{ "cells": [ { "cell_type": "code", "execution_count": null, "id": "850e7703", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [intercept, slope]\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "570fd1615d6640639a2795169dea6d2a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
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Increase `target_accept` or reparameterize.\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'Frequency')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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\n" ], "text/plain": [ "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 200 seconds.\n", "There were 8 divergences after tuning. Increase `target_accept` or reparameterize.\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pymc as pm\n", "import arviz as az\n", "from scipy.io import loadmat\n", "\n", "# === 1. Load and prepare data ===\n", "\n", "# Load .mat files\n", "suv_file = \"../data/suv_percentilesSLOthenUWM.mat\"\n", "flags_file = \"../data/flags_combined.mat\"\n", "\n", "suv_data = loadmat(suv_file)\n", "flags_data = loadmat(flags_file)\n", "\n", "# Extract data\n", "suv = suv_data['lung_SUVperc_COMBINED'][0:58, :, :] # SUV shape: (58, patients, percentiles)\n", "flags = flags_data['flags'][0:58, 3] # Binary adverse effect (0 or 1)\n", "\n", "# Choose SUV percentile (94th) and reshape\n", "p = 94 # Use 94th percentile (0-indexed)\n", "X = np.nanmax(suv[:, :, p], axis=1).reshape(-1, 1) # Shape (58, 1)\n", "y = flags.flatten().astype(int) # Shape (58,)\n", "\n", "# === 2. Standardize X ===\n", "X_mean = X.mean()\n", "X_std = X.std()\n", "X_stdized = (X - X_mean) / X_std\n", "\n", "# === 3. Build and sample Bayesian logistic model ===\n", "\n", "with pm.Model() as logistic_model:\n", " # Priors on coefficients (robust heavy-tailed)\n", " intercept = pm.StudentT(\"intercept\", mu=0, sigma=5, nu=3)\n", " slope = pm.StudentT(\"slope\", mu=0, sigma=5, nu=3)\n", "\n", " # Linear predictor\n", " logits = intercept + slope * X_stdized.flatten()\n", "\n", " # Sigmoid transformation to probability\n", " theta = pm.Deterministic(\"theta\", pm.math.sigmoid(logits))\n", "\n", " # Likelihood\n", " y_obs = pm.Bernoulli(\"y_obs\", p=theta, observed=y)\n", "\n", " # Sample from posterior\n", " trace = pm.sample(2000, tune=1000, target_accept=0.95, return_inferencedata=True)\n", "\n", "# === 4. Plot sigmoid curve with uncertainty ===\n", "\n", "# Grid of x values for prediction\n", "x_grid = np.linspace(X_stdized.min(), X_stdized.max(), 200)\n", "\n", "# Extract posterior samples\n", "intercept_samples = trace.posterior['intercept'].stack(samples=(\"chain\", \"draw\")).values\n", "slope_samples = trace.posterior['slope'].stack(samples=(\"chain\", \"draw\")).values\n", "\n", "# Compute predicted probabilities\n", "logits_samples = intercept_samples[:, None] + slope_samples[:, None] * x_grid[None, :]\n", "probs_samples = 1 / (1 + np.exp(-logits_samples))\n", "\n", "# Mean and 95% credible interval\n", "mean_probs = np.mean(probs_samples, axis=0)\n", "lower = np.percentile(probs_samples, 2.5, axis=0)\n", "upper = np.percentile(probs_samples, 97.5, axis=0)\n", "\n", "# De-standardize x-axis\n", "x_plot = x_grid * X_std + X_mean\n", "\n", "# Plot\n", "plt.figure(figsize=(8, 5))\n", "plt.plot(x_plot, mean_probs, label='Mean prediction (sigmoid)', color='blue')\n", "plt.fill_between(x_plot, lower, upper, color='blue', alpha=0.3, label='95% CI')\n", "plt.scatter(X, y, color='red', alpha=0.6, label='Observed data')\n", "plt.xlabel(\"Max SUV at 94th Percentile\")\n", "plt.ylabel(\"Probability of Adverse Effect\")\n", "plt.title(\"Bayesian Logistic Regression\\n(Sigmoid Curve with 95% Credible Interval)\")\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "112beb58", "metadata": {}, "outputs": [ { "data": { "image/png": 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/oZZ2reWt+9WU+/fv4/z58+jatWuJpV6urq4IDAxEQkICrl+/jjlz5mD9+vUqXYJLo057hJycnEJfuor2JYrXVPFjVvA9rGiyYmNjg4cPHxYqMUpMTEROTo7W3zNt/H0sWLAApqammD9/fqF13t7eqF27Nvbt21dqKVlxTpw4gQcPHiAoKAiTJ09G9+7d4e3trVJipC7F+1BQce2MCtq+fTueP3+Oc+fOoVatWsqpRYsWEAQBe/bsKdc/PUXp27cvcnNzcejQIZXlzs7OyoRG8Q9EQQX/LtT5zijrd5hCUa9dQkKCSkKtib/16oTJSBWjaKxYlv8GPTw8ULduXWzbtk3lyy89PR27d+9Gp06dYGpqqnYMc+bMgZmZGaZNm4aUlJRC6xVfQAr169fHpUuXVLa5ceMGrl+/Xuw5rK2t8cYbb2D69Ol4/Pgx7t69C6D46+/VqxcAYMuWLSrLw8PDER0djd69e5f9AjXsxYsXmDx5MnJycjBv3rwy7+fu7o4FCxagefPmuHDhgnJ5RUoDirJ161aV59u2bQMA5QBU9vb2MDY2LvQe7tu3r9Cx1Pl89u7dG2lpadi7d6/K8s2bNyvXa0JxMWnj78PGxgYffvghfvnlF5w7d05lnYGBAT788ENcu3YNS5YsKXL/xMREnD59utjjK35QCzZa/v7779WKMz8fHx88e/YM+/fvV1mu+ByUJjAwEBYWFjh+/DhCQkJUplWrViEzM7PQZ6y8Jk+eDHt7e8ybN6/IJEId6nxnqPsdtn37dpXPVGxsLMLCwood1K24v/WahL1pqpjmzZsDAL7++muMHz8eBgYG8PDwKPI/Iz09PaxcuRKjR4/G4MGD8Z///AeZmZlYtWoVnj59iuXLl5crBjc3N+zYsQMjR45Eq1atlIOeAcDVq1cRFBQEQRAwfPhwAMDYsWMxZswYTJs2DSNGjEBsbCxWrlwJW1tbleMOGTJEOeaKra0tYmNjsWbNGri6uqJx48YlXr+Hhwf+7//+D+vWrYOenh58fX2VLeOdnZ0xZ86ccl2ruuLi4nD27Fnk5eUhJSVFOehZbGwsvvjiC/Tr16/YfS9duoQZM2bgzTffROPGjWFoaIgTJ07g0qVL+Oijj5TbNW/eHDt27MDOnTvRoEEDGBsbK18XdRkaGuKLL75AWloa2rVrp+xN4+vrq+xJIpPJMGbMGAQFBaFhw4Zo2bIlzp07V+SPlTqfz3HjxuHbb7/F+PHjcffuXTRv3hx//fUXPv/8cwwcOBB9+vQp1zUV1LBhQ5iYmGDr1q3w9PSEubk5nJyc4OTkpJW/j9mzZ+Pbb7/F4cOHC63773//i+joaCxcuBDnzp3DqFGjlIOenTp1Chs3bsTixYvRpUuXIo/duXNn1KpVC1OnTsXChQthYGCArVu34uLFi+WKFRDfh6+++grjxo3DsmXL0LhxYxw6dAi///57qfv+888/OHfuHN577z3lj3t+Xbp0wRdffIHAwEDMmDFDufzp06dFlqwaGRkpv0uKYm1tjb1792LIkCFo2bKlyqBnycnJOHXqFBISEtC5c+dSY1fnO6Os32EKiYmJGD58OKZMmYKUlBQsXLgQxsbG8Pf3B1D2v/UaRbKms6T2OCMK/v7+gpOTk6Cnp1emcUb27t0rdOjQQTA2NhbMzMyE3r17C6dPn1bZRp3eNAq3b98Wpk2bJjRq1EgwMjISTExMhKZNmwp+fn4qvSny8vKElStXCg0aNBCMjY0Fb29v4cSJE4Vaon/xxRdC586dhTp16giGhoaCi4uLMGnSpEJjFRR3/YoxA9zd3QUDAwOhTp06wpgxY4odZ6Sg4sY/wMsxLkqieK8Uk1wuF2rVqiW0bdtWmD17tnDlypVC+xTs4fLw4UNhwoQJQpMmTQQzMzPB3NxcaNGihfDVV18JOTk5yv3u3r0r9OvXT7CwsChynJGi3sOSxhm5dOmS0LNnT8HExESoXbu28N577xUasyIlJUWYPHmyYG9vL5iZmQlDhgwR7t69W6g3jSAU//4UN87I1KlTBUdHR0FfX19wdXUV/P39ix1npKDiejkUtH37dqFJkyaCgYFBoZjL8vdRlJJ6UG3cuFH5WVD0pslv3759wqBBgwRbW1tBX19fqFWrluDj4yNs2LBByMzMLPG8ivFxTE1NBVtbW2Hy5MnChQsXCn1XKN7fghS9fPL7999/hREjRgjm5uaChYWFMGLECCEsLKzU3jSzZ88WAAhRUVHFbvPRRx8JAITz588LglByb5q6deuWeO0KCQkJgr+/v9CiRQvBzMxMMDAwEJycnIQhQ4YImzdvFrKzs5XblvQ9W9bvjLJ+h+UfZ2TWrFmCra2tYGRkJHTr1k2l915Z/9ZrEpkglLPykoiIiJRCQ0Ph4+ODn3/+uVAvMSoZ24wQERGRpJiMEBERkaRYTUNERESSYskIERERSYrJCBEREUmKyQgRERFJqkoMepaXl4cHDx7AwsKiQrfeJiIiosojCAKePXsGJycnlRtSFlQlkpEHDx7A2dlZ6jCIiIioHO7du4d69eoVu75KJCOKoaTv3bsHS0tLiaMhIiKiskhNTYWzs3OpN3OsEsmIomrG0tKSyQgREVEVU1oTCzZgJSIiIkkxGSEiIiJJMRkhIiIiSVWJNiNERKRdgiAgJycHubm5UodCVYhcLoe+vn6Fh91gMkJEVMNlZWUhPj4ez58/lzoUqoJMTU3h6OgIQ0PDch+DyQgRUQ2Wl5eHmJgYyOVyODk5wdDQkINLUpkIgoCsrCw8evQIMTExaNy4cYkDm5WEyQgRUQ2WlZWFvLw8ODs7w9TUVOpwqIoxMTGBgYEBYmNjkZWVBWNj43Idhw1YiYio3P/REmnis8NPHxEREUmKyQgRERFJim1GiIiokK+O3ajU883p616p5ytNaGgofHx88OTJE1hbWxe5zaJFi7B3715ERUVVamzVEUtGiIioypkwYQJkMhmWL1+usnzv3r2FegMJgoCNGzeiQ4cOMDc3h7W1Nby9vbFmzZoKdWeeO3cujh8/XqZtFy1ahFatWpX7XNUdkxEiIqqSjI2NsWLFCjx58qTE7caOHYvZs2dj6NChCAkJQVRUFD755BPs27cPR48eLff5zc3NYWNjU+79tSUrK0vqENTGZISIiKqkPn36wMHBAQEBAcVus2vXLmzduhXbt2/H/Pnz0a5dO9SvXx9Dhw7FiRMn4OPjU+I5zp8/D29vb5iamqJz5864fv26cl3B0o7Q0FC0b98eZmZmsLa2RpcuXRAbG4vg4GAsXrwYFy9ehEwmg0wmQ3BwMAAgLi4OQ4cOhbm5OSwtLfHWW2/h4cOHKjEsXboUdnZ2sLCwwOTJk/HRRx+pnHfChAkYNmwYAgIC4OTkBHd3scpry5Yt8Pb2hoWFBRwcHDBq1CgkJiaqxCuTyfD777+jdevWMDExQa9evZCYmIjDhw/D09MTlpaWeOedd7Q+IB7bjBBVFyHFfyEX4uOvvTiIKolcLsfnn3+OUaNGYdasWahXr16hbbZu3QoPDw8MHTq00DqZTAYrK6sSz/Hxxx/jiy++gK2tLaZOnYqJEyfi9OnThbbLycnBsGHDMGXKFGzfvh1ZWVk4d+4cZDIZRo4ciX/++QdHjhzBH3/8AQCwsrKCIAgYNmwYzMzMcPLkSeTk5GDatGkYOXIkQkNDlfEvW7YM69evR5cuXbBjxw588cUXcHNzUzn/8ePHYWlpiWPHjkEQBABiCcmSJUvg4eGBxMREzJkzBxMmTMChQ4dU9l20aBG++eYbmJqa4q233sJbb70FIyMjbNu2DWlpaRg+fDjWrVuHDz/8sMTXqiKYjBARUZU1fPhwtGrVCgsXLkRgYGCh9Tdv3oSHh0e5j79s2TL06NEDAPDRRx9h0KBByMjIKDS4V2pqKlJSUjB48GA0bNgQAODp6alcb25uDn19fTg4OCiXHTt2DJcuXUJMTAycnZ0BAD/99BOaNWuG8PBwtGvXDuvWrcOkSZPw7rvvAgA+/fRTHD16FGlpaSrnNzMzww8//KAyJPvEiROV8w0aNMDatWvRvn17pKWlwdzcXLlu6dKl6NKlCwBg0qRJ8Pf3x+3bt9GgQQMAwBtvvIGQkBCtJiOspiEioiptxYoV+PHHH3H16tVC6wRBqNDw9i1atFDOOzo6AoBKVYdC7dq1MWHCBPTv3x9DhgzB119/jfj4+BKPHR0dDWdnZ2UiAgBNmzaFtbU1oqOjAQDXr19H+/btVfYr+BwAmjdvXujeMJGRkRg6dChcXV1hYWGBnj17AhCrhoq7Rnt7e5iamioTEcWyoq5Zk5iMEBFRlda9e3f0798f8+fPL7TO3d1d+cNeHgYGBsp5RVKTl5dX5LabNm3CmTNn0LlzZ+zcuRPu7u44e/ZssccuLlEquLyo3kEFmZmZqTxPT09Hv379YG5uji1btiA8PBx79uwBULiBa8FrzP9csay4a9YUJiNERFTlLV++HL/99hvCwsJUlo8aNQo3btzAvn37Cu0jCAJSUlI0Gkfr1q3h7++PsLAweHl5Ydu2bQAAQ0ND5ObmqmzbtGlTxMXF4d69e8plV69eRUpKirKKx8PDA+fOnVPZLyIiotQ4rl27hqSkJCxfvhzdunVDkyZNtF66URFMRoiIqMpr3rw5Ro8ejXXr1qksf+uttzBy5Ei88847CAgIQEREBGJjY3HgwAH06dMHISEhGjl/TEwM/P39cebMGcTGxuLo0aO4ceOGMqmoX78+YmJiEBUVhaSkJGRmZqJPnz5o0aIFRo8ejQsXLuDcuXMYN24cevToAW9vbwDAzJkzERgYiB9//BE3b97E0qVLcenSpVKrnlxcXGBoaIh169bhzp072L9/P5YsWaKRa9UGNmAlIqJCdG1E1LJYsmQJdu3apbJMJpNh27Zt2LhxI4KCgrB06VLo6+ujcePGGDduHPr376+Rc5uamuLatWv48ccfkZycDEdHR8yYMQP/+c9/AAAjRozAr7/+Ch8fHzx9+hSbNm3ChAkTsHfvXsycORPdu3eHnp4eBgwYoJJQjR49Gnfu3MHcuXORkZGBt956CxMmTChUWlKQra0tgoODMX/+fKxduxZt2rTB6tWr8dprr2nkejVNJhRV+aRjUlNTYWVlhZSUFFhaWkodDpFuYtdeKoeMjAzExMTAzc2t3Ld/p8rVt29fODg44KeffpI6FAAlf4bK+vvNkhEiIiId9fz5c2zYsAH9+/eHXC7H9u3b8ccff+DYsWNSh6ZRTEaIiIh0lEwmw6FDh7B06VJkZmbCw8MDu3fvRp8+faQOTaOYjBAREekoExMT5ait1Rl70xAREZGkmIwQERGRpJiMEBERkaSYjBAREZGkmIwQERGRpJiMEBERkaTYtZeIiApTZ0RfTdCRUYHv3r0LNzc3REZGolWrVkVuExwcjNmzZ+Pp06eVGlt1xpIRIiKqssLCwiCXyzFgwIBC6+7evQuZTFbkdPbs2XKfc+TIkbhx40aZtg0ODoa1tXW5z1VTsGSEiIiqrKCgIMycORM//PAD4uLi4OLiUmibP/74A82aNVNZZmNjU+5zmpiYwMTEpNz7a0t2djYMDAykDqNcWDJCRERVUnp6Onbt2oX33nsPgwcPRnBwcJHb2djYwMHBQWUq7Uf7zp078PHxgampKVq2bIkzZ84o1xUs7bh48SJ8fHxgYWEBS0tLtG3bFhEREQgNDcW7776LlJQUZYnMokWLAABPnjzBuHHjUKtWLZiamsLX1xc3b95UieF///sfnJ2dYWpqiuHDh+PLL79UOe+iRYvQqlUrBAUFoUGDBjAyMoIgCDhy5Ai6du0Ka2tr2NjYYPDgwbh9+7ZyP0WJ0a5du9CtWzeYmJigXbt2uHHjBsLDw+Ht7Q1zc3MMGDAAjx49KtubUUFqJSPfffcdWrRoAUtLS1haWqJTp044fPhwifucPHkSbdu2hbGxMRo0aIANGzZUKGAiIiIA2LlzJzw8PODh4YExY8Zg06ZN0NSN6D/++GPMnTsXUVFRcHd3xzvvvIOcnJwitx09ejTq1auH8PBwnD9/Hh999BEMDAzQuXNnrFmzBpaWloiPj0d8fDzmzp0LAJgwYQIiIiKwf/9+nDlzBoIgYODAgcjOzgYAnD59GlOnTsX777+PqKgo9O3bF8uWLSt07lu3bmHXrl3YvXs3oqKiAIhJmp+fH8LDw3H8+HHo6elh+PDhyMvLU9l34cKFWLBgAS5cuAB9fX288847mDdvHr7++mv8+eefuH37Nj799FONvJ6lUauapl69eli+fDkaNWoEAPjxxx8xdOhQREZGFioCA4CYmBgMHDgQU6ZMwZYtW3D69GlMmzYNtra2GDFihGaugIiIaqTAwECMGTMGADBgwACkpaXh+PHjhW4i17lzZ+jpqf7vnZKSArlcXuyx586di0GDBgEAFi9ejGbNmuHWrVto0qRJoW3j4uLw3//+V7mucePGynVWVlaQyWRwcHBQLrt58yb279+P06dPo3PnzgCArVu3wtnZGXv37sWbb76JdevWwdfXV5m8uLu7IywsDAcOHFA5d1ZWFn766SfY2toqlxX8fQ0MDISdnR2uXr0KLy8vlWvs378/AOD999/HO++8g+PHj6NLly4AgEmTJhVb2qRpapWMDBkyBAMHDoS7uzvc3d2xbNkymJubF9sQaMOGDXBxccGaNWvg6emJyZMnY+LEiVi9erVGgicioprp+vXrOHfuHN5++20AgL6+PkaOHImgoKBC2+7cuRNRUVEqU0mJCAC0aNFCOe/o6AgASExMLHJbPz8/TJ48GX369MHy5ctVqkSKEh0dDX19fXTo0EG5zMbGBh4eHoiOjlZeX/v27VX2K/gcAFxdXVUSEQC4ffs2Ro0ahQYNGsDS0hJubm4AxKSpuGu0t7cHADRv3lxlWXHXrGnlbsCam5uLn3/+Genp6ejUqVOR25w5cwb9+vVTWda/f38EBgaW2NAmMzMTmZmZyuepqanlDZOIiKqhwMBA5OTkoG7dusplgiDAwMAAT548Qa1atZTLnZ2dlSX6ZZX/90kmkwFAoWoOhUWLFmHUqFE4ePAgDh8+jIULF2LHjh0YPnx4kdsXV5UkCILyXPnnS9rPzMys0LIhQ4bA2dkZ//vf/+Dk5IS8vDx4eXkhKyur1GssuKy4a9Y0tRuwXr58Gebm5jAyMsLUqVOxZ88eNG3atMhtExISlNmWgr29PXJycpCUlFTsOQICAmBlZaWcnJ2d1Q2TiIiqqZycHGzevBlffPGFSmnHxYsX4erqiq1bt1Z6TO7u7pgzZw6OHj2K119/HZs2bQIAGBoaIjc3V2Xbpk2bIicnB3///bdyWXJyMm7cuAFPT08AQJMmTXDu3DmV/SIiIkqNIzk5GdHR0ViwYAF69+4NT09PPHnypKKXp3VqJyMeHh6IiorC2bNn8d5772H8+PG4evVqsdsXl9kVXJ6fv78/UlJSlNO9e/fUDZOIiKqpAwcO4MmTJ5g0aRK8vLxUpjfeeAOBgYEq2ycnJyMhIUFlysjI0EgsL168wIwZMxAaGorY2FicPn0a4eHhyqSifv36yrYsSUlJeP78ORo3boyhQ4diypQp+Ouvv3Dx4kWMGTMGdevWxdChQwEAM2fOxKFDh/Dll1/i5s2b+P7773H48OESfzsBoFatWrCxscHGjRtx69YtnDhxAn5+fhq5Vm1Su5rG0NBQWdzl7e2N8PBwfP311/j+++8Lbevg4ICEhASVZYmJidDX1y+xj7eRkRGMjIzUDY2IiDRFR0ZELUpgYCD69OkDKyurQutGjBiBzz//HBcuXEDt2rUBoFCDVgDYvn27sr1JRcjlciQnJ2PcuHF4+PAh6tSpg9dffx2LFy8GIDaenTp1KkaOHInk5GQsXLgQixYtwqZNm/D+++9j8ODByMrKQvfu3XHo0CFlNUmXLl2wYcMGLF68GAsWLED//v0xZ84cfPPNNyXGo6enhx07dmDWrFnw8vKCh4cH1q5di549e1b4WrVJJlSwH1Tv3r3h7OxcZIvbDz/8EL/99ptKycl7772HqKgolT7bpUlNTYWVlRVSUlJgaWlZkXCJqi91hu/W4R8aqlwZGRmIiYmBm5sbjI2NpQ6HSjBlyhRcu3YNf/75p9ShqCjpM1TW32+1Skbmz58PX19fODs749mzZ9ixYwdCQ0Nx5MgRAGL1yv3797F582YAwNSpU/HNN9/Az88PU6ZMwZkzZxAYGIjt27ere61EREQ1yurVq9G3b1+YmZnh8OHD+PHHH7F+/Xqpw9IKtZKRhw8fYuzYsYiPj4eVlRVatGiBI0eOoG/fvgCA+Ph4la5Dbm5uOHToEObMmYNvv/0WTk5OWLt2LccYISIiKsW5c+ewcuVKPHv2DA0aNMDatWsxefJkqcPSCrWSkYKNggoqqqqmR48euHDhglpBERER1XS7du2SOoRKw3vTEBERkaSYjBAREZGkmIwQERGRpJiMEBERkaSYjBAREZGkmIwQERGRpJiMEBERFeH06dNo3rw5DAwMMGzYMISGhkImk+Hp06dSh1btMBkhIqIqZ8KECZDJZFi+fLnK8r179xZ5g9aNGzeiQ4cOMDc3h7W1Nby9vbFmzRo8f/682HP4+fmhVatWiImJQXBwMDp37qwc9BMQx9aytrbW+LXVRExGiIioSjI2NsaKFSvw5MmTErcbO3YsZs+ejaFDhyIkJARRUVH45JNPsG/fPhw9erTY/W7fvo1evXqhXr16sLa2hqGhIRwcHEq9cy6pT+279hIRUfUlCEAJhQVaZWoKqPM736dPH9y6dQsBAQFYuXJlkdvs2rULW7duxd69ezF06FDl8vr16+O1115DampqoX3u3r0LNzc3AMDEiRMxceJEbNq0CfXr14ePjw+ePHmCqKgovPvuuwCgTE4Ud+Ql9TEZISIipefPAXNzac6dlgaYmZV9e7lcjs8//xyjRo3CrFmzUK9evULbbN26FR4eHiqJiIJMJlNWueTn7OyM+Ph4eHh44LPPPsPIkSNhZWWFv//+W7lN586dsWbNGnz66ae4fv06AMBcqheuGmA1DRERVVnDhw9Hq1atsHDhwiLX37x5Ex4eHmodUy6XK6tjrKys4ODgABMTE5VtDA0NYWVlBZlMBgcHBzg4ODAZqQCWjBARkZKpqVhCIdW5y2PFihXo1asXPvjgg0LrBEFgG48qgMkIEREpyWTqVZXogu7du6N///6YP38+JkyYoLLO3d0d0dHR0gRGZcZqGiIiqvKWL1+O3377DWFhYSrLR40ahRs3bmDfvn2F9hEEASkpKeU+p6GhIXJzc8u9P73CZISIiKq85s2bY/To0Vi3bp3K8rfeegsjR47EO++8g4CAAERERCA2NhYHDhxAnz59EBISUu5z1q9fH2lpaTh+/DiSkpJKHLOESsZkhIiIqoUlS5ZAEASVZTKZDNu2bcOXX36JPXv2oEePHmjRogUWLVqEoUOHon///uU+X+fOnTF16lSMHDkStra2xXYvptLJhILvnA5KTU2FlZUVUlJSYGlpKXU4RLopJKDs2/r4ay8OqlIyMjIQExMDNzc3GBsbSx0OVUElfYbK+vvNkhEiIiKSFJMRIiIikhSTESIiIpIUkxEiIiKSFJMRIiIikhSTESIiIpIUkxEiIiKSFJMRIiIikhSTESIiIpIUkxEiIqJ8rl27ho4dO8LY2BitWrXC3bt3IZPJEBUVJXVo1RaTESIiqrLCwsIgl8sxYMCAQusUSURR09mzZ4s95sKFC2FmZobr16/j+PHjcHZ2Rnx8PLy8vAAAoaGhkMlkePr0qbYuq8bRlzoAIiKi8goKCsLMmTPxww8/IC4uDi4uLoW2+eOPP9CsWTOVZTY2NsUe8/bt2xg0aBBcXV2VyxwcHDQXNBXCZISIiF4RBOD5c2nObWoKyGRl3jw9PR27du1CeHg4EhISEBwcjE8//bTQdjY2NmVOJmQvz3/+/Hl89tlnWLhwISZMmAA3NzdERkbC2toaPj4+AIBatWoBAMaPH4/g4OAyx02FMRkhIqJXnj8HzM2lOXdaGmBmVubNd+7cCQ8PD3h4eGDMmDGYOXMmPvnkE2VCUR7x8fHo06cPBgwYgLlz58Lc3BxJSUnK9c7Ozti9ezdGjBiB69evw9LSEiYmJuU+H4nYZoSIiKqkwMBAjBkzBgAwYMAApKWl4fjx44W269y5M8zNzVWm3NzcIo/p4OAAfX19mJubw8HBAeYFEjO5XI7atWsDAOzs7ODg4AArKysNX1nNw5IRIiJ6xdRULKGQ6txldP36dZw7dw6//vorAEBfXx8jR45EUFAQ+vTpo7Ltzp074enpqbJMLpdXPF7SGCYjRET0ikymVlWJVAIDA5GTk4O6desqlwmCAAMDAzx58kTZngMQq1YaNWokRZhURqymISKiKiUnJwebN2/GF198gaioKOV08eJFuLq6YuvWrVo9v6GhIQAUW9VD6mPJCBERVSkHDhzAkydPMGnSpELtNd544w0EBgZixowZymXJyclISEhQ2c7a2hrGxsblOr+rqytkMhkOHDiAgQMHwsTEpFDbElIPS0aIiKhKCQwMRJ8+fYpsODpixAhERUXhwoULymV9+vSBo6OjyrR3795yn79u3bpYvHgxPvroI9jb26skPlQ+MkEQBKmDKE1qaiqsrKyQkpICS0tLqcMh0k0hAWXf1sdfe3FQlZKRkYGYmBi4ubmVu6SAaraSPkNl/f1myQgRERFJiskIERERSYrJCBEREUmKyQgRERFJiskIERGhCvRlIB2lic+OWslIQEAA2rVrBwsLC9jZ2WHYsGG4fv16ifuEhoZCJpMVmq5du1ahwImIqOIMDAwAAM+lulMvVXmKz47is1Qeag16dvLkSUyfPh3t2rVDTk4OPv74Y/Tr1w9Xr16FWSnDByvubqhga2tbvoiJiEhj5HI5rK2tkZiYCAAwNTWt0F1vqeYQBAHPnz9HYmIirK2tK3S/H7WSkSNHjqg837RpE+zs7HD+/Hl07969xH3t7OxgbW2tdoBERKRdDg4OAKBMSIjUYW1trfwMlVeFhoNPSUkBAOXtlEvSunVrZGRkoGnTpliwYAF8fHyK3TYzMxOZmZnK56mpqRUJk4iISiCTyeDo6Ag7OztkZ2dLHQ5VIQYGBhq5A3K5kxFBEODn54euXbvCy8ur2O0cHR2xceNGtG3bFpmZmfjpp5/Qu3dvhIaGFluaEhAQgMWLF5c3NCIiKge5XK6RHxYidZV7OPjp06fj4MGD+Ouvv1CvXj219h0yZAhkMhn2799f5PqiSkacnZ05HDxRSTgcPBHpGK0OBz9z5kzs378fISEhaiciANCxY0fcvHmz2PVGRkawtLRUmYiIiKh6UquaRhAEzJw5E3v27EFoaCjc3NzKddLIyEg4OjqWa18iIiKqXtRKRqZPn45t27Zh3759sLCwQEJCAgDAysoKJiYmAAB/f3/cv38fmzdvBgCsWbMG9evXR7NmzZCVlYUtW7Zg9+7d2L17t4YvhYiIiKoitZKR7777DgDQs2dPleWbNm3ChAkTAADx8fGIi4tTrsvKysLcuXNx//59mJiYoFmzZjh48CAGDhxYsciJiIioWih3A9bKVNYGMEQ1GhuwEpGO0WoDViIiIiJNYTJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESS0pc6AKLSfHXsRonr5/R118q+RERUOVgyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSUisZCQgIQLt27WBhYQE7OzsMGzYM169fL3W/kydPom3btjA2NkaDBg2wYcOGcgdMRERE1YtaycjJkycxffp0nD17FseOHUNOTg769euH9PT0YveJiYnBwIED0a1bN0RGRmL+/PmYNWsWdu/eXeHgiYiIqOrTV2fjI0eOqDzftGkT7OzscP78eXTv3r3IfTZs2AAXFxesWbMGAODp6YmIiAisXr0aI0aMKF/UREREVG1UqM1ISkoKAKB27drFbnPmzBn069dPZVn//v0RERGB7OzsIvfJzMxEamqqykRERETVU7mTEUEQ4Ofnh65du8LLy6vY7RISEmBvb6+yzN7eHjk5OUhKSipyn4CAAFhZWSknZ2fn8oZJREREOq7cyciMGTNw6dIlbN++vdRtZTKZynNBEIpcruDv74+UlBTldO/evfKGSURERDpOrTYjCjNnzsT+/ftx6tQp1KtXr8RtHRwckJCQoLIsMTER+vr6sLGxKXIfIyMjGBkZlSc0IiIiqmLUKhkRBAEzZszAr7/+ihMnTsDNza3UfTp16oRjx46pLDt69Ci8vb1hYGCgXrRERERU7aiVjEyfPh1btmzBtm3bYGFhgYSEBCQkJODFixfKbfz9/TFu3Djl86lTpyI2NhZ+fn6Ijo5GUFAQAgMDMXfuXM1dBREREVVZaiUj3333HVJSUtCzZ084Ojoqp507dyq3iY+PR1xcnPK5m5sbDh06hNDQULRq1QpLlizB2rVr2a2XiIiIAKjZZkTR8LQkwcHBhZb16NEDFy5cUOdUREREVEPw3jREREQkKSYjREREJCkmI0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkKX2pAyCS0lfHbhS7bk5f90qMhIio5mLJCBEREUmKyQgRERFJiskIERERSYrJCBEREUmKyQgRERFJir1pqErIfCFD6mN9GBgJMLfKgb6B1BEREZGmMBkhnXfrkgmCPnVCxnM5AMDcOgeTPnsA1yYZEkdGRESawGoa0mmnTwM/LKiLjOdy6BvmQU9PQNpTfWycXxf3bxtJHR4REWkAkxHSWVevAr6+QFaGHtzbpGPZr7exbM8t1G/6Ai/S5NjwYT0k/sv6GiKiqo7JCOmsTz8Fnj0DGng9x8RFD2BgKMDIRMCUZffh7JGB9FQ5fttoK3WYRERUQUxGSCddvw78+qs4P2JmIgyNBeU6E7M8jP4wHnp6Aq6cNcfZsxIFSUREGsFkhHTSqlWAIABDhgCOblmF1tvVy4Z331QAwMcfV3Z0RESkSUxGSOfcvw9s3izO+/sXv12/McmQG+ThxAng+PHKiY2IiDSPyQjpnK+/BrKzge7dgU6dit+utn0OOg9KAQAsW1ZJwRERkcYxGSGdIgjAzp3i/OzZpW/f840nkMmAkBDg7l1tRkZERNrCQc9Ip0RFAXFxgKkpMGBA6dvXssuBjw9w4gTw00/AJ59oPcTihQSUfVufEuqfKkNVipWqN34WCSwZIR2zb5/42K8fYGJStn0mTBAff/xRLFkhIqKqhckI6RRFMjJ0aNn3ef11wNwcuH1bHLGViIiqFiYjpDNiY8VqGj09YPDgsu9nZga8+aY4HxysjciIiEibmIyQzlCUinTpAtSpo96+48eLj7t2AZmZmo2LiIi0i8kI6QxFMjJsmPr7dusGODqKw8eHhmoyKiIi0jYmI6QTnj8H/vxTnB8yRP3981ft/Pab5uIiIiLtYzJCOuHcOXGgs7p1gUaNyncMRRKzfz971RARVSUcZ4R0wsofkwDUgW2jVKz5I6Fcx+jdW+wOfO8ecOkS0LKlZmMkIiLtULtk5NSpUxgyZAicnJwgk8mwd+/eErcPDQ2FTCYrNF27dq28MVM1FPOPOKiIW7OMch/D1BTo00ecZ1UNEVHVoXYykp6ejpYtW+Kbb75Ra7/r168jPj5eOTVu3FjdU1M1lZsL3L1qDABw83pRoWPlr6ohIqKqQe1qGl9fX/j6+qp9Ijs7O1hbW6u9H1V///wDZDyXw8g0F45uFeuXq2jEGh4OxMdrIDgiItK6SmvA2rp1azg6OqJ3794ICQkpcdvMzEykpqaqTFR9/fWX+FjfMwNyecWO5egIeHuL80ePVuxYRERUObSejDg6OmLjxo3YvXs3fv31V3h4eKB37944depUsfsEBATAyspKOTk7O2s7TJKQIhlxa1axKhqFvn3Fx+PHNXI4IiLSMq0nIx4eHpgyZQratGmDTp06Yf369Rg0aBBWr15d7D7+/v5ISUlRTvfu3dN2mCQRQXg1vkhF24so9O4tPv7xB7v4EhFVBZKMM9KxY0fcvHmz2PVGRkawtLRUmah6iosD7t8H9OQCXDzK35Mmv86dASMjsc1I4j1DjRyTiIi0R5JkJDIyEo6OjlKcmnRMeLj46OSWCSMTzRRjmJgAXbuK8zcumGrkmEREpD1q96ZJS0vDrVu3lM9jYmIQFRWF2rVrw8XFBf7+/rh//z42b94MAFizZg3q16+PZs2aISsrC1u2bMHu3buxe/duzV0FVVmRkeJj3caavbtd795im5GbkaboNuypRo9NRESapXYyEhERAR8fH+VzPz8/AMD48eMRHByM+Ph4xMXFKddnZWVh7ty5uH//PkxMTNCsWTMcPHgQAwcO1ED4VNUpkpF6DTVTRaOgaDdy65IJcnNR4V46RESkPWonIz179oRQQqvA4OBglefz5s3DvHnz1A6MagZlyUgjzZaMtG0LWFkBKSly/HvDGK6emk12iIhIc3ijPJJMQoI4yWSo8GBnBcnlgKIA72YU240QEekyJiMkGUWpiIcHNNZ4NT9FMnL7sonGj01ERJrDZIQko0hGWrfWzvG7dxcf714R240QEZFuYjJCktF2MtK8OWBslovMF3p4cNtIOychIqIKYzJCktF2MiKXvxpi/g6raoiIdBaTEZJESgpw+7Y4r61kBAAaNBeTkduX2YiViEhXMRkhSVy8KD46OwM2Nto7T4OX97uJ+ceE96khItJRTEZIEtquolFwds+AvmEe0lPleBjH+9QQEekiJiMkiX/+ER9btNDuefQNgPovBzxjuxEiIt3EZIQkceWK+NismfbPpWg3wmSEiEg3MRmhSicIlZyMKNqNXGEyQkSki5iMUKV78ABITRW73rq7a/98Lk1eQKYn4EmiAZ4mqX07JiIi0jJ+M5PGfHXsRrHr5vR9lXUoSkUaNwaMKmEsMmNTAY71M/HgjjFirxrDunua9k9KRERlxpIRqnSKZKRp08o7Z/2mYiPWu9HGlXdSIiIqEyYjVOkqs72IQv2mYruRu1fZboSISNcwGaFKd/Wq+Fi5yYhYMvLvLSNkZ8kq78RERFQqJiNUqSq7J42CjWM2zK1ykJuth39v8qZ5RES6hMkIVar791/1pGncuPLOK5O9Kh2JjWZVDRGRLmEyQpVKUUVTWT1p8qv/8g6+MVfZiJWISJcwGaFKJUUVjYJiWPi7V3nTPCIiXcJkhCqVlMlIPfcM6MkFPHusjycPOcQOEZGuYDJClSo6Wnz09Kz8cxsaCajbKBMAcJftRoiIdAaTEapUN14O0tqkiTTnfzXeCNuNEBHpCiYjVGmePAGSksT5Ro2kiaG+Jwc/IyLSNUxGqNLcvCk+OjkB5ubSxKDo3vvgthEyX3DwMyIiXcBkhCqNooqmMscXKaiWXQ6s62QjL0+GezdZVUNEpAuYjFClUSQj7u4lb6dtroqb5l1hMkJEpAuYjFClUVTTSJ2MKBqxciRWIiLdwGSEKo0uVNMAHPyMiEjXMBmhSiEIulMyUrdRBvQN8pCeKsej+wbSBkNERExGqHI8fAg8ewbo6QENGkgbi74B4OwuDn4Wyy6+RESSYzJClUJRRePqWvk3yCuKq2K8kWg2YiUikhqTEaoUulJFo6AYb4TDwhMRSY/JCFUKXWm8qqAYiTXhriEynnPwMyIiKTEZoUqhK2OMKFja5KKWfTaEPBnirrOqhohISkxGqFLoWjUN8Kp0hI1YiYikpS91AFT95eUCt26J89qopvnq2I1y7efqmYHIUEs2YiUikhhLRkjrnj7SR2YmYGAg9qbRFflHYuXgZ0RE0mEyQlr36L4hAKBRI0AulziYfJwaZELfMA/Pn8nx6F8OfkZEJBUmI6R1ilFOdaUnjYI4+Bm7+BIRSY3JCGndo3/FkhFdaryq8Oo+NWw3QkQkFSYjpHWKahpdKxkBxEasAO/gS0QkJSYjpHWKahrdLBnJN/hZOv8ciIikoPa376lTpzBkyBA4OTlBJpNh7969pe5z8uRJtG3bFsbGxmjQoAE2bNhQnlipCsrJBp4k6G4yohz8TODgZ0REUlE7GUlPT0fLli3xzTfflGn7mJgYDBw4EN26dUNkZCTmz5+PWbNmYffu3WoHS1XP4wQD5OXJYGYGODpKHU3RFKUjbDdCRCQNtQc98/X1ha+vb5m337BhA1xcXLBmzRoAgKenJyIiIrB69WqMGDFC3dNTFaNovNq4MSDT0VvAvBr8jO1GiIikoPURWM+cOYN+/fqpLOvfvz8CAwORnZ0NA4PC4ztkZmYiMzNT+Tw1NVXbYZKW6HJ7EQXl4GfXjJGXB+jpUtORp0+Ba9eAR4/EgVoaNRJHjyMiqka0/rWbkJAAe3t7lWX29vbIyclBUlJSkfsEBATAyspKOTk7O2s7TNISXe5Jo6AY/OyFrgx+JgjAvn1A27ZArVpAp07Aa68BTZsCZmbAW28BZ89KHSURkcZUyv+AsgLl88LLsbcLLlfw9/dHSkqKcrp3757WYyTt0OUxRhTyD34We03iqprYWKBjR2DYMODCBXGZkxPQsiVgbg5kZwM//ywmKP36AXFxkoZLRKQJWk9GHBwckJCQoLIsMTER+vr6sLGxKXIfIyMjWFpaqkxUNSXp6OirBenE4GdRUWKSce6cWAIyfz6QmAjcvy+uS00VHydOBAwNgWPHgObNgZ9+ki5mIiIN0Hoy0qlTJxw7dkxl2dGjR+Ht7V1kexGqPjJfyPA0SffbjACvBj+7e1WikpEzZ4Du3YH4eMDLC4iOBpYtA2xtX20jk4klJIGBwD//iCUoqanAuHHARx+Bd/sjoqpK7WQkLS0NUVFRiIqKAiB23Y2KikLcy+Jif39/jBs3Trn91KlTERsbCz8/P0RHRyMoKAiBgYGYO3euZq6AdFbSAzERMbXIRTGFYDrDrZnYiPVhrCGeP6vkFqwPHwIjRgDPngE9egB//gmU1k6qcWNxu08/FZ+vWAEs/wXIydV+vEREGqb2t25ERARat26N1q1bAwD8/PzQunVrfPrySzE+Pl6ZmACAm5sbDh06hNDQULRq1QpLlizB2rVr2a23Bkh62Xi1Tt0siSMpnUWtXNjWzYIgyCq3dCQnB3j7bbFExNMTOHAAsLYu2776+sDixUBQkHg75GORQMAuIDdPqyETEWma2l17e/bsqWyAWpTg4OBCy3r06IELisZ4VGMoetLY1csGoPtjeLh5vcCj+4a4848JmnZIr5yTLl4MhIaKbUR27xYbqarr3XfF6pzhw4CQy4CZMTBnmO4O7EJEVIAujahA1YxijBHbKlAyAgANvMSqmph/Kilxun5drF4BgB9+EEtGymvwYGD+m2ICciAcCDpW+j5ERDqCyQhpjaJbb1WopgHEkhEAiLthhOysSihVmDNH7Ko7aJBYVVNRPVsAfsPE+a2hwB9RFT8mEVElYDJCWqMsGamXLXEkZVPHKRsWtXKQm62HezeMtHuygweBw4fF0VS/+kpzxx3UDninhzi/6lcgmmP0EJHuYzJCWvH8mR7SU8QmSXWcqkbJiEz2qlfNnctarKrJzRVLRQDxUdODsEzqC3RqAmTnAJ9sAR4/0+zxiYg0jMkIaYWi8apl7RwYm1ad8S8aNH/ZbuSKFpORkMvAzZtio9MFCzR/fD094OORgKudmIgs28keNkSk05iMkFYo7vFiW69qlIooKEpGYq6YIE8bv9+CAGw/Kc7Png1YWGjhJABMjYBFowBjQyDyDrD5uHbOQ0SkAUxGSCuSHigar1aN9iIKTg0zYWSSh4x0Of75Rwsn+Ps6EPNQTEKmTdPCCfJxtQM+GCbObwkFLtzW7vmIiMqJyQhphbJkpIr0pFGQywFXT7F05K+/tHACRanI1KllH9ysInq3Ehu1CgKw4hfg2Qvtn5OISE1MRkgrFN167apYNQ3wqouvxpORK3HA5VjAQC5W0VSWaYOAejbAoxRgzb7KOy8RURkxGSGNEwTg0cv70lS1ahoAaPCy3ciff2r43nMHzomPvVoCTk4aPHApTAwB/7fEhq0hl4DjUZV3biKiMmAyQhr37Ikcmc/lkMkE1HGsesmIS5MM6MkF/PsvkO82SxWT9gIIvSzOD26voYOqwdMZGOcjzq/ZDyQ8qfwYiIiKwWSENE5xg7xadjnQN6w63XoVjEwE1GuUAUAsHdGI4xeBzGygvh3QtJQ78mrL6J7iudMzxPYj7O5LRDqCyQhpXGIV7dabn2K8EY20GxEE8X4xgNiYVKob2MnlYnWNsSFwMQb4WRstdImI1MdkhDROMeBZVU5GFOONaCQZuX4fuB0PGOgDfVtr4IAVUNcGmDFYnN90DIhJkDYeIiIwGSEtSHp5T5o6TlWvvYiCWzOxmubKFSA5uYIHO3JefOzhBViaVvBgGuDbFujYBMjOBZb/AuTkSh0REdVwTEZI4xTdeqtyyYi5dS6aNBHnT5+uwIFycoGTLxuu9pO4VERBJhMHQ7MwAW4+ALaFSh0REdVwTEZIo/LygKSX3XrtqsjdeovTrZv4ePJkBQ4SeRtIeQ5YmwGtG2gkLo2wsQRmDRHnfwoRkxIiIokwGSGNevpIHznZepDrC7C2q9rJSK9e4uOJExU4yIlL4mMPL7EBqS7p1RLo1kzsVbPiFyArR+qIiKiGYjJCGqWoorFxzNK531519ewpPl68CDx+XI4DZGUDf10R531aaCoszZHJgNlDAStT4E4C8FNFsi4iovJjMkIa9ei+4p40VbtUBAAcHABPT7Fnbrmqas7dBNIzAVsrwMtV4/FpRC1zYM4wcX77SSD6nqThEFHNxGSENKo6dOvNT1FVExJSjp1DLoqPPZuLQ7Hrqu5eQO+WQJ4ALP9ZHJyNiKgS6fA3JFVFyp401aBkBAB8Xo6grna7kaxs4Mx1cb5nc43GpBUzhwA2FsC9JCDomNTREFENw2SENEpRTVOnbvUoGenRQ3y8cgVITFRjxwu3gYwsoI4l0KSeVmLTKEtT4IPh4vwvp4FLMdLGQ0Q1CpMR0picbOBJgmIo+OpRMlKnDtCypTgfGqrGjqejxccuntIN/66ujk2AAW3FRjIrdwMvqkdCSUS6j8kIaczjBAPk5clgaJQHK5vq001U7aqavDwgTJGMNNVKTFozbRBgZwU8eAxsPCJ1NERUQzAZIY1RNF6tUzeryhQGlEXv3uLjH3+UcYfof4EnaYCZEdDSTWtxaYW5MTD3dXF+31ngwi1p4yGiGoHJCGnMo3+rVxWNQs+egIEBcPu2OJXq9FXxsYOHeHO8qsa7MTCkvTi/8lcgNVXaeIio2mMyQhqj7NZbTRqvKpibA506ifPHytLRRJGMVLUqmvym+gKOtYDEp8AHH0gdDRFVc0xGSGOS7levbr359esnPh49WsqG95LESV8OtHfXelxaY2IEzHtDbHz7ww/A4cNSR0RE1RiTEdKYRGU1TfUqGQFeJSMnTgA5JbXN/fvl2CIt3QAzY63HpVUt3YDXO4vzkycDT55IGw8RVVtMRkgjnj0DUpJe3q3XufolI23aALVqASkpQHh4CRsqkpGqXCqS3+R+gLs78OAB8P77UkdDRNUUkxHSiOsvf4MtauXA1CJP2mC0QC4H+vQR54utqnmR+WqwsA4elRKX1hkZAD/+KA5n/9NPwN69UkdERNUQkxHSiOiXw2pUx1IRhVLbjUTeAbJzAcfagHOdSotL6zp2BP77X3H+P/8BkpKkjYeIqh0mI6QR166JjzUhGTl7Fnj8uIgN8lfRVKeBVgBg8WKgWTNxTPxp06SOhoiqGSYjpBE1IRlxcRF/j/PygN9/L7BSEIC/b4jz1aWKJj8jI7G6Ri4Hfv4Z2LlT6oiIqBphMkIaoUhG7F2qbzICAIMHi48HDxZYcfWqOCaHoT7QqoqNulpWbdsCCxaI89OmAQkJ0sZDRNUGkxGqsJwc4OZNcb46l4wAwKBB4uPhw0Bubr4VR17ex6VVA8DYsNLjqjQffwy0bi3WU737rlhMRERUQUxGqMJiYoDsbMDAKA/WttXnBnlF6dRJ7OL7+LHYdkRJ0aq1XWNJ4qo0BgbA5s2AsbGYgH3xhdQREVE1wGSEKkzZXqReFvSq+SdKXx/o31+cV1bVvHgBnDolzntX82QEALy8gLVrxfn58wtkZURE6qvmPx1UGWpC49X8CrUb+fNPICMDsLUCXGwli6tSTZ4MvP22WEf39tscnZWIKoTJCFVYTUtGBgwQxwC7dAmIi8OrKhrvRtWvS29xZDLg+++Bhg2B2Fhg0iSxRxERUTkwGaEKqyk9aRRsbIDOL2/Zsm8fak57kYIsLcUuvgYGwJ49wLffSh0REVVRTEaoQgShZoy+WtDrr4uPodvjgcuXxZKC1o2kDUoKbdsCq1eL8x98APz9t7TxEFGVxGSEKuTRI7G5gEwG1KmbLXU4lWb4cPHR4uwxccbbG7AylS4gKc2cKb4gWVnAiBEcf4SI1FauZGT9+vVwc3ODsbEx2rZtiz///LPYbUNDQyGTyQpN1xRl+1SlXb4sPjZsCBga1Zw2A/Xri8Nt9BVeDsWqGCu+JpLJgOBgoEkT4P594M03xcSEiKiM1E5Gdu7cidmzZ+Pjjz9GZGQkunXrBl9fX8TFxZW43/Xr1xEfH6+cGjeuYfXr1dQ//4iPzZtLG4cUXh+Wh754WTJSk5MRQGw/snev+PjXX4Cfn9QREVEVonYy8uWXX2LSpEmYPHkyPD09sWbNGjg7O+O7774rcT87Ozs4ODgoJ7lcXu6gSXcokhEvL2njkMKoZhdhh0d4BnOkNuskdTjS8/AAtmwR57/9Fti0Sdp4iKjKUCsZycrKwvnz59GvwH+B/fr1Q1hYWIn7tm7dGo6OjujduzdCQkJK3DYzMxOpqakqE+kmRTVNTUxG3G6KvWhOoBcOHjWQOBodMWSIeIdfAHjvPSA8XNp4iKhKUCsZSUpKQm5uLuzt7VWW29vbI6GYRmuOjo7YuHEjdu/ejV9//RUeHh7o3bs3TilGrCxCQEAArKyslJOzs7M6YVIlycsDrlwR52tiNY3smJiMHEU/7NghcTC6ZMECYOhQIDMTeO01cRwSIqIS6JdnJ1mBgZ0EQSi0TMHDwwMeHq9uqd6pUyfcu3cPq1evRvfu3Yvcx9/fH3756pxTU1OZkOiguDggLQ0wNAQaNQLwr9QRVaL0dLFtBMRkJPYw8GSSMWpZZEgcmA7Q0xPvX9O1q1h0NmiQ+FpZW0sdGRHpKLVKRurUqQO5XF6oFCQxMbFQaUlJOnbsiJuK27wWwcjICJaWlioT6R5FFU2TJuK4VzXKyZNij5H69WHi1QjZ2cDuUx6l71dTWFoChw4BTk5i8dmIEexhQ0TFUisZMTQ0RNu2bXHs2DGV5ceOHUNnxZCUZRAZGQlHR0d1Tk06qCb3pFGOutqvH94ZJZYKbj/RVMKAdFC9euINfMzNgRMngClTOGQ8ERVJ7d40fn5++OGHHxAUFITo6GjMmTMHcXFxmDp1KgCximXcuHHK7desWYO9e/fi5s2buHLlCvz9/bF7927MmDFDc1dBkqjJjVeVyUj//nj7bXE2JMoVD5LMpYtJF7VqBfz8MyCXi1U3n30mdUREpIPUbjMycuRIJCcn47PPPkN8fDy8vLxw6NAhuLq6AgDi4+NVxhzJysrC3Llzcf/+fZiYmKBZs2Y4ePAgBg4cqLmrIEnU2JKR2FhxDHy5HOjVC27WQKdOwJkzMuwK9cTsN9iDRMWAAcB33wH/93/AokWArS0wbZrUURGRDilXA9Zp06ZhWjFfJsHBwSrP582bh3nz5pXnNKTDsrNf3SCvupaMfHXsRpHLmx/YgT6AmIG8bJQ5ahRw5gyw+agXk5GiTJkitnheuhSYPh0wMwPGj5c6KiLSEbw3DZXLjRtiQmJhAbi4SB1N5aof8fL2BwMGKJe98w5gaJCDyFsOiLxZ9sbcNcpnnwHvvy/OT5woVt8QEYHJCJWTor1Is2birUlqCr3sLLhEvhzgz9dXudzGBhjWRSxJCTzUUorQdJ9MBnz1FTB5sjhIzahRwIEDUkdFRDqAyQiVy/nz4mPr1tLGUdmcrkbC8MVzpFvbiI0z85nkewkAsPV4U7zILFcNaPUnkwEbNoiJSE4O8MYbwB9/SB0VEUmMyQiViyIZadtW2jgqW/1wceTgWO9u4uBe+fRpGwMXuxQ8TTPBnr/cpQivapDLxbv8DhsmjtI6eLDYBZiIaiwmI6Q2QQAuXBDna2oycrddt0Lr9PSAdweIpSOsqimFgQGwY8erYeOHDQN27ZI6KiKSCJMRUtvt20BKCmBkJLYZqSnMkh7CNuYGBJkMsW27FLnNuwMuQSYTcCKyPq7F1a7kCKsYIyOxEauiyuadd4CgIKmjIiIJMBkhtSmqaFq0qFnDwCtKRRI8WiDDslaR27g6pGJIJ/FWB9/s8a602KosAwNxMLT/+z+xUeukScDatVJHRUSVjMkIqa3Gthd52aX3bruib/CoMOv1CABA8O/NkZJmpPW4qjy5XGzUqrg55vvvAx99JCYnRFQjMBkhtdXEZESWmwOXC2KX3rvehduL5NerdSyauj5CeoYhNh1pURnhVX0yGbB6NbB4sfh8xQrgrbeA58+ljYuIKgWTEVJLTW286hgdBeP0Z3hhaY2H7iUPOSuTvSodWbenLXJza9BALBUhkwGffipW2xgYALt3Az4+QIG7hBNR9cNkhNRy5w7w9ClgaFizGq/WDxeraGLbdoUgl5e6/Zg+V2Bt/gJ34mthf1hjbYdXvYwdK449Urs2cO4c0LHjqxshEVG1xGSE1KKoomnZUkxIagpFMlJaFY2CmUk2pg0Vi5A+39YZgqC10Kqn7t2Bs2eBxo3FGxN26ABs2yZ1VESkJUxGSC01sb2I6eNHsL91BQAQ6921zPvNHhEOE6NsRFx3xLEIN22FV301biwmJH36iG1HRo8Wb7KXmSl1ZESkYUxGSC2nT4uP7dpJG0dlqh/xFwDgYaNmeF6rTpn3s7V+gf8bFAUAWLa1szZCq/5q1waOHAE++UR8vn490K2bWFpCRNUGkxEqs4wMIDxcnO9WttqKaqHBmeMAgJgOPdTed+7Iv2Ggn4tTl1zw56V6mg6tZpDLxTv+HjokJifh4eJNkX75RerIiEhDmIxQmZ07B2RlAQ4OQKNGUkdTOfQzXijHF7nVpa/a+9ezfaYcIn5BUA+2HakIX1+xK1e7dsCTJ8CbbwJjxojzRFSlMRmhMvtT/E1Gt25iL8yawPX8aRhkZiDFvi4eNfQs1zEWjDkNI4McnLrkgsN/N9RwhDWMqyvw11/Axx+LNwPauhVo3hw4dkzqyIioApiMUJnlT0ZqikanxR+52517lzsDc7Z7phx35KMfenLckYoyNASWLhUbMDVuDNy/D/TrB7z3ntjvnIiqHCYjVCa5uUCYOABpjUlGZLk5aPB3CIDyVdHk5z/qDKzNX+DyHTtsPV6DBmjRpo4dgchIsYcNIA4p36SJ2AWY9WFEVQqTESqTixeBZ88AS0uxVLwmqHcpHMbPUvDcqhYeNKtYX+ZaFhmYP+oMAMD/fz3x7JkmIiSYmQHffAOEhAAeHsDDh2IX4L59gRs3pI6OiMqIyQiViaKKpksXsXNDTdAw7A8AwJ2Ovco06mppZr4egYZOT/Ag2QKLFlX4cJRfz55ixrx0KWBsDBw/LmbNc+eygStRFcBkhMqkprUXkeXmwP3kYQDAra79NHJMY8NcfDPrKADg66+BS5c0clhSMDISG7ZeuSL2vMnKAr74AmjYEPjySw6WRqTDmIxQqXJzgZMnxfmakoy4RJ6B2dNkvLC0RmzbLho77oD2d/BG92jk5gJTp4qvLWlYgwbAwYPiuCReXmLJyAcfiO1Jtmzhi06kg/SlDoB0y1fHCtez371qjKQkFxib5eLss9sIL0cvyqKOq8uanPgNAHCjuy/y9A3U3v/MneRi140Z/AuOXPgEZ84AX30l1iRUdaW9v3P6uldSJC/JZGLpSL9+QHCwOILr3bviTfiWLBFLUEaNAvT5FUikC1gyQqW6+rcZAMCzXTrkNeC7Wz/jhbJL77XeQzR+fLvaKfjiC3H+44+By5c1fgpSkMuBSZOAmzeBZcvEEVxv3ADGjxcbvAYGsvqGSAcwGaFSXTlrDgBo2iFd4kgqR4OzITB88Rwp9nXxoGkbrZxjyhRg0CCxWcPYsfw91DozM2D+fLF0ZPlywNYWuHMHmDwZqF9fLC159EjqKIlqLCYjVKLHD/URH2MEmZ6AJu1qRjLS5MR+AMC1XkO0NtSsTAb88ANgYyN2AvHz08ppqCALC+DDD4GYGGD1asDJCUhIAD79FHB2FpMTtiwmqnRMRqhE0S+raNyavoCZZZ7E0WifWXIi6oeLXYeu9dJ8FU1+Dg7Ajz+K8+vXA5s3a/V0lJ+ZmdioNSZGHFLe21ssngoMBFq2BDp0ELNFDghDVCmYjFCJlFU0HWtGqUjzQ7sgz83B/WZt8NhV+3cDHDQIWLhQnP/Pf8T7wFElMjQUG7KeOyfe8+aNN8RGrefOiXVpTk7i459/AnnVPxknkgqTESpW5gsZbl00AVAz2ovo5WSj+cEdAICLr42utPN++ikwcCCQkSEmJzExlXZqUpDJxBH9fv4Z+PdfYOVKwN0dSEsTS0i6dxfblnz4oVivxuHmiTSKyQgV6+IpC+Rk68G2bhbsXbKkDkfrGob9AfPHj5Beqw5uamigs7LQ0xNvp9Kihdh8oX9/tqWUlL098N//AteuiQPsTJgg3gfh3j0xSWnVCvD0FBOT06c5bgmRBjAZoWKdPWwFAGjfP0Vb7Th1Ssv92wAAl33fRJ6BYaWe28oKOHwYcHUVe6H27w8kFz9UCVUGmUwsEdm0Sbznze7dwIgR4kiv16+LiUnXroCjIzBxIrB3L5Be/UsQibSByQgVKSHWEHevmkBPT0C7vqlSh6N1dW5fg/Olc8jTk+PyoLclicHJCfj9d7HXaWQk4OMj/gaSDjA2Bl5/HfjlF/FN2bFDbGtiZSUWY23aBAwfDtSpAwwYAKxaBZw/z1ITojJiMkJF+vuIJQCxrYilTfX/Qu300zoAwM1u/ZFm6yBZHB4eYs2Ao6M4GFqPHuJwGKRDrKyAkSPFXjiPHok35Zs1S2xTkpEhZpTz5ok9dGxtxSTm22/Fah+2NSEqEpMRKiQnG4j4Q0xGOvimSByN9tnfuIxGYX8gT08PZ8fOkDoceHoCp06Jw15cvw60b//qRoWkYwwMgF69xDsf3rkjjlHy1VfA4MHimCZPngB79gAzZohvrJ0dMGSIOBrsiRPsOkz0Ug0Y3JvUdfFPC6Sn6MPSJqdGDHTW6ce1AMRxRR67NJQ4GlGjRsDZs8DQoUBEBNC7t1jyP2uW1sZho4qSyYDmzcVp9mwgJ0d8806cEEtPTp8GkpKAAwfECRBbL3t5AR07Am3aAK1bi89NTSW9FKLKxmSEVOTmAL9vtgEAdB70FHK5xAFpmdOV83ALP4U8PTnOjpG+VCQ/Jyexyubdd4Fdu8Tft2PHgKAg8R9s0nH6+mKS0bGjOBR9ZiYQFQWcOSNmmmfOAHFxYmlK/lFf9fTEOwy3aiUmJy1biqUqdesyE6Vqi8kIqTh72ApJDwxhbp2DHiOeSB2OVsmzstB7jTji2JX+I5Di5CJxRIWZmoptJbt3FwcMPXhQ/F1atUpMUvjbVIUYGYkju3bo8GrZgwdiYvL332KiEhkptkO5elWctm17ta25uZikNGkifggUj40aidVFRFUYkxFSSksDjm4RS0X6jUmGkUn1bmzXYeu3qBN7E8+tauOviXOkDqdYMhkwfTrQrZt4s9moKPFGtIGBYlLSubPUEVK5OTmJDVxff118LghAfLyYlERFidOlS8Dt2+IfaESEOOWnrw80aAC4ub2a8j+vVYtZK+k8JiOktGIF8OyJPmycstCxmjdctbvxD9rt/B8A4PisRciwqi1xRKVr0QIIDxfbSn76KRAWJg4a+tprYi1Ah9IPQbpOJhMTFCcncThehawsMSGJjhZ75Sger10Tk5QbN8SpKJaWYlJSvz5Qr5441a0rTop5M7NKuTyi4jAZIQDA0aNiA38AGDQxCfrVuNTX9PEjDFo2G3p5ubjeYyBudesvdUhlpq8vVte8/TawaJHYfmT/fnHq0XIUpg+9gKFdbsDQgPdRqVYMDcUqGU9P1eWCANy/LyYiMTGq05074pgoqaniEPYXLxZ/fCsrMTFxchJHoLW3Fxsm5Z/s7cWuysbG2r1WqpGYjBBiY8XxmwQB6DAgBa26p0kdktYYpqdh+MdTYB1/DykO9XBixidSh1QudesC//ufmJisWCEOeXHyoitOXnSFrXU63upxDcO63kCPlnEw0GdiUm3JZK9KO4ry/Dlw966YnNy9KyYuiunff8XHtDQgJUWcrlwp/ZyWlq8SFBsbsRqodm3xUTHlf66YZ7sWKgGTkRru3j1x2IPkZKBtW+D1GYlSh6Q1Jk8fY/BnM2F3Oxrp1jbYHRBUJapnStKkiTj455IlwPf+pxF4uAXiky3w7b62+HZfW1ibv8DgjrfxWueb6Nr8Hhxtqn9XbcrH1BRo2lScipOa+io5efAASEx8NT18qPo8O1vcPjUVuHVLvVjMzMTExNpaTGgsLMQp7Q5gYgSYvpxMDAEz45fLDF8ue7nu2TPxOHocIqu6KVcysn79eqxatQrx8fFo1qwZ1qxZg27duhW7/cmTJ+Hn54crV67AyckJ8+bNw9SpU8sdNGnG2bPAsGHi942dnXjrjV9vVM9Gq3UvR2Dg53NgnpyITFMz7F32P6TUdZU6LI2pVw9YMvEUFo7/E0fDG2DPX+7YF9YYj56aYcsfXtjyhxcAwM3xCTo3u48uzf5F68YP4emSDCvzTImjJ0lZWopTwSqgggRBLD3Jn6A8fixOT568mgo+f/pU3D89XZzu3atAsMvFBxMTcTI1Faf88wWfF7fOxETs4VTWSV+fDYG1SO1kZOfOnZg9ezbWr1+PLl264Pvvv4evry+uXr0KF5fCXSNjYmIwcOBATJkyBVu2bMHp06cxbdo02NraYsSIERq5CFLP3bti+5DgYHFcpubNxTYHrq4AimkDV1XZxFxH++3fw+PkIcgEAcnODXBwwddIdnOXOjSt0JcLGNjxNgZ2vI0NuUdw5mpd7PnLHccv1MelO3aIia+FmPha2PoyOQGAunVS0dQ1GR7OyajvkAIXu1S42KfC1T4FtlbPUc2HmqGyksnEUg1ra/G+BWWVmysmMfkTlGfPXk1RvwHPM8XpheIxC0jPePk869W6vJf/LL14IU6PH2vjSosmk5WesBgavno0MHg16etr77m+vjjJ5eKkmC/LMj09nUmw1E5GvvzyS0yaNAmTJ08GAKxZswa///47vvvuOwQEBBTafsOGDXBxccGaNWsAAJ6enoiIiMDq1auZjFSCvLxX7dvCw8U7w+a/6/kbb4iNIC0spI1TE+RZWbBIvI/a92LgGB2F+uGnYHc7Wrn+ap9hODHzU2Sb1IyeA3K5gK7N/0XX5v8CAFLTDfF3tBNO/1MPZ67WxT8xtniQbIH7SZa4n2SJY+fdCh1DJhNQq5Z4/7f8k42NOOyFmZk4RcRYwNBYgKFxHgyNXj4a50GuL0CuL/4znf+71MAA1X5APXpJLherZ2oXUyUaUsYh8QUB6DhbTGAUycjz56+m/M+Lm8///MULcSC6kqb8NzoUBPHeQxkZFX5JdIoiOZHLgR9/BN58U5Iw1EpGsrKycP78eXz00Ucqy/v164ewsLAi9zlz5gz69eunsqx///4IDAxEdnY2DIpo1JSZmYnMzFdFxykpYjfT1FTN3j321MAA1L4YgmIrJoRCMyU+lSnmSt4cMkEowznVPXfh9bm5QG7eq/XtAbR/uYGlhXgzNos7gNATULyyg1Nf/qGV8YZeMq3c+Ktsx9TLy4XB8+cwfJEOgxfp0M/JKbRNCoBbXfrg/IhJYmlIngCka6aBbqHPY/qrL6n0FyVXfWj6s1zw/EXLQAfPVHTwvKZc8jTdCDfibHDtXm3celAL9x9Z4N4jC/z7yAIPki0gCHrKkvjieo6KSk7wPkPR12tg8OqfSD29V/+o5X8sahlQ+jYyWdn+6dPUNmVRmfHoyD+8pUsdWvZtLXMAmLycNEAOwPTlVAQ9IRcGeZkwFDKhL2S9nM+Cfl6mct4gLxMGiseX83JkQz8vG/pCNuRCDuRCDvSFbOi/fNQTciBXPM/LVq5XPuLVenm+5fp5qs8Vx5YLudBDDvSEPMiFHOgJuZAjV9wOpdzoNDdXmXRdOZeGZv01+92k+K4TSvutENRw//59AYBw+vRpleXLli0T3N3di9yncePGwrJly1SWnT59WgAgPHjwoMh9Fi5cKED8ReLEiRMnTpw4VfHp3r17JeYX5WrAKiuQcguCUGhZadsXtVzB398ffn5+yud5eXl4/PgxbGxsSjyPulJTU+Hs7Ix79+7B0tJSY8clEV9f7eFrq118fbWHr6126drrKwgCnj17BicnpxK3UysZqVOnDuRyORISElSWJyYmwt7evsh9HBwcitxeX18fNjY2Re5jZGQEIyMjlWXW1tbqhKoWS0tLnXjTqiu+vtrD11a7+PpqD19b7dKl19fKyqrUbdTqrG1oaIi2bdvi2LFjKsuPHTuGzsXcIKNTp06Ftj969Ci8vb2LbC9CRERENYvaI8f4+fnhhx9+QFBQEKKjozFnzhzExcUpxw3x9/fHuHHjlNtPnToVsbGx8PPzQ3R0NIKCghAYGIi5c+dq7iqIiIioylK7zcjIkSORnJyMzz77DPHx8fDy8sKhQ4fg6uoKAIiPj0dcXJxyezc3Nxw6dAhz5szBt99+CycnJ6xdu1YnuvUaGRlh4cKFhaqESDP4+moPX1vt4uurPXxttauqvr4yQdBK30wiIiKiMuEA/0RERCQpJiNEREQkKSYjREREJCkmI0RERCQpJiNEREQkqRqdjKxfvx5ubm4wNjZG27Zt8eeff0odUrVw6tQpDBkyBE5OTpDJZNi7d6/UIVUbAQEBaNeuHSwsLGBnZ4dhw4bh+vXrUodVbXz33Xdo0aKFcvTKTp064fDhw1KHVS0FBARAJpNh9uzZUodSLSxatAgymUxlcnBwkDqsMquxycjOnTsxe/ZsfPzxx4iMjES3bt3g6+urMkYKlU96ejpatmyJb775RupQqp2TJ09i+vTpOHv2LI4dO4acnBz069cP6enpUodWLdSrVw/Lly9HREQEIiIi0KtXLwwdOhRXrlyROrRqJTw8HBs3bkSLFi2kDqVaadasGeLj45XT5cuXpQ6pzGrsOCMdOnRAmzZt8N133ymXeXp6YtiwYQgICJAwsupFJpNhz549GDZsmNShVEuPHj2CnZ0dTp48ie7du0sdTrVUu3ZtrFq1CpMmTZI6lGohLS0Nbdq0wfr167F06VK0atUKa9askTqsKm/RokXYu3cvoqKipA6lXGpkyUhWVhbOnz+Pfv36qSzv168fwsLCJIqKSH0pKSkAxB9M0qzc3Fzs2LED6enp6NSpk9ThVBvTp0/HoEGD0KdPH6lDqXZu3rwJJycnuLm54e2338adO3ekDqnM1B4OvjpISkpCbm5uoTsN29vbF7rDMJGuEgQBfn5+6Nq1K7y8vKQOp9q4fPkyOnXqhIyMDJibm2PPnj1o2rSp1GFVCzt27MCFCxcQHh4udSjVTocOHbB582a4u7vj4cOHWLp0KTp37owrV67AxsZG6vBKVSOTEQWZTKbyXBCEQsuIdNWMGTNw6dIl/PXXX1KHUq14eHggKioKT58+xe7duzF+/HicPHmSCUkF3bt3D++//z6OHj0KY2NjqcOpdnx9fZXzzZs3R6dOndCwYUP8+OOP8PPzkzCysqmRyUidOnUgl8sLlYIkJiYWKi0h0kUzZ87E/v37cerUKdSrV0/qcKoVQ0NDNGrUCADg7e2N8PBwfP311/j+++8ljqxqO3/+PBITE9G2bVvlstzcXJw6dQrffPMNMjMzIZfLJYywejEzM0Pz5s1x8+ZNqUMpkxrZZsTQ0BBt27bFsWPHVJYfO3YMnTt3ligqotIJgoAZM2bg119/xYkTJ+Dm5iZ1SNWeIAjIzMyUOowqr3fv3rh8+TKioqKUk7e3N0aPHo2oqCgmIhqWmZmJ6OhoODo6Sh1KmdTIkhEA8PPzw9ixY+Ht7Y1OnTph48aNiIuLw9SpU6UOrcpLS0vDrVu3lM9jYmIQFRWF2rVrw8XFRcLIqr7p06dj27Zt2LdvHywsLJSle1ZWVjAxMZE4uqpv/vz58PX1hbOzM549e4YdO3YgNDQUR44ckTq0Ks/CwqJQ2yYzMzPY2NiwzZMGzJ07F0OGDIGLiwsSExOxdOlSpKamYvz48VKHViY1NhkZOXIkkpOT8dlnnyE+Ph5eXl44dOgQXF1dpQ6tyouIiICPj4/yuaK+cvz48QgODpYoqupB0RW9Z8+eKss3bdqECRMmVH5A1czDhw8xduxYxMfHw8rKCi1atMCRI0fQt29fqUMjKtG///6Ld955B0lJSbC1tUXHjh1x9uzZKvObVmPHGSEiIiLdUCPbjBAREZHuYDJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkmIyQkRERJJiMkJERESSYjJCREREkvp/Vgb6vk2W/t0AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.hist(X_NC, bins=20, density=True, alpha=0.5, label=\"NC histogram\")\n", "plt.hist(X_AE, bins=20, density=True, alpha=0.5, label=\"AE histogram\")\n", "plt.plot(xs, f_XatNC_opt(xs, popt_NC), label=\"NC fit\", color='blue')\n", "plt.plot(xs, f_XatAE_opt(xs, popt_AE), label=\"AE fit\", color='red')\n", "plt.legend()\n", "plt.title(\"Fit of Custom Distribution to NC and AE Groups\")\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 31, "id": "a1f40976", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NC params: [ 0.24241006 0.18097191 -0.16096395]\n", "AE params: [ 0.39013584 0.04654894 -2.02453446]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.io import loadmat\n", "from scipy.optimize import minimize\n", "import os\n", "\n", "# === 1. Load data ===\n", "suv_file = \"../data/suv_percentilesSLOthenUWM.mat\"\n", "flags_file = \"../data/flags_combined.mat\"\n", "\n", "suv_data = loadmat(suv_file)\n", "flags_data = loadmat(flags_file)\n", "\n", "suv = suv_data['lung_SUVperc_COMBINED'][0:58,:,:]\n", "flags = flags_data['flags'][0:58, 3]\n", "\n", "# === 2. Prepare data ===\n", "p = 94 # percentile index\n", "X = np.nanmax(suv[:,:,p], axis=1).reshape(-1, 1)\n", "flags = flags.flatten()\n", "\n", "# === 3. Define distribution and helper ===\n", "g = lambda x, mu, sigma, l: np.abs(x)**(l-1) * np.exp(-(((np.abs(x)**l - 1)/l)-mu)**2/(2*sigma**2)) / (np.sqrt(2*np.pi)*sigma)\n", "fun = lambda x, mu, sigma, l: (l-1)*np.log(np.abs(x)) - np.log(sigma*np.sqrt(2*np.pi)) - (((np.abs(x)**l - 1)/l)-mu)**2/(2*sigma**2)\n", "\n", "def safe_divide(numerator, denominator, eps=1e-10):\n", " return numerator / np.clip(denominator, eps, np.inf)\n", "\n", "def myfitter(data, fun, cov=True):\n", " nllf = lambda p: -fun(data, *p).sum()\n", " p0 = (1, 0.6, 0.3)\n", " bounds = ((0, 10), (0.01, 10), (-5, 5))\n", " res = minimize(nllf, p0, bounds=bounds, method=\"L-BFGS-B\")\n", " if not res.success:\n", " raise RuntimeError(\"Fitting failed\")\n", " if not cov:\n", " return res.x, None\n", " return res.x, res.hess_inv.todense()\n", "\n", "# === 4. Separate groups ===\n", "X_NC = X[flags == 0].flatten()\n", "X_AE = X[flags == 1].flatten()\n", "flags_NC = flags[flags == 0]\n", "flags_AE = flags[flags == 1]\n", "\n", "# === 5. Fit distributions ===\n", "popt_NC, _ = myfitter(X_NC, fun)\n", "popt_AE, _ = myfitter(X_AE, fun)\n", "\n", "print(\"NC params:\", popt_NC)\n", "print(\"AE params:\", popt_AE)\n", "\n", "P_NC = np.count_nonzero(flags == 0) / len(flags)\n", "P_AE = np.count_nonzero(flags == 1) / len(flags)\n", "\n", "f_XatNC_opt = lambda x: g(x, *popt_NC)\n", "f_XatAE_opt = lambda x: g(x, *popt_AE)\n", "f_X_opt = lambda x: P_NC * f_XatNC_opt(x) + P_AE * f_XatAE_opt(x)\n", "P_AEatX_opt = lambda x: safe_divide(P_AE * f_XatAE_opt(x), f_X_opt(x))\n", "\n", "xs = np.linspace(1e-3, X.max()+1, 200)\n", "yopts = P_AEatX_opt(xs)\n", "\n", "# === 6. Bootstrapped CI ===\n", "n_boot = 500\n", "ysamples = []\n", "\n", "for i in range(n_boot):\n", " try:\n", " X_NC_boot = np.random.choice(X_NC, size=len(X_NC), replace=True)\n", " popt_NC_boot, _ = myfitter(X_NC_boot, fun, cov=False)\n", "\n", " X_AE_boot = np.random.choice(X_AE, size=len(X_AE), replace=True)\n", " popt_AE_boot, _ = myfitter(X_AE_boot, fun, cov=False)\n", "\n", " f_XatNC_boot = lambda x: g(x, *popt_NC_boot)\n", " f_XatAE_boot = lambda x: g(x, *popt_AE_boot)\n", " f_X_boot = lambda x: P_NC * f_XatNC_boot(x) + P_AE * f_XatAE_boot(x)\n", " P_AEatX_boot = lambda x: safe_divide(P_AE * f_XatAE_boot(x), f_X_boot(x))\n", "\n", " ysamples.append(P_AEatX_boot(xs))\n", " except Exception as e:\n", " continue # skip failed fits\n", "\n", "ysamples = np.array(ysamples)\n", "\n", "if ysamples.shape[0] < 10:\n", " print(\"Too many failed fits. Try reducing complexity or increasing data.\")\n", " lower = upper = np.full_like(xs, np.nan)\n", "else:\n", " lower = np.percentile(ysamples, 2.5, axis=0)\n", " upper = np.percentile(ysamples, 97.5, axis=0)\n", "\n", "# === 7. Plot ===\n", "plt.figure(figsize=(8,5))\n", "plt.scatter(X_NC, flags_NC, label=\"NC\", alpha=0.5)\n", "plt.scatter(X_AE, flags_AE, label=\"AE\", alpha=0.5)\n", "plt.plot(xs, yopts, label=\"Fit model\", color=\"red\")\n", "if not np.all(np.isnan(lower)):\n", " plt.fill_between(xs, lower, upper, color='red', alpha=0.3, label=\"95% CI\")\n", "plt.xlabel(\"Max SUV at 94th Percentile\")\n", "plt.ylabel(\"Probability of Adverse Effect\")\n", "plt.title(\"Bayesian-like model with Bootstrap Confidence Interval\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "3679f66e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MAP Estimate: Intercept (β₀) = -3.010671713120543\n", "MAP Estimate: Coefficient (β₁) = 1.6928177590872044\n" ] }, { "data": { "image/png": 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fNWrUwJ49e5CQkIBOnTqhYMGCKFOmTJI+/+nx5s0bAF/vKvUt69evx6VLl3D06FH06tULQUFBSYqkxHMthg8fnuxLY9++fQFA8+UxvesmpfX96tUr7Nu3L9mySpcunWRZHTt2xJo1a/D06VP88ssvsLa2hpubm+aLN/C568hvv/2GPXv2oHbt2jA3N0fz5s2/ejndxO2c2nvhv11oLCwskrXT1dX9ZhGTOF5PTy/ZuHr16iEuLg6nT5+Gv78/LC0tUaFCBdSrV09zbsCRI0dQr169ry7jWwwMDJItX1dX95uXby5UqBCA5Oc1lShRQvP5/O/5FSEhIfDw8MCLFy+wcOFCnDp1CpcuXcKSJUsAIE1F33+NHj0ac+fOxfnz5+Ht7Q0LCwvUrVs3ySWrt23bBh8fH6xatQru7u4wNzdHp06dEBYWlup805v1e98DiX766SdcunQJly9fxp07dxAZGYlFixZBR0cnSbuU3pP/9e7dOwgh0rQvS8t89fT0IIT45nuCKKfhORZEOUTnzp0xYcIELF++HNOnT0+13f3793H69GkA//ui8l///vsvGjZsqHkul8s1JxdnNgsLC4SGhiYb/vLlSwDQ/ApvYWGR7MRmAF/9ovKlZs2aoVmzZoiLi8P58+cxY8YMtGvXDo6OjnB3d09X5sQ+2M+fP092pCWtnJ2dNeu0du3aUKlUWLVqFXbu3ImWLVtqXvfo0aPx888/pziPEiVKAEj/uknpRHRLS0uUK1cu1fdO4pcj4PNJyV26dEF0dDROnjyJiRMnonHjxrh//z4cHBxgaGiIyZMnY/LkyXj16pXm6EWTJk1w9+7dFOef+CUxNDQ0WcH28uXLJEdjMiJxOW/fvk02zs3NDUZGRggICMCTJ09Qt25dyGQy1K1bF/PmzcOlS5cQEhKS4cLie9WqVQva2trYu3cvevbsqRmur6+veS/t378/yTR79uxBdHQ0du3aBQcHB83wlC6Fq6enl+IJ5OHh4UnWv7a2NoYOHYqhQ4ciMjISAQEBGDNmDOrXr49nz57BwMAAlpaW8PX1ha+vL0JCQrB3716MGjUKr1+/xqFDh1J8fenJmhlMTU3TtF9Ly/1W8uXLB7lcnqZ9WVrm+/btW+jq6mb4nidE2Q2PWBDlEAUKFMCIESPQpEmTr95fIvGk7ZUrV+LYsWNJHoldA77nhM7vVbduXRw9elTzxzfR+vXrYWBgoLn6VM2aNXHr1q0kJwkDSPeVU3R1dVGzZk3MmjULwOeuF4nDgbT9guvl5QUtLa00Xe8+rWbPno18+fJhwoQJUKvVKFGiBIoVK4br16+jcuXKKT4S71FSs2ZNHD16NEn3F7VajR07dqR5+Y0bN8atW7dQpEiRFJf1ZWGRyNDQEN7e3hg7dizi4+Nx+/btZG1sbGzQuXNntG3bFvfu3UNMTEyKy69Tpw4AJDvh/NKlSwgKCkLdunXT/Fq+RkdHB4ULF8ajR4+SjVMoFKhRowb8/f1x9OhReHp6AgA8PDygra2NcePGaQqNr0nPeyk97Ozs0LVrVxw4cCDN7/vEL6+JmYDPN89cuXJlsraOjo64ceNGkmH3799P1oXnS2ZmZmjZsiX69euHt2/fJrkCWaJChQqhf//+8PT0xJUrVzIla3ZjaGgINzc37Nq1K8l2T7yZYcGCBZN1P/yax48fJ+v2SZQb8IgFUQ4yc+bMr45PSEjA+vXr4ezsjO7du6fYpkmTJti7dy/evHmT4Ss+JTp//nyKw2vWrImJEydq+vdPmDAB5ubm2LRpEw4cOIDZs2fD1NQUADB48GCsWbMG3t7emDJlCmxsbLB582bNL+Byeeq/g0yYMAHPnz9H3bp1UbBgQURGRmLhwoVQKBSoWbMmAKBIkSLQ19fHpk2b4OzsDCMjI+TPnz/FL9SOjo4YM2YMpk6dik+fPqFt27YwNTXFnTt3EB4errl8a3rky5cPo0ePxsiRI7F582Z06NABf/75J7y9vVG/fn107twZBQoUwNu3bxEUFIQrV65oCoexY8di3759qFu3LsaOHQt9fX0sX75cc/fer62bRFOmTIG/vz+qVauGgQMHokSJEoiNjcWTJ09w8OBBLF++HAULFkSPHj2gr6+P6tWrw87ODmFhYZgxYwZMTU0157K4ubmhcePGKFeuHPLly4egoCBs2LAB7u7uMDAwSHH5JUqUQM+ePbF48WLI5XJ4e3trrgplb2+PIUOGpHudpqZWrVr4559/UhxXt25dDBs2DAA0Ryb09fVRrVo1HD58GOXKlUvx/Iwvpee9lF6+vr4IDg5G+/btsXfvXjRr1gz58+dHTEwM7t69i61bt0JPT09zToCnpyd0dHTQtm1bjBw5ErGxsVi2bFmKN2Ls2LEjOnTogL59++KXX37B06dPMXv27GT7gSZNmqBMmTKoXLkyrKys8PTpU/j6+sLBwQHFihXD+/fvUbt2bbRr1w4lS5aEsbExLl26hEOHDqV69C29WbOjGTNmwNPTE7Vr18bw4cOho6ODpUuX4tatW9iyZUua7zSvVqtx8eJFdOvWLYsTE0lA0lPHiShVqd1o7b++vCrUnj17BADh6+ubavtDhw4JAGLevHlCiIzd0CvxqlCpPRKv5HTz5k3RpEkTYWpqKnR0dET58uVTvKLOrVu3RL169YSenp4wNzcX3bp1E+vWrRMAxPXr1zXt/nu1mf379wtvb29RoEABoaOjI6ytrUXDhg3FqVOnksx/y5YtomTJkkKhUAgAYuLEiUKI5FcwSrR+/XpRpUoVoaenJ4yMjESFChW+eYO9r223T58+iUKFColixYqJhIQEIYQQ169fF61atRLW1tZCoVAIW1tbUadOnWQ3dzt16pRwc3MTurq6wtbWVowYMULMmjUr2dWwUroxWKI3b96IgQMHCicnJ6FQKIS5ubmoVKmSGDt2rPj48aMQQoh169aJ2rVrCxsbG6GjoyPy588vWrVqJW7cuKGZz6hRo0TlypVFvnz5hK6urihcuLAYMmSICA8P17RJaZ2qVCoxa9YsUbx4caFQKISlpaXo0KGDePbsWZJ2NWvWFKVLl06W/1tXGUp05MgRAUBcvHgx2bjr168LAKJYsWJJhk+fPl0AEEOHDk02TUpXU0rtvZTa5ym191hKVCqVWL9+vfD09BSWlpZCW1tbmJqaCldXVzF+/PhkN63ct2+fKF++vNDT0xMFChQQI0aMEP/880+yq6mp1Woxe/ZsUbhwYaGnpycqV64sjh49muyqUPPmzRPVqlUTlpaWQkdHRxQqVEh069ZNPHnyRAghRGxsrOjdu7coV66cMDExEfr6+qJEiRJi4sSJSW76ltL2SmvWjL4HvvY5SJR45ac5c+akOu6/n/dTp06JOnXqCENDQ6Gvry+qVq0q9u3bl6TNt/bdie/PwMDAb74OopxGJoQQP6iGISJKt549e2LLli2IiIhIdtJlXufl5YUnT55815V/crty5cqhevXqmdqdjSgzdOzYEY8fP8aZM2ekjkKU6dgVioiyjSlTpiB//vwoXLgwPn78iP3792PVqlUYN25cni8qhg4digoVKsDe3h5v377Fpk2b4O/v/913As/tZs+ejRYtWmDs2LEZuroXUWZ69OgRtm3bprl5J1Fuw8KCiLINhUKBOXPm4Pnz50hISECxYsUwf/58DBo0SOpoklOpVJgwYQLCwsIgk8lQqlQpbNiwIc13Us9rGjRogDlz5iA4OJiFBWUbISEh+OOPP/DTTz9JHYUoS7ArFBERERERZRgvN0tERERERBnGwoKIiIiIiDKMhQUREREREWVYnjt5W61W4+XLlzA2Nk7zzWyIiIiIiPIiIQQ+fPiA/Pnzf/OGrHmusHj58iXs7e2ljkFERERElGM8e/bsm1fZy3OFhbGxMYDPK8fExETiNDmDUqnE4cOH4eXlBYVCIXWcPInbQFpc/9LjNpAet4G0uP6ll1e3QVRUFOzt7TXfob8mzxUWid2fTExMWFikkVKphIGBAUxMTPLUByk74TaQFte/9LgNpMdtIC2uf+nl9W2QllMIePI2ERERERFlGAsLIiIiIiLKMBYWRERERESUYSwsiIiIiIgow1hYEBERERFRhrGwICIiIiKiDGNhQUREREREGcbCgoiIiIiIMoyFBRERERERZRgLCyIiIiIiyjAWFkSUJmq1GtHR0RBCSB0lx1KpVIiJidGsS5VKlWXLiouLQ1xcXJbNn4iIsp5KpcpRf3slLSxOnjyJJk2aIH/+/JDJZNizZ883pzlx4gQqVaoEPT09FC5cGMuXL8/6oER52IMHD9CtWzcYGxrCyMgIVhYW+O233xAeHi51tBzj6tWraNO6NfT19GBoaAg9hQJGRkbQ19ND+3btcOPGjUxZjhACO3bsgLubG/T09KCnpwfXSpWxefPmHPNHiYiIgFu3bqFD+/Yw0NeHkZER8tvYYuLEiYiKipI62ldJWlhER0ejfPny+OOPP9LUPjg4GA0bNoSHhweuXr2KMWPGYODAgfjrr7+yOClR3nTlyhVUqVQJe9dvQot4QwyX2+KnSIGl8xbArXIVhIWFSR0x2zt8+DDc3ari9K69aK82wzC5LeoII+hABrME4Mj2Xajq6opjx45leFljx45Fq1atEBt4BwPkNhgot4Hq+j20b98eQ4cOZXFBRJQDnDhxAm5VquDo9l1oqzLFMLktKobHYfb03+FRrToiIyOljpgqbSkX7u3tDW9v7zS3X758OQoVKgRfX18AgLOzMy5fvoy5c+fil19+yaKURHmTEAId2raD9ScVpomCMJRrAQBqwQRNhBK/vXiJQYMGYdu2bRInzb5iY2PRrk0blFXrYCxsoZB//i2nNkzgLcwwWvUMnmojhCQkoF3rNnj6/Bl0dHS+a1lnzpzBjBkz0EVuiV9k5oDs83AvmGKf/B18fX3RuHFj1K1bN7NeHhERZTKlUol2rdugmFIbE2AL3S/+bjQUcRh19x7Gjh2LJUuWSJw0ZTnqHItz587By8srybD69evj8uXLUCqVEqUiyp1OnjyJoPv30EVtDkOZVpJxtjIFflGbYNdff+HVq1cSJcz+du7ciYh379ADllDIku5ui8r04C0zw1ERBR9hjrA3r/H3339/97KWLlmCAtr6aCHLl2xcY5kZHLUNsCSNR4eJiEgae/fuxctXYegOC+j+5++Go0wXjdXGWLfWDx8/fpQo4ddJesQivcLCwmBjY5NkmI2NDRISEhAeHg47O7tk0/z3BMbEvmlKpZLFSBolrieuL+lIsQ2uX78OU0NDlJGZQchkycZXFubYoPqI27dvw9zc/IflksL3rv+bN2+iiKkF8quNkVInpCpqC/yjjoWxlj4Kyc1x8+ZNNG/e/Lsy3rl1C646ppBp6aW4LDeVKW7euZNjP8fcD0mP20BaXP/fJoRAQkKC5jtefHy85v9fPhLbpDZeqVRCpVJBrVZDpVIhISEBKpUK8fHxCAoKwq1btwBAMzwtj5TaJg5LXI5arcajR4+gq6WN5XgDtQCEANQQaKNrjSraJqgiLPC36jkePXqEUqVK/ZD1mp73nExkk063MpkMu3fv/uof1eLFi6NLly4YPXq0ZtiZM2fw008/ITQ0FLa2tsmmmTRpEiZPnpxs+ObNm2FgYJAp2YmIiIjyMiEElEol4uLiEBsbi/j4eM3/E3/kTfwyn5CQkOxLfXqHJ375T0hISPKlPbcaMGCAZF1ZY2Ji0K5dO7x//x4mJiZfbZujjljY2tomO1n09evX0NbWhoWFRYrTjB49GkOHDtU8j4qKgr29Pby8vL65cugzpVIJf39/eHp6QqFQSB0nT5JiG7x8+RJlSpeGD8zRQG6WbPxy1SvcttDD7btBuf598b3r/8qVK6hduzaGy+3gKjdMMk4Igd/VoYgSKjSRmWKReI1z58599y9Qs2fPxrwZs/CHzB4m/+m6Fi1U6Idn6DN4ECZMmPBd85ca90PS4zaQVmav/4SEBHz48AFRUVGIior65v8/fPiAT58+ITo6GjExMYiOjk7yPPFS2tmNlpYWFApFuh9aWlrQ0tKCXC6HtrY2tLS0IJPJ8ObNGxQoUAA6OjqaNt96JE7/teFyuRxaWloICwvD+PHj0VBuhlIyfcgAyGUyOK05DC2/45irDkOkkw0uBgZClkJvgqyQnitR5ajCwt3dHfv27Usy7PDhw6hcuXKqHzJdXV3o6uomG574xqG04zqT3o/cBg4ODvjll1+wauMmGCIB1WVG0JLJEC/U2CcicUAdjnlT5+WpI3/pXf9ubm5wd3PDotNnMVxtBReZAWQyGWKEGlvUETgv3uFXmTmWyF+iVr06KF++/Hdn6969O+bNmYOpH59iOKxgK/t8EvgrocQCvIZSX45evXrl+M8w90PS4zaQ1pfrPz4+Hm/fvk3yiIiISPF5YqHw/v17REVFISYmJkszGhoawsDAQPOvgYGB5jLYurq6Gf5XV1cXCoUCOjo6Xy0Q5PLMO51YqVTi4MGDaNiwYZZ+Bk6fPIUj/x6Gi1CgsswQMpkMsUKFjeoXOCHeYt2Iud99oY/vkZ7XKmlh8fHjRzx8+FDzPDg4GNeuXYO5uTkKFSqE0aNH48WLF1i/fj0AoHfv3vjjjz8wdOhQ9OjRA+fOncPq1auxZcsWqV4CUa62bPlyREZGYvbevbBR6MFWrY0nsni8V8Vj+PDhGDJkiNQRs70df/2Fpo0bY/y5c8ivpYt8CXI8RCziIWAi18YO9VvUrOaBzVu3Zmg5NjY2+NffH429G6JHxBMU1zaEDMA9VTTM8+XDP/v3o2DBgpnzoogoS6hUKoSHh+PVq1fJHqGhobh9+zYmTZqkKRoy4wRePT09mJiYfPNhZGSUrFhIqXgwMDBg4ZlBGzdvQotmzTD5xAnkV+jDUq2Fx4hDNBIwffp0dOrUSeqIqZK0sLh8+TJq166teZ7YZcnHxwd+fn4IDQ1FSEiIZryTkxMOHjyIIUOGYMmSJcifPz8WLVrES80SZRF9fX3s3rMHFy5cwKZNmxAREYEGhQqhS5cuKFGihNTxcgRzc3OcPH0aR48exc6dOxEaGgqLyEiYmZkhf/78aN26NWrWrJkph7SrVKmC4JCn2Lp1K44fPw4hBIbWqIF27drB0NDw2zMgoiyhVqvx5s0bPH/+PNnjy+LhzZs36e5OJJPJkC9fPlhYWMDc3DzJI3FYvnz5YGZmBhMTE5iammqKBWNj4x/6yzeljampKY4cO4YTJ05g27ZteP/+PZoVLYquXbvC0dFR6nhfJWlhUatWra/esMnPzy/ZsJo1a+LKlStZmIqIviSTyVC1alVUrVpV6ig5llwuR7169VCvXr0sX5aBgQG6du2Krl27ZvmyiOiz+Ph4PH36FI8fP0ZwcDCCg4Px7NkzTfHw4sULxMfHp2leMpkMlpaWsLGxSfKwtLREWFgY6tWrB1tbW03RYGpqmqndfSh7kMlkqFWrFmrVqiV1lHTJUedYEBEREUnh3bt3uHv3Lh4/fqx5BAcH4/Hjx3j+/Pk372wvk8lga2sLe3t7FCxYUPOwtbVNVkBoayf/epbYv9/b25tdjSjbYmFBREREhM/nODx9+hR3797FvXv3cPfuXc3j9evXX53WwMAATk5OKFy4MJycnFCoUCEULFhQU0jY2dmxIKBcj4UFERER5SlCCLx8+RLXr1/XPO7cuYP79+8nuanufxUoUADFihXTFA9f/mttbf3DLv9JlF2xsCAiIqJcKz4+Hnfv3sW1a9eSFBLh4eEpttfV1UXx4sVRsmRJlChRAiVLlkTJkiVRvHhxGBsb/+D0RDkLCwsiIiLKFdRqNe7evYuLFy/i4sWLuHDhAm7evAmlUpmsrZaWFkqUKIHy5cujfPnyKFOmDJydneHg4AAtLa0U5k5E38LCgoiIiHKkyMhInDlzBmfOnMGFCxdw+fLlFO8SbGpqqikgEh+lS5eGvr6+BKmJci8WFkRERJQjvHz5EqdOndI8bt68mexqTAYGBqhUqRLc3Nzg6uqKypUrw9HRkec/EP0ALCyIiIgoW3r79i2OHTuGgIAABAQE4OHDh8naFC1aFD/99BPc3d3h5uaG0qVLp3i5ViLKevzkERERUbYQGxuLM2fOaAqJwMDAJEck5HI5ypcvDw8PD3h4eOCnn36Cra2thImJ6EssLIiIiEgyoaGhOHjwIPbv3w9/f39ER0cnGV+6dGnNnes9PDxgamoqUVIi+hYWFkRERPTDCCFw5coV7Nu3D/v370dgYGCS8XZ2dvDy8kK9evVQt25d2NnZSZSUiNKLhQURERFlKSEELl68iB07dmDnzp14+vRpkvGurq5o3LgxGjduDBcXF55oTZRDsbAgIiKiTKdWq3HhwgVNMfHs2TPNOAMDAzRo0ACNGzdGw4YNYWNjI2FSIsosLCyIiIgo0zx48AAbNmzAhg0b8OTJE81wQ0NDNGnSBC1btoS3tzcMDAykC0lEWYKFBREREWXI27dvsX37dqxfvx7nzp3TDDcyMkLTpk3x66+/on79+rwhHVEux8KCiIiI0k2tVuPIkSNYsWIF9u7di/j4eACfLwlbv359dOrUCU2bNuWRCaI8hIUFERERpVlERAQ2btyIP//8M8kN68qWLQsfHx+0a9eOV3IiyqNYWBAREdFXCSFw7tw5LFiwAOfPn0dcXBwAwMTEBJ06dUK3bt3g4uIibUgikhwLCyIiIkqRUqnE9u3bMW/ePFy9elUzvGLFiujTpw/atGkDIyMjCRMSUXbCwoKIiIiSeP/+PVatWgVfX188f/4cAKCnp4fq1atj6tSpqFq1Ku81QUTJsLAgIiIiAMCzZ8+wcOFCrFixAh8+fAAA2NjYYMCAAejWrRsuXLiAypUrs6ggohSxsCAiIsrjgoODMX36dKxbtw4JCQkAAGdnZwwfPhzt2rWDnp4elEqlxCmJKLtjYUFERJRHpVRQ1KpVCyNGjECDBg0gl8slTkhEOQkLCyIiojzmyZMnmD59Ovz8/DQFhZeXFyZOnIhq1apJnI6IcioWFkRERHlEaGgoJk+ejNWrV2sKCk9PT0yaNIkFBRFlGAsLIiKiXC46Ohrz5s3D7NmzER0dDeBzQTFx4kRUr15d4nRElFuwsCAiIsqlVCoV/Pz8MH78eISGhgIA3NzcMGfOHHh4eEicjohyGxYWREREudC///6LESNG4ObNmwAAJycnzJw5E7/++isvF0tEWYKFBRERUS4SHByMgQMHYv/+/QAAMzMzjB8/Hv369YOurq7E6YgoN2NhQURElAvExcVh7ty5mDZtGmJjY6FQKNC/f3+MGzcO5ubmUscjojyAhQUREVEOd+TIEfTr1w/37t0DANSuXRtLliyBs7OzxMmIKC/hnW+IiIhyqNDQULRr1w716tXDvXv3YGNjg02bNuHIkSMsKojoh2NhQURElMMIIbB27VqULFkSW7ZsgVwuR//+/XH37l20a9eOJ2cTkSTYFYqIiCgHefHiBXr27ImDBw8CAKpUqYJly5ahUqVKEicjoryORyyIiIhyACEE1q9fjzJlyuDgwYPQ1dXFrFmzcO7cORYVRJQt8IgFERFRNhcaGopevXph3759AD4fpfDz80OpUqUkTkZE9D88YkFERJSNbd++HaVLl8a+ffugo6ODGTNm4OzZsywqiCjb4RELIiKibCgmJgaDBg3CqlWrAACVKlWCn58fypQpI3EyIqKU8YgFERFRNnPr1i1UqVIFq1atgkwmw7hx43Du3DkWFUSUrfGIBRERUTYhhMDKlSsxaNAgxMbGws7ODps2bULt2rWljkZE9E0sLIiIiLKByMhI9OzZEzt27AAAeHt7w8/PD9bW1hInIyJKG3aFIiIiktjVq1dRsWJF7NixA9ra2pgzZw7279/PooKIchQesSAiIpLQ5s2b0b17d3z69AlOTk7YunUrXF1dpY5FRJRuPGJBREQkgYSEBAwfPhzt27fHp0+f4O3tjcDAQBYVRJRjsbAgIiL6wSIiItCgQQPMmzcPADBmzBjs27cP+fLlkzgZEdH3Y1coIiKiH+j69eto3rw5njx5AkNDQ/j5+aFly5ZSxyIiyjAWFkRERD/Ijh074OPjg0+fPqFw4cLYs2cPypYtK3UsIqJMwa5QREREWUwIgVmzZqFVq1b49OkTvLy8cOnSJRYVRJSrsLAgIiLKQgkJCejXrx9GjRoFABg0aBAOHjwIc3NziZMREWUudoUiIiLKItHR0WjTpg32798PmUyGBQsWYNCgQVLHIiLKEiwsiIiIskBYWBgaN26MwMBA6OnpYdOmTfj555+ljkVElGVYWBAREWWyoKAgNGzYEE+ePIGlpSX27t0Ld3d3qWMREWUpFhZERESZ6OzZs2jcuDHevXuHokWL4p9//kHRokWljkVElOV48jYREVEmCQgIgKenJ969ewd3d3ecO3eORQUR5RksLIiIiDLB33//jUaNGiEmJgYNGjRAQEAALC0tpY5FRPTDsLAgIiLKoC1btuCXX35BfHw8fv75Z+zZswcGBgZSxyIi+qFYWBAREWXAypUr0b59e6hUKnTs2BHbtm2Drq6u1LGIiH44FhZERETfaf78+ejZsyeEEOjTpw/8/Pygrc3rohBR3sTCgoiI6DtMnToVw4YNAwCMGDECS5YsgVzOP6tElHdxD0hERJRO06ZNw4QJEwB8LjBmzZoFmUwmcSoiImnxeC0REVE6zJ49G+PHjwcAzJo1CyNHjpQ4ERFR9sAjFkRERGnk6+uL3377DcDnoxYsKoiI/oeFBRERURosXboUQ4YMAQBMmDABY8eOlTgREVH2InlhsXTpUjg5OUFPTw+VKlXCqVOnvtp+06ZNKF++PAwMDGBnZ4cuXbogIiLiB6UlIqK8aNWqVejXrx8AYNSoUZg0aZK0gYiIsiFJC4tt27Zh8ODBGDt2LK5evQoPDw94e3sjJCQkxfanT59Gp06d0K1bN9y+fRs7duzApUuX0L179x+cnIiI8or169ejZ8+eAIAhQ4bg999/54naREQpkLSwmD9/Prp164bu3bvD2dkZvr6+sLe3x7Jly1Jsf/78eTg6OmLgwIFwcnLCTz/9hF69euHy5cs/ODkREeUF27dvR5cuXSCEQL9+/TBv3jwWFUREqZCssIiPj0dgYCC8vLySDPfy8sLZs2dTnKZatWp4/vw5Dh48CCEEXr16hZ07d6JRo0Y/IjIREeUhAQEB6NChA9RqNXr06IFFixaxqCAi+grJLjcbHh4OlUoFGxubJMNtbGwQFhaW4jTVqlXDpk2b0Lp1a8TGxiIhIQFNmzbF4sWLU11OXFwc4uLiNM+joqIAAEqlEkqlMhNeSe6XuJ64vqTDbSAtrn/p/ehtcPXqVbRo0QJKpRItW7bEokWLoFKpoFKpfsjysyN+DqTF9S+9vLoN0vN6ZUIIkYVZUvXy5UsUKFAAZ8+ehbu7u2b49OnTsWHDBty9ezfZNHfu3EG9evUwZMgQ1K9fH6GhoRgxYgSqVKmC1atXp7icSZMmYfLkycmGb968GQYGBpn3goiIKFcIDQ3FqFGj8P79e5QtWxYTJkyAQqGQOhYRkSRiYmLQrl07vH//HiYmJl9tK1lhER8fDwMDA+zYsQMtWrTQDB80aBCuXbuGEydOJJumY8eOiI2NxY4dOzTDTp8+DQ8PD7x8+RJ2dnbJpknpiIW9vT3Cw8O/uXLoM6VSCX9/f3h6evKPq0S4DaTF9S+9H7UNwsLCULNmTQQHB8PFxQUBAQH8W/H/+DmQFte/9PLqNoiKioKlpWWaCgvJukLp6OigUqVK8Pf3T1JY+Pv7o1mzZilOExMTA23tpJG1tLQAAKnVR7q6utDV1U02XKFQ5Kk3RWbgOpMet4G0uP6ll5Xb4P3792jSpAmCg4NRpEgRHDp0CBYWFlmyrJyMnwNpcf1LL69tg/S8VkmvCjV06FCsWrUKa9asQVBQEIYMGYKQkBD07t0bADB69Gh06tRJ075JkybYtWsXli1bhsePH+PMmTMYOHAgXF1dkT9/fqleBhER5XCxsbFo3rw5rl+/Dmtra/z777/JzgEkIqKvk+yIBQC0bt0aERERmDJlCkJDQ1GmTBkcPHgQDg4OAD73c/3ynhadO3fGhw8f8Mcff2DYsGEwMzNDnTp1MGvWLKleAhER5XBqtRodO3bE8ePHYWxsjEOHDqFIkSJSxyIiynEkLSwAoG/fvujbt2+K4/z8/JINGzBgAAYMGJDFqYiIKK8YNWoUdu7cCR0dHezZswcVKlSQOhIRUY4kaVcoIiIiKa1atQpz5swBAKxduxZ16tSROBERUc7FwoKIiPKko0ePok+fPgCAiRMnol27dhInIiLK2VhYEBFRnnPv3j388ssvSEhIQNu2bTFx4kSpIxER5XgsLIiIKE+JiIhAo0aNEBkZiapVq2LNmjWQyWRSxyIiyvFYWBARUZ4RFxeHn3/+GY8ePYKDgwP27NkDPT09qWMREeUKLCyIiChPEEKgV69eOHnyJIyNjbF//37eq4KIKBOxsCAiojxh9uzZWLduHeRyObZv344yZcpIHYmIKFdhYUFERLneoUOHMHr0aADAwoUL0aBBA4kTERHlPiwsiIgoV3v8+DHatWsHIQS6d++Ofv36SR2JiChXYmFBRES5VnR0NFq0aIF3797Bzc0Nf/zxB68ARUSURVhYEBFRrpR4hOLGjRuwtrbGzp07oaurK3UsIqJci4UFERHlSgsWLMDWrVuhra2NHTt2oGDBglJHIiLK1VhYEBFRrnP06FGMGDECADB//nzUqFFD4kRERLkfCwsiIspVnj59itatW0OtVqNTp07o37+/1JGIiPIEFhZERJRrfPr0CT///DPCw8NRsWJFLF++nCdrExH9ICwsiIgo1xgyZAiuXLkCS0tL7Nq1C/r6+lJHIiLKM1hYEBFRrrBlyxb8+eefkMlk2LRpExwcHKSORESUp7CwICKiHO/+/fvo2bMnAGDs2LHw8vKSOBERUd7DwoKIiHK0T58+oVWrVvj48SNq1qyJiRMnSh2JiChPYmFBREQ52pAhQ3D9+nVYW1tjy5Yt0NbWljoSEVGexMKCiIhyrC/Pq9i4cSPs7OykjkRElGexsCAiohzpy/Mqxo0bB09PT4kTERHlbSwsiIgox/nyvIpatWrxvAoiomyAhQUREeU4X55XsXnzZmhpaUkdiYgoz2NhQUREOcru3bt5XgURUTbEwoKIiHKMly9fonv37gCAESNG8LwKIqJshIUFERHlCGq1Gt26dcPbt29RsWJFTJ06VepIRET0BRYWRESUI+zduxdHjhyBvr4+Nm/eDB0dHakjERHRF1hYEBFRtnft2jVs3LgRAODr64sSJUpInIiIiP6LhQUREWVrMTEx6NixIxISEtC0aVP06NFD6khERJQCFhZERJStDR8+HPfu3UO+fPmwfPlyyGQyqSMREVEKWFgQEVG2tW/fPixbtgwAMGjQIFhaWkqciIiIUsPCgoiIsqWwsDB07doVwOcb4rm4uEgbiIiIvoqFBRERZTtCCPTo0QPh4eEoX748pkyZInUkIiL6BhYWRESU7axduxb79++Hjo4ONm7cCF1dXakjERHRN7CwICKibOXp06cYPHgwAGDatGkoU6aMtIGIiChNWFgQEVG2oVar0bVrV3z48AHVqlXD0KFDpY5ERERpxMKCiIiyjaVLl+Lo0aMwMDDAunXroKWlJXUkIiJKIxYWRESULTx48AAjR44EAMyePRtFixaVOBEREaUHCwsiIpKcSqWCj48PPn36hLp166JPnz5SRyIionRiYUFERJKbO3cuzp07B2NjY6xZswZyOf88ERHlNNxzExGRpG7evIkJEyYAABYuXIhChQpJnIiIiL4HCwsiIpKMUqmEj48P4uPj0aRJE3Tu3FnqSERE9J1YWBARkWTmzJmDq1evwtzcHCtWrIBMJpM6EhERfScWFkREJIk7d+5g8uTJAD53gbK1tZU4ERERZQQLCyIi+uFUKhW6deuG+Ph4NGzYEO3bt5c6EhERZRALCyIi+uEWL16M8+fPw9jYGMuXL2cXKCKiXICFBRER/VCPHj3CmDFjAHw+x8Le3l7iRERElBlYWBAR0Q8jhECPHj3w6dMn1K5dGz169JA6EhERZZI0FxazZ8/Gp0+fNM9PnjyJuLg4zfMPHz6gb9++mZuOiIhylZUrV+LYsWPQ19fHypUreSM8IqJcJM179NGjR+PDhw+a540bN8aLFy80z2NiYvDnn39mbjoiIso1nj9/juHDhwMApk+fjiJFikiciIiIMlOaCwshxFefExERpUYIgV69euHDhw+oWrUqBg4cKHUkIiLKZDwGTUREWW7z5s04ePAgdHR0sHr1amhpaUkdiYiIMhkLCyIiylIREREYPHgwAGD8+PEoVaqUtIGIiChLaKen8apVq2BkZAQASEhIgJ+fHywtLQEgyfkXREREiYYPH47w8HCUKVMGI0eOlDoOERFlkTQXFoUKFcLKlSs1z21tbbFhw4ZkbYiIiBIdPXoUfn5+kMlkWLFiBXR0dKSOREREWSTNhcWTJ0+yMAYREeU2nz59Qq9evQAAffv2hbu7u8SJiIgoK2XaORYRERHw9fXNrNkREVEON23aNDx8+BAFChTA77//LnUcIiLKYhkqLIQQ+Pfff9GqVSvkz58f06dPz6xcRESUg928eROzZ88GACxevBgmJiYSJyIioqz2XYXFkydPMGHCBDg4OKBhw4bQ09PDgQMHEBYWltn5iIgoh1Gr1ejZsycSEhLQvHlztGjRQupIRET0A6S5sIiLi8OWLVtQt25dODs749atW5g/fz7kcjlGjRqFevXq8brkRESE5cuX4/z58zA2NsbixYuljkNERD9Imk/eLlCgAEqVKoUOHTpg586dyJcvHwCgbdu2WRaOiIhylhcvXmDUqFEAgBkzZqBgwYISJyIioh8lzUcsVCoVZDIZZDIZj0wQEVGKBgwYgA8fPqBq1aro3bu31HGIiOgHSnNhERoaip49e2LLli2wtbXFL7/8gt27d0Mmk2UowNKlS+Hk5AQ9PT1UqlQJp06d+mr7uLg4jB07Fg4ODtDV1UWRIkWwZs2aDGUgIqKM27t3L3bv3g1tbW2sWLGCP0IREeUxaS4s9PT00L59exw9ehQ3b96Es7MzBg4ciISEBEyfPh3+/v5QqVTpWvi2bdswePBgjB07FlevXoWHhwe8vb0REhKS6jStWrXCkSNHsHr1aty7dw9btmxByZIl07VcIiLKXNHR0Rg4cCAAYOjQoShbtqzEiYiI6Ef7rqtCFSlSBNOmTcPTp09x4MABxMXFoXHjxrCxsUnXfObPn49u3bqhe/fucHZ2hq+vL+zt7bFs2bIU2x86dAgnTpzAwYMHUa9ePTg6OsLV1RXVqlX7npdBRESZJPFvQqFChTBhwgSp4xARkQQydB8LuVwOb29v7Ny5E8+fP8eYMWPSPG18fDwCAwPh5eWVZLiXlxfOnj2b4jR79+5F5cqVMXv2bBQoUADFixfH8OHD8enTp4y8DCIiyoA7d+5g7ty5AIBFixbB0NBQ4kRERCSFNF8V6lusrKwwdOjQNLcPDw+HSqVKdpTDxsYm1fthPH78GKdPn4aenh52796N8PBw9O3bF2/fvk31PIu4uDjExcVpnkdFRQEAlEollEplmvPmZYnrietLOtwG0uL6T50QAn369EFCQgIaNWqEhg0bZsl64jaQHreBtLj+pZdXt0F6Xm+mFRbf678nfwshUj0hXK1WQyaTYdOmTTA1NQXwuTtVy5YtsWTJEujr6yebZsaMGZg8eXKy4YcPH4aBgUEmvIK8w9/fX+oIeR63gbS4/pM7duwYTp48CR0dHTRt2hQHDx7M0uVxG0iP20BaXP/Sy2vbICYmJs1tJSssLC0toaWllezoxOvXr1M9V8POzg4FChTQFBUA4OzsDCEEnj9/jmLFiiWbZvTo0UmOpERFRcHe3h5eXl4wMTHJpFeTuymVSvj7+8PT0xMKhULqOHkSt4G0uP5T9u7dO/To0QMAMH78eHTp0iXLlsVtID1uA2lx/Usvr26DxN4+aZGmwiIqKirTv4Tr6OigUqVK8Pf3R4sWLTTD/f390axZsxSnqV69Onbs2IGPHz/CyMgIAHD//n3I5fJUb8Kkq6sLXV3dZMMVCkWeelNkBq4z6XEbSIvrP6mJEyfizZs3cHZ2xsiRI3/IuuE2kB63gbS4/qWX17ZBel5rmk7ezpcvH16/fg0AqFOnDiIjI78r2H8NHToUq1atwpo1axAUFIQhQ4YgJCREc1Ol0aNHo1OnTpr27dq1g4WFBbp06YI7d+7g5MmTGDFiBLp27ZpiNygiIsoaFy9exJ9//gng8/2IdHR0JE5ERERSS9MRCyMjI0RERMDa2hrHjx/PtJNWWrdujYiICEyZMgWhoaEoU6YMDh48CAcHBwCfb8r35T0tjIyM4O/vjwEDBqBy5cqwsLBAq1atMG3atEzJQ0RE36ZSqdCnTx8IIdChQwfUqlVL6khERJQNpKmwqFevHmrXrg1nZ2cAQIsWLVL9dero0aPpCtC3b1/07ds3xXF+fn7JhpUsWTLPnTRDRJSdLF26FFeuXIGZmZnmMrNERERpKiw2btyIdevW4dGjRzhx4gRKly7NKyoREeVBoaGhGDduHADg999/T/eNUYmIKPdKU2Ghr6+vOe/h8uXLmDVrFszMzLIyFxERZUPDhg1DVFQUqlSpgp49e0odh4iIspF0X2722LFjmv8LIQAkvxcFERHlPgEBAdiyZQvkcjmWLVsGLS0tqSMREVE2kqarQv3X+vXrUbZsWejr60NfXx/lypXDhg0bMjsbERFlE3FxcejXrx+Az+fGVapUSeJERESU3aT7iMX8+fMxfvx49O/fH9WrV4cQAmfOnEHv3r0RHh6OIUOGZEVOIiKS0Jw5c3D//n3Y2NjwSnxERJSidBcWixcvxrJly5LcX6JZs2YoXbo0Jk2axMKCiCiXCQ4OxvTp0wF8/nHJ1NRU4kRERJQdpbsrVGhoKKpVq5ZseLVq1RAaGpopoYiIKPsYOnQoYmNjUatWLbRt21bqOERElE2lu7AoWrQotm/fnmz4tm3bUKxYsUwJRURE2cOhQ4ewZ88eaGtr448//uDFOoiIKFXp7go1efJktG7dGidPnkT16tUhk8lw+vRpHDlyJMWCg4iIcqa4uDgMHDgQADBw4ECULl1a4kRERJSdpfuIxS+//IILFy7A0tISe/bswa5du2BpaYmLFy+iRYsWWZGRiIgkMH/+fDx48AC2traYOHGi1HGIiCibS/cRCwCoVKkSNm7cmNlZiIgom3j27Jnm6k9z5syBiYmJxImIiCi7+677WBARUe42bNgwxMTE4KeffkL79u2ljkNERDkACwsiIkriyJEj2LFjB+RyOU/YJiKiNGNhQUREGvHx8RgwYACAz3fYLl++vMSJiIgop2BhQUREGosXL0ZQUBCsrKwwZcoUqeMQEVEOku7Cws/PDzExMVmRhYiIJPTy5UtMmjQJADBz5kzky5dP2kBERJSjpLuwGD16NGxtbdGtWzecPXs2KzIREZEERo4ciY8fP8LNzQ2dO3eWOg4REeUw6S4snj9/jo0bN+Ldu3eoXbs2SpYsiVmzZiEsLCwr8hER0Q9w8uRJbNq0CTKZDH/88QfkcvaUJSKi9En3Xw4tLS00bdoUu3btwrNnz9CzZ09s2rQJhQoVQtOmTfH3339DrVZnRVYiIsoCCQkJ6N+/PwCgR48eqFy5ssSJiIgoJ8rQT1LW1taoXr063N3dIZfLcfPmTXTu3BlFihTB8ePHMykiERFlpWXLluHmzZswNzfH77//LnUcIiLKob6rsHj16hXmzp2L0qVLo1atWoiKisL+/fsRHByMly9f4ueff4aPj09mZyUiokz26tUrjB8/HgAwffp0WFhYSJyIiIhyKu30TtCkSRP8+++/KF68OHr06IFOnTrB3NxcM15fXx/Dhg3DggULMjUoERFlvtGjR+P9+/eoWLEievToIXUcIiLKwdJdWFhbW+PEiRNwd3dPtY2dnR2Cg4MzFIyIiLLWuXPnsHbtWgDAH3/8AS0tLYkTERFRTpburlA1a9ZExYoVkw2Pj4/H+vXrAQAymQwODg4ZT0dERFlCpVJpTtju0qXLV38sIiIiSot0FxZdunTB+/fvkw3/8OEDunTpkimhiIgoa61cuRJXrlyBqakpZs6cKXUcIiLKBdJdWAghIJPJkg1//vw5TE1NMyUUERFlnYiICIwdOxYAMHXqVFhbW0uciIiIcoM0n2NRoUIFyGQyyGQy1K1bF9ra/5tUpVIhODgYDRo0yJKQRESUecaMGYO3b9+iXLly6NOnj9RxiIgol0hzYdG8eXMAwLVr11C/fn0YGRlpxuno6MDR0RG//PJLpgckIqLMc/nyZaxcuRLA5xO2v/yRiIiIKCPS/Bdl4sSJAABHR0e0bt0aenp6WRaKiIgyn1qtRv/+/SGEQPv27eHh4SF1JCIiykXS/VNVbrnxXXx8POLj45MNl8vlSX7BS6lNIplMBoVC8V1tlUolhBA/tC3w+ejS97RVq9WIj49Ptf2XbRMSEqBWq1Odr0Kh0Jynk1VtVSoVVCpVprTV1taGXC6XtO2X612tViMhISHVtlpaWprLhmaHtkIIKJXKTGn75eczq9oCyT/LSqUSKpUK8fHxkMlkOXYf4efnh8DAQOTLlw+///57inm+dx/xrc9nRvcRX26DLzNxH5G8bVZ+7lPaBhmdb27YR3xv2/TsI/67PnPa94is3kdkdtuUPnNf7oe0tbXzzD7ia+/LZMtJSyNzc3Pcv38flpaWyJcvX4onbyd6+/ZtmhcupXnz5qV41KVYsWJo166d5vncuXNT3dk4ODigc+fOmucLFy5ETExMim3z58+f5OZTS5YsSfHqWgBgZWWFvn37ap6vXLkSb968SbGtqakpBg8erHnu5+eHly9fptjWwMAAI0aM0DzftGkTnj59mmJbhUKBMWPGaJ4/efIEc+fOTbEt8L8jWgCwe/du3LlzJ9W2o0eP1uxA9u/fj+vXr6fadvjw4TA0NAQA/Pvvv7h8+XKqbQcNGgQzMzMAwJEjR3Du3LlU2/bp00dzwuqpU6dw4sSJVNt2794dBQoUAACcP38eAQEBqbb18fGBo6MjACAwMBD//PNPqm3btm2L4sWLAwBu3ryJv//+O9W2LVq00Pw/KCgIO3fuTLVts2bN4OLiAgB4+PAhtmzZkmpbb29vuLq6AgBCQkKwbt26VNvWq1cP1atXBwCEhoZi1apVqbatWbMmatWqBQB48+YNli1blmpbd3d3eHl5AQDev3+PhQsXptq2cuXKaNSoEQAgJibmq+/J8uXLa7pwKpVKzJgxI9W2pUqVwq+//qp5nlrbmzdv5th9xLt37zBq1Ch06dIFBQoU0Ny/4ksZ2Uds374dDx48SLEtkHn7iJs3byZpy33EZy1btkTp0qUBZN0+4tmzZ7h582aybZCI+4jPsmofYWdnBxsbG83znPY94kftI/4rK/YRN2/ezFP7iJT+XqQmTYXFggULYGxsrPn/1woLIiLKfiZMmIA3b95AX19f6ihERJRLycTXjmHlQlFRUTA1NcWbN29gYmKSbDy7QiVvq1QqsX//fnh5eSVZVmrzza6HML+3bXY4hCmEwKFDh9CwYUNoaWlJ3r0pr3VzUCqV+Pfff1G/fn3o6urmuH3EnTt3ULFiRajVahw+fBg1a9ZMNUd27ebw5Tb48rVzH5G8bVZ9luPi4nDgwIFk2yCj880N+4jvbZverlD+/v5o2LAhFApFjvoekZg/N3SFStwPGRgY5Jl9xNu3b2FlZYX379+n+N05yXK+Ovb/RUVFpaUZAHxzgdmFjo5Okjfx19qlZ55pldoX9OzaVi6XQ0dHJ03TpOcqM1nV9ssPRW5o++UfvMRtkRbZoa1MJstRbYHkn2WZTAYtLS3o6Ogkex9m932EEAL9+/eHWq3Gr7/+Ck9PzyzJkNWf+y+3QWq58vI+4ktZ+bn/1jb4nvlmh899RvcRP6Ltf3uLZIfvBtlpH5HZbVP6zH25H/pye2SHz3122EcAaSwszMzMvtn9KfHGeV+rloiI6MfauHEjTp8+DQMDA8ybN0/qOERElIulqbA4duxYVucgIqJMFhUVpTnRcvz48bC3t5c4ERER5WZpKiy+1h+XiIiyp0mTJuHVq1coXrw4hgwZInUcIiLK5dJUWNy4cQNlypSBXC7HjRs3vtq2XLlymRKMiIi+361bt7Bo0SIAwKJFi6CrqytxIiIiyu3SVFi4uLggLCwM1tbWcHFxgUwmS/EqADzHgohIekIIDBgwACqVCi1atED9+vWljkRERHlAmgqL4OBgWFlZaf5PRETZ17Zt23D8+HHo6elhwYIFUschIqI8Ik2FhYODQ4r/JyKi7OXjx48YNmwYAGDMmDHcZxMR0Q+T9gv6fuHevXtYvHgxgoKCIJPJULJkSQwYMAAlSpTI7HxERJQOU6dOxcuXL1GkSBHNFaGIiIh+BHl6J9i5cyfKlCmDwMBAlC9fHuXKlcOVK1dQpkwZ7NixIysyEhFRGty9exfz588HACxcuBB6enoSJyIiorwk3UcsRo4cidGjR2PKlClJhk+cOBG//fYbfv3110wLR0REaZN4wnZCQgIaN26MRo0aSR2JiIjymHQfsQgLC0OnTp2SDe/QoQPCwsIyJRQREaXPrl27EBAQAF1dXSxcuFDqOERElAelu7CoVasWTp06lWz46dOn4eHhkSmhiIgo7aKjozU3wPvtt99QuHBhiRMREVFelKauUHv37tX8v2nTpvjtt98QGBiIqlWrAgDOnz+PHTt2YPLkyVmTkoiIUjVjxgw8e/YMDg4O+O2336SOQ0REeVSaCovmzZsnG7Z06VIsXbo0ybB+/fqhd+/emRKMiIi+7cGDB5gzZw4AwNfXFwYGBhInIiKivCpNhYVarc7qHERElE5CCAwaNAjx8fFo0KABmjVrJnUkIiLKw9J9jgUREWUP+/btwz///AOFQoGFCxdCJpNJHYmIiPKw77pBXnR0NE6cOIGQkBDEx8cnGTdw4MBMCUZERKn79OkTBg0aBAAYPnw4ihcvLnEiIiLK69JdWFy9ehUNGzZETEwMoqOjYW5ujvDwcBgYGMDa2pqFBRHRDzB79mw8efIEBQsWxNixY6WOQ0RElP6uUEOGDEGTJk3w9u1b6Ovr4/z583j69CkqVaqEuXPnZkVGIiL6QnBwMGbOnAkAmD9/PgwNDSVORERE9B2FxbVr1zBs2DBoaWlBS0sLcXFxsLe3x+zZszFmzJisyEhERF8YPHgwYmNjUbduXbRs2VLqOERERAC+o7BQKBSaEwRtbGwQEhICADA1NdX8n4iIssbBgwexd+9eaGtrY/HixTxhm4iIso10n2NRoUIFXL58GcWLF0ft2rUxYcIEhIeHY8OGDShbtmxWZCQiInw+YXvAgAEAPh+1cHZ2ljgRERHR/6T7iMXvv/8OOzs7AMDUqVNhYWGBPn364PXr11ixYkWmByQios9mzJiBx48fo2DBgpg4caLUcYiIiJJI9xGLypUra/5vZWWFgwcPZmogIiJK7v79+5g1axYAYOHChTAyMpI4ERERUVLfdR8LAHj9+jXu3bsHmUyGEiVKwMrKKjNzERHR/xNCoF+/foiPj4e3tzdatGghdSQiIqJk0t0VKioqCh07dkSBAgVQs2ZN1KhRA/nz50eHDh3w/v37rMhIRJSnbdu2DQEBAdDT08Mff/zBE7aJiChbSndh0b17d1y4cAH79+9HZGQk3r9/j/379+Py5cvo0aNHVmQkIsqz3r9/jyFDhgAAxo4di8KFC0uciIiIKGXp7gp14MAB/Pvvv/jpp580w+rXr4+VK1eiQYMGmRqOiCivmzBhAsLCwlC8eHGMGDFC6jhERESpSvcRCwsLC5iamiYbbmpqinz58mVKKCIiAq5cuYI//vgDALB06VLo6upKnIiIiCh16S4sxo0bh6FDhyI0NFQzLCwsDCNGjMD48ePTHWDp0qVwcnKCnp4eKlWqhFOnTqVpujNnzkBbWxsuLi7pXiYRUXanUqnQp08fqNVqtG3bFnXr1pU6EhER0VelqStUhQoVkpws+ODBAzg4OKBQoUIAgJCQEOjq6uLNmzfo1atXmhe+bds2DB48GEuXLkX16tXx559/wtvbG3fu3NHMOyXv379Hp06dULduXbx69SrNyyMiyilWrVqFixcvwsTEBPPmzZM6DhER0TelqbBo3rx5lix8/vz56NatG7p37w4A8PX1xb///otly5ZhxowZqU7Xq1cvtGvXDlpaWtizZ0+WZCMiksrr168xatQoAMC0adM0NyUlIiLKztJUWGTFHV7j4+MRGBio+eOZyMvLC2fPnk11urVr1+LRo0fYuHEjpk2b9s3lxMXFIS4uTvM8KioKAKBUKqFUKr8zfd6SuJ64vqTDbSCtH73+hw8fjsjISLi4uKB79+7c7uBnIDvgNpAW17/08uo2SM/r/e4b5AUGBiIoKAgymQylSpVChQoV0jV9eHg4VCoVbGxskgy3sbFBWFhYitM8ePAAo0aNwqlTp6CtnbboM2bMwOTJk5MNP3z4MAwMDNKVOa/z9/eXOkKex20grR+x/m/fvo0NGzZAJpOhXbt2OHz4cJYvMyfhZ0B63AbS4vqXXl7bBjExMWlum+7C4vXr12jTpg2OHz8OMzMzCCHw/v171K5dG1u3bk33Hbj/e6MnIUSKN39SqVRo164dJk+ejOLFi6d5/qNHj8bQoUM1z6OiomBvbw8vLy+YmJikK2tepVQq4e/vD09PTygUCqnj5EncBtL6Ues/Pj4eo0ePBgD06NEDgwcPzrJl5TT8DEiP20BaXP/Sy6vbILG3T1qku7AYMGAAoqKicPv2bTg7OwMA7ty5Ax8fHwwcOBBbtmxJ03wsLS2hpaWV7OjE69evkx3FAIAPHz7g8uXLuHr1Kvr37w8AUKvVEEJAW1sbhw8fRp06dZJNp6urm+IlGhUKRZ56U2QGrjPpcRtIK6vX/4IFCxAUFAQrKyvMnDmT2zoF/AxIj9tAWlz/0str2yA9rzXdhcWhQ4cQEBCgKSoAoFSpUliyZAm8vLzSPB8dHR1UqlQJ/v7+aNGihWa4v78/mjVrlqy9iYkJbt68mWTY0qVLcfToUezcuRNOTk7pfSlERNnG06dPNd02586dy/sCERFRjpPuwkKtVqdYuSgUCqjV6nTNa+jQoejYsSMqV64Md3d3rFixAiEhIejduzeAz92YXrx4gfXr10Mul6NMmTJJpre2toaenl6y4UREOYkQAv369UNMTAxq1KiBjh07Sh2JiIgo3dJdWNSpUweDBg3Cli1bkD9/fgDAixcvMGTIkHTfwKl169aIiIjAlClTEBoaijJlyuDgwYNwcHAAAISGhiIkJCS9EYmIcpSdO3fiwIED0NHRwfLly1M8z4yIiCi7S/edt//44w98+PABjo6OKFKkCIoWLQonJyd8+PABixcvTneAvn374smTJ4iLi0NgYCBq1KihGefn54fjx4+nOu2kSZNw7dq1dC+TiCi7ePfuHQYMGADg81HaL7uZEhER5STpPmJhb2+PK1euwN/fH3fv3oUQAqVKlUK9evWyIh8RUa42atQovHr1CiVKlNBcEYqIiCgnSldhkZCQAD09PVy7dg2enp7w9PTMqlxERLne6dOnsWLFCgDAihUrUryCHRERUU6Rrq5Q2tracHBwgEqlyqo8RER5QlxcHHr27AkA6N69e5JuoERERDlRus+xGDduHEaPHo23b99mRR4iojxh1qxZCAoKgo2NDWbPni11HCIiogxL9zkWixYtwsOHD5E/f344ODjA0NAwyfgrV65kWjgiotzo3r17mD59OgBg4cKFvGcFERHlCukuLJo1a8ZLIRIRfSe1Wo2ePXsiPj4e3t7eaNWqldSRiIiIMkW6C4tJkyZlQQwiorxh7dq1OHnyJAwMDLB06VL+UENERLlGms+xiImJQb9+/VCgQAFYW1ujXbt2CA8Pz8psRES5SmhoKIYPHw4AmDJlChwdHaUNRERElInSXFhMnDgRfn5+aNSoEdq0aQN/f3/06dMnK7MREeUaQgj069cPkZGRqFSpEgYNGiR1JCIiokyV5q5Qu3btwurVq9GmTRsAQIcOHVC9enWoVCpoaWllWUAiotxg586d2L17N7S1tbFmzRpoa6e7JyoREVG2luYjFs+ePYOHh4fmuaurK7S1tfHy5cssCUZElFuEh4ejX79+AIAxY8agXLlyEiciIiLKfGkuLFQqFXR0dJIM09bWRkJCQqaHIiLKTQYPHow3b96gdOnSGDt2rNRxiIiIskSaj8ULIdC5c2fo6upqhsXGxqJ3795J7mWxa9euzE1IRJSDHThwAJs2bYJcLseaNWuS/UBDRESUW6S5sPDx8Uk2rEOHDpkahogoN3n//j169eoFABgyZAhcXV0lTkRERJR10lxYrF27NitzEBHlOiNHjsSLFy9QtGhRTJkyReo4REREWSrN51gQEVHaHT16FCtWrAAArFq1CgYGBhInIiIiylosLIiIMll0dDS6d+8OAOjTpw9q1qwpcSIiIqKsx8KCiCiTjRkzBsHBwbC3t8fMmTOljkNERPRDsLAgIspEx44dw6JFiwAAK1euhImJicSJiIiIfgwWFkREmSQqKgpdunQBAPTq1Qv169eXOBEREdGPw8KCiCiTDBs2DE+fPoWTkxPmzJkjdRwiIqIfioUFEVEm+Oeff7Bq1SoAny/PbWxsLHEiIiKiH4uFBRFRBr19+xbdunUDAAwePJhXgSIiojyJhQURUQYNHDgQoaGhKFGiBH7//Xep4xAREUmChQURUQb89ddf2LRpE+RyOdatWwd9fX2pIxEREUmChQUR0Xd6/fo1evfuDQAYNWoU3NzcJE5EREQkHRYWRETfQQiB3r17Izw8HOXKlcOECROkjkRERCQpFhZERN/Bz88Pu3fvhra2NtatWwddXV2pIxEREUmKhQURUTo9fPgQAwYMAABMmzYNLi4u0gYiIiLKBlhYEBGlg1KpRLt27RAdHY1atWph+PDhUkciIiLKFlhYEBGlw+TJk3Hp0iWYmZlh/fr10NLSkjoSERFRtsDCgogojU6dOqW5T8WKFStgb28vcSIiIqLsg4UFEVEafPz4EV26dIEQAp07d8avv/4qdSQiIqJshYUFEdE3CCHw559/IiQkBIULF8aiRYukjkRERJTtsLAgIvqGzZs349SpU9DS0sKmTZtgbGwsdSQiIqJsh4UFEdFXBAcHY+DAgQCAcePGoWrVqhInIiIiyp5YWBARpSI+Ph5t2rTBhw8f4OzsjFGjRkkdiYiIKNtiYUFElIrRo0fj4sWLMDMzw+DBg3lpWSIioq/QljoAEVF29Pfff2P+/PkAgFWrVkFbm7tLIiKir+ERCyKi/3jy5Ak6d+4MABgyZAiaNm0qbSAiIqIcgIUFEdEXEs+riIyMhKurK2bOnCl1JCIiohyBhQUR0RfGjBmDCxcuwMzMDNu2bYOOjo7UkYiIiHIEFhZERP9v7969mDdvHgBg7dq1cHR0lDYQERFRDsLCgogIwNOnTzXnVQwePBjNmzeXNA8REVFOw8KCiPK8xPMq3r17hypVqmDWrFlSRyIiIspxWFgQUZ43dOhQnD9/nudVEBERZQALCyLK0/z8/LBkyRIAwIYNG+Dk5CRxIiIiopyJhQUR5VmXL19G7969AQCTJk1C48aNJU5ERESUc7GwIKI86c2bN/j5558RFxeHJk2aYPz48VJHIiIiytFYWBBRnpOQkIA2bdrg2bNnKFasGDZs2AC5nLtDIiKijOBfUiLKc0aNGoWjR4/C0NAQu3fvhqmpqdSRiIiIcjwWFkSUp2zdulVzEzw/Pz+ULl1a4kRERES5AwsLIsozbty4gW7dugEAfvvtN7Rs2VLiRERERLkHCwsiyhNev36NZs2aISYmBp6enpg+fbrUkYiIiHIVFhZElOvFxsaiefPmePLkCYoUKYItW7ZAS0tL6lhERES5CgsLIsrVhBDo1q0bzp07BzMzMxw4cAAWFhZSxyIiIsp1WFgQUa42depUbN68Gdra2ti5cydKlCghdSQiIqJciYUFEeVaW7duxcSJEwEAS5cuRd26dSVORERElHuxsCCiXOn8+fPo3LkzAGDYsGHo0aOHtIGIiIhyORYWRJTrPH36FM2aNUNcXByaNm2KWbNmSR2JiIgo12NhQUS5SlRUFBo3bozXr1+jfPny2LRpE68ARURE9AOwsCCiXCMuLg4tWrTArVu3YGdnh3379sHIyEjqWERERHkCCwsiyhVUKhU6duyIo0ePwsjICPv374e9vb3UsYiIiPIMyQuLpUuXwsnJCXp6eqhUqRJOnTqVattdu3bB09MTVlZWMDExgbu7O/79998fmJaIsiMhBAYNGoQdO3ZAoVBgz549qFixotSxiIiI8hRJC4tt27Zh8ODBGDt2LK5evQoPDw94e3sjJCQkxfYnT56Ep6cnDh48iMDAQNSuXRtNmjTB1atXf3ByIspOfv/9dyxZsgQymQwbNmzgZWWJiIgkIGlhMX/+fHTr1g3du3eHs7MzfH19YW9vj2XLlqXY3tfXFyNHjkSVKlVQrFgx/P777yhWrBj27dv3g5MTUXaxatUqjBs3DgCwcOFCtG7dWuJEREREeZO2VAuOj49HYGAgRo0alWS4l5cXzp49m6Z5qNVqfPjwAebm5qm2iYuLQ1xcnOZ5VFQUAECpVEKpVH5H8rwncT1xfUmH2yBl+/btQ69evQAAv/32G3r37p0l64jrX3rcBtLjNpAW17/08uo2SM/rlaywCA8Ph0qlgo2NTZLhNjY2CAsLS9M85s2bh+joaLRq1SrVNjNmzMDkyZOTDT98+DAMDAzSFzqP8/f3lzpCnsdt8D9BQUGYOHEi1Go16tati6pVq+LgwYNZukyuf+lxG0iP20BaXP/Sy2vbICYmJs1tJSssEslksiTPhRDJhqVky5YtmDRpEv7++29YW1un2m706NEYOnSo5nlUVBTs7e3h5eUFExOT7w+ehyiVSvj7+8PT0xMKhULqOHkSt0FSV65cgY+PD+Lj49GwYUPs3LkT2tpZtzvj+pcet4H0uA2kxfUvvby6DRJ7+6SFZIWFpaUltLS0kh2deP36dbKjGP+1bds2dOvWDTt27EC9evW+2lZXVxe6urrJhisUijz1psgMXGfS4zYArl+/Dm9vb7x//x4eHh7YsWMH9PX1f8iyuf6lx20gPW4DaXH9Sy+vbYP0vFbJTt7W0dFBpUqVkh1O8vf3R7Vq1VKdbsuWLejcuTM2b96MRo0aZXVMIspGbt++jXr16uHdu3eoWrUqDhw4wC6NRERE2YSkXaGGDh2Kjh07onLlynB3d8eKFSsQEhKC3r17A/jcjenFixdYv349gM9FRadOnbBw4UJUrVpVc7RDX18fpqamkr0OIsp69+7dQ926dREeHo5KlSrhn3/+gbGxsdSxiIiI6P9JWli0bt0aERERmDJlCkJDQ1GmTBkcPHgQDg4OAIDQ0NAk97T4888/kZCQgH79+qFfv36a4T4+PvDz8/vR8YnoB3n48CHq1KmDV69eoXz58jh8+DDMzMykjkVERERfkPzk7b59+6Jv374pjvtvsXD8+PGsD0RE2cqTJ09Qp04dvHz5EqVLl4a/v/9XLzFNRERE0pD0BnlERF8TEhKCOnXq4NmzZyhevDgCAgJgZWUldSwiIiJKAQsLIsqWHj58CA8PDwQHB6NIkSI4evQobG1tpY5FREREqWBhQUTZzu3bt+Hh4YGQkBAUL14cx44dQ4ECBaSORURERF/BwoKIspXAwEDUrFkTYWFhKFu2LE6ePAl7e3upYxEREdE3sLAgomzjzJkzqFOnDiIiIlClShUcP378mzfMJCIiouyBhQURZQsBAQHw8vJCVFQUatSogYCAAF79iYiIKAdhYUFEktu7dy8aNWqEmJgY1K9fH//88w9MTEykjkVERETpwMKCiCS1cuVK/Pzzz4iPj0eLFi3w999/w8DAQOpYRERElE4sLIhIEkIIjBs3Dj179oRKpYKPjw+2b98OXV1dqaMRERHRd2BhQUQ/XHx8PDp16oTp06cDACZMmIC1a9dCW1tb4mRERET0vfhXnIh+qMjISPz88884duwYtLS0sGLFCnTt2lXqWERERJRBLCyI6Id59uwZvL29cfv2bRgZGWHnzp2oX7++1LGIiIgoE7CwIKIf4urVq2jcuDFevnwJOzs7HDx4EC4uLlLHIiIiokzCcyyIKMtt2bIF1atXx8uXL1G6dGmcP3+eRQUREVEuw8KCiLKMSqXCyJEj0a5dO3z69Ane3t44ffo0ChUqJHU0IiIiymQsLIgoS7x9+xYNGzbEnDlzAACjR4/Gvn37YGZmJm0wIiIiyhI8x4KIMt2tW7fQrFkzPH78GAYGBli7di1atWoldSwiIiLKQiwsiChT/fXXX/Dx8UF0dDScnJywZ88elCtXTupYRERElMXYFYqIMkVcXBwGDRqEli1bIjo6GnXr1sWlS5dYVBAREeURLCyIKMMePHiAatWqYdGiRQCAYcOG4dChQ7CwsJA4GREREf0o7ApFRBmyadMm9O7dGx8/foSFhQXWrVuHRo0aSR2LiIiIfjAesSCi7xIdHY2uXbuiQ4cO+PjxI2rUqIFr166xqCAiIsqjWFgQUbpdv34dlStXxtq1ayGTyTBx4kQcPXoUBQsWlDoaERERSYRdoYgozZRKJWbNmoUpU6ZAqVTCzs4OmzdvRq1ataSORkRERBJjYUFEaXL79m34+PggMDAQANC0aVOsWrUKVlZWEicjIiKi7IBdoYjoqxISEjBr1ixUrFgRgYGBMDMzw4YNG7Bnzx4WFURERKTBIxZElKp79+7Bx8cHFy5cAAA0bNgQK1euRP78+SVORkRERNkNj1gQUTJxcXGYOnUqypcvjwsXLsDExARr167F/v37WVQQERFRinjEgoiSCAgIQN++ffHgwQMAQP369bFy5UrY29tLnIyIiIiyMx6xICIAwMuXL9G2bVt4enriwYMHsLW1xZYtW/DPP/+wqCAiIqJvYmFBlMclJCRg0aJFKFmyJLZu3Qq5XI4BAwbg7t27aNOmDWQymdQRiYiIKAdgVyiiPMzf3x/Dhw/HjRs3AACurq5YtmwZKlasKHEyIiIiymlYWBDlQbdu3cKIESNw6NAhAICZmRlmzJiBHj16QEtLS+J0RJQVVCoVlErld0+vVCqhra2N2NhYqFSqTExGacH1L73cug0UCkWm/e1nYUGUh4SGhmLixIlYvXo11Go1FAoF+vXrh3HjxsHCwkLqeESUBYQQCAsLQ2RkZIbnY2tri2fPnrGLpAS4/qWXm7eBmZkZbG1tM/y6WFgQ5QEfPnzAggULMHv2bERHRwMAfvnlF8ycORNFixaVOB0RZaXEosLa2hoGBgbf/cVBrVbj48ePMDIyglzOUzR/NK5/6eXGbSCEQExMDF6/fg0AsLOzy9D8WFgQ5WIfP37EH3/8gblz5yIiIgIA4Obmhnnz5qF69eoSpyOirKZSqTRFRUaPSqrVasTHx0NPTy/XfKnKSbj+pZdbt4G+vj4A4PXr17C2ts5QtygWFkS50MePH7FkyRLMmTNHU1AUK1YMU6dORatWrXLdIVwiSlniORUGBgYSJyGi7CxxH6FUKllYENFn0dHRWLp0KWbPno3w8HAAQNGiRTFhwgS0bdsW2tr8yBPlRfwxgYi+JrP2EbnnOA5RHvb69WtMnDgRDg4OGDlyJMLDw1GkSBGsW7cOQUFB6NixI4sKIqLvUKtWLQwePDjN7Y8fPw6ZTJbhk+UdHR3h6+uboXkQ/WgsLIhysHv37qFXr14oVKgQpkyZgoiICBQuXBhr167F3bt30alTJxYURJTjyGSyrz46d+4sdUQiSgG/cRDlMEIInDlzBnPnzsXevXshhADw+eZ2I0aMQIsWLXgvCiLKdBEREbhx4wasra1RpkyZLO1eFRoaqvn/tm3bMGHCBNy7d08zLPFk00RKpRIKhSLL8hBR2vCIBVEO8enTJ6xatQoVK1aEh4cH/v77bwgh0LRpU5w8eRLnz59Hy5YtWVQQUaYKDQ1Fh/btUSB/ftSrVw/lypVDyWLFsHHjxixbpq2treZhamoKmUymeR4bGwszMzNs374dtWrVgp6eHjZu3IhJkybBxcUlyXx8fX3h6OiYZNjatWvh7OwMPT09lCxZEkuXLk1Xto0bN6Jy5cowNjaGra0t2rVrp7lU55fOnDmD8uXLQ09PD25ubrh582aS8WfPnkWNGjWgr68Pe3t7DBw4UHM58JRMnjwZZcqUgb6+PvLnz4+BAwemKzfRj8DCgiibu337NgYNGoRu3bqhb9++uHbtGnR1ddGjRw8EBQXh77//hoeHB0/OJKJM9+rVK1Sv6o5/tv+FjmozLNJywBR5AVgEv0bHjh0xd+5cybL99ttvGDhwIIKCglC/fv00TbNy5UqMHTsW06dPR1BQEH7//XeMHz8e69atS/Ny4+PjMXXqVFy/fh179uxBcHBwil2zRowYgblz5+LSpUuwtrZG06ZNNVfpunnzJurXr4+ff/4ZN27cwLZt23D69Gn0798/xWXu3LkTvr6+WLBgAe7du4c9e/agbNmyac5M9KOwKxRRNhQTE4M9e/Zg+fLlOHXqlGZ40aJF0bt3b3Tu3Jl3yiaiLDdt2jS8fRmK+aIAbOT/39VIpouKMMRqoY3Ro0ahQ4cOsLW1/eHZBg8ejJ9//jld00ydOhXz5s3TTOfk5IQ7d+7gzz//hI+PT5rm0bVrV83/CxcujEWLFsHV1VVz47REEydOhKenJwBg3bp1KFiwIHbv3o1WrVphzpw5aNeuneak8GLFimHRokWoWbMmli1bBj09vSTLDAkJga2tLWrVqgULCws4OjrC1dU1Xa+d6EfgEQuibEKtVuPkyZPo1q0bbG1t0b59e5w6dQpaWlpo3rw5Jk+ejFu3bmHYsGEsKogoy8XHx8NvzVrUVxnBRpb8/IXWcnNoCaTr1/7MVLly5XS1f/PmDZ49e4Zu3brByMhI85g2bRoePXqU5vlcvXoVzZo1g4ODA4yNjVGrVi0An7/8f8nd3V3zf3Nzc5QoUQJBQUEAgMDAQPj5+SXJUb9+fajVagQHBydb5q+//opPnz7BxcUFPXv2xO7du5GQkJCu10/0I/CIBZHEHj58iA0bNmD9+vV48uSJZrijoyM6d+6M7t27w9raGgcPHsxVd/okouwtIiICH2OiUUJumuJ4I5kWCsn18Pjx4x+c7DNDQ8Mkz+VyueZiFokSux4Bn3+8AT53h3Jzc0vSLq3npkVHR8PLywteXl7YuHEjrKysEBISgvr16yM+Pv6b0yd2WVWr1ejVq1eK50kUKlQo2TB7e3tN19dz586hb9++mDNnDk6cOMGT1ilbYWFBJIHg4GDs3LkTO3bswKVLlzTDjY2N0apVK3Tq1Ak//fSTppD48o8jEdGPYGJiArlcjtdIef+TIATCkQBzc/MfnCxlVlZWCAsLgxBC8wX+2rVrmvE2NjYoUKAAHj9+jPbt23/XMu7evYvw8HDMnDkT9vb2AIDLly+n2Pb8+fOaIuHdu3e4f/8+SpYsCQCoWLEibt++jaJFi6Z52fr6+mjYsCHatGmD/v37o2TJkrh58yYqVqz4Xa+FKCuwsCD6QR4/fowdO3Zgx44dCAwM1AyXy+Xw9PREp06d0Lx5cxgYGEiYkojoM0NDQzRp3Bj/HPRHfWEKHVnSI6YnxAe8U8WhTZs2EiVMqlatWnjz5g1mz56Nli1b4tChQ/jnn39gYmKiaTNp0iQMHDgQJiYm8Pb2RlxcHC5fvox3795h6NCh31xGoUKFoKOjg8WLF6N37964desWpk6dmmLbKVOmwMLCAjY2Nhg7diwsLS3RvHlzAJ9PPK9atSr69euHHj16wNDQEEFBQfD398fixYuTzcvPzw9KpRKlS5eGtbU1NmzYAH19fTg4OHzfyiLKIuxXQZRF1Go1Ll++jEmTJqFixYooUqQIRo0ahcDAQMjlctSuXRtLly7FixcvcOjQIbRr145FBRFlK+MnTMBruQpTEIbHIhYAECvUOKCOxFK8wa8tW6J8+fISp/zM2dkZS5cuxZIlS1C+fHlcvHgRw4cPT9Kme/fuWLVqFfz8/FC2bFnUrFkTfn5+cHJyStMyrKys4Ofnhx07dqBUqVKYOXNmqlfGmjlzJgYNGoRKlSohNDQUe/fuhY6ODgCgXLlyOHHiBB48eAAPDw9UqFAB48ePh52dXYrzMjMzw+rVq9GgQQO4uLjgyJEj2LdvH8+3o2xHJv7bITGXi4qKgqmpKd6/f5/kVwxKnVKpxMGDB9GwYUP25fyGjx8/IiAgAPv378eBAwcQFhamGZdYTLRs2RItWrSAjY1NmufLbSAtrn/pcRt8n9jYWAQHB8PJySnZlYbS6ujRo+jUvgNehIXCVFsHn9QqKIUaHTt0wJ8rVnz3fCl91Go1oqKiNF3U6MfLzdvga/uK9Hx3ZlcoogxQq9W4evUqAgICEBAQgFOnTiEuLk4zPvFKH40bN0ajRo1gZWUlYVoiovSrU6cOnjwLwb59+3DlyhVYWFigefPmyW48R0TEwoIoHYQQePz4MY4cOYKAgAAcOXIEb9++TdKmcOHCaNKkCRo3bgwPDw/o6upKlJaIKHNoa2ujWbNmqF27dq78tZaIMgcLC6KvUKvVuH37Nk6dOqV5vHjxIkkbY2Nj1K5dG/Xq1YOnpydKlCjBu2ATERFRnsPCgugLHz58wOXLl3HhwgWcPXsWp0+fxrt375K0USgUqFq1qqaQqFKlCrS1+VEiIiKivI3fhijPio+Px+3bt3Hx4kVcvHgRFy5cwJ07d5LdYMnQ0BDu7u7w8PBAjRo14Orqyqs3EREREf0HCwvKEyIiInD9+nVcv34d165dw/Xr13Hnzp0Ubzzn4OAAV1dXVK1aFR4eHnBxceFVaIiIiIi+gYUF5SqxsbF4+PAhgoKCkhQSz58/T7G9qakpqlSpAjc3N7i6usLV1RW2trY/ODURERFRzsfCgnKk8PBw3L17N9kjODgYarU6xWkKFy6M8uXLw8XFRfNvoUKFeKI1ERERUSZgYUHZkkqlwsuXL/H48WM8fvwYwcHBmv/fv38fERERqU5ramqKkiVLomzZspoColy5crwhIhEREVEWYmFBkoiLi8OLFy/w/PlzPHv2DM+fP8eTJ080BcSTJ09SPP/hS46OjihZsmSyh7W1NY9CEBFRjjRp0iTs2bMH165dAwB07twZkZGR2LVr13fPM3Eee/bsyZyQX7F69Wps27YNhw8fzvJl1apVCy4uLvD19f3ueRw/fhy1a9fGu3fvYGZmlmIbPz8/DB48WHPfqsmTJ+Pvv/9Oto1+xPr9Hvv378f48eMRGBiY5fegYWFBmSohIQFv3rzBq1evNI/Q0FBN8ZD47+vXr785L21tbTg6OsLJyQmFCxdG4cKF4eTkhGLFiqF48eK8MhMRUS7WuXNnrFu3Dr169cLy5cuTjOvbty+WLVsGHx8f+Pn5JRl39uxZeHh4wNPTE4cOHUoy7smTJ3ByctI8NzMzQ9myZTF16lTUrFkzy15LRixcuDDZ1QpTk/j6rl69ChcXl++aR0bExcVhwoQJ2Lp1a5Yv60dq3bo1GjZsmOr4/67fzCh4vvT8+XPN96C7d+8mG5/aj6lbtmxBmzZt0LhxY0yYMAGbN29Ghw4dMiVTalhY0FcJIfD+/Xu8evUKgYGBePfuXZKiIfERFhaGV69eISIiIs07Lz09PRQsWFDzKFSoEIoUKaIpJAoWLAgtLa0sfoVERJRd2dvbY+vWrViwYAH09fUBfL5Ix5YtW1CoUKEUp1mzZg0GDBiAVatWISQkJMV2AQEBKF26NF6/fo0xY8agYcOGuHXrVpKiIyOUSmWmXU3Q1NQUAFI9fzA988hqf/31F4yMjODh4ZGh+cTHx0NHRyeTUmWcvr4+9PX1U90GWb1+/fz80KpVK5w8eRJnzpxB9erVk7VZu3YtGjRokGTYl0dgunTpgsWLF7OwyE0SEhJw4MABBAQEQKVSwd3dHb/++iv09PS+a35CCFy8eBE7d+7Ehw8fUKJECXTs2BGWlpZJ2qnVanz48AFRUVGax9OnT7Fv3z48ffoUMpkMhQoVwvPnz3H58mXExcVBJpNBoVAgNjY23b9yyOVyWFpawsbGBjY2NrC1tYW9vT3s7e1RsGBBzb/6+vrYtm0bLl26BB0dHVSuXBkRERFYuHAhnj59Cjs7O1SrVg1v377FiRMnkJCQgEKFCiEqKgqvXr2CUqmEo6MjypUrh4IFC+Lo0aN49OgRIiIiEBsbCx0dHbi4uGDlypVQqVSYOnUqrl69ivfv30OlUsHY2Bjly5fH0KFDsXz5cpw9exaRkZFQKBQwNzdHhQoVMHDgQFSqVCnZa4yMjMTGjRtx69YtGBgYoG7dunj06BHu3LkDPT09aGlpYe/evXj+/DnUajVMTU3h6emJrl27YunSpbh9+zaio6OhUCigVCqhq6sLKysryGQyfPjwAUqlEvny5YOzszPy5cuHuLg4eHp6YtmyZQgNDdW8xnv37iE0NBRCCLi4uKB48eKIi4tDQkICypYtiw4dOvywPyjpFR8fj127duHUqVOQyWSoVasWmjVrxkv7Eq5evYpt27bh3bt3KFKkCDp16gQLCwupY5EEKlasiMePH2PXrl1o3749AGDXrl2wt7dH4cKFk7WPjo7G9u3bcenSJYSFhcHPzw8TJkxI1s7CwgK2trawtbXFn3/+iYIFC+Lw4cPo1atXsraJ3WD8/PwwcuRIhISEwMPDA2vWrIG9vT2A/3VfGjhwIKZNm4YnT55ApVIhKioKI0aMwJ49exAbG4vKlStjwYIFKF++vGb+M2fOxIIFCxATE4NWrVrBysoqyfL/2xVKrVZjzpw5WLlyJZ49ewYbGxv06tULY8eO1RRGFSpUAADUrFkTx48fT9ZVJy4uDiNGjMDWrVsRFRWlyVWlShUA/+seFBAQgN9++w137tyBi4sL1q5dixIlSqS6vbZu3YqmTZummL9ChQpYsmQJYmNj0bZtWyxevFhTPNSqVQtlypSBjo4O1q9fj9KlS+PEiRM4ceIERowYgevXr8Pc3Bw+Pj6YNm1akpvSJiQkoH///ti4cSO0tLTQp08fTJ06VfMr/saNG+Hr64t79+7B0NAQderUga+vL6ytrZPkPHPmDMaMGYN79+6hfPnyWLVqFcqWLZvkPZDYFeq/vly/nTt31mRfuHAhAODx48fw9PRE7969MXz4cM10t27dQrly5fDgwQMUKVIkxXkLIbB27VosXboUBQsWxOrVq1MsLMzMzL56VcumTZti4MCBePz4cYqfnUwjJLZkyRLh6OgodHV1RcWKFcXJkye/2v748eOiYsWKQldXVzg5OYlly5ala3nv378XAMT79+8zEjvd7t27J4oUKSYACCPTQsLErLAAICytrMXZs2c17dRqtfj06ZOIiIgQz549E3fv3hVXrlwRp06dEv/++6/YtWuX2Lhxo/D19RXFixcXAISWtr5Q6JgIQCZkMplwcnISzs7OokCBAsLY2FgAyPBDR0dHABByuUJoaev9/3CZkMu1hb6hrVAoDAQA0bp1a/Hp06dvro+AgABhZpZPyGQyYZKvqNAzsBSAXAAQ+kYOQlffRrMMAEKupS8MjIsIuZb+F7nkwsDYSWgrTAVkck07AEJbYSIMjAsLmUz7K/OQ/f/jf8vV0bMWAIRMrtC08fb2Fh8/ftRk37Ztm9DXNxRyubYwNS8u9AysPk8j0xJGpoWFTEv//+f5OZ9C1+J/y/v/nPqGhYSugd3n4TK50NG3FboG+f9/PgqhZ1Dg8zxkWgKAyGdRROzZs0fo6+sLbYWRMDQpLORy3c+vVcfs/1/H57Y6uhbC2Kzo521jYCh27NiRJe/pjAgMDBR2dgUEAGFs5iSMTR0EAGFv7yBu3rwpdbxk4uPjxZ49e0R8fLzUUXK1mJgY0bx5CwFA6BmYC1PzEkJbW09oayuEr68vt8F3+PTpk7hz506S/bJarRYfP35M9yMqKko8f/5cREVFfdf0Hz9+FGq1Os3ZfXx8RLNmzcT8+fNF3bp1NcPr1q0rFixYIJo1ayZ8fHySTLN69WpRuXJlIYQQ+/btE46OjkmWGRwcLACIq1evaoa9fftWABCLFy9OMcfatWuFQqEQlStXFmfPnhWXL18Wrq6uolq1apo2EydOFIaGhqJ+/friypUr4vr160KtVovq1auLJk2aiEuXLon79++LYcOGCQsLCxERESGE+Pz3REdHR6xcuVLcvXtXjB07VhgbG4vy5csnWw8qlUq8e/dOjBgxQuTLl0/4+fmJhw8filOnTomVK1cKIYS4ePGiACACAgJEaGioZjmJ80g0cOBAkT9/fnHw4EFx+/Zt4ePjI/Lly6dpf+zYMQFAuLm5iePHj4vbt28LDw+PJK85JWZmZmLr1q1Jhvn4+AgjIyPRunVrcevWLbF//35hZWUlxowZo2lTs2ZNYWRkJEaMGCHu3r0rgoKCxPPnz4WBgYHo27evCAoKErt37xaWlpZi4sSJyaYbNGiQuHv3rti4caMwMDAQK1as0LRZvXq1OHjwoHj06JE4d+6cqFq1qvD29taMT3ytzs7O4vDhw+LGjRuicePGwtHRUbO/Wbt2rTA1NdVsgwkTJqS4jYQQIjIyUri7u4sePXqI0NBQERoaKhISEsT06dNFqVKlkqybIUOGiBo1anx1nR45ckTY2tqKhIQEcevWLWFoaCiioqKStAEgdu/e/dX5CCGEtbW18PPzS3FcSvuKROn57ixpYbF161ahUCjEypUrxZ07d8SgQYOEoaGhePr0aYrtHz9+LAwMDMSgQYPEnTt3xMqVK4VCoRA7d+5M8zKlKCyioqJEgQL2wsjUQZStvkzks64qTCxchIFxYSHX0hMymUxYWloKIyMjIZfLM6UQSOmhUCg0hYa2jqkwzldWWNjWEDq6VgKQCQvbGqJw2SGiZKWpwrnKTGFj3+jzH3g9fbFnzx7h5rVOVG98XFRvfFyU91jx/1/ELYVb/f3C3fuwKFJ2qJDLtcWAAQO+uj7u3LkjdPX0RT7rKqJS7c2iQq11Qq6lJ0wtK4lKtTeL6o2Pi2qNjgnr/1++o3NvUdX7kKje+Lio6v2vcCzVVwAykb9wK+HmtU/o6FoIAyNHYWZVRci19ETxCuNEtYYBonrj48LVa6+wc/pFABBFXUb//zwOCQfn3prCwtSysqhUZ4tmuWWrLRa6+rZCR89SyGQ6Qi7XFr/80lIIIcTJkyeFXEtLWBWoI6rU+0szTSnXWUJbx0zoGRYUgExY5q+dZHzR8qMEZFrCOF9pUbHWBs16LPfTcqFvVEjo6tsItwYH/3+9OgqFroXQ0jYShqYlRIWafsKpZBuxZ88eUaryCOHufVhUb3xcuDU4KOyLdxYAhK6+jdBWmIpSrrNFtUbHRPXGx0XlejuFVf7aQq6lJU6fPv0j3uppEhoaKszymQsTc2dRoeZazbpwqbFKmJgVFVZWNiI8PFzqmEmwsPgx2rZtJ7QVeqKYy1jNZ9jNa5+wc2op9PX1uQ2+Q0pfFj5+/Jhlf2e+9fjyR5pvSfyy9ubNG6GrqyuCg4PFkydPhJ6ennjz5k2KhUW1atWEr6+vEEIIpVIpLC0thb+/v2b8fwuLjx8/il69egktLS1x48aNFHOsXbtWABDnz5/XDAsKChIAxIULF4QQnwsLhUIhXr9+rWlz5MgRYWJiImJjY5PMr0iRIuLPP/8UQgjh7u4uevfunWS8m5tbqoVFSEiI0NXV1RQS/5VS4fTlPBJfs0KhEJs2bdKMj4+PF/nz5xezZ88WQvzvy3ZAQICmzYEDBwSAVH