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@manashmandal
Created December 15, 2022 22:36
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "8ff751b8",
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.random.seed(42)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "9c62f78a",
"metadata": {},
"outputs": [],
"source": [
"data = pd.read_csv(\"./data.csv\")\n",
"data.columns = ['x', 'y']"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "279e5d73",
"metadata": {},
"outputs": [],
"source": [
"n_train = 15\n",
"n_test = data.shape[0] - n_train\n",
"\n",
"randomized_data = data.sample(n=data.shape[0]).reset_index(drop=True)\n",
"train_data = randomized_data[:n_train]\n",
"test_data = randomized_data[n_train:]\n",
"\n",
"X_train = train_data['x'].to_numpy()\n",
"Y_train = train_data['y'].to_numpy()\n",
"\n",
"X_test = test_data['x'].to_numpy()\n",
"Y_test = test_data['y'].to_numpy()\n",
"\n",
"# Generate polynomials from 1D array\n",
"def extend_feature(data: np.ndarray, n: int):\n",
" if not isinstance(data, np.ndarray):\n",
" raise ValueError(\"data must be numpy array\")\n",
" \n",
" assert n > 0 and n <= 3\n",
" assert len(data.shape) == 1\n",
" \n",
" if n == 1:\n",
" return np.array([[1, sample] for sample in data ])\n",
" \n",
" elif n == 2:\n",
" return np.array([[1, sample, sample**2] for sample in data])\n",
" \n",
" elif n == 3:\n",
" return np.array([[1, sample, sample**2, sample**3] for sample in data])\n",
" \n",
"# Perform regression using pseudo inverse\n",
"def regression(x_train, y_train):\n",
" return np.linalg.pinv(x_train).dot(y_train)\n",
"\n",
"def mse(pred_y, y):\n",
" return np.square(y - pred_y).mean(axis=0)"
]
},
{
"cell_type": "markdown",
"id": "cb2c84ee",
"metadata": {},
"source": [
"# 1. Linear Regression"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "53fc575e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Computed Theta for Linear Regression: [-16.78020346 8.55726112]\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1324d9250>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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VqiSX/NauXYuPj0+y/5QTn5NVzM3NsbKyAtRLlo8ePSI+Ph4/P78kl9HSq3379lhYWLB69WrDutOnT3P27Fk6d+5sWOfi4sKZM2eSNLNnRN++fXFzc6Nw4cK0bt2ayMhIli5dip+fX5LtXvx7XbduHXq9nk6dOiV5D3p4eFC6dGnD3+eRI0e4f/8+gwcPNpwfUC8nOjs7pxlbSEgI//33H3379qVYsWJJHsvs7+6vv/6iZs2aSS5fOTg4MHDgQK5du8bZs2eTbN+nT58kcSe2uGXXyKhu3bpx+fJlDh8+bPiZ0mUfUFveTpw4weDBg3n8+DHz58+nW7duuLu78+WXXya7DGtjY8O2bduS3b7++usk2127du2lrSkAQ4YMITQ0lM6dO3P8+HEuXrzIyJEjDSNBo6KiMncS0mH48OGcPXuW2bNnY2GR+y6U5L5XZIJsbGySNc3my5cvSd+TS5cuERYWhru7e4r7uH//vmH5zJkzfPbZZ+zYsYPw8PAk24WFhSW5X6RIkSQfPOmxdu1anJycCAkJ4ccffyQoKChJcpT4JZFW82tYWBjR0dFERUWlODIltdEq3t7eSe6HhIQQGhrKwoULWbhwYYrPSTw3Y8aMYfv27dSsWZNSpUrRvHlzunXrRr169Qzbfvvtt/Tq1QtPT098fX1544036NmzJyVKlEj1tVy/fp3ChQvj6OiYZH358uUNjz/vxS8ZSP77zoiEhARWrVpF48aNDX0pAGrVqsV3333HP//8Q/PmzQH1UsY777yTqeNk1NKlS/nuu+84f/48cXFxhvUv/g7To0CBAjRt2pQ1a9bw5ZdfAuplAAsLC9q3b2/Y7osvvuCtt96iTJkyVKpUiZYtW9KjRw+qVKmSruOMHz+e+vXrY25uToECBShfvnyKH/wvvoZLly6hKEqqTfuJl2UT3wsvbpc4HDoticlApUqV0vVa0uP69espDmV//r37/PFefO8mXurI7Hv3ZapVq0a5cuVYuXIlLi4ueHh4GPoNpaRQoULMmzePuXPncunSJbZs2cI333zD+PHjKVSoEP379zdsa25uTrNmzbIs1latWjFr1izGjh1ruExcqlQpJk+ezMcff5xkxFFWmjZtGosWLeLLL7/kjTfeyJZjaE0SFSOQnuFwer0ed3f3VDtIJiY6oaGhNGzYECcnJ7744gtKliyJjY0Nx44dY8yYMcmG1WamQ1eDBg0M10HbtGlD5cqV6d69O0ePHsXMzMxwjGnTpqXaF8HBwYHo6OgMH/vFeBOP9e6776aaGCV+SZUvX54LFy7w559/snnzZtauXcvcuXMZP368oaNmp06dqF+/PuvXr2fr1q1MmzaNb775hnXr1qXaypNRqf2+X/yPL7127NjB3bt3WbVqFatWrUr2+IoVKwyJyqtK7T/3hISEJK9r+fLl9O7dm3bt2jF69Gjc3d0xNzdn6tSp6eqYmJIuXbrQp08fAgMDqVq1KmvWrKFp06ZJrsk3aNCAK1eusHHjRrZu3Yq/vz8zZ85k/vz5Sb6kUlO5cuV0fXml9D7U6XT8/fffKf5+s+tLKqdl9Xs3Pbp168a8efNwdHSkc+fO6RperdPpKFOmDGXKlKF169aULl2aFStWpOs98CqGDx9Onz59OHnyJFZWVlStWpWffvoJgDJlymT58QICAhgzZgyDBw/ms88+y/L9GwtJVExEyZIl2b59O/Xq1Uszudi1axcPHz5k3bp1ScbtP/+fdlZycHBgwoQJ9OnThzVr1tClSxfDZQ0nJ6c0P/Td3d2xsbFJcdRAekcSuLm54ejoSEJCQrq+YOzt7encuTOdO3cmNjaW9u3bM3nyZD755BPDqIBChQoxdOhQhg4dyv3796levTqTJ09ONVEpXrw427dvJyIiIkmrSuJltuLFi6frtWTWihUrcHd3Z86cOckeW7duHevXr2f+/PnY2tpSsmRJTp8+neb+0rqMkC9fvhQnErt+/XqSFoHffvuNEiVKsG7duiT7e7EzbEa0a9eOQYMGGS7/XLx4kU8++STZdq6urvTp04c+ffrw5MkTGjRowMSJE7P1S6pkyZIoioK3t3eaX0iJ74VLly4laRmIi4sjKCgIHx+fVJ+beH5f5feXUjwXLlxItj6n3rvp0a1bN8aPH8/du3dZtmxZhp9fokQJ8uXLx927d7MhuuTs7e2pU6eO4f727duxtbVN0nKbFTZu3Ej//v1p3759in/7uYn0UTERnTp1IiEhwdDs/bz4+HjDl0fifzzP/4cTGxvL3Llzsy227t27U7RoUb755hsAfH19KVmyJNOnT08yG2SikJAQQ6zNmjVjw4YNSfqEXL58OVm/jtSYm5vzzjvvsHbt2hQ/wBOPBeoIp+dZWVlRoUIFFEUhLi6OhISEZJfG3N3dKVy4MDExManG8MYbb5CQkGAYIpto5syZ6HS6TLfEpGd4clRUFOvWrePNN9+kQ4cOyW7Dhw8nIiKC33//HYB33nmHEydOsH79+mT7SnzP2NvbA6SYkJQsWZIDBw4QGxtrWPfnn38mG4Kb0vvw4MGD7N+/Px2vPGUuLi60aNGCNWvWsGrVKqysrGjXrl2SbV78HTs4OFCqVKk0f39ZoX379pibmzNp0qRkrQuKohji8vPzw83Njfnz5yc5hwEBAS+dSdbNzY0GDRqwePHiZO+L54+Z1u/vRW+88QaHDh1K8nuJjIxk4cKFeHl5JekPppWSJUvy/fffM3XqVMNowZQcPHiQyMjIZOsPHTrEw4cPkwwbzoj0Dk9Oyb59+1i3bh39+vV7aR+k1KT0OfDff//RpUsXGjRowIoVK0xmEr/MkhaVLLZ48eIU58R4//33X2m/DRs2ZNCgQUydOpXAwECaN2+OpaUlly5d4tdff+WHH36gQ4cO1K1bl3z58tGrVy9GjBiBTqdj2bJl2do0a2lpyfvvv8/o0aPZvHkzLVu2xN/fn1atWlGxYkX69OlDkSJFuH37Njt37sTJyYk//vgDUIeTbt26lXr16jFkyBDDF36lSpXSPYX7119/zc6dO6lVqxYDBgygQoUKPHr0iGPHjrF9+3YePXoEQPPmzfHw8KBevXoULFiQc+fOMXv2bFq3bo2joyOhoaEULVqUDh064OPjg4ODA9u3b+fw4cN89913qR6/TZs2NG7cmHHjxnHt2jV8fHzYunUrGzduZOTIkUk6zmZEeoYn//7770RERNC2bdsUH69duzZubm6sWLGCzp07M3r0aH777Tc6duxI37598fX15dGjR/z+++/Mnz8fHx8fSpYsiYuLC/Pnz8fR0RF7e3tq1aqFt7c3/fv357fffqNly5Z06tSJK1eusHz58mSv8c0332TdunW8/fbbtG7dmqCgIObPn0+FChVSTF7Tq3Pnzrz77rvMnTuXFi1aJJt5tUKFCjRq1AhfX19cXV05cuSIYbh5dipZsiRfffUVn3zyCdeuXaNdu3Y4OjoSFBTE+vXrGThwIB999BGWlpZ89dVXDBo0iCZNmtC5c2eCgoJYsmTJS/uoAPz444+89tprVK9enYEDB+Lt7c21a9fYtGmT4e/F19cXgHHjxtGlSxcsLS1p06aNIYF53tixY/nll19o1aoVI0aMwNXVlaVLlxIUFMTatWuN5gswPZ+fy5YtY8WKFbz99tv4+vpiZWXFuXPnWLx4MTY2NsnmiIqPj2f58uUp7uvtt982nK/0Dk++fv06nTp1om3btnh4eHDmzBnmz59PlSpVmDJlSrJtE1uHEjvbfvXVV4DaitWjRw/Dti9+Dly/fp22bdui0+no0KEDv/76a5J9V6lSJUmfrGXLlnH9+nWePn0KqElO4rF69OhhFK1mL5Xj44xyqcThyandbt68merw5JRmSEwcoveihQsXKr6+voqtra3i6OioVK5cWfn444+VO3fuGLbZu3evUrt2bcXW1lYpXLiw8vHHHytbtmxRAGXnzp2G7Ro2bPjS4bopxfTizLSKos786OzsnGR45fHjx5X27dsr+fPnV6ytrZXixYsrnTp1Uv75558kz/3nn3+UatWqKVZWVkrJkiUVf39/5cMPP1RsbGySbMcLwxGfd+/ePWXYsGGKp6enYmlpqXh4eChNmzZVFi5caNhmwYIFSoMGDQzxlCxZUhk9erQSFhamKIo6xG/06NGKj4+P4ujoqNjb2ys+Pj7K3LlzkxzrxeHJiqIO6fzggw+UwoULK5aWlkrp0qWVadOmJRk2mtZrSGnYL+kYntymTRvFxsYmzRmFe/furVhaWhqGbz98+FAZPny4UqRIEcXKykopWrSo0qtXryTDuzdu3KhUqFDBMEz8+ffsd999pxQpUkSxtrZW6tWrpxw5ciTZ8GS9Xq9MmTJFKV68uGJtba1Uq1ZN+fPPP1M8d2RgyGR4eLhia2urAMry5cuTPf7VV18pNWvWVFxcXBRbW1ulXLlyyuTJk5XY2Ng095vazLQvSutvQFEUZe3atcprr72m2NvbK/b29kq5cuWUYcOGKRcuXEiy3dy5cxVvb2/F2tpa8fPzU/77779k5zClzwtFUZTTp08rb7/9tuLi4qLY2NgoZcuWVT7//PMk23z55ZdKkSJFFDMzsyRDlVN6n125ckXp0KGDYX81a9ZU/vzzz3Sdn9RiTElmhien5cW/pZMnTyqjR49Wqlevrri6uioWFhZKoUKFlI4dOyrHjh1L8ty0hic/f74S407P8ORHjx4pb731luLh4aFYWVkp3t7eypgxY5INV1aUZ+czpduLf/MvrkvruSn9LSVOQ5HS7fnvA2OmU5Rs/FdbiExq167dKw0zFUIYl8RZcU2xKJ7QlnG064k87cX5BS5dusRff/2VZEp2IYQQeZP0URGaK1GiBL1796ZEiRJcv36defPmYWVllaxqqhBCiLxHEhWhuZYtW/LLL78QHByMtbU1derUYcqUKdlaF0MIIYRpkD4qQgghhDBa0kdFCCGEEEZLEhUhhBBCGC2T76Oi1+u5c+cOjo6OWVr9VQghhBDZR1EUIiIiKFy4cJqTC5p8onLnzh08PT21DkMIIYQQmXDz5k2KFi2a6uMmn6gkFoG7efMmTk5OGkcjhBBCiPQIDw/H09MzSTHXlJh8opJ4ucfJyUkSFSGEEMLEvKzbhnSmFUIIIYTRkkRFCCGEEEZLEhUhhBBCGC1JVIQQQghhtCRREUIIIYTRkkRFCCGEEEZLEhUhhBBCGC1JVIQQQghhtCRREUIIIYTRkkRFCCGEEEZLEhUhhBBCGC1JVIQQQghhtCRREUIIIUTKTpyApk3h7l3NQpBERQghhBBJxcfDV19BjRqwYwd8/LFmoVhodmQhhBBCGJ+zZ6FXLzhyRL3frh1Mn65ZONKiIoQQQghISIBp06B6dTVJcXGBZctg3TooWFCzsKRFRQghhMjrLl2C3r1h3z71/htvwKJFULiwpmGBtKgIIYQQeZdeDz/+CD4+apLi6Ag//QR//mkUSQpIi4oQQgiRNwUFQZ8+8O+/6v1mzdQkpVgxbeN6gbSoCCGEEHmJosD8+VC5spqk2NvD3LmwdavRJSkgLSpCCCFE3nHzJvTrB9u2qfcbNIAlS6BECW3jSoO0qAghhBC5naLA4sVQqZKapNjYwPffw86dRp2kgCQqqbt8GYYMUWflE0IIIUzVnTvQpo3akhIeDrVrq99t778PZsafBhh/hFr5/HP1Gt60aVpHIoQQQmScosCKFWoryqZNYGUF33wDe/ZAmTJaR5dukqikZvRo9eeqVXD9uraxCCGEEBlx/z688w68+y48fgy+vnDsmDoVvrm51tFliCQqqaleXR2qlZAAM2dqHY0QQgiRPr/9BhUrwvr1YGEBX3wB+/er60yQJCppSSzCtGgRPHyobSxCCCFEWh4+hK5doWNHePAAqlSBw4fVrgyWllpHl2mSqKSlWTOoWhWePoV587SORgghhEjZH3+ofVFWrVIv7Xz2mZqkVK2qdWSvTBKVtOh0z1pVfvwRoqK0jUcIIYR4XmioWqOnbVsIDoby5dXLPF9+qXaezQUkUXmZjh2heHEICYGlS7WORgghhFBt2aK2oixdqv5jPXq02mG2Rg2tI8tSkqi8jIUFfPihujx9utq5VgghhNBKRAQMHAgtW8Lt21C6tDrk+Ntv1YncchlJVNKjb19wdYUrV9Re1EIIIYQWduxQa/QsWqTeHzECAgOhbl1Nw8pOkqikh709DB+uLn/7rTqJjhBCCJFTIiPV76GmTdW5vby9Ydcu+OEHsLPTOrpsJYlKeg0frjapHT78rCS2EEIIkd327AEfH5gzR70/eDCcPAkNG2obVw6RRCW93NzUS0CgtqoIIYQQ2SkqSu0j2aCB2vWgaFHYulWdLsPBQevocowkKhkxapRawOnvv9VsVgghhMgOBw+qM6TPmKF2N+jTB06fhtdf1zqyHCeJSkaULAkdOqjL06drG4sQQojcJyYGPv1U7Rx7/jx4eKiTuS1eDM7OWkenCUlUMiqxWOEvv8CNG9rGIoQQIvc4flydA2XqVNDroVs3OHMG3nxT68g0JYlKRvn5QZMmEB8vxQqFEEK8urg4mDQJataEU6fUPpFr18KKFerUGHmcJCqZ8XyxwkePtI1FCCGE6Tp9GmrXhokT1X+AO3RQW1Hat9c6MqMhiUpmNG+uVqWMjJRihUIIITIuPl69xOPrq0577+qqdilYs0ZtUREGkqhkhhQrFEIIkVnnz8Nrr6mdZmNjoU0btRWlSxf1+0UkIYlKZnXqBMWKwf378PPPWkcjhBDC2CUkqMONq1VThx87O0NAAGzcqI7uESmSRCWzLC2lWKEQQoj0uXwZGjVSvzeio6FFC7V/Sq9e0oryEkaRqMyZMwcvLy9sbGyoVasWhw4d0jqk9OnXT72uePkybNigdTRCCCGMjV4Ps2erU+Dv2aPOKLtwoTpxaNGiWkdnEjRPVFavXs2oUaOYMGECx44dw8fHhxYtWnD//n2tQ3s5e3sYNkxd/uYbKVYohBDimWvX1Jlk33sPnj6Fxo3V4ccDBkgrSgZonqjMmDGDAQMG0KdPHypUqMD8+fOxs7Nj8eLFWoeWPs8XK/zvP62jEUIIoTVFUaevqFwZduxQqxvPmgXbt4OXl9bRmRxNE5XY2FiOHj1Ks2bNDOvMzMxo1qwZ+/fvT/E5MTExhIeHJ7lpyt1drcEAUqxQCCHyulu34I03YOBAePIE6tWDEyfUf2rNNG8bMEmanrUHDx6QkJBAwYIFk6wvWLAgwcHBKT5n6tSpODs7G26enp45EWraEosV/vWX2qwnhBAib1EUdQRopUqweTNYW6sDLf79F0qV0jo6k2Zy6d0nn3xCWFiY4Xbz5k2tQ1LfhO+8oy5LsUIhhMhbgoOhXTt1BE9YmFqv5/hxdYSPubnW0Zk8TROVAgUKYG5uzr1795Ksv3fvHh6pjCm3trbGyckpyc0oJBYrXLkSjCF5EkIIkf1Wr4aKFeH339VpK6ZMgX37oHx5rSPLNTRNVKysrPD19eWff/4xrNPr9fzzzz/UqVNHw8ggPkHPov+uEh2XzvlRatRQe3THx8P332drbEIIITQWEqJO/Nmli1rzrVo1OHoUPvkELCy0ji5X0fzSz6hRo1i0aBFLly7l3LlzDBkyhMjISPokdlDVyAdrTjD5r3OM/u0ken06hx0nTqu/cCE8fpx9wQkhhNDO+vVqK8qvv6pJyYQJ6kyzlStrHVmupHmi0rlzZ6ZPn8748eOpWrUqgYGBbN68OVkH25zWtYYnFmY6/jhxhxnbLqbvSS1aqG/UJ09g/vzsDVAIIUTOevQI3n1XrWwcEqJ2nD14UK18bGmpdXS5lk5RTHuWsvDwcJydnQkLC8vy/iq/HrnJ6N9OAvDtO1XoVCMdI4yWL4cePaBgQXWyHxubLI1JCCGEBjZtUidqu3tXHeU5ZozakmJtrXVkJiu939+at6gYs45+nrzXRB1W9un6U+y59ODlT+rcGTw94d49KVYohBCmLiwM+vaFN99Uk5SyZdXOslOmSJKSQyRReYlRr5fhraqFidcrDFl+lIv3ItJ+gqWlOq8KSLFCIYQwZdu2qZfzlyxRp7wfNUoddlyrltaR5SmSqLyETqfj2w5VqOGVj4iYePosOcz9iOi0n9S/P+TLB5cuqeW7hRBCmI4nT2DIEGjeXJ1uomRJdeK2774DW1uto8tzJFFJB2sLcxb28MO7gD23Q6MYsPQIUbFptJQ4OMDQoeqyFCsUQgjT8e+/UKXKswERw4apU+DXr69tXHmYJCrplM/eiiW9a5DPzpITt8IYufo4CWkNW37vPfX65aFDsHt3zgUqhBAi454+hZEjoVEjCAqCYsXUIoKzZ4O9vdbR5WmSqGSAVwF7Fvb0w8rcjC1n7jH1r3Opb1ywIPTurS5LsUIhhDBe+/dD1arwww/q/f791bptTZtqGpZQSaKSQTW8XJneyQcA/z1BLNt/LfWNP/pI7YC1aROcPp0zAQohhEif6Gh1mPFrr6l9CgsXVovLLloExlKeRUiikhltfQozukVZACb8foYd5++lvKEUKxRCCON05Aj4+qot3no99Oyp/kPZqpXWkYkXSKKSSUMblaSTX1H0CgxfeZwzd8JS3jBxWv0VK+DWrZwLUAghRHKxsfD551C7Npw9q16m37gRli5VR2sKoyOJSibpdDomv12ZeqXy8zQ2gb4Bh7kbFpV8wxo11M5ZUqxQCCG0deIE1KwJX32lznHVpQucOQNt22odmUiDJCqvwNLcjLndfSnt7sC98Bj6BhzhSUx88g0TW1UWLIDQ0ByNUQgh8ry4OPjyS/DzU5OVAgVgzRr45RfIn1/r6MRLSKLyipxtLVncuwYFHKw5dzec4SuPEZ+gT7pRy5Zq8SopViiEEDnrzBmoUwfGj1dbtt9+W+2L0rGj1pGJdJJEJQt4utrxUy8/bCzN2HUhhIl/nCFJrUed7lmryg8/qD3NhRBCZJ+EBLWjbPXqcPQouLioRWPXrlX7pQiTIYlKFvHxdOGHLtXQ6WD5gRv47w5KukGXLmqxwuBg9Y9FCCFE9rh4UZ1JdswYtfPsG2+oLSvdu6v/OAqTIolKFmpR0YNxb5QHYMrf59h8+u6zBy0t4YMP1OVp09ThcEIIIbKOXq+2Wletqk7i5ugIP/0Ef/6pzpEiTJIkKlms32ve9KhdHEWBkasDCbwZ+uzB/v3V5seLF+H337UKUQghcp+rV6FJE3Ua/KgoaNZM7YvSt6+0opg4SVSymE6nY0KbCjQu60Z0nJ7+Sw9z89FT9UFHRylWKITIFsduPGbpvmvsunCfGw+fpl2LLDdRFHWQQpUqakFBe3uYOxe2blXr9QiTp1MU0/62DA8Px9nZmbCwMJyMaMrjyJh4Os7fz9m74ZRyd2DtkLo421qqfVS8vCAmRi1W+NprWocqhDBxO8/fZ+CyI8QlPPs4tzI3o1h+O7wL2FOigD3eiTc3e9wcrNHlhlaGGzegXz+1eCBAgwawZAmUKKFtXCJd0vv9LYlKNgoOi6bdnL0Eh0dTt2R+AvrUxMrCDAYNgoUL4c034Y8/tA5TCGHCdl8Kod/SI8TG66lQyIkEvULQw0hi41PvB+dgbYF3AXu8/p+8lHguiXGysczB6DNJUdSE5IMPIDwcbGzg66/VqvVmcqHAVEiiYiTO3gmn4/x9RMYm0MG3KNM6VEF36RKUK6f+sZ0+DRUrah2mEMIEHbj6kN5LDhEdp6d5hYLM6V4dS3MzEvQKd8OiCHoQSdCDSK6GRBqWbz1+SlpXhQo4WD1rfSngoCYybvYUc7XDxtI8515cau7cgQED1OKBoM6REhAAZcpoGpbIOElUjMjOC/fpF3AYvQIfNS/D8Cal1WKF69ZB797qfwZCCJEBR649oufiQzyNTaBxWTfm9/DF2uLliURMfAI3Hz1Nkrxc/f/PkIiYVJ+n00ERF9sXWmAcKFHAnsIutpibZfOlJEWBlSvVVpPHj8HKSp0Kf9QoMDeCBEpkmCQqRmbZget8vuE0AD90qcpbMbfUoliWlmpv9aJFNY5QCGEqAm+G8q7/QZ7ExFO/dAEW9fTLktaOiOg4rj14ytUHTwxJTNCDSIJCIolIqTzI/2V7f5h792DIEFi/Xr3v56cWEaxQ4dX2KzQliYoRmrzpLIt2B2Flbsby/rWo2ftt+O8/+OgjdW4VIYR4idO3w+i26ADh0fHULuHKkt41sbXK3hYFRVF48CSWaw/VpEVtgVGTmWsPn6arP0zirYSbvaF/TLr6w/z6qzpa8sED9R+78ePVidwsTaAvjUiTJCpGSK9XGLriGJvPBONiZ8nfpcIp1L2jOmz5xg11jhUhhEjF+eBwuiw8QOjTOPyK52Np35rYW1toGlOCXuFOaFSSFpjERObW46g0Z2Eo4GCdpCNvYotMsfx2WIeFwrBhsHq1unGVKvDzz+DjkyOvS2Q/SVSMVFRsAl0WHeDEzVC8XG3ZvnQEFmfPqD3Wx4zROjwhhJG6fD+CzgsO8DAyFh9PF5b3q4mjkY/QiY77f3+Y5y4hJSYyD56k3h/m9csH+XrLbPI/eUyCmTmnewwh7KOxeBfOlzP9YUSOkETFiIVExPD23L3cehzFh3cP8N7PX4GHB1y7BtbWWocnhDAyQQ8i6bxgP/cjYqhY2ImV/WvjbGfcScrLpNQf5v6NYLqsmMFbJ9V5US7l9+TD1h9wstCzET1W5mYU/39/GG+3xD4x6uikAg5WuWN+mDxCEhUjd+leBO3n7SM6MopDiweT79E98PdXJy8SQoj/u/noKZ0W7OduWDTlPBz5ZUBt8tlbaR1W1tu8WS0zcvs2ik5H8IDh7OkxnMsRCYaWmOsPnxKbkHp/GEdrC8MlpBdvxt76lBdJomIC9l1+QM/Fh+h1YB2f7/wJypaFs2dlwiIhBAC3Q6PoNH8/t0OjKOXuwKqBtSngkMtaXcPD1QEFixap90uXVudFqVs32aaJ/WGuPogkKOSJ4TLStYeRr9YfJh3DukXWk0TFRPx65CYTVxxg/7w+OMVEwoYN8NZbWoclhNBYcFg0nRfu5/rDp3gXsGf1wNq4O9loHVbW2rED+vRRBxMAjBgBU6eCnV2Gd5XZ/jBmOiiSzxbvAg5Jh1bn1PwweZgkKibku60XsJnwOcMO/Ep49Ro4HT2kdUhCCA3dj4imy8IDXA2JxNPVljWD6lDI2VbrsLJOZKQ6eGDOHPW+t7c68WXDhtlyuPDoOK6lMEtv0INInqQ1P4yFGV6J/WESE5n/t8bkt5f+MK9KEhUToigKny/YzufD38A6IZ4bv2+lWJvXtQ5LCKGBh09i6LroABfvPaGIiy2rBtbG0zXjLQxGa88edUbuK1fU+4MHq/NIOTjkeCiKohDyJMbQ+vL8LTP9YUoUcMCrgJ30h0knSVRMTEx8Arsbt6fZnt/ZXb4uZQ/+g7tjLmvmFUKkKfRpLF0XHeTc3XAKOlmzZlAdiue31zqsrBEVBZ99BjNnqtPhe3rCTz/B68b5T1lq/WGCHkRyOzTt/jBujtbJZukt4WaPp6v0h3meJComKOz4KRx9fTBTFIaNW8b08V2zfcZJIYRxCI+O413/g5y8FUYBB2tWD6pNSbecb2XIFgcPQq9ecOGCer9vX5gxA5ydtY0rk6LjEriRpF7SsyHWD57Epvo8Mx0UzWeXfJbe/HmzP4wkKiYq8s222G/6g9WVX2fH6CnM7e6b5968QuQ1T2Li6fHTQY7fCMXV3opVA2tTpqCj1mG9upgYmDgRvv0W9HooVEgd3dO6tdaRZZuwqOf6wzx4LpEJiSQyNiHV5+XF/jCSqJiqAwegTh1izSx4bfBPtG3lx2dvSuEtIXKrp7Hx9F58mEPXHuFsa8kvA2pToXAu+Cw7dkxtRTmtFmOle3f48UdwddU2Lo2k1B/mqqE/TCRxCal/FTvaWDx3GcnBMNGdVwF7HDQuofAq0vv9bbqvMLeqXRvq18dq9276Hv2drx3zUzy/HT3qeGkdmRAii0XHJdB/6REOXXuEo7UFy/rVNP0kJS4OJk9Wb/Hx4OYGCxbA229rHZmmdDod7o42uDvaUKtE/iSPxSfouRManaxq9dWQSO6ERRERHc+JW2GcuBWWbL/uif1h3J5LZArY5ar+MNKiYoz+/BPatCHG3gG/AT8RaWOPfy8/mpQrqHVkQogsEhOfwMCfj/LvxRDsrcxZ1r8W1Yvl0zqsV3PqlNqKcvy4er9DB5g7V01WRKZExyVw/eFTgh48+X/HXnWCu8z2h/EuYE9hZ1vMjKBLgVz6MWV6PVSuDGfPsund9xlW5HXsrMz5dXAdKhY2zc5nQohnYuP1DF1xlO3n7mNrac7SvjWp6W3Cl0Ti49UhxhMmqC0qrq7qHCmdO0Mu7FthLDLbH8bawgyv/Mln6fUuYI9rDvaHkUTF1AUEQJ8+KIUK0fvzVfx7PYKCTtZsGFYvd038JEQeE5+g571fjvP36WCsLcxY0rsGdUsV0DqszDt3Tp0X5dD/J6ps0wYWLlQLrQpNKIpCSETMc8lL4kR3T7jx6Gma/WGcbCzwdlM783rlf77woz32WdwfRhIVUxcbq87WeOcOT+ct5K2nZbh0/wnlCznx6+A6Jt2BSoi8KkGv8MHqQH4/cQcrczMW9vSlUVl3rcPKnIQE+P57GDdOHd3j7Aw//AA9e0orihGLT9Bz2zA/jJrEXHv4rD9MahnB4IYlGduqXJbGIp1pTZ2VFXzwAYwejd0PM1i8+zBvzz/AubvhDF95DP+efliYS/FCIUyFXq8wZu1Jfj9xBwszHXO7VzfdJOXyZbUVZe9e9X6LFmr196JFNQ1LvJyFuRnF89tTPL89jcsmfSyl/jCJLTIlCmg38aC0qBiz8HAoVgzCwmDjRk5Ua0DnhfuJjtPzbu1ifPlWpVw5tl6I3EZRFD5df5pfDt3A3EzH7K7VaFW5kNZhZZxer3aOHTMGnj5Vp72fMQP695dWlFxOr1eyvANuer+/5V9yY+bkBEOGqMvffouPpws/dKmGTgfLD9zAf3eQtvEJIV5KURQm/n6GXw7dwEwHMzr5mGaScu0aNGsG772nJimNG6ujfAYMkCQlD9BylJAkKsZuxAj1MtDevbB3Ly0qejDujfIATPn7HJtP39U4QCFEahRFYcpf51i6/zo6HXzbwYe3qhbROqyMURS1c2zlyrBzJ9jZwezZsH07eHlpHZ3IAyRRMXaFCqmd00Ad/gf0e82bHrWLoygwcnUggTdDtYtPCJEiRVGYvvUCi/7f8jnl7cp08DWxPhy3bkGrVjBoEDx5Aq+9BidOwLBhYCZfHyJnyDvNFHz0kdq0unEjnD+PTqdjQpsKNC7rRnScnv5LD3Pz0VOtoxRCPOfHfy4zZ+cVAL54qyJdaxbTOKIMUBRYuhQqVYItW8DaGr77DnbtglKltI5O5DGSqJiCsmXhrbfU5enTAbXn9uxu1alQyIkHT2LpE3CYsKg4DYMUQiSat+sKM7dfBOCz1uXpaUolMIKD1c+b3r3Vjvw1a0JgIIwaBea5Y0p2YVokUTEVH3+s/ly2DO7cAcDe2oLFvWvg4WTD5ftPGLL8KLHxeg2DFEL4777KN5vPAzC6RVn61y+hcUTppCiwahVUrAh//AGWljBlito/rlzWzp8hREZIomIq6tRRrw/HxqoVSP/Pw9mGxb1rYG9lzr4rD/l0/SlMfMS5ECZr2f5rfLXpHADvNy3NsMYmcpkkJAQ6dYKuXeHRI6hWDY4ehU8+AQuZbktoSxIVU5LYqjJvnjrHyv9VKOzE7O7VMdPBb0dvMWfnZY0CFCLvWnXoBp9vPAPAkEYlGdmstMYRpdO6dWorym+/qUnJhAlw8KA6ykcIIyCJiilp3RrKl1eTlIULkzzUuKw7k96qBMD0rRfZGHhbiwiFyJPWHr3FJ+tPAeqovI9blDX+yRgfPYLu3eGdd9QWlUqV1ARl4kT1so8QRkISFVNiZgajR6vLM2eql4Ge06N2cQbU9wZg9K8nORT0KKcjFCLP+ePEHUb/dgJFgZ51ivNZ6/LGn6Rs2qQmJitXqp8rn3wCR45A9epaRyZEMpKomJpu3aBwYbVD7cqVyR7+pFV5Wlb0IDZBz8BlR7ga8kSDIIXIGzafvsvI1YHoFehSw5OJbSoad5ISFgZ9+8Kbb8Ldu+qIwn371E6z1tZaRydEiiRRMTXW1jBypLo8bZpae+M5ZmY6Znauio+nC6FP4+gbcJhHkbHJ9yOEeCX/nLvHe78cJ0Gv0L56Eaa8XVnTacZfautWtRVlyRJ1XqZRo+D4cahVS+vIhEiTJCqmaOBAtQ7Q2bNqE+4LbK3M8e/pR9F8tlx7+JSBPx8hOi5Bg0CFyJ3+vRjCkOXHiEtQaONTmGkdfIw3SYmIgMGD1QrHt25ByZLw33/qBG62tlpHJ8RLSaJiipyd1Q8egG+/TXETN0drlvSugaONBUeuP2b0byfR62XYshCvat/lBwz8+QixCXpaVvRgRicfzI01Sdm1C6pUgQUL1PvDh6tT4L/2mqZhCZERkqiYqvffV3vm79mjXmNOQemCjsx/1xcLMx1/nLjDjG0XczhIIXKXQ0GP6Lf0CDHxepqVd+fHrtWwNDfCj9GnT9XPiMaN1arHxYvDP//ArFlgb691dEJkiBH+hYl0KVwYevRQl/9frDAl9UoVYGp7dT6E2Tsvs+bwzZyITohc59iNx/RZcoiouAQalHFjTvfqWFkY4Ufovn1QteqziSEHDICTJ6FJE03DEiKzjPCvTKTbRx+pP/9frDA1Hf08ea+JOkPmp+tPsefSg5yITohc49StMHotPkRkbAJ1S+ZnYQ9frC2MrO5NdLQ6KWT9+nDpEhQpAn//rc655OSkdXRCZJokKqasfHlo21at0fHdd2luOur1MrxVtTDxeoUhy49y8V5EDgUphGk7eyecd386SER0PDW9XPHv5YeNpZElKfHx0KzZs5GAPXvC6dPQsqXWkQnxyiRRMXVjxqg/f/5ZnRchFTqdjm87VKGGVz4iYuLps+Qw9yOicyhIIUzTpXsRvPvTQcKi4qhWzIXFfWpgZ2WEtW++/14tHujkpLawLl0KLi5aRyVElpBExdTVrQv16iUrVpgSawtzFvbww7uAPbdDoxiw9AhRsTJsWYiUXA15Qjf/gzyKjKVyEWcC+tTEwdoIk5QrV2D8eHV55ky1lVWIXEQSldwglWKFKclnb8WS3jXIZ2fJiVthjFytTlglhHjm+sNIui06SEhEDOULObGsX02cbY2w/o2iwKBBEBWldpbt00friITIcpKo5AZvvgnlyqnTYy9a9NLNvQrYs7CnH1bmZmw5c4+pf53LgSCFMA23Hj+l26KDBIdHU6agA8v71cTFzkrrsFK2dKk67NjGRp0rxZin7xcikyRRyQ1eUqwwJTW8XJneyQcA/z1BLNt/LRsDFMI03A2Lotuig9wOjaJEAXuW969FfgcjrYFz7546DT7ApElQqpS28QiRTSRRyS26d4dCheD2bfjll3Q9pa1PYUa3KAvAhN/PsOP8veyMUAijdj88mu6LDnLj0VOKudqxckBt3B1ttA4rde+/D48fQ7VqzxIWIXIhSVRyi5cUK0zN0EYl6eRXFL0Cw1ce58ydsOyLUQgj9fBJDN39D3L1QSRFXGxZOaAWHs5GnKT88QesXg3m5uDvDxZG2MlXiCwiiUpuMmgQODrCmTPqRE/poNPpmPx2ZeqVys/T2AT6BhzmblhUNgcqhPF4HBlLd/+DXLr/BA8nG34ZUJui+ey0Dit14eEwdKi6PGoUVK+ubTxCZDNJVHKTdBQrTImluRlzu/tS2t2Be+Ex9A04wpOY+GwKUgjjERYVR4/FBzkfHIGbozUrB9SiWH4jTlIAPv1UrYJcogRMnKh1NEJkO0lUcpvEYoX//QcHDqT7ac62lizuXYMCDtacuxvO8JXHiE9I3+UjIUxRRHQcvRYf4vTtcPLbW7Gyfy1KuDloHVba9u6FuXPV5YULwc7IkyohsoAkKrlNkSLw7rvqchrFClPi6WrHT738sLE0Y9eFECb+cQZFkTlWRO4TGRNP34DDBN4MxcXOkuX9a1G6oKPWYaUtJkYtMKgo6nwpTZtqHZEQOSLbEpXJkydTt25d7OzscEllKucbN27QunVr7OzscHd3Z/To0cTHyyWHV5ZYrHD9erh4MUNP9fF04fvO1dDpYPmBG/jvDsqGAIXQTlRsAv2XHuHwtcc42liwvF8tyhcygaJ9U6bAuXNQsCBMn651NELkmGxLVGJjY+nYsSNDhgxJ8fGEhARat25NbGws+/btY+nSpQQEBDA+cSpokXkVKkCbNup/Xpn4QGtZyYNxb5QHYMrf59h8OvUaQkKYkui4BAYuO8L+qw9xsLbg5741qVTEWeuwXu70aZg6VV2eNQtcXbWNR4gcpFOyuW0/ICCAkSNHEhoammT933//zZtvvsmdO3coWLAgAPPnz2fMmDGEhIRgZZXyTJAxMTHExMQY7oeHh+Pp6UlYWBhOUsr8mT171HLvVlZw/Tp4eGTo6YqiMH7jGZYduI6NpRmrBtahqqdL9sQqRA6IjdczePlRdpy/j52VOUv71qSGlwl84SckqPW8Dh5U6/hs2CAz0IpcITw8HGdn55d+f2vWR2X//v1UrlzZkKQAtGjRgvDwcM6cOZPq86ZOnYqzs7Ph5unpmRPhmp569aBOnXQVK0yJTqdjQpsKNC7rRnScnv5LD3Pz0dNsCFSI7BeXoOe9X46x4/x9rC3M8O/lZxpJCqidZw8eVKcemDNHkhSR52iWqAQHBydJUgDD/eDg4FSf98knnxAWFma43bx5M1vjNFk63bNihXPnQkREhndhYW7GrG7VqVDIiQdPYukTcJiwqLgsDlSI7BWfoOeD1YFsOXMPK3MzFvX0o27JAlqHlT43bsAnn6jL33wDRYtqG48QGshQojJ27Fh0Ol2at/Pnz2dXrABYW1vj5OSU5CZS0bYtlC2b7mKFKXGwtmBx7xp4ONlw+f4Thiw/Smy8DFsWpiFBr/Dxbyf58+RdLM11zO9RnQZl3LQOK30UBYYMgchItYV00CCtIxJCExlKVD788EPOnTuX5q1EiRLp2peHhwf37iWtLZN43yOD/SlEKjJRrDAlHs42LO5dA3src/Zdecin60/JsGVh9PR6hU/XnWLd8duYm+mY1bU6TcoVfPkTjcWqVfDXX2o/s0WL1L9nIfKgDL3z3dzcKFeuXJq31DrBvqhOnTqcOnWK+/fvG9Zt27YNJycnKlSokLFXIVL37rtqR9pbt9QPvkyqUNiJ2d2rY6aD347eYs7Oy1kYpBBZS1EUxv9+mtVHbmKmgx+6VKVlJRP6B+jBAxgxQl3+7DMoX17beITQULal6Ddu3CAwMJAbN26QkJBAYGAggYGBPHnyBIDmzZtToUIFevTowYkTJ9iyZQufffYZw4YNw9raSMuqm6LnixV++63anJxJjcu6M+mtSgBM33qRjYG3syBAIbKWoih8+ec5lh+4gU4H33Xy4c0qhbUOK2M+/FBNVipWhDFjtI5GCE1l2/Dk3r17s3Tp0mTrd+7cSaNGjQC4fv06Q4YMYdeuXdjb29OrVy++/vprLDJQCTS9w5vytNBQKFZM7VC7aRO88cYr7W7yprMs2h2ElbkZy/vXoqa3iYyeELmeoih8s/kC8/+9AsC371ShUw0TGxm4dSu0aKF2iN+3D2rX1joiIbJFer+/s30elewmiUo6jR6tTv7WsCHs2vVKu9LrFYauOMbmM8G42Fmybkhd46+RIvKEGdsu8uM/lwD4sl0letQurnFEGRQZCZUqwbVr6qWfH37QOiIhso3Rz6MiclhiscJ//1XnZHgFZmY6Znauio+nC6FP4+gbcJhHkZnrqCtEVpmz87IhSRn/ZgXTS1IAPv9cTVKKFYOvvtI6GiGMgiQqeUXRotC9u7qcwWKFKbG1Mse/px9F89ly7eFTBv58hOi4hFferxCZ4b/7KtO2XABgbKty9H3NW+OIMuHQoWctKPPnqxO8CSEkUclTEosVrlsHly698u7cHK1Z0rsGjjYWHLn+mNG/nUSvN+kricIELd13ja82nQNg1OtlGNywpMYRZUJcHPTvD3q9+g9Fq1ZaRySE0ZBEJS+pWBHefFMd+fPdd1myy9IFHZn/ri8WZjr+OHGHGdsyVq1ZiFex8uANJvyultwY3rgUI5qW1jiiTJo2DU6dgvz51TmPhBAGkqjkNYnT6gcEwAsT7mVWvVIFmNq+MgCzd15mzWEpayCy329HbzFuwykABjYowYfNy2gcUSZduABffKEuf/89uJnIzLlC5BBJVPKa115ThzvGxKjl4rNIRz9P3mtSCoBP159iz6UHWbZvIV60MfA2H/92AkWB3nW9+KRVOXSmWKxPr4eBA9W/xxYtnvUjE0IYSKKS1zxfrHDOHPj/BHxZYdTrZWjrU5h4vcKQ5Ue5eC/jhRCFeJm/T91l1JoT6BXoVqsYE9pUMM0kBcDfH/77D+zs1A60pvo6hMhGkqjkRW3bQpky6kRw/v5ZtludTse0jlWo4ZWPiJh4+iw5zP2I6CzbvxDbzt7jvV+Ok6BX6OhblK/eqmS6ScqdO89qcU2eDF5emoYjhLGSRCUvMjd/NgJoxgx1xEEWsbYwZ2EPP7wL2HM7NIoBS48QFSvDlsWr23XhPsNWHCNer9CuamG+fqcKZmYmmqQADB8O4eFQowa8957W0QhhtCRRyat69ICCBeHmzVcqVpiSfPZWLO5dg3x2lpy4FcbI1ep/wEJk1t7LDxi47CixCXpaVy7E9I4+mJtykrJuHaxfDxYWaqumubnWEQlhtCRRyatsbNTZauGVixWmxLuAPQt7+mFlbsaWM/eY+te5LN2/yDsOXn1Iv6WHiY3X83qFgnzfpSoW5ib80RUaCsOGqctjxkCVKpqGI4SxM+G/dvHKBg8GBwc4fRo2b87y3dfwcmV6Jx8A/PcEsWz/tSw/hsjdjl5/TN+Aw0TH6WlU1o3Z3aphacpJCqj9UoKD1X5in32mdTRCGD0T/4sXryRfPnVoJKitKtmgrU9hRrcoC8CE38+w8/z9bDmOyH1O3Ayl9+JDRMYm8FqpAsx/1xdrCxO/RLJz57MO7IsWqS2bQog0SaKS133wgXqdfNcutdZINhjaqCSd/IqiV2D4ymOcuROWLccRuceZO2H0+OkgETHx1PR2ZVFPP2wsTTxJiYp69o/BoEHQoIG28QhhIiRRyeuyuFhhSnQ6HZPfrky9UvmJjE2gb8Bh7oZFZcuxhOm7EBzBu/4HCY+Op3oxFxb3roGtlYknKaDOPnv5MhQuDN98o3U0QpgMSVTEs6HKa9eqH6TZwNLcjLndfSnt7sC98Bj6BhzhSUx8thxLmK7L95/Q3f8Aj5/G4VPUmYC+NXGwttA6rFcXGPjsH4G5c8HZWdNwhDAlkqgIqFQJWrfO0mKFKXG2tWRx7xoUcLDm3N1whq88RnyCPtuOJ0zLtQeRdFt0gAdPYqlQyImf+9bCycZS67BeXXy8Whk5IQE6dIC33tI6IiFMiiQqQpU4rf6SJVlWrDAlnq52/NTLDxtLM3ZdCGHiH2dQsnhotDA9Nx89pduiA9yPiKFsQUeW96+Fs10uSFIAfvgBjh4FF5csra8lRF4hiYpQ1a8PtWqpxdFmz87WQ/l4uvB952rodLD8wA38dwdl6/GEcbsTGkXXRQe4ExZNSTd7lvevhau9ldZhZY2rV+Hzz9Xl6dPBw0PbeIQwQZKoCFU2FitMSctKHox7ozwAU/4+x+bTd7P1eMI43QuPptuiA9x6HIVXfjtWDqiNm6O11mFlDUVRR/dERUHjxtC3r9YRCWGSJFERz7z1FpQuDY8fw08/Zfvh+r3mTY/axVEUGLk6kMCbodl+TGE8QiJi6LboANcePqVoPltWDqhNQadcNK/Izz/D9u3qXCkLFkhlZCEySRIV8Uw2FitMiU6nY0KbCjQu60Z0nJ7+Sw9z89HTbD2mMA6PImN51/8gV0IiKexswy8DalPYxVbrsLLOvXvqHEUAEyeq/wAIITJFEhWRVM+e4O4ON27AmjXZfjgLczNmdatOhUJOPHgSS5+Aw4RFZW+CJLQV9jSOd/0PcuFeBO6O1qwcUBtPVzutw8paI0eqLZNVq8KoUVpHI4RJk0RFJJXNxQpT4mBtweLeNfBwsuHy/ScMWX6U2HgZtpwbRUTH0XPxQc7eDaeAgxUrB9TGq4C91mFlrT//VCuSm5mp0+Vb5pLRS0JoRBIVkdyQIWBvDydPwtatOXJID2cbFveugb2VOfuuPOTT9adk2HIuExkTT+8lhzlxK4x8dpas6F+bUu4OWoeVtcLD1b8fUFtSfH21jUeIXEASFZFcDhQrTEmFwk7M7lYdMx38dvQWc3Zmzyy5IudFxSbQb+lhjl5/jJONBcv61aKsh6PWYWW9Tz+FW7egRAmYNEnraITIFSRRESkbOVItVrhjBxw5kmOHbVzOnUlvVQJg+taLbAy8nWPHFtkjOi6BgcuOcODqIxyt1SSlUpFcOIX83r3q9PgACxeCXS7rdyOERiRRESkrVgy6dlWXc7BVBaBH7eIMqO8NwOhfT3Io6FGOHl9knZj4BIYsP8ruSw+wszInoG8NfDxdtA4r68XEwIABap+uPn2gaVOtIxIi15BERaRu9Gj1ZzYWK0zNJ63K07KiB7EJegYuO8LVkOydgE5kvbgEPcNXHmfnhRBsLM1Y0rsGvsVdtQ4re0ydCufOqSPmpk/XOhohchVJVETqKleGVq1Ar1fnVclBZmY6Znauio+nC6FP4+gbcJhHkbE5GoPIvPgEPSNXBbLt7D2sLMzw71mDWiXyax1W9jhzBqZMUZdnzQLXXJqMCaERSVRE2p4vVnj/fo4e2tbKHP+efhTNZ8u1h08Z+PMRouMScjQGkXEJeoWPfj3BplN3sTI3Y0EPX14rXUDrsLJHQoJaGTkuDtq0gY4dtY5IiFxHEhWRtoYNoWZNiI7O9mKFKXFztGZJ7xo42lhw5PpjRv92Er1ehi0bK71eYezak2wIvIOFmY453avTuKy71mFln3nz4MABcHRUO9LKNPlCZDlJVETani9WOHt2thcrTEnpgo7Mf9cXCzMdf5y4w4xtF3M8BvFyiqLw+cbT/Hr0FuZmOn7sWo3XKxTUOqzsc+MGfPKJuvz111C0qLbxCJFLSaIiXq5dOyhVSp0SfPFiTUKoV6oAU9tXBmD2zsusOXxTkzhEyhRFYdIfZ1lx8AY6Hczo5MMblQtpHVb2URR1YrcnT6BuXRg8WOuIhMi1JFERL/d8scLvvsv2YoWp6ejnyXtNSgHw6fpT7Ln0QJM4RFKKovD13+cJ2HcNgG/fqcJbVYtoG1R2W70a/voLrKxg0SJ1unwhRLaQvy6RPs8XK/z1V83CGPV6Gdr6FCZerzBk+VEu3ovQLBahmrHtIgv+uwrAlLcr09HPU+OIstnDhzBihLo8bhxUqKBtPELkcpKoiPSxtX324ZxDxQpTotPpmNaxCjW88hERE0+fJYe5HxGtSSwCZv1ziVk71Dl2JrapQLdaxTSOKAeMGgUhIVCxIowdq3U0QuR6kqiI9EssVnjiBGzbplkY1hbmLOzhh3cBe26HRjFg6RGiYmXYck5b8O8Vvvt/x+ZP3yhH73reGkeUA7ZuhZ9/VjuZL1qkXvoRQmQrSVRE+rm6qtOEQ45Pq/+ifPZWLO5dg3x2lpy4FcbI1cdJkGHLOWbxniCm/n0egI+al2Fgg5IaR5QDIiNh0CB1+b33oE4dbeMRIo+QREVkzAcfqJ1r//kHjh7VNBTvAvYs7OmHlbkZW87cY+pf5zSNJ69YfuA6X/x5FoARTUoxvElpjSPKIePHw7Vrah2sr77SOhoh8gxJVETGPF+scNo0bWMBani5Mq1jFQD89wSxbP81bQPK5dYcvslnG04DMKhhCT54vYzGEeWQw4fh++/V5fnz1QnehBA5QhIVkXGJxQp//RWuXtU2FuCtqkX4qLn6hTnh9zPsPJ+zU/3nFeuP32LMupMA9KnnxdiW5dDlhZlY4+LUafL1eujWTa1/JYTIMZKoiIyrUgVattSkWGFqhjUuRSe/ougVGL7yGGfuhGkdUq7y58k7fLjmBIoC79Yuxvg3K+SNJAXUasgnT0L+/M9aVYQQOUYSFZE5idPqL16sDtXUmE6nY/LblalXKj+RsQn0DTjM3bAorcPKFbacCeb9VYHoFejs58kXbSvlnSTl4kWYNEldnjkT3Ny0jUeIPEgSFZE5jRqBnx9ERWlSrDAlluZmzO3uS2l3B+6Fx9A34AhPYuK1Dsuk7Th/j+Erj5GgV2hfrQhT2lfGzCyPJCl6PQwcCDEx0Lw5vPuu1hEJkSdJoiIy58VihZGR2sbzf862lizuXYMCDtacuxvO8JXHiE/Qax2WSdp9KYTBy48Rl6DQukohvu1QBfO8kqQA/PQT/Psv2NmpHWjzSiuSEEZGEhWRee3bQ4kS8OiRZsUKU+LpasdPvfywsTRj14UQJv5xBkWjmXRN1YGrDxnw8xFi4/W0qFiQ7ztXxcI8D31c3LnzrNP4V1+Bdx6YzE4II5WHPnlElnuxWGG88Vxm8fF04fvO1dDpYPmBG/jvDtI6JJNx5Noj+gYcJjpOT5Ny7szqWh3LvJSkAAwfDmFhUKPGs9IRQghN5LFPH5HlevdWOxhev65pscKUtKzkwbg3ygMw5e9zbD59V+OIjF/gzVB6LznM09gE6pcuwNzu1bGyyGMfE+vWwfr1YGGhTpNvbq51RELkaXnsE0hkOSMpVpiafq9506N2cRQFRq4OJPBmqNYhGa3Tt8Po+dNBnsTEU6dEfhb28MPGMo99SYeGwrBh6vLHH4OPj6bhCCEkURFZYehQtcNhYCBs3651NEnodDomtKlA47JuRMfp6b/0MDcfPdU6LKNzPjicd386SHh0PH7F8+Hfyw9bqzyWpICanAQHQ5ky8PnnWkcjhEASFZEVjKhYYUoszM2Y1a06FQo58eBJLH0CDhMWFad1WEbj8v0Iui86SOjTOKp6urCkTw3srS20Divn7dqlXuoB9aeNjabhCCFUkqiIrJFYrHD7djh2TOtoknGwtmBx7xp4ONlw+f4Thiw/Smy8DFsOehBJt0UHeRgZS6UiTiztWxNHG0utw8p5UVHqnCmgVkhu0EDbeIQQBpKoiKxRvDh06aIuG0GxwpR4ONuwuHcN7K3M2XflIZ+uP5Wnhy3ffPSUbosOcD8ihnIejizrWwtn2zyYpAB8+SVcugSFCsE332gdjRDiOZKoiKyTOO/EmjUQZJzDgSsUdmJ2t+qY6eC3o7eYs/Oy1iFp4nZoFF0WHuBuWDSl3R1Y3r8W+eyttA5LGydOPLtkOXcuODtrG48QIglJVETW8fGBFi2MqlhhShqXc2fSW5UAmL71IhsDb2scUc4KDoum26ID3A6NwruAPSv616KAg7XWYWkjPl6tjJyQAO+8A+3aaR2REOIFkqiIrJU4rf5PP8GDB9rGkoYetYszoL462+joX09yKOiRxhHljPsR0XTzP8D1h08p5mrHygG1cHfKw51Gf/wRjhxRW1FmzdI6GiFECiRREVmrcWPw9VU7J86Zo3U0afqkVXlaVCxIbIKegcuOcDXkidYhZauHT2J41/8gV0MiKeJiy8oBtSjkbKt1WNq5ehU++0xdnj5d7Z8ihDA6kqiIrPV8scJZs+Cp8c5ZYmam4/vO1fDxdCH0aRx9Aw7zKDJW67CyRejTWN796RAX7z3Bw8mGlQNqUTSfndZhaUdRYPBgNaFu1Aj69dM6IiFEKiRREVkvsVjhw4ewZInW0aTJ1soc/55+FHGx5drDpwz8+QjRcQlah5WlwqPj6Ln4EOfuhlPAwZoVA2pRPL+91mFp6+efYds2sLaGhQulMrIQRkwSFZH1LCzgww/VZSMrVpgSN0drAvrUwNHGgiPXHzP6t5Po9blj2PKTmHh6LT7EyVthuNpbsXJALUq6OWgdlrbu3VPn/QGYOBFKl9Y0HCFE2iRREdmjd28oUEAdprx2rdbRvFTpgo7Mf9cXCzMdf5y4w4xtF7UO6ZU9jY2n75LDHL8RirOtJcv71aJMQUetw9LeyJHw+DFUrfosoRZCGC1JVET2sLOD995Tl42wWGFK6pUqwNT2lQGYvfMyaw7f1DiizIuOS6D/0iMcuvYIRxsLlverRYXCTlqHpb0//4RVq8DMDPz9wTKPTnAnhAmRREVkn2HD1ITl2DH45x+to0mXjn6evNekFACfrj/FnkvGO8Q6NTHxCQxadpR9Vx5ib2XO0r41qVxUJjEjIgKGDFGXR41SR6cJIYyeJCoi++TP/2w0hREWK0zNqNfL0NanMPF6hSHLj3LxXoTWIaVbbLyeYSuO8e/FEGwtzVnSpybVi+XTOizj8OmncOuW2tF70iStoxFCpJMkKiJ7jRqlFivctg2OH9c6mnTR6XRM61iFGl75iIiJp8+Sw9yPiNY6rJeKT9Dz/qrjbD93H2sLM37q5UdNb1etwzIO+/Y9m9dnwQK1pU8IYRIkURHZy8sLOnVSl420WGFKrC3MWdjDD+8C9twOjWLA0iNExRrvsOUEvcIHa07w9+lgrMzNWNjTj7qlCmgdlnGIiVGnyVcUtZN3s2ZaRySEyABJVET2S5wAzoiLFaYkn70Vi3vXIJ+dJSduhTFy9XESjHDYsl6v8PFvJ/njxB0szHTM7V6dhmXctA7LeHz9NZw7B+7u6gy0QgiTIomKyH5Vq0Lz5mrht5kztY4mQ7wL2LOwpx9W5mZsOXOPqX+d0zqkJBRFYdyGU6w9dgtzMx2zu1WjWYWCWodlPM6ehcmT1eUff1T7TQkhTIokKiJnJLaq+PsbdbHClNTwcmVaxyoA+O8JYtn+a9oG9H+KojDx9zP8cugmZjqY2bkqLStJvRoDvV695BMXB2+++ewSpBDCpGRbonLt2jX69euHt7c3tra2lCxZkgkTJhAbm7SWysmTJ6lfvz42NjZ4enryrQmNDhEZ0KQJVK+u1laZO1fraDLsrapF+Kh5GQAm/H6GnefvaxqPoihM+escS/dfR6eDaR18aOtTWNOYjM68ebB/Pzg4qO85mSZfCJOUbYnK+fPn0ev1LFiwgDNnzjBz5kzmz5/Pp59+atgmPDyc5s2bU7x4cY4ePcq0adOYOHEiCxcuzK6whFZMqFhhaoY1LkUnv6LoFRi+8hhn7oRpEoeiKEzfeoFFu9X+PlPfrsw7vkU1icVo3bgBY8eqy19/DZ6e2sYjhMg0naLk3JSh06ZNY968eVy9ehWAefPmMW7cOIKDg7GysgJg7NixbNiwgfPnz6drn+Hh4Tg7OxMWFoaTk8y8adTi46FMGbVD7Zw5MHSo1hFlWFyCnt5LDrH38kMKOlmzYVg9Cjnb5mgMP2y/xMzt6hT/X7xVkZ51vHL0+EZPUdRLPX/9BXXqwJ496ky0Qgijkt7v7xz96w0LC8PV9dm8Dvv376dBgwaGJAWgRYsWXLhwgcePH6e4j5iYGMLDw5PchIkwsWKFKbE0N2Nud19KuztwLzyGvgFHeBKTc69j3q4rhiTls9blJUlJyerVapJiZaX2iZIkRQiTlmN/wZcvX2bWrFkMGjTIsC44OJiCBZOOUEi8HxwcnOJ+pk6dirOzs+HmKU26pqVPH3XkxdWrsG6d1tFkirOtJYt716CAgzXn7oYzfOUx4hP02X5c/91X+Waz2tL4ccuy9K9fItuPaXIePoQRI9TlceOgQgVt4xFCvLIMJypjx45Fp9OleXvxss3t27dp2bIlHTt2ZMCAAa8U8CeffEJYWJjhdvOm6RaOy5NMsFhhSjxd7fDv5YeNpRm7LoQw8Y8zZOdV1GX7r/HVJnVo9MhmpRnaqFS2HcukffghhIRAxYrP+qgIIUxahvuohISE8PDhwzS3KVGihOFyzp07d2jUqBG1a9cmICAAs+eaYXv27El4eDgbNmwwrNu5cydNmjTh0aNH5Mv38hol0kfFBD14AMWKqSOA/vlHHRFkojafDmbIiqMoCox7ozwDGmR9K8eqQzcYu+4UAEMblWR0i7LoZARLctu2qfP16HSwd6/aP0UIYbTS+/1tkdEdu7m54eaWvlkvb9++TePGjfH19WXJkiVJkhSAOnXqMG7cOOLi4rD8f7n1bdu2UbZs2XQlKcJEFSigFiucPVttVTHhRKVlJQ/GvVGerzadY8rf5/B0tc3SuUzWHr3FJ+vVJKX/a96SpKQmMhISLysPHy5JihC5SLb1Ubl9+zaNGjWiWLFiTJ8+nZCQEIKDg5P0PenWrRtWVlb069ePM2fOsHr1an744QdGjRqVXWEJYzFqlNrJccsWOHFC62heSb/XvOlRuziKAiNXBxJ4MzRL9vvHiTuM/u0EigK96hRnXOvykqSkZsIEdTSZp+ezmWiFELlCtiUq27Zt4/Lly/zzzz8ULVqUQoUKGW6JnJ2d2bp1K0FBQfj6+vLhhx8yfvx4Bg4cmF1hCWPh7W2SxQpTotPpmNCmAo3LuhEdp6f/0sPcfPRq88RsPn2XkasD0SvQtaYnE9pUlCQlNUeOPCvNMG8eODpqG48QIkvl6Dwq2UH6qJiwY8fA1xfMzeHKFSheXOuIXsmTmHg6zd/P2bvhlHJ3YO2QujjbWmZ4P/+cu8fg5UeJS1B4p3pRpnWogpmZJCkpiouDGjXUVrmuXWHlSq0jEkKkk1HOoyJEEtWrQ7NmarHCGTO0juaVOVhbsLh3DTycbLh8/wlDlh8lNj5jw5b/vRjCkOXHiEtQaOtTmG8lSUnbd9+pSYqrK3z/vdbRCCGygSQqQlvPFyt8yWgyU+DhbMPi3jWwtzJn35WHfLr+VLqHLe+7/ICBPx8hNkFPq0oezOjkg7kkKam7eBEmTlSXZ84Ed3dNwxFCZA9JVIS2mjWDqlXV2j8mWKwwJRUKOzG7W3XMdPDb0VvM2Xn5pc85FPSIfkuPEBOvp1l5d37oUg0Lc/nzTJVeDwMHQkwMvP469OihdURCiGwin4RCW88XK/zxR3VulVygcTl3Jr1VCYDpWy+yMfB2qtseu/GYPksOERWXQMMybszpXh0rC/nTTNNPP8G//6oTCC5YIJWRhcjF5NNQaK9jR/DyUieCCwjQOpos06N2cQbU9wZg9K8nORT0KNk2p26F0WvxISJjE6hXKj8LevhibWGe06Galjt3YPRodfnLL9URZEKIXEsSFaG954sVTp+udq7NJT5pVZ4WFQsSm6Bn4LIjXA15Ynjs7J1w3v3pIBHR8dT0cmVRTz9sLCVJean33oOwMHW0z/vvax2NECKbSaIijEMuKFaYEjMzHd93roaPpwuhT+PoG3CYR5GxXLwXwbs/HSQsKo7qxVxY3KcGdlYZnig671m3Tr1ZWMCiRerQdiFEriaJijAO9vbq1OcA33xjssUKU2JrZY5/Tz+KuNhy7eFT+gQcptuigzyKjKVKUWcC+tbEwVqSlJcKDX32Hvn4Y/Dx0TQcIUTOkERFGI9hw8DWFo4ehV27tI4mS7k5WhPQpwaONhacuBnKgycxlC/kxM99a+Jkk/FJ4fKkMWPg7l0oUwY+/1zraIQQOUQSFWE83Nygb191+dtvtY0lG5Qu6MiCd32xtTSnfCEnlveriYudldZhmYZ//4WFC9XlhQvBxkbbeIQQOUam0BfG5epVKF1anSfjxAmoUkXriLJceHQcDlYWMuNsekVHq++DS5fUuVMWLNA6IiFEFpAp9IVpKlFCHa4MJl+sMDVONpaSpGTEl1+qSUqhQmr/JSFEniKJijA+iXNk/PILXL+ubSxCWydOPLsMOGcOuLhoGo4QIudJoiKMj68vNG2qzqcihebyrvh46N9f/dm+Pbz9ttYRCSE0IImKME6J0+ovWgSPks/oKvKAH3+EI0fA2RlmzdI6GiGERiRREcbp9dfVeTIiI2HePK2jETnt6lX47DN1edo0KFxY23iEEJqRREUYp1xarFCkg6LA4MHq77xhQ+jXT+uIhBAakkRFGK+OHaF4cbh/H37+WetoRE5Ztgy2bQNra/XSn5l8TAmRl8kngDBelpYwapS6nMuKFYpU3L8PH3ygLk+cqM6pI4TI0yRREcatXz9wdYXLl2H9eq2jEdlt5Ei187SPz7OK2kKIPE0SFWHc7O3VGkCgzqdh2hMpi7Rs2qTOnWNmBv7+aouaECLPk0RFGL/hw9XaLocPqzVfRO4TEQFDhqjLH3wAfn7axiOEMBqSqAjj5+6eq4sVCmDcOLh5E7y9YdIkraMRQhgRSVSEaRg1Sr0k8PffcPKk1tGIrLR/P8yerS4vWKBe7hNCiP+TREWYhpIloUMHdXn6dG1jEVknNladJl9RoFcvdaI/IYR4jiQqwnQ8X6zwxg1tYxFZY+pUOHsW3Nzgu++0jkYIYYQkURGmw88PmjRRi9RJsULTd/YsTJ6sLv/4I+TPr208QgijJImKMC2J0+ovXAiPH2sbi8g8vV695BMXB61bQ+fOWkckhDBSkqgI09K8OVSpIsUKTd28eWonWgcHmDtXre0khBApkERFmJbnixX+8ANER2sbj8i4mzdh7Fh1+euvoVgxbeMRQhg1SVSE6enUSf1yk2KFpkdRYOhQePIE6tR5NsmbEEKkQhIVYXqkWKHpWrMG/vxT/R36+0tlZCHES8mnhDBN/fpBvnxw6RJs3Kh1NCI9Hj6E995Tl8eNgwoVtI1HCGESJFERpsnB4Vmxwm++kWKFpuCjjyAkRE1QEvuoCCHES0iiIkzXe++BtTUcOgS7d2sdjUjL9u0QEKB2hvb3V39vQgiRDpKoCNPl7g59+qjLUqzQeD19CgMHqsvDhqmdaIUQIp0kURGm7cMP1f/SN22C06e1jkakZMIECAqCokVhyhStoxFCmBhJVIRpK1UK3nlHXZ42TdtYRHJHjsCMGeryvHng6KhtPEIIkyOJijB9iRPArVypTiYmjENcnDpNvl4PXbrAm29qHZEQwgRJoiJMX40a0KiRFCs0Nt99BydOgKurOouwEEJkgiQqIncYM0b9KcUKjcOlSzBxoro8Y4ba8VkIITJBEhWRO7RoAZUrq1Ozz5+vdTR5m14PAwZATAy8/jr07Kl1REIIEyaJisgdpFih8Vi8GP79F+zsYMECqYwshHglkqiI3KNzZ/D0hHv3YNkyraPJm+7eVWegBfjyS/D21jYeIYTJk0RF5B5SrFB7770HYWHg5wcjRmgdjRAiF5BEReQu/furxQovXoTff9c6mrxl/XpYuxbMzdVp8i0stI5ICJELSKIichcHBxg6VF2WYoU5JzT0WZHIjz8GHx9NwxFC5B6SqIjcJ7FY4cGDsGeP1tHkDWPHqv1TSpeGzz/XOhohRC4iiYrIfQoWhN691WUpVpj9/vtPHd0DsGgR2NpqG48QIleRREXkTonFCv/8E86c0Tqa3Cs6Wp0zBdSfDRtqG48QIteRREXkTqVLQ/v26vL06drGkpt9+aXacdnDQ1qvhBDZQhIVkXuNHq3+XLECbt3SNpbc6MSJZ8nJnDng4qJpOEKI3EkSFZF71aqlXoqIi5OieFktIUEdCh4fD2+//az1SgghspgkKiJ3S5xWf8ECdQityBo//ghHjoCzM8yerXU0QohcTBIVkbu1agWVKkFEhBQrzCpBQfDZZ+rytGlQuLC28QghcjVJVETuptM966sixQpfnaLA4MHw9Kl6Wa1fP60jEkLkcpKoiNyvSxcoWhSCg2H5cq2jMW3Ll8PWreqEegsXgpl8hAghspd8yojcz8oKPvhAXZ42DfR6beMxVffvw8iR6vKECVCmjKbhCCHyBklURN4wYIA6fFaKFWbeBx/Ao0dQpQp89JHW0Qgh8ghJVETe4OgoxQpfxV9/wcqV6qUef3+wtNQ6IiFEHiGJisg7EosVHjgAe/dqHY3piIhQO9CCeumnRg1NwxFC5C2SqIi8w8MDevVSl2W69/QbNw5u3gQvL/jiC62jEULkMZKoiLwlsVjhH3/A2bNaR2P89u9/NqHbggVgb69tPEKIPEcSFZG3lCmjTvkOUqzwZWJj1WnyFQV69oTmzbWOSAiRB0miIvKexGn1ly+H27e1jcWYff212urk5gYzZmgdjRAij5JEReQ9tWpBgwZSrDAtZ8/CV1+pyz/+CPnzaxuPECLPkkRF5E2JrSrz50NYmLaxGBu9Xp13Ji4OWreGzp21jkgIkYdJoiLyplatoGJFdejtggVaR2Nc5s+HffvAwQHmzlU7HwshhEYkURF5k5nZs2KF338PMTGahmM0bt6EsWPV5alToVgxbeMRQuR5kqiIvKtrVyhSBO7ehRUrtI5Ge4qizt4bEQF16sCQIVpHJIQQkqiIPEyKFSb166/w55/q9PiLFoG5udYRCSFE9iYqbdu2pVixYtjY2FCoUCF69OjBnTt3kmxz8uRJ6tevj42NDZ6ennwrM4aKnDRgADg7w/nz6pd0XvXokVpiAODTT9X+O0IIYQSyNVFp3Lgxa9as4cKFC6xdu5YrV67QoUMHw+Ph4eE0b96c4sWLc/ToUaZNm8bEiRNZuHBhdoYlxDNOTs8ucXzzjbaxaOmjj+D+fShfHj75ROtohBDCQKcoOVdG9vfff6ddu3bExMRgaWnJvHnzGDduHMHBwVhZWQEwduxYNmzYwPnz51PcR0xMDDHPdXwMDw/H09OTsLAwnJyccuR1iFzm7l21jk1sLOzZA/XqaR1Rztq+HV5/XR3ds2cP1K2rdURCiDwgPDwcZ2fnl35/51gflUePHrFixQrq1q2L5f9LxO/fv58GDRoYkhSAFi1acOHCBR4/fpzifqZOnYqzs7Ph5unpmSPxi1ysUCF1injIe8UKnz6FgQPV5aFDJUkRQhidbE9UxowZg729Pfnz5+fGjRts3LjR8FhwcDAFCxZMsn3i/eDg4BT398knnxAWFma43bx5M/uCF3nHRx+pLQq//w7nzmkdTc6ZMAGCgqBoUZgyRetohBAimQwnKmPHjkWn06V5e/6yzejRozl+/Dhbt27F3Nycnj178ipXm6ytrXFyckpyE+KVlS0L7dqpy3mlWOHRo89q+Mybp/bXEUIII5PhPiohISE8fPgwzW1KlCiR5HJOolu3buHp6cm+ffuoU6cOPXv2JDw8nA0bNhi22blzJ02aNOHRo0fky5fvpfGk9xqXEC914IA6f4ilJVy7BoULax1R9omLg5o1ITAQunSBX37ROiIhRB6T3u9vi4zu2M3NDTc3t0wFpf//PBWJnWHr1KnDuHHjiIuLM/Rb2bZtG2XLlk1XkiJElqpdG+rXh9271WKFuXkU0IwZapLi6iqFGYUQRi3b+qgcPHiQ2bNnExgYyPXr19mxYwddu3alZMmS1KlTB4Bu3bphZWVFv379OHPmDKtXr+aHH35g1KhR2RWWEGnLC8UKL12CiRPV5RkzwN1d03CEECIt2Zao2NnZsW7dOpo2bUrZsmXp168fVapU4d9//8Xa2hoAZ2dntm7dSlBQEL6+vnz44YeMHz+egYmjEITIaW+8ARUqQHg45Mb5fBRFHeUTHQ3Nmj0b7SSEEEYqR+dRyQ7SR0VkuYAA6NNH7aNy9Sr8P7HOFX76Cfr3B1tbOH0aSpTQOiIhRB5ldPOoCGEyunVTk5Q7d2DlSq2jyTp376rDsAG+/FKSFCGESZBERYgX5dZihSNGQGgo+PrC++9rHY0QQqSLJCpCpGTgQHVekXPnYNMmraN5dRs2wG+/qRWR/f3BIsMD/oQQQhOSqAiRkueLFZr6tPqhoer0+ACjR0PVqlpGI4QQGSKJihCpGTFCvQy0Zw/s26d1NJk3dqzaP6VUKRg/XutohBAiQyRRESI1hQtDjx7q8rRp2saSWf/9BwsWqMsLF6qjfYQQwoRIoiJEWhJHyWzcCM/VsDIJ0dEwYIC63L8/NG6sbTxCCJEJkqgIkZZy5eCtt9SJ0r77TutoMuarr+DiRfDwMN0WISFEnieJihAvkzit/s8/q309TMHJk89qFc2ZAy4umoYjhBCZJYmKEC9Tty7UqwexsaZRwC8hQb3UEx8Pb78N7dtrHZEQQmSaJCpCpEdiq8q8eWodIGM2axYcPqwOsZ49W+tohBDilUiiIkR6vPkmlC9v/MUKr12DcePU5WnT1JFLQghhwvJMUcKEhATi4uJyMDKRnSwtLTE3N8/Zgy5ZAn37ql/+QUHqHCvGRFGgVSvYsgUaNICdO8FM/hcRQhin9H5/5/p5tBVFITg4mNDQUK1DEVnMxcUFDw8PdDpdzhywWzf47LNnxQp7986Z46bXihVqkmJtrbb6SJIihMgFcn2ikpikuLu7Y2dnl3NfaiLbKIrC06dPuX//PgCFChXKmQNbW8PIkWp/lWnToGdP40kGQkLU2ECdfbZsWU3DEUKIrJKrE5WEhARDkpI/f36twxFZyPb/M6zev38fd3f3nLsMNHCgOj/J2bPw119q3xVjMHIkPHwIlSur9XyEECKXMJJ/B7NHYp8UOzs7jSMR2SHx95qjfY+cnWHwYHXZWIoV/vWXeinKzEytjGxpqXVEQgiRZXJ1opJILvfkTpr9Xt9/X00Gdu+G/fu1iSFRRMSzxOn996FmTW3jEUKILJYnEhUhspQxFSv87DO4eRO8vODLL7WNRQghsoEkKiJDevfuTbt27bQOQ3uJxQo3bIALF7SJ4cABdXI3UCsk29trE4cQQmQjSVRyoYkTJ1K1alWtw8jdypeHtm21K1YYG6tOk68o6uij5s1zPgYhhMgBkqgIkVmJ0+ovXQrBwTl77G++gTNnwM0NZszI2WMLIUQOkkTFSG3evJnXXnsNFxcX8ufPz5tvvsmVK1cMj9+6dYuuXbvi6uqKvb09fn5+HDx4kICAACZNmsSJEyfQ6XTodDoCAgK4du0aOp2OwMBAwz5CQ0PR6XTs2rULUIdz9+vXD29vb2xtbSlbtiw/mEIRPq3Uq6cWLIyNhR9/zLnjnjunDpEGtUiiDL0XQuRiuXoelRcpikJUXIImx7a1NM/QKJXIyEhGjRpFlSpVePLkCePHj+ftt98mMDCQp0+f0rBhQ4oUKcLvv/+Oh4cHx44dQ6/X07lzZ06fPs3mzZvZvn07AM7Ozty7d++lx9Tr9RQtWpRff/2V/Pnzs2/fPgYOHEihQoXo1KlTpl97rvbxx9CuHcydC598Ao6O2Xs8vR4GDFCTozfegC5dsvd4QgihsTyVqETFJVBh/BZNjn32ixbYWaX/dL/zzjtJ7i9evBg3NzfOnj3Lvn37CAkJ4fDhw7i6ugJQqlQpw7YODg5YWFjg4eGRoRgtLS2ZNGmS4b63tzf79+9nzZo1kqikpk0bdRbYCxdg0SIYNSp7j7dgAezdq3acnTcPZOi9ECKXk0s/RurSpUt07dqVEiVK4OTkhJeXFwA3btwgMDCQatWqGZKUrDRnzhx8fX1xc3PDwcGBhQsXcuPGjSw/Tq5hZvZsJtiZM9WWjuxy6xaMGaMuT50KxYpl37GEEMJI5KkWFVtLc85+0UKzY2dEmzZtKF68OIsWLaJw4cLo9XoqVapEbGysYfr4jDD7f02a54tlvzij66pVq/joo4/47rvvqFOnDo6OjkybNo2DBw9m+Hh5yrvvqvOZ3LoFv/wCvXpl/TEUBYYOVSd4q11bXRZCiDwgTyUqOp0uQ5dftPLw4UMuXLjAokWLqF+/PgB79uwxPF6lShX8/f159OhRiq0qVlZWJCQk7Yvj5uYGwN27d6lWrRpAko61AHv37qVu3boMfe5L8PkOvCIVicUKx45VJ4Dr0SPrixX++iv88Yc6I66/P+RUbSMhhNCYXPoxQvny5SN//vwsXLiQy5cvs2PHDkY91/eha9eueHh40K5dO/bu3cvVq1dZu3Yt+/8/nbuXlxdBQUEEBgby4MEDYmJisLW1pXbt2nz99decO3eOf//9l88++yzJcUuXLs2RI0fYsmULFy9e5PPPP+fw4cM5+tpN1qBBakfaM2fg77+zdt+PHsF776nLn3wCFStm7f6FEMKISaJihMzMzFi1ahVHjx6lUqVKfPDBB0x7bqp2Kysrtm7diru7O2+88QaVK1fm66+/NlQQfuedd2jZsiWNGzfGzc2NX375BVA75MbHx+Pr68vIkSP5KnGI6/8NGjSI9u3b07lzZ2rVqsXDhw+TtK6INLi4qMkKZH2xwo8+gvv3oVw5+PTTrN23EEIYOZ3yfKcFExQeHo6zszNhYWE4OTkleSw6OpqgoCC8vb2xsbHRKEKRXYzu93v7Nnh7Q1ycWqywdu1X3+f27fD66+ront271blbhBAiF0jr+/t50qIiRFYpUkTtWAtZU6zw6dNnrTRDh0qSIoTIkyRRESIrJRYrXL8eLl58tX1NnAhXr0LRojBlyiuHJoQQpkgSFSGyUoUK6iRwr1qs8NixZ8+fNw/SaBYVQojcTBIVIbLaqxYrjIuDfv3U6fI7d4Y338za+IQQwoRIoiJEVqtXD+rUgZgYmDUr48+fORMCAyFfPrXooBBC5GGSqAiR1XS6Z60qc+eqs8mm1+XLMGGCujxjBhQsmPXxCSGECZFERYjs0LYtlCkDoaHqTLLpoSgwcCBER0PTptkzFb8QQpgYSVSEyA7PFyucMUPtd/IyixfDzp1ga6tWSZbKyEIIIYmKENnm3XfBw0MtVrhqVdrb3r37bGjzF19AyZLZH58QQpgASVQEXl5efP/994b7Op2ODRs2vNI+s2IfJs/GBt5/X13+9lv10k5qRoxQLxNVr64WOBRCCAFIoiJScPfuXVq1apWubSdOnEjVqlVfaR+52uDB4OAAp0/D5s0pb7NhA/z2m1oR2d8fLIy/wrcQQuQUSVRyidjY2Czbl4eHB9bW1prvI1d4WbHCsDAYNkxd/ugjqFYtx0ITQghTIImKkWrUqBHDhw9n+PDhODs7U6BAAT7//HMSa0h6eXnx5Zdf0rNnT5ycnBg4cCAAe/bsoX79+tja2uLp6cmIESOIjIw07Pf+/fu0adMGW1tbvL29WbFiRbJjv3jZ5tatW3Tt2hVXV1fs7e3x8/Pj4MGDBAQEMGnSJE6cOIFOp0On0xEQEJDiPk6dOkWTJk2wtbUlf/78DBw4kCdPnhge7927N+3atWP69OkUKlSI/PnzM2zYMOLS0wnV2I0cqbaS7NoFhw4lfWzsWLhzB0qVejYsWQghhEHeamNWFLXQmxbs7DI8imPp0qX069ePQ4cOceTIEQYOHEixYsUYMGAAANOnT2f8+PFM+P8X3JUrV2jZsiVfffUVixcvJiQkxJDsLFmyBFATgjt37rBz504sLS0ZMWIE9+/fTzWGJ0+e0LBhQ4oUKcLvv/+Oh4cHx44dQ6/X07lzZ06fPs3mzZvZvn07AM7Ozsn2ERkZSYsWLahTpw6HDx/m/v379O/fn+HDhxsSG4CdO3dSqFAhdu7cyeXLl+ncuTNVq1Y1vF6TVbQodO+uzlQ7bRr8+qu6fvdumD9fXV64UB3tI4QQIinFxIWFhSmAEhYWluyxqKgo5ezZs0pUVJS64skTRVHTlZy/PXmSodfVsGFDpXz58operzesGzNmjFK+fHlFURSlePHiSrt27ZI8p1+/fsrAgQOTrNu9e7diZmamREVFKRcuXFAA5dChQ4bHz507pwDKzJkzDesAZf369YqiKMqCBQsUR0dH5eHDhynGOWHCBMXHxyfZ+uf3sXDhQiVfvnzKk+fOwaZNmxQzMzMlODhYURRF6dWrl1K8eHElPj7esE3Hjh2Vzp07p3KGUvj9GrNTp9T3gU6nKBcvKkpUlKKULauu699f6+iEECLHpfX9/Ty59GPEateuje65Vpg6depw6dIlEhISAPDz80uy/YkTJwgICMDBwcFwa9GiBXq9nqCgIM6dO4eFhQW+vr6G55QrVw4XF5dUYwgMDKRatWq4urpm+nWcO3cOHx8f7O3tDevq1auHXq/nwoULhnUVK1bE3NzccL9QoUJptvaYlEqVoHXrZ8UKJ0+GCxfU4csp9V0RQggB5LVLP3Z28Fy/iBw/dhZ7/osf1Ms0gwYNYsSIEcm2LVasGBcvXszwMWxz8HKEpaVlkvs6nQ69Xp9jx892H38MmzZBQAD8P9lk9my1po8QQogU5a1ERaeDF77cjdnBgweT3D9w4AClS5dO0urwvOrVq3P27FlKlSqV4uPlypUjPj6eo0ePUqNGDQAuXLhAaGhoqjFUqVIFf39/Hj16lGKripWVlaGFJzXly5cnICCAyMhIQ3K1d+9ezMzMKFu2bJrPzVXq14fateHAAfV+u3bQvr2mIQkhhLGTSz9G7MaNG4waNYoLFy7wyy+/MGvWLN5PnEAsBWPGjGHfvn0MHz6cwMBALl26xMaNGxk+fDgAZcuWpWXLlgwaNIiDBw9y9OhR+vfvn2arSdeuXfHw8KBdu3bs3buXq1evsnbtWvbv3w+oo4+CgoIIDAzkwYMHxMTEJNtH9+7dsbGxoVevXpw+fZqdO3fy3nvv0aNHDwrmpaJ7zxcrdHJSW1NkmnwhhEiTJCpGrGfPnkRFRVGzZk2GDRvG+++/bxiGnJIqVarw77//cvHiRerXr0+1atUYP348hQsXNmyzZMkSChcuTMOGDWnfvj0DBw7E3d091X1aWVmxdetW3N3deeONN6hcuTJff/21oVXnnXfeoWXLljRu3Bg3Nzd++eWXZPuws7Njy5YtPHr0iBo1atChQweaNm3K7NmzX+HsmKh27eDnn2H7dihSROtohBDC6OkUJa15vY1feHg4zs7OhIWF4eTklOSx6OhogoKC8Pb2xsbGRqMIM6dRo0ZUrVo1ydT2IilT/v0KIURel9b39/OkRUUIIYQQRksSFSGEEEIYrbw16seE7Nq1S+sQhBBCCM1Ji4oQQgghjJYkKkIIIYQwWnkiUclVs5sKA/m9CiFE7per+6hYWVlhZmbGnTt3cHNzw8rKKkntHGGaFEUhNjaWkJAQzMzMsLKy0jokIYQQ2SRXJypmZmZ4e3tz9+5d7ty5o3U4IovZ2dlRrFgxzMzyRMOgEELkSbk6UQG1VaVYsWLEx8e/tCaNMB3m5uZYWFhIC5kQQuRyuT5RAbUKr6WlZbLqvEIIIYQwbtJmLoQQQgijJYmKEEIIIYyWJCpCCCGEMFom30clsfhzeHi4xpEIIYQQIr0Sv7cTv8dTY/KJSkREBACenp4aRyKEEEKIjIqIiMDZ2TnVx3XKy1IZI6fX67lz5w6Ojo5ZPlQ1PDwcT09Pbt68iZOTU5buO7eRc5V+cq7ST85V+sm5Sj85V+mXnedKURQiIiIoXLhwmvNhmXyLipmZGUWLFs3WYzg5OcmbOZ3kXKWfnKv0k3OVfnKu0k/OVfpl17lKqyUlkXSmFUIIIYTRkkRFCCGEEEZLEpU0WFtbM2HCBKytrbUOxejJuUo/OVfpJ+cq/eRcpZ+cq/QzhnNl8p1phRBCCJF7SYuKEEIIIYyWJCpCCCGEMFqSqAghhBDCaEmiIoQQQgijJYmKEEIIIYxWnk5U5syZg5eXFzY2NtSqVYtDhw6luf2vv/5KuXLlsLGxoXLlyvz11185FKlxyMj5CggIQKfTJbnZ2NjkYLTa+O+//2jTpg2FCxdGp9OxYcOGlz5n165dVK9eHWtra0qVKkVAQEC2x2ksMnq+du3alex9pdPpCA4OzpmANTJ16lRq1KiBo6Mj7u7utGvXjgsXLrz0eXnxMysz5yqvfl4BzJs3jypVqhhmnq1Tpw5///13ms/J6fdVnk1UVq9ezahRo5gwYQLHjh3Dx8eHFi1acP/+/RS337dvH127dqVfv34cP36cdu3a0a5dO06fPp3DkWsjo+cL1CmX7969a7hdv349ByPWRmRkJD4+PsyZMydd2wcFBdG6dWsaN25MYGAgI0eOpH///mzZsiWbIzUOGT1fiS5cuJDkveXu7p5NERqHf//9l2HDhnHgwAG2bdtGXFwczZs3JzIyMtXn5NXPrMycK8ibn1cARYsW5euvv+bo0aMcOXKEJk2a8NZbb3HmzJkUt9fkfaXkUTVr1lSGDRtmuJ+QkKAULlxYmTp1aorbd+rUSWndunWSdbVq1VIGDRqUrXEai4yeryVLlijOzs45FJ1xApT169enuc3HH3+sVKxYMcm6zp07Ky1atMjGyIxTes7Xzp07FUB5/PhxjsRkrO7fv68Ayr///pvqNnn9MytRes6VfF4llS9fPsXf3z/Fx7R4X+XJFpXY2FiOHj1Ks2bNDOvMzMxo1qwZ+/fvT/E5+/fvT7I9QIsWLVLdPjfJzPkCePLkCcWLF8fT0zPNDD0vy8vvq1dRtWpVChUqxOuvv87evXu1DifHhYWFAeDq6prqNvLeUqXnXIF8XgEkJCSwatUqIiMjqVOnTorbaPG+ypOJyoMHD0hISKBgwYJJ1hcsWDDVa93BwcEZ2j43ycz5Klu2LIsXL2bjxo0sX74cvV5P3bp1uXXrVk6EbDJSe1+Fh4cTFRWlUVTGq1ChQsyfP5+1a9eydu1aPD09adSoEceOHdM6tByj1+sZOXIk9erVo1KlSqlul5c/sxKl91zl9c+rU6dO4eDggLW1NYMHD2b9+vVUqFAhxW21eF9ZZNueRZ5Wp06dJBl53bp1KV++PAsWLODLL7/UMDJhysqWLUvZsmUN9+vWrcuVK1eYOXMmy5Yt0zCynDNs2DBOnz7Nnj17tA7F6KX3XOX1z6uyZcsSGBhIWFgYv/32G7169eLff/9NNVnJaXmyRaVAgQKYm5tz7969JOvv3buHh4dHis/x8PDI0Pa5SWbO14ssLS2pVq0aly9fzo4QTVZq7ysnJydsbW01isq01KxZM8+8r4YPH86ff/7Jzp07KVq0aJrb5uXPLMjYuXpRXvu8srKyolSpUvj6+jJ16lR8fHz44YcfUtxWi/dVnkxUrKys8PX15Z9//jGs0+v1/PPPP6lel6tTp06S7QG2bduW6va5SWbO14sSEhI4deoUhQoVyq4wTVJefl9llcDAwFz/vlIUheHDh7N+/Xp27NiBt7f3S5+TV99bmTlXL8rrn1d6vZ6YmJgUH9PkfZVt3XSN3KpVqxRra2slICBAOXv2rDJw4EDFxcVFCQ4OVhRFUXr06KGMHTvWsP3evXsVCwsLZfr06cq5c+eUCRMmKJaWlsqpU6e0egk5KqPna9KkScqWLVuUK1euKEePHlW6dOmi2NjYKGfOnNHqJeSIiIgI5fjx48rx48cVQJkxY4Zy/Phx5fr164qiKMrYsWOVHj16GLa/evWqYmdnp4wePVo5d+6cMmfOHMXc3FzZvHmzVi8hR2X0fM2cOVPZsGGDcunSJeXUqVPK+++/r5iZmSnbt2/X6iXkiCFDhijOzs7Krl27lLt37xpuT58+NWwjn1mqzJyrvPp5pSjq39i///6rBAUFKSdPnlTGjh2r6HQ6ZevWrYqiGMf7Ks8mKoqiKLNmzVKKFSumWFlZKTVr1lQOHDhgeKxhw4ZKr169kmy/Zs0apUyZMoqVlZVSsWJFZdOmTTkcsbYycr5Gjhxp2LZgwYLKG2+8oRw7dkyDqHNW4vDZF2+J56ZXr15Kw4YNkz2natWqipWVlVKiRAllyZIlOR63VjJ6vr755hulZMmSio2NjeLq6qo0atRI2bFjhzbB56CUzhGQ5L0in1mqzJyrvPp5pSiK0rdvX6V48eKKlZWV4ubmpjRt2tSQpCiKcbyvdIqiKNnXXiOEEEIIkXl5so+KEEIIIUyDJCpCCCGEMFqSqAghhBDCaEmiIoQQQgijJYmKEEIIIYyWJCpCCCGEMFqSqAghhBDCaEmiIoQQQgijJYmKEEIIIYyWJCpCCCGEMFqSqAghhBDCaP0PMA1gmyi9CwEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"train_x = extend_feature(X_train, n=1)\n",
"test_x = extend_feature(X_test, n=1)\n",
"\n",
"theta_lr = regression(train_x, Y_train)\n",
"\n",
"pred_y_lr = test_x.dot(theta_lr)\n",
"mse_lr = mse(pred_y_lr, Y_test)\n",
"\n",
"print(\"Computed Theta for Linear Regression: \", theta_lr)\n",
"# Plot\n",
"\n",
"plt.plot(Y_test, label=\"actual\")\n",
"plt.plot(pred_y_lr, color='r', label='prediction')\n",
"plt.title(f\"Linear Regression: Actual vs Prediction | MSE: {mse_lr:.2f}\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "5daf8531",
