diff --git a/building_energy_statistical_models/README.md b/building_energy_statistical_models/README.md new file mode 100644 index 0000000..8660316 --- /dev/null +++ b/building_energy_statistical_models/README.md @@ -0,0 +1,3 @@ +# Building Energy Statistical Models + +See https://github.com/srouchier/buildingenergygeeks \ No newline at end of file diff --git a/kalman_and_bayesian_filters/01-g-h-filter.ipynb b/kalman_and_bayesian_filters/01-g-h-filter.ipynb new file mode 100644 index 0000000..6c3447d --- /dev/null +++ b/kalman_and_bayesian_filters/01-g-h-filter.ipynb @@ -0,0 +1,910 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "0c36bffb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vPq2trSotLdXEiRM1cuRI5efna+fOnUFtGHd6dtPh+eLFi5oxY4ZefvnlXtsUFRWpvr4+8HjjjTeCnl+9erXef/99/f73v9fBgwd17NgxPfLIIzffewQJR20k6emnnw5qs2HDBie7PSz0V5uamhrdfffdmjp1qo4cOaJTp07pRz/6kZKSkgJtNm7cqAMHDmj//v06evSo6urqtGLFikgdwpAWjvpI0rp164JeO9u3b49E94e0/mpz/d+7vr5eu3fvlsvlUnFxcaANY44zwlEbiTHHKf3VZ9OmTaqoqNC+fft05swZPfbYYyotLVV5eXmgDeNOL0wIJJnf/e53QcsefPBBs3z58l7XOX36tJFk3nvvvcCyt99+27hcLvPxxx+H0h1cZyC1McaYnJwc87Of/cyxfqHn2qxcudKUlJT0uk5TU5MZMWKE2b9/f2DZmTNnjCRTWVnpVFeHpYHUxxhj5s+fb773ve851zH0WJvPWr58uVm0aFHgd8acyBhIbYxhzImUnupzxx13mKeffjpo2cyZM80PfvADYwzjTl8cmfN85MgRpaena8qUKXr00UfV2NgYeK6yslJjx47VF7/4xcCyxYsXy+12691333WiO7hOX7Xptm3bNqWlpekLX/iCnnvuOfn9/ij0dPjo7OzUoUOH9PnPf15LlixRenq6Zs+eHfQR28mTJ9Xe3q7FixcHlk2dOlXZ2dmqrKyMQq+HD5v6dHv99dc1btw4TZs2TU8++aQuXboU+Q4PYw0NDTp06JDWrl0bWMaYExt6qk03xpzomDt3rsrLy/Xxxx/LGKPDhw/rgw8+0H333SeJcacv8eHeYFFRkVasWKHc3FzV1NRoy5Ytuv/++1VZWam4uDh5vV6lp6cHdyI+XqmpqfJ6veHuDq7TX20k6bvf/a5mzpyp1NRUHT9+XE8++aTq6+v1wgsvRLn3Q9f58+fV2tqqbdu26Sc/+YmeffZZVVRUaMWKFTp8+LDmz58vr9erhIQEjR07NmjdCRMm8LpxmE19JOkb3/iGcnJylJWVpVOnTumJJ55QdXW1fvvb30b5CIaP1157TcnJyUEfKzPmxIaeaiMx5kTTiy++qEceeUQTJ05UfHy83G63du3apXnz5kkS404fwh6eH3jggcC/p0+froKCAk2ePFlHjhzRvffeG+7d4SbY1GbTpk2BNgUFBUpISNC3vvUt/fSnP+W+9w7p7OyUJC1fvlwbN26UJN155506fvy4du7cGQhniA7b+lw/h3b69OnKzMzUvffeq5qaGk2ePDnyHR+Gdu/erdWrV98wFx3R11ttGHOi58UXX9Sf/vQnlZeXKycnR8eOHdP69euVlZUVdLYZN3L8UnW33Xabxo0bp7///e+SpIyMDJ0/fz6ojd/v14ULF5SRkeF0d3Cdz9amJ7Nnz5bf79eHH34YuY4NM+PGjVN8fLzy8/ODlt9+++2BqzlkZGTo6tWrampqCmrT0NDA68ZhNvXpyezZsyWpz9cXwuedd95RdXW1Hn744aDljDnR11ttesKYExmXL1/Wli1b9MILL2jp0qUqKChQaWmpVq5cqeeff14S405fHA/P//znP9XY2KjMzExJ0pw5c9TU1KSTJ08G2vzxj39UZ2dnYLBBZHy2Nj2pqqqS2+2+4WNPhE9CQoIKCwtVXV0dtPyDDz5QTk6OJGnWrFkaMWKE/vCHPwSer66uVm1trebMmRPR/g43NvXpSVVVlST1+fpC+JSVlWnWrFmaMWNG0HLGnOjrrTY9YcyJjPb2drW3t8vtDo6BcXFxgU/bGHd6d9PTNlpbW4POpJw9e1ZVVVVKTU1VamqqnnrqKRUXFysjI0M1NTV6/PHHlZeXpyVLlkjqOltTVFSkdevWaefOnWpvb1dpaakeeOABZWVlhe/IhqFQa1NZWal3331XCxcuVHJysiorK7Vx40aVlJTolltuidZhDQl91SY7O1ubN2/WypUrNW/ePC1cuFAVFRU6cOCAjhw5IklKSUnR2rVrtWnTJqWmpsrj8WjDhg2aM2eOvvSlL0XpqIaOUOtTU1OjX/3qV/ryl7+stLQ0nTp1Shs3btS8efNUUFAQpaMaGvqrjST5fD7t379fO3bsuGF9xhznhFobxhxn9Vef+fPna/PmzRo5cqRycnJ09OhR7d27NzDfnHGnDzd7eY7Dhw8bSTc8HnzwQXPp0iVz3333mfHjx5sRI0aYnJwcs27dOuP1eoO20djYaFatWmXGjBljPB6Peeihh0xLS0u4riAybIVam5MnT5rZs2eblJQUk5SUZG6//XbzzDPPmLa2tige1dDQV226lZWVmby8PJOUlGRmzJhh3nrrraBtXL582XznO98xt9xyixk1apT52te+Zurr6yN8JENTqPWpra018+bNM6mpqSYxMdHk5eWZzZs3m+bm5igczdBiU5tf/vKXZuTIkaapqanHbTDmOCPU2jDmOKu/+tTX15s1a9aYrKwsk5SUZKZMmWJ27NhhOjs7A9tg3OmZyxhjHM7nAAAAwJDg+JxnAAAAYKggPAMAAACWCM8AAACAJcIzAAAAYInwDAAAAFgiPAMAAACWCM8AAACAJcIzAAAAYInwDAAAAFgiPAMAAACWCM8AAACApf8HDd8Fp5OE1J4AAAAASUVORK5CYII=", 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vXLmiGTNm6OWXX+6xTUFBgerq6gJfb7zxRtDra9as0QcffKDf/e53Onz4sE6cOKFHHnnk9kePIOGojSQ988wzQW02bdrk5LCHhb5qU11drXvvvVdTp07VsWPHdObMGf3oRz9SQkJCoM3mzZt16NAhHTx4UMePH1dtba1WrlwZqVMY0sJRH0nasGFD0Htnx44dkRj+kNZXbW7+edfV1Wnv3r1yuVwqLCwMtGHOcUY4aiMx5zilr/ps2bJF5eXlOnDggM6dO6fHH39cxcXFKisrC7Rh3umBCYEk89vf/jZo29q1a82KFSt63Ofs2bNGknnvvfcC295++23jcrnMxYsXQxkObtKf2hhjTFZWlvnZz37m2LjQfW1WrVplioqKetynsbHRjBgxwhw8eDCw7dy5c0aSqaiocGqow1J/6mOMMfPnzzePPfaYcwNDt7X5tBUrVpj7778/8HfmnMjoT22MYc6JlO7q8/nPf94888wzQdtmzpxpfvCDHxhjmHd648ia52PHjik1NVVTpkzRo48+qoaGhsBrFRUVGjt2rL74xS8Gti1evFhut1vvvvuuE8PBTXqrTZeSkhKlpKToC1/4gp5//nn5/f4ojHT46Ojo0JEjR/S5z31OS5YsUWpqqmbPnh30Edvp06fV1tamxYsXB7ZNnTpVmZmZqqioiMKohw+b+nR5/fXXNW7cOE2bNk1PPfWUrl69GvkBD2P19fU6cuSI1q9fH9jGnDMwdFebLsw50TF37lyVlZXp4sWLMsbo6NGj+vDDD/XAAw9IYt7pTWy4OywoKNDKlSuVnZ2t6upqbdu2TUuXLlVFRYViYmLk9XqVmpoaPIjYWCUnJ8vr9YZ7OLhJX7WRpO9+97uaOXOmkpOTdfLkST311FOqq6vTiy++GOXRD12XLl1SS0uLSkpK9JOf/ETPPfecysvLtXLlSh09elTz58+X1+tVXFycxo4dG7TvhAkTeN84zKY+kvSNb3xDWVlZysjI0JkzZ/Tkk0+qqqpKv/nNb6J8BsPHa6+9psTExKCPlZlzBobuaiMx50TTrl279Mgjj2jixImKjY2V2+3Wnj17NG/ePEli3ulF2MPzgw8+GPjz9OnTlZeXp8mTJ+vYsWNatGhRuA+H22BTmy1btgTa5OXlKS4uTt/61rf005/+lOfeO6Sjo0OStGLFCm3evFmSdPfdd+vkyZPavXt3IJwhOmzrc/Ma2unTpys9PV2LFi1SdXW1Jk+eHPmBD0N79+7VmjVrblmLjujrqTbMOdGza9cu/fGPf1RZWZmysrJ04sQJbdy4URkZGUFXm3Erx29Vd+edd2rcuHH661//KklKS0vTpUuXgtr4/X5dvnxZaWlpTg8HN/l0bboze/Zs+f1+/f3vf4/cwIaZcePGKTY2Vrm5uUHb77rrrsDdHNLS0nTjxg01NjYGtamvr+d94zCb+nRn9uzZktTr+wvh884776iqqkoPP/xw0HbmnOjrqTbdYc6JjGvXrmnbtm168cUXtWzZMuXl5am4uFirVq3SCy+8IIl5pzeOh+d//OMfamhoUHp6uiRpzpw5amxs1OnTpwNt/vCHP6ijoyMw2SAyPl2b7lRWVsrtdt/ysSfCJy4uTvn5+aqqqgra/uGHHyorK0uSNGvWLI0YMUK///3vA69XVVWppqZGc+bMieh4hxub+nSnsrJSknp9fyF8SktLNWvWLM2YMSNoO3NO9PVUm+4w50RGW1ub2tra5HYHx8CYmJjAp23MOz277WUbLS0tQVdSzp8/r8rKSiUnJys5OVlPP/20CgsLlZaWpurqaj3xxBPKycnRkiVLJHVerSkoKNCGDRu0e/dutbW1qbi4WA8++KAyMjLCd2bDUKi1qaio0LvvvquFCxcqMTFRFRUV2rx5s4qKinTHHXdE67SGhN5qk5mZqa1bt2rVqlWaN2+eFi5cqPLych06dEjHjh2TJCUlJWn9+vXasmWLkpOT5fF4tGnTJs2ZM0df+tKXonRWQ0eo9amurtYvf/lLffnLX1ZKSorOnDmjzZs3a968ecrLy4vSWQ0NfdVGknw+nw4ePKidO3fesj9zjnNCrQ1zjrP6qs/8+fO1detWjRw5UllZWTp+/Lj2798fWG/OvNOL2709x9GjR42kW77Wrl1rrl69ah544AEzfvx4M2LECJOVlWU2bNhgvF5vUB8NDQ1m9erVZsyYMcbj8ZiHHnrINDc3h+sOIsNWqLU5ffq0mT17tklKSjIJCQnmrrvuMs8++6xpbW2N4lkNDb3VpktpaanJyckxCQkJZsaMGeatt94K6uPatWvmO9/5jrnjjjvMqFGjzNe+9jVTV1cX4TMZmkKtT01NjZk3b55JTk428fHxJicnx2zdutU0NTVF4WyGFpva/OIXvzAjR440jY2N3fbBnOOMUGvDnOOsvupTV1dn1q1bZzIyMkxCQoKZMmWK2blzp+no6Aj0wbzTPZcxxjiczwEAAIAhwfE1zwAAAMBQQXgGAAAALBGeAQAAAEuEZwAAAMAS4RkAAACwRHgGAAAALBGeAQAAAEuEZwAAAMAS4RkAAACwRHgGAAAALBGeAQAAAEv/D+Nj+N1Ko4o8AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "#format the book\n", + "import book_format\n", + "book_format.set_style()\n", + "\n", + "import kf_book.book_plots as book_plots\n", + "from kf_book.book_plots import plot_errorbars\n", + "\n", + "\n", + "plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))\n", + "\n", + "plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180))\n", + "\n", + "plot_errorbars([(160, 1, 'A'), (170, 9, 'B')], xlims=(150, 180))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f3bf8cdc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average of measurements is 164.9986\n", + "Average of measurements is 164.9884\n" + ] + }, + { + "data": { + "image/png": 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", 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", 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "measurements = np.random.uniform(160, 170, size=100000)\n", + "mean = measurements.mean()\n", + "print(f'Average of measurements is {mean:.4f}')\n", + "\n", + "mean = np.random.normal(165, 5, size=100000).mean()\n", + "print(f'Average of measurements is {mean:.4f}')\n", + "\n", + "import kf_book.gh_internal as gh\n", + "gh.plot_hypothesis1()\n", + "\n", + "gh.plot_hypothesis2()\n", + "\n", + "gh.plot_hypothesis3()\n", + "\n", + "gh.plot_hypothesis4()\n", + "\n", + "gh.plot_hypothesis5()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "a453991c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gh.plot_estimate_chart_1()\n", + "\n", + "gh.plot_estimate_chart_2()\n", + "\n", + "gh.plot_estimate_chart_3()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "3cfdc9ee", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "previous estimate: 160.00, prediction: 161.00, estimate 159.80\n", + "previous estimate: 159.80, prediction: 160.80, estimate 162.16\n", + "previous estimate: 162.16, prediction: 163.16, estimate 162.02\n", + "previous estimate: 162.02, prediction: 163.02, estimate 161.77\n", + "previous estimate: 161.77, prediction: 162.77, estimate 162.50\n", + "previous estimate: 162.50, prediction: 163.50, estimate 163.94\n", + "previous estimate: 163.94, prediction: 164.94, estimate 166.80\n", + "previous estimate: 166.80, prediction: 167.80, estimate 167.64\n", + "previous estimate: 167.64, prediction: 168.64, estimate 167.75\n", + "previous estimate: 167.75, prediction: 168.75, estimate 169.65\n", + "previous estimate: 169.65, prediction: 170.65, estimate 170.87\n", + "previous estimate: 170.87, prediction: 171.87, estimate 172.16\n" + ] + }, + { + "data": { + "text/plain": [ + "[158.0,\n", + " 164.2,\n", + " 160.3,\n", + " 159.9,\n", + " 162.1,\n", + " 164.6,\n", + " 169.6,\n", + " 167.4,\n", + " 166.4,\n", + " 171.0,\n", + " 171.2,\n", + " 172.6]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from kf_book.book_plots import figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, \n", + " 169.6, 167.4, 166.4, 171.0, 171.2, 172.6]\n", + "\n", + "time_step = 1.0 # day\n", + "scale_factor = 4.0/10\n", + "\n", + "def predict_using_gain_guess(estimated_weight, gain_rate, do_print=False): \n", + " # storage for the filtered results\n", + " estimates, predictions = [estimated_weight], []\n", + "\n", + " # most filter literature uses 'z' for measurements\n", + " for z in weights: \n", + " # predict new position\n", + " predicted_weight = estimated_weight + gain_rate * time_step\n", + "\n", + " # update filter \n", + " estimated_weight = predicted_weight + scale_factor * (z - predicted_weight)\n", + "\n", + " # save and log\n", + " estimates.append(estimated_weight)\n", + " predictions.append(predicted_weight)\n", + " if do_print:\n", + " gh.print_results(estimates, predicted_weight, estimated_weight)\n", + "\n", + " return estimates, predictions\n", + "\n", + "initial_estimate = 160.\n", + "estimates, predictions = predict_using_gain_guess(\n", + " estimated_weight=initial_estimate, gain_rate=1, do_print=True) \n", + "\n", + "# plot results\n", + "book_plots.set_figsize(10)\n", + "gh.plot_gh_results(weights, estimates, predictions, [160, 172])\n", + "weights" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "4fc70aae", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "e, p = predict_using_gain_guess(initial_estimate, -1.)\n", + "gh.plot_gh_results(weights, e, p, [160, 172])" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "c9f6a06a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "weight = 160. # initial guess\n", + "gain_rate = -1.0 # initial guess\n", + "\n", + "time_step = 1.\n", + "weight_scale = 4./10\n", + "gain_scale = 1./3\n", + "estimates = [weight]\n", + "predictions = []\n", + "\n", + "for z in weights:\n", + " # prediction step\n", + " weight = weight + gain_rate*time_step\n", + " gain_rate = gain_rate\n", + " predictions.append(weight)\n", + " \n", + " # update step \n", + " residual = z - weight\n", + " \n", + " gain_rate = gain_rate + gain_scale * (residual/time_step)\n", + " weight = weight + weight_scale * residual\n", + " \n", + " estimates.append(weight)\n", + "\n", + "gh.plot_gh_results(weights, estimates, predictions, [160, 172])" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "8a2fbf9c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pylab as pylab\n", + "from kf_book.gh_internal import plot_g_h_results\n", + "def g_h_filter(data, x0, dx, g, h, dt=1.):\n", + " x_est = x0\n", + " results = []\n", + " for z in data:\n", + " # prediction step\n", + " x_pred = x_est + (dx*dt)\n", + " dx = dx\n", + "\n", + " # update step\n", + " residual = z - x_pred\n", + " dx = dx + h * (residual) / dt\n", + " x_est = x_pred + g * residual\n", + " results.append(x_est)\n", + " return np.array(results)\n", + "\n", + "book_plots.plot_track([0, 11], [160, 172], label='Actual weight')\n", + "data = g_h_filter(data=weights, x0=160., dx=1., g=6./10, h=2./3, dt=1.)\n", + "plot_g_h_results(weights, data)\n", + "print(weights)\n", + "print(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "e52ce31e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy.random import randn\n", + "def gen_data(x0, dx, count, noise_factor):\n", + " return [x0 + dx*i + randn()*noise_factor for i in range(count)]\n", + "\n", + "measurements = gen_data(0, 1, 30, 1)\n", + "data = g_h_filter(data=measurements, x0=0., dx=1., dt=1., g=.2, h=0.02)\n", + "plot_g_h_results(measurements, data)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "0a35e6e9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ffok8CItLcx1nazUejpYpSZSjJTltzclpa46LjRkutmY4W5thavzfSkR3HsfgczWYuVuOkmCR478L6fXk0IUT8M88gnxTFsL19PTk9u3brz3t5m3eCxmS9xxJmIQQQgghRGZ5/Pgxbdq04ejRo2na8ufPz5YtWyhVqlQ2RPZia9asoWvXrgD079+fRYsWGbQvXLiQYWN+xMG7P5YFU6rg5bQ1o6KnIw+fxuEfHkdEXPIr76NSgZOVGhcbc5K0Om6HxvzXqNcR/+AKcTeOEnfrBLrYCKXJ1taWvXv3UqlSpZdePzY2ln/++YfAwEAcHBxo3LixUkn7dcmQPCGEEEIIId6RhIQEGjVqxIULF9Jtv3v3Lt7e3pw9e5Y8eTJW7vpdCgoKUrbr1Klj0BafpOWBbWnc+s5HZaJGpdfSv24hhnkVwjrVELzI+GQehsfxMDwlgXr4NI6QqERCoxMJjUrgcXQiGp2eJzFJPIlJAsDESEWNgs40KelKORdjZk7ZwR83D6H7/yp8RkZGtGjRgkmTJlG8ePEXxq/T6fjpp5+YOXMmkZGRyn61Wk337t2ZNWsW1tbWmfJevS1JmIQQQgghxCdr9erVSrLk5ubG9OnT8fb25vLly4wePZoLFy7w+PFjpk6dyvz587M52v84Ojoq2xcvXqRLly7o9Xp8rgbz004/AiLiUZmoib93niY5YxnTpEWaa9hZmGKX246Sue3SvYdOpyc8LonQqERCohNITNZRLb8Tdpb/DVFctGgR06ZN49KlS2g0GooVK0auXLleGrter2fAgAEsWbIkTVtSUhJLly7Fz8+PvXv3KksXZScZkieEEEIIIT5ZVatW5dSpUwAcO3aM6tWrK21Pnjwhb968xMbGYm1tzZMnTzAzM8uuUA2EhITg4eFBcnIyVrb2jF+8hVNhppx78DTlgNgwQncvJP7WCfbv30+9evWyN+BU/v33Xxo1agSk9Eh1794db29vLl26xMKFC4mNjQVg6tSpjB49+pXXkzlM6ZCESQghhBBCZAY7OzuioqLw9PTk/v37adpbt27Nli1bALhz5w758+fP2gBfouOAr9lzNx7rEnUxMk8ZvqbSaYg69TdPj/+FXpNI+fLlOXv27AvXU80OrVq1YuvWrQAsXryYzz//XGk7c+YMVapUQa/X4+npyd27dzEyMnrRpQCZwySEEEIIIcRriYqKYvXq1Zw4cQKNRkPJkiXp3bs3uXPnfuE5z3qMIiMjSUpKQq1WG7Q/qzSX+tjsFJOoYdvFQNad8eeygze2FVL2ayKCibm8h5gre9DGhAMpVeo2btz4XiVLkNKTB+Dk5ESvXr0M2ipVqkTdunU5cOAADx48ICAgAA8Pj2yI8j+SMAkhhBBCiA/e2rVrGTBgANHR0cq+9evX88MPP/Ddd9/x/fffp5s41KlTh40bNxIREcHChQv54osvlLYjR44olfMKFCiAm5vbO32G2EQNm84/IiQqkZhEDTGJGmJT/Tc2UYt/eBzxyVoATI1VeBfJgVnAWbZvmEHk3TtASiLSt29fRowYQY4cOV52y2yRnJxSnc/CwgJjY+M07TY2Nsq2RqPJsrheRIbkCSGEEEKID9qWLVto06YNL/tY+8MPP/D999+n2X/w4EGD+T2tW7dWij6sWLGCpKSU6nAzZ87kq6++yvzg/19QZDx9VpzFLyjqlcfmz2FF50p5aFM+N07WKb1eer2e0NBQNBoNrq6u6SYi74uaNWsqvUzPz68KCgoif/78JCQkYGdnR2hoaJpev+fJHKZ0SMIkhBBCCCEAtFothQoV4t69ewB06NCBb775BisrK1asWMGMGTPQ6/WYmJjw8OFDXF1d01xj+PDhzJ49+4X38Pb25p9//nnlB/c3dTUgkj4rzhAanYiztRnNSrlibW6ClZkJ1mYmWKn/23ayVlPU1SbLhtn5+/uzaNEiduzYQXR0NO7u7nTv3p2uXbtiaWn5RtdcuXKlMhTP2dmZn376SSn6MG7cOPz8/AD44osvXvrn8owkTOmQhEkIIYQQQgDs2bOHhg0bAlCvXj327dtnkEx8/fXX/Prrr8CLq67p9Xpmz57N1KlTCQkJUfZbWVnRr18/pkyZgrm5+Uvj0Ov1nD17luPHj6PRaChVqhTe3t6v7OnZ4xvCF2svEJ+spXBOa5b1qoS7w5slIm8jJiaGx48fY29vj4ODAwAbNmyge/fuJCYmpjm+YMGC+Pj4UKBAgQzfKykpibp163LixIkXHuPm5sbZs2dfWaIcpOiDEEIIIcQ7FRwczM2bN1Gr1ZQuXfqNvzUX2ePatWvKdrdu3dL0vPTo0UNJmHx9fdO9hkqlYvjw4QwePJj9+/cTFBSEvb09Xl5e2Nmlv0ZRahcvXqR///6cOXPGYH++fPmYNWsWLVqkXQNJr9ez7Nh9ftrpi14PtQo581vX8tiam6Y5FuDx48fs3btX6eWpX79+pvR4nT59mp9//pmtW7ei1abMjapVqxbNmjXju+++U+YQqVQq7O3tefo0pWz57du3ady4MRcvXsTKyipD91Sr1ezcuZMuXbrg4+OTpr1EiRJs2rTptZKlrCAJkxBCCCE+SZcvX2bcuHHs2LEDnU4HpJSY7t27Nz/88MNrfVAW2c/U9L8EIzIyMk176n0JCQnKkC+1Wk3t2rXp2rWrUmRArVbTuHHjDN3/4sWL1K5d+79iEyqjlB+dhnv37tGqVSvWrVtHhw4dlHM0Wh0/bvdl9ckHAHSpkocfW5TA1Dht+eyoqCi++uor/vjjD2U+FUDOnDn53//+x9ChQ994eN769evp1q1bmsIKR44c4ciRI8rrLl26MGPGDFxdXTl9+jS9evXCz8+P27dv88cffzBgwIAM39vBwYFdu3Zx9uxZ1qxZoySpLVu2pGHDhq8sJZ6VZEieEEIIIT45R48epXHjxsoCmc8rXbo0Bw8eVIYmif+EhISwdOnSNHNa2rVr987m+LzMpUuXKFu2LACFChXi3LlzSgKk0+lo2bIlO3bsAFJ6SZ7/6GtnZ8eyZcto06bNK+8VFRXF4cOHleeuUaMG1apV4/xNf8zzlsOlVG1MchcnSW+EcUIEUY9ukRz2ENP4MDavXEDJPDkwUsGwtRc4eOMxKhWMaVKUfrXyp5v0xMbGUq9evTQ9V6mNGTOGyZMnv+7bpbh16xYlS5ZUkjBXV1dq1qzJlStXuHHjhnJcjhw5CAgIMEhMz549S6VKlQCoVq0ax48fz/D9M5PMYUqHJExCCCGEeFMJCQnky5eP4OBgIGWuRJs2bQgPD+fvv/9W5mv06NGDlStXZmeo750dO3bQqVOndBPNEiVK8M8//5AnT54sj6tGjRrKh/b8+fMzYMAArK2tWbVqFadOnXrl+UZGRuzatUuZC/W8+Ph4xo4dy5IlS4iJicHIzApzzzI4lqiBLkdhTB1ef+iYuakRCck6zE2NmNWxLI1Lvvjc8ePHM3HiRACsra3p168fRYsWxcfHh82bNyvHnTlzhooVK752DABffvklc+bMAaB79+4sWbIEtVqNXq9n+PDhSpurqytBQUFpzndxceHx48e4u7vz8OHDDN07s0nClA5JmIQQQgjxplatWkXPnj0BqF27Nj4+PlhYWABw48YNKleuTFRUFKampjx8+JCcOXNmZ7jvjbNnz1KjRg2DYWFmZmYGBQGKFSvGuXPnlPczq1y7do2aNWsSERHx0uNMTEz47rvv6NKlC+Hh4UydOpUtW7YAULJkSS5fvpympychIYEGTVtwzj8CszylMPcoiTpnAVRG/xVz0Gs1uFsk06lOGWoWcsbN3oI7j2PYffwSc1f+hamzB/YeRUk0TnlfnK3NWNqzImU87F8Ya3JyMu7u7oSGhmJsbMy5c+coU6aM0j5lyhTGjh0LQK9evVi+fHkG3rGURW39/f0xMzMjKCjIoDf15s2bFClSRHn95MkTnJycDF67urqi1WopVqzYC+eGZZV3nRu8P4MDhRBCCCGyQOpJ5hMnTjT4cF+kSBE+//xzIOUD68GDB7M6vPfWxIkTlWSpdevW3Lt3j/j4eA4cOKBUSvPz82Pt2rVZHluJEiU4duwYderUSdOW+oP+uHHj+P777ylUqBBVqlTh77//Vnpmrl69yunTpwGIjE9mr28IP+3wpcaE7fhXHIpLu++xq9wGs1yFURkZYxofTtTZbYRu/JGHczpTX3WFYd6FKJfHgZy25lQv4EzLEg483fc7oevHUTV0O1d+aMjOL2pyeFTdlyZLkJK0hIaGAtC0aVODZAlSeoieVe5LPd/odYWHhwOQJ0+eNENPCxYsiLW1tfJ6/fr1yrZWq2X06NFKgYimTZtm+N4fGkmYhBBCCPFJiYmJUbbz58+fpj11meTUx37Knjx5oswDyp07N+vWrSNv3ryoVCrq1q3L6tWrlWMz2tORWYoXL87Bgwe5evUqv//+O/Pnz+fIkSPUrFlTOaZbt24G5xgZGdG1a1fl9ZVrvsz89wYVJu7h81VnWXL0HmE6S1RGxiSHB+DlacasjmU5McaLW7O70yxXHPF3zqBPimfRokVK8ZBnUr8XpUuXxsbclBJudliqX113LXVPnr29fZp2c3NzJWFKTk5+5fWe5+bmBsCdO3fw9/c3aNNqtQbl0IcMGUK9evUYPHgwRYoUYdmyZUBKwY1BgwZl+N4fGkmYhBBCCPFJyZs3r7L9LAlIbfv27eke+ynz9/dXkoHGjRunKe5QrVo1nJ2dAbh//35Wh2egRIkS9OvXj0GDBlGzZk2DYgXpDdl7VibbxMGN5Q8dmbP/NhqdnvzOVjQpbMPjbdN49FsPyjzawrJB9WlVLje57FJ6JefNm6dcJyQkhFatWnHgwAHOnDnDkCFDlHa1Wk2PHj0y9BwFChTAzMwMSPl7+nwFwH/++Ud5nmLFimXo2pBS+Q5SCmN0795dmYcUGRnJwIED09zv4MGDLFiwgDt37gApyebSpUvfaB2mD40kTEIIIYT4pDybvwQwevRo1q1bh0ajITw8nNGjRytD9vLkyUPdunWzKcr3S+rhWXfv3k3THh4ernx4z+iaPO9arVq1lO1p06YZVMkLCwtjyZIlWJdpTK5ecwiIN8HOwpR5Xcqxf0Rd+pezIc7vMNqY8HTnstna2hq8N9u3b8fLy4vKlSszf/58Zf+PP/5Ijhw5MhS3ra2tUor86dOn1K9fn927d+Pv78+iRYsM/h4/G0aaEQMHDsTR0RGAw4cPkzdvXooVK4arq6vSg2RkZMRXX32VJiny9vZm3759dO/ePcP3/RBJ0QchhBBCfHJat26tTPaHlB6A5ORkgw/Ty5cvp1evXlkf3HtIp9NRqFAhJVnatWuXsl6RXq9n6NChSoLwxRdfMHv27GyL9XkRERF4eHgowyurV6+uFH1YtHINSWU7YFmwMgA1CjrxS/sySg9SREQEOXLkQKPR4OzszL179wwSpL1799KgQQMgpaDE8+sZqdVqJkyYwKhRo95oraTbt29TuXJlpRcsPXXq1GHfvn0GQ+he18mTJ2nWrJkynyk1ExMTli9fTrdu3dDpdNy4cYOoqCjc3d3JnTt3hu/1LkmVvHRIwiSEEEKItxETE0OHDh3YtWtXmjaVSsXUqVMZNWpUNkT2/po1axZfffWV8rpZs2YUK1YMHx8frl69CoCxsTG+vr4ULlw4u8JM19q1a+natatBQmxRoDJOTb7A2MoevTaZITXdGdG8AkZGholNp06dlKIHtWvXZurUqRQrVoxdu3bx9ddfK+Xpn81XOn78OBqNhpIlS9KjRw9lqOKbOn/+PG3atOHBgwdp2po1a8aff/75VossBwcHs3DhQv744w9l8dhWrVoxbNgwihYt+jahZxlJmNIhCZMQQggh3pZOp2Pv3r0sXrwYX19f1Go1derUYdCgQQYllUUKjUZD+/btDXrmnvf777/Tr1+/rAsqA3bs2MGIESO4HfgEuxpdsCnTCACz+CfM714Z74rpzwPy8/OjcuXKLy0AUrlyZY4ePWowXyozJScns2XLFnbs2EFUVBQeHh50795dWTz2UycJUzokYRJCCCGEyHoajYYZM2Ywd+5cAgIClP1Vq1Zl/PjxNGnSJBuje7m7j2NYeOgOf597hPb/P/22K+nATx2rYG768uFsx48fp02bNoSEhKRpq127Nps2bTIoXy6yliRM6ZCESQghhBAi+2g0Gi5duqTMaSlUqFB2h/RCVwMimX/wNruuBvPsU2/lfI583aAwVfO/fpITFxfH2rVr2blzp/LcPXr0oF69eq89P0mn0xEeHo5arZbPsJlIEqZ0SMIkhBBCCCFeRK/Xc/JuOPMP3ubIrSfKfu+iLgyuV4AKno5ZGs/jx4/59ddfWbp0qbIYbdmyZRkyZAi9evXCxOTV6zKJF5OEKR2SMAkhhBBCiPQERcYzYsMljt0OA8DYSEXz0rkYWLcARV2z/nPj7du38fLyUtY5el7z5s3ZuHFjmrWtxOt717mBpLNCCCGEyFZarZYDBw7g6+uLmZkZtWrVonjx4tkdlsgGSUlJ/P3336xZs4bAwEDs7e1p2bIlPXv2fK1KcHt9Qxix8RIRccmYmRjRoaIH/Wvnx8PRMguiT0ur1dKyZUslWTI1NaVmzZqEh4dz6dIlIGXtpnHjxvHzzz9nS4zi1aSHSQghhBDZZtOmTYwYMYJ79+4Z7K9Xrx6LFi16r+fGiMx17949mjZtyvXr19O0OTk5sXnzZoNFaFNL1GiZuus6y4/dB6Bkblvmdi5PPufsXUR3+/bttGjRAoCiRYuye/du8uTJA6SsZdWyZUuSk5OxsbEhMDDQYI0n8fredW5glOlXFEIIIYR4DatWraJt27ZpkiWAAwcOUKNGDW7fvp0NkYmsFh0dTcOGDQ2SpdSFFMLCwmjatCk3btxIc+69J7G0mX9cSZb61szH34OqZ3uyBPD3338r29OmTVOSJYAmTZrQo0cPIOX59+zZk+XxidcjCZMQQgghslx4eDiDBg1SXterV4/Fixfz888/4+npCaRMlB86dGh2hSjeUFRUFAsWLKB79+507tyZyZMnExgYCKQMUdu2bRvNmzenYMGCFC9enEGDBvHTTz8pyXHhwoU5cOAAWq2WK1eu4OXlBaQsNjxlyhSDe22+8IjP5hzhWmAUDpamLO1ZkXGfFcfM5OVlwrNKWFiYsl2xYsU07an3hYeHZ0lMIuNkDpMQQgghstzKlSuJi4sDoGvXrqxevVrpUejfvz+lSpXi0aNH7N69m9u3b1OwYMHsDFe8pnXr1jFgwACioqIM9n3//feMGDGC06dPs3//foNz/Pz8DF5v2LCB0qVLA1CyZEm2bNlCnjx5iIiO5a9tuxjp/4RklQmrTzzg7/OPAKiSz5HZncrhamf+jp8wY3LmzKlsHzlyhA4dOhi0HzlyRNl2cXHJsrhExsgcJiGEEEJkufbt27Nx40YALly4QNmyZQ3aJ0yYwPfffw+kDN3r3r17VocoMmjr1q20bt2a1/1oaWVlRWJiIhqNRtnn7JKT7SeucejmY87cCyc8NomoBA1hUXHojdL2Ghmp4Evvwgz1Koix0euthZSV9u7dS4MGDQDIkycP27dvp3Tp0uh0Ov744w969eqFXq/H0dGRR48eYWFhkc0Rf5ikSp4QQgghPjrJycnKto2NTZr21PtSf6AW7yetVstXX32lJEvt27fn66+/xtramhUrVjBjxgzlWHt7e5YvX06LFi2IiYnh+1/msWTHMSzylcfcszSdfj+Z9gb/nyzp9TqsTI0w1iVhoU+kUa5Eupev9l4mSwBeXl5UqlSJM2fO4O/vT5kyZShVqhRPnz7l0aNHynFfffWVJEvvMUmYhBBCCJHlSpYsydatW4GUHqQff/xRadNqtaxevVp5XaJEiSyPT2TM/v37leIddevWZf369coQy19++YW9e/cqZbRrNWiKukAVvt/my+Fbj3mQVAanhmWUa5lqE2hWIT81C+XAw8GCcyeO8MXg/ugSYrFSG+MfE60cewb4ZbQ5X375JZMmTcLY+P2Yu/SMkZERmzdvpkGDBsrQwytXrhgc07NnT8aOHZsd4YnXJAmTEEIIIbJc3759mTx5Mnq9nkmTJpGUlETXrl0JCwtj2rRpXLhwAYAyZcpQqVKlbI5WvMq1a9eU7e7duxtUuIuIS8I0X0UcnKtg7lmayznyMvjP80q7iZEKB+1Tbh7eSsK98ySF3OV0tarYeHuz6tIltm/frhwbk5T23gkJCfz888+EhoaydOlSg3u/D3Lnzs3p06dZvHgxixcv5vr165iamlK7dm2GDh1KixYt3ruYhSGZwySEEEKIbDFy5Eh++eWXF7abmJiwe/dupUqaeH/99ttvSkXDGTN/pVbrHuz1DeHIrSf4BUfx/KfNIjltqFbAieoFnKhe0JnvRo9g9uzZr3WvXLly8c0331C0aFF8fHxYuHChMmzzwIED1K1bNzMfLdM9++gtSVLmkTlMQgghhPgo/fzzzxgbG/PLL7+g1WoN2pycnFixYsVHnyxptVqePHmCWq3GwcEhu8N5Y+UrV8OiUDUsC1Vmjn8u5iw8YdBuFBNK5M3TJPhfIZdxDH+fOqos0nr16lWWLl0KgLGxMYUKFTJYjylXrlw8ffqUhIQEzMzMOH78OHnz5gWgWbNmlCpVigEDBgCwYMGC9z5hkkTpwyM9TEIIIYTIVo8ePWLFihX4+fmhVqupXbs2HTt2xNLSMrtDe2dCQkKYMWMGy5YtU9bqKVmyJEOHDqVv376YmLz9d9q+vr6cOHECjUZDyZIlqV69eqZ+WI9J1LDtYiB7fIM5dieMJI3uv8akOApbJ1HEVsOpbas5c2Sfwbk5cuSgVatWhIWFsW3bNqWHqE+fPixZsoTLly8TGBiIvb09ZmZmVKhQAYB27dqxYcMGg2slJSXh6OhIbGwsefPmTXchZPFxe9e5gSRMQgghhBBZ6ObNm3h5eREQEJBue7Nmzdi0aRNqtfqNru/n58egQYM4dOiQwf7ixYsze/Zs6tev/0bXTe1heBy9lp/mzuNYZV9OaxP8j2/n6bXDJD7yBZ1hr6FKpcLc3Jz4+Ph0r1mhQgX279+f5rPdpUuXlLLznTp1Yu3atQbtGo0GR0dHoqOj8fT05P79+2/9fOLD8q5zA6NMv6IQQgghhEiXVqulZcuWSrKkVqtp0KCB0oMCsHPnTv73v/+90fV9fX2pUaNGmmTpWVvjxo3Ztm3bmwX//y4+jKD1/GPceRyLq605IxsV4d+vanPyfw3ZO30QlT3t0yRLRYoUYdeuXZw7d44OHToY9KA5OTnx7bffcvDgwXQ/7BYsWBArKysAtm/fTlBQkEH7+vXriY5OqZxXrly5t3o2IdIjPUxCCCGE+Ojp9Xr0ej1GRtn7XfG2bdto2bIlkNLjs3v3bnLnzo1Gp2fX7j2079QZjU6Pta09x06cwtTMAp1eT0EXa0yNXx17zZo1OXbsGAD58+enf//+WFtbs2rVKk6fPg2kJCj+/v5vNOTR52oww9dfICFZR/FctizvXYmctuZpjrty5YoyHLBUqVLUrFnTYDhgWFgYt2/fRq1WU7x4cczMzF5630GDBrFw4UIAChQowNixYylWrBi7du1i+vTpJCQkALBr1y4aN26c4ecSHzYZkpcOSZiEEEII8So6nY6//vqL+fPnc+LECbRaLSVKlKBfv358/vnn2TJHqlevXqxcuRKAeWu2E2qZl+2XgwiPTadedipOVmpals1NuwruFHdL/7NP6qFrBQsW5MzZczyK0aNSQdGc1rRs2ZKdO3cCsHz5cnr16pWh2JcevcdPO33R66FekRzM7VIea7OsqR8WFBRE5cqVDRZ7fV6bNm3YuHGjFFX4BEnClA5JmIQQQgjxMsnJyXTq1IlNmzal2162bFn+/fdfcuTIkaVxNWrdiZPBOqxLemHq5JHuMXq9Dr0mGQszU6wszEnS6IhJ1CjtxXPZ0raCOy3LuuFs/V/PzLx5v/HVD1Ox8CxLpc+68sTIkcj4ZADKethT0ymekV0agV5H3759WbJkyUtjDQkJISgoCFs7e1ZdiWXF8fsAdK2Shx9blMDkNXq8MtPdu3fp1KkTZ86cMdhvZGTE559/zpw5c17ZUyU+TpIwpUMSJiGEEEK8zPNrPOXLlw8rKyuuXr2q7PPy8mLfvn3pnZ6pohKS2esbwt/nH3Hs1hP4/x4QE5WepqVz07aCO2Xd7VGbGNGnVw/WrV0DpAzfa968OclaHYdvPubv84/Y6xtKkjalGp2JkYq6RVyoUdCJSw8j2HPZn1idYY+PjZkJiVqdUsEuOTyAqNObaVkmF3+sXJZuvAcOHGDy5Mns3bsXlakZzs1HYlmoKgBjmhSlf+382daLo9frOXHiBDt37iQqKgp3d3e6dOmCh0f6yaf4NEjClA5JmIQQQgjxIhEREeTOnZu4uDhMTU1Zt24drVu3RqVScfbsWZo3b05wcDAAp0+fplKlSplyX71eT2h0ItcCI7kWEIVvUBTXAqPwD48zOC7B/wqx1/bjEH2frX+vp1y5cmi1WlatWkXfvn3R6/U4OTnx6NEjzM0N5wdFxCWx/VIgG8894tKjyDQx6JITSQzww804mmVTRlMqtx1P45JZdeI+C/f5kawyBcBCpWFw/eJ0r+aJvWVKNb7YRA3zlv3BDz/PwtjaEWNrJyyL1sTMtSB6TRJPdszg80YVmDVrlgx7E+8VWbhWCCGEECIDduzYQVxcSpLSr18/2rRpo7RVrFiRiRMn0q9fPwDWrVv3WgmTTqcnIj6ZsJhEHsckEhaTxJNU/w2IiMc3MIqwF8xFyutkSety7rQq50bHZhM5dfkUMUD58uUpXrw4T58+Naj+9tVXX6VJlgDsLdV0r5aX7tXyciskmo3nH+EXFE0Zdzuq5HOgW+MahN69TSjws/Y+X3/9NdbW1oTsXcHd2fOwKlUf28qtibd1Ycaemyw4dAc3ewtCIhOITtQAOcjZaZLBPVVJsQT/9T2JAdeZc+MY1apVo1OnTq98z4T4WGQ4YTp8+DDTp0/n3LlzBAUFsXnzZlq1aqW0p57M+EyjRo3w8fFRXoeHhzNs2DC2b9+OkZERbdu2Zfbs2cqKz0IIIYQQbyokJETZrlmzZpr21PtCQ0PR6fRsPPeIi48iiE7QEJOQTEyihuiEZz8pr3WvMSbHSAUFXawplssWTeg9zuzZzKWDO/GPjSCsRAmM+vdnzZo1tGjRgmvXrgEp5b5T69OnD2PGjHnlvQrltGFMk2IG+2bNmE7r1q2BlHLb69evN2iPPred4c0qUKF1QxYduotvUBS3Q2OUdl1iHNqYMFztLKhdqTQeDpa0r+jBP0WeMnDgwJR7zJolCZP4pGQ4YYqNjaVMmTL06dPH4Bub1Bo3bszy5cuV189PwOvatStBQUHs2bOH5ORkevfuTf///wUihBBCCPE2nJ2dle0zZ87QuXNng/bURQMcHR1ZevQek/7xe61r21mY4mytxtna7P9/1DhZm5HT1oyirrYUcbXBGB2dO3fm77//Njj36tWrfPHFFyxfvpwdO3awbds2Fi9ejJ+fH2q1mtq1azN06FCaNWsGpAwX/PPPPwkMDMTBwYGWLVvSuHFjjI2NXxhfq1at+OOPPxg4cCAxMTEGbcbGxowdO5YffxiPSqWiRRk3zvtHkJCsJaetOXUrlyHgwV3Mzc3xCwkxGNrUv39/5s2bx9WrVzl16hSPHz/O8oIZQmSXt5rDpFKp0u1hioiIYMuWLeme4+fnR/HixTlz5gwVK1YEwMfHh6ZNm/Lo0SPc3NxeeV+ZwySEEEKIF3ny5Anu7u4kJiZiYWHBzp07qVevHgC3bt2iQYMGPHjwAIBV2w8w4UQcyVo9nSt7UNDFBhtzE2zMTLA2N8HG3BRrMxNszU2wt1SjNnl1ZbjnC07kzZsXKysrpUcJXl5wIjw8nM6dO/Pvv/+maStWrBibN2+mSJEiL40hMjKSP/74g+PHjytrIfXu3ZvcuXO/8BxbW1uio6MpWLAgt27dStPesWNH/vrrLwBu375NgQIFXhqDEFnlvS768KKEacuWLajVahwcHPDy8uKnn37CyckJgGXLlvHNN9/w9OlT5RyNRoO5uTkbNmxQupFTS0xMJDExUXkdFRWFh4eHJExCCCGESFfqhU4BypUrh7W1NceOHUOnS6kYV6l6TaxaT+Tek1galcjJwm4V3rqYwfMFJ9auXUubNm1eu+BEUlIStWvX5tSpUy+8R65cuTh79uxrfcmcEcWLF8fPzw+VSsWtW7cMEqKEhAQ8PT0JDQ3FxMSEp0+fylQK8d541wlTphfQb9y4MatWrWLfvn38/PPPHDp0iCZNmqDVagEIDg7GxcXF4BwTExMcHR2VXyDPmzJlCnZ2dsqPlI4UQgghxMvMnDkTb29v5fWFCxc4cuSIkiwVKlSIygOmce9JLK625kxtUzpTKr89X3Cibdu2ynWfFZx4Zt26dWnOX7NmjZIs5ciRg8WLF3P37l02b95M8eLFgZRFXKdOnfrWsT6ve/fuQEq1v86dO+PnlzJMMTg4mJ49exIaGgpA69atJVkSn5RMr5KXehJgqVKlKF26NAUKFODgwYMGv7gyYsyYMXz99dfK62c9TEIIIYQQ6bGwsGDXrl0sWbKE+fPnK+sv5c6dm379+lGsUVdGbbmBSgW/diyLg5X6je4TFxfHiRMniI6Oxt3d3eDL39cpOPG8xYsXK9sbNmygTp06QMo6UlWrViV//vzEx8ezcuVKfvnlF9TqN4s7Pf3792fOnDkEBwdz5swZihcvTq5cuQgJCVESTbVazbfffptp9xTiQ/DOl2jOnz8/zs7O3L59GwBXV9c0vyA0Gg3h4eG4urqmew0zMzNsbW0NfoQQQgghXsbU1JRBgwZx5coVoqKiCA8P5+HDh/T9YiQTfe4AMKRuQaoVcMrwtRMTExkzZgzu7u7Ur1+f1q1bU6lSJWbOnKkck7q4RHr7HB0d07Q/m+fk4eFB7dq1DdpcXV1p2LAhkPLlcUBAQIbjfhknJyd8fHzIlSuXsi8oKEhJlszNzVm/fj3ly5fP1PsK8b575wnTo0ePCAsLU/7nq1atGhEREZw7d045Zv/+/eh0OqpUqfKuwxFCCCHEJ8jGxgYHBwe0Oj3D110kOkFDWQ97vqxfKMPXSkpKonnz5kydOtVgTjZgsJbSwoULOXjwoPL61q1bjB8/Xnndrl27NNc2NU1ZWDY2NlaZzpBaZGRkmmMzU5kyZfD19WXGjBmUL1+eXLlyUaxYMb799ltu3LhhMG9diE9Fhos+xMTEKL1F5cqVY+bMmdSrVw9HR0ccHR358ccfadu2La6urty5c4dRo0YRHR3NlStXlPLiTZo0ISQkhIULFyplxStWrPjaZcWlSp4QQggh3sSsvTeZtfcW1mYm/PNFLfI4Wb70eK1Wy/HjxwkMDMTe3p5atWoxZ84cZZ0kExMTOnbsSNGiRfHx8eHYsWNprlG+fHmsra05evSo0ltTpUoVTpw4kWbeVOvWrZVKw4sWLaJ///5K26lTp6hatSqQUnnvzp07GBm98+++hXjvvfPcQJ9BBw4c0ANpfnr27KmPi4vTN2zYUJ8jRw69qamp3tPTU9+vXz99cHCwwTXCwsL0nTt31ltbW+ttbW31vXv31kdHR792DJGRkXpAHxkZmdHwhRBCCPGJOn0vTJ/v2x16z9E79FsuPHrpsTqdTr9o0SK9p6enwecde3t7va2trR7Qq1Qq/eHDhw3OGzVqVLqfk1L/FCpUSP/w4cN07/vvv/8qx6lUKn3Xrl31y5Yt0w8fPlxvaWmptP3888+Z9r4I8aF717nBW5UVzy7SwySEEEKIjIiMT6bp7CMERMTTplxuZnYs+9Ljx44dy5QpU156TMOGDdm9e7fBvqioKHLkyEFSUhIuLi7kyJFDmZfk5uZG//79+fLLL7G3t0/3mnq9noEDB/L777+/8L41a9Zkz549mJubvzQ+IT4V7zo3yPQqeUIIIYQQ75OYRA1fr79IQEQ8nk6WTGhV8qXHHzt2zCBZatSoEd7e3ly+fJk1a9Yow+qioqLSnGtjY4ONjQ1hYWGYmZlx9epVoqKi0Gg0ODg4vLJ0uUqlYsGCBeTJk4cZM2YYzJEyMzOjZ8+ezJw5U5IlIbKQJExCCCGE+GhdehjBl+sucD8sDlNjFbM7lcPa7OUff+bNm6ds//zzz4waNUp53apVK6VYw5kzZ4iLi8PS8r95UIcOHSIsLAxAWfg1o994GxkZ8b///Y+vvvoKHx8fgoKCsLe3p1GjRjg7O2foWkKItydD8oQQQgjx0dHp9Px+5C6/7L6BRqcnl505szqWpUr+V5cQz5kzJ6GhodjZ2RESEqIUrXrGycmJ8PBwAGrXrs3s2bMpWrQou3btYtiwYUq579WrV9OtW7fMfzghhAEZkieEEEIIkQEhUQl8tf4ix++k9PQ0LeXKlNalsbN8vTLcCQkJADg4OKRJliClSvC+ffsAOHz4MOXKlUv3mA4dOrzpIwgh3iOSMAkhhBDio7HHN4RRGy/xNC4ZC1NjfmhRnA4VPV45dyi1woULc/bsWe7fv8+ZM2eoVKmS0vb06VNOnz790vOrVKnC1q1bUavVb/wcr+PixYvs2LGD6Oho3N3d6dChAzlz5nyn9xTiUyQJkxBCCCHeGzqdnscxiTwIi+NBWCz+4XEp2+FxBEfGY2VmgrOVGc42apytzZQfJ2s1R289YfXJBwCUcLNldqdyFHSxznAMffr04ezZswC0b9+eWbNmUb9+fS5dusSIESOIjo4GoGfPnlSqVIkdO3YQFRWFh4cHPXr0oFGjRhgbG2fem/Kchw8f0qNHD4NFcQG++eYbhgwZwrRp097JorZCfKpkDpMQQggh3im9Xs+hQ4c4ceIEGo2GkiVL8tlnnxl8qI+IS+LLdRc5eTeMRI3ure7Xr1Y+RjQqgpnJmyUtcXFxVK5cWSkHnh4HBwfOnj1L/vz53zTMN/L48WOqVKnCvXv3XnhMly5d+OOPP17aq/b06VPWrFmDn58farWaOnXq0KxZM0xM5Lt08eF517mBJExCCCGEeGdOnjxJ37598fX1Ndjv6urKrFmz6NixI3q9nn6rzrHXLwQAYyMVbvbmeDpakcfJkjyOlng6WuJmb0FckpYnMYn//UQnKdtGRiqG1y9MncI53jruwMBAWrRowblz59K05c6dmy1btlCxYsW3vk9GDRs2TKni5+HhwejRoylatCg+Pj7Mnj2b5ORkAPbs2UP9+vXTnK/X65k2bRo//vgj8fHxBm2enp6sWrWK2rVrv/sHESITScKUDkmYhBBCiPff6dOnqVu3bpoP5qmtXLkSTf5aTNjhi9rYiFV9K1PB0wFTY6MsjDR9Wq0WHx8f/vzzT6W0d6tWrejQoQMWFhZZHk98fDw5c+YkOjoaCwsLbty4gYeHh9K+fPly+vTpA0C7du3YsGFDmmtMnDiR8ePHv/AeZmZmHDx4kKpVq2b+AwjxjkjClA5JmIQQQoj3m16vp0KFCly4cAFIqRo3bNgwrK2tWbFiBf/88w8A9vnL4NRxMhqdngktS9CjWt4017pw4QJr1qwhMDBQSVq8vb0xMsr+pCorXb58mTJlygDQoUMH1q9fb9CenJyMo6MjMTEx5M2bN82wvUePHpE3b160Wi0AAwYMoGvXroSFhfHLL79w7NgxACpXrsypU6ey4ImEyBxSVlwIIYQQH5zTp08ryVKpUqU4ceKEUqK7Xbt2dOnShfWbtmFZfyganZ5GJXLSvaqnwTUiIyPp1q0bO3bsMNg/f/58Spcuzd9//03BggWz5oHeMxmp+vfMsmXLlGRpxIgRTJ8+XWlr2rQp5cqVw9fXl9OnT3Pp0iUlORPiU/dpfTUjhBBCfKRiY2NZsmSJ0vvSs2dP9u7dS3YNJEldenvAgAEG6xmpVCqGDh2KU+OhmDrkwlwby7S2ZQySgOTkZJo1a5YmWXrm8uXL1K1bl+Dg4Hf3EO+ZQoUKYWNjA8C2bdt49OiRQfuaNWuIiYkBoEKFCmnOf5bAAvTr18+gTa1W06tXr3SPFeJTJwmTEEII8YE7evQo+fPnp1+/fmzdupX9+/ezatUqGjRoQJ06dXjy5EmWx6TT/VfpLr0S14cDtFgVq41eq6FYxMk0i8quXbtWGSLm5OTEb7/9xvXr1/nrr78oUqQIAAEBAUydOvUdPsX7xcLCgh49egAp85lq1KjBggULOHDgAKNHj6Z///7KsQMGDEhzfuohjM+KQ6SWet+nNtxRiJeR/xuEEEKID5ivry9NmjQhNDQ03fYjR47QrFmzdD8gZ7bo6GiCgoJISkqiXLlyyv6lS5cqQ8EArgdHsfhcBAARh1dRp0SeNNdavHixsr1+/XoGDx5MkSJFaN++Pfv378fc3ByAFStWkJSU9I6e6P0zfvx48ubNC4C/vz+DBw/Gy8uLadOmKe9Dp06d0q2QV7lyZWV77ty5Bm2xsbEsXbpUeZ16sV4hPnWSMAkhhBAfsAkTJijDsOrUqcPJkyeJiIhg3bp1uLq6AinD4zZu3PjOYti6dSv16tXD1tYWNzc37OzsWLZsmbJG0enTp2nUqBE7duxg994DtPllJzqVMfF3zpJ0eRfdu3dPc80rV64A4O7ujpeXl0Gbm5sbDRo0AFLmOQUEBLyzZ3vfuLi4cPjwYWrVqpWmzcTEhC+++IJVq1alO8epd+/eqNVqABYtWkTbtm3ZtGkTixcvpkqVKty9exdI+XtUrFixd/sgQnxApEqeEEII8YF6+vQpLi4uaDQanJ2duX//PlZWVkr73r17lcTC29ubvXv3Zur99Xo9o0ePNigekJparUar1Rr0Ljk1+RLr0g3QRIcRtHwYM6dM4Msvv0xzrrOzM2FhYTg5OREcHJxmQVUvLy8OHDgApPS0pC6v/ak4d+4cO3fuJCoqCnd3dzp16qQkyS8yb948hg0b9sJ2W1tbjh49SqlSpTI7XCHemXedG0gPkxBCCPGBun//PhqNBoDPPvvMIFmClCTJ0dERgJs3b2b6/deuXWuQLBUsWJBmzZphZ2cHQFJSEqampuTMmRMA69INsC7dAL1OS8yeucyeNindZAmgRo0aAISFhbFq1SqDtnPnznHw4EEgpbdp6dKlVKxYkSJFiuDt7c3KlStJSEjI7Md971SoUIHx48fzyy+/MHz48FcmSwBDhw5lyZIlODs7p2krW7Yshw4dkmRJiOdID5MQQgiRAVFRUezYsUNZE6hZs2bkypUrW2Lx8/OjePHiADRp0kRZ2+iZ6OhonJ2dSUpKolChQi9Nms6dO8eSJUvw8/NDrVZTu3Zt+vbt+8Jn0+v1lC9fnosXLwIwa9YsvvjiC1QqFTExMXTu3FmpcNd77HTuWRTmXowxALXsI/lt8Gcv/Tfcx8eHJk2aACkFCHr27Im3tzeXL19m/vz5yjBEU1PTdOdnFS1alF27dinzfYShxMREtm7davDnXb169TcqVy5EdpOFa9MhCZMQQoisptVq+eGHH5g1a5byYR1S5o106dKFuXPnZvm/SRqNhrx58xIQEICRkRHHjh2jatWqSvu4ceP46aefAGjUqBEqlYrjx4+j0WgoWbIk/fv3p0OHDgwaNIg///wzzfXVajXz58+nb9++adru379Pvnz5gJSejrNnzxq0P/D3p3jDLthWbY+Za8paSWpjI7pWzcN3zYpjbPTyD+Z6vZ6+ffuyfPnyFx6jUqkMyqZbW1sb/NkULlyYCxcuYGlp+dJ7CSE+bJIwpUMSJiGEEFlJr9fTu3dvVq5c+cJjKleuzIEDB7L8w/mkSZP47rvvgJQEp1u3bhQtWhQfHx/279//yvOdnZ1fWXZ848aNtG3b1mDfuXPnqFixIpCyps/vv/8OQLJWx9aLgSw4eJs7j2MB0GsS6Ve3KP1q5yenrflrP5tWq2XixIn8+uuvREVFKfufDfN7tg5R+/btmTFjBu7u7hw/fpzevXtz69YtAH7//fc0aw4JIT4ukjClQxImIYQQWSn18DBjY2N69+6tDA+bN28e0dHRQEryMnbs2CyNLSEhgcaNG3Po0KHXOt7V1RULCwvu3btnsN/CwoLp06fTtWtXwsLCmDJlilJmulChQly/ft1gbZ6AgADc3d0BKFasGLuPnmX75UD+POlPQEQ8ANqEGKLPbSe/xp/zJw6/8TPGxMSwY8cOgoKCsLe3p1KlSpQuXRq9Xo+Hhwe3b99Wqr9BSlW+KlWqAClzoY4ePfrG9xZCvP8kYUqHJExCCCGyUosWLdi+fTsAy5Yto3fv3krb+fPnqVixovLh/f79+1m+6Gd8fDzfffcdixcvVpI3gHz58hEUFERCQgImJiYsW7aMrl27YmRkxOHDh2ncuDHx8SnJzfDhw/n111+Vc/V6PXXq1OHIkSNAyrpIN27cUOZutWrVih+m/MLlp8ZYlaiLuXsJ5VxHCxM0vv9ydcsC9Enx/PLLL3zzzTeZ9rznz5+nQoUKAPTt25clS5akOcbFxYXHjx/j7u7Ow4cPM+3eQoj3jyRM6ZCESQghRFZKXeI6JCQEY2Njg3Zvb29l+Ft2lriOjo7myJEjREVF4eHhwb1795Q1jvr378+iRYsMji9TpgyXL18GDIfVPTN37ly++OILg30qU3MsC1XFsngdLPOVB6OU90Kv16EJ8MX26U1u7VuLNjElEXNxceH69es4ODhk2nPevHmTIkWKAClrBj2rmPdMWFgYOXPmRKvVUrRoUfz8/DLt3kKI98+7zg1MXn2IEEII8Wl7Vrrb3Nw83d6j1OW8nx2bHWxsbGjatKny+uTJk8p2nTp10hyfO3duJWHy9/dP0/7w0SNM7HOhzlUIs1yFUecqhDpnQYxMzZRjNKF3ibq6nzi/I2hjwghMdb6zszP//PNPpiZLkFK+vECBAty5c4dDhw6xfft2mjdvDoBOp2Ps2LHK2k+NGzfO1HsLIT49kjAJIYQQr1C6dGmOHDlCQEAA+/bto379+kpbQEAA//77LwD29vbkzp07u8JM49kaTAAXL16kS5cuBu1ubm7K9vXr10lITOLUg0jO3g/n1K1gTiaWI/eA2mmu62ym4+mlPfgf2YQmPIBOnTphUqSJwSKqPXr0YPDgwa+1NlBGGRkZ8cUXXyhrOLVo0YKGDRumzKXavZvr168DKRUMBw8enOn3F0J8WmRInhBCCPEKq1evpkePHkBKEvLDDz8oRR/Gjx+vVGR7fh5QdgsJCcHDw4Pk5GSsrKzYt2+fUgzB39+fevXqcffuXUwc3LAu1QD7cg3Rm9sZXEOvSSIp9C5Nq5SgWbWSlPGwJ7+zFUFBQRQoUICEhATs7OwIDQ01KLzwrmm1Wjp16sTGjRvTbVepVCxdutRgvpkQ4uMkc5jSIQmTEEKIrJScnIyXl9dLq615eHhw5swZcubMmYWRvVrfvn1ZtmyZ8rpmzZpYW1uz/9BRTAtUxrp0Q8w9Sirt2rhI4u+cJjHwJklBN0l6/AA3VxcePXqUZlHT1MUw7t69q6zLlFW0Wi2zZ89mzpw5PHjwQNlfq1Ytxo0bR4MGDbI0HiFE9pCEKR2SMAkhhMhqUVFRdO/enW3btqVpK1u2LH///Tf58+fPhsheLiYmhiZNmijJntq1INZlGmNVrDZGZilrRqnQow6/w6NDfxF3+zToNKjValQqFYmJiTg5OREcHIyJieFIfi8vLw4cOABkb7ELrVbLtWvXlOGAefPmzZY4hBDZQxKmdEjCJIQQIrtcunSJNWvWKGsCtWzZEi8vrzS9L2/i6dOnrFmzBj8/P9RqNXXq1KFZs2ZpEpWMiomNY+TsP9h1NwGcCyj7rfXx9KhViO61CpPLzgI/Pz/l3lWqVOHzzz9XEsSlS5fSp08f5dxz585RqVKlbC2nLoQQIAlTuiRhEkKIj1toaCirV69WPrzXrl2bNm3aZOkcmayk1+uZNm0aP/74o7Iu0jOenp6sWrWK2rXTFl94lcj4ZP4685AVx+8ri8maGKnwKmhHz1qFqFYgB0ZGL070Ui/Ya2RkRM+ePZW5W/PnzycmJgaAyZMnM2bMmAzHJ4QQmUESpnRIwiSEEB8nvV7Pjz/+yOTJk0lOTjZoc3V1ZdWqVR/lvJSJEycyfvz4F7abmZlx8OBBqlat+lrXu/8klhXH7/PX2YfEJaWU13a0UtO1Sh66V/XExdb8ta6j1+vp27cvy5cvf+ExVatWZf/+/VhYWLzWNYUQIrNJwpQOSZiEEOLjNG7cOH766acXtpuamrJ//35q1qyZhVG9W48ePSJv3rzKukEDBgyga9euhIWF8csvv3Ds2DEAKleuzKlTp156rbgkDRN3+LHujD/P/nUvktOGPjXz0rJsbsxNjV96fnq0Wi0TJ07k119/JSoqStlvampK165dmTNnDjY2Nhm+rhBCZBZJmNIhCZMQQnx8Hjx4QP78+dHpdKhUKr788ku6dOlCeHg406ZNY//+/QCUL1+es2fPZsqcoffBhAkT+P777wEYMWIE06dPV9qSkpIoV64cvr6+QMpaSmXKlEn3OlcDIvli3QXuPo4FoF6RHPStmZ8aBZ0y5b2KiYlhx44dytytJk2avJM1loQQIqPedW4gC9cKIYR4LyxbtgydTgfA6NGjmTJlitLm7e1NhQoVuHz5MufPn+fChQuUL18+u0LNVBcuXFC2+/XrZ9CmVqvp1asXo0aNUo59PmHS6fQsPXqPabuvk6zV42przsyOZahewDlT47S2tqZTp06Zek0hhPgQSDkbIYT4xMXGxhIZGUl2Dzi4fPmysp26GhuAiYmJsnAspFSq+1ikriz3/Lyt5/c9X4UuNCqBnstPM+kfP5K1ehqVyMmuL2tlerIkhBCfMkmYhBDiE5ScnMyiRYsoU6YM1tbW2Nvb4+npycSJE4mMjMyWmIyN/5tfk5CQkKY9dfW41Md+6CpXrqxsz50716AtNjaWpUuXKq8rVaqkbO/1DaHx7CMcufUEc1MjJrcuxcJuFXCw+jgrCQohRHaROUxCCPGJiY+Pp2XLluzZsyfd9sKFC7N//35y586dpXH98ssvjBw5EoDevXuzdOlSZe5NdHQ0pUqV4sGDBwDcuHGDwoULZ2l870poaCgeHh4kJSUB0KZNG9p27ELAk0iWr/qDOw8eojIxo3SFSvw4cTLxyVrO3H/K2tP+ABTPZcuczmUp6CKFF4QQnyYp+pAOSZiEEOLNDRkyhPnz5yuvn/UynThxQplDVLVqVY4fP56lhRWePHmCh4eH0rvUpEkTpVrcvHnzuHXrFpAyn2nv3r1ZFldGREREsGrVKrZv3050dDTu7u706NGDZs2avbRX7LfffmPol8OxyF8J6xL1sChQCZWJ6Svv93nNfIxsXAQzk4+nx00IITJKEqZ0SMIkhBBv5smTJ7i7u5OYmIi5uTk7duzA29sbSOm1adiwIf7+KT0XR44cyfLy3YsXL6Z///4vbHdwcODYsWMUK1YsC6N6Pfv27aNdu3ZERESkaatYsSLbt29PU1VOr9dz7sFTNl0IYNOZ+yTo/hspr0tORJ+cgIlKj5uLMw62lhijIyrsMbqkOMrZxjGkrTeFChV6148mhBDvNamSJ4QQItPs3LmTxMREAAYOHKgkSwBFihRh4sSJ9OzZE4CNGzdmecLUr18/rKysGDlyJIGBgQZt1apVY8mSJe9lsnTx4kVadu2L3qU49qXyo85ZEGO7HOgS49DFR3MvPpo6w2czsE8PnG0ssLdUcyskms0XA3gY/mxulhEuNmYUs4jGPvIWrnZa6tSpQ7Vq1UhOTmbEiBEsWrRIGbp3GJg9Blq2bMnSpUtxcnLKtucXQoiPmSRMQgjxCXny5ImynbrYQHr7wsLCsiSm53Xp0oX27dvj4+ODr68varWaOnXqvFdlxJO1OnyuBnPxYQTXAiM5cysI516/vfScRGD2/rtp9lupjWlcMhety+WmWgEnjI0Mh0Hq9Xq6du3Kxo0b073u1q1buXfvHkePHpUFZIUQ4h2QhEkIIT4hOXPmVLaPHTtG586dDdqPHTumbOfIkSPL4nqeqakpzZs3p3nz5tkWw4uExSQy6M/znL4X/t9OYzP0mmT0EQF0aFCNMnkcyetsRWyiltMXrzJj7kKMLGzIna8QNbwaEhGXjI25Kc3L5KJB8ZxYql/8z/G2bduUZEmtVjNs2DC8vLy4fPkyM2bM4MmTJ8r2Dz/88I6fXgghPj0yh0kIIT4hERERuLm5ER8fj1qtZv369bRs2RKVSsX58+f57LPPCAoKAuDkyZNUqVIlmyPOenfu3GH58uX4+fmhVqupXbs2Xbt2xdbWlmuBkfRfdY6AiHiszUxoV8EdG00EYwZ2JznMn949e7Bs2TKD6+n1enLkyEFYWBgeHh7KHLHX1aRJE3x8fABYt24dHTt2VNp8fX0pXbo0Wq2WXLly8fDhw4+q5LoQQrwOKfqQDkmYhBDizX3zzTfMnDlTeV2gQAGsrKwMFo6tW7cu+/fvz9IqedlNq9Xy9ddfM3fu3DSL+Nra2vLlLyvY4G9BfLKWvE6WLOlZkYIuNly/fl2ZV9WgQQP+/fdfg3MjIyPJkSMHycnJFC5cmBs3bmQoLicnJ8LDw3FxcSEoKCjN4rWNGjVS7nn//n08PT0z+uhCCPFBe9e5gSxcK4QQn5gpU6bQqlUr5fWdO3cMkqXSpUuzfv36d5osnT9/ns8//5wSJUpQpEgR2rZti4+PT5pEJSt9/fXXzJkzJ50YVKjKtGDVHTXxyVpqFXJm65CayrpHhQoVIk+ePADs2bOHQ4cOKWfq9XomTpxIcnIyAPXr189wXM9KvRsbG6f7Z2Ji8t9wvg/wO1AhhHjvSQ+TEEJ8grRaLX/99Re//fabsv5S8eLF6d+/P/369cPS0vKd3Fev1/Ptt98ybdq0dNtbtGjBunXrsLCweCf3f5Hbt28r5blNTEwYN24cXbp04VHIE75ce55I65ReG9M7h/FdOxnT59Y9mjZtGqNHjwZSEpt27dpRrFgxfHx8OHnyJAAqlYorV67g5ubGhQsX0Gg0FC9eHHd395fG5uXlxYEDB4CU+Uyp53Xdu3ePIkWKkJycjLOzM0FBQQYJlBBCfApkSF46JGESQojMo9Pp0Ov1WTL3ZebMmXzzzTfKa1NTU0xMTIiPj1f2de3alT/++AOAyLhkHj6NIzpBQ0yihuiEZKIT/vtvTKIGrU6PTq9Hpwe9PiUp0+n16AFzE2OqF3SiTuEc2FuqXxjX2LFjmTJlCgATJkxg3LhxPAiL5fOVZ7kVGgNaDU92zSH22n5OnDhB1apVDc5PSkqiRYsW7N69+4X3mDBhAvfu3WPt2rXK4rwqlYqmTZsydepUSpYsme5569evp1OnTgBYW1vz7bff4u3tzaVLl5g0aRIPHz4EYPTo0UydOvWF9xdCiI+VJEzpkIRJCCE+PPHx8bi7uxMenlJdbsqUKQwbNgwzMzM2bNhAv379iI2NBeCary8nw8yZ6nOdJI3ure9tpIKKno54FXOhfjEXCuSwNhje1rJVK3buP45Z7iIM+m4adyN1XA2IIkmrI6etGfVMbvHz6MEALFu2jN69e6e5R2JiIj/99BMLFiwwKMlesmRJhg4dys8//8y9e/fSjc/a2po9e/akScQgpTewadOmaeZGpVawYEFOnTqFo6Pja78nQgjxsZCEKR2SMAkhxIfn77//pl27dgB07tyZNWvWGLRPnz6dUaNGYWztSMUhcwjGHgAnKzV2lqbYmJtia26CjbkJNmamWJubYG1mgqmxCpVKhZFKhZEKVCowUqXsexydyMEboVwPjja4Vx5HS7yKuuBqZ85F/wj2XbpDsolVmpgrejowv2t5fpsxhQkTJgCwevVqunXr9sLnTEhI4NSpU0RFReHu7k7ZsmVp3rw5O3fuBFIKSHTu3BkrKyvWr19PQEBASkx58nD79m1MTU3TXDMuLo4BAwbw559/ppmnVLt2bdasWUPu3Llf9vYLIcRH671LmA4fPsz06dM5d+4cQUFBbN682WDysF6v5/vvv2fx4sVERERQo0YNFixYoIwNBwgPD2fYsGFs374dIyMj2rZty+zZs7G2tn6tGCRhEkKID0/q4XjpJR2+vr5UbP05To2HYWxhi5mJEd81K0a3qp5vXYDi0dM4DlwPZd/1UI7fCUu310qv1ZAUeo88VlpGf96R8nkc8HSyJDw8nNKlSxMYGIhKpeLOnTvky5fvte+den6Uq6srZ8+eVZKbuLg4vL29lXlOGzdupG3bti+81t27d1m3bh1BQUHY29vTsmVLKlasmJG3QgghPjrvOjfI8MzQ2NhYypQpQ58+fWjTpk2a9mnTpjFnzhxWrlxJvnz5GDduHI0aNcLX1xdzc3MgZXx6UFAQe/bsITk5md69e9O/f/803zYKIYT4eNjY2Cjbt2/fNmiLSdTw4647uLT+HwC22gg2fd1CqUSXml6vZ9++faxZs4bAwEDs7e1p1aoVbdq0Qa1WGxyXnJyMWq3G3cGS7tXy0r1aXmITNRy7/YQDN0KJitdQxsOOQg6mtKhdjpiIcIKBXy7+TZcuXQgPD2fRokUEBgYC0LRp0wwlSwD79u1TtocMGWLQE2Rpacm4ceNo1qwZkFJl72UJU/78+Rk7dmyG7i+EEOIt6d8CoN+8ebPyWqfT6V1dXfXTp09X9kVEROjNzMz0a9eu1ev1er2vr68e0J85c0Y5ZteuXXqVSqUPCAh4rftGRkbqAX1kZOTbhC+EECIL3b9/X69SqfSA3snJSX/79m29Xq/Xn70frq8xZa/ec/QOfZ5R2/T2tXvo/968Nd1rBAcH66tVq6YH0vx4enrqL168qD906JC+TZs2ejMzMz2gz5Ejh/7rr7/WP3jw4KXxrV27VokvvR9XV1f93bt3M/zcM2bMUK6xatWqNO1Xr15V2rt3757h6wshxKfuXecGmboO07179wgODjZYZ8LOzo4qVapw4sQJAE6cOIG9vb3BEIL69etjZGTEqVOn0r1uYmIiUVFRBj9CCCFSCgIcPXqUv/76i3///deg2lx2On/+PL169cLJyQm1Wk3+/PlZvny50pMSFhZG6ereVBv8C+3mH+VRRAKayFBC1ozBOfA4LZs3S3PNhIQEGjVqpPx78rwHDx5QvXp16tSpw6ZNm0hMTATg8ePHzJw5kzJlynD8+PEXxtypUye2b99O0aJF07Q1bdqUEydOZLh3CVIWBn5my5Ytado3b96sbL/J9YUQQrxbmbpYQ3BwMAA5c+Y02J8zZ06lLTg4GBcXF8MgTExwdHRUjnnelClT+PHHHzMzVCGE+KDp9XoWL17M5MmTefDggbLfwcGBwYMHM378eIPhaVlp3rx5fPHFFwbFCe7du8ePP/6Ik4sreeu0Iz5Xecw9SxP0/+0x1w4QvmchDlZmbNyxP90S56tWreLSpUsA5M6dm5kzZ+Ll5cXly5cZNWoU586dIy4uTjnexcWFAgUKcP78eRITE4mIiKB58+bcuHEDZ2fndGNv1qwZTZs25dixY/j6+qJWq6lVq5ZB0pNRjRs3xsXFhdDQUDZt2sSYMWMYMWIElpaWrFy5kkmTJgEpJcZ79OjxxvcRQgjxbmRqD9O7MmbMGCIjI5WfZ2tOCCHEp+q7775jwIABBskSwNOnT5k0aRJt27ZFo9FkeVw+Pj4MGzZMSZZsbGwoVaoUZi55cfDuj0WnX9FX7YW5Z2n0Oh1xd84QsuEHov+dS+e2LTl9+jRlypRJ99pLly5Vtjdu3EiHDh1wdnbGy8sLHx8fjIz++ydt7NixPHr0iOPHj+Pv70/dunWBlKJDS5YseekzqFQqatasSf/+/enVq9dbJUsAZmZmBl/6TZ06FWdnZywtLRk0aJCyJtPnn3/+1vcSQgiR+TK1h8nV1RWAkJAQcuXKpewPCQmhbNmyyjGhoaEG52k0GsLDw5Xzn2dmZoaZmVlmhiqEEB+s48ePM3nyZOV1o0aNlJ6WdevWodVq2bFjBwsXLmTo0KEvvVZ0QjL/23wV//A42pbPTctyubE1T1vW+nU9W/wVIxN6fvUd5Rp24MCtcKIeRijHaCJDqeFmxOTPm/M0IBcaTWMKFy78yjWErl+/DoCnp2ea9Yri4+PR6f6rfNenTx+lPLeLiwtLliyhYMGCAPz11198++23b/yMb2LAgAGEh4fz3XffpSkLDtCtWzfmzZuXpTEJIYR4PZmaMOXLlw9XV1f27dunJEhRUVGcOnWKQYMGAVCtWjUiIiI4d+4cFSpUAGD//v3odDqqVKmSmeEIIcRHae7cucr21KlTGT16tPK6Z8+eNGzYEEgZGjdkyJAXluT2D4uj78oz3AqNAeDiwwgm/ePHZ6Xd6Fw5D+Xz2L92Oe+4JA3/nrvNJZ07OTtNxty9GAeNTTm4/y4AJkYqqnpY8vf0b0i4f5E75ctRYFxPyPX6C60+++IsMjKSpKQkgyGHz38R96wq6zMFChQgZ86chISE8Pjx49e+Z2ZRqVSMHTuW9u3bs3DhQo4fP45Go6FUqVL0798/3QVrhRBCvB8yvA5TTEyMUg62XLlyzJw5k3r16uHo6EiePHn4+eefmTp1qkFZ8cuXLxuUFW/SpAkhISEsXLhQKStesWLF1y4rLuswCSE+ZTlz5iQ0NBQ7OztCQkLS9MBXr15dKYwQEBCAm5tbmmucuBPG4D/P8TQuGRcbM7pX9WT75UBuhsQoxxTOaU3nynloXS439pZqEpK1BETE8+hpPI+exhHwNGX7flgsvoFRaHSG/5w4WamplNeRKvkd+ay0GzlszHB1dSUkJAR3d/cMD6/u0KEDGzZsAODXX39l+PDhStv69evp1KkTAGq1mvj4eIMhevfu3SN//vwAlClThosXL2bo3kIIId5f7906TGfPnqVevXrK66+//hpI+VZzxYoVjBo1itjYWPr3709ERAQ1a9bEx8fH4Nu+P//8k6FDh+Lt7a0sXDtnzpxMeBwhhPj4PZvz4uDgkO5w5dRDop8dm9qaU/6M33oVjU5PGXc7fu9RkZy25gz1Ksh5/6esPf2QHf+fPP243Zcpu65ja27Kk5jEl8Zlpo0jzO8kiY+uUdBOxdmD/xj0UD169EjpCXJwcMjwcw8ZMkRJmL766isOHDiAt7c3ly5d4o8//lCOS0pK4ueff2bUqFEYGxsTHh7OgAEDlPb27dtn+N5CCCE+XRnuYXofSA+TEOJTVrFiRc6dOwfA6dOnqVSpktL29OlTPD09iY6OxtLSkrCwMOULK41Wx087/Vhx/D4ALcq4Ma1dacxN01aki4xPZtvFAP485c/14Ghlv7WZCY5meu5ePUfc44doIkPRRoWSGHQTbZThULc5c+YwdOhQVCoVMTExdO3alW3btgHw/fff88MPP2T42b/55htmzpz5Wsfmzp2bwoULc+rUKaV6nr29PTdu3EhTrVUIIcSH613nBpIwCSHEW9LpdJw+fZrAwEDs7e2pXr16mjk0mWnBggUMHjwYSCmAMHv2bKWnZeTIkcpwvH79+vH7778DEBmXzJA15zl6+wkAIxsVYXDdAq+co6TX67kZEkOyVoeHgyUJ0eGULFmSJ09SrqNSqShQoAD+/v4kJSWlOb9w4cIUKVKEo0eP8vTpUwCsra25ceNGukMFX0Wv1zNv3jymTp1KYGCgst/GxoYBAwZgbm7OTz/9lO65NjY2bN++nTp16mT4vkIIId5fkjClQxImIcT7YsWKFfz000/cuXNH2efs7MzQoUMZO3asUqktM8XFxVG5cmWuXbv2wmMcnHOyafcBjG2cCXgaz6LDd7n3JBZLtTEzO5Slccn0q5K+ysSJExk/fjwANWrU4I8//iBv3rw8ffqU4cOHs2rVqpeeb2FhwaZNm2jcuPEb3f+Z5ORkDh48SFBQEPb29tSrVw8bGxsA9uzZw6xZs9i9ezdarRY7Ozu6devGV199pZTtTkpK4vbt22g0GvLnz4+1tfVbxSOEECL7SMKUDkmYhBDvg++//54JEya8sL1Vq1Zs2LABE5NMLUgKQGBgIM2bN+f8+fOYOLpjXboBpva5MLbNgdrBFZW5TZpzcttbsLhHRYq7vfnvzaJFi3Ljxg1UKhX37t3D09NTaUtKSiJv3rwEBQWhUqmoVq0ax48fB1Iq3HXs2JFRo0ZRokSJN75/RiQnJxMfH4+1tbVSACIqKoopU6awZMkSpZfMwsKCLl26MH78ePLkyZMlsQkhhMg8kjClQxImIUR2O3HiBNWrV1dee3l54e3tzeXLl9mwYYOyJtDcuXPx9PRk586dREdH4+7uTrdu3ShVqtRbx3AzOJKxfx7lbKge0hlaZ6U2JreDBW72FhTMYc3AugVwtn67Ne1sbW2Jjo6mUKFC3Lx5M017x44d+euvvwC4ffs2OXLkIDo6Gmdn52xfT+/p06fUq1ePS5cupdvu4uLCgQMHKF68eBZHJoQQ4m1IwpQOSZiEENmta9euylIIkyZNYuzYsUqbj48PTZo0AVJKXKc3t6dt27asWLECa2trdDodgYGBaDQacufO/cphfLdDo5mz7zbbLwfy7Dd4/WIu1C6cAze7lAQpt70F/neuM2/ePHbs2KEka927d2fAgAGvXCT2RfLkycPDhw8xMzMjODgYe3t7pU2v11OiRAn8/PwAePz4Mc7Ozm90n3ehc+fOrFu3DgATExOaNWuGtbU127dvJyoqCkjpQbt27ZpBSXIhhBDvN0mY0iEJkxAiuz1bT8jW1paQkJA0RR7KlSv3yrV+vLy8qF+/PgsXLsTf3x9IqeLWu3dvRo8eTc6cOdHpdBw6dAg/Pz8i9ZZcN8nH4fsxSqLUsHhOvvAuRMncdgbX/v333xk0aJDS0/V87Lt376Z06dIZfu5hw4Yxb948AHr37s2iRYswNTVFr9cza9YsZamJGjVqcPTo0Qxf/1159OgRnp6e6HQ6HBwcOHbsGMWKFQMgLCyMunXrcvXqVQB27txJ06ZNszNcIYQQGSAJUzokYRJCZDc7OzuioqLIly8fd+/eTdOeN29eHjx4AECxYsWYMmUKRYsWxcfHh/Hjxys9Gi/i4eHBqG/H8uuKjTzWW2OepzQWBSuhUqX0fNTMa82YFmUp4WaX5ty9e/fSsGFDnv16t7CwwN3dndu3byv73Nzc8PX1xc4u7fkvc+PGDUqWLIlGowFSSnfXqlVLWaD8mY0bN9K2bdsMXftdWrJkCf369QPgf//7X5pKen///Tft2rUDYPDgwfz2229ZHqMQQog3865zAxlzIIQQb6BgwYIA3Lt3j/Pnzxu0PXz4UEmWIKVqW8uWLSlSpAhffvklK1asMDhepVJRt149GrTugl1pbxy8+5Nc9yum33NF6/UVjt79sCxUBZXKiNgbxwhcNow933fAPP5JurFNnjxZSYyGDBlCSEgIN2/e5ObNm1SsWBFIKRrxfByvo0iRIqxcuRJj45S1mwICAli3bp1BsvTtt9++V8kSYJCgPutZSi31vKVXJbNCCCE+LZIwCSE+CCEhIUyfPp0+ffowcOBA1qxZQ2JiYrbF06dPH2W7ffv27Ny5k8TERE6fPk2LFi2UtgIFCpA7d26Dc6tUqQKAykSNRYFK9F24l/j6/+Nm4S7YN/kK24otMHMrjMrYFG3sUyzCb1HHIZL21jewPP8nyY/vERoayrBhw9LEFRQUxIEDBwAoVKgQc+bMUcptFyxY0CBJ+vPPP9/o2bt06cKRI0do0aKFwVyfatWqsXHjRqZMmfJG132XPDw8lO3du3enaffx8VG23d3dsyQmIYQQHwYZkieEeK/p9Xp++OEHpkyZQnJyskGbq6srK1eupGHDhlkeV2xsLBUrVuT69esvPa5+/frs2bNHeR0SlcD3izaw6eQtzPOWwcj0v7lPamMjirvZ8vj6aS7u20JS4A3yuthy8//LeENKpbdSpUoREBAApFSie7a2EMD58+epUKECYLhwbWrP5l+5u7vz8OHDN38TgMjISEJDQ7Gzs8PFxeWtrvUuxcXF4ebmRmRkJCqVil9//ZUBAwagVqvZtm0bPXv2VHqWrl69mmWlz4UQQrw9GZL3EqFRCdkdghDiHfvuu++YMGFCmmQJIDg4mM8++4zDhw+/8jrx8fEcOHCAbdu2cf78eWXIml6vZ9euXTRv3hxnZ2fs7e2pWbMmK1euTPeez1hZWbFnzx7KlCmTbvuzBOfgwYOcvniFZUfv0XzuUapM3odPmCOWhapgZGqOcWIU3armYXmvSlz+oSFbhtTA5tZu4vwOo4kMoXChQsq1ABwcHJS5OJBS3jy11FXrLl++nCauwMBAQkND0xz7puzs7ChUqNB7nSwBWFpaMnr0aCDlz3z48OE4OTnh7OxM69atlWSpXbt2kiwJIYQwkPmrKWahzRcCGOn+fv8jLYR4cw8ePGDq1KlASgIyfPhwunbtSnh4ONOmTWPv3r0kJyczfPhwzp07Z5BYPJOYmMjEiRNZsGAB4eHhyv4SJUowbtw4du3axcqVKw3OOXbsGMeOHWPx4sXs3LnzhYUR3N3dOXv2LDt27ODPP/8kKCgIe3t7WrVqxfXr15mzehM25ZrRfvVNVKl6khIDbxB/+zRxt0/TuFopfvp1q8F1g4KClO3nh/MBBt+ePZ/U5cuXj1KlSnHlyhVOnTrF4sWL+fzzz1GpVMTHx/Pll18qyWKrVq3Sfa6P1ejRowkKCmLu3LlASq9TXFyc0t6wYUOWL1+eXeEJIYR4T33QQ/Iqf7+NE+M/w8go7YckIcSH7/vvv2fChAkAjB07lkmTJiltGo2GChUqKL0oZ8+eVYaiPZOUlETz5s35999/X+t+zs7OmJub8+jRI2XfZ599xvbt21875kSNll1Xgll+9C6XAv4rHpAUeo/oi7uIu3kcXWyEst/Y2JjFixfTo0cPjIyMOHDgAJ999hnx8fEADBgwgIULFyrHa7VaKleurBSaOHXqFJUrVzaIYcWKFfTu3Vt5XapUKYoWLcrBgwd5/PgxkFI57+bNm5/kfJ3jx48zf/58jh07hkajoVSpUvTv3z/NnCwhhBAfhnc9JO+D7mEKikzgyO0n1CmcI7tDEUK8A6mHlKVOACBl4dEePXowYsQI5djnE6Zff/1VSZaMjY3p0KGDUto79VC29JKW9u3bEx4ezo4dO7h48SJly5Z9aazhsUksPnKX9WceEh6bslCtiZEK++h7+G5bSLz/VeVYR0dHypUrx759+9BqtfTp04dRo0ZhYWGRZk7RkiVLcHZ2pmvXroSFhfHzzz8ryVLp0qWpVKlSmlh69uzJuXPnlPWSrly5wpUrV5R2MzMz1q9f/0kmSwDVq1enevXq2R2GEEKID8QHnTABrD3lLwmTEB+pZ6WrAYOhU+ntS30spPTEzJ8/H0gZzrd//35q164NwLhx42jevDk7d+4EoHDhwgYJmZeXFxMnTmTIkCEArFmz5oUJU7JWx+oTD5i19yZRCSlrE+WyM6dL5Tx0rOyBi405Ad+24t9//yUqKgp3d3eaNm2KWq2mb9++ynDAJ08MS4S7ubkRGBiIVqtl0qRJBr1rz5535syZ6Q5DVKlUzJkzhxo1avDrr79y+vRpICXJbNu2Ld9+++0rE0AhhBBCpPjgxx7s9QuR4g9CfKSqVaumbP/666+kHkEcFRXF0qVLlddVq1Y1OPfWrVv4+/sD0KBBAyVZgpSEIvW1nz59mubeXl5eynbqOUWpHb75mCazjzBhhy9RCRqK5bJlYbcKHBlVj2HehXCxSZm3lDt3bnr37s2XX35J27ZtsbCwwNjYmOXLl7Nr1y4+++wzHB0dsbW1pUaNGqxcuZK7d+8yYsSIdIeIOTg4sGnTJry9vdN/4/7/GTt16sSpU6cIDQ3l9u3bPH36lHXr1kmyJIQQQmTAB93DVMbdjiuPk9lw7hFD6hXM7nCEyBSHDh1i/vz5HD9+HI1GQ8mSJenfvz9t2rRJ04vysevZsyffffcdCQkJrFixguDgYLp06UJ4eDjz5s1TFoetX78+hQsXNjj32RwgSL9wgqurq7IdGxubpv3ixYvK9vPV5O49iWXSTl/2+qVUm3O0UjOiYRE6VvLAOANzKlUqFY0bN6Zx48bptk+fPp1hw4axfPly/Pz8UKvV1K5dm86dO2NlZfXa98mRIwc5ckhPvBBCCPEmPuiiDysOXON7n3vkcbTk4Ii6UvxBfNB0Oh1Dhw5lwYIF6bZ7eXmxZcsWZRHST8WSJUsMymg/z9HRkWPHjlG0aFGD/eHh4bi4uKDVanF1deXu3btYWFgo7Zs2baJt27ZAyvC2A0eP81Dlyr0nMaiSE1i2YA5B92+hjY9m0ZwZNPaqhamxEYsO32HZ0Xska/WYGKnoWT0vX3gXws7C9N28AdkoOTkZHx8fg2StfPny2R2WEEIIYeBdF334oBOm4Mfh1J93mugEDX/0rULNQs7ZHZoQb+ynn35i3LhxymsbGxvMzMwM5ra0adOGv//+OzvCy1br1q1jxIgRymKtz9SoUYPFixdTrFixdM9r166d8n41atSI6dOnU7RoUXbt2sXQoUN5+PAhxrY5sCn/GTZlGmFkbv3aMdUtkoPvmhWnoMvrn/MhWbNmDSNHjiQwMNBgf9WqVVm6dCnFixfPpsiEEEIIQ5IwpSP1m/LLAX9WnXhAs1K5+K2rfPMpPkyxsbHkzp2byMhIVCoVc+fOpV+/fpiamrJz5066detGZGQkkFLxrGTJktkccdbTaDRpejvKlSv30nMuX75M1apVDYbnPWOWuzg2lVpiWagaqv+fJ5QcHkj8ndMYmVliZGGLhZ0znoWLE5sMT+OS0Okhfw4rxjUrTr2iH+8acK/q1XNwcOD48eNpevWEEEKI7CAJUzpSvymPYqDpnCOYGKk4McabHDZm2R2eEBn2119/0bFjRwB69eqVZvHMOXPm8OWXXwIpi28+W8z1faPX67l8+TKBgYHY29tTsWJFTE2zd6ja/v37adeuXUphByMTrIrVwqZiS8xc/5v3mNskmkf7VuN/chegx97ent69ezN69Ghy5swJgE6nJyZJg42ZSbqV6T4WT548wcPDg4SElGI6TZs2VeaNzZ07l1u3bgHg7e3N3r17szNUIYQQApB1mF6puJstZT3sufgwgr/PP2JgnQLZHZIQGZZ6odQGDRqkaU+97/lhae+LdevW8dNPP3Ht2jVln5ubG19++SXffPNNthWs8PLy4ubtO3y7aAsHH5ujUaf8IjU10tOmvAd9auaniKsNugkdCAwMRKPRkDt37jSJnpGRClvzj2+e0vNWrFihJEu9e/dm6dKlSoLYq1cvSpUqxYMHD9i3bx83b95MU2xDCCGE+Nh88GXFAbpUzgPAutP+6HQfXIeZENjZ2SnbqROO9PZlxjcner2e5OTkt77OM1OmTKFz585pYg8MDGT06NF07doVnU6Xafd7XclaHX+deUirxRfYG+mCRm1LDhszRjYqwqn/NeTndmUo4ppSRMPIyAh3d3fy5s2b7b1i2enkyZPK9vDhww1602xsbOjbt2+6xwohhBAfq48iYfqsTC6szUy4HxbHybth2R2OEBnWuHFjpQfmt99+4+rVq0pbaGgoP/zwg/K6RYsWb3yfY8eO0aFDB6ysrFCr1bi6ujJq1CiDHq6MOnPmDGPHjlVeV69ene+++84gzvXr1zN16lRGjBhB0aJFyZ07N1WqVGHevHnExMRk6H5XAyI5fvsJj57GoX3BFyQarY6N5x5Rf+YhRv19mUdP43G2NmPcZ8U5MqoeQ+oVxNFK/WYP/JHTarXKduqqgs9YWlqme6wQQgjxsfrg5zA9+7b9uy1X+OOkP5+VzsW8LlL8QXx4unbtypo1a4CUMteNGjXC2tqanTt3KusEFS9enCtXrqS7mOmrTJ8+nVGjRqXb5uDgwD///JNm8dfX0aNHD1avXg3A+PHj+fHHH5W2LVu20Lp1ayBlzaH0ft3kzZuX3bt3v3JoV2R8Mj9uu8amC/8NSTQ1VuHhYImHoyWeTpbkcbTEzMSIZcfuc+9JynvmZKVmYJ0CdKvqiYX601rH6k18//33TJgwAYBvv/2WKVOmKG0ajYby5ctz5coVAM6dOydlxoUQQmQ7KfqQjvTelGuBkTSbcxRTYxUnx3jjZC3FH8SHJSIiAm9vb86fP59uu6urKwcOHHijymTbtm2jZcuWymtnZ2cKFCjA+fPnlaF5Tk5OXL9+HWfnjJXnz5UrF8HBwVhbWxMaGpqmV6JYsWJcv35deW1iYoKzszPBwcHKvrx583LlyhWsrdMv0X3s9hNGbLhEUGQCRirwdLLi0dM4krUv/vXlaKWmf+389KjmiaX6g5+umWUePHhA/vz50el0qFQqvvjiC7p27UpYWBjTp09n//79AJQvX56zZ89+1AUwhBBCfBjedcL0UQzJAyjhZkdpdzuStXr+Pv/mw4uEyC729vYcOnSI8ePHK5XZAKysrBg4cCBnz5594zLOqavqfffddwQEBHDy5En8/f2pU6cOAGFhYSxdujTD137W++Xi4pLuEK6nT58q223btiUoKIigoCAuXLiglEe/f/8+q1atSnNufJKWH7Zdo+uSUwRFJpDXyZINA6tzYERdrk9swrFvvVjTrwpT25RiUN0CNCuVi8r5HBnZqAhHRtVjYJ0CmZYsPXr0iH379nHkyJEMDyP8kHh6ejJmzBggZa7b7NmzqVy5Mk2aNFGSJVNTU2bNmiXJkhBCiE/CR9PDBLD2tD9jNl0hv7MV+76pI/+Yiw+WRqPh7t27aDQa8ubNazBvJKMePnxInjwphVFKlizJ5cuXDf7fuH37NoUKFQKgXLlyL+zhepFy5cpx8eJFAC5dukTp0qWVtjt37lCw4H/lu5//f/bixYvKWkpVq1bljz/+4OTJk2g0GszdirDocgJ3H6ckZN2q5mFs02JZ3lt04cIF/ve//+Hj46MMKbS2tqZXr15MnDgRe3v7LI0nK+j1eiZMmMDkyZNJSkoyaHN1dWXVqlXpVnMUQgghsoMMyUvHi96UmEQNVSbtJTZJy7r+Vama3ykboxTi/XDu3DkqVqwIQP/+/Vm0aFGaY1xdXQkJCcHd3Z2HDx9m6PqzZ89m+PDhABQuXJiFCxdSt25drl27Rp8+fThz5gwAhQoV4ubNm2nOz5kzJ6GhoZiZmZGYmAhGxthV64hd9Y6ojIyxN1Mxq0tF6hbJ+oViDx06RJMmTdJd+BagRIkSHDp0CCenj/N3TWhoKKtXr8bX1xe1Wk2dOnVo06YNarUUzBBCCPH+kHWYMsDazIQWZXOz9rQ/a075S8IkBBjMSTp9+jR6vd6gh+n+/fuEhIQAvNEH/z59+jB37lzu3LnDzZs38fLySrfAQ3q/wEJDQ3n8+DEmdjkxyVMKa49SmOctg4lNSsyxfocJOrCYhGproEjjDMf2NuLj4+nQoYOSLHl4eNCuXTvCwsLYsGED8fHxXLt2jeHDhytFLz42Li4ufPPNN9kdhhBCCJGtPpo5TM88W5PJ51owkXGZt86MEB8qT09PpYfp4sWLTJs2TSkHHRERwcCBA5Vj27Vrl+Hr29jYsGfPHooVK6bsS50sPSuXfu7cOdatWwfAw/A41p26T/Of/sJtwBJyD1yKc9PhWJfyxsTGGTOVFouL63iybRpJ0U/p0aOHsphqVlm/fj2hoaEA1KtXj5s3bzJz5kxWrlzJ5cuXlbWz1q9fb1DAQgghhBAfl49qSB6kfFBrPOsIN0KimdS6JF2reGZTlEK8G3FxcWzevBk/Pz/UajW1a9emTp2Xz9nbsGEDHTp0UF57eHhQpEgRTpw4oRRtsLOz48aNGwYFJzIiKSmJTZs28ccffxAUFIS9vT2tWrVCq9Xy1VdfgcoIy0JVcfPqTrKdh8G5eq0Gwh/weYs61C3uRgVPB9RG0KxZM/79918AVq1aRffu3d8otjfRuXNnJcE7fPgwtWrVMmgfMWIEM2bMAGDt2rV06tQpy2ITQgghxH9kSF4GqVQq2lbIzeR/rvP3uUeSMImPyqJFixgzZoxB5TlIKeawYsUKKlSokO557du3Z9y4cUycOBFIKQSReq6StbU1mzdvfuNkCUCtVtOpU6c0iUN0fBI7bsbgp8uFqb0ryYBepyUp6BYJ/pdJ8L9CYoAf0yZPZETLMgbnjho1SkmYDh8+nKUJ07NEEiBfvnxp2lPvS32sEEIIIT4uH92QPIBWZXNjpILz/hHcffzxlv8Vn5ZZs2YxcODANMkSwNWrV6lbty6XLl164fkTJkzAx8eHRo0aKQvf2tjYMHDgQC5cuEC9evVeK46kpCQePHhAUFBQugvRPhMcmcDUXdep8fMBbtuWw9TeFZJiiTi+jkfzexLy50hyPT5Dwv0L6JMT0l3/KfW+xMTE14ovs+TPn1/Z3rp1a5r21PvSS6iEEEII8XH4KBMmF1tzahfOAcCm8wHZHI0Qby84OJhRo0Yprzt27Mi2bdtYsWIFZcqk9MrExMQwbNiwl16nUaNG+Pj4EBcXR3h4OE+fPmXBggUGpb9fJCAggC+//BIXFxfy5s2Lm5sbRYoUYfbs2Qalpx+Gx/H1+ovU/Hk/Cw/dISpBQz5nKya2KonvlDacX/Ej544eIDg4mJkzZyrnrVmzJk0CtnbtWmX7TdegelM9e/ZUtseMGcPq1atJTk7myZMnfPPNN+zZswdImSP2bC0rIYQQQnx8Pro5TM9svxTIsLUXyG1vwZFR9TAykjWZxIdr6tSpymKigwcP5rffflPa4uPjKV26NLdv3wbg2rVrFC9ePFPv7+vri5eXl1JN73n169fn781bWXU6gLn7b5Oo0QFQOZ8j/Wrlx7uoS7r/D2q1WvLly6cMD+zZsyfffPMN1tbWrFixgkmTJqHVajE2NubBgwfkzp07U5/rVdq3b8/GjRuV18bGxkrBjGeyem6VEEIIIQzJHKY31KB4TmzMTQiIiOfk3TCqF0w73Ed83OLi4ti9ezeBgYHY29vTqFGjdId9fQierWUEMGTIEIM2CwsL+vTpw9ixY5VjMzNh0mg0tGrVSkmWLCws8Pb2Jjw8nOPHjwNw9NZjqk/YQYyRFQDV8jvxbZOilPGwf+m1jY2N+eWXX+jYsSMAK1euZOXKlWmOGzly5EuTpYiICJYtW8aaNWuUP++WLVsyaNAgZdHeN7Fy5UoSExPZvn07gEGyZGRkxPTp0yVZEkIIIT5yH23CZG5qzGel3Vh72p+N5x9JwvQJ0el0TJkyhRkzZhjM9zEzM6Nnz57MnDkTKyurbIww49Ir051a6n2Z3Wm8fft2bt26BUCpUqX4999/cXV1BWDz7gMMXPgvFkVqEgM4W5kyrnkJWpRxe2nVvtQ6dOhATEwMQ4cOTbNArEqlYsSIEUyaNOmF51++fJnGjRsTFBSk7AsKCsLPz4/Zs2ezdu1aWrZsmcGnTmFpacnWrVs5cOAAixcvNqhMOHDgwNcayiiEEEKID9tHOyQP4NyDcNouOIGl2pgz/6uPldlHmx+K/6fX6xk0aBCLFi164TE1a9ZkyZIlLF++nB07dhAdHY27uzvdu3ene/fu72Uy9dNPPzFu3DgAvvrqK4O5P4mJiZQtW5br168DcOnSJUqXLp1p9+7ZsyerVq0CYOfOnTRt2hSNVseK4/f5dc9NYpO06HVaos/vZE6/hnTr2PaN7vPkyRNWrFjB8ePH0Wg0lCpVir59+xoUX3heWFgYJUuWNFgHKVeuXISEhKDTpQwLVKvVnDhxgvLly79RXEIIIYR4v73rIXkfdcKk1+vxmnGIe09i+aV9GdpVcM/CKEV22Lt3Lw0aNABSeie6du2Kl5cXly9f5vfffycuLg5Ify4KpFRG271793vXcxAYGIinpycajQaA3r1707VrV8LDw5kxYwanTp0CoGrVqpw4cSJT7928eXN27NgBwMlrdzgbomPT+UfceZxSStvNLJGzC0eSHHqXJUuW0Ldv30y9/8tMmTJFGYpYqVIlVq5cSbFixQgODubLL7/kr7/+AlLmIj3bFkIIIcTHRRKmdGTkTZm3/xa//HuTavmdWNu/ahZFKLJL69at2bJlCwALFy5kwIABStupU6eoWtXw74CRkRGOjo48efJE2Zc/f34uXbqEtbV1lsT8ulInB+mxsLDg0KFDVKpUKVPv223Q12y/+AirojVR5yyg7Le3NOXbxkXZNGMkG/4/GdmxYwfNmjXL1Pu/TPHixfHz80OlUnHr1i0KFPgvvoSEBDw9PQkNDcXExISnT5++d3+mQgghhHh7kjClIyNvSkBEPDV/3o9eD0dG1cPD0TKLohTZIUeOHDx58gRHR0dCQkIwMTEchuno6KjMa2rbti2//fYbOXPm5Ny5c/To0QNfX18AFixYwMCBA7M8/pfR6/XMmjWL8ePHExNjuL5YgQIFWLVqFdWrV3/ldeKTtEzc6cv2S4HYmJngbGOGs7UZztbq//+vGc42ZjwMj2Pn5SB8g6L+i0GnpXROc7rWKkqDYjn4648VDB48GEh57x8+fIiZmVnmPvhL2NraEh0dTcGCBZV5Vql17NhR6Vm6ffu2QUIlhBBCiI+DJEzpyOib0mXxSY7fCePrBoX5wrtQFkQosou9vT2RkZF4eHjw4MEDg8IDISEhSrECgJs3b1Ko0H9/H86fP0+FChUAqFatmlIB7n0TFRXF+vXr8fX1Ra1WU6dOHRo1aqQUftBqtRw7dkypFle7dm0sLVO+KLgVEs2QNee5GfL6CzobG6kwDbtDwMkdxN06iS4+ivz58xMZGUlYWJhy3LRp0xg5cmTmPuwruLu7ExAQgIWFBcHBwQa/D/R6PWXKlOHKlSsAhIaGkiNHjiyNTwghhBDvnpQVzwRty7tz/E4Ym84/YphXwdeu3iU+PCVKlOD48eM8fPiQw4cPGywoeunSJWXb1NQUT09Pg3PLly+Pi4sLoaGhyrpA7yNbW1v69euXZr9er2fRokVMmTIFf39/Zb+9vT2DBg2idMv+/LjjOvHJWnLYmDG1TSmcrM14Ep3Ik5hnP0k8jknkSXQiVmYmNCqRk4bFXUmOrUijRsu4GJ/S23T37l2Dew8aNIgRI0a82wdPx2effcaiRYuIj4/n22+/Ze7cuUriuHjxYiVZqly5siRLQgghhHgjn0QPU2yihkqT9hKXpGXjwGpUzOuYBVGK7LBixQp69+4NpAwRmzx5Mt7e3ly6dImRI0cqi7u6ubkREBBgcO7jx4/JlSsXWq2WYsWKKcPzPhRjxoxh6tSpafarTM1xbDAI61LeANQs6MyvHcuSwyZjQ+fi4+NZvXp1mvLaQ4cOxdvbO1u+iLh27RplypRRCngUKFCAunXrcunSJc6ePasct2bNGjp37pzl8QkhhBDi3ZMheel4kzflm78u8ff5R3Su7MGUNplXclm8X5KSkqhdu7ZSNe5l/vrrL9q3bw+kLM76+eefK4umjhgxgunTp7/TWDPT0aNHqVWrlvK6SZMmeHl5ccL3ASeNS2Dq5IFep6WmfSSrv+2GkdHH08u6dOlS+vXr98L1p4b9X3v3HVdV/T9w/HXZeyogCoop7oG4Z+6ZM/feM1MzR2ZmVqhlmXsVommappm4tdTcW9yCCwdDUQSUee/5/cHP8+UGmChwhd7Px+M+uud8Puec98WPed+c83l/PviAH374Qe4sCyGEEPlUTidMRtl+xrdUJ9/CAASeDyMhOX05aZE/mJmZsX37drW0+D+lncPUpUsX6tevz9ChQ/H29laTJVNTU7WQQV6xYMEC9f3s2bPZGriNwvW7cNG9FabOHqTERhHxyyecCviS/JY3DBw4kL1799KkSRO9/ZUqVSIgIECSJSGEEEK8kf/MHSadTqHe7L+4Hx3PvO4+tK3knsNRCkNSFIWTJ0+yZs0awsLCcHBwoF27djRr1owBAwbw888/Z3icsbExq1atokePHrkc8ZtxdXXlYXQszuXq0mvCTA4GRxH1LAmAd0sV5GrAFI4f2AvA/fv3cXfPn+M/PDyc8PBwHBwcKFq0qCRKQgghxH+AFH3IJkZGGjpWKcz8P0P47fQ9SZjyOY1GQ/Xq1alevXq6toCAAGrXrs3cuXO5fv26ur9Zs2ZMmTKF+vXr52aobyQ06jl7r0Rg0mQsHu6l0RibsvlcGAC2FiaMaliCwfWK0znwf//zSEhIMFS4Oc7NzU3vLqIQQgghxJvK9jtMn3/+OdOnT9fbV6pUKa5evQqkfln76KOPWLduHYmJiTRv3pxFixbh6ur6ytd43Szy1qNnNPx2P0YaODq5Ma52Fq98rMh/dDodISEhxMTEUKRIkTz1Rfv83Wim/H6Bi/dj9PYnR92jQ82S9Hy3ElWLOWJqbMTjx48pVqwYsbGxWFlZERUVhYWFjH0hhBBC5A95cg5TuXLlCAsLU1+HDh1S28aOHcvWrVvZsGEDBw4c4MGDB3Ts2DEnwkjHq4A1vkUd0Snw25l7uXJN8fYyMjLC29ubqlWr5plkKVmr4/s91+m4+AgX78dgbKShVnFnGjk+4f6yITxYMYytX/QnPOgg8c/i+Pvvv2nVqhWxsbEA9OrV65WSpfj4eOLi4jItpCCEEEII8V+RI4/kmZiYZPgF9OnTp/z444+sXbuWRo0aAeDv70+ZMmU4duwYNWvWzIlw9HSt5sHpO09Ysv8GnX09slxaWQhIvTt14MABLl++jLm5OfXq1aNUqVI5es2QyDg++vUc5+89BaBNxUJMb1sOZxtz4uMrcWL1TC49eUBoaGiGv4RwcnJi0qRJmZ4/JSWFlStXsmjRIs6ePQtA0aJFGTJkCKNGjcqR39gIIYQQQrztcuQOU3BwMO7u7hQvXpyePXuqi2iePn2a5ORkvWpWpUuXxtPTk6NHj2Z6vsTERGJiYvRer6ujT2HKudsRk5CC3/Yrr30e8d/1+++/4+3tTaNGjRg1ahSDBw+mdOnSNG3alBs3bmT79XQ6hZWHb9F63t+cv/cUOwsTfuhWmQU9quBsk5rwW1pasnv3bqpWrZrhOQoXLszu3bvx8vLKsD0hIYE2bdowePBgNVkCuHPnDlOmTKFGjRo8ePAg2z+bEEIIIcTbLtsTpho1arBy5Up27tzJ4sWLuXXrFvXq1SM2Npbw8HDMzMxwcHDQO8bV1ZXw8PBMz+nn54e9vb368vDweO34TIyN+KpDBTQa2HT2PsduRr32ucSryy+Pdq1Zs4YOHTpkmBjt3buX2rVrc+3aNbZs2ULXrl2pV68e7733HitWrOD58+dZvl7Y03j6/HSCz7deJjFFR72SBdg1tj7tKhdO19fd3Z3jx4+zfft2evbsSaNGjejYsSMBAQGEhITg6+ub6XU+/vhjdu3apW5XqFCBmjVrqlXmrl69SufOnfPNn6MQQgghxKvK8bLi0dHRFC1alO+++w5LS0v69+9PYmKiXp/q1avTsGFDZs2aleE5EhMT9Y6JiYnBw8PjjSZ2Tdl8gTXHQynhYsP20fUwM/nPLEmVa0JDQ5k/fz5r167lwYMHamnvMWPGULlyZUOHl2VPnjzBw8ODZ8+eAVC/fn169OjB48ePWbJkiXon1dbWVp0zlJabmxtbtmzJsHJfRnZeDGPCxiBiElIwNzFicsvS9KlVLNsXnY2KiqJw4cIkJiZiYWHBli1baNasGQBXrlyhefPm3L17F0hdILdOnTrZen0hhBBCiDeRJ4s+pOXg4IC3tzchISG4ubmRlJREdHS0Xp+IiIiXTro3NzfHzs5O7/WmJjQvTQEbM0Ii41hx6OYbn0/oO3jwIBUqVODbb79VH+WKjo4mICAAX19fVqxYYeAIs27VqlVqstS9e3f279/P0KFDmTx5MufOnaNQoUIAGSZLkLpGUPPmzV/psb2jN6IYufYsMQkpVCxiz7bR9ehXxyvbkyWAbdu2qb+QGDp0qJosAZQpU4YZM2ao2xs2bMj26wshhBBCvM1yPGGKi4vjxo0bFCpUCF9fX0xNTdm3b5/afu3aNUJDQ6lVq1ZOh6LH3sqUT1qVAWDevmDuPs7641IiYw8ePKBt27bqXDMzMzOqVKmCra0tkFowYciQIRw8eNCQYWZZ2mqPEyZM0FsU1dHRER8fH3W7YMGCBAYGEh8fz7Fjx9S7MtHR0cycORNA/eWBVqvVu8796HhGrT2DVqfwXiV3fhtemxIuNjn2uR4+fKi+r1GjRrr2tPuiouQRViGEEEL8t2R7wjR+/HgOHDjA7du3OXLkCB06dMDY2Jju3btjb2/PwIEDGTduHH/99RenT5+mf//+1KpVK1cq5P1TB5/C1CzuREKyjulbL+X69fOrxYsX8/RpaiW3pk2bcvfuXU6fPk14eDgjR44EUuc0zZ4925BhZllycrL6PqO7nEFBQer74cOH07p1aywsLKhRowaBgYFqwrhq1SqaNWuGpaUljo6OODo6Mnz4cEJCQkhI1jJs9WminiVRzt2O2Z0qYmqcs7/XcHFxUd8fOXIkXXvafQULFszRWIQQQggh3jbZ/k3s3r17dO/enVKlStGlSxecnZ05duyY+kXr+++/p02bNnTq1In69evj5ubGpk2bsjuMV6LRaPiyfXlMjTXsvRLJ7kuZF54Qr27dunUAGBsbs3LlSvULuZWVFXPnzsXT0xOA7du3q4lVXlCuXDn1/apVq/TatFqtXhW51q1b67U7ODjQtGlTIPXO0p49e9DpdEDqI3xLlizBx8eHgYv3cuH+UxytTFnSyxdLM+Oc+jiqNm3aYGlpCcCyZcvYunWrWtzh/PnzTJ06Ve3bpUuXHI9HCCGEEOJtkuNFH3JCdk/smr3zKov236CwgyV7xtXHyixHlqf6z7C1tSUuLg5vb2+uXbuWrr1bt26sX78egJCQEN55553cDvG13Lx5kxIlSqAoCsbGxkyaNImePXsSFRXFrFmzCAwMBFIXxH327Fm6BWJLlSrF9evX1W0PDw+8vb05duwYz549w7ZKG5yaDsNIAz8PrEHtEgVy7bONHTuWuXPnqtslS5bExsZGr8R4/fr12b9/v96jiEIIIYQQhpbniz7kBR80KklhB0vuR8fzw75gQ4eT5zk7OwNw69atdHNeFEXhzJkz6rajo+MbXevKlSts2rSJwMBAvbk4OaF48eKMHTsWSL2j9NVXX1G2bFnq1aunJkuQOkcrbfIBsGvXLr1kyc/Pj1u3brF3717u3r1LvY79cWw8GIBqpvdyNVkCmDVrFm3btlW3g4OD9ZKlChUq8Ouvv0qyJIQQQoj/HEmYAEszY6a3TX3c6se/b3EtPOMqZ+LVdOrUCUid8zNixAh1/SGtVssXX3xBcHBqUtqwYUOcnJxe6xqHDh2idu3alC1blk6dOvHee+9RuHBhevfuTURERPZ8kAx88803jB8/HiOj9H91XsxRApg8eTJNmjTBz8+Pbt260bJlS7WtSJEiTJw4EWPj1MftnmssiKnQBY2RMXGX/uLqH4tzLP7MmJmZsWnTJlavXk2tWrXUxKhUqVLMmTOHo0eP4urqmutxCSGEEEIYmjySl8bgVafYczmC6sWcWD+0pvw2/TXdvHmTcuXKkZCQAKTeRapVqxYXL15U1yqC1HLWrVq1yvL5d+zYQbt27fSKMKRVvHhxDh8+/NJS9W8qNDQUf39/rly5gpmZGfXr16d79+7MnDmTL7/88qXHDho0iOXLlwOQkKyl85KjXLj/FF1UKPdWjqWwW0F13SND0Wq16HQ6TE1NDRqHEEIIIcS/yelH8iRhSuN+dDxN5hwgPlnLrE4V6FrNM9vO/V+zZcsWunTpQlJSUobtX3/9NZMnT87yeePi4vD09OTJkydA6jpBXbt25fHjx6xatUpd4+v99983yJpBiqLg7+/PV199xc2b/1vfy8HBQY2tXLlyXLhwAYDxG4L47cw97MyNuTy3L9qYSHx8fPQeWxRCCCGEEJmTOUy5qLCDJWOblgTgy21XiIhJMHBEeVe7du04efIkvXv3xtzcHEitStiiRQt27979WskSwNq1a9VkqVWrVgQFBTFt2jR++OEHLly4QIECqXN/Nm/ezL1797Lnw2SBRqNhwIABBAcHc/jwYTZu3MjevXsJCwtLXWtMY8T1h/F0+XQRgwJO8tuZexhpwPLsWrQxkQB07do11+MWQgghhBAZkztM/5Ci1dFx8RGC7j2lWVlXlvb2lUfz3tCLBVptbW3V8tWvK22FvaNHj6Zbv+uTTz7Bz88PgDVr1tCjR483ut6bSkjWcv5uNKfuPCHw+FUuRTzHyNxar0/M/p94cjy1tL6zszNXr15VEz8hhBBCCPFyOX2HSepn/4OJsRGz369Im3mH2H05gu0XwmldsZBBY0pISGDjxo0cPXqUlJQUypcvT69evd64wlxuMTMz01scNasSExPRarVYWloSHx+v7i9UKP2fS9p9L+ZQ5TadTuHYrSjWn7zLzovhJKbo/r9Fg5G5NbrE5yTev0LCvUsk3D5HUlhq9TxHR0e2bt0qyZIQQgghxFtEEqYMlHazY0TDEszbF8y0Py5S+x1nHK3NDBLL1q1bGThwYLqS2RMnTuTLL79k7Nix+fIOWEpKCgEBASxatEidz+Pl5UXhwoXVPr/99hvjxo1TtxVFYePGjep2iRIlci9gICImgY2n7/HrqbvciXqu7i9gY051L0eqFXOiWjEnHt+8wPx5vxJ4NpCkhARcXV3p06cPo0ePpkiRIrkasxBCCCGEeDl5JC8TiSla2sw7RHBkHB19CvNd18o5cp2X2b17N61atUKr1Wba50WZ6/wkMTGRDh06sGPHjpf2s7S0ZPbs2fTq1YuoqCj8/Pz48ccfgdSFV69evZph+e9XFRkZyenTp0lJSaFcuXIUL148XZ8UrY6/rj1k/clQ/rr2EK0u9a+TjbkJbSu707WqBxWL2GeY1CqKQkpKilSiE0IIIYR4A1IlLwO5kTABnA19QsfFR1AU8O9fjYalXu+xstjYWAICAli7di0PHjzAwcGBdu3aMXToUNzd3TM8RqfTUaZMGXWx0xYtWjBu3DhsbGxYuXIly5YtA8Dc3Jx79+7lq8e4Ro8ezfz589XtcuXKYWNjw4kTJ3jV4bpx40Z1Paisun//Ph9//DEbN27UK13epEkTZs+ejY+PDwnJWtadCGXJgZuEpykOUq2YI12redKqghtWZnIDVwghhBAip0nClIHcSpgAZgRe5sdDt3C3t2DX2PrYWmTtbsClS5do0aJFhhXbrK2tWb9+Pa1bt07Xtn//fho2bAhArVq1OHTokN7dkhEjRrB4ceoCp3PmzNF7NC0vi4qKokiRIiQkJGBubs6WLVto3rw5AJcvX6Z58+YvrX5nbm7OwoULGThw4GtdPzQ0lLp162a6DpKVrT0fLfyNXXcVImISAXC2NqOTbxG6VPWghIvNa11XCCGEEEK8Hin6YGAfNfNmz+UIQh8/Z/bOa8xoX/6Vj33y5AnNmjXjwYMH6j5nZ2eioqIAePbsGZ06deLYsWNUrlxZ79jz58+r7/v375/u0bIBAwaoCVNQUFBWP9Zba9u2bWqxhqFDh6rJEkDZsmWZMWMG/fv3B1Ir5jk4OHD58mXMzMxo0KABgwYNeqMFa4cOHaomS46OjvTu3RsbGxvW/rqRKPtS2NV4n1WXUuNzt7dgRMMSdK5aBHMT49e+phBCCCGEeHtJwvQvrMxMmNmxAj1WHGf1sTu8V8md6l5Or3Ts8uXL1WTJx8eHlStXUrFiRe7du8fo0aPZvHkziYmJzJo1i19++UXvWGPj/30Bz6jaW2Jiovr+TebpvG3SFreoUaNGuva0ZcRNTEzUpDE7XL9+nZ07dwLg7u7OqdOnsbB14vdz9ylg9S5KbOoivCkxkXQpZ4/f0BaSKAkhhBBC5HP555t2DqpdogDdq3sAMPG3IBKSMy/CkNaqVavU9+vXr6dixYoAFClShDVr1lCwYEEgdb5NXFyc3rFpE4MlS5boJU2KovDDDz9k2DevS1t+/NixY+najx49qr7PjnlbIZFx+G2/wrhfzzH8lyBce32D+6Al2PZZRJ0fTuMzYw/Tt17mYWwSjuYQtXMB95cN4VnQLkmWhBBCCCH+AyRhekWTW5XB1c6cW4+eMXdv8CsdExoaCqSWty5ZsqRem6WlpTpHKSUlhYiICL12X19fqlatCqTO3alevTpLly5lzZo1NGvWjA0bNgBgZ2dn8MVZs1ObNm3UxW2XLl3Ktm3b1EIPQUFBTJ06Ve3btWvXN7rW2dAndFh0mKUHb7LpzH1uxFtiUbgMps5FSFBM+P+Cd3g6WfFVh/L81NGTuPM7QZuitx6UEEIIIYTIv+SRvFdkZ2HKV+0rMGjVKZYdvEHDUgWpUdz5pcfY2toSGxvL/fv3iY2NxdbWVm1TFIWrV6/q9U1Lo9GwZMkSGjRowLNnz7hw4QLDhg1Ld43FixdjY5N/Cg04OjoyZMgQfvjhB5KSkmjTpg2lSpXC2tpaXY8JoF69ehk+sveqTt95TN+fThKXmEJlDwdalHcjNPgyc2f7oYuPoUHNqqz+cQn2VqbqnaTPP/9cPf6dd9557WsLIYQQQoi8Q+4wZUGTsq50rFIYnQIf/HKWh7GJL+3/ovpdfHw8U6ZMQafTqW0rV65UizX4+vrqPYr2gq+vL/v3709XEALAw8OD3377LcfvLgUHBzN+/Hhq165N9erVGThwYIaPymWnWbNm0aZNG3X72rVreslSuXLl+PXXX197wd7jN6Po8+MJ4hJTqOHlxJpBNRjW4B0+79Mc+9hbJN67xO6NAfhNm8yjiHCePn3K3Llz8fPzA1KT2b59+77ZhxRCCCGEEHmClBXPoudJKbRfeJjrEXHUfseZ1QNrYGyU8Rf3CxcuULlyZTVRKlWqFI0aNeL8+fMcOXJE7bd69Wp69eqV6TUVReHYsWMcPnyYlJQUKlSoQPPmzTExydkbhH5+fnz66ad6id4LvXv3ZsWKFZiZmb32+bVaLdu3b2fbtm3ExsZSpEgRevXqRYUKFdBqtaxZs4ZFixZx/PhxIHUx2iFDhjBs2LDXvqt2JOQRAwNOEZ+spW6JAizvUxVLs//NRfrxxx8ZNGjQS88xYsQIFi5c+FrXF0IIIYQQ2UvWYcqAIRMmgJDIWNouOMzzJC0fNCrBR81KZdp3yZIlDB8+PNP2YcOGsWjRote+W5JT/i1ugCFDhrB06dLXOv/Fixfp1KmTujBvWp06dWLlypVqUpSSkoJWq8Xc3Py1rvXCwesPGbzqFIkpOhp4F2Rpb18sTNMXbpgzZw4TJ05Eq01f3GPgwIEsWbIkx5NVIYQQQgjxaiRhyoChEyaALefu8+G6cwCs7F+Nd0ulf6TuhV27dvH1119z8OBBdV/ZsmUZN24cAwYMeOuSpaSkJDw8PIiMjARg4sSJjB8/HisrKwICAhg7diyJiYloNBpCQkIoXrx4ls5/+/ZtqlWrxqNHjzLt07RpU3bu3JltJdP/vBrBsNVnSNLqaFLGhYU9q7y0yt3t27dZvnw5R44cISUlhfLlyzN48GCqVKmSLfEIIYQQQojsIQlTBt6GhAng098v8POxUBytTAkcXY/CDpYv7X/37l3Cw8NxcHCgRIkSb12i9MKWLVto3749AB06dGDTpk167TNmzOCzzz4D4LPPPmP69OlZOv+AAQPw9/cHoFKlSkyfPp3SpUuzc+dOPvvsM2JiYgDYvHmzGseb2H0pnJFrz5CsVWhezpX53atgZiLT94QQQggh8oOczg3kW+MbmNqmLBUK2/PkeTIj15whKSX9XJ+0PDw8qFatGiVLlnxrkyWAGzduqO87dOiQrj3tvlu3bmXp3LGxseoivXZ2dvz555+0a9eOUqVK8eGHH7Jy5Uq17/Lly7MYeXp/Xo1gxJrUZKl1xUIs6CHJkhBCCCGEeHXyzfENmJsYs6hnFewsTDh3Nxq/HVcMHVK2sLa2Vt+/WEsqrbT7XqyZ9Kpu3LihLsLbtm1bnJyc9NrbtWuHvb09kDrP6U0E3Ytm5JqzpOgU2lV254eulTE1liEvhBBCCCFenXx7fEMeTlbM6VIZAP/Dt9l+IcywAb0GRVG4desWQUFBPHr0iMaNG6ttCxYs4MGDB+p2fHw8X375pbrdtGnTLF0rbbGE2NjYdO2JiYkkJSWl65tVdx8/Z8DKk8Qna6nvXZBvO1fCRJIlIYQQQgiRRfINMhs0LevK0AaphQ8mbAzi1qNnBo7o1SiKwooVK6hQoQLFixenUqVKuLi4MGbMGGrXrg1AeHg4ZcqUYdiwYYwfPx5vb2+OHj0KgKenJ+3atcvSNb29vSlQoAAA27Zt4/Lly3rtixcvJj4+HoA6deq81ueKfp5EP/8TPIpLomwhOxb1rCJ3loQQQgghxGvJ00Uf9u3bR8OGDd+K+UApWh09lh/nxO3HWJgaUbdEARqVdqVRaRfc7C0MHV46iqIwcOBAtfjCPxkbG+Pk5MTDhw8zbLexsWHPnj3UrFkzy9eePHkyM2fOBMDBwYHhw4dTpkwZduzYoc5vAjhy5Ai1atXK0rkTU7T0/vEEJ249xt3egs0j6+Bq9/b9/IUQQgghRPaQKnkZePFDgdQqa99//z0NGzY0cFQQEZNA7x+Pcz0iTm9/OXc7Gpd2oVEZVyoWtscok4Vuc9OyZcsYOnSoul2zZk3KlCnD3r17uXv3LgBmZma0bduWrVu3kpiYCIBGo6Fly5bMnDmTChUqvNa1Y2JiqF+/PufPn8+0z5gxY/j++++zdF6dTuHD9efYev4BtuYmbBxem1Jutq8VoxBCCCGEyBskYcpA2oQJUue6bNmyhVatWhkwqlSKonAlLJY/r0aw72ok5+5Gk/YnXMDGnFEN36Fv7WIGuzOmKAply5bl6tWrAKxdu5bu3bsDkJycTP/+/VmzZg2QugbThAkTOHv2LCkpKZQtWxYPD483juHJkyeMGjWK9evX6y0Q6+TkxKRJkxg/fnyWfz4zd1xlyYEbmBprCOhfndolCrxxnEIIIYQQ4u0mCVMGXvxQKlasSFBQEAAFChQgNDQ0y1XbctqjuET2X3vIn1cjOHj9EXGJKQA0Ku3CN+9XxNnGPNdjCgkJoWTJkkDqPKFDhw7ptUdERODu7o5Op6Ns2bJcunQpx2K5f/8+u3btIiYmBg8PD1q1avVaf4arj91h6u+pVfW+61KJjlWKZHeoQgghhHhFWq2W5ORkQ4ch8glTU1OMjY0zbZeEKQMvfiiPHz+mR48e7Ny5E4CAgAD69Olj4Ogyl5SiY+3xO3y94ypJKToK2przXZdK1CzmwO+//05gYKCaOPTu3Ztq1arlSBxnzpzB19cXgMGDB7Ns2bJ0fVxdXYmMjKRIkSLqI3qZuXfvHteuXcPMzAwfHx9sbGxyJO7M7LsSweBVp9ApMK6pN6Mbl8zV6wshhBAilaIohIeHEx0dbehQRD7j4OCAm5tbhk8gScKUgbQ/lNOnT9OoUSMABg4cyIoVKwwc3b+7EhbD6F/OEhz5/3OdruzhTuBC0KXo9WvVqhVr167Ve/wwO0RERODm5gaAl5cXwcHBeln7uXPn8PHxAaBGjRocO3Ysw/OcPXuWKVOmsHPnTl4MIxsbG/r168eMGTNwcHDI1rj/KT5Jy9KDN1i8/waJKTq6VC3CrE4V34oiIEIIIcR/UVhYGNHR0bi4uGBlZSX/Jos3pigKz58/JzIyEgcHBwoVKpSuT04nTK+/0M1bIu3Cpy/W73nblSlkxx+j6vLx2qMEXn0KZZri5lCUR398Q0r0/9Zx2r59O+3atWPfvn0vvQ2ZVa6urjRt2pQ9e/Zw69YtBg8ezDfffIOzszNBQUF6d+l69+6d4TkOHDhAy5Yt1RLgL8TFxbFgwQL++usvDhw4gLOzc7bF/YJOp/DH+QfM2nmVsKepi+A2KePKVx0qyP+YhRBCCAPRarVqspQT//6L/64X0zUiIyNxcXHJ1u/FryLPL07zojgBQJkyZQwYSdZYmhkT8+cyIjd9hTY+FvNC3hQfsZx528/wyVx/Cparg0XRShwPjeXrlVvYdyWCPZcjuJ1Nazx9+umnGBml/vH7+/vj5uZG4cKFqVSpEhcuXACgaNGiGT7iGB8fT5cuXdRkycPDg7Fjx9K3b191QF+6dIkxY8ZkS6xpnQl9QsfFRxiz/hxhTxMo4mjJop5VWN7HV9ZaEkIIIQzoxZwlKysrA0ci8qMX48oQc+Py9CN548eP57vvvkOn02FiYsKdO3dwd3c3dHivJCYmhoIFC5KUlIRTkeI0nLySU6Ex/3qckQYW9KhCqwrpb0dm1c8//8yAAQMyHHhFixZl165dlCpVKl3bypUr6d+/PwANGzZk+/btWFikrnUUEhJC1apVefr0KaampoSGhqqP/72JB9HxzNp5lS3nHgBgbWbMiIYlGFjXCwvT3P0tgxBCCCHSS0hI4NatW3h5eanfC4TILi8bX/JI3kt8++236vsJEya8cbKUlJTEqVOniI2