diff --git a/.vscode/launch.json b/.vscode/launch.json new file mode 100644 index 0000000..e0121b7 --- /dev/null +++ b/.vscode/launch.json @@ -0,0 +1,15 @@ +{ + // Use IntelliSense to learn about possible attributes. + // Hover to view descriptions of existing attributes. + // For more information, visit: https://go.microsoft.com/fwlink/?linkid=830387 + "version": "0.2.0", + "configurations": [ + { + "name": "Python Debugger: Current File", + "type": "debugpy", + "request": "launch", + "program": "${file}", + "console": "integratedTerminal" + } + ] +} \ No newline at end of file diff --git a/simulations.ipynb b/simulations.ipynb new file mode 100644 index 0000000..7ce5be2 --- /dev/null +++ b/simulations.ipynb @@ -0,0 +1,266 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n", + "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from distrx.transforms import (\n", + " delta_method,\n", + " transform_data,\n", + " transform_percentage_change,\n", + " transform_percentage_change_counts1,\n", + " transform_percentage_change_counts2\n", + ")\n", + "NREP = 300\n", + "Q = 1.96" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Univariate Simulations" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/55/53rfb8cd7bd3rvs9lvgv5zyw0000gn/T/ipykernel_12398/746050651.py:15: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n", + " mu_txs[i], sigma_tx = transform_data([x_bar], [sigma_hat], \"log\", \"delta\")\n", + "/var/folders/55/53rfb8cd7bd3rvs9lvgv5zyw0000gn/T/ipykernel_12398/746050651.py:16: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n", + " ci_uppers[i] = mu_txs[i] + Q * sigma_tx / np.sqrt(N)\n", + "/var/folders/55/53rfb8cd7bd3rvs9lvgv5zyw0000gn/T/ipykernel_12398/746050651.py:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n", + " ci_lowers[i] = mu_txs[i] - Q * sigma_tx / np.sqrt(N)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CI coverage rate: 288\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# log transformation\n", + "MU = 4\n", + "SIGMA = 1\n", + "N = 100\n", + "LOG_MU = np.log(MU)\n", + "coverages = np.zeros(NREP)\n", + "mu_txs = np.zeros(NREP)\n", + "ci_uppers = np.zeros(NREP)\n", + "ci_lowers = np.zeros(NREP)\n", + "\n", + "for i in range(NREP):\n", + " data = np.random.normal(MU, SIGMA, N)\n", + " x_bar = np.mean(data)\n", + " sigma_hat = np.std(data)\n", + " mu_txs[i], sigma_tx = transform_data([x_bar], [sigma_hat], \"log\", \"delta\")\n", + " ci_uppers[i] = mu_txs[i] + Q * sigma_tx / np.sqrt(N)\n", + " ci_lowers[i] = mu_txs[i] - Q * sigma_tx / np.sqrt(N)\n", + " if (ci_lowers[i] < LOG_MU and LOG_MU < ci_uppers[i]):\n", + " coverages[i] = 1\n", + "\n", + "coverage_pct = (coverages == 1).sum()\n", + "print(\"CI coverage rate: \", coverage_pct)\n", + "\n", + "# plotting\n", + "line_width = 0.75\n", + "cap_size = 2\n", + "marker_size = 3\n", + "plt.figure(figsize=(17, 6))\n", + "for i in range(NREP):\n", + " if coverages[i] == 1:\n", + " plt.errorbar(i, mu_txs[i], elinewidth=line_width,\n", + " yerr=[[mu_txs[i]- ci_lowers[i]], [ci_uppers[i] - mu_txs[i]]],\n", + " fmt=\"o\", color=\"blue\", ecolor=\"blue\", capsize=cap_size, markersize=marker_size)\n", + " else:\n", + " plt.errorbar(i, mu_txs[i], elinewidth=line_width,\n", + " yerr=[[mu_txs[i] - ci_lowers[i]], [ci_uppers[i] - mu_txs[i]]],\n", + " fmt=\"o\", color=\"red\", ecolor=\"red\", capsize=cap_size, markersize=marker_size)\n", + "\n", + "plt.axhline(y=LOG_MU, color='gray', linestyle='--')\n", + "plt.xlabel('SampleID')\n", + "plt.ylabel(\"Mean\")\n", + "plt.title(\"95% CIs using Delta Method SE for log transform\")\n", + "plt.legend([\"True Mean\"], loc=\"upper right\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Bivariate Simulations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Percentage Change\n", + "* the function that currently works as intended calculates percentage change in prevalence rates\n", + " * note: prevalence is analogous to mean, just with binary data\n", + "* the function that simply calculates percentage change in counts does not currently work\n", + " * in my experience, the RV is a function of consistent estimators, counts don't fall into that category\n", + " * not completely certain that the above *must* be the case, perhaps just computing variance incorrectly?\n", + " * tried both the formula in our overleaf and simply $np(1 - p)$ for variance" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True percentage change in proportions: 0.04081632653061229\n", + "10 replications of incidence counts in year 1: [473 507 492 479 491 475 465 509 504]\n" + ] + } + ], + "source": [ + "# parameters for population sizes and prevalence\n", + "Y1_POP, Y1_PREV = 1000, 0.49\n", + "Y2_POP, Y2_PREV = 1050, (Y1_PREV + 0.02)\n", + "\n", + "# simulate incidence from 2 years w/differing aforementioned parameters\n", + "y1_incid = np.random.binomial(Y1_POP, Y1_PREV, size=NREP)\n", + "y2_incid = np.random.binomial(Y2_POP, Y2_PREV, size=NREP)\n", + "\n", + "# true difference in prevalence\n", + "TRUE_DIFF = (Y2_PREV / Y1_PREV) - 1\n", + "print(\"True percentage change in proportions: \", TRUE_DIFF)\n", + "print(\"10 replications of incidence counts in year 1: \", y1_incid[0:9])" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CI coverage rate: 0.95\n" + ] + }, + { + "data": { + "image/png": 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WKuXl5UpOTo5y0003+bZHmy/oOU6h3HXXXQoAZc2aNZr7eM+xM844Q6msrPRt/+yzzxQAyooVK8J+v6NHjyr16tVTFi5c6NvuPQ+mTJnit//8+fMVAEppaamiKIry9ddfKwCUW2+91W8/73VfOw8vKChQ6tevr+zcudNv3wceeEABEHQsiYiInIQ9gYmIiFzqL3/5C7777jtcf/31+Omnn/Djjz/i2muv9Q3JrT2c/KabbsJNN92EwYMHY/DgwZg7dy6efvppfPvttygqKvLt16xZM2zYsAHbt2/HTz/9hDfffBOJiYkoKCjAzJkzkZOTgxdffBGdO3dG48aNMXLkSPz444+mfs/27dvjpJNOwq233oolS5YE9dozQs+ePfHll19iypQpePfdd3XNSdu8eXP07NnTb9uZZ57pNzR67dq1OP3009GpUye//bzTIhhBURTf/7dt24Zvv/0WV1xxBQD49RodPnw4SktLQ06BEI3Nmzdj1KhROPnkk5GYmIjk5GRceeWVqKqqwnfffRf1+wwYMADt2rXDE088gf/+97/4/PPPNaeCeOONN9CoUSNccMEFft+lS5cuaN68ua7pNEaNGuX3/MwzzwQA3++1fv16HD9+PGgIeqtWrTBo0CBfr8utW7fi559/xuWXXw6Px+PbLysry9d7PpLhw4dj165dePnll3HzzTejc+fOeOWVVzBq1KiQvUFvvPFGfP7550GPLl26RPv1fbzpnzBhgl9eUb9+fVx88cX49NNP8fvvv/u95uKLL9b1Gd7zz6tPnz7IysrCBx98AABYt24dfvvtN0ycONHvd62ursb555+Pzz//HMeOHQubhrfffhsAcN1112mm491330VlZSWuvPJKv89JS0vDgAEDgs4fj8cTNHIh8JoOp7KyEvfccw86deqElJQUJCUlISUlBSUlJX5TikSbL8RynGp7++23ceqpp0a1cOSIESOQmJjo970B+H33o0eP4tZbb0X79u2RlJSEpKQk1K9fH8eOHQs5ZUqka27t2rUAgLFjx/rtd8kllyApyX8JnDfeeAPnnHMOTjnlFL9jMWzYML/3IiIiciIuDEdERORSV199Nfbt24e5c+fiscceAwDk5ubi5ptvxn333YcWLVqEff2YMWNQr169oPkeA+dRvffee5GQkIC//e1vvsDiK6+8gv79+2PKlCkYP3582Ip369atUVJSgmPHjvnNNxyt9PR0rF27Fn//+99x++2348CBA8jMzER+fj5mzpyJ5ORk3e8ZaPr06ahXrx6WL1+OJUuWIDExEf3798d9993ntxBbKCeffHLQttTUVN8UBYA6/2t2dnbQfkYt4nbs2DH8+uuvOOOMMwAAv/zyCwDg5ptvxs033xzyNaGGbUeya9cu9OvXD6eddhoWLlyINm3aIC0tDZ999hmuu+46v+8cicfjwVVXXYVHHnkEJ06cwKmnnop+/fqF3PeXX37BwYMHkZKSEvd3Cfy9vNOneNMebq7eU045BWvWrPHbr3nz5kH7NW/ePKrpHQCgTp06uPDCC3HhhRcCUI/xsGHDsGjRIvz5z39G586dffu2bNky4vkYrUjfs7q6GgcOHPCbc1xr/mItWsfG+9ne8zTcnOC//fabX74RmIZ9+/YhMTEx5Gd5eT/n7LPPDvn3wPmX69ati7S0NL9tqampvvnRI5k2bRoWLVqEW2+9FQMGDMBJJ52EhIQETJ48OaZ8IZbjVNu+ffvQunXrqNIe6foAgMsvvxz/+te/cMcdd+Dss89Gw4YN4fF4MHz48JB5QLTXXOD3TkpKCnrtL7/8gtdff10z348lXyMiIpIFg8BEREQuduutt2Lq1KkoKSlBgwYNkJWVhYKCAtSrVw/du3eP+HpFUcIuQLV161bce++9eO+995CcnIz33nsPnTt3xvnnnw9ADXacddZZOHr0KOrXrx/yPYYOHYrVq1fj9ddfx6WXXhrT9zzjjDOwcuVKKIqC//znPyguLsZdd92FOnXq4LbbbtN8XVpamm8xp9r279/vt7hdUlISpk2bhmnTpuHgwYN47733cPvtt2Po0KH48ccf/QJhsTj55JN9gZza9uzZE9f7er355puoqqryLfjl/W7Tp0/HRRddFPI1p512mu7PeeWVV3Ds2DG89NJLyMrK8m3fsmWL7vcC1Llc77zzTixZsgR///vfNffzLijlnYc1UIMGDWL6/FC8QadQCyv+/PPPvmPr3S/UbxjP79q6dWtcc801mDp1Kr7++mu/ILCRIn3PhIQEnHTSSX7ba/d4jobWsWnfvj2AmvP0H//4B3r37h3yPQIDg4FpaNKkCaqqqrBnzx7NILX3c/75z3/6nbdmWb58Oa688krcc889ftv379+PRo0a+Z5Hmy/Ecpxqa9KkScRFNKN16NAhvPHGG5g1a5Zf3ltWVhY0x3y0vOfiL7/84td4WVlZ6QsQe2VkZODMM8/UzC9OOeWUmNJAREQkA04HQURE5HKpqak4/fTTkZWVhV27dmHVqlXIz89HnTp1wr7un//8J37//XfNoAIAFBQUYNKkSb7h7Yqi+A07Pnr0qG+7lry8PDRv3hy33HILfvrpp5D7vPTSS2HT6uXxeHDWWWfh4YcfRqNGjbBp06aw+7dp0wb/+c9//LZ99913YadCaNSoES655BJcd911+O2336Lu0RnOgAED8NVXXwVNZbFy5cq433vXrl24+eabkZ6e7luc7bTTTkNOTg6+/PJL9OjRI+QjXOA0VO8/oCYAV3tBQkVR/KYU0aNFixb429/+hgsuuAATJ07U3G/kyJH49ddfUVVVFfK71A5oB/bC1is3Nxd16tTxW9gPAHbv3o33338f5557LgD1GGdmZmLFihV+5//