Files
FYS-STK4155/doc/Programs/JupyterFiles/Dylan Smith Total Examples/My Own Examples/Random Walk Fit.ipynb
T
2020-08-23 19:35:43 +02:00

194 lines
62 KiB
Plaintext

{
"cells": [
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2nd degree coefficients:\n",
"zero power: -1.18201632336\n",
"first power: 0.197334533426\n",
"second power: -0.000300186922806\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAIABJREFUeJzsnXdcVtUbwL+HJQg4cAIONDfKUEBN\n/bm1cubITE0bmqvSpiNztbPS1FypaZKWWmlmmuae7wvuQU5AhgwFFGS/5/fHfXkDBUSGiJzv53M/\n3nvuGc+9vJ7nnnOe8zxCSolCoVAoSi9mxS2AQqFQKIoXpQgUCoWilKMUgUKhUJRylCJQKBSKUo5S\nBAqFQlHKUYpAoVAoSjlKESgeGkKIGUKINcUtR2aEEEOEEH/nMe8jJ39hIoQ4K4ToUNxyKB4+ShEo\nHhghRKAQIlEIES+EiBBCrBRC2BW3XPlBSukrpexW0HqEEB2EEAbjO7kthPhXCPFSYcj4sJBSukop\n9xS3HIqHj1IEivzSS0ppBzQHvIEPilmeR4Ew4zspB0wElgkhGhZ2I0IIi8KuU1G6UYpAUSCklKHA\nX0BTACGEkxBisxDiphDikhBiZHblhBB/CiFevyvtlBCir/FcCiFGCyEuCiFihBALhRDCeM9MCPGB\nECJICBEphFgthChvvOdiLPuSEOKasexoIYS3sf5YIcSCTG2OEEIcyHQ9z1julhDCXwjRLh/vREop\ntwI3AbdMdTcSQuwwvpt/hRDPZbpXSQjxh7FdvRDio7vkkkKIcUKIi8DFPNT3jBDinHF0EiqEeMeY\nXlkIscX4Hm4KIfYLIcyM9wKFEF2M52WEEHOFEGHGY64QoozxXgchRIgQ4m3j+w8vaaMfRVaUIlAU\nCCFETeAZ4LgxaS0QAjgBA4BPhBCdsym6ChiaqR53wBnYmilPT7TRhjvwHNDdmD7CeHQE6gJ2wAKy\n0hKoDwwC5gJTgS6AK/CcEKJ9Do+kBzwAB+AnYL0QwjqHvNliVFS9gcrAJWOaLbDDWGdVYDDwnRDC\n1VhsIZAAVAeGG4+76Wt8riZ5qG858JqU0h5NSe8ypr+N9vepAlQDpgDZ+ZmZCrQyvgt3wIeso77q\nQHm0v9krwEIhRMU8vB7Fo4iUUh3qeKADCATigVggCPgOsAFqAumAfaa8nwI/GM9nAGuM52XQvpjr\nG6/nAN9lKieBtpmufwEmGc//AcZmutcQSAUsABdjWedM928AgzJdbwQmGM9HAAdyedYYwP1u+bPJ\n1wEwGN9JsvE9TMh0fxCw/64yS4DpgLlR/oaZ7n2UWS7jM3XKS33G82DgNaDcXXlmAZuAejn8XbsY\nzy8Dz2S61x0IzPSsiYBFpvuRQKvi/m2qI3+HGhEo8ktfKWUFKWVtKeVYKWUi2ijgppTydqZ8QWhf\njVmQUiajde5DjVMTg4Ef78p2PdP5HbQvf4ztBN3VhgXaF24GEZnOE7O5znZx2zjdcV4IESeEiEX7\n6q2cXd5sCJNSVkBbI/gW6JTpXm2gpXFKJtZY9xC0L+sqRvmvZcqf+Ty7tNzqA+iPNlILEkLsFUK0\nNqZ/iTZK+VsIcUUIMSmHZ8nuHTtlur4hpUzLdJ3576MoYShFoChMwgAHIYR9prRaQGgO+VehdV6d\ngTtSysMP0E7tu9pII2tn/8AY1wPeR5uGqmjs1OMA8SD1GJXc+0CzjDUPtE58r1F5Zhx2UsoxQJRR\n/hqZqqmZXdWZznOrDymlXkrZB23a6Hc0pYuU8raU8m0pZV2gF/BWDlN32b3jsAd5D4qSg1IEikJD\nSnkNOAR8KoSwFkK4oc0f++aQ/zDadMpX3DsayI21wEQhRB2hma1+Avx81xdqfrBH65CjAAshxIdo\nX/cPjJQyBe25PjQmbQEaCCGGCSEsjYe3EKKxlDId+BWYIYQoK4RoBLx4nyZyrE8IYSW0/RHlpZSp\nwC20qSqEED2FEPWMC+8Z6enZ1L8W+EAIUUUIUdn4HI/tHorSjlIEisJmMNo8fRjwG9qc9Y5c8q8G\nmvFgncwKNMWxD7gKJAGv51oib2xHs4C6gDYVkkT2UzR5ZQVQSwjRyzhd1g14Hu3dXAc+R1srARiP\nNg11He3Z1qKtNWRLHuobBgQKIW4Bo/lvYb4+sBNtjecw2rrMnmya+AjwA04Bp4FjxjTFY4iQUgWm\nURQfQogXgVFSyrbFLcujhBDic6C6lDI76yGFolBRIwJFsSGEKAuMBZYWtyzFjXFPgJvQ8EGbUvut\nuOVSlA6UIlAUC0KI7mhz8RFotvClHXu0dYIEtIXdr9DMPBWKIkdNDSkUCkUpR40IFAqFopRTIpxX\nVa5cWbq4uBS3GAqFQlGi8Pf3j5ZSVrlfvhKhCFxcXPDz8ytuMRQKhaJEIYQIun8uNTWkUCgUpR6l\nCBQKhaKUoxSBQqFQlHJKxBpBdqSmphISEkJSUlJxi6IoZqytralRowaWlpbFLYpCUSIpsYogJCQE\ne3t7XFxc0PxnKUojUkpu3LhBSEgIderUKW5xFIoSSYmdGkpKSqJSpUpKCZRyhBBUqlRJjQwVigJQ\nYhUBoJSAAlC/A4WioJRoRaBQKBR5ISU9hWX+y0gzFDRkRf4IiA5g+6Xtec4ffjucWXtn8eHuD7l4\n42IRSqahFEEBMDc3x8PDg6ZNm9KrVy9iY2MLpd7AwECaNm1aKHVlEBsbS6VKlTLiy3L48GGEEISE\nhAAQFxeHg4MDBoMhxzpmzJjBnDlzAOjQocN9N/l16NCBhg0b4ubmRqNGjRg/fnye3tEnn3yS18dS\nKPLE7wG/M2rLKLZe3Fos7U/5ZwoD1g8g3ZBdDKB7Wey3mOl7pvPRvo+4HHO5iKVTiqBA2NjYcOLE\nCc6cOYODgwMLFy4sbpFypEKFClSvXp3z588DcOjQITw9PTl06BAAR44coWXLlpiZFe5PwtfXl1On\nTnHq1CnKlClDnz597ltGKQJFYaML1QGgD9UXW/vxKfEERAfkLX+YDvdq7himG3iq3lNFLJ1SBIVG\n69atCQ3VQvPGx8fTuXNnmjdvTrNmzdi0SfMmHBgYSOPGjRk5ciSurq5069aNxMREAPz9/XF3d6d1\n69ZZFEpSUhIvvfQSzZo1w9PTk927dwPwww8/0LdvX3r16kWdOnVYsGABX3/9NZ6enrRq1YqbN2/e\nI2ObNm1MHf+hQ4eYOHFilusnn3wSgGXLluHt7Y27uzv9+/fnzp07OT63wWBg+PDhfPDBB7m+Hysr\nK7744guCg4M5efIkAH379qVFixa4urqydKkWkmDSpEkkJibi4eHBkCFDcsynUDwIGYpAF6Z76G2H\n3gol9HZoFjlyQ0qJLlSHewV3XnjhBf7999+iFrHozEeFENZooQTLGNvZIKWcLoSoA6wDHNDC3w0z\nxnfNNxO2TeDE9RMFFTkLHtU9mPvU3DzlTU9P559//uGVV14BNLv23377jXLlyhEdHU2rVq3o3bs3\nABcvXmTt2rUsW7aM5557jo0bNzJ06FBeeukl5s+fT/v27Xn33XdNdWcohdOnTxMQEEC3bt24cOEC\nAGfOnOH48eMkJSVRr149Pv/8c44fP87EiRNZvXo1EyZMyCLnk08+yb59+3j11Ve5cuUKAwcOZMmS\nJYCmCCZPngxAv379GDlyJAAffPABy5cv5/XX740EmZaWxpAhQ2jatClTp06973syNzfH3d2dgIAA\n3N3dWbFiBQ4ODiQmJuLt7U3//v357LPPWLBgASdO/Pf3zC5fpUqV8vS3USjSDGn4h/sD2ohASvlQ\nDQz0Yfos5y95vpRr/isxV7iZeJPoHdFsXbuViRMnFrWIRToiSAY6SSndAQ/gKSFEK7S4qt9IKesD\nMWiRmEokGV+ulSpV4ubNm3Tt2hXQNPqUKVNwc3OjS5cuhIaGEhERAUCdOnXw8PAAoEWLFgQGBhIX\nF0dsbCzt27cHYNiwYaY2Dhw4YLpu1KgRtWvXNimCjh07Ym9vT5UqVShfvjy9evUCoFmzZgQGBt4j\nb8aI4OrVq7i4uGBtbY2Ukvj4ePz9/fHx8QE0BdOuXTuaNWuGr68vZ8+ezfb5X3vttTwrgQwyx7/4\n9ttvcXd3p1WrVly7do2LF7NfFMtrPoUiO85HnedO6h3a125PTFLMQ5lzz4w+VI+FmQVP1nwyTyMC\nfZge4uCfn/7hhRdewNvbu8hlLLIRgdT+x8cbLy2NhwQ6AS8Y01cBM4BFBWkrr1/uhU3GGkFcXBw9\ne/Zk4cKFvPHGG/j6+hIVFYW/vz+Wlpa4uLiY7NzLlCljKm9ubk5iYmKuXyi5BQ7KXJeZmZnp2szM\njLS0e60j6tevT0xMDH/88QetW7cGNGW0cuVK6tSpg52dHQAjRozg999/x93dnR9++IE9e/Zk2/6T\nTz7J7t27efvtt7G2ts7lTWmkp6dz+vRpGjduzJ49e9i5cyeHDx+mbNmydOjQIdu9AHnNpyjdLPNf\nxpaLW2hevTmT203m3b/f5e0n3+ZIyBHmHNIMHMZ6j2Vv0F6G/TaMd598l36N+xWozf1B+zl07RDv\nt30/13y6MB3Nqjbjf7X+x5zDcxi0YRBfdfuKGuVqZJ8/VIfZ32Yg4eOPPy6QjHmlSNcIhBDmQogT\nQCSwA7gMxEopM3qpEMA5h7KjhBB+Qgi/qKioohSzwJQvX55vv/2WOXPmkJqaSlxcHFWrVsXS0pLd\nu3cTFJS7J9gKFSpQvnx5Dhw4AGgLrBn873//M11fuHCB4OBgGjZsmG9ZW7duzbx580yKoHXr1syd\nO9e0PgBw+/ZtHB0dSU1NzSLL3bzyyis888wzDBw4MFvFk5nU1FQmT55MzZo1cXNzIy4ujooVK1K2\nbFkCAgI4cuSIKa+lpSWpqakAueZTKDKYvmc6m//dzMy9M9lxeQff6r5lzak1fLL/Ey7evEj/xv15\nttGz9GnYh/NR5/ni4BcFbvObI98w+Z/J3E6+nWMegzTgF+aHj7MPA10H4lndk1/O/sLGcxtzLPPX\nlr8wnDUwffp0HlYcliJVBFLKdCmlB1AD8AEaZ5cth7JLpZReUkqvKlXuG1eh2PH09MTd3Z1169Yx\nZMgQ/Pz88PLywtfXl0aNGt23/MqVKxk3bhytW7fGxsbGlD527FjS09Np1qwZgwYN4ocffsgyEnhQ\n2rRpw7Vr1/Dy8gI0RXDlypUsimD27Nm0bNmSrl273lf2t956i+bNmzNs2LBsTU+HDBmCm5sbTZs2\nJSEhwbRw/tRTT5GWloabmxvTpk2jVatWpjKjRo3Czc2NIUOG5JpPoQBtMTY8Ppyn6j2FRLLYfzEA\n+4L2cSbyDOO8x7HhuQ1Ymlvy+/O/82rzVzlx/QQp6QVamkQfpkciTesP2XHp5iVik2LxdvKmuWNz\ndCN1ONk7ZVk3yEzQtSACVgRQuW5l3nnnnQLJ90BIKR/KAUwH3gWiAQtjWmtg+/3KtmjRQt7NuXPn\n7klTlF7U76H08uu5XyUzkJsDNktmIMUMkeXfTQGbsuT/+czPkhlIv1C/fLcZeitUMgPJDOTnBz7P\nMd+PJ3+UzECeun7KlNZ3XV9Z/9v69+RNTEyUHt4eEkvkl5u+lNJgkPLsWSnv3Mm3nICfzEP/XGQj\nAiFEFSFEBeO5DdAFOA/sBgYYsw0HNhWVDAqF4vFHF6rDwsyCrk90pU6FOkgk5sIcaZxs8HbKutia\ncZ35q1xKSXR0NFevXuXKlSsEBQWRkJCQY5sZ+xHMhXmOX/cZ+cpalqVxlf8mQ3ycfLh48yIxiTGm\ntPT0dIYPG8YJ/Ql6NoLRi7ZBlSrg6goHDz7A28gfRel91BFYJYQwR5uC+kVKuUUIcQ5YJ4T4CDgO\nLC9CGRQKxWOOPkyPezV3rC2s8XH24WrsVfo26svG8xupWa4mjvaOWfK7VHChQnwFfljyA/u+3oe/\nvz9BQUEkJyffU7etrS1169bF1dUVNzc32rZti7e3N/owPebCnB4NeuRqCaQL09HCsQUWZv91tT7O\nmnXe8Yv76RRhQ9Lu3Qz9/ns2RkUxB3j7NMjEIOjdG9q2hWbNCudF5UJRWg2dAjyzSb+Ctl6gUCgU\n+Sb0Vijd13QnIDqAkc21fS/eTt78fPZnRjYfyaZ/N+Ht/N9oIDIykmXLlrFu3Tpiz8RylKOEOIfQ\nsmVL+vTpw5nEM1jZWvFs42dJT08nKiqK1QdXc/HyRc5tP8e6deu0iizArIYZVZpUoUblGmy+sZla\n39TCTJgxo8MMRniMACA1PZXj4ccZ7zNeK3fnDhw6RJvtf3JkLbSY1YcLBhiMtqHq8ydbEe4azvNu\nLqwbv+ehvUfjIykUCkXJY8eVHZyNOsvgpoMZ5zMOgBfdXyQ+JZ7OdTuzqMci3Ku5c/XqVT799FNW\nr15NcnIy7dq146nXn2Kb+TbOf3Ye+zL2ADh/7Uy6IZ3fXvwNIQR3Uu8wNXkqnr08aVq1KUm3kog8\nH0nEuQgizkUQtS2K77Z+h0UZCwyuBmKdY1kUv4gX3V7EzMyM06HHaHE1meHXg+GTDnD4MKSkYG1h\ngVm9GjxlEc3ua0mUKWsNPZOo8t4opvwxkslNhuXy1EWDUgQKhaJEog/VY29lz5p+azAT2nJnFdsq\nTO8wHYCBTwzk448/Zt68eZiZmTF8+HAmTpxIo0aN2HpxK9t+2sax8GO0d2lP6K1Qwm6HARByK4Sa\n5WtyPPw46TKdaf+bRu+Gve9pPzY2lr1797Jz50527txJ6B+h6P7Q4fCxLR5ly9IsLo4+6eDHevxr\n1SK2TRtCHRw4eO0aR/R6hJnA0Awav9iEY7ePscR/Ceky3TR19DBRikChUJRIdGE6vJy8TEogM5s2\nbeK1114jMjKS4cOH89FHH+Hs/N+WpcwLxu1d2mdZ8NWF6qhZvqZp7v/uxeYMKlSoQJ/27emTkgJ3\n7nAhMoxDN29xNCmJ48D3GDBtfQwOhuBgrKys8PT0ZObMmbh1daPv9r4cu30MgKOhR7X2nIt+J/Hd\nKKdz+eTatWt07NiRxo0b4+rqyrx58x64jpxcOefXffPDIsP9dsYRGBiIn58fb7zxBqDtBs5wZqdQ\nFAXJacmcvH7ynq/n2NhYhg0bRt++fXF0dESv17Ny5cosSgC0kYNLBZf/nNEZLY8szSyzOKi7Z7HZ\nYAB/f/joI20ht3JleO452LiRam1bsa83dP17HkcSE6k335Wu33fl8uXLXLlyhZs3b3Lnzh2OHDnC\ntGnTeMrrKSzNtDjbZS3LAlCzXE2q21UvqteWI2pEkE8sLCz46quvaN68Obdv36ZFixZ07dqVJk2a\nFEr9vr6+eHl5kZKSwuTJk+nTpw979+4tcL1paWlYWBTsz57hWiMzLi4upk1qe/bswc7OLssmNYWi\nMDkZcZJUQ2qWr/UTJ04wYMAAgoKCmDFjBlOmTMHS0jLHOnycfTgacpSYxBiOhByhWdVmmJuZcyT0\nCDGJMehCddrXeVwcbN8OW7Zo/0ZGahW0aAGTJsHTT0PLltiZCX75rDxWyedoeSuUc1Hn6NeuH3Xr\n1s22/TIWZfCo7oE+TM8wt2Es8V9SLKMBUCOCfOPo6Ejz5s0BsLe3p3HjxiY31B06dOD999/Hx8eH\nBg0asH//fkBzUvf888/j5ubGoEGDTC6ocyM7981r1qzBx8cHDw8PXnvtNdLTtWAXy5cvp0GDBnTo\n0IGRI0cyfrxmrTBixAjeeustOnbsyPvvv09CQgIvv/wy3t7eeHp6mnb7pqen8+677+Lt7Y2bm5vJ\nM2le2LNnDz179iQwMJDFixfzzTff4OHhYXp2haIwybDjzxgRrF69mtatW5OUlMTevXuZPn16rkoA\noKVzS4LignD4woHdgbtp6dySls4t2Re0D/cpDjy97Qpz5pzW7PkHDYKtW6FLF1i9GiIiwM9PGxm0\naQMWFpibmePl5MUS/yXU+KYGBmmgZY2W95XBwsyCMV5jTNfFweMxIpgwAU4UrhtqPDxgbt6c2QUG\nBnL8+HFatvzvj5iWloZOp2Pr1q3MnDmTnTt3smjRIsqWLWsK1JKhSO5HZvfNVlZW/Pzzzxw8eBBL\nS0vGjh2Lr68vXbp0Yfbs2Rw7dgx7e3s6deqEu7u7qY4LFy6wc+dOzM3NmTJlCp06dWLFihXExsbi\n4+NDly5d8PX1pXz58uj1epKTk2nTpg3dunWjTp06WeTJ8LoKmjfV3377zXTPxcWF0aNHY2dn93C3\nyCtKFbowHdVsq+Fs78y0adP46KOP6NixI+vWraNq1ap5quMVz1ewtrAmNT0VMwSDUhpg89cOpv/q\nTJUL2kdden2p9S+9e0Pr1mBunmudC59ZyM4rOwGws7Kj2xPdcs3/wf8+oH+T/rhXd2fL4C20d2mf\nJ9kLm8dDERQj8fHx9O/fn7lz51KuXDlTer9+mmfDDFfTAPv27TPNo7u5ueHm5pbndqTRC+k///yD\nv7+/yTVtYmIiVatWRafT0b59exwcHAAYOHCgyV11xrW58Uf8999/s3nzZlPYyaSkJIKDg/n77785\ndeoUGzZsADSHbxcvXrxHEWQ3NaRQPEx0oTq8qnnx4osv4uvry6uvvsp3331331FAZspb2DL2VkP4\n9VfYvBlCQkAI7J98El59E3r3xvwBHTy6VnXFtaprnvNXs6tGNbtqAPRo0OOB2ipMHg9FkMcv98Im\nNTWV/v37M2TIEFPHn0GGYzhzc/MsnjnzExAjs/vmDCuITz/9NEuezF/l2WFra2s6l1KycePGe7yY\nSimZP38+3bt3f2AZFYqHRVxSHAHhARjWGLhw5AIff/wxkydPztv/rdRU2L0bNmyA336D6GgoWxa6\ndYPZs6FHD20qqJSh1gjyiZSSV155hcaNG/PWW2/lqUxml9Jnzpzh1KlT9y1zt/vmzp07s2HDBiKN\nC1Y3b94kKCgIHx8f9u7dS0xMDGlpaWzcmLOb2+7duzN//nzTKOP48eOm9EWLFplcQF+4cCFXfys5\nYW9vz+3bObvmVSgKwsErB2EtXDx6kSVLljBlypTclUBKCmzbBq+8AtWrQ/fusHYtdO0KGzdCVJSm\nFEaMKJVKAJQiyDcHDx7kxx9/ZNeuXSYzyq1bt+ZaZsyYMcTHx+Pm5sYXX3xhigiWHTm5b27SpAkf\nffQR3bp1w83Nja5duxIeHo6zszNTpkyhZcuWdOnShSZNmlC+fPls6542bRqpqamm+qdNmwbAq6++\nSpMmTWjevDlNmzbltddeu2+cgezo1asXv/32m1osVhQ650POM/L5kXAV5i+Zz6hRo7LPmJICf/6p\nde7VqmmWPRs2wDPPwO+/a53/Tz9Bv37aiKCUIzK+Ch9lvLy85N329ufPn6dx4+zCG5Re4uPjsbOz\nIy0tjWeffZaXX36ZZ599trjFeiio38PjT0JCApWaVSI5MBmn4U6ErgzNmsFggAMHwNcX1q+HmBgo\nXx769oUBA7QRQAFieZREhBD+Ukqv++V7PNYIFADMmDGDnTt3kpSURLdu3ejbt29xi6RQFArJyck8\n0+sZkgOT6TGlB0veM5o2SwmnTmlf92vXwrVrYGurdf6DB2udv5VV8QpfAlCK4DEiwwpIoXicSEtL\nY/DgwezbvQ/6wtTXpuJ8IwUWfKJ9/Z87BxYW2tz/559rpp6ZjCMU90cpAoVC8chiMBh49dVX+e23\n33j61Q64ROzD57mJcETzy0PbtvDddzBwoObuQZEvlCJQKBSPLO+98w6rVq1iVtOmvL9qH1apBnCN\nh08/heefh4cU3P1xRykChUJRbGy/tJ2WNVpSwbpC1hsXLrDojTf4avt2xgNTQ0L4voUF0YN6MuXN\nDZCP/TiKnFHmowqFolgIvRXKU75PMfeIcUPorVvw/ffQpg3bGjbk9e3b6Vm1KnPXrePSmX289lQK\n1dv3UEqgCFCKoAC8/PLLVK1alaZNm2ZJv3nzJl27dqV+/fp07dqVmBgtSPXd7plHjBhhcueQGxlu\nn11dXXF3d+frr7/GYDAU7sPkkz179lC+fHnTXoouXboAsHjxYlavXg3ADz/8QFhYWHGKqXgE0YXq\nQMKt3ds0e//q1WHkSE6HhfFcmTI0c3Vl7eXLmA8ahO6G5nAxp9gAioKhFEEBGDFiBNu2bbsn/bPP\nPqNz585cvHiRzp0789lnnwH599Of4dvn7Nmz7Nixw+TIrjDI8FxaENq1a8eJEyc4ceIEO3dqDrdG\njx7Niy++CChFoMiG2FgsFi7i1CL4etZR5K+/wrBhhG/ZQo/0dOwrVeKPbduws7MDNKVha2lLkyqF\n4+ZdcRdSyiI5gJrAbuA8cBZ405g+AwgFThiPZ+5XV4sWLeTdnDt37p604uDq1avS1dU1S1qDBg1k\nWFiYlFLKsLAw2aBBA3n16lVZrVo16eTkJN3d3eW+ffvk8OHD5euvvy5bt24t69SpI9evX59tG7a2\ntlmuL1++LB0cHKTBYJBpaWnynXfekV5eXrJZs2Zy8eLFUkop09PT5ZgxY2STJk1kjx495NNPP22q\nv3bt2nLmzJmyTZs2cu3atfLSpUuye/fusnnz5rJt27by/PnzUkopIyMjZb9+/aSXl5f08vKSBw4c\nuEe23bt3yx49etyTPn36dPnll1/K9evXS1tbW9mgQQPp7u4u79y584BvOG88Kr8HRS4YDFIeOiTl\niBFS2thICVLnhHy1F/JK8CkZHx8vW7RoIW1tbeWxY8eyFG31fSvZbkW7YhK85AL4yTz010W5WJwG\nvC2lPCaEsAf8hRA7jPe+kVIWmtH7hAkTCt0bpoeHB3Pz6cwuIiICR0ctqpGjoyORkZHZumdevnw5\n4eHhHDhwgICAAHr37s2AAQPuW3/dunUxGAxERkayadOmbF1H+/v7ExgYyOnTp4mMjKRx48a8/PLL\npjqsra05cOAAAJ07d2bx4sXUr1+fo0ePMnbsWHbt2sWbb77JxIkTadu2LcHBwXTv3p3z58/fI8/+\n/ftNbqkHDhzI1KlTTfcGDBjAggULmDNnjilwjaKUERsLa9bA0qVw+jTY2SGHDaOD1U8ku7tyNPQo\nHW+e5pfXp3H8+HE2bdqEp6enqXhKegrHw48z3md8MT7E402RKQIpZTgQbjy/LYQ4DzjnXqr00bdv\nX8zMzGjSpAkRERF5LieNrkHIJ+oKAAAgAElEQVRych194MABBg4ciJmZGdWrV6djx45Zyg8aNAjQ\n3FIcOnSIgQMHmu4lJycDsHPnTs6dO2dKv3XrFrdv38be3j5LXe3atWPLli0P8NSKUsHJkzB/vrbr\nNzFRi+i1ZAkMHsyF5DD2LVzKEs+XORlxkgnvTCBqZxRfz/0ava2eJxOfxMFGc6l+JvIMyenJan2g\nCHko5qNCCBfAEzgKtAHGCyFeBPzQRg0x2ZQZBYwCqFWrVq715/fLvaioVq0a4eHhODo6Eh4enmug\njDKZfJ9kdO7348qVK5ibm1O1atUcXUf/+eefudaR4ZbaYDBQoUKFbEdUBoOBw4cPY2Njkye5FApS\nUzVPnvPna35/bGxgyBAYPVpTBEZ0V7S4wE/WfBKfMB/27dyHeStz6j9dn15re1HNrhpjvcdqeY0x\nhO+OT6woPIp8sVgIYQdsBCZIKW8Bi4AnAA+0EcNX2ZWTUi6VUnpJKb2qlDDXsL1792bVqlUArFq1\nij59+gCF4545KiqK0aNHM378eIQQObqObtu2LRs3bsRgMBAREcGePXuyra9cuXLUqVOH9evXA5oy\nygiJ2a1bNxYsWGDKm9/pN+WWuhQQEaH583dx0cI6hoXBV19BaCgsW5ZFCQDow/TYWtoS5BfEwSUH\nad6+Oend0ll5YiXwX+cPWljKymUr41LB5SE+UOmiSBWBEMISTQn4Sil/BZBSRkgp06WUBmAZUGLV\n/ODBg2ndujX//vsvNWrUYPny5QBMmjSJHTt2UL9+fXbs2MGkSZOA/LtnzggN6erqSpcuXejWrRvT\np08HcnYd3b9/f2rUqGFKa9myZY5uqX19fVm+fDnu7u64urqaXF5/++23+Pn54ebmRpMmTVi8eHG+\n3tOIESMYPXo0Hh4eeYrTrChBHD0KQ4dCzZrw4YfQrJkW5P3CBXjrLahYMdtiulAdjdIbMfj5wTRr\n1oyVq1eCGWwK0H57+jD9f3nDdHg7eecrqJMij+RlRTk/ByCA1cDcu9IdM51PBNbdr65H2WroUeb2\n7dtSSimjo6Nl3bp1ZXh4eDFLVHSo38NDJDlZyh9/lNLbW0qQ0t5eyjfekDIgIG/F05Kl1XtW0r6K\nvXRycpLXrl2TBoNBOnzuIJmBFDOEFDOEjEuKk7eTb0uzmWZy+u7pRftMjyk8AlZDbYBhwGkhRMac\nwhRgsBDCA5BAIPBaEcpQqunZsyexsbGkpKQwbdo0qlevXtwiKUoyMTGa5c/8+dqUT6NGsGABvPgi\n3GVAkBu6qzpSfkxBxAu2HNxCjRo1AG0NYNulbTxT/xn+vPgn/mH+mJuZY5AGtVBcxBSl1dABtFHB\n3eQexktRaOS0LqBQPBBXr2pxwZcvh4QE6NxZm/fv3h3MzFh1YhWXYy4zq+Os+1aVnp7OuFfGwXVY\n+NPCLGai3k7ebLu0jbHeY/nz4p/ow/SYCW322ttZKYKipEQ7nZNSqnlDRZ6trRQPyOHD2oLvb7+B\nubkW6GXiRDDuGclggX4BZyPP8mH7D7Ewy71Lee+99zi17xS2fWx5edDLWe6N8BhBQkoC3Z7oRt2K\nddGF6jA3M6d2+dpUtc3Z8k5RcEqsIrC2tubGjRtUqlRJKYNSjJSSGzduYG1tXdyiPB6kp2sxfb/6\nSlMEFSrAe+/B+PHgfO82oOS0ZE5eP0mqIZWzkWdxr+6eY9Xz58/n66+/xqGDA62ea3XP/9u6Fevy\nVXfNiNDH2YeDwQcxNzNXZqMPgRKrCGrUqEFISAhRUVHFLYqimLG2tjbNMyvySVISrFoFX3wBV65A\n3braWsCIEWD095MdJyM0JQCaJVBOimDTpk28+eab9Ozdky0eW/Bxyr1z93byZt2ZdQCM8x6Xv2dS\n5JkSqwgsLS2pU6dOcYuhUJRsbt2CxYvhm2/g+nXw8YEvv4Q+fbTpoPuQYe9fxrwM+jA9I1uMvCfP\n0aNHGTx4MN7e3oz/bDxbftly3zn/zKMAtVBc9JRYRaBQKApAVBTMmwcLF2q+gLp00eL/duz4QP7+\ndaE6qttVx62aW5ZNYBlcvnyZXr164ejoyB9//MGqi9pGy/t17p7VPTEX5kgkLZxa5JpXUXCUG2qF\n4j78ePJHLGZZYP+pPZduXmLg+oF8uPvDe/KN/XMsY7aMKQYJH4DgYHjjDahdGz75BDp