA3kufInHA1VRO+5Tizx7F8N2T6L5/Glf+ZvaXhd5roMzu4eIBofs8RqOk90E/vJE+qt+qx1pWTvlvb1D63bMYFk5CKflINa0nLSkGVdl63FYrJV8/hWP7cvxmHZ7inZT//ibGxb8SMOQfc/vKuCTS+gym3U1PkzLoBlIG30zbO8eR3j4NZdHyJrm+qNbRFEso3cwcdSo+Pz8fq9XK6aefXuuY3W5n3rx5XH311c0VX1QTac/zRNaxMh+V/07EuTt0atC4HgNJvmgUxpmf4tq9GkVCKtp2p4Ak4SrcRtBlJ+eWlyifPB7JUztneOa1TyHreBZFOgPtAzpM87/Hq8tHptaS0Hs4yf2vxK1OZGkjrsfh8WExm0l2llH+8yu1YpBr48i8420CcWkkxDRd/53XNZ3tew289s2qkH2XnRbL+IfPR6VW1CofsBlxzvkUd/6W6vPV2Z3JGvlfPDGpR+2P/WVGuviKqJzyflW62wPEdu9PykX3sqjIw8Au6cRrFLgKtlf56UF/jfgS+l5K6qAbcMu1+PI2YfzzzdoXIZPT5p53WWrQ0D/EXgN+X4AfZ+5g/urC6mVomSkxjLn1LDpkJZAQo26Uj+r3BdD9+Taekt01w1JpaXPHODRZHfGbKyj+5qnq/ApH0vbe99AYt0Gn84/d181bUqU1cZH3lRvxjII9qMHm8OB12YmNTyAlKQalzyE89jCIdeyC4xZvZRHFX/8XAjU/+GUKFW3vfRdFbCJlv7yKt7z2WvvYbv1QJWdhWT0tZN3VDxgdWE/ud1jA7wOZHHlsQpPmr7eYLLhK9uBb9uOBB55kaDqejmzAzXw6V8djN/U56jrzhuD1BXj7x7V1plb931NDaZ+VEPJYwGkj4LYTdFqQaxOQx8SH3ZM9FMGAj4Ddgs9YQtDtRJ3ZAUVsIoqYmu0F/T78lgosq6bhLt6JMj6F5HOuRp3VEUVsIn6HmbJJL+OrLArZTmyPc8i8/CHkmtB953T7sDq8mG0etBolibFqUpOaZi25ffsyKv6eEPKYpt0pZF/3NH5rJSVf136O4CDJ515D6uCbmySe45kyvYNPJm9k04GZl1itkuuGdeXCs0+qfm5FUJOjTsUf5Mknn+Spp56q9ff888/z8ccfs3Nn7SeBWzvR5DmfiNoXn0H6LePQtO1WfU807U4h5843UKVk45WpUGV1DnnvNFmdcBVuD3tv/WYdAY/rsHX7Sbg0Scwr9ODwh77/drePTYVGKs0uXB5/yFzlR+rcXRXsKHHy2kwreb1GI418E+mat1iRdhXf5BoYfFZ7HC4fRosbh6dp+s/jC4S85vgYFad2SqVLu6Q6yzvlWtSpOfjSu7CgXI5LEdug9h0+UCWlE8w5lXXyLnjiMlHEJNQ63+GHReVy4ofcTptbXib5qsdZ5c3CKa8aqANeb9hBHcBTvJsygzlsPAFgY5mVttkJdMxJRKWpO29CfX3UgN2Edd3sOuLaSdDjQDriC+mRBH0eKFwZPb5wBLS+vJynP1laPagDON1+vp++g5kr8vEWrhUeewjqPbAnJCQwf/58JEkiOzsbSZJYsGABcrmcffv2ccMNN/DPP/80Y6jRR1R5ziegXrLPxD3TK/ANf4z2D/2PlHs+YlXX21hpiUOmULJ0vwX/aRdX5Q8/gqDPg1xTxw5eMjlOP3W2v6vcyur9BraUWHC4fOSVWJgydzcvfr6cCT+vI6/Uyt7y8Ovkl+3V8+PKAkr1DgrLbbzz5x4e+2oHY77aRnJqCt1PSuGnWTt46J2FjPkwl3mrCyEgNbr/NhSbuaj/IY85Tqvk4evO4JHre9OjYyoDe7VBLpexp7x595tfulcf1pM/qF+fvoPcfWYUcUnk5tl5ccq26uNWTwBZHfdQEZfImgJzk8Vbbx/VXHDUQVuSJJQqZZ1r/ONO7g2zn4keX7ildcl6tu6tqF5KeSR/LtiD2aMUHnsI6j0Vf/fdd/PQQw9x1llnVb+2YcMGPvroI7799lsWL17MG2+8waxZoffWbo1Ek+csdGidV2aks78Y/b8fEnQfWN0hk5M86AY0mSehm/xWyHsb2+1ski57iNw8W636B3VKROm2YNuSi99UjrrXcFbo4vj0ry216rl/5Omc17sNSXGakPGtzjOSpVbwzP+WVZe5dmhXTDY389fU/jV6Yf8O3HpJD1ITtY3qH583wOvfrqKg1Mqzd53NpFk72VNkrm5HJoNRV/eiQ/tkOmclRM39PFw7XR7sy3/HHmbJY8ZVj7FZewqnt0tukvbq66NKXYZi3bw4bPrdg5v4yOUyrBvmYlxUezmmpm13skaOQVm8PHp84RbWAY+Dt3/dxvLNhzIaHslHj55Np6w44bEfQb0H9rPOOotVq1ahVB5an+rz+RgwYADr1q1DkiT69Okj1rQLog4pECDgMFXt8ObzoErJQh6TgOT3op/xBc7dNR8iU8Sn0Ob211EdtrwrcOBLgUyuwLFr1YF96Kv+6ahveJuHP98WMqWsUiHj86eH17m/t9Hi5ulPllJmcCCXy3hl1Dm88PnysOd//vQw2mQ0fq2z0eJmT5GJZZtLWbgudDKTDx6/gC7tkhvdVnPhtxkpnzweb9neGq/HnXIOaZfcizIuOTJxWfWUfP8cAav+iCNVSXZUyZnIFEpQqHDlbca06Gf8lgpkmlgS+1xMUr/LUIZZFXCiIEkSn/21hRnLQ+9HAfDp2KG0ywz9LMiJTL2n4nv06MH777+Px1O1xMjj8fDhhx9yyilVa4SLi4tJSqr/AzStgUh7zELXT9t9QZSJ6fjSO7PclYlbm4pCE4tLEUfwvNvJuulFYk/ui/akniQOv4ecO99ClZKNze1Dr9Nh27oE3eTx6Ca/hddYVmNQVyZnsU/nDpsn3h+Q2FtsrjM+tUbBq6PPoXPbJLJSYykoq9uH25FvCF2fy8u+Mit7i83kl1qoMDlZsa8ybP+oNAqy0uNYsrE0bFt/5+7F5vQ2y/1xORyUlpThttXdP3XpRUVeMq4dS84tLxHf8wLieg8n5443SbtkFC5F7VzxC3boqvMUNKQ9v92Ms2gnFfN+xLj0D7z6YgJ2Q1gfVZmYTptbXyX+9MHIFFUPWmradCXrhmewb15I0f8eovjLJ7BvnEdsp9Npc+cbtH/wE9rf9hIp51xVNahH2geOsJZ5bFzSN3wq3o45icT7KoXHHoJ6D+xvvfUW69at46yzzuLcc8/lrLPOYu3atbz1VtVUptls5qWXQu2i1XqJtMcsdMP1q9O2V+2DDqzab+DGH7ezxpdN5sgx2C54iJf2ZLKg6MDDeTYjzqnvUDnlA9yF25CCQZy7VnF4vnKZQonHFz7BDIDN5aszvqV79WSnxfHA9b15+MYzSUqoe79wJQEkSapRn93pZfH6Ep79eAmPv5/LI+8t4r8fLsZp8bCrrGoDp+X79ExeW8SWA180lu3VU2Zxh91mFkBndJJ3IAd8U92PfWVGvJWFmGd9hu/PF9H/9hq2LYtxWky8O3tXg+/nwkIPMR1Pp/TMW/nYdx7LbYkoQ+xV4LYY6BosxbVhNo696/BZ9Py7oajO+t+ZvRO/zYTuj/GU//Ac9lX/YM79heLP/4N55VQCDlNYH1VVvpb0GBPt7xpH+wc+Jr7XYAyzv8a+dTEAQbcd46Kfsa6Zhlwbh6psNcpfr0GetzBkfSeiTi+ezvVDOnMkcTEq/nvDaSTPeVh47CFo8HK30tJSKisrycjIoE2bNs0V13FBpD3GcPr8rulofA4CHhdOfxBtXAIx8YlRE1+ktNnhwWTzsL/YjN3ho0enVCSFnDZpsbXOj9coMK+ahmn+99X3O+bkPigT07Gtn3PoTaBQIhv5Jo9+XttfP8jBpWP1jbd3dgKjxy8gGGIWQC6X8ckDp5OdkYhLlVB9v7ft1fPaN7XX9Mtl8P7jgzkpTYHfbsGVtxkZQWI69iKoTaTYJuPZj5fi8oR+2OuygZ249bJTSIhRN8n92FJspreiLGS+95hu/QieeyepKUkovXaCfh9Wn4y45DRitcfe/nknp6NxGSib9Ap+S8WhvtHEknrdcyiyOhGnDf0MRJ7OTJtdU7GumR6yf3JueIaYdt1BmxDeV+0yFEf+9kPpeI9AplTT7v6PUGk00eUDR4m2tRuKzuJn2tL9GG1u+nTPZODpbUjXBqq+BIl17LU4pnXskiRxeDG5vN4//AXNTNDjwl28C8Pcb/AZSji4z3faRfegSs05YfNDuzx+Vm0t44NfN9SYNu/eIZln7jy71jpxv91M6ffP1thgRpmSTfI5V6Of8VmNczXn38Gk/eks2VJZq90hZ7Xjvqt7ER9b96/ww7FbrcxeUcB3c/bXOnb78I6cE1hN1nlXoUqumqY029w8++lyinShE52ce3oO954VxDrlnRqvx/caTMrgm/lteQW/zd1dq5xCLuPzZ4aTVcfzAeGwOb0EAhKxMUrUh+Vc99uMlH73LH5r7b4CyLn9dRx712FbPR3J70Uek0DyOVcTf/qQBq2VPxy//cB6d33thxFl6hja3fc+qqSMkGV9Vn3VZjRhshzGdOpN5sgnUGjD95EkSVT++1H1L/VQtL3nXTTZnY5yJSc2fn8QfzCIRqU4YT/H6ku9R2SdTsdDDz1E//79OfXUUznttNOq/05UosVDPqgdHh/Wgp2U//ragUEdQMK1fyOl3z+Dz1IZVfHWRy/ZXYG9juOr9utxWwz4bQZcdisLd4beX73S7GLCL+treeG7Cs18N207Lo+vZv1SkKDXVeNcv6kcRWwSioS0Gq97lk3itn5abh7emfiYKj81IVbFrZeewtVDuyLJZQ26foUczk038trtp9KrSxqpiVp6dk7l1dtOZWBsHv5dS5HJFdXnu72BsIM6wO5CMy5X7YHJvmURzl0rGXHuSVzUvwOHf1b26JTCj0+djapgBRVTPsS05Hc8hlK25Iffv97m9rGn1MLyzaW8/s0qnvt0GV//u42SSjuBQBCb24fDagk7qAPYNswlYK6o3tUt6LJhXPAj5mV/4nLYG/z+mb2tDL/dHHJQB5C8LtwHssOFKm93uutMXey3GfB6Dxw/wkcNuB04irbi93qQx9b9pUSmUEbe941yrfTb0e6dgcxjO/r5URZ71HrsL730EiqViu+++47Y2Fj+/vtvhg4dyiuv1E6FeaIQDZ7x4dpiMGBb8G3IWIMuO5bNi1i0ozxq4g2nV+434HdaCRqK6GDYiC9/Iz6Lnl0lNffX9lhNtC1ZRsVPL1D02aOY/plAd7meAp2xRn17dDZmLssj3NzUko0lWB3eGvHINbFoO55R61zDvO/IvPIRNG26HvaqhDJvJZf0b8fom/rw/pjBfPTEEDp3SefuH9c2+PpXl7hJTEkiZfG7PNijnNcvi+GhU3WkLnkXz9IfSeh7KfLYRFbnGXhn9k7sHj+xWuWRoVaTFK859GF4BJY1M1C7Tdw9oicfPDGYh286k/GPnM+r152E4cexmGf8D/vWxZgW/0bJZ4+Spt9GXlnN/j0Yf6nByaTp23nz+zVszzNSqLMxY1ke/3lvEXllVjYUmrA4vSHjqO7JgB9ZiLwD1rUz8Toavq5+4vw9OC2GOtt06QrDlt+j96A4kH0wFPLMTuw3H7AxDviovrLtlFba+WHOPl7/18znU3YQ23Nw2DpUqTnIYxIOlH8R8pfVqC9qfOHjSUdTLKF0M1Pvqfj+/fuzcOFCYmNj6du3L2vXrsVsNnPjjTeeUGvXDyfSnvGR2mMoo+Szh8PGq87uhPei/5KRUTt3dkvp1XkGzu4Uvv0V+/QMbq9G/+9HuAu2VscuU2nJHPkEuxXtODknhRi/g4opH9TIWX7gTDKvG0tc17OwewIs26tnQKdU3v1xHZv2hP+l+MmTQ0hJjqnZn/oSSr96Aingq3GuIj6VnFteRgLcLhfa+ARUcUk4grVzqx+rjpXcmJb/g/WINdoxXfuROugGkIIEnDZ86ng0iSnM3GDim6nbQl7bf6/tRuctX+CrLKx9UCan7d1vo8nuhM3tY22+gYFtNfhL9yAF/LiLdmDfsohgdT59GW0fmIgmNadW/Jv2VPL8Z6GX6XXMSeSleweAx4J90tNh86NnjHgY0+Lfa3jhB8m6+SVWuDJD5n4Pp5fv1XNBpo/SL8Nvv5tx7VgSup8dsvyOUjPdTOsxzvoiZN+l3/kOstS21evcAyUb2S6dwotfrMQfOPTResfwkxik2op91d81q1BpaXPrK2janEzAbqxalumwVaXpjU1Eod+GrO1Z0eELH08aoieWaPbYzznnHHJzc1Gr1QwdOpQ//viD+Ph4+vfvL9auRwk+cwVFnzzI4U9tH462/alkXT8Whbbxa6AbFJc/gNnmocLkwuML0CY9jsQ4NbHa2vnWgx4X+plfYN+2uHZFckXVft2pObgKt1P24wsh21PEJ9P27neQqdRIXg+SQsWkhUX8uXBvyPNVSjmfPT2MzJSaPqkU8OOtLEQ/4zM8Zfuqzs1oT/ol96HJ6YJc1bR5qiUpSMBuBqSqqVmZAr/NiGP7UqSAH+1JPVEmpmGY/TXuwkODuDI5i8xrn+bjOTpyj1i6Nqh3G27rq8b516uhrz2jPRlXPIy2zclA1XvIvOIf7NuWQMBPTJczSTrrEoyLf8NTXJU2OnXYHSQPuLJGPT5/gHcnrQubTCQuRsVHYwajVcvBkI/h99dqbAIDVZvJJPe/koopH4Sso80db6Bt1z3ksbrwOyyU/zYO74F7eDjymATa3fsuysT0sOUDTiuWNTMwr/i7el8CeUwCmVc+ivak02q8DwxmF49OWITVUXtmYtSlnRjeXYtt7XQCdhMxJ/Uk/vQLUCamE3Ba0c/68sCqiyoU8SlkXTcWTXZnZHJFrfoEgnDUeyr+jDPOIDc3F4DzzjuPxx57jIcffphevXo1W3DRTjR40IdrvzIGbZczw8ab0O8yVhS5WjS+DfkGVm0r56F3FvL0J0t56YsVjH5rPr/M2YXB6qp1vtVsxL59aegLCAYwb1yA2+fDtmlB2OvUtjsFv9WA7s93Kfz4fko+f5RhZ6SjkId+4Oai/ieRFK+u/cyCT2K9I5G0656l/YOf0Ob+iciueJpgVlfkKk2T9pffbsa8ejol346l8KPRlP38Gu6S3bh1+3Hlb8FTsgdvZSGGud/WGNShKq99+c8v8fAVHXlx1AAuPLsDl5/biff+M4ibLulBgir8crakvpchPzDV7DVXUvr9s9jWz0byOJH8Xpy7VlE++S1Szr8eeWzVLw2/pbI6/oU7ddjdPoJB8HgDIdsYcV5nnri5D9/P2M5LX67imxVOZDd+SMzAGwCQaWJJOuf/yLrmv+hnfxWyDrk2Dll82jH1r1sRS9Y1T9baHleRkErqDS/iVh8tN34MyQP/j7ajJ5J606vk3DWedve+h9TuNObsMlafj9uKwWgOOagDfDkzj8UFkHHpKLKuf5rksy9FVboKyWXDuHBSjUEdIGA3UfbTy9X9HXFf+HjS0RRLKN3M1Htgf/vtt+nXrx8Azz77LAMGDKBz5860b9++2YKLdqLFkz6olxc5CQ64ucqvOwLtST1xpnbm2b+3tFg8q/Yb8HurdhI7fDlVMCjxT+4+Fm8oYfbWshrlLVZ7rWVQhxOsLKDS7CCcYa5Kb0fcqedR+v2zVdP0UrBq2nfFD7xwa0/ijvCizz4tm4vP7YRGpayOf1eJCZ9Fj69oO20tO/A67Mi18eSWy7j5p+0s2dO0/WUxGqmc9gmmed8RsBkBCa8uD91v45DsFhTxybiLdqDJ6hTCejjQL04rzpI9fLeuiPPP6cgdl5+K1enlnR/Xst0aT8qQW0F