n03_modelling_purchase_probability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelling Purchase Probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we explore how to model purchase probability i.e. whether a customer will buy a product from a specific product category when they enter a store. The main objective is to develop a statistical model which estimate purchase probability for each customer at each shopping trip based on historical data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "import plotly.express as px\n",
    "\n",
    "sns.set(style='whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "segment_labels = pickle.load(open('models/segment-labels.pickle', 'rb'))\n",
    "segment_colours = ['lightskyblue', 'red', 'gold', 'green']\n",
    "segment_colour_palette = sns.color_palette(segment_colours)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_elasticity_cross_point(df_data):\n",
    "    return df_data[df_data['Elasticity'] < -1]['Price'].iloc[0]\n",
    "\n",
    "def calc_elasticities_with_promotion(df: pd.DataFrame, promotion: int = 1, segment: int = None, price_range=(0.5, 3.5)):\n",
    "    df_data = df.copy() if segment is None else df[df['Segment'] == segment].copy()\n",
    "    \n",
    "    # df_data['Avg_Promotion'] = (\n",
    "    #    df_data['Promotion_1'] + df_data['Promotion_2'] +\n",
    "    #    df_data['Promotion_3'] + df_data['Promotion_4'] +\n",
    "    #    df_data['Promotion_5']) / 5\n",
    "    \n",
    "    X = np.array(df_data[['Avg_Price', 'Avg_Promotion']])\n",
    "    y = np.array(df_data['Incidence'])\n",
    "    \n",
    "    # Fit a model\n",
    "    lr = LogisticRegression(solver='sag')\n",
    "    lr.fit(X, y)\n",
    "    \n",
    "    # Generate predictions for the chosen price range\n",
    "    price_range_arr = np.arange(price_range[0], price_range[1], 0.01).reshape(-1, 1)\n",
    "    promotion_arr = np.ones(price_range_arr.shape[0]).reshape(-1, 1) * promotion\n",
    "    X_test = np.concatenate([price_range_arr, promotion_arr], axis=1)\n",
    "    y_preds = lr.predict_proba(X_test)\n",
    "    \n",
    "    # Compute the price elasticities\n",
    "    purchase_probability = y_preds[:,1].reshape(-1, 1)\n",
    "    beta = lr.coef_.squeeze().item(0)  # Get the model coefficient for price\n",
    "    price_elasticity = beta * price_range_arr * (1 - purchase_probability)\n",
    "\n",
    "    # Create elasticity DataFrame\n",
    "    elasticity_data = np.concatenate([price_range_arr, price_elasticity], axis=1)\n",
    "    df_elasticities = pd.DataFrame(elasticity_data, columns=['Price', 'Elasticity'])\n",
    "\n",
    "    return df_elasticities\n",
    "\n",
    "def calc_elasticities_for_segment(df: pd.DataFrame, segment: int, price_range=(0.5, 3.5)):\n",
    "    df_data = df[df['Segment'] == segment]\n",
    "    x = np.array(df_data['Avg_Price']).reshape(-1, 1)\n",
    "    y = np.array(df_data['Incidence'])\n",
    "    \n",
    "    # Fit a model\n",
    "    lr = LogisticRegression(solver='sag')\n",
    "    lr.fit(x, y)\n",
    "    \n",
    "    # Generate predictions for the chosen price range\n",
    "    price_range_arr = np.arange(price_range[0], price_range[1], 0.01).reshape(-1, 1)\n",
    "    y_preds = y_preds = lr.predict_proba(price_range_arr)\n",
    "    \n",
    "    # Compute the price elasticities\n",
    "    purchase_probability = y_preds[:,1].reshape(-1, 1)\n",
    "    beta = lr.coef_.squeeze().item(0)  # Get the model coefficient\n",
    "    price_elasticity = beta * price_range_arr * (1 - purchase_probability)\n",
    "\n",
    "    # Create elasticity DataFrame\n",
    "    elasticity_data = np.concatenate([price_range_arr, price_elasticity], axis=1)\n",
    "    df_elasticities = pd.DataFrame(elasticity_data, columns=['Price', 'Elasticity'])\n",
    "    \n",
    "    inelasticty_end = df_elasticities[df_elasticities['Elasticity'] < -1]['Price'].iloc[0]\n",
    "    \n",
    "    return df_elasticities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Backed by research, we build a simple model where the assumption is that the purchase probability is influenced by the average price of a product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_purchases = pd.read_csv('data/fmcg-store-purchases-augmented.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_purchases['Avg_Price'] = (\n",
    "    df_purchases['Price_1'] + df_purchases['Price_2'] +\n",
    "    df_purchases['Price_3'] + df_purchases['Price_4'] +\n",
    "    df_purchases['Price_5']) / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(df_purchases['Avg_Price']).reshape(-1, 1)\n",
    "y = np.array(df_purchases['Incidence'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='sag', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression(solver='sag')\n",
    "lr.fit(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us look at the slope of the linear model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.34856916]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So there is an inverse proportionality between price and purchase probability. The coefficient of the independent variable tells us that a decrease in the average price will lead to an increase in purchase probability. This does not come as a surprise. The model quantifies the exact relationship between price and purchase probability.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Price Elasticity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Price elasticity of purchase probability is the percentage change in purchase probability in response to a 1% change in the respective aggregate price for the product category.\n",
    "\n",
    "Per definition, elasticity measure the percentage change in the output variable (in this case purchase probability)\n",
    "given a 1% change in the input variable (in our case the average price). If percent change is greater than 100%,\n",
    "then the output (the purchase probability) is elastic. For changes less than 100%, it is inelastic. \n",
    "In other words, if $|E| < 1$ i.e. the absolute elasticity value is smaller than 1 then it is **inelastic**, \n",
    "otherwise it is elastic. \n",
    "\n",
    "The general recommendation is to increase the price, for price points which are inelastic because it would not cause a significant decrease in the output variable (purchase probability). On the other hand, if a price point is elastic, then we should decrease the price.\n",
    "\n",
    "Calculating the price elasticity can help us answer this question:\n",
    "\n",
    "> How does demand for the product change with the given change in price?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elasticity can be calculated as follows:\n",
    "\\begin{align}\n",
    "E\n",
    "&=\n",
    "\\frac{\n",
    "  \\Delta Pr(purchase) / Pr(purchase)\n",
    "}{\n",
    "  \\Delta Price / Price\n",
    "}\n",
    "=\n",
    "\\frac{\n",
    "  \\Delta Pr(purchase)\n",
    "}{\n",
    "  \\Delta Price\n",
    "}\n",
    "\\cdot\n",
    "\\frac{\n",
    "  Price\n",
    "}{\n",
    "  Pr(purchase)\n",
    "}\\\\\n",
    "&=\n",
    "\\beta \\cdot Price \\cdot(1 - Pr(purchase))\n",
    "\\end{align}\n",
    "where $\\beta$ is the coefficient of the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can analyse a range of values for the mean price and determine how they effect the purchase probability. The range of prices can be determined by looking at the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_1</th>\n",
       "      <th>Price_2</th>\n",
       "      <th>Price_3</th>\n",
       "      <th>Price_4</th>\n",
       "      <th>Price_5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>58693.000000</td>\n",
       "      <td>58693.000000</td>\n",
       "      <td>58693.000000</td>\n",
       "      <td>58693.000000</td>\n",
       "      <td>58693.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.392074</td>\n",
       "      <td>1.780999</td>\n",
       "      <td>2.006789</td>\n",
       "      <td>2.159945</td>\n",
       "      <td>2.654798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.091139</td>\n",
       "      <td>0.170868</td>\n",
       "      <td>0.046867</td>\n",
       "      <td>0.089825</td>\n",
       "      <td>0.098272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.100000</td>\n",
       "      <td>1.260000</td>\n",
       "      <td>1.870000</td>\n",
       "      <td>1.760000</td>\n",
       "      <td>2.110000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.340000</td>\n",
       "      <td>1.580000</td>\n",
       "      <td>1.970000</td>\n",
       "      <td>2.120000</td>\n",
       "      <td>2.630000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.390000</td>\n",
       "      <td>1.880000</td>\n",
       "      <td>2.010000</td>\n",
       "      <td>2.170000</td>\n",
       "      <td>2.670000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.470000</td>\n",
       "      <td>1.890000</td>\n",
       "      <td>2.060000</td>\n",
       "      <td>2.240000</td>\n",
       "      <td>2.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.590000</td>\n",
       "      <td>1.900000</td>\n",
       "      <td>2.140000</td>\n",
       "      <td>2.260000</td>\n",
       "      <td>2.800000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Price_1       Price_2       Price_3       Price_4       Price_5\n",
       "count  58693.000000  58693.000000  58693.000000  58693.000000  58693.000000\n",
       "mean       1.392074      1.780999      2.006789      2.159945      2.654798\n",
       "std        0.091139      0.170868      0.046867      0.089825      0.098272\n",
       "min        1.100000      1.260000      1.870000      1.760000      2.110000\n",
       "25%        1.340000      1.580000      1.970000      2.120000      2.630000\n",
       "50%        1.390000      1.880000      2.010000      2.170000      2.670000\n",
       "75%        1.470000      1.890000      2.060000      2.240000      2.700000\n",
       "max        1.590000      1.900000      2.140000      2.260000      2.800000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_purchases[[f'Price_{i}' for i in range(1, 6)]].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The minimum price is 1.1 and maximum price is 2.8. We can extend this range to [0.5, 3.5] because it allows us to gain a better understanding of how the purchase probabilities and corresponding elasticity change. A big enough range may give us valuable information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "price_range = np.arange(0.5, 3.5, 0.01).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the simple model to generate predictions for the price range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_preds = lr.predict_proba(price_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the price elasticities\n",
    "beta = lr.coef_.squeeze().item(0)\n",
    "purchase_probability = y_preds[:,1].reshape(-1, 1)\n",
    "price_elasticity = beta * price_range * (1 - purchase_probability)\n",
    "\n",
    "# Create elasticity DataFrame\n",
    "elasticity_data = np.concatenate([price_range, price_elasticity], axis=1)\n",
    "df_elasticities = pd.DataFrame(elasticity_data, columns=['Price', 'Elasticity'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price</th>\n",