1Ap0OduzQ\nzvOoBG4l38LpKyd+PPUj3k7e+Dj5cDLiJLaf2HIq4hQAN27c4OmnnyYtPY2b/W5SbVE13tv5Hi4V\nXKhim7u3AFsrW5pWbUrjyo2xs8p5akpROKgRgUJxH/648Ac2ljbEp8Tz54U/+T3gd846nM1iLiml\n5JezvyCRfNfju0fPgOH8efj8c+2rH7TdwO+/r+0FyAdHQ44SHh/OK56v8GbLN6lctjJmwoxZ+2ax\n4/IO6trWpWfPngQHB/Ph8g+Zemkqo1uMpqptVf5X+395amNJzyVIlEXYw0ApAoXiPujD9Dxd72l2\nXd3FsmPLSDOkERAdwK3kW5QrUw6Aq7FXuZF4w3Ret2Ld4hT5P86c0XwArV8P1tYwbpzm+uE+jhzv\nR4YLiDnd5pjiDc/sOJNVJ1dxOOgw22dsR6fTsWHDBvzK+WFxxYKvu3+NjWXeHRi2rNGyQDIq8o6a\nGlIociEqIYrA2EB8nH3wdvbmbNRZACQS/zB/Uz59aCbfONnMlT90Tp+GgQM13z9bt8KkSRAUpG0M\nK6ASAO0ZG1RqcE/QeS9HL/76/C927NjB999/z7PPPosuTEezqs0eSAkoHi5KESgUuZDx5ZsxDw6Y\nOr/MHb4uVEcZ8zJYW1gXryI4eRL69wc3N9i+HaZOhcBAbT2gEL346kJ199j3SykJXhPMnZN3mPXZ\nLF566SUM0oBfmJ+y/HnEUVNDCkUORN+J5q+Lf2EmzGjh1IL4lHgA2tduz5nIM+jCMimCMB3NHZsj\nhMjiOTM7YhJjsC9jf99duA/EiRMwa5a2C7hcOZg2DSZMAAeHHIvEJcVhY2mDlblVtvellNxIvEHl\nspUBuJN6ByklsUmxhMeHZ+ncDQYD48ePR79FD+2gaueqnIo4ReitUGKTYtWmsEccNSJQKLJBSonH\nYg8W6BfQrGoz7Kzs8HH2wcLMgjY12+Dt7G2aDkozpHEs/BjeTt54O3njH+ZPmiEt23oTUxOp+21d\nvj36beEIevw49O0Lnp6waxdMn66NAGbNylUJSCnxWOLBtF3Tcszz0+mfqPlNTa7HXwfgufXP8dyG\n5+4JFGMwGBg3bhyLFi3izbfexKKLBaP/HI37Ynee+ekZAFrXbF04z6soEtSIQKHIhisxVwi9Hcrr\nPq/zZss3AahiWwX/Uf40qNSARfpFrDuzjvDb4UTdieJO6h18nH0QQjDv6DzORZ3DrZrbPfWeuH6C\n2KRYdl3dxVut38q/gGfOaF/9v/+uuYGYOVMzC61Q4f5l0Ra0A2MD2RW4K8c8u67uIiktiSMhR+jV\noBd7AvcgkbhWccXCzAKP6h4YDAbGjBnD0qVLmTRpEp988glDw4cSHBdsqsfBxoEmVZrk/1kVRY5S\nBApFNmR89b7s+TJPODxhSs/o3DO+hvVheiITIrOkZZTPThFkTBvpw/T5c5p46RLMmKHFAba3184n\nTIAcgg7lRMbznbx+kuS0ZMpYlLk3j3HqSxeqo75DfRJSEwDwPe2LWzU3LLBg5MiRrFixgqlTpzJ7\n9myEEHg5eeHl5PVgz6UoVtTUkEKRDfowPdYW1rhWcc32vqejtvNVH6pHH6qngnUF6jnUo55DPSpY\nV8hxwTgjPTIhMstX830JCYHXXtPs/n/9VXMEd+WKNhX0gEoA/rNySjWkcjLi5D3341PiORd1Tssb\nps/yPGG3w/B08OTZZ59lxYoVTJ8+3aQEFCUTNSJQKLJBF6ot/lqaW2Z7v6xlWZpWbYouTEdkQmSW\nUIreTt45Lhjrw/TULl+boLgg7bxC7dwFiYyETz+FRYvAYIAxY2DKFHB0LNjzhelMcmRnAXQs/BgG\naaB2+droQ/U8UfEJypUph0AQdzOO3TN3E3gukEWLFjF69OgCyaIoftSIQFHiCYgOIPRWaLb3ou9E\ns+bUGjYFbMpT3IKktCTWnVnHsfBj9/WQ6ePsw5GQI5yOOJ2lI/Vx9uF0xGnupN7hWPgxVp9czamI\nU8QkxnDhxgVGeIzAytwKXaiO1PRU9gXtu7fymBjN9LNuXfj2WxgyBC5e1DyC5kMJnIs6x+qTq03H\nsfBj9GnYh+p21bNVWhkjhtFeo4lLjmPj+Y14OXnhauEKyyHschi//vqrUgKPCWpEoCjx9PipB02r\nNmXT85vuuTd772y+1WkWOkdeOXLf3aprTq1h5B+aB802Tm0IDAwkPDyc6OhokpOTSUlJwdraGltb\nW2rF1+LWjVtgCx1cOpjq8HH2IV2mczz8OP1+6UdkQiQuFVxY2nMpAG1rtcWjuge6UB0/nvqRVza/\nwukxp2latSncuaN1/J9/rjmDGzRIWwhu2LBA72jQhkGciTyTJa1jnY5cjb2a7TRWxohhQJMBTN01\nleg70TiFO7Hxo42YGczYsWMHbdu0LZBMikcHpQgUJZqI+AiuxFzhdvLtbBdfj4QeoWGlhvx741+O\nhOSsCKSUXL58mZXLVmJ1xAqXZBcGfzSYtLTszUAzY21jzRu/vIGrqystWrTApbEL3IFfzv5CZEKk\nqf0/LvwBgJeTFz5OPvxw8gfqVNRcqR8JPEjTLTr48EMtHnDPnppriLuigeWH28m3ORt5lrdavcU4\nH823v5W5FTXK1eBM5Bm2XNhCXFIc5a3/W2vQh+rxcfahnkM9QieE8sVnXzB35lzc3d1Z+8taGtXP\nn48ixaOJUgSKEk3GtEbUnSiC44KzzLmnpKdw4voJ3mz5Jj+d/inLBrAMAgIC+Omnn1i3bh0XL14E\noEzFMjRo04ABzw6gbt26ODk5UblyZaytrbG0tCQ5OZmEhASioqIICgoiKCiIq1evcuzYMTZs2GCq\ne8GPC8AF2g9sz7/J/7Lq5CqTWwZvZ28W6Bfw67mNPH0Bnlo5GYJitHgAP/0E/8ubY7a84B/uj0TS\n9Ymu9/hA8nby1txlhPvTqU4n7V0mRHE19ipjvMYQFBTEsGHD2L9/P0OHDmXJkiWULVu20GRTPBoU\nmSIQQtQEVgPVAQOwVEo5TwjhAPwMuACBwHNSypiikkPxeHO3m4fMiuBUxClS0lPwdvLm0s1Lpnlv\ng8HAn3/+yTfffMPu3bsxMzOjY8eOjBk/hrcvvc27fd9ldqfZ+ZInJiaGY8eO8cayNzinOwd6WHp4\nKVjArTq3aNSpEeHh4fg4++AVCl/suE3HQAiukqA5huvf/4HiAeSFjHeUnUlnRoAYXajOpAj0YXow\nQOT+SNw+dUNKyerVqxk6dKiyDHpMKcrF4jTgbSllY6AVME4I0QSYBPwjpawP/GO8VijyhT5MT6PK\njbAyt7pn0TPzDlhvJ28u3riI73pf3N3d6d27NxcvXuSzzz4jJCSEnTt34tXHC1lJFsjrZcWKFenc\nuTPDxg+D4eDzrQ87duygcvvKEA26JTqcnJwY3rANfZeB+XX4ZJATDcakkdD76UJXAqC9o7oV65pc\nRWTGwcaBeg71sry7Lfu3wA8wZ/IcPDw8OHnyJMOGDVNK4DGmyEYEUspwINx4flsIcR5wBvoAHYzZ\nVgF7gPeLSg7F44uUEl2ojn6N+lGuTDmTFc4n+z8hLjmO3YG7qWpblVrla+EQ5wArYOi1odSqU4uf\nfvqJAQMGYGn5n3loZgdzBSXDiqiVSyu6dOlC3zt9+XX/92y43J1Dm3awOTaWDwCSoMrBVJKDDfQr\n04/GHo0xM9e+z+ys7JjSbgrWFtYFkkUXqqN1jZxdPHg7ebM/eD9BQUFMnz6dVatXYV7WnO9Xfs/w\n4cOVAigFPJQ1AiGEC+AJHAWqGZUEUspwIUTVHMqMAkYB1CoEt7mKx48rMVe4mXgTb2dvrC2sWXli\nJbuu7mLG3hmUtSyLuTDnhYYv8M477zBv3jzMy5pj6GXAdYArgwcPvqc+XaiOWuVrUc2uWoFl83H2\nwbO6J882fhaSk3n7oOSbBebYpuyg4yuvMHXGDL485cvq9aupdq0a/+z6h78P/80O2x1YNLLArLEZ\nybWTae7YnL6N+uZbjoj4CILjgk1uMrKjRmINQlaH0GBSA4QQ2LSzoe+rfRkxbES+21WUMKSURXoA\ndoA/0M94HXvX/Zj71dGiRQupUNzN2tNrJTOQx8OPy1UnVklmIF/Y+IJkBvLmnZvy6NGjsl69ehKQ\no0aNkjdv3pTDfxsuq35ZVRoMhnvqqzO3jhzwy4DCE9BgkPLXX6WsW1dKkPKZZ6Q8ezbbrHFxcXLd\nunXy+eefl+XKlZOAxBJZ16uu/PLLL+Xx48dlenr6A4vwx79/SGYg9wXuy5IeHR0tFy9eLNu1a2dq\n6+kXnpYHTx+UzEB+p/suX4+seLQA/GQe+ukiHREIISyBjYCvlPJXY3KEEMJRaqMBRyCyKGVQPL7o\nQnXYWNjgWsXVNH2y/ux66lesz+K5i5k2bRpOTk7s2bOH9u3bA9qX+qqTq7h26xq1yv830oy+E22y\nlCkUTpyAiRNhzx5o0gS2bYPu3XPMXq5cOQYNGsSgQYNISUlhz549DPl0CNf/vc67774LQIUKFfDy\n8sLLywtvb28aNWqEi4tLrlY8ulAdAkG19Gps3bqVw4cPs3PnTnQ6HQaDgUaNGjHr41nMuDWD5t2a\nEyJCTO9JUXooSqshASwHzkspv850azMwHPjM+O+9u4AUijygD9Pj6eiJpbklDSo1oFyZctyKu0Xi\nH4lM0U9h0KBBLF68mAqZPHJmzP9nTAOZ6jJaFGVY0eSbiAj44ANYvlxzA71wIYwaBRZ5/69mZWVF\nt27d6Jfcj1/O/ULAkAB279rNwYMH8fPzY86cOVn2N1StWpVatWpRvnx57OzsMDMzIyUlhYSEBPT/\n6hExgoYztA1pZmZm+Pj4MHnyZPr374+HhwdCCH5d8iv6ML3mgM68DM2qNSvYe1CUKIpyRNAGGAac\nFkKcMKZNQVMAvwghXgGCgYFFKIPiMSXNkIZ/mD+vtXgNADNhRhPzJhz5/ghhMWHMmzeP119//Z6F\nTrdqbpqFUaieAU0GmNIzvpxbOLbIn0BJSTBvHnz8MSQmaqOBDz6AihXz/Yw+zj4sPbaURJtEXnzx\nRV588UVjU0mcOnWKS5cuERgYSGBgINeuXePWrVtERmoDbCsrK2xsbEipnEKj5o0Y98w43NzccHNz\no1y5cve05e3kzYZzG0hMTcSjukeOwWoUjydFaTV0AMjJ3KBzUbWrePw5dO0Qk/+ZTGJaomkKw9/f\nn1OfnIJkmL92PmMHjs22bBmLMrhXc0cXpuNm4k1e2vSSydNmkypNsC9j/2DCSKl5A333Xbh6FXr3\nhi+/hAYNCvqYpmfLiA+cgbW1NT4+Pvj45Dx9cyz8GO/ueJfUq6m82fNNRrUYdd+2lh1bxsFrBxnn\nPa7AsitKFsrpnKLEseL4CnShOp6q9xRdn+jKzp076dChAxXsK9BvTj9e7fdqruV9nH3wC/Nj68Wt\nbP53M7eTb1PPoR4TWk14MEHOnIFOnWDAALC1hR07YNOmQlECAI2rNKasZVnTtNWDsPrkavYH7afb\nE93oUb/HffP3qN+Dbk9043+1/8dQt6H5EVdRglEuJhQlDl2ojg4uHfhryF/8/PPPDBs2jEaNGrFt\n2zacnJzuW97byZuF+oX8eOpHbCxsOPjywRzdTWdLXJwWEGb+fC0WwHffwciRD7QOkBcszCxo4dgi\nW9cY90MXqqNljZZsH7o9T/kd7R3znFfx+KFGBIoSRUJKAmejzuLj5MOaNWsYPHgwrVq1Yt++fXlS\nAvDflMvfl//ONebAPRgMsGqV9sU/bx68+ipcuKDFCChkJZBZ1uPhx0lJT8lzmdT0VI5fP14oG+MU\npQOlCBQlioyAKUknkxg+fDgdO3Zk+/btWSyD7kfDyg2xt9LWAvLcWR47Bm3bwogRWowAvR4WL4ZK\nlfLxFHnH28mb5PTke1xI58aZyDMkpSUpE1BFnlGKQFGi0IXq4Dx89c5XtGnThs2bN2NjY/NAdZgJ\nM5MDtvt2ljdvwtix4OUFly/DypVw8CC0yKd10QOSecE4r2T2saRQ5AWlCBQlik1bNsEG8Pb25s8/\n/8TW1jZf9WR0kjnuG0hPh6VLtWmgpUvhjTfg33+1EYHZw/tv41LBhcplKzNx+0QqfVEJ1+9ciU+J\nB2DyzslM2nmvz0Z9mJ5KNpWoU6HOQ5NTUbJRi8WKEoNOp+PAnANUqFWBv/76C3v7BzT1zMR4n/HU\nKl+LJyo+ce9NPz9t3t/PT4sLsGABNCueDVZCCL575jv2Be3jesJ1NpzbgC5UR0eXjqw8sRKJ5NPO\nn2bZL6EL1eHt7K2cxSnyjBoRKEoEly9fpkePHkhbyevzXn+gNYHsqFGuBmO9x2btLOPi4PXXteAw\noaHg66u5iCgmJZDBQNeBzH9mPkt6LgG0jv7arWtEJEQQmRBJcFywKW/GYrpaKFY8CEoRKB55oqOj\nefrpp0lOS4ah0KlZp8JtQEotKEzjxppLiHHj4Px5eOGFIokPkF8yYgfoQnVZ1gwyxxLIWExX6wOK\nB0EpAsUjTWJiIn369CE4OJiBswYiKhfADUR2XLkCzzwDzz0Hjo6g0/23P+ARxNvJG32YHn2oHksz\nS6zMrbJVCmpEoHgQ8qwIhBC1hRBdjOc2Qoj8T9AqFHlASsnIkSM5fPgwvr6+RFSKyJ8biOxISYFP\nPgFXV80KaN48OHpUsw56hPFx9iHkVgibL2zGo7oHHtU9TJ1/XFIc+4P3F1pMBUXpIU+KQAgxEtgA\nLDEm1QB+LyqhFAqAr7/+Gl9fX2bPnk2/fv1Mi6AFZt8+8PCAqVOhRw9tGuiNN4psU1hh0qpGKwAC\nogNo6dwSbydv/ML8iEqIwvErR34P+J2WzvkPtakoneT1lz8O8EGLMIaU8mJOkcUUisJg+/btvPfe\newwYMIApU6YQHBdM1J0ofJwKMPcdHQ3vvaftBXBxgS1bNEVQgmjp3JINAzdwK/kWPRr0YNulbSzU\nL+SHEz+QmJbItP9NY2TzkcUtpqKEkVdFkCylTMmwsBBCWACyyKRSlGouXbrE888/j6urKytXrkQI\nYZoHz9eIQEpYuxbefBNiY2HSJJg2DXIJ6PKoIoSgf5P+puuMtYDv/L7DTJjxXpv3sLOyKy7xFCWU\nvK4R7BVCTAFshBBdgfXAH0UnlqK0kpCQQN++fTEzM2PTpk3Y2Wmdmj5Mj5W5FW7V3B6swuBg6NkT\nhgyBJ56A48fh009LpBLIjgx3GYGxgbhWcVVKQJEv8qoIJgFRwGngNWAr8EFRCaUovYwbN45z586x\nbt066tT5b2esLlSHZ3XPvAdMMRg0U1BXV20vwNy52qJw06ZFI3gxYSbMTKMkZSmkyC95VQQ2wAop\n5UAp5QBghTFNoSg0Vq5cyapVq/jwww/p2rWrKT3dkI5fmF/eO7rz56FdOxg/Hp58Es6e1aaFzM2L\nSPLiJeO9qL0DivySV0XwD1k7fhtgZ+GLoyitnDlzhnHjxtGpUyemTZuW5V5AdAAJqQn37+hSUmD2\nbM0iKCBAcxm9bZu2MPwY09GlI2bCjHa12xW3KIoSSl4Xi62llPEZF1LKeCHE4zHJqih24uPjGThw\nIOXKlcPX1xfzu77c8+RNU6fT4gOcPg2DBmn7AqqVDlv67vW6EzIxBEd7x+IWRVFCyeuIIEEI0Tzj\nQgjRAkgsGpEUpQkpJWPGjOHChQusXbuW6tWr35NHH6anXJly1K9U/94KEhLgrbegdWvNZfTmzbBu\nXalRAhkoJaAoCHkdEUwA1gshwozXjsCg3AoIIVYAPYFIKWVTY9oMYCTawjPAFCnl1gcVWvH4sGLF\nCtasWcPMmTPp2LFjtnl0oTq8nbwxE3d9t+zfDy+9pMUJGD0aPvvskXUNoVA8yuRpRCCl1AONgDHA\nWKCxlNL/PsV+AJ7KJv0bKaWH8VBKoBRz4cIFXn/9dbp06cLUqVOzzZOUlsTJiJNZp4Xu3IGJE6F9\ne806aPduWLRIKQGFIp88yJ56b8DFWMZTCIGUcnVOmaWU+4QQLgWSTvHYkpaWxrBhw7CxsWHVqlXE\nJMewN3CvabPUkZAj2FjYkJSWRJoh7T+LoYMHtVHAxYual9DPPgM7ZTuvUBSEvPoa+hGYA7RFUwje\nQH69c40XQpwSQqwQQlTMpc1RQgg/IYRfVFRUTtkUJZRPP/0UnU7HokWLcHJyYt6ReQxYP8DkW3/o\nr0MZu3XsfwvFDs3g7bc1s9DUVPjnHy1gjFICCkWByeuIwAtoIqUsqFuJRcBsNPcUs4GvgJezyyil\nXAosBfDy8lLuLB4j/P39mTVrFoMHD+a5554DQBemdfi6UB22lrZcjrlM6O1QapWvRc/oSjj/rwdc\nuKCtBXzxBRQgOplCochKXhXBGaA6EF6QxqSUERnnQohlwJaC1KcoeSQmJjJ06FCqVavGwoULAc1y\nSB+quVLWh+r/c5OQmITP3PW8cTAdatrCzp3QuXNxia5QPLbkVRFUBs4JIXRAckailLL3gzQmhHCU\nUmYok2fRFIyiFDF58mQCAgL4+++/qVhRmxm8HHOZmKQYQBsZ2FnZ4RMCP/wOjaPTOd7LG881O6Fc\nueIUXaF4bMmrIpjxoBULIdYCHYDKQogQYDrQQQjhgTY1FIjmt0hRSti1axfz5s1j/PjxWVxIZKwD\ntK3VlpPX/Bj12zUObYbwcmZ0HWbgvekfKyWgUBQheVIEUsq9D1qxlHJwNsnLH7QeRckgJjGGWXtn\nMbvTbH4+8zPO5Zx5qt5/1sMz/prB4lcX07BhQz7//PMsZfWhemwsbJhQrju1px7AKzye/Z2eYO7z\nLuwM+4dfnB7tqGEKRaTN1a4AAB78SURBVEknT4pACNEKmA80BqwAcyBBSqk+0xQA/B7wO3OPzqV1\nzda8/ffbNKvWzKQIou9EM3PSTMR1wR+//0HZu1xA60OO8snZ6vT76GNiLSyY+JozT7/7HS/8v707\nj6uqzB84/vkimwguuKCgNqK2uKIiZpTm5DhpvzSnaaFl1HFpczKrMcs0p2WqKcuZFpf8OWVl9msl\nMzNNXDMuYEgmauYOhrjgCiLc5/