{ "cells": [ { "cell_type": "markdown", "id": "4dd50260", "metadata": {}, "source": [ "# Basic GP Regression\n", "\n", "Your first Gaussian Process model in LightGP. We will:\n", "\n", "1. Generate noisy synthetic data\n", "2. Fit a GP with an RBF kernel\n", "3. Visualize predictions with uncertainty bands\n", "4. Improve the fit by optimizing hyperparameters\n", "5. Compare different kernel smoothnesses" ] }, { "cell_type": "code", "execution_count": 1, "id": "ac20d085", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:05.800349Z", "iopub.status.busy": "2026-05-15T06:51:05.800132Z", "iopub.status.idle": "2026-05-15T06:51:06.045727Z", "shell.execute_reply": "2026-05-15T06:51:06.045260Z" } }, "outputs": [], "source": [ "import os\n", "import sys\n", "\n", "# Make the locally-built lightgp importable. Real users install via 'pip install lightgp'.\n", "sys.path.insert(0, os.path.abspath(os.path.join(\"..\", \"..\", \"..\", \"python\")))\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import lightgp as gp\n", "\n", "rng = np.random.default_rng(0)\n", "plt.rcParams.update({\"figure.figsize\": (8, 3.5), \"figure.dpi\": 90})" ] }, { "cell_type": "markdown", "id": "a474a0fe", "metadata": {}, "source": [ "## Generate noisy data\n", "\n", "Sample 40 points from `y = sin(x) + noise`." ] }, { "cell_type": "code", "execution_count": 2, "id": "8262d852", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:06.046898Z", "iopub.status.busy": "2026-05-15T06:51:06.046805Z", "iopub.status.idle": "2026-05-15T06:51:06.049275Z", "shell.execute_reply": "2026-05-15T06:51:06.048966Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X: (40, 1) float32 y: (40,) float32\n" ] } ], "source": [ "X = np.sort(rng.uniform(-3, 3, 40)).reshape(-1, 1).astype(np.float32)\n", "y = (np.sin(X[:, 0]) + 0.15 * rng.standard_normal(40)).astype(np.float32)\n", "X_test = np.linspace(-4, 4, 250).reshape(-1, 1).astype(np.float32)\n", "print(\"X:\", X.shape, X.dtype, \" y:\", y.shape, y.dtype)" ] }, { "cell_type": "markdown", "id": "5cbdee21", "metadata": {}, "source": [ "## Fit a GP\n", "\n", "`GPExact(kernel)` is the simplest entry point. We start with an RBF kernel\n", "at a deliberately bad initial length scale so the un-optimized fit looks rough." ] }, { "cell_type": "code", "execution_count": 3, "id": "8ce0c17b", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:06.050191Z", "iopub.status.busy": "2026-05-15T06:51:06.050138Z", "iopub.status.idle": "2026-05-15T06:51:06.052077Z", "shell.execute_reply": "2026-05-15T06:51:06.051780Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log marginal likelihood before optimize: -20.182\n" ] } ], "source": [ "model = gp.GPExact(gp.RBF(length_scale=0.3), noise_var=0.1)\n", "model.fit(X, y)\n", "pred_before = model.predict(X_test)\n", "ll_before = model.log_marginal_likelihood()\n", "print(f\"log marginal likelihood before optimize: {ll_before:.3f}\")" ] }, { "cell_type": "markdown", "id": "004e262c", "metadata": {}, "source": [ "## Optimize the hyperparameters\n", "\n", "LightGP uses Adam on the log-hyperparameters to maximize the log marginal likelihood." ] }, { "cell_type": "code", "execution_count": 4, "id": "2ce37f54", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:06.052941Z", "iopub.status.busy": "2026-05-15T06:51:06.052884Z", "iopub.status.idle": "2026-05-15T06:51:06.057287Z", "shell.execute_reply": "2026-05-15T06:51:06.057005Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log marginal likelihood after optimize: 4.990\n", "improvement: +25.172\n" ] } ], "source": [ "model.optimize(steps=80)\n", "pred_after = model.predict(X_test)\n", "ll_after = model.log_marginal_likelihood()\n", "print(f\"log marginal likelihood after optimize: {ll_after:.3f}\")\n", "print(f\"improvement: {ll_after - ll_before:+.3f}\")" ] }, { "cell_type": "markdown", "id": "5b7fa0a7", "metadata": {}, "source": [ "## Plot before vs after" ] }, { "cell_type": "code", "execution_count": 5, "id": "67d5acea", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:06.058191Z", "iopub.status.busy": "2026-05-15T06:51:06.058131Z", "iopub.status.idle": "2026-05-15T06:51:06.142511Z", "shell.execute_reply": "2026-05-15T06:51:06.142155Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3oAAAE7CAYAAACLyPOYAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAN1wAADdcBQiibeAAAwGtJREFUeJzsnQd81PX5xz+3L3sR9g57TxmCgqCyRATErbhHtVVb7bJW29rW9be1ztY9ENkyBQcgiiJ7r4SZQCB73/79X5/vcSF7XpJL8rzbM9wvN353ufs+32d9Hp2maRoEQRAEQRAEQRCEJoO+oU9AEARBEARBEARB8C/i6AmCIAiCIAiCIDQxxNETBEEQBEEQBEFoYoijJwiCIAiCIAiC0MQQR08QBEEQBEEQBKGJIY6eIAiCIAiCIAhCE0McPUEQBEEQBEEQhCaGOHqCIAiCIAiCIAhNDHH0hGbFM888A51OV3gJDg5G//798d///rdGj3f27FlMmTIFERER6vE2bNiAxs6CBQvwwQcflDo+btw4zJ492y/P0blzZ/zmN79BXTB9+nQ8++yzhdenTZuGv/71r3XyXIIgCIFEly5dlC2Kj48v9bu8vDzceOONiImJUbfhOk/bt2zZMjQmyjtnf9oVvj+vvfYa/I2maRg0aBA+/PDDwuvcg3z88cd+fy5BIEZ5G4TmBp2yL7/8stDwrVixAvfffz9CQ0Nx8803V+uxnnvuOezevRufffYZoqOj0adPHzQFRy81NRVz584tdvyNN96AyWTyy3MsXbpUbTb8zZYtW/Dtt98Wc1R/+9vfKufvkUceQWRkpN+fUxAEIRD48ccfceLECfVv2qQ//elPxX7/5ptvKnv30UcfoV27doiLi8PkyZPRr18/zJgxA43J0SvrnP1pV/he0mmuC/uanp5euNegQ/nkk0+q4ORNN90Eo1G25YJ/kYye0OzgQjpy5Eh1mTBhAv71r39h+PDhNYpqHjp0CCNGjFBZPT5eeHh4jc/LZrMhkKET2717d7881uDBg9GxY0f4m1dffRXXXnutcrp9jB07Vhl/iZgKgtCUoXMXEhKibBL/XZa96tmzJ2bNmqXsVWxsrF+f3+12w+FwoKHwp13h+9OqVSvUhY267bbbigVNr7/+epw7dw5r1qzx+/MJgjh6ggAgLCwMTqez2HvBqNt9992nFnur1YrRo0erjJEPRuK++eYbFUXkv1k2UjRqx3IMi8WCDh064I9//CNcLlfh75lx4n1+/vlnVRIZFBSEF198Uf1u3759mDp1qjonXmgEkpOTK/07MZNFA89z5Tk/9NBDyM3NLfw9y0r5nOvWrVPljNwQ0Ci+9dZbhbdhFm/x4sXYuHFjYXkry13LKt3k8RYtWqj3ZNiwYeo1jBkzBsePH8f58+dVtJVZ0t69e6tzK6/EhhHoouW0RS9FS2G/+OIL9Tx8fa1bt1ZR0KJ/s5ycHPW3KKu8lBsbRrEFQRCaInSyaHdYvXDXXXfh4MGDqtqk6Jr77rvvYufOnYXrK9f07du3qzJC37Gi1RDvvPMO+vbtq+xYp06d8MILLxR7TtoLrskMkvJ2XJuL2siSVNUubt26VQXoaFN69Oih1nUfFZ1zydJN3/mtWrVKBSrZqkHbStvO0tbx48crO8jb7Nmzp9zSTZ/tLOviy6BW5f3ic27evLmUjeL7xmCx2CihTtAEoRnx5z//WYuJidGcTqe6ZGVlaR9//LFmMBi0Dz/8sPB2NptNGzx4sNalSxd1fM2aNdr06dO10NBQ7ezZs+o2P/74o7rN+PHj1b937Nihjq9du1bjV+v2229X93v++ec1s9ms3X///YWP//7776vbdO3aVXvppZe0b7/9Vt3/6NGjWnh4uHbFFVdoy5Yt0xYtWqT17t1bGzZsmObxeMp9Xfv27dNMJpM2ZcoUbeXKldqbb76pRUREaFdffXXhbdavX6+es3379trvf/977csvv1TnxGMrVqxQt4mPj1evh6+Lr4mX06dPq99dfvnl2qxZs4q9l0FBQdqAAQO0Tz75RFu6dKnWoUMH7dJLL1Xn/+KLL6r3YsKECVp0dLSWl5dXeN9OnTppv/71rwvfa99z+S6zZ8/WrFarOh/y+eefa3q9XnvwwQfVY77xxhvq9fkeg/D18LUkJyeXen/4Xup0Oi09Pb2anxhBEITA56uvvlLr3xdffKGlpaUpe/Db3/628Pe0L7QPvXr1Klxn9+/fr67zuO/Y+fPn1e1feOEFzWg0an/4wx+0devWaf/4xz+UHfvPf/5T+Jh33HGHsqfdu3dXdpTn4LMXJamOXaTdpf1YvXq1NnPmTGWfd+3apW5T0TkXtSu+84uNjdWGDBmiLV68WJ1jZGSksmNDhw7V3nrrLfUcAwcOVHa2qI3lefheK/cJJW0U7VyLFi20zMzMKr9ffL6QkBDN7XaXen/+9a9/aVFRURXaeUGoCeLoCc0KOidcwEtefvnLXxa73TvvvKMM5ZEjRwqP0TGkY/ab3/ym8FhJ54eMGDFCGzduXLFjNGp0VHxG0GfQuLgX5dZbb9V69Oih2e32wmM8B96XDlx53HDDDVq3bt00l8tVeIzOEZ9j8+bNxRy9e++9t9h9J06cqM7ZB18PX1dJynL0+HgbNmwoPPb666+rY88++2zhMRpmHqNB9VHSIBeFTiedsg8++EBdp+Hr2LGjNnfu3GK3e/fdd5UzmJqaqq4/99xzyvCWxfHjx9U50AALgiA0Ne666y7lxPhsx9SpU9U6W9RxoONDB6covM7jRaFjQ4fkmWeeKXb8T3/6k9aqVatCO8P7cV3duXNnpedXHbvItdwHnaKePXsqG1fROZfn6NFJ9AUMyRNPPKGeo2hgd9WqVerYgQMHynT0SkI7x8f95ptvqvV+0fYyaFsWPvtcdM8hCP5ASjeFZinGwtIQXr7//nv8+9//VmUgRZUav/76awwdOlQ1Y7O0xFdecvnll2Pbtm0Vls/s2LFDlVsW5YYbboDH41EN3kVhGUlR+LzXXXcd9Hp94fPyHFiSUtHzsgSU9zMYDMXKFdmPyNdYFN6uKDNnzlSlMDz36mI2m1WJjY9u3bqpn1dccUWpY0lJSZU+3pEjR3DrrbfiwQcfxB133FF47NSpU5gzZ07he8ILn4N9jSx1JSxvZSlpWfiOV6UEVhAEoTHBvrglS5aotZ1rMqG65smTJ0vZnKrA+1CojHas5JrLXrLExMTC21LUhSqSFVFdu1jURtEWsu+aNq4m0HZSdMZfNor29NFHH8U//vGPwseo6vslNkpoCETeR2h20PlhTb6PSy+9VC3Kv//975UyI4U8qDr5008/lakyWdRolIT3Y99YySZu33X2BpR1vOj9n3/+eXUpyenTpysc81Dysej0UYSk5HO2bNmy1HW+fj53dZvP2UNIQ+zDt8koqm7pO1aZ2Ax77NjXxx4HCuT44HkR9jCUhe994eOzN6IsfMcDXfBGEAShulDEIzMzU62R/OnrZeO6R1EW9pdXB9+ay7W4vDWXPWikKjajunaxLBtFG1cTSiot18ZG0RFkfx3t1BNPPFHt94uPzz7BshAbJdQV4ugJAqAEQxgVTUhIUI4eL3QGKUddkvKcCV/miM4hxUiKwqgeKaoGSdjMXRT+ntHMe+65p8zHLo82bdqUek5GUdPS0ko9Z8nb8Tqd34oev65hpQwzeBkZGUrgpqiD7Tt/SmpTVa0kPgls3s63ySmJ73jJ90IQBKGx41PYLJkxIwsXLlSBs6LVHpXhWydXrlxZpiNH5c7ybJg/7CJvV3RMAq/TxjUkdrtdVcnwtbz33ns1er94u/KqSsRGCXWFOHqCcEHpklAJjHDsAtUpqUpZMrpYETSmLPmkcWX5YVG1MWa+Ro0aVeH9+bz79+9Xj1EVA+qDaptUJvv73/9eaNBZysNMHZUwi8LbcXZS0et8Pt/9GN2s78zX3/72N2Ukqc5Z0qDTSLI8iOpm9957b7mPwdudOXNGGeSSzrhPGY0KboIgCE0F3yxYzmCjSnRRqLD5+OOPq3X1yiuvLPP+Za33tFNUvOR6WrK9oCZU1y7SJjH4SljaScXlSy65pMJzrmuoYs3xFCwhpZp0Td4v2qjySmlpo/he+MpIBcFfiKMnNDvo/LAskzCLx/40OhrsA6BsP7n99tvV2AGWv1CuuWvXrio7xkWet3nsscfKfXz2+l199dW48847VZ/E3r171eBaOint27ev8Nw4soAGjcaCEtmMHrJc5KuvvlJS0TyfsnjqqadUtoslJTSk7AngoHCeR0kjyjIfylqz35DOIB+bhtRHr1691HVKZvN827Ztqy51BXse/vznP6v3i5lF39+GUBKbswlffvllNXsoOztbOak09MeOHVPnuGjRIlUOwxJclgfx/S5amkvY38jezPJKawRBEBojXKvz8/Pxq1/9SgX8isI18bnnnlMZv/IcPa73a9euVRdm0VghwZ+0RXxM9vlddtllyuFiv/T69euLjTuoKtWxixxTwDWeQ9H5b44lKDoXsLxzrivmzZunsni0mywzLWqjaHdZBlqV94t/j7/85S9ISUkpNcOQNor2iXZKEPyKXyRdBKGRqm5SWZNqlU8++aSWnZ1d7LaUTaYaJ8cR8Hbt2rXTrrvuOu3777+vUHWTzJ8/X+vXr1/h/Si5TNVOHz51sZycnFL3PXjwoHpMSi1TVTIuLk677777ypWt9vH1119rl1xyiWaxWJSkNEcRFH18n6oXxxBMmjRJjUbguVFBrCgpKSnajBkz1PPz9nzPynqtvlEVRfE9x969e4sdL6lgVlQdzfdelHXh4/mgaueYMWO04OBgLSwsTEli//GPfyz2vvI9/8tf/lLqveFojJKqnYIgCI2dadOmqfEG5UE7wFE0HGNTlupmQkKCGoHDsT5cc7ke++A4Ao4moB2ioifty8svv1z4+7IeryKqahe3bNmijR49Wtky2meOGarKOZelulny/MqyvT5VZt+YoZI2qzy1bl5436q+X1RE5aihjz76qNR7wzFFJVU7BcEf6Pgf/7qOgiAEIhz6ygGxjKQyUtoUeeWVV9RQYF8pLsnKylJ9E1Q0LVnGKgiCIAQGHHzOjB+FuUqWRzYVmPVjhpJD3H0cPnxYZfN4nCqhguBPZLyCIAhNBvaosCyGTp0PCuqMHDlSnDxBEAShQaFaJ8s5WdZZNEDJsULi5Al1gTh6giA0GUJCQtRMRAoU+GDPw6uvvtqg5yUIgiAI7Edkv59vXASL6thjyN49QagLpHRTEARBEARBEAShiSEZPUEQBEEQBEEQhCaGOHqCIAiCIAiCIAhNDHH0BEEQBEEQBEEQmhhNdmC6Tqdr6FMQBEEQGgmBNGlI7JcgCILgD/vVZB29QDPcgiAIQmASiI6V2C9BEAShtvZLSjcFQRAEQRAEQRCaGOLoCYIgCIIgCIIgNDHE0RMEQRAEQRAEQWhiiKMnCIIgCIIgCILQxBBHTxAEQRAEQRAEoYkhjp4gCIIgCIIgCEITQxw9QRAEQRAEQRCEJoY4eoIgCIIgCIIgCE2MgHX07HY77r33XnTp0gVhYWHo1asX3nvvvYY+LUEIeM6dO4ebb74ZXbt2xdChQzFq1CgsXbpU/W7Dhg2IiIjAoEGD0Lt3bzz77LMNfbqCIAiCIAh1zrlmuD8yIkBxuVxo06YNvv76a/UH2bJlCyZPnoz27dvjqquuaujTE4SARNM0zJgxA3fccQfmzZunjp08eRLLly8vvM3YsWOxcuVK5OXlqQXtmmuuwZAhQxrwrIWmSp5NQ06BB/k2DQ4XoNcDZiMQZNHBYtTBatbBYgJ0Ol1Dn6ogCILQhNGa6f4oYDN6ISEh+Mtf/oK4uDi1CRg5ciTGjx+P77//vqFPTRAClm+//RZmsxkPPPBA4bFOnTrhkUceKfM7xohWfHx8seOMal1++eW49tprVZDld7/7HT799FNccskl6N+/PxISEtTtUlJSMGvWLAwfPlxdfvjhB3X8559/VlGywYMHY/To0Th8+LA6/sEHH2DmzJmYNGkSunfvjieffLKO3w2hobA7NcQnubArwYEjiS6cy/QgO9+DjBwPzqR5cDTRhb0nXNge78DOBCfiz/A2bmTleWBzaPB4NPnjCYIgCH7j22a6PwrYjF5JbDabeoOYchWExsBz83Nx8JTL74/bu6MRf7wxtMzf7d+/v8rRp7S0NPz000/405/+VOp3u3fvxsGDBxEdHa0Ws3vuuUd9//7973/jP//5D/71r3/hV7/6FR577DGMGTMGp06dwtVXX63uwzLrTZs2wWg0qoz8H/7wByxevFg97q5du7Bz505YLBb07NlTLbAdOnSo5TsiBBK5BR4cTnQh364hKlQPo6H8bJ3bo8HuBFKyPDibTudOB71eg9moU1m/YDOzfoDRwMcB9DrAoAd0ev5bp/5tMUk2UBAEoTEh+yNjve2PjI0l3cqNJr1cerxl8cwzz9RJPS2j0gVOTW1WTAZv2RE3Ier6hX+z9EjPHYggFIFO3s9H/O/oVYdf/OIXKgvOKNbWrVvVMTphjCbp9XoVjerbt2+p+zECxdJpwqy6r1yaEav169erf3OROnDgQOF9srOzkZubi6ysLFUacfToUZWNdzqdhbeZMGGCqoEnffr0UWUT4ug1LSfv4GkXXG4gNsJQ6e0Neh2CLUCwRVfM+XO6gAK7hpx8DW6POgpo3tvwh05juaemnLy+nUzKKWzM1JX9EgRBCERkf3S03vZHxsbg5D300EMqvcmNJTen5RlKXnz4q+cjM8+jekuMBg2sJuKmw8ONh+5C9BkazCYdIkP0iAjRI8SqUxdBYOatvh+XTpsvOkRef/11pKamYtiwYaVq0CuCESUf/M75rvPf7J8lHo9HZQStVmux+z788MOqzJoNzidOnMC4cePKfFyDwVD4WELjx+HSkJDsdfKYyaspdP4MZsAKXaW2IS3Ho9blxk5d2S9BEIRARPZHS+ttfxTQjh4NOTMSFGL55ptvCj3d+obR4iBz2YaX0Wc6gtxwJGe4VWlRZKgeraMMiAxlaZEY7OZKeeWVdckVV1yhSgHefPNNPPjgg+pYfn5+nTwXs3ws43ziiScKyw7YvMyMXrt27QrrzoXmQWKqG9l5GlqE10/rtzhDgiAIjRPZH6He9kcBK8biywywgfGrr75CVFQUAhE6cnQCmdFjqRKdvNwCDftPurDvpBPpOR7lsApCfW1+ly1bho0bN6rRJGwQZhnl888/7/fnevXVV7Ft2zYMGDBAlRm89dZb6jibiH//+9+r8lDJ2DUPKLRCkRWuf+KACYIgCIGGrpnuj3RagHohrE3t3LmzSmVS1MHHrbfeWviGVfYH9cdL23bEAYOh/IxeefC5cwo02F1Amyg9OrY0qH4+QRCEpgQVMg+ddiEr3yu+Up+kZrsxOM5c63J5f9kLfxFo5yMIgiAEJpXZi4At3aTkaWM2dHzjw4N1cLk1nE13KwW67m2NjV40QBAEoSiZeeyV0xATLmubIAiCIAQSAV262RSgOid7Vqged/C0Uzl8giAITQEG485leC6MPhBHTxAEQRACCXH06im7FxOuh80BHEl0qoHAgiAIjR32I6dle1T1giAIgiAIgYU4evVIdJgeOQXAsbOUIBdnTxCExs35LA+YyBN1YUEQBEEIPMTRq2fYx5KS7UFSmru+n1oQBMGvc/NSsz0IDZJsniAIgiAEIuLo1fcbrtMhOlSP0+c9yMzl5HVB8B+ZmZl444036uwttdvtmDhxopqX9/nnn9fZ8wiBD2fm2R2AxSSOniAIghDYZDbT/ZE4eg2AyaiDyQicTJESTqH+FjJ/zGzZuXNn4XD0G264odaPJzReUrI8MJsa+iwEQRAEoXIym+n+SBy9BoLiBZm5GlIypYRT8B+/+93vkJCQoCJKTzzxBDZs2ICxY8di+vTpamjniRMn0K9fv8Lbv/TSS3jmmWfUv3m/SZMmYejQoeo+hw4dKvbY58+fV3Mst27dqh6ftxeaJwV2Dem5boTWcn6dIAiCINQHv2um+6OAnaPXHJQ4w4L0OJXqQUy4BrOUPwl+4J///Cf27dunIkqEC9mOHTvUsS5duqiFrDzuu+8+vPXWW+jevTu2bNmChx56CN9++23h71u2bIl33nlHLX4rV66Uv1czJqdAg9vtHR8jCIIgCIHOP5vp/kgcvQYk2KJT5U/nMt3oECt/iqZIfoENBQW2YsciI8JhMOiRkZkNj+din6bJaER4eCicTheyc3KL3Sc0JBgWixlut0fdtzpccsklahGriNzcXGzevBnXX399sXpzQSiLtByP9OYJgiAINUb2R/WDeBcNTHiwHmfSPWgVKVm9psj6737CmnUbix179o+/Qkx0JF557T2kZ2QVHu8W1wmPPjQXx08m4tU3Pyx2n1tvuBYjLxmEzKxsdd/qEBISUvhvo9FYzLm02bxOKI9FRkYWRroEoTwcTg1ZuR6ESNmmIAiCUENkf1Q/iKPXwFCxLivPg7RsN9rEyJ+jqTH+spEYOXxQqYweeezhu0pl9EiXTu2VM1gyo1f0vuURFhaGnJyccn/fqlUrVUuelpaG0NBQVWLAuvPw8HCV9Vu4cKHK6mmahj179mDgwIE1eNVCUy/bdLiASKOUbQqCIAg1Q/ZH9YN4FgFAaJA3qxcbqUnPSxMjOMiqLmURFVm202YyGcvN2lVWthkTE4NLL71UNRRPnjwZU6dOLfHYJjz99NOqnLNdu3bo1atX4e8+/fRTPPjgg/jb3/4Gp9OJG2+8URw9oRSZeR4YDfLGCIIgCDVH9kf1g05j6L6Jip3446VtO+KAwaBDkLluo9fnszzo29GImHARQhUEITBxezTsjHfWy5pYFVKz3RgcZ651Gam/7IW/CLTzEQRBEAKTyuyFeBUBgtkInM+UAeqC0JBwsczM9eBMmgvJGW7VjyYUH6tgcwJWmZ8nCIIgCAGPlG4GCJxHlZ7rQZ5NE5EDQWigbNXpFDdOp3oAzev0WS069GxnRESIxMRIrk1T74tOJ++HIAiCIAQ6Yq0DBM6j8ng0ZOTIAHVBqG/ovJw678bJ825EhugQG6FHy0iDcvgOnnIhO1+y7SQ9W5OxCoIgCILQSBBHL4AItuhVrx4dPkEQ6o/UbA2JqR5Eh+lhKjIEnONPdDog4Yyr2ZdxOlwacgo8sAZAb54gCIIgCJUjjl4AEWwB8uze8ihBEOoHu1PDiXMuBFt0xZw8Hyzb5EiBUynuZi2Qwf48jlUwy1gFQRAEQWgUiKMXYMo53GZSDEIQhPrhbLobNkfFvbHM9CVneJCZ13wdvTybR2U3BUEQBEFoHIijF2Awq5CS5VHCEIIg1C25No+aYVmZ2Ap7aE0GKLGW5vrdzMz1qgMLgiAIgtA4EEcvwAgyA/kOILegeW4mBf/yzDPP4KWXXir398uWLcOBAwea7duenO6B5qlaOWJ4sA4ZuR6kZDY/wSTpzxMEQRCaEs80k/2ROHoBWL5JpT9R+RPqg6aykNU0m3cu04PwEF2Vv5thQXqcTPGovr7mhPTnCYIgCM2JZU1kfySOXgASZAFSszzNWvihuRAfH4/77rsPw4YNUz95vbY899xz6NGjB8aMGYPDhw+rY//73/8wfPhwDBw4ELNmzUJ+fj42b96M5cuX44knnsCgQYOQkJBQ5u2adDZPQ5kCLBWVVnOIOvv6mhPSnycIgiDUJ7I/8g86rYl6E4y+++OlbTvigMGgQ1A9SoqzBygjV8OgOCNCreKLN+VFbMiQIbDZbHA6nTCZTLBardixYwe6detWo8fcvn075s6diy1btsDlcqnHf+CBB3DnnXciJiZG3eapp55Cq1at8Mgjj6jbTps2DbNnz1a/S0tLK/N2TY08m4ZdxxxqfEJ1HD3idGnIytfQv3PzGaR+8LQLOfke9X4FEqnZbgyOM1copFOf9sJfBNr5CIIg1CeyP/KfvQgsqy0oDHrvH0369Jo2L7zwQqGTR/iT11988cUaP+amTZtw3XXXITg4GOHh4Zg+fbo6vm/fPowdOxb9+/fHp59+iv3795d5/6rerrFzTvXZlT1OoTJMRh2MBuDEeZdy+po6LremSsktJpHcFARBEOoe2R/5D3H0AhRuqtKzm/4msjnDzJ3PyfPB6zzub5i5e+2117B37178+c9/Vg5lbW7XmMm3a6psMyyo5o5LRLAOWbkaTp5r+iqcHD3hVPPzGvpMBEEQhOaA7I/8hzh6AQpLRRlFZz+Q0DRhWSXLNYvC6zxeUy677DLVQFxQUICcnBysWLFCHee/27RpoxxJZup8hIWFqd/5KO92TYkzaW7QN6vN4G+WSsSE65GU7saJc24lVkI8Hk0JteQWeNSlKYi25NuhKgyUUJQgCIIg1DGyP/If4ugFKCwPc7qBvAsbSKHp8eSTT6qePJ+z5+vRozhKbRbHG264QYmpTJ48WQmrkL/+9a8YMWIELr30UvTq1avw9jfeeKMqFR08eLASYynvdoFcVpiZ60F6jkdl6iqDzte5DM7N0/mlxDomTI+z6R7sOuZU/bzb453YftSJXcdc6rIj3omjSS6l8NlYYcCJcwQFQRAEoT6Q/ZH/EDGWABRj8ZGW7UGHWD06tpSaqabccExHi2UKdNLo5NVUiKU5wQzT+UwPElPdKuNE9DoNLcIN6NDSoNQxS8ISyyNJbmTkeBAd5t8YF3v1XB52/TFI43UCfcdzCjTwalxbI2IjGldsjRnKnQlOlc0r6z1taESMRRAEoWki+yP/iLGIoxfAjh6VAbl5HRRnkrIpQSjisJ0870ZSigfBVjog3oVOZffyNOVoxbU2IiZcV+x7cybNhaNnPIiN0EFfz2WIzDby+xzXRo820YZG833mee+MdyAyVF/ovAYS4ugJgiAIzRmdqG42Xqxm70arwNHQZyIIgePkHT/rxukUN6LCdEpW3+c0sbywRbh3XALHARy/0DvHrNrZNBeOJXsQGVL/Th5hNiw8WIeEs55GNYOPQiweTReQTp4gCIIgCBUjNYEBDDdXFI3It2kBWTYlCPUJSxNOMZOX7lYOXXnOB78rzOqdSfModU2DHrA7ofryGnJEAJ87PBjK2dPr3WgdZUCgw55G8fEEQRAEoXEijl6Aw81sVr4HLRpZb48g+JvkdDcSU7z9dZVlmJjVaxFOQSMN0ICwYPbwNXywhM5eWBAQn+RW59MyMrC/1yyFtRQXhhUEQRAEoZEgjl6AYzXrlKogRRH0EloXmilU1UxI9iA8pHpDzmsyEL0+vtPM1B9JcqklOFCdPYdLU9UELI8VBEEQBKHxEZg7DKFYnx579KRPT2iusE81/owLVpM3I9YUYHkpL3T2ktNdFSpmNRSqv9HtHfUiCIIgCELjQxy9AIflXRq0Ks0IE4SmBoVUEs664HIDoUFVX65OnojH0799ELOnjlA/eT3QoKMXatXhyBkPTqW4ldBMIFHg0MDVRxAEQajfsQL33Xcfhg0bpn7yuiDUFBmvEMDjFXxk5HoQG6lHtzZSaSs0H5jlSjjrViqVFF/xqWvSaXv3zZdxYN8O9Ok3BHc/+Gt06nxx9iB/P2vycNjtdrhcThiNJlgsFixes7XY7QLJmU3P9aixC51bGWAOkAza4USXKhuPCAnceKCMVxAEoTFBp+2FF14onJ3LweBFZ+fy9zxus9ngdDphMplgtVrV7WXGrlAWMl6hCcBytawLfXqC0Fw4l+FWyplRocWdPDpxSxd+iP17d6ifvF40Y0cn0OfkEf7k9ffe+j8EIiyNpCNLsZkjiS7YnQ3/PWd2kSJQTaVUVhAEoaHxOXEffPABtm/frn7yetGMHZ1An5NH+JPXX3zxxQY8c6ExE7ihWqEQqt5xnpX06QnNhay8C+IrwTo1H686Thwzfb7f++B1Hg9UqCIaG6FXKpeHEp3q+97QZZsOp3ftEQRBEGpPVZw4Zu58v/fB6zwuCDVBHL1GNE+P4giC0NRhRot9eSaDV6GyKFVx4ljOyXLNovA6jwcyzFoys5eTDxw941Kqlw1Fgd1bOuvLpAqCIAi1oypOHDN8LNcsCq/zuCDUBHH0GgkcrZBT4Gno0xCEOoXlySeS3ci3A+HBpZenqjhx7NljT57vdnRWPB43cnIyA1KUpSQxYd6RKifOuRusXDsnn4PmxckTBEHwF1Vx4tizx5483+1ov9xuNzIzM7H/wFFV7XI+04PTKS7En3Xh4CkX9p5wYs9xp/q5/6RLqTmfOOdCcoZbjSbKtXng4kxZoVkiYiyNQIyF5Nk06HUaBsWZJMouNFkSU1yqZJPDzstyNKoqtMLb/fvFP2PtqkXg5AJN8/hdlKUyUZja9silZWvo1laPtjH1K8LETN6uBCeouUll0EBGxFgEQWgsVFVohbd76qmnsHDhwmL2y2y24J1FW9C+Q5zaBxr0rPiiOjt381y81f/h8dCGQFWC8f78Ff3GMKseUaFASJAeZxMT8PJLL5YrCiM0HkSMpQnN08t3aLA5GvpMBMH/0LDNveteTBw3Aq8+9xASTyWUeTs6UnTUZs6Zi34DhqqfZTluvB4aGg693qCMpL9FWaoiClMb6ORGhOhw4rwHufWcyecaw3Eu0p8nCILgv3EIdKToWN15553qtvxZ0slzODVExHaFWx9Wyn45HHYs++RfiI0wqDJ/CpWx8oWjh0Kt3p9hQXqllBwdple3Ye93TLgOVpNOZfbiz7qxasMh5dy9X4EojNB0CGi9/tdee019APfu3YvJkydj2bJlaNZ9eh6dEkkICvAouyBUBxqXwYO9UU4as4Qje7F25eflZt547Nl/vlHp49alKEtZojCETmRVzq0qUPGSmfyT593o1aHsDGddQCfPo9Xf8wmCIDSVLN2ePXswf/78csch8Njbb79dqooip0BDSpYHqVke2F0a9u3xn/1ixoeBO5+K8n8++T84itgvX9/gP59/Ee/8r/i5CY2fgO7Ra9u2rUpf33vvvQ19KgEB9115NunTE5qgEpnd6+T5M/NWl6IsNXEiKxviXtbvI0N1SM3WkJLpRn3BXmB9QFsGQRCEwKA24xDo4HFO8qHTbuw57sK5DI8SIGsZYUD/AWXbr9adBmHTPgdWb7Vj/kYb5m0oUBf+e+UWO77b58Du407lNHpYt1kGB/btLGW/eN4//Lgdx5NdKvNX3YylDHkPXAI6ozdz5kz1c9euXUhMTERzx2zi8HQNHWIb+kwEwX9s+Xk7XM6qO02qh+yYCxv2OFTjOb8TtGdtovXo09GIy/qb0K+TUfXMrV4+v/DxfD16dz3weK3Pmc7i4YN7ixnLipzIkr2FvC/PzZe1rOj3sW3icDLFg6gwllPWbZZNbTxyPKrMRxAEQaiYmoxD4DqblachKY1iKRqMBiAqtHgVxc13PY4Vy+arPjuP2wnoTXDrLDhqvQ8vLs6v0p+FWbz2LQzo2c6AXh2Myj62jNSXa7/69h+MpDQPzqR70CpSj9bReiQnHqs0Y1ndrKZQvwS0oycUx3qhlIuy62ajbMSExg8jh116DMaB/VVzmuLPuPDGygLVZ1CS06kenE51YO0OB7q1NeCOiZ2Uo8TM4L4929C5aw9cNWUm8nJz1e0TT5/AV2uXw+VyQfN4VC/ExKunI65bL/y0eQMyMtIQERGFiMgotGzZBi1iWxUKIdGJXPnFZ0oNjffT6fSqsf7mux6D06WpIejVKfWs7Pcs5+GmoGtrY7305zGTKAiCIFQMHRw6NkWdvYrGIdDmJaV4cD7Loxy86LCLDh6zez8dcqrLnuOxaDXtG2TseR3OtJ0Ii+2GboOnQxem4bwLaGM6jO7WzTDADZ2OGTgN2/KuQ7a7JfoErYcBThR4wpGXGokN51ph9bYo9RwdYvXo1v8XMCydV9x+mc2496Ffq74+p1tT2cVzmR785x/Pl8pYEmYsfSWoZWU1S95GaDiajKP3zDPP4Nlnn0VThptHfgE5T08cPaGxQ4fo2Fk3br7zcXy9+vMKM2+MgC75wY6Pv7WpCKcvWjmwi1FFLHmMvWx7j7vg8gDHzxTg6Y8cmDi4LfoPGYXY1u2g1+uRlpqCsLBIdf/IqGiMGj0ORpNZjS+hExfbso36XUxMSxTk5+P8ubM4cmgfPB4P7rz3V6oZfvfOny80yTOT6D0Z/ixwAr96Owfm8Cw16J3O5uCuzDCaKy31rOz3EaF6nE2jGimHyNddXaX05zUMzcF+CUJThGqVzF6RokqaTzzxRCl7dzbdjcRUb1mkz8FjeeWOeKcKUP582KnUMo2wwQ0LLOGdMWvSYAQbugI6A0xB+WjbyY6Bg8PgcXRFXlYwrEo1S6fUNm+Obg+b24L9e9vhfPJZ5Oacg8t2ALmucGzJnQ2rLhuGrHh8fwywu5ThunB2F+Q5L2Ay6JSAC895VxUyljLkPbBpUo4eLz6a7qBfr6MXEdLQ5yEItRsfcPycW80E6t+3e2HmzTeqgE6eT4iFt31tRQG+2eWVnKWc9MzRFswYbVEKY0Udo337j2HLtn2wZ5/CrvxJ+GpnZ3QJ64/rxl6OsUPawWAwFN6eqpy9+gwo8/y69+yjLj7YuM41JS83B0eOHMaS+f+Dw27zGkgF62ucKvraaszLyM6n8Xapy/tf2aAL7Q+DcS/c5WQtKysFpeHV6TQkpniFWeiY1gWMKDPKLNQvzcd+CULTwqekyeyVb1QBnbyiJYtcV08ku5TgChUxWYLPoP23O+1Y/L1dlUoaYUcb81G0NsUjynAGhk63YUT/1jDbx6FNq1hEx8SqYOVFYoH2ZffxdLziksJ/MwiZb7MjMc2IrXtSkRJ/CEnffwidxw7tgv3ibWx2J55//iW89sab0F9Yf5hcGDBwiBJIK2qbSmYsq5vVFOqXRjFHjwaQfXrVUd2sbK5EY5uj54Mb48hQPXq2bzI+utDM4BDwUylulYFjmUhF6o7Hjx3Fo797HieP7oKlxQB0G/0I/vpg/1IljBnpqVg4/wNluLp1742Y1t2xZGcr7Dp+8TZTh5sx98qgGve5Mdu1dLMNy360I37RFbCl7i11m7ZdBuHev2xSg2r3nXSrwbbEkX0Mp5dNADx21W9RcqZfVeYDMvKbmqWhd0ejksz2NxyouyPBCbNBpwQBGgMyR08QhEDlwKGj+MtzL6isWK++g/HgI79B+45xWLfDgYWbbEpoi0QbEjE4ZCX0BjM6dOmDoQN7om27jsUCk/5k+lVDcfTQnlLHLS0GYtRd32LOWKvqdadtLs82/fTzDvTr071a8wGFuqEyfyegvQX2zvguLJ3ih4gRDbPZjOYKN2BZ+R6V5RD5cyHQHDiHy6sOy6xQWVknloLQwTuT5lFzfir6DJ84fhTXXn0JnE67ypY5Mg7gUOJSGO7cCk2LQ1LiSSVBPeGqaxARGY1xV0xGl7geysiQgf00lQX835cFKHAAq7Y6sOeEC49fF4y4NsZqOUBf7XRg3gabaqAn5phBsKcfgua5GMFkOWdMhAntsAnXXDkSwcFhOJzkxvKf7Phhf1d0mOHtt9Cy9mDMqKH41WO/KXTifPMBy8tqqsfX6RBiBU6ccyE82OR3YRb2/9odQFi4Xx9WEASh2bFzzxGMGT20cIyBb2zQwNvWI93dCS2Nx9Ev6BjOGidi+vAO6NHiWvTq0aPOnLuiDBp8CY7HHyyWpePeuksbCyy5W/CfZQPw+XdBuOEyOnxxxWxT736DMfPWx5Cn76QCmi0j9FXKagoNR0Bn9MrqW7j88suxYcOGZpvR42tKy9YwqJtRDcgUhIaGA17PZnizVxQKokNiNgIRwXqEhfDfOvDbU2D3qnnRoYipJJNHbrn9Xuz47lPl5PkwGIxo276jaiKPjGqBGbNvx8w5tyEkJKzcx6Ex+r8l+TiU6BVw4dNeM8KCGy6zqAGz5cFgCpU952+0q6Z0H+y9u6pnEv54/6hCI84op9liwUv/+QRnzyQiKysTV06arrKLJOGsC2+uKsCRJO85sK3i1zNDMLJXcfnsqpCa5UbrKAPi2hr8WuKXmOJSA9qZZW0sSEZPEIRAC3ieSXPjoYcewJplHxXvvdYZYY1oj2CzG61atcRlk+/EfXfNRXCwpcJAIwOotK1O9tVB8+5vvf9ke576edESeH9vMnpLL2mLS9rasrJ0ZrMFdzz+XzjzzkAPB3bmTUOmuw3aRutxx0SrslVF7Q0rXHILNMRG6tGppQHBMt+5wajM3wloR682NFVHj6RksU/HVCflW4JQHXILPDiS5FILfliwXhkVfu2cbio4aspZgub97rCsMtiiR4i18u/SlsNO3H/jKNjTdpd7m7LKG8uD57HgOzsWbLKpZncSYgEmDrZgbD8TurY2wGjQqdsx47j1iAtf73QUc/BaRuhw24QgdXs6szSWZWXguO7EHz2I1m3aIywsXP27U+c46A0mLNzknX3Et4Xvwp1XWXHtSEu1HDaeI4M93dvq0SbGP0UZfMw9x5xwa2hUASRx9ARBCBTsTg0nkt1IzvTgwZtH4WAFc1XLs18s0S+we+0n7QR70q1mqH50+oNmE4Ok3uM0Gxf8PHg8vC9tLyszNOTZgXybBzanBo+HPd7ex+Fe1leSWZb9yre5sGzdTnx1tDPSco1obTqKc8449OtswT2TgtCllaHYuWZcGA/RqZVBjWSQ/uL6Rxy9Jujoped40CpKX63yM0HwN5SJPnTKpZy6qFD/OQdUJnv8vzk49s3jyD46v1hGryxjOXPOXDWCoCqcOOfGm6vycfB08fEMDHgGWXRK6Min6umD6mjsWbhysLnU2ITKsNkKMO/j/6qF+NKxE9C9Rx9sO+rCi4vyYLvwsq4ZYcY9VwdVy0ByQ5GTr6FbWz1aRdU+s0exgH0nXGgR7lUfbSyIoycIQiCQk+9R439ybZpqS3jysQew5ouPi5X3l2e/nvnH66q9gFkyem0s0WfVC4OnzJQxgFqTdVmJrDiAAjp+No/aOzIoy2An24D42AxwlmdjVnx/Fom7PoXdE4yDBZch09MBVw0x49YrrMXUn33ZPc7dY3avrue9CsURR68JOnr8UjFxPyiueCpdEOoL9todPO3N5NGo+QsalyffzcHxcx4lYJK8YjycDjs8ntJz83z0GzAUC1f+VC3jx4zd8i127DmuamHKpHMrPa4eYsHEweZaGS6Hw4Ed2zZjx7Yf0b5DZ0y4ahrO5QThr/PykJbj9SpnjLLgziut1fo+M+JLZ4+lM8zuM8JLJ5WltLl2DS4XYNQDocE6ZZQrKq05muRCSpa3b7IxIY6eIAgNDddOOnlcviOCdVizzYE3F+7D8cXjoblpvy5WhpSkV7+heHveZuXcMSNGsT1WvdTF3k6NAXKwEkdTlWGZeR6VCWSQM8RS9nOmpOdi4Rfr4c7cg7POHjhYcDlCgi24d1IQLut3cQ/KqpCMXA1WE9C1jbHR2ZLGjDh6TdDR4xeKX9AhcWb1BRWE+ubkeRdOnnMrB8OfBuk/y/OV8AnDmpM7fIv0U5tx+mQ8Us8nq7l2J0/Gw00PpoYZvbIMNDNZialu5Nk1ZeyYLe/X2Yg2Uf59benpqdjy40ZcMXEqLBarMrR//DAPyRneTcCcsRbcekVQtR6T/RuU7Ha5L/Zo0HVkKQ0dP0ZueRuW6rSJ1qNdC0OpGZzsmdx9zImwIPZ1NK71RBy9iu0EM9jcPFbUiyoIQs378ZLS3DhxzqOcM7Yt/PuLfGw9lI9Bwauhy92PfQeOwp1/BrZy7Nd1c+birbfeQkTIxcHp9Zk0yMp142wGe+e9doMzYMs6j137T+Hr737GpvPjoYHriQ5Duxnx4NRgtIzUF2vnYLUKB7O3i/G2RAh1izh6TdDR821Q+3aSqInQMCUqzITRIPjTMfjxoAP/WJAPPVzo3cmC6/sfQLv2HdCqVVv1+6qMIGgsJMQfwv69OzFwxBT8ZQG/z97M3u0TrJg9xlonGVgGh7gZ6dzq4rpBZ+DwaZeKxLJUqLEhjl75ULxhx1EndHqge1uxFYLgT5SC9Dk3ktI9iArVISnVg38uyEVyhks5Qv3Dt2L6lQMxol+rQvs1c/LwYgJe3hEE29G9u3dMQUNBO0BFafakp2V7VNAwPESn5reWzAj+cMCJL77cDJM7BYcKLoPRZMHtE4MwZbi5cP4e+wRZJko706W1oVH1fTdGxNFroo4ev4wdW+rRIVb69IT6jWAeTnSrni5/lmbw8X75ZgbaaRsRbCjAL+69qUzHo7wG8sZGRkYavvryC6XOOXjEJLy2vh3SL5RxPjErGGP71c0Imex8KqNCRWDZV5mZ61GKqVTa9BnpxoQ4epU7ety1ud1AXBv/9HMKQnOH5fEJZ92qKoN2avMBJ17/Ih09zd8g3xOG8I5X4LEZwcUy6aycOHzkKJZ++goSDu3C8OGBN4KAjhzLOunw8cIMZUQZDt+xk4lYteIL2Bwu7Mu/EhnuthjYxYhfzQguVG3mY2Xmsc0I6NxahFrqEnH0asnWw3YYjfqAc/SYHjebdBjQpfry7IJQUxil23/Chehw/5WZ0CD845NE6M6vgklnR99LpmPymC5N8o9ER/XdN1/2ziPqOwjDR12O06dOoFufkXh/+xDk2wGTAXjujlD06lA3QRxGW2nMfSWdYczMNtLyGnH0Knb0th9xIDRYrxy97AINnVvq0b6FocwZl4IgVA4Fu46ecSErj8FOHRZucmDVphMYELwWbs2Mjv2n48Yr2xYGzrjOMqBmMevQqaVRCV41hu8fxdaS0z04l+Hx9h6G6JB4KqHQfvXqMxAdug+HIz9FCbUkOvqpipEHpgTh8v7mYuWheQWaah3o2NKg9q2CfxFHrxYUFNjwwqsfY9jIcYjr2iXgygYYIRrS3VSq50YQ6iqbt++kS4mAFFXcqi0rvjuJhO2f41SqHglH9sOUf0Bl6+5+8NeNMltXHuWVnr71wXK079gVZ/Nb4tlPc+DR9Kqh/8V7QtW8PKF8xNErn+SUDLzxzgLVE9q6dWtlM9JzNbSL0aNzK+mdEYSaOD9HEl1q/EFYEPDaygLVgzcoeA2Op4XDlroLKaf3FNqvmFZdlfgJnZwOsY1TjZJJBZal7th7BPfMGVGs9JT264XXFmBfRl98vT+YuwRqWKsRRA9ODSos2WRpKIPEoVadEmqJCJFSzvp09OTdrgCz2YzYVu3w5YrPsGvHz36Zy+cv2BtFWXtGlwShPmAfV2auhtAg/xgrKpGdTXfh0x9CsTO5M9bOfw7Htn+O/Xt3YOnCD5VTROeoqcBIqM/JI/zJ6yuWfobWbdqhW8sCTG71OaIMicjK1/CPz/OUCqkg1ISQkGCEhUdh2aIPcfTwAWUzmE04k+5Gwhm3yvgJglD1sveDp1ywO7n/Ap7+OAcb9jiR6WqNQ5m9sHHRU/h+3aeF9mvmpOFKSIxaCnFtGqeTR1h+2qO9AV8ufKXQyStqvzZ+tRS/nN0Wv5qUgzHhnyNUn4pN+5x49O1cNWOXsHIkNsKg2gYYLE5McXln7Ar1gjh6FWAw6HHJ6IkYe8U0/PjDt/h63YoKZXLrG6bTORBTEOoaLsqJaS41cNUfvVx2mw3Ll87Huwt/RL7DgEM7voROK21E2I/XVGC5i+/1+eB1HifBwSHo3TMOw0OXo5N5J46fc+ONVfkBFWASGg8Wsxljxl+LoZeMxbovl+HHH9arDRd7aM5lulVmQgIJglA5LL3kOCFu/6hw/Md3kxGe8TlijcfQvUMIwnPXqjFARe2Xw2HHqgX/Vr3sjb0vludP8bCK7NfYwa3Qq2tLjApbjNamIzif6cHv3svFFz/aCm0YM3nM6iUkc/1xe+cGCnWOOHpVoHvP/pg553aEhoYF1BeWQzQz8xr6LITmQEYOZZhZrlL7z39mZjoWff4BklOysPdcR3XMUrAX7gqMSE1hRvDp3z6I2VNHqJ8NmSFkOQ/LXYrC6zxODAYDLht3FSZcdQ16BG1Bb+sGrN/twJfbOW4i8F+fEHjQXg0aOgrTrr0BQUEsrfIGajgWhUIJhxKdstkShEqEwg6ddilREQ5D/8v78ejk/BxuzYg+PTrgr7eHIv5Q2U7Q7l21s1/x8fG47777MGzYMPWT1xuKIUOGwGQqbb+69RqsHDlWwF0zfSYuHXMZBgR/ja7W7XB5gHfX2fDc/DzkFHiTEsxscv3Zs/8Ibr7tXgwcPLTBX1tTR6c10XBxZTWrNVXd5GP++MMG9OrTH9HRLdCQMBprc2oY2s0ks0qEOs3m7TvphN3BGTu1iw2dPXMaK5cvRHhUayw6OgF2twVto/WIOfUkli/+qJixrO2MvEAbx1Cd8zmScAr/++IkDuf0V0PP/3FnKHq2Nwb062sIpEevctXNkKCLYjtutxs/bPoaQ4aNRkhIqHfAsRno0c4os/YEoQTsK6OTx6A6R+C88uluxOnXIdnZHV36XYl7JoepwMnTv30ASxcWt190iu688068/fbbNXpf6fjQubLZbHA6nerxvOMYdjSIUmdZ58N5sJ8u+wmRLeOUirNv3NKxhMM4fd6Bj7d0xPkLo4NYNv7E7BD07mAsbbv42ixW7NzZMK+tsSM9en7G43YjIz0Viz//EGeSTqEh4eLjcEqfnlC3UPY/K88/2bygoBD07jMIm9OnKCeP4mOPXheM+37xG+Wk+DJePqeF4xPKg2pmDHYUODSVlWCjPKOGbB7n8XfffKnMnriGKgel80UnjM5rvwFD1c/ynLIecR1x1/WjYNS70c38Hf5v4Tk1B68qPX9NqdxV8C8upxPnz53F4s8/UHaMZWXsOWJZGnuQBEG46OQdTnTBbAJOp3rwhw9zkVEQhATbJeg/fAruveDkMRA645bHYbZYCjNePqeM4xNqygsvvFDoVBH+5PUXX3yxQf5EdMDoZNJ5ZYaRP+mYTb68Nzq1Mqi+ciqRkq5xPXH5qP54Ya4J49psghF2pGZr+P37ufjiJ1tp23zhtf31uRekVaEOkIxeDebosU/vuw1rcXD/blw56Vp0694bDQXnuHRvZxR1PqFOYFZg73EnGJOrzdDTvbu3o2XrNmr4+UffFGDR93Z1fM5YC269IqhKM/KYTafSLB07RrAMekCvB5is4L/5PWUPkkfzOn63zxyFIwdKl87QyVq48ic0Br74IQt7flyMIH02ciNn4E9zOxWOtWC5Jhv/G/Prqy2S0ateRs+3Yfzqy2VISjyFKddcj3btOyonjwUwzBpHhkpHh9C8KczkmYATyW68v2AjEm09UKCF4+6rrbh2pLUw2JiW40HrSAPcecfx71deUs4QM1+1nZFHZ2r79u1lHt+6dSsCsY/xxDkXcgo0ld0zGnTIycnG8qXzkFsAbEidhjxXqLpt+torkZa4q9Rj9Ow7FCvX/oT2sQZYA2ykWWPO6Mm07Rqg1+tx+fhJCAuLwNYt36NL1x6qv6YhYKo8K09D66gGeXqhiZOc7lbOVcvImn2+ufhwof/o3f/AbstH196jEG+5H8bwruja2oAbLvcaTEKnrrwyTWbomNEKD9KpwEaIRadq/fm1o99TsneWBviSYUNw7MjeUuWgvp64xsD00eGIT56FzGNrEJ25CO+vmIl7ru2qfsfXcfhg4359Qv3DbMOkqbOwaeM6bN/6A9q266BKspkNP3DKpeY3MtMnCM21J09l8ox08lx4553/4eSOT3A6OQ8DhozEoNZPMr+lAilUoebYhE4tDTDou9e4TLMs6Czu2bOnMKPn++7yeCDCAFEfqwmnU9w4k+ZBsAUICwvHrDl3YNXyhZigW4rtedORlB0BZ0h/6PT7oXmK264BAwcjOdOD9FyPek/Zy9cYZg4GOpLRq0FGrygulwtGo1EJTERGRqO+kT49oSZ4yx69/7aYUGaPJ6Oa3PiFB+tqNKuRme+Fn72P5/78S/Vvt8sFnd4EGCyIm/kN/nBjKNYseKUwg1fe3DyWZNocUMOeW0dXff4XewoGD/b2FDTmHjbOLXzy3SwE53wLs64AV06+HmP7maVHTzJ6NcroFQ3CsGevqP3id43rQq/2RsSEi7MnNC9YesgRCgwgnjpvx/vvvIl1856Gy+2G5nEV2pDPlv+MHJuGlfNfwZEDO5Xz9eSTT/q1vyzQevSqCteVtGwNCckuuFxAVJhO2f41KxchKDQKG8+OwbbdR3Bq2QRobjvgKW2bVStGgYaYcJ1ypP05t7cpIgPT69jRIzZbAT587zUMHDQcI0ZdXq/KnPxSsfZ5UFcjwuTLIFRh83cuw42zGR441Iw2nZoJRMn1mDC9mpHHjy9VNhPOulRJJOfo1ITTp47j1w/fgoP7qEjmnaej0JswYMR0JOxZW6mQCDee7EOtaZbh6NGj+NNfXsTunTswYGDpctDGwtl0N379vxzk27wG/y83etC7a3Sl5a5NHSndrLmj5yMjPQ2fffJfXDb+avTrP0RtsjiftUd7o4qoC0JzIIdz8k577VRyhgevz/sZJ9Y/iSMHtgOei/aLtuqyK2dgy6Y1aq5cXTphdPbYk+evctD6hOvI8WQXUrM9iA7VQ6/z9u9p0OHjtSn4/JskZOx5HfY0DpgfjOeeeQJdunYvvD9bMFit5vYAbWP0aBNlQJBFsntlIY5ePTh65MTxeKxZuRj9BgzBmMsm1quzl5rlRjfp0xMqgX04x856a+jpvFkvKCVziCnLM7mgsieBH10qbAZZataXxywBM3g0fjMnD8fB/aVr8aOiWyAnO6tClU2fyErvWpaS8TF2JTiVmIxPFawuMut8X1UzIzSYTToEW3R+VcPdHu/EXz7NQ4g+FSPDFmLchGswoH8/NGfE0au9o0cO7NuF9d+sxqVjJ2DQkBHqO8NL97YGtIpqmLYEQagvGFA8dIpDvIHkNBuemWdDnl2H019MgC11b6nbR8d47VfJssraqGw21cqhpDQ3TqV4EGzWIcSqw/FjR7BuzRfoPOg6vPddCxRcmB40OM6IX88MLpW9c7q9Dh/Vp9u30Ks2EtpX4SKiullPdO7SDdfMuAEH9u3Ed+vXoj7h5pUy2YJQHizD3H+SA5KB2AiDClxwceCFvW50pCh/bDXpYDHyuq7GTt7