logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "from scipy import stats\n",
    "stats.chisqprob = lambda chisq, df: stats.chi2.sd(chisq, df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Exploration\n",
    "This data consists of only two independent variables, with the goal of prediction the third variable `Admitted`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>SAT</th>\n",
       "      <th>Admitted</th>\n",
       "      <th>Gender</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1363</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1792</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1954</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1653</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1593</td>\n",
       "      <td>No</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT Admitted  Gender\n",
       "0  1363       No    Male\n",
       "1  1792      Yes  Female\n",
       "2  1954      Yes  Female\n",
       "3  1653       No    Male\n",
       "4  1593       No    Male"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_data = pd.read_csv('College_Admissions.csv')\n",
    "raw_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = raw_data.copy()\n",
    "data['Admitted'] = data['Admitted'].map({'Yes': 1, 'No': 0})\n",
    "data['Gender'] = data['Gender'].map({'Female': 1, 'Male': 0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling\n",
    "We will first try one variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_1 = data['Gender']\n",
    "y = data['Admitted']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.572260\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Admitted</td>     <th>  No. Observations:  </th>  <td>   168</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   166</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 29 Aug 2022</td> <th>  Pseudo R-squ.:     </th>  <td>0.1659</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>19:38:45</td>     <th>  Log-Likelihood:    </th> <td> -96.140</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -115.26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>6.283e-10</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>   -0.6436</td> <td>    0.222</td> <td>   -2.901</td> <td> 0.004</td> <td>   -1.078</td> <td>   -0.209</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Gender</th> <td>    2.0786</td> <td>    0.363</td> <td>    5.727</td> <td> 0.000</td> <td>    1.367</td> <td>    2.790</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:               Admitted   No. Observations:                  168\n",
       "Model:                          Logit   Df Residuals:                      166\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Mon, 29 Aug 2022   Pseudo R-squ.:                  0.1659\n",
       "Time:                        19:38:45   Log-Likelihood:                -96.140\n",
       "converged:                       True   LL-Null:                       -115.26\n",
       "Covariance Type:            nonrobust   LLR p-value:                 6.283e-10\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.6436      0.222     -2.901      0.004      -1.078      -0.209\n",
       "Gender         2.0786      0.363      5.727      0.000       1.367       2.790\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x_1)\n",
    "reg_log = sm.Logit(y, x)\n",
    "results_log = reg_log.fit()\n",
    "results_log.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the `Log-likelihood` is adequate and higher than the `LL-Null`. The `LLR p-value` (log-likelihood ratio) is also quite small (<0.05) as well as the single dependent variable; indicating model and feature significance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: The `Logit` is the same as the `Logistic`, just a further transformation on the equation to yield an equation more similar to the linear form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we assigned `Female` to the integer value 1, `Male` is our benchmark value. The `Gender` variable coefficient is 2.07, meaning that females are 7.99 times more likely to be admitted to college."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us add the `SAT` score variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.120117\n",
      "         Iterations 10\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Admitted</td>     <th>  No. Observations:  </th>  <td>   168</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   165</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Mon, 29 Aug 2022</td> <th>  Pseudo R-squ.:     </th>  <td>0.8249</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>19:45:58</td>     <th>  Log-Likelihood:    </th> <td> -20.180</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -115.26</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>5.118e-42</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>  <td>  -68.3489</td> <td>   16.454</td> <td>   -4.154</td> <td> 0.000</td> <td> -100.598</td> <td>  -36.100</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Gender</th> <td>    1.9449</td> <td>    0.846</td> <td>    2.299</td> <td> 0.022</td> <td>    0.287</td> <td>    3.603</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th>    <td>    0.0406</td> <td>    0.010</td> <td>    4.129</td> <td> 0.000</td> <td>    0.021</td> <td>    0.060</td>\n",
       "</tr>\n",
       "</table><br/><br/>Possibly complete quasi-separation: A fraction 0.27 of observations can be<br/>perfectly predicted. This might indicate that there is complete<br/>quasi-separation. In this case some parameters will not be identified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:               Admitted   No. Observations:                  168\n",
       "Model:                          Logit   Df Residuals:                      165\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Mon, 29 Aug 2022   Pseudo R-squ.:                  0.8249\n",
       "Time:                        19:45:58   Log-Likelihood:                -20.180\n",
       "converged:                       True   LL-Null:                       -115.26\n",
       "Covariance Type:            nonrobust   LLR p-value:                 5.118e-42\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -68.3489     16.454     -4.154      0.000    -100.598     -36.100\n",
       "Gender         1.9449      0.846      2.299      0.022       0.287       3.603\n",
       "SAT            0.0406      0.010      4.129      0.000       0.021       0.060\n",
       "==============================================================================\n",
       "\n",
       "Possibly complete quasi-separation: A fraction 0.27 of observations can be\n",
       "perfectly predicted. This might indicate that there is complete\n",
       "quasi-separation. In this case some parameters will not be identified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_2 = data[['Gender', 'SAT']]\n",
    "y = data['Admitted']\n",
    "\n",
    "x = sm.add_constant(x_2)\n",
    "reg_log = sm.Logit(y, x)\n",
    "results_log = reg_log.fit()\n",
    "results_log.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the `Log-likelihood` is even higher, indicating that the addition of the `SAT` variable helped the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 1.00, 1.00, 0.23, 0.02, 0.99, 1.00, 1.00, 1.00, 0.01, 1.00,\n",
       "       1.00, 0.76, 0.00, 0.60, 1.00, 0.11, 0.12, 0.51, 1.00, 1.00, 1.00,\n",
       "       0.00, 0.01, 0.97, 1.00, 0.48, 0.99, 1.00, 0.99, 0.00, 0.83, 0.25,\n",
       "       1.00, 1.00, 1.00, 0.31, 1.00, 0.23, 0.00, 0.02, 0.45, 1.00, 0.00,\n",
       "       0.99, 0.00, 0.99, 0.00, 0.00, 0.01, 0.00, 1.00, 0.92, 0.02, 1.00,\n",
       "       0.00, 0.37, 0.98, 0.12, 1.00, 0.00, 0.78, 1.00, 1.00, 0.98, 0.00,\n",
       "       0.00, 0.00, 1.00, 0.00, 0.78, 0.12, 0.00, 0.99, 1.00, 1.00, 0.00,\n",
       "       0.30, 1.00, 1.00, 0.00, 1.00, 1.00, 0.85, 1.00, 1.00, 0.00, 1.00,\n",
       "       1.00, 0.89, 0.83, 0.00, 0.98, 0.97, 0.00, 1.00, 1.00, 0.03, 0.99,\n",
       "       0.96, 1.00, 0.00, 1.00, 0.01, 0.01, 1.00, 1.00, 1.00, 0.00, 0.00,\n",
       "       0.02, 0.33, 0.00, 1.00, 0.09, 0.00, 0.97, 0.00, 0.75, 1.00, 1.00,\n",
       "       0.01, 0.01, 0.00, 1.00, 0.00, 0.99, 0.57, 0.54, 0.87, 0.83, 0.00,\n",
       "       1.00, 0.00, 0.00, 0.00, 1.00, 0.04, 0.00, 0.01, 1.00, 0.99, 0.52,\n",
       "       1.00, 1.00, 0.05, 0.00, 0.00, 0.00, 0.68, 1.00, 1.00, 1.00, 1.00,\n",
       "       1.00, 0.00, 1.00, 1.00, 0.04, 1.00, 0.02, 1.00, 0.99, 0.97, 0.94,\n",
       "       0.01, 0.00, 0.00])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the model training set predictions\n",
    "np.set_printoptions(formatter={'float': lambda x: \"{0:0.2f}\".format(x)})\n",
    "results_log.predict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0,\n",
       "       1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0,\n",
       "       0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1,\n",
       "       1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0,\n",
       "       0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0,\n",
       "       1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(data['Admitted'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Predicted 0</th>\n",
       "      <th>Predicted 1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Actual 0</th>\n",
       "      <td>69.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual 1</th>\n",
       "      <td>4.0</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Predicted 0  Predicted 1\n",
       "Actual 0         69.0          5.0\n",
       "Actual 1          4.0         90.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm_df = pd.DataFrame(results_log.pred_table())\n",
    "cm_df.columns = ['Predicted 0', 'Predicted 1']\n",
    "cm_df = cm_df.rename(index={0: 'Actual 0', 1: 'Actual 1'})\n",
    "cm_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating the accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9464285714285714"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cm = np.array(cm_df)\n",
    "accuracy_train = (cm[0,0] + cm[1,1]) / cm.sum()\n",
    "accuracy_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the decision boundary\n",
    "For this bit we will use sklearn and a new points csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = np.loadtxt('linpts.txt')\n",
    "X = pts[:,:2]\n",
    "Y = pts[:,2].astype('int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = LogisticRegression()\n",
    "clf.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Retrieve the model parameters.\n",
    "b = clf.intercept_[0]\n",
    "w1, w2 = clf.coef_.T\n",
    "\n",
    "# Calculate the intercept and gradient of the decision boundary.\n",
    "c = -b/w2\n",
    "m = -w1/w2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jjQd24/f7+NtLb3LBGafg0UWYXjA+GY+RnFLRu7bJhlxt03honSNa/AjGK+IngaAHkixTXT+Ty9/zMd7+kS/R6J/PQy/s5tPf+CFnX3sr37r7Fxxubh3tYQoEReHYNsa+7VixVlBUrFgrxr7tOPbR8es/W9vkpGPYRgonFUP2BkRtk0BQZoTIEvSLqvsI1M5i2bnv5D+/cyfHn3gSv97wGOfd8CG+8cOfYNvWaA9RICiIcq1Sc2zbFS1jXKxla5uUYA1YpqhtEghGCJEuFAyKrKjMXriamxeu5uqWQzzzl99TG5A52LCHI20d7Gxs4dJzzsLn9Yz2UAWCvJRjldp4Sz8qgUq8C9aK2iaBYAQRnzJBUVTUTuHid36IFRe+h0b/Ah59cTdf+d5POesd7+OOH/yYhkNHRnuIAkEfSh3JGa/pR0mW3UjeOBBY4yVKKBAMhIhkCYaEqntRa2dw4bs/wfLTLuDxB+/jD489za/+9Bif/sD1XHPphciyaN0jGDuUMpIz3gvJxzrjLUooEPSHEFmCYSHLCjOOW867/205V72nib/95Q/UzZhCQ8NunnnuZVA8XHHB2QT8vtEeqkBQslVqwiSzfHSPEkqeYC5KKFrpCMYj4o4VlIxQVT3r33ErNUvP43BwIZt3HeHrd/+Ss97xPr78/+5i74GDoz1EgaAkiELy8iFa6QgmEiKSJSg5iubFXz2Dd//7HZz/tjfYuOG3PPTUk/zmz4/zs6/fzsply1BkcesJxjeikLw8iCihYCIhnnSCsiHLCtOOXcT1H/kCV9zYygtPP4JaUc+Bhj189+d/YPH847j6ovMIBwOjPVSBYEiMRZPM8e6OLlrpCCYSQmQJRoRARQ1nXPJOLNPgQOtBIhmJ7/7st/zPvfez/sy13HDlJcw7dtZoD1MgGNeM14Lx3sJQRAkFEwUhsgQjiqLqhCfN5sNf+D5NB3ax8c/38eTGx3nsb8/x4N13UFVTjyxroz1MgaBslCvSNF4LxvsThmMxSigQFIsQWYJRQZJlJs08jnd84D+47Pr3s/f1lzgQh0PNr3L7N+7m7ZecwxXnn0M4GBztoQoEJaOckabxaCsxXoWhQFAo4i4WjDq+UDULT1iHPP1EDunHMvOYOXznJ7/ljLe/j9vv+A6v7tg12kMUCIZNuQ1MB+tPmM/cc7iGn8PeXqwkFExwRCRLMGaQVY2pc5fy4c9/l1s6D/On3/6CJ//6GM2tbXznPz6IHqhGlmU0Vdy2gvFHuSNNAxWM54ugAcOKqpUiKidWEgomOpLjOM5oD2IikTBMtuxqwbJEK4ihoigy4ZCPSDRJItpB28E91OkJXnvxOe769Z+4+sKzufbS9dRWV472UMc8iiITDnuJRFLiniySPsXYw5xLx7ZJvf5sLjWWFRSFpMaKqePq/d4+x03HkAPVgIMdb8+9pgQLG0vecyli+97zOF6L9ccC4vNdOirmrkBWNCixwBchAcGYxuMPM2XucmwzQzCms2T5Pn52/wbu+c2fOOeU1bznbVeweP6c0R6mYIKR98Efrs773nwCKN9rhVgTZNNvQK7HYLEipHfBeDaChh5AUlQcPYCdjLrvHWJUrZRRObGSUDCRESJLMC6QVY1jFq3m1gUruaa5gaf+/DuefPwvzP77JmbUB8igEwqE0HWxMlEwPPorxtYWn9LnvcWm4QYSFFa8g9TOzZitBwEHtXoanjkryTS8NqzCcEnVQVawWvZjIiE5DmrdDCTNgx1vH1KartRpPrGSUDBRESJLMK6QZJnqSbO44qZ/46Jr30ey8zA7O1v431/9hH+8uJ2rLjiLay+/iMl1NaM9VME4ZaAoDfjfel8eMZbeu43uabh8oiifoHBsm/TeVzCb9+PYFiBhtuwHWcEx0/nHouoFRX8c28axTXJ1IRIgSegzF5NpeG1Ihp/CMFQgKAwhsgTjFt0XRPfNxbZmc/oVKqZyH//74GP89HcPcdaaFXzkpncyZ9aM0R6mYJyRi9JEW7FtE8dI5Y3S5BVjQ0zDOaaBnYzhICHpvq7XMtjphLtiMNnZI2JkpxNkdm7GSsaQdS/67KWoob7pTDPaRnrXFsyWRiRNR62cBJIMloWkedGPXQm8lZoshkLSfOPdfV4gGC5CZAnGPbKicszC47l54fG8rbmRpx75PU/+9RGaDh+gNqRyqD3BrGnT8Xk9oz1UwThAkmXUuhlkWhqwIy3IHj+eY1f0EQn5UmZy8K2C8mLSaJKqI/uC0H4IO50AJGRZQfGHuyJOr+YiRtqMRWQaXsXsOIydTmIaScz2Q/hXno8aqsrt04y2k9jyKFYiArYNZhoTCcUfQvIGSO96ESedQPL40acdhxysAdssShANlOYTBe0CwQQQWfv27eOee+5h69atvPnmmxx77LFs2LBh0O3WrVtHY2Njn9dffvllPB7xMB6vhOumcckNH+aCa95LJtrMzo6DfOoL3yQai3P5uWdw/ZUXM21y/WgPUzCGcWwbs7kByeNDDVbjZJKYzQ049TN7vK97ysxKxZD8FegzFyPJUtFpNEmW0epnkWnahxPvBFlGqZ6KZ/YSlEAlSreIkWMaWMkYdjoJVgZUHTsZJb33ZZTFp721onDPVldgqTqSbeKYJmTSSL5pYFvY8TaQNcxDb2Ic2omseZC8QWR/GM/sZT0E21DmsD+TURQR0RIcPYx7kfXmm2/y1FNPsXz5cmzbphhHivPPP5+bbrqpx2u6LvxZJgKax4fmmYldPY2PfuYOnnjwt/z+0af45R//wqmrl/LVT/4L1ZWVoz1MwRgkmwaUvSE35aeoeWuywE2ZaTMW4ux9BdtIkWl4FX3W4qJXy2WFneIPo1TU46TjyP4Qsi8M9IoYqTqy7sU0kqBoSI4Nuh8nk8qlJa1IM1bLfrBMsEwc3QtdQs4z93jSr/8d9AB2pBnbssA0sIwExDuROg5jtR/Cv/K8vCnIYuYwby2ZNu4fOwJBwYz7u33dunWcc845ANx+++1s27at4G1ra2tZsWJFmUYmGAvIssLMect598eXc9V7jvC3Rx9g2+Zn6ew4gmwleG77Xk45fiUBv2+0hyoYIxSzcs6xbbd4PNnZJ2IjF7FaLidKvMGcsHPSyby1XJIso06ahdH4Bk4yiqNoKEE/ijfoRrpsG6NxB9gWKCqYBqTjyKFaPHNWonj9yN4AZqSpyy7CAUkCxwHHBN2LnYxi7H0lFxkr5xwKBBOZcS+yZFFMKSiQUPUk1r/jVs676kaaos3sObiDf//ad/F6dC4++xTeddWlzJo2ZbSHKRhlilk5Vyq/qGKFndXSiByqxkkncDJpwEGbsQhJlt02N+kkStVkpHgE20iCJOFfelYuMqXPWoyz18FORMFRQNFwEp1dRowOku5z91PkeXQvdBerDwWCCSCyhsODDz7Ib3/7WzRN4/jjj+cTn/gE8+fPH/Z+FVlCtIUcOu78lW8eFcWP7p1FoGY6//3Dn/P4g//Hw08+yW82PM66k1by/774SVR1YvhtyYrU7b/iniwUJVyNtviUHim/fHMpe7wo/iBWpBVHliAdRwnXoGg6WEWkCyXwTJ+HcWAHtpFAqajFO2sJSp7Umm0ZOEYCNVyDpE11jUYdB80fQFbkHmNSK+uwExHUcB2emsm5sSjharQlp2LOmI9xYAdmrB3TMsABWdWRdR9qIITq6bvqMCukkNUehfJWrIP0vm25QnfvrCUEes3hW/Mn7slSIOZy7HPUiqx169axbNkypk6dSkNDA3feeSfXXXcdDzzwADNmDG/ZfyAgTPVKwUjMY+WK1SxcsZob/6WZjRt+R7y1gZbWRjyKwsObXua6Ky4gHAyUfRzlJhgQizmGhr/PK73n0r9kNdEdL2Em46i19fimHkNyz/Puv30BQvNWoA1QRJ6JthPd9RJWMo7u9RNccCJ61aRcAbudSbtF6Tk3eR07HMbobEXRFSzbQK+spaI6nHtPjzHVT+kaQ99zoXIWzowZ2Jk0ZiJGdMdLWEYKzR/Mu012rEakDSseRQmE0MPVBOcuI3boNaRkB7o/iJXowDn0GuGVZyDJeY6bZx4FQ0fMZQmQpPLsdiL1LszWZBWyurA3TU1NrF+/nksuuYQvfOELQx5DwjB5eU8rlj1hpnXEUWSJQMBLPJ4a8Xm0TIN0pIntz/6Vb333B+iqyoXrTuZdV13CvGNmjehYSoGsSAQDHmLxNLY1Me/JkfJiGmguu0d3km/8AyvSiuQLYiejKP4K/ItPQ87T2NyxbRKv/T33ficZQwnX4F94MnYiQqpXZEgJVgJgxTr6/VvvMRUzLwNtkx2r2dmCnYzmji37Qyj+CuxMGknVXCf5ruhaYMnpbtF+r0jWRL8nRwoxl6UjeMwy0buwnNTX17N69Wq2b98+7H1ZtiOadQ4L98t4VOZRUvFUTGXledfzzUUn8cSG+3h84+P87uEnue6Ss7ntQzejyOPpY+POpW1NzHvSineQ3vsKdjKG7Avimb00rxdTaYTYIHOp6NhGCisRA08Ax3Gw4lHMzhYcBzzHLu8ztu7vl1QPjsfBSsTIJBMYe17JWSCYkRaSe155yzneF8Yz76TcOSHLecfkSCpOOlXceSs6jgP02l9urJrXtZnQPDi2jaR5sYwUsubFirZgp5M4RhJJ9xHf/jew7V4+WRP7nhxZxFyOdcbT00IgGDEkWWbSzHlc+8FPc/kNH+AfT/yZWp9NQ8Ne9jUc5PV9Tbz9kvOpDIdGe6hHLY5tu73+mve7Tukdh3FMA//Ss/r0BBwpU8zubvFWIoqTjiF5AliJjrw9B/sreAcGLajvrz1PVnjZyUhJzzs7VjPa4qZW0inwBtzC9nAt2vSFmFv/mhNYTiaN2dKAUjtT+GQJjlrE3d7FkSNH2Lx5M0uXLh3toQjGGL5QNWdddgOL1l1LU3Axf9/RxJ2/+j3rrr2VT/3X/+O1N3eP9hCPSmwjhdl6EMe2kFQNx7YwWw922RK4dDfFRFFzD3vHLs+v/uzKRMlf0dVzMIBaPRXZG+rmtdX3/UqwBiwztwpP1r1uO51UDDsVc93kvYEBLRCseAep158lue1pkq/9ndTOzVjRVpDAig7/vLNjVUO1KIFKJE8Ax8pgJ6M4GQPJsZCDVah1s1Crp7p9F5GQVQ3JE8x7/gLBRGfcR7KSySRPPfUUAI2NjcRiMR555BEATjzxRKqrq7nxxhs5ePAgjz32GAAbNmxg48aNnHHGGdTX19PQ0MDdd9+Noii85z3vGbVzEYxtFFXHVz2Vi278OGvOvZKND93PU088xoOPb+IzH7yeqy+5EFUZ9x+pcYaD2/GYrv/2qpUqkcVCMSiBSnwLT0ECrESHO44BLBn66wFYSGuf3Hn2dliPNmPFOpAUDeKdIMk4kjTgeQ9Wj+WYBrIvjHfBWmwjRWrnC9ixViRvGMeIkz7wBjhgtjcCktuyR9OxzYy76nKUfLJE/0TBaDLunwitra189KMf7fFa9t+/+MUvWLNmDbZtY1lW7u/Tp0+nqamJr33ta0SjUUKhECeddBIf+chHhr2yUDDxkWSZuulzuOZ9t3HpO9/Pc08+zNTZNTQ07GXD45uQFJ13XLae2qrK0R7qhEbWvajV0zBb9uOYGSRJRq2e1sMEdDRNMdX62diHd+OYxqA+Ub1Tf/219lFrphfk1+XYNk7bEZDSoPvASOAoimu7kIfeKVVtxkJkj7/ftKOkecFIIfsqkHUvlmWQObIXuhpqS5oHSdPd93WL0I20yCm0Zk8gKBcTanXhWCBhmGzZ1SKKEIeBosiEQz4i0eS4mUfbzJCOtnDfz37A448/gePYnHPy8dxw1SUsWzhv1MalKDLhsJdIJDVu5rIY3IfoNuxkFNkXyvX66/2eodQm9Y6AFDqXmeb9JF55Gjvh9iBUa6fjW3hqUb0AbSNFctvToKhuBM5I4VgZfPPXIPvCeSNNqdefdSNZegA70YEVj7iRrC5HdyVQiX/FOX2c6Hts6wlixdogYyCHqt2UZcbAMVwB56RjKMEaPPPWkN7xz9zxzJb9OI7tRswsE9kTRKmoA8fKjRlcMah6vFRU+st+Tzq2TeKVjW/V7OGg1s3sU7M3npnon++RpGLuCrG6UCAYq8iqhq9qCjd89EtcfN0tPPnn3/HU43/h4ac/w/9+8z9YtHARqmgpUnLc1NzJA6aD+kvH5SMrrKxkjMz+7dhGCsUXdIVZePA+frZpknx1E3a8HbcYKoPZ3EDa/wrKolMLfrj3jsDZ8XYcM0Pi9X8g674+DZyz9VKpnZsxWw8CjmunoHuRfWEcI4kSrMrvIJ+NgukBHMvE6mwBK4NtW8jJqLttV4Qwm27FNt9qjp2IgKyghCbhJCNd6dg0TjqGGq5D9oV7RMMUfxD/ktVAeVtZ9ajZ0304RjJXs6d483t3CQSlRogsgaCESLJM9aRZXHnTv3Hxte9j+wvPYIaq2Newjy9992esWLSA6664iEm1Q2u8K+hLvlV2Q3lPNuJlxtqw2g4BjlvcnY4BoC0+ZdCxOOkYdjrhrr5TNHBssC3sRKToOjBt6lycRgc7HccxMyCBHWnFMhJ5GzjLvjCS6kH2B906qUSHu53joIZr+03XSaoOikKmaR9OOun2OtR0JNvsatkDTiqCLUk90q2y7s3VZ6V3vYgdb3ML/tPJLtHlpgiBnvVikVaiO15CmbNmBOqlBq7ZEwjKjRBZAkGZ0H1BVp62HtsyOdzWSOWk6fzqT3/hp7/7M2etWcH1V13C8UsXIZXJaVhQONnCcTPagh3vxDGSoGpuRCcNVjLWtTJu4AiI5Akie/xY6QSYGcAGWUX2hwuuA+ue3pQ8PjwzFpLa/yp2pBUsA1Q9bwNn20hhJ6NI3jCKx+eKoq4Uo+QJuhG6VAJZ79sqx9UejisKu5pFO8hgJFHrZiJ7AjjpRJ/aKkmWUbx+PLOX5MasTT0OfdpxKOG6XC/FHvVisoSZjON0NpM+sKNs1ho9a/YMkCTU6ilFNe4WCIaLEFkCQZmRFZVw3Szee9vXeVtzI0898nuefOxhPvGVb/P773+Biuo6kFRURRntoR615FJmmg+IuHUZtgVIOEbSFSYFiCRZVfEtOqVbTZaOVj8T7zHLCuth2GuVoB1vJ9MEkubFMRKg6kiODb0aOGcLvK1IC9gmVE4GK4MSqnFrrrY9idna6AqNmml4567OCRrHNMC2UGpnYXc2YSej7rmbaWR/GO9xJ6IEKoacks23+ECuqibd8AZWvK2rDqw1r4/YcJBkGe9xq0nidJ07gIydjIjid8GIIUSWQDCCVNRN49IbPswFb7uZw3teZV/CIt3wCv/+tR9wydmncf2VFzNtcv1oD3PC0ztN1dtoUwIcWQUzg+wPoc9eWvDDX6ubSej0d7hiRdFQvP7C29rksZxw0kk8s5dhdxx296n7kDSvG5GR1Zwws2PtKMEqzEgzVqQZbdKxaDMWkdq5mczBHa5wkiQyZgZJ1V2biW7nbnccxrEybrRMUlDqZuKbd2Ku9qvYlGz3Oc7Wb5mxNjASZKIymUg7cri2rNYasi+MrHlRAuGc1USpxZxAMBBCZAkEo4Du9TNz4fHYtkmcCk5cezK/f/QpfvXHv3Dq8ct419WXcNLKZaM9zAmJGW3D2PtKz6L2QKVbP7RvO5akYCsqkieA7A/3KTIvBFlVkYvcpmtDJM3Tx19LCdfiW3IGxoE3XPPPdBwrGSG9459oU+dixtqwE1FwbCRFc1dazlnlnm/bAVdgKSrYNk46QSbSip5KoPqDSLKMNmMRmZYGMA0kfyWS5kHWvLlVgcWSb0WnZ94anNc2YTsOSiCE096M1X4YSdFxyuSj5ZgGTjqRs5qwJansPmkCQXeEyBIIRhFZVpk0awHv+fjXuPo9R3jmL39g46N/5ld/2MCCmbVo3jCSrOL3iQdCKTCj7SS2POrWLum+XFG7d8HaXMrLNlJuTz5Zzl+/VLaxueLPTHRCOokjucXjat0M0jv+6a7q072uB1VXUb4Va8U+YOEkY+65dPlXOYrqelwZKbcPIY6bRjQtwMZuPUDi+QfxLToFrW4msseHHKhCDlaDrGC1HyJzZDdIEt48PRcHoo8xalcqUD92JU4mjewPoXr9qNVTMDuaCvIRGyqj6ZMmEIAQWQLBmCFUPYkLr30/5111I5HmBnbFOnjh4T/zk/v/zKVdqcRZ06aM9jDHLY5tk977sptyU/U+Re2S7i15v79CVs85to3Z0UTylY3YqRiS7kPWfUi+EPrcEzB2Pv9WjVa0FTsR6WGp4KTiSB4/km3hdqIOIHuD2LFWjMYdrriybbeoHQAJyRPATkZIvroJ6YRqZN2L4gu6hf+JqLtPbxAn0Vl0eq0/l33ATUvG2rB0BcwM2qRj8RyzAroE7XDnsjdZa4ucfcQImqIKp3kBCJElEIw5VN1H9bR52LbFrLVBzmhJsuGJJ/n1g4+xduUibr3+bRy/dPFoD3Pc4ZgGTiaFpPvBMnAkd/Vctqi9vwhMIQIj3wO1EBPUrJlq5vCurpWBAVf8GSAZKcgkcoIFyRUrdjKG07IPqqe6NWPBKkBy/5/m+kHJgQqMxjexYm3IioYtK4AClgmajuzxYxtgRdtIbnsSNViFWjfD9cmKtCJ5g6g1U9wAWJHptf6iR7LuRZ+1mEzDqzhmCiVcg1IzHWPv1kFF7WBzOZCgKcYnrVSMZFNywdhGyGuBYIwiywrTjl3EDR/9It/+6e95z3vfz6HWCK+8+iodLY00HDxINJ4Y7WGOGyRVR/EGkT1eUHQwDWTfW0XtvSMwhTY17t6YOfX6s1jxjoIaU+feE2123dJxi9wd5LdWNHqCuUbRZushnHQc2RcEJKzOFqRAJfq0eegzF6GGapHA9cSaNq+rd6APJBnJFwZfyE0nWia2kcRJxly7Bs2LFWvFbG7AM38t2uQ5KP6Q6+hQQGPqPvPcT9NrSZZd1/mFJ1Nzwtn45p+E2dwwaPPuweYy3/znG9NIpX5Huim5YGwjIlkCwTggUFHDeW+7mXWXv5N0ZzM744e55+67eP7l17jorJO54YqLmXvMzNEe5pgm+/AHsFIxJM3bo6h9KPU7A9UfDdaYOifqvGFkI41tmjiW4Yq/rhWNsqq6Tu67t+JEWpA8AdTqqTiOg5OKgW2T3r21q9/gImSPLzdeyePHijQBEmRSyN4ghLw4iUiuEF6tnorq9WPLsjsWbLzHLh9yeq13I+m8lg6yjKzp2KkmrGRs0ObdAzX5RtWHFH0sZypvNJqSC8YuQmQJBOMIVfOi1s7AsadxxS3/TuWG+/jrk0/wu0eeZPWSeXz6w+9l3jGzR3uYY5YB/ZyGUL8zWP3RQIKtu6iTu5zSJd2DWjsTzzHLc+LPbR10ChL0WHXoGEkcSULyuuKChldz4sKKd7itbZJxHNt0V0oGwqjBatRpC5BkmfS+bdjxNrcmzUiihmt7OLn3nqPBhEmhKTIr1kH7m6+R6OzEjrcjqRpQlZsjZBXbSPWx1+jhsxWscsfTy+i0EEFT7lSeKLYXdEeILIFgHCLJMlNmzee6D32GK971QZ59fANPPbaBaKSNjhaVNxpamT/nWGqqKkZ7qGOOgVrsFFu/M1j90UCCrbeo6+2U3h1ZVfF0jzAFKrEkGUn3IGkeoG90x0nHUaunYicjSP5KfMedgNzNs8uun0nq1QaszlZkrx+1bkYPJ/fuc1RITVQhESXbNEnvfgkpHUXS/EiqhmNmsE0D2V+BUvvWSsrux+k+T1JX0+rUq39D8vhAVtx2RgwuaIZTd1cowym2F8XyEw/JcRzRzKmEJAyTLbtaREf0YaAoMuGQj0g0KeaxCCzTwIi04EQOcPt/fJrOSIz1Z5zEh268hhlTp4q5HCaKIhMOe4lEUj3mMp8AkX1hV/DIKtjmoKsLC32wvtXAOk5y62NdVhR+ZI8XtXJyTiAmtz3t+mJJuLVcZhp98hw8XXYMZrQtZ2WB5kX2+NGqJucVG45tu7VOXcLEScdQgjU93msbqdwxZd2LbaTAMvEtOT23atCKd5DavRXzyG4Ujxe5cjKO7bjz5vFjmxmcRAeSqiEHqvocx7Htnn0Su8YieQJIqsf1wxokMlXIOEtFsYJpKBG2/u5JQfFUzF2BrGjuyuMSIiJZAsEEQVF1fNVTcSon89mv38nGh+7n6Sce449//RsrFs7hu1+6neoKEdkqhGIekL2jX3Yy4oqSZMyNaM1eijrAA7yQ5tXd34uqYzZuRlI11+vLSOAoCtqMRbm/y94AVrQVKxHFScWQPL7cQ9wzb41rxtplZSHZJo6RwkrF+tZD2TZ2MjJo7dRgKbJsBMlJdLpzlIhiW7ZrE2EksbGRNB9Wl2hUKj3gOFiJiGsa2xWBk2TZLejvNhYsE8/8VbnU4kDXayRTecVc15GIsAlGByGyBIIJhiTL1E2fwzXvu40r3vVBXtr0KFuefZqOtiakdIRHnn2Fc08/mdqqytEe6phkKBGF7AM112i64zB2OolpJDHbD+Ffef6grvGFCrtsHZgcqEKpnOwKHsdGkiVs0wTbRJuxEHvvKzgdTTiOA7aNnYxhyjJ6OubWPOk+sDJdVhYJJK1nf8bsPFipWN7aqR71ZYOkyN4q8g+i+UPY7YcxDbcYX5IVJI/fFXyaG5GyY+1YkWaQFdK7XsQzewlKoHLA9Gyhhe6j5Zs1EKJYfuIiRJZAMIHxBio476p3ccK6y2npaOKN/dv5xt2/4ut33cs5Jx/PDVddwrKF80Z7mGOGgSIKKAXU1JgGVjKGnU6ClQFVx05GSe99GWXxaf0+zIsRdt2FBoCTiuKYGRLbnsFJuzVLarAafcYizNZGnGQEJAknHcNRFND8rilostN1g88k3TY8s99qYt17HrK1U06XL5c2dW6fcRXaJNrxhVCDYWR9Kvq8tRg7n8+JUjuddFOckWYkQAnXYcfbekR1ihVJ+eZ2pH2zBkMUy09cRv/uEggEZUdRNXxVU5i2dB3f+vH/cvmVb+OF7Tu47qOf4X23fQFzEC+oo4WhemVlya7Oc1f+yUiOjaT7cTKpfvdRrK9Sdx8qxzRwjDSOrGAnOt3/H49gRVsxGl5F9oXcaJEkuysMvUGcRLu78tBI4zgWau1M/CvPy0Xa8qUI3ZY7VXhmLgQk0ru35vWk6s+Pqrd3ll5Zi2/OShRdR5ux0BVwRhLZG0QOVIIko9TMQAlU9LkGWTHnXXQq+rEr3fq3rnqtQj22gBFtmTQYA3mLCcY3IpIlEBxFSLJMzeTZXHnzx7n42vfx/N8eJd3awP4D+3EyBg8+/SLXXnYhk2qrR3uoo8JwIwqSLKPPXorZfsiteeoqSle8wf5XvA0hVaQEKtFmLMTatQXLSCJlW+doXrdJtO7FyaRQ/GHABtXrRrn8FRiNO95aeZiKInv9uajZQClCOVhFpml/rujcirWS3rsNz5xVuaLxgaJDWXEkOyYV1WGiMQPLspE9fuRgFUqo2m33Y6Sw2hrdFYOynPcadG9/hKKAA9hWnyjgeErDjYYzvaD8CJElEByl6P4Qp5x3FbZl0hJtYduzf+WXDzzCT+/fwFlrVnL9lRezeukiJEka7aGOGKXodaeGqvGvPJ/03pddoeMNDrwPWUXSPD08sAoxQc00vAbpOLLmxU5FwcG9Vt4gjpFCCdWgzVhIetcWzLZGQMLxBnDMTE50uGnEZF5jz+4pQiVUgzZ1LundW3PbWpk0mSO73RWOqo6D47b58YVyNVT55ldWvH1SiUrW60tWIR1HrZ4GqoaTiiMHq3rWd3VPZeoBzOb9ACi1M/sUjI+3NFwxxfKC8YEQWQLBUY6sqPgqJ3PC+uv59uqzeOrh+3nyr4/w7k98kXdcdCa3f+hmVNUz2sMcMUoRUVBDVSiLTxt0H7nIUTLiih1JKUjY2UYKKxFxHeB9QcxWsI0Eksfvpty6hInsC4OqIXsDyL4KHCOBnU4gORbQU3T0jvpAFY6VwTd/jbsf3jJYtRwHq/0wbuGURqZpD07GQPL4kDoOYxspfAtPLigll0/YqnUzyDTtx/UX6inyu48TWXHryiSQVQ1HCvaIVI1mg2iBAITIEggE3aisn8ZlN36U9W9/Ly/9/a9UaRn2HWjg1dfe5PV9h3nnFRczdVLdaA+z7BS7/L4/B3m6xAt5hFb3iIzsCeI4DpIvhGfeGmS1/6/mbFNpK9IMtoVSNRnFH0KpqAXNB+k4WWFiRZoxm/bh2BaOaSIHwkhSAMUXxsmke4qO/lbu+cK5sWcFi5WIgKKiVNS6Ea+M4bbq6XJrtw+9iWMaqIGKwvyeuglbZNU1JO1KS/YufM9Gp7LF8k46DpLs1pDZZp9IlUjDCUYTIbIEAkEfdG+AE9ddhm2ZtMVaebV5O797eCP3/uERTjt+GddfdTEnrVx2VKUS8zHQqsBBXdLz1AuRSYNt0t9Xcw9hFqzG6mzC6mxBrZ8FZgYn2ZETJum929zG0131WnYqimMk0KbMxTt/bR+T1EKiPlnB4pqCbsaOt2MlI2AakO2naJkgSUjdCs37Mznt0T6nS9javVrlWHn8srQZi8i0NLjF8r4QjpXBjragTTo2b6RKpOEEo4WQ9AKBoF9kRcVbMYkLb/gY3/7xfVz3rvewq/EIt9z+Ve7704NkjPRoD3FQ+lt5Vor99rcqsJAVg9mIjNPlW+WkYsjeQI8oTO+xO6aBFWt3zTxj7aBoyP4wnllLwLZ6ropMRnFScZTKycjegFvvJCvo0+Yhq2reVJ4SqMQzbw3e+Sfimbem37oqxevHM3spcqAKO9ruussrKmQMV2R5Au659LM6MxNtJ/Ha30lue7rPKsXu82LFO7Ga92NFWkjv2px7n+zxIQeqUOtmoU2Zi1Z/DEq4Ds+cVSXtQygQDBcRyRIIBAURrp3MRdd9gPOuejcv/2Mj06eE2Nd4gP/9w0MompcbrryEmdMmj/Ywe1DOZsADrVyj638P6JI+SOQo39hd0RJzU2SaF4wUjqq5x+nTRLkacLDj7cjhOqRkBCVchxLuP91bzHwpgUo8c1ZjJ2M44VrsWBt2vAMskGwTOxEBK9On6bMjQXTXS5iRFiTN69pNdE8Hds1Leu82Mkd2gwRKuAYr2kp67ytus2xVR/G5xfJORsVJx3OmpLnrI/oACsYAQmQJBIKi0Dw+Vp9xIbZt0R5rI+35B0/89TH+b8NfWbtiEddfdTGnHr8SebRdtMvcqmSwlWuFrGrrr16ov7Hrx65E8gaQLAscG7xB99/YeQUb8NZrFfUDFn0PZb5k3YviD2NGW9zVjbIK3iDgYEWa0SYdi1rXs+mzZ/o8MpE27EQUx+4EScaRpB4C1BVwq1wbDMBORLCNJHYiij5tHmrlpKIFqohwCUYDIbIEAsGQkGUFb7iOd3zwM1xy3fvZ9OgDbHx0Ax/67Nf5zbc/zdy581BVfdTEVp9IU6/anuHSOxIlB6tzTugDRal6R1i61wtl/+bYdt5IGIAarMZyHNcLy0ihBKtzJqjdi8ezNVeeeWuwkxEkRUce4LyH6imlTZ2LvT+DFWlF8oVQa6aA7eCYBp5jVmDs3dpDuKUOvIETj7jno3mgq/cics/Hkax7kX1BMod24tgWbjG/g9H4phuRK1Kgij6AgtFAiCyBQDBsApW1nHfNe1l3+TvZ+/pLJAIKe/Y38PGvfpfjly3ihqsuYc7M6SM6pu6RJstMu5YDvXrhDZfsg96KNGM07iC9e2uPyElvEVBoobzk8bn2BOlYnx59A0VwJFnGzqR6GHU6Rhor2gJIqDVT8c5dnb/WqkhPqe7jRfei1kxzC/cdcuk7ZLmPcHOSMRRvACtjurVmXU70vQv+JVlGnzaPzJE9gOSKLn8FTjrRw6KhtwAcTwakgomPkPUCgaBkqLqPucvWok1fTXPFIpauXsNjm17gsvf+G+/5+Of466Z/YJe4AL0/stEkOVCF1dkC9OyFV8pC+MzBndjx9j5F7t3bzBRTKG/H213vp0B1nzYrWfHmW3I6nnlrkDTvW4Xx3fcjK2Sa95Np2oudMXDMNGbzftJ7X8l77sW0duk9XifRgSSryMGqHtvKurdHcb+djCJ5fGgVNci+EErlJPe/waq8Yk4J16FNOhYlWIEcrgMr02dxQJ/zKGBBgUAwUohIlkAgKDmyrFBRO53rPvRZLn/XB3n2rxvY+JcH+cadv2DVcdMIVNRiWhDw+0p+bMt2SGUcvJrUozgbVUfx+HIWAaWKbBQaOSm2UB7LxDN/Vc4bqns6zDEN7HSCTMNrPQvjNW9uP5Kiuu1mHBtJ87hCz8y4her9nHuhnlJ57ScsE8+c1X3Gm/PWirW7PR2TCo4aQvYFcUwTJVzbr5iTZBnP7CVvRf8KMBMVBqSCsYQQWQKBoKz4QzWcfcWNnHnJtbQd3MOuZJTOnS9x29e+zwWnn8QNV17MgrnHlORYTRGLp95MEUnYhP0yZxznpS7oFmdbsVZsSSp5a5VC02xDKZTvbbPQo7dgzO0tKAeqclExz7w1uf2gB9wyJknGyaRBAklWkH3991GE/j2letSS9WdcOoAtRPK1TciOjeQNYCXjyJ4KtHknDeoKPxQz0e5+XkCPVYcCwUgipL1AIBgRFFWnbuZ8PNNXoc5ay/qLL+WZF17m6g/exvUf+RR/3fTPYe3fsh2eejPFoQ4LXYVDHa7gspEKToNl9xNP21i2U9BxC02zDfS+QvbRo6BbkrCTUexUEmQFSQ+4tVG2+dZ+bAutbiZa/WxkTUdSPah1M/HMXlp0VMeKd5B6/dmcr5WdjBQ1p9gmTiaFpHuRNQ+KP+i2Aeo690LmeCAxls8LzU5GMHZvIfXq3/p4cQkEI4XkOE5h3ySCgkgYJlt2tWBZI1N3MhFRFJlwyEckmhTzOEzG+lwmY508t9FNJR43o57bbroaR/XjSCo1VRVF7Suetvm/5+LoKgQ8MvG0jWHCO04M4NfoEdXo72GdLxJWH1aArrkMe4lEUnnnslBfpoHeN9DfbCNFctvToLgNpY1DO3GSUdB9rgt63Uz8S8/qs4Ixu23vcy9mvKnXn82t1nPSMZRgDd4Fa92/91rNmG9fZrSNxJZHsZNRZI8fLRBACtXjmXfSsNN4+RYTyL5wv2OeSGnDwe5JQeFUzF2BrGhQ4to9kS4UCASjhi9YwRmXvJPT1l9DouMIb6aaeeaPf+SXf3iEc089gRuuuISlC48raF9eTSLslznUYQE27QmHKZUKutFJaterg3omdY+EVfmlXCTsypV+FHnw9kGFtm4ZaouX7ik6HKerBY8F6QSO7K4i7O8YvS0regsTbcYiZI8vv/AboJZM1r1Y6STpvS/jZFIo3mDf9kG2TabhNSRVQ9J9br9BTcM7c9GwBc9AfmJihaFgLCBElkAwgbFth2Qqg11g6mu0kFWNYO10HHsqqy+uIiqFeOrxv/DQk/9g8dxZfPSm6zj5+JUD7kORJc44zpuLRE2pVDhjjo7Z8FJBnkmpjEMkYVPllwh4ZMAmkrBJZRwCnvL3aBzMQDPbs8/e+7JbvG5boPmQPD6cjGvTUIgHWG9hYnYcJtPSgByoQvH1FUkD1ZJ1j1BJut/tXQg95jcr0uRAFUrlZBwjgarKyB4/w70r+xOAUJgZrEBQboTIEggmKB3RFNt2tpLJ2GiazJK5NVSGxvaveEmWqZk8m6tu/jiXXPs+nn/mL2x8+AEaDjbSdqSGpqhBdVU19TXVebevDytcudKfW10omWmSBUY0+ouEebXyC6xCDDSteAeZhldxjBSS5gHNi+RY7t8l6Po/effdPS3YXZhImgc7ncIxEm7D6TzH7W+1HoCx9xXXlV3VwTKw02Cleq5e7BGBAzBSaOF6t8XOMFXWQAX4YoWhYCwgRJZAMAGxbYdXdrTQFklRXemjtSPJKztaOGXlNOQCUl9jAd0f4pTzr2btOZeTjrawK3qY/7nr27y47XXOOmkVN1x5CauWLECSep6PIku5yJNThMGmIkucMUdn05tR2pMKUypVzjjOW1CqcLgMZgPRW4Q5qRiyquGYDo6ZQZIV1JqpfVbR9VevlBM9toljJJB0n+stlVHzitB8K/xsI+X2I9R9YGVwJBmMBJLm7TG/fURauIbQvBUkHRmGWUc0kF3DUFYlCgSlRogsgWACYmQs4skMQb+O36th+N1/GxkLr2d8fexlRcVXORkqJnHTJ77GnIfu58nHH+HGj3+eebOn87XbPsSCOXPybluMZ5IV7yB0cDvnKDHsKj/+2UvQQoFyn547zkHEYD4RJksSsjeIY6SQfcE+qwZzwizaiqT3bMSc865KxZB9ISRVw8mkBxSh2Tqv7Eo+ZBXF5xaV22nASCL7QnhmL8tr45AVPKrHixbyk4ykSjJ3A4mpoda/CQSlYnx92woEgoLQNYWAT6MtkkLXFWIJg+qwF11TRntoQ0eSqKyfxmXv/ijr3/FetvztMZ557EHS6QRtR/ax+fUDLFk4nyn1tT02KySi0T1SJHuCSMl2zIZXUUdoNdpgYjCfCFNDNXjmrel3VZ9jGpgxtxEz8Z6NmLvPSXdT00HtLXpFxtS6Ge7ryZibopu9FDVU1e85SoN4Yg0VIaYEY5VxL7L27dvHPffcw9atW3nzzTc59thj2bBhw6DbOY7Dj370I/73f/+XtrY2Fi5cyKc+9SlWrFhR/kELBEPEth2MjIWuKQOm/WRZYum82lxNVk2ljyVza8ZNqnAwdG+ANedczglnXYwRa2FH50G++j8/p62jk9NPWM71V13MmhVLc6nEwR7CY6Hf3WARmXwiTFZV+v0al1WcVBwnHQPN26cRc3ZOZN2LUojLe566MWBAoScQHO2Me5H15ptv8tRTT7F8+XJs26ZQ268f/ehHfPe73+UTn/gE8+fP51e/+hU33XQTf/zjH5kxY0aZRy0QFE9HNMUrO1qIJzMEfBpL59UOWMheGfJy2qrpeDwa6XSm4M/GWKa3yJQVFW/FZKiYzFe/fy/PPPp7Nj76EO+97SscO2MK937rS1RUDO63VWxz5HIxkBgsusbINt10omW6lg/9NGIe7LhZ+l3JZ5vCUV0g6Idx/7Nj3bp1PPXUU3z3u99l8eLFBW2TTqe56667uOmmm3j3u9/N2rVr+da3vkVlZSX33HNPmUcsEBRPrpC9M4WmyrR1uoJrMGsGWZbwebUJEcHqiKbYtKWRJ59vYNOWRjqiPWt6wrWTuei6D/Kfd93HJ/7jiyxdvoLmtmaaD+3m+z/7X/YfPNzvvotpjjyaDOZ83uO9qo4SrEL2D96IuaBjj2Dj5XwO7gLBeGTcR7LkIXwJvvjii8RiMdavX597Tdd1zj33XB577LFSDk8gKAlvFbJrucL18VrIPhS6i8ygX8uJzHyrJTWPj9VnXMjK086nPdbGa2++xC//+Ch3/fqPnLxyMe+88iJOPX5ln++O8bwaLZ97e1Y4klvV17MRc49G2gWarY6ELcJgfmFjhUId8wVHNxP/2zkPu3fvBuDYY4/t8fqcOXP4+c9/TiqVwusV4W/B2CFXyN7pRm+i8Qw1leO8kL0IhiIyZVnBG65j9upz+fY9K9j02ANsfPTPfPAz/8UJS+dx139+Br1Xmms8FlAPJEr6E44DtQ8aiHIL0UL8wsYC40UICkafo1JkRSIRdF3H4/H0eD0cDuM4Dp2dncMSWe6vwrHzhTDeyP6qLvU8Flo0PhZRFFixoJ6tO5qJJzLUVvtYPq8ObRCRVa65HGl8Xo1gQKe1IwmSRCyZoabSV1Aq1LYdPKEaLnj7+zjvqnex/flniLfso+HwQZKRdn731+e48erLmDNr+oD7kRWp23/Hxlw6tk2q4VXsWBuSL4gdayPT8CrawpPfEiWKDNpbX/WW7fDMzjSHOy2qAjKHOy2e2ZnmqtWBwjzBeu2vWAaaR9syXGNUX8it+5Il99+OiayMDfFb0JyPEGPxnhT05KgUWeUmEBgbXwbjnVLOY1tHkhe2HyYWNwgGdI5fPIXqSl/J9j8ShEM+pk2pwDAsdF1BKeILfSLck6esnMEL2w8RixtMrQ9x/OIpVFYMfA3zXffTLrgM27ZIRVrZ+uTDPPa3F7jvoY2sXbmIm6+9nPNOX4Oi9C9egwFPv38baax0krSVQq2oQPH4sHQFx0wR9EkonvzXPJaySZgJJlXphLwyum6TyDhoXg9B78g9qPPNo2Pr2OEwRmcriq5gZRLolbVUVIfHTCRrKHNebsbSPTlukcrzw/uoFFnhcBjDMEin0z2iWZFIBEmSClqNNBDxeAprjPeKG8soskQg4C3ZPNq2w6YtB2jtSBL06xxsirLJMDlt1fRxF9HKksmYBb2v1HM5mqgKnLhkcrdoJESiyX7fP+h1V0KsPPsavn3C2fz90T/xxF8e5L2f/BrXXnQWt33oPXg8PXsAyopEMOAhFk9jW2NjLh3bwVK8WJ2tSD4LJxlDCdcQSzpI6fxmn5bt4FcdDrZnMAIy7XGbqZUqmVSaiDG8z0MhdUqDzaM0ZSGOsQ0jGUf2VyFNWUg0ZgxrXKVkKHNeLsbiPTleCdY4ZYkFHpUiK1uLtWfPHhYsWJB7fffu3UydOnXY9ViW7WANs13E0c1bhbmlmMdU2nQjGT4Nr66AoxGLGyRTmaOgaLy0cwmjn3bVVBnHcbAGeagUet29gSrWXXEjZ1xyLa+/+HdCcoLdBw7y/PObeW3vYa6/4mIWzD2G7Fza1tj6fGszFuFk64OC1W4TaYcBW9acNtfDU2+6DbEnVyicNtcDBczpQBRep/TWPJoZs68o84XxzDsp9zqyPKbmG4Y25+VhbN6TgreY6E+YvKxatYpgMMjDDz+cE1mZTIZHH32U008/fZRHJyg1R3vReCkp1qtrNCn2uiuqzuITz8SxbSLxdg6ZO3jq+b/wwGPPsGLhXN511cVcddFZI3kKBTGUYvTejbSH259xKAXrVqyD1J5X8oqysb4AYTyvRBWMLONeZCWTSZ566ikAGhsbicViPPLIIwCceOKJVFdXc+ONN3Lw4MGcPYPH4+HWW2/le9/7HtXV1cybN49f//rXdHR0cPPNN4/auQjKQ9b9PCsOaiq9LJ1XO25ThaNFMTYKY4GhXndJlvGEajj/HR/g9Iuv47mNG9j4yJ/4t698B8eMc/Zpp6Ko3j6NqQeiWLuEYhmKKOneSHu4FOuY79g2qX3bxvwqwoEY60JQMDYY9yKrtbWVj370oz1ey/77F7/4BWvWrMG2bSzL6vGeW265Bcdx+MlPfpJrq3PPPfcIt/cJSmXIyykrp43b1YVjgfHo1TXc6+4LVnDGJe/ktPXXsPvVF5g62c/eQ4f53o9/jdfn44YrLmbJguMG3MdQ7RLGE8U65tuZ9Ki3MRIIRgLJmQi9NsYQCcNky64WkR8fBooiEw75iESTYh6HSSnmMluDpSoyz249mItkZdNvYzWSVWoURSYU8NBy5BAP/t9PeeKxh2lpbWfJcbO59vL1XHjmaWi9rA0s2+H3WxIc6rCo8ku0JxymVLqpunJEtEaTQmuyFEUmFNQ5/M8nMCMtSJ5gTpSNp0jWWEBRZMJhL5FISnxXDpOKuSuQFQ1K3MFgbP78FAgEY4LeNVizpoYBjtq0qyTLeILVXPGef+Wit7+X555+hI0PP8Dnv303S2bVM33mMSCreHT3izqVcYvLq/wSAY8M2EQSNqmMU7JU3VihmDolSZbxzlpCsqsma6y2MRIIhosQWQLBGGK0V+71HkvvGiyAtcunYlr2mBjjaKL7Q5x6wds4+dwrOLJ/B22qQWxfAx/+zNdZvWQ+77rqEpYunE/YL3OowwLsXCTLq43deRtKu5ju2xTaLFoJiuJxwcRHiCyBYIww1lbu9VeDZVr2mK3BGg1kRWXKMYtwbJt4xxTOu/Aynnz8EW74t88z/5jpXHLBeiZPP4loCqZUKpxxnLdHqrB3Ufxo9sQbSruY4bSYEcXjgomO+KYUCMYAY3HlnrC+KA5JlglWT+Kyd3+U9e94L1v+9hhPPPwHHvzLI9z5+XnIvmqMTIr6cCC3TZ+i+OlpQq2vjUpPvN42DGa0BWf3VrwLT0FW8z8qxkuvQYFgtBAiSyAYA4zFlXvC+mLo6N4Aa865nBPOuph420H2pttofH4zn/vvH3L6iSu44cqLWb1sMU+9mcoVxR9uz9DQsZV5wSiyd+QFS3cbBgA7EcWKtOIA3mOX5xV7xVo3CARHG0JkCQRjgLEaNRop64uxUItWjjHIkkS4ohZHnUaddzLX3pDkycce4ubbvszs6VNYcPxFLF+5loBHRrPTSJ0JrOoA6igIlqwNgxltwU5EcVJxJG8QJ9HZr9gr1rpBIDjaECJLIBgDjOWokSxLZY2mjYVatHKMQYm3ENj3D5R0BMsTRpl1Ehe/84Ocf/V72PrsEzzx0O9pb27gSPtSfLJBezTNcdV+FCOKLUsjLlgkWUaftRhn91asSCuSN4haMwWc/sVedptsTZZYJSgQ9ESILIFgjHA0GqYOtRatlFGnstTD2RaBff9AjR3G8lagxg4T2PcPIgvWo3l8HH/mRaw6/QKaDh3m1R2H+cdTf2HLsw+za8l8rj9lHifO8qCOgmBRApV4F56CAziJTnAGj06JFjMCQf8IkSUQlJliBEG5o0ZjjaHUopU66lTUGGwLyUiApIHcfypXMtNuBMtbgaMHsAAlHUEy0zi6HwBZVpg8bRr1U6aybNFUnl8wjScf+zMfvetPzJhcy23vfzdnLqoc8nkNFVlV8R67vKjo1GisEhzNVZgCQaEcPd/mAsEoMJKpsLFQ11QsxdailSPqVOgYlHgL2pvPE460Yuph4rNOwgrU5t2no3qwPGE3kgUoqU7M4GQc1dPnvbIsUTtpCuvf8T7OvfIGtr3wNBv//HtiiRgth/ay90gHNTX1HDNj6pDObyiM9ejUcGwjBIKRZGx9cgSCCYRp2mx5tYnWjiSaKucEgW2XvpNVRzTFpi2NPPl8A5u2NNIRTZX8GOUgW4tWXeElY9qD1qL1jjoF/Vou6lTWMdgWvr1/R+48hK3oufQfdj/HlRXis07CDE5GtjKYwcnEZ500YPQLQNV9rDj5fD765f9h0omXscuq5f/94vdccvPHuOkTn+Pxv/9zxNqnSLKMrHvHnMDqbhuBouZWYTq2aCsjGHuISJZg3DGSEZuhHqsjmmLLa03sOtCBR1MIBfQegqCUKcGBojvKOLC0KqYWrVyrMAcbg2SmUVIRbH8lDh4sx+mT/uuNFaglsmC9+x7VM6jA6o4sK3hDtRCq5cNf+A6bHvsTG/+ygY9+4ZtMqavmu1/4BAuPmzuscx6vCNsIwXiiJN/0yWSSPXv2MHPmTILBYI+/bd68mdWrV5fiMALBiKbfhnqsrOjpjKbRVYVYIsPBphhBv05tla/ktgz5aopiCYNIPE1V2FfSY5WLQmvRyrkKc6AxOKoHyxtGT7QgqUHkAdJ/PXeq9CvCCsUXquGcK9/DWZe+k9de3MTfHv0TpmPRcmg3jz//OisWL2L+nNnDOsZ4QthGCMYTkuM4w8pdvPTSS7z//e9H0zQikQi33norH/zgB3N/X7VqFS+++OKwBzpeSBgmW3a1iI7ow0BRZMIhH5Fossc82rbDpi2NuYhNLJGhusJbFlf04RwrlTZ58vkGNNVNszQeiWGYFnOmV7JyUX3JRWHvsbZ1pjAyFtUVXkJBD6esnIGq0Gcux1v9VndGY/x6qo3Kg8+T6WwlrQZIzj4ZJ1Q36HalHqtj2xjxdtLtB/jspz5JU0sbqxYdx3VXXMQ5p65BHePhS0WRCYe9RCKpIX9Piposl1LMpcClYu4KZEWDEov1YUey7rjjDj73uc9x4YUXsnfvXj75yU+yd+9e/uu//gtJkhimhhMIcoykK/pwjtU9pRX0a4SDOhUhD6etmo6qlq6+pfvDe/HcGra+3kwy7Y5R1xV0TaG1I8kL2w9x4pLJue3Ggi/VcBmNVZhWoJYjs8/juS276egA/440S+elBpy7csy1JMt4QjV4QjXccddv+ccTD/LkI3/iE1/9DlPqqrn/f+6goqJyWMcY64z1wnyBIMuw78ydO3dy4YUXAjB79mzuvfdeOjs7+dCHPoRhGMMeoECQJSteYokMqbRJNO4+uMrhij7UY2WFz+K5Nd0KqX2sXFhfUoHVvdD98X/uY/P2I6QME01TCPo1qsPersJwnVjcyBWGd6/fKncx/ljEth1SaXNI52vbDi+81sThiIOqqYPO3UjMtS9YwVmXXs/nv/srPv+f32bduedxpL2Ng/t38qXv3Mm2N3aW7FhjjbFamC8QdGfYPwVDoRBHjhxh0qRJAHg8Hn7wgx/wyU9+kptvvllEsgQlYyRd0YdyrN5Ri8Vza/F71ZKntLo/vAM+lb0HI0hIzJoaIpbIEE9myH7sookMk2oCqIr7ICplNHAsL0DI9/7hRpWMjEUsbhD063h1V2wPNHcjGXmVVY0Fq05l/oqTicTbeXXHVp74x4v89qEnWDJvNu+8/CIuOOMUNK3/4wrfKYGg9Az7k7R27Vp+97vf9XhNVVW++c1vMmvWLFKp8bGUXDA+yK4CO/OEGZyyclpZ01zFHCtf1GL7zpYhC5CBIi7dH96aqiBJIEmgqe4qxlBApyLoIZ7MkEhm6Iym2PSSa+tQqmjgSFpGFHusjmiKv714gMf/sY+/vXiAjmiqJFElXVMIBnRiCaOguRvJyGuWbCpxzup1fPOe3/Ohj/07tqzzqa//gFs++XnSqUTe7ax4B6nXnyW57WlSrz+LFe8o2xgFgqOJYRe+G4aBZVn4fPlXMR08eJCpU0fORG+0EYXvw6e/wvdSUY4ITPdid69HJZU2yZg2Z54wo+ioxWARl+6F7n0jWSY1lV7WLJ3Cpi2NdMbT1FT5aetIUh12RWMknh5WRKccCxD6uybFHsu2HR7/xz72H4oiSeA4MHNKiFNWTuPpzQeGdX0URca0YNOWBmJxo6C5Gwv1b46ZYddrL5Jo2sfxc2poOXyQ3z36LDdcdTErFi8Ax3GFVawVyRPEScdQgjV5G0KXAlGsXTrEXJaOMVP4fscdd3D77bfn/q3rAw/oaBJYgrFPuR56pfJvKsTRvHcqc9bUMDhgWk4urWk7DumMRSjgwe/VMPxWLlU13B6JpU6DDXRNCjlWd4GWSps0NsWwHBufppI03H/btlOS61Nd6eO0VdNJpjIFzd1Y6EcpqRpzl67BsU8glozwxpvtbN2xm0f/7fPMP2Y61118LmfVO3i8wndKICg1RX8j/vKXv6ShoYFvfvObeL35P4CNjY1MmzZt2IMTCEpJWRoBd1GqerFCBUzvh3d22+yDPCcqIil0XSGWMKgOvyUqhrM6rxSCMiuMVEUe8JromoLfq9HSkcBxnFykLnus3gJt7sxK9wAOIHX9l9LW8xU7d2OlH6Uky+iBSk4492qWn7aeF//2KBsf+gOf/95PefOMpXzwrCWA8J0SCEpJ0Z/8u+++m4997GNcd9113HXXXdTVveUT09jYyJ133skDDzzAK6+8UtKBCgTDZSDTznDAM2yhVYqoRTECpvfDu/v/zoqKbTtbyWTcFY5L5taUzLRzOIKluzDyaArRhNGvqIzE06QNk0jMIBIzmDYpmDtWPtH85r4OptYH2H8oipGxkGWJaZOCeD0qfp826lGlsYLuDXDSOVdw4lmXsH/HVoLJQ3Sm9/CnR5/ltUMRrr/mCtZIR+/8CASlomiRdfLJJ/PrX/+a97///Vx99dXceeedhMPhnLiSJImrr766HGMVCIZFbwGTNe189qWDBP36mPCLKmXEpTLk5bRV0/F4NNLpTElX+g5VUPYWRp2xNPFkJleA3l1UZt+bSJlMnxSkM5ZGkSWCPjfCkk80J1IZVi6sx6trRONpQgEPy+bX9ki1joWo0lhBVlRmL3Q7cjRF27AOennzlQd47+e+xZyZU7j2sgu49Jyz8PtE2lAgGApD+raZM2cO9913H7feeivXXXcdpmmiKArXXnst733ve6mvry/1OAUCYHhF690FTCxh9DDtLEXqsFT1XqWs45FlCZ9XI5MxsazS2qkMRbDkE0ayLBEK6KQN16V+3uyqPu8FiCdM2jo7sGyH1YsmUxny5I361VX5qavy90ilptJmj1SqiGb1RQ9Vc9ZVt3Dqxdez9dnH2fjQH/jq939GpU/hzJPXoug+NFUIVIGgGIb0iTl06BA/+tGPeO211zAMA0mS+NSnPsV1111X6vEJBDlKIWKyAiYST/PsSwfRNaUkxdulrveaqBGX/tKha5dPpbUzyRt72tjyWlPOZyzg02jtSBKJGUQTrrnxroYOmloTrD/tmAGjfl6P2ueemTU1zL6DkXHtdl9uNI+P48+8mFWnr+fg7lep0E32HGnjP//fXfh9Pm646mJOXr0CSaQTBYJBKXp97qc//WnOO+887r//fq655hqeeOIJrr76ar7yla9w9913l2OMAkFJ3bNlWSIc8Lhu6CXyMOodoQn6tZxomygMxy09Szaa+JYb/lvCaMfedtoj6R4+Y4vn1lAR8pDOmABomoxHd5tub329mXDA06+XWe97prUjyTObD9DakSz4HirFOY9XZFlh+tylBGeuJF63kqUnncX+Iy3c+h//yUXv/jD3/m4DyVR6tIcpEIxpiv6p/OCDD3LNNdfwvve9L+fy/uUvf5lZs2bxrW99iz179vClL30JTdNKPljB0UupbQNK7R5fKguHsUp/UcShpN7ypUNTaTPv9fV7NU5bNR3TstnV0IGmytg2+L0qKcPMXf9CHNdNy6alI0ltpQ+PrmCadi5tnG/73ue8YkE94VB+P8CJjidQwQVvfx/nXHEDrzz/FBv//Ht+cO99nLHyOOomTyFtSlSGQ6M9TIFgzFH00+mxxx7LiavuvPe972X27Nn8+7//Ow0NDfzyl78syQAFAiiPiCl17dNItfwZafpLhS6eW8v2nUNL3/ZOhw50fWVZYvWiyTS1JoglMvi9aq4v40DXv/c+E0kTn0elM25wpDVB0jAJ+jQSqUwfkZXvnLfuaGbalIpip29Coeo+Vp5yAcvXnkuk5SCHMh0c2dPIB27/MssXzOGdV17EmWuORxZteQQCYAjpwnwCK8s555zDvffey759+4Y1KIGgNwOlmYa7X69HLYkYGsmWPyOJkbGIJQy8HgWPrnQ5rxtsfaOpZM2PB7u+1RVe1p92DPNmVVFb5WNybWDQ6997n7VVPk5ZNY1MxiKZNvF73L6S23e29hl33vRvIoNhTJz073CQZYXK+hn4py3Fnn4C73z3e2nujPORz/83F7zrQ/zktw+IvrUCASVoq5OP7g2jjzZEW53hM1BbnaN5ZVgx556tJVIUmbraIPF4esj3ZFtnioef2d0jilRb6SNlmLmFA8NpI9R73AOd41Cuf/dtjIzFxuf2I8sSAZ9G2rDyjrt3O59oPENttY8Lz5g7rLmcyFimwWsvbuKJDfdjJqN84+M34glUcaQ1ytxjZubeJ1rBlA4xl6VjzLTVKYSjVWAJys9EXXU3GMWsrOyIpnj+lcM0NsVAgjnTq1ixoI5QoPgvD9t23EbXuoLPcoinMgAsnlvDG3vbS16D1vv69hZVQ7n+3bfRNYWgX6etM4WqyP2OO1/6d/m8OpQB0mBH8w8AAEXVWXLiWSw+/gxS0VZ2xZt488lnuOP797Bq8XG884qLOPuUNSiKSCUKjh6OvqeVQDDOKMYewrYdXn6jmf2HoliODQ7sbGgHyeGUFcXbSWTTZtVhL07I4cCRGCnDZPuuVubMqAQoWw3aQMJyqIKmmNq53jV7Wjch1vv4bZ1Jtr7eTMowx4yx7WghyTK+ijqoqGNeeDrvc4I8+cif+PhXvkN9TSUfuP4q3nf9FaM9TIFgRBAiSyAY4xSzstLIWETjBpIEPk0FScKybaKx/lfRDUS2eLy1I0k0bpBMmQR8Gp3RNPsORli7fCqmZZc8ejOQsOyIpoYlaIpZ8JAvctYRSfHS60058TdjSohNLzbm0qmxhBvtK0VPzPGOL1jBWZdezxkXvp0dL/+TJzbcx6GWVhr376SpPU08abN4/pzRHqZAUDaEyBIISkyp00aDrazsfjxdUwgFdA63uKvncNy6jZBfR1XkHs7nhZCN/Gx5tYmWjiQBn8a0SUHgLaFXinPsPWf9CcsjrQme+Oe+vIIGKGjeh3N9LNtm647mnPhr7Uiy72AnsWQGj65gmDZgDmgNcbTQY55VjQWrTmX+ipOxUp3sNtv4ze9/xB8eepyl847huisu4oLTT0bTjt75EkxMylL4fjQjCt+Hz0CF72OdUrXWKXS/+V4HeP6Vw+w/FCVlmAR8OnXVPnRNxrKcIY3LNG2eefEAndE0oYDeZd6q4tFVEqnhnWu+cwgHPH0Kz6srvJiWxZv7O9A11y9LV2Vqq3ysWjSJHXvbB533wa7PQAJMkiRsJP7yzC40VcbrUYklDPYfiqBpCpblIMtgGDbzZlVxxgkzjtpI1kDznP18Nx85wrOP/5mNj/yR1954k5rKMJ/98E2cc9rJozz68YMofC8d5Sp8FxWIAsEgFOr6XUpX+t7ks4cwTZstrzb1cTAPBzycdeJMjpkeZkptgGNmhDncHGffwQiqIg1pXKoqs3JhPTWVPjKmTXWFByRojxR3rr3nsr85A/pYOsw/poq0YeHTFSzTQZYgkTLx6Apv7GkfdN4Huz4d0RSbtjTy5PMNbNrSSEc0ldu2I5rimRcPsPEfe2nrTNEWSZFKmySSJn6vht+roigSacMi6NdYvqCu4BWgI+kmPxLHLPRz4PGHOe3Ct/OZb/2cL33j+yxdsRJHlmg6uJsnntnES9vfEDYQgnGPiM0KBuRoXzFVTGSq1K70veleH9QRTbHltSZ2HejA05Ui7N3Kx8jYVIS9eHSVbJs5TVUI+CASS5NKm/h9hXdm6F7LZNsOT28+UNS55ptLXVXojKbw6G67nO77qQy5PQ1jSYOgz/11KUkSKcMibVjYjkNlyMvCY2vY+kZz3rFkbRuy/+3v+uia0m8NGOD+LZKiutKHpskYhoWRsait8lEVruSl15vIZCyCPo1TVk2jumJgZ/hyRTzHwjGL/RzIqsZxy9Ywd8kJGMkO9nQ2c8/vf8bW7a+z4NiZvPOK9Vx41ml49NJGGASCkUCILEG/jMaDYCxRbNPnkWqtkx1XZzSNrrp9/A42xQj6dWqrfLnjBXwabZEUmibjOOAAsYTBoZY4qiLzwvbDLJtfV9Q1zQo923aKOtd8c/n8tsPYtsPegxFMyyEc0AgFPEyuDaBrSo/7T1EkbNum4XCUVNrE63GF45S6AHVV/rxjSaRMnt92OHf/ZhtO5xvzQMIg+7+Dfh2/V6O6wodhmKxdMRXTdPjLpj3EEhl8XeamDYeizJwc7vdHSX/3VbkWEQx0zHIU5w/1cyDJMp5ANQSq+bev3cnmZ/7Cxocf4LPfvItv3v1LfnzHp1lw3NySjlUgKDciXSjISzlTX+OFYps+l8uVvr9xhQI60yYFXVPNjEVlyJM7XnYsNZU+LNNh1rQwM6eEaW5PIiFRX+2nPZIeVpPtYs6191wGfCqNR2LsbezEtGwsy6Y9miaeNFg8twYgd/+pisSeA528scetubIdB11TmD01jG07mJbdZyyL59awfWfP+zfbcDrfmLPCIF/D8Lf+ZpBIZYglDIJ+naBP55U3m92id4+CaTukDStX9D7Y9et+X7VHUjyz+UDeVGUpGMkG5qX4HOjeAGvPvZLbv/ET/vM7d3LaGWdiKRJHGnfzw5//mudeekWkEgXjAhHJEuSl3Kmv8cBQfpGXsh9iIeMK+jXCQZ2KkIfTVk1HVd/63VQZ8nLaqul4PBrpdIZ4wmDjc/vx6Ao+r5ZryjzUazrQufZOM/eey0jcwHZcUSLLEqoik7FsLBu8utrj/lNkKZce1BQZw7SJxg0icY366kDOdb77WPq7f/1eLe+Y+/PPAvezsHhuDa/ubiOTsamp9LFkbg2mZZNKm/h0lYxlI8tujZhXV4vqqRiNG654tB1CAb0sUaaRbmBeqs+BrKjMXria2QtXk4p3sqN1Pw888Xd+8Ks/MHfmVK69/AIuPecsfF5Pic9AICgN4/5puWvXLr7yla+wZcsWAoEAl112GR/72MfQB8nfr1u3jsbGxj6vv/zyy3g84gM70l/KY5GhNn0utyt933H5WDqvtofA6v5en1cjk3FTbOGgh7bOFJIk9bmmpmnn6p9UVS6oHi+vj1Q/aebuY66t9OPzqOyIG2A72LKELElkD9P9/vPoMrbjIEkSfp+GGTdwgKqwr8f16O3s3vv+ra7w5qJ2+a5Pb2EQiafZtKUxdx7L5tUxqS5EOp3BcRxs2yHo14klM5A03YbTBRS9975+FSFPrs1PuX7QjEYD81J/DvRABXpgKf9513289Pe/8sRDf+Ar3/spP7z3fh68+xuEKqpKdiyBoFSMawuHzs5OLrroImbPns2tt97KkSNHuOOOO7j00kv53Oc+N+C269atY8mSJdx00009Xl++fDmSNPQvnolk4TBaNVmjZeHQn6gYqeL/Yo9TyPt7z2V/13T/oQjPbD5AMm3i86isXFhPa0dqwGuf7/i9e/7FEq64yUZlum/TEU3z4FO76OhMIcsSmiYza2qYc0+ajarKubHGEgZN7UlSaRNVkXAcmD4pxDknzcorLLP0runCAcsuzMIi33nUVPXtXdh9jF6PyvL59VRXFPYZyc6Fqsg8u/VgD7uKmkpvv5Gs4dyPY2EhS6k+37ZtcWDnNvZsf45zVs7FYyf5f/f+ibddfB4nr14xrO/x8YKwcCgd46p34Ujxf//3f8Tjcb7//e9TWVkJgGVZfPGLX+TWW28dtIdibW0tK1asKP9AxykjkfoaKwwkKEeiX+JQBO1QxpXvmpqmzTObDxCJGXi9CpGYwVMvNDC5JpCLfPVOX/U33nxpuljCIBJPEw54eoy5usLLJWccy0uvN9MRSZJMW2QyNs9uPZjbX3asiVSGbW+2Eo2nCQU8LJufP3KX71xTaZMXth+mPZIuuOg7b7oxkcEwetYwDecz0n0uCo0yDfeHz0Tq/SnLCjPnLWfmvOXEExFee/1Fduw/yK3/8Z/MmlrPtZdewBUXnE3AP/BKT4GgnIzrwvenn36atWvX5gQWwPr167Ftm02bNo3ewCYQ2S/liSywSl3kX6wX0WgvMoglDZJpE69XceuJdBnDsNF1JW+RdO/xtnYk2fJaE6Zp9ykgb4ukaOtM8exLB/sUdNu2g9+rcerKaVRV+Aj4tFyKL3v+2fuvusLHqaumcfZJszh11bSChUV2EUAiZRZV9J23EN6voet90+Wl+Izk80HrzWjfJ2MZ3R9m7qoz+eoPf8MnP/dl6qdM4+t3/5J/+exXSSaioz08wVHMuP5Js3v3bq666qoer4XDYerq6ti9e/eg2z/44IP89re/RdM0jj/+eD7xiU8wf/78cg1XMEIUmxIxMlZXukfp49VU7K/+oUQaSrnIYLBz7z2+xXNr0FUFr64QjbstalyB5XpBZQVG99qt7uMFiMQMWjqSOA4snlvD4rm1bN/pptAM4612P90jSJF4OjcOj6YQTRiEAnre8+9+ToXMx2BF94XUF+arYVo+rw5Fzv+7tBRpuMGiTMO9T8ZCqrDcqLqPladcwPK153Jo7xvEmvay50g7+3b9g/v/8jeuv/JizlizGrmf6ygQlJpxLbIikQjhcLjP6xUVFXR2dg647bp161i2bBlTp06loaGBO++8k+uuu44HHniAGTNmDGtciiwxzoOEo4rS9QAYyjx2RFJs3dFMPOFGHpbPq6MyPLDISRsW7ZE00YSB36vi9ahMqQvi82pFPYxs22HbzlbaIimCfp22SIptO1s5bdX0Affj82oEAzqtHUmQJGJdxezFHj/fuddUuqkSRZawbanH+A63xmk4HKW6wkt1hQ/bcR/kFSEPqxfV09yRIp7IUFvtY/m8OrQuUZIbb3uSSCxNPOX27dvZ0M6+QxHmzqxk2Ty3+HvTlkY0TcHncZtVJ1ImGdPuMY7OeJpE0sRx6HP+kVi6qOvZ3/VfsaA+93rv8+mPmko/px8/IydMtK70ZO/7cij33FAYzn0yUmMshOF8vgs+hiIz87glcNwSMskIzfsiNHfG+PDnv8G0SbVce9l5vO2i8wkHA2U5/kghK1K3/4pnzlhkXIus4fCZz3wm97+PP/54TjnlFNavX88999zDF77whWHtOxA4egw7y0mh82jZNoZhoagyr798iEjMIBTUicQMXt/bztlrZ/cbgbBstwbI41GxgWQyg66prF0+ncoKf1HjTaYyZDI21ZU+/F43tZTJ2Hg8Gj7vwM7qp6ycwQvbDxGLG0ytD3H84ilUDuIa3vs8/pH33CsAdy67j8/rUTncEieRzDC1PkQilWHeMTWcsGQK4ZAHXVVy86rrSp/5O2XlDP6xtZHWziR+n0oiaWIYFhnVpqk1wQ5PB2eumUVNVTvNbQl0XSFlWNRX+wkGPX3myasbVIS8pNJm7vxDIQ/PbTtc8PXsfw5mEw75mDalInefWKad97wKoft9OdAxh7LvwRjKfTLSYyyUEfueDPlYd9k7OG395bz8z6d4+A//x3fu+Q3xaCcfveVa/L4Qijq+V00HA2JF/LAp00KJcS2ywuEw0WjffHtnZycVFRVF7au+vp7Vq1ezffv2YY8rHk9hiTqJIaPIEoGAt6B57P4L3aO7RdsBv4YiSXh0hbaOJK1t8X7TKUdaYry6qwXLcvB5VabUBrrsCywi0WRR47ZtB01za5QMv5uCrKn0kU5nyGTMAbdVFThxyeRu6RyKOn4qbdLWkcSjKz3Ovb0jQW11kHg8Rca0c+PLNjf2e1Q01X1/ZySFbVmkkgbdrTDzjV1V4KRlU0ilM+zc307asJAk19YgnszQ2p6goyPBgtlVpA2TeCJDRVBnwewqzIyVd55OWjalm+M5tLbF855Tf9ezvzno/v62jiRbXm8ilTYJBvSCIzpZ09OqSj+ppJG7Lws5ZikZyn0y0mMcjGI+36XmuBWnM3fZqbz9wE6kZDvbdh/mvt//iJ37D3HDlRdz9qlrUJXxI7hkRSIY8BCLp7Et8cwZDsEapyyxwHEtso499tg+tVfRaJTm5maOPfbYURqVu0xcLKcdDu6tPtg82rbDS6835Za+d0RSXaaONjhOrvZGkaW8+7Fth1d3tWKZDpZjE4sbJJIZ5s2q7nebwVgytyZXx1Md9rJkbg2O42AV+AWoqXJR78+iyBJ+r+rWHXU7d1mS3AiWaeM4Tm58sYRB0OdGkbrXXRVz3pIEi+bUsO9gBEW2AHcMyZSJR1NQZIlQQOfk5VN71AJ1H0f3eZKknuff3zkpskQmY+XsD7LCbKD3W5ZNW2eKh5/ZTSyRwe9VicYNHNvJ9Sfsr14pW8eWSJlUV/pYMLuKgE/LHX+gY5aLYu6TweZl5Cns811Oaqe57XkSqSi18w7z4hu/42Nf+haTaqt424XncO2l66kIB0dlbMXhzqVtiWfOWGVci6zTTz+dO++8s0dt1iOPPIIsy5xyyilF7evIkSNs3ryZyy67rBxDFZSBfIXAsiwR8uukM1ZBrV4SKZMpdQE6om7DZFmWmH9M1ZALg4txQS8l+Qq1Z00Ns+mlRjIZN4K1ZG5NL1sEk+07h25OadsOIb/OMdMqONwaJ502SRpWH0POfAXdhVgf9GegmS2ab+tMEokZhIM61RWuMWl/VgiuID9CNG7g0RUM0wZMYgmD5vYEO/a2512s0KPnX0CnuS1BJOqu7kukTAI+jVlT3e+ekTL5LJbRMCIdL2jeEKeufzsnn3slO7b+g8c33Mdd//sHFs2exOoVy7AdlVBoPIgtwVhlQpiRHnPMMT3MSC+55JIeZqQ33ngjBw8e5LHHHgNgw4YNbNy4kTPOOIP6+noaGhq4++676ezs5He/+92wCt8nkhnpaFGoWWFvw8jsL/RCG+123z7gU+mMGdRV+Th1kEL13vsoRDiNlLFrH4PLSIrqSh9tHUmqw30NLgsZf7739DD6lCWQXMf4Yg05izmn7GrATVsaOdwSo7k9Sbpr9WJ9tY/JtcF+o1JHWuM8/MweonEDAL9XxbQcjptViaootEfym6em0iZPPt+Apsr4vBqWbbOroYOw321llH1/OZs7l4qxsrpwtMyGC8GxbdqP7MfjJAikm/jM175NwOflnVdcxHmnr0VTx1ZcQpiRlg5hRpqHiooKfv7zn/PlL3+ZD33oQwQCAa6++mr+9V//tcf7bNvGst7yxJk+fTpNTU187WtfIxqNEgqFOOmkk/jIRz4y7JWFgpGjv1/oqioPalSZb/v6an9Rv/ALFU49oiEFmmEOlWzUKNuXMOjX8Xs1DL+Vd7l/vihT94dxd6uF7DmGA54e5xNLZKgKezhlxbS8flFDFXL5xphKu9GneNcqRUWRMC2beNLMNWb2etQe52TbDm/sacOy3Jq5tGERS2aorfSx8Ngatr7R3K8tQg/7B0kikcoAEuFgT7sJ07LHvMnnRDIiLReSLFM9ZTYAmdQszrviOp585AFuu+N7fP3On3P1hWdz89uvwO8Ti5sEhTHuP3Fz5szhZz/72YDvuffee3v8e8WKFX1eE4xPhutKP9TtixFOo9FsOycOIil0XSGWMKgOD957srtw9HlUkqkMKcPq0bh49aJJfc4nkTJzxp/97a8/IVpMlE/XXMPUVMpEltyaIkWRSaX7b8zcOy2cVDPIksS6NTOZVBMg4Ovo10OruxBPpEwm1QTweVTiiUze/o/FMFYiS4L8aN4Ap1/4dk4970p2vbqZxzf8lgcefYor162GqjpaOpPMnD51tIcpGOOMe5ElEAz3F/pQti9GOI1Gs+2sONi2s5VMxqam0seSuTWDpk9ffqOFlo4EHk1hx742UmmLiqBOKKDnnNKBgs6nECFabJRPliWOmV7B63tbyVg2tuVgY6Oq7uv5tuk+//XVPjpjCnVVPibVBAqqV8oKcct2qKkO0Hiok5debxpWfdNo9QUVFI+sahy37CTmLjmRZKyVA7FWdu3cwYf/46vMmz2d6y5fz0VnnY6uD2zTIjg6ESJLIBgCxQin7g/yWMKgIqSzeG75C48rQ15OWzUdj0cjnc4wWPllc3uC3Qc6sCy7qzDcJZbIcLApRtCvU1vlemwVUkhdiBDt/h6PrmCado+0X29s26HhcJSaCp9bk+VYeFSFmgofDYejzJwSzptuHCgtXGgRvqa5vlqV4eFFT0cyfSwoHZIs4w/XQbgOtWo6H/xYhicf+SOf/eZdfPNHv+LtF53Nh9/zztEepmCMIUSWQDAEil2xVRnysnhuDVtfbyaVdlf1lSN60TsFJcsSPq9GJmMOuNy/e92SaTukDRNJkqkKe3Bsh3TGYnrIkzvH/oRJ9+MXIkSz7zncGieZNEkaJkGfRiKVySuysqKsIuTpeo9r3RAO6kRi7gpRv0/rMw+VIbc4PZY0CPr0PjV7xUQzh5vmG430saC06L4gJ593FSedfRn7drzEE3+6j10HDnGkcTe6L8DOAy0cv3QRUpkMLgXjB/GJFgiGyGAP7u7YtsP2na1E4kbZohf5UlA1lX4s2yaVNlHy1Exl6Vm3lMIwLGzHoTKkkzEdqsIeTls9vcc59hYm+Y4/mBCVZYnFc2vZfyhCMm3i97p1Vdt3tuadm6woa+1IosgyyVQGj0fhwJEYqiLzwvbDzJ5Wwb6DkR7jAEqSnmvrSLJpywFicWPI+xmN9LGgPMiKyjELj+fmhcdjxDvYEz3Ctice4zt3/5y5s6Zx3WUXcMk5Z+LzCkf2o5VxbeEwFhEWDsNnLC/x7k4xdTXdrQCyq/8yps2ZJ8woSfSit51F1lpg2bw6duzvoK0jid+rDrgCsrudRUtHilT6Laf3afVBTlg6uc+2pmkTSxr4PRr/fOVQn+MPZvSZnZuNz+1HliUCPo20YQ04N9l5b4+kiMaNrnFKTKkL5KJEAZ9GKKDnVj6C1K9NQ6FIksRz2w5zsClK0FfYfvqLeh3NNVnj5fM9VDLpJC/9/a9sfOj3vPTKdkIBHx+47gpuuLr0HozCwqF0CAsHgWAMUWxdTbmjF/lSULGEwZbXm0ikTLeVSmeKl99o5vjFk/tYLfROf06tC5AyTGLxDOGgTjxp9jm//YciPLP5AMm06/Du0RWqK7x5U2ADCUldU9yG2p0pVEUedG66pypN0+apFxrw6Ao+r0YsYdDSkaS20odHV8iYFu2dSRRV6ZOey5rPFpr2MzIWsbhB0K/j1ZU+59ibgYTUcFfFCsYumsfHCWddwuozLuTAzm088eBvMWyHwwd20dyRIJqyWLt6uUglHiUIkSUQDIFi62qG67o9WB1QPhFXEdJJpU1CQR1FkkinTXYf6CQaNwgHPX2iJ90f/Lbt8PTmA1SEPHg9KpIk9Tg/07R5ZvMBIjEDXZNp6XD750ViaeprAti2Q02lryAROZS5yaYqbc0hHPTQ1plCkiQSSROfRyUST3OwOU4klkZRJEIBD36fSnXYSzSeIeBXeWH74ZxreyGRJF1TCAZ0DjZFwdGIxAwqQx5UpW+auD8RvrarxRAwqPgUjG9kWWHmvOW8++PLMRIR9kaO8MAjP2LDoxuZPW0S1156AVdccLbw3JrgiHRhiRHpwuEzHtIJ/bnND5aCKrZo2rYdmtsTvLGnbVBB0DtysnhuLa/ubs0Job2NEcBh9tQw8aQ5YKprsPPriKa4/9EdKLJE2rBIZ0xs20GSZGRZoqbCy2mrpzNzSrjg8x9qQXnv854xOcSmLY054efRFWTJTUVWV3gJ+HTShkkiZRaVPlQUGdOCTVsaaOtIEo0bhAI6VWFvn2uSLz0cT2bQNYXDLXGg/xTsRGc8fL7LhWkkefm5J9n45z/w4ktb8Xl0vvxv7+O8M04d0v5EurB0iHShQDCK5Fu1N5TIVDGr2DqiKV5+o6XLVsFhSl1gwLRkvkL85fPqeH1vO02tcVRFor7aj8+r9YlM5RtnD9uJoM7ibj5bQZ+Oz6PSGU1j2jaWBY4DkmQjSzKKIrHvYITpk0J5W/HkE4tD9TvrnXozMhYVIY9bFK+7+8uYNhVBnbUrpqKrCk9vPjCk1X3VlT5OWTGNJ5/fj207uSL8La81cdqqtxYG9I4sRmIGiVSGZNoVo0iw/1AUj64U1cZJML5RdR+rTl3PipPP49DeN3jiwd/gDYY41LiLf2x9k6rqGk4/cTWyPHjHCsH4QIgsgWAQ+hMH+epqSuXinU03tXQksGwby3HoiKapq/L2sCoYbJw1lX7OXjub5pYY/3z5EO0Rt6C9kJow13ailq1vNJFKm2x7s5X5x1RRV+VHVWVOWz2dZzYfoLUzBdhIEiiKhCRJGIbVw++q3N5Q3QWarimEAx4Ot8RJpk2QQJZkwkEP4YC7yqu3AOov7ZcP07JJd7ngZ7dv6UiCAysX1VMZ8vYR4ZUhD0gOKcPE51XBcYVfNN6/J5hg4iLLCtOOXcQNH/0imWSU/Z1H+MMTv+TFl7czfVItb7/0PK6+8DxCAf9oD1UwTIRcFkw4bNshlY0YlGBfWXGgqXJOHGT3nX24Z1Nom7Y08uTzDWza0khHNDXk42ZrvsIBHa+u4tgOsYTB3oMRmtuTvLD9SI/9DzRORZbx+zSWHFdLOKhjZKyCIm+u7UQLkZiB4zjs2NfGw8/s4W8vHqAjmmL6pBCXnTWXC06dTUXIg64qyJKM36uSNN7q/df9fLLRo6x7fLY+qZTIssSy+bXMnBJCVWQ0RWbWlBDL5tf1iEJWV3jdPohJg0jc4NmtBwu6ZtkoVTRu0HgkRjyZwaMpdMbSPe6NrAg/84QZnLZ6OjUVfhwHkinXD8x2IBTQhXXDUY7mC+GfPJd//dpd/McX72D6rNl8557/46x3vI8du97EsUUacDwjfj4JJhSlXhpfaIF7qSM1OZPOljhGxiKZMnFwIzD11T7aIz33P9A4AToiKbbvbMn1+Fs8t2bQeXnLDkGlqS2JbTvYkkNLe5Lntx3GoykkUiY+j8LUuiCdsTRGxibZVeu0fH597txLtbqymEihV9eor/Hj96qsWDCpT5H/wmOreeRve4glM9g2GKYFO2Dt8qmYlj2g+/vSebVsea2Jlo4kQb/G1Pog0Pfe6B5hWza/lnTGpPFIDHBrsrLCTyBQNQ9LTzqbJSeeRdOBnTz35ENkJJ1Djbu55/d/5aTVy1m3dg1KgRFXwdhAiCzBhKEcKalCxUEpXbyzQmLhsTXsPxQhbXTVGHUJpHDQQ9qweux/oHFats3WHc25eYnEjZzZZ3bs+QRFdp/N7QmS6QxI7oq4UECj8UjMjbJ5VHbu7wQcvB6ViqDOjEkhli+oo7qiZ73VcFZXArR1pnKpy6BfH9DzK+ujlS3a374zf8/EeNK1t8hYNiRN2jqTPLP5AOmMlRPp4YAHI2Ph876Vns22LMKBzli6z5znozLk5ew1s3L+Y71tNMYTorl1+ZBkmUkz53HJu+aRTkXZ0dTAi6/t5jd/foJJtVVcc9G5vP2S86kMh0Z7qIICECJLMGEoR7uSQsVBqSI13SNxDg7JtImqSOiaDKgkDZN4IkMybfXYf+9C9XBQZ+7MSndeDIt4ou+8NLcn2LG3fcBC9KXzann5DTdliONQGfIQTbhNokMBjeb2FJZjo0gSmiYTCvR1hs8ymDdUfw9u23Y40hrniX/uJ5bM4NNVYskM7CCvgC60Z2LKcB3mDdNGliGRziDLbgF/KOD6dj3/ymE8ukoilSEY0Dll5QzUrkuqqjIrF9UXbT3Ru5ZuvHE0G6mONJo3RM3MRXz+e79ix0v/4PEN93Hnr37P//7xYf70o69TVVUz2kMUDIIQWYIJQ7kMPwttIDzcSE33SFzAp7KnMUIqbeHRFeJJN10Y9GnYjpN3/9lC9edeOcT+Q53sPxRh+uQQZ504m4Bfo7U9mZuX6govb+xpoz2SHjDqVxnycuqqacw/pipnI1Fb6Sfk13Nu65blYOEQjRkkkiatnUkm1QTynmN/Kwj7e3B3RFNsfb2ZN/e3E+uyTMhGnfprJF1oz8Sg33WEhy47hy6X+KDfjdA5jsOBIzHCQZ2KoIfWjiQvbD/EiUsm95ifo8lUVDS3Hh0UVWfh8aezYNWpvP3gHva9/iINbXEOHTrAf//k91x90bmcfcpJaKp4pI81xBURTBhKIXQG2vdg0bDhPnC7R2BURe46poLPo2FkLGRZYt2amVSFvf1Ggra92cKBI9GcTcC+xggvvHqIpXNreXlHc25e5s2uYstrTQVF/WRZYlJNgLoqf+7cIvE0W19voiOaxjRtVE3Gchyw3EbTdVX+ooxW+zPufP6Vw+w92EkimcFyHGJdiwGShtmjsL73eAvpmZjtaRiNp5msKiyfX88be9ty4qwzZgDk0qJIErGu1YBaPz0cJ3oaTTS3Hl0kWaZu+hzqps/BSMXZtWMr0bTFJ776XWqrfsbV68/mHZetp7aqcrSHKuhCfCoEE4rRjiwM1esJekZgAj4Vx3GtBybV+IjEM9RV+ZhUExiwyXM0nkaS6GETEImm8fu0Hh5a2T6BxUT9+p6bRMDnptJUWSLg06kMeUikzKIeuv09uCPxNI1NMRwHNFXByljYlptCrQh6ehTW96aQ+6C3RcUbe9uYNTWcO35dlS/XUkiSJGLJDFPrQ+iaQj4P59FOo42EwBPNrccOmjfAcStP5es/PpMXn32avz74W35y3wZeef0Nvv3pj+L1h5EVcV1GGyGyBBOO4Qid0aR3BGbW1DA4YNkO9dX+XOQllTZRFblHe5ZsD75QwMOhljjJlOsPpUgy4ZCHRDKTi2RlBcBA0Z7uD2zoWRxv2w7Pv3KY/YeiIDk4tjvGuiov8aRV9EO33we36ooZx3Hwed3idAmYO7OS4xdP7lFY39985rsPsuemKnLOoiIbQYOeqwsj8XS3OfJx/OIpyDJYltNnn6OZRhspgVfOaLFgaCiqxvwVJzNn8Ylc09xA5PA+drdE2fbSU/zu0b/xzssv5MKzTkPXx3ct4Hhl/D2JBIIJTO8IDNAjRbdpSyPtkRTtkTSmaaEoMtMmBTlhiduepbdNwPTJIY5fNIVntx7oIQCyjaLz2RV0f2ArsgSSKyqyD29dVWhsimE5Nj5NJaPbWJZD2ijMf6s3/T24DdNGVmRSMQMjY+P1qMyaEmbdibPyFtb3R3fB2F00eTSFaMLoE0EzLTv37+7Xw+fVqKxw28H0ZjTTaCMt8EY7WizIjyTLVE+aRfWkWWSMBObBFIrnRT7zzTv55o9+yZUXnMV1l1/EpNrq0R7qUYUQWQJBEYxESqZ3BCbbkHnLq010RFNE4wbtETct6NUV9h2M4NFUTl01rY9NQMCv4/FoPVYXpg2rT6Po7jVF3Yvv9x2M4nT1O8w+vFcuqHcH5tDlpi7h9SmcvHJazu282HnLJy43bWnE71WRHK+7us+nceLSyUUJrO6C0e9VSWcsEknXx6szliaezOTMQ/tLfXU3nO2P0UyjjYbAG6/R4qMFVfez/OTzWbrmbPa9sYXHH7yPX/3xL/h1meuvWI+k+vB5vUiSEMjlRnxKBENiohf45mO0am46oim2vNbErgMdqIqMaVrIMki4DzrTsonG07mHatYmIHuN/AFPbnWh4zgcbI4DDh5d6RP16F18n/0O1lSFoN/tdyjLEtMmBdl3MJIryJ82KdSvwCp03rIPbtt2iMTTxBIG1WEvnlqFeCKD7Tj4vQOnPHqnObtHeFrak0TiBtMnBXuYhYYC+qBRONt2yJgmgUB+9+3RTKOJOilBf8iKyjGLTuC9i07gbc2NWIlWdrd0cO+vfsKOfY288/ILuOScs/B6StsUWfAWQmQJima0C3xHg9GqucketzOaRlcVN/LiOFiWgyy79VmK4vpTdX+oZq9RImVSXenjmKlhHNshEksP2Ci6d/F9tjNRxrSIJUxqKr14PSonLJmMR1OJxtOEAh6Wza/N27ux2HnLjjuWMNwWQZpMRcA1Yq2p9A0oHHrfl/NmV/WI8DiOQyTuttCRJIlo3KAi5OGUFdOwHaffHwy953LB7CpCAb3PuY5WGk3USQkKoaJuGjAN00ix8JQIBzt+x5e++xO+fc+vufzc07np7VdSW1052sOccAiRJSiK0S7wHS36S8mk0mau6Lwc5589biigEwroNB6JkTRM/F4Ny7aRJYnpk4M5kQO9rlFAp7ktQdowWbt8KkbG4oXtR/ptFN2n+H5KCCQwrZ7eXFn/rO6CIp/49upqwams3veWJEm0diTpjKbxezVWLZrU7xznuy/f2NOO36vSHnEd2WMJk2n1QTy6Skc0lYvK/fOVQz1Spv3ut9tcLjq2hu07+/7QGK00mqiTEhSKqns5/syLWXXaBRzYuY3HN/yW3//lKdadsAifMo9I2mJyXa1IJZYIIbIERXG0+uTkS8kEfCovbD9CIlW+iF734wb9GuGgzoxQiMVzatm2s5lEMoNX7znv3a+Rz6Oi6266zbRs/D6NZfMHjnoMVHzf22sqXy1Xb6+rQlNZ3cft0RUsy0aSJKbWBcmYNvsORpg+KZRXQOS7LxOpDCsX1udc7bPnGvTpPLP5ALbt5MbW3w+FfHMZixtsfaOpx6rEsfBDQ9RJCYpBVlRmzl/Be+av4Jr3NmMmO9jRcpB//9zX8Oo61152PlecfzZ+38TOUpQb0WlSUBTZh34skclFQgI+bcLXf2QjPNUVXjKmTXWFByRoj6TQVDn3oM0WUZfruDWVvpxpZjSewefVaI+kexy7+zVKpk0iMYOA/61rlBVRZ54wg1O6itXzHbeY3nq9RU7ApxKJuXViPcfffyqr+7jjyQyJlInfo1ER8hAK6D0aXg+0bff7sqbCx+pFkzh99fTcuZqWTTpjEeoyGQ36tX73nW8uvR61q3+iNuj2AsF4IFBRR2DycTD9RG5438eorZ/Mf/3wF5z1jvfxle/eTSKZGu0hjlvEzx5BURzN9R/dIzy27fD05gMjEtELBzysXjQJcFcaDhZN7H6NEimT+mo/C2ZX9RuFGohC6++6R9zShsXB5jiqIvHC9iMsm19bUCqrd//FoF9D1xXShjVoMXe++3LW1DDPbj3YZ+zFFIrnm8t5Myt5uavh9mDbl4Luvl697TYEglKi6j5Wnb6eFaeex6E9r/PEht+yefs22pv3Y1VUsbOxleUL5iHLIj5TKJKTz7pYMGQShsmWXS1YVv5VSBOFcq4uVBSZcMj1Ixor85ivoHvTlsZceiz7oC11yiifyAkHPAUd27YdLNuhpjpAPJ4uei57n2Ms4fY8HKho/eU3mtl9oBPTsplaFyBjOgNu099xjYxFImXmrXsqZFtVkXl268F+x17s4o3ec9nakRjy4o9iPjvZcbZHXOuOUECnKuwd14tNxuLne7wyEnNpJCKYkSYiB7bxr5/+KtMn1/GOS87jqgvPJRTwl+WYo0HF3BXIigZqaVdaCpFVYo4WkVVOxtqX8EDNi8u5ynIgkdPdVHOgYw9nLlNpkyefb0BT5VyKLGPanHnCjH6jYIlkho3P7cejK3g9as6H6qwTZw4pwjeYIOnv76m0ycbn9iNLEgG/Rtqw+oy92B8KvedyKD80irlnste/tSNJJGbkopehgE5NpW/Ua8CGylj7fI9nRnIuTSPJay/+ncc33M8Lm19E01SuXn8Wt73/PUgTILJVLpEl0oUCwQAMtJqy3Cu6BkoLjsRqsqH4L3k9KuGgh8MtcVLpOImUW7uUSJk5D6xixjxQWrO/KJ+RsYglMrR1pogm3Boqv1djSm2gx9iHWyhe7PbFrszNXn+fR6UzlsbrVbAdB59XPSoWmwjGFqruY+lJZ7PkxDM53LCTjRvuI2HEOdS4G0nR2b7nIGeddCKKMv4FVykRn1CBYAAKqX8q9kHbn8jo/bfBRE6pV5P1Pv5Q6u9kWWLx3Br2H4qQSJu5FXnbd7aweG4N23e2liTyl0+wPL/tMB7N9RJr60xh2a6fWHskRTKV4cSlk0c18lPsytzs9W/tSCIhkcoK1qRJbdXAnmFjlcFMXQVjH0lWmDJrPtd96DNkUlH2R5rZ8tQGfvDje5lSV801F5/LNRedT0U4ONpDHRMIkSUQDEAp3bR7R14Wz63B79X69NTrLkBGapFBf2ms3kX3gwlDAL9Xo7rCS22lL5eqiyUMtr7eTCQ+PNuD7PFs2+ljNHrgSIxQQMOrq0TjBpbt4NFkvB6FTMZmT0MnMyeHy24e25+ILvZe6i5yZVlCUaQeNVnjLVXYn6mrYPyieUNo3hBrr3g/1bOX8/if7+MH997PD3/5Oz54w5XcfM2VEyKVOByEyBIIBqBUqyl7R14Ot8TZfyhCdYWXgE8nbZi51FrvlOTa5VOJJQ2CPr2gvn3dH/RKAVqwvzTW4rm1Axae9yfMdE0h6Ndp60yhqjLReIaKkN7D9gCKW41p2w7N7Qne2NNOIuX2IZRl6Iylc07uluUQi2dcgWU5GKaF16MAEgGfRsowy5piG6zeaij3Uve08HheXdifqevJy6eOu3MR9EVRdRadcAYLV59Gy8E9bHzofnyhCg427qLhUDutcYPzTjsJTT36JMfRd8YCQZGUov6pt9FmKm2SSJvUVvpo6UgQifXsqZcVICnDHPDB3Tty0vtBv2JBPeGQr+CxZY8fSwxsuDlYfVFvMZEVbEOJCOZbtXikNUEilcF2IBIzmFIXIBo3SCRNvF4Fx3GQJMhkbAK+rHeX28/Rtp2CInLFUGi91VDupe5p4WKaY48l+jPIFXVlEwtJlqmbPodr3ncbmVSchmgzf9x0Fw8+/Ff++86fc/WFZ/OOS9dTU1Ux2kMdMcTdLRAUwHDrn7qnikzLJpFy65UCfg1FkYjEDCKxbE89V4Coijzgg7tv+vEtIZN9/9YdzUyeFHZ7HHbVWQ00NnAFUEVw4MjTYPVF+cTEUCKCWfHS0p7MCaT2SBrLdkgZFrMmh0ikTDRVpjLkQZYkbMehIuTB61GoDHsxTRtVkUlnLJ7efKCPWC3FKtFi6q2ORmf2HveYJJEyLCqC+risKxMUhuYNoHkDvONfvsTxZ17C43++n3t++yA//s0f+a9PfoBzTz/1qEglHl2fdIFglBjIaDOWMJk2KYhHU0ikzJwAMS273we3ril9BNjWN5r6CKP2ziSPbdpDNJbG71XzCoj8kSe3SL2/yFMh9UW9xcRQojhv9W50VyhmLItEOoNlOvi9GsGAm0JNJDOE/DqOAz6vmisO792vsbdYBQqKQA1WsF3K2r2JSCEGuYKJiaxqzFtxMsctO4lrmvbz1J9/R7i2ngMHdvHXv2+hurqW9Weehq5roz3UsiBElkAwQnQXGd2NNrOiKms/0N3wtL8Hd77ISSpt4tVVInGj6/0GiZSJLCfxetQBi82LjTwNNTJVbBRH1xQUWWL/oSi2Y2MYNj6PQiigo+sKkZjBweb4/2/v3sObqvJ+gX+TNGnatEkptNUCI7Rja7lIy61yKMULokVHUSii8z4w4jCVA4OgnAGxUyvyIo9HB17re0QRzzAz3ricZ3xlAEXhlVKwMwiiwIuOpMrNAlKaS5t79vmjJG/Ta5rsney038/z8DxkNTtZ+e3V7F/XWnstqJRAxgAFErVx8ArAgH4JGJkzAHFxyms9hx0nq77/d9UDFcyE7Z7EQ8qFfOXM18bCWSCXYpdCqUT/64bgwceegtvRjPOWy6g+tg1//2IbXnrjL3jw7tvwyPR7kDEgNdpVFRUXIxUZFyMNX19ZrDCYi21nQ1mdrTjfepmEeI0KliYX+qVooVIoYLO7ul1MtKd1lDph8HoFfFr7A364YIZCAQgCMCgjGWOHX4eTp3+C8ZwJDpcHmjglnC4vkhLVuL3wZ8jor/PXp6vV+QF0uXp+wLE6DRxOD/RJmk4nbHcXD6kXsI0FfeX3OxJiPZZejxt1/3UUe3dsxcGDNXC53fh//74aQ4cMhVIZ2V5gLkZKFGO6u+AG06vT2RBbZz0nbe9G+/zrH2G2Ov0JV0+HsLqro9Tzi5wuDzweAUMy9VDHqeBye+D2CEhKVGPs8OtgtjrQYHbA5fZCo1HCanPhVF0DMvrrAurYVS9TR0Olvnj3dMJ2V/EIZnJ8X+3lor5JqYpD9ohxyB4xDrMun8fRA5/ApojH+TNGvPR/t2FS4Rjce8et0MbH7lIfTLKIJCBmj0VnF+62CRjQMmSoUav8zx+Vk4ZT319FQ6MtqCE9uV3kW891SkpUwNrsDkgUdQkanL/UBI1GCa8HSNC0bP/TNgnqKFn1fVa9Lr7DYVzfzQRiTdjubnI8e7moLzOkDcStD8yFy2nDdz9+j58sTjz3b5uw7s13MH3qZPzygXuRmZEW7Wr2GIcLRcbhwvB11wUut0SgrZ5urCyGzi7QKpUSOl08rjQ0dXp3YXevEW1d1avBZMOu6jpYbS4kaOKQkBCH6/rruo11MBtv+86bbwg23EU0ezJsGYk2I4ZQfhdjfYhLTnpzLL0eN85+9zX2frgFBw4cQFKiFh/8nzXQGfpJMpTI4cJOnD59GqtXr8bRo0eh0+lw//33Y8mSJdBoug6UIAjYuHEj3nnnHTQ0NCAvLw9PP/008vPzI1NxColcE4HWgr2dX6xksathKJUKUClbNnju6ku4p/vqRVJXdyWmGhJQMimr1Z2VmqB66zr6rAU3pcNsdUCXEBdw3hK1alEmbHc1bGl3uHu05Y4cxMLvIsUupSoON+QW4NHcAsz4VT3OffcVjI12OL//Aqv//R08dO9UTL/rdiQmyLvNyfO3N0gmkwlz587FkCFDUFVVhYsXL2Lt2rWw2+2oqKjo8tiNGzfilVdewbJly5Cbm4u3334b8+bNwwcffIDBgwdH6BNQT0Q6EQg1CQrmdn4xL1BdJXXqIIe1erqvXqR1Ndcp1aDF5LGD252rzs5fR5/1qtmOvx//EZev2uDxCLg+TQeny+s/b0qlAmq1Cqow1/XpLGGMtSUg5JyUU++jH3Adhg24Dm6nHRcsx5DSPw1rX9uMf/vje7h/yiT8y4O/wM8yr4t2NTsU/W/PMLz33ntoamrCq6++ipSUFACAx+PBc889h7KyMmRkZHR4nMPhwOuvv4558+bhV7/6FQBgzJgxuPvuu7Fp0yZUVlZG5gNQj0QyEQgnCepuorXYFygxLtCxdpFvq20S1tlwoO+GgNaf1Wx1tqwe7xWQnpqAC5ebcKmhGVmDDJLsEdhRwijW9k2RIveknHqnOI0WWSML8eSasbhQ91/Y+x/v4z8+3Y/LP/2EVUvnQ5OYDLVKDaWMFjmN6d+G/fv3Y8KECf4ECwBKSkrw7LPPoqamBg8++GCHxx05cgRWqxUlJSX+Mo1GgzvvvBN79uyRutoUokglAmIkQV0NcYl9gRLjAh3pi7yU8+o6On//OF7vX+xVl6DGDZl6AC1xT0mOh0ql8G+/o1G3LBI7dvh1SEyI3AKJYmzfFCmxnpRTbFMqVRiUPQJzlo7AjEd/guXSDzBeteHvOz7B9o+q8fB9d2FGyRQk6RKjXdXYTrKMRiNmzJgRUKbX65GWlgaj0djlcQCQlZUVUJ6dnY3NmzfDbrdDq5X3OG9fFKlEQKwkqLMhLikuUGJcoCN1kZd6Lk/b8ycIAs5dtEKv08CQHO+P+4RRmXB7WrbcOXTsgr/cdwdjNHpkYmXLnVjreaPeS5cyALqUAfC47DDkujHw5A/4w5vv4NU/bcE9t03Eo7Om44aB10etfvL/be6C2WyGXq9vV24wGGAymbo8TqPRID4+PqBcr9dDEASYTKawkiyVUgFAPt2VsUZ17Yu6ozj2T0lEcQfzb8SUcG27liuNNkChgNXmQv+UBCRo1aK8n0oF5N+UjmPfXkZTswsDUhMwKict6PlTXb1u29foKpbBvoaYvF4Bx7+7ggazHUmJGjSY7Tj+3RVMGj1ItE2b254/S5MLUCigT45HglYNKBRotrshANAlttwgE8z56Gkse7tQfxcZR/Ewlv9NpUrEiPG3Y9jYybh45jvs/fB97Nn7KXIHpyPtrslwCRoY9MlQqSLb2xrTSZZc6XTsBRNDNOM4sWAwDp/4EdYmJzLTkzF2+PVIMSSI9vr65AQMvN4Ap9MDjSb8CdUA4PF6O309ubRJm90Fl8uL1JQEJGpb9m90ubyIj1e3JEDXNDTacPhEPaxNTiTpNBg7/HqkpgQf/9bnb+B1yejv8MDa7ER8fMvG0umpieifqvPHqSfnQy6xjHWMo3gYy0ApI/OROzIfc/7nFdjMF3HBfhnrq6rwrfEc5swowb/MuAf9DMmBBymk6YWN6SRLr9fDYrG0KzeZTDAYDF0e53Q64XA4AnqzzGYzFApFl8cGo6nJDo+Xy4+FSqVUQKfTRjWOcSpg/IjrWv2VDpgtNkney+Vyh/0ajWa7vydGl6jGqJw0pOi1sohla16vALVaiSuNNjgTWxKf/ikJcDhc/ji0rCd1DlcabUhK1ODCJQtqnO4Oe7s60/b8ma0Of3z0OjWGZuphsdg7fL3OzofcYhmrGEfxMJbdUCVC028obO6BKL5vDpwfbsVLG9/Fuk3vo2TyLVg87xFcn96ywGlSf0GSvsCYTrKysrLazb2yWCy4fPlyu/lWbY8DgLq6Otx0003+cqPRiMzMzLDnY3m8Qq9bGC6yWpq6HOKojlNCEAR4PPL9AvN6BXx56pJ/oveVqzZ8eepSyyKX14a8ohXLjob8Rvy8v38uT6peixE/7x8QY7vD3dKDlaCGVqMCBDWsTU7Y7K4ez1fynb9kXct+g5evNuObugYcPlEfwnww+bTL2MY4ioexDIoiDnljinFTQRF+ulCHvX/bioP79+Gh898jQenBhavNGDfkZkneOqYHcYuLi3Hw4EGYzWZ/2e7du6FUKjFx4sROjxs9ejSSkpKwa9cuf5nL5cLHH3+M4uJiSetMJLa2E72TEtX+ifrR1Gixo+boefznP86i5uh5NFpaJpb7JtjfOm4wJhYMbJfk+G4MsDa7YHe4YWlqmSAvxp1r335/FVfNDqjjlP67Rr3sASDqExRKJdIGZeOhshX4329uR1PGaJy64sBj/2sVfmo0QYD43wUxnWTNnj0bOp0OCxcuxIEDB7B9+3a8+OKLmD17dsAaWXPnzsWdd97pfxwfH4+ysjK89dZb2Lx5Mw4dOoSnnnoKjY2NeOyxx6LxUYhCJmVSEqrWyyh0lND47qLrbOPskTkDkGrQwuX2inbnmlyTUSKKPE1CEnTpWdDcMAFLyv8V2gQd3BJ0Bsb0cKHBYMDmzZvx/PPPY+HChdDpdJg5cyaWLl0a8Dyv1wuPJ/CLdP78+RAEAW+99ZZ/W51NmzZxtXeKOb6k5KtvfoKlyYF++njkDOkX1TqFuwyGFMtJcG0nImpLGadGbv7/QJxWB0GCRUy5QbTIuEF0+HrzpqdSabTY8dU3l3Gl0YYmmwv6pHj002uRf1M6fjawX8Rj2dVmyNFcSymcNbrYLsXBOIqHsRTPmBvToVYpoYkTN9GK6Z4somiRcsXyUOriG5qzNrtgbXbB620pP/btZQy8Pry7ZUMh18Uqxeohk9P5JyL5YpJF1ENSr1jeU76huQRtHExWB7RaFQQISIiPQ1OzC05ndOYcyXWbmHBXVW802/HlqUuyOf9EJF8xPfGdKNK6m9AdDb65Rja7G0qFAna7BwooYHO4oUtsWfAzWrqa4B4Or1eA3eGOeNw9Xi+OfXtZVuefiOSLPVlEPSD25s5iaD00p1QqoFQqkKzToJ9ei1E5aaKsJi+FYIfc2j4vmj2JTqcHTc3yOv9EJF/8ViDqAbneodZ6aC5OpYTb44VGrZJ0H8JwBJsotX3e8J/3x4nvrvgn1Pt6kiI1oV6jUUF3bcFXQD7nn4jkSZ5/4hLJlFRrOIlVN218HOLilJIM0XWmp0N3wQ65dvS8Y6cuw9rsjNpaVyqlEqNy0mR5/olIftiTRdRDcp3QHQ2te5oStWrkDu2HtH6JXcYk2CHXjp5nd7qhjY+D2eoEEJ2epBQ9zz8RBYc9WUQhkGpCdyxp3dPk9Xrx7Q8N2FVdhwNHzvm30OlIsCvUd/S8pEQNRuWmS9qTFEzPHM8/EQWDPVlEFBJfT5MuIQ6XGmzwegV4FQJ+umrrcp5UsGtodfY8KXsSozmpnmtvEfU+TLJINnwXmQStOtpVoSD4epouX22GzeECFIA2Pg76JE23d9wFmyh19rxw17rqSOueuUhPqpfb2mtEJA4OF5IsNFrsqDl6Hv/5j7OoPnIODY22aFeJuuHraRqQkgiVUgmVQomU5HhYm91BbVAd7JBbpIbmorWBtBzXXiMicTDJoqhre5G50mjD4RM/8iITA1KStSgaPRAlk4bixhtSoFQqYvaOu2DnioktWskdEUmPw4UUde3uIlMoYG1ywunyQC3yZp0kPqVSgYz+OqT1S4zpOUXR2m9RrmuvEVH4mGRR1LW9yFhtLmSmJ0OjVkEQ2JsVK6SYJxVp0VieQ66baRNR+GL7G5F6hfYXmQSMHX49lErA42GSRZEVjWSRa68R9U5MskgWWl9kErRqpBgSYLZw8jv1Hb2hJ5CIAnHCC8kGF3gkIqLehEkWERERkQTYN01EsuVboDZOpYTb4+V8JSKKKUyyiEiWfKugXzXbYWlyIlmnQT+9lquhE1HM4HAhEcmOb4HaK402NJodMFudMFkcuNJo42roRBQzmGQRkez4FqhNiI+DAAFarQpeQUCCNo6roRNRzGCSRUSy41ug1uZwQwEF7HYPlAoFmm3B7YtIRCQHnJNFJCLfRG1O0A5P6wVqlUoFVCpFwJwsxpaIYgGTLCKR+CZqN9laNhbmBO3wtF6glncXElEs4nAhkQh8E7UbTHao45RoMNk5QVsEvgVq4+KUIS9U6/UKsDvcPBdEFHHsySISgW+idlKi2r81im+CNrdKiR72LhJRNLEni0gEvona1mYX7A43LE0uTtCOMvYuElG0MckiEoFvonaqQQuX24v+KZygHW1texeTEtVc/oGIIorjGEQiaT1RmxO0o8/Xu9hgsgMALE0u9E/RsneRiCKGPVlEIvJN1GaCFX3sXSSiaGNPFhH1WuxdJKJoYpJFRL2ar3eRiCjSOFxIREREJAEmWUREREQSYJJFREREJAEmWUREREQSYJJFRLLCvQaJqLfgLTdEJBvca5CIehP2ZBGRLHCvQSLqbWK+J2vv3r1Yv3496urqkJmZid/85jeYMWNGl8ecO3cOd9xxR7vyUaNGYcuWLVJVlYi60HavQQD+vQa5zhURxaKY/uY6fPgwFi1ahJkzZ2LlypX4/PPP8cwzz0Cn0+Huu+/u9vgnn3wShYWF/sc6nU7K6hJRF7jXIBH1NjGdZL322mu4+eabsWrVKgDALbfcgrNnz+KVV14JKsm64YYbkJ+fL3EtiSgYvr0GfXOyuNcgEcW6mJ2T5XQ6UVtb2y6ZmjZtGk6fPo1z585FqWZEFCrfXoO3jhuMiQUDOemdiGJazPZknTlzBi6XC1lZWQHl2dnZAACj0YhBgwZ1+RqVlZVYunQpUlJScMcdd2DZsmVISUkJu24qpQIxnL9GnepazwXjGL5YjKVKBahlOEQYi7GUI8ZRPIyl/MVskmUymQAAer0+oNz32Pfzjmg0Gjz88MMoKiqCXq/HsWPHsGHDBhw/fhxbt26FWq0Oq246Hf/6FgPjKB7GUjyMpTgYR/EwluFTKqSZliCrJMtiseDSpUvdPm/w4MFhvU96ejoqKyv9j8ePH48bb7wRZWVl2LNnD6ZNmxbW6zc12eHhbechUykV0Om0jKMIGEvxMJbiYBzFw1iKx5umgwriJ1qySrJ2796N8vLybp+3c+dOGAwGAC2JWWtmsxkA/D8P1uTJk5GYmIgTJ06EnWR5vAI8Hm9Yr9G3tXR7M45iYCzFw1iKg3EUD2Mpd7JKskpLS1FaWhrUc51OJ9RqNYxGIyZNmuQvNxqNANBurhYRERFRJMXsTDmNRoPCwkJ89NFHAeU7d+5EdnZ2t5Pe29q3bx+am5sxcuRIMatJREREfZSserJ6asGCBZgzZw4qKytRUlKC2tpa7NixA+vWrQt43rBhwzB9+nSsWbMGALB27VooFArk5+dDr9fjq6++wuuvv44RI0ZgypQp0fgoRH2G1yvA6fJAo1ZxDSwi6tViOskaO3YsqqqqsH79emzbtg2ZmZlYvXo1SkpKAp7n8Xjg9f73eHV2djbeffddbNmyBXa7HRkZGZg5cyYWL16MuLiYDgmRrHEDaCLqSxSCIPCWBBE1O904evonTkIMg0qlhD45AWaLjXEMk5xi6fUKqDl6Hg0mO5IS1bA2u5BqaFl8NBZ6tOQUy1jGOIqHsRTPmBvToVYpoYkTdxYVu22IKCK4ATQR9TUxO/GdiGKLbwNoa7MLdocblqaWIUNuAE1EvRWTLCKKCN8G0KkGLVxuLzeAJqJej330RBQxvg2geXchEfUFTLKIKKKUSgXnYBFRn8DhQiIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJMMkiIiIikgCTLCIiIiIJxHSSVVNTg6eeegpTpkxBbm4uVq1aFfSxFosFK1euxPjx41FQUIDFixfj0qVLEtaWiIiI+pKYTrKqq6tx6tQpjBs3Dnq9vkfHLlmyBDU1NaisrMRLL72Euro6zJ8/H263W6LaEhERUV8SF+0KhON3v/sdVqxYAQCora0N+rijR4/iwIED2LRpE4qKigAAQ4cOxbRp0/Dxxx9j2rRpktSXiIiI+o6Y7slSKkOr/v79+6HX6zFx4kR/WVZWFvLy8rB//36xqkdERER9WEz3ZIXKaDRi6NChUCgUAeVZWVkwGo1hvbZWrcKY7AFhvQa1JNDedF20q9ErMJbiYSzFwTiKh7EUh0atkuR1+2SSZTabkZyc3K7cYDDg+PHjYb22IADesF6BAMDrZRTFwliKh7EUB+MoHsZSHIJw7T+KLp/WY7JKsiwWS1B3+A0ePBgajSYCNeo5lVKBRI2swkpERERRIKtsYPfu3SgvL+/2eTt37kR2dnbI76PX61FfX9+u3GQywWAwhPy6RERERD6ySrJKS0tRWloq+ftkZWXh0KFDEAQhYF5WXV0dcnJyJH9/IiIi6v1i+u7CUBUXF8NkMuHQoUP+srq6Opw8eRLFxcVRrBkRERH1FrLqyeqp8+fP4+uvvwYA2Gw2nDlzBrt37wYA3H333f7nDRs2DNOnT8eaNWsAAAUFBSgqKsLKlSuxfPlyxMfHY926dcjNzcXUqVMj/0GIiIio14npJKu2thZPP/20/3F1dTWqq6sBAN98842/3OPxtLsDY/369XjhhRdQUVEBt9uNoqIilJeXIy4upkNCREREMqEQBP+Ni0REREQkkj45J4uIiIhIakyyiIiIiCTAJIuIiIhIAkyyiIiIiCTAJIuIiIhIAkyyiIiIiCTAJCsMNTU1eOqppzBlyhTk5uZi1apVQR9rsViwcuVKjB8/HgUFBVi8eHFQm2P3Vnv37sV9992HkSNH4q677sL27du7PebcuXPIzc1t92/WrFkRqHH0nT59Go8++ijy8/MxceJEvPjii3A6nd0eJwgC3njjDdx66624+eab8dBDD+HLL7+UvsIyFmosb7/99g7boMPhiECt5eeHH35ARUUF7r//fgwbNgz33ntvUMexTbYXaizZJgPt2rULCxYsQHFxMfLz83H//fdj27Zt6G71KrHaJFfeDEN1dTVOnTqFcePGwWQy9ejYJUuW4LvvvkNlZSXi4+Oxfv16zJ8/H9u3b+9zC6IePnwYixYtwsyZM7Fy5Up8/vnneOaZZ6DT6QJW7u/Mk08+icLCQv9jnU4nZXVlwWQyYe7cuRgyZAiqqqpw8eJFrF27Fna7HRUVFV0eu3HjRrzyyitYtmwZcnNz8fbbb2PevHn44IMPMHjw4Ah9AvkIJ5YAcNddd2HevHkBZRqNRqrqyto///lPfPbZZxg1ahS8Xm+3FzIftsn2Qo0lwDbZ2h//+EcMHDgQK1asQL9+/XDw4EH8/ve/R319PRYtWtTpcaK1SYFC5vF4/P+/7bbbhOeeey6o444cOSLk5OQI1dXV/rLTp08Lubm5wt/+9jfR6yl38+bNEx566KGAsieffFIoKSnp8rizZ88KOTk5wq5du6Ssnixt2LBByM/PF65eveove++994S8vDyhvr6+0+PsdrswevRo4eWXX/aXORwO4bbbbhOeffZZCWssX6HGUhB69nvfF7T+Tly+fLlwzz33dHsM22THQomlILBNtnXlypV2ZeXl5cLo0aMDYtyamG2Sw4VhUCpDC9/+/fuh1+sxceJEf1lWVhby8vKwf/9+saoXE5xOJ2pra9v1WE2bNg2nT5/GuXPnolQzedu/fz8mTJiAlJQUf1lJSQm8Xi9qamo6Pe7IkSOwWq0oKSnxl2k0Gtx55519ru35hBpLai+U70S2yY6Fen2hQKmpqe3K8vLyYLVa0dzc3OExYrZJnsUoMBqNGDp0KBQKRUB5VlYWjEZjlGoVHWfOnIHL5UJWVlZAeXZ2NgAEFY/Kykrk5eVhwoQJKC8vR2NjoxRVlRWj0dguZnq9HmlpaV3GzPezjuJ94cIF2O128Ssrc6HG0ufDDz/EiBEjUFBQgPnz5wfsm0rdY5sUH9tk17744gtkZGQgKSmpw5+L2Sb71uQfmTCbzUhOTm5XbjAYcPz48SjUKHp8c9n0en1Aue9xV3PdNBoNHn74YRQVFUGv1+PYsWPYsGEDjh8/jq1bt0KtVktX8Sgzm83tYga0tKGuYmY2m6HRaBAfHx9QrtfrIQgCTCYTtFqt6PWVs1BjCbRMMr755puRmZmJs2fPYsOGDXjkkUfw17/+tc/OJeoptklxsU127fDhw9i5cyeWL1/e6XPEbJNMslqxWCxB3eE3ePDgPjuJMBg9iWM40tPTUVlZ6X88fvx43HjjjSgrK8OePXswbdq0sF6fqDvl5eX+/48dOxYTJ05ESUkJNm3aFNA2iSKFbbJz9fX1WLp0KQoLCzFnzpyIvCeTrFZ2794d0EA7s3PnTv9wVij0ej3q6+vblZtMJhgMhpBfVy56Ekff57VYLAE/M5vNANDjeEyePBmJiYk4ceJEr06y9Hp9u5gB3bchvV4Pp9MJh8MR8Fea2WyGQqHoFe2vp0KNZUfS09MxZswYnDhxQqzq9Xpsk9Jim2xhNpsxf/58pKSkoKqqqss5b2K2SSZZrZSWlqK0tFTy98nKysKhQ4cgCELAvKy6ujrk5ORI/v5S60kcnU4n1Go1jEYjJk2a5C/vbEycWnQ0f89iseDy5ctdxsz3s7q6Otx0003+cqPRiMzMzD45LBNqLEkcbJMkNbvdjrKyMlgsFrz//vsdTtdpTcw2yYnvUVBcXAyTyYRDhw75y+rq6nDy5EkUFxdHsWaRp9FoUFhYiI8++iig3NdbOGjQoB693r59+9Dc3IyRI0eKWU3ZKS4uxsGDB/09fkBLD6JSqQy4a7Wt0aNHIykpCbt27fKXuVwufPzxx32u7fmEGsuOXLx4EV988UWvb39iYpuUVl9vk263G0uWLIHRaMSbb76JjIyMbo8Rs02yJysM58+fx9dffw0AsNlsOHPmDHbv3g0AAUsSDBs2DNOnT8eaNWsAAAUFBSgqKsLKlSuxfPlyxMfHY926dcjNzcXUqVMj/0GibMGCBZgzZw4qKytRUlKC2tpa7NixA+vWrQt4Xts4rl27FgqFAvn5+dDr9fjqq6/w+uuvY8SIEZgyZUo0PkrEzJ49G3/+85+xcOFClJWV4eLFi3jxxRcxe/bsgC+RuXPn4sKFC9izZw8AID4+HmVlZaiqqkJqaipycnLw7rvvorGxEY899li0Pk5UhRrLHTt2YN++fZg8eTLS09Nx9uxZvPHGG1CpVHj00Uej9XGiymaz4bPPPgPQ8v1otVr934njx49Hamoq22SQQokl22R7zz33HPbt24cVK1bAarUGrNo+bNgwaDQaSdskk6ww1NbW4umnn/Y/rq6uRnV1NQAE3DLr8Xjg9XoDjl2/fj1eeOEFVFRUwO12o6ioCOXl5X1utXegZXJmVVUV1q9fj23btiEzMxOrV68OWKMEaB/H7OxsvPvuu9iyZQvsdjsyMjIwc+ZMLF68uNfH0WAwYPPmzXj++eexcOFC6HQ6zJw5E0uXLg14ntfrhcfjCSibP38+BEHAW2+9hYaGBuTl5WHTpk199s6jUGM5aNAgXLp0CWvWrIHFYkFycjJuueUWLF68uM/G8sqVK3jiiScCynyP//SnP6GwsJBtMkihxJJtsj3fWndr165t97NPP/0UgwYNkrRNKgShB2v1ExEREVFQOCeLiIiISAJMsoiIiIgkwCSLiIiISAJMsoiIiIgkwCSLiIiISAJMsoiIiIgkwCSLiIiISAJMsoiIiIgkwCSLiIiISAJMsoiIiIgkwCSLiOiaixcvYuTIkQF7kgLAwYMHMXz4cP/m5EREwWCSRUR0TUZGBkpLS/Hhhx/i/PnzAIDTp0/jiSeewKRJk7BixYoo15CIYgmTLCKiVsrKyqBQKLBx40ZcvXoVjz/+OAYOHIg//OEPUCr5lUlEwYuLdgWIiOQkIyMDs2bNwpYtW3Dy5EnY7Xb85S9/QWJiYrSrRkQxhn+WERG1MW/ePDidTnzzzTd47bXXkJGREfDzd955Bw888ACGDx+OqqqqKNWSiOSOSRYRURsbNmwAAHg8HhgMhnY/T09Px6JFizB16tRIV42IYgiTLCKiVt58801s3boVFRUVUKlU/oSrtSlTpuCOO+5AcnJyFGpIRLGCSRYR0TWffPIJXn75ZTzxxBP45S9/iVmzZuGDDz7A2bNno101IopBTLKIiAAcP34cy5Ytwy9+8QssWLAAAPDrX/8aCoWiw94sIqLuMMkioj6vvr4ejz/+OPLy8rB69Wp/eUZGBmbMmMHeLCIKiUIQBCHalSAiikUVFRVIS0vDb3/722hXhYhkiD1ZREQ95Ha74XA44PV6/f/3eDzRrhYRyQx7soiIeqiqqgqvvvpqQNkLL7yABx98MEo1IiI5YpJFREREJAEOFxIRERFJgEkWERERkQSYZBERERFJgEkWERERkQSYZBERERFJgEkWERERkQSYZBERERFJgEkWERERkQSYZBERERFJgEkWERERkQSYZBERERFJ4P8DVBHJlH6ldyUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the data and the classification with the decision boundary.\n",
    "xmin, xmax = -1, 2\n",
    "ymin, ymax = -1, 2.5\n",
    "xd = np.array([xmin, xmax])\n",
    "yd = m*xd + c\n",
    "plt.plot(xd, yd, 'k', lw=1, ls='--')\n",
    "plt.fill_between(xd, yd, ymin, color='tab:blue', alpha=0.2)\n",
    "plt.fill_between(xd, yd, ymax, color='tab:orange', alpha=0.2)\n",
    "\n",
    "plt.scatter(*X[Y==0].T, s=8, alpha=0.5)\n",
    "plt.scatter(*X[Y==1].T, s=8, alpha=0.5)\n",
    "plt.xlim(xmin, xmax)\n",
    "plt.ylim(ymin, ymax)\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.xlabel(r'$x_1$')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('ml-env')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "6e92f738de8b90cde63de865266dbc2f0731dfead426ea1479c0e54561778e9d"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}