"metadata": {},
"source": [
"# Quadratic Regression"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "d6263f3f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Computed Theta for Quadtratic Regression: [-5.57311345 9.13923833 -1.66392306]\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1323ed8d0>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"train_x = extend_feature(X_train, n=2)\n",
"test_x = extend_feature(X_test, n=2)\n",
"\n",
"theta_qr = regression(train_x, Y_train)\n",
"\n",
"print(\"Computed Theta for Quadtratic Regression: \", theta_qr)\n",
"\n",
"pred_y_qr = test_x.dot(theta_qr)\n",
"mse_qr = mse(pred_y_qr, Y_test)\n",
"\n",
"# Plot\n",
"\n",
"plt.plot(Y_test, label=\"actual\")\n",
"plt.plot(pred_y_qr, color='r', label='prediction')\n",
"plt.title(f\"Quadratic Regression: Actual vs Prediction | MSE: {mse_qr:.2f}\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "5eb329c4",
"metadata": {},
"source": [
"# Cubic Regression"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "359ff24e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Computed Theta for Cubic Regression: [-1.78631221 -0.03780323 -2.09099404 0.53326138]\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x132500410>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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YkOGb+fP8/Y4dO8a9e/cYMmRIuo6e7du3p0KFCvz9998ZnvP0iJiAgACuX7+e62PnhKmpKd26dePnn38G1E60Xl5eWV4S6devH5s2baJ58+bs27ePqVOnEhAQQNmyZTlw4ECG9p06dWLr1q0ZHi1atNC1ad68OYqiPLNjuYuLC926dWPlypXMnTuX69evs3fvXrp3766r/jxrhOeMGTNISkrKUAUtqiRR0QMHBwcAoqOj8+0YZcuWTfezv78/JiYm2ZYMr127RpUqVZ77mPXr12fr1q1s2rSJOXPm4OTkxMOHD9NdF75y5QqRkZG4ubnp3vhTHzExMdy7dw9A98FcpkyZdMcoVqxYhktJqfz8/NL9fOXKFUD9YH76WFu2bNEdy9LSkpkzZ/Lvv//i7u5O06ZNmTVrFqGhobp9NWvWjC5dujB58mRcXFzo1KkTy5cvz3Z4alhYGHFxcZQvXz7DtooVK6LVarl582a69d7e3ul+Tv1ds0qgnmXLli2EhYVRr149rl69ytWrVwkMDKRFixb8/PPPuj4SqR/yL/L3z6kHDx4wYsQI3N3dsba2xtXVVfe3e57+Il27dsXExER3eUxRFNavX6/rFwTqa2P06NEsWbIEFxcX2rZty6JFi3J8PCsrK92H1Z49e7h58yb79+9Pl4CmHudpV65cYdOmTRleg6lDbJ98zXt6emJnZ5fu+Zm9fp527do1TExMqFSpUo5+n2dJ/f+X2bErVKiQoU9Q6pDbJzk7Oz/36zYn3nrrLc6fP8/p06f56aefePPNN7NNytq2bcvmzZuJiIhgz549DB06lBs3btChQwfd3yBVqVKlaN26dYZHdpfKsvPdd9/xyiuv8MEHH+Dv70/Tpk2pWrUqHTt2BMjwN39SUFAQs2fP5vPPP8+2XVEifVT0wMHBgRIlSnD27Nkctc/qP19uOqrl9bfizLi4uOjefNu2bUuFChXo0KEDCxYsYPTo0YDaQfbpb/NPevrNLjeevgac+iG8atWqTDuYPTmMeOTIkXTs2JHffvuNzZs389lnnzF9+nR27NhBzZo1dXMWHDp0iD///JPNmzfTr18/5s6dy6FDh/LsDeTJitCTFEV5rv2lnudu3bplun337t3pviU+r9y8Rrt168aBAwf48MMPqVGjBnZ2dmi1Wtq1a5ehc2lOlChRgoCAANatW8fHH3/MoUOHCA4OZubMmenazZ07lz59+vD777+zZcsWhg8fruvD9ax+C6amplnO3fGkzPohaLVaXnrpJcaOHZvpc553yKsxyep1m5/q16+Pv78/I0eOJDAwMMMQ46zY2NgQEBBAQEAALi4uTJ48mX///TfHfYGeh6OjI7///jvBwcEEBQXh4+ODj48PjRo1wtXVNUMV80kTJkygZMmSNG/eXPdFM/VLVFhYGEFBQXh7e+fpVBPGThIVPenQoQPff/89Bw8epGHDhtm2Tf1W/XTv/8xGOqS6cuVKum93V69eRavV6jqPZsbf3z/HyVNOtG/fnmbNmvHFF18wePBgbG1t8ff3Z9u2bTRu3DjTN/VUPj4+urif/D3u37+f429pqZ3s3NzccvQh4+/vz5gxYxgzZgxXrlyhRo0azJ07lx9//FHXpkGDBjRo0IDPP/+cn376ibfffps1a9YwYMCADPtzdXXFxsaGS5cuZdh28eJFTExM8PLyytHv8jxiY2P5/fff6d69O2+88UaG7cOHD2f16tW0aNFCd67Onj2b7bnKKiHJ6Wv04cOHbN++ncmTJzNhwgTd+tTq1/Pq3r07Q4YM4dKlS6xduxYbGxvdt9UnVa1alapVq/Lpp59y4MABGjduzLfffsu0adNe6PjZ8ff3JyYm5pmvwdQOnzExMekS38xeP5kdQ6vVcv78eWrUqJFlu5x+YUn9/3fp0iVatmyZbtulS5d02w2tR48eTJs2jYoVK2b7e2elTp06gDrvkz54e3vrqqYREREcP36cLl26ZPuc4OBgrl69mqF6B+gujT98+DDbZKewKTopmYGNHTsWW1tbBgwYwN27dzNsv3btmm5YqIODAy4uLrpr2am+/vrrLPefOow01cKFCwF4+eWXs3xOly5dOH36dIbr7vD83+g/+ugj7t+/z+LFiwH123RKSgpTp07N0DY5OVn3QdeqVSvMzMwyzKL61Vdf5fjYbdu2xcHBgS+++CLTfiWpw37j4uIyjCTy9/fH3t5ed2nn4cOHGc5B6htjVpd/TE1NadOmDb///nu6S253797lp59+okmTJrpLE7mR0+HJGzduJDY2lqFDh/LGG29keHTo0IENGzaQkJBArVq18PPzY/78+RmSjSd/b1tbWyBjQuLj44OpqekzX6Op37yfPpepI1+eV5cuXTA1NeXnn39m/fr1dOjQQRcrqP3CkpOT0z2natWqmJiY5Pvsst26dePgwYNs3rw5w7aIiAhdXK+88grJycnpXvMpKSm6/7vZ6dy5MyYmJkyZMiVDVerpv19mw52fVqdOHdzc3Pj222/TnZ9///2XCxcu0L59+2fuQx8GDBjAxIkTmTt3brbttm/fnun61D57Obm89rScDk/Oyvjx40lOTmbUqFHp1l+8eJHg4GDdz9OmTWPjxo3pHqnvn2PHjmXjxo3pXutFgVRU9MTf35+ffvqJ7t27U7FixXQz0x44cID169en6yw5YMAAZsyYwYABA6hTpw579uzh8uXLWe4/MDCQV199lXbt2nHw4EF+/PFH3nrrLapXr57lcz788EN++eUXunbtSr9+/ahduzYPHjzgjz/+4Ntvv832uVl5+eWXqVKlCvPmzWPo0KE0a9aMwYMHM336dE6dOkWbNm0wNzfnypUrrF+/ngULFvDGG2/g7u7OiBEjmDt3ru73OH36NP/++y8uLi45+mbo4ODAN998Q8+ePalVqxZvvvkmrq6uBAcH8/fff9O4cWO++uorLl++TKtWrejWrRuVKlXCzMyMjRs3cvfuXd58800AVq5cyddff81rr72Gv78/0dHRLF68GAcHB1555ZUsY5g2bRpbt26lSZMmDBkyBDMzM7777jsSEhKYNWtWrs8n5Hx48urVqylevHiWQ+BfffVVFi9ezN9//83rr7/ON998Q8eOHalRowZ9+/bF09OTixcvcu7cOd2HbO3atQG1GtO2bVtMTU158803cXR0pGvXrixcuBCNRoO/vz9//fVXhmv/Dg4Ouj5ASUlJlCxZki1bthAYGPhc5yKVm5sbLVq0YN68eURHR9O9e/d023fs2MGwYcPo2rUr5cqVIzk5mVWrVmFqavrMb7Qv6sMPP+SPP/6gQ4cO9OnTh9q1axMbG8uZM2f45ZdfCAoKwsXFhY4dO9K4cWPGjRtHUFAQlSpV4tdff81RP5oyZcrwySef6DqJvv7661haWnL06FFKlCjB9OnTAfXv98033zBt2jTKlCmDm5tbhooJgLm5OTNnzqRv3740a9aMHj166IYn+/r6ZvhwNRQfH58czZLcqVMn/Pz86NixI/7+/sTGxrJt2zb+/PNP6tatm6H6dvny5XSV1FTu7u689NJLQM6HJ4PaGfbs2bPUr18fMzMzfvvtN7Zs2cK0adOoW7duurYVK1akWbNmujltmjRpkmF/qdWTunXr0rlz53TbvvrqKyIiIggJCQHUqTBu3boFqIMRnmcovtEx2HijIury5cvKwIEDFV9fX8XCwkKxt7dXGjdurCxcuFCJj4/XtYuLi1P69++vODo6Kvb29kq3bt2Ue/fuZTk8+fz588obb7yh2NvbK87OzsqwYcPSDTNUlIzDkxVFUe7fv68MGzZMKVmypGJhYaGUKlVK6d279zOHz2U2M22qFStWZBgm9/333yu1a9dWrK2tFXt7e6Vq1arK2LFj083Sm5ycrHz22WeKh4eHYm1trbRs2VK5cOGCUrx4ceXdd9/VtctsOOKTdu7cqbRt21ZxdHRUrKysFH9/f6VPnz7KsWPHFEVRlPDwcGXo0KFKhQoVFFtbW8XR0VGpX7++sm7dOt0+Tpw4ofTo0UPx9vZWLC0tFTc3N6VDhw66faR6+u+R+ty2bdsqdnZ2io2NjdKiRQvlwIED6dpk9TtkNuw3J8OT7969q5iZmSk9e/bMsk1cXJxiY2OjvPbaa7p1+/btU1566SXF3t5esbW1VapVq6YsXLhQtz05OVl5//33FVdXV0Wj0aQbIhsWFqZ06dJFsbGxUZydnZXBgwcrZ8+ezRDrrVu3lNdee01xcnJSHB0dla5duyohISEZzl1uZ6ZdvHixAij29vYZXuvXr19X+vXrp/j7+ytWVlZKsWLFlBYtWijbtm175n4zm5k2M9n9H4iOjlbGjx+vlClTRrGwsFBcXFyURo0aKXPmzFESExN17e7fv6/07NlTcXBwUBwdHZWePXvqhlZnNzw51bJly5SaNWsqlpaWirOzs9KsWTNl69atuu2hoaFK+/btFXt7ewXQDVXOanj52rVrdfsrVqyY8vbbbyu3bt3K0fnJKsanPc/w5Oxk9n/p559/Vt58803F399fsba2VqysrJRKlSopn3zyiRIVFZXu+WQzPPnJod05HZ6sKOqw7nr16in29vaKjY2N0qBBg3TvL08f/1mzB2c3PDl1mHxmD0PP8pxXNIrynDV+IfQgIiICZ2dnpk2bppu0SghRcO3atYsWLVoQGBiYbR86IVJJHxVhNDKbWyC1L0Pq1N9CCCGKFumjIozG2rVrWbFiBa+88gp2dnbs27ePn3/+mTZt2tC4cWNDhyeEEMIAJFERRqNatWqYmZkxa9YsoqKidB1s83MoqRBCCOMmfVSEEEIIYbSkj4oQQgghjJYkKkIIIYQwWgW+j4pWqyUkJAR7e3u93N9GCCGEEC9OURSio6MpUaJEtvcuKvCJSkhISL7eP0UIIYQQ+efmzZvZ3ii0wCcq9vb2gPqLPs99VIQQQgihf1FRUXh5eek+x7NS4BOV1Ms9Dg4OkqgIIYQQBcyzum0YRWfaRYsW4evri5WVFfXr1+fIkSOGDkkIIYQQRsDgicratWsZPXo0EydO5MSJE1SvXp22bdtmuAurEEIIIYoegycq8+bNY+DAgfTt25dKlSrx7bffYmNjw7JlywwdmhBCCCEMzKB9VBITEzl+/Djjx4/XrTMxMaF169YcPHgw0+ckJCSQkJCg+zkqKirf4xRCCJG/FEUhOTmZlJQUQ4ci8oipqSlmZmYvPHWIQROV8PBwUlJScHd3T7fe3d2dixcvZvqc6dOnM3nyZH2EJ4QQQg8SExO5c+cOcXFxhg5F5DEbGxs8PT2xsLB47n0UuFE/48ePZ/To0bqfU4c3CSGEKHi0Wi2BgYGYmppSokQJLCwsZPLOQkBRFBITEwkLCyMwMJCyZctmO6lbdgyaqLi4uGBqasrdu3fTrb979y4eHh6ZPsfS0hJLS0t9hCeEECKfJSYmotVq8fLywsbGxtDhiDxkbW2Nubk5N27cIDExESsrq+faj0E701pYWFC7dm22b9+uW6fVatm+fTsNGzY0YGRCCCH06Xm/bQvjlhd/V4Nf+hk9ejS9e/emTp061KtXj/nz5xMbG0vfvn0NHZoQQgghDMzgiUr37t0JCwtjwoQJhIaGUqNGDTZt2pShg60QQgghih6DJyoAw4YNY9iwYYYOQwghhCjw+vTpQ0REBL/99puhQ8kTclFQCCGE0LNJkyZRo0YNQ4dRIEiikoXTNyMY+tMJTgQ/NHQoQgghRJEliUoWfjx0g7//u8OSvdcNHYoQQhQpiqIQl5is94eiKLmKc9OmTTRp0gQnJyeKFy9Ohw4duHbtmm77rVu36NGjB8WKFcPW1pY6depw+PBhVqxYweTJkzl9+jQajQaNRsOKFSsICgpCo9Fw6tQp3T4iIiLQaDTs2rULgJSUFPr374+fnx/W1taUL1+eBQsW5MVpN1pG0UfFGPUP8GP98VtsOhvKzQdxeBWT8f1CCKEPj5JSqDRhs96Pe35KW2wscv6xGBsby+jRo6lWrRoxMTFMmDCB1157jVOnThEXF0ezZs0oWbIkf/zxBx4eHpw4cQKtVkv37t05e/YsmzZtYtu2bQA4OjpmmFMsM1qtllKlSrF+/XqKFy/OgQMHGDRoEJ6ennTr1u25f3djJolKFip4OBBQ1oW9V8JZtj+QiR0rGzokIYQQRqRLly7pfl62bBmurq6cP3+eAwcOEBYWxtGjRylWrBgAZcqU0bW1s7PDzMwsy8lNs2Jubp7uNjJ+fn4cPHiQdevWSaJSFA0IKM3eK+GsO3qTka3L4WhtbuiQhBCi0LM2N+X8lLYGOW5uXLlyhQkTJnD48GHCw8PRarUABAcHc+rUKWrWrKlLUvLSokWLWLZsGcHBwTx69IjExMRC3TFXEpVsNC3rQjl3Oy7fjWHNkWAGN/M3dEhCCFHoaTSaXF2CMZSOHTvi4+PD4sWLKVGiBFqtlipVqpCYmIi1tXWu95c6i+uTfWWSkpLStVmzZg0ffPABc+fOpWHDhtjb2zN79mwOHz78Yr+MEZPOtNnQaDQMaFIagBUHgkhK0Ro4IiGEEMbg/v37XLp0iU8//ZRWrVpRsWJFHj5MGyVarVo1Tp06xYMHDzJ9voWFBSkpKenWubq6AnDnzh3duic71gLs37+fRo0aMWTIEGrWrEmZMmXSdeAtjCRReYZONUvgYmfJnch4/jlz59lPEEIIUeg5OztTvHhxvv/+e65evcqOHTsYPXq0bnuPHj3w8PCgc+fO7N+/n+vXr7NhwwYOHjwIgK+vL4GBgZw6dYrw8HASEhKwtramQYMGzJgxgwsXLrB7924+/fTTdMctW7Ysx44dY/PmzVy+fJnPPvuMo0eP6vV31zdJVJ7B0syUXg19AFi893quh68JIYQofExMTFizZg3Hjx+nSpUqjBo1itmzZ+u2W1hYsGXLFtzc3HjllVeoWrUqM2bMwNRU7QfTpUsX2rVrR4sWLXB1deXnn38G1A65ycnJ1K5dm5EjRzJt2rR0xx08eDCvv/463bt3p379+ty/f58hQ4bo7xc3AI1SwD95o6KicHR0JDIyEgcHh3w5xoPYRBrN2E58kpY1gxrQoHTxfDmOEEIUNfHx8QQGBuLn54eVlZWhwxF5LLu/b04/v6WikgPFbC3oUqsUgEwAJ4QQQuiRJCo51K+JHwDbLtzjeliMgaMRQgghigZJVHLI39WO1hXdAFi6L9DA0QghhBBFgyQqudD/8VDlDSdu8SA20cDRCCGEEIWfJCq50KB0MaqUdCA+ScvqQzcMHY4QQghR6EmikgtPTgC38uANEpJTnvEMIYQQQrwISVRyqX01TzwcrAiPSeD3UyGGDkcIIYQo1CRRySVzUxP6NPYFYOneQJkATgghhMhHkqg8hx71vLGxMOXS3Wj2Xgk3dDhCCCFEoSWJynNwtDanWx0vAJbIUGUhhBD5zNfXl/nz5+t+1mg0/Pbbby+0z7zYhz5IovKc+jX2w0QDey6HcSk02tDhCCGEKELu3LnDyy+/nKO2kyZNokaNGi+0D0OSROU5eRe3oW1lDwCW7pNp9YUQQmQvMTHv5t/y8PDA0tLS4PvQB0lUXsCAAHWo8m8nQ7gXHW/gaIQQopBQFIiN1f8jl4MjmjdvzrBhwxg2bBiOjo64uLjw2Wef6QZZ+Pr6MnXqVHr16oWDgwODBg0CYN++fQQEBGBtbY2XlxfDhw8nNjZWt9979+7RsWNHrK2t8fPzY/Xq1RmO/fRlm1u3btGjRw+KFSuGra0tderU4fDhw6xYsYLJkydz+vRpNBoNGo2GFStWZLqPM2fO0LJlS6ytrSlevDiDBg0iJibtljF9+vShc+fOzJkzB09PT4oXL87QoUNJSkrK1XnLLbN83XshV9vHmZreTpwMjuDHgzcY3aa8oUMSQoiCLy4O7Oz0f9yYGLC1zdVTVq5cSf/+/Tly5AjHjh1j0KBBeHt7M3DgQADmzJnDhAkTmDhxIgDXrl2jXbt2TJs2jWXLlhEWFqZLdpYvXw6oCUFISAg7d+7E3Nyc4cOHc+/evWzCjqFZs2aULFmSP/74Aw8PD06cOIFWq6V79+6cPXuWTZs2sW3bNgAcHR0z7CM2Npa2bdvSsGFDjh49yr179xgwYADDhg3TJTYAO3fuxNPTk507d3L16lW6d+9OjRo1dL9vvlAKuMjISAVQIiMjDXL8v/8LUXw++kupMXmzEpeQbJAYhBCioHr06JFy/vx55dGjR2krY2IURa1v6PcRE5Or2Js1a6ZUrFhR0Wq1unUfffSRUrFiRUVRFMXHx0fp3Llzuuf0799fGTRoULp1e/fuVUxMTJRHjx4ply5dUgDlyJEjuu0XLlxQAOXLL7/UrQOUjRs3KoqiKN99951ib2+v3L9/P9M4J06cqFSvXj3D+if38f333yvOzs5KzBPn4O+//1ZMTEyU0NBQRVEUpXfv3oqPj4+SnJz2Wde1a1ele/fuWZyhLP6+j+X081sqKi+oTSV3Sjlbc+vhI349eYu36/sYOiQhhCjYbGzU6oYhjptLDRo0QKPR6H5u2LAhc+fOJSVFnbm8Tp066dqfPn2a//77L93lHEVR0Gq1BAYGcvnyZczMzKhdu7Zue4UKFXBycsoyhlOnTlGzZk2KFSuW6/hTXbhwgerVq2P7REWpcePGaLVaLl26hLu7OwCVK1fG1NRU18bT05MzZ84893FzQhKVF2RmakK/xn5M+es8S/cG0qOuNyYmmmc/UQghROY0mlxfgjFWtk/9HjExMQwePJjhw4dnaOvt7c3ly5dzfQxra+vnji+3zM3N0/2s0WjQarX5ekzpTJsHutX1wt7KjOvhsey8lPV1RCGEEIXL4cOH0/186NAhypYtm67q8KRatWpx/vx5ypQpk+FhYWFBhQoVSE5O5vjx47rnXLp0iYiIiCxjqFatGqdOneLBgweZbrewsNBVeLJSsWJFTp8+na5T7/79+zExMaF8ecP2v5REJQ/YWZrxVj1vABbvlaHKQghRVAQHBzN69GguXbrEzz//zMKFCxkxYkSW7T/66CMOHDjAsGHDOHXqFFeuXOH3339n2LBhAJQvX5527doxePBgDh8+zPHjxxkwYEC2VZMePXrg4eFB586d2b9/P9evX2fDhg0cPHgQUEcfBQYGcurUKcLDw0lISMiwj7fffhsrKyt69+7N2bNn2blzJ++//z49e/bUXfYxFElU8kjvRr6YmWg4dP0BZ29HGjocIYQQetCrVy8ePXpEvXr1GDp0KCNGjNANQ85MtWrV2L17N5cvXyYgIICaNWsyYcIESpQooWuzfPlySpQoQbNmzXj99dcZNGgQbm5uWe7TwsKCLVu24ObmxiuvvELVqlWZMWOGrqrTpUsX2rVrR4sWLXB1deXnn3/OsA8bGxs2b97MgwcPqFu3Lm+88QatWrXiq6++eoGzkzc0j3v+FlhRUVE4OjoSGRmJg4ODQWMZseYkv58KoXONEsx/s6ZBYxFCiIIgPj6ewMBA/Pz8sLKyMnQ4udK8eXNq1KiRbmp7kV52f9+cfn5LRSUPDWiiTgD31393uBP5yMDRCCGEEAWfJCp5qGopR+r7FSNZq7DiQJChwxFCCCEKPBmenMcGBJTmcOADfjoczPCWZbG1lFMshBCF0a5duwwdQpEgFZU81qqCG6VdbImOT2bdsZuGDkcIIYQo0CRRyWMmJhr6NfEDYNn+QFK0BbqvshBC6EUBH9chspAXf1dJVPJBl1qlcLYx5+aDR2w5F2rocIQQwmilznQaFxdn4EhEfkj9uz49o21uSAeKfGBtYco7DXxYuOMqi/de5+WqnoYOSQghjJKpqSlOTk66uwPb2Niku3eOKJgURSEuLo579+7h5OSU5Uy9OSGJSj7p2dCH73Zf50RwBMdvPKS2j7OhQxJCFGJX78Vw9V4M9f2K4WxrYehwcsXDwwNAl6yIwsPJyUn3931ekqjkEzd7KzrVKMH647dYuu86tX1qP/tJQgjxHKLjk+j23UEexCZiooHqXk40L+dG8/KuVC3paPQ3StVoNHh6euLm5kZSUpKhwxF5xNzc/IUqKakkUclH/QP8WH/8FpvOhnLzQRxexXJ/C3EhhHiWlQeCeBCbiIWZCYnJWk4GR3AyOIIvt12muK0Fzcq50qy8K03Luhp1tcXU1DRPPthE4SKJSj6q4OFAQFkX9l4JZ9n+QCZ2rGzokIQQhUxUfBLf71Fvhjr7jWrU9S3G7sth7Lx4j/1Xw7kfm8ivJ2/z68nbBbLaIoTc6yef7b4cRu9lR7C1MOXA+FY4Wj9/z2chhHjagm1X+HLbZcq62bFpZFNMn0g8EpO1HLvxgN2Xwth1KYxLd6PTPbe4rQVNy7nSvABUW0Thk9PPb0lU8pmiKLSdv4fLd2MY/3IFBjfzN3RIQohCIvJREk1m7iA6Ppmv3qpJh2olsm0fEvGI3ZfD2HXpHvuv3icmIVm3TaotQt8kUTEi647eZOyG//B0tGLP2BaYm8r0NUKIF/fl1sss2H6F8m52bLqyBs2BA9CxI3TrBlWrQjbDfKXaIgxNEhUjkpCcQuMZOwmPSWDBmzXoVKOkoUMSQhRwkXGPqykJyaz3jqDu0HfSNyhfXk1YunWDypWzTVpAqi1C/yRRMTL/236FeVsvU6WkA38OayITGgkhXsjcLZdYuOMqlVyt+XvZ+2jOn4fXXgNFgX//hYSEtMYVK6YlLZUqPXPfUm0R+iCJipF5EJtIw+nbSUjWsmZQAxqULm7okIQQBVREXCJNZu4kJiGZvy3OUnnqOCheHK5eBScniIqCP/+Edetg0yZITEx7cuXKasLStauawOSAVFtEfpBExQh9vPEMPx0OpnVFd5b0rmPocIQQBdTszRdZtPMadZxMWD+vN5qwMFi4EIYNy9g4MhL++ENNWjZvhicnVKtSJa3SUr58jo6dmKzl+I2H7Lp0T6ot4oVIomKEroXF0GrubjQa2D66GaVd7QwdkhCigHkQm0jAzB3EJqawM3wTfku/UpOMM2fgWTd+i4iA339Xk5YtWyA5rTJCtWppSUvZsjmOJ7tqi0YDNaTaIrIgiYqR6r/iKNsv3uOdBt5M61zV0OEIIQqYmZsu8s2ua7SyimHJ9F5oEhPVyzwdOuRuRw8fwm+/wfr1sHVr+qSlRo20y0NlyuR4l7pqy+V77Loo1RaRPUlUjNTBa/fpsfgQVuYmHBzXSv6jCiFy7H5MAgGzdhKXmMKh/xbj8e/v0KqVmmi8SAf9Bw/UpGXdOti2DVJS0rbVqpWWtJQunavdSrVFZEcSFSOlKAodFu7jXEgUH7Qpx7CWOS+xCiGKtun/XOC7PdfpmnST2fPeUz/tT56E6tXz7iDh4WlJy44d6ZOWOnXSkhZf31ztVqot4mmSqBix307eZuTaU7jaW7LvoxZYmslNuIQQ2QuPSSBg5k4eJSZzevMkHE8fh/79YcmS/DtoWBhs3KgmLTt3glabtq1u3bSkxccn17uWaouQRMWIJaVoCZi5k9CoeGa/UY2udbwMHZIQwsh9/vd5Fu8NZOi943y4fCLY2sKVK+DpqZ8A7t2DX39V+7Ts2pU+aalfX01a3ngDvL1zvesnqy27L4VxMVSqLUWBJCpG7tvd15jx70UqeNjz74gAmQBOCJGle9HxNJ21E+VRPKd/HoFVyE2YMgU++8wwAd29qyYt69bB7t3qJHOpGjZMS1pKlXqu3d+JfMSuS1lXW6qXcqJ5eVdalHeTaksBJomKkYuMS6LhjO3EJaawqn89Asq6GjokIYSRmvrXeZbuC2TKxb/o9fu3ULIkXL4MNjaGDg3u3ElLWvbuTZ+0NG6sJi1duqgxP4fcVFsCyrpSTKotBYYkKgXApD/OseJAEE3LufJDv3qGDkcIYYTuRcUTMGsndpEPOLz8XcxiY+CHH6BnT0OHllFICGzYoCYt+/alrddooEkTtT9Lly5QIvu7PGdHqi2FhyQqBUDw/Tiaz9mJVoHNI5tS3sPe0CEJIYxM6hea7w4soe3e36B2bThyBEyM/C7st2/DL7+oScuBA2nrNRoICEirtHh4PPchpNpSsEmiUkC89+Nx/j0bSrc6pZj1Rh4OMRRCFHihkfE0nb0TnzuBbFnxPhqtVu0T0rSpoUPLnZs305KWQ4fS1ms00KyZmrS8/jq4u7/QYe5EPtLdSHHf1XCpthg5SVQKiOM3HtDlm4NYmJqwf1xLXO0tDR2SEMJITPz9LCsP3uDXvz6n1rmD6of5hg2GDuvFBAenJS2HD6etNzGB5s3TkhbXF+u3J9UW4yeJSgHy2tf7ORkcwfCWZRjdJmc3BhNCFG53Ih/RbNYuGlw5yg/rJ6r38Tl/PldT2hu9oKC0pOXo0bT1JibQsqXap+X118HF5YUPldNqS/PyblSTaoteSKJSgPxz5g5DVp/A2cacg+NbYWUuE8AJUdR9+tsZfj4QyK7VI/EKCYRRo2DePEOHlX8CA9U5Wtatg+PH09abmqpJS7du8NprULz4Cx/qWdWWYrYWNJNqS76TRKUASU7R0nzOLm49fMTnr1Xh7fq5n+VRCFF43I54RPPZO3nj+L9M3/wVFCsGV6+Cs7OhQ9OPa9fSkpaTJ9PWm5mp9zbq1g06d1bPSx6QaothSKJSwCzbF8iUv85T2sWWbaObyX8EIYqwjzee4Y89F9m/dDCO0Q9hwQIYPtzQYRnG1atpScupU2nrzczgpZfUpKVTpzxL4qTaoj+SqBQwMQnJNJy+nej4ZJb2rkOrii/W+10IUTDdehhHizm7GLljBUMPrYdy5eDsWbWPSlF3+XJa0vLff2nrzc2hTRs1aXn1VXByyrNDSrUl/0iiUgCl3hm1QelirBnU0NDhCCEMYPyv/7Fn63F2LnkXi+RE+P139cNXpHfxYlrScvZs2noLC2jbNi1pycPPhaQUtdqy85JUW/JCgUhUfH19uXHjRrp106dPZ9y4cTneR2FKVEIiHtF01k6StQp/vd+EKiUdDR2SEEKPbj5Qqylzf5tFpwu7oUUL2L5d/eousnb+vJq0rF0LFy6krbewgHbt1KSlY8c8TVpAqi0vqsAkKv3792fgwIG6dfb29tja2uZ4H4UpUQEYseYkv58KoXONEsx/s6ahwxFC6NHYX05z+Y/t/LZqjPpJd/w41JT3gVw5d06tsqxbp1ZdUllawssvq0lLhw5gn7czgeek2tK0rAvNy7vRtJxUW6AAJSojR45k5MiRz72PwpaonLkVScev9mFmomHvRy3wdLQ2dEhCCD24cT+WlnN2sXbVh9S5fQH69oVlywwdVsGlKOolodRKy+XLadusrOCVV9SkpX17sLPL88NLteXZCkyiEh8fT1JSEt7e3rz11luMGjUKMzOzLJ+TkJBAQkKC7ueoqCi8vLwKTaIC0P27gxwOfMDgZqUZ/3JFQ4cjhNCDD9afJm71Gr7+fYZ6V+QrV17o5n3iCYoCZ86oVZa1a9WRRKmsrdVkpVs3NXnJRUU/p1KrLak3U5Rqi6pAJCrz5s2jVq1aFCtWjAMHDjB+/Hj69u3LvGwmNZo0aRKTJ0/OsL4wJSpbz99l4A/HsLcy49D4VthaZp24CSEKvqDwWF6etZXN37+Ld+RdmDQJJk40dFiFk6LA6dNpl4euXUvbZmOjXhbq1k29TGRjky8hSLVFZbBEZdy4ccycOTPbNhcuXKBChQoZ1i9btozBgwcTExODpWXm97wpChUVrVah1bzdBIbHMrFjJfo29jN0SEKIfDR63SlcvvkfH+9arlZRLl/Ol2/24imKok4ol5q0BAambbO1TZ+0WOfPZfiiXG0xWKISFhbG/fv3s21TunRpLCwynuxz585RpUoVLl68SPnyObvnTWHro5Jq1aEbfPbbWbyKWbPrgxaYFtKMWoii7lpYDN2n/cGObwfikBgHK1ZA796GDqvoURS183Jq0vLkiFQ7O3XUULdu6igiK6t8C6MoVVsKxKWfp61evZpevXoRHh6Ocw5nGSysicqjxBQazthORFwS37xdi5ereho6JCFEPhi55iS1Zn1Gr5N/Q61a6s35TEwMHVbRpijq3yF1npbg4LRt9vbq/CzduqmTzOVj0lLYqy1Gn6gcPHiQw4cP06JFC+zt7Tl48CCjRo3i5ZdfZuXKlTneT2FNVADmbL7EVzuvUtvHmQ3vNTJ0OEKIPHb1XgzvffIj/y4dipmihZ07oXlzQ4clnqQocORIWqXl1q20bQ4O6vT93bqp0/ln0WUhrzxZbdl/NZzoAl5tMfpE5cSJEwwZMoSLFy+SkJCAn58fPXv2ZPTo0Vn2T8lMYU5U7kXH02TGThJTtPw6pBG1vIvIDcmEKCKG/3ySTp8NptW1o+pN9jZuNHRIIjtaLRw+rCYs69fD7dtp2xwd0yctmXRvyEuFodpi9IlKXinMiQqoQxZ/OX6L9lU9WfR2LUOHI4TII1fuRjNlxAJWrf0MxcwMzblz6n19RMGg1cLBg2lJy507aducnNTEs1s39W7P+Zy0AIRGxrP78j12Xsy82lKtlBMtjKzaIolKIXExNIp28/diooHdH7bAq1j+DJcTQujXsB+PMnR0NyqGBcGIETB/vqFDEs9Lq4X9+9Wk5ZdfIDQ0bZuzM7z2mpq0tGypl5tLFpRqiyQqhUjPpYfZeyWcfo39mNCxkqHDEUK8oEuh0Szv9wkz/l1IipMTpteuQbFihg5L5IWUlPRJy927aduKFYPXX1eTlhYtIJvJTfOSsVZbJFEpRHZfDqP3siPYWphyYHwrHK3ldu9CFGSjluzh45GdcI2NgC+/hBe4jYgwYikpsHdvWtISFpa2rXjxtKSleXO9JS3GVG2RRKUQURSFtvP3cPluDB+/UoFBTf0NHZIQ4jlduBPFti6DeP/gWhL9SmNx8YJe+jAIA0tOhj171KRlwwYID0/b5uICXbqoSUuzZmBqqrewUqstuy6Fse9K5tWW5uVcaVfFg4qeefsZK4lKIbPu6E3GbvgPT0cr9oxtgbmpzLMgREE0fv7fTPzwdaySE9VRPp07GzokoW/JybBrl5q0/PorPDlJqptbWtISEKDXpCW7ast7zf35qF3GGeVfhCQqhUx8UgpNZu4gPCaRBW/WoFONkoYOSQiRS+dCIrnU5jVeP7eTuIZNsNm/R/3aKoqupKT0ScuDB2nb3N3hjTfUpKVxY70mLZC+2jIgoDS1ffJ2igxJVAqh/22/wrytl6la0pE/hjVGI29wQhQon09aySeT+6g/HDsGtWsbNB5hZJKSYMcONWnZuBEePkzb5umZlrQ0alQoZi/O6ed3wf9Ni5C363tjaWbCmduRHAl88OwnCCGMxtlbEby0dBYAUd16SJIiMjI3h7ZtYelSdYjzP/9Anz7qZHJ37sDCherlIC8vtQP2/v3q0OhCThKVAqS4nSVdapcCYPHewGe0FkIYkz0zvqPerfMkWljhMHeWocMRxs7CQr1r8/LlcO8e/PUX9OqlTtsfEgILFkCTJuDtDaNGqZPPFdKkRRKVAqZfYz8Atl+8y/WwGANHI4TIiTPX7tJ+9XwAYt8fCaVKGTQeUcBYWED79rBypZq0/PEHvPOOeoPE27fVyQIbNQJfXxgzRp3mv2D36khHEpUCpoybHa0quKEosGy/VFWEKAjOfzIdn4hQIp1dcJ70iaHDEQWZpSV07AirVqlJy++/w9tvg50d3LwJ8+ZBgwbg5wcffqjeBbqAJy2SqBRAAwJKA/DL8Vs8jE00cDRCiOz8d+oqL/+2BICkSVPVDxQh8oKVFbz6Kvz4o5q0bNwIPXqArS3cuAFz5kC9elC6NHz0kdqBuwAmLZKoFEANShejcgkH4pO0rD58w9DhCCGyEfrBJzgkxHLbtzwuQwcaOhxRWFlbq3Py/PSTOgPuhg3QvTvY2EBQEMyaBXXrgr8/jBsHJ04UmKRFEpUCSKPRMPBxVWXlwRskJKcYOCIhRGbObj9Myx2/AGA2b57e58EQRZS1tTo9/5o1atKyfj107aquDwyEmTPVUWdly8LHH8OpU0adtEiikpXr16FdO7h82dCRZKp9NU88HKwIi07gj1Mhhg5HCJGJxDEfYKZoOV+7Ge6vvWLocERRZGOjzr+ybp2atKxdq858a2UF167B9OlQsyaULw+ffgr//Wd0SYskKlkZPRo2b4bevdXpjo2MuakJfRr7ArB0XyAFfN4+IQqdS6s3Uuv0PpJMTHFeNN/Q4Qih9l3p1i3tBolr1qiVFysruHIFPv8cqleHihVhwgQ4e9YokhZJVLKycKE6Xv3QIfXanhHqUdcbGwtTLoZGs+9q+LOfIITQj5QUrMZ9BMDRdt3wrF/DsPEI8TQ7O7UPy4YNakfcn35S+7hYWsKlSzB1KlStCpUrw8SJcPGiwUKVRCUrXl5qsgIwaZJ6Dc/IONqY062OFyATwAlhTK7P+RqfW1eItLLF938zDR2OENmzt1dHC23cqCYtP/6ojiaysIALF2DKFFiyxGDhSaKSnZ494bXX1Psv9OwJCQmGjiiDfo39MNHAnsthXHriTpdCCAOJicF5+hQA9r/5HiX8vQwckBC54OCgzsvy++9q0vLDD9Chg1p9MRBJVLKj0cB334Grq3qtbsIEQ0eUgXdxG9pW9gBg6b7rBo5GCHHr48k4R4Zzw9mTGjNkcjdRgDk6ql/S//xTHdpsIJKoPIurKyxerC7Png379hk2nkwMCFCn1f/tZAhh0cZX9RGiyLh1C9dv1UvGBwZ+SAl3J8PGI0QhIIlKTnTqpI7+URT13xjjusdObZ9i1PR2IjFFy6qDQYYOR4gi697wMVgmJXCsVGWajx9s6HCEKBQkUcmpBQvUDrbXr8MHHxg6mgwGNFEngFt16AbxSTIBnBD6phw9itvGdQAcH/Epnk42Bo5IiMJBEpWccnSEFSvU5e++g3//NWg4T2tb2Z1SztY8jEtiw4lbhg5HiKJFUYgaOgKA36u0oPOgzoaNR4hCRBKV3GjZEoYPV5f794cHDwwbzxPMTE3o21jtq7J0XyBareEn6RGiqFA2bsTx6EHizSy4Pupj3B2sDB2SEIWGJCq5NX26OtXwnTswbJiho0mne10v7C3NuB4Wy85L9wwdjhBFQ2Ii8aPVy8HL6r/O2280MXBAQhQukqjklo2NOq7c1BR+/lm9b4KRsLM0o0d9bwCWyARwQuiFsmgR1jcCuWfrTNSI0bhJNUWIPCWJyvOoV0+94yTAkCFqdcVI9Gnki6mJhoPX73P2dqShwxGicHvwgOTJ6uRu/2vek/7tqhk4ICEKH0lUntenn0KtWmo/lQEDjOLGTQAlnKxpX9UTUPuqCCHyjzJ5MuaREVxw9cVm0ABc7S0NHZIQhY4kKs/LwkK9BGRpCf/8Y9D7IDwtdQK4P0+HcCfykYGjEaKQunwZ5euvAZj90iAGtSxn4ICEKJwkUXkRlSurt8UGGDVKnWPFCFQr5UQ9v2IkaxVWHrhh6HCEKJSUsWMxSU5mu39dyr7TGRc7qaYIkR8kUXlRI0dC06YQGwt9+kCKcUy2NjBAnQDup8M3iE1INnA0QhQyO3ei+f13kjUmfPnSAAY39Td0REIUWpKovChTU3UiODs72LsXvvzS0BEB0KqCG34utkTFJ7P+2E1DhyNE4aHVoowZA8Dqmi8T0KkpxWwtDByUEIWXJCp5wc8vLUH55BP1TssGZmKioV8Tta/Ksv1BpMgEcELkjVWr0Jw8SZSlLYubv8Ogx9VLIUT+kEQlr/TvD+3bQ2Ii9Oql/mtgb9QqhZONOcEP4th6PtTQ4QhR8MXGojyemuCrht3o3KYmzlJNESJfSaKSVzQaWLwYihWDkydh6lRDR4S1hSnv1PcBYLFMACfEi5szB01ICMGO7mxo9JpuhJ0QIv9IopKXPD3h22/V5enT4fBhw8YD9Grog4WpCcdvPORE8ENDhyNEwXX7NsqsWQDMaN6Xt5uVw8lGqilC5DdJVPJa167Qo4c6+qdXL4iLM2g4bg5WvFqjBABLpaoixPP79FM0cXEcK1mRvdWb0b+J9E0RQh8kUckPX30FJUrA5cswfryho9GVp/89e4ebDwybOAlRIJ04gbJyJQDTWg6gX5PSONqYGzgoIYoGSVTyQ7FisHSpuvy//8H27QYNp4KHAwFlXdAqsHx/kEFjEaLAURQYMwaNovBbpWZcL11ZN6JOCJH/JFHJL+3awbvvqst9+0KkYW8QOODxEMq1R4OJik8yaCxCFCh//gm7dpFgZsGsZr0ZEFAaR2uppgihL5Ko5KfZs8HfH27ehBEjDBpK07IulHO3IzYxhTVHgg0aixAFRmIifPABAEvqdCLWvSR9G/saNiYhihhJVPKTnR2sXKkOXV65EjZuNFgoGo2GAY87/63YH0RSitZgsQhRYHz7LVy5wgM7Z75p0JWBAX7YW0k1RQh9kkQlvzVuDGPHqsuDB8O9ewYL5dUaJXCxsyAkMp5/ztwxWBxCFAgPHsCkSQDMbvw2Zs6O9G7ka9CQhCiKJFHRh8mToWpVCAuDQYPUznkGYGVuSq+GvgAs2RuIYqA4hCgQpk2Dhw+57uHHumovMTCgtFRThDAASVT0wdISVq0Cc3P4/Xf44QeDhfJ2fW8szUw4czuSI4EPDBaHEEbtyhV1mgFgYtO+ONpbSzVFCAORREVfqldXKysAw4dDsGE6tBa3s6RL7VKATKsvRJY++giSkjhUvh57/WoxqGlp7CzNDB2VEEWSJCr69OGH0KABREWpQ5a1hunQ2q+xOgfE9ot3uR4WY5AYhDBae/bAxo1oTU35tEkfitta0Kuhj6GjEqLIkkRFn8zM1Ms+NjawY4eutKxvZdzsaFXBDUWBZfulqiKEjlYLo0cD8Hvd9lx18WZws9LYWEg1RQhDkURF38qWVedXAbW8fPGiQcLo/3ha/V+O3+JhbKJBYhDC6KxeDcePk2Rrx7Q63XCxs+CdBlJNEcKQJFExhPfeg5degvh46N0bkpP1HkLD0sWpXMKB+CQtqw/f0PvxhTA6cXG6e3MtCXiT+7ZOvNvMX6opQhiYJCqGoNHAsmXg6AhHjsCMGQYIQaO7WeHKgzdISE7RewxCGJW5c+H2bWI8SzG/8iu42ltKNUUIIyCJiqGUKpXWR2XyZDhxQu8htK9aAg8HK8KiE/jjVIjejy+E0QgJ0X1hmNW8DwlmFrzXzB8rc1MDByaEkETFkN5+G7p0US/99OypXgrSIwszE93cEEv3yQRwogj77DOIiyOsSk1+8KqPm70lb9X3NnRUQggkUTEsjQa++Qbc3eH8efXNUs/equeNjYUpF0Oj2Xc1XO/HF8LgTp+G5csBGN+kL2g0DGku1RQhjIUkKobm6gqLF6vLc+eqczjokaONOd3qeAHqtPpCFCmKog5HVhQCW3dkm2NpPByseLOeVFOEMBaSqBiDjh2hXz/1TbN3b4iO1uvh+zX2Q6OB3ZfDuHxXv8cWwqD+/ht27ECxtGR0je4ADG0h1RQhjIkkKsbiyy/BxweCgmDMGL0e2ru4DW0reQCwVKoqoqhISoIPPgDgbNe+nDR1ooSjFd3qehk4MCHEkyRRMRYODrBihbq8eLH6TU+PBjZVhypvPHmbsOgEvR5bCIP47ju4dAnF1ZURfu0AGNKiDJZmUk0RwphIomJMmjeHUaPU5QED4P59vR26lrczNbycSEzRsuqQTAAnCrmHD2HSJAAO9BrO9UQzSjpZ6/prCSGMhyQqxubzz6FiRQgNVWew1dOQYY1Gw8CA0gD8eOgG8UkyAZwoxD7/HO7fR1uxEmMc6gIwtEUZLMzkLVEIYyP/K42NtbV640JTU1i/Htas0duh21Z2p6STNQ9iE/n1xG29HVcIvbp2DRYuBGBLvw8IjUumlLM1b9QuZeDAhBCZkUTFGNWpkzanytChcFs/SYOZqQn9mqh9VZbsu45WKxPAiUJo3DhITCTlpTZ8Gq9e6nm/pVRThDBW8j/TWH38MdSurV5LHzBAb5eAutUphb2lGdfDYtl1+Z5ejimE3uzbB7/8AiYmbHxrJOExCXgXs+H1WlJNEcJYSaJirMzNYdUqsLSETZvg++/1clh7K3N6PJ46fPEeGaosChGtVp3cDUjq24/pN9W7Ig9rWQZzU3krFMJYyf9OY1axYtqdlUePhqtX9XLYPo18MTXRcPD6fc7ejtTLMYXIdz//DEePgp0dP7UfwP3YRHyK2/B6zZKGjkwIkQ1JVIzd8OHqsOW4OOjTB1LyfzROCSdr2lf1BNSbFQpR4MXFqX1TgMSx41hwNgqA4S3LYibVFCGMWr79D/38889p1KgRNjY2ODk5ZdomODiY9u3bY2Njg5ubGx9++CHJycn5FVLBZGKi3jDN3h7271fvB6QHAwLUTrV/ng4hNFK/d3UWIs99+SXcugXe3iyv14kHsYn4udjSqUYJQ0cmhHiGfEtUEhMT6dq1K++9916m21NSUmjfvj2JiYkcOHCAlStXsmLFCiZMmJBfIRVcvr4wf766/Nln8N9/+X7IaqWcqOdXjGStwooDQfl+PCHyTWgoTJ8OQPzUz/nmcAgAw1uVkWqKEAVAvv0vnTx5MqNGjaJq1aqZbt+yZQvnz5/nxx9/pEaNGrz88stMnTqVRYsWkZiYmF9hFVx9+6o3L0xMhF691H/zWeoEcD8dvkFsglS6RAE1YQLExkL9+iwtVZ+IuCRKu9ryanXpmyJEQWCwrxMHDx6katWquLu769a1bduWqKgozp07l+XzEhISiIqKSvcoEjQa9R5ALi5w+jRMnpzvh2xVwQ0/F1ui4pNZf+xmvh9PiDz333+wdCkAsdNn8f3jm26OaFUWUxONISMTQuSQwRKV0NDQdEkKoPs5NDQ0y+dNnz4dR0dH3cPLqwjdm8PdHb79Vl2eMQMOHszXw5mYaHQTwC3bH0SKTAAnChJFUe9ErtVC164s1XoS+SiJMm52dKgmfVOEKChylaiMGzcOjUaT7ePixYv5FSsA48ePJzIyUve4ebOIfdPv0gXeeUd98+3dWy1p56M3apXCycac4AdxbD2fdQIphNH591/Ytg0sLIiaNJUle68DUk0RoqAxy03jMWPG0KdPn2zblC5dOkf78vDw4MiRI+nW3b17V7ctK5aWllhaWuboGIXWwoWwcydcuQIffQRffZVvh7K2MOWd+j58tfMqi/cG0q6KZ74dS4g8k5SkVlMARoxgWYiGqPhkyrnb6YbeCyEKhlxVVFxdXalQoUK2DwsLixztq2HDhpw5c4Z799Kmad+6dSsODg5UqlQpd79FUePkpA5ZBli0CLZuzdfD9Wrog4WpCcdvPORE8MN8PZYQeWLxYrh4EVxciBz5oW4+oBGtymEi1RQhCpR866MSHBzMqVOnCA4OJiUlhVOnTnHq1CliYmIAaNOmDZUqVaJnz56cPn2azZs38+mnnzJ06FCpmOTESy+pNywEdUTQw/xLINwcrHj18XwTS/fKBHDCyEVGwsSJ6vLkySw9+4Do+GQqeNjzcpWsq7VCCOOUb4nKhAkTqFmzJhMnTiQmJoaaNWtSs2ZNjh07BoCpqSl//fUXpqamNGzYkHfeeYdevXoxZcqU/Aqp8Jk5E8qUUe+uPHx4vh6q/+NOtf+evcPNB3H5eiwhXsgXX0B4OFSsSMQ7fVi2PwhQ+6ZINUWIgkejKHq6LW8+iYqKwtHRkcjISBwcHAwdjv4dPAhNmqida3/5Re1sm096Lj3M3ivh9Gvsx4SOcnlOGKHAQKhQQZ1n6K+/mGNWhq92XqWipwN/v99EEhUhjEhOP79lWsaCrmFD3T1MGDxYnYUzn6RWVdYeDSYqPinfjiPEcxs3Tk1SWrfmYbPWLN+vXqoc2VqqKUIUVJKoFAYTJ0L16nD/PgwapM4fkQ+alXOlrJsdsYkprDkSnC/HEOK5HTgA69apkyPOncvifYHEJqZQuYQDbSq5P/v5QgijJIlKYWBhAT/8oP7755+wYkW+HEaj0ehuVrhifxBJKdp8OY4QuabVwqhR6nL//jzwr6C7R9XI1uXQaKSaIkRBJYlKYVGtGqR2RB4xAoKC8uUwnWqUxMXOgpDIeP45cydfjiFErq1dC0eOgK0tTJ3Kd3uuEZeYQtWSjrSu6Gbo6IQQL0ASlcLkgw+gUSOIjoY+fdRvmXnMytyUng18AVi6L5AC3hdbFAaPHqX10xo/nnA7Z344cAOAUS+VlWqKEAWcJCqFiampegnI1hZ274b//S9fDvNOA28szUz471YkRwIf5MsxhMixBQsgOBi8vGD0aL7fc51HSSlU93KiRXmppghR0EmiUtj4+8OcOeryuHFw4UKeH6K4nSWv1yoFwJJ9MgGcMKC7d9V5UwC++IKwZBN+OBgEqCN9pJoiRMEniUphNHgwtG0LCQnQq5d635M8ljpUeduFuwSG5++NEYXI0sSJ6qXOOnXgrbf4bvc14pO01PByonk5V0NHJ4TIA5KoFEYaDSxdqt4T6NixtG+ceaiMmx0tK7ihKLBMqirCEM6eVe/pAzBvHvdiEll1KLVvioz0EaKwkESlsCpZEr7+Wl2eOlVNWPJY6lDl9cdv8jA2Mc/3L0S2PvhA7TDepQsEBPDN7mskJGup5e1E07Iuho5OCJFHJFEpzN58E7p1g5QU9RLQo0d5uvuGpYtTydOB+CQtP8kEcEKfNm2CzZvB3BxmzuRuVDyrD6uvwdEvlZdqihCFiCQqhZlGo1ZVPDzUTrWffJLHu9cwsOnjCeAOBJGQnJKn+xciU8nJMGaMujx8OPj7882uayQma6nr60zjMsUNG58QIk9JolLYFS8OS5aoy19+Cbt25enu21ctgbuDJWHRCfx5WiaAE3qwdCmcP6++tj/9lDuRj3QVvVEyC60QhY4kKkVB+/YwcKC63KcPREXl2a4tzEzo00itqizZe10mgBP5KyoKPvtMXZ44EZyc+HqnWk2p51eMhv5STRGisJFEpaiYOxf8/ODGjbR7ouSRt+p5Y2NhysXQaPZfvZ+n+xYinenTISwMypWDd98lJOIRa4/eBKSaIkRhJYlKUWFvr96sUKOBZcvUmxfmEUcbc7rV8QJg8d7rebZfIdIJClIvX4I6qaG5OYt2XiUxRUvD0sWlmiJEISWJSlHStCmMHq0uDxigfjPNI/0a+6HRwO7LYVy+G51n+xVCZ/x4dRLDli2hQwduPYxj3bHH1ZSXyhk4OCFEfpFEpaiZNg0qVYJ79+C99yCP+pR4F7ehbSUPAJbulQngRB47eBDWrFErgnPngkbDop3XSEpRaFymOPX8ihk6QiFEPpFEpaixsoJVq8DMDDZsgJ9+yrNdpw5V3njqNmHRCXm2X1HEKUpaJbBvX6hRg5sP4lh/LK1vihCi8JJEpSiqVQsmTFCXhw6FW7fyZrfeztTwciIxWaubylyIF7Z+PRw6pN4VfOpUAL7acZVkrUJAWRfq+Eo1RYjCTBKVomr8eKhXDyIjoV+/PLkEpNFoGBhQGoAfD90gPkkmgBMvKD4ePvpIXf7oIyhRguD7cfxyQk2uR0o1RYhCTxKVosrMDFauVC8Fbd0K33yTJ7ttW9mdkk7WPIhN5NcTt/Nkn6II+9//1NE+JUvqZqNduOMKKVqFZuVcqe3jbNj4hBD5ThKVoqxCBZg5U13+4AO4cuWFd2lmakK/Jo8ngNt3Ha1WJoATz+nePfj8c3X5iy/Axoag8Fh+PakmwDLSR4iiQRKVom7YMHW456NH0Lu3eh+VF9StTinsLc24HhbLrsv38iBIUSRNmqTORFurFrzzDgALd1wlRavQorwrNbycDBqeEEI/JFEp6kxMYPlycHBQh4DOnv3Cu7S3MqdHfW8AFu+RocriOZw7B999py7PmwcmJlwPi2HjSembIkRRI4mKAG9vtS8AqPdPOX36hXfZu5EvpiYaDl6/z9nbkS+8P1HEfPghaLXw2mvQrBmgVlO0CrSq4EZ1qaYIUWRIoiJUvXpB586QlAQ9e6ozgL6Akk7WtK/qCcDSfVJVEbmwZQv8+y+Ym+v6UF0Li+H3U9I3RYiiSBIVodJo1FK7qyucOaNWVl7QgAC1U+2fp0MIjYx/4f2JIiAlRTe6h2HDoGxZAP63/QpaBV6q5E6Vko4GDFAIoW+SqIg0bm5p/QJmz4b9+19od9VKOVHPrxjJWoUVB4JePD5R+C1bBmfPgrMzfPopAFfvRfPH6RAARrYua8johBAGIImKSO+119TLQFqtOgooJuaFdjfg8VDlnw7fIDbhxUcUiUIsOlqXnDBxIhRTZ5xdsP0qiqLO0VO5hFRThChqJFERGS1YAF5ecO2a2qnxBbSu6I5vcRui4pN192YRIlMzZqhzp5Qtq94wE7h8N5q//kutpkjfFCGKIklUREZOTuqQZYBvv4XNm597VyYmGvo/rqos2x9EikwAJzJz44Z6V2RQLztaWACwYNsVFAVeqepBRU8HAwYohDAUSVRE5lq1gvffV5f79YOHD597V11ql8LJxpzgB3FsPR+aRwGKQuXjj9WRZs2bw6uvAnAxNIq/z9xBo4ERraSaIkRRJYmKyNqMGVCuHISEqCMwnpONhRlvP54AbsleGaosnnLkCPz0kzrybO5c9V/UagrAK1U9Ke9hb8gIhRAGJImKyJqNDfzwgzp77U8/wbp1z72r3g19MTfVcOzGQ04GP391RhQyigKjR6vLvXur0+UD50Oi+PdsKBoNjGwlI32EKMokURHZq19fLcuD2sHxzp3n2o2bgxWvVi8JwBKZAE6k2rBBHQZvYwPTpulWz992GYAO1UpQ1l2qKUIUZZKoiGf77DOoWRMePICBA9Vvwc8hdQK4f8/c4eaDuLyMUBRECQkwdqy6/OGHUFJNZM/ejmTL+buYaGCEVFOEKPIkURHPZmGhXgKysIC//4alS59rNxU9HWhSxgWtgkwAJ2DhQggMBE/PdMPg5z/um/Jq9RKUcbMzVHRCCCMhiYrImSpV4PPP1eVRo9QPmOeQWlVZe/QmUfFJeRWdKGjCwmDqVHX5iy/A1haAM7ci2XZBraYMl2qKEAJJVERujBoFAQHqbLW9e6v3ZcmlZuVcKetmR0xCMmuPyARwRdbkyRAVpV5S7NVLtzq1b0rnGiUp7SrVFCGEJCoiN0xNYcUK9dvv3r0wf36ud6HRaHRVleX7A0lK0eZtjML4XbigTiQI6nBkE/Vt6NTNCLZfvIepiYb3pZoihHhMEhWRO6VLw5dfqsuffALnzuV6F51qlMTFzoKQyHj+PSsTwBU5Y8eq1bhOnaBFC93qJ6spfi62hopOCGFkJFERuTdgALz8sjpqo2dPSEzM1dOtzE3p2cAXgCV7r6M85ygiUQBt2wZ//QVmZjBrlm71ieCH7LoUhqmJhuGtyhgwQCGEsZFEReSeRqOO/ClWDE6eTDf/RU6908AbSzMT/rsVydEgmQCuSEhJgTFj1OUhQ9RZjx9LHenTpVZJfIpLNUUIkUYSFfF8PD3hm2/U5S++UKdBz4Xidpa8XqsUAIv3Xs/r6IQxWrEC/vtPvenlhAm61cdvPGTP5TDMTDS831L6pggh0pNERTy/bt3gzTfVb8q9esGjR7l6eupdlbdduEtgeGx+RCiMRXQ0fPqpujxhAhQvrtuU2jfljdql8CpmY4johBBGTBIV8WIWLVKrK5cuwfjxuXpqGTc7WlZwQ1FgmUyrX7jNmgWhoVCmDAwdqlt9NOgBe6+EY2aiYWgL6ZsihMhIEhXxYooVS5updsEC2LEjV09PHaq8/vhNIuJy1ylXFBA3b8KcOeryrFnqDMePfblVraZ0q+sl1RQhRKYkUREv7uWXYfBgdblPH4iMzPFTG5YuTiVPB+KTtKw+HJw/8QnD+uQTiI+Hpk2hc2fd6sPX73Pg2n3MTaWaIoTImiQqIm/MmaPOsXLzJowcmeOnaTQaBjZVqyorDgSRkJz72W6FETt2DFatUpfnzlVHjD325eO+Kd3relHSydoQ0QkhCgBJVETesLODlSvVD6IVK+C333L81PZVS+DuYElYdAJ/nr6TbyEKPVMUGD1aXe7ZE+rU0W06cC2cQ9cfYGFqItUUIUS2JFEReadJk7S74A4aBPfu5ehpFmYm9GmkVlVkArhCZONG9VYL1tZpN7QEFEVh/lZ13pQ363nh6SjVFCFE1iRREXlryhT1TsthYfDuu+q36hx4q543NhamXAyNZv/V+/kcpMh3CQnqVPkAH3wAXl66TQeu3edI0AMszEwY0lyqKUKI7EmiIvKWpaXaJ8HcXP1Gndo/4RkcbczpVkf9MJMJ4AqBRYvg2jXw8EhLWFCrKakjfd6q542Ho5WhIhRCFBCSqIi8V6MGTJqkLr//vtrBNgf6NvZFo4Hdl8O4fDc638IT+ez+fZg6VV3+/HO1/9Jj+66Gc+zGQyzNTBjS3N9AAQohChJJVET+GDsWGjSAqCjo2xe02mc+xae4LW0reQCwdK9MAFdgTZkCERFQvTr07q1b/WQ15e36Prg5SDVFCPFskqiI/GFmpo4CsraG7dvVSwE5kDoB3MZTtwmLTsjPCEV+uHQJvv5aXZ47F0xNdZt2Xw7jRHAEVuYmvNu8tIECFEIUNJKoiPxTrhzMnq0uf/SR+iH2DLV9nKnh5URispZVh27kc4Aiz40dC8nJ0KEDtGqlW60oCl8+vkPyO/V9cLOXaooQImckURH56733oHVr9YaFvXqpH2LZ0Gg0uqrKj4duEJ8kE8AVGDt2wB9/qFWU1AT1sV2Xwjh9MwJrc1MGN5O+KUKInJNEReQvExNYtgwcHeHIEZgx45lPaVfZg5JO1jyITeTXE7f1EKR4YSkpMGaMuvzee1Chgm6TWk1R+6b0auiDq72lISIUQhRQkqiI/OflBQsXqsuTJ8PJk9k2NzM1oW9jXwCW7ruOVisTwBm9H36AU6fUhHTixHSbdly8x3+3IrGxMGVQU+mbIoTIHUlUhH688w68/rp66adnT/UmddnoXtcLe0szroXFsutyzma4FQYSE6PeeBDgs8/AxUW3KX01xZfidlJNEULkjiQqQj80Gvj2W3Bzg3PnYMKEbJvbW5nzZj11ArglMlTZuM2eDXfuqDelHDYs3aat5+9y9nYUtlJNEUI8J0lUhP64usLixerynDnqfWCy0aexH6YmGg5cu8+5kEg9BChy7fbttI6zM2eqMxM/pigK8x+P9OnT2JdithaGiFAIUcBJoiL069VX1QngFEWdDCw66xloSzpZ80pVT0AmgDNan3yijuhq3Bi6dEm3afO5u5y/E4WdpRkDA6SaIoR4PpKoCP2bPx98fCAwUL1hXTYGPh6q/MfpEEIjs+/XIvTs+HF1Uj+AefPUy3uPabUK8x/3Tenb2BcnG6mmCCGejyQqQv8cHGD5cnX5++/hn3+ybFqtlBP1/IqRrFVYeTBIP/GJZ1OUtOHIb78N9eql27z5XCgXQ6OxtzRjQBOppgghnp8kKsIwWrSAkSPV5QED1BvZZWFAE7WqsvrQDWITsp8wTujJ77/D7t1gZQVffJFuk1pNUfum9G3ih6ONuSEiFEIUEvmWqHz++ec0atQIGxsbnJycMm2j0WgyPNasWZNfIQlj88UX6sRgd+7A0KFZNmtd0R3f4jZExSfzy/FbegxQZCoxET78UF0eMwa8vdNt/ufsHS7djcbeyoz+j5NMIYR4XvmWqCQmJtK1a1fee++9bNstX76cO3fu6B6dO3fOr5CEsbG2VicKMzWFtWshiyTVxESj+8Bbui+QFJkAzrC+/hquXgV3d/UeTk9I0SoseFxNGdCkNI7WUk0RQryYfEtUJk+ezKhRo6hatWq27ZycnPDw8NA9rKzkZmVFSt268Omn6vKQIRASkmmzLrVL4WRjTvCDOLaev6vHAEU6Dx7AlCnq8rRpYG+fbvPfZ+5w5V4MDlZm9G3iq//4hBCFjsH7qAwdOhQXFxfq1avHsmXLUJTsvy0nJCQQFRWV7iEKuE8+gdq14eFD6N9f7aj5FBsLM96ur15iWLL3ur4jFKmmTlX/TlWrqsPMn6BWU9SRPgMDSuNgJdUUIcSLM2iiMmXKFNatW8fWrVvp0qULQ4YMYWHqPWGyMH36dBwdHXUPLy8vPUUr8o25uXoJyNISNm1SRwJlondDX8xNNRy78ZCTwQ/1HKTg8mX46it1ee5c9ZLdE/48HcK1sFicbMzp8/heTUII8aJylaiMGzcu0w6wTz4uXryY4/199tlnNG7cmJo1a/LRRx8xduxYZj91e/injR8/nsjISN3j5s2bufkVhLGqVClt9MiYMXDtWoYmbg5WvFq9JABL9skEcHr30UfqvZpeeQVeeindpuQULf/brvZNGRhQGnuppggh8ohZbhqPGTOGPn36ZNumdOnnnzOhfv36TJ06lYSEBCwtM795maWlZZbbRAE3ciT88Yc67LV3b/Xfp761DwjwY8OJW/x75g43H8ThVczGMLEWNbt2wW+/qX+PTL5M/HE6hOvhsTjbmNO7ka++oxNCFGK5SlRcXV1xdXXNr1g4deoUzs7OkogUVSYmsGKF2v9h/351ttPUYbCPVfR0oEkZF/ZdDWfFgSA+61DJMLEWJVotjB6tLg8erFa/nvBkNWVQU3/sLHP1tiKEENnKtz4qwcHBnDp1iuDgYFJSUjh16hSnTp0iJiYGgD///JMlS5Zw9uxZrl69yjfffMMXX3zB+++/n18hiYLA11edYh/U0UBnzmRoMuDxtPprj94kKj5Jf7EVVatWwcmT6ozCkyZl2PzbqRCC7sdRzNaCXg199B+fEKJQy7dEZcKECdSsWZOJEycSExNDzZo1qVmzJseOHQPA3NycRYsW0bBhQ2rUqMF3333HvHnzmDhxYn6FJAqKfv2gQwd1YrGePdV/n9CsnCtl3eyISUhm7RHpo5SvYmPVUVmgJo5PVVSTUrQs3KFWUwY3LY2tVFOEEHlMozxrPLCRi4qKwtHRkcjISBwcHAwdjsgroaFQpYo6tf4nn6hzdjxh7dFgPtpwhhKOVuwZ2wIzU4OPtC+cpkyBiRPVSteFC+qU+U9Yd/QmYzf8h4udBXvGtsDGQhIVIUTO5PTzW97dhXHy8IBvv1WXp0+HQ4fSbe5UoyQudhaERMbzz9lQAwRYBISEwMyZ6vLMmRmSlKQULQt3qtWUd5v5S5IihMgXkqgI4/XGG+qdebVa6NUL4uJ0m6zMTenZwBdQJ4Ar4IVB4/Tpp+o5b9gQunbNsHnD8VvcfPAIFztL3q4vfVOEEPlDEhVh3BYuhJIl4cqVDPeVeaeBN5ZmJvx3K5KjQTIBXJ46eVIdgQXq6CuNJt3mxGQtC3dcBeC95v5YW5gihBD5QRIVYdycnWHZMnX5q69g2zbdpuJ2lrxeqxQAi2Va/byjKOqke4oCPXpAgwYZmvxy/Ba3Ix7hZm+pu7WBEELkB0lUhPFr00a9YSGo95eJiNBtSr2r8rYLdwkMjzVAcIXQn3/Czp3qLQ2mT8+wOSE5ha8ej/R5r7k/VuZSTRFC5B9JVETBMGsWlCkDt27B8OG61WXc7GhZwQ1FgWUyrf6LS0pKm2Rv9Gjwydj3ZN2xW4RExuPuYEmPelJNEULkL0lURMFgawsrV6qz165aBb/+qts04HFVZf3xm0TEJWa1B5ET336r3nzQzQ3GjcuwOSE5ha93qn1ThrYoI9UUIUS+k0RFFByNGqV1qB08GO7eBaChf3EqeToQn6Rl9eFgAwZYwD18mDbz7JQp6ky0T1l79CZ3IuPxdLSie125c7kQIv9JoiIKlokToVo1CA+HQYNAUdBoNLpp9VccCCIhOcXAQRZQ06bBgwdQuTL0759hc3xSCoseV1OGtCiDpZlUU4QQ+U8SFVGwWFqql37MzdU7La9cCUCHaiVwd7AkLDqBP0/fMXCQBdDVq+pQcIC5c8Es4+Rta44EczcqgRKOVnSrU0rPAQohiipJVETBU62aemkC1I61N25gYWZC70a+gEwA91w++kjtSNuuHbRtm2FzfFIKi3ZdA2BoS6mmCCH0RxIVUTB9+KHaZyU6Gvr0Aa2Wt+v5YG1uysXQaPZfvW/oCAuOPXvUzskmJjBnTqZNVh8OJiw6gZJO1nStLX1ThBD6I4mKKJhMTdXLPjY2sGsXLFyIo4257pLEkn0yAVyOaLXq5G6g9vmpXDlDk0eJKXzzuJryfssyWJjJ24YQQn/kHUcUXGXKpFUAxo2Dixfp18QPjQZ2XQrjyt1ow8ZXEPz0Exw7Bvb2MHlypk1WH75BeEwCXsWs6VJb+qYIIfRLEhVRsL37rtqnIj4eevbEx8GCtpU8AFgqE8BlLy4Oxo9Xlz/+WJ075ekmicl8u/txNaVFWcxN5S1DCKFf8q4jCjaNBpYuBScntTIwfbpuqPKvJ28TFp1g2PiM2bx56ky/Pj4wcmSmTVYdvEF4TCLexWx4rVZJ/cYnhBBIoiIKg5IlYdEidXnqVGqHX6eGlxOJyVp+PHTDsLEZqzt3YMYMdXnGDLCyytAkNiGZ7/aofX2Gt5JqihDCMOSdRxQOPXpA166QnIymVy8G1VUv/6w6dIP4JJkALoPPPoPYWPXOyN27Z9rkh4M3eBCbiJ+LLZ1rlNBzgEIIoZJERRQOGg18/TW4u8OFC7T7eRElnax5EJvIxpO3