{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Multi Dimensional Scaling (MDS)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Les méthodes de MDS consitent à projeter des données dans un espace de dimension réduite tout en conservant au mieux\n",
"une distance entre les données.\n",
"\n",
"De nombreuses méthodes existent (voir par exemple http://en.wikipedia.org/wiki/Multidimensional_scaling, ou http://scikit-learn.org/stable/_downloads/plot_lle_digits.py) nous n'en présenterons ici que quelques une."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"L'intérêt de ces méthodes est (au moins) double :\n",
"* il permet de représenter dansun espace de petite dimenstion des données a priri décrites dansun grand nombre de dimension\n",
"* il permet d'associer des axes à des données uniqueent décrite par une distance. Ceci permet de faire ensite une ACP dessus pour interpréter les données, faire des régressions, ou utiliser des algorithmes uniquement prévu pour le cas euclidien (comme les $k$-means par exemple)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Données iris"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"\n",
"current_palette = sns.color_palette()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.pairplot(iris)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On a toujours 3 espèces que l'on représentera en 3 clouleurs différentes. Les 50 premières sont de l'espèce *setosa*, les 50 suivantes de l'espèce *versicolor* et les 50 dernière de l'espèce *virginica*\n",
"\n",
"**Attention** : ces 3 espèces sont des *meta* données : ce sont les botanistes qui ont répartis les iris en espèces, ce n'est pas inhérent aux données."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Méthode 1 : les 2 premiers axes de l'ACP"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On y reviendra, mais lACP est une méthode qui permet de conserver l'inertie du nuage de points.\n",
"\n",
"Prendre les 2 premiers axes correspond à maximiser la projection des points."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ACP de données non centrée/réduite"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.decomposition import PCA \n",
"import numpy as np\n",
"import pandas"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"X = iris\n",
"\n",
"pca = PCA()\n",
"pca.fit(X)\n",
"\n",
"U = np.transpose(pca.components_) # vecteurs propres\n",
"I = pandas.DataFrame(np.transpose(pca.explained_variance_ratio_), columns=[\"pourcentage\"]) # information véhiculée\n",
"\n",
"C = pandas.DataFrame(X @ U, index=X.index) # nouvelles coordonnées"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Pourcentage d'inertie (l'_information_) conservée :"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
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},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"fig, ax = plt.subplots(figsize=(10, 10))\n",
"\n",
"sns.scatterplot(x='0', \n",
" y='1', \n",
" data=data,\n",
" legend=False,\n",
" hue = [0] * 50 + [1] * 50 + [2] * 50,\n",
" palette=current_palette[:3],\n",
" ax=ax)\n",
"\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Méthode 2 : le hasard"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cela peut sembler idiot, mais sur des données de grandes dimensions c'est (prouvé) assez efficace."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On utilise un module de sklearn https://scikit-learn.org/stable/modules/random_projection.html"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On choisi ici 2 nouveaux axes aléatoires"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"from sklearn import random_projection\n",
"\n",
"rp = random_projection.SparseRandomProjection(n_components=2, random_state=42)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On projette nos données dessus"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
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},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"data = iris_random\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 10))\n",
"\n",
"sns.scatterplot(x=\"0\", \n",
" y=\"1\", \n",
" data=data,\n",
" legend=False,\n",
" hue = [0] * 50 + [1] * 50 + [2] * 50,\n",
" palette=current_palette[:3],\n",
" ax=ax)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Méthode 3 : le MDS classique"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nos données sont ici décrites par une distance (pas forcément euclidienne) et on veut trouver $k$ axes telle que cette distance corresponde à la distance euclienne de points sur ces $k$ axes. \n",
"\n",
"voir : https://fr.wikipedia.org/wiki/Positionnement_multidimensionnel\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ici nos iris sont décritent dans un espace à 4 dimensions. \n",
"\n",
"On va commencer par déterminer une distance entre nos iris. Nous allons utiliser la distance euclidienne mais il y en a plein d'autres de possible : \n",
"\n",
"https://scikit-learn.org/stable/modules/classes.html#sklearn-metrics-metrics\n",
"\n",
"voir aussi https://towardsdatascience.com/3-basic-distance-measurement-in-text-mining-5852becff1d7 pour les 3 distances les plus utilisées (la dernière va vous surprendre)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Distance euclidienne entre nos données"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[0. , 0.53851648, 0.50990195, ..., 4.45982062, 4.65080638,\n",
" 4.14004831],\n",
" [0.53851648, 0. , 0.3 , ..., 4.49888875, 4.71805044,\n",
" 4.15331193],\n",
" [0.50990195, 0.3 , 0. , ..., 4.66154481, 4.84871117,\n",
" 4.29883705],\n",
" ...,\n",
" [4.45982062, 4.49888875, 4.66154481, ..., 0. , 0.6164414 ,\n",
" 0.64031242],\n",
" [4.65080638, 4.71805044, 4.84871117, ..., 0.6164414 , 0. ,\n",
" 0.76811457],\n",
" [4.14004831, 4.15331193, 4.29883705, ..., 0.64031242, 0.76811457,\n",
" 0. ]])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.metrics import euclidean_distances\n",
"\n",
"d = euclidean_distances(iris)\n",
"\n",
"d"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# c'est une liste de liste. Par exemple distance entre l'élément 0 et l'élément 42\n",
"d[0][42]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# ou au format numpy\n",
"\n",
"d[0, 42]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On cherche ensuite 2 dimensions pour les quelles cette distance serait bien conservée\n",
"\n",
"https://scikit-learn.org/stable/modules/generated/sklearn.manifold.MDS.html#sklearn.manifold.MDS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On trouve 2 axes permettant de recréer la distance de façon approchée"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"from sklearn import manifold"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
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" [ 0.60897716, -1.947802 ],\n",
" [-0.54227218, -1.45200678],\n",
" [ 0.21372511, -2.61383132],\n",
" [ 0.02255158, -2.55194666],\n",
" [ 0.30917529, -1.98904671],\n",
" [-0.21410352, -1.54433219],\n",
" [ 0.13543943, -1.78232486],\n",
" [-0.42540724, -2.0592374 ],\n",
" [-0.35314598, -1.43655156]])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mds = manifold.MDS(n_components=2, max_iter=3000,\n",
" dissimilarity=\"precomputed\", n_jobs=1)\n",
"\n",
"pos = mds.fit(d).embedding_\n",
"pos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On représente graphiquement le résultat"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = pandas.DataFrame(pos)\n",
"data.columns=(str(x) for x in data.columns) # pour ce fichu bug\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 10))\n",
"\n",
"sns.scatterplot(x='0', \n",
" y='1', \n",
" data=data,\n",
" legend=False,\n",
" hue = [0] * 50 + [1] * 50 + [2] * 50,\n",
" palette=current_palette[:3],\n",
" ax=ax)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Méthode 4 : isomap"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On essaie non pas de conserver toutes les distances mais seulement les $k$ plus proches.\n",
"\n",
"https://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html#sklearn.manifold.Isomap"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On trouve 2 axes permettant de recréer la distance des 10 plus proches voisins de façon approchée"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/homebrew/lib/python3.13/site-packages/sklearn/manifold/_isomap.py:359: UserWarning: The number of connected components of the neighbors graph is 2 > 1. Completing the graph to fit Isomap might be slow. Increase the number of neighbors to avoid this issue.\n",
" self._fit_transform(X)\n",
"/opt/homebrew/lib/python3.13/site-packages/scipy/sparse/_index.py:108: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil and dok are more efficient.\n",
" self._set_intXint(row, col, x.flat[0])\n"
]
},
{
"data": {
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" [ 9.67266439e-01, 4.41029277e-02],\n",
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" [ 2.58579712e+00, -1.35720529e-01],\n",
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" [ 3.12179890e+00, -2.61041068e-01],\n",
" [ 3.04956661e+00, -4.53702652e-02],\n",
" [ 2.55189140e+00, -8.42338776e-02],\n",
" [ 1.87415352e+00, 2.47829190e-01],\n",
" [ 2.21731747e+00, -2.18160079e-01],\n",
" [ 2.65731718e+00, 2.20462258e-01],\n",
" [ 1.71467523e+00, 6.97100503e-01]])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mds = manifold.Isomap(n_neighbors=10,\n",
" n_components=2, max_iter=3000, \n",
" metric=\"precomputed\")\n",
"\n",
"pos = mds.fit(d).embedding_\n",
"pos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### On représente graphiquement le résultat\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
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Pf5xzzjmnW9ntt9/O7373Oz72sY91lS1ZsoRvfOMbnHDCCV1loVBon74PERERERGRLco+jOVyOW677Ta++MUvcswxxwBw0003MWfOHB566CFOO+20bo9PJBIkEomu3y9atIhf//rXXHPNNUyaNAmATZs2sWnTJqZNm8bgwYN77b2IiIiIiIhsUfZrxhYvXkwymWTWrFldZVVVVUyZMoWFCxfu8PlXX301RxxxBGeeeWZX2ZIlSzDGsP/++++TNouIiIiIiOxI2Y+MrVu3DoBhw4Z1Kx8yZEhXXTGPPvooL7zwAn/5y1+6lS9dupTKykquvvpqnnrqKeLxOKeccgqf/vSne0x73FWOU/b5FgDbtrr9V6QcqF9KOVK/lHKkfinlSP1y15V9GEun0wA9QlIkEmHz5s3bfe7tt9/OscceywEHHNCtfOnSpWSzWaZOncpFF13E66+/zvXXX8/atWu5/vrrd7utlmWorU3s+IFlpKoqVuomiPSgfinlSP1SypH6pZQj9cudV/ZhLBqNAp1rx7b8P0A2myUWK/4XvXbtWubPn8/Pf/7zHnVXX301V1xxBdXV1QBMnDiRUCjE5z73OS6//HLq6+t3q62+H9DWltqt5/Y227aoqorR1pbG8/xSN0cEUL+U8qR+KeVI/VLKkfrlVlVVsZ0aISz7MLZlemJTUxOjRo3qKm9qaurakKOQRx55hLq6Ot7znvf0qHMcpyuIbTFhwgSgc1rk7oYxANftWx3P8/w+12bp/9QvpRypX0o5Ur+UcqR+ufPKfkLn5MmTqaioYP78+V1lbW1tLFq0iOnTpxd93rPPPsuMGTNwnJ558/zzz+crX/lKt7JXXnmFUCjEmDFj9lrbRUREREREiin7kbFwOMx5553HjTfeSF1dHcOHD+eGG26goaGBk046Cc/zaG5uprKysts0xkWLFnH22WcXfM2TTz6Za6+9lqlTpzJ79mxeeeUVrr/+ej7xiU9QUVHRW29NREREREQGsLIPYwCXXXYZruty5ZVXkslkmD59OrfeeiuhUIg1a9Zw/PHHc91113HWWWd1PWfDhg3U1NQUfL3zzjsPYwx33HEH1157LYMHD+ZjH/sYl156aS+9IxERERERGehMEARBqRvRX3ieT3NzstTN2CmOY1Fbm6ClJak5vVI21C+lHKlfSjlSv5RypH65VV1dYqc28Cj7NWMiIiIiIiL9kcKYiIiIiIhICSiMiYiIiIiIlIDCmIiIiIiISAkojImIiIiIiJSAwpiIiIiIiEgJKIyJiIiIiIiUgMKYiIiIyF5mhwwm5OOEdKklIsU5pW6AiIiISH8ROB5t3mb+vvhRNqQ2cUD9BOaMmknUT+B7QambJyJlRmFMREREZG9wfF7a9Aq/eO7OrqLXN7zJ3974F9845nPUWIPwfQUyEdlKY+ciIiIie0HeynLb83f1KM+6WX727G/w7FwJWiUi5UxhTERERGQPGWN4a/PbeIFfsH5l6xrSfqaXWyUi5U5hTERERGQPGQNe4G33MQGaoigi3SmMiYiIiOwh3w8YXT0CgylYP6xyKDEr2sutEpFypzAmIiIishdEgihnHfDeHuW2sbjksHMJ+QpjItKddlMUERER2Rtcm2NHzWbCoP35y+J/0JxuZULdGD4w+WQqqMLzCq8nE5GBS2FMREREZC8xeYfR0TH89+Efxws8QiaEn7e0WkxEClIYExEREdmLfD8A38HGQWNhIrI9WjMmIiIiIiJSAgpjIiIiIiIiJaAwJiIiIiIiUgIKYyIiIiIiIiWgMCYiIiIiIlICCmMiIiIiIiIloK3tRURERMqAMRAKOUCA6/qdW+SLSL+mMCYiIiJSYjErh5XaRMf8fxJkU8SnzMEePIZUECNQJhPptxTGREREREooZuXIPHcfbQv/2lWWfP1pwkPHUH/Wl2n3oiVsnYjsS1ozJiIiIlIixoCV2tQtiG2RW7+S5KuPEnJMCVomIr1BYUxERESkREIhh46X/1m0vuOFhwh5qV5skYj0JoUxERERkZIJCLLFw5afz2LQojGR/kphTERERKREXNcnfuCcovXxCUfgWlozJtJfKYyJiIiIlIjvB9iD9yc8dP8edSYcpfqos8l6ulwT6a+0m6KIiIhICaX8KIPOupzUq/+m48WHCXIZYhOOoPqos0lZ1eCXuoUisq8ojImIiIiUUBBAhxfDOfhU6qccgyHAtaK0e5aCmEg/pzAmIiIiUgZcN8Al1vkbr7RtEZHeoUnIIiIiIiIiJaAwJiIiIiIiUgIKYyIiIiIiIiWgMCYiIiIiIlIC2sBDREREZCfYtkXOSpPxs4QshwhRcC2CoNQtE5G+SmFMREREZAcCx+W1zW/wm5fvoSW9GWMM0/ebxkcPPotQPkagRCYiu0HTFEVERES2w7Ytlrev5Efzb6clvRmAIAhY8PaLfOepH+OFsiVuoYj0VQpjIiIiItuRszL89pU/F6xrbF9PY3I9xphebpWI9AcKYyIiIiLb4eGyvmND0fqlm5Zj2wpjIrLrFMZEREREtsPCIupEitYPSQzSJh4islsUxkRERES2I0KMk8YdXbAuZDlMHDQOz/N7uVUi0h8ojImIiIhsh5cPOGnsXKYNPaBbecSJ8OXZ/0XYi5WoZSLS12lrexEREZEdMNkwlxxyHu1eBytbVlMVqWBE1TBCXpTAK3XrRKSvUhgTERER2QkmH6KKWg6prSMIIMgFaKmYiOwJhTERERGRXeD7imAisndozZiIiIiIiEgJKIyJiIiIiIiUgMKYiIiIiIhICSiMiYiIiIiIlIDCmIiIiIiISAkojImIiIiIiJSAwpiIiIiIiEgJKIyJiIiIiIiUgMKYiIiIFGVZBmNK3QoRkf7JKXUDREREpPzErSwmu5n8htXYFbXYNQ2kiOP7pW6ZiEj/oTAmIiIi3VTYaZr/+iOyqxd1lVmxCoZ8+Eoy8QY8r4SNExHpRzRNUURERLpEHJ/2p/7YLYgB+OkOmn5/DTE/WaKWiYj0PwpjIiIi0iXkpeh47fGCdX4midf8NkaLyERE9gqFMREREekSeHnw3KL1bvsmLEthTERkb1AYExERka3sCFa8qmh1eMhoPE+7eIiI7A0KYyIiItIlayWomfMfBevCDWMhXtfLLRIR6b+0m6KIiOwzYdsn4qdw2zZgbAeroo6MieN6muZWrlwvIDZ2OrUnemx+4g/4mQ4wFvHJM6k55nw6/Gipmygi0m8ojImIyD4Rs/PkXn+MtY/fBX7nGiQTiTP49M9iBk0g7yuQlau0F8aZcDRDxh4O+QzGCZN34rS7dqmbJiLSr2iaooiI7HWWZWDjclr//ZuuIAYQZFM0/ek7RNzNJWyd7AzXDUgGCZLOIDqoJKsgJiKy1ymMiYjIXhchy+an/li4MvBJvvIooZAu7kVEZGBTGBMRkb3OBB751qai9flNq7ECrxdbJCIiUn4UxkREZK/zLYfw4FFF6yP7TcLTV5CIiAxw+iYUEZG9LuuHi26PbkIR4pOPwnV1VpWIiAxsCmMiIrLXBUFAvmIY9Wd8rtsBwk7tMIZ+5Buk7MoStk5ERKQ8aGt7ERHZJ3K+gzPsEIZc8B3IdIBlEYQryJgYnheUunkiIiIlpzAmIiL7jOsFuMQhHO8s8AEUxEREREDTFEVEREREREpCYUxERERERKQEFMZERERERERKoE+EMd/3+eEPf8icOXM45JBDuOSSS1i9enXRx993331MmjSpx681a9Z0PebBBx/k1FNPZerUqZxxxhk888wzvfFWREREREREgD4Sxm655RbuvPNOrrnmGu666y583+fiiy8ml8sVfPySJUuYMWMGTz75ZLdfw4YNA2DevHl86Utf4pxzzuHPf/4zs2bN4tJLL2XZsmW9+bZERESkjDi2IWFSJLxmKkw7EccrdZNEpJ8r+90Uc7kct912G1/84hc55phjALjpppuYM2cODz30EKeddlqP5yxdupRJkyYxePDggq/5i1/8ghNOOIELLrgAgCuuuIIXXniBX/3qV1x99dX77L2IiIhIeYpZOdwVz9L0+F34qTYwFvFJM6g55gI6gjiBNgEVkX2g7MPY4sWLSSaTzJo1q6usqqqKKVOmsHDhwoJhbMmSJRx33HEFX8/3fZ5//nm+/OUvdyufOXMmDz300B6313H6xGAjtm11+69IOVC/lHKkftn/2bbBW/YizX//+dbCwCe1eB75TY3Uf+h/yBArXQMLUL+UcqR+uevKPoytW7cOoGuK4RZDhgzpqtvW5s2bWb9+Pc8++yx33nknLS0tTJ06lS996Uvsv//+tLW1kUqlaGho2KnX2xWWZaitTezRa/S2qqry+nIRAfVLKU/ql/2X27aJtx+7s2BdfsMqTHITtSMm9XKrdo76pZQj9cudV/ZhLJ1OAxAOh7uVRyIRNm/e3OPxb7zxBgBBEHDdddeRyWT4yU9+wrnnnsv999+P67pFXy+bze5RW30/oK0ttUev0Vts26KqKkZbWxrP80vdHBFA/VLKk/pl/xfNp/CSrUXrM43LyFaOxPfLZ66i+qWUI/XLraqqYjs1Qlj2YSwajQKda8e2/D9ANpslFuuZuo844gieeeYZamtrMcYAcPPNN3PMMcdwzz338KEPfajr9bZV7PV2lev2rY7neX6fa7P0f+qXUo7UL/sxy8HYIQIvX7Darqwn5/plFca2UL+UcqR+ufPKfkLnlumJTU1N3cqbmpoYOnRowefU1dV1BTGAWCzGiBEjWL9+PTU1NcTj8V16PREREem/clacxNRjC9aZcAynflRZBjER6fvKPoxNnjyZiooK5s+f31XW1tbGokWLmD59eo/H//73v2fmzJmkUlunC3Z0dLBy5UrGjx+PMYbDDjuMBQsWdHve/PnzOeKII/bdGxEREZGylPMsKmedRXTUgd3KrWiCoed8jbSpKFHLRKS/K/tpiuFwmPPOO48bb7yRuro6hg8fzg033EBDQwMnnXQSnufR3NxMZWUl0WiUuXPncuONN3L55Zfzmc98hkwmw/e+9z3q6uo466yzALjooou49NJLmTJlCnPnzuXuu+/m9ddf59vf/naJ362IiIiUQocbpfrUz1CTbSW/4S3sRA127X6kieNpVExE9pGyHxkDuOyyy/jgBz/IlVdeyUc+8hFs2+bWW28lFArR2NjI7NmzeeCBB4DOaY2//OUvSaVSfOQjH+FjH/sYlZWV/PrXvyYSiQAwe/Zsrr32Wn73u99x5plnMm/ePH76058ybty4Ur5NERERKaGUHyYZGoI7YjqZmvF0+HEG+B4EIrKPmSDQMYZ7i+f5NDcnS92MneI4FrW1CVpaklpgKWVD/VLKkfqllCP1SylH6pdb1dUldmo3xT4xMiYiIiIiItLfKIyJiIiIiIiUgMKYiIiIiIhICSiMiYiIiIiIlIDCmIiIiIiISAkojImIiIiIiJSAwpiIiIiIiEgJKIyJiIiIiIiUgMKYiIiIiIhICSiMiYiIiIiIlIDCmIiIiIiISAkojImIiIiIiJSAwpiIiIiIiEgJKIyJiIiIiIiUgMKYiIiIiIhICSiMiYiIiIiIlIDCmIiIiIiISAkojImIiIiIiJSAwpiIiIiIiEgJKIyJiIiIiIiUgFPqBoiIiIjsLMsyRElhMu342SR2RR2uEyfjhUrdNBGRXaYwJiIiIn2CZRnibjMb/vQd3Nb1XeXxA46i+tgL6XAjJWydiMiu0zRFERER6RNiJGm66+puQQwg9frTdCy8n7ATlKhlIiK7R2FMRERkNxhjiNp5ElaKhJXGcUypm9SvGQN+6zq8jpaC9R0vPETYS/Vyq0RE9oymKYqIiOyikOUTyWyg5d+/JfPWa9ixCiqPeB8VU+bS4UVL3bx+ybIM7ub1ResDN0fgZsFO7JWf5zg2xkA+7+2V1xMRKURhTEREZBdYliGcWkfjHVdC4APgJTfT+tidZFa8RPWpl5HytXZpb/P9gEjdiKL1JhIHJwJ7OFMxauVwcm2kFi0A3yMxYTp+rI60H96zFxYRKUBhTEREZBdEyNDyyG1dQWxbmbdeozq5ERMfTqDlS3tVEICprCdUN4x8c2OP+uqZHyBnV4C7+3/wMStH5rn72LDwr11lm5++m/jko6g69kKSnkK2iOxdWjMmIiKyC+wgT3btm0XrMytewrbtXmzRwJEK4gz+0FeJDJ/cVWbsEFVHnkH0wGPI70EQM8Zg2hpp2yaIdf3cxU/jrn0d29Zlk4jsXRoZExER2SUGbAc8t2CtFY2zx3PlpKAgCOgwFVSf/nnsfJLAzWEiCXJWnKS3Z0EpbPu0P/u3ovXtC+6n+gNTSKPpiiKy9+gWj4iIyC7I23ESU+YUrY/ufyiu23MKo+wdQQBpL0yHVUsyPJSOoILcHgaxzhf28dMdRau9dAcEfX8zD9s2eKEcHXYrbaYFN5TFsrUTqEipaGRMRERkF2RdQ/V7PkR2zeu4Leu61dWdcmnnuiVlsT7HMyFiE6aTWb2oYH1s3GF4dhQKD4j2CZYNTe56frzgl6xPbgSgJlrFJYefy5j4aPA0vVaktymMiYiI7KKOIEH9f3wdr2k56TcWYlfUEZ8ym1yoipyvC9q+yHV9KifOoG3+vXjJ1m51Jhyl8vD30u727RGktJXkmsd/QN7Ld5W1Ztq48