{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Linear Regression"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Environment setup"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Python version: 3.7.5\n",
"NumPy version: 1.18.1\n"
]
}
],
"source": [
"import platform\n",
"\n",
"print(f\"Python version: {platform.python_version()}\")\n",
"assert platform.python_version_tuple() >= (\"3\", \"6\")\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import plotly\n",
"import plotly.graph_objs as go\n",
"import pandas as pd\n",
"\n",
"print(f\"NumPy version: {np.__version__}\")"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Setup plots\n",
"%matplotlib inline\n",
"plt.rcParams[\"figure.figsize\"] = 10, 8\n",
"%config InlineBackend.figure_format = \"retina\"\n",
"sns.set()\n",
"\n",
"# Configure Plotly to be rendered inline in the notebook.\n",
"plotly.offline.init_notebook_mode()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"scikit-learn version: 0.22.1\n"
]
}
],
"source": [
"import sklearn\n",
"\n",
"print(f\"scikit-learn version: {sklearn.__version__}\")\n",
"assert sklearn.__version__ >= \"0.20\"\n",
"\n",
"from sklearn.model_selection import train_test_split\n",
"from sklearn.linear_model import LinearRegression, SGDRegressor, Ridge\n",
"from sklearn.metrics import mean_squared_error\n",
"from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
"from sklearn.pipeline import Pipeline"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Linear regression in a nutshell\n",
"\n",
"A linear regression model searches for a linear relationship between inputs (features) and output (target).\n",
"\n",
"[![Linear Regression example](images/linear_regression.png)](https://en.wikipedia.org/wiki/Linear_regression)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Problem formulation\n",
"\n",
"A linear model makes a prediction by computing a weighted sum of the input features, plus a constant term called *bias* (or sometimes *intercept*).\n",
"\n",
"$$y' = \\theta_0 + \\theta_1x_1 + \\dotsc + \\theta_nx_n$$\n",
"\n",
"- $y'$ is the model's output (prediction).\n",
"- $n$ is the number of features for a data sample.\n",
"- $x_i, i \\in [1..n]$ is the value of the $i$th feature.\n",
"- $\\theta_i, i \\in [0..n]$ is $i$th model parameter. $\\theta_0$ is the bias term.\n",
"\n",
"The goal is to find the best set of parameters."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Example: using a linear model to predict country happiness\n",
"\n",
"(Inspired by [Homemade Machine Learning](https://github.com/trekhleb/homemade-machine-learning) by Oleksii Trekhleb)\n",
"\n",
"The [World Happiness Report](https://www.kaggle.com/unsdsn/world-happiness#2017.csv) ranks 155 countries by their happiness levels. Several economic and social indicators (GDP, degree of freedom, level of corruption...) are recorded for each country.\n",
"\n",
"Can a linear model accurately predict country happiness based on these indicators ?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Data loading and analysis"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Dataset shape: (155, 12)\n"
]
}
],
"source": [
"# Load World Happiness Report for 2017\n",
"dataset_url = \"https://raw.githubusercontent.com/bpesquet/mlhandbook/master/_datasets/world-happiness-report-2017.csv\"\n",
"df_happiness = pd.read_csv(dataset_url)\n",
"\n",
"# Print dataset shape (rows and columns)\n",
"print(f\"Dataset shape: {df_happiness.shape}\")"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"RangeIndex: 155 entries, 0 to 154\n",
"Data columns (total 12 columns):\n",
" # Column Non-Null Count Dtype \n",
"--- ------ -------------- ----- \n",
" 0 Country 155 non-null object \n",
" 1 Happiness.Rank 155 non-null int64 \n",
" 2 Happiness.Score 155 non-null float64\n",
" 3 Whisker.high 155 non-null float64\n",
" 4 Whisker.low 155 non-null float64\n",
" 5 Economy..GDP.per.Capita. 155 non-null float64\n",
" 6 Family 155 non-null float64\n",
" 7 Health..Life.Expectancy. 155 non-null float64\n",
" 8 Freedom 155 non-null float64\n",
" 9 Generosity 155 non-null float64\n",
" 10 Trust..Government.Corruption. 155 non-null float64\n",
" 11 Dystopia.Residual 155 non-null float64\n",
"dtypes: float64(10), int64(1), object(1)\n",
"memory usage: 14.7+ KB\n"
]
}
],
"source": [
"# Print a concise summary of the dataset\n",
"df_happiness.info()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Country | \n",
" Happiness.Rank | \n",
" Happiness.Score | \n",
" Whisker.high | \n",
" Whisker.low | \n",
" Economy..GDP.per.Capita. | \n",
" Family | \n",
" Health..Life.Expectancy. | \n",
" Freedom | \n",
" Generosity | \n",
" Trust..Government.Corruption. | \n",
" Dystopia.Residual | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" Norway | \n",
" 1 | \n",
" 7.537 | \n",
" 7.594445 | \n",
" 7.479556 | \n",
" 1.616463 | \n",
" 1.533524 | \n",
" 0.796667 | \n",
" 0.635423 | \n",
" 0.362012 | \n",
" 0.315964 | \n",
" 2.277027 | \n",
"
\n",
" \n",
" 1 | \n",
" Denmark | \n",
" 2 | \n",
" 7.522 | \n",
" 7.581728 | \n",
" 7.462272 | \n",
" 1.482383 | \n",
" 1.551122 | \n",
" 0.792566 | \n",
" 0.626007 | \n",
" 0.355280 | \n",
" 0.400770 | \n",
" 2.313707 | \n",
"
\n",
" \n",
" 2 | \n",
" Iceland | \n",
" 3 | \n",
" 7.504 | \n",
" 7.622030 | \n",
" 7.385970 | \n",
" 1.480633 | \n",
" 1.610574 | \n",
" 0.833552 | \n",
" 0.627163 | \n",
" 0.475540 | \n",
" 0.153527 | \n",
" 2.322715 | \n",
"
\n",
" \n",
" 3 | \n",
" Switzerland | \n",
" 4 | \n",
" 7.494 | \n",
" 7.561772 | \n",
" 7.426227 | \n",
" 1.564980 | \n",
" 1.516912 | \n",
" 0.858131 | \n",
" 0.620071 | \n",
" 0.290549 | \n",
" 0.367007 | \n",
" 2.276716 | \n",
"
\n",
" \n",
" 4 | \n",
" Finland | \n",
" 5 | \n",
" 7.469 | \n",
" 7.527542 | \n",
" 7.410458 | \n",
" 1.443572 | \n",
" 1.540247 | \n",
" 0.809158 | \n",
" 0.617951 | \n",
" 0.245483 | \n",
" 0.382612 | \n",
" 2.430182 | \n",
"
\n",
" \n",
" 5 | \n",
" Netherlands | \n",
" 6 | \n",
" 7.377 | \n",
" 7.427426 | \n",
" 7.326574 | \n",
" 1.503945 | \n",
" 1.428939 | \n",
