2463 lines
2.3 MiB
2463 lines
2.3 MiB
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "e268ad08",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"\n",
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"<style>\n",
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".output_png {\n",
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" display: table-cell;\n",
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" text-align: center;\n",
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" vertical-align: middle;\n",
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"}\n",
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"</style>\n"
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],
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"text/plain": [
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"<IPython.core.display.HTML object>"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"from IPython.core.display import HTML\n",
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"\n",
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"HTML(\n",
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" \"\"\"\n",
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"<style>\n",
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".output_png {\n",
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" display: table-cell;\n",
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" text-align: center;\n",
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" vertical-align: middle;\n",
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"}\n",
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"</style>\n",
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"\"\"\"\n",
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")\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "58fa497c",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import seaborn as sns\n",
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"\n",
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"plt.rcParams[\"figure.figsize\"] = (8, 8)\n",
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"sns.set_theme()\n",
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"sns.set_context(\"talk\")\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "51539fa1",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# A second partitionning-based algorithm: Gaussian Mixture Models\n",
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"\n",
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"## Outline\n",
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"\n",
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"- Recap of Kmeans and limitations\n",
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"- Derivation of GMM in 1D\n",
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"- Implementation in scikit-learn\n",
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"- Parameter selection"
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]
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},
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{
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"cell_type": "markdown",
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"id": "48cd7431",
|
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"metadata": {
|
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"## Kmeans: recap and limitations\n",
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"\n",
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"### Recap\n",
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"On a simple 1D example, present how the Kmeans algorithm works\n",
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"- Training\n",
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"- Inference"
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]
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},
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{
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"cell_type": "markdown",
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"id": "eaf998b0",
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"source": [
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"### Exercise\n",
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"\n",
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"Build a 2D toy example containing 2 natural clusters (coming from two multi-variate Gaussian distributions). The clusters should have different scale (one very dense and one more spread out). Each cluster contains 500 points.\n",
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"\n",
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"_Use the code from the Agglomerative clustering slides as a starting point_."
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]
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},
|
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{
|
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"cell_type": "code",
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"execution_count": 3,
|
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"id": "d02121b3",
|
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"metadata": {
|
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"slideshow": {
|
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"slide_type": "subslide"
|
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}
|
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},
|
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"outputs": [
|
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{
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"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([4.5, 4.5])]\n",
|
|
"covariance = [np.array([[0.1, 0], [0, 0.1]]), np.array([[2, 0], [0, 2]])]\n",
|
|
"n_points = 500\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance[i], size=n_points)\n",
|
|
" for i in range(2)\n",
|
|
"]\n",
|
|
"data = np.r_[data[0], data[1]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1])\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ac0dab3e",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Exercise\n",
|
|
"\n",
|
|
"- Build a 2D toy example containing 2 natural clusters (coming from two multi-variate gaussian distributions). The clusters should have different scale (one very dense and one more spread out). Each cluster contains 500 points.\n",
|
|
"\n",
|
|
"- __Try to cluster these points using Kmeans? What do you observe?__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "bd1dfe95",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"from sklearn.cluster import KMeans\n",
|
|
"\n",
|
|
"km = KMeans(n_clusters=2)\n",
|
|
"clusters = km.fit_predict(data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1f829a11",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Exercise\n",
|
|
"\n",
|
|
"- Build a 2D toy example containing 2 natural clusters (coming from two multi-variate gaussian distributions). The clusters should have different scale (one very dense and one more spread out). Each cluster contains 500 points.\n",
|
|
"\n",
|
|
"- Try to cluster these points using Kmeans? What do you observe?\n",
|
|
"\n",
|
|
"- __Can we solve the problem by normalizing the data?__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "6aa5c368",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"from sklearn.preprocessing import StandardScaler\n",
|
|
"\n",
|
|
"ss = StandardScaler()\n",
|
|
"data_scaled = ss.fit_transform(data)\n",
|
|
"\n",
|
|
"km = KMeans(n_clusters=2)\n",
|
|
"clusters = km.fit_predict(data_scaled)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data_scaled[:, 0], y=data_scaled[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "520d81fb",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "slide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Gaussian Mixture Models\n",
|
|
"\n",
|
|
"Derivation on a 1D example"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "47e24912",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x144 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [1, 4.5]\n",
|
|
"scale = [0.1, 1.5]\n",
|
|
"n_points = 50\n",
|
|
"\n",
|
|
"data1D = [\n",
|
|
" np.random.normal(loc=means[i], scale=scale[i], size=n_points) for i in range(2)\n",
|
|
"]\n",
|
|
"data1D = np.r_[data1D[0], data1D[1]]\n",
|
|
"labels = [0] * n_points + [1] * n_points\n",
|
|
"\n",
|
|
"plt.figure(figsize=(8, 2))\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "be07984f",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"Let's suppose we manage to find the true cluster centers (using KMeans for example). Then, the decision boundary is:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "e4ab9fe2",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x144 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(8, 2))\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"\n",
|
|
"plt.scatter([1, 4.5], [0, 0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"plt.axvline(x=2.75, color=\"k\", linestyle=\"--\")\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b4bbef06",
|
|
"metadata": {},
|
|
"source": [
|
|
"Does not allow to properly cluster the points. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "aa7b582b",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"Now if we also have access to the true variances of the distributions of the centers:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "ce7d1263",
|
|
"metadata": {
|
|
"scrolled": true,
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import scipy.stats as stats\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b8fd29f9",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Question: In which cluster should we place the black point ?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"id": "4c49e48a",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
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"\n",
|
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"x = np.linspace(-1, 9, 1000)\n",
|
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"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
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"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
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"\n",
|
|
"plt.scatter([2], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "87da1c72",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can correctly classify a point $x$ (cluster with maximum likelihood)\n",
|
|
" - Likelihood: $p(x|C_k) = \\frac{1}{\\sqrt{2\\pi\\sigma_k^2}} \\exp \\left(\\frac{||x - \\mu_k||^2}{2\\sigma_k^2}\\right)$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "9d11296f",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Question: In which cluster should we place the black point ?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "87e7c92c",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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+/Xpcc801IY9dvXo12tvb8Yc//AFlZWUAgIkTJ2LmzJlYtWoVHn/88fhKT2kVagCc6K2pawxzIqKUiKnPXJZl5OXlwWAwDLrf5s2bMWXKFH+QA0BhYSFmzJiBTZs2xfLUlEHUEFPTfOGucAAcEVFKhK2Z+2iaBk3T0NzcjPXr1+Po0aN4+OGHQ+7f09OD+vp6XH311QMeq62txVtvvYXm5mYUFxfHVHBBAGw2S0zHZiNZlgBk1msWvKFtsRj7lMts9rytZFnKqPJm4jXMNryG8eM1jN+5eA37rc01QMRhfu+99+Ldd98FAOTm5uLnP/85rrzyypD72+126LoOm8024LGCggIAQFtbW8xhTunna0aX2WdORJRWEYf5Qw89hNtvvx1NTU146623cO+99+Lpp5/GN7/5zUGPE8J9nYiRrgN2uyMp585Evm+gmfSanU4FAOB2q33KpXmXcXU43BlV3ky8htmG1zB+vIbxOxevYXFx7qC184jDvLq6GtXV1QCAq666CnfccQeeeOIJzJkzxz/gKZDNZoMgCGhraxvwmG+br4ZO2UnVw60Axz5zIqJUiHnRmAsvvBB2ux0tLS1BHzebzaiurkZdXd2Ax+rq6lBUVMQm9iwXfgU4NrMTEaVCTGGu6zp27tyJ/Pz8QWvXs2bNwrZt23DmzBn/tra2NmzduhWzZ8+O5akpg4SemsYwJyJKpbDN7A888AAqKytxwQUXoLCwEGfOnMGGDRvw4Ycf4tFHH4Use06xcOFC7Ny5E/v37/cfu2jRIvzpT3/C4sWLceedd0KWZaxatQqyLOOOO+5I3quilNBCLOcqcQU4IqKUChvmF198Md58802sX78eHR0dyMvLw/jx47Fq1SpcddVVgx5bUlKCdevWYenSpXj44Yeh6zomTZqEV199FRUVFQl7EZQein+eef/lXHnXNCKiVAob5gsWLMCCBQvCnmjt2rVBtw8fPhyrVq2KvmSU8TT/2uzBm9k1DoAjIkoJ3jWNYhb6fubsMyciSiWGOcUsZJhLvuVcGeZERKnAMKeY+Qa4hRoAxxutEBGlBsOcYtZ7C9S+byP/ojEczU5ElBIMc4pZ+D5zDoAjIkoFhjnFLOQtULkCHBFRSjHMKWa+mnf/PnOuAEdElFoMc4qJpuvw3mcl9C1Q2WdORJQSDHOKSeBI9f41c5l3TSMiSimGOcUksNbdfzS7yKlpREQpxTCnmAT2h3MFOCKi9GKYU0wCm9C5AhwRUXoxzCkmgU3oA6amcdEYIqKUYphTTNRBBsBxOVciotRimFNMIukz90xfY6ATESUbw5xi0jfM+63NHtDszkFwRETJxzCnmAxWMw9sdmeYExElH8OcYqKqvaPZQy0a49mPYU5ElGwMc4pJJH3mnv24ChwRUbIxzCkm2mBhHtBnzhHtRETJxzCnmKiDzDNnnzkRUWoxzCkmfeaZC6Gb2bkKHBFR8jHMKSa+vnBJFCAMCPPAAXDsMyciSjaGOcXE1xfev7+8/zb2mRMRJR/DnGLim3LWf1oawEVjiIhSjWFOMVEjrJkzzImIko9hTjEZPMzFAfsREVHyMMwpJv4+c2ngW6hPzZwD4IiIko5hTjFRvKPZ+09LAzz96L6trJkTESUfw5xi4m9mlwaGeeB2hjkRUfIxzCkmg01NA3pHuTPMiYiSj2FOMfFNTQsV5r5BcLxrGhFR8jHMKSa+GneweeZAb8jzrmlERMnHMKeY9C7nGvwt5AtzrgBHRJR8DHOKicYBcEREGYNhTjHxj2YPMjUNCGxmZ5gTESUbw5xiEnZqmn8AHPvMiYiSTQ63w/bt2/HHP/4Ru3fvRkNDA2w2GyZMmIC7774btbW1gx67YsUKrFy5csD2kpISfPDBB7GXmtIu8gFwrJkTESVb2DD/7W9/i7a2Ntx6660YNWoUmpqa8NJLL+HGG2/E2rVrMXHixLBP8vLLL8Nqtfp/NxgMcRWa0s/XZy6HGQDHMCciSr6wYf7jH/8YxcXFfbZNnToVM2fOxOrVq7FixYqwTzJ+/Hjk5+fHXkrKOIPdAhXgADgiolQK22feP8gBID8/H8OGDUNDQ0NSCkWZr3dqGleAIyJKt7A182BaWlpw4MABXHPNNRHtP2fOHDQ3N6O4uBjTp0/HfffdF/RLQjQEAbDZLHGdI5vIsgQgc16z5C2P2SQHLZPJ6HlrGQxSxpQ5065hNuI1jB+vYfzOxWsYYuKQX9Rhrus6Hn30UWiahkWLFg26b3V1Ne6//36MHTsWBoMBu3btwksvvYTt27fjjTfegM1mi/bpKUP4RqkHuwUq0FtjVzianYgo6aIO82eeeQabN2/GU089hVGjRg2679y5c/v8fvnll2PixIm47bbbsG7dOixZsiTap/fTdcBud8R8fLbxfQPNlNfc41QAAKqiBi2Trnua1x0Od8aUOdOuYTbiNYwfr2H8zsVrWFycO2jtPKp55suXL8eaNWvwyCOP4IYbboipQFdccQVKS0uxZ8+emI6nzKD455mHqJkL7DMnIkqViMP8F7/4BV544QU89NBDuOWWW+J6Ul3XIYaY0kTZIdwtUH0hz7umERElX0SJunLlSjz//PO45557cPvtt8f1hO+//z6amppw0UUXxXUeSi9/nznvmkZElHZh+8zXrFmDFStWYMaMGZgyZUqf5nGj0Yhx48YBABYuXIidO3di//79/sfnzp2LuXPnYsSIEZBlGbt378bq1asxbNgw3HzzzYl/NZQyqh7ufuZsZiciSpWwYb5161b/376ffSorK7Fly5aQx44cORKvvfYaGhsboSgKysvLMW/ePCxZsoSLyGS5sIvGMMyJiFImbJivXbs2ohMF22/ZsmXRl4iyQvg+c4Y5EVGqcBQaxUQNF+a+u6YxzImIko5hTjHxL+caYmqafzlXLhpDRJR0DHOKif8WqCFWMWCfORFR6jDMKSb+ZnaJfeZEROnGMKeYhB0A592uMcyJiJKOYU4x8U1NCzsAjn3mRERJxzCnmPSOZh/8rmlsZiciSj6GOcXEP5qdi8YQEaUdw5xiooUbAMcwJyJKGYY5xSTs1DSJi8YQEaUKw5xiEnZqGheNISJKGYY5xSTccq4im9mJiFKGYU4x6Z2axtHsRETpxjCnqOm6Dk0PcwtUrgBHRJQyDHOKWmBAh1s0hivAERElH8OcoqZFFOa+mjkHwBERJRvDnKLWp2YedjQ7a+ZERMnGMKeo9W1mDzEAjn3mREQpwzCnqAUGdMgBcEJvmOs6A52IKJkY5hS1wD5zOeRo9t63lsYwJyJKKoY5RS1wVbeQNfOA7ew3JyJKLoY5RS2SqWmBIc9+cyKi5GKYU9Qim2fOMCciShWGOUWt79S0UKPZe7czzImIkothTlELHAAX6haogQPjuAocEVFyMcwpakrAqm6hFo3p02fO26ASESUVw5yiFs1yrgCb2YmIko1hTlELnGoWMswD+swVhjkRUVIxzClqqu/2p4IAIUSfucQ+cyKilGGYU9R8NfNQC8YA/ZvZ2WdORJRMDHOKmq+mHWrwG8AV4IiIUolhTlHz1bSlEE3sAFeAIyJKJYY5RU2NtmbOMCciSiqGOUXNF86D9ZkLguAPdPaZExElF8OcoubrAw91+1Mff5izz5yIKKkY5hQ13/3JB6uZBz7OqWlERMklh9th+/bt+OMf/4jdu3ejoaEBNpsNEyZMwN13343a2tqwT1BfX4+nn34aO3bsgKZpuOSSS/CDH/wANTU1CXkBlHq+5VklcfDvgr3N7AxzIqJkClsz/+1vf4uTJ0/i1ltvxa9//Wv88Ic/xMmTJ3HjjTdiz549gx7b3NyM+fPn48SJE1i6dCmWLVsGu92OBQsWoKGhIVGvgVIskgFwnsc9by+FfeZEREkVtmb+4x//GMXFxX22TZ06FTNnzsTq1auxYsWKkMeuXr0a7e3t+MMf/oCysjIAwMSJEzFz5kysWrUKjz/+eJzFp3Twh/kgU9OA3po5m9mJiJIrbM28f5ADQH5+PoYNGxa2dr1582ZMmTLFH+QAUFhYiBkzZmDTpk0xFJcyQSSLxgAcAEdElCpha+bBtLS04MCBA7jmmmtC7tPT04P6+npcffXVAx6rra3FW2+9hebm5qBfFiIhCIDNZonp2GwkyxKAzHjNstFTFqNBGrQ8Bm+ZjSY5M8qdQdcwW/Eaxo/XMH7n4jUM0xAa/Wh2Xdfx6KOPQtM0LFq0KOR+drsduq7DZrMNeKygoAAA0NbWFu3TUwbQVF/NPMwAOIkD4IiIUiHqmvkzzzyDzZs346mnnsKoUaPC7h/qrlrx0nXAbnck5dyZyPcNNBNec5fDBQDQNX3w8ngzvLPLlRHlzqRrmK14DePHaxi/c/EaFhfnDlo7j6pmvnz5cqxZswaPPPIIbrjhhkH3tdlsEAQhaO3bt81XQ6fs4usDD3Uvc5/emjlHsxMRJVPEYf6LX/wCL7zwAh566CHccsstYfc3m82orq5GXV3dgMfq6upQVFQUc385pZd/NHuYMJc5AI6IKCUiCvOVK1fi+eefxz333IPbb7894pPPmjUL27Ztw5kzZ/zb2trasHXrVsyePTv60lJGiGRt9sDHOTWNiCi5wob5mjVrsGLFCsyYMQNTpkzBnj17/H/27t3r32/hwoUDVoRbtGgR8vLysHjxYmzevBl/+9vf8L3vfQ+yLOOOO+5I/KuhlOhdNCayFeAUhjkRUVKFHQC3detW/9++n30qKyuxZcuWkMeWlJRg3bp1WLp0KR5++GHouo5Jkybh1VdfRUVFRZxFp3TxLeca9kYr3rBnnzkRUXKFDfO1a9dGdKJQ+w0fPhyrVq2KrlSU0SLtM+cKcEREqcG7plHUIl6bnQPgiIhSgmFOUeutmfOuaUREmYBhTlHz9ZmHG83OPnMiotRgmFPUIu0zFwXWzImIUoFhTlGL/H7mDHMiolRgmFPUfM3s4frMuQIcEVFqMMwpar6pZuHmmXMFOCKi1GCYU9QiXc7VV3NnMzsRUXIxzClqSpR95gpHsxMRJRXDnKLWewvUCOeZs8+ciCipGOYUNd+8cS7nSkSUGRjmFDUt2uVcGeZEREnFMKeo+eeZC1wBjogoEzDMKWqRLhrDFeCIiFKDYU5Ri3TRGK4AR0SUGgxzilqka7NzBTgiotRgmFPUIl+b3fP24mh2IqLkYphT1KK/axoHwBERJRPDnKIW8aIx/hXgWDMnIkomhjlFRdd1aHpkNXOuAEdElBoMc4pK4Mj0SBeNYZ85EVFyMcwpKn3CPOza7LxrGhFRKjDMKSqBTeZhm9klDoAjIkoFhjlFJTCYI+4zZ82ciCipGOYUlVj6zHUd/kFzRESUeAxzioqmRdHMHtCnzhHtRETJwzCnqCjRDIALqLmz35yIKHkY5hQV301WgMjvmgZwehoRUTIxzCkqgX3mYoSj2QGuAkdElEwMc4pKYN+3HOFo9v7HERFRYjHMKSqBo9LDLxrDZnYiolRgmFNU+iwaE3ZqWsBodg6AIyJKGoY5RSUwlKPpM+fCMUREycMwp6j4BrIJQt/R6sGwz5yIKDUY5hSVSO9l7tmHNXMiolRgmFNUfAPZwvWXA/37zBnmRETJwjCnqPj6zMNNSwO4AhwRUarIkezU0NCAl156CV988QX27duH7u5uvPLKK5g8eXLYY1esWIGVK1cO2F5SUoIPPvgg+hJTWvlq2OHWZQf6DpDj1DQiouSJKMyPHTuGt99+G+PGjcNll12GLVu2RP1EL7/8MqxWq/93g8EQ9Tko/Xx95uFGsgOeAXKC4LlrGleAIyJKnojC/NJLL8X27dsBAJs3b44pzMePH4/8/Pyoj6PMonibyyMZAOfbT1E1jmYnIkqiiD6RxQg/uOnsF80AuMD92MxORJQ8EdXME2HOnDlobm5GcXExpk+fjvvuuw/FxcUxn08QAJvNksASZjZZlgCk/zUbjZ63jNEgRVQWWRTgBGAyy2kve6Zcw2zGaxg/XsP4nYvXMMyyHskP8+rqatx///0YO3YsDAYDdu3ahZdeegnbt2/HG2+8AZvNluwiUAIpUQyAAwBJ8rTqcGoaEVHyJD3M586d2+f3yy+/HBMnTsRtt92GdevWYcmSJTGdV9cBu92RgBJmB9830HS/5q4ul//nSMriy/yODmfay54p1zCb8RrGj9cwfufiNSwuzh20dp6WzvArrrgCpaWl2LNnTzqenuKg+gfARVgz9+7HmjkRUfKkbWSbruscWJeFopln7tnP18zORWOIiJIlLWn6/vvvo6mpCRdddFE6np7i0Ls2e3Sj2VkzJyJKnoj7zN955x0AwGeffQYA+Oijj9Da2gqLxYJp06YBABYuXIidO3di//79/uPmzp2LuXPnYsSIEZBlGbt378bq1asxbNgw3HzzzYl8LZQC/pq5FOk8c4Y5EVGyRRzm99xzT5/fV6xYAQCorKwcdBGZkSNH4rXXXkNjYyMURUF5eTnmzZuHJUuWcBGZLBRtn7lvpTguGkNElDwRh3lgbTuUtWvXDti2bNmy6EpEGS3qZnb2mRMRJR1HoFFUVJ195kREmYZhTlHx18wj7TMXuJwrEVGyMcwpKlHPM2fNnIgo6RjmFJWY55lzABwRUdIwzCkq0Q+AY82ciCjZGOYUFf8tUCO+n7kvzDmanYgoWRjmFBU1xvuZs2ZORJQ8DHOKihLrjVbYZ05ElDQMc4pK79S0KFeAY82ciChpGOYUFV8oyxH3mXMFOCKiZGOYU1RU1dvMzj5zIqKMwTCnqChqlKPZuQIcEVHSMcwpKr4BcDJr5kREGYNhTlHxDYCTI76fuW8FOPaZExElC8OcoqJE22fO0exEREnHMKeo+EezR1wzZ5gTESUbw5yi4q+Z865pREQZg2FOUVFi7jNnmBMRJQvDnKKiRjmanSvAERElH8OcotK7nCvvmkZElCkY5hQxTdcDlnNlnzkRUaZgmFPEAvu9o62ZcwU4IqLkYZhTxJSAhV8iXgGOfeZEREnHMKeIBQZy1HdN4wpwRERJwzCniAUGMleAIyLKHAxzipgS0GfOFeCIiDIHw5wipgRML+MKcEREmYNhThGLrWbOFeCIiJKNYU4RU2MYze5bAU7Tdeg6A52IKBkY5hSxwKbyaOeZ9z+eiIgSh2FOEYtpnrnEMCciSjaGOUUssM9cFCIL88D56Ow3JyJKDoY5RczXZy5LAoQIw1wMaGbX2GdORJQUDHOKmBLlHdOAfn3mXAWOiCgpGOYUMf+9zCOcYw707TNX2MxORJQUDHOKmC+MI51jDgCGgH0V3tOciCgpIvpUbmhowJNPPol/+7d/w8UXX4za2lrs2LEj4iepr6/HkiVLMGnSJFx88cX47ne/i4MHD8ZcaEoP32j2SNdl9+wbEOasmRMRJUVEYX7s2DG8/fbbsFqtuOyyy6J6gubmZsyfPx8nTpzA0qVLsWzZMtjtdixYsAANDQ0xFZrSwze1LNI7pgGAIbCZXWHNnIgoGeRIdrr00kuxfft2AMDmzZuxZcuWiJ9g9erVaG9vxx/+8AeUlZUBACZOnIiZM2di1apVePzxx2MoNqVDLDVzuU/NnGFORJQMEVWxxChqYv1t3rwZU6ZM8Qc5ABQWFmLGjBnYtGlTzOel1FNj6DNnmBMRJV9ENfNY9fT0oL6+HldfffWAx2pra/HWW2+hubkZxcXFUZ9bEACbzZKIYmYFWZYApPc1y0ZPGUxGKapyiKIATdNhMhvSW/4MuIbZjtcwfryG8TsXr2G4pT2SOprdbrdD13XYbLYBjxUUFAAA2traklkESiDFv2hMdG8b34h2N/vMiYiSIqk1c59IVwuLhq4Ddrsj4efNVL5voOl8zV1dLs8Puh5VOWRJgNMN2Nt70lr+TLiG2Y7XMH68hvE7F69hcXHuoLXzpNbMbTYbBEEIWvv2bfPV0CnzxbICXOD+7DMnIkqOpIa52WxGdXU16urqBjxWV1eHoqKimPrLKT38zexRrAAH9E5P4zxzIqLkSPoKcLNmzcK2bdtw5swZ/7a2tjZs3boVs2fPTvbTUwL5w1yO7m0js2ZORJRUEfeZv/POOwCAzz77DADw0UcfobW1FRaLBdOmTQMALFy4EDt37sT+/fv9xy1atAh/+tOfsHjxYtx5552QZRmrVq2CLMu44447EvlaKMl8YWyIspndF/5uhjkRUVJEHOb33HNPn99XrFgBAKisrBx0EZmSkhKsW7cOS5cuxcMPPwxd1zFp0iS8+uqrqKioiLHYlA6+0ejRjmb3rRjH+5kTESVHxGEeWNsOZe3atUG3Dx8+HKtWrYq8VJSR3N4wNkTbzC4L3uNZMyciSgbeNY0ipsRYM/c1y3NtdiKi5GCYU8R6B8BFN5qdU9OIiJKLYU4Ri3UAnL9mzj5zIqKkYJhTxGIeAOefZ86aORFRMjDMKWK+AWzRD4Dj1DQiomRimFPElBhugQoETk1jmBMRJQPDnCLmG40ee82cfeZERMnAMKeIuf23QI1uNLu/z5xT04iIkoJhThGLfQAcp6YRESUTw5wipsQ6AI5hTkSUVAxziljs88x5C1QiomRimFNEdF2PfTQ7p6YRESUVw5wiEthEHvX9zDk1jYgoqRjmFBG30ttEHvv9zNnMTkSUDAxzikhcNXNOTSMiSiqGOUUkMMwNUc8z52h2IqJkYphTRAIHr8V8P3OGORFRUjDMKSJuJfZmdt+8dDeb2YmIkoJhThHp28we3dvG6A1zl6JB1zkIjogo0RjmFBElcDR71DVzqfc8bGonIko4hjlFJLDPXBKjGwAXGP5saiciSjyGOUVEUXtvsiII0YW50dD7NnMxzImIEo5hThFx++9lHl2QA3372BnmRESJxzCniMR6kxUAMBh6+8zZzE5ElHgMc4qI/17mUQ5+A3pHs3vOoyasTERE5MEwp4j4mseNASPTIxU4AM7lZs2ciCjRGOYUEZfbU6M2xlAzl0QBvjFzvA0qEVHiMcwpIv6auSH6mrkgCP4avZs1cyKihGOYU0R8fd3RLhjjY/CvAsc+cyKiRGOYU0R8fd2mGGrmANdnJyJKJoY5RcTln2ce21vGyDAnIkoahjlFJJ4BcEBgMzvDnIgo0RjmFJF4BsABvTdb4TxzIqLEY5hTRHw1czazExFlHoY5RcQdd82czexERMnCMKeIJKrPnDVzIqLEY5hTROLtM/cdxz5zIqLEkyPZqaurC8uXL8c777yD9vZ21NTU4M4778TMmTMHPW7FihVYuXLlgO0lJSX44IMPYisxpUXv2uwx1swlNrMTESVLRGF+1113Ye/evXjwwQdRVVWFDRs24K677sILL7yAadOmhT3+5ZdfhtVq9f9uMBhiLzGlRbwD4AwGNrMTESVL2DB/7733sG3bNqxcuRKzZ88GAFx22WU4fvw4nn766YjCfPz48cjPz4+/tJQ2vhCOdQU4jmYnIkqesNWsTZs2IS8vr0+TuiAIuP7663H48GEcPHgwqQWkzBB3zdw7z9x3HiIiSpywNfMDBw6gpqYGotj3Q7y2thYAUFdXh5qamkHPMWfOHDQ3N6O4uBjTp0/Hfffdh+Li4jiKDQgCYLNZ4jpHNpG9YZiO16zrur+vu7DAElMZCvLNAABF09P275bOa3i24DWMH69h/M7Fa+i7jXQoYcO8ra0Nw4cPH7DdZrP5Hw+luroa999/P8aOHQuDwYBdu3bhpZdewvbt2/HGG2/4z0GZLXDQWqzN7L7jelysmRMRJVpEA+CEQb4SDPbY3Llz+/x++eWXY+LEibjtttuwbt06LFmyJLJSBqHrgN3uiPn4bOP7BpqO19zpcPt/djmVmMqgq54vBI4ed9r+3dJ5Dc8WvIbx4zWM37l4DYuLcwetnYftAC0oKAha+7bb7QAQde36iiuuQGlpKfbs2RPVcZQ+gf3csU5NMxtZMyciSpawn8w1NTU4dOgQNK3vKOS6ujoAwJgxY6J+Ul3XB/TBU+YKHIEe6wA4kzfMnRwAR0SUcGE/mWfPno329nZs2bKlz/aNGzdixIgRYQe/9ff++++jqakJF110UXQlpbQJDOBYV4Dz9Zkrqg5F5fQ0IqJECttnPm3aNEyePBmPPPII2traUFVVhY0bN+Ljjz/G888/799v4cKF2LlzJ/bv3+/fNnfuXMydOxcjRoyALMvYvXs3Vq9ejWHDhuHmm29OziuihAtsGvc1l0crcOCcy61CltgyQ0SUKGHDXBAEPP/881i2bBmWL1/uX8515cqVuOqqqwY9duTIkXjttdfQ2NgIRVFQXl6OefPmYcmSJVxEJov0uBQAgCyJMYdw4JeAHpcKq5mrABIRJUpEo9lzc3Px2GOP4bHHHgu5z9q1awdsW7ZsWewlo4zhq5nHWisHevvMAfabExElGts6KayEhLmhb82ciIgSh2FOYfU4Pc3sZmNEDTlB9e8zJyKixGGYU1j+mrkp9pq5KAr+OeqsmRMRJRbDnMJKRDM7wLnmRETJwjCnsHyj2eNpZge4PjsRUbIwzCmsRNXMzayZExElBcOcwkpYM7u3Zu5kzZyIKKEY5hRWwprZebMVIqKkYJhTWA5v+FrirJlbvF8GfF8OiIgoMRjmFFaimtktZk+Yd/cwzImIEolhTmElqpk9xxvmXQxzIqKEYphTWImqmfturtLtdMddJiIi6sUwp0Fpmu4ffW42xVczt5rYzE5ElAwMcxpUV09vLdrXTB4rNrMTESVHfJ/OdNYLDN5cS3z3IPc3szPMzyq6uwd6Vyu07jboXa3Qu+3QnV3QXd3Qnd3ev7sAtxO6pgCqG9BUQFU8vwOAKEEQJUAQAVHy/G4wQzBaAO/fgtHq+WO1QbDYIFhtEL1/w2CGIAjpvRBEacQwp0F1Onpr5vGHueftpqgaXG4VRkN8ffCUGrqmQO9ogmZvRKe7BUrraTjOnIDecQZaVyvg7knM84T5fVAGC8T8Uoh5pRC8f4v5pRDzyyDklUIQ2QhJZzeGOQ3KF+ZGWYw7fAOb6bt6FIZ5htF1DXpHE9SWr6C1fAWt5bjnb/tpQNcAAI5BzyBAsORBsBZAMOd6atEmK+CrURstgChDkGRAkgFR9tTAIUDXVUDTAO/fuqYArh7obgd0lwNwOTw/93RCd9ihddsBZ1fvU7sd0JrroTXXDyyWZIRYMBRiYQXEokpIhZUQC6sg5JWwNk9nDYY5DarLG+Y5cdbKgd5mdgDodioozDPFfU6Kja5r0OwN0BqPQG08DLX5GLSWrwavZQsS5IIhkAvLoVpLIOYPgZBTCDGn0BPgVhsEMXUfKbrqhu5oh95th9bZBK29CXpHI7T2M9A6zkDvaPZ8OVBd0JqPQWs+1vcERiukkmEQS4ZDKh0OqWQ4hPwhDHjKSgxzGpQ/zM0JCPOA0fDdPZyelkpaVyvUxsPQzhz2hPeZo4A7RD1bMnhrsVWQiqogFlZBtJVDyC1CQWEuAMBuH7yOngqCZICQWwzkFkMaMnLA47qmQu84A7X1BLSWE9BaT0JrPQGt7RSgKYCrG+rJL6Ge/BL+d6PRAqlkOKSyGkhloyGVjYJgyknp6yKKBcOcBtXpDd1cS/xvFYMswiiLcCkaR7Qnmdbd5g8q5eQ+6O2NwXc0WiENGQmpdATE4mqIRVWefmYx+7tABFGCYCuHaCsHhk/yb9c1FZr9NLSmo1DPHPX83VzvaZVwOfzXzUcsrPQEe7kn4Fl7p0zEMKdBdTo8oRvv4DefHIsBrg6nv8ZPiaF126Ge2u8PIs3eMHAnSfY2KY/wBvjIczKYBFGCVFgBqbAChtFTAAC65u12aDrqabk4fdDT/65rntp86wm49/3Nc7wlH1L5GEgVYyFVjIVYMPScu4aUeRjmNCjfALhEhXm+1YjWDifau1wJOd+5SuvpgHpyn+fPqS+htZ4cuJNs9IbO+ZArxkIsHuYZfEYDCKI4MODdPVDPHIHacADq6QNQTx/0DMRztEM58g8oR/7hOdaSD2no+f7rLNjKGe6UcvyfTYNK5AA4ALDlGoHTQFsnwzwaurMLyql9/gDXWo4P3EkyQCof7Q2WsZBKRzC84yAYzJArxkKuGAvAO2iw9STUhjrvl6h9ngF4jnYoh3dCObwTTgCCtSAg3M+HkF/GcKek4/90GlRHd2Jr5rYcIwDA3uVMyPnOVrqrG+qpOignv/SEd3M9Bsy8FmVIZaP8zb3SkJEQpMT8O9FAgiBC8g4KxLiroOs6tLZTnq4N7xctvacDencblEMfQjn0oSfcc4ogVYyFXOH5kgVbdbpfCp2FGOY0qNYOz1SlRE0js+V6zsOaeV+6y+Fpyj25D8rJL6E1HQX0/uEtQRoyCpI