NpUiRIpQtWzbHHvG6efOm+ghh64Z18B9Wl6UHb/D72ftodQrGGg1XrlxGm5KMqYkJlStV5FmSlpDIOD5cdxYrM2PeLeXyStc6deoUa9eu5cGDBzg4ONCuXTuaN29Or169qFWrFgsXLmTbtm3ExMRQpEgR+vTpQ79+/bC1zXgNo127dqnvp0+frjdoS5QowaBBg5gzZw7Jycns37+fbt26vfbPKSImgZVHbuN/+BYJyTo0GujsW4TxzUrhIgvSCiGEEEKIHJanEyYAIyMjJkyYwIwZM177HMnJyfj5+bFw4UIiIyPV/T4+PkybNo127dplR6h6TE1N1ffR0dEYG2kY8W4JRrxbAoDnz5/j7NyChIQE3nnnHbYsD0GrUxi97izbgsIY9vNpAvpXp0bxzJ8RfvLkiV4VwReWLl1KuXLl2LRpE97e3nz33Xd89913rxz7s2f/eyzQy8srXXvafWn7ZkXQvWh+OnSLwKAwUnSpN0GrF3NiapuyVCiSvUUwhBBCCCGEyEyenvQxYcIEbt68iZ+fnzofJ6uSk5Pp0KED06ZN00uWILUKXPv27Vm0aFF2hKvH29sbF5fUO0Tbt2/n/Pnzeu3z5s0jISG1oEG9evUAMDbS8H2XyjQq7UJCso6BAacIuhed4fmTkpJo3bp1umTphUuXLtGwYUPCwsIybH+Z4sWLq++3bNmSrj3tvowSqsykaHXsuBDG+4uP0HbBYX4/94AUnUL1Yk4s7e3L+qE1JVkSQgghRK5599139eZkFytWjLlz5xosHmEYeTphmjJlCkWLFn2jc8ybN49t27YBqXerOnbsyCeffKKuUwTwwQcfcPXq1Te6zj+ZmpoydOhQILWqTN26dRk7dizLli2jQ4cOTJ48We07cuRI9b2ZiRGLelahZnEn4hJT6PvTCa5HxKY7/y+//MLRo0eB1EV9ly5dSnBwML/99ptaHOPBgwfMnDkzy7H37dtXfT958mRWr15NcnIyjx494qOPPmLPnj1A6jyoBg0avPRcSSk6giNiWX7wJg2+2c/wNWc4decJpsYaOvoUZuuouvw6rBbNy2Vcd18IIYQQ4k3169cPjUaT7jV79uyXPsWk0Wj4/fffcy9QYRB5uujDm07s0mq1lChRgtu3bwOwd+9eGjduDKTWfB87diw//PADAKNGjWL+/PlvHHtaz549o2HDhpw8eTLTPpMnT+brr79Otz8uMYWeK45z/m40LrbmbBxWG0/n/1WlqVu3LocPHwbgzz//pGHDhmpbWFgYxYsXJyEhAXt7eyIjIzEzM8tS7J07d2bjxo3qtrGxMVqtVq/PqlWr1LLkz5NSuBH5jJCHsYRExhEcEUfIwzjuRD1Hq/vfEHSyNqNnDU961ywqc5SEEEKIPCQvF33o168fERER+Pv76+0vWLCgXgnrYsWKMWbMGPWuk0ajYfPmzbRv3/6Nrp+cnKw3XUOkZ8iiD3n6DtObCgkJUZOlxo0bq8kSpP4F+Pzzz9XB++KuSXaytrZm7969DBw4MF3C4ubmxvz58/nqq68yPNbG3ISA/tUo5WpLZGwiPVYcI/z/1yQCuHjxIpBa8vvdd9/VO7ZQoUI0a9YMgKdPn3L//v0sxx4QEMB7772nbqdNloyNjfnuu+/o3bs3iqKw4u+bVP5iD+8tOMTY9edZ+NcNdl+O4ObDZ2h1CjbmJvgWdWRWpwocmdSIj6SggxBCCJHnKYrC86QUg7xe536Aubk5bm5ueq/GjRtnukxKsWLFAOjQoQMajUbdhtTpCVWqVMHCwoLixYszffp0UlJS1HaNRsPixYtp27Yt1tbWmX7fE2+HPF/04U2kLUiQ0aN99vb22Nvb8+jRI548ecLQoUM5evQoKSkplC9fnsGDB9OkSRM0Gg1BQUH8+OOPXLlyBTMzM+rXr0///v0pWLDgS2Ows7NjxYoV+Pn5sW/fPrVSXZMmTf71ro+DlRmrB1Wny5Kj3I56Ts8Vx/h1aC2cbczVRO/58+dotVpMTPT/qGNj//cY3z/bXoWVlRVbtmzhr7/+Yvny5Xqfe9iwYZQoUYLEFC1TNl9k4+l7ADhbm/GOiw0lXGwo+f//LeFig5udhTxuJ4QQQuQz8clayn6269875oDLXzTHyixnv+aePHkSFxcX/P39adGihXon6u+//6ZPnz7MmzePevXqcePGDYYMGQLAtGnT1OM///xzZs6cydy5c1/ru5jIPf/pP52iRYtiZGSETqdjx44dJCQk6N3iO3z4MI8ePQJSVxZetmyZ2nblyhU2bNhA27ZtcXBwYNWqVXrn3rZtG59//jlLlizJcPHXfypYsOBrld92sbXg50E16LzkKDcePqPN/EMMrV+cWnXrs/X3TURFReHv78/gwYPVY06cOMH+/fvVn0HhwoWzfF1I/e1Io0aNaNSoUbq2yNgEhq0+zZnQaIw08GnrsvSvU0wSIyGEEEK8lQIDA7GxsVG3W7Zs+dL+L34p7uDgoLfm5PTp05k0aZI657t48eLMmDGDCRMm6CVMPXr0UNe1FG+3/3TC5OzsTNu2bfn9998JCwujc+fOzJkzhxIlSrB7926GDx+e7hhjY2NMTExITEwE4I8//sj0/PHx8fTt2xd7e/scKU3+QhFHK9YMqkHvH09wPzqez7dexrb8AOzCNMSe3c7QoUM5dOgQjRs35vz58yxdulS9VT18+PDXrjCYmYv3nzJ41SnCniZgZ2HCgh5VqO/98jttQgghhMhfLE2NufxFc4NdO6saNmzI4sWL1W1ra2u6d++e5fOcP3+ew4cP6z1mp9VqSUhI4Pnz51hZpc45r1q1apbPLQzjP50wAUydOpUdO3aQmJhIYGAggYGB6l2nf/ryyy8ZPXo0FhYWrF+/nsGDB6ulv83MzJg5cyY9evTg8ePH+Pn5sXr1agAmTpxI27Ztc/TuSvGCNuz7qAEbTt9jyf4b3I+Ox/Hd/tjV7Ezs6T/4+dfN6e6C1a5dm9GjR2drHNuCwvhowzkSknUUL2jNij5VKV7Q5t8PFEIIIUS+otFocvyxuOxkbW1NiRIl3vg8cXFxTJ8+nY4dO6ZrS/skk7W19RtfS+SOvDOK/4WiKBw4cEBvPk2DBg0YOnSo3rpB/1SlShW2bNlCly5diImJAcgwWerWrRtTpkxRt3v16sWKFSs4cOAAgFoWHMDV1ZWAgABu3rzJ4cOHuXbtGocPH6Zu3brZ+ZHTsTA1pnfNonSr5sGWcw9Y9FcINx+BQ50e2FXrQOy5HSTevYhRYiwdWjZm/jdfY2lpme48KVoddx4/T61kF/n/Ve0i40hKSU2CXsw9eqdg6sva3ASdTmHuvmDm7QsGoIF3QeZ198HeUiq+CCGEECJ/MjU1TVcluEqVKly7di1bki/xdsgXCdPz58/p0aNHukVUjx8/zpw5c5gzZw4ffvhhpsc3b96cmzdv4u/vT2BgIDExMXh4eODo6EhAQAAArVu3Tndc2kfZ/lnCUKPR0KVLF7W09/Xr13M8YXrB1NiI932L0MGnMDsvhjNv3zWuRYB99Y5QPfW3HX8DPn4HcbY2o6CtBS625liYGnHr0TNuPXpGsjbj6jLBkXHsuhSht8/d3gI7S1OuhqcWkhhU14vJrcpgbCTzlYQQQgiRfxUrVox9+/ZRp04dzM3NcXR05LPPPqNNmzZ4enry/vvvY2RkxPnz57l48SJffvmloUMWryFfJEz9+vXTS5Y0Go06R0er1TJmzBicnZ3p1atXpudwdnZm/PjxjB8/Xt23bNkyNWEKCQlJd0xSUpLeNf8pMjJSfW9ubp6FT5Q9jI00tK5YiFYV3PjrWiS/nrzH/eh4ImMTeBSXhFan8CguiUdxSVwJ0z/WysyYdwr+fzU7VxtKFLTB3NSYG5Gp6yeFRMZx82Ecj+KSePA0gQdPEzAzNuKrDuXpXNUj1z+rEEIIIURumzNnDuPGjWP58uUULlyY27dv07x5cwIDA/niiy+YNWsWpqamlC5dmkGDBhk6XPGa8vzCtTdv3sTHxwcAW1tbFixYQLdu3YiOjsbPz4+5c+cCqb8BCAkJ0Vt87N/cvn2b4sWLoygKBQoU4MSJE3h5eakxlC9fnrt37wJQvXp1jhw5op4/LCyMypUrExkZiZGREbdv38bD4+1JJLQ6hcfPkoiMTeBhbCKRsYk8T0yhaAFrSrrY4G5vidEr3CGKfp5ESGTqArSVPBwo4SLzlYQQQoj/ory8cK14+xly4do8f4dp5cqV6vuvv/5aLeHt4uLC999/z8WLF9m7dy+3b9/m4MGDNGzY8JXPXaxYMdq3b8/mzZt59OgRZcuWpWPHjtjY2LBp0ya15DikluquUqUK3bp14/Hjx/j7+xMVFQVAu3bt3qpkCVLvPhW0Naeg7Zvd+XKwMqNqMSeqFnPKpsiEEEIIIYR4e2RvPeksWrhwIcWKFcPCwoIaNWpw4sSJLJ/j5s2b6vuMSne3b98+w76vasmSJZQqVQpIzWzXrl3LsmXL1GTJ2tpaXWwsKCiITz75hG+//VZNlooWLcr8+fOzfN2sUhSFJ0+e6C3GK4QQQgghhHgzBkuY1q9fz7hx45g2bRpnzpyhUqVKNG/eXG/ez6tIW5Lxzp076dpv376dYd9X5eLiwpEjR/jggw+wtbVV95uYmNC1a1fOnj3L7t2709XSf9F+5MiR114Y9lU8evSITz/9FHd3d5ycnLCxscHX1xd/f/90VVuEEEIIIYQQWWOwOUw1atSgWrVqLFiwAEgt5e3h4cEHH3zApEmTXnps2ucUf/vtNwYMGABAo0aN2L59u1pg4caNG1StWpXo6GhMTEy4e/eu3krMWfXs2TMuXbpESkoKpUqVwtnZWa/9/PnzXL58GTMzM2rXrk2hQoVe+1qv4saNGzRq1IjQ0NAM29u1a8eGDRswNZXS3kIIIYTIWTKHSeQkQ85hMkjClJSUhJWVFRs3btR7ZK5v375ER0enKw+emJhIYmKiuv2i7PfTp08xMTGhWLFiPHz4EEh9BO79998nKiqK9evXEx8fD0DPnj35+eefc/7D5RKtVkulSpW4dOkSkHpHq06dOjx+/JgLFy6o/SZOnMjMmTMNFaYQQggh/iMkYRI5yZAJk0EeyXv06BFarRZXV1e9/a6uroSHh6fr7+fnh729vfpKW0DBysqK9evXqwuw3rlzhzlz5rBy5Uo1WSpbtiw//PBDDn6i3Ldz5041WSpVqhTBwcHs37+foKAgtm7dqs6rWrx4MXFxcYYMVQghhBBCiDzLoEUfXtXkyZN5+vSp+npRyvuFhg0b8vfff9OiRQu9/dbW1owYMYJDhw6le3wur9u4caP6fvbs2RQrVkzdbtOmjVotMCYmhj179uR2eEIIIYQQQuQLBikrXqBAAYyNjYmIiNDbHxERkeEcI3Nz839d+NXX15cdO3YQGhrKtWvXMDMzo0qVKnqFGvKTtCXNq1Wrlq69WrVq/PTTTwA8fvw41+ISQgghhBAiPzHIHSYzMzN8fX3Zt2+fuk+n07Fv3z5q1ar1Ruf29PSkadOmNGjQIN8mS4De44yHDx9O1552X8GCBXMlJiGEEEIIIfIbgz2SN27cOJYvX05AQABXrlxh+PDhPHv2jP79+xsqpDyla9eu6vuPP/6YixcvAqmJ55o1a1i7di0Ajo6ONG3a1CAxCiGEEEJk1Z07d1i5ciWLFy9m7969ubJMSr9+/dBoNAwbNixd28iRI9FoNPTr1y/H48jPNBoNv//+u6HDeC0GeSQPUr/wP3z4kM8++4zw8HAqV67Mzp070xWCEBlr3LgxVatW5dSpU9y+fZsKFSpQqVIlnjx5oldmfMyYMWpBDCGEEEKIt9WDBw8YMWIEf/zxB2mLOBctWpSZM2fSrVu3HL2+h4cH69at4/vvv1e/OyUkJLB27Vo8PT1z9NpvKikpCTMzM0OHkW8ZtOjDqFGjuHPnDomJiRw/fpwaNWoYMpw8xcjIiM2bN1OqVCl13/nz5/WSpd69ezNlyhRDhCeEEEII8crCwsKoU6cOW7Zs4Z8r3ty5c4fu3buzaNGiHI2hSpUqeHh4sGnTJnXfpk2b8PT0xMfHR92n0+nw8/PDy8sLS0tLKlWqpFeMS6vVMnDgQLW9VKlS6ao179+/n+rVq2NtbY2DgwN16tThzp07QOrdrrTL7kDqL8Dfffdddfvdd99l1KhRjBkzhgIFCtC8eXMALl68SMuWLbGxscHV1ZXevXvrzXt/9913+eCDDxgzZgyOjo64urqyfPly9SkvW1tbSpQowY4dO/Su/yrnHT16NBMmTMDJyQk3Nzc+//xztf1FcbIOHTqg0WjU7fPnz9OwYUNsbW2xs7PD19eXU6dO/cufVO7LE1XyRMaKFCnCyZMn+fbbb9XEycTEhEaNGrFp0yYCAgIwNjY2cJRCCCGEEC/38ccfc/v2bQBcXFz47LPPWLJkCU2aNFH7jBkzhvv37+doHAMGDMDf31/d/umnn9JNF/Hz82PVqlUsWbKES5cuMXbsWHr16sWBAweA1ISqSJEibNiwgcuXL/PZZ5/xySef8OuvvwKQkpJC+/btadCgAUFBQRw9epQhQ4ag0WiyFGtAQABmZmYcPnyYJUuWEB0dTaNGjfDx8eHUqVPs3LmTiIgIunTpku64AgUKcOLECT744AOGDx9O586dqV27NmfOnKFZs2b07t2b58+fA2TpvNbW1hw/fpzZs2fzxRdfqJWaT548CYC/vz9hYWHqds+ePdXvs6dPn2bSpEmYmppm6eeQK5Q86OnTpwqgPH361NChvFVSUlIUnU5n6DCEEEII8R8UHx+vXL58WYmPj8/ScZGRkYqpqakCKA4ODsr9+/fVNp1OpwwbNkwBFECZNm1aNkedqm/fvkq7du2UyMhIxdzcXLl9+7Zy+/ZtxcLCQnn48KHSrl07pW/fvkpCQoJiZWWlHDlyRO/4gQMHKt27d8/0/CNHjlQ6deqkKIqiREVFKYCyf//+l8aS1ocffqg0aNBA3W7QoIHi4+Oj12fGjBlKs2bN9PbdvXtXAZRr166px9WtW1dtT0lJUaytrZXevXur+8LCwhRAOXr06GufV1EUpVq1asrEiRPVbUDZvHmzXh9bW1tl5cqVGf4c/ull4yuncwODzWEyBEVRuHLlCg8ePMDBwQEfH598dQcmP30WIYQQQvw3nDhxguTkZCB1OoG7u7vaptFomDhxIkuWLAHg0KFDORpLwYIFad26NStXrkRRFFq3bk2BAgXU9pCQEJ4/f56uoFZSUpLeY3sLFy7kp59+IjQ0lPj4eJKSkqhcuTIATk5O9OvXj+bNm9O0aVOaNGlCly5dKFSoUJZi9fX11ds+f/48f/31FzY2Nun63rhxA29vbwAqVqyo7jc2NsbZ2ZkKFSqo+17UE4iMjHzt8wIUKlRIPUdmxo0bx6BBg1i9ejVNmjShc+fOvPPOOy89xhD+MwnTxo0b+fLLLzl//ry6z9PTkw8//JAxY8ZgZCRPJwohhBBC5LYXyRKAg4NDuva0+9L2zSkDBgxg1KhRQGrik1ZcXBwA27Zto3DhwnptL9YMXbduHePHj2fOnDnUqlULW1tbvvnmG44fP6729ff3Z/To0ezcuZP169fz6aefsmfPHmrWrImRkVG6eVwZfW5ra+t0sb333nvMmjUrXd+0ydg/H3nTaDR6+148GqjT6d74vC/OkZnPP/+cHj16sG3bNnbs2MG0adNYt24dHTp0eOlxue0/kTB9++23fPzxx+n2h4aG8tFHH3HmzBlWrVolSZMQQgghRC4rW7as+n7dunVMnTpV78v36tWrM+ybU1q0aEFSUhIajUYtppD2+ubm5oSGhtKgQYMMjz98+DC1a9dmxIgR6r4bN26k6+fj44OPjw+TJ0+mVq1arF27lpo1a1KwYEF1uZgXzp07969ze6pUqcJvv/1GsWLFMDHJvq/42XVeU1PTDEvEe3t74+3tzdixY+nevTv+/v5vXcKU7zOE06dP6yVL1apVY+LEibRs2VLdt2bNGr0JfkIIIYQQInd4e3tTv359AIKDg2ndujUHDx4kJCSEmTNnMmHCBLXvoEGDcjweY2Njrly5wuXLl9NNd7C1tWX8+PGMHTuWgIAAbty4wZkzZ5g/fz4BAQEAlCxZklOnTrFr1y6uX7/O1KlT1SIHALdu3WLy5MkcPXqUO3fusHv3boKDgylTpgwAjRo14tSpU6xatYrg4GCmTZuWLoHKyMiRI3n8+DHdu3fn5MmT3Lhxg127dtG/f/83Wssqu85brFgx9u3bR3h4OE+ePCE+Pp5Ro0axf/9+7ty5w+HDhzl58qT6c3ib5PuEaf78+er7yZMnc+LECWbOnMn27dvZsGGD2jZv3rx0tz+FEEIIIUTOmzVrlvpI2549e2jQoAElS5Zk8uTJJCQkANCnT59083Zyip2dHXZ2dhm2zZgxg6lTp+Ln50eZMmVo0aIF27Ztw8vLC4ChQ4fSsWNHunbtSo0aNYiKitK722RlZcXVq1fp1KkT3t7eDBkyhJEjRzJ06FAAmjdvztSpU5kwYQLVqlUjNjaWPn36/GvM7u7uHD58GK1WS7NmzahQoQJjxozBwcHhjZ6iyq7zzpkzhz179uDh4aHWEYiKiqJPnz54e3vTpUsXWrZsyfTp01871pyiUfJglhATE4O9vT1Pnz7NdDC/UKhQIcLDw7GxsSEiIgIrKyu99qpVq3L69GkgdQ0ANze3HItbCCGEECK/SkhI4NatW3h5eWFhYZHl4/fs2UPPnj15+PBhuraBAweyaNEiWZz1P+xl4ysrucHryPdzmJ49ewakVvz4Z7IE4OXlpSZML/oKIYQQQojc1bRpU+7cucP69ev5888/iY+Pp0SJEvTr109db1IIQ8j3CZOXlxdBQUHcuHGDixcvUr58ebUtLi6Offv2AWBmZpblco5CCCGEECL7WFpa0q9fP/r162foUIRQ5fs5TGn/wnXp0oVDhw6hKArXrl2jU6dOPHnyBICuXbtmeAdKCCGEEEII8d+V7xOmgQMHqpPwrly5Qr169TA3N6d06dLs3r0bSK1jP2nSJEOGKYQQQgghhHgL5fuEyc7Ojj179lCyZEl1X9rFvxwdHQkMDMyVuv5CCCGEEEKIvCXfz2ECeOeddwgKCmLDhg2sWbOGBw8e4ODgQPv27enXrx9OTk6GDlEIIYQQIl/Q6XSGDkHkQ4YcV/m+rLgQQgghhMh5Op2O4OBgjI2NKViwIGZmZmg0GkOHJfI4RVFISkri4cOHaLVaSpYsmW79JykrLoQQQggh3npGRkZ4eXkRFhbGgwcPDB2OyGesrKzw9PR8o0V4X5ckTEIIIYQQIluYmZnh6elJSkoKWq3W0OGIfMLY2BgTExOD3bGUhEkIIYQQQmQbjUaDqakppqamhg5FiGyR76vkCSGEEEIIIcTrkoRJCCGEEEIIITIhCZMQQgghhBBCZCJPzmF6UQk9JibGwJEIIYQQQgghDOlFTpBTqyXlyYQpKioKAA8PDwNHIoQQQgghhHgbREVFYW9vn+3nzZMJk5OTEwChoaE58kMR4oWYmBg8PDy4e/euLJIscpSMNZFbZKyJ3CJjTeSWp0+f4unpqeYI2S1PJkwvFqyyt7eXv4AiV9jZ2clYE7lCxprILTLWRG6RsSZyS04taitFH4QQQgghhBAiE5IwCSGEEEIIIUQm8mTCZG5uzrRp0zA3Nzd0KCKfk7EmcouMNZFbZKyJ3CJjTeSWnB5rGiWn6u8JIYQQQgghRB6XJ+8wCSGEEEIIIURukIRJCCGEEEIIITIhCZMQQgghhBBCZEISJiGEEEIIIYTIhCRMQgghhBBCCJGJPJkwLVy4kGLFimFhYUGNGjU4ceKEoUMSeZifnx/VqlXD1tYWFxcX2rdvz7Vr1/T6JCQkMHLkSJydnbGxsaFTp05EREQYKGKRX8ycORONRsOYMWPUfTLWRHa5f/8+vXr1wtnZGUtLSypUqMCpU6fUdkVR+OyzzyhUqBCWlpY0adKE4OBgA0Ys8iKtVsvUqVPx8vLC0tKSd955hxkzZpC2CLOMNfE6Dh48yHvvvYe7uzsajYbff/9dr/1VxtXjx4/p2bMndnZ2ODg4MHDgQOLi4rIcS55LmNavX8+4ceOYNm0aZ86coVKlSjRv3pzIyEhDhybyqAMHDjBy5EiOHTvGnj17SE5OplmzZjx79kztM3bsWLZu3cqGDRs4cOAADx48oGPHjgaMWuR1J0+eZOnSpVSsWFFvv4w1kR2ePHlCnTp1MDU1ZceOHVy+fJk5c+bg6Oio9pk9ezbz5s1jyZIlHD9+HGtra5o3b05CQoIBIxd5zaxZs1i8eDELFizgypUrzJo1i9mzZzN//ny1j4w18TqePXtGpUqVWLhwYYbtrzKuevbsyaVLl9izZw+BgYEcPHiQIUOGZD0YJY+pXr26MnLkSHVbq9Uq7u7uip+fnwGjEvlJZGSkAigHDhxQFEVRoqOjFVNTU2XDhg1qnytXriiAcvToUUOFKfKw2NhYpWTJksqePXuUBg0aKB9++KGiKDLWRPaZOHGiUrdu3UzbdTqd4ubmpnzzzTfqvujoaMXc3Fz55ZdfciNEkU+0bt1aGTBggN6+jh07Kj179lQURcaayB6AsnnzZnX7VcbV5cuXFUA5efKk2mfHjh2KRqNR7t+/n6Xr56k7TElJSZw+fZomTZqo+4yMjGjSpAlHjx41YGQiP3n69CkATk5OAJw+fZrk5GS9cVe6dGk8PT1l3InXMnLkSFq3bq03pkDGmsg+f/zxB1WrVqVz5864uLjg4+PD8uXL1fZbt24RHh6uN9bs7e2pUaOGjDWRJbVr12bfvn1cv34dgPPnz3Po0CFatmwJyFgTOeNVxtXRo0dxcHCgatWqap8mTZpgZGTE8ePHs3Q9k+wJO3c8evQIrVaLq6ur3n5XV1euXr1qoKhEfqLT6RgzZgx16tShfPnyAISHh2NmZoaDg4NeX1dXV8LDww0QpcjL1q1bx5kzZzh58mS6NhlrIrvcvHmTxYsXM27cOD755BNOnjzJ6NGjMTMzo2/fvup4yujfUxlrIismTZpETEwMpUuXxtjYGK1Wy1dffUXPnj0BZKyJHPEq4yo8PBwXFxe9dhMTE5ycnLI89vJUwiREThs5ciQXL17k0KFDhg5F5EN3797lww8/ZM+ePVhYWBg6HJGP6XQ6qlatytdffw2Aj48PFy9eZMmSJfTt29fA0Yn85Ndff2XNmjWsXbuWcuXKce7cOcaMGYO7u7uMNZFv5KlH8goUKICxsXG6ilERERG4ubkZKCqRX4waNYrAwED++usvihQpou53c3MjKSmJ6Ohovf4y7kRWnT59msjISKpUqYKJiQkmJiYcOHCAefPmYWJigqurq4w1kS0KFSpE2bJl9faVKVOG0NBQAHU8yb+n4k19/PHHTJo0iW7dulGhQgV69+7N2LFj8fPzA2SsiZzxKuPKzc0tXVG4lJQUHj9+nOWxl6cSJjMzM3x9fdm3b5+6T6fTsW/fPmrVqmXAyERepigKo0aNYvPmzfz55594eXnptfv6+mJqaqo37q5du0ZoaKiMO5EljRs35sKFC5w7d059Va1alZ49e6rvZayJ7FCnTp10yyNcv36dokWLAuDl5YWbm5veWIuJieH48eMy1kSWPH/+HCMj/a+TxsbG6HQ6QMaayBmvMq5q1apFdHQ0p0+fVvv8+eef6HQ6atSokbULvlHJCgNYt26dYm5urqxcuVK5fPmyMmTIEMXBwUEJDw83dGgijxo+fLhib2+v7N+/XwkLC1Nfz58/V/sMGzZM8fT0VP7880/l1KlTSq1atZRatWoZMGqRX6StkqcoMtZE9jhx4oRiYmKifPXVV0pwcLCyZs0axcrKSvn555/VPjNnzlQcHByULVu2KEFBQUq7du0ULy8vJT4+3oCRi7ymb9++SuHChZXAwEDl1q1byqZNm5QCBQooEyZMUPvIWBOvIzY2Vjl79qxy9uxZBVC+++475ezZs8qdO3cURXm1cdWiRQvFx8dHOX78uHLo0CGlZMmSSvfu3bMcS55LmBRFUebPn694enoqZmZmSvXq1ZVjx44ZOiSRhwEZvvz9/dU+8fHxyogRIxRHR0fFyspK6dChgxIWFma4oEW+8c+EScaayC5bt25Vypcvr5ibmyulS5dWli1bpteu0+mUqVOnKq6uroq5ubnSuHFj5dq1awaKVuRVMTExyocffqh4enoqFhYWSvHixZUpU6YoiYmJah8Za+J1/PXXXxl+P+vbt6+iKK82rqKiopTu3bsrNjY2ip2dndK/f38lNjY2y7FoFCXNUsxCCCGEEEIIIVR5ag6TEEIIIYQQQuQmSZiEEEIIIYQQIhOSMAkhhBBCCCFEJiRhEkIIIYQQQohMSMIkhBBCCCGEEJmQhEkIIYQQQgghMiEJkxBCCCGEEEJkQhImIYQQQgghhMiEJExCCCGEEEIIkQlJmIQQQgghhBAiE5IwCSGEEEIIIUQm/g9zcFPhokO4hwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "zs = gen_data(x0=5., dx=2., count=100, noise_factor=10)\n", + "data = g_h_filter(data=zs, x0=100., dx=2., dt=1., g=0.2, h=0.02)\n", + "plot_g_h_results(measurements=zs, filtered_data=data)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "856e1df3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_data(x0=5., dx=2., count=100, noise_factor=100)\n", + "data = g_h_filter(data=zs, x0=5., dx=2., g=0.2, h=0.02)\n", + "plot_g_h_results(measurements=zs, filtered_data=data)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "14d24b7a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(100)\n", + "zs = gen_data(x0=5., dx=5., count=50, noise_factor=50)\n", + "data1 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.1, h=0.01)\n", + "data2 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.4, h=0.01)\n", + "data3 = g_h_filter(data=zs, x0=0., dx=5., dt=1., g=0.8, h=0.01)\n", + "\n", + "with book_plots.figsize(y=4):\n", + " book_plots.plot_measurements(zs, color='k')\n", + " book_plots.plot_filter(data1, label='g=0.1', marker='s', c='C0')\n", + " book_plots.plot_filter(data2, label='g=0.4', marker='v', c='C1')\n", + " book_plots.plot_filter(data3, label='g=0.8', c='C2')\n", + " plt.legend(loc=4)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "66114596", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "zs = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n", + "for i in range(50):\n", + " zs.append(14)\n", + "\n", + "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.1, h=0.01)\n", + "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.5, h=0.01)\n", + "data3 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=0.9, h=0.01)\n", + "\n", + "book_plots.plot_measurements(zs)\n", + "book_plots.plot_filter(data1, label='g=0.1', marker='s', c='C0')\n", + "book_plots.plot_filter(data2, label='g=0.5', marker='v', c='C1')\n", + "book_plots.plot_filter(data3, label='g=0.9', c='C3')\n", + "plt.legend(loc=4)\n", + "plt.ylim([6, 20]);\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "750aeb7b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "zs = [5,6,7,8,9,9,9,9,9,10,11,12,13,14,\n", + " 15,16,16,16,16,16,16,16,16,16,16,16]\n", + "data1 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.302, h=.054)\n", + "data2 = g_h_filter(data=zs, x0=4., dx=1., dt=1., g=.546, h=.205)\n", + "\n", + "book_plots.plot_measurements(zs)\n", + "book_plots.plot_filter(data2, label='g=0.546, h=0.205', marker='s', c='C0')\n", + "book_plots.plot_filter(data1, label='g=0.302, h=0.054', marker='v', c='C1')\n", + "plt.legend(loc=4)\n", + "plt.ylim([6, 18]);\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "45944b79", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "9d0aea88c65d49e38aea3d8bf2c1aafd", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=0.0, continuous_update=False, description='x', max=200.0, min=-200.0),…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "from ipywidgets import interact\n", + "\n", + "# my FloatSlider returns an ipywidgets.FloatSlider with\n", + "# continuous_update=False. Filtering code runs too slowly\n", + "# to instantly react to slider changes.\n", + "from kf_book.book_plots import FloatSlider\n", + "\n", + "zs1 = gen_data(x0=5, dx=5., count=100, noise_factor=50)\n", + "\n", + "fig = None\n", + "def interactive_gh(x, dx, g, h):\n", + " global fig\n", + " if fig is not None: plt.close(fig)\n", + " fig = plt.figure()\n", + " data = g_h_filter(data=zs1, x0=x, dx=dx, g=g, h=h)\n", + " plt.scatter(range(len(zs1)), zs1, edgecolor='k', \n", + " facecolors='none', marker='o', lw=1)\n", + " plt.plot(data, color='b')\n", + " plt.show()\n", + "\n", + "interact(interactive_gh, \n", + " x=FloatSlider(value=0, min=-200, max=200), \n", + " dx=FloatSlider(value=5, min=-50, max=50), \n", + " g=FloatSlider(value=.1, min=.01, max=2, step=.02), \n", + " h=FloatSlider(value=.02, min=.0, max=.5, step=.01));\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "b934de15", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xmpiOI5Wqjvc4CSuCIAiCIAgbwWZYMSjAgqgmUqrgCgBIiTPf85UKCSuCIAiCIAgbEcko/6NyQKKaODEawWQ0Aa/LAY9TkiKhKikHJGFFEARBEARhIyaj6YtMCrAgqok9Z6QywJVd9aj3uQBUzywrElYEQRAEQRA2Qt1jBZBjRVQX+2RhtWpuPepr3ABIWBEEQRAEQRBFILPfZDpOPVZE9cCCK1bNaUDAJwsrKgUkCIIgCIIgrCaSIazYIFWCqHREUcTeM1Jwxaq5DaivoVJAgiAIgiAIokiEM0oBozYXVsOTUfyhd7Tch0FUAKfHphCcisPtFLCsI4B62bGaqJIhwSSsCIIgCIIgbESmY2X38Iq7f7oLf/rwazhwNpT7ysSsZq/cX7W8MwCPy6H0WFEpIEEQBEEQBGE1mY7VVMzePVbHh8MAgFOjkTIfCWF3WCLg6rkNAECpgARBEARBEETxmOFY2bwUMCSXcWXGxBNEJnvlwcDnzpGFFXesSFgRBEEQBEEQFhPOHBBsY2GVTImYkMu4wiSsTBFNJPHy4WEkkvZ2JK1CFEVV1DoTVsyxqo73DgkrgiAIgiAIGxHJHBBsY2E1qeqNmYza9zjtyGOv9uIT//k67n96f7kPpSScDU5jJByD0yFgRWcAAHh4BTlWBEEQBEEQhOUwx0oQpH9HE/Z1NIKq3hhyrMzx9slxAMCTr5+cFf1pLLhiaXsdatxOAFQKSBAEQRAEQRQR1mPVKO/mT8Xs6wSphRX1WJmDhX4kUiJ+8OLhMh9N8WH9VawMEFCHV1THe4eEFUEQBGGIH7x4GP9v5+lyHwZBVD0sFbC51gPA3qWAaqeBhJVxUimRCysA+H9vncaxockyHlHxYY7Vqjn1/DLmWNEcK4IgCGLWcGo0gu8//y7u3bwHyZRY7sMhiKqGOVYtdV4A9g6voFLA/DgzPoVoIgW3U8CG5W1IicA/V7lrxYTV6nlqx0qZYyWKlX9uIWFFEARB5GR4MgpA6vXoD02X+WgIorphjlULd6wqo8eKHCvjHJPdqgUttfhf1y4HADz1Th8O9U+U87CKxmBoGoMTUQgCsLJrpmOVTImI2Ljk1SgkrAiCIIicqBdPJ1TlKwRBWE+YO1aysErYd8EZImGVF8flsr9FrbVYNbcB71/VCVEEHnjh3TIfWXHYJ/dXLW6rg9/j4pfXuB1wOaSUlmoIsCirsNq0aRPWrl2LQCCA9vZ23HzzzTh06FDadTZs2ABBENJ+Pv/5z+veryiK+PrXv46uri74fD5cc801OHy4uu1VgiCIYqIWVr0j1Z9eRRDlJMJ7rKRSwGkb7+RTKWB+MMdqUVsdAODLf7QMggA8s7efl8xVE3tYGaAquAIABEFQygGrIMCirMJq+/bt2LhxI3bs2IHnn38e8Xgc1157LcLh9N3Qz372szh79iz/+e53v6t7v9/97nfxgx/8AA8//DBef/111NbW4rrrrsP0NJWvEARB5IN6V/rECDlWBFEsYokUYvLAWF4KaGPHKl1Y2fc47caxIVlYtdYCAJZ1BHDjmjkAgH96vvpcKyYWz1UFVzD4kOAqcKxcua9SPJ599tm0fz/66KNob2/Hzp07sX79en653+9HZ2enofsURREPPPAA7rvvPtx0000AgMcffxwdHR341a9+hVtvvdW6B0AQBDFLSCsFJMeKIIqGOlqdlQLaOW49lDYguPIdh1JxnDtWtfyyL129FE/vPosXDw7i7ZNjeM/8pnIdnuXs04haZyiOVeULK1v1WAWDkpptbm5Ou/wnP/kJWltbsWrVKtxzzz2IRLKf1I8fP47+/n5cc801/LKGhgZcfPHFeO211zRvE41GEQqF0n4IgiAIhfRSQHKsCKJYsP4qt1NAQG7sr6TwimpIdis2U7EkzoxPAVBKAdn/f+g9cwEA368i12o0HOOPV9uxqp4hwbYRVqlUCnfffTfWrVuHVatW8cs/9rGP4YknnsDWrVtxzz334Mc//jE+8YlPZL2f/v5+AEBHR0fa5R0dHfx3mWzatAkNDQ38p7u724JHRBAEUT2oF08nRyO0eCKIIsGi1v0eF3xuJwB7z7FSfzckUyKiCfuKQLvA3KoGnxtNfnfa7+66eincTgEvHR7G68dGynF4lsPKAHtaa/lmgRo2JHhiuvIdT9sIq40bN2Lv3r346U9/mnb5HXfcgeuuuw6rV6/Gxz/+cTz++OPYvHkzjh49atnfvueeexAMBvnPqVOnLLtvgiCIakC9eIrEkhiS49cJgrAW1qdU63Gixi0t0+wsrCYyyreoHDA36jJAQRDSftfd7MdHLpQ2+L/3/LtVsYm1ty97fxWgcqyoFNAa7rzzTjz99NPYunUr5s2bp3vdiy++GABw5MgRzd+zXqyBgYG0ywcGBrL2aXm9XtTX16f9EARBEArBjBMe9VkRRHFgpYB+rws1zLGysQuU+d0wWQWuQ7E5xqPW6zR/f+f7lsDjcuCN46N45Ujlu1Z7syQCMtRDgiudsgorURRx5513YvPmzdiyZQt6enpy3mbXrl0AgK6uLs3f9/T0oLOzEy+++CK/LBQK4fXXX8ell15qyXETBEHMNoJyDC6bN9JLs6wIoiiwqPVar1IKaNfwClEUubBixgs5Vrk5phFcoaarwYePXTQfAPDznZVfRbX3TPbgCgAIeOVUQHKsCmPjxo144okn8OSTTyIQCKC/vx/9/f2YmpIa3I4ePYpvfvOb2LlzJ3p7e/HUU0/htttuw/r163Heeefx+1mxYgU2b94MQMrDv/vuu/Gtb30LTz31FPbs2YPbbrsNc+bMwc0331yOh0kQBFHxsBPe8s4AAHKsCKJYMMeq1uOEl5UCJpK2LAmbiieRSEnH1RGoAUCzrIzAhVWrtrACgPO7GwEAI5OxUhxS0QhG4jg5Kp0vspYC+qonvKKscesPPfQQAGkIsJpHHnkEt99+OzweD1544QU88MADCIfD6O7uxi233IL77rsv7fqHDh3iiYIA8Fd/9VcIh8O44447MD4+jssvvxzPPvssampqiv6YCIIgqhG2K33evEbs6wvhxCgJK4IoBhHZnVKHV4giEE2keGmgXWDfCy6HgPZ6L/pD01wYEtqIoqiUArZplwICSqBDpYuNfXJ/VXezD41+j+Z1+GOtggHBZRVWuXZfuru7sX37dtP3IwgC7r//ftx///0FHR9BEAQBJJIpXt6zZl4D/usNGhJMEMWCOT61XmeakIrG7Sus6n1u1HqqJ9mtmAxPxjAxnYAgAAta/FmvVy2BDiy4YtUc7TJAgOLWCYIgiFmEuqGY1chTjxVBFAe1Y+V2Onhf43TCfn1WzGFo8LlRK/fJsFRDQhvmVs1t9OkK5Qa5PC4zHKSSEEURv9sjjTo6b15j1uvRgGCCIAhi1sBO7LUeJxbLpSuh6QTGI5Vd+08QdkTdYwWAL77tGGChdqwCNUxYkWOlhxK1nr0MEEhPyrNjf50RXjs6gl2nxuF1OfCnF2RP/WaOVTW4nSSsCIIgCF3Y4qnR74HP40RHvRcA0EsBFgRhOUyY+GUHqEYVYGE3uLCqcaHWKwlASgXUx0hwBaCIjWRKRNiGotoI/7ZNGo1069putAW8Wa+n7ierVBHJIGFFEARB6KLelQaABS3SgoD6rAjCeiKqAcGAvR0rVrqlLgUkYaUPKwVcnCVqnVHjdsDjlJbplVgi9/bJMbxyZAQuh4DPrl+ke92ALCLjSRHTcfvObDMCCSuCIAhClyBfPEkLp4Vyw3XvMDlWBGE16gHBgCKs7LjgDKqEVZ2HSgGNwByrnizDgRmCIFR0MuC/bT0KALj5PXMxryl7SAcgbSLIrYQV+VjVkLAiCIIgdFEvngCVYzVKjhVBWA0Lr2COFYtct3UpoM+NuhpyrHIRT6ZwUi6hzjYcWA2rEghGKktsHOwP4YUDAxAE4AsbFue8viQiqyPAgoQVQRAEoUtohrCSdh9pSDBBWA/vsfJk9FjZsRRwemYpIDlW2Tk1GkEiJcLndqKzPvdsVSWGvLKe04e2SW7VDau6eOBRLqolcp2EFUEQBKFLpmO1kHqsCKJocMfKm95jZUfHSr3pUkc9VjlhiYALW2vhYLVvOlSii9M7HMZv3ukDYMytYlTLkGASVgRBEIQurAyFCav5smM1PBmjRRRBWAzvsfKk91hNxezbY1Vfow6vsJ8AtAvHhljUeu4yQKAyZ1n9+++PIiUCVy1v43MPjUCOFUEQBDEryHSs6mvcaK71ACDXiiCshqcCZjpWcfsJFvWA4DoqBczJsWE5ETBH1Dqjvqaywiv6g9P4xc7TAICNVy0xddtKLXvMhIQVQRAEoUtm3DpQ2X1WlT4nhahulAHB0qLaJ/dYTdlQWAU1SgFJWGWHOVY9Bh2r+gpzrP7jpWOIJ0Vc1NOMCxc2m7qtUgpYGY81GySsCIIgCF0yHStA6bPqrTDH6vRYBBd9+0U88MK75T4UgphBMqXM8anNiFuP2lBYMSel3qcMCJ4gYZUVZTiwsUCHBt5jZf/ndDQcw5OvnwRg3q0ClFlWleLOZYOEFUEQBKGLlrCa3yw5VicrzLHaeWIMQxNRPLdvoNyHQhAziMSUBbTfkxleYa8eq3gyxYM21I5VLJFCPGmvY7UDE9NxDE1EARjvsaqkvqNHXjmOqXgSq+c2YP3SVtO354+1AkSkHiSsCIIgCF0y49YBYGGrPCS4whyrCbl+fzQcLfOREMRMmFBxOgR4XdISTQmvsJdjpS5PC6jCKwAqB9SClQG2BbzcnckFK4+zeyngxHQcj77aCwDYeNViCELuxMNMKnkYshoSVgRBEERWkimRl/Y0pPVYscj1ynKsFGEVo14rwnYoM6ycfHHK51jZrBSQbbgEvC44HQLcTgcXg5QWOhMWtd5jMLgCUJcC2ltsPLHjJCamE1jSXodrz+nM6z4Ux8rejzUXJKwIgiCIrKhPcmnhFXIp4NngtO0WfHpMyLuh8aRIvSCE7eAzrDyK++NjjpXNPmdaoTY0yyo7x4bkRECDZYCAIjYmbJ6Ut/ltKQnwjvWLDM3n0oLP7LL5Y80FCSuCIAgiK2zxVOtxwu1UThnNtR4E5EXUqdHKca3UC5TRyVgZj4QgZsIEiV8OggDUcev26lvS6r2sq6FkwGwcNRlcAVTGHKu+8Sm8OzAJhwBce05H3vfDouUnbPxYjUDCiiAIgsiK1uIJAARBwALeZ1VJwko5aY+ESVgR9iKSEbUOKKWA0YS9HCvmLLDeGEA5bhoSPJPjQ+ZLAZmLMxlNIGHTQJDt7w4BAM7vbkSj35P3/ZBjRRAEQVQ9WuU+DKXPqnICLNSO1cgkBVgQ9iIsCxKWCAioSgFtGl7RoFEKSI5VOqmUyHusjCYCAkCgRhGtdi0H3HZoEACwYXl7QfejCCtyrAiCIIgqJZtjBSh9VpUUYJFWCkiOFWEzuGOlStjz8rh1ewkr1n9Zr0q4Y7OsJm0qAspFf2gaU/EkXA4B3fL3phHcTgdqZZFtR8ERS6TwypERAMCG5W0F3RcTkbFEqqL6djMhYUUQBEFkRU9YVeKQ4BCVAhI2ppIcK60xDHU1SukaocDcqvnN/rReVSPU23hI8M4TY5iMJtBS68GqOQ0F3VedxwWW0m5HEWkUElYEQRBEVnQdqxZyrAjCSrR7rCoovEJ2rKgUMB2WCGimDJDBHEE7Bliw/qr1y9ryTgNkOBwCD0Syo4g0CgkrgiAIIitau9IM1mN1ZnwKcZs2VmeiDq8gYUXYjbDsSqlTAX1cWNnLsdLqv+ThFbHKXRgXg6NDrL/KeCIgo8HGvUdKf1VhZYCMauizImFFEARBZEXPsWoPeFHjdiCZEnFmbKrUh2YaURTTSpSoFJCwG5Fo9lRAuwkrtvhVfzew3jDqsUqHB1eYSARksNRFuw3O7Q9O42D/BAQBuGKpRcKqCoYEk7AiCIIgssKFlX+msHI4BCxorpw+q3AsiZSo/Hs0XJ2pgFOxJB7adhRHBifLfSiESZhjpQ6v4KWAiRREUdS8XTnQ2nQJ0BwrTY4NS59FM1HrjHqbzrLa/q7kVp03rxHNtfnHrKvhIrKChTkJK4IgCCIreo4VUFl9VhMZ5SXVOiD4uX39+M6zB/G3T+0t96EQJlFSAWcOCE6mRMST9hNWaXOsvDTHKpPpeBKnZUc/n1JA7uLYrDyO9VdtWGaNWwUojzXzu7qSIGFFEARBZEVvjhVQacIqfRd0JByzlQNgFYMT0wCAN4+P2S5JjtBHSQWcWQoI2CtynQUMaJUCkmOlcHI0AlGU3LzWOvPOjh0dq0QyhZcODwOwrr8KAAI19k1ANAoJK4IgCCIruR2ryhkSzHZBW+u8AIBoIoVIFQoP9prFkim82Tta5qMhzKCkAiqOlcfpAAtcm7bJ+zWVErmDUq+RCkhx6wo8EbC1FoJgPjmvwYZx62+dHMfEdAJNfjfOm9do2f0qpYD2EZFmIWFFEARBZCWXsKqkWVasbr+j3guvSzr9jVRhOaB6AfbK0eEyHglhFu5YqXqsBEGwXeT6RDQBZvaqBwTXeaX/J8dKoZBEQACor7Gf2GD9VVcsbYOzwJh1NRReQRAEQVQtyZTIy+dy9VidGp1CMmXvsjr2WAI1LrTIzdYjVRhgoS4ZeuUICatKQsuxAtQBFvZwrNjC1+ty8GMDlN4wcqwUWCJgPsEVgD1LAbcdkvurLCwDBNRx65X7/iFhRRAEQWiibiDOJqy6GmrgdgqIJVPoD02X6tDygj2eQI0bzXKvQzXOslLvbO/rC2GsCh9jtcLnWKl6rABllpVdeuayOdl1PLyichfGVtMflL4X5zX58rq9UgpoD2E1ODGNfX0hANJgYCvh7pxNHms+kLAiys4bx0fx4oGBch8GQRAZsMWT3+OE26l9unA5HehukgMshu1dDqh2rJprpT6rapxlpd7ZFkXgtWMjZTwawgyshE6dCggAXpvNsgplCbVh4RWRWBIpmzvYpYJtOHXU1+R1eyUV0B5idbvsVq2e28D7Va2CBgQTRIGIooj/77E3ccePd2I8Un0LHIKoZHL1VzHmy+WAvTZPBmSOVX2NG6211etYsdftnK56AMDLVA5YEaRSIg9TyepY2UVYaQwHBhTHCgDCMXsIgXIzUKiwkgMd7FIKyGPWLS4DBKjHiiAKJhxLIjSdQDIlVuUChyAqGaPCamGFJAOmO1bVK6xYeMUNqzsBUJ9VpaAWTZmOld3CK7J9N3hdDrjkMIMwzbJCJJbg3zsd9fm5O+w5jiVSZXcsixWzzmAiMnM0RiVBwoooK+odmGqMPSaISibXDCtGpcyyShNWco9VtaUCiqLId3v/6JxOOB0CToxEcGrU3q8NoTg8ggDUuDKFlbRci9okvIJ/N9SkO2uCIKiGBFeu62AVgyEpHMfvcaa5eWao9bh43H65S+TeOT2O4FQcDT431lgYs86w6zBkM5CwIsqKuvyPhBVB2AuzjpXdI9fV4RUt3LGqrlTA6XgKsaTkasxt8uH87kYAwKsUu257Iixq3e2EIyPC2m7hFVrDgRlKgIU9jrWcqPur8plhBQAOh6D0HpW5RI6lAV6+tBWuLH23hcCE1XQ8ZZtNBLOUVVht2rQJa9euRSAQQHt7O26++WYcOnRI87qiKOL9738/BEHAr371K937vf322yEIQtrP9ddfX4RHQBRKumNVudYvQVQjZnusTo5GIIr2bVgPaYRXVFspINvpdToE1HqcWLekFQDw8pHqCrAQRREnRyJVFZDAHCu/hrPh5aWA9lhs6n03MGFFs6zU/VWFhTwwwREs85Bg3l9lcRogo07lgFZqOWBZhdX27duxceNG7NixA88//zzi8TiuvfZahMMzdz0feOABU2r/+uuvx9mzZ/nPf/3Xf1l56IRFBCNUCkgQdsWosOpu8sPlEBCJJXF6bKoUh5YXSimgm/dYVVsqoLpESxAErFvcAgB49chwVYmQ5/b1Y/0/bMU/v3i43IdiGewcqFUypoRX2KPHigl4rTJhmmWlwEoB8w2uYLDeo3I6VsOTUew+HQQAXFmE/ipA2hAKeMv/WAshv4JPi3j22WfT/v3oo4+ivb0dO3fuxPr16/nlu3btwve+9z384Q9/QFdXl6H79nq96OzstPR4CeuhHiuCsC9s4yOXsPK4HFg1twG7To3jjeOj6G72l+LwTKOUArrQ7K/OHqtQhhh+z/wm+NxOjIRjODQwgZVyUmCls/PEGADg3YGJMh+JdTCHx58xHBhQeqzs5lhpCyu5FLBCHQcrKTQRkNFggxjy38tu1blz6tEeKOzx6FHvc2MimrBNvLxZbNVjFQxKSri5uZlfFolE8LGPfQz/9m//Zkoobdu2De3t7Vi+fDm+8IUvYGQkexlENBpFKBRK+yFKw7hKWE1RKSBB2AqjjhUAXNQjfW+/2Tta1GMqBOZY1avCK6biSdv0rVhB5oLX43Lg4kXSa1NN6YCnRiVntJpcEba5WOuZuefNwizsJqx0SwHpnM57rNoD1pQCltPFYf1VVxapDJARqPAhwbYRVqlUCnfffTfWrVuHVatW8cu//OUv47LLLsNNN91k+L6uv/56PP7443jxxRfxne98B9u3b8f73/9+JJPaX0ibNm1CQ0MD/+nu7i748RDGGFeVAoaraHFDENWAKWG1UFq8v2FTYSWKIl+EB2rcCHhdcDul8vKRKgqw0HrN1i1mfVbVI6xOyimH1SSsuGPlnelY+Tz2ElZ8QHCNXnhF9bw2+cJKATsbCiwF5D1W5REboijyQePriyys2KZQpfZYlbUUUM3GjRuxd+9evPzyy/yyp556Clu2bMHbb79t6r5uvfVW/v+rV6/Geeedh8WLF2Pbtm24+uqrZ1z/nnvuwVe+8hX+71AoROKqRFApIEHYFzPC6sKFTQCAY0NhDE9G0VpX2A6t1URiSSTlHqOA3H/UUutFf2gao+EY5jXZs3zRLCGNEi0WYPHG8VHEEil4XLbZU82bU2OSsKqmgARdx8p2c6yypwLWUngFZ2DColJAPysFLM9zemp0CkMTUbidAk8aLRYswr9SI9dt8e1655134umnn8bWrVsxb948fvmWLVtw9OhRNDY2wuVyweWSnuxbbrkFGzZsMHz/ixYtQmtrK44cOaL5e6/Xi/r6+rQfojQEp5T+BioFJAh7YXSOFQA0+j1Y3hEAALx53H6uFds9dzoEHgRQjQEWbMGrdhJWdAbQUutBJJbErlPjZToy6whG4nw3u5r6eHgqoGaPFQuvKP8GpHpWGlvwq6mjHisA0vPEe6wK7EmqL3N53M6T0nf6qrkN/L1YLOxQ9lgIZRVWoijizjvvxObNm7Flyxb09PSk/f5rX/sadu/ejV27dvEfAPinf/onPPLII4b/zunTpzEyMmI4+IIoHWrHikoBCasYmojiX7ccxqB8UiPyw4xjBQBreyTXyo7lgOrgCpYw2yL3WY1WUYCF1mvmcAi4VE4HrIZywJOqYcfVVG7G5ljVaqQC2im8IppQZqVlDggGVOEVs3yOVWgqwR3G9kLj1n3lLQVkYTEXzG8q+t+qt0FQRyGUVVht3LgRTzzxBJ588kkEAgH09/ejv78fU1NSU2pnZydWrVqV9gMA8+fPTxNhK1aswObNmwEAk5OT+OpXv4odO3agt7cXL774Im666SYsWbIE1113XekfJKGLuseqmhrIifLy49d68Y//8y7+8+Xj5T6UiiWZErkrYFRYXdQjLd7tGGChnmHFaOZDgqtHWCkx2OkL3svlcsBXq0BYsTJAQNqQs/PsNDPoOVY+GzlWbHHvdAia0fBsFtFsLwVkZYCNfnfBLo+VqYC7To1j75mgqdvsPDEOALhgQQmEFXfnKvP9U1Zh9dBDDyEYDGLDhg3o6uriPz/72c9M3c+hQ4d4oqDT6cTu3btx4403YtmyZfjMZz6DCy64AC+99BK8XnvV/BMZjtUs/xImrGNwQmoYVu9sE+aYUJ3ADQsrOcBif18o7fZ2gM+w8iqPpTpLAbVdRtZn9fapcdu9NmY5pfpcJ1OibfqOCoWdA7UdK2lhHrXBY82clZZJnRy+MdtTAa0qAwSsC6+IxBL4+H/swEf//TXDbu/EdByH+qW07PeWQlhVuGNV1vCKfHaZtG6jvszn8+G5554r6LiI0qEeEGyHnTiiOmBO6NkglQLmCzuB+9xOw2EHnQ016G724dToFHaeGMOG5e3FPERTqEsBGS3csaqeVMDMOVaM7mY/FrT4cWIkgjeOj+LqlR3lODxLUDtWgFQO6NNweSoNVg6vO8cqUf7zpFZAihoWvlGpqW5WMSAnAhZaBgioxEaBLs7QRJS/z3YcHcE15+T+HnjnVBApEZjX5Cs4hMMI1GNFEHmSSKYwodoxoVRAwirG5VCUfhJWeWO2v4px0UJ7lgNyx6pG7VhJC55qKgUM6sRgX1Ylsesn5RlWjGrps4owx0onFbDQkvmJ6Tiuf+D3+MrPduV9H7m+G+ooFRCA4lh1WiBGGnzWJOWNqTazXzo8ZOg2vL+qBG4VoJQx04BggjBJ5odmtn8JE9bBktEGJ6aRSJa/dKYSyVtYyQEWbx4fs/yYCkHLsWKlgMNVFF6RzbEC1H1WIyU9Jqs5nVHiWy3nDu5Yacyx4nHrBTpW298dwsH+Cfzy7TMYj+T3vs8prKjHCoCqFNACYaV2cVKp/HsK1a/5S4eNbbDsPFliYVXD5liRY0UQpsisFaZSQMIqgvLJIyUCQ5PVU+ZVSvIVVmvlPqtdp8cRtUHZEmNCI7yCpwJWkWMV0gkcuXRxCwQBODQwgcGJynRzUykRp8ckx4oFOlRLyVkklt2x4uEVscI2il5WLab/0Jvf5ofecGBAnQpYHa9LvijCyrpSwJRYWO+aOjDs2HAYp8f0+5BTKRFvy47Ve0uQCAgoVQUUXkEQJsncLaNSQMIqxlWinfqs8sPMDCs1Pa21aK3zIJZIYfdpc8lTxURLWFVbKmAimeKLWa3XrbnWg3O6pDmNlepaDUxMI5ZMweUQsLi9FkD1OCMsbl1vjlW0gA1IURTTXIo3T+RXrstnpeUoBZyMJqomsTEflB6rwh2rGlWvayElcpnrrpdzuFaHBycxEU3A73FiRWcg779rhnqLyh7LBQkromywxS/7Eo5UycmRKC+xRCpNpFOfVX7k61gJgoCLeiTX6g0bDQoO8VJA5fG0yj1Wk9GErdy1fFEvuLTmCwFKOeArFdpndUrur5rT6OPvzWpxRpgToTvHqoD36fHhMM6MK/1p+Q7yzvXdwI4/JaJqEhvzwcoeK0CVDBjJX3CwHisW5pirHJD1V53f3QiXszSSgT3OSCyJeAWW8pOwIsoGKyfoapC+dCLx6plHQpSPzBJTcqzyI19hBSjlgHYSVlqOVb3PBZdDWmFUg2vFvlNrPc6si6BLFknhIrtOjZfqsCyFRa13N/vSnJFqQG9AMCsFjCfFvPtGWWjJghY/AGDPmWBeA4ezzUpj+N1OvnCvltfGLKmUyMd+WJWkZ0WABftev6RHGRie1OnZKnVwBZD+HV2JZb4krIiywWp9O2VhJYrSRHeCKITgVPoCuT84leWahB56IQi5YMLqrRNjuiftUjKh4VgJgoAmNsuqCgIsjIjh7mZpUV2pTi6LWp/f7K+qXh5RFBXHSqcUEACm8zxPMnfiIxd2o6Pei3hSxNsnx03fT673mcMh8D6xainTNMtIOIZkSoQgAK1yL2ehsNLLQmZZjcmlgFcub0OgxoXgVBx7dIYF75TLRUsprFxOB/8MVGLkOgkromwEMxwrYPZ+CRPWQY6VNSiLJ/PjDld21SPgdWEimsCBsyGrDy0vtBwrQD3LqvKFleIkZBdWbCNrIpqoyO9bNvR7XpO/qmK9o4kU2B6EX8Ox8qpmyeUTuZ5IprDjqNRXd8XSVr758Yc8xiIYEfC1crJhNYjefGBlgK11XstK6Bp8hc93YqWALbUerJPHL7z0rnbs+vBkFL0j0uftPSUKrmBU8pBgElZE2WCOVXOtl580KMCCKJTxjPrzSt2ZLzd88eQ371g5HQIuWCidiItVDvj6sRHc8M8vGZ6XxYRVZu9RNQVYGAkcqfO6uCDpD1XeZ+O03GPV3awIq0osF8pELQ597pmOlSAISp9VHuV775wex0Q0gUa/G+fOaVD6IPMQVrlSAQFKBrS6vwpQRa4X8H5niblNfg+uWCYLqyx9Vm/JZYDLOuryqlwohPoKTgYkYUWUDfWuF0tBImFFFAoTVgH5xE6OVX4U0mMFKOWAxRoU/Ktdfdh/NoSn3+kzdH2tUkBAEVYjVSSscr1mLP55oAI/G6wUsLvJxxfv1eBYsXOfz+2EU+77y4TPsspDWP3+XWnxvG5xK5wOARcuUMp1zfZsGSkTDlTRa5MPLBHQiqh1ButpK6wUULpto9+N9UvbAABvnRzTnBlV6vlValhlQSXOsiJhRZQN1gvT6HfDL9djRwqYz0AQgHLSWS5Hww6EpgsaqDhbKVRYsR3xN3tHixJKw9LNjAz3FUXRQClg5c87Y7u7uV4zVg5YaY5VNJHkxzy/2c9fy2pwRZREwJluFcPHhZX5HisWXHH5UsmlWN4ZQKDGhXAsiQNnJ0zdl7FSwOp5bfKBOVZWRK0zrCgFZHHrjX4Pupv9WNDiRyIlYsexmRtgb5V4fpUaKgUkiDzQcqzyqR0nCDUsxn9pRx0cApBIiRiugkVzqWGRvvkKq/PmNcDjcmB4Mobjw2ErDw0A0CcLKyMDoKfjKSRkcT3TsZJ2lKspvEKvRAtQUsoqTVidGZuCKEpznpprPTwgoRoW72E+wyp7TyN3rExGroem4zwFksXtS66VXK5rwlVOJFMIy+dpvZLT2S6s2ADujkAxSgHzExuJZIqXETbJJd5XyEL75cPpfVaxRArvyHMIy+FYsZJtKgUkCBOwkq1Gn5s364ZJWBEFwmrIW2q9aAtIi2Y791k9v38A33hqn63mdaRSIiZ0Bs0awety4vzuRgDW91mJosiF1fBEbmHFykkcwszEtea62VcKyPo+Kq0U8NSY3F/V5IcgCKirqZ5yM/YYtIYDM5iwMrsBuePoCJIpET2ttTwVEgDW9pgPsDAyKw1AVQWL5AM753Q2WFkKWJhjpX7t2HfEFXI5YGaf1b6+IGKJFJr8bvS01ub19wqBHCuCyAN1o7XfzXqsZueXMGEd7H3V6Hejs8EHwN59Vv/43CE8+mov/tA7Vu5D4UxMJ8Cq9wppWr5oYf4N8noEp+K8J2XIgLBiC4o6rwuCkN6/Uu5UwGNDk3js1V5LhHWu+UKMSi0FPKmaYQWgquZYRXSGAzPyDa9gi2bmVjHUfZBGy3XZ92ud16Wbdqe8NrNzs5T1WBWnFDC/9zuLWg/UKK/dpYtb4HQIODYc5jPigPT5VZnfmaVACa8gYUUQhhBFkZdsST1WVApIWMO4SrDPYQtIGwsrtlBhJz07wI7J53bC68q+g56LtT3FCbA4PabMJpuIJnIuNLMFVwDlF1Z/95v9+Nun9uG5ff0F35fR2WNKKWBllcie5sJKcl0UV6TyzxtKKaCOYyV/FqdMCqvM/ipGPuW6SiKgvnivpmCRfChmKWC+4RXjquAK9X2+R64sYO8TQAq0AID3lqEMEFA2hwpJQCwXJKyIsjAdTyEmDzls9HuoFJCwDHWJKduZt7NjxZrW7bQzV2hwBeOCBU1wCMCp0SmctXBQMysDZORyrbIFVwBACysFNNCrVQzeHZCCAw6aDBDQwqiwqtxSQJYIKAmrWm/lJodlwh0rnR4rnyy6oibCK06PRXB8OAynQ8Cli1vSfud1OXH+vEYAxjc/jET6A0Adm2NVgQvjQoknUzxUpxipgPmWx42rotbVKOWAUp+VKIqKY1WG4AqAHCuCMA37cnY6BNR6nLwUcIpKAYkCCXEn1MOHT/dbuKi3ElEUeUlbIRG6VmOVsKrzunDunAYA1vZZZQqr4RyiSJlhNfPxsPCK0HSi5H1u0/EkF/3HhicLvj+ji172uRicmDYdtZ0PO0+M4l9ePFzw3zqlmmEFKEI5HEsWJXmylLBNRb9OKiAvBTQRXvGyXAZ4fnej5vt/bY+0cH7TYCmy0fcYD6+Yhef0QXmjx+0U+DgHKyg0FXAsSyDR5TzAYhjJlIgz41MYCEXhcgg4TxbepYZ6rAjCJOMsat3nhiAIfCeOHCuiUMZVosDuPVbRRApJOa3OTicQq4QVUJx5VmdMO1asFHCmG9Doc4ONDRorcTngiRGlp+HoYOHJiUZft5Y6L5wOASnRWFx9oXz91/vwveffTSs1ygfWYzW/Od2xSqbEvCLI7UQkmtuxyie84qUj2v1VjAtNfj7Z91Su99hsDq/gUeuBGkv7k5gwDseSeW0CZXOs1sxrQKDGhdB0ArtPj3O36tw59XxtVmqUOVaV9/4hYUWUhcwoZza7g3qsiEIQRTEtvKLL5k366kWHHR2rfBMB1VzEdsSPWxfO0Tee/nrmEgd6pYAOh8AXGqVOBlT3tRwfCXORnQ+iKPJ+hFyLXqdDQDtLzDTx2fj+/xzCPzx30PRxHR2S3Dh1b5xZQtNx/r6c1yRtmPjdTrB1a6UHWLBNRf3wCnNzrJIpEa/IwuqKpdrCSgonkET+oIH3glHxPpuFFXserSwDBNK/v/IRHKxMvsmf/tq5nA6sWyy9P146PKwKrmjO91ALhkoBCcIk3FWQP+A0IJiwgslogi9OG3xu3ktyNjhty1IhddO9neZ1FMOxOjQwwXdMC4U5VqzMxrhjpf14mssUYNE7ogirWCKFMwUIj3Asyd/7ueZYAaoAC4Nu7lg4hh9sOYJ/23rU0AKcMTgR5UJgoIANDpZY1lLr4eLD4RCqZpaV0mOVe0Cw0fCKfX1BjEfiqPO6sEYOKMikvsaNlZ31AIyld7LvqVzvMaX/rbJfl3xgn6kOCxMBAUkAMcGaj+BglUIN/pnliVcsU8oB1YmA5UIpBay89w8JK6IsZC7c/FQKSFgA25HzuhyocTv5iS2WSPH6cjsRjtnbsbJCWLXUebnAPamK8y0EJqzWzJP6t3L1WIV0HCtAEVa57sdqToykl/8xZycf2GvmcTp4L44ePMDCoNhRv3ZmBj6ryx0LKcllwmqeag4TUD3OCE8FtDBuncWsX7KoBW6daPSLWHqngT5Io98NPBVwFm6WDsgbPVYLK0BJY8znfDGWxbECgPVygMVbJ8dw4GwIAPDeBY15HmXhsMc5GU2UpA/USkhYEWUhqEpuA0Bx64QlqMsAAcDjcqC1TirHsDKVzirUDm219lgBUA1yLfzzHU0kuUPFduGNpwJqPx6WDFhqx4oJFLdTqmcrRFjxGGzfzFldWpidZaUWVr0jxoWV+rqFOVbS53d+hrBiZeSV7owYcaxY3LpRYcWCK9Yv0y4DZFy40HiAhZI8qR+3HrDwM19pDISK41gBhYU6BDXi1hndzX4sbPEjkRKREoG5jT50yT3K5UD9XV1pbjQJK6IsZC7cfFQKSFgAF1Y+pdShy8azrCbTSgHtI6yMLp6MwhaLU/HCP9/sdaxxO7CsIwDASCpg9vAKoIylgMOSWLm4R4rBPjqUf4CF2b64DpOR6+mOlXHnUe3KFfIZVKLW0xd7s8mxYkECRoRVJJbgJV3ZgisYbJD3gf5QzgW7MoTaYCpghQvefBgMMcfK2h4rQHne83Os5NAwjVJAQIldB8o3v4rhcTl46audyuSNQMKKKAuZtb5s4RUhx4oogHGNOFm2M99nQ2EVSQuvsM/JI5jRA1korIfSit1r1oc0t9GHNjmAYchg3Hp2YSXdTynDK6ZiSe4WvW9FOwDgmAWOlVGXsbPBXHjFqTRhZfw4e1WlgAUJq4zhwIy6mtnTY+U1EV7x+vFRxJIpzG30oae1Vve67fU1WNDihyiCi7FsGA6vkD/zsaQys3K20F9Mx4qHOuQfXtGY5bVTD5C+YH6j+YOzmELndpULElZEWWCLSMWxImFFFI4i2JUTh51nWal7Cu108rC6FJCVa1nhSLP+qjmNPl7mOZyrFDAq77JnKQVsZaWAJYgeZ5wYlZycBp+bl2JZ4lgZCK4AVOEV+ZQC5ulYTUQTeTtL7O+z4cCMagmv4HOs9AYEmwivYGWAly9pNVQaysci5OizMt5jpQjESncTzVLMUsCGAkoBs8WtMy5d3AKnPHuinImAjEpNBiRhRZQF9gFXeqykkwn1WBGFoJQCznSs7DjLSr3giCVShnsnio3VwspKx4pFrasdq3AsqSvacjtWpS8F7JX7qxa21nJHYXgymneIidnXrNNkKaA6hKJ3JIyUgWh4URTTbgfkN/pAFEUe1Z7ZY6X071X24p3PsTIyINiEsLoiR38VY60s7v+Qo88qZLDk1KUKUal00WuGSCzBv2+KUwqYX3hFLJHi4l2rxwqQhMzff2g1/vKPlmHV3PrCDtQC2Pd1pSUDkrAiykJm2UotTwWsrA8QYS8y56MB9u6xyny/22Vnzs6OVZ/Ksar1OPnibXgiuyjKFV7BhNVIuHSpgKxPqafFj0CNmy/C8i0HNDrDisE2HMKxJO9By0YskUoLf4kmUoYE0lgkzp/7uY1Sb1Q+n8OhiSiiiRQcAtDVmO4CsB6rSl+8G3GsjIZXDIamcWhgAoIAPp8oF8yx2nV6HNGE9v2bmZUGVM9rYwbWX+X3OPnjtxLuWJk8V7BqDoeg72p/+MJufPHqpZYONs6XQoI6ygkJK6IsjGekt1EpIGEF4xqpR531+S/oik3mLrsdItdTKdFwg7pRuGNlweeblQLObfRBEARVn5X26yuKYs7wiha5x6ocjtWCFsmtWtRaByD/ckB1KqAR/B4Xfz5ypfX1jU8hJUpjDBa2SI5Rr4HIdZYI2NVQw125fD6HrAywq8E3Iza8Ghbvoijy7wI9x0oJr9DvWdp9OggAWN4RQFOtdtlXJj2ttWit8yCWSPHbZ5I5JzAXtVUSLGIGdX9VMcQJL48z6eKo+48djvKLJiNQKSBBmCBzAczq5GOJVMXNLCDsgxK6MDMV0I5DgjNL4+ywMzcRTYA9TZY5VmzjxIIFltqxAsD7rIayOFbRRArxpPSAcpUCjk/F+cKx2DDRwQTH4nbpv3k7Vnm4jJ18SLC+U8eEzfxmPz/e4wYi11l/1YIWv+meLjUsETCzDBCojvS5WDKFhPy+03WsWClgFkeJwcJcmEtoBEEQuGv1RpY+K7aY9zgd8LpyLx+rpf/NDEp/lfVlgED+qYDKmsuY0LYDSnhFZb1/SFgRJUdrR9ynSkKK2KTPhKg8eHiFRo/VVDxpu9jWzNI4OzhWbIFe43bA68q+e24Gv9cax0oUxTTHCgDa6vSTAdl3jSAoC71M2MBMUVQiiYsNE1YLWzMdq/yEldnwCsD4LCu1sGLHa8ixkssdF7bUKimEeThWbIZVd/NMocDnJVVwGXlEtcHi15tj5TY275GFubBNB6PwAItebWHFSq3rfW5DboyV8+sqBSVq3frgCiD/UkAlat2azbJSQI4VQRhkYnrmjrjX5QBzpynAgsgXrTjZGreTL5zPhuyVDDjDsbKB8LO6vwpQj1Mo7PGNhGOIJlIQBEUUtLJSwCzJgKzHp87ryloC43I6+IJjpATJgJFYAgPyAqynhTlWkrA6lmcpYD6vG59llUNYqaPOuWNlQFhxQdbiR6c8bDQvxypLIiCgiOVKHhDMRKHH5ZhR6qimxm2sx4ptMrAyWaMwYbWzd0yz7055jxkrN1XKNCtrYVwIxUwEBIB6Fuhg2rFKDwyrBKjHiiAMwr6cfW4n3xEXBIGfIGdTPTZhLaGM3j0GW9TZLRlwRniFDU4gxRBWVqUCsjLA9oAXHrkUiTlW2YYEswV3LienlAEWzMlp9Lv5aIBFzAkaCedVDs3eO/mVAhpzrBa0mBNW3JVrqVVSCPMQViezzLACqiMVkPUW682wAtTCSv/9wT4LbIyAUVZ2BdDd7MNENIFvPLV/xu/N9l7yMk2dz/14JIafvXnSNomohcI2DtpNilqj5Cs22KZjtqh1O1LIzK5yQsKKKDmsXCtz8UsBFkShjGcRBXZNBmQlQGwXkpXalJOiOFYWpQJm9lcBRhwr/eAKRksJI9dPqAQHY26jD16XA/GkEi1uhqDBGGw1eZUCysd8anQqZz8ai1pf0OLnwiqfzQ32fGgKqyoIr1CCK/Tfo2yOVSyZ0n3u2Weh1eTi3uV04HsfPh8OAfh/b53Gb3efTfu92e+GOvlzryd6//nFw/jr/7cHf/vrfaaO1a6wUkD22bIapRQwYapneIyFV1RQKSD7zs6WUmlXSFgRJSfblzOrLTcy/JAgMoklUlyUN/rSd+XsOsuKLQaZUCDHSh+2wFY35Rt1rHILq9IlAx7PCK4AAIdDwKK2/Pus8nndjDhWoiji5IgirOY0+uBxOhBLprjQzXY87Llc0FLLP4PDk1HETThy6qh3rR6rOm/l9/EojpX+e5SFVwD6i81huZy1zWSPFQBc1NOML2xYDAC4d/OetJh9swEpdQZSAd86Ic3N+vnOUzg8MGH4OAcnpvHF/3obLx4YMHybUjAwUeRSQPm5jyVTOZ1LNcEp/eHAduT6VZ04/H/ejx9/5uJyH4opSFgRJWdcY9YQoF58Ve7OI1E+2MJSEGYuorv4ArJ4PVbf+59D+Ncth03dhjk4zFGzQ3hFPs5HLvwW9ViphwMz2gLSQiG3Y5WjFFAumypFjxUfDqxyrABgURtLBjTXZxVNJPkiy2rHKjgVx4T8nTyvyQ+nQ8B8OXJdrxyQibHWOi/qvC601HrgdgoQxeyvlRYs6r3G7dAUCszlyTWLy86wc55fJ2odUOZYAfq9yMN5OlaML129DKvnNiA4Fcf/+vk7fBh0yGRACn9tspzT48kUDvRLYiolAt997pDhY/ybX+3Fb97pw98/c9DwbYqNKIpKj1WgOMKq1uOEU+4VNbMRNxZmpYCV41i5nfo9h3alrEe8adMmrF27FoFAAO3t7bj55ptx6JD2B0sURbz//e+HIAj41a9+pXu/oiji61//Orq6uuDz+XDNNdfg8GFzCx6ieOR0rKgUkMgDtiNXXzNzTkexHavRcAz/suUIvvf8u6Z6BVjvQRdzrGxQS15Ux6rAz7ZWKWBbneKEaJXGGHesSlcKyNPyWtNL2xbn6Vix940gAAETQ0nZrrqei8TKANsDXl6uzQRhr07k+olRJWodkBy59oD5zyGLWp/X5NdMoqtTJU7abZyCUYw6Vg6HwHsLpxPar9d0PMmFjNlUQIbH5cADt54Pn9uJV46M4EevHAeQTymg/mbp0aFJxBIpeF0OOB0Cnt8/gD9kSSRU88L+ATy3T3KqDg9O5tW3VwxCUwm+wdFepLh1QRDyCrDgibkV5FhVKmUVVtu3b8fGjRuxY8cOPP/884jH47j22msRDs/8sn7ggQcMD1v77ne/ix/84Ad4+OGH8frrr6O2thbXXXcdpqft8eGb7QSzBAxQjxVRCFrDgRldLJGsSMKKRdmKorl0MubgzLGhY1WUHqsC3ei+oFaPlbRQmI6nNPtsQgaFVXMphZVGjxUALM7TsWI71wGd5EMtjLhI6v4qRo8sCPWOU91fxWAbHGYWwixqXWuGFaCEVyRToqnSKDvBQmz0otYZNbKwyrYByV5Hj8vBF+D5sLitDvd9cCUA4LvPHsL+vpDp74ZcA4L3ngkBANZ0N+IjF3YDADY9c1BXIEdiCfztU1I/FlsSvnJk2NDxFBtWBtjod/OgkWKQzywrJbyichyrSqWswurZZ5/F7bffjnPPPRdr1qzBo48+ipMnT2Lnzp1p19u1axe+973v4Uc/+lHO+xRFEQ888ADuu+8+3HTTTTjvvPPw+OOPo6+vL6fTRZSGbF/ObLeu0HIhYnbCBbvGSb+zyOEV6hOc0ZKkVErkmwhM+FV7j1UknuRlRflwRqPHyu9x8TS1YY0yPsOlgCVKBQxHExiUF78LWzOFVX6OVb7lm2oXKVs54IkRLWElHaeeY6VV7mg0hVANc6y6m7SH3fpVC9hKDbBgITa5wisAZQMymzPOeg3b6ryGN6Oz8bGL5uOale2IJVO4+2dv8xj3etNx69mEVRAAsGpOA+6+Zilq3A7sPDGG5/dn75v65xcO48z4FOY2+vDJSxcCAF62i7AqchkgoyGPZEA+x8pHjlWxsVXxYjAofciam5v5ZZFIBB/72Mfwb//2b+js7Mx5H8ePH0d/fz+uueYafllDQwMuvvhivPbaa5q3iUajCIVCaT9E8eDzFDIsaT85VkQBjEeyLy6ZsJqIJorSi6FO8zO6uFMPwu5qlI7PDsLKbIO6EZhjJYrAdJ4JT9PxJEZkN0ktrABlXo+W62K38AomRpprPTOeYxZmMRKO8e9JIxQihjvkkqWBLGLnlEbUOSth1BsSrOVYsdJDM7Os9KLWAUkcGglJsDOmHKscs6zyTQTUQhAE/P0t56G1zoN3BybxypERAOZLAbN9J+7vk9Zaq+bWo6O+Bp+5vAeA1GulNXLgYH8I//dlqSzx/pvOxbXndAAAXj48bIsyUDabrlhlgIx8Ysj1KjoIa7GNsEqlUrj77ruxbt06rFq1il/+5S9/GZdddhluuukmQ/fT398PAOjo6Ei7vKOjg/8uk02bNqGhoYH/dHd35/koCCNkDa9g0awkrIg8GOclpjN35Oq8Lr6wLkY9frpjZVBYyYsNhwDuGlRr3HqNy8nLdvJNb2P9VbUe54wd81adZECzjlXRhdXwTMHBqPW6eJDJURPlgIWI4VwBFtqlgHLk+thU1t4srXLHfMYenM4hrABFuFesYxUz4VjlmGWlJAJa40y01nnxD3+6Ju0ys3OstD7zqZSIfX2yYzW3AQDwuSsXo9HvxpHBSfy/t07PuP69v9yDZErE9ed24uqVHXjvgiZ4XQ4MTkRxZNB8kqbVFHs4MIN9/xktBZyKJRGVe/JIWBUf2wirjRs3Yu/evfjpT3/KL3vqqaewZcsWPPDAA0X92/fccw+CwSD/OXXqVFH/3mwne3iF9GUxRaWARB7olQICyqKuGAEWanfBqLAKqxrW2WdhIpooqFTOCoohrBwOgZds5Vvqe0YWVnObfDNKnIw4Vrn6TVrqFGFVzNeACY6ejP4qRj7lgGbT2tTkcpG4sFI7T4Ea1LgdSKa0Z25FYkq5Y5pjZXBulppTbIZVU3ZhVemzrHgqoAHHymvUscozuEKLq1a0488vWcD/bTwVMLvg7R0JIxxLwuty8OHY9TVu3HnVEgDAPz1/OK2P7KdvnsJbJ8dR63Hib288B4Dk3l3UI1U42aEckAmrziILK2WWlTFhxYIrXCp3lygethBWd955J55++mls3boV8+bN45dv2bIFR48eRWNjI1wuF1wu6Q1xyy23YMOGDZr3xcoFBwbSa3QHBgaylhJ6vV7U19en/RDFI2t4hZtKAYn8CcriJpsgYH1MxRBWQVVJhtFSQ3XEMtuBFMXs0cSlohjCCgD8Bc4b0koEZOg7VsZKAdl8l5SouJ/FgPcetWoLq3wi1wt5zdgiUKsUMK6aVaV2rBwOQUkG1CgHZGKswedOc5DN9lhNRhPcQdSaYcXgwspEcIyd4AOCc6QCAoBPnmWVbd4j77GyoBRQzb03rMR58xrQFvCmzV/TI+CV3o9aJZr75DLAlV31cKkitf/80gWY2+hDf2gaj7wqlf0NT0bx988cAAD85bXL+Xc5AKxb0grAHgEWimNVmlJAo44Vi1pv9LsL7rsjclNWYSWKIu68805s3rwZW7ZsQU9PT9rvv/a1r2H37t3YtWsX/wGAf/qnf8IjjzyieZ89PT3o7OzEiy++yC8LhUJ4/fXXcemllxbtsRDGyRpe4SVhReTPeBbBzsinDMko+ZQC8sWU1wWvy8mHf5qJ0LWaVEosmrCq5QPA83WspNdNS1jpO1bGSgE9LgcXX6NFDLBgjpVWKSCQp2Mlv+ca8ijz0SsFZDOkvC4H2jMW6kxYac2y4nHyGY+xS/W3jPTEsP6uRr9b9/VjyYDhCq12YO51rjlWQO4eKyasrHSsACk045dfuAyv/PX7DJUsAunn9GSGC7yXlwGmb2R7XU785bXLAAAPbTuKsXAM/+e3BxCaTuDcOfW47dIFade/XBZWO46Nmho8XQyUHqtilwKaC69gjpVWmTxhPWUVVhs3bsQTTzyBJ598EoFAAP39/ejv78fUlLRD1tnZiVWrVqX9AMD8+fPTRNiKFSuwefNmAFKz5d13341vfetbeOqpp7Bnzx7cdtttmDNnDm6++eaSP0ZiJryJMiOdxkepgEQB5BIExZxlxU5cgPFyJLYIZLvUZnchi8FENAG23rVyQDCgHgCe38aJViIgQ8+xYq9HLsdKfT/FHBJ8XBYd2Xb9FcfKuLBivXn5xGuzUkC2KFSj7q/K3OlmjpuWsDrBxWP6Y2RN/bFEip8H9Dil0d+lBfsMmRl1YCciMeOOFRsSXMpSQIbL6eBztIygFmCZonefHLW+ak7DjNvddP5crOgMYGI6gb/4yVvY/PYZCALw7T9ZneZuAcA5XfVo8rsxGU3gnVPjJh6N9ZSqFJALK4PhFRS1XlrKKqweeughBINBbNiwAV1dXfznZz/7man7OXToEE8UBIC/+qu/whe/+EXccccdWLt2LSYnJ/Hss8+ipqa4b3YiN9FEkpcwzOixolJAogCyhaIwFMdqZk9IoYTyiFtnAoP1VeQToWs17HF4XQ7L57Aou9f5LX5ZSZqWsNJzrJQ5VrkXFcUOsJiMJrj4y1YKyByrEyMRwzvw7D1TSClgf3Cmi6QVXMFgfTFakeu9I9qOldfl5M+xkQ0OI/1VgMqxqtgeq/TvAj2UuPVs4RXFKQXMB6/LAZc8V0392oiiyB2rczWEldMh4K/fvwIA8NoxKYnwtksWYE1344zrOhwCLpNdq3L2WaVSIu8rLHp4RY258Arl3EiOVSnIu4utr68PL7/8MgYHB5FKpX/A77rrLkP3kU88ptZtMi8TBAH3338/7r//ftP3TxQX9kUgCDN3kKkUkCiEoE4qIAB0FrXHKo+4dVlgsP6QepMNycWgWGWAQOGOldZwYEarHDyRKayiiSRichqWEcdKmWVVHGHF+pFaaj1ZAwA662vgczsxFU/i1GgEi2ShpUe+c6wAxcmdiicRmk6kvfZ6Ued6jtXJUemy+RoBHR31NRgNxzAQmsY5c/T7mZnzNU+nvwqo/PAK7lgZKLFjJcPZSwGl926rRamAhSAIAupqXBiPxNOEVV9wGuOROFwOAcs6td/fG5a14ZJFzdhxbBTtAS/+8rrlWf/O5Uta8dvdZ/HKkWHcfc0yyx+HEUbCMSRTIgSh+M+92U04NsOKHKvSkJewevTRR/G5z30OHo8HLS0taSUCgiAYFlbE7EOdXuVwpJeWKKWAJKwI82QLRWF05ZFIZhR1WVPIYDnSJNullhdTDSbLO4oB6z9jAsNKCnGsUikRZ3mP1czdYLY7PzwZgyiK/JykLg0zUmbVUmTHKld/FSDtwC9qq8W+vhCODoWLLqxq3E40+NwITsUxEJpOE1Z6pXhsllXf+BSiiSS8LsVtydZjBUifwwNnQ4Y+hwfOSuViKzoDuterdGEVNjEgmDnJWuEVU7Ekfw7s4FgB0uduPBJP+yyywcDLOgJp7xs1giDg//zJanzz6f343PrFukmErM/q7ZPjmIwmypJ8x8oAW+u8M8oVrcZ0jxWfHUrCqhTk9er/zd/8Db7+9a8jGAyit7cXx48f5z/Hjh2z+hiJKkJvSB1vbqceK8IkqZTITx65eqzGI/G0GF8rSHOsTM6xqpMFByvvKGcp4O4z2ctzCoU7Vnk898OTUcSSKTgE7f4F1k8SS6bShClbzNV5XXA6cqdhFbsUMFciIGORyQCLQkoBgezBLnqlgG11XtR6nEiJigADJJeQuYuZPVaAKt49h3MsiiIOnp0AICXH6VFb4amASo+VmfCKmaWArAzQ63LYJla7TiMNdN8Z7eCKTBa31eHRT12ESxe36F6vu9mPBS1+JFIiXpdLB0tNqfqrAFU/rsG5h8q6q/wu5mwgL2EViURw6623wuGwRVo7UUHolRqx2nEaEEyYZTKWAAudyra4DHhdfOFitWsVzKfHiiWBedJLAcsZXsGav9d0Wy+s2HMfycNVYDOsOutrNHeDa9xOXuo3pAqwUBIBjS0yi14KKPceZZthxVhsMsBCCa/IT1hlm2V1cmTmDCuGIAiqckBFWJ0anYIoSq+3VkmU0cj102NTmIgm4HE6eN9ZNgJVkwpoPLxCy7EaUiUC2iVWW2uW1V45at3KDZx1Ze6zYuEvxY5aB2B67uGYzoY2YT15KaPPfOYz+PnPf271sRCzAL2AAWVAMAkrwhxsYVnjzh66IAiCKhnQugCL6bgy1R4wkQoYTd+lNjv00WpEUcTu0+MAgPPmNVp+/3yOVR6f7z6dqHVGW93MAAujM6wYypDg4sStG3WslMj13LOsUimRzz7L17HSmmU1HonxstZs4RHscahnWakTAbUW90ZLcvfLZYBL2uvgzlFaVcmpgPFkivcBGnGsfB7puYhqCasJ+wRXMOpqZs6y2pclar0QLrdontWh/gnsOR3MfcUMmGNV7Kh1QPk+Mzr3MDjFeqzIsSoFeXnFmzZtwgc/+EE8++yzWL16Ndzu9C/z73//+5YcHFF9jOs4VrXcsUqk9UkQRC6Mhi50NfhwdChs6SyrTIfJ8ByrjIb1csetnx6bwlgkDrdTwMou/Z6WfOCOVR6uwplxyRGZ25RdWLUGvDg2HE6LXDc6w4rRXFvcuHXWY7Uwh2NlJnI9PSI/v/KvDg2xw8oA2wJeXk0w4zhlYXUsTVjJ/VWt2mKM/a2BXMJKdjVyBVwAymeoElMB1T3FfiNx66wUMDFTWBVrhlUh1GU4VoMT0xgIRSEIuUs8zXDpohYIAvDuwCQGQ9N5CZypWBIffvhVxJMiXrvnfaZK5wYn5OHAgeILqxq3E16XA9FECqGpeM7zHjlWpSVvYfXcc89h+XIppSUzvIIgsqEXMMBO3qIIRBMpy+Oeieol22y0TIoxyypzHo/RPg+2CJwRXlGmXfd3ZLdqZVd91obyQigkFTBfxypk0rFiUe5HBidxbGjSUHCEUSam4zyxLZvoYCxqlf7uWCSO0XBMN0yEOZw1bkfer5tWeZ5efxWDCUQtx2p+s7Z4ZH8r12eQBVcYWXyz17cSwyvYRoPbKRiaEcXDKzScX8Wxso8zwdxE9trskwXz4rY6Q0LSKE21Hqye24Ddp4N4+cgwPvTeeabv483eUf6dsa8vxMsLjcA+O50NpRG1DT43BieihnpyjZ4fCWvIqxTwe9/7Hn70ox/hwIED2LZtG7Zu3cp/tmzZYvUxElVEkKXTaHzA1V+ylAxImIE7Vjl25LI16Vvxt3kyWcxY3Tt7jzMnh7kN5XKsWH/VefOs768CCksFZD1WusIqMHNI8ISJGVaAVHZ21fI2JFIivv27g6aPUw/m5LTWeXIej8/j5CIvl2tlRUQ+WwxqOVa6wkpjllW2GVbK35I+g8GpeNbIcAA40M+EVW73tFYjIKFSUGZYGRMZRsIr2uzkWGXMGNvHA3Ksc6sYhfZZqW/HHFOjsLEDcxv1N02swmhPrigqwU5NteRYlYK8hJXX68W6deusPhZiFqC3CHA6BHjlHbtKLOkgysf4lH4iIKMYjhV7T8+Ty9RE0VgTPe+xsskcq3fkvoJi9FcBhTlWZ+RBsfN0hJXWLCuz4RUA8L8/sBJOh4AXDgwU3K+hhi28cpUBMlg5YK5kQPUIi3xh4RXq8jy9qHVGjyyszganuYOi7rHSor7GBZ8sDrJtcISm4zg1Kr3m5xhwrCo5bt1MIiAA1MjnSK3wiuEJeYaVnXqsMso0mWO1qgjJo+o+q3zmpL58WPm8M8fUCBPTcb6hYKR01Qp4imyO8RyT0QQS8kYfOValIS9h9aUvfQn/8i//YvWxELOA8RzOAps8r3XSIIhsKKUOxhwrK8Mr2G5ge30N3M6Z85OywWfXeNJ7rMoRt55MiXy2zJqiCav8HSu94cAMfcfKuLBa0h7An1+yAADwzaf3I2nAfTQCK5fLJjgyYQEWx3IEWFjiWMnCangyxoMUjDhWTX43X+CdGA0jkUzhtCyCs5U7pofIaAsrFrM+p6HGUJ+LWljls6AuJ+Go8URAQCmZ13L7hmzoWLGNIxaysFcOrjjXwuAKxgULmuB1OTAQihoeVcAYnozywBQAaf+fiwOq92sxZgBqYXRIMDs3el2OrL2ShLXkJazeeOMNPPbYY1i0aBH++I//GB/60IfSfggiG7kWAX4aEkzkQSjHcGBGZ720MC9GKWCDz81LvAwJKx5ekZ4KWI5SwKNDk4jEkvB7nFjSbl1fkZp851iFowm+ONAaDsxgDftacetm3ZwvXb0UDT43DvZP4L//cMrUbbNxXHZyenL0VzEWG3WsCpxhBUgx8x45eY814XNhpTPMWBAE7lr1DofRNz6NREqE1+XQbeLv1HDI1JjprwKUcrNkSkxL6DRLOJrAO6fG08R5sclMB82FUgqoE15hI8dKHSwSjChOZDFm5dW4nVi7sBlAuvtkhFePSvOv2PfI0aFJvsmQC7YpdU4RHlM2jFY46M0OJYpDXp2DjY2NWQUUhVcQegRzOAv+AmbdELMXvRh/NcyxGgnHMB1PWhKQwkWdz406rwuj4Rgmo7nFEe+xyigFnI6nEE0kixIgkQ3WX7VqboOhQbr5wHusTH62++T+qkCNS7c3iTtWE0qiXz6OFSA1wt919VJ88+n9+N7/HMIHz+sy3KeVDSUtz2gpoLHIdSbE6wsQVoIgoL3ei9NjUxgITaOjvoYHhug5VoBUDvjO6SCODYe5eJ7f7IdD533UmSNy3ayw8qs+xxPTiZyf60Qyhd6RMA72T+BQ/wQO9k/gYH+IL/rnNfnw+69epfsYrIJtsBjtsfLp9VhN2C8VMKDqf2Mx693NvoI2AvS4fGkrXj4yjJePDOP2dT2Gb/fy4SEAwM3nz8F//+EUQtMJHB6cMCQA9/G5XKUpAwSMj+cYp6j1kpOXsLr22mvxZ3/2Z5q/++pXv1rQARHVTa6QAaVciBwrwji8xyrHyaPR7+YxtYOhqO5uvPG/rXas5Lp3A44V6wdh7/mA1wVBkHq0QlMJtAVKKKzkRMA1RQquAPJ3rFhwxVydMkBAWUwOT0aRSolwOIS8hRUA/PklC/CTHSdwbDiMB7cdxV9fv8L0fajpNdljxUoBT45GEEuksibGWVEKCEgu0umxKfQHo2irm0ZSdp5ylZWpZ1mxRXSucseOHEOCWRmW0X4Vh0NAndeFyWgC4WhCd47TeCSG9//zS7p9lqfHpnB6bMqS74dcKBssRh0r6X2QGbceiSX4Z8tOc6xqVWWaxeyvYrA+qx3HRhFPpnLOQAOkgAfmcF2xrA17zgTx+vFRHDhrVFgVL5AjG0bHc1DUeunJqxTwC1/4Ap555pkZl3/lK1/BE088UfBBEdWJKIp8EZqtiZKXAlKPFWGC4JS+E8oQBMHyPiv1wpb3euQQVuqhoOw2DofAF6al7rPaXeTgCiD/VEDmnOQSVmy4byIl8teEh1d4zS8qPC4H7r1hJQDgP186zsMc8iE0HcdImEWtGxNWHfVe1HqcSKZEnBzN7lqx5vVCHCsgfZYVKwPszuE8AVCVAkZyJgIy9NI5E8kUDvVLPStm5hzVZsxLysY7p4M4G5yG2ylgTXcjbl3bjb/943Pw5Gcvxlt/80c8LONgv7lUuHzhYxdMpgJmxq0zp7bG7TBcVlgK1K/LXj4YuHjC6pyuejT63ZiMJvjA81wcHw6jLzgNj9OBixY28/edkQCLaCKJI4NSue65RXxcmbAU2VybeHpJzERxyEtY/eQnP8Gf/dmf4eWXX+aXffGLX8RPf/pTbN261bKDI6qLcCzJG8Gz91hRKSBhHqOlgEDuMiSzqF1Yoz1W2YaCGo3QtZJoIskXEMUKrgCUxxlPioZ7FwBlOLBecAUAeF1OvivL+qwKcawA4OqV7Vi3pAWxZAp//0z+8evMrWqt83IhnQtBEAyVA/JSwDwfI0Pd92QkuILBHLjjI2ElETCHeOSOlcZnsHckjGgiBb/HiQUG/j7DaDIg6+u6dHErfr1xHf7+lvPwqXU9uGxxK5prPVghx7sflMVdsTHvWEnXiyZSaWMdhialx9Va57VVS4Y6FXBvEaPWGQ6HgHWL5dj1wyOGbsNi1i9Y0ASfx8nFtRFh9W7/JBIpEU1+N+Y0FH84MMNoKSBzrChqvXTkJaw+8IEP4MEHH8SNN96InTt34i/+4i/wy1/+Etu2bcOKFYWVSxDVC0tP87gcvJwhEx+VAhJ5oDd4OpOuBmmBblXkulrUKYNK9U92bJc6cyio0ZOllRw8O4F4UloYdDfri5dC8Kt20c24Vtyxasp9bLwcUO41CZmcY5WJIAi47wPnwCEAv91zFm/2juZ1P8zJMRpcwWABFiwlTwsrwiuA9CHBJ0bZkF8DwkoWUUMTUT77J5dj1anjWLFyseWdAVM9Tkbd4gE2yLVeu1xuZWeJHSset27OsQKQFtQxJDtWdioDBJTXZTQcwzF5g6EYwRVq2Dyr7e8OGro+KwO8fKl0O1aCuv9sKGfKJE85nNNQUkHLSgHHIjHd67HfN5BjVTLyElYA8LGPfQzf+ta3sG7dOvzmN7/B9u3bsWzZMiuPjagy1CVT2b6AankqIDlWhHHMTJbXW9TlQ0ijxyq3Y5U+w4phtG7eSli5zHnzGou6MHA7HVxEmumzMjIcmNGWkQyYzxyrTFZ21eOja+cDkOLXjQx/zsRsfxXjggVNAIAdx7LvvFsRXgGklwKeUpUC5qLB5+YR033yZ2pBs/7jZKWAQ5PRGXH2LLrayPwqNXwQbY5zB3PJmGuWSckdK5Nx6zWqjRh1MiBPBLRRcAWgCKtoIgVRlEpciy3+rlrRBqdDwFsnx3O6TolkCq/JiYCsP2tJex2cDgHjkXjOyoZy9FcBSh/j4cFJXfHHAsOaqMeqZBg+23zlK1/RvLytrQ3vfe978eCDD/LLvv/97xd+ZETReOXIML7x1D58+0OreTRpKciVCAiQY0WYJ5pI8rlnhkoBczTOm0XtlrFFRC5hNZkxw4qhzCYp3cbCrlNsflXx+wNqPU7EEilMmXKsWHhF7jIbFjM9NBFFLJHiO/qFDM8FgK/80TL85p0+7D4dxOa3z+CWC+aZuj0XVgb7qxiXyiVNO0+OZU2xtCq8gomdgdA0F/5GHCtA6rMalXvIXA5BNxYfkBb/ToeAZErE8GQ0TeSYTQRksM9Srs/eQEgSINmE1fJOSVj1DocxFUsWffYPE/9G+6JcTgfcTgHxpJgWYMEGY9vNscrcPCpmcAWjq8GH68/txG/3nMUjrxzHd/90Tdbr7j4TxEQ0gQafm/d+1bidWNxWi3cHJnHgbIhXOWjBHNZSDQZmLO2og8flwMR0AidHI1kDY5hjReEVpcOwY/X2229r/ixZsgShUIj/e9euXUU8XMIKfrvnLA4PTuLpd/pK+nfHDSwAKBWQMAtbWAqCMWeChRyM5iihMII6kMXMHCvWQ5jZV8EbksvkWBUbngwYNfb5TqZELoDnNuZe5KsdqwlVAEhdgf1HbQEvNl61BADwj/9zyLRrxWZYmXWsFrfVoj3gRSyRwlsnxjSvw8IrrCwFPDlivMcKSH9c3c1+uHIksTkdAn+tMkty8xVW6l4ePViPVWcWYdVW50VLrQcpETg8WHzXipW6dproz9EKsLCrY+X3OKE2wksV8PDpyxcCAH61q093LhkrA7xscUvaqAmlzyr7eyCZEvn7tdjljZm4nQ6slDcB9si9a1rwwDCKWy8Zhs82FEpRPTDnqM/CIamG/q6BPhi2u0WlgIRRgqoeJyM9Gc3yCYbtsBeCOpCl0efhC/icPVbygigzCYw5K6USVpPRBI7IA2jP6y6BYyULyVzlWozBCWngrMshGNqJbw1Ir+3QRJSL21qP05LZXJ9atxD/9MK7OBucxqmx7DvEmaRSIg4PSM/x4nZzwkoQBKxb0orNb5/Bq0dHcJlcqsQQRZG/VwotBWyXe46iKqfPaM+dundsgcGI8s6GGvSHpiXh3C1dNjwZxeBEFIIArJAXjUZRPnvGSgGzCRlBELCiK4BXjozgYP9E0TccTo2ZE7GAJKwmphNps6yYeGirs9cCWhAE1HlcmJBfl1KVzL13fhPWdDfinVPj+MmOk/jSNUs1r8eCK9ZlfLZWdtXjV7v6eN+gFseGJjEdl4JWeky60Vawam4D3jkdxN4zIXzwvDma1xk3UClEWEvePVZE5cJm/lgVN2347/IFcPYvfjb8kBwrwihmS6Ga5YXHmAXCigeyOKVAlnqDPVbhLI6VUgpYGmG190wQogjMaahBe6D4iVZ8nIJBx4qVAXY21BgSR218llVMlQhozYKixu3kO8R7zxgPNjgxGsFkNAGvy4ElcsqfGS5d3AIAeOXo8IzfTcdTiCWlxXWhjpXX5eS9UoDk0hmNAFeXOBp15dQphAy2+7+wpXZGCVkuag2kAiaSKS5A2rOEVwDA8g45wELHrbCCaCLJhZ6RfjYGC3+aitu/FBBILwcsZtS6GkEQ8Ol1CwEAP95xAtHEzO+ccDSBt09KTvAVS2cKK0A/GZCVAa7sqi/aYHU92HO5V8+xks9RTbX2EtzVDAmrWQhbiJ4dL49jpbcAYAvNzBkdBJENsztyzLEai8TyCiJQow4OEARBlQqYQ1hlSQIrddx6KcsAAfOO1ekx48EVQHqPlRXBFZmwMiaWBGYEtuhZ0VWfs0ROi8tkYbX7dDCtvBFQBLjTIVgyu0jdd2TGQVGLKaO36+Tz5GYKq5Vd5twqwFgp4NBkFKIo9YG11mYXIEqARXGTAc+MTUEUpXK5FhMLX7YBGU0Lr5AW0HYrBQSUz32pI8lvWN2FjnovhiejePqdszN+/8bxUcSTIuY1+Wa8b5mwOj4SzlpBU67gCsZq+ftoz5mgZoBFSjXTj3qsSgcJq1kIW4iOhGNpqULFJjiVu4nSx3owqBTQlgxOTGvu/JUT3uNksIac7dylxMIFTOZJq85rtMeKza7JEl4xVZr3/ztycEUpygABlWNlcOOE9Z/MMyisFMcqqopat05YscZ7vR3iTPhQ1DwXX/Oa/FjQ4kcyJc6Ie1fPsLIi0VEdQW5KWKkdK4OR8p0NWo6VPBi40/xzZWSOFevXaw94dcuGlcj1iZxx24XABzE3+U29frzHSsOxsqOwYq9NqSPJ3U4Hbrt0IQDgR68cn/FaviT3V12xtHXGcbUFpPRCUcyeEMkcq3IJq2UdAbidAoJTcb4JpSY0HQfbO6QBwaWDhNUshPWkANbN8jH0d42EV2SZKk+Un5MjEaz7+y347OM7y30oaZgtBXQ7HXyxPVJgOWAwYzCxEreuL9jY4s/v0Q6vKJVj9Y7sWBVzMLAa5qrkChhg9JmIWgeUMqiRySjvPbKqFBBQFlD7+nLPt2Hsk8sGVxdQAsVcq1eOpMeuhyxKBGSo+47MlKbVeV1Y3FYLp0PACoOiSCudc39ffsEV7BgAJXFTCybi2rMEVzCWdtTBIUh9mEM6wQeFYibWXg0TVqzHKhxNcJFlx1JA1v927tzSC5CPXTQfNW4H9vWF8Mbx9I2JV7L0VzH0ygFFUVQJq9IGVzA8LgdPsdTa7GGb6LUeZ9q8RKK40DM9y4gnU7yJFADOjpeuz4qXbOk4Vn5eKkTCym68fGQY8aRoare+FARZnKyJxSUru8k1XDHn385Y2BqNW2elJXXZHKsS9FiNTEb5Lmep+h78XnOOFVsIdxgsH2qu9UAQJDeSDbm10rFa3hmA0yFgNBwztCkliqLiWBXwHLPY9VePpgsrq6LWGfmWAgLAjz9zMX71F+sMi2D2t1iPUTSRxFE5SCWf6GreY6Xz2WFR69kSARk1bid34YrZZ3VK/vyZHcytCCvpc8T6xnxup+netFLAetauXNpW8r/dVOvBh94rjUf4z5eP88sHQ9M4NDABQQAuW5xNWEmiRUtYnR6bQnAqDrdTwNIO872TVqEuB8xEiVont6qUkLCaZWSmjZ0pobAyMsiSlQqRY2U/3jk1DkD6sk4kU/pXLiHjedSQs3LAkUlrhBUTdSzVL5pIIZbI/hyxXfVypgLulk/Ei9pqLVuY54I7VgZLfdlra3S4pdvpQJO8iDg+zISVdY+txu3E0nZpEbVPJy2McWZ8CuORwhdfly6SHKsDZ0NpaZZWDQdmdBYgrOY0+rDaxCy0LtWgblGUkhMTKRENPjf/nRmYgNaL8s+VCKhGKQcsXp+V2Vh7BhsSzFwqOwdXAMB9H1iJV7/2vhmplqWChVg8f2CAP+csDObcOfVpoS1q9CLX2ed/aXsAXldxZ53psUpHWOVzbiQKh4TVLGM8Y8FWylJAIyEDyhwr6rGyG6xsTBStmQFlFfns2lvlWI1nLGzVKX96vR7s/Z09FTBR1N4OQBHKpSoDBMynAipDxY3vuLI+q2NDkrCqt9CxAowlcTFYeuCyjsIWX20BL5Z3SLvnr6lcK6ui1hlqZ9DsYt8sTNxMxZMITSewXxVckU8fjpFUwAH5fJdtOLAaVmKVrb/GCljUeneTueeaDS3OdKxabRa1znA4BMNOZjFY0h7AlcvaIIrAo6/2AlD6qy5fkt1FO0dVCpgZdLS/zMEVjNWq76PMc8Y4DQcuCySsZhnjkUxhVTrHykg/gN9DpYClIGkyDS8cTeDdAWWBUajTYyXjEfPCqsmiWVaZos7ldPD3sF6fVThLeAVbICdTYs7PwNsnx/D/PfbmjL4Bo+w+LQdXmHAZCsVsKmA+iVZslpXiWFksrHifVW5htY8HVxT+HLPY9VdVsetBOeSk3iJXbk6DtPj1uhxoL7L7UeN28s9Nf3A678HADCPhFQMTTFjlfmxsjlYxSwFZeMV8g7O/GDWudGE1ZONEQLvw6ct7AAD//YdTmJiO8/6qy3VctJ7WWnhcDkRiSf5aMcodXMFY1hGAyyFgLBKfMZtUab+wp+CuVkhYzTJYMh/jTIki19W9XXofcrajHUukTC/+q5FgJJ4maKzgN+/04ZyvP4sf7zhh+DZ7zgShfjlsJazymCzPZllZJazUC38jfVbhLOEVXpcDHjmSO1eAxWOv9uKFA4P4xP99Hb96+4yp4xZFseRR64CS+mnUsWIz98yIZuZYsSG3VpYCAqrIdQOzrJirtcqCpn3WYK92rKzusVrWUYfbLl2Ae29YaWjYdqHwcsCQIqzOsUBYZXN7WVBGrh4rQBF4RwYnES9C6XMwEuffEfk7VtJx2b0U0A6sX9qKJe11mIwm8O3fHcRAKAqvy4ELFzZlvY3L6eBOcWafFeudPLdE/anZqHE7sUw+xj2n0zd7xiLmSqkJayBhNctgOxhup3TSLFV4hbpnRK80R73QpHJA4C9/vgvXP/B77Dg2kvvKBjgzPoV7f7kH0UQKv9h52vDtWNkYY7iISVlmyScZrdkqx0rDLQsYGBKcLbxCEATuWuXqs+qVewViyRTu/tku/PMLhw2XD/YFpzE8GYPLIZR0x9VMj9V0PMkXjg1mHKuMXXurHauVXfUQBEkMsAWtFqIoYo8svqxYfF3U0wyHABwbDvNKAxZyYpWwEgQB99+0Cp+8bKEl95cLHmARnFKi1vMVVvLrnEyJXFRnwsIrjIShzG30oc7rQiyZQq/sfloJc0Ba67xcKBnFKw8InlkKSMIqG4Ig4FNyr9V/vXESALB2YTMPAsnGORrJgMOTUQyEohCE/N+vVrI6S3kyLwWkqPWSQsJqlsGE1dJ2aYejb3yq6L0cgLKzGvC6dIdkel0OsI1So8lh1cyhgQmkROD/vnQ895VzkEqJ+OrP3+HO4d4zMweOZoP1VzHsJKzyqSNnzcpWlwICQJ3skOiVJLEyv8zwCsB45PqJEWmx9/5VnQCAf3rhXfzlf79jaM7YblkoL+8M5FxYWImZOVZMWDoEoE7jecpG5q691Y5VndeFHjkxTq8ccHAiiuHJKBxCfnOZMmnwufkC6lU5dl0Jr7BfEpwRmHP09slxBKficDnyD/nwq97HWpsak9EE/0wa6bFyOAQsk4/lQBH6rFh/1XyTiYCAUgqYGV7RSo6VLh96z7y088TlS3OHabBkwP0qYcXKAHtaamdsjpUD5ohnBlgYSWImrIeE1SyDlU2xXZZwLMkHaZbi7+ZqshYEwfQQ0WqGOSIvHlTSjPLlsdd68erREfjcTrTWeZFMifjDiTFDt911chyA8r4ZtkkpYNpkeTOOlcXCSn3iqjcwy4qVAmaGVwDqIcHZbx+MxHmZx/c+sgb/509WwekQ8Mu3z+C2/3yDi81s7CpDGSCg6rEyMMdqXCVazZSlFduxApSeKb1kQLZ7vKS9zrQjkQ2WqsZi162eY1VqWIDF1kODAKTnKt+QD4dD4ItcrfcXi+6v87oML4ZXyN93BzXitgvlZJ4zrICZpYBso6uNHCtdfB4nPnbRfP5vvf4qxkqNZEC2oZLPWIBisCpLgAXFrZcHElazDHYi7mqo4YvBUgRYmGlCp2RAiVRK5O6SKAI/3tGb930dGZzE3z9zEABw7wdW4n0rpCSkHUdzlxgOhqbRF5yGQwCuWi7dbsQmjtVkLMF7v8wko1klrJiASXOsDDTRK8JKw7GSHRY9x4rNaGoPeOH3uPDxixfgR7evRZ3XhdePj+JDD73KHS0tdp+SFgZrShhcAZhzrIJ59M4BWo5VEYTV3NwBFqwHy4rgCgYbFPza0WGIomh5j1WpYcKKlegVWlbFhLvWZ09JBDQuPlbKARaHiuBY8eCKPIQVi1vPLAVsC9ACOhe3XboQgRoXFrXWGurnY+L6zPgU3+gs92DgTFZ21cPpEDASjvGRAoDyHUo9VqWFhNUsQ102xRKgzpYgwCJowpJWhNXsdqwmogmoqzR/9uapvMRmPJnCV/57F6KJFNYva8MnLp6PS+S5OEZ6t96RG2KXtgf4IsAupYDsfVXjdpgqaWu2IG49qRK+Daoa9lw9VqKoJP7VapS4qSPXs8H6qxao0sSuXNaGX3zhUsxpqMGxoTD+5MFX8d1nD+LXu87gUP8Eb8BPpZQhz+VyrIy8j1kZi9ko8UzHyqrEPDVsQaUXYFGM5vYLFzTD7RTQF5xG70hEiVsvwmMsBZkhEqzsKl/0ItfNzLBiLOezrIpQCjiaX9Q6kB63LoqiEl5RZ37+12yjs6EGL/7lldj8F+sMOeENPjfmNUlrpQPyTLN9Z+wRtc5Qz9dTB1iMUdx6WSh/cShRUtTlNXMaa7D/bKgkQ4LN7Kz6qBQQgOIuel0OdNTX4ORoBL96uw8fu3h+jlum8+DWo9h9Ooj6Ghe+e8t5EASBC6s9cp+VXh/KrlNSueCa7ga+aB0p0OmxivE85hwByoDgSCyJ6Xgyrz6jiek4F77p4RVu+ffa4iGqSrz0a5QCsn4ZvVLAk7IbtaClNu3yFZ31+NXGdfjMY3/AnjNBPLjtKP+d2ylgUWsd5rf4MRFNoMbt4D0kpYIJSb0hrgyl8drcoqAUjhVbUJ0cjSAYiWuGa7DF1yoLF18+jxPvmd+EN46P4tWjw1x8V7pjxSjUsQrolgLKwRUBM8JKEnpnxqcQnIpb+jyfKqAUkH1fTSeSCMeUkJdWcqwM0W7iPQBI78vTY1PY3xfCuXPq+caWXYQVIJUDHuyfwN6+EK49V+q7pbj18kCO1SxD/UHrYo5VCUoBlVlDuT/gLDksYqAPo5pRl0/edukCAFLEtpmwkT2ng/iXLYcBAN+8eRVfyMxp9GFBix8pEfhDr36f1Tty2dj53U1okWPKh3XS0EpJvqVQAa+LJ2PmWw7I/rbP7YTHpXyVKnHr2sJIvWGg5VgZKQVkJ/aFGvNv2utr8N+fuxT/509W4c8umo/3zm9EndeFeFLEoYEJPL9/AICUJKUXJFMMmBs9FU/mHKeQzwwrQHIj1RvRxWgub/R7+C72vrMzywFHJqN8pozVfRjrFkt9IS+9O8ydGasGBJeamY5VoaWA2R0r1mNlJBGQ0eBzY6482NbKcsBkSuQbmt35hFfIwmoqluTfxX6PUzMMhyiclapkQNZr1dVQgxYb9bRlJgMmkim+uWd2c4ooDPoUzjLUixU2Cb0kpYCmHCsqBQSQVubz4Qu78b3/eReHBiaw49goHxaqx3Q8iS//9y4kUiI+sLoLN66Zk/b7S3pacGIkgh3HRnDVinbN+0ilRJ4IuKa7gS/6h8MxiKIIQSj+rBs9+Jwjk4tvQRDQ5PdgcCKK0XCMfxbMkG3hzxySbD1WbDe9xu2AU6MURSkF1OmxyuJYMXweJz5+8QL+b1GUFnKH+idwaGACp8em8JELu7Pef7FQ95RNxZO6oidf0ex0CGiu9WJ4Mgq/x1k08bhqTgNOj01h35kQLluc3gTPejAWtdZankp42ZIW/NMLwPZ3h/hleiMs7Eyj3w2Py4FYIoX2gLfguHC9/kYzM6zULO8MyJ+dEC7qaS7o+PixhKYRT4pwOQS+wWkG7ljFUxiapBlWxYZHrveHeF+lndwqQAmwYMmA6o25SnW0K5WyOlabNm3C2rVrEQgE0N7ejptvvhmHDh1Ku87nPvc5LF68GD6fD21tbbjppptw8OBB3fu9/fbbIQhC2s/1119fzIdSMaib7ec0SieYUpQCsgWwkd1ntosfiVePsDobnOIndqOoF5YNPjc+9N65ACTXygj/+NwhHBmcRFvAi2/evGqGCLpksbRI0OuzOjYcxsS0VDa2vCPAFz6xREo3nKFUKKWA5k8chQZYjGvMsAJy91iFs8ywYhiZY6XVY6WHIAiY1+TH1Ss78BcbluDbf7Ia53c3GrqtlaSPU9B//xTy2rJFZjHKABl6ARbFHB66Zl4jfG4nj9quyzHCws4IgsCHBFsxD4gLK43PHuuxMhK1rmaFXA5oZeQ6KwOc1+TT3FzJhTq8gjlWNMOqeDBh9W7/JJ/peI5NgisY53TVwyFI0fsDoWmeGltfU7nfD5VKWZ/t7du3Y+PGjdixYweef/55xONxXHvttQiHlTSrCy64AI888ggOHDiA5557DqIo4tprr0Uyqb/ovv7663H27Fn+81//9V/Ffji2JzOaWikFLL5jZSYW2F9lpYCxRAof+MHL+MAPXuIBAkbIHP7Jhnb+z/7+nGL45cPD+M9XpNlX37llNRcRai7uSe+z0oKdRFjZmM/j5KWadohcLyQVrVBhpcwQyhRWrMdK+zll/UXZynaUuPXsjhdrVl/QrO1Y2RVBEJSNkxx9VtmeXyO0yiWrVrtFaniAhUbk+j6eCGj9rrbH5UhzTirVrWIwoWOJsKrJ3mM1GDKfCggUJ3K9kKh1ID28YogPB6Y+mmIxr0kZFv3CAWk0gN0cK5/HiSVygMXeM0FVUBm9L0pNWYXVs88+i9tvvx3nnnsu1qxZg0cffRQnT57Ezp07+XXuuOMOrF+/HgsXLsR73/tefOtb38KpU6fQ29ure99erxednZ38p6mpqciPxv5MRNOjqZlj1R+cRipHv0OhmNl9rrZSwIHQNEbDMYyEY/x5MELmwnJZRwCXLW5BSgSe2HEi6+1ePzaCO378B4gicOvabrxvRYfm9dR9Vm/2jmpeh5cBqtLjWF25mcj1fX1B7Dg2Yvkw6nz7cADrhFXme1rpsdIvBfRnmW2Uq8eKLcqa/G7TJZB2gAV2hHM5VnnGrQOlcazOlR2ro0OTM9w35litKoJjBSix60Dl9lcxLl3UkjbKoRBYqelEhrBKpUQMypsRZlIBAcWxendg0rLz5OkChRXvsVI5VlQKWDwcDoG/D1ilRrE+24WgLgdkaw2KWi89tvIHg0HpZNTcrF3HHA6H8cgjj6Cnpwfd3fr9Adu2bUN7ezuWL1+OL3zhCxgZyV7uFI1GEQqF0n6qERZN7XM7UeN2oqO+BoIAxJIpDIeLG0YwbsJZYCfHqSopBRxSCZBcg1vVaLkxzLX66Rsn+QwTNa8fG8Htj7yJSCyJK5a24hs3nqv7Ny7pYbHrWYSV7FitUZWN8QALg8IqmRLxsf94Hbf+cAdu+9EbODxgXUlNIbtyVgkrs6WAkRylgLl6rHL1V9mdWoOpn/kMfmawQanFdKzaAzVoD3ghilJTOyM4FceJIqeGqXu6Kr1/4st/tAx7vnEdLl6Uu280F9kGBA+Ho0ikRDgE80N0e1pr4XE6MBlNWFY2f7KAqHVAOocDrMdK+v6iUsDiog6hkcbV2C/aftUcJcCCRa03kGNVcmwjrFKpFO6++26sW7cOq1atSvvdgw8+iLq6OtTV1eGZZ57B888/D48n+5vl+uuvx+OPP44XX3wR3/nOd7B9+3a8//3vz1o+uGnTJjQ0NPCfXKKtUsnsc3I7HWiXd7mKHWDBF6EGdk/YSUOrnMMK3jg+iusf+D1eOTJclPvPZDCkElY6fTOZsFIw9Y70NSs7MLfRh7FIHE+905d2/R2yqJqKS6LqP267MGeMuF6f1XQ8if3yglHdj8NO4EZLAUcmo/z1f+nwMK7/55fwjaf2caFfCIWUi3Fhlecsq1zCKlsP2iQrBczaY6Uft66XCFgJcMcqx+c7GMkvmAQA79tpLvJu7aq5M+dZ7ZdLA+c1+YpWhnPOnHr+vqt0xwrQHpSdD9nCK9h3cGud13S/idvp4CVWB3TKAXefHsfmt08bus9TY5JAy2c4MAB43XKPVSKpzLAix6qoqEtVz51TX/bgJi1Wz1McKxoOXD5sI6w2btyIvXv34qc//emM33384x/H22+/je3bt2PZsmX4yEc+gunp7ELg1ltvxY033ojVq1fj5ptvxtNPP40333wT27Zt07z+Pffcg2AwyH9OnTpl1cOyFVrN9jwZsIiR66Io8kW0mR6rqSKUAiZTIu7dvAcH+yfwf186Zvn9a5HuWOVRCqgqZ3I6BPy5HL3+6CtK9PprR0fwKVlUrV/WZkhUAeDzrPaeCc5wSA6cDSGeFNFSq0RLA0otv1HHisVON9d6cO05HUimRDz6ai+u+t42/OT1Ezljt/WwJLwiz16xbEOvmUsyGU1olj4yx6o2Sykg+4yEY0nNnjzmWM2vUMfKb9CxGi/Asbr5PXPxufWL8BdXLTF/gCZgPVQs4lj9/6uK2NzudAi4ZJG0KVLpjpWVKMIq/b3FgoPMBlcwWBlYtsj1Q/0T+Oi/78CXf/YOdp7QH18BqHuszCcCAkopoCgCfbKLRo5VcUkXVvYrAwSkAAtBkGa2HR6YBEBR6+XAFsLqzjvvxNNPP42tW7di3rx5M37f0NCApUuXYv369fjFL36BgwcPYvPmzYbvf9GiRWhtbcWRI0c0f+/1elFfX5/2U41o9aPMkQMs+oroWE3HU4jJC0QjO7hsJ78YPVa/fOs0jgxKXzg7jo0imih+ueFQSHluCy0FBICPXtgNr8uB/WdD+MOJMbx2dASfflQRVT/88wsMD7ztavBhIZ9nlV4OqC4DVO/O8SHBBgVJvyzaF7T48cPbLsSPP3MRlrbXYTQcw//evBd//C8vz/jbRrGkxypPx4pHvWfpsUqmRM1yVhZekW2XXl0iqFVO2Dtc2Y4VE5R6jlUqJSqBN3m8to1+D+65YSWWdQTyO0iDsGSwfaoAC6W/qrjnkT95zzw4HQIuWmhNBHg1wOdYZWwS5ZsIyFjRJb2PDmoIq9B0HJ9/Yif/rL92VL8SYiqmuEz5OlY+1ff7qTHp+4CEVXFZ3hHgiaZ2C65g1HpdWNwmuasvyxU5FF5ResoqrERRxJ133onNmzdjy5Yt6OnpMXQbURQRjRrvCTp9+jRGRkbQ1dVVyOFWPMoOsPJBYyUzfUWMXGfOhsfpyLpLr8bvNtbcbpZoIokHXjjM/z0VTxraXSyUQdUwXb2hr5lkpgIymmo9uPl8KXr9m0/vx6cefQNT8SSuNCmqGMy1yuyz2sWElSq4AgBaZEEyYrAvj6VOMhF/xdI2/O5LV+Bv//gc1Ne4sP9sCB//v6/n9R4sKBXQb1GPVcaJy+9x8hOwljBigiLbZ8HldHBxpfV+YbvdldpjZWTjRB20Y2dHhomndwcm+CYNc6yKEbWu5vpVndh//3X4yNrqLF3PhwBPBUx/b7HhwJ0N+YmPFZ3KHCM1qZSIv/zvd3B8OAy29/T6cf1NotOyEAp4XXm/t91OZQYe+45pp1LAouLzOLFuSSsCXhdP1LUjzEVn/YBUClh6yiqsNm7ciCeeeAJPPvkkAoEA+vv70d/fj6kp6Q1x7NgxbNq0CTt37sTJkyfx6quv4sMf/jB8Ph9uuOEGfj8rVqzgDtbk5CS++tWvYseOHejt7cWLL76Im266CUuWLMF1111XlsdpF4KRmbOklFLA4jlWJ1UzO4zUJRerFPDJ10/izPgUOuq9uGF1JwCp56fYDE0UWAqocfJlIRa7TwcxHU9hw/I2/HseogpQhNVrR9P7rN45LS0Qz5/fmHZ5q3wCH54wJkjYe0udxuV2OvCpdT3Y9tWrsKi1FtFECrtPz5wHlAulFDCP8Aq5pHEsb2ElLWgyF0eCIOgmA7INA72+EiVyPf39Mh1Pok92ACvesdLZOFEH7Xhd5t/TpWJuow+NfjcSKRHv9k8iHE3g2LBUqlnMUkCGnZ+bclCbpceKCauOQGGOVe9wOC006OHfH8Xz+wfgcTrwnQ+dBwDYeWIMCZ2xGuqo9UL6dHwZ3/XkWBWfH/75hXjpr68ynSxZSjLTCsmxKj1lFVYPPfQQgsEgNmzYgK6uLv7zs5/9DABQU1ODl156CTfccAOWLFmCj370owgEAnj11VfR3t7O7+fQoUM8UdDpdGL37t248cYbsWzZMnzmM5/BBRdcgJdeegle7+z+4uE9VmnCSnasithjxRKy5htcCLId7bCFwmoymsC/bpFKQe+6eimuWSlFkL9cAmGldqzGTJSd6c3+OmdOPS6WZ9lsWN6Ghz+Rn6gCgIvlXo19fUrD63gkhuPyAnHNvPQv6pZaWViZdKy6NE5GzbUe3nDbOxKe8Xs9ookkL7/Jp1yMOVZjkVheMcrBiHYpIKA/yyqSoxRQur22Y3V6LAJRlMoFtWaTVQJ+A3OsCnEiS4kgCEoSV18QB86GIIrSrCQKEyg9dXIwSqaw6pfDKzryXBC31XnRXOtBSgTvXXn58DD+8blDAIC/u+lc/OkF89DgcyMSS6aVhmZyqsD+KkaNW1m+1XqcfEwJUTx8HqfthcrqGcLK3t+h1UhZJwvmmmkzZ84c/O53vzN1Pz6fD88991zBx1aNaJcCsh6rIgqrUTke2mA9ueJYWVcK+KOXj2MkHMPCFj8+cmE3dyn29gUxMhnls5mKQZpjZbAUUBRFngqYbXH5z7e+B68eHcYHzusqaOea9Vn1jkTwh95RXL2yg7tVC1v8M04kbQE5vGLCmLBiPVbZdvlYSdsJk8KKLb4FQSqrMUuTLExSonRfTSaFil4cuF4y4GRMf44VkD1ynfVXLWgpbLe7nNQamGOVmWBqZ86dW4+Xjwxj75kgorLQL4VbRcykzpseHMM+IwPMNc+zx0oQpDlGrx4dwYH+EJrrPLjrp28jJQIfuXAebl3bDUEQsHZhM144MIA3jo+mjahQc3K0sERAhvo7n0Q8wTgno//L7kKwGrFFeAVRGvRSAQcnopoJZFZwkjtWxnpC/BYPCB4Lx/Afv5cSAL9y7XIpZr6+Bis6AxBF4JWjM6PGrSKVEtPS84xGjKsDP7LFKXc21OBD751nSTmQ0mclPRcsuOJ8jcUBc6xC0wnEErnfMywYhYn4TFhJGxMNRlEnTToc5kWG2+ngAmjEZDlgPJnijqq2Y5W9FDASzV0KyF7zTMeKuXoLK7S/CjDmWGl9V9mVc1UBFntlp6LY/VWENky0J1MioqrvpoGJmeXIZmF9VntOB/EXT+zEaDiGVXPrcf9Nq7iAY1UEen1WLGyiUGGldqioDJBgBGrcWNSqnB+ox6r0kLCaRQQ1doFbaj3wOB0QRaUO3Wp4s71hx8raVMCHth/FRDSBc7rq8cHVSoDJ+mVtAICX3h2y5O9oMRqJIaEqM2M78blgC2qnQzAU+FEomQEWWoOBGQ0+N2+czhVgkUqJ/H2lVQoIAAvlk4DZUsBC4rgZLIjDTIkmkC54tIQvj1zXDK+QSwE9Rnqs0m+vBFdUZn8VoGyc6PZYVUgpIKA0ix84G+Kfm8xyHKI0qD9TzC2ejie5UM+3xwpQItd/8voJvHM6iAafGw99PL0Ee60srN7sHc1aXsxKAecVKKzUpYDkWBFq1H1W+fQfE4VBwmoWoTXzx+EQ+C5eMSLXRVHkjpXRxaDiWGnPATLD2eAUHnu1FwDw1euXpzkbly9pBSDFkhb6d7IxlFEuZzS8gpWA1de4SlLyxYQV67N65/Q4AG1h5XAISjJgjsj14XAUiZQIh5A9tYq5L2eD02mN4bngjlUBpQ5NBh/HjL8tL/wDNS4uMtWw8IrMUj5AERRsUK4W9TVZSgH5cODKdaxqDWycFBKjX2oWttSi1uNENJHCYXmUQ7Gj1gltHKqNKLapwTZ2atwOPnw7H1iARUqUyo8fuPV8dGeIo3Pn1MPvcSI4Fce7gzOj2UVR5MKqYMfKTY4VoQ37/nEISvUEUTpIWM0ixrPMhWEBFsUYEjwWiWNC3jnMPAllgwmrlIi0co58+MGLhxFNpHDRwmZskB0qxkU9zfC4HDgbnMbRocmC/k42WHAFOwkaLQUs9Y59Z0MNelprkRKBX719BsOTMbidAs7p0l4gsp60oRxDgs/KYr09UAOXU/vrpsnv5l/+zJExwrgFz1G+jlWuUjXdUkBZUNTplgJqh1cow4Er2LFiPVY6c6wUYWX/3VaHQ0gbGNpS68m7l4conLqM/sZ+VX9VIZtUS9sDcMmbKHdfvQxXLW+fcR2304ELFjQBAN7QKAccDcd4CfHcxkLDK0hYEdowx6rJ78mrTJ4oDBJWswRRFPmiPnOxUswhwWwh2FlfYzi1zq8q5yikHPDY0CT++w+nAQB/df3yGSfVGreT18T//t3ipAMyx2pJuzS0byKaMNTLFixDj8klcjrgf7wk9aOt7KrP+pq11hlzerSi1jMRBIE7MCyJ0Ahs2HIhpYBNec6y0ktsBGYu7tSwywyFV6iEVTyZwukxFrVe3Y7VuE7ioh05V+VQnTu3oWKDRaqBzMj1Afk7ON/hwAyfx4lvf2g1/te1y/DF9y3Jej02sFmrz4ptHJk5H2aDwiuIbFy0sBkfvbAbd//RsnIfyqyEhNUsYSqe5GEImQvRLha5XoRkQHYiMbPD7nQI8Likt2akgGTA7z//LpIpEVevaMeF8skukyuWSuWALx0uTp/VoNw0zYQVYGxIMC8FLKmwksoB2eI9czCwGrZDOpLDsWKJgNn6qxisz8pMMmDIgnIxNsvKrLDKVapWrxu3Lr2ndR2rmpnhFWfGppBMiahxOyp6GKiRHqtKCq8AkOZYrZpDZYDlhCWEMkeUJQIWKqwA4CMXduPO9y3VdQEukjfr3jg+OqPE/JT83Vpo1DqQGV5hf2eXKB0upwPf+dPz8OeXLCj3ocxKqPhylsAWaG6nMGOnXBkSbL2wYjOsjAZXMGo9TsQSKd0hwQ9tO4oHXniXz/RpqvWg2e9Bc50HfrcTT+8+C0EA/td1y7Pex+VL2gAcxI5jo4gmkpYP3ByU56d0NtSgvsaF0HQC45F4ztINveHAxSJzmrxWIiCDnciHc5UCBvUTARk8GXCktKWAfJaVSWGVy1GpyzKoNJUSEZH7yPxGwitUpYQneAhMbUWXdzBHoRrmWDHUPVWZAzqJ0pLpWPWHCk8ENMOa7kZ4nA4MTUTROxJBjyqh7ZRqOHCh1LiUffHWCt5oIYhqg4TVLEHZAfbMKFMpbilgfilmfo8LY5G47pDgX751GtFECtFELGtc9o1r5mBllj4hQEp6aq3zYngyirdOjOPSxS1Zr5sPrAeprc6LRr8HoekET2fUoxwLS9ZnxQcD6wirFu5YGSsFzOVYsVlWvSZKAdnfLuQ54uEVph0r/Rlj2XqspuJJsE3sWr3wCo1SwGrorwLMpQJWQngFACxpq0N9jQvhWBLnzSNhVU4yNzVYeIUVjpURatxOnN/diDd6R/HG8RFtYdVU+GdY7Vi1UY8VQdgGElazBJ4IqLFQ4aWABhyrRDKVNYRAi5PycGCzO3TqZMBsx8HiuR//9EVwOQSMRmIYC8cwGo5jNBxFUhTxpav1a4wdDgFXLG3F5rfP4KXDQ9YLK9mxaq/3otHvxslRY8mALGablYSViksWNeP4cBgBryttFkYmrQbDK/oN9FgBQE+r9P44YcKxOjQgpW4tVpVZmqXQuPWGLFG2bHGXKayYmBCE9FSvTLR6rNicr4UVLqy4YxVLpg1xVaMkmFZGiZPL6cCjn74Ioak45lmwaCbyhwur6UxhVTrxcVFPM97oHcXrx0fx0bXz+eUnLUoEBNLDK6jHiiDsAwmrWQKfYaWxw85KAccjcUzFkmk7YWoO9ofwJ//2Kj5xyXz87w+cY+jvKo6VuWZ7LqyylAudGptCPCn1m1y+pLWg0ihFWA3jr67P+240UTtWbLFsRFiVqxTqquXt+K83TuGSxS26z2mLwfAKJtZZ8mQ22PujLziF6XgyZ2P3dDyJY3KS48rO/Hta8o1bZ/PIsjtW2j1W6hlWegEHLBUwNB3n4oM5VmY/S3aDfbaTKRGxZEqz/LbSSgEB4L3zm8p9CASU4JhwZilgCZMaL+ppBrbOTAZkw4EtKQWUvyMDXlfBQRgEQVgHhVfMEvQcq/oaN9/l03OtfvbmKUzFk/jdnn5Df3MqluRx42Z7rJi4i2SZa3RUnhezqLWu4H4TNs9qb1/QdIhBLgblk3p7fQ1PoBs3EF5RroXlH53Tgcc+fRE2fWi17vVY6Ylej5V6OHBnjh6rlloP6rwuiCJweiy3a3VkcBIpUXo/F7ITna9jlSs4I5AlFTBsIBEQUF73eFLElPwZYA5tJScCAhmpnxobJ9FEkj/mzNEQBJEL5ohORKU5iAMha1IBzfDeBU1wOgScHpvioVCJZIqX21vjWEnLN+qvIgh7QcJqljCeIwyhq0E/GVAURTy3VxJUZ8anDM1jYmUPgRqX6V4JFsk8laUU8NiwJKwKKQNjtNfXYEVnAKIIvHLEutj1cDTBe8TaA17+HAQNLOKVVMDSmsqCIODKZW05wzVaVGl6qZT2cOWRcAzxpAhBZziw+u8ulMsBjw/nFlb7z4YASG5VIdHWzLGKxJLmhhPnEL7ZeqyMzLACpDJBNjMnNJVAMiXi1Kj02TTbr2g3nA6BLwq1+qzYcysISsIbQRilTpUKOB6JIybPQmwvYSlgndfF0yHf7JVcq7PBaSRTIjwua1I9a2SnlxIBCcJekLCaJeTqWeDJgFkCLPacCaIvqPzuQH8o599USpf8phe/zLEKZykFPDoo3bdeH5AZihG7zmZY+T1O1HpdvAxzzFCPlb1LoZplQZJIiVwEZsJSJtvqvHAb6MtjJW5GItcPnpX6q1Z0BQwdbzYCXhfcTum9acatzD0gWLo8EksiqRKe3LHSCa4AJKHJNkGCU3H0h6YRS6bgdgr8s1rJ6M2yUs9wq+T0Q6I8qMMrWBlgc63H8sTXXLDYdTbPim00zmvyWfK+ZuWESzsK+w4kCMJaSFjNEniPVRbnaE6OAIvn9qWX/x04m1tYnVTFQ5uFlUpNZSsFHLLOsQKAK5a2AQBeOjw8Y/ZIvrAySLY72VABpYBG8bqcqJddmWzlgDwR0KAQUCLXDQirfsWxKgRBEPIaEpzr9VE7UpMq14o5NLU6UesMJXI9jhNyWmJ3kx/OKhAbTFiGNQYos89HIYOfidmLEree5MKqlGWAjIvk8RWsz+qUhcEVAHD1inb84vOX4n/fsNKS+yMIwhpIWM0S9HqsAGXOULZSwGflMsBFbZJIMiOs8omH9vMdbe1SQC6s2qxxrC7qaYbH5cDZ4DS/70Jhw4FZYlMjD68wUArISjdLnApohlbeZ6X9eFgiYJfBRc1CHrmuXwooiiJ//+lF6RuFuW+mHKscwsrjcsArz5mZiCpCmvUU1RoocWPCNRiJ8/lelV4GyDDqWBGEWdSlgIM8uKL0fUhrF0phJkcGJzE8GeXnQyui1gEp0fbChc2GvksIgigdJKxmCblKl5QhwTNLAY8MTuDoUBgepwOfv3IxAKXHRY98hwMDqlk3GqWAo+EYL6db1GqNY1XjduKihVLpxkuHremzGuKOlSQseI9VDscqnkzx3iw7Ly5bcwRYMPfT6GDOhXJZZy7HanAiirFIHA4BWNpR+OtvVlhNx5O8b0MvXEGrz2rSYHgFoJplNR2vmkRAhvL5zu5YMYeXIMygjlvvD5Y+uILR6PdgRadUpveH3lFLo9YJgrAvJKxmCby8JstiZY5OeMVz+wYAAJctaeHi492BSSSSKd2/WYhjxXbhpjR2tFnM9txGX9Zo+HxQ+qysEVasFJA7VqwUMEePlXp2EVuc25FckevMscoVtc5gbkzf+BSiiexBEsyt6mmttSRm2KywYsLY6RB0wxWUyHVFPDAHNld4BYC0Hiu2SVHpM6wY6llWmTBHl0oBiXyoq5nZY1UOYQWk91mdGpPOrd3Nld8jSRBEdkhYzRJCOfoWulSOVWaPESsDvP7cTsxv9qPW40QskcKx4ezOQjIl8tjsfHbZ2fBUrdQwVqq3yKIyQAbrs3rt6Ijuwt4oQzOElbFSwNC0svg2M4y51ORyrM4GjUWtM9rqvKj1OJESwRPwtDjYLwVXWFEGCJgXVkwY19foz6JSmugVoTwpO7B+Mz1WUwnu4lWdY6Xx+bZ7cAthb+rk/r3JaEI17qG8wuqN46O8x8qKGVYEQdgX+67aCEvhu8BZe6ykE08klkwrVTs9FsGeM0E4BOCaczrgcAhYIS9o9fqs+salAb4epyOvwYw8vEJjR/vokLTIXNxmTRkgY0VnAK11HkzFk3jrxHjB95cZXtHIS7sSum6f3YMrGMyxytZjxVIBuwwuagRBMJQMaGV/FaASVgZnWRl9fbRKAZljVZsjFRBQ+uvUjlXV9VhplPqO55gRRhB61Hml9004muCueSmHA6thFR77z4b4xg0JK4KobkhYzQJiCaVnJ1vceo3byYel9qki11kZ4IULm7lDsVKOuNbrs+LRss2+vFLM/DqlQscsTgRkOBwCHxZsRew6a5xmjpV6IR6a1g7lAJSFe7aZY3ZBz7FKpUQMyP0NRoUVAD7LioU1aMGj1jutiRnmwiqLQMwkaLAHiDlWamEVNhNeIc8wOzI0ial4Eg4BmGdR43u54amAOnOs7L6xQNgTtmmRSIncJSrlDCs17fU16GmtBSsCafS7bR1IRBBE4ZCwmgWkDdzU6dnpknthzqoi11nM+vXndvLLVnLHaiLrfbEd9nwbdf1yKaBWKqDiWFlfFsUicvf15Q7nyAUTHCy8wuV08J4cvXJAJRHQvv1VgDKYckRDWI1GYoglU/JwYOPCagFPBtR2rKKJJC8FXVEmx4q9drkdq5k9ViysodZAbyC7/z2nxwEAc5t88Liq4yvbr5MKmCtohyD0UI8ymJA/b+VyrADFtQKsSwQkCMK+VMdZmtCFzbDKNXBzTkbk+tBElE+Nv26VlrDKLj5OjMo9IfkKKw8TVukLr2giyd0wq0sBAcVdydY3ZJREMoURufSDOVaAkiKnN8uqUnbsW2THakSjN4mV4LTWeU2JgZ4W/WTAo4NhJFIi6mtcPHClUJpNzrEyWwqo7rHic6wMxa2nD5TOZx6cXTGSCpgtaIcg9HA4hLSNC4/TwTdPysHaHkVYUSIgQVQ/JKxmAUZ3gFnkep+8KH7hwABEEVg9twFzVUNeV3QGIAiS8GIBDZmcZI5Vns322UoBT45EkEyJqPO6eO+SleQKZDDKSDgGUZSS41pUJ3U2jDaokwxYKcKKP1ca7wEmzs2KH9ZDdCJLKSAT8yu66nWDI8zQLDtvYwaFVa4gGIZ2j5X58ApGtfRXAfpzrCi8giiUOpXb317vtey7Ih8uVgkr6q8iiOqHhNUsgA8HzrFQYW7NWXlRzMsAVW4VIC0K2TDXbK5VITOspL+hXQqoHgxcjJNla0AJZEilxBzXzs5gSBIbrXWeNJeQJwNO6ZQCTldGjxULrwjHkjNCRvrzTONis6xOj0X4rCg1B/vl4AqL+qsAxbEaixh7zXMNB2ao5+kweCmgkfCKjPtfWCWJgICqx0rLscoRtEMQuVA7wuWKWmfMa/LxcytFrRNE9UPCahZgdOAmd6zGpxGajuOVI9I8p+vO7Zxx3XN0ygFFUeTlevnusvvc2qWAxUoEZLTUSi5MMiXqluvlYnAiPbiCwRbjerOsKmXHPuB18TK/TIePRa13GYxaZ7QHvPC5pch1FtevxuqodQBokh3FlJh7eDOgXCfXwp/1WKmDSsyUAs5GxyqVEpXn1+bvf8K+qOfLlbO/CpDSTj97xSIsaa/D1Ss6ynosBEEUHxJWswCjAzfZINe+4BS2HhxEPClicVstlmik77FkQC1hNRqOYVLeic639IEtPKOJFJIqF+FokRIBGR6Xgy+YCykHHJpID65gsPseq4JSQEEQ0CqLksw+K+Z6mkkEZPepVw6oLgW0CrfTwcv2tPrFMuFzrPLosWLx4rUGSgEzw0uYm1cNZJtjNRlLgH3c7e7YEvbFTo4VAHz68h688JUryzZPiyCI0kHCahZgdIeduQsDoWn8bs9ZADPLABl6yYAnZLeqs74GNe7cJU9a+FXNx+pyQOZYLSriIlOvd8gobIZVW126Y8Xi7oO6qYDS42Vx23amNaD9XCnDgc0vJBZmCbAYmohieDIGQQCWdVgrrFlz+5iBZECjwrdOo8eKbTj4DaQCZgqLamp8ZwvfzDlWrPewxu3I+7uDINKFVXmi1gmCmJ2QsJoFGO2xag944XQIiCdFvHBgEIB2GSCgCKujQ5OYjqcvjtjskPkFlC55XQ6w1iTWvyOKIo4NFtexApQY8SErHKuMk3pjFaUCAuDBHCPh9OeK9ViZLQUEFGcmM3Kd9VctbKk1FP5gBh65bsCxMhpeUc8dK0lMJZIpROW+sToDpYBup4MLsEI2KexINseqkt77hH1JKwUkl4ggiBJCwqqC2X16HP/58vGcDfdGB5q6nA50BJQeozkNNVg9t0Hzul0NNWjwuZFIiTgiix1GocEVgFQSxhbPbLjx0GQUE9EEHEJx+02YY5Ut8dAIrMcqM7nQSI8VHxBcAYMklRRFRZCIoqjqscrHsdIeEswGA7MyVCsxE7mu9CzmCq9In2MVVvUT+Q2EVwDKe6Ca+qsAlWOV0WOlbAJR1DqRP3YrBSQIYvZAwqpCefvkGD767zvwzaf3Y/vhId3rjptoBu9Sxapft6oza/KeIAh8gbs/o8+KC6sCF4O+jGTAo4OSgzG/2Q+vq3i79yxwQi0WzMJLATOEFYtb13OsWCpgJezat2jE04+GYzzRL59FDRsSfCKjFJD3V3Va11/FMOpYiaJoeo7VxHQcoijy97HLIcDjNPbVy/5GNSUCAtlTP1laZi7RShB6qOPWyx1eQRDE7IKEVQVybGgSn370TUzJJXj7+7IP6gWUfh4j8cVz1MIqSxkg45wuyc3KDLA4KQ8HzneGFYMNeWSlgErUevHKAAFrZlkNcWGlHV6RrccqlRIrJhUQUMomR1Qi9Gyew4EZPXIp4KmxKcSTSuT6ATkRcIWFUesMo8IqHEvyMJVcrgpb3MWTIqKJFMIsuMLrMjwqgPXZFVJWa0dYeMd0PD2chkoBCSuoI8eKIIgyQcKqwhgMTeO2H72BsUgcbqe0ODs8MDNAQs24wfAKQBno2lLrwdqFzbrXzZYMaEUpIAD4MkoBmbBa1Fbc3fu2AoWVKIrcscosBczVY1VpqWhaIrSQMkBAes5q3A4kUyLOjEnpgvFkCkcGrY9aZ/DwihzCiiVsepwO1Lj1vz7rVH1gE9MJZYaVgeAKxrlzpM2Li3r0P4uVhroUUu1aGe0HJQg9mLCqr3HxygeCIIhSQMKqgghNx/HJR97E6bEpLGzx41s3rwIAvDswqXs7tlhpMNC38J75TQCAD713LpwO/V11dTKgKEpqYCqW5KKi0BQzP3espIXXsSLPsGIoQ4LzE1ah6QQvhZs5x0pOBZyKp+3U89vKgsvjqoxUtBYNx6o/mF/UOsPhELCgOT0Z8OjQJOJJEXVeF+Y1WT9ksylLbHwmvP/N587pOjkcgjIkOJowNcOK8TcfPAc77rk65yZHpeFxOuCSv1/UfVZGE0wJQg/2GaPgCoIgSo3985wJAEA0kcTnf7wTB86G0FrnxeOfvhgipIX50aFJJFOiphBKpkRTPTvXnduB5+5ej8UGXKGlHXVwOQQEp+I4G5zGnEYfHwwcqHEVvDhS+jAySgGLmAgIAG110sk43/CKITm4or7GNUMcsddAFKXem8aMQJFKK4UqhmMFSP15hwYmpGTA5UpwxYrOgOEyOjO0GIxbN7vwD9S4MBlNYGI6zqPF/SaEldMhVOXiUAqncSKkcvIAJW69Ut7/hD1h4xhWz20s74EQBDHrIMeqAkilRHzlv9/Bq0dHUOd14dFPrcX8Fj+6m/yocTsQTaS4oMlEapyX/t/IYkUQBCzvDMBloLne63Jy94iVA7LAgQUt/oIXwEokcxJTsSTOyENnS+VYjUzGciYuajEY0g6uACQnipWCaSUD8hlWNZWx58Ecq9FIjDtwygyr/J0l1mfFkgEP9LPBwNb3VwEqxypHYInZhT93rKZVjhWVJgHQTgZUwisoFZDIn/PmNeKVr70Pf3/L6nIfCkEQswwSVjZHFEXc//R+/Hb3WbidAh7+xAVYJUegOxwClsjuzbtZ+qzY4r3W48wrSCAXPBlQDtBgAo+VchUCa3CfiiVwfDgMUZScAtYPUyxaaiVBlEgpCXBmYPOv2gPaTkOjTjJgpTlWzX4PBEFy4Jjbc1YuBZzTWIhjlZ4MqEStW99fBZh3rIy+PiwZUHJmlPAKQrVxonasKuz9T9iXuY0+uA2mbxIEQVhFWb91Nm3ahLVr1yIQCKC9vR0333wzDh06lHadz33uc1i8eDF8Ph/a2tpw00034eDBg7r3K4oivv71r6Orqws+nw/XXHMNDh8+XMyHUjT+/ffH8OirvQCAf/zwGly+tDXt98vaJWGTLcBCCa4ojhg5Z47cZ9XPHKvChwMzfKpSwGPDpUkEBCRXiS3s8umz0nOsAFWAhcYivpISAQFp9hmLkGfPVT9zrApI48qcZVXMqHVAcawiseSMgddqgiZGFwBAnTyHajKaX3hFNaPpWFF4BUEQBFHBlFVYbd++HRs3bsSOHTvw/PPPIx6P49prr0U4rMyvueCCC/DII4/gwIEDeO655yCKIq699lokk9kXP9/97nfxgx/8AA8//DBef/111NbW4rrrrsP09HQpHpZlnBmfwvf/510AwH0fWImbzp874zpLOyRhlS3Agi3ei7VQVwdYAMCJUWsSAYH0His2w8pI75cVsBjxfPqsFMdKX1hpuWGsH64SEgEZ6sj19OHA+ZcCLmSR66MRDE5M80CU5UWIWgeAgNfFUzb1ItfHp8y9PupZVqwU0EyPVTWjlPrOdKwovIIgCIKoRMp6hn/22WfT/v3oo4+ivb0dO3fuxPr16wEAd9xxB//9woUL8a1vfQtr1qxBb28vFi9ePOM+RVHEAw88gPvuuw833XQTAODxxx9HR0cHfvWrX+HWW2+dcZtoNIpoVFlAh0L6c6FKxdxGH350+1q8cXwE/98VizSvw5p0s5UCFnuhwoRV70gYkVgCJ0fYDCsrhBXb0U5wF6QUjhUguU1Hh8JcJJlhMCQda3t9FmHlyx7tXYmlUFLp5CSGJ6MYi8QRZcOBG7QfvxE662vgcTkQS6Sw5cAgAKlvr65IokQQBDT5PRiciGI0HEub56bG7OeJ9cpNTie4M1Osx1BpsFJfFuoBVOb7nyAIgiAYtipADgaDAIDmZu1o4XA4jEceeQQ9PT3o7u7WvM7x48fR39+Pa665hl/W0NCAiy++GK+99prmbTZt2oSGhgb+k+2+y8HlS1vxlWuXZ/39MtmxOjYURkI1TJVRbGHVWudFW8ALUZT6rE7Lc4cWFDgcGFA5VtFkyYYDM5S0O/2eGy0GJ/RLARt0ZllV4sKyNaA8V6y/qrXOA68r/5I3KXJdEufP7O0HUJzBwGqMDAnON7xiIprApFwK6KdSQABKqS9zrKKJJBefuYYvEwRBEIQdsY2wSqVSuPvuu7Fu3TqsWrUq7XcPPvgg6urqUFdXh2eeeQbPP/88PB7tE29/v7QI6+joSLu8o6OD/y6Te+65B8FgkP+cOnXKgkdUGuY2+uBzOxFLpngZnhozM6zyhblWWw4OIpES4XE6CuqvYahLhdgMq2IPB2ZoxYgbZWgiR3iFj/VYaaUCyqVmNZUjrFjww/BkFGfHWSJg4a8/Kwd89egwgOL1VzEMCSvT4RXS9SamE4jIwoocKwnuWMliij23gqCUUBIEQRBEJWEbYbVx40bs3bsXP/3pT2f87uMf/zjefvttbN++HcuWLcNHPvIRS/ulvF4v6uvr034qBYdDwFK5HFArwII3gxexZ4ElAz4rOwvzmn05hwsbgZUCHhsKYyqehNspoNuC3i0jMLdpOI8eq1yOlV6PVUU6VrzHKoqzocL7qxgswCKelGLci5UIyDAjrIx+nrhjNR1HWBYQ7H092/F701MB1ZsKDgu+PwiCIAii1NhCWN155514+umnsXXrVsybN2/G7xsaGrB06VKsX78ev/jFL3Dw4EFs3rxZ8746OzsBAAMDA2mXDwwM8N9VG0vbswdYsLkwxUzZOkde8B4blmdYWSR+mGN1RC4DXNBSW7L4XB5eYdKxmo4n+eI7e3iFHLeukQoYNBmOYAfUZZP9cilgIcOBGZnlpCuLNMOKYURY8TlLpsMrVKmAXioFBGY6VqXYBCIIgiCIYlJWYSWKIu68805s3rwZW7ZsQU9Pj6HbiKKYFjahpqenB52dnXjxxRf5ZaFQCK+//jouvfRSy47dTugFWARLsFg5J8NJsKK/ClDS09iA41IlAgIqx8qksGLX9zgdWRffvBRQMxVQHhDsqxxXo0UWViMWlwKyIcGAJLK7m4rrVnJhpTPLymyPFRNWk9EEd6xqybECMNOxqkS3liAIgiDUlFVYbdy4EU888QSefPJJBAIB9Pf3o7+/H1NT0q73sWPHsGnTJuzcuRMnT57Eq6++ig9/+MPw+Xy44YYb+P2sWLGCO1iCIODuu+/Gt771LTz11FPYs2cPbrvtNsyZMwc333xzOR5m0WEBFoc1HaviL1Z6WmvThg9bVa6X2eRfquAKQOXCTJgLr1CXAQqCdjkTc6yCGj1Wlbi4ZO6eFF7BSgGtcKyU99HyzkDRy8O4sMoSWJJMiZiQRYDRnkWlxyrOBYSfHCsA2R2rSnrvEwRBEISasm6dPvTQQwCADRs2pF3+yCOP4Pbbb0dNTQ1eeuklPPDAAxgbG0NHRwfWr1+PV199Fe3t7fz6hw4d4omCAPBXf/VXCIfDuOOOOzA+Po7LL78czz77LGpqCl/s2RHWY3VseBLxZCqtXE6ZY1W88AqX04HlHQHsOSO9BlaVAvrc6QvQRWUQViPhKERRzCqSMhnK0V8FKO7hmE4pYCUtLtVBH2wWlBU9Vl0NPnicDsSSqaL3VwG5HauJ6Th3T82mAk5OK7OayLGSyJxjVexh5gRBEARRbMp6hhfZKiULc+bMwe9+9zvT9yMIAu6//37cf//9BR1fpTC30YdajxPhWBInRsJY0q70opRq4ObKLpWwsmCGFQDUZqSnlbIUsEV2YeJJEcGpuOHFXq7gCkApBQxOxZFKidyJmY4nEZNnQFVSjxV7rqKJFE6NWddj5XQI6G724ehQGCuLHLUOAM3+7PPFAMVR8bmdaQ6tHuoeK/Y6Z76vZyvseWBzrJRNBXp+CIIgiMrEFuEVRGEIgoAlHTMDLERRLFlDuNpRKFYpYCkdK6/LyV2JIRPJgENsOLCOsGJzrFIieGkZoKSiOQSgroJcDb/HxV+rZEra5OiwIG4fAD58YTcWtPjxvpUdua9cIE05wiue2HECgLmNgzrWYxWj8IpMMh2rYIQF7ZBjRRAEQVQmJKyqhGXtMwMswrEkEvJCt9iLldVzGwBI7lmN25qFo08lrNoC3pKXx+WTDMiuq+dYeV1OvqhU91mpEwErLW6alQMC0lwrq94Dn79yMbZ/9SrMbSy8tDAXbB7XWCSGVCrdBd9zOogfvXIcAPDX168wfJ9sHpkogn8WybGS4I4V67EqkbtOEARBEMWChFWVsIw7VoqwYv1VHpcDNe7ivtQXLGjCvTeswHf/9DzL7tOvWpwvai1dGSBDHSNulMGQ/nBghpIMqNx3aLryhgMzWDkgYE0iYDlg5Z4pMX3GWCKZwtd+uRspEfjjNXNw1Yr2bHcxA6/LAVeGSPZbJDorHba5EImlpwJWUhksQRAEQaghYVUlLOWR60opIO+v8rkNhy/kiyAIuGP9Yqxb0mrZfbqcDt7Lsri9dGWAjNY8hgQzx0qvFBAAGvgsq5mOVSUFVzDUjpUV/VXlwONy8J4odYDFj145jn19ITT43Pj6B88xdZ+CIPD7BGShVaJZbHaHpwJGM+ZYVeD7nyAIgiAAElZVA3OseofDPAChFDOsik2tvKtdyqh1RpssFsyUAjLHSq8UENCeZVXZwkpxrKxIBCwXmUOCT41G8P3n3wUA/O8bVuZ8XbUIqBzIOioD5PA5VrEERFHkPYaV+P4nCIIgCICEVdXQ1VCDgNeFRErE8eEwAFXPQgU3g/vlXe1FJUwEZLSZdKxSKZEPCG6vzyGsZLE7rnJGQlOVNxyY0VKrPN5KLQUE0oWVKIq4d/MeTMdTuGRRMz584by87lMtpmiGlQJzrFKilChJcesEQRBEpUPCqkqQkgHTAyz4wM0Kdqz+/NIFuGJpKy5d1FLyv60MvjUmrMYiMR5QoBYaWijCqhodqwoWVn5FWP16Vx9eOjwMj8uBb//J6rzLadWlgDTDSkE9p24ymijZaAiCIAiCKBZ0lq8ilrUH8PbJcRxmwmqKxRdX7kLl81cuxuevXFyWv202vILNsGqu9eScc9So02NVmeEV6h6ryi8FPDY0if/31hkAwF3vW1JQ1H+asKJSQI7DIcDvcSISS2IwFOVR/ZW4sUAQBEEQAAmrqiIzwIL1WNFCJT8UYWXMsWLzrnIFVwBZUgErOBWtGsIrAEVYPfJKLxIpEcs7ArhjfWHCXt1jlTmbbbbj97gQiSXRNy4Nlva6HJZF9RMEQRBEqaFSwCqCR64PppcCUmlNfvAeq8koRFHMcW3FsTIScMBeE605VpUohFurIG4dUIRVIiVCEIBvf2h1TvcxF+oeKwqvSIcNS+4LSsKKvqsIgiCISobO8lUEE1YnRiKIJpLcDWmgZvC8YLOZ4kkRwal4zqb6wYlpAMaEVYMcKKKVCliJjtWCllqs6AxgjoUDostBU63yGv/5JQtwwYKmgu9TXQropx6rNNjz0TcufXYqcVOBIAiCIBh0lq8iOuq9CNS4MDGdwLGhMM2FKRCvy4n6GhdC0wkMT0ZzCquhPByrMXUq4LSUCliJi0uPy4FnvnRF0eelFZv5zX4AQGd9Db563XJL7rMurceqckVnMWDjFFgpYCUnmBIEQRAElQJWEYIgKOWAAxOUsmUBbEjw0ETuAItB3mOVuxROqxSw0uf4VLqoAoCLe5rxwEfPx88+d0lab1QhqO+HwivS8cnC6qxcCliJbi1BEARBMEhYVRnL5ACLwwOTirCiXeC8MRNgYS68QikFZP1bSiogLb7LhSAIuPk9c7Ggxbq5aQGvOm6dHCs1tRmlgLQJRBAEQVQyJKyqjKXtimNF4RWF08YdK+PCykwpYDIlYjKaQCKZwmS0cksBiexQj1V22MDk/pAsrOi9TxAEQVQwJKyqDFYKuK8vhKl4EkBlDwguN20mHKtBeXFoxLGqcTtR45Y+fuOROCbk/iqAyqGqDUoFzA5zrGiGFUEQBFENkLCqMlgp4Bm5GdzpENJKkQhzsBjxXMIqHE0gHJOErBHHClDKAYNTcV4G6Pc44XbSx7KaSJtjReEVaWQ+H+SuEwRBEJUMreCqjLaAN23Xt8HnropQgXKh9Fjph1ew4Aqf22nYlWCLyPFIHKHpyg6uILITSEsFpE0ONbUZpZE0GoIgCIKoZEhYVRlSMmAd/zf1LBSG0R6r/X0hAMDi9lrDQpaJqLFIrKKHAxP6pAkr6rFKw58R5kHvf4IgCKKSIWFVhSyV+6wA6tcpFKOpgLtPjwMA1sxrNHzf3LFSlQLWWxTxTdgHtYOZKSRmO5kOHm0EEQRBEJUMCasqZFm7yrGinoWCYHOsRiZjPBZdi12nxgEAa7obDd93k1z2FIzEEJqSwitICFcfLqeDOzFNtVTqpoYcK4IgCKKaoLqUKmSZyrGiHeDCaJEXwrFkCqGphGbCYjIlYs+ZIADgfBPCqkHVY+V0SHsctLCsTr5zy3noG5/C3EZfuQ/FVmSWRtJGEEEQBFHJkLCqQtSlgI3UDF4QNW4nAjUuTEwnMDQZ1RRWRwYnEYklUetxYnFbnca9aKMeEuySkwDrffSRrEauX9VZ7kOwJepUQEFIT1AkCIIgiEqDSgGrkNY6D5pkAUAOSOHkCrB4R+6vWjW3AU6H8QRGSgUkZjtqxyrgdZn6/BAEQRCE3SBhVYUIgsBdKyqtKZxcARbvyP1VZsoAAaVMc5xSAYlZSq3KsSJ3nSAIgqh0qO6oSrn9soWIJVJ434r2ch9KxdOWS1ixRECTwqpBlQrok5v4KRWQmE34VY4VbQIRBEEQlQ4JqyrlhtVduGF1V7kPoyporZN20rWE1XQ8iYNnJwAA581rMHW/vMcqEketLKzIsSJmE+pSQHrvEwRBEJUOCSuCyAErBdTqsdp/NoRESkRrncd04ltTrbSQDE7FUCeXRGmFYxBEteJTxa2TsCIIgiAqHeqxIogcsPCK4cnYjN+x/qo18xohCOYa75ljFU+KOBucBkClgMTswuNywOOkUQMEQRBEdUDCiiByoBde8U4eg4EZNW4HPC7pIxhNpADQ4pKYfbDIdeqxIgiCICodElYEkYNW5lhplAK+c1oaDGy2vwqQ0hszBzjTHCtitsH6rJiDSxAEQRCVCgkrgsiBEl4RgyiK/PJgJI7jw2EAUilgPqh36d1OAT63U+faBFF9+Cm4hSAIgqgSSFgRRA7+//buPajqOv/j+OvI5QByAAUBUREwQs0bafoz87KJSmNOajbZYOlurbMt5C3btd0xm3WUbLed0nW1bXbQ0qStjd2idNcFwWiUEDU1S2u9UCreWAQEATmf3x/pyaOoxFHOQZ+PmTMj38+n7/f9dd4pLz/f74eLjwLWNdhVUXPecXzXkXJJUtfQALVr27x/bb/0X+mD/X1+9HtaQGt3MVCFBrJiBQBo3XjuCLgOPx8v2fy8VXnuvE5W1Tp27rt044rmunTFio0rcDuaOyZBuV+d0H3xYe4uBQAAlxCsgCboEGhV5bnzOlVVqzvCAyW59n7VRU7BikehcBv6v7hQ/V9cqLvLAADAZW59FDA9PV333HOPbDabwsPDNX78eO3bt88xXlZWpmeeeUYJCQny9/dXdHS0ZsyYoTNnzlzzvNOmTZPFYnH6JCcn3+zbwS3s8p0BjTHaeWHFql8zdgS8KCTA+VFAAAAAtE5uDVb5+flKTU3V1q1btXHjRtXX12v06NE6e/b7DQGOHj2qo0eP6g9/+IP27NmjVatWacOGDXryySeve+7k5GQdO3bM8Vm3bt3Nvh3cwsJsFzawuLAzYGnFOZ2srJVXG4vuimr+itWlYYoVKwAAgNbLrY8CbtiwwenrVatWKTw8XMXFxRo2bJh69eqlv//9747xbt26adGiRZoyZYrOnz8vb++rl2+1WhUZGXnTasftpcOFFauTF1asLr5flRBhk79v83fyu/RRwGC2WgcAAGi1PGpXwIuP+LVv3/6ac4KCgq4ZqiQpLy9P4eHhSkhI0NNPP63Tp09fdW5tba0qKiqcPsClHI8CVtZJ+uH9qr5dmr9aJV25KyAAAABaJ48JVna7XbNmzdKQIUPUq1evRuecOnVKCxcu1PTp0695ruTkZL355pvKycnRkiVLlJ+frwceeEANDQ2Nzk9PT1dwcLDj06VLF5fvB7cWxw8JvmzFypUdASWpHbsCAgAA3BI85tmj1NRU7dmzRwUFBY2OV1RUaOzYserZs6defPHFa55r8uTJjl/37t1bffr0Ubdu3ZSXl6eRI0deMf/555/XnDlznK5FuMKlLt28wm432uVYsQpx6bzBTo8CEqwAAABaK49YsUpLS1N2drY2bdqkzp07XzFeWVmp5ORk2Ww2ZWVlycfnx30DGhcXp7CwMH3zzTeNjlutVgUFBTl9gEt1uLBidbKyVgdOVamq9rz8fNoo/sLW683FroAAAAC3BrcGK2OM0tLSlJWVpdzcXMXGxl4xp6KiQqNHj5avr68++OAD+fn5/ejrfPfddzp9+rQ6dux4I8rGbSgs8MKugFV12vnt96tVvTsFy9vLtf+FQtgVEAAA4Jbg1mCVmpqqNWvW6O2335bNZlNpaalKS0tVU1Mj6YdQdfbsWf31r39VRUWFY86l70t1795dWVlZkqSqqio999xz2rp1qw4dOqScnBw99NBDuuOOOzRmzBi33Cdav4uPAtY12FXw9UlJrr9fJUkBvl7y8bJIYsUKAACgNXPrO1YrVqyQJI0YMcLpeEZGhqZNm6bt27ersLBQknTHHXc4zTl48KBiYmIkSfv27XPsKOjl5aVdu3Zp9erVKi8vV1RUlEaPHq2FCxfKarXe3BvCLcvPx0s2q7cqa89r074LwcrF96skyWKx6O7odtp/vFJdQwNcPh8AAADcw63ByhhzzfERI0Zcd87l5/H399e//vUvl2sDLhdms6qy9rzO1NRLujErVpK09qlBqmuwK8DXY/aSAQAAwI/kEZtXAK3BxR8SLH2/TXqX9v435LzeXm0IVQAAAK0cwQpoojDbDzv49e0SIovF4sZqAAAA4EkIVkAThV2yYnWjHgMEAADArYFgBTSRU7DqEuzGSgAAAOBpCFZAE138IcGS1IcVKwAAAFyCYAU0UfiFYNUpxN9p9QoAAABgKzKgie7tFqbx/aKU1DPC3aUAAADAwxCsgCby9/XSq5MT3V0GAAAAPBCPAgIAAACAiwhWAAAAAOAighUAAAAAuIhgBQAAAAAuIlgBAAAAgIsIVgAAAADgIoIVAAAAALiIYAUAAAAALiJYAQAAAICLCFYAAAAA4CKCFQAAAAC4yNvdBXgiY4wkqaKiws2VAAAAAHCni5ngYka4GoJVIyorKyVJXbp0cXMlAAAAADxBZWWlgoODrzpuMdeLXrchu92uo0ePymazyWKxuLWWiooKdenSRd9++62CgoLcWgtaD/oGzUXvoDnoGzQHfYPmauneMcaosrJSUVFRatPm6m9SsWLViDZt2qhz587uLsNJUFAQf+jgR6Nv0Fz0DpqDvkFz0DdorpbsnWutVF3E5hUAAAAA4CKCFQAAAAC4iGDl4axWqxYsWCCr1eruUtCK0DdoLnoHzUHfoDnoGzSXp/YOm1cAAAAAgItYsQIAAAAAFxGsAAAAAMBFBCsAAAAAcBHBCgAAAABcRLDycMuXL1dMTIz8/Pw0aNAgffbZZ+4uCR4kPT1d99xzj2w2m8LDwzV+/Hjt27fPac65c+eUmpqq0NBQBQYG6uGHH9bx48fdVDE80UsvvSSLxaJZs2Y5jtE3aMyRI0c0ZcoUhYaGyt/fX71799a2bdsc48YYvfDCC+rYsaP8/f2VlJSkr7/+2o0VwxM0NDRo/vz5io2Nlb+/v7p166aFCxfq0v3T6B1s3rxZ48aNU1RUlCwWi/7xj384jTelR8rKypSSkqKgoCCFhIToySefVFVVVYvdA8HKg73zzjuaM2eOFixYoO3bt6tv374aM2aMTpw44e7S4CHy8/OVmpqqrVu3auPGjaqvr9fo0aN19uxZx5zZs2frww8/1Lvvvqv8/HwdPXpUEydOdGPV8CRFRUV6/fXX1adPH6fj9A0u97///U9DhgyRj4+P1q9fr7179+qVV15Ru3btHHNefvllLV26VCtXrlRhYaHatm2rMWPG6Ny5c26sHO62ZMkSrVixQn/605/05ZdfasmSJXr55Ze1bNkyxxx6B2fPnlXfvn21fPnyRseb0iMpKSn64osvtHHjRmVnZ2vz5s2aPn16S92CZOCxBg4caFJTUx1fNzQ0mKioKJOenu7GquDJTpw4YSSZ/Px8Y4wx5eXlxsfHx7z77ruOOV9++aWRZLZs2eKuMuEhKisrTXx8vNm4caMZPny4mTlzpjGGvkHjfv3rX5v77rvvquN2u91ERkaa3//+945j5eXlxmq1mnXr1rVEifBQY8eONT/72c+cjk2cONGkpKQYY+gdXEmSycrKcnzdlB7Zu3evkWSKioocc9avX28sFos5cuRIi9TNipWHqqurU3FxsZKSkhzH2rRpo6SkJG3ZssWNlcGTnTlzRpLUvn17SVJxcbHq6+ud+qh79+6Kjo6mj6DU1FSNHTvWqT8k+gaN++CDDzRgwAA98sgjCg8PV2Jiot544w3H+MGDB1VaWurUN8HBwRo0aBB9c5u79957lZOTo/3790uSPv/8cxUUFOiBBx6QRO/g+prSI1u2bFFISIgGDBjgmJOUlKQ2bdqosLCwRer0bpGr4Ec7deqUGhoaFBER4XQ8IiJCX331lZuqgiez2+2aNWuWhgwZol69ekmSSktL5evrq5CQEKe5ERERKi0tdUOV8BSZmZnavn27ioqKrhijb9CYAwcOaMWKFZozZ45+85vfqKioSDNmzJCvr6+mTp3q6I3G/t6ib25v8+bNU0VFhbp37y4vLy81NDRo0aJFSklJkSR6B9fVlB4pLS1VeHi407i3t7fat2/fYn1EsAJuEampqdqzZ48KCgrcXQo83LfffquZM2dq48aN8vPzc3c5aCXsdrsGDBigxYsXS5ISExO1Z88erVy5UlOnTnVzdfBkf/vb37R27Vq9/fbbuuuuu7Rz507NmjVLUVFR9A5uKTwK6KHCwsLk5eV1xS5cx48fV2RkpJuqgqdKS0tTdna2Nm3apM6dOzuOR0ZGqq6uTuXl5U7z6aPbW3FxsU6cOKG7775b3t7e8vb2Vn5+vpYuXSpvb29FRETQN7hCx44d1bNnT6djPXr0UElJiSQ5eoO/t3C55557TvPmzdPkyZPVu3dvPf7445o9e7bS09Ml0Tu4vqb0SGRk5BUbvJ0/f15lZWUt1kcEKw/l6+ur/v37Kycnx3HMbrcrJydHgwcPdmNl8CTGGKWlpSkrK0u5ubmKjY11Gu/fv798fHyc+mjfvn0qKSmhj25jI0eO1O7du7Vz507HZ8CAAUpJSXH8mr7B5YYMGXLFj3PYv3+/unbtKkmKjY1VZGSkU99UVFSosLCQvrnNVVdXq00b5285vby8ZLfbJdE7uL6m9MjgwYNVXl6u4uJix5zc3FzZ7XYNGjSoZQptkS0y0CyZmZnGarWaVatWmb1795rp06ebkJAQU1pa6u7S4CGefvppExwcbPLy8syxY8ccn+rqasecX/ziFyY6Otrk5uaabdu2mcGDB5vBgwe7sWp4okt3BTSGvsGVPvvsM+Pt7W0WLVpkvv76a7N27VoTEBBg1qxZ45jz0ksvmZCQEPPPf/7T7Nq1yzz00EMmNjbW1NTUuLFyuNvUqVNNp06dTHZ2tjl48KB5//33TVhYmPnVr37lmEPvoLKy0uzYscPs2LHDSDJ//OMfzY4dO8zhw4eNMU3rkeTkZJOYmGgKCwtNQUGBiY+PN4899liL3QPBysMtW7bMREdHG19fXzNw4ECzdetWd5cEDyKp0U9GRoZjTk1NjfnlL39p2rVrZwICAsyECRPMsWPH3Fc0PNLlwYq+QWM+/PBD06tXL2O1Wk337t3NX/7yF6dxu91u5s+fbyIiIozVajUjR440+/btc1O18BQVFRVm5syZJjo62vj5+Zm4uDjz29/+1tTW1jrm0DvYtGlTo9/TTJ061RjTtB45ffq0eeyxx0xgYKAJCgoyP/3pT01lZWWL3YPFmEt+7DUAAAAA4EfjHSsAAAAAcBHBCgAAAABcRLACAAAAABcRrAAAAADARQQrAAAAAHARwQoAAAAAXESwAgAAAAAXEawAAAAAwEUEKwBAq5KXlyeLxaLy8vIWud7jjz+uxYsXt8i15s2bp2eeeaZFrgUAuLEsxhjj7iIAALiaESNGqF+/fnr11VclSXV1dSorK1NERIQsFstNvfbnn3+u+++/X4cPH1ZgYOBNvZYknTp1SnFxcdq5c6fi4uJu+vUAADcOK1YAgFbF19dXkZGRNz1USdKyZcv0yCOPtEiokqSwsDCNGTNGK1asaJHrAQBuHIIVAMBjTZs2Tfn5+XrttddksVhksVi0atUqp0cBV61apZCQEGVnZyshIUEBAQGaNGmSqqurtXr1asXExKhdu3aaMWOGGhoaHOeura3V3Llz1alTJ7Vt21aDBg1SXl6eY7yhoUHvvfeexo0b51TTn//8Z8XHx8vPz08RERGaNGmSY8xutys9PV2xsbHy9/dX37599d577zn991988YUefPBBBQUFyWazaejQofrvf//rGB83bpwyMzNv4O8iAKAleLu7AAAArua1117T/v371atXL/3ud7+T9H0wuVx1dbWWLl2qzMxMVVZWauLEiZowYYJCQkL08ccf68CBA3r44Yc1ZMgQPfroo5KktLQ07d27V5mZmYqKilJWVpaSk5O1e/duxcfHa9euXTpz5owGDBjguM62bds0Y8YMvfXWW7r33ntVVlamTz75xDGenp6uNWvWaOXKlYqPj9fmzZs1ZcoUdejQQcOHD9eRI0c0bNgwjRgxQrm5uQoKCtKnn36q8+fPO84xcOBAfffddzp06JBiYmJu0u8sAOBGI1gBADxWcHCwfH19FRAQoMjISEnSV199dcW8+vp6rVixQt26dZMkTZo0SW+99ZaOHz+uwMBA9ezZUz/5yU+0adMmPfrooyopKVFGRoZKSkoUFRUlSZo7d642bNigjIwMLV68WIcPH5aXl5fCw8Md1ykpKVHbtm314IMPymazqWvXrkpMTJT0/QrY4sWL9Z///EeDBw+WJMXFxamgoECvv/66hg8fruXLlys4OFiZmZny8fGRJN15551O93KxnsOHDxOsAKAVIVgBAFq9gIAAR6iSpIiICMXExDi9GxUREaETJ05Iknbv3q2GhoYrQk1tba1CQ0MlSTU1NbJarU7vco0aNUpdu3ZVXFyckpOTlZycrAkTJiggIEDffPONqqurNWrUKKdz1tXVOcLXzp07NXToUEeoaoy/v7+k71fhAACtB8EKANDqXR5ULBZLo8fsdrskqaqqSl5eXiouLpaXl5fTvIthLCwsTNXV1aqrq5Ovr68kyWazafv27crLy9O///1vvfDCC3rxxRdVVFSkqqoqSdJHH32kTp06OZ3TarVK+iE0XUtZWZkkqUOHDk26dwCAZyBYAQA8mq+vr9OmEzdCYmKiGhoadOLECQ0dOrTROf369ZMk7d271/FrSfL29lZSUpKSkpK0YMEChYSEKDc3V6NGjZLValVJSYmGDx/e6Dn79Omj1atXq76+/qqrVnv27JGPj4/uuusul+4RANCyCFYAAI8WExOjwsJCHTp0SIGBgY5VJ1fceeedSklJ0RNPPKFXXnlFiYmJOnnypHJyctSnTx+NHTtWHTp00N13362CggJHsMrOztaBAwc0bNgwtWvXTh9//LHsdrsSEhJks9k0d+5czZ49W3a7Xffdd5/OnDmjTz/9VEFBQZo6darS0tK0bNkyTZ48Wc8//7yCg4O1detWDRw4UAkJCZKkTz75REOHDm3S6hYAwHOw3ToAwKPNnTtXXl5e6tmzpzp06KCSkpIbct6MjAw98cQTevbZZ5WQkKDx48erqKhI0dHRjjlPPfWU1q5d6/g6JCRE77//vu6//3716NFDK1eu1Lp16xyrSwsXLtT8+fOVnp6uHj16KDk5WR999JFiY2MlSaGhocrNzVVVVZWGDx+u/v3764033nBavcrMzNTPf/7zG3KPAICWYzHGGHcXAQCAJ6qpqVFCQoLeeecdx05/N9P69ev17LPPateuXfL25qESAGhNWLECAOAq/P399eabb+rUqVMtcr2zZ88qIyODUAUArRArVgAAAADgIlasAAAAAMBFBCsAAAAAcBHBCgAAAABcRLACAAAAABcRrAAAAADARQQrAAAAAHARwQoAAAAAXESwAgAAAAAXEawAAAAAwEX/D9fZ5ufrHa/OAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from numpy.random import randn\n", + "\n", + "def compute_new_position(pos, vel, dt=1.):\n", + " \"\"\" dt is the time delta in seconds.\"\"\"\n", + " return pos + (vel * dt)\n", + "\n", + "def measure_position(pos):\n", + " return pos + randn()*500\n", + "\n", + "def gen_train_data(pos, vel, count):\n", + " zs = []\n", + " for t in range(count):\n", + " pos = compute_new_position(pos, vel)\n", + " zs.append(measure_position(pos))\n", + " return np.asarray(zs)\n", + " \n", + "pos, vel = 23.*1000, 15.\n", + "zs = gen_train_data(pos, vel, 100)\n", + "\n", + "plt.plot(zs / 1000.) # convert to km\n", + "book_plots.set_labels('Train Position', 'time(sec)', 'km')\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "b5bd61c7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos=pos, vel=15., count=100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.01, h=0.0001)\n", + "plot_g_h_results(zs/1000., data/1000., 'g=0.01, h=0.0001')\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "bd5645ea", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Ozv7que7evQs9PT00aNAAU6dORVJS0reERgghhBBCCCHlrswL6YpEIgwYMACpqal4+PAht33fvn0wMzODoaEhAgMD4eLigtatW+Ps2bNFnuv48eNQU1ODubk53r17h0WLFkFDQwNPnjyBvLy81P58Ph98Pp97nJ6eDhMTE1pIlxBCCCGEkB9cRS+kW+YEaurUqbh69SoePnwIY2PjIve7ffs2unfvjrCwMFhaWpbo3OHh4bC0tMTNmzfRvXt3qfZly5Zh+fLlUtspgSKEEEIIIeT7lp6ejsDAQAgEAlhZWZX7NJ6KTqDKNIRv+vTp8PT0xJ07d4pNngDAzs4OABAWFlbi81tYWEBXV7fIYxYuXIi0tDTuFhUVVfLgCSGEEEIIIZXu06dPmDx5MgwMDNCxY0d07doVRkZGGDhwIEJCQmQdXomVqogEYwwzZszAuXPncPfuXZibm3/1GH9/fwCAgYFBia/z8eNHJCUlFXmMsrIyVekjhBBCCCGkioiLi0PHjh2lOkhEIhHOnz+P27dv49atW2jVqpWMIiy5UvVAOTs7w93dHUePHoWmpibi4uIQFxeHnJwcAMC7d++wcuVK+Pr64v3797h48SLGjBmDTp06oWnTptx5rKyscO7cOQBAZmYm5s+fj6dPn+L9+/e4desW7O3tUa9ePfTu3bscnyohhBBCCCFEFiZPnswlT+rq6hg3bhxmzJjBDd9LT0+Ho6MjBAKBLMMskVLNgeLxeIVud3V1hZOTE6KiojBq1CgEBQUhKysLJiYmGDhwIBYvXiwx/pDH43HH5OTkwMHBAX5+fkhNTYWhoSF69eqFlStXok6dOiWKq6LHORJCCCGEEFKe0tLS4O7ujidPnkAgEMDa2hrjxo2DkZGRrEMrd+Hh4ahXrx4YY9DT08OzZ89gamoKQNyZ0r17d/j4+AAAzp49i4EDB37T9b7bIhLfE0qgCCGEEEJIVXH06FFMmTIFGRkZEtvl5eXx559/YtmyZUV2XFRF+/btw+TJkwEAK1aswF9//SXR7unpiV9++QWAuKdqz54933S9is4NSjUHihBCCCGEEFJ258+fx6hRo1BYH4ZQKMSKFSsgJyeHpUuXyiC6ipGZmcndL6yGQsFtWVlZlRLTt/imhXQJIYQQQgghJSMUCjFnzhwueRo6dCi8vb3x6tUrzJ8/n+t1WrVqFeLi4mQZarkqmCBduHBBqr3gtrp161ZGSN+EEihCCCGEEEIqwe3btxEREQEA6Nq1K44fP47WrVujUaNGWL9+PX7//XcAgEAgwKFDh2QYafn6+eefoaurCwA4ffo0lixZgtTUVPD5fBw8eBCrVq3i9h07dqyswiwxSqAIIYQQQgipBK9eveLujxo1Smqe05gxY7j7wcHBlRZXRVNWVpYYkrhy5UrUqFED6urqmDBhAlfRe9y4cahXr56swiwxSqAIIYQQQgipBIqKitz9tLQ0qfaC2wruWx04OztLzesSCoXc/aFDh2L37t2VHVaZUAJFCCGEEEJIJejQoQN3f9euXRJV+EQiETZu3FjovtUBj8fDsmXL8OrVK8yYMQMtW7aEjY0NRo4ciXv37uH48eNQVlaWdZglQmXMCSGEEEIIqSTt27fH48ePAQAWFhaYPHkyNDQ0cOjQIW4tpJo1ayIqKgpqamqyDLXKonWgSoASKEIIIYQQUhW8evUKHTp0QGpqaqHt8vLyOHPmDOzt7Ss3sGqkonMDGsJHCCGEEEJIJWncuDEePXqEzp07S7U1bNgQV69erfDkKSsrCwcPHsSECRPg5OSEjRs3IiEhoUKvWZ1QDxQhhBBCCCEy8OrVKzx+/BgCgQBNmjRB+/btpSrzlbczZ85g4sSJSElJkdiupKSEZcuWYcGCBRUeQ0Wr6NxAodzPSAghhBBCCPmqxo0bo3HjxpV2vcuXL2Po0KEQiURSbXl5eVi0aBEAYOHChZUWU1VEQ/gIIYQQQgip5kQiEWbNmsUlT/b29rh37x58fX0xY8YMbr9ly5bRcL6voB4oQgghhBBCqrm7d+/i3bt3AMQl0s+ePQs5OXFfSosWLQAA27dvR15eHg4fPox58+bJLNbvHfVAEUIIIYQQUs0FBgZy98eOHcslT585OTlx91++fFlZYVVJlEARQgghhBBSzSko/DfwLDs7W6o9Kyur0H2JNEqgCCGEEEIIqebatWvH3d+1a5dEEsUYw+bNmwvdl0ijMuaEEEIIIYT8ANq0aQNvb28AQIMGDTB16lRoaGjg0KFDePDgAQBAR0cHHz9+hLq6uixD/SYVnRtQAkUIIYQQQsgPIDAwEB07dkR6enqh7TweDydPnsSQIUMqObLyVdG5AQ3hI4QQQggh5AfQtGlT3L9/H3Z2dlJtFhYWuHjxYpVPnioDzRAjhBBCCCHkB2FjY4OnT5/ixYsXePz4MQQCAZo0aYKuXbtKVeYjhaMEihBCCCGEkB9MixYtuPWfSOlQmkkIIYQQQgghJUQJFCGEEEIIIYSUECVQhBBCCCHkhxQUFARnZ2c0b94cTZo0wYgRI3Dnzh1UgyLVpAJRGXNCCCGEEPJDYYxh6dKlWLlyZaHtQ4YMgbu7O5SVlSs5MlIeqIw5IYQQQggh5Wj79u0SyROPx4OCwn+11U6fPo0pU6bIIjRSBVACRQghhBBCfhi5ubkSydOyZcuQkpKCrKwsuLq6QlVVFQDg5uaGt2/fyirMbyYSiRAaGornz58jNjZW1uFUK5RAEUIIIYSQH8bVq1eRmJgIAHB0dMTSpUuhra0NJSUlODk54a+//uL2PXz4sKzCLDORSIRdu3bBysoKVlZWsLW1haGhIXr27In79+/LOrxqgRIoQgghhBDyw4iIiODuDxgwQKq94Lb3799XRkjlRiQSYezYsXB2dpbqPbt58ya6desGDw8PGUVXfVACRQghhBBCfhgaGhrc/fDwcKn2gtsK7lsV7N27F+7u7tzjzp07Y/LkybCwsAAACIVCjBs3rtDnTUquVAnUmjVrYGtrC01NTejp6cHBwQGhoaES+3Tp0gU8Hk/i9rVJeIwxLFmyBAYGBlBVVUWPHj2q9JhTQgghhBDyferZsyd4PB4AYMeOHfjw4QPXlpmZiRUrVnCPe/fuXenxlRVjDFu2bOEenzp1Cnfv3sWePXvw5s0bODk5AQDy8/Oxe/du2QRZTZQqgbp37x6cnZ3x9OlT3LhxA/n5+ejVqxeysrIk9ps4cSJiY2O52/r164s97/r167Ft2zbs2bMH3t7eUFdXR+/evZGbm1v6Z0QIIYQQQkgRzM3NuWF6nz59QqNGjbhhb5aWlnj+/Dm3X//+/WUZaqm8e/cOb968AQB07NgRQ4YM4drk5eWxfv16yMvLAwAuX74skxirC4Wv7/Kfa9euSTx2c3ODnp4efH190alTJ267mpoa9PX1S3TOz9ny4sWLYW9vD0A8Ya9OnTo4f/48hg8fXpoQCSGEEEIIKdbevXsRHByMt2/fIjs7W6pYhLa2Nk6dOiVR2vx7l56ezt1v0KCBVHvt2rVRq1YtJCQkICMjozJDq3a+aQ5UWloaAKBmzZoS2z08PKCrqwtra2ssXLgQ2dnZRZ4jIiICcXFx6NGjB7dNW1sbdnZ2ePLkybeERwghhBBCiJQ6derg8ePHmDp1KtTV1bnt8vLyGDx4MLy9vdGyZUsZRlh6xsbG3P0bN25AIBBItL948QIJCQkAABMTk0qNrbopc1otEonw+++/o3379rC2tua2jxgxAmZmZjA0NERgYCBcXFwQGhqKs2fPFnqeuLg4AOI3ckF16tTh2r7E5/PB5/O5xwUzbkIIIYQQQr5GV1cXu3btwrp16/Dy5UsIBAJYWVlBT09P1qGViZ6eHvr06YNr167hw4cPGDduHDZu3Ig6derg+fPnGDt2LLfvmDFjZBipWG6+EDl5QtRQV5J1KKVW5gTK2dkZQUFBePjwocT2SZMmcfebNGkCAwMDdO/eHe/evYOlpWXZIy1gzZo1WL58ebmcixBCCCGE/Lg0NTXRrl07WYdRLhYvXowbN25AKBTC3d0dR48eRY0aNZCUlMTtY2FhgdGjR8swSiAxkw/7HY+Qmp2HE5PbwtpIW6bxlFaZhvBNnz4dnp6euHPnjkR3YWHs7OwAAGFhYYW2f54rFR8fL7E9Pj6+yHlUCxcuRFpaGneLiooq7VMghBBCCCGkWmnfvj2OHj0KZWVlAOIRYwWTJ0tLS3h5eUkMW6xsQhHDrON+iE7NQVaeEFM9fJGWky+zeMqiVAkUYwzTp0/HuXPncPv2bZibm3/1GH9/fwCAgYFBoe3m5ubQ19fHrVu3uG3p6enw9vZG27ZtCz1GWVkZWlpaEjdCCCGEEEJ+dEOHDkVoaCgWLFgAa2trmJqaon379ti7dy8CAgJQr149mca39eYbPApLgqqiPIx0VBGVnIP5pwLAGJNpXKXBY6WIdtq0aTh69CguXLggUd1DW1sbqqqqePfuHY4ePYqff/4ZtWrVQmBgIGbPng1jY2Pcu3eP29/Kygpr1qzBwIEDAQDr1q3D2rVrcejQIZibm+Ovv/5CYGAggoODoaKi8tW40tPToa2tjbS0NEqmCCGEEEKqmMTERPj6+kIgEKBx48aoW7eurEMiFeBOaALGuT4DAGwd3gzmuuoYsvsJ8oQiLO7XEBM6WpTLdSo6NyhVD9Tu3buRlpaGLl26wMDAgLudOHECAKCkpISbN2+iV69esLKywty5czF48GBcunRJ4jyhoaFcBT8A+OOPPzBjxgxMmjQJtra2yMzMxLVr10qUPBFCCCGElIZIJEJoaCieP3+O2NhYWYfzQ4uJicHo0aNhZGSEPn36oH///jA3N0efPn0QEBAg6/BIOYpOzcHsE/4AgFFtTGHfzAhNjXXwV/+GAIC1V1/D90OyDCMsuVL1QH2vqAeKEEIIIV8jEomwZ88ebN26lVtwFAB69uyJxYsXS6xpSSpeVFQUOnTogMjIyELb1dXV4eXlhfbt21dyZKS85QlEGLr3CfyjUtHUWBunprSFsoJ4UV/GGGYe98elgBjoa6ng8swOqKWh/E3X+656oAghhBBCqiKRSISxY8fC2dlZInkCxGvmdOvWDR4eHjKK7sc0efJkLnnS0dGBs7MzXFxcYGZmBgDIysrC8OHDkZ9ftQoMEGl/XwmBf1QqtFUVsXNECy55AgAej4c1g5rAorY64tJz8fsJf4hE33f/DiVQhBBCCKn29u7dC3d3d+5xp06dMGnSJK4gllAoxLhx4xARESGrEH8ob9++xdWrVwEAhoaGCAkJwY4dO7B27Vq8fv2a63X6+PEjzp8/L8NIybfyDIyB2+P3AIDNQ21gUlNNah8NZQXsHtkSKopyePA2ETvuFF69+3tBCRQhhBBCqjXGGLZs2cI9PnXqFO7du4e9e/fizZs3cHJyAgDk5+dj165dsgnyB1Ow+rKzs7PE0jUqKipYvHgx9/jmzZuVGhspP+8+ZcLldCAAYGoXS3RvWKfIfRvoa2KVQxMAwD833+BRWGKlxFgWZV5IlxBCCCGkKnj37h03bK9jx44YMmQI16agoID169fjyJEjEAqFuHz5MjZs2CCrUH8YOTk53P3C1hQtuK3gvuT74fshGZOP+EJJXg4GOqow0Fb5/00VhjoqqKOlggVnXiIrTwg785qY2/Onr55zSEtjPItIxonnUZh13A+XZ3ZEHa3vr6gcJVCEEEIIqdbS09O5+wWXYfmsdu3aqFWrFhISEpCRkVHsuXJycnD+/HmEhIRASUkJnTp1QseOHcHj8co97urM0tKSu3/u3DmMGTNGov3s2bPcfQuL8iltTcrXPzfeIjEzDwAQk5Zb5H61NZWxfURzKMiXbODbcvvGCIxOQ0hsOqa4++LIeDtoKH9fKcv3FQ0hhBBCSDkr2Jtx8+ZNCAQCKCj89xXoxYsXSEhIAACYmJgUeZ79+/djwYIFSE6WLLXcpEkTuLm5oUWLFuUcefXVp08f1KlTB/Hx8Th//jzmzZuH+fPnQ11dHa6urli9ejUAcYGBsWPHyjha8qW38Rl4GJYIOR5wcKwtcvKFiEnNQWxaLmLTchCTKv6vQMiwc0QL6GmWvBdJRVEeu0a2gP2Oh/CLTMU4Vx+4jWsN9e8oiaIy5oQQQgip9vr27Ytr164BAEaNGoWNGzeiTp068PX1xZgxYxAcHAxAvObllClTpI7ftm0bZs2aVeT5NTU18fDhQzRt2rRinkA1dODAAUycOLHYfaZOnUrz0r5Di869xFHvSPRuXAd7R7eqkGsEfkzFyAPeyMgVoHXdmnAdZ1viJKqicwNKoAghhBBS7T169AidO3eGUCgEAMjJyaFmzZpITPxvorqFhQUCAwOhrq4ucWx8fDxMTU2RlyceruTo6IiRI0ciOTkZW7ZsQWCgeJJ8p06dcO/evUp6RtXD+vXrsXDhQohEIqk2Jycn7Nu3D4qKijKIjBQlLTsfdmtuIjdfhOOT2qCNRa1C90tNTUVGRgZ0dXWhqqpapmsFRKVi1MH/J1HmNeHqVLIkitaBIoQQQgj5Ru3bt4eHhweUlJQAiNeF+jJ58vLykkqeAMDV1ZVLnqZMmYKTJ0/C3t4e48aNw5MnT7j5PPfv3+d6skjJ/PHHHwgLC4OLiws6duyItm3bYtKkSXj27BlcXV0pefoOHX8Widx8ERoaaMHOvKZEG2MMZ86cQYcOHVCjRg2YmppCR0cHo0aNQlBQUKmvZWOigyPj7aCprACfiGT85vYM2XmC8noqZUY9UIQQQgj5YXz48AG7d+/G5cuXkZ6eDmNjY4wZMwajRo0qNHkCgMGDB3NFDYKCgtC4cWOJ9jVr1mDRokUAADc3N5qzQ6otgVCEzhvuIjo1B+sHN8VQ2//mDDLGMHfuXPzzzz+FHquiooKzZ8+ib9++pb6uX2QKxhz0QQZfgDYWNfGvky3UlIruiaIeKEIIIYSQcmJmZoa1a9fi5cuX+PDhAx49eoTJkycXmTwB4i+GnxUsPlHYtmrwuzQhRboZEo/o1BzUVFfCgGaGEm0eHh4SyZOVlRUcHBxQs6a4lyo3NxeOjo6Ijo4u9XWbm9bAofGtoaGsgKfhyRjv9hw5ecJvezLfgBIoQgghhJBiNG/enLu/b98+iba8vDy4urpyj6kSH6nO/n30HgDwa2sTqCjKc9sZYxLrp+3cuRPBwcE4d+4cIiMjYW9vDwDIysqS+hsqqRamNXDoN3ES9SQ8Cb+5PZNZEkVD+AghhBBCihEdHQ0zMzOuAMX48eO5IhIbN27E06dPAQB2dnbcfUKqm1cxaei37SHk5Xh45NIN+tr/lSaPiIjg1uuytbWFj4+PxLEfP36EqakpGGOwtrbGy5cvyxyH74dkjDnog6w8ITrU08Xh31pDTk5yHTYawkcIIYQQIkNGRkZYsWIF9/jgwYPo1q0bhgwZwiVMKioq2LZtm6xCJKTUGGNYdvEVxrs9w6cM/lf3d/t/71Nfa32J5AmAxNpozZo1kzrW2NgYenp6AMTV+b5FS7OaODy+NTRVFGDfzFAqeaoMlEARQgghhHzFwoULsXHjxkLnSpmbm+PGjRto3bq1DCL7sWVkZGDXrl3o0KEDLCws0KJFCyxfvhyxsbGyDu27d/xZFNwev8et1wkYeeApkjKLTqKSMvm4EBADABjX3lyq3cDAgLt///59qbmAr1+/Rnx8PABAX1//m2NvaVYT9+d3hWOrohe+rkg0hI8QQgghpITS0tJw/PhxBAcHQ0lJCZ07d0bfvn0hLy//9YNJuQoODkbfvn0RGRkp1aauro5Tp06VqeLbj+BjSjZ6/3MfWXlCKCvIgS8QwUpfE0cntkFNdSWp/XfcfouN19/Axlgb553bg8eT7vXp3Lkz7t+/DwD4/fffsWrVKqirq+P9+/cYPnw4vL29AQCbNm3CnDlzKvT50UK6JUAJFCGEEELIjyMlJQVNmzbFx48fuW01atRASkoK91hFRQVPnz6FjY2NLEL8bolEDKMOeuPxuyS0MquBtYOb4Nf93viUwUdDAy0cm2gHHbX/kqh8oQgd1t1GfDof/wyzwcDmxoWe18vLC3369OEea2howNTUFK9fv+YWStbX10dwcDBq1KhRoc+R5kARQgghhBBSwP79+7nkqVmzZvDz80NycrJExbfc3FysXbtWlmF+lzx8IvH4XRJUFOWwwdEG9fQ0cWyiHXQ1lBESm46RB7yRlp3P7X81KA7x6XzU1lRGvyaGRZ63d+/e2LlzJ9c7lZmZieDgYC550tPTw5UrVyo8eaoMlEARQgghhJAq5fDhw9z9EydOcIULTExMcOzYMejq6gIAzpw5g8zMTFmE+F2KSs7GmishAACXPlYw1xXP6fucRNVSV8KrmHSM/tcbaTniJMr1UQQAYKSdKZQUik8dpk2bhhcvXsDJyQm1a9eGsrIyLC0tsXz5cgQFBUksCVCV0RA+QgghhBBSpWhpaSEjIwOWlpYICwuTah86dChOnToFAAgLC4OlpWVlh/jdEYkYRhx4iqfhyWhtXhPHJ7aRqmAXGpeBX/c/RXJWHmxMdDC/VwOMOugNJXk5PFrQDbU1lWUUfenQED5CCCGEEEIK0NTUBADExsZK9TAxxvDmzRupfX90R55+wNPwZKgqymPjEJtCy3830NeExwQ76KgpIiAqFU6u4vWc+tsYVJnkqTJQAkUIIYQQQqqUn3/+GQCQnZ2NxYsXS5TNPnz4MAICAgAALVq04NYf+pF9SMrC2quvAQALf7aCaS21IvdtaKAFjwl20FZVhEAkfl3HtZMuXf4joyF8hBBCCCGVJCwsDFeuXEFGRgaMjY0xcOBA+u5SBoGBgWjevDlXoKBhw4bo1q0bAgIC8PDhQ26/w4cPY/To0bIK87sgEjEM3/cUPu+T0daiFjwm2JVo8dmg6DT85vYMLc1qYPeolpUQafmhMuYlQAkUIYQQQr5nCQkJmDhxIi5evCixXV1dHXPnzsXSpUshJ0cDg0pj165dcHZ2LrJ90qRJ2LNnT6FrFv1I/n0YgRWewVBTkofX751gUrPo3qcviUSsRMnW94bmQBFCCCGEVGEpKSno3LmzVPIEAFlZWVixYgWmTp0qg8iqtmnTpuHKlSvo0KGDxHYrKyvs27evSidPQqEQ586dQ79+/WBhYQErKytMmjSJG5pYUuGfMrHeSzx0b9HPDUuVPAGokslTZaAeKEIIIYSQCjRv3jxs2rQJAFC7dm3Mnj0bVlZWuHbtGg4cOMANQ7t37x46deoky1CrrMjISMTGxkJHRwc//fRTlU2cAPH3WgcHB9y5c6fQ9mXLlmHJkiVffY65+UI47nmCl9Fp6FBPF0fGt67Sr0tp0BC+EqAEihBCCCHfIz6fDwMDA6SkpEBJSQnBwcESJbULDkMbNGgQOnTogCdPnkAgEMDa2hrjx4+HmZmZrMInlYwxhv79++PKlSvcNk1NTfD5fOTl5XHb9uzZg8mTJxd7nj9OB+KU70fUUFOE58yOMNJRrdDYvyeUQJUAJVCEEEII+R69fPkSTZs2BSBOkM6cOSPRzufzUbNmTWRnZ4PH4+HLr2VycnL4448/sHr1apoj9QPw8fGBnZ0dAKBmzZpwc3NDv379kJ2djU2bNmHZsmUAACMjI7x//x4KCgqFnsfD+wP+PBcEOR5w6LfW6Fi/dmU9he8CzYEihJDvCGMMFy9eRJ8+faClpQU1NTXY2dnhwIEDEr8OksoXHByMM2fO4NKlS0hISJB1OIQAADc8DwBUVFSk2hUUFLikqbDftEUiEdauXYslS5ZUXJDfOYFAAE9PT2zYsAFbt26Fv79/uV9j550wLDwbiCy+oNzPXRqHDx/m7q9btw6//PIL5OTkoKGhgaVLl6J///4AgOjoaNy+fbvQc7yITMGyi68AAPN7W/1wyVNloASKEEJKSCAQYPTo0bC3t4eXlxcyMjKQk5MDHx8fTJw4EZ06dUJKSoqsw/zhPHjwAG3btkXjxo0xZMgQDBgwAMbGxhg1ahTi4+NlGltSUhLWrVsHGxsb1K5dG/Xr18e8efMQEREh07hI5alXrx7U1MQT9y9evCiV3J88eRI5OTnc41GjRsHPzw9v377Fn3/+yfU6rVu3DjExMZUXeAX49OkTwsPDpRa+Lc7x48dRt25d/PLLL/jjjz/w+++/o3nz5mjfvj1CQkLKJa7LgbHY4BWKYz5RmOLuizyB6OsHVZDIyEjuft++faXaC26LioqSav+UwcdUd1/kCxn6WutjSmeLign0B1eqBGrNmjWwtbWFpqYm9PT04ODggNDQ0EL3ZYyhb9++4PF4OH/+fLHndXJyAo/Hk7j16dOnNKERQkiFW7JkCTw8PLjH+vr6sLD47x8nb29vjBgxQhah/bCuXLmC7t274+nTpxLb8/Pz4eHhgbZt2yI2NlYmsfn5+aFx48ZYsGABAgMDkZiYiLCwMGzatAkNGzaUGspFqid1dXWMHDkSAJCZmYlOnTrBw8MDvr6+WL16NcaNG8fta2Njg8OHD6NZs2aoV68eVq1ahTlz5gAQ/4Bz6NAhmTyHb8EYw/Hjx2FnZwc9PT1YWlqiRo0aGDZs2Fd7kg4cOIBff/0V0dHRUm2PHz9Ghw4d8Pr162+KLymTj78uBHGPH7xNxLxTARCJZDPDRVNTk7v/5s0bqfaC2wruCwD5QhGcj75AfDoflrXVscHR5ocpGlHpWCn07t2bubq6sqCgIObv789+/vlnZmpqyjIzM6X23bx5M+vbty8DwM6dO1fseceOHcv69OnDYmNjuVtycnKJ40pLS2MAWFpaWmmeDiGElFhaWhpTV1dnAJi8vDw7cuQIEwqFjDHG7t+/z3R1dRkABoD5+vrKONofQ0ZGBqtRowb3ujdq1IgtX76czZo1i+no6HDbhwwZUumxffr0ienp6XExAGCmpqZMQUGBe6yoqMiePXtW6bGRyvfx40dmYGAg8X4o7Hbw4EGpY/38/Lj20aNHyyD6shOJRGz69OlFPl9lZWV28eLFQo/99OkTU1FR4fbt06cPO3LkCNuyZQurV68et71Hjx7fFOM0d19m5uLJev9zj90MjmOWCy8zMxdPtvRCEBOJRN907rLw8PBgAJiciiZr3n8s++usHxu86xGbeewFO3HrGdPQ0OBeu0+fPkkcu/ziK2bm4skaL7nG3sZnVHrs35OKzg1K1QN17do1ODk5oXHjxrCxsYGbmxsiIyPh6+srsZ+/vz82bdqEf//9t8TnVlZWhr6+PnerUaNGaUIjhJAK5enpiaysLADA+PHjMWrUKG5oTceOHbFy5Upu32PHjskkxh+Nh4cHN2SyX79+CAgIwJIlS7BlyxYEBQVBV1cXAHD27Fl8/PixUmPbu3cvN1SrTZs2ePPmDT58+ICYmBiulzI/Px9r166t1LiIbBgZGeHevXto1qxZsfsVNgS44DYlJaXyDq1CHT58GDt27OAeN2nSBI6OjqhdWzwnh8/nY/jw4YX+fR46dAi5ubkAxCOVrly5glGjRmHWrFnw9fXlKhPevHmz0J6akrgcGIvLL2MhL8fDRkcbdG9YB5uG2gAA3B6/x66778p03rKIT8/FxYAYBCk3humkvTCZdQzJjR1x2Dsazz+k4IJ/DP64Hg+NQSuh3rgbRowaw33GAcAF/2j8+0g8NHjTUBvU09OotNh/RN80ByotLQ2AuErIZ9nZ2RgxYgR27twJfX39Ep/r7t270NPTQ4MGDTB16lQkJSV9S2iEEFKuCg4D69y5s1R7ly5duPtxcXGVEdIPr+AE6sWLF0tUozIyMsLEiRMBiCfh379/v1Jjc3d3BwDweDx4eHigfv36AMRrAP3777+oU6cOAOD8+fPIyMio1NiIbNSvXx8vXrzA7du3MXfuXEycOBHLly+XKFe9a9cu7rsVIF5Mdf369dzjqrRGFGOMW/sKAPbt24eAgACcPHkSHz58wODBgwGIvzfu3btX6vgnT55w92fPni0xFE1LSwvjx4/nHn85hLckEgsM3XPuYglrI20AgH0zIyz9pREAYINXKI77RBZ5jvIy5Ygv7P6+hZnH/HD02UfwahgBAPISI5HhdxWJl/9BZuB1iPL5UDaoD93+c+BvOgSbr4ciPj0XIbHpcDkTCACY3rUeejcu+fdvUjaF1z4sAZFIhN9//x3t27eHtbU1t3327Nlo164d7O3tS3yuPn36YNCgQTA3N8e7d++waNEi9O3bF0+ePIG8vLzU/nw+H3w+n3ucnp5e1qdBCCElUvCHIn9/f6m5Tn5+ftx9HR2dygrrh/b512kAMDAwkGovuK3gvpXh85wNS0tLiXlygHjERefOnXHy5EkIhUIkJCRIzWUg1ROPx0PXrl3RtWtXie0dO3bEgwcPEB4ejqZNm2LixInQ0NDA4cOHuc8WXV1dODo6IjY2Fm/evIGSkhKaNm0KdXV1WTyVr4qIiMDLly8BAK1bt+Z+0AAAVVVVbNu2DWfPngVjDOfPn5foxQfEyeNnn4twFFRwW8F9S2rphVdIzsqDlb4mpnerL9E2rr05EjP52HnnHRadewkdNSX0sa6YpCQgKhXXXsWBxwMaG2qhdd1aaG1eEzWEydiy1h2nb5+GQCBAVtAtyL28hHaj5yFW/SfEZ/Cx7XYYdt19B00VBeTmi9Dpp9qY3fOnComTfKGsY/+mTJnCzMzMWFRUFLftwoULrF69eiwj479xlyjBHKgvvXv3jgFgN2/eLLR96dKlhY6lpTlQhJCKEhcXxxQVFRkApq6uzp48ecK1vX//nllaWnKfRbdv35ZhpD+OuXPncq/5xo0bJdpEIhHr2LEj137v3r1Kjc3Y2JgBYCoqKiw1NVUqtsaNG3OxJSQkVGps5PsTEhLCatWqVeRcIQUFBbZ9+3bWv39/xuPxuO1aWlps1qxZUu+x74Gvry8X58SJEwvdp06dOgwAMzY2lmr766+/uOMXLVok0Zafn8+aNm3KtT9//rxUsXkGxDAzF09msfAye/mx8NdOJBIxl9MBzMzFk9X/8wp78i6xVNcoqfmn/JmZiyf7/bhfoe1JSUnMx8eH+fv7Mz6fzxhjLF8gZJcDY5jjnsfMzMWTmbl4sg7rbrGULH6FxFgVVfQcqDIlUM7OzszY2JiFh4dLbJ81axbj8XhMXl6euwFgcnJyrHPnzqW6hq6uLtuzZ0+hbbm5uSwtLY27RUVFUQJFCKlw48ePl/hS0759e9a7d28usQLAWrRoIZOJxz+ioKAg7nVXVVVl27ZtY8nJyezt27fst99+49rq16/PFfyoLFOnTpX48pifn88YE38p2759O9fWpk2bSo2LfL9CQ0NZz549pZInGxsbtmXLFqamplZkgtWkSZNSFd+qDDExMcX+Db569Yprt7W1lTr+/fv3TE5OjgFgPB6PzZ49mz1//px5eXmxHj16lPkz91NGLmu+4jozc/Fkm7xeF7tvvkDIJh56xsxcPJn1kmvsVXT5fs9Mzc5jDRZfYWYunuxZRFKZzhEUncq23HjD3idKF3T7kX1XCZRIJGLOzs7M0NCQvXnzRqo9NjaWvXz5UuIGgG3dulUq2SpOVFQU4/F47MKFCyXan6rwEUIqQ0ZGBuvQoUORX2LMzMxK9VlHvp2Tk9NXK5udOXOm0uMKDg7mfkT8/N4YM2YMs7GxkYjtxIkTlR4b+br09HT28OFDdvfuXRYXF1ep1w4NDWVubm7swIEDzNvbm2VlZXE9NQCYkZERmzFjBhs5ciRTVlbmto8ZM6ZS4yyJLl26cPFNnz6dpaenM8YYe/v2LWvVqhXX9s8//xR6/KJFi4r921ZUVGT3798vVUxT3Z9zVff4+V//YSUnT8D19DRb7sX8I1NKdb3iuD4MZ2YunqzX5nv0w1s5+64SqKlTpzJtbW129+5diZLj2dnZRV+gkCF8DRo0YGfPnmWMib+QzJs3jz158oRFRESwmzdvshYtWrD69euz3NzcEsVFCRQhpLLk5OSwTZs2SQzZ09XVZS4uLlIlZUnF4/P5bPTo0YV+uVJWVi60LHRlcXNz435BL+w2Z84c+tL0nUlISGCTJ0+W6O2Rl5dngwYNYiEhITKJyc3NjYulc+fOEt+5QkNDmZaWFpdMVHay9zXXr1+XGHKopqbG6tevL7HN0NCwyCGIIpGILVmyRKKX//OtTp06zMvLi9s3J0/ALgfGsFshcexDYhYTCqX/tkoydK8wqdl5bMD2B8zMxZM1+usqe/Dm2z/rRSIR677pLjNz8WSHH0d88/mIpIrODXiMMYYSKmoxLldXVzg5ORV5zLlz5+Dg4CCx7fMxOTk5cHBwgJ+fH1JTU2FoaIhevXph5cqVXJWir0lPT4e2tjbS0tKgpaVV0qdDCCFlxhhDQkICBAIB9PX1Cy14QyrPixcvcODAAQQHB0NJSQmdO3fG+PHjS1UNtiLcv38fa9euxbVr1/D5n9tWrVphzpw5GD58OC1y+R2Ji4tDx44dERYWVmi7trY2bt26hZYtW1ZqXCNGjOCWRrh3755UJb65c+di8+bNAIDjx49j2LBhlRrf1+zbtw9Tp06FSCSSajMwMMC1a9fQtGnTYs8RHx+Pw4cPIyQkBEpKSujUqRMGDx4MZWVlAEB0ag4mH3mOoOj/ioopK8jBorYG6ulpoF5tDdTVVcPyS8FIzsrDzG71MKdXg1I9j0y+AJOPPMejsCQoyvOwZVhz9GsqXbympLzDkzBs31OoKcnDe1F3aKoolvlcRFpF5walSqC+V5RAEUII+Z4lJiYiPj4eOjo6MDIyknU4pBAODg64cOECAEBdXR2Ojo7Q0NDAqVOnEB8fDwAwNzfHmzdvJErmV7QBAwbg0qVLAICoqCgYGxtLtO/cuRPTp08HABw4cECivPf3IigoCNu2bcPly5eRnp4OY2NjjBkzBpMmTUKtWrW+6dxPw5Pg7PECSVl50FFTRB1NFUQkZiFPKJ2wAYCVviYuTu8AJYXSr+TDFwgx+4Q/rrwUV81baW+NUW3MyhT3zGN+uBgQg19bm2DNoOITSFJ6FZ0bVN4nACGEEPKD0tXVlVj0knxfIiIicPHiRQCAnp4enj17BlNTUwDAmjVr0K1bNzx79gwRERG4dOkSBg4cWGmxmZubc/cvXryIadOmSbR/jhsA6tatW1lhlYq1tTX27dtXrudkjOHQ4/dYeTkEQhFDY0Mt7B3dEsY11CAUMUQlZyMsIRNhnzLx7v//zeYL8c+wZmVKngBAWUEe239tgRpqQfDwjsTi80FIzsrDjG71StWbnJjJx9Ug8dqCI+3KloAR2aIEihBCCCkGn8/H2bNn8fjxYwgEAjRp0gQjRoyg9b6qkRs3bnBDLJ2dnbnkCQA0NDSwZMkS/PLLLwAALy+vSk2gxo4di23btgEAFi5ciBo1asDR0RHp6elYu3Ytrl+/DgAwNTWVWNC7OsvNF+LPc0E48+IjAMChmSHWDGoKVSXxUGp5OR7q6qqjrq46eqBk00FKSl6Oh1UO1qilroRtt8Ow+cYbJGflYUn/RpCTK1kSder5R+QLGWxMdLgFfEnVQgkUIYQQUoTLly9j/Pjx3BCuz+bPn4+///4bM2fOpHlM1UBmZiZ3/8uFjwHJXqCsrKxKiemzFi1aYODAgTh37hzS09MxYsQIjB07Fvn5+RL7rVix4oeYixmbloMpR3wR8DENcjxg0c8NMb6DeaX+HfJ4PMzp1QA11ZWw7FIw3B6/R0p2HjYMsflq75ZIxHDU5wMAYKSdabH7ksKFhITg2LFjiImJgY6ODuzt7dGhQ4dKfQ9QAkUIIYQU4saNG7C3t4dQKJRqy87Oxu+//w6hUIg5c+bIIDpSnr4cJjdq1CiJdlkPkzty5AiGDh2KK1euAIBE8iQnJ4e1a9di7NixlR5XZfOJSMY0D18kZornO+34tQU61Jfd0Fin9uaooa6EuScDcME/Bjl5Quwa2QIK8kUnUQ/CEhGVnAMtFQX80tSwEqOt+jIyMvDbb7/h9OnTEts3bdqE1q1b4+TJkzAzq5whkVREghBCCPkCYwwNGzZEaGgoAKB3796YPXs21NXV4ebmhoMHDwIAlJWVER0d/c0T4asiX19fHDhwQKIy2vjx42FgUPbKZLLC5/NhbGyMxMREAMCSJUswe/ZsqKqqwsPDA9OnT0dOTg4A4O3bt6hXr16lx8gYw82bN7F//36J13zKlClo0KB0FeWqmpjUHPxz4w3OvPgIEQMaGmhh3+iWMKmp9tVjk5OT4ebmhkuXLiEjI4MrYDFgwIByKwZyNzQBk474Ik8gwqDmRtjoaFPkcL5Jh5/jenA8xrWvi6W/NC6X61c3z58/l/pscXJywtixY3Hnzp0ij6tbty58fHxQu3btis8NKqQ4eiWjdaAIIYSUp7t373LrzbRp04YJhZILbk6ZMoVr37x5s4yilI3c3Fw2cuTIQte2UlJSYgcOHJB1iGWybds2iefC4/EkFkMGwMaNGyfrMFm+QMgehX1ikUlZsg6lwqVk8dnfl4NZ/T+vMDMXT2bm4slmH/djWfz8Eh3v5eXFtLW1C32vNm/enEVHR5dbrNdfxTGLhZeZmYsnW3L+ZaFrvMWkZjPzBeLn8TY+vdyuXV0U99lS8G9RW1ubbdq0ifn5+bFDhw4xCwsLrm3u3LmMsYrPDcpWhoQQQgipxvz9/bn7v/32G+TkJP+5LFgqOiAgoLLC+i5MmTIFHh4ehbbl5eVhwoQJOHPmTCVH9e2mT5+OJUuWcI8ZYxLDNx0dHbF7925ZhAZAvNbR5htv0GHdHYzY741+2x4g8GOqzOKpSLn5Quy59w6d1t/B3vvhyBOI0Nq8Js5Oa4fNw5pBTenrPUd+fn6wt7dHWlpake19+vRBbm5uucTcs1EdbB5qAx4POPTkAzZdfyO1z3GfKIgYYGdeE/X0NMvlutXJ5MmTi/xsKfi3eOLECcyZMwfNmjXDmDFjcOfOHSgpKQEQr0375fzAikAJFCGEEPKFggkTn8+Xai+47cvkqjp79eoV3NzcAACqqqrYsWMHUlJSEBYWJpFULly4sNCFU79nPB4Py5cvR1BQEKZPn44WLVqgadOmGDFiBO7evYsTJ05wC7dWFoFQhOuv4jDO1Qcd1t3GtltvEZeeCzkekJ4rwKgD3tUqiRIIRTjxLBJdNtzF2quvkZ4rgJW+JlydbHFiUhu0MK1R4nOtXLmSS4769euH169fQygU4sqVK9w8mZcvX+LEiRPlFr99MyOstLcGAOy4E4a9995JPLfjzyIBACPLuHZUQfn5+Th9+jQGDRqENm3aoE+fPtizZw8yMjK++dyy8OrVKxw6dAiA5GfLu3fvMGHCBG4/BQUF9OjRQ+JYU1NT9OrVC4B4yGZ0dHSFx0tzoAghhJAvPHv2DK1btwYANG7cGM+fP4eKigoAcc/E8OHDcfLkSQDAnj17MHnyZJnFWpnmzZuHTZs2AQA2btyIuXPncm2MMXTu3BkPHjwAANy7dw+dOnWSSZxVXWxaDo56R+Lk8yjEp/+XrLezrIVfW5uiQz1dTDryHM/ep0BLRQHuE+zQ1FhHdgGXA6GIYdQBbzwJTwIAGOmoYk7Pn+DQ3AjyJSwP/llSUhL09PQgEolgYGCA8PBw7u8XAB48eMC9Nzt16oR79+6V3xMBsPvuO6y79hoAsHqgNUbamcHrVRwmH/FFLXUlPFnYvcxrUQFAZGQk+vfvj5cvX0q16enp4fz582jbtm2Zzy8LBT9bNm3aJFGchzEGJSUlCAQCAMDt27fRtWtXieN79uyJmzdvAgA+fPgAHR2dCs0NfpyfzQghhJASatWqFVq2bAlA/MuonZ0d9u/fj2PHjqFPnz5c8qSpqYkRI0bIMtRK9fbtW+7+kCFDJNp4PB4cHR25x2FhYZUWV3VyLSgWPTffx/bbYYhP56OWuhImd7bAnXldcHRiG/xiY4ga6kpwHdcatnVrID1XgJHVoCfqqE8knoQnQU1JHov7NcStuZ0xuKVxqZMnQPwF+nMPaN++fSWSJwDo0KEDV/glIiLi24P/wtQulpjWxRIAsPh8EC74R8P9qbh0+VBbk29KnjIzM9GzZ89CkycASEhIQJ8+fST+VquCgvEOHjxYoo3H40kUSvlymF9gYCBu374NADAyMoKxsXEFRipGCRQhhBDyBR6Phz179kBNTVzlKzAwEJMmTcKIESO4hUsBYPfu3dDU/HHmMhT8IhobGyvVXnDbl19aSfHyhSKs8gzGFPcXyOQLYGOsjZ0jWuDJwu5Y2LchzHXVJfbXUFbgkqiMKp5EJWXysdFLXPHSpY8VJnS0gIpi2de0Ulf/77WKjIyUak9LS0N6ejoA8XCxijC/dwOMbmMGxoA5JwPw4G0ieDzgV9tvW/vJzc0Nb96I51dZWlri2rVryM/Ph6+vL9er9nmR5aqk4P+Hwj5bGjVqxN13c3ODs7Mzzp49i6VLl6Jz585cwjx58uRKGVZNCRQhhBBSiFatWuHu3bto2rSpVJuRkRFOnTqFkSNHyiAy2enevTt3f+XKldyQGgD4+PEj9u/fDwCQl5en4XulEJ+eixH7n+LAQ3FvyMSO5jg9tR36NTUotreisCQqICq1kqIuP+uvhSItJx8NDbTKZXHZevXqcfOcbt68yfVOAOLhYMuXL+cKDfTs2fObr1cYHo+H5QMaY2BzIwhF4tkynerXhmmtr5deL86///7L3T99+jR69+4NBQUFtGjRAhcvXoS2tjYA4OjRo1zp/bLKyclBaGgoIiIiKnxOY7du3bj7hX22FPx/KBQKsWvXLgwePBgrVqxAamoqAPGi05W1Lh/NgSKEEEKKwRjDo0eP8PjxYwgEAjRp0gR9+/YttzVkZCUgIADbt2+Hp6cntz7O6NGjMWXKFOjqFr44aWZmJkxNTZGSkgIAaNiwIYYNG4akpCQcOXKE+yIzZMgQnDp1qrKeSpX2+F0iZh7zQ2JmHjSVFbDBsSn6WJduLa1MvgDjXH3w7H0KNFUU4D7eDjYmOhUTcDl7EZmCQbseAwBOT2mLVnVrlst5N27ciPnz5wMQF3oZOHAgGjZsiGvXruH58+fc9qCgIDRs2LBcrlkYgVCEmcf9cDUoDh7j7dCu3rct/KutrY309HSYm5sjPDxcqn3IkCFcFcx3797BwsKi1Nf48OED/v77b7i7uyM7OxsAYGZmhqlTp2LWrFkV0rv85WeLlZUVhg0bhuTkZBw+fJirpvjTTz8hKipKIjmUk5PD0KFDsXv3bujo6ACo+NyAEihCCCHkB7Nnzx5MmzYNhX0FqFOnDry8vGBjY1PosVeuXIGDg0ORpYItLCzw8OHDKrmgbmUSiRh233uHTddDIWKAlb4mdo9qKTVUr6S+TKL2jm6Jdpbf9mW9oglFDPY7HyIoOh2DWxhj09DC33NlkZ+fDwcHB1y5cqXIfbZv347p06eX2zWLwhhDBl8ALRXFbz6Xvr4+4uPjoampiYSEBKlkpk2bNvD29gYAxMTElPrvMDAwEN27d+cWlf5Sp06dcPXqVW54c3m6evUq7O3ti/1sefToEVRUVHDu3DnExsZCR0cH/fv3h6mpZM8lLaRbArSQLiGEEFIyXl5eEgtUqqurMysrK8bj8bhtBgYGLCUlpchzPHjwgLVr105qEd3Ro0ezuLi4ynsyVVRqVh77zdWHWxx2zgl/ls0XfPN5M3Lz2ZDdj7jzLjgTwFKz88oh4q/Ly8tjN27cYIcOHWIXLlxg6elfXyj2yJP3zMzFk1kvvcYS0nPLPSY+n8+WLVvGateuLfFebdasGTt37ly5X68yFFxoduXKlRJtnp6eXFujRo0KXcy3OHl5eczc3Jw7h4aGBnN0dGTdunWT+HxwdnYuz6ck4eHDh6x9+/ZSny1jxowp1WdLRecG1ANFCCGE/EC6du2Ku3fvAgBmzpyJv//+G+rq6oiIiMDw4cPh4+MDAPjnn3/w+++/F3uu4OBghISEQElJCW3atEHt2rUrOPqqLyM3H7/uf4qg6HQoKchh+YDGGG5rAh6v9NXmCpPFF2DV5WAc84kCANTWVMayXxrj5yb65XaNghhj2L59O9auXSsx+V9TUxOTJk3C6tWrC10/KzkrD1033kVaTj6W/dIITu3Nyz22z/h8Pp4/f4709HQYGxvD2tq6Ql6LyuDt7Y02bdpwjzt16oTu3bsjMDAQZ8+e5XqVd+/ejSlTppTq3KdPn+YqabZo0QLXr1/nqhU+ffoUXbt2RW5uLlRVVRETE8MNl6sIISEh3GeLnZ1dqT9baAhfCVACRQghhHxdTEwMjIyMAIjnEoSEhEhUrAoJCeGqXbVq1QrPnj2TSZzVVW6+EE6uPnganoxa6kpwG9caTYy1K+Ra3uFJWHjuJcI/ZQEAejTUwwp7axjqlG/VuYLr9xSmV69e8PT0hKKi5PC1BWcCcfxZFBoaaOHS9PZQkKe6ZiW1YsUKLF26tMj2QYMG4eTJk5CXL10lw9GjR8Pd3R0A4OXlxS1O+5mzszN27doFADh16pTUUgbfk4rODejdSgghhPwgCvYQdO7cWarcb8OGDVGnTh0AQFxcXKXGVt0JhCLMOOaHp+HJ0FBWwKHfKi55AgA7i1q4MrMjZnavD0V5Hm6GJKDn5ntwexTBVYX7Vvfv35dInuzt7bF161aMHz8eSkpKAIDr169j586dEsf5Rabg+DNxD9lK+8aUPJXSkiVLcPjwYfz0008S2/X09LBy5UqcOHGi1MkTAK5QAwBYW1tLtRfcVnDfHxG9YwkhhJAfRM2a/1U48/f3l2qPjo5GQkICAFTo8Jzq4FMGH1l8wdd3hHiY24KzL3EjOB5KCnLYP6YVrI0qLnn6TEVRHnN6/oTLMzuipVkNZOUJsexSMAbtfgyfiORvPv+OHTu4+5s3b8b58+cxc+ZMHDhwAF5eXlzbzp07uaFlQhHDkguvAACDWxiXW9W9H83o0aMREhICHx8fXLhwAffu3UNUVBQWL15c5gqhn3unAXH59y8V3GZoaFima1QXlEARQgghP4i6dety61o9e/YMe/bs4b7YZmdnY8aMGdzjgQMHyizO793ruHR0Wn8Hbdfcwv774eALhEXuyxjD31dCcNr3I+R4wI5fm6OtZa1KjBb4qY4mTk1ui5UO1tBUVkBAVCqG7n2C0Qe94fshpczn/TyXTkdHB87OzhJtXbp0QYcOHQAAYWFhiImJAQAc84nEy+g0aKooYEFfqzJfm4jLd9va2mLAgAHo1KkT1+tXVgXXtfvjjz9w9+5dMMbA5/Pxzz//4OzZswDElToLrgn3I6IEihBCCPlB8Hg8zJ07l3s8depUWFtbY/DgwTA1NcW5c+cAAGpqapg8ebKswvzurb4cgpx8IdJzBVh9JQQ9Nt+DZ2BMoWXhd997h/0PxAvkrhvcFL0a61d2uAAAOTkeRrcxw825nTHCzhQKcjw8eJuIwbsfw8nVp0wL8PL5fADitYkK+/JecOI/n89HclYeNniFAgDm9vwJtTWli0sQ2Wnfvj26du0KAIiPj0fXrl1hbGwMPT09iQVqFyxY8M3JWlVHCRQhhBDyAxk9ejRmzpzJPQ4ODsbZs2eRlJQEAFBWVsbJkyclhvNUJsYYrl27hgEDBkBXVxc6Ojro0KEDDh8+XOT6MJXpbmgCHrxNhKI8Dwv7WkFPUxlRyTmYftQPg3Y/hu+H/4bGHfOJxPpr4oRhcb+GcGxlIquwOXW0VPD3wCa4M68LhrYyhrwcD3dDP8F+5yNMOPQcr2JKPrfFykrcg/Thwwc8ffpUoi0xMRHXr18HAKirq0Ovjj4Wng1EWk4+rPQ1MaqNWfk9KVIueDweTp06BVtbW25bTEwM0tPTucezZ8/GrFmzZBHed4Wq8BFCCCE/GMYYTp8+jX/++QdPnjwBACgqKsLR0REuLi7cML/KJhQKMX78eBw6dKjQ9vbt2+Py5cvQ1q74+UOFEQhF+HnbA7yJz8SEDuZY3L8RsvME2Hc/HHvvhSMnXzyU7+cm+rAzr4Xll15BxIBpXSzxR5/vc7ja+8QsbLv9Fuf9ovG5toR9M0NsGGIDJYXif2fft28f11NpZGSETZs2oXv37ggICICLiwt8fX0BAJOnTIF61yk48+IjFOV5OD6pLVqa1ajQ50XKLi8vD8ePH8f+/fu5UuKdOnWCs7MzOnbsKOvwSoTKmJcAJVCEEEJI2SQlJSEjIwN6enpQU1Mrl3NmZmbC3d0dR48e5daLsbe3x8SJE6GvX/QQtiVLlmDlypXcY11dXaioqODjx4/ctv79++PSpUvlEmdpHfOJxMKzL6Gtqoj787tCW+2/0twJ6bnYfOMNTj6PQsEid7+2NsHfA5t89+sOhSVkYtutt7gUGAPGgIkdzfFnv0bFHpObmws7OzsEBgYWuY+uri5GbL6IC6+SIS/Hw84RLdDHWjbDGMmPgxKoEqAEihBCCPk+hISEoG/fvvjw4YNUm4aGBk6dOoU+ffpItWVkZMDIyAgZGRmQl5fH/v37MWbMGMjJyeHOnTtwdHREcrJ4eJyfnx+aNWtW0U9FQhZfgM4b7iIxk4+/+jfC+A6FL/z6Oi4df195jftvPqFfUwNsG94c8nLfd/JU0LWgOExxF/ccHRzbCt0b1il2//j4eAwcOJDrySzIzMwMDssO4fzrTPB4wJZhzWDfTDZDQ8mPhRKoEqAEihBCCJG91NRUNGnSRKLH6PO/z5+pqKjA29tbapjg8ePH8euvvwIAxo8fjwMHDki079y5E9OnTwcAzJ8/H+vXr6+op1GozddDse12GMxqqeHG7M5fHd4Wn54LPU3l777nqTDLL72C66P30FFTxNVZHWGgXfziu4wx3L59G+7u7oiNjYWOjg4cHBzwUccGO+6GAwDWDmqC4a1NKyN8QmghXUIIIYRUDfv37+eSJxsbG/j6+iI1NRXv37/HgAEDAIiHfa1du1bq2M9lrgGgW7duUu0FyyYXXBC4MsSl5WLfA3EisKCP1VeTJ0BcrKEqJk8AsKCvFZoYaSM1Ox8zj/lBIBQVuz+Px0P37t3h6uqKa9eu4fjx40gzsOWSpyX9G1HyRKoVSqAIIYRUexkZGTh27Bg2bdqEgwcPVvoX8B/F4cOHufsnTpxAixYtAIiHch07dgy6uroAgNOnTyMrK0vi2IIL9xY2pyYgIKDQfSvDxuuhyM0XoZVZjR9i/o6ygjx2jGgODWUFPHufgq233pbq+CNP3mPN1dcAgPm9G+C3IoY7ElJVUQJFSi0hIQFHjx7F3r17cfnyZeTl5ck6JEIIKZRQKMRff/0FQ0NDjBgxAvPmzcOECRNgamqKsWPHSpTnJd/u87wnS0tLNGjQQKJNTU2NW2MmPz8fcXFxEu0///wzFBQUAAC7du3iKrgBQHR0NJYsWcI9dnBwqIjwC/UqJg1nXoh71f7s17DK9iqVllktdawZ1AQAsONOGB6+TSzRcaeeR+GvC68AAM5dLeHctV6FxUiIrFACRUosPT0d48ePh4mJCUaOHIkpU6agf//+MDU1xfbt2wtdQJAQQmSFMYYJEyZg1apVyMzMlGgTCAQ4fPgwevXqhezsbBlFWP1oamoCEA+x+/I1B4C3b//rydDQ0JBo09fXx8iRIwGIewxtbW3RrVs3DBgwAJaWlnjz5g0A8dDAwob4VQTGGP6+EgLGgF9sDNHc9Mcqvf2LjSF+bW0KxoDfT/gjISO3yH2jkrOx+PxLuJwR9x6Oa18X83o1KHJ/QqqyUiVQa9asga2tLTQ1NaGnpwcHBweEhoYWui9jDH379gWPx8P58+eLPS9jDEuWLIGBgQFUVVXRo0cPiQ9ZIntZWVno0aMH/v33X6kep/j4eMycOROLFi2SUXSEECLNy8sLbm5uAAB5eXlMmDABR48exYIFC7gv+t7e3ti6dasMo6xe+vbtCwDIzs7GkiVLJH5YO3LkCPz9/QEAzZs3R5060tXdtm/fjjZt2gAQfze4c+cOLl26BD6fDwAwMTHBmTNnKq0X6G7oJzwKS4KSvBz+6P1jJgNLf2mEBnU0kZjJx+wT/hCKJH8sfRufgTkn/NFl4124P42EiAEj7EyxpH+jKt9bxxjDjRs3MGzYMDRt2hStWrXCnDlz6DsqAVgp9O7dm7m6urKgoCDm7+/Pfv75Z2ZqasoyMzOl9t28eTPr27cvA8DOnTtX7HnXrl3LtLW12fnz51lAQAAbMGAAMzc3Zzk5OSWKKy0tjQFgaWlppXk6pBQWL17MADAATENDg82ZM4ft27ePDRo0iNsOgPn4+Mg6VEIIYYwx9ssvv3CfTf/++69Em6+vL+PxeAwAMzExYUKhUEZRVi/+/v7c6wqANW7cmM2YMYN16tRJ4t+KQ4cOFXmO7OxstmbNGmZqasrtr6Ojw2bPns3i4uIq7bnkC4Ssx6a7zMzFk62+HFxp1/0evY1PZ1aLrzIzF0+2/dYbxhhj/pEpbNLhZ8zMxZO7jTrwlD15l8hEIpGMI/52mZmZrF+/fhLv2883OTk5tnHjRsYYY0KhkD1+/JidPn2a3bx5s8TfXUnFqujcoFQJ1JcSEhIYAHbv3j2J7X5+fszIyIjFxsZ+NYESiURMX1+fbdiwgduWmprKlJWV2bFjx0oUByVQFSsvL4/p6ekxAExeXp4FBARItK9Zs4b7UHFycpJRlIQQIqlWrVoMAKtVqxYTCARS7d26deM+uyIjI2UQYfW0Y8eOQr90fr5NmDChRF+whUIhi4yMZOHh4SwvL68SIpfk/vQ9M3PxZDbLvVhqduVf/3tz6nkUM3PxZOYLPJnjnscSidPkw89ZQFSKrEMsV1/+QKygoCD1Xh4/fjyzsLCQ2FarVi22dOlSmbxnyX8qOjf4pjlQn9d1qFmzJrctOzsbI0aMwM6dO4tdbfyziIgIxMXFoUePHtw2bW1t2NnZFbooG6l8b968QUJCAgDxJN8v1+6YOXMmVFRUAAAPHjyo9PgIIaQwAoEAgHjdITk56X/u1NXVpfatKIwx+H5IRkpW9S+64+zsDE9PT7Rr105i+08//YQ9e/Zg3759JRraJScnBxMTE5ibm0NRUbGiwi3U+8QsbPAST1GY1b0+tFUr9/rfoyEtjTGohRFEDPCJSIa8HA+DWhjhxuxO2DO6JZoa68g6xHLz4sULnD17FgCgpaUFDw8PZGdnIzExEfPmzeP2O3jwIMLDwyWOTUpKwvLly+Ho6FjhnytEdhTKeqBIJMLvv/+O9u3bw9ramts+e/ZstGvXDvb29iU6z+cqPF+Oha5Tp45UhZ7P+Hw+Nx4aAFVRqmD5+fnc/cJKx6qoqEBFRQW5ubkS+xJCiCw1bdoUDx48QHR0NG7duiXxQ110dDSuX78OQPy5ZmRkVKGxbL31FltuvoWCHA9dGtSGQ3Mj9GhYByqK8hV6XVnp168f+vXrh/fv33MLqzZo0KDQRPZ7k5qdh9/cniE1Ox82xtoYaWcm65C+GyvtrcEDD5oqChjfwRwmNdVkHVKFOHToEHd/zZo1GDFiBACgVq1a2LBhA+7fvw8fHx9unx49eqBbt24IDAzEyZMnIRKJcOHCBezbtw/Tpk2r9PhJxStzAuXs7IygoCA8fPiQ23bx4kXcvn0bfn5+5RJcUdasWYPly5dX6DXIfywsLKCsrAw+nw9PT0+kpaVBW1uba79y5QpSU1MBAA0bNpRRlIQQImnixIlcr/iwYcOwfPlydO/eHQEBAVi6dCn3Q5yTkxOUlJQqLI6g6DRsvx0GABCIGG6GJOBmSAI0lBXQu7E+HJobop2lLuTlqvaE+8LUrVsXdevWlXUYJZYnEGGKuy/CE7NgpKOK/WNblWjR3B+FurICNg21kXUYFS4iIoK7/3kB6IKEQiF3f9CgQThz5gz3eOzYsVwxle3bt2Pq1KlVvpgGkVamT4Xp06fD09MTd+7cgbGxMbf99u3bePfuHXR0dKCgoMCt5zB48GB06dKl0HN9HuYXHx8vsT0+Pr7IIYALFy5EWload4uKiirL0yAlpKWlhaFDhwIAUlJS0KNHD3h5eeHDhw/Yu3cvxo4dy+07YcIEWYVJiATGGJ4/f44jR47gxIkT9DnxAxo+fDjat28PAEhOTsaMGTPQqFEj/Prrr1xJbGNjYyxYsKDCYuALhJhzUly5rF9TA9yY3QnOXS1hpKOKTL4AZ158xOiDPmi75hbWXXsNvkD49ZOSCsEYw5/nXuJpeDI0lBVw0KkV9DRVZB0WkYGCJfYLJlOfhYSEcPe/HHHVp08frpLk69evixxNRaq40kyYEolEzNnZmRkaGrI3b95ItcfGxrKXL19K3ACwrVu3svDw8CLPqa+vz1UzYUw88YuKSHxfwsLCWI0aNYqdGNy5c+dCJ2oTUtmuX7/ObGxspKomDRw4kEVFRck6PFKJUlNTJarxFbzZ2NiwsLCwEp8rJYvPPqZkl+r6666GMDMXT9Zy5XWWlMnntguFIuYTkcQWnQ1kNsu9uMn4m7xel+r8JfHhwwf29OlT9vr160qvjpaancfO+31kiRm5lXrdsthx+y1XJOH263hZh0NkyM3Njfuc6NKli0RlvTdv3kh8jhRWGbJgAYp3795VZujk/yo6N+AxVvLVT6dNm4ajR4/iwoULEiuMa2trQ1VVtdBjeDwezp07J7FquJWVFdasWYOBAwcCANatW4e1a9fi0KFDMDc3x19//YXAwEAEBwdzxQmKk56eDm1tbaSlpUFLS6ukT4eUkp+fHwYNGoT3799LtfXv3x8eHh70+hOZO3fuHBwdHSWGWBRkbGyMx48fw8TEpJIjI7IUEBAADw8Pbj6Og4MDunXrVuKhNZFJ2Ri46xFSc/KxeagN7Jt9fc6UX2QKBu9+DBED9oxqiT7WhY+qyBOI4P70A1Z4BkNTWQEPF3Qrl6IF165dw+rVqyWG2ltZWWHu3LkYP358hQ4rSszk4+DDCBx58gGZfAH0NJWxa2QLtKpb8+sHy8DlwFg4H30BAFhp3xij29aVbUAVgDGGhw8fwtPTExkZGTA2NsaIESO4IZZCoRBXrlzB48ePIRAI0KRJEwwZMgRqatVznlNxcnJyYG5uzo2OMjIywuDBg5GcnIzTp08jN/e/BYV9fX3RokUL7nFqairMzMyQnp4OVVVVJCUlFfkdmVScis4NSpVAFfVh6+rqCicnpyKP+TKB4vF4EscwxrB06VLs27cPqamp6NChA3bt2oWffvqpRHFRAlV58vPzcf78eVy+fBnp6ekwNjbGmDFj0KpVK1mHRgjS09NhYmLCFZZp2bIlhg8fjuTkZBw8eJCrJmlvb//VBb4J+SwtJx+Ddz9GWEImAIDHA9YPbgrHVkUn4bn5QvTb9gDvPmXBoZkhtgxvXuw1RCKGvlsfIDQ+A7/3qI/fe5Ts37+i7NmzB1OnTi2yffLkydi9e3e5J1ExqTnYdz8cx59FIjdfBABQUZRDbr4ICnI8/NmvIZza1S3RdQM/puLvKyHIyRPiwFhb1NZULtdYP/OLTMHwfU/BF4gwrn1dLP2lcYVcR5bevXuHYcOGwdfXV2I7j8fDb7/9BkdHR0yePBkfPnyQaNfR0cHGjRsxfvz4ygz3u3D//n307dsX2dnZxe5nbm6Obdu2oUePHggICMDcuXPx6NEjAMD48eNx4MCBygiXfOG7SqC+V5RAEUIAYNeuXXB2dgYADBw4EKdPn+aqfsXHx8PGxgbx8fHg8XiIiIiAmRlV1yLFEwhFGOf2DA/eJkJfSwXt6tXC2RfRAIBVDtYY1abw99Dqy8HY/yACtTWVcWN2J+iofb1IhWdgDKYf9YOWirgXSkulbL1QL1++RLNmzSASiRMYKysrrkJYwd6oI0eOYNSoUWW6xpfeJ2Zh9913OOv3EflC8dcKG2NtOHeth3b1dLHgTCA8A2MBAANsDLFmUBOoKxdexyo5Kw8bvF7j+LMofP6GYlu3BjwmtCn3gg5RyeKexcTMPHSz0sP+Ma3KpZhHVFQUYmJiUKNGDdSvX1+mRQRiYmLQunVrREdHF7mPnJwc934pzO7duzFlypSKCO+7FhAQgMWLF+Py5cv4/HVZS0sLo0aNws2bN7m5lIXR1taGr68vLC0tKytcUkBF5wZUWoYQUm3cvXuXu79w4UKJksl16tTBxIkTAfw3lIWQ4jDGsOzSKzx4mwhVRXkcGNsKmxxtMK59XQDA4vNBOPhQeoL58/fJOPD/7WsHNSlR8gQAP1sboL6eBtJzBTj06H2Z496+fTv3ZXjWrFkIDg7Gzp078eDBA7i6unL7bdmypczX+Cw3X4i5JwPQbdNdnHgehXwhQxuLmnAfb4fzzu3Rq7E+NJQVsP3X5ljSvxEU5Hi4GBCDgbseIfxTpsS5hCKGI0/eo+vGuzjmI06e+jU1gKayAp69T8GyS6++Od6C0nPzMf7QMyRm5qGhgRa2/dr8m5MnLy8vdOrUCaampmjTpg0aNGiAxo0b48CBA5DV79UrVqzgkqd69erh0KFD8Pb2xvLly7lpEp/fLx06dMCpU6dw9epVDBs2jDvH3LlzkZKSUvnBy5iNjQ0uXbqEqKgo3L59Gw8fPkRMTAx27tyJW7duoVmzZoUep6+vj+vXr1PyVI2VuYw5IYR8bwquD1e7dm2p9oLbCu5b1WRmZiIoKAgCgQANGjQo9LmSb3fo8Xu4P40EjwdsGd4M1kbi5RuW9G8EFUV57L77Dis9g5GbL4Rz13oAgOw8AeadCgBj4oVHuzesU9wlJMjJ8TC9Wz3MOu6PAw8jMK6DOTSK6KUpzuXLlwEAampqWLVqlUTvx9ixY7FlyxYEBATA19cXCQkJ0NPTK/U1AHGCufDsS5zzE38579qgNqZ3q4eWZtLznHg8Hn7rYI4mxtqY5vECb+IzMWDHI2x0tEEfa308e5+MpRdeIThWPPzWSl8TK+yt0dq8Ju68TsBvh57hqHckGhtqldu6TKs9Q/AmPhN6msr416lVmV7rgooaNhkSEoKJEyfi+fPnFTJssjhZWVlwd3cHIF44+uHDh9y6m61bt4ZIJOKWhdHW1sadO3e4Csp9+vSBqqoq3NzckJ2dDXd3d8yYMaPSYv+eGBkZSa0VZ2xsjGfPnuHy5ctS8yt//fXXH3Lu2I+EeqAIIdWGlZUVd//48eMSbYwxiW0FC+FUFUlJSZg+fToMDAzQtm1bdOzYEYaGhhg6dGixQ0lI6d0JTcAKz2AAgEsfK/Ru/F8BCB6Phz96N8Ds/89T2uAVis3XQ8EYw/proXiflA19LRX81b9Rqa/bv6khLGqrIy0nH4cevy9T7BkZGQAAQ0NDiXLMn2MvOL84IyMDOXlC+EellrqHZM+9cJzzi4a8HA9u42zhOq51oclTQbZ1a+LyjA5oXbcmMvkCTHH3heOex3Dc8wTBsenQUlHACvvG8JzRAa3NxefqaqWHeb3Ef69LL7yCT0RyqeIsTCZfgIsBMQCArcObw0D72yb5v3z5khs+DIg/i6ZNm8aV0QeAvXv3wsPD45uuU1phYWHIysoCIF7P6HPy9FnBNR3l5eW55OmzgsP2vpw/RQAFBQXY29vj5MmTePDgAS5duoTx48dT8vQDoASKEFJt/Pbbb9z9pUuXYt26dfj48SMCAwMxYsQIPHnyBID4y027du1kFWaZxMfHo127dti5cycyM/8b+iQQCHDq1CnY2dnhxYsXMoyw+giNy8CMo34QMcCxpTEmd7KQ2ofH42FWj/pY0FectG+7HYZpHi/g9v+kZ92QpmWqpCcvx8OMbuLerAMPwpHFF5T6HKampgDEX56/TKxzcnJw584dAICioiKUNWti4K5HcNj5CHNOBiBfWPQ8mIJuBMdjvddrAMCyXxqhS4OS92LpaanAY6IdxncwBwA8e58CHg/4tbUJ7szrgjFt60JBXvLrybQulujf1AACEcM0D1/EpOaU+HqFufoyFjn5QljoqqONxbdXBiw4bHLmzJncsMmHDx+W+7DJr4mPj4e/vz/ev38v0duVn58vtW/BpLmwnrGvtZOv8/Pzw8qVK/HHH39g27ZtUuuekqqJEihCSLXRoEEDTJ48GQCQl5eHBQsWwMTEBDY2NlzvE4/Hw4YNG6rcl4EpU6ZwX4ZVVVUxevRoTJkyhRu+l5qaCkdHRwgEpf/C/aN4E5+B1ZeDsetuGO6/+YSUrDypfRIz+fjN7Rky+QK0Nq+J1QObFPtemdLZEkt/Efc0XQ0SL5j5a2sTdP6p7MMqf2lqCHNddaRk5+PI0w9fP+ALY8aM4e4PHz4cAQEBAMSFDUaMGIHExEQAgP2Q4Zh64hVex4l7rM75RWP8oedfTdpex6Xj9+N+YAwY1ca0TCW/FeXl8Ff/RtgzqiUGNTfC+WntsWZQU9TSKLzSHo/Hw/ohTdHQQAuJmXmYdOQ5cvLKvujw50Igg1oYlctnQcFhk6tXr5YaNmljYwMA3LDJinDnzh306NED+vr6aN68OczNzTFq1CiuN+TSpUtSi8IWXORVKBRKJVm7d+/m7lO13dKJiopCly5d0KJFCyxZsgQbNmzArFmzYGJigt9//73QhJZUHVSFjxBSreTn52PGjBnYu3evVJu6ujr279+PX3/9VQaRld379+9hYWEBxhhq164NHx8fbu2WjIwMdO3alRtec/78edjb28sw2uKlpKQgLi4ONWrUgL5+4esilbe0nHxsvfkWh568h1Ak+U+ekY4qrI20YG2oDWsjbWy//RYvIlNhVksN56e1Rw31khWAOOodiT/Pv4RJDTVcntkBmmWsoPfZad+PmHcqALXUlfDApSvUlEo+PyclJQVNmjSRqLpWs2ZNJCf/N/RNRUMbnZacQmhSHmqqK+H3HvWx5spr5OQL0dRYG/862UK3kGQmKZMP+52P8DElB20tauHw+NZQlK+832KjkrNhv/MRkrPyYN/MEFuGNSt1AvQxJRsd1ol74R4t6AYjnW9fo0dLSwsZGRmoV68e3r59K9U+dOhQnDp1CoC4Z7C8iwscPHgQEydO/OowzDp16mDOnDmwsrLCtWvXsHfvXonqe23atMHMmTOhoaEBNzc3nD17FoD4szM6OlpiyB8pWkJCAuzs7ApdN/OzESNGwN3dvcr9mFdVUBnzEqjIF4kxhpycHKioqEhU9CKEfN9CQkJw8OBBBAcHQ0lJCZ07d8bYsWNRs+b3uZBncfbt28f1rC1fvhxLliyRaL906RIGDBgAQNxTVfBX4+/Fo0ePsGbNGly5coX7kmdnZ4c5c+bA0dGxQr5EiEQMp30/Yr3XayRminubulnpQU1JHq9i0hGRmFXocVoqCjg7rT3q6WkU2l6UqORs6Kgplil5YowhLy8PSkpK4PF4EAhF6LbpHiKTs/Hnzw0xsZBhhMUJDg5Gnz59EBUVJdWmrl0DbVyOICwN0FZVxLGJbdDIUAv+Uan4ze0ZkrPyULeWGg7/ZgfTWv/N5cgTiDDqoDd8IpJLnWCWpyfvkjDqoDeEIoZFP1thUqfSJSM774Rhg1co2lrUwrFJbcolJmtra7x6Ja4SGBoaKjHPLCcnB6ampkhMTISioiKSk5Ol5qZ9i1evXsHGxoZbPNzS0hJdunRBYGAgnj17VqJzyMvLF7n4OADs378fEyZMKJd4fwQzZszAjh07AAAmJiZYsGABl7Ru3boVeXniz6MbN26gR48esgy12qrwzhVWDaSlpTEALC0trdzO+fbtWzZ16lSmra3NADBlZWXm6OjIHj9+XG7XIISQkti0aRMDwACwI0eOSLW/evWKax81alSFxREbG8tWrVrF+vXrx3r37s3mzp3LXr9+/dXjDh8+zOTk5LgYv7zNnz+fiUSico3VLzKFDdj+gJm5eDIzF0/WbeMddi80QWKftJw89uRdItt//x2bdewF677pLmu58jp79PZTucZSnHv37rGBAwcyJSUlBoDp6uqy2bNnsw8fPrATPpHMzMWTtVx5g2XzBaU+d3p6Otu5cydr27Ytq1u3LmvWrBlbvHQ5G7LjHjNz8WTWS64x/8gUiWPeJWSw9mtvcdd9+TGVMcaYSCRiLqcDuOPexqeXx9MvM7dHEczMxZOZL/Bkd7/4/1ockUjEum68w8xcPNnJZ5HlFs+6deu493Pz5s2Zv78/Y4yxyMhI5uDgwLUNHz683K752ZQpU7jzT506lQkE/71X9uzZw7Xp6OhI/e2pqamxP//8k92+fZtZWlpKtdesWZO5ubmVe8zVWXZ2NtPU1GQAmKqqKouKipJo//fff7nXd/DgwTKKsvqriNygIOqBKsSNGzfg4OBQ5OrT27Zt+2FLeRJCKh5jDO/evUN6ejqMjIzw6NEjDB48GAAwbNgwqQqD69atw4IFCwAAf/75J1atWlXuMe3ZswezZs3ifjktaObMmdi8eTPk5eWl2l6/fo0mTZpwc7NMTEzQuXNnBAQE4OXLl9x+p06dwpAhQ745zk8ZfKy/9hqnfD8CADSUFTCre32MbVe33Bdh/VZr1qzBokWLCm3T1tbGRc/LWPSIj48pOfirfyOu6EJZ5QlEmOLui9uvE6CmJI8j4wuvmpeQnouxrs8QEpsODWUF7B3dEm/iM7D8UjDkeMBBJ1t0LUXRiIrAGIPLmUCcfP4RuhrKuDe/S5EL8xbkH5UKh52PoKIoh+eLe35z6fLPSjJsUllZGd7e3tx8qPJibGyM6OhoqKioID4+XuJ7EGMMTZs2RVBQEADg8ePHePr0KdLT02FsbIzBgwdDR0cHgHgtqOvXr+Px48cQCASwtrbGoEGDuLWiSMkEBgZy/4+HDh2KEydOSLTn5+ejZs2ayMzMRN26daXmpZHyQT1QJVCeWWZkZCRTV1eX+HWmY8eOTFdXV+JXmRs3bpRD5MVLSkpir169YjExMRV+LUKI7AmFQrZ7927WoEEDic+bHj16cL3hANiKFStYWloay8vLY4cOHWJqampcW2hoaLnH5e7uXmTv0efb3LlzCz3W2dmZ22f8+PEsPz+fMSbuCdi6dSvX1q5du2+OMzY1h7VYcZ3rdZpzwp/Fp+d883krwrlz5yRePz09PdauXTumrKws8ev/vluvmJmLJ2u16gbLySt9L9RneQIhm3T4GTNz8WQ//XmFPQ5LLHb/tJw8NmzvY2bm4snqLbrMzBeIX9P999+VOYbylpsvYJ3X32ZmLp7snxsle9//df4lM3PxZLOOvSj3eF69esVMTEwK/ftQV1dnly9fLvdrMsa43o569eoV2j506FAujrCwsAqJgfwnICCAe72HDh0q1Z6Xl8c0NDQYAFa3bl0ZRPhjqOgeKEqgvuDi4sK98fv3789SUlIYY4zx+Xw2b948rq1Xr17ffK2iPHjwgP3888+Mx+Nx12vdujU7fvx4uQ9zIaQ4QUFBbMqUKczY2Jhpa2uzxo0bs7Vr17KkpCRZh1alpaamssOHD7O1a9eyPXv2sKioKCYUCtmYMWOKTFAKfh4AYHJyctywr8+3MWPGlHus+fn5zMjIiLvGpEmTWGhoKIuOjmarV69mCgoKXDxfDlVhjDFjY2MGgKmoqLDU1FSJNpFIxBo1asSdOyGh5EOxCvP5y3HXjXfY8/fJ33SuitamTRvueS9dupTl5eUxxhhLSEhgXbt25dpW/b2WtVsjHlLn+jC8TNfi5wvZ9KMvmJmLJ6u/6IrUUMai5OYL2DR3Xy4hnXfS/7v7N+hSQDQzc/FkDf+6yhLSc4vdl58vZDbLvZiZi2eJX4PSSk9PZzt27JAYNrl06dIK/SG0YcOG3GfElwlSTk4O09PTYwCYgoICy8jIqLA4iNjXhvC5urrSEL5KQAlUCZTni2RhYcF90MTFxUm0CQQCVrduXe6N/zm5Kk+HDh0qdq7AvHnzvrt/wEj1tH///iLfi4aGhuzly5eyDrHKyc/PZwsXLpToMQLA5OXlma2trcS2Dh06sAkTJkh85hT32TBo0CCWk1P+vS2XL1/mrtGnTx+pz59FixZx7StXrpQ6/vMXifr16xd6/vL6dTw2NYfVX3SFmbl4VuocprKIjIzknrO1tbXUaxoWFsa1N2/enB158v7/c5Kus1PPo0rcE5WRm8/233/H2vx9k5m5eDLLhZfZjVdxXz+wAIFQxHbcfsuWXQxiufll7wGrKCKRiJvrtvhc8Z9J14JimZmLJ7NddYMJhNXn39G///6be7/Y2tqy4OBgxph4zmLBvy9HR0cZR/rjmD59Ove6m5qasp07d7Jbt26x+fPnS/zwdf36dVmHWm1RAlUC5fkife5WLeof+2HDhlVYV3hwcDD3a+7nP7rRo0ezpk2bSnxROnnyZLlel5Av3bx5U6LHQ1VVVWqCsZGRkVSPAimaSCRio0eP/upQOADsxIkT3HH5+fkSPVNjx45lU6ZMYU2bNmWNGjViw4YNY7du3aqwH1Y2b97MXdvV1VWqveBwldGjR0u1W1lZcb+Oh4dL9qDk5uYyfX19LolMTy97YYKlF4KYmYsnG7L7UZleCx8fH7ZkyRI2e/ZstmnTJhYdHV3mWL7m+fPnEj16halTpw4DwIyNjVluvoB12XCH6wlqsvQaW3ohiL2JK/z1ik/PYeuuhjDrpde4Y1qtusG8gmIr7DnJ0uOwRC5BDP+UWeR+Ew+JhzD+fTm4EqOreImJidzf0eebgYGBxA8uSkpKzNfXV9ah/jDi4+Mlfvwq7Pbrr7/SD+IViBKoEijPF8nc3LzIHiihUMi1A2DJyeU7RGTatGncuSdMmCAxV2Dbtm1cW9u2bcv1uoR8qVu3btz7bdq0adzf1ps3b1jLli25tq1bt8o40qqjYE+OvLw8mzJlCjt58iRbvHgx98MNAGZmZiZ1bHx8PJOXl2cAWKNGjSo17l27dnGxrVu3Tqr9xo0bEp9bX1q5cqXEZ9fnH54SExPZqFGjJHrQyio+LYf99Ke49+n+m9INzXr//j1r166d1JcbeXl5Nm3aNMbn88scV1E+fPjAXcfGxkbqS1R4eLhEO2OMJWXy2Y7bb7kKeZ9vQ3Y/YmdfiHulwhIy2IIzAVxP3OfhjMd9PnyXvUflyelfb2bm4smmuj8vtD0pk8/qLbrMzFw82etY2VYQrAgBAQHMwMCg0C/qqqqq7Pz587IO8YcTGRnJOnXqJPX/Q1FRkc2aNYsbtksqBiVQJVCeL9Iff/zBvckHDBjA/cLO5/Ml2nr27PnN1/pSZc4VIKQoMTEx3Pusfv36TCgUSrQHBQVJDBchJdO/f3/udfuyLPDRo0e5NnV1danXnDHGzWMwNjaurJAZY5Il0k1NTVli4n/FB/Ly8iSSbXd3d6njExISWO3atbl9eDweMzc3Z4qKitw2BQUF5u3tXeYYV1wSF1oYuPNhqX7RjYuLY6ampsX+Sjx06NAK+ZW44JDN1atXc6Wnk5KSWM+ePbm2VatWSRwnFIrYndfxbOKhZ8xi4WUuUbJeco3VXfBfYjVw50PmFRTLhNVoqFpxQmLTuOf/4oP0j5uHHovLnv+89b4MoqscKSkpbNOmTaxFixbMwMCANWzYkC1YsIB9+PBB1qH90Hx9fdmKFSvYvHnz2JYtW6R+nCcVgxKoEijPF+nDhw8S8xPU1dVZ586duS8vn28VMW61suYKEFIcX19f7n02ceLEQvcpOLyIlEytWrUYIF7np+A6LYyJv8gX/Hx5906y0lnB/ydt2rSpzLAZY5I9kvr6+mzhwoVs9erV3OR1AKxOnTosKiqKbd68mU2cOJE5OzuzEydOMD6fz54/fy6RRBW8KSkpSQxZLK2E9FzWYLG4x6U06wExJtnrX7duXbZ371527949tnDhQolqeF5eXmWOryinT5+WeB2MjIxYly5dmKqqKrdNR0eHxcfHF3mO2NQctvXmG9b2/3OczFw82Xg3H+YT8WMWeZl70p+ZuXgyxz2PpZLeATseMjMXT3bwQdkKcRBCqhZKoEqgvF+ka9euSfwj9uVty5Yt5XKdL1XWXAFCivPu3TvuvW5nZyfVHh0dzc2Paty4sQwirJo+L2JpZGRUaI9GwQRj0KBB3BfnFy9esMaNG3Ntu3bt4o6prN6FsLAwLmkuKgkaO3asVFVAQFxw5NatW+zTp0/s77//Zo0bN2Y1a9ZkFhYWbPbs2d/8Y9AqT3Hv04Adpet9ysrK4oZOqqmpsY8fP0q0Hzp0qFyGFxZn2bJlRb6mmpqa7N69eyU6j0AoYj4RSexdwo9dYe1jSjar//+hnLdC/vuV/218BjNz8WQWCy+zTxnFV+ojhFQPlECVQEW8SKGhoWzy5Mlcr5CioiIbNGgQe/jwYbld40tFzRX49OkTGzlyZIX/Y06qNoFAUC5jqkUiEbO2tubebwcOHOC+mObk5LAhQ4ZwbX/++ec3X+9HUXAs/Jc9GpGRkRJD2j7/UPJlz7e5uTlLTk1j7k/fs3ZrbrF2a259tXRzeQkPD2f29vZSlQDbtm3Lxo0bV+wwOCUlpQr57PyUkcusFl9lZi6e7HZI0T01hSlY/GLYsGFS7fn5+dznf2Hz0srLjRs3WL9+/bg5btra2mz69OlSvZCkZP6+HMzMXDxZr833uEp766+FMDMXT/abq4+MoyOEVJaKTqB4jDGGKq4iVxsWiUTIzs6Gqqoq5OXly/XcX/r06RMaN26MT58+cdvq1q2L6Oho5OfnAwAUFBTw+PFj2NraVmgspGoQCoU4evQodu3aBW9vbzDG0KBBA0ycOBFTpkyBurp6mc7r5uaGcePGcY9tbGxgZWWFO3fuICEhAQCgqqqK0NBQmJiYlMtzqe7c3d0xevRoAICOjg6WLl2K7t27IyAgAMuWLcO7d+8AAPLy8hAKhVLH17WwxO9bjuHkqwxEp+Zw24e0NMZGR5sSxxEYGIhjx44hJiYGOjo6sLe3R9euXcHj8Up0fFRUFJ4+fQqBQIAmTZpAS0sL5ubmEIlE4PF4mD59OkaOHInk5GRs2LABd+7cAQC0bNkSz58/L3GcRfn8TxaPx8OaqyHYey8cTY21ccG5fYmfAyB+HWxsxK+bo6MjTp48KdGen5+PmjVrIjMzE3Xr1kVERMQ3x16c/Px85OTkQENDA3JychV6reosLTsfnTbcQVpOPtYPaYohLYzRYd1txKTlYueIFujX1EDWIRJCKkFF5gYAQD1Q3xlfX1+pX51R4FdcKmFOPuPz+WzAgAFF/urfpEmTMk9WFYlEEvNDCnsvXrhwoZyfUfWWn59faEWmgjdTU1Pm4+PD5s+fzxo1asSMjY2ZXdt2bPK6Q6xdgXkurVbd4H5pN3PxZL6FTJr/UlpaGrO3ty/0us2bNy9zj8fSpUu587i4uEi05eXlsSZNmnDtL168KNM1hEIhO3XqFOvatStTVlZm8vLyrEmrtqzegovMzMWz1GsbMSZe7FJLS4sB4sI9X060P3DgABf3kCFDyhQ3kY2998KYmYsna/P3TXY7JF5cZGPptRKvn0UIqfoqOjegn7m+My1atEBwcDDWrFkDa2tr1KpVC5aWlpgzZw5CQkLg6Ogo6xDJd8LFxQUXL17kHtevXx/NmzfnHr98+RLDhg3jfrEvDR6Phx07dsDDwwOtWrXitisoKMDR0RFPnjzBgAEDvu0JlABjDOHh4QgICJDoma2KFBQU4OnpiYEDBxba3rJlS9y9exe2trZYv349/ANfYtPZx1B0WIlrybUQnZYLXQ1lLO7XEA/+6IqFPzeEY0tjAMDSC68gFBX9/zk/Px/9+/fHhQsXCm338/NDly5dEB8fX+rnFRAQwN0fP368RJuioiLGjBnDPX7o+xJrroagw7rb2Hw9tNiYC8Y+fPhwODo64s6dO+Dz+RAKhYhSq498Jgf59BjY1C79P2WqqqpwcnICAOTm5qJdu3bYunUrrl+/jtmzZ2Pq1KncvlOmTCn1+YnsjGlbF0Y6qohNy8Xsk/4AgP5NDaGiWLGjSAghPw4awkdIFZSSkgJDQ0Pk5uZCSUkJp0+fRv/+/cHj8RAQEICff/4ZMTExAIAnT56gTZs233S9+Ph4ZGRkoE6dOtDU1CyPp1AskUiEgwcPYsuWLQgODgYgTur69u2LP//8E+3atavwGCrSq1ev4OHhgdjYWOjo6MDBwQGdOnUCj8dDVHI2jj+LxMnnH/Epgw8A0NVQwpTOlhhpZwZVpf++BH7K4KPbxrvI4Avw98AmGGFnWuj1Cg4frFGjBpYvX45u3bohMDAQS5cuxdu3bwEAs2fPxubNm0v1XIYMGYIzZ84AEA+La9KkiUT76tWrsWzjDmi1HowaLfpAwP4bZtexvi62Dm+OmupKRZ7fxcUF69ev5x6bmppCVVsX2d0XQE5ZDQlnVqJ9XU3cuHGjVHED4mHTbdq0QXh4eJH7jBo1CocPHy7V8EAie2d8P2Luqf+S+9NT2qJV3ZoyjIgQUpkqOjegBIqQKujIkSPcL/vTp0/H9u3bJdr//fdfrjegLF+KZUkkEmH8+PFwc3MrtF1BQQEeHh4YOnRo5QZWgfKFItwKScBRn0g8ePsJnz+VdTWUMamTOUa1MYOakkKhx/77MAIrPINRQ00Rd+Z1gY6adDLSqVMnPHjwAABw/fp19OzZk2v7+PEj6tWrBz6fDx0dHSQkJEBRUbHEsW/cuBHz588HIO6BOnDgANf2/F0chizeC2bSHDw5ceLX0qwGujaojZ133iEnXwgjHVXsGtkCNiY6UudOS0uDoaEhsrOzoaioCHd3dzg6OmLT9TfYcScMouRIRO2fBgDw8fEp09zQ6OhojBkzBrdv35bYrqSkhBkzZmDt2rVQUCj8tSffL6GIod+2B3gdlwHTmmq4N78LJcGE/EAqOjegfxUIqYI+F3IAUGhvTMFtVW3o24EDBySSp7Zt26Jhw4a4efMmIiMjIRAIMHr0aLRu3Rp169aVWZwAsOtuGEJiMzCpowWaGGuX+viPKdk47hOFk8+jkPD/3iZA3DPza2tT9GhYB0oKxQ9PG9PWDCeeRSE0PgObrr/BSgdrqX1evnwJADAyMkKPHj0k2oyNjdGrVy9cunQJqamp+PjxI8zNzUv8HJycnLB48WLw+XwcPHgQcfEJaPPLKNyO4SE8Vw0wawUeALXUCLj+8Stam9cEj8dDz0b6mOLui4jELDjueYJlAxrj19YmEl9yPT09kZ2dDQCYMGEChg4dirTsfLg9fg8AcGyogc8/DRw/frxMCZSRkRFu3bqFwMBAXLlyBenp6TA2NoajoyNq165d6vOR74O8HA+rHKzx+wl//N6jPiVPhJByRQkUIVVQwS923t7e+PXXXyXavb29ufu1atWqtLi+FWMM//zzD/f46NGj3HPLz8/Hb7/9Bnd3d+Tl5WHPnj1Yu3atrELF+8QsrL8WCgC4FBCDATaGmNerAUxrqRV7HGMMzz+k4MCDcFwPji/Q26SEIS1N8GtrE5jVKnn1RAV5OXHysf8pPLw/YHhrEzQ2lEzmPlcQ5fP5EIlEUhVFs7Ky/jtfKXtbdHV1sXLTDqzYdxIq5i0RWLcZgsLF8TORENmhjyB6dQ1XLh5DI4v/3osN9DVxYXp7zDsZgOvB8Vh07iX8IlOw0sGam6sSFxfH7d+hQ0fEpOZgz713yOQLYKWvifG9LbB5jri94I8KZdG0aVM0bdr0m85Bvi+t6tbEQ5dusg6DEFIN0RA+QqqgpKQkGBkZgc/nQ0VFBRcvXuSGZYWEhKB3796IiooCADx8+BDt27eXZbglFhYWhvr16wMA2rdvj4cPH0q0x8fHw9DQECKRCI0aNcKrV69kESYAYO3V19hz7x1qqSshKSsPAKAoz8NIOzPM6FYPtTSUJfYXCEW4EhSHgw/CEfAxjdvevl4tjGhthp6Nvt7bVJzpR1/AMzAWrcxq4NSUthK/uP/yyy/w9PQEALi6unLFEwDgxYsXaNWqFRhjMDY2xocPH75aRjtPIMLz98m49+YT7r35hNdxGRLtwpwMZIc+RLr3WbT4yQT//vsvGjduXOi5GGPYcy8cG7xeQ8SAxoZa2D2yJYSMYefRizh41gtKdSyhXdcaebz/hifuHNECqS9vY9SoUQCAmTNnYuvWraV6zQghhFRPNISPECKlVq1amDhxInbs2IHc3Fz06tUL1tbW0NDQ4NaDAsRD+apSwYX09HTufsOGDaXa69SpA11dXSQkJEjsW9nyBCKc9hUnqH8PagIjHVWsu/YaD94mwu3xe5z2/YjJnSwwvqM5BCKGEz5RcHv8nlu/SUlBDoNbGOG39uaoX6d8inL82a8hboUk4PmHFJz3j8bA5sZc27Rp07gEasKECXj8+DG3BtXOnTu598vUqVO/mjxdfxWH5ZeCJdai4vEAG2MddKxXE/IJb5AVFQEVU3N0Wnnhq8PqeDwepnaxRFNjbcw85odXMenotOHO/1u1oN1GXHk0D4AcD/ipjiZ+bmKAn9Sy0Puvv7jzDB48uKQvFSGEEPJNqAeKkCoqNzcXDg4O8PLyKrTdysoKt27dgqGhYSVHVnbx8fHQ19cHAJibm+Pt27cSw838/f25Uu1t2rTBkydPZBLn5cBYOB99AT1NZTxa0A2K8uKk4+HbRKy9FoKgaHFyp6uhjJw8AbLyhP9/rITRbepiZBtT6H7RQ1Uedt4JwwavUNTWVMbtuZ2hqSIuBsEYg5OTEw4fPgwAkNesBWVDK+TFhUGQJi5d3rp1a9y5cwdqaoUPQfyYko1lF1/hZoh4qFwtdSV0aaCHzg1qo2M9XdQoppJeScWm5WCaxwv4RaZCWUEOVgZaSArzR8CdS8iLD0fep/ewbdEMGhoauH//PrfgsK2tLby9vX+4eS4ikQjXrl3DgQMHEBISAiUlJXTq1AlTp05Fo0aNZB1esVJSUuDm5gZPT0+kp6fDxMQEo0ePxi+//EJFOwgh34yq8JUAJVDkRyUQCODm5oZdu3bBz88PAGBmZoZJkyZh+vTpVfLvoXfv3rh+/ToAYNy4cVi/fj10dXUREBCA0aNHcwURdu7ciWnTpskkxlEHvPEwLBEzutXD3F4NJNpEIgbPl7HY6BWKyGRxAYSf6mhgQgcLDGhWsWvR8AVC9P7nPt4nZWNSJwss+lnci8cYQ0hMGhbuPAbfuHwo6Flyx+S+90dzrWy4r5uPWjV0pM6ZJxDh4MMIbL31Brn5IijI8TCxkwVmdKtXZGXAb8EYQ1x6LmprKENBXg7Z2dno378/7ty5U+j+lpaWuH37NkxNCy/hXl1lZmZi8ODB3N9KQTweD6tXr8bChQtlENnX3bhxA46OjkhLS5Nqa9GiBTw9PWFgYCCDyAgh1QUlUCVACRQh4h4pgUAAdXX1Kv1L/P3799GtWzeud0FBQQG1a9dGbGwst0/dunXx8uVLaGhoVHp87xOz0GXjXfB4wP35XWFSs/AemzyBCLdfx0NLRRFtLWtV2v+TO68TMM7tGRTkeNg8rBkCo1JxPTieS+YAgAcGHfk8pAj/6wWrqa6EwS2MMMzWFPX0xK+rd3gSFp8PwtuETACAnXlNrHKwLrdhhyWVl5eHffv2YefOnXj9+jUAQF9fHxMnTsTs2bNRo0aNSo3ne+Dg4CCxMLKKigry8vIgEom4bQcPHsRvv/0mi/CK5O/vj7Zt2yI3N7fIfZo2bQofHx8oK5d/Ly0h5MdQ0blBqWYsr1mzBra2ttDU1ISenh7+195dh0WVvn0A/w6dgnQjCIqBip0goAIWdgfqioGB3bWuuvbarrFgdy52ImIhIgYIBgJSIkjnzDzvH7ycH7ODCggM4P25rrk8c54z59wzHGfOfZ7q06cPwsLCRLaZMGEC6tatC0VFRWhra8PV1ZX7wfsWNzc38Hg8kYezs3Pp3w0hvzAFBQWoqKhU6+QJKJiz6MCBA9xcRHw+XyR5MjU1xdWrVyWSPAHA8YCCvk+2ltrfTJ6Agn5Ozo310d5Cq1L/JvZWOujSQAd8IcO0Y0HYdz8CUclZkJORgqOVDtb2t8aTRV0RtKof/ObaY4q9BXRrySM5Mw97/SLQZZMvBu5+gKnHgjB4zyO8/ZwBTWU5bBzYFMfd21Z68gQUzMk0ZcoUhISEIDk5GZ8/f0ZMTAx+//33XzJ5evr0KZc8qamp4dSpU8jIyEBSUhIWLlzIbbd8+XLuRkRV8fvvv3PJU/fu3RESEgI+n49Lly5xtYgvXrzA8ePHJRkmIYR8V6lqoJydnTFkyBC0atUKfD4fCxcuxKtXrxASEgJl5YJha/fs2QMrKyuYmJggOTkZy5cvx/PnzxERESE2dG4hNzc3JCQkwMvLi1snLy9f4h9GqoEilSE2NhbXr19Heno6jIyM4OLiAgUFBUmHVWO9f/8eO3fuxKVLl7i5eUaNGoXRo0dDVbXyL+KBglql9n/ewpeMPOwe0QLOjfUkEsePRCVlwXXHfQgZ4Gilg26NdNHJUhvK8sU3ueMLhLgblojjAVG4/eYzhP//q8DjAUNbm2CuU/1iJ+glkjFt2jRu8uzdu3djwoQJIuXdu3fHlStXABQ0l/vv3F+SkpSUBF1dXQgEAujr6+PDhw8i36F+fn6wtbUFANjZ2eHu3bsSipQQUt1VqVH4rl69KvLc29sbOjo6CAwM5L703N3dufI6dergjz/+QNOmTfHx40fUrVsX3yIvL891HiekKklJScGUKVNw4sQJ8Pl8br2mpibmz5+PWbNmVftan6qobt262LhxIzZu3CjpUDg3QhLwJSMPOqrycGygI+lwvslEUwlPFnWBFI8Haakfn5sy0lLo0lAXXRrqIj41B6eeRiP6axaGtjaBjcmvV8NT1X38+JFb7tGjh1h5z549uQQqMjKyssL6oaioKK5GrLgbUB07doSmpiaSkpLw4cMHSYRICCEl8lM9gAs7gGpoaBRbnpmZCS8vL5iZmcHY2Pi7+7p79y50dHRQu3ZtODg44I8//qhWE4CS6k8oFOLJkyeIjY2Furo62rdvj/z8fDg4OHADNBSVlJSEOXPmIC4urkpd5JPyk5OTg6ysLKipqUFaWhrHnkQBAAa1NOZG3quqyhqfnpoCpjpalnM0pDwVbb767t07GBkZiZS/ffu22G0lTVFRkVuOiooSK09NTeWmJyi6Lak6BAIBPn/+DDk5OWhoaNDNQ/LLKvMVgFAohKenJzp06IDGjRuLlO3cuRMqKipQUVHBlStXcOPGDcjJfbv5h7OzMw4ePIhbt25h7dq18PX1hYuLyzfbbufm5iItLU3kQUhJ5OfnIyoqCvHx8SjaetXLywuWlpZo164d+vfvD0dHRxgbG6N79+5c8qSmpob58+fD29sbQ4YM4V67adMmPH78uNLfC6k4V65cgZOTE5SUlKCpqQl1dXWMnDQD9999AY8HDG71/RtC5NciFApx+/Zt7NixA3v37v1hv9+f5eLiwi0vXboUWVn/GyAkNDQU+/fvB1DQd8ze3r5CYykNS0tLmJqaAgBu3rwpMrIiYwy///478vPzAYCbGJxUDfHx8ZgzZw50dHRgYGAALS0tWFtbY9euXSItMwj5ZbAymjhxIjM1NWXR0dFiZSkpKSw8PJz5+vqyXr16sebNm7Ps7OwS7/v9+/cMALt582ax5cuWLWMAxB6pqallfTukhouJiWHTpk1jampq3PliaWnJtmzZwhYtWlTs+VT0ISMjw169eiWyzw0bNnDlI0eOrPD3IBQKWX5+foUf51e3ePHiYs8BdbvRzHSeD+ux7rKkQyRVyLlz55i5ubnY+eLo6Mjevn1bIcfMzs5m+vr63LH09PTYpEmT2KBBg5icnBy33s3NrUKO/zPWrVvHxSclJcUGDBjAlixZwlq2bCmy/