" 0.810696 | \n",
" 0.585384 | \n",
" 0.470490 | \n",
" 0.282662 | \n",
" 2.294804 | \n",
"
\n",
" \n",
" 6 | \n",
" Canada | \n",
" 7 | \n",
" 7.316 | \n",
" 7.384403 | \n",
" 7.247597 | \n",
" 1.479204 | \n",
" 1.481349 | \n",
" 0.834558 | \n",
" 0.611101 | \n",
" 0.435540 | \n",
" 0.287372 | \n",
" 2.187264 | \n",
"
\n",
" \n",
" 7 | \n",
" New Zealand | \n",
" 8 | \n",
" 7.314 | \n",
" 7.379510 | \n",
" 7.248490 | \n",
" 1.405706 | \n",
" 1.548195 | \n",
" 0.816760 | \n",
" 0.614062 | \n",
" 0.500005 | \n",
" 0.382817 | \n",
" 2.046456 | \n",
"
\n",
" \n",
" 8 | \n",
" Sweden | \n",
" 9 | \n",
" 7.284 | \n",
" 7.344095 | \n",
" 7.223905 | \n",
" 1.494387 | \n",
" 1.478162 | \n",
" 0.830875 | \n",
" 0.612924 | \n",
" 0.385399 | \n",
" 0.384399 | \n",
" 2.097538 | \n",
"
\n",
" \n",
" 9 | \n",
" Australia | \n",
" 10 | \n",
" 7.284 | \n",
" 7.356651 | \n",
" 7.211349 | \n",
" 1.484415 | \n",
" 1.510042 | \n",
" 0.843887 | \n",
" 0.601607 | \n",
" 0.477699 | \n",
" 0.301184 | \n",
" 2.065211 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Country Happiness.Rank Happiness.Score Whisker.high Whisker.low \\\n",
"0 Norway 1 7.537 7.594445 7.479556 \n",
"1 Denmark 2 7.522 7.581728 7.462272 \n",
"2 Iceland 3 7.504 7.622030 7.385970 \n",
"3 Switzerland 4 7.494 7.561772 7.426227 \n",
"4 Finland 5 7.469 7.527542 7.410458 \n",
"5 Netherlands 6 7.377 7.427426 7.326574 \n",
"6 Canada 7 7.316 7.384403 7.247597 \n",
"7 New Zealand 8 7.314 7.379510 7.248490 \n",
"8 Sweden 9 7.284 7.344095 7.223905 \n",
"9 Australia 10 7.284 7.356651 7.211349 \n",
"\n",
" Economy..GDP.per.Capita. Family Health..Life.Expectancy. Freedom \\\n",
"0 1.616463 1.533524 0.796667 0.635423 \n",
"1 1.482383 1.551122 0.792566 0.626007 \n",
"2 1.480633 1.610574 0.833552 0.627163 \n",
"3 1.564980 1.516912 0.858131 0.620071 \n",
"4 1.443572 1.540247 0.809158 0.617951 \n",
"5 1.503945 1.428939 0.810696 0.585384 \n",
"6 1.479204 1.481349 0.834558 0.611101 \n",
"7 1.405706 1.548195 0.816760 0.614062 \n",
"8 1.494387 1.478162 0.830875 0.612924 \n",
"9 1.484415 1.510042 0.843887 0.601607 \n",
"\n",
" Generosity Trust..Government.Corruption. Dystopia.Residual \n",
"0 0.362012 0.315964 2.277027 \n",
"1 0.355280 0.400770 2.313707 \n",
"2 0.475540 0.153527 2.322715 \n",
"3 0.290549 0.367007 2.276716 \n",
"4 0.245483 0.382612 2.430182 \n",
"5 0.470490 0.282662 2.294804 \n",
"6 0.435540 0.287372 2.187264 \n",
"7 0.500005 0.382817 2.046456 \n",
"8 0.385399 0.384399 2.097538 \n",
"9 0.477699 0.301184 2.065211 "
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Show the 10 first samples\n",
"df_happiness.head(n=10)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {
"image/png": {
"height": 701,
"width": 928
}
},
"output_type": "display_data"
}
],
"source": [
"# Plot histograms for all numerical attributes\n",
"df_happiness.hist(bins=20, figsize=(16, 12))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Univariate regression\n",
"\n",
"Only one feature is used by the model, which has two parameters.\n",
"\n",
"$$y' = \\theta_0 + \\theta_1x$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Example: predict country happiness using only GDP"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"def filter_dataset(df_data, input_features, target_feature):\n",
" \"\"\"Return a dataset containing only the selected input and output features\"\"\"\n",
" \n",
" feature_list = input_features + [target_feature]\n",
" return df_data[feature_list]"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"# Define GDP as sole input feature\n",
"input_features_uni = [\"Economy..GDP.per.Capita.\"]\n",
"# Define country happiness as target\n",
"target_feature = \"Happiness.Score\"\n",
"\n",
"df_happiness_uni = filter_dataset(df_happiness, input_features_uni, target_feature)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Economy..GDP.per.Capita. | \n",
" Happiness.Score | \n",
"
\n",
" \n",
" \n",
" \n",
" 89 | \n",
" 0.982409 | \n",
" 5.182 | \n",
"
\n",
" \n",
" 146 | \n",
" 0.397249 | \n",
" 3.591 | \n",
"
\n",
" \n",
" 121 | \n",
" 0.792221 | \n",
" 4.315 | \n",
"
\n",
" \n",
" 67 | \n",
" 1.101803 | \n",
" 5.525 | \n",
"
\n",
" \n",
" 97 | \n",
" 0.596220 | \n",
" 5.004 | \n",
"
\n",
" \n",
" 123 | \n",
" 0.808964 | \n",
" 4.291 | \n",
"
\n",
" \n",
" 32 | \n",
" 1.433627 | \n",
" 6.422 | \n",
"
\n",
" \n",
" 93 | \n",
" 0.788548 | \n",
" 5.074 | \n",
"
\n",
" \n",
" 26 | \n",
" 1.343280 | \n",
" 6.527 | \n",
"
\n",
" \n",
" 78 | \n",
" 1.081166 | \n",
" 5.273 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" Economy..GDP.per.Capita. Happiness.Score\n",
"89 0.982409 5.182\n",
"146 0.397249 3.591\n",
"121 0.792221 4.315\n",
"67 1.101803 5.525\n",
"97 0.596220 5.004\n",
"123 0.808964 4.291\n",
"32 1.433627 6.422\n",
"93 0.788548 5.074\n",
"26 1.343280 6.527\n",
"78 1.081166 5.273"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Show 10 random samples\n",
"df_happiness_uni.sample(n=10)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Data splitting"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"def split_dataset(df_data, input_features, target_feature):\n",
" \"\"\"Split dataset between training and test sets, keeping only selected features\"\"\"\n",
" \n",
" df_train, df_test = train_test_split(df_data, test_size=0.2)\n",
"\n",
" print(f\"Training dataset: {df_train.shape}\")\n",
" print(f\"Test dataset: {df_test.shape}\")\n",
"\n",
" x_train = df_train[input_features].to_numpy()\n",
" y_train = df_train[target_feature].to_numpy()\n",
"\n",
" x_test = df_test[input_features].to_numpy()\n",
" y_test = df_test[target_feature].to_numpy()\n",
"\n",
" print(f\"Training data: {x_train.shape}, labels: {y_train.shape}\")\n",
" print(f\"Test data: {x_test.shape}, labels: {y_test.shape}\")\n",
"\n",
" return x_train, y_train, x_test, y_test"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Training dataset: (124, 2)\n",
"Test dataset: (31, 2)\n",
"Training data: (124, 1), labels: (124,)\n",
"Test data: (31, 1), labels: (31,)\n"
]
}
],
"source": [