3FKQhoyDIxrSUlwBBEPxN87hgpifcW0/6xy2op/ZDd3ZC72qBcuADKAc+AAD02MpgHnYB1JLRnj53a0F6XwidFRjmFJLTrfpHnRflmRNyzoJcb82889yumeuK09MX6wvvM0f8C7P4CSLE0hGQK8Z6ArxsNAQD5+ZnKkEQIBVVQiqqBMbP8jTLt5yAenKv9995H+B2QLWfRtenpwFsAQCIBUN7W1cqzodozkvvC6GsxDCnkFo7egO3KD9BNfMcb838HBsApysuqI2HvLW2fVAbD3nWJw8kCBBLhvcNb6MlPQWmuAmCCKm4GlJxNXDhNzwj5puPwdB8AD3H98J5/EtAcUJrOwWt7RTce73hXlTt7W8fB2noGM5zp4gwzCmklnZPE7sgAPk5iWnO9dXMnS4VPS4FZuPZ+RbUFSfU04c8famn9kM9fcizUEkfAsTi8/yjoKWhYyAYrWkpLyWfIIqQSkcgr2Yc8iZfh7bWDmiNR7zjIr6EevoAoCreZXSPw/35Jv8XPGno+ZArx0IqHwPBkJhWMjq7nJ2fpJQQvpq5LccIWUrMjSpsub1fCto6XSgvOjvegrrb6enzPrXfU/M+c3hgzRu9tS6pYizkobWsdZ3DBFH2zD4oHw3807UDW29OHwJ0FdqZI9DOHIH7078AggRxiK/rZSykshqOmyAADHMahK9mXpSfuJpAQa4JkihA1XQ0tjpQXpSdNVHd2eX54D1VB+XUPmiNRzzrgPchQCyu8kxTGloLaWgt+0MpJEE29p0K5/uCeGIvlJP7oDV53mPa6YNwnT4I7H4zYEbDOM8XgyEjWXM/RzHMKaTmdk/NvDA3cYOuZElEaYEFDS3daGjpxoRRxQk7d7Loug7Nfgra6UP+xUOCLtIS0GwuDa2FXD4Ggjk35eWls4NgMEGuGg+5ajxM6D9d8UvPdEVN8bQGndrvPUjwtP6U1fj/CHmlnOd+DmCYU0gnmzy3mCwvTmztubzI6g/zTKS7uqGeOQr19EHPn8ZDfW+36SOIEEuGeYJ7aK2nP5PN5pQkgtEKedhEyMMmAgD0nk7vQkJfQj25H1rrCUDX/beC9Q2oEyz53pvG1EAsGwWpeBhnRZyFGOYUlK7rONHUCQCoKk1s7bK82AocBBqagwRkiunOLqhNx/w33VCbjkFvPx18Z1NOn7tpSaUj+aFIaSOYc2EYcQkMIy4B4P0S2njYu/zsQaiNhwG3d/nZox9DOfqx90DBc3/3Es9tX8XS4ZCKz2PzfJZjmFNQLe1OOJyePuCq0sTWNn395Kmsmeu6DsXeCHfTcTi/OgytqR5q09HQdxOD4L1b1ih/gAs2LstJmUswWv3N8oD35jFtJ6A2HITa6Gll0u2nPbX31pPQWk9CObDNd7Q34IdBKjnPc9vboirPfer5ns8KDPMMo6oqGhpOobKyKuJjTpz4CuXlQyFJibtt5VdnPLVySRRQluBBapXeLwdtnS60djgTtroc4AltvafDc6erlq+gtXwFteUraK0n0OnuCXGUALGgfGBNhXO8KYsJogipqBpSUTUwbgYAT9O82nQMatNRf2uU3nEGgA6t7SS0tpNQDm7vPYkpB1JhpefWuEVVni+4RVXsTspADPMMoqoqHnvsP7Bt29/x4ou/wejRtWGPOXBgPxYvvhVTpnwdTzzxVMIC/cipdgBAZUlOwqal+Qwry4PJIMHpVrH/eCsuG1ce9Tl0V7fnntT2055bVwb8DdcgNX5RglhQAbGoisFN5xzBnAu56gLIVRf4t/UPeK3lhOcWuroGOLs8N5ZpqOt3njwItjKItjKItvLev/PL2PWUJhGFeVdXF5YvX4533nkH7e3tqKmpwZ133omZM2eGPba+vh5PP/00duzYAU3TcMkll+AHP/gBampq4i782aah4RS2bfs7WltbsXjxrWED3Rfkra2t2Lbt7xHX6AVBgMHgCWi3W4Pefw1wAHuPtQIAxlQX+LcZjSKsVhNE0dPspmme43y/h9LT40ZPjwJJEmEwSNB1HTVVNnxxpAX769uChrnuckDrbILe0Qx0t0DoboXacQZK2xloHWegO9rDvUoI+UMgF1fBNGQYDKXVMA05D1JBOdo7k3cvdVEUIMu+a6sOWF59MIIAGAy+L2Oea6qqGjRN828P9u8lSSIkSYSu695/VwGKokGWPdtcLhWq2m+p2CjLoyia/99bEACjUYYoCtA0HYqi+h/rz2CQ/O8PXdf7nEeSBJhMBv85NQ1wOt3+xw0GCYIg9Dm/77klSYSqanA6+y7EE1hmt1vz/y5JIhRFhcs1cO6/wSB5y+lZDt/t9uxnMgV/nmDlCmQ2yxDF0M8Xjskk+/+fOJ0qFCX6c0TzPgwa8IrL8+XY17rlbenSO5s9j/d0eFrATh8ceL6cQoh5pRByiyHnl0DKL4WQWwTNWgQxtxiC3Bv2wa5luOsbTuC/uabpUFUNihL9+z/bCHqwT/J+vvOd72Dv3r148MEHUVVVhQ0bNuDNN9/ECy+8gGnTpoU8rrm5Gddddx2Ki4tx9913Q5IkrFq1CvX19di4cSPKy6Ovkflomo7m5s6Yj89UgQFdWFjoD3SbzVNztNsdg+43GEEArJILQncruvZ/CADIqb0curUQXUrv3bZaO5x48LkPoAO4d94ETBxdCkUQYO9yIc9ihL3TCVkSseOLUxhdXYjSAgu2f34K3U43JtWWwWqWsWt/Iy4cVYLSAgtEAcgVHFDOHEXXwV0QZBN2ttiwY089hphdmHtJEYSedmjdduhdrdA6mwevXQe+JskAyVYKQ8l50AsqgbwhEG1lMBRVINekQ9Bc6N63A0pHM0xV58NcOQZdyIHbndj/3IIA5Egu6J1N6N7/IQTJAOvYKdBM+ehWwt/JzCq7ITrboTSfgLG4Ao6jn0Fpb4Kp+nyYykei++BuKO1NsI75GpBbgm7VCFEUYBUccJ2sg2QwQsorguvMcZiHjkLPV/vgbDwGY3ElLMMvhG6woEs1QVUj+3C0ym5Irg50fbkduuKEZfSlkArLIekaHEc+gavxGAxF5TBXjYWqKBBzC9Glmv0fvhZJgax2oXvfdmg9nbAMGw8pxwZNB8TcYoiCDr2nC4JsgNbTha792wFVhfX8yyDll0JT3Oj+chu07naYR06EXFINXTRAUh1wN9bDcfQziNZc5Jw/BYqci25F9lzDHju6922HrirIOX8yJEsuOj97D7qmwDpmMqScAjh1I3pUGUZJg0V0Qnc6IMgyXI316KnfCynHhpyxl0PpaEHXvg9hLKmGddTFUEUj4HZ4XpOjA+YREyEXV6FL87xuq0GFUXfCUf8FnKcOwVBYDuuYS+GEFT1K7xfe/v+XfSwGFSbdie5Du+BuPgljaTXM1ecDxhw4VBkuNXwLWbzvw3B0l8PTHB+kVQwhu7H6ldGcBymvCJIlF7qrGxBlmCrGwFBaDdFogfPUQUBTYamZBLmo9/oGCnUNc2QXJMUBaAp66r+Au6UBxrLhMA2bAIduhjv670UZo7g4d9CKU9gwf++997B48WKsXLkSs2fPBuD5hj1//ny0tbXhL3/5S8hjn3nmGbz66qvYtGkTysrKAACtra2YOXMmvvWtb+Hxxx+P5TUBOHvDHAge1JdcMhGA580bS5ADQJ7BhZa3V6Ln6Kd9tltGTkThnDvR4fL8Z39960G8s6MeuRYDlt8zFQ2tPWhqc6C00IouhxvbPz2JbbuP4v+7dgzqj5/Brk+PIEd0wiq4YBWcGJqr42s1efhiXz3Kc3VU5SpwN3018EYiMTIPnwDT0FGwb9/g3yblFKDs5sfRLRV6XqvQhe5Du9D8f6v7PK9ozcfQ+f8Fh6kU7gT+z843uNC08WdwnujbHGk9fwoKZn3Hf22DyTW40b71fyBZ82EoLEPz5v/pW2ZLHsquvx/Nf/0fuE4fhanqfJRc/yC07jacXvdfKJq5EM4TB6B2tSFv4iw0blgGXeld+16QjRhy3T2QiqvRLdnCBnquwY32v7+Grk+3+rdZRl2M/H/6xsBzSwaUXns3uo98Btvl16NTz4FFdKHrH39Cx843+5zXUFSBkmuWQNc1dO59HwWTr0XLllfQvX9nn/1MFaNR+s0lOPHyf0D3BoRxaA3K5t6LhvX/D+6WU32v/eRrkX/pN9GyaQ26vV9S/eeqHIOi6fPR8PpT0N1OWGu/hoIpN0K3FkJtPAjZkg+IIho3LIdi7zsY0jb5Wki5hWj56/94ruEND6Bjz2Z0133k30cuKEPZv/0YmmwG7Cdx+vWnoPUEzNIQRJRedw9QcSF6FE8YBwsiq0GDfnofGt9Y1mfZX8FoQdn19wGyGUp+FZxhAn3Q9+HM76DDnZxb5Oq6Dt3RDs3eAKHjNITmI+j64j1Pc0s8RAmGkmropnzAlAPBnAvBlAtrQSFESy4cmhGCKQeCwYJcq4yeuu0wDjkPTW+uhK72tsAJshFlNz0KV1511gZ63GH+ox/9CO+88w527twJUex9I73++ut49NFH8fbbb4dsMv/nf/5njBw5Ei+88EKf7Q888AC2b9+Obdu2BT0uEmdzmAMDA/21136H888/H//4x56+Qf6rl1Ezqsaz+pimApoGXfP9rEBX3IDqhkFww/3l39D95QdBn89UPQ7ikFE41diOvQdPwQg3hhcbMCRfwlcnzqCywICujg6YBDcExYkwLesRceoyWrUcdMOKqmEVyCksgWgtgJBXjJzCAnR++Aacx/cFPbbkmiVo/+htuBqP+bfJBWUonf8EIIoQu1txYs3DQY+V8kswdOF/w+5OTD+5Wdbg+GAdOj/5a9DHC2feCqH2KriDNPUZDCJw4D20/u01lN/4ME69FvwLrpRXhJKrv4vT/7sUAFBx61NoeP0pyHnFyJ/0DTT9+VcYuvAJNLz2RJ8PMR9BNqJ8/mMQckvQoYSegiTLIsSj29H851V9tg9d8AQafvdknyDvLZyMofN/jJa/voLC6x+GevoQzvz+6aDnN583DgVTb4SuuOE6fRSt7/026H65E2ZAzitB2wf/CwAomnkLug/8Az31e4PuP+SGB9D699fhPnM86LlEgwntH78DACicPh85tZfBvvMt5NR+DS1/ew2uhsPBz3v9A2jZ+iqUttOe1/lvj+HUqz9G4L3lTRWjUTr3Xpx8+YfQHB0DTyKIqFy8HO26DUDwMLdJnfjqhe8H/cIrmKwo+5eHIOaXokMLPU00nvdhIuUbenDy1/dCdwWpqQsiimbcjJatr/pv8SvIRogmK9SutqSWC4IA65jJcIsWQDZCkAyAbIAgGQP+NgKSAYJsACSjZ6lcyQCIEgRRAnx/JLnv74KU9FH/cYf5v/7rv0IQBPzud7/rs/2TTz7Bt7/9bSxfvhxz5swZcFxPTw8mTpyIxYsX4/777+/z2Isvvohnn30W27ZtQ3FxbCuAJTLMj33yMTo+fw+CfzlOHQL03jcbdPj+8wr+y+Xbp9/j3uO8vYTe/bz764Hbei974DECNAjQIegaoClQnA4I0CGLgEEWoasKJEGHBEASfedOP0UX0aWb0KWZ0K2b0K0bMe7882A2iFD2/z3oMS1qDn7aeR26VRmCAAwvz0NxvhkGWUKOQQ35xQPw1FYNRRVwntjfZ7tlzNcgGoxwnTwEd+upEEfrsI6+FIohb+A9w2NgEFR0ffl+yJYHwWCCZfRkKPrAwYmyoMJxYCcM+cWe/tqWEyGfxzLiIvR8tQ+CIMI0tAaOY5/BXHU+3M0nIUgypPwSOE/WhTzeXDEGYm4hFDkn5OuWBRU9B/8BLaCbQ8opgKFgCHpOhD63aWgN1I4WmKrHoqf+i0E/mHPGfA2CbEDXgX9Ad4e4Fa4gIqd2Mrr2eUZWW0dfiu4DHwXfF4BktcFQWI6efu8HwHP3Msuoi9F90DPP2lBU6VldLa8QEAR0H/hHyPPKuUWQ8oo8Tb8Br1PpbOn7ms6f4i1r8OtqHDIcYulIaJoOo/fmQi6XpwYuySK0M0fgDPGFAgDM1eM87y9bRejxCXG8DxNFEAQIXU3oOfZpyH1M5SOhdndAaT8DwPO+dNsboXa1QYIKs+CGRXDDLLhgEhQYBQU5JWWQVReMmgNGrQcmzQGD1gOD2g0xxDVPNQ0iNEGEDsn7t4ge2zBU/cuDEMT4BxGHC/OwA+Da2towfPjwAdttNpv/8WDsdjt0XffvF6igoMB/bKxhLgi933Dj5frodQzTQiwUkm7976EQx/9DTQfckKHoItyQoOgS3Lrs/bl3m9Fixfk1Q2HNzcU/DtlRWVGC460KhlWVYt2Wo3DqBtx0zUX4n3cPw+4U0K2b4IYE9Ptq8f8umQJrRx0QIsyLpC7cNfRj/KbzSjS2OXHkVAeOnAqs2YwJ/WKcANr0gft81ub9Ic/7J4TP2wGEG0QXjdGhH3IC2D3Y+2sY4P9eOkh3yb4eAMM9P3e4PPse0gEM9WxrDnP8EQBo8/4ZTHXfX50AWsKc+ygAlALNTQDKvH9C+Mzu/WH44MX4pKX3OT9vH/z5nQBaBynjF529j/m/4/kuepjzBl7XowBQ6v0TWNZmDPp+PQ7geOgvaoBh8HIc9FU0BjsHEN/7MJEGeS3HAKDI+wfe92WY90zIepsOE9wwC54/JkGBWXDBLCgw+bf1/dsAFQbB+wdKwM8qDIICGSqMggpZiK4FQ4QGUdcAKP7vdIaWLwHVAVthSVTnCiZcxT+i0eyDNR+Ea1rIhgUHLJf/K47s+Rug6556tOCvS8MXULr/dfh+F/2/Bz7mrysL3p+Fftu959cDfvbV7T3bRej+v0XogoTGpmbsqzsAVReg6UDt+eNQWj7U+7jo3xeCBF0QoXl/1wTZ80eUoWkaOr/4e9A+LAE6IMmovnw2akdVYOzwQs83bEFAt/Ew6o0S9BIdzbkmnLQY0dLegyapHChwwN4QpFnRS5ZESLlFg177UWVm/PK2y/HJ0U4cPmFHa6cTiqLB5ej216SCEU05kAvL4Wo41Ge7ecQECLIJ7tNHoLQ3DTjO9x3ePOwCiJaBXzRjori8ZQ1eQxAkAywjJ3qa6/pT3XAc3gM5rxi6rg3otw1kqhwD1+ljEEQBhpJqOE8egKl8FNytpyDIRkjWfLjO1Ic83lg6DFKObfD14lU3HEc+ha701pglaz6k3MI+XRoDzl1SDdXRAWP5SDhP1EHrCd1qZhk+AYIkw3H0s6BdAh4CLCMnwnF4t+eYYRfCceyzkOcUzbkw2IbAeTpY7VaEZdg4OI59DgCQbWUQZBlSTiEg6Og59kXI8/Z/7b7X2b/lwTJiIhxHPkGo94ChcCgMQ0Z4/8v3ju73cZ85Bndz6KA2lY+EruuQC4eG3Ceu92ECqe1Ng7YQGYoroTsd/tYNY9kIqO1NUIN1UXhZR/0TELBC3YBrqLrhajgE0VQAV5Onq0WBiE7dhE69d/S8qXwUpIJBvjQEEHQNoq5A0hV/UAtQIeoaRGgQ9H4/B9knv2I4/rkk/iCPRNgwLygoCFr7tts9366D1bx92wVBCHqsb5uvhh4LXR84kjFWVRf8E6ou+KeEnCvRDhzYj8e8feQ+hR9HPg/dxyTrcBZ+gY6Pgw9YzP/at2C8ZBScCtDe3tvXdcVFFXhk1Qd4fPHlePnNLzDniuF49S/78Nd/HMfVlw3HixuDf8COG1GEuuOtOC9fRklhOZTWhuDPe/n1cKoSRlfkY3RFvn97rsGNlo1/GdCM7lP8jdvR+elWODt7w1zKK0LZvAXQRQFCRwlO/s9/Bj1WyinA0JvmJ7TPvPtvH6Fr7/tBHy+48t8gXngR3O6BH7IGgwB9byPs2zdiyNz70PC7PwQ9h2jNx5Crv46G9asBABU3PI2G362HIb8BuVO+juZNv8HQGx/HqVd/G7yZVZRRMe8bQJg+c4NBhF7XhtZNawK2Chj6L0/g1LrfBbknOwBBxNB5j6P5/9ag+MZvwX1CQtPGZUHPb6oYjcJpngVMeuoL0PbBG0H3yxk3BcayZrQ2elp1iieNQafpFJwnB06FAoDSa++GfedbcHUdCXKuKyDnfgV7s+dcBVO+jZyxk9GxaxOsNZPQvPko3E0D+9o95/0+2t7/Pdy5J/2v89SrPwZye6+xccgwlP3LTfhqzWrozuCzMCpvXY52wTM4M2ifuViJr164B8GCWDCYUH7dLAg5hehA/oDHfcK+D6fNhzg++PswkfLlHpx8cW3w8RWCiMqFP8OJlx8Gcj3vJWNOPfKnz0HT26sG7g/AWD4CRTcsRJfS20zZ/xqaDIDr48PIGT0Wp179Xcj/A5UL56NdTe2aEonKqeLi3EFr52Eb8mtqanDo0CFo/Wp0dXWeb15jxgRvWjKbzaiurvbv1//YoqKimJvYzxWBg+CKiorw85//AoWFhf556AcOBA+6YJyKgPzL5sI0dOBgRVPlGOR97VtwBvmclqFj0bXjcfRUO/558jCMqLDhkrFDUFffivxcI66YUDHgmNJCC26ZMw4b3zuEzZ/bUfovP4RoHfghlHPptRAKqoKOru5WjSi99m5I+QO/1eZcMBWSORfOU71BLpqsGPLtR9Ctm+FQjRBzClA47aYBxwpGC8q+/R9wCIlb1c6piiiYsQCG0uoBj5mHT4B1wlUhP0Ddbh2WC6bBVFGDnuN7UXjlvwYpsxlDrr0bre//HoAnPIS8Ygz59iNwnamHZLUhp3Yy2ne9i9Lrvg8I/f5bixJKv7kEutEKhz74+ttutwbLmMthGX1JwFYd7R+9jSHfussz2KdP4USUXnMHOr94HyVz70O3aoKhcixyJswYcG4prxhFM2+BaDCj4/P3kDdhJszDxg/Yz1BSjcKv/yvs23pnK3R8uhWl37obUt7Az4zcCdNhOu9CiKaBLQ6G0vOQP+lqtHsHhZmHXwhrzSXQDTkwVoyGaM5B6ZzvQcopGHBs3sSZ0N1OuFs8QV567d1o3/Vun6CQcgtQcv0D0GQLyq5/IOi9xYuvXgy3IXQIA4BbsqLkW3eif1eVIBlQ+q27obldcEmDr7o26PtwxARYx89IepADgEM3Yci8/wCkfnVFQUTJt74PmPOQU3uZf7Or8RgEQUTuhdMHnEvKK0LJdffDoQ2+EI3TDeRNmoPuI5+iZM4dQf8PDLnxYfTg7F1/PuwAuL/97W/43ve+h+eeew6zZs3yb7/55pvR3NyMd955J+SxS5cuxbp16/DXv/4VpaWePqa2tjbMnDkT11xzDZ544omYC87R7NFNSwN656BqbafQ9flWACJyLpwO0VaOLtUYciyYIIpw6zrau13IMxth73ZC04D3dn2FSWOHID/HhK0fH4ejR8HXLijHkEILtn16CuNHFaNqSB4kUUe+0APn8c/Rc3g3BIsNeRNnQTXmwaGEbhySJAG5omcedXfdRxBMFuRNmAExpxCay4nOT7dA7WyGedgEmIdPQJdu8X8xkCUBOZIDcDrQ/ulWqB0tMFfXwlpzCRywwpngDzVRFJAj9kBpPo7uL/4OQTIgZ8IMCHmlg15bnxzZBXQ2QW07DUNRObr274DS3gRz9ThYRkxA574PoTQdR84F0yAVVaFTNUESdVgFBxyHdsOQVwjRnANXy0mYK2vRfeAjuBrrYSyuhPX8yyAYrejWTBFPy8mRXUBXC7o+2QxdccE6dioMZcMh6Cq69n4A1+mjMBRXwDr6EqjOHsi2Mu/19wSdVXJDdNrR+clm6D3dsIycAENxJVSXE1JhBURBh9bVBtGcA7W9CZ2f/90zN/yCK2AsPQ+KswddezZB7bbDMmoSjFVjAYMJoqsLzuP74DjyCQRzDvIumgnNXIBu1eCZX91xBp2fbgFUBTnjvw6DrRTt/3gHuuJCzrgpkAvK4YYR3aoBJkmFGT3QFScEUULP8S/hOPY5JGs+8iZcBdXRjo49W2EoHorc8VdCk4zQHR3o/OSv0BztsNRcClPl+f7XnWt0Q1Kd6N6/A86GI5ALhyDvwulwiblwKL3hEmqOtNWgwKA60PnF3z3zzIecB2vNJAgmK3o0I5xq+AEz8b4PE8Ug6bDAge79O+BqOARDSRVyxk2FU7DAqUqeNQEcrej85K/QnQ5Yzr8cpvIRUHs60blnC7SedlhGfw3Gilp0B7yvfIJdQ9/nG3raIUBDd91HcLecgrFsOKznT0EPLHCpmd/tG0rco9l1Xce///u/Y//+/XjooYdQVVWFjRs3YuPGjXj++edx1VVXAQAWLlyInTt3Yv/+3tpiU1MTrrvuOgwZMgR33nknZFnGqlWrcPToUWzYsAEVFQNrdZE6m8M8WfPMfTyrQ/lW9op8lSWz2QCTWYYkClA1HaIgQNc9X4IFwbMaWO8ofgGC4OkOcblU9PS4PasyiZ7xAQ6HK+IPFs8KXSIEQUBPj9sf2EajDAE6VE0PucKTLEuwWgyArkMyiNC0xDV7BSNJgnfltb6rpkXCt2qX4O1X1TUdmu5ZBc633e0eeE6DQYIoAIIoQJI8y5hpOiAKnn8Jt1uLaU69b6VAQQAUxbOSls1mgSAIcDickCQJqqKGvP6+1dp8P3tWgNP9H8yyLMFkFD0jfb1ldjo9/76eVbwG/vuKogCj0fM+0nTP6oKB76PAa+hbAc5olCAKAhRVh8ulDHjfmUwyDLIIURKgqToU74pvZrMBouAZOOpwuPu+Jj34+04QAIvF6C23p3z9hQpzH4vFAFnyjLNxuZSYVpGL532YSL73pg4MeB2C4Pm3BHrfF+Gur89g19D3+SbLnn9PVdMTuqZEusQd5gDQ2dmJZcuW4d133+2znGtgTT1YmAPA0aNHsXTpUuzYsQO6rmPSpEn4wQ9+gNGjBxl1GYGzNcyTuQLcuS7chyiFx2sYP17D+J2L1zAhYZ6JzsYwP3HiKyxYMC9oQAd78/YP9Fdf/d+o7rZ2rjkXPwASjdcwfryG8TsXr2G4ME/s7bAoLuXlQzFlytcjrmmPHl2LF1/8DQoLCzFlytdRXj7ItBUiIjprsWaeYULdz3ywb6LJuJ/52ehc/DafaLyG8eM1jN+5eA3jXgGOUkuSpKibytm0TkR0bmMzOxERUZZjmBMREWU5hjkREVGWY5gTERFlOYY5ERFRlmOYExERZTmGORERUZZjmBMREWW5rF0BTtf1lN3OLxP4bkp/Lr3mROM1jB+vYfx4DeN3Ll5D390UQz6erWFOREREHmxmJyIiynIMcyIioizHMCciIspyDHMiIqIsxzAnIiLKcgxzIiKiLMcwJyIiynIMcyIioizHMCciIspyDHMiIqIsxzAnIiLKcgxzIiKiLMcwJyIiynIM8wzX1dWFJ598ElOnTsWECRNwww034K9//Wu6i5U1tm/fjh/+8If4xje+gYsuughXXnkl7rrrLuzfvz/dRctqK1asQG1tLa677rp0FyWr7NixA7fddhsuueQSXHTRRZgzZw7Wr1+f7mJljb1792LJkiWYOnUqJk6ciDlz5uDFF1+Ey+VKd9HSTk53AWhwd911F/bu3YsHH3wQVVVV2LBhA+666y688MILmDZtWrqLl/F++9vfoq2tDbfeeitGjRqFpqYmvPTSS7jxxhuxdu1aTJw4Md1FzDoHDhzAr3/9a5SUlKS7KFllw4YNeOSRRzBv3jzceuutMBgMOHz4MNxud7qLlhUOHTqEm266CSNGjMB//ud/orCwEB9++CGWL1+OgwcP4plnnkl3EdOK9zPPYO+99x4WL16MlStXYvbs2QAAXdcxf/58tLW14S9/+UuaS5j5mpubUVxc3Gdbe3s7Zs6cicsuuwwrVqxIU8myk6ZpuOmmm3DhhReirq4O7e3t+OMf/5juYmW8U6dO4eqrr8Zdd92F7373u+kuTlZasWIFVq5ciU2bNuG8887zb3/ooYfw5z//GXv27IHBYEhjCdOLzewZbNOmTcjLy8PMmTP92wRBwPXXX4/Dhw/j4MGDaSxddugf5ACQn5+PYcOGoaGhIQ0lym6/+c1v0NDQgPvuuy/dRckqv//97wEACxcuTHNJspcsexqSc3Nz+2zPy8uDLMuQJCkdxcoYDPMMduDAAdTU1EAU+/4z1dbWAgDq6urSUays19LSggMHDmD06NHpLkpWOX78OH75y1/iscceG/CBSoP76KOPMGrUKPzf//0fvvGNb2Ds2LG48sor8bOf/Yz9vRG67rrrUFBQgP/6r//C8ePH0dnZic2bN2PDhg34zne+M+Bz8lzDPvMM1tbWhuHDhw/YbrPZ/I9TdHRdx6OPPgpN07Bo0aJ0Fydr6LqOH/3oR5g6dSpmzZqV7uJkncbGRjQ2NuLJJ5/EPffcg5qaGnz44Yd48cUXcerUKTz77LPpLmLGq6iowPr163HnnXf2eQ/ecccduPfee9NXsAzBMM9wgiDE9BgF98wzz2Dz5s146qmnMGrUqHQXJ2u8/vrr+Pzzz/HnP/853UXJSrquo6urC8uWLcM111wDAJg8eTJ6enqwZs0afP/738ewYcPSXMrMduLECdxxxx0oLS3Fc889h7y8PHz00Uf41a9+BUEQzvlAZ5hnsIKCgqC1b7vdDqC3hk6RWb58OdasWYNHHnkEN9xwQ7qLkzVaWlrw05/+FN/73vdgsVjQ3t4OAFAUBZqmob29HSaTCSaTKc0lzVwFBQUAgKlTp/bZfuWVV2LNmjX44osvGOZhPPvss+jq6sLGjRthNpsBeL4QAcBzzz2HG2+8EVVVVeksYlqd250MGa6mpgaHDh2Cpml9tvv6yseMGZOOYmWlX/ziF3jhhRfw0EMP4ZZbbkl3cbLK6dOn0dHRgWeffRaXXnqp/8+uXbtQV1eHSy+9lLMCwgj3f/Vc7++NxN69e1FTU+MPcp/x48dD0zQcPnw4TSXLDKyZZ7DZs2fj97//PbZs2dKnj2jjxo0YMWIEampq0li67LFy5Uo8//zzuOeee3D77benuzhZ57zzzsMrr7wyYPtPfvITdHd348knn0RFRUUaSpY9Zs+ejddffx3vvfcerr32Wv/29957D4Ig4MILL0xj6bLDkCFDcODAATgcDlgsFv/23bt3AwDKysrSVbSMwDDPYNOmTcPkyZPxyCOPoK2tDVVVVdi4cSM+/vhjPP/88+kuXlZYs2YNVqxYgRkzZmDKlCnYs2eP/zGj0Yhx48alr3BZIicnx9+cGSg/Px8Agj5GfV155ZW48sor8cQTT6C1tRWjR4/Ghx9+iFdeeQU33XQTKisr013EjHfLLbfgzjvvxKJFi/Dv//7vyMvLw44dO7B69WpMmTLFP8vnXMVFYzJcZ2cnli1bhnfffRft7e2oqakZMJqTQlu4cCF27twZ9LHKykps2bIlxSU6eyxcuJCLxkShu7sbK1aswFtvvYXW1lYMHToU8+bNw+23385m9ght27YNL774Iurq6tDd3Y3KykrMmTMH3/nOd2C1WtNdvLRimBMREWU5fh0kIiLKcgxzIiKiLMcwJyIiynIMcyIioizHMCciIspyDHMiIqIsxzAnIiLKcgxzIiKiLPf/A7eOMQ3wLuHiAAAAAElFTkSuQmCC",
|
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"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
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"\n",
|
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"x = np.linspace(-1, 9, 1000)\n",
|
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"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
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"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
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"\n",
|
|
"plt.scatter([0], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "03d5be72",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Question: In which cluster should we place the black point ?\n",
|
|
"\n",
|
|
"Let's zoom in!"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"id": "fdacd9f9",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"x = np.linspace(-0.7, 0.7, 100)\n",
|
|
"\n",
|
|
"plt.figure(figsize=(8, 4))\n",
|
|
"\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.scatter([0], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "48509178",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Question: In which cluster should we place the black point ?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"id": "65280fcc",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
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"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
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}
|
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],
|
|
"source": [
|
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"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
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"\n",
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"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.scatter([1.315], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "13867b50",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Question: In which cluster should we place the red point ?\n",
|
|
"\n",
|
|
"Let's zoom in, and compute the likelihoods. __Can we really conclude that the point is in the blue cluster?__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"id": "b50b205b",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"x = np.linspace(1.3, 1.33, 100)\n",
|
|
"plt.figure(figsize=(8, 4))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.scatter([1.315], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"id": "f08f136c",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"0.02794258414879452 0.027912633932334185\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"p_x_blue = stats.norm.pdf(1.315, means[0], scale[0])\n",
|
|
"p_x_orange = stats.norm.pdf(1.315, means[1], scale[1])\n",
|
|
"\n",
|
|
"print(p_x_blue, p_x_orange)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "62cb755e",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can compute the probability that a point $x$ belongs to a cluster $C_k$\n",
|
|
" - Likelihood: \n",
|
|
" $$p(x|C_k) = \\frac{1}{\\sqrt{2\\pi\\sigma_k^2}} \\exp \\left(\\frac{||x - \\mu_k||^2}{2\\sigma_k^2}\\right)$$\n",
|
|
" - Probability: \n",
|
|
" $$p(C_k|x) = \\frac{p(x|C_k)}{\\sum_j p(x|C_j)}$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"id": "383c80a2",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"P blue = 2.6043079246504417e-19\n",
|
|
"P orange = 1.0\n",
|
|
"Sum = 1.0\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"x = np.linspace(-0.7, 0.7, 100)\n",
|
|
"\n",
|
|
"plt.figure(figsize=(8, 4))\n",
|
|
"\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.scatter([0], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"p_x_blue = stats.norm.pdf(0, means[0], scale[0])\n",
|
|
"p_x_orange = stats.norm.pdf(0, means[1], scale[1])\n",
|
|
"\n",
|
|
"p_blue_x = p_x_blue / (p_x_blue + p_x_orange)\n",
|
|
"p_orange_x = p_x_orange / (p_x_blue + p_x_orange)\n",
|
|
"\n",
|
|
"print(\"P blue = \", p_blue_x)\n",
|
|
"print(\"P orange = \", p_orange_x)\n",
|
|
"print(\"Sum = \", p_blue_x + p_orange_x)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"id": "90a00923",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"P blue = 0.5002681058054131\n",
|
|
"P orange = 0.49973189419458686\n",
|
|
"Sum = 1.0\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"x = np.linspace(1.3, 1.33, 100)\n",
|
|
"plt.figure(figsize=(8, 4))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], scale[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], scale[1]))\n",
|
|
"\n",
|
|
"plt.scatter([1.315], [0], color=\"k\", marker=\"x\", s=200)\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"p_x_blue = stats.norm.pdf(1.315, means[0], scale[0])\n",
|
|
"p_x_orange = stats.norm.pdf(1.315, means[1], scale[1])\n",
|
|
"\n",
|
|
"p_blue_x = p_x_blue / (p_x_blue + p_x_orange)\n",
|
|
"p_orange_x = p_x_orange / (p_x_blue + p_x_orange)\n",
|
|
"\n",
|
|
"print(\"P blue = \", p_blue_x)\n",
|
|
"print(\"P orange = \", p_orange_x)\n",
|
|
"print(\"Sum = \", p_blue_x + p_orange_x)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "a1f46623",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can compute the probability that a point $x$ belongs to a cluster $C_k$\n",
|
|
" - Likelihood: \n",
|
|
" $$p(x|C_k) = \\frac{1}{\\sqrt{2\\pi\\sigma_k^2}} \\exp \\left(\\frac{||x - \\mu_k||^2}{2\\sigma_k^2}\\right)$$\n",
|
|
" - Probability: \n",
|
|
" $$p(C_k|x) = \\frac{p(x|C_k)}{\\sum_j p(x|C_j)}$$\n",
|
|
" \n",
|
|
"#### How do we find these papameters ?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"id": "5f5da58f",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 864x144 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(12, 2))\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0])\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e43506b9",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can compute the probability that a point $x$ belongs to a cluster $C_k$\n",
|
|
" - Likelihood: \n",
|
|
" $$p(x|C_k) = \\frac{1}{\\sqrt{2\\pi\\sigma_k^2}} \\exp \\left(\\frac{||x - \\mu_k||^2}{2\\sigma_k^2}\\right)$$\n",
|
|
" - Probability: \n",
|
|
" $$p(C_k|x) = \\frac{p(x|C_k)}{\\sum_j p(x|C_j)}$$\n",
|
|
" \n",
|
|
"#### If we knew the correct cluster assignements for the points, would we be able to compute the Gaussian parameters?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"id": "5a4da38d",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 864x144 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"plt.figure(figsize=(12, 2))\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "02e988d0",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can compute the probability that a point $x$ belongs to a cluster $C_k$\n",
|
|
" - Likelihood: \n",
|
|
" $$p(x|C_k) = \\frac{1}{\\sqrt{2\\pi\\sigma_k^2}} \\exp \\left(\\frac{||x - \\mu_k||^2}{2\\sigma_k^2}\\right)$$\n",
|
|
" - Probability: \n",
|
|
" $$p(C_k|x) = \\frac{p(x|C_k)}{\\sum_j p(x|C_j)}$$\n",
|
|
" \n",
|
|
"- If we know the correct cluster assignements of the points we can compute the mean and variance of the Multi-Variate Gaussians\n",
|
|
" - Mean:\n",
|
|
" $$\\mu_k = \\frac{\\sum_i p(C_k|x_i).x_i}{\\sum_i p(C_k|x_i)}$$\n",
|
|
" - Variance:\n",
|
|
" $$\\sigma_k^2 = \\frac{\\sum_i p(C_k|x_i).(x_i-\\mu_k)^2}{\\sum_i p(C_k|x_i)}$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "5a208100",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Gaussian Mixture Model algorithm\n",
|
|
"\n",
|
|
"- If we know the correct parameters of the clusters (mean and variance): we can compute the probability that a point $x$ belongs to a cluster $C_k$\n",
|
|
" \n",
|
|
"- If we know the correct cluster assignements of the points we can compute the mean and variance of the Multi-Variate Gaussians\n",
|
|
"\n",
|
|
"__Does it ring a bell?__\n",
|
|
"\n",
|
|
"__How can we compute the means and variances ?__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d17f69b1",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### The Expectation Maximization Algorithm for 1D GMM\n",
|
|
"\n",
|
|
"- Fix K, the desired number of clusters\n",
|
|
"- Initialize the K means and variances at random\n",
|
|
"- Repeat:\n",
|
|
" - Compute the soft allocations of data points under current parameters of the Gaussians\n",
|
|
" - Update the parameters using the new soft allocation values\n",
|
|
"- Stop when the total likelihood is not changing anymore\n",
|
|
"\n",
|
|
"__Exercise:__ Try to implement EM to fit a GMM to the 1D toy example"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"id": "800f6b20",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Initialization\n",
|
|
"\n",
|
|
"means = [0.5, 0]\n",
|
|
"stds = [np.sqrt(0.5), np.sqrt(0.5)]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], color=\"k\")\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"id": "5053cfe5",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 23.403336833443856\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"id": "f554246b",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"id": "0a3549db",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 40.54875472662691\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"id": "2e683d8d",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"id": "e6914262",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 75.62518759531767\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"id": "7c983975",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"id": "391e5c32",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 106.90526584779028\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"id": "4d1af9dc",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"id": "de2c408b",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 132.1856163952867\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "2f7810ef",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"id": "4e622b8c",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 148.44003898677062\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "b23cdf1d",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Parameters update\n",
|
|
"\n",
|
|
"means = [np.sum(p_Ck_x[k] * data1D) / np.sum(p_Ck_x[k]) for k in range(2)]\n",
|
|
"stds = [\n",
|
|
" np.sqrt(np.sum(p_Ck_x[k] * (data1D - means[k]) ** 2) / np.sum(p_Ck_x[k]))\n",
|
|
" for k in range(2)\n",
|
|
"]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 32,
|
|
"id": "77c8bf21",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Total likelihood = 149.84601632054645\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Allocation update\n",
|
|
"\n",
|
|
"p_x_Ck = [stats.norm.pdf(data1D, means[k], stds[k]) for k in range(2)]\n",
|
|
"\n",
|
|
"p_Ck_x = [p_x_Ck[k] / np.sum(p_x_Ck, axis=0) for k in range(2)]\n",
|
|
"\n",
|
|
"labels = [np.argmax([p_Ck_x[0][i], p_Ck_x[1][i]]) for i in range(len(p_Ck_x[1]))]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data1D, y=[0] * data1D.shape[0], hue=labels)\n",
|
|
"x = np.linspace(-1, 9, 1000)\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[0], stds[0]))\n",
|
|
"plt.plot(x, stats.norm.pdf(x, means[1], stds[1]))\n",
|
|
"\n",
|
|
"plt.legend(\"\")\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"print(\n",
|
|
" \"Total likelihood = \",\n",
|
|
" np.sum([np.max([p_x_Ck[0][i], p_x_Ck[1][i]]) for i in range(len(p_x_Ck[1]))]),\n",
|
|
")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "0366af23",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "slide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Extension to multi-dimensional data\n",
|
|
"\n",
|
|
"- The mean value becomes a mean vector\n",
|
|
"- The variance becomes a covariance matrix\n",
|
|
"\n",
|
|
"The principle remains the same: EM-algorithm\n",
|
|
"\n",
|
|
"- Use current estimate of the parameters to allocate soft clusters to the data points\n",
|
|
"- Use the soft allocations to compute the new estimates for the parameters\n",
|
|
"- Stop when the total likelihood stops changing"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1b1f7634",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"### Exercise: Understanding covariance matrices\n",
|
|
"\n",
|
|
"Play with the parameters of a covariance matrix to understand what they represent"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 33,
|
|
"id": "da23dc88",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"mean = np.array([5, 5])\n",
|
|
"cov = np.array([[1, -0.5], [-0.5, 1]])\n",
|
|
"\n",
|
|
"n_points = 500\n",
|
|
"\n",
|
|
"data_test_cov = np.random.multivariate_normal(mean=mean, cov=cov, size=n_points)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data_test_cov[:, 0], y=data_test_cov[:, 1])\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7572f6f5",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## GMM using sklearn\n",
|
|
"\n",
|
|
"__Exercise:__ Solve the initial example problem using GMM.\n",
|
|
"\n",
|
|
"- from sklearn.mixture import GaussianMixture\n",
|
|
"- GaussianMixture(n_components=2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 34,
|
|
"id": "1bb3f99f",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([4.5, 4.5])]\n",
|
|
"covariance = [np.array([[0.1, 0], [0, 0.1]]), np.array([[2, 0], [0, 2]])]\n",
|
|
"n_points = 500\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance[i], size=n_points)\n",
|
|
" for i in range(2)\n",
|
|
"]\n",
|
|
"data = np.r_[data[0], data[1]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1])\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 35,
|
|
"id": "c1d47c17",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"from sklearn.mixture import GaussianMixture\n",
|
|
"\n",
|
|
"gm = GaussianMixture(n_components=2)\n",
|
|
"clusters = gm.fit_predict(data_scaled)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data_scaled[:, 0], y=data_scaled[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fcda2826",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## GMM using sklearn\n",
|
|
"\n",
|
|
"__Exercise:__ What is the probability of the point $[-0.5, -0.5]$ to be in the blue cluster? The orange?\n",
|
|
"\n",
|
|
"- gm.predict_proba"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"id": "3fa2d2e3",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"new_point = np.array([-0.45, -0.45])\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data_scaled[:, 0], y=data_scaled[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.scatter(new_point[0], new_point[1], color=\"k\", marker=\"x\", s=200)\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"id": "e90c9136",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"image/png": 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BmkeOadMxcc0Ri23bDMpKbPacIVkJGAJ0rrpmfyzT4OnvtvLMnC1UB8JIAccO6sGdpw2m+btKczBUBS2KqgMxj7+5aAdXTu6DqxPHdCg5cpYrGs1+WJZiaFYCSR5H1OOGFJwzJptwSLc51TTGkpK/zFrDQ19soDoQWeLZCj5ZVchFj82l1Bc6xCM8fAm3UFoaPMLyWLQR1xzRuIEXrp1IoqexU8phCP598RjiDe0a1TSl1lK8tXhn1GM7K/x8vjq6RLDm4En2OPA6Y+epHD0oA9cR9LPV7vQjBMOQ+BXYAgTgEqCOsBVrNGzLpl+6l1m3T+f7zaUs3VFBXloc0/un4xIKtBqcZj8MQ/L9hpJmz3l7yU5OHtqzk0Z0ZOGRcMsx/bh31pomx1ym5PZj+yPsI0drXhvxIwBLStaV+vjLh6tZur0Clyk5Z0xvbjq6gDjaX/msuyGFIM3r4KjcZKb3TcG2VbsLymgOL4wWktekEOj8to7BDtvMHNkLpyl54LP1VNSFLgb2SOAvM4eTZArUESTSpI34YY40JN9sLuNHry5peC0Qtnlx3jY+W13E6zdOxnkIx9eVsCwbS4e/NS1gWTbj8lKabY974fgc4pwG5bWdO7YjBcOy+MGwHpw8pAe1IQtDCjyGxC2OvE2Jjokf5viA37+7Muqx3ZV+Xvl+G8YRVI6h0bQHbiG45qi+UY/1z4xnYn7aEacc1tnYYRuXbZNiCBIFOGz7iDPgoI34YU9JdajB3RSNNxbtoFYXQmsOUxwOA4fTwOlsX6ejtG2uPSqPv8wcRu9kDwBep8GVU/J45qrxpLi1k1PTOeg77TAn3ILudzB85CSAaI4chCHxKXh3+W4Wbi0nN9XLuWOyiTNEu2nhG2GLk/qnM60gHUuBFOCRAjusYzKazkMb8cOcHokuXKaMqg0OcNzgTDyGQIW1KdccHkhDsKkiwKVPfoc/tPe+f/iLDfzfWUM5YUBGuxnycNjem1OiQPfK0XQ22p1+mOMWcP30/KjHPA6DG6bl6zIqzWGFTwmuenp+IwNez2/fXkF50NKZ45rDBm3ED3NU2OaS8Tn88uRBjQRNhvVO5L83TCLeiJ1hq9F0NwxDsHJ3FVWB2EK5z3+3BWnqpjaawwPtTj8CMMIW54/M4vThPakNWjgMicsQuIXC0kltmsMIKSWbW2hqs7mklrCt0JtxzeGANuJHCFbYwgW4TEEkeKfQ6Tea9sY0JX4bbKVwG7LTk7wsy6Z/j/hmzxmQGY9DCnT+meZwQBtxjUZz0AgBIcNg7pYynp6zhSp/iCn5aVwxJY94SaQ7SCdg24r+mfGkxjkprQk2OS4FXDwht1VNbYQQOJwGSilsSx2RNciaro824hqN5qAJGQa3v7KYeZvLGl5bW1jNS/O38fw1E8hPcmN3khH0oHj26glc8vh3jTQSTCm474JRJJiyxTTysCHZVRng5e+3URu0OHV4FiN7J+FWNvYRJOmp6fpoI67RaA4Kh8Pgs7XFjQx4PYGwze0vL+a/10/qNHlf21JkeUzev+UoFm8vZ/G2Cvqkejl6YAYuQLRgwC3T4K53V/DRyr2dyN5buovsFA8vXjMRrwCls0E1XQSdna7RaA6KWkvx1OzNMY/vrPBT7o+dLd4R2FZEknNKTjK3Tsvj9MGZuG27RQNumpJPVu9pZMDr2V7m41dvLiMsdUqcpuugjbhGozkobKUoq20af96XKn/okNRmW5ZNMGgRbmUWW40N//l6Y8zj324owa8rOjRdCG3ENRrNQeGUglE5yTGPCwFZSe5uoUcgBOws9zd7jq8VSXEaTWehjbhGozkopK247dj+MXfaJw7pgau7uKAV9E2Pi3lYCvC2czMVjeZg0EZco9EcFEopMtwmD188hnhXYwN3zMAMfn/6EMxuIirulXDz0QUxj58wuAdu/dTUdCH0klKj0Rw0wrYZ1yuBWbdPZXNJLVX+MP17xOM1JQ7L6haudIg0NJncN5XLJuXy3NytjY4N7ZXI704fgmFbuvOfpsugjbhGo2kfbIUTxcAUD0JEhFewOq/VrWFKfDbUhCykEHgdEo+IGOY2vU/Y4uZp+VwxOY8PV+ymJhDm2EGZ9E5y47TtbrMg0RwZaCOuOaIQQqCkIGgrDCFwdpNQbXdCKdXphs4yJF9vLOPuD1dTVBUAoE+alz+eNYyBaR5kGwVaDNsmScKlY3oj6hYCdicuSDSa1qKNuOaIwTYkxb4w//5yAyt2VpKR4OK6qX0ZnWOQ6NY/ha6MlAJhSGwFBqrR7to0JbM3l/Pj/y5p9DdbSmq54ql5vH7jZPISnAfU7CekM9E1XRz95NIcEShDMHdrOXe8srhhl7ipuIZ5m0o5c2QWd54+5NAOUBMVISAoJZtKanlx3lb8YZtTh/VkUt80PNhYlqLWhrs/WB3175WC/3t/NQ9dOBJT76M1hyHaiGuOCIJIfv7a0qhu3neW7OLiiX3on+TqVrrY0pT4FVT4w+zeU016vAuHKVFtjAF3yNikICQEflvhD1nEOU3cAmijfnrYMPjpa0uZvaGk4bVPV+0hK8nNS9dNJEEKfGGb3ZWxa7sXbi0jrPTDTnN4ou9rzWGPYUiWbi8n0Ixxe/KbTfzpjMEd1m1LiIg7P2CDZSscUuCVbU+6qsc2JAt2VPLbt5ZTXB1RS3M7JDdOL+DCcdkYh7DPpmFIKi3FL99cytyNpUCk+ciZI3vxsxMHtDpb3TAN3ly6q5EBr2dXhZ9fv7mcf5wzHCmafzNDCt07XHPYoo245rBHCKK2pdyXcl8IywajA65vGJIqG/76wRo+XL6bsK3ISfXw4+MHMDkvFcNqm8GVUrClIsCNzy9s9Lo/ZHPfp+twmpILRvXq9F7eDeNAcOFjcxvtjsO24o1FO9hd4ePv547AbMWO3Gcrnvh2U8zjszeUELAjfcsH9Uxg9e6qqOedMLiHTmDUHLZo2QLNYY9l2YzITm72nCn5abg66NdQi+Dc/8zhvaW7CNft9LeV+vjRq0t4e9kuMNp24aAQ/OXD6DFggEe+3IDvIDwKUgqUIQkIgW1IZBvU1kzT4JsNxTHd27M3llLqC7dOR11AYWWg2VN8QQu3gD+dPQwzyjjjXSY/O2lAm7PTNZrugjbimsMepSA9zsHQXolRj3scBueMzT5g13ZzmKbk9YXbG8qe9uefn6yleTPVFBtYsLVp2896Kv1haoIHtgu3DMmWqiC/eXclVzyzgF++vYL15X6sVi40wij+t3x3s+fM3lCMYbTC56GgICM+5mFTCuJcJpZlk5vg4p2bj2LGgHSEAIchOGNkFu/cfBRJptStQzWHLdqdrjkicCnFfy4dy20vL2bhPgawR6KL/1w6lnSvg+qq9nc/11qKtxfvjHncH7LZVuqjf7K7TYbG4zCobcZQm0bb/ce2FLy9bHejTO8NRdV8vqaIHx5dwOUTcjBacIMLBC6zeQPtdhjQikxxr4Tbju3H7a8sjnr8jJFZkWQ5ANumh9vg3rOHEa4biQOFtG2U7jqmOYzRRlxzRGDbCrewefCCkVSHLLaW1pIW5yIz3kl6vKvD2mQqWjZXdht3iS4B547J5tm5W6IeH9AjHo8hoY165c2Vaj38xQbOHtWLlBYWB8K2uXRiDrNWRN+NCwHT+qW3yusRDttM7JPCtVP78vg3jWPjE/um8PMTByKsvRKotq2QKJz7nKfNt+ZwRxtxzRGDUgqHUqQYgrQe8RFlMdvu0D7XXkNy2vCePPj5hqjHXaakT5oX1YbSKxW2uW5aX2at3N0kZuwyJfeeMwK3gLb4FRwOg1nNeAwA/rtgO7dM7UswGI55jm0rCtLjmdQ3lbmbSpscv35afqSBSCuna1gW107uwyUTc/lybRG+kMXUfumkex1NstylaVBrK8IN2f8C6xBm6Ws0nYE24pojks6qB7fCFheOz+HFeduiZsj/8OgCXAfwvnECXr9xCi/O28rrC7cTDNscPTCTm48uIMkUWG2sxxZCtJhEtqcqQGtqtZy2xT/PH8nbS3by5Leb2VMVoF9mPLcf24/xfVLaXP5m2DbxwFlDMhFCEA5bqH0kUIUQhAzJo19v4pXvt1EbtEjyOLhqSt4hL7fTaDoaobpZxodSiuLi6kM9jIMiKckDQEWF7xCP5ODQ82gdhiEoD8P/vb+Sz9cWoRRkJri47dh+HD8ws80lZvsiTQOfZWOYBvEug0BN4IB0yw1DsnBXFdc+tyDmOX8/bwTH5qe2OgHQqNsZCwEoWlUXfyDfRcgwuPGFhSzdUdHk2AmDM/nDGUNaVdLWnhwOv43DYQ7Q/eeRlhbfbIWI3olrNB2MZSkSpeDus4YSsCFs2zgN2S7uXjts4QKSvA4A/Ae4JLcsm8FZCfRIdEXdkad4HUzq23oDDhEvxL5eho4QkpNSsKG4JqoBB/h41R5+dPwAMl1Sdx/THJboEjONpoOQUmAYEiEiHiRp2XiUTYIAl213uXitB3jp2klNyrpyUj28fP0kPF0wTcwwJa8t2N7sOR+vKsRsIWNeo+mu6J24RtPOSEPgQ7ClpJbCykg8OD3OgUupLq3Nblk2yabg2avGUVYbYme5j55JHtK8DjyCNsfZO4v2zv4/UpBSIKXAtrv2falpHm3ENZr2RArWlwe44fkFlNeGGl7unxnP45ePI152XlLdgWBZCieKHi6DrKyEhgz+ruUz2Itt2ZwzpjfvLImdWX/i4B6Eu5jX41AiDIkf2FBUw9bSWvplxJOb6sGDOqB2rZpDizbiGk0z1JeftXYzV6sElz85r0mzlXV7qrnq6fk8d/V4nF3QLR2NrrzYqMeyFP0z4hjaK5EVOyubHJ8xIINUr6NNJXyHM8IQbKsKctUz8xstMnskunj2qglkuKQ25N0MHRPXaKJhSAKGZGNlkM1VIQJSIszmfy71EquxuqVtLK5hV0UA0ZGF6YcQKUWH1tzHwmkrHrtsLBdPyMFV9x3Fu0xumpHPPTOHdXpmelfGpwQXP/5dIwMOEY36ix//Dp/u99bt0DtxjWY/LEPy6qIdPPT5hgaD7HUa/OKkgZw0ODOm9GhQwfwtsTXNAZbvrKBgSCbhcOt2O4YpqbUjPcMtW5HqdeCWdIme4RDxVISlpDas2LynhiSPg54JLtxCYXfQjq4+WdCybJSqE/EJW/z4mAJumlFAyIpk/3sk2KGOc6ObpsRnKaQQOLtwzkA9DofBe8t344vxmZTUBFmxs5JxvRK7/Fw0e9FGXKPZB9M0mLV6D//4eF2j12uDFne9u5LMRDeTshOjllqZAjLim5duyUhwtdo1b0vJnC3l3PXOCsrqdk5ep8HNxxRwzqheGIfYkAsBQcPgN28t5/M1RQ2vp8Y5uf+CUQxK90A7GnIlJQHg+81lVPpDjMlNiSi32SoSuw/buCGip27bbVWdbTXCkPgUvP79Dr5YW4THaXDZpD6M7p2Ew25dr/RDgaLlReaCreVMzEniIKQLNJ2MNuIazT7U2Ir7P10f8/hfZ63huavGN9LnrkdZiqum5MVMsnKZkpHZSa3a5RiGZG1JLbe9vLjR67VBi7/OWkuc0+TMIZlYh9CQh6RsYsAh0rv9qqfn8+Ht00g2Wp9P0By2IZm1eg9/eG9VQztXgFHZSTx08RhcnWQ8DUOy2xfmgkfnUhXYKz87Z0MJ4/qk8MCFozC7aBKdFNA72dPsOb2T3R22+NF0DDomrtHsQyBsU1QdW350Y3EN4RjWQilFzwQnl03KbXJMCrjvglGtllj1K7i7mZ7h//psPb5DvOPzhVUTA15P2FY8+vVGlDz4R4yUgi0Vfn73zspGBhxg8fYKfv3WMsLtcJ3W4Fdw+yuLGxnwer7fUsaslYWYLeROHCqCQYvzx2bHPG5IwdEDM3Umfzeja95tGk0UDIeBMiSGw+iwBKqWWng6DIHRzMVNy+aH0/N59fpJHD84k+G9k7h4Qg6zbp/G2N4J0MpYowUs39E027qe0prgAfcMbw+kFGxqQf74+81lBNohwz0kBPd/si7m8S/XFuPvpIzq2rDNuj2x5/3U7M3UdmEbmOAw+NUpg5q8LgT87dwRuLtJ5YRmL9qdrunyCENSbSten7eNRVvL6Znk4opJeaTHOdo989glBVMK0pi9oSTq8VOH9cTZwgLCtGwKklzcfcYQQrbCZUiUZbWpr7UQ4DQkwWbm5zAkh6rZplKKJE+0oMJekjyOyILnIP3cYRvWFFY1e86eqgD5ic4Od6k318MdoLQ6iOrCCd6GbXPW8J4cVZDG07M3s6W0loE9Erh8ch+SHBLRDcoKNY3RRlzTpZGGZE2pjyufmt/IoL22YAc3zSjg8gk5mO0YxHMoxR/OHMrMR2ZT6WvsMs2Id/HjEwYibbtllTA70kncQUTfvK24gDNH9YopKToiOwm3FHCIHrpKQVaiixSvoyHpbn+uOioPtzx4zXQpIgmBxdVNu8DVk+RxdEpMPMXroLmPfWivxC7/UDUsm55ug1+dMIBQXdtWO2wdsntJc3Bod7qmS+MHbnhuQdQd6b+/3EBhTbBd665tW5HikLx/y1Sum9aX7BQPualebju2H2/+cAoJsn0StVpC2Da3HdOP9Pimu123Q/Lns4fhEof2oesWivsuGIUZpcPS5PxUxvdJaVPDlFh4JFw3NT/m8YKMOBKcnaON7hJw+oismMd/dMIAHN3AJa1UZHFp2PYBLTI1XYcOWzTOmTOHt99+m0WLFrF7926SkpIYMWIEt956KwMHDuyoy2oOI6QUrCmsjppEVM+T327mdycPhHZ8ENlWpFTpxil9uGJiJEnNa0Q6jnXW404piJOKt344hWfnbuWtRTsI24rjBmVy04wCEo229wxvb2xLMTg9jg9un8Z/vtrIgi1lDX28J+Sl4LCsdjFn4bDN5PxUjhuUyaer9zQ6lug2+fMPhuMwJQQ7/vMQls2vTh5ElT/cKKnPZUp+d/oQ8pLd2LrGWtOJdJgRf+mllygvL+fKK6+koKCA4uJiHn/8cc4991yee+45Ro0a1VGX1hwmSCnYVe5v9pxdFT5CtuqQG9kO2w3Z5FYrxVna9fq2woXihsm5XD4hFwS4ZMSQqC7i+hS2TYoBvzi+H4E64ROPhHC4fQx4PbatOH1EFmeP7s27S3ZSFQgzPi+Fqf0yuOfD1Vw3tS8TeneOSInDsvjzWUOpCdks31FBnMtkcFZC5F7RBlzTyXSYEb/rrrtIS0tr9NrUqVM57rjjeOKJJ3jggQc66tKawwTLUgzoGd/sOcN6JeEyxGH97GxYTCjAPlSpbLERQhBWkXEJIklv7YmUgnVF1fzo1SVkp3g4fnAPPA6DpdsqePCz9dgqkgQ46tzhdIZTXalI8mKShOl5KSil9O5bc8joMCO+vwEHSExMpE+fPuzevbujLqs5jFBK0SvJTU6qh22lvibHDSm4dFIuVgdKa7YnUgqCCHyWTbkvRIrXidsQOLt4i9LmsAzJulIfD36+ns3FNWSnevnhjHwGZcbHlKeNhRDgD1tUB2yCCBxS4JWR+6DKHwmpbC/z8fTszU3+ttIfwlaq3Y24MCWBuq/GUOAUjTt9HeqQhkbTqYmUpaWlrFu3jtNOO+2g3icpqXnVoa6OaUYeNXoerePZqydw2RPz2F6215C7TMlDF48hM8GFyzi4/MzOmseuqgC3v7yYxdvKG16b0DeVf5w/ksyE5su1WuJQ3FM1QYvn52zh/k/31nDvrPAzb1MpV03J49ZjC4h3tu4RIwTsrgry+7dW8OHy3YRtRU6qh5+cMJBp/dMZ0iux2b+f1j+dlDgXRpQkuwOhJmRRHbD4zxcbeH3hDvxhizG5Kfz61EH0S4/D42h+uXA4/MYPhzlA959HS3m7QrW37ysGSiluueUWvvrqK9566y0KCgoO+H1C3WTnFYv6m6q7KyN15jxKfSE2l9SyfEcFPZPcjMlNIcll1NVKHxydMY9SX4gfPDybXRVNY/x90+N4+bqJpHgcB/z+h+Ke2lHp55i/fRnz+Kw7ptE31duq9yqpDXHmQ99SVNVULe9XpwzinDHZ/OjVxXy9rrjJcbdD8vGPZtAjSiZ/WwlYNuv31CCk4Ibnvqewsul4/nPZWGb0S0M2J/pzGPzGD4c5QPefh8NhNFuB02k78XvvvZdPPvmEu++++4ANeD0VFU1dq92J+hWhnkfrMYD+SS4GpvREKYUVClMbip213hY6eh6GIVmwvSKqAQfYVFzDusJqBqd5Dtit3tn3lMNh8N6SXc2e8+r8bdw2PZ9gsPnvyTQlry7YEdWAA/zzk7WcNrwn984czl3vruTjVYUNZX7ZKR4evGg0HtRBz90wJBsrAzw7Zwupcc6oBhzgN28u4+0fTsHZjCt93+9DSkFYCEJ1Y/bKSKVDV0c/p7oGaWnxze7GO8WI//Of/+TJJ5/kN7/5DTNnzuyMS2oOQ2xbYdtd/+G3P4Yp+XhlYbPnfLG2iOHT+rZo8LoKQghKa2KLr0CktWVr2lPXWoq3F0dvGgPgD9lsK/UxIMXNH08fzG9OHURhZYAEt0miy8QjFJZlIwQoQ+K3FAJBnEGr6tSdTgMQ+G3F799dwXXT8vnz/1bFPL+4OkilP0y6o2UvkDIEu2rD/P3jtXy3qZQ4p8kF47O5eEIuLtvutrkQmq5Dhxvx+++/n0ceeYSf/exnXH755R19OY2myyGIKIo1R4LbbPes7rYiTYNaWxGs68ftri9nizIsy7KYPiCdp6IkmdVzzMDMhqxtaRr4bIUQEa+KY59kPkXLGfe2UigF0rbxwl6JVduO1O5LQYWl+Pfn6/lyTREuh+TcMdmcNzYbt4puLMNSUhWyeH/edqr8IY4ZmMmvTx1MVqKbYAvGP2QpaCH6oYAVe2q55pn5DWJotUGLBz/fwDtLdvHSdRNxdsNFqaZr0aFG/MEHH+Thhx/m9ttv59prr+3IS2k0XZZgMMx5Y7N5Zs6WmOecPjzrkOZ6WKbBs/O28sycLVT6wzgNyVmjenHHcf2jGkHLUgzIjCc7xdMo4bCejHgX4/pEyq/8huTxrzbyxsId+EIWUwrS+NlJA+nhMRG2wmtIThvekwc/3xB1bC5T0ifNi9rHfb3vwsIwJFurg1zw6FwC+xjf+z5dx2sLt/PKdZNw7ifTYxmSR77e1Og7efLbzeSnx/HQJWM4ZVhPXpy3Lep4PA6DtDgnLTXdLqsN8fPXl0ZVM91aWsvrC3dw6Zheh7SdrKb702Gyq08++SQPPPAAxxxzDFOmTGHx4sUN/1u5cmVHXVaj6XIoBWleR8w2kNdO7UtcK1yzB4uUAtuQBKQkKCWOugzrsCG5672VPPD5BirrSrmCls1/F2zniqfnExDRx+ZB8cI1ExjWu3Hm+IAe8bx8/UQ8KGqBmf+ewzNztlAVCBO2FV+tK+ash75ldYkPw5BYYYsLxueQGhc9Me2HRxc028LVr+Cnry1tZMDr2V7m46nZm5H7tAc1TcmiHRVRF1Ubi2v443sruXJKHq4YLUVvnJHfKsnbMl8oZpwf4NXvt1HbSd3XNIcvHbYT//zzzxv+rf//9fTu3ZvPPvusoy6t0URFSkFISPy2TU3AIsFl4uyk7gGmZfPj4/szY0AGD3+5ge1lPvqmx3HLMQUM65nQ5prqtmJJydaqAPd9so4VuypJi3Ny7dS+TO+fTnUgzKwV0WP26/dUs2xnBeN7NVVDsyxFvBQ8evEYakI2hVV+MuJdJDgN3EKhhODJbzZFNWS2gl+9sYxXr5uIE4hD8doNk/i//63m8zV7UCrS9OT2Y/tx/KDMZmV1a8M265tpD/rq99u4anIf6pcIPhs+XFHIXWcMITXOya5yP69+v42NxTUAzN5Qgi9k8+9Lx3LPB6sbOqgluk1uOrofPxiZhWpFYlqohR12bdBCReRxWnwvjSYWHWbEn3vuuY56a42mzUgpqFaCn/53MfM3lzW8PmNAOnfPHEG698DLu1qLEbaYkpvE6EvGYKtIdy636ATBEEPyxfpifvnG8oaXSmuC/OKNZUztl8bPT27aX3pfXlu4g7G9k6Ies22FA0WyASkpnkhcvy5OHZCK1xfuiPm+O8p91IQsnIbAshRJhuDv546gJmQRDFk4DdmqTO5wC59fTdBqnGAnBePzUnlp3lZ2lvvIz4jn1uP6U1YT5I/vr0SpyOdz74eruPKovuSmerFsha0iIQQjyniEACUlQVs1NIRJj3c12072qH5puCV0miC/5rCkq3fN02jaBZ+QXPzYXHaUN47ffrm2mCuenMfz10zolJZ+4bC9Nx9Kdc7zOwDc9U70ENY360u4pMxHQUY8G4qi72aliLwHUuKVsTO+oyXmBVowwJatwIgYPdtWJDgN4pxGpBzItlslpxvnMvE6jZi9vsf3SUHWDS1sSO6ZtaZRNvyCLWUs2FLGtdP6cv20fP7z1Ua8LoPVu6v51RvLGs4b2COBpy4f2+T9bSkoDVg88tV6VuysJCPBxY3T8xmclcCVR/Xh0a82NfkbhyG49Zh+iFa0tdVomkO3ItUc9rhcBgu3ljUx4PWs21PNpuIaZDNqX0IIXC4Tp9PEaAeBmc7CMAQrdlZGjRfX89K8rZwwJDPm8eMH9+CKp+ZzyZPzWF5Uiy1bN3+HgKn90mMej3eZJLgPfh/hlYJrp/aNekwI+PnJA3GiEEKwuyoYs5zt8a83ceygTCb1TWXp9oomx3996iA8+01dGYK52yo49YFveHvxTtbvqWbOhhKueGo+93y4hisn53HD9PxG8fWcVA/PXz2BFKfRKW1tNYc3eieuOewJIflk1Z5mz/l09R4GT80jGGU3FzYke6qDvPbNJmqDFqcNz2JQjwRcMUqXIJIxLeoWBcq2G+ltdy6iIVktFtWBMIN7Rpc1HZyVQLLX0RBzvvypebx6/SQKktwNYQDTlCghkAKs8N7PxLAVPz1hAF+sKSIc5XP64dEFeAQcbDDBDltcPD6HoGXz1LebGxYsqXFO/nT2MHonuLAtG4fT5MV50TPg65m7qZS/njeS6579vuG1jAQXvz9jCIMy4pp4IYIIfv7a0qjG+PWFO7hgfA43TOnDpRNzqfSHcBoGXodsqG3XaA4WbcQ1RwQeZ/Na13EuM3o9tGnw/95bxYcr9jbteX3hDvqmx/HcVeNxi8ZuZCEEQSlZVljF6wt3IAScNzab/hlxOG3V5lrweslFy7IOaCFgWTYjYsSz65kxIIOjClL5+UkDefybTZTWBPE4DM4a1YuzR/fmlhcXNpyrFPzf+6t45KLRuAyBH8ncLWX8b/luPA6DiybkkJ3kxrRslFKkuQ1euGYCv3hjGZtLagFIcJncfEw/zh6Rhd2KBDHTNKipWwSYonGNeT1G2OKaSblcOjGXPVUBnIYkxevAw96cA1upZnvT139eKS7JE5ePpTpgIQTEOQw8kialYIYhWbytolkvx9PfbuYPpw3Gbdu46+/B+tr2ZpCmxGdDddDCYQg8huyc/AlNt0Mbcc1hTzgc2T2/Mj963S/AqVHqtE1T8sGqPY0MeD2bimu4690V/PnMoch9jGvQkFz9zPes3l3V8Np7S3cxvHci/7l0LI5Wym1aUuKzFR8u2klRdYCjCtIY1DOhkVFqLQkug8n5qczZWNrkWLzLZObo3qhAmAtHZXHmiCwClmJbWS0fLN/NlU/Nwx9qfL0l2yuwEFTbcNHjjfMM3li0g2MHZfDns4ZFEsAsxYBUDy9cPYHasI1l2cS7TTxCtGjAhRCEDMnrS3by/HdbKa8NMSY3mR+fMICsOCfS3u9zqGvZmlOfpGg1NpZCKY4flMmHy2N3UTyqXzoBfxinrUg168IrMWLzhiEproldQgaRWvFwG7urWabBC99v57GvN0aS8oBBPRO495wR9PI6UPvP+xBiOiT+urxBVzP5EpqOo/sE9zSaA8SBokeii5OG9ox6/KIJOSRGic3W2vDo1xtjvu9na4rw7/PMEqbB/Z+tb2TA61m2o5LHvt6EMFt+nFuG5M1luzjm719yz6w1PPntZq55dgHn/mcuFZZqNnYfDY9Q/O28kZwwOLORBnPf9Dhevn4S3rrXrLCNKSBk2Vz51Hxemb+tiQGHSJxZSPjlm8ui5hl8trqIWSsLMeviwOGwjdO2SZaQ5pC4LLtVO/CgIbnm2QX85cM1bC/zUR0I89W6Ys5+eDbfbStHtDE3IRy2mZyfRkZ89Krz/pnx5CS7WyWFKg3JtuogualxzZ43KT8VZxu+L2VInpqzhfs+XddgwAFW767i/EfnUFWnetdWTDOiDRCQkrCUGMbBdXszDEnQMHh9WSE3v7KY215byqcbSgmZRpvvT83BoY245rDHshRJToObji7gztMH0y8zHrdDMjgrgb+cM5xbj+1PajRZVEFUNbJ6lALfPlrnPlvx1qLYJVWvfL8NfwsGQkrB9ooA93y4psmxXRV+bnh+AYE2PsWrbcHFj33HsOxkXr5+Eo9cOpYXrp3Ircf2o6jKv7f6ypC8u3w3328pY2gzrT9nDMggZClmbyiJec5j32yithWbMsM0CEhJDYKAlNhKUeoL4ZcGX64tYuWuyqh/95s3l9P8Hjg6HhQvXz+xyfwm56fx1JXjcbUy3FFtK857ZA6VvhADeyREPcftkPxgdO829bsPKnjq281Rj/lDdmRR2dbFi2nwwdpiLn96Pqf86xtueXUJK0t8WAeYoCnrJG7Pfng2//f+KhZuLWfeplJ++tpSLn9qPoFWJj5q2gftTtccERiWTU+vg1OH9mRkdjKmFHhdJiluM7auuYI+aV4qfSHOHt2b3skeSmuCvLNkJ9vLfEgBXqcJKmKtQpbdbHy0NmgRslWz6mNhIXj4y/Uxj68trKailc03IBJbfebbLWwpreWfH69FCJjeP72hS9fawirevmkKTiCA4O8fryUnxcsvTxnEDc8taJKQ5nEY/OqUQY0WL9HYWe5rsRGyZRo8//12np69mQpfiFuP60f/jHju+XANl0/uw7tLYzdFqQqE2Vbmo1+Su015BpZlk2wIHrtkDD7Lprw2RFqcE5chcNg2diveS5qS577dgi9k8ZcPVvOvi0bzf++vbJTRnpHg4tHLxhLXhsQ9ISL92GPVlQN8vrqIm6fnN3sP7UvIkPzqzeV8ubao4bUFW8q49Il5/PqUQZw1rAeyjU1YQgjuemc5RdVNl1Hr91TzxLeb+OFRedjatd4paCOuOWIwbBts6JfsBiIPdDsYhhhG3CvhnpnDCVqKV+Zv49v1xfRMdPPLkwdRVhtizoZiXPuIdTgNSbzLpDpG8lSy14FDCqKKadcRshWbimubnceOch+ZPeJb5fb12Xs7hJ04pAfXTOvLdxtL2VJSw/i8VG4/vj9+y8YlBVtLavCHbNbtqea1Bdt56qrx/OfLjXy7oRgBHDsok1+cPIgUh6DWjmSjxxpCfkY8ohmDGDYkv3hjGV/V9Qcfk5tMXloct728GACnKfHFqPuupzYYSTxra5lWvUCNQ0BinINIwb5qdb2231J8sz4y7t2Vfm59aSG3H9efn500kG2ltaTHu8hLiyM3xUNVZevbXyoVmXdzuNogzyulYENxbSMDvi/3zFrDycN64mljpXpAKb5e37Svez0vz9vGVZPzWr3Q0Bwc2ohrmmAYkqCCsFI4pUAeQFZ1V6a1jUZCtmJrmY+fv7a04bW1hdV8ta6YC8fn8NvTBmNYVsMj0CPh8sl9ePiL6GVMVx+Vh1fSrICJQwpyUjxsqpMAjUbPxNbFbSMIwrbN8YMzOXNULy57fF6jnd5Dn6/n4UvGMDorodGO8YPlu1m8rZyLJ+Zy/fR8lFKs2V1FvClRlo3bEJw0tCcfxEgSu+3YfngkRNuMCSEorA42GHCASyb14YFP1zX898qdlUzom8qGouifgxCQnxF3SFp5SiEiHpg6CisD/PrN5bgdkvR4F5X+EA9fPIa8VE+b3zs93kmSx0GFLxT1+Hljs/GaslUueiUlz86N3XTHshXzNpVybH5qm5IlA+Hone3qqQlaR6yAjRDU9SQQWJbdKdUEOnihaYRlSBbtrua215ZyyVPzufP9Vez0hbG7kcBJexFA8Ot9FLv25eX52yiuDrKvnqcdtrl8Yi7HDspocv7JQ3ty/pjsFjtWmUpx44yCmMfz0ryktkEi1iUiYi3XTc/nJ68uaeKqDduKH76wEJ8NfVK9OPf5nndV+Pn7R2u5/Ml5XPHUfCr9YVx1SUvStrnztMFRy9eumNyHCX1SYmYqOxwG7y7Z1ei1jHhXQwkawLtLd/KD0dm4Y+w8zxrZC88hSqByS7hsUm6T1/0hm+1lPsKWoiAj/oDe2wP88ayhUY9lp3iY2YYYu6UUtS2EPaoD4TYnynkcEVW9WOSleY9IwxI2JLv8Fn/7fAN3/m81c7ZVEDKMg04ibAm9E9c0EDYkf/tkXSO96y0ltcxaUcg9M4dzTEEqogN3PoYhCCiBRcQ0xhnikLXnNE3JnPUlUUVK6nl27hZ+fUL/Rg9VI2zxpzOHUnZCmE9X70EKOG5QJkluM6rm9v7YtiI/1cMN0yPyn/uSGufk0cvG4qb1cq3Ctrnj+P68u2RXzHh92Fb8b/kuLhyTzfXT83nw86Yx+RSvgwvGZzfomCsFTsvmkUtGU1gV5PM1e/A6TU4YnInXlC3Odf/Ys9zPkvhDdp2XYCx/eHdFg4E3peCcMb350fEDkKHmDVRHEQ7bTMxLZVR2EoujKLv9+exhJLoij1ZlSEK2wm3IVmXk25bNxJwkXr1+EvfMWsPCrWXEO03OH5/NVVP64rLtVsfYnQKOHZjJt+tjJyCO65OCZdkIAbaU+BXUBsJ4nAZGMEy8s6mJ8Eq4YkpeTI/THcf3xytFVC/M4YplGvzt47WNnp3vLNlJVpKbl66dSIIUHeY10kZcA0TiZzsqAzEbVvz27eV89uMZuDvIUWYZkjXFtfzz03WsK6wiI8HN9dP6MqN/equMX3sjhGi2jSRASXWQIBCWjRt1mJZNpkty2djeQKROXbXBrWZYNldNzGXm6N68+v02iqqDzBiQzqS+qXhom9KXUpBgypiSs/Ws2l2FRHHphBzS4p089Pl6iquDCAHT+qdz1+lD8KIaGRClFA5LkRPn4OoJOUBdqKKFOub6uv2nZm9ueG19UTUjspMaJYd9ubaIoqoAtx3XP9KERClQsGhrGZZlt6n2ur1x2hb/vmQMH67YzdNztlBWG2RUdjI/On4AvRKc+MIWi7ZX8ehXGympCTI6J5krp+SR6JCIFr4/aSv6Jbt48PyRWAKEiuz+7bDVJnW7cNjmpKE9eODz9ZTXNnXPj+uTQprXAbYiaEj++L9VzFq+uyHPYXJBGveeM4K4ugY1EHlOhBVcNjGX3RV+3tinGsOQgpuPLmBSn1TCh+A3e6gwTcmcLWVRn527Kvzc8eoS/n3hKMwOenYK1c2CnUopiotjtx3sDiQlRWJlFRWtT3rpaKRp8P8+WM07S3fFPOfv543gmL5742ftNQ/bkLy5dBd/iVJWdfSADO4+eyhmB8aWos1DSsHaMj8XPf5dzL/78QkDWLqtnMXby7lgXA4XT8jF3YwUa1uJxNci62zbtpsV0mjuuzBNyQdri/n1m8ubHKvnV6cM4oKREcEbw2FQaykCYRvTkLhkdJW0gyFkSG59ZTELtpQDUJARx29PG8L1z31PaD9lOrdD8sQV4/nF60vZXubD6zT46PZpuLqA6InpkNSEFQjRoCYXFIJ7P17Hm/uVGxpS8NhlYxnRI75Ni7qDQRqCkqDN7a8sZtWuiH6BEHDC4Ex+f8ZQnJZFUEpuenERS6J4FXone/jv9ZNwWBa2IdlVHeT+T9exprCKm2YUMD4vldW7q3AYghG9k3AKkF1MVa6jn7chKbj2+UUxyyEBPvvxDBJa0YM+Gmlp8c3W3uuduAaIxM9Ko6zW96W0JoQ4EKWJFggquHdWUwMO8MXaIjaV+BiY2pZkroPHthW5qR76pHnZUtI0WzzOaTAxP5V/frIWpeChLzbwztKdvHztJJzt1JtMKQi2ENNsDeGwzfR+6bhMGdWlbkrBKUN7NoQurJCFi4gCF8oG6+D1zffHadvcd/5oHvxiPW8v3sGGohpeW7CNF6+bxAOfrePrdZGM+GMGZXLt1Hwe/mJ9Q81+XlocsoukToVDEZW4hkwvKdhYUtvEgEMkkey2lxcz6/apDb3NOxrbUqQ7JU9cOhafZVPtD5PsdeKWYFiRwNXuqkBUAw6RSogFW8uYkpfCF+tL+Nk+SZ53vr0CpyGZOaY3Pz6uH+IQhb4ONTaC7WXNV5RU+kMkeDrG3B6J+QeaKDikYGq/tGbPGZub3O7ZlqYpmbOxpLmqK56duwV1CAQk3Erx7FUTGNSzsZhHZoKLhy4Zw/0fr2sUy91W6uO1hdsxTYmUAtM0ukzHM7cgImayXwmTwxA8etnYJt25OhqlQKAwBTx62TievXoCF4zP5bNVhdw4PZ9Xb5jMU1eOZ1DPRG57aRFf75PJfvPRBYcsqa0lLCl44pvNMY9XB8Ks39N8x7x2H5OlcNg2iQJ6eUy8ykZakQxz05QxS9DqeW/Zbnw2/Patpp6coGXz8vxtrNhV1eEJXF0VCeSlN6/clxxLi6Id0DtxDQDhUCRO+cBn6xvJPdYzoEc8PRJcHaLbHKuuup6aYBgbRWc/ImxbES/hycvGUuYPs6WkhowEN5ayCYRsfnhMP66zbFwOyXtLdvHy/K18v6WMc8Zks6W0lpW7KslO8TC8V1KkUcohdDMqy6Z/iptPfjSdL9cWsWJXJQN7JHDcoEzc0HzdWwfhEpGwxeVPzmv0+n8XbOffl4zl/727ko37ldpdMjGXsbnJHR5zlVKgVPQe6c0RthQlLeipF9cEUVnxmEoRjiJr29l4oySv7UtuqoflO1to9DJnC389eyiii3hIOhO3gFuP6cd1zy2IenxyfhouQ0AHdTLURlzTgFfAy9dN4obnF7Czwt/w+qicZB64cBTu/RKb2gPLshmfl9rsOccNysQBHIpc5HphkB4uSc/eiZSFFat3V/Gn/61iV91n5DIll0zM5YkrxuF1mpz7yBx2V+79/DwOg/9cOpbBGd5mjaXDIbEQGCKyqGr3bBVb4UZx2qBMzhzaA9tWhyz7HwDL5uYZBYRtxavfb8eqc8coBf5QmOevnsCG4ho+WVVIgtvkjBG9SHIZHZroaBmS2rBi/a4q4lwmfVK9bVqAuQzBmNyUmO5pgKxkNz9/YwWTC1I5ZVgWHmzsQ9SqNhSyOH5QJnd/sDrmOWeO7BW1H8C+VPlDWOrINCiWZTM8K4Frp/bl8W82NTpWkBHHvecMx2G3XkyorejEtkNAV0xsq8cwBD4lKKkNUVwdIDvFQ7zDwEXTxKb2mkfYkPzwpcUs2lbe5FiK18G7txyFq5MT26LhdBqUhxUPfb6ez1cXNZGdfPOHU7jx+QUUVjbdiTkMwcd3TCcuyk9ZGJJaFRFYWbCljKwkNxdPyCXJaURU5tpxDm0hEhKQKNV6gZwDQRmSgIpItXrdDjLinREJ1LDdEJaAyILjQJ5WpimptcEftlGAx5R4orT1DJsGf3h/FR8s382Y3BRG5iQhiWRpD++R0LRrWgyqlOCk+79qkqAHMLRXIldOyWuILSd7Hfz3+kmkOuQhEa6ByMLlkW828/Q+1QL1HDMwg7vPGkq5P8zJ//om5nvcflw/rhyX3SW7mHXW89YyJNUhmw+W76bSH+KYARnkpXlxHWRSaEuJbdqIHwK6shGvR4hImVVzN197zUMIQdCQ/O6dFXy6ek/Dg3pwVgL3XzCKdKc8oF7araWleRiGxIdg9sYSPllViNdpcsqwnhRVBfjDeysJhG16J3v4xckDG2RDo3Hrsf24ekIO4X0MojQEmyqCXPrkd006hv3sxAGcM6oXRisWMO15T0kpCAjB1jIfX64tIt5tcvKQnsSZstWLigNBCEhMbN/fhm1IVu6p4a53VrC1NJJ8lJPq4f+dMZShmfENhlkZkrs/XsvS7ZX84ayhrNxVyez1JbgckpOH9mRkThJJktbdh4ZkbamPm15YQKVvr/9oWO9Efnf6UG59aWGjhd7QXok8dskYHIcw294yDeZtKeOBz9azoaiaXskerp+WzynDekIgRNiQ3PHfJXy3qazJ33qdBrNun4a7C1QLRKOzn7cOh4EQkYTS9liYaSPeBekORrw1tOc8hIj00PbbUF4bjPScNiRuoTrUgEPz85BSUG4pLnz0uyY775OG9uSMEVnc8tIiJvRNZULfVB78LHbzkun90/nbD4Y1qhMOGJJTH/im0cN+X9695Siy3EaLO9D2XFD5peSqp+ezbk/j39n10/py9eS8uqzmjqE97ynDkKwqqeWSJ+ZFPf7c1RMYluElHLbxScmFj83lvgtGNzGyABP7pnLfBSMxW+mRiE9wU+4Ps7GomuLqIGnxTraX+/jHR2vZE0V/4LMfTyfhEOeF1XssEICKNHGByHchBAQNgzvfXs6nq/cmwuWmennootH0ijMPWUigJbr781aXmGm6BUpF6ku9gLe+FMO2my3WklIQEhHxCQCHiMiWtqdbMoDgtpcXRe3YNGvFbiYXpDEyO4mymiA9EtzNvlfvFA+mFNTbQCkF6/ZUxzTgAE/P3syvTxiA6iTxjJAU/PKNpU0MOMCjX29ifF4qY7MSOkUT+mDxK/jDe6tiHv/j+yt56vJxOIkI91w+KY9/fLwmajjku02lvLNkF+eNyGoQ9WkOQwrSvA6cqR5C6XGc/tC3dTK90akNWiS4WidfY5qSMCAQSGW32yI3HLZjlr5FFPoiaoR3nqYorPST6HGQ6DKjhiY0nUfXqH/RdBqGIQlJSdCQBKXEaKFrUpfFkBT6LX72xjKm/e0Lpv3tC3759gqKgzaiHcu6fJbNip2xRRxenreVmWOyWbenmoE9E2JqfQNcNrFPI+lNKQXbSpvfHWwr8xHqxFhpwFJ804xM5wOfr8ffjsMxDInTaWC24T40TUlICoJCNHv/Bm3FmsLYCVlrC6sJ1n22cU6DUbnJzN1YGvP8J7/dhK+N34VtK5StyE31xjxHCkhsRQmSYQiChsGnG0r52Vsr+M17K1lWVEvIkG3WPz8QlIqoCcahKEhyke6QOO3OafKhiY3eiR9BWIZkVXENf/toLct2VJDidXLpxFwuHJ8T0WQ+RIk1bcUwBNtrQpzzyOxGyUOfryli9oYS3vzhFHq4jHaZT3O7ZIjIKqbGOTGlwOOQPHLJWK599vsmmus/PmEAqR6zUZazbSsG9Gi+Ucbgngk4ZItKpu1Gpb/5+W4sqmmXCgVhSPzA4m3lrNhZSd/0OKbkpxGybBwxFmFSCgJS8tGaIl6ev42QZXPC4B6cPy6buCi7wf312KO+Z53rOM5pUFQTe6cMRNzgB2AsXULxo+MHcNmT0d36pwzLwtXC+wohqLIFFz42p6EqAmDWikIm5KXwrwtGdao8cfcKwh7eaCN+pGBIPl5dxJ3vrGh4qbQmyL8+W8+sFYU8deU4HHb3UFwKKMGdby+Pmv0bCNv88b1V/PPc4RjtUNSR0kLHsIKMOISA926dSqpT0tNr8vGPpvPfBdtZur2C3sluLp+cR5rHbJKgZtuKnGQPWUnuRg/meqSASyf1we7EjN94V/OPhN7JnjbbsfrSOSkianBIyY7qIJc9Oa/RosFlSh69bCxjc5Mbdub7Zjv7peSyJ+Y1qh1fvbuKZ+Zu5rUbJpO2X4a3U8D4vBTmb26ajAUwtk8KThmp3/VK6JXkxpQiZtObgox4DuSWsizFgHQvvzplEPfOWtNQSgcwOT+V3546qFFL22iEpeC3byyLep/M21zG64t2cNGY1nc40xw+aCN+hBAA/u9/0eODawqr+Hp9MSf2S48qoiGlICwEIVthSoGTjk82a46ArZqtw52zsYSgHWnreLC4DcFRBWl8uyG6i/m2Y/szvGc8Kmyj6h7O8cB1E3MITcjBFALbit0AxSPgmavGc8kT8xo1XHEYgn+eP4oksxO34UTmOzonOWq5H8BNM/LxxugTvj9CSnzAG0sipXM9Et1cMiGHBI9sYsAhYsR3VfjZUurju00leJ0mk/NTcYuINOzTszc3EX+BiLfkl28s46H9mkw4UPz+jKHM/PfsJkIlTkPy+zOG4FQR7YNw2CbeYXDmyF6Nmnrsy+3H9mv13PdHWjY/GNaTU4f15PstZVQHwozrk0Ky28RhtVw6F7AUXzcT5njy282cPbJXp8m5aroO2ogfAUgpWL+nulnFpZfnbWNafhr77zstQ7Kp3M+Dn69nY3ENvZI93DQjn8GZCVHfpzNojSuvvaQVTFtxzzkjuOaZ7xvFV0WdStPgzHjsKLufcNhG0HLLUMuySXdK3rppMmsKq1m8rZxeyR6OKkjDhUJ0ctmOC8U/zh/JRY9910iwBuDMEVlM6tu6DlVSCjZXBbjkicalc8/N3cLtx/Xn2mn5/OPjtQ2vxzkNHrlsLPd9so5f7tPDXYpIad55Y3N4ed62mNdbuLWcgKWaPNB6xTt45+ajuPvD1Q3yotP7p/OrkweRtn/IJWTxsxMHsLPcx9xNe2PjQsD10/IZn5tyUEpxwrZxAzPyUiLVGJaNsuwmd6phSAwjUt5Z74nwt7ByKKkJoo5M1dMjHm3EjxD2r0FucjxsNZGYtKXgjSW7GjUn2V7mY96mUi6dmMuPju9PQgvu147AaQgKMuLYUNR0VwaRulunEO0SuFNK4VE2T10xlp0VAb7ZUEyC2+TYgZl4pEC2Q7mVZSmcKEb1iGNMVgJKqU4RzTBNA5uIkVJWJCfCthVJhuT1GyezcGsZs1YWkuAyuXB8DpnxzlbHXf1CcM2z30e97+7/dB1PXjmeFK+DsrqmO5dN7sMLc7cyb1PjxDJbwf2frueMkb2oakGeNxC2iTMFUgr8QrC93M+CLWXkpHr509nDIreDUs1WMTgsi3+eN4JSX5jZG4pxOwym9UvHbYh2K62LlQgmDYEPwYqdlSzZXkF2iodp/dJxofA6JQ5DRA0hAfRNj+MAm2RpujnaiB8B2LZiUM8EmrNrxw/qgceQjcpnfDb89aPo3cWe/24rl0zKPSRG3CvhztOHcOVT85scEwLuPG0wLtHyLri11Euv9k100m9cNlDfN7t9n5qWpbA6sAa7noh4DXy2rpiPVhXidRhcOrEPuSluTCuSbewEpvZJZlrfFAQQCtmtlh6VUrC+qCZqD+t63ly4nR+M7k3IUhw/OJPsFC8n3vdVzPNX7KxkcFZCQzvN/fE6DeKcBhJFtRJc8eQ8Nu/Tfc6UgrtnDmd6firSsmMm5ykV6QffwyU5b0TW3gVVB4ePDENQ6Le45Il5lO6TYOcwBP+6cDRjc5L4wejevPr99qh/f+tBuPo13ZtuWl+kaStuQ3DWyF5RjyW6Tc4fl93IgDscRiP1tGi88N3W9h5mqwiHbQZlxPH45WPJSd0b+e6bHsfTV46nb7KnQ8pe6rXGD6ne+EEipaA8bHP2w3P4xRvL+HTVHt5duosLHpvLb95ZgWXurVUOh21CQYtgsKmXpqVr1LcNjcXOCj/nj8+hJhjm+ucWsKPc1yjha38e+2ojPz1xYMzjV0zOw2NElOZufGFBIwMOELYVP3ttKcW+cMx2uoYZKbssDtnsqA1TbakGvX4pRYeWcfkQXP7k/EYGHCBkKW5+cSHVAYsfHdefo6J0Grxmah5T+qZ2SclTTcejd+JHCIZl88uTBpLidfLivK0N8fFhvRP527kj8IrGPaOFiMTZmqO0Joh9iGpNDMtmbFYCL18zEV9d/NltyshuRD/MYhJA8Pqi7ZwztjclNUFmrdjdUEb32eoiPhtcxCkD0g/qM7QsRf/M5kvnBvVMIBCy+GRlIYGwjbOFOvGy2hCDeyZw1+lD+MuHqxvuXyng/HHZXDEpFztkUR60Y+7WAR75agO/O3kgDQpBdShDsrKolp++trQhF6AgPY4/zRxOgstkR1ktPRLdpMc58bSziqCUgg3FNVEFhSDi8Hnx+2388Kg8/jZzOGW+MN9uKMZlGkzrn45Hik4tL9N0LbQRP4IwwhY3T8vj6qPyqA6EcZkGbkPUSZvu1wwibDMlP42Hv9gQ8/2OGZiJcQj7OtcrTDnrn/+2rd2JzWFIfGFFlT9MIGRx4uAeXD8tn+LqAH+dtZaFW8t4/OtNzOiX1qYsZ8NhUGspbAWGAK8U9E520zvZw47ypjtyIeDU4Vn87aO1/Oui0Vz19HxW7qxkTG4yC7eWR73GNVPz8AjF6UMyOWFID9bvqSZoWQzskYBLRIyYlKJBHz0Wq3dVEbRUo/kJISj2h7ni6fkN3oC8NC93nzOC3761jLWFe9Xreid7eOyysfTwmNjt5O2RUja6RjRW7aqMVIdYNpkuybnDs4A6V3830XfQdAzanX6EocI2btsm3SFJEAqHHV220bYVfdPjYipNpcY5mdovvdNFH5xOA9Nh4HS2TqJSU4eULNpVxUn3f0X/zATG5qXyr8/Wc/ZD33Ln2yuYOaY3D108JpLl3IZKcMs0eHnRTs56eDbT//YFZz8yh9eW7cZlSJ6+ajyZdfrb9ZhS8H9nDeP9pbtYv6eaCl+Ii8bn8sQ3m/jFyYPIiHc1ucbkgjROHdoz0nvbsnFZFsMzvIztmYBXqYamLEqpJtfbn6y6WvB9saXgn5+sa+TO/81pQ/jxq4ubGNcd5T4ufGwu7anCrZRNn2YU3QD6pMbhqBu3UhAOW9rjpAH0TlzTDG5l8/zVE7j5pUUs27G3Ljs/PY5HLh1Dmrfzbh8lBT4FL3+/g9W7qxjQI56zRvbCK0Wnl2F1RwICbnlxETdML2B9UTXP7NN2cv2ean771nJOGNKDP/1gGK1dHoUNyS/fXM7mkhouGJ9DvMtkU3EN//g4sqv/wxmDee3GKczfXMrq3VWkxzsZlZPMxysLmTEwg8kFaazZXcWYPimcNaoXn6wq5IGLR7NoaxmzN5TgcRhcNqkP/dK9mPuJoUTLLFcKeiS46JHoiqp/DnDD9PxIZvo+rwVVRBu9nuwUDzWBcMy4fqU/zBdrijh9cGa75EdYlmJwzwQSXGbMDPzLJuU2kuzVaOrRRlwTE9tWxEn4zyWjqQ5a7K7wk5HgItnjQAK7q4KYUuIwJMK2O2xXrqRgaWE1Nz6/sEFN6/1l8K/P1vPgRaMZ1zsRtH5zTExT8tXGUoSAaf3TufDRuVHP+3hlIddN64tbihbDElIKdlcFOH1EFqYheXPhdkpqggzrncRTV43nhblb2FMdyU7/12fryE31UukL8dL8rdwzcwQ/+e+SRkbSaUh+f+YQ3l2yk/V7qvnHeSNxS8CysaPUUsfCLRSPXjaOix+bS02wsdG7ZGIuBWnepm7wOtnVCl9kvAUZ8Y0WrdH4en0Jpw7ObOWoWjfuJ64Yx2VPzmui53DnaYNJcZkovVjVREEbcU2z1JdXpRiC1DQvYUPw7cYS/vnJOraX+TCl4JThPfnpCQNJMDqmm1EAwU0vLGwih2nZilteWsRnP55B887IIxshBDvKfIzOTWb2huJmz311/jZ+e+KAFt/T4TCoDVl8unoPHy7f3fD6ip2VvL5gO/+8YBRLd1QwtSCN7WU+ttRli//rwlH88o1lTXa5QcvmN28t5/lrJvLZqkIcQoHV9o50tqXIjjP58PZpfLB8N7M3lpAW5+TySX0ide5R7s84Ay4Yn8M/P1kHQE0gTHILcrvp8Y6IjGybRhcbZSnyk9188qPp/G/5bhZtKycn2cMF43NIcEikXqRqYqBj4ppWo6TgjcW7+Ml/lzY8hMO24t0luzjvP3PwHUh3iBaoL3WLJXJh2Yr/Ld+Fw6Fj5BDZITscBuY+pWKWZTM8OwmnIakNNm92qoNWqxqcCAEVvlAjA15P2Fb85q1lDO2ViNeUnDa8JwBJHgcep8GmKNKpEHGHv7N4B9dNz2f+1nJWFNcSMGQkW64N2JbCbducN7Infz17KL85cQC9vQ7MGIYwHLY5b2w2fdIiS8FF28qZ0DeV5nI2L57Qh/A+rnTTjHQGrLChVgiqg80L00RDWZF8lQtGZvHn0wdzy7Q8kiTagGuaRe/ENa0mQERtKxp7qgK8tbj9mzAIIVhf1DRzd1jvRC4an0tOqhenGWmp2lXqt6UUh6QjXJkvxKZyP3M2lpDidXL0gAw8hgDLZkBGPEVVAS6amMvjX2+K+R4nDemBaEVcxB9WvNSMDGqlL0xZbZBsr4NfnDyIoqogQcuiOEYZVT2rd1fx2oLt/O2jiCRrnNPgr+eNZFxuMkHLptIfxmlIPKZssY+1bSmMeu36KFMynCa+usWhIeDl6yby2oIdvDx/Gx+vLOSXpwzmz1H6DVw2KZfimgAeh5c4Q6Ck4K1lu3j4iw0NCnST8lP509nDSTZlm7PY6+/j9r6bTVMSUpEeLk6hSzH3R0pBSAgCtiIQtvE6DDxSdPlcBG3ENa1CCMHm4tpm9dffWryTs0dktWsTBtu2GZqV2Oi13585FJcpeerbTawtrCYtzsmVU/I4d0zvVjWT6AikFPgRlPlCFFcH6ZXsJsFh4KTtLuEDuXZRTZDLn5zXSIpWCPjZiQOZOTILD4r7LhzF5pJaBvVMYPXuprXUPRPdTMhrnTZ60LKbCJPsT0WdQXOiuG5aX/r3SGB5C7HmHonuBkMIUBO0uPnFhbx6w2Rue2lRQxevgow4/n7eSLLjnQ1KckIILCkIqMjfOQ1BeW0ApyFJ8zpw1X0X0jSothX//nQd7y/ZRdCyOXpgBjdML2D6gHTOHt0LocCQgol9U/n3FxtYt6ea3sluzhuXQ0lNkKuemo8CXrluEl+sLWpSijl3Yyk/+Pe3vH/LVNwtfpodi5SCgJB8s6mU1xZuRyn4wejeHJWfhkvtbUHc0Oio7natCVrEHSFVIIYhqbQUv3t3OV+vK0bV5UlcNrkPV07q06Xr8LUR17SalpqK2OqAOjU2SzhsR7SrHRJ/yObqo/LYWe7j0a82NpxTUhPk7x+v5dPVhTx80RgcnSBdui/SkBT6wtzwwgK2le6N9Y7KSeaBC0fhldGzqQ8E05RIKeokWiPGK4jg1pcWN9GSVwrunbWGsbkpDEh1k+V1kORK5JFLx3LXOysaGoIAjM5J5h/nj8SDatUO0GVIRucks2JnZcxz+mfGY9s2AsGgngncO2sNZ43q3UgzfX/OGZvNnW8tbzKPx7/eyBkjezV87xuKarjg0bl8cPs0EkXEgPuE5K53lvPZmiJUnRE+fnAPrj4qj9+/spK/nzeCBKek1G9x3n/mNJKFnbWikM9XF/Ho5WN5evYWfn7iAEK2Yt3uKn53xmAWbClj9e5q7vlwdaN4vgIe+3oj0aj0hXlx3laundTnkO3mhAC/iHSN27cD3OwNJeSmennxmgm4hUIJQVHQ5u4PVvHVukjexLR+6fzq1MGku4zDPnHUh+C8R+c06iRYE7R45MuN7K7w88sTB0TNp+gK6Ji4plUoFakbdxqxb5kzRmThbWP8sjW4gWevmkCc0+CkYT15PMZDc/G2CpbvqsTYb4xCAKbELyU1CIJSNvSrbg98wIWPzW1kwCPjKefKp78n0B56nTIy/lnrSnhk9hbmbq8gICXSkNSGbRZujd4zuyAjDoVieVEtT3y3lU/XFOE2BffOHMaXPz2ad285is9/MoOHLxxFomx9YqIKW1w5Ja9JzXU9I7OTSHKZKBW5dyxb8f6yXTz8xXruPXckbkfTz//aaX1RSlFW23SHv2x7BX3T4xq9FgjbPPrVRpSUBOoM1aerixo8MZatmLViN394byVXHpXH5U/Nx2cJ/vXpuqi67kHL5p4PVzM+L4VF2yvYWe7H5TR48but7Cj3M31AOuP6pDacnxrnZHelP2a+BsAHy3fj2+czFUJgG5JA3ZgNs4N3uobBA3UdCPdna2ktf/t4LcI0KPJbnPXQt3y5trjuO4Ov1hVz5oPfsKsmhNEBv+uGIZoGQRnJKQhJ2eT329GYpuSjVYWNDPi+vLV4Z0PYpSuid+KaVuMEbpyRz78+W9/kWGqck3PH9sbqgDibsm3yk9x89pPpfL62uFmBqufnbmH0OcOxkARshRSgEPxj1lreX7aLkKXITvFwx3H9mZqfetCra9OUvLeisElv7Ho2FFWzvdxPQZKr0W5cStEQO29pl64MyZJdVdz84iKC+4w30WPy4jUTY2qO90nz8ueZw/nxK0saKaf9Tgru/sEwZhSk4XUZgAJbtSqhbV+SHIInrhjHrS8tajT/EdlJPHTxmIirtu41X8giZCnmby4jzrmFZ6+eyBdr9rByZyXpCS5mjunNrnI/8zeV8vy1E3ni6018tLKw4T1T4pxUR6mh/mptEbcfW8CqXZUxE+ZW7KzEkIJg2GZbWW3MBQ/Aql1VDM5KxFaKm19Y1KgdqykFd50xlHi3yfNzt2CrSMy9OQy51yApQ1Dks7jv03XM31xKgtvBJRNzOWNEFi7b7pCwi89WvBmjPzrA+8t28dMTB/KH91ZGDZWFLMXv313BQxc07tXeHkgpCEjJ099t5YV5W6nwhRiZnczPThxAvzRvpyX0+W3F+0t3NXvOwi1lHJOf2iHVNweL3olrWo2wbC4en8MfzxxKRp0ylhRw3KAMXr9xMt52d6bvRdk2TluhWnjQBS2b8oDFI99s4pi/f8nOigAXPDqXtxbvbNgxbS/z8dPXlvLqoh2og1z1h4Ev1zVftjV/c2nD7kIakSYbK0pqeWtFIcuLaht21LGotRQ3vrCwkQGHiLv20ifnkRwXPQvhR8cP4NdvLGsifWrZip+/vowSf/jgmnpYiqHpcfzv1qk8d/UE7r9gJP+7dSqPXDwaj2pslFym0XCtL9YWcdFjcxmdm8yZo3ohBPzwhYX85L9LeOLbzVz2+Dx+MKY3kwv2Nvs4d2x21Aet22HgNCTvLW2aJb8vczeWMKx3Iku2V9Ar2dPsuQlukzteWdykn3rYVvzuneWcMqwn8S6T8toQqfFOPM1URswc0wuvKZGGYHlhDac/+A0frSykrDbE1tJa7v5gNVc9/T0B2TGP4nBdklYsQpYibKtG/dP3Z+HWcoIdkGgSkBHvyUNfbKC8NoRSEe/VJU/M4/P1xdBJO3KBwGzB0+DoZO9AW9A7cU2bMMIWpw/O5JiBGYSUwiElDhSG3b5NIaIRDtuM7ZPS7DlH9Uvn3g9Xc/mUPDaX1PLN+uKGZKj9efCzDcwc1btV1zZNg5BSmFJgh+2Grl6GEKR4m0/lS4tzoZRCGpJdtSEuf6pxt6oUr4OnrxxPdryzSSaz6TD479ytMXfb5bUh1u6uYsaAjEYx7gSXSYLbjNlzHSKdwX5z0kBoZbzWNCW1NgQthSEFLhnpy+2yFUPSPIh0L7YdaVm6v9lwSzh2YAafro6MMTPBRTCs+PGrS5pcJ2jZ/OL1pdx/wWjmbChhcn4avZM9LN5W3uTcC8fn4JQiqnt+X5ymJGwp0uOcZKd4mb85+m68X2YcJdXBJqGRepSCNxft4LQRWbwyfxtvLNjOz06K7GTrEQKOKkjnwgk5jMpOxmcpnA6Dn722NKoXaU1hFbNWFnL2kMx2zxh3SEFGvCtmc5Vkr6PFXBdof3l205R8sGpPzPvzD++tYuod02heRLd9cEm4YFwOczdGX8gYUjAqN7lL7sJB78Q1B0A4bOGybXonusmMdyItu02tKg+GBKfBsQMzoh7LiHcxIS+VT1bvYVtpLaeNyOKTVYVRz4WIsVjfjJEDEIbALyUvLt7BT95czh9mrWVbTYhw3crcDttcPqlPzL83pGBKvzTCYRs/gosf/65JVndZbYhLnpgXVY/bUoqVzXTlAli4rZw/nDWU1H125BkJLra10A50TWE1gVY+mCxD8s2Wci584juO+ceXzPj7F/z8reWUhSOLE9uOJNrFug0MW/H7M4Y2aPGfNiKLNxZF740NES9DbTDMgxeP5s7Th/CT/zY19n3T4zh9RBYBf5jzx+U0O/4ZAzJYsq2ccXmpnDq8Z0wPxB3H9WflrtjJegAb9lTTK9mDy5ScPbo3pw3twb8vGUNBRhxuh+Sxy8YxrX86d/9vNVPv/ZxLnpzHZ2uKuPP0ITFzCF74biu1HWAjvFJww4z8mMevmxpR6BuyXwXIvvTLjMfVzo2OfBa88n3sEsXaoMWWktqYbWPbk3DYZmJeaszOezfNyMd16Po8tYg24kcYptm+SV2djWnZ/OkHwzl/XHajJLvxeSk8ePFo7npnBUrB5pJa4pwmLSlVNtdKVUrJ9uoQJ973NX+dtZav1xXz1qId/ODfs3ngiw2EDYlSip4JTs4fmx31Pe46fTAuIp/7vM2lMWPn1YEw36wvbvLdGFLQN715PbqsJDdPfrOJd285irt/MIyThvZg+oB0BvdMaPbveiW7cbQiYcnhMlm8o5LfvLW8YYeqFHy5tpiZ/55NdSuMj1IKL4qXr53IwxePZnjvJIpjJBLVU+EL8c7inbw8fyv/vGAUkwvScJmS9Hgntx7TjxeumYDLthu+gxNiyKCeMSKLVbuq+OPZw3AbAl/Q4u/njSQraW/xV6LH5HenD8HrNJsk0O1Pr2Q3k/um8umPpzMw1YMMW0zKTuTZK8fzyY+m89L8rdz9weqGMMbmklp+8foyvlxbxE9iqOHVBMINC2EpI8lvQSFQhjwoQ2aFLU4f1pNLJuQ2OXbu2N6cM7o3LiLSrrEuc+dpg/G08yPDRuEPNX/j+MN2h/Zw3xeXsnnmqvFcN60v8a6Igzovzcs/zx/JpRNyurTgjnanHyGEDUltyOa7tcVIEal/9UjR0AGqO+FGMX1ABmeN6o1lK5ymZPG2cu54ZXGD6zwnxcv8TaUcOyiTNYXRd7KmFM32vfYD1z+3AF8UEZkX523j1OFZDE71YFo2PzquPycP68kjX21kV4WPgT0SuPnoArLiXUjbxnCYfL8ldtwRYP7mMk4d1NilGg5aXDQhlye/3Rz1bzwOg4KMeH739gqumJLHyQMyOHFgBoYQ1FiKjARXzKzb66fnYzST0GZLQQDBV+siIYl/XTSaXRV+/vLB6gad8Up/mMe+3sgdR+ejWnAFRyR8LSZlJ4Epmb+plCXbY9eND+2VxMjeyZTWBOiTFsc/zhmBVWfovDJioOqvaFo2fzxzKEf1S+fRrzays8JPbqqXK6b0YXjvZJLdJskuAxG2GJ+bTHXI5r4LRiGFwDAE6XFOlA2mBIRotgzuumn55CU6Ce1jhMJhG7cUbKkM8umqPVH/7s1FO3jh2ol4nUYT5bzJBWm4pMBCsLaklv98tZEd5X76Z8Zz04x8etZ5vA4EI2xx29H5XDutL/M2l6IUkd+/EWnhagH5KW6evnI8d72zgs11Erk5qR7+35lDGZge1+5ufo8hOG5wJhuiCDlBJNemf0akRLEzsG2Fw7a4cUofrpzcB1tFdrheKVqlm3Ao0Ub8CMAyDe6ZtYa3Fu9s9PolE3K59ZiCLi1kEI1wyGJwzwSO/+dXUd23cU6D/Iw4fv/uCl66bhL/XbCN4uqmZUvXTu0babJBJMEnICWVgTAOQxLnkOyuDLCnmd3io19t5K8/GIZEYVoWo3rE89AFI7GUQiowlGp4CNm2Iiel+R11bqo3algiwSH5v7OH8dv96qddpuTv549sqJ22lWp44NiA2xA8cfk4LorSDOT6aX3JTXLHVBOzDMk7y3Zzz6w1jeLx4/JSeOvmo3js6w28On87YVvxwfLd3DAtv9WiJpYVaSl65ZQ8Xpq/LWq8v39mPOleB07bpofbi1I2WHsfWNGGbYQtzhqSyQmDMqnfwjklEQU6y24QhTEtmxRDkJbqIWzvzXNAKJQNwpA8ccV4Lnn8uyYLuFuP7UfP+MYGvB7TYfDy97FDBABfrytibJ8Uvt4nGdJhCG6aUYAF/OebzTy1T4e5DUXVfLhiN388cygnDsxAHqBRk5ZNPHBCQRqiXq1tnxwWaStGZMbxwtUT8IcjDWcS3CYpHgcVFdHDMkJwwMJKdtjm0om5vPjd1qhVB+ePy8YlaX/ZulaMa98Ml+4gaqeN+GGONA1e+H57EwMO8MK8rfTLjOesoT2wOtiQCwFhKQnYETdpvMvEY4gDVjRLMCR/P3cEP3ltaaMHicuU3HfhKB7+Yj2Wrfjd28t56JIxPPLFRr5cuwdbQXq8k2un5TMqJ5lN5X56IXjxu608+e2mBhff5IJULpkQO9YNsKvCT9hWOAElJTUKlm+rIGTZDO+dFPF01CUNhUIWpwzryb2z1sRMEjpzZC+CUbTNDcvmuIEZDL5pCu8t3cmuCj/9MuOZ3j+Dx77eyJdri8hMcEXcgPtodtuWonecg1m3T+OjVYXM3VhKRoKLSybkkuI2Y5bXGYZgTUktf/5gdZNj328u4+7/reLcsdkcM7AHt7y4EKizmar+7yX1wuPKil06lWhKHrlkDLe9vLiRsSzIiOPxy8fhJuIlaEu+RXi/hzBWdAEipRRWyEIA+2sDKcumT4KTj+6INFGZt7mUrCQ3F0/IJdkV+3NTCvwtSP+GLYVrn5BJryQ3fz9/JCkOye7aUCMDvi93vbuCGQOOpvm8+pZpLjmr/rNz1g0vydO0CYxhSHwKKgJhagNhMhPduMSB6bvHCXj1hkn87LWlDaJBbofksol9uOaoPGQ321wcKoTqrIykdkIpRXFxdBdMdyEpKfJTjLXCbU8CUnLqA9/EjMVmJLh488bJuA5ghd/aeQgRqQf97dvL+WLtXjGOEdlJ3Hf+SJJNeUCZn7aU+GzFO0t3srGollE5SRw3OBOl4P+9u5LP10SM9rg+ydx1+lASvQ52Vfip8IX47/fb+HT1Hi6d2AfTEDy1n7va6zT496VjuOLJ+TGvf9aoXvz2xAFYCF5bvIP7PlnXqNPaOWN687MTBjR4Omwp+WpTKT97bWmT9/rT2cM4vn8aMobBk1JQ6Ld44PP1JHsd7Cjz8c36vTXz/7xgFKcO7UFljO/C4TCwiGTTh0PhZndQYSm55dUlLNgSPYNbCnjp+kk8M3szw3olsbPcxx1H5yNshV9Ilmwv5+0luzCl4MLxORSke3HGaFUrDIkfWL6jkj1VAYZnJ9EryY0Ztg6J/vz+OBySsBIYEqxQ85K+hiH5fmcl1z+/MOY5r904maxEN4VVfjxOk0SngUdESg/v/XQdLzajR/+HM4dy9rAeBMIKUJgdrH/e5PdtSDaU+fjRq0sawlaGFJw9qhc/PWEA5gEYXcMQ+JXAbymClk2c08AjaTE0c1Dz6GakpcUjm0ks1Dvxw5xAXdOIWBRVBQjbqkNLOUJScP3zC5pIdC7dXsEFj33HWzdNOSC9dWnbxAFXjMsGIVC2IhSyEELw5zOHEFRDsGyFQwriHJJ/fLaBZ+duafQep43I4oon5zV579qgRWFlgCFZiVGzlYWAG6bn45Dw3ZbyhoYd+/L6wh2kx7u4fnJEdlPaNtPzU/nojmk8N3cL6/fUkJ8Rx+WT+pDsNJp1ldq2It1jcM1RffnNW8sb4vw9E9386pRBTOuf3mwPufqmGq15NFrAmija6g1jUVDtD/PRikKumJzH6SOyEHYkHPHe0p3kpcdzxogsPl+zh2uf/Z5hvRN58MLRUR/yyrJxARN6JyBEIvHxLqoCFoGwjcdx6Jva1LvNW9OTzLJshvVKok+at6H16r4M65VI70QXpmWRU9/q1LaxiHQIjBbyqScjwcXoPsl8s6WcV7/fhlJw9qheTMxLbaR/3lEIARUhm8uenNdIoc6yFa8v3IFlK3514oA278gtK9Lq2CEAU4Bto7qBC7sroY34YY7TkJhSNOnFXY/bETne7oWgdQgh2FUZiKmxXVQVYM7GEo4rSD3gXcX+LmilFNJSe2O0tqIqBK8uaLzLcZmSKn84phjGfR+v5V8Xjebnry1tJFvpMAT3zBxOmtukxqKhD3U0npu7hUsn5jaMRVo2qabgR0cXELQVDiFQloVqhSdEWIr8JBdPXT4Wv2Vj2eB1SLySdm1UIYjUcUeLVdYT5zIJ24qNxTXMXl/MRRNy2FnuZ/7mMu77ZD1uh+TU4Vk8f+1EfvXGMl6av40rxmdHYs9RUAr8CGYt3skbCyMKYz8Y1YtpAzJwEGmi0pG7TsOQiLquaAfjm3Qpm+evnsCdddr09RruJw7twZ2nDsZpN62hBzCAqf3SG6nU1eN2SB64aDQ/fXVpoyTNL9cW0SfNy/NXT8AjVMc2/jEM/vPFupgSs28v2cmPju9P81kfmo5AG/HDHJeAU4b15N0YsoLnjsnGLemw1a9pSr7dUNLsOR+tLOSYfmnNnnOwBMN2k5IWy24cn9yfnRV+7v5gNc9ePZ7dFQEWbSsjPd7F+D4pOEVEwc6WMmaGLUR29L6QhXufUi6lIq5Zg9g7YyHAqsshqA6G8TgM3IZAKoXDrtu5GIBtH1TyTX2MszZkYytFnNMgwSG5dmpffr1fIl09Q7IS2Vg3Z3/QYkNxDZtKfFz2xHcNi0VfyOKF77by8cpCHrpkDLe8sJDzx2ZH9fgIAbUILn68sf78vE2l5KR6eOCi0ewoq2VMTkq7d6lTUhKou1Z1IMyY3BTSvI6IOmCMC0kpsIQgpBROKRDW3nNtW+ER8M/zRlIdtKgJhPE6DZxGRPZ1a4WfJI+DRJeJR+wVSAqFLI4dlMHfPjKbeM7OGtWbdxbviFplsaWklns/WsPvThrYoU1K/JbN7GZ+x0rB1pJaBqdFT87UdBzaiB/mSNvm5ycNZMn2CraWNnbx9cuM56YZBagOTCBRioa6y1jEuQwkrXP1HihOU+JxGI0SqMK2wh+ymlW0mt4/Ha+AvAQnBcOzIglR+za0IDK/5natLlO2KY1XCEHQkPy/91by8crCBifJmNwU/n7eCJKMtuUQSFPisyN1t05D4pIR8RVbCFaW1PKrN5c1GM8kj4MfH9+fE4f2ZFr/9EZZ1BBR+Lrz9CH86o2lCAFj+qSQGufkV28sjert2VMV4PUF25k+MCOms0cZkn98tDaqStq2Uh9PfL2JjAQXr8zfzj0/GI7ZTl3qLEPyv5WF/Pl/qxuNfXROMg9dPBpnlAWDZUg2V/j5z1cb2V7mo19mPDdMzyfT42gIh6i6xVCc06DStghKwW/eWt6gVgeR8q2HLhpD7zgTu86Qe4CXr5vEdc8taCSVe9bIXlzzzPcx5/HBst38/MSBHdryVIhItnpzxLlMQCGEQJoyoi3Poe1bbpqROvvDeWGhjfhhjlLgFYqXr5vInI0lvLFoB1IIzhubzbjclEZNKjqCcNji6IEZ/L/3Yp9zyYQ+MUud2guPhAvGZfP0nMYx8admb+ZXpw7iJ/9d0uSBnZ3i4dwx2Q2Z+9HqRT0SLpqQw2Nfb4p63Un5qRG1qzZI0gal4IcvLGTxfjXUC7eWceFjc3njxtbnEFimwbPzt/H0t5upCkS00o8dmMHvTh+KP2hx+ZPzGhnXCl+Iu95didOU3DtzOOuKanh2zmZqghaT+qYyqSCNP72/is0ltVwxuQ97qgIM7JnQUFscjfeW7uJfF46KJKxH+Rj8duScWHy4YjdPXDGeJ7/dzMrdVYzuGX/QEphSCjaU+fjDe6uaHFu0rZw7317Bn84c0igTPSwlz83b1qh3+OrdVby3dBf/d9ZQThiQ3iQxMSQkP3p1Cd/tp02+rdTHhY/N5cPbp+Gp+1Bsy6anx+DV6yZSXBOksNJPdooXr8uMqlXQMC47khQmTcmeqiBKKTITXbhF+yWIeaXgsol9YnpnUrwOMhNchATsrgry3HdbKK8NMb1/OscPzsRTN7/OwpaSgIIvVhVRVB1gYt9U+qZ5I612u3BHsgNBG/EjgHohg2PzU5naNxUBOETEKHXGz8orBbceU8ADn29ocuzkoT3pneTq8B+4CtvcMD2fFTsrmb9P1vWcDSVM75/O6zdN4Z8fr2X+5lLinCbnj8vm0ol9cLewyLHDNldNyeOLNUWs29PYrZ4W5+TPZw/DoVrfIUwIwZ7qYBMDXk9hZetzCCwp+evHa3l94d4uVkrBp6uLWL5zDv+5bBynDc/i3LHZDdmv1YEwz87Zwr2z1jCtXzqjs+IZPHM4C7aU8dqC7dz36Tp6J3v4zWmDSfY4uOG573nm6gnNjsMfsshKchMno9fdhi3VbDvPfY89NXszw2YOO2ipyZAQ3Pdp7FyGz9bsIWAPaYjxCgHlgXAjA74vv3tnBVN/cjQJBg07a4iUYu1vwOupDVq8tmA7V47Pbuj+Z1kKJ4reXpPsuARsWxEUNCvak+AyCVo2Zz80m6o6j5DHYXDbcf34wYheGO3guQiHbY4ZmMGwXoks3y+/RQr423kjcRqR++2/C/bWyn+2eg//+GQtr1w3iUyX0SkVB7aUfLy2iN+9s6JhgfoAkUX581dPIKGue+DhgjbiRxDhsN3w8GtNtm17IW2bSybkMDo3hX99tp71e6rJSnJz/fR8phWkHbDYTL2b2FZgiIiKV3OGzWFZ3H/BSHZWBnhnSaRufsaADHxBi4Vbyrhn5nCUiiQIeaTAbuUix2VHJBtnbyjh5fnbCFk2pwzryekjeuHFbtPK3zQl365vvivahyt2c3RB8zkEQkBAwdtR9AEA+mcmkOg2mdovnR+9uqRBz71Hoos7TxtCnzQvIaV4c1khllJM7ZfOnacP4Zqj+mIakj1VfnZV+Bmfl4pSEUNSFSOkMDk/jRSvg3CM3aTDEKTHO2NmZ6fFORt2opX+EJatYhpxKUVEyx2QKnYyXFhFdtGxUAqKqwPkxkWyyB0Og5e/3RLzfFvBu0t3cnT/DHrW/Y0QNDF4+/P1umIuGpvd5EFc34cdIovgm2bkR/UaAFw2uQ///mJjo8/fF7K458M1JLodnDIwo110IByWzWOXjWXWykKem7uFSl+YsX1SuO24fmR6HSzeWdHIgNdT6Qtzw/MLeemaCTg7sNMh1C2Ca0P89u0VTY5tL/Nx3XMLeOaKcTgOcBymQ1IbVg1iSuIgEyHbA23ENZ2CEbYZ1SOehy8chQ0I1AFLGgoBIcPgpfnbeGbOFip8IbKS3Nw0o4ATB2fGXBQoFXkQ9U1w8pOjC5CGpCoQxjAlSW4HVZV745BtKZuv93QcV5DKUX1TUSg8UhKuk7RsC0qB19n8z9LrNJAiupiVNAQ+JSisClBcHeT5ayeyaGsZD32+oSFu/4PRvZk5ujdzN5bw6zcbu0cLKwPc8tIiHr1sLAkBB8U1Af71aaR//I9P6M9JQ3vy2NebmLeplHiXyRkjs0j1Orlqal7DeY3GI+DmY/vhD9vESxk1C98rBTdMz+dP/2sqLgMRI/VanXE4qiANlyGx9/uO63tT+0I224qrWbiljLy0uIi8KKqJ+70+A788hrQqNBY7sRXNqvcBlNYE+dfn6/jVyYNJIvJdthRHTnCbtCRfHw5bnDq0J+sKq3lpfuMKi9OGZzG5II2rnoquZ3Dfp+s4un/6AZVw7o9SCrNBFS8DpQROGVF7C1uK/9QpB0Zja2ktZb4QPVztV0URdYxS8PBX0b0lAOv2VFPmj4yjLca3/v56e9luXpoXUZmbUpDOD48uINkhOzSpsCW0Edd0GpZls68GVKyyt5YISsltLy/m+33c4rsq/PzunRUs31HBj4/rF1NVCyJGN1inbOYAkjztUyUfDtsNP6iwfWA7n9bmEKgo8wtaNiuKfdzxyuJGndKOHpjBfy4by43PLUAIOG9cNqU1QR6KEt6o5/5P13HRhFwchuTSSX1Ytr2cwVmJnPHAt436mq/cVcn7vXZx34WjcEjJI19uaJB47ZXk5penDOL1Bdt5d+lO3rhxCj3cTV2qVtjijOFZbCv18dx3WxoerkLAeWNzKMiI5/5P1+F2SC4cn9vEgNuGZH2Zj398vJaVOytJi3dx3rhsUuOdXPHUfB6/YmwTF6pXCq6bms/PXm8qvAMR2VevKRtWc4LIAuKD5bH7lg/rlcTnq/fw9OzN/OKkgTiMSHcwlyljljFeOSUPE9XiYs8IW9x+TAHXTctn9oaIyM/k/FTcToPj//FVzN9SUVUgktDYjg1M9qriqQZFvDDEbPlbT0lNkJ7ujs1eD9qK9YXNi4FtLfXRs1dCm8YRkJIrnprfKGT25qIdvLd0J89dPYEBKZ5D1qpUG3FNt0JKwcbi2kYGfF9eXbCd66fnk9R9G7XhkREt7X9/2dTIHjMwg5yU6JrnhVVBrn56fpMH+hdrIlnRNx/Tj50VPl6et41zx2Y3yoDenxU7K8lN9fK7t5fz0vWTmJyfyu/fWdnIgNezfGcl7y/dxcUTcpnaP50qfxhDCsprQzz17aaG7+q3by/noQtHYUZxZRphix9O68u10/qyYGsZ1f4wA3om8PW6Yu54ZTFZiW4evHg0cRLUPhZPGYIPVxdx1zt73ac1pbX8/aO1jO2Twk9OGsDPXlvKv84b2ei64bDFtH5pHDMwg8/XFO07FJI8Dh64aDTufbwdoVBkcZXobloCBpFOcsleB5tLavE6y6gNWSQZJi4Ufzp7GD+NotI3rX86g3u0PknPsGwSBJw2KKNuDjYBRcxe8/WYxkGInLcShxQM6BHP9mba32YluTs8S9whBb2SPU3yU/alZ2LbxmGYBq8t3hn1PUOW4if/Xcqr101sF2/HgaCNuKZbIQzJy/NjS1MCfL5mD+eNyDrkal8HimHbXDEpl1E5SQ05BD2T3Fw/LZ9jB2ZEVT4LWjaPfLUh5o7sizVF3DijgLhCg8e/2cQF45vvv12v8miriF76uD4pzRr9Nxft4Aeje3PuI3NiGpWFW8sJWCrmQ8ewbXomeTh9WE8qaoNUBmwm903l5CE9SPE4cAvVZPESVII/vR89VrxgSxnnj8uhvDZEwG56XSNs8aezhrKppJZn5myhOhDmmIEZnDKsJ16a6ozHScFz10zkhucWsLty766zb3ocfzlnOL+pC00keRwNfcOFrZjWN5W3fjiFBz5bx9IdlWTEu7hmah5H5R9YPsi+cX6nbF4H4kCqIw4EUyluProfn60uinp8VE4y8Q6jbXGqA8BQihun5/Pl2ujjyEpyk5ngjOrJikWtbfPCvK0xj+8o91EVtEgzD03TcW3ENd2OUAs7j2B3aD3UAkbYYnyvRB67ZExdDkF94l70h35N0GJ+jCzoeraV1iKAZI+DtYVVjMpJZvG28qjnHj0wk3mbI+9X7Q83W+IEkdI0Rcu7wnB9j8dmUApU0CJBQGKKJ7JriqJ0ZhiCZTsqonoH6nl3yU6OH9yD2pBFnKPphR2WzaBUD38+YzC2AoeEcMiO6t62whamhOevncDGohp2VfjJTvFQ5Q/zy9eXsalO1e/qqXnsqQqQ4HHgMCTSssmJc/DnM4cStBVSiGa/y7YgLZufnjiQORtLmiQGJrhM/nDm0DZVRxwotq3ITnTx+zOG8Mf3VzW6Dwoy4nngwlG46Jxx5KV6uGZqHk98s7nRsUS3yeOXj4vkSLTpXUWzOhBQ1/jGPDTmVBtxzSHDMCIP1TbFkmzFWSOzmLUidmzy6AEZXbYHsGlKai2FAtyGhGYUyJrmEDTzvoZgUM8ECisDDQY3N9XLOWN6k5noZk9VgEE9E+iR4CLe7eC+T9byh7OGcd2z3zeJ18a7TK6fns+tLy4CYEivRBJcJoYUMY302D4pOKVgcFYCq3ZFz/rukejCvU+cuTU07/YU1ASa/55rgxYuhyTeacaUJbRtBbZCAM3dNkpBstvBvR+t5fghmTw7ZzN7KgONssKPrqt2OOn+r3E7JDdOL+DCcdkQtpDUSQEr1ei7rM94VoBLCkSMZjGxxpRgKN764RRe+G4rby/eia3g5KE9uOqovsTLzqvPlpbNqYMyOXZgJt+sL6a0NsiEvFSyk9241IF1KzwQTMvm2sl5zBzdmxfnbaW4OshRBekcOygDD2183hApxx2fl8rHUSRxIVJdkRbn7HAvQyy0Edd0OrYUBBEs3lqOL2QxJjeFeIdsNhmtHsuyGZWdTF6aN6rAyFH90kj1OtrkLmtPhBCR+dkKKSLx7XDYbshufW9lIS9+txVfyGJKQRo3TM8nyZQHPF5Z1wVqR1ENJw3rycUT+1AbDNMr2UNpTZD/fLWRrSW15KR6GJ2TTIbXwYS8FHomuXny2008c/UEnpm9mU9X7UFKOHFITy6d1Id7P1xNUXWAPmlenKbk41WFnDWyF28s2tFkDELA7cf1xw388pRBMTu//fTEgcQZ7dej2bJsRmYnNXvOpPxUHFK0W29qt1BcN60vL87byv+dPZxX5m9j2Y4KUuMcnDM2mzinyc/r4t/+kM19n67D6zQ4d0RWkzKv+nvinWW7eXHeNmqDYaYUpHHTjAKS2pDxbFkKF4prJ/XhkvE5gMBtCFTY4gDzKw8YYdt4gFMGpiOEwLJsbKtjBaWiYdo2PVwGPzu2P06XicOQlJfXHtA4DFtxx3H9+XRVYVTVwQvG5eA6NJ50QLciPSR099Z49RzIPCxD8saSXfzj47WN4rfHD87kj2cObVU7QykFPiH58/9W4XJIzhjZG1MKkutUoxzhcJsWxe31fdiGpKg2xIOfb2D5zgrS4pxcO7Uv43JTQMAVT89n7X6Zs05D8sK1EyhIcrVZSUoYknVlPn74wkLK9imVGpGdxD3njOCKJ+c1KYu6flpfrpmSR1XQYs7GUj5dVcjpI7IY2yeFrWU+Pl+9hzcWbqfSH2Zor0Tunjmc5+dsZUROEjMGZHDvh6t5b9muhp1iksfBX88ZwcheCSgFX24owVKKf3y8tsG9m+gxuXF6AWeO7IWrBeGR1nwXQgjMOs17H/CL15fz1bqmMdBEt8mz10wgM94VVUL1QDEcBjU2Df3px+amsGR7Oc/O3kJhlZ+wpRrtzpM8Dt6/5agm7X5DptEk4xkiO7vnr5lI/+S23xP7IqXAMCSqmXr55jiSn1P7owzB8sIafv760ob72pCC88dmc/ux/Q5Y66I1tNSKVBvxQ8CR+uMwDMnC3VVc++yCqMcvHJ/DT44taNVWTQgImybPf7eFZ2ZvoSoQxmEIThuexU9PHICnDe67dvk+DMnsLeXc/sriJofuOL4/TkNy76w1Uf80J9XDy9dMxNlGd1wNghPv+zpqTHhor0SunJIXtXf5R3dMI8lp8Pn6EkpqgnidBspWTO6Xzu4KP0XVAbKS3JTVBtmwp4Yqf4h5m0u58/QhzN1QwqSCNEprgmQmuOgR78IjIi7bagTH/P1LZgzI4NJJfXA7ZINoySvfbyMzwc2t0/o2KhETIqKw5bcjAiVxLpN4l0HYF2xidIWAkJTsqQ7y6eo9uEzJaSOz2Fnm54XvtvLB8l0NO6WBPRL423kjyIh3YYatdsuKFoZkU4WfH76wkH49EihIj+Ocsdn8b9lujh+SSWGFH5fDwG1Knq9rAAPw0e3TSNkn8ckwDV5ZvJN7YtwT2SkeXrm27fcERHIFfAjW7qlmybYKeqe4mdw3DadQiDYsCo7U51QsZF2zoNLaUIMKoauuEVJHovuJa7oMfgX/+Di21OUbC3dw89EFrWrkEBaSP76/iveX7c3KDVmKtxbvZPG2cl68ZiKO9vCftpKAgl+8Eb3muHeyh/ubkfjcVuqjJmjhbEN2qzQNXpi9OWZS14qdlWQkuKIqqb2xaAc3TcnjmII0AgrmbymlNmjhdRo8+c1G1u6pjmR077OYunB8DrPXl3D/p+uQn67jmasnkOJx4KpLOJNSsL5OAe3LtUUN2cFin+qmfpnxXDelT0MpjhARd/L//W8VH60sjCixCThxSA/+3xlDEcomZClchgDLJmQY3PHqYr7bFClZO2loDyr8YZ6fu4Urp+Tx0nWT8IUs4l0mpTVBfv/OCu48Ywi5cc5208uuseHSJ+YRCNsUVZcwb1MpVx3Vlyp/iEse29vFLdFt8vOTB9EnzcvjX2/CNCT7CsfXWs1nPG8v81EdtEhtY8azYUhKgtb/Z++8o+Morzb+e2e2q/derGJZbnLvFTCmGNOLwdj03hNK+BISCAkJIUDoxaaD6cWA6bhh3Huvki25qHdtm/L9MdJaa+1KsrEdHPScw+F4d7Q7M7v73vfe+9zn4dKZy/xkWs2y4KlL+jMwJeywAnkXDkJTNaxAkk1G2OVO2QcfD3QF8S4cN+gCNh8ILkPpUTUa3Aq2ACziQ1HvVf0CeGsUVTaxYk81ozMij4uDkiQJNh+ob2N12gK7WabOFVwZDAyHMUwdq1mZTBJNzTaZy4sCz8q3YFtpAylR9jbyopUNboQw5HAdwnBqe23xbqa8tJh/nF/A4p2VvL+iGLfiISPGwfThmYTbD/Z6x3SPo7iqiZSIg9stXYcQq5lD0ToBDrOaEK2iukcSXP3GCr/zC7OZuGJkN8oa3OyrdbGiqIoGl8KVI7uxeleFL4AD9EgM56cdFTR5VJ6bt5Pn5u1sQ77bsLeObvnxh0VmMpll1GYpX1U5WIaXTRIfLCv229xcODCVWcv2tBl7rHMp/PHTDbx0+UAKKxqxywK/hqoQHX8nmhnPLa2DznyXnTpMe3V5G511r6pz8zur+PaOMb9aDQXRLKMswLBH/hVPmfya6tfHNIgfOHCAGTNmsHHjRrZs2UJTUxNvvPEGQ4cOPZZv24VfKXQdYkOC234C2MwyAa2uWsFkkli0razdYz5evZfhGZFHcJYdQ5Ylw++7WTdZCEGNM/iCvLW0ngHpUT7RlUNhlgVRDnOH7FbVJLNwVyXPz9/FhJ4JRDnal5eIDjEHHI0Z1z3eFxC8ksT9H633CZ5c+dpyTuoRz8Pn9CY3IYw6p5dn5+3gh81lxIVZuXRIOn1SI3hu7g7G5cT6zlnXdTKiHe3ask4bnoG92QRFkgRFlU1+AXxQRhR/P68Pry0q4sctZciS4NReCZw3MJXbZq3mmjHdODk/nh82G5+906sSdojN7aHs+egQC2onDUCELNGkwacrS1hTXEtqpJ1Lh6YTaZGRNQ23Bkt2+Y/xTeqbzDVvBCbyAby8cBf/PL8P1kNkcs0CBmdE88OWwN/jEItMbJiVOq/Ksm0VSJJgSGY0dlkEJYBKkqC4xhlUOU3T4e2le7h1TDfUX5GGgpAlGjV4ce5Ovt5otB9O75XIdWOyjjm7XjLJNGk6Tq+K1SRjlcDUjpf8rxHHNIjv3r2bL7/8kp49ezJs2DB+/PHHY/l2XegAQghUSeDWwKWo2M0y9uO443VIMH1EBo99uy3g8wPSI7FJh2QsQSCJ9suMHT1/RJAFbgRrS2qpavRQkBpJrMOMpOv0Tg4P+mfvLS/mmUsHMH9becAd/MWD0rB1pJ8tSfzj66181mzc4lJU7j41j7lbgweBxHB7GwWtuDAr/dIifJlpo1fzUyxTNZ3vNpXy3aZSJAEPn9Obq0d2Y/rwTOpcXj5cWcJLC3by7rXD/BTNACxoPHp+H26etbrNdfZPi2RoZrRv9M9kkvlq48GRnZRIO3dPzOP85372K/+/uqiIL9bu59nLBnD7rFU8emGBL4h/t6mUW07KYV4QYQ+rSaJvSkSngriQJLZVObni1eV+LYo3luzm3tPyOLdPEibJ2BS0hqbrQSswAKv31GCV5TbnYNJ17jwll7lby9p83eVmUZnHvt3KJ6sPGtgIAZcPS+emMdkBiVSSJNoQJw/Fpv11eFTD5/vXAEkSVHs1zj3kc3972R5mr93HJzeNIMp0bFzHVJPMSz8X8dYSY1pENFelHjyrF+Gy9F+TUT1cHNPCyuDBg1m8eDEzZ87k/PPPP5Zv1YUOYDC6BX/8YjPj/j2PU59cyClPLOCp+YUoJpljEfMOhaponN8/JeBYUHSIhUfP79splyNF0RiZ076L10UDU5GP4u9ekyUWFdVw8uMLuPmd1fzps41MfnYR1769CqeQiLKbGZAeGfBv610KKZE2Xpw60Mi4myFLgosGpXLzuOx2x4mEgIomL7PX7SM5wkZqlJ291U6cXsMt7VDIkuDxi/vx7Sb/WfruCaG8e+1Q