a1Uvw7VcrVbaJ2W5mDYuilDU1r0pkeXPzuLjTcYprY6h1vxAdrpaR7EGqm++It8zEgw6xevTuaFRBl2Are2c9SiyJDjZfT23hGJVbrrAi19MCRwtGYeM3y3Ho4D6/vAahedOn3yBcefW12Pz9t9ix7Uf1neGm7OgZN5Iz3A19eoJQZ3D9PpLogtMNpGcVYMmieWiDLXBkH0e4xV7KftGhY9tYUSeP8Dozb8JFGOjsGGtA7/ZGOF2a6n9kxUmfvgNxfOdi/O6adHRo4bXvOxNcePy/OaqSqNj7bdCpiiNm846fc2PnMSfOpLkuVCQ1bpyu+nkNIsbiR9p36Izp192MgoL6nWJOdSK1mXRpdZaxEBovKVkeZcj4OeHmrTy8Tl/Nn0fV4a9arOTbhw0frebksL/gQppLoTcYVYnmyDHj8dWaZWUKibAcOSOHjpMBrSL9UzrGx0lO9ygpbJ9qpb8yefk2Db06mNCiSJlb6yiDypJm57mRmuPtN2B0k9lSOtlsVK9J1v/6MRbEn3Hjp0ODVAmMbu1y1azeo2dfv70moXnSo1dfGE1GNQKFqGAQy8fOuNkjgNbRsl0QmhZcv4+ecaoe8IKCAiz4fB50mhPxKeFIXjEBLmdx+8V+VpZoTpgwAUuWLGk0QikNCe1ciwgdrGajcuI4rmnU2Inqd1s2LMTjU2/Awm2x2HzAqWbuPfluLh6aFoQJgyzFHsc7aN2gKn0SzrrVyIs2UXq0iDCowFRjwenyBrHPZ3rUHOx+nYx1PgdbCvD9TJu27dUMkYKCfBUZrY959PwCsI+JkSlBKOnkUUGM0bCKnLzawkze6pWLkHI+GdfNvg2L5r+v+u/c7uLRuU5dvLPkfvXEX8qdm5eZpykFr/YtDH4rgWbvYXiITjlf/oQBlk6taGxKL6V8v9vEGNG/s0ll4/p1NqJTSz10Og2pWd4sYHXh+/HojGD1OKccA3GwYAx+ir+oXFpdmHV9+rcPqlEN/MnrQvOFtos2LDsrE/v2bFfBoVCV2fMgOb34d1kQGjMsbT6a5EJOPoOUNsybN08JrmzLm4GwlA/gdpW2X75Zcn/729+Uw+fPuXlNHbaL9O5gUs5aWo6GEWMmYsiw0YiJDMdvZwfjziut3kypG/j3FwV4c1V+mZUwDEDxMVh5tHnbEdx46z1qpNAdd96Lw0eOIhBxe7wzBk+ed6mMJKur0rI9sNk1eOph2y4hujoiOysDW7dsQm5uNsZeflW99OyxmTgiRHx3obiTx2hXXUe82JNnsQYpJy8yKlqVYJYszSQhwSGFYiF0+EoKibRqG6cCFhy94M/sNL9/raL0KrPpL3ie3AhXpYeJPQW8cL5QuxhNRTW56LNRPSbMW0JbVfi3fObWUPz23RyczhqA09uA8LBz6N82A3HdelX5cejUMevqE8ThqIbVy+c3OlVSwf+kpZ7HxvVr4XS5MHjICHWMzp6muVTwQhAaM6yuYFaILQ0MyP35wxxYHOE4bBuLq4dH4sste8q0X6GhoYViKHT4GqtQSkNBG9itnQEWM1Tf3oAhY5QNPXfuDC7p6ETX29rixUX5yM7XsGabA8eS3fjd9SFlKgCfO5OAe+aMKGa/Fi2cjy+/2YrBA3qov2t9amWU9RljJQ+DwdyL5Tu8mTW2dYRH6JQTm1dH7SQlEa+gjmjVuh2mXXsjDuzbje+/+7rOM3sUzuDgzvrIIAYKSnE0y4PTKS4VbWbURPDC9+VIPTh5dPCorsmI5lWTrlVOHonrOdg7SqEIJWe8+ebmcbg3f3boFIesfA1dWlH90/9LU3gQZ/J4F2B/NfCzv6C6oydYaskMYL/OJkSH6pSzV9n3tmTmLTftGJ69LRQRwd7nXvs9xaCWICH+UJXP4903Xy40koQ/eZ3Ot9C86RLXA1dNmoHNm77Brh0/q80Yx6zEn/XgbJpk9oTGi8ejqSHo5zPdCLG68NKnR3Ek2YK9BVfj0v4RuHtSEPr2G1JYbVJeaSadOgqvcHg5f4qTV75y6H333acGvfPn8WMJakZej7Z65No0ZUePxR/Gyi8+R0vLObxyXxh6tPMGTw8nuvHof3Ow74SrSvaLKqgvvfwydiW4lAAb94aZuR6Vva1ruP/ka2FJJjPFFE/be8KlHFpVvhqmUw5rZcKOdYGE5uqQdu07Ytq1c7Bi2edo1aqt6oGoK/jh4QeateZ0+prDYn061Y1T5zzezbsHyMiDEu+oycy3pubk+co169LJo3Oy4ds1SDh6CLfOfRBBQcGFfQ/ZrR8EDJ97b1hkTg6zduXB4bMtI/RoWUcqf3w/okMNKsIWEVK794WvUYnYhNf8XHl/Dn/XklyqlIViONXJvP3nf4sQc2oB9m/ejnPRA+AaNg5YtQzXXDsHnTp7h6pXRFlZ16KCOELzpnvPPvBoHny9djlatW6rSjrDg6GcPZ3OJT17QqODNov7hqR0DyKDPXjrvUUIykuHDjdjeA8LHpkeDL1OhzvufRwrv5iveqqLjk+Q0szazQLkAPj58+cXitb876XnseXnHejVdxAGDRmunL3rZt+Kf8xtif+uKcDaHQ6luPnUR7mqtHP6SEthlq48+3Xs8E5Eh+tQYAdOnmcQ1QOzEUp9mIHREKteqYuz9LOmVUPss6NauZpj7fAgpwDIyvfA4WBHp6Z67rj3Cg+qWS++vxFHrx4EWmbfcAdiWrSs0+ehwAQTFYyQNIdZI4zGnTznUcM4qcrEmSscM8GRAV1aN9+PNUtRDifVj5P3/cavcPTwfiVA5HPyePy1FflIKuiEjjO+QciZN6HL2asipBXNeGODNevzO7Y0+FUspSTMpFGSv7awmbpdTPWzeSWhoenW1oiDp5zIzPMgsozS67Iil3yf77v9msLrtrQD+OHYUhjnvAht2UJcc/296NzOm10tD2ZX6TSWJYgjCKRnr36IiopBbMvWhcEJOnss4wTE2RMa3zxSBocjQzS8//FSuPLPY0f+dejZ3ownZoeoDTorPsJaxOHLb7fi0/dekdLMWvDCCy8UOnnE9/Opp57C6tWrC3+XcGQvvlq1AI/97u9YvvQz3HLHA/jFNcHo3s6At1YXwOUG3l1nw5EzbjxyTbCqMKjIftFZD7F6++QJM3qcDcpgMh0/HuX8YF4sJr0qJTUbvPaYfpnPN2OhDS8XHTteKHzo7SX0FeLQkeTaGBoO6HWBVyip05porV9lcyX8PUevKmz5cSPCwiPQp+8g1AWUruXQaw66bcrwC7vnuFPVexf9u/jmrfTtZFS9UM0NNvseOOVSi1dNRiNUB/afbvt5M66ZcSPad+hUeHzBdzZ8sp5KZUCfjgb89fbQSmd40UlPydJUKUdd9//ws7MjwYGIYH2Nla5YosFxJgO7GBFWYuZPbfprWeZBB73kWsNyzf17y8qy8XYX1ziWyoZ1vwn9xj2MfENnXD82CFMvsSgDVJVMYXlD6wMZmaPnnzl6lUFbyjl77AHt1DkONodXOa57W71k9oRG1bPOearzFy1H2tl4bM2bgYjIWLxwd6ia38a1naX0VHzu0sp/YmDNFZZrbt++vdTxFi1aICur+BxC2p9J196OX/zyN2pcmQ+WQf5jQR5Ss722jkJkv78hBM7s4zW2X5pGFWyvs8a/Of/Nzh+P54KTd8F3oLI1YdWYofDC9ZSjI2qXrfP16A3pbqp1wFjm6AUQISGhWP/1asQfPVQ3j2/lPL36qUduSDiAk1/Qkhtibmb4BUxM5cDupv0elIRqkkeSXGohqq2TVxUlxo6d4zDlmtnFnLwvfrro5HFu3e/nhFRpg8koG8sW66pksyh0pChYVBuFWr7X7Feikqe/oMPYtY0BufkcXF/83PqU0S/ipfjtNI8T5vy9SHF1Ua/vx++/woOvnMTbq/OxI95ZSuWTxpBGkUPqqVrGn43JyRPqD24krNYgrFm5GGfPJKqIOjfMLOMUNU4hkHvCeJ1tLUfPeHvW9xx34bvjnbE9bzqM1hb48y0hysljwJFKiG2iDaqHTJy82sOyTZ8yqQ/f9ZJzCOmsHT+yCyHRXeBw2FVgKT8vV7U3sG+PgVXCcsxf/zcH5x2damy/dDpv2SY/D2FBepUYYJIkNoLzhL0jG3jhdV74O1bb8La8jzfz13iCAJLRq8eMnnq8n3/Az1s2Ydr0OejYqfI+mupyPsuj5nLUdsh0ychHoMzn4wZ2Z4JDLcxlORHexVpTUvbNJavHsoJDiZSJ1mr9d68sy3P0yAG0iG2lyrmKsupnO95ew+HoUE7Q3+eGqkGplcEadzYwD+xiqhMBlrLgAGhGCSnRXBM4BJ3Gh7Py/Am/awln3Dib4S52bmX9TbydAN7ZhT54nMbumrv/jffX5qJFwSqEGtKwNXcmbFpYYTAoxOJ1eAu/0xf8RYMBiAzxKoOyxLV7WwP6dDSWmxEMBCSjVz8ZvaI9uUcPH8DM629T6wAze2wX6NbW4PfvgyDUtieMToXFYsUHi39Cx87dsHXbDryzqS1yncGq3I52qgf7pNn6oRSQ9WptD5T9TlP8e7DXccqUKWXOIbzjjjvx6FOvITm1AN9/PR+ax62UvC1WqwqAfvyNDUs2c4i9lxsvs+DGcRzL0Pj+Xk7J6DVdhg4fjYGDhuO7DeuUYqG/Meq9fVq1hRkxRmp3JjixI8GJ+CSXKntraNiHp2nlb1z4hWdKPTmjeSiQ8jWePO9WEcuo0NovdhUpMR4/dgTr1izDmaRTxe6zcstFJ49R/r/eVjUnz1du2qGFod6cPMKoHD8nNVFpZf8GyzhY+ulvGCFkjyLfQ/brVZR5++9HK2G1WMucQzisuwmvPhSJCVdfB4M5EkNDlsOkKyjMRnIoLaOiHIStLme9FyqcbTnswpfbHfjkWxv+/EkebnkhC3//PA/bjzpVEEVovvDzefn4Sap0k0rShJk9Bg/4OTqXUfveV0Hwd08Yr3/8zivYs3sH9m9bB4uWovrB2ZNHJ4+wFJ9zVtkvLU6e//DNHbzzzjtVhpU/K5pD+NvfPqEc7bYtg3HphDlwezxYufxztQ9hyeTcK4Pwu+uDEWT2Pv787+x45pM8VckmlI9k9Oo5o+fbnNsK8hEUHKL+7c8UsFIBcmoYHFfzul86eZxfcibNO2OGjhPnmoRagT6dTA0W4Xc4NTVs0mrSVXgO3MCzHHBgnLHOe9UaGpaasC+PTl5Ne86q0g/Wo3d/TJp2A4YMG4kRoy4vdHo++MqG5Vu8ETZ+Vv52ewji2lStzy6nwKNKTTlmoD6VUvmd23PCCe4Fqutg0jFlNrl3x7rrJaQq6L5y+vWKwkxfyTmEJctWKDe9aMHH0FtbwNhmkvq85Ds05NtYIlr88VgOzYABNz38vpeEvRG3jLdiRE9TwJStSEav/jJ6PtxuN5xOhyrl9Nkviimx34T94SzbFoRA6gmL694XV18zB/vzx+GMsw8emBKEKcMthWs67RD3NnU9b1Yonu0rbw4hq5QYfDyZlIkNaz5G774DCvcd5HSKWwUgk9K8Roz7n8dnBqvKoMaCsx4zek1btSNA4R+FTl5qyjklXT1txo0IDfWWVtUWOkAUJMnO09AiQlfjHjh+gdg35VNAjI3wzvuiA8gZJ3WpjFgemXmacmQry6bw3FjYlpnjadKOHt+L48kuFd3yh5NHylOysliC0KtPf1wy8jJ17FymG/+3JB8HT3uj+Cz5e/rmqjt5zA7Z7DSuxnofh8HvX2y4HsfOuhEaVL372l38XtXtZyr8Qr/ekSS3CrKUt0n3zSGsCLPFgmtn3giDwaAiplWFm5+Dp1346ZATPxxwKrUxZgH//nk+hvcw4oEpwap3QWh+8LNkMATh1Mlj+Pmn7zD9upsQZLYo/QL2Cet0RvlsCA0CHQZK+BcX+TDCYg3CUdsI5eRdN9pS6OSxwoGFHb3bG8XJq2d8cwjLVaNuY4AekfBcfTPatQov9nuK5bx8bxjeXJWPjXudKjj59Ed5uOEyC2643Nog+9NARjJ6DZDR88HFaNniT+F2OTHz+tvVpswfsOwrooZZB5Z9MkPEPquSG3A1wiBbQ+8O9W/IGa3Yf8qlMhHcCFell4/3GRRnarJf+mPJLiSlFu/nqi1l9YPxc/mvtz7HpWMnwu3RYeXPdny2wQbbBVvauZUeT90YWq1IPkst+BnjZ4kDxOsbCpNwqCrn7VS1vp8ZEn7+hnQzKcXXuoSf3VMpbpw451bN4f74DHMo7Y7tm7FnxxYc2LdTOfV3P/jrSpvXuRlas82OpZvtSmmRMLhwx8QgTB5mbtDsnmT06j+j56MgPw+LFnyIiIgoTJ0+RzmAXHdZ4t+zvbHOAyKCUF5PWIHNBpfTa790Bgv6X/c+ckIux8heZvxujndWHgOlXM9ogzjIWgg8mNljQJaB5eQTO3H61DFs+WF9sSqWo5kd8fbqAjX+gPTvbFTZPfZbBjLOeszoiaPXgI4eKSjIx6LPP0R4eASmXXuDMpa1hSV1jMgPijMXzhGp6sZgP0va3N6sQnkbZPYoDehi8lsWqSpQsIMbc6boq7Lp9TZXa+pLH9kERVlY3kf1MA7+9vcmzlcSuG/PNsS2bIPf/ulFtO7QHd/scmDZZpvq8fIxaagZd18dVK1yXt94Av5tqIDZEPDzsSvBqWZPVjXrS+eUThd7COoDvk/Hz3K4r3+cvW1bvsddt1wNj9sDt9tV7XEK/My9u64A63dfjJaP7mPCL6cHN1g0XBy9hnP0SFZmBhZ9/oH6/Ey4apracPicvV6ygRYagM1bD+GfL7yMowe2IiiiPdLb/wnm8Dh0aW3AP+8MVXs57pHScygipEfbOh7pI9QOXxnnmjVr8LuHZytti5L2SxfcBc8vysPpFG8pJwejP3ZdsArKBioixtKM4KDp6dfdiLS0FCQlnvTLY9IBYzlCRo672sNEcyvJmNFxZBSMZZz1CcswSVU3u9xw8KZNsUmXPZSsUWdfgT82cCXHKZCn//Yqbpr7MIaPmYJFO1rgthez8N81BYVOHoeF//W2EDw0LbjaPZssLabjwoxeQ6HKNyP0sDmqfh+qz9Zn5Jef9S5tDErum983bk5qw/IlnxYayZJCO1WB68JjM0Lw7K0hqqybbD7gxGP/zcHxZBHiaI5EREapAOWJ40eRnpaijtHpZ38plYDZEyoI9TVO4Y4778WpVA/++OzLmDrrbvQcfh0s4Z0RHarDn24KUU6eUubO8aB9rF6trUJg4yvj/GnD8nLtF0XMXr4nDBMGeVVasvI1PPNpHt5fx0yfiIhJRq+BM3o+ODfEbLaoD7KeKbNawuZ4fsCrKsrCgc17TrgQzuhvJbdnVo9Duft3NtVL2R0zG7uPMYvgnXtSVSj97XBrGBJXv9nHuobltftPuhAdVrXsZnVLNU1mC2bd9VcEmZz4MWc27Bek+UnrKD1mXmrBlYPNNXruQMjmFSvfPFa1LDE/S+zP42epvlXZ+J5RWTUxxYPI0NIl1bUV2qGS58KVP1XrsZjde2VpPrbHe40upcp/eW0wLut3QQ6tnpCMXsNm9CqyXyz5pTAYS+P8Ne5HECqS7/e1Gtz14B+Q6wrFlpyZ0Bst+MfcUFWJwUoOBh9iIgwNpjUg1IyhQ4dhx47tldqv9XsceHNlfmFrSaeWepXd69o6sDK3ktFrhtBIchH6Ysk87N1d+sNcXeiYsgY9Pdtd5QwRl7yqbGKDrTpkF1A1sX4iJbkFGvLs3r6g6mAxAXaH9/5NBW76T6e61Gvzh5Eqa5wCjeb2jZ9ie+405eTxuS7rZ1IR0TcfDsOkoZYaPzfVHFk735DZvKLZ6bBgbz9nZTDTTSe3IaS3+V53bmlAl9Z6Famk01kTyhq8zus8Xl2Y3fvTzSG49QrOMKJTAby0OB/vf1VQo7EVQuO3X9xofz7vXTWGxff9okIyM3v+GPkjCJWNU1BZHlsBvl77hbJfLljw6IzgwnJ7CrqFhegQ11qcvMbG0KGlh6+XZb/GDzDj/+4LU7M9ycnzHvzmf7lYuMnWbG2ThNkCCJaT9erdH99tWItjCYdr/XjMflE9kzXOFZGW4+1nY79XVWAjMwPEKVn1Y7wpLsMPanVFH3h7ljc2pfLNjBwNWbneeXX+gE3NRRU2ieZx4WRyAbp3bYPHrwvGR7+JwG9mhWB4j9oJ2zCQwfneraL0ASHPz3Nopco3K/5++IxDQzZ3M3PeIdaohpgzcFEV57QkFF5hT0PR2Xt6gwHX33x3zc5Jp8OcsVb8+ZYQhF7oBaZgy7Of5qnRGULDwTVv1t8y8b8vC7B6q10pqNY0QFBVuAnrGtcTa1cvRfLZpEJnj9lecfaEuoDS/EUVNn3jP06ezYNNC1PjYMb0NRdWcHA/QGXouhbTEvzPk08+WWz2nuGC/bp5rrfdpCjtWxjwwl2huOlybyDS5QE+/taG33+QizPpza/NQBy9AKN334G4ZORYrF29rNBY1hSKTLB8pqJBtsz6nTjnUga5Opv40CCdKoHgbLu6hH1J5zM9KotYE9grwvNsCpEcvoakNM5Xq77TW155rzOkP6AvHiXTG0yYOG4UnrklFOMGmP1Wtpxn19Q4g6oGFOqDiBCDKuutqI6f3yGWTFZH2KiuaB1lULPK6Ojxu1sdSg5ev+762/HL3/wVu3Zuhc3mHaheE1ge/vK9oapEhrAc9tf/y1WKoULDQOXkw4lubNrvxLtrbfjte7m44R9Z+MXr2XhteT6+3e1Acoa7QqW2mkDb1b1nX6xcvgCZmemFdkicPaEuGDx4CIwlsjy0Z6aYIbi8vwlzxnqVzLlWckQMB6I35ZFLzWX4+pAhw3DNdbfi7od+h/17d8LNCHIJaNdvGmfFi3eHKk0Bcui0G4++lYOVW+xNYk9YVaRHL0B69IpC47v+61UqMnXlpGtr9Vhc4LgppEpmyY0qnyfhjBtnM2om0c+MHvsv6lJG29ePRvGHmjg3Sn0zR8OAAOgJqy2pWd7RF5xpWFtHj87zX+blIj4hHqeWTQDcNpXJ885bC6qyEmP1ntM7g7F1tDHgxlScUXMj9WV+flKyNfSp4895dTmT5kL8GY/q06xN/6ndbsPiBR9dEIW6qVaqvwwc/PuLfCXQQqwm4BfXBOPy/nXXtyc9emWz5ZADr68swN4TTuTZyn//YsJ0GNDFqNTpBscZqzS6pjJot1YtX4CWrdpg5OhxxZSTWeLbq7307Am1h2vzdz8fxuQrhsPhsKnNvk5vBAxWjH9gA155bIDqZ2awOOOCwmYbUdhsMnA92XYgHauWfogOHTvjyqunl7svsjs1fPR1AVb8fFF9jXuRR6YHo1PLhhHkkfEKfqCyuRKB7Oj5jCXhxov/rs0GjM5SWLBOzTYqKuSQnO7CkSQPYooMRq9ueRCb7Pm4dUX8GZdySmrTzE+HlLPeWPrWWGH0ad9Jp+o5rO1mjJH8P36Yi5QLCpo9wg4i8bsnkZ56HiPHXIG7H6h8tlp18c2gG9zNVG2VzvoSZeHQ95JOE0VHLGagX6fAmseogjRn3Uopt7ZzFHOys7Bw/vsYMfpy9O03uNbnteh7Oz751gbf6jt+gAn3T6mbEQzi6FX8ndt+xIF8B/tU3Goe1eEkNw6zjLN4tZuCf53u7QwY1t2EUb1N6Bhb8xJrl8sbNCIUaPH9W5w9wV+o/csZD07H/4x/PPM4Es9kQIsejW6XPoLXnxiAyBC9Utik/eeA7S6tDAHRMiD4D9rnTdsT8dXKTzB1+vXo0LFLhbfffcyJ11YU4FymT8UdmHWpBXMus9Z6ll11EUfPDzR2R8/H/n07cejAXlw782YYjTVzVFRWIsuD2EgDOsYaVBlNSpYbx5I9qrfGWsPXxt6/vDrcvHOjsjPeqc6vNo/PzQX37xye3lgXepafMrNZ22wenfMn3skpHJMw7RITorMX8VOCGbNuKezfohonhVp8g0mrMli7wvPP8aBVpF6VzgQiRxJdOJ9VPKvHTUJqloY+HQMrm+eDZdN0/jn2obbOf25ONkJCw/z2/dh+1IlXluUr8R3SMlKPR64JwsCu/p1rJI5e9VU3meHgOIz9p1zYd9KFvcddKChjzAjLnUb3NqlZiV1b12yT/NPmDcjMSMfVU64rvL9PjZOZPRlULdQ0eM3qliCTG/M/eRunslpgZ97Vap/2wt1hQP5xZb/27N6BAQOH4C9/fhK9enaXN7sJwj3NtoPpiImKqFIw0e7UMG+DDV/8aFdjyAiF1u6dFKR0COoLcfT8QFNx9HJzs7Fo/gdo3aZ9MWNZk4xQZq4G3p1RDNars1eqtg7a+Sw3+nQw1clG2FeqyE1ibfBJ+g+Ka5z1+VRF5YaMYgq12dBzgWMm70iSN1vMSNbtE6w4f+4MwsMjERQcUu7IheoM1m6Mw+s54JllblSG52ekqAx3z3aGehkj0tCjNsjG9WvRuk079OzVzy/nxlLOnQkX+yfoNNx9VZCaYegPxNGr/XgFbjgOnXZhR7wL2+OdOHGutJBOh1g9rhhoVj271RElSk09jyULPkLf/oNx6dgJhcd9zl7PdoEZRBECF1ZgcM1jkpgVLs+8cxCnc1oBOiOeuikEsaaTxewXxTso4sH+LvZ5CU0PJjIOnrJj66blGDhoGNp36FSlarHXVhTgWJEZsMO6G3HP1UFoG1P35ZwyXkEoJDQ0HNNm3IhTJ49h8/ff1vid4SaQ0VOqNTLqwcyQP7Jw3EDUlaolSzbNfgiw8LVz456b3ziVACkJzQsFcGrD/9YUFDp5Ewea0Cdsuyrba9W6XaGTV97IheoM1i5ThMXKrFNgOks+0R7O2WEPER08Dij3yXAHqpNHOAOwZYReDaH3BxERUfjmq5U4k3Sq1o/FcmsqctJwsl+PsH/vwdey8b8v89X3W2h4uIZzJuodE4Pw6gPhePuRMNwx0ap6WHycTvHgw69tuPuVbPz5k1x8v9+hMoOV0aJFS0yeNgu7d/6MPbu3FR5nvziDp1TjlM+BUFUY7DyS5ILL7cHOnzfi75+l4mROO3hgxF1XBamy45L2i6qcHMHw4osvyhvdRGHgsHtbE4yWUKxeuQgZ6amV3qdbW6MSEaN9CvFq9mDbURcefjMHH35doCrBmgoBHUrjF/Thhx9GVFQUoqOj8cgjj6ja/+aGz1gePbwfBfl5tXoszgHjxV8lWnQa03MrH+FQXfglowPprzECdGopytLYoIPKPiyW21LOvqZs3OvAup3e+qw+HQ0Y3W4Ptv78PXJzc6o0coHXebwm2OyaGqkQyA4TYWaBoj2to/Xo1oaZPFPAy3Dze9w+1rshr0g5tKoMHDwcffsNwqoVi5CRkVbrx+NndvpIC958OFzNYvSeJ7BiiwP3vZqNFxfnqTJPRjeFwKBNtAGzLrXipXvC8M6vwnHHBCvat/BuFVjqxAztC4vycc+/sjFvQ4EKjFQE+2bGT5yq5sMWVcej7eCFZdPsGxaEiuD6xiwMs8F7t32FXTu3I+m8dz80aagZ14zwij7t31vafnEvyYye0HRpHW3AtVOvREzL9lix7PMq7ZUN+gv26ZFwXDnYrPqU2Qqx+Ac77n81B0s32/xiVxuagHb0/va3v+H777/HgQMHsH//fmzatAl///vf0Ryhsbx17kMq8+ITagkE6EA5nN6B0v4kI8ejeqT8JYDBDUV2Xs2HTTcUzNSk52q1cnjpML+12iufz8e5YchpbNm8HhOvugZt23Wo08HaLJvV6XVqjEFjIDRIr+YsUZ2tpr2r9Q2zI+1aMKvn8YvjOPbyq9C6dVts2rAO/oLVBJzF+I+5oRjU1VjoNGza58Sz8/Jwx0vZeGVZHtbtsCMx1f+y/0LNYNn8rDFWvP5QGF66JxRThpkLZyZyXZq/0Y67/5WN5xfm4WhS+UHY3n0G4Iab74bBaCxmv7gus1LhaJJbKcnK310oz45wXAttWWL8VuzbuxvbcqYg3xOFgV2NuG9ykFq7eLuuPQeXGrnA8s0hQ6pvv4TGA//+HVuacN2M66A3WfDTjxurfN/IEL1S4OQa17O9d6+SU6Dh/a9seOA/2fh6Z+Mex1Ct8Qp9+/bF3XffjVtvvRUtW7ase+emQwe88sormD17trq+cOFC/OY3v8HJkyebTY9eSbKzs7B04ceYNG0mWrVqW+nt/S2qURaM6LaN0aNLa/8IbTA7SHUkZoD8qdRHAZreddRPWBfw88u5LxwYH1WL3raXl+Rh415vhPOxqXYc+vEDDB8xBsMuubTM2/uzR4+qWHREKGjSWIVwGgPsv9x1zKnK8PzxnXE47GpDzrELdUHCWZcarv7jQWbzSv8+yEwxEINaV1iWw35i9qdGBHsdA69AE3u9PBjd24KoWg6zr6298LdtrM8evZp81jbtc2D1Vgfizxb/47EPl72/HNVQ1vf93LkzWLtqqRJ+Co+ILPaYWfkaurTSq2HHvG98fDxeeOEFlYnhJp0Dk6XHqvnB7wFVY3lx5CTii8WfYk/+RCQ7e6hM8wt3hxb2VbNXy551HLOmXKLKNZnJkx695gVLyvcezUKmjdU5lmrvO/g5+umQEx99Y0NS2sXgKQVbuLaxV5lVcU1WjGX+/Pn44IMP8N133+Gqq65SgwunTZtWK+n/8sjIyFDlmkePHi1c3PnvHj16IDMzExEREXVqKDNzPZj5t0wlXMKNk+pts+pUNJO9J1Tn4wakY0v2vdWf48DX9PW6FTh98hhm3zC3mLEsib9FNcqDc/ooGEL1TX9k4NizcSjRiZa1lI0vCaOBFBLgwOnGAD+De0/UTGjD5+Bv274dabp+iBrwMC67pCd+PycYJ47Ho3OXbhUugLw/e/J8AYK7Hni8Rp8ZivX0am+qtaCOUDln0yg37lY9e/5yqk8ej0dCwmGMnzClThx1rh1bjzhVzxc/6/n26j/GUzeG4PaJQbU6j9raC3/bxkB29IrCLN7Kn+34bp8T7iIJ5S6tDZg52oIxfYvbBAYPViybj7zcHMy64Q41s7Po+VIwjDbVkXUcw4YNlc16M6Wok9+r72BMnfMY+vXtjoMnHXh1/iGcd3ZSezJmYFhq7BN/YhCoVwcjTp1IUD15viDBE088IUGCZgTXksOJLuzcuQseR1axeZ5VhRm8b3Y58NkGG9KKtP1w9uh1o624eqi5VjoXAevo+UhKSsJHH32kLnTIbrvtNmXY+vTpA39x+vRpdOzYESkpKWjRooU6xn8zWsrftW/fvtjtn3nmGTz77LPFjtXGUJ4678bEP2RU6bbciFN+mtFMlhF0bmWoVT9VZVRkLIvy9G8fxNKFHxarV6ezN3POXDz7zzf8dj4+VUW+9trKvPPLteeYd9PAMjp/f/mprkiHtL5nptRnNq+kgw+9CXqDGU///XXMnn1jnQRmGtvsvCYbyTzuzZD5Y/A1STmfjCULP8KgISMwYtTlqEv43T913oODp10qes8h9klpLNfSijkRJfnb7aFqDlJt8FcFSE1to7/tV305ej6YSVn+kx1rt9uLzehjFPymcVbVn+lz+Ox2GxYv+EjZrWuvu0mVcxbd/HDD/uY/H8aShR+qjIwPZmb4Xr799tt1+lqEhnfy6Jz5MnLcs5jNFvz2L2/hixNXI6cAMBq833tWiviUOFlZ17eTSVWQCAL3el//cBjrVi9Qgco+/QbV6E1htcFXOx1Y8oNN7XN98HPGvr4pw81oHWVoeo6ej40bN+LRRx/Fnj17EBwcrL6c//73vzFoUM3e0LIyevzSx8XFqWP8d/fu3eslo5ec7sZLS/KRmOJGgcPb25Vn9y4olUWdOXj5sn5mXDHIVGdDOu02GxYv/AjDhl+KHr36lnmb2VNHqMbkkvQbMBQLV/7k1/OhSiHLbtq1MPpBJrf28+LKg7PS+nUy1moAe33A7OO+GmbzynLw9XoDBg0diffnrYXZckFiqo7hhk2pYbVrHBnUpgDLqDmSxF/jFsiJ40exavlCXHHlNNVrVd9wHadyK3tsWd6XW6Ap48sRMek5bsy6NAh9OhkDwtHzl21sLBm9kuQUeFRJ58otdvW38sHh6zePt2JUL+8s05ycbBVAmHjVdLRr37GUwz9zyggcObCz1OMPGzYMW7durZfXIjQM9913n8qOF3Xyab+69bsUGL4AGgx4dEawKqEjXAvYT0WnL9DtulC/cL++7Mut2LJ5HabPuLHSgeqVOWYb9jiw+Hs7zqRfjDxyZR3ew4jJwy2q/7yqdrc+Hb1qW0f2x3344YcqYkkFzLlz52LZsmUq0/bqq69i1qxZSEhIQG2h0iazdrt27Sp09Phv9u1V5uT5S8GHqmNl9eix3IgbquQMj2oQPnHejcOnOXDZ+0ZTCn/5Fru6MNM381ILLu3jn7JGHxarFXNuuksNUWeGT68vXa7FkrvDB/eWyujVRFSjMqxmr7PXNoaz+nQ13picOu9CsNX7wa0LjHqvExXIBoFlsBSkMBm9qlDVpSzVTI/HrVSo6svJ46LDLIwMRK5f6OBR4ZTlzy3C/fMd6tylO8aOuwobv/0SnTvHFRvFUR9wLWDJPEd0tI0pPUevU6vAEPqpL9sYyLCN4YbLrJgxyoJ1OxxYuMmm7OGpFA/+uSAfcW0MuHW8FUO6heGW2x8otF9Fqwy45nHI9bEj+4qtYyKo0TxguWVRJ89nv06dyUQHGDBnrLdPylfFQMGy7m31AW3ThYaBVWFTrxyOrKwMfL12BW6/86FiFQTVgcGyKwd7P3tbDjux6mdvuwF3/T8fcalLdKgOl/c3Y/xAs6rsCxSqldEbP348fv75Z0yfPl2VUFx55ZWlNuTh4eHIzs72y8k9/fTTWLlyJVavXq2uT5kyBTNmzFDHA02Mhc9Fx2/3MRc27XeqD0BR2kTr1QLFgbP+dPjI6hULERXdAqMuHV9hCZ/BwAZ5oHNcTwweMsqvwiy+geyD4mpeOnHyvEuVzMb6uTevKIz+cVDvkDiTXxpq6ywrc9KFmAhdjUqAmdFbvOBDeNxFHXwjZs65068lu1Xp2+TnwVhP2QTBC6sPOPyd77o/y58zM9IRGRUdUG9zoAxM97dtbKwZvbI+i6u22rHkB7vKuvjo18mAu68OUlUgC+e/rwaq9+s/pJjtmjl5OBxFhl6bzWbV9+gr7RNxlqbJ3ffch48+/KB4sFJvRHj3mzHzvlfxxOxgZRepyp2a5UG7FgYVUBexL6E8zme6sf1AKtq2jvZrGwkTPau32rF+j0NVmBSFa9voPmaM7GVSFQ0lP58BW7rJqCRVxVhSWR4ej0dll/wBozosf5k3b566zuemCic3rYGuusmI+re7HVj1c/ESFi5I904KQt9alhqVFExYuXwBxl0xWRnMskQ1dm7fjOMJR6BBU7OM6kKYhaqWLNOrSb0yy/xYcsah2nXdP8fy0H6djbVSsqwrqDi674QTLo83Ol4Tfth6BPfeOAKa2w542ONghMVi9bsIT0Uwu9uppR4dYqVssyFg1pq9blZTaRVOlqJzFpVveaSiZVW/c/l5uVj/zRqMmzAZISGhaGgCxdHzt21sKo6eD37e2MO37EcbCrzjPFUgYvxAE0a1O4xtm7/EtOlz0KlLt1K2a++eHWjboSt+3LgaTqdDlBSbMPzMfvX9IcyZeolS/qWzp9OztMWKy+7bgH8/PqBwo56W40FUiE6Jq0kwUaiMxBQXdh9OwaE9G3Hl1dNV4Mif69sPBxzK4dt/srSMNHuVR/Q0YWh3I3p3MKrPcMA6eo2Jhnb0imaQWMKy+Acb0oso94zta8JdVwX5rbRt394dqrSqpLGsT2EWSukHWXSqB6460TVmf/af9H8GojxoIPjF47y0QIOzpChZHhtec+XEP3+Si0O7v8f5Pe8iXHcKgwYNrbFqZm2yuwPjjEr2WmgYGO0+esYFj4el1d4ZU8ywWMw6tI3WI8SqR3aeR5XVxYRXraePwbdliz6BR/Ng5vW3wWTyn7FszI6ev2lqjl5RG7Fwk10FQBnMIhyTManzVjjTd2LWnNsR27J1qfv94YkHsGIxS2JFnKWpwjLMhDNunMt04+DOr/DRR59g++7DsMQMQNfRD+ONJwYWBmc5M5StDX06mhrNvFOhYdE0DQeOZeOjjz9Ai5gWmDr9er8lpYqSnOHGhj1O5fidPF9aRYxCQpzVx30yS9lnj7HWet8rjl6AzNHjBmvJZpsqYXG4Ls6KunmcFdNGWPxSzvnjD+uRlpainL2GEGbxbvA9GNzNXOVZXg6nhkOJLiWwUF819oFavkmHl4qj3IjX9PO2M8GJ5+clYkTIYpijeuMXd05FfUMjTJlrmZ3X8DDSeDbdrebNcR3jWJjoUD3MF6LiLK9lYOFcRtVLpvPz87Bo/geIbhGLKdNm14mxrCri6DUuR8/HmTQ3PvjapuZVedEwNPxr9OgYihtnTioV5CrPfok4S9OA69Cxs24kpbvhyk3CsiXzcLRgJI7ZBql90j/vDFMjO3x2kjacVVH+UhcWmgduj4Zt+8/j888+QI+efXD5+NJrjT+h7WU/Hy8HT7mVMmxJ/nxLCG4ZX7fjgeRbUk8w6nTzuCC8+XC4mi1EWMLy7jobHvtvjipbrC2cFTJ56iz1b5ZnFoUCLMzgFcXfwix0VvlBZtS2yhG8ZLfKKkSF1t9GhGlz1lMX7RlpaPglpQALo9w1dfLYs/DxV+kYErwS2Vob3Djr6hqfDx+Li2JNXgfl1VtFSs9EIMBMV7e2HPtiRr9OJlVW7XPyiF6vQ8dYgyod4eapKgQHh+CaGTfgbNJpHDq4tw7PXmiqtI0x4A83hOC5O0JUOwMLOXdkX4HP9o3Enz7Ow8lz9krtl4izNA1oM06l0MnzwOTJxKoVi3DW2RvHbAPB+PdvZoUUOnkMXjB4xTVNnDyhJnvUwb1bYvLU2TiwbzeSEk/W6ZvIGY8zRlnxj7lh+PiJcPzhhmBMu8SsevZ8sKSzrpHSzXrK6JWVeXl7dUExmdaJg8yYe6W11gvY9p37sH3rZhTEXo+0XJPawOnyj2PNq5fD7bLDXYfD0+nk0anlTMGKIiW+CN6ZdDdaROjrdO5gYxieTgGW/adcahhnTbO7G/bY8d26z2DU2dF50E24eUJ4tR+Dzh37JX2nwL8he7iqek40wozOD+wqIiyNiYSzLpzLqJ4abWZmOiIiohpUBEEyeo0zo1dyzVm/24EPv7EpBcXO5h1oYTqNzgNn4YZxISowV1JYzDdb7euNWzFiSE8VsBAaH74A5/FkD8KDPfj80/8hKSsMW7KmQIMeD00LwqShlsLPCeeYdW0tvd8Cal1h99OeZFhCYhpMq4GaFruOuXDf5CBYTHVbuikZvQZicJwJ/3kwDLeMt8J8wdf4epcDD76WgzXb7CrbVV0Hi/f73fs5eG5FC2TkOJGZsBy7j9lx8LQbB9I6os013yCow1SYg2MQHBKOy66YXCcZhOx871ybiuDizggeexTr28kjLC2kYAiHajY0dMSPJ7sQbKnZOAXCxt5P19sRb7sE8do0zBgTVu3H8BlSZn1YfktnLSpMr94nZviqAksE2f8lzfGNC5Z0csmp6t+ZREZ6hUe+/+5rxB89VIdnJzRluOZNHGzBm78Iw5RhZpxzdkOIPg2Hdn6JX7yepcqeGIxkUPLKydcphemwsAiMGTcZx895VOlxVbPRQmDBecUnznkQqSp6DDhqG4OtWVcpJ48q5T4nj5tYBiBpW9rFBI5svdA4sZp1GNavFXRwY/WqL3D2TGK9n0NkqB7Du3vnitY1ktFroIxeyebN/64pwLajF8stW0boMGW4dxxDeVF2Onc0gj8edGJXgquwuZ0E6bIxImwRHKZOyAm9Cum5Go4fj8epZRMK1Rj1BhOsVguW+Dmrx+xU6+jyxU6oesm+vIh6UNisLKLSrY0BbWIaLqtHAxZ/xq0+A7UZKzHvi5+wdHc72LUw3D85CFMvsdRIgrhttAFd2xgKI+QMOBw940ZKJs+vYoEYqjkyizC4q6lYeaAQ+DDDzpEMTlf1BZG2/fwDtm75HjNm3YI2bdujPpGMXuPP6JWEAkLvLT+B1gWLccI+CAn2EWog8ZS+Z3D/DSOKZ/UsFry7cAu6d+uGLq1lYHZjgn3BtC2cj7lv109Yc6QHtiZ4bTHVWB+9NrjQ3jDYGBmiQ8/2xoDqqxcaNxk5bnw4fyUSTxzG7BvnFgYv6wNR3WxCqptVhefKxvT/fVmgsipFYX06+xg4jJHrXkaupuZ3JJwt3dzJ0r/L+plxWX8TgnEOa1cvwczZtyE8IhJPPvYAVi37qNh8NTp7M+fcgb8+/6bfXgs3GPk27wy1kopYFOrYf9KljldVsKWuyLV5SxSZufL3bMOqQgfvSKK7yqqHZbF9+zZs/m4dduRPgymsM17/RVi1N3b8u1D9rk+n0lK//HseTnQhJ798wRx+fs9nedCjbcM6zkLtFF+PJXPQevUcPf7t13+zGscSjuD6G+YiIjKq3v4M4ug1PUfPV12w9KsDOL5/PTbnzIEbZqRufhxZR+aXmA/qVY5+4s+vqZ73di30aN/C23MqBLYiMIO9rADaseVb7NyxHZuzZyLX0wKDuhrxp5tDCj+ztE1UKqTCJlW9BcGfnMtw4Z33P0Nebgauv3EugoKCm5yjJzuyAIF/qFG9zRjW3YRvdjmwfIsdianeFN3xZNawl57N4YOZsRG9TLi8v0kpUV0shWyH2+Y+BIPBoMRZjh3ZWcxIEl5fv2m7Mqz+cnb4oc12e1R5JuVjfVE59m/Fn3GpRbuhnTwSYtEhNUtTfSHRYfV/Pjn5HvV3DQuuuZOXEH8IP25ah/0F45Hm6ognrrBWe1PHrJ3TDdWvWNaCw2PMzh446VRZ5LJ6SFmqy89hbKSU1TRWmMnT4FEGozrlJLwt1ctysrOx4ds1uHbmzXV6nkLTh+vh7Kv7Im1UD5jXO/HtrgLkn99Tyn4xs3dg3w712bWYNSSlupXyc+dWnJPKwGjD2xmhdMXP4SS2KuhwZP827Nz+M7bnTVVOHoPav5tz0cnzzfvkfF5x8oS6oFWUETffOBPvvvcRfvh+PSZeWf9K5XWNOHoBBssSJg2z4OqhZhxOdGPrEacS6aDTxxEEJCxIpyKX3dsalYPXu4OhXEeBTl5Bfh4+/+w9VZ55+ODeYrOIoDfBGdIf/1tTgPunBPnNMLL++Gy61yloEc7smdfJ42iJQBlUztdqMnnl5+t7U8BmYJYo8Slrmi3OSE/FujVf4ITjEpxx9lZlqJdeUHStDpl5GlpH6lVpTHnQKNPYHjzlQk6Bp9gwd5ZsKkexnQyubczwb8ysLhVprdUcj8d1ZvLUmXAWXVsEoZbEhJtw29gsBJ39FAva9kRSxgHVdlCWcjSdA5a/MxjFqpE20RTtMBQO2BYaHvbZ0cmzmnRIP38SmzZ+hb35E1SQMjZCh6dvDikMArPvkraFA6ZFYVOoSzq3CcZNN9+I5EyjX5MegYI4egEKnY5eHYzqUpTqRttJUHAIunXvjfPJSTCbvTs4X4+DprcgasAvsHqbAx1bGlRfoD+gGEeIFarkL9HK2TfeQZGB4uT5oNPM/kVm9bwN4XUPZwfS6eV7Ut0yuaJERsVAazUZRw52UNfvmGittrANjalRz5KnyschRITo0bODEUeSXKpnggaZ93d7gO5tDcq5Fxov/M5yxh57aGsyhJj9UrycPnUcRw/vx/iJUyWjItSaqKgYdOjQHlMuT8MHR8xw0s+js6f32q9x1/6q2O3pFLBKgUIfGReye2xpEGXOAHDyEl1KfI4lmz+ltcKOvClIdXVGeLAOz94aqpSwfWVt2Xka4trqlWCbINQlOp0OvTtHwnLWjR+37oGzIA2jx4xvMm+6OHqNjMo245ShfvfNl1U5CyOddz/4a5XJu3TsBOTkZMFkMiPl3Bns27MNbpcbmk6P3IOvA71/gXe+7KqEOHr5aeQAHQFmBgrsdPBqrihZl/CcjHoNSWluZWzqejPATB6l7FleVFMDlpubo4YHx3YejXWHOqpj7Gtgr2F1Yf8D+z+rWhZDR31AZ5N6v1h6yveMM7ECzYEXakZkCDPx5ZeJVwX2OFCF02A04bJxV4mz1wxgAJJiYG434PJo8Hh4jCquF29D06W/cGHfOwNMDP4VtWnl2a8rr74Webm5eODhJ3D46Als3rwFdqcLOr0Bv3v6ecy69TE8clO/wuoIBi1aRBhU6R+rEGIj9ejQQl9toSHBv06eyQjYc1PxzYajeP/nPvBonZXa9LO3hqjeSsKMCh10Bp45h0wQ6gO9XofOrQ04FhuGlctWwRoUhCFDRzaJN19UNwNEjMUflDVrqOisPB5btngeIiIj8ftH5xbejhsyTWdBhxnfoGOnbvjX/WEB0UNXX1BSnr16vTsalbJknTyHR1MlkhyjQNEARphrUipqt9uwZOHHymHfmjMdB5N0auP0yv1h6NKqekbR2/+gYQBVMkW8QAAz7xp2xjtUdrY2gZmkxFNYvnQehl0yBsNHjKmz91bEWOpfjIUbcZb3MpvPzJkOOs47V46bwQBVKsnnM3E50ntnOKnpmh46gd5sDasaXG7vv6F575+cGI87Zo2Aoxz7VVCQr9a+Ll264ZH7ZsNms3t79vQm6AwWDLr1W/zmtn4Y0s1U6nxZscH/dWhhQOtoEWupbyfv0IVMnubMxWefvo/E3FbYlXe1sjvP3BqKfp28wWXaI1aLtIoyqP7+QAwOC00bh1PDym93Y/1XyzHhymno1WdAnTyPiLEINYKRUJ/zRnw/33vr//DsP99QhvO62bfi2T88XOx2HKCuNwAZe16HOfxlvL+uAL+4pn6UhwIBljsGWzWcPOdCeLCpWj0d3ERQYdTm9IqaEN2F6BBtFI/YHR6k5XqQncdNUM3LNSmos3rFInjcboR0vxYHv/Qenz7SUm0njwaVjl6P9rLpES5iNXlnDHEjz0h7TWnXviOunnwd1q5Ziu49+iAyqv5kqwX/wjXO5vBWIzBDp9drKvDJoBjnkXK95Iad2Ro6d1UJYKkMoJvOqNdhtDk8ePW5VwqdvLLsFzPFN95yj7JfvF2hMIvHqdbZhM2v4Rn9y7hioAl3Xx1U2EdMZ4FiW3weqlWzNLlTS45ikHLO+lDX9PXkGWDDZwvmISUvDHvyJqq/y2+vDyl08khajlfZuXMrcfKEhsFs0mHyuIHIz8/Hxg3r0Llrd1itQY36zyGlm00IlrsUE1opokpWVDShrNvRaOpz9qp/r93hwCU9TRjeo/qlgI2VUKt3MPixZDd6tKvcyNBJSst241ymR22KvdK2F++j0zF+7DuiUxtojlCozXD4HzdvQEZGGq6+5nY8+REfR0OLcB1uGmet9mNRHCc8uHY9gkLTgwEK9mJyM1zbrH7Xbj2V6m9oWHiNeouFhoNBK2Z36RypQJgF6BDrLX30ifbU5u+phLDoGF7o12Lej6rQZdmv3bt3KCeTAQjar/1l2C86e870Peqf3+52Yke8Cw9MDcLo3hdVheiQtow0ILfAo8o5W0RwFIMeYWWoCAv+GR3EGbH8vPDy+YKVOJ+lYXvuFGgw4rEZwcX2GCzX5Ew9KjxLhYnQkARZdJgxaSTadewBh8cCSyO3X7LCNSHY08CsXVGKqpIVv52x1O3Gjh5aGMX/z/J8pV7WnGCEl0PUOfLAl50rCTcJFFLZdcyBUymc76NTZZhUe2OE23dpEW5AbLhB/aQzxQ1SbZw8MmTYKCVdv+AnsxpnQO6ZFFTtsmKWqrJvskOsqGQKpfGJWfgDOnlOpwNLF32MpMST8nYHeOaOa/75TDey8zXlgHHkCueh8tJRZcH0yuGqi03PkCFDYDIVt1+8PnTIENhdnNPpVoq/ffsNhqEM+zXx8mEY2s17nGXy/1yQj38uyFMORFG4FkeH69TxPSdcqpyeDq3gHxjU4UzOo0lu9Rmik8f+vNXHhmNb7jS4YcUvrw3G5f0vOuH83DEb3L1d6dm7gtAQhAbpMaRXNHJzc/H5Zx8gPS2l0f4hxNFrQrBxnT0NPmfP1+Nw1wOPl3E7a6GxNBiM6na/+OWvce+k4EJD+fbqAjQn6IhRdfBMmlsZJvYWFNjpFGnePoPTLuw+5sK5DN/YCL1ysuo60rPlx404eTwewcEhOJgcgfW7vdHsYd2NGNWr+llXDj6PCtOpkRKCUBIGeyobwFoduA61iG2FVcsXIjXlnLzhAQYzd6xmyMjVVCSbyrqD4ziT1YRWkQa1Wa+PaPaTTz4Jq9Va6OzxJ68/+/ST6nx6tWcvMTDjlse99stwwX4ZL9ovyvM/dl2wUlMmmw868YvXc/Dtbkexz7O3nFOP8CCdmve665gTyekuvwU4mivsRT+d4kbCWa9Ql8Wo4YsVq/Hip8eQYY+EXQvDw9ODMGGQuVjwlOI9DCp4s7uCEBhEhOjRPy4cVmsovljyGXJystEYEUevCcGGdTauz5wzF/0GDFU/fY3sZd1u1pw7Ede9N4YMvxQLV21Rx9nfMPKC87BpvxM/HXKgOeFVa9OrjNm+Ey7siHeoC+cyMQIcEaJTapn+FDeoiG0//4Dt236ETq9XpTCvr/Q639zIPDQtuNobMEbt2RdDhTORGxfKghF1ltTxc+IP+Bkde/lV6NQ5Dl8smYf09FR54xsYr0CJB+ezuMnW0KmlHoPijKpfis5dQwyn7tatG3bs2IE777wTw4YNUz95ncdZytcyUo9+nU24emwvzF+xBVOum4tOXXpgxKhxhXaOn7XxA8x47aEwXNrHVFim/q9l+Xh2Xp4qSS45t5bVGFzPDye5sf+kUwX1/BXkaE7QSWbrw/FzHjWTlU45nbzj8ftR4PB+nh6+JghXDr7Y/KvKg11eJ09m5QmBSGykEbfedB2Cw6KwdNGnyMvLQWNDVDebkOpmTfF4PNDr9eoDHBISpgzdw2/kKAPJrA+NZtEB2c0JljmS2pZd1oQ9u7dh04Z1mDR1Jtp27Ikn383ByfPejcrv5wRjVJH+k6pCZ5US+r06VD43T2i+HDjpQq7Nm7n2F263G1+uWoKQ0FCMu2KyXx5TVDerp7rpdGkqiEVRFa7traMMKnjFAFdjc1TTsjWcOu9UGaGoMCNcjlxlv4ry40EH3lpdoLKVJMjMeaNBmDTMXGpNp3PH94bCWiy/bx8j/XtVhaWvx866VXktK13Y4r5s5Vc4Fb8T2/KuRZa7NR6aFoRJQy86eey7zC3Q1KxgBlcFIZA5fiYP7380D92798TwS0Y3KtVN+XYJyslLOZ+Mj957AydPJKiSFvZ+ERrId9Y2rxLOonAz0BBOXk52Fn747msl79uxS0+8uCiv0Mm7dqSlRk4eN0eUN28TrRcnT6iQiBD/ZfR8UEhj0pTrcNm4q9V1KicK9bcRT1U9bprKjA3sYkSfjkZVndDYnDxf6SVfx4CuZsS1NeHwkSP45MO3kZx8ttjtuE6+/lBYYakgR9vQ8fvjh7mqRL/kZomBDfZcZ+R4sOe4S/Vjs3RfKB+vuI0TaTke5SDzb/PNlpM4Fb8DO/OmIMfTWmXyijp5/Dzys9itrV6cPKFR0LlNMO647VZ07D4CDpcHDkfjqXYTR09QsIdm4ODhWLNykZqBNX6ASfWAEfaEbT1SQuVMqDMYmQkLj8CtdzyIbj374+Ul+dh21LvrHhxnxNwrq6+ySSiw0CJMryL4glARQRa9Gnjtb9hPxcDSwf278fln7yI3t/GVwTQ2WKHB7AkHUFNUpVtbo1KabAoZfUbCKSo16bKe6NylG1Ys/QxJZ8+XElX41bXBeOaWEMRGeF/z/pNu/PKtHCz5waYCYEUp7N8L0SE5w4Pdx5w4neJS87WE4qRle1RbAx1obyZPh2932fHaukj8kHMLsrUO+M2sYFw1xFIs05yVryGujR6to0X4XWgc6HQ6dG1rVevo95s2qTYEh6NxBCvF0WtGcIFlJK2sFC8/xKMuHY8+/QZh5Ref4/y5M6oHzKfC+cbKfDVSQKj9UPunf/sgZk8doX7yelGOJRzGovkfwOl0wmgNx18/y8PmA14nm2MfOHeoJkNkJZsnVAeWqut1WqlNsL+I695LzUWjsSzIz5M/Th1g0Ht7eeNaGwpVM2s7MiNQCQ824qE7Z6Bz5474csVnOJ6YVuqzy0Hq/3kwHFOHe7N7zFh/8LUNT7ybq+brlYTlrkpwy6JTv9993CvYwvLX5kp8fDzuu+8+DB06DDffdi+++uGQyghHhTIwpOGTZT9h41cLVMuDxxCGP94YgjF9L1af8L3LytXQpZUebaKrN/tVEBoanU6HTi0NuHTkEOTl52PFss/VXi3QkR69ZtCjxwWYg0gpX8zBbk5X+fPTeNtNG79Ct+690LZdR6zbYcdrK7ylmxMHmZUsslAz6NTNmjy8cFi9TxXVJyRAJ489TMMuGYO23UbjHwvycDrFW67Zva0Bz94aoqLTNYHCC+zV6dvR2CQi+ULdQoGOnQlOJdhTV2uf3WbDsiWfQvN4MGP2rTUaSis9ekJRnC4XPv18JXr2GwmnPloNdC/LuT1wyqVGCCWleQqd4uvHWHD9ZdZyhbYoHMLxDnSemUXkOJ6aBN0as5PHERg2m80biDSaYLZYsGTNVrTvGIe3P/sJ7vPrsb9gPDL1vfGnm0LRt8gwdDp5bAXp3EqPDrHSIy40XtweDbuOZODzeR8iOjoG066dU2pkWWVIj57gV7i4Uup4QBcTBnQ2qaGkmSVmC/mgE3DZuKuUk5edlYkBbVIxqKv3A/z1Lgc27m3YumQKRFC+mRfKYlNFzSeYEui8++bLhU4e4U9ef++t/yt08oYOvxRJnuF49O2cQiePs6GeuyO0xk4enXdGr9tGi3EVqgYdPJb31eV8MYvViunX3YSg4FDYCppvH7DgP0xGI+beMgMjB7RCuDEFaWlpqnS1pI1gf+K/7g/DrEstSjjE7QHmf2fHY2/n4FBi2c2pdBhbRujVKICDp13Yd8KpShfrKusdaLzwwguFTp7PfrHP9r+vv4wX39tc6OTZrH2UvRInT2iqGPQ6DOwehdlzblUOm91uQyAjBdJNHG7UaMjYl+GTzO7axqgazWmgKopIHti/C7t3bcXNV96AY8kRqsfr9RX5iGtjUPL8dQ3P79BpN7YddaoI7Jk0j6rtL4nFBLSLMaBLa4PqK+TMpUAsUTqwb0ehk+eD13n8WPwRxPUZjfl7ByPh7MVFY85YC24aZ61V5Jglt2FBFNgIvPdECFw4Y+x8Zt0+B8s3r515k/o3BaFCQkIRHBJat08qNHkYsNy9YwsOx5/A1GtvRkpWlFIbtpguroH8NxU4OYbh1eX5OHHOg1MpHjz5bi6uGmLG7ROspVRn+bjMEoZYvWIi7E+LCAXaxxgRGdp0M3zsT/xxy/ZSZWq0X19v3IYpLUfihHM8LDH98LebQopVDLFlJFMyeUITw2jQYXCvFgiLuAUpmW5kJp1CbGxrmM3VF8qra8TRa+Jk53vQuZWhmOPD0hOqrTGrV9HQ7BGjLkdBQT42rvscd182C698Ga2kp59fmIeX7gkrZjQrKldkJovOTJ9+Q9Sw9pJz/UrC4b1f/GhXGcSq9AXanVDze3j5ZpcDRj3UTKhrRlhUNjJQShX5+g8f3FvM2WP5S88+g5Gon4Blmx3waN5ekXYxevzimmA116q25Ds09GhnbLKbEKHu5unVZ7L8xx/WK7XZa2fdgtDQ4jL5glBdbr5hOt79cCFWLfsUc264Gbm2GBQ4NEQEFx8AzyDo/90bhsU/2PH5dza43MC6HQ6s//EwIs6/iayzu9G3hO3yKnTqEBZU3OFrF21EVBMq6WQ1CCuCTpxzoXP3QTh0oLj90umNQMQAbM+fjmHdTXhidkixUm8Gmhkg7tJar4LDgWKLBcEfcA4nEx9ulxvzlq1BSJAV18y4UZU0BxLSo9eEe/SotGZ3aRjc1QRzCaeM89Q4EDwmvOLxAVzov9uwFgf374G1661YstXbozdugAmPzah4YHdlPWklYSnmkh/s2LDHocYA+OAz8MtEh7VtjF5JONOOsmKGjiDvdzrVg0OnXcrpKwoHAc+81IrL+5saZExCRe+HweBVIBx9xzKc0YYX9orMHG3BDZdbaz1bxWdobc6yPwOCUNn6sT3eoTIh9bFxZRnY8mXzUVCQhxmzbkVYWHil95EePaEiXC433vtoIY6fSsSjjzyE5CyjcjwoHlLWWAmOXHh7TQG27DyCU8smQHPbAY8TBqMJ1gpsV+EMPgcDqUC7FkYVROVGsLHCnkTa1nMZHljNQPq5Y8Xsl05vgNFgQJcZazB14jDcfXVQsXWi0MlrpUc7cfKEJozDpWHn4QwsW/wpgoOsmD7jJtWaECg9euLoNWFHj5mxjrF6pbZWltgCZaPdGhBqrbj3ix8g9pB16tIDT32YiwOnvV4Y+xtY+lIeVJVcuvDDUhmsmXPm4tl/vlF47OgZFxZ/b8fGLYeRvuc12FP3wNJiAEZOfhQzJvTC4G5Gtdmsypdt73EXfjzoxMZ9jmJOH8VM7p0chF7tjQ3q6P37hafx0+b16j1p1boDWgz7HdKCvHPFurUx4JHpwdDbjlc7C1rRZ6BDrB6dyvgMCEJl3/sd8U5lROqrFJqziaj6m5OdiZtuu7/SMhhx9ITKcLvdOHAoHv379oTd6UFiqke1AfAzHWLVlfm5f+CB+7Fp7SfQPBeNiN5gwjUz78A/X36z3MqV/ft2oEfvwbj+jsfRvVs3tInSIybcUNg20RigHT2X4UZSqkcFXOmw0oHja3zpH0/ju43fQPO40LFjJ0QPfwa3z7kaEwdfzGDwdm+//hIO7N2J4cOG4OmnnkT37t0b9DUJQn2UN+8+molli+fBYjFh9g1zVSC/PMTR8wOVebhN3dFjf1tGjqZKGMsT8UhMceHEeU+5Cpxl8eWXq7DxcCT2Z/YtdPbYy1BWZo8jBPbv3VHqeL8BQ7FgxY+qT3DR93bsPu6CI/tYtSKolUF1tLXbHVixxa5KT3xwcO69k4LqvYevZDaPC4DOYEX7GesRHNUVN4+z4rrRFiSeSqhWFrQqn4GBXb1zswShuhxNcqlByFUJtPgLfu5PnTiGrt16VnpbcfSEquJ2e/DuhwswYvggtOvYAwnJLrhcUKWWJas9yrNdQbGD8LtXNuHaUZbC1oXyKlc+/eJnRLfqqpwkVqHwwnJPCh0FqoOXluVGYppHDYmPKNLTyNc4Y9Jw2G125fz67Ndb83/GmOEXv6e83czJw1V2nu+FyWSC1WrFjh070K1bzYKVgtCYnL29CdlIOHkG/Xt3q7DiTVQ3hVrDkkYOfC0rYukjPMQ7FLk6DnHHDu3QHhvRN2wrY5+qr+GlJfmqzKMkzEbR6BWF12PaD8Rv3snFnz7OU04eydz7GnQer5NH3EUUKWtCWJAes8dY8dYj4UrQRI2WAFQPHwflsqeiIRU3PR4P3G4n3PFv4F/3halz5YagImXOmn4GKB4gCDWB/bzsWapPuEbQyWMmZtXyBThxvPisSUGoCXSw2rdrjXc/WoCjh3ejf2cTosP1SMnyzpetzHZBb4IpegA+WW/Dg69lY/1u9lRr5a7Z8957BbERBvUdOp/lwd6TLuw94cTZNJdypAKpRPtMmktV+Bw961Z2qGWkodDJ41iE3z71PGwXnDyf/dJpTny1+N/FHuvN/7xU6OSp+zqdSqnzxRdfbIBXJgj1C9tj+seFo2+vbjiTmo+liz7BueQzDf5nkDB/E4WLd6sofYURBTqBHIheUI2JCX36DsLkqbPQwbgdQyI2QQcPNu1zKufpu32OYlLTLDlkZNNnMFn6ouksOBFyP46ecRcqZl4zwozW+v3wuMtWpKwNzMTeekUQXv9FGAbHecsXz2d68McPczFvfUG9jWbYv3d7KcVNOrXhrn3o2NJQJWXO6sLevNZR0gAv1BwLKxkaaE/KrEFMi5ZYvWIhDh3Y0zAnITQZaAunXD0Os2dMxrwFK7Bp0/fo3lavLnl2io54CoOeJW2X8UKFSb9xj6jrqdkaXlmWj1//Lxdbt2+vcM1mn15MmB4xYTo1wzb+rBs7Ehw4cNKlbFFDOH1s3eBs1fgzLuxKcCLB5+BFFBdu46iJx/+Xg8MHthcGYct6jWpWb7YHRw7sLPVe0NljRk8Qmouz172dES0jLTBawrB08Sc4dfJYg56TNO40QbxjE7xZrYrgwt4iQo/EFG+/QlVhtH3GrJvx/XfrgWgNO457naeXFufjnS91yqFqo2a2tcfMJ77D+i/+jZTTu2GJGYCoAb+AObwrQq06TBthxrRLLErC+vT6IUg4UlqRkpFVf0CH58+3hOCjLw7i7TdeQkHKHvx70wDs3vco/nxf/zot5czNzYbRHKya1zWPu9jr69d/SJWUOav7PrAMx2LUIVJGKgi1wGrSQafXKh3FUlcb85GjxyEoOATffLUSmZnpSglYlPuE2nDZpcMRFhaCH7fsxMTxo9E2hu0NHhw/51JzWSnUwjJ5lsuzksLXK33XA4+rweDf7nbg029tSM/VlIOUrusHnX5fsX6+stZsloeyuiI0CHC5vcPX03LcYBsPbSAdQbZZ0BaVJRTjG1rOeXZ0nDi8/Mknn6xySSSfk1UeVOLm68yzecW/eE5mSlWXmFf70dc21f4QrE9Hx9bBiE83wFPCfvE1cm3grMLIUD1GjRiK+CN7i41hYPkmz1UQmgtmow49O1pgmDYd33zzjeo753xqti01BCLG0gR79GhAWHbRv3PlowW4QLOMkf0D1YVRPMYil3x1CF/uDsH5/MpV8qieeeVgM8YPNBd7T6ur0FkTfM9hs9tVaShLcXQGC0bcuR7PPdgfbWMMNRoHURGpKeewaNHnOJ6Uh5WfPQ+P26Eio+W9Pn+9D/y7tozUK+lwQaitIAvL3hpyDTx+7AgO7NuFSVNnwWC4mAGXHj2hNp9t2sdtO/ehV/eusFiDcCbdjdMpHpiNXuerPDimYdlmO774yYbMlBL95QYTLFYLllRxzaYDxtYH9vdoOjpdnGHJfj4gyOLtk+OxkycSlMPkG1peVv+bzxHcvn0HBg0egod/+Ru06RCHrDwNmXkeOJwXq3mCzN5gSslz4WiJzzbY1MzaaEMiBoasgdNtxufvPlNYlumzS/NX/IywFnFoE61XqtinqnCOgtBccLo0HDvrxuaftyMv8wwmXDmt8DsnYix+oDmLsaRmudG1DUcRVL7JZ28CN3KM6pnKiSJWBN9jlladPZOIlr2uxc6kVqo0hYbFZ1Dat9CreXBj+poQ16b8c6KTUzKC6i8nrzwVUDp74d1vQteJ/4fbRp7F0w+M8quz+fmqndi7/wj2FUyAJ/8UOub8F+dO7arw9dX2feDfhKVF/TpT4luqs4XacTjRpWZuUpwhEDh4YA86dOiM0LBwcfSEWsE+0JdefRcFBTbcf9dNaNM6VpVwnkh2IdemqSxVRXaRQVXOfF207iDObn8d9rQ9qnKl19hHcMPk3rhioFnNo6zO2u1wee0yVaN9fhh7zJ9/5iGsWPxRMftFR2rOTXPx9xffUE7e9KuKBwnNZgveXbgFnbt2U3sYOoxlBX/ZwrDlkBMff2tTqqQ+RrfegUGdnLjqqitx+tSxYnbpxjsfRWybbmqEUbsYQ6HIDM+DPXm+rOMTTzwhTp7QbHG5NZxIdiMp3Y3oUB0O7t+Bnj37QW+yyHiF2tJcHT0u2OlUWuxSdaXFPcedyrBUVupZkbHctGEdDuzfhUsvm4gBA4fB7aHR8vYnBArlKalZWgxCx2u/wvnvH0dO/PxivYJljYOoDDaq79qxBccL+uLDb2k0NfX5+fMtoejTse4zbIwO87M/KM7UZAb3Cg0HhRqOJVdPnbeu4HeLs4oyM9IwedpsmELbYHCcuULRqfq0F/4i0M6nKWO3O/Dhp0twJP64GrI+ZGBfVfqelOpGUppHOVlUy6yoOsbn8K382Y58+8XjbFG4aogZEweb1cDwmsDPAQWRbrhmpNoklqRX36F4Z8FmvPDMQ1i9tLgjWJn9Ytnl5gNOLNhkw8nzXgdPDyf6RuzFpAmjcWlfcymJeN8QdaPBO2w+Oqzh1wVBCGTcHg0nz7txLCkfG9Z8pI5dNWUWzEEx9TJHT76hTQwObGVJRnU2PuwN4P1qCkupLr9iEsZdMRlbNm9EVlaG6jEIJCevIhXQS4YPUZFOW+qeWgvC5Ofn4Ysl8/Djj5uxZEOyOkYH+m931I+Tp87BrqlSXHHyBH/A8rGGEmQpCTed1153Ezp37Y6liz7G+bOnGvqUhEaOxWLGPXNvwMQrLsWCJauRX2BTG68urY2qEoXDwqmaWVKZsyhc4yn69d5jEbjn6iBVNk+YFVyy2Y6HXs/Bk+/lYN0OOoJatTdxtKX9BpRtvwYMHKLEXhIOlRZCKc9+UYhl8fc23P+fHLy4OL/QyYuxZmNym6XoHnYAAzvZSzl5dID5XkSE6NCPqqXi5AlCpXAv1rmlAT06BGPclNsRHhGFpQs+QFZmGuoDaeBpomqb1ZnVE6IGpl8s16gJNEZ9+g1CXPdesFisyMrMgNPpQIvYVggU2G+3evl89e+ipZl//P0TcFlCcffmgTiXcaCYulh1hFCSEk9h3ZfLkOuwYlPG9bBp4UoM5S+3har+hfpAqZ5qEAMs+FeQRdcwgixlYTAaccXEqejUOQ6hMe0a+nSEJgDt5aSJl+HySy9BUJAVpxPPIiQ4CNHRkQixmpCc4capFDfybDrl5JT3PaCQyvSRFky9xKxKIZdvsePAKa+AyaHTbhw6XYD/rinAoK5GXNLThOE9TFUury/PfrG0vypCXnRUtx914rv9Tvx82FlsbEpEsA5X9zqF/NPr0KpFG1w1eQaCgoKLPT9FXFhW2qUV20IM5QrGCIJQ9hrTIdYAkyEYFvNsJJ8+jPCIaNQHIsbSxEo3U7Lc6N3BpNQ0qwqjdDvjncpI+SMLxx6zvz/zaxzcvwv9Bw7DE3/8Jzp36Y5AoKL+t30HjuCm6SPgcnmb6nV6ryFdtrZqPXprVi/HnhMafky5FB4Y0SpSj2duDVH9C/UFS4jMJmBAZ5OoEwp+k2LfHu9UvUrV6TeqD0SMRfA37DG7+94HcfjQQYweNRIvvPBP1WOWW+DB6VQPUjM9CLJQrbJqNjYpza3mt1Ktk20VReG3qWd7AwZ2NaqKj14djBXuNSqyX2UJeZnMFjz24g84nd9JzckrOUqpY6weU4ZbMH6ACWtXfoY2bdtj+IixxTJ5FI1gjy7LUDu3lr5vQagtqVkeHElygfGi+ijdFEevCTl6jLhzQR7czVztcQH7TjrVPJ+a9un5KGlsaDCMJjPmLdmIviVGCQQixxKO4rd/egFHD+2CKayzt7/OdRKjRw7Fg4/8ppTDl5Z6HscSDsMcOxL/WZ6L81ne953G+483hiCyngUs6Oh3b2tA62hJ1gv+4+BpF3LyPRUqETYE4ugJ/nbyiqpG0n6ZzWb8+NMWDBo4QAU96KydSnEht0BT34eqBj9on3cluPDDASe2HnEqVcuScOPXLkaPzq0NqtSrdZRelYGyP9Y7BqG4mAo3d3TeeC4cmbB3/1Esn/8KTh7dBS2ok3LSnNknYGnB0UYPq9FGbO0Y0cuEqwZbEGVMUjZswKDhqv+1qIPHx87O1+B0A21j9KrHsLYbUkEQLpZPn0lzo0d7Y60rZcTRa0aOHmfk6HVeEY7qzppKSnXh+LnaCy6UpWypNxgwfuJUvPa/xWgsfLb6AP72yKXwXJDMpjonFcxe//QnjB7WA5rHgx3btuDnLd/BbuyEjSlXQYM3c3dpHxMenRGsZLHrExr1nHwNg+NMCKrDuYBC88Nf64O/EUdP8Cf33XcfPvjgg2Jz4Gi/rrtuFhYt/LyYbPq5DK9YC/8dHqKvlhNEp+9IkluVdzJb7uuRqwyOu7OYvC2zDOCzlJLCZyVxZBcf+cDqFKPJgmff3Iwpl/dSgis//7RJiYb17T8Yl4+fVGzPwPERLNWMDNWhU6xRqY8KghCYVOboSdi/ifXntWuhr1HJXrBVD02rXZ8eYUlJyYZwj9uN5LNJSp1z4/ovMXDQcMS0aIlA5uDG/0Cv2eHx9et5nHA4gF//4QX0GP8n9A/6Eibk4nDBZTjj7K2KcGiA77wyCJOGmdVw3PqGUV1uxMXJE+pEkKWWfbyCEOhwJEBRJ89nv06eOKZEWpYuX4vJV41DdFQE2sca0SJCw9l0N86me5TiNXvdqtL+wAh+7w5GdZl7ZZByqg6qHj4XTpxz4/g5d6kyT+LyAOwsqAg+u+PI69B57IVD3PlTcwO7vv4PRvX9I9auXgqP5sGUa2ajS9cehfel08pMg8mkQ4+2BsRGSi+eIDR2xNFrQlCHo6allyz1NOi9Mz9q02RdXkN4335D4HDYkZuTjfmfvqNKRS4ZMRYWqxWBSFkOK509e9pu5DqDkWJoi+P2YXBowUpmeuIgM64fa63R4Hl/wGiO04Vq9WYKQlVheZoOmtrMNkQQQxDqA5Zt7tmzp5izx1l1PJ6Xl4+zySn46/Ov4eoJYzFh3GhYzUalztkyUsO5TDeSLzh8YUEM/FX9e8IS0BE9eTEVq9ChwuX5TA/SczzIt2lKxZOD1enN8RtpMtLm61RZJxUwWerJ3vCbrt2Hs+UoSIeEhqFbj94YPmKMqlLxVYNw9i1Fl9q1MKBNtCHg+nEFQagZ0qPXREo3a9Of53MUOE+P9fihSoWzZpTVEF506Dif58Sxo/hu4zo4HA7MufFORERGIdAoswRVr8fQsTMx7rb3lEQ2FTU7tTRgaHdT4XvO1//umy8XNstTKc2fQ9/Lg+fD/hGW7YoamlAX6wtLzCzG6m1g6xop3RTqskePTp7ValWZPgqycI3dsm0Xvlj1NUxGI/7wxEMIsnqdJZ9zxs/kWZZ0ujUEW/QItpQ9pLwh7Ne0627G86+8X3iMSpzsw2NrHh3EvIxjeP3fLxUOO3/yySdl2LkgBDjSo9dMHD3fkGz2Z1VntEJRTp53ITHFg5ha9uFUpAzmw+1yIf7oQfTo1U+NYTh0YA969x0Ik8mMQICvYSYdVpsNbrcLer1BOaxLvtxWroJoZU5uXZKa5UanVgZ0iJUkvVA3HDzlUqqugSTIIo6eUBfO3osvvljo7DzxxBOlnJ0Cmx0HD8VjyKC+SE/PxJGEExg2uD+MLO+44ECl0eFL96gB6jzMrBuVa+vXfhWolomi9ou2KM+uKfE1ng/HMcVG6pGceKxCJ1cQhMBEHL1m4uhl5HpU2WC3tjXf6Kdle3DglBOxEfU3DoCwf2/l8gXKUR0wcKhS5wwNDUNDkZGehrDwcJw+dRzP/P4XSEs9hyHDRuPuB0urblYWRaWzN3POXDz7zzfq7HwZOWaPx+C4mmVzBaGxCrKIoyc0NLv3HsJHny1Vmb1xY0di1IjBagafLxPOkkjKqafleFRrBEVbgq115/SlppxTPfDxRw/gL0/9CpnpKRg8dBRuufvXiG0Tp8RbQq1QZZ5RYRdLNMsSoqGzd+edd+Ltt9+uk3MVBKGZOnpnz57F/fffj23btql/79y5E4MGDfLrC29qjh5l9Xu2Nykp5prCspNdCQ5EhenrvQ+HxoVZPaqAZWdn4va7HkZYWHgpyee6gv2DxxKOqHNIPH0Ck6fNQly3XtV6jNlTR2D/3h2ljvcbMBQLV/6EuoL9G+zN69FOsnkC6vRztv+kq8H6UMtCHD0hEKBQy/ebt2HD91vgdDjx3DO/VqWd3IP47BfF0lgmSacvK59OH8spofYWFPKqjcR6QUE+Eo4exMEDe3Au+Qzm3HQXolu0Vs9pc3oVOi1mIDZcrwa0hwfrSlX+DBs2DNu3by/12Dy+devWGp+bIAh1S6NU3eTCOGnSJDz11FMYMWJEQ59OwMM/MP/Q7AWoDZyvw+ie3en9d33CyGH/gUPRb8AQZajo5OXn5eLTj95Gx85x6BrXA+3bd0JQcIjfnrMgP089XnZ2Fj798C0YDAbEde+F62+ci1at2/lNiIbH6wpGjCnCw/4KQahL2JtHsQYRZBGE4gQHWXHVhDFKoCXxTDLMJhNOnkrCm+/MQ/++PTGgX09069oJLSOtKhjL0k6qJLMSg9U4mbn8XnkdLwqsMNvHck9eynIAafNtBfmwBgXjzJlELFv0MSzWIHTq2geDR02BzhqrnMqQIKjSTIq0sXS0ov7tioRoBEFovARkRq8odGAko1cxNBo2p4ah3WovxBGf5EJKtkdF/RoaGpzjx47gWPxhnDyRoHr5Jlx1DXr3GYAzSaeVsYuKilbOWlWa3dPTU3H65DGcP5+snMmszHTc88DjSnns1MljypE0GGse+2iIHj1mWZiB7dXeUO8N/0LzIhAFWSSjJwQq+fkF2LX3oCrtPHz0GNxuDx554Db06NYFBw8nwGIxo2VsjHIS7U6dml1nc1BdE8ize1Qmzu2mmrYGDTqkp57F+TMnkZ6ajLTUM3C7nJhx0yOcnYC0lNPo1KkTwoKMyqGzmnRqzE51vqeVCdEIghCYNMqMnlB9Ry/MqveL2mJYiA5nMwLD96eh6dGzr7qwoTzlfLLqnSMskTx8aF9hBjgyKgY333afKmFZtXwhPB43nA4HHE4H+g8YgmGXjMGx+EM4dHAfWrZqg379B6Nd+07KyeOXpFPnuFqfL505OnWVCdH4C/Z7MJvXLqZmsxMFoTows8B1hoIsgeLoCUKgEhwchNEjhqiL0+nCiVOJaN+ujfrd2q83If7YSfVvo8GAnj264sF7bkbS2RQsX7IKLrcbNptdib5MuXoiBg3sjyV79iD5dCLatW2DQf1Go3vXzmjZ0qzm9hn79qhV6SehM0enrjIhGkEQGhf1ntGbNm0aVq1aVe7vjx8/js6dO1c7o/fMM8/g2WefLXasufTopWZ70KWVHu1a1N5vz8n3YNcxF1qEs0wrcF8zYdQxKytDlXi6nE507dYTDrsde3ZvhU6nh9lshslsQWxsK9Wc7itxDQR8pTt01HhGjNnSUa+OMhv7MttEGRDXVrJ5QvMUZGkqGb26sl9C4FJQYENaeiaysnNUsLJ3zzhkZGRhy7bdqo3AarXAajGjS+cOaBETFVD2SxCEwCHgxFiys7PV/LTyiI6OLia+IaWblcPm7j6djGpgqj+yRCzPYumHRO39D79umXkchQG0idYjIoTZOKhh55yDSKeds5rCgvUVvv/s7eCA+/6dTTBLdkVopoIsTcXRC/TzEQRBEAKTgCvdDL9Qeif4r29Gp9f8lnFkVonlWbk2Kc/yN/wipuVoSvGsaxtDqcH0bNLvYNdUpi4pzYOcAu9tKcddFJbOUbGNKpvi5An1CcWa9DpNrTu1LRUTBEEQBKFuCdgePTYE+2AGkNdZilcfUvuNCa9Cpg5WP6pkRoYC6bn+ezzBS0YuM3VeB803u6gkbKDv2NKI2AgNyRluJGd4kOX2qD4M3sPh0mAx69CnoxGRASCYIzQvrCao4ILDVf/KvIIgCIIgNBFHLyjIO3CU+EYsrF+/HuPGjWvAswo82OvFMip/1u6HWPXQNI/fHk8A8u0amACJa1O+k1fS4evS2ojWURqyCzzIZrknxXKsQHS4QcpqhQaBs7fCg/WqzDiQ+5YFQRAEQQhgR0/6E6reUxcW7N8NF50Mk4F9Y5rKJNUWPo7LQ9U+lCpDbA6wzI3CKz3aly7XrMrfIshiQKvIOjs9QagW4UEUApI3TRAEQRACnYB19ISq4n9FUDpjIUE62By1c/Q4/4eDYL2PybJDICtPA6tvg9WMH0DfDFTE/r+9O42Nqvr/OP69d6Yt3dvpAnRDQPmBioqQGDc0BKJGImCQRCUEoohBTEzEwAMRTVCJmuADTYwPQGLyeyCiPJDEFYNLUENYRIj+NIKC+kdl6Ubbaefef75nrAKxdJvl3DvvVyxCC+VwO50zn3vO+X61cW1NhSu1lhSwAIajsIAVfwAAgoCgF2DdCd+svGmFzFSLlTjy4//5UvrPDtpBO9nqS2WJIxeNjJqqeHq+TFe2tHLfqTZtDOuLJ3r2TMNg8pxhcUHm2zro9ld9UxpAU9GP8OzVTG2h0FDlmm1vQNDpKrOuzutuglR+rwAAgNQi6AWYhpPCgmRxhFTTc3oiQz+nl6zaee6ZNF0pjJXqm2u2M2ohGbOtMyHS0eXJH82e/N7sSazETcmW0f7oGDR06rjKipNjam7TXkXJgJqKwNnc7kl9dcS0SwDCQFfntRCLfv9GI9keDQAA6AtBL8D0hVa6GhfrClxyu6U/6HN1umWzo1NkUlPfhUe0NHtRgYgU9H7clVExX345kZCfj3tSWZps9ZAuGuq0Z93oWETG1P5T3KStw5PDxxPmY1Vl7rC2lmoQ13/DqEpeDSM89AaI9n/