OnTuxbt26iJ9z5MgR3/UTyDuk3syA1mmnnYYWLVrgueee80v/sWPH8OKLLyI3Nzfuxo9nn33W7/m6deuwc+dOX2NF37590ahRI3zzzTea56lW728v7zQA3tEQoQwdOhRJSUn4/vvvNT9HL61rBFCvk8BFO998882g/C/afCHe4zRs2DB89913US1YGInH44GiKEHf7/HHH/dbXFGP/v37AwBWrVrlt/2f//xn0MKHI0eOxFdffYV27dqFPA4MAhMRkZOxJzAREZFLffXVV3jxxRfRo0cPpKam4ssvv8S9996LnJwc3H333b79du7cicsvvxyXXnop2rdvD4/Hg7Vr12LBggXo3LkzJk+eHPL9n3jiCXz33Xd49dVXfdvOPfdc3HTTTbjzzjvRr18/zJo1C3379g0bUExPT8err76KkSNHomvXrrj++uuRm5vrmyNz+fLl+PLLLzV7rL7xxhtYvHgxLrzwQrRt2xaKouCll17CwYMHMXjw4LDHaMKECRg/fjymTJmCiy++GDt37sT8+fPRpEkTv/0uuOACnH766ejRoweaNGmCnTt3YsGCBcjKykJOTk7Yz4jG1KlT8cQTT2DYsGG466670KxZMzz33HP49ttvAQQPR9fy1Vdf+ebA3Lt3Lz766CM8+eSTSExMxMsvv+z3vQoLCzFs2DAMHToUkyZNQosWLfDbb7/hf//7HzZt2oQXXnhB83O800rcd999GDZsGBITE3HmmWdi8ODBSElJwWWXXYZbbrkFJ06cwGOPPYYDBw7EfGzuvffeiPtceumlePbZZzF8+HDceOON6NmzJ5KTk7F792588MEHGD16NMaMGeNL+8qVK7Fq1Sq0bdsWaWlpvu8TjUaNGuGOO+7A7bffjiuvvBKXXXYZfv31V8yZMwdpaWmYNWsWAPU3u/vuuzF58mSMGTMG+fn5OHjwIGbPnh12agKvrVu3YujQobj00ksxYMAAZGZm4sCBA3jzzTexdOlSDBw4MGhu4V27dgVN3wKoPT3btWsX9Xf0pn/+/Pm44oorMHLkSBQUFKCsrAz3338/Dh48GNXvEskXX3yByZMn4//+7//w448/YsaMGWjRogWmTJkCQJ1/+B//+AcmTpyI3377DZdccgmaNm2Kffv24csvv8S+ffvCBncBoF+/fpgwYQLmzp2LX375BSNHjkRqaio2b96MunXr4i9/+QvatGmDu+66CzNmzMAPP/yA888/HyeddBJ++eUXfPbZZ6hXrx7mzJmj67t5R168+uqrOPfcc9G4cWNkZGSgTZs2GDlyJIqLi9GhQweceeaZ2LhxI+6//360bNnS7z2izRfiPU5Tp07FqlWrMHr0aNx2223o2bMnjh8/jrVr12LkyJE455xzov7eDRs2RP/+/XH//ff7vu/atWuxbNkyv17OenTu3BmXXXYZHnzwQSQmJmLQoEH4+uuv8eCDDyI9Pd0vf7zrrruwZs0a9OnTBzfccANOO+00nDhxAjt27MBbb72FJUuWBB1nIiIix7BrRToiIiKy19atW5X+/fsrjRs3VlJSUpT27dsrM2fOVI4ePeq332+//aaMGTNGadOmjVKnTh0lJSVFycnJUW655Rbl4MGDId977969SuPGjZUXXngh6G/PPvuskpOTo9SvX18ZPHiw8sMPP0SV3j179ii33nqr0rlzZ6Vu3bpKamqq0r59e6WgoED573//69tv1qxZCgBl3759iqIoyrfffqtcdtllSrt27ZQ6deoo6enpSs+ePZXi4uKIn1ldXa3Mnz9fadu2rZKWlqb06NFDef/995UBAwYoAwYM8O334IMPKn369FEyMjKUlJQUpXXr1kpeXp6yY8cO3z7ele63b9/u2zZgwAClc+fOQZ87ceJEJSsry2/bV199pZx33nlKWlqa0rhxYyUvL0956qmnFADKl19+GfZ7eD/b+0hJSVGaNm2qDBgwQLnnnnuUvXv3hnzdl19+qYwdO1Zp2rSpkpycrDRv3lwZNGiQsmTJEt8+H3zwgQJA+eCDD3zbysrKlMmTJytNmjRRPB6P3/d+/fXXlbPOOktJS0tTWrRoofztb39T3n777aD3CPc9Pv/887D7de7c2e/3URRFqaioUB544AHfZ9evX1/p0KGDUlBQoJSUlPj227FjhzJkyBClQYMGCgDf7+D9noHn9Pbt2xUAypNPPum3/fHHH1fOPPNMJSUlRUlPT1dGjx6tfP3110Fpffzxx5WcnBwlJSVFOfXUU5Unnngi5O8f6MCBA8rcuXOVQYMGKS1atFBSUlKUevXqKV26dFHmzp2r/P7770Fp1HpcccUVYT9L67sriqK88sorSq9evZS0tDSlXr16yrnnnqt88sknfvsEXpOReH/n1atXKxMmTFAaNWqk1KlTRxk+fLjfb+W1du1aZcSIEUrjxo2V5ORkpUWLFsqIESP80hsuDVVVVcrDDz+snH766b7fKzc3V3n99deDvus555yjNGzYUElNTVWysrKUSy65RHnvvfd8+0ycOFGpV69e0Gd4P7+29957T+natauSmpqqAFAmTpyoKIr62+bl5SlNmzZV6tatq/zpT39SPvroo6B8R1H05QvRHCctBw4cUG688UaldevWSnJystK0aVNlxIgRyrfffqsoSs05dv/99we9FoAya9Ys3/Pdu3crF198sXLSSScpDRo0UM4//3zlq6++UrKysnzHQFG0r/dQec6JEyeUadOmKU2bNlXS0tKU3r17K+vXr1fS09OVm266ye/1+/btU2644QYlOztbSU5OVho3bqx0795dmTFjRtD9j4iIyEk8ihJm/CURERERCeuaa67BihUr8Ouvv0Yc9k4ki+LiYlx11VX4/PPPDVvIzk2YL6jWrVuHvn374tlnn8Xll19ud3KIiIhsx+kgiIiIiCRw11134ZRTTkHbtm1x9OhRvPHGG3j88ccxc+ZMVwd6iNyM+YJqzZo1WL9+Pbp37446der4TW+kNVUQERGR2zAITERERCSB5ORk3H///di9ezcqKyuRk5ODhx56CDfeeKPdSSMimzBfUDVs2BCrV6/GggULcOTIEWRkZGDYsGGYN28e0tLS7E4eERGREDgdBBEREREREREREZGDRbeUNBERERERERERERFJiUFgIiIiIiIiIiIiIgdjEJiIiIiIiIiIiIjIwbgwnAGqq6vx888/o0GDBvB4PHYnh4iIiIiIiIiIiBxOURQcOXIEp5xyChISwvf1ZRDYAD///DNatWpldzKIiIiIiIiIiIjIZX788Ue0bNky7D4MAhugQYMGANQD3rBhQ5tTQ0RERERERERERE53+PBhtGrVyhebDIdBYAN4p4Bo2LAhg8BERERERERERERkmWimp+XCcEREREREREREREQOxiAwERERERERERERkYMxCExERERERERERETkYJwTmIiIiIiIiIiISGJVVVWoqKiwOxlkguTkZCQmJsb9PgwCExERERERERERSero0aPYvXs3FEWxOylkAo/Hg5YtW6J+/fpxvQ+DwERERERERERERBKqqqrC7t27UbduXTRp0gQej8fuJJGBFEXBvn37sHv3buTk5MTVI5hBYCIiIiIiIiIiIglVVFRAURQ0adIEderUsTs5ZIImTZpgx44dqKioiCsIzIXhiIiIiIiIiIiIJMYewM5l1G/LIDARERERERERERGRgzEITERERERERERERORgDAITERERERERERERORiDwERERERERERERGQJj8cT9jFp0iTL0jJp0iR4PB5ce+21QX+bMmWK5ekxE4PAREREREREREREZInS0lLfY8GCBWjYsKHftoULF/rtX1FRYWp6WrVqhZUrV+L48eO+bSdOnMCKFSvQunVrUz/bSgwCExEREREREREROUh5ebnmo7KyMup9AwOwWvvp0bx5c98jPT0dHo/H9/zEiRNo1KgRnn/+eQwcOBBpaWlYvnw5Zs+ejS5duvi9z4IFC9CmTRu/bU8++SQ6duyItLQ0dOjQAYsXL46Ynm7duqF169Z46aWXfNteeukltGrVCl27dvXbV1EUzJ8/H23btkWdOnVw1lln4Z///Kfv71VVVcjLy0N2djbq1KmD0047LSioPWnSJFx44YV44IEHkJmZiZNPPhnXXXed6cHuJFPfnYiIiIiIiIiIiCw1b948zb/l5OTg8ssv9z1/4IEHNAOQWVlZftMhLFy4EL///nvQfrNmzYo9sSHceuutePDBB/Hkk08iNTUVS5cujfiaoqIizJo1C48++ii6du2KzZs3Iz8/H/Xq1cPEiRPDvvaqq67Ck08+iSuuuAIA8MQTT+Dqq6/Gv//9b7/9Zs6ciZdeegmPPfYYcnJy8OGHH2L8+PFo0qQJBgwYgOrqarRs2RLPP/88MjIysG7dOlxzzTXIzMzE2LFjfe/zwQcfIDMzEx988AG2bduGcePGoUuXLsjPz9d/sKLEIDAREREREREREREJY+rUqbjooot0vebuu+/Ggw8+6HtddnY2vvnmGxQWFkYMAk+YMAHTp0/Hjh074PF48Mknn2DlypV+QeBjx47hoYcewvvvv4/c3FwAQNu2bfHxxx+jsLAQAwYMQHJyMubMmeN7TXZ2NtatW4fnn3/eLwh80kkn4dFHH0ViYiI6dOiAESNG4F//+heDwERERERERERERBSd6dOna/4tIcF/dtibb75Zc1+Px+P3/MYbb4wvYVHq0aOHrv337duHH3/8EXl5eX6B1MrKSqSnp0d8fUZGBkaMGIGnnnoKiqJgxIgRyMjI8Nvnm2++wYkTJzB48GC/7eXl5X7TRixZsgSPP/44du7ciePHj6O8vDxoKovOnTsjMTHR9zwzMxP//e9/9Xxl3RgEJiIiIiIiIiLxlZaqj0CZmeqDiHxSUlJs3zce9erV83uekJAARVH8ttWewqK6uhqAOiVEr169/ParHWwN5+qrr8b1118PAFi0aFHQ372f8eabb6JFixZ+f0tNTQUAPP/887jpppvw4IMPIjc3Fw0aNMD999+PDRs2+O2fnJzs99zj8fje3ywMAhMRERERERGR+AoLgVrDrH1mzQJmz7Y8OURknSZNmmDPnj1QFMXXO3nLli2+vzdr1gwtWrTADz/84JvXV6/zzz/ft8jd0KFDg/7eqVMnpKamYteuXRgwYEDI9/joo4/Qp08fTJkyxbft+++/jyk9RmMQmIiIiIiIiIjEV1AAjBoFVFYCvXoBGzYASUnsBUzkAgMHDsS+ffswf/58XHLJJXjnnXfw9ttvo2HDhr59Zs+ejRtuuAENGzbEsGHDUFZWhi+++AIHDhzAtGnTIn5GYmIi/ve///n+H6hBgwa4+eabcdNNN6G6uhp/+tOfcPjwYaxbtw7169fHxIkT0b59ezz99NN49913kZ2djWeeeQaff/45srOzjTsYMUqIvAsRERERERERkc0yM4Fu3QDv3Jtdu6rPGQQmcryOHTti8eLFWLRoEc466yx89tlnQXMZT548GY8//jiKi4txxhlnYMCAASguLtYVgG3YsKFfYDnQ3XffjTvvvBPz5s1Dx44dMXToULz++uu+z7j22mtx0UUXYdy4cejVqxd+/fVXv17BdvIogRNqkG6HDx9Geno6Dh06FPZEISIiIiIiIqI4VVQAKSlAeTkQMK8mkducOHEC27dvR3Z2NtLS0uxODpkg3G+sJybJnsBEREREREREREREDsYgMBEREREREREREZGDMQhMRERERERERERE5GAMAhMRERERERERERE5GIPAREREREREREREElMUxe4kkEmM+m0ZBCYiIiIiIiIiIpJQYmIiAKC8vNzmlJBZvL+t97eOVZIRiSEiIiIiIiIiIiJrJSUloW7duti3bx+Sk5ORkMD+nk5SXV2Nffv2oW7dukhKii+MK10QePHixbj//vtRWlqKzp07Y8GCBejXr1/IfV966SU89thj2LJlC8rKytC5c2fMnj0bQ4cO9e1TXFyMq666Kui1x48fR1pammnfg4iIiIiIiIiIKB4ejweZmZnYvn07du7caXdyyAQJCQlo3bo1PB5PXO8jVRB41apVmDp1KhYvXoy+ffuisLAQw4YNwzfffIPWrVsH7f/hhx9i8ODBuOeee9CoUSM8+eSTuOCCC7BhwwZ07drVt1/Dhg2xdetWv9cyAExERERERERERKJLSUlBTk4Op4RwqJSUFEN6eHsUiWaO7tWrF7p164bHHnvMt61jx4648MILMW/evKjeo3Pnzhg3bhzuvPNOAGpP4KlTp+LgwYMxp+vw4cNIT0/HoUOH0LBhw5jfh4iIiMgSpaXqI1BmpvogIiISWUUFkJIClJcDycl2p4aIyDZ6YpLS9AQuLy/Hxo0bcdttt/ltHzJkCNatWxfVe1RXV+PIkSNo3Lix3/ajR48iKysLVVVV6NKlC+6++26/nsKBysrKUFZW5nt++PBhHd+EiFyJARciEklhITBnTvD2WbOA2bMtTw4REREREZlLmtmi9+/fj6qqKjRr1sxve7NmzbBnz56o3uPBBx/EsWPHMHbsWN+2Dh06oLi4GK+99hpWrFiBtLQ09O3bFyUlJZrvM2/ePKSnp/serVq1iu1LEZF7FBYC3bsHPwoL7U4ZEblRQQGwcSOwYYP6fMMG9XlBgb3pIiIiIiIiU0gzHcTPP/+MFi1aYN26dcjNzfVt//vf/45nnnkG3377bdjXr1ixApMnT8arr76K8847T3O/6upqdOvWDf3798cjjzwScp9QPYFbtWrF6SCISJu3J3BlJdCrlxpwSUpiT2ASA3uquxeH0xIRkYx4/yIiAuDQ6SAyMjKQmJgY1Ot37969Qb2DA61atQp5eXl44YUXwgaAAXXFvbPPPjtsT+DU1FSkpqZGn3giIm8wraJCfd61KwusJA5ODUBERERERORo0kwHkZKSgu7du2PNmjV+29esWYM+ffpovm7FihWYNGkSnnvuOYwYMSLi5yiKgi1btiCTPZ+IiMgtODUAERERERGRo0nTExgApk2bhgkTJqBHjx7Izc3F0qVLsWvXLlx77bUAgOnTp+Onn37C008/DUANAF955ZVYuHAhevfu7etFXKdOHaSnpwMA5syZg969eyMnJweHDx/GI488gi1btmDRokX2fEkiIiKrsac6ERERERGRo0kVBB43bhx+/fVX3HXXXSgtLcXpp5+Ot956C1lZWQCA0tJS7Nq1y7d/YWEhKisrcd111+G6667zbZ84cSKKi4sBAAcPHsQ111yDPXv2ID09HV27dsWHH36Inj17WvrdiIiIiIiIiIgoSlzXgkgXaRaGE5meSZiJyOW4iAWJjOen+/A3JyIiGfH+RYC6dgXXtSCXc+TCcERERETkTuzoQ0REREEKCoBRo4DKSqBXL3Vdi6QkFg6INDAITERERERCKyxkRx8iIiIKwHUtiHRhEJiIiIiIhMaOPkRERERE8WEQmIiIiIiExo4+RGQWTjdDRERukWB3AoiIiIiIiIjsUFgIdO8e/CgstDtlRERExmJPYCIiIiIiInIlTjdDRERuwSAwERERERERuRKnmyEiIrfgdBBEREREREREREREDsYgMBEREREREREREZGDMQhMRERERERERERE5GAMAhMRERERERERERE5GIPARERERERERERERA7GIDARERERERERERGRgzEITERERERERERERORgDAITERERERERERERORiDwEREREREREREREQOxiAwERERERERERERkYMl2Z0AIiIionBKS9VHoMxM9UFEREREREThsScwERERCa2wEOjePfhRWGh3yoiIiIiIiOTAnsBEREQktIICYNQooLIS6NUL2LABSEpiL2AiIiIiIqfiaEDjMQhMREREQvMW9Coq1OdduwLJyfamiYiIiIiIzFNYCMyZE7x91ixg9mzLk+MIDAITERERERERERGRMDga0HgMAhMRERERERFFgcOTiYiswdGAxmMQmIiIiIiIXItBPdJD9uHJPN+JiNyLQWAiIiIiInIt2YN6ZC3ZhyfzfJeb7EF82dNPJDsGgYmIiIiIyLVkD+qRtWQfnszzXW6yB/FlTz+R7BgEJiIiIiIi15I9qEekB893uckexJc9/USyYxCYiIiIiIiIiEhwsgfxZU8/kewS7E4AEREREREREREREZmHQWAiIiIiIiIiIiIiB2MQmIiIiIiIiIiIiMjBOCcwEREREREREREZqrRUfQTKyLA+LUTEIDARERERERERERmssBCYMyd4+8yZ1qeFiDgdBBERERERERERGaygANi4EdiwQX2+YYP6PD/f3nQRuRV7AhMRERERERERkaEyM9VHRYX6vGtXIDm55jkRWYtBYCIiikhrPi9vwY6IiIiIiIiIxMXpIIiIKKLCQqB79+BHYaHdKSMiIiIiIiKiSNgTmIiIIiooAEaNAiorgV691Pm8kpLYC5jIKUpLgdL9wdvZ25+IiIiIyBkYBCYiooi05vMiImcoLErAnLnB22fNAmbPtjw5REREluCUZ0TkJgwCEzkUCzRERBStgvxqjBqTyN7+RETkKoWFwJw5wdvZCEpETsQgMJFDsUBDRETRyswEMluztz/Fhg3PRCQrTnlGRG4i3cJwixcvRnZ2NtLS0tC9e3d89NFHmvu+9NJLGDx4MJo0aYKGDRsiNzcX7777btB+L774Ijp16oTU1FR06tQJL7/8splfgcgSBQXAxo1qQQZQ/924Ud1ORETkZKWlwKZNwY9QgUqKHxcPJSJZZWYC3bqpjZ+A+m+3bgwCE5EzSRUEXrVqFaZOnYoZM2Zg8+bN6NevH4YNG4Zdu3aF3P/DDz/E4MGD8dZbb2Hjxo0455xzcMEFF2Dz5s2+fdavX49x48ZhwoQJ+PLLLzFhwgSMHTsWG7yRMyJJsUBDRERuxaCktdjwTERERCQ+j6Ioit2JiFavXr3QrVs3PPbYY75tHTt2xIUXXoh58+ZF9R6dO3fGuHHjcOeddwIAxo0bh8OHD+Ptt9/27XP++efjpJNOwooVK6J6z8OHDyM9PR2HDh1Cw4YNdXwjIvNVVAApKUB5OYf2CkHyH0Ty5FMkgv/AgidPTgEHVfRjHG36vNMThBrey8ZQ84h+/kQie/opPnp/f9nPF9nTb/QXkO14yJ5ew9Mv2wEhXfjzhqcnJinNnMDl5eXYuHEjbrvtNr/tQ4YMwbp166J6j+rqahw5cgSNGzf2bVu/fj1uuukmv/2GDh2KBQsWaL5PWVkZysrKfM8PHz4c1ecTERERkfm8wV7OcUyhaM1hnJFhfVqIiIiIrCJNEHj//v2oqqpCs2bN/LY3a9YMe/bsieo9HnzwQRw7dgxjx471bduzZ4/u95w3bx7mhFpxi4iITMFFh4iIyChai+fOnGl9WojMxkYPIiLykiYI7OXxePyeK4oStC2UFStWYPbs2Xj11VfRtGnTuN5z+vTpmDZtmu/54cOH0apVq2iST0REMdCqsM+aBcyebXlyiIhIYgUFwKhRwdOFZGQAc+fanTqKhA3D+rDRg4iIvKQJAmdkZCAxMTGoh+7evXuDevIGWrVqFfLy8vDCCy/gvPPO8/tb8+bNdb9namoqUlNTdX4DIiKKlVaFnZU9IiLSS2u6EO9ztxM9yMqGYX3Y6EFERF7SBIFTUlLQvXt3rFmzBmPGjPFtX7NmDUaPHq35uhUrVuDqq6/GihUrMGLEiKC/5+bmYs2aNX7zAq9evRp9+vQx9guQ44heQCZyEs7vSUREZA3Rg6xsGNaHjR5E5GSMy+gjTRAYAKZNm4YJEyagR48eyM3NxdKlS7Fr1y5ce+21ANRpGn766Sc8/fTTANQA8JVXXomFCxeid+/evh6/derUQXp6OgDgxhtvRP/+/XHfffdh9OjRePXVV/Hee+/h448/tudLkjRELyATEREREeklepCVDcNEROTFuIw+UgWBx40bh19//RV33XUXSktLcfrpp+Ott95CVlYWAKC0tBS7du3y7V9YWIjKykpcd911uO6663zbJ06ciOLiYgBAnz59sHLlSsycORN33HEH2rVrh1WrVqFXr16WfjeSj+gFZCIiIiIivRhktRd7tRGRLETIrxiX0cejKIpidyJkd/jwYaSnp+PQoUNo2LCh3ckhi1VUACkpQHm5mAVk0dPnOpL/IHYn3+7PdzzBD7DgyZNTwEEV/RjrTZ/o38dpZDvegemVLf1mE/14GJ0+UfKX2bPN6dXmuPPd4C8g2/GQPb2Gp1+2A+IQZuVXgaL5ed18CuiJSUrVE5iIiIiI/InQC8NuWscgI8P6tBARxYO92ohIFsyv5MMgMEWNlUwiIiLxcC407WMwc6b1aSEie8leZ+F0HEQkC+ZX8mEQmKImeiVT9gIfEcmD+Q2JhL0wtI9BRgYwd67dqSMiK4leZyEiIrILg8AUNdErmSzwEZFVIuU3DBKTldgLQ/sYeJ8TkXuIXmchIiKyC4PAFDXRK5ks8BGRVSLlN2yUIiIisofodRYiIiK7MAhMjsECHxFZJVJ+w0YpIiIiIiIiEgmDwEREMeBwfwqHjVLh8fohIiIiIqdhGZdExyAwEVEMONyfKHa8fojITKyEExGRHVjGJdExCExEFAMO9yeKXaTrRyuAk5FhbTqJSE6shBMRkR1YRyTRMQhMRBQDDvcnil2k60crgDNzpjXpIyK5sRJO4bChkYjMwjoiiY5BYCIiIhKKVgAnIwOYO9fu1BGR6FgJp3DY0EhERG7FIDAREREJRSuA431OREQUKzY0EhGRWzEITERERERERK7AhkYiInKrBLsTQERERERERERERETmYU9gIiIiIiKyjdZCXd4em0REREQUP/YEJiIiIiIi2xQWAt27Bz8KC+1OGREREZFzsCcwERERERHZRmuhLvYCJqJISkuB0v3B2zmSgIgoGIPAREQkHK2hwRkZ1qeFiIjMpbVQFxFRJIVFCZgzN3j7rFnA7NmWJ8dxOF0PkbMwCExERMIpLATmzAnePnOm9WkhIiJys9JSYD97WpKgCvKrMWpMIkcSmESrTM4gO5GcGAQmIiLhaA0NzsgA5obo7WE09nogkbGnPBFZqago9L2XQSASQWYmkNmaIwnMwul6iJyFQWAiIgOwl4yxtIYGe5+bjb0eSGTsKU9EVsrPB8aMYRCIyI04XQ+RszAITERkAPaScRb2eiCR2d1TnojcJTMTaM2elkRERNJjEJhMI9pwatHSQ87CXjLOwl4PJDK7e8oTuR3LlERERCQjBoHJNKINpxYtPaxAOAt7yRAREbmDaGVKIiIiomgwCEymEW04tWjpYQWCiIiISD6ilSndTmtdBi6WSURE5I9BYDKNaMOpRUtPvBUI9iQmIiKr8J5DVEO0MmUgt12vWusycLFMIiIifwwCE9kk3goEexITEZFVeM8hkofbrletdRm4WCaRflqNSOxZT+QMDAITSYpDEYmIyCq85xDJw23Xq9a6DFwsk0g/rUYk9qynaGhNz+PUkSgyYhCYSFKiD0Wk+LhtKCcZi+cPGY33HCJ58HolkpfdZTitRiT2rKdoaE3P49SRKDJiEJiISEBuG8pJxuL5Q0RERCQfu8twWo1I7FlP0dCanoedUMTBIDARRcXqVmm7W8Ht5rahnGQsnj/Wcnt+BfAYEFmJ15tc+HuRHizDkcy0puchcTAITLZhgUguVrdK290KbjcO5aR48PyxltvzK4DHgMhIkcrIvN7k4rTfS28dzrQ63+7dNf9mZ8fxRmJhGY6IzMQgMNnGaQUip7O6VZqt4EQkC+ZXPAZERopURub1Jhen/V5663Cm1PmWLQOuuUb9f/v2wNKlwJV5Mb4ZEZF7MAhMtpGtQKTVip2RYX1a7GB1qzRbwYlIFsyveAzIXk4ro0UqI/N6k4vTfi+9dTjD63y7d6sB4Opq9Xl1tfohg4YCaBnjmxIRuQODwGQb2QpEWq3YM2danxYiIiIiUjmtjGZ1GdlpQXQyl97z0/DzuaSkJgDsVVUFz/fbwCAwEVF4DAITRUmrFTsjA5g71+7UERFRtDgnPZGzsIwWH6cF0cnhcnKAhAT/QHBiIpR27e1Lk8BY5iGi2hgEJoqSViu29zkREcmBc9ITOQvLaPFhEJ2k0rKlOgdwQQFQVQUkJqo39pbsBRwKyzxEVBuDwERERGSr0lJg//7g7WYNRQ4MeLz5JnDggPp5mzbV7MdeMkTkBgyik3Ty8oBBg4C2bdXpIbKzAZ6vIcm2Dg/pw57epBeDwER/YAZKRGSPoqLQvc3MGoocGPBYvz7057OXjHF4jyUiIkN5e/6yB3BYoq/Do9URgOWD6LCnN+nFIDDRH5iBEhHZIz8fGDPGvqHIWp/PyodxRL/HMkhNRERkPa2OAKKUDyKxe2HNeHt6s/zjPtIFgRcvXoz7778fpaWl6Ny5MxYsWIB+/fqF3Le0tBR//etfsXHjRpSUlOCGG27AggUL/PYpLi7GVVddFfTa48ePIy0tzYyvQILiUBl34Q2PSByZmUDr1vYNRdb6fDKO6PdY0YPUZC+7K/lERE4le0O83QtrxtvTm+Uf95EqCLxq1SpMnToVixcvRt++fVFYWIhhw4bhm2++QevWrYP2LysrQ5MmTTBjxgw8/PDDmu/bsGFDbN261W8bA8DuI/pQGTIWb3hERNYR/R4repCa7GV3JZ+IyKnsboiPt2OQ7AtrsvzjPlIFgR966CHk5eVh8uTJAIAFCxbg3XffxWOPPYZ58+YF7d+mTRssXLgQAPDEE09ovq/H40Hz5s3NSTQRCYk3PCIi8hI9SE32MruS77aexhyNRUSiiLdjkOwLa7L84z7SBIHLy8uxceNG3HbbbX7bhwwZgnXr1sX13kePHkVWVhaqqqrQpUsX3H333ejatavm/mVlZSgrK/M9P3z4cFyfT0TW4w2PiEhcbguKiYZBOn9mV/Ld1tOYo7HkwvyYnIwdg8htpAkC79+/H1VVVWjWrJnf9mbNmmHPnj0xv2+HDh1QXFyMM844A4cPH8bChQvRt29ffPnll8jJyQn5mnnz5mFOqJILURgsQBEAYPfumn+zs+1NC1Egnp/uI+hv7ragmGgYpLOW7MOJ9WLQRS7Mj8lJtOrk3oHhZncMYiMr2U2aILCXx+Pxe64oStA2PXr37o3evXv7nvft2xfdunXDP/7xDzzyyCMhXzN9+nRMmzbN9/zw4cNo1apVzGkgd2ABirBsGXDNNer/27cHli4F8vLsTRORF89P9wn1m18pxm/utqCY1SJVQs0O0rFh3J/sw4n14mgsuTA/Jiexu07ORlaymzRB4IyMDCQmJgb1+t27d29Q7+B4JCQk4Oyzz0ZJSYnmPqmpqUhNTTXsM8kdWIByud271WBLdbX6vLpaPSmGDgVatrQ3bUQ8P91H6zcfNBSA/b+524JiVotUCTU7SGd3JZyIosf8mJzE7jo5R0KQ3aQJAqekpKB79+5Ys2YNxowZ49u+Zs0ajB492rDPURQFW7ZswRlnnGHYexIBLEC5XklJTbDFq6oK2LbNEUE2Dm2SnMPPTwpB4zf3fL8NIgSByVx2V0LtroQTEVFsSkuB/fuDt8tS5re7Ts6REOaT/Rw1mzRBYACYNm0aJkyYgB49eiA3NxdLly7Frl27cO211wJQp2n46aef8PTTT/tes2XLFgDq4m/79u3Dli1bkJKSgk6dOgEA5syZg969eyMnJweHDx/GI488gi1btmDRokWWfz8icrCcHCAhwT/okpioDsF2AA5tElvEwpDDz08KQeM3V9rxN3cDuyuhdlfCiYhIpXd6nqKi0I11tpf5BV3jgKwn7DkqCKmCwOPGjcOvv/6Ku+66C6WlpTj99NPx1ltvISsrCwBQWlqKXbt2+b2ma9euvv9v3LgRzz33HLKysrBjxw4AwMGDB3HNNddgz549SE9PR9euXfHhhx+iZ8+eln0vp5BtfjetoIgo6bW6ZyV7cpqsZUt1vs2CArWHZWKiGjl1SC9Lu3uVyc7s6y9iYcjh5yeFwN+ciIjIdQLrwIWFanEgkNb0PPn5wJgxgpX5ua4F1SLkOSoQqYLAADBlyhRMmTIl5N+Ki4uDtimKEvb9Hn74YTz88MNGJM31ZJvfTSsoIkp6re5ZyZ6cFsjLAwYNAtq2VYdiO6iV2u5eZbIz+/qLqjDk4POTNIT6zdkTk4iIyLG06sB5eWosNdL0PJmZQOvWApX5I6xrYXdHNdE7njmRcOeoYKQLApO4ZJvfTSsoIkp6re5ZyZ6cFvH2smNvO6rF7Osv6sIQz0/34W9ORETkGuHqwMuWSTg9T4R1LezuqCZ6xzNyHwaByTCyze+mFRQRJb1W96w0+vM4vUR4paVAKSespz+wJzVRdESZ8o/3OCLniTV/4SJEJJJIPV9FrwPrFmFdC7s7qone8YzcJ8HuBBCRMxUWAt27Bz8KC+1OmRgKixJ4fIiIdFi2rGatwvbt1ed24T2OyFniyV+KipgfkDi07k9FRXanzCTeNQ4SE9XnAWscZGYC3bqpwW5A/bdbN+saaOz+fKJA7AlMRKbg9BLhFeRXY9SYRB4fIqIoRJjyz3K8xxE5R7z5CxchIpHY3fPVFlzXgihqDAITkSk4vD28zEwgkxPWExFFZdu2sFP+Wc5p9zguXGMtuxcqspro3zfe/IWLEJFIZJui0TBc44AoKgwCExGB87mRu2ie7xkAT3cSUfv2wVP+JSQAx48DmzbVbBMlqCQbLlxjrEhzRtu9UJHVRP++ofKXWlOKEgmNjXgUDtcwoEAMAhNRTJwWNNWqAM+aBcyebXlyiEyldb7PmQncaX1yyGBOy5+Bmin/CgrUHnoejxqwGT7cfz9Rgkqy4cI1xtIKenrLFG4bri369w3MXwKmFCUSGhvxKJxI9yNyHwaBSVqiDy1zOqcFTTmfG7mJ5vmeAUCACjnFx2n5s1ftKf/Wr1eHt4oaVJKN41aLt1mkOaPdNlxbhu/LKUVJVm5rxNPs2crRbCFxDQMKxCAwSUv0oWVO57SgKedzIzfRPN8FqpAbyW2Nhk7Ln2vz9szr1s0/iCRiUIncy2lzRrsFpxQlGbmtEU8rBsDRbKHxfkSBGAQmaYk+tMzpGDQlIlm4rdGQ+TMRERE5kWbPVo5mI4oKg8AkLRmGllENJ85RaSQu6kBkHjYaEhERyYnD/6k2zZ6tjAEYgnV252MQmIgs4dQ5Ko3CRR2IzMNGQ+uxYYuIiIxg9fB/BsHIzVhndz4GgYnIEk6eo9IIXNRBJWoBmwEtiods57sRIjVssZJNRFbhPVxuVg//ZxCM3Ix1dudjEJjIIKzQhsc5KsPjog4qUQvY7KlN8ZDtfDdCpIYtVrLN5caGByItvIfLzerh/wyCkZuxzu58DAITGYQVWiJtgQGJ3Fxg+XKgUSNg5EjxC9hu66lN4WkF2LR6lWn2YhL0fDdCpIYtVrLN5bSGBwa1KR68h5vLaR1hGAQjquG065sYBCYyDCu0RNq0AhLeXjiiF7Dj7aktewGKARh/kc7nQJq9mCwk2sI6rGSby2kND04LapO13DbaymrsCEPkXLy+nYdBYCKDxFuh5Xxl5GRaAQm39MKRvQDFAIy/eM9nOxoFrF5Yh+wlQsODkZwW1Lab3tEMZCzZG4YDsSMMOYnTrs948fp2HgaBSRhuz3A5Xxk5mVZAwi29cGQvQIkSgNm9W/1306bQAS2r7heRzudIjXp2NApYvbAOkZGcFtS2m97RDGQs0RuG9TYScGQHOYno16fVeH07D4PAJAzRMlyre+aaPV+Z24PsRHaSvQAlQgBm2TLgmmvU/+fmAooSvI8oBfRIjXp2NApYvbCOXhwNQ2Qdt4/OsZvoDcNObyRgT3gKR/TrUzaMQYiHQWAShmgZrtU9c82er0y0IDsRuUe8Fa7du9UAcHW1+lxRgIQE4JVX1ECG3feLQJEa9WRvFDADR8OYy2lBdqd9H6u5fXSO3US5B3hH1+zeDWRn12x3eiOBU4LcWr8fxUeU69MpzIhBsCEnPgwCkzBEy3CdtpKwaEF2o3HhKiJxxVvh2ratJgDsVV0N1Kmj/t/u+0UgLkKkn9PuuWbTe89zWpDdad+HyGq1R9e0bw8sXQrk5anPnd5I4IQgd6jf78or7U2TXgxiu4NRMYja58tTTzmjIccuDAITaXBaJV60ILvRuHAVkbjirXC1b6/2/K0dCE5MBNq1My/NZC2n3XPNpveeF2+QXbThnGY1GjAoQXrIer4Ejq6prlbv00OHAi1b2ps2K8ge5Nb6/QYNsjddejghiE3RMSIGEXi+zJ8PbNwod0OOnRgEJiJHEGXhKnIno4cmRwq4iNbzPVJ64q1wtWypVhAKCoCqKjUAXFjojsoqUSh673nxBtlFm1LKjEaDcD0jiQLJHMQKNbqmqkrdzvuq+EpKQv9+339vT3r0ckIQm6wT6ny59VZgxw6gWTN1m2wNOXZjEJjIpZw2n