88fPfunQCQ7AdiHx8fYW5uLqKjozXDli1bJoyMjIRKpRJCfC4QXFxckkw3ZswYUaJEiSSF4ZIlS5JN5+zsnKTNb7/9JpydnVPMKMT/iq8PHz4kea1fFkQRERFCX19fbNu2TQiRvsIiMdegQYOSLPfly5dCS0tL856Jj48XVlZWqX7RT9SuXTsxePBgzfPy5csn2/6fv6vpCUNDwySPR48eJWlXoUIFMWnSpBSXk1mFRdaeGv4N8+fPR7du3dC9e3c4OzvD19cX9vb2WLZsWYrtly9fjkKFCsHX1xfOzs7o3r07unbtirlz5/7g5Omzfv16vAx9iRKVZsIknzMiwwMRFXENMR8eQ6363NUoPDwcHz9+TNJ/T0dHB2ZmZihQoACKFSsGFxcXVKtWDW5ubgAAY/NysHVojoJF28OhZA8ULjMYxcqPgaGxE0o6l8KVK1fw8OFDvH79GrGxsYiLi0OBAvYwt3GHq+celKu+GE6lByI+LhyOzr1QsvIU2Dk0g4WdB8xtqqJo+RGwzF8PMvnn8xwMDP/XT9XItDhKu82GMu4dXj//F3ItHdg6NEXBYp2xfPmfePPmTarrY8GCBZBrGaFEpWnQM8yPl493QFvbCM5VfoeeYX4AgFoVi4jQ48hfuBUKFGkDLa3P3cW0tHRRoHArFCjcGq9CDiD06d9Qxr9H4bKDEfnmEpxK94dVgXqQyT8fJlXomMCpVH+YWbnh+YMNEEJAS0sPBYu0gZ3TL5DJ5ChecTz0DOwAfD4BysS8LJyr/I742HBYF/SEWp2Av/7aibt37+L332fAyLgwirmMhY6ehWaafNZuKF5hLGKjX8DA2BHFK4xLMj7mw2NoaxuglOts6BvZa9aFsVlJlHKdhbjYN3jz/PD/1mt8JNSqOJR2mw2FjhlePTsIALCxbwi51udDx9raBihUvDPMrFwR9+kVSlQcj3zWrprDv7p6lijmMhaGxk6YMWPmd713s8Ly5csR/fETSlaeAQPj//VnNjQpihKVZ+Ht23dYvXq1hAlJCo8ePcKWLZvhULIfrAt6aj7D2jrGcCrVD+Y2n/d74gecgErZi6WlJRo1aoR169Zh7dq1aNSoUbIuvwBw7949XLx4EW3atAHw+QIgrVu3xpo1a5K1rVatGoyMjGBsbIx9+/bBz89P0+0lJdra2qhcubLmecmSJWFmZoagoCDNMAcHhyTdmAIDA/Hx40dYWFjAyMhI8wgODsajR48AAEFBQXB3d0+yrP8+/9L9+/cRFxeHunXrptrmWx49egSlUpmkO41CoYCrq2uS1wMA5cqV0/zfzu7z38nULr7y6dMnAEixe3f58uWTXHDF3d0dHz9+xLNnzzTDvly/wP/WzZcnJlevXh0fP35MctPbqlWrJmnj7u6OBw8eQKVSAfjctbJZs2ZwcHCAsbExatWqBQAICQlJsrwv17u5uTlKlCiRbH1khJ2dHRo1aqR5P+7fvx+xsbH49ddfU50msQvcl+dFdOjQIcX39IIFC3Dt2rUkj8Sueon09fURExOTSa8oZZKdYxEfH4/AwECMGjUqyXAvLy+cPXs2xWnOnTsHLy+vJMPq16+P1atXp3qiVFxcHOLi4jTPo6KiAHw+sepblzPNLPv27YedfXWYmNoCEChZYThkcm1oaelBrqWLVyEHoSN/hH8PHYKBgQEMDQ2hr6+fal/z33//HffuP4GLxzzNH98v6ekp8PDGbFhZWcHGxkYz/N69e3j6NBglKk6Erg4ACLx5dhT6+vqwL9IQ2orkf7AdijVD8M0rAACd/4zXUVjDrlANRL+7AJ3iPwMAChVtjDf/1959x0Vx9H8A/+zdcQXujt4EREEE7CgWDLEES0xsKfZEVCwYbPhLVCyxRoIx0ZjniUmMouYRzeuxGzTRR0U0msSGPRYsGAVRaUc5uOPm9wfeynEHUj3F7/v18iU7OzM7O7Nzt3O7O5uyCXv37sXw4cPLqY94uDV6GzKpGABDfvZJNGzydBkAMjPPQ2yhQ8Mm/Y22CwAePv2QkboLuRmJcPXsiqKC67CS28K9UQ8IhMbxGzV9B1fPLIROcw8yK7eSsvr0Q1ZaPLT51yC3MvxAE9s3hqNrOwgFBbCS2wIoxtatW5GYeASe/hMhEQv4surZO7WATCaFZ9N3jdYXZJ+Ce+M3n3ywlqlHaxe4egQjL/MPiH0GQGzhiAYNX0du9nVYWSnx8P5BSCUik20AAFZWSqDYE46ubcFxZdcL4ebVD4cPf4/c3FxIJBKj9M/b7t2/wNWzB6ysrGFUFxZ2cPXshl279iAyMtI8BTRB/1nxvD4zXkW7du2CQmkLt8Y9ITTRh90bvw2g5HPMz8/veRfvpaXRaMAYg06n43+4kkql/HdhVTDGoFKpoFAoqj2lt1QqrfRDyKzkrgrodDqMGjUKU6ZMAQB888030Ol0BusB4Mcff4RWq4Wbm5tBHhYWFnj8+DFsbW35uJs3b0azZs1gY2PDP79TXrn04aW3VTp/fVmsrKwM1hcXF8PV1RWHDh0yytPGxoaPW7pt9HmW3a7+n/6kvWyasmU1lae+rPoT7rL7YyqtUCg0KAdQ8kyDqW3b2tqC4zg8fvy4wv0pu2/6vy0tLcstj56psle0H/n5+ejVqxd69uyJjRs3wtHRESkpKejTpw/UarXBvlZUp2XroLw2KrvfZfMbM2YMQkND8eWXX2LdunUYPHhwhX1i06ZNUKvV/A/KpfO9ePEimjVrxoc7OTmZfHaidN4ZGRlwcHAodz8ZY9BoNEYT51Tlu89sA4tHjx6huLjY4MQXAJydnZGWlmYyTVpamsn4Wq0Wjx494kfTpUVHR2PhwoVG4fv3739u05VOnBj+5K/sJ/93LBOj5MPy6tWrlcqvTZs2WB/7PYC8cmIEANiM06dPG63ZvHlzmbL0evJPVyqsNA8AJSPjicNNfBGFTi2TH4BxJdvYu3evydJ99923hmlCvzfOA74Aypa1NCtg4uYyYT0BqJ/8K8vPRH7WwEcVbCN0nlFQXFxcBWUCEFZOfqFfVZwudLrh+tBppZYDUXEbTHryR3knCl0BdMXBgwfLWf98zZ+vr9dy6gIfASj/+DGnAwcOmLsI9Za3tzd+2hiL8vuwDwDwL8oklSMSieDi4oLc3FwUFRXVOL+yJ89VpVKpKh1Xo9FAq9UiJycHnTt35n8kDAoKQk5ODrRaLTQaDf/3xo0bsWTJEnTv3t0gn9DQUKxduxbjx49Hbm4ugJJfpPVXF541yFKr1dBqtThy5Ag/mcf169eRlZUFDw8P5OTkoLCwkH9YW8/X1xdpaWlQq9UmZ6bKycmBj48Pjh49ioEDB/Lhx48fN8hLXw8qlQre3t6QyWSIj4/HyJEjjfLU15F+ohZTdenk5ASxWIwDBw7wv5ZrNBqcOnUK4eHhyMnJ4X/VVqlU/HsP8vJKzjlyc3PLrTNfX1+cPXsWnTp1Mth2UlISHjx4wM/slZCQALlcDqVSybdfUVGRQb7e3t7Ys2cPsrOz+YHsoUOHoFAooFAo+HQnTpwwSJeYmAhvb2/k5eUhKSkJjx49wuzZs+Hu7g4AOHr0KL8/pff18OHDeOeddwCUXCm4du0aP2GMfiIb/fFbVFRkso30ywKBAAUFBUb1FBwcDEtLS6xcuRK//vor4uPjKzz+1qxZg0mTJmHYsGEG4bNmzcL333+PxYsX82GmtleaWq1GcnIymjZtajJeUVERCgoKkJiYCK1Wa7CuKlc5zD4rVNlfPRhjFf4SYiq+qXC9qKgoTJ8+nV/OycmBh4cHevXq9dzexBwREYHtOw+g5Ws/guOMp0+9cnImWvhZY+/e+Erl95///AeTJk1C6y5rIZUZzwBw99p6ZKfvQ3LyDYNLkjk5OWjSxAdOnkPh5jUYAJDx4ASunV2M5p2+hMLG3yivtJRf8ODWeqxbtxar45Qo0jytZ8Z0OHd0HOS2zdCk5f+VbOPxOVw+GYX4+HgEBwebLH9w8Ou4ly5D04D5AIALx6fAQmILv3ZPB4D5qls4/3sEmraZAzsX49kPMh4cx7WzS2DjEAh1QSrcvT/AjfMxaBW8GpZyT6P495J/xj83NqHdG3EQWcgBAI9Tj+L6uWiTaXTFhTiTMBI2Th3w6F7JCfmaNWswe/ZcCKTt0Lj5JKNtFBVm4kzCSDi79zZaf/mvWWBMh+YdlxmlY6wYSYlhUNq3gXeLaWBMh6TEMBRrCxAYsgU5Gedx68JCrFu3zqgNAODa2c+Qmf4n2nb/CRZia6P8b15aBa7oHP7++3KdvxinMgYNGowTf91Es44rTfbnSyfC0eONQGzYsN48BTRBo9HgwIED6NmzJ81aVUd27dqFkSNHotVr/za4RU7v0b1tWDy7Bzp27EgzRFWBWq3G3bt3IZfLqz0DoV5tXLGoCgsLC4hEIv67+vLlywDAL4tEIlhYWECpVGLnzp3IysrCRx99ZDQT3qBBg7B582Z8/PHHkMtLPv+trKwqfQ4glUphYWGB2bNnY+XKlbCwsMDUqVPRqVMnfhAjkUggFAoN8uzfvz+CgoIwcuRIREdHw9fXF/fv38e+ffswYMAABAYGIjIyEqNHj0ZQUBCCg4MRFxeHv//+G15eXnxe+npQKBQAgE8++QQLFiyAUqnEa6+9hocPH+LSpUsICwuDpaUlZDIZjh07Bl9fX0ilUlhbWxvUpVKpRHh4OBYsWAA3Nzc0bNgQX3zxBQoKCvDRRx9BqVTyP7wqFAq+HFZWVgDADwhM6dOnD06dOmWwXj/74fTp0zFnzhzcuXMHMTExiIiI4KdDFYlEEIvFBummTZuG7777DnPnzkVERASuXr2KmJgYREZGGqS7d+8eFi5ciPHjx+PMmTNYs2YNvvjiCyiVSvj7+0MsFvPvQ7l48SK++uorg2NAv69ffvkl3N3d4ezsjLlz58LBwQHDhg2DWCyGVCoFx3FQKBRQqVQQi8UG7V32WPX29kZSUhIyMjIgl8thZ2fHf/+OGjUKixYtQpMmTdCjR49yj7ukpCScO3cOcXFxRldpR4wYgXnz5mH58uX8d1JhYaHRAEChUPDtdubMGUgkEoSEhJj8YV2tVkMmk6FLly5GnxVVucJptoGFg4MDhEKh0dWJ9PR0o6sSei4uLibji0Sicr9oJBKJyds/LCwsntsJwrhx47BmzRrcuroV7t5DDdY9up+AtH/+wsrlWypdnsGDB2PatOm4fu47NA2YZ3A7VL7qNlJubEP4hDH8h5Cevb09Bg4cgC0/b4HcLhgyKzdY2XZCkVaIq0n/RvNOX/LPMgBAYcFDJF/cAKGg5L7JIg1ncFJ77+Z2ZD6+CXe//0ORhkOxNh83Lq2Bu3tDdOvWrdwvnnHjxmL8+PGwdvoLtk4dYe3cG8nnv4StS8kyAIikXhBJvXHtwhq0VLSChfjph422SIXr59dAJGkMe/dBuHhiCqwd06HVSXE16Vv4t/8MAsHTuizIu4ebVzbB1ikIOihQpAE0RTm4fmENCgoKocpOh0jSiI/PGEPK1f9AlZMOCFNQWKiDtY0c77//Pm7cuIElSz6H0qknFDZ+pdLocOPCjyjIz8OdG7uN1ls79ca1s4tge+cIHBp0M6iPf5K3IivjDho2i0KRhsP9m9uRlXG7ZN2tA3B06wkIS+4nLigoQDGz4tMWqR/j4YPzKCrIw7Xza9Ck1f+B454OHlSZV3Dv5l58+umcF+I2KAAYP34cdu16G9a39sPJw3DO7dTbu/DwwTWMG/fdC3kC/zw/N141/fv3h0Jhjevnv4NvuyX8s0QAoM67j39ubAfQA/b29tQGVVBcXAyO4yAQCGr8w4L+SoU+v7rGcZzBtsq+Fbn0+tjYWPTo0QO2trZG+bz//vuIjo5GUlIS7OzsAKBK9SEQCGBpaYmZM2figw8+wD///IPg4GCsW7eOz0P/fVc2z71792LOnDkYO3YsHj58CBcXF3Tp0gWurq4QCAQYNmwYbt26haioKKjVarz33nuYOHEifvvtN4O89f8AYN68eRCLxViwYAHu378PV1dXhIeHQyAQQCwWY9WqVVi0aBHmz5+P119/HQkJCUZ1GRMTA8YYQkNDoVKpEBgYiN9++40/l9LHK11PpsLKGj9+PNq2bQuVSsUP8DiOQ0hICJo2bYpu3bqhsLAQQ4cOxcKFCw3yKXtceXh4YO/evfjkk08QEBAAOzs7hIWFYd68eQbxRo4cCbVajU6dOkEoFGLy5MkIDw8Hx3FwdnbG+vXrMXv2bHzzzTdo27Ytli9fjv79+/P7oc/r888/R2RkJK5fv47WrVtj9+7d/Al22XYu295l6/eTTz5BaGgoWrRogYKCAty6dQuNGjUCAIwdOxbR0dEYM2ZMhcdgbGwsmjVrZnC7k967776LiIgIxMfH4913S25FDwsLM4oXHR3NP3Lw888/Y8SIEfzguiyBQMC/aqDsZ2yVPnOf+Xh3HerQoQObOHGiQZi/vz+bNWuWyfgzZswwetI/PDycderUqdLbNNd0s1FRUQwAs3cOYk0D5jHfdguZo1sPxnECNnToMH6Gg8ravn07EwpFTGnjw7xaRjL/9ktZA6/BTCyWM3//5iwjI8NkugcPHjAvryZMIlUyN+9hzL/9Uubs0Z8BAiaxdGWNm0Uw//ZLmYdPKBNZKBg4IbO2ach27tzJ3Bv3Zr5tF7CmAfOYrVOnkqlCbVsw//ZLWSP/icxK4cYsLeUGM2eYotFo2Ntv92UCgYg5uZfkaaX0YeAEzNG9N/Nrt5j5tJnN5Db+DJyAWUjsmKffOObffinz9BtXMn0rJ2QODXowv8DPmLV9OwaAya39GccJmUzuybyaT2H+7ZcyN+9hTCiyZBwnYu5NPmD+7Zeyhr5jmYXEjoETMk4gNtqutX3bUtO4CphQKGLx8fGMsZLZNNq378hEFlLm4jmQ+QV+xpq0+oTJrX0ZAObk0Z8JRVaME1gYrLdS+vKzUDk0CGG+7RaypgHzmI1jRwaA2TkHG9SrrXMwk8kblRwzLl1Y01bhbOfOnczGrhFr5D+xpI2ajmIWYhsmslAyuW2Lkjqw8WNNWs1gfoFLmIvnQCYSSVnHTkEGs3GYm06nY2PGjCmZDa1Bt5Jjqu2nzN41mAFgkyZNqtKUlM8DzQr1fOzfv5+JxRImt25Uqg8PZxKJkvn5NaM2qIaKZnqpKv2MOFX9vnrZ6WcEMreXpf4HDRrEli5dyi+XnTHpZVYbbXDs2DEmEolYWlpaLZasYunp6czOzo7dvHmz3Dj1arrZtWvXssuXL7Np06YxKysrdvv2bcYYY7NmzWIffvghH18/3WxkZCS7fPkyW7t27Usx3SxjJSdTP/30E2vZsjU/7V7jxt5s5cqVTKvVVivPo0ePst6932RcyRO7zNrGln388ccsMzOzwnQPHz5kU6dOZQqFNQPABAIBa9cukFlZyZn+nQ+AgJ/6Vj/NY4MG7nzZfX39Wbdu3ZhEUvJOCKFQxIYMGcouXrxYqbIXFRWxmJgY5u7ekM/Tzc2DKZU2T6cm5ATMwkL8pBz6cnFP/+aeTs0rk1ny73x4GheM4wSsadOmrHPnzozj43MG+dna2jKh0OLpdvE03muvvWY0UMrNzWVz585lDg5OfBpPz0ZMoVDyywKBoFR5npZVqVQyTiAqE86VWi6V5km4WCLj28DJyZkJSp5OZ5yJ/EUiMR/m4ODE5s2b90INKvSKi4vZ6tWrmY+PL19ef//m7Mcff3zhBhWM0cDiefrrr79Yv379+c8fhcKaTZkyhd2/f5/aoBpoYFFzNLComtu3b7NVq1bxyzSwKKFWq9n169dZ9+7d2fDhw+ugdOX7888/jd4vUlZtDSw4xsw7d9+3336LZcuWITU1FS1atMCKFSvQpUsXACX3od2+fRsJCQl8/CNHjiAyMhKXLl1CgwYNMHPmTISHh5eTu7GcnBxYW1sjOzv7uT1jURpjDBkZGSguLubftFxTKpUKeXl5Vb5FQKPR4PHjx/wUeEDJrWXnz5+Hr68vPDw8kJmZifz8fJw6dQp9+vRBdnY2BAIB7OzswHEcCgsLkZGRAWtr62o9DK/T6fDw4UOIxWJ+xo5Hjx6hoKAAUqkU9vb2YIzh3r17/GwfGo0GKSkpsLW1hVAohKWlJZRKJTIzM5GamgqFQoEHDx5Aq9UiICCAvwWooKAAKSkpkEgkYIwhLy8PTZo0gVQqhVarxd9//w2xWAyZTIaioiI4OzuXe8kQKJkZ4/Hjx5DJZFAqlQbLCoUCqampuHHjBhhjcHR0hLe3NyQSCQoKCnDjxg0oFAqIRCIUFBSUTFn7ZEaNjIwMyGQycBwHiUQCW1tbPHjwAH/99Rf69OkDrVaL7Oxs2NnZITc3F/fu3YNSqYRMJoODgwNyc3OhVqv52w1fZOzJVMscx8He3v653LddHRqNBnv37sVbb71Ft+E8J3l5eVCpVLCzs4NYLKY2qCa1Wo1bt26hcePGNX7GQqfTIScnB0ql8oV4Xut50b91OSsry6zleFnrv+xbv19mNWmD9evXIywsDG3atMHu3bsNZi97EVT0WVGVc2ezDyyeN3MPLF5G9IVuftQG5kX1b37UBtVDA4v6g+rf/OpzG9TWwKJ+1QohhBBCCCHELGhgQQghhBBCCKkxGlgQQggh9dwrdtczIaSKauszggYWhBBCSD2lfx6lKm/OJYS8evSfETV9hs3sb94mhBBCSN0QCoWwsbFBeno6AMDS0rLas6/pdDoUFRVBrVbXuwdXXwZU/+ZXH9uAMYb8/Hykp6fDxsamxrNJ0sCCEEIIqcdcXFwAgB9cVBdjDAUFBfx02OT5ovo3v/rcBjY2NvxnRU3QwIIQQgipxziOg6urK5ycnKDRaKqdj0ajQWJiIrp06UJT/poB1b/51dc2sLCwqLX3XtHAghBCCHkFCIXCGp08CIVCaLVaSKXSenVS9bKg+jc/aoNnqx83iBFCCCGEEELMigYWhBBCCCGEkBqjgQUhhBBCCCGkxl65Zyz0LwDJyckxc0leHhqNBvn5+cjJyaF7Cs2E2sC8qP7Nj9rA/KgNzIvq3/xe1TbQnzNX5iV6r9zAQqVSAQA8PDzMXBJCCCGEEEJeDiqVCtbW1hXG4VhtvcP7JaHT6XD//n0oFIp6NwdxXcnJyYGHhwfu3r0LpVJp7uK8kqgNzIvq3/yoDcyP2sC8qP7N71VtA8YYVCoVGjRo8MwXA75yVywEAgHc3d3NXYyXklKpfKU60ouI2sC8qP7Nj9rA/KgNzIvq3/xexTZ41pUKPXp4mxBCCCGEEFJjNLAghBBCCCGE1BgNLMgzSSQSzJ8/HxKJxNxFeWVRG5gX1b/5URuYH7WBeVH9mx+1wbO9cg9vE0IIIYQQQmofXbEghBBCCCGE1BgNLAghhBBCCCE1RgMLQgghhBBCSI3RwOIVl5iYiH79+qFBgwbgOA47d+58ZpojR46gXbt2kEql8PLywnfffVf3Ba3HqtoGCQkJ4DjO6N/ff//9fApcz0RHR6N9+/ZQKBRwcnLCwIEDcfXq1Wemo35Qe6rTBtQPatfq1avRqlUrfn7+oKAg7Nu3r8I01AdqT1Xrn47/uhcdHQ2O4zBt2rQK41E/MEQDi1dcXl4eWrdujX/961+Vin/r1i289dZbeP3113H27FnMnj0bU6ZMwbZt2+q4pPVXVdtA7+rVq0hNTeX/+fj41FEJ67cjR44gIiICf/zxBw4cOACtVotevXohLy+v3DTUD2pXddpAj/pB7XB3d8fnn3+OU6dO4dSpU3jjjTcwYMAAXLp0yWR86gO1q6r1r0fHf904efIkfvjhB7Rq1arCeNQPTGCEPAGA7dixo8I4M2bMYH5+fgZhEyZMYJ06darDkr06KtMGhw8fZgBYZmbmcynTqyY9PZ0BYEeOHCk3DvWDulWZNqB+UPdsbW3Zjz/+aHId9YG6V1H90/Ffd1QqFfPx8WEHDhxgXbt2ZVOnTi03LvUDY3TFglTJiRMn0KtXL4Ow3r1749SpU9BoNGYq1aspICAArq6uCAkJweHDh81dnHojOzsbAGBnZ1duHOoHdasybaBH/aD2FRcXY8uWLcjLy0NQUJDJONQH6k5l6l+Pjv/aFxERgbfffhs9evR4ZlzqB8ZE5i4AebmkpaXB2dnZIMzZ2RlarRaPHj2Cq6urmUr26nB1dcUPP/yAdu3aobCwED/99BNCQkKQkJCALl26mLt4LzXGGKZPn47g4GC0aNGi3HjUD+pOZduA+kHtu3DhAoKCgqBWqyGXy7Fjxw40a9bMZFzqA7WvKvVPx3/d2LJlC86cOYOTJ09WKj71A2M0sCBVxnGcwTJ78o7FsuGkbvj6+sLX15dfDgoKwt27d7F8+XL6QqmhSZMm4fz58zh27Ngz41I/qBuVbQPqB7XP19cXSUlJyMrKwrZt2xAaGoojR46Ue3JLfaB2VaX+6fivfXfv3sXUqVOxf/9+SKXSSqejfmCIboUiVeLi4oK0tDSDsPT0dIhEItjb25upVKRTp064fv26uYvxUps8eTJ2796Nw4cPw93dvcK41A/qRlXawBTqBzUjFovRpEkTBAYGIjo6Gq1bt8bXX39tMi71gdpXlfo3hY7/mjl9+jTS09PRrl07iEQiiEQiHDlyBKtWrYJIJEJxcbFRGuoHxuiKBamSoKAg7NmzxyBs//79CAwMhIWFhZlKRc6ePftKXnKtDYwxTJ48GTt27EBCQgIaN278zDTUD2pXddrAFOoHtYsxhsLCQpPrqA/UvYrq3xQ6/msmJCQEFy5cMAgbPXo0/Pz8MHPmTAiFQqM01A9MMNdT4+TFoFKp2NmzZ9nZs2cZAPbVV1+xs2fPsjt37jDGGJs1axb78MMP+fg3b95klpaWLDIykl2+fJmtXbuWWVhYsK1bt5prF156VW2DFStWsB07drBr166xixcvslmzZjEAbNu2bebahZfaxIkTmbW1NUtISGCpqan8v/z8fD4O9YO6VZ02oH5Qu6KiolhiYiK7desWO3/+PJs9ezYTCARs//79jDHqA3WtqvVPx//zUXZWKOoHz0YDi1ecfsq6sv9CQ0MZY4yFhoayrl27GqRJSEhgAQEBTCwWs0aNGrHVq1c//4LXI1Vtg5iYGObt7c2kUimztbVlwcHBLD4+3jyFrwdM1T0AFhsby8ehflC3qtMG1A9q15gxY5inpycTi8XM0dGRhYSE8Ce1jFEfqGtVrX86/p+PsgML6gfPxjH25CkTQgghhBBCCKkmenibEEIIIYQQUmM0sCCEEEIIIYTUGA0sCCGEEEIIITVGAwtCCCGEEEJIjdHAghBCCCGEEFJjNLAghBBCCCGE1BgNLAghhBBCCCE1RgMLQgghhBBCSI3RwIIQQkildenSBXFxcc9lW926dcO0adOey7ZeZOvXr4eNjQ2/vGDBArRp06bS6dPT0+Ho6Ih79+7VfuEIIaQUGlgQQkglpaenY8KECWjYsCEkEglcXFzQu3dvnDhxgo/DcRx27txplHbatGno1q0bAKBfv37o0aOHyW2cOHECHMfhzJkzdbELNfLLL78gLS0NQ4cO5cOSk5PxzjvvwNHREUqlEoMHD8aDBw9Mpi8sLESbNm3AcRySkpL48ISEBHAch6ysrDregxdfo0aNsHLlSoOwIUOG4Nq1a9XO08nJCR9++CHmz59fw9IRQkjFaGBBCCGV9N577+HcuXPYsGEDrl27ht27d6Nbt27IyMioUj5hYWE4dOgQ7ty5Y7Ru3bp1aNOmDdq2bVtbxa41q1atwujRoyEQlHx15OXloVevXuA4DocOHcLvv/+OoqIi9OvXDzqdzij9jBkz0KBBg+dd7BpjjEGr1Zpt+zKZDE5OTjXKY/To0di0aRMyMzNrqVSEEGKMBhaEEFIJWVlZOHbsGGJiYtC9e3d4enqiQ4cOiIqKwttvv12lvPr27QsnJyesX7/eIDw/Px8///wzwsLCADz9Jf+3335DQEAAZDIZ3njjDaSnp2Pfvn3w9/eHUqnEsGHDkJ+fz+fz66+/Ijg4GDY2NrC3t0ffvn2RnJzMr9+4cSPkcjmuX7/Oh02ePBlNmzZFXl6eyTI/evQI//vf/9C/f38+7Pfff8ft27exfv16tGzZEi1btkRsbCxOnjyJQ4cOGaTft28f9u/fj+XLlxuE3759G927dwcA2NraguM4jBo1il+v0+kwY8YM2NnZwcXFBQsWLKiwbkeNGoWBAwdi4cKFcHJyglKpxIQJE1BUVMTHYYxh2bJl8PLygkwmQ+vWrbF161Z+fel6DwwMhEQiwdGjR6HT6RATE4MmTZpAIpGgYcOG+Oyzz/h09+7dw5AhQ2Brawt7e3sMGDAAt2/fNirb8uXL4erqCnt7e0RERECj0QAoufXrzp07iIyMBMdx4DgOgPGtUKbExsbC398fUqkUfn5++Pbbbw3Wt2zZEi4uLtixY0eF+RBCSE3QwIIQQipBLpdDLpdj586dKCwsrFFeIpEII0eOxPr168EY48P/+9//oqioCCNGjDCIv2DBAvzrX//C8ePHcffuXQwePBgrV65EXFwc4uPjceDAAXzzzTd8/Ly8PEyfPh0nT57EwYMHIRAI8M477/BXEUaOHIm33noLI0aMgFarxa+//orvv/8emzZtgpWVlckyHzt2DJaWlvD39+fDCgsLwXEcJBIJHyaVSiEQCHDs2DE+7MGDBxg3bhx++uknWFpaGuTr4eGBbdu2AQCuXr2K1NRUfP311/z6DRs2wMrKCn/++SeWLVuGRYsW4cCBAxXW78GDB3HlyhUcPnwYmzdvxo4dO7Bw4UJ+/dy5cxEbG4vVq1fj0qVLiIyMxAcffIAjR44Y5DNjxgxER0fjypUraNWqFaKiohATE4N58+bh8uXLiIuLg7OzM4CSQWH37t0hl8uRmJiIY8eOQS6X48033zQY1Bw+fBjJyck4fPgwNmzYgPXr1/MDzO3bt8Pd3R2LFi1CamoqUlNTK9xPvTVr1mDOnDn47LPPcOXKFSxduhTz5s3Dhg0bDOJ16NABR48erVSehBBSLYwQQkilbN26ldna2jKpVMo6d+7MoqKi2Llz5wziAGA7duwwSjt16lTWtWtXfvnKlSsMADt06BAf1qVLFzZs2DB++fDhwwwA+9///seHRUdHMwAsOTmZD5swYQLr3bt3ueVOT09nANiFCxf4sIyMDObu7s4mTpzInJ2d2ZIlSyrc9xUrVjAvLy+jfJVKJZs6dSrLy8tjubm5LCIiggFg48ePZ4wxptPp2JtvvskWL17MGGPs1q1bDAA7e/as0X5mZmYa5N+1a1cWHBxsENa+fXs2c+bMcssZGhrK7OzsWF5eHh+2evVqJpfLWXFxMcvNzWVSqZQdP37cIF1YWBhf9/ry7Ny5k1+fk5PDJBIJW7Nmjcntrl27lvn6+jKdTseHFRYWMplMxn777Te+bJ6enkyr1fJxBg0axIYMGcIve3p6shUrVhjkHRsby6ytrfnl+fPns9atW/PLHh4eLC4uziDN4sWLWVBQkEFYZGQk69atm8nyE0JIbaArFoQQUknvvfce7t+/j927d6N3795ISEhA27ZtjW5pqgw/Pz907twZ69atA1DyEPTRo0cxZswYo7itWrXi/3Z2doalpSW8vLwMwtLT0/nl5ORkDB8+HF5eXlAqlWjcuDEAICUlhY9ja2uLtWvXYvXq1fD29sasWbMqLG9BQQGkUqlBmKOjI/773/9iz549kMvlsLa2RnZ2Ntq2bQuhUAgA+Oabb5CTk4OoqKjKVk25+w4Arq6uBvtqSuvWrQ2ujAQFBSE3Nxd3797F5cuXoVar0bNnT/4qlFwux8aNGw1uFwOAwMBA/u8rV66gsLAQISEhJrd5+vRp3LhxAwqFgs/Tzs4OarXaIN/mzZvzdVPZ/anIw4cPcffuXYSFhRnsz5IlS4z2RyaTGdwyRwghtU1k7gIQQsjLRCqVomfPnujZsyc+/fRTjB07FvPnz+efC1AoFMjOzjZKl5WVBWtra4OwsLAwTJo0Cf/+978RGxsLT09PkyeuFhYW/N8cxxks68NKPyzdr18/eHh4YM2aNWjQoAF0Oh1atGhhcEsOACQmJkIoFOL+/fvIy8uDUqksd78dHBxMPvjbq1cvJCcn49GjRxCJRLCxsYGLiws/mDl06BD++OMPg9ulgJKT9hEjRhjdrlPRvpva16oonTY+Ph5ubm4G68uWsfRtYTKZrMK8dTod2rVrh02bNhmtc3R05P+uzf3RbxcouR2qY8eOButKD2AAICMjw6AshBBS2+iKBSGE1ECzZs0MHnj28/PDyZMnDeIwxnD69Gn4+voahA8ePBhCoRBxcXHYsGEDRo8ezT+wW12PHz/GlStXMHfuXISEhMDf39/kgOD48eNYtmwZ9uzZA6VSicmTJ1eYb0BAANLS0sqdVcjBwQE2NjY4dOgQ0tPT+Ye8V61ahXPnziEpKQlJSUnYu3cvAODnn3/mH3wWi8UAgOLi4mrvd2nnzp1DQUEBv/zHH39ALpfD3d0dzZo1g0QiQUpKCpo0aWLwz8PDo9w8fXx8IJPJcPDgQZPr27Zti+vXr8PJycko37IDyoqIxeIq1YOzszPc3Nxw8+ZNo+3qB3d6Fy9eREBAQKXzJoSQqqIrFoQQUgmPHz/GoEGDMGbMGLRq1QoKhQKnTp3CsmXLMGDAAD7exx9/jNDQUPj5+aFXr14oKCjADz/8gOTkZERERBjkKZfLMWTIEMyePRvZ2dkGsyFVl35Goh9++AGurq5ISUkxus1JpVLhww8/xOTJk9GnTx80bNgQgYGB6Nu3LwYNGmQy34CAADg6OuL3339H3759+XD9bESOjo44ceIEpk6disjISH4Q1bBhQ6N9BgBvb2+4u7sDADw9PcFxHH755Re89dZbkMlkfLzqKCoqQlhYGObOnYs7d+5g/vz5mDRpEgQCARQKBT7++GNERkZCp9MhODgYOTk5OH78OORyOUJDQ03mKZVKMXPmTMyYMQNisRivvfYaHj58iEuXLiEsLAwjRozAF198gQEDBmDRokVwd3dHSkoKtm/fjk8++YTf12dp1KgREhMTMXToUEgkEjg4ODwzzYIFCzBlyhQolUr06dMHhYWFOHXqFDIzMzF9+nQAJQ+Xnz59GkuXLq18RRJCSBXRwIIQQipBLpejY8eOWLFiBZKTk6HRaODh4YFx48Zh9uzZfLzBgweDMYbly5djzpw5kEqlCAgIwNGjR+Hp6WmUb1hYGNauXYtevXoZnYRXh0AgwJYtWzBlyhS0aNECvr6+WLVqFf9yPgCYOnUqrKys+JPM5s2bIyYmBuHh4ejcubPRLUJAyW01Y8aMwaZNmwwGFlevXkVUVBQyMjLQqFEjzJkzB5GRkVUqs5ubGxYuXIhZs2Zh9OjR/IxZ1RUSEgIfHx906dIFhYWFGDp0qME0tYsXL4aTkxOio6Nx8+ZN2NjYoG3btgbtaMq8efMgEonw6aef4v79+3B1dUV4eDgAwNLSEomJiZg5cybeffddqFQquLm5ISQkpMJbzMpatGgRJkyYAG9vbxQWFhrMGlaesWPHwtLSEl988QVmzJgBKysrtGzZ0uCt5bt27ULDhg3x+uuvV7oshBBSVRyrzKcWIYSQV96DBw/QvHlznD592uQg6UUwatQoZGVlmXz7+ausQ4cOmDZtGoYPH27uohBC6jF6xoIQQkilODs7Y+3atQazS5EXX3p6Ot5//30MGzbM3EUhhNRzdMWCEEJIvUFXLAghxHxoYEEIIYQQQgipMboVihBCCCGEEFJjNLAghBBCCCGE1BgNLAghhBBCCCE1RgMLQgghhBBCSI3RwIIQQgghhBBSYzSwIIQQQgghhNQYDSwIIYQQQgghNUYDC0IIIYQQQkiN0cCCEEIIIYQQUmP/D6mt3LYcvF+8AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.io import loadmat\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.preprocessing import StandardScaler\n", "\n", "# === 1. Load and prepare data ===\n", "\n", "# Load .mat files\n", "suv_file = \"../data/suv_percentilesSLOthenUWM.mat\"\n", "flags_file = \"../data/flags_combined.mat\"\n", "\n", "suv_data = loadmat(suv_file)\n", "flags_data = loadmat(flags_file)\n", "\n", "# Extract data\n", "suv = suv_data['lung_SUVperc_COMBINED'][0:58, :, :] # SUV shape: (58, patients, percentiles)\n", "flags = flags_data['flags'][0:58, 3] # Binary AE flag (0 or 1)\n", "\n", "# Choose SUV percentile (94th percentile, index = 94)\n", "p = 94\n", "X = np.nanmax(suv[:, :, p], axis=1).reshape(-1, 1) # Shape (58, 1)\n", "y = flags.flatten().astype(int) # Shape (58,)\n", "\n", "# Optional: Standardize the input\n", "scaler = StandardScaler()\n", "X_scaled = scaler.fit_transform(X)\n", "\n", "# === 2. MAP Logistic Regression ===\n", "\n", "# Gaussian prior on coefficients: β ~ N(0, τ²)\n", "tau_squared = 1.0\n", "C = 1 / tau_squared # C is inverse of regularization strength in scikit-learn\n", "\n", "# Initialize logistic regression with L2 penalty (MAP estimation)\n", "model = LogisticRegression(penalty='l2', C=C, solver='lbfgs')\n", "model.fit(X_scaled, y)\n", "\n", "# === 3. Output MAP Estimates ===\n", "\n", "print(\"MAP Estimate: Intercept (β₀) =\", model.intercept_[0])\n", "print(\"MAP Estimate: Coefficient (β₁) =\", model.coef_[0][0])\n", "\n", "# === 4. Optional: Plot decision boundary ===\n", "\n", "# Generate predictions for plotting\n", "x_vals = np.linspace(X.min(), X.max(), 200).reshape(-1, 1)\n", "x_vals_scaled = scaler.transform(x_vals)\n", "probs = model.predict_proba(x_vals_scaled)[:, 1]\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.scatter(X, y, c=y, cmap='coolwarm', edgecolor='k', label='True labels')\n", "plt.plot(x_vals, probs, color='black', label='MAP prediction (probability AE)')\n", "plt.axhline(0.5, color='gray', linestyle='--')\n", "plt.xlabel('SUVmax (94th percentile)')\n", "plt.ylabel('Probability of AE')\n", "plt.title('MAP Logistic Regression (with Gaussian Prior)')\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 38, "id": "cbf195fe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Collecting pymc3\n", " Using cached pymc3-3.11.6-py3-none-any.whl.metadata (15 kB)\n", "Requirement already satisfied: arviz>=0.11.0 in c:\\users\\zahra\\anaconda3\\lib\\site-packages (from pymc3) (0.21.0)\n", "Requirement already satisfied: cachetools>=4.2.1 in c:\\users\\zahra\\anaconda3\\lib\\site-packages (from pymc3) (5.3.3)\n", "Collecting deprecat (from pymc3)\n", " Using cached deprecat-2.1.3-py2.py3-none-any.whl.metadata (1.6 kB)\n", "Requirement already satisfied: dill in c:\\users\\zahra\\anaconda3\\lib\\site-packages (from pymc3) (0.3.8)\n", "Collecting fastprogress>=0.2.0 (from pymc3)\n", " Using cached fastprogress-1.0.3-py3-none-any.whl.metadata (5.6 kB)\n", "Collecting numpy<1.22.2,>=1.15.0 (from pymc3)\n", " Using cached numpy-1.22.1.zip (11.4 MB)\n", " Installing build dependencies: started\n", " Installing build dependencies: still running...\n", " Installing build dependencies: finished with status 'done'\n", " Getting requirements to build wheel: started\n", " Getting requirements to build wheel: finished with status 'error'\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " error: subprocess-exited-with-error\n", " \n", " × Getting requirements to build wheel did not run successfully.\n", " │ exit code: 1\n", " ╰─> [33 lines of output]\n", " Traceback (most recent call last):\n", " File \"C:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\pip\\_vendor\\pyproject_hooks\\_in_process\\_in_process.py\", line 353, in \n", " main()\n", " File \"C:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\pip\\_vendor\\pyproject_hooks\\_in_process\\_in_process.py\", line 335, in main\n", " json_out['return_val'] = hook(**hook_input['kwargs'])\n", " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", " File \"C:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\pip\\_vendor\\pyproject_hooks\\_in_process\\_in_process.py\", line 112, in get_requires_for_build_wheel\n", " backend = _build_backend()\n", " ^^^^^^^^^^^^^^^^\n", " File \"C:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\pip\\_vendor\\pyproject_hooks\\_in_process\\_in_process.py\", line 77, in _build_backend\n", " obj = import_module(mod_path)\n", " ^^^^^^^^^^^^^^^^^^^^^^^\n", " File \"C:\\Users\\zahra\\anaconda3\\Lib\\importlib\\__init__.py\", line 90, in import_module\n", " return _bootstrap._gcd_import(name[level:], package, level)\n", " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", " File \"\", line 1387, in _gcd_import\n", " File \"\", line 1360, in _find_and_load\n", " File \"\", line 1310, in _find_and_load_unlocked\n", " File \"\", line 488, in _call_with_frames_removed\n", " File \"\", line 1387, in _gcd_import\n", " File \"\", line 1360, in _find_and_load\n", " File \"\", line 1331, in _find_and_load_unlocked\n", " File \"\", line 935, in _load_unlocked\n", " File \"\", line 995, in exec_module\n", " File \"\", line 488, in _call_with_frames_removed\n", " File \"C:\\Users\\zahra\\AppData\\Local\\Temp\\pip-build-env-pniegcuk\\overlay\\Lib\\site-packages\\setuptools\\__init__.py\", line 16, in \n", " import setuptools.version\n", " File \"C:\\Users\\zahra\\AppData\\Local\\Temp\\pip-build-env-pniegcuk\\overlay\\Lib\\site-packages\\setuptools\\version.py\", line 1, in \n", " import pkg_resources\n", " File \"C:\\Users\\zahra\\AppData\\Local\\Temp\\pip-build-env-pniegcuk\\overlay\\Lib\\site-packages\\pkg_resources\\__init__.py\", line 2172, in \n", " register_finder(pkgutil.ImpImporter, find_on_path)\n", " ^^^^^^^^^^^^^^^^^^^\n", " AttributeError: module 'pkgutil' has no attribute 'ImpImporter'. Did you mean: 'zipimporter'?\n", " [end of output]\n", " \n", " note: This error originates from a subprocess, and is likely not a problem with pip.\n", "error: subprocess-exited-with-error\n", "\n", "× Getting requirements to build wheel did not run successfully.\n", "│ exit code: 1\n", "╰─> See above for output.\n", "\n", "note: This error originates from a subprocess, and is likely not a problem with pip.\n" ] } ], "source": [ "!pip install pymc3\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "79080223", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import scipy.io as io\n", "import matplotlib.pyplot as plt\n", "from scipy.ndimage import gaussian_filter1d\n", "from sklearn.utils import resample\n", "\n", "# --- Load Data ---\n", "data_path = \"../data/\"\n", "suv_file = data_path + \"suv_percentilesSLOthenUWM.mat\"\n", "flags_file = data_path + \"flags_combined.mat\"\n", "\n", "suv_dict = io.loadmat(suv_file)\n", "flags_dict = io.loadmat(flags_file)\n", "\n", "suv = suv_dict['lung_SUVperc_COMBINED'][0:58, :, :]\n", "flags = flags_dict['flags'][0:58, 3]\n", "\n", "p = 94 # Percentile index\n", "X = np.nanmax(suv[:, :, p], axis=1).reshape(-1, 1)\n", "\n", "# --- Handle missing values ---\n", "valid_indices = ~np.isnan(X).flatten()\n", "X = X[valid_indices]\n", "flags = flags[valid_indices]\n", "\n", "# --- Binning parameters ---\n", "n_bins = 20\n", "bin_edges = np.linspace(np.min(X), np.max(X), n_bins + 1)\n", "bin_centers = 0.5 * (bin_edges[:-1] + bin_edges[1:])\n", "\n", "# --- Bayesian Estimation (Beta posterior mean) ---\n", "alpha_prior = 1\n", "beta_prior = 1\n", "\n", "probabilities = []\n", "counts = []\n", "\n", "for i in range(n_bins):\n", " bin_mask = (X.flatten() >= bin_edges[i]) & (X.flatten() < bin_edges[i + 1])\n", " bin_flags = flags[bin_mask]\n", " n = len(bin_flags)\n", " k = np.sum(bin_flags)\n", " if n > 0:\n", " prob = (k + alpha_prior) / (n + alpha_prior + beta_prior)\n", " probabilities.append(prob)\n", " counts.append(n)\n", " else:\n", " probabilities.append(np.nan)\n", " counts.append(0)\n", "\n", "probabilities = np.array(probabilities)\n", "counts = np.array(counts)\n", "bin_centers = np.array(bin_centers)\n", "\n", "# --- Remove NaNs before smoothing ---\n", "valid = ~np.isnan(probabilities)\n", "probabilities = probabilities[valid]\n", "bin_centers = bin_centers[valid]\n", "counts = counts[valid]\n", "\n", "# --- Smooth with Gaussian filter ---\n", "smoothed_prob = gaussian_filter1d(probabilities, sigma=1)\n", "\n", "# --- Bootstrap 95% Credible Interval ---\n", "n_bootstrap = 500\n", "bootstrap_curves = []\n", "\n", "for _ in range(n_bootstrap):\n", " sample_probs = []\n", " for i, n in enumerate(counts):\n", " k = int(probabilities[i] * n) # Approximate AE count\n", " if n > 0:\n", " beta_samples = np.random.beta(k + alpha_prior, n - k + beta_prior, size=n)\n", " sample_probs.append(np.mean(beta_samples))\n", " else:\n", " sample_probs.append(np.nan)\n", " sample_probs = np.array(sample_probs)\n", " sample_probs = np.nan_to_num(sample_probs)\n", " smoothed = gaussian_filter1d(sample_probs, sigma=1)\n", " bootstrap_curves.append(smoothed)\n", "\n", "bootstrap_curves = np.array(bootstrap_curves)\n", "lower = np.percentile(bootstrap_curves, 2.5, axis=0)\n", "upper = np.percentile(bootstrap_curves, 97.5, axis=0)\n", "\n", "# --- Plot ---\n", "plt.figure(figsize=(12, 7))\n", "\n", "# AE and NC points\n", "plt.scatter(X[flags == 1], np.repeat(1.0, sum(flags == 1)), color='red', alpha=0.6, label=\"AE\")\n", "plt.scatter(X[flags == 0], np.repeat(0.0, sum(flags == 0)), color='blue', alpha=0.6, label=\"NC\")\n", "\n", "# Smoothed Bayesian probability curve and 95% CI\n", "plt.plot(bin_centers, smoothed_prob, color='blue', label='Smoothed AE probability')\n", "plt.fill_between(bin_centers, lower, upper, color='blue', alpha=0.2, label='95% CI')\n", "\n", "plt.xlabel(r'$SUV_{94}$ (max per patient)')\n", "plt.ylabel(\"Probability of AE\")\n", "plt.title(r\"Nonparametric Bayesian Naive Bayes: $P(\\mathrm{AE} \\mid \\mathrm{SUV})$\")\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 5 }