amf8e3jL6fGDNLGMyK9TNMURUREdlEQBCT9GLkhBxE5+mLsw86kw64j5+seZ1+WpIKh511DYsrszmEkDLHxh9NwwbWkrKpSN2+POCGLx1Y+0y2IbREQcM/rD4KjIV2R3qZvDRERkd3k+wG5XB+etybd+H5AO5XEjr6IqjkfAQOuiZD0nUInGfQpHh5vtqwsWr+idTX5II+Dtu8X6U0aGRMRERHZRtaz6QgSdPgJMp7TL6bu2VjsVzG0aP3QxGAco3v0Ir1NYUxERESkn3PzASeOm4uh8Lq3Mw84BctTGBPpbQpjIiIiIgNAgko+O+tiIs7WqYi2ZXPBtLMZFm3A9/vBEKBIH6NbICIiUpAxEDNZrHwHXqodO1GN5yTIBOF+MW1LZMDxLCZUjOf6E77KpnQLXuAxOD6IsB8l6OM7RYr0VQpjIiLSgzFQYZJsuvcmso1vdpVHR02h7n3/jw4/rkAm0gcFnsHxogy1h3UW5ED/lEVKR9MURUSkh6jJsum+H3QLYgCZtxbR8vefE7F6bo8tIiIiu0ZhTEREerDzSbJrlxasS694EcdN9nKLRERE+h+FMRER6cHPbj9sBblML7VERESk/1IYExGRHqxY5XZqDSYS77W2iIiI9FcKYyIi0oPnJIjtf0jBuvgBs3BthTEREZE9pTAmIiI9pL0Qtad8kvjE6bDlkFhjkZgym+pjLiCjw2GlRBzHwnF0+SIi/YO+TUVEpKB2L0bi+E9SffR5BLk0JhInbyfo8OxSN00GoKiVw8m3k37jRQAqxh6KG6og44dL2zARkT2gMCYiIkVlPAdMNUSqOwu80rZHBqaYnSM1/246nv9HV1nro3dQNf00YoefTlqBTET6KI3zi4iISNmyLAObVnYLYlu0LfwrtK7BGFOClomI7DmFMRERESlbYZOnbf59RevbF9xH2HZ7sUUiInuPwpiIiIiUr8DDS7UVrfbS7Rhf82dFpG9SGBMREZGy5VkRYmMPKVof2/8QPEtrxkSkb1IYExERkbKVd6HikBMx4ViPOisSJ3HwseQ1S1FE+iiFMRERESlrKauShvO/TWz/aXSee2eIjT2Moed/m6SpLHXzRER2m7a2FxERkbLmeZB0BlFxyn9T42cAcK0oSd8h8IMSt05EZPcpjImIiEjZC4Kg89w7KjoLtGeHiPQDmqYoIiIiIiJSAgpjIiIiIiIiJaAwJiIiIiIiUgIKYyIiIiIiIiWgMCYiIiI7xRiDMaVuhYhI/6HdFEVERGS7IpZLyE/hbliDcULYtcPIWnHynu7piojsCYUxERERKSpm5ci+/Hc2PvMXCHwAjBNm0Gn/j3DDgeR8u7QNFBHpw3RLS0RERAqyLEOw4U02P31PVxADCNwcG/9yE+H85hK2TkSk71MYExERkYIiZNn89N1FagM6XnqEUEiXEjKwWZaBkIsbzuCFs9ghLayUnadpiiIislNCDth+nsByyHmGICh1i2RfM4GL17axaL3b0kgk8ABdfMrAZOyAZm8jd7x4D4s3vknUiXDC2DmcPO4Y7FxYn5OyQwpjIiKyXbYF8aCd5Iv/JrnyZeyKOipnnIZfMZSMHy5182Qf8q0w4aHjSC9/vmB9ZOQUPGzAL1gv0p9ZlqHZ28jXHr0R/51pvBk3y1+XPsKrTUv4wpGfxMrpM1K2T2FMRESKMsYQy22g8TdfI8ilu8pTS+dTc/S5RA44lqwfKmELZV/K+g7Vcz5MevkLQPdb/CYcIz5pFu2ugpgMTL6d544X7+kKYtta2bqaxuR6RoRHEWh4TLZDE71FRKSoqJWj+aH/6xbEtmh97HeEvFQJWiW9JQggHxvMkA99Bbuqvqs8PGQ0DR+9mpRVUcLWiZSWa1wWb3yzaP0L617FcXSpLdunkTERESnKdtNk1ywuUhuQe3sJ9uiZeJ7u/PZXOd/Grp/M4HOvgVwKYyy8UJwUUXz9vcsAZjBEnQgZN1uwvipcqTVjskOK6yIistsCX5s3DASe55P0YySdQXTYtaT9CL6vq0wZ2MJ+hOPHzi5aP334NFzX68UWSV+kMCYiIkV5TpTIsHFF6yMjD8DztGZIRAYez4VTxh3LmJqRPeouPuwjxIiXoFXS12iaooiIFJUNItSefCnrf/M1AjfXra5q5unk7YQ20hORAcvOhfnCkZ9kXaqJ5xtfoSpcyfTh0zqDmGuXunnSByiMiYhIUb4fkI0OoeGiG2h/9m9k33oNO1FL1ZEfgLrRpLWToogMYEEAVi7M8NBIRo8dTRCgqYmySxTGRERku1zf0GGqiRz5EeIzcgSWTTYIac2QiMg7giAgn1cIk12nMCYiIjsl5xkgAh68+8wpERER2XXawENERERERKQEFMZERERERERKQGFMRERERESkBPpEGPN9nx/+8IfMmTOHQw45hEsuuYTVq1cXffwbb7zBpZdeysyZM5k1axaXXXYZa9eu7ar3PI+pU6cyadKkbr9+9KMf9cbbERERESnIGB2iLjKQ9Ikwdsstt3DnnXdyzTXXcNddd+H7PhdffDG5XK7HY1taWrjooouIRqPccccd/OIXv6C5uZmLL76YbDYLwMqVK8lms9x77708+eSTXb8+/vGP9/ZbExERkQHOGPBDedqtVpan36SFjXjhHJalYCbS35X9boq5XI7bbruNL37xixxzzDEA3HTTTcyZM4eHHnqI0047rdvjH3nkEVKpFNdffz3RaBSAG264gWOOOYbnn3+eWbNmsWTJEioqKpg8eXJvvx0RERGRbtxwllsW/pLFG5d1lQ1N1HP57E8Tp1LHSIj0Y2U/MrZ48WKSySSzZs3qKquqqmLKlCksXLiwx+NnzZrFLbfc0hXEACyr8222tbUBsGTJEsaNG7ePWy4iIiKyAyGf37x8d7cgBrA+uZHrn7yFvJ0pUcNEpDeU/cjYunXrABg2bFi38iFDhnTVbWvEiBGMGDGiW9nPf/5zotEo06dPB2Dp0qW4rssnPvEJFi9ezNChQ7nwwgv5wAc+sMftdZyyz7cA2LbV7b8i5UD9UsqR+qXsS0mSLHz7pYJ165Mbacu3M9iJ9ahTv5RypH6568o+jKXTaQDC4XC38kgkwubNm3f4/DvuuIPf/OY3XHnlldTV1QGdG3z4vs9ll11GQ0MDjz32GF/5ylfI5/N88IMf3O22Wpahtjax288vhaqqnh/wIqWmfiml4OezeMnNBJ6LFY7iVNZ1q1e/lH1hc0sLwXYOUW/PdTBx8P5F69UvpRypX+68sg9jW6Yb5nK5blMPs9kssVjxv+ggCPjBD37AT37yEz71qU9x/vnnd9X99a9/xfM8EonO4DR58mTWrl3LrbfeukdhzPcD2tpSu/383mTbFlVVMdra0nieX+rmiADql1I6MVK0PfVHOl59DDwXu6qeuuPOx9rvQDw7qn4p+0zYChOyHPK+W7B+UKyWlpZkj3J9Xko5Ur/cqqoqtlMjhGUfxrZMT2xqamLUqFFd5U1NTUyaNKngc/L5PF/5ylf461//yle+8hU+9rGPdavfNtRtMXHiRO677749bq/r9q2O53l+n2uz9H/ql9KbElaGjffeSK7xza4yr20jG/5yE/VnfA5GHt5Zpn4p+0DEiXHy+KP569J/9qg7YPAE4lYcN1+836lfSjlSv9x5ZT+hc/LkyVRUVDB//vyusra2NhYtWtS1BuzdLr/8cv7+97/zv//7vz2CWFtbGzNmzOCee+7pVv7KK68wYcKEvd5+EREpX8ZAkNzULYhtq+VfdxBy23u5VTKQ+C6cMvY4Tpt4AiGr8x65MYYjhx/Kp4+4AJMPlbiFIrIvlf3IWDgc5rzzzuPGG2+krq6O4cOHc8MNN9DQ0MBJJ52E53k0NzdTWVlJNBrlnnvu4YEHHuDyyy9nxowZbNiwoeu1Kisrqaqq4sgjj+Smm25i0KBBjB49moceeoj77ruPn/3sZyV8pyIi0tssyyK39o2i9V7bRnB7nmkpsjeZXIj3jTmJE/afQ9rLELHDRIhBtuzvmYvIHir7MAZw2WWX4bouV155JZlMhunTp3PrrbcSCoVYs2YNxx9/PNdddx1nnXUWf/3rXwG4/vrruf7667u9zpbHXHvttfzoRz/i61//Ops2bWLcuHH88Ic/ZM6cOaV4eyIiUiJBEOBUDir+ANvB2H3iq1L6ON+FEDFCxGAAz+4yxmDbBt8PdL6aDAgmCAL19L3E83yam3susi1HjmNRW5ugpSWpOb1SNtQvpRQqTAfrbv08QYERsIppxxOfcz4V1ZXql1JW+tvnpWUZ8k6GdckmVm9ey7DKIQyvHEbEi+F5ulTtK/pbv9wTdXWJ/rGBh4iIyL6UMQmGfPh/aPrDtd0CWXjYOKqO+iBpX1PFSsUYCFs+jp8hMIacFcd1d+7C3HEsHL/zwGTXig74C8NyZowhbXfw7cd/yKZUS1d5VaSSK+deRqVVo1Ey6bcUxkREZEBzfQNVY2j4xPfIr1+B19FMeNh4TGIQHX4U2y51Cwcm2w6I5VvZ/PgfSS9/ESsco/LwU6g4YA4dXs9dkbcwBhJWmuzyF2l7uXOHwoppJ1AxZhpJP4bmA5Uf38nxowW3dQtiAG3Zdm58+mdcOfsz2H6kRK0T2bcUxkREZMBzfeigAqthauddet8n0EBKyRgDsXwL63755a7RSi+bovXfvyX9xnPUvP+zpPzCgSxhpdn4p++Q37Cqqyy79k3CQ/dn0FmX0+HpMNpyk/bTrGhZXbCuKbmRpJeiCoUx6Z8090JEROQdvh/geb5GT0osbLm0PnZnwXV82bcXE2xuxBjTo85xLLLLX+gWxLbIrV9BbtUrO7WG490itk8F7SSy66gIWolZeQr8eNlNOW/7O5Zm3EwvtUSk92lkTERERMpKKMiRfvP5ovXpxc8Qfs94cjmvW7njZ9j8cs/Dk7foeOkRqkYfisfOn91VYWdpf+ZPbHz5X+B3/rzo/lOpO/mTdJBQcN8LEqE4juXg+m6POoOhOlIF+RI0TKQXaGRMREREykqAwYTCRetNJN4rISjiBHQs+AsdLz7cFcQAMiteZuNfvkfMyu77RgwAkSDGaROPL1h37P6zOs9cE+mnFMZERET6INs2JEyKRK6JRH4DCSu9W1PwylHeilExrfDFOUBiymzyea9HuWtFqZha/HkV004gvwtrj0JekvYXHy5Yl1u3DCvTttOvJcX5ruGEMXM5f9rZVIYTAMRCUc6ecipnTXof5PtHvxYpRNMURURE+piw5WE1LaXpwZ/gpzoDgV05iPr3X0aualTnDpF9WM6FyiNOI7P8RfKb3u5WV33UB3HD1QUPRnZdn4qxhxIeMoZc08pudeGhYwmPOpgOb+d3ZglyafB6Tp3r+nltGzD1Q9CRrXvO5ELMHnokRzRMww1cHOMQCWJ4uV37s7VtQ87OkHRTGAwJJ0bIi+Htwt+7SG9SGBMREelDjIFQZiPr7r4e2Hqh6rVvYv1d1zDsEzfSYWpK1r69pcOPU/+hK8mvX0b69aewYpUkph2PF60l4xdf85X0Yww6+wpyK1+i46V3trY/5ETCow8m6e/adDcTioKxKLa1pl1RpyC2F7lugEO06+LUYxf/bB2fFam3+Nmzv6H1nVHL+ngdn55+IcPCDfhe375JIf2TwpiIiEgfErF82p6+GwpdqPouHS8+TGj6h8nv5OHI5SoIAjqCGNbQg4kOnwZAMucVHBHr/jzo8GI4+x9F1ejDAEPeRHZpRGyLvB0nMWU2ydce71EXGjScIFazw/ZI7zAG2vzNXP/kTwi2+bexMdXMt5/4Idef+FWiXkUJWyhSmCbhioiI9CHGz5Fr6rl1+xa5xmXYQf/Zes73A3I5r8fOiTviuj4ZP0zGD+32FLWsZ1M191xi4w/rVh4aPIrBZ3+ZjDaWKB9OwF8W/6NbENvC8z0eXvYEdkgjY1J+NDImIiJSJsKOwQo8XGPjFhnZ8i2HUG0Dbuv6gvWh+hH4Rl/ve0uHF6XyxE9Rc2wSP9mKFa3AD1fQEcQI/L49+tifuEGeVa1ritYvb1mFG+QxuvSVMqMeKSIiUmJhyyWca6V9wd9xW9cTHXUglQfMJmUqePegTs4PUfWeD5Je8VKBVzJUHvZeOorvOSG7Ie2FwNRARU1ngQ8Fp4lKyTjGYWhFPY0dTQXrh1UMwTEOuza+KrLvaZqiiIhICYUsD1a/QONtX6TjxUfIrHyF1sfvovH2LxHLbsCyuk+tCoIAr6KBulM+iXG2nsVlwjEGn/kFcuGaXn4HImXAtTlj8ikFqwyG9044Fq//zN6VfkQjYyIiIiUUCdI0PvizHuVBLs2mB2+h5oyvkKb7AchZP0RozJE0fGIqfkczGIOVqCVjxXG1Y5wMQEEQUB+u5xOHnsOvX/oTeb9zeDjiRPjk4R+lyqoutimmSEkpjImIiJSIMQZ342rwC88rzK1bge2mwAr3qMv7hjwJSHQekksAmoMlA5lxHQ6vP5SDTzqATelmLGNRG60h4kXxXd2kkPKkMCYiIlIixkCwg7lTgW7ni+y0wDOEvBgN9vDOgpxOH5DypjVjIiIiJeL7AaEhY4DCd+2d2gaCULxX2yQiIr1HYUxERKSE8lac6lln9KwwFoNO+SRZozAmItJfaZqiiIhICWV9h9gh72XIiMlsfupPuO3NRPabQPV7ziYbHrTbBxaLiEj5UxgTEREpsbQXxho0merTv4QJPDwrTNK3tfubiEg/pzAmIiJSBnw/2LqFvXZFFBEZELRmTEREpJ+xbQvHsTFG23mLiJQzjYyJiIj0EyHbJ+Inya54Da99I9GRU7Bq9iMVRAmCUrdORETeTWFMRESkH3CsAGfjmzTefX23Q6RD9SMZ/KGv0O5pV0YRkXKjaYoiIiL9QCxI0nRP9yAGkN+4ms1P3EXE1m4gIiLlRmFMRESkj7MsQ67xTfDcgvXJRU8T8lO93CoREdkRhTEREZE+zhiDl2wt/gDfBU9bNIqIlButGRMREenjPM8nMXxS0XqnZii+EwHNVCzIGAgcH8/kAQgHUby8djwRkX1PYUxERKQfCOJ1REZOIbt6UY+62hMuImviKI31ZNnQzmbuevk+Xlr3GmEnzPH7z+bkccdg58LahVJE9ilNUxQREekHUn6EutMuo2rm6ZhwFIBQ/QiG/MdXCerH4XkKYu9mDHSYNr76r+t5vvEVvMAnnc/w16WP8N2nfowbypa6iSLSz2lkTEREpJ/o8KKEDjuLoYeegvE9fCtM1sQUxIpxfP746l/Je/keVWvaGnmrbQ3j4uPxfQ2Pici+oZExERGRfiTvQdKP00ElKT+iILYdefK8tP71ovXPrH4Ox9GlkojsO/qEGWCMgVDYxtaXi4iIDHAGiDmRovWVkUTvNUZEBiRdkQ8gvjFsaM/xywcX86M/vcLTL68l6wcYU+qWiYiI9L5wEOWkcUcXrZ87eha5nI4EEJF9R2vGBgjfGO57cgX3PbG8q2zeq42MGlrJ1z4+AxvNhxcRkYHFcwPmjJrJ842v8Gbzym51Zx9wKlVOFfRcTiYistcojA0QLR25bkFsi7fWt/PQ/Lc47ajReK7WFYiISHkzxmBZBt8PCPbCvvN2LsxnZlxMY3I9899+gUQoxlEjp1NhVWDyxS+TLMtg2xZBEODq+7MHy4acnSGZT2IZi7gdJ+xrMxmRd1MYGwDCYZt/PdYziG3xj/mrOHHGSHUGEREpW5ZliJPCa1lLfuNqooOGY9cNJ0Vij3Y7DAKwcmFGhEex/8QxBAHk817RI9mMMbihLKs7Gnl1wxLqY3VMHXoAET8GnlZ/AOB4LNq8lNte+D3JXAqAwfE6/t/MixjsDCXQzE+RLrr+HhAMmaxbtDaX9zoPtdTaMRERKUOWZUh4ray/65t47c1d5XZFDUPO+Topp26Pt58PgmCn1oflw2m+8+SPaWxfv7V9xuJzsy5hbGIseAP7y9QYQ1NuAz+af3u38g2pZr71+A+5/oSvEvbiJWqdSPnRLZwBwHU95hwyvGj9jAMbCNvqCiIiUp6iZNh47/e6BTEAr6OVjffcQJR0r7TDhAL+8Nr93YIYgB/4fH/e/5G3eqcd5SxwXP606G8F6/JenidXL9BxASLb0L+GAcD3A0YOqWDiyJoedbGIw3+cMJHA1xxuERGBiO1RYaWosFJE7PL4brByHeSaVhWsyzevxcp19Eo7cmSYt/q5HuXDqxr4j4PeT8pLQ9jDsgbu6JiLy+rNa4vWv9m8ksCUR78SKQeapjhAOCbgS+cdzhMvreXBp1eSzrrMPKiBs48dT9yx9nh6h4iI9G22bYh7m9n82O/ZuHgeAPFJM6mZcw5Jq7qk3xOBm9t+fT7bK1c0XuDhBd2DxPmHnI1j2Tyy7En+/Prf2b9mJP9x0OnUh+rBtfd9o8qMjc2Qino2Z9sL1o+qHo7BouiiPJEBRmFsgAgCsAk4/rDhzJ46DGMMtVVRUsmsdoESERHiQQfr7vgqfnrrRXTq9afJrHyZhgu+QzsVJWubiVV0bs/nF1jTZSxMrLJX2hE2YYZVDKGxowmAE8fNZV37Bh5e9njXYxZteIOvP/q/fOGoS5mQmIDnDaybnbYX4kNTTuPaJ37Uo84yFkePPhI3r+sOkS00TXGA8VwfB4jYhkhYWVxERCDkGJKvPtYtiG3hpztIvvoYoRJ+ZeStBJVHvLdgXcUhJ5C3E73SjpAf5cJDPtT1+8P3O5hHlj1R8LG3vfB7clamV9pVTnw/YL/4MC6Y9kFC1tZOkwjFufw9nyJewlAvUo526aN14cKFu/Ti06dP36XHi4iISO+z/Swdbxb/jk+/uZCag04gT6QXW7VV1rNIHP5+7Hg1bfP+gp9JYkXiVM14P9GDjiPp9c50QM/zGRkfwZVzP8Pdix5gU6qZgMIjXy3pzaS9NBUl+jMrJZN3OHLodA4bdjAtmc04xqYqUkXYi+AX39xZZEDapTD26U9/mo6OzkWyQRBgTOEFqlvqXn/99T1voYiIyD5g2xaOFRAYQz7vsxfOD95pITsg4icJcmmME8Z14mT9UK+2oRtjYUWKjy5ZkQSBZUMJz4dKehFCU05iyKT3YLwcgR0iZ1eQdHv5D821GR4ewX8dcRFvp4pvVAFgm4G3ZmyLwDWEiDHEinUW5LRKTKSQXQpj999/Px//+Mdpbm7mu9/9LrFYbF+1S8qQbVvYdmcA35mzWEREypExhoRJkn97CanFT2PFKqmYdiJevJ6MH9rnPz9u58guepR1T/+ZIN85jS065mDqTvkkHVQSlCCR5YIQlTPeT2bVqwXrK2e8n1wQgiKjQL0l7wbkiYMV72xKbwexd/h+gMk5NMSHELHDZL2eG4yMqRlB1IqWNMCKSPkzwS5+6jc2NnLmmWdy5plncsUVV+yrdvVJnufT3JwsdTN2iuNY1NYmaGlJ7nADD8syZH14bfkmFr6+nsE1MY6fPpKKiIMp2W1c6Y92pV+K7K5KK0XT76/GbVnXrbx61lmEp51Cxg93K9+ZfmkMOzWq5TgGlv6blkdu71EXqtuPQR++iqQf3fk3sxfF7SwdT/yO5Kv/7iqLjT+M6pmnY4XjBE4Ez4mTKeUIXpkxdsDy5HL+95mfdwvR8VCMrx/9Oaqo3We7UOrzUsqR+uVWdXUJ7J04x3eXwxjAPffcwze+8Q0efvhhhg4dulsN7I/6YxgzBjIefPWnT9Pc1n0h8qfPnsoREwfv3BWIyE7Qh7jsa2EnIDfvLtqf/0fB+mEfv5EOp75bWbF+aVsQJUWQbCbIZbCrh5C34mT94pNOEiZF06+vKLhRBsDQj15DumJkyT5WY1YWK91Cask8oiMPIL/pbVqf/CNBrvMw4+jIKdSd+imSpkpHorzD2D4pk+TJtxbwdvs6pgyeyKENBxFx4/v0z0ifl1KO1C+32tkwtlt7I5155plMmTJF0xQHgMBY/PJvr/QIYgA/vedlbv7ScUT34Z6ctm1hWQbfD/C8gf2PWkT2XNjP0PzKv4vWp15/itBhZ5HPb39umWMHhNvX0HT39dsEK0Pl4aeQmHEGSa/Ipg1ermgQA8hvWIVVNbpkn3dpPwKRBiLTP4i37Cla/vXrbvWZ1YtouutqBn/kajroG9cAIcdg+zkCyyHnmb0edAPPIkYlp44+CUxA4IOb8/FLPKVTRPqG3QpjxhgmT568t9siZSjn+ixctL5gnR/AouWbmD5p8F6/cLAsQ8YLeP3NjSxbs5lxw6s5YP86oo7BH2BntojI3hQQuPmitX4uw85suRDzkzTedc27DiMOaH/uQUL1I7DHzin4uWhsB+OEix5i7NQMJVMGI05Orp0Nj99VsM7dvAGvZS2mZnxJ1rftLNsOiHvtdDz3T5JrFuNUD6Zy+mm4sUFk98HawB0FeBGRQnTQlGyXFwRs77ogndv7e9RalqEllefKnz5NMrP19WMRh2//51EMqggNuEM0RWTvcE2Y2LhDSb/5XMH6+OQjSe9gao1tW2SWv1w0UG1++m7q9z+MVIGRo5ydoOKQE2l/9m896qxYJXbdcIIyCGPGz+N1tBStz61bhj1oAu67NtCI2B4hL0mQbseEIvjhCjLEen1Ko2UZoqlGGn/79a6/p+zbS0guepK6Uz5JeMwMcv7A3elQRMqHDn2W7Yo4FmOGVRWtP2jsoL0+Kpbz4bt3PNstiAGksy7X/XohWd18FJGdELPyVAStJDJrqQhaidl5sr5DzdEfxTjhHo+PjjoQKofucLTHsgz5jauL1nvtzVhFNvHOuYaKGe8nNqH7OZx2RS1DP3IVKbpvL29ZhpiVo8JvJeE1k7DSO7UGYYuQAwkrTYWV7FwPZhU+kubdAsvGROLFX7duvx4BK2FnyTzzexp/8VnW3fFVGm/7Is1/vIa427LTP3dviZJh0wO3FAzMzQ/dSiRI92p7RESK0ciYbJdj4D/PPJj/+enTPb54j5o6jMpYaK9v4JHM5Fm3KVWwbkNLmo5Mnpqouq6IFFdpp2n5+89Ir3ixqyw29lBqT76UVKiOhouup+3pe0gvfwErEqfyiFOJTphJh7fjnQx93ycyfCLtzz1YsD5Utx/+diY7drhRKk+4lJqjz8VtXY8dq4REHSm6b/hgWYZ4fhPND/6U7NqlADjVg6k7+VK8urE7HNmpsDOkXvonTc89gJ9JEm7Yn9rjLsStGrnD5+bsCqqOOJXNT/2pR52JxHGG7N9tOmXIMaRffoSOFx/q9tj8prdpuuubDD7v2yQpHu72NstNkd9QJDD7LvmNqzH1U8p6mqWIDAwaGZPt8v2AodVRbvzvORw+eQixiMOwQQk+ddZUPv6+KVj74Ivs3dNe3i2f10YeIlJczM7T8vefdgtiAOnlL9Dyj58TNnk6TA2xuR9j8IXXM+icbxJMOHanghiA5wWE9puIFS88a6DmmI+SNdsPHmkvRIdVS3bQZJKx4ST9nlP5EkEH6397VVcQg871Wk1/uJZQqgljio82xe0sLQ/+hM1P/RE/07nLb27dCtbf+Q3slhU7HF3LuwHxqScSn/KebuV2opqh51xF2uo+ghf2krQt7Dn1EsDraMFvWbvd9u51O/pu8j16szkiIsVoeEF2KAgCauMOnz7rYDwvwBhDxDFdW5bajkUm75P3fBzbIhay8PZgO9PKRIiQY5Ev8BqObVFd0XN6kYjIFnY+SXrFSwXr0stfoMZNgqkh61nQta5r1z6z0qaCoed+k033/5Dc+hUAWJE4NcecB0Mm7PT07WKZwXEs0m88h5/pKPQsWp/4HZUnX0YmKPw1blItZFYW/jNoefg26j58FSm2Hz47vAiJoz9G9VEfwm1dhxWtwKp4ZwTvXdPFjZcjyBae0QCQb16LVTex19b7+qE4Tu0w3JbGnpXGwhk8uiw2ShERURiTnRIEYIIAxwAEXaNXvjE8u6iJOx9eQmt7lmjY5r1H7c/7jhqD5e9eIIs4hg+fMJHf/n1xj7qzjx1PxLEItM29iBQRZLd/3mOQTUG0Zo9+hucFpJw6as78MnY+SeC5mEiCrJ0gsxf2NbINpFa9UrQ+17gMO8hR6Gvcti2ya3p+fm6Rb16L5WXB7HgkMOOFwKrBDKrpDI5FPnoDO4QVieMXCWShQcN7NfxkTZxBp/4n6393Ne9OjjVzzyFvxXc1f4uI7BMKY7LbLNviiZfWcvtfF3WVZXIef/73m6zblOTi06ZgdmMaY+AFHHvocIbUxLjzoSWsb04xuDbGR06cxNRxgxTERGS7TCSxg/q9s3bJ9wPSRMCOgA0EwF7aYDYwBqd2WNF6u7IO39gUPsoqwIpVFn9xy+78tQsfzzv6KM/ZCapmfoDWx39XoK2DsGv269VdIj3PJ181kmEX3UDbgnvJvb0Uu6qeqllnQfVw0tpJUUTKhMKY7LaM63PXw0sL1j3zSiPnnjSJRGj3liVaQcCh4wcxZcws/CDAetfUSBGRYrxQguj+U8mseLlHXWz/Q/CcBJT5rqy5nEfFwcfSNv9+CqWm6llnkzMxCg3veF5AfPjEzsD17vmEQGLyLPJWbK/+GeRdSBx4DJXpNtqf+3vXzw0PGU39Bz7/zuYdvTstMO9Z5O06YnM+RsLLElgO2SDU69vsi4hsj8KY7LZ01iWdLX4buHFTkgnDqnZ7tyrX7dyPzH7X1EgRke1JeyHqTvkUzX//SbdAFtt/GrWnfJJ2b+8f+Lsv5Jwq6s/4LJvuv5nA23pQdeXhp2IPP4DsdmYJZEyCwWd8jg1//h4EWx/n1A6jeu5HaPf2/shQ0osQOeJsKg49hSDT0XnOWChBkmhJA1DWNUD0nfCp7xERKS8KY7Lbws72v8wr42FtGywiJdHuxag65b+pzScJcilMOI4XSvSZIAaQ821Cww6m4eKbcDetIchnCQ0ZQ95OkPK2//Wd9y0YcgDDLvk+mWXP4bZtIjrmYJxBo+gI9t0oVdazyFIJ0XemSfrss58lItIfKIzJbouGLaaOr+flNzf2qKupiFBXFSlBq0REOqXf2Xyia7OOMp+aWEjes8hTgRl0AMZA1g92euOJvG+Tpwpn0vGEjCHn+e9soqFwJCJSLnTOmOw2Kwj49NlTGVbffbF8Ihbia5+YScTSIS4iItuyLEPcypBwN5DINFJhkoTtHYejIAh2e6qf6/rk815JpgoaAxEnIGrlCen2r4hID/polN0WBBCxDFdfciTrm1Msf3szDYMSjG6oJOIY/F46T0ZEpC+wbYhlmtjwl//FbVkHgHHCVM/+MLHJc0n7/esMxYjl4qQ20L7wftzNTYSHT6Ly0JNIW9UMhL2YjIGole88+iDbgYkk8EIJMn54h7tTisjAoTAmeyQIAmxgeF2MkfWJrru3CmIiIt3F/A7W3/n1bmdxBW6O1n//hvqqeuzhh+30YdHlLmx5+CsWsO4fP+8qy659k44XHmboud/Ajw/v17saGgMVVprmB35MZtWrXeXR0QdRd+p/0eHHFMhEBNA0RdlLgqDzXJf+/OUqIrK7bNsit2ZR0UORW5+4i0hQuK4vigRpmh++rUd54ObY9MAtRMkAEHIMMStL1HKx+tHU9qiV79zNc5sgBpBZ9SrND95C1MoXeaaIDDQaGRMR6YfCDoS9JPgugR0mayV0Tl8J2bYh17isaL3bsg5rZ3fmKHPGGPKb1oBf+OiT/MY1WPkUlU6ejhf+Sfubz2FHE1ROfz/W0HGkvL6/+ZOdTxY85w4gs/IVavMdYNX2cqtEpBwpjEnZsiyDZXcO3voadRPZaRV2ho5n/0bzCw8R5LPYFTXUzP0IsVGH9rt1SX2F5wWEh44tWu9UD8HvT5NV/O0HS4PHul9diZ9JApAHMqtfJ3HQXBKzP0ra79uBLMhtf5QzyKUhqjAmIpqmKGXGtg0uhs0Zj3Wbs7y1oYOHFq5mRVMHnuk/U1hE9pWYlaP14V/QvuB+gnwWAK+jlU0P/IT8snna0a5EPM8nPOpATDhasL569ofJWfFebtW+EQQBTv1IMIUvMZzaYbit67uC2LaSrz6OlW7Z103c50xk+3+XJtw//q5FZM8pjEnZsCzDxvYcV/3iGT73/cf48o+f5Fu3LSAAXlvezE/ueUWBTGQH7HwH6TefK1i3+Ynfd05dlN0SsnwqrBQVJknUdtnVj6O0qWToR76BXTloa6HlUP2eD+KMmtqvppHmrBi1x3y0Z4XlUH/qf9Ly2O+KPjf9xgJCIXsftm7fc50EsbGHFayLjT0Uz0kUrBORgUf3SKVsZLyAK3/2DOns1nUGmZzHb/++mP/+8CE8/fJa3lyzmQNGVmvKokgBlmXIN71dtN7PJCGfBl0I7hJjDPnW9SQf/yPJRU+A7xMbdyg1x5xH2qllZzdA9PyATHw/Bn/0W5hsO76bx4pXk7PipLz+dW805ztEJ81l6LDxtM37M+7mDYT3m0jVzNMx4Rj5TWu38+y+f9Mt44WoPfkSePj/ut0ciY07jNqTLqHdC5WwdSJSThTGpCw4jsX819Z3C2Lbuu/xZZw4czR/e3oFk/7jkN5tnEgfEQQBdrxqO48wGEdrxnZV1G9n7W++hte+qass/eZzZFa9xrCLrqed7f2Zd+d5PkliEIpBCAgAb++3uRxk/BCmcgyJk/8by8/jWxE6PEMk8IlPPpLU608XfF5s4gyS+b7/h9Luxag48VPUHJskyKYwkTiuk6Dd06WXiGzVv27FSZ9lWRZL3yq+TmB1UweDa2Pk8z4aFBMpLAjAVA7GilUWrI+NPQTX1lqVXeE4FpkVL3YLYlsE+QxtC+4n7OhDqZggCMh6NukgStbrHPHK+RY1c84p2E8rDjkBfx9ubGFZhriVpcJrJpFdR4XpIGzvu7+/jOfQYapJRofRYarJKIiJyLvoU0HKgu/7jBtezaPPrSlYv199gubNGY4+bDghy+DpUGmRgjJWnCEf/h/W33UNwTZnWoXqhlF70sV0+PrY3xU2Lskl84rWp5c9T2LmWeSI9WKr+rYggJRdTcMF3yH1+hOk31iIFa2kcsZpmNpRpPbRjp+WZYi7LWy893vkN7wFgLFDVB35AeJTTyLl9fy5jmNhLAMB5PvaaF3II0OGtkwbUSdKwkkQ8iKa5i9SZvStLGXBdX0OnzyUOx5cTLbAF95ps8cy/9VGPnXWVLydXaAhMgB5HmRiw2j42A24G1aSb20i0rA/pqqBjiBGEOhCbJcYCytaUbTajlUQGKtzuqHsNM8LaCeBc9B7qZpyHIGxyQbOPg0KcZI0/e4beMnWrrLAy7P5qT9hJ2pxxs/GdTt/vmUZsk6K59Yv4rUNSxlRNYyjRh5BLEgQuOW/pi2I5PnDovt4YtUCgnc659CKwXzxqE9Saap1Q1OkjGiaopSNqGO4+tJZ1FRuPV/GsS3OPnY8DXVxPnXWVMLqsSI75PnQESTIDTkIM/l40pVjSPpRBbHdkHOh8vD3Fq2vnH4aOaNRsd3lugEZP0zWs/dpELMsg7vxrW5BbFubn/ojET/V9dh208pX//ldbnvh98xf8wJ3L3qALz30LVYmV2HKfKNH24FHVjzO46vmdwUxgPUdG/j24z8kZ2dK2DoReTeNjEnZCPyAodURrv+v2bSlcrieT3VFhJBtCBmD5/k7Okd0rzAGLNvC8wMcy/Sr7aZlYPH9QFOS9lAQAFUNVB95Opvn3detLjb+cEKjDiZX5qP1jmNjDLiux0DN45ZlyK1fUbTeS7Zi/M4NpDw7x08W/JpkvvvBzX7g84P5t3L9CV/F8QqfF1cOMibNg2/+u2Bda6aNdckmRoRH6eaMSJlQGJOy4vsBDlAX32bbXz/A66U5QIExbGzPct8Ty2luy3DIxMHMPWQ4UdvoolZkgMoSoeaos4lPmUtq8TP4bo74pCMhUU/Si+z4BUokYuUJ5dtJL16Al00TG38EVA4h5Zdvm/cV3w8I148sWm/FKgksG3xI+2lWtKwu+Lism6UptZHhoRFlG2xd3yXrZovWN3Y0Map+dK9PVXQcC8uy8Dxfyw1EttEnwpjv+9x888388Y9/pL29nenTp3PVVVcxcmThD9aWlha+9a1v8fjjj2OM4X3vex+XX345sdjWqSQPPvggP/rRj1izZg1jx47liiuuYNasWb31lqQMBcbw+Etr+dUDr3eVLVrRzL2PLeO6T8+mMmLrTqLIAGXHKshkDPahZ2ADadcjKOPryYiVx138bzb++7ddZW3z7yU66kBq3/ffdJTxyM6+4PsBzpD9saIV+JmOHvXVR55B1kp03vzbwV9s1s1CyFCuCwVDVohEKN5jZG+LEZUN+L0xzeQdxoaslWJe4yusblvL5PrxHFA/gbAb001OEfrImrFbbrmFO++8k2uuuYa77roL3/e5+OKLyeVyBR9/2WWXsWrVKn75y1/ygx/8gMcee4xvfOMbXfXz5s3jS1/6Eueccw5//vOfmTVrFpdeeinLli3rpXck5Sjj+vz6wdd7lCczLj+/9xXK+LpLRHpJPu+Rz5f/dL9QtoXWbYLYFpm3XiOz5Gkcp/w3odjbUqaCoed+A6d68NZCY1F5+HuJHDCna/OOmB2jJlr47DiDYb/KhrK+MRcJYrx/0gkF6wYnBjE4Xt9r/deyoDH7Nl96+Fvc8fLd/HvlM/z02Tv46r++S4fZjGUNvH4o8m5lH8ZyuRy33XYbl112GccccwyTJ0/mpptuYt26dTz00EM9Hv/CCy+wYMECvvvd73LggQcya9Ysrr76au69917Wr18PwC9+8QtOOOEELrjgAsaNG8cVV1zBgQceyK9+9avefntSJmzb4vUVzUW/oF5dtoms1o6JSIlF7IAK00HCayZhkoQKzG8Jh206Xn606Gu0PfsAYa/wqEl/5vsBqfBg6j9yNcMuup6hH72GYZd8n8iMs0m6W7e1j/hRLjr0Pwq+xvsmHk84KO9RRc8NmD1iJqdNOgHH2tpBxtaO4n9m/zcht/fan7MzfO+ZX+C+sx5vi45ckpsX3o5rF76pLjKQlP00xcWLF5NMJrtNIayqqmLKlCksXLiQ0047rdvjn332WQYPHsy4ceO6ymbMmIExhueee45TTjmF559/ni9/+cvdnjdz5syC4U4GDm8H0yXK9z6oiAwEFXaG9mfuZuMrj4LnYkXiVM06k/gBc0m9a+2an9xc9HX8TAfGBAPyQ833A5LEIBSDLUuT33WaiucFjK8cy9eP+Rx3vXIfK1tXUx+v48wDTmFy3QRMrsy3UwRMLsT7xpzI8WNmk8qniThhoiaK5Ybxe3FUrz3fTnW0kryfJ+flu9Wtan2bjJ8mTqjIs0UGhrIPY+vWrQNg2LBh3cqHDBnSVbet9evX93hsOBympqaGxsZG2traSKVSNDQ07NTr7SrHKfvBRqBzJGjb//Ymx7EwXbsjls/VwIFj64rWTRhZQyxsMwBn9vSqUvZLkWLKoV9GyNL695+RXv5CV5mfTdH6799S7eWJTnsfrr/1Ayo2eSbJxU8XfK3YmKkEdhTH0r+z4iyGR0bwmRkX4wUuFhZhop3fWWVy5bTDfhlAnAriTkXX77EB9v0XmbEgTYpNba3MGT2DEdXD2JRq4Xev3NdtcxE38PrMdZPsnHL4vOxryuQjpbh0Og10BqptRSIRNm/ueecvnU73eOyWx2ezWTKZTNHXy2aL7z60MyzLUFub2KPX6G1VVb13Pk4m67KhNc3j899i/aYUR0wZygFj6hhcG++1NmxPKJXn/XPGcv8Ty7uXOxafOnsqg+v61t9tX9ab/VJkZ5WqXwaeS25DU7cgtq22efcyYuqxhGqHdJW55gCc2gbclnfdZLQd6o7+COGaavSJtjN2/vvJy3QQZDNgDFaiCsvunRGfcvu8dH2PNzYt57rHf0xmm+A1cdBYLjvyIr739C/wfI+KcILqaAW1CfXE/qjc+mU5K/swFo12zm3O5XJd/w+QzWa77Y647eMLbeyRzWaJx+NEIpGu13t3faHX2xW+H9DW1jfm4du2RVVVjLa2dK9sMRsALy1r5qa7nu9al/Xo82uor4nyrU8eRTxUHndQzpw7lmnj67n70Tdpbc9y4LhBnDl3HFUxh5aWZKmb1+/1dr8U2Rml7pcxt4Vc4xtF64N8FjfdQUew9aLWmBhDzrmKtnl/IfnyowRenuiYg6k97gIy4VqS+jzba2zjE0pvoOVfvyaz8lVMKELlIcdTMf00MiaxzzbLKHW/LCZjJbn2sZvJet2vs5ZuWs7Ct1/iyBGH8dRbCzl/6lmE3Ii+W/uZcu2XpVBVFdupEcKyD2Nbphw2NTUxatSorvKmpiYmTZrU4/ENDQ088sgj3cpyuRytra0MGTKEmpoa4vE4TU1N3R7T1NTE0KFD97i9fe2AYM/ze6XNWR++//sXenwpbWzN8Mu/LeLS0w+iV0503gnjh1XyxY8ciucHhByLwPPJ570dP1H2mt7qlyK7ohT9MmJ7tD7+eyqmbO/oFQNOuEfb8sSJzPoIlTPPAAJcEyHphwjyAWh/2L3CGIjmN9D4y6/AO5tUBPkMbQv/RnrFywz64P+Q9PftCEE5fV5almFF2+oeQWyLp956ls8fdQlzRs1gRHw4uVx5tFv2vnLql+WuPIYjtmPy5MlUVFQwf/78rrK2tjYWLVrE9OnTezx++vTprFu3jlWrVnWVLViwAIDDDz8cYwyHHXZYV9kW8+fP54gjjthH72JgsyzDkrdaiq4PW/DaurLaqdD3A0wQ4BgIBvhdHREpLSfIkn7zWYJcFruy8LrW2NhpuHbhqV4519Dhx+nwE2Q8p6y3ZO+LIpZL67/v7Api28pvXI236a0BtX27MYZNqZai9Xkvz5D4IEZHx2Dcsh8PEOkVZR/GwuEw5513HjfeeCP//Oc/Wbx4MZ/73OdoaGjgpJNOwvM8NmzY0LUWbNq0aRx22GF87nOf4+WXX2bevHlcddVVnHHGGV0jXxdddBF/+9vfuP3221m2bBnXX389r7/+OhdeeGEp32q/ZYwhlen5RbWFH4BXJqNiIiLlxWDCUVqeupvB7/sUdqKmW21o8EjqTr6UrK8L21KwgxzplS8XrU8vmY/jlP/ui3uL7/uMqxtdtH5QrJYQ4bLavEuk1PrEp/dll12G67pceeWVZDIZpk+fzq233kooFGLNmjUcf/zxXHfddZx11lkYY7j55pv55je/yYUXXkgkEuGUU07hK1/5StfrzZ49m2uvvZZbbrmFm266ifHjx/PTn/6023b4svd4ns8BY2qL1o8YUkHEsRmQ+yyLiGxHzopRechJbH76T2x66HYGnfAxgsDHa2/GqR1KaPAo2v142R9C3X8ZrGgCP9VWsNaOVw2o0cgggEHROsbUjGBl65oe9edOPYNIEMPVNFmRLiYYSJ8S+5jn+TQ3942FqI5jUVuboKUl2Stzen1j+L/7X2Peq9139jIGrr50FqPq43ieuuJA19v9UmRnlLpfVtppNt5zPbn1KwCwohVYsQoSBx1N+MATyPg6p6lUQg54Lz/A5if/ULB+2Cf+lw570D752aXul8UYA244yx9eu59nVj+LF/jUxqo59+AzOaBmoqYn9nPl2i9Loa4u0T828JD+wQoCLj79IA4aO4i/PL6M1vYsk0bXcuGpU6ivjOz1IGaMwQdcP8AyELaNwp6I9Ekdfoy6My/H37Sa5KInsWKVJA4+Gi9SqyBWYnkXKg4+jszyF8iu7b7jZe1xF5APVQ24vVJ8x8X18pw64VjOOOAk/CAgakUJezG8AX5xLlKIwpj0Gsv3mTt1GDOmdB64bZvORYt7fXDWMmxoy/Lbfyxh2ZpW6mtifPj4CUwcVYOleeoi0scEASSDGNagSUSPnQIEJHNev7/ID4VsjDG4rrfDNUbhsI0JAryg93c1TvpRak//Av7mRtJvLMSKVhCfdCT5UCXZARaWg0ieu167lyff2rpJWm20mstnf5oQ0e08U2Tg0jTFvUjTFEvPcSyWvt3Gd+9YyFFTh3PkgQ1goCOVJ5tzmXVQA0aBrGz1134pvc9xDE6QA2xygb1HGwaoX+49xnTuQGj7OQJjkbPiPf5MI5ZLKL+Z1GtP4CVbiE2YgTNkLMkg3uPmXdjyCLttJF95FLelkcjog4mNO5wkFb2+SYQxBsfpnJLUG8ehlFu/tB3DQ6v/xT2vP9ijLhGKc+3xX8bJKZD1d+XWL0tJ0xRlQMq4Prf/9TWuuGA6z7yyjpt+9zw512dwbYwPHjuBvBcQ3oNdhm3bIuMGpDJ5LMsQi9iELaOdoUTKhG0b4n4HqVefpO3NZ7GiFVTOOA1qRpL2w6Vu3oAWsnwi2Y20PnYX2bcXYyeqqZp5Bokxh5D0IgCELRdv2TNsfPjWrud1vPIYobphDP7w12gP4ltfz/Yxja/R+Jeb2LIBVGrpQjY/8QeGfvRqUqFB+H5A1MrjeCm8jmasSAKilaSJ7/XP7SAIBvSZlFmT5sE3Hy1Yl8yneGvzGsYnJuj7UuRdFMakX0lnPU49an/++M83WLJq61knG1rS/OSel/nMOYdy+PhBu3e3xjK8vrqVn97zCq0dWaBzJ8jPnnMo9RXaqlek1IyBuLeZdb+5stvudunlL1Bx2MnEZpxNRoGsJCzLEOp4m8bffh2Czs9fP5ti04M/IXHgXBJzziPthwl7HTRuE8S2yDc30jbvz0SOOpec23lHLeKnWHf/j3j3Trx+poPmB39C9elfwrYD2p74LclXn+h6nFM9hMEfvIJ0uH6frCW2bMjZGdpy7RAEVIWrCAfRQkeR9Stu4JHOZ4rWr+toYmLlxD7xXbnlbLi+0Fbp+8r+nDGRXWHbhvqaWLcgtq3fPPg6md0IYsYYNmzO8p1fP9sVxAByeY+X3thAxgvwjMG2B87hniLlJmx5tD5+Z8Ftxjue/wdObnMJWiUAUTI0/+PnXUFsW8nXHsfOt+M4Fuk3nyv6GslX/k3YTwOdn8nupjUEXr7gY7Nr38DxUqRe/DvJVx9n28Dmbm6i6a6riQV7f1mBcXze6HiTr/zzOr72rxv42qM3csU/v82rrYvA6d+jZo5xqI5WFa0fXTOyLDbSshxDPpSmzWoh43RAyMVs+ep2fPLhNEs7lvJ6++tkQ0mCfv73JqWnkTHpVxJRhzVNHT3KHdviPdP2Y+r4ejwfImFrl3Z18oE7H1rcrez0OWMZP6KG+55Yzh/++QbDBiX4yIkTGTe8GktLMUV6XSjIkFqyoGh9aulCQtPeP6CnkpWK5WXIb1hdtD67+nXsSUPJZ4sHpMDLs+VANWMgcHPb/6G+S9tzPdcvAXjJzXjNb2NqJ+7VTaTa/TZueuYXBNuEv4yb5ccLfsm3jrucOlPfb8+EiwRRPnjAqdz6wl096gbH62hIDCHIlfbNB6E8TzU+x92LHiDtdo7iHTh4Ipcc/lHCQZgXN77Krc//Du+dmwYGw+mTT+LE0XMx+YG1GYv0Ho2MSb9iA/sNTnQrG1af4KpPzMQyhtvuf40rfvwk9zy+HBfTNRVhRzw/YMXarXfbD504mEHVUb73u+d5c00r2ZzHysY2rvv1szz24tuYnXxdEelF/sBeTF5SxgKKfy6acBTX9YiOPbToYyIjJuNZndNMfT8gNHh00cc61YMxTpggV3zaXL6lcae/A3aGFYIH33y0WxDb1l8W/wOc/tsHPTfg0CEHc85BHyDiRLrKJw0ax//MuYyQW9rNO2zH8OKGV/nNy/d0BTGA1zYs5X+f/imtXis/f+63XUEMICDg3sX/4K2ONXu1r4hsSyNj0q94ns/YYVVEwjbZnIdl4JNnHsz/3vkcmzu23kW99/HlPPNKI9/65FE79Y/AsgxD6+K0JTtf46SZo/nRH18s+NjfPbSU90zdb482ChGRXZc3UWLjDyP9xrMF62MTp5PUqFhJuHaM2NhDSC9/oWelsQjvN4kOL4CKwURGTSH71qLuj7Fsao//GOkgzJYph3k7TuUR76P92b+9+wWpO+kSfCeKFa3Az/ScLQEQqh9JZi8GdC9wWdPWWLS+sX09buBi03/XLZp8iGP2ew9HDj+MtJfGsR0sDH7g49k5rCC894+z2UlZk+GPi97dVzqNqN6Pf7z5WNHn/mXxP/jMEReDr8tm2fs0MiZ9nmUZ8hg2duRY0ZQk7wVc//9mE484HDZ5KM++vr5bENuiqSXN80uburYi3h7HwH+cMLHbz0xlCq/Gdj2f5rZswToR2Xdyvk3NMedhReI96hIHzcWP1vR+owSArO9Qe/zHsBM1PeoGvfeT5KwYACk/St37LqPm6HM7H2s5xPY/hGEXfodcbEi3DRWyfoj49NOp/8BnCQ0eiRWJEx0zlYYLrsUbNI5sEKF61pkF2+NUD8GqbtirUwYdE2J0zfCi9SOr9yNk+v9UN8/tXD/2xKoFfPnh6/jCP67hCw9dzU0Lf042lCzZCJMb5Nmc6bmeFKAqUsHGVHPR5zanW3ED3ciRfUMRX/o0yzK0pPJcc9sCmtu2TjuYPXU/fvD5o2lqTfOTu18u+vwnXlzLjMlDdvhzfD9g/4ZKPnryJO56eOkOv0xCOxHwRGTvCgJI2TU0fOy7dLz4COllz2FFK6iacTrW0HGkvMiOX0T2iSCApF3DkPO/TW7VK6SXP49dNZiKqceRC1WT22bEocOL4hx4MvUHzMEQ4JkwSd8ptPcHKS+Cvd9h1J59AFbg4VlhUn6IwA/AD4hPnkN1NkXb/Pu6NvuI7DeBQaddRpI4796JcU94+YCTxx3LoyuewX9XYw2GD0w6icDt/1Mm7JDhkbee5oE3/tWtfFnzKr7zxM18dc5nsXO9PzroGIeoEyHj9rxZ+nbbOiYPGsdrTUsLPnd83RhCJrwXe4vIVgpj0qdl/YCrfv4M7anuO2o9+fJaBtXEmDSqhkjILvr8aNjGMgZ/m49YyzIYY/C8d32ZBgHHHz6C2dOGk3M9GgbFWbcp1eM1qxJhquL9/+6nSDnyfWinktDhZ1J7yKkElkUuCOOXwS5uA53vB3SQwB5zFLGxR4ExdOS8zh2S3sV1A1xiO/W6nueT5p2g7cG2ASvlhQkfchoNBx9LkOnAhCJ4oQQdfqQzsO1lCSq5/D2f4icLf83mbDsAleEElxz+UarsGoJ+vr09QJY0f1v6z4J165Mb2ZTexFBnWK9vZBIhxsnjjubeJQ/1qFvRsppPHHYOD7zxaLf1ZAC2sTjzgFNgAARpKQ2FMemzLMuwurG9RxDb4h/zVnLoxOnMPXQ4y94uvKX1ae/Zv2t3LixDzgtY9lYr7akck0bVUhkLdd8Z0Q+IWBCPOXzxo4dz5U+fJpPbOnXBsS0uP/8IIrYOghYppbwLeSI9Ls6l9DzPx+vFGV8515CjAiIV7zQA9lmf8AyjY2O45pjL6XA7d4ZMhBJE/CieOzD6Yc7P9wg021rbsZ5hdfv1+jb3Xj7gxLFzWdexgflvb127WB2p5IrZnyYeJPj6MZ/j58/9luUtbwEwrHIolxx2LpWmut/ugimlpzAmfZYxhsZNxbdBzuQ8MjmP2sooB40bxKvLNnWrn3PIcEYOqcD3A4xleLOxne/++lncbUbEpk8ZyifPOBjrXYu8PS+gviLM9z93NAsWrWfxqmbG7lfNUQcPIxayFMRERAYo3wuwvQjVW0brcuANoBsCIcshYofJeoWPHhiaGFyy70iTDXP+QR/iQweexvqODSTCCeqiNYTcKG4+oNqq4/MzPkkmyBAEAVErSsiP7tJROCK7SmFM+izf9xnTUPyAyapEmEzO5ZY/vcQnTj+IE2eM5vnF67Esw7GHj2R4fRzzzhdCOu9z3a8W9viCWLhoPZNG1XLiESN6fBj7fkDYwDHThnHsoftBAPm812PqizEG30Am7+P7AdGwTdiiLA6/FBER2ZsiQYwTx83lr0sf6VFXF6thSLyeYAdHxO1LJu8Qo5L9Y1WdOzvm6Fqq4PsBxg8R452lBh54hebRiuxFCmPSZwUBDB0UL7p268MnTGTJqhZyrs9P7nmZmsoIU/avY/TgSvbbJog5jsWzrzUWvVN33xPLmXvIfkX/sbjbuWNmWYa2jMctd7/E4lUtAIwcWsmnzprKsJpoybb4FRER2Rd8F04Zdyybs+08uWpB17lrwyqH8sVZnyTkRrut0y4Vff9KuVAYkz4tbOAbFx/Jj/7wIq+t6NyWNhK2+eCx4znywKH4U4YydXw9Dy94C8syHHf4SEY3VGJtE7yMMTQ19wxzW7Qlc51zxXdj7W7GC/jKLU+S3GYb/NXr2/naz57me5+ZS1XU1jx0EZEBzLIMEbLYuPhYZE28xwZSfY3Jhjhn8hmcMfkU2rPtRJ0IcTtByItoGr/IuyiMSZ/mv7Ohxuc/cijpnE8u7xGPOkQdC9/zsYADRlZzwKipnU8Igh5fBJ7nM3VCPX99akXBnzF2eDW2ZdjV1OQ4Fv9+/u1uQazrZ/oBv//nG1zy/inQx790RURk90SsPHbraloe+y35prdwaoZQ/Z4PERl+QN8/iiFvEyVB1Ep07pjpUxYjYiLlRochSZ8XBGD8gLhjqIk5hA342wQc3w/wPb/zV4E7cr4fMKahiqF1PQ+KBbjotCk4uzEq5gfw0hsbi9YvXtlMXouCRUQGJMc28PbLrL/ranKNywi8PPlNb7Pxvu+TfvHvROz+eciwMdoiXmRbCmMiQNiCqy85kiMPamDLec4Ng+JcedEM9quL79a0CsvAkNri5+QMqo7u8PBoERHpnyJ+B82P3F6wrm3evYT84tPn+6SQRybUwfL0m6zz1uKGM1i6ChXRNEUReGdnRAsuPf0gLjz1AFwvIBKyidg9D3/eWa7rc+pRY3h4wVsF6z947AQc0zmCJiKlYwyE3jkcPp/3tbBfekcuiZ/uKFwX+Hit6zE1lf1iXXEQzvPnJQ/wzxVPdZXFQzG+eNQnGRbeD79/DgKK7BTdkxB5RxAAvk/EMiRCFg7BHi+iroqF+PTZU3uMgJ0+Zyzjh1dpIbNIicWtLLGOt8g+diuZR39BdPMy4lbxA2t7izEQsT0SJkXcyuA4+rrub4y1/fvhJhTpF0HMcSyeXfdStyAGkMqnue6Jm8lY/WwEUGQXaWRMZB8yQcAREwfz4y8dy7I1reRcn0kja4mGLEx/+JYV6cPiVpb2f/+S1OJnusqSrz1OdMw0at77KZJetCTtcqyAaL6ZzU/8nsyqV7HiVVTNOJ3E2MNJ9vVNHaSLH0oQGjyS/IbVPeqsaAKrYhD94YirrEnzl8V/L1iX911eaVrMzMFHbPeYGJH+TLfaRHaBbRss28J27J1f7xUERAwcNLqWw8YNIuYYBTGRErMsg79pZbcgtkVm5UvkV7+Gbff+V6RlGSLp9TTefgWppQvwsynclnU0/+PnbH7k/4hZ2V5vk+wbGaLUv/8zWJF3bR5lOQw+4wukTeFNpfqawAS0ZtqK1r/d1qhNPWRA08iYyE4wBvKB4fVVrfzr2dWEbIuTZ41mxOAK7J0MVpqSKFI+wpZHx7MPFK3veO4BqkccTJpwL7YKImRpefi2zpNz3yX9xkKq3/NBCA/t1TbJvuH7AalwPQ0fu4HMyhfJrl5EaPBo4pOOJG1V4vWTdVRWYDG8qoG329YVrJ9UP77Pn6smsicUxkR2govhu3c8y7K3N3eVzXttHUce2MAnTj9wpwOZiJSJwMfPFx9l8vNZCHr/AtH2s2TXLi1an1nxEs6Bp2hKVz/h+9BOAmfcHKITjiYIAtrzXr+YnrhFyI9y7sFncMNTP+1RVx2tYnztaPycvkNl4NI0RZEdcByLea+u6xbEtpj32jrWNHVoi3qRPiZPmPgBRxWtj088EtcuwZoxY3X+KlYdLs06Ntm3XNcnl3PJ5/vJcNg2PM9ndGIU/3nE+VSGE13lE+r256qjP0vILX4EjMhAoJExGbAs25DzIADCloHAL7hzVcb1+cf8VUVf54GnV/JfZx1M5yuJSF/geT4V447AmX8/btuGbnV2oprEwcfS3nOm4D6Xt2LEJx9J6vWnC9ZHx0yjQ6Ni0scY1+GQuqkccNwE0m4ax3KImhiWG8LXzBIZ4BTGZMCxLEPaDfj9Q4t58qW1+H7A9ClDOf+9B1ARsfG9AMsyBEHQFc5GDq3g2MNHYlmGV5dt5PklTV11+V6e627ZhqwXkEy7GCARc945D01faCK7IkWCIed+g47n/07Hq4+B7xOf8h6qpr+fpKmgFPuKZz2Lmrnnkl2zBK99U7e62hMuImcn+tUUNhk4PDfAIUol0a4+HOgmpojCmAw8WR/+5ydP0dK+db3I/NfW88qyTfzvZXPJuR6rGtuojIcZPjiBZVlMHFnLv55bg+v6HDFlKO+fPZYf3/0SG1rSHH/ESHptkqIxLGts50d/fInWd9o/qDrKZ//jUEbUxwm0SYjITvP9gHYShA4/myGHngoG8iZKu2dKEsS2SJpKhnz0GnKrXyP9xkLsiloqpp1APlJL1tfXtohIf6JPdRlQHMfiyZfWdgtiW6QyLvc+sYy2ZI6nX24E4MsXTucPjyxh+dtbt+W9/4nlPPXSWi778CH88m+vsd/gClzf3+eBzBhoTef59u0L2DZzbdqc4Rv/N4/vf+5oEiEtAxXZVXkP8sTKZqax7wd0EMceNZPY/jMJAkNHP9vUQUREOunKTQYU1w+Y92rh7XUBXlq6kfEjagA4aNwgcnmvWxDborktw0tvbuBTZ0/l6794hoy776/ijGVx96NvUmjwy/MDHnh6Bbajf9Ii/YXn+eRyfr/c1EFERDrpyk0GBNux8ABjDPsNTvSoT8RCjBxaydC6GJlc54XPR0+ezL+fW1P0NZ9+uZGVa9sZXl/Bm2tad+mAWNuxCEznAdI7e9Zl3vNZ2Vj84Mxlb7fhat2YiIiISJ+haYrSr23ZrOPBx5bz4tINVCXCnD53LKOGVnH7X1+jtjLKBacegGUZ1m9KMWa/KoIAJoysIQgCbLtwUqqrivLx9x8IwJSxdbhuQMbziVhmu4c7W3Zne/71zCpeemMjdVURTp8zlqE1McwO1qg4lmG/+gRrmjoK1o8YnMCxDV4vjNKJiIiIyJ5TGJN+yxjD5ozLl3/8FOns1j2qX12+iZNmjuIjJ01i0ug6bvnTS6xvTnXV11ZG+MJHD+ftDR0cedAwFi5a3+11E7EQnznn0B7Pi4ZtvnnpLIZWRQoGMmMMm1MuX76le3vmvbqOc0+exPGHDcdsL0cFAWcfN4EF72pP52vD++eMxdOW1yIi8i62bchaabJ+lpAVIkIUXKuU+9SIyDs0TVH6LR+49b7XugWfLR6a/xazpw3nNw++3i1QAbS0Z/nxH19i//2qcV2fQycN7lb/3lljuPtfb/R4Xibn8a3b5pMtMjLmG/jZX14p2J47/7Fkh+vOggDqKyP894emEQnZXeWxiMMXzz2c6nhou88XEZGBJ3BcXtn8Gl9/7EYuf/jbfP6hb3LbK78jH8pgdnaevIjsMxoZk34r5wW8/ObGovXtqRxvrG4tWNe4KYkfwJ/+tZQPHj+R2dOG88wrjeRdn5kHNvCnf71R5DXzbGjNMLw22uOOYzbvs2hFc9H2LFrezIzJg/G2c26ZCQIOm1DPDz5/NC1tWYzpHMkL20bb2ouISDe2bbGkfTk/XvDLrrIgCHh27Uu83dbI/8y+DCsXLl0DRURhTPovYzp/FZuGkd/BlL583uOqi4/kul8uJOd6HD55KLYx5Haws1l7Mge1MXZ1n2x/J+eLBH5A2MDQ6ki3MhERkW3lrAy/ffkvBesaO5poTK5nRHgUQQnmK9ohQz7I4RiHwDWaMikDlsKY9Fth2+LQiUN4fklTwfraygiObeEWGInaMuIUD1l88+IjSWZdMjmX6kQEDFTEQnSk8wVfd8SQioJfbGHHYuLIGpYWGY07cGzddkfFREREdoUbuDQli88QeaN5BaOHj8btxY2fjB2QNkkefONR3mxewZBEPadNPIG6UB3G1WWpDDxaMyb9lgl8Lnr/FBLRnh/uZx49jnjY5v2z9y/43GMOG0EkZOH7ATYBVRGbhuooiajD/FcaOfu48QWfd9TBw4iH7YJ1joFPnjW123qvLT4wdyyxAuUiIiK7yzYWUSdStH5wfFCvjorZtmGD28QVj1zLI8ufYGXrGha8/SJXPXojL2x4GRzdkJSBR7cgpN8KAqgM2/zvZ+by6HNreH5JE9UVYT4wdxzD6uIEns/7jtqfRCzEn//9JsmMSzRsc+pR+3PqUWMwfueXgjGGfAAr3m5jwaJ1xCMh3jNtP676xEx+cvfLbGhNE486nDhjFO+dNaboFvW+H1CXCHHTZ+dy/5MreGXZRmorI5x1zHhGDqnY4db2IiIiuyJCjJPGHc19Sx7qUReyQ0wcNBYv13vfPXkry08W/hrX77mR1S9f+iMHn3QAIWJFn29ZhsD28AOfEGFc7SAs/YDCmPRr/jvrq049chQnTh+JbRnwg647gVbgc+LhI5gzbT9yrk/IsYiFLDzXx7IMbgBeAN/8v3ms3Zjset37n1zOhadO4dMfnEom5+F6Po8//zYt7VmGVhW/Cxn4AVHb8B/Hjeeso8diWxYWwXbPJhMREdkdXj7gpLFzeat1DS+uX9RVHnUiXP6eTxP2Yru4unnPpL006zo2FKzzfI/G9vWMjo4puH7MD+dZ2baaB998lKyX48gRhzF92DRCbkzfodKnKYzJgGAZQ8g2WAby71qX5Xk+IQOhUOesXc/1CYxhxfoOFq1oZuPmTLcgtsWvHljEVZ+YyQ13PIsfgGMbPvHOQdA74ns+NoDvo/t6IiKyr5hsmIsPOY8Or51VrWuojFQyvLKBsBfF3/5+VHvdjiJTUOQRfijPb175E/PffqGr7I1NK3hg6b+46ujP4uSKj6aJlDutGZN+zViGtBdw/zOruPnul/nbvFVkvADLLn62imVbPLdkA9+8dT77D6/myZfeLvrYxStbGDeiBoCzjp1A2NGZLSIiUl5M3qHSr2VqzVTGRPfHyfV+EAOI2TGGVgwuWGdbNvtVDO0xKmYMbMxu7BbEttiUbuHvb/4bS0ML0ocpjEm/ZdmGtc1pPvO9x/jDI0tZ+Pp67np4KZ+56THWNmewrMLBKev63P63zukcljHb3QI/nXUZVp/gs+ccyknTR4KmSoiISJnyt5mmXwphP8p/HnEettVzw6rzp55NOIj2KA+FHB5b+UzR13z8rfnkTHavtlOkN+leguxztm2R83xsy2DBXp3bbdvvTC0ssCV8zgu44bfP9di6Pu/63Pjb5/jOp48q+A+gLZUnne1cXLxqXRuTRteyZFVLwZ9/1NRh1FdHiNiWFhKLiIhsh+f5DA018N0T/ocH3vgXbzavZEhiEO+feCKDwoMI3MJjBNs7hzMIAjQnRfoyhTHZZyzLkHID/v7Ucl58YwM1iQhnHD2OUUMrsPbwzpxvDO3pPK8u30Qs4jBl/0FE7e4nPLen87S2F75b1tyWoSPtUhPr+U/A2WYK4z/mreJTZ0/lO79aiPeuEHng2EHUV0exg0BBTEREZCcEniFGJR+a+AHcIL/10OeeGywCkM97HD36SB5fNb9g/exR0wkR0fpr6bMUxmSfMMbQlnG54sdPdY0yvUU7Ly/byPveM4Yz547b7UDmW4bb/rqIp19u7CqzDHz6g9M4dHw9JgiwLIPnbf/13x2utkhEHYbWxVnfnKK5LcMDT6/gfz42g/ueWM6ryzZSGQ/zvveM4djDR2L5+vgXERHZVX4eLEI7DFFBEDAkPoRDGg7kxXWvdaurjlbxvgnH4+f2XTtF9jWFMdknfAO/uO/VriC2rb89tZKTZ46mosjhyNtj2xbzF63vFsSgc6nWzX98iR98/mgqIg7rNmeoiIeJhG2yuZ6rlGMRh6p4qODPiNiGL370cL72s6fJ5DxeWLKBZWs2c9LMUVxyxkH/v707j4+qvvc//j7nzJLJSgJJQBbZd9nXKrggqEW0llqvV6UqrdZblP5ca6GKcl1alLYuV1ulXpdae93obaVSrFcUqpGwiIosSmRREpaQBLLMcs75/UGJppkgQjJnknk9H488NN9vzsxnzNdk3vkuR0GfqaBlMBsGAEACmBG/Zg67WFv2b9VfP/4/1cXCGtdlhE7pOkaBWEhOQg/oB5oXYQwtIhJz9f7H+5rsX7dlj04besLXDjRh29Hi5Z802f9/q3fqlKEnKC3g0/LVO/XdSX319F8/avR1V5w7UEGfKSfOXjPbdpWfFdCv/t+pendDqTZtq1DPztn6xkmdFPKbcmxXsRg/+AEgVZmmoaDqZNm1kmHKtkKqcwKeHo7R1pmRgAZmD1TfUb3luo78CsqOuAQxtHqEMXjCOMbttq6kyoNf7AMb1LO9xg3uKJ9l6qNPy9UlP1MffVquyoMRvfD6Fl1wWi9df/EIvbKyRJ/vPajOBZm6eHJ/de6QHjeIHXb4ZtGnDT1Bpw/vLLmH1q07X7H0EQDQtvlMV8Gaz1W+9LeKlH0qSUo7cZByJ39fNb48bkDcgmzbkWH7ZEiyCWFoIzjaHi0i6DM0rE/8e4lI0tA++ce0zM9vmhrQPU+hoE+3fm+0BvVor1dWluh/Xtssn2VqQI885Wal6bVV2yVJL7/xiZ7+60ca1jdfM745UEN65evTXZUK+o5u6MdijqIRW9GoBzdkAQAknbTYfpU+c1t9EJOkum0fquyZnynDPeBdYcfBNA25/pii/lrF/HUy/AQdIFGYGUOLMFxXM88bpJ88vELVdQ33jV1wai9lBC01urPjUT2uo0vPGaDtZQf0/N+36OOdFfV9rxfvUNGHpbr3R6eoqvqL3bx7Kmr1x9c2139+5uhuMgwOwgUAfD1By1HVipckp/F+aKfuoGo2F8k3YHKr2lNsWK72O/v038XPa/O+rTINU2M7D9NFg89XMJbe5mf6DJ8UMWtVUVclyzSVHchSwPbmpthITYQxtAjXlbKClu6fPVF/L96hdZv3KDsjoPMn9tIJ7dNlHOO6eteV2mcHtGe/r0EQO6y6NqqSzyo1oHuePtwaf8/ayAEFisX4KQsA+HosJ6y6HY33IR8WLnlPmQNOV6yVLDwyDOmgqnTb/92v2D8DpuM6envnGm3c94nuOPUGWZHGN2JuM/wxvVu2Vr9f/7Ki/3z9GYF0XTvmCnVL7yY3xh9u0fJax08LtEqH912dO+5E3XLpSM2aPkRd26d/rSPtTctSnSNV1sVUa7uSz5TftLRi3WdNXvPH1zbpkrP6y4zzM7QwL129Tshp83/pAwA0P9ewZGW2a7Lfymovx/j6JwUfiWEcmpFLN2oUMsOyrGZ86+Zz9OJHS+qD2Jftr63Uh3s3N+/zJRHTNPRZzS7997rn64OYJFVHarRg5SOqVbWH1SGVMDOGFmfbjkxJ7tc4/MIwpJgMPfXXj/TWus9kO66y0v06f2IvnTL0BAWDTf+yqw3bqqmL6qZLR+l//r5ZJZ9XyTINnTz0BF1yVn/5jWNaIQkASHERI6jscd/S3pfvj9ufOfJsVUeb7xeMz3SVFtuvyjdfUHjHBlnpOcoe9y2ldR6osELH/fhRRfTh7s1N9hd/vl4jOgyT2uBiEtuK6sUNS+L3uY7e2Pa2zu1+lmLR1rPkFK0TYQxJx7BMRR1XK9d/rtUby+pvznygJqpnXt0oV9K0CT3191U74l5/+sguapcV1Mr3Ptf5E3upU4cMZWcEDh1LH3MIYgCAY2LbroId+ypzxFk6uGbpFx2GqdxJlyuWlqevvIvxUTJNQ8HaXdr19M/q96jZByu0939/rYyTTlPmhEskZRzXcxgylRXI0MFI/Fmg3LQcGW30d6YtW6UHdzfZv73yMznN9c0EjoAwhuRhGKqqi+mlNzZp62eVKsxL14++M0zrP9mrJStL6r/sT8s/0ZiBHTVlbDf9rWh7g4foWpilyWO6yWcaumBiD9m2K9M0ZMccOa1oQzUAIDnV2EGFxnxHWSPOVnjnRhk+v4In9FPYTFfYab4likGFVb70sbiHhVS//4ayx0yTlHd8z+GmaWrfSXp8zR/i9k/qcbKibXRmyCefumR3UuWe+Cdg9s7tLtM1CWRocYQxeMowTdXFHLmuq9Lyav3n74p0eDvXzt0HtXrjbn1v6kCNGdRR735YKkk6WBtVeVWd/u3MvjptRBe9+s421dbFdNrILurbtZ18cuW6rmL/XCpisz8MANCM6hy/ZObK6nGyJFcHbLfZZsQOs+w6RUq3Nl3D9g8V6tj9uJ4jFnM0rGCwRp0wVMWfv9eg79Ih31aWlS01zoJtghHz6cJB5+rDNxY26vObPp3SbTRLFJEQhDF4xjYMPbt0o95c+5lmXThMT//1I8XLTc8u3aibLxtVH8ZM01Ao6FPAb6pTuzR9/9yBh5Yeuo5s2+U2kACAhLDtFnyzbhiSDKmJ32qmL9A8TxPx6/KTvqsLBpyt9aUbFPQFNbRwoNIUkmLNexhJMnFdVx0C+Zo15nI9sfZ/VB2tkSR1SM/TrDGXK83JYE4MCUEYgyccw9DDL6zXui17JEnpaT6VV9XF/dpozFFdJKag31I4amvc4I7KSvfX7/+KcUNmAEAbE7NCCvUcptqta+P0Ggp2Hdhsz2VE/Wqn9jqj86mHnjtFlvUbMUuDcwbp7kk/UXW0WoZhKsNKV8AJtWzQBr6kbZ5XiqRgWKZiMhSVJNPQl++zXBOO1Qexo3osw5DjuurdpZ0untJPQb+VMr8sAACpJ+z4lDvpcpnp2Y36cid9T1Hf8R3eEU8s5iTV71bTNGT7I6oy9qvM3qWwv1ryN+8fYG3blS+Sphy3vbKdXFnRIEEMCcXMGJqNaRoyDEOu66rOdvXcqxu14p/H0o/qX6gZ3xygrKAl13W1e39tg2sP1kaV3y6kPRW1jR43GLB0QocM3XnVeKWn+RT0W/Ibbls8aRcAAEmHbsFS42unjjPuUe0nq1X3yRpZWe2VOXyKYml5isnvdYktyjQNHTQrdd/K36js4KE/3hoydMqJo3XRwPNlhNv260fqIIzhuBmmobDt6tOdlao4ENbQPvma8+g/Giw7XPVRmT7Yuk/3z56gNNNQTmbDte7/++YnumLaIC18drVi/3I/sh9NH6qsdL/SAz75fYZM15VNEgMAtHG27eqAMuTrc5oy+kyQa5iH7mPmSL42vrYp6qvT3W88qP11lfVtrly9te1d5abl6JsnTpbdRg8XQWpp4/8ro6UZpqGd+2r057e2qrS8RlHb0cr1n8fd/1UbjunPb5XItEzlZARUmJde37et9ICWvbtNP5s5TlPGdlOfru102oguWjh7ogb3yJXluAqYkuG43CcMAJBSYjFH4ZihSDPeUDqZGYah0urdDYLYly395E3VGY1X0gCtETNjOC5RV4rEHO2prFPxxt2aenIPrf94b5Nfv3pjmS6Y2FMBy9DcK8bozkVF9UsT127ao5raqG6ZMUqu48oyDDm2o7hHLAIAgDbJNI36pYnxhGNhRZ22vlATqYIwhmPm91vasr1C9z61qn62altplTJCTf94zEwPyDQNOY6rrKClu374De2rqtO+yjp16pCu7PSADNuRXMnhkHoAAFKO4zjqnN2xyf50f0gB0y82j6MtYJliG2JapqKuVFkXU23MlfsvJxg2t7qYo9+8/H6DZYOrNpTp5KEnNHnNeRN6ym8eKspxXPnkqjA7qMEntlNuyC/LZRkiAACJYPpd2YGw7EBYht9t0fcMX4frSvmhDirI6BC3f1q/yUpzQwmuCmgZzIy1EY5hqGhDmZ55daOqa6OSpGF98vXDb5+kNOvQTFRzq66NNdobVlUd0a491Tpr3Ila+s62Bn3jBnXU4B55cY+MbYn6AABAY6ZpKOyr0csb/6qV24vluI5GnTBEFw06T+lOppwkONndFwvq1gmz9NC7T+iT8kPvJ3ymT+f0OV0TuoxVLML7BrQNhusyD9FcbNtReXl1wp/Xsgyt/bhcv/pj4xtDdmyfrjt/MF6+f1ny5/OZys3N0P791cd8T5GqsK0f/3J53L7pp/fW+JM6adWGMkVijsYP7qi8rKBMhhuOoDnGJdDcGJdIRsczLu1AnW5/4/5GB2Sk+0O6a9ItCkTSm7gysQzDkOOLqNapVdiOKNOfoaDS5ESTZAoPjfDz8gt5eRmyrK9ehMgyxTYgbEvPLP0obl/pvhrt2lctowXWHqQHferYPv4P7L+sLFFmKKBzx5+ob0/oofysAEEMAACPWZapVbvWxz2psCZaq2WfvCkrSdZNua4rI+pXup2tXHWQPxoiiKHNIYy1ATHb0d6KxkfJH7ZlR4Usq/l/eAUtQz++aLj8/3KzE8OQrr1wmNIsKRq1FY3a7AMDACAJ2GZMqz5b12T/ml3vK6JI4goCUlyS/O0Dx8MyDYWCPtWG49/9sFP7jCb3ZBmGJNNUzHEluQr6TNlHOa1s244K26XpV//vVL327nZt2r5fnfMzNfXkHsoO+dgHBgBAkjFlKiPQ9DLEdH9IpsHf6oFEIYy1AWk+U1NP7q4XXv+4UV8o6FPvLjlxg1EkZmvvgaie/utHem/LHmWE/Dr35B46Y1QXmUcZpFzHVcgy9K0JPWQ73WWZxqEwRxADACDpuDFD5/Q+Xas/Xx+3f2qfSfI5AdlK7f0+QKLwp482wLYdnT2uu8YPbnhPjqx0v+74wTgF4yxRNAxDO0oP6KYH39SaTbtlO66qqiN69m+bdP+za2V/zT1mhwPY0c6qAQCAxHNdVx1DBZrSa2KjvtEnDFXfvN5xTz0G0DKYGWsjTMfR96cN0sVT+uuzPQeVlRFQfrs0BS1Djt14lirmuHr8fz9QLE7fR5+Wa/f+Wp2QGxKHbQIA0LYYUb+m9T5bp3f/ht7ZuUYx19bYzsOVG8iVGfF7XR6QUghjbYjhusoMmOrfJUfSoZsnxwtikhS1XX3wyb4mH2vVR2WaPrGnolFubw8AQFtjRn3KVp6mdj9LkhSL2XKjHhcFpCDCWBt0VLNZhhT0Wwo3EbYyQ35mxQAAaOP4oyvgLfaMpaiQ39TkMd2a7B87qGPK36wPAAAAaEmtIoyFw2HdcccdGj9+vIYPH64bbrhB5eXlR7xmzZo1uuyyyzRy5EhNmDBBc+bMUUVFRX1/WVmZ+vXr1+jjpZdeauFXkxxcx9W3T++tLgWZjfq+f94gpQcsD6oCAAAAUkerWKY4b948FRcX68EHH1QgENDtt9+u6667Ts8880zcry8pKdHMmTM1ffp0zZs3T/v379cdd9yh2bNn68knn5Qkbdy4UcFgUK+99pqML50cmJWVlZDXlAzyc9N1+8yx2lZ6QG+/v0vtsoKaOLyzMoM+GSxRBAAAAFpU0oexsrIyLV68WI8++qhGjRolSVq4cKHOPvtsrV27VsOHD290zeLFi1VQUKA5c+bUB63bb79dl1xyiXbs2KGuXbtq8+bN6t69uwoKChL6epJN0DLUu1OW+ndtJ9d1D60dJ4gBAAAALS7pw9jq1aslSePGjatv69GjhwoLC7Vq1aq4Yey8887T6aef3mDG6/C/V1ZWqmvXrtq0aZN69erV7PX6fK1i5acsy/zSPx05zqH9Ya2lfrRNDcclkBwYl0hGjMvEM01DhiHZTZxUDcblsUj6MFZWVqbc3FwFg8EG7QUFBSotLY17TbyQ9dhjjyk/P1/9+vWTJG3evFm5ubm65JJLVFJSohNPPFHXXHONJk5sfBPEo2WahnJzM475ei9kZ4e8LgFohHGJZMS4RDJiXLa8mmitKuqq9OHuzbIdW4MK+io3lKPMQOt6z5dIjMuj53kY27lzpyZNmtRk/+zZsxUIBBq1B4NBhcPho3qOn//853rjjTf00EMPye/3KxaLaevWrerdu7d+8pOfKDMzU6+88oquuuoqPfHEExo/fvwxvRbHcVVVVXNM1yaaZZnKzg6pqqpWts2piUgOjEskI8YlkhHjMjFsM6o3P3tHz73/pwbtZ/Y8RRf0+6Z8duP3qKmMcfmF7OzQUc0Qeh7GCgsLtWTJkib7ly9frkgk0qg9HA4rFDpy6o5Go7rtttu0ePFizZ8/X2eeeaYkyefzqaioSJZlKS0tTZI0ePBgbdmyRYsWLTrmMCap1R0Hb9tOq6sZbR/jEsmIcYlkxLhsOYYh7YvuaxTEJOm1rSs0pHCg+mT0keOwbPFfMS6PnudhzO/3H3Hv1qZNm1RRUaFIJNJghmz37t0qLCxs8rqDBw9q1qxZKi4u1sKFC3XOOec06M/IaDy13KdPH61YseIYXgUAAADaEtMnvbrhjSb7/7x5mWaP6i7D8fztNFqxpN9dN3LkSDmOU3+Qh3To6PqysjKNHj067jWRSERXX3211q9fr0WLFjUKYlu2bNGIESNUVFTUoP2DDz5Q7969m/9FAAAAoFWx5ai8rrLJ/sq6A3JkJ7AitEVJH8YKCws1depUzZ07V0VFRVq/fr2uv/56jRkzRsOGDZN0KHzt2bOnfjnjb37zG61evVrz589Xz549tWfPnvqPSCSiXr16qWfPnrrzzjtVXFysTz75RPfcc4/WrVuna665xsNXCwAAgGRguZaGFg5osn9Qfh/5xZ4xHJ+kD2OSNH/+fI0fP16zZs3SzJkz1bNnTz3wwAP1/WvXrtUpp5yitWvXSpL+8pe/yHVdXX/99TrllFMafKxdu1amaerRRx/VkCFD9OMf/1gXXHCB3nvvPT3xxBPq27evVy8TAAAAScKOuRrXZaQyAumN+vymT1P7niknasS5Ejh6hutyh9/mYtuOysurvS7jqPh8pnJzM7R/fzUbLJE0GJdIRoxLJCPGZWKYpqFqs0pPvfeC1pd9JEnqk9dDlw//rvLM9nJYpdgA4/ILeXkZreM0RQAAACAZOY6rdDdbVw+boYjCcl1XASMoy/bL4ebPaAaEMQAAAKAJrutKUUsBfbFc0RFBDM2jVewZAwAAAIC2hjAGAAAAAB4gjAEAAACABwhjAAAAAOABDvAAAABAUrAsUxGzTjJcGa4pvxOUbaf2Eelo2whjAAAA8Jzrj+r9/Zv14oYlKju4V52zO+qiQdPUI7u7jChvWdE2sUwRAAAAnjJ8rv5v+0o9/O6TKj24R65c7azapfvf/q2Ky9bJJIuhjSKMAQAAwFMRo1aLN74at++5D/6kiFGX4IqAxCCMAQAAwFP7w1Wy3fh7w+piYR2MVie4IiAxCGMAAADwVMDyH7HfZ1oJqgRILMIYAAAAPJXly1ROWnbcvk6ZBUq30hNcEZAYhDEAAAB4ym8Hdf34HzSaIQv503TduJny2UGPKgNaFmfTAAAAwFOOIxX4CvXzyXP0XukGbavcqd553TUov5+CdkiO7XpdItAiCGMAAADwnGNLATtd4wvG6OSOY2XbruyII275jLaMMAYAAICkEYsRv5A62DMGAAAAAB4gjAEAAACABwhjAAAAAOAB9owBAAAgJfn9lgxDchyXvWrwBGEMAAAAKcWwXNWZNVq+c422Ve5U37yeGnnCEAXtdI7RR0IRxgAAAOA5w+8qpogkQ0E3rcVmqkzL0Ofhz3TPiocVc2KSpKKda/U/G/6i2ybOVnsrXzaBDAlCGAMAAIBnDEuqMQ7opQ1L9MHuzcoMpGtq3zM1NH+gjIi/2Z8vYtbqV+88Xh/EDgvHwnrg3Sc09+TZMu1Asz8vEA9hDAAAAJ4wDEOVbrlu+/sCRf8ZjqrCB/TY6t9r1AlD9L2TLpIZbd5AVhU9oAOR6rh9ZQf3qMauUaYIY0gMTlMEAACAJ1xfVE+/90J9EPuy4s/XqzJaKcNo3ueM2Y2f68ts127eJwSOgDAGAAAAT0QV1YY9W5rsX1f6oSzLatbnzA21k2XGf8x0f0gZ/oxmfT7gSAhjAAAA8IRhGLKMpt+OBi2/pOY9TCPgBPWdAd+M23fZ0OkKOqFmfT7gSNgzBgAAAE8E3KDGdRmplTtWxe0f1mlws5+q6MZMTegyXl2yO+mFj15R6cG96pLdUf826Hx1Su8kO3r84c+yDEXMOlXbNZKkDCtdASeNUxrRCGEMAAAAnnCihi4cdK4+2rtF5bUVDfouGjRNIaW3yPMaUZ/6ZPbRjWP/Q45sWfLJsv1ymiGIyXK1vW6HHil+SvtrKyVJuaEcXTNqhjqndZHsZt4Eh1aNMAYAAADPBGPpmnfqDfpwzya9+/k6tUvL1pk9JijHnyMj2nJvVW3blWn7ZerQaY1OMy2HrNEB3bviYTnuFzN6+2srde+Kh3XvmbcqQznN8jxoGwhjAAAA8IzjuLIiQQ3PG6YR+UNlyFA04khRryv7+ky/9MqmvzcIYoc5rqMlW17XRX0vUJzDI5GiCGMAAADwnG07ki0194EdiRRTVCUVO5rsL6nYrpgRrZ+NAzhNEQAAAGgGPvnUKTO/yf5OmQXyMReCLyGMAQAAAM3AjRma1m9Kk/3T+k2WG+MAD3yBMAYAAAA0A9eV2lnt9B+jZyhgfbEUMWD59R+jZ6idlSu39a7CRAtgnhQAAABoLjFLg9sN1oLJc1VeVym5rvJC7eS3Q3I5uAP/gjAGAAAANCPXlnx2SAVm6FBDpDUfS4KWxDJFAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAAD3CfMQAAAKANMU1DPp8p15WiUdvrcnAEhDEAAACgDTAMQzF/nT498JnWfP6+ckM5GttlhNKVIcUsr8tDHIQxAAAAoA2IBep074qH9PmBsvq2FzYs0VUjL9HQ9idJMXYoJRu+IwAAAEArZ/pdLd74aoMgdthjq59V2KjxoCp8FcIYAAAA0MpFjLDe2lYUt8+Vq3WlG+Tz8dY/2fAdAQAAAFo513UVdWJN9h+M1EgyElcQjgphDAAAAGjlfPKpV96JTfYPLRwg2+ZkxWRDGAMAAABaOcsO6PKhF8o0Gr+979+hl/LScuW6HhSGIyKMAQAAAK2c47jK83XQ/DNu0sD8vjJkKDOQoe8MnKpZo6+QGQl4XSLi4Gh7AAAAoC2wTeUaHfSjEZcrZtgyJAWcNNlhpsSSFWEMAAAAaCNc15WiPvn++TbfFkEsmbFMEQAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAAD7SKMBYOh3XHHXdo/PjxGj58uG644QaVl5cf8ZpHHnlE/fr1a/TxZb///e81adIkDRkyRP/+7/+uDRs2tOTLAAAAAIB6rSKMzZs3TytWrNCDDz6oJ598Ulu3btV11113xGs2bdqk888/XytWrGjwcdjLL7+sX/ziF5o9e7ZeeukldenSRVdcccVXhjwAAADAK6ZpyPS7MvyOfL5W8VYeR5D038GysjItXrxYc+fO1ahRozRkyBAtXLhQq1at0tq1a5u8bvPmzRo4cKDy8/MbfBz26KOP6tJLL9V5552n3r176+6771YoFNLzzz+fiJcFAAAAfC2OP6ptdZ/qt+uf1kNrFql43xrZgbAMw/C6NByjpA9jq1evliSNGzeuvq1Hjx4qLCzUqlWr4l4TiUT06aefqmfPnnH79+3bp08//VTjx4+vb/P5fBo1alSTjwkAAAB4xfFH9YcNL+veFQ9r7a4PtGHPFj22+lnd9davFQvUel0ejpHP6wK+SllZmXJzcxUMBhu0FxQUqLS0NO41H3/8sWzb1tKlS3XXXXcpHA5r9OjRuummmxpc16lTp0aPuXHjxuOqt7VMF1uW2eCfQDJgXCIZMS6RjBiXqcUwpM/D+/SPHcWN+sqq9+rvW1fo3J5T5NgeFPcljMuvz/MwtnPnTk2aNKnJ/tmzZysQCDRqDwaDCofDca/ZvHmzJCkUCunXv/619u3bp4ULF2rGjBlavHixamsP/fXgXx/3SI95NEzTUG5uxjFf74Xs7JDXJQCNMC6RjBiXSEaMy9Tguq6eeXdlk/1vfPq2zul7uvKy2yWuqCNgXB49z8NYYWGhlixZ0mT/8uXLFYlEGrWHw2GFQvG/0d/61rc0ceJE5eXl1bf16dNHEydO1Ouvv65u3bpJUqPHPdJjHg3HcVVVVXPM1yeSZZnKzg6pqqpWtu14XQ4giXGJ5MS4RDJiXKYWn99UzG562st2HUWjMe3fX53AqhpjXH4hOzt0VDOEnocxv9+vXr16Ndm/adMmVVRUKBKJNJjJ2r17twoLC5u87stBTDq0BLFdu3YqLS3V2LFj6x/jy8/9VY95NGKx1jXwbNtpdTWj7WNcIhkxLpGMGJepwXFcnXriuLjLFCVpXJcR8rnBpBkLjMujl/QLOkeOHCnHceoP8pCkkpISlZWVafTo0XGv+eUvf6mzzjpLruvWt+3cuVP79+9X79691b59e/Xo0UNFRUX1/bFYTMXFxU0+JgAAAOAFx3F1QmZHDczv26gvO5ilc/ueKSfqQWE4bkkfxgoLCzV16lTNnTtXRUVFWr9+va6//nqNGTNGw4YNk3RoueGePXvqlx1OnjxZn332mebNm6eSkhKtWrVK1157rUaMGKEJEyZIkq688ko98cQTevnll/Xxxx/rpz/9qerq6vSd73zHq5cKAAAAxGVGArpm5AxdNfISndiuszpm5uv8flM0//QblWane10ejpHhfnn6KEnV1NTo7rvv1tKlSyVJEydO1Ny5c5WbmytJKioq0owZM/TUU0/VL0F8++239etf/1qbNm1SIBDQpEmTdMsttygnJ6f+cRctWqSnnnpKFRUVGjx4sObOnasBAwYcc5227ai83Nu1ukfL5zOVm5uh/furmUZG0mBcIhkxLpGMGJeJZ/mliHHooDe/G5AT9ebeXj6fqYgRlitXATcoO5Y8b+UZl1/Iy8s4qj1jrSKMtRaEMeD4MC6RjBiXSEaMy8QxTUMRX61e2fJ3vbWtSLZra2zn4fr2gHOUZmfKcXgrfRjj8gtHG8Y8P8ADAAAASFZRX63mv/kr7a0pr297a/u7WlP6ge464xb5IxzjjmOX9HvGAAAAAC/4fKbWlW1oEMQOq47UaNnWN2V5OLVhGJL8jiL+GtX5DsrxR2Wa3iyfxLFhZgwAAACIwzZiemfn6ib7iz97T2f1OE2Wgokr6p9M01CdVa2n17+otbs+kCtXXXNO0JXDL1KBv1CymXNpDfguAQAAAHEYMhXyN70MMc2fJsOjt9NRX63uXP5Lrdn1vlwd2re2o/Jz3bn8V6p0KmQYzJC1BoQxAAAAIA43Zujs3qc12X9O79PldxI/K2ZZpj7a97H211U26nNdV8998Ce5vljC68LXRxgDAAAA4nBdV51ChTq9+/hGfUM7DtTgDv1l24k/NdC0DK3Z9X6T/Zv2bZVtEMZaA/aMAQAAAE0won5N73euzuh5it7aVqSYE9Mp3cYoP5QvI+L3pihXKkhv32R3TjBLclmm2BoQxgAAAIAjMKJ+tTfydWGf8yVJ0agjN+Ld/cWiUVsTTxynP29+LW7/tH6TFXTTFFNq3+urNWCZIgAAAPAVXFeKRGxFIrZc1/sbPacbGfrhqMsaHdQxrssIDS8YnPI3XW4tmBkDAAAAEsQwDLm+mGzFZMqSZfvlOMcQ7mKWTsobpIVTbtfmfZ+oNhZW/w69lWlleLd8El8bYQwAAABIBJ+tfdFyvfDeK9pe8ZkKMzvo2wO+qRPSO8mIHsPb8pipgNI1NHeIJOPQYSJMiLUqhDEAAACghVk+Q5sOfKJfvv14fdv+ukrd/daDumzIdI3rOFqKHdsOItt2JXm/dBJfH3vGAAAAgBYWNmr1+Jrn4vb94YM/KWqGE1wRkgFhDAAAAGhhNbEaHQgfjNsXc2LaV1ue4IqQDAhjAAAAQAszjCO/7fYZ7B5KRYQxAAAAoIWlW+kqyOgQty/kT1O7YE6CK0IyIIwBAAAALSzgpGnWmMvltxoeO28YhmaNvlwBJ82jyuAl5kMBAACAFmbbjvJ9BfrFmT/VW9vf1cfln6pzdied0eMbynAz5dheVwgvEMYAAACABHBsKWBn6KyukzS5my3TNRWLuRxKn8IIYwAAAEACxWKOJEMOMSzlsWcMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA84PO6AAAAAACJZVmmomadIm5ElmEpoKDcKPM0iUYYAwAAAFKJz9anNdv05LrntevgbpmGqbFdhuvfBp0nfzRdrut6XWHKIP4CAAAAKcI0DZWGy3Tvioe16+BuSZLjOnp7x2rdveIhxfx1HleYWghjAAAAQIqIWRE9s/7FuH1lB/do54HPZZpGgqtKXYQxAAAAIEU4hq2S/Tua7P9g9yZZFhEhUfgvDQAAAKQIQ4Yy/OlN9rdPz2XPWAIRxgAAAIAUEXDSdE6f0+P2GYah4R0HKxZzElxV6iKMAQAAACnCjrk67cRvaEjhgAbtlmnp+nE/UNBpetYMzY+j7QEAAIAUYoT9umrYpaqMVWnz3q3KCmaod253BZyQXJvDOxKJMAYAAACkGCPqVzu11/iCfLmuKyfqip1iiUcYAwAAAFKUbbM/zEvsGQMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA0l/tH04HNa9996rV199VXV1dTrjjDM0Z84c5eXlxf36n/zkJ3r55Zfj9l177bWaNWuWJGnKlCnatm1bg/4LLrhA9957b/O+AAAAAACIw3BdN6nv73brrbequLhY99xzjwKBgG6//XZlZGTomWeeifv1Bw4cUF1dXYO2e+65R++++65efPFFFRYWqqamRiNHjtQjjzyiQYMG1X9dWlqasrKyjrlW23ZUXl59zNcnks9nKjc3Q/v3VysW4/4SSA6MSyQjxiWSEeMSyYhx+YW8vAxZ1lcvQkzqmbGysjItXrxYjz76qEaNGiVJWrhwoc4++2ytXbtWw4cPb3RNVlZWg0D1+uuva8mSJXryySdVWFgoSfr444/lOI6GDx+unJycxLwYAAAAAPiSpN4ztnr1aknSuHHj6tt69OihwsJCrVq16iuvD4fDuuuuuzR9+nSNHTu2vn3Tpk3q0KEDQQwAAACAZ5J+Ziw3N1fBYLBBe0FBgUpLS7/y+ueff1579+7Vj3/84wbtmzZtUnp6uq677jqtWbNGubm5mj59umbMmCHTPL586vMldb6td3ja9GimT4FEYVwiGTEukYwYl0hGjMuvz9MwtnPnTk2aNKnJ/tmzZysQCDRqDwaDCofDR3xsx3H05JNP6sILL1R+fn6Dvi1btqiqqkpnnXWWfvSjH2n16tVasGCBKisrNXv27GN7MZJM01BubsYxX++F7OyQ1yUAjTAukYwYl0hGjEskI8bl0fM0jBUWFmrJkiVN9i9fvlyRSKRRezgcVih05G/ymjVrtH37dl188cWN+h577DGFw+H6vWX9+vXTwYMH9cgjj+jaa6895tkxx3FVVVVzTNcmmmWZys4OqaqqVrad2hsskTwYl0hGjEskI8YlkhHj8gvZ2aHkP8DD7/erV69eTfZv2rRJFRUVikQiDWbIdu/eXX8YR1OWLVumgQMHxn38QCDQaMatb9++qqmpUWVlpXJzc7/mK/lCazs5xradVlcz2j7GJZIR4xLJiHGJZPRV49LnM+W6SvnAJiX5AR4jR46U4zj1B3lIUklJicrKyjR69OgjXrtq1SqNHz++UbvrujrzzDP10EMPNWh///33lZ+ff1xBDAAAAEB8rj+mg1aFVpS+rXf2vKta3wG5PtvrsjyV1Ad4FBYWaurUqZo7d67uvvtuhUIh3X777RozZoyGDRsmSYpEIqqsrFROTk79bJdt29q8ebMuv/zyRo9pGIYmT56sRYsWqWfPnho8eLDefvttPf7445ozZ04CXx0AAACQGtxAVC9v+qv+XrKiQft3Bk7VaV1PlhFN6ljSYpL+Vc+fP1933323Zs2aJUmaOHGi5s6dW9+/du1azZgxQ0899VT98fUVFRWKRqNq165d3Me84YYblJmZqYULF6q0tFRdunTRnDlz9N3vfrfFXw8AAADQFhjGoX1ijuPKcdwmv840DW2p3NYoiEnSCxte0UmF/ZVvFspt+iHaLMN1U/FltwzbdlReXu11GUeFO6QjGTEukYwYl0hGjEt4yTAk2x/Rntp9+qS8RO3T26tXbjeFlKF2OY3HpeuP6dfFj2nLvpK4jze+y0jNGHSRnGiiXkHLy8vLSP4DPAAAAAC0LrFAnRasfFQ7qj6vbwtaAd06YZYys3o2+nrHtVVVd6DJx6sIV8qRoyQ/zqJFpN4rBgAAAHBMDL+jZ99f3CCISVLYjujeFQ9rf21Fo2v8CmpwQf8mH3No4SBZrtXcpbYKhDEAAAAARyWsOr372bq4fXWxsHZUfi7DaNjuxKRv9j1DAcvf6JrMQIbGdxkhO5aaO6cIYwAAAACOStSJyXGb3qdYWXdAxr+mMUnpTqbuOP1G9e9w6B7AhgwN6zhQ8067XoFYeovVm+zYMwYAAADgqKRZQeWkZauyripuf/fcLnFPVnRsqZ2Zp1kjZyqqiCQpoKCMmCUnhc8TZGYMAAAAwFEJOGm65KQL4vYNyu+rvFBuk9c6jisj6lMgmq5ANF2KWil5nP2XEcYAAAAAHBU75mpgbj9dO/YKdUjPkyQFLL/O7n26rhn9PeWkZXlcYevCMkUAAAAAR82I+TQ4Z5Bum9BTUTcmn2EqqJCMGPM8XxdhDAAAAMDXEos5shSUpaAkyZbkI1l8bcRXAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAECrZhiSaRpel/G1+bwuAAAAAACOhWFKUV+dSg/uVlX4gLrldFaGlSEj6ve6tKNCGAMAAADQ6piWVBYt1c+X/5dqo3X17cM6DtL3h18sIxzwsLqjwzJFAAAAAK2Kz2dKgZgeeOd3DYKYJK0r/VBLty6X1QqmnVpBiQAAAAAgyWerVjVaW/qBDoQP6tJh31Z1tEbPrHtJYTtS/2XLPnlTZ/aYIJ/SPCz2qxHGAAAAACQ/n601e97TorXPNWju076HZo27XAtXPiZXriSpLhaW7dhJH3ZYpggAAAAg6dWoulEQk6Qt+0q0ee9WnVTYv74tPz1PPiPZoxhhDAAAAECS8/st/WN7cZP9b3z6jsZ3G1n/+b+ddL6CbigRpR2X5I+LAAAAAFKaYUgV4aom+6sjNUrzBZUdzNLFJ52vfjl9FIs5Cazw2DAzBgAAACCpxWKORnUaIkkyDEM9crupb/ueCvkOHdAxqKCPuud01fzTbtLwvKEyYq1jzql1VAkAAAAgZTmOq67ZnXVevykaWNBHW/aVKGyHNbXfGSqvqVD/Dr0VjGbIdV3Z/zzEozUgjAEAAABIepbjU24oR/e+9XCD9iGFAzT6hGFy61pPCDuMZYoAAAAAkt5B54CeXPd8o/b1ZR+p6LN1h24E3cq0vooBAAAApJRAwNIb295psv+vW15X2KhNYEXNgzAGAAAAIKm5kirqKpvsPxCprr/hc2tCGAMAAACQ1Bzb0ahOQ5vsH5TfVz75E1hR8yCMAQAAAEhqtu2qT14P5We0b9RnGaa+O2iajJjlQWXHhzAGAAAAIOn5Y2maO+E6Teg2RpZ5KHj1bd9Td5x+o7KNHLmtb5UiR9sDAAAASH6O48oXCeni/tM1fcBUuXLlV0CW7Zdjt8IkJsIYAAAAgFbEjRnyK1T/udMKD+44jGWKAAAAAOABwhgAAAAAeIAwBgAAAAAeIIwBAAAAgAcIYwAAAADgAcIYAAAAAHiAMAYAAAAAHiCMAQAAAIAHCGMAAAAA4AHCGAAAAAB4gDAGAAAAAB4gjAEAAACABwhjAAAAAOABwhgAAAAAeIAwBgAAAAAeIIwBAAAAgAcIYwAAAADgAcIYAAAAAHiAMAYAAAAAHiCMAQAAAIAHCGMAAAAA4AHCGAAAAAB4gDAGAAAAAB4gjAEAAACABwhjAAAAAOABwhgAAAAAeIAwBgAAAAAeIIwBAAAAgAcM13Vdr4toK1zXleO0nv+clmXKth2vywAaYFwiGTEukYwYl0hGjMtDTNOQYRhf+XWEMQAAAADwAMsUAQAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAAADAA4QxAAAAAPAAYQwAAAAAPEAYAwAAAAAPEMYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDE0UFxcrAEDBqioqMjrUpDidu3apeuvv14nn3yyRo8erZkzZ2rLli1el4UU4ziOHnjgAU2YMEHDhg3TD37wA+3YscPrspDCKioqdNttt2nixIkaMWKELr74YhUXF3tdFlCvpKREw4cP10svveR1Ka0CYQz1Dhw4oJtvvlmO43hdClJcJBLRVVddpT179ujRRx/Vs88+q4yMDH3ve99TeXm51+UhhfzXf/2Xnn32Wc2fP1/PPfecHMfR97//fUUiEa9LQ4q6/vrrtXbtWi1cuFAvvviiBgwYoJkzZ2rr1q1elwYoGo3qxhtvVE1NjdeltBqEMdSbN2+eunbt6nUZgIqLi7V582bdd999Oumkk9SnTx8tWLBANTU1ev31170uDykiEonod7/7na677jqddtpp6t+/v375y1+qtLRUf/vb37wuDylo27ZtWrlypebNm6dRo0apR48e+tnPfqaCggL9+c9/9ro8QA8++KAyMzO9LqNVIYxBkvSnP/1Ja9eu1U9/+lOvSwHUp08f/fa3v1VhYWF9m2ke+nFVVVXlVVlIMRs3blR1dbXGjx9f35adna2BAwdq1apVHlaGVJWbm6vf/va3Oumkk+rbDMOQYRj8bITnVq1apT/+8Y+69957vS6lVSGMQTt37tRdd92lX/ziF8rIyPC6HED5+fk69dRTG7Q9/fTTqqur08knn+xRVUg1paWlkqROnTo1aC8oKKjvAxIpOztbp556qgKBQH3b0qVLtW3bNk2YMMHDypDqqqqqdPPNN2vu3LmNfmbiyHxeF4CWtXPnTk2aNKnJ/pUrV+qmm27SRRddpFGjRmnnzp0JrA6p6qvG5dtvv628vLz6z5ctW6b7779fl19+ufr165eIEgHV1tZKUoM3vpIUDAZVWVnpRUlAA2vWrNGtt96qKVOm6LTTTvO6HKSwefPmafjw4Zo2bZrXpbQ6hLE2rrCwUEuWLGmy/7nnnlNtba2uvfbaBFaFVPdV4zInJ6f+3//whz9o/vz5Ou+883TzzTcnojxAkpSWlibp0N6xw/8uSeFwWKFQyKuyAEnSa6+9phtvvFEjRozQfffd53U5SGGLFy9WcXEx+xaPkeG6rut1EfDOGWecod27d8vv90uSXNdVbW2tgsGgvvWtb+nOO+/0uEKksgULFujxxx/XFVdcoVtuuUWGYXhdElLI+vXrdeGFF2rZsmXq1q1bffvFF1+sfv36ad68ed4Vh5T2zDPP6K677tLZZ5+tn//8541mb4FEuuyyy7RmzZoG47CmpkaBQEBjx47V448/7mF1yY+ZsRT39NNPKxaL1X9eVlamyy67TP/5n//J3hx46nAQu+WWW3TllVd6XQ5SUP/+/ZWZmamioqL6MFZVVaUNGzbo0ksv9bg6pKrDt1q47LLLNGfOHP5IBc/dd999qqura9A2ZcoUXXfddTrvvPM8qqr1IIyluM6dOzf43LIsSYeWkbVv396LkgAVFRXp8ccf12WXXaZp06Zpz5499X3p6ekcNIOECAQCuvTSS3XfffcpLy9PnTt31oIFC9SxY0dNmTLF6/KQgkpKSnT33Xdr8uTJuvrqq7V37976vrS0NGVlZXlYHVLVl08+/rL27ds32YcvEMYAJJ2//OUvkg7N3D799NMN+mbNmsUeRyTMddddp1gsprlz56qurk6jR4/WokWL6pd2A4m0dOlSRaNRLVu2TMuWLWvQd8EFF3CkONAKsWcMAAAAADzAfcYAAAAAwAOEMQAAAADwAGEMAAAAADxAGAMAAAAADxDGAAAAAMADhDEAAAAA8ABhDAAAAAA8QBgDAAAAAA8QxgAAaAYrVqzQ9OnTNXToUJ1xxhlatGiRXNf1uiwAQBIjjAEAcJzWrVunH/7wh+rZs6cefPBBTZs2TQsWLNBjjz3mdWkAgCRmuPzZDgCA4zJz5kxVVVXp+eefr29bsGCB/vCHP+gf//iH0tLSPKwOAJCsmBkDAOA4RCIRFRUVafLkyQ3azzrrLFVXV2v16tUeVQYASHaEMQAAjsOOHTsUjUbVvXv3Bu0nnniiJKmkpMSDqgAArQFhDACA43DgwAFJUmZmZoP2jIwMSdLBgwcTXhMAoHUgjAEAcBwcxzliv2nyqxYAEB+/IQAAOA5ZWVmSpOrq6gbth2fE/nXGDACAwwhjAAAch27dusmyLG3btq1B+/bt2yVJvXr18qIsAEArQBgDAOA4BINBjRo1SsuWLWtwk+elS5cqKytLQ4YM8bA6AEAyI4wBAHCcrrnmGr333nuaPXu2li9frl/96ldatGiRrr76aoVCIa/LAwAkKW76DABAM1i2bJkeeOABlZSUqLCwUJdccomuvPJKr8sCACQxwhgAAAAAeIBligAAAADgAcIYAAAAAHiAMAYAAAAAHiCMAQAAAIAHCGMAAAAA4AHCGAAAAAB4gDAGAAAAAB4gjAEAAACABwhjAAAAAOABwhgAAAAAeIAwBgAAAAAe+P+q9QROcCIHLgAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = pandas.DataFrame(pos)\n",
"data.columns = (str(x) for x in data.columns) # pour ce fichu bug\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 10))\n",
"\n",
"sns.scatterplot(x='0', \n",
" y='1', \n",
" data=data,\n",
" legend=False,\n",
" hue = [0] * 50 + [1] * 50 + [2] * 50,\n",
" palette=current_palette[:3],\n",
" ax=ax)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"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": "3.13.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}