54IC1eRexk9NDlSwEW0nu9WpCcvT60gtG2rVoCys1nYI/ey+p7n9Cml3N4zkvSRPYilNbqmfXv70kTRy8mRe3SUViOELEFsspZWo8e2bTVBYNKHQWAil+J8evpwAnoKx+ihyZECLqL1fLcqPd5gDIMyRNZy+pRS7BlJesjeE5Oja+wV72gu2X8/TvFFtUW6HrQaPdhoFTsGgYlciovw6OOUlYSjFW/Q2+6e5lZPl2D00ORIARfRer6Llh6ieJk9B65oU7q4HXtGkh6y98QEQo+uIWsYMXpK5tFRsgexyViRrodw54ss57xoGAQmcikuwqOPE1YS1iPeoLfdPc1Fmy6BiOSidw5cvUFj5lFiYVCC9HDK+cLRNfYwavSUzL+fzEFsMlY01wMbrYzFIDARURRkX0lYr3iD3np7mhvdc1i06RKISC5658DVGzRmHiUeVjJJDwaxKFZuHT21e3fNv9nZcgexyTjRXg88X4zDIDAREQWJN+itt6e50T2H3VrAJiJj6J0DV2/QmHmUmFjJJD14vhBFZ9kydTFFQJ1mZ+lS4Mor7U0TkVsxCExERLbjHNVEJLPAoHHz5urohsC5fznnLxERucnu3WoA2DuHdnW1Ohpm0CB700XkVgwCExFR1AKHchmFc1STkeJd2JAoXnqnhyAi0mL2QpVEZiop8V9EEVDn0v7+e3vSQ+R2DAITkRRYAPZnx8ryoYZy5eWZ81lE8Yh3YUOieOmdHoKISItsjUpGr/NAcsvJARIS/APBiYlAu3b2pYnIzRgEJiIpyFYANpvVK8trDeUaOpRz4ZF44l3YkCheeucUJiLSIlujktHrPJDcWrZUO44UFKg9gBMT1XoM6w9E9mAQmMjhzBq+bzXZCsBms3pl+W3bQg/l2raNhTgST7wLG7qZU+4ZZA+eP0TGk61RSdZ1Hph/mScvT50DuG1bdXqI7GyWyYjswiAwkYM5aSVW2QrAZrN6Zfn27UMP5Wrf3rzPJCJrOXHKF6Mq9RzeHJkTzx8i0k/GdR6cVGcSlbfTCDuPyI3lIfkl2J0AIjKH1vB9b4WYSA/vUK7ERPU5h3IROYsT7xnLltU0VLVvrz6PVVER0L178KOoyJi0ys6J5w+RVUpLgU2bgh+h1n4g4zH/Iooey0PyY09gIpPY3UrGlVgpnFgWlgs1lIuInKFkm8dRU74YPY+5rMObraJV5pD1/CGyEufQtZfWlGesMxEFY3lIfgwCE5nE7gIdV2KlcGJdWI5DucgNtBrxwjWSyC6nveKoKV+Mnsc83uHNdjcMm02rzCHr+UNkJQZV7KU15RnrTNFxY5nJzWSc7oX8MQhMZBK7C3RcidXdIvX0tXphOdHE0hOa3EOrES9SI4nMnHbPEG0ec7sbhs3mtPOHyEoMqhhLb1CS+Vd83FhmIpIZg8DkWHb3uhGhQMeVWN0rUk9fqxeWE02sPaHJHbQa8ZzeQOCkKV9Eq9Tb3TBsBSedP6QyamFFt7G7DuJ2sQQlWWeKnVvLTESyYhCYHMvpvW6ixeH77uTUnr5GVUgDj8+bbwIHDqgVtE2bavZjhc2dtBrx3MBJ9wyRgpIiNAxbQbbzh0FObcuWqfNqA2oP+qVLgSuvtDdNsmAdxF6xBiWjzb84msyf0WUmTi9BZK4EuxOg1+LFi5GdnY20tDR0794dH330kea+paWluPzyy3HaaachISEBU6dODbnfiy++iE6dOiE1NRWdOnXCyy+/bFLqyUr5+cDGjeqNH1D/3bhR3U7kdJmZQLduakEMUP/t1k3uwtOyZTVDudu3V5/HKvD4rF8PjB8PnH8+V7olchLZgpJkHSPvKU6jtbCiN2hO4RlVB6ndSEHRM7sMXFjoX1b0PgoLjXl/tysq4vGVEfMreUjVE3jVqlWYOnUqFi9ejL59+6KwsBDDhg3DN998g9atWwftX1ZWhiZNmmDGjBl4+OGHQ77n+vXrMW7cONx9990YM2YMXn75ZYwdOxYff/wxevXqZfZXIhO5pdcNkRtoVUiHDjUmuCP6UG0OLQ2Px8d6POYkM617yqBB9qZLFFoLK37/vT3pkY0RdRD2xBaXU0fbiYLTS8iH+ZVcpAoCP/TQQ8jLy8PkyZMBAAsWLMC7776Lxx57DPPmzQvav02bNli4cCEA4Iknngj5ngsWLMDgwYMxffp0AMD06dOxdu1aLFiwACtWrAj5mrKyMpSVlfmeHz58OK7vRWQEVsjJSlafb1oV0m3bjAkCi95oxKGl4fH4WI/H3FwcbmyukhIGOcPRWlixXTv70hSKU6fzcHojhezD/d2+robZ3Dwll4ycnl85kTTTQZSXl2Pjxo0YMmSI3/YhQ4Zg3bp1Mb/v+vXrg95z6NChYd9z3rx5SE9P9z1atWoV8+cTGUVr6AyHs5MZrD7fvBXS2hITa4byOh2ntwmPx8d6oh5zpwxH5HBjc+XkhL6niBbktIt3YcXERPW53QsrhuLk6TzM6oktSv7I4f5EziHSyBFR8jjRSRME3r9/P6qqqtCsWTO/7c2aNcOePXtift89e/bofs/p06fj0KFDvsePP/4Y8+eT/ETJbEStkJMzWX2+yVAhNZMT53g2Eo+P9UQ85k4KChUUhM5jCwrsTZdTuP2eEo28PLXHNKD+m5dnb3pqc/qcxVoN31qNFKWl6qK2gY/aowlEyh+1ypDM34jkoze/MotIeZzopJoOAgA8Ho/fc0VRgraZ/Z6pqalITU2N6zPJGUSa/0b04ezkLHacb3l56tCitm3VCqmThn4SUXz0DkfUmm5BlCmUONzYfKHuKaKWmeya8kvUhRWdPp2Ht5GioED9XpEaKQoLgTlzgrfPmgXMni3ecG0O9ydyDr35lRlEy+NEJ00QOCMjA4mJiUE9dPfu3RvUk1eP5s2bG/6e5A7MbPxxTmKygqgVUnI2WfI3p86PGY1IwxEDf8PCQrXSEohzGruLLPcUzsHtzzudh+hzFsdDTyNFpIXKnB40J3ISGdcEsLtRVaQpKWQgzXQQKSkp6N69O9asWeO3fc2aNejTp0/M75ubmxv0nqtXr47rPZ1OlOkP7MbMxp9ocxJHMzSOiCgaouVvobh9GFyk4YiBv6E3AOwd4s4plEhknPLLn1um84i2kSLS9DycA5tIHrKuCWBno6ooU1LIQpqewAAwbdo0TJgwAT169EBubi6WLl2KXbt24dprrwWgztX7008/4emnn/a9ZsuWLQCAo0ePYt++fdiyZQtSUlLQqVMnAMCNN96I/v3747777sPo0aPx6quv4r333sPHH39s+feTQajpD0SaIwywrieULCsnWyU/HxgzJrgXQkZG6N4rZtPqNeMdGkdE2kpLgdIwPV+N6hkrS89V0fK3QByZEnk4YrjfcNkyTqFEYuOUX8Gi6Xkmyz3GbCIM1yai6ETq2U/BmMfpI1UQeNy4cfj1119x1113obS0FKeffjreeustZGVlAQBKS0uxa9cuv9d09TaJAti4cSOee+45ZGVlYceOHQCAPn36YOXKlZg5cybuuOMOtGvXDqtWrUKvXr0s+16y0KpkDh0qzgVm5Ry9zGz8iVZB0arwG30DZQXD3SL9/lp/F316gcKiBMwJM/TYiKHJIs2pHolo+VsgjkxRhQsKif4bEsnM7OHLkebwDlX2lukeYwW7h2uHo1UmEnn4O5FZuCZAbETO40QjVRAYAKZMmYIpU6aE/FtxcXHQNkVRIr7nJZdcgksuuSTepDme1nxS27aJEfi0oycUMxtxWbHoBCsY7hbp9w/3d9HndyzIr8aoMYmaPV/j7RkbbX7NRpbocGRKDVnmeCVykkgLk5n1/lr3TLffYyI1NIuWP3L0Xniidxwg0sPM85llwOhIFwQm+2gtwuCdg9BudvWEYmbjTk4bfs0Cpj6Rfv9Ifxd9eoHMTCAzTK/JeHtVRpNfs5ElehyZQkR2Mnv4stb7a90z3X6PEb2hOZBVo/dkJdvvaTTWUZzF7eezCBgEpqiJXslkTyiykt6V6L0yMwARy7S8IesT6feP9He3D02PlF87rZHFChyZQkR2MXv4stb7a+Vxbr/HiN7QHMiK0Xsyk+33NBrrKM7i9vNZBAwCky6hKpmiED1ITc4SqYKhVWCZMxO405ok6sIbsj6Rfn82SoUXKb/mHLex4cgUIn9OHe5P4bn9HuP2hmbRRJrTOhK3/56soxjL7p7Vbj+fRcAgMOkmciWTPaHIKrGuRJ+ZAUDAAgtvyPpE+v3ZKBVZuPyaQXQiileo4f55efamiazDewyJQu+c1uSPdRRjsWc1MQhMMbO7FUmLyEFqcpZYVqIHCyyOEanRiY1SkWnl1wyiE1E8tIb7Dx3KfMRNeI8hEeid05rcxeqYCntWE4PAFDO2IpGR4h0qZRc2OrhbpN+f50fsGEQnolhpDfffto35Mal4jyGr6J3Tmpwh2umIrI6psGc1JdidAJJXfj6wcaPaegSo/27cqG4n0quwEOjePfhRVGR3yojILgyiE1EsvMP9a0tMVLcTefEeQ0RmWLas5n7Tvr36XAtjKmQ19gSmmLEVieIROPQlNxdYvhxo1AgYOZJDU/QSdXoWIiIiq8U73J/3VCL5cCFIskKk0ata0xENGhT6/RhTIasxCExEtog09IU3QH04PQsREVGNUMP9o8V7amgMspGoQi0EeeWV9qaJnCnSQn9a0xF9/735aSOKBqeDICJbcOiLsZx6PGtXOEkepaXApk3Bj1A9J4iIzBLrcH+n3lPjoWd4M5GVtHpesuxoLJbJVQUF4e8PWtMRtWtnbTqJtLAnMBHZgkNfjOXE4ylCrw72eooNe9ERUSxEyXOdeE+Nh1aQbehQzqdL9ivZ5gnb85LTu8RPhDK5KCIt9BfvdEREZmNPYCIKiT35yE4i9Opgr6fYsRcdEenFPFdcWsObt22zJz1EteW0V8L2vCwq4uLT8RChTC6bvDx1GiJA/Tcvz970ENXGnsBEFBJ78sVGlF5MgWTrBWH3fFp6F3Ugf+xFZw1R8xsivdjTVGze4c2178uJiTVBeyI7Rep5mZ8PjBkDVFYCvXpx8Wm97C6TyyrW6YiIzMYgMBGFxAKTfiIPlZItqK9V4bRqPi0WeEl0Iuc3RHqF62nKCrT93D68ubQ09Eg4uxrSZWvYt0KohSC9Dc9smI6P3WVyIjIWg8BEFBILTPqI3nNUtqC+3RVOFnhJZKLnN0R6saep+EIF2dyisBCYMyd4u10N6bI17FuFPS/NYXeZnIiMxSAwmY7DVcPj8XEGs3qOGnV+yBjUD9erw2ws8JLISkrYU52cRdY8121lOLcG2QoKgFGjxGlIl61h3+m0emZ7FxCL9fUi9ey2s0xORMZiEJhMFWq4qt0To4tUYOdwXnHpLZCZ0XNUxOvHanZWOFngJVHl5LCnOjmPbD1NZbhHi1TmtYJZ39cbzBOlIV3Ghn0n0+qZPWsWMHt27K8XrWe3WxuBZAjSE+mREHkXotiIuJKoSCtPG3V8ahd4yTh6VxL29mJKTFSfx9uLScTrx43cWuAlsRmd3xCJQpY8V4Z7tEhlXiu47fuSOPLzgY0b1R7ZgPrvxo1qnhDP6/PzzUkv6aO3Tkgkuph6AldVVaG4uBj/+te/sHfvXlQHjEl8//33DUkcyU20RT5Em0PRiOkD2JPYPLEMtTOy56ho1w+JTauXgvf8c0svMDdhT3WqjT2VrCX6PVqrzDt0qBjpM5poZXxyF62e2fG+3u57uttGEmjh9CvkNDEFgW+88UYUFxdjxIgROP300+HxeIxOFzmA0Yt8xLsyr1lztsYq3ukDWOA1V6wFMqN6MYU6PxISgOPHgU2baraxgk+A9lBC7+2ZjUTOJGKvSVYa7SHLcGKnEH0hO615w0UJUgeKd05V0cr4RLJjR6MaogbpRcfyoLhiCgKvXLkSzz//PIYPH250eshBQi3ycfvtwN696sMr2iBWvCvzmjFnazziXQTFroWBrM7Q3XoDCTw/PB719w7MdlnBJyC4l8JrrwEXXshGIjJeuDyZlUbzROrpy55K1hJ9ITutecNFCVIHindOVdHK+EQyY0cjihfLg2KLaU7glJQUtBe1FEFCyctTg5UAcN11wN13xz6fTkFBfPMliTiHYu3jU1Kib0ERbwG/NrMLvFbPt+b2+d1qnx/r13O+MNKWmQl066b2TgCAtDT2iiLjhcuTZZgjVWaR5iQMzAO6dlWfR9OLkmITTxnOKFrrQohY5g0n3jlVZfu+JJfSUnUUXuAj1AhVI9m17gt71lM8WB4UX0xB4L/+9a9YuHAhFEUxOj3kQN4C2F//Gl8Qy4gKjggF9kCxDue1usBrdYbOG4jK+3t268YKPkXP2yuqNvaKMp+TF+qMlCez0mguLhwUHauvQTunZInUUC5imVeLU8v4Tqf3epP1HmnHwmBmdISJ9vizDEnxYHlQfDEFgT/++GM8++yzaNeuHS644AJcdNFFfg+iUPQW8MxqdRVxDsVYWVngtTpD5w2EKHbsFWU9p49ciDQFESuN5mJP38iceA1qBW2ibSh3Upk3GqJ/X1mDoKHovd5kvj6tboQzoyOMnuPPMiTFg+VB8cUUBG7UqBHGjBmDAQMGICMjA+np6X4PIj20CkR2tLpGQ7QCnFUFXqszdN5AiOLDXlGRGZWfu2HkQqQpiFhpJDs58RoMF7TRaijfts269JnJruH3ZpI5CBpI7/Um+/VpdSOc0R1hYjn+LENSrFgeFF9MC8M9+eSTRqeDXCrcpOEiLnLi5knOrV4ERfRFV4hkIHqvKDsZmZ+7YeRCNHlyXp66cEzbtmqlMTubq2eTNZx2DUZamElrIbR4l2wRZTFerYXiZF0M12kLbem93px2fZrN6IUOYz3+LENSrFgeFFtMPYGJjBCpVdKuoY/xDr1zMqtbhdkKTURm0MrPP/+85u96uGXkQjR5MiuNZAenXYORgjZm9LQSqaeq0+bAdloQVO/15rTr02xGX988/mQHlgfFFXMQ+J///CfGjh2L3r17o1u3bn4PomiIWCCKZeidrAW4WFmdofMGQuQeVk23o5Wf9+un/l9vAMTsoW8iDY1mnkyAWOck4Lzhp9EEbYxsKBeto4PT5sB2WhBO7/XmtOvTCkZe3zz+RFRbTEHgRx55BFdddRWaNm2KzZs3o2fPnjj55JPxww8/YNiwYUankRxKtAJRpAKwaOklInISK3uhhcrPgfgCIGaOXCgsFHOOfHIvEddtcNLooWiDNtE2ykQK2tvV0UG0dTbM4sQgnN7rzUnXp1WMbHSV4fi7JT8wC48fRSumIPDixYuxdOlSPProo0hJScEtt9yCNWvW4IYbbsChQ4eMTiM5lGgFIjuG3hERkfW90ALz81AB4VgCIGb1ki0ocNbQaJGxEhUdUYfrO6mnupFBm0hBezs6Oog0/YQVZAjC6aX3enPS9SkjkY+/CPmBzPd/EY4fySOmIPCuXbvQp08fAECdOnVw5MgRAMCECROwYsUK41JHjidSgcjqoXdEFDvRhiJTfOzohVY7P//oI7FGegSe397zunlz9V+Zh0aLXMliJSp6ThuuLyqjgjaRgvZWd3QQbfoJq4gchCOyiwj5gcz3f6OOn8jlMzJWUiwvat68OX799VdkZWUhKysLn376Kc466yxs374diqIYnUZyOFEKRNGsfO7dr/a/JDdRVsImfbRWDp81C5g92/LkUJyMXgk7Wt58/Oyzo8v/rVJYCMyZE7x95kzr02KkZcvUigqg/uZLlwJXXmlvmry0KlGDBlnz+aWlwP79wdszMqz5fC28RzpDZibQunXN6uxduwLJyf6rtetZzT3e85XrbIgl2t+T+QGZwe78wKj7v13XR0lJ6OP31ltAjx4128LlzyKXz8h4MfUEHjRoEF5//XUAQF5eHm666SYMHjwY48aNw5gxYwxNIJGV2NPXXWRu9XU7rV5NBQX2potiI8J0OyLl/06c/kGEnj7h2F0JFXGOXSPvkRy9ER27e2JF29Eh3vOV62yIJZrfk2VmMovd+YER9387r4+cnNDTmhUURJc/i14+I+PF1BN46dKlqP7jLLn22mvRuHFjfPzxx7jgggtw7bXXGppAIquxp6872N3ri+Kj1auJ5KWnF5pZRMn/MzPVR7hee7KxO8gaiV290b3y84ExY4DKSqBXLzXwn5Sk9twJNerBbEbfI53au91IMvXEivd8jXb0HVkj0u/JMjOZye78IN77v93XR6jjd/vtwMiR0eXPopXPRB0Z5SQxBYETEhKQUKu5YezYsRg7dqxhiSJyMg6lEoPW0BlRAhJEbiRKEJaMZ3eQNRK7K6HRDNe3UryVwsBKXG4usHw50KiRWjG1O8gtGruDCHoZcb6K0PBHqki/p2hBInIeO/KD2j1d47n/x3p9GBkTCHf8IuXPopXPtKb8Y6OxcWKaDgIAPvroI4wfPx65ubn46aefAADPPPMMPv74Y8MSR+Q0HEoljlBDZ0QKSMjK7qGsRCSmWKf8sDJPEWlKELvFOzw3cHj5+ecD48cDn36q/t27kFxVlfrc7fcMtwbZ2PAnB7uH65M7WJkfBNbJgdjv/7FcH2bEBGI9fiJMyVZbpIVMKX4xBYFffPFFDB06FHXq1MHmzZtRVlYGADhy5AjuueceQxNI5BScb0csot3wnICNHEQUjt4gqx15ituCUlpB9njvkdFU4mS8Z5jVKMEgG4mMZWZyEq06uZfZQVQRYwIiNYJnZqqNxF27qs+9jcaZmfalyWliCgLPnTsXS5YsQVFREZJrTcLYp08fbNq0ybDEETmJW3t5iEykG57sRCzQEJF4og2yMk8xX6QgbDz3yEiVOBl/XzOD1gyykehYZqZAso7+M6NOruf6EDUm4LZGcDeLaU7grVu3on///kHbGzZsiIMHD8abJpKcbHPeWpVe0ebbIRVveMYQtUBD/mTLn8m9mKeYK9o5aM26R8r2+1oxZy/nyCXRCVNmLi0F9peqK9kBwObNf0wyngnA/u6CbljYSqaFLAOZVSeP9vrQ+/la55N3EWHSxnpPaDH1BM7MzMS2bduCtn/88cdo27Zt3Ikieck2tM/K9MowHyJRrDiU1RhmXu+y5c9uUloKbNoU/CgttTtl9mGeYi67g7Cy/b5WHS9hgmxEAksoKlQnG+/VS93Qq5f6vKjI3oT9IXBOdO9DkOTFTcaRHLXZPfJC7+drnU+FhdakV1as92iLKQhcUFCAG2+8ERs2bIDH48HPP/+MZ599FjfffDOmTJlidBr9LF68GNnZ2UhLS0P37t3x0Ucfhd1/7dq16N69O9LS0tC2bVssWbLE7+/FxcXweDxBjxMnTpj5NRxJthuCHemVYT5EozGI7Q52F6icwMzrXbb82W2cXmGMBfMUc9kdhLX69423ocXu40VENarzC9RJxgMfgqwcJevCVtHW2exuRDSC3dOb6Pl8rfOp9jzG5I/1nvBiCgLfcsstuPDCC3HOOefg6NGj6N+/PyZPnoyCggJcf/31RqfRZ9WqVZg6dSpmzJiBzZs3o1+/fhg2bBh27doVcv/t27dj+PDh6NevHzZv3ozbb78dN9xwA1588UW//Ro2bIjS0lK/R1pammnfw6lkuyHYlV43zYfohCA2Rc/uApXMzL7eZcuf3UbWCqPZmKeYR4Qgu5W/b7wNLSIcLyL6g3fS8cCHIGPjRVnYSk9HHD11Nqc0ilk98iLw94j280U5n2SiVe8JMZmBK8UUBAaAv//979i/fz8+++wzfPrpp9i3bx/uvvtuI9MW5KGHHkJeXh4mT56Mjh07YsGCBWjVqhUee+yxkPsvWbIErVu3xoIFC9CxY0dMnjwZV199NR544AG//TweD5o3b+73IP1kuyGInl67Mi+jeu46IYhtBaf1lOZQ1tiYHaQVPb9zOxbwtTFPMY8IQXarfl8jGlriOV6c8oWIrKQnqKu3ziZro5iddS4ROkY5rc4Zjla9x/sbuJ2uheGuvvrqqPZ74oknYkpMOOXl5di4cSNuu+02v+1DhgzBunXrQr5m/fr1GDJkiN+2oUOHYtmyZaioqEBycjIA4OjRo8jKykJVVRW6dOmCu+++G129NbEQysrKUFZW5nt++PDhWL+Wo3hvCAUFavBC9BuC6OkNNWl8QgJw/LhacfAycpEBIyf5Z8/DyGReVIGMZfbCkaLnd2QOLohhPtmPsVuC7JmZQOvWNQutde0KJCfrX3gt1uNVVATMnRu8feZMfe8jO9mvl0ic/v1IDtEuZOk9X9ev119nk20hSzvrXEYvLBrLwoNuq3Oy3hOerp7AxcXF+OCDD3Dw4EEcOHBA82GG/fv3o6qqCs2aNfPb3qxZM+zZsyfka/bs2RNy/8rKSuz/48rp0KEDiouL8dprr2HFihVIS0tD3759UeJt6g9h3rx5SE9P9z1atWoV57dzDhF6leghcnoDW1k9HvWmMXy4OXNGGt1zlz0Pw2NPaarNil4VIud3ZDwRep04nROPsZt6CllJqyfyyJHqczccbydeL7U5/fuRPKLpiFP7fB0/Xq1n1hZNnU2WRkS761xGd4zSO72R3d/fLqz3aNMVBL722mtx6NAh/PDDDzjnnHOwbNkyvPzyy0EPM3kCcihFUYK2Rdq/9vbevXtj/PjxOOuss9CvXz88//zzOPXUU/GPf/xD8z2nT5+OQ4cO+R4//vhjrF/HkWS5IXiJnN7amdf69ebOGRnrDUqrwijrUCGrlGzzsKe0hWQYimtFYUXk/I6M49YCv5WceIwZxDJPqClfNm8G+vRRnzv9eDvxeqnN6d+P5BKpI07g+fpHeMSxdbaSEntHpxrdMUrv9EZuHp3Lek9ouoLAixcvRmlpKW699Va8/vrraNWqFcaOHYt3333XF1w1S0ZGBhITE4N6/e7duzeot69X8+bNQ+6flJSEk08+OeRrEhIScPbZZ4ftCZyamoqGDRv6PYjM4s20vGsemDVnZCw3qEgVRhlb4KzqBZXTXmFPaQvFuyiQVWxbpGLTL2pUfPNmdcPmzeJFySlqXBDDfE6rVDGIZS23HW+7gzBmc1p+QHKqnX+E64gT6nxVFOCZZ9T/y1Jni1ZOjr2jU43uGKV3HQmOzqVAuheGS01NxWWXXYY1a9bgm2++QefOnTFlyhRkZWXh6NGjZqQRAJCSkoLu3btjzZo1ftvXrFmDPt5m9AC5ublB+69evRo9evTwzQccSFEUbNmyBZlcjYVcRu8NKtoKjEwtcFb2gmJPaWsZsSiQ0/id77lNsKz7IqBXL3VDr15iRskpKlwQw3xOq1QxiGUOrYZltx1vu4MwZnNafkDyCazDANodcbTO19691f87rS4iQp3Lzo5RInx/EovuIHBtHo8HHo8HiqKgOrAkY4Jp06bh8ccfxxNPPIH//e9/uOmmm7Br1y5ce+21ANRpGq6sNcP1tddei507d2LatGn43//+hyeeeALLli3DzTff7Ntnzpw5ePfdd/HDDz9gy5YtyMvLw5YtW3zvSeQmem5QTqvA2NErR8ae0rLS22rudEHnu5KAgoTHsfut/6jRce/DYVFyt8x36qYCv12/qdOOMYNYxgvXsOy24+206yWQ078fiU2rDuMVeB668XwVoc5lZ8coEb4/iUN3ELisrAwrVqzA4MGDcdppp+G///0vHn30UezatQv169c3I40+48aNw4IFC3DXXXehS5cu+PDDD/HWW28hKysLAFBaWopdu3b59s/OzsZbb72Ff//73+jSpQvuvvtuPPLII7j44ot9+xw8eBDXXHMNOnbsiCFDhuCnn37Chx9+iJ49e5r6Xcg4bqnUWyXaG1SsFRhRfy+7gtqBx1vU40POEvJ8r/ZgW50zauaecViU3G3znbqhwG/3b+qkY+zGoICZIjUsu/F4O+l6CcXp34/EFUsdxgnnq946k0yjU83g9u9PNZL07DxlyhSsXLkSrVu3xlVXXYWVK1dqzq1rlilTpmDKlCkh/1ZcXBy0bcCAAdi0aZPm+z388MN4+OGHjUoeWWzZMrWQDagVwKVLgVqdwclE3gpMQYFa0IimAmPn71VaCuzfH7w9I6MmPQkJ/oUoQ3vllJYC+0uBykr1+ebNQFISkJEJQA208Xwmq2id706dLkArIDNokL3pMpuTC/yi/KZOOsZ5eerxa9tWDQpkZwMVFXanSk7RzIHrxuPtpOslFKd/v0hqB+Wys2N/n0hldvIXax1G5vM1VJ0pj3UmQxl1PZN4dAWBlyxZgtatWyM7Oxtr167F2rVrQ+730ksvGZI42ZSXl6O8vDxoe0JCApKSkvz20+LxePzmK9azb0VFheYCfUbuW1EBJCcD5eXqJPIeT4rfvuXlit/fa++fnFyzb2VlJRSlOuj9vM+Bmn2TkipRXl7t9/ft24FrrklGdbUHQE0FsH//SiQnV4f8fPVrJAPw+NJQXl6tmd6kpJp9q6qqoChVmulVlJp9ExOrUF5eFfLzKyoAjycJ3o74VVVVSE6u0kyvovjvW15epZnexET/fcOlt7q6Zt+EhGqUl1dqpjchIRFA4h/HuRrJyZUoLwcmTAD69QM6dfLgm28UtGkDVFX571teXhnm91IwaJDHb1+t9FZVJSI5OfGPc1RBeXkFQp3CFRVAYmJNGhRFQXJyBYqKgPvuC97/1lsTACShZUugsFDBtdcCVVUeJCYqWLSoCk2b1pwfHo+6r/d9y8srNNNbWZmA5OSa676yqBDKffeoT5KTgT/9SU3vrTOQlDQDu3cnhQhoKOjXr8Lv/SsrPX+cw6ry8nLN80E9H/2vZa3rs6Ii9HUf+vv5v29Skvq+WudP7Wu5oqICycmK5vleOz+JdH2Gyk9CnQ/B12dwfuKfXv88Itr8JNL1qSc/qX19mpGftGwJLFlSjT//2RN0vntvO+p9K+GP8zH66zPW/CTU/tXVofOTUPvXft/A6/N///Ogutp/LQBvQKZ2fhIqvYmJ/td9cnKFZnqrqoLzCK301s5PAPVajjY/KS8v10xvUpL/9ZmcXF7rfK31ml17gN9+QbL3D5s3owJA+cnNkZzc3O81gHbZIFIesXs3kJBQie3bq9GmjXF5hFbPp2+/rXm9njIH8wj1+Smn1OQResocZuYRld7GU5iXR0Rb5ogmj6ioqEBWFpCQUFPmUX8nBVlZVX77Nm2q5hFNm6rvaWQeEep4RcojAvcPLHOEuz5DlTkC6xqxlTkA/zpB9GWOSNdnpDJHbWp6a657o/ITj8f/ug93ferJT2KvE4TPTxISQucnTzyRgClTEgF40L69gsWLqzBpUgIC84hors+iomrcd1/Nde91663B12ftPCL09RlbmSPSPVxPfuJ/fRpf5qjpmKNEVYcBwucngdenvjJHzfUZKN78xFuHCVmnvEbB0KZfoSWAii++gJKYCDRvrj587xFdjCHW/CTWGIO+/CTS/T76/CRcjCHwel6yRPnjejYvP9FbJ6isjDZuUFPmCCUxMfGPfCK4zBFuX+/93oh9a8cLY903XNwwkEfRigSGMGnSJHg8noj7Pfnkk1EnwAkOHz6M9PR03HbbbUhLSwv6e05ODi6//HLf83vuuUfzh83KysKkSZN8z++//378/vvvIfc95ZRTkF9rvsYFCxbg0KFDIfdt0qSJXw/qxYsXY9++fSH3TU9Px9SpU33Pi4qK8PPPP4fct27dupg69W9ISVEvvmefLcbOnTtD7pucnIzbb78dFRVASgrwzDPP4fvvS0LuCwC33z7rjxsRcMUVL6Bz52/8/r59exs89dTEoNfNmfMxFOVfmu97440346ST6qG8HFi9+k188cUXYfa9EfXqNUJKCvD226uxYcN6zX3z8/+MU05piu3bgTFjtmDQoPeRnn4k5L5Ll07Gjh0tkJwMfPTRJ3j//fc03/eKKyYiJ6cNysuBzZs/w9tvv62572WXXYbs7FORkgJ88cUWvPHGq5r7jhlzCc48szMqKoAuXb7G2LH/1Nz3lVdG47PPuvwRTPkOzz+/QnPfIUOGoU+fnigvB376aQeeeuopANq/15o1wODBwI4dP6G4+HHN9/3Tnwbg3HMHoqICaNFiL6677jHNfT/5JBdvvjkEycnAvn0HsXjxQs19O3TogUsvHYHycqC8/BjuuKMQv/3WGI0b/xb0+5111lkYMeJCpKQAR4+W44EH5oV5304YN+7/fOf77NlzNPf97rscTJp0OYYMCf7bxInFyM6uuaZat87C1VdP+iPAAcyffz+OH9fOIyZNyvddn4sWaecRGRlNcN11U3zpffTRxdi/P3QecfBgOubPn+q7Pq+7rggtWoTOI+rUqYtbb/2bL71PPlmMXbu084i//e12X3pfeOE5lJRo5xGzZs3ypXflyhfw7bffaO57883TUa9eCioqgLFjX0GXLl9q7jt//s04eLAekpOB119/E5s21eQRhw41wG+/nYzGjX9FevoRTJlyI5o2bYTycuCDD1Zj/XrtPOLPf/4zjh1rirZtgRUr1mPr1tWa+06aNBlZWS1QUQEMHPgJhgzRziOKiyfiu+/aIDkZWL/+M6xerZ1HjB17GTp1OhXl5cDXX2/B00+/r3m+X3LJJTj11M5ISQG+/PJrvPyydh4xcuRodO/eBRUVQOfO3+GKK7TziDffHIZPPumJ5GRg27YdePbZpzT3HTToPPTv3xfl5cDevT/h8ce184gBAwagb9+BSEkBfvppL4qKavKIQ4caYMGCqVCUmjlsEhPV3nfduh3E1KnaecRnn/XAK6+MQHIycPDgMSxc+IDmvmeccRYuvvjCPwqj5Zg3zz+PqH3+5Oa2woUX/p/vfL/nHu08ol27HIwff7nvfP/737XLETt2ZGHp0km+63PGjPtRr15NHlE7DR2Pfov8Wov/LZg6FYcaNQr5vt5yhJ484umna3rrejzVuOCCN9Ct22a/fcvKmmLevD/jhx/UnibR5hE//AC0a6dAUWrKpR5PNaZOXeA7l+3IIwLpzSNOOqkpUlKA9977Nz7+OHRnC8C6POLVV7XLEVbkETt21JQjgOA82Kg8IlCvXrk4//whqKgAmjaNPo84duwYHnhAzSM2beqK118fCUVJ8J3/EydWh80jauvUqZPuPMIrXF0jUh5RW2bmKSgoyPfdwyPVNfLzp/jSW1QUua7hvT4LC4tQWhq6HHHsWF38/e9/86X3mmuK0aaNdh4xY8btvvQuXx65ruFN7yuvvIBvvtHOI6ZPnw6PJwUpKcCLL76C//5XO4+48cab0ahRPVRUABde+CZ69tTOIxYsuBF79zZCcjLwzjuR6xotWjRFeTnwySf/1uyQBQCTJ09G06YtkJICfPhh5LpG+/ZtUFEB9O37GUaM0M4jnn32Mnz99alITgY2blTrGqHusR5PNd59twRDhpyG8nLgu+++xj//qZ1HjB49Gp07d0FKCvDxx9/hvfeC8wjv9T9mzJkYPVpd5CEwjwi0evV5+Pe/+yI5Gdi5M3Jd47zzBqK8HDhwYC/uvXe5X35TW25uLs45ZwhSUoC9e8PXNbp164ELLhiBigqgUaNjuOUW7XLEli1n4fnnL/wjP4lc17j00v/zne/Tpj2kWabLycnB//3f5b7z/f77tfOI1q2zcNVVk3zX5333adc1fvrpFCxalO+7Pm+5ZQEaNdKua1x//RRfehct0i5HpKen47rrpvrSW1xcE4/QqlN+gIEYiLUonjQJO9u0Cfm+5eXJmD37dl96J016Dqeeqp1HzJ49y5feVasilyPq109BeTnw5puv4MsvtfOIm2++GSkp9ZCSArz2WuRyRJMmjVBRAYwYsRp9+2rnEYsW/Rk//dQUycnAv/4VuRzRpk0LlJcDn332Cd57T80jQpeZFZSUeNC2LbBuXeRyRMeOp6KiAujZcwsuvFC7HPH885dgy5bOSE4G/vOfyOWIHj26oLwc2L79O6xYET4ekZvbExUVwKmn7sCkSdp5xHnnnYe+ffsCAH76KXI5YuDAgQCAvXv34rHHtMsRubm5GPJH5f7gwYNYuFA7j+jRowdGjBgBwL8cEcpZZ52FCy+8EIAa+PWWI06cOIF7770Xhw4dQsOGDTVfD+jsCRxqugUiuzRu/Cs8nuqgSn1m5lFoxKxN5x2aUl3dBf/5z5khK7xuFer3SkhQ0K5d5IYlM9Wt6/88Pf2IZvDeTKGGcnk81Wjc+DfL02Km336ri+3b24QsUIsuVIVej2efTYN3XdIrruiNkSP32Z4/2HW+Wy09/QguuOAN3++XkKCgsNBj6RDIwPPn+PGN+KMMZ1saJoz9F/I31loI9733gOPHDfmswOkaFCUBr78+Eu3abfOdc970ADXDOQPnmtfSsiUwefIGPP54T79r0g3ns1uFyoNFntKlW7fNaNduW0BQ5iy7k+VqgY0Idjt0qAEqKpKkH279228n+5XvATXP37UrReMV4TVuHLyt9vX/zDOKOvzfxHlsn302zRcI02rEFI1bynQhYwAJCtq/