fHuSAaICr3Hrn3+369eN3LOc+55/t46H57zvOc5zlxhIhtl9Kg\ndoWDy5RS1aCqt4ZeB27HWocgFvgLUM7z/spXldzeef/H9zl04hBp2WkUOYvw9/Pn1dmvQgaE9w+n\ne/fTZxA9uWMb/3ghmet+ccINN9Bg1ixeLTPNRNlFWJRS7lHlxeuNMVuAWsaYYmPMf7Hu/ysFnBr+\nOX+TtV5RflE+P+39iT179jB1wlSIhP2x+8kryDt10Lx5SOfOXLnTiWPScJg/H8qZa0gp5V5VTQTH\nRSQQSBeRf4nIWKCOG+NSNUhBUQEZORn4iR8GUzonkCPLwYgRIyjIL0D+JFALUrNT4eBBSEiAhAT2\nt2xE53uh4ZjHwbUUqlLKs6qaCO52lR0NHANaAH9yV1CqZkn/NZ0iZxGDLhsEQHyLeBoEN2DO7Dl8\n9dVXhAwIYWC8NdI4N/ED6NgRPv4YnnmGif+4loPNw4luEG1nFZTyaVVNBDcZYwqMMYeNMf8wxjyM\nNbOoUqUPgz3Q/QEAekT1oL1/e1bNWkXtS2tztPNRBjT/Pf9Nqk/Cw7MpDAninidjOPDI/STnpNE9\nsjuirQGlbFPVRDCknG1DqzEOVYM5sh00C23G71v9nmf7PMuILiPI+yCPAP8A+j3SjwmNBzPsvhkM\nXZ7H7Pg6vD5tGDNJ5cvNX7J+73pdYlEpm1U6akhEEoA7gFYi8kWZXXWB/e4MTNUcjiwHcVFxiAgT\nek3ghRdeYH3aet57913uPHYMxo2FOnVIfHkkw4++Rc/t1uzjM9Jm4DROXXRdKZudbfjod1jzCzXC\nmiCuxBEgw11BqZojryCPzfs3M6Sz1WhMT09n0qRJ/HngQO74+GNITIR+/eDtt2lStB1mv8Wa3WsA\n+G7XdwB0j9JEoJSdKk0ExpgdwA4R6QvkG2OcInIp1iI1P3oiQHVxS81OBaB7ZHcKCgq4++67aRgW\nxnSHA9m/H6ZMgYceAj8/Yk7Wx9/PnyJnEbX9a5NflE/Lei1pGqpDRpWyU1X7CFYAwSISBXwLDMNa\ngUz5uJKO4tjIWCZOmMD69euZfeAADevVg+Rkaz1hP+vPrHZAbTo26QjAnR3vBNDbQkpdBKqaCMQY\ncxxryOhrxpjBQDv3haVqCke2g7bhbcn4bCFTXnmFe4D+I0ZAWhp06fKb8j2ieuDv58993e8r/V0p\nZa+qTjEhItITuBMYfo7HKi/myHLwyOYohsy8i2g/P15++224++4Ky0/sPZGb291M12Zd+fTWT+kb\n3ddzwSqlylXVL/OHgMeBz4wxP4lINJDkvrBUTZCdvZnn38lmeUY2u4CVn3xC6ODBlR4TGRZJZFgk\nAIOvqLysUsozzmUa6uVlft8KPOiuoFQNkJFB2KD+hG2H2cDjjz3GVWdJAkqpi9PZniOYaox5SETm\nYy0mc5pzXaFMeQFj4K234MEH2RtSi9uCodNlnZj89NN2R6aUOk9naxG863p92d2BqIvbwfyD1Dp6\njLoP/h3mzeNI76uI37+Boo35vP/e+wQGBtodolLqPJ3tOYI01+tyEWnsep/ricDUxWXsC9fyz5m/\nUDe3gP1PPkKj9CmwHOKHx9OhQwe7w1NKXYBKh4+KZbKI7AM2AptFJFdEJnkmPGU7Yyj8z6vMeC4D\njudjkpKY3T0CFsEVcVew4LUFdkeolLpAZ3uO4CEgHuhujGlojGkA9ADiXWsSKG+Wlwe33ELgmIdZ\nHA2d7nGy+bImTPn7FKgFCz9aSL3a9eyOUil1gc6WCP4CJBhjtpVscI0Yusu1r0IiMltE9orI+jLb\nwkVksYj87HrVxWgvVikp0LUrJCayYvRABibA/jrwxFNPkLM5hyuGXcElLS+xO0qlVDU4WyIIMMbs\nO3Ojq58g4CzHvg1cf8a28cC3xpi2WFNVjK9inMpTjIHXXoP4eCguhhUrmNEnlKZ1mxGYHchnMz/D\nL8aP/xmsy1Eo5S3OlggKz3MfxpgVwIEzNg8C3nG9fwe46SznV5509Ki1hOSDD8L111OclsqckJ9Z\nvn053Rp2Qz4TpJ7gvF6njlbKm5xt+GhnETlcznYBgs/jfBHGmD0Axpg9ItKkooIiMgoYBdCyZcvz\nOJU6Jxs2wM03w+bN8PzzMG4cS7YuZsjn1vTSLZe1pHB/IWaIITg0mPiW8TYHrJSqLpW2CIwxtYwx\ndcv5CTPGnO3W0AUxxsw0xsQaY2IbN27szlOpefMgLg4OHIAlS2D8ePDzIzkrGUGY3mo6a+av4fHx\nj7P3tb3k/j23dJoIpVTNV9XZR6tLjog0A3C97vXw+VVZhYXWbaCEBIiJgbVroU+f0t2OLAdt/Nvw\nxNgniI2NZfLkyTSu05jQwFAbg1ZKVTdPJ4IvOLX+8RAg0cPnVyV274beva2O4bFjISkJoqJKdxtj\ncOxycOj9QxQWFjJ37lwCAtzaCFRK2cRtU0mLyAfAtUAjEdkNPAW8APyfiAwHdgK3uOv8qhJLllit\ngIIC+Ogj+POff1Nk56Gd5H6ZC5kwd+5c2rZta0OgSilPcFsiMMYkVLDrOnedU52F0wn//CdMmgTt\n2sEnn8Bll5VbdMa8GbAKBt85mISEii6lUsob6OIyvuLAAWvBmK++gjvvhBkzoE6dcotmZWUxdfxU\nJEL47/T/ejhQpZSnaSLwBRkZMHgw7NoFb74J994LIuUWLSoqIiEhgRMFJ+jwaAfqheoUEkp5O093\nFitP+/BD6NnT6g9Yvhzuu6/CJAAwefJkVq5cScDAAHp17eXBQJVSdtFE4K2KimDcOLj9dmsR+bQ0\nKyFUIjExkeeee47BCYM50f4EcVFxHgpWKWUnTQTeaP9+6N8fXnoJ7r8fli6Fpk0rPWTjxo3cfffd\nxMbG0n9MfwBNBEr5CO0j8Dbp6VZ/wJ49MHs2DBt22u68gjxu/ehWDp04VLqt6HgRG1/YSEhwCF3G\ndGHy6snUDarLpQ0v9XT0SikbaIvAm8ydC1ddZd0WWrnyN0kAYOm2pSzeupigWkGE1w6nQVADtv93\nO8d/Pc59L97H7K2zCQsMY1KvSfiJ/nko5Qv0v3RvUFQEDz9sDQvt3t3qD+he/uygKVkpBPgF8M3d\n37DwzoXE/RzHgfQD+PX3Y5XfKopNMS/2fZFHrnrEw5VQStlFbw3VdLm5cNtt1hQRY8ZY/QKVTAXh\nyHbQKaITwf7BzJkzh2eeeYZhw4bxQ9wPJG1PAqB7lE4xrZQv0RZBTbZ2LXTrBmvWwJw5MHVqpUnA\naZykZqcSFxXH8uXLGTFiBH369GH69On0aN4DgKiwKJ1ZVCkfo4mgpvq//4Orr7ber15tPTV8Fpv3\nb+bwicO0ONmCwYMH07p1az755BMCAwNLRwjpSCGlfI8mAg/KP5lPzPQYFmxecP4f4nRacwXddpu1\npnBqqvXqMn7JeEZ+MfK0Q/704Z8IejaIjtM6wlGY/vB0/P39WbBgAQ0aWMtGlyQAXXlMKd+jicCD\n1u5Zy7qcdXy28bPz+4CjR62ZQp95Bv76V/j2W2hy+iJvH6z/gHk/zaPYWQxAQVEB8zfPp2fznozu\nNJrmXzQn99dcEhMTiY6OLj2ufeP2zLpxFvfE3nPe9VNK1UyaCDwoJTvltNdzsn27taB8YqLVFzBr\nFgQFnVYk52gOOw/t5GjhUTbt3wRA+q/pFDmLuK/zfaS+nErOthw+/fRTep7xlLGIMLzrcMJrh59X\n3ZRSNZcmAg9yZDkAWL93PccKj1X9wJUrreGgO3fCwoXW6KBy5gsqm2BKzuXIckARTB83ndWrV/Pe\ne+9x/fXXX1hFlFJeRROBB6Vkp1A/uD5O42TtnrVVO2jWLLjuOmjYEJKToV+/Cos6shz4iR+hgaGl\niSB5ZzLB84NZtmQZM2fO5NZbb62OqiilvIgmgmp0svgkRwuPApB9JJuN+zZS5CwC4ED+AbYc2MLQ\nzkMBWLhlIYcKDp12fEFRAQVFBQDkHd1nrSc8ciTO3/fh+MqlcOml5BXklXvu7CPZrNy5kg5NOtA9\nsjurd61m3e51JD6TSMG6Al555RVGjBjhpporpWoyTQTV6KllT9F5eme2522nxastuOKNK3hy6ZMA\npGanAnDjZTfSqn4rnl/1PD3/9/T79Ld8dAu3fXwby9Z+SmrnJtZ6wg8/zD33RHHdFzeT/ms6Df/V\nkO93f3/acTvydtDi1RYs276MK6OupGfznmTsziCmTwzHfjzGwIcGMnbsWM/8IyilahxNBNVoydYl\nbD24lbk/zsVpnDQOaczyHcuBU/fsuzXrxpd3fMmwmGFk7ssk91guAMXOYpK2JbE7eQkdbhzONTsM\nK54aBlOmsHjHUpJ3JzN/03ycxsnSbUtPO++qnatwGidT/ziV5657jtFdRtNhSQfkF+Hef9zL3Bfn\nevYfQilVo2giqCYnik6wLmcdANNTpxMSEMIdHe/ghz0/cLL4JI4sB5c3upx6wfVo17gdQ2OGAqc6\neDP3ZXLlxmN8O+045vBh+gyBubGB7D22lx2HdmAwvLX2rdOOKZGSnUJIQAgPxD3AyUMnGfjHgWxI\n2cCcOXOYNmkadQLLX5JSKaXApkQgIttF5EcRSReRVDtiqG4ZORkUFhcCsOvwLro260rP5j05UXyC\njJwMHFmO0x7W6tqsK37iV9pSyHvtJb5+D3bWg9gRTta0tFoRKVmnvvR3Hd4FcNo2sBJB12Zdyfwp\nkx49epCZmcnnn3/OXXfd5e5qK6W8gJ0tgj7GmBhjTKyNMVSbki/0FnVbABAXGVf6tO5nGz8j51jO\nadM3hAaG0q5xO1J3JcOjj3L1s3NY2taf/veGsrO+9TkZORms2LECP/GjWWiz0s/POpJF9pFswOqg\nXrtnLU2ymxAfH09xcTErV67kxhtv9GT1lVI1mN4aqiYp2SlE1Ilg0GWDAGvKht/V/x2NQhqV3tI5\ncx6fq8O7cP8L38KUKbzbqz4vj7+GS6OtvHhPt3soNsW8ve5t2jduzzWXXAPAvbH3AvC643XmrZ/H\nv7//NwVJBXz+1OdER0eTnJxMly5dPFVtpZQXsCsRGOAbEUkTkVHlFRCRUSKSKiKpubm5Hg7v3Dmy\nHMRFxdE3ui9BtYKIbxmPiND7kt7sPbaXekH16BTR6dQBWVk8O3kFf8w8yd/6w19+n8c10X3o26ov\nkWGR/LXLXwmsZfUR9L6kN31b9aVuUF1GdB1B3aC6PL/qeRLmJPD3oX+Hb+GGQTewcuVKmjdvbt8/\nglKqZjLGePwHiHS9NgHWAb0qK9+tWzdzMTtUcMjIZDFPL3vaOJ1Ok5efV7ov/2S+yczNNLnHck8d\nkJZmTGSkcYaGmux5s0xmbqbZtG+TKSouMkXFRebIiSPGGGN+PfKryczNNIVFhabYWWwOFRwyxhiT\neyzXvPP5O6ZJ0yYmMCjQvDj1ReN0Oj1aZ6XUxQ9INVX4TrZlYRpjTLbrda+IfAbEASvsiKU6pGWn\nYTDERcUhItQLrle6L9g/mMsbXX6qcGIi3HEHNGyIrF5Ns06daHbG54UGhgIQERpBRGhE6fa6QXU5\ndOgQkx6fxLRp02jTpg2LFi4iJibGndVTSnk5j98aEpE6IhJW8h7oB6z3dBzVqaSjODaykn5vY2DK\nFGth+Q4dwOGATp0qLl+OxMRE2rdvz4wZMxg7diw//PCDJgGl1AWzo48gAlglIusAB7DAGPO1DXFU\nG0e2g9YNWtMwpGH5BU6ehHvugUcftaaRXrYMmjat8uevW7eOAQMGcNNNNxEeHs6aNWt45ZVXCA0N\nrZ4KKKV8msdvDRljtgKdPX1edzhRdIKXvnuJ5duX0691BZPBHT5sffkvXgxPPGGtJeBXtfy7bds2\nJk6cyNy5c6lfvz4vvfQSY8aMIaCS5SiVUupc6eL1F2DhloVMTJpIbf/aDLxs4G8L7N4NN9wAGzbA\n7NkwbFiVPtfhcDB16lQ++ugj/P39GTduHI899ljpamJKKVWdNBFcgJSsFPz9/Nk/bj+1A2qfvjMj\nAwYMsFoEX30Ff/hDpZ919OhRPv/8c958803WrFlDWFgYo0eP5tFHHyUqKsqNtVBK+TpNBBfAke2g\nY5OOv00CixfDzTdD3bqwalWFncLHjx/nm2++4YMPPmD+/Pnk5+fTunVr/v3vfzN06FDq1q3rgVoo\npXydJoLz5DROUrNTua39bafvePttGDkSrrjCagmUecArPz+f9PR0kpKSWLx4Md999x2FhYU0btyY\nYcOGkZCQwFVXXYVfFfsQlFKqOmgiOE9bDmwhryDv1ERyxlgdwU89RX6fPmz95z/ZkpbGlg8/ZP36\n9aSlpbFhwwaKi61F5WNiYhgzZgz9+vXj2muvxd9fL4VSyh5e/+2Tk5NDZmYmxhicTmfpk3Rne3/m\nNqfTyfHjxzl+/Dhrtq0haXMSHIBFWxex8MgC9n73HXtzcsgJDCQvKQnKLA7fpEkTunXrxsCBA+nW\nrRtXX301jRs3tvFfRSmlTvH6RLBo0SKGDBnils+uFViLpE1LaVxQQJNjx+jcvj1Nrr2WiKZNad26\nNW3atKF169aEh4e75fxKKVUdvD4R9OvXj6VLl+Ln54eIICJnfV/RtpCQEAKCA/jdG79jTPwYXurw\nkDUy6ByHhyql1MXE6xNB06ZNaXoOT/GeTWp2KidrnaTv8aZw5ZWQlwcLFkC/Ch4oU0qpi5zXJ4Lq\n5shy0Hsb/GHKPyAsDFauBJ3vRylVg+k4xXNkPv6IRe+BNG8O33+vSUApVeNpIjgXb77JfS8t45fo\nBsiqVdCihd0RKaXUBdNEUBXGwMSJ8MADfNkWPn/tftCRQEopL6GJ4GyKimDUKHj2WfbcOoA/3QZd\nouPtjkoppaqNJoLKHD9uzRk0axY8+STv/q0XxbWge1R3uyNTSqlqo4mgIgcOWDOGzp8Pb7wBzzxD\nyp5UWtVvRaOQRnZHp5RS1cbrE4Exhm0Ht2Gt41w1xTu2wzXXYFJTMR9+CPffz8H8gyTvTiYuKs59\nwSqllA28PhHMTJtJ9H+i2XV4V5XK7/rua/Z0akXRrh1MfvxKEuQTkrYlEf6vcHYd3kWPqB5ujlgp\npTzL6x8o69KsC2AtItOyXsvKC69eTZP+N7PfwIxX7+DV3HnU+iWD1g1aU0tqMe2Gadze4XYPRK2U\nUp7j9S2CzhGdCfALwJHlqLzgl19C374crBvAVcPhlePfcqTwCHkFecz7aR4dIzoysttIwoLCPBO4\nUkp5iC2JQESuF5FNIrJFRMa781xB/kHENI3BkV1JInj/fbjpJujQgTvGtmRHA9h6cGvp7q0Ht55a\nd0AppbyMxxOBiNQC3gD6A+2ABBFp585zdo/sTlp2GsXO4t/ufP11uOsu6NWL/EULWHFsAxF1IgAI\nDQwlJCAEQDuJlVJey44WQRywxRiz1RhTCMwDBrn1hFFxHCk8wqb9m05tLFlR7G9/g0GD4KuvSD/2\nC8WmmFHdRgEQGxlL12ZdSz9DKaW8kR2JIAooO4Rnt2vbaURklIikikhqbm7uBZ2w5Eu8tJ/A6YSx\nY2HSJBgyBD7+GIKDS/cP7zKcBsEN6H1Jb6695Foa1m5Iu8ZubbQopZRt7Bg1JOVs+80gf2PMTGAm\nQGxsbNUfAijHZY0uIywwjJSsFIZ2uAuGD4c5c+Chh2DKFHAtFp+SnUJUWBSX1L+EDQ9soEFwAwBG\nx43G38/rB1gppXyUHd9uu4Gy03Y2B7LdeUI/8SM2Mpb0Hd9bU0Z88YV1W2jCBJBTecmR5SidPqJp\n6KnFbCJCI9wZnlJK2cqOW0MpQFsRaSUigcDtwBfuPuk19Tvz7Ms/WEng9dfhySdPSwIH8w/y84Gf\niYvUvgCllG/xeIvAGFMkIqOBRUAtYLYx5ie3nnTfPsZMmE/YDsMvrz1N6wce+E2R1OxUQCeUU0r5\nHltufBtjvgK+8sjJdu2Cfv2ov303N94O/eMaMLqcYiUdxbGRsR4JSymlLhbe/WTx5s1w9dWQnY18\nvYi0LhGkZKeUWzQlO4VLG15K/eD6Hg5SKaXs5d2J4PnnIT8fli1DevcmLiquwqkmHFkOfVZAKeWT\nvDsRvPmmtcB8F2viubioODbu28ihgkOnFcs6nMWeo3u0o1gp5ZO8OxHUrg3R0aW/lswXlLYn7bRi\nJa0E7ShWSvki704EZyj5oj/z9lBKdgr+fv7ENI2xIyyllLKVTz0uG147nDbhbZiZNpOMnAzCAsOY\n8scpOLIcdIroRLB/sN0hKqWUx/lUiwBgZNeR+Pv5s2b3GmauncnXW74mJTtF+weUUj7L5xLBuPhx\nbP7bZjIfyCTAL4D3f3yfwycOa/+AUspn+VwiKBHsH0znpp35YpM1u4UOHVVK+SqfTQRgjSJyGid1\nAupwRaMr7A5HKaVs4dOJoKQV0C2yG7X8atkcjVJK2UMTAWhHsVLKp/nU8NEzXd7ocib2mshdne6y\nOxSllLKNTycCP/Hj6T5P2x2GUkrZyqdvDSmllNJEoJRSPk8TgVJK+ThNBEop5eM0ESillI/TRKCU\nUj5OE4FSSvk4TQRKKeXjxBhjdwxnJSK5wI7zPLwRsK8aw6kJtM6+QevsGy6kzpcYYxqfrVCNSAQX\nQkRSjTGxdsfhSVpn36B19g2eqLPeGlJKKR+niUAppXycLySCmXYHYAOts2/QOvsGt9fZ6/sIlFJK\nVc4XWgRKKaUqoYlAKaV8nFcnAhG5XkQ2icgWERlvdzzuIiLbReRHEUkXkVTXtnARWSwiP7teG9gd\n54UQkdkisldE1pfZVm4dxfIf13XPEJGu9kV+fiqo72QRyXJd53QRGVBm3+Ou+m4SkT/aE/WFEZEW\nIpIkIpki8pOIjHFt9+brXFGdPXutjTFe+QPUAn4BooFAYB3Qzu643FTX7UCjM7b9Cxjvej8eeNHu\nOC+wjr2ArsD6s9URGAAsBAS4Eki2O/5qqu9k4NFyyrZz/X0HAa1cf/e17K7DedS5GdDV9T4M2Oyq\nmzdf54rq7NFr7c0tgjhgizFmqzGmEJgHDLI5Jk8aBLzjev8OcJONsVwwY8wK4MAZmyuq4yBgjrF8\nD9QXkWaeibR6VFDfigwC5hljThhjtgFbsP7+axRjzB5jzFrX+yNAJhCFd1/niupcEbdca29OBFHA\nrjK/76byf+CazADfiEiaiIxybYswxuwB648NaGJbdO5TUR29+dqPdt0GmV3mdp/X1VdEfgd0AZLx\nket8Rp3Bg9famxOBlLPNW8fKxhtjugL9gQdEpJfdAdnMW6/9NKA1EAPsAaa4tntVfUUkFPgEeMgY\nc7iyouVsq5H1LqfOHr3W3pwIdgMtyvzeHMi2KRa3MsZku173Ap9hNRVzSprJrte99kXoNhXV0Suv\nvTEmxxhTbIxxAm9x6paA19RXRAKwvhDfN8Z86trs1de5vDp7+lp7cyJIAdqKSCsRCQRuB76wOaZq\nJyJ1RCSs5D3QD1iPVdchrmJDgER7InSriur4BfAX16iSK4FDJbcWarIz7n8PxrrOYNX3dhEJEpFW\nQFvA4en4LpSICPC/QKYx5pUyu7z2OldUZ49fa7t7zd3cIz8Aqxf+F2CC3fG4qY7RWKMI1gE/ldQT\naAh8C/zseg23O9YLrOcHWE3kk1j/VzS8ojpiNZ/fcF33H4FYu+Ovpvq+66pPhusLoVmZ8hNc9d0E\n9Lc7/vOs89VYtzkygHTXzwAvv84V1dmj11qnmFBKKR/nzbeGlFJKVYEmAqWU8nGaCJRSysdpIlBK\nKR+niUAppXycJgKlyhCRCa5ZIDNcsz72EJGHRCTE7tiUchcdPqqUi4j0BF4BrjXGnBCRRlgz136H\nNUZ9n60BKuUm2iJQ6pRmwD5jzAkA1xf/n4FIIElEkgBEpJ+IrBGRtSLykWuemJJ1IV4UEYfrp41r\n+y0isl5E1onICnuqplTFtEWglIvrC30VEAIsAT40xiwXke24WgSuVsKnWE90HhORx4AgY8zTrnJv\nGWOeE5G/ALcaY/5HRH4ErjfGZIlIfWNMni0VVKoC2iJQysUYcxToBowCcoEPRWToGcWuxFocZLWI\npGPNfXNJmf0flHnt6Xq/GnhbREZiLZik1EXF3+4AlLqYGGOKgWXAMtf/yQ85o4gAi40xCRV9xJnv\njTH3ikgP4AYgXURijDH7qzdypc6ftgiUchGRy0SkbZlNMcAO4AjWMoIA3wPxZe7/h4jIpWWOua3M\n6xpXmdbGmGRjzCRgH6dPI6yU7bRFoNQpocBrIlIfKMJaBnAUkAAsFJE9xpg+rttFH4hIkOu4J7Fm\nuQUIEpFkrP/JKmk1vORKMII1e+Y6j9RGqSrSzmKlqknZTmW7Y1HqXOitIaWU8nHaIlBKKR+nLQKl\nlPJxmgiUUsrHaSJQSikfp4lAKaV8nCYCpZTycf8PshNhntlIyoEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1d845320>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1ed48ac8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"\"new_dist=distance_list[-1]\\nstep_max=2500\\nnew_x=steps\\nnew_dist_list=[]\\nnew_steps_list=np.arange(steps,step_max)\\nwhile new_x>=steps and new_x<step_max:\\n dist_prediction=clf.predict(new_x)\\n new_dist_list.append(dist_prediction)\\n new_x+=1\\nplt.plot(new_steps_list,new_dist_list, color='red')\\nplt.show()\""
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"steps=250\n",
"\n",
"distance=0\n",
"x=0\n",
"distance_list=[]\n",
"steps_list=[]\n",
"while x<steps:\n",
" distance+=np.random.randint(-1,2)\n",
" distance_list.append(distance)\n",
" x+=1\n",
" steps_list.append(x)\n",
"plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
"\n",
"steps_list=np.asarray(steps_list)\n",
"distance_list=np.asarray(distance_list)\n",
"\n",
"X=steps_list[:,np.newaxis]\n",
"\n",
"#Polynomial fits\n",
"\n",
"#Degree 2\n",
"poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
"X_poly=poly_features.fit_transform(X)\n",
"\n",
"lin_reg=LinearRegression()\n",
"poly_fit=lin_reg.fit(X_poly,distance_list)\n",
"b=lin_reg.coef_\n",
"c=lin_reg.intercept_\n",
"print (\"2nd degree coefficients:\")\n",
"print (\"zero power: \",c)\n",
"print (\"first power: \", b[0])\n",
"print (\"second power: \",b[1])\n",
"\n",
"z = np.arange(0, steps, .01)\n",
"z_mod=b[1]*z**2+b[0]*z+c\n",
"\n",
"fit_mod=b[1]*X**2+b[0]*X+c\n",
"plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
"plt.title(\"Polynomial Regression\")\n",
"\n",
"plt.xlabel(\"Steps\")\n",
"plt.ylabel(\"Distance\")\n",
"\n",
"#Degree 10\n",
"poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
"X_poly10=poly_features10.fit_transform(X)\n",
"\n",
"poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
"\n",
"y_plot=poly_fit10.predict(X_poly10)\n",
"plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
"\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"\n",
"#Decision Tree Regression\n",
"from sklearn.tree import DecisionTreeRegressor\n",
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
"regr_1.fit(X, distance_list)\n",
"regr_2.fit(X, distance_list)\n",
"regr_3.fit(X, distance_list)\n",
"\n",
"X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
"y_1 = regr_1.predict(X_test)\n",
"y_2 = regr_2.predict(X_test)\n",
"y_3=regr_3.predict(X_test)\n",
"\n",
"# Plot the results\n",
"plt.figure()\n",
"plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
"plt.plot(X_test, y_1, color=\"red\",\n",
" label=\"max_depth=2\", linewidth=2)\n",
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
"\n",
"plt.xlabel(\"Data\")\n",
"plt.ylabel(\"Darget\")\n",
"plt.title(\"Decision Tree Regression\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"\n",
"\"\"\"new_dist=distance_list[-1]\n",
"step_max=2500\n",
"new_x=steps\n",
"new_dist_list=[]\n",
"new_steps_list=np.arange(steps,step_max)\n",
"while new_x>=steps and new_x<step_max:\n",
" dist_prediction=clf.predict(new_x)\n",
" new_dist_list.append(dist_prediction)\n",
" new_x+=1\n",
"plt.plot(new_steps_list,new_dist_list, color='red')\n",
"plt.show()\"\"\"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}