{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Support Vector Machines\n",
    "\n",
    "### Verschiedene Methoden um Daten zu simulieren\n",
    "Eine Sammlung von verschieden Methoden um Daten zu simulieren:  \n",
    "* Methode um Daten mit zwei Klassen zu simulieren, welche linear trennbar sind (`seperable=True/False` gibt an ob die Daten perfekt trennbar sind oder teilweise überlappen):  \n",
    "`generate_linear_data(n_samples=1000,seperable=True,scaled=True)`   \n",
    "  \n",
    "* Methode um Daten mit zwei Klassen zu simulieren, welche nicht linear trennbar sind:  \n",
    "`generate_non_linear_data(n_samples=1000)`    \n",
    "  \n",
    "* Transformiert Daten von $\\mathbb{R}^2$ in $\\mathbb{R}^3$:  \n",
    "`transform_data_2_3d(X,y)`    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import pylab as pl\n",
    "import matplotlib\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "\n",
    "from plotly.offline import init_notebook_mode, iplot\n",
    "from plotly.graph_objs import *\n",
    "import plotly.tools as tls\n",
    "init_notebook_mode(connected=True)\n",
    "\n",
    "import scipy as sp\n",
    "from sklearn.datasets import make_circles, make_blobs\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "'''\n",
    "Generate  Linear Seperable Data for SVM Demo\n",
    "'''\n",
    "def generate_linear_data(n_samples=800,seperable=True,scaled=True):\n",
    "    if seperable:\n",
    "        X1, Y1 = make_blobs(n_samples=n_samples,n_features=2,centers=2,shuffle=True,\n",
    "                            center_box=[-4,4],random_state=42)\n",
    "    else:\n",
    "        X1, Y1 = make_blobs(n_samples=n_samples,n_features=2,centers=2,shuffle=True,\n",
    "                            center_box=[-3,3],random_state=42)\n",
    "    \n",
    "    if scaled:\n",
    "        scaler = StandardScaler()\n",
    "        X1 = scaler.fit_transform(X1)\n",
    "        \n",
    "    return X1, Y1\n",
    "\n",
    "'''\n",
    "Generate Non Linear Seperable Data for SVM Demo\n",
    "'''\n",
    "def generate_non_linear_data(n_samples=800):\n",
    "    X1, Y1 = make_circles(n_samples=n_samples, noise=0.05, factor=0.4,random_state=42)\n",
    "    return X1, Y1\n",
    "\n",
    "'''\n",
    "Map 2D data into 3D Feature Space\n",
    "'''\n",
    "def transform_data_2_3d(X,y):\n",
    "    #transform data using the following transformation: [x1, x2, x1**2.0 + x2**2.0]\n",
    "    poly_kernel = lambda x1,x2: sp.array([x1,x2,x1**2.0+x2**2.0])\n",
    "    newX = sp.array([poly_kernel(x1,x2) for x1,x2 in zip(sp.ravel(X[:,0]),sp.ravel(X[:,1]))])\n",
    "    return newX, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Methode um Daten zu visualisieren\n",
    "Diese Methode plotted die simulierten Daten, entweder statisch oder interactive (`interactive=True/False`). Falls, ein SVM Model mit übergeben wird, wird zusätzlich die Entscheidungsfunktion und die Margin geplottet. Falls, die Daten in $\\mathbb{R}^3$ sind werden diese in 3D geplottet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_data(X,y,svm=None,interactive=True):\n",
    "    if X.shape[1]==2:\n",
    "        fig = pl.figure(figsize=(11,6))\n",
    "        if svm:\n",
    "            w = svm.coef_[0]\n",
    "            b = svm.intercept_[0]\n",
    "\n",
    "            x0 = sp.linspace(-1,1,50)\n",
    "            decision_boundary = -w[0]/float(w[1]) * x0 - b/float(w[1])\n",
    "\n",
    "            margin = 1/float(w[1])\n",
    "            margin_up = decision_boundary + margin\n",
    "            margin_down = decision_boundary - margin\n",
    "\n",
    "            svs = svm.support_vectors_\n",
    "            pl.plot(svs[:, 0], svs[:, 1],\"o\",markersize=17, \n",
    "                                             markeredgecolor=\"#8e44ad\",\n",
    "                                             markeredgewidth=2,\n",
    "                                             markerfacecolor=\"#ffffff\",alpha=0.5)\n",
    "            pl.plot(x0, decision_boundary, \"k-\", linewidth=2,label=\"Entscheidungsfunktion\")\n",
    "            pl.plot(x0, margin_up, \"k--\", color=\"#16a085\", linewidth=2,label=\"Margin\")\n",
    "            pl.plot(x0, margin_down, \"k--\", color=\"#16a085\", linewidth=2)\n",
    "            \n",
    "        pl.plot(X[y==0,0],X[y==0,1],\"o\",color=\"#e67e22\",label=\"Negative Class\",markersize=10)\n",
    "        pl.plot(X[y==1,0],X[y==1,1],\"s\",color=\"#2980b9\",label=\"Positive Class\",markersize=10)\n",
    "        pl.xlabel(\"x1\")\n",
    "        pl.ylabel(\"x2\")\n",
    "        \n",
    "        if interactive:\n",
    "            plotly_fig = tls.mpl_to_plotly(fig)\n",
    "            iplot(plotly_fig, show_link=False)\n",
    "        else:\n",
    "            ax = pl.gca()\n",
    "            ax.spines['top'].set_visible(False)\n",
    "            ax.spines['right'].set_visible(False)\n",
    "            ax.spines['left'].set_visible(True)\n",
    "            ax.spines['bottom'].set_visible(True)\n",
    "\n",
    "            #turn off all ticks\n",
    "            ax.yaxis.set_ticks_position('none')\n",
    "            ax.xaxis.set_ticks_position('none')\n",
    "            pl.legend(ncol=4,loc=\"upper right\",frameon=False)\n",
    "            pl.ylim([-2,3])\n",
    "            pl.show()\n",
    "            \n",
    "    else: #3D plots\n",
    "        if interactive:\n",
    "            negClass = Scatter3d(x = newX[y==0,0], y = newX[y==0,1], z = newX[y==0,2],\n",
    "                                 mode = 'markers',name=\"Negative Class\",\n",
    "                                 marker=dict(opacity=0.5,size=3))\n",
    "            posClass = Scatter3d(x = newX[y==1,0], y = newX[y==1,1], z = newX[y==1,2],\n",
    "                                 mode = 'markers',name=\"Positive Class\",\n",
    "                                 marker=dict(opacity=0.5,size=3))\n",
    "            if svm!=None:            \n",
    "                tmp = sp.linspace(-1,1,51)\n",
    "                x0,y0 = sp.meshgrid(tmp,tmp)\n",
    "\n",
    "                decision_boundary = lambda x,y: (-svm.intercept_[0]-svm.coef_[0][0]*x-svm.coef_[0][1]) / svm.coef_[0][2]\n",
    "\n",
    "                db_pl = Surface(x=x0,y=y0,z=decision_boundary(x0,y0),\n",
    "                                opacity=0.8,\n",
    "                                autocolorscale=False,\n",
    "                                surfacecolor=\"#8e44ad\",\n",
    "                                showscale=False,\n",
    "                                cauto=False,\n",
    "                                showlegend=False,)\n",
    "\n",
    "                plotData = [posClass,negClass,db_pl]\n",
    "                \n",
    "            else:\n",
    "                plotData = [posClass,negClass]\n",
    "            \n",
    "            layout = dict(title=None,\n",
    "                          font=dict(family='Optima', size=15, color='#7f7f7f'),\n",
    "                          margin=Margin(l=0,r=0,b=0,t=50,),\n",
    "                         )\n",
    "\n",
    "            fig = dict(data=plotData,layout=layout)\n",
    "            iplot(fig,show_link=False)\n",
    "        else:\n",
    "            fig = pl.figure(figsize=(11,6))\n",
    "            ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "            ax.scatter(X[y==1,0],X[y==1,1],X[y==1,2], c='#2980b9', marker='s')\n",
    "            ax.scatter(X[y==0,0],X[y==0,1],X[y==0,2], c='#e67e22', marker='o')\n",
    "\n",
    "            if svm!=None:            \n",
    "                tmp = sp.linspace(-1,1,51)\n",
    "                x0,y0 = sp.meshgrid(tmp,tmp)\n",
    "\n",
    "                decision_boundary = lambda x,y: (-svm.intercept_[0]-svm.coef_[0][0]*x-svm.coef_[0][1]) / svm.coef_[0][2]\n",
    "\n",
    "                ax.plot_surface(x0,y0,decision_boundary(x0,y0), color='#8e44ad',alpha=0.6,shade=False)\n",
    "\n",
    "            pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beispiel 1\n",
    "In dem ersten Beispiel simulieren wir linear trennbare Daten, plotten diese und wenden eine lineare SVM auf die Daten an. In diesem Beispiel betrachten wir die Hard Margin SVM, hierzu wird der Parameter C auf einen hohen Wert gesetzt.\n",
    "\n",