+2LXLFSQNuArS2rPT6EcK+DGvn0vAbqpVt+TzYFk9jYQzhlUVbXcaAbcDyaKji3MPvqKtyF0mrjy3Q62yg/u0Iy1Zy6tfr2LxhhL2FpuZv6aIRz9cxp6kgXDbx8Tf+jYpF9zAPgso+1xe++JkcjKv+g+bDMFj6t+le/WokjKIu/oZMu94m9QrHyfrtnGk3DyOFxabWFqP+uQqDQtLAlz7dyWLjXEoE9NYsrfmfu/kL8Vtrd1/h2MwWpGXb0KhiUW2fyHMfYGA3YB9S27I8yWfG+fOFVUi0r7w8aSjKZZQuplp1LatHo+H3r17s2PHjqaM6bgh0p56KL2p0MTZmeDYugTHrpXIVVoS+l1KTPseuJTxLRqPxeHh0z83s2xT6MxmyQkaXrzvHLJTD60jD1gqMX79n7CDe8KA/yPuvBuQle2ibFLthEhpl4zCunZWyKegVR16ohr2EBVOOU63j3aZ8Vg8fjpkxB9at1xupLOngMp/P6wxVRzXcxDJQ25nUaGbgU38zMHARBtl3z0d8nplai2ZVz9Oxd/vk3HZ/WGnqQESB1xNfpfL6J6VyOoDS/sO8uT1PejXORa/Lg8CflTpbZFpYslzqmibmUqM307p98/VWN5XMxA5Wdc+hX72l7S5bRymJb9h37zw0GGVlvQRD/PPnhh+zy2ofv3V0efw8pcrQ67J16gUvPPYINKTY6r7o0JvJEcyY135D35LJaqsTiQPuBJVciaOgPyY+9vr8fO/PzaxaY+epHg1dpePnLQ4Hr3xTDLTYonXNE0u+XKzh9HvLidMIkLGj+7LqR0Sa6x796T2rHP71rhTBpD5f2OQeevYf1xo4bEfRqMGdq/Xy+mnn95kW7bm5eXx9NNPYzabSU5OZvz48XTs2LHGOYFAgNdff50lS5Ygk8m47777uO6665qk/daEFAwQdDtBLkehjYtIDGabh2f+t5TiCnvYc758djjZaYfiC3pcVM74DEeo6XiZvMpjT2uD325G9/d7eI7YejXr+mfQ/f5m2Pa0HU4j67qxYfvEqy+m+IvHQ36xSBo4smpKugn3YgcwzP8RS5iNTACyrh2L7q/3yL5+LOW/jgt7XvplD5B45nD0ZicPv7MQh7tm0plYrZLL+7fl8gHtSElJqOEN++0mSn94Hr8pzB7tMjnZNz2PKrUN9s0LMS3+LdRJ5Nz7Hl8vNjF/TSHZaXFcek5HvpyytcZZGrWCob2z6JYTw2knZ5DTJqtWTUGvG8nvRabWIq9jB7T6YHN6eeentWzYVfvhyYyUGN555Pwm2+/e6fbxzdStzF5ZWOtY57aJvHzvOaQk1tzz3Wcso+jT8A+9in3ZBQ2l3lPx4WjKRAEvvfQSN998M7Nnz+bmm2/mxRdfrHXO1KlTKSwsZM6cOfz2229MnDiR4uLQG1g0N5H21OvSMrkCp1zL3L3WiMWDrOqDMxyxWiV2j79G+fl7LaQMvR1N+x41zpUp1WRe9zTbrUpsbh/K+GTSr3qcxMG3oUhIBYUSTbseKOp4CKqqIhneAylUj4zX5XJjWjU97GyBde0MTHp9k/bX2nwDHOXfkEylBilY9Qs2PbT1JVOoUGeehKlSh9XhqzWoQ9U+1pNzC/h1cXGtZwQUMYnE97wgbAyxXfuiSsnB6wtgWTU1zFkSltVTufuybnzxzHBeGXUOsiOeazj7lDQ+urcHV2lX0X3bZwTnfIht50r8DnONeORqLU55DHN2Ghrd32abJ+SgDlBpclXn5m+K+7lkr54bLzqF64d1I0ZTZX0o5DIGndmWF+7qR0rZwlq+q1ytQXtSmGeVZHLiew6qcX7U+MTRrKMpllC6mTnqwL5ixYqwfytXrmyyQAwGA9u3b+eKK64A4IorrmD79u0YjcYa582YMYPrrrsOuVxOamoqw4cPj9hyu0h76tGuNxSbGTagY9j+u3hAR75fXVij/GvTt7O4xEf2NU+SdsfbKIeMInnkWNrd/xE7Fe14dPKh/bsXFnp4s7gD6utepcOD/8M77BFWlAVQZ4XP4BU4ZTDrSt0h4y3RW/BX5octK3ndmG2OOq//rZk72FZalZt9XYHpqP31wj9bUXbtH7ZNuSYWkrJpc/treI3lZFz+QNUXmcOQKVQHlon9in3qBFLVda8VP/hl/PB4ZAoFih6DQn4xkqm1JPa9lJJvnkRmrzxs6Vtt/BUFlBstZKTEsqnMSuZhu9CdlJ3AqPMScE9+Fs/WhfiMZXhKdlH55zsYZn2FxWhs8vfjxwv2UFwZfsYIYFte6HX5x6LHzdjB2iIzN17UnU8e6cP/7juZz8f05+HrziC9PBdmPV3Ld1WUrCZjxIOoUnOO6Hg5mZfchdJRWuP8qPGJo1lHUyyhdDNz1Kn4oUOHHrWSBQvCP6FcX7Zu3crYsWOZPv1QTubLLruMd955p0Z2uxEjRjBu3DhOP/10AL788kt0Oh3PP/98o2NoKNHgqUe7Lqy0s3mHjp9n76rRd2d2y+DRG89kXZG5Ts96Y5GZM9snE1/P9jYUmugXZ6Hsx+erlyYdRJ3VGe2I/6JJSg1Z3uVyYZnzJc6toR9kkinVJN35HqqkjNC56O0ejDY3m3ZXYrS4OaNrBinJMWSlxNQZ/+CTYrDM+zak/ZA84j9ouvUnTqvB6fVToLfTJcaNp3Ab3ooiFAmpqDM6YFn1L668TQBk3f4GT0wqoqTSEfI63n30fLqflForHrvHR8BqwLd5Lo4tC5ECfmK79CGh93CMC3/CU7qHrGvHUjHlg/ApVnucS/Il9xMTG4vN7aNY7+C3mTtYt7OC527sTps1H+M3hV4Sl337OFbaU+jXKfT9ORa9Yp+eTolaxnywOGSbAP+58UyG9+vQ5O//hvqufkslvsoCXCX7UCamEtOxJwpLPvLs06LDFz6eNERPLMebx96UHI8Du6B+ONw+LDYPG3ZX4PIEOLNbBunJMSTFN+068IME/T7+v73zDo+qeNvwvX3TOyn0ItJFBQQFpAoqSFHsDTuKiB3Lz4oKduy9+1lQQURUeu+9l4SE9La91/P9EY2G7IZAym7C3NfFpU/OnJl3zpzsZOeZ4jWWYFj9A47s3cg1EcScO5qYHoNPeMa1qySbgk8eCngt5pxRJI24Gbmquudrd3pYv7uIt37cUWXCfmpiJC9MOZ/UxJrnOfhsJuxHd2JcPw+fVY86rQOJF16DKqU1Ck3V9fX27F2UL3wfZXwLfA5LtY1nEi68mqKMYcx4b221xQMDeqZzzxVn1fjsvTYzzty9SB43zvyDWPeuruzIo3sMRqaOwLL9r4D3trzlZTTpHav8TG92Mm9lJqO6qHHPfSxoudE9LiRl7FRk9Xz2hN7k4KG311BmcFS7plTI+XDGcFqcwn74AkG4Ur+/QXUgPT2dkpISfD4fUDFJrrS0lPT09GrpCgv/nWVdVFREWlpao8b6D+HkqYez9gMZKdEM6dOGVu0SaJEcRVx0/a4D/6+2eUGd3IrYUXehvXYWLW54gfjzxmKWIjlcYKLc5Ah6v1kWRdLFd8Jx25pq2/Yg9oLLWXo4sOerMzmZ88OOah1pid7OnB92YLG7A5a3Iascm8uLIioOeecLYMwM0m57ndSJD+FN7sCSI6Yq6ZfsKwaVFq+57O8lcO1IvfIxUq98jLSrnyRh8FXIoxLp0CqOV+8bzLldWhAXraZNWgzTrz6bK0d1Qa6U1/j8vF435Ys+oOy3t7HsWFLl27l1/3oiO52Dtn2vqhWVyUkcdTvHPNHV8lOpFdxwSVeSYmueBCd5XewtMNT7+6DRKnnq1vMq9/H/B6VCxiM39kHz9xLI+nwffU4bLn0xxoJsXIYS/B5XNZ/VbbehK8hBb7Dg9fpD7/s2Jx1OsQTSDUzYdOxJSUl07dqVhQsXArBw4UK6du1KYmLVb1ijR49m7ty5+P1+9Ho9S5cuZdSoUaEIOeQedlPTa46U8chPuxutvFXZZq78+gBHTHL2ZOmZ/dUWnvlgHTM/28TGPUUU6Gy89N/zus0GXKu/xpV3gLSrnyRx+I3ED7qS9JtepMW4+1id72Hm79XLO1xsZunmf5d4Hc+eTB0W+7970a/PKsf39174rfJW49jxF25dIQWlOq77dj8r8zwoIqJZG6B+z/++H4cqFnlEDCljpyKPiKF03uuU/PgSxd/PxJGzF23rLmjVSvKtbtI6JvO/Owbwwl3nE5EQUau96wstPtQpbQNXxu/FsGYuKZfeUzEHYtANxF18N63vfof85N7c9v2+gPmrlQpsMk3APRb+QdVlILP+OlLv78OaI+W0SY3lxakDuXVCT0YPaMcd43vy+v1DWHColA1HdfVW3gersvBbdJTOf5OC96ei/+IhCj+8D92yr/Gay2H5c0j5WynR2/nyzyPc//FB7n9rPV//cYBSkwu2fNyIvu8qvNnrMZaVYLG7oWB7ePnQwmM/ZcJmKB4gKyuLGTNmYDabiY2NZfbs2XTo0IHbb7+dadOm0bNnT3w+H8899xzr1lUclHD77bdz1VVXhSTecPCwha5ZHy4yU5hv5KP5e6u137jBHejXuyXtU2OIUoJh9feYNsyvvK5Kbo1MpcajL6blzS/iik4NWN7ATsm89f0ONuwJ7B0DvPXgEJITI1mXWc7QNlqMSz7F9s/GI38T23889q4XkZBYs8c8qGMiCmMBlp1LAw6JK2KTaXnzizhUsaf0/AZ2SkZReqT6lr0yOXK1luSx9xL9997qe/JNnNU6jqharAO3Od24DqzBuOi9ajGrklrS4pqnWZHnbth9HvKMnNM2gUi1skHydxh1uOa/+J/TFf8lusdgks4dSpm2PQ++tbbaDnWJsVpeuescWsRpGtzn9amiKTPYWLTuKFsP6YjUKLlscHt6pstIiI8NDx9aeOynTFh17AJBfVNqsHPnS8vw+gIvYftwxnAyUqLxmMrJ//A+JI8zYLqYc0eTNHIyckXgU9R+XZ3FJ79W/+MBKnzcD2YMJzUxEsnvw7R5IfplXwVMm3b1E0R2POeE9fIYS8j7YFq1CYL/kHrFI0SdGXy2/YnwOW3YDm5Et/hT5JoI4s+/HFViBpLPgzI+FWVUHIpTOB/dYjTiyT+Abc23ePRFyJRqonoOIXHg5TXu195UcBzbS9E31TdOqkBGqynv8OHSIhZvyg2YYvyFHbnxkm6olA07mHqsyMzDb6+psiMkQO/OyTxw7bkkxGiD3CloCoTNUHxTJFw8bKEDa6vTQ2aBKWinDrDlYAk2lwfJ6wraqQO4S7JxOexByxvQI71y3fLxjOzXpnIv+tKSUkwbfw1ajmHtTzitphPWz++wBe3UAWyHt+Bwe0/5+Sm0USjPPJ/EW94k/bpnsexeTvH3z1MydxYFH99P0fczcRlKWHGw5vPZ/6uLym3c/eZGnlvs4tjZ9+CbOAvnmOdZLA3AJEWF/H3RmR0czjeyZNMx1u4soEhnY1t27dfR291eLFm7g7YJSLgMpWzZH2R3P2Dltnwslr9XMzSQz2s2W3l77s5qnTrAzsPlZOYaGrR84bE3PKJjrwOh9qyFrllvztFjdnhqbEOr08uuPBMypRqZIviOcqrElmTq3UHLS4qP4Ok7+lfZkEcug0G9W3LxwPZo1RV70eutTnw2U9ByvKYy9Gb7CesnO8Hud8roRPYVnvz55f/VG4+Z8fmh5KeXcRdnV8nfXXyU0h9eQO221Co/p9vL/y0+iNHiIqvAxOy5h3n4swMs3W3gvA6RyE1FSOYyckv0bKxHz7u22mBx8tG8vTz4xire+nEns7/eypRZy8jM1nG0xFKr/HblGXGp/l23HwhJpQ16WA6AX5KQ7H93rA3k89qsNg4dC76n/cJ1ORWdfqh9aOGxnzJiKL4OhIOHLHRVvTVHz1kZcfj9En5Jwun2Me3VFfiCbN792v0Xkp4cRZTCT/mSz7HuWBIwXcvbXsMd17LG8q1OD4V6O0oJnG4v8TEadHYP7Vr8uxe91aDD8/OzAc8bB9C2P4uEy+4nIjqmxvpGeG0Uff0/PPrA+/C3unNO0DkBtdU6kwNvcRa2n4INLUPi9S+iSO1wwvxcTi+3v7ik8oxypULGczd2J/HYCtx7lyF53SCTE3Fmf5JG3IQ6LrnR3p+BHZNZuPYo3/4ZeGvsYOv+A2m/qRTdp9MD7l6oiI4n7toX+fivPFbvqO7BA1zcvw23XXoG6sjoBvN5C5Iu5K6XVwZt0x4dknjylvOIkjnCy5cWHnutER27oNngcnvJK7XyxW/72J1VjkalYMrlvSgqt/H9ksPV0g87txW3jO5IpNyFXBuF5PVQOu+NqseiyuQkX3IXUV0HVFtPfqpY9qykbMHbAa8df+a40+3FZHVjtLjQqOTERGlIjNUgk8lwleRQ+PX/kI7bCS5x+I3E9B5R5zMCCstt+A6txrPyk6BpUsZOJabX0BPmVWa0c8vz//7RdOOItgywr8B9sPqmPOrUDqRe9Tgmnxa3x4dKKScuWoNa1TBnkpcbHUx9dQW2IKM7/Xuk8cC15wa1Wv6L3+3EdnADZb+9U+XnMqWa9OueQdPyDIrK7Ux/Y1W1ofDoCBVv3H9hlbMTGgK92ckjb6+hRB94B8EpE3tx8fnt6nW7cEHjIobi60CoPUGhq+qsAhMPzlnNrsxyJAmcbh9vfLeDpLgIHr7+XFq1qBgmbZEQwd0Te3DN2Up0H9xO3rt3U/Lzq3gdVhQXTSP9lldIuuhWksfeS9Jtc1Ce0R+FJrLe4lW16038wCtA/m9HJVOqSb70bo754yvTl5scfLXoAHfNWspDb63m3tdW8tBbqzh4zIDX58cTl0HiTS+TMOJmIjudS8zZF5F00ytoegxFoa27Z20wO5BFJ1V/8f+DPzIRay3y06qV9OpUMTlOJoMBnWNxH1wXME93yVGspQU88f467py1jLtfXs6mXcdw6ksw5hzAWXQUr1mHzemul/ZweXxBO3WAwjIbLre3VvktPmxA0bEvre6cQ2zfS4nodA4JQ66l1Z1v4ktqx1/7SoiJVvPm/RcyqHdLlAoZKqWcoee25vX7BtHCuLnBfd5EjZc7JvQMWNekOC39uqVUdOqh9qGFx37KiI69DoTaQxb6X220uPjgl90Bjwd996ddyGUyHrqxL09NOZ+XbjubXpmfY//lucohU2fOHoq+fBy308Y6QyRxfS9hV0R3xn5xkNXZ5nqNd+UxB/EDxpN06xyUYx4m4cqnaH3XW2TF9eT2v9eBe7w+/tyQw29rjlYOXwOUG508+f46yo0O1mXqGPv5AY6kDKDFxIco6H4FV87NY1WOrV7iVamVWJRJQdeeyyNiKJbF1+o885hINddf0hWlQkZMpBrJXAIEHyy0Ze8lPqZid7z7xp9Bh/LVFH44Df23T1L42cMUfPYI3vwDrDtUVOf2cHh8xEQGn7PQskU0mr/nSNQmv9XZFtTJrcg7cxw/xo0nM2MIqvhU1mT9vRd+lo6MlGjuvVDDx7em8fH953L3Fb1I161GvnB6w/u8Wcvp3iGJ5249hzapFW2rkMsY3Dud2Te0J7l8Y8OWLzz2BkcMxdeBcPCUm4tWymQYLU4MVjexkWriotTIFDLW1vJ+q9XNHS8tDdpWZ7ZJ4LHJ/bBZjcj/eLXaZLB/iO47lujBVxOp1TZK/Tdn6+kXYG90p8PDPa+sCDhzGeDqkZ0ZN6RTrZ/Pqehyk4OvF+7lmr5ROBa8VGXIX6aJJPWap9lpj6Vn64Ra5Weyu8kvsfD94oPcNTAa1/zngraXavBkXtsSTWKMmts6F+Nc+231RHIlyZNfRRafVjePvVMyi9Ye5es/Anvsr903mM5tEur9+Ybc53VZMZaX4dQko1AoiFb7ichbDe0GhocPLTz2U0Z07IKQozc7+fL3/azcnl/5jbtHxySmX332CfdY/4dinY3bXwzesXdtl8hTt56Hxm0k790pQdOpEjNIv+F5lNHxJ1WH+iavxMLdLy8Per1HxyT+d8t5RGrr92z44ynV2/n6972M65eM1pSDzJAPCa2J79ANTXwSSuWJfefjsdjcKF1GSr54GL8jwMlrMjmqK2dzzwd7mHlDN2KXvYDfYQmYV0yfi0kafhPyE6wSOBFGi5PPftvHim3/HgGtVMi5+/JeXHBWBnK5HLPVhcvjQ6NSEBejRqM6+boLBI2BGIqvA6H2lJuD3ptn4MN5e1i+Na/KMPreLB1PfrCerCJTrfKL1Co5s21C0LYaPaAdMoUMi8tXxds+Hplag8cf+vZVq+TIa5i7lBwfgU+i4dun1MKNY3tCZCJ5kV2wdhmLpnN/IhJb4PBKp5Q/Chna+CRaTHwYAmz4ox16K/M3lyFJEK2WgnbqAO6Cw7gc9jrXNz5Gy01juvPGA0N44NpzeGJyP95/dBhJqdHYnF4+mr+70u+fMnsZn/+2n3Kjg8X76u95h9z3bU46nGIJpBsY0bHXgXDymJuqdrt9rN8deMlWsc5OTrGFrTn6E+YXG6Xh1nE9UAfYsatdeixnnZHMmiPl/LBbT0QNO7JJ3Ueyo8xbJf+9BSYsNjfHSq0s2l3YKM8nJlJNv+7BDzcaN7gjm7J1Ddo+WSUWVBJYHB4yUqKQtCoeWrCXrflG5HJZnfKXyRUc8LdAdfUsovtPIKJdL6LOvoiUya+xrCyVxduKAfAhD9j5/4MsJokcg7te6rsl18Dt321HEaOhf490dhaZySmz8fq321iyKbdyoyO318/v67J5/5ddlBqd9fa8Q+77NicdTrEE0g2MGIqvA43hwTZ3feCojuc/3RT0GV8x7Awmjexcu729HW5KDQ4WrMpi+8FStBoFI89ry9BzW5ESXzGrfdNRHYPSoPjrJ/BZjVXK0rTsjOaS6WhiEyvXpZcZHRzO0bNkUy4+v8TA3hkM6t2SFgmRDf58SvQ2nv5oIwVlVYerb7ykKxcPaIf0d+da7+u6OyVjtbn59q+DrN1ZiF+S6NctlRsu7ka+1UnPVvH1Vt76zHIGnZGEFh9OScHeAhMyl4+Zn2/G75cY078lY1QbcO1bGfD9SLz2eZTpZwQ97357roEeabH8c+ze/hILvdvUbk6Axekhr9jCo2+vCfp+vn7/haQlRzUPz705aQifWITHLjjdyMo3Mv2NVUGv3315Ly4+v/1J5el0e7E5PMhlMuKiNcgDjGl7TeVY96/DdmAdMqWa2HNHo23THWXMv8P5OpODpz7aQG5x1aHglIQIZt8zkJSEhj/DW292cqzIzOb9xcRFqRnYuyUJMRqiImo+ArUulOht3P/GKiz2qkvANGoFb0y/kNZ/z6RuKFxuL6UGB/NXZZJbbOHBCR3w/PUmnpKqEx7jB15JXL9LUASZtW+1u8nMN/LNnwcpKLWSlhTF1Rd1pmu7RGKjgp9H/1/+WJ/Dez/vCnr9kev7MOjslrWvnEDQCIih+DoQDh51U9d+uYzk+MAHTsjlMrq0Tzrp/D1+iaS4CJRqBYv3FwdMr4xLRnX2xbhGPkDCxEeI7j4Qhyq68rrPL7F8W161Th2gzODg5xWZmB0nt47aYHGyP8+A0eaqdX025xo4o20Cd07oxWVDOrGvzIr/741DGqI9th/TMX9VVrVOHcDl9vHl7/sxWqvGb3N5MFldlBrs7M8zYnMFzt9ht6ErKcJlKMVnt2B1BY7H7ZdonRrDTWO6c+P4nkQmppB+9ROkXf8c0X3HEn/hNbS68y0izrmYJVnWgPVxuLws3pzL/z7cwKFjBqwOD5n5RmZ+tplfVmRic3hO+DysLg9qdc2b4ihV8lqt4z8VHXIfuCnrcIolkG5gRMdeB8LBo27q+oU/D/LQ9X2q7eoll8F9V5/NF5uONVj5azJ13Pzd/oDrvk1WF39tCH7G+tItuZQZnScs76VFB8gvt7HjUCkvf72VN7/Zxvs/7eJogYkjxbXby/2fdeKrD5fxQoDz4OtTF+ocrN8d/PjZLQdK0Ftclektdjdb9pfw5Afrufvl5bz/ww627i/BbHNV5r8j14DHWIppySeYPptOwXtTKP7hBXxFmew8WhI0nvVHddzz/Q7WZ+tRRiewyZHMK6beZLYcijq5JauO2YLWx2xz89Xv+wPW4ZeVmZhtLtaf4HmsPVJOXHwESkXgWYxatQKZWlGrdfynokPuAzdlHU6xBNINjBiKrwMN7bGeNrpjEg6Hl037i9l/VEfLlGiG9mlNVKSKjdn6kMTndnmZ/vqqym+nxyOTwSdPjGR7ganG/LJLrWzdWci8VZnV7p9xY1/kUWq6t4xr8PpEaxQ4LUb0FheJifFEREQETF9QbuPlzzdTZnQErLdSIeeDx4aTmhCJwepi/spMflmRWS3dVSM6c+nADmw6pmdYKyVFXz2Oz6I/7iHKSbr6aZQtz6zVee611QM7JbMvq5yZn20O+rs77arenH9WBmuO1JzfwUIzdqOD1/5vG//9pJTLZTx+U1+IUNGtgdov5D5wU9YQPrEIj11wuuP3SwE98cbG6fbywS+7WbYlL+D13mck8+iNfYmOrNnrrmk9epRWyTsPDyM5PiLg9frCa9FjO7AB847FSB4XkWf0Ia7fGJRxKciOW/rn9fn5bvEhflxafW99gCHntuKeK85Cq1ZSVG7jzllLCfQJIpfBh4+NIDUxAtOmheiXfRkwP3WLtqRf+/Qpne1eExv2FPHiF8E79qmTzmJU/3YnzMfh8uJ0e7HY3Py+Lpu8EivtM2K5+Px2pMRHoFGLteyC8EMMxdeBcPCom5sO5ok3ttaqlVwxrDOaAB6rQi5j8tgeIJfVmJ/d5WVdkKV8ADanl4JyW4PWR1daQvH3L6Bb8hme8ny8pjLMW/8g/5OHcOsKWX6g6nnqyw6UcNF5bUkJ8MdGTKSKiUPPwPP3fgOHjukDduoAfgkO5RrIK9Zh21/9oJd/cJcew+us+zr043X7jNga9wHo0SG5xvvNNhe7jpQx++stPPvJRpZuzeWKYWdw84QeXDOqC61axOD217yO3+Z0UV5SjD13P7bDm3GV55NTUPvz64/XwX1bC3anB53BgjE/E1zWE6Q/DXQ4xRJINzCiY68D4eBRC91wOs/iYMYt59G9QxJatYJLLmjP83eez+vTLyQmSsX+QlON9+8tNGE5wXnwBpurwc4f31tgwp65HXdpTrVyJbcD3ZLPKSrTVbn/hUUHOFhmZfa9A7l8WCdS4iNIjNVy2aAOvHjPQJ7949/83b6aB/vcXj878kxQwzn3APa/dwSqz/rHRqkZP6RTwPJGnteGuGh10PuPlVn5fvEhnvxgPdsOlJKVb2LeiizunLWMMr2DXQXGE5Yv+bx4i45g/fZRir/+HyVzZ1Pw4X0o13yCx2I4pfoF8m2d2ZvILrXz+v9t57431/L4/+WyZFsRBrMTslefnO+btxmWPx8+PrTw2E8ZMRRfBxrSExU6PPTWHD1ntYzD7fbx7Z8HWbOzAJ9fIjFWyzWjzqRt63haJQVfx5xdYOKJ9wKfYqZUyHn9gQtJjo9okPgdFhP6uS/gKsoK8gbLSLjtLZRxKQHvtzo85OlsJEWpiY/R4PL6q1wvKLMyZfaygN/aZTL44NHhZJsc9HQcoHzBnIARaNr2IGn8g2ijY+u9/jqzgx2Hyvhp2REKyqykJkYyYWgn+vdIJyk28FkAG4/q6BCnZfrrgZdgpiZG8tI9A0mJDzxH4R+tdejJ//A+JF/1P+yieg4hZfRt2PzKk6rP8T6t5LSy86iRZz7bxvFnH/Xpmsp9k3oQX7C8Rt9XKtyFL/FMPMYSfDYj6oQWKGKSUMQkh96HFh77KSM6doHgBOhNDh5/f321jWIAJo/tztiB7VEpAy+LMlpcvPLNFnZn6qpdu+aiM5k4pBPaWpzzfSr4bCaKvnsOd0lO0DSt73kPVXzqKeVvc7j5cekRfllZffLcFcM6ccXwzkRpVXitBop/nIW76LgJhGotLW+ehTql9SmVX1sMFic+X8XcjcTYwEsr/8vH83ezYE3gQ4IA3nl4KG3Tav5wNqz7GcPK/wt8Ua6g9ZS3T/m5/4PO5ODBOavRmZwBr8+6ZyDdOyQFvd/v8+DKP0TJ3Nn4/3PAj7ZdT1pcNg1lTGKd4hOEDjEUXwfCwZMWumH16sOlHMk3BuzUAb5ffAi92Rn0/i15Bu6/5lwmDT+DSG1FB54SH8G0q3ozakBbVh4pa7D4nYoINGeeHzBuAE16R4rsnHL+fpmMAee04pEb+tAmNQalQk6b1BgeuaEPE4Z0wk/FXvYOZTRpk2aQdPGdqFu0RRmfSmzfS8m49TW2mTQN3p5KlYLk+AhUasUJ0+/MNWB1eIM+MwCP119jeQ6nC1dh9T92KvH78LucJ4zfYbNyJK8E2z8n/B3n01ptrqCdOsDiTcfw520N6vP6TOUUffd8lU4dwJmzB93SL/DZDOHlSwuPvdaIjr0OhNoDFrrh9fKDpazdGXwCnMPlRWd2Bb3/+YX72ZZv5NpRZ/LCPQN57I4BzLjlPEb0bcOWXGODxr8mU4e1dV8U0QEOx5HJiR42mUcXHj1hfjtyDfgcVsy6cgrLDGzJ/nfv/ju+3YY8Ws0LUy7glfsHM3RIR+TRamKjNFXyU8YkcCDuHLb3vAP5+P+ROOwGVhZJPPrL3rBq71l/HqRvDXv0a9UK5H+fRxAsv/3FVlTJLYPmATLkam3A++csPYzDpMd6YAOG+a8SteIdHLuX4TXrIHdTFZ9W8gTv1AF8Pj/s/SWoz2vdtxp8gf+IsR3YgN+qDy9fWnjstUYMxdeB+vYEhQ693pVn5Nx0DWq5DKdcw6ESK1u25bNwXfCh2bcfGkq79Pr3iOtD78g1cF6KhGntj1j3rgW/F02rriSNvBlffAZrjta8Dt+g15Noy8e07me85jJULdqRMOhK1MktsUuqkNevIdq/S0oU//twA/ml1Udprru4C5ec357YSHWN+WlsZeR/eB9I/mp5RHTqQ4tx07Cjrna/y6zHtehNXAVVlxsq41qQfv0zqIq2QPvBoI2l3GBl+ptrMFndAd/L5+/oT2/5bmh9XjWf16+KpHTea9gPBV8S2PLWV9Do94aPLy089lojOnaB4G+8VgPO3P2Yt/6J5HMT1WUA0d0GkWtVct/rKwPek5YUyeypg2rl3YYSv8eF32FBkiTkam3Q/dX/i89pxbj2Z0ybFlS7ljLuPqK6DAh4Drrf7cRnN+P3OJGrNCgiYpFrGnatfn3gtehw5h7EnrUN/9mX839rilizsxCvTyIhRsO1o7pwfs90YqNPvM+83+3EfnQnpfPeAP+/34rVLdqRdtVjKGOTq90jSRKW7Ysp//Ojyp+pklsjV2vx6IuI6no+SSMnI1dV7J3g80us21XAK99sq5ZX5zbxPDn5PBJqeC/1q77HuHZukKsyWt/9LqqEus0DEIQGMRRfB8LBAxa6frTXYqDk51cpnfc6zrz9uAoz0S//moLPHyExQuLSC6ofRKNSypl65dloNIqQx38iLVdpcKjjWJbnxS7T1up+r9UYsFMHKF/0IR6rsdr9+rJSyhd/Tt7791Lw0f3kvTeVskXv4zXrTin+pfuLsbr+XReuKynGfmwf1oMbcJbmkltYP/seeExlFH79FKXzX8e6ZxWO7x7hqvhdvDPlLD54ZAhv3H8hA89uyfocfe2et1qLvM1ZJN76JsmXTSNx+E2k3fgiyrGP4FTHBbzfZTFi2voHAFFn9ift2qeJ6T2ciPa9SLl0CtpWZ2IwGCrTK9wWzk0y8MJdA+jYqiLP6AgVV4/szBOTzyNB7a7R543pMQhkgbuAyM59Kv6ACCdfWnjstUZ07HUgHDxBoeuu9+SbcGTvxJV/sFob+2xGHCs+45oRnXjq9v6c06UFnVrFM25wR16dPpgvt+Wx5kh41ae+tPlw9W+C/yB5nDj0xby59HBlep1Oj33Zx1h3Lf33W6rkx7Z/HSW/vIrFoD+p8ov1drR+iQ27i8grMiKVHMXy7QyKv3mK0p9fpfDj+5Evew+vRV+r/ILpvFIjhlXf4zUUV6mfa8ciXP/3AJG6gyTFRbD2JPNffdTIZV8cYJe2G/H9L2ODNY4rv9oXdG95ncWB3+0guueFRLTvRfH3M9Ev/QLjup8p+fkVTJsXopX7K/c94OhKouZdTy/ZHp69fQCfP9yPd66N5aou5ooRpBP4vApLLmlj70SmrLp7ojq9I8mjbkeRvyG8fGnhsdcaMRRfB8LBExS67vrCthHo5r6IO9h6b5mc1ve8h0sTz9FSKy3jI4iLVOPw+sIi/obShnW/YFj5bdD3P/Xap9ngaMF5HZKI0apwleVT8NF9QdOnT36ZdcaoyvTByh94RjJGk5OnP9pAqaFiz/p3p/TC9/PjSN7qfnLkmeeRMuaegJ51bfTQVkoK3p9aZcj8v2hbdyP1ykexo6kxP6vLQ06JlRaxGmIj1Xj80knFY7fbsaz4kpiu51P83fNA9Y/myDPPI+7iKURExdSL7+sv2oMvoROu4mx8ViPaFq1QxKdVWAWh9qGFx37KiI5dcNrjtRop+uYpPLqCoGnqst67qeIqzqbg04cCX5QraT3lHVTxKZU/sh7cSOnPryBTa4k992Ii2vVA8nmRKZQ48w6iiEkk7pyLTliuzuTgobdWU26smPXdrX0i03qW41r7TZA76uYHewzF5L13T9DrqpTWZFz3bI372ZusLg7nGvhp+REMZhed28QzaXhn0pIiT2o/eY9Zh2n9L5i3/Rk4gUxO67vfOe3eRcHJIYbi60A4eahCn7p2K7REntE3aDurU9sjU2nDJt7G0lJUAtpO5wZ8JvEXTMSjiqySXq6JQq6JJHXiw3jK8yj+biYlP75E8XfP4yo8QkTrrmzIqnnd/vIDJRSUWSs7dYCUhAiU+pyg7QMSfpf9lOvrk6tRJgRf4hbRticyTWTQ+3VmB9/8cYDnPt3E/mw9RTobq3YUMO31lew4UnZS57UX2GV4TKU1VNWPzxV434SQ+8bhpMMplkC6gREdex0ItQcqdP3oNUcNxJ57EXJNZIBWlhEz7CaUUXFhE29j6dW5Dkp6X0vM4GuRR1YMHyrjU4m/dCpxfS5mdXbV8+SlmBQShlyHYe2P2I9s5b9DyY6jOyn99S3icdRY/tcbj5FdVPXDz+v1Q5chqAfegLb7hcgC7D0fbF14bfT2cj+Jw24I0PYgU6pR9x6FXKkKeP8bSw9TanDw58Zj1e71+yXenbuLYr291vG8tyYXZWrgPe4rKqrEiSrg/SH3jcNJh1MsgXQDI4bi60CoPVCh609HaxS4ywvQ/fUpzmN7gIqlRjHDJ6NO70hkVHRYxduYenCnJNQeKz6fF73DT2xiMlEaZbX0bpMOv1VH4RePBf2dSbvxRXwpHYKWtyVHT4JcxlMfbgDgxku6kpYUxYpteehNTs5sFcUl56ag2PoD7syKNdgR7XvRYsKD2GU1e+A16Uhc2A5vQb/sK/x2c2X7x158N8qUtkRFaALef6jYwu49hcxbGWR+BvDmAxfSsWV8reJZn1nOkAwo+Gh6wM1jos4aTuywm4iIjKp2f8h943DSED6xCI9dcLog+X1IHjcypQqZInzOtPY5rPhdNvBLyNRalNHxoQ6pyeC1GLAf3lxlHfbxJI2+nbhzR9eYT7nRwf1vrmJkvzbYnF4WHbc5kFIh4+nru5O05UPwuUm76glUcSlBcqs9kt+Hz2qsaH+5Arkmqlbt/8Evu/m9hg2M3rj/Qjq1OnE+/1Cxh/thSn56Gb/z301yIjv3I/niO1AG2klQIPgPYii+DoTaA22KevvRUly6IvSrvqfkp5cp/etTnKXH8LscYRHfkiwLTm0iqsQ0HMqokMfTlLRHrkZewwQzACkyoXJderD8tFolM+88nx4dk6t16gBen8Qb8zLRjp2B6rIZuDTx9RK/1e1naa4bV0w66qSWtWr/FQdLOL9XetD6atQKYiLVJxWPzQPa1l1Iv/VVEq95lhZXzKDVXW8RP/oulh9zBr0/5L5xOOlwiiWQbmBEx14HQu2BNjW9L99AmquAgo+mY1r/C46c3dh2LKbw4wewHdxAdtHJrXMWOrz02mMW5MltkGujCIRMpaFMncraE6z7X5tZTpu0GPZmlQfMB0BvdqJzwpVf7Q+6Lrwx9NML9hERqaZzm/iAcY4f2ok8s+Ok85fJFazI93LNAh1bpDaok1qy8pidmb8Hvz/kvnE46XCKJZBuaCTBKWN2uKU/9hRKZodb6Fpop6FUyn7tRilr5sTq/164QnLqi8MqXqFPXu88Vi7Zs/dIR1+6qmr7vnilZM3cKW3JLKl1fu//vEsa88D8oP8O5uhCXt9/dLnRIX3y6x5p0mMLpTEPzJdunblYWrEtT9qXp6/b88wplZyGUsltKJEcxnJpfWZZ0PSSwyRJ+36t+O/prsMplkC6gREeu6DRcOYdpPCrJ4JeT750CrG9RzRiRIKGQPJ58Zp12A5uwFWUhTqtPdFdz0cRkxRwb/lg7DpSxpMfrA94TaWU88GM4bRICLSSITR4vH5MVhc+vx+VUlHn8wO8Fj2mjb9i3rEUyeNEGdeChCHXEtmxd632+hecvoih+DoQak+zqWmv01bj8/TZzGw/Vru9uIUOX231SKgSUlGfM4bivpPR9LkMVUIaNi8nlV9GShTt0gPPIJ407Aw0mhOfr96Y2un1sTXfSGSkmsTYuu174LUaKJ47G9PmhZXHs3pNpZT9+ibmXSvwez0nzC/kPrLw2IXH3hQJtafZ1LQ/pubdstRp7Uh3F1FUWre9v4UOD736SBn3freT1YfLTun+3UVmbp7Qk+F9W6NUVHxUxUdruHVcdy65oD0bjjbPORlbc/R4dAW4izIJhHH1D/hsphPmF3IfWXjswmNvioSDp9mUtN1ikgp/eT2gx573yYOSI/+QZDuyVTLvWyf53M6Qx9sc9J97CiWbwyl5rUbJYTZKa4+UhlV8J9J/7S2UTDanVKK3SXklZulwgVGyhlF8DaHtLo9U+seHgeei/P3PWZh5wvxC7iMLj1147ILTA6/ViHHDPCzbF1cc6CGTE3VmP2LOvojSea8jUyhoMf5+VIkZKGOTQh1uk0aSJLzmMiw7l2E7tBm5SkNsn4uJaN9LrIUOc3TLvsS0cUHQ6y1vew1NarvGC0jQpAiLoXiHw8H06dMZOXIko0ePZsWKFQHTbdq0ibPOOotx48Yxbtw4Jk2a1MiRViXUnl5T1MtyHEQNvIaWt75K6qQZpF31GIqYpMrNOHw2E7oln+NzWsMi3qas3bpCCj55GOPan/CU5eIqPELZgrco+flVvFZDyOMTOriO7nEhwVBEx6OIjD1hfiH3kYXHfnp77J9++inR0dEsWbKEDz74gCeffBKbLfBEq44dO/Lrr7/y66+/Mnfu3EaOtCrh4sk1Jf3CogMcNbiw7ltNydxZFH//AuYtv1dOEAJwlx4Dv5/N2c3TQ20M7XPa0C35vMrOZf/gyj+I49heduUZwyZeoatqZUwSkWcFWCEikxN38T0oouNPmF/IfWThsZ/eHvsll1wi7d69u1Lfcccd0qJFi6ql27hxozRhwoTGDK1GwsWTa2ra7vJIJb+9U6OH6Cg4HDbxNkXtNpRIWTMvD/p88794TLJbTGETr9DVtcNskPQHNksFXz4hHXv3Hql4/puSqSBbstlstbo/5D6y8NhPb4/97LPPZtmyZSQmJgLwzDPP0LZtWyZPnlwl3aZNm5gyZQpt27ZFqVRy7bXXMmHChFCELKgjlj2rKFvwVuCLMjmtp7yNqoajNAU1c6IzxtWp7Um/9ikUkQ1/IEVTRvJ7kXx+5Cp1yGLwOa1IXi9yTQRylSZkcQiaDo0yFD9hwgTOO++8gP98Pl+t8+nevTurVq1i3rx5vP7667z77rusXx94A4vGIJw8uaamtW27Vx4FejzRPQYjj4yrc3nlJgdH8o0cOqanqNyGweJkyb7isKh/Q2uZWosqpXXA5wsQ1aU/Lrk2bOINN+2zm3HkH6b0t/co/eVVzDuW4jKWseZwaaPHY0eDMjoem09ep/xC7isLj715eezz5s1j06ZNAf8pFAoyMjIoKCioTF9UVERaWvVva9HR0cTExADQunVrRowYwfbt2xujCgEJJ0+uqWlVbDKJVz9TtfORydF2H4y8/1UoNBGnnP/2XANF5VZmfrqJB95YxUNvreHOWUt5d+4u4jRKNh7Vhbz+Da2VUfHEDr8FkHE88shYonteyOpMXdjEG05ar9NhWDOXoi8fw7Z3FfbMbZQvep/iL2fQTm1jS3bT3Gch5L6y8NhPL4/9rbfekp544glJkiQpOztbGjBggGSxWKqlKykpkfx+vyRJkmQwGKQxY8ZIS5YsadRY/0uoPbimri1Ot5RXUCQ5SnMlR+ERyakrkg7m1n4v8WC6RG+Tbn7uz4D7iz/z8Qap3OQIi/o3tLZZLZIhc5eU99H9lfvxF/4wS3KWFwRO7/RIO3P1ks3lCYv4Q6GX7S+WbLkHgs5NKPj6acluMYVNvCejQ+4rC4/99PLY7XY7M2bM4MCBA8jlch5++GFGjKiYETpnzhxatGjBNddcwzfffMN3332HUqnE5/Mxfvx4brvtthBHLwg3th0o4ZlPNga9/sGM4bRMiW7EiEKL12ZCcjtBLkeujUKhqbq/uuTz4rXosR3ajKvwCJq0DkR16Y8iJvGk9nZvDvi9HsoWvIXtQHCLr/Xd74r5H4KwJiyWu0VGRvLWW2+xZMkS/vrrr8pOHeC+++7jmmuuAeD666/n999/59dff2XhwoUh79TDyRMUukJvztaxP0dfY7uVGexhE29jaIciElVCKk5NPEuOmKpc33K0DEf+YfI/mIZ+6efY9q9Fv/wr8j6chjPvAFuySho0vk1Hyyk12MkrsVBYbmVfnhFrIz0fm8vD4QITheVWyo0OLA43R4oM+Ow1+6A+b/2Ub3V6WLyv8d6HkPvKwmNvXh57cyXUnpnQ1fWHq7JIOMGpWmq1MmzibWz90qIDFJQa8BhL8ebuoXu0k9K5LyH5PFUfks9LydzZxEqOBosnt8xGYb6JB+es5u6Xl3PnS8v45rd9lOjtAdNvztaRU2ql1OCgWGcjv9zGVxtyTql8s83Fmh0FzPpsE3e+tIy7X17OD0sO4fYrUXfqE/TdkUfEYPWf+vvz9vIjGPQ63GV5uI/topvKgM3QOHM+Qu4rC4+90Tz2sBiKb6pYnB7WZZZzQadkYrQqocNEn5Uey92zl+H1VX+1UxMjeemeC0iJjwybeBtTW4wG1Hv/wLx5IYrIGBKH3UjZb28HfcfjJz6Kuv3ZRNdzPJFqJUs3H+OdubuqlRkXreaN6ReijVBVpo/WKCkos/LZgn1sO1iCX4KOreK4eUx32mXEEh+lqXX5A9onsnjjMb5adKBa2V3aJjDj+t5YPp+KP8BphHEjbiHirJFEatWnVH+fRYft97dxFRyszFMZn0ralY/hiU1jzZGGa3+c5oqOpcMQ0MY2bw3hE0sg3cCIjl3Q7HB7fOw8UsaLn2/G5//39Y6OUPHSPRfQLj0uhNGFDknyY972F7q/PgFAlZhOzNkXoV/2ZdB7ki+dQmzvADug1ZFyo4Ppb6zEZHUHvH7nhJ5cekF7ZLKKWf0lejvTX1+J1VF1ZEEug1lTB9G1XWKtyy412Llr1jI8Xn/A6y9PHUjHGCelC+bgLsqqKEcbRcKgK4nuMfiU1/777GaK576MK7/6HxTyyFha3voKqtjkU8pbIPgvYii+DoSLhyp0Ve3y+TnrjBTee3QYN4/pxsUD2vLgtefy5gNDKLC6Qh5fIO13O3EZy9GXFOGwWhqkPJdZj3HdT5Xvr9eiR5WUQU1IiW0apL52pydopw6wcW8xJru7Ir3DzV8bc6p16gB+CT6evweTzVWr8tcdKaPc6AjaqQNs2FuMOrklyZMeJ/GWN8i47XVa3f46ql4jWXLUdsr199rMATt1AL/djKs4m1WHGm6dvNXpobi4GHv+IYwbfsWyazme0qP4bcaKIELtOwuPvd4QHXsdCAfPVOjAWqNSsLvYwrJCM/37tmHIua3YUWjisXl7wyK+f/R3m44hmUopW/QBBe/fjfGTqRgWvI6rJIdDhfW7V77d7sRnNVa+v5LHhddUhqZlZwKhSuvATr28Xuv71rIj7Mw1oFbV/NETHaEkR2fnxUUHyC23sWFPUdC0R/KMOF2+E5afU2rFZnJgd3prLFuprIht5TEHl32dycoyNcrYZFZn1q097MbyGsu15x9h3o6CBnvfvBYd7oWvUPzl4+iXf0XZwnfJ+3QGtqzt+N2O0PvOwmOvN8RQfB2obw9M6NNPS5Zy9F8/ht9hqfpyKZRkTJ7NBkMEfdol1kt5LmM5hZ/cj+SyVxYj10bRYsKDmDYvxJG1A6j4OIjocDZJF9/JmiIf/don1Uv5ZUY7heU2yo0OWsRH4PH6+XTBPnJLjqs7MOuegbTNiGVtZjl9Wscz89NNZBWYAv4eyuUyPnl8RBVP/vjyFUBRuQ2dyUlCrIZnPt6I2RZ4xODth4bSLj223tvbWZJD4ScPBv08Sb5sGru13TirdXy9v2+ReChb+A72Q5sClCyj1Z1zUEfHhJcPLTz2U0Z07AJBiPD7PBhWfY9pw/yA17Xte5E64UEUEfWz5l7yedGv+RHTup+r/FymjiCuz8VE9xiE5PMiV0cij4xGoa2/tf5F5Tae/ngDReX/TkhLjNVy/zVn8+mCfeQU/TtEObxPayaP7U5c9L/7ov+1MSfgRDuA83umc9/VZxOpDbzmvtRg57u/DrFyez5en58RfVvTt1sas7/agv+4T7+xA9tzzaguxETW/97wXquBom+exqMrqHZNplTT6q63UMWl1Hu5AB5jCXnvTQUpsAUR128sicNvQCZXNEj5gsZFDMXXgXDyaIVuetptNWM7sCHwywU4s3djMlvqrTyrR4LuI9C271WlHMntAIUSf0Q8K8ojcEYmodBGn3T+NpeHJfur78VfZnTw3Kcbq3TqAHqzk1e/3ca0K3vRo2MS/Xuk8vwNXbnu/ARio9RV8u/bLZVOrapPeoyNUnPjpd2I/Psb6vHxZRdbePy9dSzdkovXV9GpLd2Sx/rdhbwybTADe2WQkRxFj45JPHt7fwb3bVMxI68e21tndnK0wMR3a4qJvOQBFDFVJ/rJVBrSrvkfbnVMg71vkscVtFMHcOsKkFzW8PKhhcd+yoiOvQ6Eg0crdNPVZVY3MoUy8MsFIJNTbHbVa/lXf70f/5C7aHnrK8QMvhbVoBtJvnUOcf3GsDLHdtL5bcwsp9zoYNX2fJZsyiVGLqNAZ6u8/triQ5Qa7OSXVj8XHsBkdWPUGbmvRxm3pO4lYdXLeNZ8gd/tqFJeYmwE915zDjdd1p1OreJpkxbDpBGdeejmfhw1BF73vrfAxLaDJZXr4v/Lqh0FvP3jTi65oB2jB7RjzAXtUcdouOP/ttfr8y42OFiwOov7Xl/Jj0sP8/i3mViHPYp2zCPEDboa9aipJNz8GtqWnVmTZWiw902m0oI8+LumyeiErHR/ePnQwmM/ZcRQfB2obw9O6NNL25xu7FsXYln1bcD3K7LrAIx9b6RlSkKDlG93edmVb6RHy7hTut9gdbJ5Xwnv/7SryrLCnh2TeOi6Pqg0CrYd06N2+Xjpyy1Bf49uHtmW/kXf4yo8UlHvM/rSYsL92HzyauXvKTDROTkKpUKOUilnbQ3xGa0uXvl6K7szg09a+98t5/H8Z5t4ffpg0lKi6729jxWZeeydtdXKTYmP4LweaQzr35a0hMgGf9+iFH7KF3+GdefS6g9BoaT1nXNQRUSGlw8tPPZTRnTsAkEI8Vp0Fb6rvuqsb7k2mpaTZ6FKTA9RZCfmWJGZqa+uCHhtdP+23DauBxq1ksx8I/e/sSpoPk9PPpdO1m0Y1/2C32kl7dqniTzOLjgVnG4vs77cwraDpUHTPHXreazYls+dE3pW8fTrA6/Pzztzd7FsS27QNB89NoL05Kh6LTdoPFYDuj8/wXbo33MU5BHRpF7+CJpWnZErTq9zAZozYii+DoTaoxW66es1BV5Sr32GhKHXo0xIRxmbQmy/MbS89RVckcknXJd8tMjMut2F/LDkEBv3FnG0yNwoe617vH4WrMkiGMu25mGwuPhzbxFx0WoygnResVFq0hVGHEd3kXr5Q0T1HoE8uXW9xOuVJEac1zZojJ1axRMTpebWyyom6tX387K5vBgtzqDlAxjtjbevgkMZjb3/jbS88y1Sr3yMtBtmEn3dbPypnSo69VD7zsJjrzdEx14HQu3RCn1y+mCRme+35IZNPOsyy3l6wT6W53mI738Z8nFPkHn+AxR0HoMqvgVra7jf55c4VmTm8XfWMOvLLXzz50Fe+Hwz/3t/HQWlViRJatD43R5fUN8cwOP1Y7J7eHHRAfaXWHn6tv6kJlY9VS4+WsOz13fFv/ZzHNm7KP/jQxTnXMaqXGe9xLv2SDl2GfTsWH03N41KwV0Te/Hp5ly25Bkb5n0rNnNGDTviRWqV6O2eRn3fbvq/fawslhN1Rh/WWxOY+OV+1mT+fWhSqH1n4bHXG2Iovg40pCcmdP3oXXkGzkiK5mi+kSN5RlokRdG7czLJcRE4PL6Qx3eq2uX0cu+rKwLuxpYYq+X16YNRa5QNVn6EUsHHv+5l0frsgL8bGrWCdx4eys5Cc+X9pQY7ZXoruceKSU3QkKpx4l/7JZ6yY5X3JVz5P1Stu9fb3vQbj+ronRHHnsxyFqzOwub0cM6ZLRh3YUdiotSsy9I1aHuVGx08/s7agO10wyVd6dgxic5psSF/n2K0zWwveQifWITHLhDUHb/bie/vDV8KbSoe/2BDlc1INCoFz9zeny7tElEqwm/Qyue0IXlcyJTqoGvYtx0s4ZmPg585P3vqQLq1T2qoEAHIL7FwzyvLq60FBxg/uAM3XNINtarqumhH3gHK//gQv92Mz1Z9w5m4Cy4naci1DRKv2erC55eIilBVi6uhkCSJvBILr/3fdo7+vcGOVq3g8mFncPGAdvXu6wsEIIbi60Q4eLRCV/WcTWVFlP3xIXnvTaU0J4fnPttcbYcxl8fHM59spNzkCKv4HVYzxux9lPzyKgWfP0rxjy9hOLwdp6WiQ3BYjBQVFuG0WwMu4fov5UYHVlfg8mwuD16bEZepnOKiImwu9ynFGx+r4aV7BtEmNaZK2Rf0ymDisDNw+fzV7nejwlOWF7BTB5C0cdhc3gZ5vpJchtHuZvP+YhauPcqhXD2HC0wN1p4Wp4e/9hWTmBDBc3cM4L1HhjF72iDefngoE4d2Qq6Uh9X7Vxuf2Ja3j+JyC5n5RvJLTJgKssBpqfX9wmMXHnvYEw4erdD/ardZh+mHZ7HtXY1MLsesTKTU4AjYdi63j33Zer7eeCxofvsKTHy7Kfj1+tR+jwv7gfXo/+8pnNm78Vn0uPIPYpj7Atatv+MszET/0yzcPz6J4be3aZMcEbBe/5CRHM2GLF218pxWM+4jWyj6+ikK3rkT19yncOxYjNdmZH1W7eLNL9Hj1hXg2DyPxP1zeWlcLN882p8ZN/Xl2SkXMGZYJxJitAHvP2KWVdug5V9k2FK7s+ZIWb0/X5fby97Mch58YxWzv9rKh/P28NCcNbz7ww70pvrx9IPptUfKiYvWsK/Myl0/7GRnoRm1UhHy35fj9Yl8Yb3ZzjvLzNwxazn3v7GKKS+v5Okf8ijUO2t1v/DYhcfeJAi1J3a6aZvLQ26pkXZJUUREVj9P3bRrObqF7wKgiIqn6PyHeOGHw0Hb78ZLutK6fSLdM/5dx701R0+PtFhK9XYO5OiJiVJzVqdkEmO1uHz+Bquf1mUk//17kXzVvViQkXbtUxR/93zl7mGayx7n6QX6gN/c26TGMPOu81GqFVXKs9ts2Lb/iWX1/1W7J6rLAOIuuo2Vxxw1xltUqqNF0Rb0S7+ocr8yPpW0a59mbbFE3xr2lt+dZ+CcSCPF3z5TsRvaf0i+9B6OxXenXVr97I3/X22xupgyezn+AL7Bed3TuP/ac/BDWL3vja1r8oWtfi1v/biDDXuKqz2/pDgtr903mCSNJ3x8bAifWITHLhAExmvR48w/iGXnMpDJiT17JJqWZ6CMTgAqfPWSn1/BcXRnxQ1yJdLEl5j+0Z6geT5/5wB6d25R5WelBjtPf7ShyoxvpULOYzf15awzktGoa9gprg7Ys3ZQ/P3MoNcThlyLbf863KUVE82UcS2QXfIoL/10lLz/HKLSPiOWJyb3IzWx+vIyj6mMvPengs8bsIyWt7+OpkXw5WGSJOEsOUbRp4EPMonocDYtJtyPQlvzumzJ58Vr0WM9sB5X3gGUienE9h6BMiYRuSayxntPlW/+PMAPSwL/kSeTVawnT0tqnPXkTZGicit3vLQs6PWnbj2Pvt3SGjEiQU2Iofg6EGpP7HTQf+0twm3SUfz9C5T+8hqOoztxZG2n5KfZlMydhb60pCK9XI5M+Z+DO/xetIYsurSND9h2yfFaMlKiq5SnNzt587sd1ZZxeX1+XvhiM+UmZ4PU1+r0IPl9AeP8tz4++M8BHV5TKf7fX+Lp67vx5gMX8sxt/XnrwSHcffXZRP19gMnx5bn1xUE7dQD7kW1sPFoeMF6L3c2Bo2UYN/8e9H7H0Z1YTMbK+60uD1uyddhcx9XXI6GKb4H6nEvR9b+dyEHXoU5uhU1SNczzdVTsABcMSQKnyxsW73s46f/6wnpz1dGV49mTpQO3LXx87FB76MJjb7qE2hMLF72vwITO5KCwzEqiWkFema3e8l9zuATj9r9wl+ZUe/6uwkzs+9dysNCEXKlG0/uiKtc9677h/ktb0r19VU+3TWoML9x1AQfLrFXKM1hd7MkqD9jWfr/Eyu35/LWvuP492Mxy1MmtQRb811GTcQae8vwqP/OZy3EVHyHP6uLcrqkcNti549vtrA1SnifQ9PX/4EXOV+tzqsW3v9DElv0lbNiVDzZ9DTlIGM02duYaKDc62HGwjG27ClmxNZ9SvZ39haYq8aw5Us6U73ez+kjDvp8His10ah0fNGq5XEbE30sDw+H3KVz0f33hKG3NI1WpiRGQvy18fOxQe+jCY2+6hNoTCwd9tMSC2eDg0wV70f09CenMtgncO6k3SQkRNe7lXRttN5bj+L8A55X/jTIuhRY3vIA2Lgmn2YD+j/dxZm6rvC7XRqM6/zr87fqit3rRapQkxmpJiY+oVt6Jtj4d1Lslo4Z0pENKdL0/z0iZB8PanzFvnF+t3Kgz+6NO74Bh5XHeuExO0m1zkMem1Ko8l7GMwo/uq+Zt/0PLO+awqlTBgI5V7z+nZRwPzllN+/QY7uyUj2vjjwHvl6k0JNz8GhaieeK9dRgs/5ajVMh58pZ+eNUKumWc2t70ddE2m5u7X16Ox1v9hLMLz2nJPZf3xosU8t+ncNL/9YX1bjWPvrOGYl31OR1yuYwPZwwnLcoXPj42hE8swmMXNDXW7ynkpS+2VPt5pFbJWw8OCej1ngxes47cd6dUDEUHQK6JpNUdb6KMrViz7bUaceYfxLRpAX6nnYgOZxHX52KUsck1n6QGFOts3PnS0oDrsgHuGN+DsYM61qk+NeGzm7Ef2YphzY94TWUoouOJ6z8eTVp7iv7vuWrPIG7ABOIvmIiilr603+PGum8N5b+/V+1a7LmjSLjwWhQR0fhdDvyuig9wuTaKQqOHKbOXI5PBu1N64f35SSRP9a1S486fgKbvRB59byO5JdX/EFMqZHw4YwTJ0XL8zopRHbkmErmm5hn+9YHH6+PgMQMvfLYJm/NfO+LszilMv/ocEuO0DR5DUyenyMzj763FYv93gqdcLmPGjX0558yUBpt/Ijh5xFB8HQi1BxZqXWqw89mCfQGfjd3pZfGmXLZm6+pU3jGzF22brkHbQNOmOx7Fv57y0hwHsvbnknbl46Rc8zQFncfgjEhCplCesDyNRsGAXhmBy1Er6NstrUGfp10ewb7oXrS44QVaT/2AtJtncyRlAPLEViSNvKVymZgyPpWUy+4lqu9Ylhyp/Tpsm09GcWIP0m54Hm2b7sgjYlCntSdl4kMkDLoap0yFuTiP0oXvkPvePeS+fy8lv79PstxCx5axSBK8+0ceEeMeRxn3n0mHcgWxfS4hus+lFBhcATt1qLBAtG49ZX98QO57d5P77hRKfnsHV3kBkt/XoO+rSqmgbUYsL0wdyMy7zufRG/vwzkNDufrSbqg0igZpz6auj/eF2ybImDP1XB645mxG9mvDzZd25YMHBnBOh5iKTj3UvrXw2CsRHXsdCLUHFmpttLlr3Chl28ES9uab6lTeQwuOED3ousD+s1yB1Gci63OrevprjpSjiIhmZa6Te3/YU+vyth4zMmxAO84+bqZ8fLSGF+66gGyjvcGf7yM/72ZlnhtVXAor8jw8+NNuVhxzEHvuKDSTnsd55asoJzxFTM8hrDx28vHc9v0+NjuSSL3iEbRXv8j27rexS9kJRVQsPlMplpXf4Os6GvdlL+C89Dn83S9Bv+FXHr+iA2qlnH3ZBp7/tYSi/tPRTHoRzYRnaHHrmyQOvY5VuU6Kg+wboFbKeWRCO/TfPoFt75qKSXx+H45DGyn87BE8hhI2Ha2+7r4mfbDIzMajOvbkG2uVfn2Wjslfb6Pc62PgWS05qLdxVz2fv96c9PG+sOzoClK+v4ihCUeZdtXZXN6hjPS5F6E5tjxgeuGxC4+9SRJqDyzUukhn464ahq57dUrm6ku70a5F3TzpwR3ikJVmUbboQ7yGiuNNVUktSbrkLg75kumUXn/nlW88quOcVvE4nB4Ky6xoNErSkqJIiYvA5vaG1fOvTx0l91G+cw1HaMM7C7Iq9zbXqBRcO6wNA9v4+XW/nwXr8qq08aDeGdxyWQ+S4yrmLJTq7Ux/bWW1d+GiPhlMjNqGa8+SgO9KVLcLiL3oTlZlm0/8PrSPReUyY9m3Do++AG3bHkS274VLE8fazNrv/W51edDr9KRqfMhkMvxKLVtKvPRuHR/y9ggHHXIfWnjsp4zo2AWnjN3p4Y3vtrNxb/VNK6D+17Z6rUb8rr+9WW0Uyqj4esv7dMdr0XO0wMRDn+wm0CfCw5O60LdrCxZsKWPL/mKiI1WMH9yRdhlxxP9nv3OL3c1r326rdgb6/67uTIu1L+O3BxmKVChpc/d7lXMlguF3O7FnbqN0/puVm/VAxfuQfsPzNa7Dr5KP1427NJfyPz7AXVxxkI0qpQ0pF9+JOq09cpXYw13QdBFD8XUg1B5YqLUPuHZ0VxJjq0886t8jjfYt4+q1PIcyiuVFclxRLVBGxYe8/s1JO/1KflhbHLBTB/h2RR42n4IOHZN4/OZ+PHpDXzq1SWBjjr5Kfhtz9NxzxVmcfWZVO0OtUiCTB/+4kcnk+CSp5jkCLg86sxODPAn1xGfRnjMWmbpi4p3faaNk7myKimpXX6+hhMKvnqjs1AE8ZbkUfv0/3LrCkLdHOOqQ+9LCY681omOvA6H2wMJBP7FwH8/ceT5TJvaiV6dk+nZL5clbz+OeK85ie74x5PEJXTvtkpQcrWETl8JyG3YPPDh3F5tzDURolAHPi39+4X52Fpl5+LpzeeOBIdx/Qx9evm8QnTq1IqL74KD5R3UfRKZJChqf3enhQLae577Ywd0fH2Lqp5l8W9oF1eXPo0yoGBXyGkvw2cwnrG9BqQH9mh8Cb9Yj+dEv/waf0xZW7RMOOuS+tPDYa48kOGXMDrf0x55Cyexwn/ba7/dLBotT2nlML1nCIB6hT06brC7pgTdXSWMemB/w39VP/C6V6G0nnf/ifUWV2mUokXLm3CZlzZxY5V/2azdJbn1x0PysTre07UCJNPbB6nHd+MyfUsGRw5V5GbL2nDA+p6FMyn71hmpxVP57cZLkMZWHVfuEg5YcJkna92vFf8Ndh1MsgXQDIzx2gUAAwMa9Rbzw+eaA16656EyuGtEZRR3Pr/eYyjBv/wvrnlUgSUR1u4C4vpeijEtBJpNVS+/3uPFYjRhKy/DL5JQ7lHy9spCDucbKNLeNbk+form48g7Q+u53UCXUPK/DazFQ8MUMfObygNfl2mha3fEGyqCn0AkE4Y0Yiq8Dofa8hBa6PnWn1vGM6NuG4+nZMYnRA9ph9/jqXN7yPC8R/SfRcvJsUm+eTeEZY3BqE5DJZNXSOy1GdOvnU/jRfdh/egrn3CeJWzGLB4ZFMrBHSmV86w6akFr2JLLrAI7Z5CeMx6WKIvacqtsP/5eYs0eiiIwNeXuEmw65Ly089lojOvY6EGrPS2ih61NvzTOS2DqeV+4bzNUjOzNucAcendyPm8b1JDE28PnqJ6tfWHSA1Vl6lDGJrMxzM/XHwPsMSJIf26FNWNb+gOR18w8+mxHHwle4cXALNKqKjWVUKjma5AzUg27grh/3nzCeNZk6YnoNRdWiHcejSsxA0XMkMoXYO/54HXJfWnjstadRBvybKaH2vIQ+sV6yr0iyOd2Sz+eTrM7Qx9OUtM3lkZbuLwpJ+R6zTsp589agPnjB/Hekt7/bLI15YL60fle+5HU5Tro8p7FcKt+5Uir46n9SwZdPSsYdyyRdSZGYIxJEh9yXFh57rREeu6DZYra5KTPY+WtjDha7hwvOyqBr20SS4ht+b/LTDb3ZidvjQ6GQERelQa1SnPimGvAYisl7756g11UpbdjdcTLrDpl5+Po+JARYcllbfE47IJ3wHHmBoKkghuLrQKg9L6GDa5PNxXeLDzL9jVX8seEYa3cVMvurrTz67lqKdbaQx9dc9N48A2t25vPoO2u4/cWlTJm1nE8X7KXc6MBal/zlCmTKijMAAqGITqBLhxbcOqEXSnXd9nq3o0KhjQqL59mUdMh9auGxB0V07HUg1J6X0IH11hw9+SVWFq79d/ORfyjR2/l0wV7sTk/YxNtU9cEiM/szy3n5622Vx3m6PD4Wrc/hmU82UGJwnHL+isg4InsOqdZ+/xA3YDx6VEz+emvYPI/TTYfcpxYee3AaZcC/mRJqz0vowNpoc0kzP90YdE32ZQ/Ol4p11rCJt6nqYp1NuurxhUGf85b9RdLKgyWnnL/LWCblfvxQNX+9bPEXktdmCnn9T3cdcp9aeOxBER57M8Hr82O2upCAqAg1WnXdPM6mjNXu5tlPN3IwxxA0zfuPDqNVi5hGjKr5kV1gYtrrK4NeH3JOSx649tyA69Nri9dqwKMrxHZwA3JNJNHdB6KITkARIdpOIAiGGIqvA3X1qJwWA8ZjByn740NKF76LLXsPxcUlJ5XfykMllBrsfLf4IPe/uZp7X13B+z/vorDMisXhDitPrrE0chm9Ov27zvl44qM1aNUnPp+9rtphtWAqKcB+bB+u4mxcJh3rjpSG/PnUlw50ku5/0WqU7Mwz1qm8pTlOfKmdSR51G9rzr2RlqQq7TBsW9T/ddW18ZUfebkp1FvJLLZTrrfiObRQeeyMQFh37r7/+ytixY+nWrRvffPNNjWl//PFHRo4cyYgRI3juuefw+/01pm9I6uJReW1G9H99gv6bJ7BsX4x113JK/u8ZPH+8icdiqHV+0UoFj7+3jh+XHkFvdmKxe1i+NY/7Xl9Jsc7Oeyszw8aTa0w9sl+boKMWk0Z0JqGe1mUH0uszy/FajZiWfYHuk/so/uYpCj59iOIvH6M95ezPr337hpv+fksuR0utSJKEF2iREHyFwYXntGZTVjnZpRZ8fumUy1/7t159uIyZv4fX8zid9Yl85DKTi3eW27hj1gqmzF7OtDdWs+CQFpNeX6v7hcd+6oTFUPzhw4eRy+V89NFH9OrVi+uvvz5gury8PK677jrmz59PfHw8t99+O2PHjmX8+PGNG/DfWJyndt7xoDOS8R/ZQNmvcwLmGzdwEokDr8DqkWrMz+b0sHBtNt/8cSBgPud2bcHlo7rQLqVu56E3RR2hUpBdaOL1/9tOfqkVgAiNkiuGn8Hwvm1IitU2WPmDO8RhX/N/mLf+Ua1NZCoNGbe/gSYhNayeV210qcHOrsxytu0vITZazZiBHTCYnTzz8Qa8vqofI0PPbcWEIZ34atEB7E4PfbqmMqh3SzL1Ns5qnRAW9RG64c5r17vVPPH+usrfvf9y5fAzuHJEZzR+e9D7xXnsdSMsOvZ/mDFjBj169AjasX/yyScUFhby1FNPAfDnn3/yyy+/8NFHHzVmmHXGZzNR9N1zuEtyAl6Xa6NodcebJ9yr2mhx8fj768grsQS8LpPBJ0+MpEVCZF1DbrIYLE6sdg9en5/oCDXxMWpUyoadf+AxlpL3wb2BTw8DEofdSPyAcQ0aQ31TrLPx2HtrKTc6q/x86hVn0a1DEvNWZnIgR09slJqJQzqhUMiY+dlmfP5/P16iI1S8fO8gWqcKf7y5s+NQKU99tCHgNZVSzgczhp/Wn0sNTVgMxdeWoqIiMjIyKnVGRgZFRUUhi+dUPSqP14PPZgyar99pA8l/wvw8Ph81/V0mSRX3hIsnFwq96ZiB+Dgt7TPi0EYoWXaw4T1un8setFMHcObtx+/1hMXzqY02WJy899Ouap06wDs/7cLu8nDnxJ48d+cAbhrfk9hoDc9+sqlKpw5gdXh4Z+5OdGZnWNVP6Hr22N12Nu4N/rns8foxWV218qWlY5vwmkrxWvT4HWbY/5vw2GtBo3TsEyZM4Lzzzgv4z+fzNUYIDcKpelTHzH40GZ2D5qtu0RYUqhPml2Nw0LdHetB8zjojmVWZ5WHjyZ0u2oUyaJsAyONSkSkUYRPvibTe4mLnkbKg9Vmw+ihyZGzLN7FobzE/Lz8SNO3+bD0Gqyus6id0PXvsRbuIiQq+uRCASiE/oQ/tsejRH9xNwVf/o+DzRzGs+QlPdCuk/K01ly88djEUXxcszlP3qNSmAgo+fRik6pP/Uq96gqhO59QqP53JyTMfrkdnqvptSq2U8+p9g8kxO+nTLjEsPLnTRV/YLgrjgjk4sncGfG8y7ngTbUrrsIn3RLprUhRTX10R9PegV6dknpjcDx+QXWrlh9/3s/ufD/8AvPPwUNqmxdY5Prvby+FiC51So4nWhM/zOl10TT5yrhHueSXwO5MSH8Er0waTpHEHvd/jclH45eP4LPoq98ojY2l580sVR/MKjz0oTapjDzR5bsyYMUyYMKGRI607frcTZ+5+yn5/F5/VCFR460kjbiaycz8UEdG1zqvUYGfeykyWbcnD4/XRt1sqN1zcjfTkSJSK03c9eyjxmEop+vY5vIb/DknKSL50CtFdz0euaTr71ZcbHUx9dQU2hyfg9Rsv6crEoWegkMuQJImFa4/y0fy9AdMmxGh44/4LSYo79fpbbG7KTQ6WbsnFYvcwsFc6HVvF1ylPQf1itbuZvzqLH5YcrvJzlVLOzLvOp2u7xKD7G/i9Hgwr/w/TpgUBr8ecPZKkkZORqzT1HndzISw89oULFzJ48GD+/PNP5syZw+DBg8nMzARgzpw5fPfddwC0bt2au+++myuvvJKLLrqIVq1acdlll4Us7rp4VHK1Fql1DyKvmknGba/R8tZXSb/1dQ7F9sQu05xUfhERKiaP6c47Dw/l1fuHcPek3rROjcHh8YeVJxcKvexAMeVGB5n5RpZszmXD3iJK9Da8vhPPYaiLVsW1IPW6Z0mY9CRxAyaQNPIWWk55m9z4HtgkZdg8n9porUbJ1SMCW0eRWiWDerdEIa84T/2vfcX0655GfHTgD93rLu6KRnPq9d+fZ+THZYeZ9tpKFqw+yoqteTz/2WYef28dJXobS/YXh/x5na76vz5ydKSacee35pUpfRl4VgZd2iUwcUhH3p3en85pmopOPYgP7bcZsO5dFfD9AbDuXYPfYRUeew2ERcc+ZswYVq9ezc6dO9myZQurV6+mU6dOANx3331cc801lWmvvvpqli5dytKlS3n22WdRhPAbaV09qjVHdFz+1QFWlmnQpLVnRb6HB+YGPp/6RFqtUrC9wMTkr7eyMVtfL/E1db3pqI4EjYqZn23i/jdW8dYPO3jx881Me20lh44Z2FdgatDyV+S5uX2ZnaMdLiau36WsKIS7f9wXNs+ntnptVjlD+7Tm2lFdquwN0CYthodu6kuW3l4l/WGdndlTB3J25xT++VKWFKdl2lVnk+/yVq5LP9l4tuToKTPYmb8qi+MpLLfx+cL9HCgwhfx5na76eB85Jn85XZZfy/ShKp6+tT839LKT/tNolNnLA6av1HY9kr+GuVf/2JfCYw9Oo2xc20wJ9V7NQtesdSaH9MT7awPuYz7xkQVSYbk1rOINd22yuaTMQpOUmW+QcovNUpnBLq06FHwveJ3ZIWUWGKVjxSap3GiXrM66lW+0uaTnazoD4KFfpcxCY9g8r9NN19d+6j6bUSr9/f1qZwT886/4l9ckn8su9oqvgbDy2AWC+qSw3MqdLy0Lev3OiT0Zc0GHRoxIUBcsdjfPfryRQ7nBzwD4YMZwWqbUfn6KIDzxGEoo+PQh/C57lZ/LVFpa3vYK6sSMIHcKIEyG4psqofa0hK5ZB5vs9Q9Z+SZ25BrCJl6ha9YymYyu7YNv2hQXrcbh8YVNvKebrk8fWhmfQsvJs4jqej7IFSCTE9mlPy1vfA5VZPSJ8wu1hy489qZLqD0toWvWckXNr3fbtBg+Wp0VNvEKfQKdVc45PdJRKwO36+XDzuCDtUfDJ94w0pLPh8NYTjutE4u+cTz2umiZTI6qbBcpCR7a3PoSbaZ+QMp5I1DPvwlZbfILtYcuPPamS6g9LaGFx3666Q2ZpdKBbJ102wuLK9vy8hm/ST8sOSiVm+whjy/c9OK9RZLTpJP0q36Qsl+9UcqaOVE69u49kmXvWslhNoalxy7OY687wmMXNGvKjHZe+HwzWfmmyp9FapU8dWt/zmwbL9b5N1H0ZidWuxuvTyI6UkV8tAa1SrTl8fhsJkrmz8GZs6vatYSh1xPX91Lkqpp3iRM0PcRQfB0Itacl9In17iIzT04+jzfuv5BpV53N45P78daDQzizbUJYrPNffbgUp9mIR1+EsyyfkqJibGH0/MJVJ8ZqSYiP4LDBTkSECrVKEVbxhYu2lBcH7NQBjGt+xGzQ1Vt5IfethcdeiejY60A4eWhNWW8/ZsBocVJUbiNOIafM4MDh8rC+HvJ/9rf9bM030qlVPNqECF5elcWOQjNKhTzk9T9QYKCjXEf5jzPJe38qhR/dh+vnZ/Bk78DntIc8vuP1pqM6sootlBrsFOlsFOhsfL85N2ziE7qqPlhkxnpoE8GQvG4s+jI2ZIWfx15nHU6xBNINTaMM+DdTwsFDa+p6zeESKbvQJN09e1mlZzruoV+ld+bukMqMdunPMIu3PrWzvEA6OuvqgGt17dm767zuu751QalFmvnZRumyByva6e7Zy6SN+4okvdkRFvEJXVXbXB6pdMX3QdeDZ82cKBlzDtZbeSH3rYXHXonw2AUhpcxg577XV2KxV1+adsn57Zk8thtadc2npTVF/F43usWfY9mxOOB1dWo70q55CmVUXCNHFpgyg50H5qzGaHFVu/bM7f05t0tqCKISnAhXaS4FH98f8JpcE0nLO95AFZvcyFEJGhoxFF8HwsFDa8ra5vKy+UBJwE4dYPGmHAp19rCJtz6132nDkR3Y+wRwl+TgczvDIl6r08PaXYUBO3WAj+btwWB2htXzFbpCF7g1xJwzKkCryUi69G52lvvrrbyQ+9bCY69EdOx1INQeWlPXmaUW9v7t7wXC65MoMTrCJt761DK5Ark2KmjdZQoVVrc/LOLNLrWybldh0FgLy204XN6wer5CV+hbvtuHu/c4UifNQJNxBoqYJCI69aHlLbPJjejAgz/trbfyQu5bC4/9XxplwL+ZEmoPralrm8sjfbpgb9C9v8c8MF86km8Im3jrW5t2rQjqfZb+9p5ks9nCIl69xSE9/l7g/QD++VdUbg358xS6Zm03G6X8/ALJbrU0SP4h962Fx16J8NgFISW/1MKU2csDXjujdTxP39afuCBHgDZ1vFYjpb++VW05kjI+lfTrn0UVlxKiyKqzYU8RL36xOeC1Xp2SeOymfkRHivXQAkE4IIbi60A4eGhNXZfZPdx9ea9qzzYhRsMD157D9nxjWMVbn9qhjEI+/A5Sr3qCiE7nENGuF3EX303q9c+hiksJeXz/1V3aJtCrU/VJVlFaJXdM6EV0pDqs4hU69Fp47MJjb5KEg4fW1PV9P+4kNSOWD2YM58oRnRnapzXTrz2H16dfyFGjg6cXNL3zy09GX/nVfrb6WpE68SFMg6cwY28sK/I8YRPfPzohVsvk8T25/fJedGmXQLv0WCYO7cSM2/qT//ekunCKV+jQa+GxC4+9SRJqz6y5aZvLI20/ppeszvCIR+jqes3hUqnc5JCMFqdktrua9T4DQjdhzz3UHrrw2AUCgUAgENQXYii+DoTawxJaaKGFDlctPHbhsTdJQu1hCS200EKHqxYeu/DYmySh9rCEFlpoocNVC49deOwCgUAgEAjqATEUXwdC7WEJLbTQQoerbsoeu9dhpaS4lD/WHeX9n3exdHMOpcWl+ByW+om1gREdex0ItYcltNBCCx2uuql67F6vn4N5Zqa8sYn3ftnDovU5zPlhF1Pf2sLRYht+vyQ89uZMqD0soYUWWuhw1U3VYy/V26RJjy0MeCbCdU8tksoMduGxCwQCgUDQVNi0t4iZnwc+FwFg1j0D6d4hqREjOnnEUHwdCLWHJbTQQgsdrrpJeuwuK2VGBzWhNzvBZREee3Ml1B6W0EILLXS46ibpseesoWOreGqiVYtoOLpKeOzNlVB7WEILLbTQ4aqbqseuMzmku2YtDeixP/DmSslgdgqPXSAQCASCpkSJ3s4rX2/lUK6h8mdnnZHM9KvPJjk+MoSR1Q4xFF8HQu1hCS200EI3Fd0kPPa/dWqkj/9dkc4Hjwzl1WmD+fDRoTw6Jplkrbd+Ym1gRMdeB0LtYQkttNBCNxXdJDz2Sr2CuJ+uoKVuJWe2TSCjfCUxP18p9oo/HQi1hyW00EIL3VR0U/HYG0U3MMJjFwgEAoGgGSGG4utAqD0roYUWuvba6vSQU1CCS1eIuzwfl6mczUfLwia+5q6bkscuzmM/jQm1ZyW00ELXTkuSH7++ANXiNyj44F7yP7yP4s8fpVX5LkrL9CGP73TQTctjb2Dd0DTKgH8zJdSeldBCC1077TaUSNmvXC9lzZxY7Z95z2rJ7/eHVbzNUQuPXXjsAoFAUC9Ifh/Gdb9gWP19wOuKmCRaTp6FMiaxkSMTCBoGMRRfB0LtWQndtLTV5aG0uBh73kGse9fgKDhCcVEx1jCJr7lqp82KPWs7wfBZdPjdzrCJt7lq4bELj71JEGrPSuimpf36Qhxzn6b4qyco/fVNir6YgWf+TPym0rCIr656b4GJWMmGT1+Ex1CMTqfn49VHQx5frtGFXBNFcGTIFIqQP7/mroXHfpp57PPnz5fGjBkjde3aVfr666+Dptu4caPUq1cv6bLLLpMuu+wy6YorrmjEKKsTas9K6KajPaZyKefNWwN6vLnvTZU8Fn1YxXuy2uuwSZaDm6Rjb99VWa/8Lx6XTAXZksXhCml8FqdbsmXtDPjss2ZOlAq/f0HyOqxh9TyboxYe+2nmsR8+fBi5XM5HH31Er169uP766wOm27RpE7Nnz+aXX35p5AgFgrphz95N8f89G/R6xi0vo03v2IgR1S/2zO0U//BCtZ/LNJG0uu1VVPGpIYjqX7w2E7rFn2Hbv7bKzxXR8WTcOBNVQnqIIhMI6p+wGIrv3LkznTp1Qi4Pi3BqTag9K6Gbhra5PHjK82t6lfAaSrC6wiPek9VOsx7dks8D1kty2TFvX4Lk84Y0XmVUHHEjbibx6qeJPPM8Itr1Imn07cRd8wKuyOSwep7NVQuPXXjsQcnJyWHChAlMmjSJefPmhTSWUHtWQjcNvTlbjyoxo6ZXCWV8ChuydGER78lqu82OR18YtG6OrO34nbaQx7vymJNb/jKj63cLqVc8woH4Plz2xX7WHgmv59lctfDYm5nHPn78eKlfv34B/3m93sp0jz76aI0eu8VikcxmsyRJkpSbmysNHz5cWrduXYPHH4xQe1ZCNx3tMZVL2a/fHNDjPfbOFMlj1oVVvCejnfoSKeuFK4J62PlfPC557ZawiVdo4bGHXDcwYeGx/8OMGTPo0aNHUI/9eGbNmkV0dDRTp05t4MgEgrohSRLuslyKvn0Gv/3f4ThFTBLp1z2NOqllCKOrG36Xg9KF72A/uDHg9RaXP0x0l/6NHJVAcPrSpIbiS0tL+efvEKPRyLp16+jSpUvI4gm1ZyV009EymQxPbAbR175E6jVPkTT6DtKuf47IK5/DHd0i5PHVRdskJUnDbkQRncDxaNv3RpXROaziFVp47CHXDUxYdOwLFy5k8ODB/Pnnn8yZM4fBgweTmZkJwJw5c/juu+8AWLx4MWPGjGHcuHFcf/31jBs3jhEjRoQs7lB7VkI3Lb02s5yJX+5nszuNuHNHsdGezOVfNQ+PV5WQSty1M1FfeBPa1t2I6NCbhMtnkN3zWlbluUIen9Ch18Jjb2Yee3Ml1J6V0EKHm96YWSbZLSbJ53JIFmfo4xE6fLTw2E9Tj10gEAgEAkHdCIuh+KZKqD0roYUWWuimooXHfpp57E2VUHtWQgsttNBNRQuPXXjsTYJQe1ZCCy200E1FC49deOwCgUAgEAhOATEUXwdC7VkJLbTQQjdVLTz2hkN07HUg1J6V0EI3J70lR89by46ETTxCN2HPPdQeuvDYmy6h9qyEFro5aLvVLLn1xZLl8FbJcGSn5DSUSj6PO2ziE7oJeu6h9tCFxy4QCE5XfDYThjU/YN62GKj4KJKptKSMnUpkh97INRGhDVAgaIKIofg6EGqPSmihm7K2O90Ydi7HvO0v/unUASSPk9JfXsNtLGHp/uKwiVdo4bELj/00INQeldBCN2VtM+qwbvqVwEgY189jX2552MQrtPDYhcd+GhBqj0pooZuyduoKg57hnjVzopT74XQpOy984hVaeOzCYxcIBIIa8JrLyfvwPiS3M+D1yDP60GLcdOGzCwQniRiKrwOh9qiEFropa7cqmqjeFxGM2AETWXnUHDbxCi08duGxnwaE2qMSWuimrNdkGShtNwRtu15URUbisBspksXzzG/7wiZeoYXHLjz204BQe1RCC93U9eK9RZLDbJCcxUcl/YZfpbLNf0pOXaHkc9rDIj6hhcfeILqBER67QCAQCATNCDEUXwdC7VEJLbTQQjdVLTz2hkN07HUg1B6V0EILLXRT1cJjb0AaZcC/mRJqj0pooYUWuqlq4bE3HMJjFwgEAoGgGSGG4utAqD0qoYUWWuimqoXH3nCIjr0OhNqjElpooYVuqlp47A1Iowz4N1NC7VEJLbTQQjdVLTz2hkN47AKBQCAQNCPEUHwdCLVHJbTQQgvdVLXw2BsO0bHXgVB7VEILLbTQTVULj70BaZQB/2ZKqD0qoYUWWuimqoXH3nAIj10gEAgEgmaEGIqvA6H2qIQWWmihm6oWHnvDITr2OhBqj0pooYUWuqlq4bE3II0y4N9MCbVHJbTQQgvdVLXw2BsO4bELBAKBQNCMEEPxAoFAIBA0I0THLhAIBAJBM0J07AKBQCAQNCNExy4QCAQCQTNCdOwCgUAgEDQjRMcuEAgEAkEzQnTsAoFAIBA0I0THLhAIBAJBM0IZ6gAAnn32WTZs2IBarSYyMpInnniCnj17Bkz77rvvMm/ePAAmTJjAPffc05ihCgQCgUAQ1oRFxz548GAef/xxVCoVK1as4P7772fp0qXV0m3ZsoU///yThQsXAjBp0iT69etH3759GztkgUAgEAjCkrAYih86dCgqlQqA3r17U1xcjN/vr5Zu0aJFjB8/Hq1Wi1arZfz48SxatKixwxUIBAKBIGwJi479v3z77bcMGTIEubx6aEVFRWRkZFTq9PR0ioqKGjM8gUAgEAjCmkYZip8wYQKFhYUBr61fvx6FQgHA77//zm+//ca3337bGGEJBAKBQNDsaJSO/Z/JbjWxZMkS3njjDb744guSk5MDpklPT6/yB0JRURHp6en1FqdAIBAIBE2dsBiKX7FiBS+99BKffvoprVq1Cppu9OjRzJ8/H6fTidPpZP78+Vx88cWNGKlAIBAIBOFNWJzH3r9/f1QqFYmJiZU/++KLL0hISOCJJ55g2LBhDB8+HIC3336b+fPnAzB+/HjuvffeUIQsEAgEAkFYEhYdu0AgEAgEgvohLIbiBQKBQCAQ1A+iYxcIBAKBoBkhOnaBQCAQCJoRomMXCAQCgaAZITp2gUAgEAiaEaJjFwgEAoGgGSE6doFAIBAImhGiYxcIBAKBoBkhOnaBQCAQCJoRomMXCAQCgaAZcdp27M8++yyjR4/msssu4+qrr2bPnj1B07777ruMGDGCESNG8O677zZilDXz66+/MnbsWLp168Y333wTNN2mTZs466yzGDduHOPGjWPSpEmNGGXN1LYOAD/++CMjR45kxIgRPPfcc/j9/kaKsmYcDgfTp09n5MiRjB49mhUrVgRMF47tkJ2dzVVXXcWoUaO46qqryMnJqZbG5/Px7LPPMmLECEaOHMncuXMbP9AaqE0d3n77bQYMGFD57J999tnGD7QGZs+ezbBhwzjzzDM5fPhwwDTh3g61qUO4t4PBYOD2229n1KhRjB07lqlTp6LX66ulq+3vfMiQTlOWL18uud3uyv8fPnx4wHSbN2+WxowZIzkcDsnhcEhjxoyRNm/e3JihBuXQoUPSkSNHpIcfflj6+uuvg6bbuHGjNGHChEaMrPbUtg65ubnSoEGDJJ1OJ/l8PumWW26R5s2b13iB1sDbb78tPfHEE5IkSVJ2drZ0/vnnS1artVq6cGyHG264QZo/f74kSZI0f/586YYbbqiWZt68edItt9wi+Xw+SafTSYMGDZLy8vIaO9Sg1KYOb731ljRr1qzGDq3WbNmyRSosLJSGDh0qHTp0KGCacG+H2tQh3NvBYDBIGzdurNSzZs2SHnvssWrpavs7HypO22/sQ4cORaVSAdC7d2+Ki4sDfgNctGgR48ePR6vVotVqGT9+PIsWLWrscAPSuXNnOnXqhFzedJuxtnX466+/GDFiBImJicjlciZNmhQ27fDHH39w1VVXAdCuXTt69OjB6tWrQxzVidHpdOzfv58xY8YAMGbMGPbv31/tG8qiRYuYNGkScrmcxMRERowYwZ9//hmKkKtR2zqEO3369CE9Pb3GNOHcDlC7OoQ78fHxnHfeeZW6d+/eFBYWVksX7r/zTbdHqEe+/fZbhgwZErBzKSoqIiMjo1Knp6dTVFTUmOHVCzk5OUyYMIFJkyYxb968UIdz0hzfDhkZGWHTDoWFhbRs2bJSp6enU1xcHDBtOLVDUVERqampKBQKABQKBS1atKj2XAP9DgSrX2NT2zoA/P7774wdO5ZbbrmFHTt2NHaodSac2+FkaCrt4Pf7+e677xg2bFi1ayfzOx8KlKEOoKGYMGFCwL+0ANavX1/5QfD777/z22+/8e233zZmeLWitnU4Ed27d2fVqlXExMSQl5fH5MmTSU1N5fzzz6/PcANSX3UIJSeqQ20JZTuc7lx99dXcddddqFQq1q1bx913382iRYtISEgIdWinFU2pHZ5//nkiIyO5/vrrQx3KSdNsO/bafBtasmQJb7zxBl988QXJyckB06Snp1f5UC8qKmq04ab6+kYXHR1d+f+tW7dmxIgRbN++vVE6lPqqw/HtUFhYGDbtkJGRQUFBAYmJiUDFO/Lf4bx/CGU7BCI9PZ2SkhJ8Ph8KhQKfz0dpaWm15/rPs+/VqxdQ/ZtjKKltHVJSUir//4ILLiA9PZ0jR47Qr1+/xg75lAnndqgtTaUdZs+ezbFjx/jggw8CjuTW9nc+VJy2Q/ErVqzgpZde4tNPP6VVq1ZB040ePZr58+fjdDpxOp3Mnz+fiy++uBEjrTulpaVIkgSA0Whk3bp1dOnSJcRRnRyjRo1i6dKl6PV6/H4/c+fODZt2GD16ND/88ANQMdS+Z88eBg0aVC1duLVDUlISXbt2ZeHChQAsXLiQrl27Vn5Y/cPo0aOZO3cufr8fvV7P0qVLGTVqVChCrkZt61BSUlL5/wcOHKCgoID27ds3aqx1JZzbobY0hXZ4/fXX2bt3L++++y5qtTpgmtr+zocKmfTPJ81pRv/+/VGpVFU+AL744gsSEhJ44oknGDZsGMOHDwcqlmjMnz8fgPHjx3PvvfeGIuRqLFy4kJdffhmz2YxKpSIiIoLPPvuMTp06MWfOHFq0aME111zDN998w3fffYdSqcTn8zF+/Hhuu+22UIcP1L4OAN9//z2ffPIJUPHX/lNPPRUWQ/l2u50ZM2Zw4MAB5HI5Dz/8MCNGjAAI+3bIyspixowZmM1mYmNjmT17Nh06dOD2229n2rRp9OzZE5/Px3PPPce6desAuP322ysnDoUDtanDo48+yr59+5DL5ahUKqZNm8aFF14Y6tArmTlzJosXL6a8vJyEhATi4+P5/fffm1Q71KYO4d4OR44cYcyYMbRr1w6tVgtAq1atePfddxk3bhwfffQRqampNf7OhwOnbccuEAgEAkFz5LQdihcIBAKBoDkiOnaBQCAQCJoRomMXCAQCgaAZITp2gUAgEAiaEaJjFwgEAoGgGSE6doFAIBAImhGiYxcIBEEZNmzYSW2bWxv+97//MWrUKLp06cIvv/xSr3kLBALRsQsEgkamS5cuPPPMM3Tr1i3UoQgEzZJmu1e8QCBoGEwmE4888gi7du3C5/Nxzjnn8Oyzz5KWlgZAXl4eM2bMYP/+/Zx11lm0b98ei8XCq6++CsB1110HgEajCVkdBILmjPjGLhAITgq/38/EiRNZsWIFK1asQKPR8Nxzz1Vef+ihh+jVqxebNm1i6tSp/PrrryGMViA4/RAdu0AgOCkSEhIYNWoUERERREdHM2XKFLZs2QJUnLq3Z88epk2bhlqtpk+fPgHPsxYIBA2HGIoXCAQnhcPh4KWXXmLNmjWYTCYAbDZb5ZGpcXFxREREVKZPT0+nqKgoVOEKBKcd4hu7QCA4KT777DOys7P58ccf2b59O99++y0AkiSRkpKCyWTC4XBUphedukDQuIiOXSAQ1IjH48HlclX+M5vNaDQaYmNjMRqNvPPOO5VpW7ZsSY8ePXj77bdxu93s2LGDFStWVMnP7XbjcrmQJAmv14vL5cLv9zd2tQSCZos4tlUgEARl2LBhFBQUVPnZxIkTyc/PZ+/evbRo0YLJkyfz9NNPs2/fPpRKJbm5uZVnVffq1Ys2bdrg8/l48cUXAbjhhhvYvHlzlTy/+uorzjvvvEarl0DQnBEdu0AgaFCmT59Ohw4dmDZtWqhDEQhOC8RQvEAgqFd2795Nbm4ufr+f1atXs2zZMkaMGBHqsASC0wYxK14gENQr5eXl3HvvvRiNRtLS0sQucwJBIyOG4gUCgUAgaEaIoXiBQCAQCJoRomMXCAQCgaAZITp2gUAgEAiaEaJjFwgEAoGgGSE6doFAIBAImhH/D22d1ekVjdvBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "ax.grid(b=None)\n",
    "ax.set(facecolor='w', aspect=1)\n",
    "\n",
    "sns.scatterplot(x='Lag1', y='Lag2', data=df_test, hue='Direction_Up', s=75, zorder=2)\n",
    "\n",
    "\n",
    "x_min, x_max = plt.xlim()\n",
    "y_min, y_max = plt.ylim()\n",
    "\n",
    "nx, ny = 100, 100\n",
    "xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))\n",
    "Z = np.c_[xx.ravel(), yy.ravel()]\n",
    "plt.scatter(Z[np.where(qda.predict(Z) == 1)][:, 0], Z[np.where(qda.predict(Z) == 1)][:, 1], \n",
    "            s=1, c='tab:blue', alpha=0.7, zorder=1)\n",
    "plt.scatter(Z[np.where(qda.predict(Z) == 0)][:, 0], Z[np.where(qda.predict(Z) == 0)][:, 1], \n",
    "            s=1, c='tab:orange', alpha=0.7, zorder=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **4. K-nearest neighbours.**\n",
    "We'll now see how a nonparametric model performs against parametric ones. Again, `statsmodels` does not support $K$-nearest neighbours, so we'll use `sklearn`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix:\n",
      " [[43 58]\n",
      " [68 83]] \n",
      "Score: 0.5\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn1 = KNeighborsClassifier(n_neighbors=1)\n",
    "knn1.fit(X_train2, y_train)\n",
    "\n",
    "print(\"Confusion matrix:\\n\", sklearn.metrics.confusion_matrix(knn1.predict(X_test2), y_test),\n",
    "     \"\\nScore:\", knn1.score(X_test2, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's... not great. Let's try to increase $k$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion matrix:\n",
      " [[48 55]\n",
      " [63 86]] \n",
      "Score: 0.5317460317460317\n"
     ]
    }
   ],
   "source": [
    "knn3 = KNeighborsClassifier(n_neighbors=3)\n",
    "knn3.fit(X_train2, y_train)\n",
    "\n",
    "print(\"Confusion matrix:\\n\", sklearn.metrics.confusion_matrix(knn3.predict(X_test2), y_test),\n",
    "     \"\\nScore:\", knn3.score(X_test2, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slightly better. Can we improve this further?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k = 1 score: 0.5\n",
      "k = 2 score: 0.48412698412698413\n",
      "k = 3 score: 0.5317460317460317\n",
      "k = 4 score: 0.5158730158730159\n",
      "k = 5 score: 0.48412698412698413\n",
      "k = 6 score: 0.49603174603174605\n",
      "k = 7 score: 0.4642857142857143\n",
      "k = 8 score: 0.48412698412698413\n",
      "k = 9 score: 0.49603174603174605\n",
      "k = 10 score: 0.5198412698412699\n",
      "k = 11 score: 0.5317460317460317\n",
      "k = 12 score: 0.5158730158730159\n",
      "k = 13 score: 0.503968253968254\n",
      "k = 14 score: 0.45634920634920634\n",
      "k = 15 score: 0.48412698412698413\n"
     ]
    }
   ],
   "source": [
    "for k in range(1, 16):\n",
    "    knn = KNeighborsClassifier(n_neighbors=k)\n",
    "    knn.fit(X_train2, y_train)\n",
    "\n",
    "    print(\"k =\", k, \"score:\", knn.score(X_test2, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks like we can't. For comparison, here are the decision boundary visualizations (in somewhat low definition) for $k=1, 5, 10$ and $15$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12,12))\n",
    "\n",
    "k = [1, 5, 10, 15]\n",
    "i = 0\n",
    "\n",
    "for ax in axes.flat:\n",
    "    ax.grid(b=None)\n",
    "    ax.set(facecolor='w', aspect=1, title=f\"k = {k[i]}\")\n",
    "    \n",
    "    plt.sca(ax)\n",
    "\n",
    "    x_min, x_max = plt.xlim()\n",
    "    y_min, y_max = plt.ylim()\n",
    "\n",
    "    nx, ny = 50, 50\n",
    "    xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))\n",
    "    Z = np.c_[xx.ravel(), yy.ravel()]\n",
    "    \n",
    "    knn.set_params(n_neighbors=k[i])\n",
    "    \n",
    "    plt.scatter(Z[np.where(knn.predict(Z) == 1)][:, 0], Z[np.where(knn.predict(Z) == 1)][:, 1], \n",
    "            s=5, marker='o', c='tab:blue', zorder=1)\n",
    "    plt.scatter(Z[np.where(knn.predict(Z) == 0)][:, 0], Z[np.where(knn.predict(Z) == 0)][:, 1], \n",
    "            s=5, marker=\"o\", c='tab:orange', zorder=1);\n",
    "    \n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The decision boundary appears to smoothen somewhat as $k$ increases, with fewer \"pockets\" of color and larger overall areas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **5. Application: Caravan Insurance Data.**\n",
    "We wrap up with the `Caravan` dataset, available from the ISLR package and provided here as a .csv file. This dataset consists of 85 predictors measuring demographic charactersitics for 5,822 individuals.\n",
    "\n",
    "Our dependent variable is `Purchase`, indicating whether a given individual purchases a caravan insurance policy. Only 6% of the people in the dataset purchased one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     5822\n",
       "unique       2\n",
       "top         No\n",
       "freq      5474\n",
       "Name: Purchase, dtype: object"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "caravan = pd.read_csv(\"data/Caravan.csv\")\n",
    "caravan['Purchase'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main issue with KNN is that of scale: since we look at the points _nearest_ to our obesrvation to perform a classification, we need to have a notion of distance that is robust to different scales and units (eg. a difference of USD $1000$ in annual salary is small, but a difference of $50$ years in age is big).\n",
    "\n",
    "The best way to insure we are judging things on the same scale is to _standardize_ our data, by subtracting the mean from every feature (hence all features have a mean of 0) and dividing each feature by its standard deviation (so all features have a standard deviation of 1).\n",
    "\n",
    "Note: This is not the only possible way to scale our data. See [here](https://sklearn.org/auto_examples/preprocessing/plot_all_scaling.html) for a comparison of scalers `sklearn` has to offer and their uses.\n",
    "\n",
    "First we look at the mean and standard deviation of (some of) the features in our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:\n",
      " MOSTYPE     24.253349\n",
      "MAANTHUI     1.110615\n",
      "MGEMOMV      2.678805\n",
      "MGEMLEEF     2.991240\n",
      "MOSHOOFD     5.773617\n",
      "              ...    \n",
      "AZEILPL      0.000515\n",
      "APLEZIER     0.006012\n",
      "AFIETS       0.031776\n",
      "AINBOED      0.007901\n",
      "ABYSTAND     0.014256\n",
      "Length: 85, dtype: float64 \n",
      "\n",
      "Standard deviation:\n",
      " MOSTYPE     12.846706\n",
      "MAANTHUI     0.405842\n",
      "MGEMOMV      0.789835\n",
      "MGEMLEEF     0.814589\n",
      "MOSHOOFD     2.856760\n",
      "              ...    \n",
      "AZEILPL      0.022696\n",
      "APLEZIER     0.081632\n",
      "AFIETS       0.210986\n",
      "AINBOED      0.090463\n",
      "ABYSTAND     0.119996\n",
      "Length: 85, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "X = caravan.drop(columns='Purchase')\n",
    "y = caravan['Purchase']\n",
    "\n",
    "print(\"Mean:\\n\", X.mean(),\n",
    "     \"\\n\\nStandard deviation:\\n\", X.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To scale our data, we use the `StandardScaler` class from `sklearn.preprocessing`; we fit the scaler to our predictor dataframe, then apply the `transform()` method to it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:\n",
      " MOSTYPE    -1.015639e-16\n",
      "MAANTHUI   -5.891695e-16\n",
      "MGEMOMV     5.059123e-17\n",
      "MGEMLEEF    2.968433e-16\n",
      "MOSHOOFD    3.783378e-17\n",
      "                ...     \n",
      "AZEILPL    -1.518214e-16\n",
      "APLEZIER   -9.635599e-16\n",
      "AFIETS     -3.440795e-16\n",
      "AINBOED     6.019413e-16\n",
      "ABYSTAND   -1.696465e-16\n",
      "Length: 85, dtype: float64 \n",
      "\n",
      "Standard deviation:\n",
      " MOSTYPE     1.000086\n",
      "MAANTHUI    1.000086\n",
      "MGEMOMV     1.000086\n",
      "MGEMLEEF    1.000086\n",
      "MOSHOOFD    1.000086\n",
      "              ...   \n",
      "AZEILPL     1.000086\n",
      "APLEZIER    1.000086\n",
      "AFIETS      1.000086\n",
      "AINBOED     1.000086\n",
      "ABYSTAND    1.000086\n",
      "Length: 85, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(caravan.drop(columns='Purchase'))\n",
    "X_scaled = pd.DataFrame(data=scaler.transform(X), columns=X.columns)\n",
    "print(\"Mean:\\n\", X_scaled.mean(),\n",
    "     \"\\n\\nStandard deviation:\\n\", X_scaled.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scaler.transform()` returns an array, so if we want to keep our column names we can make it into a dataframe. Note that the mean and standard deviation is not exactly equal to 1, but for the purpose of predicting things, that's fine.\n",
    "\n",
    "We now split our observations: for the test, we'll take the first 1000 rows, and the training set will be the rest. We then fit a KNN model (with $K = 1$) on our data and evaluate the performance on the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.882"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train = X_scaled.iloc[1000:]\n",
    "X_test = X_scaled.iloc[:1000]\n",
    "y_train = y.iloc[1000:]\n",
    "y_test = y.iloc[:1000]\n",
    "\n",
    "knn_car = KNeighborsClassifier(n_neighbors=1)\n",
    "knn_car.fit(X_train, y_train)\n",
    "knn_car.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our error rate is just under 12%. Not bad, eh? Except..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.059"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.value_counts()['Yes'] / y_test.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...only 6% of purchases are a 'Yes', so predicting 'No' for every observation would result in a 6% error rate.\n",
    "\n",
    "That said, maybe the total error rate is not the right metric we should use; ultimately, if our plan is to sell insurance to clients, we want to target the customers that are more likely to buy our product. So a better question to ask is, when our model preditcs someone will purchase insurance, how often is that prediction true?\n",
    "\n",
    "Let's display our confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[873,  50],\n",
       "       [ 68,   9]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sklearn.metrics.confusion_matrix(knn_car.predict(X_test), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Among the 77 customers KNN predicts will buy insurance (second row), 9 really do (bottom right). So we are right in $11.7\\%$ of cases, which is far better than random guessing (which would be right in at most $6\\%$ of cases).\n",
    "\n",
    "Let's see whether we can improve our rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[921,  54],\n",
       "       [ 20,   5]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_car.set_params(n_neighbors=3)\n",
    "sklearn.metrics.confusion_matrix(knn_car.predict(X_test), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $K = 3$, we have a true negative rate of $20\\%$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[930,  55],\n",
       "       [ 11,   4]])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn_car.set_params(n_neighbors=5)\n",
    "sklearn.metrics.confusion_matrix(knn_car.predict(X_test), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $K = 5$ we reach $27\\%$. There is not much point in increasing $K$ further, however: once our number of neighbors becomes large enough, the KNN algorithm will automatically pick up more \"No\"'s than \"Yes\"'s, since these are overwhelmingly present in the data.\n",
    "\n",
    "To conclude, we compare KNN with logistic regression. Note: the fit with default parameters was throwing a \"max iterations reached\" warning so I increased it to 125 (default is 100) so it converges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[934,  59],\n",
       "       [  7,   0]])"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_car = LogisticRegression(max_iter=125)\n",
    "logit_car.fit(X_train, y_train)\n",
    "sklearn.metrics.confusion_matrix(logit_car.predict(X_test), y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our model does not pick up any true \"Yes\". We can try to play with the probability threshold a bit; what if we make it declare a customer as a \"yes\" if the probability is $25\\%$ or above?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True positives: 11 \n",
      "Total predicted: 35 \n",
      "Accuracy: 0.3142857142857143\n"
     ]
    }
   ],
   "source": [
    "true_pos = np.intersect1d(np.where(logit_car.predict_proba(X_test)[:,1] > 0.25)[0], \n",
    "               np.where(y_test == \"Yes\")[0]).size\n",
    "total_pos = np.where(logit_car.predict_proba(X_test)[:,1] > 0.25)[0].size\n",
    "print(\"True positives:\", true_pos,\n",
    "     \"\\nTotal predicted:\", total_pos,\n",
    "     \"\\nAccuracy:\", true_pos/total_pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we get an accuracy of $31\\%$. Not bad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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