Lectura_9_Kmeans.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# ***K-means clustering***\n",
    "\n",
    "## ***Universidad Central***\n",
    "\n",
    "## ***Maestría en analítica de datos***\n",
    "\n",
    "## ***Métodos estadísticos para analítica de datos.***\n",
    "## ***Docente: Luis Andrés Campos Maldonado.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mglearn\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import KMeans\n",
    "from utils.plots_clustering import (\n",
    "    cluster_biplot,\n",
    "    elbow_plot,\n",
    "    plot_silhouette,\n",
    "    gap_statistic\n",
    ")\n",
    "\n",
    "plt.style.use(\"ggplot\")\n",
    "plt.rcParams[\"figure.figsize\"] = (15,6)\n",
    "url_base = \"https://raw.githubusercontent.com/lacamposm/Metodos-Estadisticos/main/data/\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***$k$-means clustering***\n",
    "\n",
    "El k-means clustering es uno de los algoritmos de agrupamiento más simples y más utilizados. Es de los métodos no supervisado para dividir un conjunto de individuos (registros del Dataset) en un conjunto de $k$ grupos (es decir, ***$k$ clusters***), donde $k$ representa el número de grupos preestablecidos. Este algoritmo busca que los objetos ***dentro del mismo cluster*** sean lo más similares posibles (es decir, alta similitud intraclase), mientras que ***distintos clusters*** sean lo más diferente posible (es decir, baja similitud entre clases).\n",
    "\n",
    "En el $k$-means clustering, cada grupo está representado por su centro (es decir, ***centroide***) que corresponde a la media de puntos asignados al ***cluster***."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ***Algoritmo de $k$-means.***\n",
    "\n",
    "El primer paso cuando se usa el algoritmo es indicar el número $k$ de clusters que se desean obtener. El algoritmo comienza seleccionando aleatoriamente $k$ objetos del conjunto de datos para que sirvan como centroides iniciales de los cluster. Seguido, cada uno de los registros restantes se asigna a su centroide más cercano (_asignación de cluster_), donde más cercano se asigna por la distacia euclideana. Después del paso de asignación, el algoritmo calcula el nuevo centroide de cada cluster (_actualización del centroide_). Ahora que los centroides se han vuelto a calcular, para cada observación se verifican las distancias para determinar si podría estar más cerca a un clúster diferente. Todos los objetos se reasignan nuevamente utilizando el  centroide  actualizado del clúster. Los pasos de asignación de cluster y actualización del centroide se repiten iterativamente hasta que las asignaciones de clústeres dejan de cambiar (se logra la convergencia), es decir, los clusters formados en la iteración actual son los mismos que los obtenidos en la iteración anterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***El algoritmo $k$-means se puede resumir de la siguiente manera:***\n",
    "\n",
    "1. Especifique el número de cluster ($k$) que se crearán.\n",
    "\n",
    "2. Seleccione aleatoriamente $k$ registros del conjunto de datos como centroides de los clusters iniciales.\n",
    "\n",
    "3. Asigna cada registro a su ***centroide*** más cercano, basado en alguna distancia.\n",
    "\n",
    "4. Para cada uno de los $k$ clusters, se actualiza el ***centroide del cluster***.\n",
    "\n",
    "5. Iterar los pasos 3 y 4 hasta que las asignaciones de los ***clusters*** dejen de cambiar o el número máximo de\n",
    "iteraciones se alcanza."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Se asume que entre los individuos se puede establecer una distancia euclidiana.***\n",
    "\n",
    "La idea básica detrás de $k$-means clustering consiste en definir grupos de modo que el total de la variación ***intra-cluster*** se minimize (conocida como ***inertia, within-cluster sum-of-squares criterion, o within-cluster variation***).\n",
    "\n",
    "El algoritmo estándar define la variación ***intra-cluster*** como la suma de las distancias al cuadrado (euclidiana) al centroide y los elementos del cluster:\n",
    "\n",
    "$$W(C_k) = \\sum_{x_i \\in C_{k}}||x_i -\\mu_k||^2$$\n",
    "\n",
    "• $x_i$ es un registro que pertence al cluster $C_k$.\n",
    "\n",
    "• $\\mu_k$ es el valor promedio de los registros asignados al cluster $C_k$\n",
    "\n",
    "Cada registro ($x_i$) se asigna a un cluster de tal forma que la suma de los cuadrados de la distancia de la observación a sus ***centroides*** $\\mu_k$ sea mínimo.\n",
    "\n",
    "Definimos la ***inercia*** o ***within-cluster sum-of-squares*** como sigue:\n",
    "\n",
    "$$WCSS =\\sum_{n=1}^{k} W(C_n)= \\sum_{n=1}^{k} \\sum_{x_i \\in C_{n}}||x_i -\\mu_n||^2$$\n",
    "\n",
    "El algoritmo $k$-means tiene como objetivo elegir ***centroides*** que minimicen la ***inercia***. Esto mide la compacidad (es decir _goodness_) del agrupamiento, se desea que sea lo mas baja posible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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aLSqVyuQDbe/YrE5BQQFjxowhLS2Nzz//3OIkpynGs1G7rKXmNR63FLdi6d9Ho6n8miwvL7/uvgk3F5988glAjaQuPj4+PProoyQkJLB+/XomTJgAVC4s7tixg3/+85/Ex8fz17/+FQAPDw8iIyN54403cHd3ByrHSuvWrfnoo4/44IMPeO+991CpVAwdOpS3337b4iS7Knl5efj4+Jj+fqti7XvdSEOOg6FDh9ZZ58uWMXv27Flyc3NtynjXUP3v0qUL+/fvZ8GCBWzdupXExESg0piZN28ec+fOrbMNo75VT8LTEBQVFZk9o6UhBkgz4MKFCxaPZ2RkAJgNOLW6ctPKYDDUEBZLX6j1xfjMuvpWlfXr17N//36mTJnCypUrzc6lp6ebMl7ZysWLF/nggw/o3bs3X3/9dQ0XktWrV9vVniDcihgMBhYsWED79u35/vvva3zJN0RBsPLyciZNmsT333/P66+/zmOPPVbjmqYaz0btsqRRgCkLlqTuFa6HzMxMkpKSAHjssccs/s1DpZFiNECgciX83Xff5d133+XEiRPs3r2bpUuXsnjxYnJzc1m1apXp2oiICCIiIsjNzeXrr79m3bp1rFixguDgYH777TfatGljtX+enp5kZ2dbnCtY+16/UVQds5ZS697IMduzZ0/Wrl2LwWDg0KFDbNu2jQ8//JC//OUvuLm5MX369Frv9/LywsnJyeaMWfZgbLNt27YN3nZTIC5YzYDdu3fXOFZeXs6XX34JwF133WU6btzGS0tLq3HPd999Z7F9BwcHu1ctjM/88ssvLd5raUXjxIkTAISGhtY4Z+kdjX0Dy6sSJ0+epKKigqCgoBqTlXPnznHy5MnaX0IQbkLsHc9ZWVnk5uZy33331TA+8vPzTe4P18MzzzzDpk2bmDZtGi+//LLFa+oznmvTB2sYtcuSRhkMBvbu3QvAH/7wB5vbFITqGGt9/PGPf2T69OkWf9q0acO2bds4deqUxTa6d+/O9OnT2b17N+7u7qxfv97idV5eXjz88MMsW7aMKVOmkJ2dzZ49e2rt31133UVFRQVff/11jXPGuUVzobYxe+LECc6dO0e3bt2s7iBfD7ZqjEaj4Y9//CN//etfTYslRgO0Lvr06UN6enqDp8s1Fiy0Jatpc0QMkGbAjh07atQBWLx4MampqQwfPpwuXbqYjt9zzz0ANYLbtm/fbnUF0dfXl8zMTNN2nS106tSJkSNHcurUKRYvXmx2bv369RYNCmNqzOoicvLkSdNWs6W+geUgKmN71Y2g/Px8Zs6cicFgsPV1BOGmwd7x3LZtW7RaLQcPHiQ/P990vKysjL/85S/X7T/83nvvsXjxYkaMGMGSJUusXlef8VybPlgjJCQEHx8fVq9ezbffflujr6dOnWLEiBGNVqxRuDUwfgd/9NFHREVFWfz585//bApUh8q6F5YM7ZycHEpKSsxcaXbu3Gkx1uDixYsAZumtLWEMin/llVfMYkzy8vJYuHChnW/buEybNg2oDJivGudSXl7OvHnzqKioqHOnob7UpjEHDx606AJv3EGq69/AyLBhw6ioqGjwRBZGfastfXtzRlywmgGPPvoo48ePZ/z48XTv3p0ff/yRLVu24OPjU6Pg0NSpU3n77bd54403OHToEL169eLYsWOmOiIJCQk12n/ooYc4cOAAo0aNYsiQITg7O9OvXz8effTRWvv13//+l3vvvZdnnnmG5ORk+vXrx4kTJ1i3bh2PPvooGzdurPEe3bt35z//+Q8//fQTd911F2fPnmXTpk088sgjFgf48OHDUavVvPTSS/z888+mHR5jNoxJkyaxZs0a+vfvT1BQEHl5eaSkpODi4kL//v358ccf7fy0BaFlY+94VqvVzJ07lzfffJM+ffowbtw4SktL2blzJ9nZ2QwfPpydO3fWqy8ZGRk8//zzqFQqevfuzeuvv17jmv79+xMSElKv8RwYGIifnx9r1qzB0dGRLl26oFKpeOKJJ8wWZqri7u7OihUr0Ol0DB06FJ1Oh7+/PwcPHiQ5OZn27duzdOnSer2vIEDlItuxY8fo06ePaVHQEtOnT+f1119n5cqVvPrqqxw6dIjQ0FDuvvtuevbsSceOHcnMzGT9+vWUlZWZLdSNHz8ed3d3Bg0aRNeuXVEUhb1793LgwAH++Mc/MmLEiFr7GBERwZo1a9i6dSu9e/dm7NixlJWVkZCQwN13383Ro0dNLt03mvvuu48XX3yRf//73/Tu3ZsJEybg5ubGli1b+Pnnn3nggQd44YUXGuXZDz30EG+//TYzZ84kLCwMDw8PvLy8eOqpp1i1ahVLly7lgQceICAgAG9vb1JTU9m4cSPOzs5mtZhqIywsjEWLFqHX6y3+uyUlJZl2U4yuo998840ptqh169amjGFGKioq2LZtG4GBgfTu3bve739DuXEZgFsu1JLnv3refCOW8nRXzWG/ceNGZdCgQYpWq1VatWqlhIaGKkePHrXY1s8//6yMHj1acXd3V9zc3JShQ4cqu3btslo3ID8/X5k1a5bi5+enODg41NrP6hw/flwJCwtTWrVqpWi1WmXQoEHKpk2brD7r7NmzyuTJk5WOHTsqLi4uSq9evZS33npLKSsrs5oTfNWqVUq/fv0UFxeXGp9tQUGB8vLLLysBAQGKs7Oz0qlTJ2XOnDlKVlZWrTVRBOFG0Rj6UJW6xrOlcVZWVqYsWrRI6dmzp+Li4qK0a9dO+dOf/qScPn3aYh58W+uAVK1vYu2nahv1Gc/79+9XHnzwQcXT01NRqVRmdYOsfUbG+0JCQpTWrVsrjo6OSufOnZVZs2Yp58+fr3FtbbUA6qpFItx6TJ48WQGU999/v85rjfW0EhMTlbS0NOWll15S7rvvPqVdu3aKk5OT4ufnp4waNUr54osvzO77+OOPlZCQEKVbt26Kq6ur4u3trfTv31956623atT0sTZ2ioqKlL///e9K165dFScnJ6VLly7Kyy+/rJw7d04BlHHjxpldX1tdrro0rDq11QGxxurVq5X7779fcXd3V5ydnZVevXopr732mlJUVFTj2trqgFjSA0WxrI2KoiiLFi1S7rjjDsXJyUkBTO1+++23yqxZs5S+ffsq3t7eiouLixIQEKBMmTJF+emnn2x+L0VRlP79+ysdOnRQDAZDjXPGz93aj6W6T3q9XgGUd999165+NCdUimJHPjGhQfn000+ZOnUqK1eurJFFQxAEQRAEoaFJSUkhKCiIv/3tb7zxxhs3uju3BKtXr2by5MkkJiaa0g9fD2FhYezevZvU1NQWm1Cjeey/CYIgCIIgCA3G77//XuPYpUuX+Nvf/gbQIBNhwTYmTZrEwIEDWbBggV11RCzxww8/sG7dOhYsWNBijQ+QGBBBEARBEISbjueee45Dhw5x33330aZNG86dO8eWLVvIzs7mz3/+c63xK0LDolKp+OSTT0hMTOT33383K1xpLxkZGSxcuJBZs2Y1YA+bHjFABEEQBEEQbjJCQ0O5cOECGzduJDc3FxcXF+68805TmmChaenbty99+/a97nZGjx7N6NGjG6BHNxaJAREEQRAEQRAEocmQGBBBEARBEARBEJoMMUAEQRAEQRAEQWgyxAARBEEQBEEQBKHJEANEEARBEARBEIQmo95ZsHJycjAYDA3ZF0EQ7ESj0eDt7X2ju1EvREME4cbTkjUEREcEoTlQHx2ptwFiMBgoKyur7+2C0KxQFIWcnBwKCgpwc3PD29sblUp1o7t1UyMaItxMiIbcGERHhJsJRVEoKSmhrKwMR0dHnJ2db1odkTogwi1NXl4ecXFxxMTEkJqaajoeEBBAREQEOp2uRVcaFQShcRENEQTheikpKeH48eMcPvwLBQWXTcfd3Dzp2/dOevTogbOz8w3sYcNT7zogmZmZsuogtGh27drFrFmzKCoqIiwsjLCwMLy9vcnJySEhIYGEhARcXV1ZsmQJw4YNu9HdtYijoyNt2rS50d2oF6IhQktHNOTGIzoitHTS0tJISdlOWZmBI0c8+OUXT4qL1bi4VHDnnZfp2fMKjo4aRo58iM6dO9/o7lqkPjoiBohwS7Jr1y4iIyMJDg4mKiqK9u3b17gmIyODGTNmoNfriY6ObpYTiJY8eRANEVoyoiHNA9ERoSWTlpbG1q16TpxwIympI/n5NR2T3N0NhIT8TvfuBYwaFdwsjRAxQIRbFnv8r/Py8hg4cCBDhgwhKSkJjca6J6LBYCAkJIQ9e/awb9++ZudK0ZInD6IhQnPDVh0RDWk+iI4IzQl7YjhKSkr4/PPVHD3qzP/+15mKCuuxHmq1wuTJaQQGlvD44481O3es+uiIxIAILZr6+F/HxcVRVFREVFRUrRMHqMzssGzZMvz9/YmPj2f69Ok1rpHgU0Fo2dirIw2tISA6IggtmfrEcBw/fpyyMgNJSd1qNT4AKipUJCV14LnnTnD8+HF69+5d45qWFsAuOyBCi6U+/teKojB06FAGDBjAmjVrbH5WeHg4Bw8eZPfu3aYB3RyCT1vy6qVoiNAcsFdHGlJD4MbrSEvWEBAdEW489YnhUBSF1atj2b8f4uI62fwsne4c99wDjz020aQjzSGAXVywhFuG+vpfZ2dn06dPH2JjY9HpdDY/LzY2lvDwcH766Sd8fHyaTfBpS548iIYIN5r66Ejfvn0bREOMz7/ROtKSNQRER4QbS31jOIqLi1m1ahWxsZ349VdPm59355156HTneeKJJ3BxcWk2AezigiXcEuTl5TFr1iyCg4NN/teKonDp0iXy8/Nxd3fH19eX9u3bk5SUREhICLNmzWLfvn0UFBQA2F0wx3h9QUEBhw8frnXSotPpTJOWyMjIZht8Kgi3MvXVkcTEROD6NMS4iCE6Iggtl5KSElJStnPihFuVGA4FrbYcJ6cKSkvVFBY6kJ+v4X//68zkyZXGwuOPP2YymouL1XY9s6jIAYCysjIyMzOrGD/dahg/v/7qaTJ+ysv1zS6A3b43F4QbjKIoREdHm/yv8/Pzef/99+nZsydt2rShW7dutGnThp49e/L++++Tn5/PsmXLKCoqIj4+Hjc3N6Cyeq49GK+vqKgwm7RYWjEFTJOW4OBgZs2aRV5e3vW9uCAIDcb16Mi2bduA+muIm5tbDeNHdEQQWh7Hjh27GsPRESenCgYOvMRTT6Xy4ovHeOaZE7z44jGeeiqVgQMv4eRUQVJSB8rKDBw/fhxHR0cAXFwq7Hqmq2s5UDkXqWr8WNp5AUzGz4kTbqSkbKekpOT6XroBEQNEaBHk5eURFRXFkCFDWLRoEaGhoRw6dIguXbowb948+vfvT2xsLCkpKcTGxtK/f3/mzZtHly5dOHz4MKGhoURHR+Pl5UVAQAAJCQl2PT8hIYGAgACSk5PtDj41Gj+CINxYGkJH4uLirktDvL296xXELjoiCM2DkpISfvrpJ775Zj+//upBu3bFPPPMcYKCLpCR4UJsbCdiYvyJje1ERoYLQUEXeOaZ47RrV8KRIx4cPvwLTk5OuLl5cuedl+t+YBV69bqCm5snZ8+eNRk/tgawG42f5oIYIEKzZ9euXQwcOJCFCxfSt29fDAYD3bt3Z8yYMQwePJi0tDTWrFmDTqdjxIgR6HQ61qxZQ1paGoMHD2bMmDEEBASQmppKbm4uERERJCQkkJGRYfYcRVHIysri9OnTZGVlYQyPSk9PJzExkYiICFatWkVYWJjVFcvqdOjQwWT81DPcShCEBqChdOTkyZNMmDDBooaAZR0xakhkZCQAMTExoiOC0AJJS0vj889X8/XX36JSVXDpkhOTJ5/l7Fkt7757O/HxlTEdJ0+68+uvnsTHd+Ldd2/n7Fktkyef5dIlRwoKLlNaWkrfvnfSs+cV3N0N1Z6ioNUa8PIqRas1AJVj3t29jJ49r9CnTy9++ulXjhzxsLrzUZ38fEeT8dNcNEQMEKFZY/STHjJkCGlpabz77rsAvP/++3a5L3zwwQdApf+1TqfD1dWVGTNmYDAYyM3Ntep+8Z///IcpU6bg4uLCpUuXSE1NJSwszK53CAsLIzU11W6XDUEQGoaG1pERI0aYaQhQq46MGDECFxcXgoKC+OCDD0RHBKEFYgw4P3rUmaiobgDce+8lUlPdWbOmdjeoNWs6k5rqzqBB2UBlDEePHj1wdNQQEvI7arWCi0u5VTeuQYMuERqajqOjhvbt21NQcJlffrE9eB3g1189KCi43GzcsCQIXWi2WAoSzcrKAiq3QO3NwQ+V/tetWrViyZIlREZGcv/993PkyBFTFpqFCxeaZaF58cUXAXBwcOC///0vUP/g0/Pnz0uOf0FoYhpDR9q3b2/SkJCQEB5//HFmzZpFYWFhDR2Jj48nISEBR0dHhg8fTmlpKSA6IggtieoB5y4ulbEYDg4KGzbY5ga1YUMHnn220gXKWKdj5MiHKC/XM2PGKXx9S9FoKjhyxJMdO9qasln16nWZoKALANx2Ww82bNgE1D+APT8/v1nUChEDRGi2WPKT9vHxwdXVlUcffdQu94Xx48ezceNGKioqSEtLo2/fvjz77LO88847jBo1ihUrVljNQjNt2jT0ej0ff/wxf/7zn+sdfDpq1CjTsaasFSIItzKNpSMBAQEsXryYZ555hi+++EJ0RBBuYqoXDSwsVFNWpuLoUfvdoO68M5+KigquXLlCmzZt+OMf/4CiHOT4cTc2bPCzms1q3LjfUamOk5HhTIcOhnoHsK9bt850rClrhVRHDBChWaIoikU/6ezsbIqKipgwYYLNbeXm5qLVajEYDPTr18903MHBgVGjRrFhwwarK6Dt27dnw4YNhISE8MILL9C9e3cSEhLsyv8fFxeHl5cXS5cuxcfHx7S7snDhQt55551GrxUiCLcqoiOCIFwviqJw+PAvZjEXWm0Fjo6KXTU8XFzKKStTU1Gh8Pnnn5uOV1TAiRNurFnjb3UnJT9fw+rVnZk0KQ1//0IuXXKkV6/Ldj2/V6/LFBWp2bixA8XFDqZaIVeufMv+/d81eq2Q6ogBIjRLcnJySE1N5Y033jA7np+fD9juvqDX65k4cSKFhYWMHz8enU6Ht7c3n3/+OatWrWLFihV2uV/06dPHFHxqy8ppeno6SUlJLFq0iIkTJ5qOS45/QWh8REcEQbheSkpKrsZcXKtY7uRUuftgqxtUQEA+Ot05HB0rXax+/bWyYGCfPnn065fHhg1+drlxXbjgRs+el3F3N9i0A+PuXsYdd1whObkdv/56bbf0RtYKkSB0oVlirWCgu7s7YFsOfr1eb5bhxli5+KGHHuKbb75hwoQJdmeh+fnnn2sEn1rDYDAwc+ZMtFotERERNc5Ljn9BaFxERwRBuF4sFQ0sLa38f1vcoAIC8q1kynKjc+cifv3V0043Lk/atSuhrEzF2LGVAey1oVYrjB2bTlmZmkOHvCy0eWNqhYgBIjRLrBUM9PHxMbkv1EZubi4TJ060mOHm0qVLHD16tF5ZaI4fP87y5cvR6/WEhISQnp5u8dr09HRCQkLQ6/Um1wlLSI5/QWg8REcEQbheLBUNLCxUm9ygasPFpRyd7pzFTFlabTmtW5fa5UYFcOSIB76+paxf35GAgHwmTUrD3b3M4rXu7mVMmpRGQEA+cXGdKC52sHjdjagVIgaI0Czx9vY2K/ZlTHHZq1cvTpw4QXx8vMUc/Eaio6MpLCy0mOHGXveLqn0CuPvuu9m0aRN79+7F39+f8PBws+JlOp2Ozp07s3fvXjZv3kxQUFCt7UqOf0FoHERHBEG4XpydnU1FA6+lyj2Jr28ZvXpdtlDH4xr9+uXi6FhhMVOWvW5cRozZrNLTXfnf//zx9y/k2WePM2HCOe68M4/bbsvnzjvz0OnSeO654/j7F/K///mTmupea7tNXStEDBChWaJSqUwFA1evXm1WqXjlypW4uLgwffr0Gu4LiqKQmZnJhx9+aLXQlz3uF1UxXu/h4UFwcDBnzpxh0aJFHDp0iPDwcIKCgggPDycpKYknnniCs2fP1jlpMCI5/gWh4amPjhgLCZ46dYrFixeLjgjCLY5KpbpaNPAyzz57reL5unUdMRisuUEpaLVlDByYzZEjll2s7HHjqooxm1VJiZrUVHfee68HycntaN++GJ3uPBERZ9HpznPHHVc4dKgV777bo07jw0hT1goRA0Rotuh0OhwdHfnTn/5kVql4ypQpJCQkkJycbHJfqFoErG3btrUW+vL19SUwMLBO94vqJCQkEBgYiI+PDwBeXl7MnTuXI0eOmCYsI0eOxGAw8Pjjj9uVFtO4Kmr0WRcEoWGwVUd+++03s0KCt912GydOnBAdEQQBrVaLSgVnzlyL4zh0yIu1azubuUGZFxM8jo9PmVUXq8JCB7KynOp046pOz55XyMpyMu2EFBc7sG+fL4sXB/DWW7fz3nvdWbKkGw4O8NNPrSgpsex2ZQljm8a4l8ZEDBChWaNSqSz6XwcHB5vcFzp16kT79u2ZN28e/fr1Y/HixYB11wiVSsXs2bNNWWhsIT09ncTERObMmVOjaI9KpcLX1xdnZ2d27NgB1H9V1OizLghCw1GXjuzcuZPevXvz/PPP069fP2JjY1m1ahUgOiIItzolJSXs2rWHEydqxnGkprqbuUHNm3fMtEOyaVOl1lh3sVJx4IC3KZuVLbi7l9Gz52UOHPAGqmfNUlFUpCE314ny8spz9d1dMca9NCZigAjNlri4OEpLS62muAwODmbFihWoVCoefPBB0tLSWLt2LeHh4UDtX96RkZFotdoGyUJT/ZpOnToRFxdnx5tWrooGBATY7U8uCELt1KUjAKWlpQQHB3Pu3DnWrl2LTqczFfwTHRGEWxtjEcL16y1XPE9NdWf9+o6oVHDypHmmK6jdCDh0yIuyMrUd2ax+t5rNqup1I0dewGDA7t2VXr2u4Obm2SRFCcUAEZol1gqIVSU3N5dp06aZioAZr7PFNcLLy4vY2FibstCMHTuWLVu2sGTJEotZaKpmqomPj+ehhx4iMTHR7lXRyMjIGquigiDUn7p0pGqWq/Xr15tdIzoiCIKlIoTVcXEpZ9y436/ukPibrrPFxaq42IG4uE42ZrM6S48eBWRlOaLRWDZqrmW9KuCHH7zqsbtyhb5972wSDZFChEKzxFoBsapYy1BjdI2YN29erYW+jO4XEydOxN/fn5CQEFOBsZycHOLj41m3bh2Ojo44OjryxBNPkJiYaHZNQkICiYmJaLVaU6aajz/+GJVKxYwZM0hKSqq1QJlxxdPV1dWuqsyCINRNXTpSW5Yr0RFBECwVIayO9UxXlS5WQUEXai0YaHTj0unO8eyzx/ntNw9+/dWToiIHXF3L6dnzMj17XqG8XMVPP3nSq9cVnnvuOEeOVL/uCj17XqasTM3//ufP+fOu3HVXHuPG/c7q1Z1rLXSoViuEhGTg6KihR48e9f247EKl1DPXVmZmZpMEqQi3JmlpaQwaNIiUlBRGjBhR47yiKPTs2ZN+/fqxdu3aGudzc3Pp0qULgwcPrvPLOysri6FDh17dZr32Nx0YGMicOXOIjIw0raR++OGHnDhxwnRNQEAATz/9NFOmTKFVq1akp6fj7+/PY489xurVqwkODmbZsmV06NChxnPT09OZOXMmer2emJgYhg4dau/HhKOjI23atLH7vuaAaIjQ2NSmI0YN6d+/P2vWrLF4/62gIy1ZQ0B0RGhcrly5wpo1a4iJ8efkSUuZpBSeeiqVjAwX4uNrGikuLuU888xxzp7VsmZN7UaAq6uBqVNP4+tbikOVuPGsLCcOHPDmxx+9KClxwMWlnLvvzub++y+ZuXdduuTI/v3e/PijNyUlDri7l/Hcc8dRqVSkprqRlNSB/PyasR3u7mWEhKTTvXsBo0ePolMn68aWNeqjI7IDIjRLrBUQM2IsArZw4UKL542uEWPGjCEkJKTWL+/p06dz5MgR1Go1t99+uyldp4+Pj9k2ZEREBBUVFfz3v/81TR5SU1P5+OOPAXj88cdNq5AvvfQSo0aNYtasWfj7+xMaGkpoaCgODg5kZGSwbds2Nm3ahFarrbfxIQhC7ZSXVwZUWtKRujQEREcE4VbHUhHCqhiLCe7Y0dbieaOL1eTJZ5k0KY0NG6wbAWPH/k6bNqWoVFBcrGLfPl9++MGL3FxHqgacFxc7cOCAD2VlKoYNyzL1zde3jLvvzgVUHD7c6uqOhiPDhg1Bo9nDc8+duLpr4k5FhQp3dwMBAQXcfns+jo6OBAXVz/ioL7IDIjRLFEXhD3/4A0OHDiU2NrbG+cOHD9OvXz+rOyRG9Ho9EydOpLCwkNDQUMLCwmq4Rjg7O/PMM89w7Ngx1q1bh1arJTY2luDgYIvthIWFmbWTkJBAQkICarUag8HAZ599ZpoI5OXlsWrVKj755BPy8vLMAlXbtm3L9OnTeeKJJ+xKtVmVlrx6KRoiNDbLli3jtddeIywsrMYux+nTp+nWrVudGgLm43/8+PFMmDDhptGRlqwhIDoiNC6KohAd/Rk//OBkcYejXbtiZs8+WcsOSSUBAfnodOdwdKzgyBFPjhzxMLlO9epV6WJlMKjYvbs1OTnOV49VulPFxXUyq+NRva1ff/WkuFiNi0uF6T5FUaHRKIwePZpOnTpRUlLCkSNHOHToMEVFJWY7LI6OLvTv34eePXvWO/hcdkCEm4ry8nJTEGZ1/+uNGzcCdaepNBb6iomJ4Z133jEzZgIDA1m0aBGRkZGmL+6MjAxmzJjBmDFj2LRpE8HBwej1esaMGUNwcDBRUVE1+qLT6cjIyGDatGkkJyebVRD94YcfWLx4MUVFRRYnHG+//TaLFy9myZIlDBs27Ho+LkEQqqAoCqtWraJPnz6mVLlVx649hQSr6shrr71mlp1KdEQQbm5UKsVU8bx6HEePHleAutPdGgsG9uuXy91359C797XA9EuXHNHr25lcrAB+/dUTd3cDY8f+zuTJZ02VzAMC8pk8+Sypqe5s2NCxRn+M940bd54ePQpNOnLx4kW+//5HysoM/PabJ7/8cs1oufPOy5SUfMf33//IyJEP0blz5+v+zGxBdkCEZkl2djZ9+vRBq9UyfPhwM/9rRVG44447uHjxIsHBwVb9t6uSm5uLv78/99xzD0uWLMHb27uGa4QRg8FASEgIe/fu5fDhw/Tt29cmH3CDwcC4cePYu3cv+/bt44cffiAyMtLqhAOuTVT0ej3R0dF2Tx5a8uqlaIjQmBg1ZOXKlfzlL3+pMYYrKipwd3fn0UcftRhHZonc3Fzatm3LkCFDbhodackaAqIjQuNSXFzMqlWrKC1Vcfq0W7U4DoWnnjqBm1s5qanuFndILOHiYmDevGOcPetKQkInCgo01KzpUYlarTBpUhr+/oV8/PFtzJ590qZ4ErVaYfLkNAIDSxg2bAjbt+/gxAk3kpJqGi0A7u4GQkJ+p3v3AkaNCrbbCKmPjkgaXqFZYqzk+8orr9RIcXnp0iWOHTtGSEiIzUXAoqOjKSoq4rPPPqN79+74+vpaTTOn0WhYtmwZhYWFPPvss1az5Fi6LyoqisLCQubOncuf//xni8XPqtK+fXuSkpIIDg5m1qxZ5OXl1fkugiDUjVFDOnXqZDFVbnZ2NkVFRXaluv3www+pqKgQHRGEWwSjcbtnT+saqXIr4z/K+O03D7vS3d5zTzZqNSQmdqagwDy+ozoVFSo2bOiAo2MFwcEXrGTbsnxfUlIHysrK2L59JydOuPG//3W2mokrP1/D//7XmRMn3EhJ2U5JSYlN73I9iAEiNEuMQejdu3c3VTz39/cnPDzctOMxbtw4m4qAKYrCxx9/TGhoqNUv8Op06NCB0NBQtm7dWq/7duzYQVFRkc0TjmXLllFUVER8fLxNzxEEoXaqJrIwpsq1pCPOzs42FRIsKyvjnXfeqbU2UXVERwShZWMMQs/OdjareD5hwjnuvLPS0P/tNw87iglWcN992fz6q6dVY6A6+fmOHDniQY8e+bXWI7F034ULzlRUVJCUZI/RYuD48eM2PeN6EANEaJZ4e3sTEBBAQkKCyf960aJFHDp0iKeffhqonBDYUgTsl19+4ejRo3bnxw8LC6OoqMgsiNTW+9Rqdb0mKitXruTs2bNkZ2dTT+9IQRAw1xDAqo785S9/samQ4COPPMLly5dbhI4sX76cS5cuiYYIwnXi7OyMm5snd9552RTHkZzcjvbti3nkkQsAODhgczHByZPTcHGpMFVJt5UjRzxxdFQ4ccJ6oHtNFLTa8noZO4cO/czly5cpLi5uNB0RA0RolqhUKiIiIkwuVl5eXsydO5cjR46QmZlpZpxUX9mMjY0lJSWF2NhYwsPD6d+/P1A5IbEH4/VOTk523efg4IDBYKjXROXUqVPce++99OnTh6FDhxIVFSXuFIJQD6prCGBRR1JTU+vUEH9/f7755hugZejImTNn6Nu3r2iIIFwnKpWKvn3vpGfPK7i7GygudmDfPl8WLw7grbd6kJ3tSK9el03FBKvvkNx2Wz533pnHhAmVRQY7dy4EoLjYvul3UVFlcHp5ue0VyrXaclq1Mtht7Pz6qweFhVdYu3Ytq1atYvXqWH7++ecGd8sSA0Rotuh0OlxdXc3cI1QqFa1bt+bpp582TSyqr2yGh4cTFBREeHg4hw4d4p///CdgW7abqhivLy0ttes+42SnvhOVVatWERsby4ABA1i4cCEDBw5k165ddrUlCIJlDYGaOtKvX79aNcR4HFqOjixevFg0RBAagB49euDoqCEkpKqLlYqiIkf27fMxxX9U3yHR6c4TEXEWne487dsXk5zcjuhof6DurFnVcXWtrGnk4GD7boSTU+Uz6mvsJCR0JDa2E/v3w1dffcvnn68mLS3NrrZqQwwQodnSqlUrlixZYtE9IjIy0iz+o+rKZlZWFqdOnSIrK4sjR47wwgsv4OnpaZY60xYSEhJwdXVFr9fbdd+2bduA+k9URo8ejU6nY82aNaSlpTFkyBAiIyNlAiEIdlKbhsA1HZk2bRru7u5WNWTu3Ll07ty5RenIpEmTREMEoQFwdnZm5MiH6N69gMmTzV2sDh3yMov/MN8huZ333uvOW2/dzuLFARw44MOwYVkYDNCr1+VanliTypogKrp3z7f5ntLSyil+fY2dEyfc+fVXT+LiOvGf//Tg6FFntm7VN5gRIgaI0KwZNmwY0dHR7Nmzx8w94sCBA/zf//0fW7ZsYezYsaaJhUqlwtfXl65du+Lr60tGRgbjx48nPz+fdevW2ZztJj09nYSEBPr06WNXlpz09HQ2bdpE+/btTb7ntpKQkEBgYCA+Pj6mY5LdRhCuD2sakpKSQnJyMr169WLr1q2MGzeO9PT0GhqiUqlIT09vsToiGiII10/nzp0ZNSqYwMASnnvuBDpdpYtVx45F7N/vTffu+UyadLaKcaKiqEhDbq4TRUUa3N0NTJqURkBAAT/84GVX1ix39zJ69rzC77+7mFzBbEGtrqC8vD7GzhWyspxMOyHQOFmypA6I0CLIy8sjPj6e6OhoUlNTTcfbt2/PxYsXUavVNSqdJyQkkJiYiFarZeXKlUydOtXmPPyPPvooKSkplJeXo1arCQ4OZsOGDXXeZ8z7/9JLL/H3v/+dtLQ0mwJI09PT8ff3Z9GiRcydO9fq+fnz5zN9+nTT8Zacw180RGhKrGmIh4cHV65cwc3NjZKSkptWR25GDQHREaFpKSkp4fjx4xw+/AsFBdcm9leuOODmVo6iUKPSec+eV8yqmp8/78ozzxy3uZ7HY4+dJSCgALUaKioqixquXl33fZMmpdGtWwFqtcK7795uUyC6u3sZzz57nOTkduzb52vx/HPPneD++wfRu3dv0/H66IgYIEKLQlEUcnJyWL58OR9++CE//vgjffr0YcqUKXzzzTccPXrUdG1gYCBz5swxVSiuWol42bJldOjQoUb76enpTJ8+na1bt/LRRx/xwAMPsH37dubNm0dQUBBRUVFW75s5cyZ6vZ7Nmzdzzz330KVLF5snKsYJx5kzZ/Dy8rJ4XXh4OAcPHmT37t2m2gMtefIgGiLcCIwaUlBQwLp163j77bepqKhg5cqVXL58mY8++sgmHalLD6ZPn05KSgqffvop/fr1s6gj1auzN7aO3GwaAqIjwo1BURRKSkr4+eefOXjwBz7++Db+7/9O8sMPrejcuYjWra/FfGVlOXHggLdZpXPziuYdyM93rPEMd/cyxo1Lp0ePAh58cDht27YlMzOT7dt3cOyY9moldEfatSvmwgUXs/vGjk0nICCfuLhOhIT8brOxYyx6+N57PSgudrB4nU53jnvugccem3hdOiIGiNAiycvLY+DAgQwePJjU1FT69+/P6tWryc7O5sqVK3h4eFisUKzX65k4cSIFBQWMHz8enU5nWumMj48nMTERgMcff5w33njDdN+uXbuYNWsWhYWFhIaGMmHCBIsrpHFxcQQFBZmeNWbMGEaOHMny5cttMlyM91rCmJHnp59+MrlXtOTJg2iIcKPJy8vjnnvuQa1WM3r0aNasWYOiKDbpyLhx4zAYDISFhZntmMTFxbFu3TqcnJxYvnw5Q4cONd1XVUcmTpxIr169uOuuuygoKGgSHbnZNARER4QbS0lJCZ9/vpqjR53w8iojI8OF+Hg/XF3LcXauoKREfdWVqebEPyAgn8ceS0OtVvj1Vw+OHPE07Zr06nWZnj2v4ODgwKhRQXTqdK3KelpaGl98oQcUjh1zp1u3Atav74hKRY3dltRUd5uNHaPR8r//+ZOaaj3d75135qHTneeJJ57AxaXS8BEDRLil2LVrF5GRkdx+++0cO3bMZjeF3377jTvvvJO2bdua+WRrNBo6duxIdnY2+/fvp1WrVmb35eXl8fzzz5OSkmKWUaf6CmlVVq9ezRNPPAFQw3CJj49n3bp1NSYc1khJSSEoKIhvv/2Wzp07Ay178iAaIjQHdu3axRNPPIFKpeLcuXM2uzp17tyZcePGmeoMGXFzc8NgMLBnzx6zSYORvLw8nnvuOQAGDRrE119/TXJyss06Un3hxJrhYombTUNAdES48aSlpbF1q57MTEd8fErtdnc6etSDtm1LzHZNSktVODurCA+fiIeHR417f/zxR/btO0BJiRpX12tB5pZ2WwB6984lNPT3qy5i5sZOz56Vxk5Vo6U2brstn4iIs0yaNMnUt/roiG2VSQShGWIMLv3zn/+MoihMmzbNJv/q559/HldXV15//XU2bNjApk2bcHV1pWfPnvzwww/ExMTUmAAY6devH8nJyTz00EMsWbIEb29viyukxmd9/vnnaLVa/t//+3+sXLnSLIOOn58fixYtsjjhsIQxu42xwrMgCNfPsGHDWLJkCbNnz7ZZQ2bMmIGLiwtjxozBwcGBEydO4OLiwu23387hw4dZtWqVVeMjLi6OM2fOEBoaCsDgwYNZtmwZnTt3tklHoqKizCqdBwYG2qwjoiGC0PAYA9STk7dhMMDYsb/b5O40dmw65eUqjh1zp6ICvL1LMRhUZGc70aFDCaNGjbJofFQNAHd2rjQ+yspULF3ajawsZ6rvtqjVCn37Xqa0VMXevW24665cevc+bzqfl6chObldDaPFGsYsWcYq8fVFdkCEFk9eXh5vvPEGn3/+OcHBwbW6KRjjO4x/9n5+frRp04affvoJrVbL0qVLzVwmjBhdJ4qKirjvvvv46quvCA4OtjkmJCgoyOTakZ2dzR/+8AdGjRplV0rPm81/WzREaE5s3ryZ2bNnExQU1OgaMnv2bHx9rwV49unTx2SQVH+eJR25cOECPXr04MEHHyQpKcmi4WKJm01DQHREaD6UlJRw4MABfv31CMePu5liNKpT6e70Oz16FGAcunl5GgoLHWjXrgRHR0eCgkZYXMRIS0sjJWU7ZWUGrlxxoFWra94YX3/tQ3Ky+Q6uZdcqBVfXclxcDPz5z6c4ccKd+PjONr+nxIAIQjV27tzJrFmzKC4utprJRqPR4O7uTlZWlum+gIAAIiMj0el0eHrWrBhqdPUyGhzt27c3xZIYY0KsZc2x5hKxcOFCXn31VbtcPm62DDaiIUJzo6qRMH78eIuxXhqNBg8PDzIzM0332aMhH3zwAatXrzZz4ywrK+PkyZOEhITYrCOiIZWIjgjNjbS0tKu7IeUcOeLBr796VIntuELPnldQq9U4OTlSWlpsus/NzZO+fe/k9ttvx8nJyWK7W7fqOXHCjeTktsyceQpHx2tT+IoK2LSpPbm5Thazb1lyrRoy5CLDhmXxn//Y7jYmWbAEwQLWUm1WnSB4eHiYsuC4ubnh7e1tdQXRGOw+ZMiQGllocnNziYmJqTNrjiVyc3Np3749Dz74oM1pOffs2cO+ffvM2mzJkwfREKE50tgasn37dr799lsACgsd0Gor3Rn279/PF198YbqvLh0RDalEdERojlhL11vVyHB0dKSkpISysjIcHR1xdna2qiPXgt2d+d//OjNy5AXuvTcbMNeRqliLB6mKi0s58+Yd49QpN5tS+06efI7AwGIef/wxnJ2dTefEABGEq1RNtVnXBKE2oqKiWLhwYa0B7pmZmbRt25bFixczadIkqzEh1Xn55Zd58803GT16tE2uXDExMTVcO1ry5EE0RGjONIaGuLu78/7772MwGCgrUxEV1Y0ZMypXMcvKyujSpQsjR460mn2rOre6hoDoiNC8MabrtcXIqI2ff/6Zr776lv/8pwcAf/nL8au6Ya4jACkpbfj+e2+r2beq8+CDFxg8+BInTrizfr31LFkhIel0717A6NGjariHSRC6IFxFpVLh4+NjVlXcXhRFISYmhrCwsFpdHAoKCoDKFcuqft11MXz4cN544w1ThWZrrlyurq4WJw6CIDQejaEher3e5Hp14IA3Fy648N133tx7b7YpoLNr1642ty8aIgjNG5VKhYuLiyldbX1QFIXDh3/hyBEP8vM1BAdnmIyN6joC0LFjMV99Zfv0/vRpN4YMuURgYDHPPXfCqtuYo6OGoKCaxkd9EQNEEKyQk5NDamqqWT0QS7i7u5uut7d9qMzzv337dqKjo4mNjTWdDwgIYP78+Vb9ygVBaN5U1ZD8/Hy+++47oDJjzddftwbgq69aM2BADo6OCunp6eTn55s0xZb2QTREEG5mSkpKKCi4zC+/dMLd3cCAAZXj3pqOBAbm4+5usCmmA65ltdLpwjh79iweHr9w553XsmRVuo0NshqbUl/EABEEKxh3Nry9vWu9ztfXl8DAQBISEtDpdDa3n5CQQEBAAF26dGH69OlMmzatQVw+BEFoHlTVkK+++sps98M4OcjP15hWLxVFMWXYswXREEG4+TG6GBYXq7n//iyz3Q9LOqLRKNx3X1aNjFjW6NXrCm5unnh4eNC7d2/uvPPOBnEbqwt1g7coCDcJxlz5de1sqFQqZs+eTUJCgllhw9pIT08nMTGRyMhI08A2unx07tzZ5jgSQRCaL0YNyczMtLj7YeSrr1pTVlY53r/77jvy8/PrbFs0RBBuDYzumV5eZRZ3P4xU1ZG7787B3d1AXbi7l9Gz5xX69r3TTEdcXFzw8PDAxcWl0XREDBBBsIK3tzcBAQEkJCTUeW1kZCRarZYZM2aYpde0hMFgYObMmbi6ujJhwoSG6q4gCM0Mo4Z88803Fnc/jBhXL6FSH7788sta2xUNEYRbB2dnZ9zcPLnvvksWdz+MVNURR0eF++/PqtFWVdRqhZCQDBwdNfTo0aNxOl/b85v8iYLQQlCpVERERNi0s+Hl5UVsbCx6vZ6xY8eSnp5u8br09HRCQkLQ6/UsXbrUpgrogiC0TFQqFU888YQp/sLSqqWRqquXX3/9tVkK4KqIhgjCrYVKpeKOO3rg61sK2K4jAwdm07ZtkcXr3N3LmDw5je7d8wkKGmGWUrepkDS8glALtdUBqY7BYOD+++/n4MGDqFSqWjPSWKuWbC8tOYWmaIhwK7B7926OHTsGWK5UXJXg4AxTJptvv/0WT09P0ZA6EB0RbgW+/PJLjhw5AtinI4oCv/7qWUtWK8sV1+1F0vAKQgPTqlUrlixZQmRkJCEhISxbtqzWXPvff/89S5YsIT09XTLSCMItTmFhoWkno7ZVSyNVM9kMGjSIuLg40RBBuMUpLCw0LWLYqyMODmoGDKhokqxW9iI7IIJgA7t27WLWrFkUFRXZvLPRUIXMaqMlr16Khgg3O9988w0///wzAOXlUFBQ95qfm5sBh6tFi3v37k1gYKBoSC2Ijgg3Ow2hI3fddVejZrWSHRBBaCSGDRvGvn37iI+Pt3lnoyEKmQmC0DIpLCw0uUwAODiAp2fdWWmqcuTIEfr16ycaIgi3KA2pIx4eHg3dvetCDBBBsJFWrVpJrn1BEGzi2LFjVqsfK4qCoihUVFSgVqtRqVRWNeTYsWP079+/EXsqCEJzpS4dMf63agpda+00Nx0RFyxBaMG0ZPcJ0RBBuPG0ZA0B0RFBaA7UR0ckDa8gCIIgCIIgCE2GGCCCIAiCIAiCIDQZYoAIgiAIgiAIgtBkiAEiCIIgCIIgCEKTIQaIIAiCIAiCIAhNhhgggiAIgiAIgiA0GWKACIIgCIIgCILQZIgBIgiCIAiCIAhCkyEGiCAIgiAIgiAITYYYIIIgCIIgCIIgNBligAiCIAiCIAiC0GSIASIIgiAIgiAIQpMhBoggCIIgCIIgCE2GGCCCIAiCIAiCIDQZYoAIgiAIgiAIgtBkiAEiCIIgCIIgCEKTIQaIIAiCIAiCIAhNhhgggiAIgiAIgiA0GWKACIIgCIIgCILQZIgBIgiCIAiCIAhCkyEGiCAIgiAIgiAITYbmRnegpaAoCjk5ORQUFODm5oa3tzcqlepGd0sQhBaE6IggCNeDaIhwsyAGSB3k5eURFxdHTEwMqamppuMBAQFERESg0+lo1arVDeyhIAjNHdERQRCuB5OGrFxJ6unTpuMBXbsSMXWqaIjQ4lApiqLU58bMzEzKysoauj/Nil27djFr1iyKiooICwsjLCwMb29vcnJySEhIICEhAVdXV5YsWcKwYcNudHeFWxBHR0fatGlzo7tRL24FDQHREaF505I1BG4NHdm1axezZs6s1BA3N8JcXfFWq8mpqCChqIiEgoJKDVm2TDREuCHUR0fEALHCrl27iIyMJDg4mKioKNq3b1/jmoyMDGbMmIFeryc6OloGvtDktOTJw82uISA6IjR/WrKGwM2vI7t27SIyIoJgFxeivL1pr6npuJJhMDAjJwd9cTHRMTGiIUKTIwZIA5GXl8fAgQMZMmQISUlJaCwMeCMGg4GQkBD27NnDvn37ZAtUaFJa8uThZtYQEB0RWgYtWUPg5taRvLw8Bg4YwBCViqTWrdHUEuthUBRCsrLYoyjs++470RChSamPjkgWLAvExcVRVFREVFRUrZMGAI1Gw7JlyygqKiI+Pr6JeigIQnNHdEQQhOvBpCHe3rUaHwAalYpl3t6iIUKLQQyQaiiKQkxMDGFhYRbdJSzRoUMHQkNDiY6Opp4bSoIg3ESIjgiCcD0oikLMypWEublZdLuyRAeNhlCtlugVK0RDhGZPoxogiqKQnZ1NWloa2dnZDTogGqvtnJwcUlNTCQsLs+u+sLAwUlNTycnJaZB+CILQMjUEREcEoTnREnUkJyeH1NOnCXN1teu+MK2W1NOnRUOEZk+jpOFtzJST9rRdn3zZBQUFAHh7e9vVL+P1BQUF+Pj42HWvIAjmNBcNAdERQWipGMf6pzGfcir1lOl4t4BuTImY0iA6Ykvb16UhavvWiY3Xi4YIzZ0GN0Cqp5x84403zFJOLly4kHfeeadeKSdtbXvRokWkp6fXa/Li5uYGYPfqgfF64/2CINSP5qAhS5Ys4a677qq3ESQ6Igg3ll27dvHkrCcpKiqiY1hH7n7jbhy9HSnLKSM9IZ1XF77Kv9/5N58s+aReOmJL2+8uerdyLlKP2h0mDamosKtvxutFQ4TmToNmwapvyklbVgdsbXv69Ols2bIFlUqFTqcjNDQUBwcHMjIy2LZtGxs3bkSr1VqdvCiKwtChQxkwYABr1qyx+fMIDw/n4MGD7N69W6qSCk1GS85g05AaAnWvMtrT9tatW3FycqKsrIzQ0FCCgoJwdnampKSE5ORkEhMTa63dIToitBRasoaAdR2JiIygTXAb+kf1x6W9S437ijOK+XHGj2TqM4mJjrFLR2xqe/qPZGzJQK2Azt2dUBcXHFQqMsrL2VZSwsaCgsq5iJXaHYqiMPSBBxiQlcWa1q1