    "### Simuliere Daten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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ffy5J+sEPftDodu3bt1efPn0ajR0wYIDy8/PrjXXO6aSTTmLDi49s375dTz75pIYPH67q\n6mr16tVLp5xyiqRAecK8efOUkZGh+++/v97vcLt27fSnP/1JGRkZevzxx7Vly5a66z7//HPtt99+\nKikpafT9OnfurKOOOiquP9N+++2nYcOGqbKyUo888kij64O9BjT3dTGUeL0GdO7cWYMGDWpU5rDf\nfvvprrvukhTda0BBQYH69+9f9/UXX3whSerdu7cOOOCARuN79eoV858pWiS3QAi2pyym47zSu3dv\nnX/++fr66681Y8aMkGPXr1+vzz77TD179mzyj0ztH7d//OMfdZetWLFCkprc+BRuQ9THH3+sP/7x\nj/rlL3+piRMnavz48Ro/fry2bt0qSXr33XdD3j4atX+0GvaH3Lhxo1577TV17NhRZ511Vt3lL730\nksrLy3XKKac0+aId7DHxSlVVlZ5//nlNnz5dl1xyiS6++GKNHz++ru664WN5wgknSAr8H61atarJ\nulwp8Fxq1aqVHnjgAc2cObPujyL849RTT62rXy0qKtLQoUP14Ycfqnfv3lq4cGFd0rRy5UqZmfr1\n69co2ZOko446SieccIKqq6v197//ve7yE044QTt27NBFF12kdevWycwS9rPVauo1YMeOHXryyScb\nlSU193XRK2aml19+WTfeeKMuvfTSuteA3/72t5Kafg346U9/qhdeeKFRT919HXHEEWrTpo0WL16s\nG2+8sVENdjKg5hYIwWXn12wiCz8u2f32t7/V/Pnzdd999+mXv/ylunQJXiP873//W5L01ltv1avL\nDGbfWeBPPvlEkpq836Yul6SpU6fqxhtvVFVV07PktfV+sTB69Gj94he/0OLFi/XVV1+pffv2kgIb\nU6TADuZWrVrVja99TBYvXhzVYxJKhw4dtGXLlrpZkFh59913NWzYsKAb8Wo1fCxvuukmrV+/Xs8+\n+6yeffZZ5efnq0+fPho0aJAuvPBCHXLIIXVjDz30UN1xxx264oordNlll+myyy7TIYccopKSEg0d\nOlTnnntuvccOqWffGtCcnBwdeOCBGjBgQF3SW6v2d75h66p9HXrooXrllVfqxkrSzJkzNXjwYD30\n0EN66KGHVFhYqBNOOEFnnHGGLrzwwoTUa59xxhk66KCDtG7dOr3xxhs65phjJEmPPfaYvvnmG40Y\nMaJenXBzXxdD6dChg955552YvwZ8/vnnGj58uFavXt3kmIavAb/+9a+1cuVKLV26VGeeeaZycnLq\nZukvuOCCusdHCmwunDVrliZMmKBrrrlG11xzjQ466CD1799fgwcP1ujRo+vV83qB5BYIIbd4qHav\nnRu6NCEjU7nHDktcUM3UvXt3/fjHP9Z9992nKVOm1CVyDdXO2h100EE6/fTTQ95nsNmapl74m9oJ\nPH/+fF1//fVq06aNbr/9dg0aNEidOnWq2xU8duxYPfroozGd3SksLNS5556rRx99VI888oh+9rOf\nqbq6um45seEmktrHpEePHurXr1/I+470sIU+ffpoy5Yteu2112Lag3jEiBHauHGjzjnnHP3f//2f\njjzySBUWFqpVq1Z699131aNHj0aPZceOHbV27VotX75cL7zwglatWqVXX31Vf//73/Xb3/5Wf/zj\nH+uVmvzsZz/TyJEjtXDhQr388st6+eWXNWfOHM2ZM0e9evXSihUr1LZt25j9TEishn1um1L7PAqV\n7AX7vT3yyCO1adMmLVmyRMuWLdOqVav00ksv6YUXXtC0adM0f/78eisn8ZCRkaGLLrpIN910k2bP\nnq3bbrtN0rdvcJt6DWju62Iwffr00cqVK/Xaa69FGX1oP/7xj7V69WqddNJJmjZtmoqLi7Xffvsp\nKytLe/bsCbqBNS8vTy+++KJeffVVPffcc1q1alXdJtRbbrlF06dP15QpU+rGjxgxQqeffroWLVqk\nv//971q1apXmzZunefPmadq0aVq5cqUOPvjgmP5cUYmmQDfdPthQhsqvPrJPb+gZekPZDT2t8quP\nvA61noYbymp9+umnlpeXZxkZGfbGG28E3VD28ssvB91MEU7tpqRZs2YFvX7RokVBN5SNGjXKJNkf\n/vCHoLc7/vjjg26aaO6GslpLliyp2xhlZvbcc881+XPPmTMn6Cazlpg1a1bdxraKioqobx9so8y+\nm+Wqqqoa3aZ2o0ywTX0N7dq1y26++WaTZK1bt7adO3eGHL9+/Xo75phjTJL95je/ifbH8Q2/bigL\n5qGHHjJJVlJS0uSY/v37mySbM2dOyPsqLS21yy+/3CTZgQceWO+6WG8oq7Vp0yaTZAcccIBVVlba\nO++8Y5KsY8eOjX5/mvu6GMqyZctMkmVnZwfdmBVOsMdl165dlpGRYa1atWq0SdfM7K233jJJFkj/\nQvvmm2/swQcftMzMTHPO2TvvvBNy/Pvvv1/3d2DMmDFR/zwRYEMZEAuZRV3UbtTdUlaulNFgoSMj\nU8rKVbtRdydtG7CGOnXqpMsvv1zV1dW6+uqrg4454YQT1L59e61bt07vv/9+xPdd24f10UcfDXp9\nU5eXlpZKUtB3+Rs3btS6deuC3q72QIpQpQyhnH766ercubP+9a9/6c0332xyxqZ2bFZWll588UXt\n2LGjWd+voR/96Efq0qWLvvjiC1155ZVhx69cuTLsmNrH8sADDwxaGlDb3igS+fn5uvLKK9W5c2dV\nVFRo06ZNIccXFxfr8ssvl6SQPYThH7Vt+1555ZWgNfEbN27Uq6++qoyMjLB9mtu1a6ff//73ysjI\n0KeffhrR0n5LXwMOP/xw9e/fX59//rmee+65JsuSpOa/LoZy6qmnqn///tqzZ48uueSSsMekr127\ntsketbV27typ6upqtWnTptEmXSm614Ds7GyNHz9e/fr1k5np9ddfDzn+0EMP1TXXXCPJ+9cAklsg\njNaHDVSHSxcrr89ouZwCyTm5nALl9RmtDpcuVuvDBnodYlSuvPJKFRUV6amnntKHH37Y6PqsrCxd\nd9112rt3r4YNG6Z//vOfjcaUlZXp0UcfrVfXOXHiROXm5uqFF15oVPLw5JNP6m9/+1vQeGqX8P70\npz9pz55vG9t/8cUXGjduXJN/uGqP1A1VWxpK7bKkJN11111auHBho00ktQ444ABddtll2rFjh845\n5xy98847jcZs375df/7znyPeYJWdna25c+cqJydHd955p3784x8Hrb375JNPNHnyZA0bFr705bDD\nDlNGRobefPPNeht4JOnBBx9s8g3GrbfeWm83e601a9bos88+U0ZGRl2HiGXLlumZZ55p9P+yd+/e\nuu4Toeqr/a59fmSnAEY6Lpl16dJF5513nqqrqzVp0iTt3Lmz7rodO3Zo0qRJqq6u1vnnn1/35nX3\n7t26/fbbgyavixcvVnV1tdq2bRs0MWuopa8BkuoOgpg1a1aTZUlS818Xw5kzZ46Kioq0YMECDRs2\nLOhhMKWlpbruuut00kknhdzoJQVeq9q1a6cdO3Y06gTx3HPP6fbbbw96u5kzZwZ9A/vvf/9bb731\nlqRvf6/XrVunuXPnBk20n3rqqXpjPRPNNG+6fVCWgFTVVFlCrVtuuaVuaUpNLNn98pe/rLv+2GOP\ntXPPPdeGDh1qvXv3try8PJNkzz77bL3bzJ4925xzJsn69OljY8eOrVuWrL2/ww47rN5tPvjgAyss\nLKzrmzhixAgbPHiwFRQU2JFHHmnDhg0LuiT52Wef1cUxYMAAGz9+vE2cONEWLVrU6HEIVpZgZvbu\nu+/WexxClR3s2bPHzj//fJNkrVq1sj59+tiIESNsyJAhVlxcbNnZ2SapUf/LcFavXm2dO3c2SZaZ\nmWn9+/e3UaNG2XnnnWe9evWqezz79etX73ZNLbdOnjzZJFlGRoadeuqpNmbMGDv66KPrygUUpCyh\n9vE/8sgjbfjw4TZmzBg7+eST6/qaXnXVVXVj77jjDpNkhYWFduqpp9rYsWNt2LBh1qlTp7ol3Y8+\nSq4yHUQm2rIEM7Nt27bVPb+Kiops+PDhNnz4cGvXrp1JsuLiYvvqq6/qxm/fvr3ud6hXr142cuRI\nGzVqlPXt27fu9/Dee++t9z2aKkuoqKiwjh071r3eXHTRRTZx4sR6pVGhyhLMzHbu3Gm5ubl13ztc\n2UFzXhfDeeedd+yoo46q+73t3bu3jRgxws4//3w78cQT63qEd+vWzXbv3h32cbn11lvrYuzfv7+N\nGTPGTjjhBJNkV199ddCyhOLiYpNkhxxyiJ1zzjk2duxYGzRoUN3r2r69ihcsWGCSLC8vz04++WQb\nM2aMnXfeeXbIIYeYJGvTpk2Tf3taKOL8zfMEMpk/SG6RqsIlt+Xl5XUJVagX/hUrVtjo0aPt4IMP\ntuzsbCssLLQjjjjCRo0aZQ8//HCjJv5mZkuXLrVBgwZZQUGBFRQUWP/+/W3evHm2cuXKuhfbhj74\n4AMbPXq0de7c2XJycuyQQw6x//3f/7UdO3Y0+QJuFqhZGzhwoBUWFtYlgfvW4IZLbs3MTjrppLrH\n4emnn25yXK1FixbZ0KFDrVOnTpaVlWVFRUXWs2dPGz9+vC1YsMD27NkT9j4aKi8vt3vvvdd+8IMf\n2IEHHmjZ2dmWm5tr3bt3tx/96Ef21FNPNTrEoqk/2nv37rX777/fjjvuOMvPz7f99tvPTjvtNHv2\n2Wftww8/DJrczpkzx8aNG2c9e/a0du3aWevWra1bt242dOhQW7Kkfm3o+++/b1OnTrVTTz3VDj74\nYMvJybH27dvbcccdZ9OnT7cvvvgi6p8fyaE5ya1ZoMn/DTfcYMccc4zl5uZabm6uHXvssTZjxoxG\nrxGVlZV277332qhRo6xHjx7Wtm3buuf62LFjgx5AEuo1YP369TZ48GArKiqqezO2bw1uuOTWzOxH\nP/pR3WvA3XffHfbnbc7rYjhVVVU2Z84cGz58uB188MHWunVry8nJsS5duth5551njzzySKPXllCP\ny7x586xfv37Wtm1ba9OmjfXv37+u7jlYcvvUU0/ZpEmTrFevXvad73zHsrOz7eCDD7YzzjjDHn/8\n8XoHQnz22Wd200032VlnnWVdu3a13NxcKywstKOPPtp+9atfxfPNbcT5mwv8nAimb9++tmbNGq/D\nAHzhhhtu0JQpUzR58mT94Q9/8DocAEBqCd2DbR/U3AKImf/85z9Ba06feeaZulPSxo0b50FkAIB0\nQZ9bADHz/PPPa9KkSerVq5e6dOkiM9OmTZvqNlhce+216tu3r8dRAgD8jOQWQMyUlJRo3Lhxevnl\nl7V06VLt3r1bRUVFOvvss3XJJZdoyJAhXocIAPA5am5DoOYWAAAgKVBzCwAAgPRDcgsAAADfILkF\nAACAb5DcAgAAwDdIbgEAAOAbJLcAAADwDZJbAAAA+AbJLQAAAHyD5BYAAAC+QXILAAAA3yC5BQAA\ngG+Q3AIAAMA3SG4BAADgGyS3AAAA8A2SWwAAAPgGyS0AAAB8w1fJrXMuyzl3mnPuNufcK865z5xz\ne5xznzjn5jnnBnodIwAAAOIn0+sAYuwUSS/U/HurpLWSyiQdJek8Sec5524wsykexQckVFXpZpWt\nfkDlGxbJ9pTJZecrt3io8ksmKrOoi9fhAQAQc76auZVULWm+pO+ZWSczG2Jmo8zsGEmjJe2VdJ1z\n7lRPowQSoOK95do2c7B2r50r27NLksn27NLutXO1beZgVby33OsQAQCIOV8lt2a2zMxGmNnKINfN\nlTS75ssLEhoYkGBVpZu1fe5kqbJcqq6qf2V1lVRZru1zJ6uqdLM3AQIAECe+Sm4jsK7mc2dPowDi\nrGz1A9LeytCD9laqbPWsxAQEAECCpFtye1jN5888jQKIs/INixrP2DZUXaXy1xcmJiAAABIkbZJb\n51xHSeNrvpzvYShA3NmespiOAwAgVaRFcuucy5Q0R1KhpKVm9pTHIQFx5bLzYzoOAIBUkRbJraT7\nJJ0maYvYTIY0kFs8VMoI0+kvI1O5xw5LTEAAACSI75Nb59ydkiYq0Pf2NDPb6nFIQNzll0yUWmWF\nHtQqS/klExITEAAACeLr5NY5d5ukn0vapkBi+57HIQEJkVnURe1G3S1l5Taewc3IlLJy1W7U3Rzk\nAADwHd+e6H0bAAAgAElEQVQmt865WyT9r6SvJJ1hZm97HBKQUK0PG6gOly5WXp/RcjkFknNyOQXK\n6zNaHS5drNaHDfQ6RAAAYs6ZmdcxxJxz7mZJV0rarsCM7bowNwmqb9++tmbNmpjGBiA4jgoGAITg\nIh3ou5lb59wNCiS2OxSYsW1WYgsgcTgqGAAQK76auXXOnSNpUc2XayS91cTQd8zs5nD3x8wtEH9V\npZu1bebgwFHBTcnKVYdLF8dlBpcZYwBICRHP3IbpFZRyivb5d9+aj2BWSAqb3AKIv2iOCi4cMj2m\n37viveXaPndy4PvXnOhWO2O8e/0TajfqbmqTASDF+Koswcxmm5mL4GOg17ECCPDqqOCq0s2BxLay\nvPH3r66SKsu1fe5kVZVujun3BQDEl6+SWwCpx6ujgqOZMQYApA6SWwCe8uqoYK9mjAEA8UVyC8BT\nXh0V7NWMMQAgvkhuAXjKq6OCvZoxBgDEl9+6JQBIMbVHBTfsWiApMKPbKisuRwXnFg/V7rVzQ5cm\nxGHGuCm0JAOA2GDmFoDnvDgq2KsZ42A4xAIAYsdXhzjEGoc4AP4WrM+tpHozxvHuc+v1IRYAkCLS\n9/hdAIiUFzPGDdGSDABii5nbEJi5BRBvW2cU15QihOZyCtTx6g0JiAgAkhIztwCQCmhJBgCxRXIL\nAB6iJRkAxBbJLQB4yKtDLADAr0huAcBDydSSDAD8gOQWADxUe4iFsnIbz+BmZEpZuXE5xAIA/Irk\nFgA8lgwtyQDAL2gFFgKtwAAAAJJCxK3AwuxiAJAuqko3q2z1AyrfsEi2p0wuO1+5xUOVXzKRJXEA\nQMqgLAGAKt5brm0zB2v32rk1BwqYbM8u7V47V9tmDlbFe8u9DhEAgIiQ3AJprqp0s7bPnSxVlkvV\nVfWvrK6SKsu1fe5kVZVu9iZAAACiQFkCkObKVj8g7a0MPWhvpcpWz1LhkOkx/d6UQgAAYo0NZSGw\noQzpYOuM4ppShNBcToE6Xr0hZt+34r3lgRnjvZX1Z4wzMqVWWWo36u6gXQJilRCTWANASol4QxnJ\nbQgkt0gHn03tLimC1wHn1Gna+zH5nlWlm7Vt5uBAKURTsnLV4dLF9RLN5ibEDcXqfpINCTsAH4s4\nuaXmFkhzLjs/puMiEU0pRK1Y1Qb7tcaYTYEAEEByC6S53OKhjU/GaigjU7nHDovZ9yzfsKhxYtlQ\ndZXKX19Y92VzEuJgYnU/ycSvCTsANAfJLZDm8ksmSq2yQg9qlaX8kgkx+562pyzqcc1JiIOJ1f0k\nEz8m7ADQXCS3QJrLLOqidqPulrJyG8/gZmRKWblqN+rumNZsNqcUojkJcXOuj3ZcMvBjwg4AzUUr\nMA+x+QPJovVhA9Xh0sUqWz1L5a8v/Pb5eOww5ZdMiPnzMbd4qHavnRs6IWtQCuGy8yPr6hAmcY7V\n/SQTPybsANBcJLceCbZbu3bzx+71T6Tsbm2krsyiLiocMj3mvWyDyS+ZqN3rnwid3DYohWhOQhxM\nrO4nmfgxYQeA5qIswQNs/kC6a04pRKxqg72oMY43LzYFtkRV6WbtfHqKts4o1mdTu2vrjGLtfHoK\nr3kAYoLk1gNs/gC+LYXI6zNaLqdAck4up0B5fUarw6WLG61cxKo22Isa43hLpYSdlmUA4o1DHEKI\n1yEOXp0IBfhBoFa95bXBsbqfZJEKB1M09/AOABAnlMVGvJJbL06EAuB/yZ6w73x6SkT1znl9Riek\n9htASok4uWVDmQfY/AEgHhK5KbA5omlZlqw/A4DkR82tB1Jt8wcAxAItywAkAsmtB1Jp8wcAxEpz\nDu8AgGhRluCB2t3a4TZ/JEONHFIHh4Ig2fmxxzCA5MPMrUeibYMEhEJ7JaQCVq0AJALdEkKIV7cE\nIJZor4RUkgotywAkJbolAOkimkNBmtqBTkkDEqV21SqZW5YBSG3M3IbAzC1SQXMOBamfzNbe1qle\n/2Vm0gAAySPimVtqboEUF217pcb1uXUj6t+gukqqLNf2uZNVVbo5RtECABBfJLdAioumvVJV6eZA\nvWNlefhm+rVqShoAAEgFJLdAiovmUJCI6nMbqjkxCgCAVEByC6S4aNorRXT8aRCcGAUASBV0SwCa\nKVk6DERzKEhzk1ROjAIApAqSW6AZgvXqrD00Yff6JxLeYSDS9kouOz+izgr1RHliVLIk/QCA9EQr\nsBBoBYZgUvnQhJ1PTwl//GlDUfwsNOiPH940AEhztAID4iWaQxOkQFKy8+kp2jqjWJ9N7a6tM4q1\n8+kpnrTXiqg+t1ZGppSVW1fSEE7ITgy0FWsRjlcGgMiR3AJRimhTVk2HgWRLSmrrc5WVG6TDwrdv\nil1OgfL6jFaHSxdHPNMabdKPyPCmAQCi47uyBOdcD0lnSTpeUl9JhyvwV3ukmc2L5r4oS0Awn03t\nrkYHHjQlKzcpyxcCS9yxPf60OSelJVoqLu1HVEqSkam8PqObPF4ZAHwg4rIEP24ou0TS5V4HAf+K\neFNWRmbEM5mJTkoyi7qocMj0mH7faE9KS7Rk2wQYqWhWCkhuAcCfZQlvSvq9pFGSukta4W048JtI\nD02QXMRJiR9Ec1JaoqXy0n6yv2kAgGTju5lbM/vzvl87F/EsNtJUtEvV+SUTtXv9E6ET11ZZUmVF\nRN/fL0lJbvHQiJbPo2krFivR1AMn2+xnpCsF9CIGgAA/ztwCEWvOhq+Qm7L26TCQzDOZ8RDNSWmJ\nFs3SfiJE00EjmuOVAQAkt0hjLVmqrj00Ia/PaLmcAsm5Rh0G0i0piTTp92LjVjIt7Uf7hiqZ3zQA\nQDLyXVkCEKmWLlWH25QVaflCopOSeHYMiPSktERLlqX9em+oGqqukqqrtH3u5HodNKI5XhkAwMwt\n0li8l6qTcSYzEX13a5P+jldvUKdp76vj1RtUOGS6p8lXssyiN7cXcCQrBQCAAN/1uW3IObdc0imi\nzy0aiLhfrXPqNO39Zn+fePSUbW4cqXpscEsly8+eCr2AASBJpXWfWyAiiVqqjkdP2eZI5Y4BLZUs\nS/vJVPsLAH5FWQLSVrIsVSdKsnUMSLRkWNpPtw4aAOAFZm6RtpJ1w1e8MGvo/Sx6MvcCBgC/YOYW\naSsZN3zFE7OG3qOtFwDEH8kt0loyLFUnSrqVYSSjdHtDBQBe8F23BOdcb0kz97noKEltJL0nqbT2\nQjPrF+6+6JYAP0mWjgFIng4aAJBCIu6W4MfkdqCkl8KNM7OwDxLJLfym4r3lYTsG+Gm2Gkh1A25d\nrq/K9oQd1z4/WyuvGBj/gADvRJzc+q4swcyWm5kL9+F1nIAX0qkMA/CDSBLbaMYB6YBuCUCa8bpj\nAAAA8URyC6CmBvQBlW9Y9G0NaPFQ5ZdMpAYUAJBSfFeWACA6Fe8t17aZg7V77dyaE9tMtmeXdq+d\nq20zB6viveVehwgAQMSYuQXSWFXp5sAGs2AdFKqrpOoqbZ87OeIOCswAg+cAAK+R3AJprGz1A4HO\nCaHsrVTZ6llha3SDdWKonQHevf6JqDoxkCClplg+BwCguShLANJY+YZFoY+ClaTqKpW/vjDkkHoz\nwA3vr7pKqizX9rmTVVW6OWxMlEmkplg+BwCgJZi5BXws3Ayo7SmL6H7CjYtmBji/ZEKTMUkKXybx\n2GVqfeSZ+mbTMmZ1k0gsVwEAoCV8d4hDLHGIA7wSzbJ8U2MzDzxa/33m+pAHNux4/PKa2dHQXE6B\nOl69ocnrt84ojuh+lNlacq7JmHK6nqhvPng5/GyynKR9Xrs4hMJzkT4Hwj2XUN9R05+PeOzbU8+M\nYySA5yI+o4CZWyDJRFO32OTYNY9Jtjf4N9hno1jrI85QxVvPhE4mMzKVe+ywkDFHOgOsqoqQMX0T\ncclBgzflzdj8htiK1SoA6mufnx3xCWXNwQlo8COSWyCJRNO9QAqxhN9UYruvvZWBWdRWWaGT21ZZ\nyi+ZEPKuXHZ+ZDO38cayt2cifQ647PwEROMf8U4oOQENfsSGMiCJRFO3GNHYUKqr9M2mpWo36m4p\nKzewtL+vjEwpK1ftRt0ddiY0t3ho49t7IYLNb1LgTcTOp6do64xifTa1u7bOKNbOp6ew2akFInoO\nRLAKAAAtlQR/jYDESIX2UlF1LzBFUJsamu0pU+vDBqrDpYtVtnqWyl9f+O1jc+ww5ZdMiOixyS+Z\nqN3rn2hxPLEQbtmbdlXxEdFzIIJVAABoKZJbpIVUSWiiqluMwV7Q2iXizKIuKhwyvdnL+ZlFXdRu\n1N2NHmNJdZu9JJMqm6i5jaFQy96xPrQC34rkORDJKgAAtBRlCfC9VOq/GWk9osvOb3ntYoMl4pYu\n1dfOAOf1GS2XUyA5J5dToLw+owOX9zovomXrnMNODV4mEclG2TDL3tGUfSB64Z4DyfAGEoD/RdQK\nzDl3iqQLJHWW9JmkeWb2TIjxV0r6vpkNilWgXqAVmD/sfHqKdq+dG7YjQF6f0Z5vRIomVsnCjw0l\nK7duhjLYzHbt94pVi62q0s3aNnNw8FnTBjFJalQmkdPjNFW8/ZxU9U1EP1MwtKsC6qPVGFJI7FqB\nOeemSbquwR2Pc869KOlCM/siyM2OkHRKpEEA8RRNHavXyW1EdYvVVaqu+K/yeo+MrM41o5VUvU/3\nhAZLxIlaqo922TpYmUTFsee0aNmbdlWJkQr17QD8K2RZQs2M7RRJ1ZJmSZos6S5J/5V0hqRXnXOH\nxDtIoCVSKaGpTQCDL8t/q+KtZ1T6yP+o4ORJITsdtB16k/L6jAm5RJzIpfqWLlu39PbRlH2geTg+\nGYDXQpYlOOf+Jmm4pNFm9rd9Lj9A0sOSBkn6VNJpZrZpn+sflHSRmbWKV+CJQFlCYsVrticVl6Kr\nSjfr62V3quKNRaEHZuWqaOz9qnh7SbM7HaTi49NcqVSikoqiKT1hBjc5UJaAFBJxWUK4DWX9Jb25\nb2IrSWb2uaTvKzCbe6Ck5c65o6ONEqgVz9meVOy/mVnURRmtC8LHvbdSFW8vUeGQ6ep49QZ1mva+\nOl69QYVDpkecPKTSzHZL5ZdMrOncEALtqpqNDXupJ9KTzZp7AhrghXA1tx0krQx2hZntlfRj51yZ\npJ9JWuqcO8PMXo9xjPC5eNd8pmr/zUTVCqfTyVK0q4qvVKpvRwBH6sKPwiW3X0kK+RfNzC53zlVJ\n+qUCCS7rFohKNLM9zfmDmKoJTaJmVHOLh0a0VJ9MM9st0ejQim/KambITaos147HL2fzUzOl0yoA\nEmPArcsjOvq3fX42iTrqhCtL2CypT7g7MbNfSbpVUntJL0o6quWhIV1EdSpXM6Vi/81EbX5Kx6X6\n2kMr9ht5p5TVWpI1OtyDzU/RY8MeYi2SxDaacUgP4ZLb1ZI6OudKwt2Rmf2fpFsktZPUNwaxIU0k\naranNqFpbm1qoiWqVjhkh4aargvJOLPdUql0uEeqSMX6dgD+Ey65XazA7rRfRHJnZnaVpBmKYkcb\nEI/ZnpaetpUMEjmjmooz2y3F5qfYS8dVAADJJ1zN7d8V6GdbHekdmtl1zrl/SipqSWBIH7Gu+Qx2\n2lbtUvPu9U/E5LStREh0rXDtzHa6bPRh81PspWp9OwB/CTlza2ZVZrbUzF6K5k7N7ClJT7QoMqSN\nWM72+G2pOR1nVBOFzU/xwXMWgNfCHr+7L+fcIgUOZ9gZZlwfSY9JOqwFsSFNxHK2J96dF7yQbjOq\niZJOLdASjecsAC+Fq7lt6IeS1jvn+jU1wDn3M0kvS+JYXkQsVrM9iei8kM78UMtci81PAOBPUc3c\nSvqrpIskrXDOXWNmt9Ze4ZwrlPSgpKGSvpF0ScyiRFqIxWwPS83x45da5lqpergHACC0qGZuzWy8\npIslVUr6nXPuaedckXPuREnrJQ2TtEnSCWZ2f6yDBcKhz2Z8+K2WWUrfFmgA4HfRliXIzP4i6XhJ\nGyX9QNJbCnRV6KLAzG5fM3szlkECkWKpOT782jaLzU9Acmufnx3TcUgPzsyad0PnOkt6Q1KhJJP0\noJn9OIaxea5v3762Zs0ar8NAFKpKN2vbzMGBGcamZOWqw6WLmZGLwtYZxZFtvsopUMerNyQgIgBA\nmon4DIVoa24D9+5cfwW6IbRV4Ije70q62Dm3U9KVZhZmRw8QH/TZjA9qmQGksgG3Lo/oiN72+dla\necXA+AeEuIq6LME5d6Wk5ZIOlvRnSUcoUJ7wpQInmb3snOsaswiBKLHUHHvUMgNIZZEkttGMQ3KL\nts/tM5K+L6lM0ngze7Tmquedc8WSHpE0UNK/nHM/MbP5sQwWiBR9NmMr1qfIAQAQL9HO3J4l6XVJ\nffZJbCVJZrZV0mmSrlegXGFuTCIE4LlYniIHAEA8RZvc3i+pn5m9F+xKC5gm6QxJn7cwNgBJgrZZ\nAIBUEVVZgpn9NMJxLznnejUvJADJqLaWuWz1LJW/vlC2p0wuO1+5xw5TfsmEmCW2VaWbVbb6AZVv\nWPTt9ygeqvySiSTPAICwmt0KLB3QCgxIrGCnoEmq1+mCDYEAonXU9OcjHvv21DPjGAlaIOJWYFF3\nSwCAePDjKWgAgMQjuQWQFPx6ChoAILFIbgEkhfINi0K3GpOk6iqVv74wMQEBAFISyS2ApMApaADi\npX1+dkzHIbk16/hdAPWxw7/lXHa+bM+uiMYBQDQ4Uje9kNwCLRRsh7/t2aXda+dq9/on2OEfIU5B\n400SAMQCZQlAC7DDP3bS/RS0iveWa9vMwdq9dm7NDLbVvUnaNnOwKt5b7nWIAJASmLkFWiCaHf6F\nQ6YnJqgUVXsKWrg+t36cwaz3Jqmh6iqpukrb505Wh0sX+/Lnj4cBty7XV2V7wo5rn5/NkjXgM8zc\nAi3ADv/Yqj0FLa/PaLmcAsk5uZwC5fUZrQ6XLvZteQdt0GIvksQ2mnEAUodvZ26dc2MlXSLpWEmt\nJL0j6UFJ95pZtZexwT/Y4R97mUVdVDhkelrNdEfzJimdHhcAaA5fztw65+6R9LCkvpJWSnpB0uGS\n7pY0zznXysPw4COR7txnhz9C4U0SAMSO72ZunXPnSbpU0lZJ3zOz92ouP0DSS5LOlTRZ0p2eBQnf\nYIc/YoE2aEgk6pHhd36cuf1NzecraxNbSTKzzxUoU5Ckq5xzfvzZkWDpvsMfsZFbPDSwaS4U3iQh\nRqhHht/5KsFzznWW1EfSHkl/a3i9ma2Q9ImkjpL6JTY6+FHtDn9l5TZOTjIypazcsDv8q0o3a+fT\nU7R1RrE+m9pdW2cUa+fTU2gflkZ4kwQAseO3soTjaj6/ZWZBeupIkl6TdFDN2NUJiQq+VrvDv2z1\nLJW/vvDb5vvHDlN+yYSQiS0HQETOzwccpHMbNACINb8lt91qPoea8vpPg7FAizVnh38q9DZNloQy\nHd4EtORNEgDgW35LbgtqPofaUly7a6NNnGMBQkr2AyCSJaFMhTcBsZKObdAAINb8lty6ms/maRRA\nBJK5t2kyJZTJ/iYAyal9fnbEHQEQHbotINn5Lbn9uuZzQYgxtdd9HWIMEHfJ3Ns0mRLKZH4TgORF\nUhU/dFtAsvNVtwRJH9V8DjWVdHCDsYAnkvkAiGQ6VjiZ3wQAAJKP35LbdTWfezrncpsYc3yDsYAn\nkrm3aTIllMn8JgAAkHx8ldya2RZJ/5KULWlkw+udc6dI6qzA6WX/SGx0QH3J3Ns0mRLKZH4TAKSi\nSOuMqUdGqvJbza0k3aTAAQ6/c86tNrP3Jck5t7+kmTVjbjazaq8CBKTk7m2aTMcK55dM1O71T4SO\nhQMOgIhRjwy/89XMrSSZ2TxJ9ypwCtkbzrmnnHNPSHpP0lGSFkq628MQgTq1vU3z+oyWyymQnJPL\nKVBen9HqcOliz3q3JtOscixOgQMApA9n5s+uWc65sZIuk3SMpFaS3pE0S9K9kc7a9u3b19asWRO/\nIIEkFqzPraR6s8qJTL4DB0pwwAHgtaOmPx/x2LennhnHSJBmXPghNQP9mtzGAskt0h0JJYCGSG7h\nkYiTWz/W3AKIEU7MAgCkGpJbAGkrMDP9gMo3LPp2Zrp4qPJLJjIzDTSB0984pS3ZkdwCSEvBaopt\nzy7tXjtXu9c/kfCaYiBVkKxxSluy8123BAAIp6p0cyCxrSxv3GKsukqqLNf2uZNVVbrZmwABAM1G\ncgsg7ZStfiAwYxvK3kqVrZ6VmIAAADFDcgsg7ZRvWBT6UAhJqq5S+esLExMQACBmSG4BpB3bUxbT\ncQCA5EFyCyDtuOz8mI4DACQPuiUA8K2mWn3l9BikireeCV2akJGp3GOHJS5YAEBMkNwC8KVQrb6U\nkSm5MAtXrbKUXzIhAZECAGKJ5BaA73zz79Xa/sj/SNV7G19ZXRX4aJUtZeYExuw7g5uRKbXKUrtR\nd3OQA2KGpv9A4pDcAkgp4U4Vq3hvubY//D+SBUls92XVat1zsDJy2qj89YXf3texw5RfMoHEFjHl\n56b/6Zi4c0pbciO5BZAywp0q1vbsKfrvM9eHT2wlqbpK32xaqo5Xb1DhkOlxjhzxlo4JVrLwc+Le\nFJ5DyY3kFkBKqHeqWEM1pQb/ffJayUV+n7T68o90TLC8FukbCiDRSG4BpISIThWzvZJFfp+0+gKa\nj8T2W6wcJBeSWwApIaJTxaJBqy+kGBKo5MXKQXLhEAcAKSHmJQS0+kKKIYECIkNyCyAlxLSEIKMV\nrb4AwKcoSwCQEnKLhwYOYAhVmuBaBTaUBetvu8+YogtnK+eQkpjHiOZhuR1ALDFzCyAl5JdMlFpl\nhR6Uma22P/ytlJUbOIxhXxmZUlau2v3ofhLbJMNyO4BYIrkFkBIyi7qo3ai7Qyeuo+5Wfu/z1eHS\nxcrrM1oup0ByTi6nQHl9RqvDpYvV+rCBnsSP9BZpM3+a/gMtR1kCgJTR+rCB6nDpYpWtnhXyVLHM\noi4qHDKdwxmQNCinIHFH4pDcAkgpJK4IhuNQk99XZXt01PTnG11OLTVijeQWAJDySI4SL9I3FOFQ\nS41YI7kFAABRC/eGItgsrV+xcpBcSG4BACkjkoTJr8vcJFDJy4/Pt1qp2KqP5BYA4Ct+XeZOlsQB\n6SUVW/XRCgwAAAC+wcwtAMBTsdqYlG5Scbk4FfC4pj6SWwCApyJJENJpc1KkErVcnG7JXiouw6M+\nyhIAAECTSPaQapi5BQDA55qa+Y71bCsz7EgGJLcAAKSQSMsEIpEMs620LkOskdwCAJBCkiEhjdbb\nU88MOybdansRP9TcAgAAz1Hbi1hh5hYAkPSiaRcWy2VuZhOR7lLxZDySWwBA0vMqcWQ2EekuFd+0\nkdwCAJihBOAbJLcAAF/PUJK4IxqpuAwfb6n2O0RyCwDwNT8n7omQbscjJ0NylmxS7XeI5BYAADSp\nqWSPAxuQrGgFBgBAmmrJ0nqkt02n5XskB2ZuAQBR2XfGLllq7NJJNDWh8fy/4f8dyYrkFgDQbMlS\nY5dO/JpUspELsUJyCwAAPOfXpB2JR80tAABNoK4USD3M3AJACki1PpN+wWMJpB5mbgEgBcS7zyQz\njwD8wlczt865fEnDJB1f83GcpFxJi81siJexAUAyazhD6acepmxUio+WriawGpE6Uu13yFfJraTD\nJM3xOggAQPIgMYqPlq4mpNqpV+ks1X6H/Jbcfi1plqQ1ktYqMHN7n6cRAQAAIGF8ldya2QeSJtZ+\n7Zw7ysNwAAAAkGBsKAMANEILLACpylcztwCA2Ei1GjsAqMXMLQAAAHyD5BYAAAC+kTRlCc65WySd\n04ybnmZmn8Q6HgBIJqnWZxIAvJI0ya2kAyX1aMbtsmIdCAAkG2pgASAySZPcmtkFki7wOg4AQPrg\nlKzma+lqAqsRiJekSW4BAEg0TslqvpYm+7xZQLywoQwAAAC+QXILAAAA3/BdWYJzboGkTjVfdqj5\nfJJz7pV9ht1gZosTGxkAAADizXfJraTjJHVpcNl+kk7c5+sOAgAAgO/4Lrk1s65exwAAAABvUHML\nAAAA3/DdzC0AAIgePX/hF8zcAgAAev7CN5i5BQCktJbMOHJKFuA/JLcAgJTWkhlHltcB/6EsAQAA\nAL5BcgsAAADfILkFAACAb5DcAgAAwDfYUAYAAFqEHrlIJszcAgCAFqFHLpIJM7cAACSxRM2K0vMX\nfkFyCwBAEkvUrCjlAvALklsAQEqLdMZRko6a/nyT90FyB/gDyS0AIKWFSkqbSmYbohYULcWmuuRB\ncgsAAJJesiePbKpLHnRLAAAASY/kEZFi5hYAAPhSss/2Ij6YuQUAAL7EbG96IrkFAAAtEmnvW3rk\nIhEoSwAAAC3Ckj6SCTO3AAAkMWZFgegwcwsAQBJjVhSIDjO3AADfYtYTSD/M3AIAfItZTyRKpMdA\n80Yq/khuAQBA0kv25JE3UsmD5BYAACQ9kkdEiuQWAIA05fcTvJJ9thfxQXILAICPRZrAhpKqJ3il\nYkKOlqNbAgAAPpaqiSnQXCS3AAAA8A3KEgAAQERSsUY3FWNGyzBzCwAAIhJpiUMylUKkYsxoGZJb\nAAAA+AZlCQCAhGOpGEC8MHMLAEg4looBxAvJLQAAAHyD5BYAAITECV5IJdTcAgDgY9EcQUt9c3Kg\nJr1lSG4BAPAxkp/UQ016y1CWAAAAAN8guQUAABGJtPY2mWp0UzFmtAxlCQCAtEAdY8ul4uOSijGj\nZZi5BQCkBeoYgfRAcgsASDiWigHEC2UJAICEY6kYQLwwcwsAAADfILkFAACAb/gquXXO9XDO/dI5\n96xz7n3nXIVzbqdz7h/OuV845yjeAgAASY2a9JbxW83tUkkHSaqQtEbSa5IOkNRfUj9JFznnTjez\nUu9CBAAAaBo16S3jq5lbSZskTZTUwcwGmNkYMxsk6UhJb0k6TtIdXgYIAACA+PFVcmtmp5nZLDPb\n1eDyjyT9tObL8ylPAAAA8CdfJbdhrKv53FpSey8DAQAkHnWMQHrwW81tKIfVfN4jiZpbAEgz1DEC\n6To1FSQAAAgTSURBVCGdZm6vqvn8tJl942kkAAAAiIu0SG6dc+MljZK0W9LV3kYDAACAeHFm5nUM\nkiTn3C2SzmnGTU8zs09C3O9pkp6RlCXpIjObE0VM2yRtbkZMAAAAiJ0vzeysSAYmU83tgZJ6NON2\nWU1d4Zw7WdIiSdmSfh5NYitJZtahGfEAAADAI0kzcxtrzrkSSc9JaiPpSjO7xeOQAAAAEGe+rLl1\nzvWT9KwCie21JLYAAADpwXfJrXPuBElLJLWVNM3MZngcEgAAABLEV2UJzrk+kpZKKpR0g5lN8Tgk\nAAAAJJDfkttSSe0k7VBgI1lTrjCzLxMTFQAAABLFb8ltpD9MNzP7KJ6x+IlzroeksyWdqcBJb50l\nfSPpbUlzJc00sz3eRYhEcc7lSxom6fiaj+Mk5UpabGZDvIwN8eOcGyvpEknHSmol6R1JD0q618yq\nvYwNiVPzt+AsBX73+0o6XJKTNNLM5nkZGxLHOZcl6XsK5AUnSeoiqb2kbZL+IeluM1vuWYDyWXKL\n+HDOfSzpIEkVktZI+ljSAZL6S2otaZ2k082MY419zjnXS4H/74ZIbn3KOXePpEsV+P1fKqlS0mkK\nbNhdoEBis9e7CJEozrn/J+nyIFeR3KYR59zpkl6o+XKrpLWSyiQdJenomss9LQ313YYyxMUmSRMl\ndTCzAWY2xswGSTpS0lsKzN7d4WWASJivJc1SINk5UdJPvQ0H8eScO0+B/+utko41syFmdq4CKzgb\nJZ0rabKHISKx3pT0ewVO/OwuaYW34cAj1ZLmS/qemXWqeV0YZWbHSBotaa+k65xzp3oVIDO3aJGa\ngzJWKjCrU0h5QnqpOdr6QTFz60vOuTWS+kgaZ2Z/bXDdKZKWK5D4HkR5Qvpxzi2XdIqYucU+nHN/\nVmBCbJaZTfQiBmZu0VK1S9StFai5AeADzrnOCiS2eyT9reH1ZrZC0ieSOkrql9joACSx2rygs1cB\nkNyipQ6r+bxHEjW3gH8cV/P5LTMrb2LMaw3GAkBtXvCZVwGQ3KKlrqr5/LSZfeNpJABiqVvN580h\nxvynwVgAacw511HS+Jov53sVB8ktmq2m3nKUpN2SrvY2GgAxVlDzuSzEmF01n9vEORYASc45lylp\njgIHaS01s6e8iiXTq2+MxHDO3SLpnGbc9DQz+yTE/Z4m6Y+STNIkM9vUzBCRIPF6LsC3XM1ndh0D\niMR9CrQJ3CLpAi8DIbn1vwMl9WjG7bKauqKmQ8IiSdmSfm5mc5oZGxIr5s8F+NrXNZ8LQoypve7r\nEGMA+Jxz7k4FOiRsVWBCZKuX8VCW4HNmdoGZuWZ8fBTs/pxzJZKekZQv6Uoz+0Mifx40X6yfC/C9\nj2o+dwkx5uAGYwGkGefcbZJ+rsAJZaeZ2Xseh0Ryi8g55/pJelaB+rprzewWj0MCED+17Xx6Oudy\nmxhzfIOxANJITbnb/0r6StIZZva2xyFJIrlFhJxzJ0haIqmtpGlmNsPjkADEkZltkfQvBcqPRja8\nvuYQh84KLEP+I7HRAfCac+5mSb+WtF2BxHaDxyHVIblFWM65PpKeVyCxvcHMpnscEoDEuKnm8++c\nc91rL3TO7S9pZs2XN3M6GZBenHM3SLpS0g4FEtukWr3h+F2E5ZwrldROgSfxohBDrzCzLxMTFbzi\nnFsgqVPNlx0kHaLAc2Pfjhk3mNniRMeG2HPOzZR0iQJHbL8oqVKBHdFtJS2UNMLM9noXIRLFOddb\n376pkaSjFChTe0/7HOJjZpxY52POuXP0bS6wRtJbTQx9x8xuTkxU9ZHcIiznXKRPkm5sPvI/59xH\nCr3JSJIuNrPZ8Y8GieCcGyvpMknHSGol6R1JsyTdy6xt+nDODZT0UrhxZubCjUHqqulx/2AEQ1eY\n2cD4RhMcyS0AAAB8g5pbAAAA+AbJLQAAAHyD5BYAAAC+QXILAAAA3yC5BQAAgG+Q3AIAAMA3SG4B\nAADgGyS3AJAGnHM9nHOXO+fmOOfecc5VO+fMOTfC69gAIJYyvQ4AAJAQl0i63OsgACDemLkFgPTw\npqTfSxolqbukFd6GAwDxwcwtAKQBM/vzvl8757wKBQDiiplbAEgxzrk/1tTLPueCZKnOudk11z8V\n7HoA8DOSWwBIPZdL2iDp+5Ku2vcK59w4SeMkbZE0zsws8eEBgHdIbgEgxZhZhaTzJe2SdL1z7iRJ\ncs4dKWmmpCpJY8ys1Lso/397d69qxRUGYPhdloKIFsKBaGcTsTmVEBDPFVha2dgIFklnJbmAdOkC\nKQ4oEdEbSCFY2cgpBBuJKNja5QqWxT7+FAErGWbyPNVmZrP5pntZrFkbYBniFmCF5pz/VLfbvTvx\naIxxvnpSnazuzTmfLzkfwFLELcBKzTkfVn9WP1SvqkvV39VvS84FsCRxC7BuP1fvq9PVh+qmfbbA\n/5m4BVi3q9WF489nq4sLzgKwOHELsFJjjL3qQTWqw77svz2z6GAACxK3ACs0xjhR/VWdq36fc96q\n7rdbxT1ccjaAJYlbgHX6tTqojqq7x9fuVK+r62OMX5YaDGBJw3sHAOsyxjionrY753Z/zvn2q3uX\nqxftFi9+mnMeHV/fb3cG7ic/VqeqN9Xn83DnnFe++wMAfEfiFmBFxhjnqpfVXnVjzvn4P75zu/qj\netcufv8dY1yrnn3r9+ec/q4XWDVxCwDAZthzCwDAZohbAAA2Q9wCALAZ4hYAgM0QtwAAbIa4BQBg\nM8QtAACbIW4BANgMcQsAwGaIWwAANuMjD5vT26gD+U8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a76dbd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = generate_linear_data(n_samples=100,seperable=True)\n",
    "plot_data(X,y,interactive=False)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wende Hard-Margin SVM auf Daten an\n",
    "Beachte, ein hoher C-Wert führt zur Hard-Margin SVM!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "marker": {
          "color": "#FFFFFF",
          "line": {
           "color": "#8E44AD",
           "width": 2
          },
          "opacity": 0.5,
          "size": 17,
          "symbol": "dot"
         },
         "mode": "markers",
         "name": "_line0",
         "type": "scatter",
         "x": [
          0.09262402675366854,
          0.7365703225667646,
          -0.21695235241603567
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "svm = SVC(kernel=\"linear\",C=10**6)\n",
    "svm.fit(X,y)\n",
    "plot_data(X,y,svm,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beispiel 2\n",
    "In dem zweiten Beispiel simulieren wir Daten die nicht perfekt trennbar sind und klassifizieren diese mit einer Soft-Margin SVM.\n",
    "\n",
    "### Simuliere nicht perfekt linear trennbare Daten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R1dXVdvfdd9v48ePt6KOPtm7dujX+X584cWLQA0hCvQZs3LjRRo0aZfn5+Y1v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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8a5790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = generate_linear_data(n_samples=100,seperable=False)\n",
    "plot_data(X,y,interactive=False)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wende Soft-Margin SVM (C-SVM) mit kleinem C auf Daten an"
   ]
  },
  {
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     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "svm = SVC(kernel=\"linear\",C=10**-1)\n",
    "svm.fit(X,y)\n",
    "plot_data(X,y,svm,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wende Soft-Margin SVM (C-SVM) mit großem C auf Daten an"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "svm = SVC(kernel=\"linear\",C=100)\n",
    "svm.fit(X,y)\n",
    "plot_data(X,y,svm,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beispiel 3\n",
    "\n",
    "Im dritten Beispiel simulieren wir zwei Klassen, welche nicht mit einer linearen Funktion trennbar sind, z.B. zwei inneinanderliegende Kreise.\n",
    "\n",
    "### Simuliere nicht linear trennbare Daten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,y = generate_non_linear_data(n_samples=1000)\n",
    "plot_data(X,y,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transformiere Daten von $\\mathbb{R}^2$ in $\\mathbb{R}^3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "newX, y = transform_data_2_3d(X,y)\n",
    "plot_data(newX,y,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wende SVM mit linearen Kernel auf transformierte Daten an"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "svm = SVC(kernel=\"linear\",C=0.1)\n",
    "svm.fit(newX,y)\n",
    "plot_data(newX,y,svm,interactive=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Beispiel 4\n",
    "In unserem viertem Beispiel wenden wir einen polynomiellen Kernel auf unsere nicht transformierten (orginal) Daten an. Dieses Beispiel ist ähnlich dem dritten Beispiel. Nur müssen wir mit einem polynomiellen Kern den Feature Space nicht explizit berechnen und können die Daten somit trennen.\n",
    "\n",
    "### Wende SVM mit Polynomiellen Kernel auf nicht linear trennbaren Daten an"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0wTSaNGnK/AXzuG7UtW6LV5SUlPDCf57nwouGeJ2kCJCZmUmTtCaUHit1eTgu\nWfojb739ptv1PvzwA/76+y+X5Xv27CF3hzlrg9VDu2nTn3z77Wy3ov/7HxYB0DrMK3KGmph2Z5N4\n0/+I7TYS4pIAAXFJxHYbSeJN/yOm3dkN3UWfON8HHhg/gSZNmvL9D4vcfk9jY2P51yPma2SUj2vE\n3gd84w03ER8fz88//+QyyXDRooXMmfOd2/6ddqp5Avann39CVVWVbXlRUSF3jhvr0bdtTT35V4D3\nDavtDOC9999l4cIFLrmzrWRmZnHH7WMpPVbKdddfw19/ue7zaOlRPvv8U9WTA+Pi4vjkk89p1KgR\n7773Dvfed7cto4c9+fn5PPTIBK4ffZ3PbZ5yyinodDq279jOb7/96vDZ9Omfmy04bvjvm69z4OBB\nF8G9YeMGCgoK0Ol05FhGM5cv/4XFP/7g8ncxGo38uMScxaV1K/c+/XBHWkckgPZtIvbiuqGJhLLq\n9tgEdQDemtdee52//t7JypUr6HbG6ZxtSf23cuUKjpYepVu3bkyZ/JqtfVVVFU88+Tj/fvopunbp\nyimndECn07Fnz242bNwAwPPPvkBsrO+XkL59zyQrK4s/N/3JOYMH0alzZ2JjYunXrx83jFE3LD/i\nqhE8+tgjzF8wD8Ald7Y9d4+7h/0H9vP2229x3vmDOf3002nXtj0mxUTewYP89fdfVFRU8L9vv6NT\nx06q9t+uXTuWLlnG6DGj+P77RSxe/APdu3Wnbdt26HQ69h/Yz8aNGzAajbRt09bnMLFer+fhhx/h\nyaee4Lbbb+X9D96nTevW7Nmzh3Xr1/HwQ48wecokl/U++exj2+Skzl26kJSYyOHDh1m9ZjVVVVWM\nHDHSlplk/4ED3HzrTSQkJHDGGT1omZNDVVU1mzdvYs/ePSQnJ/PkE/9WdfxaRpfWisYXPKk6V3Y4\nIwSkpaUy4cEJ/PvppzxWfL173D0cOLCft995i/OHDOb0rqfTrl17TCYTeXm118i3s7+jo+Uaadmy\nJVOnvM7d99zFuLvv5IMP3rMVrPn997Xcc/e9vP3OW8Q6lYG/++57mDVrJosX/0CPXt3o07svhkoD\nv/32Kzk5LRl26XAWLJzv0scLhlxAQkIC8+bPZejF/0e7du3Q6/VccvGlXHLJparOx6hRY5g8ZRKf\nfvYJgEvubHteeP5FCgoK+N9333JW/75079adNm3aUllZSV7eQXb+tZOqqirW/b5BtX2sb5++LJj/\nPTffcgORsUhmAAAgAElEQVSff/EZM7+cQa9evWnZshXGmhr27NnNlq1bbFmhfJGensHtt43lgw/f\n49LhFzNo4CAys7LYvn0b27dv56EJDzNlqmup90mTXuWpfz9Jx46d6HhaR+IaxZGXl8fatWswmUxM\nePAhsrPNLzZbt23lsSceJTUllTPOOIPs7GwqKgysW/8HBQUFZGVl8eD4CaqOP9xoeNUhaXC0ahOx\nRq9rFJO0h/hJsNKApTdLZ9mSn/n3U0/TokVzliz9kSVLfySnZQ5P//tZlixe5pC9IykpidenvsEV\nl1+JobKSZT8tZdH3Czl27BjXXH0NPy37hdtuu13Vvhs1asR3387hoouGsnffPr76ahaff/EZvzpF\nZLyRkpLCZcMvs/3beRKkMy9PfIXvFy1m5IiRlJaWsvjHH/j115VUGAxcPPQSpn30MQP6D1S9fzBP\nnlyzai0ffTiNYZcOp/hIMT8s/p6FixZQWHiYYZcO5+Npn7Bh/Z+qSrDff994pn8+g759zyQ3dwc/\nLP4BnV7PRx9O45mnn3W7zr+feoZbb7mN5ORk1q5dy5y5c/hn9z8MGjiIzz/9gmkffWJre2bfvjz7\nzHMMHDCQ/Lw8FixcwC/LfyY+IZ777r2fNat+D3oxDUl4cNed4xxyQbu7f7w08RW+X7iYESNGUnrM\n8RoZOvQSPvrQ9RoZPWoM8+YsYPA5g/l71998/715ZOSLz2Zw2fDLAWjWrJnDOu3atmPFit8YMWIk\niqLw/Q+L2LlzJzffdAtLf/zJ46S6rKxsvp41m7MHncO2bVuZ+eUMPv/iM/7c9Kfq89DhlA7061db\njXaUG9uIldjYWD795HNmzfyaoRddzKGCQyxctIC1v6+lxljD1SOvYeb0WbRr1171/gHOOvMsNq7f\nzGtT3+C8887nwIH9LFgwjx+XLOZEeTlXX30NX82azdIff1K1vVdfmcR/33iLbqd3Y/2G9SxdsoTM\njEy+nf0dN990q9t1Jk+eyqjrR6PTCVasXMGCBfM5lJ/PxUMvYc7/5vLcM8/b2l588SU8/ugTnHHG\nGezes5u58+ayavUqsjKzePLxp1j921qPGW3CHdEQOWqjmU6ndVWmvTmzobsBaDddn/0ER3/EdUqG\nnnbt/buZaYkImqcrkUgikFDIjVdefZkXJ77A2DvuYvKkKcHfgSRkhPKRs3v3bsoKPefttmfQ0B7r\nFUXpE6q+SOtIFKJVm0igAjuakeJaIpHUF/b3G39E94EDB2jUKM7FOrH4xx+Y+tpkhBCMGjU6SL2U\n1Bf22Um0jBTaUYYWo9hSYPuHFNcSiaSh8Ud0//TzMsY/cB/du3WnVavWKIrC37v+tk2afOThR+nV\nU9qRIhX73NtaRArtKEHrUWwpsL0jxbVEIglXfInus848i1HXj2b1mtUsX/ELFRUVNGnShP/7v4u4\n7dY7bPn2JZGLlqPbUmhHAVqOYkuB7RkpriUSSaThTnR36tSZd95+r2E6JKlXtBjdlkJbw2gxii0F\ntnekuJZIJFohUE+3JLLRWnRbCm2NorUotvRhe0cKbIkmMFWjrypFX3MCFBMIHcaYJIxxaaDzkTu9\nLutKwh7rPU4K7uhBK9FtKbQ1hhTY0YMU15L6RHFbULkW4e6R6If4FTUVxFYWOCopxYS++jj6mjKq\nG2ejxCS433cd1pVEFjLKHV1oIbothbaG0JLIlgLbPVJcSxxwI2RNMQmggM5Y4SJuFV3gt3ydqQad\nG9FsiktDsYhmezGuq6kgtvKwF/GbZe4rIEw1rkLZHkUhtrKAqoRWrtFpU3Wd1pVR8MhFRrmjh0iO\nbkuhrQG05sVuKB+2yaRgMpnQheE5lAI7uvAVPQbPQlZXfcJpY7XitqZxtk3c+oOupoIYLxFj63at\nUW1hqnbtm0OfFGIrD1Od0ApFF4u+qtS3WlIU9FWl1DROd1gc48e6xsYZtkVeo+DVxy2NpPCOBGSU\nOzpQG902Go2YTOHzRQg/RSHxCy2VT2/oculVBhMVhvJ63683glEGXRJGmKrRVxYRd2IPcWX/EHdi\nD/rKIjBVo9j9B2Yrhqf/dKYa70LWHYpCTGUBwlTtV5eFqdpVZPvYrk6l+NVVlQKYI8oq0FcfJ6ay\nGJ2pxnYuVK9bc6L2/PqKgtv6aBbecRUHEDUVqvYjaVjkPVP7+LrrHTt+jMoydVUh64PIVmZuEEJ0\nFEKMF0JMF0LkCiFMQghFCDGyjtsdJYRYKYQ4JoQ4IYRYJ4S4RwjRYOdQK1YRq8CGhrWJVBkUDh8q\n5ER5GSa7UYL6xvqgkA+LyEVx85+oKSeu4oA5Wmq1RtkJOX2NwUFMe0OVkHXbsVpxqxZ/RTP4J5xj\nyw/Ung+161QcQGcVvmrXVUy14tzf82exn+DnS4qk4ZD3UW3jfPUqisLJqpMUFhVSVFCC8WSDdMst\nWrSOjAPGB3ODQoi3gbuBSmAZUA0MAd4ChgghrlYUpd5en7QksK2EhQ9bEZwoMVJlKCAuXodOF/o7\ntP3NQj4QIhhTNTFVR9FXlwEmQIcxNhljXBMUXSzCVE1c+T68x2L+tvx2XNcdjcr+sewnEHScTD5F\ndWv1+6rdbqOyv320DQa7qEpsQ1z5ftT3z3yRBXb+BMbYQmoaZ/q5niRcsH+3itbbrRYmF1qxPxZF\ngZpqE1XlRkzVgnA6Qi0K7a3AJGAdsB6YBgwOdGNCiBGYRXYBcI6iKH9blmcBPwNXAvcCb9St2+rQ\nmsgOC4FtjyKoqoCqitBGtI12D/mYhhsUkajAhOd3aD064ks2kJk7GWGqQdi1VSwDhoouBmGqAtTf\n+hX0KLoYCjs9jKFpL2IMBaTkzSO5aAXCWAkoAT9GFARHBs1W3T7914cQKjzjCpCMQNE3RhirHM5F\nKFDQczz7QhQUUgqWet2fAlTFt+JYl8eoic9WfUzOmPTx7Os/HXC8hu3Rofd7u5L6xT7Io9fewL4q\nrFoi0p8/RpOzlgi/49Gc0FYU5SP7f4u6hwkft/x+1CqyLfs5LIQYB/wCPCaEeFNR/Bj/9BOtTHgM\nuyh2PSLFdfjjSVRbH8bOglfRxSFM1Qg3osu6zCqy/UFgRJiMZOZOojLpVOKPb7MsrzuKvrF/7XWx\nqo7B3DcFYTSgWGRsKGNKAiPJRcvJ6zGZ5MJfECbPQlsAcYY8cjZOoLDTw5aXAYP/+7Rbx5NAM3r4\nDkkBHj7Y33+tz6RoE9wxOh01JjvbZoQ+k/Q6HUaTiRqTKWw1RXj2KkwQQrQEegNVwDfOnyuKshzI\nA7KBfqHqh1YmPNpHscP1gggFRkw2kR0jdBF7Q9MaJttfpvYHzA9c5x+A+JIN5GycQErBUnRGAwIF\nnekkgVs4fCNMVcQf30awBkIVoCxD/QBfjKEAYarxez+iDhF3v/ZjrKQmPpvCTg9j0jWyjSK475MJ\nnekkmbmTKW/aByVA4RtjKPD6uafvj6fvm6Rhsd6T7f8y0YL9s7gmdHHCkGPVRjUWwR1uyCe+d3pa\nfm9TFMVT+OMPp7ZBRQtWkYbOJtJQSIEdPvgrqp2JMRSQmTsZnemki0UhtFHbYG9fx/Gc4apbN909\njbq8SCj4zhBQFxQRS3ru62RtfxlheenxtT9hqgFFBJxTPG3fV36vo1Z8SxoO+3t0NApucExMEIlY\ndVK4iW3NWUeCTDvL731e2ux3ahsUtGYViTaBbUWK64bBWbTEGApokreg1vKhb0xZxjkcz7kMwNEO\nYvdZTXy27fNAIrvhhAIUd7jLdkwuNhin444xFJBwdEOdhL6gVmwH+4VEAYRSRVLxSr+2LTCSWLKW\nwk4Pu/XWe18Xkop/ozgI8+2dX+rMf4+5JBWtRGesxKRvzImMszmWc4XtbyYJPdZ7do1SK7ajwVYS\nYydSaxRTxD67wtFKIoW2d5Isv70lV7bmsUr21EAIMRYYC5CV2dznTrUSxQYpsCX1g7tooL3lw1lQ\nCaOBlIKlJB/+CVAQiuL6WeEvtsmIyUUrQj65L1SYI7w6ijvcxYnsIcQYCmi6exoJRzcAtQLY+bjj\nS9YFrQ9GfSJ6o8Gtlz1Q6vQCYDLn/srrOZWUvPkkFy1HGA0qtxn874G776jeaCClYBnJhcsp6PQQ\nFU3Ng6bS610/SMEdud5t58h2Q+sQKbS9Y73v1mn0U1GUD4APADqd1tXrtiJdZEfjZEcpsOsfb8La\nHnvLhzMCI8JDVs7ayYiTyes51ZLpI7Kw3mgqmvSmpP2t1MRnWwTdJISpyq2otD9ufGbzVocA9MYw\nKwQFZG1/iUOnP01Jhzso6XAHbX8d0SB98fkdNRnJzp1CXs+pnIzPdPnuxxmKSM2b6zIycSznchkJ\nDwLRLLhldDs4SKHtnTLL7yQvbayflXlpowqtiGwpsCVqiDEUqBYIaoW18/Yzbd7dwBCmGrMnV+ig\n/lLl1xkFOJ49lOM5wx2sImZBpyKDiKmGYEZunSMW9gLe2VZinqRorIfJlCaab32ew10ex9C0lx/r\n+e6Zoy3HAOgtPhojCL3lRBhR9PFUx6X7rNYpTDWk5M2npMMdDssblawnO3eK+9Gawl843OkRP49N\n4oloFNxaiW43tNiWQts7ey2/23hp08qprd9owY8dTSJbCuy6E1+ygazcSV4FQnnTMxzWUSOsHcWN\nmbp5jI0kFa+owxYaCuEiyvzxmQuMIZnE6Cy4FRFLdePmxJ4sRJhOWl62BqMzlpNUtCqkdh1zX0xk\nbX/RzxU9fw892XLAaHfQtcckjAbiDAd8fketqQzt/6YxhgKyc6d4jYRn5U7iYM/XZGQ7iESr4I7k\n6HZDi20ptL2z0fK7qxAi3kPmkb5Obf1CRrEjBymwg0OMoYCs3Ek+BUJez6mqBYKnojHBIHzqi6nH\nXa7sQHzmCvqQiN1awS0o7PKoy985xlBA4pHfvebGDnZfVOMhK4MvW05d9+9sX1Lz4mSOhM+luMPt\ngPR3BxNnwR1NYhsi7xnYkGI7ss5UPaMoygFgAxAHXO38uRBiMNASc9XI1f5uX4rsyECm6QsuqXlz\nVQqE+T63FWMosKR3e9Ft6j0t4ivSrKB3myvbX5+5omsUcAo8tQilyu3f2TE3tqM4VNCjoAtp2kCv\nCFexam/LCdWLmfPLk5oXJ4GRlKIVbtMJSoKDcx5uLRPpebcbKt+2jGgDQoiXMJdS/05RlMedPn4J\nc7GaV4QQqxRF2WVZJxN4x9LmZX+rQkayyI4WgQ04CGwt4Y8/OtgkqRQIzkPlztRGsU9GVNTZXFTF\nFFCfzeLS7GH22EYX45Ar22qp8WdOt4Ke8qZnoTOecGODCF66PgEe/86Gpr2csoJU2qwl5en9yN42\nEaH4X3Wzzijm8+jJqhSSXbp5eVL74mRtZx9xNWJyENsy0l13YoQuauwk0kriH5oT2kKIXtQKYIAu\nlt8ThRAPWxcqimJfybE50NHy2wFFUWYLId4FxgFbhBBLgWpgCJACzAHe8qePUmSHP1oV2KDOHx3s\nCVQOD3XVAsFAm9VjXHJag/dMDeFKbRaQnpj0CSQVB+JBFhzu8phbm4yCHkUXQ2Gnh23nytFS40df\nhSCxZA3CZHQR2AAnEzsQV7EfoRid+uC/APcmGGvis21ZQZwp7PwIWdtfbICXLGNIrUrucH55Avwo\nI6/Q9teRjrnj7a6lYIjuhnxxDyeiyb8d6RMl7cV2qNGc0MYsfs9ys/zUQDeoKMrdQohfgXuAwZhD\nSrnAx8C7/kSzFUs0RIrs8ETrPmy1/uhAJlA5P2ytBTeO5gxHxLfwO7IqcJ/TGkJfQMZddgzvbX17\nma3bij+2lYIuj5NY4r8HWdE39hrpdZ9lRP3LiLm4TCyA2+wk1mOIMxygoOsTJBavqe2DrhHCVIW/\nlSTtLRG+iujYY2jay7LP+n3ZUnSNQ/aS5y4Di/PLk5Xypn1IKvoV4eV6qt2e4vFaqmukuyFe3MOd\naBPckRrdri8dJqzCT1I/dDqtq/LRmzMbuht+IQW2dmi2631SCpZ6FYUKeo5nX8iRDmNdPvMUuTqZ\n1IH03R95jLKW5lxBWt6cOkUATbpGtgmSbVaPQRfC4XpFxICiLgpsTaVnLXoC3gW69fwamvb2Kypq\nXc+bncaeprs+8Pm3tj8GMOfcNsUk+Mz44akv/tp5rOeupMMdHqPE9mLTWbCpOcZgVqVU0FMV34I4\nQ37QI9kKUBXfmtiqIo8vT1biSzaQuWMSQgnME25/LXnC2W/sTnTHGApoufFBry8dJl2jqM98Yn2G\nalVsQ+RGtgHOHtpjvaIofUK1fSm065lIE9rRJLIj8QbhL21Xj1YlUE36ePb2n+GwzF3kCtR5joMh\nduzFXdtfR3qN5NUVfyLaJl1j9g0wnyu1LwAmfTz7+k+3RHDnk1z4s09xqkYc2aO2L845t/09Bmdi\nDAWk7fuKpOIVPs+fScSR1+s1AHI2TvAp2JyPP8ZQ4Hs9EQNCZ7HB1E0cm3SNAEIWzT7Y+22HEQl3\n0f3y9P5kb3/Jax98XW/urhxF14iyzHPdjh54Et11fXGPJuwnD0rBHV6EWmhHzpmQ1DtaF9nO2USi\nAX8nUFmxt5w4P1RFgBP7/EVgJKXgB9qsHkOgty5/pLm6iKyOssxza9fx8/xaPcj7BszkcJcnPWbZ\nMOkaubUPqNmHipaUdLjDtu1AvyNWauKzKe403nw8Ita9qMMsgAs7P0JNfLYfqeocM5T4yk5i0jWi\nsPOj5PV8jePZF2LSx1vsMd5x/tz+byBUFPzxFwXzaIK9tz5n4wRSCpaiMxoQKOgsdozmW5/3XeDG\nx/6Emx+d6SQpBUvI2TiB+JINDu316Gw/MYYCmu16jzarR5NSsFj1xOZoxz5jlZazk0RyVpJQoUWP\ntqSOaF1gQ3RFse1RO4HKOZWYmpR83giWELf6thVLPDvQzB1qhIiqbeliHSapBXp+wXuWDXf2ATX7\nCKQvdTkGewxNe5HX63XS9n9FUvEqUKzfHz0n0gdS2uZa2zGpTVXnLkOJ2vNmP6nSu01FjyG1G/HH\nt7vdlvpJiOpRdHGUtL8V8F2SPZQITAjTSTJzJ7sdPQl0Eqi/qSW1jL1/G7QZ3Y5k33YokEJb4oDW\nRXa0CmwrZRnnqBrqtU8lZsKoKiVffRKobSSYXl13k9QCOb/2eMuy4S+B9qWux2BPTXw2xR3HU9xx\nvNd2wYii+3Pe6vJSo+78WPqroi8KUNjpEds+Qz3RVw3W0YPjOcNdUhgG9HLr46UsGtF6OkAptmuR\nQltiQ8siO1omO/riWM7lJBf+4jXbhaKL4VjOZQGl5Ktv/BE0rusJB8GuNkJu9jRf6FaQHc+5TNX5\ndU7VFgoC7UtDHEOwouj+EOhLjbrz4182FPtJnoFU8Aw2AiPJhT9Z5g7ULYWh2peyaETr1SUjPQVg\nsIjOo5a4EA0iW1Z1NIuLw50e8eppLej0EFXxGUCtNzNcI1JWf6kVtXFu8zo6i2dXYNLH+7VXe0+z\nPao8w356rQMl0L40xDGUZZzjsi9nwkWwqT0/isrvlHO7YNgsgjFNWJiqglJt1friLvGMvXdbi/7t\naPdtR7fqkFCjWIZ27EqraoVonOyoBkPTXhx0mBwmMOrjOZZ9Aft7TuZk0942gW1FjRAKB/yLbJvY\n1386ewfNZl//6X4IIxXe5J5THc6vSR/P8ewLyes5tV5zCgfal/o+huM5l/ks915fIwFqUHN+An15\nCNZLrZpJn6HE+cVdln33jtYnS0az2Jbp/eqZcErvFy1RbIln7B9+3oYt1aRRM99JdIggPCQCtYT4\ng3N6OnU5mf3LZS1RTyB5tMMZVakH3aQs9Cf/uSfqev3UJR2ngjlK787vbi8gZdl3z2g5FWA42khk\nej9JSNCqyJZRbHWYLGcKcIleu8P7cLnlR8RS1SirTlE0c9q3OI5nD+VE+tkhi6IrQHmTvg7LIi2q\nqjXCaSQgGARqwVHzPfSFs6WqvjC/iA5lX//pbu1V9vca+3uQxBEtR7ejMbItJ0NGIVoW2SAFtjfU\nRrDd4ZCpwVJgBWof6EKpJu7koYD6ZRXnioilLOs8m5gNpEy5apyUiFUY+YqqRnOFu1ATzKwr4UAg\n2U28fw99C+hgFIcKOJqt8kXUeu+xL/kuI9yuaDUzSbRNkpTWkXqmoa0jUmRHJ/bRa08V59xVhHOH\nmiFxf3AWBvaiFggob68avFU2DFYua4kkUPypGtrQ1NXeYx+1jTMUkZo31+X+dCzn8qi+/rSadzsc\nxLYswa4xGlJoa1FkS4HtHXuBDcHxwQbDQ6oGq38VcBC+2Eq+1+3epSDYO2h23TsqkYQQtddbfcxr\ncN2fCOqLaKOS9WTnTvF4fzrc6ZGIsxAFEym2Q4P0aEuCghTZ0YXV/2jvibSvOOdaRt2IzlIRLsZQ\n4HXbwcrz60smW4tm2MqUWzKEHOz9XxRdXN33H6YpCyUSe1RfbyIGRdco9B1yQIcwGkguWk5K3jyf\n9w5vxBgKyM6d4vX+lJU7qU77iHS0mgZQ675tqVCiAC2m74tGkR1jKKDZrvdpu3o07X4dQdvVo2m2\n632HB487gW1dN3P7yz6LaFjFrdc2QSpe47sMurnktjNqJmb6IlxyMkskvlB9vSlGyjLPDcoEYjXX\nkHnCpREB6IwGUgqWkrNxAvElGwLap5qKmMJUQ2revIC2rxW0OlFSy2I7elRKlGIV2VrB+iYfbcVn\n4ks20HLjg6QULEVnNCBQbA+3lhsfpHHJOrcC27puzsYJxBkOBCxu7anPSLAnkeEuQ4XV662quqPM\nHiKJENReb4q+cVAylgRqyLJFnbe/SNtfR9Bm9Ria7vpAdQRaTeRezf0pWpBiO3KIHqUSZdgXotEK\n0RjFBnM0Oit3ktch1ezcKTQyFLqs26h0C1nbX7Ksqw5fETR1hTiCgzeRYW8pOZ79f6AikqdAvVZn\nlEjqij+Fb+o62qMgAH2dfN7Wl11/o9xqI/fBGlHTAlJsRwbRpViiBOnH1hapeXNVDak6Wz7iSzbQ\nfOvz4PdNWKHtryNosf4BGpVucfk0GFEzdb1Qb+/wx8caiTmZJdGLv/ndPeUjP5F+joq5DQoEcZKz\nfZS7zarRXiPc/kTuZQ7uWqyju1rybWtNbEefatE4