"x_train_uni, y_train_uni, x_test_uni, y_test_uni = split_dataset(\n",
" df_happiness_uni, input_features_uni, target_feature\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Data plotting"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"slideshow": {
"slide_type": "skip"
},
"tags": [
"hide-input"
]
},
"outputs": [],
"source": [
"def plot_univariate(x, y, input_features, target_features, model_list=None):\n",
" \"\"\"2D plot of features and target, including model prediction if defined\"\"\"\n",
"\n",
" plt.scatter(x, y, label=\"Actual\")\n",
"\n",
" if model_list is not None:\n",
" predictions_count = 100\n",
" x_pred = np.linspace(x.min(), x.max(), predictions_count).reshape(\n",
" predictions_count, 1\n",
" )\n",
" for model_name, model in model_list.items():\n",
" y_pred = model.predict(x_pred)\n",
" plt.plot(x_pred, y_pred, \"r\", label=model_name)\n",
"\n",
" plt.xlabel(input_features)\n",
" plt.ylabel(target_feature)\n",
" plt.title(\"Countries Happiness\")\n",
" plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
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eOza4Z/az/dAXt1sqLXcSbgEGFDfh1qZNm/Tee+9p3Lhxuv7668P+vOHDE5SZmRL25wxErNeH6GJ+wBfmCPrD/IAvzBH0h/kxOAxNGBrUuGOtHUHNkXXv1OrJ5RV+b4P0prquWUc73coex2KJWMbfIfiiuOm5VVRUJEn6zne+o2HDhkW3GAAAAAAY5EaYg1tLEcy4yhrXgIOt7nvtdA38JgAiKi5Wbn388cd66623lJKSohtuuCEiz2xv79ChQ8ci8qxAeVJsl+tIlCtBLGJ+wBfmCPrD/IAvzBH0h/kxuEwYnRTUuLwzMgOeI8+tdYQk2JKkAwc/Y47GKP4OiW+pqSM0fHhwMVVcrNxau3atJGn27NlKSgruL1AAAAAAQOhkZSYrx5IW0JjJE0cHvCUwmMb1/TEnxsUaEGBQiYtw6/XXX5ckXXXVVVGuBAAAAADgUZhvlb/nHpokfX2WLeBnBNu4vi/27PSQ3g9A+Bk+3Pr0009VU1OjlJQUTZ8+PdrlAAAAAAA+x9/dgsHuKmxt6whyZG82S5qyMpNDdj8AkWH4cKuyslKSNGXKFCUksHwUAAAAAGJFSbkzoOtfeKM64GeEahuhySQV5FtDci8AkWX4cOvDDz+UJJ155plRrgQAAAAA4BFML6wPdx1U7d7DAY0JxTZCk0maNydXdmvGgO8FIPIMH27t2bNHkmSxWKJcCQAAAADAI9heWJU7XQFdH0zj+s+zWdJ0141n6eK88UHfA0B0GX4fX2NjoyRp3LhxUa4EAAAAAOARbC+sY62BjyvMt2pRcYXcfjbuyp88ThPGpcienU6PLSAOGD7ceu6556JdAgAAAADgC4LthTXCHPg4uzVDc+fkamlZVb8Bl2f7Iau0gPhi+HALAAAAABB7gu2FlXdGZlDjZuSN15hUs0rLnar20uvLZklTQb6VvlpAHCLcAgAAAAAErN7VIkdtk1rbOmROTOi1xc/TCyuQpvKTJ45W9rhRcrmOBFWT3ZohuzXDZ20A4gvhFgAAAADAbw5no0rKnV5DqxxLmgo/tzoqkF5YJpP09Vm2kNSYlZlMmAUMIoY/LREAAAAAEBmbKxu0qLiiz9VYNXXNWlRcoS2VDZL+0wvLZOr/vp5eWHk5wW1JBDC4sXILAAAAAOCTw9nos2G7JLndUlFZlUanmmW3ZtALC0DYEW4BAAAAAHwqKXf6tb1QOhFwlZY7uwMremEBCCfCLQAAAABAv+pdLQE1hpek6rpm1btaejWZJ8yCP7wFoZmZKdEuCzGKcAsAAAAA0C9HbVPQ4wizEIj+DiyYdNpofWO2TePTzVGoDLGMhvIAAAAAgH61tnVEdBwGJ18HFuzYfVD3PvNW94EFgAfhFgAAAACgX+bE4Db9BDsOg0+gBxY4nI2RKQyGQLgFAAAAAOiXPTs9ouMw+ARzYAHgQbgFAAAAAOhXVmaycixpAY2xWdLotwW/DOTAAkAi3AIAAAAA+KEw3yqTyb9rTSapIN8a1noQPwZyYAEgEW4BAAAAAPxgt2Zo7pxcnwGXySTNm5MruzUjMoXB8DiwAANFdz8AAAAAgF9m5I3XmFSzSsudqvayjcxmSVNBvpVgCwHhwAIMFDMBAAAAAOA3uzVDdmuG6l0tctQ2qbWtQ+bEBNmz0+mxhaBwYAEGinALAAAAABCwrMxkwiyEhOfAgkCaynNgAT6PnlsAAAAAACCqOLAAA0G4BQAAAAAAoooDCzAQbEsEAAAAAABR5+vAgskTR+vrs2wan26OQnWIZYRbAAAAAAAgJvR3YMFZ9pMlSS7XkShXiVhDuAUAAAAAAGIKBxYgEPTcAgAAAAAAgGERbgEAAAAAAMCwCLcAAAAAAABgWIRbAAAAAAAAMCzCLQAAAAAAABgW4RYAAAAAAAAMi3ALAAAAAAAAhkW4BQAAAAAAAMMi3AIAAAAAAIBhEW4BAAAAAADAsBKiXQAAAAAAIPrqXS1y1Dapta1D5sQE2bPTlZWZHO2yAMAnwi0AAAAAGMQczkaVlDtVU9fc670cS5oK862yWzOiUBkA+IdtiQAAAAAwSG2ubNCi4gqvwZYk1dQ1a1FxhbZUNkS4MgDwH+EWAAAAAAxCDmejlpZVye3u/zq3Wyoqq5LD2RiZwgAgQIRbAAAAADAIlZQ7fQZbHm63VFruDGs9ABAswi0AAAAAGGTqXS19bkXsS3Vds+pdLWGqCACCR7gFAAAAAIOMo7YpouMAIJwItwAAAABgkGlt64joOAAIJ8ItAAAAABhkzIkJER0HAOFEuAUAAAAAg4w9Oz2i4wAgnIjdAQAAAERM7d7DKn9vj1rbOmROTJA9O11ZmcnRLmvQycpMVo4lLaCm8jZLGt8rADGJcAsAAABA2DmcjXr1xUrt2H2w13s5ljQV5ltlt2ZEobLBqzDfqkXFFXK7fV9rMkkF+daw1wQAwWBbIgAAAICw2lzZoEXFFV6DLUmqqWvWouIKbalsiHBlg5vdmqG5c3JlMvV/nckkzZuTS/gIIGaxcgsAAAAIQL2rRY7aJrbV+cnhbNTSsiqfq4PcbqmorEqjU82EKBE0I2+8xqSaVVruVLWXLYo2S5oKWFUHIMYRbgEAAAB+cDgbVVLu9NqjiG11fSspd/q17U06EXCVljv5HCPMbs2Q3ZpBcAvAsAi3AAAAAB82Vzb0u/rIs61u3pxcXZw3PrLFxbB6V0tADcslqbquWfWuFkKVKMjKTOZzB2BI9NwCAAAA+hHotjqHszEyhRmAo7YpouMAAIMTK7cAAACAfrCtLnitbR0RHRdNbOkDgOgh3AIAAAD6wLa6gTEnBvfrRrDjooFebAAQfcb5rwYAAAAQYQPZVhcL4Va0VxPZs9MjOi7S6MUGALGBcAsAAADog1G31cXKaqKszGTlWNICWv1ms6TFRDDoS6C92EanmlnBBQBhQkN5AAAAoA9G3Fa3ubJBi4or+gyUPKuJtlQ2RKSewnyrTCb/rjWZpIJ8a1jrCZVgerEBAMKDcAsAAADog9G21cXiyY52a4bmzsn1GXCZTNK8ObmGWN00kF5sAIDQY1siAAAA0IdobasLtldWrJ7sOCNvvMakmlW2vU4f7jrY632bJU0FBmq8bvRebAAQbwi3AAAAgH4U5lu1qLjCr9BooNvqBtIrK9ZPdrRbMzTzvGzV7j2s8vf2RK3JfSgYtRcbAMQrwi0AAACgH55tdb62+w10W91AT94zymqi7HGjlHSuJWLPCwcj9mIDgHjG364AAACAD55tdaXlTlV7WR010G11oTh5j9VEkWO0XmwAEO8ItwAAAAA/2K0Zslszgu6H1Z9Q9MpiNVHkRKsXGwDAO/5LBgAAAAQgKzM5pCFFqHplsZoosiLZiw0A0L8h0S4AAAAAGMwG0ivr8zyriQLBaqLgeXqxmUz9XzfQXmwAAN8ItwAAAIAoCmWvrMJ8q8+wxYPVRAM3I2+87rrxLNn6CBVtljTddeNZXg8AAACEDtsSAQAAgCgKZa+sSJ3sONh9se/aNy/PkaSQ92IDAPiHcAsAAACIolD3ygr3yY6DmcPZqJJyp9ceaTmWNBXyuQJAVBBuAQAAAFEUjpP3wnmy42C1ubKh3xVxNXXNWlRcoXlzctmGCAARRrgFAAAARFm4Tt4L9cmOg5XD2ehzq6ckud1SUVmVRqeaWcEFABFEQ3kAAAAgyjh5L7aVlDv9Ch6lEwFXabkzrPUAAHpi5RYAAAAQA+iVFZvqXS0BbRmVpOq6ZtW7Wlg1BwARQrgFAAAAxAh6ZcUeR21T0OP4ngFAZBBuAQAAADGGXlmxo7WtI6LjAACBo+cWAAAAAPTBnBjceoBgxwEAAke4BQAAAAB9sGenR3QcACBwhFsAAAAA0IeszGTlWNICGmOzpLGtFAAiiHALAAAAAPpRmG+VyeTftSaTVJBvDWs9AICeCLcAAAAAoB92a4bmzsn1GXCZTNK8ObmyWzMiUxgAQBKnJQIAAASs3tUiR22TWts6ZE5MkD07nS1IiFv+zPfB8DMxI2+8xqSaVVruVHVdc6/3bZY0FeRbCbYAIAoItwAAAPzkcDaqpNypGi+/2OZY0lTIL7aII/7Md0mD6mfCbs2Q3ZoxKMI8ADASk9vtdke7CCNqb+/QoUPHol2GV5mZKZIkl+tIlCtBLGJ+wBfmCPozmOfH5soGLS2rUn//cvJsSbo4b3zkCosxg3mOxBO/5rskX79IfPFngvkRG2I5nGOOoD/Mj/iWmjpCw4cHtwaLlVsAAAA+OJyNPn/RlyS3Wyoqq9LoVHNcrVbB4OL3fPfjXvxMxBZWnwKIVzSUBwAA8KGk3OnzF30Pt1sqLXeGtR4gnAKZ7/7gZyI2bK5s0KLiCq/BliTV1DVrUXGFtlQ2RLgyABg4wi0AAIB+1Lta+vxlsC/Vdc2qd7WEqSIgfIKZ7/7gZyK6Al196nA2RqYwAAgRwi0AAIB+OGqbIjoOiKZwzlt+JqKH1acA4h3hFgAAQD9a2zoiOg6IpnDOW34mooPVpwAGA8ItAACAfpgTgzt/J9hxQDSFc97yMxEdwa6Y2/hefYgrAYDw4b8wAAAA/bBnp0d0HBBN4Zy3/Ez4p97VIkdtk1rbOmROTJA9O11ZmclB3y/YFXPvf3xQujzoxwJARBFuAQAA9CMrM1k5lrSAtvXYLGkD+mUUiJZg5rs/+JnwzeFsVEm50+tnn2NJU2G+VXZrRsD3DXbF3IHDrap3tfB9A2AIbEsEAADwoTDfKpPJv2tNJqkg3xrWeoBwCmS++4OfCd82VzZoUXFFn6FiTV2zFhVXaEtlQ8D3HsiKOQ4BAGAUhFsAAAA+2K0Zmjsn1+cv/CaTNG9OblCrK4BY4fd89+Ne/Ez45nA2amlZlc/TDN1uqaisSg5nY0D3z8pM1uhR5qBq4xAAAEbBtkQAAAA/zMgbrzGpZpWWO1XtZXWFzZKmgiC3DQGxxt/5LomfiQEqKXf6DLY83O4Tn3egn+mU00dr478CbxDPIQBA7Al1X754wd9WAAAAfrJbM2S3ZvAPSwwK/s53fiaCV+9qCbi/WXVdc8C9sC6dmhVUuMUhAEDsCFdfvnhBuAUAABCgrMxkfnHHoOHPfOdnIjjB9rRy1DYF9HlzMAZgbJsrG/rdvuzpyzdvTq4uzhsf2eJiBD23AAAAENfqXS16/d06lZZ/otffrVO9qyXaJQGSgu9pFcw4DsYAjCncffniBSu3AAAAEJfYwoFYF2xPq2DGeQ4K8PVLMocAALElEn354gHhFgAAAOIOWzhgBMH2tAp2HAdjAMYSqb588YBwCwAAAHEl0C0co1PN/DKPqIhGLywOxgCMI1J9+eIB4RYAAADiCls4YCSF+VYtKq7wa86GshcWhwAAsS+SffmMjobyAAAAiBsD2cIBRIOnF5avZu/0wgIGn0j25TO6wfcVAwAAIG6xhQNGRC8sAN5Eui+fkRFuAQAAIG6whQNGRS8sAF8Ujb58RkW4BQAAgLjBFg4YHb2wAHxetPryGQ09twAAABA32MIBAIgn9OXzD/8XFQAAAOIGWzgAAPGGvny+EW4BAAAgrrCFAwAQb+jL1z/CLQAAAMQVzxaOpWVV/QZcg30LBwDAeOjL5x3hFgAAAOIOWzgAABg8CLcAAAAQl9jCAQDA4EC4BQAAgLjGFg4AAOLbkGgXAAAAAAAAAASLcAsAAAAAAACGRbgFAAAAAAAAwyLcAgAAAAAAgGERbgEAAAAAAMCwCLcAAAAAAABgWIRbAAAAAAAAMCzCLQAAAAAAABgW4RYAAAAAAAAMi3ALAAAAAAAAhkW4BQAAAAAAAMMi3AIAAAAAAIBhEW4BAAAAAADAsAi3AAAAAAAAYFiEWwAAAAAAADAswi0AAAAAAAAYFuEWAAAAAAAADCsh2gUAAAAAQDyqd7XIUduk1rYOmRMTZM9OV1ZmcrTLAoC4Q7gFAAAAACHkcDaqpNypmrrmXu/lWNJUmG+V3ZoRhcoAID6xLREAAAAAQmRzZYMWFVd4DbYkqaauWYuKK7SlsiHClQFA/CLcAgAAAIAQcDgbtbSsSm53/9e53VJRWZUczsbIFAYAcY5wCwAAAABCoKTc6TPY8nC7pdJyZ1jrAYDBgnALAAAAAAao3tXS51bEvlTXNave1RKmigBg8CDcAgAAAIABctQ2RXQc8P+zd+/RUdX3/v9fm0sygUBuBDBxyCCQhCgNKnhpIHrOARupyVesStGqoNZqvRetF/ydVW1Fu2rsxdpaaUusthixVIlYKooK5pyq4EkKxARBJsREIZJwiZLEwPz+oJNKSSZz2XPZs5+PtbpWzew9+x3YTGZeeX/eHwD/QrgFAAAAACHq7OqJ6HkAgH8h3AIAAACAEDkSh0T0PADAvxBuAQAAAECICnLSInoeAOBfCLcAAAAAIETZmcnKdaYGdE6eM1XZmclhqggA7IMeWAAAAADQ0R0P6xrb1dnVI0fiEBXkpAUUPpUVuVReWSOPZ+BjDUMqLXIFXywAoBfhFgAAAABbq3O3aVW1W9ua9h33WK4zVWVFLhW40gd8ngJXuq4qyddTa+p9BlyGIS0oyffrOQEAAyPcAgAAAGBb62tbfIZR25r2qbyyRgtK8jWzMGvA5ysuzNKoFIeqqt1q6CMsy3OmqtTPsAwA4B/CLQAAAACWFuxywjp324BdVpLk8UgVa+qVkeLwu4OrwJUe8jJHAIB/CLcAAAAAWFKoywlXVbv9mo8lHQ24qqrdAXVcZWcmE2YBQAQQbgEAgF50GQCwilCXEza3dvQZivnS0LRPza0dvC4CQIwh3AIAAKYNUwaASDBjOWFdY3tw125sJ9wCgBgzKNoFAACA6Fpf26Lyypp+Oxi83Q8balsiXBkA9C2Y5YT/rrOrJ6hrB3seACB8CLcAALCxQLsfare1RqYwAOhHKMsJv8yRGNwilmDPAwCED+EWAAA2Fmj3w7OvNoS3IAAYQCjLCb+sICctqOcJ9jwAQPgQbgEAYFPBdD9s2bFXjZ8cCFNFADAws5YTZmcmK9eZGtBz5DlTmbcFADGIcAsAAJsKtvuh9gOWJgKIHjOXE5YVywM1EgAAIABJREFUuWQY/p1vGFJpkSuoawMAwotwCwAAmwq2++FQJ8OUAUSPmcsJC1zpuqokf8CAyzCkBSX57BoLADGKaYgAANhUsN0PSQ7ePgCIHu9ywkCWVftaTlhcmKVRKQ5VVbvV0Mdz5jlTVVrkItgCgBjGu1MAAGwq2O6HwkmZJlcCAIEpK3KpvLLGrw0x/FlOWOBKV4ErXc2tHaprbFdnV48ciUNUkJPGjC0AsADCLQAAbCqY7odTJmQoZ+xItbYeDGNlAOCbdznhU2vqfQZcgS4nzM5MJswCAAti5hYAADYW6DDlb87KC29BAOCn4sIsLZo3VXn97HiY50zVonlTNbMwK8KVAQAiLS46t5qbm/X444/rrbfeUltbm9LS0nTuuefqlltuUWYmSycAAOhPoN0Phbn8XAUQO1hOCACQ4iDc2rx5sxYuXKiDBw8qNzdXU6ZM0ZYtW/Tcc8/p73//u55//nmlpKREu0wAAGIWw5QBWB3LCQHA3iwdbnV3d+uOO+7QwYMHdd999+mKK66QJHV1denOO+/U3/72Nz322GO67777olwpAACxje4HAAAAWJWlw62XX35ZbrdbpaWlvcGWJCUmJuqee+7Rpk2btHPnzihWCACAtdD9AAAAAKuxdLj1yiuvSJIWLlx43GMnnHCCqqurI10SAAAAAAAAIsjS4VZdXZ2GDh2q/Px8ffzxx6qqqtKuXbuUmpqq8847T1/5yleiXSIAAOgHSyABmIXXEwCwN8Pj8bU3Uuzq7u7WlClTNHbsWH3/+9/X4sWLdejQoWOOueaaa/T9738/ShUCAIC+1G5r1fK1Ddr64d7jHjv5pAzNn53HrowA/GKX15PGTw6o9oNWHersUZJjiAonZSpn7MholwUAMcOy4VZbW5vOPvtsJSUlqaenRyUlJbrxxhuVkZGht956S/fff7/27dunBx54QPPmzYt2uQAAQNIrbzfqlytq5Ovdh2FIN18yVbPPzIlcYQAsxw6vJ3YJ7wAgVJYNtz7++GOde+65kqQZM2bod7/73TGPv/HGG/rOd76jMWPG6M0335RhGKZev7u7R/v3Hxr4wCjIzBwhSWptPRjlShCLuD8wEO4R+BLK/VHnblN5pe8Pol6GIS2aN1UFrvSAr2NF8bSkitcQ+GLW/WGH15P1tS16ak39gOHdgpJ8zSzMilxhYcZrCHzh/ohvKSlJSkgIbnqWZWduJSUl9f7/+fPnH/f4ueeeqzFjxmj37t1qbGyUy+WKYHUAAODfrap2+/VBVJI8Hqmq2m25D6OBqnO3aVW1W9ua9h33WK4zVWVFrrj/MwCCEe+vJ3XutgGDLeno91axpl4ZKQ5LfX8AYLZB0S4gWCNGjNDQoUMlSSeeeGKfx2RlHf0NRnt7e8TqAgAAx2tu7egzwPGloWmfmls7wlRR9K2vbVF5ZU2/fy7bmvapvLJGG2pbIlwZENvs8HoSTHgHAHZm2XBr8ODBmjBhgiRp9+7dfR7z6aefSpLS0/ktBgAA0VTXGNwvmoI9L9YF2pVR526LTGGABcT764kdwjsAMJtlwy1JKi4uliStWbPmuMc+/PBDNTc3a/To0XI6nZEuDQAAfElnV09Ez4t1dGUAwYv315N4D+8AIBwsHW5985vf1LBhw/TCCy+oqqqq9+v79+/XfffdpyNHjujyyy/XoEGW/jYBALA8R2JwYz6DPS+W0ZUBhCbeX0/iPbwDgHCwxit8P7Kzs/Xggw/qzjvv1B133KFly5Zp9OjRqqmpUXt7u8466yxdc8010S4TAADbK8hJi+h5sSyUrgyr7qAImCneX0/MCO/iaQdWAPCHpcMtSZozZ47Gjx+vX//613rnnXe0fft2OZ1OXX311Vq4cGHv0HkAABA92ZnJynWmBtSxlOdMjcsPY3RlAKGJ99eTUMI7dmAFYFeWD7ckafLkyfrFL34R7TIAAIAPZUUulVfW+DVryjCk0iJX2GuKhnhfUgVEQjy/ngQb3u1oOeBzowrvDqwLSvI1szDLpGoBIDYwjAoAAEREgStdV5XkyzB8H2cY0oKS/LjtLoj3JVVAJIT6etLc2qG1G5tUVb1Tazc2xdxMu7Ii14Dfm5dhSF+ZkMEOrABsjV8BAgCAiCkuzNKoFIeqqt1q6KMrIc+ZqtI4XzYT70uqgEgJ5vXEKsv2vOHdQIGVN7yr3vJJwDuwxsL3CQBmIdwCAAARVeBKV4Er3dYDj+N5SRUQSYG8nqyvbbHUsj1/w7uU4Qla9tf6gJ7buwOrXV5zAcQ/wi0AABAV2ZnJtv1gFWhXBh0WgG8DvZ7UudsCWraXkeKIiX93/oR3azc2BfXc7MAKIJ4QbgEAAEQBSzSByFlV7bb0sj1f4R07sAIA4RYAAEDUsEQzNvH3EV+aWzsCmnEnWWvZHjuwAgDhFgAAQNTZeYlmLLHKsHEEpq6xPejzrPDvkh1YAUAaFO0CAAAAgGhbX9ui8sqafjt8vMPGN9S2RLgyhCrel+15d2ANBDuwAog3hFsAAACwtUCHjde52yJTGExhh2V7ZUUuGYZ/x7IDK4B4RLgFAAAAWwtm2DjM09zaobUbm1RVvVNrNzapubXD1Oe3w7I97w6sAwVc7MAKIF5Z59cRAAAAgMnifdh4LIvUjDPvsr1A/p6tuGyPHVgB2BnhFgAANsaucLC7eB82HqvW17b4XArqnXG2oCRfMwuzQr5eWZFL5ZU1fnXoWWHZXn+v3ezACsCuCLcAALAhdoUDjor3YeOxqHZba0AzzjJSHCG/HnmX7Q103Vhftufvazc7sAKwG8ItAABsJtIdE9FGBwN8idSwce7Df1m+tiHgGWdmhE1WX7Znt9duAAgE4RYAADYS6K5wZnRMRAvdafBHuIeNcx8eq/GTA9r64d6AzulrxlmwYaFVl+3Z6bUbAIJBuAUAgI0EsyucFT8g0eEAf4Vz2Dj34fFqP2gN6jzvjDOzwkKzlu1FKiSzy2s3AASLcAsAAJuwy65wdDggUOEYNs592LdDncHPOIulsDCSHXl2ee0GgFAMinYBAAAgMkLZFc5KgulwgL15h40bhu/jAhk2zn3YtyRHcL9b3/9Zd0BhYZ27Lajr+GN9bYvKK2v6DZy8IduG2hZTrmeX124ACAXhFgAANmGHXeFC6XCAvRUXZmnRvKnKc6b2+XieM1WL5k31qyOI+7B/hZMygzpvR8uBmAgLA+3IMyNks8NrNwCEimWJAADYRKR2hYumUDocWL4Ds4aNcx/2L2fsSJ18UkZAQ+VdY0fI/cnBgK4TrmV50Zh9ZYfXbgAIFZ1bAADYRLh3hYsFdDjADNmZyZo9zanSovGaPc0ZcEDCfejb/Nl5Ay4B9TIMaXzWyKCuY/ayvGh15NnhtRsAQkW4BQCATXh3hQuEv7vCxQo6HBALuA99K8zNDGjGWerwhKCuY3ZYGK3ZV3Z47QaAUBFuAQBgI2VFroA6JvzZFS6W0OGAWMB9OLBAZpzFSlgYzY68eH/tBoBQ2ePXQwAAQNK/doUbaCByILvCxRJvh0MgS4focIDZuA/94++Ms1gJC6MZssX7azcAhIpwCwAAmykuzNKoFIeqqt1q6OPDd54zVaVFLst+OCorcqm8ssavoc90OCBcuA/9l52Z7DPYi5WwMNohW7y/dgNAKAi3AACwIbN2hYtFdDggFnAfmisWwsL9n3UrKXGwDnUd9vscs0O2eH7tBoBQEG4BAGBjA3VMWBUdDogF3IfmiXZYuL62ZcBr91VLuDry4vW1GwCCRbgFAADiEh0OiAXch+aJVlhY524LKtiiIw8AIodwCwAAxDU6HBALuA/NEY2wcFW1O6BgKylxsG6cO4VgCwAiiHALAAAAgKVEKixsbu0IaJC9JB3qOqyU4QlhqggA0JdB0S4AAAAAAGJRXWN7RM8DAASHcAsAAAAA+tDZ1RPR8wAAwSHcAgAAAIA+OBKDm+IS7HkAgOAQbgEAAABAHwpy0iJ6HgAgOIRbAAAAANCH7Mxk5TpTAzonz5nKzpgAEGGEWwAAAADQj7IilwzDv2MNQyotcoW1HgDA8cIabjU0NGjp0qW69957dcstt0iSPvvsM/35z39Wd3d3OC8NAAAAACErcKXrqpL8AQMuw5AWlOSrwJUemcIAAL3CMulw//79Wrx4sV577TVJksfjkfHPnwZNTU1avHixfvGLX+jJJ59UXl5eOEoAAAAAAFMUF2ZpVIpDVdVuNTTtO+7xPGeqSotcBFsAECWmh1vd3d26+uqrtXXrVg0fPlxnnXWWNm/erNbWVklHg66RI0dq9+7duuKKK/TCCy8oKyvL7DIAAAAAwDQFrnQVuNLV3NqhusZ2dXb1yJE4RAU5aczYAoAoM31Z4jPPPKOtW7dq+vTpWrt2rR5//HGdeOKJvY9PnjxZ69at0/Tp03Xw4EEtXbrU7BIAAAAAICyyM5M1e5pTpUXjNXuak2ALAGKA6eHWSy+9pCFDhuiRRx5RenrfbbnJycl65JFHNGTIEG3YsMHsEgAAAAAAAGATpodbO3fu1MSJEzVmzBifx40ZM0YnnXSSdu/ebXYJAAAAAAAAsAnTwy3DMHTo0CG/jj1y5IgSEhLMLgEAAAAAAAA2YXq4NX78eH300Uf66KOPfB63a9cubd++XSeddJLZJQAAAAAAAMAmTA+3SktLdfjwYd11113at+/4bXIlad++fbrjjjskSeeff77ZJQAAAAAAAMAmhpj9hJdddplWr16tTZs26fzzz9dXv/rV3i6uiooK7dixQ6+88or279+vSZMm6fLLLze7BAAAAAAAANiE6eFWQkKCfvvb3+quu+7SG2+8odWrV/c+9uMf/1gej0eSNH36dJWXlysxMdHsEgAAAAB8SXNrh+oa29XZ1SNH4hAV5KQpOzM52mUBAGAK08MtSUpJSdETTzyhLVu26LXXXtOOHTvU0dGhpKQk5eTk6Nxzz9UZZ5wRjksDAAAA+Kc6d5tWVbu1ren4cSG5zlSVFblU4EqPQmUAAJjH9HDrj3/8oyZMmKCzzjpLp5xyik455RSzLwEAAABgAOtrW/TUmnr9c+HEcbY17VN5ZY0WlORrZmFWZIuLY3TJAUDkmR5uPfHEE+ro6NCbb76pkSNHmv30AAAAAAZQ527zGWx5eTxSxZp6ZaQ46OAKEV1yABA9pu+WuH//fo0fP55gCwAAAIiSVdXuAYMtL49Hqqp2h7WeeLe+tkXllTV9BlvSv7rkNtS2RLgyALAH08OtyZMnq7GxUe3t7WY/NQAAAIABNLd29Buy9KehaZ+aWzvCVFF8C7RLrs7dFpnCAMBGTA+3lixZohEjRmj+/PlasWKFPvjgA+3bt0+HDh3q938AAAAAzFHXGNwvmYM9z+7okgOA6DN95tZtt90mwzDU2Nio//7v/x7weMMwVFdXZ3YZAAAAgC11dvVE9Dw7C6VLjiHzAGAe08OtDz74IKDjPf7+mgMAAADAgByJwb3FD/Y8OwulS45wCwDMY/pPsNdee83spwQAAADgp4KctIieZ2d0yQFAbDA93MrOzjb7KQEAAABbam7tUF1juzq7euRIHKKCnLQBO36yM5OV60wNaLlcnjOVTqIg0CUHALEhrK+q+/fv19///ne53W599tlnGjZsmMaNG6ezzjpL6enp4bw0AAAAYFl17jatqnb3GVDlOlNVVuRSgav/99NlRS6VV9b4NejcMKTSIlcI1doXXXIAEBvCEm55PB499thjWrZsmTo7O497fPDgwVq4cKFuu+02DR48OBwlAAAAAJa0vrZFT62p7zeY2ta0T+WVNVpQkq+ZhVl9HlPgStdVJfk+n0c6GmwtKMn3GZShf3TJAUBsCEu4deedd2r16tXyeDzKysrS5MmTNWzYMB08eFDvv/++du/erd/+9rdqaWlReXl5OEoAAAAALKfO3TZgICVJHo9UsaZeGSmOfoOp4sIsjUpxqKrarYY+wpc8Z6pKB+gAw8DokgOA6DM93FqzZo1eeukljRw5UkuWLNGsWbOOO2bt2rW677779PLLL+v888/v8xgAAADAblZVu/0KSaSjAVdVtdtnOFXgSleBKz2o2V3wD11yABB9podbzz33nAzD0KOPPqoZM2b0eczs2bOVmJio6667TitWrCDcAgAAgO01t3YEtLxNkhqa9qm5tcOvIfOEWeFDlxwARJfp4dbWrVuVlZXVb7DlVVxcrKysLG3dutXsEgAAAADLqWtsD/o8gqvoo0sOAKLH9HDr888/17hx4/w6NiMjQw0NDWaXAAAAAFhOZ1dPRM9DeNAlBwCRZ3q4NXr0aH344Yfq6upSYmJiv8d1dnZqx44dGjVqlNklAAAAAKaKRDeOIzG4t+bBngcAQLww/SdhUVGRVqxYofLyct177739HldeXq5Dhw7p61//utklAAAAAKaoc7dpVbW7z1lYuc5UlZk4R6kgJy2i5wEAEC8Gmf2E11xzjRITE/X000/rO9/5jt544w3t3r1bHR0d2r17t15//XVdd911euaZZ5SYmKhrrrnG7BIAAACAkK2vbVF5ZU2/Q963Ne1TeWWNNtS2mHK97Mxk5TpTAzonz5nKEjgAgO2Z3rmVk5OjRx55RIsWLdKbb76p9evXH3eMx+ORw+HQT37yE7lcLrNLAAAAAEJS527TU2vq5fH4Ps7jkSrW1CsjxWFKB1dZkUvllTUDXleSDEMqLXKFfE0AAKzO9M4tSZo1a5ZefPFFXXTRRcrIyJDH4+n9X0ZGhr7xjW9o5cqVmj17djguDwAAAIRkVbXbr4BJOhpwVVW7TblugStdV5XkyzB8H2cY0oKS/JACtebWDq3d2KSq6p1au7FJza0dQT8XAADRFLbpky6XS0uWLJEkdXR06LPPPtPw4cOVnEzbNAAAQKgiMeDcrppbO/pditifhqZ9am7tMOXvoLgwS6NSHKqqdquhjzrynKkqDWHWVyTniAEAEAlhC7daWlq0evVqffvb31ZycnJvqPWrX/1KBw4c0GWXXaZx48aF6/IAAABxiWAi/Ooa24M+z6yAscCVrgJXuukh5vraFp/LLb1zxBaU5GtmYVbQ1wEAIJLCsixx5cqV+trXvqZHH31Uzc3Nxzz2P//zP6qoqNAFF1ygF154IRyXBwAAiEuRHnBuV51dPRE9z5fszGTNnuZUadF4zZ7mDCnYCnSOWJ27LehrAQAQSaaHW9XV1br33nv1xRdf6JxzztGQIcc2h1177bWaM2eOuru7dd999+kf//iH2SUAAADEHYKJyHEkBre4IdjzIiVac8QAAAg308OtZcuWyTAM3XPPPXriiSc0ZsyYYx4/99xz9eijj2rx4sXq6enRb3/7W7NLAAAAiDsEE5FTkJMW0fMiIZQ5YkC8YlMFIH6Y/uulzZs3a/To0brqqqt8HnfFFVfoiSee0Lvvvmt2CQAAAHEl2gPO7SY7M1m5ztSA/szznKkx/WcdC3PEgFjB7EIg/pjeudXZ2anMzEy/jj3hhBPU0UE6DgAA4EsowQSCU1bkkmH4d6xhSKVFrrDWE6pYmiMGRBOzC4H4ZHq4NXbsWH344Yc6dOiQz+O6u7vV2NjodxAGAABgVwQTkVfgStdVJfkDBlyGIS0oyY/5Lo94nSMGBILZhUD8Mj3cKi4u1qFDh/Twww/7PK68vFwdHR0qKioyuwQAAIC4QjARHcWFWVo0b6rynKl9Pp7nTNWieVM1szArwpUFLh7niAGBYnYhEL9Mf8dz1VVX6YUXXtBzzz2nhoYGXXTRRZo0aZKGDRumQ4cOafv27XrxxRe1ceNGORwOXXfddWaXAAAAEFcIJqKnwJWuAle6mls7VNfYrs6uHjkSh6ggJ81Ss6jicY4YEAhmFwLxzfRw68QTT9TPfvYzLVq0SDU1NaqtrT3uGI/Ho5EjR+rRRx+V0+k0uwQAAIC4QjARfdmZyZb/8ywrcqm8ssavzhUrzBEDAsGmCkB8M31ZoiQVFRXpr3/9q2677TZNnTpVGRkZGjx4sIYPH66TTz5Z119/vVavXq0ZM2aE4/IAAAAhicXt4eNtwDkiL97miAGBYHYhEN/CNoghLS1N119/va6//vpwXQIAAMBUsbw9vDeYGGgYMsEEfCkuzNKoFIeqqt1q6OM+z3OmqjSK9zkQLswuBOIb/1IBAAB0dHt4X8GRd3v4BSX5URsgTjABM8TLHDEgEMwuBOKbaeHWgQMHtG3bNk2dOlVDhhz7tOvXr9dzzz2nxsZGpaamasaMGZo/f75Gjhxp1uUBAACCFuj28Bkpjqh2cBFMwAzxMEcM8BezC4H4FnK4deTIEf3kJz/R8uXL1d3drbVr1yo7O7v38Z///Od64oknJB0dJC9JGzduVGVlpZYuXaoJEyaEWgIAAEBIgtkePtrdUQQTABAYNlUA4lfIA+W///3vq6KiQp2dnUpISFBnZ2fvY//7v/+rX//61/J4PMrIyNA999yj8vJyzZo1Sy0tLbrpppvU3d0dagkAAABBC2V7eACAdbCpAhC/Qurc+vvf/66XXnpJw4YN03333afS0lINHTq09/Gf/vSnRy8yZIh+97vfKS8vT5L09a9/XXfffbdefPFFrVy5Ut/85jdDKQMAACBobA8PAPbB7EIgPoUUbr344osyDEP33HOPLrroomMe++ijj/SPf/xDhmHovPPO6w22vG677Ta98MILWrNmDeEWAACIGraHBwB7YXYhEH9CCrfee+89JSUl6eKLLz7usQ0bNvT+/1mzZh33+NixYzVu3Dht3749lBIAAABCwvbwAGBPzC4E4kdIM7daW1uVnZ0to49Fy++8807v/z/77LP7PD81NVX79+8PpQQAAICQsD08AACAtYUUbnk8Hjkcjj4fe/fdd2UYhiZNmqS0tL7f/O3fv1/JySTlAAAgerzbwweC7eEBAABiR0jhVmZmpj7++OPjvl5fX69PP/1UklRUVNTnuW1tbWpqalJmZmYoJQAAAISsrMg14O5ZXmwPDwAAEFtCCremTZumvXv36t133z3m6ytXruz9/33N25Kk5cuX68iRI5o+fXooJQAAAISM7eEBAACsK6Rw69JLL5Uk3X777XrjjTf06aef6s9//rOWL18uwzCUm5ur008//bjzXn/9df3mN7+RYRiaM2dOKCUAAACYorgwS4vmTVVeP0sU85ypWjRvqmYWZkW4MgAAAPgS0jY/U6dO1VVXXaWKigrdcMMNvV/3zuJasmTJMcdXVFTo9ddf1zvvvCOPx6MLLrigz/ALAAAgGtgeHgAAwHpC3sP67rvvVk5OjpYuXaqWlhZJ0le+8hUtXrxYJ5988jHHLl++XI2NjZKkkpISPfTQQ6FeHgAAwHRsDw8AAGAdIYdbkjR//nzNnz9fBw4c0JAhQzRs2LA+j/vP//xPffHFFzr//PPp2AIAALAwutsAAECsMCXc8ho5cqTPx++66y4zLwcAAIAIq3O3aVW1W9ua9h33WK4zVVfOKVBhLrthAwCAyDE13AIAAED8Wl/boqfW1Mvj6fvxbU379P89+T+6+ZKpmnoSO0oivOgeBAB4EW4BAABgQHXuNp/BlpfHIz22okaL5k1VgYuAC+YbqHuwrMjFvQcANjMoWhf+8MMPNXnyZBUUFESrBAAAAPhpVbV7wGDLy+ORqqrdYa0H9rS+tkXllTV9BlvS0e7B8soabahtiXBlAIBoilq4JUkej0cef98lAQAAICqaWzv6DRP609C0T82tHWGqCHYUSPdgxZp61bnbIlMYACDqorYscfTo0XrooYeidXkAAAD4qa6xPejzmIEEswTTPcjyRACwh6iFW8nJyZo7d260Lg8AAAA/dXb1RPQ8xK5oDXEPpXuQgBUA4h8D5QEAAOCTIzG4t4zBnofYE+0h7nQPAgB8Ces7jkOHDikpKan3v+vq6rR69WodOXJExcXFOvvss8N5eQAAAJigICctouchtqyvbfE568o7xH1BSb5mFmaFpQa6BwEAvoRloPy6det03nnnHTNT67XXXtOll16q3//+91q2bJmuvvpq/eAHPwjH5QEAAGCi7Mxk5TpTAzonz5lKx0wciJUh7nQPAgB8MT3c2rx5s26++Wbt2rVLzc3Nko7uivjggw+qp6dHEydO1EUXXaSkpCRVVlbq1VdfNbsEAAAAmKysyCXD8O9Yw5BKi1xhrccMza0dWruxSVXVO7V2YxO7O/YhmCHu4UD3IADAF9N/lVFRUaHDhw/r8ssv15133ilJ2rRpk1paWjRixAgtX75cycnJuvDCC3XllVdqxYoVmjVrltllAAAAwEQFrnRdVZI/YBePYUg3XzI1pnepi/b8KKuIpSHu3u7BQOqhexAA7MP0zq333ntPKSkpuvvuu+VwOCRJr7/+uiTpnHPOUXLy0R8wZ5xxhrKzs7V582azSwAAAEAYFBdmadG8qcrrZ4ni6NQk3XRJoWafmRPhyvy3vrZF5ZU1/YYk3vlRG2pbIlxZ7AlliHs4xGP3IADAHKaHW3v37pXT6dTQoUN7v/bWW2/JMAzNmDHjmGPT0tJ04MABs0sAAABAmBS40nXX5adpwfl5ykxNOuaxPfsO6bHnanX342+FbfZSKGJlfpRVxNoQd2/34EABl2FIC0ry6b4DABsxfVliSkqKPvvss97/3rNnjxoaGmQYxnG7I3788ce9nVwAAACwhqO75zX0GxJt/XCv6nbuDevuecEIZn6UGQFJc2uH6hrb1dnVI0fiEBXkpFliuVwsDnEvLszSqBSHqqrdauij+y7PmapSlpUCgO2Y/pPH5XJp06ZN2rFjhyZMmKCqqipJUn5+vsaMGdN73KpVq7R3716deeaZZpcAAACAMAm0+ykjxRETQUM05kdZfbZXrA5xL3Clq8CVbtnQEABgPtPDrbKyMr377ru68sordeqpp+qNN96QYRi6+OKLJUktLS168skn9fzzz8u2AiG1AAAgAElEQVQwDM2dO9fsEgAAACLGbh+wo9X9FKpQ5kcF+vfZ3Nqhqv9x65339/R7jHe2V6x1t31ZrA9xz85Mjut/awAA/5kebl1yySXavHmznnvuOb366quSpNmzZ+uyyy6TJH366ad69tlnJUkLFy7UhRdeaHYJAAAAYWf1rpxgxNLueYGKxPwoX/dEXwbqbouF4LSsyKXyyhq/Ak2GuAMAoiUsC+IfeOABXXnlldq2bZucTqemTJnS+9hJJ52kefPmqbS0VNOmTQvH5QEAAMLq6Myp/pfmWaErJxiR7H4yW7jnRw10T/Snr+62WApOvUPcB/reojnEPRZCQABAdIVt2uPEiRM1ceLE476enJys+++/P1yXBQAACCurzpwyQ6ztnheIcM6P8vee6M+Xu9tiMTiN1SHusRQCAgCiK3xbmUg6dOiQkpL+tUV0XV2dVq9erSNHjqi4uPi43RMBAABinVVnTpkhFnfP89f+z7oDPsff+VGB3BP9qWts1/7PumM2OI21Ie6xGAICAKInLO801q1bp4cfflhnnXWWHnjgAUnSa6+9pltvvVWHDx+Wx+NRRUWF5s2bpx/84AfhKAEAAMB0Vp45ZYZY3T3PH6uq3QGf48/8qGDuib50dvVYIjiNhSHudu6eBAD0bZDZT7h582bdfPPN2rVrl5qbmyVJHo9HDz74oHp6ejRx4kRddNFFSkpKUmVlZe/QeQAAgFgXysypeODdPS8Qkdw9rz/BBlApwxMGPMasv9uuLw4HHZzaTTAhIAAgvpkeblVUVOjw4cO6/PLL9fjjj0uSNm3apJaWFo0YMULLly/XkiVL9MQTT8jj8WjFihVmlwAAABAWVp45ZZayIpcMw79jY2X3vHCGktH+u42X4NRfoXRPAgDil+nh1nvvvaeUlBTdfffdcjgckqTXX39dknTOOecoOfnob+7OOOMMZWdna/PmzWaXAAAAEBZWnjllFu/ueQMFXNHcPe/fhTOUNOPvNs+ZqsShg4M6N9rhWqTZvXsSANA3099p7d27V7m5uRo6dGjv19566y0ZhqEZM2Ycc2xaWpp2795tdgkAAABhYeWZU6Hoa4j4onlT+90975QJGSqZ7oyJYEsKbygZ6t+tt7ut+dPPgjo/noJTf9A9CQDoi+k/DVNSUvTZZ//64bxnzx41NDTIMIzjdkf8+OOPezu5AABAdMTK7mdW4J05FciyqFiYORWsOnebVlW7+/x+c52pKity6VvDE465f4pOPVE5Y0eqtfVgFCruWzhDyWDuCa8vd7f5M9+rL1YPTgNF9yQAoC+mv8q7XC5t2rRJO3bs0IQJE1RVVSVJys/P15gxY3qPW7Vqlfbu3aszzzzT7BIAAIAf/AkuYqXzJpaUFblUXlnj10DrWJk5FYz1tS0+d6Tb1rRP5ZU1WlCSr9nTnL1fz8wcEaEKffv30DZn7Ag1fuJ/4BZIKBnIPfHl5y/90r8xuwWnwbJr9yQAwDfTw62ysjK9++67uvLKK3XqqafqjTfekGEYuvjiiyVJLS0tevLJJ/X888/LMAzNnTvX7BIAAMAAAgkuZhZmRba4GOedOeXrz0+KrZlTgapztw34/UlHd6KrWFOvjBRHzHyfvkJbfwUaSvp7T0jSGZNHq/Srrj5DKbsEp6EgBAQA9MX0gfKXXHKJLr30Uu3du1evvvqqenp6NGvWLF122WWSpE8//VTPPvusenp6tGDBAl144YVmlwAAAHwINLioc7dFpjALKS7M0qJ5U5XnTO3z8TxnqhbNm2rZYHBVtdvvLiSPR6qqdoe1Hn+tr21ReWVNyMFWMKGkP/fEHd+cquv/3yn9Bi1WHNYfDVbcsRMAEF5hWXz+wAMP6Morr9S2bdvkdDo1ZcqU3sdOOukkzZs3T6WlpZo2bVo4Lg8AAHwIJriw64doXwpc6SpwpcfdzLLm1o6Aw6GGpn1qbu2I6vftb2jry78vFQyUGfdEcWGWRqU4+h3WH2qN8cAO3ZMAgMCEbbLixIkTNXHixOO+npycrPvvvz9cl0WA4u0NOQDAN6sGF7EsOzM5rv5s6hrbgz4vmn8OgYS2kuQaO0JnnzI2LO+BQr0n4jU4NRMhIADgy8K6bcjhw4e1detWffjhh+ro6NC3vvUtffHFF/r44481bty4cF4aA2CIMADYk1WDC0ROZ1dPRM8zQzChrfuTg7rm65Nj+r6Ot+DUbISAAACvsIVbf/jDH/Tkk09q7969vV/71re+paamJl1wwQWaNWuWlixZouRkfvBEGkOEAcC+rBhcILIcicG9PQz2PDMQ2tobISAAICzvQhYvXqyVK1fK4/EoJSVF3d3d6uzslHR0oPyRI0e0du1aNTU16U9/+pOSkpLCUQb6YOXdjwAAobNicIHIKshJi+h5ZiC0BQDA3kzfLfFvf/ub/vznPyszM1NLly7V22+/rcmTJ/c+fsYZZ+iZZ55RZmam6uvrVVFRYXYJ8MGqux8BAMxhxeACkZWdmazcfnb860+eMzWqnTOEtgAA2Jvp4dby5ctlGIZ+/vOfa+bMmX0eM23aND3++OPyeDxas2aN2SWgH6EMEQYAxAcrBheIvLIilwzDv2MNQyotcoW1noEQ2gIAYG+mh1t1dXUaN26cTj31VJ/HTZkyRTk5OWpsbDS7BPQjlHkUAID4YbXgApFX4ErXVSX5A94nhiEtKMmP+ggDQlsAAOzN9HCrq6vL7xlaDJOPLOZRAAAk6wUXiI7iwiwtmjdVef2ERnnOVC2aNzVmNp8htAUAwL5MHzRwwgknaOfOnfr88881bNiwfo/r6OjQ9u3bdcIJJ5hdAvrBPAoAgFdxYZZGpThUVe1WQx9L1vOcqSotchFs2VyBK10FrnQ1t3aorrFdnV09ciQOUUFOWsx1PXlD24E2ziG0BQAg/pieWvzHf/yHli1bpocfflgPPPBAv8ctWbJE3d3dOuecc8wuAf1gHgUA4MusFFwgurIzky1xTxDaAgBgT6aHW9/+9rf14osvasWKFWpsbNScOXO0f/9+SdL777+v7du367nnntPGjRs1cuRIXX311WaXgH5451EEMlSeeRQAEP+sElwA/iC0BQDAfkwPt9LT07V06VLdeOONevvtt/XOO+/0PnbRRRdJkjwej9LS0vTYY49pzJgxZpcAH8qKXCqvrPHZru/FPAoAAGBVhLYAANiH6QPlJenkk0/WSy+9pDvuuEOnnXaaRo4cqcGDBys5OVknn3yybrrpJq1evVrTpk0Lx+XhA0OEAQAAAABAPAnbpPDk5GRde+21uvbaa8N1CQSJeRQAgGjzLhnb0/a52ju6lZacoNHpw1g6BgAAgICxDZ5NMY8CABANde42rap2+5z/mOtMVRm/ZAEAAICfwhZubdmyRTU1Nero6NDhw4fl8THk6aabbgpXGRgA8ygAAJGyvrZFT62pH3Du47amfSqvrNGCknzNLMyKTHEAAACwLNPDre7ubt1+++1at27dgMd6PB4ZhkG4BQBAnKtzt/kVbHl5PFLFmnplpDjo4AIAAIBPpodby5Yt02uvvSZJGjdunMaPH6/ExESzLwMAACxkVbXb72DLy+ORqqrdhFsAAADwyfRwq6qqSoZhaPHixfrWt75l9tMDAGIMs/swkObWDp8ztnxpaNqn5tYO7ikAAAD0y/Rwa9euXTrhhBMItgAgzvkaDM5AcHxZXWN7yOcTbgEAAKA/g8x+wuHDhys5mTegABDP1te2qLyypt9uHO9A8A21LRGuDLGos6snqucDAAAgvpkebk2bNk07d+5UW1ub2U8NAIgB/g4G9w4Er3Pz88DuHImhNYqHej4AAADim+nh1o033ihJWrx4sbq7u81+egBAlAUyGNw7EBz2VpCTFtXzAQAAEN/CMnPr4osv1vLly1VcXKwzzjhDY8aM0dChQ/s83jAM3XnnnWaXAQAIg2AGgzMQHNmZycp1pgY1VD7PmWq5e4dNFgAAACLL9HDrlltukWEYkqR9+/bplVde6f3vf+fxeAi3AMBCgh0MzkBwlBW5VF5Z43fXnyQZhlRa5ApbTWZjkwUAAIDoMD3cuvDCC/sNs8LhhRde0F133dXv49dff71uv/32iNUDAPEs2MHe0RoITgdN7Chwpeuqkny/5rVJR4OtBSX5lgmD1te2+PzevJssLCjJ18zCrMgWBwAAEOdMD7cefvhhs5/Sp/fff1+SVFRUpPT0498AT548OaL1AEA8C3awd6QHgtNBE5uKC7M0KsWhqmq3GnwsUcxzpqrUQn9HgW6ykJHisMz3BgAAYAWW336orq5OkvTQQw9pzJgxUa4GAOJbsIO9IzkQnA6a2FbgSleBK723q25P2+dq7+hWWnKCRqcPs2R3XTCbLBBuAQAAmCekcGv79u2SJJfLpSFDhhzztUBMnDgx6Brq6+s1atQogi0AiIBgBoNHciA4HTTWkZ2ZbLkQqy9ssgAAABB9IYVbF1xwgQYNGqTVq1dr/PjxkqTS0tKAnsMwjN7uq0A1NTXpwIEDOuecc4I6HwAQuEAGg0d6IDgdNIg0NlkAAACIvkGhPsGRI0eO+W+PxxPQ//79/EB4521lZGTohz/8oWbPnq0pU6boa1/7mh5//HF1dXWF9L0BAI7nHQw+0N4hkR4IHkoHDRAsq22yAAAAEI9C6tyqr6/362vh4u34WrlypVJSUnT66adrzJgx2rJli37xi19ow4YNqqiokMPhMP3aCQlDlJk5wvTnNVOs14fo4v7AQHzdI9+YlaeJ49L17KsN2rJj73GPnzIhQ9+clafC3MxwlniM/63fE9R5u/Z+rqkFJ5hcTfzjNeSoURnDgz4v3v8M4/37Q2i4PzAQ7hH4wv2Bf2fpgfLezq3zzz9fS5Ys0bBhwyRJH330kW688Ub93//9n372s5/p7rvvjmaZABCXCnMzVZibqcZPDqj2g1Yd6uxRkmOICidlKmfsyIjXc6gzuE6YYM8DJKlwUnABbrDnAQAA4HiGx+PvdJLgvP/++2psbNTBgweVlpamiRMnyuVymfLcXV1dampq0rhx45SQkHDcdefOnaukpCS98847Gjp0qCnX9Oru7tH+/YdMfU6zeFPs1taDUa4EsYj7AwOx6j2ydmOTlr/6QcDnzZ81SbOnOcNQUXyy6v0RTg//8b2AN1m46/LTwlhRdHGPwBfuDwyEewS+cH/Et5SUJCUkBNeDFZbOrSNHjmj58uV68skntWfP8ctEJkyYoFtvvVWzZ88O6TqJiYn97rQ4efJkjR07Vh9//LHcbrcmTZoU0rUAALGtICctoucBXrG8yQIAAIAdhDxQ/t95PB5973vf049+9CPt3r1bDodDeXl5Ou2005Sbm6uEhARt375dt9xyix555BGzL3+MUaNGSZIOHYrNDisAgHmyM5OV60wN6Jw8Zyo71iFksbrJAgAAgF2Y3rn1/PPPa82aNUpOTta9996r0tLSY5YEdnd368UXX9TDDz+s3/3ud5o+fbrOOeecgK/T0dGhH//4x9q/f78effRRDRly/Lfy0UcfSZLGjBkT/DcEALAMOmgQLcWFWRqV4lBVtVsNfSxRzHOmqrTIRbAFAAAQBqaHW88++6wMw9Djjz+uM88887jHExISdMkll2jMmDG67rrr9Ic//CGocGv48OFau3at2tvb9e677+rss88+5vH169ervb1dubm5hFsAYBPeDpqn1tT7DLjooEE4FLjSVeBKV3Nrh+oa29XZ1SNH4hAV5KTRIQgAABBGpodbO3fu1Pjx4/sMtr6suLhYOTk52rJlS1DXMQxDl156qX7zm9/ohz/8oZYtW9YbYu3atUv333+/JOmGG24I6vkBANZEBw2iLTszmTALAAAggkwPtxITEzVokH+jvJKSktTe3h70tb773e9q48aN2rRpk0pKSnT66adLkt5++211d3dr4cKFmjNnTtDPDwCwJjpoAAAAAPswPdz66le/qpdfflmbNm3qDZv64na7tW3bNs2aNSvoazkcDlVUVKiiokJVVVV6++23lZCQoKlTp+qKK67QeeedF/RzAwCsjw4aAAAAIP4ZHo8/Y3f9t2fPHl166aXq7OzUww8/rHPPPfe4Y7Zt26Zbb71VbW1tev755+V0Os0sISK6u3u0f39s7sKYmTlCktTaejDKlSAWcX9gINwj8IX7AwPhHoEv3B8YCPcIfOH+iG8pKUlKSAiuB8v0zq1f/epXKigo0Lp163TDDTcoKytLp5xyilJSUnTo0CHt2LFD77//viQpMzNTt99++3HPYRiGVqxYYXZpAAAAAAAAiDNh2y1Rkjwej5qbm9Xc3NznsXv27NGePXuO+7r3fAAAAAAAAMAX08Othx56yOynBAAAAAAAAPpkerg1d+5cs58SAAAAAAAA6NOgSF3o8OHDkboUAAAAAAAAbML0zi2vTz/9VE8//bTeeOMN7dq1S52dnUpOTtaECRN03nnnad68eRo+fHi4Lg8AAAAAAAAbCEu49be//U333nuvPv/8c3k8nt6vHzx4UDU1NaqtrdVTTz2ln/70pzrttNPCUQIAAAAAAABswPRwa+vWrVq0aJF6eno0ffp0XXLJJcrNzdXw4cPV0dGh+vp6rVixQu+9956++93vauXKlcrKyjK7DAAAAAAAANiA6TO3fvOb36inp0cLFy7U008/rbKyMuXn58vpdGry5MmaO3eu/vSnP+nyyy/Xvn37tHTpUrNLAAAAAAAAgE2YHm699957Sk9P1x133OHzuLvuukspKSl68803zS4BAAAAAAAANmF6uPXZZ58pKytLgwcP9nlcQkKCxo0bp7a2NrNLAAAAAAAAgE2YHm5NmjRJO3bs0IEDB3we193drcbGRp100klmlwAAAAAAAACbMD3cuuGGG9TZ2ak77rhDnZ2d/R63ZMkSHTx4UNdee63ZJQAAAAAAAMAmTN8tMSMjQ/Pnz9ef/vQnzZkzRxdddJGmTJmikSNHqrOzU9u3b9eLL76orVu3auLEiWpvb9cf//jH457n8ssvN7s0AAAAAAAAxBnD4/F4zHzC/Px8GYYh79MahnHcMb4e83r//ffNLMt03d092r//ULTL6FNm5ghJUmvrwShXgljE/YGBcI/AF+4PDIR7BL5wf2Ag3CPwhfsjvqWkJCkhIbgeLNM7t6ZPn272UwIAAAAAAAB9Mj3cevrpp81+SgAAAAAAAKBPpodbAAAAgCQ1t3aorrFdnV09ciQOUUFOmrIzk6NdFgAAiDNRDbcOHDigdevW6cILL4xmGQAAADBR7bZW/eHlOm1r2nfcY7nOVJUVuVTgSo9CZQAAIB6FJdzauHGjli5dqu3bt6uzs1NHjhw55vHDhw+rq6tL3d3dkkS4BQAAECdeebtRv1xRo/62LNrWtE/llTVaUJKvmYVZkS0OAADEJdPDrbq6Oi1cuFA9PT0aaCPGwYMHa8qUKWaXAAAAgCioc7f5DLa8PB6pYk29MlIcdHABAICQmR5u/f73v9cXX3yh/Px8XX311XI4HLrlllt03nnnad68efrkk0/0l7/8RRs3btTpp5+uP/zhD2aXAAAAgChYVe0eMNjy8nikqmo34RYAAAiZ6eHWpk2bNGTIEP3yl7/UiSeeKEk68cQTtWvXLhUVFUmSvvGNb+h73/ue/vrXv+ovf/mL5s6da3YZAADgnxjqjUhobu3oc8aWLw1N+9Tc2sH9CAAAQmJ6uLV3715lZ2f3BluSlJ+fr9dff11dXV1KTEyUJN1zzz165ZVXtHLlSsItAADCoM7dplXVboZ6IyLqGtuDPo9wCwAAhGKQ2U84ePBgjRgx4pivjRs3TkeOHNHOnTt7v5aZmSmXy6UPPvjA7BIAALC99bUtKq+s6beTxjvUe0NtS4QrQ7zq7OqJ6HkAAABepodbY8aMUUtLyzHD5MeNGydJqq+vP+bYIUOGqKOjw+wSAACwtTp3m55aU+/3UO86d1tkCkNccyQGtyAg2PMAAAC8TA+3pk2bpvb2dj311FO9X8vNzZXH49HatWt7v7Z3717t3LlTo0ePNrsEAABsLZih3kCoCnLSInoeAACAl+nh1hVXXKFBgwbpxz/+sebPn6/u7m6deuqpysnJ0bp167R48WI988wzuvrqq9Xd3a1TTjnF7BIAALCtUIZ6A6HIzkxWrjM1oHPynKnM2wIAACEzPdzKy8vTj370IyUmJqq+vl4JCQkyDEOLFi2SJK1cuVIPPvigGhoaNHToUN16661mlwAAgG2FMtQb8Fdza4fWbmxSVfVOrd3Y1BuOlhW5ZBj+PYdhSKVFrvAVCQAAbCMsQw7mzp2r4uJivf32271fO++887R06VL9/ve/V3Nzs8aPH68bbrhBEyZMCEcJAADYEkO9EU7+7MB50yVT9csVNT6XxhqGtKAkn906AQCAKcI2wTMjI0Nz5sw55mszZszQjBkzwnVJAABsj6HeCJf1tS0+Nyrw7sB58yVT9cPrvqqnX65TQx8hWJ4zVaVFLoItAABgmpDeyb7wwgumFHHhhRea8jwAANgdQ70RDoHswPnYihr98Lqv6q7LT1Nza4fqGtvV2dUjR+IQFeSkMWMLAACYLqRw6+6775bh72CFfhiGQbgFAIBJvEO9Axkqz1BvDCTQHTiffbVB37ukUNmZydxbJiIsBACgbyGFW1lZWT4fb2lpUUJCgkaNGhXKZQDANHwwgB2UFblUXul75pEXQ70xkGB24NyyY6+aWzt4fTWJP7POWOYJALCzkMKtdevW+Xw8Pz9fU6ZM0R//+MdQLgMAIeODAeykwJWuq0ryB1xGxlBv+COUHTgJt0Ln76yzBSX5mlno+xfPAADEK6bHAoh7fDCwJrrsQlNcmKVRKQ5VVbsZ6o2QsANn9AQy66xiTb0yUhz8mwYA2BLhFoC4xgcD66HLzjwFrnQVuNIJChESduCMnkBnnVVVu3l9BADYEu86AMQ1PhhYC1124cFQb4SCHTijI5hZZw1N+5h1BgCwpUHRLgAAwiWUDwaIvEC77OrcbZEpDLA57w6cgThlQgYBS4hCmXUGAIDdEG4BiFt8MLCWYLrsAERGWZFLhuHfsYYhfXNWXngLsgFmnQEA4D/CLQBxiw8G1kGXHRDbvDtwDhRwGYZ08yVTVZibGZnC4hizzgAA8B8//QDELT4YWEcoXXYsfQIiw98dOM+ZnhOF6uIPs84AAPBfSJ/gWlpaBjymu7t7wOOyshgKDMB8fDCwDrrsAGtgB87I8c46C6SrNc+Zyt8DAMCWQgq3/uu//svn44ZhaMuWLT6PMwxDdXV1oZQBAH3ig4F10GUHWAs7cEZGWZFL5ZU1fs0jNAyptMgV9poAAIhFIc3c8ng8If/vyJEjZn0vAHCcQIcg88EgOuiyA6ytubVDazc2qap6p1Zt2KHGTw5Eu6S4EMisswUl+SpwpUemMAAAYkxIv/J+7bXXzKoDAMLC+8HgqTX1Pn/zzQeD6KLLDrCmOnebVlW7+/y3m+tMVVmRi9fVEPk764w/ZwCAnYUUbmVnZ5tVBwCEDR8MrIHlN4C1rK9t8fmLg21N+1ReWaMFJfmaWch81VAw6wwAAN8YVgLAFvhgEPvosgOso87dNuC/VUnyeKSKNfXKSHHwb9YEzDoDAKBvhFsAbIUPBrGNLjvAGlZVu/3qspSOBlxV1W7+3QIAgLAh3AIAxBS67IDY1tzaEdB8PElqaNqn5tYO/g0DAICwINwCAMSkQLvsCMOAyKhrbA/6PP5NAgCAcCDcAgBYGru1AZHV2dUT0fMAAAAGMijaBQAAEKz1tS0qr6zpd4mUd7e2DbUtEa4MiF+OxOB+NxrseQAAAAMh3AIAWFKgu7XVudsiUxgQ5wpy0iJ6HgAAwEAItwAAlhTMbm0AQpedmaxcZ2pA5+Q5U5m3BQAAwoZwCwBgOaHs1gYgdGVFLhmGf8cahlRa5AprPQAAwN4ItwAAlhPKbm0A/qW5tUNrNzapqnqn1m5s8jsALnCl66qS/AEDLsOQFpTks6kDAAAIKyZ7AgAsh93agNCYsctocWGWRqU4VFXtVkMfz5PnTFUpu5UCAIAIINwCAFgOu7UBwVtf2+JzMwbvLqMLSvI1szDL53MVuNJV4EpXc2uH6hrb1dnVo1EZw1U4KVPDBvu5bhEAACBEvMsHAMSUL39IdiQOUUFO2nGDqNmtDQhOoLuMZqQ4/Oq8ys5M7v13mpk5QpLU2now5HoBAAD8QbgFxBF/QgEgVgWyTMq7W1sgQ+XZrQ0IbpdRlhUCAIBYR7gFxAEzZqfYAeFf7ApmmVRZkUvllTV+fVBntzYgtF1Gea0EAACxjHALsDgzZ6fEK7uHf7Ee6gW7TMq7W9tA57JbG3BUKLuMxtJrBgAAwL8j3AIsLJhQ4Jx/zkKxCzuHf1YJ9UJZJsVubYD/2GUUAADEK8ItwMKCCQXOmZ4T3qJiSLgGJ1uBVUI9M5ZJ9bVbWyx2qAHRxi6jAAAgXvFuBbCoYEOBxk8OKGfsyDBVFVvsOjjZSqGemcukvrxbG4DjscsoAACIV4OiXQCA4AQbCtR+0GpyJbEplI4gqwsm1IsWqy6Tam7t0NqNTaqq3qm1G5vi4r5B/PPuMhoIdhkFAABWQOcWYFHBfrg/1GmP2Sl2HZxstd3QrLZMyipzzID+sMsoAACIR3RuARYV7If7JIc9Mm2rdgSFKpRQLxqstExqfW2Lyitr+g0PvXPMNtS2RLgywH/eXUYNw/dx7DIKAACsxB6fcoE4FOyH+8JJmSZXEpus1hFkFquFet5lUoF0m0VjmZSV5pgBA2GX0eCxcQUAALHJ2p/iABsLNhSwyzB5K3UEmcmKoZ4VlknZdXMCxC92GQ0MS5IBAIhtLEsELKysyDXg0hIvu81OsevgZCuGerG+TMrOmxMg/mVnJmv2NKdKi8Zr9jSn5V8Dw4ElyQAAxD7CLcDCYj0UiPHLtIYAACAASURBVDY7hn9WDfWKC7O0aN5U5fVTe54zVYvmTdXMwqwIV2a9OWYAzBPokuQ6d1tkCgMAAMdgWSJgccxO6Z83/Bvog0m8hX9WWObXl1hdJmW1OWYAzMOSZAAArIFwC4gDsRoKxAI7hn9WD/WyM5Nj6r614hwzAKELZUlyLL2G+cL7BgBAvOCdNxBHYi0UCIdg3ojbMfyzY6gXLlacYwYgdKEsSY71ny0MyAcAxBvCLQCWYMYbcTuEf19mx1AvHILdmZQ/Y8Da4nVJ8vraFp+dvd4B+QtK8qMy5xAAgGAQbgGIebwRD43dQr1wsOocMwDBi8clyYEOyM9IcdDBBQCwBHZLBBDT2KkKsYCdSQH7icclycEMyAcAwAoItwDENN6II1YUF2Zp0bypynOm9vl4njNVi+ZNpXsQiBPeJcmBiOUlyaEMyAcAINbFbt80ANuzw05VsBbmmAH2Ek9LkuN5QD4AAIRbAGIWb8QRq5hjBtiDd0nyQMvjrbAkOV4H5AMAIBFuAYhhvBEHAERbcWGWRqU4VFXtVkMf3cR5zlSV+rFjb7TF44B8AAC8+GkFIGbxRhwAEAviYUlyPA7IBwDAi0+AAGIWb8QBALHEykuSvQPyA5llGcsD8gEA+DJ2SwQQs+JtpyoAAKKprMglw/Dv2FgfkA8AwJcRbgGIabwRBwDAHN4B+QP9XLXCgHwAAL6McAtATOONOAAA5ikuzNKieVOV109ndJ4zVYvmTdXMwqwIVwYA/z979x7fZHn/f/wdKLSUbpRCRVprg46kC2gpIKAVPMw55kZ1TkVFpD70xzxvCm7iccqc4tbN74bD0xQFpp0OpVVE8TDR4EDEFiVSFAjGVlhGW10pLbS9f3/wSGdtekia0528nv8ouQ+5Qi+u3vc71/25gOBRcwtAzIuXlaoAAIgF8VAgHwCAryPcAmAKXIgDABBaZi6QDwDA1xFuATAVLsQBAAAAAF9HzS0AAAAAAACYFuEWAAAAAAAATItwCwAAAAAAAKZFuAUAAAAAAADTItwCAAAAAACAaRFuAQAAAAAAwLQItwAAAAAAAGBahFsAAAAAAAAwLcItAAAAAAAAmFZStBsAAABQ7W2Qa3edmppblJKcJEfuUGVnpkW7WQAAADABwi0AABA1LnetypxubffUd9pmy0lXUaFVDmtGFFoGAAAAs+CxRAAAEBXrKmtUUlrhN9iSpO2eepWUVujtypoItwwAAABmQrgFAAAizuWu1ZNrtskwut/PMKSla7bJ5a6NTMMAAABgOjyWCAAAIq7M6e4x2PIxDKnc6daQwQOpywUAAIBOCLcAAEBEVXsbunwUsStVnnrd/teNnV6nLhcAAAAItxCTWDULAOKXa3ddyM7lq8tVPD1PU/OzQnZeAAAAmAfhFmIKq2YBQPxram4J6fl8dbmGDUnhdwQAAEACoqA8YgarZgFAYkhJDv13a766XAAAAEg8hFuICayaBQCJw5E7NCznrfLUq9rbEJZzAwAAIHYRbiEmBLNqFgDAnLIz02TLSQ/LuUNZzwsAAADmQLiFqAt21Sy+nQcA8yoqtMpiCf15Q13PCwAAALGPcAtRF+y37Hw7DwDm5bBmaM70vJAHXOGo5wUAAIDYxhUgoi7Yb9n5dh4AzG1afpaGD0lRudOtqgBn8HYlXPW8AAAAELsItxB1wX7LzrfzAGB+DmuGHNYMVXsb5Npdp6bmFqUkJ8mRO1TLXt0e0GPr9px0ZWemhbG1AAAAiEWkA4i6YL9l59t5AIgf2ZlpnYKpokKrSkorerXgiMUizSi0hqdxAAAAiGnU3ELUBbNqFt/OA0D8621dLotFKp6eJ4c1IzINAwAAQEwh3EJMCGTVLL6dB4DEMS0/S/NmjpO9iy9B7DnpmjdznKbmZ0W4ZQAAAIgVPJaImOD7dv7JNdu6ffyEb+cBIPF0V5eLWbwAAAAg3ELM6GnVLHtOumYUWgm2ACBB+avLBQAAABBuIabw7TwAAAAAAAgE4RZiEt/OA31HSAwAAAAgERBuAUCccblrVeZ0a7ufx3ttOekq4vFeAAAAAHGEcAsA4si6yppuF2bY7qlXSWmFiqfnJeTqcsxmAwAAAOIP4RYAxAmXu7bHFUclyTCkpWu2adiQlISZwcVsNgAAACB+9Yt2AwAAoVHmdPcYbPkYhlTudIe1PbFiXWWNSkor/AZb0v9ms71dWRPhlgEAAAAIBcItAIgD1d6GLsObrlR56lXtbQhTi2KDy12rpS/3fjaby10bmYYBAAAACBnCLQCIA67ddRE9ziyWvVLV630TaTYbAAAAEE8ItwAgDjQ1t0T0ODNYV1mtvXUHAjomEWazAQAAAPGGcAsA4kBKcnDrgwR7nBm89O5nQR0X77PZAAAAgHgTv3c1AJBAHLlDI3pcrKv2NshbH9isLZ9wzWar9jbItbtOTc0tSklOkiN3qLIz08LyXgAAAEAiIdwCgDiQnZkmW056QEXl7TnpcRuu9GX2Vahns7nctSpzuv3+bGw56SoqtMphzQjpewIAAACJhMcSASBOFBVaZbH0bl+LRZpRaA1re6KpL7OvQjmbbV1ljUpKK7oMHbd76lVSWqG3K2tC9p4AAABAoiHcAoA44bBmaM70vB4DLotFKp6eF9ezhYKdfXVE+qCQzWZzuWv15JptMozu9zMM6YmXt2ldZXVI3hcAAABINDyWCABxZFp+loYPSVG5060qP7OF7DnpmpEAj8EFO/vqrBOPDlkbypzuHoOtr1v6cpXWf7SXxxQBAACAABFuAUCccVgz5LBmJHQB82BqkB2ZMUjT8rND8v7V3oaA3tvH95hi8fQ8Tc3PCklbAAAAgHhHuAUAcSo7My1hwix/igqtKimt6NXsKYukS860h+y9+1LQ3jCkpWu2adiQFGZwAQAAAL1AzS0AQFwKqAbZD0Nbg6wvBe2lwwFXudMdmsYgJlR7G7R2k0flzl1au8mjam9DtJsEAAAQN5i5BQCIW9GqQRZsQfuvq/LUq9rbkNCz7+KBy12rMqfb72Oqtpx0aqwBAACEAOEWACCuRaMGWbAF7b/JtbuOcMvE1lXWdLtiJjXWAAAAQoNwCwCQECJZgyyYgvb+9PXxRkSPy13bbbDlQ401AACAvqPmFgAAYVBUaO2x3ldPQvF4I6KjzOnu1WIGEjXWAAAA+opwCwCAMOhtQftuzxGixxsRWdXehoBn7flqrAEAACBwhFsAAITJtPwszZs5Tvac9ICPteekU2/LpFy76yJ6HAAAQKLjeQcAAMLIV9B+XWW1lr5c1atjLBZpRqE1vA1D2ARbK40aawAAAMEh3AIAIAKm5WdLsvRYZNxikYqn51Fc3MSCrZVGjTUAAIDgcBUFAECETMvP0vAhKSp3ulXlpyaTPSddMwqtBFsmF2ytNGqsAQAABIdwCwCACPI9pljtbZBrd52amluUkpwkR+5QamzFiezMNNly0gMqKk+NNQAAgOARbgGICwQFMJvszDT6aBwrKrSqpLSi20dQfaixBgAA0DeEW0AACFBij8tdqzKn2+8MCVtOuop4xAtAFDisGZozPY8aawAAABFAuAX0AgFKbFpXWdPtjeN2T71KSitUPD1PU/OzIts4AAmPGmsAAACRQbgF9IAAJTa53LU9zoiQJMOQlq7ZpmFDUriBBBBx1FgDAAAIP8ItoBsEKLGrzOnuVS0b6fDPp9zp5mcDIGqosQYAABA+/aLdgFCrr6/XySefLLvdHu2mIA4EE6Ag/Kq9DQGtQiZJVZ56VXsbwtQiAAAAAEC0xF24ddddd8nr9Ua7GYgDBCixy7W7LqLHAQAAAABiV1yFWy+++KJWr14d7WYgThCgxK6m5paIHgcAAAAAiF1xE27t3btXCxcuVEFBgfr37x/t5iAOEKDErpTk4MoFBnscAAAAACB2xU24deutt6q5uVmLFi2KdlMQJwhQYpcjd2hEjwMAAAAAxK64CLf+9re/6e2339b8+fOVm5sb7eYgThCgxK7szDTZctIDOsaek85KZQAAAAAQh0wfbn322Wf63e9+pylTpmjWrFnRbg7iiNkClGpvg9Zu8qjcuUtrN3nivrB9UaFVFkvv9rVYpBmF1rC2BwAAAAAQHRbDMIxoNyJYra2tmjVrlrZv364XX3xRWVlZkiSHw6HW1lZVVVVFuYUwu8rtXt3+yHr15l+JxSItnHuS8m2Z4W/Y11Ru9+rptVXaunNfp21jjhmmi75vj3ibIuXVDbu1+NmKbn8+Fot03fnj9P3JzOoEAAAAgHhk6plbjz32mD744AMtWLCgPdgCQinflqlrzx/X4wwhX4AS6RDp1Q27dfsj6/0GW5K0dec+3f7Ieq3dsDui7YqUMyfnauHckzT22GF+t489dpgWzj2JYAsAAAAA4phpZ25t27ZN5513nk466SQ98sgjHbZFYubWwYMt+vLLA2E7f19kZn5LkuT1/jfKLYkfLnetyp1uVXnqO22z56RrRqFVDmtGxNtUUtr9rCUfi0WaN3OcHNaMuO0f1d4GuXbXqam5RSnJSXLkDqXGVpDitY8gNOgf6Al9BN2hf6An9BF0h/4R34YMGaSBA4NboM20y7r98Y9/1KFDh9TS0qL58+d32NbW1iZJ7a/fcsstysiIbPCA+OKwZshhzYipAKXM6e5VsCVJhiGVO90RD+AiKTszjTALAAAAABKQacOtxsZGSZLT6exyn/LycknSL37xC8IthESsBCjV3gZt9zOLrDtVnnpVexvav+1AbIml4BQAAAAAzMS04dayZcu63EZBecQ71+66oI8b5xgZ4tagL1zuWpU53X7DSltOuoqi8MgrAAAAAJiJqQvKA4mqqbkloschPNZV1qiktKLLWXjbPfUqKa3Q25U1EW4ZAAAAAJgH4RZgQinJwU26DPY4hJ7LXasn12zrsW6aYUhL12yTy10bmYYBAAAAgMkQbgEm5MgdGtHjEHrBLAgAAAAAAOgsLsMtl8tFvS3EtezMNNly0gM6xp6TToHyGNGXBQEAAAAAAB3FZbgFJIKiQqsslt7ta7FIMwqtYW0Peq8vCwIAAAAAADoi3AJMymHN0JzpeT0GXBaLVDw9jxX3YggLAgAAAABA6FBdGjCxaflZGj4kReVOt6r8POZmz0nXjEIrwVaMYUEAAAAAAAgd7pQAk3NYM+SwZqja2yDX7jo1NbcoJTlJjtyh1NiKUSwIAAAAAAChQ7gFxInszDTCLJPwLQgQSFF5FgQAAAAAAP8ItwAktGjNeCsqtKqktEKG0fO+LAgAAAAAAF0j3AKQkFzuWpU53X5nT9ly0lUU5lplvgUBnlyzrduAiwUBAAAAAKB7hFsAEs66yppuQ6XtnnqVlFaoeHqepuZnha0dLAgAAAAAAH1HuAUgobjctT3OlpIkw5CWrtmmYUNSwj6DiwUBAAAAACB4hFsAEkqZ092rOlfS4YCr3OmOyMwpFgQAAAAAgOD0i3YDACBSqr0NAa1QKElVnnpVexvC1CIAAAAAQF8RbgFIGK7ddRE9DgAAAAAQfoRbABJGU3NLRI8DAAAAAIQf4RaAhJGSHFyZwWCPAwAAAACEH+EWgIThyB0a0eMAAAAAAOFHuAUgYWRnpsmWkx7QMfacdFYxBAAAAIAYxrM2ABJKUaFVJaUVMoye97VYpBmF1rC3yayqvQ1y7a5TU3OLUpKT5MgdShAIAAAAIOIItwAkFIc1Q3Om5+nJNdu6DbgsFql4ep4c1ozINc4kXO5alTnd2u6p77TNlpOuokIrf28AAAAAIoZwC0DCmZafpeFDUlTudKvKT0Bjz0nXDAIav9ZV1nQbDG731KuktELF0/M0NT8rso0DQoiZiQAAAOZBuAUgITmsGXJYM4K+gU3EG1+Xu7bHGW+SZBjS0jXbNGxICgEhTIeZiQAAAOZDuAUgoWVnpgUUSiXyjW+Z092rWmXS4YCr3OmO278LxCdmJgIAAJgTqyUCQC+tq6xRSWmF32BL+t+N79uVNRFuWfhVexu6/NxdqfLUq9rbEKYWAaEV6MxEl7s2Mg0DAABAjwi3AKAXEv3G17W7LqL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\n",
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