7C3HyRIb9wW2PAVjLzVrWTENboVbZq3ing/XEWo1MfuWUSSHmNsucqrOwJRwZt80kpN7xBMTYiE7LoSHJvfiuUv7Yzlk3ql12+Ty4Rn8+7ttAZ3QyhvcvLG4iDP6JlNa52JyQRLPXTaAByf3okdCGK9eMSjgd+qvZ/fqtGuWWwiufWNFQI7BP7/eSpVbQdZ1rhyR6fecqQP3kjCbKWDtVdN04u1mXrp8oN/GQJYED03uxYJt5X4BHIyXeWPxHr7eVIopQMtJ03RSo+xtHm+N1Cg75nZIUscbXiF46MtNAT/3erfCw3M2oxyDxUmRJB7+agsvLyz06SroOszfVsHFLy/Bya/nHnWEY5qJS9KvtPnyG4RbSFw6YwnFVQczM7ei8caS3RRVNvLPc3tjOg47T7Oq8vylA1i7t5a3l+7BrahM7JnIab0TD8u2M8QkcdHAVN4PYH2YlxDW6QysMxBCUN7k5Y7317Z5buO+Om5/bw3PXFzA05f0596P1/HTjkrf80kRNp67dAA2XWdgUhhf3DySsgYPTq9KaqQdmwSig/EUi8XE9j21vHvdMHZXNqFqOllxISzcVsHJ+fFM6JnAR6tKqGzw0Dc1ggsGpvLdxlLyk8J56+qh1Lk8dIsNJcIiY23l6KXrOiHW9peAEKtMQXI4c24ZZZxLcy9dD5IZSZpOssPEI5N7ImSBpoNdFrhdil849XoVzilI5uWFhQD0SYngH18FdjED+GbjAWZMG0RxtZOJPRN56PNNPunTzBgHD5zVkzXFtby3fA+9ksK57eRckkItnWIOtyi/tRi3BMLrP+/m7gm5ZEbbObsg2VcR2VPVRPeE0KAZ8CWD07BJImCnRGga/RPD+PzmEVQ0fyeSI+0I4Mynfwp6Ls/N28kpPeI51LZH03S6J4QG1XcHuHJEJvpR+l0cDXg0w441GOZvK8etQ/tbk8NHk6LxRRCp2tI6Nz9uLWNSj7jjwqn5pTghiW0tIwMnKkzNBKbjdR1CwFcbS/0CeGss2F5BrVslK8ZxWK/7S67jlB5xjMiKQdV1QizyEe177zktj+6JYbw4fxflDW7sZpmLBqdy49hsou1tSVbB0NF1uBSNF4K0AMDQ6G5SdNIirfzn4n7Uu1VKqpuIcliICbUQZTP7Kh1hGCXtw0G9W2V3ZSP3frQOb/MmRxJw0aA08hLDePL7bdxzWg8GpkdhNxsqZhcOTqPRrRAbaiXcGobdHLiA2lOW23XZmj48k+hQy2EReZo8KpWNHt5auJuSaicFqRGcNyCVaLsZc6vM1WvyMrFXAt9sLO1QrtWr6ghhuIJNf2WZX+ZWVNnE1a+v4KMbRnD5sHTMksAR5HoDQQgoqWmfY1FS08TOyiZ6JITyxzPzOXdACi8u2MX3m0p5cHIvrnxteZuyemaMg2kjMgnr4LsYBsSFHvxO7K1zBQ3CYFiiakIE/L6qus7MKwYzdcbSNp/p3RPzSIm0E2Lp3L05HutUU7273e+WrhsMmV9yDodehxAwb23gAN6CL9btZ1KfJCJC/vuNh44KESdkEO/C4cGtaL7MIRgWbi8nOzbjuLEudR3snWCht4cIm5nLh6YzqU8SHlXDJEtE2ExHvVzo9Kps2Bu87AxQXN1EWqSNMKuJMKuJ5PCjY28qBPy8q5L/HOLVrenw7vJiokMs5CeFE24zEx1iQVFUIu0SkZ3cxIRbZP56dm/uCWDJOSgjioEZUYf1nWj0qny4ai9/m3PQlOTHLWU8O3cnr14xmP5pET5zkEa3wrn9U+mbGomq6cSFBic95sSH0uD2UtPkbVN6ndAzgUsGp+FRNWqavITbTL4grunQ6FEwSVLQ75uuQ35icE6D8f5hvLlkN78/NY/kcCsjukVTkBKBV9WxWSS+uWMMMxbuYu7WcqwmmSlD0jirIJmoDvzEA8EiS5gkEdTMxmaWfPcQdKqdCpWNHqoaPSRF2OkW4+CHu8byxbr9rNxTTXKEncuGphMXaul0AD9esJok0qLtQROMjBiHIdV7CJq8Kg0eFY+iYTPLRNlNyIdRdjd30AYxyeK4tBiPBk7IIN4lPnB4kMxyqx99YJhkiYYGz2Fpjv83xCAMIQuJbaX1/LSjgrgwKxN7JWKXBLJXocnbvlFBILR3HUKAJsvEhVkDyry2IMpupq7OedQ3QR5J4t/fBhYEAXhr6W6eu3QAWbEhKIp6RJ/F2OxoPrh+GE98v71Zac7KlcMzOK13ImZVpba2/VGoFggBFR7NL4D7rkPVuOaNFXx3x2ismoYQgv01Tm54ayUjc2LonxbJzeOz+cvnmwK+9s3jchiQHs1Zz/iXme8/Ix9d1/n9B2t9qnVp0XaevqQ/caFWthyop8Gj0OBSyIh1kB0TgjmAeltmjJ34MGsbhTsw+tSn905k+ivLSI92cP3wDJ8fvQDcHnAAt4/N4vpR3RBCEBtmRXBkvw2zLDGxV2LQEcrzB6RiQae+wU2pU+GGt1exp+rgd3NAehT/ubiAKf2TuKAgCVkC1auiOD0czukcj9+31SRx78Qe3DJrdcDn752Yh0XTfecgSYImBA/P2cx3mwwZ1FCriStGZDB1SHpAwl+g6+ifFkV7HNpLBqWhexRqmzyBDziOiIkJbXdD0dW0/g1AaBqXDE5v95ixub9e05AWSJKgVoULX1zMla+vYOaiIv7x9VbG/3s+n6zfjyof3a+zIUYiM/PnIi4YGNy6MyHcSmyIpXncDJAlPJLxHybpF+3oVZ12Nw91ToX4cBtRdmM/Lpsk1Ob3bU/lqTUkVSMr3Mrj5/Vhzi2jePvqwZyUn8Cyomp+3FlFnU6n7q1kknlzaXABE6dXZe3eWp8UaGxzW2HRjkounbEUi0nipnHZfoS3MKuJv5/bm6HdomjyKn7zzyf1iEcS8MhXW/xkZ+NCrdjMMquKa3jl50Ke/H47P2wpw+nRWLSrEpckt7k3dnTevHqIX1kbjCDzz/MNjXS3olFU2YgWZKemKxpWXceiab+IFiVpGvedlheQpJYTH8rkgmQ2HKjHLQkueXmJXwAHWLWnmqvfWEGjqqMrKorn6EnOHm0oisagtAj+fm5vwu0Hc8pwu4lHzu3NgNQIv3XJJSQueXkp32w8qGPe4FZ4Zu5O/v71VpRO8rBsAm4Ymx3wuR6JYQxMjzoh+uFwgmbiXTg8qKpOXnwI/dMjWb2nps3zlw1JbytG8SuEG8ENb61kX4A52H9+vZXBGdF0C7cctXGU1mIkj19UwMReiW3c0+xmmRenDsQmdHRZUKvo/Oe7rXy7qRSB4LTeidx2Ug7hMmhHoJQlCdrtWQsBVllCQ6ei0ctHK/eyaGclETYTV4zIJCvG0SnCoqbpyOggS3y4eh9Pfr/dr5x7eu8E/nxmT2RFxWSSEMIwdmk9T6toepuRtkNRXNXEyPRIVBXCrSay40LZWW6Qwu7/ZAMXDkrllSsGU+dUiA6xkBxhw4YOqkqTip9L2pQhafzh4/Vt3uMvk3vxxuLdvNNKEa2wopEft5Rx54Tu7G42hHGIgy5pqqoTZTfzxtVD2LSvjm2l9SSE2+iZHM6ri4p8n3uflIgjDtCSJPAKgbf5lpkFhk3oId9XXYcQSeeda4by7aZSftxShiQEE3omkB7t4LZ3V1Pr9PLpTSOD9s63lTawv85NRqjlVz/zLKsaE7vHMjZ3FDVO43oi7CZDzrfV995kkvlhe3lQX/vZa/dx+0k5hHcijkuaxrSh6eTEhfLkD9vZU9VEmNXElKHpXDE8A4uqdXKu4b+PriD+G4FF03huSn/eWVbMG0t2U+v0khJp56Zx2ZycF3dMBfyPFmrdCltLA9tcAjw7bwf/OLsX0lH4+UmSoLCVGMkfPl7PQ2f35qyCJD5bs49ap5dhWdFcMCCVEAHoOhUeY961tff2J6v38u3GA3x60whirTIqAlXXMUuiU4IbNgnOH5DCO8uKAz5/yeA0bGaJDfvqmfbKMppaMay/21zGab0T+cuZ+Z36fE0miVV76wLO8X+1oZS4MBs3jMni+23l1Dq9DMmMJjHc6rOZNEuC3snhPsnVQMhPCvex4+1C58WpA7jk5SU+U4kPVpTwwYoSrhyRydWjMps18I3jQ60yv5uQxw1vrUTRdKwmuY2HdnyYFV3HL4C3xpPfb+PjG0ewtriWIekRSK02Voqi0ehWmPnTLiIdFn7aUcFDXxxUGLTIEmf2SUJVNVRZ6jAY+0GS2O/08vCczSzZVYUQMDo3lj+c1oNYq9x2Ay0knv1xOzvKGxmSGY2m63y4soT1rbgZa4pryI0PbWOg0oIVRdVk90vC+ysSdgkGTdGwAPGW5ggcwPnMo+l81gEhbWlRFad3j+1UFi0rKuOzohmaOcSQDhZGhq4p6gkTwOE4BPGvv/4agPXrjR3z8uXLqa6uxm63M3bs2GP99l1ohq6DSVG5ckgalwxKNb60GAIsh5bRhQBdlnCrOpIQhsrWf7m0JEkiqBJVC3ZVNOLV9DajN0cCs1nmi1Y9Sbeice9H60iJtDOxVwLdE8JICLMRYZLweBQUSeIvszf6BfAWeFWdXZVNVNvNvPZzEdVNxgbg3P4phIiDilRSs+xkvVtB05uzEeCmcTks3FHRhvxTkBrB1aO6saaklgdnb/QL4C34esMBJhckMyItosPF3Km1r23/3vJiTu2ZyB8+2eB7rGdSOC9fPhCr0FC8KhcMTOXFBbsCkrLiQq1kx4WiNY84qapOtFnw2U0jWVZUxdyt5USHWLh4cBqRNhNmVfMrXcuaTnmDm1euGMxLC3YhB2gXTMhP4P2VgTc8YPwOFm6vID8pDI+On06/TYDDLHPvaT247d011LZS4bObZV6aNpBQs8T+eg9/n7OZRTuNUcIR2TH83xn5xNtNAef9ZVliT4OHC15Y7Lsvug4LtlWwdNfPfHLjCBJsst8mQEFnf62LlburWbk7sLxuaZ2LSEdwAmNUiPlXn4UfFgQdktdMknRYrQNFUWkt33NiFND9ccyD+O233+7376effhqAlJSULgW3/wLUQ760bWJzs4HC899vY8XuaiLsZq4ckcnI7JiAhKDjBU3Tie9gNCutRcjiFxg8tGxgPEJgDaBlvrfGySuLigC4dlQ33+MeXWdJYVWb4wH+fl5vZq/Z50dUWryrkhfm72LWtUNJDLeiaYa61wOzN1LZaGSXoVYTd5ySy1m9E3nv2mF8t6mUD1ftRdV0zuyTyOR+Kdz01kruOjUvYIuhBS8v2EXfKf063NzognYrHW5Fa9MP3rS/jt9/uI7Hz++DVYLaBi//urCA+z5a59cCiA218OQl/Tg07qqqjgWVcd2iOCk7BofDKP/W1jrbZkOqxvjcWN5fVcLw7GjSouzkxIeyo1UmqqNT3dA+Ea/O6aWq0dsmwKmqRqzNhKrrvNiseV5Y0Uh6tIMR2TFE2WRqXMb43DWjs0iPcfDp6n38vLOSc55bxEc3jCA1xNRG68Clw58+2xhwY+NWNP765WaeuKCP0c5ohlkI+qZGsqCdGer+6VFtNNtbIEuC4Vkx//XN99GERcBFg1L5aUfgeyIEDMmMOmGU1o4WjnkQ37o1OLO2C78uCFmwvqyRa95Y4ZvbLal28vsP1zEkM4r/XNyvU37fxwpRdjOZMY6gRK8bx2Zj0vUj3k23MF8f/3Y7i3aU8/fz+vLaz0VBjz+7XzLeZjZ8sDnn7LhQBCIg09jpVbn+rZX864K+NHlUbj6EodvgVnj4y83YzTKn58UxuWc8Z/ROwKXomISgxqVwoM5NVQcM2vIGN40eFbtZClryNfTgDU/2mqbgQdB8CMFtQHokFwxMxanpKJJgW2k9S3ZV8vpVQ9i8v47SOhc58aHEhFj5+5zNTB+ewYSctsHF+LeGvYPROFlRmdI/BZcOsiRx72l53PjWKl+A3FbawFkFyXy14UDQ1xiRE8OXa/cxJicG/GxRBSaTIDXMigqkRtgYlxuLLIxZ5R+3VfLkD9sornJiM0ucVZDMa1cN5q731rK3xslfPt/Isxf3w3TI9sOj6X5l8EOxeFclHs1f0ETxqlwwIIWXFuwKqCKXFGEjKzaEod2i+XRN2/HRP0/Kp31l/RMPiqIxKD0qqLjOFcMzOy3b/L+Erp54F5BlCZcOii648/01AQPSsqJqlhRWMa7bf4+1aRfwxlWDWbe3jvBmARVd1xEIHFaZjEg7mufwR8xa4BYSU15e4iNnlda6GJ8XH1Cf/LReicQ4zOjNC6xVlsiIcbD7kA3G5IIkPminvFta58Ysy7zy046gxzz5/XZOyotDR/DjpjI+XLWXcJuJS4emU+P0kNyBEEZ+UjgHal0kJISiHSJ9KssCVZbZXN7A9gMNTBmczvPzdwZ8ncGZUX7B6HendicuzMozc3dQWNGILAlOyovjmjFZPPzFZlRNJ9Jh5qsNB3z3JVDJ/7ChatgAIcH+GhevXjmYmQsLWbijgvV7a/nL5F5E2M1+5fAWpEbZiXJYmNgnya8qoMgSB+o9vLV0N3UuhfHd4xjTPRarruHVBW+vKOGpHw9+Ri6vxgcrSlheWMU/zu/D5TOXsWpPDR5Nb7Oodiam6AG6sCGy4JUrBnH9myv91OSSI2y8cdUQHOjce2oeZ/RJ4oX5uyitc5GXGMot43NIDrUi/UqsMo8mrLrGa83tlPdXltDkMXy9bx6XzSk94k8Ibs/RRlcQ/41DkiX2NXn565ebuXJkt3azsFd/LmJoRiSd10I7uvAIwaLtlTw7bwcl1U7CbSYuHJTKyfkJ3PPBOs7un8KFA1KOuOz/w9YyP3b1Q19s4plLB9AvLYK3l+6hrN5NQriV68dkcUavRL8FwyEJ/nB6D254a5Xfa0Y4LJTVBXdtA6hp8rTL6m70KCg6TJ251BcMrSaJ68dm41V1Nu2vZWi3aJYGKedfNjSdepd/+VgIw8Gs3KWwYHspdrNMz5RwBllMLNhezsZ9/paxMSEWfn9qHne+twaA03snYjXJ3PfRQXa4qul8t7mM5burmTFtEJcFUA0b2i366JU7VY2TesRz67urGJMbz/QRmai6zk/by3nnmqHc8PZKPx5Bj8QwHruwgP21LuZvLSc/IQwboMoy328tJS06hLP7peCwytQ5FTbtryc3IRSHWeLZeYE3NkWVTWzcV8fgzCiWF1UHrAJZZeHHwj8UfVIisARqA6kaeTEOvr1jDBv21bK3xkl+UjjpUXbsGOV/EzAoKYxnLy7wESZNrciA/2vQNB2zpnLLmCyuGdUNVdeRhSAkALfnt4KuIP4bhhBQp+pc8OJiIuxm6jvwN653Kf+1SpUqSzy/YBevL97te6zOpTDzpyKWFVZzz+k9uP7Nlfy4pZTnpgzAfJj60PVuhU9W7/V7zK1oXPfmCsbmxvHApJ7kJYbhMEvYBeiahiJLeJtZ2Zqm0S85nMcvLOBvczb7+tqVDW7yk8PZVdEY9L3TYxztekuf2z+F5+bu8Mvy3YpmZF4JYTw7dyfPTx3Aw19s9suUrSaJ+8/I5+cdFVw+LMNXQRECPLLMne+v8fPnNsuC+0/P5x/n92VtcQ1frt+PRzFMVsbnxfPPr7fQJzWC7PhQpgxJ45Z3Agt01DR5+XT1Xs4qSObDVtr2I7KiibSZfNWLXwpdB7uu8eyUAXy3qZQnvt+GqulM6pNEpMPMPRPziA6xUu/ykhLpwGqW2FPVxAvzd1JU0cj1Y7KQZYk6RaWo0sk/v97GpUPTGdItmtcWFbFhXy3RDguXD89g5vRB3PbuauqcbSs9324sZWxeHHVOBavcNhg7JHhgUj7TX21rWSoE/OnMfKz4O8L5oBqs7cHJYQxJCUfTdDRV8zu2JZibANTOt5OEScKl6gjAIYsTqn+uK+pBjoeut+X2/IbQFcR/y5AlXvxxJy6vhqJ6SItuXzt9cGYU1l9IHDtSOFXdL4C3xvq9tdQ5veTEh7KmuJb1+2oZnBx+2BlfoOxd12HetnLmbSvn9SsHkxsXQpVHo6G5vLlgWzmr91Rx7ehssqLtjMuKZujNI2hwG8+HWWWqnQpz1u8P+Pr90iKpbvQwtnt8UIWuswqSmf7KsjaPP/n9dl6eNpBpryzj5rdXce9pPYgNtbJ5fx3x4Vb6pETw7NydjOse52d1qkoSf5690S+Ag8Gif/CLTbwwdSA/binlpLw4Tu+dSJhJ0KDC2f1TWLyzkgibmYRww2v7hfm7Ap7zt5tKuff0Hny4sgSTJJjUN4l7J+YZVZKAf3FkaMnMJveMZ0KPeHR07M3toW82ljJ3SxnhdjPVTR4/bfObxmWDruOSJP793TbmrD/ApL5JJEXYuOb1Fb7japq8PPj5JgakR/GvCwq4/s2Vbc5B1TQkYfSh7QIODfOKopEXG8Ir0wfx4BebfJuxFoe3jAhbh99Vgyx3dO6ckCXqVZ2Z83Yxf3s5drPMJYPTOK1XIlZNOya2n104dugK4r9hOFWdH7cY/V5F01m1u5qTesT7HmsNsyy4bnQWQjv+Iggmk8SiLcFnjwG+3niAMbmx7Chr4O2le+h/bu/DEuUIs5o4u18yq4trAj4/IjuG6BALl7+6wlcWNUmCyf2SmT6iG1e9vpyrR3bj8iFpWFSNaFPzu6sasXYTj19YwH0fr/crL+clhHH/Gfn84eN1PHJeXxbvqqSq0Z+kZjNLxIRYAoq9GFnlLt6+Zigrd1ezek81SRF2TukZz6Z99Tw3dwc3jM0mxuY/+uTSdL4P8Bm34PWfixiRE8O/vtnGpD5JVLk1Lp2x1G/E79l5O7hhbBb3ndaDf3zd1n1M16FvSgRvXDWEUJuJ5DAr8hHM3wohsDTrfXu9atAAoyiar82jairIEtNHZLKjrME369+CUTmxDOkWjSQETR6VOesNEtylQ9O56jUjW3ZYZMJsJmqavLgVjVV7qqmod9MrObxNq+Hk/ATG5MaSHGalUdWp92rU1jgJs5owN/tSy5pG/8RQ3rlqCE7FUHSzm6TjPr4pyxLFDR4ufnmJ36bmoS828/bSYt68ajBm7bdZlj4SmJqVETVN/69VMrqC+G8YArC0Mhd4bt5OXpg6ECHgh80HF/nYUAv/ubgfEWbpF5dChUnGqek0uBWsJgm7SWq2x2x/eQ9mBuF7XtV9UpoeVUPT4XCtHk7tmcBLC3b5jWvFhVk5u18ylwxOZ/IzP/kRsxRN5+NVe2l0q9x6Ui7/+mYr5/ZPIeIQxShJ1RiZEckPd45hdXENlU0e0qNDqHV6uW3Wag7UuXjw8428ePlAPluzlznrD6CoGmO7xzF1eAYl1c6gJhGfrN6LpmvcO7EHufFhBgNdh4HpkYzKjjYC5yGfWWWjp13OwOYDdUwZkkZmrAMVuPHtVQFn9F+Yv4vnpw4gJdLeRkXrpPx4ZvxUyHvLi7HIEnN/N+awP48WstnHPxXiVnQm900iKzYEi6Z1OP9sE4JtB+q5/ZRcPIrGwu0VmCTByfnxVDd5mb1mH388LY+FO41xpeQIG/tqnGTGhHDz+BxCrSYqGtwkRdjZU9XIUz/sYPbafZySn+AXxOPCrJzXPwWzBLNWlPDCgl2+70hqlJ1Hz+9LTpQN0bzIW4AWPRM07biXgZ063PXB2jaOawA7yxt4f0UJ0waloB7HE9NkCbduVD0cFhmHScIm+HWPikkCN4K5OyrZWd5IfmIYgzKjsKMfkTLjL0FXEP8NwyELzuuf4mPdNrgVrn9zBTeOy+G60Vnsr3WREeMgPsRiKBn9wh+VapJ5cWEh7yzb48sseyWH868L+pJgMwV9fVXVGJ4V0+5rj+0ex+fNTm2n9UrEKgWYge8ANl3jveuG8c9vtvLtxgPcfVoP30jbW0t2B2VWf7PxAFeNzMQsCz5bu49rhqbhOeRYoelY0RmZHoksC+oUnbs+WOvzxN60v46X5u/kT5N6MrkgmbJ6N6t2V3Pt6yvITwrnqpHdeDCIOcj4vHicXo1XFhUyd0sZZpPE2QXJXDOqGyGSaLNBCuvAQzw21EqdS+EvZ/WkssHTJpNtjVlL93DegBSebsXcDrOauHBgKpfPNFoAkQ6zITbULGbj1Q0RIasw/McDBWTVJHP/pxuYu/VgBeb9FcX0SAxj5rRBWLX2yYuqonJyXhx/mr2RLaX19E+LwqXr3P/xBqJDLLwyfRBC0zA1a21bzTI2s8z/nZnPHz5e70c07JMSwVNT+vPC/B2ENruSCQHjuxtciRBZ8ObyYh7/3l8op6TaybRXlvHFLSOJtci/CuEVp6Kxszw4P+PtpXu4YEDKURFM6ghCgFeW+ftXW/hy/X4f3yYnPpT/XNyPBPvR408cTQhZYnNFE9e8scKvQhZikXnjqiFkhluOayDvCuK/YaiKxsWD0vhgZYkv02r0qDz27VZkSfDMlP6kh1rQAkggHi40WeJf323jo1X+5LGN++q46MUlfHXbKD/1rNbQdQi3ypycH+9XIWhBapSd7glhrC6uIS7UyoT8hCNiqqqqjl3oPHBaHved1oPXFxfxty83c/8Z+SzZVdnu3+4oayAxwkZFvRsRRFVKiJZ5bAiV4KkLC3BpOk0elVCrYcpx09uruG5MNre2mhlfWljF5IJkrh2dxauLCn1VCUnAnafk0i02lDOeWnhwQfGovL54N5+v288nN44gROi+OXBV1QiRpHbZ0hcOTKXJ7SUzJpSlhe1fd2FlI5MLkn3XNyI7hlvG5/LIV1vISwwjIdzGKT3isciClfvqeOSrrewsb0CWBKf2TOCeiXmEy8Jv0dN1nU/X7vML4C3YcqCef36zhT9NzAuojtYasqLy0Fk9KW/08tGqElyKxhMXFZAVG4JV11BUnUGZUQgB+2ud9EoO5+xnFrXRI1+/t5b7PlrHYxcVkBJuY3z3OCyyhFUyVOQ8GGSya0dn8cPmUj8So6Lp/Pv77Tw8Kd9P4vW/hUAz563RHsHyaMMrSfzh0w3MO+Rz3lHWwCUvLWFOO2vCL4EkCSRJoOsdVwADoUmHq19f0eZeNnpUpr2yjG/uGI31ODYdu4L4bxx2NN6/bhgvLtjFh6tKcHk1ClIjuO+0HmRF239x9t0Cp6rz8SHs7xY0uBXeWbaHa4ZloAUJviZV42+Te5Ee5WDW8j24vAaZaFxePDeMzebuD9cyODOKf57XBzt6YKZvJ6DrRnZY5fTy8sJCADyKht3cfjHYbpHxKEYJPFBvTJEkatwKHy8ppMbp4ZT8BHonRxAh64RaJATGpMClQzPolxbZpkT9x882MG14JrOuG0ZlgwdN0+iVHI5JElz75qqAPfOqRg9P/bid303ozvebSymv9zCkWzTd40N4Zko/Ln5pSZuANSonhjP7JCHrOrquERPafk6WHuVgYEYU3905hooGNyt2V/Pe8j3cPTGPdSW17K5sJDbMwrztlX6e5aqm89WGAyzZVcnsm0caJifNqHYpzPipMOh7zll/gN9PyKP96XgDJlUj2W7irnHZRubnVdFU1bcplYVgyuB0iiob+W5TKXUuhb6pEZzbP4XoEAt7q518sLKEXRWNeBQNk6oa7RJdQ0KiSQg+W7mXn3dW4rDI3Dw+B4tJ4g8fr6eh2ff8p+0VeHWOS3Z7KIz9pPBVAcKspnYNdfqnR2I6HDLJL0CDR20TwFtQ71b4aNVepg9KOWq9ZlkWuBCU1LjYtL+OxHAbfVLCseh6pwVizGaZT9btD7oZavSoLC2s5qSs46en0RXEf+NQVR0bOneMy+LGMVnoGL1k61HsSUmSYPuBhnbLnz9sKWPq4LR2VaZkReXm0ZlcNTITp1fFZpaRJYOc9PoVg7HKAouu/+LzlkwSry8uOnhum0s5qyA46c1ulkkIt6HrRulVPWS8TTVJPDNvF2+3sun8YOVekiNsvHPtUMIkgSoEczeWMjInlj9+sp7HLy7gj59s8Jlb6LpxHhcOTGXh9jJuHZ+L7FWoV3Q27fcnWrXG52v3M6lvMg/Mbi7FzzUqF+9eO5Q5t41i9tr9zNtWjsMic+WITPISQjEpRqnaI0k0uBWy40KClmCnDEnnQJ0bTdNIj3FQXNVEj8Qwrnh1ma/vemrPBB6eE7gVUN3k5bXFRdw0MtPnWKVqehtjk9ZQNB2XohrOe52Arus+/+9D4fKqDMyI4tReCbyzbA9PT+lPVaOH95YXs7/WSU58KHeeksuBOjcriqroMSAFTVORZYlSl9JmIzRvaznDs2J44uJ+XPuGwXK3Ww6XDXAU0NxnLqlx4lU0MmNDsAqwC8FlQ9N90sGH4u5T8wwzl2N9erLE+j2BNeFbMG9bORcPSDlqQapWhWmvLvXjltjNMs9dNoDe8Y5OTd0IIdiwN/jvDWDjvlpOyYnheCmxdwXxLgCGF3LrAHq0+amtPaIDPy8bWUMHvyNdMdS6bLIATQOthSikH9aMbHtQdJ2yVr7Vq4truPXkXHqnhAf8Ad9zWh5zt5Ty7rVD21QBZNlwBns7gM/2vloXt7+7hhem9EfVdPqkRlJY0cj87RUUVjZx+8m5xIZa2FvjIj7cisursmFvDUWVTXy4qoRLB6SgBLGibIFH1doYhZRUO7nq9RW8Nm0Ql/RL5ry+ScgSyLqO6j3IIHdIoGkafzu3D7e8s6pNYJ06LIOKRg/3fbyemdMHIXQYkR3LKU/M9wVwkyTQdALOV7dg9tr9XDks05epypIgLszq5x3eGmZZYDXL1Cqaj+GtKhpCgNlsLGmKEpzJ3hoOs8wjX23mmtHdmDIknXeXFfvZzS4vqmZ5UTU3js1mdG6sL6N16XDbu2uocynEhlq4fFgGQ7rF4FWN8/AoGiNzYli0o5ILBqZil4yv6/GAKkt8v62Cv3252WfIY5IE04ZncN2oblw3qhtOr8r7K0p86ozhdhN/O6c3qeHWo1Z9aw+6rhNibX9z47DIbbT2jxTVTi/TX13ehhzq9Kpc+8YKvr1jDGGdei+d7LiQdo/Ijgs9rmI7XUG8C8ccmqbTLTYEu1kO6PIFMGVwGnZJdMhCPx4wC8GgjCgWtjKf+P0Ha3nqkv4sK6rko5V7qW7y0Dc1gjtO6U5CmBWrJJpZ9v4/XpdusP6DYW1JLU5VI0SWsMiCdSWGWMueqiZ+98FaHBaZ6BALtU1e6t0KJ/WIJzc+jPdXlHBO3yQcZpmYEItPXOZQDEiPZHtZW2LattIGql1e4i2ywRrX2m7cWrSq520v542rhrC8qJrVe2qIcJg5JT+e1XtqeGtJEb87tTthNjO6EJTWuYh2WHwMfyFoY5pyKHRdR0j4TiDKbua60Vn8bc7mgMef0TuJ138u4pVFRSRH2Pjjmfn0S4ukstHD7CXFuBSNM3onkhHt6JDJ7pAEvz81j1cXFfLQ2VFt/OJb8MKCnVw0ONVXIm1SNLaXNZAVG8Ij5/fh2R938OQP29F1Q2TnvAEpPDi5F9e8voLp7bSJjjZkWWJDWQN//HSD3+OKpvPKoiLC7WYuH5jCneOyuXFsNrsrm7CbZRIjrNjguBHJNE2nV3J4u6X9acMyMHN0EoqSaid7qgJ7LiiaztvLdnPTyG4dfk4ej8rZBcn854ftASvwFlliTG7nrFCPFrqCeBcCQgjQJEM0w+VRsVlkbJIxLnUkJFsrOg9MyvezsWxB94TQ5l7y8ZtPFUIY1xjgl6h4Vc7pl8xz83b6FpiqRg/TXlnKmO5x3Hd6DwpSI7CAwYJXNNACVwE08Fs8cuJDuXJEJt3iQlBUHVXTUXQdi2S05SIOsZZs8qg0eQ5mD1EOM40eBWdzxhwiwR2n5PKnzzYGuEa4YWw2//iq7Rw3QHGVk8TkML97YDJJaAhj/lDVQFGZkJ/AA7M3sbuqkdz4MA7UurjhzZWc0TeJe0/L55kft/uY8yOyY/jXhQW8vGAX87aV41UN3+8Qi+yn/90aJ/WIp6zBQ1KIUQsSwFl9Elm5u5qvDwmqvVPCmTI0naub57n317mQZYkHv9jENxtLfce9uWS3YZM6bSDWdmR4VUVlXE4MGTF23l0e2IMcmq1Dt1YwuWc8iqL6+t1/Pac3d7y7xm8Ez61ozFpWTFm9mzevHopJ4JslPtZw6fCvb9r6wbdg5sJCzu+fgk3TsAP50XZAR1ePv/6DFfjzpJ7c/2nbNWFIZhR9A7SmjgRCwOZ2JiwA1u+tw6vpnRqDtEvwxMX9uPO9NX6B3CQJXpg6wE9Y6XigK4h3oQ2EELhliX98vYWv1h9A0XRMkuCMPoncd1oPLGrHc7ptoOqclBvLO9cM4bFvt7G2pJZIu5mpw9K5eFCaoRR1bC7HD0KWcGNoXte7FHLjQ5E8CmEW/59CiCR446ohXPfmSp+RhqbD7someieHEyoMZmt7G25JEiAJMmNCqG6qYWz3OK4cmcmjX2/19bHD7SZuGJvNeX2TiQ21MCA9ElkSQV3RzhuQym2zVjO+Rzw2SaAqGhPy4vBMyufJ77ZT3xxc4sOs/OGMHvy0oyKo5GtihM33OUqSwCUkFhVV8cW6/ZhliUuHpJEdG0KIppEVF8KX6/f72gm9U8IZ1z2e699c4beQ/byzkpW7q3nlisFsPlBHaZ2bD1YWc93YbJ74rm1wCbWauGhQGpfNWMoj5/XhtJ4JCAz+wwNn9uCW8dl8vs6Qfx2RE4vTo3DjWwcNQcbkxrH1QL1fAG/Bpv11/ONrg8ku2skwZVUjLy6U+g5aE3UuLy2DB9EOC4Mzo9i4ry6oz/0Pm8u4ckQ3Xl64k/tPzyfWKh3z0SMN2uVI1LsVnB4VWzN77b869qZqnJQby/vXDePx77excW8d0aEWrhyRycSeCUdN3U/XDde39pAQbsUkCfROLEKSpjMsLYIf7hrLx6v3srO8gZ5J4Uzum4xdosOpiaMNof8ahhcPA7quU1EReDTmREFEs+tUbW1w04v/JryyxNVvrmTz/ra7155J4cy4fABmVTui65BlgUsX6ML4cTma+5nHA7okseZAPb97f60v2IExY/7o+X2RvV6/jE2SBU4Euyoa2V/jontCGPGhFuyic6MpXpPM/Z+sZ1JBMg/O3sSMKwYxbeaygOXD20/OZergVObtqKCywRtQBe3iQWn0Sg7nb3M2M+e2UURIB6ViQ8Js1LoUqps8yEIQapWpavRy1rOLAp5bcoSND64bhkXTEELQJASXzljaxohlSGYUT17cjyavyrbSBt5fXsy8beX8+8ICnpu3IyjhbWz3OPqnR/Jk8+z0n8/qia7DSwt2+Wbjh2VFc8/EHjS6FS5/ZRnxYVZm3zKSaLvZ950y+twyXkli0tOLfH/bgqen9OfhLzdRGsRkxiQJfrxrLPYOVmeTSebrbeUBK0Ut+PD64XQLt6BpOrpJ4sftFXy5/oBf2+VQ3DWhOz9uKWNbaT1f3jqKMKEfUSWrs/DIEhOeXNiuW9y8340lpBPh8XitU5Ik8CIMuVpdJ+Qo67hHRNipbPJyyuPzg1aDPr1pBKkO82FvaiwWGU03xj0P1YY4WoiJCfUJWQVC+2yjLvzmIEmCosqmgAEcjF3+7ipnu1+q9qCqOmZNw6JqWDXtuAVwIQSVboUb3lrpF8AB5m8r5/8+XY8i+f8cNFXHqmr0inEwISeG9FAzoSYJ2SRjMrX/0zGZJJYWVjFvWwVur8ZDZ/finaV7gvb/XlywE7emMzo7loEZUXx443BO7ZlAZoyDYVnRzJg+iAm9EnhzyW5mXTuUcFn4BQOTJIhxmIkzS0SbBBZVIzbEzNWjMtu8V7jNxMvTBmEXxguokuCB2RsDOqktK6rmzSV7ePTrrTz4+UaGZ8fw93N7Ex9ubVc0ZMH2cgakR/n+/fCXm8mKC+HJS/rxxlVDePuaoYztHsfvPlhDcqSdEItMWb27TTas68bi6PKqlDe0DdQRdnPQAA7NTPYgPAy/4xSVsd3jiAkJPB+RlxBGcoTVVxKXNZ3RufFt/NUPhUWWUDSNJo/K8/N3ondw/C+FVQguHJga9PkB6ZGGY9qvCJqmI2vGemDVj418aaTNxAtTB2IOMNFw3ehuJIZajqgq4fGoKF71mAXwzqCrnN4FP5jNMl9sCGzE0YIvN+yn5/ic43RGRweaJHh23s6g46Dfby7jj2fkE4h3ajJJeBBUNXn5YLFhSTq2eyxDu0XjCCIZ69Xh0zWGgtyfPtvA+9cPZ9GO4Bmby6tR0eAhIczKoh0VfL7OkPic0CuBbjEhpEbZaXApvDZ9EPZOjv+ZVI1rhmdyfv9UNuyrJTM2hHCbmVCrTKgs8DYvPC5NZ/624Nr0768o5q/n9ObbTaU88tUWbj0phz6pke2+t64bcr2TC5JJi3Ywpnss7yzdw2fN96Q16t0Kp/ZK5JPVewmik4MZOLlHPN9u8i+b1zm9xIdZ/aYJWkOWBDazTHt1UqOVINhb3cQrVwzm3o/W+anUjciO4dHz+2BtNXqlaTqySef8ASkBvQbAqCL0T4/ksW+3AvD1hgPcNj7nmM6L64rKtaOz+HFrWRsmdpjVxCPn9sHKsR8h+7VBlgQ9Yh18d8cY3ltRzJqSWhLCrFw5IpP4UAvyr1AZrrPoCuJd8IOug0Vun95h7eD5XyM8ms7qPTXtHlNS46RHlN23I1cliQZF40BZI/O3lfvEXwBmr91HlMPMu9cOI84qBwyqLfFI06GworHDrM0kS9z+/hqWNbuL7Sw/6BB2xYhMbhiZiaxph8XWtaATYTez+UA9D36+iUaPSq/kcO4+NY8e8SHIqobL2z5ZsbLRQ2grqdaXFuzivAGppEc7gjJ+h2VFs7VZu/yxb7bywvydAfv8gzKiDEGYUCuJ4bagkrCypnPPxDx+2lHhVyr+cGUJlw1N54lDJE9bcFqvRGytmO+HQpIEDbrgsuZWQkaMg+vHZNMtNgSvqpEWZccmCcya3oZlL6k6yZF2+qRE+FnAtuCyIenM31bum7gIpuTXEWTZ0Ol2q3rz71PgaMc4xa5rvHftML5Yv58PV5bgVXUm9Ezg8qHpOI6CfPIJC1UjBLh2WDpezahe6ar2q5R2PRx0ldO74AevV+W8/intHnNOv2S83vZJQMcSJpOE2SwfVklfEoKoEHO7x4TbDvbEVFni3VV7mf7qcupcil8Ab0F1k5dr31yJM0AANAt8Zc2C1AgyYhyc2859jQ6xEGKVfQH8ULz2cxFNR0CKcksGczs6xMJtJ+dydr9kdpQ1cMVry/lxWwXCJOGwyFja2WCkRzv8ZrbdikZJVSN3npIb8HiTJLh7Yh4hVhNb9tfTLy0yYAAXAq4fm83O8kZK61z8ZXJPImxtg7gwSTiFoTo257bRPH5RAXGhRtm7yaNwbv8UTu0Z73vNcd3jeObS/sy6dhj3nd4DuZ3g6UZw67urfa2E3ZVN3P/Jei6dsYTr31xJcXUTVhFY312oGsnhVh67sC83j88mwm723a8/n9WTgrRIXph/cLzwjD7NG4rDgSzY26hw06w1jPv3fMY/Pp/LX13OmtIGtCCfmabpmBWVC/ok8crlA3nzikFcPzwdm6b9dgN4K6iKhqRpaIr6q9Cz/6XoysS74Add14kLMXNqz3i+3dS2THhqzwRiQ8zHbfcqhECVBF6MKoEQghUlNewoa6QgNYLsuBDsdFxetktw5YhMfvfBuoDPJ4RbiQkxg6oZvIBaF0/+sJ2bxmXz3vLioK+7p6qJqiYvSXbZL5tVFI3+6ZFMG57BqJxY7v5gHf+6sICPVpUE7OHePTEPdwe924Xby5tHnDp3701mifImL8OzY/h87X6cXoXBmdG8dc1Qnvx+Gw/P2cyY3NHYBJw7ICXodU4fkdFm/KrWqVBU0cgTF/fjqR+2U9jMgO+VHM79Z+TzyWrDjW1wZjR/OjOfRo/CzIWFPmJRXJiVe0/LY8G2cib3SyYvIZQNe+tICLfRIz704H00yby4oJB3VxhSuy3GIx/eOMLo7Wo6FnQenNSTW8bn4lE1lhdV8dDnmyirdxNikblkSBrXjOyGOcBURZOi+WbzW0PXDSGQZ+bu5KkL+iIHIIIJYQjkhFpkzuufwum9k5AlwaZ9dby7fA/Liw5uyMJtJq4fk31YzGVJEpS5VM5/YbGfzOeuikaufG0Fz182gCFpEWhBvjeqovpK95py4gerLgRGVxA/gSGEUfJ1aVDv8hJiNWGTBBb0XzSTalI1HjqrF4MzY3hp4S7K693Eh1m5bkwWk3onIh+neW5JlqhVdP719Ra+3VSKqukMSI/kxnHZ7Kt18u/vtpEYbuPta4YQZZLaDeSKojEiK4bhWdEs3lXl95xFlnh6ygBsGCM6qhA+gZa4MCsl1YFLxi3YX+sk2RHWJkDYdI1pwzM44z8/4VE1/vDxOp6eMoAPV5bw+dp9OL0qA9IjuW5MNsuLqnzl5EOJdy3wqNphlWSdusR9H6/3C1Kb99fzwYoSnp86gH98tYWSGic5ETbuOCmH6kYP0SEWYkKt7K128vXG/UwuSCHSYfELSFaTREFaJEmRNqIdFt64agheVUPVdNbtreUvszf65GK/2XiAsjon/7qwgGHNimayJNHoUXhzcREXDEzD5VV5du5ONu2vY+ZPhXx35xisGHrzf5y90c/0Rtfhx63lbH15KR9cPwxz82iiCZ34EDNP/LiD91aU+I5v9KjM/KmIxTurmHH5QMyt5o6FgIoAZLnWKKpoxKu3nR8WskSdovHygp38vLOSUKuJyQXJjMqJxWKSfL7wkoAx3eO4a0J3ws0CNbiabBsoQvCPr7cE1el++MvN/OeSfqSGW0/onm4Xfhm6gvgJipZZ7j/P3sgPW8p8WWBBagRPXFRAZAdBrSPIisr5fRI5vVcCOkbfxS4J1OMUwIWAelXnnOf8XaVW7anhujdX8uTF/dhW2sDK3dVMf3U57107tF3ddQCzqvL4hQWsKq7h1UVF1Lm8DM+K4aqR3YgNsdDUYIwveTSd3ZVG4C6tc5ERE1w7HCAl0h5w06QJwYyFu3yL8M7yRq54dRmTC5J55tL+mGWJxAgbN761kp3ljQzPjsFqlgjC0WJkTmynBXFMZonZ6/cHzDKdXpWHPt/EzeNzfGx5Sde57eQcXl1UxIqiKronhvHZzaPYWV7PrbPW+P39zeOzeXbuDt5tztxTIu08flEBxVVN/P7DtpWO1cW1/POrLTxwVi/WldSwancNUSEWbj05l1lLi/l0zUFjHKdX5fN1+7ikXzJVTiWgax3A3honP++s5OTsaF9lotGr+QXw1ti0v44N++sYmhpOo6L77FA7MnhJjXJgEoLWZRZZlthR42LqzGV+AXbjvjp6p4Tz57N6ceO4bOLDbAgBa/bUEG23oB4mg9kLLGhnfG1vjZMmj0pRtZPcSNtxEZPpwq8PXT3xExQeSXDDWyv5fnOZXxl3bUktF7+8FCe/fIxEVVSsmoZN07Bo2nEL4AC6LPHU3B1tXLbAWE//9c1WrhiRCRiSivtrg1uAtv47GzqD06N4/KICXp42iBvGZmG3yLSeLjNLgowYBwAfr9rLlCFpQV8zJz6USHvgXrtL1Vm0038RbvKovLu8mKtfX8G0V5axcV8dNU1eJAE5caE4gphljM6NJcpq6vSMcZMCbyzZHfT5XRWNJEXayIoNQRGCD9fsY9LTi/ho1V6WFlbx5uLdnP6fBTi9Gmf2SQQM45S/n9ubMJvZF8DBCCaXz1xGZmyIHwGuNb7bXEaTR2F0ZhQDMyKZt7WMKS8t8QvgLVhaWAWSYEkHNqifr9uPt/l+mEwSC9th/4OxIdtc0cS1b69i7GPzGfPYPAorGumZFB70b24el431kK+VU4c73lsTMEPesLeOpbsq+WT1Xqa9sox/fr2Fk3vE+8b5Dgs6Hf6KhYDn5+9COULSXBdOfHRl4icghBCU1ntYH8RNp7zezaKdFUzIiTmuGr5HEx4NvlwXfNStpNpJlONg7r29rJ7syFiUVr0/IcBiMdGk6qi64a2yv8HN3R+uZ2upMUI0tFs0t52cS2mdkxHdYpAVFZOuc9O4bOZuLaes3s3m/fXcdnIOT/2ww+8cEsNtvDR1ILYgIztCEDSotSCk2cL07H4pOGR466qh/OXzjczdVo6uQ4/EMG49KYeC1EgsovMmGrqA6iB66r7zA2wCqtwq//q2rZqapsN9H63juzvHcsHANFIi7fzfp+tZckg7AoxS/9tL93BO/xTeWrKbQ5JX4xhFQ1WNmekVu4M7WMWHWZGEwCx1xOYXSOKgZ04wlbtwu4m/nt2bUKuJS15e6ntc1+GhLzbx74sKuG3W6jZchWnDM+iVFNZm81rnVnza8IHwyeq9zJg+GAFYBNjEkTnrmYUhSft9kGpEerSDqkYPJdVOvPx3rE678N9HVxA/AWEySfy8s/2s49tNpZyUE3uczugYQNChGUrrkZ+UKP+StiJJeHRYvqeGZ37cwcZ9dYTbTZw/IJWHzu7FrbNWU1bvZmlhFVe/vpzXrhzC0/N2cuvYLISmERdm5YaxWbwwfxePf7eNq0d1473rhrFwewWNHoXhWTH0Sgo3XMuCLNAOSXDpkAz+9FlgFbBIhxmzSeL0PonceXIuQlEJkSQeOac3bs0o924rrWfmokKem7eTQRlRTB+eQZhJ6pAgZRLQNzWCn3YEzmZlSZAYYUc2y7wTgHnfAq+q8+2mUuZvLWP6iMyAAbwF20rr+cvkXpxVkOTT21+zp4aZPxVS6/QSaTejKBpDu0VjlgXeIGz7acMz8boNQl57mDI4DUk3pscURWNc9zi8qk5BWqSvR//1xv2c2z8Vt1fl/wJodJdUO/njJxt4YepA9lY7+WFzGdEhZi4YmEqk1RSQ/9EYhLPQglqnF7tZ8inPHWn9qmWsbuH2ioAiQXdO6M7rP+/2WcX2iQ85buJJXfj1oCuIn4AwbPw6yPCsJmQB/71BsF8GEzCueyw/bAksQhITYvEtbBF2M1mxIb7xGdUk88PWMqqbvPy7VYZZ51R4dVERP22v4PGL+zF1hpGVubwary4qpFtsCI1ejVibiTcX7MJikpl17TDmbi2jpsnLrvIGTu2VwCer91JS3cTQ1HA8nuCLpqpqjM6NoWdSeBs9a0nAI+f2ITHMyp0n52JSVDRJYl+jh2fn7eC8Aal8sKKEH1oJiWzcV8c7y/bw+hWDyYuxt6vDbdZ17prQnZ92LA74/Fl9k3h/eTF9UiLazSrBqOw4LHK737nEcBt/Pac3T363za+PO7RbNE9f2p+1e2qwyAKnbniUf3HrKBZsr2DmwkI/KdXrRmeRFG5Dc3mwS4KrRmYG9L7umxJBz6RwahRjxt1ukdE9GnO3lvkka8NtJq4YmYlHMSYOAinSAWwva+CCFxaz+N7xjOkWha6D16ugByl7xIfbaCbGB0T/9Eg2768n1GoiJcJqiMQcQb9a13WizTKf3jSCh77czOKdxoasZ1I4N4/PYfGuSlbtqWbm9EE89MUmXr9icFc2/htEVxA/AdGSdQQqWbbgsqHpJ/RMqEnXufvUPBZsrwiYsd08PodZy/ZgM0vMnDYIe7Oalskk8c2WMnITwpj2yrKAr729rIE9lU2c0TuRORsMl6wfNpfx8rRBLNpZyfkFidS7FN5fWcQriwoZnh1DqNXE64t3+5S8Lh+WQUcdS10HgeD+M/JZubuKT1bvpc6l0C8tkitGZPLdpgO8s7SJf53XG00S/LCjgvs/2UBOfCh1LsUvgLfAq+rcPGs1n988Ems7+teappMSauXxC/vyx882+gmknJIfz3kDUrnuzRWMyIphcLdovtvU1kCkBXmJoXy76QBWk0Skw0xNk7fNMX+e3JN7PlzHjjJ/X4OlhVX89fNNvHj5QP78+Wa+3XTAF/wGZUTx8rSBPDfPEIK5dnQ3suJCCLPI1LpA1jSuG9WNvMQwnpm7g+IqJ+F2E9OGZXDRoDR2VzXx0oJC1pZUM2P6YK56bbnfudW5FJ76YQdThqQ1f17Boem6wf7vxG/GKuDsfsl8srqt+pwk4PJhmdz1/hoqGjzkxofySrPK3pHMJOuaRqLdxD/P78PeaideVae4qomnf9zO1tJ6fndqd9YU17CzvBGnV6MDi+4u/A+iK4ifoLBLglvGZfP03LZe1RPy40mLsJ3QQVzTdGJsJt6/bjj/9+kGXyabEG7l9pNzCbGaGJQRxV/O6umnQtWkwcer9zJlSHpQnXIwpET/fm5vXxBvgcEPElw+LJ0ftpRR2ehh3tZycuJDuWpkJpmxhoVocqStQ59sAJMMT/2wDZtZ5vqx2djNMttKDROW8gY371w7FKuABl3wQLOd6KS+SXy8KjDLGgyRmX21LrLCre0GBknTGNYthlevGOxjMufEh7J6TzXXv7kSl1dj3rZy/jipJ09+vz3g/YoLtRITYmV3ZRPP/riDf57flxvfWumXhaZE2tF12gTwFlw1qhs3v72KNYcw5VfsrubaN1by4Q3DsaIj6XobNzlZUTk1J4ZRWTFo4OuBL9tdze/fX4umw+m9E/lq/YGAmwuA91eUcPWoLJIjbEGrDuO7x9G+FNBBSKrGPafmoWo6n6/b79tIR9jN/GlSPl9t2E9Fg8FH2F7WwJ3vr+WpiwowH6GwiKJoWEwyTo9KtdPLjvIGTu+dyINn9+LLdft5Y7FBYDR0wTv3HrJJpkkzNi5mWcImGeI1/wPaJ785dAXxExSSpnHZkDT6pUXy5A872FneQGK4jWtHd2N897jjNst9TKFqZIRZmDF1AG5VQ9HAYZEIMxtkMDkzCsXrb1eoA+UNbrwdbGA8ika9S6FvagTrSmo5OT+epYWVnNMvhQe+3IxFlnjswgL21TiZu7WMqcMyePy7bWzaV4ei6YTbTdw8Loez+ya1e68bPCq/n9iDP366nj98vN73uCTgzlNy2VvtpHtsCEt2Vvg4AKFWE5UN7ZPSKhs9pEXbaXSryJIAlxJQ7UzTdO79aB1Or4rFJFFa6/ZjVWs6eBWNt64ewtWvr/CbBkgMt/HExf346xeGV/jcbeWMyYvjoxtH8MzcHazaXU243cxdE7qzMghRLSbEQpjN1CaAt+BAnYtlhZWMz4pGCdIeUBTNNz6oyRK7a108/MVm30ZiYEYUHwQZLQOD8LaupIb7zujBbYeMy4GhE3DPaT0w6Z3XFDcpKv83MY/fTehOYWUTmqYjSYLXFhUx7xAd+hW7q3GqGuZfQCA3YczcLymsIis2lEaPwnvLixmWHcNFg9LQdR2bLKATqn6qSebtFSW88nMhdU4Fsyw4qyCZu07pjl3X2pT+ZVnCqUOdR8XpUYgLtWIVdKpq0YVjj64gfgJDVjT6J4bx4qX90BAIIEQWeDvh2nSiQFU1zBhMXWRA1XA3Lx6B+v0CI0DnJ4W3224YlRvL0sJKBmdGs620nitHduOz1Xv5cUsZH60yxp5mLS/m7IIk/jQpn301Lm47ORezJFB1eGNxEY98tQWXV+WygSnoAbJYSRLsq2zivo/X88cze2IxSawtriHMZmJARhRfrN3PR6v2MjYnxicOAobOeu+UCJ9gSiCkRNm5+KUl7Gk2ueidEs7fz+1Dkt3k16x1mAQXDEzlsQDsczCY26FWmVirxOe3jmJ5URX7alxkx4XQIzGcO99bgyQZve2iykYe/HwTp/dO5IFJPXF6VBo9ChE2c9AsPC8xLGiAb8FXG0sZ2wGJrQWKDvUuxe9+qZqOKYA7VWvoQHGlk8cu7MszP+6gqFkHoF9aJHdPzGNHWT0R6VGYdbXT2aikajiA7rEhTH11eVDfdoCyejcREdYjz3RVlVtPymHBi0tYsquSB8/uRYTdzLcbD9DkUTijTxKaEJgl0W7/XZEl/v7VFj5vNfnhVXU+XrWXNXtqeOuqIZhbUfG8qsb2Ghd3vrfGV8UwSYLzBqRw18m5vzhZkGWBWxe4NB1V07GbpOOqR/G/gK4gfoKjJci1lNG8v/HNsV0WXDEik0376jinXwqfrG47hxxhNzOhZwIzFuxiaFY0r0wfTHFVI2Py4rht1mq/Yy8Zks4HK/cyY+EuXM03N8ph5u6JeWTHhfL8/J2cPyA1IKFI03QSw22U1rm5ddZq4kKtZMeH4PSoPPbtNlRNZ2z3WHSMYNeCz9bs4+Vpg5i9dl/AsanBGVEoms70EZl8u7GUpYVVbNhbxwXPL+aLW0cSbZIOasB7Vc7tl8K7y4sDErsePKsXVgzbVYssWFtcw7qSWt5e6uLa0Vk8cXE/5m8rp6LBzfQRmZhlgdOjYhVgt5tZtaea5+ft5B/n9+XpH3e0eX2vqmE3t9+odVjkzqsaCNqU/Rdur2Bir0Q27gs8cmk1SaRE2vnd+2sZkB7F7ad0JybEgsMiYzXL3DZrNYUVjQzrFs0TF/bFdAQZZtghVRBJwLi8eM4qSCbcZiIpwoYkiSMWYNJ1cKDz4fXDqXF6efSbrX7Oc1+s209atJ13rh7abv+9waP6BfDW2FXRyMo91YzKiPSNppY2eJg6c6kfL0XRdN5fUYKmw90n5yAd4TUJSWJfk8L/fbqetc2VmrhQK3dOyOWk3NguFbpOokvspQv/U1C9KucWJDNvaxm3n5LLtOEZ2MwHv+b90yJ5fuoA/v7lZi4YmMrpfRLJiHHw/eYybn57ld9idUafRNaW1PLMjzt8ARyMnvT9n2xgUGYUKZF29lQ1oZoCB6oIm4m8BCNAlze4WbKrirUltb7gfOv4HOpcCvUuhdxmzfAGt8IHK4v51wV927h6DUyP4i+Te/Hnzzbw4coSxuXF8cZVQ4gJseBRNR7/bjvaIcYwNl3j3WuHceWITEKaxWT6pUUy65qhjMiKRjQv+CZV4+ax2ZzRJ4mLBqUhBEx8cgEPfbGJ5+bt5Ka3V/H3OVvolxaJWdcRXoVTcmOZdc1QYkIsTB2W3ub61xbXMi4vvt3P7LIh6Z3W4rcL6BYbYrQQmrFoZwWDM6NJj3YE/Jvfn5pHUriVCwamUt3k4Y2fi9hd2URZvZtLXlzs031fUljFzsqmwzLWAWPW/oaxWb5/RzrMvHblEHolh/PPr7Zww1sruf3dNawvb0TvhBd9MKiqjkPSWV5UFdA6trjKyf99tgElyPmbTBI/72pfQOej1XtRdOPv3arG8/N3Bh0F/HhVCe4jjLNCQJ2qccGLP/sCOBi/kfs/2cCXG0sRx9h7/X8FQj/BbFx0XaeiIniZ8URARIQdgNrawCMvJwp+rdchBHgkiQaPyuriGpKbiVdmWWLz/jpe/bmQCJuZl6YaWtpVis7E/yxs8zqvXDGYO99bQ60zMGGqX1okkwuSyY4LYc76/dx1UtusRJIEdRpcOmMp+w8hVd15Si6XD0njozX7eGVREf+5pD9/n7OZNcU1AIzLi+O60Vl4VI2Kejd5iWGs31vHv7/dSmWrcnKv5HDuO70H015ZhlmSmPu7MVgCBEXJJOPSDX344qomPl5VgkfRmD4ik+Rwqy8DNZllShq9nPX0TwGvu2dSODOmDsDcagRLCIEqS6zYU8PTc3dQVNlISqSDm8ZmMSI7htcW7+bFBbvavNb4vDj+dnYvzM3v3ZnvlGKWeezbbb62Bxhqcv++qICPV+1l9hpDlz47LpTfn9qd/inhmDQNYZbZVe1ieWEVX67fHzBzP713Ig9Pyg9qKhIMqizz6Hdb+Xj1Pl66fCDPzt3hF5xacO9pPeidHEZqlAO7LA472/RIEhe+tCQoQU8ImPe7sTgCLOsmk8Tnm8t5YPbGoK8/Pi+eR8/pCYqGajZx/guL2VsT/LN4++oh5LWy7+00TBKPfLedj1e1rZSB4X3+1e2jsB6FbPzXuk51FjExoe1uLLvK6V34n4DJJNGo6YBAAmyA1Swxvnsc32wq5dm5OzlQ5yLMamLK0HSuHJ5huFoBDqspYP/cJImgARxgTXENd0/Mw+lV+WBlCTeNy+HQXFDTdCJkiQ+vH8aWA/Us3FFBbKiVM3on4ZAFkqajabC/1sUt76zilpNyuHtiHvtqnMSEWqls9LCjtI6JvZO4ddbqgBruG/fVsWp3NaNyYtvvP+s6ZfUeLp2xFGerIDV73X4uGZzG7eOzMakaiqbz4vy2Uw8t2LS/jmq3QpTNhF0YxDNd15EUlRHpEfS/fCAaBj/B8L1WuXJ4Ov3SInnqx+3sLGskMcIgYU7oEd9uX1U2yThVg/Fhl5tJbqrG70/Nw2KSfH7ZJdVO/u+T9Tw7ZQC3jc9B03Uk3/sbn7NJh1VF1Tz6zdag7+dW2jqddQayqnL3hO5cNzqbDftrAwZwgMe/28pbVw/lpMfnM2VwGreNzzm8vrIQ7c716zo4PSoOc9ssVlE0RnbAPbhwYApys4COJEFIBzNrDouJzjLiW8Otwfebg4811rsVap0K8ZaubLwjdAXxLpzQEAIUWWbOplJmLiqirN5FXkIYd57SnR7xIcgehUn5cYzvHoemG71Ku4ThJdz8GmFWmZN7JLRZVDoiS1lNEjEhFh75aguaDrsqGugbF9KGWKSqBru6f2IYg1Ii0HXdIB9qOooOY7rH8sjXBvnpgc82YjVJRNjNNLgVmjwq/zivD06v2q4Jyyer93LdmGySImxYhQi4rDp1eGnBLv5+Xh9iQixIQrCupIa3l+7h3eXFnNkniZ4xdlya7puHD4a1xTXGe47Oom9iKFLzNSuK5jeq1dK+lhWNYanhFEwdiN48CdUS4ANBkgROIfH5mn18sX4/siS4YEAKp+QnYNU0TF6F352Uy41js6lq9GA3y4Ra5WYFPbXN+xvnpjIyp/0gdmafRMyyRL1mmLFIQmAzSb7NQHswqRrRdlPQ7BIMEtn2sgYyY0J4Z1kxufFhnN0rofNELl2nW2yIrwVwKGRJ4LCagurzhpgkLhiYwocr255j94RQ+qVG+u5fpM3M5cMy+NNngTP36BAL8WGWI7YlNnUgq3u4bY3fKrq2OV04oeGRZO76cB1//nwTe6qacHk11pbUcsVry/l47X40WULxalg1Dbtu/F87ZDF2mGX+enYverQil4FhQ9krObg5xjn9kqlu8vj6k3az3C77WFU1PB7Fb3pA1yHSZmJCz4N9Y7eiUVbvpsljlISHZ/uz1wOhzqUQZpO5eVwOqP4BQZYlvLKEV9c5syCJJ7/fxrRXljF15lIWbC/n0Qv6Mjw7hhcXGEYaJlmQGG5r9/1iQ61sLa3n2jdXsqWiqVN9XkXRMGtGJm3RtHaDYp0G5zy3iH9+s5WN++pYV1LLA7M3cfHLS3A2m33oXgW7ppFiNxFtElhUDbWdEStdhxiHmWHdogM+nxxhY1hWDAsLq7jgxSVMeHIhJz+xgKmvLmdTRVMbrkEgeHX8+BOB4PSqzTPd8Nz8nTQdhpqbo1kfIhgm9krA1s5pyprG70/pzh9O70FMiDG4ZzNLTB2azqtXDMaq+5/7qb0SyU8Ka/M6koBHz+9D+9+S4LBLgrP6JgV9PibEQniXck2n0JWJd+GEhSwLNpY18PPOwGSdf3+3jUl9krB34rViHGZemTaQkhoXP2wpw2GRGZ8XR058KNNeWdZmYY4Ps3LRoDRCbSZenjaQJo9KVpwD3X34ozEmVeOvZ/UiJy6UN5fsocGtYJElJhUk8btTuuMQOnkJYciSMMZwzDLn9E/m1J6JyM0l/20H6uifHmUo17U6BUmWKHOrvLlkN7kJYfzlkH7okl1VrCtZwWtXDuGROZvRgcomhYsGpfFTEFewxHAbkQ6zb677r19u5o3pg/wycCEEmiTwAuhglYBOiok4FZU3FhcFdKUrrnLy3Lyd3DU+O+BYX0cwaxpPXFTAY99tY/bafT7S1sjsGP59YQGr9lRzyyGz5IUVjVz+yjI+vGE4mWGWdjcKJhmGZUWzak/wtkav5HD+XWWMuJXXu1EPo3yvKCojs2O4dEga7ywr9nuuT0o4fzwjH0lVA1ZiJEngFQKvpnNOvyTO7JOIourIksAuga6obebko2wmZk4bxJfrD/DW0t3UuxQGZkRxx8m5xNlMQQWlWmbLG70qDW6FmBArNsnYROi6UQm7elQ3Zq/dR3UAkZ6/TO6JXXDEuvO/JXQR2/4LONGJFi34r1+HSeK+2ZuCek4DPHZBX07Kim53tKf1dUiSwGSS0HVoUHQe/W4rU4dl8s7SPSzYXo5FNgxLzuiTxB8+Xs+fJvXklndWEWo15EDP6Zds9NqP4GclmSScmsEKthyioqWbJP71/Q4Wbq/gP1P68eHKEj5fuw+XVyMpwsbN43I4rXcCust/QXTLMmc8vZDHL+rHPR+uC5rRTy5IZnRuLCOyYpj4n4X84fQerC6u4cOV/iIqIRaZl6cNYsXuKgZlRvPF2v0sLazi1SsGITfzCuyyoNKl8Ph325m7tQyzLDGpbxI3jM0mwixQgvhqC1nglWQ2769j0/56suIMFvq/vtnqN4duNUn8cNeYX0R60mUJlwZNXhW7WcIqCVTgopeWBiVyDUiP4tlLCtodQXPLEvtr3VzzxoqAfIpxeXGMyonl4S83A0b15rs7RmPtrD1dM1RJot6r8u2mUpo8Kif1iCcp3IpF0wN+93RJ4kCTl7/P2cySwiokASfnJ3DvxDwizQI9wMak9e9CNkk4NR1NF1gkw5wl2HdckiX2N3m57d01vtl5IeC0Xon86cx8LKoxiy/JgnoNHv9uG3PWH0DRdHolh3P/6T3IiXYgHeY9CYb/+jr1C9FFbOvC/yxaSDztodGjcDhWy5qm42l5TSFYVljN3C3lnDsghQcm9UTVdOZvK+eyl5fiUTW8qoZH0djvcvHPb7YyZ8N+XrzMYL23QAjQJCNoeFQNW7OghXZIH1RTNKyAo3nOW1N0X0YlFI3fnZLLpUPT+f0Ha/364/trXfzxsw0UVTVy7bAM3+JnMsl8tHYfdU4js2+vJP/95lJ+d2p3Vu2ppsGt8MDsjdx/Rg9mTB/EF2v3U+P0UJAayWm9E7HIEi/O38UT32/n/euGMzYvjtveXcOmfXUMyIjkzlO6c/nMZT5lOLei8e7yYr7eeIC3rh5KlMOETTvEFEQS7Kxxc+0b/qpxKZEG6/yBzzawrbTB93q/dH0XqoYdsJuadx6qToNGu0zsVXuqUfT2F00LMHdrKS9MHcjf5mxiQ7NdsFkWTOqbzLn9U7jhrZW+4y8alGp8FzQjU1aaM2WTJDC3Y5wiaxqRsuCyASkGL0TR0JqJmm2OlSV21LiYMmOpb7RR0+G7TaUs2lHBZzeNJMok2t14qj7VPIP11t4WtUmHi19aQqPHv2301YYDNLi8PHpuH0y6hqbqhAr448Q87jk1D0033PdsgiOep/8toiuId+GEhVnAhJ4JQcvpAIMz28/C24O9Oet+dVERbyze7dOobkGIRcZqkvzER9bvrWPZ7irGZkahNLtnNSF4+MvNfL+5DFXTCbHITB2WwZXDM/yYyYok0aRorC+pxmGW6ZkUjgUQzRHLis6u8sagBLdXfirk8qEZPoa8W9N9EqAdbWQEYJaET6Ne1XT++sVmokMsnJKfQFZsCKv3VLO9tJ7B3aK59aRcdlY0sLSwise+Pcj2PqtvMg9+vslP2rUFNU1enp+3k6y4EC4ckIpD6L7yulMX3PDWSoZ0i8ZhMbH1QD1bS+vZW+PkjnfX8PC5vbnm9RWA4aN9GDLhnYbUwU2SREeWN4Yc8gUD0rhl1mouGZLGnyaFEWIx4fKqfL3xANe9ucLXmumeEMr1Y7LQFBVVltjR3CoorGwkI9rBTeOyyY5xtDuG1hl1RpcO//fphoDCQU0elUe/3crDk/KROiHZ2hFkk8SHK0r8AnhrLNxRSb1XJaqZE6DrxobKJ5akd5XQDxddxLYunLBQFI1T8xOIDrEEfH5Yt2iibKYjlroUusb04ZmE2wPvdW89OTegZvdbS/bgal533UJiyoylfLOx1LeINnpUXlywiwe/3ITaLGihmGT+9MUmTn5iAXe8t5br3lrFSY8v4OutZWjNx7g12pS3W0PTYUlhJaJZ0EUWLSNABtkqNjTwfQI4vU8SVgmy4kL8Hq9q9PD+imJeWVTEgu0VJEXaWbyzkn7pkVw4IJWnftjud3xmbEgb29XW+HbTAQZlRPH03B3ozexkk1mmqKqRZy4dQEZMCFaTxPQRGbxx1RBy4kM5UOeiwaWQGmWURe88JZeQDiYHjgQ2WQQkcbXgpB4JHeqf6zpEmATPTx3Aqt3VTJ2xlBvfXokQ0CMxjCGZ0YzrHsezl/bntemDsWoaqiTx9vISpsxYysIdFbia/QAe/347by4r9n1HjhQuVWtXwveHzaV4j9KGyKXB/G2BuRQt2LC3DrlLyOWooetOduGEhh2N968bRp+UCN9jkjCcwJ64qMBPkORw4UTw59kbeOnyQT7rVzCERR46uxcn5cUFtPB0elV0dJ9CVjAf6682lFLvUdFNEo9/v53vD+nte1SNB2ZvYmdVEzabCdkkOnROq3MpNCrGMTI604cbFpxvL9nNHad0D/g3IRaZq0Zl4tFgeFYM1iBMcyHg1J4JzNtazu7KRvbVutpk3IGyvdbwqjpCCD5bsw9382NuYO7Wci6bsZSZPxXywcoS7v9kA3d/uJa/ndub9GgH20rryYxxcNeE7gzPjDom/gA2AX89uzemAP1Hh0XmvtPykDvBJNdUjaQwKw9N7sW8343j3WuGkRpmZUJODI+d25tHz+nF8NQIzKqKpuk0KBpPz91BXKiV/1zSj7+f24eC1EjGdo9jTF4c7iPwIvc7nw7+XNOPXlFDFh3Ploda5SPijHQhMLrK6V04oaGqOlEmwYuX9sel6ji9KuE2E2ZJYEJv1qs+ApKZJCisbGL+tgo27a/n0iHpXDM6C03XqW7yMGvZHjbvr+O03olt9NkvHJgKQqJB15m9tq3ndGss3lXFab0TSY60MaRbNMsKq9oc89i32/ndhFxW7q7hjN6JLA1wTAv6pkTw5uLd3DwqE8Wr0j0uhDG5sczbVk6vlAievLgfT/+4nZ3ljQgBo3JiuWlcDg/O3sTeGicfXDeMl6cN4urXl/vJbQph6Kyv31vDSfnxJEbY2VfT1Ob9XV6VuFAr5Q3uNs+BIXu7vaweTzNhT5IEW8saeXVRUZtjS+vc/Pmzjdw8PgdJwLTmfv+xcs9SVY30cAuf3TySf3y1mZ92ViIJwYT8BO4+tTuRZoF2GN8lm0nC3Yob4VEPluNbHrVYZGYvLSbSYeaZy/rz0Oeb/JTkhIAbxmRz5fB0RCc2LrIscOkCt6bjVTUcZpkws9SuDevgzChMR6mwYQamD8tg0Y7ALS6rSaJncvgvskmWZQkvhoa7VRadnnr4X0VXEO/CCQ9N0zGjYzNJWE1m5m4t46uNB7CZZaYOSScvIRSLdng/dEkSPkZ0eb2b/xxSNm7BgPQov3+f0iOegRlRXPXGCkbmxHYoWKHpOk9+v42d5Y2c1COe20/O5Q8fr2dP1cEAuXFfLU1elce/38YnN40IuiBPLkhmaWEVO8sbUZov1qxp/PO8PizYXsGMnwrpk9Kdeyb2wG6REQJW7anhzvfWcKDOeL0XF+zitnHZfHnbaGav3UdheSPJkXbO7peMJODztfuJcphpdCsM6xZDTnyoH3N81rJirh+b5WNft4YQcOO4bP7x1Rb6pEQgA14heGZeW+OUFmw5UE9qlJ2MaDuyN5Bv3dGFUHUSbTL/Oq8PiiEAiAUMZb2j0DNu835CUN7g5upR3Xh+7s42UrC6Ds/P38nQbtH0jQ9pl98hyRL7mrzc98l6H6Euwm7mlvHZzLxiMGc8tbDNb0AS8H9n5GM5DBvW9qCqGn2SIxjWLZolATabD07uSfCmTsdQZIn1pQ28/FMh1Y0eBqRHctXIbkSYO2fD+r+IriDehf8JSJKgRtG5+KXFflngD5vLGJIZxX8u7ofpMOQtNU0nIyawoUYL0qIcVLdifPdLi+D+M/M586mffLKm00dkMm9rW7OKFuQnhfP3OVvwqBpLC6tIjbLz+EX9uOaN5dQ5jaAVE2LxMbYf/24br101hMe+2coPWwyiXLjdxKVD0umXFsWts1Zx3egsTEKgYAQBk6Jyam4so7JjcGs6J/17ftDzeX9lCdeO7kaYRcbpUQmxmuifHsFXG/bz7NyDUqyzlhWTEG7lpcsHcdu7q9ndbO05d2sZI3Ni+OOZ+Tz94w7fmFViuI27T8tjwfYKdlU08vbVQ7AJaNJ09lS2zehbw62o2DjqPLag0DQdGZ3WRWEhiWOS7SmKxrjucUSGWHj8u8B2sQBP/rCd5y7p5zeL3xqGoYjOhS8u8ZPUrXV6+ducLdx5isoH1w/ntlmrfRvAnPhQHj67F8khFrSjNM4FYNZUnryogB+3ljNzUSGVjR56JYVz14TupIZbj7iSosgSD365ma83HmxhbTlQz/srSpgxfRC9Y0PQj+J1nCjoCuJd+J+ARwju/mhtwDLusqJqZq/bz4V9kzotb6lpOrnxoUTYzUH1068cmUm4zcTlwzOwmiRCLTLPzd/lW0S3HKgnNtRKz6TwgGSviwal8fPOSr++ckm1k9d+LuSiQWnMWFgIwAWDUvm8uSy/cHsF5fUueiWHM31EJqqmo2g6n67ey8sLVxnHD0xFOaT0qigqFvD1y4OhyWPM8Jo1lWtGZrK0qAqzJPkF8BaU1rn5/Qdr+du5fbjy1WW+8vsnq/fy7KX9Oa1XIuUNhvJcrdPL6z8Xsa20nv9c0o+cGAeqqmGSJTJiQtrVA0+JtOPSwWKSkI5j6VSSBG4EdW6FfbUu4sKsRNvNhgjJUSrpq6pG7+RwtpU1tntdO8oa2s+UZZnnf9juF8Bbw7DMTeGD64bhVDSEAJvcOTnZw4Wug6yonJ4Xy9jcGHQEJoExMneE902WJTaUNvgF8BYoms5ts1Yz59ZRAS2B/9fRFcS78D8Bl6q3a/7xyqJCJvVOPKxSnl3XeWX6IKbOXNZmcfzjmfnEWE3GqJPVhKrreFSjX94af/h4HU9PGcCc9fv5eJUxepMUYWP68EwSI2z87oO1bd73242lvHrlYGYsLKQgNYLBmdE808qr+1/fbOOuCd256e1VfhsMsyx49tIBhMrBS4sOi0yY1US9O3BpuldyOBIHM/iR3aK5+5MNQe/R9rIGoh1m5t41lnq3gtUkYZMl7JKOoqikhVlwaVBlNfHApJ5ENpumtARBs65z8/hsFgexyMxPCmN1cQ1//GQDp/dO5K4J3QmXxBFnjpJJxtnM9LIIYyQsUPCUJEG9Dje9vcpvA5YR4+ClqQOJtUpHrbxuh6A2qi1IirARWBHfgEvVmbsleMXH5dUor/eQ6jDh8xTRNI5y/PaD0nq2HH5Rud4LzFhUGPT5OpfC7qomekTbg87W/6+iK4h34X8Crg5IP+X17o6HpQ+Bpulkhlv59o7RfL+5lBW7a0iJtHPRoFQirDIeDZ6Zv4sPV5bg9KqkRNq5cmQmo3PjuPejdWg6VDR4uOLVZZzZN4n/TOlPZkwIFllw/ycbgsqaKpqOxSTx7wsLCLebuXXWaj+G8ZriGp78fhsf3jCc7aX1rN9bS0ZMCKNzYw02fjvZjl2Ca0Z344nvA/f475mYZ4htNP/brWhBzTZasL/WRUJ8CA6bCSdQ7VTY4/KSFGHDpoNV00iyyS031W8OWNN0cmKMmejn5vln+4nhNv4yuRe//2Atiqbz+br9zN9ezuc3jyJMFuiShKrpmITosMIiy4JGXTBzYSGfr92HoumcnB/PzeOyiZClNmVYlxBMnbG0zWTB7somLn55CV/cMgrrUZpoVlUNh0mib2oE64K4n103JguHJFDaCVAdGfZ09PyvGYqmU90Y3FEQoLrJg4jpjMjy/xa6gngXjhtkWSDLhqTp0R4RCrGaMLWzyOUlhiFapVySJHALQY1TYfmWMuLCbCSFW7EJ/FyZNFXDBpzbO5Fz+yQiEIaJiQbTXl3mJ7yyt8bJw19uZtrwDK4ZncVLzf7ZbkXj41V7+W5jKV/fPgpdh62lwV3CohxmUiJspEXaGf2veaiaTqTDzBm9k4gOtbC32smi7RXYTRLDUiMYmRGJw2FB1zuWltQUjYsHplLn8vL6z7t99yvEIvPHM/PJi/MnT5klQUa0w9fzDoTEcBuagKIaF7e9t8bnm94itfnAmfmYm6U2g6F/WiTvXDuUH7eU0ehS6J8RRUKYlfs/3kBx1cFrcnk0iiobsZtlXl9cRK1TYVRODGf2ScIhCFiuFQLqNcG5z//sp1r38aq9zFm/nw+vH06yw+SbYpAkwc6KxqCjgTVNXhbtqODU3NigLmyHC4uu88RFBVzy0tI2LaGJvRIYnR3T7nvZZcG5/VPabIRaEOkwE2U3B3U3+7XDJksMSI9sV4MgJy7siCZRTnR0BfEuHHO0mCFsLW1g8a5K4sOsTMhPwC6Jo6aPbBNwdr9kPgpiA3nHybm+DFOSBI0IbnxrlR8bOCbEwouXDyQz3NrGXrH1psNkkpi/szKoctpbS3Yz67phzPyp0G9u+qGze2HFsIu8aWw2D36xKeDfXzs6ixABXk3n2Uv7s620nj4pkXyyei87yhvIjgvhzWuGYJUMOUxVBfthJCCyonL9iEyuGJ7J7qomzLJESqTNII8dct0mXefGsdks2B64apAVG0KUzUS9onNZK6lVOCi1qWo6D03KD6g8JssSm8oaufbNldjNMsOzY7hnYh63zlodUKDknxf0ZdbyYr7ecMD32E87Knhm7k7evXaoXzD2nYcs8fjX2wLKzrq8Gv/36QZemNIfU3PZ12SSWNyOCiDA/O3lnNo9tt1jDgeaphNlkvj0puH8vLOKbzeXEmqVuWxIBikR1g49xzVF5bIh6Xy4soSy+ra8kAfP6mVY8J6YMRxNUblyZCbvLi8OuFEfkB5JuE1utwr1v4ousZcuHFO0sMYveGkJV72+gpcXFvK3OVsY//h8Pt9U+ovVqFogVI3fT+jOqBz/hVUScNtJORQkh/syTLcQXP36ijbjPJWNHi6bsZSmDtYBtwYfdKCcVljeSN+UCCQBAzOieO+6YYzIjEJXNRRF5fReCUwfnuFX4RcCpgxO47x+ySiKhtA0CpLDAcGVry1n9tp9LCusYtayYk7/z0KWFdeiN4+wCWHca4ulc/aNQtWwaRo9ouxkh1uwqhq6qmEySXgkiUYELklClQRZMXZuHNvW/jI21MJLlw/EJgte/bkooNQqwLebSnGqOh5hVD8k08FzdOvw1Fyj3+/0qvy4pYyyenfAAJ6XEIZbUf0CeAsa3Ao3vL0Kp962ZOzSYc6G/UHvxdqSWlytAoOuG1ar7SEmxMrRtrtWVcOm9ZScaP4xuScPTMyjW7ilXcOV1rCj89ENw7lkcJpPsKdvagTvXDOUYRmRbSx4TzSEmyRemT6YCLs/R39gehRPX9Ify2+sF96Crky8C8cULiG47q0VvhJrC3QdHv5yM4Myokh1mI+KgpNZVfnXeb2pdSksLarCbjYxrFs0Vgmk5oVQCMGBIEECjNL3R6tLmD4oFTXIoqejd6hMZpYlnp/aH6dHo8mjEmYz8jwhDrJ3bxzVjatGZrJqTw2apjMwIwqbLHxZlxBQ51b9Ro8kAeN7xNM7OYJN++oYmBGJoup8sGovK3ZXkxHtYHJBMg7JmG3uCK3vuypLrCyp49FvtrKrohFZMoRO7j0tj6uGp3Nuf6PSUdHgZkxuHIMyorCj4VS0dvXrATbsq2PWsj0cqHUxsVcClw5JxyF0VA12V/pXNLyqRqTDTM0hFpVn90vm/eXBN08l1U5qXF7iW21kJEngUXQ/4ZpAUDXdl9J4vSon94jn4TmbDW3v5s+sNaYMTjuslpAQAlUSeHRDG8AsRFCjjxa2+OGGXFXVsAv4/UnZ3Do+2xDT4X/IUETV6Bln58tbR7Knykl1o4ec+FDCrTJm7cicA/8X0BXEu3DMIITRP9zRjm7z8/N28tez8hEdjD51BrpueHPHWiQm58cDzQtiq7VWlgXr9wYmD7VgWWE1lw5MDVqmskmCyQXJrGiHDd8nNYJJTy+iouFgCffk/HgentzL1x+WNQ0HMDbTEIxRVc2PVS6bZd5ZtMv37wHpkdx3ej7ztpbx044KHBaZFbtriLCb+cdXW3yz5E/+sJ1Hzu3N+OzYTrcrhCzx4/YK7m/FRFc1na83HmBpYSWzbx5JlCy4aWQmAJpmVBSM9oREmK39pUQIY+SuqtHD8/N38c6yYj66YTihZkF6tMPvPr23vJgbx2bzyFdb/F4j0mGmrD74KBoYRMKEGIdvQTebZYor6umVHN6m8tKCuFArDosMrUrWoWaJz28ZRXWTxxfAP1hRzOfr9nPFiExDk7+T91aSJWoUjX/O2cL3m0vRdENH/f4z8uke40A+ijVuXQd8rHADJ7qhiM+b3KPidqtE2s10j3EgRduM1kkQ97bfCrrK6V04ZhBCUNKOtSPAjvJGPEeZjKLrRvAONP+q60YptD3EhJiR22GyK4rGKfnxJEXYAj5/wcAUvt5wwC8wgSE885cvNqFI/j87VdUCZkqajm9+Ois2hN+dmsc1byznuXk7Wbm7moXbK7jlndU89cN2nprS31ea13W47+MN1B5GpujS4ZE5WwI+V93k5Y0lu5FMEh6Pgsej+N1bm4RPoz0Qwm0mwm1mv550rdPLnz7biEkS3DTOv1T/bbMe/QOTehIXdvCzavKo9EgMblACEBNqRZglTGbZdz/Wl9Rw47i27YAW3DQ+m1Dzwc9EkwTL9tRwxavLuHzmMqa9soyb315FfnI439wxmhtGZWLq7OZIQIMG5z73M99uKvVNGWw5UM+0V5axoqQWKYhW/ZGiI5XAEwm6LNha7eSil5dy6n8WctYzizjliQW8sKgIj+gKX9AVxLtwDKHrOonhgQNdC1Kj7FiO46Kjqhr90iKCmnwAXDGim8/+Mxhsus671w5lQs8EX2803GbijpNzuWhQGk//GHiE69tNpbg6uWmR0RmYHgnAtWOyeOjzTT4Vt9ZYXlTN+r21jMiO8Xv8raV7kM2d65FXNnqCzo6DIbfqbLUnMJlkzGbZ8MBWNIZlRjMoI6rN3wkBf5rUM6A2+uJdlTQqGr0Tw5k2PN3vuUe+2sLa4ho+umE43905hrl3jWFSr0RuHp8T9BwHZkRR3eTh7k828sS8XVR6dZyKxsjsWDxejTm3jeKtq4cyY/ogJhckE+kwc+cpuYzrHoenuYohyxI7q13c9M5qv01YvVvh0a+3smp3NZbDGFXUJYnn5u3w80hvjQc/34TzKCTisizwyBIHXCpryxqpVnUUSTqhA7oQghqPxuUzl/n5vLsVjRk/FfLyT4XQ5YbWVU7vwrGDrkNsiIXUKHvQcZ0bx2YhHyXd5s7Cgs6/Lyzg1ndXt+l1XjwolZQIa4fKUqqqESIED0/K509n5ONRNWwmCbMsuPDFpUF7sLoOJTVOekTZO+zheb0aZ/ZJ4onvt5MZE9LuWNqHK0u4aVyOn/HErvJGvJreqZ16R9sKwz1NR5MMg415m0qpbPQwLCuGjGg7djSevqQfc7eV89rPRdQ6vfRLi+SyoRl8veEAc7eWBXxdr6rj0FVuHJXFpUMy+GhVCVWNHk7OT6AgJQI7OvaWC1BVIuxm7j8jn399s8XvHvdIDOO+03pw49srfcH3jSW7uf/0HkwqSOaL9fv58+yN1LsVwm0mLhuWzqc3jeSbjfuxycLHynfp8Lc5bXXfW/D499sZnRPbaWUwtw5z1rcl4rWgvMFNo0fF+gscSCRZ4oBT4bq3Vvr9zgpSI3hmSn8cEiekAIomC576dkfQsdE3l+zhyhGZv0mVttboCuJdOKawoTNj2iAufmlJG/nSG8ZkkRll/0WORkcCoeoMSYvg69tG8/JPhWzYW0t8uJXrRmWRExuCrHauDK3rOpKqY8cQUUHT8CII7aA/HGbtPJHPLuCtq4fQ6Gn/nCrq3X6+58kRNsZ0j8UqCzpTVY8NseCwyDQFeZ/TeydiNUvMXneAv83Z7CsLP/XjDjJiHLx55RBChMbp3WMZmx2DjpHV3jJrNSv31AR8zSiHGZvJmHsyaRqxZsE9p+YBOvX1blRVbdPPtUiC4qpG3rpmKBv21lLvUhiZE8uBWhc3v7OqTQvj719toW9aJO+vKKGhudJQ51J4ft4u1hbX8tgFff009RWdoL1zMESDXIqG9TASwI7sY43njzyIO3W4+KUlbSopa0tqufL1FbxxxSDMJ2DX2K3SLmHSo2qUNxgqdL9l/LavvgvHHJqmE2eVmXPrKH7aUcFPOyqIDbVy8aA0Iq1ywNnh4wGhasTbZO46ORe3piEQWCUjS/8lRCC7JHHFiAzu+Wh9wOfjwqzEhnRedENXNbIirDTqAkkE94bOTwpnd0UTQ7pFc/O4bKqavDg9CturnCSH2zrU+7YJuPOUXP4WoC8eZjVx1chulNS4+GsAd7LdlU3cNGsVL106AHMrUpUJnWtGZ7Hy7VUB3/PGcdk4pIOjvbp+kC0f7FztknGtl7y0hB6JYeTGh5ESaefuD9cFvbaPV+3l1F4JfHyIhsDPOysprXOTFnJwUyUJ2hUNAmPOv7N2LBYBp+TH89nawCNukQ6zQQo8wt+B2Swxe31p0FbIjrIG9ta6yAq3nnDZuEDHYZGpakcw0GbuKqd33YEuHHNoqoZFVTk1N4aHzuzBHWO7EWsRR5WVe9jnJAm2Vjm56o0VjH9sPuMem8fVb65iR43LN3t9JFAUldE5sQzObNsfjgu18NbVQ1CBCq9GkxBosoTooMeqqTo2AWf2SQp6zJUju7GrooFrR2dx27truPO9Ndz/yQYufHEJF89YSpVXQ26nf6irGmf1TuTR8/v48RhGZsfw8Y0jCDEJnp4b3DJ0w946GtqYrmj0TwnngUn5foutWRbcODaLyX2Sgo7xBYOmaJyUG8szl/Sn0a1yoM5FUQcuaAdqnUQ5Aqvmf75uH+ZWvAGzLDi9T2LQ1ypIjcB2GN8PSdO47eTcoMHmnol5OH5B29qrG6Y47WHF7up2P/tfKxyy4OJBaUGfjw+zEt5B1eu3gK470IXjhqPtlnSkkGWJXTUupsxY6tcT37S/jkteXsL71w0nK8LIXIQ4/H6iWVV56uJ+LCms4vXFu6lzepnQM56pwzL5y+yN/Li1zDd/PLZ7HA9P7oW9g/cRqsb9p/egxun1W7TNsuD/zsgnOdLG9BGZnP/8z7i8/ve5pNrJ1JnL+OiGYe0awMiqxoTcGEZmxeBSDIcxq2SYlDgVjR1l7Wuo76txEhMX4ncdsqpxVs8ETu2ZQHGVE0XTyYxxYBUgjlCyVFY1RqRHMuvqIWg67Kxs/7xy4kPZF2RKovUtV00yLy8s5PJhmSzcXtFmTt1qkvjbOb2xCh3JLKMCsgBvO60OXYcIWeLjG0bwx882smqPMZaYHGHj7ol5DM+MOuyNTGvIQhAZ0r6tT5TDckLOUKuKxvkDUvhoVUmbjZok4NEL+mLnxB+h+6XoCuJd+M3BpRus4EDrmqbDg19s4sWpAyiuc1Hn9JIdF4pdFpj1ztlgtjiAjesWxbCMKFRdR5Ilpr+63E9kRtdh3tZypr26nLeuGtxh39Ksqjx6bm/qPSprimsIsZjomxqBBZ3ocBszF+1uE8BbcKDOxc7yRnrFOtrdLCheoxxukQDdmLHXAFmSSI60sacqeNYbFxqkZKtqWIHcSCPDPxqezy3WqgC5cSHEhVkNk5tDYJIEE3slcvnMZQFf56y+SSiKislkzMnPXFTE0qIqXp42iI9WlvDNxgMoqs74HnHcfnIu4RaZOq/GxyuK2XKgnuy4UC4cmEqIHFxCWNc0Emwyz15SgFs1hIJspqNjA6opGtOGpfPp6sByw7IkGJkd86vZQB8urJrGO9cM5f0VJby7vJhGt8LQrGjuOqU7sTbT/4aIzS9EVxDvwm8Obk1v10hh/d5aGjwqF7+0xPfYoUItnYGiaJgwyFhbKhqDqsTtqmhka1kjBfGOdg0cWsRsomTBKc3jZC2LmEfRWL67qt3zWV1cQ9+EUDTt8HMXq9C5YUw2S3YFfo+MGAeRHRhsHKts0I7OW1cN4bKZS/2IbVaTxNNT+rNwe0VASdghmVEkhRuTCC4Otgs27K1j2sxlnFWQzF/P7o0QgjXF1djNMqv31nHj26taKfaV8sKCnTx+YQEjMqKCBnJN0zGhGwtuMwnyaMRVXddJCrNy4cDUgFLAD57V87Dsd39t0DQds6YybVAKFwxIAcAsQNb0o7IZ/F9AVxDvwm8OnWlpappOerSDPVVNpEbZ2V/j4tFvt3LvhO6HTcYzmWS+aRYwCYavNuxn4KndUdXgs9qtcWgGIstShzP5SRG2Iw6kqqrTIz6Uy4ak8/ayPX7PRdjNvDh1oEGeO6JX/2VQVZ04q8Tsm0eyak8NG/bVkhBuIz8pnFnL9nDx4DQqG918unofTq+KwyJz8aA0rhvdzdiUYdDUWo9nOb0q768o5v0VxYDR+pg6NIOb31nVRnJX1+GuD9Yy966xhAaQaD3WMKkad52cwyWD06ho9BBqNeFWVNIi7YRZZJ/k8IkMVdH8RslOvObAsUNXEO/Cbw4WWdAnJSKo/OqA9EjKG9yc3juRUbnG+FJls06zBwiRxGH2yQ2WbXtwWEztLv6yLHAj8GpGQDELo1fdch4ScPmwDN5euifg35tlwfCsX1ZWlVWVW8dlccngNN5etofqJg+jc2IZnxePHf2/WtpUVR2LUMlPCuOdZXuoaarwVVu+qcQASgAAeHZJREFU3nCAc/qn8MLlA0iNdGCVBXZJoCmqLxgIDBe7ygBOZwCDM6KYv6283fn/T9fu4/ReCQgh0F1eIm3mgMceCwgh2FXRyHPzdrK7spG0aAc3jMlifPe443YOXfjvoCuId+E3B4csce/peUx/ZXmbrMokCW49KRcJ6J0SwQ1vrvSb0e6eEMqMaYMIaUdAQ5IEUjMbWNd0vF6VyQXJvDB/V8DjAc4fkILXGzgL1yVBUb2Hv36xmdXFNQgBo3Niuf+MfGKtsk+oJD7Myu0n5/CfH/xZ5ELAExf1w3oU8hdZ1Uiyy/zhlByQJCTA5fL+KshFug4hssSQzGie/OGgYp5b0Xh/RTEjsmPIjxEITWtT9bdLcPWoTHaWN3JWQTKSEEhCMH9bOe8t38OY7nEUVrRPoNtV3sjLPxXx4coSuieE8vxlA4kyicP2uJZlgVMX1HtUGtwKCWFWgwgYZJOkyBL//m47H646WE7fXdnEHz7ZwKS+SfzfxLxOy8R24cSD0E8w2qKu61RUBDfUOBEQEWGYP9fWtq8r/mvHiXodQkC9LiisbOKZH7ezqlmMZEB6FLeelMOcdfu4Zkw2Zzy1MKBbWV5CGK9OG4j5kIVRCPBIErsqmnhvRTGqrnNuvxR6JYUjC3j0u20B/c7P6pvE/aflBbScNJkktlQ6uWzm0jYz4laTUUKOtUiEhRml9Kp6N6WNHmYuKqKk2knPpDCmDc8gormsajJJNGngVDRUTSfEIhuz2p3M0IUAryRR7VRYuL0Cs0kwNjeOELN0VGb+j8Z3SpUlShu8zFxUSEm1k/ykMKYPzyDSIiNUY9ROl4Qhr6JpviCrmE3M+KmQd5ftodGjYpIEp/ZK4JpRWaRF2Vi4vZK7Plgb9H3vnNCdJbsqfV7kMSEWZt88EksnxYPAMKLZXefm9vfW+Mr7koCzC5K5Z2KenzANGJ9HuUfj9Kd+Cvqan98ykiSbfNhl/hP1930oTvTriIkJbVc+tysT78JvCrIsIcuCEE2not7FpL7J3DmhOwBbD9Tz8JebeOTcPrz+c1FQu9GtpfVUNnlJsvsvjF5Z5tZ3V7Nyd43vsTnrD5ATH8rrVwzmngndGdotmufn72J3ZSPp0Q5uGJvNuNxYn/3ooXBq8KfZGwOKvLgVjX9+vYVHzu518Po0jRSHmQdOy8OraVglCVVRDTERWbCt2sV9H6/3ZZWRDjO3n5zL6fnxnQrCXlnmvk82MH9beatHNzNlSBq3js/BCmgBrkWSBIoQeDUdWQisQj/sDLWzkFWNFIep+R7oWCSBrqoIXccty6zcW8sna/YihODigankJYQhC50/z97oM18BUDSdOesPsGlfHe9cPZQh3aIIscgB1fP+v73zDo+iWv/458xsyaYXQk8CIfTeOwgCCooVGypiw4a9Xuu99+e9dr32Ligiig1UVEBAihQBpffeS0ivuztzfn8c0sjuJoEkJDCf5/GRTD87u/POecv3ddo0eiVG87/fitrGHst288f2ZIYmlT+MkWlIRn+0jPxi25sSvl91gHzD5OnhrUrcJ7td58cVvjPTC/j2r/3cPzARt7t8+RYWtQvLiFucFWi6Ri6wam8aGw5mklgnhL5JMWTlGUxetoc9KTm0axTOxzd0Z1dyNusPBG5XuvlwJo0SowvjwJpNZ9KyPSUMeAHbjmTx0qzNPDGsJUOT6tA3MUYFYSXHy4z8z9RyDTNgK9d5W47iPsEWSinBa2ADjOOZ6JomOJxncO1Hy0qokaXleI6X20kublsPM4CxETaN9xbsOMGAK6b8uZeE6BDCXTYGt4gt8VJi6Bo7UvN4a942diRn0yjKxZ0DE2lVN7TKFPuKfwbm8TyCPKFxw8TlJT7PX9cdol3DcN67vqvPcQHsOpbDX3vT6Nskkkk39+CGT5aXUEhz2XVeubIjHyzYUWq2O2fTUYY0r1OuaxY2nYkLdpQw4MX5ee0hHh7WktCSe5EdoHENQHa+hwr0bLGoZVSpEc/Ozua1117j119/JSMjg6SkJO666y7OPffcqjythUUJNF1jX5ab6z7+s8TD12nT+GRMNx49vwWmBG++F8OrkqPqhAZuq1A33Fki0zvXlHy+dLff7WesPciDQ1sQZJTs9VzWBK0sF2i5y92E4KWZm/3Kif5vzlaGta4XsJlErglfHc/W9sVnS3bx6PBW/G/uNu47pxm6aWJqGt+sOsDLs4pmqPvTcvlzZwpjesdzR/9En2GEykbqGq/M3uLzhWjdgQw+WriTCzs08BnuAPh+1X56xUeSEOrgl3v7sXpvOpsOZ9I4ykV8dAjvzd/u8yUg0mVHE6JcOQN5hsmibYHV13YczaJTvdDCfAyv12BYm3p8uqT0d69vUgyjeySQGBtCqtvAoWs4iiVDWpwZVKkW3/jx4/nxxx+59957ef/990lKSmL8+PHMnz+/Kk9rcQaiaQJD18jXNPI1Ue4WmwB5UMqAg3JHj/10OSk5Xpy6htdjFAq13Nq/qd/jhQfZSKxTUpnMkNJvu0lQ3br8zbAC4bJpxEW7/K7vlRiNvRyzLC+B5Tkzcr2FDUL8kesx/IrJgOp9HhXsYOqKveQff7vINWUJA16cz5bsITXPWy2zxDwTflx9wO/6r1fs5YIODf2u145fpGlKnIZJ77gIbu4RR79mdRj90VK/s/jRPeLwlrOvuyYgxBl4XhXiLFnFYJqSpjHBNK9bcn7+j+GtGNqmPs/O2MDw1xcy8OX53PXlag7nGwjdmpafSVSZEZ8/fz6LFy/m2Wef5YorrqB379688MILdOrUieeff76qTmtxmhFCIHUNt66Rr2sY+qn3NDZ1jb3ZHh75fh3nv7GIKz9YxpS/9+Ox6WUeW9c1/tqT5rdBhMeQ/LTmQAn9ctOUJES5uLp7ad1muy54Z3QXTjSruhDEBpi9u+w6QXb1WVTEaAVr8PQFbXyu0zXB48NbYy/ndNwRoIe6Ol7g9UE2PWCNfbjLRp7HwJSw5XAmDoetRIzZF18u31tCu9zndekaHk0jQ0KKV5KvaWg2DZtNQxzva17WZ+o2TL/lYUBhIps/rurWGK3Y52wYJh6PgU1KHhjSwuc+l3dpRN2Q8kueujTB9b0S/K4PD7LR2EcLW6eUTBzbnXNb1UUIOL9dfaSEf/6wnoPpeYXb/bUnlcvfXUKGF8u9fgZRZe702bNnExYWVsJ1LoTg0ksv5amnnmLbtm0kJSVV1ektTgOaJkg34OWZm5i5/jCGKemXFMM/hremrkuHk0hkErrGyn3p3DWlqPd3Vr6Xl2ZuYfqqA0wc2x17AAUyXRcB1dkA1uxLxzgh09xmmNw7qBmXdmrEx3/sJDnLTef4CK7rmUCoLkq1Tw3RBOMGNPXZBQzgqu5xeAyTdYeyaBDhok6onaByuDa9XpP29cP4aExX/m/GRnYf15Bu0yCcf1/clvrBtnK5R50CLu7UkCl/+naHx0W7CLZrARXXgjQY0rqeX8N8Rdc4fjg+23XYlGH1V3ddQEq2O2Dhm9A19ma5eeTbtYX91Ae1iOXREa1YtDWZpTuOERvm5Loe8UQH2/265p265jcpDVQmub8mJW0bhtOmfpjPOnjNNLmic0O6JkTx5txtbDuaRcOIIO4clETX+EhknsfHEX3j9Zr0axZDx8YRrN5XMidDCHj+sg4EUVroxDQlTmHw34vakGeqF76Rb/vOVs/1GLz9+zYeG9q87FiORa2gyoz41q1bSUpKQjvh7b5ly5YAbNmy5aSNeEHJQG3FZlMzjzNtHPvS8xj51qISD8pF245x8dt/8NW4XnRoFF7hMpdjOR4e+36tz/22HM5izqYjXNW1sd/9hYCmsaF+1wM0iw3FYbf5vB8xoU5euaIDHkPismnH21CWJt9rcmGHhqzZl8GPa0q6bfsl1WF4u/qc//qiQpd64ygXH9/QjSZRweWaFQ0Md9J+XC9yPAYagmCHTqSryLVanu/UXeckMXP9YVJOMKzacQMRGxY4DwDgmZFt2HQos5SGeqe4SC5o34BXZm8mOsRO83phBAXZ6d+8Du8v8F8fP7hVXUKCHUiX73HsT8/jyg+WFn5uHRpHMLZvEy5/Z3GJ79mUP/cyrn8itw1IJMxZembvNSXX907wW6t/64BEmtcN5ZmRbXjn9+0czcwnxKFzTc94bu2fSFQZ3bKiQ528Pbozbq+JTRdEh6jP8qipwizZbi91QpyEOnWCy/A8fDimG7+uO8TExbtIy/XQOT6S+4e0ID7Kpfqvl8GOYzlk5PoPjcxaf5iHh7UkOiLw/T5Tn1O1jbKeD1VmxNPS0mjSpEmp5REREYXrzzay3F7cXonDZhDppzVibSXXa/Lir5t8znS8puSJaeuYdFMPIirYOvBAem7AB9LkZXs4r219Iv0cV0ro1ywGp03zGZMWAkYFeAkANYvzYRcKyfEYzN54hH/+sJ77h7bgyu6NWbL9GFLCiPYN2HYkk5smLi9x/n2puVz1wVJ+uac/McFlK3tJCVEuO1Eue4llFaFuqJ3pd/Xl7XnbmLZqP26vSZ9mMTx6fiuaRAeX6xixIQ6+vq0Xf+5KZfqq/dh0jcs6NyIxNpSf1x6gc3wUj57figJb07xuKHHRLvamlK7RjQlx0Dsxxu848r0mb/++rcTnNn5QEg99s8bn9+yDhTsY2qYeHRuFl1pn0wQ3923K1iNZzNl4pMS6izs1ZFSXRoTYdUZ3j2N4u/p4DIlNE0QE2QK62YsT6tDhuDKf1zDZfDiL8VP+KvSeaAIu7NCAJy9o4/f7ChAZZOPqbo05r209pFQ9s8sy/MUp66Eval9XUosAVGl2eqA+yWX1UA5EbSvaN3SNrcnZvDlvOzuPZtMwUrnbOjYM91sfXBsoLqKQr2nMPuHhWJxNhzLJzPNAfvndi0IIsgMkiwHkuA3cbi/pAY7r0DXev64rt05aUSIuKgS8dHkHolx2vF7jpL5XQggO5nl5+Js1ADw7YyMhDp2OcZE0inSx61gW90/1LRCSluNh0bZkhjSLPuUuU+UVtHAJeHBQM+4e1AyJegDYpSQvO5+8gHsWoQH9EyLp0SSKXI/JO79vY+qklYXr35q7jYs6NODx4a2wmyaf39STu6b8xbr9RWGNZrEhvHdtV5ymQXp60T0u8Z0Sgt83FyWMRQXbMaT02a2sgPcXbOe/I9v4VTd7dmQbHhragt+3HEUXgnNaxhJu15F5HtKPu7714/9hQLYfFb2yyNN1rnx/CbnFktpMCT+sPkiu2+TfI1uXmZVfYGs9HijuXNdsGnkmIEBICBIltfRD7HpACdmRHRpik2aZ35WICBdeU+LO8+ApZ3JeTeRMEHsJZC6rzIhHRkb6nG2np6uvY8GM/EzH0DW+WLGPN+YWSWEezcrntkkrubJrY+4fnHRGSCJK8CuOUoApUfXR5T2mlCTEhKAJfIqdAAxoXocgXSC9Abp/GSZt64Yw5/6BTF99gPUHM0isE8KoLo0J0cHlJxZaHkxN8Na8kjKn2W6DxduPMbRNPf7cmRpw/4VbkxnavA6q4WfVI9WNKlHmdjJn9nhU+84pf+5h6orS3bN+WHOQ1g3DuapjA0JNyQeju5DlMTicnkedMCfhThuusgRfhMChF92bqGAHhzP8G3BQ5WseU/rt3GUzTGIdGtd0alg4DgTkaRqpOR6cNo1Qp676VJ9k6Ztm0/h8ye4SBrw4szce5rHhLQmv4DxG0wR5QuPTJbv58s89ZOR5adconIeHtaRlbEhhzX2wgKcvbMO9X60qdYxwl41x/RORAV4aDU0jw2Pw/qwt7E3NKQyVBAsKJX4tag5V5lhJSkpi+/btmCcYqC1bVLlJixa+MzrPNHINWcKAF2fqyn0k55wZQgx2AV0TovyubxARhKsc8bwTCdLg8i6+3d1Om8bN/ZoGfCAVYpi4pMmYbo3474WtGdcrnjAh0U6xZtZtSjYezPS5LivfS2QZrvLYUEdF3mtqFDkmAWvjP1q4kxyzoJ2kaqHaOiaYOnYNRzG5U38Ea6LEvT+amU9cVOC4Zst6YTjKKKGSUhlvr9fAsNt4e9Euzn11ARe9/Qfnvb6Qqz5cxtbUXNBP7vGYZ0gWbPVdclbA5kOZFa7ayNc0rv/kTz5YsKOwnHHd/gxumLCc37YkF16vYZj0jI9k4tjutKwXBqhKhvPa1mPaHX0IDXBaQ9eYseEww/63kI8W7WTm+sO88Otmhr62