8Q+gWQWwbh3w6682plBuoa7nqioPPv1U/f/evckhXkVSUShuhw4dUgAo+/btU8rKyoIeFRUVfvuH2sf7KC8vj3nf8vJyS/Y9erRMSU5W/1X3VwcUlJer+wb+vfZz9f3U/X//vSLk+3mfe5NRXq4oSUkVId9vyZIKJTGxWgEUJTFRUR5/XH1frc9Xv0O1L70VFRVh01tdXe1L7/HjlWHT+/331UpCgrqv95GYWK1s3Rq8v8dT5ft+x49Xhk3viRNVvvRWVlaGTW9VVVXU6T1xosp3fBMSqjQ//+jRMiUhodKX3hMnqsKm9/jxSl96q6qqwvxe1crSpTXpPXGiKmx6jx+v9KXX46mu9XuWBZ2fiYk16S0rqw6b3t9/r/Clt7q6Ouzxraio8KW3rKw6bHp//73C73wPl96kJPV9H39cPY+9x2fJkuDz89ixcl96FUUJm97y8vKor89jx8r90nvsWHmY71cecH2Whz1/vJ//+OOKkpCg/v4JCaG/X+30Rro+Q+UnoY5vcrJ63Xv3T0wMnZ/UpLfa9/28+cnWrWW+tNe+vr//vjqq61Pr9aHyh8DrMzGxMmx6jcxPaj9q5yfe63Pr1jIlMbFc2bpV+/q0Kj8J3L+ysjLi9elNf0lJ6Pwk1PsnJlbEnZ9o/f4//FBzvseSn4TaPynJ//r0/v3770On4ccf/e/3vvfctlMp27DB9yjfsEFRNm5Uynf+HFUesXq1//3Q+3jrrfIwx0RRvvuuPOwxDswjtM5JrTxC6xjHm0do7V+7zBHpHq6nzBFtHrF1a5kCVCk//GBumUPPPVxPHlFVpb6v1vlbUmJsHhEqvXryiOrq6rBl5ljLHNHmEV5anx8ujwi1f2CZ49gx7eszVJlD656sr8wRWCeIrswReH0uWVIRVAbxfv7OnYry2WcVyiefqO/3ySdlyoYNZcrOnTVpr319GpGf+KdHLSNFuj715Cex1wnClzkSEoLLHFr3uG3bqmK6PgPzE637xY8/1uQR2ten/jLHDz8oEctsevIT/3u4OWUORQlfJ9CTnwRen+HSG5yf1FyfgY9485PA66d2nfLxx/3LMuHqBNHEGGrun4rv/mlWjEFffhKpTlAddH1q7a91vw91vXk8NXEOrTpcvPmJ3jpB9Pfwqlq/UfCjsrLSd+7Uzk8i7Rt4v49n39rxwlj33bdvnwJAOXTokBIJg8AG8AaBozngTlA7QxbhubcS7c2g7UqPVoV3zRoeLzM/P5Ddxzfe9Nr9+5j1XC1Q+18biYmKXxDMiuNr1/UtS/4Q7vipQXxvAVB9bnd6ZXkuwu///vuh0/DBB6F/88qZs0K+oHzmHEOuea1j8txzzswD7XjuhGvWS+v8lSkPdcPni5qeSPnRzJmhz69Zs8xJv1VlIqvzm5qODMbmN1r3C637l1mfJ1p+I/rzQEa/f2CdKRK957Ps90+jrueEBEXxeMTLr2J9jVPpiUlGOeiOSFyirGzqHc5fWzQrs1pp2TI1nYD677Jl1qfBsN+rtBTYtCn4UVoadxrtJMr5bDStRZy8Q4u8K9CKKtrru/ZKurG8XlSBQ/u9C3Ha/btpHW/RaP3+3ulorEh/Tk7oNHjvCYGq8wuAjRuBDRvUDRs2qM9rrUUQjnehmj/WxEBiIlBYWJO3hTomHg8wfnzN3+24RzmFqNdsrLTOX1nyUFHJkofGS6sM8v336v/z89XsLfBRUGBPemSUl6fOsw+o/xo5VYPWPVTr/mXW5zG/EYtZdSan3T9jUft6fuYZNfRbWyz5lVvuNzJgEJjIIJEqvNEyK4N02g0toagQ6N496LH7wZUA5P1eTiV7wCea6ztcI4tR+YNdRKywitCoFa1Qv//48UC/fupzK9Kv+xzMzAS6dQO6qovvoGtX9XlmZtSfGS4oEJgeb/6gdY/ytvtt3qw+37zZEe1+phHxmo2H7HmoiGTKQ+MVKajnze4CHzqyO0PTIyuzgnJWX//Mb9zNaffPWHnP99zc+PMrs+43DCzHhkFgIgPF2wpuZoHcaTe0UL3Ult2xA+0fnQrA+RUa2egN+Igo3PUdTSOLmb1kzCZahVWURi09hc/av/+HH6o9K6xOvx3nYLiggJ6eJkVFaltfr17q81691OdFReakW3aiXbNGkDkPFY0oeahVRAvqiZYeGZhx/Ye7hzO/cS8n3j/jEW9+Zdb9xk0NmUZjEJjIYLG2gptdIHfcDS2gl9ruJl1xzd+zUF3tAeD8Co2MzBhaZDWt6zvaRhaje8lY1QIuWoVVhEatWAqf3uN17Jh96Rdtyploe5poDdeOcnYKx9LKA0S7Zo0SeP6yF1BsRMhDrSZaUE+09IQi2vVl5P0rmnu4aPdLsoZT75/xiCe/ivZ+oye/cVtDptEYBCYShNkFcqff0Eq2eSyp0IhWIJaNkUOLRGJHI4vVLeAiVVjtbtSKtvDp1DmizRDpHmX1cG0ZRMoDQl2zTrqHCdULSLJ1CtyaB4kW1BMtPbUJdX0ZjAEkhzMgPxapzCuKWPOraO43evObkhL3NWQaiUFgEo5oFRSr0mNFgdzJN7Sc9orpx8/JBWKrOa1RwurvY1cFJt4Kq1H5qd3nTzSNdk6eI9osIt6jRCuTeEWbB9S+Zo24h4lyPEQL4mitUyDqfCXMgygc0a4vo7mxJ7yrFBqTH4vcSCOTSPebWPIbLhYbHwaBSSiiBdmsTI9VBXKn3tDMPn5OLxDbQcSATzys/D4yVmCMzk/tPH8iNdo5fY5oM4l0jxKtTFKb3jzAiHuYSMdDtDww1DoFls5XEkPPN+ZBpEW068tobu0J7xoFNufHFCTc/SaW/IYNmfFhEJiEIVqQzY702FEgF6VXjxHMPH5OLxDbRaSAjxGsmvNX1AqMVnrNyk/tOn8iFT7tmiOajCNamSSQ3jwg3nuYaMdDuDwwYJ0CdO1q6XwlsfZEZh5EoQh3fRlMlACSk+pgQrE5P6bQtO43seY3bMiMHYPAJAzRgmx2pcfKArlIvXqMYtbxc3qB2Cx2F3Dt/vx4yDadQLj0ipa/GyFc4ZP5hfxiPWf15jmx5lF684B4z0nRrmER80A72d4TmRzFDdeX3QEkJ9bBiGIRT37DhszYMAhMwhCt0ixaeowmWq8e0bmhQBxKPEFUuwu4dn9+PGSbTiBSep2an2oVPt2aXzhJLOes3jwn3jxKTx4Q7zkp4jUsUh5oO/Z8I4O54fqyK4DEOhiRPzfkNyJhEJiEIVqlWbT0GE20Xj0ycNsNKp4Ahd0FXLs/P16yTScQKb1Oz09DcVt+4TR6z1mtPOfzz2v+Hs3+sfQIrv1vOPGck6Jew6LkgUROxOvLHKyDEQVjfmMdBoFJKKJVmkVLj5FE7NUjA9FuUGZNdxBvgMKqodRaSkrkLmDLdn1Gk14n56daRMsvSB8956xWntevn/p/UaZIieecdOM1TDGKYaE6IreQrYxHRM7CIDAJR7RKs2jpMYqovXooemZOdxBvgMKKodR+AiqcOSf+i4QERdfni0S26zPa9Do1PyXnivacDZXnAc6bIsWya5hBRKnFulAdkRvEW8bzZo+bN6vPN29m9khE0WMQmMjF2KtHXmZPdxBvgMKoodTRfp/ACmfL4WdiafVkJHqqo/p8Ecl2fYqYXpkXBiS5BOZ5oQLCbp8iRQ8GEeXGherExiCi/eIpMxUVqdlhr17q8169mD0SUfQYBCZyOfbMk5PZQ4mNCFAYMZQ62u8TqsKZt/E6lKzfF9Xni0q261Ok9Mq8MCDJqXae99FHnCIlHgwiSo4L1ZnCqIZNBhHFEGuZKT9fzQ4DH8weiSgaSXYngIiI9PP21K0dODV6KHFeHjBoENC2rRqgyM4GKir0vYfeodQxf5/MTKB1Zk0Cu3YFkpPRsiK6zydn0epZPmiQveki5/PmNWefrTakFRSoDVqcIkUnjTwdOu9BRE6xbJl6XwPUMtPSpcCVV8b2Xvn5wJgxwdszMoC5c2NPY6DaQevsbOPe1+0yM4HWrYO36y2jE8WD17e82BOYiKTC4d0qq4YSWxWg4NBoCkfv0FWuvE0iYE9fItJDq4xr9BRg3o7agQ8jO2pzNA5p4XQk8uP1LTcGgYlIGrzh+IsmwCBT0JwBE9Kid+iqrItukfj05qmBDWky5cluwqAE2S1cGVe2hk2z160gMfnub5t+CbuwJ6cjkRuvb/kxCExEUuANJ7RwPXVlDJpzaDSFonf+O/YsJzPEm6fKmCe7BYMSZKdIZVzZGjZlC1pT/Pzub7lNsKz7Is2FPTmnsdx4fcuPcwITmYzz5RhD64az7XsPGNcJxjlRyUlimf/OiDmtibzizVOZJ4vNqjlSSRKlpaG7gWdkAshEaSmwfz9QWalu3rwZSEpSz5dYRAqqeBs2I80xLgor1q0gcQTd35QEFCQ8jqGvXI+Wo7qpC3smJanXz1zOaSw7Xt/yYxCYyERGLuLgdlo3nPbtFPsSJbBoW2nZSEFOFm/Pcl4f5BVvzxf2nBEbgxLkp7AQmDMnePvMOQDuRFGRf+OAtwf5zJmxfVw0QRWZGjZlC1pTfELe36o92FbnDLWjDhf2dBSrr2+tRrfMzNgb3tyO00GQ49k1/x6nLzAWh3frE83QQQ5NDsb5OsmL1wfVFu9wbNmGcxO5WkGBOj59wwb1+YYNfuPVjR7OHm0ZV6Yps0RY54FlOmto3d/i7ajD309cVl7fWtM1FRaa95lOxyAwOZqdlXj2+jGeCAVKWUSqULCRQlW7gClD0I8FYmvw+qBA8TZEsiGTSCKZmUC3bmoPRkD9t1s3dXutPwc+/vizj557thPLuHYGra0o07FMpop0f4tl4U0ZyuRuZ9X1rdXoVlBg7uc6GYPA5Fh2V+LZ68ccMvWCsFu4CoVRjRQyF4BrFzDbtVMLGSIH/Vggtg4b8SiUeIM0TgzyEFFosdyzWcY1hhV1QJbJ/IW7vxUWJejqyWl3HZ7EEm2jG0WPQWByLLsr8Xb1+pE5KEfG06pQGNFIIXMBOLCAqSjqozaRgn4sEEfHqPyPjXjuofeciTdIo/f1vKcTyYf37OiYlb+ZXQfk7xua1v2tIL9aV09Ou+vwRE7HIDA5lgiVeKt7/QQG5e68U9/QG3IPvY0UgUO53nlH7gJwqAJmIJGCfiwQR2ZkowSH7kdP5iCl6A1ZoqePiELjPTsyM/M3s+uA/H310duTU4Q6PJGTMQhMjiVKJd6qoV2hWqXvvjt46E1RkbnpIHnoaaQInJR/1Ci5C8ChCpgej/35hRYWiMMzo1cOh+5HJnKQMtIchKL35BI9fYFimfOR9JO50cVNeM8Oz+z8zew6IH9fc4lShydyKgaBydHcVInX6tlYWGjMysXRYgVFLtE2UgROyv/WW3IXgEMVMIuKxM0vWCAOz6xeOYHXB/O3GqIHKbVWk37wQfX5+vViN2TJ1tNM63iz4dk4Ije6kD/es8OzIn/TUwfU24jF39d8bqrDE1ktye4EEJnNLYsseFulaxeqEhOB4cP9v3tFhXlpWLZMDQp407N0KXDlleZ9HlknMxNo3dp/29KlatCnqkrOAnBeHjBoENC2rVrAzM6uuT5E/B7h0ut2WvmfkY0STs/fSkvVR2Wl+nzzZiApCcjMAEKN2BQ9SJmfD4wZ47/tlVeAv/9d/f/48Wrv/9pzgYvUkGXFOW2kUMcbADIygLlzrU+P02g1ugwaZG+6SBvv2dq08re6ddX/796tHq94RVsHLCryz6e8jVkzZ2q/hr+v+dxShyeyGnsCEzmE3a3SovcKI+M5oZVetgKm1emVpeer2fmfG/K3wkJ9PTlFHw4bOAdh06ZqALj2YpCAuD257L6n68XVu80leqMLhSZbGcMqofK38eOBfv3U51b3dA8c7Rbt6En+vkQkIwaBiRzEzqAcKyjuxAKwc8k29NjM/M8N+VtBgb5KsGxBypKS4N9QUYBnnqn5u2gNWU5oaCNjiN7oYhVZGibtEnh8RD5etfO3Dz9U82K7GlrZiEUiEvn6NYLTv5/IGAQmchi7gnKsoBA5h6w9X83K/9yQv8VSCZYpSJmTE/o37N1b/b+owWs2tBFgfaNLrAv9mVmpl61h0mqBx2fSJPGPl/f8PXbM+Q2tRmDQzD1kyu9iuV/I9P2ciEFgIjKEqL3CWGAi0i9Ur0k3V8hEzd9EIEuQkr8hyc7KRpdYFvozs1Iva8NkrPQGVUIdn6eekud4uaGhNV4MmrmHbPmd3vuFbN/PiRgEJiLDiNYrjAUm/Rg0t5aox1ur12RghUzU9JtBtPyN9ONvSLKzqtFF7xypZlfq3TAlT216gyqhjk8gkY8XG+nCY9DMXazK74wqw+u9X7gtPxcRg8BEZChReoWJUmCSKUgmctA81qGpIhP5eEdTIRM5/WYRJX+j2PE3JMCZ9xQj6Z0eRqtSv+17jyHpcVtPUb1BlVDHJ5Dox8sNjXSx1gk0r69txqRLFjLVqeJhRX5nZBle7/3Cbfm5iKQLAi9evBjZ2dlIS0tD9+7d8dFHH4Xdf+3atejevTvS0tLQtm1bLFmyJGifF198EZ06dUJqaio6deqEl19+2azkO5JbMmSSiwitjDIFyUQJmmuJZWiqyEQ/3kD4CpkM6Sci0qJ1TykstDddstKq1Ldvpxjy/m7rKao3qBLq+EycKN/xcnIjXTx1As3rq71x6ROdTHWqeJmd39ldhndbfi4iqYLAq1atwtSpUzFjxgxs3rwZ/fr1w7Bhw7Br166Q+2/fvh3Dhw9Hv379sHnzZtx+++244YYb8OKLL/r2Wb9+PcaNG4cJEybgyy+/xIQJEzB27Fhs2LDBqq8lNTdlyCQXu1sZ7b7B6iVC0Dwcvb1iRCf68fbSqpDJkn5yD/bsJD207ikFBXanTE5WVOrd0FM0HoHHp7iYx0sU8dYJ3B40k61OZQQz8zsRyvDMz+0lVRD4oYceQl5eHiZPnoyOHTtiwYIFaNWqFR577LGQ+y9ZsgStW7fGggUL0LFjR0yePBlXX301HnjgAd8+CxYswODBgzF9+nR06NAB06dPx7nnnosFCxZY9K3k5cYMmcxnVM9yuwtMdg3divX42R00j0RvrxjRiX68I5E9/eQ87NlJejjtniICKyr1Tu4paoTA48PjJQYjgm5uDpqJELS0g1nXryhleOZP9pEmCFxeXo6NGzdiyJAhftuHDBmCdevWhXzN+vXrg/YfOnQovvjiC1RUVITdR+s9AaCsrAyHDx/2e7iRWzNkMo/RPcvtLDDZMXQrnuNnd9DcbWQ/3rKnn5yHPTuJ7MdKPVEwo4Jubr2+RAlaOoUTy/AcDaaPNEHg/fv3o6qqCs2aNfPb3qxZM+zZsyfka/bs2RNy/8rKSuzfvz/sPlrvCQDz5s1Denq679GqVatYvpL0mCG7g1VzPpvVs9yuApPVN1gjjp+bexnYQfbjLXv6yVnYs5PIPVjhJ5k4MehmJbccPyvXWXJaGd5pa8eYTZogsJfH47/KrKIoQdsi7R+4Xe97Tp8+HYcOHfI9fvzxx6jT7yRuyZDdzMo5n53Ys9zKG6xRx8+tvQzsIvvxjjX9kSrwrODrw+NFZA4ufiymeCv8zDPJak4LulnN6cfPjnWWZK+D1Oa0tWPMlmR3AqKVkZGBxMTEoB66e/fuDerJ69W8efOQ+yclJeHkk08Ou4/WewJAamoqUlNTY/kajpOXBwwaBLRtq2bI2dnAHzNtOF5pKbB/P1BZqT7fvBlISgIyMuxNl1G0epYOGmT85wBAvXpqz/LagUyRe5ZH+/tbdYP19syX5fiRO9QOoGRn12wvKgLmzq157q3Iz5wZ/u+zZgGzZ5uWXGlFOp5EpN+yZWo5CFDvsUuXAldeaW+aSJWfD4wZE7w9I8M/L9TitnuMVpk1M5OjJazkpKCbHZx6/KyqcztZZibQunXwdrfEpfSSJgickpKC7t27Y82aNRhT666/Zs0ajB49OuRrcnNz8frrr/ttW716NXr06IHk5GTfPmvWrMFNN93kt0+fPn1M+BZyKy1VH1pBL7szZKuDsk6vdFvRM7d2BatfP2DCBGD5cvVzRO9ZLtrv7+2ZX1Agx/Ej5wsXQIlUgdf6OyurocUbECEif6yUiy3eCr/b7jFuC3oTycSJo2FJbNIEgQFg2rRpmDBhAnr06IHc3FwsXboUu3btwrXXXgtAnabhp59+wtNPPw0AuPbaa/Hoo49i2rRpyM/Px/r167Fs2TKsWLHC95433ngj+vfvj/vuuw+