DR2dcTl9GpYtU5fnzVPP3VNiEpL5fk/aSB8zqaYIIQxE3n1E4eHiAkuWAGCyYD7jbdV7AS3Zex2tViaAA0BR1OHIiqJWUho2zLTZygNBPIxLorSLLa9Wl2qKEMJwJFERhUuHDjBgACgKr8z9GA8SuBYWy+7LYYaOzDj88w9s3w4WFjB9eqZNouOT+P6JvilSTRFCGJK8A4nCZ9488PXF5EYQ3578CYDFe2UCOJKS4IMP1OWRI8HPL9NmK/YHEfkoCX9XWzpKNUUIYWCSqIjCx94eVqwAjYYaWzbQ+tpRDly7z7mQSENHZljffw8XL6qXyD7+ONMmUfFJuqRuROtymJpk7L8ihBD6JImKKJyaNYNRowCYt/UrnOMiWbq3CE8AFxEBEyeqy1OmgKNjps2W7wsiKj6Zsm52tK/qqb/4hBAiC5KoiMLr88+hUiUcIu8zbcvX/HHqNqGR8YaOyjA+/xzu34eKFWHgwEybRD5K0t0jaUTrslJNEUIYBUlUROFlZQU//ABmZrS/tJ9Xzu1i5cEgQ0elf9euwf/+py7PnQtmZpk2W7YvkOj4ZMq72/NKFammCCGMgyQqonCrXVud3AyYuuUbtm05RmxCsoGD0rNx4yAxEdq0gXbtMm0SGZfEssf3RhrRuiwmUk0RQhgJSVRE4Td+PErdujgmxPLZxnn8cuymoSPSn/374ZdfwMREvdN0JpO7ASzZd53ohGQqeNjTrrKHnoMUQoisSaIiCj9zczQ//ECyhSVNg05yf+4CUorCBHBaLYwerS737w9Vq2baLCIukeX7gwAY2bqcVFOEEEZFEhVRNFSogPaLLwB4969v2b/pkIED0oM1a+DIEbCzU0f6ZGHx3uvEJCRTydOBtpXd9RigEEI8myQqosiwGDWSG9XrY5OUgPuwQZBSiG9W+OiR2jcFYPx48Mj8cs6D2ERW6KopZdFkcWlICCEMRRIVUXSYmGDz40piLKwpH3iWkE+yrjIUeF9+CTdvgpeXbj6ZzHy/5zqxiSlUKenAS5WkmiKEMD6SqIgixbVKef7qr1Ya3OZ8od5JuLAJDU27j8+MGWBtnWmz+zEJ/PB4uPao1uWkmiKEMEqSqIgip9onI9hStgFmKckkvv0OJCQYOqS8NWECxMRAvXrw5ptZNvt+z3XiElOoXsqRlhXc9BigEELknCQqosipVNKR396dwH1rByzOnYVJkwwdUt45cwaWLlWX581ThyVnIjwmgR8O3gDUkT5STRFCGCtJVESR1LV9bT5uNwwAZdYsOHDAwBHlAUWBMWPUYclvvAGNG2fZ9Lvd13iUlEINLyeal3fVY5BCCJE7kqiIIql5OVeuN2nDhsot0Gi10KuXermkINu0CbZuBQsLtW9KFu5Fx7PqUGo1RUb6CCGMmyQqokjSaDT0b+LH5NaDuevoqt4PZ+xYQ4f1/JKT1WoKwPDh4O+fZdNvd10nPklLTW8nmpWTaooQwrhJoiKKrM41S2JevBij241QV3zzDWzebNigntfixXDhAhQvDp98kmWze1HxrD6sVlNGvyR9U4QQxk8SFVFkWZmb0rOhD/t9a/BX09fVlf36wcOHhg0styIj1ZE+AJMng5NTlk2/3nWNhGQtdXycaVLGRT/xCSHEC5BERRRpPRv4YGlmwgd13uKRnz+EhMCwYYYOK3e++ALCw6FCBRg0KMtmoZHx/HQkGIBRUk0RQhQQkqiIIq24nSWv1ypFvLkV89/5RB3O+9NPsH69oUPLmcBAmD9fXZ49G8zNs2z6za6rJCZrqedbjEb+xfUTnxBCvCBJVESR17+JHwDfJ7kRMeJxh9T33lNneDV248dDYiK0agXt22fZLCTiET8fuQnAyJdkpI8QouCQREUUeWXc7GhZwQ1FgQWNekCNGnD/PgwcqM5NYqwOHoS1a0Gjgblz1X+z8PWuqySmaGlQuhiN/KVvihCi4JBERQhgwOOqyprTd4n6fpk6F8lff8GyZQaOLAuKknazwX79oHr1LJvejnjE2qNqNWVU63L6iE4IIfKMJCpCAA39i1PJ04FHSSmsirGHadPUDSNHqv1AjM3atXD4MNjawtSp2TZdtPMqSSkKjfyLU7+09E0RQhQskqgIgToB3IAAtaqy8kAQicNHQpMm6my1ffqo09Ibi0eP4KOP1OVx48DTM8umNx/Esf7Y42rKS1JNEUIUPJKoCPFYh2olcHew5F50An+evQsrV6oViz170kbWGIMFCyA4GEqVgtGjs22aWk1pUsaFur7F9BSgEELkHUlUhHjMwsyE3o18AVi89zqKn596B2KAjz+G8+cNF1yqe/fUeVMApk8HG5ssm958EMcvx28BMOqlsvqITggh8pwkKkI84e16Plibm3IxNJoD1x6P/Hn5ZUhIgJ49ISnJsAFOnAjR0VCnDrz1VrZNF+64QrJWoWk5V2r7SDVFCFEwSaIixBMcbczpVqcUoFZV0GhgyRJwdoYTJ9I62RrCuXPw/ffq8ty56uR0WbhxP5YNJ24DMKq1VFOEEAWXJCpCPKVfEz80Gth1KYwrd6OhRAn1hoUAn38OR48aJrAPPlA79b7+OjRtmm3ThTuukqJVaF7elZreznoKUAgh8p4kKkI8xae4LW0quQOwdN/jocndu6uPlBT1EtCjR/oNatMm9WFuDjNnZts0MDyWjSfVaspImTdFCFHASaIiRCYGBpQG4NeTtwmPSVBXLlqkDgW+dEmdul5fkpPVagrA++9DmTLZNl+4/QopWoWWFdyo4eWU//EJIUQ+kkRFiEzU9nGmupcTiclaVh28oa4sXlztrwLqEOGdO/UTzNKlav+UYsXg00+zbXotLIbfTqX2TZFqihCi4JNERYhMaDQaBj6eAO7HQzeIT0pRN7zyCgwapC736QORkfkbSFQUTJigLk+apHbqzcbC7VfQKtC6ojtVSznmb2xCCKEHkqgIkYV2lT0o6WTN/dhEXZ8PQB1xU7q0Oula6v128suMGercKeXKwbvvZtv06r0Y/jgdAsBIGekjhCgkJFERIgtmpib0bewLwJK919FqH99J2c4OVqxQhy4vXw6//54/Ady4kTbh3OzZakfabPzvcTWlTSV3qpSUaooQonCQREWIbHSv64W9pRnXwmLZfTksbUNAQFoH10GDICws8x28iPHj1YnmWrSAjh2zbXr5bjR//pdaTZG+KUKIwkMSFSGyYW9lzpv1vIDHE8A9acoUqFJFvTQzeDAoSt4d+NAh+PlntWozd676bzYWbL+CosDLVTyoVMIh7+IQQggDk0RFiGfo09gPUxMNB67d51zIE51nrazghx/AzAw2boQff8ybAypK2s0G+/SBmjWzbX4pNJp/ztwBYIT0TRFCFDKSqAjxDCWdrHmlqicAS/cGpt9Ys6Y6GgfUOU5u3nzxA65fDwcPqjcczMGU/Qu2X0ZRoH1VTyp4SDVFCFG4SKIiRA4MaKIOVf7jdAihkfHpN370EdSvrw5V7ttXneb+ecXHq/tL3W+JEtk2v3Anin/OhKLRSDVFCFE4SaIiRA5U93Kinm8xkrUKKw8Gpd9oZgYrV4K1NWzfDl9//fwHWrgQgoLUBGXMmGc2n7/tMqBWU8q52z//cYUQwkhJoiJEDvV/PAHc6kM3iE1ITr+xfHmYNUtdHjsWLl/O/QHCwtIu9XzxBdjaZtv8XEgkm8/dVaspraSaIoQonCRRESKHWld0x7e4DVHxyfxy/FbGBkOGQKtW6g0Le/VS79GTG5MmqTPR1qql3vjwGeZvuwLAq9VLUFaqKUKIQkoSFSFyyNREQ7/HfVWW7Q8kRfvUcGQTE3UCOEdHOHz4mXc5Tuf8efjuO3V57lx1X9k4ezuSrefvYqKB4VJNEUIUYvmWqAQFBdG/f3/8/PywtrbG39+fiRMnkpiYmK7df//9R0BAAFZWVnh5eTErtXwuhBF6o3YpHK3NuXE/jq3n72Zs4OUF//ufujxpEpw8mbMdf/ghpKRA587QvPkzm6f2TelUoyT+rnY5O4YQQhRA+ZaoXLx4Ea1Wy3fffce5c+f48ssv+fbbb/n44491baKiomjTpg0+Pj4cP36c2bNnM2nSJL7//vv8CkuIF2JjYcY7DbwBWLrveuaNevaE115TL/306qXOLpudLVvgn3/UTrk5SNT/uxXBtgv3MNHA+y3L5PZXEEKIAiXfEpV27dqxfPly2rRpQ+nSpXn11Vf54IMP+PXXX3VtVq9eTWJiIsuWLaNy5cq8+eabDB8+nHmp9zcRwgj1auiLuamGo0EPOXUzImMDjUa9jOPmBmfPpt39ODMpKWlT8Q8bBmWffRnny61qNaVzzZKUlmqKEKKQ02sflcjISIoVK6b7+eDBgzRt2hQLCwvdurZt23Lp0iUePnyY6T4SEhKIiopK9xBCn9wdrHi1eklAvVlhplxdIbUyOHs27NuXebvly+HMGXB2hs8+e+axTwY/ZOelMExNNAxvKX1ThBCFn94SlatXr7Jw4UIGDx6sWxcaGoq7u3u6dqk/h4aGZrqf6dOn4+joqHt4eXnlX9BCZKH/4061/54N5dbDuMwbdeqkToGvKNC7N8TEpN8eHQ2ffqouT5gATyTxWUkd6fN6zZL4umQ/fFkIIQqDXCcq48aNQ6PRZPu4ePFiuufcvn2bdu3a0bVrVwYOHPhCAY8fP57IyEjd42ZeTFkuRC5VKuFAkzIupGgVVuwPyrrh/Png7Q3Xr6dd4kk1cybcvQtlyqhDm5/h+I2H7L4chpmJhvelmiKEKCLMcvuEMWPG0KdPn2zblC5dWrccEhJCixYtaNSoUYZOsh4eHty9m37kROrPHh4eme7b0tISS0vL3IYtRJ7rH+DHvqvhrDl6k+Gty+JgZZ6xkaMjrFgBLVuq/VY6dYKXX4bgYHUYMqiXhp64/JmV1JE+XWqVwru4TR7+JkIIYbxynai4urri6uqao7a3b9+mRYsW1K5dm+XLl2Py1NwQDRs25JNPPiEpKQlzc/VNfuvWrZQvXx5nZ+fchiaEXjUv50pZNzuu3Ith3dGbDAgonXnDFi1gxAhYsAD691c72H78sXpfn2bN1OTlGY4FPWDvlXDMTDQMk5E+QogiJN/6qNy+fZvmzZvj7e3NnDlzCAsLIzQ0NF3fk7feegsLCwv69+/PuXPnWLt2LQsWLGB06i3uhTBiGo1G11dl+f4gklOyuRnh9OnqNPt37kDHjrB6tTo6aN489d9n+PJxNaVrHS+8ikk1RQhRdORborJ161auXr3K9u3bKVWqFJ6enrpHKkdHR7Zs2UJgYCC1a9dmzJgxTJgwgUGDBuVXWELkqc41S1Lc1oLbEY/492zmHcAB9YaFP/wApqZw4IC6rlcvdbr8ZzgS+ID9V+9jbirVFCFE0ZNviUqfPn1QFCXTx5OqVavG3r17iY+P59atW3yUeot7IQoAK3NTejb0AdShyk+/vtOpVw8++URdtraGzz/P0TFS503pVseLkk7WLxSvEEIUNLnuoyKESK9nAx++3nWN07ciOXbjIXV9sxlm/OmnasfZmjWhZMln7vvgtfscvH4fC1MThraQaooQouiRmxIK8YKK21nSpZaadCzek8UEcKnMzdWqyiuvPHO/iqLo+qZ0r+tFCammCCGKIElUhMgDqZ1qt164S1B4bJ7s8+C1+xwJfICFqQlDWvjnyT6FEKKgkURFiDxQxs2eFuVdURRYtj/whff3ZDXlrfreeDpKNUUIUTRJoiJEHhn4eB6V9cduERGX+EL72n/1PkeDHmJpZsJ7zaWaIoQouiRRESKPNPQvTkVPBx4lpbD6cPBz7+fpaoq7g1VehSiEEAWOJCpC5BGNRsPAALWvysoDQSQmZzMBXDb2Xgnn+I3H1ZRmUk0RQhRtkqgIkYc6VCuBu4Ml96IT+PN0SK6frygK8x7Pm/JOAx/cpJoihCjiJFERIg9ZmJnQu5EvAIufNQFcJnZdDuPUzQiszE14V6opQgghiYoQee2tet5Ym5tyMTSaA9fu5/h5iqIw/3E1pVdDX1zt5S7hQgghiYoQeczJxoJudUoBalUlp3ZeusfpW5FYm5syqGkWd2IWQogiRhIVIfJB38Z+aDSw61IYV+5GP7O9oih8ufUKAL0a+eBiJ9UUIYQASVSEyBe+Lra0qeQOwNJ9z54AbtuFe5y5HYmNhSmDm0rfFCGESCWJihD5ZMDjCeB+PXmb8JiELNspisL8x/Om9GnkSzFbC73EJ4QQBYEkKkLkkzo+zlT3ciIxWcuqgzeybLfl/F3OhURhZ2mmm91WCCGEShIVIfKJRqNhwOObFf546AbxSSkZ2mi1CvO3qX1T+jTyxVmqKUIIkY4kKkLko5ereFDSyZr7sYlsPHk7w/Yt50O5cCcKe0szBjye1VYIIUQaSVSEyEdmpib0bewLqJ1qtdq0CeC02rSRPn0b++JkI9UUIYR4miQqQuSz7nW9sLc04+q9GHZfDtOt//dsKJfuRmNvZUb/JtI3RQghMiOJihD5zN7KnDfreQGwZJ86AZxWq7BguzrSp38TPxxtzA0WnxBCGDNJVITQgz6N/TA10bD/6n3OhUTy95k7XL4bg4OVGf2aSN8UIYTIiiQqQuhBSSdrXqnqCcDiPddZsF3tmzIgoDQOVlJNEUKIrEiiIoSepA5V/u1UCFfvxeBoba7raCuEECJzkqgIoSfVvZyo51tM9/PAAD/spZoihBDZkkRFCD1KnSvFycac3o18DRuMEEIUAGaGDkCIouSlSu7M714Df1c7qaYIIUQOSKIihB5pNBo61yxp6DCEEKLAkEs/QgghhDBakqgIIYQQwmhJoiKEEEIIoyWJihBCCCGMliQqQgghhDBakqgIIYQQwmhJoiKEEEIIoyWJihBCCCGMliQqQgghhDBakqgIIYQQwmhJoiKEEEIIoyWJihBCCCGMliQqQgghhDBaBf7uyYqiABAVFWXgSIQQQgiRU6mf26mf41kp8IlKdHQ0AF5eXgaORAghhBC5FR0djaOjY5bbNcqzUhkjp9VqCQkJwd7eHo1Gk6f7joqKwsvLi5s3b+Lg4JCn+y5s5FzlnJyrnJNzlXNyrnJOzlXO5ee5UhSF6OhoSpQogYlJ1j1RCnxFxcTEhFKlSuXrMRwcHOTFnENyrnJOzlXOybnKOTlXOSfnKufy61xlV0lJJZ1phRBCCGG0JFERQgghhNGSRCUblpaWTJw4EUtLS0OHYvTkXOWcnKuck3OVc3Kuck7OVc4Zw7kq8J1phRBCCFF4SUVFCCGEEEZLEhUhhBBCGC1JVIQQQghhtCRREUIIIYTRkkRFCCGEEEarSCcqixYtwtfXFysrK+rXr8+RI0eybb9+/XoqVKiAlZUVVatW5Z9//tFTpMYhN+drxYoVaDSadA8rKys9RmsYe/bsoWPHjpQoUQKNRsNvv/32zOfs2rWLWrVqYWlpSZkyZVixYkW+x2kscnu+du3aleF1pdFoCA0N1U/ABjJ9+nTq1q2Lvb09bm5udO7cmUuXLj3zeUXxPet5zlVRfb8C+Oabb6hWrZpu5tmGDRvy77//Zvscfb+uimyisnbtWkaPHs3EiRM5ceIE1atXp23btty7dy/T9gcOHKBHjx7079+fkydP0rlzZzp37szZs2f1HLlh5PZ8gTrl8p07d3SPGzdu6DFiw4iNjaV69eosWrQoR+0DAwNp3749LVq04NSpU4wcOZIBAwawefPmfI7UOOT2fKW6dOlSuteWm5tbPkVoHHbv3s3QoUM5dOgQW7duJSkpiTZt2hAbG5vlc4rqe9bznCsomu9XAKVKlWLGjBkcP36cY8eO0bJlSzp16sS5c+cybW+Q15VSRNWrV08ZOnSo7ueUlBSlRIkSyvTp0zNt361bN6V9+/bp1tWvX18ZPHhwvsZpLHJ7vpYvX644OjrqKTrjBCgbN27Mts3YsWOVypUrp1vXvXt3pW3btvkYmXHKyfnauXOnAigPHz7US0zG6t69ewqg7N69O8s2Rf09K1VOzpW8X6Xn7OysLFmyJNNthnhdFcmKSmJiIsePH6d169a6dSYmJrRu3ZqDBw9m+pyDBw+maw/Qtm3bLNsXJs9zvgBiYmLw8fHBy8sr2wy9KCvKr6sXUaNGDTw9PXnppZfYv3+/ocPRu8jISACKFSuWZRt5balycq5A3q8AUlJSWLNmDbGxsTRs2DDTNoZ4XRXJRCU8PJyUlBTc3d3TrXd3d8/yWndoaGiu2hcmz3O+ypcvz7Jly/j999/58ccf0Wq1NGrUiFu3bukj5AIjq9dVVFQUjx49MlBUxsvT05Nvv/2WDRs2sGHDBry8vGjevDknTpwwdGh6o9VqGTlyJI0bN6ZKlSpZtivK71mpcnquivr71ZkzZ7Czs8PS0pJ3332XjRs3UqlSpUzbGuJ1ZZZvexZFWsOGDdNl5I0aNaJixYp89913TJ061YCRiYKsfPnylC9fXvdzo0aNuHbtGl9++SWrVq0yYGT6M3ToUM6ePcu+ffsMHYrRy+m5KurvV+XLl+fUqVNERkbyyy+/0Lt3b3bv3p1lsqJvRbKi4uLigqmpKXfv3k23/u7du3h4eGT6HA8Pj1y1L0ye53w9zdzcnJo1a3L16tX8CLHAyup15eDggLW1tYGiKljq1atXZF5Xw4YN46+//mLnzp2UKlUq27ZF+T0LcneunlbU3q8sLCwoU6YMtWvXZvr06VSvXp0FCxZk2tYQr6simahYWFhQu3Zttm/frlun1WrZvn17ltflGjZsmK49wNatW7NsX5g8z/l6WkpKCmfOnMHT0zO/wiyQivLrKq+cOnWq0L+uFEVh2LBhbNy4kR07duDn5/fM5xTV19bznKunFfX3K61WS0JCQqbbDPK6yrduukZuzZo1iqWlpbJixQrl/PnzyqBBgxQnJyclNDRUURRF6dmzpzJu3Dhd+/379ytmZmbKnDlzlAsXLigTJ05UzM3NlTNnzhjqV9Cr3J6vyZMnK5s3b1auXbumHD9+XHnzzTcVKysr5dy5c4b6FfQiOjpaOXnypHLy5EkFUObNm6ecPHlSuXHjhqIoijJu3DilZ8+euvbXr19XbGxslA8//FC5cOGCsmjRIsXU1FTZtGmToX4Fvcrt+fryyy+V3377Tbly5Ypy5swZZcSIEYqJiYmybds2Q/0KevHee+8pjo6Oyq5du5Q7d+7oHnFxcbo28p6lep5zVVTfrxRF/T+2e/duJTAwUPnvv/+UcePGKRqNRtmyZYuiKMbxuiqyiYqiKMrChQsVb29vxcLCQqlXr55y6NAh3bZmzZopvXv3Ttd+3bp1Srly5RQLCwulcuXKyt9//63niA0rN+dr5MiRurbu7u7KK6+8opw4ccIAUetX6vDZpx+p56Z3795Ks2bNMjynRo0aioWFhVK6dGll+fLleo/bUHJ7vmbOnKn4+/srVlZWSrFixZTmzZsrO3bsMEzwepTZOQLSvVbkPUv1POeqqL5fKYqi9OvXT/Hx8VEsLCwUV1dXpVWrVrokRVGM43WlURRFyb96jRBCCCHE8yuSfVSEEEIIUTBIoiKEEEIIoyWJihBCCCGMliQqQgghhDBakqgIIYQQwmhJoiKEEEIIoyWJihBCCCGMliQqQgghhDBakqgIIYQQwmhJoiKEEEIIoyWJihBCCCGM1v8BS8ePHT7Xi/gAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"train_x = extend_feature(X_train, n=3)\n",
"test_x = extend_feature(X_test, n=3)\n",
"\n",
"theta_cr = regression(train_x, Y_train)\n",
"\n",
"print(\"Computed Theta for Cubic Regression: \", theta_cr)\n",
"\n",
"pred_y_cr = test_x.dot(theta_cr)\n",
"mse_cr = mse(pred_y_cr, Y_test)\n",
"\n",
"# Plot\n",
"\n",
"plt.plot(Y_test, label=\"actual\")\n",
"plt.plot(pred_y_cr, color='r', label='prediction')\n",
"plt.title(f\"Cubic Regression: Actual vs Prediction | MSE: {mse_cr:.2f}\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "70ae5b90",
"metadata": {},
"source": [
"# Conclusion\n",
"\n",
"Based on Mean Square Error values, **Cubic Regression** task gives the best fit line. It is also visible from the chart that the prediction is closer to actual value. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3cc2fbf5",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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