vXr15IOlfy/N2/eMAMDg2/+Prq4uLCcnBxJh0mIiNTU1ArNDcqUQHl4eDAjIyP24cOHH26bm5vLlJSU2NGjR0t1DC0tLbZ79+5iy3Jyclhqair3iI6OpgSKfFNISAjT09P7YZJUeNGzatUqNnjwYMbj8bj1TZo0EdtvVlYWU1RUZACYubl5hcV///59NnDgQO5Yenp6bM6cOcXevCA/58SJEyLng6mpKevatStTqaXGjKYcYqbzfJhmUwcWHx8v6VBJFXDo0KHvfp/o6Oiwd+/eVcix/f39mYqKyjeP3axZM/b169cKOfbPyMvLYy4uLt/93LZu3SrpMMn/y8/PZ/Xr1+f+NnJycszJyUkk4QXAZs2aJelQCRFRpRIooVDIPDw8mIGBAQsPDy/Ra3JycpiioiLz8vIq8XGio6MZj8djFy5cKNH2Ff0hkeorPz+fWVpacl/yCgoKrGfPnqx9+/ZiP9qrVq0See327du5slq1ajGhUChSLhAImLq6OgPATExMKiT+ondr//uoXbs2e/jwYYUc91dV9KJg3bp1TCAQMMYYO/XoHTOd58MMPQ4ySEmzlStXSjhSImnJyclMWVmZO1/s7OzY33//zdasWcNMTEy49c7OzhUWw8uXL1m/fv2YtLS0yPfC7Nmzy/X3UCgUin3//Yzc3Fy2bNkypq2tLfKd1qRJE3b27NlyOw75eefPn+f+Po0aNWKfPn3iym7cuMFkZWUZAKaiosLS0tIkGCkhoqpUAjVp0iSmpqbG7t69y+Li4rhHVlYWY6yg6d3q1avZ06dPWWRkJPP392e9evViGhoaLCEhgdtP/fr1uS/J9PR0Nnv2bPbw4UMWERHBbt68yZo3b84sLS1LXCVMCRT5lrNnz3Jf/tbW1iwuLo4ru3PnjsiPd9FzlDHG0tLSRGqh/tukpOgPi4uLS7nHfvHiRZH4tLS0WOvWrbkfLABMU1OTffnypdyPXVKRkZFs0aJFzMHBgdna2rLJkyezoKAgicVTnOw8foku/j5+/Mh9rjY2NiKvGb73ETOd58PUO438Zo0k+bVs3ryZO1+GDRsmcr4kJyczIyMjrryiaqEKJSQksPv377MnT55wv8c/SyAQsBMnTjA7OzsmJyfHpKSkWJMmTdi2bdvK7Rg5OTnMz8+PXbp0iQUHB5drkkbKx+jRo7nz2MfHR6x8/PjxXPmZM2ckECEhxatSCdS37oQX1i7FxMQwFxcXpqOjw2RlZZmRkREbNmwYe/Pmjdh+Cl+TlZXFunXrxrS1tZmsrCwzNTVl48ePL1UTGUqgyLeMGjWKO08vXbokVl40GTl9+rRYedE7yQ0bNmQXLlxg4eHhbMuWLSL9qSrirmnRWrJFixax3NxcxhhjcXFxzNbWlitbu3ZtuR+7JDZt2iRy57voY/z48VWiv9abuDTWbMU15rDhDnsT9/27o0+fPuXid3d359Z//JLBTOf5sDrzfZhe3UYMADMyMqro0EkVN2DAAO58Ke6mwfLly7nyQ4cOVX6APyEvL0/k/f33YWNjwxITEyUdJqkEPXv25P7uMTExYuW7du3iyvfu3SuBCAkpXkXnBqUaxpz9YM5dAwMDXL58uVT7UVRUxLVr10oTBiEllpyczC03a9ZMrFxPTw/R0dEAgODgYPTv358rS0lJEXl9SEgIXF1dxfbh6OiI3r17l2PUwKdPn/DgwQMAQKNGjbBy5UpuuFg9PT3s378flpYFQ00fP34cc+fOLdfj/4iXlxdmzpz5zfK9e/dCXl6em+xTEnLyBZh+PAhfs/LxNSsffXb4Y00/a/SxMSx2e11dXW75/v37YIyBx+PheEDB+dHCQAln3r8GAGhra1f8GyBVWuFocQCKnaSx6Lqi21YHCxcuxOnTp7nnpqamUFZWRkhICAAgKCgIQ4YMwc2bNyUVIqkk+vr63PK9e/dERqAFAF9fX26Z5vIkv5KqPZEJIT/JwMCAWy5uVnstLS1uec+ePbh06RJyc3Px5MkT9OzZExkZGQCKv0ACgH79+uH8+fOQlpYu17gTEhK45Q4dOojNtWFhYcFd8CcmJpbrsX8kPz8fCxcu5J5Pnz4d0dHRSE5OxqZNmyArKwsA2LFjh8iEn5Vt3dUwvIlPh6ayHDpaaCE7XwDPE8+x+PxL5PLFp0gwMjJC+/btARQky4sXL0Z6ZjZOPS1IoD7eOsJt+9+LCPLradSoEbd88OBBkTKBQIDDhw8Xu21Vl5KSgp07dwIAZGVlcerUKUREROD169d4/Pgx971z69YtBAQESDJUUgmKftfNmTMHz549A1Bwju/fvx8nTpwAUDCxfJcuXSQSIyESUSH1WpWMmvCRbynaz8nAwIA9evSIMVYwuETRpgffe6ipqbGwsDB24cIF5u7uzoYMGcJmz57NgoODKyzuov1xmjVrJtY3ICIiQqTjdWUq2jerV69eYuVLly7lylesWFGpsRXyDfvMTOf5MNN5PuxWaDzjC4Rs4/Uwbl3vbX4sOjlT7HWi/c54TLdDf2Y6z4cZ/f/gEfj/vmiS7HdGqob3799zfSSlpaXZwoUL2evXr9m9e/dEmj01adKkWvXtOXz4MBf7pEmTxMr37NnDlc+cOVMCEZLKJBQKWdu2bUV+E62srMRGtl29erWkQyVEREXnBlQDRWo0Ozs7dOjQAQAQGxuLtm3bom7dutDX18ekSZO47Yo2UyhKT08P165dQ7169dC7d2/8/fffOHbsGNavX48mTZpUWNympqZo2bIlAOD58+dYt24dN7F0SkoKJk6cyG07cODACoujOO/eveOWBwwYIFZedF3RbStLcmYeZp0KBgCMamcKBytdSEvxMLNrPXiNaQV1JVkEf0pFz233cTfss8hrbbs4w/2P3dDsMRNGUw5BoeMYAEDGixuAUIDatWvDx8cHmpqalf6+KkNGRgb27NmDXr16oXPnzhgxYgSuX78OoVAo6dCqHHNzc8yYMQNAwd341atXo1GjRrC1tYWPjw8AQFpaGps2bRKrQa7K4uPjueVOnTqJlRdd9/nzZ7FyUrPweDycPXsWjRs35ta9efNG5Dz57bffMG/ePEmER4jElKoPFCHVTeGXv5OTE54/fw4A+PDhg8g2kyZNwpYtW3D58mUcOXIEcXFxUFdXh6urK4YOHQplZWUJRF7QXGLw4MEAgPnz52Pnzp2oV68eHj58iMzMTAAFTQvHjx9fqXEpKipyy7GxsWLlRdcV3bYyMMYw78wLJKbnwkJHBQu7NxApt6+vg3+ndITH0Wd48SkVY7wDMLlzXagqyOL2m88IjPwKgdAIKo2NAADC3CxkhT+E4kc/TJg3D1OnToWhYfF9qIoSCoW4c+cOQkNDIScnh06dOqFBgwY/fJ0k+fn5oX///mJNQo8cOYIOHTrg3Llz1PfrP9avXw9paWls3LhRLMnU0NCAt7c3HB0dJRRd2RS9OfD06VMMHTpUpPzp06fcsoaGRqXFRSRHX18fjx8/xj///IO9e/dy32u2traYMmUKXFxcqtVNAkLKA4+xH4wMUQ2kpaVBTU0Nqamp3+yrQv4nPz8fV65cEfkSbNGihaTDqlDZ2dk4ePBgsV/+Xbp0qbJf/kuWLMEff/xRbJmKigouXrwIe3t7MMZw5HEUUrPzMcmuLqSkKu79hIWFwcrKCgBgaGiIZ8+eQUdHBwCQm5uLrl27ws/PD0DBABeFSWBlOPo4CgvPvYSctBTOebRHIwO1YrfL5Qvw+78hOPI4SqzMQkcFDlY66FxfG63qaEAKrFR93M6dO4fZs2eLJeqOjo7YvXs3LCwsSvemKsHr16/Rpk0bLjEvTsuWLeHv7w85OblKjKx6iIqKgre3N0JCQiAnJwc7OzsMGTJEYjdffkZiYiKMjIyQl5cHRUVFXLlyBXZ2dgAKapS7du3K9W309fWFra2tBKMlhJDiVXhuUCENAysZ9YEqucOHDzN9fX2xfj5t2rRhr169knR4NVpmZiZ78+YN+/DhAzdBa0lcuXKFOTk5MSkpKW7CwokTJ3KTWefxBWzWyedc/56rr+J+sMef161bN+7c0dDQYNOnT2eLFi1i5ubmIn3OCoderwxvE9JZ/cWXmek8H7b33vsSveZMYDTruPYWG/3PY+btH8GiksT7RZXGoUOHvtufTltbm719+/anjlERBg4cyMXo4ODAnjx5wtLT09nJkydFvi8OHz4s6VBJJZgwYYLIeduiRQtmZ2cnMm1B69atJdq36+XLl8zT05M5OTmxXr16sfXr19PQ6oQQTkXnBlQD9QvZu3cv3N3dv1leu3Zt+Pv7V/mmRtXNx48fsWrVKhw9ehRZWVkAABMTE0yaNAmenp5QUFAo0X5yc3ORmZkJNTU1rkYkM5ePyUeewTf8f82ubEzUcXZS+wqtVYuMjETHjh3x6dOnYssVFRVx9erVSrs7nccXot8uf7yKSUNHCy0cHNu6QmvhivP161cYGRlxf2M7OzsMHz4cycnJ2LVrFyIjIwEAzs7OuHLlSqXG9j1fv36Fjo4O+Hw+dHR0EBERASUlJa789u3bXDM0BwcH3Lp1S1KhkkqSnZ2Nnj174vbt28WWW1hY4Pbt2zA2Nq7kyApaUEyaNAn79+8XK1NUVMSePXswYsSISo+LEFK1UA1UCVAN1I8lJiYyBQUF7u5hjx492JEjR9i2bdtYvXr1uPWOjo6SDrXKSsnKY39eCWV9dtxnZwKjmUDw47uvwcHBTFNT85s1Era2tiwzs2y1HonpOazXNj9mOs+H1V98mZ14EsUsFxXUwDyJSCrTPksjOjqaDRkyhMnIyIi8JwcHBxYYGFhux0nOyGU+wbHs8YcklpieU+xd7zWXQ5npPB/WdMU1Fp+aXW7HLo3Nmzdzn8GwYcNE4kxOTmZGRkZc+bt37yQSY3GePXvGxeXm5iZWLhQKmYaGBgPAjI2NJRAhkYTc3Fy2fft21rBhQ+780NfXZ0uXLmXJyckSi8vd3f27tbw8Ho9dvHhRYvERQqoGqoEqAaqB+rENGzZgzpw5AICxY8di3759XA1Feno6mjRpwrVrf/PmDerXr1+m4zDG8OTJEzx8+BB8Ph+NGzdG165dy32epMqUxxfi8KNIbLv9Fl+z/jchZiODWljYvQE6WGgV+7r8/HzUr18fERERAABVVVU4OzsjOTkZt2/f5iaU9vDwwPbt20sVU2RSJkb98wSRSVmorSSLf9xawcakNhacfYljT6LQpYEO9o1uVcZ3XDoJCQl4+vQp+Hw+GjVqVK59fN4mpGPUP08Ql5rDraulIANzbRWYayvDXEsZinIy+ONSCBgDdo9oAefGkpnMceDAgdzko0FBQWITN69YsQLLly8HUDBv0MiRIys5wuKFhoaiYcOGAAAnJydcvXpVpDwtLQ3a2trIy8uDpaUlwsPDJREmkaDU1FTw+XxoaGhItL9o0XNVXl4eq1atwrBhw5CcnIw1a9bgyJGCudrq16+P0NDQKtu3lRBS8So6N6BR+H4Rjx494pY9PT1FflhUVVUxbtw4LFmyBADw+PHjMiVQQUFBGD9+PAIDA0XW16lTB1u2bEHv3r3LGL1kMMbg8yIO66+FISq5oFmWhY4KHBvo4OijKLyOTcPwfY/Rub42Frg0QH09VZHXX7hwgUuemjdvjuvXr3MjXD169AgODg7Izs7GP//8gz/++APq6uoliuvFpxSM8QpAUmYejGor4uDY1jDXVgEAjO9khuMBUbgZ+hnhCemop6v6g739PF1dXfTo0aPc9xsY+RVjvQOQmp0PvVoKkJHmISYlG2k5fDyPTsHz6BSR7Ye2NpZY8gQUJMyFivuyLrqOz+dXSkwlYWlpCUNDQ8TExOD69et48OABN6EwAKxduxZ5eXkACprwVaSMjAzcv38f6enpMDIyQps2bSAlRbNtSJqaWvGDsVQ2Ly8vbnnFihWYNWsWgIJR4g4dOoSIiAg8ePAAYWFh8Pf3R8eOHSUVKiGkhqNfpl9E4RxCAIrtc1N0uOmi25ZUUFAQbG1txZInoKAPUJ8+fbgZy6uDxx+S0GeHP6YeC0JUcha0VeWxpp81rk7vhAUuDeA71x5u7etARoqHu2GJcNlyD3NPByO+SE3J+QsXIF1LBwpmzdFl8h/Y7BeLkfsfY8O1MDRt3gpjxhTMMZSdnY2bN2+WKC7f8EQM2fMISZl5aGRQC2cnt+eSJwAw11aBU8OCJGLPvQ/f2k2Vd/tNAobve4TU7HzYmKjjyvROuD/PAaG/O+OqZyfsHN4cs7vVQz8bQzQ1VoejlQ6W9Gwo0ZiLzpNy8OBBkTKBQIDDhw9zzxs1alRpcf2IjIwMJk+eDKDgpoG9vT3c3Nywdu1adO7cGatXrwZQMCVA4XblLTs7G7Nnz4ahoSFcXFwwaNAgtG/fHvXr1xf53MivLSwsjFv+7+iePB5PZB3VlBJCKhLVQP0imjRpgvPnzwMA/vnnH6xZs4Yr4/P5OHDgAPe8adOmpd7/hAkTkJGRAQBo2LAhPDw8oKysjAMHDuDOnTtgjGHChAno0aMHVFRUfrA3yfn4JRN/XArBzdCCCSKV5aQxwa4ufutkBiW5//130VCWw/LejeDWvg7WXXuDyy/jcfLpJ1wMjkVHC218+pqFMP3+MJo0BABw4q0QeFswZLbf2y+49DIO7S2ac/tLTU39blw5+QJ4P/iIDdfCwBcydLTQwq4RzaGqICu27QQ7c1x9HY8Lz2Mwq1s96KtV/FxMjDHk8oWQ4vEgI8X7qQEcTgd+wrwzLyAQMtjX18aO4c25z15BVhpWerVgpVf1muqOHTsWq1evBmMMf/zxB/Ly8rhBJNauXYtnz54BKPi/2KpV5TSvLKlZs2bh5s2buHPnDvLy8kS+DwqtWbOmQiaPzs3NRY8ePXDnzh2xsnfv3mHkyJGIiYmhiToJ5OXlueXExETUqVNHpLzoxL5FtyWEkPJGfaB+EVFRUTAzM4NQKASPx8PUqVMxfPhwJCUlYf369dzFS4sWLRAQEFCqtuOBgYFo2bIlAKBBgwYIDAzkarQYYxgwYADOnj0LANizZ0+lT/xaErl8Af72/YDtd94hjy+EtBQPQ1sbY7pjPWir/viHODDyK1ZfDkVg5FeR9Yyfj/yUWDQz04N9y4bQVJbHnnsfEJ+WAzCGtIDzSPE7hEsXz8PFxUVsvwIhw9lnn7D5Rjhi/792y7WZAdYPaAo5mW9XIA/6+yGeRCTD3dZcbDLZ8pQvEOLcsxjs8n2PiC//m0OIxwOkeTxISxU8pACYaymit40xulvrw0BdPKljjOHvex/w55U3AIB+zQ2xtn8TyEpXn4ry2bNnY+PGjd8sl5aWxrVr16rk5KrZ2dlYunQp9uzZg7S0NG69paUlli1bhuHDh1fIcVevXo1FixYBAOTk5DBs2DBYWVnh6tWruHv3LoCC2oXnz59XSAJHqo9du3ZxtaCurq44c+YM1782Pj4eTZs2xefPnyElJYWIiAiYmJhIMlxCiARVdG5ACdQv5HuTsgIFFy+3bt0qdbvx7du3Y+rUqQCALVu2YNq0aSLlfn5+3HDWY8aMwT///FPKyCvWg3dfsPj8K3z4/wSgk6UWlvVqBAud0tWUMcZwNywR7xMzYK6tjOTINxjo4gAwIXR1dXHs2DF07twZX1IzMfqviwjJKehXIEyNx8lZvdDWQkdkX7dCP2PdtTcITyio2dNXU8CMrvUwoLnRD2t4br9JwFjvp1CRl4H/fAeoKYrXVP2MXL4Ap55+wq677xGTkl3q1zczVkPPJgZwsdaHoboihEKG1ZdDse9+QZ8xd1tzzHe2+uH7ZIzh8+fP4PP50NPTk/hgJUKhEAsWLMCGDRsgFApFyjQ0NODt7Y1evXpJKLqSycjIgL+/P9LS0iq8HxKfz0edOnUQExMDHo8Hf39/tGvXjitftGgR14RwwoQJ2L17d4XEQaqHtLQ0mJiYcDX2zZo1w5AhQ5CUlAQvLy98+fIFANCnTx+cO3dOkqESQiSMEqgSoASqZBhjWLlyJVatWsV1Ci+kr6+PgwcPokuXLqXe7+a/tmDuyvWQ060L11GTIa1dB6FxaVCQlca4jmawkk1C+zYFTZZGjRpVbPOgksjMzMTRo0fh4+PDdTIfOXIkHB0dy3SBl5iei9WXQ3EuKAYAoK0qj6U9G6JnE/1yGb2JMQZHR0eRpkkGBgZIT09Heno6FMxbQtN5KmRUNcHjAeM7mWNm13p4FZOKP6+8wdP/r81SU5SFh31djGpXBwqyJUsQhEIG5y33EJ6QgXnOVpjUue5Pvx8AyM4T4NiTKPx97z0S0nIBAFoq8nC3NcOAFsaQluJBIGQIf/sW/foPxOcvX8DjSYEnKw8FkyZQsuoIeaOG4PH+9/dqaqyO2kqyuBtWMJfVwu5WcLf9frw5OTnYsWMHdu7ciQ8fCvp6aWpqYty4cZg9eza0tbXL5f2WVXR0NLy9vRESEgI5OTnY2dlhyJAhIvMrEdFR1YqbHys9PR1aWlo0AiDhXLhwAf379/9mX10TExP4+/vDyMiokiMjhFQllECVACVQpZOYmIhDhw4hNDQUcnJysLW1Rd++fSEnJ1fifbxPzIC3/0e8jk3F65gU5H5n3Al5YQ7ibnkjPfgaNqxdw42cVJw3b97g2LFjiI2Nhbq6OlxdXdGhQwfcv38f/fv3R2JiothrOnTogHPnzpX4olkoZDgWEIW1V94gLYcPHg8Y1dYUs5zqo1YxfYp+RlJSErp3744nT54UWz5l5lzItRmKM88KkjhNZTkkZRYkt/IyUhjTwQyT7OpCTan0cZ0J/IRZp4KhrSqP+/PsIS9T9tqZnHwBDjz4iL1+H/AloyA+vVoKmGhnjiGtTUQSu8Lh6ws7fMvLy8Pe3h7Jycl48uQJpFU0oFSvPeo5DkaSdG0UfgPJSPGwbkAT9Gv+/QufjIwMuLi44P79+8WWm5qa4s6dOzAzMyvz+yWVIygoCM2bF/QFdHNzExllDSi4CaGlpYXk5GQYGxsjKipKEmGSKub27duYM2cO168QKGge269fP2zevBmGhoYSjI4QUhVQAlUClEBVLsYYem/3x8uYIgMf8POQm/ABeZ8/wEpXGWP6dkNCriwOPUtEjlRBfxdBehLmuzbHbw4NxC7mMzIyMHbsWJw6dUrseNbW1vgQHYNcyEFaWR1SSrUBJkD2h0BAWJC5tWrVCvfv3/9hEhiZlIkZJ57jWVQKAKCxYS2s6mONpsbqZf9AfiAvLw8nTpzA3r17RWokPDw8uOaSt0ITsODsS3xOz4UUDxjU0hieXepBT018xMQSH5cvhN36O4hLzcHa/tYY3Kps/QEYYxjrHYA7/19DZFRbEZM618WAFkbFJmUXLlxAnz59ABSMNnf9+nUYGBgAAG7duoXu3bsjLy8PKioqCA6LgH9kBh59SMaQ1sboZPnjJPi3337D/v37uecdO3aEsrIybt++zQ0l3rx5czx9+pTmganivn79Ch0dHfD5fGhrayMiIgLKyspc+e3bt7n+Yg4ODrh165akQiVVDGMMz58/524Etm/fnvueIYQQSqBKgBKoyvX4QxIG73kEeRkprO3fBI0N1RD29B569+ol1u8D0jJQse4KtXaDIFOr4OJYX00BkzvXRRtzTXzNzENSRg6WrlqHt5ExkFKsBWlF1YJ/ldUhpaQOaSV1SMmJJxIGigJEnliJ2NCnAIAjR45g2LBh34z7wvMYLDr3Chm5fKjIy2B2t3oY2a4OpH9ixLjylJqVj4vBMWhXVxMWOuUzf9M+vw/441IozLWVcXOGXZlGxzv5NBpzT7+AnIwU/nBtjL7NDb87sMPo0aO5Ybx9fHzE5ohyd3fH3r17AQBnzpxBv379ShxLQkICjI2NkZ+fD2VlZdy8eRNt27YFAERGRsLR0RHv378HUHDxbW9vX6r3Sirf4MGDcfLkSQCAvb091q5dCysrK1y5cgWenp6Ii4sD8OP/34QQQkghmkiXVDl7/Qo6+vdvYYQ+NgVNJSy6d8fZs2cxbtw4JCUl/W9jAR/5obcxZagD9DvaYdfdD4hLzcGSC69Fd2rWDbV/0OKK5efAWFsd2rUU8CExE7HZgKLrctSq5Y20J2exf//+Yi+wsvL4WHbhNU4FfgIAtK6jgb+GNCt2JDhJUlOSxch2dcp1n0Nam2DLrbf4kJiJm6EJ6NaodBPNJqTlYKVPCABgZtd6GNTK+IevSU5O5pZtbGzEygubbAEFNRClcfnyZa6WafLkyVzyBBQ03Vu5ciV3Dpw9e5YSqGpg6dKluHz5MjIyMnDnzh20bt1abJtWrVphwIABEoiOEEIIEUcJFCmVD4kZuPUmAQAwtoNoxuPq6opu3brh5MmTePDgAfh8PqytrTFy5EhoamoCAAa3MsGJgGjsu/8B6Tl81FaSQ2xEOL4mxECYnYY+Ll1h06ge1JVkoaUij7cvAzFj4jgIslIhyxPiXUYGZGVl8Tk9BwvPvsTN0M+o3dkNSvXa4m3gcbF4Q2LTMPXYM7xPzIQUD5jqYImpDhaQqUZDY/8MFXkZjGxrip133+Pvex9KlUAxxrDo3Euk5/DR1EgNv3UsWZ8ifX19bvnevXsYMmSISLmvry+3rKurW+J4ANHkrFmzZmLlRRO2lJSUUu2bSEajRo1w+fLlH/ZxLE0fTUIIIaQiUQJFSuUf/wgwBjha6RQ7zLeioiJGjx6N0aNHF/t6BVlpjG5fB6Pb1+HW1a7dFykpKTAwMMBen00i/VZMpMzBTy1I2PIAxMTEoE6dOtBRVcDeUS1x5ME7LDwdBHkDK0B3Ifbfj8CY9nXA4wEHH0Zi1eVQ5PGF0KulgL+GNENbc81y/TyqA7cOdbDPLwKBkV/x9GMyWtbRKNHrLjyPxc3Qz5CV5mHdgKYlTjqHDh3KNdGbM2cOLCws0LJlSwgEAvzzzz84frwg0dXS0ir1qI9FkzNfX1+xGsfCeYMAQE+vdLVtRHI6deqEDx8+4OjRo7h06RI3hPqoUaPKPMomIYQQUlEogSIl9jUzD6f/vxncb53My22/hRdH+fn5EAqFInP5WFpaQl5eHrm5BUNmBwUFcbPP83g8vLlyALH7/4amyzQomjXHSp8QXHsdDzVFWdwIKUi8HK10sH5gU2go/5p3sHVUFdC/hSGOPYnGumthODCmNRTlvj8iX2J6Lpb/W9DMcpqDJerrlbxPVufOndGuXTs8fPgQnz59QqtWrVCvXj2kpKTg8+fP3HYzZ86EgkLpBsno2bMnlJWVkZmZif3796NTp04YOnQopKWl4efnhyVLlnDbDh06tFT7JpKloqICd3d3uLu7SzoUQggh5Lvotl4VlpqVj803whEWny7pUAAARx5HIidfiEYGtdDWvGS1GCVR2I8lMTERx44dEykLCQkRmbNqyJAhGDNmDNatWwd7e3usWrUKgvQv+HxyKSa3qg0lOWk8iUjGjZAEyElLYVmvhtg3uuUvmzwVcretCzlpKTyJSMbAvx8gLvX7k98uvfAKKVn5aKhfCxNLOYcUj8fD2bNnYW1tza0LDw8XSZ7Gjx+PefPmle5NAKhVqxY3UbNAIMDIkSNhZGSEunXrwtbWlptI09nZWaSvFSGEEEJIeaFR+H4gPCEdC86+hJaKHJoaq6OZkToaG6mV+3xBxZly9Bl8XsRBTVEWJya0hZWe5EYYzOUL0HHtHSSm5+Kvwc24wSPKg4+PD3r16gUAkJGRwYQJE+Do6Ijg4GBs2bKlRH1Z1qxZg/nz5yMqKQtLLrxCcmYe1vSzRmNDtXKLs7p7/CEJk448Q3JmHrRU5LFnVAs0N6kttt2lF3HwOPoMMlI8XJjSAY0MyvYZZmVlwdvbW2z49ilTpsDJyanMQ4zz+Xy4ubnhyJEjxZa3adMGV65cQe3a4u+NEEIIITUfDWNeAhX1ITHGMHjPIzyJSBYrq6utjKbG6mhqpI5WdTTQ0KB8/zgBH5MxcPdD7rmWijxOT2yHOlrK33lVxTn1NBpzTr+AXi0F+M2z/+4w1qXFGMPw4cPFap+KatasGWxtbeHt7Y20tDRuvYWFBZYuXYqRI0eWWzw1WXRyFsYffIo38emQk5bCmn7W6N/ifxPXJmfmoesmXyRl5mGagwVmdqsvwWi/jTEGHx8f7Ny5E/7+/tyAJe7u7hg5ciQNOEAIIYT8wiiBKoFvfUgRERHYs2cPNyJc48aN4e7ujhYtWpRov3fefMYY7wDIyUhhuqMlQuLS8OJTCqKTxZs/TXOwwIyu9cpl4k6hkMF1R8FEtb2bGuDt5wyExqXBUF0Rpye1g75a5Q6/zRiDyxY/vIlPx3wXK0y0K12TrpLg8/lYuHAhtm/fjuzs/32+UlJSGDhwIHbv3g11dXVkZGTAz88PaWlpMDY2Rtu2bamDeSll5PIx48Rzro/YBFtzzHW2grQUD9OOBeFicCzq66ri36kdISdTcZ8tYwy+vr44evQoYmNjoa6ujj59+sDV1RWyshVfw0sIIYSQmokSqBIo7kPasGED5s+fD4FAILb92LFjsXv37u9epAmEDD22FiQNE2zNsaB7A64sKSMXLz6l4nl0Cp5FfYXf24J+F5M618Vcp/o/nUQVTlyqKi+DO3M6gzFg0N8PEfElE3W1lXFyQjtoqsj/1DGAggvYksTq9zYRI/c/gZKcNB4ucISaYsVd3H79+hXnz59HXFwc1NXV0aNHD5iamlbY8X5VQiHDphvh2H7nHQDAvr42ejU1wMyTwZDiAecmd0BTY/UKO35iYiL69+8PPz8/sTJzc3OcP39epA8VIYQQQkhJUQJVAv/9kPbt24fx48d/9zWTJ0/Gjh07vll+JvATZp0KRi0FGdybaw91pW83Cdp/P4KbbHR8JzMs7N6gzElUek4+7Df44ktGLhZ1b4DxtgWj3cWkZGPgrgeITc1BY8NaODq+7U/1w7oT9hmLzr6EiaYSNg5qBsPvTCo76p8nuBeeCLf2dbC8d6MyH5NUPReDYzHnVDBy+UJu3US7upjvYlVhx8zJyUH79u0RFBT0zW20tbURGBgIY+MfT9xLCCGEEFJURSdQNa7tU15enshQxjNnzkRcXBzS0tKwZcsWrm/Erl278PHjx2L3kZMvwKYb4QCAyfYW302eAGBcRzOs+P/EYq9fBH73CUFZ89Idd97jS0YuzLSUReZKMlRXxKHf2kBTWQ6vYtIwzjsA2XnitWs/kscXYvXlUIzxCkBsag4efUhGj61+uPn/zbn+Kyw+HffCEyHFE584l4hijOHz58+IjY0ttuazKurd1ACnJraDXq2C4cTNtZXh2cWyQo95+PBhLnnS19fHkSNHEBcXh2vXrnET4SYmJuLPP/+ssBgyMzOxZ88edO7cGfXq1UPr1q2xatUqkZECCSGEEEKKU+MSqKtXryI+Ph4A4Orqio0bN0JPTw+qqqqYNm0aFi5cCKDgYvfAgQPF7uPwo0jEpGRDr5YC3IokMd8zun0drOrbGADg5f8Ryy6+hlBYuiQqMikT/9yPAAAs6t5ArP9JXW0VHBjbGqoKMgj4+BUTDwcir0jNwY9EJWVh4N8PsefeBwDA0NYmaGKkhpSsfPx28ClWXQpBvkB0f/vvF2zr1EgPJppKpXo/v4qcnBxs3LgRlpaW0NXVhaGhIfT09DBv3jxuWO2qrImROi5O6YA5TvVxYExrKMh+f46on7Vv3z5u+fTp0xg2bBj09PTQrVs3XLt2DUpKBefZwYMHufm/ytObN2/QuHFjTJgwAb6+vnj79i0CAgKwePFiWFhY4Pr16+V+TEIIIYTUHKVKoNasWYNWrVpBVVUVOjo66NOnD8LCwkS2mTBhAurWrQtFRUVoa2vD1dUVb968+e5+GWNYunQp9PX1oaioiC5duuDt27elfzcA3r9/zy3369dPrLx///7FblsoLSef6xcyo6tlqS4mh7cxxdr+1uDxgIMPI7Ho/KtSJVGrL4ciTyBEJ0stODbQKXabxoZq8HJrBUVZafiGJ8LzRBDiU3N+uO9LL+LQY6sfgqNTUEtBBrtHtMCaftY4NbEdxnSoA6Cg9mzQ3w/x6WsWgILJVM8HxQIo34lza5LMzEx07doVs2fPFjmfvnz5gnXr1qFVq1bfrOmsSnRqKcDD3gLGGhWfJIeGhgIATExM0L59e5EybW1tdOvWDQCQkZGBmJiYcj12SkoKunXrJvI3UVX93yTB6enp6NOnD16+fFmuxyWEEEJIzVGqBMrX1xceHh549OgRbty4gfz8fHTr1g2ZmZncNi1atICXlxdCQ0Nx7do1MMbQrVu37zZpWrduHbZu3Yrdu3fj8ePHUFZWhpOTE3JyfpwY/Jei4v/68hRefOULhFyTuk+fPhW7baG/fd8jJSsfFjoq6N/cSKy8qNzcXPj5+eHy5ct48eJFwbDnrUywfkBT8HjAsSdRmH/2BQQlSKIevP+Ca68TIC3Fw5KeDb/bh6plHQ38PbIFZKV5uPwyHm3X3ELXTb5YfvE1boYkID0nn9s2J1+AhedewuPoM6Tn8tHCtDYuT+8E58Z6AAB5GWks69UIu0e0gKqCDIKiUtBj631cfx2PQw8/Ik8gRHMTdbQwpTl1ijN9+nTcv3+fe96hQwc4OTlxA5R8/PgR/fv3L3OTzppIXr5gAJT09HTk5+eLlSclJYltW1727duH6OhoAIC1tTUCAgKQlpaGDx8+oGfPngCA7OzsCm0+SAghhJDq7acGkUhMTISOjg58fX1ha2tb7DYvXrxA06ZN8e7dO9StKz78NWMMBgYGmDVrFmbPng0ASE1Nha6uLry9vTFkyJAfxlG0o1hCQgKsmrSAvGEDaFq1QgungQhNyIKKvAyW9qiPDdOHcxe8J0+exMCBA7n9JKTlwG79HeTkC7FnZAt0a6RX7PHy8vKwatUq7Ny5U6SJVpMmTbB8+XL07dsXF57HYMaJ5xAyoGcTfSzq0eCbw48XHfFvdDtTrHBt/MP3DBQMBLH5RjhexqSi6F9RWoqHZsbqaF9XE9dfJyAsIR08HjDJri5mdK33zTmcopOzMOXoMwR/SgUAyMlIIY8vxM7hzdHdWr9EMf1KEhISYGxsjPz8fCgrK+PGjRto164dACAyMhKOjo5crdTt27dhb28vyXCrjIEDB+L06dMAgK1bt2Lq1KlcmZ+fH/ddUrduXbx9+7ZcpgYoZG1tjVevXgEoqAmzsvrfYBmZmZkwNTVFUlISZGVl8fXrVygrS2beNUIIIYSUXUUPIiHzMy9OTS240NbQ0Ci2PDMzE15eXjAzM/vmaFoRERGIj49Hly5duHVqampo06YNHj58WKIEqtCS8y/xMjEfxtP/NyHr85gMAEAuPw/TT75EulJT8GSewFCvoAliUVtuvUVOvhAtTGuja0PdYo+Rn5+PPn364MqVK2JlL168QL9+/biLQmkpHqYffw6fF3G4+ioePZvo47dO5mhsqCbyuuMBUXgTnw41RVl4dqlX4vdrX18H9vV1kJKVh4fvk3D/3Rfcf/cFkUlZCIz8isDIrwAALRU5bB7cDJ0stb+7P2MNJZya2B5rr77B/vsRyOMLYayhCKdvJJJlxefzkZCQADk5OWhpaZXrBXJlunz5MleDMnnyZC55AgBTU1OsXLkSw4YNAwCcO3eOEqj/5+HhwSVQ06ZNw927d+Ho6Ijg4GCRfomTJ08u93MjMjISQEFyVjR5AgBlZWU4ODjg1KlTyM/PR3x8fLE3fQipTGlpaTh06BAePnzIzWc4ZswYGBoaSjo0Qgj5ZZU5gRIKhfD09ESHDh3QuLFojcnOnTsxd+5cZGZmon79+rhx4wY3+t1/FQ74oKsrmrDo6upyZf+Vm5sr0rk8LS0NAHAuKBZS8gV9OFhqPDI+BiM35g3yYt9AubED1NoOhKqNCxRNGmFd34Yi80C9T8zAiYCCpj3znK2+eeH2119/ccmTtLQ0+vXrBysrK1y9ehUBAQEAAE9PTzg6OqJnk4bQVJbHXzfD8TgiGeefx+L881i0NdfA+E7msK+vg/RcPjZeLxjxb0YXS9RW/v6If8VRV5KDi7U+XP6/lig6OQv+777A/30SVORlMKOrJXRUFUq0LzkZKSzp2RBtzDSw/34EJttbQFqqfC5i4+LisH79enh5eSElJQUAYGVlhSlTpsDd3b3aTZ6anJzMLTdr1kysvHBEOaBgfitSoHPnzpg2bRq2bt0KADh79izOnj0rso2joyOmTJlS7sdWUVFBeno64uLikJmZKVbDVLTvpYqKSrkfn5DSOHbsGCZMmID09HRu3YkTJ7B8+XIsWrQIy5cvr7Y3oAghpFpjZTRx4kRmamrKoqOjxcpSUlJYeHg48/X1Zb169WLNmzdn2dnZxe7H39+fAWCxsbEi6wcOHMgGDRpU7GuWLVvGAIg9anccxrq5zWS+j56ymJgYNmLECCYrK8uVK9RpxsxnnmCm83xYvUWX2aGHH5lQKCx4P4eeMtN5Pmyc95Nvvmc+n89MTEy4/d2+fZsrEwqFbMaMGVyZh4eHyGtfRKewaceeMfMFl5jpPB9mOs+H2W+4w0buf8xM5/kwx413WR5f8M1jV3ehoaFMX1+/2L8bAObk5MRycnIkHWapHDlyhIvf3d1drHzXrl1c+axZsyQQYdUlFArZpk2bmK6ursh5oKyszDw9Pb/5ffGzxo0bxx1r5syZ3P9/xhg7fPgwV2ZjY1MhxyekpM6dO8d4PN43vzMBsOXLl0s6TEIIqZJSU1MZAJaamloh+y9TH6gpU6bgwoULuHfvHszMvj83UF5eHmrXro19+/Zh6NChYuUfPnxA3bp1ERQUJHIX387ODs2aNcOWLVvEXlNcDVTRJoLy8vI4ffo0evbsicTERAQGBoLP56NRo0ZQ1TbArJPB8A1PBAA4N9LD4NbGGOMVACkecGW6LerrqYodEygY/rhBgwYAgC5duuDGjRsi5SkpKdDR0UF+fj7q1asnNkIhAMSmZOPAg484+iQK6Tl8bv2Bsa1hV+/7Teyqq8LPPjy8oKZNXl4eDg4OSE5OxuPHj7ntZsyYgU2bNkkqzFJLS0uDgYEBMjMzIS0tDW9vbwwbNgxSUlLw8/NDv379uD5ygYGBaN68+Tf3lZqaiosXLyI2Nhbq6uro0aMHjIy+P4hJTZCXl4dbt24hLi4O6urqcHR0hJqa2o9fWEbBwcGwsbHhBvWwtraGg4MDgoODcffuXW47b29vjB49usLiIOR7BAIBLC0tERFRMK3FoEGDMGvWLCgrK8Pb2xsbN24EYwwyMjKIjo6Gnl75NrMmhJDqrqL7QJWqBkooFDIPDw9mYGDAwsPDS/SanJwcpqioyLy8vL65Tz09PbZhwwZuXWpqKpOXl2fHjh0r0TEKs0xNTU3uzpySklKxtWOMMSYQCNnee++ZxcL/1QaZzvNhs04+/+5xAgMDuf2PHTu22PdSGIOxsfF395Wek8/2+31gTpt92ZLzL0v0Pqurc+fOcZ9b48aNWUxMDFd269YtJicnx9U+VNSdgoqyYMECkTvCenp6zNzcXGSds7PzN1+fn5/PFixYwJSUlEReIy0tzYYNG8ZSUlIq8d38GrZu3frdu/pjx44VqZkipLJdv36dOx/t7e3FzseirR3+/PNPCUVJCCFVV0XXQJUqgZo0aRJTU1Njd+/eZXFxcdwjKyuLMcbY+/fv2erVq9nTp09ZZGQk8/f3Z7169WIaGhosISGB20/9+vXZ2bNnued//vknU1dXZxcuXGAvXrxgrq6uzMzMrMTNeAo/pPj4eNavXz/uh2Xx4sXffV1w9Fdmt+42M53nwywXXWafvmZ9d/svX74waWlp7kL5v/Hdu3ePO7adnV2JYv8VjBo1ivtcLl26JFbu7u7OlZ85c0YCEZZdfn4+GzZs2Dcvxlu3bs2Sk5OLfa1QKGQjR4787sV8y5YtWUZGRiW/q5rv33//ZW3bthX5rC0sLNiOHTsoeSISt3nzZu683L9/v1h5UFAQVz5q1CgJRFj1ffjwga1Zs4ZNnTqVLVmyhAUGBko6JEJIJapSCdS3LvIKa5diYmKYi4sL09HRYbKysszIyIgNGzaMvXnzRmw/RWukhEIhW7JkCdPV1WXy8vLM0dGRhYWFlTiuoh9STEwM1268cePGP3xtek4+23YrnN0KjS/Rsfr27cu97+7du7OQkBDG5/OZj4+PSP8ob2/vEsdf0/Xs2ZP7XIrWPhUq2ldo3759Eojw5wiFQnbhwgXm5OTEVFVVmaKiImvVqhXbu3fvd/t1Xbp0SaTGaeLEiezkyZNs8eLFTE1NjSv7448/KvHd/Frev3/P7t+/z169esUEgprbB5FUL9u3b+f+/2/atEms/O7du1z5uHHjJBBh1ZWVlcVGjRpVbP+xzp07F/sbRAipeapUAlVV/fdDKuyYbmRkVO7HCgoKYgoKCt+tNWjSpEm1GxChIo0fP577bI4ePSpWPnjwYK7833//lUCEklE0sfxvwh0UFMRdABgZGdHFPSG/kOfPn3PfDZaWliwtLY0rEwgEIt8d32oe/yvi8/nM2dn5u7/PlpaWLCkpSdKhEkIqWEUnUMXPqFqNhYSEICEhAQAqpGNts2bNcPHixW92dG/evDmuXLkCeXn5cj92SWVkZGDPnj0YM2YMRo4cibVr135zSPjKUHTwkDlz5nDDvQsEAuzduxcnTpwAAGhpaYnMB1bTPXz4EEDB+x4xYoRIWbNmzeDg4AAA+PTpEz59+lTp8ZHq6+vXrwgMDMTLly+Rl5cn6XBIKTVt2hTt27cHUDC0frNmzbBu3Trs3LkT7du3h4+PD4CCORgHDRokyVCrlDNnzuDq1asACuZ1W7lyJfz9/bFr1y5uUJ63b99i/fr1kgyTEFITVEhaVskKs8ygoCDWsmVL7k7T5s2bK+yYycnJbNOmTczBwYG1bNmS9e3bl507d47l5+dX2DFL4uTJkyLNvwofsrKybOXKlRLp3yEUClm7du3E7gLq6OiIrFuzZk2lxyZJ6urqDAAzNDQs9u9S9C7zhw8fJBAhqW7CwsLY0KFDRaZv0NbWZosXL6a+dNXMq1evuO+I4h7S0tLs/Pnzkg6zSnFwcOA+nwsXLoiUvX//nvt/oaWlJfHfakJIxaImfCVQ+CEVfRgYGPxyI5hdvHjxh/OGrFy5UiKxxcXFsSZNmnwzLnd3959uphYdHc2WLVvGunbtyuzt7dnUqVPZy5dVd4RDW1tb7v1fu3ZNpCwqKorJy8szAKx27dosLy9PQlGS6uLJkyfF3jwpfLRq1arajXL5q3v9+jWzs7MT+1s2aNCAXb9+XdLhVTm1a9dmAJi+vn6xN6VcXFy4zzAiIqLyAySEVBpKoErgvwmUnp4eCw4OlnRYlUogEIgMn923b192//599vz5c+bp6SlSExUfX7IBM8pbZmYm27FjB2vWrBmTl5dnqqqqrEePHuzKlSs/XTO2detWJiMjU+yF46RJk6rk3cZDhw5xMaqrq7PNmzezFy9esEOHDrG6detyZTNmzJB0qKSKy8nJYUZGRtw5o6mpycaMGcNcXV25kUMBsN9++03SoZIyePXqFduzZw/buXMn8/Pzo5Eiv0FDQ4MBYDo6OsXekOvWrRv3f+Hjx48SiJAQUlkogSqBwg/J0tKSrV69mn358kXSIVW6mzdvcj8Mtra2Yj+w06ZN48rXrVsnoSgrhre393dr3QCw6dOnSzpMMfn5+SK1UMU9TExMRKYAIKQ4R48e5c6Ztm3bigw68Pz5c6asrMwAMHl5eZaYmCjBSAmpOE5OTtz/gxMnToiUhYSEiExDwufzJRQlIaQy0CASpfD06VMsWLAAmpqakg6l0r18+ZJbHjVqFHg8nkj56NGjueVXr15VWlwVLT8/HwsWLOCee3h4ICIiAomJiVi3bh1kZWUBANu2bUNUVJSkwiyWjIwMfHx80Ldv32LLW7Rogbt370JHR6eSIyPVzaVLl7jlVatWQVVVlXvetGlTjBs3DgCQm5uL27dvV3p8hFSGiRMncsujRo3CnDlzcPXqVaxduxZ2dnYQCAQAAHd3d0hLS0sqTEJIDSAj6QBI+ZCR+d+fMiMjQ6y86Lqi21Z3165dQ1xcHACgZ8+e2L59O1c2Z84cpKenY+XKlRAKhThw4ACWLFkiqVCLpaqqirNnz+L169c4cuQI4uLioK6ujj59+sDW1lYsESakOGlpadxy/fr1xcqtrKy45fT09EqJiZDK1rt3b/Tt2xfnzp1Dbm4uNmzYgA0bNohs07hxY8yaNUtCERJCaooaVQP1K+vQoQO3vHPnTmRmZnLPhUIhNm3aVOy21d3bt2+55QEDBoiVDxw4sNhtq5pGjRph9erV8PLywubNm2FnZ0fJEykxExMTbrlwGOeirly5wi0bGxtXSkyEVDYpKSkcP34cU6ZM4VofFNWrVy/cuXMHtWrVkkB0hJCapOZURfzibGxs0LZtWzx69Ajh4eGwsbHBpEmToKKiggMHDsDf3x8AULt2bQwePFjC0ZYfBQUFbrmwJqqoouuKbktITTJy5Ejs2LEDADB37lzo6uqie/fuyMrKwubNm/Hvv/8CAAwMDLj5xQipieTk5LBt2zYsXrwYp0+f5mr1e/fujXr16kk6PEJIDcFjjDFJB/Gz0tLSoKamhtTU1GpxZ0kgEMDHxwf79u1DaGgo5OTkYGtri8mTJ6NJkyZl3u/Lly/RqVMnpKamFlsuJSWFkydPon///mU+RlUTFhbGNU8yMjLCs2fPoK2tDQDIy8tDt27d4OvrCwA4duwYhgwZIrFYCakojDH06NFDpKZJTU0N2dnZIhPp7tq1S6SfCCGEEFITVXRuQAlUJUtLS0Pfvn2/2ZF7xYoVWLp0aZn3//LlS0ycOBEPHjwQWW9paYktW7bAxcWlzPuuqrp164YbN24AALS0tDB69GioqKjgyJEjePfuHQBAX18fHz9+hJycnCRDJaTCpKamwtXVlbth8F9Lly7F8uXLqWkoIYSQGo8SqBKoLgkUYwy9evUSGTFLRUUFubm5yM/P59bt2bMH48eP/6ljBQcHw9/fH3w+H9bW1rCzs4OUVM3s8vbx40d06NABsbGxxZYrKCjgypUr6Ny5c+UGRkglEwgEuHjxIvbu3YuQkBDIycnBzs4OkydPho2NjaTDI4QQQioFJVAlUF0SqCdPnqBNmzYACvoieXl5oVevXsjMzMTGjRuxYsUKAIChoSE+fvxYo0bLq2jR0dGYNWsWzp49yw1VCwB2dnZYv349WrVqJcHoqraIiAicOHECsbGxUFdXh6urK1q0aCHpsAghhBBCyoQSqBKoLgnUlClTuI7exdUy9ezZk6udun79Orp27VrpMVZ3sbGxCAgIAJ/PR+PGjYsd0pkUyMrKwqRJk3Do0CH892vAzs4OR48ehYGBgYSiI4QQUpMIBAKR1jaE/Cw5Oblvtq6q6NyAqjgqUdGJXIvri9S9e3cugapqk75WFwYGBnB1dZV0GFWeQCBA//79ix3yGgB8fX3RuXNnPHr0CBoaGpUcHSGEkJqCMYb4+HikpKRIOhRSw0hJScHMzEwi/dspgapEqqqq3PLbt29hZGQkUh4eHl7stpUtODgYx44dE2nS5eDgQJ3Pa5AzZ85wyZOysjLmz58PBwcHvHjxAqtWrcKnT5/w9u1brF+/HmvWrJFwtIQQQqqrwuRJR0cHSkpKdC1ByoVQKERsbCzi4uJgYmJS6ecVNeGrREeOHMGIESMAAO3bt8e1a9egoqICAHj16hXatWuHjIwMyMnJISYmBlpaWpUaX2pqKkaNGoWLFy+KlTVr1gxnzpyBubl5pcZEKoajoyM3EuSFCxfQu3dvruzDhw+wsrJCfn4+tLS0EBcXR/3xCCGElJpAIEB4eDh0dHSgqakp6XBIDZOamorY2FhYWFiITZ5d0blBzRyWrYoaMGAA16fkwYMHMDc3x/jx49G/f3/Y2NggIyMDADBixIhKT57y8/PRq1evYpMnAHj+/Dk6d+6MhISESo2LVIygoCAABcO79+rVS6TM3NwcXbp0AQB8+fIFnz59qvT4CCGEVH+FfZ6UlJQkHAmpiQqb7hUdPKyyUAJVieTl5XHmzBkuE05MTMS+fftw9uxZ8Pl8AECLFi2wefPmSo/t+PHj8PPzA1AwQuC2bdvw+vVrHDt2DJaWlgAKRrr7888/Kz02Uv4Kq7oFAoHYABKF6/+7LSGEEFIW9DtCKoIkz6tfOoESCAS4fv06tmzZgl27duH169cVfsy2bdvi0aNHGDx4sEizKC0tLSxYsAB3796VSDPEvXv3cssnT57ElClT0LBhQwwZMgR37tyBvLw8AMDb2xt5eXmVHh8pX4XDun/+/BmnT58WKQsNDcWtW7cAAHp6emJ99QghhBBCfmW/bMeG06dPY/bs2YiMjBRZb2dnhz179qBevXoVduwGDRrg+PHjSEpKwrt37yAnJ4eGDRtySYokvHjxAkDBHFSOjo4iZYaGhujWrRv+/fdfpKSkICYmBmZmZpIIk5STiRMn4tq1awCAUaNGISAgAI6OjggODsaGDRu4Gih3d3dIS0tLMlRCCCGkyujcuTOaNWuGv/76CwBQp04deHp6wtPTU6Jxkcr1SyZQBw4cgJubW7Flvr6+6NChAx48eMA1XasompqaVaZTZWFtWG5uLoRCodhFc2Zmpti2pPpydXVFv379cPbsWeTm5mLDhg3YsGGDyDbW1taYNWuWhCIkhBBCJMfNzQ0HDhwQW//48WM0aNDgm6/j8Xg4d+4c+vTpU4HREUn75ZrwJScnY/LkydxzR0dH7N+/H+vXr+dqVb58+YKpU6f+1HEiIyOxaNEi2Nvbo1OnTpg0aRLXcb8qat++PYCC937w4EGRsmfPnuHOnTsAAGNjYxgaGlZ6fKR88Xg8HDt2DFOmTBEbuQYAevXqhdu3b1fpUS0JIYSQiuTs7Iy4uDiRR4sWLSplqhmadLhq++USqAMHDiArKwtAwWh3N27cwNixYzF79mw8e/YMxsbGAIBr167h3bt3ZTrGpk2bULduXaxevRp3797F/fv3sXv3bjRv3hzjx4/nBowoq7dv32LGjBmwsLCArq4uWrRogS1btiAtLa3M+5w0aRK3PH78eIwfPx7Hjx/HggUL0LlzZ26ggYkTJ35z1mdSvcjJyWHbtm2Ijo7Gjh07sHjxYmzYsAFhYWG4ePFipY8ESQghhFQl8vLy0NPTE3k4Ojp+s7lenTp1AAB9+/YFj8fjngMFU4Y0b94cCgoKMDc3x4oVK0SuB3k8Hnbt2oXevXtDWVkZq1atqsB3Rn7WL9cWy9/fn1uePXu2yAge6urq+O2337Bs2TIAwMOHD2FhYVGq/e/fv/+7zZ727dsHeXl5bN++vZSRFzh06BDGjh0r8p/u8+fPePbsGTZt2oRr167Bysqq1Pt1dnbG6NGjceDAAQgEAuzbtw/79u0T2aZNmzbUxrcG0tXVFamVJYQQQioKYwzZ+ZU/7LSirHSFj9oWEBAAHR0deHl5wdnZmesO4efnh1GjRmHr1q3o1KkT3r9/D3d3dwDgrjkBYPny5fjzzz/x119/UXeJKu6X++sUTTwKJ7Etqui60tYU5efnY/HixdzzGTNmYPbs2VBWVoaXlxfmzZuHvLw87Ny5E7Nnzxa5M1ESvr6+cHNzg1AoBADIyspCV1eXm6cnKioKTk5OePXqVamrl3k8Hvbv3w9jY2P89ddf3JxUQEGfp2HDhmHbtm00lwMhhBBCyiw7X4CGS69V+nFDfneCklzpLnt9fHxErgtdXFy+u722tjaAghvyenp63PoVK1Zg/vz5GD16NICC+RZXrlyJuXPniiRQw4YNw5gxY0oVI5GMX64tlrW1Nbfs7e0tUiYQCHDo0CHueePGjUu176tXryI+Ph4A0Lt3b2zatAkGBgZQU1ODp6cnFixYAKDg7ktxHRN/ZNWqVVzyNG7cOMTHxyM6OhovX75EkyZNABQkUf/tw1RS0tLSWLlyJWJjY3HkyBFs2LAB+/btQ2RkJA4cOED9YQghhBDyy7C3t8fz58+5x9atW8u0n+DgYPz+++9QUVHhHuPHj0dcXBzXrQQAWrZsWV6hkwr2y9VAjR07FqtWrQJjDKtXr0ZeXh6GDx+O5ORkrF27Fs+fPwcANG3atNQnctE+U/379xcrHzBgAFasWAEAeP/+fan2HR8fjxs3bgAouHPx999/c1XDjRs3xqFDh9C0aVMABc38PDw8SrX/olRVVTFs2LAyv54QQgghpDiKstII+d1JIsctLWVl5VJ35ShORkYGVqxYgX79+omVKSgoiByPVA+/XAJlZmaG2bNnY/369RAKhVi3bh3WrVsnso2MjAw2b95c6rayioqK3HJMTIxYeWFTu/9uWxKxsbHcsqOjo9gw402aNIGOjg4+f/5c7LEJIYQQQiSNx+OVuilddSIrK8vNpVioefPmCAsLK5dkjFQNv1wTPgD4888/sWDBgmInCNXS0sKFCxdgb29f6v06ODhwyzt27EBCQgL3PDc3F6tXr+ae/3ey2h9RU1Pjll+/fi1WnpCQgC9fvgAANbUjhBBCCJGAOnXq4NatW4iPj8fXr18BAEuXLsXBgwexYsUKvH79GqGhoTh+/LhIv3lSvZQqgVqzZg1atWoFVVVV6OjooE+fPggLC+PKk5OTMXXqVNSvXx+KioowMTHBtGnTkJqa+t39urm5gcfjiTycnZ3L9o5KQEpKCqtXr0ZkZCRWrVqF4cOHY8yYMfD29kZUVBS6d+9epv3Wq1cPTk4F1dIxMTFo2LAhpk+fjkWLFsHKygp+fn4AAENDw1JPsGZubs5N3PbgwQMcOXKEK8vLy8PMmTO5/lG9e/cuU/yEEEIIIaTsNm7ciBs3bsDY2Bg2NjYAACcnJ/j4+OD69eto1aoV2rZti82bN8PU1FTC0ZKy4rHCCX5KwNnZGUOGDEGrVq3A5/OxcOFCvHr1CiEhIVBWVsarV6+wbNkyuLm5oWHDhoiMjMTEiRPRpEkTnD59+pv7dXNzQ0JCAry8vLh18vLyqF27doniSktLg5qaGlJTUyVe+xIVFYWOHTsiOjq62HIlJSVcvXoVnTp1KvW+9+7dyw17CQCtW7dGgwYNcOvWLa55oLy8PMLCwug/JSGEEEIkKicnBxERETAzMxPp60NIefje+VXRuUGpEqj/SkxMhI6ODnx9fWFra1vsNqdOncKIESOQmZn5zTHt3dzckJKSgvPnz5cpjqqUQAEFtU9z587FqVOnRGaS7tKlC9atW8fdkSgtxhjGjx+P/fv3F1suIyODY8eOYcCAAWXaPyGEEEJIeaEEilQkSSZQP9UHqrBpnoaGxne3qVWr1g8nBLt79y50dHRQv359TJo0CUlJST8TmkQZGhriyJEj+PTpEy5duoQLFy7g3bt3uHHjRpmTJ6Cg4+XevXuxf/9+kSHWeTweevXqBT8/P0qeCCGEEEIIqUBlroESCoXo3bs3UlJScP/+/WK3+fLlC1q0aIERI0Zg1apV39zX8ePHoaSkBDMzM7x//x4LFy6EiooKHj58WOxAD7m5ucjNzeWep6WlwdjYuMrUQFUGxhiio6ORlpYGfX19aGpqSjokQgghhBAO1UCRiiTJGqgyjyPp4eGBV69efTN5SktLQ48ePdCwYUMsX778u/saMmQIt2xtbY0mTZqgbt26uHv3brGj1a1Zs4abT+lXxePxYGJiIukwCCGEEEII+aWUqQnflClT4OPjgzt37sDIyEisPD09Hc7OzlBVVcW5c+cgKytbqv2bm5tDS0tLZGLaohYsWIDU1FTu8a0BGwghhBBCCCGkPJWqBooxhqlTp+LcuXO4e/cuzMzMxLZJS0uDk5MT5OXlcfHixTJV2X769AlJSUnQ19cvtlxeXh7y8vKl3i8hhBBCCCGE/IxS1UB5eHjg8OHDOHr0KFRVVREfH4/4+HhkZ2cDKEieunXrhszMTOzfvx9paWncNkVnZbayssK5c+cAABkZGZgzZw4ePXqEjx8/4tatW3B1dYWFhQU3pxIhhBBCCCGEVAWlqoHatWsXAKBz584i6728vODm5oZnz57h8ePHAAALCwuRbSIiIlCnTh0AQFhYGDeCn7S0NF68eIEDBw4gJSUFBgYG6NatG1auXEm1TIQQQgghhJAqpdRN+L6nc+fOP9zmv/tRVFTEtWvXShMGIYQQQgghhEjET80DRQghhBBCCCG/EkqgCCGEEEJIlZWamoqTJ09i586dOH36NDIyMir8mG5ubuDxeJg4caJYmYeHB3g8Htzc3Co8jpqMx+Ph/Pnzkg6jTCiBIoQQQgghVU5eXh5mzZoFQ0NDDB48GB4eHhg4cCAMDQ2xePFi8Pn8Cj2+sbExjh8/zg2WBhRM3nr06NEqPxdnXl6epEOo0SiBIoQQQgghVQqfz0e/fv2wadMmZGZmipSlpaVh1apVGDFiBIRCYYXF0Lx5cxgbG+Ps2bPcurNnz8LExAQ2NjbcOqFQiDVr1sDMzAyKiopo2rQpTp8+zZULBAKMGzeOK69fvz62bNkicqy7d++idevWUFZWhrq6Ojp06IDIyEgABbVhffr0Edne09NTZFC3zp07Y8qUKfD09ISWlhY3kvWrV6/g4uICFRUV6OrqYuTIkfjy5YvI66ZOnQpPT0/Url0burq62Lt3LzIzMzFmzBioqqrCwsICV65cETl+SfY7bdo0zJ07FxoaGtDT08Py5cu58sKB5fr27Qsej8c9Dw4Ohr29PVRVVVGrVi20aNECT58+/cFfqvJRAkUIIYQQQqoUb29vXLp0CQAgKyuLCRMmYP/+/Rg7diykpaUBACdOnMCZM2cqNI6xY8fCy8uLe/7PP/9gzJgxItusWbMGBw8exO7du/H69WvMmDEDI0aMgK+vL4CCBMvIyAinTp1CSEgIli5dioULF+LkyZMACpLFPn36wM7ODi9evMDDhw/h7u4OHo9XqlgPHDgAOTk5+Pv7Y/fu3UhJSYGDgwNsbGzw9OlTXL16FQkJCRg0aJDY67S0tPDkyRNMnToVkyZNwsCBA9G+fXs8e/YM3bp1w8iRI5GVlQUApdqvsrIyHj9+jHXr1uH333/HjRs3AAABAQEACkbyjouL454PHz4cRkZGCAgIQGBgIObPnw9ZWdlSfQ6VgtUAqampDABLTU2VdCiEEEIIIYQxlp2dzUJCQlh2dnapX2tjY8MAMADs8uXLImXHjx/nyuzs7MopWlGjR49mrq6u7PPnz0xeXp59/PiRffz4kSkoKLDExETm6urKRo8ezXJycpiSkhJ78OCByOvHjRvHhg4d+s39e3h4sP79+zPGGEtKSmIA2N27d78bS1HTp08Xee92dnbMxsZGZJuVK1eybt26iayLjo5mAFhYWBj3uo4dO3LlfD6fKSsrs5EjR3Lr4uLiGAD28OHDMu+XMcZatWrF5s2bxz0HwM6dOyeyjaqqKvP29i72c/iv751fFZ0blGoYc0JI9fTp0yeEh4dDTk4OzZo1g4qKiqRDIoQQQoqVmZmJoKAgAIC1tTVcXFxEygcNGoR58+YhMjIS/v7+YIyVurampLS1tdGjRw94e3uDMYYePXpAS0uLK3/37h2ysrLQtWtXkdfl5eWJNPPbsWMH/vnnH0RFRSE7Oxt5eXlo1qwZAEBDQwNubm5wcnJC165d0aVLFwwaNAj6+vqlirVFixYiz4ODg3Hnzp1if/Pfv3+PevXqAQCaNGnCrZeWloampiasra25dbq6ugCAz58/l3m/AKCvr8/t41tmzpyJ3377DYcOHUKXLl0wcOBA1K1b97uvkQRKoAipwYKCgrBo0SJcvXqVm39NRUUFbm5uWLlyJdTV1SUbICGEEPIf+fn53HJxv1M8Hg/q6uqIjIwEn8+HUCjkmvVVhLFjx2LKlCkAChKhogpHBLx06RIMDQ1FyuTl5QEAx48fx+zZs7Fx40a0a9cOqqqqWL9+PR4/fsxt6+XlhWnTpuHq1as4ceIEFi9ejBs3bqBt27aQkpISm2e16GdUSFlZWSy2Xr16Ye3atWLbFk3O/ttEjsfjiawrTE4L+5v9zH5/1Gdt+fLlGDZsGC5duoQrV65g2bJlOH78OPr27fvd11U2SqAIqaF8fX3h4uIiMnoQUPDFt337dty5cwf37t2DhoaGhCIkhBBCxKmpqcHAwACxsbF48OAB3r9/L1IL8eLFCwQHBwMArKysKjR5AgBnZ2fk5eWBx+NxgzMUatiwIeTl5REVFQU7O7tiX+/v74/27dtj8uTJ3Lr379+LbWdjYwMbGxssWLAA7dq1w9GjR9G2bVtoa2vj1atXIts+f/78h32DmjdvjjNnzqBOnTqQkSm/S/7y2q+srCwEAoHY+nr16qFevXqYMWMGhg4dCi8vryqXQNEgEoTUQNnZ2Rg0aBCXPBkbG8PT0xOjRo2CgoICAOD169eYPn26JMMkhBBCxPB4PPz2228ACkawc3JywqlTpxAZGYmjR4+iZ8+e3LaF21UkaWlphIaGIiQkRCxZU1VVxezZszFjxgwcOHAA79+/x7Nnz7Bt2zYcOHAAAGBpaYmnT5/i2rVrCA8Px5IlS7hBEwAgIiICCxYswMOHDxEZGYnr16/j7du3aNCgAQDAwcEBT58+xcGDB/H27VssW7ZMLKEqjoeHB5KTkzF06FAEBATg/fv3uHbtGsaMGVNs4lJS5bXfOnXq4NatW4iPj8fXr1+RnZ2NKVOm4O7du1zzzICAAO5zqEoogSKkBjpx4gTXztje3h7h4eHYvHkzDhw4gBcvXkBNTY3bLj4+XpKhEkIIIWKmT58OMzMzAAW1NYMGDUKdOnUwfPhwREdHAyio/ZkwYUKlxFOrVi3UqlWr2LKVK1diyZIlWLNmDRo0aABnZ2dcunSJi3/ChAno168fBg8ejDZt2iApKUmkNkpJSQlv3rxB//79Ua9ePbi7u8PDw4N7b05OTliyZAnmzp2LVq1aIT09HaNGjfphzAYGBvD394dAIEC3bt1gbW0NT09PqKurQ0qq7ClAee1348aNuHHjBoyNjWFjYwNpaWkkJSVh1KhRqFevHgYNGgQXFxesWLGizLFWFB77b6PKaigtLQ1qampITU395slNyK9k6NChOH78OADg3r176NSpk0h5YVtsADh27BiGDBlS6TESQgip2XJychAREQEzMzOu9UNpfPz4EX379sXz58/Fytq2bYuzZ8+WeqAFUnN87/yq6NyA+kARUgMVnXSw8A5YUUXX/XeCQkIIIaQqqFOnDgIDA3Hr1i2cPn0aSUlJ0NbWxpAhQ2Bra1thI+8R8iOUQBFSAxVNkC5cuAAPDw+R8gsXLhS7LSGEEFKVSElJoWvXrmLDhBMiSdQHipAaaPTo0dzyggULcPjwYeTn5+PLly+YNWsWNxO4qanpN0cNIoQQQggh4iiBIqQGat68OQYMGAAASE9Px8iRI6GoqAhtbW1s2rSJ227lypUVPvwrIYQQQkhNQgkUITXUgQMHRIZ6LTq0qJSUFDZu3IiRI0dKIjRCCCGEkGqL+kARUkMpKSnh4sWLuHPnDvbu3YvQ0FDIycnB1tYWEydOhIWFhaRDJIQQ8gsQCoWSDoHUQJIcSJwSKEJqMB6PBwcHBzg4OEg6FEIIIb8YOTk5SElJITY2Ftra2pCTk6OR80i5YIwhMTERPB4PsrKylX58SqAIIYQQQki5k5KSgpmZGeLi4hAbGyvpcEgNw+PxYGRkJJG+3JRAEUIIIYSQCiEnJwcTExPw+XyRvriE/CxZWVmJDYRFCRQhhBBCCKkwhc2sJNHUipCKQKPwEUIIIYQQQkgJUQJFCCGEEEIIISVECRQhhBBCCCGElFCN6ANVOA58WlqahCMhhBBCCCGESFJhTlBRc0XViAQqKSkJAGBsbCzhSAghhBBCCCFVQVJSEtTU1Mp9vzUigdLQ0AAAREVFVciHREihtLQ0GBsbIzo6GrVq1ZJ0OKQGo3ONVBY610hloXONVJbU1FSYmJhwOUJ5qxEJlJRUQVcuNTU1+g9JKkWtWrXoXCOVgs41UlnoXCOVhc41UlkKc4Ry32+F7JUQQgghhBBCaiBKoAghhBBCCCGkhGpEAiUvL49ly5ZBXl5e0qGQGo7ONVJZ6FwjlYXONVJZ6FwjlaWizzUeq6jx/QghhBBCCCGkhqkRNVCEEEIIIYQQUhkogSKEEEIIIYSQEqIEihBCCCGEEEJKiBIoQgghhBBCCCmhGpFA7dixA3Xq1IGCggLatGmDJ0+eSDokUs2tWbMGrVq1gqqqKnR0dNCnTx+EhYWJbJOTkwMPDw9oampCRUUF/fv3R0JCgoQiJjXBn3/+CR6PB09PT24dnWekPMXExGDEiBHQ1NSEoqIirK2t8fTpU66cMYalS5dCX18fioqK6NKlC96+fSvBiEl1JBAIsGTJEpiZmUFRURF169bFypUrUXTcMjrXSFncu3cPvXr1goGBAXg8Hs6fPy9SXpLzKjk5GcOHD0etWrWgrq6OcePGISMjo1RxVPsE6sSJE5g5cyaWLVuGZ8+eoWnTpnBycsLnz58lHRqpxnx9feHh4YFHjx7hxo0byM/PR7du3ZCZmcltM2PGDPz77784deoUfH19ERsbi379+kkwalKdBQQE4O+//0aTJk1E1tN5RsrL169f0aFDB8jKyuLKlSsICQnBxo0bUbt2bW6bdevWYevWrdi9ezceP34MZWVlODk5IScnR4KRk+pm7dq12LVrF7Zv347Q0FCsXbsW69atw7Zt27ht6FwjZZGZmYmmTZtix44dxZaX5LwaPnw4Xr9+jRs3bsDHxwf37t2Du7t76QJh1Vzr1q2Zh4cH91wgEDADAwO2Zs0aCUZFaprPnz8zAMzX15cxxlhKSgqTlZVlp06d4rYJDQ1lANjDhw8lFSapptLT05mlpSW7ceMGs7OzY9OnT2eM0XlGyte8efNYx44dv1kuFAqZnp4eW79+PbcuJSWFycvLs2PHjlVGiKSG6NGjBxs7dqzIun79+rHhw4czxuhcI+UDADt37hz3vCTnVUhICAPAAgICuG2uXLnCeDwei4mJKfGxq3UNVF5eHgIDA9GlSxdunZSUFLp06YKHDx9KMDJS06SmpgIANDQ0AACBgYHIz88XOfesrKxgYmJC5x4pNQ8PD/To0UPkfALoPCPl6+LFi2jZsiUGDhwIHR0d2NjYYO/evVx5REQE4uPjRc43NTU1tGnThs43Uirt27fHrVu3EB4eDgAIDg7G/fv34eLiAoDONVIxSnJePXz4EOrq6mjZsiW3TZcuXSAlJYXHjx+X+Fgy5Rd25fvy5QsEAgF0dXVF1uvq6uLNmzcSiorUNEKhEJ6enujQoQMaN24MAIiPj4ecnBzU1dVFttXV1UV8fLwEoiTV1fHjx/Hs2TMEBASIldF5RsrThw8fsGvXLsycORMLFy5EQEAApk2bBjk5OYwePZo7p4r7TaXzjZTG/PnzkZaWBisrK0hLS0MgEGDVqlUYPnw4ANC5RipESc6r+Ph46OjoiJTLyMhAQ0OjVOdetU6gCKkMHh4eePXqFe7fvy/pUEgNEx0djenTp+PGjRtQUFCQdDikhhMKhWjZsiVWr14NALCxscGrV6+we/dujB49WsLRkZrk5MmTOHLkCI4ePYpGjRrh+fPn8PT0hIGBAZ1rpEao1k34tLS0IC0tLTYiVUJCAvT09CQUFalJpkyZAh8fH9y5cwdGRkbcej09PeTl5SElJUVkezr3SGkEBgbi8+fPaN68OWRkZCAjIwNfX19s3boVMjIy0NXVpfOMlBt9fX00bNhQZF2DBg0QFRUFANw5Rb+p5GfNmTMH8+fPx5AhQ2BtbY2RI0dixowZWLNmDQA610jFKMl5paenJzbQHJ/PR3JycqnOvWqdQMnJyaFFixa4desWt04oFOLWrVto166dBCMj1R1jDFOmTMG5c+dw+/ZtmJmZiZS3aNECsrKyIudeWFgYoqKi6NwjJebo6IiXL1/i+fPn3KNly5YYPnw4t0znGSkvHTp0EJuOITw8HKampgAAMzMz6OnpiZxvaWlpePz4MZ1vpFSysrIgJSV6iSktLQ2hUAiAzjVSMUpyXrVr1w4pKSkIDAzktrl9+zaEQiHatGlT8oP99BAYEnb8+HEmLy/PvL29WUhICHN3d2fq6uosPj5e0qGRamzSpElMTU2N3b17l8XFxXGPrKwsbpuJEycyExMTdvv2bfb06VPWrl071q5dOwlGTWqCoqPwMUbnGSk/T548YTIyMmzVqlXs7du37MiRI0xJSYkdPnyY2+bPP/9k6urq7MKFC+zFixfM1dWVmZmZsezsbAlGTqqb0aNHM0NDQ+bj48MiIiLY2bNnmZaWFps7dy63DZ1rpCzS09NZUFAQCwoKYgDYpk2bWFBQEIuMjGSMley8cnZ2ZjY2Nuzx48fs/v37zNLSkg0dOrRUcVT7BIoxxrZt28ZMTEyYnJwca926NXv06JGkQyLVHIBiH15eXtw22dnZbPLkyax27dpMSUmJ9e3bl8XFxUkuaFIj/DeBovOMlKd///2XNW7cmMnLyzMrKyu2Z88ekXKhUMiWLFnCdHV1mby8PHN0dGRhYWESipZUV2lpaWz69OnMxMSEKSgoMHNzc7Zo0SKWm5vLbUPnGimLO3fuFHt9Nnr0aMZYyc6rpKQkNnToUKaiosJq1arFxowZw9LT00sVB4+xItNCE0IIIYQQQgj5pmrdB4oQQgghhBBCKhMlUIQQQgghhBBSQpRAEUIIIYQQQkgJUQJFCCGEEEIIISVECRQhhBBCCCGElBAlUIQQQgghhBBSQpRAEUIIIYQQQkgJUQJFCCGEEEIIISVECRQhhBBCCCGElBAlUIQQQgghhBBSQpRAEUIIIYQQQkgJUQJFCCGEEEIIISX0f+anVd6j0HqfAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos=pos, vel=15., count=100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=.2, h=0.0001)\n", + "plot_g_h_results(zs/1000., data/1000., 'g=0.2, h=0.0001')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "7f700f11", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zs = gen_train_data(pos=pos, vel=15., count=100)\n", + "data = g_h_filter(data=zs, x0=pos, dx=15., dt=1., g=0.01, h=0.1)\n", + "plot_g_h_results(zs/1000., data/1000., 'g=0.01, h=0.1')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "36a84129", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.96, 0.24)" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "\n", + "from filterpy.gh import GHFilter\n", + "f = GHFilter(x=0., dx=0., dt=1., g=.8, h=.2)\n", + "\n", + "f.update(z=1.2)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "615cee5f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.96 0.24\n" + ] + } + ], + "source": [ + "print(f.x, f.dx)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "0a25fd75", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(1.965, 0.375)\n" + ] + } + ], + "source": [ + "print(f.update(z=2.1, g=.85, h=.15))" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "53dd5056", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1.965 0.375]\n", + " [2.868 0.507]\n", + " [3.875 0.632]\n", + " [4.901 0.731]]\n" + ] + } + ], + "source": [ + "print(f.batch_filter([3., 4., 5.]))" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "76065dec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " x = [ 3.8 13.2 101.64]\n", + "dx = [8.2 9.8 0.56]\n" + ] + } + ], + "source": [ + "\n", + "\n", + "x_0 = np.array([1., 10., 100.])\n", + "dx_0 = np.array([10., 12., .2])\n", + " \n", + "f_air = GHFilter(x=x_0, dx=dx_0, dt=1., g=.8, h=.2)\n", + "f_air.update(z=np.array((2., 11., 102.)))\n", + "print(' x =', f_air.x)\n", + "print('dx =', f_air.dx)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2eeea6e2", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/02-Discrete-Bayes.ipynb b/kalman_and_bayesian_filters/02-Discrete-Bayes.ipynb new file mode 100644 index 0000000..cdb2f29 --- /dev/null +++ b/kalman_and_bayesian_filters/02-Discrete-Bayes.ipynb @@ -0,0 +1,1099 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "f134bd92", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import book_format\n", + "book_format.set_style()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1c25fbb6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "belief = np.array([1/10]*10)\n", + "print(belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "e0b5572a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hallway = np.array([1, 1, 0, 0, 0, 0, 0, 0, 1, 0])\n", + "\n", + "\n", + "import kf_book.book_plots as book_plots\n", + "from kf_book.book_plots import figsize, set_figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "belief = np.array([1/3, 1/3, 0, 0, 0, 0, 0, 0, 1/3, 0])\n", + "book_plots.bar_plot(belief)\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e3c452e9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.333 0.333 0. 0. 0. 0. 0. 0. 0.333 0. ]\n" + ] + } + ], + "source": [ + "\n", + "\n", + "belief = hallway * (1/3)\n", + "print(belief)\n", + "\n", + "belief = np.array([0., 1., 0., 0., 0., 0., 0., 0., 0., 0.])" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3b00c961", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "belief: [0.3 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.3 0.1]\n", + "sum = 1.6000000000000003\n" + ] + }, + { + "data": { + "image/png": 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T7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAULhDqj3Ab4Op3/hxtUd4T/3oMx/s9zHWAAB+xX8TqQZX2gEAoHCiHQAACifaAQCgcKIdAAAKJ9oBAKBwoh0AAAon2gEAoHCiHQAACifaAQCgcKIdAAAKJ9oBAKBwoh0AAAon2gEAoHCiHQAACifaAQCgcKIdAAAKJ9oBAKBwoh0AAAon2gEAoHCiHQAACifaAQCgcKIdAAAKJ9oBAKBwoh0AAAon2gEAoHD7Fe0rVqzIxIkTM3To0MycOTMbNmzY57533nlnzjnnnBx55JE58sgj09TU9Lb7AwAAffU72levXp3m5uYsXbo0mzZtyuTJkzNr1qxs3759r/s/+uijufDCC/P9738/69evz4QJE3LuuefmlVdeedfDAwDAYNDvaF+2bFkuu+yyzJ8/P6ecckpWrlyZww47LPfcc89e9//mN7+ZP//zP8+UKVMyadKk3HXXXenp6Ulra+u7Hh4AAAaDfkX77t27s3HjxjQ1Nf36DYYMSVNTU9avX/+O3uOtt97KL37xixx11FH9mxQAAAapQ/qz844dO9Ld3Z2GhoY+2xsaGrJly5Z39B5XXXVVxo0b1yf8/19dXV3p6urq/bmjo6M/YwIAwEFlQJ8ec/PNN+e+++7Lgw8+mKFDh+5zv5aWlowcObL3NWHChAGcEgAAytKvaB81alRqa2vT3t7eZ3t7e3vGjBnztsf+3d/9XW6++eZ873vfyxlnnPG2+y5evDg7d+7sfW3btq0/YwIAwEGlX9FeV1eXadOm9fkS6f9+qbSxsXGfx33pS1/KjTfemDVr1mT69Om/8XPq6+szYsSIPi8AABis+nVPe5I0Nzdn3rx5mT59embMmJHly5ens7Mz8+fPT5LMnTs348ePT0tLS5LklltuyZIlS7Jq1apMnDgxbW1tSZLDDz88hx9++Ht4KgAAcHDqd7TPmTMnr732WpYsWZK2trZMmTIla9as6f1y6tatWzNkyK8v4N9+++3ZvXt3/uiP/qjP+yxdujRf+MIX3t30AAAwCPQ72pPk8ssvz+WXX77X/+3RRx/t8/NLL720Px8BAAD8HwP69BgAAKD/RDsAABROtAMAQOFEOwAAFE60AwBA4UQ7AAAUTrQDAEDhRDsAABROtAMAQOFEOwAAFE60AwBA4UQ7AAAUTrQDAEDhRDsAABROtAMAQOFEOwAAFE60AwBA4UQ7AAAUTrQDAEDhRDsAABROtAMAQOFEOwAAFE60AwBA4UQ7AAAU7pBqDwC/LaZ+48fVHuE99aPPfLDfxxxMazDYzz+xBok1GOznn+zfGuDPQTW40g4AAIUT7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAUDjRDgAAhRPtAABQONEOAACFE+0AAFA40Q4AAIUT7QAAULj9ivYVK1Zk4sSJGTp0aGbOnJkNGza87f7/9E//lEmTJmXo0KE5/fTT88gjj+zXsAAAMBj1O9pXr16d5ubmLF26NJs2bcrkyZMza9asbN++fa/7/+AHP8iFF16YSy65JD/60Y9ywQUX5IILLsgzzzzzrocHAIDBoN/RvmzZslx22WWZP39+TjnllKxcuTKHHXZY7rnnnr3u/+Uvfzm/93u/lyuvvDInn3xybrzxxpx55pm57bbb3vXwAAAwGBzSn513796djRs3ZvHixb3bhgwZkqampqxfv36vx6xfvz7Nzc19ts2aNSsPPfTQPj+nq6srXV1dvT/v3LkzSdLR0dGfcd8z3f/zZlU+90DZn3W0BtYgObjWYLCff2INEmsw2M8/sQaJNUiq15j/+7mVSuU37tuvaN+xY0e6u7vT0NDQZ3tDQ0O2bNmy12Pa2tr2un9bW9s+P6elpSU33HDDHtsnTJjQn3HZh5H/X7UnqD5rYA0G+/kn1iCxBoP9/BNrkFiDpPprsGvXrowcOfJt9+lXtA+UxYsX97k639PTk9dffz1HH310ampqqjjZgdPR0ZEJEyZk27ZtGTFiRLXHqQprYA0G+/kn1iCxBok1GOznn1iDZHCsQaVSya5duzJu3LjfuG+/on3UqFGpra1Ne3t7n+3t7e0ZM2bMXo8ZM2ZMv/ZPkvr6+tTX1/fZdsQRR/Rn1N9aI0aMOGj/YL5T1sAaDPbzT6xBYg0SazDYzz+xBsnBvwa/6Qr7/+rXF1Hr6uoybdq0tLa29m7r6elJa2trGhsb93pMY2Njn/2TZN26dfvcHwAA6Kvft8c0Nzdn3rx5mT59embMmJHly5ens7Mz8+fPT5LMnTs348ePT0tLS5Jk4cKF+ehHP5pbb701559/fu6777489dRTueOOO97bMwEAgINUv6N9zpw5ee2117JkyZK0tbVlypQpWbNmTe+XTbdu3ZohQ359Af+ss87KqlWrct111+Waa67JBz/4wTz00EM57bTT3ruzOAjU19dn6dKle9wWNJhYA2sw2M8/sQaJNUiswWA//8QaJNbg/1VTeSfPmAEAAKqm379cCQAAGFiiHQAACifaAQCgcKIdAAAKJ9oLsWLFikycODFDhw7NzJkzs2HDhmqPNGAef/zxzJ49O+PGjUtNTU0eeuihao80oFpaWvLhD384w4cPz+jRo3PBBRfkueeeq/ZYA+r222/PGWec0fsLNBobG/Pd73632mNVzc0335yamposWrSo2qMMqC984Qupqanp85o0aVK1xxpQr7zySv7kT/4kRx99dIYNG5bTTz89Tz31VLXHGjATJ07c489ATU1NFixYUO3RBkR3d3euv/76HH/88Rk2bFhOPPHE3HjjjRlszwzZtWtXFi1alOOOOy7Dhg3LWWedlSeffLLaY1WdaC/A6tWr09zcnKVLl2bTpk2ZPHlyZs2ale3bt1d7tAHR2dmZyZMnZ8WKFdUepSoee+yxLFiwID/84Q+zbt26/OIXv8i5556bzs7Oao82YI455pjcfPPN2bhxY5566qn8zu/8Tj7xiU/kP//zP6s92oB78skn87WvfS1nnHFGtUepilNPPTWvvvpq7+uJJ56o9kgD5mc/+1nOPvvsHHroofnud7+b//qv/8qtt96aI488stqjDZgnn3yyzz//devWJUk++clPVnmygXHLLbfk9ttvz2233ZZnn302t9xyS770pS/lK1/5SrVHG1CXXnpp1q1bl2984xt5+umnc+6556apqSmvvPJKtUerrgpVN2PGjMqCBQt6f+7u7q6MGzeu0tLSUsWpqiNJ5cEHH6z2GFW1ffv2SpLKY489Vu1RqurII4+s3HXXXdUeY0Dt2rWr8sEPfrCybt26ykc/+tHKwoULqz3SgFq6dGll8uTJ1R6jaq666qrKRz7ykWqPUZSFCxdWTjzxxEpPT0+1RxkQ559/fuXiiy/us+0P//APKxdddFGVJhp4b731VqW2trbyne98p8/2M888s3LttddWaaoyuNJeZbt3787GjRvT1NTUu23IkCFpamrK+vXrqzgZ1bJz584kyVFHHVXlSaqju7s79913Xzo7O9PY2FjtcQbUggULcv755/f598Fg8+Mf/zjjxo3LCSeckIsuuihbt26t9kgD5tvf/namT5+eT37ykxk9enSmTp2aO++8s9pjVc3u3bvzD//wD7n44otTU1NT7XEGxFlnnZXW1tY8//zzSZL/+I//yBNPPJHzzjuvypMNnF/+8pfp7u7O0KFD+2wfNmzYoPp/3vam378RlffWjh070t3d3fsbZf9XQ0NDtmzZUqWpqJaenp4sWrQoZ5999qD7rcFPP/10Ghsb8/Of/zyHH354HnzwwZxyyinVHmvA3Hfffdm0adOgvm9z5syZ+frXv56TTjopr776am644Yacc845eeaZZzJ8+PBqj3fAvfjii7n99tvT3Nyca665Jk8++WT+8i//MnV1dZk3b161xxtwDz30UN5444386Z/+abVHGTBXX311Ojo6MmnSpNTW1qa7uztf/OIXc9FFF1V7tAEzfPjwNDY25sYbb8zJJ5+choaG/OM//mPWr1+fD3zgA9Uer6pEOxRkwYIFeeaZZwbl1YSTTjopmzdvzs6dO/PAAw9k3rx5eeyxxwZFuG/bti0LFy7MunXr9ri6NJj831cTzzjjjMycOTPHHXdc7r///lxyySVVnGxg9PT0ZPr06bnpppuSJFOnTs0zzzyTlStXDspov/vuu3Peeedl3Lhx1R5lwNx///355je/mVWrVuXUU0/N5s2bs2jRoowbN25Q/Rn4xje+kYsvvjjjx49PbW1tzjzzzFx44YXZuHFjtUerKtFeZaNGjUptbW3a29v7bG9vb8+YMWOqNBXVcPnll+c73/lOHn/88RxzzDHVHmfA1dXV9V5FmTZtWp588sl8+ctfzte+9rUqT3bgbdy4Mdu3b8+ZZ57Zu627uzuPP/54brvttnR1daW2traKE1bHEUcckQ996EN54YUXqj3KgBg7duwef0k9+eST88///M9Vmqh6Xn755fzbv/1bvvWtb1V7lAF15ZVX5uqrr86nPvWpJMnpp5+el19+OS0tLYMq2k888cQ89thj6ezsTEdHR8aOHZs5c+bkhBNOqPZoVeWe9iqrq6vLtGnT0tra2rutp6cnra2tg+5+3sGqUqnk8ssvz4MPPph///d/z/HHH1/tkYrQ09OTrq6uao8xID7+8Y/n6aefzubNm3tf06dPz0UXXZTNmzcPymBPkjfffDM/+clPMnbs2GqPMiDOPvvsPR73+vzzz+e4446r0kTVc++992b06NE5//zzqz3KgHrrrbcyZEjfNKutrU1PT0+VJqqu973vfRk7dmx+9rOfZe3atfnEJz5R7ZGqypX2AjQ3N2fevHmZPn16ZsyYkeXLl6ezszPz58+v9mgD4s033+xzJe2nP/1pNm/enKOOOirHHntsFScbGAsWLMiqVavyL//yLxk+fHja2tqSJCNHjsywYcOqPN3AWLx4cc4777wce+yx2bVrV1atWpVHH300a9eurfZoA2L48OF7fIfhfe97X44++uhB9d2Gz3/+85k9e3aOO+64/Pd//3eWLl2a2traXHjhhdUebUBcccUVOeuss3LTTTflj//4j7Nhw4bccccdueOOO6o92oDq6enJvffem3nz5uWQQwZXpsyePTtf/OIXc+yxx+bUU0/Nj370oyxbtiwXX3xxtUcbUGvXrk2lUslJJ52UF154IVdeeWUmTZo0aLpon6r9+Bp+5Stf+Url2GOPrdTV1VVmzJhR+eEPf1jtkQbM97///UqSPV7z5s2r9mgDYm/nnqRy7733Vnu0AXPxxRdXjjvuuEpdXV3l/e9/f+XjH/945Xvf+161x6qqwfjIxzlz5lTGjh1bqaurq4wfP74yZ86cygsvvFDtsQbUv/7rv1ZOO+20Sn19fWXSpEmVO+64o9ojDbi1a9dWklSee+65ao8y4Do6OioLFy6sHHvssZWhQ4dWTjjhhMq1115b6erqqvZoA2r16tWVE044oVJXV1cZM2ZMZcGCBZU33nij2mNVXU2lMsh+zRYAAPyWcU87AAAUTrQDAEDhRDsAABROtAMAQOFEOwAAFE60AwBA4UQ7AAAUTrQDAEDhRDsAABROtAMAQOFEOwAAFE60AwBA4f5/AI1lGsKw/y4AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def update_belief(hall, belief, z, correct_scale):\n", + " for i, val in enumerate(hall):\n", + " if val == z:\n", + " belief[i] *= correct_scale\n", + "\n", + "belief = np.array([0.1] * 10)\n", + "reading = 1 # 1 is 'door'\n", + "update_belief(hallway, belief, z=reading, correct_scale=3.)\n", + "print('belief:', belief)\n", + "print('sum =', sum(belief))\n", + "plt.figure()\n", + "book_plots.bar_plot(belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "296d5895", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.188, 0.188, 0.062, 0.062, 0.062, 0.062, 0.062, 0.062, 0.188,\n", + " 0.062])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "belief / sum(belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "9d5d77a7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sum = 1.0\n", + "probability of door = 0.1875\n", + "probability of wall = 0.06249999999999999\n" + ] + }, + { + "data": { + "image/png": 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w/cWLF5WTk6P169crLS3tiue94447dPr06eD21ltvhTsaAAAAEJXCjvrNmzfrwQcfVEVFhaZMmaKtW7fqpptu0vbt2wdcP2PGDP3whz/U4sWLFR8ff8XzDhs2TGlpacEtNTU13NEAAACAqBRW1Pf19amtrU0ul+vSCWJj5XK51NLS8pUGOXr0qDIyMpSTk6OlS5eqo6Pjimt7e3vl9/tDNgAAACBahRX1Z8+eVX9/v5xOZ8h+p9Mpr9c76CGKior00ksvqampSVu2bNHx48d199136/z58wOur62tVXJycnDLzMwc9PcGAAAATHdDfPrNvHnztGjRIuXm5qqkpESvv/66urq69Oqrrw64vrKyUt3d3cHtxIkTEZ4YAAAAuHEMC2dxamqqHA6HfD5fyH6fz3fVN8GG6+abb9Y3vvENHTt2bMDH4+Pjr/r6fAAAACCahPVMfVxcnAoKCuTxeIL7AoGAPB6PiouLr9tQFy5c0Mcff6z09PTrdk4AAABgqArrmXpJcrvdKi8vV2FhoWbOnKm6ujr19PSooqJCklRWVqYxY8aotrZW0udvrv3ggw+Cfz558qQOHTqkESNGaMKECZKkRx99VPfdd5/GjRunU6dOqbq6Wg6HQ0uWLLle1wkAAAAMWWFHfWlpqc6cOaOqqip5vV7l5+erqakp+ObZjo4OxcZe+geAU6dOadq0acGvN23apE2bNumee+5Rc3OzJOmTTz7RkiVLdO7cOd16662aPXu29u/fr1tvvfUrXh4AAAAw9IUd9ZK0YsUKrVixYsDHvgj1L2RlZcmyrKueb9euXYMZAwAAAIBukE+/AQAAADB4RD0AAABgOKIeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADEfUAwAAAIYj6gEAAADDEfUAAACA4Yh6AAAAwHBEPQAAAGA4oh4AAAAwHFEPAAAAGI6oBwAAAAxH1AMAAACGI+oBAAAAwxH1AAAAgOGIegAAAMBwRD0AAABgOKIeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADEfUAwAAAIYj6gEAAADDEfUAAACA4QYV9Q0NDcrKylJCQoKKiorU2tp6xbXvv/++vvOd7ygrK0sxMTGqq6v7yucEAAAAcEnYUd/Y2Ci3263q6mq1t7crLy9PJSUl6uzsHHD9xYsXlZOTo/Xr1ystLe26nBMAAADAJWFH/ebNm/Xggw+qoqJCU6ZM0datW3XTTTdp+/btA66fMWOGfvjDH2rx4sWKj4+/LucEAAAAcElYUd/X16e2tja5XK5LJ4iNlcvlUktLy6AG+DrOCQAAAESTYeEsPnv2rPr7++V0OkP2O51OHTlyZFADDOacvb296u3tDX7t9/sH9b0BAACAocDIT7+pra1VcnJycMvMzLR7JAAAAMA2YUV9amqqHA6HfD5fyH6fz3fFN8F+HeesrKxUd3d3cDtx4sSgvjcAAAAwFIQV9XFxcSooKJDH4wnuCwQC8ng8Ki4uHtQAgzlnfHy8kpKSQjYAAAAgWoX1mnpJcrvdKi8vV2FhoWbOnKm6ujr19PSooqJCklRWVqYxY8aotrZW0udvhP3ggw+Cfz558qQOHTqkESNGaMKECdd0TgAAAABXFnbUl5aW6syZM6qqqpLX61V+fr6ampqCb3Tt6OhQbOylfwA4deqUpk2bFvx606ZN2rRpk+655x41Nzdf0zkBAAAAXFmMZVmW3UN8VX6/X8nJyeru7rbtpTjTdhy15ft+Xd75m4lhH8M9AADgc/w3EdfLtXaukZ9+AwAAAOASoh4AAAAwHFEPAAAAGI6oBwAAAAxH1AMAAACGI+oBAAAAwxH1AAAAgOGIegAAAMBwRD0AAABgOKIeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADEfUAwAAAIYj6gEAAADDEfUAAACA4Yh6AAAAwHBEPQAAAGA4oh4AAAAwHFEPAAAAGI6oBwAAAAxH1AMAAACGI+oBAAAAwxH1AAAAgOGIegAAAMBww+weABhKpu04avcI1807fzMx7GOG0vVL3AOJexDt1y9xD6TB3QMMrZ8DE34GeKYeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYLhBRX1DQ4OysrKUkJCgoqIitba2XnX9z372M02ePFkJCQmaOnWqXn/99ZDH77//fsXExIRsc+fOHcxoAAAAQNQJO+obGxvldrtVXV2t9vZ25eXlqaSkRJ2dnQOu/+1vf6slS5bogQce0DvvvKOFCxdq4cKFOnz4cMi6uXPn6vTp08HtlVdeGdwVAQAAAFEm7KjfvHmzHnzwQVVUVGjKlCnaunWrbrrpJm3fvn3A9c8995zmzp2r1atX6/bbb1dNTY2mT5+u+vr6kHXx8fFKS0sLbikpKYO7IgAAACDKhBX1fX19amtrk8vlunSC2Fi5XC61tLQMeExLS0vIekkqKSm5bH1zc7NGjx6tSZMm6eGHH9a5c+euOEdvb6/8fn/IBgAAAESrsKL+7Nmz6u/vl9PpDNnvdDrl9XoHPMbr9X7p+rlz5+onP/mJPB6PNmzYoH379mnevHnq7+8f8Jy1tbVKTk4ObpmZmeFcBgAAADCkDLN7AElavHhx8M9Tp05Vbm6uxo8fr+bmZt17772Xra+srJTb7Q5+7ff7CXsAAABErbCeqU9NTZXD4ZDP5wvZ7/P5lJaWNuAxaWlpYa2XpJycHKWmpurYsWMDPh4fH6+kpKSQDQAAAIhWYUV9XFycCgoK5PF4gvsCgYA8Ho+Ki4sHPKa4uDhkvSTt3bv3iusl6ZNPPtG5c+eUnp4ezngAAABAVAr702/cbre2bduml19+WR9++KEefvhh9fT0qKKiQpJUVlamysrK4PqVK1eqqalJzz77rI4cOaJ169bp7bff1ooVKyRJFy5c0OrVq7V//379/ve/l8fj0YIFCzRhwgSVlJRcp8sEAAAAhq6wX1NfWlqqM2fOqKqqSl6vV/n5+Wpqagq+Gbajo0OxsZf+rjBr1izt3LlTTz31lJ544glNnDhRu3fv1p133ilJcjgcevfdd/Xyyy+rq6tLGRkZmjNnjmpqahQfH3+dLhMAAAAYugb1RtkVK1YEn2n/c83NzZftW7RokRYtWjTg+sTERO3Zs2cwYwAAAADQIF5+AwAAAODGQtQDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADEfUAwAAAIYj6gEAAADDEfUAAACA4Yh6AAAAwHBEPQAAAGA4oh4AAAAwHFEPAAAAGI6oBwAAAAxH1AMAAACGI+oBAAAAwxH1AAAAgOGIegAAAMBwRD0AAABgOKIeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADEfUAwAAAIYj6gEAAADDEfUAAACA4Yh6AAAAwHBEPQAAAGA4oh4AAAAwHFEPAAAAGG5QUd/Q0KCsrCwlJCSoqKhIra2tV13/s5/9TJMnT1ZCQoKmTp2q119/PeRxy7JUVVWl9PR0JSYmyuVy6ejRo4MZDQAAAIg6YUd9Y2Oj3G63qqur1d7erry8PJWUlKizs3PA9b/97W+1ZMkSPfDAA3rnnXe0cOFCLVy4UIcPHw6u2bhxo55//nlt3bpVBw4c0PDhw1VSUqJPP/108FcGAAAARImwo37z5s168MEHVVFRoSlTpmjr1q266aabtH379gHXP/fcc5o7d65Wr16t22+/XTU1NZo+fbrq6+slff4sfV1dnZ566iktWLBAubm5+slPfqJTp05p9+7dX+niAAAAgGgwLJzFfX19amtrU2VlZXBfbGysXC6XWlpaBjympaVFbrc7ZF9JSUkw2I8fPy6v1yuXyxV8PDk5WUVFRWppadHixYsvO2dvb696e3uDX3d3d0uS/H5/OJdzXfX/vwu2fe+vw2DuJfdgaN2DaL9+iXsgcQ+i/fol7oHEPZC4B3Y25hff27Ksq64LK+rPnj2r/v5+OZ3OkP1Op1NHjhwZ8Biv1zvgeq/XG3z8i31XWvPnamtr9fTTT1+2PzMz89ouBF8q+e/snsB+0X4Pov36Je6BxD2I9uuXuAcS90DiHtwI13/+/HklJydf8fGwov5GUVlZGfLsfyAQ0B//+EfdcsstiomJsXGyr5ff71dmZqZOnDihpKQku8exRbTfg2i/fol7IHEPJO5BtF+/xD2QuAfRcv2WZen8+fPKyMi46rqwoj41NVUOh0M+ny9kv8/nU1pa2oDHpKWlXXX9F//r8/mUnp4esiY/P3/Ac8bHxys+Pj5k38033xzOpRgtKSlpSP/wXotovwfRfv0S90DiHkjcg2i/fol7IHEPouH6r/YM/RfCeqNsXFycCgoK5PF4gvsCgYA8Ho+Ki4sHPKa4uDhkvSTt3bs3uD47O1tpaWkha/x+vw4cOHDFcwIAAAC4JOyX37jdbpWXl6uwsFAzZ85UXV2denp6VFFRIUkqKyvTmDFjVFtbK0lauXKl7rnnHj377LOaP3++du3apbffflsvvPCCJCkmJkarVq3SM888o4kTJyo7O1tr165VRkaGFi5ceP2uFAAAABiiwo760tJSnTlzRlVVVfJ6vcrPz1dTU1Pwja4dHR2Kjb30DwCzZs3Szp079dRTT+mJJ57QxIkTtXv3bt15553BNY899ph6enr00EMPqaurS7Nnz1ZTU5MSEhKuwyUOHfHx8aqurr7spUfRJNrvQbRfv8Q9kLgHEvcg2q9f4h5I3INov/4/F2N92efjAAAAALihhf3LpwAAAADcWIh6AAAAwHBEPQAAAGA4oh4AAAAwHFFvkIaGBmVlZSkhIUFFRUVqbW21e6SIefPNN3XfffcpIyNDMTEx2r17t90jRVRtba1mzJihkSNHavTo0Vq4cKE++ugju8eKqC1btig3Nzf4S0aKi4v1y1/+0u6xbLN+/frgRwJHi3Xr1ikmJiZkmzx5st1jRdzJkyf113/917rllluUmJioqVOn6u2337Z7rIjJysq67OcgJiZGy5cvt3u0iOjv79fatWuVnZ2txMREjR8/XjU1NYq2zz05f/68Vq1apXHjxikxMVGzZs3SwYMH7R7LVkS9IRobG+V2u1VdXa329nbl5eWppKREnZ2ddo8WET09PcrLy1NDQ4Pdo9hi3759Wr58ufbv36+9e/fqs88+05w5c9TT02P3aBFz2223af369Wpra9Pbb7+tb33rW1qwYIHef/99u0eLuIMHD+rHP/6xcnNz7R4l4u644w6dPn06uL311lt2jxRRf/rTn3TXXXfpL/7iL/TLX/5SH3zwgZ599lmlpKTYPVrEHDx4MORnYO/evZKkRYsW2TxZZGzYsEFbtmxRfX29PvzwQ23YsEEbN27Uj370I7tHi6i//du/1d69e7Vjxw699957mjNnjlwul06ePGn3aPaxYISZM2day5cvD37d399vZWRkWLW1tTZOZQ9J1muvvWb3GLbq7Oy0JFn79u2zexRbpaSkWP/8z/9s9xgRdf78eWvixInW3r17rXvuucdauXKl3SNFTHV1tZWXl2f3GLZ6/PHHrdmzZ9s9xg1l5cqV1vjx461AIGD3KBExf/58a9myZSH7vv3tb1tLly61aaLIu3jxouVwOKxf/OIXIfunT59uPfnkkzZNZT+eqTdAX1+f2tra5HK5gvtiY2PlcrnU0tJi42SwS3d3tyRp1KhRNk9ij/7+fu3atUs9PT0qLi62e5yIWr58uebPnx/y/wfR5OjRo8rIyFBOTo6WLl2qjo4Ou0eKqP/8z/9UYWGhFi1apNGjR2vatGnatm2b3WPZpq+vTz/96U+1bNkyxcTE2D1ORMyaNUsej0e/+93vJEn//d//rbfeekvz5s2zebLI+d///V/19/df9ktKExMTo+5f7/6vsH+jLCLv7Nmz6u/vD/7W3i84nU4dOXLEpqlgl0AgoFWrVumuu+4K+c3M0eC9995TcXGxPv30U40YMUKvvfaapkyZYvdYEbNr1y61t7dH7etGi4qK9NJLL2nSpEk6ffq0nn76ad199906fPiwRo4cafd4EfE///M/2rJli9xut5544gkdPHhQ//AP/6C4uDiVl5fbPV7E7d69W11dXbr//vvtHiVi1qxZI7/fr8mTJ8vhcKi/v1/f//73tXTpUrtHi5iRI0equLhYNTU1uv322+V0OvXKK6+opaVFEyZMsHs82xD1gGGWL1+uw4cPR+WzEZMmTdKhQ4fU3d2tf/u3f1N5ebn27dsXFWF/4sQJrVy5Unv37r3s2alo8X+ficzNzVVRUZHGjRunV199VQ888ICNk0VOIBBQYWGhfvCDH0iSpk2bpsOHD2vr1q1RGfX/8i//onnz5ikjI8PuUSLm1Vdf1b/+679q586duuOOO3To0CGtWrVKGRkZUfUzsGPHDi1btkxjxoyRw+HQ9OnTtWTJErW1tdk9mm2IegOkpqbK4XDI5/OF7Pf5fEpLS7NpKthhxYoV+sUvfqE333xTt912m93jRFxcXFzwWZiCggIdPHhQzz33nH784x/bPNnXr62tTZ2dnZo+fXpwX39/v958803V19ert7dXDofDxgkj7+abb9Y3vvENHTt2zO5RIiY9Pf2yv8Tefvvt+vd//3ebJrLPH/7wB/3617/Wz3/+c7tHiajVq1drzZo1Wrx4sSRp6tSp+sMf/qDa2tqoivrx48dr37596unpkd/vV3p6ukpLS5WTk2P3aLbhNfUGiIuLU0FBgTweT3BfIBCQx+OJutcTRyvLsrRixQq99tpr+s1vfqPs7Gy7R7ohBAIB9fb22j1GRNx777167733dOjQoeBWWFiopUuX6tChQ1EX9JJ04cIFffzxx0pPT7d7lIi56667Lvs429/97ncaN26cTRPZ58UXX9To0aM1f/58u0eJqIsXLyo2NjTfHA6HAoGATRPZa/jw4UpPT9ef/vQn7dmzRwsWLLB7JNvwTL0h3G63ysvLVVhYqJkzZ6qurk49PT2qqKiwe7SIuHDhQsizccePH9ehQ4c0atQojR071sbJImP58uXauXOn/uM//kMjR46U1+uVJCUnJysxMdHm6SKjsrJS8+bN09ixY3X+/Hnt3LlTzc3N2rNnj92jRcTIkSMvew/F8OHDdcstt0TNeyseffRR3XfffRo3bpxOnTql6upqORwOLVmyxO7RIuYf//EfNWvWLP3gBz/QX/3VX6m1tVUvvPCCXnjhBbtHi6hAIKAXX3xR5eXlGjYsulLmvvvu0/e//32NHTtWd9xxh9555x1t3rxZy5Yts3u0iNqzZ48sy9KkSZN07NgxrV69WpMnT46aLhqQ3R+/g2v3ox/9yBo7dqwVFxdnzZw509q/f7/dI0XMG2+8YUm6bCsvL7d7tIgY6NolWS+++KLdo0XMsmXLrHHjxllxcXHWrbfeat17773Wr371K7vHslW0faRlaWmplZ6ebsXFxVljxoyxSktLrWPHjtk9VsT913/9l3XnnXda8fHx1uTJk60XXnjB7pEibs+ePZYk66OPPrJ7lIjz+/3WypUrrbFjx1oJCQlWTk6O9eSTT1q9vb12jxZRjY2NVk5OjhUXF2elpaVZy5cvt7q6uuwey1YxlhVlv4IMAAAAGGJ4TT0AAABgOKIeAAAAMBxRDwAAABiOqAcAAAAMR9QDAAAAhiPqAQAAAMMR9QAAAIDhiHoAAADAcEQ9AAAAYDiiHgAAADAcUQ8AAAAYjqgHAAAADPf/AdMLV+AzLK+dAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.discrete_bayes import normalize\n", + "\n", + "def scaled_update(hall, belief, z, z_prob): \n", + " scale = z_prob / (1. - z_prob)\n", + " belief[hall==z] *= scale\n", + " normalize(belief)\n", + "\n", + "belief = np.array([0.1] * 10)\n", + "scaled_update(hallway, belief, z=1, z_prob=.75)\n", + "\n", + "print('sum =', sum(belief))\n", + "print('probability of door =', belief[0])\n", + "print('probability of wall =', belief[2])\n", + "book_plots.bar_plot(belief, ylim=(0, .3))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "7cb8c66c", + "metadata": {}, + "outputs": [], + "source": [ + "def scaled_update(hall, belief, z, z_prob): \n", + " scale = z_prob / (1. - z_prob)\n", + " likelihood = np.ones(len(hall))\n", + " likelihood[hall==z] *= scale\n", + " return normalize(likelihood * belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "fe27e7d8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.188, 0.188, 0.062, 0.062, 0.062, 0.062, 0.062, 0.062, 0.188,\n", + " 0.062])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from filterpy.discrete_bayes import update\n", + "\n", + "def lh_hallway(hall, z, z_prob):\n", + " \"\"\" compute likelihood that a measurement matches\n", + " positions in the hallway.\"\"\"\n", + " \n", + " try:\n", + " scale = z_prob / (1. - z_prob)\n", + " except ZeroDivisionError:\n", + " scale = 1e8\n", + "\n", + " likelihood = np.ones(len(hall))\n", + " likelihood[hall==z] *= scale\n", + " return likelihood\n", + "\n", + "belief = np.array([0.1] * 10)\n", + "likelihood = lh_hallway(hallway, z=1, z_prob=.75)\n", + "update(likelihood, belief) " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "4df5518f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def perfect_predict(belief, move):\n", + " \"\"\" move the position by `move` spaces, where positive is \n", + " to the right, and negative is to the left\n", + " \"\"\"\n", + " n = len(belief)\n", + " result = np.zeros(n)\n", + " for i in range(n):\n", + " result[i] = belief[(i-move) % n]\n", + " return result\n", + " \n", + "belief = np.array([.35, .1, .2, .3, 0, 0, 0, 0, 0, .05])\n", + "plt.subplot(121)\n", + "book_plots.bar_plot(belief, title='Before prediction', ylim=(0, .4))\n", + "\n", + "belief = perfect_predict(belief, 1)\n", + "plt.subplot(122)\n", + "book_plots.bar_plot(belief, title='After prediction', ylim=(0, .4))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "720e464c", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "756ae341066643029d9fd9e1ed809275", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=0, description='time_step', max=19), Output()), _dom_classes=('widget-in…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "\n", + "from ipywidgets import interact, IntSlider\n", + "\n", + "belief = np.array([.35, .1, .2, .3, 0, 0, 0, 0, 0, .05])\n", + "perfect_beliefs = []\n", + "\n", + "for _ in range(20):\n", + " # Simon takes one step to the right\n", + " belief = perfect_predict(belief, 1)\n", + " perfect_beliefs.append(belief)\n", + "\n", + "def simulate(time_step):\n", + " book_plots.bar_plot(perfect_beliefs[time_step], ylim=(0, .4))\n", + " plt.show()\n", + " \n", + "interact(simulate, time_step=IntSlider(value=0, max=len(perfect_beliefs)-1));\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "bcec2eec", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def predict_move(belief, move, p_under, p_correct, p_over):\n", + " n = len(belief)\n", + " prior = np.zeros(n)\n", + " for i in range(n):\n", + " prior[i] = (\n", + " belief[(i-move) % n] * p_correct +\n", + " belief[(i-move-1) % n] * p_over +\n", + " belief[(i-move+1) % n] * p_under) \n", + " return prior\n", + "\n", + "belief = [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.]