t/jzCMzM52KYNu7/8UjREaDJuaBre+qSc3L17N08//TSxsbG1rjDW1raiKFy6dIn8/Hzc3d1p1aoV48aNY+/evfy///f/+PTTTzl69Kjp+u7du+Pk5MTRo0eJsZIvOyoqioULF5KWlmZTAGl6ejr+/v7Mnz+f6dOn13m9IDQULXny0BAasmfPHlJSUtDr9bXuVAC1tl1VR1xcXJg6dSrbt2/nhRdeICEhwUxDAgMDefzxx/nyyy/ZsWOH1dodoiNCS6AlawhY1pG7B96NxxAP7km6B7XGugtThaGC/SH7ubLnCttTtqPX62t1qQKstq0oCqWXSjHkG9C4a9C00rB/3D6upGTxirsn0fn5HDUYTNd312hwUqs5ajAQs2qVdQ1ZsIA0Pz+bAtHTDQb8z59n/quvioYITcoNNUDs/bJdvXo1TzzxBCqVqs7qwCdOnKjRdm5uLtHR0Xz88cc1Jgf33HMPn3/+OWq12mrbarUatVrN999/X2MLVPL3Cy2Fljx5uF4NSU9Pp1OnTjg7O1NWVlarjoSEhLB69eoabVvTET8/P37//XfUajUTJkyw2K5WqyUwMJAjR46wf/9+0RGhRdKSNQQs68irC18lKC3I4u5EdYrTi9F30uPo7IihzEDHsI50COtg5lL1e8LvuLq6EhoSyuerPzdruzS3lLToNE59fIr8o/mmdt0D3en0eCd+W/Ab6grQabWEubldq2BeUEBCYSFqQO3szPc//GBZQ6QOiNACuGEGiL3uBnq9njFjxjBy5EhWrFhRp5uFr68vQ4cOZe3atab7J06cSGFhYY1JR3x8PAkJCTg4OPDpp5/y2GOPWWzb6Ko1fPhwVq1aVeOaqu4ay5Yto0OHDjWuSU9PZ+bMmabV16FDh9b57oLQkLTkycP1aAhU6sDDDz9McHBwnTqyZcsWHnjgAXbv3m12vzUdiYuLIzExEa1WS1xcHMHBwRbb1ev1lJeX86c//Yk333yzxvNFR4TmTkvWEKipI4OHDqZsQBkD1gyw6f4L+gt88/A3tAtux10r7qrVXSvjiwx8B/syePdg070HJh6gvLCcjmEd6RjW0WS4/J7wO78n/I5KraKNoiK9Y6caLlEZBgPTL11iS1ERwx980Ppc5Gol9GXe3nSwsJCRbjAw82ol9JhVq0RDhCbnhhkg2dnZ9OnTh9jYWNM2pTVyc3Pp0qULgwcPtmlVcNy4cWzdupXly5czZcoUk/Fiq4/4pk2bakwejG2PHTuW5ORkwsLCWLBgQY0Vg6oBq6GhoTVWQY1+4EuXLpUBL9wQWvLkob4aAtd05IEHHmD9+vV16sjYsWPZvXs358+fx8vLq0F0pKqGVFRUsGTJEsaMGVOjHdERoTnTkjUELOvI3bF346fzq/Pe0txSkrsk4/uALwPXD6zTXevbsd9yafclgs8Hk7Mvh2/HfEvb4LbcFWXdcPlh+g9c2HKBWN/W6Nzda1xjUBTGXrxIclERYRMnWp+LzJxZqSFaLWFa7bWdlMJCEgsLKzUkKko0RLgh3DADJC0tjUGDBpGSksKIESNqve/9999n3rx5drlZdO7cmSeffJLnn3+e/v37c++997J582YcHR2t3md0adi7dy9nzpzBy8vLatsVFRW4ubmxdOnSGn6Yubm5xMTEsHr1as6ePWs6HhAQQGRkJBMmTKC8vNyu9HqC0FC05MlDfTUE6qcj/v7+vPPOO4wZM6bBdKSqhqjVaj7++GMeeeQRs2sUReHMmTPEx8ezbt06TlfNhiM6ItxgWrKGgGUduS/lPtqOaFvnvanvp/LzvJ8JTgu22V1ra+et3P7S7aS+l4rPvT4M2jwIB0cHq/cYDZeClCzOdfDDy6HmtekGA53PnaMCcNNqWWohMN00F/nsM86eP286HtC1K5HTpomGCDeU+uhIgxQitDXlpKIofPzxx3ZVB3Z1daV3796sWLGC7t27k5+fT0pKCn369OH9998nNzfX4n0ajYZly5ZRWFhITEyMxWs6dOhAWFgYAQEBDB48mMjISHbt2gVU+l5GRUUxduxY3nrrLZPx0aVLF/7617/y2WefoSgKjz76KH369GHQoEH06dOHoUOHEhUVRV5enk3vJwiCfWlrr0dHXnrppQbVkaoaMnLkSGbPnl1DQ4YOHcr999/Pu+++y+nTp+nWrRvPPvssX331FRs2bBAdEYQGwqgjZTlldVxZqSOnPj5Fx7CONhkfpbmlnI89j8Zdw7HXjlGeX05mSiY7++wk9f1USnNLLd6n1qj5w/I/UKQoxFyt7VGdDhoNYVotARoNgxWFyIiImnORRx6pnItcNT66dOpUORdZvbpSQx5+2FxDHnhANERo1jRpDEhWVhZt2rSx2c2iqo/2+PHj0el0FgNBY2NjLbpZQWVay0OHDnHkyBGLqwGxsbGEh4eb4kL27NnDokWLeP755021AiwFoCqKgqIo6HS6WgPo7c0vLgj20JJXL+sbA9LcdKSqhkydOpUvv/yyVg2Jj48nMTERJycnFEWpM4BedERoTFqyhkD9Y0BKskrY0maLTe5aZrEeoR3pOKFmrIeD1oG7Y++mXXA7i218p9uPy6ZMjrXraHkuUlBAeGYmGZ06MT0nhz2KwqL33uP5Z56p1BE3N8JcXa+5XhUVkVBQUDkXoTLVr6Xzrq6uVlP9CkJD0eyzYBlX/2xxs2ioWA/j5CArKwtfX98a51NSUggKCuLUqVM4OzvTqVNloNioUaNqfe60adNISUmx+FxrdQoEoaFpyZOH+mbBam46cj0aotfrWbp0KTNmzKi1X6IjQmPRkjUE6p8Fq+B0ASndUup017qgv2BbrMeMH7iov8igTYMsGiHnY89zIPwAWZ0742vBDSulqIigCxc45eeHs0pFp3PnKnVEqyXK29tiGt4Mg4Fply6RUlTEpnbtCHZ1rXF+xtXg9GgrZQcEoSG4YS5YADqdDldXV2bMmIGhSq7rqrhfDcCqy80iNzeXiRMnEhwcTFJSktXJSPv27UlKSiI4OJiJEydadKPw9vYG4MqVKxbbMPbFw8MDV1dXHB0dCQoKqvO5GzZsYOTIkYSFhdV4btV+zZo1S7ZABcEGbNEQaH46Ul1DNBqNzRpi1IiEhIRa+yU6Igi2YdSRH2f8SIXBehVxjXvlhL42d63S3FIOTDxA2+C2DEwaaNWgcWnvwsCkgbQNbsuBiQcsumM5elfGml2xUtncWMHcQ63GVaXCEQhycSGpdWurNUDaazRsaNuWka6uhF28SG55eY3zSa1bE+ziwqyZM0VDhGZFgxkgrVq1YsmSJej1ekJCQkhPT69xja+vL927dyc+Pr7WtqKjoyksLCQqKqrW7DZQt4921cmBJRISEggMDMTHx4fo6GjKy8tZsWKFTc9dvnw5xcXFvPTSS1b7VVRUVOf7CoJgm4YAlJaW4unpSVxcXK3tNZWOVNeQiooKuzQEYOLEiej1eqv9Eh0RBNto1aoVnyz5hEx9JvtD9lOcXmzxuorSCjSeGs7Hnbd4HiAtOo3ywnLuirqr1gxZUBnrcdeyuygvLCctJq3GeaOh46G23E5CQQGBGg0+ajXRBQWUAyt8fWut/QGgUalY7utLsaLwkoXFE41KxTJvb9EQodnRYC5YRmpLORkXF2cqAnju3DmLq4OKotCzZ0/69+9vcz0AsO6jXZvvtjEzzqJFi3j66afp2bMn/fr1M9UbsYWJEyeyfv16MjIyTKuk1ft18OBBdu/eLRkphAanJbtP1FdD1q1bh4ODAxUVFaSlpXHhwgX69etn1kZT6UhDaEh4eDhbt25FURTOnj1rMWOf6IjQWLRkDYHadeTJWU9SVFREh9AOZjU6zsedJ31dOjgAFXDv1ntp+5C5G5aiKGzvuZ1W/Vtx95q7be7PgfAD5B3K46EjD5mN1f26/bDxIufa+9WcixgM+J87xyIfH5728KDn+fP0c3Jibdu6M3kZmXjxIusLC8no1AlvC4sf4ZmZHGzTht1ffikaIjQ4N9QFy8iwYcPYt28f8+fP5+DBg4SHhxMUFER4eDgpKSkoioKzs7NVN4tLly5x9OhRwsLC7HpuWFgYR48eJTs723QsPT2dxMRE5syZU2PAGQwGZs6ciVarJSIiwvTcCRMm2PXcCRMmUFpaypIlS6z2KzU11absPoIg1K0h5eXlvPvuu2i1Wv70pz/x4IMPkpGRYdZGU+hIQ2lIWFgYly9frjVjn+iIINjHsGHDOLDvAAvmL8DpoBMHwg/wddDXHAg/wMWUiyjlCr3f7Y3aRc03o7+h8Fyh2f2ll0rJP5pPx7COdj23Y1hH8o/mU5Z9zSgqTi8mfV06WWXl5FVzwTIoCjMvXUKrUhHh5saligqOGgxMuJrRy1YmuLlRCizJz7d4PkyrJfX0adEQodnQ4AYIVG6BTp8+nd27d/PTTz+xdetWAJYuXUpgYCADBgyw6maRf3XwWNpNqI3qPtrVJwdVSU9PJyQkBL1eT1xcHF5eXtf93KioKCxtJhnPF1hJvycIQk3q0pA9e/YQGxvLjh07yM7OZsGCBWb3N7aONIaGjBo1io8++kh0RBAaCKOO7N2910xH+i3th3ugO9l7smk7si1KmcKXQ740c9cy5FcukBpjN2zFeH3ZlUoDpMJQwQ8zf8BB60Ap5ql40w0GQi5eRF9URFzbtng5OJB/1UDxtuKqZQ3j9VFXrljWkKvnRUOE5kLtTsrXiUqlwsfHx/QH7+vry+zZs5k3bx4xMTHMmjULf39/MzeLM2fOALbVA6hKVR/t9PR0pk+fztatW7n//vtJTk6uUXlYq9WyefNmgoKCANsDW6099+TJk2RnZ9fIkGM872bnaoYgCLVryMsvv4yjoyOlpaUsXbqU33//nT/96U8NriN6vZ6//e1vHDhwoFE1ZPz48cyYMUN0RBAamOo64uzrTLfZ3fjp+Z9QO1ZOzAtPFbK181b8wvwqdz2uzv9tqSlSFeP1jh6OFKcX88PMyuxY926+l9PLTvPWxou0U6tJvFrBXKtSsbldO4KuZrByv2oo5FgJVreG8fqT5eVkV1TUyLRlPC8aIjQXGmUHpDpVi4xFRkai1Wr5/PPPSU1NZdGiRRw6dMjkZjFz5kxcXV3tDpaKj4/Hz8/PZNR8+eWXKIrCvn37zFw4Dh06xKJFizh79qxp4gCVKyW2BLZWJyEhAX9/f8ByhpyEhAQCAgLsXhUVBOEaljQkJCSE0tJr2Wa+/PLLBteRnTt3AvCvf/3Lbg05dOiQTc80BrF37twZEB0RhMaiaqHCzpGdUTmoqCi+NtFvPbg1eYfyOBB+gAO6A6g0qlqD1C1xPv48Ln4u/Dj7R/T+ei7tvcS9m++lbVBb/HR+/F5iYFJWFodKS1nk48PZzp1NxgdAK5UKT5WKuIICDpVaLm5oiYSCAvyvGh2WMm0lFBYS0LWraIjQbGgSA+TQoUNoNBri4+Px8vIiNjYWvV7PlClT0Ol0HDlyhKysLE6dOkVWVhb/+te/SExMrOHXbQ2jj/b58+dJSkpi/vz5bNy4EYAFCxbg4ODA8OHD+fnnnzly5Ahz586lVatWZvePHz+e/Px81q1bZ/dzH3zwQaBmhhzj+cjISAn6EoTrwNvbGz8/P5O705IlSzh16pTZNcXFxfzyyy8mHfnb3/5GQkJCvXVk3rx5rFu3joqKCrs15PDhwxZjU6w9c86cOab0v6IjgtA4HDp0qNKoiD9vZngYydmXw/077+fhrIcZeWokd7x6B+nr0inOsJxJqzrF6cWkJ6ZTfL6YS3sv0fO1ngSfDaZtUGUwudE9S9+mDUf8/Jjr6UmrKq5W6QYD4zMzyVcUEgsLGZ6RQUYtKcmr3pdYWMiDLpVpgqtn2jKej5w2TTREaDY0ugGSl5fH7Nmzuf32201GRXBwMJs2bWLv3r34+/szadIktm/fzvHjx9m+fTu7d+9GURSmTZtWaz0AqPTRnjFjBlqtlj179qBWq3nnnXdMBXd69OjB5s2bOXjwIP3792fSpEnExsaSkpJiKi7m7+/P3r17iYuLw8nJyebnGn3Dc3NzTWk4q593dXW1OyhVEARzLl++TFZWlklDDhw4YDrn6FP5pV5UVMT8+fPZv38/c+bM4Z///CcA06dPt1lHXF1dmTdvHiqVijfffJPRo0cD8Ne//tVmDdFqtYwbN47s7GzefvvtWp9ZNb6kajrf6teIjgjC9ZGXl8efZ/8Z99vdSU9M58g/jqCUVsZKGDWkvKicH2f+SO73ueTuzyX3QC6KovD9tO9rrSkCV2M9ZvyA2klN24fbUpJZwrF/HSP722sJLYzuWQ9nZjIpM5PYggJSiooqq6BfvIj/uXPsLS4mrk0bVFS6Tb1VR+2OqkHsuRUVplS+ZudzckRDhGZHoxsgcXFxFBUVmXymjdmvgoODOXPmTA0XrPDwcI4cOYKfnx9bt26ttR6AMRA0OTmZv/3tb4wZM4aKigqCg4NZu3Yt/v7+xMfH1/qsQ4cO8c477/DDDz/whz/8gb59+9r8XL1ez5IlS9i0aZNZhpyq55cuXWq2UioIgv3ExcVhMBhMma8+/vhjABxcHXhgxwOoXSqlLCEhwTSuAwMDcXJyIjk52WYdqaio4L333mP8+PHExsaSnJyMn58fJ06cqFVDFi1axJkzZxgyZAj//Oc/OX36NAAfffSRxV2Q6kHsRo0UHRGExsE4zu5JvAe1i5ozUZVxYtU15MLmC6ZsWVeOXMHVz5WLWy+yL2Sf1ZoixenF7AvZx8XkiwxMGsh9m+9j1LlR+A725dsx33JBfwGA83Hnuc3FkUXe3hwqLSU8M5OgCxcIz8zkUGkp73h780PHjnR2cMBYUvCDK1c4VFJi8blVg9iX+PqyqaiIOZ6e1zTEYCAkKwt9cTFLo6JEQ4RmRYPXAamKoigMHTqUAQMGsGbNGvR6PWPGjCE4OJhly5bRoUMH03XZ2dlcuXKFgoICXnzxRZKTk3n11Vd56623KCwsZPz48UyYMMEUTB4fH8+6devQarX89a9/5R//+AfBwcFERUWZ6ou8//77zJs3j7S0NNOxqs+qqKhgw4YNLFmyhKNHj5r67eDgYBrA1esQVA1AXbNmDR9++CG7d+/ms88+o6yszHTe1dWVpUuXMnTo0Pp8vIJgEy05h78tGgLmOjJ16lRGjx5tyvIS8FwAfRb14afnfiL13VQAIiMjyczMJDk5mc2bN6MoChMnTrSoI8bx6uzsTFFREaNHjzbTEKipI1U1xMPDA7VaTUxMDB9//LGZjhi5/fbbWbhwoUUNiYuL48EHH2Ts2LGiI8INoSVrCNg+Fxk8dDBlA8oYsGYA+0L3VdYBwbKG+E/3p/uz3fn5xZ/JTM7kjlfv4PhbxykvLKfD+A74TfAz1RT5PeF3fk/8HQetA/fE3WNyt4LKXZF9Ifu4tPcSQ/cNZUfvHbzXypu5np6VOlJRwZWKCiqADYWFLLlyhaMWdmtVgE6rJczNDW+1mpyKChIKCkxB7GvatOHDK1fYXVzMZ61bU0ZlzEdiYWGlhkRFiYYIjUp9dKRRDZDs7Gz69OlDbGwsOp0OAL1eX+dkwPjFHBQUxG+//UZYWBjHjh0zc6Pw8/PjxRdfZNy4cfTt25fBgweTlJRkVn04NzeXLl26WDxXtR9hYWFmRkZ8fDzx8fGoVCrat2/P+fPXgtACAwOZM2cOwcHBPPfcc2zdupWKKgFfAQEBREZGotPp8PT0rM9HKwg205InD7YaIFV1ZPDgwXTp0oXS0lIcXB0YeXIkLu1dKM4oJrlbssmv293dnYSEBFOQuDUdCQwMZOrUqbz++usMGTKkhk6AfTry0EMP8dRTT5kFx1fHqCGRkZEUFhYyY8YM0RHhhtGSNQTsm4vcHXs3voN9TVphTUNUDioUFDRuGpNRceW3K+wP20/+sXwUw7Vpk3ugO93mdMM/0h/HVjVT9hanF6P31+PW3Y3i4wWkd+xE6yoZqvRFRUy8eJFCRSFMq+UhV1eeunSJ6grSXq0mo4pGBGo0zPH0JNjFhedyc9laWEhVJ7GArl2JnDZNNERoEuqjI42ahteY8q5q1gWjO1RMTAwfffSRWdYpLy8v/vSnPzFu3Dhyc3OZOHEi69atw8XFhbZt23LPPffwyiuvMHDgQO677z7mzp3L+++/T2FhIVFRUTUmDsaA9zFjxhASEmLadam6E1N9tRNAp9ORkZHBtGnT2LJlC/feey+TJ0+mQ4cOGAwGEhMTef7553F1dWXVqlX07duXgoIC3Nzc8Pb2liAvQWhAqurIv//9b9Pkvuvsrri0rwy6dGnvQrfZ3UwrmPfffz8qlYrY2FjTbqlRRwYMGMChQ4fo168fSUlJfPDBBxQVFVnUELBPR5577jlT/3zUarKrTBjuuecennzySTp37kxubi5PPvmkaZdDdEQQGg+jhjh6O3L838dNCxXWNEQpV/C404Oer/WkLLeMAxMPkL4u3aQh6nvU9H63N44ejjj6ONY6Vl06uNBhfIfKHZdyhSlZWSzz9aWDRoO+qIgxFy4Q7OpKlK8v7TUansvONhkfVTUko6KCe52cmOzuTgcHBwyKQmJREc9fje9Y9fnnoiFCi6LJd0CqYnRlOH/+PJs3b+bTTz/l2LFjpvPdunVj6tSpjBgxgvvuu4/Y2FjuvvtuunXrhkaj4ezZswwfPpz+/fuzZs0aq/2ouko5ZswYkpOTGTZsGOvXr7c44TBiMBgYN24cycnJZqumsjopNBda8uqlvTsgn3zyCXPnzqW4uNhs5dJI9V0QI5Z05Oeff+b1118nLS3NJg0Bcx155JFHSElJMdORjIwMunXrRnFxMa4qFd906MCg9HSKFQW1Wo1KpaK8vNzUnuiI0BxoyRoC9s1F+n/Sn8NzD9fY/TBiTUP8u/kzY+oMk4bcHXs3fjo/m/t4PvY8B8IPENumDTOysihUFMa4upJcXMwwFxfWt22LRqUiw2Cg2/nzFCtKTQ2h0hWrvEq7ssshNBfqoyONGoTu7e1NQEAACQkJFs+rVCp8fX3p27cvL730Er/99htZWVk88sgjdO3alT179jB9+nTUVzM6eHt7m4p9OTk5ERkZydGjRwkLC6u1H1WD0L/++mtKSkpYvnx5rcYHgEajISoqCoCpU6cCla5fu3btYvr06TLgBaEJMOrIO++8Q3FxZRBo1ZVLI8YVTCPdunWzqiMREREoikJERIRNGgLmOrJr164aOvLvf//b1L/ZHh70c3Ji9tWUuhUVFVRUVIiOCMINwNvbm24B3TjxzgmLux9GqmuItpsW/67+fLXnKzMNqW919LudnDjTqROLfHz4uqSEEkVhua8vmqs7Ff++fJniq2vCNTTk6s/Uq7VM/Nq3Z9fevaIhQoulUQ0QlUplSi9pSy5+lUpFaWkper2eadOmmQZ71SJkvr6+BAYGMmDAAHbs2AFgU2EdLy8vnn76aby9vQkLC6vhdmWNDh06EBoaSnJyMgDnz5835esXBKHxUalUjB8/3rQ76uDqQI8Xeli8tseLPUzZbE6dOoVOp7OoI7fddhsdO3Zk+/btgG0aAtd0xNPT00xHMjIyTJm5XFUqXrg6IXjR0xOXq5MLtVrNli1bANERQWhKVCoVYePDyD+WD9iuIYWnCgnXhdfQkPpWR/dQq/FycOBpDw+81WrCtFraX13AyDAY+PhqEVKrGgJsKSoC4HxGhmiI0KJp9DS8Op0OV1dXU/rd2rCW877qTopKpWL27Nl8/fXX/Pe//wUqJxS2cOnSJY4ePWp3LuywsDDOnz+Pn1/llqvRn1QQhKYhMzPT9P+WVi6NVF/BvHjxoun/q+vIvHnzTOds1RCo1JG0tDQzHam++2GcVLTXaEwrmOXl5WRkZIiOCMINoKE0pFtAN9ITLKf0tkZ63Hm6uzia6nNcqqjgqMHAhKsGDdTc/bCoIVTGgvhdbUc0RGjJNLoB0qpVK5YsWYJer7e5tkb1nPfVd1IiIyPRarVs2LCB7t27Ex8fb1Nf8vMrVz9sXe00Yrx+0KBBwLVVEEEQGp+LFy+ydu1aoPaVSyNVVzDXrl1rmkBY0hF3d3c8PDxs1hCoqSPWdj+MVF3BBOjfvz8gOiIITUVDasiUiCn8nvC7XdXRf1+XztNaD1NQeP7VwHLvq4aEtd0PIzU0xMkJEA0RWjaNboAADBs2jOjoaPbs2YO/vz/h4eEWKwnv2bOHmJgYi/mqq+6kuLu7m4qEOTk5maoj14UxfsSe1c6q1xcVFREQEGC3ASMIQv356KOPTLsLFYYKdg3YxdZOW63+7BqwC6W8ciWxuLjYZBxATR2Ji4ujoKDAZjdRuGaAGHXB2u6HkaormAC//vqr6IggNCGNoSE/zvjRpuroh6b/gFalIqKKseB+1fDIuWqIWNv9MFJDQwwGArp2FQ0RWjRNYoBApRGyb98+5s+fz8GDB80qCR88eJD58+ezf/9+q8Vyqu+k9O3bl02bNpGWloaiKEybNq1WFy9FUSgrK8Pd3Z3PPvsMe5J/xcXF4efnh16vJzIyssWktjNmGUtLSyM7O9uudxaE5sDFixdZtWqV6XelTKH4fHGdP0rZtb/1mJgY0wqmJR2JjY0FqFNDAMrKynj22WdxdHTkf//7H+np6bXufhipuoJ56tQpQkNDW4SOiIYILZ3G0JBPlnxCpj6T/SH7a62OfmDsPi5uvUCCbxu8rtb+UBSFsooK3IHP8vNJr2P3w4iZhhgMhOp0LUJDQHREsEyjpuG1hqIo5OTk1Ctf9a5du5g1axZFRUWEhoYyatQoEhIS+OKLLxg1ahTLly83VViHyiJi0dHRLF68mBMnTpiOd+/enaeeeorIyEi8vLysPi89PR1/f39uv/120tLS2Ldvn5l7WHMkLy+PuLg4YmJiSE1NNR0PCAggIiICnU7X7N9BsI2WnELTFg1ZvHgxK1eutHq+oqICRVFQqVSmQFFLTJ06laeeesr0e1UdGT9+PJ07d+a9994jODi4hoZApY58+OGHvPPOO1y+fNl0vFWrVuTl5QHwnKcni3x8rPbhuexs3r16b2RkJP/6179qffcbiWjIrUNL1hCoW0caU0OenPUkRUVFdAjtQMewjqbq6OfjzpOxLh2tSkWCbxuCXF3JLS8nuqCAxZcvc6LKQkcrlYq8q9Owm0lDoIqOrFxJ6unTpuMBXbsSMXWq6MhNRLOrhN5Y5OXlER8fT3R0tNmXozEdZmhoKGFhYaSmpvLaa69RUlJCaGgoOp3OrNq5sep6bGwswcHBNZ5jrAOybds2ysvLWbVqldUdmuZC1YlV9QrvCQkJJCQk4OrqypIlSxg2bNiN7q5wnbTkycON1BC49uX45ptvUnQ1s4yxXkdoaCgTJkzA29ubnTt38p///AeDwWCmI6dOnWL27NmUl5fjqlJx0s+vhutEVarm+HdxceGbb76hbdu2TfW6NiMacmvRkjUEmsdcZGX0Sk6lnjIdd9CoUAwKY11deczdndSyMl7Ly6NEUQjVatG5ueGtVnPKYGD2pUuUw02lIXBVR2bOrNQRNzfCXF3xVqvJqaggoaiIhIKCSh1Ztkx05CbgljFAjFy6dIm+ffuyePFiJk2ahFqtZtWqVXz00UccPXoUlUrFqFGjWLFihcW0uxkZGcyYMQO9Xs+mTZvMjJD09HSmT5/O1q1bcXFxYfny5S3C+IiMjLRa4R3M3zk6OloGfgunJU8emoOGGAuULV++nAcffJCKigo2btzIxx9/zNGjRwGs6shzzz3Hu+++C4Aj0Paqi0VtXCwvx/jGTz75JP/4xz8a+pWuC9GQW4+WrCHQPHTENBfx8WGSmxtqRWFVYSEfXb7MUYMBFTDK1ZUVV6udG6m6o3GzaAhc1ZGICIJdXIjy9rZoVGUYDMzIyUFfXEx0TIzoSAvnljNA0tLSGDRoECkpKYwYMcJ0PCcnBz8/P4YNG8aGDRvqrHY+duxYdu/ezWeffUZZWRlxcXGsW7cOlUrF5MmTeemll5p9oZ+8vDwGDhzIkCFDSEpKqvOdQ0JC2LNnT4twKROs05InD81ZQxRF4dSpU9x5550MHz68ho5UrXpeX5rbCqZoyK1JS9YQaGY60q4dI1xdTcdzysvxO3eOYS4ubLha7dxI1d2M+tLcNASu6siAAQxRqUhq3drsnatjUBRCsrLYoyjs++470ZEWTLOrhN7YVC0sVpWYmBjKyspYsWKFTdXOly9fbnLTCg8P58CBA7zwwgscPnyYN954o9kbH1AZKF9UVERUVJRN77xs2TKKiorsSj8qCDcb1jREpVKxceNGDAaDRR359NNP8fX1xc/Pz/RTPW7EwcEBDw8P2rVrR/v27Wv8eHl5mQLgmwOiIYJQP0w6UmGeFSumoIAyRWFFlWrnRj7Nz8dXrcbPwcH006HaDkhL0xCooiPe3rUaHwAalYpl3t6iI7coLXoHRFEUhg4dyoABA1izZo3pWM+ePenfv7/pmC3odDq+/PJLkpOT8fHxaTHZJcDy52ALxgxku3fvblHvK1yjJa9eNlcNMR6/lXRENOTWpSVrCDQjHXngAQZkZbGmdWvTsZ7nz9PfyYk1duxQ6C5e5EutluQdO1qUhoDlz8EWwjMzOdimDbu//LJFva9wjVtuB6R6YTG4Vu08LCzMrrZ0Oh0ZGRmoVKoWNwBycnJITU21+52Ngfr21kURhJsFSxoCt56OiIYIQv1RqVRETJ1KQkEBGVczXBmrnYfZWSxQ5+ZGRlZWi9MQuKojp08TVsUNzRbCtFpST58WHbnFaNEGCJgXFjMYDNdd7bygoKDB+9gYVM2rff78eeDmf2dBaAyqawjUrHZuKy1pTImGCELDYdKRnBwMilKj2rmtGK9vKWPKoo7c5O8sNAy1O/q2AIyFxSIjIwkJCeHNN98E6l/t3M3O1Yqmxlp+frh531kQGpPqGrJs2TLc3d2Bm3NMiYYIQsPTqlUrlixbRmREBCFZWbx5NXa0elxIXRivb+5jylqND7h531loWFr8DghUVlmPjo5mz5499O/fHy8vL7sDmhISEggICLB7BbAp2bVrFwMHDmThwoUMGDCA2NhYUlJSWLt2rSkYLSsri9OnT5OVlVVntVFr7yxVS4Vbjaoa4u/vz5w5c/Dz87vpdEQ0RBAaj2HDhhEdE8MeRaF/ejpeajXxdq7qJxQWEtC1a7PVELiqIwMGsHDBAgZkZRHbpg0p7dqxtnVrvNRqYvPzySov53RZGVnl5XXriJV3Fh25uWnRQejVMRYFev/998nNzeXcuXMW89hXx1jtfP78+UyfPr0Jemo/teXnz83NZdq0aaasPUYCAwOZPXu2xWrvlt5Zqh+3PFpyAGlz1hBjkVMHB4ebRkdEQwRLtGQNgeatI++/9x652dmc69Sp1gKDRtINBvzPn2f+q682Sw2B2mt85JaXM+3SJTYWFmKock+gRsNsT08i3dzwqpbpy9I7SwX1lsctVwfEGrm5uaZ89uvXr282+ewVRSEnJ4eCggLc3Nzw8vIiNzfX9Lu3t7fFoLPa8vPr9XomTpxIYWEh48ePN6v2bqxaXL3au6V3lurHLZOWPHlozhqiKApnzpwhODi4WemIaIjQ0LRkDYHmrSO5ubkMvPtuhgDr27RpNjUxrktHrNT40BcVMfHiRQoVhfFVqr3nVFSQUFBAQmEhWpWK2LZtCb4apG7pnaWCestEDJAqVF3tW7ZsWY0c/VC5gjdz5kz0ej0xMTGNVunc2qqgq6srRUVFpt+trRJGRUWxcOFC0tLSzFYt9Xo9Y8aMsblq8aZNm+jbt2+Nd5bqxy2Xljx5aO4aAs1HR0RDhMaiJWsINH8dqbpjsMzbmw4WFjLSDQZmXq0KHrNqVePPRartLLhqNBRV2fm0ttMQFRXFwgULSPPzM9v50BcVMebCBYJdXYmqVu3dSIbBwIxLl9AXFbGpXTv6OjrWeGepoN5yEQOkGlVX5EJDQ2usyCUmJuLq6srSpUsbbcDXtioYHx9PYmIizs7O/OUvfyE1NdVslXDo0KFkZ2fz6KOPMmjQILP8/Lm5uXTp0oXBgwfbVLV43LhxbN++HYPBgFarNb2zVD9u2bTkyUNL0BC48ToiGiI0Ji1ZQ6Bl6EjVVf1QrZYwrfbaqn5hIYmFhZUaEhXVuHMRKzsL8QUFJBYW4qxS8RdPT1LLy812Gkw68vDDDMrJYU2Vv5fc8nK6nDvHYBcXkqpVe6+OQVEYd/Ei24uKMECljlx9Z6mg3rIRA8QC1X26jQQEBBAZGYlOp2u0Suf2rgpu2rSJfv36MX36dPR6Pa1bt+bChQsAxMbGotPpTPe9//77zJs3r8aKpjXS09Pp3LkzwcHBLFq0yPTO1lZGa2unOfu532q05MlDS9EQuHE6cr0a0rZtW9LT0wHREMEyLVlDoOXoiElDVqyoEdcQOW1a489FbNlZqLJD0c/RkenZ2eiLiirnIpmZAMS2aYOuSraq9y9fZl52Nml2xLl0PneO4IcfrqkjFnZXamunucfL3EqIAVIL1X0erfk4NhT1WRXcu3cvZ86cwd3dnbFjx7J9+3Zef/11XnjhBVJSUhgxYoTpXepbpfmbb75h3759qFQqqX58E9CSJw8tTUOgaXWkITRkx44dvPbaa6IhglVasoZAy9ORGzIXsWdn4eJF9hYXc6ZTJ9zVasZe3bF43cuLF3JzSWnXjhFXYziup9r7Nx4e7Dt48JqOSAX1Fs0tVwndHlQqFT4+PnTu3BkfH58G/WO1lCouLi6OoqIioqKiap04AGg0GpYtW0ZhYSExMTFoNBqWL19ORUUFpaWlgHl+/pMnT9a7SvP58+c5c+aMqU2pfiwIttNYOtJYGlJeXm5RQ66n0rtoiCDUnxs2F/H2rtX4ANCoVCzz9aVQUYgpKECjUrHc15cKoPTqNVVrfFxPtffzFy6Y64hUUL/luGUMkMYgLy+PqKv+i3369GHQoEH06dOHoUOH8sEHH/Doo4/a5JIA0KFDB0JDQ/noo49QFMX0e3R0NIGBgSQkJACVQaP9+/cH6l+1eOzYsURFRZGRkXFd7UjVUkG4Pm6EhgBs3rwZEA0RhJsBk4488IC5jjzwAB+8/z6ParU2uTUBdNBoCNVq+ejy5Uodufp79JUrBGo0JFQZs5uvJsCob+XzsQ8/bK4jUkH9lkIMkHpiraBXbGwsAwYMIDc3F71ej16vt7nNsLAwjh49SnZ2tun3Y8eOERERQUJCAqtXr2bMmDHce++9QP2rFt9///0sXLiQ8ePHX1c7UrVUEOrPjdCQjIwM9Hq9yWdaNEQQWjbWigLGtmnDgKwscrOz0RcWoq+SLa8uwtzcOGowkH11tyPMzY1j5eVEuLuTUFhIhsGAvqiI6VlZQP0rn99fWsrCBQsYP27cdbUjOtIyEQOkHhgDQ4cMGUJaWhpr1qxBp9MxYsQIdDoda9as4dy5cwwbNowxY8bYPIEwrgpeuXLF7PcxY8bg6urKlClTCA4OZvPmzXTv3p24uDi7+p2QkEBgYCBJSUmkpaUxdOhQ1Go1ixcvtrud5lztWRCaOzdCQ7RaLZGRkUycOJHg4GDREEFo4RiDy4eoVKT5+bGmdWt0bm6McHVF5+bGmtatOdepE8NcXBhz4YLNRohxZ+HK1Qm+8fcxrq5oVSois7KYePEiwS4udNdoiLO32ntBAYEaDUlt25Lm58dQlQo1sPiqbtncTguoGi9YRwwQO8nLy2PWrFkEBweTlJRk1T2iffv2rF+/nuDgYCZOnEhubm6dbRtXBT08PMx+9/Pz4/HHH6e8vJyoqCgcHR2ZPHkyiYmJpq3LukhPTycxMZE5c+agUqlo3749SUlJjBo1iq+++oqjR4/a1U5kZKQEfQlCPbhRGhIbG8u2bdsoKChg+fLloiGC0ILJy8tj1syZBLu4kNS6tVUXq/YaDeuvFv+bePEiueXldbZt3FnwuGp4GH/302iIbduWbcXFFCgKy1u3ZrKbG4lXd0VsId1gILGwkDmenpU6otGQ1Lo1o7Raviou5mhpad2NVGkncto00ZEWihggdnI9gaF1YVxd9PHxQVEU/ve//3HbbbdRXl7Ojh07CAsLM01WIiIiUBSF6dOnY6hj4BsMBmbOnIlWqyUiIsKsf1FRUQCEhoba3I6rqysTJkyo830EQahJU2kIQHx8PAEBAVy+fJk//OEPdOzY0aQjoiGC0HK5nuDyujDuUPio1ZVzkfx8bnNwoEJRGOnsjJ+DA2FX40oi3N1RgOmXLmGoI6mqQVGYeekSWpWKiCpuUxqViqirmhWalWVbOzk5oiMtHDFA7EBRFGJiYswMgbqoHhhqDeOq4JQpU/jggw+4/fbbWb9+PSdPnqRdu3acPHkSrVZrWgW97bbb6NixI1u3biUkJMSU699SuyEhIej1euLi4vDy8rLYv2PHjjFu3Dib2lm6dCmtWrWymHFDEATrNIWGzJkzh7y8PBYuXMi6detITU3ltttuo23btmRkZJh0pDloiPEzER0RBNtRFIWYlSsJc3Ord3C5NYw7C1Pc3fngyhVuP3+e9UVFnCwvp+25cwT+/jtp5eWMvpqx6jaNho5qNVuLigi5eJF0K4sQ6QYDIRcvoi8qIq5tW7wcHGr2z82NY6WljMvMrL2drCz0xcUsjYqSuUgL5papA9IQZGdn06dPnxoFveoiNjaW8PBwsrKy8PX1rXHemMN/586daDQaCgsLCQ0NZcKECaaKx3Fxcaxbtw6tVktsbCzBwcG8//77PPfcc7i5udVapVmr1RIXF0dQUFCt/XN3d6e4uLjOas/9+/cnLi6OmJiYGkXZIiIi0Ol0Upm0iWjJOfxFQxpeQ/bu3cuKFSuYNm0aBQUFhIaGotPprOrIb7/9dkM0xFj5WHTkxtOSNQRucR2pVhSwLmILCgjPzCSrc2d8qxkAcK0OyM6iIjQqFYWKQqhWywQ3t2uV2wsKiC8sxEWlIuGqa9f7ly/zXHY2bioVRVfvCat2T2JhIVqViri2bQmykm7X2D93V9dKHamjarxpLrJyZY3ijhFTp4qGNCH10RHbTGcBuJbqrb4pJ69cuVJj8pCens7MmTPZsmULarWa4cOHW6x4rNPpTBWPx4wZw6ZNm4iMjGT+/PkMGjSIUaNG8d///pfY2FjTPYGBgSxatIjIyMhaB6Gxf+vWreObb74hOjrarJ2AgADmz5+PTqfj+++/Z+DAgRQVFREWFsYbb7xhNslYuHAh77zzDkuWLGHYsGF2fU6CcLPTmBqi1+t59dVXmTRpEiNHjmTFihV16siaNWtwd3dvMA15+eWXMRgMtWqIp6cnu3btYtasWaIjglAPTDpSz7S1Vyoqahgg6QYDMy9dYktREWpguIsLUb6+NXZYdG5uZBgMTL90iTEXLrCpXTsi3dyYn5PDIGdnRrm68t8rV4gtLDTdE6jRsMjHh0h3d1rV0mdj/17++98rdWTFCmKrGRbzr1aN//777xk4YEClhri58UabNtcMlawsFi5YwDtvvcWSZctEQ5opYoDYgTHVW31TTj7zzDNMnjzZ9EUbHx/PunXrcHJywsnJieHDh9da8dgY9BkSEsLEiRM5c+YMsbGxjBkzBkdHR9atW0ffvn1ZvHgxkyZNsrnIkbF/qampTJ8+nWnTplms1GrM3BMcHFynkRQZGUl0dLQMfEGoQmNpiLOzM3PnzuXVV19l5MiRbNiwwSYdmTZtGitWrGDSpEkNoiF///vfiYmJYffu3VarPYuOCML1YdKReqatfSYnh8lVdijiCwpYV1iIE+CkUjHcxYWktm2txpYYA9tDLl5k4sWLnOnUidi2bRlz4QKOKhXrWremb0YGi318mOTmho9abZuOXO3f3195hZhVq9j95ZfW5yIREQS7uBDl52fZSPLyYkZODpEREUTHxIiGNEPEBcsOFEVh6NChDBgwgDVr1th8X3h4OLt27cLd3Z2TJ0+ajjs5OZmqFDs4OHDu3Dmb/MLT09Px9/dn0aJFzJ07F71ez8SJEykoKMDDw4OgoCDWrl1rV/+2bt1KRUUF+/fvt7jSmZeXx8CBAxkyZEitRhJccwfZs2cP+/btky3QRqQlu0+Ihly/hmg0GrPA7/rqSGBg4HVryKFDhwgICGDv3r1Wx73oSPOjJWsI3MI68sADDMjKYk3r1jbfF56ZyS5nZ9w9PDh5tQo5gBPXKp07AOc6dbIptiTdYMD/3DkW+fgw19MTfVEREy9epEBR8FCpCHJ1ZW3btrb37+JFDpWWEuDkxF5g33ff1Rj3eXl5DBwwgCEqFUmtW9cagG9QFEKystijKBbbEhqO+uiIBKHbgUqlMivoZQvGwNCnnnqKPXv2sHfvXtO5mJgYMjMzCQgIYMKECfUOSg0ODubMmTP85z//wcnJqV79mzdvHsXFxcTHx1u8rj6Ze4qKiqy2Jwi3Ig2hIT/99BNbt24FKifpy5cv5+TJk/To0aPeOhIUFHTdGjJnzhyioqJqHfeiI4Jw/ahUKiKmTiWhoMDu9LdPPfMMe776ip9++sm0yBDj60tmp04EaDRMuI6q6cGurpzp1In/+PjgpFKZihba0785np5E+fhYHfd2Z//y9hYNaaaIAWInOp0OV1dXZsyYYXfKSZVKhaOjo+m80Zc7NTWVsLAwu/pRveKxl5cXc+fOZdeuXTg4ODBt2jS7Ums+/fTThIaGEh0dXSODxPVk7rHUniDcylyvhvj4+JhlovL398fDw4Pjx49fl44YNeS3337D1dXVbg2JiIioddyLjghCw2HSkZwcu9PWGnXEOB/x1WhApSLVYCDMzqri1aumezk4MNfTk9/8/HBVqZhWj/S8RsMmesUKs3F/Pdm/qrcl3HjEALGTVq1asWTJEvR6vc2pK6umnHSrMrhzcnLIz88H6h+Uunr1alJSUkxZaPr27YuDgwNbt261OSWmMbVmWFgYqampNfzTc3Jy6m0kWWpPEG5lrldDoHF1ZNasWRQWFrJ161bGjh1rd3pe0RFBaHxatWrFkmXL0BcXE5KVZVfaWiPGRdCcigryq1U9txXj9ZGZmcQWFJBSVERsQQGzLl2iUFHYWlTE2Hqk5w3Takk9fdps3Ofk5JB6+jRhVrJoWcNSW8KNR4LQ68GwYcOIjo5m1qxZ+Pv715pyMiYmhqFDhwKVvosJCQm4uLjg7OxMQkICw4cPB2oGpSqKwqVLl8jPz8fd3R1fX1+zIC7j9U8//bTpmDFjzbBhw+jXrx+7d++utX9arZbNmzebUmsaJyMFBQWmQmbG36uetxVr7QnCrU59NQRs15G6NKTq9dV15N133+Xw4cOsXLnSLg0B0RFBaCqGDRtGdEwMs2bOxP/8+VrT1sasWmU2F4mLi+PT5cvRAPEFBQx3cQFqBrYrisKlqwaKu1qNb7WAcuP1R8vKCM/MNB0P1Gh418eHwyUlrCwowP/cuVrT825u184sPa/RsKk67q83+5doSPNCDJB6MmzYMPbt20d8fHydKScBs7STffr04dChQyQkJPDuu+8SGBhIQkICOp2O3NxcoqOj+fjjjzl69KipzcDAQGbPnk1kZCReXl6misdffvkl+fn5eHh4mDLWZGVlAbB48WIuX77MRx99ZFNqTeNkxK3aFuz1Zu6p3p4gCPZrCNimIyNHjrRJQ4BadWTs2LFUVFQQERHBN998Y3N6XtERQWg6hg0bxr7vvqvUkVrS1prNRWbONKWvbePkREJhIe95exOo0ZBQUIDOzY3c8nKiCwr4+PJljlbZvQjUaJjt6UmkmxteDg6mqum/duxIjqJwpaICD7XalPlq7IULVAARbm58U1Jic3peo2FTddxfb/Yv0ZDmhWTBagAURbGachJqpp10cXHB39+fkpISRo4cyYMPPshf//pXYmJiTO4PYWFhNVYcExIS0Gq1LFmyhIiICFMWrOr8/vvvdOnShfHjxxMbG2uqEnrlyhWzCUZ1wsPDOXjwILt37zY7fz2Zeyy1JzQcLTmDjWjINerSELBNR1544QVTUcHaNCQ2Npa+ffuaZdOrSnp6Op06dUKtVjN+/HjWrl1rk4aA6EhLoyVrCIiOVMWmuYgxfa23N+01Gs6UlRFw/jxBrq6McHHhrzk5xLRubXKhCrOwa5Fwdddiia8vEVlZpixY1Uk3GOh07hxqYLxWy9o2bciuqKhhpFgiPDOTg23asPvLL03XXE/2r+ptCQ1LfXREDJBGxlraSb1ez8MPPwzAiBEj2Lt3LyUlJYwePdpibnzAlBt/y5YtuLi4cP78ebNgVKgMCn300UfZsWMHFRUVpKWl2ZWSc/78+UyfPr3G+aioKBYuXNhg7QkNQ0uePIiG2I4tOtK/f39++OEHRo0aZbEIIVzTEL1ezx/+8Ad+++03zpw5Y6YjBoOBsWPHkpyczMSJE4mLixMduYlpyRoCoiO2Ulv62tdzc/l7bi4PubjwVXExJcBoV1eLhQgBMgwGZlwtWugCnO/c2RS7YcSgKDx64QJ7S0p41tOTN/PySLMnve/588x/9dUa4z4qKoqFCxaQZqH+h71tCQ2HpOFthlhLOxkcHMwXX3yBi4sL27Zto7S0lODgYJKSkqx+MRsLiAUHB1u04o1BocnJyTg4ONidycaYIcMS15O5RxCE66MuHXF2dubQoUOMGjWKDRs21KkhI0eO5ODBg6xcudLM+DBqSEpKCn/84x/ZtGkTarVadEQQWji1pa/9f15eLPTyYkdxMaVAsKsrSW3bWp3gt9doSGrblmBXV8tzkauB5cnFxSiKwhR3d9Rge0asKhm7qnM92b+E5oUYII1IXWkng4ODOX/+vGkFc8WKFTblxl++fDnFxcU8++yzZhmw/P392bt3L5999hllZWV4e3vblQ2reqadqjRE5h5BEOzHFh2ZP38+KpXKLg0B2LhxYw0N2bNnD5s2bSIpKYnCwkLKyspITk5ukHEvOiIITY8t6Wv/n5cXr1wdZyt8fW2qsbHc15diReHZ7GxT9qvwixfxP3eOvcXFfNa6NaXA2MxMDGo1ySUl9c7YZaQhsn8JzQNxwWpEsrOz6dOnD7Gxseh0OovXKIpCz5496d+/v11+0TqdjqSkJNMqorEicvfu3XnqqafYsWMHW7Zs4bnnnuOjjz6iqKio1kw7S5cuNcu0Y42qQbAN0Z5wfbRk9wnRENuoS0caWkPgWsD6jh07OHjwIG+99RazZ88WHbkJackaAqIjtmDSkDZt0FkJxFYUhZ7nz9PfyYk1dlQv1128SFJhIUYzQAMYgO4ODjzVqhU7iorYUlzMp599BmAKgK8tY9fSqKg6x33VYPrrbUu4fiQGpJmRlpbGoEGDSElJYcSIERavycrKok2bNrUaKZYwrlgGBQURHh5O586dyc3NNQWaOjk5UVhYyE8//YSDg4Mp005qaqqpjYCAACIjI2tk2rFE1eC28vJytm3bRkxMTL3bExqGljx5EA2xjbp05Ho1RK1WM3bsWB577DF8fHzMAtYbUkeqB8iq1WoSEhKuS5eE66clawiIjtiCSUPatWOElRoaWeXltElLq9VIsURsQQHhmZkEOTsT7u5OZwcHchXFFKzupFJRqCj89NNP+Pj4kJeXZ8rYlVotY1dktYxdlrA4F1m5sl5tCQ1HfXRE0vA2IraknbzeAmJLly6la9eupuM6nY6MjAymT5/Oli1b2L59OzqdjunTpzNt2rQ6M+1Ux5gv3JKx8cQTTzBy5EgcHBxsbk8QBPuoS0euV0O+/fZb7r77brNzDakjtWlIREQEGzZsoKKiwi5dEgTBdmxJX3u9hQiXtm5N16uV1QF0bm5kGAxMvxqsbtSQVq1aXZ+OWDA2npgyReYiLRCJAWlEvL29CQgIICEhweo17u7uQP1z43t4eNQ41759e9avX8+oUaN45ZVXyMvLA0ClUuHj40Pnzp1rTaNpZNeuXQwcOJCFCxcyYMAAYmNjTf7iAwYM4LXXXmPUqFGkpqba1J4gCPZTl45cr4bcdtttFs83hI7UpSELFy5k0KBBHD582GZdEgTBPry9vQno2pWEoiKr17hfNSTqW2PDw4Lh0l6jYX3btoxydeWVl182aQjUQ0cGDGDhggUMyMoitk0bUtq1I7ZNGwZkZfHaq68yauRImYu0MMQAaURUKhUREREkJCSQkZFh8RpfX19TATF7MBYQs1bVs2qwenx8vN19N9YcGDJkCGlpaaxZswadTseIESPQ6XSsWbOGtLQ0hgwZQmRkJLt27bL7GYIg1E1dOtJYGgLXpyOiIYLQPFCpVERMnUpCQQEZVoK2fdVqUyFCezAWIvSxsnNiClYvKqr/XCQigiEqFWl+fqxp3RqdmxsjXF3RubmxpnVr0vz8GKJSERkRITrSghADpJGpK+2kSqVi9uzZtRop1UlPTycxMZE5c+bUaul36NCB0NBQoqOjsSfUJy8vj1mzZtmVFnjWrFlmqxuCIDQctelIY2oI1E9HREMEoXlRV/palUrFbE9PEgoLrRop1Uk3GEgsLGSOp2ftcxGNhlCtlugVK+yfi8ycSbCLC0mtW9eeFrh1a4JdXJg1c6boSAtBDJBGxpa0k5GRkXbX7NBqtURERNT5/LCwMFJTU+1yz7BWc8ASGo2GZcuWUVTP1Q1BEOqmLh2JjIxEq9XaXF9jxowZNmsI2K8joiGC0LywJX1tpJsbriqV7fU6Ll1Cq1IRYUPQephWS+rp0/Wbi1ioXVIdjUrFMm9v0ZEWhBggTcCwYcOIjo5mz549+Pv7Ex4ebuYLPXPmTAoKCti6dStjx46tNTf+uHHj0Ov1xMXF1aiCbgljoGmBjduqddUcsER9d1oEQbCd2nQkOTmZvn378sUXX9SpIcYq57ZqCNinI6IhgtA8GTZsGNExMexRFPzPnyc8M5PYggJTDY+Zly5RoChsLSpi7MWLtdbYGHfxIvqiIuLatq1RBd0SxmB1u+YiddQuqU59d1qEG4NkwWoihg0bxr59+4iPj2fp0qXExsaazvn5+TFr1ixcXV1ZvHgxnTt3Zvz48eh0OrPc+AkJCTg7O7N582aCgoJseq5xtcHNxrR6OTk5pKam8sYbb9j1fmFhYcTGxpKTk1OrT7kgCPWnLh155JFH2LFjh1UNSUxMpKKigpdeeslmDQH7dEQ0RBCaL8OGDWPfd9+ZUuHGVsko5aVWE+HmRheNhrcvX6bzuXOM12rRubmZ1dhIKCjAWaVic7t2BFlJ61sdY7C6XXOR06d5w87UrmFaLbFXd1pER5o3YoA0Ia1atSIgIICMjAxGjhzJ66+/zm233WaWteGVV15h8eLFvP3222bbiAEBAXh5eTFkyBC7Jg4JCQkEBATYnKLTuDpR35SeBQUFMugFoRGpS0dyc3OJiYnhww8/rKEhf//731m5ciUnTpyw65n26IhoiCA0b4ypcG+77bbKAG9nZxZ7edHTyck0F3nG05OYggI+vHyZ+MJC070BXbvi5ezMkJISm40PgITCQgK6drV/LlLPtMCiI80fccFqQoyBmaNGjeKLL77g7rvvxtfX1yx4y8vLi1deeYWsrCxGjhyJm5sbX3/9Nbt372bu3Lls3LjR7kDTyMhIm9PS2VK7xBL27rQIglA/6tIRLy8v5s6dy7Fjx8jIyGD48OG4u7uzYcMGZsyYwdSpU+sVsG6rjoiGCELzJy8vj9lPPskoV1eS27all7Oz+VzEwYG5np4c8/Mjo1Mnhru64u7qyobNm5n7l7+wsR7B6pHTptk/F6lnWmDRkeaPGCBNiD2BmY6OjkRHR1NSUsK2bdtQqVR1ZtSqijFY3dXVlQkTJtjcR1tql1jC3p0WQRDqh606olKpaNeuHZ9//jnFxcWmMd3YOiIaIgjNH1sDvFUqFe00Gj739TXpSF0ZtapiUBRm5uTUby5SR+0SS9i70yLcOMQAaSIaIjDTloxaULliGRISgl6vZ+nSpbRq1crmftpSu8TS8+zdaREEwX5ago6IhghC8+Z6A7w9PT3rzKgFlTsfIVlZ6IuLWRoVZf9cpI7aJZaeZ+9Oi3DjEAOkiTAGZoaFhdl1X/X0l3Vl1AoPD8ff3589e/YQExPD0KFD7e5rU+y0CIJgPy1FR0RDBKH5YgzwDrMjhgPMU+nWlVErPPP/s3ff8U3V+//AXyerSdO9B22BsgsIAoICtmxEBaRUEBWQ9QNxIF6v8wrce73K97pQr4iUVRCRJSAKZSggKlBkqGwKhVK6dzPajM/vjzQhaUaz2ibl/Xw8eCjJyclJ6Hn18znn83l/ihGfl4cjjCFj/XrX2iJNeKeFtByahN5M3Dkx07gSzrp160wq4SQmJuLtt99GWloaAgICnDpW/RXSadOmYfz48Vi5ciWio6PNtsvPz8fs2bORmZmJjIwMh65uEEIc5y05QhlCiOdy1wRvWxW1Etu2xdszZrjeFlm5EtOmTsX4khKsDA5GtIU7NvlqNWaXlyNTqUTG+vWUI16COiDNxN0TM/VVLGbMmIHy8nLIZDJIpVIEBwe75daj/grp3LlzER8fjwkTJiA1NdWspKdEInH6TgshxDHelCOUIYR4JndO8G6WtkhGBubOno34vDxM8PVFqq+vSVng7XK5LkecvNNCWgbHnFytpbi4GCqVyt3H02oxxpCcnIy+ffti06ZNdr9u0qRJ+P3333H48OEWGdNYWVlpuEKanZ1teDwxMRHTpk1z6eoGcZ1QKES4g3XSPQVliOO8MUcoQzybN2cIQDniDMYYkgcNQt+SEmwKC7P7dZOKi/F7eDgOHz3acjmyejWyG9xpmebinRbiOmdyhDogzSg9PR3/+te/kJuba9cE0vz8fMTHx+Ptt9/GzJkzm+EIrWOMNcnVDeIab248UIY4x1tzhDLEM3lzhgCUI85KT0/HvxYvRm5srF0T0fPVasTn5eHtJUsoR4gZZ3KEJqE3I2+emMlxHEJCQhAXF2eycCIhpHl5a45QhhDiObx1gjflSOtBHZBm1BxldAkhrRvlCCHEVfoJ3k1ZSpcQW2gIVgs4dOgQ5s6dC4VCYXNi5ooVK2hCFbHJm4dPUIa4hnKEuIM3ZwhAOeKqQ4cOYe7s2bocsTHBe0V6OuUIsYrmgHgRmphJ3MGbGw+UIa6jHCGu8uYMAShH3IEmeBNXUQfEC9GEKuIKb248UIa4D+UIcZY3ZwhAOeJOlCPEWc7kiNPrgAjsqJpA7BMZGdnSh0C8lDefh9587J6IcoQ4w9vPQ28/fk9DOUKc4cx56PQdEEIIIYQQQghxFFXBIoQQQgghhDQb6oAQQgghhBBCmg11QAghhBBCCCHNhjoghBBCCCGEkGZDHRBCCCGEEEJIs6EOCCGEEEIIIaTZUAeEEEIIIYQQ0myoA0IIIYQQQghpNtQBIYQQQgghhDQb6oAQQgghhBBCmg11QAghhBBCCCHNhjoghBBCCCGEkGZDHRBCmklycjJ69OgBrVbr0n7Gjh2LxMRE1NXVuenIiDeZPn06OI5DTk5OSx9Ks0lJSQHHcS19GA5Zs2YNOI7DiRMnXNrP9u3bwXEcDh486KYjI4TczTylLeJwB4TjOJM/fD4fISEhSElJwdq1a8EYc+pAiHVr164Fx3FYu3Zts72nTCbDxx9/jKFDhyIiIgIikQhBQUG477778Oabb+LatWvNdix63tzw2rp1K44cOYIlS5aAx7tz2qlUKixbtgzPPPMMevXqBZFIBI7jkJ6ebnVf//znP3H9+nV88sknzXHoXoOyqeXk5OSYff8CgQCRkZF4+OGHsWfPnpY+RADA4sWLwXEcDh061KTvU1NTgzfeeAOPPvoo7rvvPsPjMpkMX331FaZMmYIuXbpAKpXC398fffv2xQcffGDxF/ljjz2Ge++9FwsXLnS5wdCa0Pne/KgtotMa2yJXrlzB0qVLMXToUMTFxUEkEiEyMhLjxo3DTz/9ZHFfrrZFBE69CsCiRYsA6BpQV69exbfffovDhw/j5MmT+Oyzz5zdLfEAx44dw8SJE5GXl4c2bdpgzJgxiImJgUwmw+nTp7F06VL897//xbFjx3Dvvfe29OF6PMYY3nzzTXTq1AmPPfaYyXMymQwLFiwAAERGRiIqKgq5ubk299erVy+MHj0a77zzDp599ln4+vo21aF7pdaeTe+++y5ee+01xMbGtvShmAkMDDT8PCuVSpw9exY//PADfvjhByxbtgwvvPCCU/vNyMiAXC5345E2rU8++QQFBQV47bXXTB7/+eef8dRTTyEkJARDhgzB+PHjUV5ejl27duFvf/sbtm/fjoMHD0IsFhtew3EcXn31VUyaNAmbNm3ClClTmvvjeLTWfr7fzagt4l622iL/+Mc/8M0336Bbt24YM2YMQkJCcOnSJezatQu7du2ymN8ut0WYgwAwSy87evQo4/F4jOM4du3aNUd3S2xYs2YNA8DWrFnT5O914cIFFhAQwHg8HnvvvfeYSqUy2+batWssLS2N/fTTT01+PMamTZvGALDr16836/u6at++fQwAe+edd8yeq62tZT/88AO7ffs2Y4yxRYsWMQBs5cqVNve5adMmu7a7m1A2tZzr168zACwhIcHsudWrVzMATCqVMplM1vwHZ0R/fjVldqnVahYXF8c6depk9tzp06fZhg0bWG1trcnjVVVV7N5772UA2Pvvv2/2OoVCwYKCgtjAgQOb7Li9DZ3vzY/aIjqtsS2yZs0adurUKbPHDx06xIRCIROJRIZ2ijFX2iJu64Awxli3bt0YALZlyxaz544dO8ZSU1NZZGQkEwqFrE2bNmzOnDksLy/P4r5KS0vZG2+8wZKSkphEImEBAQGsZ8+e7NVXX2U1NTUm216+fJk9/fTTLCYmhgmFQhYdHc2efvppdvnyZbP9Gv8C2rhxI7v33nuZRCJh0dHR7KWXXmJKpZIxxtjBgwdZcnIy8/f3Z0FBQeypp55iJSUlZvtLSEhgCQkJrKKigs2fP5/FxMQwHx8f1rVrV7Zs2TKm1WpNtv/pp58YALZo0SKLn1u/P73k5GTDd97wj/EPv0qlYv/73/9Y//79mb+/P5NIJKxXr17s008/ZRqNxuJ7WTJ8+HAGgL3++uuNbqv/rvRKS0vZa6+9xrp06cLEYjELCAhgQ4cOZZmZmWavNQ6yH3/8kSUnJzM/Pz/m7+/PxowZw86fP2+yvbXvoGGDx9lj2LNnD0tOTmYBAQEmP99HjhxhjzzyCIuNjWUikYhFRkay/v37s8WLFzf6/ehNmjSJAWBXr15tdFt7OyAKhYKJxWI2YMAAu4+jtWuObDp58iR74YUXWM+ePVlwcDDz8fFhHTp0YAsXLmRlZWVm29fW1rJly5ax3r17s6CgICaRSFhCQgIbO3Ys279/v8m29v6sWfvlp9Vq2ccff8y6du3KfHx8WExMDJs/fz6rqKgwyxXGHD8HbbHVAdFqtUwqlTIA7MSJE4bHDxw4wEaNGsWCg4OZSCRiHTt2ZK+++iqrqKgw24c+B40ZZ+np06fZmDFjWGBgIJNIJOzBBx9kv/zyi8n2CQkJVnNEr6CggL388susU6dOzNfXlwUGBrJOnTqxadOmsezsbLu+iz179jAA7K233rJre72vvvqKAWCPPPKIxeenT5/OALALFy44tN/Witoipqgtcge1RSxzpC1ibMSIEQwA27p1q9lzrrRFnB6CZYtQKDT5++rVqzFnzhz4+Phg7NixiIuLw5UrV5Ceno7vvvsOx44dQ3x8vGH769evY8iQIbhx4wb69OmDefPmQavV4vLly/joo48wd+5cSKVSAEBWVhaGDx+O6upqjB07Ft26dcPFixexYcMG7Ny5EwcOHEC/fv3MjvHTTz/Fnj17MH78eKSkpGDfvn346KOPUFZWhnHjxmHy5Ml4+OGHMWfOHPz666/YsGEDSkpKLI5lrqurw/Dhw1FRUYHJkyejrq4O27Ztw4svvohLly7hf//7n9Pf5fTp0xEUFISdO3di3Lhx6NWrl+G5oKAgALpbz48++igyMzPRuXNnTJkyBWKxGD/99BOef/55HD9+HOvXr2/0va5fv44DBw5ALBbj73//e6Pb+/j4GP7/xo0bSElJQU5ODgYPHozRo0dDJpNh9+7dGD16NFasWIHZs2eb7WP37t3YuXMnHnroIcydOxfnz5/HDz/8gKysLJw/fx5hYWEAdLfZd+zYgbNnz+LFF180fHb9f105hq1bt2Lv3r2GY7hx4wYAYO/evXj44YcREBCAsWPHIjY2FmVlZbhw4QI+//xzw61/Wxhj+PHHHxEVFYXExMRGt7eXWCxGnz59cOzYMVRWViIwMNBt+27NXM2mlStX4ttvv0VycjKGDx8OrVaL33//HR9++CH27NmD48ePw9/f37D99OnT8fXXX6N79+6YOnUqJBIJbt++jaNHj2Lv3r0YPnw4APf8rM2fPx/Lly9HTEwM5syZA5FIhF27duHEiRNQqVRmn13P3nPQFax+PL5+IvmKFSswb948SKVSpKWlISIiAocOHcLSpUvx3Xff4ZdffjE5t205efIk/u///g/3338/Zs2ahZs3b2Lbtm0YNmwYzpw5g86dOwMAFixYgB07duDw4cOYNm0a2rZta7IfuVyOgQMHIjs7GyNGjMCjjz4Kxhhu3LiBnTt3YuLEiWjfvn2jx3PgwAEAwKBBg+z8dnT0/z4CgeVfywMHDsTatWtx4MABdOnSxaF9362oLUJtEWqL6LjSFrGVTS61RRztscDKVYfDhw8zHo9ndpvm0qVLTCgUssTERHbr1i2T1xw4cIDxeDw2fvx4k8fvv/9+BoD95z//MXuf4uJiplAoGGO6K2tdunRhANiGDRtMttPfFurcubNJr1t/1SEgIMCkZ6tUKlm3bt0Yj8djISEh7NChQ4bnNBqNoTd++vRpk/fRX1UbOHCgSS+8tLSUtW/fngFghw8fNjzu6FUHxhq/7an/TM899xxTq9WGx9VqNZsxYwYDwHbs2GHxtcYyMjIMn8VRycnJjOM49vXXX5s8Xl5ezu655x4mFotZQUGB2Wfi8/nswIEDJq957bXXGAC2dOlSk8cbu+3p7DFwHMf27Nljtr8JEyYwAOzMmTNmzxUXF1v+Ihq4cOGCzauaDdl7B4QxxhYsWMAAsO+//96ufbd2zZFNOTk5JueYXnp6OgPA3nvvPcNjFRUVjOM41qdPH4uvMb6K6cjPmqXz4MiRIwwA69SpEysvLzc8XltbywYPHmzxCp0z56A1tu6ArFq1yjAESy6Xs5ycHCYSiZi/v7/Z1fx58+YxAGz27Nkmj9u6A2IpG7/44gsGgM2bN8/kcVtDsHbt2sUAsAULFpg9V1tby6qqqmx8A3f079+fAbB4ldqW0aNHMwDsiy++sPj8mTNnGACWlpbm0H5bK2qLnDZ5H2qL6FBbxDJH2yJ6OTk5zMfHh/n6+lq8y8+Y820Rp8vwLl68GIsXL8abb76JSZMmYfjw4WCM4f3330d0dLRhu+XLlxsq/TScNDls2DCMHTsW3333HaqrqwEAv//+O3777Tf06tULr776qtn7hoWFGSbo/frrr7h48SLuv/9+PPnkkybbTZo0CYMGDcKlS5dw9OhRs/288MIL6Nq1q+HvPj4+mDRpErRaLR5++GEkJycbnuPxeHjqqacAAGfPnrX4fbz77rsmvfCQkBD84x//AKArx9hUtFotPv30U0RFReGjjz4Cn883PMfn8/HBBx+A4zh89dVXje4rPz8fANCmTRuHjuHs2bM4fPgwUlNTMXnyZJPngoKCsGTJEiiVSmzbts3stZMnT8awYcNMHpszZw4AOFS+0pVjGDduHEaPHm113xKJxOwxe68K37x5EwBMzgl3iYqKMnkPotNU2QQACQkJJueY3owZMxAQEIDMzEzDYxzHgTEGHx8fk2ojeqGhoWaPOfuztm7dOgDAm2++aXIlTiQS4d1337X5WnedgwBQUVFh+P5fe+01jBkzBjNnzgQA/Oc//4FEIsGGDRtQV1eH5557zuxK/jvvvAN/f3+sX78etbW1dr3nwIEDMX36dJPHZsyYAYFA4FQJXEv/BiKRyOTOli03b96EUCi0+O9rzWeffYa9e/eiV69emDFjhsVt6Hy3jNoipqgtQm0RS5xpi9TW1uLJJ59EbW0tFi9ejODgYIvbOZtNTg/BWrJkicnfOY7DqlWr8Mwzz5g8/ttvvwEADh8+jKysLLP9FBUVQaPR4PLly4bbOAAwatQoi7+0jZ06dQoAMHToUIvPDx06FEePHsXp06fx4IMPmjzXt29fs+1jYmIAAH369DF7Th9Yt27dMntOIBDggQceMHs8JSUFAHD69Gkbn8I1ly9fRllZGTp27Ih///vfFreRSCS4cOFCkx2D/t+4srISixcvNnu+uLgYACweg6V/h7i4OABAeXl5sxyDcZlMY08++SS2b9+O/v37Y9KkSRgyZAgGDhzoUCiWlpYCgNUT1xUhISEAgJKSErfv25s1VTYBuiEGK1aswKZNm3D+/HlUVlaalEbNy8sz/H9AQAAeffRRfPfdd+jVqxdSU1MxePBg9O/f36xaiKs/a/qMsTTsZ8CAAVaH9QDuOwcB3fmn//71ZVEfeughPPfccxgzZgwA27kdHByM3r1748iRI7h48SLuueeeRt/T0vELhUJERkY6dPzJycmIjY3Fe++9h1OnTmHMmDEYOHAgevXqZbHTaU1paalD5/v27duxYMECREVFYdu2bVaHytH5bhm1Re6gtgi1RaxxtC2i0Wjw9NNP45dffsGkSZPwt7/9zeq2zmaT0x0QVj+mVyaT4bfffsPMmTMxd+5cJCQkmJyE+g/93//+1+b+ampqAOiuoAGwq8RkZWUlAOs9Ov3j+n0aszROTf9L2tZzKpXK7LmwsDCLv6D0vUL9cTYF/fd75coVsyA2pv9+bdF/X8aNKEeOYf/+/di/f79Dx2BpnLf+u9ZoNM1yDPp/p4YmTJiA3bt344MPPsDq1auxYsUKALpfCu+++y5GjBjR6HHpr1golcpGt3WUQqEweQ+i01TZBOiuZn777bdo3749xo0bh6ioKMPVxo8//tjsqv0333yDpUuXYuPGjYZxumKxGBMnTsT777+PyMhIAK7/rOkzRr8/Y3w+3+bVeHedg4DuDlFjtfFdyW1LrM0VEQgEDh1/QEAAjh07hkWLFmHXrl2Gu1lhYWF49tln8dZbb1ntHBiTSCR2n+87duzA5MmTERERgZ9++snmHBM63y2jtsgd1Bahtog1jrRFNBoNnnrqKWzZsgWPP/44NmzYYHMhWGezyeWV0KVSKYYPH47vvvsOGo0G06ZNM6nXrj+BKisrwXRVtyz+0d9m1P8Q2PODp993QUGBxef1t/GaeoJuSUmJxR9Q/XEZv7/+Soparba4L3t/6erp9/3YY4/Z/H6vX7/e6L70V09PnjzpUFDpj2HZsmU2j6Epb/+6cgy2TqyHH34YP/74I8rLy3Hw4EG89NJLOHfuHB555BGcP3++0eOKiIgAcCeU3Em/T/17EFPuzqaTJ0/i22+/xfDhw3Hp0iWsWbMG7777LhYvXoy3337b4iJyEokEixcvxuXLl3Hz5k1s2LABgwYNwoYNGzBx4kSTbV35WQsICAAAFBYWmj2n0Wia5OfPWZ6S25a0adMGq1atQlFREf766y988sknCA0NxT//+U/885//tGsfERERqKqqsthANLZlyxakpaUhMjIShw8fNkyWt4bOd9uoLUJtEWqLWGdvW0SlUuGJJ54wrDm0ceNGm3fQjffpaDa53AHR69mzJ2bPno1bt27ho48+Mjw+YMAAALoFmOyh3z4zM7PRVV979+4NAFZXtdWv3tjUC9So1Wr8+uuvZo/rj0t/nMCd21+WFpu7evWqxZNNf0XDUrB06dIFQUFBOHbsWKO/8BrTrl07DB8+HEqlstGrRAAMV3sd/Td2lq3voamPQSqVYujQofjwww/xxhtvoK6uzq7VnZOSksDn83Hx4kW3H5N+n8bVSIg5d2XT1atXAQBjx441C+QTJ04YrgJZExcXhyeffBKZmZno0KEDjh49avGXgTM/a/qMsTTG/NixY1YbGS3BVm5XVFTgzJkzEIvFJuPi3cVWhhjjOA5JSUl4/vnnDVcxd+zYYdd79OzZEwBw6dIlq9t89dVXeOKJJxATE4PDhw+jY8eOje6Xznf7UFuE2iLUFjFnT1ukrq4OaWlp2LJlC6ZOnYr169fbNfzU2WxyWwcEAN566y34+Pjg/fffN4yZe+655yAUCvHSSy/h8uXLZq+pq6sz+Yfq06cPHnjgAZw5cwZLly412760tNRwC2ngwIHo3Lkzjh49iq1bt5pst3XrVvz888/o1KmTw+UQnfH666+bDL8oKyszjIM0HovapUsXBAQEYOfOnSgqKjI8rlAorK4SrB8+YWmCj0AgwPPPP4/8/Hy88MILFhtB+fn5dvWQAd0KvgEBAXj33XfxwQcfWGy43Lx5E5MnTzaMdezbty8GDx6M7du3Y/Xq1Rb3++eff5p8XmfY+h6a4hiOHDli8fPrrzLbs+pnYGAgevXqhT/++KPRBqqjjh07hrCwMHTv3t2t+22N3JFN+rKtDRsZRUVFmD9/vtnri4uL8eeff5o9LpPJUFNTA4FAAJFIBMD1n7WpU6cC0E3iNm441NXV4Y033rD52ub21FNPQSgU4tNPPzV06vT+8Y9/oKqqCk899ZTJRFp3sZUh586ds3gHyZHzHbgz3l4/h6ChdevWYerUqYiPj8eRI0fsKu1rvL8hQ4bYtf3djNoi1BahtoipxtoitbW1eOyxx7Bz507MnDkTa9asaXTuk56zbRG3rgMSGxuLuXPnYtmyZfi///s/vPvuu+jSpQtWr16NGTNmICkpCaNHj0anTp2gUqlw8+ZN/PzzzwgPDzfplW3YsAEpKSl44403sG3bNqSkpIAxhitXrmDfvn24ePEi2rZtC47jsG7dOowYMQKTJk3CuHHj0KVLF1y6dAk7duyAv78/MjIy7P4SnRUdHY3a2lp0794dY8eOhUqlwtatW5Gfn49nn33WZNKZUCjEiy++iH/961/o3bs3HnvsMajVauzfvx8xMTGGyWfG7r//fvj6+uLjjz9GaWmpYZzg888/j8DAQPzjH//A2bNn8cUXX+C7777D0KFDERsbi6KiIly5cgW//PIL3nnnHXTr1q3Rz9K1a1dkZmZi4sSJ+Nvf/oZly5Zh2LBhiImJgUwmw9mzZ/HLL7+A4ziTyiAbN27E0KFDMXPmTHzyySfo378/goKCcOvWLfzxxx/466+/8Ntvv7k0fGDYsGH473//i9mzZyM1NRX+/v4ICgrCc8891yTH8MILLyAvLw8DBw5E27ZtIRKJ8Pvvv+PHH39EQkKCWYULa1JTUw2ve/jhh82ef++99ww//2fOnAGgq1aiv5o9aNAgzJo1y+Q1ly5dws2bNzFnzhybt22JjjuyqV+/fhg4cCC2b9+OBx54AIMGDUJhYSH27NmDzp07m527eXl56N27N3r06IGePXsiLi4OVVVV2L17NwoKCvDCCy8YKiu5+rOWnJyMOXPm4Msvv0RSUhJSU1MhFArx3XffITAwEDExMU2eg/Zq27YtPv74Y8yfPx/33nsvHn/8cYSHh+Pw4cP47bff0KVLF4sNPncYMmQIeDweXn/9dfz111+Gq8BvvfUW9u/fj1deeQX3338/OnXqhIiICNy6dQs7d+4Ej8fDK6+8Ytd7jBs3DgsWLEBmZqbZefvTTz9hxowZ0Gq1GDJkiMVhGEFBQViwYIHZ4/v27UNQUJDVic7kDmqLUFuE2iLmbLVF5s6dix9++AFhYWGIjY21OOQ0JSXFcIFFz6W2iENFe5nt1UcZ060k6+vry3x9fU3qHP/xxx9s2rRpLD4+nolEIhYcHMySkpLYnDlz2MGDB832U1JSwv7+97+zTp06MR8fHxYYGMjuuece9sYbbzCZTGay7cWLF9lTTz3FoqKimEAgYFFRUezJJ59kFy9eNNuvrTrwtmpcW6uZbbz66LPPPstiYmKYSCRiXbp0sbj6KGO6muHvvvsua9++PRMKhSwuLo698sorTCaTWay9zZhudd0BAwYYVhRGgxrUWq2WZWRksKFDh7Lg4GAmFApZTEwMGzhwIHvnnXfYzZs3zfZpS3V1Nfvwww9ZSkoKCw8PZwKBgAUEBLB7772Xvfbaa+zatWtmr6mqqmLvvPMOu/fee5lUKmVisZi1bduWjRkzhq1YscJk1djG6okDYMnJyWaPf/DBB6xLly5MJBJZXHfAncfwzTffsMmTJ7MOHTowqVTK/P39WVJSEnvjjTdYUVFRo9+hXmFhIROJROzxxx+3+LytFWYBsGnTppm95vXXX7dYC/5u1hzZVFpayubNm8cSEhKYj48Pa9++PXv99dctnrvl5eVsyZIlbMiQIYZciIqKYsnJyWzjxo0m2eDIz5q1GvQajYZ9+OGHrHPnzkwkErHo6Gj27LPPsoqKCubn58fuuecek+2dPQctsbUOiDWZmZlsxIgRLCgoiIlEIpaYmMheeeUVk3VM9BpbCd0Sa1m6fv16Qy1+45+Z8+fPs5deeon16dOHhYWFMZFIxBISElhqaqrZquqNGT9+PPPx8TGrm6//zm39sXTMly5dYgDYiy++6NBxtGbUFllk8ji1Re6gtohlttoijbVDrGWtK20RjrH6EhLEKfphGY1VfiF3t//3//4f1q1bh5ycHKuVLuxVW1uL9u3bo2vXroZVlwmx5sqVK+jUqRMmT56Mr7/+uqUP567w66+/YuDAgfjwww/x0ksvuby/l19+GZ999hkuXLhg95Atcnehtgixhye1RTzjnjwhrdw///lPiEQivPPOOy7va/ny5SgoKMAHH3zghiMjrUVBQYHZZFm5XG4YzvPYY4+1wFHdnR544AGkpaVh6dKlJpWYnJGfn4/ly5fj+eefp84HIcQlntQWcescEEKIZZGRkdiwYQPOnTsHrVbr0lhgHx8frFq1yq5F2sjd4+OPP8bXX3+NlJQUREdHo6CgAAcPHsStW7fw0EMPIS0traUP8a7y/vvvY/Xq1bh+/TqSkpKc3k9OTg5effVVvPjii248OkLI3ciT2iI0BMtFdNuTEOIJDh48iPfffx9nzpxBWVkZBAIBOnXqhClTpmDBggV2LaJHCPFO1BYh3oY6IIQQQgghhJBmQ3NACCGEEEIIIc2GOiCEEEIIIYSQZkMdEEIIIYQQQkizoQ4IIYQQQgghpNk4XYa3vLwcarXancdCCHGQQCBAcHBwSx+GUyhDCGl53pwhAOUIIZ7AmRxxugOiVquhUqmcfTkhHoUxhtraWqhUKgiFQvj4+IDjuJY+rFaNMoS0JpQhLYNyhLQmd1OO0EKE5K5WW1uLK1eu4I8/zkEmqzI8LpUGoGfPJHTs2BE+Pj4teISEEE9GGUIIcdXdmCPUASF3rdzcXOzffxAqlRoXLvjj3Lk2UCp5EIu1SEqqQnX1MZw4cRIjRgxDXFxcSx8uIcTDUIYQQlx1t+YIdUDIXSk3Nxd792bi6lUpduxoh5oa01Ph/PkA+PmpMX78bWg0mRg9elSrOvEJIa6hDCGEuOpuzhGqgkVaBcYYlEolqquroVQqwRizum1tbS327z+Iq1el2LgxzuyE16upEWDjxjhcvSrF/v0HUVtb21SHTwjxAPbmCGUIIcQSaovYj+6AEK/mzLjJK1euQKVSY8eOdtBqbU/u0mo57NgRjYULr+LKlSvo3r17k3wOQkjLcTRHKEMIIcaoLeI46oAQr+XMuEnGGP744xwuXPC3erWhoZoaIS5c8Ie//zkkJSWZVaS4m6pWENLaOJojTZEhAOUIId6K2iLOoQ4I8UrOjpusra2FTFaFc+faOPR+58/7IykpD7W1tRCLxQDuzqoVhLQmzuRIeHi42zIEoBwhxJtRW8R51AEhXqfhuEndrUsGX18NRCIt6up4kMv5hnGTU6bork48+eQThnrxSqVj058UCj4AQKVSQSwW37VVKwhpLZzNkXHjHgXgeoYAd2/1G0JaA2qLuIY6IMSrMMZw/vx5w7hJkUiLe+6pQL9+5QgLqzNsV1IiQlZWMM6eDTIZN9mhQwcAgFisdeh9JRINAEAoFN7VVSsIaQ1cyZGbN28CcC1DgLu7+g0hrcHly5epLeIC6oAQr6C/xXj27F+orq7GhQsBiIxUIi3tFoRCLS5cCMCPP0YYev7dulVh5MhCDBlSjC1b2hjGTXbr1g1SaQCSkqpw/nyA3e/frVs1pFLd9uZXPMxZuuLhibdACbmbuCNH/PwuuZQhPj4+Vq6cmqMcIcTz1NbW4vLly/jttxM4f96f2iJOog4I8XjGtxgvX5aiSxegtFSEKVNuIjvbD7t2xVjt+Y8dextTptzEL7+EQiYrRV1dHXr2TEJ19TH4+antmvzl56dC167V6NlzwF1ftYIQb+WuHJHLS9G3b19UV//uVIZwHGdy5ZRyhBDvcSdHVODxWq4tcvXqVa/PEFoHhHg0/S3GS5d88OGHHbF3bxQA4P77S5Gd7YdNm2zXzt60KQ7Z2X4YMKAMgG7cZMeOHSEUCjB+/G3weMY1uhl8fdUICqqDr68aAAOPxzB+fAEEAj5UKpXhioejVSv++OOczXrghJCm4+4ciY+Pt5IhQMMc4fG0GD++AEKhAAkJCfjzzz8pRwjxQsY5kp7eDkDzt0WEQgHi4+Nx8uRpr88QugNCPJalYQq6kxHg8xl27Yqxq+e/a1c0XnrpCgAYStONGDEMGk0mpkzJxZ49EejQQWY2drO0VAitlkN4eB0APk6cOAkeDw7dLgXuVK2oqqoCj8fzivJ4hLQWTZEjUqnUJEN27IiGWs2zOAZcPxSjR49e2LJlm+HKKeUIId6jYY6Ixbq5GM3dFunduy+2bNkGrVaN8+fDHPoMnpYh1AEhHsvScCe5nAeVisOlS473/JOSZBCJRACAuLg4jB49Cvv27Uf79tcA6BoEDcdudutWBa0WuH1biN274zFnznWnq1Zs3rzZ8Jinl8cjpLVoqhzRZ8j+/QexcOEVaLUcOI5ZHAPerVsVTp06g4ICMXbvbkM5QoiXaZgjLdEWAXg4efIkcnJ80bat2uszhDogxCNZW6TH11cLoZA5fPXwwoUAdO9ejfz8fPj4+EAqlaKurg4ajQbZ2VLs3Blrc+xmYmINgoJ0VyScrVqxY0c0qqqEXlEej5DWoKlzxN/fH+3aJeDKlau4ds0Xu3ZRjhDS2ljKkZZoi4wbl4fERBmysoLQtq3c6zOEOiDEI1lbpEck0p1wjvT8xWINEhJk0GiAH374wfC4VgtcvSrFpk3xNitIbNoUh8mTczF2bD5KS4Xo1s2xqhVdu1ahpESEM2eCAOjex9PL4xHSGlCOEEJcZSlHWiJDvv46HpMn5+LRRwtaRYbQJHTikawt0lNXp/u7vT3/xMQaLFhwBX36VODChQBs3twGGRnxOH06EACwa1es3WM3hUItCgvF6Nq1Cn5+arveX1+1IisrGPoTXk9fHu/qVSn27z+I2tpau/ZJCLEP5QghxFWWcoQyxHXUASEeSb9YV8OTWy7nGXr+jUlMrMGUKTdx86YvPvqoE7ZubYPz5wNw7ZoUcXEKnD8f4ODYzQBERtZCpeIwdqyl6jemeDyGsWPzoVLxcPZskMVt9OXxVCo1rly5YtexEELsQzlCCHGVpRyhDHEddUCIR9KNjdQt0gPobl3271+K5567htBQFbp1s93zF4s1SEu7ZbE8nq+vBmFhdRZvXUZGKq3u88IFf4SG1mHnzhgkJtZg8uRc+PmpLG7r56fC5Mm5SEyswZYtbaBU8q3u1xPL4xHSGrREjtjKEIByhBBvY5wj1BZxH5oDQjwSx3GGRXq6d6/EI4/kG1YZ/fnnMDz8cD7Gjr2NTZsargDK4OurwX33lUEo1Fosj2dt7KafnxrTpt3A558nWrwaoa8gkZ8vwcaN8UhLu4WXXrqCCxcCcOGCPxQKPiQSDbp1q0KXLtVQqXjYuDEe2dl+jX5efXm82tpaiMViB78tQoglzuWILkNEIi169Kh0KEcayxCAcoQQb3MnR35Dhw41EAioLeIO1AEhHqtjx444fvwEJkzIw9WrpquM1tQIMGXKTUyenItdu8xr8Gs0umoTlk5ea2M3Bw4sga+vBg88UIJ9+6LMXqevIFFby0N2th8+/rij4T27d79zG1ajAX7/PRgHD0agttb61QZj+kBRqVTUcCDEjezNkcxM8xr8juZIYxkCUI4Q4o18fX3BccCNG77UFnET6oAQj8aYvjqE6dWF7Gw/k54/Y3dq8B89Gorx4/OtVoeQy/koKRGZVJDw81Ojb99yAEC/fuX49dcws8Do2rUaJSUiwwmqVPJx/Hgojh8PgUSiQXBwHWbOzAGfD+TkSO0+4YE7gaIfa0oIcZ/GcmTSpFzMn29ag58xhkmT8uzOEXsyBKAcIcTb1NbW4tChI7h61c8r2iI+Plr4+akwa9YNj84QmgNCPNaVK1eg0WitVofIzvbDzp0x4Djg2rU7k7tycqQAbJXH45CVFWxSQWLgwBIIhboxj0IhwwMPlJi8QldBospiBQmAQ20tHykpJVCpOFRWCuyamGasW7dqSKUBtJgYIW7WWI4AutWMr171w4cf3pkgmp8vAWB/jjSWIQDlCCHeSL8I4c6dllc896S2iEIhQFWVEA8+WAK1Gh6dIdQBIR7J2gJixsRiDcaNu11/VSLesJ095fHOng2CSsXD2LG34e+vMlxx0OvXr9wQCLoKErehVluuIGE6ySsO165JG52Y1vD1XbtWo2fPJHCc7TJ8hBD7NZYjtiaIOpIjjz12y2aGAJQjhHgjT2uLjBt323BH15I7OSLD6dNBTpXqba4MoQ4I8Uh3Fv6xvsjOPfdUWJzcZXxb0xqlko8tW9ogMbEGM2bkGK44yOW6W5X6Kw/6k7ljRxmEQi0effQ2kpIq0b59DZKSKjFxou62a3y83DDJSxc2HMaPt6883vjxBRAKBejYsaMD3xAhpDGN5Yi1DAEcy5F27eRWMwQA5QghXsrT2iKJiTJwHDB//jWkpeXazJGDByPBGIdx4zwzQ2gOCPFI1hYQu4OhX79yK5O7dLc1R44shJ+f2upVi+xsP2zfHouJE/Pq35PDunUJmDXrOoRChgEDytC/fxlUKh6++aYNAgNVuO++MiQlVRv2UVIiwr59kThzJgi1tXz4+anQuXMNkpK6gMe7iClTcrFjRzRqaszHU/r5qTB+fD46dJBh5MjRNGyCEDeznSO2MgSwN0cKC8XQajnweMwsQ+67rxwhIXXo2LGGcoQQL+RpbZGvvopHXp4E/fqVYeDA0kZzhMdj6NBB5pEZQh0Q4pGsLSCmp6+f/eOPERafP3s2CEOGFFspj3dHmzYK6O80ZmUFo7BQjJMng3H//WXg8YDr132xaVOcYRLX8eMhkEpVSEvLQ3S0Al99FYfychEAzuQKQr9+/ZCQkID9+w9i4cKruHDBH+fP+0Gr5eDnp0ZiogydOtVAKBRi5MjRaNOmjWtfGCHEjFaryw9LOdJYhgD25cjAgSUQCHRXFxtmiEDAkJAgN2kUAJQjhHgLT22L/PxzOH75JRRTptxEXJwcX32VgJISEeRyAUxzRIiUlAchEBzxuAyhDgjxSD4+PhAKxSbVIYz5++vGNFq7KqG/rWlcHq9hz9+42oRKxeHXX8MAAL/8Eoa+fcshFDK0aaOAUMhQW6sb52lcXg8AXnwxGyUlIvzxRwDatlWgfXu54QpCXFwcnnzyCVy4cAFi8R/o0qUKfKNiFEKhGL169UB4eLjL3xchxNzNmzeh0cBijlirwW+ssRyxJ0MEAoZz5wINDQfKEUK8hye2RYA7ORIcrIKPDzBjxg0AsJgjbdq0QWxsrMdlCHVAiMfiOGaYhNnw1mXHjrrbjrYmdzUsj3fhgj8uXAgwLNIzZEixYbxlVlawSV1v/ZUH/fjL7Gw/pKXdMixi9uOPEVAqeRCLtejWrQopKbqx3n379jW5glBUVIRTp85ApVLj4sUAnDsXYHhdUlIVamtP4tSpMxgxYhji4uLc+v0RcjdjjOHPP8+jqMjHMBHT0UnmgO0cGTCg1O4M2bcvComJNZQjhHgZ97dFTBcMHDKkyKUcOXgwstEc8cQMoQ4I8Ui1tbWoq6uFWs1ZXKm4V68KKBQ8q1cl9PSL9PTpU44hQ4rQvfud8ZKsfk6W8RUHPeMrD/fdV47+/cuQnW26iJmefg0A3USv3xEWFoa4uDjk5uZi795MXL0qxY4d7ay+bvz429BoMjF69ChqPBDiJvrJo8eOxeChhwrMckQu50Gl4hrNEMA0R4YONc0RoPEM6devHHl5EkyYkEc5QogXcXdb5J57KnDffaYLBtrbFnE2RwB4ZIZQFSzikfQTv44cCUNiYg0mT86Fn5/uMd2YSxUuXvS3q8ScUsmHWs2B44DPPkvExx93QFZWkMl4y4YnpP7KAwAIBAyVlUKzMp0Nt//66zhcuSLF/v0HUV1djf37D+LqVSk2brT9uo0b43D1qu51tfr7q4QQl+gzpLpaYKgyY5ojWgiFzO4ylUolH3y+1pAjp04FGp5rLEOEQobHHsuzWO634WsoRwjxHO5uixw/HoqzZ/2h1QJfftnOobaIozly9aoU+/YdwL59BzwyQ6gDQjySfuJXWZkPNm6MR3y8HC+9dAUTJ95CUlIlAODiRX9D/WzbJebuVKkoKfGBWs1Dr166fVi64qD3yy9hUKl0yeDvr4avr8bmMWu1HHbujIZKpcK+ffugUqmxY4flhYsavm7HjmioVGpcuXLF5raEEPsYTx7VD4GwlCMaDWdHhgA8nhYPPFCG8+cDoFTy0aOH7gqmvRnC5wMHDkTYlQeUI4R4Bve2RfQ5Uo7z5wNQVSV0uC3iSI7s2BENtVoNtdozM4Q6IMQj+fj4QCoNQFJSleHW5b59kYiKUuLhhwsB6E5ES1c2GwoPr0VYWJ3h9qjxSqOWrjjoNbzyYGllY/PXCHH+vB+Ki8tw/rz1hYssve7CBX+cPfsXqqqqoFQqwZjtICOEWGecIQCs5shvv4U2miF+fipMmZILsViL8+cDnMoQjgN69aqw69hdz5E/oVAoKEMIcZE72yLNnyMC1NbycP68tVLjll7TfG0RmgNCPBLHcejZMwnV1ccME7+OHw/F8eMhkEjUmD07B926VWHr1jY2J3d17VqNrl11DRClkme12oQ1Dcdf/vprWKMncna2H7p3r2l0XHlD58/7IykpD9988w0AQCoNQM+eSejYsSPV9ifEQZYyRD8EwjhHQkPr7MoQtfrOuO+mzhDA9RzZsGEDZQghLnJ3W6Q5c8TXVwOJROuxbRHqgBCP1bFjR5w4cRLjx9/Gxo36iV8cFAohjh8PMSzuYzy5q18/08ldJSUi/PRTOIYPL4ZYrDW54sDjMcyZc63R49DfUjWuQmGLWq27sWirvKclCoWuLt62bTHQaHhISqpCdfUxnDhxkqrbEOIEyxkCNMyRvXujbGbIvn2RuHTJDwsWZOOeeyqbPEMA13Nk9+4otGsnpwwhxEXuaovs2xeJ3Fwx5sy50Sw5Yk+pcUuaqy1CHRDisXx8fDBixDBoNJlmq3g2XNzH9MqmBj4+WtTW8qBQ8MHjMQwaVIqePSuQmCgz7J/PBwICGp98asyeKw8CgfXFz2yRSHRzTK5e9YNCIaDqNoS4yFaGAMY5kodNm+KtZohuYS8tlEoOHTvWGF7fVBkCuJ4j584F4OTJEMoQQlzkvrYIMHnyTajVaJYcsbfUeEPN1RahOSDEo8XFxWH06FHo3LkWCxdeRVqabuJXTIwCJ04Eo0OHGkyefNNozCUHhUKAigoRFAoB/PzUmDz5FkQiLTp1qoFSyUdVlaDRP9XVAjCmK4+nUnGGxxUKfqPjLxMTZYbyno7o2rUaJSUiw9UHgKrbEOIqaxnSvn0NEhNrUFQkRMeOMqOx26YZAnDw81PV5wgDx+kqazmbI/ZkCOC+HKEMIcR17mmL5CIxUYb8fLFTOaLVOpYjcjnfUCLYEc3VFqE7IMTj6VcCvnLlCvz9zyEpKc/wXHU1Hx06yGyOuVSpeNi8uQ3Gj7+N/Hxxgzre5ng8hieeuIn27dXg8wE+n+HLL9vbNW7bz0+Frl2rcemSv8XFz2y/rgr79kUCMD02fWWKhQuv4sqVK+jevXuj+yOE3GErQ5RKXYnutm3dnyOTJ99Ehw5q8HgtmyOUIYS4zh1tkY0b45GXJ8GCBVecyhHAkRxRw8dH67FtEeqAEK/g4+OD7t27IykpCbW1tfjrr7/w+++nkZGRgPnzr+H06UDExSksjrk8cyYItbV8bNnCw5QpNzF5ci527TIdiqHn56fC2LG30aGDDBwHSCRSKBQKjBt3G19/3XhQjB2bD5WKh8zMSLRvL7OwcJHt1509G2RxG31lCl3oJYHjbJfTI4SYapghKpUKV69exYkTJwEA338fDbFYY3XstjM50rGjDGKxBF27dsYff/zVojlCGUKI69zRFgF0VbMcyxExOnXqiHPnLjiUI3V1uvkqntgW4ZiT9bWKi4sNC7QQ0txqa2vx1Vdf49IlEYKCVCgoEGPr1liLY7eNJSbWIC1NNyTrwgV/nD8fYHSVogrduulWOO7UqQPuv/9++Pj44NatW9i7NxNXrkixc6etoMhHYmINNm6MR3a2HxITazBlys36FUvtf501SUmVSEvLw9NPPw2xWAxAV6M8PDzchW+y5VCGkJZWW1uLDRs2Qi7X4upVP2zd2gYAsytHnngiFzwew/nz/rhw4U6OdOtWha5dq8Hj8TBs2BC0a9cOHMcZVjRvyRxpbRkCUI6QluVsWwRwLUcuX/atXwm98TwA4JFtEboDQryS8aSw4mJh/S3GKNTUCKBQWH9ddrYfVq5si/nzryE+Xo6kpGrDcxoNUFUlQEgI8MADDxjKzenHfvL5B5GYeMUsKBreXtWfuPrFz554IhcLF16x2OHp2rXa7HXW6MdjqlQqw0lPCHGej48PRo4cjr1796JbtzvDFBQK2zlSWOgDjmO4eNEfUVG16N79zlCMujoOfD4PkyY9Dn9/f8Pj7suRAJw/b314h60coQwhxL2cbYsAruWIVpuJhQuv4Px528O99HngiW0R6oAQr6U/EfftOwC1GnbfYhw1qghqNYeDB8PRuXMNOnWqgVrNoaREhNjYOowaNdqs1rV+7OeRI0fAWA66d7/TcbF0e1VPHzC3b4vRvr3MpMNTWSmw+jpL9JUp9CuzEkJcFxcXh2HDhmH//oOGalj2DFPQaDhcvuwHrRYIDq6DWs2htFSImJg6jB492qTRYPxeTz75BA4fPgzGbjicI9XVfHTpUmVYXLGx1zVEGUKI+znbFnElR/r374vjx7MQHd34cC/AM9si1AEhXi0uLg5PPTUFWVlZ4LgLmDz5ZiO3JXXjKTkOGD++AJWVAhQV+SAyshbx8VqMHDkabdq0sfp+4eHhuHYtB1ev+uL776OhVPKt3l41Hk+5YUMClEoewsLq8MgjtxEXp8CtWxIcPx5q92ft1q0aUmkALShGiJu1b98eI0YAHPcjnngit5EhUsYZkm+SIbGxGowe/ZDVDKmtrcWVK1dQXFwGjoPDObJ8eQcIBFpMmJCHhAQ5rlzxw6ZNcRZfZwllCCFNw7W2iOM5oqPrrKxe3RZCIbM63MtT2yLUASFez8fHB4MGDUJCQgL4/APo0OFq/S1Gf6PxlHdWRNdqdXW3ASAwUI2YGAl69rwXnTp1gkgksvgeubm52L//IFQqNW7e9EX79nI89FAhdu2KhqVf/g3HUyqVujcsKfFBRkZbzJuXja5dqx2sTFGNnj0H0ORRQppA+/bt8dBDQuzffxCJiY5lSFiYAL1734euXbvalSEXLvijpCQMgwaVOJEjfGzYkIB587LRqVMN/Pw0lCGEeABX2yKO5sjNmxJ06CDHuHH52LUrur5suClPbovQJHTSquivMP7xxznIZHduS0qlAejRoxsSEhIAAIwxcBwHkUgEHx8fmyeSftLX1atS7NgRg5oagWEyu1CotVlyb8uWNhbHU4aGKjF//jVkZ/vZVc1iypRb6NxZiSeffMLkqoM3TyClDCGeyFaG9OyZhI4dO0Kr1UImk9U/LoVYLHY4QwA0yBHrc0Is5QhliA7lCPFEzZUj3twWoQ4IaZUYY4ZSm0KhsNFOhjV3Klz4YONG05NTLNbgnnsq0K9fOcLC6gyPl5SIkJUV3Oh4yunTc5CQIEd2tp/ZCs16fn4qjB+fjw4dZHjoIfPhYd7ceKAMIZ6sOTIEuJMjw4cXQSi88+vYnhy52zMEoBwhno3aItbRECzSKnEcB7FY7HKllytXrkClUmPHjnZmDQelko/jx0Px558B+Pvfr2D37iicOxdgdSx3Q1lZwWjbVo5OnZRYuNDardpqCIWCRuemEELcqzkyBNDlyJ9/BuKhhwqxY0c0cnKkNkt3GqMMIcSzUVvEOuqAEGIFYwx//HEOFy742xwbKRLprlqWlYksjsG0Rl/Kbvz4scjPzzdbWVV3q3aAzbkphBDPZX+GaAEAVVVCVFTYf65ThhDS+rXWtgh1QAixora2FjJZFc6ds93br6vjAQDEYq1D+9eXspNKpWYrNLtyq5YQ4hkoQwghrmqtOcJz+x4JaSX044qVStuniVzOR0mJCN26VdncrqGGpez0t2r9/f0bnYxGCPF8lCGEEFe11hyhDgghVugX2Wn8agKHrKzg+hVQ1Xbt+04puyRqJBDSSlGGEEJc1VpzhDoghFjh4+MDqTTAZNVha86eDYJKxcPYsbfB49kuLMfjMYwfXwChUICOHTu663AJIR6GMoQQ4qrWmiPUASHECo7j0LNnkmGRHluUSj62bGmDxMQaTJ58E35+lstC+vmpMGVKLjp0qMHIkcNpRWJCWjHKEEKIq1prjtA6IITY0FgNf2M8HsOsWTmIilIA4BopZTfcLaXsvLmGP2UIuRtQhjQtyhFyN2iNOUJVsAixwcfHByNGDINGk4kpU3IbXaQnJkaJ4cOHQyaTUUlMQghlCCHEZa0xR+gOCCF2yM3Nxf79B6FSqe2+muCuFVBt8earl5Qh5G5CGdI0KEfI3aQ15Qh1QAixU21tLa5cuYI//jgHmezOZDDd1YSkFrma4M2NB8oQcrehDHE/yhFyt2ktOUIdEEIc1BxXE+zlzY0HyhByt6IMcR/KEXK38vYcoTkghDhIv0iPWCxu6UMhhHghyhBCiKu8PUeoDC8hhBBCCCGk2VAHhBBCCCGEENJsqANCCCGEEEIIaTbUASGEEEIIIYQ0G+qAEEIIIYQQQpoNdUAIIYQQQgghzYY6IIQQQgghhJBmQx0QQgghhBBCSLOhDgghhBBCCCGk2VAHhBBCCCGEENJsqANCCCGEEEIIaTbUASGEEEIIIYQ0G+qAEEIIIYQQQpoNdUAIIYQQQgghzYY6IIQQQgghhJBmQx0QQgghhBBCSLOhDgghhBBCCCGk2VAHhBBCCCGEENJsqANCCCGEEEIIaTbUASGEEEIIIYQ0G0FLH4C3YIyhvLwcMpkMUqkUwcHB4DiupQ+LEOJFKEcIIa6gDCGtBXVAGlFZWYktW7YgY80aZOfkGB5PbNsWU595BmlpaQgMDGy5AySEeDx9jqzNWIvr2dcNj7dLbIfpU6dTjhBCbKIMIa0NxxhjzrywuLgYKpXK3cfjUQ4dOoS5s2dDoVAgVSpFqkSCYB4P5VottikU2CaTQSKR4IuVK5GSktLSh0vuQkKhEOHh4S19GE65GzIE0OXInLlzoFAoEJMag+jUaAiDhVCVq5C/LR+3t92GRCLBl198STlCmp03Zwhwd+QIZQjxdM7kCHVArDh06BCmTZ2KUWIx0oODESUwv1lUoFZjVnk5MpVKrMvIoBOfNDtvbjy09gwBdDkyddpUhI8KR6/0XhBHic22URYocWbWGRRnFiNjHeUIaV7enCFA688RyhDiDagD4iaVlZXo37cvHuQ47AgLg8DG+Eo1YxhfUoIjjOH4yZN0C5Q0K29uPLTmDAF0OdKvfz/4P+iP+3bcB57Aes0PrVqLE+NPoPpINbKOZ1GOkGbjzRkCtO4coQwh3sKZHKEqWBZs2bIFCoUC6cHBNjsfACDgOKwMDoZCocDWrVub6QgJIZ5OnyO90nvZbDgAAE/AQ6+VvShHCCEGlCGkNaMOSAOMMWSsWYNUqdTisCtLogUCTPD1xbrVq+HkDSVCSCvCGMPajLWISY2xOGTCEnG0GNETorFm3RrKEULucpQhpLVr0g4IYwxlZWXIzc1FWVmZW0+Iptp3eXk5snNykCqROPS6VF9fZOfkoLy83C3HQQjxzgwBdDlyPfs6olOjHXpdTGoMrmdfpxwhxI28MUcoQ0hr1yRleJuyXJwj+3amXrZMJgMABPMc65vpt5fJZAgJCXHotYQQU56SIYBrOSIMFjp0bPrtKUcIcZ2n5AhlCCHm3D4JvSnLxdm7748++Aj5+flOrd1RVlaGHj16YHN4ONKkUruPbbNMhknFxfjzzz/ppCfNxpsnkHpyhnz5xZfo3bu3040XfY7029wPsWmxdh9f3uY8ZE3KohwhzcabMwTw7BzRt0UoQ0hr1+JVsJqyXJzd+555BgV7CsBjQJqfn8NrdzDGkDxoEPqWlGBTWJhdxwYAk4qL8Xt4OA4fPUqrkpJm482NB4/NkFlnULS3CEKRECqVyqnGC2MMg5MHQ9VXhb6b+tp1fACQNSkLot9F+Pnwz5QjpFl4c4YAHpwj9W0RjuMQmxZLGUJatRbtgLhSLi4gIMDm7Ulb+2aMoa60DuoaNQR+AggCBTgx7jhq9pfgVnQsAnk8lGq1qNFq4cfjQaXVYnZFhc21O9LT0/GvxYuRGxtr10T0fLUa8Xl5eHvJEsycOdPOb5AQ13lz48GdGRIYGGhzmENj+zbOEZ6Yh1PPnELpj6UY8scQ+HXyM8kYUagItYW1jTZe0tPTseRfSzAyd6Rdk0iV+Ursi9+HxW8vphwhzcabMwTwnByx3BY5gdKjpRh5cySEgUKT57UqLc7OPksZQloFZ3LEbXNA9OXiBqcPtrtcXGZcJl5++WVcvHzR5u1JS/uuq6hD7rpcXF9+HTWXagyv9evshzZPtkFRZhFmlJbifF0dLqnVhuc7CwSY4+8PFWOYO3u2xbU70tLS8P7SpZhVXm7XOiCzy8shkUgwceJEh74zQsgdzmTIvvh9WL9+PcRisc1hDtb2bS1HpB2k0Kq0+OvlvyC7KjPLmHbz2qH32t44Pf005sydY7HuflpaGv7v/f/DmVln7GoInZ19lnKEEBc1d4401hYpzCzE6RmnUX2+2uz5tnPaQqvSUoaQu5Jb7oA4c6uwMLMQx8cdB1MzxE60fntyxfIV+Nvf/wb+ID76fdPP8Nqsx7OgkWsQkxqDmNQYw2tvb7uN29tug+Nx0Kq1eNxHgol+fneGYclk2CaXQ8xxkDOGRUuWYNasWWbHZ7wS+srgYERbuBOSr1Zjdv1K6Bnr1yM5OdmZr5IQp3nz1UtXMwQAfk7+GeW/6qq92Boq5efnB9aD4YHMBwyvtZkjW3U5wsAQOjAU7Z9rb5YxfAkfSf9Nwh/z/8CSRZbvfpoM11jZC+JoC8M18pU4M1t3N2V9BuUIaV7enCFA8+aIr68vRMkih9oijDGAAbFpsRaf54l50Mg1WLLIeluEMoR4uhYbguXoZKnCzEIce+QYIkZGoPeq3jbHZxbuKQTTMvT6shfazm5757WjItA73fprT888jcI9hdgcGoY0Pz+T5wvUaswoLcVehQICHg9vvv02Hn/8cbOrD4cOHcLc2bOhUCgwwdcXqb6+dzoycjm2y+W6TlJ6Op3wpEV4c+PBlQwB6nPk4WMIHxmOe1ffa3ss9g8F4El4GHlNN5TB7hyZdRpFmUUYsHsAIkdFmjx3asYpFO0tAk/Cg1QoxbFfjyEoKMhsP8YTVqMnRJs1QvK350MikWDlipWUI6TZeXOGAM2cI3sK0On1Tuj2Tjf7M2TGaRTtN88Q/fOGHBHw8Pab1tsilCHEk7VYByQ3NxcDBgzAA/sfQMTwCJuvq6uow76EfQgdHIr+O/o3ektxf8f9UOQoEPloJHp81AM/9foJIfeHYMD3A8AX8m2+9tjYY5DVzwUJ4ptuq2YM44qKcEChgAaAr6+vxYnpFRUVyMjIwNcbNuBmXp7h8cS2bTFtxgykpaUhICDA5mcmpKl4c+PB2QwBjHJkUCj677Q/R9o+2xYdFnZwKEeOjz+O0p9LMfLGSIiCRKbPjTuO4oPF0Kq08BH7YPXK1WYZwhjDjRs3sHXrVmz7dhtu5tw0PNcusR2emfYM5QhpMd6cIUDz5sixscdQcrgEg48OxtEHj7qcIYbnxx1H8YFiMA2Dr6+vxYnp+rbIV19/hVs3bxkepwwhnsCZHHHLQoTS+nK1qnLzUngN5a7LhUauQe/03o2Oz6wrqUNtfi0AoPC7QhzocACaGg2K9xfjpx4/IXtZNuoq6iy+lifg4d5V90LBGDLq62kbE3Ac0kNDoQWwODAQgwFMmzoVhw4dAqCbbJaeno6xDz+MpUuXGjofCW3a4NVXX8Wu77/HzJkz4e/v32QLHBFyt3AkQwCjHFnlWI7kfJ7jcI70XtkbGrkGuRm55s+l9wbTMHRZ0gWByYGYOs08QwYnD8bAgQPx0Ucf4WbOTcS3i8dLL72EX375BT8f/plyhBA3acocUdeoEXJ/CFgdw+F7D9udIdXnqq1mCGCUI1qGzos7w3+wv8UceWTsI1i6dKmh8xGXEIdXX30Vu3ftpgwhXqlZ54AwxnCw60EE9gpEv039Gn2P4xOOI//bfMPfIx+JROKLiabjsH356Le5n9mtTb2TaScg3l2My5ExFkvSTSoqwtm6OvwZE4PHSktxhDF88PHHeHnBAigUCqRKpRZL+YolEjyWmopff/7Z4bVGCHEXb7566ezY7ZbIkaxJWag8W4lhF4aZ5Yj+uSF/DsGJ8SdQ83MNPvrgI7z08kuW1wnYmo/b211fJ4AQd/DmDAGaJ0eM53pET4hG7MRY8zlhFjJEWaDEwaSDGHZuGP588U+rGQKY5kjWY1moPlJtO0fq56aIxWKkPpaKo78epQwhLaZFy/DaUy6utqQWe8L32DU+M/frXPw+5XeTx/gSPkZcG2HYv60x2nr6RXlK4uIQyje/TapfQLAkLg51jKHNrVvgOA6jfX2RHhxssQyv8RySwWIxnvP3d2itEULcxZsbD85kCNCyOTKmZAxEoSKrz2nrtMhskwmO4xAxOsLmOgGnZ5xG4d5CgAPapLVx60JphNjLmzMEaPoccWW+2J8L/0T2R9lIXJiIkP4hVjMEcD5H9HNIwgaHod1z7ShDSItosSFYgK5cnEQiwZlZZ6BVay1uo67RlcMVBgtt7quuog6npp8y/F0Yotteo9Dgyn+vGB4XR4nRf0d/RIyKQNbjWRZvgerfq1pr+ZiCeTzD8xKOgxDASLEYO8LCrK4BEiUQYFdEBEZLJPi9thYjxGIMl0iQJpViU1gYcmNj8SDHmQzpIoTYZk+GAC2bI6pq86Edxs/xJDxwQg7hI8Nx3477rDaAxFFi9N/VHxGjI8BxHKLTohGbFouI4RGITYtF3019MTJ3JPwfNB2OQQixzZ05UldRh6zHsxAxKgL9d/S3fT43yBBlgRLXl+vuSOQszzEMibKUIcbH4WiODNg1ABGjI1D+eznCR4RThhCv4bYOSGBgIL784ksUZxbjxPgTUOYrzbYR+Oka9I2Nz7z26TWwOt3JypfwMejHQeCJdYeaszwHyoI7+7Y1Rtv4vfx5lj9qeX3HxJ/HwzqZDBoAq0NDba79AejmkKwKDYWSMbxeUWHyXJRAgB1hYRglFmPu7NmorKy0uS9CiH0ZAgCaGg2AlskRob95Y8X4udx1uWAaht6rGx9Trp+nBgBZj2ehMLPQ5HlxlBj37bgP4aPCMWfuHMoRQuzgzhxxZM5qwwy58n9XoFXq2hcahQa563W5YilDjI/D2RzRKrU4//p5k+coQ4gnc1sHBABSUlKQsS4D1UeqsS9+H7ImZSFvcx6K9hchb3Mezsw9A07AIW9LntV9MMaQ/VG24e9t57VF4D2BaDevHQDzq5cAII4WI2ZCDK5/ft1s4tXtLXnoIBYixEoHZJtMhs4CAYI5DsurqjDB19eu1c8BIFogwARfX6yurka50WKHgK6DsjI4GAqFAlu3brVrf4Tc7RrLkBNpJ/DjPT+CE3K4vfW21f24PUe23YZfZz/DXRRLzwmCBbi+/DpiJsTYtWqx/j2jU6Mh8BPgRNoJs7sv+oXSKEcIsZ87coQxpjufUx07n2MmxCD7k2zD3Q+9or1F8E30tZghgBtyZEI0bqy+gdryWpPnKEOIp3JrBwTQnfhZx7Ow+O3FEP0uQtakLPw68ldkTcpC8f5iMDVD/rf5JlcfjVWfrzZcCeBL+Oj4SkcAQMe/d7R69RLQLR5Uc6kGqrI7VzOU+Urc/jYfw4Vii5O+8tVqbJfL8WxAAMoYwyW1GhPrq2jYa6JUijoAX9TUmD2n76CsW72aKlIQYidbGVK0rwjQAnFT43B7++3my5Htt9Hu2XZmOWL8nKpMhZpLNYiZGOPQ541NjYW6Sm317ou+cbFm3RrKEULs5GqO1JXW6c7nVMfO55jUGMiz5Ya7H/oOB9Mw+Mb5WmyLuCVHJsaC1THkfJFj9