WhPZsgANJBf+ompINaXgB9twbaPSLebsIpj8\njk5ZI1JxhgM03/osqfu+dvhcTSGOYOCPvcMfH6uMZEsiiUAK3zhPIN7XfzrFncZT2OkRr9HuUBW6\nEYDOVOk1wu1P5N5qkZOCuxatRbe1JLZlwRoNoUWRDdErsMEclfY1gdGKAITRQErBYlIKFtd539YH\nbpMDX1GZ2pmTad1sn/kqxJHz58MIo8HnPsxD2fo6F4dR9I3V7S+CM43s2H2YPWVlQdmWEOEhThSl\n7hP32iUn07l9VhB6E74EUvhG7XashpH6QGBEmIxk5k4ir+drDv0+nnOZOajgpUCV88u3Hp0semOH\nfYEbLaQAjNHpqDFZbLARrANkHu16JlR5tKXI1h4xhgJabnwwaIVhAkUBquJbk9/7NdXrqMn9q6Dn\nRPpATDEJdS4Oo3Z/x7MvjLiqg1aBfVBXgamFQnp6oksbnd9RvXC5rvyLVpmchFRxcTm6fEFLU0JU\nCO5gU1858Z1RgIomvSns+oTD8rrk+bc+M6JdbIP28m2HOs92qPNoy4i2hpAiW1uk5s3x6c2uD8w2\nkv1+raM2OlXa5lrbMHddCCQaFu7YC2xa1ZDevJQuzQ6RmZjg0lZEybWiOA0jFzavYHuL5hw8lEZ+\nfhl7N5fSNilNCm6VBCsnvr8IIOHoehqVbiGxeLVDFcjypmeCECSW/OHXy3dtWXcZ3bY+O2sUGdkO\nB6TQ1gBayi4iRbYZE0aSilY2yEMwGFh9pb6iU8HyS9f3/vxhx+7DqtoJUftStafsBHm6CkytFNKb\nl9I1vYDMxERaJ7ShVcIpoepqxHEg8R+yko5QmF7AtuYtOHBIIS+/gr2bS2mXnOTQVlF8P+6iTaCr\nndtgP+4dTJtJ863POmxTGA0kFa/yGL02l6Wf51Ke/XjOZbZrW9pJarFaSSDyo9uRLLal0I5wpMiO\nPGIMBaTmzXV5WBzLuZyq+AzAfFPUhTiNVV1KNqt54AXLV6qW+t6fL+wj0umZKbbl3v3RZlFQlGog\nvfkxuqbnWwR2aymw3dAq4RRaJZzCgYR/yEw8QmF6vkVwCyprnCflur+erD7x4sLj7NlUFlUWFPVz\nG+I50u4W0ne9h+I0wTrQ+4in9lYfd9b2lzh0+tO2uSHubCXCkkIwufAXB2FeG902C24ptrXh245U\nsS092vVMMD3aWhHZ0SKwwfywyMqd5CHqqseQ2pX447n1MklJQQcqs5IowN5B3wJ181FGAw6Wjxyz\n5SM9NdmhjfDxwMuM3WkR2M2kwPaDAxX/sL/iCIXl5RRWd/TZXrHziBcfK6P4UBq6fEELY3JUCG5/\n5lIklqz1Ol/ErCR0iCBlvbBu73CXx6mOb0HOxgle92/SNSKv51SXF2r7LBzRLLi1EtmG4Hu2pUdb\n4hYtpLyB6BLZ9oVnnLFGcRKObnSJFgVbbNsL4qztL/q1boyhgMzcyV6PITN3stsHntbZsfswe0+U\nOlg+ujQ7RFZSEq0TfOUvdkZGsAPBPsINviO19uxPK7NYULI5eEixeb7bJSfRqV0WWnxcqp3bgFBU\nzBfRURXfktiThxF+FMjyhHl9E5k7XqE8vb/qWgLO8z1kdNuMFiPbkYL27hxRgFYyjESTyAaVhWd8\n/DsQFAARA4rRxUqh6ONVDx0DpOTNC/iBF+m4S69nbwPJ01VgaimcLB/SU90QBHLOHS0oBTYLSl5e\nJXs2n3Bpb7WcRHLkW+3chsydU1Xk8jcRW1XEvgEzafvr1fhfKMvDdpUakopXqS7P7um+I73b2hTb\nkaAfpNCOMKTIjlzqMsPfObJttn3UFlX2JsgVD0OqYC4SoWbouCxjsNmXfdh3KjBfD7xIZNGmXbXZ\nP00o5LcAACAASURBVJrZp9er/f42jZOe6kjHk+fbUJXj1NIEGCk+Uh7x2U7UzG3wtzz6ifSBJBWv\nDEqgQACKou6+6StoIKPbUmw3BFJoRxBSZEc2qqsXuluXWkmt6GJtQ73CLh+Aqxj3nW1D7dBxVVJ7\ncjZOANUPvNBO5Kwvcvfk8Wt5oUv2D09Iga0NnAU3HHPbrrBFudtsJ53aOQvz8MaaYtPTy7G/BaFK\n21xH4pHVCKX+05PGGAp82tbso9tWse1tkrrWbHBaEttA2E+OlEI7QpAiO/Ix6eLQ17n4jIIwVbmN\nFAlbC3MUuyzzPJ/ZNtQMHR9pfxvNdk/zq3BOpFRgXLRpl8syeztIZXYMTTvJSHW0YhXcnnCX7cSd\n1cS+AmYkWk38GfkCy32l86Nk7piEUKrqPO/En/ZqbWv2ebcTSjaSnTvFY0aTw50e0dwEb62I7UjI\nRCKFdgQhRXbkYsJITaMMdIaDAQ+nql9PT1nmeaqtG76GjtX4su2xf+CGK1a/9f6W5WSmO78U1H4/\nMzJKOT3tmBTYEreos5qYbSYAxUfKOZhXEXFpBAMpCGVo2ou8Xq853ld0jRCmKoLl33ZGgN+2tUaG\nQrJzp3id4J2VO4mDTiXjtYAU2/WDFNoRgBbS+EW7yAaIPVkc0nR9VgLxSHsbOvbXWx7OFRitAvtk\nc4FyipFzm28lMzHBY2VFc3q9M+u5l5JIQ63V5HDzE2xvXlvJkt2RUSQn0IJQ7u4rntKDBgt/bWtq\nJ3in5s3jSIexdelaWCLFduiRQjvM0UIav2gV2Sa7h4geHaLOthH1BNMj7U/1OEXXqMEqMHrDKrDz\n9WU07ZFAesZxuqXly6wgkqCixmpSW8kym9wDKTZft6fKleEixINVEMphO4U/ByUVoD3+2tbUBBKs\nwQstCm3QntgON6TQDmO04MuOdpFtf9NSO6EoOCi0WT3GpVpjQFtS3W992OXPds1tfZzz2uyXkWpJ\ng+BqNVnLtvy+7Dhc+zJr7+cGWLllM2cnZoWF4PY1aTKQ7WRue5GEoxuClMpU+G1b8zejilbRitiG\n8JscKYV2mCJFduTiTmSD2glFAiwVG+tSGVLguTyxv6idCHU8+8KwEdm5e/LYU3bCktvaLLCtExoH\npkuBLWlYHAX3drZmtLR9Zl+tUkGP6VgZO/ansGfTrojydasl/viOoEW0FV2s37Y1fzOqaBktiO1w\ntJBIoR3GSJEdeXgS2aByQpGIJa+XedJN219H1Lk/wajWGMhEqFCzY/dht8uFqLET2M7FY+SERkl4\nYRXcrRP+cfnMZAm2HEgtYUtqMkXZKazcfDjiJlL6wp9IsTWZqbMwVzDfOws7PeL3Pc7fjCpaR4rt\nEPSnoTsgcUULkx9BimxnbBOKdryCUGrcPixAofGxbcTlzQtq3+pSrTHQiVChwOq1PqirID0zBXBM\nxwd6ilINUmBLIgpv3882iafSKuFvDqTuY2tGS7bvUDiYH3mZSzzhj6VOEXGUN+tHUvFvWDO5IPRU\nx2USU11C1vaJtvzXvixzMYYCUvLmkVy4vHZbnvari+FozqVut6HF3NtaEtvhgFAUxXcrSdDodFpX\n5aM3Z3r8XCuWkWgS2b4Etu2GXrTC9kDxWskRAB1CZQostXlpTfp49vWfrmqb7jAfR90mQgWKvcA2\ntVBIb1FKZmqC7XNhd+4zY3daBHYzKbDDhGHv6Cip8P0tbZqgsODu8Hg4hiP7yv9mfdEBth9pTmF+\nM3T5gpamhIgW3E13fUBKwWKf9zAFOJ49VFUGE/sAgDvLXFLBMtJ3vQeYvOb4tt/OiaY9gNrS7fEl\nG8jKneRx31rIvV2jRK7QBmxC25ceOXtoj/WKovQJVT80G9EWQowCxgHdAT2QC3wCvKso6lN5CCGe\nBZ7x0uSkoihBMW9pRWRHE75EdiCprIRly2pR62+s62SeYE2E8gcHgd3SLLBPb3aQzMQEWiUIdG5v\noDKCHW6oEdn+tItW2iSeik7oyEwsorDZIba3aM7+/GYRHeE+nnMZyYd/RihVXtspujgHe1qMoYDM\n3Mle81+7s8yZRfY7fhf90lNbuj3OUERW7iTN5962RrYjVWyHi4VEk0JbCPE2cDdQCSwDqoEhwFvA\nECHE1YqispZ0LZuAP90sr65LX53RgsiOlmi2mki2pwdBQxBpk3kWbdrlQWC3ok3iqQ3dPYmkQbBN\npEw0pwo8HOGC21xF8hGvljp3/mu1+a/T9n2FKSZe9Yii/bq1rnAz1tLtqXlzoir3trSQ1LEPDbr3\nECCEGIFZZBcA5yiK8rdleRbwM3AlcC/whp+bnqMoyrNB7KoDkZ4vO9pEts6QR7O8+SQXrXTw5tn7\nAv2tqBhKImkyj33VRnuB3SZR5ryWSKzYZy6JdMFtriL5Bmn7vnLyX8dwIn0Apa2vdYkMq81/nVS8\nAtD7VRzHLMSNbrM26dGRVLQyanJva8mv3VD6RHNCG3jc8vtRq8gGUBTlsBBiHPAL8JgQ4k1/LCSh\nJNItI9EmshuXrCM7d4qDHcRdKj1/KyqGknCu1mjFKrArs2Mwdc7jXCmw3SL9zhJ7fAnuSKo+Wdxp\nPMWMV9Vedf5rwNdkR8/rureg6KIs97YWxDY0XH5tTQltIURLoDdQBXzj/LmiKMuFEHlADtAPWFW/\nPfRMpIpsK9EisnWGPLJzp6jyBdb3TdY8yKlv0KwggWDvw27aI4HMjCJOTy2RAtsD0u8scYcnwb08\nX4mo6LZa6rMAmHPWpmjMvW0V25FKQ1pINCW0gZ6W39sURfF0FfyBWWj3xD+h3UsI8QrQBCgB1gIL\nFcXHDA4fRHoqv2jKMGLCSLO8+Sq8eSdpueF+nP19oURBz4n0gZhiEhokK0ggOE90zGxxhHNbH6NV\nQjPaJPZr6O5JJBGJYzEcy6TJ9D7sKDBoquiNmvzXwcJqA7EK7WjNva2VyZH1rVm0JrTbWX7v89Jm\nv1NbtQy3/NhzUAgxRlGU5X5uC9COLzsasE58TFblzQP8nmsLiqUiZCBxSEUXQ2mba22ZQcIZdwK7\nS7ND9M5oJQW2RBIk7CdNWqtPFmuo6I2aQlrBxH6EUm0Rr2M5l9VH1+odaSHxD60J7STL73IvbU5Y\nfier3OY/mH3f3wN7gDigG+aUf4OBRUKIAYqibPK0ASHEWGAsQFZmc4fPIjWaHU2+bPvsIqGwg1jj\n3lXxOVQ06Ula/gJ85XetXa5D0cWGtTXEiieBLX3Y9Yf0d0cfVsHdJvEf9qVu55e4VA4eSuNgXmRN\nmHTGeyEtM8E0T9nbQNQU8TocQJXKSCDS/doNYSHRmtC2T4MZFBRF+cLN4p+Bn4UQs4ERwIvAMC/b\n+AD4AMwFayDyo9kQfSIbQuMLtH5p4wx5xBkOAMLlAeH5gSEo6PI4J9O6BbVPwcRbLmwpsOuXSPB3\nD5isd1kmhX/dsQpuIX43+7ebR2aGEnsMTXuR13OqSyEtYTQEV2S7sYG427fJln0qsitD+iLS/dpQ\nv1FtrQntMsvvJC9trJ+VeWmjlucxC+0LhRCxiqKoyqmthSwj0SiywerNW6K6aqM/1G7Tv/fExOI1\nYSm0vRebkbmwPTFwsg4lSDLBnWgNxrr+Ct+mCUqdxLuc2Bk8Bqaf6ejfjtCUgFbcFdJq++uIoO7D\nU9Ymd/u2jvZq/QkZyX7t+i5kozWhvdfyu42XNq2c2taFXMvvOCAdOKR2xUgW2dGAp2I0VUmnAIsb\noEfucZ6kEy7Yp+prmp1ARsZxuqWWSIGtgmCJ7FBSUiEYMFnvU3CrtaqoQc1Lg9oXgGi30Dj6t4vY\nmppMYXoTKgti2FNQFjEpAUNNINY8a1EbE0ZbuXYtIy0kKvZVL3upPzZafncVQsR7yDzS16ltXWhm\n9/8nPLayQ6nHTBTBJlp82Z6K0ZSn96fZ7mlhJ4PCNVdrTrsMKpuBrkklWanQJjFD2kScCKYQbQg8\n9b2hjivY1phI/tuowXo9lotmxJOIEhNDo/gYKA7Pe4pqhD6gCen2KEBVfEsKuzzqU2THGApIyZtn\nqT5pfWaczdGc4Zjic+rUj3BGKxaSUKMpoa0oygEhxAagF3A18Ln950KIwUBLzFUjVwdhl9dYfu9U\nFEW1FSVSo9mgfZEdX7KBrNxJbovRpBQsaeDeuSecc7UKzKkQhca/N4GiVSGn1ePSMgK9edK1CI9q\ntnXhRPoAS/XGwBFAXGW+z3bxJRtcJkWanxnLSC5czuFOj9iqSmoRLVhIQr6fkO+h/nkJc7GaV4QQ\nqxRF2QUghMgE3rG0edm+KqQQ4l7MZdl/VxTlRrvlrYFBwLeKopy0Wy6AMZZ9AbwWwuMJC6LBMhJj\nKCArd5LHYjThSLjmahWixvyDHhHBozgS39TFBx4Kwq0/kYRADxgtYruGSJUIpa2vI6l4NSh1fGlQ\nasjZOMGhBLs9MYYCMnMney1glpU7iYM9X9P05EiIbAtJyPcR8j3UM4qizBZCvAuMA7YIIZYC1cAQ\nIAWYA7zltFo60BFzpNuepsAM4D0hxE7MObjjgK7U5uF+S1GU99X2zzWfROSg9Wh2at4chEnVfNaA\nCXbaqXArrb5j92H2niglT1eBKVWQriula2w+SSTi6LSKDiLdGiLRPmb7yD9UlK9hm64FxdVp6E4I\n9mw+QbvkJDq1izzrQ018NhVp3Uk4uqHOUW1hOulSgt1KSt48VQXMsra/xOEuj2tWbGvBQhJKNCe0\nARRFuVsI8StwD+Zc13rMExc/Bt61j2b74AAwCbOvuwNmga3DLMi/Aj5QFOWnIHc/7IiGLCMmjOYC\nBCGO3CsiFhCIuhUUDbvS6tbJj/n6MnOGkebH6ZqeT2ZiIq0TWketN1uKbEkk0CrhFFq1OYXMxN8p\nTM9nW/MWHDiURl5+BXs2n6BtUlrETY6MP74jaAEN5xLsVpKLVqgqYBZnOEDLjQ9q2kYSyRaSUCMU\nRQ7r1iedTuuqfPTWzIbuhmq0NgEyxlBAat7c2kkrukZUN0ontrIQoVTV+cZsfzU5b0sBFBFDacsR\npOXNcVPowFwZEnQOgt+8XKDo9AhTddiVVl+0aZdZYLdwFtjNolZgW5E2Bm2i1WwkAAcq/mF/xREK\ny8vZVtyC4kNp6PIVckwJESW42/46Mqi2NQVQ9PGWPNmXUROf7fc+TLpGmraRWKPakSa2z76ox3pF\nUfqEavuajGhLgotWRLbbiY6mSuIMB4Nq6PG0LQEIpYa0vDkUdHmcxOI1DkUWyjIGU57ez+3ycBHV\n9uzYfZiV5YehVQ3pzUvpml4Q9RFsSXRgP1KhtVSBttR/Cf+QmXjELsKtmCPcEZJrO9jFxQS1E+OT\nC3+hsNPDfu9DmE7SZN8sijo9ELR+hRPSQuIeKbQlHtHSBMjGpVvI3v7/7L17lBzlee77+6p7ZtRz\n02g0MxpNSwgJ2YwkFBiBvQ0YSEJIbAewc+IkTsLJjjeGZNvJSQJi+5bkOD6xnQQFsmOHJBzj7JPl\n+HLicxLAt+zggIAgbEAyBoQcC4Gkaak1N2murRl117f/qK6e6u7q7qq+1uX7raU1munqquqZ7qqn\n3nre5/20rTWkHiLbHJHuZF1CT9M19WzRoAOT5b7dnsvFtmLNyB7YMcXO9afZ0N2tBLYilAQ1KtBe\ncA8zflrmxre/6/Ltrd7NkhjDxR4ra+0wj9tuMJsch47sY6lvN10zLziuaguge+pJFmauD6yFBPzb\nGNkolNBWlCUI1ezYzEGGD38a6nzhsHpojWTX7fRg680hM5WwTnrsv6KTocFJLls7q8aoKxQBplBw\nW8e3f/PFo56tbs/FbzX6bvTSQrumRkl9ma6Z590/DwKdRKKq2sX4X0UpGkJQGiDNyD6BXve8F4Hh\n2ZNa1LUX0KtDZkphrWJfemOan9z+Ej87sszbB9+mRLZCEQI2d17CtQNv5S1DW/jxi2bZuWOFpSvg\n1a4U33zxaKt3r4h0bJiJ0b3oWgeyARMaBc7vYhY9V0+zNvFInffIWwTpjnitqIq2ooggfUDWJh6u\nGL9UC9V6AL08ZKYU8a2DLK9Pc55JNeVREXrC2uhqfu4XWEeMHvToGqaTky3eK3tS/XtIjN1Hb+LR\nbN+LcbxutYlHkKF7cj/T2+9s8Z40BlXVzkcJbYUtQahmg7P4pVpxe9D26pCZSpgT44S6EVYSlZut\nCAtCaNmBVN6eJJmODef6YbYcuA2tjg2StaBlzqOTQWtAtd0rKK+2gRLaijyCVM0Gb1o0vDZkxglv\nLJzjfHcUmdYZbPXOeAwlrhVhRhBBiAyvHjvjSa+2FS+dD/x4V9MNqqq9ihLaiiKCUs2G+kc8FeJG\nXkk0pNbmmSEzTjAnPZ7ctJiXke2XKY+NjF5TAlsRZrp5iaW2RWOa5KY+X0T/Nfp84Hg/LHc1VVU7\n+CihrcgRtGo2VBfxVE3kUzkkILUO5od+wpN52HaYzY/LGwVyR4IbfJqRXWv0mhLTCkUxpbK2zeg/\njuFJse3kfNAMzLuaETQy6IEV26qqbaCEtiKPIFWzAWbj764Y8QSgi3aEvNCwikdi7D5fCexxbYmB\nKzoYGJxjd9+87wR2vVAiW6EoTXH0X4LDGzey/5T0ZHXbSeRfOWotwpjZVEJfJv79vbkpk8uxoRrW\n6n3CXtVWQlsRaNKxYc6M3lM0ERKM23dSizIxujdveMDFT/8i1LXiIehNPOqL3Gwzwq9/uJOrtsOu\nrmU2d7611bulUAQCa1KJXyZFOsEquDu7hjmztgd9eA0r03jKu21G/g0d2YfQl6sYVlM75jqsUyaT\no3ez1D+mqtoBJbyXGIo8gpKbbcdi/+WcGNvH3PBN6JEYEoEeiTE3fBOJsfuKJ3TVuYgpkPRM7q/v\nShtIfNM6tgz2IAL6flD4g2f2tvb2fqMJ6t0S87jh1TQSM/IPUT9R63SKQuFfXJBB05cZPvLnRFPJ\nuu2PFwmiNdUpqqKtCAUyNlJy5HnxwvU/wXup270SXj1BNppr9kUCVWVUKFqFIGLYLIQ3jyXp2DDU\nqcpqiGyNWiYPCz1NX+LrTG3/gKpqBxAltBWBvtLUbSwg0VSS3sQjRsZ25jwysibnlUvHhpGRWP19\n2nWsnjSKb754lFORec6nMwyyQDfj+CVdpF4EtcroN/o73U1aVXiHbl7iDTYxme5FpDTWLKRb3hxp\nd8zPzvatw9ojrMRGaE+dqrrJUpChd/JJprZ/oA77o/AaSmgrgOA1QVqxNmHEZg5m/Xmrfm2rV25i\ndG9jOtOld4VDrgFy8xwDG8+xa+DVbMLI+lA2QAZp4p+d/aLZr8/cBzfbVXcV/Mnq8WKcibZFXmkf\n4WS0l5OJ5ZY1R5Y65kvqkzAlyNC2PInUolU3WRr7ZNz1DHoCSRibIpXQDjlermZHU0nWJh4uqjzP\nxt/tKMFDSyVYn3iUnsmnjOdr7Qj9AsLmNQsyCD3D0JF9JHd+tKbOdHu85zc1Bfb54Sj6JXD9xlfZ\n0N0d2oQRhTOe2ZtxlU9u/b/b5wSdINqVSiWRnDi1nvFTzY3+i6aSDB3Zh6YvFz1Wz3tXQl/mzM6P\nFQl6cC7mZWRNLu5PESyU0FZ4spodmzlYlBRirTyfGb2nuImx0vP15Yo3CoWepmvqWUtneroulW0Z\nidW8jnphjfDrv6KTwcEZdq89zpauLUpgtwBr1dkv1fRqhGE1z3Eqzv3MzJLg5ge0QIltKBTck7y8\ntoeJgXW8mkzx+otHm1Ld7k08gtAb7xOXkTW5JsvexKP0TO7PFYcutA/QnkrYFnhyz8c4v205cBvz\ng9dxNn4Leize8P1uBWGM+lNCW+E5oqkkG47cW6IKYVSeNxy5l/Gx+20r2+WfXx5Bhp7J/cxsv6Pg\noJmyLOMO6xQwrxDfOsj69SDWpRleC5sDahMJg1BrJs2uNlvFp18uQqohyO9R87iywDrWsA4ZjbIm\nBkw1vkG8Z/LJhg+nsR7f07Hhoqb7aCpJ/NBdCJvzkUl+5N936JnYX7GY5EfC2hSphHaI8eotqrWJ\nhytWIYSeZm3iEaa331nV88uuO+uVKzxoGg01VuEdyfbTZMqKbyk05uK3VL0/zUDz4F0Np/h9emOj\nBGQ9RLGXIvbcXDSpCyxvIkgjmyg7mpH2ZE55LEV+dnflO6ROikkKf6GEdsjxom3ESRXCrDzbCe3a\nqxiS/qMP5lJITEpWKw7+DkKWE/be9ZwK0r7Pyw6roPKSCG4Gbq0VQamAu/HDe9l+kp+v3Rzp0ahJ\nv2Ae1SNMjO6tKIZNW0nf8a/SPfXvmD075f6q5YpJfids9pHwvFKFb3BahSi1XK1VDAH0Jh8jfugu\nYjMHyy7bm3gEUSFRREhJb+LRmvapEYQ1LzvsOK10h6kp0cs4vZD0wwWnaHKaxvzg9cgqtmkmkpRH\n4/Rlf0Cqfw/RVJL+ow+y5cBtXPz0e9ly4Db6jz6YN4SmLXWKrpnvAsY5xqmNMWh4sbjXaFRFO6R4\n1TYCzqsQRhZqMXpkDZEaqxjWFJLE2H0lKxZuqu9eHMHe7BOfovV4ueqpCAfNGmQzF7+VnjPfQbi+\nZowws+V9rDv5NZsUkQhSizIxupflvt0VI2Ont93OmtmX6J58yv3Idx8NOlOURgntEOPVK0snOdbl\nGgwXBq+jN/mdCs931tQo9DS9iUdLiuRaq++twqsT2xSKsGK1unjdBlILxsV9M21PzuWtVUSn+vew\nNHCNbV+O0JcZ+uF9LK67iq6Z76LpKzZbNYo1A0cfcLkXq+glikkKf6GEtsJzzMbfXTHHWmpRZuO3\nFv1cJ8Nc/N30TOyvkIOtIdFdpZDYTxfTcHLSKFV9bzZmtN9yt0CmdQaZC+UESEXw8XNDpF/3uxyt\nmBhpWPvKX7CYxW4ZiTE/eANz8VtydzDNvpxU/5WrVWu5WrXunnqq4j5U+5c0iknXV/ls7xMmn7YS\n2grPkY4Nc2b0nqIcbFitOJwZvaeknaNcl7f5/HPx97Du5Fcd7Y/InK9pupgX4v2s2dlsTmcnQCZD\nPQFSEWzKVYT9nlTjN8xM7Ys6X+NE3ziPt69tysRIZ9Y+0CMxjl/9RdvHmzX0phDjPHVzICdFhi3m\nTwntEJJB96xtxCTVv4fxsftZm3gkL/x/fvAGZgvSQEo93254wPzgDSwOvI3hw59xfJCURGs60Jrx\nT3YV8fnB64vSTeqJVWDrmyQDI+e4bP24mgDpc1Sjonv8Jq6DkppixRTc8L2iiZGNENz1sPY1a+iN\nFQlMjO5FxkbAw/1UCmcooa3wLOnYMNPb73Qcb6STybsVZRfHB9B/9EHHB06jWn0BdPcXJhKQop2J\n0b20pU6VbZgxPYH1xDpivX+4k8HBOXavnWFz52a2dL2prttqFn4TS9UStui+ZhCG941fuHbgrbmJ\nkS+t7WNyoJfzySivJ+fraieptbEemjP0xo6gDasJM0poK0KHmwPn6qm5mqqCYHHgbVyIjRA/dFfZ\nSZeV0k2qJb51kPO5CZARNncu+FZkgxJLCkVQ2Nx5CbrUWaCXWIMmRtbaWA8tamQX4ZBmYfFph+Ov\nqQglpawajRpgUIhA0jXzHHok5mjSZbl0k/rgjyppWKrWpVC2EEVYaPRE2rn4rY4a68tNdmzk0Bvb\n7QELA9fkvo+gkVE+bV+jhHbI8HJ+di3oBSKyXLZpMxGZ857K2vbDqPWgi2xlC1E0AnWBVoyTxvhK\nkx2dVMVL4TRGNu85oo1zF/2S620pvIsS2iHE642Q1WLegirfJW4cLKs5AFaDUQ3xZ9a2QqHwPkHI\n3BakkQ2SI+Ua461RfqVwUhUvh651FIn8Ukhg+pI7GtYcr2gNSmgrAkcrusTtkGhcaB+gPXXS2fIN\nzNpW49YVimDi9ztAogmFn1KN8U6fW6oqXgkZiZG4Yh+9iUfpPfMYyHSFAo9G+8Ix4EbX+6nwLsEs\nbSpCjdPsVDdItOw/Nz45nfZUwlkEYBOytptxQgsbz+zNKCuIQhFQoqkk/UcfZOiH9yGyd0iliObm\nJ5TDPKabIl9qbQ4GpOn0TO63fazQHqnwD6qirQgcjbBgSK2N5M6P0jX17OrtR60teztRIized4kG\nuamTzm7pVmrIUSgUrUcgkU0xnSlajV2fD2SQMoLU2kHqCFn6TmHhMb0WC6HREOlve5AdZkNk0JNH\nlNBW+J7CK/16dolbG2aW+3az3Lc77/ajkWyS7/0z7CIJnIhspw05CoWi9VhFttUb3erhMub2/erX\nFkSy9jZvSJJKfT5Cz2TLK20I9IImy9X/9SYeyQ0kc35ekmw5cFvDh5kpmoc33tWKphDEK2IT6xVx\nLV3iJhLDX1epYcbO+7flwG15Fe5y25gbvslRQ04tKH924+nvlI68sioZonU4/Rs5xYveaC/ukx8x\n+nwuVFhKIsiwtG6M2OxLCH0FWLUlCn0lbyCZ0/OSoPHDzBTNxZHQFkLcANwGbAJOA1+TUn6zzPIf\nBn5GSvmTddlLRd0IauKIlVq7xAGk1sHxq79Y1XOdW1dEw+P8VrcUrAxWr+HHKmLYKPc3anVFWuEt\neib2VyyWmNbA2OxLIO37fqwDyZI7P+rqvFQ4zCwTG3L7MhQeoaLQFkJ8AvgD89vs1/8shHgM+N+l\nlBM2TxsFGtvZVQEhxK8A/xX4MSACHAH+DvhrKd2npAsh3gHcBVwFrAGOAV8G9kkpi+8vKVpG+exU\ng3J1HwkIfbnq23f1GPurUCgU1VDqosGvtpJWIHTnfT5G5bv8nSqhX2D9aw8B0tE5KP+5xjCzye23\nO94nhbcoK7Szlew/xBgp9z+AQ8Cbgf8M3AR8Vwhxo5TyWIP30xVCiL8CPgicB74DXMDIy/kccKMQ\n4heklI7LnUKI/wb8Kcbv4QngLMaFxB8DN2d/B0t1fRGKmiiVnSoyyw4rFdXfvqvH2N8wU+9b/I2k\nUNQoMeMP6jV91E+VcL98pvyGqJg/YqSJtKdO5olrp4LbHGamhLZ/qeQj+C2M98OvSCnvkFI+KhhV\niQAAIABJREFUIKX8XYyK9b8BW4AnhRCXNng/HSOE+HkMkZ0EfkxKebOU8ueANwGvAj+H8bqcru8q\n4E+AJeBaKeVPSSl/AdgGPAm8DfhUfV+Foh6Y/unjV3+RN97+NSYuvQunKSAmggyavszQkX1EU0lH\nz5mL34rUyt8sUikjpfn6B3XfxuYpMeMP1N/JmwgR3H6SwnecsPlZyeeqYWa+ppLQvhp4WUr5j9Yf\nSinPAD8DfAEYAZ4QQlzWmF10zUezXz8spfyR+cPsPv/X7LcfEc5DhT+C8Xn4Uynldy3rWwDej6Hc\nPiiE6Kt5zxUNI5pKMvTqvVUHc5m375yQjg1zLv4e26xV82fn4u9R3eQKhUKRxUt9JFLraPUu5KFs\nhv6mktgcBA7bPSClzEgpPwB8FtgAfEcI8WN13j9XCCE2AVcCK8A/Fj4updwPJIBhjEp0pfW1A+/M\nfvsPNus7BhwA2oF3Vb3jiobTm3gEIVeqfr55+84J0VSSvsQ/21YszJ/1Jf7ZcYU8jNz8gNay2/Iq\nGUShCDfzQz+enYdQGenIPFI9ps0wgqaG1viUSu+kaaCr3AJSyt8B7scQ5d8RQozVad+qwdz2K1LK\nUt1ozxUsW45LgU5gRkr5Wh3Wp2gRxrTI2nB6+87JCHg3FfJa8Out2Fbe2jetKwqFIpwY9r82R8tK\nrQ0p2hu2L8pm6H8qCe3jGBXiskgp7wb2AeuBx4Cdte9aVWzNfj1eZpkTBcs6Wd+JMsu4WZ+iRdTD\n4+b09p2zEfDOK+S14qVbsn7gmn0RXzW5KRSK+mImV+laR8nKtgR00c7E6D1M7Lgnu2ykaBknGJbC\nwudG0LUONcwsAFQS2s8Aw0KIayqtSEr534A/A9ZhROC1gu7s18Uyyyxkv/a0YH2KFlGrx02C45SQ\nWkbtKhQKhaL1mMlVS+vGbPttQOS8geayc8M3oUdixtTISIyV2OaKFhQJICKsxEayYt147tzwTSTG\n7lPDagJAJaH9DYy30u86WZmU8iMYCRytuu9rbrdelqm6rE8IcacQ4nkhxPPnZs/WYbcUbpkfvL7m\nN4XT23dORb1qcFEoFApvE5t9uUS/jUTTV3KJVIUpV8ev/iITOz9S0YIiACEztKdOgZQsrTNcqL3J\nfyH+/b30H31Q9fP4nEpC+0mMvOy/drpCKeUfAO8G/ksN+1Ut89mv3WWWMR+bL7NMXdcnpXxQSnmV\nlPKqvrXrHGxWUW/m4rdW7aOTwNK6Kx3fvjNEfXnrgcrRDi43PxD86asKRRiotd8m34JS/pwgyKDJ\nFTrPHkTLpAwhn53lED90F7GZg1W/DkVrKRv2K6VMYwx8cYWU8lEhRCusFG9kv24ps8zmgmWdrO+i\nOq1P0SLSsWEmdtzD0Kt/ipBpV7dcpGhnZpvz60YnI+Cb2eAiybTsFlMl6jU4xEsE7fUogoFK03GP\n036b3uS/Mhe/xbYYk+rfQ3LnR1n/o7+lffl09jnl1le8fnMU+/mxfeixuMtXoWg1rkovQoiHhRBr\nHSx3JdCKy69D2a+7hBCxEsu8pWDZchwBUkC/EOKSEsu81cX6FC0k1b+HxJ7/zkrHRldNKhM77nHV\njFKuitHsBhcpyw/OaTVKlCpaQZhEpzn8SU0sdY/zPppMyapzbOYgw6/8Me3Lp10NqSnaFz3NusQ3\nqny2opW4PQvfAnxfCPHLUspn7RYQQvw2RlNk4/JuSiClPCmEOAjsAX4B+PuCfbsB2IQxNfKAg/Wt\nCCG+BfxvwK8CnyxY3zaMoT4rGH52hcdJx4aZuOz32fTCb1NpSqQEFgavr6oZpdQI+PnBG0pWPhQK\nRXMoJTqDljbjpwsKSSZbGPBOJKmMrEFkSiUFryIAoS+z4fBnkFobQl9BRtaw2H8VXZPPotXhNZlJ\nVdPb76x5XYrm4lZo/z3wa8B+IcTHpZT7zAeyle6/w/BnL7M6hbHZfAZjWM2fCiGekVIeze7fEPBA\ndpk/kVLmjrRCiN/CGMv+PSnlrxWs708wxrZ/WAjxbSnl97LP6caYjKkBD0gpzzXyRSnqRzo2zNT2\n32Tg6ANlqwtSawcp2XLgNotQvp65+K2OhLLZHDOz/Y767bxCoVBUQOXA14fF/qvonnzKRRVaR9OX\nARCZFN2TT9V1f1RSlT9xJbSllL8uhHgc+CsMIfvjGML7TcBXMLzRR4BflFK+XOd9dbqPXxNC/DWG\n0H9JCPEYcAG4EegF/hn4XMHTBjCG0xS19kopnxNCfAT4U+AZIcS/AeeAG4Ah4LvAxxv0chQOiaaS\n9CYeMTx1JURx0TKiDWQaY7bXKhINKSIgdbqnnsl59ES2MaVn4gkmRveS6t/jaLuK8GFWRvs7pbpl\nr2g6dpV59V6sApc3BOwmAdcTlVTlT1wbOKWU/48Q4nsYVeN3Aq8A/UAbRsX7g1LKpbrupUuklB8U\nQjwNfAhDEEcwLgC+APy1tZrtcH1/JoT4AXA3hsd7DXAM+Etgn5RyuZ77r3BH58whho/8OUJPlxTF\nAENH9uUvIy9kM04Fet7tvrfQNfUsmrxQtC1rY8r0tttZf+yhsttVGajhRnnQ/UV/pwzs3yyor6uR\ndJ193jON5Cqpyr9U1SklpXxVCPEO4CVgA8Z13xeklB+o587VgpTyS8CXHC77CeATFZb5NvDtmndM\nUVeiqSTDR/48d7vOSk4Uv3ovCND0FZtljGsuCYxf+TnSsWH6jz6IkBU6zfULDBz9m9zzbbd7ZB+J\nsftUZTvkXLMvoqqJPsH6NwqaX1vhnmZaNSTlK+BSizIbv7VZu6OoI1UJbSHE1RhWkV6McecXAe8X\nQswCH87GAioUDWdt4uHKOadyBWT5uoSZhTqz/Q6HkU56xbuK1nW2Glnh9Sgai6omep8gRk36BeP4\n5L2EJKfNkDVvB0h3DBK5MIvQM3nnH0kEqUVJjt6tijY+xfVkBSHEh4EnMPKjPw+MYlhIpjAmSD4t\nhLi4bnuoqBsRNNLuXDOex5koNqZ4lV8mQ2/y21z89HsdH1grnZLNdbZ6spf04AlMofAaSmS3Fi8e\np5wMH6sHUmsnedknSIzdXzTG3RzFvtQ/1vD9aDZpqRNxL0N9h6t3thDim8DPAIvAr0spv5x96H8K\nIS7HsGr8OHBQCHGHlPL/q+fOKhSF1PPWnnGarW8clgDl2VYoFAqPY9fYvth/FVJEKloJK9k+yj1P\nijYmRo1ZDUZBpvAcJMlUiKJVeBu3lxLvAH4AXGkR2QBIKZMYyR6fxLCUfLUue6hQlMEPXdiCDJq+\nzNCRfS2tbHsRP+X8KhSKYBKbOUj80F30Jh/LG3/ePfkMINGJ2Mhf45+utVOFOQAJXOjYSGLPX3Ah\nNsLQK59i0wsfojf5L0Uj2C86tJeumRdrfp2K1uD2Xs2DwO+UStmQUkrgE0KI/cAXa905haIS84PX\n05t8rKx9xDhAior2kUbTas+2y7CdpuC0QVA1pikUwaTVx6VoKsnQkX2lG+plpsSZQyBFlNTay4jN\nvgzZZnunlW2pdXDmst+nLXWKoSP3IvQV2+eazfUbjtzL+Nj9yqftQ9zmaP+mw+UeF0JcUd0uKRTO\nmY2/m56JJxB6GaEt2kGAsEkdaSbmZK9WCG0v+h/dEOTYNUVzUM2O3qWVx6fexCOVG+ptfyYR8gKd\nZw8WzGEo/3zDLtKeFztrl4hVtA49zdrEI2oypA9pmAtdSjnZqHUrFCbp2DBnRu9B1zqKmlYkEXSt\ng4kd93Au/nO5W331xs061WSv6vj6B3We2ZvJ/VMo3KJEtsIOJw315bAbUlP4r2iJ7A+diPzVZxmF\nGoX/8HeZS+EaM3kkKoLT6Zvq38P42P30Jh6mN29C4w3MxW8BssNqGrgPTpthWu0p1z1oH6mEqkQq\nFMHEOB611hbW7OKHQCL0FYaO7Mt+71zkB6lQE5bEEVBCWxEQ0rFhprZ/gLM2t9X6jz7ouGpQLSux\nzbSnErYDbExaP9nLnz5nJbIVCkWjaFZWdiHGOcldJb3VhRpFdSihrQg8td4arIQA2lMJqBDBJLVo\nrsLeDHZs28A3XzzK+PEl9BHJwMg5ltaPc3Jpmi1dg2zuvKRp+xJ2VLqKwilWa1RQm4BPLr3G8cVJ\nJhaXeHlaMnWqD+2UYJPeydaenqbui5OG+kYgKNVkaU/rCzWKalFCWxEoMhTfjmrG7TbrKHfQ8irb\n5sFU6MvEv7+X+cHrmYvf2pTu8Xddvp1Xj53h9fF5xk8JnhjpY2hkml0DJzjRNc1FneuV4K4zaty6\nQmHPyaXXOLE0zcTiIq9MDTNxahvaKcFFWYG9Y9uGpu/TXPzWig31jcLNvTo1gt2/KKEdUoLm0wbQ\niKDbVCWc3ho0BbHUOrIJJbJKX7eOFFGQpl1lNVpQZHNRmznAZse2DexgQ05wnzqts3+kj4GNc0pw\nNwBldVEoijm59BrPT57glakRpk5vNgR2pqtlAtskHRtmYnSv0cejpwvGn2uA3tD+nkqYKSVnskNt\ngkCY/NnQwNQRhXcJ0xsc3I3RlaKd6W23I7W2qg6uuS7zbNOh3fj3Vg2w2bFtA++6fDvXdo7wtrYt\nbNavYP7CT7PA7qbtQ1i4+YFwfcYUinKcXHqNw0sjzF/4aTbrV/C2ti1c2znCuy7f3lKRbZLq30Ni\n7D6b8ec/zdzGn7VNrGqGGUwCS+uuZHzPX6ipwj5GVbQVgaPQPuL01qAAhFxh4OhfU91AXeu6KlsH\nhL5C34mvMnXp79S0rWqRZFpaqQkyTqva1SaqKHuKwq/IJnuhnZKODTOz/Y68OQfRVJL4obtK5Gg3\nhzO7Pt6kLSkahRLaikBhZx/JvzW47OAAKZsyRVIg6Z58ksXB65perZAyCjQ2iUVRnlpiCxttT3G6\nb0rwK6qhVcefaCpJb+IRo0E+FwNbumfGTc61U3I9O06WjcTqum0vkPZhxGytqPubIcXM0w4L5q1B\nJzSzyiug6RYSK16tLgWBSvYRL3u5ne6bl19DISr5pfW08ngTmzlI/NBd9CYfQ8ukEEi0bM9M/NBd\nxGYOFj2nEYlV9kNsiglyykjY7KvherWKUKARIWNj3fBqI4nQ0/QmHm36dv0+lt3rzCwJ5dX2ENbp\non6hnhcHrb7QkNJMZmr+cSeaSmZHnS8XCedyPTOtHBCjUkaCgzrTKhQ2OJ30WA/M0bpWb2CzkERz\nJ0Cv0t8pHdsYvFZhnVkSgc1CbhTKtrJK0F5fqy7unVhAhJ6m7/hX0aOxnLWkOS2P+UiM5KsgpYyY\nhOkuuhUltENMEMexW7HL1EZEQFauaDVbrjW7cpJ4fZLzqSh6Os15zrKj07sHQDdiQ4la/xNE24pT\nWl11bhR6gcBKvD7Z1ME0TiwgggzdU08CkYKIv+afD8bH7g+cyDYJm20ElNBWBJRSmdoLA9fQPflU\n0w6cTg/SzRytu2PbBjgGryfnGZ9YYmqkHYDdfd9Tedo+ws1FRauqv9fu0xyl0Qsk/77X/f4Fqfrt\nJ0uLUwonQGonoqxJppuene20kGG8kwqtJeUpPMbXKsz1SCywIjusKKGtCDSFVe1zF72P7qkDlmEy\njUESQWpRzndvJzb3StkDbyuaXgqH2Eyl1/L4cC+DgwtcpgR34GhV9dfpyKdqR0O5qX7XkvKicIfd\nBMiLxrvY2hNjx+XNz812OrSs7DooFNQRpIiQ6ttNbPblXKJVqXeYk7QRSYSFgDZAhtU2Akpoh54g\n20fsqtptqVOu4pUqkX+jNwLo2cioG5iL3wJg5LDqy6XXoUVzyzYbq+B+48Vlpob7eHzzvJoYqWg6\nNz+gNbTqrER248kX2MYESBJRLtI7edfl21u2X/OD19ObfKymBBGBebwXecf4dGyY/qMP0pt8jMJq\neDHGpMnSSBYHrq56H71OGG0joIS2IgSYVe1c53kV1exStwNF7nENqUVtx6qXHu8byT2n1bcKTcH9\nrR/8kPXx3cxfuIxO5oBTLd0vhfepl0BWjaPBYIHdzF/oZZMu2N4GbV3plk9/dDq0rDKCN97+taKf\nOvOAg661IaVEyJWShZ7hw5/mzOg9gZoEGeZqNiihrcgShqp2I4YPmAh0RDYiKrnzo3RNHcgbirC4\n/q0gBV1nn7MMSlitiHgFKQ2ho/K1FU6xqxQrm0a4MY4f0YYPpnE6gCZ/aFlxwQOHU3ILe2nM7Tu1\npQh9GSnaSj+ePY9sOHJv4Boiw1rNBiW0FRgfALvc6SCRQa96+IC03DSshNCX2fjyHwEiN4ZdZFJ0\nTz5TsuLtNSRRhJoaGTis1eJKzYG1RiUqke2OIKWNNCsvOzZzsEg4i+wAmp6JJ4qOtebQst7Eo/RM\n7s8reGiZRbonnyl7fijspcnfvnM0eaHiMkJPszbxCNPb73SxZoVXUUJbkSPoVe3qI/Sct2qJ7PKF\nwlyQQegZho7cS8LjlYoXDx5HH5EMjUzTvWUeQPm0A4adTcMqvr/+QV3ZOOpIEBNFCjETRt6Y7WBi\nEmZ+cIZNemdDYvysA2gKWT3W7iMxdl9RZXtm+x1FMws6zr1E9+S/V9hqBi2zmBtqU2r79cCcrRAE\noZ2WNjG7IUMJbQUQjqq2rrUR0VccL296qMs1MrpF6Cv0H/sCE7s+Vrd11pN3Xb49l0Ry6rTOP57u\nY8eo9E0SiReH1vgFq/h2W2FVojy8mA2QZxYWODy9EU4M0plMs6tnQ8O82U4H0PQmHq04CMysTFdC\nAN2TT9E9+ZSbXS1ah+NlWziVUlFflNBW5BHUqnZ7ahLNgT/blBcyEst5qOPf31tzNJSJADrPvkA0\nlbStajv1HDaSvCSS8XNMpaM8vqGXXSPPeT6JpJamPCUWV1EXK4pKFEb4mQkj13U1PsLP6QCaShN3\ny1XG7dfZPJo5W6FRqGq2gRLaihxBrmqvTTyM08Pk1PYPsjB8Y+77ekRDFWJXaXHrOWw0puA+8nqC\n119c4PCZa3hl8xvsGjgBg8pOolCEFVNkv3xuE5OT3cy8tMSmTE/TIvwcD6CpsFwjG+QLcTPIphWz\nFRSNQ11qKIoIYhSP00ZIAaw/9lDOhwdGNJTU6ndNKoCeyf15P+s49xIbDn8GTV8u2k9BBi2baGLd\nr2YxujXO1p5uLon1sFm/gokLlzZ9HxQKhbdYYDdr2MSm6AAjTRTZ4LzaW2m5ahvkq0U6lFxSizIb\nv7XBe9NYgqgjqkUJbUUeQb3N48bvZnr7TMxoKF3rcHygdLM/sZmDbHz5k5QfZFC8X83EiOkKduyf\nU1+ycJhAo1AEmWali9gxP3h9NpavNKWqwtFUkv6jD7LlwG11swQ6RWqlo/3AqHrrWjtnRu/xdMO8\nU4KqJ9yirCMKW4Lm1XYzgtfO25cXDTXxeK5BslrPnllpMT2CwoFlx4nnsJGYmbgSnRNL04GzjlTr\n71aZ0YpyBCm6z0S3iOzE+Fma7SZ2MoDGbuKunT2veUSY3nY76489ZJPlbbC07kqmt93ue5GtvNn5\nKKGtKCKIXm23Pmu7Crg1GiqaSlYcrV4KiZartLj1CLayEz3x+iTjx5fQR9qZGukB/JFE0mhMga6a\nKRV2NHKsfLMxI/wmFpd4+fQIWnKeNcl0QyL8ylFpAI3dxF23jY/1J8P6Y59nctvtrFl4vSjLe7aJ\nDe+K5qKEtqIkQapqz8bf7WoEbyVvX/kDfaVKt87iwNsA9x7BVnWiW5NIXh+fZ/yU4PGVOAODc+z2\nSfSfQqGojuIIvzE6k2m29jQ+YaQU5QbQ2E3cbWbjox0CI9518LXPM77nvwciI9sOVc0uRglthS1B\nq2qnY8OcGb2H4cOfBvSyQtjO21cqds8Yt/5s7kCPiICsdDDX6Jp6luW+3a4q1F7oRM8T3N+fZ3pj\nfzb67wXPR/81GpXhrQgarYzwc0KpATR2uC5qZL/W+xMt5AXWnfgKk5f+bp3X3HpUA6Q9SmgryhKk\nqnaqfw+nL/s/syPSSx8QpBZlceBt9B99MCusTW+3yDXCFcbumQf6LQduQ8tUGKSAnvNau/GO23kO\nW0Ve1nbyHPunRxnYOMeugROhFdxqmmJ4cHpR5Vd/dimBbU56bNQgmkZgFkkcH2cx5igsrnsL0Qsz\nrJl92ZHYdirMBdA99UwghTaoBkg7lNBWlCRoVW2A8327Se78GBuO3FvS23cu/h6GD3/GpmGm1Fj1\n1VG/zvNdU0RTSUfecWOrkSLPoRcwBfe3fvBDEqcE+0f6GNh4LtSCWxFsrKPqg0a+wB5h6vRmtFOC\nTZke3wlsKGx+dIaMxDh+9RdX+3BcPM9xiknFu57+Q1WzS6OEtqIsEbRAVbXBqGyPj93P2sQjOcuH\nHlnDwuANLA68jeFsnrVTrKN+3VSo44fuYnrb7Uitkndc4/Rlf8By327H+9Rs3vljl+YmSSZOSSW4\nXfDM3vy/vaqKe5sgiuxigb0F7ZRks97Jxd19vhPYUF3zo9We58bTbT6vN/ntqvbV75giW1Wz7Qmk\n0BZCXAr8AfCTwHogCXwT+KSU8rTLdV0MvF5hsV+WUn7F/Z76h6CJ7XRsmOntd+Y1pOhkGDz6edcN\nM9bYvcV1V9E99ZSj24dCX2b9sYfKRD6tds97WWSb5E2SHF/gfLqPV1biTAzOAeNA8KdJKp+2wm/k\nT3nsRZzR2JxMs7Wnm9Gt8VbvXtVU0/xotee58XSbdkPnQjt4F9N+FdlpvfEXzoET2kKIG4BvATHg\nIPAkcDnwm8DPCyHeLqX8jypWvQh8rcRjlYS4rwmihaQU3VVOChOZ88RmDtI18113z9PTtC8cc9U9\n73VGt8bh9QQrsTWcj4LGOhZYB5xq9a41HLPa6TRb268e3lbxzN6Mqvg3gAV2E6OXTVHBmhi0dacZ\n3eq/KrYVV0LZJhLQqQ1QAhOje+maOuB4+YWBax0t6wf8bBlphsiGgAltIUQX8BUMkf3bUsrPWR7b\nB9wNfFkIcZWU0u0ZbkpK+eu17qP08VS5oFW1C9GIoFWZUy21juxtyhVXz7NWw512z/sBKaOWATfB\nnSZZilrsBaoqrmg2UurZz+nq59bvuBHKK7ER2pYn2HD407lEKam1O5qTILU1pPr3MPTD+xz7uc9u\neZ/DJf2BX6vZQFM0TaCENvB+YBh4wiqys3wYeA+wB3gnhpVE4RCzqh10se3GY517DpCJdhNdOVvV\nNls5hKbRSKII0rlxzYrKOBXpqrJbmUL/eynC/Lu0TnlsxTj1RuHmWN6eOpWrfpuJUkZZTCs7tVcS\nYX7ox7PPc34c99tdylL4OTO7WdVsCJ7Qfk/26xcLH5BSZoQQXwE+nl2uZUI7retENf+9OcNgIXE7\nQRIMv3V0ZarmcexWSuV2z/lketiObUb0X+L1eU5sWmRg5BxL68c53jXJlq7BwHu1vYZquFQUcnzx\nR5xcmjamPE5Lpk4tGgkj2Qg/v+M00ck4bucvYz6n0v1nq6fbqbCXkVjFZfyAny0jJs0qGgZNaI9l\nvz5X4vHnCpZzQ5cQ4qPAxcAycAR4REo57mYlou7x980nyFVttxMka0UCi+vekvez/Eiq/CqLmdud\n6t/TlP2rBbM58psvHmX8lOCJkT6GRqbZuf64EtwK1yg/e33IG6M+vYmpU9vQTgku8mFGdiH5BQp3\ndybtMM/WhdN+7TzdzoR964eO1QO/p4yk9eZqmMAIbSFEL9Cf/fZ4icVOZL9urWITA8CnC372F0KI\ne4Hfd+P5jgrN91XtoIptc4KkXc52OWq5fOqaeZbzyctoX3iNnon9CP287fpyud2v3ktiz/2+qGwD\nvOvy7Xmj258YWZ8T3Ce6VfSfIh+ndo96EvQBNBBsgQ32BQqwHyTjduqjVXBLrYP5oZ8oalQ/G7+5\nYpFGalFm47c63Kq38bPIbjaBEdpAt+X/iyWWWch+dXNfbBl4EPhH4DBwDtgG3Ab8HvAxjM/f75da\ngRDiTuBOgA1DG3M/97vYDirFOdspx5PB3ApuI+ZvhYGjD+S+r/gcuUL/sS8wsetjeT/3st0kb3S7\nEty+oplJH06EbCNEcRCzsa0cX/wRL0ye5PD0RiYCJrChfGa2VSSb31dfGIkwP/QTRU3rGXQoU6Qx\nK+BnRu9p+bG4VpRlxD3CffhGYxBC/BlQzaXejVLKhBAijhnWC21SFo9eEkK8CfgPYEVK2VH93ubW\ndwvwCHABuFhKWTG/bPTNu+TnP/slIGvB8KHQNskQzKp2IRcf+FU0J947aqtsu0EC41f+Ve6gXbqa\ns3qL00t2k1ePneH1+XnGtSWIpxnYeI6d60+zobubawfe2urd8wVuxG8tHu1n9mYcxxVWSyuq2GHA\n9GG/PLuJw6+253mw/SywC4sKoAE6ogmpXnp2cqSJWXTSstnY0VQybxiaGdU664GCR60EwTICxUL7\nundc8YKU8qpGbddLFe0R4NIqnteW/Tpv+VkXMGuzbLfNslUjpXxUCHEIw/P9U8Dfu12HX6vaJkG1\nkFhx6r1L9e4gNvdy08S2OY2yfDWneEy8SSsr4HkV7pPzjCeiPBk3pklK+azyb3sMNxVf1WjZekyb\nyMuzm5iY3M3MD5YCU8G2Lyo070LNmi5SKLLBfhhaEAiqyG4GnvmNSSlvk1KKKv69kX3+HDCTXd2W\nEpvZnP36Rh13/Uj2q+sRWuYfvBWeoXpgfuCCcCupHLPxdyO18tekUouS6VhHsz5SAuiZ3A84m4Bm\njok3ic0cJH7oLnqTj6FlUggkWrbhMn7oLmIzBxu5+zl2bNvAuy7fznVdG9h0spep5wf42ne38I1T\nHTw9+Swnl15ryn74EafWiGb7iv3sY/Y7J5de4+nJZ3lu4jj/dqKfqZcG6fw+XNdlfM78LrI7zr3E\nhsOfQdOXqxosVg/MlCg7kR10/CqyTVpVFPRSRbseHAJuBN4C/MDm8bdalqsX67NfF8ouVYKo0Hwt\nVIPeHAnlGySt1gxjYEHz/pZmZaVn4omKJx3rYJxqK+CNpLDCPXUhyhPDvezc+LxKKCndA0a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mi8gdmsaFwYut7y+GoFuvIJqvwtVRlZU7Onsx6YFhdTaDuJKBs4+gDWE68T4aJQ1BMnVepapqW2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\n+3xE3NT2mgXALQARo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac45a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotte Entscheidungsfunktion\n",
    "def plot_decision_boundary(X_,y_,svm):\n",
    "    pp = sp.linspace(-1.5, 1.5, 100)\n",
    "    x0, x1 = sp.meshgrid(pp, pp)\n",
    "    X = sp.c_[x0.ravel(), x1.ravel()]\n",
    "    predictions = svm.predict(X)\n",
    "    decision_boundary = svm.decision_function(X)\n",
    "    fig = pl.figure(figsize=(11,6))\n",
    "    pl.contourf(x0, x1, predictions.reshape(x0.shape),  alpha=0.3)\n",
    "    pl.contourf(x0, x1, decision_boundary.reshape(x0.shape), alpha=0.02,label=\"Decision Boundary\")\n",
    "    pl.plot(X_[y_==1,0],X_[y_==1,1],\"s\",color=\"#2980b9\",label=\"Positive Class\",markersize=10)\n",
    "    pl.plot(X_[y_==0,0],X_[y_==0,1],\"o\",color=\"#e67e22\",label=\"Negative Class\",markersize=10)\n",
    "    pl.legend(ncol=2)\n",
    "    pl.xlabel(\"x1\")\n",
    "    pl.ylabel(\"x2\")\n",
    "    \n",
    "#Wende Polynomiellen Kernel des zweiten Grades auf nicht linear trennbaren Daten an\n",
    "svm = SVC(kernel=\"poly\",C=1,degree=2)\n",
    "svm.fit(X,y)\n",
    "plot_decision_boundary(X,y,svm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 1,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}