\n", + "prior = predict_move(belief, 2, .1, .8, .1)\n", + "book_plots.plot_belief_vs_prior(belief, prior)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "0d0e8ffa", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0. , 0. , 0. , 0.04, 0.38, 0.52, 0.06, 0. , 0. , 0. ])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "belief = [0, 0, .4, .6, 0, 0, 0, 0, 0, 0]\n", + "prior = predict_move(belief, 2, .1, .8, .1)\n", + "book_plots.plot_belief_vs_prior(belief, prior)\n", + "prior" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "3cc1f721", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final Belief: [0.104 0.103 0.101 0.099 0.097 0.096 0.097 0.099 0.101 0.103]\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "f95e077c4b4c4c0d89153d20088458c5", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=1, description='step'), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "belief = np.array([1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n", + "predict_beliefs = []\n", + " \n", + "for i in range(100):\n", + " belief = predict_move(belief, 1, .1, .8, .1)\n", + " predict_beliefs.append(belief)\n", + "\n", + "print('Final Belief:', belief)\n", + "\n", + "# make interactive plot\n", + "def show_prior(step):\n", + " book_plots.bar_plot(predict_beliefs[step-1])\n", + " plt.title(f'Step {step}')\n", + " plt.show()\n", + "\n", + "interact(show_prior, step=IntSlider(value=1, max=len(predict_beliefs)));" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "295e37e4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final Belief: [0.104 0.103 0.101 0.099 0.097 0.096 0.097 0.099 0.101 0.103]\n" + ] + } + ], + "source": [ + "print('Final Belief:', belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "54808ae0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def predict_move_convolution(pdf, offset, kernel):\n", + " N = len(pdf)\n", + " kN = len(kernel)\n", + " width = int((kN - 1) / 2)\n", + "\n", + " prior = np.zeros(N)\n", + " for i in range(N):\n", + " for k in range (kN):\n", + " index = (i + (width-k) - offset) % N\n", + " prior[i] += pdf[index] * kernel[k]\n", + " return prior\n", + "\n", + "\n", + "\n", + "from filterpy.discrete_bayes import predict\n", + "\n", + "belief = [.05, .05, .05, .05, .55, .05, .05, .05, .05, .05]\n", + "prior = predict(belief, offset=1, kernel=[.1, .8, .1])\n", + "book_plots.plot_belief_vs_prior(belief, prior, ylim=(0,0.6))" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "2aef5bc3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prior = predict(belief, offset=3, kernel=[.05, .05, .6, .2, .1])\n", + "book_plots.plot_belief_vs_prior(belief, prior, ylim=(0,0.6))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d8c8916b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.discrete_bayes import update\n", + "\n", + "hallway = np.array([1, 1, 0, 0, 0, 0, 0, 0, 1, 0])\n", + "prior = np.array([.1] * 10)\n", + "likelihood = lh_hallway(hallway, z=1, z_prob=.75)\n", + "posterior = update(likelihood, prior)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "67bb80af", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "kernel = (.1, .8, .1)\n", + "prior = predict(posterior, 1, kernel)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, True, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "0e84159a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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g3wOAPYIK7c3Nzdq2bZuysrK+OYDbraysLJWXl7e63y9+8Qv16dNH99xzz/mvFADQbuj3AGCXLsFMPnz4sLxerxISEgLGExIStHv37hb3ee+99/Sb3/xGO3bsaHOdpqYmNTU1+V83NDQEs0wAwAWi3wOAXRx9esyxY8d0991367nnnlNcXFyb9ysqKlJsbKx/S05OdnCVAIALRb8HAGcFdaU9Li5OERERqqmpCRivqalRYmLiGfM//vhjHThwQN///vf9Yz6f7+vCXbpoz549GjJkyBn7FRQUKD8/3/+6oaGBRg4A7Yh+DwB2CSq0R0VFacyYMSorK/M/xsvn86msrExz5sw5Y/6wYcP0wQcfBIz97Gc/07Fjx/SrX/2q1cbs8Xjk8XiCWRoAIITo9wBgl6BCuyTl5+dr2rRpSktLU3p6upYuXarGxkbl5eVJknJzc5WUlKSioiJFR0drxIgRAfv37NlTks4YBwDYhX4PAPYIOrTn5OSorq5O8+fPV3V1tUaNGqXS0lL/m5UOHjwot5sPWgWAix39HgDs4TLGmHAv4lwaGhoUGxur+vp6xcTEhHs5AOCoztzzOvO5A+h8gul5XCIBAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACzXJdwLAADgYjZ69V5Hj7/97qGOHh/AxYEr7QAAAIDlCO0AAACA5QjtAAAAgOXOK7QXFxcrJSVF0dHRysjIUEVFRatzX331VaWlpalnz5665JJLNGrUKK1evfq8FwwAaD/0ewCwQ9ChvaSkRPn5+SosLFRlZaVSU1OVnZ2t2traFuf37t1bjz76qMrLy/X+++8rLy9PeXl5evvtty948QAA59DvAcAeLmOMCWaHjIwMjR07VsuWLZMk+Xw+JScn67777tO8efPadIyrr75akydP1qJFi9o0v6GhQbGxsaqvr1dMTEwwywWAi44tPY9+3zY8PQbA+Qqm5wV1pb25uVnbtm1TVlbWNwdwu5WVlaXy8vJz7m+MUVlZmfbs2aPrr7++1XlNTU1qaGgI2AAA7Yd+DwB2CSq0Hz58WF6vVwkJCQHjCQkJqq6ubnW/+vp6de/eXVFRUZo8ebKefvpp/fM//3Or84uKihQbG+vfkpOTg1kmAOAC0e8BwC7t8vSYHj16aMeOHdqyZYsee+wx5efna8OGDa3OLygoUH19vX87dOhQeywTAHCB6PcA4IygPhE1Li5OERERqqmpCRivqalRYmJiq/u53W5ddtllkqRRo0bpo48+UlFRkW644YYW53s8Hnk8nmCWBgAIIfo9ANglqCvtUVFRGjNmjMrKyvxjPp9PZWVlyszMbPNxfD6fmpqagikNAGhH9HsAsEtQV9olKT8/X9OmTVNaWprS09O1dOlSNTY2Ki8vT5KUm5urpKQkFRUVSfr6fsW0tDQNGTJETU1NevPNN7V69WotX748tGcCAAgp+j0A2CPo0J6Tk6O6ujrNnz9f1dXVGjVqlEpLS/1vVjp48KDc7m8u4Dc2NmrWrFn6+9//rq5du2rYsGF66aWXlJOTE7qzAACEHP0eAOwR9HPaw+FifG4vAJyvztzzLsZz5zntAM6XY89pBwAAAND+CO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOXOK7QXFxcrJSVF0dHRysjIUEVFRatzn3vuOV133XXq1auXevXqpaysrLPOBwDYg34PAHYIOrSXlJQoPz9fhYWFqqysVGpqqrKzs1VbW9vi/A0bNujOO+/Un//8Z5WXlys5OVmTJk1SVVXVBS8eAOAc+j0A2MNljDHB7JCRkaGxY8dq2bJlkiSfz6fk5GTdd999mjdv3jn393q96tWrl5YtW6bc3Nw21WxoaFBsbKzq6+sVExMTzHIB4KJjS8+j37fN6NV7HT3+9ruHOnp8AOETTM8L6kp7c3Oztm3bpqysrG8O4HYrKytL5eXlbTrG8ePHdeLECfXu3bvVOU1NTWpoaAjYAADth34PAHYJKrQfPnxYXq9XCQkJAeMJCQmqrq5u0zEefvhh9evXL+AHwemKiooUGxvr35KTk4NZJgDgAtHvAcAu7fr0mMWLF2vt2rVat26doqOjW51XUFCg+vp6/3bo0KF2XCUA4ELR7wEgtLoEMzkuLk4RERGqqakJGK+pqVFiYuJZ933yySe1ePFi/elPf9LIkSPPOtfj8cjj8QSzNABACNHvAcAuQV1pj4qK0pgxY1RWVuYf8/l8KisrU2ZmZqv7PfHEE1q0aJFKS0uVlpZ2/qsFALQL+j0A2CWoK+2SlJ+fr2nTpiktLU3p6elaunSpGhsblZeXJ0nKzc1VUlKSioqKJEmPP/645s+frzVr1iglJcV/L2T37t3VvXv3EJ4KACCU6PcAYI+gQ3tOTo7q6uo0f/58VVdXa9SoUSotLfW/WengwYNyu7+5gL98+XI1Nzfr9ttvDzhOYWGhFixYcGGrBwA4hn4PAPYI+jnt4XAxPrcXAM5XZ+55F+O585x2AOfLsee0AwAAAGh/hHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAckF/IiraxskP22jtgzbCURMAAADO40o7AAAAYDlCOwAAAGA5QjsAAABgOUI7AAAAYDlCOwAAAGA5QjsAAABgOUI7AAAAYDme0w6gU+PzDQAAFwOutAMAAACWI7QDAAAAliO0AwAAAJbjnnYAQIfBexQAdFRcaQcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAs1yXcCwAAAEDnMnr1XseOvf3uoY4dO5y40g4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFjuvEJ7cXGxUlJSFB0drYyMDFVUVLQ6d9euXfrhD3+olJQUuVwuLV269HzXCgBoZ/R7ALBD0KG9pKRE+fn5KiwsVGVlpVJTU5Wdna3a2toW5x8/flyDBw/W4sWLlZiYeMELBgC0D/o9ANijS7A7LFmyRDNnzlReXp4kacWKFXrjjTe0atUqzZs374z5Y8eO1dixYyWpxa8DAOxEv7fX6NV7HT3+9ruHOnp8AMEL6kp7c3Oztm3bpqysrG8O4HYrKytL5eXlIV8cACA86PcAYJegrrQfPnxYXq9XCQkJAeMJCQnavXt3yBbV1NSkpqYm/+uGhoaQHRsAcG70ewCwi5VPjykqKlJsbKx/S05ODveSAAAOoN8DQNsEFdrj4uIUERGhmpqagPGampqQvumooKBA9fX1/u3QoUMhOzYA4Nzo9wBgl6Buj4mKitKYMWNUVlamKVOmSJJ8Pp/Kyso0Z86ckC3K4/HI4/GE7HgAgODQ7wF0NBf7G7iDfnpMfn6+pk2bprS0NKWnp2vp0qVqbGz0P10gNzdXSUlJKioqkvT1m5k+/PBD/39XVVVpx44d6t69uy677LIQngoAIJTo9wBgj6BDe05Ojurq6jR//nxVV1dr1KhRKi0t9b9Z6eDBg3K7v7nr5tNPP9Xo0aP9r5988kk9+eSTmjBhgjZs2HDhZwAAcAT9HgDsEXRol6Q5c+a0+uvR0xtzSkqKjDHnUwYAEGb0ewCwg5VPjwEAAADwjfO60n4xudjfdAAAAABwpR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwXId/TjucxXPwESr8WQIAoHVcaQcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsx3PacVFy8pnerT3PO1zPEe9M5woAAFrGlXYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcl3CvQAAAHBxGL16r2PH3n73UMeODXQEXGkHAAAALEdoBwAAACxHaAcAAAAsxz3tAADAWk7eRy+1fi99OO7fD8e5huv7i+BxpR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALDceYX24uJipaSkKDo6WhkZGaqoqDjr/P/8z//UsGHDFB0drauuukpvvvnmeS0WANC+6PcAYIegQ3tJSYny8/NVWFioyspKpaamKjs7W7W1tS3O37Rpk+68807dc8892r59u6ZMmaIpU6bo//7v/y548QAA59DvAcAeQYf2JUuWaObMmcrLy9Pw4cO1YsUKdevWTatWrWpx/q9+9SvdeOONeuihh3TFFVdo0aJFuvrqq7Vs2bILXjwAwDn0ewCwR5dgJjc3N2vbtm0qKCjwj7ndbmVlZam8vLzFfcrLy5Wfnx8wlp2drddee63VOk1NTWpqavK/rq+vlyQ1NDQEs1xJkvfLL4LeJxitrcnJup2lZrjqcq7hOdfO9P1t637GmFAuJygXY7+X+PviZE2n69r0/XW6rk3nyvfX+bpt2adN/d4EoaqqykgymzZtChh/6KGHTHp6eov7REZGmjVr1gSMFRcXmz59+rRap7Cw0EhiY2Nj69TboUOHgmnRIUW/Z2NjY2u/rS39Pqgr7e2loKAg4GqNz+fT559/rksvvVQul8uxug0NDUpOTtahQ4cUExPjWJ1w1wxXXc6149UMV92Ofq7GGB07dkz9+vVzrIYtOlO/D1ddzrXj1QxXXc419ILp90GF9ri4OEVERKimpiZgvKamRomJiS3uk5iYGNR8SfJ4PPJ4PAFjPXv2DGapFyQmJqZd/zCGq2a46nKuHa9muOp25HONjY119PjnQr/veHU5145XM1x1OdfQamu/D+qNqFFRURozZozKysr8Yz6fT2VlZcrMzGxxn8zMzID5krR+/fpW5wMAwo9+DwB2Cfr2mPz8fE2bNk1paWlKT0/X0qVL1djYqLy8PElSbm6ukpKSVFRUJEmaO3euJkyYoKeeekqTJ0/W2rVrtXXrVj377LOhPRMAQEjR7wHAHkGH9pycHNXV1Wn+/Pmqrq7WqFGjVFpaqoSEBEnSwYMH5XZ/cwF/3LhxWrNmjX72s5/pkUce0dChQ/Xaa69pxIgRoTuLEPF4PCosLDzjV7UdrWa46nKuHa9muOp2pnMNJ/p9x6jLuXa8muGqy7mGl8uYMD5TDAAAAMA5Bf3hSgAAAADaF6EdAAAAsByhHQAAALAcoR0AAACwHKH9/ysuLlZKSoqio6OVkZGhiooKR+v9z//8j77//e+rX79+crlceu211xytJ0lFRUUaO3asevTooT59+mjKlCnas2eP43WXL1+ukSNH+j+gIDMzU2+99Zbjdb9t8eLFcrlcuv/++x2ts2DBArlcroBt2LBhjtaUpKqqKt1111269NJL1bVrV1111VXaunWrozVTUlLOOFeXy6XZs2c7VtPr9ernP/+5Bg0apK5du2rIkCFatGiRnH4//bFjx3T//fdr4MCB6tq1q8aNG6ctW7Y4WhPOouc7g35Pvw8V+v2ZCO2SSkpKlJ+fr8LCQlVWVio1NVXZ2dmqra11rGZjY6NSU1NVXFzsWI3Tbdy4UbNnz9bmzZu1fv16nThxQpMmTVJjY6Ojdfv376/Fixdr27Zt2rp1q/7pn/5Jt956q3bt2uVo3VO2bNmilStXauTIke1S78orr9Rnn33m39577z1H6x05ckTXXnutIiMj9dZbb+nDDz/UU089pV69ejlad8uWLQHnuX79eknSj370I8dqPv7441q+fLmWLVumjz76SI8//rieeOIJPf30047VlKQZM2Zo/fr1Wr16tT744ANNmjRJWVlZqqqqcrQunEHPd67n0+/p96FCv2+BgUlPTzezZ8/2v/Z6vaZfv36mqKioXepLMuvWrWuXWt9WW1trJJmNGze2e+1evXqZ//iP/3C8zrFjx8zQoUPN+vXrzYQJE8zcuXMdrVdYWGhSU1MdrXG6hx9+2IwfP75da7Zk7ty5ZsiQIcbn8zlWY/LkyWb69OkBYz/4wQ/M1KlTHat5/PhxExERYV5//fWA8auvvto8+uijjtWFc+j57dvz6fehQ7/v3P2+019pb25u1rZt25SVleUfc7vdysrKUnl5eRhX5rz6+npJUu/evdutptfr1dq1a9XY2NguH20+e/ZsTZ48OeD/r9P27t2rfv36afDgwZo6daoOHjzoaL0//OEPSktL049+9CP16dNHo0eP1nPPPedozdM1NzfrpZde0vTp0+VyuRyrM27cOJWVlemvf/2rJGnnzp167733dNNNNzlW8+TJk/J6vYqOjg4Y79q1q+NX1RB69Pz26/n0+9Cj33fyfh/ufzWEW1VVlZFkNm3aFDD+0EMPmfT09HZZg8Jw1cXr9ZrJkyeba6+9tl3qvf/+++aSSy4xERERJjY21rzxxhuO13z55ZfNiBEjzJdffmmMMe1y5eXNN980r7zyitm5c6cpLS01mZmZZsCAAaahocGxmh6Px3g8HlNQUGAqKyvNypUrTXR0tHnhhRccq3m6kpISExERYaqqqhyt4/V6zcMPP2xcLpfp0qWLcblc5pe//KWjNY0xJjMz00yYMMFUVVWZkydPmtWrVxu3222+853vOF4boUXPd77n0+/p96FAvz8Tob2TNvB//dd/NQMHDjSHDh1ql3pNTU1m7969ZuvWrWbevHkmLi7O7Nq1y7F6Bw8eNH369DE7d+70j7VHEz/dkSNHTExMjKO/Go6MjDSZmZkBY/fdd5+55pprHKt5ukmTJpmbb77Z8Tovv/yy6d+/v3n55ZfN+++/b37729+a3r17O/4Da9++feb66683kkxERIQZO3asmTp1qhk2bJijdRF69Hznez79nn4fCvT7M3X60N7U1GQiIiLOaKC5ubnmlltuaZc1tHcDnz17tunfv7/529/+1m41Tzdx4kTzk5/8xLHjr1u3zv8X7tQmybhcLhMREWFOnjzpWO3TpaWlmXnz5jl2/AEDBph77rknYOyZZ54x/fr1c6zmtx04cMC43W7z2muvOV6rf//+ZtmyZQFjixYtMpdffrnjtY0x5osvvjCffvqpMcaYO+64w3zve99rl7oIHXp++6Pfhw79vnP3+05/T3tUVJTGjBmjsrIy/5jP51NZWVm73IPXnowxmjNnjtatW6d3331XgwYNCttafD6fmpqaHDv+xIkT9cEHH2jHjh3+LS0tTVOnTtWOHTsUERHhWO1v++KLL/Txxx+rb9++jtW49tprz3iM21//+lcNHDjQsZrf9vzzz6tPnz6aPHmy47WOHz8utzuwbUVERMjn8zleW5IuueQS9e3bV0eOHNHbb7+tW2+9tV3qInTo+e2Pfh869PtO3u/D/a8GG6xdu9Z4PB7zwgsvmA8//ND85Cc/MT179jTV1dWO1Tx27JjZvn272b59u5FklixZYrZv324++eQTx2ree++9JjY21mzYsMF89tln/u348eOO1TTGmHnz5pmNGzea/fv3m/fff9/MmzfPuFwu88477zha93Tt8evSBx54wGzYsMHs37/f/OUvfzFZWVkmLi7O1NbWOlazoqLCdOnSxTz22GNm79695ne/+53p1q2beemllxyreYrX6zUDBgwwDz/8sOO1jDFm2rRpJikpybz++utm//795tVXXzVxcXHmpz/9qaN1S0tLzVtvvWX+9re/mXfeecekpqaajIwM09zc7GhdOIOe71zPp9/T70OFfn8mQvv/9/TTT5sBAwaYqKgok56ebjZv3uxovT//+c9G0hnbtGnTHKvZUj1J5vnnn3espjHGTJ8+3QwcONBERUWZ+Ph4M3HixHZv4Ma0TxPPyckxffv2NVFRUSYpKcnk5OSYffv2OVrTGGP++Mc/mhEjRhiPx2OGDRtmnn32WcdrGmPM22+/bSSZPXv2tEu9hoYGM3fuXDNgwAATHR1tBg8ebB599FHT1NTkaN2SkhIzePBgExUVZRITE83s2bPN0aNHHa0JZ9HznUG/p9+HCv3+TC5jHP5oKQAAAAAXpNPf0w4AAADYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFju/wHYLY9KUUhlAgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "likelihood = lh_hallway(hallway, z=1, z_prob=.75)\n", + "posterior = update(likelihood, prior)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "b972ab08", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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wR1ChvbW1VVu2bFFeXt6XE7jdysvLU3V1dZvH/exnP1NycrLuvPPOc18pACBs6PcAYJcuwQw+fPiwvF6vUlJSAvanpKRo165dZzzm7bff1q9//Wtt37693XVaWlrU0tLif93Y2BjMMgEA54l+DwB2cfTpMU1NTbrjjjv0zDPPKDExsd3HlZWVKSEhwb+lp6c7uEoAwPmi3wOAs4K60p6YmKioqCjV1dUF7K+rq1Nqaupp4z/44APt379f3/3ud/37fD7fF4W7dNHu3bs1aNCg044rKSlRcXGx/3VjYyONHADCiH4PAHYJKrTHxMRo1KhRqqqq8j/Gy+fzqaqqSrNmzTpt/JAhQ/Tuu+8G7PvJT36ipqYm/fKXv2yzMXs8Hnk8nmCWBgAIIfo9ANglqNAuScXFxSosLFRWVpays7O1aNEiNTc3q6ioSJI0ZcoUpaWlqaysTLGxsRo2bFjA8T169JCk0/YDAOxCvwcAewQd2gsKClRfX6+5c+eqtrZWI0aMUGVlpf/NSgcOHJDbzQetAsA3Hf0eAOzhMsaYSC/i6zQ2NiohIUENDQ2Kj4+P9HIAwFGdued15nMH0PkE0/O4RAIAAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWK5LpBcAAACCM3LFHkfn33bHYEfnBxA8rrQDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWI7QDAAAAliO0AwAAAJYjtAMAAACWO6fQXl5eroyMDMXGxionJ0cbN25sc+zLL7+srKws9ejRQxdccIFGjBihFStWnPOCAQDhQ78HADsEHdorKipUXFys0tJSbd26VZmZmcrPz9ehQ4fOOL5Xr1566KGHVF1drXfeeUdFRUUqKirSG2+8cd6LBwA4h34PAPZwGWNMMAfk5ORo9OjRWrx4sSTJ5/MpPT1dd999t+bMmdOuOS6//HJNnDhRCxYsaNf4xsZGJSQkqKGhQfHx8cEsFwC+cWzpefR7e41cscfR+bfdMdjR+QF8IZieF9SV9tbWVm3ZskV5eXlfTuB2Ky8vT9XV1V97vDFGVVVV2r17t66++uo2x7W0tKixsTFgAwCED/0eAOwSVGg/fPiwvF6vUlJSAvanpKSotra2zeMaGhrUrVs3xcTEaOLEiXryySf1z//8z22OLysrU0JCgn9LT08PZpkAgPNEvwcAu4Tl6THdu3fX9u3btWnTJj388MMqLi7W2rVr2xxfUlKihoYG/1ZTUxOOZQIAzhP9HgCc0SWYwYmJiYqKilJdXV3A/rq6OqWmprZ5nNvt1kUXXSRJGjFihN5//32VlZXpmmuuOeN4j8cjj8cTzNIAACFEvwcAuwR1pT0mJkajRo1SVVWVf5/P51NVVZVyc3PbPY/P51NLS0swpQEAYUS/BwC7BHWlXZKKi4tVWFiorKwsZWdna9GiRWpublZRUZEkacqUKUpLS1NZWZmkL+5XzMrK0qBBg9TS0qLXXntNK1as0JIlS0J7JgCAkKLfA4A9gg7tBQUFqq+v19y5c1VbW6sRI0aosrLS/2alAwcOyO3+8gJ+c3OzZsyYob///e/q2rWrhgwZohdeeEEFBQWhOwsAQMjR7wHAHkE/pz0SeG4vgM6kM/e8znzuweA57UDH4Nhz2gEAAACEH6EdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsFzQn4gKezn5YRt80AYAAEDkcKUdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACw3DmF9vLycmVkZCg2NlY5OTnauHFjm2OfeeYZXXXVVerZs6d69uypvLy8s44HANiDfg8Adgg6tFdUVKi4uFilpaXaunWrMjMzlZ+fr0OHDp1x/Nq1a3Xbbbfpz3/+s6qrq5Wenq4JEybo4MGD5714AIBz6PcAYA+XMcYEc0BOTo5Gjx6txYsXS5J8Pp/S09N19913a86cOV97vNfrVc+ePbV48WJNmTKlXTUbGxuVkJCghoYGxcfHB7PcTmXkij2Ozb3tjsGOzQ0gkC09j35vLyf7vUTPB8IlmJ4X1JX21tZWbdmyRXl5eV9O4HYrLy9P1dXV7Zrj2LFjOn78uHr16tXmmJaWFjU2NgZsAIDwod8DgF2CCu2HDx+W1+tVSkpKwP6UlBTV1ta2a44HHnhAffr0CfhBcKqysjIlJCT4t/T09GCWCQA4T/R7ALBLWJ8e88gjj2jVqlVavXq1YmNj2xxXUlKihoYG/1ZTUxPGVQIAzhf9HgBCq0swgxMTExUVFaW6urqA/XV1dUpNTT3rsY8//rgeeeQR/elPf9Lw4cPPOtbj8cjj8QSzNABACNHvAcAuQV1pj4mJ0ahRo1RVVeXf5/P5VFVVpdzc3DaPe+yxx7RgwQJVVlYqKyvr3FcLAAgL+j0A2CWoK+2SVFxcrMLCQmVlZSk7O1uLFi1Sc3OzioqKJElTpkxRWlqaysrKJEmPPvqo5s6dq5UrVyojI8N/L2S3bt3UrVu3EJ4KACCU6PcAYI+gQ3tBQYHq6+s1d+5c1dbWasSIEaqsrPS/WenAgQNyu7+8gL9kyRK1trbq5ptvDpintLRU8+bNO7/VAwAcQ78HAHsE/Zz2SOC5ve3Dc9qBjqEz97zOfO7B4DntQMfg2HPaAQAAAIQfoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwHKEdAAAAsByhHQAAALAcoR0AAACwXJdIL6CjGrlij2Nzb7tjsGNzAwAAwD5caQcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsx3PaAQAA0OE5+Rk6kvOfo0NoBwAA7cIHBwKRw+0xAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5bpEegEAEEkjV+xxbO5tdwx2bG4AQOdCaMd5cTLwSIQeAAAAidtjAAAAAOsR2gEAAADLEdoBAAAAyxHaAQAAAMsR2gEAAADLEdoBAAAAy51TaC8vL1dGRoZiY2OVk5OjjRs3tjl2586d+v73v6+MjAy5XC4tWrToXNcKAAgz+j0A2CHo57RXVFSouLhYS5cuVU5OjhYtWqT8/Hzt3r1bycnJp40/duyYBg4cqFtuuUX/+q//GpJFB4PniAPAufmm9XsA6MiCvtK+cOFCTZ8+XUVFRRo6dKiWLl2quLg4LV++/IzjR48erV/84hf6wQ9+II/Hc94LBgCEB/0eAOwRVGhvbW3Vli1blJeX9+UEbrfy8vJUXV0d8sUBACKDfg8Adgnq9pjDhw/L6/UqJSUlYH9KSop27doVskW1tLSopaXF/7qxsTFkcwMAvh79HgDsYuXTY8rKypSQkODf0tPTI70kAIAD6PcA0D5BhfbExERFRUWprq4uYH9dXZ1SU1NDtqiSkhI1NDT4t5qampDNDQD4evR7ALBLUKE9JiZGo0aNUlVVlX+fz+dTVVWVcnNzQ7Yoj8ej+Pj4gA0AED70ewCwS9CPfCwuLlZhYaGysrKUnZ2tRYsWqbm5WUVFRZKkKVOmKC0tTWVlZZK+eDPTe++95//vgwcPavv27erWrZsuuuiiEJ4KACCU6PcAYI+gQ3tBQYHq6+s1d+5c1dbWasSIEaqsrPS/WenAgQNyu7+8gP/RRx9p5MiR/tePP/64Hn/8cY0bN05r1649/zMAADiCfg8A9gg6tEvSrFmzNGvWrDN+7dTGnJGRIWPMuZQBAEQY/R4A7GDl02MAAAAAfInQDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYjtAOAAAAWI7QDgAAAFiO0A4AAABYrkukFwAAwDfZyBV7HJ1/2x2DHZ0fwDcDV9oBAAAAyxHaAQAAAMsR2gEAAADLcU87AACwFu8ZAL7AlXYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcjynHd9ITj63l2f2AgAA2xDaAQAATsHFIdiG0A7ACnzqIYDOLhJ9kN77zUFoBwB0GFwdBdBR8UZUAAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHK8ERVop0i9wz4Sb6zjaQIAANiFK+0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5QjtAAAAgOUI7QAAAIDlCO0AAACA5bpEegEAAADoXEau2OPY3NvuGOzY3JHElXYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcoR2AAAAwHKEdgAAAMByhHYAAADAcucU2svLy5WRkaHY2Fjl5ORo48aNZx3/H//xHxoyZIhiY2N12WWX6bXXXjunxQIAwot+DwB2CDq0V1RUqLi4WKWlpdq6dasyMzOVn5+vQ4cOnXH8+vXrddttt+nOO+/Utm3bNGnSJE2aNEn/+7//e96LBwA4h34PAPYIOrQvXLhQ06dPV1FRkYYOHaqlS5cqLi5Oy5cvP+P4X/7yl7r22mt1//3365JLLtGCBQt0+eWXa/Hixee9eACAc+j3AGCPLsEMbm1t1ZYtW1RSUuLf53a7lZeXp+rq6jMeU11dreLi4oB9+fn5euWVV9qs09LSopaWFv/rhoYGSVJjY2Mwy5UkeT/7NOhjgtHWmpys21lqRqou5xqZc+1M39/2HmeMCeVygvJN7PcSf1+crOl0XZu+v07Xtelc+f46X7c9x7Sr35sgHDx40Egy69evD9h///33m+zs7DMeEx0dbVauXBmwr7y83CQnJ7dZp7S01EhiY2Nj69RbTU1NMC06pOj3bGxsbOHb2tPvg7rSHi4lJSUBV2t8Pp8++eQTXXjhhXK5XI7VbWxsVHp6umpqahQfH+9YnUjXjFRdzrXj1YxU3Y5+rsYYNTU1qU+fPo7VsEVn6veRqsu5dryakarLuYZeMP0+qNCemJioqKgo1dXVBeyvq6tTamrqGY9JTU0NarwkeTweeTyegH09evQIZqnnJT4+Pqz/M0aqZqTqcq4dr2ak6nbkc01ISHB0/q9Dv+94dTnXjlczUnU519Bqb78P6o2oMTExGjVqlKqqqvz7fD6fqqqqlJube8ZjcnNzA8ZL0po1a9ocDwCIPPo9ANgl6NtjiouLVVhYqKysLGVnZ2vRokVqbm5WUVGRJGnKlClKS0tTWVmZJGn27NkaN26cnnjiCU2cOFGrVq3S5s2b9fTTT4f2TAAAIUW/BwB7BB3aCwoKVF9fr7lz56q2tlYjRoxQZWWlUlJSJEkHDhyQ2/3lBfwxY8Zo5cqV+slPfqIHH3xQgwcP1iuvvKJhw4aF7ixCxOPxqLS09LRf1Xa0mpGqy7l2vJqRqtuZzjWS6Pcdoy7n2vFqRqou5xpZLmMi+EwxAAAAAF8r6A9XAgAAABBehHYAAADAcoR2AAAAwHKEdgAAAMByhPb/V15eroyMDMXGxionJ0cbN250tN5///d/67vf/a769Okjl8ulV155xdF6klRWVqbRo0ere/fuSk5O1qRJk7R7927H6y5ZskTDhw/3f0BBbm6uXn/9dcfrftUjjzwil8ule+65x9E68+bNk8vlCtiGDBniaE1JOnjwoG6//XZdeOGF6tq1qy677DJt3rzZ0ZoZGRmnnavL5dLMmTMdq+n1evXTn/5UAwYMUNeuXTVo0CAtWLBATr+fvqmpSffcc4/69++vrl27asyYMdq0aZOjNeEser4z6Pf0+1Ch35+O0C6poqJCxcXFKi0t1datW5WZman8/HwdOnTIsZrNzc3KzMxUeXm5YzVOtW7dOs2cOVMbNmzQmjVrdPz4cU2YMEHNzc2O1u3bt68eeeQRbdmyRZs3b9Y//dM/6cYbb9TOnTsdrXvSpk2btGzZMg0fPjws9S699FJ9/PHH/u3tt992tN6RI0d05ZVXKjo6Wq+//rree+89PfHEE+rZs6ejdTdt2hRwnmvWrJEk3XLLLY7VfPTRR7VkyRItXrxY77//vh599FE99thjevLJJx2rKUnTpk3TmjVrtGLFCr377ruaMGGC8vLydPDgQUfrwhn0fOd6Pv2efh8q9PszMDDZ2dlm5syZ/tder9f06dPHlJWVhaW+JLN69eqw1PqqQ4cOGUlm3bp1Ya/ds2dP8+///u+O12lqajKDBw82a9asMePGjTOzZ892tF5paanJzMx0tMapHnjgATN27Niw1jyT2bNnm0GDBhmfz+dYjYkTJ5qpU6cG7Pve975nJk+e7FjNY8eOmaioKPPqq68G7L/88svNQw895FhdOIeeH96eT78PHfp95+73nf5Ke2trq7Zs2aK8vDz/Prfbrby8PFVXV0dwZc5raGiQJPXq1StsNb1er1atWqXm5uawfLT5zJkzNXHixIA/X6ft2bNHffr00cCBAzV58mQdOHDA0Xq///3vlZWVpVtuuUXJyckaOXKknnnmGUdrnqq1tVUvvPCCpk6dKpfL5VidMWPGqKqqSn/9618lSTt27NDbb7+t6667zrGaJ06ckNfrVWxsbMD+rl27On5VDaFHzw9fz6ffhx79vpP3+0j/qyHSDh48aCSZ9evXB+y///77TXZ2dljWoAhcdfF6vWbixInmyiuvDEu9d955x1xwwQUmKirKJCQkmD/+8Y+O13zxxRfNsGHDzGeffWaMMWG58vLaa6+Zl156yezYscNUVlaa3Nxc069fP9PY2OhYTY/HYzwejykpKTFbt241y5YtM7Gxsea5555zrOapKioqTFRUlDl48KCjdbxer3nggQeMy+UyXbp0MS6Xy/z85z93tKYxxuTm5ppx48aZgwcPmhMnTpgVK1YYt9ttvvWtbzleG6FFz3e+59Pv6fehQL8/HaG9kzbwf/mXfzH9+/c3NTU1YanX0tJi9uzZYzZv3mzmzJljEhMTzc6dOx2rd+DAAZOcnGx27Njh3xeOJn6qI0eOmPj4eEd/NRwdHW1yc3MD9t19993miiuucKzmqSZMmGCuv/56x+u8+OKLpm/fvubFF18077zzjvnNb35jevXq5fgPrL1795qrr77aSDJRUVFm9OjRZvLkyWbIkCGO1kXo0fOd7/n0e/p9KNDvT9fpQ3tLS4uJioo6rYFOmTLF3HDDDWFZQ7gb+MyZM03fvn3N3/72t7DVPNX48ePNj370I8fmX716tf8v3MlNknG5XCYqKsqcOHHCsdqnysrKMnPmzHFs/n79+pk777wzYN9TTz1l+vTp41jNr9q/f79xu93mlVdecbxW3759zeLFiwP2LViwwFx88cWO1zbGmE8//dR89NFHxhhjbr31VvOd73wnLHUROvT88KPfhw79vnP3+05/T3tMTIxGjRqlqqoq/z6fz6eqqqqw3IMXTsYYzZo1S6tXr9Zbb72lAQMGRGwtPp9PLS0tjs0/fvx4vfvuu9q+fbt/y8rK0uTJk7V9+3ZFRUU5VvurPv30U33wwQfq3bu3YzWuvPLK0x7j9te//lX9+/d3rOZXPfvss0pOTtbEiRMdr3Xs2DG53YFtKyoqSj6fz/HaknTBBReod+/eOnLkiN544w3deOONYamL0KHnhx/9PnTo952830f6Xw02WLVqlfF4POa5554z7733nvnRj35kevToYWprax2r2dTUZLZt22a2bdtmJJmFCxeabdu2mQ8//NCxmnfddZdJSEgwa9euNR9//LF/O3bsmGM1jTFmzpw5Zt26dWbfvn3mnXfeMXPmzDEul8u8+eabjtY9VTh+XXrvvfeatWvXmn379pm//OUvJi8vzyQmJppDhw45VnPjxo2mS5cu5uGHHzZ79uwxv/3tb01cXJx54YUXHKt5ktfrNf369TMPPPCA47WMMaawsNCkpaWZV1991ezbt8+8/PLLJjEx0fz4xz92tG5lZaV5/fXXzd/+9jfz5ptvmszMTJOTk2NaW1sdrQtn0POd6/n0e/p9qNDvT0do/39PPvmk6devn4mJiTHZ2dlmw4YNjtb785//bCSdthUWFjpW80z1JJlnn33WsZrGGDN16lTTv39/ExMTY5KSksz48ePD3sCNCU8TLygoML179zYxMTEmLS3NFBQUmL179zpa0xhj/vCHP5hhw4YZj8djhgwZYp5++mnHaxpjzBtvvGEkmd27d4elXmNjo5k9e7bp16+fiY2NNQMHDjQPPfSQaWlpcbRuRUWFGThwoImJiTGpqalm5syZ5ujRo47WhLPo+c6g39PvQ4V+fzqXMQ5/tBQAAACA89Lp72kHAAAAbEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAsR2gHAAAALEdoBwAAACxHaAcAAAAs9386Yo9SQTIXBwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prior = predict(posterior, 1, kernel)\n", + "likelihood = lh_hallway(hallway, z=0, z_prob=.75)\n", + "posterior = update(likelihood, prior)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "2146cd23", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prior = predict(posterior, 1, kernel)\n", + "likelihood = lh_hallway(hallway, z=0, z_prob=.75)\n", + "posterior = update(likelihood, prior)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "8bd9a8e7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prior = predict(posterior, 1, kernel)\n", + "likelihood = lh_hallway(hallway, z=0, z_prob=.75)\n", + "posterior = update(likelihood, prior)\n", + "book_plots.plot_prior_vs_posterior(prior, posterior, ylim=(0,.5))" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "cf4e3410", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "book_plots.predict_update_chart()" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "95505b17", + "metadata": {}, + "outputs": [], + "source": [ + "def discrete_bayes_sim(prior, kernel, measurements, z_prob, hallway):\n", + " posterior = np.array([.1]*10)\n", + " priors, posteriors = [], []\n", + " for i, z in enumerate(measurements):\n", + " prior = predict(posterior, 1, kernel)\n", + " priors.append(prior)\n", + "\n", + " likelihood = lh_hallway(hallway, z, z_prob)\n", + " posterior = update(likelihood, prior)\n", + " posteriors.append(posterior)\n", + " return priors, posteriors\n", + "\n", + "\n", + "def plot_posterior(hallway, posteriors, i):\n", + " plt.title('Posterior')\n", + " book_plots.bar_plot(hallway, c='k')\n", + " book_plots.bar_plot(posteriors[i], ylim=(0, 1.0))\n", + " plt.axvline(i % len(hallway), lw=5)\n", + " plt.show()\n", + " \n", + "def plot_prior(hallway, priors, i):\n", + " plt.title('Prior')\n", + " book_plots.bar_plot(hallway, c='k')\n", + " book_plots.bar_plot(priors[i], ylim=(0, 1.0), c='#ff8015')\n", + " plt.axvline(i % len(hallway), lw=5)\n", + " plt.show()\n", + "\n", + "def animate_discrete_bayes(hallway, priors, posteriors):\n", + " def animate(step):\n", + " step -= 1\n", + " i = step // 2 \n", + " if step % 2 == 0:\n", + " plot_prior(hallway, priors, i)\n", + " else:\n", + " plot_posterior(hallway, posteriors, i)\n", + " \n", + " return animate" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "20cdfb18", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "07f5150a20294f789c8b0bb9648b0348", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=1, description='step'), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# change these numbers to alter the simulation\n", + "kernel = (.1, .8, .1)\n", + "z_prob = 1.0\n", + "hallway = np.array([1, 1, 0, 0, 0, 0, 0, 0, 1, 0])\n", + "\n", + "# measurements with no noise\n", + "zs = [hallway[i % len(hallway)] for i in range(50)]\n", + "\n", + "priors, posteriors = discrete_bayes_sim(prior, kernel, zs, z_prob, hallway)\n", + "interact(animate_discrete_bayes(hallway, priors, posteriors), step=IntSlider(value=1, max=len(zs)*2));" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "9c5fab3b", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "3fd22407bdf34874be73cba51724e9fd", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=12, description='step', max=12), Output()), _dom_classes=('widget-intera…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hallway = np.array([1, 0, 1, 0, 0]*2)\n", + "kernel = (.1, .8, .1)\n", + "prior = np.array([.1] * 10)\n", + "zs = [1, 0, 1, 0, 0, 1]\n", + "z_prob = 0.75\n", + "priors, posteriors = discrete_bayes_sim(prior, kernel, zs, z_prob, hallway)\n", + "interact(animate_discrete_bayes(hallway, priors, posteriors), step=IntSlider(value=12, max=len(zs)*2));" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "c1d71ec8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "measurements = [1, 0, 1, 0, 0, 1, 1]\n", + "priors, posteriors = discrete_bayes_sim(prior, kernel, measurements, z_prob, hallway);\n", + "plot_posterior(hallway, posteriors, 6)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "831e733f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with figsize(y=5.5):\n", + " measurements = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0]\n", + " for i, m in enumerate(measurements):\n", + " likelihood = lh_hallway(hallway, z=m, z_prob=.75)\n", + " posterior = update(likelihood, prior)\n", + " prior = predict(posterior, 1, kernel)\n", + " plt.subplot(5, 2, i+1)\n", + " book_plots.bar_plot(posterior, ylim=(0, .4), title=f'step {i+1}')\n", + " plt.tight_layout()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "946244a8", + "metadata": {}, + "outputs": [], + "source": [ + "class Train(object):\n", + "\n", + " def __init__(self, track_len, kernel=[1.], sensor_accuracy=.9):\n", + " self.track_len = track_len\n", + " self.pos = 0\n", + " self.kernel = kernel\n", + " self.sensor_accuracy = sensor_accuracy\n", + "\n", + " def move(self, distance=1):\n", + " \"\"\" move in the specified direction\n", + " with some small chance of error\"\"\"\n", + "\n", + " self.pos += distance\n", + " # insert random movement error according to kernel\n", + " r = random.random()\n", + " s = 0\n", + " offset = -(len(self.kernel) - 1) / 2\n", + " for k in self.kernel:\n", + " s += k\n", + " if r <= s:\n", + " break\n", + " offset += 1\n", + " self.pos = int((self.pos + offset) % self.track_len)\n", + " return self.pos\n", + "\n", + " def sense(self):\n", + " pos = self.pos\n", + " # insert random sensor error\n", + " if random.random() > self.sensor_accuracy:\n", + " if random.random() > 0.5:\n", + " pos += 1\n", + " else:\n", + " pos -= 1\n", + " return pos" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "027f4891", + "metadata": {}, + "outputs": [], + "source": [ + "def train_filter(iterations, kernel, sensor_accuracy, \n", + " move_distance, do_print=True):\n", + " track = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", + " prior = np.array([.9] + [0.01]*9)\n", + " posterior = prior[:]\n", + " normalize(prior)\n", + " \n", + " robot = Train(len(track), kernel, sensor_accuracy)\n", + " for i in range(iterations):\n", + " # move the robot and\n", + " robot.move(distance=move_distance)\n", + "\n", + " # peform prediction\n", + " prior = predict(posterior, move_distance, kernel) \n", + "\n", + " # and update the filter\n", + " m = robot.sense()\n", + " likelihood = lh_hallway(track, m, sensor_accuracy)\n", + " posterior = update(likelihood, prior)\n", + " index = np.argmax(posterior)\n", + "\n", + " if do_print:\n", + " print(f'time {i}: pos {robot.pos}, sensed {m}, at position {track[robot.pos]}')\n", + " conf = posterior[index] * 100\n", + " print(f' estimated position is {index} with confidence {conf:.4f}%:') \n", + "\n", + " book_plots.bar_plot(posterior)\n", + " if do_print:\n", + " print()\n", + " print('final position is', robot.pos)\n", + " index = np.argmax(posterior)\n", + " conf = posterior[index]*100\n", + " print(f'Estimated position is {index} with confidence {conf:.4f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "421dd3d8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time 0: pos 4, sensed 4, at position 4\n", + " estimated position is 4 with confidence 99.9900%:\n", + "time 1: pos 8, sensed 8, at position 8\n", + " estimated position is 8 with confidence 100.0000%:\n", + "time 2: pos 2, sensed 2, at position 2\n", + " estimated position is 2 with confidence 100.0000%:\n", + "time 3: pos 6, sensed 6, at position 6\n", + " estimated position is 6 with confidence 100.0000%:\n", + "\n", + "final position is 6\n", + "Estimated position is 6 with confidence 100.0000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import random\n", + "\n", + "random.seed(3)\n", + "np.set_printoptions(precision=2, suppress=True, linewidth=60)\n", + "train_filter(4, kernel=[1.], sensor_accuracy=.999,\n", + " move_distance=4, do_print=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "7ddc5cfe", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time 0: pos 4, sensed 4, at position 4\n", + " estimated position is 4 with confidence 96.0390%:\n", + "time 1: pos 8, sensed 9, at position 8\n", + " estimated position is 9 with confidence 52.1180%:\n", + "time 2: pos 3, sensed 3, at position 3\n", + " estimated position is 3 with confidence 88.3993%:\n", + "time 3: pos 7, sensed 8, at position 7\n", + " estimated position is 8 with confidence 49.3174%:\n", + "\n", + "final position is 7\n", + "Estimated position is 8 with confidence 49.3174\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "random.seed(5)\n", + "train_filter(4, kernel=[.1, .8, .1], sensor_accuracy=.9,\n", + " move_distance=4, do_print=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "4036a928", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with figsize(y=5.5):\n", + " for i in range (4):\n", + " random.seed(3)\n", + " plt.subplot(221+i)\n", + " train_filter(148+i, kernel=[.1, .8, .1], \n", + " sensor_accuracy=.8,\n", + " move_distance=4, do_print=False)\n", + " plt.title (f'iteration {148 + i}')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fae54ac6", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/03-Gaussians.ipynb b/kalman_and_bayesian_filters/03-Gaussians.ipynb new file mode 100644 index 0000000..6232679 --- /dev/null +++ b/kalman_and_bayesian_filters/03-Gaussians.ipynb @@ -0,0 +1,691 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "60cbbba5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import book_format\n", + "book_format.set_style()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "73d6c1d7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sum = 1.0\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import kf_book.book_plots as book_plots\n", + "\n", + "belief = np.array([1, 4, 2, 0, 8, 2, 2, 35, 4, 3, 2])\n", + "belief = belief / np.sum(belief)\n", + "with book_plots.figsize(y=2):\n", + " book_plots.bar_plot(belief)\n", + "print('sum = ', np.sum(belief))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f1b2382a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.8" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = [1.8, 2.0, 1.7, 1.9, 1.6]\n", + "np.mean(x)\n", + "\n", + "\n", + "x = np.array([1.8, 2.0, 1.7, 1.9, 1.6])\n", + "x.mean()\n", + "\n", + "np.median(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "476edae6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.50017" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "total = 0\n", + "N = 1000000\n", + "for r in np.random.rand(N):\n", + " if r <= .80: total += 1\n", + " elif r < .95: total += 3\n", + " else: total += 5\n", + "\n", + "total / N" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "deb7db97", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.8 1.8 1.8\n" + ] + } + ], + "source": [ + "X = [1.8, 2.0, 1.7, 1.9, 1.6]\n", + "Y = [2.2, 1.5, 2.3, 1.7, 1.3]\n", + "Z = [1.8, 1.8, 1.8, 1.8, 1.8]\n", + "\n", + "print(np.mean(X), np.mean(Y), np.mean(Z))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "dc753dc7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.02 meters squared\n", + "std 0.1414\n", + "var 0.0200\n" + ] + } + ], + "source": [ + "print(f\"{np.var(X):.2f} meters squared\")\n", + "\n", + "print(f\"std {np.std(X):.4f}\")\n", + "print(f\"var {np.std(X)**2:.4f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "9ffaba4b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from kf_book.gaussian_internal import plot_height_std\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plot_height_std(X)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "81476f6e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean = 1.810\n", + "std = 0.145\n" + ] + } + ], + "source": [ + "from numpy.random import randn\n", + "data = 1.8 + randn(100)*.1414\n", + "mean, std = data.mean(), data.std()\n", + "\n", + "plot_height_std(data, lw=2)\n", + "print(f'mean = {mean:.3f}')\n", + "print(f'std = {std:.3f}')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "686f5ac2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "std of Y is 0.39 m\n" + ] + } + ], + "source": [ + "np.sum((data > mean-std) & (data < mean+std)) / len(data) * 100.\n", + "print(f'std of Y is {np.std(Y):.2f} m')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d7af759a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Variance of X with outlier = 621.45\n", + "Variance of X without outlier = 2.03\n" + ] + } + ], + "source": [ + "X = [1, -1, 1, -2, -1, 2, 1, 2, -1, 1, -1, 2, 1, -2, 100]\n", + "print(f'Variance of X with outlier = {np.var(X):6.2f}')\n", + "print(f'Variance of X without outlier = {np.var(X[:-1]):6.2f}')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "483ee44f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.stats import plot_gaussian_pdf\n", + "plot_gaussian_pdf(mean=1.8, variance=0.1414**2, \n", + " xlabel='Student Height', ylabel='pdf');" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3dc1a259", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import kf_book.book_plots as book_plots\n", + "belief = [0., 0., 0., 0.1, 0.15, 0.5, 0.2, .15, 0, 0]\n", + "book_plots.bar_plot(belief)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "7c1c6060", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_gaussian_pdf(mean=120, variance=17**2, xlabel='speed(kph)');" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "3bd0b5eb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(-3, 3, .01)\n", + "plt.plot(x, np.exp(-x**2));" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "980401a8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cumulative probability of range 21.5 to 22.5 is 19.74%\n", + "Cumulative probability of range 23.5 to 24.5 is 12.10%\n" + ] + } + ], + "source": [ + "from filterpy.stats import norm_cdf\n", + "print('Cumulative probability of range 21.5 to 22.5 is {:.2f}%'.format(\n", + " norm_cdf((21.5, 22.5), 22,4)*100))\n", + "print('Cumulative probability of range 23.5 to 24.5 is {:.2f}%'.format(\n", + " norm_cdf((23.5, 24.5), 22,4)*100))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "e5898f07", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.24197072451914337\n", + "[0.378 0.622]\n" + ] + } + ], + "source": [ + "from filterpy.stats import gaussian\n", + "\n", + "print(gaussian(x=3.0, mean=2.0, var=1))\n", + "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "b651c0d2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xs = np.arange(15, 30, 0.05)\n", + "plt.plot(xs, gaussian(xs, 23, 0.2**2), label='$\\sigma^2=0.2^2$')\n", + "plt.plot(xs, gaussian(xs, 23, .5**2), label='$\\sigma^2=0.5^2$', ls=':')\n", + "plt.plot(xs, gaussian(xs, 23, 1**2), label='$\\sigma^2=1^2$', ls='--')\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "a6a891ab", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from kf_book.gaussian_internal import display_stddev_plot\n", + "display_stddev_plot()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "ed88b83d", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a0d3e27dca3340bfa1952ebdb3afb7ad", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, desc…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import math\n", + "from ipywidgets import interact, FloatSlider\n", + "\n", + "def plt_g(mu,variance):\n", + " plt.figure()\n", + " xs = np.arange(2, 8, 0.01)\n", + " ys = gaussian(xs, mu, variance)\n", + " plt.plot(xs, ys)\n", + " plt.ylim(0, 0.04)\n", + " plt.show()\n", + "\n", + "interact(plt_g, mu=FloatSlider(value=5, min=3, max=7),\n", + " variance=FloatSlider(value = .03, min=.01, max=1.));" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "d1e43f38", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(-1, 3, 0.01)\n", + "g1 = gaussian(x, mean=0.8, var=.1)\n", + "g2 = gaussian(x, mean=1.3, var=.2)\n", + "plt.plot(x, g1, x, g2)\n", + "\n", + "g = g1 * g2 # element-wise multiplication\n", + "g = g / sum(g) # normalize\n", + "plt.plot(x, g, ls='-.');" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "9fbd8d71", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(0, 4*np.pi, 0.01)\n", + "plt.plot(np.sin(1.2*x))\n", + "plt.plot(np.sin(1.2*x) * np.sin(2*x));" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "87362ed8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def normalize(p):\n", + " return p / sum(p)\n", + "\n", + "def update(likelihood, prior):\n", + " return normalize(likelihood * prior)\n", + "\n", + "prior = normalize(np.array([4, 2, 0, 7, 2, 12, 35, 20, 3, 2]))\n", + "likelihood = normalize(np.array([3, 4, 1, 4, 2, 38, 20, 18, 1, 16]))\n", + "posterior = update(likelihood, prior)\n", + "book_plots.bar_plot(posterior)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "df6d4a02", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mean: 5.88 var: 1.24\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xs = np.arange(0, 10, .01)\n", + "\n", + "def mean_var(p):\n", + " x = np.arange(len(p))\n", + " mean = np.sum(p * x,dtype=float)\n", + " var = np.sum((x - mean)**2 * p)\n", + " return mean, var\n", + "\n", + "mean, var = mean_var(posterior)\n", + "book_plots.bar_plot(posterior)\n", + "plt.plot(xs, gaussian(xs, mean, var, normed=False), c='r');\n", + "print('mean: %.2f' % mean, 'var: %.2f' % var)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5e931c63", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.13114657203397997\n", + "0.13114657203397995\n" + ] + } + ], + "source": [ + "from scipy.stats import norm\n", + "import filterpy.stats\n", + "print(norm(2, 3).pdf(1.5))\n", + "print(filterpy.stats.gaussian(x=1.5, mean=2, var=3*3))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "f13bc1e9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xs = np.arange(10, 100, 0.05)\n", + "ys = [gaussian(x, 90, 30) for x in xs]\n", + "plt.plot(xs, ys, label='var=0.2')\n", + "plt.xlim(0, 120)\n", + "plt.ylim(-0.02, 0.09);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f122fea3", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/04-One-Dimensional-Kalman-Filters.ipynb b/kalman_and_bayesian_filters/04-One-Dimensional-Kalman-Filters.ipynb new file mode 100644 index 0000000..e63cac3 --- /dev/null +++ b/kalman_and_bayesian_filters/04-One-Dimensional-Kalman-Filters.ipynb @@ -0,0 +1,911 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "da017204", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "#format the book\n", + "import book_format\n", + "book_format.set_style()\n", + "\n", + "import filterpy.stats as stats\n", + "stats.plot_gaussian_pdf(mean=10., variance=1., \n", + " xlim=(4, 16), ylim=(0, .5));" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "77975f25", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of readings is 9.959\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from numpy.random import randn\n", + "import matplotlib.pyplot as plt\n", + "\n", + "xs = range(500)\n", + "ys = randn(500)*1. + 10.\n", + "plt.plot(xs, ys)\n", + "print(f'Mean of readings is {np.mean(ys):.3f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "81445aa7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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2tTvQsBs3EBQUxKxZswy106dP06dPH9xgzUYRcUNq6kVECiONnMNuvLANu9E7q1vo2rUrXbp0MdSWLl3KokWLTEokIpI3ffSIiBTGt8BfdrXWQKAJWaRYWCwWZs+eTWCg8T9q3759OX78uEmpRERyp6ZeRKSg9gP/s6tVBSJMyCLFqlKlSsyePdtQ++uvvzQMR0Scjpp6EZGCyAC+sKt5AR3RO6qbevLJJ+natauhtnz5cpYuXWpSIhGRnPQRJCJSEOvIOdtNJFAxl2PFbcyaNYtKlSoZav379yc5OdmkRCIiRmrqRUTy6wSw3q5WBWhmQhZxqMDAQKZNm2aoHTt2jNdff92cQCIidtTUi4jkRxbw5ZWvV3kAj6N30hKie/fuREVFGWqzZ8/mp5/s5zUVEXE8fRSJiOTHNuCQXa0FEGxCFjGFxWJhzpw5+Pn5ZdesViu9e/cmIyPDxGQiImrqRURu7jyw2q5WDmjl+ChirmrVqjFy5EhDbceOHUydOtWkRCIiNmrqRURu5hvgkl3tMcDHhCxiutjYWBo0aGCovfHGG+zfv9+kRCIiaupFRG5sH7DTrnY3UNOELOIUvL29mTdvHhaLJbt28eJFXnrpJc1dLyKmUVMvIpKHCxcu2G6OvV4poK0ZacSZNG/enD59+hhqK1euZPHixSYlEpGSTk29iEge3nzzTThrV3wEKGNCGHE6Y8aMoXLlyobawIED+euvv0xKJCIlmZp6EZFc7Ny5k0mTJhmLVYHGpsQRJxQQEMCMGTMMtaSkJIYNG2ZSIhEpydTUi4jYsVqtvPTSS1y+fPla0QPbzbF615TrdO7cmccee8xQW7BgAZs3bzYpkYiUVPp4EhGx85///If16+2Wjr0fqGRKHHFiFouFWbNmUbp06eya1Wqlb9++ZGZmmphMREoai9UNbtVPSUkhICCA5ORk/P39zY4jIi4sJSWFOnXqkJiYeK1YDugLeJsUSpzfeuBbY2n+/Pk8//zzpsQREfeR3z5XV+pFRK4zatQoY0MPttlu1NDLjTQHAo2luLg4zpw5Y0ocESl5vMwOICKSG8soy80PKmongDl2tVpAHcdHERfjBbQDPrhWOn36NK+//jpz5ti/qEREip6u1IuIAFiBr698vcoT21V6E36/EBdUA7p06WIozZs3j4SEBJMCiUhJoqZeRATgF+CAXe0+oKLjo4jrmjJlCrfddlv246s3zWZlZZmYSkRKAjX1IiJpwCq7WgC2GW9ECqBq1aq8/vrrhtpPP/3Ee++9Z04gESkx1NSLiPwAnLOrRQE+JmQRlzdo0CBq1aplqA0bNkwrzYpIsVJTLyIl20lgo12tBvA3E7KIW/D19eXtt9821E6ePMmIESNMSiQiJYGaehEpuazACuD64c4e2GYx0c2xcgvatm1LdHS0oTZ79my2b99uSh4RcX9q6kWk5NoN/GlXu5cc842LFMbUqVMpVapU9uOsrCz69euHG6z5KCJOSE29iJRMGeS8OdYfaGlCFnFLYWFhxMXFGWo//vgjixcvNimRiLgzNfUiUjJtBM7a1dqgm2OlSL366qtUq1YtR+3ChQsmJRIRd6WmXkRKnhRgnV3tTqCeCVnErZUqVYrJkycbaocPH2bixIkmJRIRd6WmXkRKnnhsw2+up5VjpZhER0fz0EMPGWrjx4/n8OHDJiUSEXekpl5ESpYjwM92tXuAyiZkkRLBYrEwbdo0PDyufeRevHiRoUOHmphKRNyNmnoRKTmswEq7mi/wsAlZpERp0KABvXv3NtQ+/vhjNmzYYFIiEXE3hWrqZ82aRVhYGKVKlSIiIoLNmzfneeyCBQt44IEHKF++POXLlycyMjLH8VarlREjRlC5cmX8/PyIjIxk7969hYkmIpK3ndiu1F+vJVDGhCxS4vzrX/8iICDAUHv55ZfJysrK4xkiIvlX4KZ+8eLFxMbGMnLkSLZu3UrDhg2JiorixIkTuR6/Zs0aevTowffff8/GjRsJDQ2lTZs2HD16NPuYCRMm8PbbbzN37lx++uknSpcuTVRUFJcuXSr8TyYicr10YLVdrQIQYUIWKZFuv/123njjDUNty5YtvP/+++YEEhG3YrEWcBWMiIgImjZtysyZMwHbYhqhoaH079+fYcOG3fT5mZmZlC9fnpkzZxITE4PVaiUkJIRBgwYxePBgAJKTkwkKCuK9996je/fuOc6RlpZGWlpa9uOUlBRCQ0NJTk7G39+/ID+OiDgpy6givmv1O+AHu1oPoE7Rfhsp2awjb/yRmpGRQf369fn999+za8HBwezZs4eyZcsWdzwRcUEpKSkEBATctM8t0JX69PR0EhISiIyMvHYCDw8iIyPZuHFjvs5x4cIFMjIyqFChAgD79+8nMTHRcM6AgAAiIiLyPOfYsWMJCAjI3kJDQwvyY4hISXMWsB+6XB2o7fgoUrJ5e3szdepUQy0xMZExY8aYlEhE3EWBmvpTp06RmZlJUFCQoR4UFERiYmK+zjF06FBCQkKym/irzyvIOePi4khOTs7eNC2YiNzQauDydY8taApLMU27du1o166doTZlyhT+/PNPkxKJiDtw6Ow348aNY9GiRSxdupRSpUoV+jy+vr74+/sbNhGRXB0EdtnVmgKVTMgicsWUKVPw8vLKfpyens6QIUNMTCQirq5ATX1gYCCenp4kJSUZ6klJSQQHB9/wuZMmTWLcuHGsWrWKBg0aZNevPq8w5xQRuaEs4Bu7WingQcdHEble3bp16devn6G2ZMkSfvjB/sYPEZH8KVBT7+PjQ3h4OPHx8dm1rKws4uPjadGiRZ7PmzBhAm+++SYrV66kSZMmhn3VqlUjODjYcM6UlBR++umnG55TROSmfgGO2dUeAm4zIYuInREjRlCxYkVDbdCgQZriUkQKpcDDb2JjY1mwYAELFy5k9+7d9OnTh9TUVHr27AlATEwMcXFx2cePHz+e4cOH88477xAWFkZiYiKJiYmcP38esK20N3DgQEaPHs3nn3/Ozp07iYmJISQkhOjo6KL5KUWk5MkA4u1qFYEmuRwrYoLy5cvnOsXlxx9/bE4gEXFpBW7qu3XrxqRJkxgxYgSNGjVi+/btrFy5MvtG10OHDnH8+PHs4+fMmUN6ejpPPPEElStXzt4mTZqUfcyrr75K//796d27N02bNuX8+fOsXLnylsbdi0gJtwlItqs9AniakEUkDy+88AJ16hjnVY2Li+PixYsmJRIRV1XgeeqdUX7n7xQR13FL89SfB97GtuDUVWHAM2jGGylWN5unPjeff/45HTt2NNTeeustXnvttaKKJSIurFjmqRcRcQlrMDb0AG1QQy9O6fHHH+fBBx801MaOHZtjAgkRkRtRUy8i7uUkkGBXawCEmJBFJB8sFguTJ0/GYrn2W+f58+cZOXKkialExNWoqRcR97IauH4EhBfQ2qQsIvl0zz33EBMTY6gtWLCAXbvsF1kQEcmdmnoRcR9/Anvsai2AABOyiBTQW2+9hZ+fX/bjrKwsLUglIvmmpl5E3EMWsMquVhq434QsIoVQpUoVBg8ebKitWLGCVavsX9giIjmpqRcR9/AzkGhXewjwNSGLSCG9+uqrOVZTHzx4MJmZmSYlEhFXoaZeRFxfOvCdXe12oLEJWURuQZkyZRg9erShtnPnTt59912TEomIq1BTLyKubyNwzq7WBi00JS7p2WefpUGDBoba8OHDs1diFxHJjZp6EXFt54D1drXqQE0TsogUAU9PT8Oq6wCJiYlMmDDBpEQi4grU1IuIa/seyLCraaEpcXGPPPII7dq1M9QmTZrEkSNHTEokIs5OTb2IuK4kYJtdrTEQnMuxIi5m4sSJeHhc+5i+ePEi//znP01MJCLOTE29iLiuVRgXmvLGNuONiBuoV68ezz//vKH2/vvvs3XrVpMSiYgzU1MvIq5pH/CHXe0+wN+ELCLFZNSoUZQtWzb7sdVqZdCgQVit1hs8S0RKIjX1IuJ6cltoqixwrwlZRIpRUFAQcXFxhtqaNWv44osvTEokIs5KTb2IuJ5twAm72sOAjwlZRIrZwIEDqVq1qqE2ZMgQMjLs7xAXkZJMTb2IuJY0ci40FQQ0NCGLiAP4+fkxZswYQ23Pnj3MmzfPpEQi4ozU1IuIa/kRSLWrtUHvZuLWevToQZMmTQy1N954g7Nnz5oTSEScjj4GRcR1JAMb7Gq1gBomZBFxIA8PD6ZMmWKonT59OscVfBEpudTUi4jr+A64fN1jC/CISVlEHOyBBx6gc+fOhtr06dPZv3+/SYlExJmoqRcR13Ac+NmuFg5UMiGLiEnGjx+Pt7d39uP09HSGDRtmYiIRcRZq6kXE+VmBb+xqPsCDjo8iYqaaNWvSt29fQ+2TTz5h06ZNJiUSEWehpl5EnN8e4IBd7X6gjOOjiJht+PDhlC9f3lCLjY3VglQiJZyX2QFExHlYRlnMjpBTJrDaruYPtDAhi4gTqFChAsOHDyc2Nja7tnHjRv773//yxBNPmJhMRMykK/Ui4twSgFN2tdaAdy7HipQQffv2pUYN47RPQ4cOJS0tzaREImI2NfUi4rwuAWvsapWB+o6PIuJMfHx8GDdunKH2559/MmvWLJMSiYjZ1NSLiPNaD1ywq0Whdy4RoEuXLtx3332G2ptvvsmZM2dMSiQiZtJHo4g4p7PARrtaHSDM4UlEnJLFYmHy5MmG2tmzZ3nzzTdNSiQiZlJTLyLOKR7bTbJXeaCFpkTsRERE0K1bN0Nt1qxZ7Nu3z6REImIWNfUi4nyOADvtak2AQBOyiDi5sWPH4uPjk/04IyNDC1KJlEBq6kXEuViBVXY1X6CVCVlEXEC1atV4+eWXDbX//ve/rF+/3qREImIGNfUi4lx+Aw7Z1VoCpU3IIuIiXnvtNSpWrGioDRo0iKysLJMSiYijqakXEedxmZwLTZUDmjk+iogrKVeuHCNHjjTUNm/ezCeffGJSIhFxNDX1IuI8/gfYz8YXiRaaEsmHF198kVq1ahlqw4YN49KlSyYlEhFHUlMvIs7hArDWrnYHUM+ELCIuyNvbmwkTJhhqBw8e5O233zYpkYg4kpp6EXEOa7GtIHu9NoDFhCwiLqpjx460bNnSUHvrrbc4deqUSYlExFG8zA4gIsIpbENvrlcPqGpCFpFbYBnlBL+F1gF+uPYwJSWFUaNGMWPGDNMiiUjx05V6ETHfKuD6STo8sY2lF5GCqwLUN5bmzp3L77//bkocEXEMNfUiYq4/gT12tRZAeROyiLiL1lCqVKnsh5cvX2bo0KEmBhKR4qamXkTMkwV8Y1crDdxvQhYRd1IOXnnlFUNp+fLlrF1rfze6iLgLNfUiYp7tQJJd7SGgVM5DRaRghg0bxu23326oxcbGakEqETelpl5EzJEGxNvVKgGNTcgi4ob8/f0ZNWqUobZ161Y++ugjkxKJSHEqVFM/a9YswsLCKFWqFBEREWzevDnPY3ft2kWXLl0ICwvDYrEwbdq0HMe88cYbWCwWw1a3bt3CRBMRV7EeSLWrRWG7SVZEisTzzz+f4/P0tdde4+LFiyYlEpHiUuCmfvHixcTGxjJy5Ei2bt1Kw4YNiYqK4sSJE7kef+HCBapXr864ceMIDg7O87z16tXj+PHj2dv69esLGk1EXMVZYKNdrRZQw/FRRNyZl5cXEydONNQOHz7M1KlTTUokIsWlwE39lClTeP755+nZsyd33XUXc+fO5bbbbuOdd97J9fimTZsyceJEunfvjq+vb57n9fLyIjg4OHsLDAzM89i0tDRSUlIMm4i4kHjg8nWPLdgWmhKRIte+fXsefvhhQ23s2LEkJdnf0CIirqxATX16ejoJCQlERl6bQNrDw4PIyEg2brS/7FYwe/fuJSQkhOrVq/PUU09x6NChPI8dO3YsAQEB2VtoaOgtfW8RcaAjwE67WlPg9lyOFZFbZrFYmDRpEhbLtYWxzp8/z8iRI01MJSJFrUBN/alTp8jMzCQoKMhQDwoKIjExsdAhIiIieO+991i5ciVz5sxh//79PPDAA5w7dy7X4+Pi4khOTs7eDh8+XOjvLSIOZAVW2tV8gVYmZBEpQRo3bkxMTIyhtmDBAn755ReTEolIUXOK2W/atWvHk08+SYMGDYiKiuLrr7/m7NmzfPLJJ7ke7+vri7+/v2ETERewC9uV+uu1wjY3vYgUq7feegs/P7/sx1lZWbzyyitYrVYTU4lIUSlQUx8YGIinp2eOcXhJSUk3vAm2oMqVK0ft2rXZt29fkZ1TREyWAay2q5UHmpmQRaQEqlKlCq+++qqh9u233/LVV1+ZlEhEilKBmnofHx/Cw8OJj782uXRWVhbx8fG0aNGiyEKdP3+eP/74g8qVKxfZOUXEZJuAZLtaG8DLhCwiJdSQIUOoUqWKoTZo0CDS09NNSiQiRaXAw29iY2NZsGABCxcuZPfu3fTp04fU1FR69uwJQExMDHFxcdnHp6ens337drZv3056ejpHjx5l+/bthqvwgwcPZu3atRw4cIANGzbQqVMnPD096dGjRxH8iCJiuvPAOrvanYCWoxBxqNKlSzNu3DhDbc+ePcyePdukRCJSVArc1Hfr1o1JkyYxYsQIGjVqxPbt21m5cmX2zbOHDh3i+PHj2ccfO3aMxo0b07hxY44fP86kSZNo3Lgxzz33XPYxR44coUePHtSpU4euXbtSsWJFNm3alGN5axFxUd8D9hcCo7BNZSkiDvX3v/+dZs2M495GjRrF6dOnTUokIkXBYnWDO2RSUlIICAggOTlZN82K3ALLqGLospOAudhmvrmqIdCp6L+ViFxjHZn3x/uGDRu47777DLV+/foxY8aM4o4lIgWU3z7XKWa/ERE3ZQW+wdjQewOtzYkjIjb33nsv3bt3N9TmzJnDr7/+alIiEblVaupFpPjsBf60q90H6A9qIqYbN24cpUqVyn6cmZnJoEGDTEwkIrdCTb2IFI9MYJVdrSxwrwlZRCSHO++8k8GDBxtqK1euZMWKFSYlEpFboaZeRIrHFuCUXa014GNCFhHJ1dChQ3NMHz1o0CAyMjJMSiQihaWmXkSK3kVgjV2tMtDA8VFEJG9lypRhzJgxhtru3buZO3euSYlEpLDU1ItI0VuDrbG/Xlv0jiPihGJiYrjnnnsMtZEjR2qKSxEXo49YESlaJ4DNdrW/YVtsSkScjoeHB9OmTTPU/vrrL4YPH25OIBEpFDX1IlJ0rMAKjFNYegJtzIkjIvnzwAMP0K1bN0Nt3rx5/PzzzyYlEpGCUlMvIkXnN2C/Xe0+oLwJWUSkQCZOnIifn1/246ysLAYMGIAbrFEpUiKoqReRopGBbaGp6/kD95uQRUQKLDQ0lLi4OEPthx9+4JNPPjEpkYgUhJp6ESkaG4CzdrVH0BSWIi5k8ODBhIWF5ailpqaaE0hE8k1NvYjcumRgvV2tKnC3CVlEpND8/PyYPHmyoXbkyBHGjx9vUiIRyS819SJy61ZjG35zlQVod+WriLiUTp060bp1a0NtwoQJ7N9vf8OMiDgTNfUicmsOAL/Y1cKxLTYlIi7HYrEwffp0PD09s2tpaWkMGjTIxFQicjNq6kWk8LKwTWF5vVLAQyZkEZEiU69ePfr27WuoLV26lG+//dakRCJyM2rqRaTwEoAku9rDQGkTsohIkXrjjTcIDAw01F5++WUyMjLyeIaImElNvYgUzgXgO7taJWxDb0TE5ZUvX5633nrLUPv111+ZPXu2SYlE5EbU1ItI4XwHXLSrtcO2gqyIuIVevXrRuHFjQ23EiBEkJiaalEhE8qKmXkQK7iiwxa52F1DNhCwiUmw8PT2ZMWOGoZaSksKQIUNMSiQieVFTLyIFkwV8ZVfzBqJMyCIixe6+++4jJibGUPvwww9Zu3atSYlEJDdq6kWkYBKAY3a1VkCACVlExCEmTJhAQIDxf/K+ffvqplkRJ6KmXkTyLxWIt6sFAs1NyCIiDhMUFMTo0aMNtV27djF9+nSTEomIPTX1IpJ/q4FLdrX2gJcJWUTEofr06ZPjptk33niDI0eOmJRIRK6npl5E8ucQsN2udje6OVakhPD09MwxnWVqaiqxsbEmJRKR66mpF5GbyyTnzbE+6OZYkRKmefPmPPfcc4bap59+yqpVq0xKJCJXqakXkZv7HzlXjn0IKGtCFhEx1dixY6lQoYKh1q9fP9LS0kxKJCKgpl5EbuYcua8c28yELCJiusDAQMaNG2eo7d27l0mTJpmUSERATb2I3MwqIN2u1h6tHCtSgvXq1YuIiAhD7a233uLAgQPmBBIRNfUicgN/Ajvtag2BO03IIiJOw8PDg9mzZ+Phca2NuHjxIv3798dqtZqYTKTkUlMvIrnLAL60q5UCHjEhi4g4nXvuuYc+ffoYal9++SX//e9/TUokUrKpqReR3P0AnLGrtQbKmJBFRJzS6NGjCQoKMtQGDBjA2bNnzQkkUoKpqReRnJKAH+1qdwDhJmQREadVrly5HKvKHj9+nLi4OJMSiZRcaupFxCgL+OLK16s8gMfRO4aI5NC1a1ceffRRQ23u3Ln8+KP9lQERKU76iBYRowTAftX3+4CgXI4VkRLPYrEwa9YsbrvtNkO9d+/epKfbT50lIsVFTb2IXJMCfGtXqwC0NCGLiLiMsLAw3nzzTUPt119/ZcKECSYlEil51NSLyDUrAPtFIR8DvE3IIiIuZcCAAdxzzz2G2ujRo9mzZ49JiURKFjX1IgLA559/Drvtig2B6makERFX4+Xlxfz58w1z16elpfHiiy9q7noRB/AyO4BISWcZZTE7gu3q/Cy7mh/QxoQsIuKywsPDefnll5k6dWp27fvvv2fhwoU8++yz5gUTKQF0pV5E4Dts4+mv1xYobUIWEXFp//rXv6hataqhNmjQIE6cOGFSIpGSQU29SEl3GPjJrlYNaGBCFhFxeWXKlGH27NmG2pkzZ3j55ZdNSiRSMqipFynJMoDldjUvbDfHOsGoIBFxTe3bt6dr166G2qJFi1i2bJk5gURKgEI19bNmzSIsLIxSpUoRERHB5s2b8zx2165ddOnShbCwMCwWC9OmTbvlc4pIEVkDnLKrtQIqOj6KiLiX6dOnU65cOUPtxRdf5MyZM+YEEnFzBW7qFy9eTGxsLCNHjmTr1q00bNiQqKioPMfKXbhwgerVqzNu3DiCg4OL5JwiUgSOABvsapWBe03IIiJuJzg4mOnTpxtqSUlJGoYjUkws1gLOMxUREUHTpk2ZOXMmAFlZWYSGhtK/f3+GDRt2w+eGhYUxcOBABg4ceEvnTEtLIy3t2mTaKSkphIaGkpycjL+/f0F+HBHTmTL7TQYwHzh5Xc0DeAGtHCsiRccKfATsNZaXL19Ohw4dzEgk4nJSUlIICAi4aZ9boCv16enpJCQkEBkZee0EHh5ERkaycePGQgUtzDnHjh1LQEBA9hYaGlqo7y1SYq3F2NADPIgaehEpWhbgcQgICDCUX3jhBQ3DESliBWrqT506RWZmJkFBxk/+oKAgEhMTCxWgMOeMi4sjOTk5ezt8+HChvrdIiXQU+NGuVhm4z4QsIuL+/MlxP11iYiKvvPKKOXlE3JRLzn7j6+uLv7+/YRORfLgMLMP2J/GrPICOgKcZgUSkJHjmmWdo166dofb+++/z1VdfmZRIxP0UqKkPDAzE09OTpKQkQz0pKSnPm2DNOKeI5OEHcg67aQXofzURKUYWi4X58+fnuAjXu3dvzp49a04oETdToKbex8eH8PBw4uPjs2tZWVnEx8fTokWLQgUojnOKSC6OAevsasHA/SZkEZES54477mDq1KmG2rFjx4iNjTUpkYh7KfDwm9jYWBYsWMDChQvZvXs3ffr0ITU1lZ49ewIQExNDXFxc9vHp6els376d7du3k56eztGjR9m+fTv79u3L9zlF5BblNewmGg27ERGH6dmzJ1FRUYbau+++y9dff21SIhH34VXQJ3Tr1o2TJ08yYsQIEhMTadSoEStXrsy+0fXQoUN4eFz7XeHYsWM0btw4+/GkSZOYNGkSrVq1Ys2aNfk6p4jcou8B+2UfHkDDbkTEoa4Ow7n77rs5d+5cdr1Xr17s3LmTwMBAE9OJuLYCz1PvjPI7f6eIMyr2eer3AwvtakHA8xTi13oRkYKzjjS2GgsWLKB3796GWnR0NEuWLMFiMWHtDhEnVizz1IuIi7kILLWreQKdUEMvIqZ57rnncsyGs2zZMt59912TEom4PjX1Iu7sayDFrtYaDbsREVNZLBbeeeedHMNtBgwYwB9//GFSKhHXpqZexF3tvLJdLwxo7vgoIiL2goODWbBggaGWmprK008/zeXLl01KJeK61NSLuKOzwJd2NV9sw270f72IOIno6Giee+45Q23jxo2MHTvWpEQirksf7yLuJgvb9JVpdvXHgACHpxERuaGpU6dSo0YNQ23UqFFs3rzZpEQirklNvYi72QgcsKvVv7KJiDiZMmXK8OGHH+LpeW3RjMzMTJ566inOnz9vYjIR16KmXsSdJALxdrUA4FETsoiI5FPz5s355z//aajt27ePQYMGmZRIxPWoqRdxFxnAf7ENv7leJ8DP8XFERAri9ddfJyIiwlCbP38+y5cvNymRiGtRUy/iLlYAJ+1q92Gb8UZExMl5e3vzwQcfULp0aUO9Z8+eHDx40KRUIq5DTb2IO9gBbLWrBQMPmZBFRKSQatWqxbRp0wy1v/76i+7du5ORkWFOKBEXoaZexNWdAr6wq3kDXdCqsSLicnr16sUTTzxhqG3atInXXnvNpEQirkFNvYgrywA+ufL1eo8Dtzs+jojIrbJYLPy///f/qF69uqE+adIkvvjC/gqGiFylpl7Ela0ATtjV7gEamJBFRKSIBAQE8Mknn+Dj42OoP/PMMxw6dMikVCLOTU29iKvKbRx9JaCdCVlERIpYeHg4U6ZMMdT++usvunXrpvH1IrlQUy/iivIaR//kla8iIm7gpZde0vh6kXxSUy/iajKAT9E4ehFxezcaX//ll1+alErEOampF3E1K4Eku5rG0YuIm9L4epH8UVMv4kq2Agl2NY2jFxE3l9v4+jNnztC5c2cuXrxoUioR56KmXsRVHAa+sqtpHL2IlBC5ja9PSEjgxRdfxGq1mpRKxHmoqRdxBSnAYiDTrq5x9CJSQlwdX1+rVi1D/f333+ftt982KZWI81BTL+LsLmNbYOq8Xb0FGkcvIiVKQEAAy5Yto0yZMob6oEGD+O6770xKJeIc1NSLODMrtiE3R+zq1YFIx8cRETHbXXfdxQcffGCoZWZm0rVrVw4cOGBOKBEnoKZexJltAbbZ1coBTwCeDk8jIuIUoqOjGTlypKF2+vRpoqOjuXDhgkmpRMylpl7EWR0EVtjVvIHuwG2OjyMi4kxGjBhBhw4dDLWff/6Zf/zjH7pxVkokNfUizigZ2zj6LLt6NBDs8DQiIk7Hw8ODDz74gLp16xrqixcvZuLEiSalEjGPmnoRZ5MOLAJS7er3A/UcH0dExFn5+/uzfPly/P39DfVhw4bx9ddfm5RKxBxq6kWcSRbwGXDcrl4TeNjxcUREnF3t2rX56KOPsFgs2TWr1UrXrl3Zts3+piQR96WmXsRZWIGVwB67egWgC/q/VUQkD+3bt2f06NGGWmpqKu3bt+fQoUMmpRJxLLUJIs5iE7DZrlYK6AH4OT6OiIgriYuL4+9//7uhdvz4cdq3b09ycrJJqUQcR029iDP4FfjGruaJbaYbrRgrInJTFouFd955h1atWhnqv/zyC126dCE9Pd2kZCKOoaZexGyHgSW51DsCYY6NIiLiynx9fVm6dGmOGXHi4+Pp3bu3proUt6amXsRE+/btg4+By3Y7HgYamBBIRMTFlS9fnq+//ppKlSoZ6gsXLuRf//qXSalEip+aehGTnD59mkcffRTsFz+8B3jAjEQiIu6hWrVqfPnll9x2m3GlvjfeeIOFCxealEqkeKmpFzFBamoqHTp0YO/evcYdNYD2gCW3Z4mISH41bdqUjz/+GA8PY6vz3HPPsWrVKpNSiRQfNfUiDpaWlkanTp3YsGGDcUcQ0BXbDbIiInLLOnTowPTp0w21y5cvEx0dzfr1601KJVI81NSLONDly5fp3r07q1evNu7wB54CfM1IJSLivvr160dsbKyhdvHiRdq3b09CQoJJqUSKnpp6EQfJysqiZ8+eLFu2zLjDD1tD75/Lk0RE5JZNnDgxxxz2KSkpREVFsWvXLpNSiRQtL7MDiJQEVquVvn378uGHHxrqZcuW5Vz3c7ahNyIibsoyygluFKoB1AF+v1Y6ffo0jzzyCOvWraNGjRpmJRMpErpSL1LMrFYrr776KnPnzjXU/fz8+PLLL6GKScFEREoST+AJaN26taF8/PhxWrduzZEjR8zJJVJE1NSLFLPRo0czadIkQ83b25slS5bQsmVLk1KJiJRA3rB8+XLuvfdeQ/ngwYNERkZy4sQJk4KJ3Do19SLFaOrUqYwYMcJQ8/Dw4OOPP6Zt27YmpRIRKblKly7NV199RePGjQ3133//nTZt2nDmzBmTkoncGou1EGsmz5o1i4kTJ5KYmEjDhg2ZMWMGzZo1y/P4Tz/9lOHDh3PgwAFq1arF+PHjbYvuXPHss8/mWAwiKiqKlStX5itPSkoKAQEBJCcn4++vuw3l5hwyvnM98G0u9WigUfF/exERyck60tb2nDx5kpYtW/Lbb78Z9jdo0IDVq1fnWJFWxCz57XMLfKV+8eLFxMbGMnLkSLZu3UrDhg2JiorK809WGzZsoEePHvTq1Ytt27YRHR1NdHQ0v/zyi+G4tm3bcvz48ezt448/Lmg0EedgBdaQe0P/KGroRUScwO233863335LtWrVDPUdO3bQqlUrjh07ZlIykcIp8JX6iIgImjZtysyZMwHbNH2hoaH079+fYcOG5Ti+W7dupKam2m4IvKJ58+Y0atQo+8bBZ599lrNnz+ac6i8PaWlppKWlZT9OSUkhNDRUV+ol34rtSr0VWzP/Yy77IoH7i+fbiohI/ly9Un/V/v37admyZY4bZWvUqEF8fDx33nmnI+OJ5FAsV+rT09NJSEggMjLy2gk8PIiMjGTjxo25Pmfjxo2G48E2tMb++DVr1lCpUiXq1KlDnz59OH36dJ45xo4dS0BAQPYWGhpakB9DpHhkASvIvaGPQg29iIgTqlatGj/88ANhYWGG+h9//EHLli35448/zAkmUkAFaupPnTpFZmYmQUHGSbWDgoJITEzM9TmJiYk3Pb5t27a8//77xMfHM378eNauXUu7du3IzMzM9ZxxcXEkJydnb4cPHy7IjyFS9LKAL4HNuexrD7RwbBwREcm/atWqsW7dOmrXrm2oHzp0iAceeIDdu3eblEwk/5xi8anu3btn/7t+/fo0aNCAGjVqsGbNmhzzyQL4+vri6+vryIgiecsElgM77OoWoCMaQy8i4gLuuOMO1q5dS2RkpGGV2ePHj9OqVStWr15Nw4YNTUwocmMFulIfGBiIp6cnSUlJhnpSUhLBwcG5Pic4OLhAxwNUr16dwMBA9u3bV5B4Io6XAXxK7g19F9TQi4i4kODgYNasWZNjusuTJ0/y0EMP8eOPuY2vFHEOBWrqfXx8CA8PJz4+PruWlZVFfHw8LVrkPr6gRYsWhuMBVq9enefxAEeOHOH06dNUrly5IPFEHCsVWAj8Zlf3BLoBdzs8kYiI3KLAwEC+++47mjdvbqj/9ddftG7dms8++8ykZCI3VuApLWNjY1mwYAELFy5k9+7d9OnTh9TUVHr27AlATEwMcXFx2ce//PLLrFy5ksmTJ/Pbb7/xxhtvsGXLFvr16wfA+fPnGTJkCJs2beLAgQPEx8fTsWNHatasSVRUVBH9mCJF7DTwb8B+VXEvoDtQ1+GJRESkiJQrV45Vq1blWPU7LS2Nrl27MmXKFAqxzI9IsSpwU9+tWzcmTZrEiBEjaNSoEdu3b2flypXZN8MeOnSI48ePZx9/77338tFHHzF//nwaNmzIZ599xrJly7j7bttlTE9PT3bs2EGHDh2oXbs2vXr1Ijw8nHXr1mncvDinw8D/A+wXHfQFngJqOTyRiIgUsbJly7JixQrDYpkAVquVQYMGMWDAgDwn9BAxQ6FWlHU2WlFWCqrQ89T/CiwBLtvV/YH/A7QAoYiIU7Ofp/5mLl++TL9+/Zg3b16OfR07duSjjz7itttuK6p4IjkU24qyIiXWRuATcjb0wcBzqKEXEXFDXl5ezJkzh3HjxuXYt3z5ch566CFOnDhhQjIRIzX1IjdzGfgK+CaXfTWBntiu1IuIiFuyWCwMHTqUjz76CB8fH8O+zZs307x5c3bssJ8GTcSx1NSL3EgKthlu/pfLvnuAHtjG0ouIiNvr0aMHq1evply5cob6/v37ad68OR999JE5wURQUy+St4PAfGw3xtprDTyObfpKEREpMVq2bMmGDRsICwsz1C9evMhTTz3FwIEDycjIMCeclGhq6kXsWYGfsF2hP2+3zwvoDDyAbYEpEREpcf72t7+xadMmIiIicuybPn06rVu3JjEx0YRkUpKpqRe5Xjq22W1WAFl2+8oBvYAGDs4kIiJOJygoiLVr1/LCCy/k2Ldu3TrCw8PZsGGDCcmkpFJTL3LVGWwLSu3MZV8NoDegRY5FROQKX19f5s6dyzvvvJNjbZ1jx47x4IMPMmvWLC1UJQ6hpl7ECmwD5gJJuexviW1RKU1DLCIiuejZsyc//vgjVatWNdQzMjLo168fnTp14uTJkyalk5JCTb2UbBewzT2/HNvQm+v5At2Bh9H/KSIickPh4eEkJCQQGRmZY9/y5cupX78+K1asMCGZlBRqVaTk2gfMBnbnsu924HmgrkMTiYiICwsMDGTlypXExcXl2JeUlMSjjz5Kv379uHDhggnpxN2pqZcS5+LFi7YbYT8k5+w2YJt//jkg0KGxRETEDXh6ejJmzBi+/PJLKlXKudT4rFmzaNKkCdu2bTMhnbgzi9UN7t5ISUkhICCA5ORk/P21tKfkbevWrcTExLBr166cO/2ADsDfHJ1KRETc0nlswzv35tzl7e3NqFGjGDx4MN7e3o5OJi4kv32urtRLiXD+/HliY2Np2rRp7g19TeAl1NCLiEjRKQP8HWiPbZ2T62RkZPDaa6/RtGlTNm/ebEI4cTdq6sXtffHFF9x1111MnTqVrCy7yee9gHbYZrcpa0I4ERFxbxagKfACuU6L/PPPP9O8eXP69+9PSkqKg8OJO9HwG3EYyygHL8Gagm3sfG43wgIEY1sdNueQRxERkaJ3GVgDrM99d0hICDNmzKBTp05YLFq2XGw0/EZKrixgMzCT3Bt6T+AhbDfDqqEXERFH8QIigV5w991359h97NgxunTpQseOHTl06JDD44lrU1Mv7uUPYB7wNTnnnQeoBvQBWpFjfKOIiIhDhNombhg3bhx+fn45dn/xxRfUrVuX4cOHc+7cORMCiitSUy/uIQnbFJUfkPuqsH5ANBCDpqoUERHTeXt7M3ToUH755RfatGmTY//FixcZPXo0NWvWZN68eVy+fNmElOJK1NSLazsHfA7MxbaYVG4aAf2ufNUQRRERcSLVq1dn5cqVfPzxx7nOa3/ixAlefPFFGjRowFdffYUb3AopxURNvbimNGw3G70NbAVye4+rBDyD7Qp9aUcFExERKRiLxUL37t357bff6NOnD56enjmO2b17N4899hiRkZEkJCSYkFKcnZp6cS0XsTXzU698zcjlmDLYFpF6EdsYehERERdQvnx5Zs+ezY4dO3jsscdyPea7776jSZMmPPbYY2zatMnBCcWZqakX15AKxAPTsDXzl3I5xht4EOgP3INe3SIi4pLuuusuvvjiC+Lj42ncuHGux3z11Ve0aNGCRx55hB9++MHBCcUZqe0R53YeWIWtmV+HbdiNPQu2Jn4Atqbe10HZREREitHDDz/Mli1beP/997njjjtyPebbb7+lVatWtGzZktWrV2vMfQmmpl6cUyK2G2CnARvIfZgNQB1sw2w6oBVhRUTE7Xh4ePD000+zZ88exo8fT2Bg7lO4rVu3jjZt2tC0aVMWLlzIpUu5/Ulb3JlWlBWHuemKspnAb9gWjjp4k5PVAx7AtiqsiIiIi7GOLFz7lZqayrx585g4cSKJiYl5Hnf77bfTu3dvXnzxxTyv8otryG+fq6ZeHCbPpj4VSAC2ACk3OgFQH1szf3sRhxMREXGgwjb1V128eJF///vfjB8/niNHjuR5nKenJ507d6Z///7cf//9WCya29nVqKkXp2No6jOxzSv/M/D7lcd58QAaAvcDFYsvn4iIiMu5jO2zdB1w9ibH3o7t87QBcF27dKu/YEjxym+f6+XATCJwHNubz05sV+hvpAwQDjRB4+VFRERy44Xts7Ixtotkm4H9eRx7EvgW22xy1bEtylin+COKY6ipl2J38OBBPvvsM5gDJOXjCXcAzYC70CtUREQkPzyAv13ZTmBr7n8m94kmrMAfVzZfeC7pOXr06EHLli3x9vZ2VGIpYhp+I8Vi9+7dLFmyhCVLlrB169abP8ETuBtbM1+lmMOJiIiUBBeB7dga/L9ufniFChXo0KEDnTt35pFHHqFUqVLFm0/yRWPqxaGysrJISEhg2bJlLFmyhN9++y1/T7wD2/i+uwG/YgwoIiJSUmUBh7Bdud8FpN/8KWXKlOHRRx+lU6dOtG3blnLlyhVrRMmbmnopdkePHmXVqlWsWrWK1atXc/r06fw90R9bI98QyH26XRERESkO6dimj94O/Jm/p3h4eBAREUGbNm2IioqiadOmeHlpfKyjqKmXInf27Fk2bNjAt99+y6pVq9i1a1e+n1uxYkVOh5623XEfhpY9ExERMVsKsAOanG3Cli1b8v20gIAAWrduTZs2bXjwwQepXbu2psosRmrq5ZYdPnyY9evXZ287d+4s0PLTVapUoVOnTnTu3JkHHngA77d0842IiIizsY60cvDgwewhtOvWrSvQ531gYCD3339/9ta4cWN8fHyKMXHJoqZeCiQ5OZmtW7eSkJBAQkICGzZs4NChQwU+T+3atYmOjqZz5840bdoUD49rl+RvuqKsiIiIOJz9PPVJSUl8/vnnLFmyhO+//560tLQCnc/Pz49mzZrRtGlTwsPDCQ8Pp0aNGoaeQPJPTb3kymq1kpiYyK5du9i2bVt2E79v375Cna9cuXK0bt2aqKgoHnnkEcLCwvI8Vk29iIiI87nR4lMXL15k3bp1fPPNN6xatYpffvmlUN8jICCAxo0b06RJE8LDw7n77rupXbu2rujng5r6Eu5q875792527dpl2P76Kx/zWuXBx8eHZs2aERkZSVRUFE2aNMn3zTJq6kVERJxPQVaUPXbsWPYkGWvWrOH48eOF/r5eXl7UqlWLevXqGbbq1atrOs3rqKkvATIyMjh27Bj79+9n37597N27l3379mVvFy5cuPVvUgqoet1WGdDQeBEREbdRkKbe8DyrlQMHDhjuv/v1119vOY/FYiE0NJSaNWtSs2ZNatWqRc2aNalRowZ33nlnier1QE29qYrkinQmcB44d+VrCpBst53DtipcUfEAgrA17iHYmvhANFONiIiIGytsU5+b06dPs2HDBjZv3pw9xPfEiRNFdn6wDeWpWrVqjq1y5crZm7+/v9vMyFMim3qGYbuy7IwuA2nYVne7AKRe+Xr9v1O51sQXwUX2G/IGbsfWwF9t4isBmnZWRESkRCnKpj7Hua1Wjh49mt3gJyQksGPHDo4cOVJs3xNsN+tebfCDg4OpWLGiYatQoYLhcfny5Z127n019UUhE8jIY0sHLmFr1C9dt+X1+HIR5ioIL2xX2ytd2W6/8jUAXYEXERGRYm3q85KcnMyvv/6afb/fL7/8wq5du25pjP6tCggIMDT95cuXp2zZspQtW5YyZcrk+HdeNU9PzyLNld+mvlC/ksyaNYuJEyeSmJhIw4YNmTFjBs2aNcvz+E8//ZThw4dz4MABatWqxfjx43n00Uez91utVkaOHMmCBQs4e/Ys9913H3PmzKFWrVoFC7YNW6N6GVtDnpnPf9s361f/nVWwb28ab6BCHltZ1LyLiIiIUwkICKBFixa0aNHCUD937hx//PFHjvsE9+7dW+wNf3JyMsnJyfz5Zz6X2s2Dr68vfn5+lCpVyrDdrObj44O3t3eOLTMzM1/ft8BX6hcvXkxMTAxz584lIiKCadOm8emnn/L7779TqVKlHMdv2LCBli1bMnbsWB577DE++ugjxo8fz9atW7n77rsBGD9+PGPHjmXhwoVUq1aN4cOHs3PnTn799dd83f2cfaXeHXkAZbA15wF2W7krX/0A9xg2JiIiIg5mxpX6wrh06RJHjhzh0KFDHDp0iIMHD2Z/PXr0KMePHyc5OdnsmMWmyIffRERE0LRpU2bOnAlAVlYWoaGh9O/fn2HDhuU4vlu3bqSmpvLll19m15o3b06jRo2YO3cuVquVkJAQBg0axODBg7NDBwUF8d5779G9e/cc50xLSzMshJCcnEzVqlUL8mOYywsoja0Zv+3KdvXfZa7sK3vdMWrYRUREpJgkxzlPIxww9hYv0mZguzcx9crXq/cpXryyXbry+NKVxxm39u0c6ezZsze+iG0tgLS0NKunp6d16dKlhnpMTIy1Q4cOuT4nNDTUOnXqVENtxIgR1gYNGlitVqv1jz/+sALWbdu2GY5p2bKldcCAAbmec+TIkVZs875o06ZNmzZt2rRp0+b22+HDh2/YpxdoTP2pU6fIzMwkKCjIUA8KCuK3337L9TmJiYm5Hp+YmJi9/2otr2PsxcXFERsbm/04KyuLM2fOULFiRbeZvqgopKSkEBoayuHDh51iqk9xbnq9SH7ptSIFodeL5JdeK7mzWq2cO3eOkJCQGx7nnHP33ISvry++vr6GWrly5cwJ4wL8/f31P4fkm14vkl96rUhB6PUi+aXXSk75uXe0QPOiBAYG4unpSVJSkqGelJREcHBwrs8JDg6+4fFXvxbknCIiIiIick2BmnofHx/Cw8OJj4/PrmVlZREfH59jSqKrWrRoYTgeYPXq1dnHV6tWjeDgYMMxKSkp/PTTT3meU0RERERErinw8JvY2FieeeYZmjRpQrNmzZg2bRqpqan07NkTgJiYGKpUqcLYsWMBePnll2nVqhWTJ0+mffv2LFq0iC1btjB//nwALBYLAwcOZPTo0dSqVSt7SsuQkBCio6OL7ictgXx9fRk5cmSOoUoiudHrRfJLrxUpCL1eJL/0Wrk1hVpRdubMmdmLTzVq1Ii3336biIgIAB588EHCwsJ47733so//9NNP+ec//5m9+NSECRNyXXxq/vz5nD17lvvvv5/Zs2dTu3btW/8JRURERETcXKGaehERERERcR4FGlMvIiIiIiLOR029iIiIiIiLU1MvIiIiIuLi1NSLiIiIiLg4NfVu6ujRo/zf//0fFStWxM/Pj/r167NlyxazY4mTyczMZPjw4VSrVg0/Pz9q1KjBm2++ie6fF4AffviBxx9/nJCQECwWC8uWLTPst1qtjBgxgsqVK+Pn50dkZCR79+41J6yY6kavlYyMDIYOHUr9+vUpXbo0ISEhxMTEcOzYMfMCi6lu9t5yvRdffBGLxcK0adMcls9Vqal3Q3/99Rf33Xcf3t7erFixgl9//ZXJkydTvnx5s6OJkxk/fjxz5sxh5syZ7N69m/HjxzNhwgRmzJhhdjRxAqmpqTRs2JBZs2blun/ChAm8/fbbzJ07l59++onSpUsTFRXFpUuXHJxUzHaj18qFCxfYunUrw4cPZ+vWrSxZsoTff/+dDh06mJBUnMHN3luuWrp0KZs2bSIkJMRByVybprR0Q8OGDePHH39k3bp1ZkcRJ/fYY48RFBTEv//97+xaly5d8PPz48MPPzQxmTgbi8XC0qVLsxcFtFqthISEMGjQIAYPHgxAcnIyQUFBvPfee3Tv3t3EtGIm+9dKbv73v//RrFkzDh48SNWqVR0XTpxOXq+Xo0ePEhERwTfffEP79u0ZOHAgAwcONCWjq9CVejf0+eef06RJE5588kkqVapE48aNWbBggdmxxAnde++9xMfHs2fPHgB+/vln1q9fT7t27UxOJs5u//79JCYmEhkZmV0LCAggIiKCjRs3mphMXEFycjIWi4Vy5cqZHUWcUFZWFk8//TRDhgyhXr16ZsdxGV5mB5Ci9+effzJnzhxiY2N57bXX+N///seAAQPw8fHhmWeeMTueOJFhw4aRkpJC3bp18fT0JDMzk7feeounnnrK7Gji5BITEwEICgoy1IOCgrL3ieTm0qVLDB06lB49euDv7292HHFC48ePx8vLiwEDBpgdxaWoqXdDWVlZNGnShDFjxgDQuHFjfvnlF+bOnaumXgw++eQT/vOf//DRRx9Rr149tm/fzsCBAwkJCdFrRUSKXEZGBl27dsVqtTJnzhyz44gTSkhIYPr06WzduhWLxWJ2HJei4TduqHLlytx1112G2t/+9jcOHTpkUiJxVkOGDGHYsGF0796d+vXr8/TTT/PKK68wduxYs6OJkwsODgYgKSnJUE9KSsreJ3K9qw39wYMHWb16ta7SS67WrVvHiRMnqFq1Kl5eXnh5eXHw4EEGDRpEWFiY2fGcmpp6N3Tffffx+++/G2p79uzhzjvvNCmROKsLFy7g4WF8G/D09CQrK8ukROIqqlWrRnBwMPHx8dm1lJQUfvrpJ1q0aGFiMnFGVxv6vXv38u2331KxYkWzI4mTevrpp9mxYwfbt2/P3kJCQhgyZAjffPON2fGcmobfuKFXXnmFe++9lzFjxtC1a1c2b97M/PnzmT9/vtnRxMk8/vjjvPXWW1StWpV69eqxbds2pkyZwj/+8Q+zo4kTOH/+PPv27ct+vH//frZv306FChWoWrUqAwcOZPTo0dSqVYtq1aoxfPhwQkJCbjjribinG71WKleuzBNPPMHWrVv58ssvyczMzL7vokKFCvj4+JgVW0xys/cW+1/6vL29CQ4Opk6dOo6O6lqs4pa++OIL691332319fW11q1b1zp//nyzI4kTSklJsb788svWqlWrWkuVKmWtXr269fXXX7empaWZHU2cwPfff28FcmzPPPOM1Wq1WrOysqzDhw+3BgUFWX19fa2tW7e2/v777+aGFlPc6LWyf//+XPcB1u+//97s6GKCm7232LvzzjutU6dOdWhGV6R56kVEREREXJzG1IuIiIiIuDg19SIiIiIiLk5NvYiIiIiIi1NTLyIiIiLi4tTUi4iIiIi4ODX1IiIiIiIuTk29iIiIiIiLU1MvIiIiIuLi1NSLiIiIiLg4NfUiIiIiIi5OTb2IiIiIiIv7/yDVRmuQQCtoAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import kf_book.kf_internal as kf_internal\n", + "kf_internal.gaussian_vs_histogram()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "621bd369", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "𝒩(μ=3.400, 𝜎²=10.100)\n", + "𝒩(μ=4.500, 𝜎²=0.040)\n" + ] + } + ], + "source": [ + "from collections import namedtuple\n", + "gaussian = namedtuple('Gaussian', ['mean', 'var'])\n", + "gaussian.__repr__ = lambda s: f'𝒩(μ={s[0]:.3f}, 𝜎²={s[1]:.3f})'\n", + "\n", + "g1 = gaussian(3.4, 10.1)\n", + "g2 = gaussian(mean=4.5, var=0.2**2)\n", + "print(g1)\n", + "print(g2)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "e8fe46d6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "𝒩(μ=25.000, 𝜎²=0.530)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def predict(pos, movement):\n", + " return gaussian(pos.mean + movement.mean, pos.var + movement.var)\n", + "\n", + "pos = gaussian(10., .2**2)\n", + "move = gaussian(15., .7**2)\n", + "predict(pos, move)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "43c42718", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "𝒩(μ=10.800, 𝜎²=0.008)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def gaussian_multiply(g1, g2):\n", + " mean = (g1.var * g2.mean + g2.var * g1.mean) / (g1.var + g2.var)\n", + " variance = (g1.var * g2.var) / (g1.var + g2.var)\n", + " return gaussian(mean, variance)\n", + "\n", + "def update(prior, likelihood):\n", + " posterior = gaussian_multiply(likelihood, prior)\n", + " return posterior\n", + "\n", + "# test the update function\n", + "predicted_pos = gaussian(10., .2**2)\n", + "measured_pos = gaussian(11., .1**2)\n", + "estimated_pos = update(predicted_pos, measured_pos)\n", + "estimated_pos" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "fbf4fb30", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "𝒩(μ=10.000, 𝜎²=0.500)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "z = gaussian(10., 1.) # Gaussian N(10, 1)\n", + "\n", + "product = gaussian_multiply(z, z)\n", + "\n", + "xs = np.arange(5, 15, 0.1)\n", + "ys = [stats.gaussian(x, z.mean, z.var) for x in xs]\n", + "plt.plot(xs, ys, label='$\\mathcal{N}(10,1)$')\n", + "\n", + "ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n", + "plt.plot(xs, ys, label='$\\mathcal{N}(10,1) \\\\times \\mathcal{N}(10,1)$', ls='--')\n", + "plt.legend()\n", + "print(product)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "20766c3e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Ci4sL/fv3JzU1tfC6+Ph4HnzwQWrVqoW3tzcjRozg8uXLReqeMmUKrVu3xtXVlYCAAMaNG4fRqK4KdeLECTQaDX/++Sf9+/fHxcWF0NBQduzYUeKf7c1+NiVtZ3H8/f35+uuvi5zbtWsXTk5OnDp16qbv8Z8/359++omePXtiMBj4448/uP3221m0yPYbyZUqac/PzycqKoqIiIirFWi1REREEBkZWex1mZmZ1K9fn+DgYO644w4OHjx4wzh5eXmkp6cXeQghhCiqlW8rxoWPq+hm3JRGoylc/vGnIz+hKEoFt0hUOEWB/KyKeZTj319UVBQ+Pj58+eWXRf4db968mV69ehV53r59+yLXxsTE0L9/f/r06cPevXuZNGkS9957LwaDgWbNml03XsGQC29v7xK1b9++fQB88cUXvPfee2zbto3ExERGjhzJ+++/z2effcb69evZt28f8+bNA+D48eO0b9+exo0bF/bwHz9+nJdeeqmwXkVRUBSFL7/8kkOHDvHtt9/yyy+/FCbB+/btQ6PRMHPmTCZNmsS+ffuoV68er776aonaXZKfTUnaeSOtW7fm0KFDRc698sorPPHEEzRo0OCm7/GfP9/p06czefJkDh48SP/+/enUqRM7d+4kLy+vRG0pq1KtHpOcnIzZbL6mpzwgIIDDhw9f95rQ0FDmzp1LmzZtSEtLY8aMGXTr1o2DBw9St27d614zbdo03nrrrdI0TQghRCU2tNFQZu6eyfHU4xxLPUbTWk0rukmiIhmz4b06FRP7tfPg6FqmS3fs2MEnn3zCyJEjWblyJbfccgsAW7ZsYeLEiYXlTp8+TZ06Rd/fM888w9ChQ3nnnXcAdVjF/PnzOXv2LA4O16ZjFouF5557ju7du9OqVasStS86Ohpvb28WL16Mj48PAL1792bLli0cPHgQFxcXADp27EhCQgIATz75JE8++WSRvOvll18ukgxrNBqmTp1a+Lx+/fpEREQUjrfft28fXl5eLF68GD8/ddL50KFD+fLLL0vU7pL8bErSzhtp1apVkaR91apV7N69m59++qlE7xHUn6+rqytLliwpMlehTp065Ofnk5CQQP369UvUnrKw+eoxXbt2ZdSoUYSHh9O7d29+/fVX/Pz8bvgXOXHiRNLS0gofZ86csXUzhRCiyvg8+nPe3PYmRy8freimlJi7o3vhOvKr4lZVcGuEKJujR48yYsQIunfvzscff1x4XlGUIol3Tk5OkUU3Tp8+zfr163n99deL1GcwGAgLC7turKeeeoqYmJhSDbvYt28fd955Z2HCDuqQkuHDhxcm7AXnGjRowOnTp1m9ejXTp0/Hzc2t8DFy5Mgi7+f06dM89dRTtGrVilq1auHm5sZPP/1U2Pm6b98+7rjjjsKEHeDUqVM0btz4pm0uyc+mpO28kX/2tCuKwsSJE3nppZfw9fUt0XsseJ9Dhw69ZnJxwRKf2dnZJWpLWZWqp93X1xedTkdiYmKR84mJiQQGBpaoDr1eT9u2bTl+/HixZQwGAwaDoTRNE0KIGsFsMfPL0V+4mHORfvX6Vake60Ehg1h/Zj1/x/3N+PDxaDSaim6SqCh6F7XHu6Jil0FWVha1atUCYOrUqfTv359Nmzbh7+9/TU+4r69vkbHW0dHRODo60rJl0fknsbGxPPbYY9fEGj9+PH/++SebNm0qdlTC9URHRxfp8Qc10Xz++ecLn+fm5nLkyBHCwsLYt28f3t7e1x17XpCIXrx4kY4dO9KvXz9mzpxJUFAQZrOZDh06FCbV+/btuyZudHR0kSFDN2rzzX42JWnnzbRq1YqzZ8+SmZnJsmXLuHDhAhMmTCjxeyxo6/WG/KSkpAAU+dJiC6VK2h0dHWnfvj1r165l2LBhgHr7Zu3atYwfP75EdZjNZg4cOMCtt95a6sYKIURNtzdpLxdzLuKud6dr7a4V3ZxS6RPcB0etI3HpcRy9fJRQ79CKbpKoKBpNmYeoVJQlS5Zw1113AdCvXz/uuOMOxo8fz+jRo3niiSeKlG3btm2R1UR0Oh0mk4nc3NzCHvi1a9dy8ODBIkmhoig8/fTT/Pbbb2zYsIEGDRqUuH3p6enExcXRtm3bwnOnTp0iLS2tyLkDBw6gKAqtW7dm8+bNZGRkUKdOnSI98f+0bNkyzGYzP/74Y+EX7c8++wyj0Uh4eDhpaWnXxAU1wX3mmWdu2u6S/Gz0ev1N23kzBV+s9u/fz6RJk5g8eTKurq4leo9w/Z9vgZiYGOrWrVvYa28rpR4eM2HCBObMmcP8+fOJjY1l3LhxZGVlMWbMGABGjRpV5NvW1KlT+fvvvzl58iR79uxh5MiRnD59+rrfLIUQQtxYwdCSvvX6otfpb1K6cnHVu9Kzbk/C/MLINtn2NrIQ1rB7925GjRpFfHw869evp0ePHoWvffrpp8TFxREZGVmY/BUYNGgQBw8eLOxtb9++PXq9npdeeomTJ0+ybNkyHn/8cYAiSftTTz3FggULWLhwIe7u7iQkJJCQkEBOTk5hmc8++4z+/ftf09Z9+/ah0+mK9PoXjHH/5zjr6OhoGjVqhJubG507d8bDw4NRo0axb98+jh8/zsqVK3nuuecKy/v4+JCens4ff/zBsWPHmDlzJm+99RZBQUH4+fmxf/9+HBwcaN26deE1p0+f5vLly4UJ742U5GdTknbe6GcD4ObmRv369XnhhRfQarWMHTu2xO/xnz/ff77PAps3b2bgwIE3fa/lVeqkffjw4cyYMYPJkycTHh5OdHQ0K1euLJycGh8fz4ULFwrLX758mbFjx9K8eXNuvfVW0tPT2bZtGy1atLDeuxBCiBrAbDGzJn4NoA41qYqm957OglsX0Nb/2t4qISqb1NRUfvjhB3r06HHNmOv69esza9as644caN26Ne3atSuc5Fi7dm3mzp3L77//Tps2bZg3bx4PP/wwjRs3LrIyzBdffEFaWhp9+vShdu3ahY/FixcXlklOTubEiRPXxNy3bx+hoaFFxtLv27fvmp7hffv2FSbD3t7eLF++nEuXLtGrVy/atWvH66+/TsOGDQvL33777Tz66KM89NBD9OjRg3PnznHfffcVJuTXi7t37168vLyKjP0u2Gzz30rysylJO2/0synQunVrtm/fzrvvvltkLPzN3mNx7xPU4UZLly4t8iXAVjRKFVh7Kz09HU9PT9LS0vDw8Kjo5gghRIXYlbCLR1Y9grujOxvv21jletpFzZSbm8upU6do0KBBldwRPTExES8vr1LPtfvrr7946aWXiImJQast2kdqsVjo06cPPXr04L333rNmcyutKVOmsHHjRjZs2HDDclXtZ/PFF1/w22+/8ffffxdb5kb/B0qT45ZqTLsQQoiKUzA0pn+9/lU+YU/LS+Ns5lla+lTujaGEKOuGkEOGDOHYsWOcO3eOU6dOcfHiRdq2bUtycjLTp0/n9OnTLF261LqNrcRWrFjBZ599ds35TZs2VemfjV6vZ9asWXaJJUm7EEJUEUFuQdR1q1tlh8YU2JWwi8f/fpzabrX5686/ZBUZUW0VjLnevn07r776KufOnSMgIICIiAh27txZ4k2TqoOdO3de93xiYmKV/tnYc46mDI8RQogqRFEUFBS0Gptvs2Ez2cZsei/uTa45l8W3LaaFj8xxqs6q+vAYIcrLWsNjqu6nvhBC1EAajaZKJ+wALnoXetbtCchGS0IIUVJV+5NfCCFqAJPFxKazmzCajRXdFKsZGKIuj7YqbhVV4IavEEJUOEnahRCikotKjOKptU9xx+93VJsEt1dQL5x0TpzLPMehlEMV3RwhhKj0JGkXQohKrmAISafATtVm0qaL3oVeddUtzmWIjBBC3Jwk7UIIUYmZLCbWnFY3VCoYUlJdFKyCs+b0mmpzB0EIIWxFlnwUQohKbFfCLi7nXcbL4EWnwE4V3Ryr6lm3J691fo0B9QdUmzsIQghhK5K0CyFEJVYwdCSifgQO2ur1ke3s4MwDzR6o6GYIIUSVIMNjhBCikjJajKyNXwtQ5TdUEkIIUT6StAshRCW1N3EvqXmpeDt50yGgQ0U3x2b+OPEHj616jAMXD1R0U4SoMCEhIXzyyScV3QxRiVWve61CCFGNdAzsyG9DfyMhO6HaDY35p01nN7EjYQfrz6yntV/rim6OENXC6NGjSU1NZenSpRXdFGEl0tMuhBCVlEajoXGtxvQI6lHRTbGp3nV7A2ryLkRVlp+fX9FNENWYJO1CCCEqVPeg7mjQcOTyERKyEiq6OUIU6tOnD+PHj2f8+PF4enri6+vLpEmTCpcoDQkJ4e2332bUqFF4eHjw+OOPA/DLL7/QsmVLDAYDISEhfPTRR0XqTUpK4vbbb8fZ2ZkGDRrwww8/FHk9Li4OjUZDdHR04bnU1FQ0Gg0bNmwoPHfw4EFuu+02PDw8cHd3p2fPnpw4cYI333yT+fPn8/vvv6PRaK65TlRN1fd+qxBCVGE/HfmJ3Qm7uafpPXSqXb2Wevw3bydvWvu1Zv/F/Ww+t5l7m95b0U0SdpJtzC72NZ1Wh0FnKFFZrUaLk4PTTcu66F1K3cb58+fz6KOPsnPnTnbv3s3jjz9OvXr1GDt2LAAzZsxg8uTJTJkyBYCoqCjuu+8+3nzzTYYPH862bdt48skn8fHxYfTo0YA6dOX8+fOsX78evV7PM888Q1JSUqnade7cOXr16kWfPn1Yt24dHh4ebN26FZPJxIsvvkhsbCzp6enMmzcPAG9v71K/d1G5SNIuhBCV0IpTK9iduJtw//Bqn7SDOkRm/8X9bDq7SZL2GqTzws7FvtYzqCf/i/hf4fM+P/Uhx5Rz3bIdAjowb/C8wueDfxnM5bzL15Q78HDpJzsHBwfz8ccfo9FoCA0N5cCBA3z88ceFSXu/fv144YUXCsuPGDGC/v37M2nSJACaNm3KoUOHmD59OqNHj+bo0aOsWLGCnTt30rFjRwC++eYbmjdvXqp2ff7553h6erJo0SL0en1hrALOzs7k5eURGBhY6vcsKicZHiOEEJVMen46e5P2AtCrbq8Kbo19FLzPHRd2kGfOq+DWCHFVly5dimz+1bVrV44dO4bZbAagQ4eiKzvFxsbSvXv3Iue6d+9eeE1sbCwODg60b9++8PVmzZrh5eVVqnZFR0fTs2fPwoRdVH/S0y6EEJXMtvPbMCtmGno2pK573Ypujl2E1gqlrltdgt2DuZx7mUBX6R2sCXY8uKPY13RaXZHnG+7bUGxZraZoH+TKu1eWq12l4erqavU6tVr1/RSMnQcwGo1Fyjg7O1s9rqjcJGkXQohKZvPZzUDN6WUHdaWcZXcuq9ZLW4prlWaMua3K3syOHUW/WGzfvp0mTZqg0+muW7558+Zs3bq1yLmtW7fStGlTdDodzZo1w2QyERUVVTg85siRI6SmphaW9/PzA+DChQu0bdsWoMikVIA2bdowf/58jEbjdXvbHR0dC+8GiOpBhscIIUQlYraYa2TSDkjCLiql+Ph4JkyYwJEjR/jxxx+ZNWsWzz77bLHlX3jhBdauXcvbb7/N0aNHmT9/Pp999hkvvvgiAKGhoQwePJgnnniCHTt2EBUVxWOPPVak59zZ2ZkuXbrw/vvvExsby8aNG3njjTeKxBk/fjzp6encf//97N69m2PHjvH9999z5MgRQF3ZZv/+/Rw5coTk5ORreupF1SNJuxBCVCIxl2K4nHcZd7074f7hFd2cCpGUnURqbmpFN0MIAEaNGkVOTg6dOnXiqaee4tlnny1c2vF62rVrx08//cSiRYto1aoVkydPZurUqYUrxwDMmzePOnXq0Lt3b+666y4ef/xx/P39i9Qzd+5cTCYT7du357nnnuOdd94p8rqPjw/r1q0jMzOT3r170759e+bMmVPY6z527FhCQ0Pp0KEDfn5+1/T+i6pHo/xzwFQllZ6ejqenJ2lpaXh4eFR0c4QQwmZ2XNjBzKiZ1HOvx/Te0yu6OXb37vZ3WXRkES+0f4HRrUZXdHOEFeTm5nLq1CkaNGiAk5PTzS+oRPr06UN4eDiffPJJRTdFVGE3+j9QmhxX7kUKIUQl0rl2ZxbfthiTxVTRTakQIZ4hAGw8u1GSdiGE+AcZHiOEEJVQTR3f3StIHce/N2kv6fnpFdwaIYSoPGrmbwUhhKiEzmeex9Pgiave+kvIVRXBHsE08GzAqbRTbDu/jcEhgyu6SaIG27BhQ0U3QYhC0tMuhBCVxPs736fHoh78ceKPim5KhSrobS9YRUcIIYQk7UIIUSnkm/PZfmE7JouJxl6NK7o5Fapgqcst57ZgUSwV3BphLVVg3QshbMJa//YlaRdCiEpgd8Juckw5+Dv709y7eUU3p0K1DWiLm96NlNwUYpJjKro5opwKliDMzs6u4JYIUTEK/u1fbxOs0pAx7UIIUQlsPLsRgJ51e6LRaCq4NRVLr9Uzvu14PA2eNPBsUNHNEeWk0+nw8vIiKSkJABcXlxr/b1zUDIqikJ2dTVJSEl5eXsXuoltSkrQLIUQFUxSFTWc3AWrSLmBE8xEV3QRhRYGBgQCFibsQNYmXl1fh/4HykKRdCCEq2Kn0U5zNPIteq6dr7a4V3RwhrE6j0VC7dm38/f0xGo0V3Rwh7Eav15e7h72AJO1CCFHBClZJ6RDQARe9SwW3pvKIS4tjTfwamtZqWjg5VVRtOp3OagmMEDWNJO1CCFHBBoUMQq/VE+ha/tun1cmKuBX8L/p/9AvuJ0m7EKLGk9VjhBCiggW6BvJg8wfpV69fRTelUukZpI7v35mwE6NFhlQIIWo2SdqFEEJUSs29m+Np8CTTmClLPwohajxJ2oUQogL9fvx3lhxdQnJOckU3pdLRaXV0qd0FgMjzkRXcGiGEqFiStAshRAWaFzOPqZFT2Zu0t6KbUil1q9MNgG3nt1VwS4QQomKVKWn//PPPCQkJwcnJic6dO7Nz584SXbdo0SI0Gg3Dhg0rS1ghhKhWErISOJF2Aq1GS6fAThXdnEqpYAnMA8kHSM9Pr+DWCCFExSl10r548WImTJjAlClT2LNnD2FhYQwaNOimGybExcXx4osv0rOnbBwihBBwdchHK99WeBo8K7g1lVNtt9o08GyAQWfg+OXjFd0cIYSoMKVO2mfOnMnYsWMZM2YMLVq0YPbs2bi4uDB37txirzGbzYwYMYK33nqLhg0blqvBQghRXRQk7bKh0o191u8ztty/hXYB7Sq6KUIIUWFKlbTn5+cTFRVFRETE1Qq0WiIiIoiMLH6S0NSpU/H39+fRRx8tUZy8vDzS09OLPIQQojqxKBYiL6ifmwXjtstfqQVSz8CZnZB+HhTFOvWWkKIonE/NIer0ZS6k5aBYKX49j3o46hytUpcQQlRVpdpcKTk5GbPZTEBAQJHzAQEBHD58+LrXbNmyhW+++Ybo6OgSx5k2bRpvvfVWaZomhBBVSmxKLKl5qbjqXWnt17r0FaSdhfjtcOk4JB9VH5dOgDH7ahlHN/BtAj5NwLepelyvK7gHFF9vCV1Iy2F33GVOXszixMVMTlzM5FRyFtn55sIyro46Gvq50dDPlUZ+bjTyc6NDSC0CPJzKHNeiWNBqZA0FIUTNY9MdUTMyMnjooYeYM2cOvr6+Jb5u4sSJTJgwofB5eno6wcHBtmiiEEJUiKMpRwsnoOq1+pJfeD4atv0XDv4GiuXa17UO4BYAGQmQnwnn96qPwtf1EDYcuj0DfqGlbvfB82l8tekkf+6/gNlybU+6g1aDn7uBpIw8svLNHDiXxoFzaUVevyM8iMd7NSQ00L3EcRcdXsTCwwt5sNmD3N/s/lK3WwghqrpSJe2+vr7odDoSExOLnE9MTCQw8Nrtt0+cOEFcXBy333574TmLRf0l4+DgwJEjR2jUqNE11xkMBgwGQ2maJoQQVcqdTe6kX71+JVsRRVHgxFrY+l84tfHq+TrtIKCF2ote0Jteqz7o9GDKh8unrvTCH1MfiQcg4QDsXaA+mt4C3Z+Fel1Ao7lBeIWtxy/x5aYTbD52dT35NnU9CQ1wp5G/Gw19XWnk70Y9bxf0Oi35JgvxKdmcuJhZ2Bt/OCGdmHPp/LLnLL/sOUvfUD8e79WILg290dwgPkCmMZNTaafYdn6bJO1CiBpJo5Ry0GHnzp3p1KkTs2bNAtQkvF69eowfP55XX321SNnc3FyOHy862/+NN94gIyODTz/9lKZNm+LoePNxiunp6Xh6epKWloaHh0dpmiuEEFWXxQIxP6vJeuIB9ZxGB63uhm5PQ+02pa/zzE7Y+ikc/gu48vFftyN0fw6aDSmSvCuKwp/7LzB74wkOnle/XGg1MKRNHZ7o1ZBWQaVf8Sb6TCpfbTrBypgECjrqw+p68p/ejRjcKrDY5P3gpYPc/+f9uOpd2Xz/5tLdnRBCiEqqNDluqZP2xYsX8/DDD/Pll1/SqVMnPvnkE3766ScOHz5MQEAAo0aNIigoiGnTpl33+tGjR5OamsrSpUtt8oaEEKKyUxTlpj3LZCXDb0/A8TXqc70rtH8YuowDr3rlb0TycYicBdE/gjlPPdfyLrj9U3DyIDU7nxeX7GNNrLqcr7Nex/COwTzaowHB3i7lDh+XnMXXW06yZPdZ8kzqHdhbWgXywT1t8HC6NiG3KBZ6L+5Nal4q8wfPl5VkhBDVQmly3FKPaR8+fDgXL15k8uTJJCQkEB4ezsqVKwsnp8bHx6PVyiQhIYQozozdM9h3cR9jW4+ld3Dvawuc3gY/PwoZ58HBCXq+CJ0eA+da1muEb2M1Qe/7Omz/4so4+V/hQjSHevyXsX8bOZeag6ODlif7NOLhriHUcrXeCi4hvq68M6w1z0c05dttcczeeIIVMQkcPJ/OZw+2pU1dryLltRotXWp3YWXcSiIvRErSLoSocUrd014RpKddCFGdDF06lFNpp5jZZyYD6g+4+oLFAls/hnXvgmJWx6jf+y0EtLR9o87sQvl5NJq0s+Qpet42jWSr1x18NqIdLevYfuOnfWdSGf/jHs6k5KDXaXj91uY83C2kyB2J3479xuRtk2nj14Yfbv3B5m0SQghbK02OK13iQghhRwlZCZxKO1W4ckyhrGRYeC+snaom7G2Gw9j19knYgcveYTzr8V9Wm9th0Bh5Rz+Pv4Pn0dL7JsN4rCQs2Is/n+7JoJYBGM0Kby47xLgFe0jLMRaW6VpH3YQqJjmGtLy04qoSQohqSZJ2IYSwo4JdUFv5tsLTcKUH+8xOmN1THb/u4ARDP4M7vwSDm13aFH0mlSH/3cwfx3J5SnmJqGYvomgd0B/+Hb7qDQkxdmmHp7Oe2SPbM+X2Fuh1GlYeTOC2WZuJubJkZKBrIF1rd+XOxneSY8qxS5uEEKKysOk67UIIIYradn4b8I9dUOO2wg/3qJsi2XM4zBVRpy8z6psdZOWbaeDrymcPtqVlnVvhzGD4eQyknIRvh8DoPyGwDJtAlZJGo2FM9wa0q1ercLjMA3O2s/CxLrSu68lXA7+yeRuEEKIykp52IYSwE7PFTOQFtae9W51uEL8DfrhXTdgb9bPrcBhQe9hHz91JVr6Zbo18+GN896vj14M7whOb1OUgc1Phuzsg8ZDd2lYwXKZjSC0yck2M/GYHB8/LkBghRM0lSbsQQtjJ4ZTDpOWl4aZ3o1VuHiy4G4xZ0KA33L/QbsNhAGLOpTHqmx1k5Jno3MCbrx/ugPu/l1p08YaRv0CdtpB9Cb4bCheP2K2Nns565o3pRLt6XqTlGBn59Q4OJ6Rjtpg5cPEAyTnJN69ECCGqCUnahRDCTrQaLQPqD6Cfbzj6H+6D/AwI6QkPLAK9s93acfB8GiO+3kF6romOIbWYO7ojLo7FjJZ08oSHfoPANpB1Eebfru6uaiduBge+faQTYcFeXM42MmLODh5b+RQPLn+Q1adX260dQghR0SRpF0IIO2nu05yZoQ/z7p7lkJcG9bqqCbtj+TcrKqnDCemM/HoHaTlG2tbzYt6YTrgabjK9ybkWjPodAlpDZqKauF86YZ8GAx5Oer57pBOtgjy4lJXP3mNewNX5AUIIURNI0i6EEPaSeBC+G6aOEa/bCUYsseuQmGOJGYyYs4PL2UbC6noy/5FOuN0sYS/g4g2jloJfc8i4oCbuKads2t5/8nTWs+DRzrSo7UH65QYA7LiwE6PFeJMrhRCiepCkXQgh7ODcuR2cXnAHSk4KBLVXx4ob3O0W/3xqDg9+vYNLWfm0CvLgu0c74/HvMew34+oLD/+hrnKTfg7mD4XMi7Zp8HV4uTiy4LHONPEKxWJyJceUzaa4KLvFF0KIiiRJuxBC2Fp+NgtWPMltvs58XLcJjPwVnOy3u3Ou0cx/FkRxMSOPZoHuLHi0M57OpUzYC7j5w8PLwLshpMXDktFgtl9vt7erIz881hVncygAU9f9Tr7JYrf4QghRUSRpF0IIW1IUWPYM25VMAFp2ewGcvewYXmHS0hj2n02jlouerx/ugJeLY/kqdQ+8MhbfDU5vgdWTrdPYEvJ1MzC2wyAAkowHmPrnQbvGF0KIiiBJuxBC2NL2L7h46BeOOzqiQUOnhoPtGn7BjniWRJ1Fq4HPHmxH3VpWmvTqFwp3zlaPt/8P9v9knXpL6LamvQHQOZ9hwc6j/LT7jF3jCyGEvUnSLoQQtnJqM/z9BtudnABo5t2MWk617BZ+d1wKb/2h9kK/ekszujf2tW6A5rdDzxfV4z+egQv7rVv/DQS5BfFihxe53X8qWPS8sTSGfWdS7RZfCCHsTZJ2IYSwhbSz6nhvxcz2Os0B6FKni93CJ6bnMu6HPZgsCre1qc3Yng1tE6jva9A4Akw5sHgEZKfYJs51PNzyYd4dPJSI5nXIN1n4z4IokjPz7BZfCCHsSZJ2IYSwNmMuLB4J2ckoga3ZfmXOZ5fa9kna800Wxv1j4umH97RBo9HYJphWB3d/DbVCIDUefn4ELGbbxLpeeK2GmcPDaOjnyoW0XMYv3IPJLBNThRDVjyTtQghhTYoCf70A5/eCszenbn2fpJyLOGodaeffzi5NeGvZQfbEp+Lh5MCXD7UvfrdTa3GuBfcvBL0LnFwPa6faNt4/rItfx3+jP+D9e+vj6qhj+8kUpq04bLf4QghhL5K0CyGENe2ZD9ELQKOFe+ZSu057ZvWbxYQOE3BycLJ5+J+jzvLDjng0Gvj0gbbU93G1eUwAAlrC0Fnq8dZP4NAfdgn71f6vWHxkMYnGGD66LxyAb7acYtm+83aJL4QQ9iJJuxBCWMulE7ByonrcfzI06ouzgzN9gvswovkIm4c/k5LNlN9jAHg+oil9Q/1tHrOI1vdA1/Hq8bJnISPR5iELhhxtv7Cdwa0CeapvIwBe/+0ACWm5No8vhBD2Ikm7EEJYg8UMS58EYzaE9IRuz9o3vEXhxSX7yMo30zGkFk/1bWzX+IX6T4GA1pCToibuimLTcF3rdAVg+/ntKIrCcxFNaVPXk/RcE6/8sh/FxvGFEMJeJGkXQghriPwMzmwHR3cY9j/QajmScoT/7vkv0UnRNg//7bY4dpxKwcVRx4x7w9BpbTTx9GYcHNX127V6OLoCohfaNFy4fzgGnYGknCROpp1Er9My874wHB20bDx6kR93yvrtQojqQZJ2IYQor8RDsO4d9XjwNPCqB8C6M+uYc2AO3x36zqbhjydl8sFKdfLla7c2t9849uIEtlKXggRY+Sqk2i5xNugMhRN8t1/YDkBjf3deHhQKwDt/HSL+UrbN4gshhL1I0i6EEOVhyoffngBzPjQdDG1HFr60/byaRNpyqUeT2cILS/aRZ7LQq6kfIzrXs1msUun+LNTtBHnp8PuTYLHdMowF698X/LwBHunegM4NvMnON/Pikn2YLTJMRghRtUnSLoQQ5bFpOiTsV5c9vP2/cGU99GxjNvsvqjuEFoy7toUvNpxg3xl1eccP77bheuylpdWpw2T0LnBqE+yaY7NQBV+KErITCsewa7UaZtwbhqujjp1xKczdcspm8YUQwh4kaRdCiLI6FwWbP1KPh8wE94DCl3Yn7sakmAhyCyLYPdgm4WPOpfHp2mMAvHVHSwI9bb+kZKn4NIIBV9ZsXz0Fko/bJEwz72Ysv2s5S25fUuRLS7C3C2/c1gKA6X8f4Whihk3iCyGEPUjSLoQQZWHMgd/+A4oZWt0Nre4q8nLk+UjAdkNj8kxmXvhpHyaLwuCWgQwLD7JJnHLr8Cg07AOmnCvDiExWD6HVaIv9YnR/x2D6hPqRb7Iw4adojLJbqhCiipKkXQghymLtVEg+Cm6BcOuMa14umBRZMN7a2mauPsqRxAx83Rx5985WlWdYzL9ptXDH52DwhHO71Y2XbMiiFE3KNRoNH9zdBk9nPTHn0vlsnW16+4UQwtYkaRdCiNI6GwXbv1CPh84CF+8iL2cZs0jOSUaDhs6Bna0ePuZcGnM2nQTgvTtb4+NmsHoMq/KsC7d8oB5v/MAmw2RyTbk8s+4Zei/uTZYxq8hrAR5OvD2sFQCfrz8uw2SEEFWSJO1CCFEaZhP8+RygQJv7oenAa4q46l3ZOHwjv93xG7Wcalk3vEXh9aUxWBS4rU1tBrYMtGr9NhN2PzSOUFfZ+WuC1TddcnJw4njqcVLzUtmdsPua14eG1SGieQAmi8IbS2Nk0yUhRJUjSbsQQpTGrq/V1WKcPGHgO8UW02q0NPJqZPXwP+6MZ9+ZVNwMDky6MsmyStBo4Nbp4OAEpzZCzC9WD1Ewf6BgaNK/vTm0Bc56HTtPpfDLnnNWjy+EELYkSbsQQpRU+oWrmyj1nwJuftcUURTFZr24FzPy+PDKJkovDGxKgEclWy3mZrwbQs8X1ONVr0FumlWrv1nSXreWC8/0bwLAe8tjSc3Ot2p8IYSwJUnahRCipFa9BvkZENQe2o+5bpG49Dgifo5gauRUq4eftjyW9FwTLet48FCX+lav3y66Pws+jSEz8eoXICvpXLszGjQcTz3OxeyL1y3zaI8GNPF3IyUrnw9WHrFqfCGEsCVJ2oUQoiSOr4WDv4JGC7d9rK6Kch2R5yNJyk4iPiPequG3nUjm173n0Gjg3Ttb46Croh/fDgYYcmVt+11fw7k9Vqva0+BJCx91yFBxve2ODlreuTIp9ced8USdvmy1+EIIYUtV9FNfCCHsyJgLy19Ujzs9AbXDii0aecH667PnmyxMWhoDwIjO9QgP9rJa3RWiYR9ofS8oFvjzebCYrVZ1wc+9YJ386+nc0Id72tcF4I2lMZhk7XYhRBUgSbsQQtzMlo8h5SS414a+rxVbzGgxsithFwBd63S1Wvg5m09y4mIWvm6OvDSomdXqrVAD31XXbr8QDbvnWq3a7kHdaeffjla+rW5YbuItzfB01hN7IZ1vt8VZLb4QQtiKJO1CCHEjl07Alpnq8aD3wMmj2KIxyTFkGbPwMnjR3Lu5VcKfScnmv2uPAfD6kOZ4OuutUm+Fcw+A/pPU47VTISPRKtV2DOzI/Fvm82DzB29YzsfNwKu3qF+APl59lAtpOVaJL4QQtiJJuxBCFEdR4K8X1LXFG/WDlnfesPi289sAdYiGVlP+j1dFUZjyx0HyTBa6NvRhWHhQueusVDo8AnXaQl46/P263cMP7xBMu3peZOWbefvPQ3aPL4QQpSFJuxBCFOfQUji5HnQGuHWGutb4DRSMo7bW0JjVhxJZdzgJvU7D28NaoblJ/CpHq4MhMwENHFgCpzZZreq0vLTrbrJUJLxWwzvDWqPTalh+IIFNR6+/4owQQlQGkrQLIcT1GHPg78nqcY/nwOfGGyUpikI7/3Y09mpM19rlT9rzTGbeXR4LwGM9G9LY363cdVZKQe2g46Pq8crXrDIpNT49np6LejJuzTjyzHk3LNuijgcPdw0B4O0/D8mkVCFEpSVJuxBCXE/k55AWDx5B0P25mxbXaDRM6DCB3+74jdputcsdfv62OE5fysbP3cBTfRuXu75Krc9r6g6ziQdg7/flri7YPRgfZx9yzblEJ0XftPyz/ZtQy0XPsaRMFu607lKdQghhLWVK2j///HNCQkJwcnKic+fO7Ny5s9iyv/76Kx06dMDLywtXV1fCw8P5/vvyfygLIYTNZCTA5iuTTyPeAkcXu4ZPzsxj1trjALw0KBQ3g4Nd49udqw/0flU9Xvt2uXdK1Wg0hXc7brT0YwFPFz0TBoYCMHP1UdKyjeWKL4QQtlDqpH3x4sVMmDCBKVOmsGfPHsLCwhg0aBBJSUnXLe/t7c3rr79OZGQk+/fvZ8yYMYwZM4ZVq1aVu/FCCGETa98GYxbU7Qit7ynRJbsTdt90KEZJzVx9lIw8defTe9rVtUqdlV7Hx9SdUrOTYfNH5a6uYF5Bwbr5N/NAx2CaBriRmm3k0yur9QghRGVS6qR95syZjB07ljFjxtCiRQtmz56Ni4sLc+def53dPn36cOedd9K8eXMaNWrEs88+S5s2bdiyZUu5Gy+EEFZ3fi9E/6AeD5p208mnAGczzjJm1Rh6L+5d7sQ99kI6i64M0Zh8Wwu02mo2+bQ4Do7q2u0A279Q18Uvh4JNlmIvxXI59+a7njrotEy6Td1N9bvIOE5czCxXfCGEsLZSJe35+flERUURERFxtQKtloiICCIjb96boSgKa9eu5ciRI/Tq1avYcnl5eaSnpxd5CCGEzSmKOhkSBVrfB8EdS3RZQW9uaK1QDDpDOcIrvPPXISwK3No6kM4NfcpcV5XUdBA07Ksusbl6crmq8nPxo0mtJigo7Liwo0TX9GziR/9m/pgsCu/9FVuu+EIIYW2lStqTk5Mxm80EBAQUOR8QEEBCQkKx16WlpeHm5oajoyNDhgxh1qxZDBgwoNjy06ZNw9PTs/ARHBxcmmYKIUTZHPod4reBgzNETCnxZQXjprvU6VKu8Gtik9h6/BKODlom3mKdzZmqFI0GBk8DjRZil8GpzeWqrlvtbkDJh8gAvDakOQ5aDWsPJ8kSkEKISsUuq8e4u7sTHR3Nrl27ePfdd5kwYQIbNmwotvzEiRNJS0srfJw5c8YezRRC1GTGXFh9ZYfO7s+CZ8nGkpst5sKe3G51upU5fL7Jwrt/qRv8PNajAcHe9p38Wmn4N1c3XQJYNbFcS0De1ug23ur2FuPCxpX4mkZ+boy6sgTkO3/JEpBCiMqjVEsS+Pr6otPpSEwsut10YmIigYGBxV6n1Wpp3Fhdsiw8PJzY2FimTZtGnz59rlveYDBgMJT9FrMQQpTa9s8hNR7c60D3Z0p82aFLh0jPT8dd705Ln5ZlDv9dZBxxl7LxdTPwZHVf4vFm+rwG+5dAwgF1fkG7UWWqppl3M5p5Nyv1dc/2b8Kve89yNDGTH3ed4aEu9csUXwghrKlUPe2Ojo60b9+etWvXFp6zWCysXbuWrl1LvpmIxWIhL886qywIIUS5FVni8U1wdC3xpdvObwOgU+1OOGjLtjTjpcy8whVLXq4JSzzejKsP9HlFPV77NuTad16Tp4ueCQOaAjDz7yOk5cgSkEKIilfq4TETJkxgzpw5zJ8/n9jYWMaNG0dWVhZjxowBYNSoUUycOLGw/LRp01i9ejUnT54kNjaWjz76iO+//56RI0da710IIUR5rHsb8jMhqD20vrdUlxaMly7P0JiP1xwlI1dd4vHu9jVkiceb6TgWvBtBVhJsmVnmapJzkllwaAFf7vuyVNc92KkeTfzduJxtZJYsASmEqARK3Z0zfPhwLl68yOTJk0lISCA8PJyVK1cWTk6Nj49Hq736XSArK4snn3ySs2fP4uzsTLNmzViwYAHDhw+33rsQQoiySjwIe68s8Tj4fdCWri9jYqeJRJ6PpGdQzzKFP3Exkx93qvN23hjSAl1NWeLxZhwcYeA7sOgBiPyfuo57CecZ/FNSdhIf7PoAV70rj7R+BL1WX7LwOi1v3NaCh+fuZH5kHA93C6m58wyEEJWCRlEUpaIbcTPp6el4enqSlpaGh4dHRTdHCFGd/HAvHPsbWtwB931n9/BPfL+bVQcTiWjuz9cPl2yJyRpDUeDbIXB6K4SPgGH/K3UVFsVCn8V9uJx3mfmD59MuoF2prn/omx1sPpbMHeF1+PT+tqWOL4QQN1KaHNcuq8cIIUSldGqTmrBrHaB/yZd4tJbdcSmsOpiIVgOvDC79hMlqT6OBAW+rx9ELISGm1FVoNdrCjZZKs/RjgVcGN0Ojgd+jz3PgbFqprxdCCGuRpF0IUTNZLFc38Gk/BnwalbqKj3Z/xB8n/iDbmF3qaxVF4b3l6gY+93UIpkmAe6nrqBHqtocWwwAF1rxZpiq61lEXSiiYNFwarYI8GRYeBMC0FbFUgZvTQohqSpJ2IUTNdPBXOL8XHN2g9yulvjwhK4FvD37LpK2TMFpKv7rIqoOJ7IlPxUmv5fkrK5WIYvSfrN4NOb4aTm4s9eUFSXtMcgzp+aVfieaFgU1x1GnZduISG2XDJSFEBZGkXQhR85jyYO1U9bj7c+DmV+oqCnZBbenTEk+DZ6muNZotfLjyMABjezYkwMOp1PFrFJ9G0OFR9Xj1ZPUuSSkEugbSwLMBFsXCrgu7Sh2+bi0XHu6mrtX+/orDmC3S2y6EsD9J2oUQNc/uuZB6GtwCoeuTZaqiYHx0QS9uaSzadYaTyVl4uzryeK+GZYpf4/R+GRzd4UK0epeklLrW7opeq+dc5rkyhX+qb2M8nBw4nJDBr3vOlqkOIYQoD0nahRA1S24abPxQPe47sVQbKRWwKBZ2XNgBqMlgaWTmmfh0zVFA3XnT3alkSxDWeK6+0ONZ9XjtW+rdklJ4IuwJtty/hVEty7a7qpeLI09d2al25uqj5BrNZapHCCHKSpJ2IUTNsuUTyEkB31AIL9smb7GXYknJTcHFwYUwv7BSXTtn00mSM/MJ8XHhgU71yhS/xuryFLjXhtR42PVNqS71dvLGRV++ddYf7hZCkJczF9Jymbc1rlx1CSFEaUnSLoSoOdLOwfYra31HvAm6Uu8vB8Dmc5sB6FK7C3pdyXvKkzJymbP5JAAvDWqGo4N8BJeKowv0ubLj9qYPISe1TNWUZeIwgJNex4Qrk4b/t+E4l7Pyy1SPEEKUhfzGEELUHBveA1Mu1OsGobeUuZrzmecB6FG3R6mu+3TNMbLzzYQFe3Fr68Ayx6/RwkeAXzPIuQxbPynVpVGJUdy37D6eWfdMmcMPaxtE89oeZOSa+Gz98TLXI4QQpSVJuxCiZkg8pG7QAzBgqrpxTxlN7T6V9fetZ3DI4BJfc+JiJot2nQHgtVuaoSlH/BpN5wARb6nH279Q756UkIejB7EpsexK2EWuKbds4bUaJt6iboT1XWQcZ1JKv0a/EEKUhSTtQoiaYd3boFig+VAI7lju6nydfXF3LPmGSB/9fQSzRaF/M386N/Qpd/warekgqN9dvWuyYVqJL2vs1ZgAlwDyzHnsSij90o8FejX1o0djX4xmhY9XHy1zPUIIURqStAshqr/47XBkOWh06kY95WCymEp9zb4zqSw/kIBGAy8NDi1XfIF6lyTiTfU4+ge4WLLEWaPR0LNuTwC2nNtSria8fOXv8bfoc8ReKP2GTUIIUVqStAshqjdFgTVvqsdtR4JvkzJXZVEs3PLrLTy26jESshJKGF7hgysbKd3ZNohmgR5lji/+IbgThA5R756sm1riy3oEqfMQypu0t6nrxZDWtVEUmL7qSLnqEkKIkpCkXQhRvR37G+IjwcEJ+rxarqpiU2JJyErgQPIBfJxKNsRly/Fktp24hKNOy/MRTcsVX/xL/0mg0ULsMji7u0SXdKndBQetA/EZ8cSnx5cr/AsDm6LTalh3OImdp1LKVZcQQtyMJO1CiOrLYoY1VyYtdn4CPOqUq7otZ9Xe2c61O5doqUeL5Wov+4gu9Qj2Lt864eJf/JtD2APq8Zo31bsqN+Gqd6Wdfzvg6tKdZdXQz43hHYMB+GDlYZQSxBdCiLKSpF0IUX0dWAJJB8HJE3o8X+7qCoZUFIyLvpm/Dlwg5lw6bgYHxl/ZTVNYWZ+JoDNA3GY4sbZElwxuMJghDYfQxKvsQ6UKPNu/CU56LVGnL7MmNqnc9QkhRHEkaRdCVE+mPFj/rnrc43lwrlWu6tLy0tifvB+AnkE3T9qNZgsf/a2OdR7bsyE+boZyxRfF8AqGTmPV4zVvgsVy00vubXov7/d8n061O5U7fICHE2O6NwBg+qrDmC3S2y6EsA1J2oUQ1dPueep29+61odMT5a5u2/ltWBQLjb0aE+h6842RFu86Q9ylbHxcHXm0Z4Nyxxc30GMCGDwg4QAc/NXu4f/TuxGeznqOJmby296SrxsvhBClIUm7EKL6ycuATdPV496vgGP5x5IXDI0pWH3kRrLzTXy69hgAT/drjJvBodzxxQ24+kC3K7ucrnsbTPk3vURRFI6kHCHyfGS5w3s663myTyMAPl59lFyjudx1CiHEv0nSLoSofiI/h+xk8GkMbR+ySpWdAjvRI6gHvev2vmnZeVvjuJiRR91azjzYub5V4oub6DIOXP3hchzsmX/T4hvPbuSeZffwzvZ3rBL+4W4hBHo4cS41hx92lG9VGiGEuB5J2oUQ1UvmRdg2Sz3u94a67b0V3NH4Dr6I+IIOgR1uWC41O5/ZG08A6pKAjg7yMWsXBjfo/bJ6vPFDyMu8YfEOAR1w0Fhn6UcAJ72O5yLUia2frz9ORq6x3HUKIcQ/yW8TIUT1snkG5GdCnbbQYpjdw/9vwwkyck00C3TnjrAgu8ev0do9DLVCICsJtn9xw6Jujm60DWgLlH/pxwL3tK9LIz9XUrLymbPppFXqFEKIApK0CyGqj8unYdc36nH/Kep291awNn5tiXZAvZCWw7fb4gB1m3ut1jrxRQk5OEK/Serxtv9C1qUbFrfW7qiF4XVaXhoUCsDXW05xMSPPKvUKIQRI0i6EqE7WvwcWIzTsA436WqXKtLw0JmyYwICfB5CUfeN1uD9ZfYx8k4VOId70DfW3SnxRSi3vgsDWkJcOW2besGhB0r4rYRe5plyrhB/UMpCwYC+y8818tu6YVeoUQgiQpF0IUV0kxMD+xepxxJtWqzbyfCQWxUIjz0b4uxSfiB9PymBJ1BkAXrmlGRor9fKLUtJqof+b6vHOryD1TLFFm3g1wd/FnzxzHrsTd1slvEaj4ZXBam/7wp3xxF/Ktkq9QgghSbsQonpY9zagQMs71fHsVlIw3vlmSz3OWHUUiwIDWgTQvn75NnIS5dS4P4T0BHM+bHi/2GIajaZwo6yt57ZaLXy3Rr70auqH0awwc/URq9UrhKjZJGkXQlR9pyPh6ErQ6KDvG1ar1qJYCpO5HnWLT9r3xl9m5cEEtBoKxzSLCqTRqHMaAPYthKTDxRZ9oNkDfDXgK55v/7xVm/DylX8Hv+87z6Hz6VatWwhRM0nSLoSo2hRF3b4eoN0o8G1staoPpxzmUu4lnB2caeffrpjwCh+sVJPCu9rVpWmAu9Xii3II7gjNbgPFcuUuzPWFeofStU5XHHWOVg3fKsiT28PqoCgwfVXxXxqEEKKkJGkXQlRtR1fCme3g4KzufmpFm85uAqBz7c7FJnWbjiWz/WQKjg5anh/Q1KrxRTn1nwwaLRz+E87stHv4FwY0xUGrYf2Ri+w4eeOVbIQQ4mYkaRdCVF0WM6x5Sz3u8h/wqG3V6guS9n7B/a4f3qLwwQq1F3VUl/oEeTlbNb4oJ79QCH9QPV7zpnpX5joSshKYvms6k7ZOsmr4EF9X7u8UDMD7Kw+jFBNfCCFKQpJ2IUTVtf8nuBgLTl7Q/TmrVz97wGw+6PkBfYL7XPf1Pw9c4NCFdNwNDjzZ13rDcoQV9ZkIOgOc3grH11y3iNFi5LtD37HsxDLS8tKsGv6Zfk1w1uvYG5/K6kOJVq1bCFGzSNIuhKiaTHnquuwAPZ4HZy+rh/Bw9ODWhrdSy+na1WDyTRY++ltdGeTxXg3xdrXumGhhJZ51odNY9XjNW2CxXFMk2D2Yxl6NMSvmwrsr1uLv4cQjPUIAmL7qCGaL9LYLIcpGknYhRNW06xtIiwf3OtD5CbuHX7wrntOXsvF1M/BIjwZ2jy9KoecLYPCAxAMQ8/N1i/Srpw6BWn9mvdXDP9G7EV4ueo4lZfLLnrNWr18IUTNI0i6EqHpy02HzDPW4z6ugt+5Y8vT8dB5a/hBz9s/BbDFf83pWnolP1x4H4Jn+jXE1OFg1vrAyF2/o/qx6vO4d9S7NvxTMW9hybgt55mtfLw8PJz1P9VGHT32y+ii5xmv/TQkhxM1I0i6EqHq2fgrZl8CnCYSPsHr1m89uJvpiNH+e/BOdVnfN619vPkVyZh71vF24v2M9q8cXNtBlHLgFQOpp2D33mpdb+LTA38WfHFMOOy7ssHr4h7rWp46nE+fTcpm/Lc7q9Qshqj9J2oUQVUv6BYj8XD2OeBN01u/lLhgiUTBk4p+SM/P4atMJAF4eHIqjg3yMVgmOruqkVICNH0Ju0QmnGo2GvsF9AVgXv87q4Z30OiYMVDdc+nz9cVKz860eQwhRvclvGyFE1bJhGphyILgzNBti9erzzflsPrsZoDCJ+6f/rj1GVr6ZsLqeDGlt3SUmhY21fQh8m0JOinq35l/61euHn7Mf3k7eNgl/Z9sgmgW6k55r4n8bTtgkhhCi+pKkXQhRdSQdhr3fq8cD3la3q7eynQk7yTZl4+fsRyvfVkVeO5WcxcId8QC8ektzNDaIL2xI5wD9p6jHkf+D9PNFXu5Suwtr7l3DM+2esU14rYZXbmkGwLfb4jh7OdsmcYQQ1ZMk7UKIqmPtW+q29M1ug3qdbRKiYGhEn+A+aDVFPyKnrzqMyaLQN9SPro18bBJf2FizIepdGlPO1SVDr9BqtNf8nVtbn6Z+dG3oQ77Jwsy/j9o0lhCieinTp9Pnn39OSEgITk5OdO7cmZ07i98ees6cOfTs2ZNatWpRq1YtIiIiblheCCGu6/Q2OLIcNLqrvaVWZlEsbDizAbh2aMze+MssP5CAVqP2sosqSqNR79IARP+g3r35F7PFTExyjI3Ca5h4q9rb/lv0OQ6dT7dJHCFE9VPqpH3x4sVMmDCBKVOmsGfPHsLCwhg0aBBJSUnXLb9hwwYeeOAB1q9fT2RkJMHBwQwcOJBz586Vu/FCiBpCUWD1ZPW43Sjwa2qTMJnGTML9w/Fz9qNz7as9+YqiMG2Fmtzd3a4uoYHuNokv7KReZ/VujWKBNW8WecloMTL418E88NcDnEw7aZPwbep6cXtYHRQF3l957ZcGIYS4nlIn7TNnzmTs2LGMGTOGFi1aMHv2bFxcXJg799oltAB++OEHnnzyScLDw2nWrBlff/01FouFtWvXlrvxQogaIvYPOLsL9C7quuw24uHowcw+M1l9z2ocdVd3OF13OImdp1IwOGiZMNA2XxiEnUW8qd61OboC4rYWntZr9TTybATA+njrb7RU4KWBoeh1GjYdvciWY8k2iyOEqD5KlbTn5+cTFRVFRETE1Qq0WiIiIoiMjCxRHdnZ2RiNRry9i5+dn5eXR3p6epGHEKKGMhvV7ecBuo4H90Cbh/zn2uwms4X3r/Syj+negNqe1t3ISVQQ3ybqXRtQ7+IoSuFLBUOjbLE7aoF6Pi6M6FwfgGkrYrFYlJtcIYSo6UqVtCcnJ2M2mwkICChyPiAggISEhBLV8corr1CnTp0iif+/TZs2DU9Pz8JHcHBwaZophKhOor6FlBPg4gvdbbOqB8ClnEvXHQ7xy56zHEvKxMtFz7g+jWwWX1SAPhNB7wrndsOh36+eDu4DwP6L+0nOsV0v+NP9GuNucODg+XSW7T9/8wuEEDWaXVePef/991m0aBG//fYbTk5OxZabOHEiaWlphY8zZ87YsZVCiEojLwM2fqAe93kVDLYbS77sxDLuWHoHb2x5o/BcTr6ZmavVFT7G922Mp7PeZvFFBXAPgG7j1eO1U9W7OkCAawCtfFqhoBROTLYFHzcD/7nyRXD6qiPkmcw2iyWEqPpKlbT7+vqi0+lITEwscj4xMZHAwBvfsp4xYwbvv/8+f//9N23atLlhWYPBgIeHR5GHEKIG2vpfyLoI3g2h/Wibhlp3Rl3qsYVPi8Jz32w5SWJ6HnVrOfNQ1/o2jS8qSLenwdVPvZuze17h6YLdcG2xO+o/PdK9AQEeBs5ezuH7yNM2jSWEqNpKlbQ7OjrSvn37IpNICyaVdu3atdjrPvzwQ95++21WrlxJhw4dyt5aIUTNkXYWts1SjyPeBJ3terkv5VwiOikauJqsJWXkFu5a+dKgUAwOuuIuF1WZwf3q5OYN0yDnMnB1XPuOCzvIMmbZLLyzo44XBoQC8OnaY6Rk5dsslhCiaiv18JgJEyYwZ84c5s+fT2xsLOPGjSMrK4sxY8YAMGrUKCZOnFhY/oMPPmDSpEnMnTuXkJAQEhISSEhIIDMz03rvQghR/aydqm6AU68bNB9q01Abz25EQaG5d3MCXdW7hh+tOkp2vpm29bwYGlbHpvFFBWs3GvyaQU4KbJoBQCOvRjzT9hm+GfQNzg62nXx8d/u6tKjtQUauiU/XyIZLQojrK3XSPnz4cGbMmMHkyZMJDw8nOjqalStXFk5OjY+P58KFC4Xlv/jiC/Lz87nnnnuoXbt24WPGjBnWexdCiOrlXBTsX6weD3pX3RDHhgqW9ivoZT90Pp2fotS5NG8MaYHGxvFFBdM5wMB31eMdX8KlE2g0Gsa2GUu4f7jNd0nVaTW8MUTdsGvBjniOJ0mnlhDiWhpFUSr9OlPp6el4enqSlpYm49uFqO4UBebdAvGR0OZ+uOtLm4ZLz0+nz+I+GC1Gfh36K429GjPi6x1sO3GJ29rU5rMH29k0vqhEFtwNx9dA89th+AK7h39s/m7WxCbSr5k/c0d3tHt8IYT9lSbHtevqMUIIcVOHflcTdgdn6D/Z5uHWxa/DaDHS2KsxTWo1YW1sEttOXMLRQcsrg5vZPL6oRAa+o264FLsM4rYAsDdpL5O3TmbT2U02D//arc1w0GpYdziJzccu2jyeEKJqkaRdCFF5mPLUjW5AXZPdM8jmIYc0GMJn/T7j6bZPYzRbeG95LACP9mhAsLeLzeOLSsS/+dVVila9BhYL6+PX89vx31h6fKnNwzf0cytcpejdv2Ixy4ZLQoh/kKRdCFF57JgNqafBLRC6P2uXkHqdnt7BvelXrx8Ltp/mZHIWvm6OPCkbKdVMfV8Dgwdc2Af7F3FLg1sA2HhmI5n5th9r/mz/Jng66zmckMFPu2WPEiHEVZK0CyEqh6zkwpU76D8ZHF3tGj41O59P1hwDYMKAUNydZCOlGsnVF3q9qB6vnUozt2BCPELIt+QXruVvS14ujjzbvwkAH/19hIxco81jCiGqBknahRCVw4ZpkJcOgW0g7AG7hHxp40t8uudTknOSmbXuOGk5RkID3LmvQ127xBeVVOf/gFd9yLiAJvIzbm1wKwDLTy23S/iRXerTwNeV5Mx8vriyV4AQQkjSLoSoeEmHr+5GOeg90Nr+o+lsxllWxq1kbsxcTl/K4rvIOADeuK05Djr5aKzRHAwwYKp6vPVTbvFrD8D289tJyU2xeXhHBy2v3aouAfn1llOcScm2eUwhROUnv5mEEBVLUeDv10ExQ7PboEFPu4RdGbcSgI4BHZm97iJGs0LfUD96NvGzS3xRybW4A+p1BWM2ITu+obl3c8yKmdVxq+0SPqK5P10b+pBvsvD+ysN2iSmEqNwkaRdCVKwjy9W1sbX6q72bdlAw1KGhS3dWH0rEQavh9Ssb3AiBRqPe9UED+xdxa61W1HOvh8HBYKfwGibd1gKtBv7af4FtJ5LtElcIUXlJ0i6EqDjGHFj5qnrc7Wnwsc+KLccvH+fY5WM4aB1YtVPdzXlM9xAa+7vbJb6oIoLaQbuHABgRs4o/7/idYY2H2S18izoejOisLgH55h8HMZotdosthKh8JGkXQlScrZ9Cajx4BF1dscMOCnrZgwxtOX1Rwc/dwDNXVuwQooj+U8DJE31CDJo939o9/AsDm1LLRc/RxEy+izxt9/hCiMpDknYhRMW4HAdbPlaPB75jtyUeFUVhxakVAJw8pSbqr93aTJZ4FNfn6gv9JqnHa98mP/0Ckecj7Rbey8WRl6/szPvJ6qMkZeTaLbYQonKRpF0IUTFWvgamXGjQC1reabewOaYcutTpggFvslOb0TGkFsPCbb/zqqjC2o+BgNbk5aUSsXQIj69+nFNpp+wW/r4OwbSp60lGnon3V8ikVCFqKknahRD2d2w1HPkLtA5wy3R10p+duOhdGOD3FMmxL6LFkbeGtkJjx/iiCtI5wJAZGBRomZUOUHi3xi7htRqm3tEKgF/3nGN3nO2XnRRCVD6StAsh7MuUByteUY87/wf8m9k1vNFsYcofBwEtD3WpT4s6HnaNL6qoel2gzf3cmpUFwIpTy1EUxW7hw4O9GN4hGIDJvx/EbLFfbCFE5SBJuxDCviI/g5QT4BYAvV+xa+iTaSeZtm4Fx5Iy8HZ1ZMKAULvGF1XcgLfoZ9RhsFiISz9NbEqsXcO/PDgUDycHDl1IZ+EOmZQqRE0jSbsQwn7SzsKmGerxgLfByb693F9Fz2PJ+Vcx+K/glcGheLrI5FNRCu6BuPZ+lV456mTQFcd+s2t4HzcDLwxUv2hOX3WES5l5do0vhKhYkrQLIezn7zfAmK3uNNnmPruGNpqNrLqym2V9l3bc2z7YrvFFNdH5CW7VegGw4thSLIp9104f0bkezQLdSc81MePvI3aNLYSoWJK0CyHs48Q6OPgbaLRwq30nnwLMifoTE1lYjO58cOswtFqZfCrKQKenZ8QHuFksJFpyOXTYvr3tDjotbw9TJ6Uu2nWGqNOX7RpfCFFxJGkXQthefhYse0497vQ4BLa2a/hco5mv9/0IQFPXvrSt52PX+KJ6MTSOYKpzE/44e55WGz8Bs8mu8TuGeHNXuyAUBSb+up98k+yUKkRNIEm7EML2NkyD1NPgURf6vWH38NP+3kq+Xl3f+t2Ix+weX1Q/A277igY6N0jYD9s/t3v8N4a0wNvVkaOJmXy58YTd4wsh7E+SdiGEbZ2PhsgrSc2Qj8DgbtfwhxPSWXzkZzQahaYe7Wnh18Cu8UU15eYPg94FwLh+GqTYb7MlAG9XRybf1gKAWeuOc+Jipl3jCyHsT5J2IYTtmE3wx9OgWKDlXRA62L7hLQqv/nIAjfNJAP7TboRd44vqLbFpBC80aMY9AV5Ylj0Ldly3HeCO8Dr0aupHvtnCxF8PYJG124Wo1iRpF0LYzvb/qcMHnLzglg/sHv77yDiiz6TikPAUH3T/nD7BfezeBlF9uTt6sM0BTjrq2XFhO+xbZNf4Go2Gd4e1wlmvY+epFBbvPmPX+EII+5KkXQhhGymnYP176vHAd9ThBHZ0PjWH6avUJfFevqUFtzbuhV4r67IL63HRuzCk0e0ALPFwh1WvQVayXdsQ7O3CCwObAvDe8liS0nPtGl8IYT+StAshrE9R4M/nwZQDIT2h7Ug7h1eYtDSGLFMW7eq7MaJTPbvGFzXHvU3vBWC9iwvJ+amwcqLd2zC6WwitgzzJyDXx5rKDdo8vhLAPSdqFENa3fzGcXA86A9z+qd3XZP9z/wXWHk7C2W8DCZ6v8/uJpXaNL2qOUO9Q2vi1waSBpe7ucOAnOLbarm1w0Gl5/+7W6LQalh9IYPWhRLvGF0LYhyTtQgjrykq+2tvY5xXwaWTX8KnZ+by17CBgws13LxnGNDwcPezaBlGzFPS2/+JbGwvAnxMgz76rubSs48nYng0BmLQ0hoxco13jCyFsT5J2IYR1rXgFclIgoBV0e8bu4d/+M5bkzHzq1j1JriUNP2c/egX3sns7RM0xKGQQ7np3zpqz2e5TD9LiYe1Uu7fjuYgm1PdxISE9l2krDts9vhDCtiRpF0JYz4GfIeZn0Ohg6H9BZ9+JnytjEvhlz1m0GggK3gfAsMbDZAKqsClnB2cea/MYL3V4iRYR6trt7PwSTqy3azuc9Dqm3aXuNrxwRzzrjyTZNb4QwrYkaRdCWEf6efhrgnrc6yUIam/X8EkZubz22wEAHuzuwqHUKDRouKfpPXZth6iZHmn1CKNajsKr+VDoeGXX3d+fgpzLdm1Ht0a+PNJd3UDs5Z/3k5KVb9f4QgjbkaRdCFF+iqImKLlpUKct9HrRzuHVTZRSsvJpUdsDr4A9AHQP6k4dtzp2bYsQDJgK3o0g/Rwsf8nu4V8eHEpjfzcuZuTxxtIDKHbe9EkIYRuStAshym/X13BiHTg4wZ1f2X1YzKJdZ1h3OAlHnZYZ97Zi2ck/gKsTBIWwh3xzPr8f/50J2yZhuXO2OkzswBKI+dWu7XDS6/hkeDgOV1aTWRp9zq7xhRC2IUm7EKJ8ko/B35PU4wFTwa+pXcOfvpTF238eAuClQaG0qFOLeYPmMbb1WHrVlQmown4sioUPdn3A6tOridQaoecL6gt/Pg/pF+zallZBnjzbvwkAk38/yLnUHLvGF0JYnyTtQoiyMxvh18fVTZQa9oGOY+0b3qLwwk/7yM4307mBN4/2UMfyNvRqyDPtnsFB62DX9oiazcnBiaGNhgLwfez30PtlqB0Ouanq8DE7D1MZ16cRbet5kZFr4sWf9mGxyDAZIaoySdqFEGW3+SM4vwecPOGO/4HWvh8pX246we7Tl3EzOPDRfWFYMNs1vhD/NqLZCLQaLVvPbSU29Tjc9ZU6bOzEWtj9jV3b4qDTMvO+cJz1OiJPXmLetji7xhdCWJck7UKIsjkXBRs/VI+HzATPILuGP3g+jY9XHwXgzaEtqVvLhfHrxvPixhc5k3HGrm0RokCwRzCDQwYD8PWBr8EvFCLeUl/8exJcOmHX9jTwdeX1Ic0B+GDlYY4lZtg1vhDCeiRpF0KUXl4m/PoEKGZoeRe0tu+yijn5ZiYs3ofRrDCoZQB3twviYPJBtp7byprTa9Bq5KNNVJxHWz8KwOrTqzmVdgo6PQ4NeoMxG34dCyb7LsM4onM9+oT6kW+y8NziaHKNckdKiKpIfrMJIUpHUeDP5+DSMXCvDUM+snsTJv8ew5HEDHzdDLx3Z2s0Go3aqwnc2uBWgtzs2+svxD81rdWUPsF9UFCYFzNPHTY27H/qMLJzUbBmil3bo9Fo+PDuNtRy0XPwfDrv/HXIrvGFENYhSbsQonR2z1WXsdPo4J554OJt1/A/7TrDkih119P/PhCOj5uBE6knWBO/BrjayylERRrbeizt/NsVDpXBsy4Mm60eb/8fHPrdru3x93Di4+HhaDSwYHs8v8sykEJUOWVK2j///HNCQkJwcnKic+fO7Ny5s9iyBw8e5O677yYkJASNRsMnn3xS1rYKISrauT2w8lX1OOJNqN/VruEPnU9n0u8xALwwMJRujXwBmBszF4B+wf1o5NXIrm0S4nra+LVh/i3z6RbU7erJZrdC92fV46VP2X18e59Qf8b3bQzAxF8PcDxJxrcLUZWUOmlfvHgxEyZMYMqUKezZs4ewsDAGDRpEUlLSdctnZ2fTsGFD3n//fQIDA8vdYCFEBcm5DEseBnM+hA6Bbk/bNXx6rpEnf4giz2Shb6gf43qryfm5zHP8dfIvAB5r/Zhd2yREqfWbDPW6QX4G/DQKjPZdP/25iKZ0a+RDdr6ZcQv2kJ1vsmt8IUTZlTppnzlzJmPHjmXMmDG0aNGC2bNn4+Liwty5c69bvmPHjkyfPp37778fg8FQ7gYLISqAosDSJyE1Hrzqq+NzNRo7hld45ef9xF3KJsjLmZn3haPVqvF/iP0Bs2KmS+0utPZrbbc2CVESl3Mv83n053xz4MpyjzoHuGcuuPpBYgwsf9Gu7dFpNXx6f1v83Q0cS8rk9d9iUOy8frwQomxKlbTn5+cTFRVFRETE1Qq0WiIiIoiMjLRao/Ly8khPTy/yEEJUoG3/hSPLQWeA+74DZy+7hp+3NY4VMQnodRo+H9GOWq6Oha89Ff4UL7R/gXFh4+zaJiFKYk/SHmbvm83XB74mI//KcBSP2nD314AG9i6AvT/YtU1+7gY+e7AdOq2G3/ae48edskSqEFVBqZL25ORkzGYzAQEBRc4HBASQkJBgtUZNmzYNT0/PwkdwcLDV6hZClFLcVlhzZZ3pW96HOuF2DR91+jLvLY8F4PVbmxMe7FXkdVe9K6NbjaZdQDu7tkuIkugb3JdGno3INGay+Mjiqy807AN9X1eP/3oBEmLs2q5ODbx5aVAoAG/+cZCYc2l2jS+EKL1KuXrMxIkTSUtLK3ycOSO9AEJUiMwk+PkRdT32NsOh/Ri7hk/Jymf8wj2YLApD2tTm4W4hha8ZLUa5rS8qPa1GW7ii0feHvifH9I8x7D1fgMYRYMpRx7fn2veu8uM9GxLRPIB8s4VxP0SRlm20a3whROmUKmn39fVFp9ORmJhY5HxiYqJVJ5kaDAY8PDyKPIQQdmbMgUUPQmYC+DWD2z626zj2PJOZJ77fzYW0XBr6uvLB3W3Q/CP+vJh5DP9zONvObbNbm4Qoi8ENBhPkFkRKbgq/Hfvt6gtaLdz5FXgEQcoJ9Quy2X4TQ7VaDR/dG0bdWs6cScnhyYVRGM0Wu8UXQpROqZJ2R0dH2rdvz9q1awvPWSwW1q5dS9eu9l36TQhhQxaLOvH07C5w8oLhC8DR1W7hFUXh1V8OsCvuMu4GB758qD1uBofC1zPzM1lwaAGxKbFczrtst3YJURZ6rZ7RLUcDMO/gPHJNuVdfdPVR/385OMPx1eqSqna8g+Tpouerhzrg4qhj6/FLTFoqE1OFqKxKPTxmwoQJzJkzh/nz5xMbG8u4cePIyspizBj1tvmoUaOYOHFiYfn8/Hyio6OJjo4mPz+fc+fOER0dzfHjx633LoQQ1rXhPTj4K2gd1ITCt4ldw89ad5zf9p5Dp9Xwv5HtaBLgXuT1r/Z/xeW8y4R4hDAoZJBd2yZEWQxrPIwAlwASshL4/tD3RV8Magd3faUe75oDO760a9ta1PFg1gNt0Wpg0a4zzNl80q7xhRAlU+qkffjw4cyYMYPJkycTHh5OdHQ0K1euLJycGh8fz4ULFwrLnz9/nrZt29K2bVsuXLjAjBkzaNu2LY89JuspC1EpRS+ETdPV49v/Cw162jX879HnmLn6KABv39GKnk38irx+Ov0038eqSc9LHV/CQetwTR1CVDZODk680OEFhjYayh2N77i2QIuhEHFlwveqiXBkpV3b1795AG8MaQHAtBWHWRljvcUlhBDWoVGqwH2w9PR0PD09SUtLk/HtQthS3Bb4bhhYjOokuf6T7Rp+d1wKD87ZQb7ZwtieDXj9ShLxT0+vfZoNZzfQI6gHX0R8Ydf2CWFTigLLnoE934HeFR5dBYH223tAURSm/HGQ7yJP46TX8tMTXWlT18tu8YWoiUqT41bK1WOEEBUg+TgsGqEm7C2GQd837Bo+/lI2j38fRb7ZwoAWAbx6S/Nrymw9t5UNZzfgoHHgpY4v2bV9QlhbtjG76AmNBobMhAa9wJgFC4dD+oXrX2wDGo2Gybe1oHdTP3KNFh6dv5vzqfbdsVUIUTxJ2oUQkJ0CC++F3FQI6gB3zlZXtrCTtGwjY77dSUpWPq2CPPj0/nB02mtXqll9ejUADzR/gIaeDe3WPiGsKTErkefXP8+jqx7FovxrtRadXt3AzLcppJ+DH4dDfpbd2uag0/LZg21pFujOxYw8Hvl2F5l59lvRRghRPEnahajp8rPgxwcg5SR41oMHfgS9s93C5xrNPP79bk5czCLQw4lvHu6Ii+P1x6lP6TqFmX1m8p+w/9itfUJYm06rI/JCJDGXYlh2Ytm1BZxrwYM/gYsPXNgHS8aAKd9u7XN30vPN6I74uhk4nJDBuAVR5JnMdosvhLg+SdqFqMmMOfDj/XBmOxg84cHF4OZvt/B5JjOPfx/FjlMpuDrq+GZ0BwI8nIotr9FoGFB/AB6OMrdFVF2+zr480eYJAD7Z8wlZxuv0pHs3gPt/BAcnOLYKfn3Mrmu4B3k5883DHXDW69h8LJnxC/fKGu5CVDBJ2oWoqUx5sPghOLUJHN1g5C8QcO3ET1sxmi2MX7iXTUcv4qzXMW9MJ1rW8bxu2b/j/iY93767RQphSyOaj6Ceez2Sc5KZs3/O9QvV6wzDfwCdIxz6HZaOA4v9erzDgr34+uEOODpoWX0okecWR2OSxF2ICiNJuxA1kdmo7r54fLW6qcuDP0FwR7uFN5ktPLc4mtWHEnF00PL1wx3o1MD7umWPpBzhpU0vcduvt5GSm2K3NgphS446x8LJ1N8d+o4z6WeuX7BJBNz7rbpnwoGfYNmz6uZndtK9sS9fPtQevU7DX/sv8PLP+7FYKv2ic0JUS5K0C1HTWMzw2xNw+E/QGeCBhRDS3X7hLQov/7yfv/ZfQK/T8OXI9nRv7Hvdsoqi8OGuD7EoFjoGdsTb6fqJvRBVUe+6velWpxtGi5EZu2cUX7DZELhrDmi0sPd7WPGyXXdN7Rvqz6wH2qHTavh17zlel11ThagQkrQLUZNYLPD7eIj5BbRXVqlo1M9u4RVF4fWlMfx6ZbfTWQ+0o2+z4sfQr4xbyc6EnRh0BiZ0mGC3dgphDxqNhpc7voxOo+NE2onrj20v0OouGPYFoFF3TV09ya6J++BWgXw8PBytBn7cGc9byw5J4i6EnclWgkLUFBYLLH8B9i0EjQ7umQuhg+0WXlEU3lp2iB93xqPVwMfDwxncKrDY8uczz/N25NsAPNrqUYLcguzVVCHsppFXIz7s9SE9gnrgone5ceGw+8GUqw6R2TZLnaTa93V1fXc7GBpWh3yThReX7OPbbXEY9FpeHdwMjZ3iC1HTSU+7EDWB2ahOYts9F9DAnV+q26bbicls4dVfDvDttjgAPrwnjKFhdYovbzHx6uZXyTBm0MavDY+1ecxOLRXC/gaGDLx5wl6g/Wi45UP1eNN0WPWaXce439O+Lu8MawXAlxtPMuWPg5hljLsQdiFJuxDVXcE67PsXqT3sw76ANvfaLXxOvpn/LNjD4t1n0Grgg7tbc0/7uje85ofYH9ibtBdXvSvv93wfvVZvp9YKUXEsioXvD33PwtiFNy7Y+QkYNE093v4/+HWsXddxH9mlPlPvaIlGA99FnubpH/eQa5R13IWwNRkeI0R1lnVJ3en0XJS6Ssx986HpILuFT83O59H5u4k6fRmDg5b/PtCWQS2LHxJT4O4mdxObEkvPoJ4EuwfboaVCVLwNZzbw4a4P0Wv1tAtoRzPvZsUX7vokuPqqd9BifobsZBi+AAzudmnrqK4heLs68vziaJYfSCAlaydfjeqAh5N8wRbCVjRKFZhJkp6ejqenJ2lpaXh4yKYqQpTI5dOw4C64dPzKDotL7Lqs4/nUHB6eu5NjSZl4ODnwzeiOdAyR1V+EKI6iKDyz/hk2nNlAA88GLBqy6ObDZo6vgcWjwJgFtcNhxBK7bpC27Xgyj38fRWaeiea1PZg/piP+N9ggTQhRVGlyXBkeI0R1lBAD3wxUE3bPYHhklV0T9qOJGdz9xTaOJWUS6OHEkv90u2nCrigKW85tkRUpRI2l0WiY2m0q/s7+nEo7xfTd029+UeMIGL0MXHzgQrT6/z7lpM3bWqBbY18WPd4FXzcDsRfSueuLbZy8mGm3+ELUJJK0C1HdnNwI826BzATwbwGP/g1+oXYLv+PkJe6dHcmFtFwa+bnyy5PdCA28+S37pceXMm7NOF7Y+IIk7qLGquVUi3d7vosGDT8f/Zk1p9fc/KKg9vDoavCqD5dPqYn7uSjbN/aKVkGe/DquGyE+Lpy9nMM9syOJOn3ZbvGFqCkkaReiulAU2PIJfD8M8tKhXjcYsxw8il+lxbrhFb7efJIHv95BWo6RdvW8+Pk/3Qjycr7ptXFpcUzbqU6sa+HTQpaQEzVal9pdGNNqDABTtk0hISvh5hf5NFIT98DWkHUR5g6G3fPstpZ7PR8Xfh7XjdZBnqRk5XP/V5F8FxknX8CFsCJJ2oWoDnLTYPFIWDMFFAuEPQAP/aqOZbeDzDwT4xfu5Z2/YjFbFO4Ir8MPj3WhlqvjTa9Nz09nwsYJ5Jhy6BzYmUdaPWKHFgtRuY1vO55WPq3INmVzPPV4yS5yD4DRyyF0CJjz4c/n4PenwJhj07YW8HUz8OPjXbilVSBGs8Lk3w8y4ad9ZOeb7BJfiOpOJqIKUdUlHlIT9pQToHOEWz6A9mPstuHK8aQMnvg+ihMXs3DQaph0WwtGda1fot7yHFMO/1n9H/Yk7cHX2ZdFQxYR4Bpgh1YLUfnFp8dzNuMs3YK6le5CiwW2fgLr3la/xAe2hvu+B+8GNmnnv6l33U7x/srDmC0KzQLd+WJkexr4utolvhBVSWlyXEnahajK9v+k7o5ozAaPujD8O3V8q538uf88L/+8n+x8MwEeBv43oj3t65esd99oMfLc+ufYdHYT7np35g2eR6i3/cbeC1HVXMq5RC2nWmg1JbxJfnID/PyouhykkyfcNceuS77uOHmJpxbuJTkzD3eDAzPuCyvRkq9C1CSyeowQ1V1+Nvz1grqpijEbGvaFJzbZLWHPNZp584+DjF+4l+x8M10b+vDXMz1LnLADHEk5wvbz2zHoDHzW/zNJ2IW4gVNpp3jgrweYtmNayceJN+yjfi7U7agOoVt4H6ydareNmDo39OGvZ3rQoX4tMvJMPPF9FNOWx5Jnko2YhCgL6WkXoqqJ26qOU718Sn3e6yXoMxG0OruE3x2Xwss/7+dkchYA/+ndiBcHNsVBV/o+gN0Ju8k2ZdOrbi9rN1OIauXvuL95ceOLKCiMCxvHk+FPlvxiUz6seg12zVGfB7SCOz6HOuE2aeu/Gc0Wpi0/zNyt6mdWE383pt8bRniwl13iC1GZyfAYIaqjvExY+xbs/Ep97hEEt/8XmkTYJXxOvpnpq44wb9spFAX83Q1Mu6s1/ZuXbgx6Zn4mbo5uNmqlENXX4sOLeWfHOwC82ulVRjQfUboKDv6m3qHLvgQaHfR4Hnq/DA4GG7T2WitjEnhj6QGSM/PRamBsr4Y8H9EUJ719OhyEqIwkaReiujm5Ef54GlJPq8/bjYKB76jjVO1gx8lLvPzLfk5fygbgnvZ1mTSkBZ4upduy/KcjP/Hlvi+ZPWA2TWo1sUVThajWvtj3Bf+L/h8A03pO47aGt5WugqxkWP6imsAD+DVXe93r2mdo3eWsfN5cdpDfo88D0NDPlen3hJVqaJ0Q1Ykk7UJUFzmpau/67rnqc89gGPpfaNTPLuEzco3MWHWE+ZHql4Xank68d1dr+oaWbpt0RVH49uC3fBz1MQoKT7d9msfbPG6LJgtRrSmKwvs732fh4YXoNDomdprI8GbDS1/Rod/VXvesi6DRQrenofcr4GifFV5WH0rktd8OcDEjD40GHu3egOcHNMXV4GCX+EJUFpK0C1HVmfIhah5seB9yUtRzHR6FAW+B4ea7i5aX0Wxh0c54PllzjEtZ6qS1+zsG89qQ5ng4la53Pd+cz1uRb/HHiT8AGNF8BK90fEU2UBKijCyKhSnbprD0+FLC/cKZN3geDtoyJLvZKbDiZTiwRH3uXhv6vg7hD9pljkxqdj5T/zzEr3vOAeDnbmDCgKbc275umebICFEVSdIuRFWlKHD4T1g9RV13HcCvGdw6HRrYfrKmoiisiU1i2opYTl5UJ5o29HPlraEt6dnEr9T1Jeck8/z654m+GI1Wo+Xlji/zYLMHJWEXopwURWHh4YUMChmEr7Nv+So7vBxWvnp1+F1AKxj4tt3u6K0/nMSbyw4WDr9rGuDGxFub06epn3xWiGpPknYhqqKzUfD36xAfqT539VN7vdo+BDrb3zI+cDaNd5cfYvtJtWff29WR5yOacH+neujL0Ot1JuMMj656lAtZF3DXuzOj94zSbxIjhCix7w5+R8+6PWngWYZNlEx56iT3TdPV5SEBGkfAgLchoIV1G3od+SYLC7af5r/rjpGabQSgR2NfXru1OS3qyO99UX1J0i5EVXIuCrZ8ArHq8BEcnKHbeOj+rF2Gwhw4m8bsTSf4a/8FAAwOWh7t0YD/9GlU6qEw/5Rvzmfs32O5lHuJWf1mlS2REEKUyMpTK3lp00u4O175glynjF+Qs1PUxH3nHLAY1fHure+D7s9AQEvrNvo60rKNfL7hON9ujSPfbEGjgaFhdXiiVyNJ3kW1JEm7EJWdosDxNbD1U4jbfOWkRh1L2vd18AyycXiFzceS+XLTCbYev1R4/q62QbwwKJQgL+cy1ZtjysGiWHDVq5PZUnJT0Gl0eBrss8qNEDXVP4ei6TQ6Hm/zOI+1fgxHnWPZKrx0Qp0Ef+j3q+eaDFQ7E+p3BxsPWzmTks2Hq46wbN/5wnO9mvrxn14N6drIR4bNiGpDknYhKiuzEWJ+ga3/haSD6jmtg9qT1e1pm9+GNpkt/HXgArM3niT2QjoAOq2GoWF1eLxXQ5rXLvv/r01nN/HejvfoGdST17u8bq0mCyFKKN+cz9TIqfx+Qk20QzxCeKPLG3Su3bnslZ7bo3YuxP4BikU9F9ReTd6b3WbzCasx59L4ctNJ/tp/HsuVbKV1kCdP9G7I4JaBMmFVVHmStAtR2aSchOiF6iNdXSkBRzdoPxq6jAPPujYNfyYlm5+jzvJz1FnOpeYA4OKo4/6O9XikRwh1a7mUue6ErAQ+2PkBa+LXABDkFsSvQ3/FRV/2OoUQZaMoCqviVvHBrg9IzkkG4JFWj/B8++fLV/GlExD5OUT/AKZc9VytEGg7EsIesMtn2NebT7J49xlyjeqXh7q1nLmvQzB3tQsq12eYEBVJknYhKoO8TDi0VE3UT2+9et7VX03UOzwCzl42C5+db2LFgQSWRJ0pnFwK4OPqyJjuIYzsUh8vlzLeOgdMFhOLDi9i1t5ZZJuy0Wl0jGoxiv+E/UcSdiEqWEZ+BrP2zmLR4UV81v8zetW10upTmRfVCas7v4Lc1CsnNdCoL4SPgGZDQF+24XUlkZKVz3eRcczfFsflKxNWNRro1siHe9sHM6hlIM6OssOqqDokaReiopjy1DHqMb/CwaVgzLrygkZdPq3tCAgdAnonm4TPN1nYfvISf+4/z1/7L5CVb1aja9SVGO5pX5dBLQPLvW34idQTvLjxRY6nHgcgzC+MSV0mEeodWu73IISwntPpp6nvUb/w+U9HfsLT4En/ev3LtrZ7gfwsdbz73h/g9Jar5w2e0Oou9VGvK+jKPpn9RnLyzayIucDPUWfZduLqvBx3gwO3hdXmtjZ16NTAu0wrXwlhT5K0C2FP2SlwbDUc+QuOr4X8zKuveTdSE/U299tscmlatpENR5P4+1AiG49cJDPPVPhafR8X7mlXl7va1y3z5NICiqIUTv7KzM9kwM8D0Gg0PN/+ee5ucjdajfxyFKIyyzJmMWDJADKMGQS5BfFQi4e4s/Gd5b8zlnIK9v2o3lVMO3P1vJOXOnk19BZ1+Ugn2/z+PpOSzS971OF/Zy/nFJ53d3Kgb6g/ES0C6BPqV67VsISwFUnahbAlswkS9kHcVjj2N5zeBor56utugeovqbD7Ibiz1VdZMFsUDp1PZ8epS6w7nMTOUymYLFf/G/u6GRjQwp8729alY0itcq+ycCHzAgtiFxCbEss3A78prG/7he00924uK8MIUUVk5mcy/9B8Fh1eRGpeKgDuju4MDx3Og80exM+l9BuoFWGxQNwm2P8THF0J2Vd7wNHqoUFPaDIIQrqDf0vQWveLvsWisONUCr/tPcva2KTC3ZwBHLQaujT0oW8zfzo38KZ5bQ90WlmBRlQ8SdqFsCZTPlyIhrgt6tj0+B2Qn1G0jH9LaHarmqzXbmvVX0ZGs4UD59LYeSqFHScvsTvuMhn/6E0HdQfBiOYBDGgRQFhdL7Tl/GWUlJ3E2vi1rD29lt2JuzFf+VIyf/B82gW0K1fdQoiKlWPK4Y/jf/Ddoe+Iz4gHwEHjwLSe0xjcYLB1gljMcGYnHFmuPi4dL/q6kyfU66Ym8PW7Q2Abq24iZ7YoRJ+5zOpDSayJTeR4UmaR192dHOgU4k3nht50buBDyzoeshKNqBCStAtRVqZ8uHgYLuy7+kg4AKacouUKfuE07K0m6rVCrBLeaLZwLDGTmPNpHDyXxsHz6Rw8n06O0VyknLvBgY4NvOnWyIcBLQKo7+NqlfjbL2zn872fE30xusj5ToGdGN1yNN2DusswGCGqCbPFzIazG5h/cD57k/by151/Uc+jHgCR5yM5mXaS/vX6E+gaWP5gycfU5P3kRjizo+gwQlBX0wpsA7XDrj58m1otkT+VnMWaQ4lsPZHM7rjLRYYRgrqaVss6HrSs40mrIE9aBXnQ2M9NEnlhc5K0C3Ezpjx1HOalY5B8FJKPQ9Ih9WHOv7a8szfU7wYhPdReoYCW5VqfON9kIT4lixMXszhxMZOTF7M4mpjB4QsZ5Jst15T3ctFf6RXyscqtXYti4WTqSfZd3EfTWk1p7dcaUJP2sX+PBaCNXxsG1BtA//r9CXYPLnMsIUTldybjTJH/58+ue5Z1Z9YB0NirMWF+YYT5hRHuH06IR0j5ht39c4jh6a1wOhLy0q4t5+AEAa3Avzn4NgGfJuqftULKNcHVZLZw6EI6O06msONUCrviUkjLMV5TzuCgpVltD0ID3Gjo50ZDX1ca+rlR38dFJrgKq5GkXQizCTLOQ9rZK48z6p+pZ9TbtKmnr24U8m8GT6hd0OMTrv7p07hUQ15MZguJGXmcT83hfGoO5wr+vJzDqeQszlzOwWy5/n89d4MDLYM8aPWPHp+Gvm5lHvJitBg5fvk4celxnEw7yYHkA+xP2k+GUR3iM7L5SF7p9Eph2V+O/kLf4L4EuAaUKZ4QoupbfHgxy08tZ2/SXhSKflb5Ovuy+p7VhavPXMi8QC2nWjg5lHFVLIv5yh3O/f+4w7n/2t74AloHNXH3bgReweoa8Z7BVx51wT2wVJ0qFovC8YuZxJxLI+ZcOjHn0zh0Pv2a3vgCOq2Get4uNPB1JcjLmTpeztTxcio89nc3SA+9KDGbJ+2ff/4506dPJyEhgbCwMGbNmkWnTp2KLb9kyRImTZpEXFwcTZo04YMPPuDWW28tcTxJ2gWmPMhJVdcFzrl85ZEKWRchK0ldO7jgz8xEyE4uPikv4OgOvo2v9t74NlUT9Foh10wezTdZSMsxkpaTT2q2kbQcI6nZRlKy8knOzONiZh4XM/JIzlSfX8rMo5icvJCro07tvfFzpaGvG4393WgV5EFwLZdSJehZxiySspO4mH2RpBz1z2D3YCLqRwBwOfcyvRZfu0azs4MzrXxbMThkMPeF3lfieEKImiMlN4XopGj2XdxHdFI0By8dJLRWKD8M+aGwzLClwziZdpLarrUJ8QwhxCOE2q618XPxI8gtiHD/8NIHtljUTekuRKtDay4du/LniX8spVsMjQ5c/cDND9wC1L0x3PzUP119wbmWurKNc60rD69reu4tFoX4lGxizqdxPEm9G3oyWf0zO9983bAFdFoNPq6O+LoZ8HU34OvmiJ+bAT93A96ujng66/Fy0ePprB57OutxdJAkv6ayadK+ePFiRo0axezZs+ncuTOffPIJS5Ys4ciRI/j7+19Tftu2bfTq1Ytp06Zx2223sXDhQj744AP27NlDq1atrP6GhA1ZLGAxqSulWExq74jFpA4nMRuvHBuvPjfnqcm2Ob/on6YcMP77ka2u+5ufqW5KlJ+h/pmXoZ4zZpe+uVo9eS61yXWpQ7ZzIJlOtckwBJBiCOaiIZgUapFjspBjNJNrNJOVZyYrz0RmnomsfBNZeWYy80xk5pquGVNeEnqdhtqeag9MHS9ngjydCPQyEFRLT11vR7xctDhoHfBy8lLbq1iISowix5RT5JFtzCYjP4P6HvW5s8mdgLqx0dClQ7mUc4ls07U/m55BPflfxP8Kn9/+2+3UcqpFiEcIzbybEe4fTtNaTcu3TrMQosYxmo1cyr1UOM7doljov6R/4e6r/9bSpyWLbltU+Hz0ytHkmnLxcPTA0+CJh6MHHgYP3B3dqeNWh8EhVyfCxiTHoEGDQWdAr9PjqHVEr9XjmHUJQ1o8htQzkHbu6p3UtDOQfl79XVRaelcwuIHBXR1fX/inGzi6goMz6J1R9M5kmB25mKslKUfDpTy4mKWQkK2QmK1wIdNCjsUBIw4Y0WFCh1FRn5uuPDejLfzTjBYFLS6OOlwNDrgZHHA16HArPHbAxVGHk16Hc8HjynMnvQ5HBy2OOi0GB616fOW5g05z5U8tDloNjg7qnw46LTqtBgetBp1Wg06jKffCBaJ8bJq0d+7cmY4dO/LZZ58BYLFYCA4O5umnn+bVV1+9pvzw4cPJysrizz//LDzXpUsXwsPDmT179nVj5OXlkZeXV+QNBQcHV0jSHjn/NbamrmK787UfAgX/zJ+/ZMDHon5LXuVqZLNL8R8YT6foCTSrZde5mFjrer1kUP0rGZfiQD2TWnazi5kVbuZryhQcjk3V0DRfbVOks8Kv7ldf1/zrmrGpJlrnqR8VO520LPB0+EdZ5R/XKDxxOYOuublosRDl5MisWsUv7/doajq9c9TtrfcZHPnI26vYsiPTMhiYrU7uPOKo512fWsWWvTc9k9uzsrEoGg7o3XjX1xMTWswFH4joCj8QPdKaQGp7khRPLuktONVZXLQyzdWfizEtDOPlHuppXQbOwfMLf0ZXy6l/mtJbY0zph4eTHncXI9k+H6PVglYDWq2CVqOgufLoGtiXFzu8gq+bgTxzDr0W98JsMWNSrv13MShkEDN6zwDUSWHh34cX+3P4dyLe6YdO5FyZIOumd8PPxQ9/Z3/8XPxo5t2Mh1s+XGxdQghhLYqicDnvMnFpcZxKO8XpjNOFd/8aeDbgjS5vFJbt/EPn63Y0gDqP5odbr/bg91/Sn6TspOuWbVqrKb8M/aXw+V1/3MX5zPPoNDoc0KABdIqCFoV6Ole+8Wiv3o3NvsQzpjOcxojWYgbFjFZRf+dpAB+zmdmJFwvrneTrzXFHtRf+H78+0ACuioWvEq6Wfc+7FocMjoWv/5ODojAv4ep7mVnLi2gntaxS+BtXU/ib/bPz6YAWCxrm1nImyrng9/SVMlcKKmh464IRg6JBQcPPXlp2u1zttf93JvBiArhb1LLLPRV2uP7rTf3j4JkkB7zN6k9mjYeZrdfNV9Sy4y7pCTRp0QAb3Eysu25Z1WOXDYW5zVZnE6vcr51PUODhywYaGdWhTrucTCzzuM6csytGpBlolq+WjTaY+OUGZe9Nd6RNnvozPeRo5rzeQseAO+nywOvFXmMrpUnaS9XNlp+fT1RUFBMnTiw8p9VqiYiIIDIy8rrXREZGMmHChCLnBg0axNKlS4uNM23aNN56663SNM1mdJdPka+9xBGDe7Flgs0nCDapCdlyjSeHb7BudaA5jqZG9R/oOo0Hhw1exZb1Uc7Q2KT+o9uKO7GG4hNbdyWB+mb1i852jRuHnLyvU0r9z6UjDX+LmuyZtS4ccPIttt5MnYID6n++VK2WvU7Fj1k8qzOSojhgwoE4jeMNywZm1CbZ5EMujpx0yGev0/Fiyx5O78/ruX3JwAWN5jyuzp9decV85XFVWp4XBrdQ9FoNQYaLpLrEF1tvE49WtGsRgrNeh1mTwsKEs8WWvatFN97qfis6rYbU3FR6Lv7HF9R/jcJx0OcS4KG+dwfFgTxzHsWx/GMIj06rI7RWKDqtDmcHZ5wcnHBxcMHZwRl3x/+3d7exTdV7HMC/5/RpZc8b0q7bugccDMau7DLhbtNLrpBLCGK8URGiY9FXvoIBThZ0GKPAHQmKDzgyo9FcJcYXwhUTJbgQAZXxMIYX1A3CGGNzD8BYy5Ztbc//vjhdpdA96dZT7PeTNF1Pf+u+2zlrf/33nP+Jxsx4/7ONfrDkA0QZojBtyrQ/fnIUIqLfSZIkJEQkICEiYdQpYasWV8Ex6EDPQA8cgw71MuCAc9B5xwHvlikWSJAw6BnEoDKIQc8gXIr6+mmQ/Xdn6XP1oXeY3WbMU6YCS//tu93y33/h4o0LgE4HwH/fd4spHli0y/cp78UL/8HZ/sBvHGIgA+nZ3k+R+3FR34Mz+sC7ZRpvGx9tMuhHfI2Mkfp8yboMRpwboTZV7kSU9/F7jQn4xRw1bO103RXc433R2m+IR6M5UG+jPlam1IxUqL1NjS4WDRGBehu1NkVcwkzvujksx6DB+wlyIFbRhNne3uaEFI2GEXqbe8QlzHarr6FnpSg0mAL1Nqo4cRmzXGpvc8E0BQ2m4XubaHEFs7yf4LcazGiVjEB387D1oWJcI+1tbW1ITk7G999/j4KCAt/yF154Ad9++y1qa2vv+B6j0YiPPvoIq1at8i1799138corr6CjoyPgzwmlkfbz9Udx9soxdHkCHNnuNceYjghZfcd8xdWFdk/3sLWzTekwy+o/X5vrKtrc1wMXShKyTWmIlNVmrMNzHVdcnYD027vyW9/LZ5nSEKOLBiSg092NlsFfAe/UfMI7hiAk9Xp6RAbiDLEQkHHdfQOXBlvU+yEBsvpRnSSp9enmLCSYpkLIenS7b6Cp76K3Rqfu9y2r1xIk2KNm4J4I9SPTHtd1NDnPAQBk7/7hkuS9QEJa1L1IikyBJAE3XT345UY9JEn9qE6S1O+R1WJkxmYiLSYdellGr9uJM1dP+er0koxbZyDMiMlAZlwmAHVf79pff9smJQzlUK9TolJwb/y9AIB+dz+Otx/31Une32notjXS6ntcl+LCmc4z3rw6v2sZMuJMcUiKSlL/9kKgvbcdOlkHWZKhl/S+j3n1sv4Pn/iIiCicCCHgVtxwCzfM+t/O8tze2w6XxwW3cMOtuKEIRb1AgUE2YEb8DF/tuavn0OfugxACChQIIdQLBIw6I+633u+rPd15Gs5BJ25tlYYOzNVJOjyY8qBfbXd/9x0H7gKADBn/SFno28W0vvM0rvV1AUKou5oKj/c4LAEoCh6y3K+OqSse/K+7ER0D19TaoRoB39cLE/8Cg6QDhIJzzkv4td9b6007NDSvCKAgdiZMkh4eATQ4r6Cl/yoUCAhFgSK8PwLq3+OvkdNhghFCCDQNdKB18Jr3b6U+siIEhpr2XHM6piACAkDLYCdaXdeGfjpu7zKzjamI1k0BINDmuo4Wd9edRd6bWYZkxOrUKY073TdwyRX4DRQAZBltiNNFQQiBqx4Hmlztw9ZmGqxI1Kn95HWPE33KAOZkFCEjZ8Gw3zNZJm2kPVhMJhNMJpPWMQAAWXMfQNbcB8ZcP57Tzswbf5wQUDTGuqkAZoxapYrF32AfU2UCEpEa+88x1UYaIvGQ/aEx1UboI/D3lDsP1gzEIBuQb80fU60kSb4GnoiI/hhJkmDQGWCA/0j7eOaSz5maM+bavGl5E1vrHeCbm1w45sfNtcxG7hhrc1CEsf52c72XsRjPpL8zRy/xGduRjTRkXIcrT506FTqd7o4R8o6ODlitgf9hrFbruOqJiIiIiMjfuJp2o9GIefPmoaamxrdMURTU1NT47S5zq4KCAr96ADh48OCw9URERERE5G/cu8esX78eJSUlyM/Px/z587Fz50709vbimWeeAQCsXr0aycnJ2LZtGwBg7dq1WLhwIXbs2IFly5bh008/xcmTJ1FdXT2xvwkRERER0Z/UuJv2J598El1dXdi8eTPa29sxd+5cfP3117BY1LMnXr58GfItZ44sLCzEnj178NJLL2HTpk3IysrCvn37xjxHOxERERFRuPtdZ0QNNp5ciYiIiIj+bMbT4/K8uUREREREIY5NOxERERFRiGPTTkREREQU4ti0ExERERGFODbtREREREQhbtxTPmphaIIbh8OhcRIiIiIiookx1NuOZTLHu6JpdzqdAIDU1FSNkxARERERTSyn04nY2NgRa+6KedoVRUFbWxuio6MhSZLWccKKw+FAamoqWlpaOEd+mOI2EN64/sMb13944/qffEIIOJ1O2Gw2v5OTBnJXjLTLsoyUlBStY4S1mJgY/sOGOW4D4Y3rP7xx/Yc3rv/JNdoI+xAeiEpEREREFOLYtBMRERERhTg27TQik8mEl19+GSaTSesopBFuA+GN6z+8cf2HN67/0HJXHIhKRERERBTOONJORERERBTi2LQTEREREYU4Nu1ERERERCGOTTsRERERUYhj005EREREFOLYtNOwWltb8fTTTyMxMRFmsxm5ubk4efKk1rEoCDweDyoqKpCRkQGz2Yzp06fj1VdfBSeb+nM6fPgwli9fDpvNBkmSsG/fPr/7hRDYvHkzkpKSYDabsXjxYpw/f16bsDQpRtoGXC4XNm7ciNzcXERGRsJms2H16tVoa2vTLjBNqNGeA2713HPPQZIk7Ny5M2j5SMWmnQLq7u5GUVERDAYDvvrqK/z000/YsWMH4uPjtY5GQVBZWYmqqiq88847+Pnnn1FZWYnt27fj7bff1joaTYLe3l7cd9992LVrV8D7t2/fjrfeegu7d+9GbW0tIiMjsWTJEvT39wc5KU2WkbaBvr4+1NXVoaKiAnV1dfj888/R0NCARx55RIOkNBlGew4YsnfvXhw7dgw2my1IyehWnKedAiovL8d3332HI0eOaB2FNPDwww/DYrHg/fff9y177LHHYDab8fHHH2uYjCabJEnYu3cvHn30UQDqKLvNZsOGDRvw/PPPAwB6enpgsVjw4YcfYuXKlRqmpclw+zYQyIkTJzB//nw0NzfDbrcHLxxNuuHWf2trKxYsWIADBw5g2bJlKC0tRWlpqSYZwxVH2imgL774Avn5+XjiiScwbdo05OXl4b333tM6FgVJYWEhampq0NjYCAA4c+YMjh49iqVLl2qcjIKtqakJ7e3tWLx4sW9ZbGwsFixYgB9++EHDZKSlnp4eSJKEuLg4raNQECiKguLiYpSVlSEnJ0frOGFLr3UACk0XL15EVVUV1q9fj02bNuHEiRNYs2YNjEYjSkpKtI5Hk6y8vBwOhwPZ2dnQ6XTweDzYsmULnnrqKa2jUZC1t7cDACwWi99yi8Xiu4/CS39/PzZu3IhVq1YhJiZG6zgUBJWVldDr9VizZo3WUcIam3YKSFEU5OfnY+vWrQCAvLw8nD17Frt372bTHgY+++wzfPLJJ9izZw9ycnJQX1+P0tJS2Gw2rn+iMOZyubBixQoIIVBVVaV1HAqCU6dO4c0330RdXR0kSdI6Tljj7jEUUFJSEmbPnu23bNasWbh8+bJGiSiYysrKUF5ejpUrVyI3NxfFxcVYt24dtm3bpnU0CjKr1QoA6Ojo8Fve0dHhu4/Cw1DD3tzcjIMHD3KUPUwcOXIEnZ2dsNvt0Ov10Ov1aG5uxoYNG5Cenq51vLDCpp0CKioqQkNDg9+yxsZGpKWlaZSIgqmvrw+y7P/0oNPpoCiKRolIKxkZGbBaraipqfEtczgcqK2tRUFBgYbJKJiGGvbz58/jm2++QWJiotaRKEiKi4vx448/or6+3nex2WwoKyvDgQMHtI4XVrh7DAW0bt06FBYWYuvWrVixYgWOHz+O6upqVFdXax2NgmD58uXYsmUL7HY7cnJycPr0abz++ut49tlntY5Gk+DmzZu4cOGC73ZTUxPq6+uRkJAAu92O0tJSvPbaa8jKykJGRgYqKipgs9lGnF2E7i4jbQNJSUl4/PHHUVdXhy+//BIej8d3PENCQgKMRqNWsWmCjPYccPubNIPBAKvVipkzZwY7angTRMPYv3+/mDNnjjCZTCI7O1tUV1drHYmCxOFwiLVr1wq73S4iIiJEZmamePHFF8XAwIDW0WgSHDp0SAC441JSUiKEEEJRFFFRUSEsFoswmUxi0aJFoqGhQdvQNKFG2gaampoC3gdAHDp0SOvoNAFGew64XVpamnjjjTeCmpGE4DztREREREQhjvu0ExERERGFODbtREREREQhjk07EREREVGIY9NORERERBTi2LQTEREREYU4Nu1ERERERCGOTTsRERERUYhj005EREREFOLYtBMRERERhTg27UREREREIY5NOxERERFRiPs/pLT6Ss1x6OkAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_products(g1, g2): \n", + " plt.figure()\n", + " product = gaussian_multiply(g1, g2)\n", + "\n", + " xs = np.arange(5, 15, 0.1)\n", + " ys = [stats.gaussian(x, g1.mean, g1.var) for x in xs]\n", + " plt.plot(xs, ys, label='$\\mathcal{N}$' + f'$({g1.mean},{g1.var})$')\n", + "\n", + " ys = [stats.gaussian(x, g2.mean, g2.var) for x in xs]\n", + " plt.plot(xs, ys, label='$\\mathcal{N}$' + '$({g2.mean},{ge.var})$')\n", + "\n", + " ys = [stats.gaussian(x, product.mean, product.var) for x in xs]\n", + " plt.plot(xs, ys, label='product', ls='--')\n", + " plt.legend();\n", + " plt.show()\n", + " \n", + "z1 = gaussian(10.2, 1)\n", + "z2 = gaussian(9.7, 1)\n", + " \n", + "plot_products(z1, z2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b15c19b2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "prior, z = gaussian(8.5, 1.5), gaussian(10.2, 0.5)\n", + "plot_products(prior, z)\n", + "\n", + "prior, z = gaussian(8.5, 0.5), gaussian(10.2, 1.5)\n", + "plot_products(prior, z)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "651ae03e", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "24ad017f78f24c47af5617910689d188", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=7.5, description='m1', max=10.0, min=5.0, step=0.5), FloatSlider(value…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from ipywidgets import interact\n", + "\n", + "def interactive_gaussian(m1, m2, v1, v2):\n", + " g1 = gaussian(m1, v1)\n", + " g2 = gaussian(m2, v2)\n", + " plot_products(g1, g2)\n", + " \n", + "interact(interactive_gaussian,\n", + " m1=(5, 10., .5), m2=(10, 15, .5), \n", + " v1=(.1, 2, .1), v2=(.1, 2, .1));" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "1bc6e653", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "PREDICT\t\t\tUPDATE\n", + " x var\t\t z\t x var\n", + " 1.000 401.000\t1.354\t 1.352 1.990\n", + " 2.352 2.990\t1.882\t 2.070 1.198\n", + " 3.070 2.198\t4.341\t 3.736 1.047\n", + " 4.736 2.047\t7.156\t 5.960 1.012\n", + " 6.960 2.012\t6.939\t 6.949 1.003\n", + " 7.949 2.003\t6.844\t 7.396 1.001\n", + " 8.396 2.001\t9.847\t 9.122 1.000\n", + " 10.122 2.000\t12.553\t 11.338 1.000\n", + " 12.338 2.000\t16.273\t 14.305 1.000\n", + " 15.305 2.000\t14.800\t 15.053 1.000\n", + "\n", + "final estimate: 15.053\n", + "actual final position: 14.838\n" + ] + } + ], + "source": [ + "import kf_book.kf_internal as kf_internal\n", + "from kf_book.kf_internal import DogSimulation\n", + "\n", + "np.random.seed(13)\n", + "\n", + "process_var = 1. # variance in the dog's movement\n", + "sensor_var = 2. # variance in the sensor\n", + "\n", + "x = gaussian(0., 20.**2) # dog's position, N(0, 20**2)\n", + "velocity = 1\n", + "dt = 1. # time step in seconds\n", + "process_model = gaussian(velocity*dt, process_var) # displacement to add to x\n", + " \n", + "# simulate dog and get measurements\n", + "dog = DogSimulation(\n", + " x0=x.mean, \n", + " velocity=process_model.mean, \n", + " measurement_var=sensor_var, \n", + " process_var=process_model.var)\n", + "\n", + "# create list of measurements\n", + "zs = [dog.move_and_sense() for _ in range(10)]\n", + "\n", + "print('PREDICT\\t\\t\\tUPDATE')\n", + "print(' x var\\t\\t z\\t x var')\n", + "\n", + "# perform Kalman filter on measurement z\n", + "for z in zs: \n", + " prior = predict(x, process_model)\n", + " likelihood = gaussian(z, sensor_var)\n", + " x = update(prior, likelihood)\n", + "\n", + " kf_internal.print_gh(prior, x, z)\n", + "\n", + "print()\n", + "print(f'final estimate: {x.mean:10.3f}')\n", + "print(f'actual final position: {dog.x:10.3f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "8dc9f8c5", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "45bb8f451db44b96958b929f53dd5312", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(IntSlider(value=1, description='step', max=30, min=1), Output()), _dom_classes=('widget-…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from kf_book import book_plots as book_plots\n", + "from ipywidgets.widgets import IntSlider\n", + "\n", + "# save output in these lists for plotting\n", + "xs, predictions = [], []\n", + "\n", + "process_model = gaussian(velocity, process_var) \n", + "\n", + "# perform Kalman filter\n", + "x = gaussian(0., 20.**2)\n", + "for z in zs: \n", + " prior = predict(x, process_model)\n", + " likelihood = gaussian(z, sensor_var)\n", + " x = update(prior, likelihood)\n", + "\n", + " # save results\n", + " predictions.append(prior.mean)\n", + " xs.append(x.mean)\n", + "\n", + "def plot_filter(step):\n", + " plt.cla()\n", + " step -= 1\n", + " i = step // 3 + 1\n", + " \n", + " book_plots.plot_predictions(predictions[:i]) \n", + " if step % 3 == 0:\n", + " book_plots.plot_measurements(zs[:i-1])\n", + " book_plots.plot_filter(xs[:i-1])\n", + " elif step % 3 == 1:\n", + " book_plots.plot_measurements(zs[:i])\n", + " book_plots.plot_filter(xs[:i-1])\n", + " else:\n", + " book_plots.plot_measurements(zs[:i])\n", + " book_plots.plot_filter(xs[:i])\n", + " \n", + " plt.xlim(-1, 10)\n", + " plt.ylim(0, 20)\n", + " plt.legend(loc=2);\n", + " plt.show()\n", + " \n", + "interact(plot_filter, step=IntSlider(value=1, min=1, max=len(predictions)*3));" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "1ab70095", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\t4.4502 2.6507 2.2871 2.1955 2.1712\n", + "\t2.1647 2.1629 2.1625 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", + "\t2.1623 2.1623 2.1623 2.1623 2.1623\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "process_var = 2.\n", + "sensor_var = 4.5\n", + "x = gaussian(0., 400.)\n", + "process_model = gaussian(1., process_var)\n", + "N = 25\n", + "\n", + "dog = DogSimulation(x.mean, process_model.mean, sensor_var, process_var)\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "\n", + "xs, priors = np.zeros((N, 2)), np.zeros((N, 2))\n", + "for i, z in enumerate(zs):\n", + " prior = predict(x, process_model) \n", + " x = update(prior, gaussian(z, sensor_var))\n", + " priors[i] = prior\n", + " \n", + " xs[i] = x\n", + "\n", + "book_plots.plot_measurements(zs)\n", + "book_plots.plot_filter(xs[:, 0], var=priors[:, 1])\n", + "book_plots.plot_predictions(priors[:, 0])\n", + "book_plots.show_legend()\n", + "kf_internal.print_variance(xs)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "f9433529", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import kf_book.book_plots as book_plots\n", + "book_plots.show_residual_chart()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "a067ab0a", + "metadata": {}, + "outputs": [], + "source": [ + "def update(prior, measurement):\n", + " x, P = prior # mean and variance of prior\n", + " z, R = measurement # mean and variance of measurement\n", + " \n", + " y = z - x # residual\n", + " K = P / (P + R) # Kalman gain\n", + "\n", + " x = x + K*y # posterior\n", + " P = (1 - K) * P # posterior variance\n", + " return gaussian(x, P)\n", + "\n", + "def predict(posterior, movement):\n", + " x, P = posterior # mean and variance of posterior\n", + " dx, Q = movement # mean and variance of movement\n", + " x = x + dx\n", + " P = P + Q\n", + " return gaussian(x, P)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "e6ee66c7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xs = np.arange(145, 190, 0.1)\n", + "ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n", + "plt.plot(xs, ys, label='A', color='g')\n", + "\n", + "ys = [stats.gaussian(x, 170, 9**2) for x in xs]\n", + "plt.plot(xs, ys, label='B', color='b')\n", + "plt.legend();\n", + "plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='g', capthick=2, capsize=10) \n", + "plt.errorbar(170, [0.015], xerr=[9], fmt='o', color='b', capthick=2, capsize=10);" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "d8ca5d45", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from random import random\n", + "xs = np.arange(145, 190, 0.1)\n", + "ys = [stats.gaussian(x, 160, 3**2) for x in xs]\n", + "belief = np.array([random() for _ in range(40)])\n", + "belief = belief / sum(belief)\n", + "\n", + "x = np.linspace(155, 165, len(belief))\n", + "plt.gca().bar(x, belief, width=0.2)\n", + "plt.plot(xs, ys, label='A', color='g')\n", + "plt.errorbar(160, [0.04], xerr=[3], fmt='o', color='k', capthick=2, capsize=10) \n", + "plt.xlim(150, 170);" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "919e90be", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Variance converges to 0.005\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def volt(voltage, std):\n", + " return voltage + (randn() * std)\n", + "\n", + "temp_change = 0\n", + "voltage_std = .13\n", + "process_var = .05**2\n", + "actual_voltage = 16.3\n", + "\n", + "x = gaussian(25., 1000.) # initial state\n", + "process_model = gaussian(0., process_var)\n", + "\n", + "N = 50\n", + "zs = [volt(actual_voltage, voltage_std) for i in range(N)]\n", + "ps = []\n", + "estimates = []\n", + "\n", + "for z in zs:\n", + " prior = predict(x, process_model)\n", + " x = update(prior, gaussian(z, voltage_std**2))\n", + "\n", + " # save for latter plotting\n", + " estimates.append(x.mean)\n", + " ps.append(x.var)\n", + "\n", + "# plot the filter output and the variance\n", + "book_plots.plot_measurements(zs)\n", + "book_plots.plot_filter(estimates, var=np.array(ps))\n", + "book_plots.show_legend()\n", + "plt.ylim(16, 17)\n", + "book_plots.set_labels(x='step', y='volts')\n", + "plt.show()\n", + " \n", + "plt.plot(ps)\n", + "plt.title('Variance')\n", + "print(f'Variance converges to {ps[-1]:.3f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "20ffb548", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sensor_var = 300.**2\n", + "process_var = 2.\n", + "process_model = gaussian(1., process_var)\n", + "pos = gaussian(0., 500.)\n", + "N = 1000\n", + "dog = DogSimulation(pos.mean, 1., sensor_var, process_var)\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "ps = []\n", + "\n", + "for i in range(N):\n", + " prior = predict(pos, process_model) \n", + " pos = update(prior, gaussian(zs[i], sensor_var))\n", + " ps.append(pos.mean)\n", + "\n", + "book_plots.plot_measurements(zs, lw=1)\n", + "book_plots.plot_filter(ps)\n", + "plt.legend(loc=4);" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "5d65cae8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sensor_var = 20.\n", + "process_var = .001\n", + "process_model = gaussian(1., process_var)\n", + "pos = gaussian(0., 500.)\n", + "N = 100\n", + "dog = DogSimulation(pos.mean, 1, sensor_var, process_var*10000)\n", + "zs, ps = [], []\n", + "for _ in range(N):\n", + " dog.velocity += 0.04\n", + " zs.append(dog.move_and_sense())\n", + "\n", + "for z in zs:\n", + " prior = predict(pos, process_model) \n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", + "\n", + "book_plots.plot_measurements(zs, lw=1)\n", + "book_plots.plot_filter(ps)\n", + "plt.legend(loc=4);" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "1fdf3cb3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sensor_var = 5.**2\n", + "process_var = 2.\n", + "pos = gaussian(1000., 500.)\n", + "process_model = gaussian(1., process_var)\n", + "N = 100\n", + "dog = DogSimulation(0, 1, sensor_var, process_var)\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "ps = []\n", + "\n", + "for z in zs:\n", + " prior = predict(pos, process_model) \n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", + "\n", + "book_plots.plot_measurements(zs, lw=1)\n", + "book_plots.plot_filter(ps)\n", + "plt.legend(loc=4);" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "5f0f97be", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sensor_var = 30000.\n", + "process_var = 2.\n", + "pos = gaussian(1000., 500.)\n", + "process_model = gaussian(1., process_var)\n", + "\n", + "N = 1000\n", + "dog = DogSimulation(0, 1, sensor_var, process_var)\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "ps = []\n", + "\n", + "for z in zs:\n", + " prior = predict(pos, process_model) \n", + " pos = update(prior, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", + "\n", + "book_plots.plot_measurements(zs, lw=1)\n", + "book_plots.plot_filter(ps)\n", + "plt.legend(loc=4);" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "f5174fef", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import math\n", + "\n", + "sensor_var = 30.\n", + "process_var = 2.\n", + "pos = gaussian(100., 500.)\n", + "process_model = gaussian(1., process_var)\n", + "\n", + "zs, ps = [], []\n", + "\n", + "for i in range(100):\n", + " pos = predict(pos, process_model)\n", + "\n", + " z = math.sin(i/3.)*2 + randn()*1.2\n", + " zs.append(z)\n", + " \n", + " pos = update(pos, gaussian(z, sensor_var))\n", + " ps.append(pos.mean)\n", + "\n", + "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", + "plt.plot(ps, c='#004080', label='filter')\n", + "plt.legend(loc='best');" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "32053950", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/05-Multivariate-Gaussians.ipynb b/kalman_and_bayesian_filters/05-Multivariate-Gaussians.ipynb new file mode 100644 index 0000000..7bc8e7e --- /dev/null +++ b/kalman_and_bayesian_filters/05-Multivariate-Gaussians.ipynb @@ -0,0 +1,1015 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "84f7aebf", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import book_format\n", + "book_format.set_style()\n", + "\n", + "from kf_book.gaussian_internal import plot_correlated_data\n", + "\n", + "height = [60, 62, 63, 65, 65.1, 68, 69, 70, 72, 74]\n", + "weight = [95, 120, 127, 119, 151, 143, 173, 171, 180, 210]\n", + "plot_correlated_data(height, weight, 'Height (in)', 'Weight (lbs)', False)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "2bddc99f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.025, 2.727],\n", + " [ 2.727, 327.235]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "W = [70.1, 91.2, 59.5, 93.2, 53.5]\n", + "H = [1.8, 2.0, 1.7, 1.9, 1.6]\n", + "np.cov(H, W)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c8c40b53", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.02 , 2.182],\n", + " [ 2.182, 261.788]])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.cov(H, W, bias=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a4b2b5e1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[6.956, 6.956],\n", + " [6.956, 6.956]])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X = np.linspace(1, 10, 100)\n", + "Y = np.linspace(1, 10, 100)\n", + "np.cov(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "3b3cd57c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 6.956 -3.084]\n", + " [-3.084 1.387]]\n" + ] + } + ], + "source": [ + "X = np.linspace(1, 10, 100)\n", + "Y = -(np.linspace(1, 5, 100) + np.sin(X)*.2)\n", + "plot_correlated_data(X, Y)\n", + "print(np.cov(X, Y))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "48467e8b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[10.635 2.885]\n", + " [ 2.885 2.254]]\n" + ] + } + ], + "source": [ + "from numpy.random import randn\n", + "X = np.linspace(1, 10, 1000) + randn(1000)*2\n", + "Y = np.linspace(1, 5, 1000) + randn(1000)\n", + "plot_correlated_data(X, Y)\n", + "print(np.cov(X, Y))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "caa35277", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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HbxqMP355GpW1Tfjoy566cy3BuF9WKtY+WoZ7RhfgwdJrVN2HDfGVcYZsELX9HKLt0Gb2i3zH0XPYcfScqc9J+kpPScKq7cf8X2u9tOZnpaBy0V1I7dMzn5tc7MKre+oU78eG+Mo4QzaIuAVZTavEaPTvmxbV/SnxdIY06leb2XVc+ffLB2/wB2PAvNd6ImBANohc5zWpVomRqKhpwL/+Z3XE9yfSwuVMx5pHyuDMSMWW6npU1jbB6xOCXuuh9HqtJwqmLAwUrvOaVFMfrVhDTGYqL8zHzFuGYtnW4NdyflYKfn5/CZKSHHBmpvTabp+bmYLlP7ghoXfqacGdeibQe6ee1yfg1hU7WbZGMWEdt05zp56diE3C9aJUWUFkF3L9nak35pBjkLvlktVDIFIlsN6elHGGbDNq0htqzr4jshPWIKvDgGwjUv0ocjNSMGtCIeZNGuEPzPksdaMYwxpkdZiysIlw/SguXOrGqu3HMPbn2/w9Kb5p6rBiiESasQZZG86QbUBNh60LHd2Ys6EKP7q9COt3nTBtbESRYg2ydgzINqC2akIA8FsGY4oRgfX2dj6kwU4YkG1Ay4KHbYvGia7IzUjBmhllGD+sH5KTHPjoywb8bEtN0GJ0z9pIEeZNuo6BOQADsgpGX9254EHxQHxHvPiPN2DCdf0BAMs/OiKZYutZG/kbXv/LCfzygRLkZaVx9gwGZEVmHMEkNmfhZg+KZc4rFUFTil0AgI++PK243nGhoxs/3ngw6HuJfFp13G2d1nM2q/YIdD1U1PT0pCWKJeVDc1HT0IaOLq//e7kZKZh5SyF+X1kX0UEG8XZadcKeOq3nbFapX4Sak3u1qqhpwMLNh3o1aCFKNEa8v6yiJY7FTR2y2nPl1NJyBJNeppYU4MDPpuDpydcjKyVu/jREmiXqluu4eNcbcaCoWUcwhUpOcuDbrr7o0ydZ18clikWJtuU6LgKyEbNZs45gCiXO9FsuMW1BlGgVSHERkI2YzVpxLI2aHXtEiSBRt1zHRUA2YjZrxhFModjnmKj3+8vrE1BZ2xR0bFS8ios6ZHE2627plJxdiiu2Wq+2Rh7BJCXR8mWUuBwIv+s08P1lxj4AO4mLgCzOZudsqOr1h452Nju1pABTil2m7MNPtHwZJa5wwfjpydf7t1OH2wcgVk7FS51yoLhIWQBXZ7MuZ3BQcznTo/7DiUcw3V96DW4e3s+wukilvDVRPHMA2LT/GwDGVE7FAkNnyMuXL8fmzZtx9OhRZGRk4JZbbsGKFSvw7W9/25DnM3M2awS5mT5RvAuthlJbOaXneZVWM3SG/Nlnn2Hu3LnYu3cvtm3bhu7ubnzve99De3u7Yc9p1mzWKFNLCvCj24vgiK1hE+nmbFunZfsArGboDLmioiLo6zfeeAMDBgzAgQMHcPvttxv51DGroqYBv911grNjSlha1lJCbxvrfZdNXdRraWkBAOTnS1c7eDweeDwe/9etra2mjEsv0b4YWIdMiS4vM8VfDaW1cioeKjJMW9Tz+XyYP38+JkyYgJKSEsnbLF++HE6n0/9v8ODBZg0vahU1Dbh1xU5Mf2UvntpUjemv7MWtK3ZK9tAIV1fJOmRKdOc7uvGnGrfmfQB697Kximnd3ubMmYOPP/4Yu3fvxrXXXit5G6kZ8uDBgzW137SCljadcldxz2UfntpUbcqYiewqyQG8PP27uGf0IFWzXis6M2qhpdubKSmLefPm4Y9//CN27doVNhgDQFpaGtLSYuuIe6XyHAd6ynOmFLuw7Yhbtq5y/uTrjR8wkc35BODHGw9iXZIjbOUUAFTWNuFsWyca2zxxU5FhaEAWBAE/+clP8P777+PTTz9FUVGRkU9nCbWNjV7b/TVe3V0nG7g37f8Grpw0uFs9ErciSiziREasnBJJzZrViIWKDENzyHPnzsWGDRuwceNGZGdnw+12w+1249KlS0Y+ranU/pF/8dFRuFuVA/et131Lp5ERxTapDo3hcsVqxMJOWEMD8tq1a9HS0oKJEyeioKDA/++dd94x8mlNpfcf+d2qv+v6eESxLHDCE2kVUix1jjM8ZRHvlBobEVHkAic8kVQhGdWZ0Shx08vCKnLlOUQUGalZbSQ5YD162ZgpLrq9WcnrE+DMSMXjEwrxfnU9mtt50gdRtAQAD98UvA9BbXpw8bRR6J+dxp16iUZqtTc7vQ/aOi9bOCqi+LBq+zFs2n/KX3NcXpSP3MwU2VPZczNTMHNCUUwF4UBMWUQo3GrvRQZjIt1o3WkXm2H4KgbkCKjp1UpE0Qvsfby3tkl2dgz0bL3Wcpix3TAgR0Dtam9+VooJoyGKb2KNfuXXjapuHwsbQMJhDjkCav/gi7//Hbhy0rHtiBt/qD6N5vYug0dGFM/UJSRiYQNIOAzIEVD7B3flpOPm4f1w8/B++Om0Yuw70Qx3ayee31KjeuFv/LB87P06dj+CEenlpqF5cDgAue0NSQ5g7NA88walM6YsIqB09p1UDaW4H9+Vk66pCqPq5PnoBksUB/IyUzD/P6tlgzHQ05joQAy/ZxiQI6C1V2sguX4WUrq8XCYkOt/RjfMKC3qiWM4hMyBHKNJTrpsvspMbkVp5mSnIzdS2OM4ccoJS06s1dLdQflaqlUMmiglZacmYfWsRbirshxmvfq76frmZKfD5BHh9QkxuDmFA1iDcmXlKvVoDTzhwOTOsGDpRTGn3ePH6X07iL7VNmu53oaMbM179PObO0hOZdoRTJLQcfWI0NUfJqDnKyecDfryxypxBEyUoqePTrKIljjEgq6Am0E4pdime6zUwJw2AQ/PCHhFpZ/VZeiLbnakXy9SemZedlqJ4lBOPZiIyTyydpSdiQA5DzBfvOX5O1Zl5ard1EpG5YqkMjgFZQiSHKP79fPycE0gUT2KpDI4BOUS4fLGSP1SfRpKjZ6eQFOaQicwl5pBj4Sw9EQNygEgPURTJBWMAeOG+7wBARAGfiNRT2jEbroTVagzIASI5RFFK6EzZFVIet/bRMjz3/iEe90SkE6X3XCA1JaxWYUAOoFfy3yfIn+s1pdiFQ/UtWPNJrS7PR5QInBl98PiEIhT2z0L/vmmAADS2ezAgOx1jh+bhwMnzijtmtx1xS35CFU8msbpumQE5gJ7J//7Zabi/9Jpe349kwZCIgJZLPV0Svz96EJKTHEFphwMnzwdNfKTeZ66cNHRe9imWsE4pdlmWvmBADiC21XS3dIbN8WanJ6Ot06v4WFLBPdIFQyLqsWr7Mby97xRuLMzD7mONuHDpatpPTDsA0us0SvsA7FC3zG5vAeTaaoraOr2Qu3hK9UIGol8wJKIe7tZO/PHLhqBgDPSkHZ7cUIWFmw9F9T6zsm6ZATlEuLaagZSqKaRWdvVaMCQiaeLbUukgVCVW1i0zIEuYWlKAz/7tTsVWmaEzZbleyLG0W4goEYX7dGsm5pDDOHDyvOKhpErVFIFiabcQUaJRqls2CwNyGGpntOGqKUKJC4ZMWxBZxwHAmZmC9D7JQTtm5eqWzcSAHIbaGa3a2yUnOXDfmAKs33UimmERkUoOIGhxT5z3vviDGyRP+uFOPRtTKoHTuk++oqYBv2UwJjJNXlZqUNoxdBZsx5acDMhhiCVwczZUhb3Sqs03seSNyHyLp42Cy5lhu1mwHAZkGWIJXK8dPxrzTSx5IzKfy5nhnwXbtZlQKAZkBeFOltbyx9x+xG3gCIkoVGD5mh7NhMwK6AzIKoSeLK1FRU0DXt1Tp++AiEiWmE4M165ASzMhM7vDcWOIgcTcMRGZ54kJhZhaUqB4HibQ00zIG27rLa72nwlNOYoBvaKmQb+BgwHZUMwdE5lvcrELgPL7L7CZkBQ9ArpWTFkEEPNE7pZLaG7vQn7fNLhyIssXeX0Cdh87Z9BIiUiKKycNPkHAlup6HDvTpuo+gZvAAnPFjW0e1QFdrxI6BuQr5PoUa80XsecxkTVaOy9jxu8+13QfcXNXpO9bPfvUMCBDuU9xg8wCQOjq6/l2D+ZuPMiaYyILdHQp9yoXBW7uiqZXuZ59ahI+IGvZtBF6moDUFTXJAQZjIpsL3NwFIKKNW0acap3wi3pqF95CFwDCrb7qmN8nIoMEtsqNZPHdqO5wCT9D1pr/OdvWya3QRDFo3p3XYcTAvr02dkSSAzaqO1zCB2St+Z+6xnaWsxHFoAnX9ZeshlAbA9T2Po9GwgdkrX2K3973DYb0yzJ4VESkJ7mTQNR2dpw5ocjw/hcJn0MWu7qp/TW7Wz1ovih/ei0R2YtcrlfucGOzTxJJ+IAMXO3qlpuRour2+VmpKHCmqw7iRGSNzNRkrFPRryLc4cZy52QaIeFTFqKpJQXITk9RVVTucmb4eyUTkX1dkqhLDte5TY/OjtFiQA4wflg/1aeEJCc5sPbRMjz3/iE0t0d37DgRGUNA8P4Bpc5t0XR21ANTFgHkcklAzx938bRRAIDK2iZ4Lvvwmx9+F/lZqeYNkog0EfcPRNq5zesTUFnbhC3V9aisbdK1mVAohyAIti2nbW1thdPpREtLC3Jyckx7Xrk97bmZPXnmCx1XZ8W5GSm4cImzZCK7WvVQKX5VcTRsNZX46Xf3gklBKQo9eiFriWOcIUuYWlKAxdOKJX92oaM7KBgDYDAmsrnmi+o7t4nM7oUMMCBL8voELNvKxvJEsc6Bnhmt2rSiuGvPil7IAAOyJO7EI4oPAoD7xhTA5cxQdXtx1160ze0jZUpAXrNmDQoLC5Geno5x48Zh3759ZjxtxPTsb0pE1vrtrhM43+6BKyf8FmlxJi3u5lMbA/SOFYYH5HfeeQfPPPMMlixZgqqqKowZMwZ33303zp49a/RTR0zP/qZEZL3n/lCDzm7pXslSu/HUxgC9Y4Xhdcj//u//jtmzZ2PWrFkAgHXr1mHr1q147bXXsHDhQkOes6OjA5s3b474/j6fgD5ff4WWzmgW63QoJnc4VD1Od9M34cfgiHIcDgccav9fwj2XpjFI3NYR5vsqH8Oh+f7oNeY+uS44kpK1PUbgc0b7d4jqMRz6jCGK+/tfQ1ENIfLX86Wghwl+jOy0PviXO4ah74Va7N5dC6Anh5x1/hia27uC8sh9cgagT863DOmFDBgckLu6unDgwAEsWrTI/72kpCRMnjwZlZWVvW7v8Xjg8VztE9Ha2qr5OQVBQGlpKY4dOxbZoIkooZwB8G+vqb/9wId+jozCUkP6WxiasmhsbITX68XAgQODvj9w4EC43e5et1++fDmcTqf/3+DBgzU/p8PhwG233RbxmImI5Hyrf75h/S1stXV60aJFeOaZZ/xft7a2RhSUX331Vbz66qtRjaWytgnTX9kb1WMQUWz4zcOluL/0Gsmfhet9YQRDA3L//v2RnJyMM2fOBH3/zJkzcLlcvW6flpaGtLQ0I4ekitcn4PJlHxxQfz5ev6xU3DumAB980YDm9i4jh0dEOpNbnDOzv4WhATk1NRVjx47Fjh078MADDwAAfD4fduzYgXnz5hn51BGL5CjwxdNG+ZtXlxfm48cbDxo4QiLSi1GLc5EyPGXxzDPP4LHHHsONN96I8vJyvPTSS2hvb/dXXdhJJEeB52ak+INxRU0Dlm39yrDxEZF+xKTD4mnFlrbcDGR4QH7ooYdw7tw5PP/883C73SgtLUVFRUWvhT6rRXpw6awJhf5grDWYE5F1nJkpeOjGa7Fsa3TNg/TEbm9XRLKIl5vRBwcWfw8AcOuKndxuTRRD8jJTcL6j914DcW6sVyWFljhmqyoLI6hdIY1oC6TDgW1H3HBmpDIYE8UYqWAM9CzkOxDc2N4scR2QtfQyjWQLZEtHN+ZsqMLjEwqjHSoR2Uhg8yAzTxCJ225vWnuZlhflw5WjreROzPW8X10fzVCJyKbMbjQWlwE5kl6myUkOTC8fovm5BADN7d3om6a1zwER2Z3ZjcbiMiBH2su0sH9WxM950SPdSYqIYk9oO06zxGVAjrSXKdtuEpFUO06zxGVAjrSXaXlRPgqcDMpEiczlTDeseZCSuKyyEAOru6VTMo8cuF0ytCzu+6NdeOX/1pk8YiKy2j+UDMR/v7kovnfqWSE5yYEl9xZjzoaqXg2CAj+ObDvi7lUWZ9HfgYgsVlnbjJcfGWtZMAbiNGUBAFNLCrD20TK4QlIQ4scRAJJlcWoOkX2gdJBu4yQie7hwqVv3Q0u1issZsmhqSQGmFLt67dQDerY6R7pn/I7rv4Vdx86huT2aI56IyG6sPuA4rgMyIN3LtLK2Kaqtzi5nBh4svQav7qmLcnREZCdWV1rFbcpCTqRXwcDaxMnFvRvsE1FssqruOFRCBuRIroKhtYliJYdc+l+Pg4aJyFhW1h2HSsiArCaYhv5dQmsTxUoOoPfJ5o4r/9ZML8Pbs8fjCTYfIrItK+uOQ8V9DlmKmrK4l6eXIS8rtddiYGVtk/97U4pdWPtoWa/SOVdIR7mWS13MNxPZzBMTCjG52GVp3XGohG5Qr6U9p9xtpSo5xD+w1yeweT2RiYr6ZWLqDS68WVmHix6f5G3EzWG7F0wyPBhriWMJHZABdQ3swx3PpHSygNcn4I09J3jOHpFNvT17vOH9jnliiAZKR3wrtfIMPVlADPDbj7jxfnU9a5WJbMzquuNQCR+QlWhp5dlyqatXWoOI7MvquuNQDMgK1F5B/3y4Aa//5aTBoyEiPQQ2GLOThCx700LtFfSNSgZjolghwB51x6EYkBWoqVkGAPsujRJRrGBAViC3AYSIYpO4GO9V097RRAzIKoRr5ZmflWLRiIgoGuHO1bQaF/VUkmrl6W7txNPvVFs9NCKKEMveYlhozXJlbZOFoyGicNL6JMFzWXqXXiC7lb0xZREFtQt+RGQupWBsl3aboRiQoxC44EdE5ipwpiM3Q/lDvlQ3RsCeZW9MWURpakkBfnR7EdbvOmH1UIji3v+cdB2KvtUXzRc9aGr34D8+/VrxPnlZqWhu7/J/HdqN0U4YkKPk9Qn44IsGq4dBlBBWf3IcOel90HLpsur7LJ42Ci5nhmwDMbtgQI6SUq8LItKPIEBTMAZ6zsA0uqObXhiQo2S3shki6mHXfhVyuKgXJbuVzRCRvRfu5DAgR0mp9M2B3ufzEZGx7HROnhYMyFFSOuwUAGbfVuQ/+JSIjDPvzuvw9uzx2L1gUswFY4ABWRfhel2IV+lF9xRL/pyI9CFu9Hh6yvW4eXi/mEpTBOKink6kel0EltdMLSmAzydgweYv0dbptXi0RPEn1vLFUhiQdSR3Pl9FTQPmbjwoeTYfEUUuNzMFL/7ghphMUYRiQDaB3EGpRBSdNdPLMGFEf6uHoQvmkE3AzSNExihwpmN8jGz6UIMB2QTbjritHgJRXIqHvHEgpixkeH1C2EU6tSpqGvDanjpjBkiUwJ6YUBg2b6zHe9cKDMhhVNQ0YOmHR4JSDQUau0SJuWMi0t/kYpdk4N12xB31e9cqDMgSKmoaMGdDVa9FOHdLJ+ZsqFK9A4i5YyL9iT0qzrd7cOuKnUHvsdzMFFzo6O51H63vXaswhxxCriJC/J7a02rZeIhIX2LS4b4xBZi78WCvCY9UMAa0v3etwoAcwOsT8MaeE7KzWi2n1aptPJSflYL/eKSMx0ERKXA507HmkTJ88EWD5jJSte9dr09AZW0TtlTXo7K2ydQAzpTFFVI5YzlqZr9i4yF3S2fYF0+/rFRULroLqX2SkJQEzNlQpWHURInh8QmFmFLsQnlRftSpQLn3rh5rR9HgDBlXc8Za/shqZr9KjYccAH7xYAlS+/T8GaaWFGDNI99ldziiAH3T+mDhP4zy96iINhUY7r0bLg6I+eeKGuNPBkr4gKx1F53W02qVGg+FXnXzstJg4xQXkekuei5j3C+3+wNipD3I5d67eq4dRSPhUxZaPv5E2vRaqfFQIC4EEvV2vqMbT26owrpHyzCl2IUCZ7qmT7RK712lOBCYfzbyOKiEnyFrCYDRNL0WGw/dX3qNbHtAnkBCFN6izYcA9FRZyMlMDQ5tSu9dtXHA6AlTws+Q1QbAxdNGYeaEIsN3+6hZCCRKVOc7uvGX442KJ713dvsw/64RKPpWlqqdemrjgNETpoSfIas5gqnAmW5KMAaCFwKJqLff7PibYrrCJwAv7TiGtD5JqhrWq40DRh+YakhArqurwxNPPIGioiJkZGRg+PDhWLJkCbq6uox4uqioOYLJ7AYm4kJgbkaKac9JFCv+38kLqm+rdiHOLnHAkIB89OhR+Hw+rF+/HocPH8aqVauwbt06PPfcc0Y8XdS0VkKYNaY1j5SZ/rxE8UTtJi7AHnHAIQiCKanKX//611i7di2+/vpr1fdpbW2F0+lES0sLcnJyDBxdD7t1iPL6BNz0i+1obrffJwsiPTnQU8mQmZqMji59jzj7zcOluL/0GtW31zsOaIljpi3qtbS0ID9fPv/i8Xjg8Xj8X7e2tho9rCByRzDpRcsfOznJgQdKB7F9J8U915XdcADwpM67VbUuxJkRB8IxJSAfP34cq1evxsqVK2Vvt3z5cixdutSMIVkikm2ZU4pdDMgUl358x3B8uyDbPzEBeuqBn5hQiM0H63E+TKMgtcSucEYvxOlJU8pi4cKFWLFihextvvrqK4wcOdL/dX19Pe644w5MnDgRv/vd72TvKzVDHjx4sGkpCyOFa+kpzo3D5ai8PqFXi0GieJCflYJfPthzOKnUZCU/KxXjivLxcU3kJ+78xyPfRV5WmqVpSC0pC00B+dy5c2hqapK9zbBhw5CamgoAOH36NCZOnIjx48fjjTfeQFKStjVEs3PIRlEKquKVfPeCSZIvloqaBt0/xhHZxb2jXfjwy95BV3wnODNT0NLRrbkuPzM1GTnpKXC3Wtuo3rCArEV9fT3uvPNOjB07Fhs2bEBycrLmx4iXgFxZ24Tpr+xVvJ3c5pOKmgY8/U41LnX7jBgikS050NN0/nxHt3/hL9rHA8J/IjWCljhmSNlbfX09Jk6ciCFDhmDlypU4d+4c3G433O7EPOxT7XbLZVu/wq0rdobtKpWRmvAbKynBCOjZnfcPJS7kZUVfl2/3RvWGvMO3bduG48eP4/jx47j22muDfmZSlZ2taFnllTpqJlz+mShRiHnk/KxUPFA6CNfkZmDZ1q8ieiyzGgVFwpAZ8syZMyEIguS/RKS0LTNQ6BVca3tQonh2vr0Lr++pQ4EzI+oTduzYWTHhe1mYQW5bppTAK7ja9qDsaU+JQJyYLNt6BIunjQIQ+Wvfjp0VGZBNEm5bppyzbZ2qr+KP3Tw00qERxRRxwpKXlSa91TknDbmZKZY3CooEV4lMNLWkAD4fsGDzl2jrvKx4ey1X8MH5mdEMjSjmnG3rxP2l10ge/rDtiBtzNlT1qsywqmGYWgzIJqqoacDcjcqLc6E7jOT6I4u3/fv5Dp1HS2S+fyq7Bi5nOl7+pFbxtuKERWqrs/iJNHSzicuCOmQtGJBNonVxLvAKvuTeYtmr/X1jCrB+1wkdR0tkjduu/xa+P3oQ3quqV5yEKKUctBydZhfMIZtE7eJcflZKr6J1ubaAax4pUzw9gShWDMhO17U3sdqj0+yCM2STqF2cW/z97wQFY7E7nOeyDyv/aQzgABovevxXey2HtBLZlTjr9fkEbKmux4DsnsnGsq2xlXKIFgOySdQu0Llyrt5OrjucmDPbfiQxdz9S/BBTcZe6vZjx6uf+7xc407F42ijLmwOZiSkLk2g9s0vcnRc6+xV38lXUNKDrsg//eeCUsQMnMlhuZs+W6Ash7TbdLZ2Yu/EgWi51xUzKIVoMyCbRkheTWwAUv7do8yGM++V2tHXqe7oCkR7Uhs2f3jMKaX2kw5Dd+04YgQHZRGrP7FLKC4sNV6Jt4E1kFDWlnQXOdBQX5MDd6gl7u8Bdq4mAOWSThZbi9O+bBghAY7sHlbVNKC/Kt+UeeyK9Lbm3GI3t4YNxoER5TzAgW0AsxamoacD/+q8vei3aPXzTEAtHR2SswJNCKmvlD7wQ2bHvhBGYsrCI3KLdS9v/JrsXnyiWBZZ2al3sjncMyBZQs2gnlgIxKFO8CSzt1HMTSDxgQLaA2kW7pyeP6LUAWOBM5+yZTJEepvohGrmZKb1mu+EWuwfmpGH+5BHwXPahsrYpISotmEO2gNoFisL+Wdi9YFLYTlZERuq8rP/5jbNukT4zMnSxu66xA2/v+warth/z38aKA0rNxhmyBdQuUIj7+kP34k8tKcCPbi+KehyPlA9GWh/Otckc6SlJmDfpurA/F1/raX2S8NL2vwWdFg0Eb4qKVwzIFoh2IcPrE6JqKCQ+/rTRg+C5HP8fA8keHr5psGIuWM36SjxvFGFAtkC0CxnRNBQKfPzGi+pqQIn0cPd3lFMNatZX4nmjCAOyRdTu2pMSTZF84OMnSm0nGcOZrn4JSm3pmtrXdrxuFOGinoUibaCtNpD2y0rFsvtLkJeVKvn4YuokXCNwIjmP3zoML23/GwD5rdIOqC9d07K+Eo8YkC0mdfyMEjWBND8rBZWL7kKqTOmSmDqROo2EKByxd/G8Sdfh266+vVrEBtJaGaH02lZ7WkisYkCOQXKBVJyD/PLBG4KCsdjoPnSmHO7sMSmBz8UAnphC1zjkerNE0r9YzWs7njeKOARBsO37qrW1FU6nEy0tLcjJybF6OLYj18A+cEai5nahAft8uwfLtn4leR8AWLLlMM60cVEw0ZhVC6z2tR0LtMQxBuQYF27mK6qoacCTEptIxFvILSDKPfYru77GLz76Svf/H7LeT+8ZieJBTjRe9EQ9442G0ms7VmiJY0xZxDi5HLTXJ2Dh5kOSPxOvwi98cBhTil2SL3S5xz51viOi8ZJ9ifnZx28dZovAF8n6Sqxj2Vsce3nn8V7H4oRyt3rw8s7jmh97cF5mpMMimxIQ3/nZWMCAHKe8PgGv7zmh6rartv9N83bUka7sSIZFNpaVlowpxS6rh5HQmLKIU/tONOPCJfVHPL3wwWFkpfbB5yeaAQi4eVh/jJc5VLK5o0unkZJdtHu8eG33CTx+q3QDIDIeA3Kc0rqTyd3qwX97bZ//65c/qUVuZgpe/MENkot+/fumRT1Gsp9ffPQVXttzIiarGeIBUxZxSo+dTBc6uvGkRHetipoGPL3JmPafsyYMNeRxSb1E6KpmVwzIcUqpo5wWL3xw2N9dSyyjO3sxuhOvQ8dV4EzHukfLcG0uFwutFthVretKc/gt1fUJ0yTeSkxZxCk9t0W7Wz3Yd6IZ5UX5eOY/v9BlfANz0jG9fAgK+2cG1Zg+v6VGl8en6Ihd1cYv34Hm9qvrBbG6OSNWcIYcx8J1lIvE2bZO/OVYIzq6vDqMDDjT2nOYa11jB8629bRT9PoEDM3nDNlOAoMxwHSG0ThDjnOBvQa2H3Hj/ep6NLdrTzcMyE7HO/u/UXXb9D5Jisf/iDP2VVe6hQE9s6/n7hmFJAfAT8b2JB68u/TDI2E3FFHkOENOAOKOp8X3fgf7fzoFb88ej988XIq3nhgXdAJwOPmZKRg7NE/17Pi26/vj7dnjMe/O4ZrG6W7pxP98+yDuGjVA1e3zMlM0Pb7REiU0xXuTeCsxICeYwDP6JozojxfuK1a8T3NHN+749SfIVtmQvLywH24e3g8jBmrbPCJOimvqW5GRIv/S7JeVis+fm4x1j5YhP8segTknw5gPnPeO1r5ZY96d1+Gt/zEOrpw0wy4U8dok3koMyAluakkB1j1ahlyF2aa7pRPvVdUrvrkdDuCxWwoBRFZ6J86+LnXLpzya2ruw/0QznBmp+Ok9xaovFkZqvXQZQGQz5X8quwY5If8Prpw0rHu0DC89XAanymAvnpf49JTrMeG6/njhvu9Ijslx5d+/3F6EgpA1BrUXuHhtEm8l61/FZBq5nshTil34y/FGPPnWAbR7eqcmxNxhZmoy2mVSFz+6rcjfh/l8u8fQfPDcjVWadiMaTQj5rxpiQ59JIwdi9/EmtHZeDvlpz6eaFf84WrJrn5TAfhTh+l27Aqolnp06Kuh1MXZoHu749ScJ2yTeSmy/mSDU9JetrG3C9Ff2Kj7W90cX4KNDDUGBNskBzL6tCIvuKfY/35wNVWxiL0Octf7o9iL8dteJXr+r0BapFTUNWLj5UNiGUXIlaVpbWYp/P0C6SbzSuY90FfshU5BwwTH0zbWluh5PbapWfLzfPFyKfygpwJuVdTjZ3IGh+Zn4bzcX+mfGXp+AW1fsjPhk7ERR4EzH4mmjeh0EEEicje5eMAnJSQ54fQL21jah8utG+AQgLzMV/bPT4MrRv19wPDWJtxL7IZOf1ydg6YdHJGeqoSVMWg6YTO2ThCduGyb5c6Wj3BPZvDuvw4iBff2zVC3H3t98pdnThBH9MWFEf8PHGukhvBQ5BuQ4p+UNr9cBk1x9D2/Cdf2Dmq7b/dj7RGwSbyVWWcQ5LW94cbs1IL0qD6hrYM7V997E6ofQi1miH3tPwRiQ45zWN3y47dYuZ7rqhRw9GxvFE6mLmdLvKlwgT2RenxC3DY+YsohzkaQhos0d6tnYKB64ctLwwn3fkbyYJfqx91rF+0IjqywSgFUlTFJvHikO9GwoieWJTrgLz9OTr8e8SdcpBtR4DzR6UFstZDcse6NerHrDi/Wv24648dqeurCzQLEWF4i9GfX8u0bgnf93Kurfbbwce28EpVLK0PJAO2FAJklWv+GVLgpqZ9Rq5Wel9mofKRIvDI9PKMRdIwfiX//rC7hbtT9vbmYKDvxsCgAwmBpI7aalt2ePt11VCOuQSVJgCZMVwVkpNx34c3fLJSzb+lXYgCpHnC199m934sDJ85JtR10hM9gX7itWvTU50Is/uME//tBAYPUFMJ7YvTxQLwzICcjKfKVSXav488rapoiDMRC8EDZ6cC4mjRwIOIDGix7J4Cg2WZLbmhwqLzMFU4qlO7ExJ6yvRCkPZEBOMOEWRsSTIOQWRsyc8UU60xFnvgB65RzFgBjugiDO0F/eeRy/3VUr20QJAM53dPt30AWK5ndM0vTatGR3rENOIErbqIGebdRSdZ0VNQ24dcVOTH9lL57aVI3pr+zFrSt2GnaUT6QzncXTeoLxnA1VvXLRao4fSk5y4KnJI/DzB29Q9XyBFw6vT8CeY41Y+N6hiH7HFJ5em5bszvCA7PF4UFpaCofDgerqaqOfjmRo2UYNXC3AX/bhYTwZYYCLVCSbSxwAlm09ghc+OBx1QFRzkgpw9cIhXrBmvPq5bEtQnrYROT02Ldmd4SmLZ599FoMGDcIXX+hzWjFFTsvCiJqKByPPV4tkc4kY7NTcZm9tk2yDHi0fkSNpNRrri09WifeGR4bOkD/++GP8+c9/xsqVK418GlJJbRqgrrFD8iO/FCNnfHqemh1q7kbl1IWaj8gAwqaB5MT64pOVAo8hEzvgxQvDAvKZM2cwe/ZsvPnmm8jMVHe0u8fjQWtra9A/0o+avgmunDS8ve8bzQHGqBnf1JIC7F4w6cqhqdfp9rgXLnUrplvUfETW2mqUvSlIjiEpC0EQMHPmTDz55JO48cYbUVdXp+p+y5cvx9KlS40YEkFd34Tp5UOwavsxzY9t5IxPnBGVF+Xjvaq/K6YRBEHAmVaPqouKUrpF6SOylgtRPC0+kTE0zZAXLlwIh8Mh++/o0aNYvXo12trasGjRIk2DWbRoEVpaWvz/Tp06pen+pExp1lfYP0vT45k541ObRhAP9lSiNt0i9xFZy4UonhafyBiatk6fO3cOTU1NsrcZNmwYfvjDH+LDDz+Ew3H1hev1epGcnIwZM2bg97//varn49Zp44SrKVa7RRWwrqmLmk0XFTUNWPjeIVWHoP7m4VLcX3pNRGMReyyEm7UDQG5GCtbMKMP4YfGV7yR1LO9l8c033wTlf0+fPo27774b7777LsaNG4drr71W1eMwIJtPTYARWbnzTM0mlT3HGzHjd58rPla0/Q94ICjJsbyXxZAhQ4K+7tu3LwBg+PDhqoMxWUMpzyw25JlS7LK03EjN0ULjh/UzZXeXmAYKnbWH9ssgUsKt09RLvAQYM5u/x3t9LJmD7TcprHjpVsZGP2Qly3PIemFAJr3Ey8WFYo/lOWQiu+Fx9hQL2O2NiMgmGJCJiGyCAZmIyCYYkImIbIIBmYjIJhiQiYhswtZlb2KJNPsiE1GsEuOXmi0ftg7IbW1tAIDBgwdbPBIioui0tbXB6XTK3sbWO/V8Ph9Onz6N7OzsoFaeRmhtbcXgwYNx6tSphN0VyN9BD/4e+DsA9PsdCIKAtrY2DBo0CElJ8lliW8+Qk5KSTO8Ol5OTk7AvQBF/Bz34e+DvANDnd6A0MxZxUY+IyCYYkImIbIIB+Yq0tDQsWbIEaWlpVg/FMvwd9ODvgb8DwJrfga0X9YiIEglnyERENsGATERkEwzIREQ2wYBMRGQTDMhERDbBgKzA4/GgtLQUDocD1dXVVg/HNHV1dXjiiSdQVFSEjIwMDB8+HEuWLEFXV5fVQzPUmjVrUFhYiPT0dIwbNw779u2zekimWb58OW666SZkZ2djwIABeOCBB/DXv/7V6mFZ6sUXX4TD4cD8+fNNeT4GZAXPPvssBg0aZPUwTHf06FH4fD6sX78ehw8fxqpVq7Bu3To899xzVg/NMO+88w6eeeYZLFmyBFVVVRgzZgzuvvtunD171uqhmeKzzz7D3LlzsXfvXmzbtg3d3d343ve+h/b2dquHZon9+/dj/fr1GD16tHlPKlBYH330kTBy5Ejh8OHDAgDh4MGDVg/JUr/61a+EoqIiq4dhmPLycmHu3Ln+r71erzBo0CBh+fLlFo7KOmfPnhUACJ999pnVQzFdW1ubMGLECGHbtm3CHXfcITz11FOmPC9nyGGcOXMGs2fPxptvvonMzEyrh2MLLS0tyM/Pt3oYhujq6sKBAwcwefJk//eSkpIwefJkVFZWWjgy67S0tABA3P7N5cydOxfTpk0Lej2Ywdbd3qwiCAJmzpyJJ598EjfeeCPq6uqsHpLljh8/jtWrV2PlypVWD8UQjY2N8Hq9GDhwYND3Bw4ciKNHj1o0Kuv4fD7Mnz8fEyZMQElJidXDMdWmTZtQVVWF/fv3m/7cCTVDXrhwIRwOh+y/o0ePYvXq1Whra8OiRYusHrLu1P4OAtXX12Pq1Kn453/+Z8yePduikZOZ5s6di5qaGmzatMnqoZjq1KlTeOqpp/DWW28hPT3d9OdPqF4W586dQ1NTk+xthg0bhh/+8If48MMPg5rie71eJCcnY8aMGfj9739v9FANo/Z3kJqaCgA4ffo0Jk6ciPHjx+ONN95QbLAdq7q6upCZmYl3330XDzzwgP/7jz32GC5cuIAtW7ZYNziTzZs3D1u2bMGuXbtQVFRk9XBM9Yc//AEPPvggkpOT/d/zer1wOBxISkqCx+MJ+pneEiogq/XNN98EneN3+vRp3H333Xj33Xcxbtw405vmW6W+vh533nknxo4diw0bNhj6QrSDcePGoby8HKtXrwbQ87F9yJAhmDdvHhYuXGjx6IwnCAJ+8pOf4P3338enn36KESNGWD0k07W1teHkyZNB35s1axZGjhyJBQsWGJ6+YQ5ZwpAhQ4K+7tu3LwBg+PDhCRWMJ06ciKFDh2LlypU4d+6c/2cul8vCkRnnmWeewWOPPYYbb7wR5eXleOmll9De3o5Zs2ZZPTRTzJ07Fxs3bsSWLVuQnZ0Nt9sNoOe0i4yMDItHZ47s7OxeQTcrKwv9+vUzJZfOgEyStm3bhuPHj+P48eO9LkLx+qHqoYcewrlz5/D888/D7XajtLQUFRUVvRb64tXatWsBABMnTgz6/uuvv46ZM2eaP6AExJQFEZFNxOcKDRFRDGJAJiKyCQZkIiKbYEAmIrIJBmQiIptgQCYisgkGZCIim2BAJiKyCQZkIiKbYEAmIrIJBmQiIpv4/96TGezeDntUAAAAAElFTkSuQmCC", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1.004 -0. ]\n", + " [-0. 