hxlCPFEbu+AALpboDNnzsTPh3/Gn3/+ib179wIAkj5I0r2piIfTs05bHJ959aOrhv9vO6+t4QqAOEps8+plwzHaWrUWp2efBvjAenkNKjQak+3VjGF2aSl8OQ5TpVLU1A/FCrZyp8Qa/fbp1dUWT+xUX19k5+SgvLzcof0ScjdrLENCB4WC78tvthzh+/IRNzXOZNuGz9k7N6Uh/faRoyMt3n0BdI2a69nXKUcIcYArOeLs+Wx8/jYc+ll2vMyss+PuHLmRfoMyhHiFJumA6HEch5CQEMPqwL4JvvDr7IegvkEoyizC8fHHTcZnKguUuPWVrsa18VVLPVtXL43HTyrzlTg+/jiKMovQZ20fyAGTtUDy1WqMLypCpkKBLRERCOLz4VffkSi3MlndGv321zQalFl4rb6DIrOwFgkhxDZrGVK0twj9Nvdrthy5b8t9JguIWXrO3jluDem3j3nM/O6Lnr5xQTlCiOOcyRFnz2f9XA/AfOinVqE1uejRFDkivyanDCFeoUk7IHr6xYHUFWq0m9cOZb+W4d6Me1H6cyky4zMN4zPPzj9ruG1pfNVSz9bVy7yteRDHinFm3hlkxmei9OdS3P/9/WjzRBtEPxaNpbIqfFNTg0lFRYi/dQs/K5X4PjISIyUSAEAgxyGA47DFwZNzm0yG+PryvpYqbek7KFIHh3YRQu5omCG3t91G4D2BGLB7QJPkyOm5p5EZl4nCvYUIHhAMVYXKMH48a1KWScZEjNStuCwIFEAQILA5x80S/dhvcZzuOC1VydE3LihHCHGeIzlScaoC4lgx8rbafz4rC5Qo3KMrJmFt6Of1/11Hzpc5TZIjknhde4YyhHiDZumABAcHIyo2Cnlb8hA3LQ58Xz5ufXULI7JHoPsH3VF5thJZk7KQv123WJilq5Z6lq5eKvOVyN+eD2WeEqU/l6Lrv7ti1M1RhhM6Ni0Wt2vVmFxSgrN1dfggJAQ34+IMnY98tRqPFRejhjF8K5ejoMGEcmv0c0iGinUNB0uVtrbJ5Uhs2xbBwcGOfWmEEIPg4GC0S2yH21tvGzLk9KzTCB8WjpE3Rro9Rwp2FKDd8+3QdnZblB8rNxk/Xnm2Et0/6G6SMcp8JU48dgLqGrXNOW4NGY/9VlfUD72wUCXn9rbbaJfYjnKEEBdYaotYy5HfRv0GZZ4S+dvsP58vLLoA1F+HtDb0U1urxZn/d6ZJciR8qG4dBsoQ4g2apQNy+PBhFOYXIn97PrRKreGW56nppxCbFothF4ah7dy2hu0tXbXUa3j18vLSyzg96zR4Ih4ixkSgtrgWl/9zGWXHygyv0d965AHoKRQiis/Hidpa3SKERndEtoSHQ8RxmFFaCnUjE7WM55BUaLXoLBCYVdrSd1CmzZhhceIZIcQ+HMdh0AODcHvbbZMMOT7+OLQKLRJfSHRPjkh4aP+39mAcw7WPryHnixwwNUPigkTw/fgAHwjoGQBxlBjlJ8rN7ojct+U+XaNmpuW5KcYajv22VmlL3zF6ZtozlCOEuMBaW6RhjowpGYMR10dgRPYI3fk8o/HzWX5LjhvpNwA0PvQTAKSdpDZzhCfi4dSMUw7liKpCRRlCvIbbVkK3prKyEv3694P0finKjpUhdHAo+u/oj+KDxch6PAsauQaRD0WicG8hmIqZrVJsibJAiX3t9umGWfAAcMADPzyAiJERFlck1Z/c/wkKwrqaGlwyusPRWSDAPH9/POrrCx6AJ4qLcbyuDmMkEqwMDUW0hZK8+Wo1ZpeWIlOhQEZYGKaWlOCDkBC8EBBg2EbNGMaXlOAIYzh+8iQCAwMd+n4JsYc3r2Jsb4YAuhzpe19fKOuUCB8RbpYhMRNiED4sHH88/we0dVqnc4TnwwOrY4iZEIOYiTEQBAlw+pnTCBkYgl4reiE3IxfXP7+Omkt3qt75dfZDu2fbIW5qHJiaoeD7ApyecRoRoyJw76p7IY62sIJxvhKnZ+ty6v7v70dAjwBkxmei+wfdkfhComE7rVqLrPFZqDpShazjWZQjxO28OUMA97ZFYibEICY1xrCaeN62PF2ZXgZEPhSpWwndyvl8ZOARyK/LAQCJCxPR44MeZtvpV0YHYHgPPb/Ofmg7ry2iH40GeEDWE1moOF6ByDGR6L3S+vvqc6RPRh/8PvV3yhDSIpzJkSbvgKSnp2PJv5ZgZO5IVJ6txLFHjiFiVAR6r+wNnoSH3IxcXFx80XAickIOPhE+je63tqgWTKU79OgJ0ei/rb/hOa1ai+Pjj6P051KMvDESZ2afge/uYlyO1JW1K9NqUa3VQgtgl1yOL6qrTTolfAD6awQTfH2RKpUimMdDuVaLbTIZtsvl8OU4bAoPx/+qq/GzUokbbdogqH4uSL5ajdnl5chUKpGxfj2Sk5Pt+EYJcZw3Nx4c6YDoc6R3Rm+cmnrKLEMadgqcyREAiHy4vpFh1HHJXpaNv/72F0bljoI4SgzGGFRlKqiqVbqhDjzojmG56TGAD3DgEJ0ajdjUWEOD4/a227i9/Tb4vnzct+U+hA0NM8kr/WR3Zb4SZ2afQXFmMdZnUI6QpuHNGQK4ty3SMEcEAQKoa9To9GYnXFt2DRq5BtGPRSN24p3zOW9rHm5vvw3UF9q0dfHD+KIHX8JHyskU8Hx5gBbI35WPnC9yzDOk/o5Fw86RcY703dQX1/93nTKEtBiP64AwxjA4eTBUfVXou6kvAKAws9BwtSH6sWhEDI/A2efPGlYsdoalE16Zr0RmfCY6v90Zl5ZcwgcBQXjJqOefqVDg8aIiyBlDaoNOxlaZDFvlcnAAovh85BmV8O0sEODZgACMEovxUnk5MhUKvBYYiBSxWNdBkcuxXS6HRCLBivR0OuFJk/LmxoO9DYeGOWKcIfpfylqtFqemnjLpTDiMB4y8MRK+bXxNHq6rqMO+hH2GK6bGKxObHEuqaQPh1sZbyN+ZD47PganvHJf+jkn8tHho5BqcmnkKRZlF6PRaJ4SlhBkaF/nb8yGRSLByxUrKEdJkvDlDAPe1RWInxkIQJIAyV4nb395G4d5C8H356L+1PyJGRqD6YjVOpJ5AzeUak/NZHCuGtKMUpYdKAVi/+6FnfBckcWEiIkZGWM2Q21tv6ybBc7pho8q8O3NC9DkSMSoCf770J2UIaVEe1wEpKytDjx490G9zP8SmxRoer6uos3i1AZyuM8GT8ACmG5utVWjBcZzuKoAIEAYJdf/fYPZK++fao9NrnUweOzHpBIr2FkFdrcZIHzHWhoUhWiBApkKBRwoLMUoiQXpoqMWVzwvUaswoLcUehQL3i0SY4ueHaD4fasawXaHAdrkcQqEQQcHByC8sNLwusW1bTJsxA2lpaQgwGpJFSFPw5saDvR0QSzliNUOgu/sh8BPoGv5aZjFHmIqBE3IQhYqgrlFDXamGT7QPEl9INMsRQNdYMb5iKo4Wmz7W4K6JnrJAid+f+R3Fe4sRdF8Q2s1pB3GcGOoKtaGBIBAKEBwUjML8OznSLrEdnpn2DOUIaXLenCFA07RFBEECxIyPQdS4KLA6ZjhXxWIx/AP8wbuPh6QPknAw6SDCR4SjZH+J4a6GI0M/eT48aNVaRI42v/NqvP2pGadQtKcIwfcHI25KHHyifXSLOm/PpwwhHsHjOiC5ubkYMGAAHtj/ACKGR5g9rx/KIM+To/D7QtxcexOyy3fK4MYlxGH2zNkYPnw4HnjgAbPwaIx+7sebAQH4tLoacsbwiESCfUolUsRi7IyIgMDGhCw1YxhXVIR9CgWM62IZdzL8/f1RXl4OmUwGqVSK4OBgmuRFmo03Nx7s7YDYyhHj4VBMy1DwXQFylpsOY7CUIzWXa3Bx0UWMzB2JX4b8gsBegei3qZ/N4zC+Yhr5cCSK9xcjLCUM/Xea3hVpSKvW4vi44yjaV2Ry5dS4gUA5QlqKN2cI0HJtkbAhYdgTvkc3Xrv+tHZm6KdvO18MvzycMoR4NWdyxPzSvxvp601bW1CH43RXIEWhIgT1DEKn1zpBVabCra9v4Y/n/8D3332P0NBQ5ObqFvZxdmXQWf7++FtgIDJkMrxTUYFaxrAqNNRm5wMABByH9NBQxN+6hWekUqyRyRAbFYVDP/8MnlHFq5CQEISEhDh0bIQQ+9jKEeMMAYAOL3ZA4guJjeZI5KORuPD2BZyaego1l2rQ9V9dGz2OyFGRGHljJHIzcnHh7QvQ1mrRe1Vvmw0HAOAJeOid3huZ8ZmIfyYeN9fcRHRsNI4cOkI5QkgzaIq2iH7FchhdwmUqZjJMyh7KfCXqSups3jWhDCGtUZOW4dXX7s/flm/X9voQKP25FO0S2xlOpMbCwxr99v48HoL4fDzv749gHg+pvr4Wh11ZEi0QYIKvL/YpdaGSV1CAiooKh46DEOK8psgRSYwE0ALFPxYDsP/ihihIhPbPt4cwQIjo1GibjQZj4mgxYibEoGhfEQAgPy+fcoSQZtIUGaJfsVzgf6ctIQoTQRwrtusPJ+DAk/AgChXh5tqbjR4TZQhpbZq0A8JxHKZPnY7b2247tKBOw3rVjoaHXv6WPHQQCw3rc5RqtbikVmOigyuBpkqlyNNoEFu/H5mDq6UTQpzXFDkiChXBr7MfgvvrFuVy5OJGXWkdFLkKxE60fzgoAMSkxkCZp4Q4VtdpoRwhpHk0ZYZEjolE3290E9vv+fwejL41utE/Q84MAVMz9FnXB6NvjbY478wSyhDSmjT5QoRpaWmQSCQ4M+uMXQvqnJ19FhKJBBMnTjQ87mx43P42H8/7+hvCo0are/9gCyuW26LffoCPbmyn1MEODCHENe7OkdrCWrSb1w7lJ8rh295XV+vfTvqhF84OCQ0ZYHo1lRDS9JoqQ25vu43QwaGQdpTanSOUIYQ0QwckMDAQX37xJYozi3Fi/Ako8y13IJT5SpwYfwJFmUVYuWKl2WI5DofHzNPw5ThMNTpB/eo7EuVa269vSL+9AroJ6MHBwQ69nhDimqbIkTZPtoFAKgBfzMft7fZf3NDU6MpyOzskVKPQoF1iO8oRQppRU2UI35ePM7PPoN3cdnbniH74FmUIuZs1eQcEAFJSUpCxLgPVR6qxL34fsiZlIW9zHor2FxkqVe2L34fqI9VWF8txJDyyxh5H0d5CbAsNNywOyBiDSquFH4ANNTVwpPjXFpkMsXw+MhUKTJsxw2sqSzDGUFZWhtzcXJSVlTn0mQnxNO7OkdPTT+OeL+5B9aVqgAecnnXarosbf736FzgRh9vb7L9rAgB5W/IgjhWjKLPIZFiHJ6MMIa1JU2VIUWYRCjMLwZfw7coRQaAAggAB8rbkOXT83pghAOUIsazJV0I3VllZia1bt2LNujW4nn3d8Lgj9aoPHTqEOXPnQKFQIPqxaMRMvLNoT96WPBR8mw9fjsO20HCMlEhQodFgnUyGz6qqcNVotfMOAgGeCwjANKnU0EmxJF+tRvytW+gkEiFXIMDxkyfNroh4msrKSmzZsgUZa9YgOyfH8Hhi27aY+ozue/b0z0Ds480lNJ3JEMD9ORJ8fzDKT5RDW1dfj3+Vbp2PhpT5SpyefRpFmUVImJWAG+k3DKujN0a/MKp/J39ocjXIOp7l0ecgZcjdw5szBPCMtkjwA8GoOFkBjVJ3d9SwroeNHCncUwiOx7XaDAEoR+4mHrcOiDWMMZfqVVsLD07AAWqGsRIJpvj5IVulwr8rK1HLGCb4+iKtwWrn2+Vy+HIcNkdEYJREYvY++nVADigU0PB4WL9hg8evJnro0CHMnT0bCoUCqVIpUiUSw2feplBgm0wGiUSCL1auREpKSksfLnGRNzceXMkQwD05smXLFvz7vX9Dpag/Dj7AgdOtjJwWe2dF4m23cXv7bfB9+bhvy30Iui/I6uroDelr+BcfKAY0wIb1np0jlCF3F2/OEMAD2yL1UcBxtnPk3jX34tQzp1plhgCUI3cbr+mAuEtpaSl69uyJz0JCMMnXF5VaLTJkMmyUyXBVrQYHYLREgtU2VjufVVqKTIUCuyMjTToh+Wo1ZpaWYq9CAbGPD1atWeMVJ/y0qVMxSixGenCw9c9cXo5MpRLrMjLoxPdy3tx48IQM0a+Q3HtVb4QNDQPTMOR9k4cbq29Ani03bOfX2Q/tnm2H+GnxEAbqJoJaWh29IWW+Eqdnnkbh3kL4iH2wZpVn5whlyN3HmzME8Iwc0bdFen7WE7GTYqGqVCE3Ixe3Nt6C7OqdSlUNc6Q1ZghAOXI3uus6IPrVTfdHRmK4UeehXKNB7K1bSBGLscuO1c7HFhXhsFKJDWFhUEE35+NbuRwcx2HK00/j9ddfb/R2rCPOnTuHpKQkt+0P0F2J6d+3Lx7kOOwIC2v0M48vKcERxrxiSBmxzpsbD56UIQ1XSNavjJy9LBuX/nMJo3JHQRJtfpfUeHX0mAkxiEk1HRKa/20+OI7DU1Oe8vgcoQy5O3lzhgCenyOX372MC29fwNA/hsK/q7/ZHZaWzJCmQDlyd3ImR5plEnpT0Zega1jVKkMmg4oxrLZztfNVoaG6YVrFxZhUXIyskBC88tpr+OPcObz77rtuPeGLiorw+OOPo6ioyG37BIAtW7ZAoVAgPTjYrs+8MjgYCoUCW7dudetxEOJNrC1yql+ILHFhIgRSAc7Mtlx9T786evcPuqPybCWyJmXh15G/ImtSFvhZfLz6yqv464+/vCJHKEMIcY6tHGn3bDsIpAKc+/s5MI359d6WypCmQjlC7OXVHZDg4GAktm2LbQqF4THGGJZXVTm82vljvr6ICgvDH3/8gV+OHcPzzz/fJL3xzz//HBUVFVi+fLnb9skYQ8aaNUiVSh1e4X3d6tVUkYLctRpb5FQUJEK/zf1QlFmE4+OPW6y+JwoSITYtFn7tfAEA4WFh+PPPP/HbL795TY5QhhDiPFs54qkZ0hQoR4gjvLoDwnEcpj7zDLbJZCior3ClX+081cEFetKkUhSUlIDjuCYrbVdUVIT169cDADIyMtx29bK8vBzZOTlItTCR3pZUX19k5+SgvLzcLcdBiLexZ5HTyFGRGLB7AEp/LkVmfCZOTDphUrrzZNoJ7IvLRM2BErwRGIjikhLDvptCU+QIZQghzmssRxpmSMPyv82dIU2FcoQ4wqs7IMCdRYFmlZdDzZjLq53LZLJGtnTe559/DqVSF05KpdKlq5fGdbXz8nS1xD3xMxPi6exZ5FQ/TCLp/5JQtLfIZJiEeHcxPgoMxq2YNkgR6yaRekOOUIYQ4j6N5YitoVbNnSHuRDlCnOX1HZDAwEB8sXIlMpVKjC8pMXRAnF3tXOrgnRN7GV+11HPm6mVlZSXS09ORPGgQevTogQEDBmD06NEAPO8zE+IN7F3kVKvQonR/MbRVamwJD8f12FiUxMXhcmQMXggIQGB9iUnAs3OEMoQQ97MnR4yHWvEArAsLa/YMcRfKEeIqr++AALrVTddlZOAIY+iVn48gHg9bHexJb5PLkdi2LYKDg5vkGI2vWobU9/YdvXp56NAh9O/bF/9avBh9S0qwOTwc+yMj8U1YGIJ4PGxx02emVUvJ3aaxFZL1QySq9xdjT2QkJkqlaCsUIpTPNxkm4ek5QhlCSNNpmCMn0qwP19wTGYmpfn7NniHuQDlC3MG+WUJeICUlBcdPnsTWrVux7OOPsa2sDAVqtV0TofLVamyXy/H2jBlNMubS+KqlhOPwY1QUBuTnQ8kYMjIyMG/ePERERNjch0ld7dhYs8+Vr9Xi5bIynKuthZTHgx+Ph1Aez+rnsfSZadVScjdLSUlB1vEsw8JiWZuzDM91EAvxUWAwpvn5IdDK8AJPzxHKEEKannGOLPtsGbK22p8jTZ0h7kA5QtzFq9cBsaaiogL9+/XDgwB2hoe3eB3qxYsXY+XKlQCAhQEB+CAkBAvLyvBRVRUAYM6cOVi0aJHV1zdWV7tCo8EX1dVYVFGBOqPHOwsEmBcQgGlSKYL4fMPjlj4zrVrqnby5hr8nZwhjDDdv3sSIoUPxAI+H78PCILQxrtnTc4QyhFjjzRkCeHaOVFRUoH/fvugH4OvQUEQ0uNthrDnXxHB2BXjKEWLNXbcOiDVBQUFYsXIl9tXWYnxJCfLrK2Q1lK9WY3xJCTKVSqxIT2+SE76oqAgZGRkAdFctX6mv4/33gACI60/edevW4fLly1ZvL9qqq52pUCDh1i38o6IC4319DbdCN4eHo5dIhL+VlSHh1i1k1pcqtvSZ9Vc0HuQ45MbGYlNYGNKkUgyXSJAmlWJTWBhyY2PxIMdh2tSpOHTokNu/J0I8CcdxSEhIwJerVuGn2lo8Vlraojly9epVrFmzBoD1HMnIyEBhYaHF11OGENL8goKCsCI9HT/X1WFmeTkKNBqL2zVHhgCW52306NEDyYMG4ZNPPsH58+dtDnWiHCHu1CrvgOgZ96Qn+Poi1df3Tk9aLsd2uRwSiQQr0tORnJzcJMcwa9Ys7NmzB8Cdq5Z6xlcvAcu3FxljSB40CH2Li7GpQe8yU6HAI4WFGCWRID001OJwswK1GjNLS5GpUGCgjw9+rasz+cy0aql38+arl96QIUDL58ihQ4cwfdo0qOo7QLZyJDAgAAtfftlyhpSUYFNYmMm+KUOIN2cI4B050tIZ0vAYGt5Z2CKTYbtcDgZAC2qLEMc5kyOtugMC6Hr8W7duxbrVq83GEk6bMQNpaWlNtrrojh07MH/+fAC6q5bXGoyXLFCr0S4vD8r6f4IBPj44WX9SfrFyJXr16oXly5fjs88+w+bwcKQZVYio0GiQcOsWBovF2BER0ejJOraoCPuVSrzy2muYOnWq4TOnp6fjX4sXI9fCWE5L8tVqxOfl4e0lSzBz5kynvhfiPt7cePCWDAFaLkcOHTqEqU8/DabVQovGc4QHgAPg6+uLL1auRHJyMs6ePYuHH36YMoRY5M0ZAnhPjrRkW8Rk3kZwcOMdBLEYv9bWUluE2I06IDY4O+bRWZWVlbinZ0+rVy31jK9eigD8ERODhRUV2KtQgGMM+hu2+yMjMdxocZ9lVVX4W1kZctu0cfpktXVl1JZJxcX4PTwch48e9diJcncLb248eFuGAM2bI/orgmF1dbjuQI5Ml0pRxBgyFQoEBQaitKICAGUIscybMwTwvhxpibaIQ3cWiorws1KJE9HR1BYhdqM5IDZwHIeQkBDExcUhJCSkyX9YV69ebeh8GI/Zbsh4DHcdgC1yOXaGh2OUWAwBgE/qy9IZ19VmjGF5VRVSfX3tOuEBIFogwHiJBMs//RRa/VoptGopIQ5pzhzZsmUL5HK5Ye6JvTnylUyGFSEhGCkWo7qigjKEEA/S3G0RW/M2GhJwHFaGhkLOGDKVSmqLkCZ113RAmlLDWtVarRYrv/zS8Pw8f3+rJ2eUQIB5/v6Gv39YWQk+gFWhodBANx6zs0CAbUZ1ta+pVLikViPVwUV70qRS5BcXY+CAAUhPT0dBQQEAWrWUkJZmKUMy1qxBolAI/XJm9uaICrocWRUaCi0sZ0ipVksZQkgrYy1HUqVShzoIE3x98XlVVaNtEcoR4opWsw5IS7BWqzouJgaV9cMhbF211Pt7QACWV1dDyRjKGcMFlQrdRCJM8PXF8upqzPX3xyvl5ShQq3FWpcLE+ko3zp6sPcrK8K/FiyGuv9pAq5YS0jKsZUi7uDhcz82FsP7vjubIFzU1+HtgoMUMiRII8H19JRrKEEK8X2M58lZoqEP7S5VKsVkuR5lWa+iQWMqRr+ob/o6O5KccIQB1QJzWsKLEu+HhhooSbxUXG7ZTM4a++fmN7k9jdAJ/WFWF9LAwQwiM9fXFoooKjCsqwqm6OgwRi7FfqXT6ZF0XFgYVY5hVXo49AD6rrjaZVNYYb1iplRBPZytDtpaXIwe6uxmA4zmiYAz/raoyy5BZpaV41t8fM0tKADj/C58yhBDP0FiO3ATwXFkZogUCjLJziJO+g1Ct1SKUz7eaIy+VlQEA1stkeNzPz+5jphwhAHVAnGJrJdACtRo3jdYLUAHIs1L725qNMhn+HRRkCAEegNVhYZhUXIyREgl2hoej2+3b2CKTOXayymToLBAgpH5V0h1hYRjHGDLlclyqq0NnkajRfXjDSq2EeLrGVhMe7OODXTU1huFXzuTI8upq3Fd/TvMAbI6IwMOFhdivUGCUWIzLajVlCCFerLEcSZNKURAUhJmlpXiksBC7IyPt6oToOwj+9W0Q47aIPkf2KRTgADAAexQKw10Re1COEIDmgDissrISc2fPxiixGDvCwsxOuLU1NQjl8RDL5yOWz4cYurKYMfV/t/VHwnEQAAjh8bC2psYkBG5pNOAArA4NhZDHwxSpFNvlchRYWRytIf3J+mxAgOFkFXAc0usr6kwoKYG6kduoasYwu7wcEokEEydOdORrI4TUayxDgPoccSFDYvl8hPB42Fk/1Mqfx8MoiQSz/f2hAbAqLIwyhBAvZk+OALr5YTsjIjBKIsHjRUWosONChnEHATDtkOhzRA3dvBAA0ABYXF9trzGUI0SPOiAOaqyixGtBQbgVF2f4c61NG/ABvBoYaPJ4wz9Z0dFQMYYPQkJwKy4OrwYGYmNNDdrz+dBotfi8stKk0sRUPz8wADNLS+07WUtL4ctxmNrgame0QIAJUiku19VhXHGxQ6s9N5zw5mRFZ0LuKvZUpTHOEWcz5FZcHNRaLRL5fFRptShWq/GjXI6J9TniCRkCmE+cpRwhpHHOVrfKaGTCdsMOAmPM0BbRMgatVov9crlZ43FlTQ1uNXIxg9oixBgNwXIAY8ylihLP+/tbvFVofFKOk0iwrKoKn1VV4Wr9CRiZlwcBgAc4DhUaDYL4fLQXCBDD42GvQoHxRUVYGRqKaAvHlK9WY3b94kLfR0YiiM8322airy+2yGQ4whji8/JsrtSasX49evXqhfT0dLMJb5ZWTyWE3NEcGTJVKkWFRoNPq6rwrUIBNYD2eXkAYJIjLZkh+pWPLU2cpRwhxLaWaotE3LqFDgIBso3uooTweCirXyj1wYIC/BIVRW0RYpe7ZiFCdygrK0OPHj3MVgJtzGaZDJOKi1ESF4fQBied8Um5JCgISysrIWcME3x9MVEqNZx4W2QyfCuXw5fjsLn+duqyqiosLCuDlOOgqH9NqtFrtslk2F7/mi0RERhpZeznfoUCIwsLsX//fvz22282V2o9deqUyYS3VInkzvspFNgmkxlWT01JSXHmayYO8OZFxChD3J8h30dGggF4vKgIsvpMSLORIxdVKrdmyH/+8x+o1epGV3tuOHGWcqTleHOGAJQjzd0WWV9Tg+/qh3ZKOA6/RUdjQH4+lPVNST5063M0dY5QW8SzOJMjdAfEAfpa086WrpxaUoJpfn4WT8olQUFYVFGBURIJ0kNDLU8mU6sxy2gy2TSpFG+Xl2OAjw9GSyT4vLoam+Vyw2s6CwT4ICQE0/z8EGjjmPXjO7OzszFz5kzMmDHD4kqt9k54m1VejmlTp2JdRgad+IQYacoM0Xc+HiksxAiJBKvtyJFNYWHw4zi3Zcg/3noLGevX4/DRkfMFuQAAiyZJREFUo1ZXe6YcIcQ1LdkW+a22FqjvgMzz98c9IhHm+fvjo/qlBwb5+OBUXV2T5ghlSOtAd0Ac4OpVh7ZxccjJzTU8HshxeMzXF8PFYswpK0OyWIxdERE2x3OqGcP4oiL8rFTiRps2OF5Xh0cKCzFKIsGK4GCkFBaii1CIteHhhgoTjZlUVIS9SiW0Pj448fvvFm9ZVlZWon/fvniwvmJFo8dYUoIjjOH4yZN0C7QJefPVS8oQ92XIOF9flGu1mFtaimESiUM5sjosDJOLi13OkLN1dUgUifAzYPW8pxzxPN6cIQDlSHO2RQrUarTLy4OSMUg4DtfqG//Gj/MAnIyMxOMlJU2SI5QhnsmZHKFJ6A4IDg5GYtu22Fbf+7eXvlb1z7/+ij///BOx0dEQAwBjWCuT4anSUtQyhtWhoQ5PJhslkWB3ZCR+VirR9vZt+PF42KtUQsWYXSe8fsLZ3/z9oVQqsXXrVovbOTzhLTgYCoXC6v4IuRu5K0P27duH4MBAyOsz5LHiYswoLYUGcDhH8jQat2TIswEBSA8JsXneU44Q4jp35UhmZqbuPLSzLfJ/VVWGoVbz/P0Ndx6iBALM8/cHoKuM1aewsMlyhDKk9aAOiAM4jsPUZ57BNpnM4dKV02bMAK/+1mNefj6UAL4MC0NxmzZIFAgMlWnsYTyZjDGGURIJbrRpgw9CQlBTPxlshoOVbZ4PCMAEX1+sW73arIKEKxPeLO2PkLuVOzIkJCQE0dHRKK+shArAqtBQXIuJQUcXcmSkWOxyhkyVSm2e95QjhLiHu3JEIpFAzZhdbZECtRrLq6sB6OZ+vBIQYPL83wMCINaX1QVQodG4PUcoQ1oX6oA4KC0tDRKJBLPKy52qVa0fuwkAIXw+wHHIVquR6sBtVABIlUpxSa1GWf2YySA+Hy8EBOBwVBTuEQqxV6HAuKIi26XsioqQqVBgS0QEgvh8pPr6IjsnB+Xl5SbblpeXIzsnB6l2rqJqOEYr+yPkbuZqhgCmORIvEMCfz8cVF3NEnyGX27TB8pAQZCoUGOtghgDWz3vKEULcxx05UlJSAsC+toi1ux96xndBVAAek0rdniOUIa0LdUAcFBgYiC9WrkSmUonxJSUO1aqurKzE9u3bDduUa7Woqe9ANJxMxhhDiUaDHJUKJRqNWc9dv/3XMhn2KxS6sZ1FRUjIy8NVtRoMwGGlEvG3bmFSURE2N9gu/tYt/KxU4vvISENFCv0+jRs3xn93dsJbw/0RcjdzJUMA2J0jjWWI8fbGOTK5uBjzy8ogAJCpUDiUIcb7pBwhpOm42hZJT0/Hi889B6Dxtsi5ujp8Xj/J3NLdDz3juyCfVFfjWTfnCGVI60JVsJyQkpKCdRkZmDt7tt017/VlJ+VyOQI5Dhx0q40OEYsB3Kn+UKHRYJ1MhuVVVbhkFCidBQLMCwjANKkUQXy+Yfvny8pMtvkgJASPSCRIzMvDZyEhqGIMn1dV2VWRQr9PaYMrIPq/65+3l7X9EXK3cyZDANiVI/ZmiH57wHKO7JHLsVepxFSpFL/V1tpd1YZyhJDm4UpbRKFQ4DGJBEUAtjrQFrF090NPfxfko6oqaACkiMUQA27LEcqQ1oWqYLmgsrISW7dutavmvaFkXHAwvpHLsbCsDDwAN2NjMaSwEL1EIjzj74/Hi4ogZ8xiHe1tRvX7V1dX42xdHY5GRaGGMfjzeIZKE7dVKiTUh9E3ERG6VUK1WlRrtSbbNTSpuBi/h4fj8NGjJs8zxpA8aBD6lpRgU1iY3d+Ptf0R9/HmCjaUIfZnCAC7ciSSz8eZujq7MmSURGKoOtMwRwo0GrS5dQuBPB5GiMXYFB5uV4YAlCPexpszBKAcAZxvi0QJBJhQVIRdcjlyrbRFxkgk2KNQQAWYVL6yxrgilpjjUMsYgtyUI5QhnsuZHKEOiBswxqzWvLdUMq5Co0F8bi5qAYyQSDBULMYr5eXgAVZrbwMw1O/PVCigBfBRSAheaHArVM0YHi0sxD6lEhyAW23a2DVZK1+tRnxeHt5esgQzZ840ez49PR3/WrwYuY2Ej737I+7hzY0HypA7bGUIYF+OxPD5SK+pwRg7MyQjLAxTS0rwQYMcUTOGsUVF2KdQQAPdwmKUI62XN2cIQDlizNG2CADcUKmQmJeHkRIJhltoi/xfVZVhjQ8hgAgLK5g3VKTRQP8vwgFgcF+OUIZ4JirD20I4jkNISAji4uIQEhJi0nCwVDIuiM/HlshIqAHsUSiwWy4HB10jYkdEhM3bmzsiIjBCIgEHYFyDiVj6yVz7lEr4APDlOMy0twKFhQlqxtwx4Y0QYpmtDAEaz5EfFAqsq6nBaDszZJREguklJZAAmGo0LEGfIfsVCvQRieAHQMxx9leyoRwhpMU42hYBgAShEEuCgrBXocCuBm0RAIbKV4BucnmeRtPoH+PuIAOwPyICEjflCGVI60EdkCZkq2TcKIkEP0RGQgzgUG0tAPvr968KDQUALK6osDiZa0NYGFQAnpBKsdeeChQWJro25OrEWUKIc+zJEQHg8BogGgADxGJk1dWZZMgRpRK7IyKwIyICSgChfL6uql5xMeUIIV6osfK1bwYF4V9BQTjSoC2ytqYGoTweYvl8i3+i6++G+HIcwuqHVEnq84cDEFI/r+Pj6mp0E4nckiOUIa0HDcFqQvasVlquVqPL7dtIEYvxTf0VB3ukFRVhh1wO/aknAKAG0IHPx3OBgTikUODH2lrUMAaxjw/qamttTlBbkZ5umOhqi/EENnfsj7jGm4dPUIbYp7EcYYyhc14eeotEbskQ4M6E9Z8UCnyvUODlV1/F559+6rbznnLEc3hzhgCUI/awpy3CGEPHvDz0cVOONGyLyAD87ZVX3JYjlCGeheaAeJjc3FwMGDAA+yMjMdxK3eoSjQbhubk2g8GSzTIZJhUXY6SPDyb5+SGOz0cFY4aJpiKOg5wxrFixAoMHD7Z7oqs9HJk4S5qWNzceKEPs01iOuJohPABjJRI8IZUipL7CXsMc+fPPP8Hn8ylHWiFvzhCAcsQentIWeeSRR9x63lOGeA5ncoTK8DYhe0rGWau93Rj99ivCwtBWKDQ8niaVokCtxszSUuxRKKBQKBAYGIiZM2dixowZNie62tJwctuMGTNc2h8hxD6N5YirGXIsKgr96ktw6jXMkYMHDyItLc2lHLE0QdbVXCKENM5T2iIAXG6PUFuk9aA5IE0oODgYiW3bYlv9iWeJX/3J62xda38LYRElEGBnRARGSyR46403UFlZCaDxia6W6BcsSh40CD169MCAAQPQo0cPJA8ahFWrVoHP5zu0P0KIYxrLEVczpL1Ro8GYu3LEVoakp6ejqqrK4VwihNjP09oigHtzhNoi3ok6IE2I4zhMfeYZbJPJUGBlolQoj4fOAgG2ObhC5zaZDJ0FAsMkr4b0k9WVCgW2bt3q8LEDujGW/fv2xb8WL0bfkhJsDg/H/shIbA4PR9+SEvxr8WL079sXhw4dcmr/hJDGNZYjTZUhgOs5QhlCSMujtgjxRNQBaWKNlYzjOA7zAgKwTS63GgwN5avV2C6X49mAAJs9/WiBABN8fbFu9Wo4OtVHv2DRgxyH3NhYbAoLQ5pUiuESCdKkUmwKC0NubCwe5DhMmzqVTnxCmpCtHGnKDAGczxHKEEI8B7VFiKehDkgTs6dk3DSp1LEa2aWl8OU4k/r91qT6+iI7Jwfl5eV2H3NlZSXmzp6NUWIxdoSF2V5TICwMo8RizJ092+T2KiHEfRrLkWlSKXw5DrPszJBZDmQI4HiOUIYQ4lmoLUI8DXVAmkFKSgrWZWTgCGOIz8vDpOJibJbJDGt4/L+yMsgYs6tG9riiImQqFNgSEYEgO1Yk1U8QkzlwW9XagkWWCDgOK4ODoXDh9iohpHG2cmSfUoleIhF+sGPdH/0q5/ZmCOB4jlCGEOJ5qC1CPAmV4W1G1krGGdff159klupab5PJ4MNx+DYiAiOtlNJrSF8i788//0RISEij2zPGkDxoEPqWlGBTWJjdn21ScTF+Dw/H4aNHaQJYM/LmEpqUIc5pLEd40C0CNkEqxUQLtfG1jOH1wED8OzjY7vd0JEcoQ7yLN2cIQDniDGsZIhEIoKjvdNjKEWqLkIaoDK+H05efa9++vWEBnUelUjwhkRjq738tl2OnTIZv5XJsNrpSkNi2LYJ8fPBgba3dJzwAbJPLkdi2LYLtbGyUl5cjOycH7zr4g5Tq64vN9bdX7QkXQohzGsuRW2o1PqmuxrcyGbY0yJB/PPMM1qxahatlZQ69pyM5QhlCiGczLoW7e/duvLxgAZRKJR718cHE4GAE83g2c4TaIsQdqAPSzA4dOoTp06ZhlFiM9DZtzMY0pkmlKAgOxsyyMmQqlfjgww8xbNgwBAcHY9WqVfjX4sUoUKutjoU0pp8g9vaMGXZfCdDfHnW2FrhMJqOTnpAm1liOTPf3R75KhWnl5fhRqcT/Pv8cjzzyiCEH/rV4MQqCgpokRyhDCPEOhw8fxnPz5zucI9QWIe5Ac0CakSMTqnaGh2O0RIJ/vPEG+Hw+OI5rtIqFMTVjmF1eDolEgokTJ9p9jPYsWGSJfnupnZNaCSHOsTdHooVC/FCfI68sXIiqqioAjVfDMeZMjlCGEOL5XMkRaosQd6AOSDNydUKVPVUsAN3VhvElJchUKrEiPR2BgYF2H6M9CxZZ4ujtVUKIczw9RyhDCPF8ruQItUWIO1AHpJkwxpCxZg1SpVK7blkClmtnN1bFYlJxMeLz8nCEMWSsX4/k5GSHjtOeBYsa0t9enebA7VVCiOO8IUcoQwjxbO7IEWqLEFdRFaxmUlZWhh49emBzeDjSHLg1aK1yhLUqFolt22LajBlIS0tDQECAU8daWVmJ/n374kGOw46wMJtXR9SMYXxJCY4whuMnTzp0hYO4zpsr2FCGOM5bcoQyxHt4c4YAlCPOcGeOUFuEAFQFy6O5e0KVcRWL8vJyyGQySKVSBAcHu9zz199enTZ1KsaXlGBlcDCiLVwlyVerMbu8HJlKJTLWr6cTnpAm5i05QhlCiOdyZ45QW4Q4izogzaSpJlRxHIeQkBC3V3vQ316dO3s24vPyLK5Lsl0uh0Qicer2KiHEcd6UI5QhhHimpsgRaosQR9EQrGbirYvqNOXtVeI6bx4+QRniOG/MEcoQz+bNGQJQjjiDcoS4mzM5Qh2QZpSeno5/LV6M3NhYu2tnx+fl4e0lSzBz5sxmOELrGGNuv71KXOfNjQfKEOd4a45Qhngmb84QgHLEWZQjxJ2oA+LhaEIVcTdvbjxQhjiHcoS4kzdnCEA54izKEeJOzuQIleFtRs1RO5sQ0rpRjhBCXEU5Qloa3QFpAYcOHcLc2bOhUChsTqhakZ5OE6qITd589ZIyxDWUI8QdvDlDAMoRV1GOEHegIVhehCZUEXfw5sYDZYjrKEeIq7w5QwDKEXegHCGuog6IF6IJVcQV3tx4oAxxH8oR4ixvzhCAcsSdKEeIs5p1IUKBHVUTiH0iIyNb+hCIl/Lm89Cbj90TUY4QZ3j7eejtx+9pKEeIM5w5D52+A0IIIYQQQgghjqIqWIQQQgghhJBmQx0QQgghhBBCSLOhDgghhBBCCCGk2VAHhBBCCCGEENJsqANCCCGEEEIIaTbUASGEEEIIIYQ0G+qAEEIIIYQQQpoNdUAIIYQQQgghzYY6IIQQQgghhJBmQx0QQgghhBBCSLOhDgghhBBCCCGk2VAHhBBCCCGEENJsqAPSjKZPnw6O45CTk9PSh9JsUlJSwHFcSx+GQ9asWQOO43DixAmX9rN9+3ZwHIeDBw+66cgIIXe75ORk9OjRA1qt1qX9jB07FomJiairq3PTkRFCiP08ogPCcZzJHz6fj5CQEKSkpGDt2rVgjLX0IbZaOTk5Zt+/QCBAZGQkHn74YezZs6elDxEAsHjxYnAch0OHDjXp+9TU1OCNN97Ao48+ivvuu8/kuf/+978YM2YM2rZtCz8/PwQEBKBHjx5YuHAhbt26Zbavxx57DPfeey8WLlzocmOhtaFzvvmtXbsWHMdh7dq1zfaeMpkMH3/8MYYOHYqIiAiIRCIEBQXhvvvuw5tvvolr164127HoefOFoK1bt+LIkSNYsmQJeLw7v75zc3Px7LPPon///oiKioKPjw9iYmIwePBgrFmzBiqVymxf//znP3H9+nV88sknzfkRCCEEAMAxD/hNr79CvmjRIgCASqXC1atX8e2330KlUmH+/Pn47LPPWvIQ3SI/Px+VlZVITEyEUChs6cMBoOuAtGvXDoGBgViwYAEAQKlU4uzZs9i7dy8AYNmyZXjhhRec2v/Nmzchl8vRpUsXl45z8eLFWLJkCX766SekpKS4tC9b/vOf/+DNN9/EL7/8ggceeMDkuQ4dOsDPzw/33HMPIiMjoVKpcPr0aRw+fBgBAQE4dOgQevfubfKazZs3Y9KkSfjqq68wZcqUJjtub3O3nPOeZO3atXjmmWewZs0aTJ8+vcnf79ixY5g4cSLy8vLQpk0bDBs2DDExMZDJZDh9+jR+/fVX8Hg8HDt2DPfee2+TH4/e9OnTsW7dOly/fh1t27Zttvd1FWPMkKMXL140ubN86NAhjBs3Dv3790f79u0REhKC0tJS7NmzB7m5uRgyZAj27dsHgUBgss8xY8bgt99+Q15eHnx9fZv18xBC7nLMAwBglg7l6NGjjMfjMY7j2LVr11rgyFq/69evMwAsISHB7LnVq1czAEwqlTKZTNb8B2dk0aJFDAD76aefmuw91Go1i4uLY506dbL4vEKhsPj4l19+yQCwhx56yOJrgoKC2MCBA916rN6Ozvnmt2bNGgaArVmzpsnf68KFCywgIIDxeDz23nvvMZVKZbbNtWvXWFpaWpOe05ZMmzaNAWDXr19v1vd11b59+xgA9s4775g9V1tbyzQajdnjdXV1LCUlhQFg33zzjdnzmzZtYgDYypUrm+SYCSHEGo/ugDDGWLdu3RgAtmXLFrPnjh07xlJTU1lkZCQTCoWsTZs2bM6cOSwvL89s25MnT7IXXniB9ezZkwUHBzMfHx/WoUMHtnDhQlZWVma2fW1tLVu2bBnr3bs3CwoKYhKJhCUkJLCxY8ey/fv3m2x75MgR9sgjj7DY2FgmEolYZGQk69+/P1u8eLHJdtZ+8Wm1Wvbxxx+zrl27Mh8fHxYTE8Pmz5/PKioqWEJCglnnwLgh8eOPP7Lk5GTm5+fH/P392ZgxY9j58+ctfpeW2OqAaLVaJpVKGQB24sQJw+MHDhxgo0aNYsHBwUwkErGOHTuyV199lVVUVJjtIzk52ezf9qeffmIA2KJFi9jp06fZmDFjWGBgIJNIJOzBBx9kv/zyi8n2CQkJhp+Rhn/0CgoK2Msvv8w6derEfH19WWBgIOvUqRObNm0ay87Otuu72LNnDwPA3nrrLbu216uoqGAAWIcOHSw+P336dAaAXbhwwaH9tmbNcc4zxlhpaSl74403WFJSEpNIJCwgIID17NmTvfrqq6ympsZk28uXL7Onn36axcTEMKFQyKKjo9nTTz/NLl++bLZf4w7xxo0b2b333sskEgmLjo5mL730ElMqlYwxxg4ePMiSk5OZv78/CwoKYk899RQrKSkx25/+PK+oqGDz589nMTExzMfHh3Xt2pUtW7aMabVak+2NzyFLGuaG/jy09Mc4j1QqFfvf//7H+vfvz/z9/ZlEImG9evVin376qcUGrjXDhw9nANjrr7/e6Lb670qvtLSUvfbaa6xLly5MLBazgIAANnToUJaZmWn2Wkez0Np30DD/nD2GPXv2sOTkZBYQEGDy823v7whbJk2axACwq1ev2v0axhj7+OOPGQD273//2+w5hULBxGIxGzBggEP7JIQQV5nej/VgDYcsrV69GnPmzIGPjw/Gjh2LuLg4XLlyBenp6fjuu+9w7NgxxMfHG7ZfuXIlvv32WyQnJ2P48OHQarX4/fff8eGHH2LPnj04fvw4/P39DdtPnz4dX3/9Nbp3746pU6dCIpHg9u3bOHr0KPbu3Yvhw4cDAPbu3YuHH34YAQEBGDt2LGJjY1FWVoYLFy7g888/NwwxsWX+/PlYvnw5YmJiMGfOHIhEIuzatQsnTpyASqWyOlxr9+7d2LlzJx566CHMnTsX58+fxw8//ICsrCycP38eYWFhznzVJlj9CD397f4VK1Zg3rx5kEqlSEtLQ0REBA4dOoSlS5fiu+++wy+//IKgoCC79n3y5En83//9H+6//37MmjULN2/exLZt2zBs2DCcOXMGnTt3BgAsWLAAO3bswOHDhzFt2jSzYRNyuRwDBw5EdnY2RowYgUcffRSMMdy4cQM7d+7ExIkT0b59+0aP58CBAwCAQYMG2fnt6Hz33XcAgJ49e1p8fuDAgVi7di0OHDjg8lC0u4mr5/z169cxZMgQ3LhxA3369MG8efOg1Wpx+fJlfPTRR5g7dy6kUikAICsrC8OHD0d1dTXGjh2Lbt264eLFi9iwYQN27tyJAwcOoF+/fmbH+Omnn2LPnj0YP348UlJSsG/fPnz00UcoKyvDuHHjMHnyZDz88MOYM2cOfv31V2zYsAElJSUW51bV1dVh+PDhqKiowOTJk1FXV4dt27bhxRdfxKVLl/C///3P6e9y+vTpCAoKws6dOzFu3Dj06tXL8Jz+fFWpVHj00UeRmZmJzp07Y8qUKRCLxfjpp5/w/PPP4/jx41i/fn2j73X9+nUcOHAAYrEYf//73xvd3sfHx/D/N27cQEpKCnJycjB48GCMHj0aMpkMu3fvxujRo7FixQrMnj3bbB/2ZuGiRYuwY8cOnD17Fi+++KLhsxtnlrPHsHXrVuzdu9dwDDdu3ADgnt8RjDH8+OOPiIqKQmJiYqPb62k0Gvzwww8ALOeTWCxGnz59cOzYMVRWViIwMNDufRNCiEtauAPEGLN+NfTw4cOMx+MxkUjEbt++bXj80qVLTCgUssTERHbr1i2T1xw4cIDxeDw2fvx4k8dzcnKYWq02e4/09HQGgL333nuGxyoqKhjHcaxPnz4WX2N8BXPChAkMADtz5ozZdsXFxSZ/t3QH5MiRIwwA69SpEysvLzc8XltbywYPHmzx6pz+ihufz2cHDhwwee61115jANjSpUvNjscSW3dAVq1aZRiCJZfLWU5ODhOJRMzf39/sav68efMYADZ79myTx23dAYGF4SBffPEFA8DmzZtn8ritIVi7du1iANiCBQvMnqutrWVVVVU2voE7+vfvzwBYvEJtbOXKlWzRokXs5ZdfZiNHjmQ8Ho8lJCRYvFLOGGNnzpxhAFhaWppdx3E3aI5z/v7772cA2H/+8x+z9ykuLjYMqdNqtaxLly4MANuwYYPJdvohKp07dza5A6D/eQwICDC5yq5UKlm3bt0Yj8djISEh7NChQ4bnNBqN4c7A6dOnTd5Hf5dv4MCBJncESktLWfv27RkAdvjwYcPjjt4BYazxIVj6z/Tcc8+Z5J5arWYzZsxgANiOHTssvtZYRkaG4bM4Kjk5mXEcx77++muTx8vLy9k999zDxGIxKygoMPtMjmRhY0OwnD0GjuPYnj17zPbnyO8Iay5cuMAAsEceecTmdsXFxWzRokXs7bffZvPmzWMdOnRgANiUKVOsvmbBggUMAPv+++/tOhZCCHEHj+qALFq0iC1atIi98cYb7PHHH2dCoZBxHMc++eQTk+31gbl7926L+xs/fjzj8/l2NTy1Wi0LCAhgQ4YMMTxWWVnJALAHHnjAbOhDQ/pfLpcuXWr0vSz94ps5cyYDwNatW2e2/dGjR212QJ588kmz11y7do0BYKmpqY0eD2N3OiCBgYGG7//VV19lDz30kOHfZdmyZYwxxv79739bHVZRVlbG/P39mVgsNmlA2eqAWGqg1NXVMYFAwPr06WPyuD0dEHuGe9gSHR3NhEJho9vpOyr6P/369WNXrlyxun1BQQEDwPr37+/S8bUmTX3Onzx5kgFgvXr1anTokP48u//++y0+P2jQILMOgP7n0dJwvSVLljAA7OmnnzZ7bu3atQwAW7t2rcnj+g7IkSNHzF6jP9+nT59ueMzdHRCNRsNCQkJYVFSUxfka5eXljOM4uzrRS5cuZQDYpEmTGt3WmL6jPnHiRIvP79ixgwFg//vf/wyPOZOFtjogrhxDww6wniO/I6zJzMy0eIGnIX1HRf+H4zj2t7/9jdXV1Vl9zXvvvccAsOXLlzt9fIQQ4iiPGoK1ZMkSk79zHIdVq1bhmWeeMXn8t99+AwAcPnwYWVlZZvspKiqCRqPB5cuX0adPHwC64QUrVqzApk2bcP78eVRWVpqURs3LyzP8f0BAAB599FF899136NWrF1JTUzF48GD079/frFLIk08+ie3bt6N///6YNGkShgwZgoEDB6JNmzZ2febTp08DsDzsZ8CAAWZVS4z17dvX7LG4uDgAQHl5uV3vr1dZWWn4/vUlUR966CE899xzGDNmDADg1KlTAIChQ4eavT44OBi9e/fGkSNHcPHiRdxzzz2Nvqel4xcKhYiMjHTo+JOTkxEbG4v33nsPp06dwpgxYzBw4ED06tULfD7f7v2UlpYiODi40e2OHTtm2P7UqVN488030adPH2zevBmjRo0y2z4kJAQAUFJSYvex3C2a6pzX/xuNGjXKpFypJbZ+rvWPHz16FKdPn8aDDz5o8pyln+GYmBgAMGSPsdjYWACwWLZZIBCYVV4DYKj6ps+KpnD58mWUlZWhY8eO+Pe//21xG4lEggsXLjTZMej/jSsrK7F48WKz54uLiwHA4jG4KwtdOYaGZbv1XP0dAeiyBkCj+dSlSxcwxqDRaJCXl4dvv/0Wb7/9No4ePYrvv//ekEXGKJ8IIS3BozogrH6+gUwmw2+//YaZM2di7ty5SEhIMGkc6MP4v//9r8391dTUGP5/0qRJ+Pbbb9G+fXuMGzfOUCsdAD7++GPU1taavPabb77B0qVLsXHjRsMYXbFYjIkTJ+L9999HZGQkAGDChAnYvXs3PvjgA6xevRorVqwAoGt8vPvuuxgxYoTNY6ysrAQAw/6M8fl8hIaGWn2tpbkW+g6LRqOx+b4NJSQkNFoXX3+s0dHRFp/XP15RUWHXe1qbKyIQCBw6/oCAABw7dgyLFi3Crl27kJmZCQAICwvDs88+i7feesuusscSiQRKpdLu9w0NDcWIESPQr18/dOnSBU8//TRu3LgBiURisp1CoTDsn5hqqnNe/zOob/Db4srPtaUx8/pz0NZzltZlCAsLs9hhjoqKMjnOpqD/fq9cuWLWKTRmnKnW6L8v44s6jhzD/v37sX//foeOwV1Z6Mox6P+dGnL1dwRwJzvszSc+n4/4+Hi8+OKLiIyMxBNPPIG3337bYmlryidCSEvwiIUIG5JKpRg+fDi+++47aDQaTJs2DXK53PC8/hd7ZWUlmG4YmcU//7+9+w6Pqs77//+cySSZyaSSAiEklNBDXxAEFJC6yiKKUSy3uhRvZG/7iuDPdbF9bauIure6IgrsoktRLHtrQJAiSpNehCQECekhIXUmmXJ+fyQzpMxMZsIkZOD9uC6uXTJnzjkJ5jXn096fMWPGADWLnb/44gsmTJjAyZMn+fjjj3n55ZdZvHgxzz77rMOdYHU6HYsXL+bUqVOcPXuWf/7zn4wePZp//vOf3HbbbfWOvemmm9iyZQvFxcVs3ryZxx57jGPHjjF16lSOHz/u8nsNDQ0FIC8vr9FrFovF/oHYFth+7rm5uQ5fz8nJqXdca+rUqRMfffQR+fn5HD16lLfffpvIyEief/55nn/+ebfOERMTQ2lpqcOHQ1fCw8O59tprKSgo4NixY41et/0bxsTEeHTeq4m3f+dtD6TuPAS3lf+uCwsLHT4s2+6r7vVtozpms9nhudztBLCxnfuWW25x+fPNyMho8ly20dx9+/Z51Giy3cPSpUtd3sPHH3/s0ffmiUu5h7r7cjR0KZ8RcDE7mvN58Pvf/x7A6Saukk9CiMuhTTZAbAYMGMDcuXM5d+4cS5YssX99xIgRAOzYscOt86SlpQEwbdq0RlOa9uzZY+8BciY+Pp67776blJQUunfvzo8//ujwg0Cv13PDDTfw5ptv8vTTT1NdXd3kTuK2jet+/PHHRq/t2rXL6QPG5WC7V0cfZBcuXODgwYNotVr69Onj9Wvbeoab6s1UqVQkJSXx0EMP2XswN2zY4NY1bFViTp486fH92R50HU2Z+/XXXwHqVR4Sjnnrd952fEpKSpO70Lv67xrghx9+AGjxzfLMZjM//fRTo6/b7qvuJpe2qTiZmZmNjk9LS3P44O/qd6h3796Eh4eza9cujxvgDXXt2pUJEyZgNBqbHLEC7KPPnv4bN5ern0NL30NzPiMAkpKS8PPzs2eJJ1xlE0g+CSEujzbdAAF45plnCAwM5G9/+5t9Lu///M//4O/vz2OPPcapU6cavae6urreB4itbGvDB4z8/Hz+9Kc/NXp/QUEBR44cafT1iooKysvL0Wg0BAQEALB9+3aHjQTbiEZTu8vee++9ALz00kv1Hhqqq6t5+umnXb63td1zzz34+/vzzjvv2Bt1Nn/5y18oLS3lnnvuqVdW01tsU9HOnj3b6LVjx445HEFy99/AxjbX3rZ+oK6zZ886vAbUlCbeu3cv8fHx9O/fv9HrtvONGzfOrfu42nnjd/53v/sdI0eO5ODBg7z66quNjj9//rx9OsuoUaPo1asXP/74I+vWrat33Lp169ixYwc9e/b0uDxzcyxatKjedNCioiL7moy662J69+5NaGgoX375Jfn5+favGwwGHn74YYfndvU7pNFoeOihh8jJyeHhhx922CmTk5PjVm89wNtvv01oaCgvv/wyb7zxhsOMPHv2LDNnzrSvuxg6dCjXXXcdn3/+OcuXL3d43iNHjtT7fpvD1c+hJe7hUj8joGZkZtCgQRw+fNjhv83+/fsdNqjKy8t55JFHgJpRGEd27dpFVFQU/fr1a/I+hBDCW9rUGhBH4uLimDdvHkuXLuW1117j5Zdfpnfv3ixfvpxZs2aRlJTElClT6NmzJyaTibNnz7Jjxw6io6PtPTvDhg1j1KhRfP7554wcOZLRo0eTl5fHt99+S69eveyLRm2ysrIYPHgw/fv3Z8CAAcTHx1NaWso333xDbm4uDz/8sH3PkIcffpisrCxGjRpFly5dCAgI4JdffmHLli107tyZmTNnuvz+xowZwwMPPMA//vEPkpKSmDFjBv7+/nz99deEhYXRsWPHJhfRtpYuXbrw1ltv8ac//YkhQ4Zw++23Ex0dzbZt2/j555/p3bu3w4c9bxg3bhxqtZpFixZx9OhRew/wM888w6ZNm3jyySe59tpr6dmzJzExMZw7d44vv/wStVrNk08+6dY1br75Zh599FFSUlKYM2dOvdf2799PcnIy1157Ld27d6d9+/acP3+eXbt2ceTIEYKDg1m1apXDOfwbN24kPDzc6SJnUZ83fucB/vnPfzJ27Fiefvpp1q9fz9ixY1EUhdTUVDZu3Mivv/5Kly5dUKlUrFixgokTJ3LHHXdw880307t3b06ePMmGDRsICQlh5cqVLf57GBsbS1VVFf369WPatGmYTCbWrVtHTk4O8+fPr7cA3t/fn0ceeYQXXniBwYMHc8stt2A2m9m0aRMdO3ZslGkA1157LUFBQbz11lucP3/evmbhoYceIiwsjL/85S8cOnSI999/n6+//pobbriBuLg48vPzSU1NZefOnbz00kv07du3ye+lT58+pKSkcNttt/HnP/+ZpUuXMn78eDp27EhFRQWHDh1i586dqFQqnnrqKfv7Vq9ezQ033MDs2bN5++23GT58OOHh4Zw7d47Dhw9z9OhRfv7550uaLjR+/Hhef/115s6dy4wZMwgJCSE8PJz/+Z//aZF7uNTPCJsZM2bY39ewMfH888+zc+dORo4cSUJCAkFBQWRmZvLtt99y4cIFRo4cyaJFixqd8+TJk5w9e5YHHnjA5RQyIYTwuhassOU2XOyKrCg1ZUyDgoKUoKCgevXXDx8+rNx3331KQkKCEhAQoERERChJSUnKAw88oGzevLneOc6fP688+OCDSufOnZXAwEClW7duyqJFi5SKiopGJSuLi4uV5557Thk3bpzSsWNHJSAgQOnQoYMyZswYZfXq1fVK8/773/9WZs6cqXTv3l3R6/VKSEiIkpSUpDz99NNKfn5+vXtwVv7RYrEob775ptKrVy8lICBAiY2NVebPn69cuHBBCQ4OVgYOHFjv+Kbq+QPKmDFjnP4863K1D4gzKSkpysSJE5Xw8HAlICBASUxMVJ588sl6+5jYNLUTuiOOSogqiqKsWrXKXoe/7n8zx48fVx577DHld7/7nRIVFaUEBAQonTt3VmbMmNFoV/WmTJ8+XQkMDFSKiorqff23335TnnjiCeWaa65RYmJiFI1GowQHBysDBgxQnnjiCeXs2bMOz3fy5EkFUB555BGP7uNK1xq/84pSs2fPggULlJ49eyqBgYFKWFiYMnDgQOXpp59WKioq6h3766+/Kvfcc4/SoUMHRaPRKB06dFDuvvtu5ddff210XldloV39fjr7b7/uTujz58+3507v3r0d7oSuKDUlxF9++WWlW7duir+/vxIfH688+eSTDjPN5ttvv1VGjBih6PV6+79B3TyyWq3KypUrlRtuuEGJiIhQ/P39lY4dOyqjRo1SXnrpJaf/nTtTVlamvPnmm8rYsWOV6OhoRaPRKKGhocqQIUOUhQsXKqdPn270ntLSUuWll15ShgwZouj1ekWr1SpdunRRbrzxRuWDDz6ot4N9c7PwjTfeUHr37q0EBAQ4zD9v3oMnnxGu5OXlKQEBAcrtt9/e6LVvvvlGufvuu5UePXoooaGhikajUaKjo5Xx48crH3zwgcPSyoqiKIsWLXK4L40QQrQ0laLUlqERbU5qaio9e/Zk5syZfPrpp5f7dq4KP/30E6NGjeLNN9/kscceu+TzPfHEE7z77rucOHHCrd3YxdXJNk20qUp04ur23//936xYsYIzZ844rbrlrqqqKrp160afPn34/vvvvXSHQgjhnrYxt+cql5ub22ihbGVlJY8++ihQU5lGtI6RI0eSnJzMq6++Wq8KU3Pk5OTw3nvv8dBDD0njQwhxyZ5//nkCAgJ46aWXLvlc7733Hrm5ubzxxhteuDMhhPBMm18DcjV46623+PTTTxk7diyxsbHk5uayefNmzp07x+9//3uSk5Mv9y1eVf72t7+xfPlyMjIySEpKavZ5zpw5w1NPPWVfBCqEEJeiffv2/POf/+TYsWNYrdZLWpcUGBjIRx995NamsUII4W0yBasN2Lx5M3/72984ePAgRUVFaDQaevbsyV133cWjjz7q1iZ6QgjfJVOwhBBCXE2kASKEEEIIIYRoNbIGRAghhBBCCNFqpAEihBBCCCGEaDXSABFCCCGEEEK0GmmACCGEEEIIIVpNs8vwFhcXYzabvXkvQggPaTQaIiIiLvdtNItkiBCXny9niBDCdzW7AWI2mzGZTN68FyEuG0VRqKqqwmQy4e/vT2BgICqV6nLf1hVNMkRcSSRDhBDCfbIRobiqVVVVkZqayuHDx6ioKLV/Xa8PZcCAJHr06EFgYOBlvEMhRFsmGSKEEJ6TBoi4amVmZrJp02ZMJjMnToRw7FgnjEY1Wq2VpKRSysp2sWfPPiZOHE98fPzlvl0hRBsjGSKEEM0jDRBxVcrMzOS771JIS9OzYUNXysvr/yocPx5KcLCZ6dOzsVhSmDJlsjxACCHsJEOEEKL5pAqWuCIoioLRaKSsrAyj0YiiKE6PraqqYtOmzaSl6Vm9Or7Rg4NNebmG1avjSUvTs2nTZqqqqlrq9oUQbYC7OSIZIoQQl0ZGQIRPa87869TUVEwmMxs2dMVqdb1I1GpVsWFDLI8/nkZqair9+vVrdIwsPhXCt3maI97OEJAcEVcHg8FAXl4eiqK47CgUbYdKpUKlUtG+fXt0Op3XzisNEOGzmjP/WlEUDh8+xokTIU57LRsqL/fnxIkQQkKOkZSUZH8okMWnQvg+T3PEmxkCkiPi6mEwGMjKyiIkJAS1+tIn4BQWFhIVFeWFOxNNsVqtZGVlERcX57VGiDRAhE9q7vzrqqoqKipKOXask0fXO348hKSkLKqqqtBqtbL4VIgrQHNyJDo62isZYru+5Ii4WuTl5Xmt8VFZWcmXX37JnXfeSVBQkBfuTriiVqsJCQkhLy+PLl26eOWc0gARPqfh/OuaKRAKQUEWAgKsVFerqaz0s8+/vuuumg/5u+++077vhNHoWQAaDH4AmEwmCgoKZPGpED6uuTly881/AC4tQ2ydGJIj4mqiKIpXGh8ABw4coKqqigMHDjBq1CivnFO4plarvTptThogwqcoisLx48ft868DAqwMHHiBYcOKiYqqth9XWBjA3r0RHDoUXm/+dffu3QHQaq0eXVenswA1w5CNH1oac9T4kWkUQrQNl5IjZ8+eBZqfIf7+/k4aP41JjogribceXisrKzl69CgAx44dY/DgwTIK0kqkASKuOrZ50ocOHaWsrIwTJ0Jp395IcvI5/P2tnDgRypYtMfbpC337ljJpUh7jxhWwdm0n+/zrvn37oteHkpRUyvHjoW5fv2/fMvT6UM6ePev1xadCiNbhjRwJDj55SRkSGBjIsWPHJEeEaKYDBw5gsdQ06M1ms4yC+ChpgIg2r+486VOn9PTuDefPB3DXXWdJTw/mq686Op2+MG1aNnfddZadOyOpqDhPdXU1AwYkUVa2i+Bgc4P3NZ5+ASqCg0306VNG//7DOXLkuNcWnwohWo+3cqSy8jxDhw6lrOwXBxkCjnIkONhMnz5lDBgwAsCri9iFuJrUHf2waSujIDExMXzyySfceOONl/U+fIU0QESb1nCetEZjpXfvNK699jzp6cF89pnr6QuffRbPzJmZjBhRBNTMv+7Rowd79uxj+vRsVq+Odzn9Yt++CHr2rECj8cNoNHpt8akQovV4O0cSEhI4cOCQPUOsVhVarcVpjiiKCo3Gj86dO3Pw4EHJESGaqe7oR2WlH0FBllYZBcnLy+Ott95i06ZN5ObmEhUVRb9+/XjggQe4/vrrvX69nTt3csstt5CamkpYWJjXzw9QXFzMokWL2LhxI2q1mqlTp/Liiy8SHBzcItdrSBogos1yNE86KMgMgJ+fwldfdXRr+sJXX8Xy2GOpAPb6+hMnjsdiSWHOnAwiI6vRaJxPvwBQFDX79x9ErW7+4tPy8nKp8S9EK2uJHNHr9fYMueuuTA4eDGXq1Fyn07j69i3FalWzZs1azGaL5IgQzVB39MNkUrFiRWfmzMnA319p0VGQs2fPMnXqVMLCwvjrX/9K3759MZlM/PDDDyxcuJCffvrJ69f0FkVRsFgsaDSNH/cffPBB8vLyWLt2LSaTiUceeYQ///nPvP/++61yb9IAEW2Wo82+KivVmEwqTp70fPpCUlI5VquVsrIyoqOj+d3vhqAov5Caquerr+JcTL/Ionv3Cr75JpZp03Kavfj0iy++sH9NavwL0TpaKkfCw8O54YZxqFRbSUwsJzW1qWlckiNCXIq6ox9790aQl6dl374Irr22qEVHQZ566ilUKhXfffcder3e/vXevXtz1113OXyPoxGMI0eOMH78ePbt20dCQgKZmZksWrSI3bt3YzKZiI+P569//Ss9e/bklltuAaBHjx4A3HHHHbzzzjtYrVbeeecdVq1aRX5+Pt26deOJJ57gD3/4Q73rfvrpp7z88sucOHGCNWvWNPq5nDp1ii1btrBx40YGDRoEwMsvv8ydd97J4sWL6dChg1d/ho5IA0S0Sc42+woKsuLvr3i0+FOrtWAyqbFaFf71r3/Zv261Qlqans8+S2hi+kUCM2dmMmlSHufP+9O3r6eLT0sxGNR8/XUsRqOf1PgXopW0bo40NY1LckSI5mo4+vHTTzUbEO7cGcXQocUtNgpSXFzMli1bePrpp+s1PmwuZXrUwoULqa6u5ssvvyQoKIhTp06h1+uJi4tj+fLlzJo1i59//png4GD75n9Lly5l3bp1vPbaa3Tr1o1du3Yxf/58IiMjGTlypP3cL7zwAosXL6Zz586Eh4c3uva+ffsICwuzNz4Arr/+etRqNb/88gs33XRTs78vd0kDRLRJzjYMDAio6TV0d/pCYmJ5vQo3x4+HYjSq6d+/hIEDS/jqqziPpl/k5enp06fUyeLTxoKDTfTuXcbGje05fvxiUEmNfyFanuSIEFeGhqMftt+b8nJNi46CZGRkoCiKvYS/N507d46pU6fSt29fgHob/EVERAAQFRVlb+RUVVWxdOlS1q5dy7Bhw+zv2b17NytXrqzXAHnqqacYO3as02vn5+c32kVeo9EQERFBfn6+N769JnlnRxghvMzZhoHV1TUf8u5MX0hMLOeuu85y9mwQS5b0ZN26Thw/Hsrp03ri4w0cPx7q4fSLUNq3r8JkUjFtWjZqtet62Gq1wrRpOZhMag4dCndwzpoa/2lpejZt2kxVVZVb9yKEcI/kiBC+z9noh83OnVGYTDW/08eOHaOystJr1/bmvhcNzZ07lyVLlnDTTTfx6quvcuzYMZfHZ2RkUFlZSXJyMl26dLH/WbNmDWfOnKl3bN2RjbZKGiCiTfL39wcuPiBotRaGDz/PrFlnsFhqpiO4otVaSE4+Z69wU3/6hYWoqGqH0x/atzc6PeeJEyFERlbz5ZcdSUwsZ+bMTIKDTQ6PDQ42MXNmJomJ5axd2wmj0c/hcbYa/yaTmdTUVJffkxDCM5cjR1xlCEiOCOEpZ6MfNrZRELi4L4i3dOvWDZVKRVpamkfvs+34XrcBYzab6x1zzz33sHfvXpKTkzlx4gSTJk1i2bJlTs9ZUVEBwOrVq9myZYv9z44dO/joo4/qHdvUNLSYmBgKCwvrfc1sNlNcXExMTEzT36AXSANEtEmBgYH2zb4SE8t59NFUJk3KIzdXx+HDYfbpC84MHHgBf3+rwwo3zqZfBAebue++35ye11aFJidHx+rVCSQkVPLYY6ncdts5kpJK6NatnKSkEpKTM3n88VQSEipZvTqB9HTXJe1si1sPHz7Wor0tQlxtWjtHmsoQkBwRwhNNjX7YtNQoSEREBOPGjWP58uX2BkBdJSUlDt8XGRkJ1JTvtWm4fwlAXFwc999/P5988gkPPvggq1atAi52ntgaXgC9evUiMDCQc+fO0a1bt3p/4uLiPPq+hg4dSklJCYcOHbJ/bceOHVitVn73u995dK7mkjUgok1SqVS1Gwb+TO/epfU2CtNqLfTpU8a0adkOFn4qBAWZGT68iBMnHE+NqK6ueWBoOP1i1KhCgoIsjBxZyMaNjStA2KrQVFWpSU8P5q23etjr/vfrd7En1WKBQ4fC+O67DlRVOe6xbEhq/Avhfc3LEdtGghauucazHGkqQ0ByRAhPNDX6YdOSa0FeeeUVpk6dypQpU1iwYAFJSUmYzWa2bdvGJ598ws6dOxu9p2vXrsTFxfH666/z9NNPk56eznvvvVfvmGeeeYYbbriBxMRESkpK2LlzJz179gQgPj4elUrFxo0bmTBhAlqtluDgYObPn8+zzz6L1Wpl+PDhlJWVsWfPHoKDg5k5c6bb31PPnj254YYbePzxx3n99dcxmUwsWrSIW265pVUqYIE0QEQb1rlzZ3bu/LnRRmFGox9r13birrvOMnNmJl99FYvZrG60Cdj337d3eN7KSj8KCwPqVaEJDjYzdGgxAMOGFfPTT1GNgq5PnzIKCwPsPZhGox+7d0eye3c7dDoLgYFWbrophx49KjhyJMzthwa42CtqMpnkwUEIL3I3R1JSYujevaLRRoKbN7uXI+5kCEiOCOEud0c/bFqqIlaXLl3YvHkzS5YsYfHixeTl5REZGcnAgQN57bXXHL7H39+f999/nwULFjB27FgGDRrEokWLmD17tv0Yi8XCwoULycnJISQkhHHjxvHCCy8AEBsby4IFC3jxxRd55JFHuP3223nnnXdYuHAhkZGRvP322/z222+EhYXRv39/Hn30UY+/r/fee49FixYxY8YM+0aEL730UrN+Rs0hDRDRZv32228ADqc/pKcHs3p1AsnJ53jssVQURYVKpXDiRCi7drVj6tRcFxVuVOzdG8GkSXn2KjSjRhXi718zbcHfX2nUgxkcbKJPn1I2bmwPNKx2o8Jg0ODnZ6Jbt5oh2ubW+LcNuwohvMOdHLnjjkz+9KfTQE1lqS1bYvDzszJjRrbbOdJUhoDkiBCeqDv6oVYrPPDA6SbfYyvq4O1RkPbt2/PKK6/wyiuvOD2mYfWo4cOHs23bNqfHvPzyyy6v+cQTT/DEE0/U+5pKpeKBBx7ggQcecPieUaNGuV3FKiIiotU2HXRE1oCINuli/X7nFWbS04P58suOqFRw+nT9CjXg+sP70KFwTCY106ZlExJisvdc2gwbVmyfx91UFZr6x6goKdE0ubi1ob59y9DrQ2UzMSG8yJ0cgZod0dPSgnnzzYsZYltz4U6O3HLLOZcZApIjQnii7ugHgJ8fhIaam/zjV2fA0NsVsYR3SQNEtEkX6/c736hLq7Vw883ZpKUF89lnCfYHjLpTI5yxTb9ITCxn1qwz9p7Lysqa9LL1YNZUoTlL9+7lfP11B4dVaOpXqonn9Gk9ffu6Xtza8P19+pQxYEASKpXrvQSEEO5rKkdcVbnyJEe6dq10miGA5IgQHvr111/RarXo9fpm/wkMDOTXX3+93N+KcEKmYIk2yVn9/rqcV6hpPMXKkfT0YD7/PI7bbsuqvaaKFSs6M2dOBv7+CiNGFDF8eBEWiwqzWcWtt2bTp08ZJ06EYjD4odPVLGLt06cUk0ltr1RT0xOqYvr0bFavdr47MtT0eE6fnou/v4YePXp4/HMSQjjXVI64qnLlbo7k5WmxWlWo1UqjDLnmmmLataumR49yyREhPDBkyBCGDBlyuW9DtCBpgIg2qWH9/sYUrr32vNOpFYcOhTNuXIGTSlkXdepkwNZZuHdvBHl5WnslDbUaMjKC+OyzeFQq6lSqybK/v6jIn40bYzh4MIKqKj+Cg0306lVOUlJv1OpfueuuTDZsiKW8vPGc7OBgE9On59C9ewWTJk2RaRNCeJnrHFEYNqzY5fQsd3Jk1KhCNJqa0Y+GGaLRKHTuXMnGje05eDBcckQIIWpJA0S0SYGBgQQFhdSrVFVXREQ14eFmNm50PLXCUaWshh/edavW1K2wUbeSRqdOBvz9FcrLNfZ529dcU0RkZE3Part2JoYNuwCoOHw4zN4LOWzYMDp37symTZt5/PE0TpwI4fjxYKxWFcHBZhITK+jZsxx/f38mTZpCp06dvPODE0LUY7WqHOaIbSPBLVucb7rVVI64kyEajcKxYxerWUmOCOEdR48epV+/fpf7NkQzSQNEtEkqlYqYmEj69j3jcPrDwIE1m/+4mqLVsFLWiROhnDgRYp/2MG5cvn3edt364nXridvmcaenB5OcfA5/fysnToSyeXN7jEY1Wq2Vvn1LmTQpj4kT89FoFCZN+j2BgYHEx8dz9913cuLECbTaw/TuXVpvgZy/v5ZBg/oTHR3t5Z+eEAKo3b1YsW84WDdHnG1I2lDjHAmxT58aMeK82xmycWMHEhPLJUeE8IK8vDxmzJjB9u3bad/ecals0bZJA0S0SYqikJ9/HqtV5XCjsP79axogTZWprLvR17XXnq+30Zdts2BH9cXr9mBec00xw4cX1dvErC7bHgA335xFjx6V9XYhzs/PZ//+g5hMZn79NZRjx0LtDxxJSaVUVe1j//6DTJw4nvj4+Gb+tIQQDdkqYJ08GULXrhWNcqS6uuZ/3Sl1WzdHrr++kH79yuq93lSGDBtWTFaWjltvzZIcEcIL3n33XYqLi/n73//O888/f7lvRzSDVMESbVJVVRWVlWXs3BlJYmI5M2dmEhxcM10hKMhCZKTJ7TKVRqMfhw6Fo9VaSEvTs3RpInv3htdb+9HwYcDWgwmg0SiUlPg3qpLT8PhPP00gNVXPpk2bqaqqIjMzk+++S+HkyUDefLMHa9fWlPc8fTqY48dDWbu2E2++2YOTJwP57rsUMjMzL+EnJoSoy1YB68iRMHvFu7o5AjW7jbtb6taWI4GBFtLSgti/P8z+WlMZ4u+vcMstWQ6rbTV8j+SIEK7l5eWxYsUKAFasWEFeXt5lviPRHNIAEW2SrXrNb78FsXp1AgkJlTz2WCq33XaOpKSa0Y+TJ4PtUyuaUlPtRmHDhjhMJj8GDSqpvY7z3VV37ozCZKpppYSEmAkKsri8htWq4ssvYzGZTPzwww9s3Pg9aWl6Vq92/cCxenU8aWkXHziEEJeubgUs2zSq+jlSM5XJ3QwBuOaa86jVsHFjB/r3L629jnsZ4ucH338f47KaFUiOCNGUd999F6PRCIDBYODvf//7Zb4j0RzSABFtUt3qNbbpDxs3tqdDByM33VTT25GVFWTfTNC2+6lj9avd1N2x2FHPpU3DHkxbTX9Xysv9OX48hN9+y8RsNrNhg6PynvVZrSo2bIjFZDKTmpra5DWEEE1rWAHLWY5YLCo3MgTUaisjRxZx/Hgogwdf8DhDVCoYNOiCW/cuOSKEY3VHP2zayihITEwM//d//3e5b8NnSANEtEmBgYHo9aEkJdX0MhqNfuzeHcm77yby6qs9KCryp0ePcqdTK+qKjq4iKqraPsfaUdUaZ+r2YDbc2diZEydCUJSaOd2udl+uq7zcnxMnQjh06CilpaUYjcZ6c8CFEJ5pmCHgOEeys3VNZkhwsIm77spEq7Vy+rS+xTMELjVHjmAwGCRDxBWn7uhHO3XNI2xrjILk5eWxaNEihg4dSqdOnRg0aBD33HMP27dvb5Hr7dy5k5iYGEpKSlrk/ABLlizhxhtvpHPnznTv3r3FruOMLEIXbZJKpWLAgCTKynY1qF6jwmDwZ/fudkyalMd333VwWenKtsEX1EzFqDv6oVYrPPDA6SbvxdYzWreajStWqwo/PxyWD3bl+PEQkpKy+Pe//w2AXh/KgAFJ9OjRQ2r7C+Eh5xkCDXPkiy/imDo1x2WGmM01jYju3ctbPEPg0nPkn//8p2SIuKLUHf3QqVRs6dCBETk5GBWFFStW8Kc//alFKmKdPXuWqVOnEhYWxl//+lf69u1rnyK5cOFCfvrpJ69f01sURcFisaDRNH7cr66uZtq0aQwdOpTVq1e3+r3JCIhos3r06IG/v4bp0xtPjzh0KNw+/SojQ19vakVychb33nuW5OQsOnQwsnVrTXnK8HCTvecSauZkh4aam/xTt+SlOz2YttebKu/ZkMFQc6H16zuyZk0n9uyBnTt38a9/fSoLS4VoBlcZAhdzZMCAEpYu7e40QzZubM8HH3QDoGfPixWwWipD4NJz5JtvOkiGiCtK3dGPB0NCGBgQwIMhIUDLjoI89dRTqFQqvvvuO/7whz+QmJhI7969efDBB/n2228dvsfRCMaRI0eIiYnh7NmzAGRmZnLPPffQo0cPunTpwnXXXcf333/P2bNnueWWW4CaDIuJieGhhx4CwGq1snTpUoYOHUpCQgJjx47l66+/bnTdzZs3M2HCBDp16sTu3budfl/z5s2jb9++Xvk5eUpGQESbFRgYyMSJ47FYUhrtBFx/g7CzfPVVR3bvjmT37nbodBYCA61UVanx87MybVoOFkvNxl8Ggx8Gg3vX1+ksaDQKZrPK/qEONfO4f/zR+bSLbt0qAPfKeza8HkBaWjAGg8Y+ZWz69GwslhSmTJksJTaF8ICrDAFbjsRx992Z3HJLNl99FdsoQwwGP4KDzUyblo3VCoqiorTUz8VV63OUI01lCFx6jhw7Fsq+fe0kQ8QVoeHox5OhNSODC0JDea+srMVGQYqLi9myZQtPP/00er2+0ethYWEO3uWehQsXUl1dzZdffklQUBCnTp1Cr9cTFxfH8uXLmTVrFj///DPBwcHodDoAli5dyrp163jttdfo1q0bu3btYv78+URGRjJy5Ej7uV944QUWL15M586dCQ8Pb/Y9tiRpgIg2LT4+nilTJjfYCbhmeoRWayErS0v37hUup06YTGr27w9nyJALLFnS06351MHBJh5/PBWVCvz8FP7xj25uv69nz3LKyvyc7uLuTJ8+ZRQWBtRr7Niq29x1VyabNm3m7rvvlKkUQnjAVYbodBb69buAWg1dujSdI7/8UpMjnuTB5c4RyRBxJWg4+tGhdkpRB42GB0NCWFJaah8F8ea+IBkZGSiK0iJrJM6dO8fUqVPtIxBdunSxvxYRUVO8Iioqyt7IqaqqYunSpaxdu5Zhw4bZ37N7925WrlxZrwHy1FNPMXbsWK/fszdJA0S0ebadgFNTUwkJOUZSUpb9taIif9Rq2LMngm7dKuptNFhYGMDGje05eLBmz4/+/UsdbGrYmFqtcPPN2QBotUEYjUZuvjmbTz9t+n3TpuVgMqnZvTuScePyHe7i7khwsIk+fUrZuLE9UP8atuo2jz+eRmpqKv369WvyfEKIi1xliNFY8/u2fn0c4eEmhg0r9nKOqOjXL4njx3+9bDkiGSJ8mbPRD5uWHAVpyUIOc+fOZcGCBWzdupXrr7+eqVOnkpSU5PT4jIwMKisrSU5Orvd1k8lE//79631t0KBBLXHLXiUNEOETAgMD6devH0lJSVRVVXH06FF++eUAn34az5/+dJozZ/T83/91aDR1ou6H8MUpW5l89VX9qRg2wcEmpk3Lpnv3CiZMGE/Xrl05d+4ckMKdd2by5Zeu3pdDYmI5q1cnkJWlY/ToQrcfVGwPHIcOhTs8xlbdpubhKQmVynVJTiFEfQ0zxGQykZaWxp49+4Ca9RyOpnE2N0duvjmHHj0q7dOeOnXqhNV6+XJEMkT4KmejHzYtOQrSrVs3VCoVaWlpHr1PXVuhq24Dxmyuv/brnnvuYdy4cWzatImtW7fy9ttv89xzzzFnzhyH56yoqJmWuXr1ajp0qF/IouGoZlBQkEf3ezlIA0T4FJVKhVarpX///hw+fJTJk/MoLAywT1MwGDRO13jYNiNLTj7H44+n1k7FCK0z1aKUvn1rFphOnDiBrl27AhencPj5bSYxMZXjx0M4cSLU4RSN1asTSE8PBjxp8Fx84DAanc8tt1W3qaqqQqvVXuJPUoirky1DtFotffv2Zf/+g1RWWutMdVK5lSN33pnJ4483zoO+fUvp06cMjUbD5MlT6NSpE9A2ckQyRPiapkY/bFpqFCQiIoJx48axfPly5syZ02gdSElJicN1IJGRkfb7t63BOHr0aKPj4uLiuP/++7n//vt58cUXWbVqFXPmzLHvY2SxXNwAuVevXgQGBnLu3Ll60618lTRAhE+qu7i0oMDfvptxU9MU0tOD+fDDLvzpT6dJSKgkKeliRRuLBdRqmDDhYuPDxjaFY/v27SjKGfr1u/i+ulM0qqr86l3riy86cuut2bVzyxs+cNQ8qDR84HDGNqfbZDLJw4MQXhAYGMikSRP47rvv6NvXvQwByMsLRKVS+PXXEDp0qKJfv4tTuiwWSErqwzXXXENAQEC999lyZNu2bSjKbx7niOOOE8cNF0ckQ4SvaWr0w6YlR0FeeeUVpk6dypQpU1iwYAFJSUmYzWa2bdvGJ598ws6dOxu9p2vXrsTFxfH666/z9NNPk56eznvvvVfvmGeeeYYbbriBxMRESkpK2LlzJz179gRqskKlUrFx40YmTJiAVqslODiY+fPn8+yzz2K1Whk+fDhlZWXs2bOH4OBgZs6c6dH3de7cOYqLizl37hwWi4UjR47Y7z042PXziDdIA0T4LFuP4saN32M24/Y0hcmT8zGbVWzeHE2vXuX06lUOgEajZsqUyfYeS0eio6M5ffoMaWlB/Oc/sRiNfo2maNS91oABpVRXq9ixI5rBgy/Ue1ApKdE4fOBwxlbdxtYzIoS4dPHx8YwfP55NmzYzbVoWn32W4NZUJ4tFxalTwVitCu3aVde+puKmm5xXmqqqqiI1NZWCgiJUKpqVI0OGFNfrOHHWcHFEMkT4EndHP2xaahSkS5cubN68mSVLlrB48WLy8vKIjIxk4MCBvPbaaw7f4+/vz/vvv8+CBQsYO3YsgwYNYtGiRcyePdt+jMViYeHCheTk5BASEsK4ceN44YUXAIiNjWXBggW8+OKLPPLII9x+++288847LFy4kMjISN5++21+++03wsLC6N+/P48++qjH39err75q33cMYPz48QB88cUXjBo1yuPzeUqlNHOFTUFBASaT411jhWhNVVVV7N27l+PHT5Caquerrzq6XN/Ro0cFtunPFgvodIEMHDiAvn37NuqxtMnMrKkgYzKZOXtWR0JCJWlpwW5PiajplVTQ6SxotWb++78zSEsLZt0690tiJief45pr4M47b7fP3/b39yc6Otrtc7QlkiGiLTl9+jTff7+FtDR9E2s0GmeIv7+GQYMG0L9/f7cy5MSJEAoLAxg9upD0dM9zRK838/DDaZw+reff/47HUcPFkSstQ4RvOX36NCG1+3a44y9/+QsffPABAP5AjF/THXX5Fgu2T5V58+Z5tSKWgLKyMrp16+aVc8kIiPB5gYGBjB49ms6dO+Pn9z3duzcutdm3b1ntvGw/RowYSUREBP7+/gQHB6PVal0uyMzMzOS771JIS9OzYUNXyss1JCaWN7n7euMpEba55Rp++imSsWMLPaxuU8aAASNk8agQLaBbt278/vf+bNq0mcRE5xni769h5Mjr0Ol0aDQaIiIi0Ol0HmcIwNmzQXVyxL01IaCiosKfnTttGWKRDBFXnLqjHwAmIKvOegh3tOTu6OLSyQiIuKLYpjgcPnyMioqLpTT1+lAGDEiiZ8+eTnsonZ3vX//6lJMnA1m9uv70Lq3WwsCBFxg2rJioqGr71wsLA9i7N8LllAit1sKf/3yKjAy9W2U577rrHL16GRvV8Pfl3kvJENEWtWaGwMUcmTAhH3//ix/HTeWIZIjwNZ6MgLz99tt89NFHl3zN2bNn8/DDD1/yeUQNb46ASANEXJEURbGX2vT39ycwMLBZvX5Hjx5l585dvPlmD6e9jEFBJhYsSOWbbzpw7Fio07ncDd1wQx7XXXeetLRgl1M+pk/PoXv3Cn7/+ymN1qf48sODZIhoy1o3Q8wsWHCKDRtiOXNG77D8ryNXe4YI3+LpFCzR9sgULCGaULfUZnMpisLhw8c4cSLE5RSHgICaNnxRUQAGg/u/UmfO6Ln++vP06mV0uENz3SkfkyY1fnAQQrSc1s0QKwClpf5cuOD+6IpkiBDCV0kDRAgnqqqqqKgo5dgx1x/a1dU1Gw5ptVaPzm+rSJOcPIOzZ8822qG5ZsrHCI+nfAgh2gbJECFaztGjR+nXr9/lvg3RTNIAEcIJ2/Qgo1Ht8rjKSr96myG6q2/fMvT6UEJCQhrt0HwpUz6EEG2DZIgQLSMvL48ZM2awfft2WWTuo1ynohBXMVut/KZ7JVXs3Rth3wzRHRcr0iTZHxBsUz5CQkKarMwlhGj7JEOEaBnvvvsuxcXF/P3vf7/ctyKaSRogQjgRGBiIXh9KUlJpk8ceOhSOyaRm2rRs1GrXdR3UaoXp03Px99fQo0cPb92uEKKNkQwRwvvqluhdsWIFeXl5l/mORHNIA0QIJ1QqFQMGJNGnT1mTvZJGox9r13YiMbGcmTPPEhzsuLpTcLCJu+7KpHv3ciZNmlCvHKYQ4soiGSKE97377rsYjUYADAaDjIL4KCnDK4QLTdXwr0utVpgz5wwdOhgAVRMVaSZ4pSKNL5fQlAwRVwPJECFqeKMMb15eHsOGDbM3QAB0Oh179uy57GtBYmJi+OSTT7jxxhsv6320JCnDK0QrCQwMZOLE8VgsKdx1VyYbNriutd+xo5EJEyZQUVEhFWmEEJIhQnhR3dEP/3b+mIpM9lGQ559/vsWum5eXx1tvvcWmTZvIzc0lKiqKfv368cADD3D99dd7/Xo7d+7klltuITU1lbCwMK+f/+zZs7z55pv8+OOP5Ofn0759e2677TYee+yxVssWaYAI0YT4+HimTJnMpk2bPaq1LxVphBAgGSKEN9Rd++Gn82P0ltFsG7ENq9HKihUr+NOf/tQioyBnz55l6tSphIWF8de//pW+fftiMpn44YcfWLhwIT/99JPXr+ktiqJgsVjQaOo/7qelpWG1Wnn99dfp2rUrv/76K48//jiVlZU899xzrXJvMgVLCDdVVVWRmprK4cPHqKi4uKi0plcy6bL0Svry9AnJEHG1kQwRV7NLnYL1l7/8hQ8++ACAxMcT6f9Gf448foT0JekAzJs3r0VGQe68806OHz/OTz/9hF6vr/daSUmJfYSi7hQsRyMYR44cYfz48ezbt4+EhAQyMzNZtGgRu3fvxmQyER8fz1//+ld69uzJ0KFD613njjvu4J133sFqtfLOO++watUq8vPz6datG0888QR/+MMfgIsjJ59++ikvv/wyJ06cYM2aNYwaNarJ7/Pdd9/lk08+Yd++fU6PkSlYQlwGgYGBUmtfCNFskiFCNE/D0Y8eT9ZUf+uxoAcZ72W02ChIcXExW7Zs4emnn27U+AAuaXrUwoULqa6u5ssvvyQoKIhTp06h1+uJi4tj+fLlzJo1i59//png4GB0Oh0AS5cuZd26dbz22mt069aNXbt2MX/+fCIjIxk5cqT93C+88AKLFy+mc+fOhIeHu3U/ZWVlRERENPv78ZQ0QITwkK3Wvlarvdy3IoTwQZIhQnim7tqPLg92Qduh5ndH20FL1we7kr4kvUXWgmRkZKAoCt27d/faOW3OnTvH1KlT6du3LwBdunSxv2ZrCERFRdkbOVVVVSxdupS1a9cybNgw+3t2797NypUr6zVAnnrqKcaOHev2vZw+fZply5axePHiS/umPCBleIUQQgghRJvkbPTDpseCHqi1NY+z3t4XpJmrFNwyd+5clixZwk033cSrr77KsWPHXB6fkZFBZWUlycnJdOnSxf5nzZo1nDlzpt6xgwYNcvs+cnJymDlzJtOmTeO//uu/mvGdNI80QIQQQgghRJvkbPTDxjYKAt7fF6Rbt26oVCrS0tI8ep9aXfN4XbcBYzbX3wvonnvuYe/evSQnJ3PixAkmTZrEsmXLnJ6zoqICgNWrV7Nlyxb7nx07dvDRRx/VOzYoKMit+8zNzeWWW25h2LBhvPHGG269x1ukASKEEEIIIdqcpkY/bFpqFCQiIoJx48axfPlyewOgrpKSEofvi4yMBKh3H0ePHm10XFxcHPfffz+ffPIJDz74IKtWrQJqikMAWCwW+7G9evUiMDCQc+fO0a1bt3p/4uLiPP7ecnJymD59OgMHDuTtt9+2N5paizRAhBBCCCFEm9PU6IdNS46CvPLKK1gsFqZMmcLXX3/N6dOnOXXqFB9++KHTTQe7du1KXFwcr7/+OqdPn2bTpk2899579Y555pln2LJlC7/99huHDx9m586d9OzZE6gp3a1Sqdi4cSOFhYWUl5cTHBzM/PnzefbZZ/nss8/IyMjg8OHDLFu2jM8++8yj78nW+IiLi2Px4sUUFhaSl5fn1elrTZEGiBBCCCGEaFPcHf2waalRkC5durB582ZGjRrF4sWLuf7660lOTmbHjh289tprDt/j7+/P+++/T2pqKmPHjuWdd95h0aJF9Y6xWCwsXLiQ0aNHM3PmTLp168arr74KQGxsLAsWLODFF18kKSnJ/t6FCxfy+OOP8/bbb9vft2nTJjp37uzR97Rt2zYyMjLYsWMHAwcOpH///vY/rUX2ARHCh/lyDX/JECEuP1/OEOFbPN0HpO6+Hyp/FYExgU2+pyq/CsVU81jbUvuCXM1kHxAhhBBCCHFFqjv6AaCYFIxZRo/O0ZK7o4tLJw0QIYQQQgjRZvz73//2yqZ4//73v3n44Ye9cEfC22QKlhA+zJenT0iGCHH5+XKGCN/i6RQs0fZ4cwqWLEIXQgghhBBCtBppgAghhBBCiBalUqku9y2IS+TNf0NpgAghhBBCiBalUqmwWq2X+zZEM1mtVmmACCGEEEII39G+fXvKysqkEeKDrFYrZWVlXq0oJlWwhBBCCCFEi9LpdMTFxZGXl4eiKDSzBpJoZSqVCpVKRVxcHDqdzmvnlQaIEEIIIYRocTqdji5dulzu2xBtgEzBEkIIIYQQQrQaaYAIIYQQQgghWo00QIQQQgghhBCtRhogQgghhBBCiFYjDRAhhBBCCCFEq5EGiBBCCCGEEKLVSBleNymKQnFxMRUVFej1eiIiIry6I6QQ4sonOSKEEEJIA6RJJSUlrF27lk9WfkJGeob9610Tu3L/vfeTnJxMWFjYZbxDIURbJzkihBBCXKRSmrkVZUFBASaTydv306Zs3bqVB+Y9gMFgoOOMjsTOiMU/wh9TsYmc9Tlkr89Gp9Pxj/f/wdixYy/37YqrkL+/P9HR0Zf7NprlasgQkBwRbZsvZ4gQwndJA8SJrVu3cu999xI9OZpBywah7aBtdIwx18jBOQcpSClg5YqV8vAgWp0vPzxc6RkCkiOi7fPlDBFC+C5pgDhQUlLCsOHDCLk+hGs2XINa43ytvtVsZc/0PZRtL2Pv7r0yjUK0Kl9+eLiSMwQkR4Rv8OUMEUL4LqmC5cDatWsxGAwMWjbI5UMDgFqjZtCHgzAYDKxbt66V7lAI0dZJjgghhBCOSQOkAUVR+GTlJ3Sc0dHhdAlHtLFaYm+N5eMVH9PMASUhxBVEckQIIYRwrkUbIIqiUFRURGZmJkVFRV79UG2pcxcXF5ORnkHsjFiP3tdxRkcy0jMoLi72yn0IIXwzQ0ByRAghhHClRcrwtmTJSU/O3Zya+xUVFQD4R/h7dF+24ysqKmjXrp1H7xVC1NdWMgQkR4QQQghv8/oi9JYsOenuuZe8sYScnJxmPbwUFRXRv39/hq0ZRlxynNv3lrUmi7137OXIkSPy4CBajS8vIG3LGfKP9//B4MGDm90IkhwRvsKXM0QI4bu82gBpbslJd3oY3T737IPkfpuLSqUiLjmODrd2QOWnoiq3ioLvC8j9OpegoCCnDy+KonDdmOswDTUx9LOhbv889t6xl4BfAtixbYfsbCxajS8/PHgzQ6DpkQpPzp3/XT7+Af6YTCZib40lelI06kA11iorBRsLyPk8x2UjSHJE+ApfzhAhhO/yWgOkOSUnS7eV8shDj/DZms9c9jC6OreiKFSfr8ZcbkYTrEETpmHPzXso3FFIz/+vJ5mfZFJ+stx+vL67HnWAmoqTFaxaucrhw8OyZct47oXnmJQ5ya0FpMYcIxsTNrL42cXMnj27yeOF8BZffnjwRoaUbS9j86bNpKSkuBypAFyeu26OqLVq9v9xP4WbC+n+ZHdy1ufUy5DgXsF0ursTRT8WcX7Lead7d0iOCF/gyxkihPBdXmuAePphm/lpJr/81y81IxUz4lxOhUhLS2t07uoL1WSuyCTjvYxGDwfh14Rz7l/nUKlVdJzRkY4zOtrPnb0+m+z12aCGAHUAB/YfaDSNwtMHob3T91K6vVTq94tW58sPD5eaIcYcIymdUvAP9MdsMrucUnXr9Fv516f/anRuZzmijdNizDaCGuJui3OYIX5BfgT3Cqb6RDX79uyTHBE+yZczRAjhu7zSAPF0ukFeSh67pu4iZmIMg5cPbnKaRbvIdgSMCWDYv4fZ37/39r1YKi2NGxjrahsYfjDkkyHE3xnv8NwHZh8g79s8bhh3A6tWrWp0TL3pGh8OQhvr4B5zjBycW3OPq1auYsyYMU1+70J4ky8/PFxKhkBNDvx848+0n9y+yRzJ/TaXqNFRjN42ut77neVI1toscj7PwS/Ij2Frh9F+cvtG5z0w5wD5KfkoFoX/uue/eOWVVxpdX3JEtHW+nCFCCN/llQaIJwsuqy9Us7HzRiKvi2T4huFNT7O4eQ+53+Uy+KPBdL6/88XGy+QYBi9z/tBhezgY8c2IRg8PtnPvmraL/I353D7jdhYvXtyo17HugtXYW2Mb9YLa5oF/+MGH8tAgLgtffnhoboZAnRwZHcnwL5vOkV3TdnF+23kmZ00mIDzAKzliO2/BxgIUq8IH73/A1KlTG51HckS0Zb6cIUII3+WVfUA8KTmZuSITS6WFwcsGu7c78LJBqFQqivcUU55ezp7b9hA1LoprvrjG6TQNbQctvZ/rTczkGPbevpfqC9UOzz3koyGoULFm7RqGXjOUrVu31jtm7Nix7Nm1hyefeBLVLhV779jLT5N+si8UXfzsYvbu3kv//v1bZC8BIa4WnpattefIR+7lyJCPhmCttnJ2xVmPcmT4huFOc8R2Xpt58+fxn//8p9F5xowZw8bvNvLIQ4/gt8dPckQIIcRVzysNEL1eD4CpuHFJzboURSHjvQyPdgdW69SE9Avh7PKzfN/9eyzlFgo2FfBD/x9IX5rusHFhzDXy06Sf6PtSXyyVFjJXZjo8tzZWS8cZHdEn6gm+Lph777vX3ggpKSlh2bJlTJ02lVdffZVzZ88BEN85nqeeeorV/1yNoijc9Ieb6N+/PyNGjKB///5cN+Y6li1bRklJiVvfnxDC/QyBS8uR44uOu50jAGXHyhj84WCnOVI3Q6ImRjHvwXmNMuS6MdcxatQolixZwtkzZ0nomsBjjz3Gzp07+earbyRHhBBCXHVadQ1IVWEV30Z/6/Y0i7pztGNviSUuOc7hQtBha+rP0T7y+BHSl6ST+HgixnNGSg6VMP7EeIdlLW1196fkTuHg7IOUbS9jyRtLeOyJx1zuFaAoCigQl+x6Ab2n+xQI4Qlfnj7R3DUgrZUjxlwjm5M2M/7YeI48csRpjtTNkAN/PED5j+WuM2RdDtmfZxMQEICiKJhMJq/vdyKEu3w5Q4QQvssrO6GrVCruv/d+nnvhOYy5Rqe9kuZyM+DeNIum5mjHJcfZ52jvmrrLPkfbmGsk472aUpxn3jtD/7f6k7UmC1ORiYDIgEbXsd2LxWBh0IeDSOmUwrwH5xEzJYbrll3n9Lr7Z+2nYFMB8X+Mr/fQYnv94JyD3HvfvU5LdAohLnI3Q6B1cgQg9bVUTEUmUl9PpeOMjk5zpG6GDP5osEcZkp+Sz6APBtFlTheHx0iOCCGEuBJ5ZQoWQHJyMjqdjoNzDmI1Wx0eowmuae80Nc2i+kI1e2/fS8zkGIZvGO7RHO3U11KxGmuubzFYyNuYV3PNMsfXtN2Lf4g/ap0alb+K6EnRXLPB9dzwEV+NIHpiNHtm7Gk0fUPbQcs1G64henI0D8x7QKZRCOEGdzIEWidHGnZk2AaKHeVIowzRuJ8hMZNjODTvEFnrsxweIzkihBDiSuS1BkhYWBj/eP8fFKQUsGf6How5xkbHBEQGoO+uJ2td4w/bujxdqG6bo3363dP2hwabvK9rGiD+IY57S7PXZxPcKxj/dv5krshEsSgMXu7BwlajleOLjjt8fdCHgzAYDKxbt87luYQQ7mUIgLXaiiZUQ9balsmRzJWZjToyMlfVrP9wlCONMsTqWYYA7L19L3kpeQ6PkRwRQghxpfFaAwRqqkatXLGSsu1lbEzYyN479pK1Jov8Tfn2edIV6RXkrM/BmOv44aI5C0y1sVo63tqR9DfT7Q8N/u1qHhSs1Vb8I/ztf6/LmGMk+/Nsus7vClBz3Vs9u27srbH8tvw3qoqrnL7+8YqPpaqNEG5oKkP23L6HjQkbsRgt5HzRQjnydnqjjoz87/IJSgxqlCNeyZAZsWiCNexJbjyaaj9GckQIIcQVxKsNEKh5gNi7ey+Ln11MwC8B9UpOnv/xPCigDlRzYM4Bh9Msqs9XU36ynI4zOnp03ejx0fapEH46P0ZvGY1aW/PtmcvNVOXVbyBYzVYOzD2AX5Af8ffGX7zubZ5dN+62OJRqhTPvn3H4escZHclIz6C4uNij8wpxtWoqQxSLQr8l/fAL8vN6jnSc0ZHK9MpGHRmKRSEoPqjeAnSvZciMOMylZpcV+yRHhBBCXEm83gCBmqkUs2fPZse2HRw5coTPP/8cgMGfDCa4VzDhQ8PJT8ln9/TdjaZZeLLAtK660xe6PNiFsIFhdH2wpldSMSmkvp5qf92YY2T39N3kp+RzzdprCAgPaPZ1bcf/tuw3h72Tttdt+xwIIZrWVIYUbS9i2JphXs+Rur/DDTsyinYX2UdcWiJD2k9pT8b/ZkiOCCGEuOK1SAPERqVS0a5dO3r06AGApcRC1we7UvRTEUNWDuH8jvOkJKTUm2ZR8H0B4N5+ADbGXCO5X+cCNQ8NPZ6suV6PBT3sDw8Zf8/gzD/OsPeOvaQkpHB+x3mu/c+1xEyKAdxf2NqQ7fjK05WYipwvULXtcyCEcJ+zDMlen03YwDBGfDPCazkC2Nd6QOOODKvByoE5B1osQzre0pHyk+WSI0IIIa54LdoAsYmIiKBDXAey1mYRf188fkF+nPvXOSamT6TfG/0oOVRin2ZxcO5B1Do12euy3T5/6mupKKaaXsMuD3axz7/WdtBefHiosnLwvw9ScqiEfm/0Y/LZyfYHBwBNmMatha0NZa/PRpegAxxXyMlen03XxK5ERER4dF4hxEURERF0TexK9rpse4YcmHOA6PHRTPptkldyxJhrJO/bmpFUZx0Zef/Jo/iXYq9nSHCvYLTxNbklOSKEEOJK1yoNkG3btpGXk0fO5zlYjVb71In99+8nLjmO8SfGc2PhjUzMmMiNhTfS9//1JfvzbKcLTOuqWy6z7kODTd2HB7VWzagfRpH4cCL+YRenSRhzjOy5ZQ/mcrPLha2Nrl27ADX6hppNnBpWyDHmGMn5PIc/3vdHh5sgCiHco1KpGD1yNNnrs+tlyO7pu7EarCQ+nNgoR3ou7En2evdyBODEX09A7XISZx0ZALHTYr2eIV3nd8V8oXYKl+SIEEKIK1yLN0BKSkp4YN4DRE+Ixk9/sdey7tSJfTP3UbC5gIrUCgo2F1C4rRBFUdg/a7/L/QAATr1yyr5gtO5Dg029URCjlZ1jdzaqzPVd/HcUbitkwLsDUAeo3bpu3QWopgsmexnOuq8fmnsInU7Hbbfd1pwfnRCiVklJCeu/WI/KT+UwQ/besZfstdlc2H+BC3sucHD+QX597lcUFA7MdrxQva7Kc5X8tuw3oOmOjNNvn+bMP87Uy5CUhBQKtxcy+KPB+On83Lpmw0Xsdcv51j1GckQIIcSVRqU0s65jQUEBJlPTc52XLVvGcy88x6TMSZQcKrm4K/GHg1Hr1GSuzCTjfzMoP1luf48mVIO5zIxKrSJmSs2x2tjGZS1LDpXww5AfwFrz0DDx9ESH5S+NuUY2dt1Y01BRAXW+44CYAFRqFVW5dapkqaD979vX7Jzs4LrGHCMH5h4gPyWf3638Hb/c+wv93uhH4sOJ9tcPzj1IQUoBq1auYsyYMU3+nIRoDn9/f6Kjoy/3bTSLuxkCF3Nk8MrB7L93v3sZUm6m5//Xk9SXU+3HO/t93j5qO5UZlQAkPp5I/zf6NzruyONHSF+S3ujr+u56QvuHUnq0lIrU2kXiKoiZEsOQj4Y0mSHX/udaQvuHkpKQIjkiWp0vZ4gQwne1aANEURSuG3MdpqEmhn42FKipVrX39r1YKi3ETo8lLjkOTbgGY6aR7C+yyfsuD78gP4avG46iKI2O9Y/wx1RsImtdVs387tq7d/bQYFP34aHrg10JHx7OkYeOYDFY6DijIx1ndLSfO/2ddIp+KkKFithbY4m77eJ1s9dnk/15Nn5Bfgz9bCgZ72RQuK2Q3/3zdygmhez12eR8noNOp+PDDz6UhwbRonz54cHdBkjDHKmXIbfGEjfDeYbETIpxmDl1f5+z1meBpeZa7nZkqHVqRm8bjeGMgQNzDmCprJ8jhT8Ukva3NBSLQuwtja9py5Br1l5D1A1R7J62W3JEXBa+nCFCCN/Vog2QoqIi+vfvz7A1w4hLjrN/vfpCNZkrM0n7WxqGTIP968G9guk6vysJ9yXY51eX/VrGnhl7KD9VjmKuUyIz1A+rwYpiUlw+NNjUe3gIVGM1W2k/pXaUw8H7yk6WseeWPZSn1r+u7R5jJsdw9PGj5H2XZ583DtA1sSt/vO+PJCcnExoa6vLnI8Sl8uWHB3cbII5yxJYhDUc+9N31dHuoW70MAec5EtwrmIDoAIp+LAI868iIvTWW3K9ya0ZXHORI9YVqTr97mrTX0zCXmutd05ZzlkoLB+YckBwRl40vZ4gQwne1aAMkMzOTESNGMHLTSGImxDR6XVEUstZlcWDWgZqRiFs71h9tWJdNzhc5aAO1VFZUMvijwYQOCmXb77bVm0ql8lcRGBPY5D1X5VfZq2UFdQ1iwqkJqDXOl8FYzVZ+/sPPFG4ppM+LfdB306OYFXI+z7H3Tv7j/X8wYMAAKioq0Ov1REREyEJR0Wp8+eHB3QaIqxxRFAVTkYmcb3I4/D+HsRgsxM2Iqzei6ShHSo+Xkr4knbH7x7Jt2LZmdWQARI2PYuR3I13miMVk4eff/8z5Hefp97d+BPcKxnzBXG+UQ3JEXC6+nCFCCN91WUZAGnLWm5nQNYE5f5zDyJEjmTBhAiM3jUTfXc+mrpuac8v1qLVqJmVMcvmwATXzsFPiU1AsF39M0jsp2gpffni4lBEQRzzJkYCYALYO3oouQYfhTM0obHM6Mrr8dxcGvT+oyfdIjoi2ypczRAjhuzQteXJb7f6c9TkuHxwCwgNIfDiRbg91w1Rk4pf7fiHwWCA7t+9ErVZTVFQzPcJUbLJv9qUJqVmoDuDfzh8/nZ/rm1HAXGHGXGJGrVMT0C6As5+cpefCni7fpo3VEjsjlqIdRRhzjMTFx7F963bU6lapYCzEVa8lciRsUBhYsTc+ABSTgjHLvfK5NpkrM+m9uHeTHRmSI0IIIcRFLdoAUalU3H/v/Tz3wnMYc41NfkirVCqs1VYKUgpY/Oxi+4dz3QeQjrd1JLhXMGGDwoj5fQwH7j/AsH8PczjFq6Gqwiq+jf6W3634ncsHmYbiZsSRvSabwA6BZGVmceHCBdq1a+f2+4UQzddSORIQFYCpxIRiUgiICkAd6F5jQLEqVOVU2Ts+3OnIAMkRIYQQwqbFu9+Sk5PR6XQcnHPQrbr4jmre2x5AstdnU5VXRdcHu5K9PpuIoTW7ApuK3SvlaS6vHTGJ8G/iyPpsx0ePrxmmrqio8Oj9QohL0xI50uuZXijWmilRA/93IFPOTXHrz/U/XQ/AsH8PY8q5KW41PkByRAghhLBp8QZIWFgY/3j/HxSkFLBn+h6MOY6nOBhzjOyZvof8lHw+/OBDwsLC6r1e9wGk092d8Avy4+iCowT3CiZ7fbZb92KbvuVug8XGdnzE8JoGj16v9+j9QohL05I5ognVuJ0hIDkihBBCXKpWmYA8duxYVq5YSdn2MjYmbGTvHXsb7Ua+MWEjZdvLnG64VfcB5MD9Bxj4/kAKNhag8lORvT4bY27Tc7cDIgPQd9eTtTbLo/vPWpuFLl7H+R3n6ZrYlYiICI/ef7koikJRURGZmZkUFRXRzHoDQrQJLZEjgz4YhLncTPY69zIEwFptRaVR1exD5AFfzBHJECGEEC2hxXdCr6ukpIR169bx8YqPyUjPsH/dk2owW7du5YF5D2AwGIgYGUHx3mKs1VbaT2rP8K+GOy2HqSgKxjwjP173IxWnK5h8bjK6WF2T92zMMZKSkEKvZ3tx6vlTLH52MbNnz/bo+25tJSUlrF27lpUff0z6mTP2ryd26cK9f6z5OTfsGRa+yZcr2DQnQ8D7ORJ2TRgXdl8gelI0I74a0WRJ3V037aJwWyGKRWFy5pWZI5IhVw9fzhAhhO9q1QaIjaIoFBcXN7vmvcMHEBXETIlhyEdD0MZeXKRafaGazBWZnH73NBVpF+dca0I19P5rbxJmJRAQHuDwOlazld3Td3N+x3kiR0RS/nM5e3fvbdMfvFu3bmXe3LkYDAZm6PXM0OmIUKsptlpZbzCwvqICnU7H+x9+yNixYy/37YpL5MsPD5eSIeC9HFn67lLO5593miFQu6ngO6dJ+1v9TQWvxByRDLm6+HKGCCF812VpgHiL1Wpl1HWjqO5XTaf/6sTBOQexGCzE3hpL3Iw4ytPLOfXiKaxV1pqvJV/c5DBrbRY5n+fgF+THsLXDaD+5fb1zG3OMHJh7gPyUfMKHhFO6v9TptI62YuvWrdx3771M1mpZFhFBB03jIme5ZjNziotJMRpZsXKlPED4OF9+eGgLGaIoCqOvH03VgCo6TO/AkYeO1MsQ/wh/Cn8oJO3NNBSzcsXniGTI1ceXM0QI4bt8ugHScIOyRhuR2Xo0lw9xWLrTmGtk/6z95Kfk0/OpnkSNi6p5qFiXRc4XOaj8VCgmhSB9EB9+8GGbfWiAmt7c4UOHcr1KxYaoKDQueoLNisL0wkK2Kwq79+1rsz2xomm+/PDgExkCV02OSIZcnXw5Q4QQvsund8GylbG0lbe0bUR2/c/Xo9apiZkSw4ivRjjdN0DbQcuIr0YQMzmGU6+e4qdJP7H3jr3kfJGDYlaIj43nucXPsW/Pvjb70GCzdu1aDAYDyyIiXD44AGhUKj6MiMBgMLBu3bpWukMh2h5nGTL+xHgmpk9Erb16ckQyRAghRGtp0Y0IW5qtjGXDcpiZKzNRTApDlg9xuaAUQK1RM+SjIaTEp6AJ0PDlhi+JiIggODjY4znll4uiKKz8+GNm6PUOp0w4EqvRcGtQECuWL2fWrFk+8X0K4W3OMkSlUpH7dS6K+erIEckQIYQQrcmnR0Dq7mxsoygKGe9l0HFGxyZ3TLbRxmqJvSWWyOhIBgwYQEJCAu3atfOZD9Ti4mLSz5xhhq7pajx1zQgKIv3MGYqLi1vozoRo2xxlCFx9OSIZIoQQojX5dAOk7s7Gthr+1eerKT9ZTscZHT06V1xyHLlZuT75QWqbRhKh9uyf03a87MgsrlaOMgSuvhyRDBFCCNGafLoBAvV3NraarZjLa0pk2uZ0u8t2vK98kNbdIKy6uhqAYqvVo3PYjpcdmcXVrGGGAFdFjkiGCCGEuFx8vgFSd2fjPdP3YCm3AI3ndDfFdnxb/yAtKSlh2bJljBk9mv79+zNixAiuv/56dBoN6yorPTrX+spKErt08YkdmYVoKQ0zxJhjRBNcsw7iSswRyRAhhBCXm883QADGjh3LyhUrKdtexg+DfkATriF7XbZH58hen03XxK5t+oN069atDB86lBcWL2ZoYSFroqPZ1L49a6Kj6a1Ws66igmNVVZwxmSi0WHBVYTnHbObzykruc7B4tG7PaFFRkcvzCHElqJshGxM2cmj+IbRx2isuRyRDhBBCtAU+XQWrrrFjx7J3917WrVvHW0vfss/pdmcBqTHHSM7nOSx+dnGbXTBab4OwuLh6lWouWCykm0wcra6mX87FxbS9NBoeDA3lPr2ecD8/+9fNisLc4mJ0Oh233Xab/eslJSWsXbuWlR9/TPqZM/avJ3bpwr1//CPJyclS719csepmyMcrPsaYZbyickQyRAghRFvh0xsROnPhwgWGDR9G6PWhXPPlNS5LaFrNVvZO30vp9lL27t7boh+OiqJQXFxMRUUFer2e8PBwLly4YP+7s3KdrjYISzEYuD0/n0pF4dagIG7T64lQqym2WllfUcH6ykqCVCrWxMQwWacjx2xmbu0uxitXXdyReevWrcybOxeDwcAMvZ4ZOt3F8xgMrK+oQKfT8f6HH8rOx22IL28i1pYzRFEUfvvtNyZOntimckQyRHibL2eIEMJ3XZENEKj5MLz3vnuJnhzNoA8HoY11sINxjpGDcw9SkFLAqpWrWmyTMGe9gjqNBoPZbP+7s17CZcuW8cLixWQ26LVMMRiYmpfHZJ2OZZGRDuv355rNzD5/nhSDgVGBgfxUXY1Op+ODZcvqPTjYe0YjIpyeZ07tQ8eKlSvlAaKN8OWHh7aeIdB2ckQyRLQUX84QIYTvumIbIFDzofjAvAcwGAzE3hpLxxkd8Y/wx1RsInt9Njmf56DT6fjwgw9brPHhqldwXUUFn1dWEqhS8UhoKOkWS71ewjFjxlBUVMQfbryREcXFfFbnQ+KCxULnc+e4TqtlQ0yMy52LzYrCtPx8NhmNPLlwIffeey+hoaGA655RR+eZXljIdkVh9759MpWiDfDlhwdfyBC4/DkiGSJaki9niBDCd10xa0AcaTine++avfbXuiZ2ZfGzi0lOTrZ/kHqbqznXAMl6fU2v4PnzvFZSwjft2/NWeDizi4q49557iIqKIq+gAIDXG3xArKiooFJRWBYZ6fIDH0CjUvFRZCQJWVnodLp63+/atWsxGAwsi4tz6zwfRkSQkJXFunXrmD17tic/DiF80uXMkUvNkJiYGHLy8gDJECGEEG3HFT0CUlfDudPO5kp7i8e9gvn57DAa+a1TJ4LVaqbl57PZYOCl8HCevHCBTe3bM6F2l2JFUeiTlcWggAA+i4lx+56S8/P5OSSE3b/8gkqlQlEUxowezdDCQj6LinL7PHcUFPBLdDTbfvyxTS62vZr4cu+lr2UItG6OeCNDthgMvCgZIlzw5QwRQviuK6IMrztUKhXt2rUjPj6edu3aefVDz1HJSXuvYESEe72CkZFUKgorKyrsvY1WoLr2mLobhJ02mThpNjPDw70GkvV6svLy+O2332rOWVxM+pkzzKh9KHHXjKAg0s+c8bndnoW4VC2VIy2VIRYcZ8h5q1UyRAghxGVzRU/BammuSk5eKC3lD0FBDhdjOhKr0XBrUBD/W1rKQyEh9r+vKCujl0bD+ooKkvV6UgwGbqudUhGh9qz9aDt+2o038vDjjzNy5MhLOk9FRQXt2rXz6L1CiIsuR4YA/MdgAGp+lw9VVzMwIMCta0iGCCGE8AZpgDRTw4WhL0dHXyw5WVjIuvJyUlQqUgwGJrvZOzhDr2dNZSVFViuRfn72v78UHs5fL1zg0/Jy7i0sZGRgINurqsioU/3GHbYe0FHV1byweDHa2vuq2zPqyXna8m7PQrR1lyNDcs1mDplMzC4sBCDDbOaOggKOdezoVkNHMkQIIYQ3XDVTsLzJtjD0epWKzLg4PouKIlmvZ4JOR7Jez2dRUZzr1ImxWi1T8/JIqe1tbIqtV7Cs9sPZ9vepOh064P7CQibrdAyu7a38W0mJR/e9vqKCXhoNG2JiyIyLY4xKhRp4t6zMs/NUVpLYpUub3e1ZiLbucmRIkErFfYWF3J6fz2Stlu4aDa+XlFBktfJ6aalb55cMEUII4Q3SAPFQSUkJ8+bOZbJWy4aoKKe9hh00Gr6s3bjr9vx8LlgsTZ7b1isYUvvQYPt7nEbD3SEhWID/Fx7OB+XlAJwymzlcVeXWfeeYzXxeWcn80FBUKhUdNBo2REUxJSiInUYjJ6urmz5JnfPcN2uWLB4VohkuV4asiYnhe6ORCkXho6gopul0pNaOor5XVkZuEyOqkiFCCCG8RRogHrqUhaFNsfUutlOrURSF1eXldPPzw2K1sqWykhlBQXxSUYGxTuGy6QUFmJsoZGZWFOaeP0+QSsW9daY8aFQqltXOv761sNC98xQXo9PpuO222xwunBVCuNZaGQKwrrycRD8/Sq1Whvj701GtZkbtupK606YMiuJyFKSlMgQcL8AXQghxZZMGiAcURWHlxx8zQ69v1sJQVx+stl7B+4ODebusjJ5ZWXxpMHDaYqF9VhanLRZQFN5rMNUhw2xmSl4eOU56L3PMZqbn55NiMLA2JoZwP7/G96fXc6q6mpsLClyfp7CQFKORN5cuZe3atYwZPZr+/fszYsQI+vfvz5jRo1m2bBklHk4NE+Jq0RoZMj80lBKrlReKi/nCYCDdYqFbVhYx586Ra7USpFJxsrqaTysr673/f52MgrREhnywbBlQs0O75IgQQlx9rpp9QLyhqKiI/v37syY62l5Nxh1rKiq4o6CAwvh4Iht8eMPFGv4/GAxoVCoqFYVbg4K4Ta+3L0pdW1HBuspKbP9Y7dRqimp7MP0BBbg1KIgZdd6zvnaX5CCVirUxMUxyspDVdn/BOh1Go7HmPEFBF89TWcnnlZXodDrmP/QQ//vOOw53ZV5vMNTbhXns2LGe/YCFx3y5hr9kiPczZIfRyPLISGadP09FbY4kN8iRLyorUXOxPG/dLOmp0fBCRESLZsgHy5ahKIrT3d0lR1qXL2eIEMJ3SRUsD1TUToFobsnJstrKNHXlmM3MPX+ebw0G1MA4rZZlkZGNekevCwzk68pKjIBOpWJLhw6MyMnBqChYgGfDwlhVUcGaOr2avTQa3mjXjvuCgwlzcc+2+/viq6/4+eefWbF8OWsalAR9dtYsYmNjeXDePNe7MoeHM6e4mPvuvZcVK1fKw4MQdbRkhqQYDDwXHs7MwkIm6nQsd5AjyXo9h6uqGJyTAzTOktTaqlg2nmbI03/5C2az2WmGJCcns3///qZ3d5ccEUKIK5o0QDxgKxnZ3JKTjxYXc1ed3sh1tb2RAUCASsU4rZYNMTEO54W/VlqKsfb/PxgSwsCAAB4MCWFJaSlWYEVFBV9GRTEgN5d327Vjpl5PO7XarUWetvtLT09n9uzZzJo1q9Fuz6WlpQwfOtS+cNbZ3HXbwtTphYXMmzuX3fv2ERYW5tHPS4grVUtlSKBKxcOhoTx34QITdTq+cpIjAJ9UVGC7esMssY2wNjdD/vLMM6xctYptP/7ocMf4hgvwJUeEEOLqJGtAPBAREUFily6sd7Mkps36ykpi2rXjSHQ0dxQUMCkvjzsKCviyshIzUAmYFIXlkZEOP5BzzWb72g+dSsWToaEALAgNRVt7fIbZzKDcXMJVKrYbjUT6+bldYWZ9RQWhajV/fuwxSkpKHO727PHC2YgIDAYD69atc/8HJcQVztsZ8kVthlQoCm+WlmIBpzkC7mUJQIrB4HGG9NJomKzVMm/uXEpLSx3uGC85IoQQAqQB4hGVSsW9f/wj6ysqmixZaWNbGPo/jz7K9p072bFjh/21lZGRFHTqRKJGw20udjx+rbTUXvnqwZAQ+3EdNBoeDAmxH3e9VkuASsX6ykqP7+/PISEYjUaHH/SXsnB2xfLlUtVGiFreyJAjR47w3XffAWAGPoqM5HTHjvRoIkfA/Sz5xmDw+P7mh4ayrF07pw0GyREhhBA20gDxUHJyMjqdjjnFxR6XnFSpVPj7+9tfj9RoQKUi3WxmhpMFqc56LG3q9lzurqpibVQUfsCs8+c9Ks/7UGio0w/64uJi0s+cYYabuzHbzAgKIv3MGYqLiz16nxBXskvNkHbt2hEeHm4/JkGjIcTPj1QXOQKeZYkC3O1uWd065XldNRgkR4QQQthIA8RDYWFhvP/hh6QYjUwvLHS75GRYWBglJSV8/vnn9mOKrVbKG+xY3JCzHkubuj2XBkVhbH4+fsB3BgM35+d7VJ7X2Qf9pS6crXBj/wIhrhaXkiFAs3IEPMsSgC1GI9M8zBBw3mCQHBFCCGEji9CbYezYsaxYuZJ5c+eSkJXlsuTkylWrGDNmDFu3bmXe3LlUVlYSplKhombe9DitFmi8KFVRFI6bTPxv7eZgjnosbRaEhvJeWRlGRUEDfBMTw/j8fLYZjSScO+eyPO9/2re3l9as+0HfrnZzMbj0hbN6D8qNCnE1aE6GAB7liKIonK9tnFTU2UPI3SyxdWR4kiEgOSKEEKJp0gBpprFjx7J73z7WrVvnsuRkaGgoW7duvVh2slMn/l1ZyeNFRayvrGRJRAS9NBrWV1SQrNdzwWJhRUUF75WWcrJOz6OjHksbW8/lktJSTMC62lK877ZrR6mi8L+lpW6V53X2QW9fOFtY6NHeBesrK0ns0oWIiAi33yPE1cKTDAHczpGJWq3DDLFxN0sstV+7R6/n56oqt0t8S44IIYRoimxE6AWKojgsOQk10yWGDx3K9SqVvezkBYuFhMxMqoCJOh03aLU8VVzMyqgo5p0/T6WicKNOx7cGAyZqeixPO6iXX1eu2UzXrCyMioJWpcJUuwnZmpgYFEWhyGqlzGolRK12WlrzjoICfomOZtuPPzZ6fdmyZbyweDGZTdyHTY7ZTEJWFs8+9xyzZ8/26Ocp3OfLm4hJhlzkKkPA/Rx5srgYvUqFQVGYUTtqoSgK9xQWNitLAP6g0/FlTIxbGQKSI77GlzNECOG7ZATEC2wLQ+tON7Cxl52Mi7OXnQz382Nt+/bcmJdX08hQFPyBewoL+b1Ox7LISF4rLcVUW6rTrCgMrd04zBVL7QODUVFQA1/UVsPqoNEQ6efncAdlG1slm2dnzXL4YJGcnMzfXn2VOcXFLuv32+637sJZIYRrrjIE3MuRHLMZBRit1dbbhPDxoiJszTxPswRqKmLlWSz2HHFFckQIIYQ7ZBF6C3JVdnKyTsf/tW+PFvjeaKS69msbYmIA7PO1AUxAlsXS5J+6fclWIBAPqmE18UF/qQtnhRDN406OBAKHTCam1G5CaDuubuUraF6WeFQRS3JECCGEG6QB0oKaKjs5WacjKz6eG2tft20g9kl5OZFqNXF+fg7/xNb2QgapVETVTofQ1elJDKr9/xq1uqYaVkGBVz7obQtntysKCVlZ3FFQwJqKCjYZDKypqOCOggISsrLYrij1Fs4KIZrPnRx5NjwcFY03IXSWJU1liB8QWufvP1RVea3BIDkihBBC1oC0oMzMTEaMGMGm9u2Z4OThQVEU+mRlMSgggM9qRz/ckZyfz4baXZABEvz8uEGrpcRq5WuDATVgAf781FP87zvvYDAYXFba+WDZMrc/6EtKSuwLZ9MbLJy9r8HCWdGyfHn+tmSIe5rKEW9lSJyfHzcHBXFNQADfGgysr6xEDYSEh7P03Xd58IEHJEeuQL6cIUII3yVrQFqQO2Unz1utnDSbecHDCi/Jej3rKivZ36EDCf7+9RaF5prNzD5/nm8NBrp27epRpR1nGi6SnTVrFrNmzXK5cFYIcemaypFLzZCNMTEMCQyslyH3hYRczJELFygvL7/kHHG00H727NmSI0IIcRWSEZAWpCgKY0aPZmhhIZ9FRTk85ozJRNesLJejJI5sMhiYlJdHRlwcXersrm5jVhSm5eezA9jzyy+EhYU1WWnHkZKSEtauXcvKjz9u1Et57x//SHJysszPvox8ufdSMsQ9TeVIS2UIeCdHJEPaNl/OECGE75I1IC1IpVJx7x//yPqKCnKdzJ0Orq2h39zNuUKc7CqsUan4KDISo9HIunXr7PfTrl074uPjadeuXZONj61btzJ86FBeWLyYoYWFrImOZlP79qyJjmZoYSEvLF7M8KFD2bp1q0f3LoRwX1M50lIZApeeI5IhQgghHJERkBbmqH5/Xc2dv31Hfj6Hqqs5ERfn8gHAVU1+V+ptehYR4bBmf67ZzJziYlKMRlasXMnYsWPdPr/wDl/uvZQMcZ+rHGnpDIHm5YhkiG/w5QwRQvguGQFpYU2VnVSpVDwYGsr62j073GGrtT8/NLTJh4EZQUGknzlDcXGx2/dcUlLCvLlzmazVsiEqyuWuyRuiopis1TJv7lxKSkrcvoYQwn2ucqSlMwQ8zxHJECGEEK5IA6QVNFV2cqvRiIIHe3acP0+QSsW9tYtTXYmonV5RUVHh9v3aNz2LiHC5URjUTNH4MCICg8Fgn6IhhPA+VzkSqlLhh/sZMseDDAHPc0QyRAghhCvSAGklY8eOZfe+fTz73HP8Eh3NHQUFTMrL446CAr6prMQCfGcwMC0/32Wt/Zvz80kxGFgbE0N4E7sSw8V53no3HzRcbXrmTKxGw61BQaxYvpxmzugTQrjBWY7MOn8eE+5lyDQPMwQ8yxHJECGEEE2RMrytKCwsjNmzZ9OtWzfmzZ2LwWDgD3o9d+p0tPPz4wejkTdKSog/d45bgoJI1uvr1dpfX1GBH/Cf9u2Z5Ga1m/WVlSR26UKEmyU6bZuevezhnOAZQUGsqZ2i0a5dO4/eK4Rwn6scSTebedFFhnxeWQnAyMBAtzMEPMsRyRAhhBBNkQZIK9u6dSv333dfzcLMTp3q9RBO0Ol4MjSUd0tLeb2sjHW1DwtQU7Jy0vXXs/HbbxngpGRmQ7Z53s/OmuX2wlHbFIsIF5VxHKk7RUMeHoRoWa5y5MGQEFZWVPBOaWmjDHl21iwMBgOvv/IKuWazWyMUnuaIZIgQQoimSAOkFTVcmOlobnS4nx/PRETwVFgYNxUW8pPVyqYtW0hISKC0tJTh27Yxp7jY6fttzIrC3OJidDodt912m9v36M7miY54OtVLCNE8TeVIuJ8fD4eG8lBICPkWC3eeP89e4Kv//Ifw8HBKSkp4d+nSFssRyRAhhBBNkTUgrciThZn+ajUr2rWjqqqK77//HpVK1WRFLZscs5nphYWkGI18sGyZR5t8RUREkNilC+sNBo++N0+negkhmsfdHFGpVLTXaPhX7T4e69evB5quzGfT3ByRDBFCCNEUaYC0Em8tzGyqotYdBQUkZGWxXVFYuWoVY8aM8eg+3dk8sSHbFI37PJjqJYTwnC/kiGSIEEKIpshGhK2kqKiI/v37syY6mmQPphjYHgaOHDlSb150SUkJ69atY8Xy5aSfOWP/emKXLtw3axbJycmEhoY2616b2jyxLrOiML2wkO2Kwu59+zwabRGXzpc3EZMM8Zyv5IhkiO/w5QwRQvguWQPSSry9MNNWCWfWrFkUFxdTUVGBXq8nIiLiknsQbVM07rv3XqYXFvJhRASxDnpbc8xm5tbuYrxy1Sp5cBCihflKjkiGCCGEcEUaIK2kpRZmqlQq2rVr5/WqMbYpGvPmziUhK4tbg4KYERTUqKSnTqdr1lQvIYTnfClHJEOEEEI4I1OwWomiKIwZPZqhhYV8FhXl9vvuKCjgl+hotv3442WZG92SU73EpfPl6ROSIZ7zxRyRDGnbfDlDhBC+SxogrWjZsmW8sHgxmXFxbtffT8jK4tnnnmP27NmtcIfOKYri9ale4tL58sODZEjz+GqOSIa0Tb6cIUII3yUNkFYkCzOFt/nyw4NkSPNIjghv8uUMEUL4LinD24paYx8PIcSVTXJECCGEr5MRkMtg69atzJs7F4PB4HJh5gfLlsnCTOGSL/deSoZcGskR4Q2+nCFCCN8lDZDLRBZmCm/w5YcHyZBLJzkiLpUvZ4gQwndJA+Qyk4WZ4lL48sODZIj3SI6I5vLlDBFC+K5m7wOicaP6inBP+/btL/ctCB/ly7+HvnzvbZHkiGgO+T0UQlwOzR4BEUIIIYQQQghPSRUsIYQQQgghRKuRBogQQgghhBCi1UgDRAghhBBCCNFqpAEihBBCCCGEaDXSABFCCCGEEEK0GmmACCGEEEIIIVqNNECEEEIIIYQQrUYaIEIIIYQQQohWIw0QIYQQQgghRKv5/wEZ2rEowBHAJAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x800 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mglearn.plots.plot_kmeans_algorithm()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***Método $k$-means***\n",
    "\n",
    "Vamos a hacer uso de [`sklearn.cluster.KMeans`](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) para realizar el $k$-means clustering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***Ejemplo 1.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Murder  Assault  UrbanPop  Rape\n",
       "Alabama       13.2      236        58  21.2\n",
       "Alaska        10.0      263        48  44.5\n",
       "Arizona        8.1      294        80  31.0\n",
       "Arkansas       8.8      190        50  19.5\n",
       "California     9.0      276        91  40.6"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_usarrests = pd.read_csv(url_base + \"USArrests.csv\", index_col=0)\n",
    "df_usarrests.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>1.255179</td>\n",
       "      <td>0.790787</td>\n",
       "      <td>-0.526195</td>\n",
       "      <td>-0.003451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>0.513019</td>\n",
       "      <td>1.118060</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>2.509424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>0.072361</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>0.234708</td>\n",
       "      <td>0.233212</td>\n",
       "      <td>-1.084492</td>\n",
       "      <td>-0.186794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>0.281093</td>\n",
       "      <td>1.275635</td>\n",
       "      <td>1.776781</td>\n",
       "      <td>2.088814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>0.025976</td>\n",
       "      <td>0.402909</td>\n",
       "      <td>0.869548</td>\n",
       "      <td>1.883901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>-1.040880</td>\n",
       "      <td>-0.736484</td>\n",
       "      <td>0.799761</td>\n",
       "      <td>-1.092723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>-0.437875</td>\n",
       "      <td>0.815030</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.585834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>1.765415</td>\n",
       "      <td>1.990786</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.150530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>2.229265</td>\n",
       "      <td>0.487757</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>0.492653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>-0.577030</td>\n",
       "      <td>-1.512241</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>-0.111300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>-1.203228</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>-0.805344</td>\n",
       "      <td>-0.758392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>0.605789</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>0.298525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>-0.136372</td>\n",
       "      <td>-0.700121</td>\n",
       "      <td>-0.037685</td>\n",
       "      <td>-0.025021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>-1.295998</td>\n",
       "      <td>-1.391029</td>\n",
       "      <td>-0.595982</td>\n",
       "      <td>-1.071153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>-0.414682</td>\n",
       "      <td>-0.675878</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.348567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>0.443441</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.944918</td>\n",
       "      <td>-0.531910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>1.765415</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>0.104398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>-1.319191</td>\n",
       "      <td>-1.063757</td>\n",
       "      <td>-1.014705</td>\n",
       "      <td>-1.448624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>0.814521</td>\n",
       "      <td>1.566544</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.708350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>-0.785763</td>\n",
       "      <td>-0.263757</td>\n",
       "      <td>1.358058</td>\n",
       "      <td>-0.531910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>1.000062</td>\n",
       "      <td>1.021090</td>\n",
       "      <td>0.590399</td>\n",
       "      <td>1.495646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>-1.180036</td>\n",
       "      <td>-1.197090</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.682898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>1.927762</td>\n",
       "      <td>1.069575</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-0.445631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>0.281093</td>\n",
       "      <td>0.087757</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>0.751490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>-0.414682</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.875131</td>\n",
       "      <td>-0.521125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>-0.808955</td>\n",
       "      <td>-0.833454</td>\n",
       "      <td>-0.247047</td>\n",
       "      <td>-0.510340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>1.023254</td>\n",
       "      <td>0.984726</td>\n",
       "      <td>1.078909</td>\n",
       "      <td>2.671197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>-1.319191</td>\n",
       "      <td>-1.378908</td>\n",
       "      <td>-0.665769</td>\n",
       "      <td>-1.265281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>-0.089987</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>1.637207</td>\n",
       "      <td>-0.262288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>0.837714</td>\n",
       "      <td>1.384726</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>1.172100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>0.768136</td>\n",
       "      <td>1.008969</td>\n",
       "      <td>1.427845</td>\n",
       "      <td>0.525008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>1.208794</td>\n",
       "      <td>2.015028</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.553480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>-1.620693</td>\n",
       "      <td>-1.524362</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-1.502548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>-0.113180</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>0.660186</td>\n",
       "      <td>0.018119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>-0.275527</td>\n",
       "      <td>-0.239515</td>\n",
       "      <td>0.171676</td>\n",
       "      <td>-0.132870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>-0.669800</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.870123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>-0.345105</td>\n",
       "      <td>-0.784969</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.682898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>-1.017688</td>\n",
       "      <td>0.039273</td>\n",
       "      <td>1.497632</td>\n",
       "      <td>-1.394700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>1.533490</td>\n",
       "      <td>1.311999</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>0.136752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>-0.924918</td>\n",
       "      <td>-1.027393</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.909380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>1.255179</td>\n",
       "      <td>0.208970</td>\n",
       "      <td>-0.456408</td>\n",
       "      <td>0.611287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1.139217</td>\n",
       "      <td>0.366545</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.460298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>-1.064073</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.179892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>-1.295998</td>\n",
       "      <td>-1.487999</td>\n",
       "      <td>-2.340661</td>\n",
       "      <td>-1.081938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>0.165131</td>\n",
       "      <td>-0.178909</td>\n",
       "      <td>-0.177259</td>\n",
       "      <td>-0.057376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>-0.878533</td>\n",
       "      <td>-0.312242</td>\n",
       "      <td>0.520612</td>\n",
       "      <td>0.535792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>-0.484260</td>\n",
       "      <td>-1.087999</td>\n",
       "      <td>-1.852151</td>\n",
       "      <td>-1.286851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>-1.203228</td>\n",
       "      <td>-1.427393</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-1.125078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>-0.229142</td>\n",
       "      <td>-0.118303</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>-0.607404</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       0         1         2         3\n",
       "Alabama         1.255179  0.790787 -0.526195 -0.003451\n",
       "Alaska          0.513019  1.118060 -1.224067  2.509424\n",
       "Arizona         0.072361  1.493817  1.009122  1.053466\n",
       "Arkansas        0.234708  0.233212 -1.084492 -0.186794\n",
       "California      0.281093  1.275635  1.776781  2.088814\n",
       "Colorado        0.025976  0.402909  0.869548  1.883901\n",
       "Connecticut    -1.040880 -0.736484  0.799761 -1.092723\n",
       "Delaware       -0.437875  0.815030  0.450825 -0.585834\n",
       "Florida         1.765415  1.990786  1.009122  1.150530\n",
       "Georgia         2.229265  0.487757 -0.386621  0.492653\n",
       "Hawaii         -0.577030 -1.512241  1.218484 -0.111300\n",
       "Idaho          -1.203228 -0.615272 -0.805344 -0.758392\n",
       "Illinois        0.605789  0.948363  1.218484  0.298525\n",
       "Indiana        -0.136372 -0.700121 -0.037685 -0.025021\n",
       "Iowa           -1.295998 -1.391029 -0.595982 -1.071153\n",
       "Kansas         -0.414682 -0.675878  0.032102 -0.348567\n",
       "Kentucky        0.443441 -0.748605 -0.944918 -0.531910\n",
       "Louisiana       1.765415  0.948363  0.032102  0.104398\n",
       "Maine          -1.319191 -1.063757 -1.014705 -1.448624\n",
       "Maryland        0.814521  1.566544  0.101889  0.708350\n",
       "Massachusetts  -0.785763 -0.263757  1.358058 -0.531910\n",
       "Michigan        1.000062  1.021090  0.590399  1.495646\n",
       "Minnesota      -1.180036 -1.197090  0.032102 -0.682898\n",
       "Mississippi     1.927762  1.069575 -1.503215 -0.445631\n",
       "Missouri        0.281093  0.087757  0.311251  0.751490\n",
       "Montana        -0.414682 -0.748605 -0.875131 -0.521125\n",
       "Nebraska       -0.808955 -0.833454 -0.247047 -0.510340\n",
       "Nevada          1.023254  0.984726  1.078909  2.671197\n",
       "New Hampshire  -1.319191 -1.378908 -0.665769 -1.265281\n",
       "New Jersey     -0.089987 -0.142545  1.637207 -0.262288\n",
       "New Mexico      0.837714  1.384726  0.311251  1.172100\n",
       "New York        0.768136  1.008969  1.427845  0.525008\n",
       "North Carolina  1.208794  2.015028 -1.433428 -0.553480\n",
       "North Dakota   -1.620693 -1.524362 -1.503215 -1.502548\n",
       "Ohio           -0.113180 -0.615272  0.660186  0.018119\n",
       "Oklahoma       -0.275527 -0.239515  0.171676 -0.132870\n",
       "Oregon         -0.669800 -0.142545  0.101889  0.870123\n",
       "Pennsylvania   -0.345105 -0.784969  0.450825 -0.682898\n",
       "Rhode Island   -1.017688  0.039273  1.497632 -1.394700\n",
       "South Carolina  1.533490  1.311999 -1.224067  0.136752\n",
       "South Dakota   -0.924918 -1.027393 -1.433428 -0.909380\n",
       "Tennessee       1.255179  0.208970 -0.456408  0.611287\n",
       "Texas           1.139217  0.366545  1.009122  0.460298\n",
       "Utah           -1.064073 -0.615272  1.009122  0.179892\n",
       "Vermont        -1.295998 -1.487999 -2.340661 -1.081938\n",
       "Virginia        0.165131 -0.178909 -0.177259 -0.057376\n",
       "Washington     -0.878533 -0.312242  0.520612  0.535792\n",
       "West Virginia  -0.484260 -1.087999 -1.852151 -1.286851\n",
       "Wisconsin      -1.203228 -1.427393  0.032102 -1.125078\n",
       "Wyoming        -0.229142 -0.118303 -0.386621 -0.607404"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Escalamos la información.\n",
    "scaled_data = StandardScaler().fit_transform(df_usarrests)\n",
    "pd.DataFrame(scaled_data, index=df_usarrests.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=2, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=2, random_state=0)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=2, random_state=0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "kmeans = KMeans(\n",
    "    n_clusters=n,       # Número de clusters\n",
    "    random_state=0      # Semilla aleatoria.\n",
    ")                                  \n",
    "\n",
    "kmeans.fit(scaled_data) # Ajustamos el modelo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "104.96163315756873\n",
      "[[ 1.01513667  1.02412028  0.19959126  0.85556386]\n",
      " [-0.67675778 -0.68274685 -0.13306084 -0.57037591]]\n"
     ]
    }
   ],
   "source": [
    "# Atributos.\n",
    "print(kmeans.inertia_)\n",
    "print(kmeans.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>centroide_cluster_0</th>\n",
       "      <td>1.015137</td>\n",
       "      <td>1.024120</td>\n",
       "      <td>0.199591</td>\n",
       "      <td>0.855564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>centroide_cluster_1</th>\n",
       "      <td>-0.676758</td>\n",
       "      <td>-0.682747</td>\n",
       "      <td>-0.133061</td>\n",
       "      <td>-0.570376</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       Murder   Assault  UrbanPop      Rape\n",
       "centroide_cluster_0  1.015137  1.024120  0.199591  0.855564\n",
       "centroide_cluster_1 -0.676758 -0.682747 -0.133061 -0.570376"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centroides = pd.DataFrame(kmeans.cluster_centers_, columns=df_usarrests.columns, index=[f\"centroide_cluster_{i}\" for i in range(n)])\n",
    "centroides"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot centroides.\n",
    "temp = centroides.iloc[0:4,0:5]\n",
    "temp.index = [\"cluster0\",\"cluster1\"]\n",
    "X_axis, a = np.arange(len(temp.columns)), np.flip(np.arange(-0.1,0.1,0.1))\n",
    "##\n",
    "for i,index in enumerate(temp.index):\n",
    "  plt.bar(X_axis -1*a[i], temp.loc[index],width=0.1, label = index)\n",
    "plt.xticks(X_axis,temp.T.index)\n",
    "plt.xlabel(\"\\nFeatures\",)\n",
    "plt.ylabel(\" \",)\n",
    "plt.title(\"Plot centroides\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1\n",
      " 1 1 0 1 0 0 1 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "# Cluster de cada instancia\n",
    "print(kmeans.labels_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>7.9</td>\n",
       "      <td>204</td>\n",
       "      <td>78</td>\n",
       "      <td>38.7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>3.3</td>\n",
       "      <td>110</td>\n",
       "      <td>77</td>\n",
       "      <td>11.1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>5.9</td>\n",
       "      <td>238</td>\n",
       "      <td>72</td>\n",
       "      <td>15.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>15.4</td>\n",
       "      <td>335</td>\n",
       "      <td>80</td>\n",
       "      <td>31.9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>17.4</td>\n",
       "      <td>211</td>\n",
       "      <td>60</td>\n",
       "      <td>25.8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>5.3</td>\n",
       "      <td>46</td>\n",
       "      <td>83</td>\n",
       "      <td>20.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>2.6</td>\n",
       "      <td>120</td>\n",
       "      <td>54</td>\n",
       "      <td>14.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>10.4</td>\n",
       "      <td>249</td>\n",
       "      <td>83</td>\n",
       "      <td>24.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>7.2</td>\n",
       "      <td>113</td>\n",
       "      <td>65</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>2.2</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>11.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>6.0</td>\n",
       "      <td>115</td>\n",
       "      <td>66</td>\n",
       "      <td>18.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>9.7</td>\n",
       "      <td>109</td>\n",
       "      <td>52</td>\n",
       "      <td>16.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>15.4</td>\n",
       "      <td>249</td>\n",
       "      <td>66</td>\n",
       "      <td>22.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>2.1</td>\n",
       "      <td>83</td>\n",
       "      <td>51</td>\n",
       "      <td>7.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>11.3</td>\n",
       "      <td>300</td>\n",
       "      <td>67</td>\n",
       "      <td>27.8</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>4.4</td>\n",
       "      <td>149</td>\n",
       "      <td>85</td>\n",
       "      <td>16.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>12.1</td>\n",
       "      <td>255</td>\n",
       "      <td>74</td>\n",
       "      <td>35.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>2.7</td>\n",
       "      <td>72</td>\n",
       "      <td>66</td>\n",
       "      <td>14.9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>16.1</td>\n",
       "      <td>259</td>\n",
       "      <td>44</td>\n",
       "      <td>17.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>9.0</td>\n",
       "      <td>178</td>\n",
       "      <td>70</td>\n",
       "      <td>28.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>6.0</td>\n",
       "      <td>109</td>\n",
       "      <td>53</td>\n",
       "      <td>16.4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>4.3</td>\n",
       "      <td>102</td>\n",
       "      <td>62</td>\n",
       "      <td>16.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>12.2</td>\n",
       "      <td>252</td>\n",
       "      <td>81</td>\n",
       "      <td>46.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>2.1</td>\n",
       "      <td>57</td>\n",
       "      <td>56</td>\n",
       "      <td>9.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>7.4</td>\n",
       "      <td>159</td>\n",
       "      <td>89</td>\n",
       "      <td>18.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>11.4</td>\n",
       "      <td>285</td>\n",
       "      <td>70</td>\n",
       "      <td>32.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>11.1</td>\n",
       "      <td>254</td>\n",
       "      <td>86</td>\n",
       "      <td>26.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>13.0</td>\n",
       "      <td>337</td>\n",
       "      <td>45</td>\n",
       "      <td>16.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>0.8</td>\n",
       "      <td>45</td>\n",
       "      <td>44</td>\n",
       "      <td>7.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>7.3</td>\n",
       "      <td>120</td>\n",
       "      <td>75</td>\n",
       "      <td>21.4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>6.6</td>\n",
       "      <td>151</td>\n",
       "      <td>68</td>\n",
       "      <td>20.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>4.9</td>\n",
       "      <td>159</td>\n",
       "      <td>67</td>\n",
       "      <td>29.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>6.3</td>\n",
       "      <td>106</td>\n",
       "      <td>72</td>\n",
       "      <td>14.9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>3.4</td>\n",
       "      <td>174</td>\n",
       "      <td>87</td>\n",
       "      <td>8.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>14.4</td>\n",
       "      <td>279</td>\n",
       "      <td>48</td>\n",
       "      <td>22.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>3.8</td>\n",
       "      <td>86</td>\n",
       "      <td>45</td>\n",
       "      <td>12.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>13.2</td>\n",
       "      <td>188</td>\n",
       "      <td>59</td>\n",
       "      <td>26.9</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>12.7</td>\n",
       "      <td>201</td>\n",
       "      <td>80</td>\n",
       "      <td>25.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>3.2</td>\n",
       "      <td>120</td>\n",
       "      <td>80</td>\n",
       "      <td>22.9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>2.2</td>\n",
       "      <td>48</td>\n",
       "      <td>32</td>\n",
       "      <td>11.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>8.5</td>\n",
       "      <td>156</td>\n",
       "      <td>63</td>\n",
       "      <td>20.7</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>4.0</td>\n",
       "      <td>145</td>\n",
       "      <td>73</td>\n",
       "      <td>26.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>5.7</td>\n",
       "      <td>81</td>\n",
       "      <td>39</td>\n",
       "      <td>9.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>2.6</td>\n",
       "      <td>53</td>\n",
       "      <td>66</td>\n",
       "      <td>10.8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>6.8</td>\n",
       "      <td>161</td>\n",
       "      <td>60</td>\n",
       "      <td>15.6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Murder  Assault  UrbanPop  Rape  cluster\n",
       "Alabama           13.2      236        58  21.2        0\n",
       "Alaska            10.0      263        48  44.5        0\n",
       "Arizona            8.1      294        80  31.0        0\n",
       "Arkansas           8.8      190        50  19.5        1\n",
       "California         9.0      276        91  40.6        0\n",
       "Colorado           7.9      204        78  38.7        0\n",
       "Connecticut        3.3      110        77  11.1        1\n",
       "Delaware           5.9      238        72  15.8        1\n",
       "Florida           15.4      335        80  31.9        0\n",
       "Georgia           17.4      211        60  25.8        0\n",
       "Hawaii             5.3       46        83  20.2        1\n",
       "Idaho              2.6      120        54  14.2        1\n",
       "Illinois          10.4      249        83  24.0        0\n",
       "Indiana            7.2      113        65  21.0        1\n",
       "Iowa               2.2       56        57  11.3        1\n",
       "Kansas             6.0      115        66  18.0        1\n",
       "Kentucky           9.7      109        52  16.3        1\n",
       "Louisiana         15.4      249        66  22.2        0\n",
       "Maine              2.1       83        51   7.8        1\n",
       "Maryland          11.3      300        67  27.8        0\n",
       "Massachusetts      4.4      149        85  16.3        1\n",
       "Michigan          12.1      255        74  35.1        0\n",
       "Minnesota          2.7       72        66  14.9        1\n",
       "Mississippi       16.1      259        44  17.1        0\n",
       "Missouri           9.0      178        70  28.2        0\n",
       "Montana            6.0      109        53  16.4        1\n",
       "Nebraska           4.3      102        62  16.5        1\n",
       "Nevada            12.2      252        81  46.0        0\n",
       "New Hampshire      2.1       57        56   9.5        1\n",
       "New Jersey         7.4      159        89  18.8        1\n",
       "New Mexico        11.4      285        70  32.1        0\n",
       "New York          11.1      254        86  26.1        0\n",
       "North Carolina    13.0      337        45  16.1        0\n",
       "North Dakota       0.8       45        44   7.3        1\n",
       "Ohio               7.3      120        75  21.4        1\n",
       "Oklahoma           6.6      151        68  20.0        1\n",
       "Oregon             4.9      159        67  29.3        1\n",
       "Pennsylvania       6.3      106        72  14.9        1\n",
       "Rhode Island       3.4      174        87   8.3        1\n",
       "South Carolina    14.4      279        48  22.5        0\n",
       "South Dakota       3.8       86        45  12.8        1\n",
       "Tennessee         13.2      188        59  26.9        0\n",
       "Texas             12.7      201        80  25.5        0\n",
       "Utah               3.2      120        80  22.9        1\n",
       "Vermont            2.2       48        32  11.2        1\n",
       "Virginia           8.5      156        63  20.7        1\n",
       "Washington         4.0      145        73  26.2        1\n",
       "West Virginia      5.7       81        39   9.3        1\n",
       "Wisconsin          2.6       53        66  10.8        1\n",
       "Wyoming            6.8      161        60  15.6        1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cluster = df_usarrests.copy()\n",
    "df_cluster[\"cluster\"] = kmeans.labels_\n",
    "df_cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.165</td>\n",
       "      <td>255.250000</td>\n",
       "      <td>68.400000</td>\n",
       "      <td>29.165000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.870</td>\n",
       "      <td>114.433333</td>\n",
       "      <td>63.633333</td>\n",
       "      <td>15.943333</td>\n",
       "    </tr>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Murder     Assault   UrbanPop       Rape\n",
       "cluster                                          \n",
       "0        12.165  255.250000  68.400000  29.165000\n",
       "1         4.870  114.433333  63.633333  15.943333"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_cluster.groupby(by=[\"cluster\"]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=4, random_state=0)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Con 4 clusters\n",
    "n = 4\n",
    "kmeans1 = KMeans(\n",
    "    n_clusters=n,\n",
    "    random_state=0\n",
    ")\n",
    "\n",
    "kmeans1.fit(scaled_data)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "58.241584331343226\n",
      "[[ 0.75759426  1.13128272  0.94567938  1.22798509]\n",
      " [-0.44878894 -0.35858791  0.56576856 -0.20455729]\n",
      " [-0.97130281 -1.11783581 -0.93954982 -0.97657842]\n",
      " [ 1.32475684  0.90930557 -0.86737678  0.29612861]]\n"
     ]
    }
   ],
   "source": [
    "print(kmeans1.inertia_)\n",
    "print(kmeans1.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>new_instance_35</th>\n",
       "      <td>-0.113180</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>0.660186</td>\n",
       "      <td>0.018119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>new_instance_22</th>\n",
       "      <td>1.000062</td>\n",
       "      <td>1.021090</td>\n",
       "      <td>0.590399</td>\n",
       "      <td>1.495646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>new_instance_3</th>\n",
       "      <td>0.072361</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>new_instance_24</th>\n",
       "      <td>1.927762</td>\n",
       "      <td>1.069575</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-0.445631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>new_instance_13</th>\n",
       "      <td>0.605789</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>0.298525</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        0         1         2         3\n",
       "new_instance_35 -0.113180 -0.615272  0.660186  0.018119\n",
       "new_instance_22  1.000062  1.021090  0.590399  1.495646\n",
       "new_instance_3   0.072361  1.493817  1.009122  1.053466\n",
       "new_instance_24  1.927762  1.069575 -1.503215 -0.445631\n",
       "new_instance_13  0.605789  0.948363  1.218484  0.298525"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 0], dtype=int32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Metodo predict en K-means\n",
    "df_to_predict = pd.DataFrame(scaled_data, index=[f\"new_instance_{i+1}\" for i in range(len(scaled_data))])\n",
    "sample = df_to_predict.sample(5)\n",
    "display(sample)\n",
    "kmeans.predict(sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>distance_cluster_0</th>\n",
       "      <th>distance_cluster_1</th>\n",
       "      <th>assign_cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>1.173345</td>\n",
       "      <td>2.525795</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>2.241206</td>\n",
       "      <td>3.915857</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>1.343111</td>\n",
       "      <td>3.039746</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>1.992482</td>\n",
       "      <td>1.649881</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>2.147210</td>\n",
       "      <td>3.933386</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>1.694303</td>\n",
       "      <td>2.949777</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>3.388652</td>\n",
       "      <td>1.130697</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>2.072609</td>\n",
       "      <td>1.625288</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>1.496565</td>\n",
       "      <td>4.168703</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>1.495708</td>\n",
       "      <td>3.318037</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>3.307732</td>\n",
       "      <td>1.653913</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>3.350149</td>\n",
       "      <td>0.876948</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>1.233588</td>\n",
       "      <td>2.624330</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>2.265107</td>\n",
       "      <td>0.773839</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>3.939475</td>\n",
       "      <td>1.161980</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>2.532264</td>\n",
       "      <td>0.381063</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>2.589281</td>\n",
       "      <td>1.385559</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>1.077478</td>\n",
       "      <td>3.017834</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>4.073342</td>\n",
       "      <td>1.451380</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>0.604721</td>\n",
       "      <td>2.995591</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>2.858145</td>\n",
       "      <td>1.553174</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>0.750115</td>\n",
       "      <td>3.241392</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>3.485322</td>\n",
       "      <td>0.746845</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>2.329723</td>\n",
       "      <td>3.427396</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>1.199539</td>\n",
       "      <td>1.859004</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>2.870059</td>\n",
       "      <td>0.791274</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>2.973730</td>\n",
       "      <td>0.238298</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>2.017757</td>\n",
       "      <td>4.200854</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>4.058382</td>\n",
       "      <td>1.289974</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>2.428732</td>\n",
       "      <td>1.965930</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>0.523620</td>\n",
       "      <td>3.130767</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>1.295806</td>\n",
       "      <td>2.930173</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>2.381503</td>\n",
       "      <td>3.539002</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>4.680022</td>\n",
       "      <td>2.084610</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>2.207752</td>\n",
       "      <td>1.139184</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>2.059215</td>\n",
       "      <td>0.801072</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>2.051799</td>\n",
       "      <td>1.556312</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>2.748280</td>\n",
       "      <td>0.688496</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>3.442513</td>\n",
       "      <td>1.994045</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>1.701486</td>\n",
       "      <td>3.248773</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>3.708679</td>\n",
       "      <td>1.409342</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>1.100953</td>\n",
       "      <td>2.455284</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1.122219</td>\n",
       "      <td>2.601086</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>2.850016</td>\n",
       "      <td>1.421988</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>4.675348</td>\n",
       "      <td>2.483361</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>1.773489</td>\n",
       "      <td>1.108040</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>2.361600</td>\n",
       "      <td>1.352362</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>3.938125</td>\n",
       "      <td>1.915696</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>3.857726</td>\n",
       "      <td>1.080112</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>2.310255</td>\n",
       "      <td>0.764605</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                distance_cluster_0  distance_cluster_1 assign_cluster\n",
       "Alabama                   1.173345            2.525795              0\n",
       "Alaska                    2.241206            3.915857              0\n",
       "Arizona                   1.343111            3.039746              0\n",
       "Arkansas                  1.992482            1.649881              1\n",
       "California                2.147210            3.933386              0\n",
       "Colorado                  1.694303            2.949777              0\n",
       "Connecticut               3.388652            1.130697              1\n",
       "Delaware                  2.072609            1.625288              1\n",
       "Florida                   1.496565            4.168703              0\n",
       "Georgia                   1.495708            3.318037              0\n",
       "Hawaii                    3.307732            1.653913              1\n",
       "Idaho                     3.350149            0.876948              1\n",
       "Illinois                  1.233588            2.624330              0\n",
       "Indiana                   2.265107            0.773839              1\n",
       "Iowa                      3.939475            1.161980              1\n",
       "Kansas                    2.532264            0.381063              1\n",
       "Kentucky                  2.589281            1.385559              1\n",
       "Louisiana                 1.077478            3.017834              0\n",
       "Maine                     4.073342            1.451380              1\n",
       "Maryland                  0.604721            2.995591              0\n",
       "Massachusetts             2.858145            1.553174              1\n",
       "Michigan                  0.750115            3.241392              0\n",
       "Minnesota                 3.485322            0.746845              1\n",
       "Mississippi               2.329723            3.427396              0\n",
       "Missouri                  1.199539            1.859004              0\n",
       "Montana                   2.870059            0.791274              1\n",
       "Nebraska                  2.973730            0.238298              1\n",
       "Nevada                    2.017757            4.200854              0\n",
       "New Hampshire             4.058382            1.289974              1\n",
       "New Jersey                2.428732            1.965930              1\n",
       "New Mexico                0.523620            3.130767              0\n",
       "New York                  1.295806            2.930173              0\n",
       "North Carolina            2.381503            3.539002              0\n",
       "North Dakota              4.680022            2.084610              1\n",
       "Ohio                      2.207752            1.139184              1\n",
       "Oklahoma                  2.059215            0.801072              1\n",
       "Oregon                    2.051799            1.556312              1\n",
       "Pennsylvania              2.748280            0.688496              1\n",
       "Rhode Island              3.442513            1.994045              1\n",
       "South Carolina            1.701486            3.248773              0\n",
       "South Dakota              3.708679            1.409342              1\n",
       "Tennessee                 1.100953            2.455284              0\n",
       "Texas                     1.122219            2.601086              0\n",
       "Utah                      2.850016            1.421988              1\n",
       "Vermont                   4.675348            2.483361              1\n",
       "Virginia                  1.773489            1.108040              1\n",
       "Washington                2.361600            1.352362              1\n",
       "West Virginia             3.938125            1.915696              1\n",
       "Wisconsin                 3.857726            1.080112              1\n",
       "Wyoming                   2.310255            0.764605              1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Distancia de las instancia al centroide de cada cluster.\n",
    "temp = pd.DataFrame(\n",
    "    kmeans.transform(scaled_data),\n",
    "    columns=[f\"distance_cluster_{i}\" for i in range(kmeans.n_clusters)],\n",
    "    index=df_usarrests.index\n",
    ")\n",
    "temp[\"assign_cluster\"] = kmeans.predict(scaled_data)\n",
    "temp[\"assign_cluster\"] = temp[\"assign_cluster\"].astype(\"string\")\n",
    "temp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***¿Cuántos cluster debemos seleccionar?***\n",
    "\n",
    "Determinar el número óptimo de clusters en un Dataset es un problema fundamental en el agrupamiento. En $k$-means se requiere especificar de antemano el número de clústeres $k$ que se generarán.\n",
    "\n",
    "Desafortunadamente no hay una respuesta definitiva a esta pregunta. El número óptimo de clusters es algo subjetivo y depende del método utilizado para medir\n",
    "similitudes y los parámetros utilizados para la partición.\n",
    "\n",
    "Una solución simple y popular consiste en inspeccionar el dendrograma producido por el agrupamiento jerárquico para ver si sugiere un número particular de grupos, de igual forma este enfoque también es subjetivo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos a describir diferentes métodos para determinar el número óptimo de clusters para $k$-means. Estos métodos incluyen métodos directos y métodos de prueba estadísticos:\n",
    "\n",
    "1. Métodos directos: consiste en optimizar un criterio, como el ***WCSS*** o la silueta media. Los métodos se denominan ***elbow method*** y ***silhouette***, respectivamente.\n",
    "\n",
    "2. Métodos estadísticos de contraste: consiste en comparar la evidencia contra la hipótesis nula. Un ejemplo es la estadística de [***GAP***]()."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ***Método del codo.***\n",
    "\n",
    "\n",
    "La idea básica detrás de los método $k$-means, es definir clusters tales que ***WCSS*** se minimiza. Recordemos que ***WCSS*** mide la compacidad del agrupamiento y queremos que sea lo más pequeño posible.\n",
    "\n",
    "El método codo analiza el ***WCSS*** como una función del número de clusters. Se debe elegir una cantidad de clusers de tal forma que agregar otro cluster no mejore mucho el valor ***WCSS***.\n",
    "\n",
    "El número óptimo de clústeres se puede definir de la siguiente manera:\n",
    "\n",
    "1. Calcule el algoritmo de clustering $k$-means para diferentes valores de $k$. Puede variar $k$ de 1 a 10 grupos.\n",
    "\n",
    "2. Para cada $k$, calcule ***WCSS***.\n",
    "\n",
    "3. Trazar la curva de ***WCSS*** según el número de clusters $k$.\n",
    "\n",
    "4. La ubicación de una curva (codo) en el plot generalmente se considera como un indicador del número adecuado de clusters.\n",
    "\n",
    "Tenga en cuenta que el método del codo a veces es ambiguo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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   "source": [
    "***Según lo observado, ¿cuántos cluster usted considera que se deben formar?***"
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   "source": [
    "### ***Coeficiente de silhouette***\n",
    "\n",
    "\n",
    "El coeficiente de silueta mide qué tan bien se agrupa una observación y estima la ***distancia promedio entre clusters***. El plot de silueta muestra una medida de qué tan cerca está cada punto en un cluster de los puntos en los clusters vecinos.\n",
    "\n",
    "Para cada observación $i$, el ancho de la silueta $s_i$ se calcula de la siguiente manera:\n",
    "\n",
    "1. Para cada observación $i$, calculamos la disimilitud (distancia) promedio $a_i$ entre $i$ y todos los otros puntos del clúster al que pertenezca $i$.\n",
    "\n",
    "2. Para todos los demás clusters $C$, a los que no pertenezca $i$, calcule el promedio de disimilitud $d(i,C)$ de $i$ con todos los puntos de $C$. La menor de estas $d(i,C)$ se define como $b_i = min_C\\  d(i,C)$. El valor de $b_i$ puede verse como la disimilitud promedio entre $i$ y su cluster \"vecino\", es decir, el más cercano al que ***no*** pertenece.\n",
    "\n",
    "3. Finalmente, el ancho de la silueta de la observación $i$ se define mediante la fórmula:\n",
    "$$S_i = \\frac{(b_i - a_i)}{max(a_i, b_i)}$$\n",
    "\n",
    "El ancho de la silueta se puede interpretar de la siguiente manera:\n",