       "      <th>Elasticity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.50</td>\n",
       "      <td>-0.096399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.51</td>\n",
       "      <td>-0.100467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.52</td>\n",
       "      <td>-0.104663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.53</td>\n",
       "      <td>-0.108989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.54</td>\n",
       "      <td>-0.113448</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Price  Elasticity\n",
       "0   0.50   -0.096399\n",
       "1   0.51   -0.100467\n",
       "2   0.52   -0.104663\n",
       "3   0.53   -0.108989\n",
       "4   0.54   -0.113448"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_elasticities.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To spot patterns, let us graph the price elasticities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "inelasticty_end = df_elasticities[df_elasticities['Elasticity'] < -1]['Price'].iloc[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "sns.lineplot(x='Price', y='Elasticity', data=df_elasticities, color='grey', ax=ax)\n",
    "ax.axvspan(0.5, inelasticty_end, color=sns.xkcd_rgb['grey'], alpha=0.4)\n",
    "ax.set_title('Price Elasticity of Purchase Probability \\n (Inelastic Price Range Shaded Grey)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The price elasticity decreases as the price increase i.e. the higher the price, the less likely for purchase. \n",
    "This is obvious. The interesting is the rate. The decrease is relatively slow in the range 0.5 to around 1.5, \n",
    "and then it becomes steeper. \n",
    "\n",
    "The price elasticities are all negative. This is because we used the model's coefficient which was negative.\n",
    "So there was an inverse proportionality between price and purchase probability.\n",
    "\n",
    "We can determine whether or not different price points are elastic or not. For example, at the price point of 1.10, the average customer has an elasticity of -0.69. This means that for each increase in price by 1%, the probability of purchase will decrease by 0.69%. Since $|-0.69| < 1$, the purchase probability is inelastic. At 1.50 price point, the elasticity is -1.7. An increase of 1% in price would translate into decline of 1.7% of the purchase probability. In this case, the elasticity of purchase probability is elastic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With prices lower than 1.25, we can increase them without losing too much in terms of purchase probability. For prices higher than 1.25, we gain more by reducing the prices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average customer elasticity curve is helpful to get an overview of the overall purchase behaviour. \n",
    "If we want to develop concrete marketing strategy, we need to further refine the analysis.\n",
    "We can create finer analysis by looking at the specific behaviours of different consumer segments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Price Elasticity by Segment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Bz8+PuXPnMm/ePFxdXRk4cCAAI0aMoEuXLgQEBDBhwgRu3bqFRCJh1KhRNG/enIULF/LHH3+QlpbG66+/jq+vL/PmzaOoqIjc3FzGjRtHu3btuHXrFqNHjyYnJ4datWpx9OhRfvvtNwoKCpgyZQqXL19Gq9Xy9ttvExYWZlLX/Px89uzZw5gxYwBDr+zw4cMBWLJkCRYWFly5cgU/Pz/mzJmDXC5n06ZNfPfdd+h0OurVq8fEiRNNykxPT+fjjz8mLy+PjIwMIiIiGDlyJBcuXGDChAloNBoUCgUzZsxg165dZGRkMHjwYFatWkX37t1ZuXIlLi4uTJ48mePHj2Nubs7QoUPp1KmTyXF27NjBt99+S1FRESqViujoaIqKitizZw+HDh3CxcWFl19+2bj9lStXuHLlClOnTiUmJqbMtqtZsyYNGzbEzMwMKysrPD09SUtLw8LCAoCBAweSnZ1Nr169eP311wEICwujV69e9OvXT6QjPYIIrAVBEAThX+jUqVOcPHnybyk7ICCAhg0bPnKbkydPYm5uzrp169DpdERGRrJv3z66du1KVFQUAwcOJD8/n5MnT/LZZ5/x0Ucf0b17d9q2bUtGRgb9+vVj06ZNAKhUKrZv3w7Au+++y7Rp0/Dx8SE+Pp7o6GjatWvH9OnT6dixI6+99ho///yzMQ3iq6++ol69enz66afk5+fTp08fGjZsiKenp7Guhw4donbt2piZlc6APXnyJDt27KBy5cr06tWL/fv34+npyfr161m7di0KhYLPPvuMb775xiS1YuvWrYSFhREREUFeXh4hISH079+f7777jjfffJOOHTuyceNG/vjjDwYPHszatWtZunQpjo6OxjJiYmJQKpXs2LGDzMxM3njjDdq1a4dcLgcMvc9r165l8eLFODk5ERsby9KlS1m8eDGhoaEEBgaaBNVgCJqnT5/O4cOHH9p2jRo1Mr4+ceIECQkJzJo1i6SkJIKDg/nkk09Qq9UMGDAAb29vWrRogb29PVZWVly8eJHatWs/8rPxIhOBtSAIgiAIT61p06Y4ODiwatUqkpKSSE5ORqlUUrduXVQqFSkpKZw8eZLQ0FDkcjkHDx4kKSmJBQsWAIYe7+vXrwPQoEEDY7mzZ89m79697Ny505jfC4ac4RkzZgDQvn177OzsADh48CBFRUVs2LABAKVSyeXLl00C6+TkZKpUqVLmedSsWdO4zsfHh5ycHG7evElKSgq9evUCDOOH161b12S/t956i0OHDvHNN99w+fJl1Go1hYWFhISEMGXKFH7//XdCQ0Np06bNQ6/h0aNH6dWrF2ZmZri4uLBt2zaT9WZmZixatIg9e/Zw9epVjhw5UuaXg7/q6NGjvP/++8yZMwd7e3sCAgIICAgwru/Rowf79u2jRYsWALi7u5OcnCwC60cQgbUgCIIg/As1bNjwsb3Kf6fdu3ezYMECBgwYQLdu3bh79y56vR6ALl26sH37dk6ePMngwYMBQ+/rd999h4ODAwAZGRk4Ozvzyy+/GFMQAPr160dQUBBBQUEEBwczevRoAKRSqbH8++l0OmbPnk29evUAuHPnDvb29ibbSCSSUjnDJRQKhcl2er0erVZLx44diYqKAgzjJD94497MmTO5fv06YWFhtGvXjoMHD6LX6+nQoQMBAQHs3buXFStW8OuvvzJt2rQyjy2TyUzSKlJSUnBzczP2WBcUFNCjRw+6dOlC06ZN8fPzY9WqVWWW9bR27drFpEmTmDdvHkFBQQAcO3YMtVpNcHAwYBjP+f7rJpVKn2tg/18kro4gCIIgCE8tPj6ejh070r17d+zs7Dh8+LAx+AwPD2f79u2kpKTQpEkTAJo1a8bq1asBSExMJDw8nMLCQpMys7OzSU5OZuTIkbRq1Yrdu3cbywwODmbLli0A7Nu3j9zcXGO5a9asAQzBepcuXUhLSzMp18vLyzgix5MICgri559/JjMzE71ez6RJk/juu+9Mtjlw4ABvvfUWHTt25OrVq6Snp6PT6Xjvvfc4ffo0ffr0YeTIkZw7dw4wBKUPBudNmzZl+/btxgeSvP7666hUKuP65ORkJBIJQ4YMMdappIyyyntSCQkJTJo0ieXLlxuDaoC8vDxmzZpFcXEx+fn5bNy4kfbt2xvX37hxg2rVqv2lY74oRI+1IAiCIAhPrWfPnowePZpt27Zhbm5O48aNSU1NBcDNzQ1HR0cCAgKMPbJRUVFMmDCB8PBwAGbNmoWNjY1JmQ4ODvTo0YPOnTsjk8lo1qwZRUVFKJVKxo8fz0cffcT69eupXbu2MRVk+PDhTJo0ibCwMLRaLWPGjCkV/AUHBzNjxgx0Ot0T9bjWrl2b4cOHExkZiU6no06dOgwePBiNRmPc5n//+x8ffvghFhYWVKlSBX9/f1JTUxkyZAjjx49n0aJFmJubM2nSJABat27N4MGDWbZsmbGMfv36MW3aNLp06QLAJ598YnJNateuTZ06dejYsSMSiYSWLVty/PhxAJo3b87cuXOxtbWlQ4cOjz2n06dPs2DBAr7++mu++uortFotH330kXH9u+++S9u2bTl16hSvvvoqOp2Ofv36GVNDcnNzyc/PF2kgjyHRl/W7yr9IcXExZ86cwd/f3+TnnH/K8ePHjd/GhYpDtEvFI9qkYhLtUjE9rF3Onz9PnTp1yqFG5W/lypU0b94cX19fzp49yyeffEJcXNwT7z9jxgyaNWv2yJznx3mRH2n+3XffIZPJKuRwe39Xu5T19/a4uFP0WAuCIAiCUOF5eXnxwQcfYGZmhkKhYOrUqU+1//Dhwxk7diytW7cWw8U9pYKCAuLj4/niiy/KuyoVngisBUEQBEGo8EJCQggJCfnL+9va2rJo0aLnWKMXh7W1NYsXLy7vavwrVKibF7ds2UKnTp34v//7v+d216sgCIIgCIIg/BMqTI91eno68+bNIy4uDrlcTp8+fQgKCsLX17e8qyYIgiAIgiAIj1VheqwPHjxIs2bNcHBwwMrKildeeYWdO3eWd7UEQRAEQRAE4YlUmMA6IyMDFxcX4/vKlSuTnp5ejjUSBEEQBEEQhCdXYVJBdDqdyV26er3+qe7aPXPmzN9RrUdyW7KEmgkJZMvl6M3N0d2b6+Vy42uTZQ+sK2uZTqFAZ2GBztLSMLewAKn0Hz+3/4KSsT6FikO0ScUk2qViKqtdZDKZ8RHfQvkQ179i+jvaRaVSPfX/HytMYF2lShWOHTtmfH/79m0qV678xPuXxzjWOmdnCvLzsZfLkRQXw8OmZ6VQgLU1WFmZzh+2zM4O7O3/nJdMJe9tbOA//khSMTZvxSPapGIS7VIxPWoc63/7OMqpqakMGDCAPXv2MHbsWAIDA+nWrdsT7z9u3DiOHDnCyJEj+fHHH0lNTWXKlCkmTxDUarWMHDmS2bNns3TpUvz9/Wnbtu1T1zU0NJSVK1fi4eEBPPl4yQsWLKB58+a89NJLjB8/nj59+lC/fv2nPn6JvXv3kpyczJtvvlnm+osXL/LBBx+wbdu2R5bz6aefcvfuXWbOnAnAyZMnmTFjBgUFBfj5+TFz5kxkMhkjRoxg1qxZ/5rP2t81jrVcLqdhw4Ymy0rGsX6YChNYN2/enIULF5KVlYWlpSW7du166jEq/2nD3LO50NMFBQqspFbYmNtgZ26HncIwOVo64mBhj53MEmuZDAuJBAuJBAWYTCXLpBoNFBWBUgkFBaXnDy7LzoabN0uv0+keXXGJxBBk3x9429mBszNUqlR6XvLa2dkQ5AuCIAhCOdm4cSMJCQncuXOHWbNmsX///lLbrFmzhpYtW2JpacnIkSP/8ToePXrUGOhPnz79mct7VCC3adMmPvvsM8zNzR9ZRnx8PBs3bqR169YA5OfnM2LECJYtW0bt2rX54IMPiI2NpV+/fvTq1YtFixbx4YcfPnPdXzQVJrB2dXXl/fffZ8CAAajVanr06EGDBg3Ku1qPdMEqkV+zfjW80d6bioA80+3MMEPxwH8WWJR6bWVmha3cFkeFI46WjjhXdqaSdQ0q2VTCxsoGS0tLLCwssLS0xNLSEmtra6ytrZHenyqi1xuC65wcw5Sb++fr+6cHl6enw/nzcOcO5Oc//KRtbf8MuCtXBjc3qFLFdF7y2tLy+V5wQRAEocIIDw/n888/x8fHh1GjRmFjY8PkyZM5efIkX331FUuXLmXp0qXs2LEDrVZLy5YtGTNmzBOVrdPpiI6OJj4+HolEQpcuXRg8eDBDhgxBr9fTs2dP1Go12dnZdOvWzeQJjHq9npiYGGJjYwGMveKBgYEMHz6cmjVrcv78eZydnZk/fz4ODg789ttvLFiwAI1Gg4eHB1OnTsXR0dFYZn5+Ph9//DE3b94kMzOT4OBgpk+fTnp6OqNHj0apVGJmZkZUVBTJycmcOXOGqKgovvjiC6ZNm8bw4cMJDAxkzpw5/PLLL0ilUnr37k1kZKTJeR85coR58+ZRVFREbm4u48aNo3r16qxduxYAd3d3unfvbtw+Ly+P3bt3M3fuXJPHkz8oOzubefPmMWTIEC5cuADAgQMHaNSokfER5VFRUWi1WgBatmzJtGnTGDp0aKnHzguPVmECazD8kYaHh5d3NZ7Y4BbLeE2Zyl21NVkac5TqIoo0ueh0uWi1OWi0eai1uai1uRSrcyhS56JUZVOgykapyiVTlUOBOo8CdR4avQZ0GALzIiDH9FgKFFg+5D9bmS32CnucLJyoZF0JFxsXXGxccHdwx8HWAWtXV2MQbmlpidnj0kCKiyEz0zDdufPw+a1bcPKkISgvq5fc3t4QZLu7Q7Vq4OVlmJe89vQEC4vn1BqCIAgvltOZOhKyHvML5V/UwMmM+s6P/rciJCSE+Ph4fHx8uHTpknH577//TuvWrfntt984c+YMsbGxSCQSxowZw+bNm58o9WjNmjWkpaWxefNmVCoV/fv3p1atWixevBg/Pz9jCsiAAQNKPdb8woUL2NraYmtrW6rcCxcuEB0dTd26dRkxYgRbtmyhc+fOfPbZZ6xcuRJ7e3vWrl3LnDlzTHqaf/31V+rUqcOMGTMwNzenc+fOnD17ll9//ZXWrVszaNAgfvvtN44fP85bb73Fhg0bGD58OH5+fsYydu7cyYkTJ9iyZQtqtZp+/frRqVMnk4Ebvv/+e6ZNm4aPjw/x8fFER0ezZcsW+vTpA2ASVIPhoTcLFy4kNTX1kddzwoQJvP/++6SlpRmXpaSkYGVlxfvvv09SUhKNGzdm7NixAEilUvz8/Dh06BDt2rV7XHMJ96lQgfW/TW95F8xIML7XSOxRSSpTjAtFVEaJCwU6V/L0buRqG5CjrUye3oUCfWWKcKRkUBa9Xo9GV0yROgeNNhutNhu1NguV5i4qdRYqTTYFqizyi++QV5RJXlEWeaq73Ci+Sa4qF51GCxqgAMg0raMCBVZYYY21ce5g7oCzhTOVrCvhau2Km70bVR2q4unsSWXHytja2mJVpQpm7u5PdiG0WkOgnZZmCLbT0kxfp6bCrl2G13q96b6VK/8ZcHt5ga+vYapZ0xB4ixs3BUEQKqSQkBBWrFhBs2bN8PX1JSkpiczMTGPvb0xMDAkJCcb86aKiItzd3Z8osD58+DARERFIpVIsLS0JDw8nPj7emMbwKMnJyVSpUqXMdc7OztStWxeAmjVrkpOTw6lTp0hLS2PAgAGAobfc3t7eZL+wsDASEhJYtWoVqampZGdno1QqCQ4OZsSIEZw/f56QkBBef/31h9br6NGjdOzYEblcjlwu58cffyy1zezZs9m7dy87d+7k1KlTz+WGvB9++AE3NzeCg4NNvoRotVr279/PunXrcHd3Z/z48SxdupQRI0YAht7xlJSUZz7+i0YE1s/AzHMbiWfX41vdFjQZyLQZyDQZWGkzQJsImgPAHZDoDVf6vqutR4bOzAWNWWXUEheKJa4USqqgxJ0CXRVy9O5ka2uRratCrsaaQg3oy6iDXq9HpclDq81Cp7uLRpuNWpNFkTqT/KLb5Bamk1OYTk7RbbILb5NSnMpp9Wk0eZpSKSsA5pgbA3B7qT3OCmdcLF1ws3HDw8GDak7V8HbxxreKLy4OLoaRW6RScHU1TI+iUsGNG7ibDkMAACAASURBVHDtGqSkGOYlr8+ehW3bDDnmxsqYQ40ahiC7JNiuUwfq1QMXF0OuuCAIwguqvvPje5X/TgEBAYwdO5aDBw8SGBiIs7MzO3fuRKPR4O7ujlarJTIy0njDXW5uLlKplLt375Yqa82aNcZ0hz59+qB74FdQvV5vTFN4HIlEgkxWdnhz/yAHEonEWG7jxo2Nj+wuLi4uFdDGxMTw008/0bVrV1q3bs2lS5fQ6/U0adKEbdu28euvv7J9+3Y2btzIt99+W+axZTKZyWhnqampODk5YWVlZVzWr18/goKCCAoKIjg4mNGjRz/ROT/K9u3buX37Nl27diUnJwelUkl0dDQ1a9akYcOGeHp6AtCxY0e+//57435SqfTxv3ALpYjA+lmYe5CjDQGHR3z71mtBmwnaDNBkGOcSbTpSTQZSbQYKTQY22kRQp4H+gVFEJIDCDr21GzqpO1ozN1RmVSjCnUJJFQr0buTp3MjRu5Ov9aZQA4VavWGuAU0Z0bghGM9Fo72NVnOHYs1tlMXp5Bemk6u8RW5hOtmFGWQX3eaM6iw5ymz0mXp44IurAgX2ZvY4yh1xsXDB1doVdzt3PBw98Knsg29lXzwdPHG0cDT8z0QuB29vw1QWnc7Qq335MiQmGqaS13v2GG7OLOHsbAiw69Y1nT8uuBcEQRCeC5lMRoMGDYiJiWHx4sW4uLgwefJkYw91s2bNWLBgAb169UKhUDBs2DAiIiIIDAwsVVbfvn3p27ev8b1Wq2XTpk20adMGlUrFli1bGDJkyBPVy8vLixs3bjzxeTRs2JCoqCiuXr2Kt7c3X375Jenp6caRM8CQj9y7d29CQ0NJSkriwoUL6HQ6Zs2ahaurK5GRkQQFBREREQEYgtIHvwg0bdqUlStX0qdPHzQaDYMGDeKrr77C+96/idnZ2SQnJ7N69Wrkcjlz5swxliGVSin+i6OM3R/ox8XFceTIET7++GPS0tJYuHAhaWlpuLm5sXfvXurVq2fc9saNG7z00kt/6ZgvMhFY/90kUpBVNkyPG1BDrwfdXdCkgeamyVyiuYlUk4ZUdQi55iY2+qLS+5vZgMwdFB4g8wRzTzRSD1RmHijxRIkH+Tp7lFpQqh1Rahwp0NREqQGlRo9SDcVlpOvp9FqKVXdQqW+hLL5BvvIGuYU3yC64QbbyJtlF6VzIv8LR7GMU3yhdL7lETiV5JapYVcHT3hMvRy98K/vi5eiFh50HHnYeVLKqZPhmXLWqYXrw5z693tDbff68oXf73DnDfM0aw82XJapUgYAA3N3coFMnCAgwBPKid1sQBOG5CwkJ4ejRo/j4+ODi4kJmZqYxXSM0NJQLFy7Qq1cvtFotL7/8MhEREU8U9Pbu3Zvk5GS6du2KWq0mPDyc9u3bP1Gdateuzd27d8nLyyszz/pBLi4uREdH895776HT6XB1dWX27Nkm20RGRjJp0iQWL16MnZ0dAQEBpKam0r9/f0aNGkVcXBxSqZRPP/0UgJdffpmJEyca3wO0b9+eM2fO0K1bN3Q6HQMGDDAG1QAODg706NGDzp07I5PJaNasGUVFRSiVSpo2bcpHH31EpUqV6N+//2PPKT09ncGDB5eZblLCzc2NKVOmMGTIEIqLi6lTp47xBkitVsu5c+dM6i88GYle/2DS679LyXiC5TGONZTTGLB6PehySgXfhvlN0KSC+rrhNQ9EymY2xqAbmSfIPAyv773XSD1Q6mxQaqBArTcG3QX3Bd8FmpLloH3g06PSFJBffIvCohvkK6+RnZ/M3fxksgquk12cRq76Dnm6LHQP1MtcYo6rlSsedh54OXnhaeeJh50H1R2qGyd7C9OcN+O1SEszBNpnzsAff8CJE+jPnUNS0lvg4ACNGhmC7KAgCA425G+LYPsfJcZLrphEu1RMjxrHuk6dOuVQo3+XlStXYmZm9sic57/i7xovuaL55ZdfOH78+CNHGqlI/q52Kevv7XFxp+ix/jeSSEDqYJgUdR++nV5jCLjV10FzHdSp9+b33hclgDad+7O3ZYCdmQN25h4gqw7m9ybL6iCvDubeYOYI93LTinUYg+0CDRSobclX21Kg9iVfA/lqPQVqQxBechSdXkt+cQa5RTfJzb9Kdv5VcvKTySlM5VZOGpfu/Eau5g4avdrkdBwsHIxBtpe9l0nQXb3lSzjcd+fyyYMHaWxubhi15ORJOHECvvoK5s0zbODuDs2bG4Ls4GBo3FiM0S0IgvAf0bdvX9599126d++OpRj69anodDpiY2OZM2dOeVflX0kE1v9lEtmfvdEPo1eB+qZpwG2cp0Dhb6DLNd3HzBbMqyMxr47FvcnJ3BssqoNtdTBzKNUbrNMbernz1VCglpKv8SBfXZUCdVPy1XryVDpyi3UU6iToMEOv11Ogus1d5TWyC5PJykvkbt4VcgpTOHTtLDuKd1GsVZocw15hj5eDIeC2KrYisFYgPiE++Lw6nBqONbBEBgkJEB9vmA4ehHvjnCKXQ5Mm0KoVhIZCixaGp1gKgiAI/zrm5uZ89dVX5V2NfyUzMzPjjZzC0xOB9YtOIjf0RMurP3wbbTaok0F99d78vkn5K+gefCKO3b2ebm+Q+4K5D2ZyH2zMfbGxrAZWD//Y6fV6irXc6+12I7fYlYycemQWFJNTrEOpNaNYIkcrs6BQncXdwhSylSncVaZwV3mVHGUyx9ISySxIYW3yWpOyq9p64Ovkg281X3wb1cd3fAQ+Ont8LmRgd/gPQ6A9dy58+qlhRJJmzQxBdmio4bVc/hcusCAIgiAILwoRWAuPJ3UAaSOwaFR6XckNlw8G3KqroLoMBT+ByY2WMkPQLfcBcx9j4G2YeyMxs8RCBhYyqGQhAVszqGRX6rBqrZabdxRcv12Z9GwrMmU+5Cp0FDuZI7GwAwtrCqVqsoquk1mQSGZBEpkFV0jOS+LEra3kFaeblOdcuTLeb/hQa2QPauXJqJWUjd+hRGrNnILN5MmGp0i+/DK0a2e4KbJuXZGjLQiCIAiCCRFYC89GIgGpk2GyaFx6vV5nuIlSfQVUV0CdaJirEqHwkOEmzPvJPO4F2iXBdi1Q+IG5L5j9+ZRGc6kUL1cnvFydTHZXqVRkZGRw9Gg8coWCtNtZZOQWo5X5gEUAUlcHLB0ro7GUc1uTQVrBNe4UJJGpvEJmwRW2Jx9gTeF19HI9tAJaQRWpM7WUltS9doy6sbvwW/IhtRVV8QgJx6xzGLRpA/eNQyoIgiAIwotJBNbC30tiBuYehskqxHSdXg+6LEOQrbpyL/hONMzzt927sdJYEJh7gdwP5LVM5zIPw3EAuVyOh4cH6enpxjvqdTodmZmZpKWlGaYbh0lLS8NapcIX8LOyw7lqGI5e1bB0qozWwpJrBakkZl4kOfsiN3MvkZR/kSPWlyiqWVKfG1iqF1Nr62L8VppR3aYG3nVDqNO2H43rNMNWIQJtQRAEQXjRiMBaKD8SCUidwdIZLINKr9fmgfoyqC5C8UVQXzLMCw+ALv++cixBXtMk4LYy04O2BkgdMTMzw8XFBRcXFxo0aAAYcrmzsrJIS0vj5s2b3Lx5kysHz6LRaACwtrampYcHvau2pkqT17Gt5E4hMq5mp3P29gUuZV4k6c45Mq4d4oDTJWJliejyE+HHbzDbBG5Uwt2lMd5uTfCrVI/6rvVoUNkPVysLbOUgFWkkgiD8B4wbN44jR47w/vvvExYWVt7V+Vv179//L9/UN378ePr06UP16tUZO3YsixYtIj09naioKL7++utnrtuHH37IqFGj2LNnD4DJw3aeVP/+/Rk+fDhBQWX8e/wI69evx8rKirCwMObPn4+/vz9t27Z96uOXSEhI4KeffmLMmDFlrk9PT6d79+7s37+/zPXr1q0jJiYGiUSCv78/kydP5sqVK4wdO9a4TVZWFvb29mzdutV47Vyf0wPmRGAtVFxSW5A2Lp1iotcbhhFUXTIE3aqLhtdFf0DeRkBLHUvgMiCtYhiSUF733rwOKOoikbrg7OyMs7Mz/v7+gGFA/IyMDFJTU7lx4wapqalcvHjReNjKlSvj4eFBiJcX/QMb4+DgABhGPMlUFnHu981c3ruOq4m/cUl6h7OVd7EhYxfae0+ENZNIcbb2xdW2Lp4OdfFxqkcdl3rUrVQLZws59gpwkEuwNcfksbeCIAgV1caNG0lISED+AtzcfeTIkb+87/Tp0wHDY8zPnz8PgKur63MJqvfu3Yurqyuurq5/KaB+VidOnDA+TXPkyJHPXF5iYiKZmZllrtu3bx/R0dHcvn27zPVXr17lm2++IS4uDmtra8aOHcvq1at54403jA/LKSwspGfPnkyaNAmAwYMHEx0dzfz585+57iACa+HfSCIBc3fDZN3adJ1eBaokEs9vx9dTA6oLUHwOcr8zHb1E6nxfsG2YS+V1cavihpubG02bNgUMf4AlQXZqaipnz57lxIkTANjb21OtWjWqVauGl5cXrV7pRUiH3obyz5+HDRsojl3LpbSznKki4Y+m1fnD14Zz+Qmcu/UjOr3hITlSiTmVbGpRxa4+bnYNqOrQgNqVGuBl74aDQoKjHBwVEhwUEuzlIDMTQbcgCOVvyJAh6PV6evbsyfLly/n999/57rvv0Ol01KtXj4kTJzJr1ix8fHzo168f69atY8WKFezYsQO1Wk27du345ZdfiI+PZ8GCBWg0Gjw8PJg6dSqOjo6EhobSoEEDzp8/z+rVq3F2djYeW6fTER0dTXx8PBKJhC5dujB48GAOHz7Ml19+iUwmIzU1lQYNGjB9+nQyMjJ45513qFGjBomJibi7uzN79mwcHBzYu3cvn3/+OTqdDk9PT6ZMmUKlSpVMjh8cHAzAgAED2LBhA35+fsaOl5LHhM+cOZPQ0FC6dOnC/v37KSws5NNPP8Xf39/YG/ztt9+SkZHBsGHDGDduHAMGDGDPnj3cuXOHCRMmcOvWLSQSCaNGjaJ58+bEx8cbnwJpb2/PZ599hpOT6b1Fy5YtY8qUKQAsXLgQgBEjRtCyZUteeeUVjh8/jlQq5fPPP8fT05OEhARmzJhBUVERjo6OTJ48GU/PP4fl1Wg0TJo0icuXL3Pnzh38/PyYO3cuGo2GDz74gDt37gAwbNgwLC0t2bNnD4cOHcLFxYVt27YRGBhIt27dWLFiBWvWrEEqldKmTZtSPdCXLl1i6tSpKJVKsrKyGDx4MJ07d2bBggUolUq++uor3nnnHZN9YmNjWbhwIeHh4WV+JuVyORMnTsTGxgaAWrVqcfPmTZNtlixZQtOmTY2Pa/f19eXGjRtcu3aNatWqPfIz/yREYC38t0jkoKhNjrYAnO97apleD5oboDpnCLRV5+8F3OsNo5qUMLMzCbgtFXXx9aqLr08rkJih0+nIyMggJSWFa9eukZSUxOnTpwGwsrIyCbSrfPwxiqgo6p8+Tf1Vq+i7ejV8cxysrCjs1pMLPdtwtpolp2+f41T6WRIyDnDqxp9DBNoqKuNm1wBXuwa42dXHzb4BLja1cVSYGwJuxb2AWy4xvldIRdAtCC+MlSth+fK/p+yBA2HAgEdusnjxYvz8/Pjxxx+5fPky69evZ+3atSgUCj777DO++eYbQkJCiI2NpV+/fhw6dIicnBzu3LlDYmIiAQEB5OXl8dlnn7Fy5Urs7e1Zu3Ytc+bMMfbwtmrVis8//7zUsdesWUNaWhqbN29GpVLRv39/atWqhaWlJSdPnmTTpk14e3szcuRIVq1aRfv27bl06RJRUVEEBQUxc+ZMvvjiC9555x0mTJjAmjVr8PDwMAapCxYsKHX8NWvWsHLlysdeOgcHB2JjY4mJiWHJkiXGYBcgKiqKAQMGsGjRIlJTU43Lp0+fTvfu3Wnbti0ZGRn069ePTZs28eWXXzJp0iQaNGjA119/zblz52jZsqVxv+zsbJKTk/Hx8SlVj9u3bxMcHMwnn3zCzJkzWbVqFR988AFRUVEsXrwYd3d3fv/9dz755BNWrFhh3O/kyZOYm5uzbt06dDodkZGR7Nu3D6VSSdWqVVm6dCnnz59n8+bNfPTRR4SGhhIYGMjLL7/Mtm3bAEM6x+rVq9mwYQOWlpYMGjTI+LTCEj/88ANDhw4lODiY69ev06VLF+ODfY4cOVIqqAZMrmVZqlatStWqVQFDuseqVauYMWOGcX1eXh7r169ny5YtJvs1adKEvXv3EhkZ+cjyn4QIrIUXg0Ty502U1v/353K9HrQZ94Ltc1B83jDP3wba+/7BMrMBuT9mivpUsWhAlfr1CXqpLXozR7Kysrh27Zox2L5w4QIAFhYWVK9eHW9vb2qMHo3z9OlIDh6EVauwXLeOgO/XEVCjhuEfsDcWQ9WqZBVmkZCewB+3/uBU+ilO3TrF4eQvUGlVAJibyfF0qIu7fQNcbBvgbNMAd7uGWModAcMQ4Q5yQ5BtCLYlONzr8baSiRQTQRD+HocPHyYlJYVevXoBoFarqVu3Lm+99RaffPIJWq2WpKQkOnXqxNGjRzl9+jStW7fm1KlTpKWlMeBeEK/T6bC3tzeW27Bhw4ceLyIiAqlUiqWlJeHh4cTHxxMaGkrTpk2pUaMGAF27dmX9+vW0b9+e6tWrG/OHX331VUaPHk2LFi1o0KABHh4eAPTu3ZulS5c+9viP8vLLLwNQs2ZNdu3a9UT7HDx4kKSkJGNAr9FouH79Om3btmX48OG0a9eOtm3b0qJFC5P9rl27RuXKlZ+oLseOHSM5OZnr16+bBK35+fkm+zRt2hQHBwdWrVpFUlISycnJKJVKAgICmDt3Lunp6bRu3Zphw4Y99LhHjx6lTZs22NraApgE7iXGjh3L77//zpIlS7h06RJKpbLUNn9Veno6gwYNonv37iY545s3b6Zdu3Ymv34AuLu7k5KS8lyOXeEC688//xypVMqIESPKuyrCi0AiAZmrYbJuY7pOm/lnoF18BopPQ94GyPkzJ04ic8dZUR/nqg0IqFEfFK3ILa5KyrVbJCUlcfXqVWOgbWtri7e3N95DhlBj8mTsdu+GZcsgKgomTIBOnXAaNIjWnTvTunpr4zHUWjUXMy9y6tYpQ7CdfopTt35i/9U/e0487WpQs1JjvBwbU8W+MY7WjdBKTH8ulJuBk0KCk4Uh0HZSSHC61+ttIRMBtyD86wwY8Nhe5X+KVqulY8eOREVFAVBQUIBWq0WhUFCnTh22bNlCjRo1CAoKIj4+nuPHjzNo0CBOnDhB48aNjTcFFhcXU1BQYCxXoVAAht7itWsNv+j16dMHnU5ncny9Xo9WqwVAKpWaLC95L5PJSi0vq5ySm9jvP35Z9Ho9EonEZPv793majgydTsd3331nvHcnIyMDZ2dn6tSpQ5s2bdi7dy+zZ88mISHBJCiWSCQm5/Wg++ui1+vR6XR4eHgY8421Wq0xtaPE7t27WbBgAQMGDKBbt27cvXsXvV5P9erV2bFjB7///jt79+5l+fLlbN++vczjymQyk/NPT0/H0tISO7s/n0vx3nvvYWdnR5s2bejUqRNbt2594uv1KFeuXGHQoEH079+fgQMHmqz75Zdf+N///ldmfc3MzJ7L8StMYJ2Xl8eMGTPYtm0bgwYNKu/qCIIhD9uqpWEqUXLjZPFp00m5APTFANghpb61H/Vfqo++hT/5al+S02y5mFRMYmIiCQkJADg7O+M9ahR1xo7Fa/dupDExsHUrVKsG77wDgwZBpUqYS83xr+yPf2V/XuM1Y1XS89P549YfnEg7wfG04xxPO8aepFjj+uoO1alfuQm1KjWmulMAbrZN0ODEjQI95+7qTU7VSmYIuh0VJcG3IfB2UIC5yOkWBOExgoKCWL58Oe+88w5OTk5MmjSJatWqMWLECEJCQli0aBEDBw4kMDCQadOm4e7ujpOTEw0bNiQqKoqrV6/i7e3Nl19+SXp6OjNnzjQpv2/fviY35mm1WjZt2kSbNm1QqVRs2bKFIUOGAHD8+HHS09NxcXFh06ZNtGrVCjDc2Hb+/Hnq1KnDhg0baNWqFQ0bNmTixImkpqbi4eHBunXrHjoqhlQqNQbRjo6OXL58mZo1a7Jnzx5jQPw4MpmsVCAO0KxZM1avXs3QoUNJTEzktddeY/fu3bz55ptMnjyZN954AwcHB3bv3m2yn6enJ2lpaU90bIAaNWqQk5PDsWPHeOmll9iwYQNbtmwhJibGuE18fDwdO3ake/fuXL9+ncOHDxMcHMz333/P9evXGTduHK1ataJNmzbk5+cjlUqNX2pKvPTSS4wePZoRI0agUCgYNWoUQ4cOpXnz5sZtDhw4wI4dO3B1dWXVqlWAoV3vv85PKz8/n7feeov33nuPV1991WSdXq/n7NmzBAQElNovNTX1ueRXQwUKrHfv3k316tV58803y7sqgvBw9984afPKn8v1GsOTJo3BdgIUHUGStw5boL4V1G9gi/6l+hTqa5GW5cr5qzls2JBDlSopWNna4jV9Ok1v3aLGtm3Ix42DyZOhb18YMQLK+B+Bq40rr/i+wiu+f9YjU5lpDLRL5lsubTCu97L3orFbYwKqNKa2S1O8nZuixZ6sYj1ZxZCUq+e0xjTotjPHGGjfH3jby8FMpJYIggDUrl2b4cOHExkZiU6no06dOgwePBiA1q1bM2nSJAIDA7G3t8fZ2ZnWrVsD4OLiQnR0NO+99x46nQ5XV1fjzXqP0rt3b5KTk+natStqtZrw8HDat2/P4cOHqVy5Mh9++CHp6em0aNGCnj17kpaWhr29PQsWLODatWv4+fkxbdo0rKysmDJlCsOHD0etVuPu7m7M735Q27Zt6dOnD5s2bWLUqFEMGTKESpUq0aRJE+7evVvmPg9ydnbG3d2d/v37m+T+RkVFMWHCBONNebNmzcLGxoYPPviAsWPHIpPJsLKyYtq0aSblOTg4UK1aNRITE/H19X3s8eVyOfPnz2f69OkUFxdjY2PDp59+arJNz549GT16NNu2bcPc3JzGjRuTmprK22+/zQcffEB4eDhSqZQxY8ZgZ2dH8+bNmTt3rjHtA6BevXq8/vrrxl8X2rdvbxJUg+EGy379+qFQKKhduzZVq1Y13nD6xRdfMGfOHEaPHv1E17VPnz4sW7aMHTt2cOfOHb799lu+/fZbAEJDQxk5ciRZWVmYm5uX+SvE0aNHmTdv3hMd63Eker1e//jN/jn339H6JIqLi40J8Y/6yebvcvz4ceODSISKo8K0izYPVGcNwXZRgiHgLv4DdLnkFdjQd9Rafj/eimaNTxPY5BhuVc+Tr7Kjyl09rU6fptq+fZgVFkKLFjB6NHTpAk/5c9Xdwrv39Wof5/jN41y5e8W43s/Zj8CqgQRVDSLIIwi/SvUp0MgNwXaRnrv3gu6sYj3F93VKmEnAQW4ItJ0tSiZwfkhqSYVpE8GEaJeK6WHtUtLjKpTt8OHDfPHFFyY9sGDokSwZgeNZFBQUYG1t/UxlPG+7d+/m2LFjfPTRR+VdlXLzLO1y4cIFvvzyS2N++/3K+nt7XNz5j/dY79ixw+RbGhh+migrsf1pnDlz5pn2fxbHjx8vt2MLD1dx2sUcaHxvAtAjl9zASnqJxfM2kZS4gU07mrBpaxsuXh1CXZ9z/L42lLQsV+IjA7A6rsRnx1nsIiJQenqSERlJVqdO6J9i3FgHHGhr0Za23m3BG/LUeZzLPseZ7DOczT7L9ovbiUkw/EMkN5PjZ+eHv6M/9Rzq4e/gTz2rqiCRoEaKEgUFKFBKFCiLFKQVKbiSI0cv+TPgl+vVWFNsmPRFWFOMFeYcO34c0cdd8VScvxXhfmW1i0wmM8lBFkwVFRWh1WpLXaPCwkJ0Ot1zuXYV7fo3a9aMzZs3k5ycjIuLS3lXp9z81XZZvHgx7777bpn7q1Sqp/7/o+ixfkait6diqkjtotfDnTtw8SJcumQ6v3oVXF3B1xfy89ScOyfhk1G/M2bwMvRFJ0F1EQmGm2tUheboL4LilBrVdWuKGvbFZtAMzBwrPYc66rmWc40jN45w+MZhDt84zPGbxynUFALgbOls7NVu5tGMZh7NsLf48859nV5PdjFk3uvlvlNk6OW+U2Tay21uBk4K/uzhvtfb7agQ43OXl4r0tyL8SfRYV0wVscda+Pva5V/RYy08ObVaTZs2bahduzbLli0r7+r8JV27diUmJsbkTuCn4efnR3x8fKkB8Z/Er7/+yqlTpxg5ciS7d+8mPj7eeMf630GphMTEsgNoAD8/w1SrFrz2muG1ry+kpUH//mBja8658+Dh0QZoY+jZ1SkNI5IUnUSfexi1/xFk/heRywqQswx98jKUR50pdm2Lrcf/IbNpBvLaIJE+oqalSSQSvBy88HLwome9ngBodBrOZJzhcOphY8C9M3EnevRIkOBf2Z/mns1p4dmC5p7NqeFYAycLM/gz3kav16PUQGaRnpOXUrB2qUZmkZ7UfNMbKCWAgwJjoO1kIaHSI9JKBEEQBKEiEoF1Bfbzzz9Tu3Ztzpw5w5UrV8ocAL6iKxnSpzycPn2anJwcwHDTSdu2bZ+5TK0Wrl0rHTz/P3tnHh/D/f/x5+xmk80pQQ5EQkhCnSFEIkQUdSXqKIpQ1R9VWj1oXXXVTd098aVVZ0sRR0sRKuKIkogQBJEoiTMJuXc/vz8m2SQkbhI6z8djHisz8/nMZ2bs7mvf8/683mfOQFISuLjIwtndHVq0gEGD5L/Ll5fnPd5LaCi8+SaMHg3DhhWRPq0yA9PGYNoYE5tBmAAIHZmpJ7gVtgSL0+uxKHcV0/LrkK6tg2ugE1rQeqA2awTahqD1BGP3xxbbRioj6jvUp75DfQZ5yvZEKZkpHLl8hND4UA7EH2B11Gp+OPoDAPbm9oWEdoMKDTAxMsFcA+YaiWvcpKFjVUP/WTo5qn0jQ3AjU3AjQ452X0gV6Ao8RzM3kiPc5XPFdnlTCVuthKkimbjQMgAAIABJREFUuBUUFBQUShmlTlgr/tX5rF69mvbt2+Pk5MRPP/3E+PHjadmyJd98842hetHHH39M48aN6dWrF9999x07duxAr9dTqVIlxo8fj729PUFBQZQpU4bz58/z9ttvU6dOHWbNmkVWVhbXrl3Dx8eHqVOnAnJp1h9//BGtVkuTJk34+eefiY6OBii2/127drFmzRoWL1583znkRZxDQkLYuXMnKpWKuLg4tFotM2bMoFq1aqSmpjJlyhTOnDlDdnY23t7efP7554W8OdPS0pgwYQJxcXHcvn0bc3NzZs+ejYuLCzt27OC7775DkiTUajWff/4558+fZ82aNeh0OiwtLXF2dubPP//khx9+4Nq1a4wfP57z58+jUqno2bOnoThBcXzwAezbB7GxskjOizy7u0PHjvKrszOoH0+74uIii2s3t8doJKkxsaqPwxuL4I1F6P75h4zRIzE/t5MsDw2J/uWQasfjUO4oRuqs3DbmoPXIF9rahmDs9thi28rEitddXud1F/lHik6vI/patEFoh8aH8vvp3wEwUZvQqFIjfBx9aOrUFLNMs0J9GaslHMzAwaywQNYLQXJWruDOXa5nQNRNPVkFLGfNjMgV2xK2prL4VgS3goKCgkJJUuqEtYLMuXPnOHbsGAsWLKBWrVoEBQXxySef0LVrVzZs2EDt2rVJTk4mLCyMr776io0bN3LmzBl+/fVXjIyMWLt2LWPHjjWIXSsrK4OR+6effspHH32El5cXd+/e5fXXXycqKgqtVsvs2bPZsGEDDg4OLFq0yOBN+aD+HzUafOTIEbZs2YKDgwNfffUVP/74IzNmzGDq1KnUqlWL6dOno9PpGDlyJMuWLeP//u//DG337duHlZUVa9euBWDcuHGsXLmSL7/8kpkzZzJ79mzq16/P/v37DZ6bPXv25NatW3zyySds2LDB0NfEiROpUqUK3377Lampqbz99tv4+fnh7Oxc7Nh794aBA8HVFZ5lGleFCvLyNKgbNMD8jx1w/DiaCROoPGQT2RYWHPZvzQnfitjbX8fd+Q6OtolYZPyIJObLDSVz0DbIFdsNQdsIjF1BenTXEbVKTR37OtSxr8P7nrKH7JXUK4QlhBF6KZQDCQeYe3AuMw/MBMDtHzd8KvvQ3Kk5flX8qGpd9b4iCiopv1x79XvSSlKz5bzta+nFC27zPMFtmhvhzhXfiuBWUFBQUHjeKMK6lLJ69Wr8/f2xsbHBxsYGR0dH1q1bR9euXenWrRsjR45ky5YttGzZEktLS/bs2cOJEyfo2rUrIFdxSk9PN/Tn6elp+Pf06dPZt28f33//PefPnyczM5O0tDTCw8Np2rQpDg4OAPTp08cwmfRh/T8KtWrVMvT92muvsXPnTkDOhT5x4gS//SYXN8nIyLivbdu2balcuTIrVqwgLi6Ow4cPG0zeO3TowNChQ/Hz86Np06b83//93wNdYg4cOMCIESMAuRrio1R7uqeKbOmkfn2kjRvhn3/QjBuHT/BWvMIrcKZ3b3YnV+b6rVtIko667sbUcc2ism0ixvoTcPsHELn3UmUtC2zTxqBtDKZeclXKx6CCZQW61OxCl5pdAEjPTufolaOsDVvLJXGJ4Jhglh9fDkAly0r4VfEzCG33cu7FViuTJAkrY7AylnApkLIvhCAlW45wX0uXJ05ez4ATNxTBraCgoKDwYlGEdSkkLS2NTZs2YWxsTMuWLQG5mtAvv/zCu+++y2uvvUZISAgbNmxg9OjRgCx033vvPXr16gXIFjF5+cUAZmb5j+H79OmDu7s7zZo1o127dkRERBjKuxY0iSlYFvZh/T8KWq3W8O+88qp5fc+fP9+QQ56SknKfuFq1ahXr1q2jd+/eBAQEYG1tTUJCAoAhkh8aGsqGDRv43//+x6hRo4odx72lVuPj47GxscHCwuKxzqfU0qCBXMFx3z7UI0ZQc/ZsatSqRfKoURyvWJHoU6eIOH0NqEjVqk2pXbsGr1WT0IoTkHEY0g/BjelArp2HkVOu0PbKfW0Aqke/VqYaU3ydfDG9ZkrDhg3RCz2nrp1ib9xe9sXtY/eF3aw6sQoAWzNbmjs3x8/Zj+bOzaljXwfVQyLokiQXqylTjOC+bhDbxQtuW9O8lBIJu9w8bqXipILCy8WCBQvYsGED/fr1K/Ficw/yzT558iTbtm1jxIgRdOrU6YnmIhXn1/0wUlNTGTlyJN988w2JiYmFnmw/KaNGjWLo0KFUqlSpyO3z5s1DrVYXmeqblJTEqFGjuH79OiqVis8//xxvb2/u3r3LyJEjuXjxoiHF08fHhxMnTrB9+3Y+//zzpxrz80QR1qWQ4OBgrK2t+fPPPw3iNiUlBX9/f/744w+6d+/O4sWLSU9PN9gx+fr6snbtWgIDA7GwsGD+/PlER0cbKg/lkZKSwokTJ1i8eDFlypTh0KFDXLp0Cb1ej6+vL99//z2JiYnY29vz66+/Gto9av9Pgq+vL8uXL2fSpElkZ2czePBgfH19GTx4sGGf/fv307lzZ9566y1SUlKYOHEi1apVIycnhzZt2vDdd9/x9ttv4+vrS/v27cnOzi62LKq3tzfr16/nk08+ITU1lX79+rFgwQJD3vorQ/PmcPAgrF+PNGoU1n360MLPjxZff801JyeioqKIiooiOHg7W1UqXF1dqV17KO7uC9GosyHjGGQcgvTDsuBOzSuXrgKT2rkR7VzBbfIaSI/2caKSVNSyq0Utu1p80OgDhBCcu3mOfXH7DGJ7/Sm5WqS11ppmTs0MQtujggdGqkc7TkHBXe2elJJ7Bfe1DDh+XU/BopM2JmCbK7bzXm1MlGqTCgqllU2bNrFs2TKqVq368J1LkGnTprFo0SLgxU/wT05O5tSpUwDY29s/tagGWeQPGTLkvvWpqalMmzaNrVu38t577xXZdubMmbRs2ZLevXtz/vx5goKC2LdvH8uWLcPZ2ZmFCxcSGxtLv3792L9/P3Xq1GHZsmXExMTg7u7+1GN/HijCuhSyevVq+vfvXyhibGVlRVBQEMuXL2fNmjVMnDixUA7yW2+9RWJiIt27d0eSJCpUqMD06dPv69vKyoqBAwfSuXNnzMzMsLe3p0GDBsTFxeHt7c2oUaMYMGAAxsbG1KxZE1NT04f2/6DJi4/CmDFjmDJlCgEBAWRnZ+Pj43Pfm/Ddd99l3LhxhnSR+vXrc+bMGYyMjBg9ejTDhw83RKKnTp2KRqOhSZMmDB8+nK+++opatWoZ+ho3bhwTJkwgICAAIQSDBg169UR1HpIE3bpBp06weDFMmACNGmH77rv4T51KixYtuHLlCidOnODkyZPExMSg0WioUaMGtWvXplq1YajL5v4/zLmWG9HOE9obIDnXBlIyk/O0C0a2jZyKtkK5b4gSruVccS3nyoAGAwCIux1XSGgHnwkGwMLYgqaVm+JfxZ+WVVvSoEID1KrHtxYsSnDneXFfy00pyXs9myzI09tGEpTTUkhs25pKWBhRbAqLgsKrihCC2bNn89dff6FWq+nRowf9+vXj8OHDzJ07l4yMDFJSUhg1ahStWrVi5MiR3L59m7i4OEaMGEH58uWZNm0aGRkZ2NjYMHHiRCpXrkxcXBwTJkzg9u3baLVavvzyS1577bX72uc90QX5cz0xMZEhQ4bw9ddfc/XqVebNm4der6dy5cpMmjSJ8uXLc+DAAaZPn44QgooVK/L111+zY8cODh8+bPhOCwoKYujQoTg7OzN8+HDS0tJQqVSMHTsWV1dXIiMjixx3dHQ0Y8aMAeQS70URFhaGra0t1tbWgDzBPyYmhoULF5KYmEhcXByXL1/mrbfeYvDgweh0OmbOnMnhw4fR6XR06dKFd955p1CfxV3v4OBglixZglqtxtHRkVmzZjF58mSSkpIYMmQIo0aNMkTVL1++zKhRo7h58yZarZbJkyffdw5z584lLCyM5ORk7OzsmDt3Lhs2bCApKYmBAweycuVKbGxsDPvv2rWLKlWqPPDpQevWrWnSpAkAzs7OhtTUoUOHGgJjCQkJlCmT/2EdEBDA//73v/tKsZcaxEtORkaGCA8PFxkZGSVy/PDw8BI57vPg0qVLYuHChUKn0wkhhPjzzz9Ft27dSnhUT8ardF+eKcnJQgwfLoSRkRBWVkLMmSNEVpYQQgidTicuXLggNm/eLKZPny4mTJggZsyYIYKDg8WlS5eEXq8v3JdeL0TmWSFurxTi6kdCXGgixGkTIU4hL2fshYjvJMT16ULc3SuOhu9/4mH/m/KvWHNijfhgywei1je1BBMQTECUmVZGBK4OFPPC5onIq5FCp9c9zdUpkiydXly5qxeR13ViV0KOWHM2WyyMzBLT/slf5kZkiV/OZIs/L+WIY9d0IuGOTmTk6B/eeSlAea+UToq7L9HR0fl/3P5JiIt+z2e5/dNDx7ht2zbRs2dPkZmZKe7cuSMCAwNFUlKS+PDDD8W5c+eEEEIcOHBAdOzYUQghxBdffCG++OILIYQQmZmZIiAgQFy+fFkIIcS+fftEv379hBBC9OjRQ5w8eVIIIcTZs2dFmzZt7mtfFP7+/iI+Pl5cv35d+Pr6ivj4eCGEEIsXLxYffvihyMzMFN7e3oZrOHv2bPHzzz+L9evXF+q3T58+4uDBg2LhwoVi8eLFQggh9u7dK5YsWSJu3bpV7Lg7duwo9u+XP+cWLVok/P397xvj5MmTxS+//GL4283NTQghxIIFC0S3bt1EZmamuH79uqhfv75ITk4Wq1atElOnTjVcsz59+ogjR46IgwcPij59+gghRLHXu2XLluL69etCCCGmT58uoqOjRXx8vGFcBf/9f//3f4ZxhYSEiI8++qjQuC9evCiGDh1q0AcjRowQS5cuLXTdi2PBggViwYIFxW7P44cffjCcUx7vvvuuqFmzpvj1118N61JTU0WjRo0KfSfduXPnof0/CYXeb7k8THcqEWsFAw4ODiQlJREQEIBarcbS0tJgw6fwimBlBbNmwYAB8PHH8OmnciR73jxUbdpQpUoVqlSpQvv27YmNjeXEiRNERERw9OhRypUrR926dalbt64cbZEkMK4uL2Xk3HtEFmSekPO00w9BehjckR91epip4UI9MPXOXzRVHymqXcGyAj1q96BH7R4AJN5JJORiCLsv7Gb3xd1sjtkMyDna/lX9aVmlJS2rtqR62epPHUnWqIq2BUzPESQViGxfS7/foaSMsTxJ0q5AhLusFtRKdFvhFeDIkSO0a9cOY2NjjI2NDWkNs2bNYs+ePfzxxx9EREQUKhVdt25dAC5evEh8fHyhlL87d+5w9+5doqKiCs2TSUtL49atW4XaP4jIyEjq1q2Lo6MjAD169ODHH38kJiYGe3t7QyW9zz77DKCQa1RBvL29+fDDDzl16hR+fn706dOH06dPFznumzdvkpSURNPcme5dunRh/fr19/UZFxdniNDei5eXF8bGxpQrVw5ra2tSU1MJCwvj1KlTHDx40HAtYmJiqF69uqFdcdfb39+ft99+m1atWvHGG29Qs2ZNw9ykezly5Ahz5swBwM/PDz8/v0LbnZ2d+eKLL/j111+5cOECx48fx8nJqci+noTly5ezdu1afvnll0Lrly5dyuXLl+nZsyceHh5Uq1YNCwsLhBDcunXriYrHPW8UYa1gQKPRMGnSpJIehsKLoEYN2L5dnuT4ySfwxhvQuTMsWACOjqjVatzc3HBzcyMzM5Po6GgiIiLYs2cPe/bsoUqVKtSrV4/XXnsNY2Pj/H4l43z7PpsP5HU51yHjIFfP/04F84uQ8hPc/kbeprYD0yb5QlvrCaqH+xnaW9gXEtqXki/JIjt3WXdyHQCOVo60rNrSILQrl6n8zC6hqZGEs6WEs2X+OpHrwZ0vtmXhfSFFkKe31RKUz00nsctd7E0VdxKFJ6BMX3kpIe6dCJ6QkEDZsmUJCgrCy8sLLy8vvL29GT58uGGfvEnser0eR0dHgxjX6XRcv34dvV5fSKQDXL161ZA6kdf+xIkThkq6tWvXZsqUKYb99foCv26R35c5OTloNJpC401NTeXu3buFJtODXPUYoGHDhmzdupWQkBC2bdvG77//zkcffVTkuO/tQ11MUQNJkgrVaChIwfLYef3pdDpGjBhBmzZtALh58ybm5uYcP37csG+vXr2KvN5jx47l9OnT7N27lxEjRjB06FDDvKx7KTgmIQSxsbGFxHtUVBSfffYZ77zzDm+88QYqlarQ+T4NM2fOZO/evaxcudLgHHb48GGqVKmCnZ0dlSpVwsPDg7NnzxpMDtRqNar7KqqVDhRhraDwX0WSICAA2rSBOXPgq6+gZk2YMgWGDDFUuzExMcHDwwMPDw9u3bpFZGQkERERbNq0iW3btlGzZk3q1atH1ar3e1IDYFQeLDryb3YFKjg1BKGTy7Snh0H6QcgIgzubc3dWg0leVDtXcGtcHhrVdirjxDv13+Gd+u8ghODszbMGkb3t7DZ+jvgZgOplq9OySku5yE3V1ylnVu5ZXlEkScLaBKxNJFwL5G/n6OUqk0m5YjspXRbbUTfzv5gsNRiEdp7oLqtMllQoxTRq1Iiff/6Znj17kpOTw3vvvcfMmTO5ePEiq1atwtjYmNmzZxvqIRTExcWF5ORkwsPD8fT0ZP369QQHB7NixQqqVKnCpk2b6NSpE6GhoYwbN46//vqrUPs6deoUO/GvXr16jB8/noSEBBwdHVm7di1eXl5UrVqVGzducO7cOapXr86SJfIcEQ8PD2JjYxFCkJCQQExMDCALPnt7e/r164eXlxedO3emSpUqxY67YsWKhISE0KJFi2JtXJ2cnLh8+fIjX+MmTZqwbt06/P39ycrKolevXkycONGw/fbt20Ve75ycHNq3b8+KFSsYNGgQ2dnZnDp1Ci8vryIn9Xt6erJ161Z69OjBgQMHWLRoEatXrzZsP3LkCI0bN+btt9/m1q1bhISEGMS+Wq0u8h4/CsuXL+fQoUOsXr0aK6t8W6eQkBCysrIYO3YsSUlJREVF8cUXXwDyEwLA8GOrtKEI65eY+fPn4+zszJtvvllqj5+amsqQIUP4+eefH6vvRYsWUaNGDVq1alXkdiEEI0eOxM3NjQEDBhS5z6ZNm1i6dCmSJGFqasqYMWOoU6cOID9yy/tlDDBgwAACAwMfa4yvDCYmMGoU9Oghl5gcNgxWrIAff4Rcr/A8bGxs8PPzo3nz5sTHxxMREcHJkyeJjIzEysoKDw8P6tev/+APPEkN2nryYiMXlUF3QxbZeWL7KaLakiThVs4Nt3JuvO/5PnqhJyopyiC015xcw4///IiERMOKDWnt0po21drg7eiNiZFJsf0+DUYqCTtTWTgX5G62LLILLgWj20aSbP2X19bOVMJOK6FVotsKpYDWrVsTFRVFly5d0Ov19O3bl7p169KtWzc6dOiAkZERTZo0ISMjg7S0tEJtjY2NmT9/PlOmTCEzMxMLCwvDZLRZs2YxYcIElixZgkajYe7cuY+V0lW+fHkmTZrE0KFDyc7OpmLFikyZMgUTExNmzZrF559/TnZ2Nk5OTsycORONRsP69etp27YtVatWNUR1g4KC+Oyzz9iwYQNqtZoZM2Y8dNyjRo1i3rx51K9fv8ixtWzZkjVr1hisax9Gz549iYuLo3PnzuTk5NClSxe8vLw4dOgQIIvLoq53VlYWH330Ee+++y4mJiaUK1eO6dOnY2VlRcWKFQkKCmLatGmG44wbN46xY8eyatUqTE1NmTx5cqFxtG/fnqFDhxIQEADITwny0kpatGjBwIEDWbJkCZUrP/yp4OrVq0lKSuKjjz7im2++wcLCgqCgIMP2H3/8kQ8++IAxY8YYUlNHjx5tsPM7cuQI/v7+j3T9SgJJPKtYfgmRmZlJVFQUtWvXLvQY5UVx9OjRYh+tKMiPBgMCAjh27NhjtQsKCqJ37960bdv2vm2xsbFMnDiRyMhIPvzwwyKFdXBwMDNmzGDDhg3Y2dmxd+9exo8fT0hICOfPn2fw4MH8+eefT3xeryxCwNq1cv71tWvy68SJ8ACP7+zsbGJiYjh+/DixsbEAVKtWjQYNGuDu7m54JPpY7xWhg8yTuUI7DDIOQlZM7kY1aOuDadP8RVO0f2pR5OhzOHL5CDvP72Tn+Z2ExYehEzrMNGa0qNKC1i6tae3SmtdsXysRp48cveBGBoUFd4YgvUCQyapAdDtvsTF5MmcS5TOsdFLcfTl16pQhR1jhxXP37l3Mn7L8bs+ePfn2229LZX7wy8DQoUP58MMPC9ntPYv7UhRFvd8epjuViHUp49ChQ8yePZuKFSty/vx5tFot06dPp1q1agarofj4eFq0aMGNGzdwdXVlwIABREREMHnyZNLT09FoNAaT9djYWKZMmcLt27fR6XQEBQXRrVu3+47bsmVLOnToQGhoKKmpqfTv39/wi3rt2rWsWLEClUpF+fLl+fLLL6latSojR440HL9OnToMHDiQ0NBQkpKSDMVkRo0aRUZGBp06dTL86s/jwoULTJo0ibt373Lt2jVq1KjBvHnz+O2334iKimLmzJmo1Wpat25daKwrV67krbfeomLFisVeR41Gw+TJk7GzswPkX9fXr18nKyuLY8eOoVKp6NWrF6mpqbzxxhsMHjy42Jy4/xSSBD17yjnXo0bJKSLr18PSpVBM2XqNRkPt2rWpXbs2t2/f5tixYxw/fpxff/0VMzMz6tWrZ6iS+ejjUIO2rrzYDJLX6W7kT4hMD4XbS+DWAnmbkTOYFRDaJrXlPorASGWEd2VvvCt7M85vHCmZKYRcDGFH7A52nt/JtrPbAKhoWdEQzW7l0go7c7vHO4cnxEglYW8G9gUmSwohuJMDSWmFxXZsSr4VoEYl+27bFYhw25pKmKiV6LaCQmli9OjRLF682JDaoPDoREZGUqlSpVLrYQ2KsC6V5OUSeXp6snr1akaMGGGYtZyRkcHWrVsBGDlyJCBHDIcMGcLkyZNp0aKFYUb1+vXr+eijj5g5cya1atUiNTWVHj16UL169SIfUyUnJ7N+/XoSExN58803adiwITdv3mTJkiWsXbuWsmXLsmHDBoYMGWIYQx5ZWVnY2NiwZs0aoqKiePvtt+natSvTpk0jICCgyFy4devW8eabb9KpUyeys7Pp0qULISEh9O7dmz/++IPevXvfJ6pBfmQFEBoaWuw1tLW1NUR7hBBMmzaNli1bYmxsjE6nw8fHh88++4ycnBwGDhyIhYXFfd6g/2lsbOD776FPH9lBpFUreP99mDkTLC2LbWZtbY2/vz9+fn7ExsZy7NgxDh06RFhYGDY2NqjV6vsnPD4q6nJg0V5eAEQ2ZETIIjs9FNJCIEWu4IjKKjd9JE9sexVbLdLKxIpA90AC3eVUoLjbcYZodvCZYH6K+AmAevb1aFOtDa1dWsuVJDWmj38OT4gkSVhqwLJMYe/t7NzodmKB6Pap23qO38jfx9pYnihpnzdR0kzCSqP4bisolBR57koKj8/LcO0UYV0KqVGjBp6engB07dqVSZMmGayGino0eObMGVQqFS1atADk6GxwcDDnzp3j0qVLhrLnIAvz6OjoIoV1r169kCQJBwcHmjVrRmhoKNevX6d9+/aGR1ZdunRhypQpRVr2vJ4b0axVqxZZWVn35dTdy4gRIwgNDWXx4sVcvHiRpKSkh7Z5XNLS0hg5ciRXr141TFTp3r17oX369+/PihUrFGFdFL6+cPw4jB0Lc+fKTiL/+x8UKMxQFKrcSo6urq7cuXOHiIgIwsLC2LRpE9u3b6dOnTo0aNDggU8dHoqkAVNPeWGYnMaSfTFfaKeHwvUJgOBx0kecrZ15r8F7vNfgPXR6HceuHmNn7E52nN/BvIPzmHVgFlojLc2cmtGmWhvaVm9LLdtaJSJUi7ICFLmVJQtOlEzKLXSTh1YN9rkiOw1rrqULymmViZIKCgoKT4sirEshRaUk5K0zMzMrctu9X+pnzpxBCIGlpWWhaPH169exLCbiWNBuR6/Xo1Kp7rMtgnzronvJyzXKG8vD0vc//fRTdDod7dq1M1QAfJYp///++y/vv/8+1apV4+effzbYNG3cuJEaNWoYqkoJIYq1P1IATE3h66+ha1fo319OCXmE6HUeFhYWNG3aFBMTE2xtbTl27JjBG7tChQp4enpSp04dNBrN041TksC4qryU6SOv093OnRQZ+kTpI2qVGs+KnnhW9GRUs1HczbrL3ri97IyVI9ojdo5gxM4ROFo50rZaW9q5tuP1qq9TRluGkqJgZcmCziRZOtn6LzFNkJguSEyHo9f06FRORJ3OwUjKj2zbm+XncGtUithWUFBQeFRKpwngf5zTp09z+vRpQM5v9vDwKGRDcy8uLi5IkmRIjTh58iT9+vWjatWqaLVag7C+cuUKHTt2JCoqqsh+Nm7cCMiCNDQ0lObNm9OsWTO2bdvGzZs3AVi/fj3W1tY4Ozs/0rkYGRmh0+mKFMz79+9nyJAhtG8vP9qPiIgwWPao1eoixfujkp6eTlBQEG3atGHu3LkGUQ1w9uxZFixYgE6nIyMjg5UrVxrGoPAAfHzk6PWnn8IPP0DdurB//yM3lyTJ4CLz2Wef0a5dO3JycggODmbOnDn88ccfXL9+/dmOWW0NFm3B9itw2g1ut8H5MNjNBdNGkLYHEofAxfpwtizEvwHXJ8HdXaC/c1935sbmtHdtz9y2c4n6IIr4T+JZErAEr0perIteR9d1XSk/qzx+y/2Y9vc0jl89/kx/LD4NxmqJSuYqGtiqaedkxDvuRnxazwhvfQwdndV4lFehUcGp23r+jNez4oyOORE5LI7OZvPFHA4l6riQoictp3Scj4KCgkJpRAnTlULKly/PvHnzuHz5MmXLlmXmzJkP3N/Y2JiFCxcydepUg3XQwoULMTY25ttvv2XKlCksWbJBRhkHAAAgAElEQVSEnJwchg0bVqwDQEJCAl26dCEjI4OxY8fi4uKCi4sL77zzDv369UOv11O2bFl++OGHRzZmt7W1pW7dunTo0IGVK1diY2Nj2PbJJ58wZMgQzMzMsLCwoFGjRly6dAmQJ1POmTOH7OxsOnfu/EjHyisYsGnTJnbs2MG///7Lzp072blzp2Gf5cuXM3ToUCZNmkRAQAA5OTm0bduWt95665GO8Z+nYPQ6KAj8/ORJjuPHw2NEnLVaLY0bNzbc8/DwcI4cOcKhQ4eoWrUqnp6ehRxFnhmSRhbUpo2Ajx8xfaQZmDUDU18wKjyB0dHKkQENBjCgwQCyddkcTDjI9nPb+ePcH4zePZrRu0fjYOFA2+ptaVe9Ha1dWmNjanP/uEoItSRhQSa1y6qonWtQkJdKkh/ZFiTcEUTfut9zOy+dxN5UjpIredsKCgr/eZ5VPfWnJTw8XHTt2lUEBgaKvn37ioSEhEdq97Ca7c+b8PDwZ9rfwYMHRYcOHZ5pn4+Cv7+/iIyMfOHHfV486/uiUAQpKUL07y8ECNGokRAxMQ/c/WH3JDU1Vezbt0/MnTtXTJgwQcyePVvs3r1bJCcnP8tRP5ycW0KkbhciaYwQF/2EOK0V4hTyEusuxL/vCXH7JyEyzwuh1xfbzb8p/4rlx5aLHr/2EDbTbQQTEKqJKuGz1EdMCpkkjlw+InR63Ys7r2J41PdKWrZeXEjRiYNXc8TmC9licXSWmP5PlpiWu8yJyBK/nMkWO+NzROR1nbh6Vy9yHnB9FB5McfclOjr6BY/k8Zk/f744cuTIM+nL399fxMfHP/P2qampYujQoUKv14vRo0c/8vffnTt3Cv3t5ub2ROMaOXKkQee899574urVq0/UTx5r164VwcHBxW7fv3+/6Nu3b5HbcnJyxJdffik6dOggOnbsKDZv3mzY9sMPP4g2bdqIjh07im+//VYIIV+DIUOGiJycnKca87Pk3vvyrCjq/fYw3VlqItYjRozg22+/pUaNGvz2229MnjyZ7777rqSHpaCgUByWlvJExvbtYeBAuZjMvHnw3nsPrZRYFBYWFjRr1oymTZty9uxZwsPD2bdvH3///Tfu7u54enoa0p6eK3npIxa5Hur6TMg4Cul/Q9rfkPobJMsTYTGqlBvRbi5HtY1fA0l+mlPBsgL96vejX/1+6PQ6Dl8+bIhmjw8Zz7iQcdia2fJG9TdoV70dbaq1obxZ+ed7bk+BqZFEFUuJKgXS6rP1eRMkZWeSxDTB8et68rJF8sq3F4xsKxaArz5HjhzBy8urpIfxQL755hu6d++OJEmFyqG/KA4dOsSQIUMAWLx48VP3988//9C4ceP71uv1epYvX84PP/yAm5tbkW03b97MnTt32LJlCzdv3qRdu3b4+/sTGRlJcHAw69evx9TUlCFDhrBjxw7atGmDt7c3a9asoXfv3k899leNUiGss7KyGDZsmGEymbu7O7/88ksJj6pk8PLyKrYU6vNk9+7dL/yYCq8I3bpBkybwzjuywN66VRbcT1j8QKVS4e7ujru7O7du3SI8PJzjx49z+vRpypcvT+PGjalXr96TWfY90YBMwMxHXsp9AUKfW5I9V2in74PUNbn72oCZb376iLYBSMaoVWqDd/Yk/0lcu3uNHbE7DEL7l8hfkJBoVKkR7au3p4NbBxpUaIBKKt3TYDQqiYrmEhUL1GXQC8GtzMKpJGdTBJEFyrfbmOSKbVMJh1zBbaZRxPbLxtWrVxk+fDhpaWmoVCrGjh3LxYsXiYqKYuzYsSxatIjk5GTmzp1LRkYGKSkpjBo1ilatWjFy5EgsLCw4efIkiYmJDBkyhK5du3L79m1GjBjB1atXqVatGpmZmYBcxnr06NEkJiaSlJSEt7c3U6ZM4fDhw8yaNQu9Xo+rqyujRo0qsn1B7ty5w+7duxkxYgQgFyQbOnQoAD/88ANarZbY2Fjc3d2ZPXs2xsbGbNy4kZ9++omcnBzq1KnD+PHjCxUHSUxMZPTo0aSmppKUlETnzp0ZNmwYp0+fZty4ceTk5GBiYsK0adPYsWMHSUlJDBw4kJUrV9K1a1d+/vlnbG1tmThxIkePHkWj0fDBBx/cN/9n+/btLFu2zFBdcerUqWRkZLB7924OHjyIra0tzZo1M+wfGxtLbGwsX331FStWrCjyPnbu3NlQUTEpKQmNRoNGoyE6OhpfX18scguENWvWjL/++os2bdrQsWNHunfvbnATU8inVAhrY2NjOnXqBMi/rhYtWlRsKeviKG5C3ovg6NGjJXZsheJR7ssLZto07FatotKiReS89hrnp07lbr16hXZ5kntStmxZ/Pz8uHLlChcuXGDbtm3s2LEDJycnnJ2dn0u1rUejSe4yHGPpMhbq41iqjmGRcwztnWAA9MKEO/o63NF5cEdXn7v6OuiRnX1qUIMazjUY5jSMU8mnOJB0gANJB5i4dyIT9k6gnEk5mto1xdfOFy9bL8yNnt95Pq/3ilXuUh3IxIhUTOUlw5S4DC2nb+cLExORhRXpWIp0+ZV0TMjhv/yVXdR9MTIy4u7duwCsOrmKn0/8/FyO3bdOX3rVenDZ7VWrVuHj40O/fv0IDQ0lLCyMvn37sm7dOgYNGoSjoyPz589nzJgxVK1alcOHDzN79my8vb3JyckhISGBxYsXc+7cOQYOHEjbtm35+uuvcXV1Zd68eRw9epTt27eTnp7OoUOHqFatGtOmTSM7O5uuXbsSHh5ORkYGFy5cYOvWrVhaWjJ9+vQi2+ddM4CQkBBcXV1JT08HMExkBznyu2HDBmxtbenXrx9//fUXjo6OrF69mqVLl2JiYsLChQv5/vvvee+99wC56t+GDRto3bo1AQEBpKam0r59e7p27cqSJUvo1asXrVu3Jjg4mEOHDtG7d29WrVrF/PnzMTY2Rq/Xk56eztKlS0lJSeG3337j5s2bvP/++/j4+Bgck/R6PStXrmTOnDnY2NiwceNGvv32W+bPn0/z5s1p2LAhDRo0KHSuFStWZPTo0YSHh6PT6Qptu5cxY8awZcsW+vfvT05ODi4uLvz+++8EBQWh1WrZuXMnQgju3r2LkZERWq2W48ePFxsJf9E86NyelKysrMf+fHzhwnr79u2F6tOD7GqxfPlysrKyGDlyJDk5OQwaNOix+lVKmisURLkvJUSjRtCrF8Y9elBj4ECYOhWGDweV6pncEyEEly9f5tChQ0RHR3P+/Hnc3d1p3LgxVatWLcHIiSfQKf/PnERI248q/W+s0v7GKnMpoEeeENngngmR5WlEI/rSF4Brd6/xx7k/2Hp2K3+c+4PN8ZvRqDT4VfGjg2sHOrh2wLWc6zMbeUm+VzJy5Ij21TRBYroJiWnGnM/M9wg0MwKHAmkkDmb/nUmSDyppnvdj0sTE5LlVjDUxMXnoj1Y/Pz8+/PBDYmNj8fPz49133zWMSavVYm5uzty5c9mzZw979+4lIiKC9PR0zM3NMTIyws/PDwsLC+rVq0dycjLm5uYcO3aMr7/+GnNzc5o3b07lypUxNTWla9euREZG8uuvv3L+/HlSUlIQQqDVanFxccHBwQGg2PYFz+Xq1atUqlTJsC5vvABubm64uLgA4OrqSmZmJpGRkSQkJNC/f3/0ej06nY7XXnvN0N7c3JzBgwdz8OBB1qxZw9mzZ8nOzkaSJFq1asWkSZM4fPgwLVu2xN/fH7VajUqlMowr798RERF0794dS0tLLC0t2b59+33X/Pvvv2f37t1cuHCBw4cPo1KpDNfzQfdMq9WiVqsfeE9nzJjByJEjCQoKokmTJrRs2ZK4uDgGDRqEtbU13t7eREREGPpwdHQkMTHx8SvrPgeeV0lzY2Nj6t0TIMoraV4cL1xYt2vXjnbt2t23/u7duwwePBhra2u+++67p/e0VVBQKBkaNYJjx+Rc6y++gJAQ+OmnZ9K1JEk4Ojri6OhI69atCQ8P5+jRo8TExGBra4uXlxd169Yt+c8PI3uw6iovALqU3FLs++T0kdvfwK058jbjmrkiWxbbtubOBNULIqheENm6bA7EH2Dr2a1sObOFT/78hE/+/AS3cm4Gkd3MuRnG6heUFvOM0RpJOFtKOBfI287SyQVt8gW34GKiIM9R3yS3uI1DAbFtY/LfLG7Tt15f+tbrW2LHb9iwIVu3biUkJIRt27bx+++/s2zZskL79OrVCy8vL7y8vPD29mb48OGGbffWPsj7tyhgUZn3w2HFihX8+eefdO/eHR8fH0OtBqCQnWpx7QsiSVKxtQsKBujy+sqrtzB27FhDVDTPGjaP6dOnEx8fT8eOHWnVqhUHDhxACEHbtm3x8PBgz549LF++nJCQECZPnlzksY2MjApdi7i4OCpUqGBIe7t79y7dunUjMDCQRo0a4e7uzsqVK4vs63GIiorCwsKCKlWqYGNjQ7NmzYiJiaF+/fq0adOG/v37A7BkyRIqV65saJf3A0GhMKXmiowYMQJnZ2fmzZv34nInFRQUng9lysC6dfDtt7B7N9Svj8WxY8/0EFZWVrRs2ZJPPvmETp06oVar2bJlC3PmzGHnzp3cvn37mR7vqVBbgcUbYDsFnPeBazI4/Q22U0FTBVLWwJUgiK0C55zg3z5w6wc0OWfxc27OzNYziR4SzfmPzrOw3UKqWlfl2yPf0mpFK8rPLE+3dd1YdmwZiXcSS/pMnxpjtYSjhYqGtmo6OBvxbg0Nn9Yzop+7mraV1dS0VpGtl4vbBMfpWHwqh7mROaw4k8OOeB2RN/Qkpgl0pcQ//FVm5syZbN68mc6dOzNu3Diio6MBWXDpdDpu377NxYsXGTZsGM2bN2fXrl33CdJ78fb2NtReiIyMNFiwhoaG0qNHDwIDA8nMzOT06dNFFjArrn1BnJ2duXz58iOfp5eXFzt37uTGjRsIIZgwYQI/3RMsCA0NZcCAAbRr144LFy6QmJiIXq/n448/5sSJE/Ts2ZNhw4bdd40K0qhRI7Zt24YQghs3btCnTx+ysrIM2y9evIgkSbz//vuGMRWs/fCwa1scERERhjz1O3fusH//fho0aEBCQgIffPABOTk5pKam8ttvvxUKjF6+fBknJ6cnOuarTKnIsY6OjmbXrl1Ur17d4FlsZ2f3TGbKKigolBCSBIMHg7c3dO+O26BBcOuWnBryDKOLRkZG1K9fn3r16hEfH8+hQ4cICwsjLCyMGjVq4OXlhZOTU+lKH1CZyJMczXyh3CgQOsg8kTsZ8m+5QE1KbiRKXd7gPFLVzI+hjQYztPFQ7mbdZdeFXWw9s5UtZ7ew/tR6ABpVbCRHs1+SCZCPgpFKooKZRIUChWd1QnAjQ54keTXXkeTETT3/5NYYUudWknTIrSSZ50iiVJJ8dgQFBfHZZ5+xYcMG1Go1M2bMAORJbuPHj2fGjBl069aNDh06YGRkRJMmTcjIyCAtLa3YPj/66CNGjhxJhw4dcHFxMURI+/Xrx4QJE/jxxx+xsLDAw8ODhISE+4Rdce0L4u3tzbRp0wwVhh9GjRo1GDp0KP369SMnJ4datWoxcODAQvsMGjSIzz//HK1Wi4ODA7Vr1yYhIYH333+fMWPG8M0336DRaJgwYQIALVq0YODAgSxZssTQR69evZg8eTKBgYEAfPnll4aJg3njqFmzJu3atUOSJHx9fQ35vz4+PsyZMwdLS0vatm370HM6ceIECxYsYPHixfTs2ZOYmBgCAgJQqVT07t3bkN7Rpk0bAgMD0el0vPPOO4b0pJSUFO7cuWMwnVDIRxLi5f5Zn5frouRYKxREuS+ljNRUbnXujM2uXXJxmWXLHqkc+pOSnJzMkSNH+Oeff0hPT8fBwYEmTZpQu3bt55aT+kwRArJj811H0vZB9nl5m8pKzs0285Nt/rQNERgRkRhhENmHEg4hEDhYOBhcRlq7tMbS5P5r/iq9V4QQ3CzgSJKXSpKRG8iTyLX/M5MMudt2pdT+70E51jVr1iyBEb1aTJs2jSZNmuDv7/9Y7Z5XLu/Lxk8//YSRkVGpsdt7XvelqPfbw3RnqYhYKygovOJYWnJ++nQa7t0r512fPAkbNsBzEghlypShVatW+Pn5ceLECQ4ePMjGjRvZtWsXjRs3pmHDhpiamj6XYz8TJAmMq8uLtZzfSHZ8AaG9F65ty93XDMnUm/pmftT3bM4Y38+4lp7KH+f+MESy/3f8fxirjfGv4k+AWwAB7gE4lXn1HuFKkkQ5LZTTSryWu04IQXJWvs/21XTBhRRBVAH7v7ImBfK2c3O3TY1Kn9hWeHYMHTqUkSNH0qJFi9L1NOsl4O7du4SFhbFo0aKSHkqpRIlYPyWvUrTnVUK5L6UPwz0JCYEePSAtTfa7fgHl5IUQxMbGEhYWxvnz59FoNHh4eODl5UXZJ/TbLnFykgoL7cxIQIBkDFqv3KI1zck2bkTo5Qi2nNnC5pjNnL15FoB69vUIcAvAVbjSp2WfVyJl5HG4k50f0b6aJovulOz87WWMC0+StDeTsHiBXttKxLp0okSsSydKxFpBQeG/S4sWcPSoLKi7d4fPPoPp06GYWfrPAkmSqF69OtWrVycxMZGwsDDCw8M5fPgwNWvWpEmTJlSuXPnlilwZ2d3jPHIL0kNlkZ22D25MhxtT0KCmhbYhLeo3Z7bPHGLS7Ag+t4/NMZuZun8qeqHni+NfyJFstwBed3kdM43Zg4/9CmChkaheRqJ6vrsfaTkiv7BNbnT7THJ+7MnCSE4jKZhKYqX5b9j/KSgoPBqKsFZQUHjxODrC3r3w6afw9dcQEQFr1z5xtcbHwd7enjfffJPXX3+dw4cPEx4ezqlTp6hUqRLe3t7UrFnz5bSQUtuARUd5AdDfgfQDsshO2we3FsDN2bgj4V6hLsOr+XGDd/n+4Ckisi6wJmoNi/9ZjKmRKa1cWhHoHkhHt444WDiU7Hm9QMyMJKpaSVS1yl+XqSsgtHNF9/kUQZ7cNlUXztl2MJOwfs5e20IIRcwrKDxnnjShQxHWCgoKJYOxMSxaBA0bwvvvg5cXbN783PKu78XS0pLXX3+dZs2acfz4cQ4ePMhvv/2GtbU1Xl5eeHh4lEh62TNDZQHmbeQFQJ8OGYdzhfZeuL2YciKdMe6AcQ2yfHqw90Z5guMT2Xx2N8Fn5OqRjSs1JsAtgED3QOrY1fnPCToTtYSThYRTvjkD2XrBtfTCqSSHrwn0ud/DJiqwKyi2TSXKap+N17ZarSY7O1uxpVVQeM5kZ2cX63f+IJQc66dEyeUtnSj3pfTxwHty4AB06SLnXa9eDR06vNjBIZcLPnPmDGFhYVy6dAkTExMaNGhAkyZNsLKyengHLxsiCzL+IeHsKhxtYiF9P+hT5E1GVYnKrMvmyyqC4y5w6N/jADiVcTKIbD9nP0yMXuIfHs+YHL3g+j32f0npgpzcb1iNCuxMpUJ52+VNQV2M2C7u/ZKUlERmZiaVKlV6OZ+svOQoOdalk2d9X/R6PZcvX8bExAQ7O7tC25QcawUFhdKPjw8cOQKdOkFAgJxzPWLEM/W7fhgqlYoaNWpQo0YNLl++TFhYGAcPHuTQoUPUrVsXHx8fbG1tX9h4njuSMZg2ITFbg2Plhrle2pGQthcpbR91xD7qON1gjBNczXZg6zUngi9n8r9jS/nmyDdYGFvQtnpbAtwCaO/anvJm5Uv6jEoUI5WEgxk4mEnkFUDW53ptF4xsRz3Aa9sh12vb6AFe2+XLlychIYGYmJjnf1IK95GVlaU8LSiFPI/7Ym5uTvnyj/+5pghrBQWF0kHlyrB/P/TvL1vyRUbC4sVQArZ4lSpVolu3bty6dYuwsDCOHTvG8ePHcXNzo2nTpi/fRMdHQVKD1kNeyn4MQg9ZpyBtHw5p+xhgupcBFa+Q7gG7r1ux+WpZtsTt5Lfo31BJKnwq+xDoFkiAewDu5dxfvevzBKgkCVtTWTzXyV0nhOBWJoao9tU0wenbeo7fkLfneW1rJEfENR0OprLXtnGu17ZKpVKq3ZUgR48epV69eg/fUeGFUpruiyKsFRQUSg9mZrBmDdStC2PHwpkzsHEjVKxYIsOxsbGhffv2tGjRgsOHD3P48GGWLVuGo6MjTZs2xd39FRaQkgpMasmLzWBD0RrTtH10KLuXDpX3oa+XzD+3IPiKhuArkXz+134+/+tzXMtWJ8AtkED3QJo6NcVIpXzV5CFJcr51Wa3EazbyuqK8thPSLfkrIb9kdzkTDB7beakkWsVrW0Gh1KF82ikoKJQuJAnGjIFataBPH/D0lCc1enqW2JDMzMxo0aIFTZs25dixY4SFhbF27VrKlSuHj48PdevWfaJJLi8VhYrWvAuAKvsSnml/41l1LxPT9xF/O4Ut/8Lmfy+w6PBc5hycg43Wkg6uHQl078wb1d/AyuQVzFd/SiRJwtoErE0k3K3ldeFHI3Cv3SA/sp0uiL8jiL6VPy3K2hiDyM57NXuBXtsKCgr384p/EygoKLy0vPkmhIVBYCA0bw6rVsnrShCNRkPjxo3x9PQkOjqa0NBQgoOD2bNnD15eXnh6eqLVakt0jC8UjROU6S0vQOWcRAZX38fgtH2kpuxh56WTbL6cypaY1fxyYjUalQp/Jw8Ca/QioEa3V7L647NCAiyNJSyNJVwLeG3fzS7ssy2nkuSLbSvNPZFtMwkLI8VrW0HhRaEIawUFhdJLnTpw8KAsrrt0kT2vP/74hU5qLAqVSkXt2rWpVasWFy5cIDQ0lF27dvH333/j6emJl5fXq+kk8jCM7MHqLbB6C0sH6FLtJl3S9qO7G0JY3DY2X4xh8+WjDP3jKEP/+Iz65e0IrP46nWoNwqNSc0X8PQLmGgkXjYRLgf9eGTkFKkjmiu6zBQrbmBsV9tq2N5Uo85y9thUU/qsowlpBQaF0Y28Pe/ZA375yQZnYWJg377lWanxUJEnCxcUFFxcXrly5woEDBwxuIq+kk8jjoi4LloGoLQPxdZiDr2cqM9MPEPPv7wSf/ZPNcXFMPrSaSQdXU8lMQ0CVGgS6BeDvPgitVolmPypaIwlnSwlny/x1WTrZ7u9qgZLtFwoUttGqKRTVdjCVsDFRxLaCwtNS8t9MCgoKCg/DzAzWrYORI2HWLLhwQZ7kaGn58LYviAoVKtC1a1datmxZpJOI4uQAqC3B4g3c3d7A3Q2G69O5fuNPtsX8zOZz+1lx5gTfR5/A3Ggqb1S0INDFkw7uPShfrgNoKpf06F8qjNUSjhYSjkUUtjFEt9Mg/JoeXa7aNlbdP0Gy3DMqbKOg8F9BEdYKCgovByoVzJwJ1arBkCHQrBls2SKXRy9FFOckUrlyZXx9fXF1dVWignmoTClv+yZ9bd+kry9kZKcQcmYpm0+vY/P542y4FIJqbwg+5SCwsg2B1ZvjXjEAzJqBxrXEU4JeNjQqiYrmEhUL1NHQ5Ra2yZskmZguOH5dbyhsYyTJhW3yItv2phK2WlA/wGtbQeG/jCKsFRQUXi4GDQJnZ+jeXS6DvnUr1K9f0qO6j4JOIv/88w9hYWGsXr0aOzs7fH19qVWrllI57x60Giva1vqEtrU+4RshOHYlnM3RS9l8ZiufH0vg82ObcLPcRGBFWWj7OL2O2sIPTJuDSW3ZIlDhsVCr5OI09mYSlJPX6YXgZgGxfTW9cGEblQS22sKOJLamEhpFbCsolB5hHR4eztSpU8nOzqZSpUrMmDGDMmXKPLyhgoLCf4+2beViMh06gK8v/PortGtX0qMqEo1GY3AMiYqKIjQ0lA0bNrB79258fHzw8PB49a36ngBJkmhQsRENKjZiQiu4lHyJLTHBbDq9mvlnDzI75hblTDbQocJvdKoEbSpYY1GmmSyyzZrLhW4kTUmfxkuJSpLLrZc3lahdVl4nhOB2llxFMm+SZMxtQcQNObSdV9im4CRJO1MJE7UithX+W5SaT/NRo0bx3XffUb16dWbPns3SpUv59NNPS3pYCgoKpZW6deHQIejYUS6DvnixXLWxlKJWq6lXrx5169YlJiaG/fv3s23bNvbu3UuTJk3+e1Z9j4lTGSc+aDyEDxoPISUzhT/P/cnmM5sJPhPMzxeTMVal8LrDLgIrBNOxIjiam4OpjyyyzZqDtjGolOv7pEiSPLnRxkSiZoHCNinZGCZHJqbLEySjbuY7kpQ1yY9s54lupbCNwqtMqRHW27ZtQ6PRkJ2dTWJiIu7u7iU9JAUFhdJOxYqwdy907QrvvguXL8vFZUpx7q0kSdSoUQN3d3fi4uLYv38/u3btYv/+/TRq1AgvLy8sLCwe3tF/GCsTK96q9RZv1XqLHH0OoZdC2RyzmU0xmxh8NJbBR6FheTMCK0USaL+TetYgqYxB61VAaHvLkykVnhhJkm37yhjnF7YBuJOdH9W+miZIuKewTZkiCtuYK4VtFF4RJCGEePhuL4aYmBj69++PkZERa9eupUKFCg9tk5mZSVRU1AsYnYKCQmlFys7GedIkym3fTlK3bsSPGAFqdUkP65FJTk7m3LlzXLlyBZVKReXKlalWrRpmZmYlPbSXCiEEF+9cZG/iXvYl7uPErRMIBBVMrWlbwZ43K2bQxj4erZEeIdSk6d1J1Tfgjs6DO7r66FDSD58XWahJxZQUTEmV5Nd0ycSw3URkYUkGVqRjKdKxIh0TslHktkJppXbt2piYmNy3/oUL6+3btzNt2rRC61xcXFi+fLnh7zVr1rBx40bWrFnz0P7yhHVxJ/i8OXr0KA0bNnzhx1V4MMp9KX0893ui18Po0TBjhlyhcdUqMDV9fsd7Dty4cYPQ0FAiIiIQQlCnTh2aNm2KnZ3dczvmq/xeSbqbxNYzW9l8ZjM7YneQlp2GpbElbat4EFjZhvZ21ygrjoLIlBuY1M7P0TZrDkYPD+48L17l+5JHhk6QlDs5Mm+S5I2M/O1mRuQXtclNIynpwjb/hfvyMvIi78vDdIS2dv8AACAASURBVOcLTwVp164d7e6ZZJSZmclff/1Fq1atAAgMDGTGjBkvemgKCgovMyoVTJ8OlSrBsGHQujVs3gxly5b0yB6ZcuXKERgYSIsWLQgLC+Po0aNERkbi5uaGr68vlSsrXs6Pg525Hf09+tPfoz/p2ensvrCbzTFyXvavZ66gltT4OvkQWPX/2bvvsCjP7P/j72cKDF0QFJCO9CJVqgKxEluiqSaburv5bYobd7+b3rNZU0xbTbLJpm66plmJFQsiiFQREWuiiUks2AEp8/vjgQETo8QAM8B5XddzqTMwHPIgfnJz7nNHM3mINUN1W+H4/+Doq+oL6Ie2h2ybkaD3s+g2o97GoFXwcVDwOcfBNh1Pktz7o5GW1uette1hu+1XFznYRlgQi+ix1ul0PP7447i7uxMZGUlOTg5xcXHmLksI0RvddRe4u8P116sTQ77+GnrZ4SyOjo6MGzeOESNGUFRURGFhIW+//Ta+vr6kpaUxdOhQCRK/kY3ehgnBE5gQPIHXjK9R/H0xC7cvZGHNQv6+5hX+DoS5hjE5+C9M9g8haUAt2vo8OPEVHHtbfRGdV3vIth0JVqEStLvYuQ62aWoxcrBePdCmLWwX/+xgm0E/C9uucrCNMBOLCNZarZYXX3yRRx55hObmZgYPHsxTTz1l7rKEEL3VlVfCoEEwZQqkpEBOjjpFpJextbUlIyODlJQU0yzsjz76CHd3d9LS0ggPD5dZ2BdBo2hIHJJI4pBEnrzkSfYe3cui7YtYWLOQ5wte5Jn8Jtxs3ZgYPJHJwf9ljJcXdk2b4fQ6OJ0Lxz9SX0jrenbriHU0KL2nt7+30GkUPGwVPDpsOWg2qm0jbUH7x9NGKg63UNy6tK1TwK3D5kj31rCtk1nboptZRLAGSEhI4IsvvjB3GUKIviIjQ511PX48jBypntKYnm7uqi6KlZUVycnJJCYmsmXLFjZs2MDnn3/O6tWrSUtLY9iwYTIL+3fwG+DHXUl3cVfSXRyrP8bXO79mYc1Cvqz+knfK3sFaa83ogNFMDpnMxKDn8TTUqSG7br3668nWf7s0jmCT1r6qbZMAipV5P7k+SqsoDLJRV6rbtBiNHGlA7dduDdxVR1oobQ3bbQfb/HzWthxsI7qSfCcWQvRdkZGQn6/2W48dC599Bpdeau6qLppWqyUmJoZhw4ZRXV1NXl4eixcvZs2aNaSkpBAfH2+WTdx9iZPBiasjr+bqyKtpbG4k79s80yi/JTuWAJDomcjkkMlMDplJVMDbKE3ftYfs0+vg4P3qiyk2YJPcuqo9Qv29xu48H138HhpFXZV2NShE/Oxgmx87bJLccdRIRYeDbQYaaB/917rCLQfbiIslwVoI0bf5+Kgr19nZamvIu+/CddeZu6rfRVEUwsLCCA0NZc+ePeTl5bFixQrWr19vmoVtZycB7vfSa/Vk+WeR5Z/FC+NeoOpglakv++Hch3k492F8nXxbQ/ZkRvq+jJXWCpoOQl1ee9A+/CQcbgG0YIgDmxFgmw426aBzM/en2ad1PNgmtMPBNicaOWvW9jcnjWztMGvb2brDRBIbdWVbZm2LzpBgLYTo+9zcYPVqdQzf9dfDkSPqJsdeTlEUAgICCAgI4LvvvmPDhg2sX7+ejRs3EhcXR2pqKk5OMpu5KyiKQsSgCCIGRXD/iPv54eQPplF+b5a8yZxNc3C0diR7aDaTQyaTPTQb58GXq+/cfAzqNraG7fVw9BWofUF9ziqkNWiPUIO23l82RHYzRVFwtAJHK4Xgnx1s82OHsP3daSPbjraHbXs9GBQ/Tn3fzCALGf8nLI8EayFE/+DoCEuXwrXXwowZcOgQPPZYnwkxQ4YM4aqrruLgwYPk5+ezefNmNm/ebJqF7eYmK6Ndyd3enVvjbuXWuFs53XialbtXmkb5fbr1U7SKlpG+I02r2QHO48F+vPrOLQ1QX9zaPpIHJz6DY2+qz+k8wSYdN50v1GvBOko2RPYQe72CvZNCYIf/F61rah//9+NpI98c0bPxxxba4ra1Bga19moPbr1cDaCVvu1+S4K1EKL/MBhg/ny47TZ44gk4fBj+/W91BnYf4ebmxpQpU0yzsEtKSigvLyckJIT09HS8vLzMXWKfY6u3NQXoFmMLm77bpLaMbF/IzGUzmblsJhFuEaa3GT5kOBrbVLBNhYH3grEFzlSpq9mtq9o+1vNg73OtGyJT29tHDMNBYzD3p9xv2OgUfB0UfFtnbRcf3kF0TByHWsf//VinBu+Kwy00tm6S1Crg2tq3PahDK4n0bfcPEqyFEP2LTgdvvgkDB8Jzz6ltIe++C1Z9a3qDk5MT48ePZ+TIkWzatIlNmzbx1ltv4evrS3p6OoGBgfIj7G6gUTQkeyWT7JXMv0b9i11HdrGoZhELty/k2Q3PMitvFoPtBquj/EImMzpgNLZ6W/XUR+tIcP4LABUlS4gOPNq+qn3qQfUDKFZgSFTbRmxHqKFb62zGz7j/0Z9j/F+L0UhtA6aV7R/rjOw4bqTiyNl9222r2m1zt+2lb7vPkWAthOh/FAWefRZcXeHee6G2Vp0Y0gc3/Nna2pKZmUlqaqppFvaHH37I4MGDSU9Pp6Wl5cIvIi5aoEsgdyffzd3Jd1NbV0vOzhwWbl/I/Kr5vFX6FgadgTEBY9RRfsETcbd3B6DR6A5OE8CpdaNt82E4na8G7bo8OPICHHkGUFqPYk/v0KctJ3T2NI2iMNAAAw0K4R02SZ5sbA3bbce2nzZS3aFv207XGrY7rGw7y0mSvZoEayFE/3XPPerK9Z//rI7kW7y4Vx2B/lv82ixsW1tbFEUhJiZGZmF3M2cbZ6ZHTWd61HTONJ9h3TfrTC0ji2oWAZA0JIkpIVMIbA4kzhjXHrC0A8FhknoBtJyG+qLW9pH1cPx9OPqa+pzOt3XqSGv7iFUYKH2n3am3UBQFBytwsFIY2qFvu75j33Zr4O54bHvbSZKDOgRuOdym91CMRqPxwm9muRoaGqisrCQyMtIs81uLi4uJj4/v8Y8rzk/ui+Wx6HvyxRfqpsbgYFixQj0SvY8zGo1s376dZcuWcfToUezs7EhOTiYhIQGDQXp4e5LRaGTLT1tMIbvo+yIAApwDmBys9mWn+6Sj1+rP8yJN0FChto3UrVcDd/OP6nMaF7BNa58+YoiTg2suUnd9H2tqMXKovr2V5KfW3u0zHQ63cTXQvkmydcOkQfq2gZ799+VCuVOWJ4QQYupUdWLIlCkwYgSsXAm+vuauqlspikJoaCgnT57E1dWVvLw8Vq1aRV5eHgkJCSQlJeHg4GDuMvsFRVGIHhxN9OBoHhr5EN+f+J5XVrxCeX05r21+jZcKX2KAYQCXBl3K5ODJjB86HifDz8YoKjo1MBvigBlgNELjrvagXZcHJxe1vq0N2CS1t48YUkAr99qcdBoFd1twt1VgoPqYsUPf9k+tgXvPcSOVHfq2B1hhCtltgdteJ60k5iTBWgghAEaNUlerL720PVwHB5u7qm6nKAp+fn74+flx4MAB8vPzyc/Pp6CggJiYGFJTU3Hpo+0xlsrTwZOpvlN5Kv4pTp05xYrdK1i4fSGLaxbz0ZaP0Gl0ZPplMjl4MpNCJuE3wO+XL6IoYDVUvQbcpD7W9GNr0G4N24f/1XpwjQasY1pXtVsvvUyPMTdFUXAxgItBIazD/tSO87bbWkq2d+jbtm3t2+7YSuJsrfaBi+4nwVoIIdqkpEBurnr8+YgRatCOjjZ3VT3Gw8ODadOmkZWVRX5+PmVlZZSUlBAeHk5aWhoeHh7mLrHfsbOy47LQy7gs9DKaW5op/K7Q1DIy4+sZzPh6BtGDo00tI/Ge8Wh+rZ9aNxgcp6kXQPMJqC9oX9U++hbUzml9W5+zg7bM07YY55q33dDcHrJ/ag3dRQeNtLTmbb0G3AxtLSRqS4mbQcFKWkm6nARrIYToKCYG1q+H0aMhIwO+/hqSksxdVY9ycXFh4sSJZGZmUlBQwObNm9m6dSuBgYGkp6fj6+srP2o2A61GS6p3KqneqTw9+ml2HN5hGuX3r7x/8c/1/8TD3oNJwZOYHDKZS/wvwUZvc54XdAC7MeoFYGyE+nKo26Bep9fC8Y/V5zQOYEhuD9uGJGkfsSDWWgVvewVv+/bHmjv2bbeublfVtlB6qP1t2kYADupwOeilleT3kGAthBA/FxLSHq5HjYJFiyAry9xV9Th7e3tGjx5Neno6mzdvpqCggPfee48hQ4aQnp5OSEiI/ANsRkEDg/hbyt/4W8rfOHz6sGmU30eVH/FGyRvY6m0ZEzCGicETuTToUjwdPM//gooebBLUi7+29ml/0x606zbAoccBI2r7yDA1ZLeFbRnzZ1G0GoXBtmoPdhuj0cjxRkw92z/V/XIEoI2Ws4L2IDlN8jeRYC2EEOfi56eG6zFjIDtbnXM9caK5qzILg8FAeno6SUlJlJeXk5+fz6effoqrqytpaWlERUWh1UqbgDkNtB3I9dHXc3309TQ0NbD2m7WmlpEF2xcAEOsey4SgCUwInkCiZyJazQXumaKAlZ96meZpH4O6gvagfewdODpXfU7nfXbQto6W9hELoygKTlbgZKUQ9LNWkoMdVrZ/qoPSQy00tebtjlNJTKMAbRRsdBK2f06CtRBC/BoPD1i7FsaPh8svhw8+gKuvNndVZqPX60lISCAuLo6qqio2bNjAggULyM3NJSUlhbi4OKz62AmWvZG1zpqxgWMZGziWOdlzqPypkiU7lrBkxxJTy4irrSvZQ7OZGDyRsYFjGWAY0LkX1zqB/Tj1gtYxf+Vwum1Vez2c+ER9TmOvto+0hW1DsrSPWChrrYKXvYJXh1aSFqORIw3q6vZPravbe382lcRB3z4CcJAccANYYLCuqqriqquuorKy0tylCCGEeoDMqlXqavW118LJk3Drreauyqw0Gg2RkZFERESwa9cuNmzYwLJly1i3bh3Dhw9n+PDh2NraXviFRLdTFIWowVFEDY7ivvT7OFJ3hGU7l7F4x2KW7FjC+xXvo1W0pPukm1azw1zDOh+MFB0Y4tWrbcxf07cdgvYGOPwEHJb2kd5Go6gtIK4dTpMEONXYPme7bcPk7uNG2uK2XtNxZbv/bZS0qGBdV1fHk08+SWNjo7lLEUKIdo6O6ibGadPgj3+EEyfg7rvNXZXZKYrC0KFDGTp0KPv372fDhg2sXbuW/Px84uLiSE5OZsCATq6Eih7hYuPCtVHXcm3UtTS3NFOwv8C0mn3Pynu4Z+U9+A3wY2LQRCYETyDTLxOD7jccGKQooPcFJ19wmq4+1ny8dfpIZ9pHotSwLiyWnV7BX6/g79j+WMcDbn76lY2SLta/bCWx74MbJS3qq/fpp5/mxhtvpKSkxNylCCHE2WxtYcECmD4dZs6E48fh4YfVICHw8vLi6quv5uDBg+Tn51NUVMSmTZuIiIggNTVVRvVZIK1GS5pPGmk+afxr1L/Yd2wfS3csZfGOxbxV+hZzi+Ziq7dllP8o02q2l+NFzLfWOoLdWPWCDqdEtq1q50n7SC931gE3rYxGI8fOcNbq9oU2Sg62VRho3bs3SlpMsF61ahX19fWMHz/e3KUIIcS5WVnBJ5+oq9aPPqqG6+eek3DdgZubG1OmTCEzM5PCwkKKi4uprKwkICCA1NRUAgIC+twKVV/h7eTNbQm3cVvCbdQ11rFm7xrTavaimkWwBKIHRzMhaAITgyeSNCTpwhsgz+WsUyLvUh9r/LZ1xF9ea/vIkx0Or4kGmxSwSVV/1QfI37leQFEUBljDAGuF4A4/uGqbud3eSnL+jZJt/du9ZaOkYjQajRd+s66Tk5PDrFmzznosICCAkydP8u6772Jvb09ISAjbt2/v1Ou1ndkuhBA9pqUF79mzGTRvHgcvv5xv77sPZCrGOTU2NvLNN9+wZ88eGhoacHR0JCAgAE9PTzSaXznIRFgUo9HInpN7yPspj7wf8yivLafZ2IyT3onUQamkDUojxS0FJyunC79YJ2k4iZ22EntNOfbacuw0W9EqpwBoNLpwqjmKky3RnGqO5lRLGEZ+Q7uKsDgtwGmsOYENJxUDJ7DhBAbOKHrT21gbz+BAPQ7UYW+sx5E6bDljtpojIyOxtrb+xeM9HqzPZf78+bz++uvY2dkBUF1dTWhoKB9++CH29vbnfd+2YP1rn2B3Ky4uJj4+vsc/rjg/uS+Wp8/dE6MRHnoI/vUvdVPje++BXn/h97MwPXVfmpub2bJlC/n5+Rw8eBBHR0eSk5OJi4szy/duS2fJf19q62pZvms5S3YsIWdnDodOH0KjaEj1TlVbRoImEDkosmt/MmFshoatULcR6vLVXxt3tD6pA0Ns+4q2TWq3bYq05PvSF7VtlOzYu324Xp2krgB/DtfhbK306H25UO60iFaQK6+8kiuvvNL055CQEBYsWGDGioQQ4gIUBZ56St3YeN99cOoUfPopGGTl7Fy0Wi0xMTEMGzaMnTt3kp+fz/Lly1m7di0JCQkkJSXh4CC9tL2Bs40zV0dezdWRV9Pc0kzR90UsqVFbRu5fdT/3r7qfIQ5DGD90PNlDsxkdMBonw+9czVa0YIhWL+fb1MeaDqoztes3wul8OPoG1L6sPqcbcnb7iHUsaOR/4Hqb822UPN1kxMkCp3taRLAWQohe6957wcEB7rhDHcn31VdwgZ+09WeKohAUFERQUBDff/89+fn55Ofns3HjRqKjo0lJSWHQoEHmLlN0klajJdkrmWSvZJ685Em+O/4dX+/8mpydOcyvms9bpW+h0+hI804je2g22UHZRA2K6prVbJ0bOExSL1CPZG+oOHtV+8Rn6nOKtToS0LSqnQI62VDbG7VtlFTXrC2PRQbrzvZXCyGERbj9djVM33wzjBsHS5aAjJm7IE9PT6644gpqa2vZuHEjpaWllJWVERQURGpqKr6+vrLRsZcZ4jiEW+Nu5da4W2lsbmTj/o3k7MghZ2cO9626j/tW3df1q9ltFH37TG3nO9XHmg6cHbRr/w1HZqvP6f3Obh+xjpZRf+J3k68gIYToCjfcAHZ2ar91VhYsXw5ubuauqldwdnbm0ksvJTMz0zSm77333sPT05PU1FTCwsJko2MvpNfqGek7kpG+I5k1ehbfn/jetJr9WdVnptXsVO9UdTV7aDbRg6O79n+mdB7gMFW9AFoaoKG0PWifXgPHP1KfU2zBZnh70DYkg86162oR/YIEayGE6CrTpsHCherx5yNHwsqVMGSIuavqNWxtbcnIyCA1NZXy8nI2btzIZ599xoABA0hJSSEmJkaOTO/FPB08uSX2Fm6JvYXG5kYK9heQs1NdzW7rzfZ08GR84Hiyg9TV7E4ftd5ZGmuwSVYvaD0pcl970K7Lh8PPAU3q81bBYEgB21T1V5q7th7R50iwFkKIrjR+PCxbpvZbjxihhuuAAHNX1avo9XoSEhKIi4tj+/bt5Ofnk5OTw5o1a4iPj2f48OGy0bGX02v1jPAdwQjfEfxr1L84cOKAaTX7822f83bZ22gVbftqdlA2wwYP6/rWIEUBvY96OV6jPtZyGuo3twftU0vh+HsAxNjawbcd2kdskkArbV+inQRrIYToaiNHwqpVasgeMQJWrIDwcHNX1etoNBrCwsIICwvj22+/paCggLy8PPLz84mMjCQ5OVlOdOwjPBw8uDn2Zm6OvZmmliZ1Nbu1N/uB1Q/wwOoH8LD3MPVmjwkc0/Wr2W00tmA7Ur1AXdVu3AV1Gzny7QLcmnfC4X+iTl8GrMLaV8ENyWAdoU4xEf2SBGshhOgOiYmwdi2MHg0ZGeoqdlycuavqtXx8fPDx8eHIkSMUFhZSVlZGRUUFfn5+JCcnExwcLBsd+widRke6TzrpPuk8NeopDpw4wLJdy8jZmcOX1V/yTtk7aBUtKd4ppt7sYe7D0Cjd1IevKGA1FKyG8u2ZcNz846H5BNRvUsf91RXAyUVw7B317TX2YEhsD9o2SaAb3D21CYsjwVoIIbpLZCSsX6+G66wsWLoU0tLMXVWv5uLiQnZ2NllZWZSUlFBYWMgnn3yCi4sLycnJDBs2TPqw+xgPBw9uirmJm2Ju+sVq9oOrH+TB1Q8yyG4QYwPHMi5wHGMCxjDYvpuDrNYB7EapF7Suau9uD9r1BWf3auv9OwTtZDDEgCJfp32RBGshhOhOQUHt4XrsWFiwQP29+F0MBgOpqakkJSWxbds2Nm7cyNKlS1m9ejUJCQkkJibi6Oh44RcSvcrPV7N/OPkDy3YuY/nu5Xy982s+qPgAgBj3GMYFjmNc4DjSfNKw0nZziFUUsApUL6fr1Mda6qC+pD1on14Pxz9ufXtrMMS1B22bZNB5q68jejUJ1kII0d18fNRwPWYMTJgA8+bBlCnmrqpP0Gq1REZGEhERwb59+ygoKGDDhg3Sh91PuNu7c2PMjdwYcyMtxhZKD5SybNcylu1axvMbn+eZDc9gp7cjyz+LsQFjGTd0HEEuQT3TNqSxAds09WrTuB/qCtWgXVcAR1+D2hfV53QeZwdtQzxo7Lq/TtGlJFgLIURPGDwY1qyB7Gx1LN///gfTp5u7qj5DURRTH3ZtbS2FhYWUlpZSUVGBr68vKSkp0ofdx2kUDfGe8cR7xvPAiAc43nCc3D25LN+1nGW7lrG4ZjEAfgP8TKvZl/hf0nUH1HSG3ku9HKepfzadFlnQoV/7y9Y31qqH1th0CNv6IFnVtnASrIUQoqe4uKjj9yZPhuuvh5Mn4c9/NndVfY6zszPjx48nMzPzF33YSUlJMg+7n3C0dmRK6BSmhKo/Hdp1ZJdpNfvDLR/yevHraBX1SPZxgeMYN3Qc8R7xaDU9ONHjrNMi71AfazoE9YXtQfv4B+rKNoDGRd0MaVrVHi7j/ixMp4J1U1MTOp1kcCGE+N0cHNRNjFdcAbfdBidOwN//bu6q+qS2Puzk5GSqqqooKCggJyeH3NxcYmNjGT58OAPk6Pl+I9AlkNtdbuf2xNtNx60v26kG7UfWPMIjax7BxcaF0QGjTSvaQxzNcMCTzhXsJ6gXgLEZzlSfvTHy0NeAUX1exv1ZlE6l5aysLKZOncpVV13FEDlFTAghfh8bG/jyS3XV+v/+Tw3Xjz4qP+LtJhqNxtSHvX//fgoKCkxXSEgISUlJ+Pr6SptIP9LxuPWnRj3FwVMHWbF7haltZN7WeQBEuEWYVrNH+IwwT7GKVg3L1hEw4Fb1sebjUF90/nF/hiT1iHZDEug9zVN7P9SpYD1v3jzmz5/P9ddfT3BwMNdeey0ZGRnyTUgIIS6WlRV8/DHY28Pjj8Px4/D88xKuu5GiKHh7e+Pt7c2xY8fYvHkzxcXFVFdXM2jQIJKSkoiKikKv15u7VNHD3OzcmB41nelR0zEajWz5aYtpNXtu0VxeKHgBg85AjHMMV565krGBY4lwizBfDtI6Xnjc35HngUb1ed2Q1qCdpLaP2CSoAVx0OcVoNBo7+8YtLS2sXr2aWbNmYTQamT59OjfccINZe9UaGhqorKwkMjISa2vrHv/4xcXFxMfH9/jHFecn98XyyD35FS0tMHMm/Pvf8Mc/wn/+A9qe+zFuf78vjY2NVFZWUlhYyI8//oiNjQ1xcXEkJibi5NSDm9p+pr/fF0tyuvE0a/euZdmuZSzYuoC9J/cC6kSS0QGjGRMwhtEBo/F0sLBV4ZZ6aChrnUKySf21cVfrkxqwDj87bFtHgNI723578u/LhXJnp/8L7tq1i/nz57N48WJiYmKYOnUq69ev569//SuvvfZalxYthBD9hkYDL72k9l4/9RScOgXvvQeyatoj9Ho9sbGxxMTE8O2331JYWEh+fj75+fmEhYUxfPhwfHx85Ce0/Zit3pbsoGyyg7L5g9sfcBvqxopdK1i5Z+VZs7PD3cIZEzCGMQFjGOk7EgdrB/MWrjG09163aTrU2kLSGrZPfAnH3lKfU2zVTZQ2Se1tJDJb+zfrVLC+9tpr2bdvH1dccQWfffYZ7u7uAGRmZpKcnHyB9xZCCHFeigL//Kcaru+7T50WMm8eGAzmrqzfUBQFX19ffH19OXr0KEVFRZSUlFBVVYW7uzvDhw8nKipKNvILfJx8uDXuVm6Nu5UWYwvlP5SzcvdKVuxewevFr/Ny4cvoNDpSvFJMq9mJQxLRaSzga0fnCvbZ6gUdWkgKWyeRbILaOWCcrT6vdW/v07YZrvZua833k5zeoFN3efr06YwfP/6svrNjx47h5OREbm5ulxTy5Zdf8vzzzzNw4EBADe0zZ87sktcWQohe4d571XB9xx0wcSJ89ZXagy161IABAxgzZgyZmZlUVFSwadMmFi5cyMqVK01tInKqowB1dnasRyyxHrH8I+0f1DfVs+HbDazYvYKVu1fy6JpHeWTNIzhZO5Hln8Vo/9GMCRzTc4fUXMhZJ0a2ztU3noH6itag3bqyfXJh2zuAVWhrn3Zr2LaOVscGCqCTwfrtt99m0qRJZz123XXXsXjxYuzsuuZUoMrKSu677z4mTpzYJa8nhBC90u23q2H65pvVI9CXLgUZCWcWer2e+Ph44uLi2Lt3L4WFheTl5bFhwwbCw8MZPnw43t7elhGQhEUw6AyMChjFqAB1U+Gh04dYvWe1aUX7q+qvAHXVuy1kj/IfhZudmznLPptipW5utElon63dXAv1m9uD9qkcOP5e69sbWo9nH97er63377ctJOcN1jfeeCNbtmyhvr6euLg40+MtLS1ERUV1aSFbtmxh7969vP7664SEhPDwww+bdeOIEEKYzQ03qOH6mmsgKwuWLwc3C/qHt59RFAV/f3/8/f2pra01tYls3boVd3d3EhMTiYyMlENnxC+42rpyVcRVXBVxFUajkV21u0wh+4vqL3i77G0AYtxjTP3Z6T7p2OhtzFz5z2idwW6MekFrC8k37Zsi6zfB0dehJHQj1gAAIABJREFU9qXWt3drDdptbSSJoHUxX/096LzB+pVXXuHo0aM88MADzJo1q/2ddDrcuvibvJubG7fccgtxcXG88MILPPHEEzz//PNd+jGEEKLXmDoVFi2Cyy+HkSNhxQrw8jJ3Vf2es7MzY8eONbWJFBUVsWjRIpYvX05MTAyJiYmmlkYhOlIUhaEuQxnqMpT/l/D/aG5ppvhAsWkj5EsFL/Fc/nNYa61J90lXg3bgGGLcY9AoGnOXfzZFASs/9XK8Sn3M2AgNlWqfdlu/9qmlmA6y0Qd1GPeXBNbDQNPz09y623nH7Z08eRJ7e3uOHj16zucv5sSqnJycs0I6QEBAAO+++67pz8eOHWPMmDFs2rTpgq/XNvZECCH6IvuSEobOnEmToyM75s6lwdfX3CWJDoxGI7W1tezdu5cDBw5gNBpxdXXFz8+PQYMGodFYWCASFquuqY6SIyUUHixk06FN7DyxEwAnvROJrokkuiYy3HU4XrZevab9SMNJbDXV2GkrsdOol5XmEAAtRj11LcGcaolQr+YIGow+QO/4O/Nr4/bOG6wvv/xyvvzyS0JDQ3/5jorCtm3buqS4EydO8Pnnn3PTTTcBcPToUbKzs9m4ceMF31fmWItzkftieeSe/A4lJTB+vPr7nBzowv+Ocl+6zsmTJykpKaG4uJjjx4/j6Oho6tG2/42bUOW+WKaevC8/nPyBVbtXmTZCfnfiO0Dtz77E/xJG+Y/iEv9LLG9+9oU07j+7haSuCIyn1Oc0TmBIaG0haZ1Cor/wid+9Zo71l19+CUB1dTVGoxFFUWhubqalpaVLT6aytbXlzTffJDY2lmHDhvHBBx8wZsyYLnt9IYTo1eLiIC8PxoxRe64XLFB/FRbF3t6ekSNHkp6ezvbt29m8eTO5ubmsXbuW8PBwEhMTZbOj6DR3e3eui76O66Kvw2g0UnO4htV7VrNqzyoWbl/Iu2XvAhDqGmoK2Zl+mbjYWHgvs95LvRymqn82NsOZ6tYWkk3qr4efA5rU53We7SHbZrgavLWWu6G7U1NBCgsLeeqpp1i4cCG7d+/mpptuYu7cucTGxnZJEVqtlpdeeonHHnuM+vp6/Pz8ePbZZ7vktYUQok8IDoYNG2DcOHX1+pNP1P5rYXE0Gg1hYWGEhYVx6NAhNm/eTFlZGZWVlQwePJiEhASio6Nls6PoNEVRCHENIcQ1hL8k/sU0P3vVnlWs3rOad8ve5ZWiV1BQiPWIZZT/KEb5jyLdJx07q66Z3tZtFK166qN1BHCz+pjp1MjWsF1fBCe/an8fq2CwGQmDXgCtmQ/i+ZlOBetnnnnG1BcdFBTEG2+8weOPP868efO6rJCEhATTCrkQQohz8PKCdevUGddXXAH//S/ccou5qxLn4erqyvjx47nkkkvYsmULRUVFLFmyhJUrVzJs2DASExNxdXU1d5mil+k4P/v/Uv+PM81nKPquiFV7VrFqzyrTRki9Rk+yV7JpRTvJKwkrbS/4H7pznRppGvnXGrQbSqHleO8M1o2NjURERJj+HBERwZkzZ7qtKCGEEL9i4EBYuRKmTYNbb4VDh+Cee8xdlbgAKysrU7/1/v37KSoqori4mE2bNuHv709CQgIhISFotVpzlyp6ISutFWk+aaT5pPFIxiOcbjxN3rd5rNq9itV7V/P42sd5bO1j2OptGeEzQl3RDhjFsMHD0Gp6ydfcz0f+WahOBWsbGxvWrVvHyJEjAdi4cSO2trbdWpgQQohfYWcHCxeq867vvRcOHoRnn+23BzL0Joqi4O3tjbe3N+PGjTNtdpw/fz52dnbExsaedW6EEBfDVm/L2MCxjA0cC0BtXS1rv1nLqt3qivY9K9X/GXc2OJPln8UlfpcwKmAUIQNDZA/A79SpYP3ggw9yxx13oNOpb67RaJgzZ063FiaEEOI8rKzgww/VFezZs+HwYXjjDdB16tu6sAB2dnaMGDGCtLQ0du3aRXFxMRs2bCAvLw83NzdsbW0JDg6WVWzxuznbOHNZ6GVcFnoZAAdOHGD1ntWmzZBfbPsCAE8Hz7Mmjvg4+Ziz7F6pU9+Bhw0bxpo1a6ipqUGr1eLv7y+bLoQQwty0Wpg7Vz2V8fHH4cgRdVOjwWDuysRvoNFoCAoKIigoiOPHj1NSUkJhYSHz5s3D3t7etIp9MWdHCHEuHg4eZ00c2V272xSyl+1cxgcVHwDgP8CfLL8sMv0yyfLPwstRDqm6kPMG6wULFjBlyhTeeeedsx7Pz88H4Oabb+6+yoQQQlyYosBjj4GrK9x1lzoxZMECcHIyd2XiIjg6OpKZmYmdnR2Ojo6UlJSQl5fH+vXrGTp0KPHx8QQHB8vBM6LLKIpCoEsggS6B/Cn+TxiNRip/qiR3by65e3P5svpL09HrQ12Gtgdtvyw8HDzMXL3lOW+w/uabbwCoqanpkWKEEEJcpDvvBBcXuPFGyMyEr7+GwYPNXZW4SBqNhpCQEEJCQjh27BglJSWUlpby6aef4uDgQGxsLLGxsbKKLbqcoihEDY4ianAUM5Jm0GJsoeLHCnL35LLmmzXM2zqP/5b8F4CQgSGmkJ3pl8lge/mec95gPWPGDABGjRrF6NGjz3ruq6++Ote7CCGEMJfp08HZWZ0YkpYGy5ZBYKC5qxK/k5OTE1lZWWRkZLBjxw6Ki4tZt24d69atIygoiPj4eIKCgmQVW3QLjaIhxj2GGPcYZqbMpLmlmbIfylizdw25e3P5aMtHvF78OgBhrmFk+WWR5Z9Fhm8GbnZuZq6+5503WK9evZqmpiaeffZZjEYjbaefNzU1MWfOHC677LIeKVIIIUQnZWfDqlUwaRKkpMCSJZCYaO6qRBfouIp99OhR0yr2J598YlrFjouLw0nagEQ30mq0xHvGE+8Zz99T/05TSxOlB0pNrSPvlb/Hq5tfBSByUKRpNTvDN4OBtgPNXH33O2+w3rZtGwUFBRw+fJj//e9/7e+k03HTTTd1d21CCCEuRkqKekrj+PFqW8hnn6mBW/QZAwYM4JJLLiEzM5OamhrTKvb69esJDAwkNjZW5mKLHqHT6EgckkjikETuSbuHxuZGig8Um1pH3ip9izmb5qCgED042tQ6MtJ3JM42zuYuv8udN1jfcccd3HHHHXz44Ydcd911PVWTEEKI3yskBPLz4dJL1dXr//4XZMN5n6PRaAgNDSU0NJSjR49SWlpKaWkp8+fPx9bWlujoaOLi4nBz638/khfmodeqpz0meyVz/4j7TadCtrWOvF78Oi8XvoyCQox7jKl1ZITPCJwMvf+nLZ0atzd27FhWrVrFqFGjmD17Nlu2bOH+++8nNDS0u+sTQghxsTw8YO1a9fjzW26B776DBx+Ug2T6qAEDBph6sXft2kVpaSmbNm2ioKAALy8vYmNjiYyMlHG5okd1PBXywZEP0tDUwKbvNplaR14peoUXCl5Ao2iI84gjy0/tz073Se+VQbtTwfr+++8nPT2djRs3sm7dOm666Sb++c9/8sEHH3R3fUIIIX4PR0dYvFg9/vzhh2H/fnX2tRwk02d1nIt96tQpysvLKS0tZdGiRXz99ddERkYSGxuLl5eXnLInepy1zpoRviMY4TuCRzIeob6pnoL9BabWkZcLX+a5/OfQKBpi3WNN/dkjfEcwwGD5U3A69Z316NGj3HTTTTzzzDNMnDiRqVOn8uGHH3Z3bUIIIbqClRX873/g5QVPPw0HDsDHH4OtrbkrE93Mzs6O1NRUUlJS2L9/PyUlJVRWVlJaWoqrqytxcXFER0djZ2dn7lJFP2XQGcj0yyTTLxOAusY6CvYXsPabtazZu4a5m+by/MbnTa0jHYO2i42LeYs/h04F68bGRhobG1m/fj1PP/00dXV1nD59urtrE0II0VUUBWbNgiFDYMYMGD0aFi0yd1WihyiKgre3N97e3owfP56tW7dSWlrK8uXLWblyJSEhIcTGxhIYGChj+4RZ2ehtyPJX+64B6pvqKdxfaArar21+jRcLXsSgM1B1exX+zv5mrvhsnQrWo0aNIiUlhbCwMCIjI5k4cSITJ07s7tqEEEJ0tTvvBE9PdeZ1WhpWzz0H8fHmrkr0IGtra+Li4oiLi+PgwYOUlJRQUVHBtm3bcHR0JCYmhpiYGJyd+97EBtH7GHQGMvwyyPDL4JGMR2hoaqDo+yJ2HtmJp4Onucv7hU4F6xkzZnDVVVcxuPUUr9mzZ8vGRSGE6K2mToWVK2HSJEJvvlk9pTEhwdxVCTNwc3Nj3LhxjB49mu3bt1NaWmo6fMbPz4+YmBjCwsJkw6OwGNY6a9J90kn3STd3KefUqWB95swZtmzZQkFBAQDNzc3k5OQwc+bMLivkp59+4qGHHuKnn37CYDAwe/ZsvLy8uuz1hRBCdJCeDhs20DJmDIwcCR99BHLoV7+l1WoJDw8nPDycY8eOUV5eTllZGV999RVLly4lPDycmJgYfHx8ZMOjEOfRqWA9c+ZM9u3bx8GDBwkPD6e8vJzhw4d3aSH33HMP48aN49prr+Xjjz9m9uzZvPTSS136MYQQQnQQHk71O+8w7OGH1VXs55+Hu++WcXz9nJOTEyNHjmTEiBHs27ePsrIytm7dSllZGc7OzgwbNoxhw4YxYIDlT2gQoqd1Klhv27aN5cuX89hjj3HzzTfT0tLCY4891mVFHDlyhOrqat555x0Apk2bRkpKSpe9vhBCiHNrGjgQcnPhhhvgb3+DXbvgpZdkHJ9AURR8fHzw8fFh/PjxVFdXU1ZWxpo1a1izZo20ighxDp36zjlo0CB0Oh1+fn7U1NSQnZ3NiRMnuqyIffv24enpydNPP83mzZtxc3Pj4Ycf7rLXF0IIcR62tjBvHtx3Hzz3HOzZA598Ag4O5q5MWAgrKyuio6OJjo7m6NGjVFRUSKuIEOegGI1G44Xe6JZbbuHyyy/H2dmZefPmmY46X7ly5W/+gDk5OcyaNeusx3x9fSkqKuK1114jKyuL+fPns3DhQt5///0Lvl5DQwOVlZW/uQ4hhBC/5Pr55/g8+yx1gYHsfPFFGls3rQvxc0ajkdraWvbt28eBAwdoamrC1tYWLy8vvLy8sJU56aIPi4yMxNra+hePdypY79mzh/nz5/OPf/yDmTNnsmHDBmbOnMn06dO7pLhvv/2Wyy+/nOLiYgDq6upITk6mvLz8gu/bFqx/7RPsbsXFxcTLqCqLI/fF8sg9sUznvC/LlsGVV6or1kuWQEyMeYrrx3rb35fGxka2bdtGeXk5u3fvBsDPz49hw4YRHh7eZ1pFett96S968r5cKHd2qhXE39+fe+65B6BbNhT6+Pjg7u7O2rVrycjIIDc3l4iIiC7/OEIIITph3DjYsAEmTFCnh3z6qfp7IX6FXq83tYq0TRUpLy9nwYIFLF26lNDQUKKjowkICJADaESfdt5gPWnSpPO+86IuPLVrzpw5PProozz33HPY29vz9NNPd9lrCyGE+I2ioqCwECZNgsmT4d//hjvuMHdVohf4+VSR8vJyqqqq2LJlC/b29kRGRjJs2DAGDx4s/diizzlvsO7JDYQBAQGd6qkWQgjRQzw8YO1a9ZTGO++EbdvgxRdBrzd3ZaIX6DhVJDs7mx07dlBRUcGmTZsoKCjAzc3NtMrt6Oho7nKF6BLnDdZeXl54ep77uMh169Z1S0FCCCEsiJ0dfPEF3H+/OjGkulqdIOLiYu7KRC+i0+kICwsjLCyM06dPs3XrVioqKli1ahWrVq3C39+f6OhowsLCzLJfSoiuct5Gpzs6/NjvrrvuOuu5F198sXsqEkIIYVm0Wnj2WXj3XVi/HpKS1NVrIS6Cra0tiYmJ3Hrrrdx1111kZGRw9OhRFixYwOzZs/n888/ZsWMHLS0t5i5ViN/svCvWHQeG7Nu371efE0II0Q/ceCMEB8Pll0NysjrrOjvb3FWJXszFxYXMzEwyMjLYv38/FRUVbN26lcrKSuzs7IiMjCQ6OhoPDw/pxxa9wnmDdccv4p9/QcsXuBBC9EMpKbBpE0yZAhMnqu0hM2fKMejid1EUBW9vb7y9vRk/frypH3vz5s0UFhbi6upKdHQ0UVFRcpS6sGidXrEWQgghAPDxgbw8dQX773+Hykp47TWQ3ljRBbRaLaGhoYSGhlJXV0dVVRUVFRWsXr2a1atX4+vrS1RUFOHh4djY2Ji7XCHOct5g3dLSwrFjxzAajTQ3N5t+D9Dc3NwjBQohhLBAdnbqJsYnnoDHH4eaGnWT46BB5q5M9CE2NjbEx8cTHx9PbW0tFRUVbNmyhcWLF7N06VKGDh1KVFQUwcHBfeYQGtG7nTdY19TUkJycbArTSUlJpuekFUQIIfo5jQYeewwiItTV68REWLgQhg0zd2WiD3J2diYjI4ORI0fyww8/sGXLFiorK6mpqUGv1xMaGkpkZCSBgYFotVpzlyv6qfMG6+rq6p6qQwghRG915ZUQGKj2XaemqtNDrrzS3FWJPkpRFDw8PPDw8GDMmDF88803bNmyxXQIjY2NDeHh4URFReHj4yMLgaJHdepIcyGEEOK84uKgqAimTYOrroJ77oGnngKd/DMjuo+iKPj5+eHn58ell17Kzp07qayspLy8nOLiYhwdHYmMjCQqKkpOehQ9Qr7jCSGE6Bru7pCbC3ffrc69LimBjz8GV1dzVyb6Aa1WS0hICCEhIZw5c4bq6moqKyspKCggPz8fNzc3IiMjiYyMxEUOOBLdRIK1EEKIrmNlBa++qvZb/+UvkJCgbmqMizN3ZaIfsbKyMh2Xfvr0aVObSG5uLrm5uQwZMoSoqCgiIiKwt7c3d7miD5FgLYQQouvdfDNERcHUqZCWBq+/DjfcYO6qRD9ka2tLQkICCQkJHDt2jMrKSiorK/n6669ZtmwZ/v7+REREEBYWJuP7xO8mwVoIIUT3SEiA4mK4+mp1asimTfDCC+qqthBm4OTkRFpaGmlpaRw8eNA0WWTRokUsWbKEwMBAIiIiCA0NxVrmsouLIMFaCCFE93Fzg+XL4f77YfZsKC+H+fPVfmwhzMjNzY1LLrmErKwsDhw4QGVlJVu3bmXHjh1otVqCgoKIiIiQGdniN5FgLYQQonvpdOrR5wkJcMstar/155+rx6MLYWaKouDp6Ymnpydjxoxh//79VFZWUlVVRXV1NXq9nuDgYCIiIuRwPHFBEqyFEEL0jKuvhvBwuPxyyMiAF1+E228HGYEmLISiKHh7e+Pt7c24ceP49ttv2bp1K1VVVWzduhWdTsd3331HRESEHEQjzskigvXhw4e55ZZbTH8+ceIEtbW1lJaWmrEqIYQQXS4qSp13/Yc/wJ13wrp18N//gqOjuSsT4iwajcY0Izs7O5s9e/awdu1aampqqKiowGAwEBoaSkREBP7+/hKyBWAhwXrgwIEsWLAAgJaWFm688UZmzpxp5qqEEEJ0C2dn9ejz556DBx+E0lK171qOQhcWSqPREBgYyNGjR4mJiWH37t2mdpGysjJsbW0JCwsjIiICX19fNBqNuUsWZmIRwbqjzz//HBsbGyZNmmTuUoQQQnQXjQbuvVfts77mGkhOhrlz1R5saQ0RFqxtY2NQUBBNTU3s3LmTrVu3UlFRQXFxMfb29oSFhREZGYm3t7ec9tjPWFSwbm5u5j//+Q+vvvqquUsRQgjRE0aOhLIyuO46+OMf1daQV18FOztzVybEBel0OkJDQwkNDaWxsZGamhq2bt1KaWkpRUVFODo6EhYWRnh4uITsfkIxGo3GnvyAOTk5zJo166zHAgICePfdd1mzZg3vv/8+b731Vqdfr6GhgcrKyq4uUwghRE9qbsbjrbfw+O9/qff3Z/czz1Dv72/uqoS4KE1NTfzwww8cOHCAgwcP0tLSgrW1NR4eHnh4eODi4iIhu5eLjIw856zzHg/W5/PQQw8RGxvLtGnTOv0+bcH61z7B7lZcXEx8fHyPf1xxfnJfLI/cE8tkcfdlxQp19frUKXjjDfX3/ZDF3RcBXNx9aWhooKamhqqqKnbu3ElTU5OpXSQ8PBwfHx/pyf6devLvy4Vyp0W1gpSVlfGnP/3J3GUIIYQwlzFj1NaQa66B669XW0NefhkMBnNXJsRFsba2JioqiqioKBoaGtixYwdVVVWmdhE7OztTyJaNj72fRQXrffv24S6ncQkhRP/m6QmrV8NDD8Ezz0BBAXz8sToDW4hezNramsjISCIjIzlz5owpZJeVlbF582bs7OwIDQ0lPDwcPz8/Cdm9kEUF6/LycnOXIIQQwhLodPD00+rmxhtvVE9tfPlldYOj9KaKPsDKyoqIiAgiIiI4c+YMO3fupKqqyjRdxNbW1hSy/f39JWT3EhYVrIUQQoizXHopVFTADTfAn/8My5apB8o4O5u7MiG6jJWVFeHh4YSHh9PY2GgK2Vu2bKGkpAQbG5uzQrYcRmO5JFgLIYSwbB4eaqCePVs9UGbTJvjoI0hPN3dlQnQ5vV5PWFgYYWFhNDY2smvXLtOR6qWlpdjY2BASEkJ4eDgBAQESsi2MBGshhBCWT6OBe+6BzEyYPh0yMuCRR9SgrZN/ykTfpNfrTXOym5qaTCF727ZtlJWVYTAYCAkJITQ0lMDAQPR6vblL7vfku5EQQojeY/hwKCmBO+6Axx6DVavggw/Ax8fclQnRrXQ6HSEhIYSEhNDU1MTu3bupqqpi+/btlJeXo9frCQ4OJjQ0lKCgILOMIBYSrIUQQvQ2jo7w/vswdizcfjsMGwZvvgm/4QwEIXoznU5HcHAwwcHBNDc3s3fvXrZt20Z1dTVbt25Fq9USGBhIWFgYISEh2NjYmLvkfkOCtRBCiN7pD3+AlBS1NeSKK9TNjc8/D/b25q5MiB7TFqIDAwO59NJL2bdvnylk19TUoNFo8PPzIywsjNDQUOzl70e3kmAthBCi9xo6FPLy4OGH4bnn1PnX778PycnmrkyIHqfRaPD19cXX15dx48Zx4MABU0/2kiVLWLJkCT4+PqaQPWDAAHOX3OdIsBZCCNG7WVmpB8lMmKCO5UtLg/vvVzc3WlmZuzohzEJRFDw9PfH09GTUqFEcPHiQbdu2sW3bNpYtW8ayZcvw8PAwnfo4cOBAc5fcJ0iwFkII0TeMHKnOvP7rX+GppyAnR129lhMbRT+nKAqDBg1i0KBBZGRkcOTIEVPIXr16NatXr8bNzc005m/w4MEochDTRZFgLYQQou9wdIR33oHJk9We67g49QTHGTPUkX1CCFxcXEhLSyMtLY1jx45RXV3Ntm3bWL9+PevWrcPZ2dkUsocMGSIh+zeQYC2EEKLvufxydWPjn/4EM2fCokXw7rvg7W3uyoSwKE5OTiQlJZGUlMSpU6eorq6murqagoIC8vPzcXBwIDQ0lLCwMHx9feVo9QuQYC2EEKJvcneHhQvhrbfg7rshKgpeeUWdIiIrcEL8gp2dHfHx8cTHx1NfX09NTQ3btm2jtLSUoqIibGxsTLOy5UCac5NgLYQQou9SFPjjHyErS93YeP31sGCBGrDd3MxdnRAWy2AwEB0dTXR0NGfOnGHXrl1UV1ebDqTR6XQMHTqU0NBQgoODZVZ2KwnWQggh+r7AQFi3Dp59Fh59FNasgVdfVedfCyHOy8rKytRz3dzczDfffGNqGamurkZRFPz8/AgNDSUkJAQnJydzl2w2EqyFEEL0D1qtOoZv4kS4+Wa48kr1mjsXBg0yd3VC9AparZaAgAACAgLIzs7m+++/NwXsnJwccnJy8PT0JCQkhLCwMFxdXfvV5kcJ1kIIIfqXqCgoKFAPlHnsMcjNVVtDrrxSeq+F+A0URWHIkCEMGTKEUaNGcejQIVPIzs3NJTc3FxcXF0JDQwkNDcXLy6vPh2yLCdb79+/n3nvv5eTJkzg6OvL0008zZMgQc5clhBCiL9Lp1NXryZPV1eurr4Z589SAPXiwuasToldydXUlPT2d9PR0jh8/zvbt28+aMGJvb09ISAihoaH4+/uj1WrNXXKXs5hg/fLLLzNhwgSmT5/O+++/z4svvsjs2bPNXZYQQoi+LCIC8vPh+efVkxrXrIE5c+Caa2T1WojfwdHRkcTERBITE00TRrZv305FRQXFxcVYW1sTFBREaGgoQ4cOxdra2twldwmLCdYtLS2cPHkSgLq6OgwGg5krEkII0S/odHDvvTBpkrp6PX26unr92mvqyD4hxO/SccJIY2Mje/bsYdu2bdTU1FBZWWnq226bMGJvb2/uki+axQTrv/71r1xzzTW8//77NDY28umnn5q7JCGEEP1JeDhs2AAvvggPP6yuZr/wgjqmT1avhegSer2e4OBggoODaWlpYd++faa+7B07dgDg4+Nj2vzo7Oxs5op/G8VoNBp78gPm5OQwa9assx4LCAigoaGBW2+9ldGjR7Ns2TLmzp3LwoULL9jk3tDQQGVlZXeWLIQQop+x3rsXvyeewL6iguPDh/PNAw9wxsvL3GUJ0WcZjUZOnDjBgQMH+PHHHzl+/DgADg4OuLu7M3jwYJycnCxm82NkZOQ521d6PFify5EjR8jOzqawsND0WHJyMkuXLsXFxeW879sWrH/tE+xuxcXFxMfH9/jHFecn98XyyD2xTHJfzqOlBV5/XW0TaWpSJ4j87W9q60g3k/timeS+9Jza2lrTSva+ffswGo04OjqaNj/6+vqaNj/25H25UO60iFYQZ2dnrK2t2bx5MwkJCRQXF2NnZ3fBUC2EEEJ0G40G/vIXtff6zjvVgP3xx/DmmyDhSohu5ezsTEpKCikpKZw6dYodO3ZQXV1tOl7d1taW2267DUdHR3OXehaLCNaKojB37lyefPJJ6uvrsbOzY86cOeYuSwghhAAvL/jyS/jiCzVgDx8OM2fC44+DnZ25qxOiz7OzsyMmJoaYmBgaGxvZtWsXP/74o0UOurCIYA0QHR3N/PnzzV2GEEKjuGigAAAYRUlEQVQI8UuKAtOmwahR6sr188/D55+rrSJjx5q7OiH6Db1ebzpwxhJpzF2AEEII0WsMGKCG6bVrwcoKxo2DP/wBDh40d2VCCAsgwVoIIYT4rUaOhPJyeOgh+OQTCAmBN95QNzwKIfotCdZCCCHExTAY4Mkn1YAdHQ233QZpaVBWZu7KhBBmIsFaCCGE+D3CwyE3F957D3btUieGzJwJJ06YuzIhRA+TYC2EEEL8XoqintBYXQ1/+hO8/DKEhsL8+WD+4yKEED1EgrUQQgjRVVxc4D//gY0bYdAguOoqyM6GnTvNXZkQogdIsBZCCCG6WlISFBWpK9f5+RAZCU88AfX15q5MCNGNJFgLIYQQ3UGngxkz1PaQyy6DRx9VA/bixeauTAjRTSRYCyGEEN3J01MdybdiBej16hHpEybAjh3mrkwI0cUkWAshhBA9YfRoqKhQT21cv15dvb7/fjh50tyVCSG6iARrIYQQoqfo9fC3v0FNDVx7LTz9tDo95OOPZXqIEH2ABGshhBCip7m7w7vvqhsb3d1h+nTIzFQPmxFC9FoSrIUQQghzSUmBwkL1OPSqKoiLgzvvRHvsmLkrE0JcBAnWQgghhDlpteqhMjU1cPvt8NprRE6dCq+/Ds3N5q5OCPEbSLAWQgghLIGzM8yZA6Wl1AUGwv/7f5CQAGvWmLsyIUQnSbAWQgghLEl0NDWvv66O6DtyBLKyYOpUOb1RiF7AYoJ1RUUF06ZNY9KkSdx2220cPHjQ3CUJIYQQ5qEocPXV6uEyTz2lzsAOD4f/+z84etTc1QkhfoVFBGuj0ciMGTP4xz/+waJFi5gyZQoPP/ywucsSQgghzMvGBh54QO2//sMf4IUXICgIXn0VmprMXZ0Q4mcsIljX1tZSX19PcnIyAFlZWeTl5XHmzBkzVyaEEEJYAI//3969B1dd3nkcf+cmyEWhu1y6OhLCXZCKQQVvSKtIDGkApeBlg1CBuogFK3KRAcQictkVhbXYCkEuWljkUsQoFRetiMwScJEVAWMREEVuMwSEEODsH781bRaBqMn5nSTv10xmOM/vJOeb+c4zfPjx/J7nxzBzJuTmBgfLDBwIP/kJvP562JVJ+jsxEaxr165NtWrVePfddwFYsWIFhYWFHDp0KOTKJEmKIW3awFtvwZIlcOIEpKUFXx99FHZlkoC4SCS6Rz3l5OQwYcKEYmMpKSk88sgjTJw4kfz8fDIzM5kxYwY5OTn86Ec/OufPKygoYPPmzWVZsiRJMSeusJA6Cxbw4xdeIOHYMfZ1786eAQM4VatW2KVJFV6rVq2oUqXKGeNRD9Zn8/HHH9O8eXMADhw4QOfOnVm3bh3x8ee+qf5NsD7bL1jWcnNzSU1Njfrn6tzsS+yxJ7HJvsSm79SX/fth7FiYMQNq1IARI+Chh4L12SpVzpfYFM2+nC93xsRSEICRI0eyadMmALKzs+ncufN5Q7UkSZXeP/4jTJ8OmzbBjTfC8OHQrBnMmQOnT4ddnVSpxExyHTt2LGPGjKFz587s2rWLYcOGhV2SJEnlx+WXw/Ll8J//CfXqQe/ewRHpf/5z2JVJlUZi2AV8o3Xr1ixZsiTsMiRJKt9uvhnWrYOFC4Ot+jp1Cr4mTQp2EpFUZmLmjrUkSSol8fHQqxds2QJPPw3r1wc7ivTuDTt3hl2dVGEZrCVJqqiqVIHBgyEvD4YOhQULoGlTGDbMExylMmCwliSpoqtVCyZODE5w7NkTJk+GRo1g6lQoKAi7OqnCMFhLklRZXHYZvPgibNgAqakwZEhwB3v2bDh1KuzqpHLPYC1JUmVz5ZWwcmXwVacO9OkDrVvD0qUQG8dbSOWSwVqSpMrq1lvhv/4LFi0K7lh36wbt2wdb9kn6zgzWkiRVZnFxcMcdsHkzzJwJn38OP/0p3HYb5OaGXZ1UrhisJUkSJCZC376wfTv8678GobptW/jFL2Dr1rCrk8oFg7UkSfqbqlXh4Yfh009h9Gh47TVo2RL694fdu8OuToppBmtJknSmiy6Cxx8PAvaDDwa7iTRuHOyHfeBA2NVJMclgLUmSzq5u3WC/623b4K674N/+DVJSYNw4OHw47OqkmGKwliRJ59egAWRnw4cfws9+BmPGQMOGwcEzR4+GXZ0UEwzWkiSp5C6/HBYvhvXroV07GD48uIP99NNw7FjY1UmhMlhLkqTvLjUVVqyA996DK64IHnhs3Biee85j0lVpGawlSdL31749vPlmcKhMSgoMHBgckz5zJhQWhl2dFFUGa0mS9MPdfDO88w688QbUrw/33w8tWsDcucGpjlIlEFqwnjp1KtOmTSt6ffjwYfr3709aWhr33HMP+/btC6s0SZL0fcTFQadO8P778Kc/Qc2akJUFrVrBwoVw+nTYFUplKurBOj8/n5EjR5KdnV1sfOrUqbRt25acnBx69OjB+PHjo12aJEkqDXFxkJERnN64aBHEx0PPntCmDSxdCpFI2BVKZSLqwXrVqlUkJyfTp0+fYuOrV68mIyMDgC5duvDOO+9Q6NosSZLKr/h4uOMO2LQJ5s+Hr7+Gbt3g6quDEx0N2Kpgoh6su3btSv/+/UlISCg2/tVXX1GnTh0AEhMTqVGjBgcPHox2eZIkqbQlJMDdd8OWLTBrVnByY3o6XHutAVsVSmJZ/eCcnBwmTJhQbCwlJYXZs2eX6PsjkQjx8SXP/Zs3b/4u5ZWq3Nzc0D5bZ2dfYo89iU32JTZV2L60bk3cyy/zoxUr+PGsWVRJT+fo5Zezp39/Dl9/fbCMJIZV2L6Uc7HSlzIL1mlpaaSlpZX4/XXr1mX//v3Ur1+fkydPcvToUWrVqlXi72/VqhVVqlT5PqX+ILm5uaSmpkb9c3Vu9iX22JPYZF9iU6XoS7t2MHo0zJlD9d/+liaDB0PbtsGJjunpMRmwK0VfyqFo9qWgoOCcN3NjZru9Dh06sHTpUgBee+012rZtS1JSUshVSZKkMpOUBL/8JWzbFux7feBA8NDj1VfD8uUuEVG5EzPB+te//jUffPAB6enpvPTSS4wePTrskiRJUjQkJUHfvrB1a7AG+9Ah+PnPgzvYf/qTAVvlRpktBTmfQYMGFXtdq1YtZsyYEVI1kiQpdElJ0KcP3HtvsIvIb38LmZnBNn1jxgRhOwaXiEjfiJk71pIkSUAQsO+7Dz7+GGbPhvx86NoVrrrKfbAV0wzWkiQpNiUmQu/ewTZ9L74IR48G+2C3aQNLlniSo2KOwVqSJMW2xMTgaPSPPoK5c+HYMejePQjYr7xiwFbMMFhLkqTyITExWH/90Ucwbx4cPw533gmtW8PLL8OpU2FXqErOYC1JksqXhAS4554gYL/8cjB2993QogVkZ0NhYbj1qdIyWEuSpPIpIQF69YJNm2DxYqhZM9i2r0kT+N3vgjvaUhQZrCVJUvkWHx881Lh+Pbz2GvzTP8G//AukpMDTTwcPPUpRYLCWJEkVQ1wcpKXBmjWwahU0bw4PPwwNG8JTT8Hhw2FXqArOYC1JkiqWuDj46U/hrbfg3XeDExxHjIAGDWDsWDh4MOwKVUEZrCVJUsV1/fXB8pD16+Hmm+Hxx4OAPXw4fPVV2NWpgjFYS5Kkii81NThUZtMm6NIFJk2C5GQYPBg+/zzs6lRBGKwlSVLlccUVwRZ9W7ZAz54wfXrwkOMDD8COHWFXp3LOYC1JkiqfZs2CPa+3b4c+fWDWLGjcOPjz1q1hV6dyymAtSZIqr4YNYcYMyMuDBx+EP/4xOGimRw/YsCHs6lTOGKwlSZIuvRSmToXPPgsebFy5MliX3bkzvP02RCJhV6hywGAtSZL0jbp14cknYedOmDABNm4MdhO5/nou/stfDNg6p1CD9dSpU5k2bVqxsTVr1tC7d++QKpIkSQIuvji4c71jR/CA4549NB4yBH7yk+Dhx5Mnw65QMSiUYJ2fn8/IkSPJzs4uGjt9+jSzZs3i4Ycf5vTp02GUJUmSVNyFF8LAgbB9O38dOzYI1HffHTz8+PzzcPx42BUqhoQSrFetWkVycjJ9+vQpGsvLyyMvL48nnngijJIkSZLOLimJg126wObNwX7Y//AP8KtfBVv1TZkC+flhV6gYEEqw7tq1K/379ychIaForEmTJowfP56LL744jJIkSZLOLz4eunaFdevgzTeDHUSGDg1OcxwzBg4cCLtChSguEim7Vfg5OTlMmDCh2FhKSgqzZ88GKFpfPWjQoKLr69atY/r06cydO7dEn1FQUMDmzZtLp2BJkqTvqNrmzdSfPZvaq1dzqmpV9nfrxt5776WwXr2wS1MZadWqFVWqVDljPLEsPzQtLY20tLSy/IgiZ/sFy1pubi6pqalR/1ydm32JPfYkNtmX2GRfYtNZ+5KaCr17w//8DwkTJ1LvpZeot2gRZGXBsGHQpEn0i61EojlfzndD1+32JEmSSkPLljBnDnzyCfTrB/PmQfPmwdHpH3wQdnWKAoO1JElSaUpOhn//9+CwmUcfhZwcaNMGbr8d/vKXsKtTGQo1WA8aNKjY+mqAa6+9tsTrqyVJkmJWvXrBITM7d8L48bB+Pdx0E9xwAyxfDm4vXOF4x1qSJKks1aoFI0cGh808+yzs2gU//zm0bh0sHSksDLtClRKDtSRJUjRUqwaDBgVrsOfODbbu690bGjWCqVPhyJGwK9QPZLCWJEmKpqQkuPde+O//hhUroGFDGDIELrsMRo+GffvCrlDfk8FakiQpDHFxwQONb78Na9dChw7wxBPBYTMPPgh//WvYFeo7MlhLkiSFrV274Kj0jz6Cu+6C3/8+2P/67ruDO9sqFwzWkiRJsaJFC5g5M7hbPXhwsHvIlVdCWhqsXg1ld2C2SoHBWpIkKdZccglMmfK3rfo2bICOHYM724sXu1VfjDJYS5Ikxaratf+2Vd/vfgcHDsAddwR3tl94AQoKwq5Qf8dgLUmSFOsuvBB+9SvYuhUWLIAaNYJj0xs2hMmT4fDhsCsUBmtJkqTyIyEBfvGL4BTHP/8ZLr88ODb9sstgxAj48suwK6zUDNaSJEnlTVwc3HILvPlmELI7dYJJkyA5GQYMgO3bw66wUjJYS5IklWepqbBwYbBM5L774MUXoVkz6NEjCN2KGoO1JElSRdC4McyYETzoOHx4sFTk6qvhZz+DN95wq74oMFhLkiRVJPXrw5NPBlv1TZ4MH38MnTtDmzYwbx4UFoZdYYVlsJYkSaqILroIHnkkOGwmOzsI1P/8z9CoETz9NOTnh11hhWOwliRJqsguuCBYe/3hh/Dqq5CSAg8/HOwkMnKkO4mUotCC9dSpU5k2bVrR67y8PO655x4yMzPp2bMnW7ZsCas0SZKkiic+HtLTg6PR160LdhWZOBEaNID77w+WjOgHiXqwzs/PZ+TIkWRnZxcbHzVqFP369WPZsmUMHjyYYcOGRbs0SZKkyuGaa+A//iPYSeSXv4T584PTHDMzYc2asKsrt6IerFetWkVycjJ9+vQpNt6jRw9uvPFGAJo1a8YXX3wR7dIkSZIql8aN4bnnggcdx4wJQvUNN8B118GSJXDqVNgVliuJ0f7Arl27AhRbBgLQvXv3oj8/++yz3HLLLSX6eZH/2zrmxIkTpVThd1dQUBDaZ+vs7EvssSexyb7EJvsSmypsXy66KDi5cfBgWLQIXngBBg4MdhXp1w+6d4eqVcOu8qyi1Zdv8mbkLFsXxkXOduUHysnJYcKECcXGUlJSmD17NvC3YD1o0KCi65FIhEmTJvH+++8zZ84catased7Pyc/PZ9u2baVXuCRJknQOTZs2/dacWmZ3rNPS0khLSyvx+0+ePMmwYcPYu3dviUM1QPXq1WnatClJSUnExcV933IlSZKkc4pEIhQWFlK9evVvvR71pSBnM3HiRI4cOcKsWbO44IILSvx98fHxJQ7hkiRJ0g9R9RxLYmIiWB88eJD58+dz6aWX0qNHj6LxZcuWhViVJEmSVHJltsZakiRJqkw8eVGSJEkqBQZrSZIkqRQYrCVJkqRSYLCWJEmSSoHBWpIkSSoFBusSWr58ObfffjudOnVi/vz5Z1yfPn06HTt2JDMzk8zMzG99j0rfkSNH6NKlC7t37z7j2pYtW+jevTu33XYbjz32GCdPngyhwsrpXH1xroRj+vTppKenk56ezqRJk8647nwJx/n64nwJxzPPPMPtt99Oeno62dnZZ1x3vkTf+XoSM3MlovP68ssvIx07dowcOnQocvTo0UhGRkZk+/btxd4zYMCAyIYNG0KqsHL64IMPIl26dIm0bNkysmvXrjOup6enRzZu3BiJRCKRESNGRObPnx/tEiul8/XFuRJ9a9asifTs2TNSUFAQOXHiRCQrKyuycuXKYu9xvkRfSfrifIm+devWRXr16hUpLCyMHDt2LNKxY8dIXl5esfc4X6KrJD2JlbniHesSeO+992jXrh21atWiWrVq3Hbbbbz++uvF3rN582aef/55MjIyGDduHAUFBSFVW3ksXLiQMWPGULdu3TOuff755xw/fpwrr7wSgO7du5/RM5WNc/UFnCthqFOnDsOHD+eCCy4gKSmJRo0asWfPnqLrzpdwnK8v4HwJwzXXXMOcOXNITEzkwIEDnDp1imrVqhVdd75E3/l6ArEzVwzWJfDVV19Rp06dotd169Zl7969Ra+PHj1KixYtGDp0KEuWLOHw4cM899xzYZRaqYwfP562bdt+67X/37M6deoU65nKzrn64lwJR5MmTYpCwI4dO8jJyaFDhw5F150v4ThfX5wv4UlKSuLZZ58lPT2d9u3bU69evaJrzpdwnKsnsTRXDNYlcPr0aeLi4opeRyKRYq+rV6/OH/7wBxo1akRiYiJ9+/bl7bffDqNU/Z/z9UzhcK6Ea/v27fTt25dHH32U5OTkonHnS7jO1hfnS7geeugh1q5dyxdffMHChQuLxp0v4TlbT2JprhisS6B+/frs27ev6PW+ffuK/Tf3nj17WLRoUdHrSCRCYmJiVGtUcf+/Z/v37z/r0gRFj3MlPLm5udx333385je/oVu3bsWuOV/Cc66+OF/CkZeXx5YtWwC48MIL6dSpE1u3bi267nyJvvP1JJbmisG6BK677jrWrl3LwYMHOXbsGCtXruSmm24qul61alUmT57Mrl27iEQizJ8/n1tvvTXEinXJJZdQpUoVcnNzAVi2bFmxnikczpVwfPHFFwwcOJApU6aQnp5+xnXnSzjO1xfnSzh2797NqFGjOHHiBCdOnGDVqlWkpqYWXXe+RN/5ehJLc8V/+pZAvXr1GDJkCFlZWRQWFnLnnXfSunVr+vXrx0MPPcQVV1zBuHHjeOCBBygsLOSqq66iT58+YZddKf19T6ZMmcKoUaM4cuQILVu2JCsrK+zyKi3nSrhmzpxJQUEBTz31VNFYr169eOutt5wvISpJX5wv0dehQwc2bdpE165dSUhIoFOnTqSnp/v3S4hK0pNYmStxkUgkEsonS5IkSRWIS0EkSZKkUmCwliRJkkqBwVqSJEkqBQZrSZIkqRQYrCVJkqRS4HZ7klQB7N69m1tvvZWmTZsWjUUiEbKysrjzzjuLvXfVqlWsXbuWUaNGRbtMSarQ3G5PkiqA3bt3k5GRwcaNG4vG9u7dS5cuXZg7dy7NmzcPsTpJqhy8Yy1JFVS9evVo0KABa9asYdy4cRw7dowaNWrQrVs33njjDZ5//nn27dvHmDFj+PTTT4mPj6dXr15kZWWRn5/P+PHj2bZtG4WFhbRv355HH33UI7Ul6RxcYy1JFdTGjRvZuXMnx48f55NPPmHu3LnMnTu32Hsef/xxkpOTef3111mwYAELFy7ks88+48knn6Rly5YsXryYpUuXcujQIbKzs0P6TSSpfPDWgyRVEMePHyczMxOAU6dOUbt2bSZPnsyBAwdo1qwZNWrUOON73nvvPYYOHQpAzZo1efXVVwFYvXo1H374IYsWLSr62ZKkczNYS1IFUbVqVZYtW3bG+OLFi6lWrdq3fk9iYiJxcXFFr3ft2kXt2rU5ffo0zzzzDI0aNQLg8OHDxd4nSTqTS0EkqRJr3749r7zyCgD5+fn07t2bHTt2cMMNNzB79mwikQgnTpzggQceYN68eSFXK0mxzWAtSZXY6NGj+fTTT8nIyOCuu+5iwIABtGrViscee4yvv/6ajIwMMjIyaNq0Kffff3/Y5UpSTHO7PUmSJKkUeMdakiRJKgUGa0mSJKkUGKwlSZKkUmCwliRJkkqBwVqSJEkqBQZrSZIkqRQYrCVJkqRSYLCWJEmSSsH/AvqdqY97JRX9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "sns.lineplot(x='Price', y='Elasticity', data=df_elasticities, label=f'average (inelastic at {inelasticty_end:.2f})', color='grey', ax=ax)\n",
    "for segment, segment_label in segment_labels.items():\n",
    "    df_data = calc_elasticities_for_segment(df_purchases, segment=segment)\n",
    "    cross_point = calc_elasticity_cross_point(df_data)\n",
    "    # annotation = f'{segment_label}: {cross_point:.2f}'\n",
    "    # ax.annotate(annotation, xy=(cross_point, -1.0), xytext=(1.6,-0.2-(segment*0.15)))\n",
    "    plot_label = f'{segment_label} (inelastic at {cross_point:.2f})'\n",
    "    sns.lineplot(x='Price', y='Elasticity', data=df_data, color=segment_colours[segment], label=plot_label, ax=ax)\n",
    "ax.set_yticks(np.arange(0, -15, -1))\n",
    "ax.set_ylim([-12, 1])\n",
    "arrow_props = dict(arrowstyle= '->',color='blue',lw=1, ls='-')\n",
    "ax.annotate(f'Average: inelastic \\nprice point at {inelasticty_end:.2f}', xy=(inelasticty_end, -1.0), xytext=(0.6,-1.5), arrowprops=arrow_props, va='center')\n",
    "ax.set_title('Price Elasticity of Purchase Probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Showing all elasticity curves at the same time allows us to compare them:\n",
    "- Standard segment becomes inelastic at price point 1.39. Notice it is 14 cents higher than the average price point. Suppose we want to target the Standard-segment. We could increase the price if the price of a product is between 0.5 to 1.39 and consider decreasing prices after 1.39.\n",
    "\n",
    "- Fewer-Opportunities segment is more price sensitive compared to the average because its curve is both lower and much steeper than the other curves. For example, notice the large difference between the curves for Fewer-Opportunities and Well-Off segments. The steeper curve suggests that we increase the price, consumers become more elastic much faster. The tipping point between elasticity and inelasticity is 1.27. It appears that this segment is more inelastic in the lower than 1.27 price points. This is also evident from the graph where the red line a bit higher than the other curves. There are two factors that may explain this:\n",
    "  1. The first reason is technical in nature. The Fewer-Opportunities segment contains the largest number of consumers. The abundance of data may result in a more sophisticated/better model.\n",
    "  2. The second reason is related to purchasing behaviour. The consumers enjoy chocolate bars so much that a price increase in the lower price range does not affect them and would not stop them from buying the products. However, once it starts to become expensive then they consider it as a luxury product and avoid buying the product. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Purchase Probability with Promotion Feature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In any purchase analytics model, price is the most prominent feature. However, there are other factors such as promotion which effect customers' decision whether to buy a product. There are three types of promotions:\n",
    "- **Price Reduction**: simply reduce the price of the product. It could be complex discounts conditioned on buying more units e.g. buy 2 and get 1 for free (get 33% discount).\n",
    "- **Display**: product is situated in another selling location which is different from the usual place where consumers can pick it up. For example, placing a new car at a shopping mall is a promotion without a price reduction.\n",
    "- **Feature**: promotions that happen when specific opportunities for product purchase are being distributed and presented to customers. For example, printed ads and newspaper inserts are feature promotions. Subtle feature promotions include using the same car brand in large movie productions like James Bond."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To consider the overall effect of promotion activities on price elasticity, we will look at two cases:\n",
    "1. Promotional activities for all brands at all price points\n",
    "2. No promotional activities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_purchases['Avg_Promotion'] = (\n",
    "    df_purchases['Promotion_1'] + df_purchases['Promotion_2'] +\n",
    "    df_purchases['Promotion_3'] + df_purchases['Promotion_4'] +\n",
    "    df_purchases['Promotion_5']) / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(df_purchases[['Avg_Price', 'Avg_Promotion']])\n",
    "y = np.array(df_purchases['Incidence'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.49408026,  0.56158995]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LogisticRegression(solver='sag')\n",
    "lr.fit(X, y)\n",
    "lr.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients are -1.49 for price and 0.56 for promotion. The promotion coefficient is positive which indicates that if we increase the promotion, the purchase probability will increase. In broad terms, this is what we would expected. But the model quantifies the exact relationship between price, promotion and probability of purchase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_elasticities_with_promo = calc_elasticities_with_promotion(df_purchases, promotion=1, segment=None)\n",
    "promo_cross_point = calc_elasticity_cross_point(df_elasticities_with_promo)\n",
    "promo_label = f'With promotion (elastic after {promo_cross_point:.2f})'\n",
    "\n",
    "df_elasticities_with_no_promo = calc_elasticities_with_promotion(df_purchases, promotion=0, segment=None)\n",
    "no_promo_cross_point = calc_elasticity_cross_point(df_elasticities_with_no_promo)\n",
    "no_promo_label = f'Without promotion (elastic after {no_promo_cross_point:.2f})'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "sns.lineplot(x='Price', y='Elasticity', data=df_elasticities_with_no_promo, label=no_promo_label, ax=ax)\n",
    "sns.lineplot(x='Price', y='Elasticity', data=df_elasticities_with_promo, label=promo_label, ax=ax)\n",
    "ax.set_title('Price Elasticity of Purchase Probability with and without Promotion');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that the elasticity curve with promotion sits above its no promotion counterpart for the entire price range. \n",
    "Without promotion, the price becomes elastic after the 1.27 price point, whereas with promotion it is 1.46.\n",
    "The different is 19 cents. \n",
    "For example, if a product's regular price is 1.30, the purchase probability is elastic.\n",
    "On the other hand, if a product costs 1.50 without promotion and is reduced to 1.30 during a promotion, \n",
    "then our analysis says that the purchase probability is still inelastic at 1.30. \n",
    "This sounds trivial. People are willing to buy products at promotional prices for several reasons.\n",
    "Perhaps, psychologically people feel they are getting a bargain or it is due to the large discount signs in the stores.\n",
    "In any case, customers are less price sensitive to similar price changes when there are promotional activities.\n",
    "In other words, it pays off to offer discounts.\n",
    "\n",
    "According to this model, it would be beneficial to have a higher original price and a constant promotion rather than a lower original price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}