1.002]]\n" + ] + } + ], + "source": [ + "X = randn(100000)\n", + "Y = randn(100000)\n", + "plot_correlated_data(X, Y)\n", + "print(np.cov(X, Y))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0cbcde24", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import kf_book.mkf_internal as mkf_internal\n", + "\n", + "mean = [2., 17.]\n", + "cov = [[10., 0.], \n", + " [0., 4.]]\n", + "\n", + "mkf_internal.plot_3d_covariance(mean, cov)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "2b9f04a6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.031507521572225645" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from filterpy.stats import gaussian, multivariate_gaussian\n", + "\n", + "x = [2.5, 7.3]\n", + "mu = [2.0, 7.0]\n", + "\n", + "P = [[8., 0.], \n", + " [0., 3.]]\n", + "multivariate_gaussian(x, mu, P)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5d0c9785", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0315\n" + ] + } + ], + "source": [ + "import scipy\n", + "from scipy.stats import multivariate_normal\n", + "print(f'{multivariate_normal(mu, P).pdf(x):.4f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "5e938c5b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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Wv/GNb+CKK67Y/nyr3vzaa6/F7bffPrSJERGNq24/xIMLGwjiCMd6x+HFfUzUDUw1zV2x6VJVZOydrqDdi7C41oEX+9jjzOPbR1Lsnaphulkpe4pERCPjvMP6S1/6Ugghzvn6p6pTJyLarda7Ph5abKMX9nC8twBJzrB/toqKtft6kDccHZah4PiKh4faD2G6OgOxLBAnKfZM1cqeHhHRSNh9zw5ERCVZ3ujj6HIH7aCNRXcRVVvF7GR15Nsx5snQFRyYr2J5PcBSdxFREgEYHAi1f6a+K95pICI6E4Z1IqICHF/tYWGthzV/Hcv9JTQdAzMTu6Ps5WwkScLMhAVdk7G4to4MGQRmkWYCB+cavI2IaFdjWCciytmRpQ5W2n0s91ew5q9ismFiqsl2hY/VrA1OZl1Y6SDNEgjsRZplePJ8i51iiGjX2r3vvRIR5UwIgQcXNrDcdrHgLmDNX8VMy2JQP4N6VcfeGRv9uI8j7SPYcH1895E1JGlW9tSIiErBsE5ElIMsE/je8Q2sdQf90ztBB3OTNlp1HgJ3NlVbw/7ZCsLUx5HOw+h4Pr5zZBVRnJY9NSKiwjGsExENmRAC3zu+jg3Xx5HOUbhhD3tnxu+gozzZpoqL5qtIRISH2g+hF3CFnYh2J4Z1IqIhO7LUQacf4GjnKILEw77ZCqo2D/s5X6au4KK5CiAleLj9MPpBgAeOrSPLzr19MBHRTsewTkQ0RAtrPax2PBzvLcCPB0F9N/ZQHxZdU3DRXBVCSvFI9xH0/BAPLbbLnhYRUWEY1omIhmS96+P4ag8r3gq6YQfz0xZsk0H9QmmqjH0zFQRpgOPdY9jo+XhkpVv2tIiICsFnESKiIXD9CA8tttEOOlj1VjHVNFGrsEZ9WExDwd5pG0eXelh0lwAAhqZgqlEpeWZERPliWCciukBBlOCBY+twoz4W3QU0qjomG2zPOGxVW8PshIXFtXXoqg4sAbqqoF7lbU1E44tlMEREFyBJMzxwbB1eFOCR7iOwLQWzk1bZ0xpbzZqBVs3AkruIXtTD9xc24AVx2dMiIsoNwzoR0ROUZQIPHFtHPwhwtHMEmgrsma5AknjaZp5mJiw4FQ3HusfhRT4eOLbOHuxENLYY1omInqBjq130/BBHu0chpBT7ZitQZAb1IsxP2jANGUe7R+FFAR5c2IAQbOlIROOHYZ2I6Ano9kMsb/Sx7C4jTEPsm6lAU/mQWhRZlrB3xoYkZTjeW4DrR1ja6Jc9LSKioeMzCxHReUrSDA8ttuHGfWwE65humjANpexp7TqqImN+2oYX97Hqr+H4ao/160Q0dhjWiYjO08OLbfhxhIXecVQsFa26UfaUdi3bVDFRN7DaX4Ef+3hwYYMnnBLRWGFYJyI6D6sdD203wGJvAQIZ5iftsqe06001TRi6jGO94/CimAcmEdFYYVgnIjpHYZTg6HIH7aCNXtTD3KQFlXXqpZMkCfNTNuIswrK7hJV2Hx03KHtaRERDwWcZIqJzIITAg4ttBHGERXcJjaoOp6KVPS3aZOgKZlomNoINuJGLhxbbSNKs7GkREV0whnUionOwsObC9UMc7x2Dqg56fdNoadYMVC0NC+4CgiTGQ4vtsqdERHTBGNaJiM6i70dYWOth1VtFkATYM2VDZj/1kTQ3aUEgw2JvAR03wGrHK3tKREQXhGGdiOgMhBB4eKkDP/Gx5q1hsmHAMtWyp0Wnoaoy5qcs9KIe2kEbj6x0WQ5DRDsawzoR0RmstD34YYxFdxGGLmOiwTaNo65qa6hXdSz3VxAmMY6xOwwR7WAM60REp5GkGY6vDVZogyTA7IQFSWL5y04w3TQhkGK1v4LVjoe+H5U9JSKiJ4RhnYjoNI6tdBEmMZb7K6hXdZa/7CCqKmOqOegOEyQBjix3IAQPSyKinYdhnYjoFPp+hNWOh9X+CgRSTDfNsqdE56lZ02FoChbdRXhBjLWuX/aUiIjO23mH9S9/+cu45pprMD8/D0mS8LnPfW77a3Ec4x3veAee/exno1KpYH5+Hr/4i7+I48ePD3PORES5O7rSRZAE2Ag2MNU0efjRDiRJEmYnLfiJj3bQwbGVLlJuNiWiHea8n336/T4uueQS3HbbbY/7mud5uPfee3HTTTfh3nvvxV/+5V/iO9/5Dn7iJ35iKJMlIirCRs9H34+w1F+Grilo1vSyp0RPkG2qcCoaVrxlRGmKxXW37CkREZ2X8y7AvOqqq3DVVVed8mv1eh133HHHSZf94R/+IS677DIcOXIE+/fvf2KzJCIqiBACx1Z7cCMXXtzHvpkKN5XucNNNE9/vu1j31qDKMqYaFeiaUva0iIjOSe67pTqdDiRJQqPROOXXwzBEGIbbn3e7bLFFROVZ3ugjiGIs9Zdhmyqqtlb2lOgCbb07stpdQ8Ns4NhqFwfnmmVPi4jonORahBkEAd7xjnfg53/+51Gr1U55ncOHD6Ner29/7Nu3L88pERGdVpJmWFh30Q7aiNIQMxNW2VMaujTL4IUx2m6AjZ6P9c2PjZ6PthvA9SMkaVr2NIdusmlCloEVbwXrXR9eEJc9JSKic5Lbynocx/h3/+7fQQiBj33sY6e93o033ogbbrhh+/Nut8vATkSlWGn3EacpVvqrqFd1mPrOLpXIhEA/iOAFMcI4QRSniJNHN1gKCGw1M5QASHi03EeRJRi6CkNXYWoqHFuHIu/cTbaKLGGyYWBpvY2WNYGFtR6evKdV9rSIiM4ql7C+FdQffvhh/MM//MNpV9UBwDAMGAZPBCSicmWZwPJGH+2gjUykmGraZU/pCRGbAb3rReh5IbJMIM4SRGmIOI0RZTHiNEKcxidE9QEJEhRZha5o0BUdeqBDVTQYio7FdQkVS0PNNuDYBuQdWMffrOlY64RY89dgKDqCKIGps3c+EY22oT9KbQX1+++/H1/84hcxMTEx7CGIiIZuteMhTlOse2twKhq0HdaqMU5SrHV9dPsB0kwgymL0Ixf9yEOcDU7vlCUJmibDNBRUVR2yLGErcwsxCPpxIhAnIXpRgDQbrMIrsoKKWoGfVOF6ESTZRdXUMVm3d1TYlSQJrbqBlfUOpuxJLK67ODDbKHtaRERndN6Psq7r4oEHHtj+/MEHH8R9992HVquFubk5/MzP/AzuvfdefP7zn0eaplhcXAQAtFot6DrbnxHR6BFCYHHdRSfoIs5i7G04ZU/pnCVZhtWOh3YvQJIl6EUu+pGLKI0gSxJsS0XLtGBoMhTl/F6ApFmGKBbwggR930U36kKVVVS0KsKkip4XwrENTDVsGNrOCO1NR8daO8Satw5d0TE/4bAzDBGNNEmc5/nLX/rSl3DFFVc87vJrr70W733ve3Hw4MFTft8Xv/hFvPSlLz3rz+92u6jX6+h0OmcsnyEiGpbVjoeHF9v43sb3YRgZ9s5Uyp7SWaVZhvWuj7WejyRN0Q076ARdQBKwTAVVS4NlKEMtV/HDFJ6fwA0SiEygqlfRMBvQFA31ioHJug1NHf3gu7IRYK0d4SkTT8Fcs4b9M/Wyp0REu8QTybnnvRTy0pe+FGfK9+eZ/YmISrW1qt6LeojSEPP1atlTOqueH2JhtYc4y9ALu2gHHQhkqFU11KtabhtBLUOBZShoQUfXjdF2+3C7LhzdQZI10OmHmGrYmKiNdr3/Vu36hr8OXVExN1HdES8yiGh32hnvWxIR5aTtBgijBGveGmxThWWO7sNiJgSW1l203QD9uI81fw1ZlsGxNTQc87zLXJ4oCRLqVR1ORUPXjdBxe3BjFw2zAbEx2OA6P+FAVUYzAKuKjKajY723gZY1geWNPvZM8Z1cIhpNo/usRERUgMV1F/3Yg5/42DcxuuUvQZTg2GoXQZxg3VtDL+rBNlW0alZpq8KyJKHhGHAqGtq9GOv9dXixj+lsCkGYYG7SgWONZrevVt3ARjdCO2hD76iYbVULe7FDRHQ++MhERLtWtx/CC2KseqswdWVkTytd63p4aLGNXuDhePc43NjFZMPETKu8oH4iRZYxUTcwO2EjzkI80juGbujikeUuFtddZCNYHqmpMupVDev+GpI0xUrHK3tKRESnxLBORLvW4roLP/HhxX1MNEZvBXirnn6r//tCbwGSkmB+yoIzgi8sLEPBnmkLpiFhub+MNW8Naz0PR5c7220gR0mrbiDJErSDNpbWXWTZ6L2oICJiWCeiXanvDw4NWvPWoGvKyIVfIQSOrfaw3vOw4q1i3V9HraphfsqGPgKr6aejyDJmWhYmGyZ6cQ+LvUX0/BBHljpIRiywG7oCp6JhzV9HnKZY63J1nYhGD8M6Ee1Kqx0PcRajF/UwUTcgjdCJnJkQOLrSQdcLsNxfRj9yMdU00aoZkDA68zwTx9YwN2EhzkIsugvoByEeXmwjTtKyp3aSybqJOI3Qj/pY6/plT4eI6HEY1olo18kygQ03QCfoQJIk1Cqjs6qeZBmOLHXQ9UIsukvwEx/TLRNVa3TmeK4MXcHslIVUJDjuLsALQzy81EYYJ2VPbZtpKDB1Be2gjb4fwQ/jsqdERHQShnUi2nU2ej7SNEM7aKNe0SDLo7FanWYZji514AYBFt0FRGmA2QkL9gi3kzwbQ1UwN2kCUorj7nG4YYCHF9uIRiiwNxwdbuQiyRKscqMpEY0YhnUi2nVWOx768aAMpuHoZU8HwKBG/fhaD/0wwqK7iFQkmJ2yYOqjW59+rjRVwfykBUUWWHQXESQxjq50R6aGvVYd3Ac6YRfrXZ+H+xHRSGFYJ6JdJYwSuP5mf21NGZlDkJY2+uh5IVb6K0iyGLOTJowR3kh6vhRFxuyUDUUZBHY/ivDIcnckgrEiS4Ne8UEbSZqh7QZlT4mIaBvDOhHtKqsdD6nI0At7I7Oqvtb1sNHzseatIUh8TLeske748kQpkoSZlokMKZbcZfTDCMfXemVPC8CgFCZKQ3iJz1IYIhopDOtEtGsIIbDW9dENOwAE6iOwsbTrBdt91HtRD5NNA5YxfkF9i6YqmG2ZiLIQK94Kuv0QK+1+2dNCxVKhKTI6QRvdfogoHq2uNUS0ezGsE9Gu0e2HiJMU7aCNqq1CVct9CAyiBMfXXLhRHxvBBpqOviO7vpwvQ1cw1TThRX2s+xtY7Xjo9MsvPWk4OjpBFxkEe64T0chgWCeiXWO14yFIAgRJUHoJTCYEjq12EcQBVr0VVG0NDWf0TlHNS8VU0aoZ6IRtuFEfi+tu6T3Y644OgQzdoMue60Q0MhjWiWhXSNIMnX6IdtCBqsioWOVuLF1u9xHECVb6q9A0CZON3RPUt9SrOiqWhjV/FVES49hqr9QNp5o6uF+0gzbCKEHPC0ubCxHRFoZ1ItoV1joeMpGhG3ZRr2qlnljq+iE2uj42vHUkIsZU09wxJ5MO20TDgCwBy/0V+GGMtV65K9oNR4efeAjTiBtNiWgkMKwT0a6w4QbohS5SkaBeLa8EJskyLKy58GIP3aiLVk0fy84v50qRJEy1TIRpgHbYwWrbQxCVd2CSY2tQZBmdoIO2GyDLym8tSUS7G8M6EY29OEnR9yP0oh4MTYFR4kFDi2s9hEmMVX8VtqGiVhmN9pFlMnUF9aqOtr+BIAlwbLWLrKRyGEmSULVV9KIeskywFIaISsewTkRjr+0GEBBwIxdOie0a226Anhdh1VuFgNiVdeqn06zp0DQJK/3VQS1/ie0cHVtDlIaI0pgHJBFR6RjWiWjstd0AXuwjEykcu5ywnmYZljcGbRq92MNkw4Ci8CF4iwQJU00TiYjR9tvY6AUI4nLKYSqWCkmS0It66PS5sk5E5eIzBRGNtTTN0PMi9MIeNEWGWdKBQysdD3GWYT1Yg22pqJjldqMZRbqqoFHV0A07CNMIi2tuKfOQZQkVU0Uv7G2XUBERlYVhnYjGWtcLIYSAG/VQLWlVPYgTtHsBNvwNZCLDRI3lL6dTq+pQFAnr3jr8MC7tsCSnoiFIfCQiZSkMEZWKYZ2IxlrbDRAkIeIsRtUuZzV7ecNFmEbohV00qhpUlr+clixJmKgb8BMP/biPlXa/lM2mVUsd7HMIXZbCEFGp+IxBRGNLCIFOP4Qb9SBLUikHIbl+hL4fY8NfhyJLqJXYNnKnsE0VlqFg3d9AlKRYL6H3uqrKsAwVbtSDH8YIS2wnSUS7G8M6EY0t148GNeubJTBFH4QkhMByuw8/CeDFHpp1HXKJhzHtJM26gSSL0Y16WOt4SLKs8DlUbRVu1EcGwVIYIioNwzoRja22GyDOYgRJUEoJTNcLEUYJ1v01GLqCqlVe28idxlAVOLaGtt9GnKZYK+E0UcfWIJDBi/oM60RUGoZ1IhpbbTeAG7mQIJWyuXSt68OLPURphKbDTaXnq+noEGLwzsiGGxS+um7oCnRNQS/qwfUjJGnxq/tEROcd1r/85S/jmmuuwfz8PCRJwuc+97mTvi6EwHve8x7Mzc3BsiwcOnQI999//7DmS0R0TvwwRhSn6IUubEuBIhdbfuL6g1X1dtCBoSuwSmoZuZMpigzH1tAJOkizDO0Saterlgo3GrSQ7HB1nYhKcN5hvd/v45JLLsFtt912yq9/+MMfxu///u/j4x//OL72ta+hUqngyiuvRBDwQY6IitPth8gg4MX9UspPVjs+gjREmAaoc1PpE1arqtur6+tdv/DOME5FQ5Il8BMfXY9dYYioeOddxHnVVVfhqquuOuXXhBC49dZb8e53vxs/+ZM/CQD40z/9U8zMzOBzn/scfu7nfu7CZktEdI56fgQv9iAgCu8C0w+iQY/woA1dlXkA0gXQVAW2paIbdFDTHbTdAC3HKmx8y1AgSRK82EfP4+FIRFS8odasP/jgg1hcXMShQ4e2L6vX67j88stx9913n/J7wjBEt9s96YOI6EK5fgQ/9qDIMgy92BKUta6HMB28WKg7XFW/UHVnsLrtRn2sdz2IAlfXJUmCZSjw4j7iJGULRyIq3FDD+uLiIgBgZmbmpMtnZma2v/ZYhw8fRr1e3/7Yt2/fMKdERLuQH8ZI0wxe7MM2iw3qQZSg78fohB2oilxKb/dxY6gKbENFJ+ggTrLCDymqmCr8eFDK6fpcXSeiYpXeDebGG29Ep9PZ/jh69GjZUyKiHc71IwgI+LEPq+ASlLWuhzhL4EV91KsaJLCv+jA0HB1xFqEf9ws/JMkyVaQiQZCEDOtEVLihhvXZ2VkAwNLS0kmXLy0tbX/tsQzDQK1WO+mDiOhCuH6EIAkgkBVaL55mGXp+hF7YgyShlHaR48rQFRi6gl7oIowS+GFc2NiWoUCCBD/xGNaJqHBDDesHDx7E7Ows7rzzzu3Lut0uvva1r+GFL3zhMIciIjqtnhehH3uQJAmGXtwbiN1+iCzL4MaDE1N5WulwObYGP/GQZEmhhxTJsgTTUODFPoIoYb91IirUeS85ua6LBx54YPvzBx98EPfddx9arRb279+Pt7zlLfjABz6Apz71qTh48CBuuukmzM/P45WvfOUw501EdEphlCBOUvixB9scdPIoStsN4Mc+0ixF1eYhSMNmWyqkjgQ3cqF7GmZa1cJeENmmgk6vD2Dwzk2jahYyLhHReYf1b3zjG7jiiiu2P7/hhhsAANdeey1uv/12vP3tb0e/38frX/96tNttvOQlL8EXvvAFmCYf2Igof1tlCl7sY6LAMpQgThBECXpRD7omw9B4CNKwKZKEqqWiF7homA10+2Fhodk2Vax1QkRpjJ5X3LhEROcd1l/60peesW2WJEl4//vfj/e///0XNDEioidiUK8eIhMpLLO4ftxtN0CapfBjH6062zXmpWpr6Hke/CRA29UKC81bG5W92IPr24WMSUQEjEA3GCKiYer5EfzEg4RBf+wiCCHQdQO48eBY+go3lubG1BVoqoxe1IMfxojiYvqeK7IEQ1PgJx68YNAalIioCAzrRDQ2tg6t6cceTEOBLBdTz9zzQ6SZQC90YVsqFG4szZVja/AiD6nICt1oapsqvHjQNrIfFNeNhoh2N57WQURjY6te3Y891J3iasa7/QhhGiLOIrSs4kpvnogoSRHGCaIkRZJmSNNBWaMsA5qiQFMVGJoCQxvdp4eqpWKjG6Efu+j6GqabxYxrWwo2eoNuNK4foVbhJmIiyt/oPhoTEZ0nL4iRZAmSLIFlFBOkhBBwgwj9yIMsy7AKPjH1XKQiG7Sz9CNESQoASLIUSRYjE4NyDgkSFFmFpqiQIA1OXzU1OJYBTR2t30lRZBi6DC/yUdNrCOIEZgEvLixjMEaQBPAK7PNORLsbwzoRjQ0/ShCkg6Poi+qv3g8iiEzATzZbRY7QiaWpyNDth+j0Q6QiQxgH8BMfQRICOH2jAF0xYGkmosRCtx+hag02cqrK6IR221Sx0fWRQcD1o0LCuqbKkCUJQRoWeigTEe1uDOtENDb8MEaYhJAkCXpBrRNdP0acJYjSCI0Cu8+cjRdGWGl7SESGftSHG7kQIoOmyXAqCjRFga5KkJTBiwuRCSQpEMUpwihGJwjRQQcVrYJUOHD9GM2ahfqI9I+vWCrWuyH8yIPr6ZisFdOhxdAVhEmIKE6RphkUhVu/iChfDOtENBbSNBsEzTSEqRe3AtzzQnhxH5JUXPeZMxEQ2Oj56PRDBEmAdtBGJjJUTBUVS4eqnjpcSrIEXQZ0TUbV1pBlGfp+Atfvw0s8OEYNoisQRDEm6zYUqdyQqioydFVGP/FQCStI0rSQlX9TV+D5g3dv/ChB1WKbTiLKF8M6EY2FIBq08AuTAKZZTJD0wxhJmqEfebB0pbDTNE8nSVMstz0EcYxu0EM/dmFqCmpV87Qh/XRkWYZT0VGxVPS8BF2/gygJkYkGoiTFdKMKo+RadttS0XU9CAj0vAhNJ/93NgxdRrsXQEDAD2OGdSLKHd+/I6Kx4EcJBATCJIRR0Mq660dIRYooDWFb5a59pFmKhXUXXhhitb+KfuyiVtHQahjnHdRPJMsy6lUdzZqBMA2w0l+FFwZYWOshLKjH+enYpopMZAiSEG4QFTKmoSub97MIflju709EuwPDOhGNBT+MEaUxBERhYb3nR/BiHwICdoklMBkEFtf7COMYK94KMpFgsmGiOsTDmSxDwXTThKxmWPXWECYhFtddxJvdZcpgaAoUWYYX9dH3Y2RnOF17aGNu3rdCbjIlooIwrBPRWPDDBGFSXCeYJB0cwOQlHgxdKW2joYDASruPII6x5q9BgsBU04CuDX8+iiJjsmFA1ySs+euI0gRLbRepKO80z4qpwkt8CCHgFbC6rsgSNEVGmITwI66sE1H+GNaJaCz4YYwwDaAqMtQCgvNWn+0wCQrd0PpY610f/SDCht9GKhK0GgbkHH9/CRJadQOKLLDmrSGMEyxv9CHO0AoyT6YpI8lipFkKr6BTRQ1dQZgG25uaiYjyxLBORDtevHka56BevZiHNS9IEG2GxLLCeqcfoOuF6AQdhGmAVs2EdgH16edKliS0agYypFjz1uFHMVY7Xu7jnoq52aJzcFBRMSvdhi5vv4vDUhgiyhvDOhHteFsb/YI0hFFQf3UvjBEmAQDAKKFe3Y9irPd89CIXXuyh4eiFvVABAFWVMVE3EIsIG8EGXD9CxwsLG3+LosjQVBlBEiCIksLq1uMsRioylsIQUe4Y1olox/PDGBkE4jQqZHNpmmUIowRBEkLXZCgFt2wUEFjreojSCL2wi6qtwjaL70ajazKajoEgDuDGfWz0fCRp8WUhpq4gSAMIIQpZ6eYmUyIqEsM6Ee14fpRsr3IXUZKyFdCCJICpFx+SO26AKEnR9tvQNBm1Snm9vi1DQcVU0Qu7SNMUaz2/8DkYuoIojQYr3UWEdU2GBAlhErB9IxHljmGdiHa8MEoQJoNOIHl0QXksLxjUqidZDNMo9mE0TlK03RBu1EciEtSr5R/K41Q1SADaURteEMMLi+l5vsXcLP8Jk2B742+eJEmCpskIk6j0XvNENP4Y1olox4uSQXBWZBmynH9Jihcm8LdW8guqkd+y4QZIsxS9sIeKpUIvYEPp2ciShFpVQxAHCJMI6z2/0O4wmjrotx4kIbwwgSigbl1TJSRZjCwTSNLyWlcS0fgr/1GeiOgCCCEQJxniLIam5h/UMyEQbJbdaKpcaH/1MEnRDyJ0oy4kCXAqwzv06ELZpgpNk9EJ24iTDK5f8Oq6oSBIfIhMICygnaKmyEiywao62zcSUZ4Y1oloR4uTbBDY06SQtoVRnEIIgTANCzspdct610OUxvBiD46tQi54Y+vZ1Cs6kiyBF/vY6AXIClxdNzQZUbq5l6CADi2aKiPOBuNFJZ7iSkTjj2GdiHa0raCUiARqAWF9KwhGaVxoCUoYJwiiBG7UgyJLqNjFb2w9G12TYeoKemEPSZbC9YpbXddUGQIZ4iwppI5cVQcr6wKCK+tElCuGdSLa0baCUpzGhaysh3GCOEsgkBUy3hbXj5BmKYIkgFPRIGG0VtW3VCsaUpEgTMJCS2GMzY3FURoWEta3/vZxmiDmyjoR5YhhnYh2tChJkYoMmUgLqVkP4wRxOgihRgGdZwAgg4DrR/BiD5AG9dmjSldlqKoEL/YQxgnCgoKsosiQZRlxGiOM8h9TVQb3tTiLWQZDRLliWCeiHS1OUsSbtcpaAZs9wyhFlMWQJamwzaV9P0ImBLzYh22MXq36Y9mGiiAJkIkMrl/cqaa6KiHMIiRphiTLt0PLoyvrMctgiChXDOtEtKNF8aBtI4Dca9aTLEOSZojSCFpBq+rAoAQmTCKkIinlpNLzZZuDlX8v9uB6UWFtHHVNQZwM7gthzptMZVmCIstIuLJORDljWCeiHS1KUsRZDAnSdmlCbmNt18dHMNRiSlHiJEUQJegnfaiKVMihTxdKlmWYhgov8gbvCATF1K7r2iA8ZyiofaMqIc7i7Y5ERER5GP1HfSKiM4jiFHGaQFUkSDmXh4TRoPtHnMbQtGJKUXp+iExkCOIAljm6teqPZRsKEpEgSiO4Qf6nigKDevnB3yfKfWUd2GzfmCbbvf6JiPLAsE5EO9bW6ZFxFhfStjGMU0RpDAEBvYCTSwUEXD+Gn/gABCrG6JfAbDENBYo02GjqBTGStICV7u2OMHEhK+uqKiMRm608WQpDRDkZ+rNbmqa46aabcPDgQViWhSc/+cn47d/+bb5FSERDtxWQimrbGKcp0s1TK7WcS24AIEoypFkGL/JhagrkAk9LHQbLUuAnPgQE/AJWumVJgizLSLNi2ikOVtY3D0biJlMiysnQl2k+9KEP4WMf+xj+5E/+BM985jPxjW98A9dddx3q9Tre/OY3D3s4ItrF4hMORLILaNsYJxkSkUBCMZ1ggihBBoE4i2BZWu7jDZupq3C9BHEaI4gSOJaR+5iqAiRZgiQd1JHnWRqlqRIyMWgdyl7rRJSXoYf1r3zlK/jJn/xJXH311QCAAwcO4FOf+hS+/vWvn/L6YRgiDB9t7dXtdoc9JSIaU0k6qBNOsxSynH+YjZMUSZpCKWBVHQCCKN7ubqLrO6defctWXX+UxQgKOKgIAFRFRrL1Ii7NoOW4EXirhWYmUqQZ3z0monwMfWnoRS96Ee68805897vfBQD8n//zf/BP//RPuOqqq055/cOHD6Ner29/7Nu3b9hTIqIxtRWQhMigyPkG6EyIQY28SIoL62GCKA0hSSjkwKdhkyBB02RESYgkyZBmRRxWJCPZLFWK03w3fW7d59JsUK5ERJSHoa+sv/Od70S328XTn/50KIqCNE3xwQ9+EK95zWtOef0bb7wRN9xww/bn3W6XgZ2IzkmWCWQQEBCQcw7r2yU3aQJVz78EJkpSZEIgSmMYqgIJOy+sA4NTXvv+oHWjHyWo5tzRRlWk7b77cZICRn7vuGzd5zJkXFknotwMPax/5jOfwX/7b/8Nn/zkJ/HMZz4T9913H97ylrdgfn4e11577eOubxgGDCP/OkYiGj9pliHbXK3Ne2V9qzVfKhKYRZyUGg/aREZZmHvAzZOuKnBFgjhLEEYpqma+46mqBIFsUEde0Mp6lqVIcx6LiHavoYf1t73tbXjnO9+Jn/u5nwMAPPvZz8bDDz+Mw4cPnzKsExE9UWkmkIpBSMp7Zf3E+nhVyT88B9FgY6YQAoa2c1o2Ppa++S5EnEYIogI2mMqD8ZIsQZJz7/Ot+1wquLJORPkZ+vKQ53mQ5ZN/rKIoyFjPR0RDlqYZMjFYWS+iDCbNUggIqAV1gonSCJBQ2AFMeZAlCaoqIUwjREm6/eIqL1un2KZZgjjn3u6yLEHCZkcYPscRUU6GvlxzzTXX4IMf/CD279+PZz7zmfiXf/kXfPSjH8Uv//IvD3soItrlTlxZz7sMJkmz7QNwlJw3e6ZZiiTNEGURdFXesfXqWwxNQRAM6tbDKIVt5PdiR1EGt1ci8l9ZBwaBnSvrRJSnoYf1P/iDP8BNN92EX//1X8fy8jLm5+fxq7/6q3jPe94z7KGIaJcb1KwXUwZz0guDHHt3A0CSis3/JjAK2MyaN02V0RcRBMR2OVGeJFlCJgTSAg7jk2UgyzLWrBNRboYe1h3Hwa233opbb7112D+aiOgkaSYeLYPJefE5ExnE5gsDKfdV/MHvlIoUcgH18Xnb7keeZdu/W77jDcbKCgjQsiSxzzoR5WrnL9kQ0a6VpoOuH7Ik5XpSJQBk2aBFH1DMynoGASEEFHnnP0xv9aVPRbr9rkGeZHnQe7+I/LxVBiM2+/ATEQ3bzn8WIKJda2tlPe969cFYGbLNFwZ5S7JHDxAqYjNr3rbCerJZi583WZKQYjNA51wKo8jS9rs73GRKRHnY+c8CRLRrbZ0cmXe9OrB5AFNRYT19NKyPQVbffOdjsLJeRKCVZQlic39B3p3I5M36eAAshSGiXIzB0wAR7UZbZQcZignrqRDIsgxFVKUkyQktKZWd3QlmiyJLm4cHDU6czZMkSdsvCvIO0CeurLMMhojywLBORDvSVjDKRP4BWggBkQ3qyPPeXApstonMEiiStOPbNm5RZRmpGPSpz3u1W5EGp5gC+QdoWcZ2lyCWwRBRHhjWiWhH2o5gQuQeaLdaAGYizX1zaQax2XYwg5xzP/ciKYqEJBv0qc97k6kkg6UpRDQ2GNaJiM5iqwVgJkTuj5ppsrVKW8zG2aLIyqMr0Hm3b5TlwTsuAAopucHmC4MC2roT0S409D7rRERFEFsBCQIF7PncHjPvVfytQgpRwGbWKBL4wC2D2/Hd75Kg6/mNJ0E64W+Wr8HfaCtAM0ET0c7GlXUiorM4Me4V9sIAYkyq1QcGt1txK9BbY+Q91uBlAV8YEFF+uLJORDuaEMUF6PzXhIsRRWLzvydeBmz9fnmssOd9aBUR0bhiWCeiHanIRcyTVtZzH2xrSTi/wbZKX0704d999LL3vze/31JA5L/aXeQqvnTyn4yIaNhYBkNENELGPfAJjP/vSEQ0TFxZJyIaIdLj/jF8737X4IdH0aMr6m//LQm6nt+YWyTk/+7EiavprL4hop2OYZ2IdqStECY92vgjv7FO+Ffuq8InpsucBnu0Jl2ccFk+teqPJUEqKEAXthP40ftiMSMS0S7DMhgiohEkFfHCoEBldUrhyjoR7XRcWSeiHWmru8igf3fOY50wZlFjDVbx8x1M16VcN5OeaHC7bf7NChiyuBab2O69z443RJQHrqwTEZ2FvHmSqCxJua8QK/LWf2WIdHzW1rNMQJEGv5ws5fvUI4TYDs55HyxFRJQ3hnUi2pEe3YiZ/wq0LMvbY2VZ3mFdgQQJiqQgybKzf8MOkWSALCkAAFXJ96knzQAZg7G2/3Y5ESc0+ufrAiLKA8M6Ee1IRZbBbK3OKpCRFVB7ragSZFlBmvMLgyJlWQZFGQRoRck31Qohtv9mW++K5DcWy2CIKF8M60S0I8myBEmSoEhy7qvdj44no4jFblWWoUgKhEAhLw6KkKYCKhTIm3+zXMcSYnsVX8k5QJ9Y3qPk/MKAiHYnhnUi2rFkWYIsFbMCrcibLwwKyM6qIkOVB2EzGZO69TQTUBQl9xIYABCZgCQXs7J+0guDnEtuiGh34iMLEe1YiixBlotZ7ZZlGZIsF9KCUFUGK+sAkI1BWM/SwR9IlmSoav5PO5kYlCwNxsx/ZX2rLp4r60SUB4Z1ItqxFFmGXFQZjCRBxiCs572hVVXk7QCYjsEm02TzV1AkBWoBq89ZJgaHL22WSuU7Fh7tcsOwTkQ5YFgnoh1LkTcDNET+LRUVaXuVNv+OMPJ2R5hx2GS69YJDlVUoBZTBZNngnZC869WBQXmPLCnbeyiIiIaNYZ2IdixFkbfrhPMOtbIkbdcm5x7Wla0SDgVJmutQhUjTwdFBsiRDzbkTDLDVDUYuZKV7a4Mp69WJKC98dCGiHUuRiw3QW4f5pDlXpmjqYGVdVzTE8c5P61GSQZM1AICm5ntwdiYEMiGgSGohATrNBCRJZr06EeWGYZ2IdixFlrfrhfMu7dYUGao8CJpJzmldhgRdU6ArOtJMbG/Q3KmiKIOh6JAlCXrOG0y3/jaKrEDLeSwhBuVXiiQXUt5DRLtTLo8ux44dwy/8wi9gYmIClmXh2c9+Nr7xjW/kMRQR7WInrqznXQajqYMXBrIkb5Z15MvUFRiKAQAIk50b1pMkQyYEdFWHoSvbBwjlN97gb6PKKrScA/TWXU6WFK6sE1Fuhv5+5MbGBl784hfjiiuuwN/8zd9gamoK999/P5rN5rCHIqJdTjmha0reZTDq5umbqqwW0vvc1NXNTZIqojiDZeQ+ZC6izRcauqLD1LXcx9t60abKCjRVyXWsrfucLLNmnYjyM/Sw/qEPfQj79u3DJz7xie3LDh48eNrrh2GIMAy3P+92u8OeEhGNqa2DioACVtY3V2kHYT3KdSwAMPTBw7Ou6ggjP/fx8hLGGVRZhSzJMPV869UBIE0zKPJgBT/vMpit+5zCmnUiytHQH8n+x//4H7j00kvx6le/GtPT03je856HP/7jPz7t9Q8fPox6vb79sW/fvmFPiYjG1FaLQwn591pXFRmSJEGV1Nxr1oFBANRVBYaiI0kHmyZ3oihKYSjGYMOslu9KNzA48VWVBi8K1KJW1iWFNetElJuhP7p8//vfx8c+9jE89alPxd/+7d/iDW94A9785jfjT/7kT055/RtvvBGdTmf74+jRo8OeEhGNqa3VTEXOP6xLkgRVkaAoamHtFE1Dhb5Ztx5FO69uPUszpJmArujQNQVyzvXqwGCDqaJshvW8a9a5sk5EBRj6e5JZluHSSy/FLbfcAgB43vOeh29+85v4+Mc/jmuvvfZx1zcMA4axQ4sxiahUW2FMKaiOXFUUKJKCLBtsmsz7KHtTU6DKCmRJRhSnMI38V6aHaWtjrKEYMPVi5p6kApaiQpKl3E9L3brPKbKS+wsDItq9hv7oMjc3h2c84xknXfYDP/ADOHLkyLCHIqJdbqusQpNVxAV0TNHU4to3Atiu8TZUE3648/qt+2E6qFeX5UI2lwKbZTBK/p1gACBOBvX4EiToOZfcENHuNfRHsxe/+MX4zne+c9Jl3/3ud3HRRRcNeygi2uU0VYEkSdBkrZCwrqsK9M3DfeIk/5V8RVZg6ips1UaaCYQ7qBQmyzIEYQpbr0CRZVhG/ptLkzSDEAKapBZSHx+fcNhTEeMR0e409LD+1re+FV/96ldxyy234IEHHsAnP/lJ/NEf/RGuv/76YQ9FRDRY7VaKCeuGrkCRFciSUtjJoo6tw1B1KJIKL0wKGXMYvGBw+9iqhYql5d5fHQCi+NE2kUYBK91xkkFVNsM6V9aJKCdDD+sveMEL8NnPfhaf+tSn8KxnPQu//du/jVtvvRWvec1rhj0UERF0VYEma4Nj5nPeZGpom+0UFb2wg4psc3Dyp63b8MNkx3SF8YIEpmZClmQ4BTWJj5IUsjQoVTIKaBO5tbKuKDzBlIjyk8uj2Y//+I/jx3/8x/P40UREJ9E1BZqyVZqSwchxI6O+WXajyxr8ODz7NwyBDAlVS0eS2uiF3UFpiZl/EL0QUZwhSQVqegWGpha26hzFApqsA0AhYT1JBTRTK6Q+noh2Lz7CENGONlhZHwSzvEthJGnQK1xTNSSJgEAxq9xV2xhs0lRN9IPRL4XxgwSKpMBUDTi2Xti4cZzCUHRIkpR7Gcx2fbxcTH08Ee1eDOtEtKPpmnJCh5b8w7OhKdAVAwICUUGlMIaqQFcVWJqFOM4KG/eJyISAFyawNAuSJME2i+kCIyAQJwKaqkHXBu+A5CnZ3GCsyRrr1YkoVwzrRLSj6ergaHm1oPaNhq5udwCJ4+JCc9U2YKomJEmG74/u6noQphACsLUKqqYGRSrmaSZKMggI6IoBo6BOMACgKhpX1okoVwzrRLSjPdprvZiOMKamQNncxBgVGdYtbbBZU6+iHyRIRnB1PRMCXTeGqVlQZQWOXdyBd1svnDRZK2xzqQQZqqRwZZ2IcsWwTkQ72lZQKqx94wkdYaKC2jcCgyPtGxVj0LdcUtD14sLGPld9P0YmBGp6Dbapbd9WRYjiDIo8eCFlFrSyriqb9wWurBNRjhjWiWhH22qbV9TKuqYOjpY3VBNhlBW2yRQAalUTqiTDMRwEYVroyv7ZZFkG10tQ0SpQZQXNqlXo+EGUwlBNAI+e/JqnOD3hQCSurBNRjhjWiWjH0xQZmqIVssEUACxDg6mayIQoNDDLkNB0LNiaDVVW0XbDQl8snEmnnwAYvJBwLL3QAJsJgSjKYKomNE2BquQ/dpKI7ZahXFknojwxrBPRjjfY9KlCCFFILbdtaoMWgZAQhMWVwgCDE011VUHDbCBJBPpe+ZtNwyiDHySoG7XBqrpjFjp+FA/e4TAVA7ZRTPeZKM6gyxo0Nf/OM0S0uzGsE9GOZ+oqDGUQEIMo//BsGxokSNAVA0GBdesAIEHCZN2GruioaBV0vRhpWl45TCYEOm4ITdZhazaajgVFLnalOYgSyJIMo6CwnqQZ0iyDrhiFlNwQ0e7GsE5EO56lq9AVDRJkhAWUpRiaAlmWYKomgrD4oGxoKhxLh2M4UKBirRMiE8WXwwgItLsRkhSom3UYmopagR1gtgRhCnOzXt028g/PYTT4mxuqAauA8Yhod2NYJ6Idz9pcTTVVA2EBK+tbh/2YmoksyxAlxa6uA0CzZkHXVLTsFtIMWO8UX7/edWMEUYqW1YSp6pis24WODwxeMIRRBkM1oSoy9AI60IRRCgkyDEXfvu8REeWFYZ2IdrytUgSjoLAODF4gGIoBCdL2SmuRFEnGbKMKQ9EwYU0gijO0e8W1c3S9GH0/Qd2sw1ItTDUqpXRFieIMmRAwVbOw4BxGKQxVBzB4V4eIKE8M60S048myNKhbV02EcQZRQEmIbQxO59QUrZA6+VPRVAUzrSoMxUDDbMIPEvT6Ue7j+mGKbj9GRauiolUwUbcK29j5WEH46Cq3bRYU1uNsu00kV9aJKG8M60Q0FrZWukVB7RQtXYUkSzBVC35QTlgHAFNTMdWwYGsWHN1Bz0vQ9/NbYQ+jDBu9EKZmom7WUK8YcKzi69S3+GECUzUhQSosrAdRCkMxYOgqZJmdYIgoXwzrRDQWLEOFoQ5CY1hAhxZJklA1NVT0CtIsK6z85lQqpoGmY8ExHFS0CjpujPVuNNRNpwICvX6EtU4AQzbRMJuomDpaTvF16ltSIRCEGSzdgqbKMAuoV4/iFEKIweZSlsAQUQH4SENEY8EyNKiSAlVWBzXklfzHrFoGel4EWVLQDxIYenmH4zQqJtIsA1CHpujohG2sbqRo1Azo6oWty2RphvVehCjO4OgOHMOBbWqYbJQX1AEgCBMICFRUG9WCutBs7U8wFYMlMERUCK6sE9FY2FrlNBSzsFXuqj3YZGhrNryg/MOJJhwb0w0bVd3GpD0FCAWrGwE6boQsO//SoEwIuF6MpY0QSQJMWJNwDAdNx8JMowoZ5ZaA9P0UuqJDlVVUTb2QMcMohSKpUGWVbRuJqBB8pCGisaBv9j43VAO9yCtkTFWWYRka7NiC2+8hTlJoJXREOVHFNKCrKpbbfSjyFPqhCzdw0Q8SVAwVlqlC1868ThMlGYIwgeenyIRARavAMRxoiorpZqWQcpOzERDwgwQ1ow5ZllApql49TrfLrbiyTkRFKP8Rl4hoCCRpsyOMYmDdz5BlopDNf46tox/akCDDC1LUq+WGdWDQJWZu0kG750ORZFT0CtzQhR/66AcBJEmCrkpQVRnyZm4XGZCkAnGSIc0EJEmCpVqo6g5UWUHV0tGqWVCk0XhDNggHLRttzUbV0iFJxazyh1GGimJAkiQYWvl/ayIafwzrRDQ2LEODubXJNEphmfk/xFUtHfKGBEsz0Q9C1KvFlGOcjQwJLcdGvWKg7YZQZAU1UUOURgiSAEmWIAgSZMgACMiQocoaTEWFbmgndVhpVC0YJb9j8FhekECVBy/OHLuY2zzLBOI4g2kMTi4t6gUCEe1uDOtENDYsXYWuDg4qCgoK64amQtcU2JqNVc9DmmVQ5NFYfQYARVYwUbPRcEz4YYx+oCEIjdN2ihmsuiuoWDqqpgpFHq2QvsXzE9hqFZIkoVJgvbrAZicYlsAQUUEY1olobFQtHTIkmKoJL0jRrBUzrmPp8CMbEiS4XjIyq+snUiQZVdNA1Ry885BmKaIk2w7tEiRoilx6zf258MMUSZbB1iuwTbWwF0fe5gFMpmoWViNPRDQ6yz9ERBfINjXIsgRLs+EX2J2lXjWhSAos3Ybr5Xcg0TApsgJL11AxdFQMHbah7YigDgCuH0OVNViqiXrFLGxcP0hgaRYkSKhao/eCjIjGE8M6EY2NrZIIW7MQpxniJP+TTIFBKYxlaHC0KqIkK+RQpt0qFQJ9P4FjOJBlCU5B/dUBwAtS2JoFRZFZBkNEhWFYJ6KxUrV0WNrgsJ4ie583qiZszYYqq3D75fdcH1eenwACcLQq6hUTcmFdYFKkWQZbq3BVnYgKxbBORGOlaulQJQW6YsAPilvhdmwdkiyhqlfh+vFpN3DShel5MSzNgiIraFSLK4HxggQSJFiaBYdhnYgKxLBORGNlq+d2RbPRL3BlXZFl1GwDVd1BJsRInGg6bsIkRRilqOpVGLoKUy+uR4IXpDBVEzLr1YmoYLmH9d/5nd+BJEl4y1vekvdQRESQ5UFvcEuzEcUpkrSYunVgUAqjySpM1UKvvzM2mu4kbj+BLA3aZBa5qg5sbS61t+9fRERFyTWs/+///b/xn//zf8ZznvOcPIchIjpJ1RpsMgVQaCmMbWjQNQWO7iCIUkQJN5oOSyYEXD9BVa9ClmTUKsVtLI2TDHGawdYsVMziTkslIgJyDOuu6+I1r3kN/viP/xjNZvO01wvDEN1u96QPIqILUbV0aLIGTdYKL0dpVE1UdBuKrKDjcnV9WHr9GCITqBs1OLYOtcCDp/r+4D5kaTZLYIiocLk92l1//fW4+uqrcejQoTNe7/Dhw6jX69sf+/bty2tKRLRLbAUqS7Phh8WubjeqJhRZRt2oo+8lhZbhjCsBga4bo6JXocoqJup2oeP7QQJDNaFKChybYZ2IipVLWP/zP/9z3HvvvTh8+PBZr3vjjTei0+lsfxw9ejSPKRHRLqIqMkxdRUWzEYQpsqy4ziyKLKPlWHCMGiRJ5ur6ELhegiTLUDfrqNo6TK3Yw7e9MIWtWtt9/ImIijT0R7yjR4/iN37jN3DHHXfANM++AcgwDBhGcbWHRLQ7OLaBjm9DYNCZpWoXtymwWbOw1vNRN2poe200HA1KgWUb40RAoONGsDUbuqxholbsqnqSZojiFJOmvX1CLhFRkYb+7HHPPfdgeXkZP/iDPwhVVaGqKu666y78/u//PlRVRZpywxUR5a9q6TAUfXBIkV9s3boqy2hUTTiGAwgJXXaGecK8IEGcZGiYDViGBrvgk0Ndb3DfqWg2+6sTUSmGvrL+spe9DP/6r/960mXXXXcdnv70p+Md73gHFEUZ9pBERI9TrxiQJAmO7sD1OsCEVej4E46Fdi+AYzjoul3UqjoUdhE5b+1eBFO1YCgGJguuVQcA14thqRZUWUW94HaRRERADmHdcRw861nPOumySqWCiYmJx11ORJQXRZFRtXRUIwcbwQaCKIWpF7dYoKkKahUDSVpHL+yi50ZoOCz5Ox9ekCCKM8xU6zB1tfBOLFk2aBc5aTehKjIq7K9ORCVgESURja1G1URFsyFLCtwSSlEmahYUedB3ve3GSNkZ5pwJCKx3Q5iqBVu1MFEv9p0RYPBiQQgBR3dQr5rsr05EpShkS/2XvvSlIoYhIjpJo2ri6LKEil6B63uYPP2RD7kwNBVNx0IqGnBjF+1ejIkGV9fPRa8fI04yTDlNWIaGml18CUqvH0NTBnsfij4xlYhoC1fWiWhs6ZoC29Tg6A78MEGSFL+yPdmwoSkqGmYDXS9CyFNNzyoVAhu9GFXdgaEYmG5WSpmH6ydwdAeyLKFm80UWEZWDYZ2Ixlq9YqKqVyFBQs8rvhRGlWVM1G3UjBo0Wcd6Oyx8DjtNuxtBZEDLbMKxjcI7wACDg5CSNINjOHBsgy0biag0DOtENNYaVROKJMPS7FLCOgC0HAu6pqJltxBEKVyfrRxPJ0xS9PoxGlYDqqpipqRV9Z4XQ5FU2KrFEhgiKhXDOhGNNdvUoGsKHMOB56dICzzNdIssSZhtVmCrFmzNxnonQiqKn8dOsN4Oocoa6kYNkzULmlpOu9+el6BqVAEM2oASEZWFYZ2Ixl69YsLRqxAQ6Je0ql21DFRtHRPWBIQA1jssh3msjhshiFJM2BODdyIKPq10SxSniOIUjl5F1dJLe8FARAQwrBPRLtComtBkDYZqotcv9jTTE800KtBUDS1rAq4Xox+wHGZLmKTY6EWo6TVYqonZZhVySa0Se14CCTIqepUHIRFR6RjWiWjsObYORZHh6FW4XgxRUgmKrqmYbVbh6FXYegWr7Yi91zHoqb66HkCTNTTtFpo1q/ADkE7U68eo6DZkSKxXJ6LSMawT0diTJAn1igFHryETAq5X3up6o2rCsQ1MWhOQIGGlHZQ2l1Gx3okQJwKT9hQsXcN0o5xNpcCgBMYPEzh6DaauwtQLOY6EiOi0GNaJaFeYqNkwVQOWaqHdi0qdy+xEFYaqYdKegh+m6LjlzqdMfpii24/QtJowVQPzk05p5S8A0HFjyJKCmlnDRL2cmnkiohMxrBPRruDYOnRNQd2sw/XjUg5I2qLKMuYmHNiqhZpew0Y3QhjvvsOS0jTD6kYAU7VQN+qYatgwtfJWsoUQ6PQi1I0aZEiYqFmlzYWIaAvDOhHtCpIkYaJmo2bUIUFGu+TV7Kqlo1Wz0LJb0BUdS2sBkl1Uv54JgaWNAAISpu0p2KaGiZK6v2zp+wniNEPdrKNeNdkFhohGAsM6Ee0aEzULiiSjZtZKL4UBgKlGBbahY6Y6AwkKltb8XdF/XUBgZSNAFAnMVGZg6hr2TDplTwttN4KhmrBUC5MsgSGiEcGwTkS7hqGrcGwDdaOOOMngBeVtNAUGhyXtna7B1AeBPUmBlXUfAuMd2Nc7EfwgxXRlCpZmYu90HapS7ip2kmZw+wkaZgOqIvMgJCIaGQzrRLSrTNZtVDQbmqKPxOq6KsvYP1WDpeqYrswgCDOstcf3wKSOG6Hbj9CyW6joFeyZrJVap76l6w563teMwcZSqcRNrkREJ2JYJ6JdpVE1oSgyGmYD3X6MNCt/FVvXVOydrsPWLEzYk+h5MTZ64xfY+0GM9W6ImlFHTa9htlUttZ/6idq9CFXDgSopLIEhopHCsE5Eu4osS2g5FhpGHRCDA3BGgW1omJ8cHJjUslpo9yKsdcYnsPe8GMvrASp6FRNWCxM1a2QOHArCFGGcomHUUbF09lYnopHCRyQi2nUm6zZW2n1U9AravQANZzRWd2u2iaQlgHVAlmSs9leRZgJTTQMSdm5ZRtsNsdGNUNNrmLAn0KiamG5Wy57WtnYvgiZrqOpVrqoT0chhWCeiXcc2NViGhrrRwLHeIwiiFKY+Gm36Wo4FWZIgrUuQIWPFW8FyJjDVMks9LOiJWuuE6PYjNMwGmmYTrZqFmREK6lkm0HEjtKwJyLKE5ois9hMRbWEZDBHtSpN1G45RhSqraHfL32h6okbVxJ4pB1WjiunqDPwww+KajzTbOX3YMyGw0g42N5NOoGk2MdWsjFRQB4BuP0YmBOpGA03HgqLwaZGIRgsflYhoV5qoWVBkGc3N+vAyTzQ9FccysG+6hqpuY86ZRRwDx5b90ttNnoswSbGw4qHvpZiyp1HXa5ibcDBZ8qFHjyWEwGo7gGPUoCsaplgCQ0QjiGGdiHYlRZEx1aigaTYhSTLWu6O3mbNi6rhopgFbM7HX2QNdNrG07mOtE45sL/ZuP8LCig8IFXPOHByjij1TzshsJj1Rtx8jTjJMWhOoVQxURqQzDRHRiRjWiWjXmmlWoMoKmmYTG91oJNo4Ppapq3jSfBO1ionZ6gxaVgu9fozjKx6iJC17etvSLNt+IeFoDuacedQsGwfmGqjZoxfUAWCtHaKiVWGqJmZbo1WeQ0S0hRtMiWjX0tRBT+04bWLdX8dGJ8Rkc/SCpaoo2D/dwHrPh7QhwVRNrPRXcXzZh1PR0HA0KHI5ay+ZEOj1Y7TdGBASZiozsDUbzZqF6UZlZDfFul6MME4xU59AxdLh2DyxlIhGE8M6Ee1qM80KVtp9NMw61rsdtOoGZHk0A2bLsWCbGo6tdKEp8+gGHXS8DnpejHpVQ62qQykoHAtshvRejCwTcHQHDbMBXVUxP+mgao12+F1th7BUCxXN5qo6EY00hnUi2tUMXUWrZiHOJtAO2mj3IrTqoxs0TU3FwbkmVtt9KLIMx3DQCbro9Lro9hPUqyqqlgY1p64mqRDw/GSwKTfNUNGraJpNaLKKetXEdMOGqoxGG8zT8YIEfphgX20Opq6OZD09EdEWhnUi2vVmW1Wsd304Rg3rnR6aNR3SiJZvAIAsSZhuVtGqWVjt+FBlFXWjNnix0XWx0Y1g6AqqloqKpV5wiUwmBLwgQd9L4IcpBARszca03YSh6HBsHZONCkxtZzylrLVDGKqJql7lqjoRjbyd8chKRJQjy9BQr5oI00l8f6ODjhuPzKmmZ6IqCmZbVbQcEysdD4qsoGE14cUevLiP9Y6P9U4EQ5ehawp0TYauytA0+bS15AICUZIhjjPESYYoyuBHKYQQMBQDTbuOqlqBIiuwTQ3TjQosQyv4N3/igjCF68eYd6ahawpaNavsKRERndHQw/rhw4fxl3/5l/j2t78Ny7Lwohe9CB/60Idw8cUXD3soIqKhmW1V0XEDOLqDtY63I8L6Fl1TsWeyhql6gq4XotPX4MRVpCJFP+7Dj314foxuP9j+HlWWIcsAtjK7ADIBpKnYbgupyAp02UDDNFHVKlBlFaoio1YxULONHRXSt6x2AmiKjprhYLZVHel3UIiIgBzC+l133YXrr78eL3jBC5AkCd71rnfh5S9/Of7f//t/qFQqwx6OiGgoqpaOqqVjIpnAQ+0euv0ItcrOCezAILRP1lVM1isI4gRdN0DX0xAnNQBABoE4jRClMeI0hhAnHAQlAZIkQzUU6IoBTdagSIPyGUWWUKuYcGwdtqHt2IAbRil6/Riz1VloioKJETukiYjoVIYe1r/whS+c9Pntt9+O6elp3HPPPfjhH/7hYQ9HRDQ0cxMOXD9CRatiZcOHY+/cYGpqKsxmFdPNKpI0RRCliJIUYZQgjFNEcYIMAMTgJE9JliBh0M7S0BQYugpTU2BoKjR1tDeMnquVjQCarKFuNjDTqo5s1x8iohPlXrPe6XQAAK1W65RfD8MQYfjoyYHdbjfvKRERnVKtYqBq6ZhOpvFg+/vY6I52Z5hzpSoKqtZ4BO4nygsS9LwY884eGKqK6Qbf6SWinSHXUzSyLMNb3vIWvPjFL8aznvWsU17n8OHDqNfr2x/79u3Lc0pERGe0d6oGUzXQMBtYbYcjeaopnb/l9QCWaqFu1DA/6XBVnYh2jFzD+vXXX49vfvOb+PM///PTXufGG29Ep9PZ/jh69GieUyIiOqOKpaNVszBlTyHLgNWN4OzfRCOt40bwwwTT1RlYhoYJdoAhoh0ktzKYN77xjfj85z+PL3/5y9i7d+9pr2cYBgxj57/NTETjY89kDRu9AJP2BFa7q2jWdOja7i4j2amyTGBlfdDlx1Yt7J2q7dh9CES0Ow19ZV0IgTe+8Y347Gc/i3/4h3/AwYMHhz0EEVGudE3BTLOClj0BVVaxtMbV9Z1qrRMiSQWmKzODlpMVLg4R0c4y9LB+/fXX48/+7M/wyU9+Eo7jYHFxEYuLi/B9f9hDERHlZrZVHWxErMzA9WO4Xlz2lOg8RXGKtXaICXsChqpj33S97CkREZ23oYf1j33sY+h0OnjpS1+Kubm57Y9Pf/rTwx6KiCg3iiJj71QNNcNBRaticc1Hxs2mO8rSWgBVVjFhT2K6WYGp89BuItp5hv7IJQSfzIhoPLRqFlY7HmbSGTy48X2sd0JMNs2yp0XnwPViuH6MPc5eGKqKuVa17CkRET0huXaDISLa6fZND1o5tqwJrHZChFFa9pToLNJMYHHNR0WromY42DtVg6Lw6Y6IdiY+ehERnYFlaJhq2JisTEKTdSys+nwHccQtr/lIEmC2OgvHNtBiq0Yi2sEY1omIzmLPZA2WrmHemUMQplhth2f/JipFrx+j7UaYrc7A1HRcNMNNpUS0szGsExGdhSxLODjbgK3ZmLQnsdoO4AVJ2dOix0iSDAurPhzdQcNsYP90HQY3lRLRDsewTkR0DiqWjrmJKibsCViqjeMrHlJ2hxkpx1c9SJAx68yhUTUxUbfLnhIR0QVjWCciOkezrSocy8C8M480lbC0xvMjRsV6J0TfTzDnzMPSdFw02yh7SkREQ8GwTkR0jiRJwoHZBizdwExlBh03QrcflT2tXS+IUiyvB2iaLVS1Cg7MNqCy+wsRjQkW8xERnQdDV7FvqoY0zeDGLhZWerANFarKcFgGIQSOL3vQVQPT1WlMNyuoVYyyp0VENDR8diEiOk8TdRtNx8JsdRaypODYilf2lHat5fUAUZxhvjqPiqFjz2St7CkREQ0VwzoR0ROwf6YOS9Mx7+yBFyRYXmf9etG6/Qjr3RBTlWlYmomDcw3IslT2tIiIhophnYjoCVAVGQfnGqhoNqYrM1jrhGj3WL9eFC9IcHzZR91sYMJqYc+kA8vQyp4WEdHQsWadiOgJcmwD+6brwDIQpxEWV9tQFQlVm6ExT1Gc4pElD5ZmY646i8m6jZlWtexpERHlgmGdiOgCTDcrCOMEAjOIsxjHlvu4aL4KU1fKntpYStIMRxb7UCQNe2t7Ua+Y2M9TSolojLEMhojoAu2dqqFZtbCnthe6YuCRxT6SJCt7WmMnywQeWfKQpTL21fahahp40lwTksQ6dSIaXwzrREQXSJIkHJxrwrEM7KvtA4SCo0t9nnA6ZMdXPQRhhn31vagYJp6ypwWF/dSJaMzxUY6IaAhkWcKT55uwDQN7a/sQxcDxZQ9CMLAPw/K6j14/xp7aPCq6jafsaUHXWGpEROOPYZ2IaEg0VcFT906gYljYU9uDvp9gcZUtHS/UeifEWifEdGUGju7gSXNN2CY38RLR7sCwTkQ0RKau4snzTTh6FbPVOXTcGMe4wv6ErW4EWFr30bImMGG1sG+6jnrVLHtaRESFYTcYIqIhc2wDB2YbwCIgSzKO947hkUxgz7TNQ3vOw9KaPzj0yJ7CpD2J2VYV081K2dMiIioUwzoRUQ5aNQuyLOH7xwFFVnC0cxRHFvvYN1uBwsB+RkIILKz66LgRZquzaJpN7JmqYZa91IloF2IZDBFRThpVE0/d20LNrOKixn5EEfDwcZdtHc8gywSOLXvoujHmnT1omk1cNNtgUCeiXYthnYgoR45t4Gl7J+AYFVzUuAhZKuOhBRdRnJY9tZGTZgJHl/pwvRR76/vQMOt40nwTk3W77KkREZWGYZ2IKGe2qeHi/ZNwTAsXNS6CJDQ8vNBHEDGwb0mSDEcWXAShwP7GftSMKp6yp4WmY5U9NSKiUjGsExEVwNRVXLzv0cCuSjoeOu5ioxuWPbXSuV6MB4+7SBIJF9UvQs2o4Gl7J1CrGGVPjYiodNxgSkRUEF1TcPH+STxwbB2ydADL7hIW1zbQ9xPMTlpQd9lpnEIILK8HWO+GqGhVzDtzsHQDT9s3AVPn0xMREcCwTkRUKFWR8bS9E3hkpQsZEip6BQu9RTx4zMX8lI2KtTselsMoxfEVD2GUYboygwmrhVpl0PJSU3kyKRHRlt3xrEBENEJkWcL+mTpqFQMPL8qwVAvHesdxZNFFq2ZgumVCksa3veNGN8TSegBN1nGgMQ9Ls7B3qsYe6kREp5Dbe6633XYbDhw4ANM0cfnll+PrX/96XkMREe1IjaqJZxyYQsup4KL6fkxXZrDRjfDQcRfhGG4+TdIMjyz1sbjmo2E0cLB5EA27ih+4aJJBnYjoNHIJ65/+9Kdxww034Oabb8a9996LSy65BFdeeSWWl5fzGI6IaMfSVAVP3TuBvVM1TNoTONA4gCxV8eAxF4trPpJ05/dkzzKB1XaA7x3twfMF9tb2YrY6i5lGFT9w0RQsQyt7ikREI0sSQohh/9DLL78cL3jBC/CHf/iHAIAsy7Bv3z686U1vwjvf+c4zfm+320W9Xken00GtVhv21IiIRpYXxHhwYQNeFGPdW8Oavw6BDBN1A626seNOPhVCoN2LsNoOkaYCDbOBSXsSpqbjotkGGlWz7CkSERXqieTcodesR1GEe+65BzfeeOP2ZbIs49ChQ7j77rsfd/0wDBGGj7Yu63a7w54SEdGOYJsafuCiKSys9aDKMhpWE+veOtba69joRphoGGg6OuQdENo7boSVjQBxkqFm1DFVm4KuaJio29gz6XATKRHRORp6WF9dXUWappiZmTnp8pmZGXz7299+3PUPHz6M973vfcOeBhHRjiTLEvZsbrZcWHOhySpaVhOr3ipW1ttY74SYbBioV0cvtAsh4HoJVjYChHEKR3ewtzEFUzXQqJqYn3RY8kJEdJ5K7wZz44034oYbbtj+vNvtYt++fSXOiIiofJqqYP9MHTPNChbWXaiyipY1gRVvBYtrHSyvB3AqGmoVDRVLLbV7jB8k6PRj9PoxkjSDrVVwoDEFS7Xg2Ab2TDqoWHpp8yMi2smGHtYnJyehKAqWlpZOunxpaQmzs7OPu75hGDAMnlJHRHQqhq7iwGwDM80Kjq/2oCsapuwpdMMOOn4XHbcPRZZRq2hwNoN7EYIoRdeN0HVjxGkGVVbh6A3UnRos1ULF0rFn0oFj8/GdiOhCDP1RXdd1PP/5z8edd96JV77ylQAGG0zvvPNOvPGNbxz2cEREu4JlaHjynhb6foSVjgfLNTBpTyJIQnTDLrr9DjZ6LlRFhmNrMA0FhibD0JULLpcRQiCMM4RRijBK0fMSRHEKRVJRM+pwqjVUNBuSJKFeMTBRt7l5lIhoSHJZgrnhhhtw7bXX4tJLL8Vll12GW2+9Ff1+H9ddd10ewxER7RoVS0fF0iGEQKcfYr3rw+6bmK5MwU98dIIuXM/FRs/b/h5NlWHqCvTN8K6rMiRJgiQBW9UzQgACgMgEklQgjFIEcYowyhDHGQQGjcM0WYOtO5ixHFT0CmRJhmPraDkWGlUTipLb8R1ERLtSLmH9Z3/2Z7GysoL3vOc9WFxcxHOf+1x84QtfeNymUyIiemIkSUKjaqJRNZFlAm03wHrPhN23IYRABoEoCREkIcI0RBiH6AQBkiw8+w8HoEgqDNVARdEH5YqqCUMxoEiDMF61dLRqFpqOBZUBnYgoN7n0Wb8Q7LNORPTEpWmGfhAjiBL4YQx/879ZNnioT0WGOI0BDAL91lOAJEmQAEiQocoKVFndvtzUVViGCsvQYOkqbFNj60UioidgJPqsExFReRRFRq1ioFY5eWNnFKfb4T1OUggBZGIQ1oUYtIyUMPivIsvb4dzQlFI7zRAR7XYM60REu4CuKdA1BfWyJ0JEROeFhYZERERERCOKYZ2IiIiIaEQxrBMRERERjSiGdSIiIiKiEcWwTkREREQ0ohjWiYiIiIhGFMM6EREREdGIYlgnIiIiIhpRDOtERERERCOKYZ2IiIiIaESpZU/gsYQQAIBut1vyTIiIiIiIhmcr327l3XMxcmG91+sBAPbt21fyTIiIiIiIhq/X66Fer5/TdSVxPtG+AFmW4fjx43AcB5Ik5TJGt9vFvn37cPToUdRqtVzGoFPjbV8u3v7l4W1fHt725eLtXx7e9uU53W0vhECv18P8/Dxk+dyq0UduZV2WZezdu7eQsWq1Gu+8JeFtXy7e/uXhbV8e3vbl4u1fHt725TnVbX+uK+pbuMGUiIiIiGhEMawTEREREY2oXRnWDcPAzTffDMMwyp7KrsPbvly8/cvD2748vO3Lxdu/PLztyzPM237kNpgSEREREdHArlxZJyIiIiLaCRjWiYiIiIhGFMM6EREREdGIYlgnIiIiIhpRDOtERERERCNq14X1D37wg3jRi14E27bRaDROeR1Jkh738ed//ufFTnQMncttf+TIEVx99dWwbRvT09N429vehiRJip3oLnHgwIHH3c9/53d+p+xpjaXbbrsNBw4cgGmauPzyy/H1r3+97CntCu9973sfdx9/+tOfXva0xtKXv/xlXHPNNZifn4ckSfjc5z530teFEHjPe96Dubk5WJaFQ4cO4f777y9nsmPobLf/L/3SLz3u/4VXvOIV5Ux2jBw+fBgveMEL4DgOpqen8cpXvhLf+c53TrpOEAS4/vrrMTExgWq1ile96lVYWlo6r3F2XViPogivfvWr8YY3vOGM1/vEJz6BhYWF7Y9XvvKVxUxwjJ3ttk/TFFdffTWiKMJXvvIV/Mmf/Aluv/12vOc97yl4prvH+9///pPu529605vKntLY+fSnP40bbrgBN998M+69915ccskluPLKK7G8vFz21HaFZz7zmSfdx//pn/6p7CmNpX6/j0suuQS33XbbKb/+4Q9/GL//+7+Pj3/84/ja176GSqWCK6+8EkEQFDzT8XS22x8AXvGKV5z0/8KnPvWpAmc4nu666y5cf/31+OpXv4o77rgDcRzj5S9/Ofr9/vZ13vrWt+Kv//qv8Rd/8Re46667cPz4cfz0T//0+Q0kdqlPfOITol6vn/JrAMRnP/vZQuezm5zutv9f/+t/CVmWxeLi4vZlH/vYx0StVhNhGBY4w93hoosuEr/3e79X9jTG3mWXXSauv/767c/TNBXz8/Pi8OHDJc5qd7j55pvFJZdcUvY0dp3HPodmWSZmZ2fFRz7yke3L2u22MAxDfOpTnyphhuPtVBnm2muvFT/5kz9Zynx2k+XlZQFA3HXXXUKIwf1c0zTxF3/xF9vX+da3viUAiLvvvvucf+6uW1k/V9dffz0mJydx2WWX4b/8l/8CwbOjcnf33Xfj2c9+NmZmZrYvu/LKK9HtdvF//+//LXFm4+t3fud3MDExgec973n4yEc+wpKjIYuiCPfccw8OHTq0fZksyzh06BDuvvvuEme2e9x///2Yn5/Hk570JLzmNa/BkSNHyp7SrvPggw9icXHxpP8P6vU6Lr/8cv5/UKAvfelLmJ6exsUXX4w3vOENWFtbK3tKY6fT6QAAWq0WAOCee+5BHMcn3fef/vSnY//+/ed131eHO83x8P73vx8/+qM/Ctu28Xd/93f49V//dbiuize/+c1lT22sLS4unhTUAWx/vri4WMaUxtqb3/xm/OAP/iBarRa+8pWv4MYbb8TCwgI++tGPlj21sbG6uoo0TU95v/72t79d0qx2j8svvxy33347Lr74YiwsLOB973sf/s2/+Tf45je/Ccdxyp7errH1+H2q/w/42F6MV7ziFfjpn/5pHDx4EN/73vfwrne9C1dddRXuvvtuKIpS9vTGQpZleMtb3oIXv/jFeNazngVgcN/Xdf1x+/TO974/FmH9ne98Jz70oQ+d8Trf+ta3znlj0U033bT97+c973no9/v4yEc+wrB+CsO+7enCnM/f44Ybbti+7DnPeQ50Xcev/uqv4vDhwzAMI++pEuXuqquu2v73c57zHFx++eW46KKL8JnPfAave93rSpwZUbF+7ud+bvvfz372s/Gc5zwHT37yk/GlL30JL3vZy0qc2fi4/vrr8c1vfjOXfTFjEdZ/8zd/E7/0S790xus86UlPesI///LLL8dv//ZvIwxDhpjHGOZtPzs7+7guGVs7pmdnZ5/Q/HabC/l7XH755UiSBA899BAuvvjiHGa3+0xOTkJRlMft/F9aWuJ9ugSNRgNPe9rT8MADD5Q9lV1l676+tLSEubm57cuXlpbw3Oc+t6RZ7W5PetKTMDk5iQceeIBhfQje+MY34vOf/zy+/OUvY+/evduXz87OIooitNvtk1bXz/c5YCzC+tTUFKampnL7+ffddx+azSaD+ikM87Z/4QtfiA9+8INYXl7G9PQ0AOCOO+5ArVbDM57xjKGMMe4u5O9x3333QZbl7dueLpyu63j+85+PO++8c7ujVJZluPPOO/HGN76x3MntQq7r4nvf+x5e+9rXlj2VXeXgwYOYnZ3FnXfeuR3Ou90uvva1r521Mxvl45FHHsHa2tpJL57o/Akh8KY3vQmf/exn8aUvfQkHDx486evPf/7zoWka7rzzTrzqVa8CAHznO9/BkSNH8MIXvvCcxxmLsH4+jhw5gvX1dRw5cgRpmuK+++4DADzlKU9BtVrFX//1X2NpaQk/9EM/BNM0cccdd+CWW27Bb/3Wb5U78TFwttv+5S9/OZ7xjGfgta99LT784Q9jcXER7373u3H99dfzhdKQ3X333fja176GK664Ao7j4O6778Zb3/pW/MIv/AKazWbZ0xsrN9xwA6699lpceumluOyyy3Drrbei3+/juuuuK3tqY++3fuu3cM011+Ciiy7C8ePHcfPNN0NRFPz8z/982VMbO67rnvSOxYMPPoj77rsPrVYL+/fvx1ve8hZ84AMfwFOf+lQcPHgQN910E+bn59kWeUjOdPu3Wi28733vw6te9SrMzs7ie9/7Ht7+9rfjKU95Cq688soSZ73zXX/99fjkJz+Jv/qrv4LjONt16PV6HZZloV6v43Wvex1uuOEGtFot1Go1vOlNb8ILX/hC/NAP/dC5DzTkrjUj79prrxUAHvfxxS9+UQghxN/8zd+I5z73uaJarYpKpSIuueQS8fGPf1ykaVruxMfA2W57IYR46KGHxFVXXSUsyxKTk5PiN3/zN0Ucx+VNekzdc8894vLLLxf1el2Ypil+4Ad+QNxyyy0iCIKypzaW/uAP/kDs379f6LouLrvsMvHVr3617CntCj/7sz8r5ubmhK7rYs+ePeJnf/ZnxQMPPFD2tMbSF7/4xVM+vl977bVCiEH7xptuuknMzMwIwzDEy172MvGd73yn3EmPkTPd/p7niZe//OViampKaJomLrroIvErv/IrJ7VJpifmVLc5APGJT3xi+zq+74tf//VfF81mU9i2LX7qp35KLCwsnNc40uZgREREREQ0YthnnYiIiIhoRDGsExERERGNKIZ1IiIiIqIRxbBORERERDSiGNaJiIiIiEYUwzoRERER0YhiWCciIiIiGlEM60REREREI4phnYiIiIhoRDGsExERERGNKIZ1IiIiIqIR9f8D4bPtrfSQK2EAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.stats import plot_covariance_ellipse\n", + "import matplotlib.pyplot as plt\n", + "\n", + "P = [[2, 0], [0, 6]]\n", + "plot_covariance_ellipse((2, 7), P, fc='g', alpha=0.2, \n", + " std=[1, 2, 3],\n", + " title='|2 0|\\n|0 6|')\n", + "plt.gca().grid(False);" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "47c71447", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from kf_book.nonlinear_plots import plot_cov_ellipse_colormap\n", + "plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 1.3]]);" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b4ddeed2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = [2, 7]\n", + "P = [[2, 0], [0, 2]]\n", + "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", + " title='|2 0|\\n|0 2|')\n", + "plt.gca().grid(False)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "75acd5ce", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = [2, 7]\n", + "P = [[2, 0], [0, 6]]\n", + "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", + " title='|2 0|\\n|0 6|')\n", + "plt.gca().grid(False)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "8572a83b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = [2, 7]\n", + "P = [[2, 1.2], [1.2, 2]]\n", + "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", + " title='|2 1.2|\\n|1.2 2|')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1ceff08d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 18.525, 135.701],\n", + " [ 135.701, 1092.29 ]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov_hw = np.cov(np.vstack((height, weight)), bias=1)\n", + "cov_hw" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "40647bd1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(height, weight, s=120, marker='s')\n", + "plt.title('Track Team Height vs. Weight')\n", + "plt.xlabel('Height (in)'); plt.ylabel('Weight (lbs)')\n", + "plot_covariance_ellipse((np.mean(height), np.mean(weight)), cov_hw, fc='g', \n", + " alpha=0.2, axis_equal=False, std=2)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3a3073c9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "max_temp = [200, 250, 300, 400, 450, 500]\n", + "lifespan = [10, 9.7, 5, 5.4, 4.3, 0.3]\n", + "\n", + "plt.scatter(max_temp, lifespan, s=80)\n", + "cov = np.cov(np.vstack((max_temp, lifespan)))\n", + "plot_covariance_ellipse((np.mean(max_temp), np.mean(lifespan)), cov, fc='g', \n", + " alpha=0.2, axis_equal=False, std=2)\n", + "plt.title('Engine Temperature vs Lifespan')\n", + "plt.xlabel('Temperature (C)'); plt.ylabel('Years');" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "da680421", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c63e7e2461784ae79fe27f0f5d50d365", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=5.0, continuous_update=False, description='var_x', max=20.0), FloatSli…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from ipywidgets import interact\n", + "from kf_book.book_plots import figsize, FloatSlider\n", + "\n", + "fig = None\n", + "def plot_covariance(var_x, var_y, cov_xy):\n", + " global fig\n", + " if fig: plt.close(fig)\n", + " fig = plt.figure(figsize=(4,4))\n", + " P1 = [[var_x, cov_xy], [cov_xy, var_y]]\n", + "\n", + " plot_covariance_ellipse((10, 10), P1, axis_equal=False,\n", + " show_semiaxis=True)\n", + "\n", + " plt.xlim(4, 16)\n", + " plt.gca().set_aspect('equal')\n", + " plt.ylim(4, 16)\n", + "\n", + " \n", + "with figsize(y=6):\n", + " interact (plot_covariance, \n", + " var_x=FloatSlider(5, min=0, max=20), \n", + " var_y=FloatSlider(5, min=0, max=20), \n", + " cov_xy=FloatSlider(1.5, min=0, max=50, step=.2));" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "ed1fb161", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P = [[4, 3.9], [3.9, 4]]\n", + "\n", + "plot_covariance_ellipse((5, 10), P, ec='k', std=[1, 2, 3])\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y');" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "c15c7d62", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P0 = [[6, 0], [0, 6]]\n", + "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "cbf589fb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P1 = [[2, 1.9], [1.9, 2]]\n", + "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P1, fc='g', alpha=0.9)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "f64dab4d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.stats import multivariate_multiply\n", + "\n", + "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", + "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", + "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.9)\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "9d86bc4f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P3 = [[2, -1.9], [-1.9, 2.2]]\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "dd36018e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "d476c9cd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import kf_book.book_plots as book_plots\n", + "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "a795569b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P1 = [[2, 0], [0, .2]]\n", + "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", + "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", + "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "6a174317", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P3 = [[2, -1.9], [-1.9, 2.2]]\n", + "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", + "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", + "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "2862db11", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P5 = multivariate_multiply((10,10), P2, (10.1, 9.97), P2)\n", + "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", + "plot_covariance_ellipse((10.1, 9.97), P2, ec='k', fc='g', alpha=0.6)\n", + "plot_covariance_ellipse(P5[0], P5[1], ec='k', fc='b')\n", + "plt.xlim(6, 14);" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "e294f927", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from filterpy.stats import plot_3d_covariance\n", + "\n", + "mu = [0.3, 5., 10.]\n", + "C = np.array([[1.0, .03, .2],\n", + " [.03, 4.0, .0],\n", + " [.2, .0, 16.1]])\n", + "\n", + "sample = np.random.multivariate_normal(mu, C, size=1000)\n", + "\n", + "ax = plot_3d_covariance(mu, C, alpha=.4, std=3, limit_xyz=True)\n", + "ax.scatter(sample[:, 0], sample[:, 1], zs=sample[:, 2],);\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "10d26757", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/06-Multivariate-Kalman-Filters.ipynb b/kalman_and_bayesian_filters/06-Multivariate-Kalman-Filters.ipynb new file mode 100644 index 0000000..93b3a19 --- /dev/null +++ b/kalman_and_bayesian_filters/06-Multivariate-Kalman-Filters.ipynb @@ -0,0 +1,33 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "e6b03f7e", + "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": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/kalman_and_bayesian_filters/LICENSE.md b/kalman_and_bayesian_filters/LICENSE.md new file mode 100644 index 0000000..0575583 --- /dev/null +++ b/kalman_and_bayesian_filters/LICENSE.md @@ -0,0 +1,9 @@ +The MIT License (MIT) + +Copyright (c) 2015 Roger R. Labbe Jr + +Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.TION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. \ No newline at end of file diff --git a/kalman_and_bayesian_filters/README.md b/kalman_and_bayesian_filters/README.md new file mode 100644 index 0000000..bec49d0 --- /dev/null +++ b/kalman_and_bayesian_filters/README.md @@ -0,0 +1,3 @@ +# Kalman and Bayesian Filters in Python + +See https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python \ No newline at end of file diff --git a/kalman_and_bayesian_filters/book_format.py b/kalman_and_bayesian_filters/book_format.py new file mode 100644 index 0000000..65dcec5 --- /dev/null +++ b/kalman_and_bayesian_filters/book_format.py @@ -0,0 +1,183 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from contextlib import contextmanager +from IPython.core.display import HTML +import json +import os.path +import sys +import warnings +from kf_book.book_plots import set_figsize, reset_figsize + +def test_installation(): + try: + import filterpy + except: + print("Please install FilterPy from the command line by running the command\n\t$ pip install filterpy\n\nSee chapter 0 for instructions.") + + try: + import numpy + except: + print("Please install NumPy before continuing. See chapter 0 for instructions.") + + try: + import scipy + except: + print("Please install SciPy before continuing. See chapter 0 for instructions.") + + try: + import sympy + except: + print("Please install SymPy before continuing. See chapter 0 for instructions.") + + try: + import matplotlib + except: + print("Please install matplotlib before continuing. See chapter 0 for instructions.") + + from distutils.version import LooseVersion + + v = filterpy.__version__ + min_version = "1.4.4" + if LooseVersion(v) < LooseVersion(min_version): + print("Minimum FilterPy version supported is {}. " + "Please install a more recent version.\n" + " ex: pip install filterpy --upgrade".format( + min_version)) + + + v = matplotlib.__version__ + min_version = "3.0" # this is really old!!! + if LooseVersion(v) < LooseVersion(min_version): + print("Minimum Matplotlib version supported is {}. " + "Please install a more recent version.".format(min_version)) + + # require Python 3.6+ + import sys + v = sys.version_info + if v.major < 3 or (v.major == 3 and v.minor < 6): + print('You must use Python version 3.6 or later for the notebooks to work correctly') + + + # need to add test for IPython. I think I want to be at 6, which also implies + # Python 3, matplotlib 2+, etc. + +# ensure that we have the correct packages loaded. This is +# called when this module is imported at the top of each book +# chapter so the reader can see that they need to update their environment. +test_installation() + + +# now that we've tested the existence of all packages go ahead and import + +import matplotlib +import matplotlib.pylab as pylab +import matplotlib.pyplot as plt +import numpy as np + + +try: + matplotlib.style.use('default') +except: + pass + + +with warnings.catch_warnings(): + warnings.simplefilter("ignore", matplotlib.MatplotlibDeprecationWarning) + pylab.rcParams['figure.max_open_warning'] = 50 + + +@contextmanager +def numpy_precision(precision): + old = np.get_printoptions()['precision'] + np.set_printoptions(precision=precision) + yield + np.set_printoptions(old) + +@contextmanager +def printoptions(*args, **kwargs): + original = np.get_printoptions() + np.set_printoptions(*args, **kwargs) + yield + np.set_printoptions(**original) + +def _decode_list(data): + rv = [] + for item in data: + if isinstance(item, unicode): + item = item.encode('utf-8') + elif isinstance(item, list): + item = _decode_list(item) + elif isinstance(item, dict): + item = _decode_dict(item) + rv.append(item) + return rv + +def _decode_dict(data): + rv = {} + for key, value in data.iteritems(): + if isinstance(key, unicode): + key = key.encode('utf-8') + if isinstance(value, unicode): + value = value.encode('utf-8') + elif isinstance(value, list): + value = _decode_list(value) + elif isinstance(value, dict): + value = _decode_dict(value) + rv[key] = value + return rv + + +def set_style(): + version = [int(version_no) for version_no in matplotlib.__version__.split('.')] + + try: + if sys.version_info[0] >= 3: + style = json.load(open("./kf_book/538.json")) + else: + style = json.load(open(".//kf_book/538.json"), object_hook=_decode_dict) + + with warnings.catch_warnings(): + warnings.simplefilter("ignore", matplotlib.MatplotlibDeprecationWarning) + plt.rcParams.update(style) + except: + pass + np.set_printoptions(suppress=True, precision=3, + threshold=10000., linewidth=70, + formatter={'float':lambda x:' {:.3}'.format(x)}) + + # I don't know why I have to do this, but I have to call + # with suppress a second time or the notebook doesn't suppress + # exponents + np.set_printoptions(suppress=True) + reset_figsize() + + style = ''' + + ''' + jscript = ''' + %%javascript + IPython.OutputArea.auto_scroll_threshold = 9999; + ''' + return HTML(style) diff --git a/kalman_and_bayesian_filters/kf_book/book_plots.py b/kalman_and_bayesian_filters/kf_book/book_plots.py new file mode 100644 index 0000000..91b6a96 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/book_plots.py @@ -0,0 +1,459 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +from contextlib import contextmanager +import ipywidgets +import matplotlib as mpl +import matplotlib.pylab as pylab +import matplotlib.pyplot as plt +from matplotlib.patches import Circle +import numpy as np + + +_default_size = (9, 4) + +def equal_axis(sz=_default_size[0]): + """ set size of axis in inches, using the same for each""" + pylab.rcParams['figure.figsize'] = sz, sz + plt.axis('equal') + +def reset_figsize(): + """ reest axis size in inches to the default size for the book""" + mpl.rcParams['figure.figsize'] = _default_size + + +def set_figsize(x=_default_size[0], y=_default_size[1]): + """ set the figure size of the plot to the specified size in inches""" + + mpl.rcParams['figure.figsize'] = x, y + + +@contextmanager +def figsize(x=8, y=3): + """Temporarily set the figure size using 'with figsize(a, b):'""" + + size = pylab.rcParams['figure.figsize'] + set_figsize(x, y) + yield + pylab.rcParams['figure.figsize'] = size + + +""" If the plot is inline (%matplotlib inline) we need to +do special processing for the interactive_plot context manager, +otherwise it outputs a lot of extra >> plot_errorbars([(160, 3, 'A'), (170, 9, 'B')], xlims=(150, 180)) + """ + + with figsize(y=2): + i = 0.0 + for bar in bars: + plt.errorbar([bar[0]], [i], xerr=[bar[1]], fmt='o', label=bar[2] , capthick=2, capsize=10) + i += 0.2 + + plt.ylim(*ylims) + plt.xlim(xlims[0], xlims[1]) + show_legend() + plt.gca().axes.yaxis.set_ticks([]) + plt.show() + + +def predict_update_chart(box_bg = '#CCCCCC', + arrow1 = '#88CCFF', + arrow2 = '#88FF88'): + plt.figure(figsize=(4, 4), facecolor='w') + ax = plt.axes((0, 0, 1, 1), + xticks=[], yticks=[], frameon=False) + + pc = Circle((4, 5), 0.7, fc=box_bg) + uc = Circle((6, 5), 0.7, fc=box_bg) + ax.add_patch (pc) + ax.add_patch (uc) + + plt.text(4, 5, "Predict\nStep",ha='center', va='center', fontsize=12) + plt.text(6, 5, "Update\nStep",ha='center', va='center', fontsize=12) + + #btm arrow from update to predict + ax.annotate('', + xy=(4.1, 4.5), xycoords='data', + xytext=(6, 4.5), textcoords='data', + size=20, + arrowprops=dict(arrowstyle="simple", + fc="0.6", ec="none", + patchB=pc, + patchA=uc, + connectionstyle="arc3,rad=-0.5")) + #top arrow from predict to update + ax.annotate('', + xy=(6, 5.5), xycoords='data', + xytext=(4.1, 5.5), textcoords='data', + size=20, + arrowprops=dict(arrowstyle="simple", + fc="0.6", ec="none", + patchB=uc, + patchA=pc, + connectionstyle="arc3,rad=-0.5")) + + ax.annotate('Measurement ($\mathbf{z_k}$)', + xy=(6.3, 5.6), xycoords='data', + xytext=(6,6), textcoords='data', + size=14, + arrowprops=dict(arrowstyle="simple", + fc="0.6", ec="none")) + + # arrow from predict to state estimate + ax.annotate('', + xy=(4.0, 3.8), xycoords='data', + xytext=(4.0,4.3), textcoords='data', + size=12, + arrowprops=dict(arrowstyle="simple", + fc="0.6", ec="none")) + + ax.annotate('Initial\nConditions ($\mathbf{x_0}$)', + xy=(4.05, 5.7), xycoords='data', + xytext=(2.5, 6.5), textcoords='data', + size=14, + arrowprops=dict(arrowstyle="simple", + fc="0.6", ec="none")) + + plt.text (4, 3.7,'State Estimate ($\mathbf{\hat{x}_k}$)', + ha='center', va='center', fontsize=14) + plt.axis('equal') + plt.show() + + +def show_residual_chart(show_eq=True, show_H=False): + plt.figure(figsize=(11, 3.), facecolor='w') + est_y = ((164.2 - 158)*.8 + 158) + + ax = plt.axes(xticks=[], yticks=[], frameon=False) + ax.annotate('', xy=[1,159], xytext=[0, 158], + arrowprops=dict(arrowstyle='->', + ec='r', lw=3, shrinkA=6, shrinkB=5)) + + ax.annotate('', xy=[1, 159], xytext=[1, 164.2], + arrowprops=dict(arrowstyle='-', + ec='k', lw=3, shrinkA=8, shrinkB=8)) + + ax.annotate('', xy=(1., est_y), xytext=(0.9, est_y), + arrowprops=dict(arrowstyle='->', ec='#004080', + lw=2, + shrinkA=3, shrinkB=4)) + + + plt.scatter ([0,1], [158.0,est_y], c='k',s=128) + plt.scatter ([1], [164.2], c='b',s=128) + plt.scatter ([1], [159], c='r', s=128) + plt.text (1.05, 158.8, r"prior $(\bar{x}_t)$", ha='center',va='top',fontsize=18,color='red') + plt.text (0.5, 159.6, "prediction", ha='center',va='top',fontsize=18,color='red') + plt.text (1.0, 164.4, r"measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue') + plt.text (0, 157.8, r"posterior ($x_{t-1}$)", ha='center', va='top',fontsize=18) + plt.text (1.02, est_y-1.5, "residual($y$)", ha='left', va='center',fontsize=18) + if show_eq: + if show_H: + plt.text (1.02, est_y-2.2, r"$y=z-H\bar x_t$", ha='left', va='center',fontsize=18) + else: + plt.text (1.02, est_y-2.2, r"$y=z-\bar x_t$", ha='left', va='center',fontsize=18) + plt.text (0.9, est_y, "new estimate ($x_t$)", ha='right', va='center',fontsize=18) + plt.text (0.8, est_y-0.5, "(posterior)", ha='right', va='center',fontsize=18) + if show_eq: + plt.text (0.75, est_y-1.2, r"$\bar{x}_t + Ky$", ha='right', va='center',fontsize=18) + plt.xlabel('time') + ax.yaxis.set_label_position("right") + plt.ylabel('state') + plt.xlim(-0.1, 1.5) + + +def show_legend(): + plt.legend(loc='center left', bbox_to_anchor=(1, 0.5)) + + +def bar_plot(pos, x=None, ylim=(0,1), title=None, c='#30a2da', + **kwargs): + """ plot the values in `pos` as a bar plot. + + **Parameters** + + pos : list-like + list of values to plot as bars + + x : list-like, optional + If provided, specifies the x value for each value in pos. If not + provided, the first pos element is plotted at x == 0, the second + at 1, etc. + + ylim : (lower, upper), default = (0,1) + specifies the lower and upper limits for the y-axis + + title : str, optional + If specified, provides a title for the plot + + c : color, default='#30a2da' + Color for the bars + + **kwargs : keywords, optional + extra keyword arguments passed to ax.bar() + + """ + + ax = plt.gca() + if x is None: + x = np.arange(len(pos)) + ax.bar(x, pos, color=c, **kwargs) + if ylim: + plt.ylim(ylim) + plt.xticks(np.asarray(x), x) + if title is not None: + plt.title(title) + + +def plot_belief_vs_prior(belief, prior, **kwargs): + """ plots two discrete probability distributions side by side, with + titles "belief" and "prior" + """ + + plt.subplot(121) + bar_plot(belief, title='belief', **kwargs) + plt.subplot(122) + bar_plot(prior, title='prior', **kwargs) + + +def plot_prior_vs_posterior(prior, posterior, reverse=False, **kwargs): + """ plots two discrete probability distributions side by side, with + titles "prior" and "posterior" + """ + if reverse: + plt.subplot(121) + bar_plot(posterior, title='posterior', **kwargs) + plt.subplot(122) + bar_plot(prior, title='prior', **kwargs) + else: + plt.subplot(121) + bar_plot(prior, title='prior', **kwargs) + plt.subplot(122) + bar_plot(posterior, title='posterior', **kwargs) + + +def set_labels(title=None, x=None, y=None): + """ helps make code in book shorter. Optional set title, xlabel and ylabel + """ + if x is not None: + plt.xlabel(x) + if y is not None: + plt.ylabel(y) + if title is not None: + plt.title(title) + + +def set_limits(x, y): + """ helper function to make code in book shorter. Set the limits for the x + and y axis. + """ + + plt.gca().set_xlim(x) + plt.gca().set_ylim(y) + +def plot_predictions(p, rng=None, label='Prediction'): + if rng is None: + rng = range(len(p)) + plt.scatter(rng, p, marker='v', s=40, edgecolor='r', + facecolor='None', lw=2, label=label) + + +def plot_kf_output(xs, filter_xs, zs, title=None, aspect_equal=True): + plot_filter(filter_xs[:, 0]) + plot_track(xs[:, 0]) + + if zs is not None: + plot_measurements(zs) + show_legend() + set_labels(title=title, y='meters', x='time (sec)') + if aspect_equal: + plt.gca().set_aspect('equal') + plt.xlim((-1, len(xs))) + plt.show() + + +def FloatSlider(value, **kwargs): + """ + Creates an ipwidgets FloatSlider with continuous update + turned off + """ + return ipywidgets.FloatSlider(value, continuous_update=False, **kwargs) + + +def IntSlider(value, **kwargs): + """ + Creates an ipwidgets IntSlider with continuous update + turned off + """ + return ipywidgets.IntSlider(value, continuous_update=False, **kwargs) + + +def plot_measurements(xs, ys=None, dt=None, color='k', lw=1, label='Measurements', + lines=False, **kwargs): + """ Helper function to give a consistent way to display + measurements in the book. + """ + if ys is None and dt is not None: + ys = xs + xs = np.arange(0, len(ys)*dt, dt) + + plt.autoscale(tight=False) + if lines: + if ys is not None: + return plt.plot(xs, ys, color=color, lw=lw, ls='--', label=label, **kwargs) + else: + return plt.plot(xs, color=color, lw=lw, ls='--', label=label, **kwargs) + else: + if ys is not None: + return plt.scatter(xs, ys, edgecolor=color, facecolor='none', + lw=2, label=label, **kwargs), + else: + return plt.scatter(range(len(xs)), xs, edgecolor=color, facecolor='none', + lw=2, label=label, **kwargs), + + +def plot_residual_limits(Ps, stds=1.): + """ plots standard deviation given in Ps as a yellow shaded region. One std + by default, use stds for a different choice (e.g. stds=3 for 3 standard + deviations. + """ + + std = np.sqrt(Ps) * stds + + plt.plot(-std, color='k', ls=':', lw=2) + plt.plot(std, color='k', ls=':', lw=2) + plt.fill_between(range(len(std)), -std, std, + facecolor='#ffff00', alpha=0.3) + + +def plot_track(xs, ys=None, dt=None, label='Track', c='k', lw=2, **kwargs): + if ys is None and dt is not None: + ys = xs + xs = np.arange(0, len(ys)*dt, dt) + if ys is not None: + return plt.plot(xs, ys, color=c, lw=lw, ls=':', label=label, **kwargs) + else: + return plt.plot(xs, color=c, lw=lw, ls=':', label=label, **kwargs) + + +def plot_filter(xs, ys=None, dt=None, c='C0', label='Filter', var=None, **kwargs): + """ plot result of KF with color `c`, optionally displaying the variance + of `xs`. Returns the list of lines generated by plt.plot()""" + + if ys is None and dt is not None: + ys = xs + xs = np.arange(0, len(ys) * dt, dt) + if ys is None: + ys = xs + xs = range(len(ys)) + + lines = plt.plot(xs, ys, color=c, label=label, **kwargs) + if var is None: + return lines + + var = np.asarray(var) + std = np.sqrt(var) + std_top = ys+std + std_btm = ys-std + + plt.plot(xs, ys+std, linestyle=':', color='k', lw=2) + plt.plot(xs, ys-std, linestyle=':', color='k', lw=2) + plt.fill_between(xs, std_btm, std_top, + facecolor='yellow', alpha=0.2) + + return lines + + +def _blob(x, y, area, colour): + """ + Draws a square-shaped blob with the given area (< 1) at + the given coordinates. + """ + hs = np.sqrt(area) / 2 + xcorners = np.array([x - hs, x + hs, x + hs, x - hs]) + ycorners = np.array([y - hs, y - hs, y + hs, y + hs]) + plt.fill(xcorners, ycorners, colour, edgecolor=colour) + + +def hinton(W, maxweight=None): + """ + Draws a Hinton diagram for visualizing a weight matrix. + Temporarily disables matplotlib interactive mode if it is on, + otherwise this takes forever. + """ + reenable = False + if plt.isinteractive(): + plt.ioff() + + plt.clf() + height, width = W.shape + if not maxweight: + maxweight = 2**np.ceil(np.log(np.max(np.abs(W)))/np.log(2)) + + plt.fill(np.array([0, width, width, 0]), + np.array([0, 0, height, height]), + 'gray') + + plt.axis('off') + plt.axis('equal') + for x in range(width): + for y in range(height): + _x = x+1 + _y = y+1 + w = W[y, x] + if w > 0: + _blob(_x - 0.5, + height - _y + 0.5, + min(1, w/maxweight), + 'white') + elif w < 0: + _blob(_x - 0.5, + height - _y + 0.5, + min(1, -w/maxweight), + 'black') + if reenable: + plt.ion() diff --git a/kalman_and_bayesian_filters/kf_book/gaussian_internal.py b/kalman_and_bayesian_filters/kf_book/gaussian_internal.py new file mode 100644 index 0000000..6ac3e2b --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/gaussian_internal.py @@ -0,0 +1,132 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +import filterpy.stats as stats +import math +import matplotlib.pyplot as plt +import numpy as np + +def plot_height_std(x, lw=10): + m = np.mean(x) + s = np.std(x) + + for i, height in enumerate(x): + plt.plot([i+1, i+1], [0, height], color='k', lw=lw) + plt.xlim(0, len(x)+1) + plt.axhline(m-s, ls='--') + plt.axhline(m+s, ls='--') + plt.fill_between((0, len(x)+1), m-s, m+s, + facecolor='yellow', alpha=0.4) + plt.xlabel('student') + plt.ylabel('height (m)') + plt.show() + + +def plot_correlated_data(X, Y, xlabel=None, + ylabel=None, equal=True): + + """Plot correlation between x and y by performing + linear regression between X and Y. + + X: x data + Y: y data + xlabel: str + optional label for x axis + ylabel: str + optional label for y axis + equal: bool, default True + use equal scale for x and y axis + """ + + + plt.scatter(X, Y) + + if xlabel is not None: + plt.xlabel(xlabel); + + if ylabel is not None: + plt.ylabel(ylabel) + + # fit line through data + m, b = np.polyfit(X, Y, 1) + plt.plot(X, np.asarray(X)*m + b,color='k') + if equal: + plt.gca().set_aspect('equal') + plt.show() + +def plot_gaussian(mu, variance, + mu_line=False, + xlim=None, + xlabel=None, + ylabel=None): + + xs = np.arange(mu-variance*2,mu+variance*2,0.1) + ys = [stats.gaussian (x, mu, variance)*100 for x in xs] + plt.plot (xs, ys) + if mu_line: + plt.axvline(mu) + if xlim: + plt.xlim(xlim) + if xlabel: + plt.xlabel(xlabel) + if ylabel: + plt.ylabel(ylabel) + plt.show() + + +def display_stddev_plot(): + xs = np.arange(10,30,0.1) + var = 8; + stddev = math.sqrt(var) + p2, = plt.plot (xs,[stats.gaussian(x, 20, var) for x in xs]) + x = 20+stddev + # 1std vertical lines + y = stats.gaussian(x, 20, var) + plt.plot ([x,x], [0,y],'g') + plt.plot ([20-stddev, 20-stddev], [0,y], 'g') + + #2std vertical lines + x = 20+2*stddev + y = stats.gaussian(x, 20, var) + plt.plot ([x,x], [0,y],'g') + plt.plot ([20-2*stddev, 20-2*stddev], [0,y], 'g') + + y = stats.gaussian(20,20,var) + plt.plot ([20,20],[0,y],'b') + + x = 20+stddev + ax = plt.gca() + ax.annotate('68%', xy=(20.3, 0.045)) + ax.annotate('', xy=(20-stddev,0.04), xytext=(x,0.04), + arrowprops=dict(arrowstyle="<->", + ec="r", + shrinkA=2, shrinkB=2)) + ax.annotate('95%', xy=(20.3, 0.02)) + ax.annotate('', xy=(20-2*stddev,0.015), xytext=(20+2*stddev,0.015), + arrowprops=dict(arrowstyle="<->", + ec="r", + shrinkA=2, shrinkB=2)) + + + ax.xaxis.set_ticks ([20-2*stddev, 20-stddev, 20, 20+stddev, 20+2*stddev]) + ax.xaxis.set_ticklabels(['$-2\sigma$', '$-1\sigma$','$\mu$','$1\sigma$', '$2\sigma$']) + ax.yaxis.set_ticks([]) + ax.grid(None, 'both', lw=0) + +if __name__ == '__main__': + display_stddev_plot() diff --git a/kalman_and_bayesian_filters/kf_book/gh_internal.py b/kalman_and_bayesian_filters/kf_book/gh_internal.py new file mode 100644 index 0000000..d839a67 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/gh_internal.py @@ -0,0 +1,227 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + + +import kf_book.book_plots as book_plots +from kf_book.book_plots import figsize +import numpy as np +from matplotlib.patches import Circle, Rectangle, Polygon, Arrow, FancyArrow +import matplotlib.pylab as plt + + +def plot_hypothesis1(): + with figsize(y=3.5): + plt.figure() + plt.errorbar([1, 2, 3], [170, 161, 169], + xerr=0, yerr=10, fmt='bo', capthick=2, capsize=10) + + plt.plot([1, 3], [180, 160], color='g', ls='--') + plt.plot([1, 3], [170, 170], color='g', ls='--') + plt.plot([1, 3], [160, 175], color='g', ls='--') + plt.plot([1, 2, 3], [180, 152, 179], color='g', ls='--') + plt.xlim(0,4) + plt.ylim(150, 185) + plt.xlabel('day') + plt.ylabel('lbs') + plt.grid(False) + plt.tight_layout() + + +def plot_hypothesis2(): + with book_plots.figsize(y=2.5): + plt.figure() + plt.errorbar(range(1, 11), [169, 170, 169,171, 170, 171, 169, 170, 169, 170], + xerr=0, yerr=6, fmt='bo', capthick=2, capsize=10) + plt.plot([1, 10], [169, 170.5], color='g', ls='--') + + plt.xlim(0, 11) + plt.ylim(150, 185) + plt.xlabel('day') + plt.ylabel('lbs') + plt.grid(False) + +def plot_hypothesis3(): + weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, + 169.6, 167.4, 166.4, 171.0, 171.2, 172.6] + + with book_plots.figsize(y=2.5): + plt.figure() + + plt.errorbar(range(1, 13), weights, + xerr=0, yerr=6, fmt='o', capthick=2, capsize=10) + + plt.xlim(0, 13) + plt.ylim(145, 185) + plt.xlabel('day') + plt.ylabel('weight (lbs)') + plt.grid(False) + + +def plot_hypothesis4(): + weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, + 169.6, 167.4, 166.4, 171.0, 171.2, 172.6] + + with book_plots.figsize(y=2.5): + plt.figure() + ave = np.sum(weights) / len(weights) + plt.errorbar(range(1,13), weights, label='weights', + yerr=6, fmt='o', capthick=2, capsize=10) + plt.plot([1, 12], [ave,ave], c='r', label='hypothesis') + plt.xlim(0, 13) + plt.ylim(145, 185) + plt.xlabel('day') + plt.ylabel('weight (lbs)') + book_plots.show_legend() + plt.grid(False) + + +def plot_hypothesis5(): + weights = [158.0, 164.2, 160.3, 159.9, 162.1, 164.6, + 169.6, 167.4, 166.4, 171.0, 171.2, 172.6] + + xs = range(1, len(weights)+1) + line = np.poly1d(np.polyfit(xs, weights, 1)) + + with figsize(y=2.5): + plt.figure() + plt.errorbar(range(1, 13), weights, label='weights', + yerr=5, fmt='o', capthick=2, capsize=10) + plt.plot (xs, line(xs), c='r', label='hypothesis') + plt.xlim(0, 13) + plt.ylim(145, 185) + plt.xlabel('day') + plt.ylabel('weight (lbs)') + book_plots.show_legend() + plt.grid(False) + + +def plot_estimate_chart_1(): + with figsize(y=2.5): + plt.figure() + ax = plt.axes() + ax.annotate('', xy=[1,159], xytext=[0,158], + arrowprops=dict(arrowstyle='->', ec='r',shrinkA=6, lw=3,shrinkB=5)) + plt.scatter ([0], [158], c='b') + plt.scatter ([1], [159], c='r') + plt.xlabel('day') + plt.ylabel('weight (lbs)') + ax.xaxis.grid(True, which="major", linestyle='dotted') + ax.yaxis.grid(True, which="major", linestyle='dotted') + plt.tight_layout() + + +def plot_estimate_chart_2(): + with figsize(y=2.5): + plt.figure() + ax = plt.axes() + ax.annotate('', xy=[1,159], xytext=[0,158], + arrowprops=dict(arrowstyle='->', + ec='r', lw=3, shrinkA=6, shrinkB=5)) + plt.scatter ([0], [158.0], c='k',s=128) + plt.scatter ([1], [164.2], c='b',s=128) + plt.scatter ([1], [159], c='r', s=128) + plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red') + plt.text (1.0, 164.4, "measurement ($z_t$)",ha='center',va='bottom',fontsize=18,color='blue') + plt.text (0.0, 159.8, "last estimate ($\hat{x}_{t-1}$)", ha='left', va='top',fontsize=18) + plt.xlabel('day') + plt.ylabel('weight (lbs)') + ax.xaxis.grid(True, which="major", linestyle='dotted') + ax.yaxis.grid(True, which="major", linestyle='dotted') + plt.ylim(157, 164.5) + + +def plot_estimate_chart_3(): + with figsize(y=2.5): + plt.figure() + ax = plt.axes() + ax.annotate('', xy=[1,159], xytext=[0,158], + arrowprops=dict(arrowstyle='->', + ec='r', lw=3, shrinkA=6, shrinkB=5)) + + ax.annotate('', xy=[1,159], xytext=[1,164.2], + arrowprops=dict(arrowstyle='-', + ec='k', lw=3, shrinkA=8, shrinkB=8)) + + est_y = (158 + .4*(164.2-158)) + plt.scatter ([0,1], [158.0,est_y], c='k',s=128) + plt.scatter ([1], [164.2], c='b',s=128) + plt.scatter ([1], [159], c='r', s=128) + plt.text (1.0, 158.8, "prediction ($x_t)$", ha='center',va='top',fontsize=18,color='red') + plt.text (1.0, 164.4, "measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue') + plt.text (0, 159.8, "last estimate ($\hat{x}_{t-1}$)", ha='left', va='top',fontsize=18) + plt.text (0.95, est_y, "estimate ($\hat{x}_{t}$)", ha='right', va='center',fontsize=18) + plt.xlabel('day') + plt.ylabel('weight (lbs)') + ax.xaxis.grid(True, which="major", linestyle='dotted') + ax.yaxis.grid(True, which="major", linestyle='dotted') + plt.ylim(157, 164.5) + + +def plot_gh_results(weights, estimates, predictions, actual, time_step=0): + n = len(weights) + if time_step > 0: + rng = range(1, n+1) + else: + rng = range(n, n+1) + xs = range(n+1) + book_plots.plot_measurements(range(1, len(weights)+1), weights, color='k', lines=False) + book_plots.plot_filter(xs, estimates, marker='o', label='Estimates') + book_plots.plot_track(xs[1:], predictions, c='r', marker='v', label='Predictions') + plt.plot([xs[0], xs[-1]], actual, c='k', lw=1, label='Actual') + plt.legend(loc=4) + book_plots.set_labels(x='day', y='weight (lbs)') + plt.xlim([-1, n+1]) + plt.ylim([156.0, 173]) + + +def print_results(estimates, prediction, weight): + print('previous estimate: {:.2f}, prediction: {:.2f}, estimate {:.2f}'.format( + estimates[-2], prediction, weight)) + + +def plot_g_h_results(measurements, filtered_data, + title='', z_label='Measurements', + **kwargs): + + book_plots.plot_filter(filtered_data, **kwargs) + book_plots.plot_measurements(measurements, label=z_label) + plt.legend(loc=4) + plt.title(title) + plt.gca().set_xlim(left=0,right=len(measurements)) + + return + + import time + if not interactive: + book_plots.plot_filter(filtered_data, **kwargs) + book_plots.plot_measurements(measurements, label=z_label) + book_plots.show_legend() + plt.title(title) + plt.gca().set_xlim(left=0,right=len(measurements)) + else: + for i in range(2, len(measurements)): + book_plots.plot_filter(filtered_data, **kwargs) + book_plots.plot_measurements(measurements, label=z_label) + book_plots.show_legend() + plt.title(title) + plt.gca().set_xlim(left=0,right=len(measurements)) + plt.gca().canvas.draw() + time.sleep(0.5) + +if __name__ == '__main__': + pass diff --git a/kalman_and_bayesian_filters/kf_book/kf_internal.py b/kalman_and_bayesian_filters/kf_book/kf_internal.py new file mode 100644 index 0000000..c3e3157 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/kf_internal.py @@ -0,0 +1,92 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +import kf_book.book_plots as bp +import filterpy.stats as stats +from math import sqrt +import matplotlib.pyplot as plt +import numpy as np +from numpy.random import randn, seed + + +def plot_dog_track(xs, dog, measurement_var, process_var): + N = len(xs) + bp.plot_track(dog) + bp.plot_measurements(xs, label='Sensor') + bp.set_labels('variance = {}, process variance = {}'.format( + measurement_var, process_var), 'time', 'pos') + plt.ylim([0, N]) + bp.show_legend() + plt.show() + + +def print_gh(predict, update, z): + predict_template = '{: 7.3f} {: 8.3f}' + update_template = '{:.3f}\t{: 7.3f} {: 7.3f}' + + print(predict_template.format(predict[0], predict[1]),end='\t') + print(update_template.format(z, update[0], update[1])) + + +def print_variance(positions): + for i in range(0, len(positions), 5): + print('\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format( + *[v[1] for v in positions[i:i+5]])) + + + +def gaussian_vs_histogram(): + + seed(15) + xs = np.arange(0, 20, 0.1) + ys = np.array([stats.gaussian(x-10, 0, 2) for x in xs]) + bar_ys = abs(ys + randn(len(xs)) * stats.gaussian(xs-10, 0, 10)/2) + plt.gca().bar(xs[::5]-.25, bar_ys[::5], width=0.5, color='g') + plt.plot(xs, ys, lw=3, color='k') + plt.xlim(5, 15) + + +class DogSimulation(object): + def __init__(self, x0=0, velocity=1, + measurement_var=0.0, + process_var=0.0): + """ x0 : initial position + velocity: (+=right, -=left) + measurement_var: variance in measurement m^2 + process_var: variance in process (m/s)^2 + """ + self.x = x0 + self.velocity = velocity + self.meas_std = sqrt(measurement_var) + self.process_std = sqrt(process_var) + + def move(self, dt=1.0): + """Compute new position of the dog in dt seconds.""" + dx = self.velocity + randn()*self.process_std + self.x += dx * dt + + def sense_position(self): + """ Returns measurement of new position in meters.""" + measurement = self.x + randn()*self.meas_std + return measurement + + def move_and_sense(self): + """ Move dog, and return measurement of new position in meters""" + self.move() + return self.sense_position() + diff --git a/kalman_and_bayesian_filters/kf_book/mkf_internal.py b/kalman_and_bayesian_filters/kf_book/mkf_internal.py new file mode 100644 index 0000000..d5ef009 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/mkf_internal.py @@ -0,0 +1,480 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" +# pylint: disable=invalid-name, missing-function-docstring +# pylint: disable=too-many-arguments, too-many-locals + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +from matplotlib.patches import Ellipse +import matplotlib.pyplot as plt +from matplotlib import cm +from mpl_toolkits.mplot3d import Axes3D +import numpy as np +from numpy.random import multivariate_normal +import filterpy.stats as stats +from filterpy.stats import plot_covariance_ellipse + +try: + import kf_book.book_plots as bp +except ModuleNotFoundError: + import book_plots as bp + + + +def zs_var_27_6(): + + + zs = [3.59, 1.73, -2.575, 4.38, 9.71, 2.88, 10.08, + 8.97, 3.74, 12.81, 11.15, 9.25, 3.93, 11.11, + 19.29, 16.20, 19.63, 9.54, 26.27, 23.29, 25.18, + 26.21, 17.1, 25.27, 26.86, 33.70, 25.92, 28.82, + 32.13, 25.0, 38.56, 26.97, 22.49, 40.77, 32.95, + 38.20, 40.93, 39.42, 35.49, 36.31, 31.56, 50.29, + 40.20, 54.49, 50.38, 42.79, 37.89, 56.69, 41.47, 53.66] + xs = list(range(len(zs))) + + return np.array([xs, zs]).T + +def zs_var_275(): + zs = [-6.947, 12.467, 6.899, 2.643, 6.980, 5.820, 5.788, 10.614, 5.210, + 14.338, 11.401, 19.138, 14.169, 19.572, 25.471, 13.099, 27.090, + 12.209, 14.274, 21.302, 14.678, 28.655, 15.914, 28.506, 23.181, + 18.981, 28.197, 39.412, 27.640, 31.465, 34.903, 28.420, 33.889, + 46.123, 31.355, 30.473, 49.861, 41.310, 42.526, 38.183, 41.383, + 41.919, 52.372, 42.048, 48.522, 44.681, 32.989, 37.288, 49.141, + 54.235, 62.974, 61.742, 54.863, 52.831, 61.122, 61.187, 58.441, + 47.769, 56.855, 53.693, 61.534, 70.665, 60.355, 65.095, 63.386] + xs = list(range(len(zs))) + + return np.array([xs, zs]).T + + +def plot_track_ellipses(N, zs, ps, cov, title): + #bp.plot_measurements(range(1,N + 1), zs) + #plt.plot(range(1, N + 1), ps, c='b', lw=2, label='filter') + plt.title(title) + + for i,p in enumerate(cov): + plot_covariance_ellipse( + (i+1, ps[i]), cov=p, variance=4, + axis_equal=False, ec='g', alpha=0.5) + + if i == len(cov)-1: + s = ('$\sigma^2_{pos} = %.2f$' % p[0,0]) + plt.text (20, 5, s, fontsize=18) + s = ('$\sigma^2_{vel} = %.2f$' % p[1, 1]) + plt.text (20, 0, s, fontsize=18) + plt.ylim(-5, 20) + plt.gca().set_aspect('equal') + + +def plot_gaussian_multiply(): + xs = np.arange(-5, 10, 0.1) + + mean1, var1 = 0, 5 + mean2, var2 = 5, 1 + mean, var = stats.mul(mean1, var1, mean2, var2) + + ys = [stats.gaussian(x, mean1, var1) for x in xs] + plt.plot(xs, ys, label='M1') + + ys = [stats.gaussian(x, mean2, var2) for x in xs] + plt.plot(xs, ys, label='M2') + + ys = [stats.gaussian(x, mean, var) for x in xs] + plt.plot(xs, ys, label='M1 x M2') + plt.legend() + plt.show() + + +def show_position_chart(): + """ Displays 3 measurements at t=1,2,3, with x=1,2,3""" + + plt.scatter([1, 2, 3], [1, 2, 3], s=128, color='#004080') + plt.xlim([0, 4]) + plt.ylim([0, 4]) + + plt.annotate('t=1', xy=(1, 1), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.annotate('t=2', xy=(2, 2), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.annotate('t=3', xy=(3, 3), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.xlabel("X") + plt.ylabel("Y") + + plt.xticks(np.arange(1, 4, 1)) + plt.yticks(np.arange(1, 4, 1)) + plt.show() + + +def show_position_prediction_chart(): + """ displays 3 measurements, with the next position predicted""" + + plt.scatter([1, 2, 3], [1, 2, 3], s=128, color='#004080') + + plt.annotate('t=1', xy=(1, 1), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.annotate('t=2', xy=(2, 2), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.annotate('t=3', xy=(3, 3), xytext=(0, -10), + textcoords='offset points', ha='center', va='top') + + plt.xlim([0, 5]) + plt.ylim([0, 5]) + + plt.xlabel("X") + plt.ylabel("Y") + + plt.xticks(np.arange(1, 5, 1)) + plt.yticks(np.arange(1, 5, 1)) + + plt.scatter([4], [4], s=128, color='#8EBA42') + ax = plt.gca() + ax.annotate('', xy=(4, 4), xytext=(3, 3), + arrowprops=dict(arrowstyle='->', + ec='g', + shrinkA=6, shrinkB=5, + lw=3)) + plt.show() + + +def show_x_error_chart(count): + """ displays x=123 with covariances showing error""" + + plt.cla() + plt.gca().autoscale(tight=True) + + cov = np.array([[0.1, 0], + [0, 8]]) + pos_ellipse = stats.covariance_ellipse(cov) + + cov2 = np.array([[0.1, 0], + [0, 4]]) + + cov3 = np.array([[12, 11.95], + [11.95, 12]]) + vel_ellipse = stats.covariance_ellipse(cov3) + + + sigma = [1, 4, 9] + + if count < 4: + stats.plot_covariance_ellipse((0, 0), ellipse=pos_ellipse, variance=sigma) + + if count == 2: + stats.plot_covariance_ellipse((0, 0), ellipse=vel_ellipse, variance=sigma, + edgecolor='r') + + if count == 3: + + stats.plot_covariance_ellipse((5, 5), ellipse=pos_ellipse, variance=sigma) + stats.plot_covariance_ellipse((0, 0), ellipse=vel_ellipse, variance=sigma, + edgecolor='r') + + if count == 4: + M0 = np.array([[0, 0]]).T + M1 = np.array([[5, 5]]).T + _, cov4 = stats.multivariate_multiply(M0, cov2, M1, cov3) + e4 = stats.covariance_ellipse(cov4) + + stats.plot_covariance_ellipse((0, 0), ellipse=pos_ellipse, variance=sigma, alpha=0.25) + stats.plot_covariance_ellipse((5, 5), ellipse=pos_ellipse, variance=sigma, alpha=0.25) + + stats.plot_covariance_ellipse((0, 0), ellipse=vel_ellipse, variance=sigma, + edgecolor='r', alpha=0.25) + stats.plot_covariance_ellipse((5, 5), ellipse=e4, variance=sigma) + plt.ylim((-9, 16)) + + plt.xlabel("Position") + plt.ylabel("Velocity") + plt.axis('equal') + + plt.show() + + +def show_x_with_unobserved(): + """ shows x=1,2,3 with velocity superimposed on top """ + + # plot velocity + sigma = [0.5, 1., 1.5, 2] + cov = np.array([[1, 1], [1, 1.1]]) + stats.plot_covariance_ellipse((2, 2), cov=cov, variance=sigma, axis_equal=False) + + # plot positions + cov = np.array([[0.003, 0], [0, 12]]) + sigma = [0.5, 1., 1.5, 2] + e = stats.covariance_ellipse(cov) + + stats.plot_covariance_ellipse((1, 1), ellipse=e, variance=sigma, axis_equal=False) + stats.plot_covariance_ellipse((2, 1), ellipse=e, variance=sigma, axis_equal=False) + stats.plot_covariance_ellipse((3, 1), ellipse=e, variance=sigma, axis_equal=False) + + # plot intersection circle + isct = Ellipse(xy=(2, 2), width=.2, height=1.2, edgecolor='r', fc='None', lw=4) + plt.gca().add_artist(isct) + + plt.ylim([0, 11]) + plt.xlim([0, 4]) + plt.xticks(np.arange(1, 4, 1)) + + plt.xlabel("Position") + plt.ylabel("Time") + + plt.show() + + +def plot_3d_covariance(mean, cov): + """ plots a 2x2 covariance matrix positioned at mean. mean will be plotted + in x and y, and the probability in the z axis. + + Parameters + ---------- + mean : 2x1 tuple-like object + mean for x and y coordinates. For example (2.3, 7.5) + + cov : 2x2 nd.array + the covariance matrix + + """ + + # compute width and height of covariance ellipse so we can choose + # appropriate ranges for x and y + o, w, h = stats.covariance_ellipse(cov, 3) + # rotate width and height to x,y axis + wx = abs(w*np.cos(o) + h*np.sin(o)) * 1.2 + wy = abs(h*np.cos(o) - w*np.sin(o)) * 1.2 + + + # ensure axis are of the same size so everything is plotted with the same + # scale + if wx > wy: + w = wx + else: + w = wy + + minx = mean[0] - w + maxx = mean[0] + w + miny = mean[1] - w + maxy = mean[1] + w + + xs = np.arange(minx, maxx, (maxx-minx)/40.) + ys = np.arange(miny, maxy, (maxy-miny)/40.) + xv, yv = np.meshgrid(xs, ys) + + zs = np.array([100.* stats.multivariate_gaussian(np.array([x, y]), mean, cov) \ + for x, y in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + + fig = plt.figure() + ax = fig.add_subplot(111, projection='3d') + + #ax = plt.gca(projection='3d') + ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn) + + ax.set_xlabel('X') + ax.set_ylabel('Y') + + # For unknown reasons this started failing in Jupyter notebook when + # using `%matplotlib inline` magic. Still works fine in IPython or when + # `%matplotlib notebook` magic is used. + x = mean[0] + zs = np.array([100.* stats.multivariate_gaussian(np.array([x, y]), mean, cov) + for _, y in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + + y = mean[1] + zs = np.array([100.* stats.multivariate_gaussian(np.array([x, y]), mean, cov) + for x, _ in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + + +def plot_3d_sampled_covariance(mean, cov): + """ plots a 2x2 covariance matrix positioned at mean. mean will be plotted + in x and y, and the probability in the z axis. + + Parameters + ---------- + mean : 2x1 tuple-like object + mean for x and y coordinates. For example (2.3, 7.5) + + cov : 2x2 nd.array + the covariance matrix + + """ + + # compute width and height of covariance ellipse so we can choose + # appropriate ranges for x and y + o, w, h = stats.covariance_ellipse(cov, 3) + # rotate width and height to x,y axis + wx = abs(w*np.cos(o) + h*np.sin(o)) * 1.2 + wy = abs(h*np.cos(o) - w*np.sin(o)) * 1.2 + + # ensure axis are of the same size so everything is plotted with the same + # scale + if wx > wy: + w = wx + else: + w = wy + + minx = mean[0] - w + maxx = mean[0] + w + miny = mean[1] - w + maxy = mean[1] + w + + count = 1000 + x, y = multivariate_normal(mean=mean, cov=cov, size=count).T + + xs = np.arange(minx, maxx, (maxx-minx)/40.) + ys = np.arange(miny, maxy, (maxy-miny)/40.) + xv, yv = np.meshgrid(xs, ys) + + zs = np.array([100.* stats.multivariate_gaussian(np.array([xx, yy]), mean, cov) \ + for xx, yy in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + + ax = plt.gcf().add_subplot(111, projection='3d') + ax.scatter(x, y, [0]*count, marker='.') + + ax.set_xlabel('X') + ax.set_ylabel('Y') + + x = mean[0] + zs = np.array([100.* stats.multivariate_gaussian(np.array([x, y]), mean, cov) + for _, y in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.binary) + + y = mean[1] + zs = np.array([100.* stats.multivariate_gaussian(np.array([x, y]), mean, cov) + for x, _ in zip(np.ravel(xv), np.ravel(yv))]) + zv = zs.reshape(xv.shape) + ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.binary) + + +def plot_3_covariances(): + P = [[2, 0], [0, 2]] + plt.subplot(131) + plt.gca().grid(visible=False) + plt.gca().set_xticks([0, 1, 2, 3, 4]) + plot_covariance_ellipse((2, 7), cov=P, facecolor='g', alpha=0.2, + title='|2 0|\n|0 2|', std=[3], axis_equal=False) + plt.ylim((0, 15)) + plt.gca().set_aspect('equal', adjustable='box') + + plt.subplot(132) + plt.gca().grid(False) + plt.gca().set_xticks([0, 1, 2, 3, 4]) + P = [[2, 0], [0, 6]] + plt.ylim((0, 15)) + plt.gca().set_aspect('equal', adjustable='box') + plot_covariance_ellipse((2, 7), P, facecolor='g', alpha=0.2, + std=[3], axis_equal=False, title='|2 0|\n|0 6|') + + plt.subplot(133) + plt.gca().grid(False) + plt.gca().set_xticks([0, 1, 2, 3, 4]) + P = [[2, 1.2], [1.2, 2]] + plt.ylim((0, 15)) + plt.gca().set_aspect('equal', adjustable='box') + plot_covariance_ellipse((2, 7), P, facecolor='g', alpha=0.2, + axis_equal=False, std=[3], + title='|2.0 1.2|\n|1.2 2.0|') + + plt.tight_layout() + plt.show() + + +def plot_correlation_covariance(): + P = [[4, 3.9], [3.9, 4]] + plot_covariance_ellipse((5, 10), P, edgecolor='k', + variance=[1, 2**2, 3**2]) + plt.xlabel('X') + plt.ylabel('Y') + plt.gca().autoscale(tight=True) + plt.axvline(7.5, ls='--', lw=1) + plt.axhline(12.5, ls='--', lw=1) + plt.scatter(7.5, 12.5, s=1500, alpha=0.5) + plt.title('|4.0 3.9|\n|3.9 4.0|') + plt.show() + + +def plot_track(ps, actual, zs, cov, std_scale=1, + plot_P=True, y_lim=None, + xlabel='time', ylabel='position', + title='Kalman Filter'): + + count = len(zs) + zs = np.asarray(zs) + + cov = np.asarray(cov) + std = std_scale * np.sqrt(cov[:, 0, 0]) + std_top = np.minimum(actual+std, [count + 10]) + std_btm = np.maximum(actual-std, [-50]) + + std_top = actual + std + std_btm = actual - std + + bp.plot_track(actual, c='k') + bp.plot_measurements(range(1, count + 1), zs) + bp.plot_filter(range(1, count + 1), ps) + + plt.plot(std_top, linestyle=':', color='k', lw=1, alpha=0.4) + plt.plot(std_btm, linestyle=':', color='k', lw=1, alpha=0.4) + plt.fill_between(range(len(std_top)), std_top, std_btm, + facecolor='yellow', alpha=0.2, interpolate=True) + plt.legend(loc=4) + plt.xlabel(xlabel) + plt.ylabel(ylabel) + if y_lim is not None: + plt.ylim(y_lim) + else: + plt.ylim((-50, count + 10)) + + plt.xlim((0, count)) + plt.title(title) + plt.show() + + if plot_P: + ax = plt.subplot(121) + ax.set_title(r"$\sigma^2_x$ (pos variance)") + plot_covariance(cov, (0, 0)) + ax = plt.subplot(122) + ax.set_title(r"$\sigma^2_\dot{x}$ (vel variance)") + plot_covariance(cov, (1, 1)) + plt.show() + + +def plot_covariance(P, index=(0, 0)): + ps = [] + for p in P: + ps.append(p[index[0], index[1]]) + plt.plot(ps) + + +if __name__ == "__main__": + #show_position_chart() + plot_3d_covariance((2, 7), np.array([[8., 0], [0, 1.]])) + #plot_3d_sampled_covariance([2,7], [[8.,0],[0,4.]]) + #show_residual_chart() + + #show_position_chart() + #show_x_error_chart(4) diff --git a/kalman_and_bayesian_filters/kf_book/nonlinear_internal.py b/kalman_and_bayesian_filters/kf_book/nonlinear_internal.py new file mode 100644 index 0000000..4a23cec --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/nonlinear_internal.py @@ -0,0 +1,60 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +import filterpy.stats as stats +import matplotlib.pyplot as plt +import numpy as np + + +def plot1(): + P = np.array([[6, 2.5], [2.5, .6]]) + stats.plot_covariance_ellipse((10, 2), P, facecolor='g', alpha=0.2) + + +def plot2(): + P = np.array([[6, 2.5], [2.5, .6]]) + circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7) + ax = plt.gca() + ax.add_artist(circle1) + plt.xlim(0,10) + plt.ylim(0,3) + P = np.array([[6, 2.5], [2.5, .6]]) + stats.plot_covariance_ellipse((10, 2), P, facecolor='g', alpha=0.2) + +def plot3(): + P = np.array([[6, 2.5], [2.5, .6]]) + circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7) + ax = plt.gca() + ax.add_artist(circle1) + plt.xlim(0,10) + plt.ylim(0,3) + plt.axhline(3, ls='--') + stats.plot_covariance_ellipse((10, 2), P, facecolor='g', alpha=0.2) + +def plot4(): + P = np.array([[6, 2.5], [2.5, .6]]) + circle1=plt.Circle((10,0),3,color='#004080',fill=False,linewidth=4, alpha=.7) + ax = plt.gca() + ax.add_artist(circle1) + plt.xlim(0,10) + plt.ylim(0,3) + plt.axhline(3, ls='--') + stats.plot_covariance_ellipse((10, 2), P, facecolor='g', alpha=0.2) + plt.scatter([11.4], [2.65],s=200) + plt.scatter([12], [3], c='r', s=200) + plt.show() \ No newline at end of file diff --git a/kalman_and_bayesian_filters/kf_book/nonlinear_plots.py b/kalman_and_bayesian_filters/kf_book/nonlinear_plots.py new file mode 100644 index 0000000..c2a5ebe --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/nonlinear_plots.py @@ -0,0 +1,339 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +import math +from matplotlib import cm +import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import Axes3D +import numpy as np +from numpy.random import normal, multivariate_normal +import scipy.stats + +from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform +from filterpy.stats import multivariate_gaussian + + +def plot_nonlinear_func(data, f, out_lim=None, num_bins=300): + ys = f(data) + x0 = np.mean(data) + in_std = np.std(data) + + y = f(x0) + std = np.std(ys) + + in_lims = [x0 - in_std*3, x0 + in_std*3] + if out_lim is None: + out_lim = [y - std*3, y + std*3] + + # plot output + h = np.histogram(ys, num_bins, density=False) + plt.subplot(221) + plt.plot(h[1][1:], h[0], lw=2, alpha=0.8) + if out_lim is not None: + plt.xlim(out_lim[0], out_lim[1]) + + plt.gca().yaxis.set_ticklabels([]) + plt.title('Output') + + plt.axvline(np.mean(ys), ls='--', lw=2) + plt.axvline(f(x0), lw=1) + + + norm = scipy.stats.norm(y, in_std) + + '''min_x = norm.ppf(0.001) + max_x = norm.ppf(0.999) + xs = np.arange(min_x, max_x, (max_x - min_x) / 1000) + pdf = norm.pdf(xs) + plt.plot(pdf * max(h[0])/max(pdf), xs, lw=1, color='k') + print(max(norm.pdf(xs)))''' + + # plot transfer function + plt.subplot(2, 2, 3) + x = np.arange(in_lims[0], in_lims[1], 0.1) + y = f(x) + plt.plot (x, y, 'k') + isct = f(x0) + plt.plot([x0, x0, in_lims[1]], [out_lim[1], isct, isct], color='r', lw=1) + plt.xlim(in_lims) + plt.ylim(out_lim) + #plt.axis('equal') + plt.title('f(x)') + + # plot input + h = np.histogram(data, num_bins, density=True) + + plt.subplot(2,2,4) + plt.plot(h[0], h[1][1:], lw=2) + #plt.ylim(in_lims) + plt.gca().xaxis.set_ticklabels([]) + plt.title('Input') + plt.tight_layout() + plt.show() + + +def plot_ekf_vs_mc(): + + def fx(x): + return x**3 + + def dfx(x): + return 3*x**2 + + mean = 1 + var = .1 + std = math.sqrt(var) + + data = normal(loc=mean, scale=std, size=50000) + d_t = fx(data) + + mean_ekf = fx(mean) + slope = dfx(mean) + std_ekf = abs(slope*std) + + norm = scipy.stats.norm(mean_ekf, std_ekf) + xs = np.linspace(-3, 5, 200) + plt.plot(xs, norm.pdf(xs), lw=2, ls='--', color='b') + try: + plt.hist(d_t, bins=200, density=True, histtype='step', lw=2, color='g') + except: + # older versions of matplotlib don't have the density keyword + plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g') + + actual_mean = d_t.mean() + plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo') + plt.axvline(mean_ekf, lw=2, ls='--', color='b', label='EKF') + plt.legend() + plt.show() + + print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std())) + print('EKF mean={:.2f}, std={:.2f}'.format(mean_ekf, std_ekf)) + + +def plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.): + + def fx(x): + return x**3 + + def dfx(x): + return 3*x**2 + + mean = 1 + var = .1 + std = math.sqrt(var) + + data = normal(loc=mean, scale=std, size=50000) + d_t = fx(data) + + + points = MerweScaledSigmaPoints(1, alpha, beta, kappa) + Wm, Wc = points.Wm, points.Wc + sigmas = points.sigma_points(mean, var) + + sigmas_f = np.zeros((3, 1)) + for i in range(3): + sigmas_f[i] = fx(sigmas[i, 0]) + + ### pass through unscented transform + ukf_mean, ukf_cov = unscented_transform(sigmas_f, Wm, Wc) + ukf_mean = ukf_mean[0] + ukf_std = math.sqrt(ukf_cov[0]) + + norm = scipy.stats.norm(ukf_mean, ukf_std) + xs = np.linspace(-3, 5, 200) + plt.plot(xs, norm.pdf(xs), ls='--', lw=2, color='b') + try: + plt.hist(d_t, bins=200, density=True, histtype='step', lw=2, color='g') + except: + # older versions of matplotlib don't have the density keyword + plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g') + + actual_mean = d_t.mean() + plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo') + plt.axvline(ukf_mean, lw=2, ls='--', color='b', label='UKF') + plt.legend() + plt.show() + + print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std())) + print('UKF mean={:.2f}, std={:.2f}'.format(ukf_mean, ukf_std)) + + + +def test_plot(): + import math + from numpy.random import normal + from scipy import stats + global data + + def f(x): + return 2*x + 1 + + mean = 2 + var = 3 + std = math.sqrt(var) + + data = normal(loc=2, scale=std, size=50000) + + d2 = f(data) + n = scipy.stats.norm(mean, std) + + kde1 = stats.gaussian_kde(data, bw_method='silverman') + kde2 = stats.gaussian_kde(d2, bw_method='silverman') + xs = np.linspace(-10, 10, num=200) + + #plt.plot(data) + plt.plot(xs, kde1(xs)) + plt.plot(xs, kde2(xs)) + plt.plot(xs, n.pdf(xs), color='k') + + num_bins=100 + h = np.histogram(data, num_bins, density=True) + plt.plot(h[1][1:], h[0], lw=4) + + h = np.histogram(d2, num_bins, density=True) + plt.plot(h[1][1:], h[0], lw=4) + + +def plot_bivariate_colormap(xs, ys): + xs = np.asarray(xs) + ys = np.asarray(ys) + xmin = xs.min() + xmax = xs.max() + ymin = ys.min() + ymax = ys.max() + values = np.vstack([xs, ys]) + kernel = scipy.stats.gaussian_kde(values) + X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j] + positions = np.vstack([X.ravel(), Y.ravel()]) + + Z = np.reshape(kernel.evaluate(positions).T, X.shape) + plt.gca().imshow(np.rot90(Z), cmap=plt.cm.Greys, + extent=[xmin, xmax, ymin, ymax]) + + + +def plot_monte_carlo_mean(xs, ys, f, mean_fx, label, plot_colormap=True): + fxs, fys = f(xs, ys) + + computed_mean_x = np.average(fxs) + computed_mean_y = np.average(fys) + + ax = plt.subplot(121) + ax.grid(False) + + plot_bivariate_colormap(xs, ys) + + plt.scatter(xs, ys, marker='.', alpha=0.02, color='k') + ax.set_xlim(-20, 20) + ax.set_ylim(-20, 20) + + ax = plt.subplot(122) + ax.grid(False) + + plt.scatter(fxs, fys, marker='.', alpha=0.02, color='k') + plt.scatter(mean_fx[0], mean_fx[1], + marker='v', s=300, c='r', label=label) + plt.scatter(computed_mean_x, computed_mean_y, + marker='*',s=120, c='b', label='Computed Mean') + + plot_bivariate_colormap(fxs, fys) + ax.set_xlim([-100, 100]) + ax.set_ylim([-10, 200]) + plt.legend(loc='best', scatterpoints=1) + print ('Difference in mean x={:.3f}, y={:.3f}'.format( + computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1])) + + +def plot_cov_ellipse_colormap(cov=[[1,1],[1,1]]): + side = np.linspace(-3, 3, 200) + X,Y = np.meshgrid(side,side) + + pos = np.empty(X.shape + (2,)) + pos[:, :, 0] = X; + pos[:, :, 1] = Y + plt.axes(xticks=[], yticks=[], frameon=True) + rv = scipy.stats.multivariate_normal((0,0), cov) + plt.gca().grid(False) + plt.gca().imshow(rv.pdf(pos), cmap=plt.cm.Greys, origin='lower') + plt.show() + + +def plot_gaussians(xs, ps, x_range, y_range, N): + """ given a list of 2d states (x,y) and 2x2 covariance matrices, produce + a surface plot showing all of the gaussians""" + + xs = np.asarray(xs) + x = np.linspace (x_range[0], x_range[1], N) + y = np.linspace (y_range[0], y_range[1], N) + xx, yy = np.meshgrid(x, y) + zv = np.zeros((N, N)) + + for mean, cov in zip(xs, ps): + zs = np.array([multivariate_gaussian(np.array([i ,j]), mean, cov) + for i, j in zip(np.ravel(xx), np.ravel(yy))]) + zv += zs.reshape(xx.shape) + + ax = plt.figure().add_subplot(111, projection='3d') + ax.plot_surface(xx, yy, zv, rstride=1, cstride=1, lw=.5, edgecolors='#191919', + antialiased=True, shade=True, cmap=cm.autumn) + ax.view_init(elev=40., azim=230) + + +if __name__ == "__main__": + #plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 2]]) + ''' + from numpy.random import normal + import numpy as np + + plot_ukf_vs_mc()''' + + '''x0 = (1, 1) + data = normal(loc=x0[0], scale=x0[1], size=500000) + + def g(x): + return x*x + return (np.cos(3*(x/2+0.7)))*np.sin(0.7*x)-1.6*x + return -2*x + + + #plot_transfer_func (data, g, lims=(-3,3), num_bins=100) + plot_nonlinear_func (data, g, gaussian=x0, + num_bins=100) + ''' + + Ps = np.array([[[ 2.85841814, 0.71772898], + [ 0.71772898, 0.93786824]], + + [[ 3.28939458, 0.52634978], + [ 0.52634978, 0.13435503]], + + [[ 2.40532661, 0.29692055], + [ 0.29692055, 0.07671416]], + + [[ 2.23084082, 0.27823192], + [ 0.27823192, 0.07488681]]]) + + Ms = np.array([[ 0.68040795, 0.17084572], + [ 8.46201389, 1.15070342], + [ 13.7992229 , 0.96022707], + [ 19.95838208, 0.87524265]]) + + plot_multiple_gaussians(Ms, Ps, (-5,25), (-5, 5), 75) + + + diff --git a/kalman_and_bayesian_filters/kf_book/pf_internal.py b/kalman_and_bayesian_filters/kf_book/pf_internal.py new file mode 100644 index 0000000..f34c792 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/pf_internal.py @@ -0,0 +1,403 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + + +import warnings + +from filterpy.monte_carlo import stratified_resample, residual_resample +import matplotlib as mpl +import matplotlib.pyplot as plt + +import numpy as np +from numpy.random import randn, random, uniform, multivariate_normal, seed +import scipy.stats + + + +class ParticleFilter(object): + + def __init__(self, N, x_dim, y_dim): + self.particles = np.empty((N, 3)) # x, y, heading + self.N = N + self.x_dim = x_dim + self.y_dim = y_dim + + # distribute particles randomly with uniform weight + self.weights = np.empty(N) + self.weights.fill(1./N) + self.particles[:, 0] = uniform(0, x_dim, size=N) + self.particles[:, 1] = uniform(0, y_dim, size=N) + self.particles[:, 2] = uniform(0, 2*np.pi, size=N) + + + def predict(self, u, std): + """ move according to control input u with noise std""" + + self.particles[:, 2] += u[0] + randn(self.N) * std[0] + self.particles[:, 2] %= 2 * np.pi + + d = u[1] + randn(self.N) + self.particles[:, 0] += np.cos(self.particles[:, 2]) * d + self.particles[:, 1] += np.sin(self.particles[:, 2]) * d + + self.particles[:, 0:2] += u + randn(self.N, 2) * std + + + def weight(self, z, var): + dist = np.sqrt((self.particles[:, 0] - z[0])**2 + + (self.particles[:, 1] - z[1])**2) + + # simplification assumes variance is invariant to world projection + n = scipy.stats.norm(0, np.sqrt(var)) + prob = n.pdf(dist) + + # particles far from a measurement will give us 0.0 for a probability + # due to floating point limits. Once we hit zero we can never recover, + # so add some small nonzero value to all points. + prob += 1.e-12 + self.weights += prob + self.weights /= sum(self.weights) # normalize + + + def neff(self): + return 1. / np.sum(np.square(self.weights)) + + + def resample(self): + p = np.zeros((self.N, 3)) + w = np.zeros(self.N) + + cumsum = np.cumsum(self.weights) + for i in range(self.N): + index = np.searchsorted(cumsum, random()) + p[i] = self.particles[index] + w[i] = self.weights[index] + + self.particles = p + self.weights.fill(1.0 / self.N) + + + def estimate(self): + """ returns mean and variance """ + pos = self.particles[:, 0:2] + mu = np.average(pos, weights=self.weights, axis=0) + var = np.average((pos - mu)**2, weights=self.weights, axis=0) + + return mu, var + + +def plot_random_pd(): + def norm(x, x0, sigma): + return np.exp(-0.5 * (x - x0) ** 2 / sigma ** 2) + + + def sigmoid(x, x0, alpha): + return 1. / (1. + np.exp(- (x - x0) / alpha)) + + x = np.linspace(0, 1, 100) + y2 = (0.1 * np.sin(norm(x, 0.2, 0.05)) + 0.25 * norm(x, 0.6, 0.05) + + .5*norm(x, .5, .08) + + np.sqrt(norm(x, 0.8, 0.06)) +0.1 * (1 - sigmoid(x, 0.45, 0.15))) + + with warnings.catch_warnings(): + # matplotlib warns about deprecated rcParams when you copy. Oye. + warnings.simplefilter("ignore", mpl.MatplotlibDeprecationWarning) + + # hack because of bug `with plt.xkcd()` doesn't return context correctly + saved_state = mpl.rcParams.copy() + plt.xkcd() + plt.axes(xticks=[], yticks=[], frameon=False) + plt.plot(x, y2) + plt.ylim([0, max(y2)+.1]) + mpl.rcParams.update(saved_state) + + +def plot_monte_carlo_ukf(): + + def f(x,y): + return x+y, .1*x**2 + y*y + + mean = (0, 0) + p = np.array([[32, 15], [15., 40.]]) + + # Compute linearized mean + mean_fx = f(*mean) + + #generate random points + xs, ys = multivariate_normal(mean=mean, cov=p, size=3000).T + fxs, fys = f(xs, ys) + + plt.subplot(121) + plt.gca().grid(False) + + plt.scatter(xs, ys, marker='.', alpha=.2, color='k') + plt.xlim(-25, 25) + plt.ylim(-25, 25) + + plt.subplot(122) + plt.gca().grid(False) + + plt.scatter(fxs, fys, marker='.', alpha=0.2, color='k') + + plt.ylim([-10, 200]) + plt.xlim([-100, 100]) + plt.show() + + +def plot_pf(pf, xlim=100, ylim=100, weights=True): + + if weights: + a = plt.subplot(221) + a.cla() + + plt.xlim(0, ylim) + #plt.ylim(0, 1) + a.set_yticklabels('') + plt.scatter(pf.particles[:, 0], pf.weights, marker='.', s=1, color='k') + a.set_ylim(bottom=0) + + a = plt.subplot(224) + a.cla() + a.set_xticklabels('') + plt.scatter(pf.weights, pf.particles[:, 1], marker='.', s=1, color='k') + plt.ylim(0, xlim) + a.set_xlim(left=0) + #plt.xlim(0, 1) + + a = plt.subplot(223) + a.cla() + + else: + plt.cla() + plt.scatter(pf.particles[:, 0], pf.particles[:, 1], marker='.', s=1, color='k') + plt.xlim(0, xlim) + plt.ylim(0, ylim) + + +def Gaussian(mu, sigma, x): + + # calculates the probability of x for 1-dim Gaussian with mean mu and var. sigma + g = (np.exp(-((mu - x) ** 2) / (sigma ** 2) / 2.0) / + np.sqrt(2.0 * np.pi * (sigma ** 2))) + for i in range(len(g)): + g[i] = max(g[i], 1.e-29) + + return g + + +def test_gaussian(N): + for i in range(N): + mean, std, x = randn(3) + std = abs(std) + + d = Gaussian(mean, std, x) - scipy.stats.norm(mean, std).pdf(x) + assert abs(d) < 1.e-8, "{}, {}, {}, {}, {}, {}".format(d, mean, std, x, Gaussian(mean, std, x), scipy.stats.norm(mean, std).pdf(x)) + + +def show_two_pf_plots(): + """ Displays results of PF after 1 and 10 iterations for the book. + Note the book says this solves the full robot localization problem. + It doesn't bother simulating landmarks as this is just an illustration. + """ + + seed(1234) + N = 3000 + pf = ParticleFilter(N, 20, 20) + z = np.array([20, 20]) + + #plot(pf, weights=False) + + for x in range(10): + + z[0] = x+1 + randn()*0.3 + z[1] = x+1 + randn()*0.3 + + pf.predict((1,1), (0.2, 0.2)) + pf.weight(z=z, var=.8) + pf.resample() + + if x == 0: + plt.subplot(121) + elif x == 9: + plt.subplot(122) + + if x == 0 or x == 9: + mu, var = pf.estimate() + plot_pf(pf, 20, 20, weights=False) + if x == 0: + plt.scatter(mu[0], mu[1], color='g', s=100) + plt.scatter(x+1, x+1, marker='x', color='r', s=180, lw=3) + else: + plt.scatter(mu[0], mu[1], color='g', s=100, label="PF") + plt.scatter([x+1], [x+1], marker='x', color='r', s=180, label="True", lw=3) + plt.legend(scatterpoints=1) + plt.tight_layout() + + +def plot_cumsum(a): + + fig = plt.figure() + N = len(a) + + cmap = mpl.colors.ListedColormap([[0., .4, 1.], + [0., .8, 1.], + [1., .8, 0.], + [1., .4, 0.]]*(int(N/4) + 1)) + cumsum = np.cumsum(np.asarray(a) / np.sum(a)) + cumsum = np.insert(cumsum, 0, 0) + + #fig = plt.figure(figsize=(6,3)) + fig=plt.gcf() + ax = fig.add_axes([0.05, 0.475, 0.9, 0.15]) + norm = mpl.colors.BoundaryNorm(cumsum, cmap.N) + bar = mpl.colorbar.ColorbarBase(ax, cmap=cmap, + norm=norm, + drawedges=False, + spacing='proportional', + orientation='horizontal') + if N > 10: + bar.set_ticks([]) + + +def plot_stratified_resample(a): + N = len(a) + + cmap = mpl.colors.ListedColormap([[0., .4, 1.], + [0., .8, 1.], + [1., .8, 0.], + [1., .4, 0.]]*(int(N/4) + 1)) + cumsum = np.cumsum(np.asarray(a) / np.sum(a)) + cumsum = np.insert(cumsum, 0, 0) + + fig = plt.figure() + ax = plt.gcf().add_axes([0.05, 0.475, 0.9, 0.15]) + norm = mpl.colors.BoundaryNorm(cumsum, cmap.N) + bar = mpl.colorbar.ColorbarBase(ax, cmap=cmap, + norm=norm, + drawedges=False, + spacing='proportional', + orientation='horizontal') + xs = np.linspace(0., 1.-1./N, N) + ax.vlines(xs, 0, 1, lw=2) + + # make N subdivisions, and chose a random position within each one + b = (random(N) + range(N)) / N + plt.scatter(b, [.5]*len(b), s=60, facecolor='k', edgecolor='k') + bar.set_ticks([]) + plt.title('stratified resampling') + + +def plot_systematic_resample(a): + N = len(a) + + cmap = mpl.colors.ListedColormap([[0., .4, 1.], + [0., .8, 1.], + [1., .8, 0.], + [1., .4, 0.]]*(int(N/4) + 1)) + cumsum = np.cumsum(np.asarray(a) / np.sum(a)) + cumsum = np.insert(cumsum, 0, 0) + + fig = plt.figure() + ax = plt.gcf().add_axes([0.05, 0.475, 0.9, 0.15]) + norm = mpl.colors.BoundaryNorm(cumsum, cmap.N) + bar = mpl.colorbar.ColorbarBase(ax, cmap=cmap, + norm=norm, + drawedges=False, + spacing='proportional', + orientation='horizontal') + xs = np.linspace(0., 1.-1./N, N) + ax.vlines(xs, 0, 1, lw=2) + + # make N subdivisions, and chose a random position within each one + b = (random() + np.array(range(N))) / N + plt.scatter(b, [.5]*len(b), s=60, facecolor='k', edgecolor='k') + bar.set_ticks([]) + plt.title('systematic resampling') + + +def plot_multinomial_resample(a): + N = len(a) + + cmap = mpl.colors.ListedColormap([[0., .4, 1.], + [0., .8, 1.], + [1., .8, 0.], + [1., .4, 0.]]*(int(N/4) + 1)) + cumsum = np.cumsum(np.asarray(a) / np.sum(a)) + cumsum = np.insert(cumsum, 0, 0) + + fig = plt.figure() + ax = plt.gcf().add_axes([0.05, 0.475, 0.9, 0.15]) + norm = mpl.colors.BoundaryNorm(cumsum, cmap.N) + bar = mpl.colorbar.ColorbarBase(ax, cmap=cmap, + norm=norm, + drawedges=False, + spacing='proportional', + orientation='horizontal') + + # make N subdivisions, and chose a random position within each one + b = random(N) + plt.scatter(b, [.5]*len(b), s=60, facecolor='k', edgecolor='k') + bar.set_ticks([]) + plt.title('multinomial resampling') + + +def plot_residual_resample(a): + N = len(a) + + a_norm = np.asarray(a) / np.sum(a) + cumsum = np.cumsum(a_norm) + cumsum = np.insert(cumsum, 0, 0) + + cmap = mpl.colors.ListedColormap([[0., .4, 1.], + [0., .8, 1.], + [1., .8, 0.], + [1., .4, 0.]]*(int(N/4) + 1)) + + fig = plt.figure() + ax = plt.gcf().add_axes([0.05, 0.475, 0.9, 0.15]) + norm = mpl.colors.BoundaryNorm(cumsum, cmap.N) + bar = mpl.colorbar.ColorbarBase(ax, cmap=cmap, + norm=norm, + drawedges=False, + spacing='proportional', + orientation='horizontal') + + indexes = residual_resample(a_norm) + bins = np.bincount(indexes) + for i in range(1, N): + n = bins[i-1] # number particles in this sample + if n > 0: + b = np.linspace(cumsum[i-1], cumsum[i], n+2)[1:-1] + plt.scatter(b, [.5]*len(b), s=60, facecolor='k', edgecolor='k') + bar.set_ticks([]) + plt.title('residual resampling') + + + +if __name__ == '__main__': + + show_two_pf_plots() + + #plot_residual_resample([.1, .2, .3, .4, .2, .3, .1]) + + #example() + #show_two_pf_plots() + + #a = [.1, .2, .1, .6] + #plot_cumsum(a) + #test_pf() diff --git a/kalman_and_bayesian_filters/kf_book/smoothing_internal.py b/kalman_and_bayesian_filters/kf_book/smoothing_internal.py new file mode 100644 index 0000000..b449b34 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/smoothing_internal.py @@ -0,0 +1,62 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +import matplotlib.pyplot as plt + + +def show_fixed_lag_numberline(): + fig = plt.figure() + ax = fig.add_subplot(111) + ax.set_xlim(0,10) + ax.set_ylim(0,10) + + # draw lines + xmin = 1 + xmax = 9 + y = 5 + height = 1 + + plt.hlines(y, xmin, xmax) + plt.vlines(xmin, y - height / 2., y + height / 2.) + plt.vlines(4.5, y - height / 2., y + height / 2.) + plt.vlines(6, y - height / 2., y + height / 2.) + plt.vlines(xmax, y - height / 2., y + height / 2.) + plt.vlines(xmax-1, y - height / 2., y + height / 2.) + + # add numbers + plt.text(xmin, y-1.1, '$x_0$', fontsize=20, horizontalalignment='center') + plt.text(xmax, y-1.1, '$x_k$', fontsize=20, horizontalalignment='center') + plt.text(xmax-1, y-1.1, '$x_{k-1}$', fontsize=20, horizontalalignment='center') + plt.text(4.5, y-1.1, '$x_{k-N+1}$', fontsize=20, horizontalalignment='center') + plt.text(6, y-1.1, '$x_{k-N+2}$', fontsize=20, horizontalalignment='center') + plt.text(2.7, y-1.1, '.....', fontsize=20, horizontalalignment='center') + plt.text(7.2, y-1.1, '.....', fontsize=20, horizontalalignment='center') + + plt.axis('off') + plt.show() + +if __name__ == '__main__': + + #show_2d_transform() + #show_sigma_selections() + + show_sigma_transform(True) + #show_four_gps() + #show_sigma_transform() + #show_sigma_selections() + diff --git a/kalman_and_bayesian_filters/kf_book/ukf_internal.py b/kalman_and_bayesian_filters/kf_book/ukf_internal.py new file mode 100644 index 0000000..58687c1 --- /dev/null +++ b/kalman_and_bayesian_filters/kf_book/ukf_internal.py @@ -0,0 +1,487 @@ +# -*- coding: utf-8 -*- + +"""Copyright 2015 Roger R Labbe Jr. + + +Code supporting the book + +Kalman and Bayesian Filters in Python +https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python + + +This is licensed under an MIT license. See the LICENSE.txt file +for more information. +""" + +from __future__ import (absolute_import, division, print_function, + unicode_literals) + +from filterpy.kalman import UnscentedKalmanFilter as UKF +from filterpy.kalman import MerweScaledSigmaPoints +import filterpy.stats as stats +from filterpy.stats import plot_covariance_ellipse +import matplotlib.pyplot as plt +from matplotlib.patches import Ellipse,Arrow +import math +from math import cos, sin, atan2, pi +import numpy as np +from numpy.random import randn + +def _sigma_points(mean, sigma, kappa): + sigma1 = mean + math.sqrt((1+kappa)*sigma) + sigma2 = mean - math.sqrt((1+kappa)*sigma) + return mean, sigma1, sigma2 + + +def arrow(x1,y1,x2,y2, width=0.2): + return Arrow(x1,y1, x2-x1, y2-y1, lw=1, width=width, ec='k', color='k') + + +def show_two_sensor_bearing(): + circle1=plt.Circle((-4,0),5,color='#004080',fill=False,linewidth=20, alpha=.7) + circle2=plt.Circle((4,0),5,color='#E24A33', fill=False, linewidth=5, alpha=.7) + + fig = plt.gcf() + ax = fig.gca() + + plt.axis('equal') + #plt.xlim((-10,10)) + plt.ylim((-6,6)) + + plt.plot ([-4,0], [0,3], c='#004080') + plt.plot ([4,0], [0,3], c='#E24A33') + plt.text(-4, -.5, "A", fontsize=16, horizontalalignment='center') + plt.text(4, -.5, "B", fontsize=16, horizontalalignment='center') + + ax.add_patch(circle1) + ax.add_patch(circle2) + plt.show() + + +def show_three_gps(): + circle1=plt.Circle((-4,0),5,color='#004080',fill=False,linewidth=20, alpha=.7) + circle2=plt.Circle((4,0),5,color='#E24A33', fill=False, linewidth=8, alpha=.7) + circle3=plt.Circle((0,-3),6,color='#534543',fill=False, linewidth=13, alpha=.7) + + fig = plt.gcf() + ax = fig.gca() + + ax.add_patch(circle1) + ax.add_patch(circle2) + ax.add_patch(circle3) + + plt.axis('equal') + plt.show() + + +def show_four_gps(): + circle1=plt.Circle((-4,2),5,color='#004080',fill=False,linewidth=20, alpha=.7) + circle2=plt.Circle((5.5,1),5,color='#E24A33', fill=False, linewidth=8, alpha=.7) + circle3=plt.Circle((0,-3),6,color='#534543',fill=False, linewidth=13, alpha=.7) + circle4=plt.Circle((0,8),5,color='#214513',fill=False, linewidth=13, alpha=.7) + + fig = plt.gcf() + ax = fig.gca() + + ax.add_patch(circle1) + ax.add_patch(circle2) + ax.add_patch(circle3) + ax.add_patch(circle4) + + plt.axis('equal') + plt.show() + + +def show_sigma_transform(with_text=False): + fig = plt.gcf() + ax=fig.gca() + + x = np.array([0, 5]) + P = np.array([[4, -2.2], [-2.2, 3]]) + + plot_covariance_ellipse(x, P, facecolor='b', alpha=0.6, variance=9) + sigmas = MerweScaledSigmaPoints(2, alpha=.5, beta=2., kappa=0.) + + S = sigmas.sigma_points(x=x, P=P) + plt.scatter(S[:,0], S[:,1], c='k', s=80) + + x = np.array([15, 5]) + P = np.array([[3, 1.2],[1.2, 6]]) + plot_covariance_ellipse(x, P, facecolor='g', variance=9, alpha=0.3) + + ax.add_artist(arrow(S[0,0], S[0,1], 11, 4.1, 0.6)) + ax.add_artist(arrow(S[1,0], S[1,1], 13, 7.7, 0.6)) + ax.add_artist(arrow(S[2,0], S[2,1], 16.3, 0.93, 0.6)) + ax.add_artist(arrow(S[3,0], S[3,1], 16.7, 10.8, 0.6)) + ax.add_artist(arrow(S[4,0], S[4,1], 17.7, 5.6, 0.6)) + + ax.axes.get_xaxis().set_visible(False) + ax.axes.get_yaxis().set_visible(False) + + if with_text: + plt.text(2.5, 1.5, r"$\chi$", fontsize=32) + plt.text(13, -1, r"$\mathcal{Y}$", fontsize=32) + + #plt.axis('equal') + plt.show() + + + +def show_2d_transform(): + + plt.cla() + ax=plt.gca() + + ax.add_artist(Ellipse(xy=(2,5), width=2, height=3,angle=70,linewidth=1,ec='k')) + ax.add_artist(Ellipse(xy=(7,5), width=2.2, alpha=0.3, height=3.8,angle=150,fc='g',linewidth=1,ec='k')) + + ax.add_artist(arrow(2, 5, 6, 4.8)) + ax.add_artist(arrow(1.5, 5.5, 7, 3.8)) + ax.add_artist(arrow(2.3, 4.1, 8, 6)) + ax.add_artist(arrow(3.3, 5.1, 6.5, 4.3)) + ax.add_artist(arrow(1.3, 4.8, 7.2, 6.3)) + ax.add_artist(arrow(1.1, 5.2, 8.2, 5.3)) + ax.add_artist(arrow(2, 4.4, 7.3, 4.5)) + + ax.axes.get_xaxis().set_visible(False) + ax.axes.get_yaxis().set_visible(False) + + plt.axis('equal') + plt.xlim(0,10); plt.ylim(0,10) + plt.show() + + +def show_3_sigma_points(): + xs = np.arange(-4, 4, 0.1) + var = 1.5 + ys = [stats.gaussian(x, 0, var) for x in xs] + samples = [0, 1.2, -1.2] + for x in samples: + plt.scatter ([x], [stats.gaussian(x, 0, var)], s=80) + + plt.plot(xs, ys) + plt.show() + +def _plot_sigmas(s, w, alpha=0.5, **kwargs): + min_w = min(abs(w)) + scale_factor = 100 / min_w + return plt.scatter(s[:, 0], s[:, 1], s=abs(w)*scale_factor, + alpha=alpha, **kwargs) + + +def show_sigma_selections(): + ax=plt.gca() + ax.axes.get_xaxis().set_visible(False) + ax.axes.get_yaxis().set_visible(False) + + x = np.array([2, 5]) + P = np.array([[3, 1.1], [1.1, 4]]) + + points = MerweScaledSigmaPoints(2, .09, 2., 1.) + sigmas = points.sigma_points(x, P) + Wm, Wc = points.Wm, points.Wc + plot_covariance_ellipse(x, P, facecolor='b', alpha=.3, variance=[.5]) + _plot_sigmas(sigmas, Wc, alpha=1.0, facecolor='k') + + x = np.array([5, 5]) + points = MerweScaledSigmaPoints(2, .15, 1., .15) + sigmas = points.sigma_points(x, P) + Wm, Wc = points.Wm, points.Wc + plot_covariance_ellipse(x, P, facecolor='b', alpha=0.3, variance=[.5]) + _plot_sigmas(sigmas, Wc, alpha=1.0, facecolor='k') + + x = np.array([8, 5]) + points = MerweScaledSigmaPoints(2, .2, 3., 10) + sigmas = points.sigma_points(x, P) + Wm, Wc = points.Wm, points.Wc + plot_covariance_ellipse(x, P, facecolor='b', alpha=0.3, variance=[.5]) + _plot_sigmas(sigmas, Wc, alpha=1.0, facecolor='k') + + plt.axis('equal') + plt.xlim(0,10); plt.ylim(0,10) + plt.show() + + +def show_sigmas_for_2_kappas(): + # generate the Gaussian data + + xs = np.arange(-4, 4, 0.1) + mean = 0 + sigma = 1.5 + ys = [stats.gaussian(x, mean, sigma*sigma) for x in xs] + + + + #generate our samples + kappa = 2 + x0,x1,x2 = _sigma_points(mean, sigma, kappa) + + samples = [x0,x1,x2] + for x in samples: + p1 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='k') + + kappa = -.5 + x0,x1,x2 = _sigma_points(mean, sigma, kappa) + + samples = [x0,x1,x2] + for x in samples: + p2 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='b') + + plt.legend([p1,p2], ['$kappa$=2', '$kappa$=-0.5']) + plt.plot(xs, ys) + plt.show() + + +def plot_sigmas(sigmas, x, cov): + if not np.isscalar(cov): + cov = np.atleast_2d(cov) + pts = sigmas.sigma_points(x=x, P=cov) + plt.scatter(pts[:, 0], pts[:, 1], s=sigmas.Wm*1000) + plt.axis('equal') + + +def plot_sigma_points(): + x = np.array([0, 0]) + P = np.array([[4, 2], [2, 4]]) + + sigmas = MerweScaledSigmaPoints(n=2, alpha=.3, beta=2., kappa=1.) + S0 = sigmas.sigma_points(x, P) + Wm0, Wc0 = sigmas.Wm, sigmas.Wc + + sigmas = MerweScaledSigmaPoints(n=2, alpha=1., beta=2., kappa=1.) + S1 = sigmas.sigma_points(x, P) + Wm1, Wc1 = sigmas.Wm, sigmas.Wc + + def plot_sigmas(s, w, **kwargs): + min_w = min(abs(w)) + scale_factor = 100 / min_w + return plt.scatter(s[:, 0], s[:, 1], s=abs(w)*scale_factor, alpha=.5, **kwargs) + + plt.subplot(121) + plot_sigmas(S0, Wc0, c='b') + plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, variance=[1, 4]) + plt.title('alpha=0.3') + plt.subplot(122) + plot_sigmas(S1, Wc1, c='b', label='Kappa=2') + plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, variance=[1, 4]) + plt.title('alpha=1') + plt.show() + + +def plot_radar(xs, t, plot_x=True, plot_vel=True, plot_alt=True): + xs = np.asarray(xs) + if plot_x: + plt.figure() + plt.plot(t, xs[:, 0]/1000.) + plt.xlabel('time(sec)') + plt.ylabel('position(km)') + plt.tight_layout() + if plot_vel: + plt.figure() + plt.plot(t, xs[:, 1]) + plt.xlabel('time(sec)') + plt.ylabel('velocity') + plt.tight_layout() + if plot_alt: + plt.figure() + plt.plot(t, xs[:,2]) + plt.xlabel('time(sec)') + plt.ylabel('altitude') + plt.tight_layout() + plt.show() + + +def plot_altitude(xs, t, track): + xs = np.asarray(xs) + + plt.plot(t, xs[:,2], label='filter', ) + plt.plot(t, track, label='Aircraft', lw=2, ls='--', c='k') + plt.xlabel('time(sec)') + plt.ylabel('altitude') + plt.legend(loc=4) + + +def print_sigmas(n=1, mean=5, cov=3, alpha=.1, beta=2., kappa=2): + points = MerweScaledSigmaPoints(n, alpha, beta, kappa) + print('sigmas: ', points.sigma_points(mean, cov).T[0]) + Wm, Wc = points.Wm, points.Wc + print('mean weights:', Wm) + print('cov weights:', Wc) + print('lambda:', alpha**2 *(n+kappa) - n) + print('sum cov', sum(Wc)) + + + + +def plot_rts_output(xs, Ms, t): + plt.figure() + plt.plot(t, xs[:, 0]/1000., label='KF', lw=2) + plt.plot(t, Ms[:, 0]/1000., c='k', label='RTS', lw=2) + plt.xlabel('time(sec)') + plt.ylabel('x') + plt.legend(loc=4) + + plt.figure() + + plt.plot(t, xs[:, 1], label='KF') + plt.plot(t, Ms[:, 1], c='k', label='RTS') + plt.xlabel('time(sec)') + plt.ylabel('x velocity') + plt.legend(loc=4) + + plt.figure() + plt.plot(t, xs[:, 2], label='KF') + plt.plot(t, Ms[:, 2], c='k', label='RTS') + plt.xlabel('time(sec)') + plt.ylabel('Altitude(m)') + plt.legend(loc=4) + + np.set_printoptions(precision=4) + print('Difference in position in meters:\n\t', xs[-6:-1, 0] - Ms[-6:-1, 0]) + + +def plot_scatter_of_bearing_error(): + def plot_scatter(theta): + theta = math.radians(theta) + d = 100 + xs, ys = [], [] + for i in range (3000): + a = theta + randn() * math.radians(1) + xs.append(d*math.cos(a)) + ys.append(d*math.sin(a)) + plt.scatter(xs, ys) + plt.xlabel('x') + plt.ylabel('y') + + plt.subplot(121) + plot_scatter(45) + plt.gca().set_aspect('equal') + plt.title("45° bearing") + plt.subplot(122) + plot_scatter(180) + plt.xlim((-101, -99)) + plt.title("180° bearing") + + +def plot_scatter_moving_target(): + pos = np.array([5., 5.]) + for i in range(5): + pos += (0.5, 1.) + actual_angle = math.atan2(pos[1], pos[0]) + d = math.sqrt(pos[0]**2 + pos[1]**2) + + xs, ys = [], [] + for i in range (100): + a = actual_angle + randn() * math.radians(1) + xs.append(d*math.cos(a)) + ys.append(d*math.sin(a)) + plt.scatter(xs, ys, c='C0') + + plt.axis('equal') + plt.plot([5.5, pos[0]], [6, pos[1]], c='g', linestyle='--') + + +def _isct(pa, pb, alpha, beta): + """ Returns the (x, y) intersections of points pa and pb + given the bearing alpha for point pa and bearing beta for + point pb. + """ + + ax, ay = pa + cx, cy = pb + + # bearing to angle + alpha = 90 - alpha + beta = 90 - beta + + # compute second point, let hypot==1 + bx = cos(alpha) + ax + by = sin(alpha) + ay + dx = cos(beta) + cx + dy = sin(beta) + cy + + # Line AB represented as a1x + b1y = c1 + # Line CD represented as a2x + b2y = c2 + + a1 = by - ay + b1 = ax - bx + c1 = a1*ax + b1*ay + + a2 = dy - cy + b2 = cx - dx + c2 = a2*cx + b2*cy + det = a1*b2 - a2*b1 + + x = (b2*c1 - b1*c2) / det + y = (a1*c2 - a2*c1) / det + + return x, y + + +def _plot_iscts(pos, sa, sb, N=4): + for i in range(N): + pos += (0.5, 1.) + actual_angle_a = math.atan2(pos[1] - sa[1], pos[0] - sa[0]) + actual_angle_b = math.atan2(pos[1] - sb[1], pos[0] - sb[0]) + + da = math.sqrt((sa[0] - pos[0])**2 + (sa[1] - pos[1])**2) + db = math.sqrt((sb[0] - pos[0])**2 + (sb[1] - pos[1])**2) + + xs, ys, xs_a, xs_b, ys_a, ys_b = [], [], [], [], [], [] + + for i in range (300): + a_a = actual_angle_a + randn() * math.radians(1) + a_b = actual_angle_b + randn() * math.radians(1) + + x, y = _isct(sa, sb, a_a, a_b) + xs.append(x) + ys.append(y) + + xs_a.append(da*math.cos(a_a) + sa[0]) + ys_a.append(da*math.sin(a_a) + sa[1]) + + xs_b.append(db*math.cos(a_b) + sb[0]) + ys_b.append(db*math.sin(a_b) + sb[1]) + + plt.scatter(xs, ys, c='r', marker='.', alpha=0.5) + plt.scatter(xs_a, ys_a, c='k', edgecolor='k') + plt.scatter(xs_b, ys_b, marker='v', edgecolor=None, c='C0') + plt.gca().set_aspect('equal') + + +def plot_iscts_two_sensors(): + plt.subplot(121) + pos = np.array([4., 4,]) + sa = [0., 2.] + sb = [8., 2.] + + plt.scatter(*sa, s=200, c='k', marker='v') + plt.scatter(*sb, s=200, marker='s', c='C0') + _plot_iscts(pos, sa, sb, N=4) + plt.subplot(122) + plot_iscts_two_sensors_changed_sensors() + + + +def plot_iscts_two_sensors_changed_sensors(): + sa = [3, 4] + sb = [3, 7] + pos= np.array([3., 3.]) + + plt.scatter(*sa, s=200, c='k', marker='v') + plt.scatter(*sb, s=200, marker='s') + _plot_iscts(pos, sa, sb, N=5) + plt.ylim(3.8, 8.5) + + +if __name__ == '__main__': + + #show_2d_transform() + #show_sigma_selections() + plot_scatter_of_bearing_error() + + #show_sigma_transform(True) + #show_four_gps() + #show_sigma_transform() + #show_sigma_selections() + diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..c62a919 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,223 @@ +aiohttp==3.9.1 +aiosignal==1.3.1 +alembic==1.13.0 +anyio==3.7.1 +argon2-cffi==23.1.0 +argon2-cffi-bindings==21.2.0 +arviz==0.14.0 +asttokens==2.4.1 +async-timeout==4.0.3 +attrs==23.1.0 +beartype==0.16.4 +beautifulsoup4==4.12.2 +bleach==6.1.0 +blosc2==2.3.2 +cachetools==5.3.2 +certifi==2023.11.17 +cffi==1.16.0 +cftime==1.6.3 +charset-normalizer==3.3.2 +click==8.1.7 +cloudevents==1.10.1 +cloudpickle==3.0.0 +colorama==0.4.6 +comm==0.2.0 +cons==0.4.6 +contourpy==1.2.0 +cryptography==41.0.7 +cwrap==1.6.5 +cycler==0.12.1 +dapper==1.5.1 +debugpy==1.8.0 +decorator==5.1.1 +defusedxml==0.7.1 +deprecation==2.1.0 +dill==0.3.2 +dnspython==2.4.2 +entrypoints==0.4 +ert==8.0.7 +ert-storage==0.3.22 +etuples==0.3.9 +exceptiongroup==1.2.0 +executing==2.0.1 +fastapi==0.99.1 +fastjsonschema==2.19.0 +fastprogress==1.0.3 +fenics-dijitso==2019.1.0 +fenics-ffc==2019.1.0.post0 +fenics-fiat==2019.1.0 +fenics-ufl==2019.1.0 +filelock==3.13.1 +filterpy==1.4.5 +flatten-dict==0.4.2 +fonttools==4.46.0 +frozenlist==1.4.1 +fsspec==2023.12.2 +greenlet==3.0.2 +h11==0.14.0 +h5py==3.10.0 +hdf5plugin==4.3.0 +hippylib==3.1.0 +httpcore==1.0.2 +httpx==0.25.2 +idna==3.6 +ipdb==0.13.13 +ipykernel==6.27.1 +ipython==8.18.1 +ipython-genutils==0.2.0 +ipywidgets==8.1.1 +iterative-ensemble-smoother==0.2.0 +jedi==0.19.1 +Jinja2==3.1.2 +joblib==1.3.2 +jsonschema==4.20.0 +jsonschema-specifications==2023.11.2 +jupyter==1.0.0 +jupyter-client==7.3.4 +jupyter-console==6.6.3 +jupyter_core==5.5.0 +jupyter-server==1.24.0 +jupyterlab_pygments==0.3.0 +jupyterlab-widgets==3.0.9 +kiwisolver==1.4.5 +lark==1.1.8 +llvmlite==0.40.1 +logical-unification==0.4.6 +loguru==0.7.2 +makefun==1.15.2 +Mako==1.3.0 +MarkupSafe==2.1.3 +matplotlib==3.8.2 +matplotlib-inline==0.1.6 +miniKanren==1.0.3 +mistune==3.0.2 +mpi4py==3.1.4 +mpl-tools==0.2.50 +mpmath==1.3.0 +msgpack==1.0.7 +multidict==6.0.4 +multipledispatch==1.0.0 +multiprocessing-on-dill==3.5.0a4 +nbclassic==1.0.0 +nbclient==0.9.0 +nbconvert==7.12.0 +nbformat==5.9.2 +ndindex==1.7 +nest-asyncio==1.5.8 +netCDF4==1.6.5 +networkx==2.8.8 +notebook==6.5.6 +notebook_shim==0.2.3 +numba==0.57.1 +numdifftools==0.9.41 +numexpr==2.8.8 +numpy==1.24.4 +nvidia-cublas-cu12==12.1.3.1 +nvidia-cuda-cupti-cu12==12.1.105 +nvidia-cuda-nvrtc-cu12==12.1.105 +nvidia-cuda-runtime-cu12==12.1.105 +nvidia-cudnn-cu12==8.9.2.26 +nvidia-cufft-cu12==11.0.2.54 +nvidia-curand-cu12==10.3.2.106 +nvidia-cusolver-cu12==11.4.5.107 +nvidia-cusparse-cu12==12.1.0.106 +nvidia-nccl-cu12==2.18.1 +nvidia-nvjitlink-cu12==12.3.101 +nvidia-nvtx-cu12==12.1.105 +openturns==1.21 +opt-einsum==3.3.0 +ordered-set==4.1.0 +packaging==23.2 +pandas==1.5.3 +pandocfilters==1.5.0 +parso==0.8.3 +patlib==0.3.5 +pexpect==4.9.0 +Pillow==10.1.0 +pip==23.3.1 +platformdirs==3.11.0 +pluggy==1.3.0 +prometheus-client==0.19.0 +prompt-toolkit==3.0.43 +psutil==5.9.6 +ptyprocess==0.7.0 +pure-eval==0.2.2 +py-cpuinfo==9.0.0 +pyarrow==14.0.1 +pycparser==2.21 +pydantic==1.10.13 +Pygments==2.17.2 +pylfsr==1.0.7 +pymap3d==3.0.1 +pymc==5.10.2 +pyparsing==3.1.1 +PyQt5==5.15.10 +PyQt5-Qt5==5.15.2 +PyQt5-sip==12.13.0 +pyro-api==0.1.2 +pyro-ppl==1.8.6 +pysip==1.0.0 +pytensor==2.18.4 +python-dateutil==2.8.2 +python-multipart==0.0.6 +pytz==2023.3.post1 +PyYAML==6.0.1 +pyzmq==24.0.1 +qtconsole==5.5.1 +QtPy==2.4.1 +referencing==0.32.0 +requests==2.31.0 +resdata==4.1.1 +resfo==4.0.1 +river==0.21.0 +RoffIO==1.0.1 +rpds-py==0.13.2 +Rtree==1.1.0 +ruamel.yaml==0.18.5 +ruamel.yaml.clib==0.2.8 +scikit-base==0.6.1 +scikit-learn==1.3.2 +scipy==1.11.4 +segyio==1.9.12 +Send2Trash==1.8.2 +setuptools==68.2.2 +shapely==2.0.2 +six==1.16.0 +sktime==0.24.1 +sniffio==1.3.0 +sortedcontainers==2.4.0 +soupsieve==2.5 +SQLAlchemy==2.0.23 +stack-data==0.6.3 +starlette==0.27.0 +stonesoup==1.1 +struct-tools==0.2.5 +sympy==1.12 +tables==3.9.2 +tabulate==0.8.10 +terminado==0.18.0 +threadpoolctl==3.2.0 +tinycss2==1.2.1 +tomli==2.0.1 +toolz==0.12.0 +torch==2.1.2 +tornado==6.1 +tqdm==4.66.1 +traitlets==5.14.0 +triton==2.1.0 +typing_extensions==4.9.0 +tzdata==2023.3 +urllib3==2.1.0 +utm==0.7.0 +uvicorn==0.24.0.post1 +wcwidth==0.2.12 +webencodings==0.5.1 +websocket-client==1.7.0 +websockets==12.0 +wheel==0.41.2 +widgetsnbextension==4.0.9 +xarray==2023.12.0 +xarray-einstats==0.6.0 +xtgeo==3.6.0 +xtgeoviz==0.1.0 +yarl==1.9.4 diff --git a/scripts/env_export.sh b/scripts/env_export.sh new file mode 100644 index 0000000..506a5df --- /dev/null +++ b/scripts/env_export.sh @@ -0,0 +1,3 @@ +#!/usr/bin/env bash + +pip list --format=freeze > requirements.txt \ No newline at end of file