jR4/Gq6++ivfeew8ff/yxLd9RZIWFwJw5Nc/tDnoFsjoo5/RKt9k9S0NVsJYvBz78EOjbV/ye5SL+/m7umU9iiRRAiVSB1/o7hcYeEETGKilhpdzJYr3HaI1uEZ3bgt5aZP39SExGnU8czUlWkyoIPG7cOPz666+46667UFpaitNPPx1vvfUWsrKyAAClpaXYtWuXb//s7Gy89dZbuOmmm7Bo0SKccsopeOSRR3DxxRf79unTpw9WrlyJmTNn4o477kC7du2watUq9PJGEMmnoAAYNSp4uyhBT6uDck6vdJvds1Sr1fP332s+X2Si/v6RhkqxAGwNp08XEwl7NRCRzHJyWCknf6FGt9g9L2m0ZTo2rHJ6FzKWkecTR3OS1aQKAgPAlClTMGXKlJB/Ky4uDto2YMAAbNq0Kex7XnLJJbjkkkuMSJ6jac0bZXfQy0vUoJzMzOxZylZP67EAbB3RpguxGq9vIpIZK+VyM7ohVmt0y9Ch9p0TLNNFT5bpXdhRQw5mnE8czUlWSrA7AUQkNrMm4fdWsBIT1eesYJlLq8DCFc9jE2llcbevUsvrm4hk5/TV6J2sqAjo3r2mAbZXL/V5UVFs71eyzRNydMu2bfGlM1Ys0+lj1eik2kFcvZYtU4P5gPrvsmXGpYuMZdb55NSF70g80vUEJiLnkKHV0ymt8hyeb6xIPX05MkGO65uIKBxWyuVk9BRxOe2VkKNbvEE7q7FMp48Vo5Pi6ZktS09lt/PWCevV42g3khuDwERkK5ErWE4aasfh+cYScWFAEYl8fRORc7l9XnajlZaqD1mOp9ENsaJND8IynT5m/37xBnEZ1Bdf7Tphv37AhAnqguYi5AdEejEITEQUgtNa5UWrwMhO1J6+Tum5TkQUD7fPy260wkJgzpya5248nqFGt9iFZTp/0TRSmDk6Kd4gLoP6YgtVJ1y+HPjwQ6BvX452I/lwTmCSTjzzLRFFS9RW+XjOf85v6GycT46IWEZSuX1edqMVFPB4AmKNbmGZrkZhYXRzQJv1+3mDuLXpCeJyHQWxadUJf/9d/T9/J5INg8AkFQY5yCrxFujMYMT5L1IFhozDRWKIiGWkGpmZQLduwY/MTLtTJiceTzGxTKeyu5HCiCAug/riErFOSBQPBoFJGgxykJVEa5Xn+U/hiNpznYiswXsEOUFgT3b2bKdoiNBIYUQQl0F9MYlWJySKF+cEJsvpnbPSu//69QxykLXMnD9ML7cF+bQW9cnMtKZQL9uiQpxPjsgdtMpQbrtHkPMELsY7YQLwzDM1z2VenJfcwalBXNnKxGYQqU5IFC/2BCZL6R2qWHv/8eMBj8f/7wxykNnsKtCVlgKbNqkFLQA4ccJdQ5GKikLP71ZYaO/nB84vJwr2UiByvnBlKA5XJZmF6sn+1FPs2U5icWvPdNnKxGZxapCf3Ic9gckyWkMVBw2Kbn9FUYPAiYlcCZecL3Bl81Gj1H89HvVacPr5n58PjBkTvN2qoX1an5+R4f+7iIS9FIicK1IZytsQVFDAMhLJJ1RP9kDs2U52Cuyp7qae6TKWie3EntMkOgaByTJ6hyqG2l9R1KFhl1/OIAeJpbRUfRh1w9cqcFVUAL17O//8z8wEWrcW7/NFP97speAOdk+XQtaLpgwlQ0OQ3inByB1CTWkUiD3byS56OzI5jaxlYrsEduTx9qCeOdOe9BAFYhCYLKN3zkqt/Xv3Vv/PIAeJpLAQmDOn5nm8N/xIBS6e/0Tu4w2gPfgg8MgjNdu9+c2sWcDs2ZYniywQbRlK5IagcD3pNBs2MgC2a+hXWgqUStQTLVRP9vHjgeXL2bOd7Mc510kP9pwm0TEITKYJLNDv2wfMmAHcc090BTqnD23kUBFnKSiombKhNt7wicgItQNojz4K3HEHcOGF/vuwF7BzyV4mitSTTqvn1JyZwJ3WJtURCosSMCfE8bzhBvVfEXtih+rJPmtWdD3btUZjcXQEGYGL75Ie7DlNomMQmEyjVaC/4Qa1B1M0QxVlGNoYKw4VcRatioZTzldRcWhxaGxkcgbv+f3558EBtHvuUbeJEgTkOWc+mctEkXrSac4DnwGADam6FeRXY9SYRL9tr7wC/P3v6v+NmtPU6HtwYE/2aHu2a43G4ugIMoLsjXBERLUxCEymCTcU4pFHor9xijy0MR7xDhVhhZvcLtTQ4jyXLNIRCRuZ5Ff7/P7Tn9Q58WurqlIDa6LcG3nOGSNSUE20MlG0QcBIPek054EXNMgt+vQVmZlAZq3juXu3GgA2ck5TkRbK0hqNxV7A+rBhXZvMjXB664xcd8AZeD2TFgaByTQcChFevMfH6gq31UFnBrkpHK2hxUMHAYLERmzF+cjkFnh+BwaAATWA1r69tekKh+dc/EQKqkUjZENcnv8+3kooYG5POquDFrJNX1FSYuycpqItlMXgVPxky3/sIFojXLT01hm19mfPennweqZwGAQm13BaUNHqCrfVQWf2KqNwtCq02773MAgMNsLJLtTQeaCmJ6WIQ1F5zsVHtKBaJJoNcUNrzstQldCSEnN60lkdtJBt+oqcHGPnNDU6qEz2ki3/IX301hk18zc2tEjB7utZa452WWMuTsQgMLmG04KKVle4rQ46s1cZhaNVoW3fLkSXSSLJaA2d//BDoG/fmgAaOYdsq89rpdc7RYlWJbSkRH1udAOG1UEL2aavMHpOU6ODymQvBvWdTW+dUTN/IynYXZ7QmqNd1piLEzEITK7BoGJ8rA46s1cZhcNFOkgkRo800Tq/zz675u/kLLKtPq+VXu8UJVYHldwWtIhlTmIj5zTlPdhZ9Ab1jZpjlj0DQ+PxonjYXZ7QmqOdMRdxMAhMrhEpqMgbLpFcQlVoRe2FRWIxOr83Y6SJzIvQkH6yBdUipZc9Rc0V65zERs5pGk8exTK3WPTmP0bNMcuegaHxeFE87C5PaM3RrrcMy4XtzMMgMNEfIt1wuVIqkXhkXaSD7GV0BcuokSaBBV6Rzu/SUqCUQRtTyRb4D9kQ9we7K6GyixQkNXpO4ljLuLHmUW4LcskQ9NaT/xg1xyx7BobG40Xxkq08ESiahWcpdgwCE/0h0g2XK6USETlDYH6/b59aQW/USH2ut4JuxPQ1oq/kXFiUgDkuCtrYRaTAfzTCpVf2SqidIgVJjZ6TWJSF9Zwa5JIl6B1t/mPUHLPMD0Lj8SIjyFae8Ipm4VmKD4PAZBvRWsUj3XC5UioRkTm0VhI2a6RFYH4/e7a9i1jYvZJzNAryqzFqTGLQdqcGbcgYslZC7SbKYrxWL6zn1CCX24LepOJw9uholQFF6ikvArecT5EWnqX4MQhMtpGlVdzLbYuOEBFZRWslYatGWti9iIXdKzlHIzMTyHRR0MbtRGuodxtRFuMlY7gt6E3ij+4RiVYZ0KqYgAz3OzedT5EWnqX4MQhMtmGrOBERAdpBWKtGWhi1iEWs7F7JmeSoBFpJtob6aLmlJxWRkbguij4yjO4Rid0N8aLf7yKdT04rv3BNAfMxCEy2Yas4EREBrEiywGs/0SuBVnNiQz0XmiGKDddF0UeG0T0isbshXvT7XaTzyYnll3ALz1L8GAQmIldyWqspEcmNi2jZS/RKoNWc1lAvykIzWj2R2dOSRMZ1UfTh6B65iH6/0zqf6tZV/z9yZHzlF1HrxFxTwDwMAhORKzmx1ZSI5MYCr31ErwRSfEpK7F9oJtycjuxpSSLjnNH6cHQPGSnU+TR+PNCvn/r3Pn1Cj2yJtvzCOrH7MAhMZBGjenlwPjtjsNeXsURtRQ7E64fIHrLkEeRMOTn2LjQTaU5H9rQkchaO7nEPK0Zy1D6fPvxQDQAbNbKFdWL3YRCYyCJG9PLgfHbGYa8vY8nQiuymlXWJRCNDHkHOZXfPvEhzOrKnJZHzcHSPO1g1ksN7Hh07ZuzIFtaJ3YdBYCKLxNvLQ5T57IhCEb0VmSs1E9lL9DyCrGXHHLh2LjTDOUKJiMRg9P1Hbx0/3pFRWvcTq0a2kPwYBCaySLy9PLR6kVg5nx2RFtFbkblSM5G9RM8jyFp2zYFrV888u3siExGRyuj7j946frwjo3g/oXgxCEyGkW1l49JS9SFLetnqRxQ79sIikotsZQrZ2D1HsxvnwOUcoUTkBFp1aFnm+Lf7/mPEyCg7R7aQ/BgEJsPItrJxYSEwZ07Nc9HTy1Y/otjx+iGSi2xlCtnYPUezW+fA5RyhRCQ7rTq0LHP8233/MWpkFO8nFCsGgckwdreq6VVQAIwaFbxdlPSG6qXTtSvwySdA797it/rZ3ctIy+7dNf+KfPzIeCL3wjL7epG91wbpE26kiyy/uWxlCtlwjmYiEh3L7GLSqkPz/iEmUevkZpJtxLfVGAQmw9jdqqaX6JlApF46orf62d3LKJRly9TFwQB1eoClS9XAILmHqK3mZl8vsvfaIH3CjXSZMcOeNOklW5lCNpyjmYhEFqrMfuWV9qaJVFp1aN4/xCRindxsso34thqDwESCkr2Xjmjp371bLUx654StrlZbsocOFS8gSO5j9vXCXhvuYuhIF3bFIqI4lZYCpZzjm6KkVWYfNMjedMmCc+pTbaLVya0g+ohvuzEITCQo2XvpWJb+KAMU27b5LwoGqHPDbtvGIDDZz+zrhb023CVcRU/Xb87hE0RkgMKiBMzhHN8UJa0y+/ff25Me2XBOfapN9phCLNjgER6DwEQUEyHmGA05Vix0gKJ9eyAhwb9QmZiobreDEMePiEgLh0+4CufPC8/onnVu66lXkF+NUWMSg7Y75buyTGcsrTJ7u3b2pUkmeufUd3p+ZPdIBN5fSTQJdieAiORUWAh0717Tutyrl/q8qMiiBGgFKLw9gwO0bKnGiBP/qIMkJqrfwa5Yhu3Hj4gonJIS7eET5Dha96TCQnvTJYqiImOPj9HvJ7rMTKBbt+CHUwIgbi/TlZYCmzapwS1A/XfTJnV7LEQrs8tG7/Xm9PyosCjB1u/H+yuJhj2BiQiA/pVD7Z5j1LMtdIDC8/02AKFLiXl56nxibduq8Q07p7e0+/gREYWVkyPW8AnBOG21bc6fF57ennVWvx/Zy+1lOjMWnw1VZnfy8HU7OT0/snskAu+vJBppgsAHDhzADTfcgNdeew0AMGrUKPzjH/9Ao0aNNF+jKArmzJmDpUuX4sCBA+jVqxcWLVqEzp07+/YZOHAg1q5d6/e6cePGYeXKlaZ8DyJR6V05VO8co0YPlVPahw5QKO3CByi8vQjs7k0QePy8x2fPHvU5hwoRGcfpQx1N4e2KVVCg9gBmVyw/Tlttm9dCeFpzKoryfmQvt8+7b1YQXJQyu9M5PT/KzAQybfx+vL+SaKQJAl9++eXYvXs33nnnHQDANddcgwkTJuD111/XfM38+fPx0EMPobi4GKeeeirmzp2LwYMHY+vWrWjQoIFvv/z8fNx1112+53Xq1DHvixAJyuyVQw3vJWBwgMLu+dy0jg8XcSAzuG1+Mi6SEiORhk8Ixo2rbRMRheL2ILjd9Jbp3FYGJCJ/UgSB//e//+Gdd97Bp59+il5/1NyKioqQm5uLrVu34rTTTgt6jaIoWLBgAWbMmIGLLroIAPDUU0+hWbNmeO6551BQUODbt27dumjevLk1X4ZIUGavHGpKL4GQY8VieyszhrLpwaFCzmZ3I0MgtzU6OH2oYzRirvSxK1ZIblxt205aC/sIN/2Gd12C3bvtaTSx+/OJyHJ6y3RuKwOSPqLVWch4UgSB169fj/T0dF8AGAB69+6N9PR0rFu3LmQQePv27dizZw+GDBni25aamooBAwZg3bp1fkHgZ599FsuXL0ezZs0wbNgwzJo1y6+ncKCysjKUlZX5nh8+fDjer0jkeKb1EjAoQGH3fG5sfXc2uxsZArmt0cHpQx2jwUofyaywKAFzRJ9+Y9kydcFaAEr79tg1Yyl+GZkHwKJKdK3PR/v26mipvDwTP5CIRKC3TOe2MiDpI1qdhYwnRRB4z549aNq0adD2pk2bYo93As0QrwGAZs2a+W1v1qwZdu7c6Xt+xRVXIDs7G82bN8dXX32F6dOn48svv8SaNWs00zNv3jzMqX1lkC1Em+ORrWZy41A2c8m+iFKkXpSR/m53I0MgNjpYS4Tz3+pKH4ebkpG0FvYRZvqN3bvVAOwf6xR4qqvR4u4C9L17KICW5leiAz4f1dXqRT90KHvxC4h1BjKS3vuq7PfhqGMAHBkRk8Dy4r596vH2LsXF/Ep+tgaBZ8+eHTGY+vnnnwMAPB5P0N8URQm5vbbAvwe+Jj8/3/f/008/HTk5OejRowc2bdqEbt26hXzP6dOnY9q0ab7nhw8fRqtWrcKmg4wn2hyPbDUj0ib7IkqRelFG+jsbGdxNhPPf6kqf2T2PGWR2F62FfYTJQ0tK/BeqBZCEKrxfuA1He9QEYU0LWof4fFRVAdu2MQgsINYZiGIXVQyAIyNiFliOmj2b+ZXT2BoEvv7663HppZeG3adNmzb4z3/+g19++SXob/v27Qvq6evlneN3z549yKx1Fu/du1fzNQDQrVs3JCcno6SkRDMInJqaitTU1LDpJvOJNsejaD39ArHXAdlJ9kWUIvWidPrQOhF6sspM9vM/FpGuicB70po1wIEDwT1NtIK6nN6ChJKTAyQk+AdiExNx6vD2QK0YrGlBa43PR/v2Jn2gXERrNBK9ziAaq0d/ss4ktogxgDhHRvD398f8ynlsDQJnZGQgI4qrKTc3F4cOHcJnn32Gnj17AgA2bNiAQ4cOoU+fPiFf453iYc2aNejatSsAoLy8HGvXrsV9992n+Vlff/01Kioq/ALHJCbR5ngUvacfex2QnWRfRClSRcPpvQ9F6MkqM9nP/1hEuiYC70kjRvj/PVJQ1+kNLySZli3VnmYFBWoP3MRE9SS3qheu3Z8vONEajUSvM4jG6tGfrDOJLWIMIM6REfz9/TG/ch4p5gTu2LEjzj//fOTn56OwsBAAcM0112DkyJF+i8J16NAB8+bNw5gxY+DxeDB16lTcc889yMnJQU5ODu655x7UrVsXl19+OQDg+++/x7PPPovhw4cjIyMD33zzDf7617+ia9eu6Nu3ry3flcgsTm/Fk2blcCIJidaTVfZeGrKn3whac85lZABNmtRs1wrqOr3hJV6O6b0v05yOeXnAoEFA27ZqEMLq9Or4fMt6Vgry+7HRSG5Wj/50ep3J8eIcGcHf31iRyryxlFdEG90hGymCwADw7LPP4oYbbsCQIUMAAKNGjcKjjz7qt8/WrVtx6NAh3/NbbrkFx48fx5QpU3DgwAH06tULq1evRoMGDQAAKSkp+Ne//oWFCxfi6NGjaNWqFUaMGIFZs2YhMTF48QkimTm9FU+KlcOJJCVaT1bZe2nInn4jiF5Qlz1Q74je+zLO6ejtZWZXD9woP9+SnpUC/X6i5zcUntWjP51eZ3K8OEdG8Pc3VqQybyzlFdFGd8hGmiBw48aNsXz58rD7KIri99zj8WD27NmYrXEmtGrVCmvXrjUqiURkI7NXDrd6PjKKkSC9jszmmF5+MZK9l4bs6XcD0QP1kfIA0Xrv6xbnnI4Unuk9K/n7EZGd7B6ZQT6RyryxlFc4uiM+0gSBiYjCMXvlcKvnI6MYhOp1dKXgvcZi5IhefnGQvZeG7Ol3A9ED9ZHyANF67+sW55yOFJ7ZPSs92/j7Ebme3R0z7B6ZQQAil3ljKa+wE1Z8GAQmEgTnthGb1fOROZ3hQ621eh0NGgq/pdkdQvpefkSCEz1Q7/g8IMKcjiwziU1pH9+cnERm4ug+Cwg0HQwR+WMQmEgQnNtGbFbPR+Z0Rg+11up15Pl+G5wYBJa+lx8RxcXxeUCEOR1ZZhJcnHNyCsPunoxkCo7uMxmngyESGoPARILg3DbkJkYPtdbqdaS0Y68jMh57EZFs4u05a8tCeWHmdGSZSQKyz8npoimmAjn9HsfRfebidDBEYmMQmEgQTilYEUXD8KHWTul1RFJgLyKKRLTFG+PtOWvbQnkaczqyzCQJWefkdNkUU4Gcfo/j6D5zcToYIrExCEykwenzzTn9+5G9bDm/avU6+uWTEvyUnI3Kzf6fb1cARi9bet2ZyGm9iiL1ImL+6j6Bv/nddwOPP17z98CgqdVB4nh7zoq+UB6RoTQWJnTqFFOB2FPWXKI1EhqOHTOIhMYgMJEGp8835/Tv53SiFyBtO7/+KGA+9kZrzAnRi8X0XmsGsa3XnUmc1qsoUi8i5q/uE/ibewPA11yj1oO9vEFTrWvCrGs83gYI0RfKIzKUxsKEbpliij1lzWV1/m8L2aeDIXIwBoGJNDh9vjmnfz+nM7sAGW/PTbvPr4L8aowakxi0XZZea7L1uovUKOG2XkV2n/9kvXC/ee3f3Rs01bomRL3GiVyFPRnJRK7J/2WdDobI4RgEJmGINvzZ6cN2nf79nM7sAmS8PTftPr8yM4HMEL1YZOm1Jluvu0iNEm7rVWT3+U/W0/uba10Tol7jRK4Tqicjr08yAPN/IrITg8AkDKcNfyYyU6QCZLzTRVjdc5NzqMrNNb1aiIjIPdiTkYiIHIZBYBKGbMOfiUQW73QRVvfc5ByqcmOvFiIiIiIiZ2PHHfkxCEzCkG34M5HIZOuZyTlUyUjxzmlNRERERET+2HFHfgwCExE5kGw9MxmcIyPFO6c1kdHYc4aItDB/IJlpnr8ZAE9f52HHHfkxCExERESOYvWc1kSRsOcMEWmJlD+Itnh2JAxqu4vW+TtnJnCnPUkiE/E6lh+DwEREROQoVs9pTc4Xb1CDPWeISEuk/EG2xbPZ6OUumudvBgABp6AjcjsGgYlIChxqRG7GXjVE9oo3qMFrlYi0RMofZFs8m41e7qJ5/go6BR2R2zEITGQSBm2MxaFGZCbRFxJjrxpryTb0lszHoAYR2UW2xbNFKTuRnFgGIzIXg8BEJmHQxlgcaiQWpzVyiL6QGANQ1pJt6C3pp7fhR9a8jYiISCYsgxGZi0Fgciy7g1QM2hiLQ43E4rRGDtEXEmMAylqyDb0l/URv+CEiedldB3E7s3uSajUisqeqMVgGIzIXg8DkWHYHqVjQI5HFW4B1WiMHFxKj2mQbekv6id7wQ0TysrsO4nZm9yTVakRkT1VjsAxGZC4GgcmxnBakioS9DkiPeAuwPK9IJMz/SC/RG37Y04xIXm6rg+gVeM9eswY4cABo1Eh9Hm9+Z3ZPUq1GRPZUJSIZMAhMjuW2yr/dvQ4YhJGL2wuwoi8ER/qYnf8xf5OfbL8he5pRbbKdv27H3yW8wHv2iBH+f483vzO7J6lWIyJ7qhKRDBgEJnIIu3sd2B2EJn3cXoDlfKDOYnb+x/wtmGxBKdl+Q7c31JE/2c5fspfoDd2B9+x9+9T0ZmQATZrUbGd+R+Q8spUfnYhBYCKHsDvjtDsITaQH5wMNT7YCmtnpYv4WTLaglGy/odsb6sifbOcv2Uv0hu5o79nM74icR7byoxMxCExEhhA1OEQUiujzgdqNBTR/zN+CyRaU4m9IMuP5S3qwoZuIRCVb+dGJGAQmIiIiPyygUSQMShGRl+b0AxmAEdmE6NMbiIYN3c4i2+gsonB43tqPQWAiIiLywwIaERFFS2v6gTkzgTtNfH+3jk4hd+HoLDISGxWIQWAiImKBgIiIiGKiOf1ABvD/7d17dBT1+cfxzwaSCCZZCUvYRAKkVkEkqMQSA62KQICKUPFCDh6kLY1iBU2FtsZ6mlA5ovSorXghokco0sZqgWKlqaAkiohKMOVSmqLCD5WEKEISooZA5vdHZCUku7nt7uzMvl/n7IG57X5nd579fveZJzPyw429uLwBwhl/nQV/4qQCSAKj00ga2Rufb3hhQAAAADrD6+UH/HRjLy5vgHDGb6/w4u3yNy6Xf56fkwogCYxOI2lkb3y+XWO1JDoDAgAAAOvhmsmhjc+na6z2m6qrvF3+5r77/PP8dn3f0H4kgdFpJI3sLdifr78HSN4GDP46i9qWYCfRuzpAYkAQXFYf0Fq9/QAA2AXXTA5tfD5dE26FSd4uf+NyNT+OgM4iCYxO48e+vQX78/X3AMnbgMFfZ1HbEuwkergNkKzO6p+X1dsPAIBdcM3k0Mbn0zXhVnjm7fI3DX66vA5AEhhASPD3AMnbgCFYZ1GDnUQPtwGS1Vn987J6+wEAsAuumRza+Hy6hsIzwL9IAgMICf4eIHkbMNj1LCoDJGux+udl9fYDAAAAQLghCQwAAPyKawYDAAAAQGghCQwAAPyKawYDsDJOZOF0FRVShR9vXgwAgFlIAgMAAL/imsEArIwTWThdwbIILfDjzYsB4BROOiLYSAIDAAC/YuAKwMo4kYXT3ZbdqMnXdWsxn+MB/kASMLxx0hHBRhIYgCkY8AQX7zcAAO1D34jTJSZKiX68eXFXMaazF5KA4Y2Tjgg2ksAATBHqAx67DbBD/f0GAABA2xjTdUyoj+lJAoY2b8ePy+Wf5w+V4xDhwzJJ4CNHjujOO+/UunXrJEmTJ0/WkiVLdM4553jdZvXq1SooKFBpaakOHz6s999/X5dcckmzderr6zV//nz95S9/0VdffaUxY8boySefVL9+/QK4NwBCfcBjtwF2qL/fAAAAaBtjuo4J9Ji+q0lCkoChzdvxM2tW07+hdlIBaItlksDTp0/XJ598oqKiIknSrbfeqhkzZujll1/2uk1dXZ1GjRqlG2+8UdnZ2a2uk5OTo5dfflmFhYXq3bu35s2bp0mTJqm0tFTdurW89hMA/wj1jtJuA+xQf7/RNaFe5QIAQHtVVEiff06f5g3vQ8cEekzvLUl4333+eX6Y68zjp6BAevpp6dlnm6atXiiE8GOJJPCePXtUVFSkrVu3Kv2bKFu2bJkyMjJUXl6uQYMGtbrdjBkzJEn79+9vdXl1dbWeffZZrVy5UmPHjpUkPf/880pOTtbGjRs1fvx4/+8MAEt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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "coverages = np.zeros(NREP)\n", + "mu_txs = np.zeros(NREP)\n", + "ci_uppers = np.zeros(NREP)\n", + "ci_lowers = np.zeros(NREP)\n", + "y1_rep1 = y1_incid[0]\n", + "y2_rep1 = y2_incid[0]\n", + "\n", + "# print(transform_percentage_change_counts1(y1_rep1, Y1_POP, y2_rep1, Y2_POP))\n", + "# print(transform_percentage_change_counts2(y1_rep1, Y1_POP, y2_rep1, Y2_POP))\n", + "\n", + "for i in range(NREP):\n", + " mu_txs[i], sigma_hat = transform_percentage_change_counts2(y1_incid[i], Y1_POP, y2_incid[i], Y2_POP)\n", + " # print(delta_hat, sigma_hat)\n", + " ci_uppers[i] = mu_txs[i] + Q * sigma_hat / np.sqrt(Y1_POP)\n", + " ci_lowers[i] = mu_txs[i] - Q * sigma_hat / np.sqrt(Y1_POP)\n", + " if (ci_lowers[i] < TRUE_DIFF and TRUE_DIFF < ci_uppers[i]):\n", + " coverages[i] = 1\n", + "\n", + "coverage_pct = (coverages == 1).sum() / NREP\n", + "print(\"CI coverage rate: \", coverage_pct)\n", + "\n", + "line_width = 0.75\n", + "cap_size = 2\n", + "marker_size = 3\n", + "plt.figure(figsize=(17, 6))\n", + "for i in range(NREP):\n", + " if coverages[i] == 1:\n", + " plt.errorbar(i, mu_txs[i], elinewidth=line_width,\n", + " yerr=[[mu_txs[i]- ci_lowers[i]], [ci_uppers[i] - mu_txs[i]]],\n", + " fmt=\"o\", color=\"blue\", ecolor=\"blue\", capsize=cap_size, markersize=marker_size)\n", + " else:\n", + " plt.errorbar(i, mu_txs[i], elinewidth=line_width,\n", + " yerr=[[mu_txs[i] - ci_lowers[i]], [ci_uppers[i] - mu_txs[i]]],\n", + " fmt=\"o\", color=\"red\", ecolor=\"red\", capsize=cap_size, markersize=marker_size)\n", + "\n", + "plt.axhline(y=TRUE_DIFF, color='gray', linestyle='--')\n", + "plt.xlabel('SampleID')\n", + "plt.ylabel(\"Mean\")\n", + "plt.title(\"95% CIs using Delta Method SE for percentage change\")\n", + "plt.legend([\"True Mean\"], loc=\"upper right\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It seems as though the CI length is wider than it should be at more extreme values of prevalence (i.e. those near 0 or 1). This is probably due to the fact that when computing the CI, the standard error was divided by the sample size of the first year. Unclear as to what it should be instead, any suggestions?" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "ihme", + "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": "3.12.3" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/distrx/transforms.py b/src/distrx/transforms.py index a93d737..0139c92 100644 --- a/src/distrx/transforms.py +++ b/src/distrx/transforms.py @@ -278,6 +278,7 @@ def transform_percentage_change( sigma_xy = cov[0, 1] delta_hat = (mu_y - mu_x) / mu_x + # TODO: add option instead of doing this by default bias_corr = (mu_y * sigma2_x) / ((n * mu_x) ** 2) p_hat = delta_hat + bias_corr @@ -290,7 +291,42 @@ def transform_percentage_change( return p_hat, np.sqrt(sigma_trans) -def transform_percentage_change_counts( +def transform_percentage_change_counts1( + c_x: int, n_x: int, c_y: int, n_y: int +) -> float: + """alternative percentage change transformation with only counts provided + + Parameters + ---------- + c_x : int + raw count in one sample (e.g. of incidence) + n_x : int + sample size + c_y : int + raw count in second sample (e.g. of incidence) + n_y : int + sample size + + Returns + ------- + sigma_trans: array_like + standard errors in the transform space + """ + mu_x = c_x / n_x + mu_y = c_y / n_y + # sigma2_x = (c_x * (1 - mu_x) ** 2 + (n_x - c_x) * mu_x**2) / (n_x - 1) + # sigma2_y = (c_y * (1 - mu_y) ** 2 + (n_y - c_y) * mu_y**2) / (n_y - 1) + sigma2_x = n_x * mu_x * (1 - mu_x) + sigma2_y = n_y * mu_y * (1 - mu_y) + + # sigma_trans = (sigma2_y / mu_x**2) + (mu_y**2 * sigma2_x / (mu_x**4)) + sigma_trans = (sigma2_y / c_x**2) + (c_y**2 * sigma2_x / (c_x**4)) + print(sigma2_x, sigma2_y) + + return ((c_y / c_x) - 1), np.sqrt(sigma_trans) + + +def transform_percentage_change_counts2( c_x: int, n_x: int, c_y: int, n_y: int ) -> float: """alternative percentage change transformation with only counts provided @@ -314,11 +350,13 @@ def transform_percentage_change_counts( mu_x = c_x / n_x mu_y = c_y / n_y sigma2_x = (c_x * (1 - mu_x) ** 2 + (n_x - c_x) * mu_x**2) / (n_x - 1) - sigma2_y = (c_y * (1 - mu_y) ** 2 + (n_x - c_y) * mu_y**2) / (n_y - 1) + sigma2_y = (c_y * (1 - mu_y) ** 2 + (n_y - c_y) * mu_y**2) / (n_y - 1) + # print("look", sigma2_x, sigma2_y) sigma_trans = (sigma2_y / mu_x**2) + (mu_y**2 * sigma2_x / (mu_x**4)) + # sigma_trans = (sigma2_y / c_x**2) + (c_y**2 * sigma2_x / (c_x**4)) - return sigma_trans + return ((mu_y / mu_x) - 1), np.sqrt(sigma_trans) def _check_input( diff --git a/tests/test_transforms.py b/tests/test_transforms.py index 6432fed..8380e05 100644 --- a/tests/test_transforms.py +++ b/tests/test_transforms.py @@ -1,3 +1,4 @@ +# TODO: CHANGE TESTS TO INCORPORATE POINT ESTIMATE """Tests for transforms.py module.""" import numpy as np @@ -7,7 +8,7 @@ delta_method, transform_data, transform_percentage_change, - transform_percentage_change_counts, + transform_percentage_change_counts2, ) TRANSFORM_DICT = { @@ -107,7 +108,8 @@ def test_percentage_change(): def test_percentage_change_counts(): x = np.random.choice([0, 1], size=1000, p=[0.1, 0.9]) y = np.random.choice([0, 1], size=1100, p=[0.2, 0.8]) - sigma = transform_percentage_change_counts( + mu, sigma = transform_percentage_change_counts2( (x == 1).sum(), len(x), (y == 1).sum(), len(y) ) + assert -1 <= mu and mu < np.infty assert 0 < sigma and sigma < 1