gO1peVZ5Wg2kyoz40KFDycjIYO7cuSWWT5s2jaZNm54Vmel2u87M9YcCbjNlxZ4yS2xqKqaElFwP+ZqGTRM8c2EbvyVIjw1vRfBJfNs0w+TBIc25rmc89mIPkCYxwXx5ay/CKvhQcbsNDI9Rae5BXQjqhftOEFqxK4V+SXUCvqRd2S3Ob+OTwnPoGl5N1ci7NVVadbIIIUDXcB///6mEtdxe02+2N6jM9BPFZSrSqsHwGlzdPY4GEUoXPjPfS0ael2YBEhVv7Z/o15VeHKFr5Gk6b87dxsTFu0r0G9+Xmst1n/xJmsc8qRdsTQhCHGXXe1cEm01j9obD7PDThOU/MzZS3EehmyYd64UwYUxX5j80kN8fHMj/XdCacE0UTqw0TWDqGrlCIxuBR9fIMyX/N2NjqePne01u/nQFedIy4jWNKnOnDxw4kJ49e/LEE0+QlpZG48aNmTZtGitXruSdd96pqtPWKISA9NzAMeD0HG+t642r64JcNN78fRvfrNxHnsdkQPM63HNuc6bd1Yd7v1xdqM1dL9zJ48Nb0zM+8qTjvrrX4N5zVOZxWq6HIJtOsF07Lll6et17TgHj+ieyfNfKUus8huSPbck8MaI1z/p4MN4xsBkRxbqQgXpYe6WaOUnDxCME6w5n8cbcbWxPzqJhhIvbByTSs2l0qWYYZWHqGkdyPHywYAc7krOJj3Jx64BEGoY5T0r+1GHTcOhaCQNYnBCHrpLCTsHb4cLk63G9+GjRTqau3Mf/ftvC/67qxN1T/i7R/1vXBM9d2o46LluZLl9d19iT5cZtSL8KdB5D8va8bTwxrIXSna8AQRqM6Z3Ait2+QynBDp1msSGlyhQDkWsqz53f9R6DXck5tIouqiP3ek3sgB0KsyALW6/qGikek//8vIH5W44iJSTVDeX+Ic2585xmvPP79lLnyMr3suFQJt0ahFaK7r2o5N7rDocOQhR2DjxbqDIjLoTgnXfe4dVXX+W1114rlF196623GDx4cFWdtkbh9Zr0S6rDuwFaUA5pXRdZy2QQc9C44v0lJYQkflxzkJnrDzPl1p58dUtPMvO9mFISbNf9GlubXSPbUEIcNk3DqYHNX+201yQIqF+QJm6aNaLM1TBM2jcM5+KODZl+giJYiENnaOt61A210y0hind/38725Gzio13cPqAZ8ZFBhcaz4MXol42HmbvpKCFOnTG9myAE3PHFX4VKaRm5mdw3dXWFW0yausYvG4/wzx83FC5bfyCDX9Yf5oGhLbiyU0P0CuZmBGkwsqN/qdKre8Spvt2ncJ8MQ+JEMn5AIrf2awoCHEIw9dZe7DiWzYpdqUQE2+maEMW2w5lkekzCbBpagJPmSnj8+3Xcc25zvzK0AH9sP0a+KQNK0frC6zXplRhDl/jIwg55xfnPJe0qfExTlq34l2+Y5TKMQkCWIbn0ncUlVPq2Hcniri/+5j+XtGNgi1ifKnS7j+XQvWE4nETzWbtdVy8RuiAr3+RgRh7BDp0olx1XBTrpnYjUBTkGfLliP9uOZtGhUQTD2tQjCHlKL5C1BasVaRXj0TWu/WS5z17EsaFOpt3ZG0ctShbRbBpvL9rFJ3/s8rk+sU4Ik27sjqOMJ7eha8zfdozXftvKoYw8hFBJak9f0IZIu8Csog5XvqiM7FWvrrEvPa+wtrdfszpc2EElA5mGiRACUxd4DInTruM+/sByaeo7fcxtcuUHS0nNKem5GdyqLqO6NubOyX+VOuf3d/QhLsSOlLLMMWQjGPTqfL8P+Nn3DyCygl56ISBf00s1FQFo3yicD67rWsJbIIQoDB15PIZP13p574Wpaazcn86U5XvJzPOyZl8apizond6RPvGRCD8P8HQTRryxiA/GdGXshOV+z9EkJpjPb+yO8yQekRERLtLyvPyy9iCfLtlNSo6bDo0juP/c5jQMc6JV8Dev2XQ+Wrrb74RAE/D7g+fgkuU4rq7x4pxtfO1nZl8n1MFzl7Xn1s9Ke5c+u6k7bWOCK6S/rumCXAS/bTzC8l2p1A1zMqRNPRZtTebd+dupF+7ktSs70TzaVWGvh6kJlu1N576vVpWw106bxoSx3WkR7SL8uJJibc5Ot1qRnkacUvLZjd25b+pqVhZzr7VuEMZb13RWWbCn7/IqTJ4J3wRw6+1IzibXa+IIYBCETWP6mkM890uRupmUMH9LMpftXcJP4/uqt+hahM0wSQx38u8LWuM1JQ4h8HqNwsxvKSW6hFwEExbuZN7mowTZNUb3iGdgi1ju/vKvUgYcYO6mI/RvXodOcZGs2ptWYt0Xf+7hiWEt8JTRYtJu15m15mDAGdo3K/dxZ98mFWpXKSUESZPPxnZn/cEMvvlrP5pQcf6WdUOwGyaSoh7khzLd/Lx2D6aECzrUp0FYEHbTOCmXaq4pS6j4Fb+mB6auZt6D5xDs5zvkNszjMqwmsaFOjmb5zni/unscIboWsMtcICKDbFzUpi5DWtVFopI/bVJWyI1egOk1GN0jns+X7vEpIXxN93icGuV6mORL+HntQb/rk7PcBPnI04kNddIsJqRUsnIgChT3Rn+0jJxi+RMTFu/i7sFJ3Htuc16fs5UbJvzJz/f0J0qvmIs9x6SUAQcVw7/p0+X8dv9ASqsGnFlYRryKMU1JsAZvXdWRXK8kOSufmFAn4UE2NI/3pMtYThuCEj9GX3gNEwLocOdJeO03300x0nM9fLZ0N7f3SQjYFrMmYpoSTAMN1XCkOLqucTDXyxXvLynx+T05fR1Tx/Vm0yHfGe4AXy3fy9U94ksZ8YKQRcBr0jXyhWB/auBZyKGMvJN6bTJNiR2Drg3C6DqydcFCjOMGHFQP8oe/XVuiQ9fHf+ykV2I0r13RscKxfYdD58sV+/0+7E0JszYc4ooODXzGRsOcNtXB7o9dPH5Bax6cWtoIJNYJ4aKODU/agBfg9Z56OV8BwQKm3dWHf/24gQXHm9kEO3Ru6N2EG3rFo1XgWit6r6NDHEy6qbsqC6zAfnnAjROX+3xmvDl3GxPGdicy2E5ajof35m/nsSHNyz0bt9t1vlu2x6/HPM9j8ufOFEZ2qF+psfeahmXEqwHTlNiQhAkID3cQHq6ybQMJlNRUdKBH02gWbz/mc32o00ao0+ZXg1sIOJSeH7Ab1s9rD3FDz/gKxw1rMnkS7p+6qtTDLMimk5ITWF/8UEYeUT5K1Ya2rosI8HQyNcFvW5KZsHgXN/fz35UNoG+zGOQpBK8Nw/Q5C9RsGpOW7fHZYnPpjhQ+XryLO/o0wayAARJCsOuY7yztAnYdy/abee/SBNf1jOfjP3bROMrFxBt7MHHxLlbsSiHUaePqHnGM6tIYp2lWU/V+2Ri6RpYh2XE0m9sHNuPZS9qp54omCNIEsgKfn1PAsDb1mLbKd1e3qGA7TWKCefHy9uxJyaFj40jaNAjDRRl1/SegaYKdyTk+PUwFfP/3fi5o34DJy/awdEdKhXIQTGDr0cDfg21Hs1DiFGeuFbeMeDVT298I7VLy6HktueTdxT7HMq5/U1yB+2iULQt5Blax5HhNthwuncuR6zHKrCVvUS+sRCY2QGyYk15NY/zOFIWAdI/JE9PWAdAwIsiv6zjcZaNPs5gqyfTPNWGSj17XBUxZtocbeiUQVIFjGoakS3yU34Q6gM5xUX7dvtJrcGu/puR7TaYs38vvm45yZfc4rujamPjoYOqHOTDzvTXGgHttOv/8cQMzizWeCXPaeHFUB7o0DCufTkIxhGlyz2Clo+9LkOYfw1sRIuDSTg0BQWZmHoZhVjjsp2milMb+iexPy6VvUgwAYUG2Cmkm6AJa1w/j13X+y3hb1Q/jTDbgUMX9xC3OPExTUj/UwYfXdy3RMCPIrnHP4CSu7No4oBtcSlV2FuzwXxs/skMDXCcptFFT8QRwEa7clcqA5nX8rr+5bxOmFiuFat8ogq9u7YkrwMNJs+lMKibE8vyvm3hzdOdSvckbRATx5S29KJ9yesXxGNJvG1hQ6naBPhtfeL0GA1vU8fsdCnXa6JUYWMpW9xrcMzCR3x8cyOtXd2JIq7q0bxhOPZcNs4y+6tWJqWv899dNJQw4qFDKnV/8xZFcb4Vr/aWEcJvg+zt606tpdOHyuGgX74zuzIBmMRheEylVLsfJhvxMU9IsNiTgNol1QgqrXK7vlUBwBXQf3G6DSzo19NuUKMSh0yU+stZPnMrCmolbVBjNMOlSP4wf7+pLep4Ht8ckKsROkKBcbr0g4KFhLfn3TxtKrYsOcTC6Z3yF3Ku1gVCnzW9N9QcLdzDxxu6kZLtZd6BIX1wT8PB5LenQKIJPx3YnLddDeJCNIF3DSeCHq8eU7EwumgVtPJjJk9PW8eh5rXDadfal5tCiXhhNY4IJkmaV5WbYdRGwBajLritp1Qq68l1IPr+5B2MnLC9ULwOIcNn57MbuuCg7/iwMVbbYIlK9jErTrHFztnwTZqzxnYQmJbw+Zyv/GdkGrYLVHNKQxDp1XhvVAbdUkslOXVSq9oJpSuIiXdQPD+JQRmllfiHgks6NuG3SSto1DGdwy9gK5yC4BLx/XRfumPxXib4IwQ6dz27qEfBF90zBMuIWJ4VhmESHOokOtqvSDaP8D0BpmIxoU5c6oQ5enrWFPSk56JpgaOt6PHp+S0KoWPJMbSBIg2t6xPGpD9dyWo4Hw5R8eF0XDme5+XNnCuEuO30SY3BqoHkNbECI6/jPtRyxWocmaFEvtEQsetuRLMZP+ZsIl506oQ7+dVEbnKZZpub9qeDSYHTPeD5cuNPn+qu6xxGkQXkqo4pjGpKEUAe/3NOPDQcz2X40i6S6obSqF0bQ8bI+UG0os02pupLpgiCh3MnFZ2c1daYmBBzOzAtY6rxqbxoek5PKHynI1bGBChubstK1F4KQfHpjd679eBnJWUW5H7omeGZkG1bsSuXhYS0Y1qZeYTVDRRCmpEP9UOY+MJB5m4+w/Wg27RpF0DsxmiBktZaqni4sI25xWtANkwFNouh6cw88pkTXBE4Bmlmx5Jlag9fkjgGJZLsNvv1rX6HhCHHo/OuitjQOVbXDjYPtNOnYACmlmhEZ6mFut9sQQrmSy/P5eD2qJGni4l2ljEB6rgdNQJOYiqmGnQym1+SmPk1YvTeNP3eVVDDrHB/Jbf2bVigpq8SxTYkDSdcGoXRvFI55Qla8YdP5Yd0h3pu/g6NZ+Th0jYs6NeS+c5Nw+RMVqkFIqTw4gYhwOdA0gV3Ty6VSJgRIXcMtAQk2AbopKySHWxFMUxLr1Jh+Zx/WH8hk5Z5UGkUGcU7LuujHXxyCdVWOebJXIAxJEJKRreuhtVWysl5vzfOqVBWW2MtpoLa3xivAGkfFMY/rU287kkWQXSchJpgg/HeH8uoaydkevvlrHzluL8PbNaBlvVCCTjBCvsZgahrL9qZx/9TVJWbb4S4bX9zSiwYuW5UbcVCGw60pMZxpf6vSsEs7N6JxZBCOE2bFlXUvDE3j3UU7fXo+EmKCmXJzT+xG1fl7Kmscbk3jqo+WlUpsLODJC1qTkeshLMjO+W3r4QrQaUzoGpnHGzL9vPYghik5p2VdHh7WgminBie8HFb270LXNXRdKfidauleRajtz6myxF4sI34aqO1fqgJq0jiEECc9mzgd49A0UZg45A/DpvN/P29ixgnCHE1igpl0Uw9csmgG5W8MUtPIQ4nG7D6WQ+f4SLrER6qYcTVrFGhaScU2XzPhyroXZSnUvXh5e4Ym1akyY1JZ49B1wc4MJZZyouxqp7hI7hvSvFB1LsiuMemmHjSNcCJPMMhCCNJNySVvLy6VaOjQNabe1ov4UEeJ3Iia9Ps+FWr7OMoy4mdWCrDFWYUQAq+mkWHCxmM5HMo3cGvqbb+mY5bhwrTZNOZuOVrKgAPsOpbDk9PX4S1HK0thmrhMk0va1uO+gYn0i4/EaZjVbsBBjTk/30t+vrdKXdm6rvHXnrSAse7v/t5Pfg13p4Mqp0sId/Lrvf0Z2zuBpLqhdIqL5JmRbbh7cBL3FesZnucxuWniCvJ9FGqZmuCFXzf7rBRwGyZPTl9HXs3/OCx8YMXELWolQgjyNY0Hv17N0p0phcsbR7l4d3QXGobYanVSS44J7y/w3zhnwdZk8k1Z7tKws6mrE5Td8rQ8Thu9WH/u04k0TEJBNYHp35R1BzN4Z952Vu9LL7VtZr6XjYcy6VwvtMSLUr6E3zYeLrV9Aev2Z5BvSgIrFljURKyZuEWtxK0Jbpu8soQBB9UL+uoPl5JT2/seC8HeAEIZUkJuGfK3ZyuGYdIlISqgaNClnRsS5MdjY2ga6SbM2ZHCot1p5GoaZg3QLZBeAzvw6eLdPg14AbuO5ZRyv8pyNPSqyioFi6rj9H8zLSwqiBBwLNvDuv0ZPtdnuw2mrTqA7qOJQ61BShJi/AtlCAHBDsuR5g+XLhjdPd7nusZRLvonxfr0Thg2nWd+3siQ1xbw8DdruOerVQx6ZT5T/z6AoZ/+75NNiOMqZP5pccIsHMCuQYfGEX73aRARhMtmmYPaiHXXLGoduq6xal9awG3+2J6Muxa704M1wZ3nNPO7/txWdVXXKguf6IbJ3YOa8dj5rYgOUS1I7Lrg4o4NmHJLT4J8FKYLm84787czc31Jt7NhSl6ZvYVV+9OxnWZDZ3gNru0Zj790iDqhjuOdxkp+953AkyNa+/VOPHZ+K4Kt71OtxLptFtWCrmt4NdVRS9i0U9JHlxKigh0BtwkPslObJxZer0H/ZjGM6tK41LrmdUP518i26KfQsORMRrNp5GsaHlNyUYf6/HpPP+Y9MJC5DwzkyfNa4ZKmz8S6XFPy1Qr/bXZf/W0LuTXgIw/TNd64ujO2Eyx5VLBdVS2I0mMzDJOECCcfj+lGo8gi6d06oQ5eHtWBngmRVaKdb1H1WP44iypF9ZLW+XNfGp/8sYu0HA/dm0RxS7+mRNhFqdrU8mAYJh0bR/iVMQW4sW8ThClrteCD7jV4cEgSt/Rvyg+rD5Cd7+W8NvVoEhOMU5plxjjPNjRNJTt+8scupvy5h2y3QZOYYO4b0pxeCdHox+vC/X1sOW6jVBlXcbYczqImpFoI06RH43DmPTiQBVuT2ZuaQ6fGkbRrFB6w05hmSjrXD2XqrT3J8ZiYUhLq1HEJgXGGyRyfTVhGvJyoul5ZYyUaayoeTeeR79eycGuR/Of2o1l8s3IfE8Z2p00d10llkTsF/OfSdjz8zZpS60a0q0+TKNdpKaOqbGyGSR274Lbe8YBStjKNmtMisyaRLzRumLCcrUeKdCR2Hcvhvq9Wc8/gJK7t1hgtwHfCWYbrJirYXmMaYglTqZSNaFkHTRMYhtLSL+t7UdDfXPWOEXAS3cksaha12OFY9WiaIFzPItq7h8ijC4nK306EnuG3a45FSWw2jZV700oY8AK8puTer1aRV6Hmg0UIw2RA02h+uKsvw9rUo3GUiy7xkbx7bReevqA1tjPAgBcgperY5HZXbX11VaFpAlPXcB//71TDKb6w2TSW7kwpYcCL8/bv28kv46Nz6oLuTaL8rh/TOwFXDXpiFggGud3GaS+Dszh9WDNxP+i6IMI8gv7VtXCkqNuWHtWUiKu+IMMRj7cWJ05VB3kmfPLHLr/rU7LdHEzPp0mY/aQ8HJpp0tBl49kLW+M2JbpQ+uuWa7DmIDXB4TyDF2dtZtHWZOy6xkUdG3DXOUmE6JXXoCJfwtSVe/2uN0zJmn3p9ImL8GvwHFLy/GXtufL9pRzLdpdY165hOFd3i6sR3y2pa7gRbDyYQVa+l3YNwwl16NhPkLC1ODuwjLgfwkhHn3QRpJ/wYEjdif7pCMLGLSIV/yUbFmBISVqOO+A2abluRLjjpCVTpZQIQ6ouTvLM635Wm7HZNLak5nHtR8vwHvcgeE2Dr1bsY9aGw0y/sy/BonJCVFJSohWlL8rqW26akiib4Ie7+vLr+kP8su4QDpvGtT3i6RwXcVJdtiobQ9f4fVsyz/ywoUT8fmCLWJ6/tB12w6gyQy5Eze34djZTg5xDNQdNE2jHNpU24AXkpqJtn4vNdvrrRk8XhmGwb5//mQ+AUxN0TShyT8qsZOQJGdVN65Quh7E4M8gx4R/frS004MVJzfHw1u/boJJqr4N0lQsRiI6NI8t0OxuGxGEYXNa+Hm9e2YHXLm9Pn/jjBvw0WzBNE+xNz+Ox79aVSsCbv+Uo//llE4ZW+Y90r66RKQVb0vJJ9pjHpY0t01FTsO6ED2w2DbFrQcBttJ1zsWln57zPMAyefvofXHzxRWzatMnvdsI0Gdc/EV0TyNR9eH/+L8biCYWGfEDzOoTU5jowi4DkeU12JGf7XT991YFK0+v2ekzOb1uf2DDfnbUv7dSQYFv5A/Fej4nNlGiGWWNKrzwIXvttq9/1P689SH4lX2pyjof7v1nD4FfnM/qjZQx/YxHXfvInh3K9aJYhrxFYd8EHUgIh9QJvE1wHydk5Ez906CCLFy8kJSWFa6+9hq1bN/vcTkqIsGv8s38Exm+vQn4W8sB6yEmhf1IMz1/WHptV61wtaJrAZtMCdkOqbHzNwIvjNkzchllpDWtcSKaO68WA5nUKE+dCHDp3DGzGI+e1RK/lyV9eYN0B/3KrpoSUMsJXFSEtz8stn65g6Y6S0sa7juUclzautFNZnAJWTNwHHo+BbDkcZj/uNwhkdhmLu5xNJZx2E5eZiWbkIXUHeE1Mm39JzZpOo0aN+eCDidx2242kpKQwbtxYPvhgIs2btyy17bbNG3nh4duQeVmER0Tx8IvvMqB7J0LsWpXG7ywUQtfIBzYfzmJHcjbNY0NJqhtCEFXfijTUoRMVbCc1x+Nzfe/EGJbvSmFAYgy2Sog2G4ZJuCZ48dJ25JuSfK9JsF3HpQnMGpCQdqoIICbESUZu6U5kBYQ4KmdiIYTgQHoeGw76ljbOyPPyy/pDXNGhPl7P6X850nUNL6oC0CGoMd6T6sCaifshV4RhDv2Pz3Vmr7twO2PLZYAi7dmErngD+/u90d/uiu2tTug/3YM952C1zooqm+bNWzJ58hSio6NJTU1l3LixpWbkW7duZty4saSmphIVFcUnH0/k4t6didBU/bNlwKsWTRfszXQz4s0/uOnTFTw7YyM3TFzOyLcXczDHU+XuUJcG9w1p4fvaBNw2IJEPF+yo1GRE05TohkmwlETpAqdpnhEGHCBYgxv7NPG7vllsCMGV1C9A1zVW7E4JuM2CLcmcbvsthMCj6yzbn8FD36/jvm/XMmPTUdy6ftbE7c+OUZ4EuYaTvFZXYtw8B9lyBMQ0QyYOwrj+R9w97yXLKLsJZKieg+23x9EWvQz5x99oTQOxYRri0wuJ0Py7xqoDhw3CtExCtSzs9op/FVq1asXkyVOIiooqZchPNOAffDCRpKSWVhJbNZKL4LqPl5GeW3ImnJLtZvRHy8it4vMbXpPBrWJ55LyWRLiKmlzGRbt445rO/LD6AHlekxqjoFLF2GwaDsfJGxev12Ro67r08FHLHuLQef2qTrgqbV4giXQFljaOcNlOu2aGR9e4bfJK7pj8Fwu2JrNk+zGenL6ey95bTIYha/VEqbxY7vQAZBtB5Aa3Iui8t9BlHqZwkiuDML3le+g4vOmIdd/6XukMR8vYQ2hkK/JMR4XdP0IIgnQvmszHEEHkG1q5Z7Y2XRAuUhGrJqNtnAZCx9lxNGbrS0g3IypkaFu1asUHH0wsNNjjxo3l4Ycf56WX/lvCgPtytVtUHTabzuzNR8n20640I8/Lit2pDGwSVaWuR13Csax8/ndVJ3RNoGuC5Kx8Pl64k7/3pvHUBa0J0UWZ8fPajNRUSGP+pqPsT8ulc3wUbRuE48L0K5HqD7th8L8rO7JmfwafLt1NTr6XgS1iuaJrY4JF5fU+93pNeiZGY9P835sbejeB05hnoNt0Pv1zL2t9dDM8nJHPU9PX8dJl7U/DlVUvlhEvA9OU5CihwuNLyvejs9k0xLY/Sq8Iqw8j34D0fWgLX8YlJc4OV2PG9/VpQDVNoOsaUsrCh22Inoczdz/akrcQabuQdVsT3ONOch2x5Bq+s3OLHy/cOIQ+YRjkHCtaPutxtD/fI3LMz6SKyAq5ups3b1nCkD/++MMAlgE/jei6YMXu1IDbrNydxqDEGKiAiKtm08gzJJoQBGllxx6DhOSKbnFc+f4SMvJKxnK7JkQyol19vOXMLamNSE1jyd40Hpy6uoQxjAlx8MUtPYl1ahUy5FKC3TDp0SicTpe1x0QSpAkMb+VL8YY7dZ4Z2Yanpq8vtW5E+/rERQadVmnjXFMyaeluv+sXbT9G/hn8cliAZcSrEnGC28weDJd/DDMehKNFpVna9jlo0YlEXv8DqVIZUF3XCCMN7dhGxP6/IKIxMqE/XuHAvnYy2tx/FZ1m33L0vz4j+OJ3kQnnkWf4d4O5tFy0GQ+VMOCFpO1BW/giQQP+j1xvxWJrzZu35OGHHy804AAPP/y4ZcBPE1JK4qMDh3wSYoLLXfssNI1sCZP+2M3CrcmEOG3c0DuBHglR2E3/CYqGIYl16vx8Tz++//sAczcdweXQuaF3Ah0aRqjkxooOrgYiBEhNJ19K1Zgmz0uky0a6x+S+r1aV+nyOZbsZM+FPvr2tN86T+AQMw0QHdJQaXVUQZNO5sH0D2jQI5425W9l0KJN64UHc1j+RLvGR2E5zroGEUqGiEusl5J/uoH01IOTpVjCoIFJKkpN96yPXNKLFUfS3Ohct6DoWTANWT4EW50NMM8hLh40/Qs4xZPsryB78Im7pJEIeQd8+ByIaQX4mrP8e9ixDjpmGeL+/7xMKDWP8KlLMaL/XFKUdw/ZWJ//SSzYn5p3LMYQNKSFHROLxM9uKiFAtDdPTc0vEwAvPVUtm4sXHUVvxNYYsBINeme9ze03AvAfPIdhHX+0T0XXBniwPV3+4lLwTHopd4iN5+5rO5Xqg63adfEOiCbDj2/VbG++FrgsyTcGrszfz87pDeAxJy3phvHJFB75asZdJS/f43XfKLT1pERVUI3NFCu5FZmYeXiHwmMoD4yqHB6Y6cGsa101Yzk4/WgRBdo3Z9w2g3nHtgNr0nSpOTExowNi+ldhWheRrYZjdbi5a0OpCZbRv+AGim8LB1eDOgovfhmHPIjb+QJCZRYSWhn5oNaz5Er4eCwf+hnMeg9vnI9ZM9X9CaSK2zsQeIENVmO7SBtwWBJ1Gw8jX4fzn0fIzsL/dBcdnw4nYMpkoh3/BDiidxPbf/77kM9nNonoJ1gX/uaRdqeVCwMujOhDko++0L3Kl4O4v/y5lwAH+2pPG7I1HsJVDtMfwGNhME80wz6iGHTkILnt3MdNXHyyUft18OJNfNxxm8+HAE46tR7JOOvlKCHA4bDidtipN4DKPi944pcRu1hzxm2AN7j03ye/6q7vF16iGNVXFWTDE00e2EYS336OYw1+GsAbgioQOV8KkS2Hxm7Djd1j7DUy5GlJ2wLnPoJlutM0z4OsblPG+9H31a50wHHJSIWNf4JNm7PPbIcrhsKHpDnAVy26N7wVjpilDvvAVdV0bpsP134HNifjlYfQf7iLGnu7zuJs2bSqVhT5ixEg++GCiZchPM5phMqR5DDPv7c+1PePp3SyGG3onMOveAfRtEoVWztlflttgb4r/WcynS3aRfZY2A9JsGp8v3VOqYQqohL6Gx2ez/kiIDj6pWbhX0ziSb/LWop28MGcr64/l4NH1syIbuwCv16RXQjR3ntOME4c9rE09bh/QFFlDXjiqEsudXg3Y7RrBZip2YSA+GAi5fhKOrpqMrNcOkb4HkrdAXgak7YaVE6FBRxj4KBzZCHP/z++5zKumkFZvYImZTpDmIVhko+1ZhKjXDjbPgN+fg/rt4YJX4fPLi0rgCghrAKM+gS+uhPxM5NVT8NbvQpqnSKTm4MHdXHvtNaSkpPh0nfsqM6uJrvXa6MI9kUBjEAI0m47HlNg1gVHBRLI92R4uf2+J3/XRIQ6m39GHoHK45suitt2LfKEx6oOlHMrIK7UuwmXnjas7ccOE5T73jXDZmXF3X5wV9EoYNp0XZ23mu78PlFjeLDaET8d2J0jKStF5ry33wtQ18kxYviuFfK9Jj6bRhNm1QoW+2jIOf1ju9BqAx2OSKSORx3b4N+AAq79E7FoIn46Evz6DZoMheTu0HwUX/k/NoFtdABe9BbE+jGFILGb9jiUMuEt3E7J/DvrbnRE/PwQ5yRCTBNd+A5e8B7OfKjLgIbEQ0Rg0HTIPwsoJ0OEqAMT6b9GzDxbWuG7dujmgAYeirHVrRn56kVK5sjXDrLABB4gNdZaa6RSnY+MIHGfpk0QiMfwYzPRcDyv3pPLY+a1KrXPZdT65oRuuChpbm01n4fZjpQw4wPaj2Tz5w3qMs2g2DsrjFCxNBidGM6JlHSI1ar3EbkU4S3961Y8QAjL2B94o8wBkHlL/PrhaGfNL3oI6LeGzi5VL/Z1e8Of7cN7zkHRu0b4RjZHXfo20uQrjk0KAy30I7ftbwfBA/XawZ4n699pvITcF9iyFtpfCmB9gxMtw7tNw0yw453HY/KtKwAPw5KLtXYqTPPbv38e4cWNJSUkhOjo64AzblyHfv7+MkIBFlWOzaeQLQb6m4S2jK5VTgws6NPC7/r5zm2M7boxsNnU8txAIm+Y3tHOm4NIFw1r777Pw4YKdjOxYn9n3D+CWfk0Z3q4+T17Qmln39adJuLPCrvQcU/LO79v9rp+/5Sh5NTBJrjowalCzmurEKjGrAnz13TVNExlb+o28BHXbQOrOor/bXQ4rPoE/Xi+53aG18NVouGUuJA2F8IaAQJgG9s9HEtHvQbxx/QCJtvCNoouRUrnJjXxYMwU6Xgn97ofwRvDlNeDOLhpAuyvg+u+VSx+g6QA4vAHR3KB+/Qb06dOfJUsWMXnyFBo0SAg4rOJ15H369Kd+ff8GwaLq8R4Xgvlo0U4OZ+TRol4Y9w1pTsvYEJ8zGM0wefz8VuR7TGZtOFy4PMSh89/L2lM/xIGUJl6bzh+7Upi4eDfpuR56NIni1v6JRNi10yoKUpVIr8mtAxKZtmq/T2GdewYn4UTg0ODu/k0wpJo5eTzGydV1C9iTkuP/eiTkuA2CT0KB0aJ2YsXEKwkhIFjPx2lmqdm0MwzDGUk2EXgNSZgtG6eZjfjiSji2zccBNBgzXSW5FRjTG36EyaPAm+/7pB2vhugkWPExJA2BnrfD9Lvg4CrkgEcQTQfAr4/B4XVqe7tLGf7pd6qkuTE/gDdPxb190fUm6H6zWn/x25iHN5DR+gY8XolhGOTkpNK4cVy5Y0379++jfv0G6JXUQ7qyqO0xMyj/GLy6xmPT1jN/y9FS6x4e1oJRHRui+eksZ+gaOV7JlsOZhDptNIkJJkiANJQBv2/qKpbtLBkusmmCiTd2p3VMcLmEQWrjvdA0wVG3wZPT1hcK7MSGOrlvSHPObRGLblRePXVZZVVCwO8PDiT4LIqJl0VtH0dZMXFrJl4JCAGRtiz0WY8hNk4vnPnqkfHol01ARjRCn3Ef4uhmuOQdmHZnyRm3LQhG/g92/VEkEGN3qVi1N18taz4MmvRTx961ALbNUTXnrS+ExIGAAG8uXP4RzHsOsW+FyoTv/4A6ritKZccjIe143WrOMfjzA/8DW/U59BkPoz6GWU8iL5+I57jkrK7rNG4cV6HPqVGjxhXa3qJy0TTBjmM5Pg04wCuztzCyQ0P85VPrhkmYgO4Nw4Dj3iWUC33BjpRSBhxUO9L7vlrF9Dv7EFiJu/ZimpJYh86bV3Yk35R4TUmo00aky0amj4S3UyFEF9wxMJFHvl3rc/3AFrE4NQFnabXA2YhlxCuBEC0H/ed7EVtmllyRtgf9r0+QYfUQW35Vy6bfBUP/DUg4vB4iE6BJXzi6FWwH4IpPVUb6vP+CZofYVnDBK7B9Hqz+Ur0xtDgfzv2nymCfOAJyjncbcoRA/4dg0OPKoK+eApt/gZYjlLFf/BZEN1MiMznHICgCDvzlf2CGG7KPwJ6lGBe9S4aM4mxpVnEmIjWNzwLIVJoSluw4xrDmMQFjiyfGcXNNmLh4l9/tk7PcHMl0ExdiO2M715mmxIZUD1QNIoLtZe1yUng8BgOS6nBp54Z87yM7/dmL22E7/nJlcXZgGfFKwGFmI4SmjOveZSUz0NtchPj21qK/U3bA1OuVhnpkAkgT6iTBjrlwdLMqH4vvo8q7bC4lwDJ1DGQVxSI5tBZWTVYSrgWuz+hE6HydUnjLPAjbZiuZ1y5jlEt9xcdw1WQICoeed8DeP8H0qhl6QTKdL4SOp901ZBihmNbbfa3GRJLjpyFKAdlu/72q/R5XStJyS9dJFycj14MItVdK6dPZju41eGRoC27tl8j3f+8ny+3l/Lb1aR4bilOamNZnfFZhGfFTQAgI17PR0g9CRJxye3e7SWWhz3wcPLmgO0rXYIMynAXGUwLJm6FxVxjwIMz9Dyz/GIb8E2Y9WdKAF5BxAJa9D52vVclqYQ1g+UdwbCuEN1ZucGmqF4rEc5SwzLz/KBd7/Y4qoW3LTOhyA8x/wfcA67ZBevLIJaRGykKeDRRkd1fGc9kODGlVl4Vbk/1u06NJdIXV1JyaoFtCNHtT/FdfxMecnKiJhW9shkldp8b4/k0RArxeA8M4yWQ5i1qNZcQrgN2u4TLSEEi8woFDM9C/uwmxZ3HRRsveU0lmV0yEL0cDQsW8vX5iY/ZgZeS3zYGjWyBlJ5z3X/j1H2qmvPln/xe06Se4ZQ6s/04Z+wKyk+HbW1TpWNIQGP4CpO9XLxnhjeHAShA6tLsUIuLVcQ6f0KnIEQLDnsWMiCfff48Bi6pCV+0rD6TlIYFGkS7VKOMUsry9XpMhrevx+txtpPhQGOuaEElMsB1ZwXMI0+SOgYn8sPqAz2YcQ1rXw6VbcdrKRkpwn4TnxOLMwspOLwdCQIQtC33jNLQ/31fNSgY+Aqm7EMs/8r3TOf+A1iNBSqQ3D7HsXcg8DP3uhZB64MmDVZMADZyhENdTGe1di8AeBO1GKQP/Ts/AF3fnUni3t/+p2jVTVAnZBwNVjL39FUon/esbVGOVXndD59HqZWHdd+DJgab9od3lmHlZ5NTpQq6frmi1PeuzgJo2DkPXmLH+MC/P2kLucXEWp03j7sFJjOrUyGe2c3nHoOuCFI/k3q9Wsf6A8hAJAcNa1+OZkW1wGP47kgU+sMb6I9ncN3UVaTlFb33ntqrLsxe3Vd3KynHcmnYvTpYzYRxnwhig9o+jrOx0y4iXg0hbFrZvrkPsX1G08Lrv4KtrlcvcF8HRqm/4V9eBM1y5xpsNUolm2+eA7lQlYg27qBj2j/fCkQ0ljzH2Z/hmLGQd8X2O8EYqEe7jIf4vvuM1MPARZaRnPqGW1e8AAx5SsXaApgOV/KrpBQF48pDB0WSZIQHbmtb2H0cBNWkcdrvOgl2p3PPlKp/r/3tJO85vWQfjhMSzioxB0wT5CHINkxy3QUSQHacGummektte0wW5UnAoI5+MPA9NYkJw6QK7LP9xa9K9OBXOhHGcCWOA2j8Oq8TsFLHZNPS9i0sa8AI8ucpF7UszOidFzaRBlYvVbQ0TL1Cx7AI2/6wyz7fNKW3AAf74H/S9T8XXfdHnHpXkFgh3FhzZBKH1Iba1irs3H6akV4f+G1Z+Cn3vhbVTVbJc1hGo1w4GPY4tpmOpwwkBQboHp8xBz83EdIT5FLexODmyDcnLs7b4Xf+/OVsZ0LwOzlM4h2lK7EjsAsKduvr+Gqded2AaEieSJmF2RLhDxcBNaWVKW1hUIZasTxk4ZTbaihNqqZv0Vxrj10+D0VOVSEvHayihMRkUWRQH73kb/P58SQNeQGxLKCg/O5Gts5QaW997QCv2vqXbleFtPlRlowei+XmqVMzwqDi9ZlOz/o/Ohd2LYfRXMP95ldyWvk9te+AvxORRODd+iUsvip3adZMoeZiQuY9if7c72ltd0X95kCh5GLtuPaorA48pAypyHcnMJ7+Gq59JWboMzeLMRNcFNpt2VnVPq2lYM/EyENIAd7GHareboHF3+OyiouxyR4hSSxv5Bvxwt1rW+TrVZhQgrgfM+bfvE3jdvmfyBXxzM4ybBy0vgOyjqh95dFNY/z282weu+1a9CBz10VgkJFbNqmc8oErQYppB3XaqKxqoevQ9S1S5mQ+0Of/C1foScnGgaYIwzwH0jwaruHnB57PmK/RNPxF28xzSbHHWw/sU0TWBTRN4/XyOQoBd8+P9sbCoJoSukSdh/YEMDqbn0bpBOI0jg3DBGdUrvjZw1s7EbTaNMD2LCC2dED3P75ukRwtBFjQaiWqiXNHT7yxZW+3OVr240/cpvfOEPqo5yaYf1XoR4F3J5iRgl4jIeHWunx5QWefz/qvc8n9+qGb6341THc4S+kKdFqq9qCMU6rWFKybAD+OVoMu6b+DjoeDNVtuDmqWv/97/uU0v7FuOrmsEixy0Xx4BaajQQJ0WRepy7my0mf/AJfzPIC3Kh1PAsLb+G2oMaF4H52n61WqawKNpZCFI9UryNQ3NdtY+Qs5edI0NR3MY9vpCbvv8L/754wau+mApV324jFSvGbCZjkXlc1bOxCPs2dh2zkNb+iZkHcZerx1Bg5/BE9GMPNOBx2MgpcRm03CRpgRT4vsoo7bsff8B4GXvwS2/wf6VKmnM8CiD7opS9eKGD0GM3X+olqPb5vg+ZtexSlmtw1UQUqd0J7SM/bDxeAeyIxtUuVrj7kqu9af7i3TTC5j9DNy55Pg12f0n5h1HHJ9122UuotkgOOcR1WFNs6uuaBt/hGXvIXb+jkPmku1XtNOiPGimyaPnteLPnSkkZ5X8vkS47Dx9YRtsUlZ7PbCmayS7Df7x3Vr+2pMGQKjTxs39mnBNtzh0b+Xpg1vUbLINyc2fLcdzQsngvtRcbpiwnK9u7VkosWvly1Q9Z50RD9ezsM+4F7H1uERqcAyiyw2I9D04Vk3GYXNitr8SGVIX7dAatLn/UsbRHgydrlWZ3qk7IXVX6YPnpSvD/du/VPkWQK871Sy43eVKBvVElr0PY2eo4x07ocVgyxHKBT5huJrZNx+qRF0yDxZtc84/VJz7gwHq3AU06Q+Xfahm8Z4s2PADbJimjPvqr2DgY0rVrUk/5VL3g2zcHV0X6Njh4CqY86+ilZqu1N9GvAwzHgRpEmQzccnjmu82J7kijDxvzWp4UpOREkI1ybQ7+jB15T6mrz6AKSUXtm/A6B7xBAtZYeW8yhCMyZYw6t0lZOYX1SVn5Xt5fc420nM83Nm/KcJyo57x2GwaU5ftLWXAC9iXmsve1FwSooNJzfWQluOmQYQLly6UHKxl0Cuds8qIa5rAlrKpyIA7QuHKT2Hmk3BwFQVObT0nGVmvHWL2U0U7e3Jg+YfK8F30poqJ+/pGCl2Vhi1+XdVdO0JgyVsqCS7zEOyYV2xboQRZso7ANVOVatumn8Aeomq5Mw7Atzer+OfW2arO/JJ34euxkJcGUU2VtvrXN5S+jl0LlUJbbEvlIehwlWot+t1tSgGuyxgIb6DK1FZ8XKS/XgyZNARhDyJs32zYuwQ2TC+5gWmosV3wCnS+Fs3uIGTxc2h/fao+L7uLkE7X4er7IGneUOsHXE5MU2V5j+0Rx5VdVOKiS9cwvRVT5JK6Rr6EfWm5BNl0YsMcuKBc3cSKo9l0pizdXcKAF2fSsj3c3K8pQRU6qkVtxCNh1d60gNusO5DBxCW7+HVdkdLkgOZ1eP6y9jgM05LerWTOKiPu1Dzoy98vWtBljEryOriqaJmmQ49xiE8v9H2Q1F0qqztxEGyfW3JdbCvlok7ZBnXbwqXnKSPuyVWJbec+rTLN9y5TdeJN+qtZtM2h4un2YOj3gEo0W/4xxLZQxn/RK8qIH1oD855VyWxHN4MzDJa963/Am35SmfELXlKSrNvnqi5qh9bAd7eqGf3F78D10+HHe1R7UlDX1O5yGPwk2h9vQqvhqhTNH0vfQV77LeLbW0qq13ly0ZZ/iDjwN+GjPifdG+r/GBalMDxGYSmZWUF3tWHTeXfBDiYv21OYJBfhsvOfS9rSvXGk33ajvsg1SvYRL3UuU7L9aDbtYy1p1TMdXRM0iAj8uhbs0Nl6uGSr1AVbk7l7yirevLojdku5r1I5qzIQNOktcnODalhSfHbZpD/cNFNlgQeKFW/8Qbm3i6M7lFzq97fB9PEq8zsoHCW76lSGW9PVLPrIRtUHHAm/PaOyzD+/RNWFZ+xXCXE7f1ez2fR9MPgp6HFb0TUe26Zc9FFNVa34dd+p3uBD/qlK3wqQpqoT1493VErZoa6jSX8Vt884AF9coa7voreUB+G672DMNAiti/j0Yug6BsLj1AtIrzshOKb055GfCVlHShrwYoj9K9DTd1plKNWEsGlMWLKbT5fsLpHlnp7rYfyUVezNzK/QvRCAvYxkJYdNO22eFl0X2B02HE6b9R2rYqTX5IbeTfyud9l1mtQJYfvR0oJcK/ekkp7nDZjHa1Fxzioj7hEuzGZDixaY3qI4cv0O0O8++HZcyS5kvjDcKjs7JFapsbW9FK7/Trml9y1X7uolb6lyM1sQdBmrzrVnGVzzJXS4GlwRqo3ozvnqmFKqJiWTr1A14Be9CXuWwsx/wLQ7VBLZ2BkqwW7a7eqcuxao7PPPL1Pu/W2/KXd74+5F12oPLhkrXz8NDhcTljE8KrN+1Rfqej6/DCZeCIvfhNQdMOlScGfAik/UC8Wl70Pvu0p+Hk3PgQ0BstwBbc1X2O1WbLw6yDPh0yW7/K5/edZm3BV4kgbbBFd09d8L3mXXSYh2VbubVNMEHl1n9ZEc/vnLJp6duZnt6fl4dM0yFFWElJK6IXbuPKdZqXU2TfDSqA58tHCn3/3X7EtH084qs1PlnFXudLdXItteDn+8qpLQNJuapRoe1dXrp/shfS9EJahZs+nHhdn8PNWo5PznlNt8w3T46vrSxj9lhyrhanMRaJoy/IvfUtrka78uaVwLMNzw27+h5fnKqIPyDPxwt2pm0vUm1Xns2HY1cy/OrkVKwW30V/DZxao2/MQEPCO/pHBMwX7nPOZ7rNlH1bmkqTwQG39QHoeO1xQm6pmJgxFHylCOE9YPt7rIzPeS5/HvLl+5O7VCsXWvx2R4u/p8umS3TyGax0e0wkn1dpoXAvKExtiJy9l6pGjW9/XK/fRuFsOrozpgszLmqwTdMLm+Rxznt63PhMW7OJieS8fGkVzdPY6f1x5k7iY/MtGokE71flPOfM66J2sGkRg3/KxkR7fOhNYXKVlUZxik7VEz4s2/Qucxvg8QFIHsdhPMekLNkDMPKMUzf7P39d8pYx5cR5V/7V8OTQcod7Y/9ixWnoET2fabyjTveI3/WHheuhKZ6XgtnP88LH6j5Ppmg1XteXGcYYHDB0c2QoNiEqyzn1ZiNkJA3TaYiYMw21zuf3/A7HANHo/1UK0OynJ9hwfZK+z6dpomU27pydg+TQh2KI9K6wZhfHJDN4a2jK1w57NTxdQ1Xpi5qYQBL2DJ9mNMXbkP3aphrzJshklDl40nh7Xgf6M6cFufBCJ0aNswwu8+TptGu0bhGFZMvFI5q2biAF4D0p1NCb32R3RvJprNAVlHEbnFsrOXvg2XfaTqs1d8UtQPPK4n5sg3EKYX4nopQ+yvxWhEHETGqZfOsAZKhGX2P5X0aVnuelCGtU4LSD5BR3vTz6qHuDff/75bZyk52B/vgeStxY553PV/4jV3uhY2zfB/PFcUtLpQvZBIqUIDh9cjr/kSWb8T6Z5QQkMboSUORuyYW2p3mdAXb3g8ptf68VYHwXaNZrGhPuOSANf0iCNYExXqaqppAs2UjOvXlDsGJuLxmgjAJU6PQle+CT+vPeR3/YTFu7i8c6NT0pi3CIyUEuk10IGCxnot64YyuFUsczcdLbX9fy5ph8PKTK90zjojDuqhk04YiDBsQiNy+AslZSxNQ5V2tbscRn0MQkc6w/GGNSJfCyN09v0qfr5jvkr0KnDJA9RtA+c+BflZqmQssolSestNh5bDYcErqo93bCs4usn3BdbvoNzYfe9VBvSn+1WcHVSi2onu8BPRbKqcrXiP8EZd4NxnVA17/weLVBjqtVMGung53YnHatxVeS2anau8AaCkaMMaYLhiMfNzyJQhRFz0LvrKD9GWf6g8As5wzG43YXa/nUxvSBl3xaKyCAJevaIDV36wlPwTup01iQnmmh7xGOV0NQsBbk1n8a5UPlu6m6w8L/2ax3B9zwRCdXHaJDbzvWZh0l7nuEgu7dKI6BAHB9LymLpiL9uOZGElylc/NsPgPxe148+OqXy4aAfJmW7aNgznnsFJ1A91WFoCVcBZ34rUZtOI2DQJzR4E675W8eET0R2Yty/GsAWjCdAOrUJsmal01F3Raua+7D1lwEe8CN/eWlKQxe5SLUPrtIBVn8PBNcol/s2Nar3QVMZ4WD1VC979Fvj9OSUyU7cNjHgJvrhKGfALXoXEc+D9/kru1Rd974OwhhDbXBlq3a6Otex99TIweqqKsXe4CuJ7wb4Vana+4KWSxxFCnW/3YpWw1/8hlUgHcPUX8NdnyA5X4WnUmwxD1YE7bRKXzECYHqRmI1eEk++t2W7N6mpVKARITdVuG1JiE4JgDbzeU3+wnTgGoWtkGpIPF+5g/pZkguwaV3WL48IODXCaZrlLwbw2nfFf/s3K3WkllgfZNabc0ouEMHulukfLey/yNI0Rby7iucvaczQznyl/7uFQeh7NYkO5vncCeR6DAUl1cFaglK4yqe3tL+HUxmCzaeSaYEqJXRNKZfA0vVXV9nth9RMvAyEEUbmb0adcAVdNUj23C+qlAaKaIkd/BX9/jvh7kpphNu4G5zyujFv99ko0Zf00ZYhn3O+7W5lmUyVcC1+BLterxDl3NuxdDm0vVrP61F1qZpw4EBa8rJLIAAY8ol4AUnZA+8th6buqlOy3f5Y+T2g9uOlXeKe3b1f/OY+rGvcj65Vk6o65ytAPfATiesKaryB9v8oZaD9KCdasnKBCCyNfVyVyMUkw+En1b0Am9MN7yUek1dI68Or4keu6RpYJr/62hRlrD+IxJE1ignloWEu6xUWgn+IMxdcYhAB0jTxDKte3rpV7Bg7qQfzTpqM8NX29z/Vx0S6+vLknjko0lOW9F8Kms+FoNpOW7ma2jxr2O89pxtie8YjTlNxW2w0HnBljgNo/DsuIB0AI9XAN1XKwT7lUuaCH/FOVjh1aqwxlfC9VdnWiJCocL+fqAQtfVrXU8T1hcoAEr153qjrwDdPVrLZBJ7X8m7EqzlyAbocrPwcEuMLh4FrYPkclky16TcXiz30aQuoqZbjkrWqfNpfBwIdVzfqhtcpFnrJDHdMZps7f7nL4/g444COxzhWlEv163Ap/fqR6jBd0LEscpD6LTTNg+AuqHj5tT+Gu5iUfkJ5wYaXMKqub6viRu3WdS99dzJHM0rkMT13Qmova1qNCQeoTqIoxuDXBmIkr/cbWAX69tz8xtsqr5yrvODRNsCvLzeXv+pYMFgLmPTCQkNOUCV3bDQecGWOA2j+Osoz4WRkTFwLCtGxs+ccQO5aCIwR55STExp+ULGr7K6H1hZBxUJVR+TLgoLK8J1+uZtDxvaEsoYkjG1W9N8Afr8Gdy+CdXiUNOKj4+tTr4caf1YtF1iHVc7zP3UVZ7XP+reLcfe9VrnMkHFgNCFg1Bbb+qmLgBf3Gg6JUBzLDAz1ugWk+jHhuKmyeoeL9f00suW7Aw8rtnzRENXc5oRGLtuwdQhIGko4V+z4R3abxzcp9Pg04wMuztnBe23o1LglLAqk5Ppr2FCMr30uMzV49F1QMzabxxbI9ftdLCXM2H+HydvWtqgiLM5qzzogLAZG2LPRptyJ2LSxaoenIQU9Bx9GIr8cqedLs5NJ64QU06a/kUQvqsB0hyuUdiPAGRRrlCf2UO/tEA16A4VYu9sPrVEJZu1EqJl6c/X+p/wpwhitXf7226lyarlzv7izVTKXpQFXfHt9LNU5Z+ErJzmqaDYa/pAx9VBM1NmcYDP037FwAW35WmewndlIDyE3FnrqJ6LBG5OrR5BqO0tucpeQYkumrfIRYjpPrMdiXmktShLNG6cvbEHRsHMG8zaUzjUG9s9YNdZ6W3uamVC8QgcjMC7zewuJMoGZnHFUBwXo++uzHSxpwANNAzPknIueYMoD2YDVz9fgpIWvaHzb/rP4dEqtizQ06qv380em6olKu0Lqly8dOJH2vakVqepUYS0S8Msz+iElSRr9Okjr2V9fBum9VjDu2pepBPvMfMOkyFY+/faFSj4tpppLcxkxTeutz/q2U2UZ9Ald+ptqkzn8ekobB9nm+z92oC2LLr+jvdCd490xceuAZ3NmGWYZ1VutrlsyYHcl9Q5r7VT8b0b7B6ettLiVDWvvvuw7QL6nOacuet7CoLs46I+6U2YgN0/xvsOw91RhFs6lZbuJAPxsKNQNpd7kydgtfUcbvsg+KtMqL0+9+5QZofbyxSuYhNWMORGSCylL/6T54u4dKMLvmK/w+VbvfDH9/rmbwCb3VsuBold3+1XUqiz5lh2qluvgN1eK0910qm90RClOuUUZ/358qlPDLI0p2ddNPqttZ6wtVDXqpj0KDrjfC6i9BSrSFLxIssojS04jS0wjRK6bVfabh0jWGt6vvd73TphEfHVzjujuZpqR+sIPXr+pEiKPky+PQ1vV4YngrtNNkJL1ekz6JMcSG+g5CtG4QRsNwp9WQxeKM56wz4uRlBHb/HdmgXMn7V6gWoR2vVq7yE9mzBLrdAm0uUYZu8wyVTR4Zr5qR9L5LqaN1ulY1FbE5YeIFqsWoblez7JYXqCQ0X9icENdDNSwBdc1/fgBHN0L3W0tv3+NWJQBzZIPqihZyfJbSeYzScc9OLr1PTgrM/be6lhUfFzWHCYpQ8qzZyeo6OlwJY6YrH2azQSWPERSpQg9rp6qYeoerYPiLaN+Pw/ZGO2xvdsD1y51Eevdj18/OWZHpNRjdI57IYN+x49sGJFJVwQdNE6f0AqWZJn3iI5l5X38+v6kH747uwtwHBvJ/I1tjN05vrNmF5MtxPWnfqKRK2IDmdfjo+m44a9hLkYVFVXDWxcSxuwKvD60HuWmqFeil78Gi1+HKSUpq9PC648cIVq7zJn1V45GCuHbDzqqP92//hBbDVY13bqqqB89LV9ts/hW63axm+45gVT/+9Q0lY9M2J1z6gWpCcuKDaNH/4JY50KSfepFwhKi68R3z4ecH1QtCbEvVb1xoat2SN/2Pd9scOOcJZbB3L1YCNF1uVDP4679XLw/7/1bZ7j/eq0rRBv5DzeZ1u5rBL3tPicDUbw+tR8KUq4t056WJ2DoTfdcCwm6ZT5qt0Vk5OwoWkm9v682/ftrAwm3JSAl1Qh2MH5TE+W3qVXoplKFr5Hglm/ZnEGTXaVEvVCXOncTMWRomTqB1jPrtmKYEQ552BWzDMInUBe+P7kyeYZKR5yUq2IFTA5tplhnCsLA4E6gyI75161Y+//xz1q9fz+bNm3G73cyZM4fGjf13Q6oOPHooeoNOJXuIF6fzdao5ScZ+mPMvGPasSurqc7eaZWu6Umlb/aVSVSveYCS0riq7MjxFNd4nkrZHzaSlhL8+hY6j4a5lsG2u6vNdvz3Uba0M+JZfS++fc0zJwIbUVcIt2clq2wIZ1v4PwZqvVT25NNV//hq5gFpfULPe+y7lwrc54ZPz1PrG3WDo/8E3N6nzznoSGnWD3nfDjAfU9RTQ4zaY+6zv83ly0X57CteId8g2a1oedtVjGpJIm+DFS9vhNsFjmDhtGsG6wKjk7GmvTec/v2zipzVFgkNOm8bTF7bh3BZ1TromvSa+fJmmxI7ELiDMZVPfZ8NqsWFx9lBl7vR169Yxb9486tSpQ5cuXarqNBUmW4ZiXPqBmmmeSEJfNcMuaA+acRBmP4MMrosR1wdPWDxGeDyGOx+j/dWYtqCS+2ccVJ3DAlGnhXrQpO8Fd66aMe/9UyWf9bhVudAnXerbgIMyuLmpMPNx6Hu/qhGXpio3u+xD5Z6XsiiBLueYMsz+CG+ojHP3m1UN+i8Pq5eRKyaqsECvu5Tb/ZJ3lEt9yL8g+wg0aF+6C1tknH8pWUBsm4VD1s5azcrANCW6YeKSJuGaaipS2QYcm8ab87aXMOCgZEqfmLaOHSk56PrZm59gYXGmUWVG/OKLL2bBggW89957DBo0qOwdqgnTlGTYGmHcuhDzvOdVR7EW52Fe+y3mpe8j13wFDbsoadKh/0a2GgnRTTHRySKSFHco6c4Esp2NkM7IkvHyQ2uUC91XDN0RorqKtbsMUrYpVbfmQ1TG+MafIK4r/PGG6nbW7jL/A2h+nnKdH/gLdv8BN/wAty+GkW9A6m5I2aVeBuwhKgFu5UToM97/8XrfBQtfhW9uhlETVFb73GehTkuV2JeXrl4YJl2q2ptunQWXvAdZR+G6b1T8vICySo2OuzddNoNgmxu71WWq0skz4ZuV+/yuf3nWVvKlZcQtLM4UqsydXpMbv3sNSQoR2FuPwd5yFFLYcEs7phdCz30JZ84exORRkH20sOjHHhJLxLXfYYbUQxxeg7bpB2R8X2TvuxHzny86+IKXYfTXqlVo+yuV8dZsygW/+HX4tVjfbt2uRFSiEuDoVhj0hIonD39BxaeLKaIBqhtan7tVpjmoZLSw+kr+VHco49/nXqWLHt8T7liqvAoxLdQMev7zRS1HbUHQe7z6//Y5atmuhSpZ76+Jyi3vilCZ8cXZ/Qd8cYWKl+ekw1WT4dg2ZOZBZEgsWmQCpO32+bnL+D5onkxC5z0KnlzMFiOQLYaTISPxWu0JK4WsfC/uAO7ydfvTMS0bbmFxxlArE9sKZPQqBxWfLcgOtuWmIz67qCgRrYDso2ifXYh2zZfwxSgApaV+8TvIfg8ilr2rJEqPbVez6YR+KtEs60iR0lm/++DwhqIEOcMD8/4Ll3+klq/+Qs3mp4+Hyz9RvcfXfq1msC3OUwIzP91XFIfOTSuKhRtuFaffOks1J/n8cgiOVYZ92XsqGW/c73B0s5oxB8fAmqlKMraAtd/ABS/D8g+V237ha74/Mne28iD0vENJ0sa2QF79JaYjAnHec4ivRpfeR9Nh4KNoX45WSXGAtn0uLHieyBt/xRPRtCI3rVKx2VT5VOV+r6qXgjG4HIF/0lEhdnRdI8JPadbp5ky4F3BmjONMGAPU/nH4qyguoFYa8apCCBA7F5Q04PU7qDi5kQ/b58LB1SoL/cDfyrhOvxPRcTTcOge8bmUsV0+BRa8WHUOayrge+Etlun96Ycnkr6XvwvkvqCz27rcow7t3qSpB8+QCQs2A579QMlu9UdfSgjE5KbDqC7h5ttrPm6+y4XOPqWyf7XOVCp2vnubSAJtLZZxLQxn0L670/WFt+VW1NM1LQzYfjmFTXcyI74N+1ReImf8ompHXbY0c/iIibY8SlknbXeR6z05GfHcr+jVfYzijynejLPwS4tBp0yCcDQczfK4f07sJUUHWz97C4kyhXL/mZcuWMWbMmHIdcMmSJURH+0gaq0SqSsje6bQRtvsP9UdMEgx/UYmj7F6sStMuehM0B8Q0L+p0JiWsmqxm0KM+gexj/ku6spOV8Ws5QkmuFnBoLThDoNcdKtFt4oXKyOWmqfOv/670sYSAHuNg2u2l162fppTYTK+qA9+34vgAw5QoywWvwne3lM4ib36e8g50ukbF5xt1UWI26771cX4NMg8i21yCt8No0jIKSuRs2OufQ/CYX9C9OQhN6ZCJ1VOOvwB1gv4PwPwXYcfvapcDf0NeBul5QaXPUw3U9gYJUDQG3evllSs6cOX7S8k8QZa0bcNwLuvUkIwMPyqENYAz4V7AmTGOM2EMUPvHERMTGnA2Xi4jnpiYyHPPPVeuE4aG1s52lKCS3mRkE0R4I7joDdUXvLhO+KrJ0Ppi6DZWiZsU5+hm0IOKSsz8seVXZUiLG/HQumqWHNUEvizmil76too5m56S2wdFwLD/KCW1rCM+TiLVMT8crDLPC8jPVEptXceqjmaLi71shNaF5kNV+9Jed8KKifDbv+Cqz30acdl6JEQnYo54hbTckq5Zj9cknXDC7DYci19GLP+gaOW235Tn4YqJ6noKGrp4sqH6+2iccRiGpG6QjZ/v6cdXK/Yxb/MRnDad63rG0SsxBrthWuVXFhZnEOUy4rGxsVx2WYCM6TMEj8dAtr0MHC4l2OKr0cfG6ZDQS9VPF8xwAaKbQn46BIUHPonQKFXF2vl65YZffMIM3pOrktj6PwA9b1dGT3dCdBOY83++Z+igkuVWTChpwIvz9yQYO0MpuSGK4vXHtkNoLLx7mTrfgIfUOZ1hRWpuAM5wZL+H8IYcr/nPLf2Gq2kCe+oWtOIGvAB3tor7X/gqfHmt+kycEXB2CrpVOqZhEgTc1COOa7o2QhOCIA28XsMy4BYWZxg1N4X8NJGrhSObDlS12/5YeVykpTjdb1Fx5og4JZbij5YjlHhMAY26KZd12m7fNdaeHFXy9dnFKgN9+h1Ko71hR9/H1+3KKG/zoXFegGkoV/2YH+H6aao2/cAq5cKffIU656JXIaqpStIr6M4mNGTz8zBunkO6iPF/fCBIy0Nb/Lr/DbIOg2lCcDSy1UjyhdXCtLIxvAYOKbGZZq3s825hYVE2VZbhkpuby/z5SjRl8+bNACxYsIDo6Giio6Pp0aNHVZ36lMg1nASb3sD9pNL3qs5lBbS/QtWWL3lLubp7j1cNUU4krIEy2DP+UG1BO12jZF4zjwtzhNX3nXAGKr6t21XjlPXfK5f8sGeVQEtBtnpsKxjyDBzbBloZvmmbE5yhgFCx8D/+V9ptvnIC8qI38YyajGbkgdBxi2ByZRBmGSVhmulBZPpvvwlA1iFk4iCMIc+S462Z2dIWFhYWNZkqM+LHjh3j3nvvLbHsX//6FwA9evRg0qRJVXXqU0Y6IwNvEJOk3No9b4cW50NYQ8hLVcYVVNew4S/AkrdVjFyzqVh637uVJvt5z6kkr8VvKS3yxW8ql3Ln62DmE77PWa+tSnIDVa6l6bBnGdw0S7m6NV1Jyc59Vr0MtLlINUPxhT0YhA4fnKP+7j1eyb2eaMSPbUNKSPeGAqHYdJ0QmUqEyEHqGkLaMIXvlwVDC0LWbYs4vN7vxygbdcOddDGZ3uAa1UfbwsLCorZQZUa8cePGhTPw2ka+CMbV7FxEgQjKifQYB7sWKBf41DGq5Kz9qKL1Pz+sarrPfRpc0SqT/OgmZThbXaBm1c0GKYnW7COwb7nar8/dkHSuakpSnOBopfb2033KWF/4uqrpbneZ2nfa7ar/984FcHi9Mt5971Pu8OM12SUY+Aj8/VnR30vegmumqOS24olyEXGI1F2ERgUhkDj2zEeb/5x6mXCGIbveiN7rTjQtrJSudp5hw9XnXvR1X5du4gJQtw0eV30yjAD91y0sLCwsAiJkTWtiXAZSSpKTs6r0HEIIovRU9ClXlprNyl53Ieq3hWl3Fi2MbQndboJfHvV/0Cb9Ia5nkbjK+S8o479phiq7ch2vkQ6JVS71Pz8AdxY0H6Y6ka37Tqm/tRyuEt6CwlVd+uynlOKa7lTa6ZFx8Pdk1Y608/VK1e3vz1UyWf326kUhdTfM+0/J62t9EYQ3gGXvFy275F1Y9Crm+S/B0Y1oM/9Relx1W+O55jvSvGGlVrl0N8F7ZqP9OL5kxn50Isa135FGbI1oqlHbS1DgzBgDWOOoSZwJY4DaP46YmNCA7YQt1QcfSClJM6MIu+Zb9LRdiG2zVEZ264vw2sOxH9uEptuLDNOxbcpACs2vfrjsdC0itqWaaUupjKo0VILa7KdVnB3UbHjAI9DxKtizFFxRyOAYRMvhyjgve18Jz2ybo8Rehv5bybV6cpSIy6af1UuBzaFqweu1h6u/QIbEIvYsUfXfBYpxxcnYp8ZQQKdr1fiSt6LN/y+0Gun7wzqyEX3PH9jiR/hOnorvjbz1d8SepcjcFEjogxHRlHQzokYYcAsLC4vajGXE/WCaknQzDC28A7YenZBSlaDhAWdUB0JuX4r48z20PUvAFYVpcyH63odY9Krqhtb9ZjW7Fjqk7UFExsGHg5RR7vcAtL0MUrYjvrmp5ImzjsDPD8GF/1MZ480GQ84x5KovEEmD1AuAJ0+59PcshYkjoHEP1b502XvqGOnFNNcProEtv6h67xkP+h9wbGvltu9yg+oJfnQTzLhfrTu8Hvrc43dX7e9Pccadg5cisRaX7iZ4169oP96lFtTvgHCEwt+T0Ea+hS2qI2708t8QCwsLC4tSWEa8DExT4naXVDbLN3TyqUdQn6ew9cpBCht5BBPctTHOFsMRRzcqoZQC2dG4njDocWh2Lmyfg5j9FLJRV8Rvz/g/8cJXYOTrkLIDMzwB+t6Ptm8pYtUXqkSs3eXI5kMBoWLUHa5GLH1XibWciCMUQusrMZni/c8LEELNvDdMU6Ir391aMks+pK4qSfP7IXk4sfbdZaQqA14QrTm4unCd9uVVhNyxHDeR/o9pYWFhYVEmVp34KZDn1cgyQ8k2gjAMk3xcyGPb4Md7Snby2rtMdSfr/0Bh7FtIo0i61Rfpe1X52brv8OghSARi+zwVe+93PwgNMfECxNZZmL3Hk+1shHn99KLYegHRicjRUxHuLJX8Ft6w5HrNpuRk9yxVcfi135Qqc5M9b1eNWPxgtrkcd7E6b4dDQ/z9me+ENgBPLmLvUnTd+vpZWFhYnArWTLwSCZbpaLOf9L3Sk6uMZOfrVElZcEzAGDoAuakY57+I1xaKY/lrSmnt7xNK8zIOoH89BtvlX5AR2oawcQvRjm5EHN0EMYngzUd8da06/1WT4eJ3IesgHFqnkujiusOmX5Adr0IsebO0AU/oh9n6IrR9y33XzofVx2x5AZ5i8XBdetFStgX8rMSxrWgJAsMIuJmFhYWFRQAsI16JaO7MIuEVX2yZCVdMUJKoUiqt8i0zfW/bsAsyMoEcPYYgbxraio/9H3f/SuxmDlmEgDsH8dN94IpUIjI5KUXbfXOj6iv++wuqvC1vCcz5JwBmzztg3ELEhmloW34BRzBGt9sw6rYjwxNKxJD/oIc3VNfhzgYhkImD4IJXyZCRFNdMNbBj1uuAtmmG30uW9dpZiW0WFhYWp4hlxKuTgpl3dKJyX/e5R3VIK65LDkpe9dynkZ48DCEQQqruZoHw5uF0mmhL3lOa775031N3qTpzd6YqSzuObDuKfNNBthGEo82N2FtfjRQ6+dKJcXyGneYJwdn9IYK7jUN4cpTiW1A4hj0c44TSDbfHQHa4Cha+pGriTyQoAtmgM4ZhSYFaWFhYnApWULISMR3hKo7tj1YjYMd8MNxK8nTuszB6qspU1x0qPt3ifLjuW2XcnWF4PAZeqau+5v6wBSEdYegyD3F4beCLTNmh5F9BzabbjsI79FmyDZVZ7vZKso0gcrz2UkY236uRakSSojUkxYzBsPtv9pIjIjGv+kKNqzjOcMzrppNJRODrtLCwsLAoE2smXolkiwjCh7+E9rWP3uvOMOh2s8o6H/ov1VTkh/Ew5RroNFqVgAmhkuC+vRl54eu4j5ds5RCOY9BTaF+MKn1cwOx6E3kiDJDIiDhEgQKcD2S99piJ5yo3e2Q8+SKEbE/l9/HOM2yYdXoQetdKxI7fIWUbskEnZKMeZBGB14qFW1hYWJwylmJbJROs5+E6thbttydVfbXQkM2HwblPI/KzYM8SWDkB+j2g3OizSmulyyYDkJe8yzFP0Ww1RM8laPO3aHOeAW++WigEsv1VeAf/izRPiFKay9uM/tFg3xfnisJz6yLSjAiE8J88Xl7Kq4Rks2lomsAwZI10odd2RSc4M8YA1jhqEmfCGKD2j8NSbKtmcowg8mN6EnLVt+hmPmgabhGMTRjo6QfQ9yyBqKZIaSLbXoqo3x4x/3ll8ENikT1uQ7a6gBRPSVd1tuHCaHk1wa0uhCMbVT14vXbka2GFM2kpJe7gxjgHPIK24MWSF2Z3YV4zlWwZfnzbavk4AKw2mBYWFhZVhDUTr0Z0XeAQHoKcGtIWQlp6LjabRijp6NKNRCdbr0O+20cyWDEK3sr8ZXeH6Lk484+grfgYkXkAM643su1lZBKBx6i8NIja/oZbwJkwjjNhDGCNoyZxJowBav84rJl4DcIwJLnYcIS4Cpd5vSZpFGseYgQ24ODfeBeQbbjIsSfg6P9/aNKDIZy4PVYQ2sLCwuJMwzLi1YgQEKLlYs9KhrQ9RDsjMF2xxxO9KtchIiXkeyTqFlsG3MLCwuJMxDLi1YQQEGnLRJ9xH2KrEnjRAT2sARGjJpIZ1gq3YTUEsbCwsLAoP1adeDURquWg/zi+0IAXknkQbdJFhJopvncshqYJHA4bdrtl7C0sLCwsLCNebdi96YhiKmkl8OYjlr+P0+Y7i1vTBJG2TCJTlxO25P8IX/U20fIQIXrtTNSwsLCwsKgcLHd6NaBpAg5tDLzNroXYe2STXzzJ7fi+kSIF/fNL4Nj2ohW/P0tQn3vQuo8n0xtcBVdtYWFhYVHTsWbi1UVQZBnrI5Ci9DtViMhGn35bSQN+HG3xGziOrLZaelpYWFicpVhP/2rANCUyupmSXvW3TY87yCOk1HK7ma101P2gLXwBF5l+11tYWFhYnLlYRryayJahmBe/p9LUT0A2HYi3YXffkqQ5yYEPfGw7uiy7ttzCwsLC4szDiolXE25DJ6d+H1zjFqEtfBmxfwUEx2D2vAMjYSAZRqjvHV1RgQ8cmYCJla1uYWFhcTZiGfFqJNewk2dvQuSFb6B5ssn3Qp4WHlBb3KOHoTfsAgf+8rne7PcgOSIcsPTJLSwsLM42LHd6NSOlxLQF43XFkmWGltkcJFuGYlz2MYQ3LLXO7HQdnoY9a2RnMAsLCwuLqseaiddwTFOSrtcj/MbfEPuXo2/+CRkUhdn5ejxB9azyMgsLC4uzGMuI1wIMwySVcPSGQ7HFDQWh4XZ7kZYkuoWFhcVZjWXEaxGGYWIYYMW/LSwsLCzAiolbWFhYWFjUWiwjbmFhYWFhUUuxjLiFhYWFhUUtxTLiFhYWFhYWtRTLiFtYWFhYWNRSLCNuYWFhYWFRS7GMuIWFhYWFRS3FMuIWFhYWFha1FMuIW1hYWFhY1FIsI25hYWFhYVFLsYy4hYWFhYVFLcUy4hYWFhYWFrUUIaWUp/siKoKUktp1xaURQv3fGkfN4EwYx5kwBrDGUZM4E8YAtX8cQoAoGISv9bXNiFtYWFhYWFgoLHe6hYWFhYVFLcUy4hYWFhYWFrUUy4hbWFhYWFjUUiwjbmFhYWFhUUuxjLiFhYWFhUUtxTLiFhYWFhYWtRTLiFtYWFhYWNRSLCNuYWFhYWFRS7GMuIWFhYWFRS3FMuIWFhYWFha1FMuIW1hYWFhY1FIsI25hYWFhYVFLsYy4hYWFhYVFLcV2ui8gEFu3buXzzz9n/fr1bN68GbfbzZw5c2jcuHG59n/sscf4/vvvSy3v2LEjU6dOrezL9cupjgNg3bp1vPTSS6xevRq73U6/fv147LHHqFevXhVeeWmSk5N56aWX+P3338nPz6dNmzY89NBDdOnSpcx9q/t+ZGdn89prr/Hrr7+SkZFBUlISd911F+eee26Z++7Zs4fnn3+eZcuWYZom3bp149FHHyUpKanSrzMQJzuGN998k7feeqvU8jp16vDHH39U1eX65dChQ3z00UesX7+eTZs2kZOTw2effUbPnj3LtX9NuB+nMoaadD+WLFnC9OnT+fvvvzl06BARERF06NCBu+++m5YtW5a5f024F6cyhpp0LyqDGm3E161bx7x582jTpg0hISEsXbq0wscIDg5mwoQJJZaFhIRU1iWWi1Mdx/bt27n++utp3749r7/+Orm5ubz22mtcf/31fP/999U2nvz8fMaOHUtOTg5PPfUUkZGRfPrpp4wdO5Yvv/ySNm3alHmM6rwf48ePZ8OGDTz00EM0btyY77//nvHjx/Pee+8xcOBAv/sdO3aM0aNHExMTwwsvvICu67z77rtcd911TJs2jfr161fJ9VbmGAqYMGECwcHBhX/b7faqvFy/7N69mxkzZtCmTRt69erF3Llzy71vTbkfpzKGAmrC/ZgyZQppaWmMHTuWZs2akZyczEcffcSoUaOYNGkSnTp18rtvTbkXpzKGAmrCvagUZA3GMIzCf0+YMEG2aNFC7t27t9z7P/roo7Jr165VcWkV4lTHcc8998i+ffvK7OzswmXbtm2TrVq1ku+//36lXmsgPv/8c9miRQu5bt26wmX5+fly8ODB8uabby5z/+q8H7///rts0aKFnDVrVuEy0zTl1VdfLc8///yA+77wwguyffv28tChQ4XLUlJSZOfOneXTTz9dZdd8IqcyhjfeeEO2aNFCpqenV/Vlloviv4HZs2fLFi1ayKVLl5Zr35pyP05lDDXpfiQnJ5dalp6eLrt16ybHjx8fcN+aci9OZQw16V5UBjU6Jq5pNfryys2pjMPj8fD7779z/vnnl3hrbNasGR07dmTWrFmVcYnl4rfffqNFixa0bdu2cJnD4eDCCy9k8eLFZGVlVdu1lMXs2bMJCwsr4XYWQnDppZeyY8cOtm3b5nff3377jT59+pQIVURFRTFo0CBmz55dpdddnFMZQ03jVH4DNeV+nCnPo5iYmFLLwsPDSUhI4NChQwH3rSn34lTGcKZxZnwrA5CTk0OfPn1o3bo1gwYN4vnnnyc7O/t0X1a52bt3L3l5eTRv3rzUupYtW7J169Zqu5atW7fSokULn9dhGAY7duwo8xjVdT+2bt1KUlJSqQdvQbxsy5YtPvfLy8tjz549fsd57Ngxjh07VunX64uTHUNxRowYQevWrenXrx9PPvlktV17ZVGT7kdlUFPvR0pKClu3bvX5nCmgpt+L8oyhODX1XlSUGh0TP1VatWpFq1ataNGiBYZhsHjxYiZNmsSKFSuYMmVKrYiBpKWlARAREVFqXWRkJHl5eeTl5REUFFQt1+LrOgqWpaamBty/Ou9HWloaTZo08XutBZ/riaSnpyOl9Pt5F+zrayZQ2ZzsGADi4uJ44IEHaN26NXa7nb/++ouPPvqIJUuW8N133/kcX02kJt2PU6Em3w8pJU899RSmaXLzzTf73a4m34vyjgFq9r04GarNiC9btowxY8aUa9slS5YQHR19yuccO3Zsib/79+9P06ZNeeqpp/j555+5+OKLK3zM0zEOUG7Uk1nnj5Mdx6lcR1Xcj0CcyrWezGdaFZzsGC655JISf/fu3ZtOnTpx0003MXnyZO68887KusRqoabcj5OlJt+PF198kd9++43nnnuOZs2albl9TbwXFRlDTb4XJ0O1GfHExESee+65cm0bGhpaZddx0UUX8cwzz7Bq1aqTMhrVPY7ib7gnkpaWRlBQEE6ns8LHPZlxREZG+ryO9PT0EtdaEU71fvijrGv197YdERGBEMLv511w7OrgZMfgj759+xIbG8uqVasq4eqqh5p0PyqbmnA/XnvtNT755BOeeOIJLrvssoDb1tR7UZEx+KMm3IuTpdqMeGxs7El/wJWJlBI4+SSV6h5HXFwcQUFBPmPfW7ZsKXf850ROZhxJSUk+47CbN29G13USExMrfB2nej/8kZSUxKxZszBNs8SxC67fV1wPICgoiLi4OJ/j3LJlC9HR0dXmLjzZMQRCSlmrErRq0v2oCk7n/Xj99dd57733ePjhh8vllauJ96KiYwhEbfttFFD7rvgU+eGHHzBNk44dO57uSykXdrudgQMHMnPmTHJzcwuX79y5k1WrVjFs2LBqu5ahQ4eyZcsWNm7cWLjM7XYzY8YMevfufVKeh6q6H0OHDiUjI6NULe+0adNo2rRpQGGKIUOGsHjxYo4ePVq4LC0tjXnz5jF06NBKvc5AnMoYfLFo0SKSk5NrzXe/gJpyPyqb03k/3nrrLd555x3uvfdebrnllnLvV5PuxcmOwRe19bcBNTyxLTc3l/nz5wNqtgewYMECoqOjiY6OpkePHoXbDh48GKDwgbd//34eeeQRLrjgAuLj4zEMgyVLlvD555/TuXNnRowYUSvGAXDPPfdwxRVXcMcdd3DTTTcVir00atSI0aNHV9s4Ro0axeTJkxk/fjwPPvggERERfPbZZxw5coT//e9/JbY93fdj4MCB9OzZkyeeeIK0tDQaN27MtGnTWLlyJe+8807hdtdffz1//vln4X0BuPnmm/nhhx8YN24cd911FzabjXfffRebzcbtt99eqddZVWO45JJLuOSSS2jatCk2m42///6bjz/+mISEBK699tpqG0Nxfv31VwDWrl0LwPLly0lNTcXlchUK19Tk+3EqY6hJ9+OTTz7hzTffZNCgQfTp06eEC9nhcBSKNtXke3EqY6hJ96IyELLAn1kD2bdvn195yR49ejBp0qTCv080Gunp6TzxxBNs2LCB5ORkpJTExcVx/vnnM27cuGrJ5i7gVMZRwJo1a3j55ZdZs2YNNpuNvn378thjj9GgQYOqu3AfHD16lBdffJH58+cXyq4++OCDdOvWrcR2NeF+ZGVl8eqrrzJz5swSkqVDhgwp3MbXjxxg165dvPDCCyxbtgwpJV27duXRRx896fBFdY/hgQceYN26dRw5cgSv10v9+vUZPHgwd95552mLIfuTw2zUqFHh96Sm34+THUNNuh8F1+eL2nIvTmUMNeleVAY12ohbWFhYWFhY+Oesi4lbWFhYWFicKVhG3MLCwsLCopZiGXELCwsLC4taimXELSwsLCwsaimWEbewsLCwsKilWEbcwsLCwsKilmIZcQsLCwsLi1qKZcQtLCwsLCxqKf8PdBjQbD4DR2oAAAAASUVORK5CYII=",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Proba new point in blue cluster = 0.5714547896575101\n",
|
|
"Proba new point in orange cluster = 0.42854521034249016\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"sns.scatterplot(x=data_scaled[:, 0], y=data_scaled[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.scatter(new_point[0], new_point[1], color=\"k\", marker=\"x\", s=200)\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"probas = gm.predict_proba(new_point.reshape(1, -1))\n",
|
|
"\n",
|
|
"print(\"Proba new point in blue cluster = \", probas[0][0])\n",
|
|
"print(\"Proba new point in orange cluster = \", probas[0][1])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "8a083be9",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "slide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"- How many parameters do we need to estimate for a GMM with $K$ components on data in dimension $N$?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d52ccd83",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"- How many parameters do we need to estimate for a GMM with $K$ components on data in dimension $N$?\n",
|
|
"\n",
|
|
"$$n_{params} = K \\frac{N^2 + N}{2}$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "31465c4f",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"To reduce this number of parameters, we can place constraints on the Covariance matrices\n",
|
|
"\n",
|
|
"- No constraint: _covariance_type=\"full\"_\n",
|
|
"$$n_{params} = K \\frac{N^2 + N}{2}$$\n",
|
|
"\n",
|
|
"- Force all components to share same covariance matrix: _covariance_type=\"tied\"_\n",
|
|
"$$n_{params} = \\;\\; ?$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "c9ad72db",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"To reduce this number of parameters, we can place constraints on the Covariance matrices\n",
|
|
"\n",
|
|
"- No constraint: _covariance_type=\"full\"_\n",
|
|
"$$n_{params} = K \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"- Force all components to share same covariance matrix: _covariance_type=\"tied\"_\n",
|
|
"$$n_{params} = \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"- Force diagonal covariance matrices: _covariance_type=\"diag\"_\n",
|
|
"$$n_{params} = \\;\\; ?$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4a5e49cd",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"To reduce this number of parameters, we can place constraints on the Covariance matrices\n",
|
|
"\n",
|
|
"- No constraint: _covariance_type=\"full\"_\n",
|
|
"$$n_{params} = K \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"- Force all components to share same covariance matrix: _covariance_type=\"tied\"_\n",
|
|
"$$n_{params} = \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"- Force diagonal covariance matrices: _covariance_type=\"diag\"_\n",
|
|
"$$n_{params} = 2KN$$\n",
|
|
"\n",
|
|
"- Force covariance matrix to be diagonal, all dimensions with equal variance: _covariance_type=\"spherical\"_\n",
|
|
"$$n_{params} = \\;\\; ?$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "01254e31",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"To reduce this number of parameters, we can place constraints on the Covariance matrices\n",
|
|
"\n",
|
|
"- No constraint: _covariance_type=\"full\"_\n",
|
|
"\n",
|
|
"$$n_{params} = K \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"\n",
|
|
"- Force all components to share same covariance matrix: _covariance_type=\"tied\"_\n",
|
|
"\n",
|
|
"$$n_{params} = \\frac{N^2 + 3N}{2}$$\n",
|
|
"\n",
|
|
"\n",
|
|
"- Force diagonal covariance matrices: _covariance_type=\"diag\"_\n",
|
|
"\n",
|
|
"$$n_{params} = 2KN$$\n",
|
|
"\n",
|
|
"\n",
|
|
"- Force covariance matrix to be diagonal, all dimensions with equal variance: _covariance_type=\"spherical\"_\n",
|
|
"\n",
|
|
"$$n_{params} = \\;\\; K(N+1)$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d262990f",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 1:__ Can we use _diag_?, _tied_? _spherical_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"id": "42f02614",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([4.5, 4.5])]\n",
|
|
"covariance = [np.array([[0.1, 0], [0, 0.1]]), np.array([[2, 0], [0, 2]])]\n",
|
|
"n_points = 500\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance[i], size=n_points)\n",
|
|
" for i in range(2)\n",
|
|
"]\n",
|
|
"data = np.r_[data[0], data[1]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1])\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "7a50c8fb",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example :__ Can we use _diag_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 39,
|
|
"id": "14578c29",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=2, covariance_type=\"diag\")\n",
|
|
"clusters = gm.fit_predict(data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b0dfbfb3",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _tied_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 40,
|
|
"id": "f98428b6",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
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"data": {
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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=2, covariance_type=\"tied\")\n",
|
|
"clusters = gm.fit_predict(data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e6ead7ef",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _spherical_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 41,
|
|
"id": "babfc60f",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=2, covariance_type=\"spherical\")\n",
|
|
"clusters = gm.fit_predict(data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "867ab7a2",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _diag_?, _tied_? _spherical_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 42,
|
|
"id": "f18d6086",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([1, 4]), np.array([1, 7])]\n",
|
|
"covariance = np.array([[5, 0], [0, 0.05]])\n",
|
|
"n_points = 100\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance, size=n_points)\n",
|
|
" for i in range(3)\n",
|
|
"]\n",
|
|
"all_data = np.r_[data[0], data[1], data[2]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=all_data[:, 0], y=all_data[:, 1])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fc3a2fc2",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _diag_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 43,
|
|
"id": "3619b61a",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=3, covariance_type=\"diag\", n_init=50)\n",
|
|
"clusters = gm.fit_predict(all_data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=all_data[:, 0], y=all_data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fa6d0f23",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _tied_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 44,
|
|
"id": "69dcda32",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "-"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=3, covariance_type=\"tied\", n_init=50)\n",
|
|
"clusters = gm.fit_predict(all_data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=all_data[:, 0], y=all_data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "625a8ba7",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Constraints on the covariance matrices\n",
|
|
"\n",
|
|
"__Example 2:__ Can we use _spherical_?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 45,
|
|
"id": "2201e847",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"gm = GaussianMixture(n_components=3, covariance_type=\"spherical\", n_init=50)\n",
|
|
"clusters = gm.fit_predict(all_data)\n",
|
|
"\n",
|
|
"sns.scatterplot(x=all_data[:, 0], y=all_data[:, 1], hue=clusters, palette=\"tab10\")\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "72aa50d3",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "slide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Selecting covariance type / number of components\n",
|
|
"\n",
|
|
"- Increasing the number of parameters (number of components/no constraints on covariance) generally results in a higher total likelihood.\n",
|
|
"\n",
|
|
"- However, models that are too large are not very informative (e.g., each point its cluster)\n",
|
|
"\n",
|
|
"- Hence, we want to find a good __balance__ between __number of parameters__ and __high total likelihood__.\n",
|
|
"\n",
|
|
"### The BIC criterion\n",
|
|
"\n",
|
|
"$$BIC = -2 \\log(L) + \\log(N)$$\n",
|
|
"\n",
|
|
"$L$ total likelihood, $N$ number of parameters"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ccb9efb1",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Selecting covariance type / number of components\n",
|
|
"\n",
|
|
"__Example 1:__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 46,
|
|
"id": "69e56569",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([4.5, 4.5])]\n",
|
|
"covariance = [np.array([[0.1, 0], [0, 0.1]]), np.array([[2, 0], [0, 2]])]\n",
|
|
"n_points = 500\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance[i], size=n_points)\n",
|
|
" for i in range(2)\n",
|
|
"]\n",
|
|
"data = np.r_[data[0], data[1]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=data[:, 0], y=data[:, 1])\n",
|
|
"plt.axis([-1, 11, -1, 11])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 47,
|
|
"id": "aafff2c4",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"spherical__2 5475.201351795416\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n_components_range = range(1, 5)\n",
|
|
"cv_types = [\"spherical\", \"tied\", \"diag\", \"full\"]\n",
|
|
"\n",
|
|
"bic = []\n",
|
|
"names = []\n",
|
|
"for cv in cv_types:\n",
|
|
" for n_comp in n_components_range:\n",
|
|
" names.append(cv + \"__\" + str(n_comp))\n",
|
|
" gmm = GaussianMixture(n_components=n_comp, covariance_type=cv)\n",
|
|
" gmm.fit(data)\n",
|
|
" bic.append(gmm.bic(data))\n",
|
|
"\n",
|
|
"index = np.argmin(bic)\n",
|
|
"print(names[index], bic[index])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4bb70f17",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"source": [
|
|
"## Selecting covariance type / number of components\n",
|
|
"\n",
|
|
"__Example 2:__"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 48,
|
|
"id": "c3d414c7",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 576x576 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"means = [np.array([1, 1]), np.array([1, 4]), np.array([1, 7])]\n",
|
|
"covariance = np.array([[5, 0], [0, 0.05]])\n",
|
|
"n_points = 100\n",
|
|
"\n",
|
|
"data = [\n",
|
|
" np.random.multivariate_normal(mean=means[i], cov=covariance, size=n_points)\n",
|
|
" for i in range(3)\n",
|
|
"]\n",
|
|
"all_data = np.r_[data[0], data[1], data[2]]\n",
|
|
"\n",
|
|
"sns.scatterplot(x=all_data[:, 0], y=all_data[:, 1])\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 49,
|
|
"id": "dade282e",
|
|
"metadata": {
|
|
"slideshow": {
|
|
"slide_type": "subslide"
|
|
}
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"tied__3 1941.9421774610244\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"n_components_range = range(1, 5)\n",
|
|
"cv_types = [\"spherical\", \"tied\", \"diag\", \"full\"]\n",
|
|
"\n",
|
|
"bic = []\n",
|
|
"names = []\n",
|
|
"for cv in cv_types:\n",
|
|
" for n_comp in n_components_range:\n",
|
|
" names.append(cv + \"__\" + str(n_comp))\n",
|
|
" gmm = GaussianMixture(n_components=n_comp, covariance_type=cv)\n",
|
|
" gmm.fit(all_data)\n",
|
|
" bic.append(gmm.bic(all_data))\n",
|
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"\n",
|
|
"index = np.argmin(bic)\n",
|
|
"print(names[index], bic[index])\n"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"celltoolbar": "Slideshow",
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"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": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|