    "\n",
    "- Las observaciones con un $S_i$ grande (casi 1) están muy bien agrupadas.\n",
    "\n",
    "- Un $S_i$ pequeño (alrededor de 0) significa que la observación se encuentra entre dos grupos.\n",
    "\n",
    "- Las observaciones con un $S_i$ negativo probablemente estén ubicadas en el cluster incorrecto."
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   "source": [
    "El algoritmo es similar al método del codo y se puede calcular de la siguiente manera:\n",
    "\n",
    "1. Calcule el algoritmo $k$-means  para diferentes valores de $k$. Por ejemplo, variando $k$ de 1 a 10 grupos.\n",
    "\n",
    "2. Para cada $k$, calcule la silueta promedio de las observaciones.\n",
    "\n",
    "3. Trazar el plot según el número de clusters y la silueta promedio.\n",
    "\n",
    "4. La ubicación del máximo se considera como el número apropiado de clusters."
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   "source": [
    "***El criterio estricto, nos diría que la mejor elección son 2 clusters.***"
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    "### ***GAP Statistic***\n",
    "\n",
    "Este estadístico compara, para diferentes valores de $k$, el ***WCSS*** observado frente al valor esperado acorde a una distribución uniforme de referencia. La estimación del número óptimo de clusters es el valor $k$ con el que se consigue maximizar el estadístico ***GAP***, es decir, encuentra el valor de $k$ con el que se consigue una estructura de clusters lo más alejada posible de una distribución uniforme aleatoria. Este método puede aplicarse a cualquier tipo de clustering.\n",
    "\n",
    "El algoritmo del gap statistic method es el siguiente:\n",
    "\n",
    "1. Hacer clustering de los datos para un rango de valores de $k$ y calcular para cada uno el valor de ***WCSS***.\n",
    "\n",
    "2. Simular $B$ sets de datos de referencia, todos ellos con una distribución aleatoria uniforme. Aplicar clustering a cada uno de los sets con el mismo rango de valores $k$ empleado en los datos originales, calculando en cada caso $W_{kb}$. Se recomienda emplear valores de $B=500$.\n",
    "\n",
    "3. Calcular el estadístico ***GAP*** para cada valor de $k$ como la desviación de la varianza observada ***WCSS*** respecto del valor esperado acorde a la distribución de referencia $W_{kb}$.\n",
    "\n",
    "$$GAP(k)=\\frac{1}{B}\\sum_{b=1}^{B}log(W_{kb})−log(WCSS)$$\n",
    "\n",
    "La estimación de los clústeres óptimos será el valor que maximice la estadística de ***GAP***."
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            "gridwidth": 2,
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            "ticks": "",
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          },
          "ternary": {
           "aaxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           },
           "bgcolor": "white",
           "caxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "#EBF0F8",
           "linecolor": "#EBF0F8",
           "ticks": "",
           "title": {
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           },
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           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "#EBF0F8",
           "linecolor": "#EBF0F8",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "#EBF0F8",
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         }
        },
        "title": {
         "text": "Gap Statistic Method"
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
         ],
         "title": {
          "text": "Number of clusters"
         }
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "title": {
          "text": "Gap Statistic"
         }
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      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gap_statistic(df_usarrests, nrefs=40, max_clusters=10, scaled_data=False, random_state=42)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso el caso el número de clusters a selecionar debe ser de ***4 clusters.***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***Visualización de los cluster.***\n",
    "\n",
    "Vamos a hacer uso de `PCA` para lograr visualizar los cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduccion a 3 dimensiones\n"
     ]
    },
    {
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       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
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       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=2, random_state=42)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=2, random_state=42)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=0.90)\n",
    "pca_transform = pca.fit_transform(scaled_data)\n",
    "print(\"Reduccion a\", pca.n_components_, \"dimensiones\")\n",
    "\n",
    "kmeans = KMeans(n_clusters=2, random_state=42)\n",
    "kmeans.fit(pca_transform)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>0.985566</td>\n",
       "      <td>-1.133392</td>\n",
       "      <td>-0.444269</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>1.950138</td>\n",
       "      <td>-1.073213</td>\n",
       "      <td>2.040003</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>1.763164</td>\n",
       "      <td>0.745957</td>\n",
       "      <td>0.054781</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>-0.141420</td>\n",
       "      <td>-1.119797</td>\n",
       "      <td>0.114574</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>2.523980</td>\n",
       "      <td>1.542934</td>\n",
       "      <td>0.598557</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>1.514563</td>\n",
       "      <td>0.987555</td>\n",
       "      <td>1.095007</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>-1.358647</td>\n",
       "      <td>1.088928</td>\n",
       "      <td>-0.643258</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>0.047709</td>\n",
       "      <td>0.325359</td>\n",
       "      <td>-0.718633</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>3.013042</td>\n",
       "      <td>-0.039229</td>\n",
       "      <td>-0.576829</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>1.639283</td>\n",
       "      <td>-1.278942</td>\n",
       "      <td>-0.342460</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>-0.912657</td>\n",
       "      <td>1.570460</td>\n",
       "      <td>0.050782</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>-1.639800</td>\n",
       "      <td>-0.210973</td>\n",
       "      <td>0.259801</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>1.378911</td>\n",
       "      <td>0.681841</td>\n",
       "      <td>-0.677496</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>-0.505461</td>\n",
       "      <td>0.151563</td>\n",
       "      <td>0.228055</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>-2.253646</td>\n",
       "      <td>0.104054</td>\n",
       "      <td>0.164564</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>-0.796881</td>\n",
       "      <td>0.270165</td>\n",
       "      <td>0.025553</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>-0.750859</td>\n",
       "      <td>-0.958440</td>\n",
       "      <td>-0.028369</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>1.564818</td>\n",
       "      <td>-0.871055</td>\n",
       "      <td>-0.783480</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>-2.396829</td>\n",
       "      <td>-0.376392</td>\n",
       "      <td>-0.065682</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>1.763369</td>\n",
       "      <td>-0.427655</td>\n",
       "      <td>-0.157250</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>-0.486166</td>\n",
       "      <td>1.474496</td>\n",
       "      <td>-0.609497</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>2.108441</td>\n",
       "      <td>0.155397</td>\n",
       "      <td>0.384869</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>-1.692682</td>\n",
       "      <td>0.632261</td>\n",
       "      <td>0.153070</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>0.996494</td>\n",
       "      <td>-2.393796</td>\n",
       "      <td>-0.740808</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>0.696787</td>\n",
       "      <td>0.263355</td>\n",
       "      <td>0.377444</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>-1.185452</td>\n",
       "      <td>-0.536874</td>\n",
       "      <td>0.246889</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>-1.265637</td>\n",
       "      <td>0.193954</td>\n",
       "      <td>0.175574</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>2.874395</td>\n",
       "      <td>0.775600</td>\n",
       "      <td>1.163380</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>-2.383915</td>\n",
       "      <td>0.018082</td>\n",
       "      <td>0.036855</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>0.181566</td>\n",
       "      <td>1.449506</td>\n",
       "      <td>-0.764454</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>1.980024</td>\n",
       "      <td>-0.142849</td>\n",
       "      <td>0.183692</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>1.682577</td>\n",
       "      <td>0.823184</td>\n",
       "      <td>-0.643075</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>1.123379</td>\n",
       "      <td>-2.228003</td>\n",
       "      <td>-0.863572</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>-2.992226</td>\n",
       "      <td>-0.599119</td>\n",
       "      <td>0.301277</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>-0.225965</td>\n",
       "      <td>0.742238</td>\n",
       "      <td>-0.031139</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>-0.311783</td>\n",
       "      <td>0.287854</td>\n",
       "      <td>-0.015310</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>0.059122</td>\n",
       "      <td>0.541411</td>\n",
       "      <td>0.939833</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>-0.888416</td>\n",
       "      <td>0.571100</td>\n",
       "      <td>-0.400629</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>-0.863772</td>\n",
       "      <td>1.491978</td>\n",
       "      <td>-1.369946</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>1.320724</td>\n",
       "      <td>-1.933405</td>\n",
       "      <td>-0.300538</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>-1.987775</td>\n",
       "      <td>-0.823343</td>\n",
       "      <td>0.389293</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>0.999742</td>\n",
       "      <td>-0.860251</td>\n",
       "      <td>0.188083</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>1.355138</td>\n",
       "      <td>0.412481</td>\n",
       "      <td>-0.492069</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>-0.550565</td>\n",
       "      <td>1.471505</td>\n",
       "      <td>0.293728</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>-2.801412</td>\n",
       "      <td>-1.402288</td>\n",
       "      <td>0.841263</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>-0.096335</td>\n",
       "      <td>-0.199735</td>\n",
       "      <td>0.011713</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>-0.216903</td>\n",
       "      <td>0.970124</td>\n",
       "      <td>0.624871</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>-2.108585</td>\n",
       "      <td>-1.424847</td>\n",
       "      <td>0.104775</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>-2.079714</td>\n",
       "      <td>0.611269</td>\n",
       "      <td>-0.138865</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>-0.629427</td>\n",
       "      <td>-0.321013</td>\n",
       "      <td>-0.240659</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     PC1       PC2       PC3  cluster\n",
       "Alabama         0.985566 -1.133392 -0.444269        1\n",
       "Alaska          1.950138 -1.073213  2.040003        1\n",
       "Arizona         1.763164  0.745957  0.054781        1\n",
       "Arkansas       -0.141420 -1.119797  0.114574        0\n",
       "California      2.523980  1.542934  0.598557        1\n",
       "Colorado        1.514563  0.987555  1.095007        1\n",
       "Connecticut    -1.358647  1.088928 -0.643258        0\n",
       "Delaware        0.047709  0.325359 -0.718633        0\n",
       "Florida         3.013042 -0.039229 -0.576829        1\n",
       "Georgia         1.639283 -1.278942 -0.342460        1\n",
       "Hawaii         -0.912657  1.570460  0.050782        0\n",
       "Idaho          -1.639800 -0.210973  0.259801        0\n",
       "Illinois        1.378911  0.681841 -0.677496        1\n",
       "Indiana        -0.505461  0.151563  0.228055        0\n",
       "Iowa           -2.253646  0.104054  0.164564        0\n",
       "Kansas         -0.796881  0.270165  0.025553        0\n",
       "Kentucky       -0.750859 -0.958440 -0.028369        0\n",
       "Louisiana       1.564818 -0.871055 -0.783480        1\n",
       "Maine          -2.396829 -0.376392 -0.065682        0\n",
       "Maryland        1.763369 -0.427655 -0.157250        1\n",
       "Massachusetts  -0.486166  1.474496 -0.609497        0\n",
       "Michigan        2.108441  0.155397  0.384869        1\n",
       "Minnesota      -1.692682  0.632261  0.153070        0\n",
       "Mississippi     0.996494 -2.393796 -0.740808        1\n",
       "Missouri        0.696787  0.263355  0.377444        1\n",
       "Montana        -1.185452 -0.536874  0.246889        0\n",
       "Nebraska       -1.265637  0.193954  0.175574        0\n",
       "Nevada          2.874395  0.775600  1.163380        1\n",
       "New Hampshire  -2.383915  0.018082  0.036855        0\n",
       "New Jersey      0.181566  1.449506 -0.764454        0\n",
       "New Mexico      1.980024 -0.142849  0.183692        1\n",
       "New York        1.682577  0.823184 -0.643075        1\n",
       "North Carolina  1.123379 -2.228003 -0.863572        1\n",
       "North Dakota   -2.992226 -0.599119  0.301277        0\n",
       "Ohio           -0.225965  0.742238 -0.031139        0\n",
       "Oklahoma       -0.311783  0.287854 -0.015310        0\n",
       "Oregon          0.059122  0.541411  0.939833        0\n",
       "Pennsylvania   -0.888416  0.571100 -0.400629        0\n",
       "Rhode Island   -0.863772  1.491978 -1.369946        0\n",
       "South Carolina  1.320724 -1.933405 -0.300538        1\n",
       "South Dakota   -1.987775 -0.823343  0.389293        0\n",
       "Tennessee       0.999742 -0.860251  0.188083        1\n",
       "Texas           1.355138  0.412481 -0.492069        1\n",
       "Utah           -0.550565  1.471505  0.293728        0\n",
       "Vermont        -2.801412 -1.402288  0.841263        0\n",
       "Virginia       -0.096335 -0.199735  0.011713        0\n",
       "Washington     -0.216903  0.970124  0.624871        0\n",
       "West Virginia  -2.108585 -1.424847  0.104775        0\n",
       "Wisconsin      -2.079714  0.611269 -0.138865        0\n",
       "Wyoming        -0.629427 -0.321013 -0.240659        0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_with_pca = pd.DataFrame(pca_transform, index=df_usarrests.index, columns=[f\"PC{i+1}\" for i in range(pca.n_components_)])\n",
    "df_with_pca[\"cluster\"] = kmeans.labels_\n",
    "df_with_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
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          "scene": {
           "xaxis": {
            "backgroundcolor": "white",
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            "gridwidth": 2,
            "linecolor": "#EBF0F8",
            "showbackground": true,
            "ticks": "",
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           "yaxis": {
            "backgroundcolor": "white",
            "gridcolor": "#DFE8F3",
            "gridwidth": 2,
            "linecolor": "#EBF0F8",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "#EBF0F8"
           },
           "zaxis": {
            "backgroundcolor": "white",
            "gridcolor": "#DFE8F3",
            "gridwidth": 2,
            "linecolor": "#EBF0F8",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "#EBF0F8"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           },
           "bgcolor": "white",
           "caxis": {
            "gridcolor": "#DFE8F3",
            "linecolor": "#A2B1C6",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "#EBF0F8",
           "linecolor": "#EBF0F8",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "#EBF0F8",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "#EBF0F8",
           "linecolor": "#EBF0F8",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "#EBF0F8",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "PCA-CLUSTER Biplot."
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
         ],
         "range": [
          -3.342225615017864,
          3.363042270287223
         ],
         "title": {
          "text": "Dim 1 (62.01%)"
         }
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "range": [
          -2.7437959866443897,
          1.9204600120431201
         ],
         "title": {
          "text": "Dim 2 (24.74%)"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot con 2 clusters.\n",
    "cluster_biplot(pca, df_usarrests, kmeans.labels_, size_text=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style>#sk-container-id-4 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-4 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-4 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-4 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-4 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-4 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-4 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-4 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-4 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-4 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-4 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=4, random_state=0)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=0)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Consideremos 4 clusters.\n",
    "kmeans1 = KMeans(n_clusters=4,random_state=0).fit(pca_transform); kmeans1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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         "text": "PCA-CLUSTER Biplot."
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          0,
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         "range": [
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     "metadata": {},
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   ],
   "source": [
    "# Plot con 4 clusters.\n",
    "cluster_biplot(pca, df_usarrests, kmeans1.labels_, size_text=6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Murder  Assault  UrbanPop  Rape cluster\n",
       "Alabama       13.2      236        58  21.2       1\n",
       "Alaska        10.0      263        48  44.5       1\n",
       "Arizona        8.1      294        80  31.0       1\n",
       "Arkansas       8.8      190        50  19.5       0\n",
       "California     9.0      276        91  40.6       1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Caso 2 clusters\n",
    "df_clusters2 = df_usarrests.copy()\n",
    "df_clusters2[\"cluster\"] = kmeans.labels_\n",
    "df_clusters2[\"cluster\"] = df_clusters2[\"cluster\"].astype(\"category\")\n",
    "df_clusters2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Box-plots\n",
    "fig, axes = plt.subplots(2,2, sharex=True)\n",
    "\n",
    "sns.boxplot(data=df_clusters2, x = \"cluster\", y = \"Murder\", ax=axes[0,0])\n",
    "sns.boxplot(data=df_clusters2, x = \"cluster\", y = \"Assault\", ax=axes[0,1])\n",
    "sns.boxplot(data=df_clusters2, x = \"cluster\", y = \"UrbanPop\", ax=axes[1,0])\n",
    "sns.boxplot(data=df_clusters2, x = \"cluster\", y = \"Rape\", ax=axes[1,1])\n",
    "fig.suptitle(\"Boxplot para features con 2 Clusters\", fontsize=14, fontweight=\"bold\",)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Comentarios:***\n",
    "\n",
    "1. El cluster 1 tiene una alta tasa delictiva y predomina la población urbana.\n",
    "\n",
    "2. El cluster 0 tiene tasas bajas de delitos y una menor tasa que el cluster 1 de población urbana.\n",
    "\n",
    "Note que la solución en este caso es bastante simple, pues solo está teniendo en consideración las tasas de crimenes altos con \"población urbana\" y tasa de crimenes bajos con \"población rural\". Esta solución parece ser buena, pues logra identificar los estados que tienen alto y bajo crimen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-5 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-5 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-5 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-5 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-5 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-5 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;KMeans<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.5/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=4, random_state=0)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 4\n",
    "kmeans = KMeans(n_clusters=n,                  # Número de clusters\n",
    "                random_state=0)                # Semilla aleatoria.\n",
    "kmeans.fit(pca_transform)                        # Ajustamos el modelo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Murder  Assault  UrbanPop  Rape  cluster\n",
       "Alabama       13.2      236        58  21.2        3\n",
       "Alaska        10.0      263        48  44.5        0\n",
       "Arizona        8.1      294        80  31.0        0\n",
       "Arkansas       8.8      190        50  19.5        3\n",
       "California     9.0      276        91  40.6        0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Caso 4 clusters\n",
    "df_clusters4 = df_usarrests.copy()\n",
    "df_clusters4[\"cluster\"] = kmeans.labels_\n",
    "df_clusters4.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Box-plots\n",
    "fig, axes = plt.subplots(2,2, sharex=True)\n",
    "#\n",
    "sns.boxplot(data=df_clusters4, x = \"cluster\", y = \"Murder\", ax = axes[0,0])\n",
    "sns.boxplot(data=df_clusters4, x = \"cluster\", y = \"Assault\", ax = axes[0,1])\n",
    "sns.boxplot(data=df_clusters4, x = \"cluster\", y = \"UrbanPop\", ax = axes[1,0])\n",
    "sns.boxplot(data=df_clusters4, x = \"cluster\", y = \"Rape\", ax = axes[1,1])\n",
    "fig.suptitle(\"Boxplot para features con 4 Clusters\", fontsize=14, fontweight=\"bold\",)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Box-plots\n",
    "fig, axes = plt.subplots(2,2, sharex=True)\n",
    "#\n",
    "sns.boxplot(data=df_clusters4, x=\"cluster\", y=\"Murder\", ax=axes[0,0])\n",
    "sns.boxplot(data=df_clusters4, x=\"cluster\", y=\"Assault\", ax=axes[0,1])\n",
    "sns.boxplot(data=df_clusters4, x=\"cluster\", y=\"UrbanPop\", ax=axes[1,0])\n",
    "sns.boxplot(data=df_clusters4, x=\"cluster\", y=\"Rape\", ax=axes[1,1])\n",
    "fig.suptitle(\"Boxplot para features con 4 Clusters\", fontsize=14, fontweight=\"bold\",)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Comentarios:***\n",
    "\n",
    "1. El cluster 3 tiene alto el índice de asesinatos. El cluster 2 tiene un menor índice de asesinatos.\n",
    "\n",
    "2. `Assault` y `Murder` tiene un comportamiento similar para los clusters.\n",
    "\n",
    "4. Note que el cluster 1 tiene una tasa más alta de asaltos que el cluster 3. A su vez el cluster 3 tiene más asesinatos. Los clusters 0 y 2 tiene un compartamiento similar en ambas features (`Assault` y `Murder`).\n",
    "\n",
    "5. En cuanto a `UrbanPop` el cluster 0 y tienen cluster 1 tiene las tasas más altas. Por su supuesto los individuos en los cluster 2 y 3 tiene una tasa baja de población urbana.\n",
    "\n",
    "Note que podemos caracterizar los cluster así:\n",
    "\n",
    "- ***Cluster 0:*** Baja tasa de delitos, y una alta tasa de población urbana.\n",
    "\n",
    "- ***Cluster 1.*** Alta tasa en todas las features.\n",
    "\n",
    "- ***Cluster 2.*** Baja tasa en todas las features.\n",
    "\n",
    "- ***Cluster 3.*** Alta tasa de `Murder` y `Assault` con baja tasa de población urbana y violaciones.\n",
    "\n",
    "Esta solución parece ser buena, en este caso podemos pensar en una segmentación basados en la feature `UrbanPop`, note que acá tenemos más información que con 2 clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ***Referencias:***\n",
    "\n",
    "1. _Análisis estadístico de datos multivariados. Díaz L & Morales M. Editorial: Publicaciones Facultad de ciencias. UNAL._\n",
    "\n",
    "2. _Multivariate Analysis I. Kassambara A. Disponible en: http://www.sthda.com/english/_\n",
    "\n",
    "3. [_Selecting the number of clusters with silhouette analysis on KMeans clustering_](https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html#sphx-glr-auto-examples-cluster-plot-kmeans-silhouette-analysis-py) [_by sklearn_](https://scikit-learn.org/stable/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.10.12"
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}