UirDD7V8HAADSh2WGANNAlVx5Sz1dUSstdM05vcFqPeNLrMyRqrLBvQjUUNRUE5H6GtestKWrII9+Xv389bGIjB99bgXLkkJXJjZEpbo8IidahjcGbWpeX+2arW5AmOgKtd4sAQAA9iLoBZQGED3dls5eVhrW4n+dXRtM+NSiK7pSNpStj/pnNOxpjzgtYpIO+nlLCx1pGhn516bPGnI1AOoY9JzhUNsp6GrmyApW8xA++rxjTtem6WYMAAAYPoJeQGmYyovKgHqyDZUWRhHHMeFtoLTYSnmxIxXFQx+Xruw11kQknkhusUx1AZvuhJgedRfakqof0/OFeo11O+dg6Ivf1g5PGqvdtJyfBLJNV6nz85PPQwAAwE4EvYDS81/aky2d59j0/I2eo+uMDzzgdHaL1MUiw64wqUGxtsw17RhSST/fqErXnDHqj1bgvLguav5NWjRmoNo7kyuGVWWs5iGcdCW8bIhbuwEAQGYQ9AJK76SXFaX379CwpsVeOroG9mKuI66rgCIVJcMPn7qFs67KNa0JUrWqZ4qjuCL1VQMPYFohtEnPDLYN7LyejrWjS2RMra4GspqH8NLv88HcAAEAAJlF0AuwdBViOVtZUTJsDSTktHdqFcvUrTKWmFWx1J3VG2pxlLqqiAm8AzmvpyuG1RWuaSMBhJmueOtJYQAAYCeCXgDpqpG+xErn+byzw1ZBvpjti/2tlum5tlRuV9RVPd1mqX32BnNOsK/x5UUcqSkf/Pg0uI4bFTV9ATUsXqgAi+5YbaxxM970Hcg0ff7pbcECAADsQ9AL6LZNbQkwIi/9f5eGnJEVrjl3diGtHb6MirnntCpIhfIibWaeLPIyHK1nPLMVdKjhuPCv83oJL9kM/ny6ha2t05dxo6Pm7CQQdnpjp7jQ4ZweAACW4hVpAOnqlPaxGm7Bk4GqKk0+TPo6K6chx3F8qU5D8RH9N9bFtCDK0IOerjhEhriadzZtt/Cfhqh094icOuvMnq7knWr35aJaV2rKWclD7oiVOFTeBADAUgS9AOrpSbYwyBStvllZ4vS5qtZ8xjd98/T3pYNW4NSVuI4hVvjTM34jK1PTuFyLs1w2Jmq2tJ5o8eWPZk96PF8m1LmmJQRbNpFr54RppQcAgJ2i2R4ABk9P6BVm4HxeLw0vGuQO/tRjVvXObjKu4SsvkmypkC5avXJ0pSs/HU9IYf7g/p6eRLJcRG25m9ICNZc2JYNnIpEsSkGFTeQifezn5yV3GaR62zYAABgeVvQCRht+a7DKZNBTuqKnYelU2z+rahr6dLVMi4+kuzCMFnlx3OS/fzB0fDUVrpQUpvahrmFXz+JpPz5CHnKVPvb1xgf99AAAsA9BL2D0znnhCJH8DN8911W9ptqIqTx5stUzxVn+bPGkvsqVUZWRjKwc1JZHpHUQrRY0iOqxQq3cCSB9N4GovAkAgH14BRwwXXE9s5adL5uecbu0KU8qS7V9gC9jR0bkopGRjBWFqa0YXAN1Xc3TPnylhWwpA9KluMAxN4IG0msTAABkDmf0Akb7yRUXZC+fa8GViQ26gpf5wiNlRY6pAHq63TOrCBeiYVBbIdTF6GkHpFPRCD0zrOd1deWdaw0AgC1Y0QtYyHMdJyXVI4dDA142qksmi8IkG6j3t6rX3O6bM4UaDgGkj55X1Wq0Q62KCwAA0oOgFyBd3SIj8rUQi+QsbStRXe6aINcXPS+kH9UG6bQ7ADLxfemK53GlAQCwCUEvQLSynb6gytSZOBtpcGusdv8uTHM+PSekzcz196S60iaAf1cywjHVgLt7WNUDAMAWvBIOEO0Jp6XMc50GuKaa5Fm987dwnmzzpbLENX3/AGSGVgEuL3GlvYugBwCALUgNAaErVbqaRbGDpNFVEdOkXVs86Mqe9tc70eKZba3jR0fpbQdkWHWZS5sFAAAsQtXNgIj3aHNiPaOXu9s2zy8AMW50xFyT46c9SSTEFIQYMzJieu4ByCwtfJQXccxNF/0/AADILoJeQGhFO92SGOUF1Dlh76KRUamvSrZSIAQD2VOQ50hFiRZK8qSimKAHAEC2sXUzILTIQUU/veNyVV7UIeQBFmD7JgAA9iDoBeV8njhSzJZEABYrL3KkIOr8a0VcAACQWQS9AOjs7Z9H0ANgefVN7XPZ3knQAwAg2wh6Aemfp2df9EwaANi+fTPhi3g+YQ8AgGwi6AWAVrGrKOZLBcB+pYWOlBUJq3oAAGQZ6SEATdIjrkjxCFbzANjPdR2pi0WloyvbIwEAILcR9ALQVqG00OV8HoDA0PYKxSNEznSxfRMAgGwh6FmuK+5LTRmreQCC1fKkLuZKW4eX7aEAAJCzCHoWM8UMHEdKi/gyAQiWqvKI2XJOBU4AALKDBGExPeNSVKBvrOgBCJb8qCONNVFp6/RNL1AAAJBZBD3Lz+fVlrumuAEABE1VmSOVJY6cbifoAQCQaQQ9SyW85Asj7Z8HAEGkvT8vGhkRzxOJ9xD2AADIJFKEpbRaXWkRbRUABFtZkSuNNa6cavNoog4AQAYR9CzV0eXLyHJXHIdtmwCCrb46IrUVETnZynk9AAAyhaBnoa5uXwryHImVRrI9FABIyRbOcaMiZpfCiVa2cAIAkAkEPQu1dvgyKuZKfh6reQDCQW9eTajLM2Hvzxa2cQIAkJNBb/v27TJ9+nSprKyU2tpamT9/vhw7dkxyQXfC19Z5UlVm5ZcGAIassMCRiQ15Eitx5I9mz+xeAAAA6WFlmmhubpZVq1bJ0aNH5fDhw1JWViYLFiyQXNDc7svomCslI6z80gDA8Ff2GqJmK2d7ly8nWz3pSRD4AABINccPQCfbr7/+WqZMmSJdXV0SjUYH9Ge0iEkq/mm7/xeXSMSRwvz0b6PUu9tahOXKcXnmzjcAhFlbhye/nvTkj9Oe6LO1Ps8WFoi4AyxC9WdLQqaMz5fiEcN7vkzVfJEqto0HAGCn/uaLgaWmLNu5c6dMmjRpwCEvqH3zTrd7cvHoCCEPQE4oKXRlQr0rdVWenGr1zHbOk60ivu+J6zqSHxWJRhyJRrSgy8ADIAAAyMLWzdmzZ5v02dfbkSNHzvn9e/fulTVr1siGDRsu+HmffPLJcz5PKp3p9KXljCdtnZ7pb6crb7rVKJV3XE+1+ab8+KgYlTYB5Bbdqt5YE5WrxuXJVeOjMqkxTxqrXSkqcCWR8KW9wzdB8M/mZBj88683reYZhuyXzvkLAJC7Mr51s6WlReLxeJ8fj8Vi4rrJ/HngwAGZNWuWvPDCC7Jw4cKsbH059kePnImLJBLJQika8LoTIp6XfF/yb/DNC478PJGCqCN50YFP1DpGLTeulej+U58nIzKwRRQAgkKfI/U5V59vE76ffO719P3Jj1cUO2b1L0xbJW0bDwDATv3NF9ae0dOQN3PmTFm/fr0sWbLEqolSt1nqi464hr4ekXiPb1b9tC2CnrGLJ8yrE7PlSIObbj/SIHg2HVtHXFspeBIrdeWSuighDwCywLZgZdt4AAB2CmTQO3jwoMyYMUPWrVsnS5cuDdREqaGvM64hzpeW9uSWT/215zt6tfU/0Z/qDwX5Ig1VrtmyqaEQAJB5tgUr28YDALBTIIOeruBt3rxZioqKznn/oUOHpKmpKVATpefpmb5kANTVP8/XggIieVExleIIeACQXbbMF7aOBwBgp0AGvVRgogQABHG+sG08AAA79Tdf0JUbAAAAAEKGoAcAAAAAIUPQAwAAAICQIegBAAAAQMgQ9AAAAAAgZAh6AAAAABAyBD0AAAAACBmCHgAAAACETFRC3kQQAICgYf4CAAyX41+onTr67ThvI8bMdeaxwfcgzxtgLmAuYC5gLmAuyO3nZ7ZuAgAAAEDIEPQAAAAAIGQIev1Yu3atBA1j5jrz2OB7kOcNMBcwFzAXMBcwF+T28zNn9AAAAAAgZFjRAwAAAICQIegBAAAAQMgQ9AAAAAAgZAh6AAAAABAyBL1BevXVV02TwxdffFFstmfPHpk6darEYjGpqKiQ6667Tj755BOx2fbt22X69OlSWVkptbW1Mn/+fDl27JjY7LfffpM77rhD6urqzONi3759YqPu7m5ZsWKFubb6mHj44Yelp6dHbPbSSy/JtGnTpKCgQObOnSu26+rqkqVLl8rYsWOltLRUJk6cKBs3bhTb6WOhsbFRysrKpL6+Xh555BGJx+MSBB0dHXLxxReb5zj0j/krfZi/0ido81fQ5i7F/BXe+YugNwi//vqrPP/88zJ58mSx3ZgxY+Stt96SEydOyKlTp2TlypVy++23mweWrZqbm2XVqlVy9OhROXz4sHnhuWDBArGZ67py6623yrZt28Rm69atk88++0wOHTokBw8elE8//VSeeeYZsZmG58cff9yEpyDQFx6jR4+WDz/8UFpaWuS1116TRx99VN5//32x2fLly+Xbb781Y96/f795e+655yQInnjiCfNch/4xf6UX81f6BG3+CtrcpZi/Qjx/+RiwuXPn+ps3b/Zvuukmf8OGDYG5colEwt+2bZuvX+4ff/zRD4r9+/f7ruv63d3dfhDo9d27d69vo4aGBn/Lli1///qNN97wm5qa/CBYu3atP2fOHD+I5s2b569Zs8YPit9//92fMWOGv2jRIt92u3fv9i+//HL/vffe88vLy7M9HOsxf2UW81fqBHX+CvLcpZi/wjF/saI3QG+++aa5471o0SIJEl0Szs/PN9sHdOy6rSwodu7cKZMmTZJoNJrtoQSarujqFtirrrrq7/fpz3/++WdzFxrp0dnZKV999ZVcccUV1l/i9evXS0lJidkyrSt6ujXK9rvPerf85ZdfNs9vuDDmr8xj/koN5q/sYP4Kz/yV80Fv9uzZ5mxVX29HjhwxTzSPPfaYvPLKKxKUMfc6ffq0tLa2yuuvvy433nhjIMas9u7dK2vWrJENGzYEZsy2amtrM/8/ex9478/1sYHU0wXe+++/Xy655BK58847rb/Eq1evNo8T3Rr14IMPyqhRo8RmuoV+ypQp5kxvLmP+suc6n435K3WYvzKP+Stc81fOL5X897//vWDhAT34+8ADD8h9991nXrQFZcxnKywslIULF8pll11mCkTccMMNYvOYDxw4ILfddps50Dxr1iwJynW2la7UKF29q66u/vvnSouGIPWTpJ57++6778x5PT3HGRS6gn7llVfK4sWLzdht9MMPP5ibbvpiOtcxf9lznXsxf6UW81dmMX+Fb/7K+aCnBT/601tcobfSpr5I3r17tzkQvHXrVrFxzH1Vrvr++++zEvQGOmadJGfOnGm2kmk4zaahXmfbaKWyhoYGUxF0/Pjx5n36c620WF5enu3hhW6SfOihh+TLL7+Ujz76KJDXt/d5wlZalOH48eMyYcKEv8erK9N6E0MrH15zzTWSK5i/7LnOivkr9Zi/Mof5K5zzV84HvYH44osvzinle9ddd5lKi/qCzlbvvPOONDU1yaWXXmruRGpI1XNaNm910mpaGvK0wtaSJUskSHvZe+m11l/rvmubVnL0ej799NNy/fXXm19rxTLdWmgz/Z7rffM8z1xXvaY2n8nSEuCff/657Nixw7xACcK2qC1btsi8efNMKP3mm2/M998tt9wittJKvPo80WvXrl3msaw3L/SMIc7F/JUZzF/pE7T5K4hzl2L+Cun8ldZSLyEVhKqbmzZt8idMmOAXFxf7VVVV/s033+zv2LHDt9nixYt9x3HMmM9+++mnn3yb6bfR+W8ff/yxb5N4PO4vX77cr6ioMG8rVqywvpqpViw7/7rq956tjhw5YsZYUFBwzuN32bJlvq3a2tr8mTNn+rFYzIx17Nix/sqVK/329nY/KPR7jaqbA8f8lR7MX+kTtPkraHOXYv4K7/zl6A/piZAAAAAAgGywZ28ZAAAAACAlCHoAAAAAEDIEPQAAAAAIGYIeAAAAAIQMQQ8AAAAAQoagBwAAAAAhQ9ADAAAAgJAh6AEAAABAyBD0AAAAACBkCHoAAAAAEDIEPSDkjh49KtXV1fLBBx+YX8fjcbn66qvlqaeeyvbQAADoE/MXMDyO7/v+MD8HAMtt3bpVVqxYIfv375dnn31W9uzZIzt27JBIJJLtoQEA0CfmL2DoCHpAjli2bJns2rVLfvnlF9m3b580NjZme0gAAPSL+QsYGrZuAjli+fLlcuDAAbnnnnsIeQCAwGD+AoaGFT0gB+i5vGuvvVYmT54sb7/9ttm2OXXq1GwPCwCAC2L+AoYuOow/CyAgVq9eLSUlJbJx40aZNm2a3H333eacnr4PAABbMX8BQ8eKHhBy7777rtx7773nnMubM2eOxGIx2bRpU7aHBwDAv2L+AoaHoAcAAAAAIUMxFgAAAAAIGYIeAAAAAIQMQQ8AAAAAQoagBwAAAAAhQ9ADAAAAgJAh6AEAAABAyBD0AAAAACBkCHoAAAAAEDIEPQAAAAAIGYIeAAAAAIQMQQ8AAAAAJFz+H7jIVZupuAT6AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_gp(ax, X, y, X_test, pred, title):\n", " mu, sd = pred[\"mean\"], np.sqrt(np.maximum(pred[\"var\"], 0))\n", " ax.fill_between(X_test[:, 0], mu - 2*sd, mu + 2*sd, alpha=0.18, color=\"#2563EB\")\n", " ax.plot(X_test[:, 0], mu, lw=2, color=\"#2563EB\", label=\"GP mean\")\n", " ax.plot(X_test[:, 0], np.sin(X_test[:, 0]), \"--\", color=\"#6B7280\", lw=1, label=\"true f\")\n", " ax.scatter(X[:, 0], y, c=\"black\", s=18, zorder=5, label=\"data\")\n", " ax.set_title(title); ax.legend(fontsize=8, frameon=False)\n", " ax.set_xlabel(\"x\"); ax.set_ylabel(\"y\")\n", "\n", "fig, (a, b) = plt.subplots(1, 2, figsize=(10, 3.6), sharey=True)\n", "plot_gp(a, X, y, X_test, pred_before, \"Before optimize()\")\n", "plot_gp(b, X, y, X_test, pred_after, \"After optimize()\")\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "b698cf3e", "metadata": {}, "source": [ "## Different kernel smoothnesses\n", "\n", "The Matérn-ν family interpolates between rough (ν=½) and smooth (ν=∞ = RBF) fits." ] }, { "cell_type": "code", "execution_count": 6, "id": "bc0b9cf8", "metadata": { "execution": { "iopub.execute_input": "2026-05-15T06:51:06.143498Z", "iopub.status.busy": "2026-05-15T06:51:06.143422Z", "iopub.status.idle": "2026-05-15T06:51:06.191022Z", "shell.execute_reply": "2026-05-15T06:51:06.190694Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 3.5))\n", "ax.scatter(X[:, 0], y, c=\"black\", s=18, zorder=5, label=\"data\")\n", "for nu, color in [(0.5, \"#F59E0B\"), (1.5, \"#10B981\"), (2.5, \"#2563EB\")]:\n", " m = gp.GPExact(gp.Matern(nu=nu), noise_var=0.1)\n", " m.fit(X, y); m.optimize(steps=60)\n", " ax.plot(X_test[:, 0], m.predict(X_test)[\"mean\"], lw=2, color=color, label=f\"Matern v={nu}\")\n", "ax.legend(fontsize=9, frameon=False); ax.set_xlabel(\"x\"); ax.set_ylabel(\"y\")\n", "ax.set_title(\"Smoothness via Matern v\")\n", "plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "cb386df2", "metadata": {}, "source": [ "## When to use exact GP\n", "\n", "`Solver.Cholesky` is **O(N³)**. The rule of thumb on a laptop:\n", "\n", "- **N < 5,000**: exact Cholesky is fine and gives the cleanest uncertainty estimates\n", "- **5,000–50,000**: switch to `Solver.CG` (matrix-free on GPU)\n", "- **N > 50,000 and D ≤ 3**: switch to `Solver.SKI` (FFT-accelerated)\n", "\n", "The next tutorial shows how to combine kernels for more complex signals." ] } ], "metadata": { "kernelspec": { "display_name": "lightgp-docs", "language": "python", "name": "lightgp-docs" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }