{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Merger rate density evolution with redshift" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Number of compact binary mergers per unit time per unit volume" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad\n", "from astropy.cosmology import LambdaCDM\n", "cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7)\n", "\n", "# calling necessary class from ler package\n", "from ler.gw_source_population import CBCSourceRedshiftDistribution" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# uncomment the following line to see the docstring\n", "# SourceGalaxyPopulationModel?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_1.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_1.pickle\n", "merger_rate_density_bbh_popI_II_oguri2018 interpolator will be loaded from ./interpolator_pickle/merger_rate_density_bbh_popI_II_oguri2018/merger_rate_density_bbh_popI_II_oguri2018_2.pickle\n", "\n", " available model list with it input parameters: \n", " {'merger_rate_density_bbh_popI_II_oguri2018': {'R0': 2.39e-08, 'b2': 1.6, 'b3': 2.0, 'b4': 30}, 'star_formation_rate_madau_dickinson2014': {'af': 2.7, 'bf': 5.6, 'cf': 2.9}, 'merger_rate_density_bbh_popIII_ken2022': {'n0': 1.92e-08, 'aIII': 0.66, 'bIII': 0.3, 'zIII': 11.6}, 'merger_rate_density_bbh_primordial_ken2022': {'n0': 4.4e-11, 't0': 13.786885302009708}}\n" ] } ], "source": [ "# class initialization\n", "# default model \"BBH popI/II Oguri2018\"\n", "cbc = CBCSourceRedshiftDistribution()\n", "\n", "# list out the models for the merger rate density wrt redshift\n", "print(\"\\n available model list with it input parameters: \\n\", cbc.merger_rate_density_model_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting differential comoving volume\n", "\n", "* This important to understand why the source frame merger rate decreases with redshift\n", "* This is with planck18 cosmology. `ler` allows you to change the cosmology.\n", "* $1/E (z)$: derivative of comoving distance with redshift, $D_c(z)$: comoving distance, $H_0$: Hubble constant, $c$: speed of light\n", "\n", "\\begin{equation}\n", "\\frac{dV_c}{dz} = 4\\pi \\frac{c}{H_0} \\frac{(1+z)^2 D_c^2(z)}{E(z)}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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SNfZvgbQulKyame5iqnsIBAI4Ozujb9++eOedd+o90sGNGzcwc+ZMBAUF4YcffsD3338PADhw4ADeeust9OvXD+vXr8fy5ctNeTpNcurUKSxZsqRJQyQRQtoG6rpuJtOmTcOjjz4KjUaDwsJCnD9/HqtXr8aXX36JH3/80WBKhIEDB6K8vBxCoVC/7NixY9BoNPjyyy8NRjg/cuQIeDwefvzxR4P1LdGpU6ewdOlSzJw506BkCADx8fG1TndOHu7AgQPmDoEQo6JkZSaRkZF4+umnDZalpqZixIgRiIqKQseOHREREQFAO7CnWCw2WDc3NxcAql3kc3NzIZFIjJqoHhyFvTmIRKJmPV5rY+lfVAhpKPrqakH8/PywYcMGVFZW4pNPPtEvf7DNyt/fH4sXLwagnV2W4zgsWbIEHMdh/fr1KC0t1Vcz3t92s2nTJnTr1g0SiQSOjo6YOnVqtekZBg8ejE6dOiE6OhoDBw6EtbU13nnnHQCAUqnE4sWL0a5dO4hEIvj4+OCtt97Sj8Ctw3Ec5syZg927d6NTp04QiUQICwvD/v379essWbIEb775JgDtJH+6eFNSUvTneH87RUFBAebPn4/w8HDY2trCzs4Oo0ePrnPA3IcpKirC66+/Dn9/f4hEInh7e2PGjBnIy8vTr5Obm4vnnnsObm5uEIvFiIiIqDaKuq5q97PPPsM333yDwMBAWFtbY8SIEUhPTwdjDB9++CG8vb0hkUgwfvx4/eDA9/v2228RFhYGkUgET09PzJ4926CKdM6cObC1ta1x1t5p06bB3d1dP3fWg21Wur+h7du346OPPoK3tzfEYjGGDRtWbQoYAPrzkEgk6NmzJ/755596tYN16tRJPyP1/TQaDby8vDBx4kT9stLSUrzxxhvw8fGBSCRChw4d8Nlnnz10Pi/d3/qDNmzYYPA3BGj/jsaOHYtjx46he/fukEgkCA8P1/8v7dy5E+Hh4RCLxejWrRsuXrxYbb83btzAxIkT4ejoCLFYjO7du+tnKiDNyFyDErZVycnJDAD79NNPa10nKCiIubi46F8/OJjprl272OOPP84AsLVr17KNGzeyy5cvs40bN7IBAwYwkUjENm7cyDZu3MiSkpIYY4wtW7aMcRzHpkyZwr799lu2dOlS5uzszPz9/VlhYaH+WIMGDWLu7u7MxcWFvfLKK+y7775ju3fvZmq1mo0YMYJZW1uzuXPnsu+++47NmTOHWVlZsfHjxxvED4BFREQwDw8P9uGHH7LVq1ezwMBAZm1trR8w9/Lly2zatGkMAPviiy/08ZaUlDDGtAO9RkVF6fd5/vx5FhQUxN5++2323XffsQ8++IB5eXkxmUxmMMCp7vNdv359nb8HhULBOnXqxPh8PnvhhRfY2rVr2Ycffsh69OjBLl68yBhjrKysjHXs2JEJBAL2+uuvs6+++ooNGDCAAWCrV6+udswuXbqw0NBQtmrVKvbee+8xoVDIevfuzd555x3Wt29f9tVXX7FXX32VcRzHZs2aZRDP4sWLGQA2fPhw9vXXX7M5c+YwPp/PevTowSorKxljjJ04cYIBYNu3bzfYtrS0lNnY2LDZs2cb/B5rGhC3a9eurFu3buyLL75gS5YsYdbW1qxnz54G+/v2228ZADZgwAD21VdfsXnz5jFHR0cWFBRksM+afPDBB4zH47GsrCyD5cePH2cA2K+//soYY0yj0bChQ4cyjuPY888/z9asWcPGjRvHALC5c+cabPvg34Lus3pQbQMGd+jQgXl4eLAlS5awL774gnl5eTFbW1u2adMm5uvryz7++GP28ccfM5lMxtq1a8fUarV++6tXrzKZTMZCQ0PZypUr2Zo1a9jAgQMZx3Fs586ddX4WxLgoWTWz+iSr8ePHMwCsuLiYMVbzyNu6f9g7d+4YbFvTCNopKSmMz+ezjz76yGB5bGwss7KyMlg+aNAgBoCtW7fOYN2NGzcyHo/H/vnnH4Pl69atYwDYyZMn9csAMKFQyBITE/XLLl++zACwr7/+Wr/s008/rXZx0XnwAlVRUWFwEWFM+1mKRCL2wQcfGCyrT7J6//33GYAaLzi6kd9Xr17NALBNmzbp36usrGR9+vRhtra2TC6XGxzTxcWFFRUV6ddduHChPnGrVCr98mnTpjGhUMgqKioYY4zl5uYyoVDIRowYYXCOa9asYQDYTz/9pI/Ly8uLPfnkkwbxbt++nQFgJ06c0C+rLVl17NiRKZVK/fIvv/ySAWCxsbGMMcaUSiVzcnJiPXr0MIh5w4YNBiPZ1yY+Pr7a75kxxv7v//6P2drasrKyMsYYY7t372YA2LJlywzWmzhxIuM4zuBvp6nJCgA7deqUftnff//NADCJRMJSU1P1y7/77rtq/2fDhg1j4eHh+t8VY9rfQ9++fVlwcHCdnwUxLqoGtEC6qcAVCoVR9rdz505oNBpMnjwZeXl5+oe7uzuCg4Nx9OhRg/VFIhFmzZplsOzXX39Fx44dERISYrAP3XxRD+5j+PDhBvNSde7cGXZ2drh161ajzuH+adfVajXy8/Nha2uLDh06ICYmpsH7++233xAREYHHH3+82nu6Kqa//voL7u7umDZtmv49gUCAV199FSUlJQYTBgLApEmTIJPJ9K979eoFAHj66acNppHv1asXKisrkZmZCQA4dOgQKisrMXfuXINOJS+88ALs7Ozw559/6uOaNGkS/vrrL5SUlOjX27ZtG7y8vNC/f/+HnvesWbMM2rMGDBgAAPrfy4ULF5Cfn48XXnjBIObp06frZ0KuS/v27dGlSxds27ZNv0ytVmPHjh0YN26cfnzJv/76C3w+H6+++qrB9m+88QYYY9i3b99Dj1VfoaGh6NOnj/617vcydOhQ+Pr6Vluu+ywKCgpw5MgRTJ48GQqFQv83n5+fj5EjRyIhIUH/OySmR8nKAukuRPdP+d4UCQkJYIwhODgYLi4uBo/r16/rO2voeHl5VWugT0hIwLVr16ptr5vK/MF93H8R0HFwcEBhYWGjzkGj0eCLL75AcHAwRCIRnJ2d4eLigitXrqC4uLjB+0tKSkKnTp3qXCc1NRXBwcHVeiV27NhR//79HjxnXeLy8fGpcbnus9Dtp0OHDgbrCYVCBAYGGhxnypQpKC8v17eZlJSU4K+//sKkSZNqbMd50IMx6hLQg7Hc38MUAKysrODv7//Q/etiPHnypP5CfuzYMeTm5hpMEJmamgpPT89qf+O1fbZN0djfS2JiIhhjWLRoUbW/e12b8YN/98R0qDegBbp69SpcXV1hZ2dnlP1pNBpwHId9+/aBz+dXe19XktOpaXR1jUaD8PBwrFq1qsZjPPiPX9NxADy08bw2y5cvx6JFi/Dss8/iww8/hKOjI3g8HubOnQuNRtOofRpbbedszM+id+/e8Pf3x/bt2/HUU0/h999/R3l5ebWZghsaY2N/LzWZMmUKFi5ciF9//RVz587F9u3bIZPJMGrUKKPsv7akrOtc8qDG/l50f1fz58/HyJEja1z3waROTIeSlYU5ffo0kpKSqnVrb4qgoCAwxhAQEKAvCTVmH5cvX8awYcPq9Q2+Phqynx07dmDIkCH48ccfDZYXFRXB2dm5wccOCgrC1atX61zHz88PV65cgUajMShd3bhxQ/++Mej2Ex8fj8DAQP3yyspKJCcnY/jw4QbrT548GV9++SXkcjm2bdsGf39/9O7d26ixJCYmGvTqq6qqQkpKSr2mlg8ICEDPnj2xbds2zJkzBzt37sSECRMMbkfw8/PDoUOHoFAoDEpX9flsdaXBoqIig1s3jFkaA6D/XQgEgmq/A9L8qBrQgqSmpmLmzJkQCoX6bt3G8MQTT4DP52Pp0qXVvkEzxpCfn//QfUyePBmZmZn44Ycfqr1XXl6O0tLSBsdlY2MDAPUawYLP51eL/ddff210m8GTTz6Jy5cvY9euXdXe0x3n0UcfRXZ2tkH7S1VVFb7++mvY2tpi0KBBjTr2g4YPHw6hUIivvvrK4Bx//PFHFBcXY8yYMQbrT5kyBUqlEj///DP279+PyZMnGyUOAOjevTucnJzwww8/oKqqSr988+bNDarCnTJlCs6cOYOffvoJeXl51Up+jz76KNRqNdasWWOw/IsvvgDHcRg9enSt+9a1hZ44cUK/rLS0tNotBU3l6uqKwYMH47vvvkNWVla19+/cuWPU45G6UcnKTGJiYrBp0yZoNBoUFRXh/Pnz+O2338BxHDZu3Fivb7D1FRQUhGXLlmHhwoVISUnBhAkTIJVKkZycjF27duHFF1/E/Pnz69zHM888g+3bt+M///kPjh49in79+kGtVuPGjRvYvn07/v77b3Tv3r1BcXXr1g0A8O6772Lq1KkQCAQYN26cPondb+zYsfjggw8wa9Ys9O3bF7Gxsdi8ebNBSaQh3nzzTezYsQOTJk3Cs88+i27duqGgoAB79+7FunXrEBERgRdffBHfffcdZs6ciejoaPj7+2PHjh04efIkVq9ebbQ2RRcXFyxcuBBLly7FqFGj8NhjjyE+Ph7ffvstevToUa2UHRkZiXbt2uHdd9+FUqmsdxVgfQiFQixZsgSvvPIKhg4dismTJyMlJQUbNmxAUFBQvUvDkydPxvz58zF//nw4OjpWK5mMGzcOQ4YMwbvvvouUlBRERETgwIED2LNnD+bOnWvQOedBI0aMgK+vL5577jm8+eab4PP5+Omnn+Di4lLv4crq65tvvkH//v0RHh6OF154AYGBgcjJycHp06eRkZHRpPv8SAOZpQ9iG6br5qx7WFlZMUdHR9arVy+2cOFCg660Ok3tuq7z22+/sf79+zMbGxtmY2PDQkJC2OzZs1l8fLx+nUGDBrGwsLAat6+srGQrV65kYWFhTCQSMQcHB9atWze2dOlSfTd7xrRd1++/50fnwS7IjDH24YcfMi8vL8bj8Qy6HdfUdf2NN95gHh4eTCKRsH79+rHTp09X66Jd367rjDGWn5/P5syZw7y8vJhQKGTe3t4sKipKfy8YY4zl5OSwWbNmMWdnZyYUCll4eHi1fdd2O4Lu96a7t0hH18X6/PnzBsvXrFnDQkJCmEAgYG5ubuzll182uAfufu+++y4DwNq1a1fj+7V1XX8wlto+r6+++or5+fkxkUjEevbsyU6ePMm6devGRo0aVePxatKvXz8GgD3//PM1vq9QKNjrr7/OPD09mUAgYMHBwezTTz/V3zqgU9PfTXR0NOvVqxcTCoXM19eXrVq1qtau62PGjKl27Jr+Rmv7PSYlJbEZM2Ywd3d3JhAImJeXFxs7dizbsWNHvT8L0nQ0+SIh5KE0Gg1cXFzwxBNP1FgVTIipUZsVIcRARUVFtfbBX375BQUFBa1m2hHS8lDJihBi4NixY3j99dcxadIkODk5ISYmBj/++CM6duyI6OhoGiSXmAV1sCCEGPD394ePjw+++uorFBQUwNHRETNmzMDHH39MiYqYDZWsCCGEWDxqsyKEEGLxKFkRQgixeJSsCCGEWDxKVoQQQiweJStCCGmAEydOYNy4cfD09ATHcdi9e3eDtq+oqMDMmTMRHh4OKysrTJgwodo6WVlZeOqpp9C+fXv97AJtHSUrQghpgNLSUkREROCbb75p1PZqtRoSiQSvvvpqraO5K5VKuLi44L333kNERERTwm016D4rQghpgNGjR9c5KrxSqcS7776L//3vfygqKkKnTp2wcuVK/egfNjY2WLt2LQDg5MmTNc464O/vjy+//BIA8NNPPxn9HFoiKlkRQogRzZkzB6dPn8bWrVtx5coVTJo0CaNGjUJCQoK5Q2vRKFkRQoiRpKWlYf369fj1118xYMAABAUFYf78+ejfvz/Wr19v7vBaNKoGJIQQI4mNjYVara42I7dSqYSTk5OZomodKFkRQoiRlJSUgM/nIzo6Gnw+3+A9W1tbM0XVOlCyIoQQI+natSvUajVyc3MxYMAAc4fTqlCyIoSQBigpKUFiYqL+dXJyMi5dugRHR0e0b98e06dPx4wZM/D555+ja9euuHPnDg4fPozOnTtjzJgxAIC4uDhUVlaioKAACoUCly5dAgB06dJFv1/dspKSEty5cweXLl2CUChEaGhoc52qRaFR1wkhpAGOHTuGIUOGVFseFRWFDRs2QKVSYdmyZfjll1+QmZkJZ2dn9O7dG0uXLkV4eDgAbdf01NTUavu4/3LMcVy19/38/JCSkmK8k2lBKFkRQgixeNR1nRBCiMWjZEUIIcTitfoOFlVVVbh48SLc3NzA41FuJoS0fBqNBjk5OejatSusrFr9ZRxAG0hWFy9eRM+ePc0dBiGEGN25c+fQo0cPc4fRLFp9snJzcwOg/aV6eHiYORpCCGm6rKws9OzZU399awtafbLSVf15eHjA29vbzNEQQojxtKWmjbZzpoQQQlosSlaEEEIsHiUrQgghFo+SFSGEEItHyYoQQojFo2RFCCGt3JIlS8BxnMEjJCTE3GE1SKvvuk4IIQQICwvDoUOH9K9b2sgXLStaQgghjWJlZQV3d3dzh9FobSZZaTQaaDQac4dBCCFNpruWKRQKyOVy/XKRSASRSFTjNgkJCfD09IRYLEafPn2wYsUK+Pr6Nku8xtBmklVubi4lq0aqUjOUV2lQrtJAWaWBtZAHmcgKVvzqk8MRQurANIBade+hUQEcB9i4NGg3eXl5AFBt1uDFixdjyZIl1dbv1asXNmzYgA4dOiArKwtLly7FgAEDcPXqVUil0kafTnNqM8nK1dWVhluqpwqVGvHZClzPVqCgtBKVVQ8meQ04rhJ2YgEcbARwshHC38kG3g6SGmc3JaTV0agBVTlQVaH9qaoAqu77WVVx970Hl1dW35e1E9Dx+QYdXjfMUlxcHLy8vPTLaytVjR49Wv+8c+fO6NWrF/z8/LB9+3Y899xzDTq2ubSZZMXj8drUOFoNxRhDRmE5rt0uRkJOCao0htNrW/E4WIusIBbwIC+vQoVKDXlFFeQVVUjNL0dMWjGkYiuEetgh1NMO9tZCM54NIQ2k0QCqMu2jsvTuzzJAVXr35/3LS7WlosbgoC1JWYkAKwkgEAMSB6CB1ybdtUwqlcLOzq7BYdjb26N9+/ZITExs8Lbm0maSFaldeaUaB6/nICm3RL/MWSpCJ087+DnZwEbEh5DP05eaGGMoV6mRX1KJwrJK5MiVSMhVQFFRhbPJBTibXAAvewnCvOzQ0d0OPB6VtogZMKZNLJUlgLIEqFTcfV1DEqqq0K7fEAZJ5+7DSlz3T4EE4IsanJyMraSkBElJSXjmmWfMGkdDULJq4zIKy7D/ajYUFVXg8ziEetihk5cMbnaiWqv0OI6DtdAK1o5W8HG0BgAM7uCCW3dKEZdVjNT8MmQWlSOzqBzRqYXo184Zgc42VEVIjIMxoEp5NwnJ7yai+xKSsgRQ3k1MrAHt1Bx3N6FYA0Ibw58CyQPL7iagFvI3PX/+fIwbNw5+fn64ffs2Fi9eDD6fj2nTppk7tHqjZNVGaTQM51IKcOZWPhgDHKwFeDTcA6524kbtT8DnoYO7FB3cpShRViHuthzRqYXIL6nE3ku34eUgwYBgZ3jIJEY+E9LqaNRARfG9h1J+97n8bhJSAOqq+u2L47QJRiTVPh5MQkJrQGCj/WklMXuJx1QyMjIwbdo05Ofnw8XFBf3798eZM2fg4tKwjh3mRMmqDWKMYf+1bMRnKwAAHT3sMCTEBSIrvlH2byuyQs8AR3T2luFCSiEuphUis7AcW8+lI9jNFv3bOVObVlumVt1NPMWGSUmXkCpL6lclJxADQtu7ScgWEOmeS7XPhXcfrTQBNcTWrVvNHUKTUbJqYxhjOH7zDuKzFeDzOAzv6IZQz4Y30NaHWMBH/2BndPaR4UxSPuKy5EjIKUFKXin6tXNGFx97qhpsrdQqoLwQKCsAygvu/Swv0lbPPQzfChDJAPH9D7v7EpMU4AtMfhrEclCyamNi0gpxMa0IADAizA0h7qZJVPezEwswIswdXX0dcPzmHaQXlOFY/B0k3SnFI6FukEnootMi6arrqiWkQm0JqS58wd0EZG+YjHTPBdYtpj2INA9KVm3I9Sw5TtzU3kw4sL1zsySq+7lIRXgy0gtXMorxT4I2aW06k4pB7V0Q5mlHpSxLpVEDZflA6R2gJBcozbtXSqqrA4NADEgcAWvHez/F9oDEvkV1TiCWgZJVG5FRWIaDcTkAgEg/B3TzczRLHBzHIcLHHn5O1jhwLQeZReU4GJeDxNwSDA91g62I/iTNhjFtZ4aSO9rEVJqrTU7lhdqEVRO+lWFCkjjcey60bt74SatGV4Y2QKXW4GBcDtQahvZuUgwMdjZ3SLC3FmJiN29cTC/EqcR8JOeVYuPpVIzu5A5/Zxtzh9f6qauAkhygJFtbUirJ1SaoKmXN61sJtUMC2bje/emkTUgiKZWQSLOgZNUGnLmVj6IyFaRiKwwPdbWY6jYej0M3P0f4O9lg/7Vs5MqV2H0pE70DndArwNFi4mzxNBpttZ38NqDI0v4svVNzaYnjaUtGtq73JSdnbTsS/T6IGVGyauVy5BWITi0EAAwNcTVa93RjcrIVYUp3HxyLv4PYzGKcTspHjrwCI8PcIRZYXrwWTVeVJ88CFLfv/syqeXggoTUg9dAmJV1ysnYCePSZE8tDyaoVU2sYDsTlgDEgxF2KQBdbc4dUKys+D8ND3eAuE+PojVzculOKLWfTMDbCA67Sxt2o3CZoNNrqvOJ0oChNW2qqqWs4XwBI3bXJyc5T+5NKS6QFoWTVil1IKUCeQgmJkI9BHVrGneqdvGRwlYrwx5UsFJersO1cOoaZ8F6wFkeXnIrStI/itOojeXM8wNYFkHoCdh7an9ZOdHMsadEoWbVSigoVziYXANCO22ctbDm/alc7MZ7q5Yv9V7ORnFeKv69lI0degUHtXdreoLgajbYThD45pVdPTlZCQOYL2PsCMi/A1o1umCWtTsu5gpEGuZBSCLWGwctBgg5uLWNytfuJBXyM7+KJM7cKcDY5H5fSi1BUXolHwz0sst3NqCrkQH4iUHALKEqtITmJtInJ3heQ+WiTE5WaSCtHyaoVUlSoEJtZDADoE+jUYnvVcRyHPkFOcJEKsf9qNlLyyrD9fDoe6+LVuka90Gi0nSHyE7WPkjuG7wvE2qRk7wfY+2h76FFyIm0MJatW6P5SlW4Kj5asnasUk7oLsPfSbeSVVGLruTQ81sWzZY/grioHCpLvlaBU5ffe4zhtJwindoBjoLbk1EK/cBBiLJSsWpkHS1WthZudGFN7+mDPpdu4o1Bix4UMjOzkjvYtqYqzQg7cuQHk3QSKMw2HKrISaROTLkHR6A+EGKBk1crcX6rydmjBJY8aSMUCTOrujf1Xs3HrTin+vJKFonYq9PB3sNyqzsoybYLKva7tHHH/1Bc2zoBTkDZB2XlT1R4hdaBk1Yq0lraquois+BjX2RMnEu7gYloRTibmoaisEsM6uoFvKT0Fq5Ta0lPudW1V3/0lKJk34NpRm6Ak9mYLkZCWhpJVKxKbUawtVdm3vlLV/Xg8DoM7uMLBWohj8Xdw7bYcpZVVGBPuCaGVmUonahWQnwTkxml/au6byVbqBriGAi4hlKAIaSRKVq2ERsNw7bZ2DqEuvm1jUsMIH3tIxVb4KzYLKXll2BGdgQldPZv3nrLSfOD2RSD7iuEgsNZO2hKUa6h20FdCSJNQsmolbuWVokRZBWshH0EWPKySsQW62OLJbt7Yc+k2cuQV2HY+HY939YK9tdB0B9WogTvx2iRVlHZvudjuXoKiHnyEGJVZW3RPnDiBcePGwdPTExzHYffu3fr3VCoVFixYgPDwcNjY2MDT0xMzZszA7du3zRewBbt6t60q1NPOctpumomHTIIp3X0gkwhQVKbCtvPpyJFXGP9A5YVA0lHg9Bogbo82UXEc4BwMdJ4M9HoZCBqqHYOPEhUhRmXWZFVaWoqIiAh888031d4rKytDTEwMFi1ahJiYGOzcuRPx8fF47LHHzBCpZSsuVyElXzt4abiXzMzRmIeDjRBTevjA1U6Esko1dkRnICWvhgFdG0qjAe7cBC5vA85+B6Sd0fbwE9kC/v2A3i8D4RO1vfqoNx8hJmPWasDRo0dj9OjRNb4nk8lw8OBBg2Vr1qxBz549kZaWBl9f3+YIsUW4llkMxgBfR2vTVn9ZOBuRFSZ288afV7KQml+GPZdu45HQRg6Cq1EDOVeBtLPaKd11HAMAz67a3nw0lQYhzaZFtVkVFxeD4zjY29vXuo5SqYRSea+hW6FQNENk5nN/x4pw77ZZqrqfyIqP8V28cDAuG9ezFPj7WjZKK6vQ3a+e92KpVUDWZSD9rPYmXkB7w65nF8Cji3ZiQkJIs2sxyaqiogILFizAtGnTYGdX+zflFStWYOnSpc0YmXm11Y4VdeHzOIwMc4eNyAoXUgrxb0IeyivVGBDsXHvCUlUAt2OAjPPaaj4AENoAPj21JSkrUfOdACGkmhaRrFQqFSZPngzGGNauXVvnugsXLsS8efP0rzMzMxEaGmrqEM3mZo625NjRo+11rKgLx3EYEOwCayEfJ27mITq1EOUqNYY/ePOwskSboG7H3BvdXCwDfHsD7p0Bfov4FyGk1bP4/0RdokpNTcWRI0fqLFUBgEgkgkh071uwXC43dYhmo1JrkHy3E0GLGiOvGXXzc4RYwMehuFzE3ZajQqXGo+EeEDCVtrNExjlAffcGXhtnwLePtus5dZYgxKJYdLLSJaqEhAQcPXoUTk50c+X9UvNLUVmlgZ1EADc7qqaqTZinDGIBH39dycKt3BLsOnIKj4liIFbf7S1o5wH49tV2Qacu54RYJLMmq5KSEiQmJupfJycn49KlS3B0dISHhwcmTpyImJgY/PHHH1Cr1cjOzgYAODo6Qihsu73edBJySgAAwa62bWLEiqYIcrbB4/5V2HvqEjIryvGrUITHA0WwDRkMOLenJEWIhTNrsrpw4QKGDBmif61ra4qKisKSJUuwd+9eAECXLl0Mtjt69CgGDx7cXGFaJJVag1t3qwCD3ahjRZ3kWUDSEXgXpWGiixV257ggz7YDtsMHT9j4wJ4SFSEWz6zJavDgwWD3T5nwgLrea+tS88tQWaWBVGwFdzuxucOxTEqFdsSJnGva1zwruAZ3x5S+3fHblTwUl6uw/UI6JnT1gquUPkNCLJlFt1mR2iXc7QUY7CalKsAHMQZkXdImKt3gsm5hQMBAQGIPGYApPSTYdTETdxRK/HohA+O7eMLbgSY8JMRSUZenFqjq/ipAV6oCNFCaD1zaDMTv1yYqOw+g20wg9DGD6Tl0o114OUhQWaXBrphMJN0pMVvYhJC6UbJqgdIK7lUBesio+gqAdnik1FPAhZ+AonTt/VHthgNdZ2gTVg3EAj4e7+qFQBcbVGkY/richWu3i5s5cEJIfVA1YAukG7Q20MWGqgABQH4biP8LKLmjfe0YCLQfWa+JDgV8HsZ19sTB6zmIuy3HgWs5qFCp0c2PhlUixJJQsmphGGNIztMOB+TnZGPmaMxMXQUkHwMyLmjbqQQSbWnKLaxBXdF5PA4jQt0gEfARnVqIEzfzUF6pQb92TvRlgBALQcmqhSkqU0FergKfx8GnLXcIKCsA4nYDihzta7cwoN0w7Xh+jaAdnskZEiEf/ybk4XxKAcpVagwLcQWPhrEixOwoWbUwuipAT3sJhFZttMkx+ypwc792hHSBBAgZox19ook4jkMPf0dIBHwcup6Dq5nFqFCpMbqTO6z4bfSzJsRC0H9gC5Oar60C9Hdqg6Wqqkrgxp/A9d+1icreF+j+rFES1f06eckwtrMH+DwOibkl2H3pNpRVaqMegxDSMJSsWhCVWoOMwjbaXlWSC8T8DGRd0bZH+fcHIqYB4kZMrFgP7VyleLyrF4RWPKQXlGFHdAZKlVUmORYh5OEoWbUgt4vKoVIz2Iqs4GzbRsZGZAy4fRGI/hkozdNOJx8xDQgYYPKR0X0crTGxmzeshXzkypXYfiEdxWUqkx6TEFIzSlYtSEq+rlRl3TZ6qWnU2rap+P2ApgpwCtJW+zn4NVsIbnZiTO7uA5lEgKIyFbZdSEOuvKLZjk8I0aJk1YKk3u1c4e/cBqoAVRXAle3A7Uvaar/AwUD4pEb39msKBxshJvfwgYtUhFKlGr9GZyC9oKzZ4yCkLaNk1UKUKKuQX1IJjgN8HVt554qyAiDmF6AwBeALgE5PAn59zDqNh+3d4Zm8dcMzXczUz9JMCDE9SlYtRGZhOQDARSqCWMA3czQmVJSmTVRl+YBICnR9xui9/RpLNzxTsJst1BqGv2KzcDm9yNxhEdImULJqIXS9AL3sJWaOxISyY4HLWwFVOSB1B7pFAVI3c0dlwIrPw6OdPNDZWwbGgCM3cnEqKY+msyHExChZtRCZRdqSVaucxoIxIPkEcP0PbacKlw5A16e1JSsLxONxGBriit6BTgCAs7cKcPh6LjQaSljE8n388cfgOA5z5841dygNQiNYtABlldr2KqAVlqwYAxIPAxnnta/9+gABgyx+mnmO49AnyAk2Ij6O3MhFbGYxyu6OdiGg0S6IhTp//jy+++47dO7c2dyhNBj9V7UAt++WqpxthZAIW1F7FWPAzb/vJar2I7S9/iw8Ud2vs7c9xoRrR7tIyi3BzpgMlFfSaBfE8pSUlGD69On44Ycf4ODgYO5wGqzNlKw0Gg00Go25w2iU9IIyMMbgIRO32HOoRqMBbu7TjvPHcUD7UYBHZ+3yFibIxQaPd/HE3iu3kVlYjq3nUjGhqxdkEoG5QyOtlO46oFAoIJfL9ctFIhFEIlGN28yePRtjxozB8OHDsWzZsmaJ05jaTLLKzc1tsRf6K0kFKC6rAt+ZIS2tFdyQyjTaYZMUWQDnALh3BlT2QFqauSNrkn7uHA7eVCClWIPv8gowrJ0MLraUsIjx5eXlAQBCQ0MNli9evBhLliyptv7WrVsRExOD8+fPN0d4JtFmkpWrqyu8vb3NHUaDKVVqaBKUkAmA7h0DYCNq4b8ydRVw43eg4iYg4gMdHwNc2ps7KqPwBRDoX4U9l27jjkKJMzkMo12dENgWbuImzYp3d6ixuLg4eHl56ZfXVKpKT0/Ha6+9hoMHD0Isbrkzi7fwK1/98Xg8/S+4JcmSlwHg4GgjgFTSwscDVFcB1/cA+YnaaefDHgec25k7KqOyk2hHu/jzShZS88vwx5UsDA1xRWdve3OHRloR3bVMKpXCzq7uwZyjo6ORm5uLyMhI/TK1Wo0TJ05gzZo1UCqV4PMtvy28zSSrlkrXZd2rpXdZ12i0JSpdouo0EXAMMHdUJiGy4mN8Fy8cvp6Da7flOHw9F4qKKvQNopmHSfMbNmwYYmNjDZbNmjULISEhWLBgQYtIVAAlK4uXVaxto/KQtdziu7Z7+iEg9wbA42uHT2qliUqHz+PwSKgbpGIBztzKx7nkAigqqvBIqBv4NPMwaUZSqRSdOnUyWGZjYwMnJ6dqyy1Zy6sXa0M0GqYf4btFJ6vUk0BmtLbXX8dxgGOguSNqFrp7sR4JdQOP43A9S47dFzNRoaKu7YQ0FJWsLFheqRIqNYPQigdHmxbaXpUZAyT/o33e7hHAtaN54zGDTl4y2Iis8FdsFtIKyvBrdAbGd/GEnZh6ChLzOHbsmLlDaDAqWVmwnGIlAMDdTtwy2zpybwAJB7TP/fsB3t3MG48ZBTjbYFI3b9iI+MhTKLH1XBqyi1vBbQiENBNKVhYsq1jbucK9JVYBFqYA1/dq26s8uwL+A8wdkdm52okxpYcvnG2FKFWqsSM6HQk0zQgh9ULJyoLl3G2vanHJqjQfuPrbvUFpg0e0qCGUTEkmEWByDx8EONtApWb440oWziUX0KjthDwEJSsLpaxSI79UO3itu10LSlaqCuDqDqCqErD30d702wLvbzMlkRUfj0V4oouvPQDgZGIeDsTloErdMkdYIaQ50FXEQuUUK8EYYCcRtJxRKzQabdVfWQEgttPe9MtvIbE3Mx6Pw5AOrhgS4goexyHuthw7L2bSILiE1IKSlYXK1lUBtqRSVcoJID8J4FkBYU8AQhpm6GG6+NhjfBdPCK142kFwz6eh4G6JmhByj1mT1YkTJzBu3Dh4enqC4zjs3r3b4H3GGN5//314eHhAIpFg+PDhSEhIME+wzazFda7IvQ6kntY+D3kUsPMwbzwtiL+zDab08IGdRICiMhW2nk9DWn6ZucMixKKYNVmVlpYiIiIC33zzTY3vf/LJJ/jqq6+wbt06nD17FjY2Nhg5ciQqKlp/l98W1blCkQPc+EP73Kcn4BZm3nhaIGdbEab19IGnvRhKlQa7LmYiNqPY3GERYjHM2qAwevRojB49usb3GGNYvXo13nvvPYwfPx4A8Msvv8DNzQ27d+/G1KlTmzPUZlWirEKpUg2OA1xsa56bxmJUlml7/qmrtEMoBQ4xd0QtlrXQCk9GeuNgXA5uZCtw6HoOCsoqMaCdM3g0RBNp4yy2zSo5ORnZ2dkYPny4fplMJkOvXr1w+vTpWrdTKpWQy+X6h0LR8u5juaPQ3gzsaCOE0Mpif0Xae6ji/wIqigGJAxA6nnr+NZEVn4dRndzRJ8gJABCTWog9l2mIJkIs9sqSnZ0NAHBzczNY7ubmpn+vJitWrIBMJtM/HpycrCXQjQdo8aWqzBggL0E7OG3Y44BAYu6IWgWO49A70AmPhntAwOeQkleG/51LQ16J0tyhEWI2FpusGmvhwoUoLi7WP+Li4swdUoPl3i1ZudpZcLIqyQWSjmifBw0FpG51r08arIO7FJPv63ix7Xw6EnNbXk0BIcZgscnK3d0dAJCTk2OwPCcnR/9eTUQiEezs7PQPqVRq0jhNQVcN6Cq10M4VahUQtwfQVAFOQYBX2x3zz9RcpWI81dMXPo7WqKzS4PfLWTiVmEcjXpA2x2KTVUBAANzd3XH48GH9MrlcjrNnz6JPnz5mjMy0KlRqFJerAAAuUgstWSUdAUrztPdRhYyhoZRMTCLk44muXuh6d8SLs8kF2Hv5NrVjkTbFrL0BS0pKkJiYqH+dnJyMS5cuwdHREb6+vpg7dy6WLVuG4OBgBAQEYNGiRfD09MSECRPMF7SJ6UpVdhIBxAILnMHzzk1tWxUAdBxLN/42Ex6Pw+AOrnCVinH4eg5u3SnFtvPpGBfh2XKnjyGkAcyarC5cuIAhQ+51dZ43bx4AICoqChs2bMBbb72F0tJSvPjiiygqKkL//v2xf/9+iMUWWj1mBPr2KkssVVXIgfg/tc99eraZSRQtSainHZxshfj98m0UlFbif+fSMKqTO4JcbM0dGiEmxbFWXvmdkZEBHx8fpKenw9vb29zhPNT+q1m4nqVA3yAn9Ap0Mnc49zAGxO4A8hMBqTsQOUPbC5CYRamyCn/GZiGzUDvSSZ8gJ/QKcGyZ856RBmtp1zVjsNg2q7ZKV7KyuPaq3DhtouLxtVPTU6IyKxuR9gbiLj72AIDTSfn440oWlFXUjkVaJ0pWFkSl1ugHMXW1pAFsK0uBhIPa5379ABtn88ZDAAB8HochIa54JNQNfB6HxNwSbD2XTvdjkVaJkpUFKSitBGOAtZAPW0uaFiTxEKAqB2xdAN/e5o6GPKCTlwyTunvDVmSFgtJKbD2XhrjbcnOHRYhRUbKyILqegE6WNHJFXiKQE6ftnt5hDFX/WSgPmQTTe/vC19EaKjXD39eycTAuByqa0JG0EpSsLIhuZmBnWwvpilylBG7u1z737kHTflg4a6EVHu/qhT5BTuA44GpmMbaeT0chzY9FWgFKVhYk727JytlSSlZJRwGlQjtIbcBAc0dD6oHH044r+ERXb1gL+chTKLHlXBpu5tAwTaRlo2RlQfJLLShZFWcAty9qn3cYBfAF5o2HNIivkzWm9/aDl4MElVUa/HklC0dv5KKKqgVJC0XJykKUVd6bw8rsIxIwdq/3n0dnwMHfrOGQxrEVWWFipDd6BjgCAC6lF2H7hQwUl6nMHBkhDUfJykLkl2jbFWQSgfnnsMq6DCiyASshEDDIvLGQJuHxOPRr54wJXb0gFvCRI6/A5nOpSMwtMXdohDQIJSsLcafEQnoCqiqA5OPa5/4DABEN49MaBDjbYHpvX3jIxFCqNPj98m2cuHkHak2rHsCGtCKUrCyErmTlbO4qwNR/tVPVWzvR1B+tjJ1YgEndfRDp5wAAiE4txI7odP0o/4RYMkpWFkI36oCzOYdZKs0DMqK1z4OH0z1VrRCfx2FQexeMi/CASMDD7aIKbD6bihvZdBMxsWyUrCwAY0w/zJKTuUpWuk4VTAM4B9OI6q1cO1cppvf0g6e9tlpwX2w29sVm0RxZxGJRsrIA8vIqVFZpwOdxcLA2U7LKSwAKUwCeFdBumHliIM1KZi3ApG4+6B3oBB7H4Ua2ApvOpCKjsMzcoRFSDSUrC6C7v8rBRggezwxTPGg0wK1j2uc+PbQ3AZM2gcfj0CfICZN7eEMmEUBRUYUd0Rk4mZhHnS+IRaFkZQHMXgWYfQUoywcEEsC3j3liIGalG1swzNMOjAHnkguwjYZqIhaEkpUF0CUrs1QBqlVAyr/a5359ASsLGD2DmIXIio8RYe4Y29nj3j1ZZ1MRm1GMVj5HK2kBKFlZAH3JyhwD2GbGaMf/E9sBnpHNf3xicYLdpHi6ty987o7gfuh6Dn6/koWyyipzh0baMEpWZsYY04+23uzDLKkqgLRT2uf+/QG+Bc2hRcxKKhbgyUgvDGzvDD6PQ1JuCTadSUVKXqm5QyNtFCUrMyutVKOySgOOA+wlzTxYbPpZbcKycQbcwpv32MTicRyHbn6OmNrTB062QpQq1dh1MRNH43NpnizS7ChZmVnB3ZEr7CUCWPGb8dehLAEyzmmfBwwCePSnQGrmKhVjWk9fdPGxBwBcSivClrNpuF1Ubt7ASJtCVygz03Vbd2zuMQFTTwHqKsDOU3sTMCF1EPB5GBLiigldvWAj4qOgtBLbL6Tj+M07VMoizYKSlZkVlt1tr2rOnoBKhXZkdUA7qSJnhnu7SIsU4GyDGX38EXq3i3tMaiE2nUlFegHdSExMi5KVmekGsG3WzhXpZwFNFSDzormqSIOJBXyMDHPHhK5ekIqtUFSmwo7oDBy5kQNlFQ3XREyDkpWZNXu39crSezMA+/WjUhVptABnGzzTxw+dvWUAgMvpxdh4OhWp+dRjkBgfJSszqlCpUVap/SbabDcEp5/TtlVJ3WmwWtJkIis+hnV0w5OR94Zr2hmTiQPXsmlQXGJUlKzMSNdeJRVbNc/swKpyIPPuFCD+/alURYzG18kaT/f2Qxdfe3AccO22HBtPpyLpDs1ITIyDkpUZFZZqJ72zb65SVcYF7fBKti6AU7vmOSZpM4RWPAzp4IpJ3X3gYC1AibIKey/dxr7YLJRXUimLNE2DhyxQKpU4e/YsUlNTUVZWBhcXF3Tt2hUBAQGmiK9V05WsHKyb4WbgKiWQcV77nNqqiAl52UswvbcfztzKR3RqIW5kK5BWUIahIa4IdpOaOzzSQtU7WZ08eRJffvklfv/9d6hUKshkMkgkEhQUFECpVCIwMBAvvvgi/vOf/0AqpT/I+tAnq+boCZgZo01YNs6AS4jpj0faNAGfhwHBLgh2leJgXDbySirxx5UstHNVYHAHF0jFzTxaSxu3du1arF27FikpKQCAsLAwvP/++xg9erR5A2uAelUDPvbYY5gyZQr8/f1x4MABKBQK5OfnIyMjA2VlZUhISMB7772Hw4cPo3379jh48KCp424VCsu01YAm71yhUQOZF7TPfXpRqYo0G3eZdvSLXoGO4HEcEnNL8MvpVFxIKaD5spqRt7c3Pv74Y0RHR+PChQsYOnQoxo8fj2vXrpk7tHqrV8lqzJgx+O233yAQ1PxtKDAwEIGBgYiKikJcXByysrKMGmRrxBhDUWkzVQPmxmmHVxLZAm5hpj0WIQ+w4vPQN8gZwa5SHLmRg9tFFfgnIQ9xWXIM6eAKH0drc4fY6o0bN87g9UcffYS1a9fizJkzCAtr/DVBpVIhOztb3yTk6OjY1FBrVa9k9dJLLwEA1Go1Tp48ic6dO8Pe3r7GdUNDQxEaGmq0AI1Fo9FAo7GcYWHk5Sqo1Nqp7G2FfNPFxhiQdg5gADwiAXDamYEJaWZONgJMjPTC9SwF/k3MQ55CiV8vpCPEXYoBwc6wEdGo//Wlu14oFArI5XL9cpFIBJGo7qHb1Go1fv31V5SWlqJPn4ZPtqpQKLBp0yZs3boV586dQ2VlJRhj4DgO3t7eGDFiBF588UX06NGjwfuuS4P+Ovh8PkaMGIHr16/XmqyMSa1WY8mSJdi0aROys7Ph6emJmTNn4r333gPXwKqs3Nxci0pWmcWVKC4uhr2Ej4yMdNMdqDQPKKwEeE6AxhVISzPdsQipB1sAQ7x5iMksR/ydcpwtLsbFxEx09bJBiKsEPKqmfqi8vDwAqFYwWLx4MZYsWVLjNrGxsejTpw8qKipga2uLXbt2NbhgsWrVKnz00UcICgrCuHHj8M4778DT01Pff+Hq1av4559/MGLECPTq1Qtff/01goONM/Zog7/KdOrUCbdu3WqW3n8rV67E2rVr8fPPPyMsLAwXLlzArFmzIJPJ8OqrrzZoX66urvD29jZRpA1XkF4EmYwh0MUGvr6epjtQ7DlAUAR4RQIBQaY7DiENFBwI5MgrcDT+DrKLK3CjGMjXcBjSwQWe9hJzh2fReHdnSYiLi4OXl5d+eV2lqg4dOuDSpUsoLi7Gjh07EBUVhePHjzcoYZ0/fx4nTpyoteqwZ8+eePbZZ7Fu3TqsX78e//zzj9GSFccaOF/1/v37sXDhQnz44Yfo1q0bbGxsDN63s7MzSmAAMHbsWLi5ueHHH3/UL3vyySchkUiwadOmGrdRKpVQKpX615mZmQgNDUV6erpFJaujN3JxKb0I3f0dMCDYxTQHKc0Dzv2g7VDR80XA2nT1yYQ0lkbDcPV2MU4m5utHvQjztEP/YGdYC6lqsCYZGRnw8fFp0nVt+PDhCAoKwnfffWfk6EyjwTcFP/roo7h8+TIee+wxeHt7w8HBAQ4ODrC3t4eDg4NRg+vbty8OHz6MmzdvAgAuX76Mf//9t87ulitWrIBMJtM/LLH9DLj/HisT9gRMvztflXMwJSpisXg8Dp297RHV1w9hntovu9duy/HzqVRcySiChnoNmoRGozH4Yl+XwsJCFBQUAADu3LmDnTt3NntPwgZ/bTly5EiD24sa6+2334ZcLkdISAj4fD7UajU++ugjTJ8+vdZtFi5ciHnz5ulf60pWlkbXbd3eVD0BK0uBnLt/TD69THMMQozIWmiFEWHu6OQlw5EbubijUOLw9VxczZRjaIgr3GVic4fYYi1cuBCjR4+Gr68vFAoFtmzZgmPHjuHvv/9+6Lb//e9/sXz5cgDAm2++ic2bNyMiIgKLFy/Ga6+9hueff97U4QNoRLIaPHiwCcKo2fbt27F582Zs2bIFYWFhuHTpEubOnQtPT09ERUXVuM2DvWHu7yljKarUGigqTHyPVdYV7TQgUndAZjnVn4Q8jKe9BE/19MXljCKcSspHjrwCW8+nIdxLhr5BzpAI+eYOscXJzc3FjBkzkJWVBZlMhs6dO+Pvv//GI4888tBtv/rqK1y7dg3l5eXw9fVFcnIyXFxcUFxcjEGDBllusgoICMCsWbMwc+ZM+Pr6miImvTfffBNvv/02pk6dCgAIDw9HamoqVqxYUWuyagnkFVVgTDuWmrUp/vE0mnvTgHh1M/7+CTExHo9DV18HtHeT4p+EO7iepcCVjGLE5yjQK8AREd72sOLT0Kb1dX+7f0NZWVlBIpFAIpGgXbt2cHHRtrHLZLJmq2UDGtFm9dprr2Hnzp0IDAzEI488gq1bt9a73rOhysrK9L1edPh8E96T1EyK7rZXySQC0/yyC24BFcWAQAy4djT+/glpJjYiK4zq5IFJ3b3hIhVBqdLgxM08/Hw6FTey5Whg/zDSCHw+HxUVFQCA48eP65eXlDTviPoNTlZz587FpUuXcO7cOXTs2BGvvPIKPDw8MGfOHMTExBg1uHHjxuGjjz7Cn3/+iZSUFOzatQurVq3C448/btTjNLeichO3V+mmAXHvDPBpDDbS8nk7WOOpnr4YEeYGqdgK8nIV9sVmY+v5dGQUlpk7vFbt0KFD+qYVmUymX15WVobvv/++2eJocNf1B6lUKnz77bdYsGABVCoVwsPD8eqrr2LWrFlNLjUoFAosWrQIu3btQm5uLjw9PTFt2jS8//77EArr19ZjjC6exqbrtt7D3xH9g52Nu/OyAuDsd9RdnbRaKrUGMamFuJBaiMoqbS1LkKstBrRzbp5BoS2AJV7XTK3RNzGoVCrs2rUL69evx8GDB9G7d28899xzyMjIwDvvvINDhw5hy5YtTQpOKpVi9erVWL16dZP2Y2mKyrXVgCYpWenaqhwDKVGRVknA56FXoBM6eclw5lY+YjOLkZRbguQ7pejsLUOvQEe6P6sZnDp1CnZ2dujUqVOzHK/Bv9GYmBisX78e//vf/8Dj8TBjxgx88cUXCAm5N+3E448/bvRxoVqTe5MuGjlZqVVA9hXtc89I4+6bEAtjI7LCsI5u6OJjj38T83DrTikupRchLkuOngGO6OJjDwF1wjCZ2bNnY86cOdWSVVJSElxdXY0+VVSDf5M9evRAQkIC1q5di8zMTHz22WcGiQrQ9hjU9eAjhtQaBnmFiWYIzr0OqCoAsUxbsiKkDXCyFWF8Fy9M7OYNVzsRKqs0+DchDz+fSsH1LOqEYSrx8fE13sp06NAhTJs2zejHa3DJ6tatW/Dz86tzHRsbG6xfv77RQbVm8nIVGAMEfA42xu62nnVZ+9OzC8Cjb5SkbfFx1HbCuJ6lwKmkPCgqqrD/ajZi0goxMNiFpiIxMjs7OxQWFlZbPmDAALz77rtGP16Dr2gPS1SkbrqegDJroXG7rZfmA8UZ2o4V7uHG2y8hLQjHcQj1tENUX3/0D3aG0IqHXLkSO6IzsOdSJvJLTHObTVs0atQofPbZZ9WW83g8VFZWGv149S5ZBQbWr1rp1q1bjQ6mLdDdY2UvMXJ7VfbdUpVjECAybl0xIS2NgM9DD39HhHna4eytAlzJKMatO6VIzitFiLsdegU4tpmeg6by4YcfomfPnnjyySexZMkShIeHo6KiAitXrkTnzp2Nfrx6J6uUlBT4+fnhqaeegqurq9EDaStMco+VRg1kx2qfe0QYb7+EtHDWQisMCXFFxN1OGEm5JbieJUd8tgIhHlL0CnA0fttxG+Hj44MzZ87g5ZdfRkREBEQiEaqqqiCTyfD7778b/Xj1Tlbbtm3DTz/9hFWrVmH06NF49tln8eijj1YbYYLUTa6rBjRmySo/CagsA4Q2gBPNWUXIgxxthHgswhM58gqcuZWPW3dKEXdbjhtZCnT0kKJXgBNkprpJvxXz8/PDX3/9hbS0NFy8eBFCoRC9evUyyfT29c40kyZNwr59+5CYmIhu3brh9ddfh4+PD95++20kJCQYPbDWqtgUyUrXscK9E8CjQT4JqY2bnRjju3hhWk9f+DtbQ8MYrt2WY8OpFByKy9H/f5L6y8zMBJ/Px/jx4zF69GiTJCqgER0svLy88O677yIhIQFbtmzB2bNnERISUmOvEGKIMYZi3dQgEiNVPVTIgYIk7XN3qgIkpD7cZWI83tUbU3r4wM9Jm7RiM4vx86kUHL6eo7+9hNTu5MmTCAgIgK+vL3x9feHm5oYFCxaYbKaLRtXhVVRUYNOmTVi6dCnOnj2LSZMmwdqauoU+TImyClUaBh7HwVZspDvsc64CjAH2PoCNk3H2SUgb4WkvwROR3pjcwwe+jtZQaxiuZBRjw8kUHLmRo5/Kh1T30ksvoWPHjjh//jzi4+Px6aef4tChQ4iMjERmZqbRj9egK+bZs2fx448/Yvv27QgMDMSzzz6L3377zegzBLdWuioGqdgKfJ4Ruq0zdm+CRequTkijedlL8GQ3b2QUluHMrQKkF5ThcnoxrmbKEe4lQ48AR9iKaAin+yUlJWHnzp1o3749AKBdu3Z45plnMHnyZMydOxe//vqrUY9X708/LCwMubm5eOqpp3D8+HFERFCVU0MZvb1KkQ2U5gE8K8Al5OHrE0Lq5O1gjYndrJFeUIbTt/KRWViOS+lFuJpZjHBvGbr7U9LS6dixI3Jzc/XJCtDe5/bBBx+gZ8+eRj9evT/169evw8bGBr/88gs2btxY63oFBQVGCaw1KjZ2t/Wcq9qfzsGAlajudQkh9ebjaA1vBwkyCstxOikfmUXluJhWhNiMYnT2sUd3PwfYtPGkNXPmTLzyyivYu3cvfHx89MuLi4thZ2dn9OPV+9Om4ZOaTte5wiglK40ayI3TPqcqQEKMjuM4fdJKLyjH6Vt5uF1UgZjUQlxJL0JHDztE+jnAsY3eXDx37lwAQHBwMJ544gl06dIFarUamzZtwieffGL049U7WbXkaeQthVGrAQuS795bZQ04BDR9f4SQGnEcB18na/g4+iA1vwxnk/Nxu6gCsZnFuHq7GIEutujm5wAve4m5Q21WWVlZuHTpEi5fvoxLly5hw4YNSEhIAMdx+OSTT7Bv3z507twZnTt3xqhRo5p8vHolK8aYaaZfb2OMmqxy7o5Y4RpGg9YS0gw4joO/sw38nW2QWVSOCykFuHWnFEm5JUjKLYGnvRjd/BwR5GLTJq6Xbm5uGDlyJEaOHKlfVlFRgdjYWH0S27t3L5YvX46ioqImH69eySosLAzvv/8+nnjiiTpn6E1ISMCqVavg5+eHt99+u8nBtSaVVRqUVaoBAHZNTVaqCiAvUfvcvXkmPiOE3ONlL4FXFy8UlFYiOrUQ17PkuF1UgdtFt+FgLUA3P0d09JDCqhXOp7Vs2TJERkaiW7ducHNzM3hPLBajR48eJpnPsF7J6uuvv8aCBQvwf//3f3jkkUfQvXt3eHp6QiwWo7CwEHFxcfj3339x7do1zJkzBy+//LLRA23pdKUqsYAPsaCJo0zkxQOaKsDGGbB1e/j6hBCTcLQR4pFQN/QJcsLl9CJczihCYZkKh67n4FRSHrr42CPCx77p//MW5P3339eXHN3d3fWJS/fTy8vLJMetV7IaNmwYLly4gH///Rfbtm3D5s2bkZqaivLycjg7O6Nr166YMWMGpk+fTvdc1cKoVYC517U/3cK0U4IQQszKVmSFfu2c0d3fAdduyxGTWghFRRVOJeXjQmohQj3tEOnrYNxh1sykR48eyMrKwqxZs+Ds7IyYmBjs3LkTy5cvh1qthouLCyIjI/HXX38Z9bgN6nvZv39/9O/f36gBtBW64VvsJE3s7lpZChSmaJ/TvVWEWBSRFR+Rvg6I8LbHzRwFolMLcUehxKW0IlxJL0awmy26+znA1U5s7lAb7ezZs9iwYQPeeecd9OjRA6tWrUJQUBCUSiUuXbqEmJgYXLx40ejHbX0VqhbKaCWrOze0I1fYeQDWphkwkhDSNHweh44edpjeyxdPRHrpxx+Mz1Zg89k0/BadgZS8UjDGzB1qo8ycORM3b95Ehw4dEBkZiYULF0KtVqNXr154+eWX8f333xv9mJSsmoluahA7cROTla4K0DW0iRERQkyN4zj4OdngiUhvTO/lixB3KXgch7SCMuy6mIlNZ9MQd1sOtablJS1bW1t88sknuHDhAq5evYp27drhl19+MdnxKFk1E6PMY1UhB4rStc+pCpCQFsXVTozR4R6Y2c8fXX3tIbTiIU+hxD8Jd1psCauqqgpKpRLTpk2Dt7c3Zs2aZbJRjNr2eCHNhDGmrwZsUrf1Oze0P+19ALHxhzMhhJieTCLA4A6u6B3ohCsZxRBa8VpUF/ePP/4YsbGxiI2NxY0bNyAWi9G5c2f07NkTL730EmQymUmOS8mqGZSr1FCptd+c7JoyNYhueCXXjkaIihBiTmIBHz0DWl678zvvvAN/f39ERUVh2rRpBgPZmlKj0nlSUhLee+89TJs2Dbm5uQCAffv24dq1a0YNrrW4f2qQRn+DKi8E5FnarurOHYwYHSGE1N+AAQOQn5+PpUuXolu3bujXrx9eeeUVrF+/HpcvX4ZarTbJcRt85Tx+/DjCw8Nx9uxZ7Ny5EyUlJQCAy5cvY/HixUYPsDWQl1cBaGLnijs3tT/tfQGRrRGiIoSQhjt+/DiKi4sRHx+PH374Af369cP169fxxhtvoGvXrrC1tTXvFCE6b7/9NpYtW4Z58+ZBKpXqlw8dOhRr1qwxanCtxb32qiZUAeraq1yoVEUIMb/g4GAEBwdj6tSp+mXJycm4cOGCSe6zavDVMzY2Flu2bKm23NXVFXl5eUYJqrWRN7VzRUUxIL99twqweeqHCSHkQWlpafD19a31/YCAAAQEBGDSpEkAgMzMTKMNv9TgakB7e3tkZWVVW37x4kWTjQnV0ulHr2hsNaCuCtDOCxBJ616XEEJMpEePHnjppZdw/vz5WtcpLi7GDz/8gE6dOuG3334z2rEbXLKaOnUqFixYgF9//RUcx0Gj0eDkyZOYP38+ZsyYYbTAWpMm32OlrwKke6sIIeYTFxeHjz76CI888gjEYjG6detWbVDza9euITIyEp988gkeffRRox27wSWr5cuXIyQkBD4+PigpKUFoaCgGDhyIvn374r333jNaYK0FYwyKiiZ0sFAqAHmm9rkLVQESQszHyckJq1atQlZWFtasWYPg4GDk5eUhISEBADB9+nRER0fj9OnTRk1UQCNKVkKhED/88AMWLVqEq1evoqSkBF27dkVwcLBRA9PJzMzEggULsG/fPpSVlaFdu3ZYv349unfvbpLjGVtppRpVGgaOA2wbc49V3s27YwF6AmLT3GxHCCENIZFIMHHiREycOLHZjtno7mm+vr51NrQZQ2FhIfr164chQ4Zg3759cHFxQUJCQouahkRXBWgrsgKf14jpPHTtVdQLkBBiwfh8vsnusQIakawYY9ixYweOHj2K3NxcaDQag/d37txptOBWrlwJHx8frF+/Xr8sICDAaPtvDvemBmlEFaCqHChK0z6nXoCEEAtm6vENG9xmNXfuXDzzzDNITk6Gra0tZDKZwcOY9u7di+7du2PSpElwdXVF165d8cMPP9S5jVKphFwu1z8UCoVRY2oo3Q3BjepckZ8EMI12RmCaDoQQYmb/+9//an2PM/FEsA0uWW3cuBE7d+40euNZTW7duoW1a9di3rx5eOedd3D+/Hm8+uqrEAqFiIqKqnGbFStWYOnSpSaPrb6aNDVI3t0qQGfTtAcSQkhDxMTEYNq0aQCABQsWYOXKlbWuFxkZadRjN7hkJZPJEBgYaNQgaqPRaBAZGYnly5eja9euePHFF/HCCy9g3bp1tW6zcOFCFBcX6x9xcXHNEmttGj1DsLoKKLilfU5VgISQZlZaWlptmUqlQnR0NABtn4La9OzZE/PmzTNY1tRp7hucrJYsWYKlS5eivLy8SQeuDw8PD4SGGk4y2LFjR6SlpdW6jUgkgp2dnf5x/5BQ5tDoklVRKqBWaW8ClnqYIDJCCKldx44d8fnnn6OiokK/7NNPP8U///yD559/HqNGjap12/DwcNjZ2WHWrFn6ZU29tanByWry5MkoLCyEq6srwsPDERkZafAwpn79+iE+Pt5g2c2bN+Hn52fU45hKk+6xur8K0MR1wYQQ8qCzZ88iPT0doaGh+Prrr1FZWQmBQIC5c+fiv//9L5544olat+U4DkuWLEFERAQmTpwIlUrV5A4YDW6zioqKQnR0NJ5++mm4ubmZtFHt9ddfR9++fbF8+XJMnjwZ586dw/fff4/vv//eZMc0prLG3mPFGJCnvcmO2qsIIebg4eGB1atX46233sLKlSvRqVMnzJ8/H8899xz4fH6d29rZaSeHnTt3LhwcHPDYY481vTaONZC1tTX7559/GrpZo/3++++sU6dOTCQSsZCQEPb99983aPv09HQGgKWnp5sowtrdLipjqw7Esx9OJDVsw+JMxo4sZ+zEZ4ypq0wTHCGkxWrodW358uWse/fuzNbWlrm4uLDx48ezGzduNOiYt2/fZq+88goLDQ1lP//8c7X3OY5jSUk1X+t27tzJHBwcGnS8BzW4ZOXj46PPms1h7NixGDt2bLMdz5gaXwV4t1TlGAjw6v4GQwghD3P8+HHMnj0bPXr0QFVVFd555x2MGDECcXFxsLGxqXPbwsJCxMfH4+bNm/rblWbNmlXjWLD/+c9/cPPmTXh4eKBz5876x9ChQ1FQUNCkc2hwsvr888/x1ltvYd26dfD392/SwVs7eWPnscpP1P50amfkiAghbdH+/fsNXm/YsAGurq6Ijo7GwIEDa9ymb9++SE5Ohr29PUJCQvSP8ePHIySk+qDaHMfhwIEDALRjyJ4/fx6ZmZnYu3cvDh8+DH9/fyQmJjb6HBqcrJ5++mmUlZUhKCgI1tbWEAgMSw1NzZ6motFoqo22YWpFZZVgjMFGyK//sSuKAUWutlOFfQDQzDETQiyf7nqiUCggl8v1y0UiEUQi0UO3Ly4uBgA4OtY+2MD333+PDh06VLvG18f27dtx6dIl/esDBw5g06ZNDd7P/RqcrFavXt2kA5pLTUNDmVpKZhGKiytRVqxBWlpZ/TYqSgVU9oDEHsimySwJIdXpJrp98NaexYsXY8mSJXVuq9FoMHfuXPTr1w+dOnWqdb3XX38diYmJcHd3N6jS69y580NHKxKLxYiLi9PHN2LECCxcuLAeZ1a7RvUGbIlcXV3h7e3drMcU3GaQsUq09/eEr1Pd9cJ6xecAQRHgEwGYeKBgQkjLxONp7zqKi4szmPS2PqWq2bNn4+rVq/j333/rXO/gwYMAqlfpHTp0CAEBAXVW6f3444+YMmUKBg8ejC5duiA2NrbJPcfrlazkcrm+U8X9Rc6aNGfni4bg8Xj6X3BzYIyhRKkGx3GQWYvqd+yqSm3JigPgEgw0Y7yEkJZDdz2RSqUNuubOmTMHf/zxB06cOFHvL+81Velt3ry5zm3CwsIQHR2N3bt3IzY2Fn5+fnj33XfrHWdN6pWsHBwckJWVBVdXV9jb29eYIRlj4DjOpEPEtyTKKg0qq7TVjtL63mNVlAZoqrTzVtk4mzA6QkhbwhjDK6+8gl27duHYsWMNmr2isVV6QqEQkydPxuTJkxsd9/3qdRU9cuSIviHu6NGjRjlwa6frCWgt5EPAr2cJqSBJ+9MpiEatIIQYzezZs7Flyxbs2bMHUqkU2dnZALRjvUokkjq3NUWVXmPUK1kNGjRI/zwgIAA+Pj7VgmWMIT093bjRtWBy3T1W9Z0ahDHtlCAA4BhkoqgIIW3R2rVrAQCDBw82WL5+/XrMnDmzzm3rW6XHTDyfVYM7WAQEBOirBO9XUFCAgIAAqga8Szfaer2rAMvytd3WeVaAPXWsIIQYT1MTSX2q9Ezd27rBLfi6tqkHlZSUQCwWGyWo1kA3eoW0vqNX6EpV9r6AldBEURFCSMtU75KVbm4SjuOwaNEiWFtb699Tq9U4e/YsunTpYvQAWyqFbh6r+pas7m+vIoQQYqDeyerixYsAtCWr2NhYCIX3vv0LhUJERERg/vz5xo+whdJNZ1+vklWVEii6297n2DwTWxJCSEtS72Sl6wU4a9YsfPnllxZ7P5WlUDRkhuDCVIBpAIkDYF378CeEENJWNbiDxfr1600RR6uiUmtQVqntaFKvEdd109dTqYoQQmpEQySYgK5zhdCKB5HVQz5ixihZEULIQ1CyMoH7O1c89Oa5soK7Xdb51GWdEEJqQcnKBBrUuaIwWftT5kNd1gkhpBaUrExA0ZAbgqkKkBBCHoqSlQnI63tDsLpKO8o6ADjWf2BJQghpayhZmUC9u60Xp2sTlsgWsHFphsgIIaRlomRlAvUuWRWmaH86+NMo64QQUgdKVkam0TCU6JPVQ0pWus4VDlQFSAghdaFkZWSllVXQMAYex8FWWEeyqiwFFDna5w7+zRIbIYS0VJSsjEx3Q7Ct2Ao8Xh1Ve7oqQFtXbZsVIYSQWlGyMjJFfasAC+5WAVIvQEIIeShKVkYmr8/UIIwZdq4ghBBSJ0pWRnbvhuA6egKWFQBKhXZWYJlPM0VGCCEtFyUrI9NVA9Y52rquVCXzBvj1nEmYEELaMEpWRiavT5uVvsu6v+kDIoSQVoCSlZE9dFxAjebeEEuUrAghpF4oWRlRhUoNpUoDoI42K0UWUFUJCMSArVszRkcIIS0XJSsjKlFqqwDFAj6EtU26qGuvsvcFePTxE0JIfbSoq+XHH38MjuMwd+5cc4dSI3l5PaYGoS7rhBDSYC0mWZ0/fx7fffcdOnfubO5QaqXvCSippQpQrQLkmdrnNB4gIYTUW4tIViUlJZg+fTp++OEHODg4mDucWj109IridECjBkRSQGK550EIIZamRSSr2bNnY8yYMRg+fPhD11UqlZDL5fqHQqFohgi1FA8bvaJQ1wvQj6YEIYSQBqjHvOvmtXXrVsTExOD8+fP1Wn/FihVYunSpiaOqmfxho1dQl3VCCGkUiy5Zpaen47XXXsPmzZshFovrtc3ChQtRXFysf8TFxZk4ynvqHL1CVQEosrXP7f2aLSZCCGkNLLpkFR0djdzcXERGRuqXqdVqnDhxAmvWrIFSqQSfzzfYRiQSQSQS6V/L5fJmiVWtYfqu6zW2WRWnawewtXYExHbNEhMhhLQWFp2shg0bhtjYWINls2bNQkhICBYsWFAtUZlTibIKjAFWPA7Wwhri0rVXUamKEEIazKKTlVQqRadOnQyW2djYwMnJqdpyc9PdY2UrtgJXU+eJohTtTwdKVoQQ0lAW3WbVktzrtl5De1VlKVByR/vc3rcZoyKEkNbBoktWNTl27Ji5Q6hRnd3Wi9K1P21dAKFNM0ZFCCGtA5WsjKTOklURtVcRQkhTULIyEnldU4NQ5wpCCGkSSlZGoitZyR4cF1CpAMrytSNW2NMU9oQQ0hiUrIyAMVb7pIv69ipXQCBp5sgIIaR1oGRlBOUqNVRqBgCwFT2YrHRVgNQLkBBCGouSlRHoqgBtRVaw4j/wkRalaX9SexUhhDQaJSsjqHXSxQo5UFagba+SUXsVIYQ0FiUrI5DXNulisa69yg0Q1G8gXkIIIdVRsjKCWrut66sAqb2KEEKagpKVEdQ6NQi1VxFCiFFQsjKCGtusDNqrvM0UGSGEtA6UrIxAUVObFbVXEUIsxIkTJzBu3Dh4enqC4zjs3r3b3CE1GCWrJlJWqVGhUgN4oGRF7VWEEAtRWlqKiIgIfPPNN+YOpdFa3KjrlkZeri1ViQV8iKzum3SRkhUhxEKMHj0ao0ePNncYTdJmkpVGo4FGozH6fovLK8EYg1TEv7d/pQIovdteJfUCTHBcQkjbpbvWKBQKyOVy/XKRSASRSGSusEyqzSSr3NxckySrhJwyFBeXwJ4nQlra3dKU/DagsgfEdkBWrtGPSQhp2/Ly8gAAoaGhBssXL16MJUuWmCEi02szycrV1RXe3sbvlZeqvANZMR8B3vbw9XXRLrwZBwiKAI92gC9VAxJCjIvH03Y3iIuLg5eXl355ay1VAW0oWfF4PP0v2JgUSjU4joPMWnhv/8UZAAfA0R8wwTEJIW2b7lojlUphZ2dn5miaB11Jm0jXwUJ/Q/D981fR/VWEEGIUbaZkZSq6oZbsJHc/St38VTYuNH8VIcQilJSUIDExUf86OTkZly5dgqOjI3xbSFMFJasmqKzSoLxSe4+VvmSluxmYhlgihFiICxcuYMiQIfrX8+bNAwBERUVhw4YNZoqqYShZNYGuVCUW8CEW3L3Hiu6vIoRYmMGDB4MxZu4wmoTarJpANyagvgqwshQo1XYppfYqQggxHkpWTSB/cLR1XXuVrQsgtDZTVIQQ0vpQsmqCYn3JSpesaEoQQggxBUpWTaCrBpTpk1Wq9idNYU8IIUZFyaoJ9CUrsRVQWXavvcqekhUhhBgTJasm0PUGlEkE97qs2zgDQhszRkUIIa0PJatGqlCpoVRpB8a1kwioyzohhJgQJatG0rVX2Yj4EPB599qrKFkRQojRUbJqpOL7O1eoyu+7v4raqwghxNgoWTWSQbIqSgcYA6ydAJGtmSMjhJDWx6KT1YoVK9CjRw9IpVK4urpiwoQJiI+PN3dYAB64x4raqwghxKQsOlkdP34cs2fPxpkzZ3Dw4EGoVCqMGDECpaWl5g4NRWW6busCoJiSFSGEmJJFD2S7f/9+g9cbNmyAq6sroqOjMXDgQDNFpaUrWdkL1UDJ3anrKVkRQohJWHSyelBxcTEAwNHRsdZ1lEollEql/rVCoTB6HGoNg+LuuICyylxqryKEEBOz6GrA+2k0GsydOxf9+vVDp06dal1vxYoVkMlk+kdoaKjRY1FUqKBhDAI+B9sy3fxVVKoihBBTaTHJavbs2bh69Sq2bt1a53oLFy5EcXGx/hEXF2f0WHTtVTKJAJy+cwV1WSeEEFNpEdWAc+bMwR9//IETJ07A27vueaJEIhFEIpH+tVwuN3o8Rbpu60IAijvahVSyIoQQk7HoZMUYwyuvvIJdu3bh2LFjCAgIMHdIAICiskoAgL2m8L72KqmZoyKEkNbLopPV7NmzsWXLFuzZswdSqRTZ2dkAAJlMBolEYra49D0BVXdLVQ40fxUhhJiSRbdZrV27FsXFxRg8eDA8PDz0j23btpk1Ll2blb0yU7uAqgAJIcSkLLpkxRgzdwjVaDRMm6zUKtizXEAASlaEEGJiFl2yskTyu93WrSrlkFppaP4qQghpBpSsGqhQVwXIisBxABz8zRoPIYS0BZSsGqhQ1xOwSjeFPVUBEkKIqVGyaqDC0kpArYQjKwI4jpIVIYQ0A0pWDVRYpgLKi2EvqAJs3QCB+brQE0JIW0HJqoEKSyuBiiI4CtV0fxUhhDQTSlYNUKFSo0SpAsqL4CCoos4VhBDSTChZNUBhWSWgKoctVw6xgAfIaPBaQghpDpSsGiC/pBIoL4KjoAqQeQN8gblDIoSQNoGSVQPk322vchJSFSAhhDQnix5uydLkK8qBimI42agBh+YbAZ4xhqqqKqjV6mY7JiHEfPh8PqysrMBxnLlDsRiUrBogPy8P0KjhZGOl7bbeDCorK5GVlYWysrJmOR4hxDJYW1vDw8MDQqHQ3KFYBEpW9VReqUZJsXbUCic3b4Bn+hpUjUaD5ORk8Pl8eHp6QigU0jctQlo5xhgqKytx584dJCcnIzg4GLxmuN5YOkpW9ZRXogQqiiATVEHk0jxVgJWVldBoNPDx8YG1tXWzHJMQYn4SiQQCgQCpqamorKyEWCw2d0hmR+m6nnILigBlCZyFVYBjYLMem75VEdL20P+9Ifo06ulOdgYAwNXelqawJ4SQZkbJqp5yc7MBAK7u3maOhBBC2h5KVvWgrFShoLAQAODm3bxVgG0Bx3HYvXu3/vWNGzfQu3dviMVidOnSpdZllmbDhg2wt7dv0Db+/v5YvXq1SeIxp2PHjoHjOBQVFZk7lIeaOXMmJkyYYO4wyENQsqqH3MwUMI0aUhEPNs40JUh9zJw5ExzHgeM4CAQCuLm54ZFHHsFPP/0EjUZjsG5WVhZGjx6tf7148WLY2NggPj4ehw8frnWZOdWUZKZMmYKbN2+aJyAL07dvX2RlZUEmk5k7FNJKULKqh6zMZACAh4tTs3RZby1GjRqFrKwspKSkYN++fRgyZAhee+01jB07FlVVVfr13N3dIRKJ9K+TkpLQv39/+Pn5wcnJqdZlDVVZWdm0E3oIiUQCV1dXkx6jpRAKhXB3d6dbLYjR0JX3YRjD7awsAICHp/lLVYwxVFZpzPJgjDUoVpFIBHd3d3h5eSEyMhLvvPMO9uzZg3379mHDhg369e6vBuQ4DtHR0fjggw/AcRyWLFlS4zIASE9Px+TJk2Fvbw9HR0eMHz8eKSkp+v3qqnc++ugjeHp6okOHDg3a7rPPPoOHhwecnJwwe/ZsqFQqAMDgwYORmpqK119/XV96BKpXAyYlJWH8+PFwc3ODra0tevTogUOHDjXoMwSAn376CWFhYRCJRPDw8MCcOXP076WlpWH8+PGwtbWFnZ0dJk+ejJycHP37S5YsQZcuXfDTTz/B19cXtra2+L//+z+o1Wp88skncHd3h6urKz766CODY9a135s3b4LjONy4ccNgmy+++AJBQUEAqlcD6j6bv//+Gx07doStra3+y4xOVVUVXn31Vdjb28PJyQkLFixAVFRUrVV0crkcEokE+/btM1i+a9cuSKVS/Y30sbGxGDp0KCQSCZycnPDiiy+ipKSk1s+7plJzly5d9H93gPbv9LvvvsPYsWNhbW2Njh074vTp00hMTMTgwYNhY2ODvn37IikpyWA/e/bsQWRkJMRiMQIDA7F06VKDL26kdnSf1UNoFNnIlKsAzgpePs03xFJtVGqGb44mmuXYs4e0g9Cqad+Uhw4dioiICOzcuRPPP/98tfezsrIwfPhwjBo1CvPnz4etrS3+85//VFumUqkwcuRI9OnTB//88w+srKywbNkyjBo1CleuXNHf9X/48GHY2dnh4MGDAFDv7Y4ePQoPDw8cPXoUiYmJmDJlCrp06YIXXngBO3fuREREBF588UW88MILtZ5rSUkJHn30UXz00UcQiUT45ZdfMG7cOMTHx8PXt35ffNauXYt58+bh448/xujRo1FcXIyTJ08C0N40rksox48fR1VVFWbPno0pU6bg2LFj+n0kJSVh37592L9/P5KSkjBx4kTcunUL7du3x/Hjx3Hq1Ck8++yzGD58OHr16vXQ/bZv3x7du3fH5s2b8eGHH+qPs3nzZjz11FO1nktZWRk+++wzbNy4ETweD08//TTmz5+PzZs3AwBWrlyJzZs3Y/369ejYsSO+/PJL7N69G0OGDKlxf3Z2dhg7diy2bNliUI28efNmTJgwAdbW1igtLdX/vs+fP4/c3Fw8//zzmDNnjsEXpsb48MMPsWrVKqxatQoLFizAU089hcDAQCxcuBC+vr549tlnMWfOHH0y/eeffzBjxgx89dVXGDBgAJKSkvDiiy8C0FZzk7pRsnqInJTrqNTwIJLaw8WeuqwbQ0hICK5cuVLje+7u7rCysoKtrS3c3d0BALa2ttWWbdq0CRqNBv/973/1JZv169fD3t4ex44dw4gRIwAANjY2+O9//6tPQvXdzsHBAWvWrAGfz0dISAjGjBmDw4cP44UXXoCjoyP4fD6kUqk+nppEREQgIiJC//rDDz/Erl27sHfvXoPSUV2WLVuGN954A6+99pp+WY8ePQBoE3FsbCySk5Ph46OdruaXX35BWFgYzp8/r19Po9Hgp59+glQqRWhoKIYMGYL4+Hj89ddf4PF46NChA1auXImjR4+iV69e9drv9OnTsWbNGn2yunnzJqKjo7Fp06Zaz0WlUmHdunX60tecOXPwwQcf6N//+uuvsXDhQjz++OMAgDVr1uCvv/6q8/OZPn06nnnmGZSVlcHa2hpyuRx//vkndu3aBQDYsmULKioq8Msvv8DGxka/33HjxmHlypVwc2v8sGmzZs3C5MmTAQALFixAnz59sGjRIowcORIA8Nprr2HWrFn69ZcuXYq3334bUVFRAIDAwEB8+OGHeOuttyhZ1QMlq7owhpTUFACAj6cneDzz178L+BxmD2lntmMbA2OsyW0Zly9fRmJiIqRSwy8QFRUVBlUv4eHhBmOr1Xe7sLAw8Pl8/WsPDw/ExsY2KMaSkhIsWbIEf/75J7KyslBVVYXy8nKkpaXVa/vc3Fzcvn0bw4YNq/H969evw8fHR59QACA0NBT29va4fv26Pln5+/sbnK+bmxv4fL7BTadubm7Izc2t936nTp2K+fPn48yZM+jduzc2b96MyMhIhISE1Ho+1tbW+kQFaD9T3TGLi4uRk5ODnj176t/n8/no1q1btQ4593v00UchEAiwd+9eTJ06Fb/99hvs7OwwfPhw/blEREToExUA9OvXDxqNBvHx8U1KVp07d9Y/1+0nPDzcYFlFRQXkcjns7Oxw+fJlnDx50qDKVa1Wo6KiQp9sSe0oWdWlOANJhSqAEyEgIOjh6zcDjuOaXBVnbtevX0dAQNOqVEtKStCtWzd9FdL9XFxc9M/vv0g1ZDuBwHCuMo7j6rxo1mT+/Pk4ePAgPvvsM7Rr1w4SiQQTJ06sd0cPiUTSoOPVpqZzaer5ubu7Y+jQodiyZQt69+6NLVu24OWXX25wHA1tB32QUCjExIkTsWXLFkydOhVbtmzBlClTYGXV+Esbj8erFpeuvfJ+95+P7stXTct0n2tJSQmWLl2KJ554otq+aDilh6MOFnUoSLmCO0oBeLbOCHKzN3c4rcKRI0cQGxuLJ598skn7iYyMREJCAlxdXdGuXTuDR13dpRu73YOEQuFDp2w5efIkZs6ciccffxzh4eFwd3c36MjxMFKpFP7+/rV21e/YsSPS09ORnp6uXxYXF4eioiKEhobW+ziN3e/06dOxbds2nD59Grdu3cLUqVMbfUyZTAY3NzecP39ev0ytViMmJuah206fPh379+/HtWvXcOTIEUyfPt3gXC5fvozS0lL9spMnT+qrP2vi4uJi0PFDLpcjOTm5MadlIDIyEvHx8dX+7tq1a9dsQyt988038Pf3h1gsRq9evXDu3LlmOa4xULKqjaoclxO11TX+vr6QCPkP2YA8SKlUIjs7G5mZmYiJicHy5csxfvx4jB07FjNmzGjSvqdPnw5nZ2eMHz8e//zzD5KTk3Hs2DG8+uqryMjIMPp2D/L398eJEyeQmZmJvLy8GtcJDg7Gzp07cenSJVy+fBlPPfVUg0tnS5Ysweeff46vvvoKCQkJiImJwddffw0AGD58OMLDwzF9+nTExMTg3LlzmDFjBgYNGoTu3bs36Dj3q+9+n3jiCSgUCrz88ssYMmQIPD09G31MAHjllVewYsUK7NmzB/Hx8XjttddQWFj40CrjgQMHwt3dHdOnT0dAQAB69eqlf2/69OkQi8WIiorC1atXcfToUbzyyit45plnaq0CHDp0KDZu3Ih//vkHsbGxiIqKMqgSbqz3338fv/zyC5YuXYpr167h+vXr2Lp1K957770m77s+tm3bhnnz5mHx4sWIiYlBREQERo4cqa+KtXSUrGrAGEP69bOILRICQht07WAZVYAtzf79++Hh4QF/f3+MGjUKR48exVdffYU9e/Y0+Z/f2toaJ06cgK+vL5544gl07NgRzz33HCoqKmBnZ2f07R70wQcfICUlBUFBQQbVh/dbtWoVHBwc0LdvX4wbNw4jR45EZGRkg84zKioKq1evxrfffouwsDCMHTsWCQkJALTVTHv27IGDgwMGDhyI4cOHIzAwENu2bWvQMR5U3/1KpVKMGzcOly9fNijNNNaCBQswbdo0zJgxA3369IGtrS1Gjhz50CoyjuMwbdq0GuOwtrbG33//jYKCAvTo0QMTJ07EsGHDsGbNmlr3t3DhQgwaNAhjx47FmDFjMGHCBIO2tsYaOXIk/vjjDxw4cAA9evRA79698cUXX8DPz6/J+66PVatW4YUXXsCsWbMQGhqKdevWwdraGj/99FOzHL+pONbUSmMLl5GRAR8fH6SmpsLbu37j+uVm38aWPw8BTIPA9uEYNyDSLDc3VlRUICUlBQEBAVSnTdocjUaD0NBQTJo0yaCLfFtRUVGB5ORkfbXd/TIyMuDn54e4uDh4eXnpl4tEIoMb7HUqKythbW2NHTt2GNy3FhUVhaKiIuzZs8dk52EsbaaDRW5ubr2rYFhVJYS2jrAXVCHU29Gg7r45qdVqqNVqqFQqmi6AtHqpqak4dOgQBg4cCKVSibVr1yI5ORmTJk0y+egjlkilUkGtViMrK6taTYSu6vnBtsnFixcb3Lx8//pqtbpa1aebm1u1m7stVZtJVq6urvUuWQHAf/yDwGNVAF/w8JVNRFeyEggENLU1afXEYjE2b96MhQsXgjGGTp064eDBgwZdxNsSjUYDPp8PDw+PaiUr3ZfXmkpWrVWbSVY8Hq9BpRPtqubtVMHj8fTD+dAYa6S18/X11Y/OQaD/v6/p2qV7LZVK69XW6uzsDD6fbzAUFwDk5OTUeWO7JWkRdUstubslIYSYm1AoRLdu3Qxug9BoNDh8+DD69Oljxsjqz+KTVUvvbmkMrbwPDCGkBsb+v583bx5++OEH/Pzzz7h+/TpefvlllJaWGgwJZcksPlm19O6WTaG7G143ejQhpO3Q/d8/OPJHY02ZMgWfffYZ3n//fXTp0gWXLl3C/v37mzTkVHOy6DaryspKREdHY+HChfplPB4Pw4cPx+nTp2vcRqlUQqlU6l8rFAqTx2kqfD4f9vb2+lKktbU1tV0R0soxxlBWVobc3FzY29sb5YZknTlz5tR7EGVLY9HJqjHdLVesWIGlS5c2R3jNQtf42ZaqPQkhgL29fYvp/NAcLDpZNcbChQsxb948/evMzMwmjZNmbhzHwcPDA66urjUOpkkIaX0EAoFRS1StgUUnq8Z0t3zwDm65XG7SGJsLn8+nP15CSJtl0R0sWkN3S0IIIU1n0SUrQNvdMioqCt27d0fPnj2xevXqFtXdkhBCSNNZfLKaMmUK7ty5g/fffx/Z2dno0qVLi+puSQghpOksPlkBTetuqRu89v7J1AghpCXTXc8aOj9aS9YiklVT6Dpn9OzZ08yREEKIceXk5MDX19fcYTSLVj+fVVVVFS5evAg3N7cGDWSrUCgQGhqKuLg4SKVSE0ZoHq39/IDWf450fi1fY89Ro9EgJycHXbt2hZVVqy9zAGgDyaqx5HI5ZDIZiouLGzSDbEvR2s8PaP3nSOfX8rWFczQWi+66TgghhACUrAghhLQAlKxqIRKJsHjx4lY782ZrPz+g9Z8jnV/L1xbO0ViozYoQQojFo5IVIYQQi0fJihBCiMWjZEUIIcTiUbIihBBi8ShZ1eCbb76Bv78/xGIxevXqhXPnzpk7JKNZsWIFevToAalUCldXV0yYMAHx8fHmDstkPv74Y3Ach7lz55o7FKPKzMzE008/DScnJ0gkEoSHh+PChQvmDsso1Go1Fi1ahICAAEgkEgQFBeHDDz9ES+4LduLECYwbNw6enp7gOA67d+82eJ8xhvfffx8eHh6QSCQYPnw4EhISzBOshaJk9YBt27Zh3rx5WLx4MWJiYhAREYGRI0e2mmnljx8/jtmzZ+PMmTM4ePAgVCoVRowYgdLSUnOHZnTnz5/Hd999h86dO5s7FKMqLCxEv379IBAIsG/fPsTFxeHzzz+Hg4ODuUMzipUrV2Lt2rVYs2YNrl+/jpUrV+KTTz7B119/be7QGq20tBQRERH45ptvanz/k08+wVdffYV169bh7NmzsLGxwciRI1FRUdHMkVowRgz07NmTzZ49W/9arVYzT09PtmLFCjNGZTq5ubkMADt+/Li5QzEqhULBgoOD2cGDB9mgQYPYa6+9Zu6QjGbBggWsf//+5g7DZMaMGcOeffZZg2VPPPEEmz59upkiMi4AbNeuXfrXGo2Gubu7s08//VS/rKioiIlEIva///3PDBFaJipZ3aeyshLR0dEYPny4fhmPx8Pw4cNx+vRpM0ZmOsXFxQAAR0dHM0diXLNnz8aYMWMMfpetxd69e9G9e3dMmjQJrq6u6Nq1K3744Qdzh2U0ffv2xeHDh3Hz5k0AwOXLl/Hvv/9i9OjRZo7MNJKTk5GdnW3wtyqTydCrV69We91pjLYxXG895eXlQa1WV5vY0c3NDTdu3DBTVKaj0Wgwd+5c9OvXD506dTJ3OEazdetWxMTE4Pz58+YOxSRu3bqFtWvXYt68eXjnnXdw/vx5vPrqqxAKhYiKijJ3eE329ttvQy6XIyQkBHw+H2q1Gh999BGmT59u7tBMIjs7GwBqvO7o3iOUrNq02bNn4+rVq/j333/NHYrRpKen47XXXsPBgwchFovNHY5JaDQadO/eHcuXLwcAdO3aFVevXsW6detaRbLavn07Nm/ejC1btiAsLAyXLl3C3Llz4enp2SrOjzQOVQPex9nZGXw+Xz9ho05OTg7c3d3NFJVpzJkzB3/88QeOHj0Kb29vc4djNNHR0cjNzUVkZCSsrKxgZWWF48eP46uvvoKVlRXUarW5Q2wyDw8PhIaGGizr2LEj0tLSzBSRcb355pt4++23MXXqVISHh+OZZ57B66+/jhUrVpg7NJPQXVvawnWnKShZ3UcoFKJbt244fPiwfplGo8Hhw4fRp08fM0ZmPIwxzJkzB7t27cKRI0cQEBBg7pCMatiwYYiNjcWlS5f0j+7du2P69Om4dOkS+Hy+uUNssn79+lW73eDmzZvw8/MzU0TGVVZWVm2iVD6f32qncA8ICIC7u7vBdUcul+Ps2bOt5rpjDFQN+IB58+YhKioK3bt3R8+ePbF69WqUlpZi1qxZ5g7NKGbPno0tW7Zgz549kEql+jpxmUwGiURi5uiaTiqVVmt/s7GxgZOTU6tpl3v99dfRt29fLF++HJMnT8a5c+fw/fff4/vvvzd3aEYxbtw4fPTRR/D19UVYWBguXryIVatW4dlnnzV3aI1WUlKCxMRE/evk5GRcunQJjo6O8PX1xdy5c7Fs2TIEBwcjICAAixYtgqenJyZMmGC+oC2NubsjWqKvv/6a+fr6MqFQyHr27MnOnDlj7pCMBkCNj/Xr15s7NJNpbV3XGWPs999/Z506dWIikYiFhISw77//3twhGY1cLmevvfYa8/X1ZWKxmAUGBrJ3332XKZVKc4fWaEePHq3x/y4qKooxpu2+vmjRIubm5sZEIhEbNmwYi4+PN2/QFoamCCGEEGLxqM2KEEKIxaNkRQghxOJRsiKEEGLxKFkRQgixeJSsCCGEWDxKVoQQQiweJStCCCEWj5IVIYQQi0fJihBCiMWjZEUIIcTiUbIihBBi8ShZEdJEKSkp4Diu2mPw4MHmDo2QVoOmCCGkiXx8fJCVlaV/nZ2djeHDh2PgwIFmjIqQ1oVGXSfEiCoqKjB48GC4uLhgz5491SYRJIQ0DpWsCDGiZ599FgqFAgcPHqRERYgRUbIixEiWLVuGv//+G+fOnYNUKjV3OIS0KlQNSIgR/Pbbb5g2bRr27duHYcOGmTscQlodSlaENNHVq1fRq1cvzJs3D7Nnz9YvFwqFcHR0NGNkhLQelKwIaaINGzZg1qxZ1ZYPGjQIx44da/6ACGmFKFkRQgixeNRdiRBCiMWjZEUIIcTiUbIihBBi8ShZEUIIsXiUrAghhFg8SlaEEEIsHiUrQgghFo+SFSGEEItHyYoQQojFo2RFCCHE4lGyIoQQYvH+H+oKkXDo7EMDAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# age of the universe (from present day) in years wrt to redshift\n", "# consider z=0 corresponds to present day t=0\n", "z = np.geomspace(0.001, 10, 100)\n", "t = 13.786885302009708-cbc.cosmo.age(z).value\n", "\n", "# differential comoving volume wrt to redshift\n", "z = np.geomspace(0.01, 10, 100)\n", "dVc_dz = cbc.differential_comoving_volume(z)\n", "\n", "# plot the differential comoving volume and age of the universe\n", "# show differential comoving volume scale on the right y-axis\n", "# show age of the universe scale on the left y-axis\n", "plt.figure(figsize=(4,4))\n", "plt.plot(z, t, color='C1', linestyle='-', alpha=0.5, label=\"Age of the universe\")\n", "plt.ylabel(\"time (Myr)\")\n", "plt.xlabel(\"z\")\n", "plt.twinx()\n", "plt.plot(z, dVc_dz, color='C0', linestyle='-', alpha=0.5, label=\"Differential comoving volume\")\n", "plt.ylabel(r\"$\\frac{dV_c}{dz} (Mpc^3)$\")\n", "plt.title(\"Age of the universe & \\n Differential comoving volume\")\n", "plt.legend()\n", "plt.grid(alpha=0.4)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Merger rate evolution with redshift (detector frame)\n", "\n", "* LeR default Merger rate follows [WIERDA et al. 2021](https://arxiv.org/pdf/2106.06303.pdf).\n", "* It is a functional fit to the population I/II star merger-rate density normalized to the local merger- rate density following Oguri (2018). \n", "* This model follows from the M10 model to the Belczynski et al. (2017), which is arrived from Madau & Dickinson (2014) with the inclusion of the metallicity dependence of the star formation rate, which is bassically the effect related to pair-instability supernova (PSN) and pair-instability pulsation supernova (PPSN). \n", "\n", "\\begin{equation}\n", "\\mathcal{R}_m(z_s) = \\frac{\\mathcal{R}_O(b_4+1)e^{b_2 z_s}}{b_4+e^{b_3 z_s}} \\text{Gpc}^{-3}\\text{yr}^{-1} \\tag{1}\n", "\\end{equation}\n", "* $z_s$: redshift of source\n", "* $\\mathcal{R}$: local mergerrate. $\\mathcal{R}=23.9^{+14.3}_{-8.6}\\text{Gpc}^{-3}\\text{yr}^{-1}=23.9^{+14.3}_{-8.6} \\times 10^{-9}\\text{Mpc}^{-3}\\text{yr}^{-1}$\n", "* fitting parameters: $b_2=1.6$, $b_3=2.1$, $b_4=30$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z_to_luminosity_distance interpolator will be loaded from ./interpolator_pickle/z_to_luminosity_distance/z_to_luminosity_distance_0.pickle\n", "differential_comoving_volume interpolator will be loaded from ./interpolator_pickle/differential_comoving_volume/differential_comoving_volume_0.pickle\n", "merger_rate_density_bbh_popI_II_oguri2018 interpolator will be generated at ./interpolator_pickle/merger_rate_density_bbh_popI_II_oguri2018/merger_rate_density_bbh_popI_II_oguri2018_5.pickle\n" ] } ], "source": [ "z_min = 0.0\n", "z_max = 10.0\n", "# class initialisation\n", "cbc = CBCSourceRedshiftDistribution(z_min=z_min, \n", " z_max=z_max,\n", " merger_rate_density=\"merger_rate_density_bbh_popI_II_oguri2018\",\n", " cosmology=cosmo,\n", " )" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.39e-08" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# looking for local merger rate density (R0)\n", "# by default, it uses results from Renske et al 2021\n", "cbc.merger_rate_density(zs=0.0) # in units of Mpc^-3 yr^-1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plots with uncertainties in local merger rate density\n", "\n", "* [WIERDA et al. 2022](https://arxiv.org/pdf/2106.06303.pdf) , $\\text{R0} = 23.9^{+14.3}_{-8.6} \\times 10^{-9} Mpc^{-3} yr^{-1}$\n", "* `ler` allows you to change input parameters for the merger rate density model\n", "* with results from [GWTC-3, PDB (pair) model](https://arxiv.org/pdf/2111.03634.pdf):\n", "\n", "| Model | $\\mathcal{R}_O$ |\n", "|-------|---------------------|\n", "| BNS | $170^{+270}_{-120}$ |\n", "| BBH | $25^{+10}_{-7}$ |\n", "| NSBH | $27^{+31}_{-17}$ |\n", "\n", "\n", "* Note: uncertainties in local merger rate density of BNS is much larger than BBH and NSBH" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### BBH" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "z = np.geomspace(0.01, 5.0, 100)\n", "\n", "# getting the median values of zs distribution (source frame)\n", "# det: detector frame, src: source frame\n", "param = dict(R0=25 * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bbh_density_median_det = cbc.merger_rate_density(z, param=param)\n", "\n", "# getting the lower bound values of zs distribution (source frame)\n", "param = dict(R0=(25-7) * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bbh_density_low_det = cbc.merger_rate_density(z, param=param)\n", "\n", "# getting the upper bound values of zs distribution (source frame)\n", "param = dict(R0=(25+10) * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bbh_density_up_det = cbc.merger_rate_density(z, param=param)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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6N04UFRUF0CmpuiccDgdjx47l6aef7vLnx+ejnOz5ANdff/1JA+S2HBFX68vf1un2s2DBAlavXs1PfvITxo8fT3BwMA6HgwsuuKDLv4GuPlsn+7wdH2j29PfT9lk4MeBRrqGBSTfMnz+/PWGzK83NzfziF7/gn//8J1VVVYwZM4Ynnnii15UhT/zSffzxx8nIyGDWrFm92p8nueKKK7j99ttZu3Ytb7311kkfl5GRwbJly5gxY0avT4ypqans3LkTwzA6XPnk5uZ2ei2QK//zzjuvV6/VG++88w433nhjhxkETU1NVFVVdXjcya7a2todGxvbq3anpqa294Ycb8+ePU59nZPx8/Pjkksu4ZJLLsHhcHDnnXfyl7/8hV/+8pederXanOoKdsyYMUyYMIHXX3+d5ORkCgoKePbZZ0/bjiFDhhAQEEBeXl6H7W2zTHJycjr0FrW2tpKXl8e4cePat2VkZPDNN99w7rnnnvYqu6ufx8TEEBISgt1uP+0xzsjIYN26dbS2tnZIAD/daxz/nk78HQPs3r2b6OjoDr0l/amyspLPPvuMBx98kF/96lft27v6TPZVT34/QPtnoS3JXLmW5pg4wd13382aNWt488032bp1K1dffTUXXHCBU/7AWlpaeO211/jud787ILoVg4ODef7551m0aNEpa0YsWLAAu93OQw891OlnNput05d3V+bNm8fhw4f573//276tqamJv/71rx0eN2nSJDIyMvjd735HXV1dp/201WdwNovF0mn44Nlnn+00rbbti+LE9zxv3jxCQ0N59NFHaW1t7bT/07X7wgsvZO3ataxfv77Dc07sperr63TlxOmgZrO5vUegq+mbbYKCgk45zPWd73yHTz/9lGeeeYaoqKhTXlC08fX1ZfLkyXz99dcdtk+ePJmYmBheeOEFWlpa2rcvXry40+9iwYIFHD58uNNnC2TI7vi6HUFBQZ2eb7FY+Na3vsW7777L9u3bO+3j+GP8rW99i7KyMp577rlOj2v7PAUGBgKdPzMJCQmMHz+eV155pcPPtm/fzqeffsqFF17YaZ/9pa2n48S/gf4ooNeT3w/Axo0bMZlMTJ8+3eltUaenPSZ9VFBQwMsvv0xBQQGJiYkA/PjHP+bjjz/m5Zdf5tFHH+3T/pcsWUJVVVWHWgfe7lS5HG1mzZrF7bffzmOPPcaWLVuYO3cuvr6+5OTk8Pbbb/OHP/zhpPkpbW6//Xaee+45Fi5cyD333ENCQkJ73gEcu6o0m8289NJLzJ8/n9GjR3PzzTeTlJTE4cOH+eKLLwgNDeV///tf39/4CS6++GJeffVVwsLCGDVqFGvWrGHZsmXtQwttxo8fj8Vi4YknnqC6uhp/f3/mzJlDbGwszz//PN/5zneYOHEi11xzDTExMRQUFPDBBx8wY8aMLr+82tx///28+uqrXHDBBdxzzz3t04VTU1PZunVr++NCQ0P79DpdufXWW6moqGDOnDkkJyeTn5/Ps88+y/jx4095lTpp0iTeeust7rvvPqZMmUJwcHCHAPfaa6/l/vvv57333uP73//+SXsUTnTZZZfxi1/8gpqamvacGV9fXx5++GFuv/125syZw7e//W3y8vJ4+eWXO+WYfOc73+Ff//oXd9xxB1988QUzZszAbreze/du/vWvf7XX2Gl7D8uWLePpp58mMTGR9PR0pk6dyuOPP84XX3zB1KlTue222xg1ahQVFRVs2rSJZcuWtdfUuOGGG/jHP/7Bfffdx/r165k5cyb19fUsW7aMO++8k8suu4yAgABGjRrFW2+9xbBhw4iMjGTMmDGMGTOGJ598kvnz5zN9+nRuueWW9unCYWFhHWqd9LfQ0FDOPvtsfvvb39La2kpSUhKffvppp54rZ+jJ7wck4XvGjBmd/haVi7hpNpDXAoz33nuv/f77779vAEZQUFCHm4+Pj7FgwQLDMAxj165dBnDK209/+tMuX2/u3LnGxRdf7Iq31i+Ony58KidOF27z4osvGpMmTTICAgKMkJAQY+zYscb9999vHDly5LTPNQzD2L9/v3HRRRcZAQEBRkxMjPGjH/3IePfddw3AWLt2bYfHbt682bjyyiuNqKgow9/f30hNTTUWLFhgfPbZZ+2PaZu2WFpa2uf3X1lZadx8881GdHS0ERwcbMybN8/YvXu3kZqa2mk66V//+ldj6NChhsVi6TSF9osvvjDmzZtnhIWFGVar1cjIyDBuuukm4+uvvz5t+7Zu3WrMmjXLsFqtRlJSkvHQQw8Zf/vb3zpMF+7J69x4441GUFBQp9dpO25t3nnnHWPu3LlGbGys4efnZwwZMsS4/fbbjcLCwg6vd+J7raurM6699lojPDzcALqcOnzhhRcagLF69erTvv82xcXFho+Pj/Hqq692+tmf//xnIz093fD39zcmT55srFy50pg1a1anacgtLS3GE088YYwePdrw9/c3IiIijEmTJhkPPvigUV1d3f643bt3G2effbYREBBgAB1+18XFxcZdd91lpKSkGL6+vkZ8fLxx7rnnGi+++GKH12poaDB+8YtfGOnp6e2Pu+qqq4x9+/a1P2b16tXGpEmTDD8/v05Th5ctW2bMmDHDCAgIMEJDQ41LLrnE2LlzZ4fX6Oln/XTThbvaz6FDh4wrrrjCCA8PN8LCwoyrr766faru8e092T5O9nmbNWuWMXr06A7buvv7qaqqMvz8/IyXXnqpW+9bOZ/JMLpRHUq1M5lMHWblvPXWW1x33XXs2LGjUxJWcHAw8fHxtLS0dJi61pWoqKhOuSX5+fkMHTqUf//731x22WVOfR+D2TPPPMMPf/hDDh06RFJSkrubo5zsiiuuYNu2bZ1yiU7nlltuYe/evSet7KoGh2eeeYbf/va37Nu3z2mJv6pndCinjyZMmIDdbqekpISZM2d2+Rg/Pz9GjBjR432//PLLxMbGctFFF/W1mYNWY2Njp1oJf/nLX8jKytKgZAAqLCzkgw8+4Be/+EWPn/vrX/+aYcOG8dVXX/X7CsPKM7W2tvL000/zf//3fxqUuJEGJt1QV1fX4eorLy+PLVu2EBkZybBhw7juuuu44YYbeOqpp5gwYQKlpaV89tlnZGdn9zqocDgcvPzyy9x4441Om/Y5GF155ZUMGTKE8ePHU11dzWuvvcbu3btPOg1Zeae8vDy++uorXnrpJXx9fbn99tt7vI8hQ4boUveDnK+vLwUFBe5uhnL3WJI3aBvrPvHWNjbc0tJi/OpXvzLS0tIMX19fIyEhwbjiiiuMrVu39vo120ps79mzx0nvYnD6/e9/b4wePdoICgoyrFarMXHiROPNN990d7OUk7Xl8gwZMsR4++233d0cpVQfaI6JUkoppTyG1jFRSimllMfQwEQppZRSHkOzKk/B4XBw5MgRQkJCBkTVVaWUUspVDMOgtraWxMREzObu94NoYHIKR44cOe3iW0oppZQ6uYMHD5KcnNztx2tgcgohISEAHDhwoMOS96r/2O129u3bR0ZGRrdWqVV9p8fc9fSYu54ec9errKwkLS2t/bu0uzQwOYW24ZvQ0ND29TNU/7Lb7QQHBxMaGqonDxfRY+56esxdT4+567UtSNrTVAhNflVKKaWUx9DARCmllFIeQwMTpZRSSnkMzTFRSinlNex2O62trb16nsPhoKmpSXNMnMRiseDj4+P0choamCillPIKdXV1HDp0iN6spGIYBjabjfz8fK1L5USBgYEkJCTg5+fntH1qYKKUUsrj2e12Dh06RGBgIDExMT0OLgzDoLm5GX9/fw1MnMAwDFpaWigtLSUvL4+srKweFVE7FQ1MlFJKebzW1lYMwyAmJoaAgIAeP7+tl8VqtWpg4iQBAQH4+vqSn59PS0sLVqvVKfvV5FellFJeQ4MKz+KsXpIO+3T6HpVSSimlekkDE6WUex2fyGi3QVM12Fo6bldKDRqaY6KUco/81VC4FVKmQkQqOGxQXw5b3wSTGcy+4BcAvkHgGyA3Hyv4WsEn4Ni/oYkQEO7ud6OUW82ePZvx48fzzDPPAJCWlsa9997Lvffe69Z29YYGJkqp/mMY0FAB1QVQdRCGXQCGA1rqoTIfSnZKD0n8WNleXwI1h48+2SQBiunov2YfMFnAbDm6/ejNbIGpt0NY91cvVWqg27BhA0FBQe5uRq9oYKKUch7DgLoSqD4IVQXyb9vQjL1FHuMXArZ6CUQSJ0J4MljDJPAITYS4MWBrBlsjtDZBa6PcbE3H3Zplf61NYG+GslxoaYTASCjPAR9/iBkhvSxKDUIxMTHubkKvaY6JUso5KvLg67/B+r/AjiVQsBbK9kLNEQkeAqPA0Qo+vhAcD3GjIHGcbDcfvUYymcDiC/7BEBQD4SkQM0weN2QqDJ0Fw+bBqEth7FUw8XqYcB2YDCjbI8ND3/wTtrwBJbvBYXfrIVH9yDAk4O3uzX7crSfP6+rWg/yn2bNn84Mf/IB7772XiIgI4uLi+Otf/0p9fT0333wzISEhZGZm8tFHH7U/Z/v27cyfP5/g4GDi4uL4zne+Q1lZWfvP6+vrueGGGwgODiYhIYGnnnqq0+umpaW1D+sAPP3004wdO5agoCBSUlK48847qaura//54sWLCQ8P55NPPmHkyJEEBwdzwQUXUFhY2MNfTN9pj4lSqm8aKmDf5xIINNfIMI1/CATHQlgShCSBf5AMu/QHH6vcrOHSmxI9DCoLJCBqbYTQBCjeIT+LGw1RmRL8KO9mb4UvO38hn5yBj80GPj5AH6ccz/wR+HS/0ukrr7zC/fffz/r163nrrbf4/ve/z3vvvccVV1zBz3/+c37/+9/zne98h4KCAlpaWpgzZw633norv//972lsbOSnP/0pCxYs4PPPPwfgJz/5CStWrOA///kPsbGx/PznP2fTpk2MHz/+pG0wm8388Y9/JD09nf3793PnnXdy//338+c//7n9MQ0NDfzud7/j1VdfxWw2c/311/PjH/+Y119/vdeHqjc0MFFK9Y6tGfK/goMbJCBprIKQOMicA0Gx0vvhaj5WSD1TbvZWaK6Fom2Q86kMHR3aAP6hEqDEjYbIoZKjolQ/GjduHP/3f/8HwAMPPMDjjz9OdHQ0t912GwC/+tWveP7559m6dSvLli1jwoQJPProo+3P//vf/05KSgp79+4lMTGRv/3tb7z22muce+65gAQ+ycmnzrE6Pgk2LS2Nhx9+mDvuuKNDYNLa2soLL7xARkYGAHfffTe/+c1vnHIMekIDE6VU75Tsgn3LoakKfAMhYzZEpHvOF73FV3JOAiJgxEXS3vJ9UF8GtUdkqCk4VoaGYke5J5BSvWfxlZ6LbjOwNTXhY7XS5x6THva4ZWdnH3uqxUJUVBRjx45t3xYXFwdASUkJ33zzDV988QXBwcGd9rNv3z4aGxtpaWlh6tSp7dsjIyMZPnz4KduwbNkyHnvsMXbv3k1NTQ02m42mpiYaGhoIDAwEZN2btqAEICEhgZKSkh69V2fQwEQp1X2tTTJNt6UeLH4yPBOfDfFjJOHUE5lMEBIvt6GzZYinLUhpKJf7MSNg+AU6s8ebmEw9Gk7BMMDiOPq5dW0Q6uvbMZAxmUwdtrVVs3U4HNTV1XHJJZfwxBNPdNpPQkICubm5PX79AwcOcPHFF/P973+fRx55hMjISFatWsUtt9xCS0tLe2DSVTt7s2BiX2lgopQ6vZZ62PuJTOUdNh+qD8nwTdb54Bfo7tZ1n8kkeS9hSdLDc3ADHN4kQzzluZA8GTLPlV4Wpdxg4sSJvPvuu6SlpeHj0/krOiMjA19fX9atW8eQIUMAqKysZO/evcyaNavLfW7cuBGHw8FTTz3VXkL+X//6V/+9iT7SWTlKqdMz+cgMm5LdkuiKIb0L3hSUnMjsA6nTYdJNEJkOdcXy3r58Gg6sdnfr1CB11113UVFRwcKFC9mwYQP79u3jk08+4eabb8ZutxMcHMwtt9zCT37yEz7//HO2b9/OTTfddMo1azIzM2ltbeXZZ59l//79vPrqq7zwwgsufFc9o4GJUqprTTXyb2MllO6E4DhIPxuSJkql1YGSk+EfJHkm4xbKzJ7qQ1BzSGYbKeViiYmJfPXVV9jtdubOncvYsWO59957CQ8Pbw8+nnzySWbOnMkll1zCeeedx1lnncWkSZNOus9x48bx9NNP88QTTzBmzBhef/11HnvsMVe9pR4zGe4YQPISNTU1hIWFUVFRQUSEdu26gt1uJycnh6ysLCwWD0miHOC6POZlubDjPYgdITNdbM0QFO25eSTOYhhSpdZkkVyE0GSpveIXDFEZTgvG9HPec01NTeTl5ZGeno7Vau3x8w3DoKmpCavVqisUO9Gpfi+VlZVERkZSXV1NaGhot/epOSZKqY4Kv4HdH0piaGOFlJEPinZ3q1zDZILwVPl/a4MUbdu/UpIsxy+ExAnubZ9Sg4AO5SilhGHAga9g1/+krLxfEAyfD9buX+kMKL6BkkcTmSaF2hqrofqwVJPVjmal+o32mCilpPhY7lI4/LXU+WibWuvb8y7zAcXiK2XwU8+UWUhHNkup/EMbIHG8rIysVWSVcioNTJQa7Bw2Qg5+hslULsM3kUMhbYZ+4R7P4nt0rR+bBCeHN8n04oPrIfvbMv1YKeUUOpSj1GDW2ohp61v4V+ZKT0ncaEg/S4OSkzH7QNJkGDZXkmJLdsGaZyHvS3A43N06pQYE7TFRarBqqoGtb0FlAQ5bM8bQqZCY3X+L7Q0UJhPEDIeINKl7UpYD296ROi9jrwJrmLtbqJRX0zOQUoNRXSls+gdUHoCmGqrjz5LS8hqUdJ+Pv8xYyjpfKuMe2gCr/gDFO93dMqW8mp6FlBpsWhthy+tSSKylASPjHOyhSQOnYJormUwQOxImXC+zlyoPwNd/hx3/AVuLu1unlFfSwESpwcbiL6sAO+wwfB6ED3F3i7xfQBiMXQDJk6ChDHI/hbV/gppCd7dMKa+jgYlSg4nDLjkRFh8YcaGUmVfOYbbItOIxV4GBDOmseRbK9rm7ZcqNZs+ezb333uvy1zWZTCxZsgSQ1YVNJhNbtmxxeTt6Q5NflRoMGiogdxnEjpLhhsAIKSCmnC8sCSZ+R+rC1JVKknFLg3cveKi8WkpKCoWFhURHe0cFZw1MlBroDAN2/RdK90DxDknW1KCkf/n4w/CLpChb7SForYPoLLC36NCZcjmLxUJ8fLy7m9FtOpSj1EBnMsGQGTLUkHKGlJpX/c9kkqnDoUlga4Rv/glf/RH2furulg0stpaT3+y2jo+1t8ity8e2dm+/fVBZWckNN9xAREQEgYGBzJ8/n5ycHEAWGYyJieGdd95pf/z48eNJSEhov79q1Sr8/f1paGjo0eueOJSzfPlyTCYTn3zyCRMmTCAgIIA5c+ZQUlLCRx99xMiRIwkNDeXaa6/t8Ws5g/aYKDXQNddCXRGknaU5Je5gMkkZe7OvFLGrL4Omane3auD48qmT/ywqA7IXtN/1WfdnMBtAFzPQwofAhOuO3V/7Z5nBdqJzHuh1U2+66SZycnL473//S2hoKD/96U+58MIL2blzJ76+vpx99tksX76cq666isrKSnbt2kVAQAC7d+9mxIgRrFixgilTphAY6Jwez0WLFvHcc88RGBjIggULWLBgAf7+/rzxxhvU1dVxxRVX8Oyzz/LTn/7UKa/XXV7RY/L888+TnZ1NaGgooaGhTJ8+nY8++uiUz3n77bcZMWIEVquVsWPH8uGHH7qotUp5iMOboHQvlOyWL8KgWHe3aHBLmyErFFtD4fBm+Z00VOmCgINEW0Dy0ksvMXPmTMaNG8frr7/O4cOH25NUZ8+ezfLlywFYuXIlEyZM6LBt+fLlzJo1y2ltevjhh5kxYwYTJkzglltuYcWKFTz//PNMmDCBmTNnctVVV/HFF1847fW6yyt6TJKTk3n88cfJysrCMAxeeeUVLrvsMjZv3szo0aM7PX716tUsXLiQxx57jIsvvpg33niDyy+/nE2bNjFmzBg3vAOlXKx8H+z9WK7OEydIrQ2tU+J+wUeDw/pKTNUHMa36D8SPgjHfAt8A97bNW8380cl/dkLBQNvUO/GxWumyx+TEv49pd/a9bcfZtWsXPj4+TJ06tX1bVFQUw4cPZ9euXQDMmjWLe+65h9LSUlasWMHs2bOJj49n+fLl3HLLLaxevZr777/faW3Kzs5u/39cXByBgYEMHTq0w7b169c77fW6yyt6TC655BIuvPBCsrKyGDZsGI888gjBwcGsXbu2y8f/4Q9/4IILLuAnP/kJI0eO5KGHHmLixIk899xzLm65Um5QVwo7lshMHP9QSbo0W9zdKnW8gHB87I0yxHbgKxk2qC9zd6u8k4/fyW+WE669LX5y6/Kxvt3bbz8aO3YskZGRrFixoj0wmT17NitWrGDDhg20trZy5plnOu31fH2PvWeTydThfts2hxvWgPKKHpPj2e123n77berr65k+fXqXj1mzZg333Xdfh23z5s1r7y47mebmZpqbm9vv19TUtL+m3W7vW8NVt9jtdhwOhx7v3mqpx7T1LagrAcwY6eeA2Q8cJx8usDsMHIaB/RSPUc5ldxg0BydhS/g2Pnv+B8W74Ks/YoxbCNHD3N08j2S32zEMo/3WU23P6c1z+8owDEaMGIHNZmPt2rXtwUV5eTl79uxh5MiR7e2aOXMm//nPf9ixYwczZswgMDCQ5uZm/vKXvzB58mQCAwO7/R5OPF4nu9/2/+P/Pdm2k71GV9+TvT2Pe01gsm3bNqZPn05TUxPBwcG89957jBo1qsvHFhUVERfXMckvLi6OoqKiU77GY489xoMPPthp+/79+wkNDe1941W3ORwOKioqyM3NxWz2ig49z+GwEZb3Ib61B7EbUJVyLkalAzh1oqXDgIraZnKpwayjPS5x7JhbscRdROih5fgWFmCUPUtD0lk0xk7QobcTOBwObDZbh4vHnrLZbKd/kJO1XWilpKRw8cUXc9ttt/Hss88SHBzML3/5SxITE5k3bx5NTU0AzJgxg5/97GdMnDgRHx8fWlpamDFjBq+//jo//OEP2x/XHS0tLTQ1NbUfs+bmZpqammhpkdlFTU1N7ftrbW1t39bGZrPhcDhO+ZrNzc3YbDby8/M7nbPbLu57ymsCk+HDh7Nlyxaqq6t55513uPHGG1mxYsVJg5PeeOCBBzr0tNTU1JCSksLQoUOJiIhw2uuok7Pb7eTm5pKZmYnFosMP3WYYsPt9TL71YDUw0s8mOqp79TLsDoNcDDLjQ7FoZOISHY95GCRdBQe+xFT4DVFV6zDCzDDqMhl2UIB8Yebn5+Pv74/Vau3x89uu+v39/TG5MOgzm81YLBasViuvvPIK9957L9/61rdoaWnh7LPP5sMPPyQkJKT98eeeey52u51zzjmn/X3OmTOH999/n3PPPbdH793Pzw+r1Yq/vz9A+7Hz85PPldVqbd9f2zDO8fv38fHBbDaf9jV9fHxITU3t9LjKysput/V4JsMd/VpOcN5555GRkcFf/vKXTj8bMmQI9913X4cywL/+9a9ZsmQJ33zzTbdfo6amhrCwMCoqKjQwcRG73U5OTg5ZWVkamPRE/mrI/QzqSyBhAiSO7/YVt91hkFNYTVZCmAYmLnLSY168A3I/B1+rVOmdcD0EhLutnZ6kqamJvLw80tPTex2YNDU1YbVaXRqYDHSn+r1UVlYSGRlJdXV1j0YdvLav3OFwnLRLb/r06Xz22Wcdti1duvSkOSlKebWS3bDvC0mejMyAhGwdBvBWcaMh+yrpASvaCqufhaoCd7dKKZfyisDkgQceYOXKlRw4cIBt27bxwAMPsHz5cq67Torh3HDDDTzwwLGiN/fccw8ff/wxTz31FLt372bRokV8/fXX3H333e56C0r1j/py2PU/mYETFC2LyOkMHO8WkgATrgVruKxrtOZPcGiju1ulPMjrr79OcHBwl7euSmh4G6/IMSkpKeGGG26gsLCQsLAwsrOz+eSTTzj//PMBKCgo6JB0c+aZZ/LGG2/wf//3f/z85z8nKyuLJUuWaA0TNbA47LD7f9BYKdMiM2Z3nvKovJNfMGRfDTnLoGwP7P9CelN8ez6EoQaeSy+9tEM9lOOdOOXXG3lFYPK3v/3tlD9vq4p3vKuvvpqrr766n1qklAco2QmV+bJQXNZc+TJTA4fZB4bNg9BE8A2Com0QOwL8Q07/XDWghYSEdEiYHWi8IjBRSnUhZiTEDJP1b8KS3d0a1R9MJskZctigrhgONUBztSzGGOI9q8Uq1RNekWOilOpCzWHpJUnSmhcDntkHQhKhbDfs+q/knTTXubtVSvULDUyU8jZF26G2GMpzpVtfa10MDiYTJIyT3jFrOFQfBHuru1ullNPpUI5S3qR8H+xcAs31MGQqRKS6u0XKlXz8YeQl0NoEZTnQ0gChSVLrRBNj1QChgYlS3sTHHwwH+AVBWJK7W6PcwWQGv0BZUK4yH7a/C8ExMPFGCIx0d+uU6jMdylHKm/hYIXESpM+QvAM1eJl9IDBckmGLd8JXf4SKPHe3SrnQgQMHMJlMbNmyBZAZqiaTiaqqKre2q680MFHKG9hbwdYs3fcWi+QYKBUQAeOvhaAYqRC77gU4vNndrVJucuaZZ7bX+/JmesmllKdrrIJN/5BcArMPhOvUYHUc30AYc4WssVO6Wz4r9WWQdZ7O1hpk/Pz8iI/3/mnk2mOilCdzOGD3+1LDomAtBEVJjoFSxzP7QNb5khDdWClTirf+a3DM2rG1dO9mP+7mcBx7vsNx9Oet3dtvD6WlpfHMM8902DZ+/HgWLVoEgMlk4vnnn2f+/PkEBAQwdOhQ3nnnnR6/DnQeylm8eDHh4eG8//77DB8+nMDAQK666ioaGhp45ZVXSEtLIyIigv/3//4fdru9V6/ZH7THRClPdmiDzMRpqoGMcyTpVamumEyQMlWG+XI+hbwV0FQJE74zsD83Xz7VzQca+Nhs4OMDo6+A2JGyuWwP7FgC4UNgwnXHHr72z9Da2Hk35zzQeVsf/fKXv+Txxx/nD3/4A6+++irXXHMN27ZtY+TIkX3ed0NDA3/84x958803qa2t5corr+SKK64gPDycDz/8kP379/Otb32LGTNm8O1vf9sJ76bvNDBRylPVlcD+5XIFHJ0FEWnubpHyBjHDpb7Nrv9KvklTDUz+rizyqDzS1Vdfza233grAQw89xNKlS3n22Wf585//3Od9t7a28vzzz5ORkQHAVVddxauvvkpxcTHBwcGMGjWKc845hy+++EIDE6XUKdht8sXSWClXu8lTNF9AdV9oImRfIzVvyvbC6mdh0k0Qme7uljnfzB9184EGtqYmfKxWMB+30F30cNnHiX9f0+50WhNPZ/r06Z3ut8206avAwMD2oAQgLi6OtLQ0goODO2wrKSlxyus5gw5WK+WJ8r+CqkNSQCv1TC2epXouIBzGXSNrKVUfhO3/Bg/KI3AaH7/u3SzH3Y5bjR6z+ejPfbu33x4ym80YhtFhW2ur63J/Tlxt2GQydbnNcXzejZtpYKKUp6kvl0TXxgqIHyVXv0r1ho8VRl8O8dkQniqzdgZDQqwHiYmJobCwsP1+TU0NeXkd682sXbu2031n5Jd4Kx3KUcqTGAbkfAJN1bLUfcJ4d7dIeTuzDwydJXVwKvaBrUlmdsWP6dxLoJxuzpw5LF68mEsuuYTw8HB+9atfYbFYOjzm7bffZvLkyZx11lm8/vrrrF+/nr/97W9uarH7aWCilCcp3iGL8zVVy/RPH393t0gNFD7+EJoAB9fK5ywhGybfChb9GuhPDzzwAHl5eVx88cWEhYXx0EMPdeoxefDBB3nzzTe58847SUhI4J///CejRo1yU4vdz2ScOPil2tXU1BAWFkZFRQURERHubs6gYLfbycnJISsrq9NVxYDX2gjrX4TKAgiNh4xzXZLwancY5BRWk5UQhsWsCbau4NZjXnMEdv5XpsuOv07W2fECTU1N5OXlkZ6ejtXa85wrwzBoamrCarVi8qBEcpPJxHvvvcfll1/u7qb0yql+L5WVlURGRlJdXU1oaGi396k5Jkp5iryVkl9iOCB5qs7CUf0jNFHqdcSMgMItUH2oY8ExpdxMAxOlPEV4GjhaJa/EGuLu1qiBzD8EQuIk/+TwZlj9Rzi8xd2tUid49NFHCQ4O7vI2f/58dzev3+jgolKewi8AkqdBuM7CUS4SEA6V+6XnpDIfGsshY4721rnQqbIp7rjjDhYsWNDlzwICAvqrSW6ngYlS7uawy0yJ8v0QECJXsUq5SsIEsLXKFPWd/4GGcinZrjN23C4yMpLIyEh3N8Pl9AyolDs118LGV6QIlo8fhKW4u0VqsDGZZPG/gDDIWQr7V0jF4QnXe+QaOzpfw7P0x+9Dc0yUcqfDG6G2CA6uk7VMtAtduUvMCBh9JThscHiTLGJXX+7uVrVrm6XX0tLzFX5V/2loaAA6V5jtC+0xUcqdUqZBxQHw9QffQHe3Rg12YUlSxn7HEijdI0mxk2/2iAUkfXx8CAwMpLS0FF9fX8zmnl1XG4ZBc3MzgEdNF/ZWhmHQ0NBASUkJ4eHhTi3voIGJUu5UWwiBkVp2XnmOgHAY923Y9T5UHYS1L8C4hZA4zq3NMplMJCQkkJeXR35+fo+fbxgGNpsNHx8fDUycKDw8nPj4eKfuUwMTpdyh8gD4BUPFfrCGgXmQFZNTns03AMZcAbnLpOdk42JovASGnuPW4UY/Pz+ysrJ6NZxjt9vJz88nNTV18BVv7Ce+vr79ciw1MFHK1Roq4Ju3JPE1YTxEZ5z2KUq5nNkHsuZJ4FywXoZ37K0wbJ57m2U296ryq91ub3+uBiaeTZNflXIlw4CcT2UtHIdNxvSV8lQmEwyZLus22VvkflONu1ulBjgNTJRypbK9UJYjgUnKGeDb8ys/pVwubhRMvBFsLVD4jczWsensGNU/NDBRylXsNtj3OTTXQFgyRKS6u0VKdZ+vVZK0W+thz4ew8reSHKuUk2lgopSrHN4ItcVga5beEpP++SkvYzJBUKz0/FXsh9zPdAFA5XR6ZlTKFVrq4cAqGcKJHiZThJXyRiYTjLoUkiZBQCSU7ZHeQKWcRGflKOUKeV9CUxWYzZA00d2tUapvzD6Qeqas8VSWA62N0Nokpe116rvqIw1MlOpvdaVwZBM0VkHKZKkRodRA4GOFkHjJOakthNLdMH6hfsZVn3jFUM5jjz3GlClTCAkJITY2lssvv5w9e/ac8jmLFy/GZDJ1uPVm7rtSfWIYsO8zqVliDYPYUe5ukVLOZfGFuDEyS+fQelj3giwCqFQveUVgsmLFCu666y7Wrl3L0qVLaW1tZe7cudTX15/yeaGhoRQWFrbfelPGWKk+Kd93bHpw8mTpAldqoIlIhexvy+e7eBes/hNUH3Z3q5SX8oqz5Mcff9zh/uLFi4mNjWXjxo2cffbZJ32eyWRyeg1/pbrNYT86PbgWQpMgPMXdLVKq/wRFyQKAO/8LlXmw5k8w4XqpgaJUD3hFYHKi6upqACIjTz2zoa6ujtTUVBwOBxMnTuTRRx9l9OjRJ318c3Nz++qTADU1UuHQbrdjt9ud0HJ1Ona7HYfDMTCOt8MOkRmYSnZjJJ0BhkmGdjyM3WHgMAzsDs9r20A1YI+5TyCM/hamnE9kOvH6lzBGXS6Jsm5eOG9AnVu8RG+PtckwPPBMeQoOh4NLL72UqqoqVq1addLHrVmzhpycHLKzs6muruZ3v/sdK1euZMeOHSQnJ3f5nEWLFvHggw922r5u3TpCQ0Od9h7UyTkcDioqKoiMjOzxsuYexzCgvhQaymXFVg/lMKCitonIECtmXXTVJQb8MTccBBV/TUDFTvCx0hQ3gbrEmW6dsTOgzi1eoqamhqlTp1JdXd2j71CvC0y+//3v89FHH7Fq1aqTBhhdaW1tZeTIkSxcuJCHHnqoy8d01WOSkpJCaWkpERERfW67Oj273U5ubi6ZmZnevdCWYUgC4KGvwRrq0bMU7A6D3KJqMuPDsAzIb0nPM2iOeeE3mPJWyEraSZMwshfITB43GDDnFi9SWVlJTExMjwMTrxrKufvuu3n//fdZuXJlj4ISkOWZJ0yYQG5u7kkf4+/vj7+/f6ftFotFP8guZDabvfuY15fDjn9LhUyLH/gHurtFp2U2mbCYTQP7S9LDDIpjnjQeAsJkOvGh9dBcDRNvcFuBQa8/t3iZ3h5nr+jPMgyDu+++m/fee4/PP/+c9PT0Hu/Dbrezbds2EhIS+qGFSh0nfxVU5MmJOCjK3a1Ryr0i02HsAskxKdsL1bq+jjo1r+gxueuuu3jjjTf4z3/+Q0hICEVFRQCEhYURECBd5DfccANJSUk89thjAPzmN79h2rRpZGZmUlVVxZNPPkl+fj633nqr296HGiSGngOV+TITx+Lr7tYo5X7BMTD+Oqg8ADVHwC8EItKkErJSJ/CKwOT5558HYPbs2R22v/zyy9x0000AFBQUdEhoqqys5LbbbqOoqIiIiAgmTZrE6tWrGTVKp66pftZQLifdsCR3t0Qpz+EXKFOHW+qgZIdMKbbbIOt8DVBUB14RmHQnP3f58uUd7v/+97/n97//fT+1SKkuNNUAJqg4IAmvunqwUp35BYMBbH5NcrAsvpA5x92tUh5Ez5xKOYOtBTa9IuW4G0qk/LxSqmv+wdJT4uMvuScNFe5ukfIgXtFjopTHO7QB6suk9HzKGe5ujVKeLyoDItKhvhiObIGY4dKDEhzj7pYpN9PARKm+aqmHgrUSlMQMl2EcdWqGQ4a+GiuhqUqOncki3fpmH/nX4gtm3+O2+XX+mRsLdiknMJshJEF6TL55S4KUsQsgeZK7W6bcSAMTpfoqf7V8uZotkDDO3a3xLIYhyY6NVdBUKf82Vkog4nBCaXCzBazhEBIHwfHyr5sKeKk+CIgAoxXqiiX3pK4Yhl2gSbGDlAYmSvVFQwUc3iRfuEmTPbrCq0s0Vcl00LYApLEK7C1dP9biK6X6rRFHc3IMcNjk8XYbOFrBfvTmaD36s7b7NtmHwy6zoBrKoXinbAuIgJB4CI6TQMXX8wvcDXomE2SeDwGRcOAr2PMR1JXIooC+GmgONhqYKNUXeSuhuQb8giBupLtb4x4OO1QVQOluqC3q/HOzRQIPa7gEDQEREpD4Bfd+YTfDcTRIaZH1iGqL5Cq7PSCqhJJd8lhrmAQqbcGKX1Av36jqVyYTJE+Wz8fej+HgOullm3ij2yrFKvfQwESp3qo5AsU7oLEa0mcOvmJqLXVQuleqebY2yjaTCUITITBago+ASPAPcX4uiMksMzp8/GX/kUNle2ujBCi1xVBXJD1aTdVyK90jj7GGHu1NiZcieIO9l8vTRGVA9rdh5xLpBVv9rJSxj+x5xW/lnTQwUao3DAP2L4fmWrmaixrq7ha5hmFAzWH5kq8+KPdBvtxjhkN0lvSEuItvgBS3i0iT+7ZmCVBqi6VXpbFCkm6baqAsRwKc8CHS9pCE3vfgKOcKioZx18Ku/0kV5XUvwNirpUdFDXgamCjVGxX7oXyfBCbD5spskYGstRHKc6SHpLn22PbQBIgZAWEpnjlDxscfwlPlBhKotA391ByR3JTKA3KzhkL0MIjK1F4UT+AXCGO/BbmfSSC8+XXJO9Gk2AFvgJ9NleoHDgfs+1y+oEMTIaxnK117lboSydWoyj82i8bHT768Y4ZL3og38fGX31fb76yhXIaiyvdLL8qhr+HIZulFiR4uwz3ai+I+Zh/ImguBUZoUO4hoYKJUTxVvl6vt1gbIPHdglp5vbZTkw4q8Y9uCYiQYiUwfOD1EgVEwZLrMqKo8IFfm9aXyvivytBfFE5yYFHtovdyPH+Pulql+4pSzS2trK0VFRTQ0NBATE0NkpGZQqwGssQKa6ySPIWiAVak0DCjPlUq2tmb5UojKlOGaoGh3t67/WHwlPyY6S3tRPFVbUmxFniQ4V0dIj6X+LgacXgcmtbW1vPbaa7z55pusX7+elpYWDMPAZDKRnJzM3Llz+d73vseUKVOc2V6l3C9xgpSfD4oeWCfF5lo4uEZ6g0CSetPOkl6FwaRDL0qe5NV06EUJk16U6Ewt5uZqQdFya6iAwq3yWTWZtVLsANOrwOTpp5/mkUceISMjg0suuYSf//znJCYmEhAQQEVFBdu3b+fLL79k7ty5TJ06lWeffZasrCxnt10p1zMMqDooX0gDZaE+w0FAxW5MRTlg2CSJNXECxI7yzIRWV7H4Hg1AhkkvSukeSXpuqpYepSObZFgrfpwuQ+BqgZESnGxcLEsVOGwwZKq7W6WcpFeByYYNG1i5ciWjR4/u8udnnHEG3/3ud3nhhRd4+eWX+fLLLzUwUd6vaBv4BED1oYFT8KmhHNOBrwgqOwzBVgiNh9QzB07Q5SyBUXJckidLr0nZXuk1K8uVIZ+oTEgc596p0oNNQAQkjpcFAO2tMuymAeKA0KvA5J///Ge3Hufv788dd9zRm5dQyrM0VcPuj6D2MKRMk1Ln3sxhkxN68Q5wOHCY/TBSz4SYYQNreMrZLH6SABwzXGaHFH4jgWrZXqjYJ70r8dky1VX1r7ak2Pgx0qN1ZLP8Xsw+AzsfahAYIKn1SvUzw4DgaGgs9/4KlLWFkL9Ggi2AiFSqYkcSFa1JnT0SHAtZ50uAcmQT1BTK1OqyvZIsHD9WZ/K4go8VQhIlONn+bynINupS6eHSz7NXcto8x3Xr1jlrV0p5Hv8QiBstped9/N3dmt5x2GQl5D0fS1DiFwiZczCGnoPDR79Aey04Vop+Db9ASt077NITte0dmdFja3J3Cwc+k0l6SWwNMmNn679g61sys0x5Haf1mFx99dUUFBQ4a3dKeZa6Yqgr9d4hHFsT7Pvi2CJ7McMhaZIEWQ7DvW0bKEISYHi8lOw/skVm8hRtk6TZuFGSTOytQa23GDoHguLks563Uj7vE74DQYNsZpmX61FgsmDBgi63G4ZBRUWFUxqklEepPizd9BarVDz1xsJiTVVS1rupRnIkhs4a2NVq3clkkmMbmiRrCR3ZLLNHjmyBkp0QNwZiR4JpkC346Comk+ScBMXArvePLgL4Bxi3EKKGubt1qpt6dJZdtmwZr776KsHBHTPPDcNg5cqVTm2YUm5nGLD/CyjaLrkCIy5yd4t6rrZQrh5tzeAfDJnnyWwG1b9MJinIFpYi5fyPbIbGKji8Sb4s48aAI8HdrRy4QuJgwkIpYV91CNa/JKXtjRR3t0x1Q48Ck9mzZxMSEsLZZ5/d6WfZ2dlOa5RSHqFiv0wNba6VRDpvq+lRliM5JYYDgmMg41xNxnQ1k0kqBIcPkZL3R7ZAUzWmQ18T2WgC3ykQO9w7e+I8nW8gjL5C/gYObcS0631CfZIhLRkCdFqxJ+vRX8O///3vk/5s6dKlfW6MUh7DMGD/8uMW6ktyd4u6zzDg8EbJbwCZRZR2ln75uZPJDJFDJUgp3wdHtmCuK8N0cL0M8SRPgoh0nUXibCazfPZD4mHPJ/jV7sW07nmY+B35u1YeqU+zcoqKipzVDqU8S/EOyS9pqZcvDW9ZqM9hk4CqLShJHA/pszQo8RQmM0RnYYy6grrYKTIzqqUO9q+QBeoayt3dwoEpKhMjeyF2n0DpSVz9LBz5xt2tUifRp7Pt3LlzndUOpTyHww4HvoTmmqML9cW6u0Xd09IgU4ErD8iwU/pMKS2vV+Gex2yhKTwTY/SV8jsy+8gMkl3/k6EHnWLsfIERVKVfAuGpcqxrjuh0Yg/Vp8sow9BphmoAOrJFpgfbmyFpond8sTdUyMybljopOJVxjnRfK89m9pFerehMqXlSkSfTiyvzJGCJHu59uU0ezLD4Ygy/UCo4O1qhcIsUw/MLAbOX9IoOAn0KTEzecMJWqidsLZC/SqbWRmZ4x5o41YdkKMDeImvcZJ6na4Z4G79gGDpbviQPrpNAs2CdBCkpUzUfwplMJghPkZ7R2iKoLYXSXTD2W5IHpNxOQ0SljndovYzzGw5InOju1pxeZb70lNhbIDRBpjRrUOK9QuJh5CWQOl16vhqrYO8nx+rQKOcxWySpvfgbCUy2vwd2m7tbpdC1cpQ6pqVerlKbaqQyqjXE3S06taqDkLdCgqioDEidod3+A4HJLD0nEeky1FCyG6oKpKJs3GhZJNCiBdqcJmsu+H0FwQmS9B4zTKfVu1mfAhOLRU+CagApWCNVUs0WSBjn7tacWvUhKf7msB+bDuwtM4dU9/j4yzBO9HA4uF4Ck8KtUJ4LSZNl2EGH0/vO7CMz1+wtUF0gFyi2RjkH6CrFbtGnM9nXX3/NkiVLqK2tdVZ7lHKPpho4tFG6zmPHePYVU80R2Pe5BCURqZA2U4OSgSwgXFYxzpwji0m2NMg6MHs+hPoyd7du4LD4SS5P6S745k1Y/Uep0qtcrk9nM4vFwsKFCyktLXVWe5RyD/8Q+YIPjoW4ke5uzcnVFkm+gcMu1UTTZ+nwzWBgMsk019GXy+KLFl+oK4Hd78OBVdDa4O4WDgwms6xlFBIvQ6Ub/iY5Ppp74lJ9vsyaMmUKeXl5zmiLUu5jOMBigZQpnrsCbF0J5C6TImphSbIYnwYlg4vZBxKypdR6VIZU+S3LkcTNou0SsKq+8Q04FgA2lMtigOtflJlSyiX6HJj84Ac/4Oc//zkHDx50Rnu69NhjjzFlyhRCQkKIjY3l8ssvZ8+ePad93ttvv82IESOwWq2MHTuWDz/8sN/aqLyYvVXqltSVQqCHLo9eXwo5S6WtoYmQMUeruQ5mfkGQfrbMwgqKlvyIQxtg13+lV031jckMaTNg1KXgaJEk5K+egcJvJBhU/arPgcm3v/1tNmzYwOjRo7n++ut56aWX2LhxIy0tLc5oHwArVqzgrrvuYu3atSxdupTW1lbmzp1LfX39SZ+zevVqFi5cyC233MLmzZu5/PLLufzyy9m+fbvT2qUGgOpDMpa852PpKfHEL/uGcsj5VL58QuI1KFHHBMfCiIsl+bltevGej6RycWuju1vn/SLTYcJ3pPpz1UHY+ApsfxdatTJvfzIZfSzfmp+fzzfffMOWLVva/z1w4AA+Pj4MHz6crVu3Oqut7UpLS4mNjWXFihVdrnQMEjDV19fz/vvvt2+bNm0a48eP54UXXujW69TU1BAWFkZFRQUREbpUvCvY7XZycnLIyspyzayvXUfH6H2tcoL3tKGRxkoJmmxN8iWUdb4k6TmR3WGQU1hNVkIYFrPO8nCFfjnmtmZZvLH0aG+yj78MR0QP09k79PGYGw44vEmWC/ANlIBl3ELvWtzTDSorK4mMjKS6uprQ0O7XV+rzZVdqaiqpqalceuml7dtqa2vZsmVLvwQlANXV1QBERp68KueaNWu47777OmybN28eS5YsOelzmpubaW4+tnZCTY0UNLLb7djtOnbrCna7HYfD4brjnTYbakuOTgs0g8ODummbqjHt/ViuzoKiMIaeByZfp7fR7jBwGAZ2T3rvA1y/HHOzH6RMh8hMTAVrJCfiwGoozcEYMt07qhj3o74dcxMkToKQJEx7P5LaMl/9EWP4fKkfpLPiutTb83ifA5ODBw+SkpLSYVtISAgzZ85k5syZfd19Jw6Hg3vvvZcZM2YwZsyYkz6uqKiIuLi4Dtvi4uJOuSLyY489xoMPPthp+/79+3sU7aneczgcVFRUkJubi9kVa1c0VkJzFBAMDdX9/3rdZG6pJfzQZ5htjdj8I6gOnopR2gg4v3veYUBFbTO51KAdJq7Rv8fcD8JmYjVyCCrfiqnuIEbxIZrCh9EQNRZjkBZnc84xD8AUdzHBhWvxL83DqPoXlTW+OAI8NDfNzdou7nuqz4HJiBEj+NGPfsTPfvYzAgMD+7q707rrrrvYvn07q1atcvq+H3jggQ69LDU1NaSkpDB06FAdynERu91Obm4umZmZ/TuUU18GFn84cgRCQmWNGU9ha8K05zOwGhAQjzHsAmJ8rP32cnaHQS4GmfGhOpTjIi455olnQMtoOLQBU+UBsOVDRSlGyhQITxt0wztOPeZJF0PpbmioIDLUDtFhMtSqOqisrOzV8/ocmCxdupQf/vCH/O1vf+ORRx7hpptu6usuT+ruu+/m/fffZ+XKlSQnJ5/ysfHx8RQXF3fYVlxcTHz8yVdc9ff3x9+/81RRi8WiVW5dyGw29+8xt9tgx7sy/TYqQ8p8e8pJ2mGDvOXQXAP+wTBsHvj1f7E3s8mExWzSwMSFXHLMrcGQeY4keR88utxC3goIy4WUaYNuXSXnHXMTxI+SGToNZVC0BXyCoLXuaB7Y4OyVOlFvz+F97is/88wzWbduHY899hi//OUvmTRpEl9++WVfd9uBYRjcfffdvPfee3z++eekp6ef9jnTp0/ns88+67Bt6dKlTJ8+3altU16ocIsEJY0VkrzmKUGJYUhyXW2RJLhmngt+/d8LqQaBsGQYdRkkjpcE7+rDsHMJHNkswbDqHZMJgmLANwi2/lNmROUsdXervJ7TBvFvuOEG9uzZw0UXXcT8+fO56qqrnFZ47a677uK1117jjTfeICQkhKKiIoqKimhsPDbefsMNN/DAAw+037/nnnv4+OOPeeqpp9i9ezeLFi3i66+/5u6773ZKm5SXsjVD/lfQVA2RGRDgQUN0hVugfJ8k0mXMHvTJisrJzD6QOEEClNAkKcZ2ZAvs/I+sw6N6zxoivZs+/mDykR4qh8PdrfJaTs8unDt3Lrfeeivvvfceo0aN4v7776eurq5P+3z++eeprq5m9uzZJCQktN/eeuut9scUFBRQWFjYfv/MM8/kjTfe4MUXX2TcuHG88847LFmy5JQJs2oQOLhe6oIAJE1wb1uOV75PviQAhkyTLw6l+oM1TIYbhs6WHrmmGtj7KexfLuvwqN6JSIXx14KPj/wtF++Afcu1nkwv9DnH5IUXXmDDhg1s2LCBXbt2YTabGTNmDHfccQfjxo3jzTffZNSoUfz73/9m8uTJvXqN7pRaWb58eadtV199NVdffXWvXlMNQC31Ms7eWA1xo2R9HE9QWyS9OADxYyFmuHvbowY+k0lqcYQlyXBOyS6oyJMhnsTxsl6MToHtOZNJemF9AyF3qawEfXAdjLtGAhfVLX0OTB555BGmTp3KDTfcwLRp05g0aRIBAceS9b73ve/x6KOPctNNN2nVVeVe+atlCMfiA/HZ7m6NaKo6bqXgNCmIpZSrWPwgZSpEZULBGlmW4eB66cEbMk1nmvSWjz/Ej4GqfCjPgbV/hmHzZRkBV5RB8HJOqWNyOrfccgu//OUv+/pSSvVeY6VUbmyski9/3/6bfttttiZZKdjWDMExkD7TcxJx1eASGAXDL4KyvXD4axnu3POhVI1NmuS5C1t6sqAYGH+dDJEV74Qd/5YgZezVEBDu7tZ5tB6HbpWVlVRUyCqLpaWl/Pvf/2bHjh2nfE5sbCyff/5571qolDPkrZQpuH5BMozjbg4b5H4u4/v+wZBxrq5/o9zLZJJhxNFXSg+KYUh5+x3vSQ+KLl7XcxZfyecZPl9yTQ59DV/9UQIVdVI9CkxeeuklJk2axOTJk3n++ee54oor+Oyzz7jmmmt46aWXTvo8k8nErFmz+txYpXqlplCWhG+qllkJ7q4xYBiyPk9dMfj4Qeb5stS6Up7AN0B674ZfIFf2rY0S2Od8IkOPqudihsGE6+V4Vh6ADX+Dnf8Fm/MWux1IenSJ9sc//pEdO3bQ2NjIkCFDyMvLIyYmhurqambNmsWtt97aX+1UqncM4+hsgzoIiISooe5ukSQbVuRJcuHQOdqtqzxTSAKMvBRKdsCRbyTA3/lfKUiYME57+HrKGirDOAfXwaENsmJ4xX5ZDDAk7vTPH0R61GPi4+NDQEAAkZGRZGZmEhMTA0BYWBgmHRtXnqhiv2TGN1VD8iT3n0wr9kPhN/L/1DMhNMG97VHqVMwWSRQffTmEp0iSduFW2LFEanWonjFb5O9+zLdkxeLinbD6j5C/RuueHKdHgYnFYqGpqQmAFStWtG/va50SpfpNawPYWyA0UapfulNDORw4blpwdJZ726NUd/mHSB5U5hzJ02qulQqn+z6XafiqZ8KSYeJ3IDwJao7A7g90mOw4Pbp8XLZsWftaMmFhxxY9a2ho4MUXX3Ruy5Ryhsihsiy52eTeugy2Ztj3hSS9hiVB0kT3tUWp3jCZIDwVQhKlSnHxTqjMly/WxAla+6SnfKww4hIpxGZvhqJtknQcHC/HehBPK+5RYHJ8MAJQVFREfHw8sbGxxMbqfHflgaoPS49JsBt7SwyHLJzWXCtXnumz9ASuvJfFF5KnyJIOBWslifvgehkyHTJda5/0hMkk9U4MQ9buOrJZko0bymHMlYP2WPbp7Dh37lxntUMp5yraLmWhq/IhMMK99UGObJYAyewDGedoTQg1MARGyjTYtBnymW6okCGJ/NXSQ6i6z2SSWjIBEZKsf2SzBHuDNO+kT4FJd0rFK+VyrY0y/r3xFZma5xfsvrZUHpBkQZATeGCU+9qilLOZTFKEbcyVx3KmSvfA9n9DWY7WPukpv0CZpRMzAjBkeKe5VpKOB5E+TVHQmTjKMx1dB6T2iIx7u0tjldQrAZliGekBU5WV6g8+Vkg7S4KT/DVSafnAqqPDO9M8axVvT+cfJKuL21ugugDqS6QHJXkKpM2UJTUGOB3oVgOPxU8WzEqfJTMI3MHWLDMW7K0yJTi5dwtYKuVVguNg5CXyeTf7yAKVO/8rFU/tre5unXex+MnsnaqDssjijvdkzZ2aI+5uWb8b+KGXGnwayqQYVFC0e17fMODAl1I7xS9Yk13V4GK2yHT4yHQoWAdVBTIkUZkHKWdA2BBdE6onkiZI0vy+zyR3rrZQpm4PneX+Ktb9pE+BicVicVY7lOq72mIpmx0YJSdHdyWZFm6RqxyzRZJdtdy8Goz8giHzXAlMDq6D5jpZHyosSVY0toadfh9KRGdCeLKUHCjLgZ3/geLtUqgtPMXdrXO6Pl3Gbd682VntUKpvDEOuKEp2yRRGdyWZVhXIbCCQqZPu6rVRylOED4FRlx8tY2+RGWo7/6PDOz3lY5VZUCMuBsMu9U/WPAd7Ph5wa+5o/7IaGMr3ya2p+tj4tqs1VUPel/L/2JFa2VWpNhZfKSo46nLJm3DYZXhnx3uyTIPO3um+qKEw8QYpxlZbLFO01zwnMwAHiD4HJqtXr2b79u3OaItSveNwwP4vZFpdaJJ7Ss87bFJ/wN4iCYDJU1zfBm9jb5HaF1UFHRP6DEPWYakthPpSmeHRVAMtDZJUPMimTg4o1lDIPE+GePxDpJz9/hWw92P5Pavu8fGHYXNhzBWAQ3qK1/wZdn0wIGrI9Pmy8q677uLuu+9mzJgxHbbv27eP2NhYQkJC+voSSp1a4Rb5YmtthKzz3JNoWrBOvmR9A2DobOmyHuwMx7Hfha1ZFi9sqZNcg+Y6sDVIUGnYpbvf7CNJkYZDZnKYTMDRJMm2/5uQsuhDZ8u+TSaZ/eQbKFNSAyJltWbN6/FcJpP8vkMTJZmzaOux2TuxI2XIR4sQdk/4EOk9yftSck72fgS+Vgn8vFifA5M9e/Ywe/bsTtuXLVvG//73P95///2+voRSJ2drPjYDJmooBMW4vg1lOVC2V0646bOkSNJg47DJTKjqg1BfJoFHWJIMqzlaobVJgjcM6RExHV27yDcQrJEQngYh8dIbYmuU/9tb5eawHXdzyP6aayWAaW2Ckt3H9mn2kaDQPxgCoiAiDWJHuPngqC6ZfSBxPERlwKENsu5O8Q4Z2kmeLCXvdfbO6Vn8JBCJGQYHN8jfSfl+SYr10lk7fQ5MQkNDqazs3AU3c+ZMfvGLX/R190qdWsEaqC+XL6bESa5//YYKSbYFSBgvNUsGC4ddgrKaQ5LQaGs6GkjY5QvF4gu2VikIFRQrK9Naw46W3o6CoCjpzrf4df4CSp0h/xqGBCCGIfttC1DMFtlua5ahs9rDEhjVHIaGSrnVl8tjA8KPXoGbIXfpsdLfAREQHCPBkXIf/xDImCPDdwfXH8vVKt0jxdm0WnL3hKXIrblWek/qiqBkJ6TPllk9XqTPgckFF1zA7373O958880O281mMy0tAytTWHmYpmooWC/LhcePAauLhw3tLZJX0rZicMI4176+qxkOOem1TfN02GUaaFO13LeGyzGIHSXBQlB0x8AjuReBo8kEpqPDYhYfoIsu/uATesla6uVLruYI+ARIG5qqJWipKTyWz2Iyy1V7SLx0iUekyfovyj3CkiEkAUp2yDIOdSWw638QMxwSJ+rwTnf5h8hQ5oGvJECpLIBZ90svopfoc2Dy0EMPccYZZ/Ctb32LRYsWMXbsWJqamnjiiSfIzs52RhuV6lreSmiulml0cWNd+9qGIYuVNVVLddn0swdmt7OtWb7Qqw/Jzd4qUxZtLfKlHjtKEhrjsyEiHfw8ILfDL0i+zGKGH9tmGJJAG511NEApkmGn2kKpOVOVD60NkDRJPk8Om+S++Fjd9z4GI7NFPkuRR4d3KvJkqK7igMzqiR42MP/OnM3sI2tzmc1g9pVgLzJTAm8vOH59DkxSUlJYu3Yt3//+9xk3bhz+/v7YbDbCwsL43//+54w2KtVZTaFcVTVVQepZkvDlSqV75KRpMksi5kD7AmuqgqIdstaJrUl6hwyHDHuYLJAwFvxDwTrXOxJ9TSYICIOA8ZLX0KaxSq4qS3ZJr0lLvSw5X3UIir6RK/jwIXI1HxjlFSf1AcEvSP6uYoZLblJjpVwIlOXAkKnuySXzNmYfWVvHYT86u+1rGVptrpaLCw/uHXRKsYfU1FT++te/Yrfb2bJlC76+vkydOpXISM9948qLGYbMxGipk1wFV4+f1pfBofXy/+TJEBzr2tfvbyU7ZSE2W5P0HATFQMxICUaih0tX8UD5gg4Il8Xn0s6Sz1VLvQxX1ZXJ/coDEoBafGWoMCINQpMlsdAdtXIGm5AEWXundLcULqwvhV3vS89J0kSdfdUdZosMVzbXwo4lsq10NwydI70qPn5ubV5X+vyX9dVXX3H99ddTUFAAQHR0NDfddBMzZszoc+OU6lJ9qXxZNNXIXH5XfkHYmqVmisMuCwXGjnLda/cXw8BkP5oPZm+Rrt/WBun6HXa+dK0PhvF9k0nG4f2DYcrNMPoyKQJWsgtKd8nn7dAmMG+B7G8fW/rg+GnRyvnMlqOrc6fD4Y1Qliuz4KoOSO5JzHA9/t3hHwLZV8tFXfUh2PkeHP4aRlwk07Q96GLDZBh9K7k3ZswYhgwZwsMPP0xoaCirV6/mD3/4A9XV1axYsYKkpCRntdXlampqCAsLo6KigogIXbbbFex2Ozk5OWRlZZ16LaaD66WLN+1M152U2npqqgrkj3zkJd79he2wQUUejsJtHGnyIyFrEhYz0kMSECG9A4NgifVusdugbI9MZ60tkmCttV4+E0c2gsVf8lfa6rGcbncOg5zCarISwrCYPecLwSvUFctMuIYKuR8YCclnnHZGnB7zowwDKvZJYTtbkyStx42BERc6vfe3srKSyMhIqqurCQ0N7fbz+hyYBAQE8M033zBs2LD2bYZhsGDBAgDefvvtvuzerTQwcb1uBSZNNZIYZ/GVAMFVirbL65otcpXhrdMYbc1yxVmyExqrcbQ2UtbqT9RZt2CJHipFysx6BXpKthZoroHqQlj3ZznBc7THJXqYDC8GxZ70KlS/JPvIcEDpXjiy6Vil0/AhMvPLGt7lU/SYn8Bhk/PZoa9l5lxglOSkDJ3ttJy93gYmfb4cGjlyJCUlJR0CE5PJxG9+8xvOOOOMvu5eqWOa66S6a22RDDUEurD0fF2JdCODLN3ujUGJvfXo0MROOZb2ZvAPxUg9m0rzUKKSJoKP9pB0i48f+ETLlOjzFsHBtVLcqq5ETvRHNkvPU9JEXTOpP5jMUjgvMk1yT0r3SE9m9SGIGQGJ4wZeQrqzmX1kodHYMZD3hcx82v2BBHvDL5Sp/24a3unzWeimm27iBz/4Af/9739JSTm2/HJPIySlTitvhQzfBEVDigvXorE1Sben4YDIoZIA6o2Kj/b4tDZJ7Y+0WZB+FviFYOTkeNQYs1cJiYNRl8HIS+UL8uC6Y4matYXH6rm0FYvz5uE/T+NjlSJsMSMkX6LqoATeFbkQP06CF01SPjVriHx2KwtkqLp8H2z6hxzTsVe5ZfZOn39j9957LwBZWVlceeWVjB8/HrvdzmuvvcZvf/vbvu5eKeFwyCJujeVSetlVV0OGIYWKWuqksFjqdO/6Am8r1W5vObqOTASMmQNDzgT/IHmMXRfFcwqTSb4IY0fAuGvg8Cb5zDRWQF3psaULojMhIhMMrTjrNAHhsjhgzREJvhsq5N/S3TJzLjzV3S30fBFDYOJ3JKg+uFYuZDJmS1kAF+ea9fnVCgsL2bJlC9988w1btmxh8eLF5OTkYDKZ+O1vf8tHH31EdnY22dnZXHDBBc5osxqMzGa5MrI1dyyc1d9KdkoXsdkCQ2fJWKw3cNiPJmoWStEwe4vMIho6W07iqn/5+EsQC5I421QFlXmyzs+RbzAVbiPSFgSOsRCTpb8TZwlNlKT08n0yJNFcC/u+kErESZMBL/n7dRezRfJ0YkdKAcKSPVJDJmKo9ADGjHBJ/lmfk1+70tTUxLZt2zoELNu3b6eqqsrZL9WvNPnV9U6a/NraKDNxHDbXdS3WlcCej6T7PXW6/FF6g5rCo2sIlclxGzZPgqrg+C5PKt2eCaX6xjBkobqCNTgOb6KivIxIfwdmHz+ZATVsnncUq/MW9la56i/aDg4bDgMKTXHEj56JJUBXve8Wh03OI9UHoXiX9AZOua3bwYnLk18ffvhhJk6cyKRJk4iLi+vwM6vVypQpU5gyxYV5AGpgsrdKfkdglMyCCHXR9HNbs+S0GA6pn+ANeSWtDZJ4WZYjw16+ATDmKlk8bzCueOxpTCZJ1oxMwxj9LWo2fEyk6bCUC29tkEDYGia/K1uz5qL0lcUXEifILKkjm6BsH/61+Zh2lkH8aIgf6z09oO7StpZUY6V8RlubZfmGsOR+Xbm414HJr371K0xHx9rj4+Pbg5S2f51Zv2TlypU8+eSTbNy4kcLCQt577z0uv/zykz5++fLlnHPOOZ22FxYWEh8f77R2KRcoWAsHvpSKnKMudU1+h2HAgVUyc8UaCqlnenZeSdvUycMbJXizt8rwzZhvDa7Vjr2J2UJL5DCMrIugpQZqS2S4ra5IEjjzVkguStuCiJ78+fN0fkGQNhMjeiQtO1aCo1qWsyjLkeUJoodpgbbTiR0pif8ttTKzr7ZIFshsrYOUaU7PQen13qZMmUJhYSE333wz0dHRbNq0iX//+988+uij2O12YmJimDhxIh9++GGfG1lfX8+4ceP47ne/y5VXXtnt5+3Zs6dD91Fs7AArHT7QNVXLkERjFcSNdF3Nkg55JbO946qqeDs0lEFwAoy9EhImaHE0bxEQITeAplTYt1yCzaLtULxTrljjx8jCdv14lTrgBUZRk3QOcYE1UhSvqVqWXijZBclTpBdAnZyPv9ysR9feyX1HctkOfQ0jLnbq0iC9PnOtW7eOxYsX8/Of/5wpU6bw9NNPk5GRQXNzM1u2bGHTpk1s3rzZKY2cP38+8+fP7/HzYmNjCQ8Pd0oblBvs+1xOHj7+MvXPFepLj9UrSZ7i2fVK2tLDGipkLZv4cTBivmuLzinnsobC6EshaYKsnn3oa0lgrjkixdtiR8lVvtbo6B2TSQqxhSdLJd8jW+TCJ2epDBMnT/boxe08gtlyLJk4b6Uk2dcckbonTlocsE+XVDfddBNXXXUVv/nNb5g4cSJ33nknv/zlL5k6dSpTp07tc+P6avz48TQ3NzNmzBgWLVp02vV7mpubaW5ubr9fU1MDSHKgXadUuoTdbsfhcGAv24epcDs0VGGkzZSS3w6n52l3ZGvBtG+5TJ+NSMWIGt7/r9kbDpskAvsGSHVR/1DImHOs0mgPP6vtx1w/4y5z2mMekgjZ18DIy6BgDab8VVJl9tBGjLBUqY2i9Tl6xO4wcBgGdochyZvRIyF8KBRtxVS6C6oPQ80RjKgsyU3RBQJPLXo4RKTDwXWYjmyBvC+hZBdG+mxZHNDi1+tzitNm5eTk5HDfffexceNGHn/8cW644QZn7LYTk8l02hyTPXv2sHz5ciZPnkxzczMvvfQSr776KuvWrWPixIknfd6iRYt48MEHO21ft26dFotzEYfDQUV5KRkVy/FtKKbRGk990ln9P8ZuGIQUfoV/3UHsvsFUDZmH4YFDOJbmakIKv8KnqQLDcFCZeRWO0JQ+rRDqcDioqKggMjISs5aid4keH3PDwLfmAObGcpqtcTLbCggp3YgtKIam0AwM7UU5JYcBFbVNRIZYObEivbmllqCyb/CvOwiAYfahIWIUjRHDNQDsBktzNUFF6/CrLwQfP+zWKOqTzqLMFM3UadNcv1YOgM1mY/fu3WzdupVnnnmGjRs3UlpaSmSk87vEuhOYdGXWrFkMGTKEV1999aSP6arHJCUlhdLSUp0u7CJ2u53Da99lSNMuTA2VGCMvltLe/a1kJ6aD68Fsxhg23zWv2ROGAeW5mA6ulbWCfK0YY66WktJ9zCWx2+3k5uaSmZmp04VdpE/H3G6Dpkqph7L9belB87FixIyQVXg9efjRjewOg9yiajLjT7FWTl0xpkMbZIosgF8gRuJESfzUBNlTMwyo3I9p/3KZVWYNoyownahzf+C66cKPP/4427ZtY9u2bezevRur1Up2djZnnHEGt99+O2FhYb3ddb8444wzWLVq1Skf4+/vj79/5yl6FotFT9iu0lxDcOkWTL7NmGOHQ4gLEpbryyQZzoSUunfFa/aEvUVmJ5XtldlJEekw8UaZeuokZrNZP+cu1utjbrGAXzwERUFAiFQmLs+Fwi1QvE0K6cVnQ3iKfpmewGwyYTGbTh6YhMbDyIulGN6hjVLxOX+VHNfECVJvRmdInYRJEmAj044uDrgRE2W92lOvA5Of//znpKWlceONN7Jw4cIOi/h5oi1btpCQoFMnPd6+zzG1NoC/v0x57W+2Zti/XLLLI1IlidSTGA7Y/aFMz3O0wtA5Mg24rZy8GrwsvjKVPfVMWYBt/3IJsCsOyG3EhRCV4d42eiOTSXpIwofIjJ2ibZKEv3+5JHYmTpQZPBqgdO34xQEL9/dqF70OTGbOnMmWLVt48MEH+d3vfkd2djYTJ05sv40ZM8ZpV191dXXk5ua238/Ly2PLli1ERkYyZMgQHnjgAQ4fPsw//vEPAJ555hnS09MZPXo0TU1NvPTSS3z++ed8+umnTmmP6icVeZiKd2LYmjCSZjht6e2TMgzIXy1lq/2DIXWGZ55sAqOkwNG4GyFlqlYHVZ1FpkHkTdB4uRQkLN4OfiFQdQgCwqCxWv7VGVvdZ/aRImzRw6SEQPFOmQGXu0wWwUycKCXwVdesIb3+vPU6MFmxYgUgSa8bN25k06ZNbNq0iddff52qqir8/f0ZO3Ys69ev7+1LtPv66687FEy77777ALjxxhtZvHgxhYWFFBQUtP+8paWFH/3oRxw+fJjAwECys7NZtmxZl0XXlIdw2GXKXnMNTUEprrnSK90DlQeO1SvxlEqbDpusaGz2lcXfEidJBdcwPQmq0wgIh9GXyXoxzTVSTbayAHa/DxjyJRs/VnKoPDEI90Q+/jKMEztSasuU7JK/y72fSAHDxIkQ7GHDv16uX9bKycvL4+uvv2bz5s08+uijzt69y+haOS5UvBO2/QtHXTk50eeTmZZ88nFgZ2goh90fSECUcoYkDXqC1gZZdKy5BpKnQXSWjNv249RFXSvH9Vx6zGuKYPvbUm/C1ix5J2HJkJAtq+4Okh44u8Mgp7CarIRTJL92R2sDFG6TOiiOo9Nhw5IhaaImHp+g8sh+Iqdc5brk11NJT08nPT2dq6++uj92rwaimBGQOAmj+jCGTz93N9tbjuWVhA+RolWeoKECcj+TCq6Y5WosbtSg+eJQ/SQ0Hs78gdTp2PeFJCZWHZTqxoGR0luoVU+7zzcQhkyV9XbaSttXH5JbRJoUwAvQC9m+6FXK9vHDJt1x+PDh3ryMGkwayuQLOKGfK7y25ZU01YBfMKS5oEZKd1QVSA9OXZG068wfwJBpGpQo5wlLgonXw9yHYexVstp0U7X8LTRVy9+G4XB3K72HX7AkHo++QoaeTSYZGt75H6mI2lTj7hZ6rV4FJlOmTOH2229nw4YNJ31MdXU1f/3rXxkzZgzvvvturxuoBriaQmiohPJ98iXc33keZXugIk+6s4fOcn9eiWHIuHXuMklwDR8CZ/1IrsY8IWBSA481RGbszH1IAuDkM8BArvj3fCy5EzWFx5Y8UKdmDYX0s2HUZdJjYhhyPtvxnkzlbqlzdwu9Tq+Gcnbu3MkjjzzC+eefj9VqZdKkSSQmJmK1WqmsrGTnzp3s2LGDiRMn8tvf/pYLL7zQ2e1WA4GtBXb8W6bCRmbIQmX9qaFcSrmDTEX2hIS14h1So6SlXto08TuSwKhUf7P4HOuhDE+B6gLI+VQ+i2V7ISRBfh6ZrtVPuyMgAjLOOVoXabMEemV7oWKflG9PGCvDQOq0evVpi4qK4umnn+aRRx7hgw8+YNWqVeTn59PY2Eh0dDTXXXcd8+bNY8yYfv6iUd6tpQ4Mu0zXjRgiPSb9tTbN8fVKwod4TrJrSAJggmEXwOjL+3+KtFJd8bXKjJ05v4L9n0PBumOLBwaES4ASM1wXD+yOoGjIOh/qiuHwJrnwKtkpQUrsSLkA0+N4Sn0KgwMCArjqqqu46qqrnNUeNZhYw2TmSVBc/yaLeVpeSWujzLJprJJE3Ol3QcwwzSdR7hcSC+OugZGXwoEvZWG2umLYt1x6UoZM02qy3RUcJxcctYVwZJNMMS7aJmUK4kbJxZEHrsflCZzeP2exWHSVUtU9NUegvli6ivtT6a7j6pW4Oa+ktlBm3kQdnQackC3LrWs+ifIkfoEwbB5kngeHN8KBVfKZrT4sQbWtWZZwCEnUz+6pmExShC0kQYZ2jmyS2XdHtkg9lPgxUm3a4uvulnoUpwcmJ5ZF2bRp0ylX9FWD0OGNkvCKCfyC+vePsq4EDn0t/0+e7N68ksoDUpWzqRr8iqS0fLCHLRao1PHMFqnzk3KGBCN1JceSZJsqj+ahZEsJd81DOTmTSfJ4wpLlPHBks5wHDm2UGk5tFWY1QAF6MCtn2bJlTJs2jVmzZrFs2TIACgsLefnll1m4cGH740wnRM9nnHFGe6XWNh9++GFf2qy8WVO11FLY/YH0ZFjD+++1bM0SCDjski3vznVwSnbDvs/l/UcPhxk/0KBEeRcff/lyTZwodTys4ZI/sedj2PyafNm2Nri7lZ7NZJIe4tGXQ/pMKdne2ihJ+dvelmNoa3J3K92u24HJ3XffzY9+9COefvpp3nvvPW6++WaGDx/OsmXLuPTSS0/6vLFjxxIaGsrNN9/cvu3//u//+tZq5Z0MQ8rON1bKjICkif3XDWwYMkbeUifT+VLPdE+Xs2HIySb/K2iqlZP6mXdphUjlvXz9IXsBzHtE8lFCk6GlAfavhE2vStExdWomM0RlSg2U1DPlHGVrliGerW/DwXWDeppxt/veAgIC2iu5jh8/npiYGHbu3Ely8qkrBppMJhYtWsQzzzzDVVddxT//+c9Owz1qkCjdLeOqjVWS69GPZdYp3ibVLd25Do5hQMEa6aptqYehZ0P2QvDrx/etlKv4Bsjsk4xzJfje/4VUQW1thPrSYwntJovmoZyM2SKznaKzoDJfkmMbyuWcUbpHhsjix/Rvz7IH6nZgUlpayltvvUVWVhbDhg0jLS3ttEEJ0F4f/9577yUiIoJLL72UxsbG3rdYeaeWBqmR0FQt3cH9uUhfbREc3iz/HzLNfb0TJpOceFobYMRF0n2rY8hqoDGbIXmS3Cry5DNffUTyUUr3SJCSkC09BJqH0jWTWYZ4ItKg5rAEKLVFEuiV50qJg7bFFweBbn9KfvSjH/Hpp5/y9NNPs2vXLpqbm7nssssYP34848eP54orrujw+H379pGRkcHy5cvbt914442EhoZyyy23OO0NKC+Ru1QKDxkOGHJm/005bG2AvBXyOlGZMpPAXVrqpJt78hhIna7TgdXA1zbDLjRJ/t4PrpMAZe+n4L9GvlxjR8i0fdWZySQJsmHJctyKtslyFZX5cgtNgPhsSToewL1Q3Q5MLr30Un74wx+238/Ly2P79u1s376dd955p1Ngcscdd5Cbm0t8fDzZ2dnttzlz5lBRUeG8d6A8X1mOrMbZWAlDpktJ7P5gOGSNipYGKQo1ZJrr/3hbGuDIRkm0tbfKAoERaXJVqdRgYbZASBzM/jkUrJb8k5ojUqL90Aa5YIgfAyHx7m6p5wqOhcxzZei7aBtU7JelAmoKpYhb/FjpSRmAdWW6HZicLNC48847CQsL6/T4pUuXAvDoo4+yYcMGDh8+zH//+18+++wz0tLSyM3Ndd67UJ6rtQn2fgxNVRLlxwzvv9c6vEn+aC2+MPQc1w+bNFXLcFVdKTRWw6QbISxlQF/ZKHVKvlbImAPpsyXva/8KqYJaslNmn2Sd7/71qjxdQLjM4EkcL7knZXulN2rfF1KkMn6MLOkxgHpkux2Y9DbQ+Ne//sWWLVva73/66ae89tprfWu18h77PpMvaocd0s7svz+etsQxgNQZrl9vpqFCgpL6MjlZjL1armaUUtJjmDBObjVHZHmIwGjpRTXs0ttZUyTDPP791KPq7fxDZJp2QvbRiQQ75WLowFcymydu9ICphdLjTKSeBhpWq5WdO3cyatQoAObOncsDDzzQ85Yq71OxX7L1GysgZWr/ZZY3VUtlSpA/zv6uJHui+lLYuxQayyU5beqdEJnq2jYo5S1CE2H8tTJrrbFSSt7v+I982R7++ugwz2gIjtfexq74BkDiBDnXle6Fkh0y6+/geij8RtbjiR3p1evx9Dgw6Wmg8be//Y1vf/vbzJ49m/Hjx7Nt27ZORdjUAGRrhj0fyfo0wfFyJdQf7K3SpWlvkfHqpEn98zonU1sIOctkHDg0AabfLf8qpU7NZILASLk5bOAfJKttl+yUICUkXvIoojJ0Nk9XLH4yjBM7Qi4Ci7bLRdqRLfL/mGESvHhhonGPf9s9DTRGjx7Nxo0bWbJkCdu2bSM1NZVf/OIXfWq08gIt9RI02FuOzkjphxOLYUjhssZKWdtj6CzXjrM6bJJs21gJ4akw/fuycJdSqmfix8qtplCGeQ6uP7a6cXAsjF2gCeQnY/aRIZyozM61UEp2Q9RQObZeVAulx98Wpws0uiqe5ufnx4IFC1iwYEHfWqu8h3+IrK8REi9XRP2hZKfUTTCZpYiab2D/vM7JmMwQOxoComDKd7Waq1J9FZoA4xdKzZ8DX8kQbUCk1PbwC5LzSkO5XABoz3tHx9dCqT0iAUpNIZTlQvk+r6qF0qvL2FMFGg6Ho8+NUl7MMOSEUXFAEkH7q5BaXfEJi/O5sKeitQEs/lIAKSpLTqKasKeU8/gGQNZ5MqOnuUZm9VUdlGGKg+t0mOdUTCapIxOa1HUtlOBYyUEJT/XYmTz6G1XOYxiw8z/Hpv8FRvTPSaOlQbp7DYdcIcSOcv5rnEzJTgmIEsbJ68aNlis5pZTzmc0ywy4gXL5oWxtlWYvaIhnm8Q+Rv8GYEbLejOro+Fooxdukh7muRG6+AUfL4Q/zuHOYBibKeSoPSHReVyzz7vujeJLDJmtytBVRS53hui7dwq1SHKq5TvJn4sf273o/SqljLL4wbK6cW9qGeWqOQP4auViITIfM8wbEdFmnCwiHtJkyOaAsR5KLWxqkB6pwK0SkSnDnIUNkGpgo5wlPlTn2ZbmSiOVshgEFR0tc+/hJN68rTkKGAUc2ydTn5qOL8Y27VopHKaVc6/hhnuJtsop48U4ZOq4vl54Tv0CZGajF2zryDZTe3rgxUH3wWO9TRZ7cAiMlQIkc6tYATwMT5Tz1pWD2g9Rp/VMmuXSPVD00mSB9lhQy62+GIb0khVtlplHmebLku49f/7+2Uurkji/aVlcmCZ8gPba1hVLcMTxV8inCkgH39wR4DLNFkmQj0qQ4ZOluSZBtqID81cfqybhpiEwDE9V3ZTmyxHnZXrBY+md2TG2RJL0BJE08eqLpZ4YBB9dC0dECRsPnw5grtatYKU8THC03gOZamW5sGMcuZgIiIGY0Zlsc4IILGm8SGAmpZ8owT3muBClNNVJTpniHnGtjR0qOj4uGeTQwUX1TUwjb/y2Z8wnj+mcIp6WuY7Jr3Fjnv0ZXDIckjbU2wKhLYeSlYNE/GaU8mn+IJHzGZ0Pel3JB01iOKW8lES0WTM3DIHWqa3pcvYmPvyQSx46S6dklu+Tf6kNys4ZKD0pUZr8PkelZVvWerQV2/VcKjJkt/bNgncMGuZ9LNn5gJKSd5brkLHsLxIyC5ClHFwXUPxelvEZwDIy9Ui4qDm+EA19hyt8BZXsgJksqp/oGHCtxoITJJL0kYcnSc1K6G8pz5P8H18tiqVEZEqT0U40qPdOq3stdKhF1ayOMmO/8ZFDDkPHOhnJZ9yFjTv/XLHDYpLxzaJIEXLEjIDrLY+f7K6VOw+IDQ6ZiJE2mMngNEcGNMuxTVyrnlkMbwT9Y/tZDEjVIOZ41VAplJk6Q82Lp7qM5KXvkFhIvAUr4EKeeIzUwUb1TsgsOb5YPadKU/ilwVrxDErJMZsiY3f9FzBw2WXenIk+S5sZcKd2WWgpbqQHBHhgNGVnyN91cIwXHdn8AVc1SoygoBuJGSeKnlgI4xuJ7rOZJXbEEKJX5kvtXWySzoKKHy/o8Tsgx1MBE9VxjlSzQ11gpPQvxo53/GlUFkhkOkDIFQvp5YTx7K+z7XGqxOGwwZJoGJUoNVCaT5JgkZMOcX0ouyqENMt1433IoWANRw46WcI92d2s9h8kkvSQh8TIhoGyv9Jy0NEg5haKtx2ZC9aH0vQYmqmccdskraSiXnoy0GU4f5rA0VWIqXiVDOTHDIWakU/ffib1FVgiuPijvb+JN8r60S1epgS8sCcZfA2OukOAkf7X01BZtk14T/xBJ9tRclI78gmSIJz4bqvKlF72uRIZ8KvYfXTusdysba2Ciemb/cvnQNdVIzoezh1daGwk98iVY7RCWCClT+/dkYGuGnKWSdW4yweRbYEg/v6ZSyvP4+EtyfdpZUFkgAUpkuqzTY2+RC5eGShmuCE/VsgFtzBYpyBY5VC5YS3bJd0RDOabKnN7t0slN7BcrV67kkksuITExEZPJxJIlS077nOXLlzNx4kT8/f3JzMxk8eLF/d7OAa90r3Rx1pdLF2dEqnP377Bh2vc5Flu9JF0Nnd2/SaeGA3I+lROOyQxTbtWgRCkFEUOkFyXlDLk4ih0NlQelzsfuD2HTP2T4p7ZQelKUCIySwC57gSyu2ss1eLwiMKmvr2fcuHH86U9/6tbj8/LyuOiiizjnnHPYsmUL9957L7feeiuffPJJP7d0AGushN3vS35JSBwkTXDuF7hhyPoX9aU4LP4YGef2fzlpk1mmOJt9Yert8oekQYlSqo3JJOvMRA2Fs38MY66SGSi2FlmmYtu7sPVNqQytjvGxQvxYjMzzevd0JzenX8yfP5/58+d3+/EvvPAC6enpPPXUUwCMHDmSVatW8fvf/5558+b1VzMHLrsNdiyRtSgwQdrZzp+2W/iNdP+ZTNQmnEmUK4ofNVRI8u7Zs6XLVimlTiYoCkZeBCMulJ6TgnWS8FlfIdWvw5Klp9fsI8n0OtTT66VJvCIw6ak1a9Zw3nkdI7V58+Zx7733nvJ5zc3NNDc3t9+vqakBwG63Y7fbnd5Or2FrxmQATbUYmeeCXzA4nNh9WZGH6fBmAOwp02i2xWJ35v6P11SD6eAajNhR4BMglQ5D4mEQ/37tdjsOh2Nwf8ZdTI+56zn1mEcMldvob0HRFunxddihpgSaqjEVfIURlSnTjkPi+2ftMC/Q2/P4gAxMioqKiIvrWFcjLi6OmpoaGhsbCQjoen76Y489xoMPPthp+/79+wkNdf1CRh7DYQfHEMxh/jgaw6Cx2mm79mkoIezwF5gMB40RI6i1xVNR20QuNZidPKpiaakh7NDnmJtraK6oozbzCiiqldsg5nA4qKioIDc3F7NOj3YJPeau13/HPKLtBcAWRED5IYJqGqF6C+Rtxe4bQnP4UJpC03H4Da7vkZrK3gWBAzIw6a0HHniA++67r/1+TU0NKSkpDB06lIiICDe2zE1a6qVXoXwvOOogIdO5QziNVZhKNkCQH4QPwRh6NnbDRC4GmfGhWJwZmTRUYMr9Csx1EBmNMe27xEekOW//Xsxut5Obm0tmZiYWi1a4dQU95q7nsmM+Khsqz4NDazEd3gRN1VCzGeq3Q1gyxtBz+r9YpIeoNMp79bwBGZjEx8dTXFzcYVtxcTGhoaEn7S0B8Pf3x9+/c8KlxWIZfCePlgbY8prM4w+IgNA48HHimGlrA+xfJtPwQmIgY5bMwHEYmE0mLGaT8wKTuhKZEtxYAcGxMP0uCE9xzr4HCLPZPDg/526kx9z1XHbMYzLklr1A8ucOrpdK1nVF0FwFJqQMfku9zFwZoEM9vT2HD8jAZPr06Xz44Ycdti1dupTp06e7qUVeqPqglBpuroHhF0iWtbPYW6WgWXOdJItlnNt/a+DUFELuMplNFJoE0++E0H6uIquUUiAJsMmT5dZUDeX75WKvtgiqj0DupzIrMGYYRKRLtVSdGegdgUldXR25ubnt9/Py8tiyZQuRkZEMGTKEBx54gMOHD/OPf/wDgDvuuIPnnnuO+++/n+9+97t8/vnn/Otf/+KDDz5w11vwPmHJUqvEsDt3HRzDIUXa2hbmyzy//9akMAw4tF6mOkekwbTvS4+JUkq5mjVMyiyAzAKsOAAHvpSe3Py1cOhrWa03KkvOV4FRgzZI8YrA5Ouvv+acc85pv9+WB3LjjTeyePFiCgsLKSgoaP95eno6H3zwAT/84Q/5wx/+QHJyMi+99JJOFe4Ow5C1Ykp2S+AQluTcfReslSqrZh/IPFd6TPqNAbGjwBoOE2/otyW6lVKqR3z8IXY4XPCYrC9zeJOUwK+vgLqv4OA6SJoka3YNQl4RmMyePRvjFNX1uqrqOnv2bDZv3tyPrRqAao5IVcP4MZKXEZrg3Ii9cIss+GQywdCz+6/3oqlapjTXFEoxpOEXyniuUkp5ErNF1ptJnCBF24q+gSNbJEjxC4aqQ+AXIEtn1BVLT0rAwJ+I4RWBiXKBphrY/q70ZlQfhGHznJv3UbJT/uAAUqbJWhP9oXiHXG1Ej5By0nGjZUlupZTyZD5+kDxFbrZmSYxtrpELrIMboGwP5K+RC7qoTIhMk97gAUgDEyXJqNvflYQse6vz8z7K90mVRJArg9gRztt3G8OQKoxHNktSrcVXen76K39FKaX6i4+/3AIjIWyInM+sYXKBV1sINYdlkcGQeAlS4kb13wQCNxg470T1jmHIGjiVB6C5FoaeI6WXnaX6EBxYJf+PHQUJ45y37zaGQ3JXinfKVUbGOZD9bfB14kwipZRyB7P52MyelgZZo+fIFlnFt/qwLBXSoRx+C1j83N3qPtHAZLDbvxwKt8ksmaTJ0j3oLHUlsO8LCRwih8rQirOzzB12yWwvy4HWRhhxEYy+XNepUEoNPH6Bsnpv2llyIXl4swz3+PhDXalMXMhdCoHREJUhOSm9XOHXnTQwGcyObG5f0ZeY4ZAw1nn7biiXPxCHTaL5tLP6JyjJ/Ux6e+zNMPYqGHaBJJQppdRA5h8ikwhAzoVN1VCyRxZdrcyX86LFV86/URkQnuY1+XYamAxW5ftgz8cSQIQly7Q0Z1UfbKySSqu2FknUGjq7f4IFk1muFBytMP47MHSWdHsqpdRgYrZIPkradMnhO7JZpiBX5Eq9lIo8Sa5NOwvixri7taelgclgVFsMO96ToMQ/BNLPdl7iVFMN5HwiwyqBUZB5Xv8NqzRXQ9QwSJ8FieMHbTEipZRqFxgBmXPk1lABhzdKoFK+DzBJ4qxvoAwF1ZVISYWgaI8qi6+ByWDTWAlb35KEKbNFAgdnJYk218LeTyRBKyAChs2VHg1naqyEwq0QO1LuJ4zVdW+UUqorgZGQdb7c6ssl36+xStbsKdwqwYplHfiHSjXa8BQISXR7jp4GJoNJSz1885ZMC3a0Sq0Sq5NWuWypPxqU1Mm0tmFznbu+Dki7cz+T4MRhhwnXyXQ5pZRSp9Y22zI4BqKGSimFI5uhZIck0B462rPiGyB1pjLOcdsUZA1MBhOTRaYHtzZIT0lQjHP229ogQUlzrQwNDZsnXYXOVHkA9q+QBK/QRJkOrEGJUkr1nNlybAqy3SYVuYu2QvF2md1TfUiGefwCj1agLZALzoBIlwyZa2AymNgaIXoYhMQ5bw2clgbY+/GxMvDD5jl/elrJTqlT0lwnC1xN/Z6MiSqllOobiw/Ej5abYRwNSorlfF5fAjVFsPsjCUgCIo4N+QTH9VuPigYmA53DDuW5EJIARdul+E5kunP23TZ80xaUDL9AekycxTAkcavwGwlKkibB5Juc+xpKKaWEySRBR1venj1TkmWrC6RXpaFCelIOfS0XoBFpEDMMQp242CsamAxshgG7P5Bxw6A4CE+WYRBnaKk/2lNSIwvkDXNyUAIyRFSyU4KSjHNg7AJZ0EoppVT/s/hARCpMvwtam6F0lywwWLRNcv2Ktsnj/EIkUDHsMiPTGtanl9XAZCAzmSRYqC+VHhNnrRbcUne0p6Qfg5I28dmyUNXIi92eKa6UUoOWr7+UZUgcLxe9FfslLyUoTiZT1BVLYbfCLTLUHpEOjUavXkoDk4GstVGGWIbMgJgs58xTb6tT0lx3LNHVmUFJUzW+DcXygXY0S42ViHQtnKaUUp7CZJJqslEZct/WIjN7muvlArK2GKqPYCK4V7vXwGSgMQyp+BeVIbkldUUQk+mcyquNlZDzqSS8tk0J9uvdB69LtYWYcj4npKoawudKFcPQJC2cppRSnszHD3yiYdwC6d0u2g7F2zAaHL3bnZObp9zJMGD/F7L+jWFAQrbMvnFG5nR9mQQltuZjRXucOSW4PFfa3ViN3T9aEl3Dkp23f6WUUv3PLxCGnCG3igrgez3ehQYmA4VhwL7PIX+1ZE1HDnVeUNJW2MzeIsV5Ms93XkVXwzi2jHdLHUbMSKqjziU2ItU5+1dKKeUevezt1sBkIDAMCRwK1hwLStLPck5QUpUvhc0cdkmezZgDFr++7xck0Mn7UpKoWhog9UwYuxAKDjtn/0oppbyOBibezjBkhsyh9VKxLyoT0s50TlBSukeCHcOQhZ6GznJuQZ3inVCWI1PMxlwJw+cDmuSqlFKDmQYm3szhgN3vyzBIfSlEZ0Hq9L4HD4YhRc2ObJb70cNkv85efTIkXuqqDJsHyWfIzBu73bmvoZRSyqtoYOKt7DbY9R/Jfq4vhZhRMGSKE4ISh5R/L90j9xPGQeIE58yMMQxZcyE0UdrsFwzTvg/BsX3ft1JKqQFBAxNvZGuG7e9C6V5oKJciZEkT+z4l2N4i+STVhyQQSZkKsSOd02aHDfLXQNkeCE6ArPNk332sEKiUUmpg0cDE27TUw9a3oOKA1BVJnACJ4/o+zNJSD7nLZC0Es8/RwmZOmhnTXCszhmqLJKiKSIP4cVpeXimlVCcamHib3R9A+X6psjdkKsSO6vswS0O5BCUtDeAbAJnnQlCMc9pbfUh6YZqqZDbPpO8eTc51QsE3pZRSA44GJt4mboxUdk0/+1g54L6oPCBTdh02CAiHzPOcU2LeMGTNhCObpXx9aKIEJdFOaLNSSqkBSwMTb9BYJbkYlQekrkjW+VJ9tS9OnHkTmiTTgZ1VOK2lTvbfVCtVXCdc1/c2K6WUGvA0MPFkhgEH10t+RtIkSU61hva9R8PeCvlfQUWe3I8bBclTnDsd2GGTYaaQeBg2X9ZSUEoppU5DAxNPV1ckSaOHNkDG7L6vT9NUI+vpNFRInseQaVKnpK8MBxRuleWuTWbwCYQRF+kifEoppXpEAxNP1lIHQbEQM0x6TPo6zFJ9CPJWyBLVvgGQcQ4ExzmhnQ1w4EupUeKww4TrIX6s5KwopZRSPaCBiaepLYLDGyFpMpTtheZqqSfSl1kshkPyPQq/keGh4FgYeo6sAtlXVflwYLVMXQYYeYm0V4dulFJK9YIGJp6kaDvs+VCGWcpzIWYEhCT2bSiktVFm3dQcXRgvdsTR8u99LcbWKsNLJbukBkpwnPSUxI3WoRullFK9poGJJ3DYJcG1YB00Vki9j9iRfa8lUlskQzctDVI0LXW6LPLXV7ZmqadSXyr/T5kG2QsgMKLv+1ZKKTWoaWDibk3VsPM/ULEf6sul3kf6TPAL6v0+2xJRC7fI0E1AOAydDQFOChzMPtLjYvGDcddJwGPRj5JSSqm+86o15v/0pz+RlpaG1Wpl6tSprF+//qSPXbx4MSaTqcPNarW6sLXdUL4Pvv67LJhXXy4Jo1nn9S0oaamHvZ9IfRLDkB6SERf3PShprITWBul9qTkC6efA2ffD0JkalCillHIar/lGeeutt7jvvvt44YUXmDp1Ks888wzz5s1jz549xMZ2vTptaGgoe/bsab9v8pTcB4cd9i+XVXwbKwEDMubI2jR9aWNFHhSsllk3Fl8YMr3v1WENBxRvh8ObpX7KkOkQPRwi05xXjE0ppZQ6ymsCk6effprbbruNm2++GYAXXniBDz74gL///e/87Gc/6/I5JpOJ+Ph4Vzbz9BoqZOimKl96SYJjIH2WFE7rLVszHFwnPTAguSnpZ/dtnyBr6OSvhtpCaGmU/SaMh7DEvu1XKaWUOgmvCExaWlrYuHEjDzzwQPs2s9nMeeedx5o1a076vLq6OlJTU3E4HEycOJFHH32U0aNHn/Txzc3NNDc3t9+vqakBwG63Y7fb+/YmDAOKtmLKXSa9JM11GHGjIWmi5Gw4jN7tt+YwpvyvZIjFZMKIz4b4bMkB6e0+HXYo+gZT0VZorgeLD8aoSyFjHvhZoa/H4hTsdjsOh6Pvx1t1mx5z19Nj7np6zF2vt8faKwKTsrIy7HY7cXEdi4HFxcWxe/fuLp8zfPhw/v73v5OdnU11dTW/+93vOPPMM9mxYwfJycldPuexxx7jwQcf7LR9//79hIb2sffBYSM857/41BXR6htCbfwsHJYoKK7v1e5M9lYCy7YQUJ0LgN03hNr4qdhMMVBc1+tmmltqCD2yCp+mSnC00hyaTv2Qc3FYoiH/YK/3210Oh4OKigpyc3Mxm70qBcpr6TF3PT3mrqfH3PXaLu57yisCk96YPn0606dPb79/5plnMnLkSP7yl7/w0EMPdfmcBx54gPvuu6/9fk1NDSkpKQwdOpSIiF4mjxqG5I3Ul4FjIpTtgdQzifUN6N3+AKoPYypYDfZ6CLZixI6ExIlEW3x7v882Nn9MpY3g648x/Fsym8eFxdLsdju5ublkZmZisfSx1orqFj3mrqfH3PX0mLteZWVlr57nFYFJdHQ0FouF4uLiDtuLi4u7nUPi6+vLhAkTyM3NPelj/P398ffvnNBpsVh6/kFuqYecTyEwWoqPVewHPz/ImtP7xfJaG+HQ11J8DcAaAqkzIDShd/sDCZyq8iF8iKyj01wn1Vvjx7otl8RsNvfumKte02PuenrMXU+PuWv19jh7RX+Wn58fkyZN4rPPPmvf5nA4+Oyzzzr0ipyK3W5n27ZtJCT04Uu8Jyry4PAm2PaO1BTxD5YApTdBiWFAWQ7sWCJBickkKwKPuqxvQUl9qRRKy1kq1WEBErIh81xNcFVKKeUWXtFjAnDfffdx4403MnnyZM444wyeeeYZ6uvr22fp3HDDDSQlJfHYY48B8Jvf/IZp06aRmZlJVVUVTz75JPn5+dx6663910iHXZJOW5vA5AO+QVLBNTKt9yXgG6ugYI1UcQUIjJQpu8FdT5HultZGCZrK9hyrChuaBMmTZUqwUkop5SZeE5h8+9vfprS0lF/96lcUFRUxfvx4Pv744/aE2IKCgg4JTZWVldx2220UFRURERHBpEmTWL16NaNGjXJ+4xx2ma57ZAuMuAiqD8q04PSZvV8oz94ii+4V75RaImYfSBwHsaN7H+Q4bLK2TeE30FwrrxE/FkZfCRFpusaNUkoptzMZhtHLOaUDX01NDWFhYVRUVJw8+bUiT4ZCao9I70ZEmgyzBEb1ftimYp+sMNzSINvCh0DKGX3vzchbCSW7pcckJB5GXQ7Jk6QYm4ew2+3k5OSQlZWl48Auosfc9fSYu54ec9errKwkMjKS6urqHs1s9ZoeE4/TWAX7PoPiXdBcI1/2MSOkLolvL0vf15XAofVQVyr3raGyEnB4Su/baTgkQLI1S7Bk8YXh8yHjXPDvQ+l7pZRSqh9oYNJTtmbJ+ShYD83VsghfcLyscdPb1YCbauDIJul9AQkeEsZJfoq5l7+ihgpZL8c3ACLTwTBB3FgYdgEERfdun0oppVQ/08CkuxwOWa33wCpoKJMeE98AKf0eObR3eR+tjTJjp2yP5KmYTBCVBYkTep+b0lQjAUnFvqPVYM1SRj56mAQkmkeilFLKg2lg0h1lObB3i6wZ01QtwyNxYyRxtDfDNrZmKNkJxTvA3irbwpIgabLMuumN5loJnMpyJeBx2CBmJIy8GGKG9z5hVimllHIhDUy6wbTjPfCzyxd+1FBInCTFzXrK3iLJp8XbJTgB6cVImgShfagbUpEnqxW3NkqgE5UBIy6WwMmiv2KllFLeQ7+1uqO+FMIyIOv83uVntAckO8DWJNsCwmXIJjy1d8MrDtvRxf/skpPSUg8RqTD8QslP8aCZNkoppVR3aWDSDcaQaTB0Ys8DiLYhm5Jdx3pIrKESOEQO7fl0YsOA+hIo2ibBTvIUsLVAQBSc/WOIzHDpujZKKaWUs2lg0h1+IT0LSlrqpDBa2d5jOSTWMCn33quAxAFVBTIEVFsklWUxIGmK9LoEx2oPiVJKqQFBAxNnaiiX4ZqKPAkmQJJZ47NlmKWnAYmtWdbGKdkJjZUSkJgt0uOSdb7MtNGkVqWUUgOIBiZ9ZTig6qAED23r2YAsrhc3Rtag6e0U3aqDsrierRn8giB9FmScA2EpYPaK9ReVUkqpHtHApLdaG6E8B0r3QHOdbDOZj5akH93zJFmHTYZrQErQN1aB2U9WJE6aDGlnamE0pZRSA54GJj1hGFBXLMFIVb7MiAHwsUJ0llRq9ethmffGKslFKd8ntUjMFhg2X4aAYkbA8Hm9L3GvlFJKeRkNTLrD1iQzYcpypMBam6AYKV4Wmd6z0vG2Zqg8IPkjtUVy394qCbJJkyShNSRO80eUUkoNOhqYdIMpdylEHK3IavGFiHQJSHo7tHJovczasTXL8E9kBqTNkIDE2v0VGJVSSqmBRgOT7jAcEBwjs2Ai0sDSzVohbXVHKvbLGjh+gbKWjW8w+IfA0NkwZDqEJWvviFJKKYUGJt1iDJ0DmZO6+WBDKsVWHpBbU7X0jDRUwJBpEBIP8eNg3ELwC+jPZiullFJeRwOT7vDvxro49lY4vFFm1jRVS2VWu01WII4bIz0j8WPAP7j/26uUUkp5KQ1MesvWDM01kgBrGBKIFO+QqcO+ATJDJ2mSFFcLiOh9LROllFJqENHApLsMA5qqoPqQ3GqLJNjIOl9+5hsAaWcfLaw2WoMRpZRSqhc0MOmOI1ugcoskrtpbpBgaQGA0WKMgMlWm+va0holSSimlOtDApBtMlfuhNQB8/CE8VXJFYkfL+je6mq9SSinlNBqYdIORdhZkTJbpwgERuk6NUkop1U80MOmOCddDRIS7W6GUUkoNeHrpr5RSSimPoYGJUkoppTyGBiZKKaWU8hgamCillFLKY2hgopRSSimPoYGJUkoppTyGBiZKKaWU8hgamCillFLKY2hgopRSSimPoYGJUkoppTyGBiZKKaWU8hi6Vs4pGIYBQE1NDRaLxc2tGRzsdjt1dXV6zF1Ij7nr6TF3PT3mrldTUwMc+y7tLg1MTqG8vByAtLQ09zZEKaWU8lLl5eWEhYV1+/EamJxCZGQkAAUFBT06qKr3ampqSElJ4eDBg4SGhrq7OYOCHnPX02PuenrMXa+6upohQ4a0f5d2lwYmp2A2SwpOWFiYfpBdLDQ0VI+5i+kxdz095q6nx9z12r5Lu/34fmqHUkoppVSPaWCilFJKKY+hgckp+Pv78+tf/xp/f393N2XQ0GPuenrMXU+PuevpMXe93h5zk9HTeTxKKaWUUv1Ee0yUUkop5TE0MFFKKaWUx9DARCmllFIeQwMTpZRSSnkMDUxO4k9/+hNpaWlYrVamTp3K+vXr3d2kAW3lypVccsklJCYmYjKZWLJkibubNKA99thjTJkyhZCQEGJjY7n88svZs2ePu5s1oD3//PNkZ2e3F/iaPn06H330kbubNag8/vjjmEwm7r33Xnc3ZcBatGgRJpOpw23EiBE92ocGJl146623uO+++/j1r3/Npk2bGDduHPPmzaOkpMTdTRuw6uvrGTduHH/605/c3ZRBYcWKFdx1112sXbuWpUuX0trayty5c6mvr3d30was5ORkHn/8cTZu3MjXX3/NnDlzuOyyy9ixY4e7mzYobNiwgb/85S9kZ2e7uykD3ujRoyksLGy/rVq1qkfP1+nCXZg6dSpTpkzhueeeA8DhcJCSksIPfvADfvazn7m5dQOfyWTivffe4/LLL3d3UwaN0tJSYmNjWbFiBWeffba7mzNoREZG8uSTT3LLLbe4uykDWl1dHRMnTuTPf/4zDz/8MOPHj+eZZ55xd7MGpEWLFrFkyRK2bNnS631oj8kJWlpa2LhxI+edd177NrPZzHnnnceaNWvc2DKl+k91dTX8//bu76WpP47j+KsGw9ChTIc/MCUJhZAhThyimaFeSHgdQ2jq7YRkeOONIfQHFAThlbsSkUKEQIcY6pWoxcBdCCZFRpuzLkQFvdj83g3ULvTL9Jwdnw8Y7LzhHF5X48X5fNhHuvJhW/h/ksmkJicndXR0pKamJqPjWF4gENCzZ8/O/K7j+mxtbamsrExVVVXq6enRz58/r3Q/h/id8+fPHyWTSRUXF5+ZFxcXa3Nz06BUwPVJpVIaHBxUc3OzamtrjY5jaRsbG2pqatLx8bHy8vI0PT2tR48eGR3L0iYnJ/X161etra0ZHeVW8Hq9CoVCqqmpUSwW0+joqB4/fqxoNCqHw3GpZ1BMgFsuEAgoGo1eeR0YV1dTU6NIJKL9/X19+PBBfr9fS0tLlJNrsrOzo5cvX2p+fl45OTlGx7kVurq60t/dbre8Xq8qKys1NTV16SVLisk5RUVFstls2t3dPTPf3d1VSUmJQamA6zEwMKBPnz5peXlZ5eXlRsexPLvdrocPH0qSPB6P1tbW9PbtW42NjRmczJq+fPmiRCKh+vr69CyZTGp5eVnv3r3TycmJbDabgQmtr6CgQNXV1fr27dul72GPyTl2u10ej0cLCwvpWSqV0sLCAmvBsIzT01MNDAxoenpanz9/1oMHD4yOdCulUimdnJwYHcOy2tvbtbGxoUgkkv40NDSop6dHkUiEUnIDDg8Ptb29rdLS0kvfwxuTfwgGg/L7/WpoaFBjY6PevHmjo6Mj9fX1GR3Nsg4PD8806u/fvysSicjpdKqiosLAZNYUCAQ0MTGhmZkZORwOxeNxSVJ+fr7u3btncDprGh4eVldXlyoqKnRwcKCJiQktLi4qHA4bHc2yHA7HhX1Tubm5KiwsZD/VNRkaGlJ3d7cqKyv1+/dvvXr1SjabTT6f79LPoJj8w/Pnz7W3t6eRkRHF43HV1dVpbm7uwoZYZM76+rqePn2avg4Gg5Ikv9+vUChkUCrrev/+vSSpra3tzHx8fFy9vb03H+gWSCQSevHihWKxmPLz8+V2uxUOh9XZ2Wl0NCBjfv36JZ/Pp79//8rlcqmlpUUrKytyuVyXfgb/YwIAAEyDPSYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAAMA0KCYAssqPHz90586dC5/zBxICyE6cLgwgq9y/f1+xWCx9HY/H1dHRodbWVgNTAcgUThcGkLWOj4/V1tYml8ulmZkZ3b3LS2Ag2/HGBEDW6u/v18HBgebn5yklgEVQTABkpdevXyscDmt1dVUOh8PoOAAyhKUcAFnn48eP8vl8mp2dVXt7u9FxAGQQxQRAVolGo/J6vQoGgwoEAum53W6X0+k0MBmATKCYAMgqoVBIfX19F+ZPnjzR4uLizQcCkFEUEwAAYBpsYwcAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKZBMQEAAKbxH23rbba5IjncAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fill between zs_low and zs_up\n", "\n", "# bbh\n", "plt.figure(figsize=(6,4))\n", "plt.plot(z, bbh_density_median_det, color='C1', linestyle='-', alpha=0.5, label=\"median\")\n", "plt.plot(z, bbh_density_low_det, color='C1', linestyle='--', alpha=0.5, label=\"low_lim\")\n", "plt.plot(z, bbh_density_up_det, color='C1', linestyle='-.', alpha=0.5, label=\"up_lim\")\n", "plt.fill_between(z, bbh_density_low_det, bbh_density_up_det, color='C1', alpha=0.2)\n", "\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"$\\frac{dR}{dz} (Mpc^{-3} yr^{-1})$\")\n", "#plt.yscale(\"log\")\n", "plt.xlim(0, 5)\n", "plt.legend() \n", "plt.grid(alpha=0.5)\n", "plt.title(\"Merger rate density (detector frame)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### BNS" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "z = np.geomspace(0.01, 5.0, 100)\n", "\n", "# getting the median values of zs distribution (source frame)\n", "# det: detector frame, src: source frame\n", "param = dict(R0=170 * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bns_density_median_det = cbc.merger_rate_density(z, param=param)\n", "\n", "# getting the lower bound values of zs distribution (source frame)\n", "param = dict(R0=(170-120) * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bns_density_low_det = cbc.merger_rate_density(z, param=param)\n", "\n", "# getting the upper bound values of zs distribution (source frame)\n", "param = dict(R0=(170+270) * 1e-9, b2=1.6, b3=2.0, b4=30)\n", "bns_density_up_det = cbc.merger_rate_density(z, param=param)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# fill between zs_low and zs_up\n", "\n", "# bns\n", "plt.plot(z, bns_density_median_det, color='C2', linestyle='-', alpha=0.5, label=\"median\")\n", "plt.plot(z, bns_density_low_det, color='C2', linestyle='--', alpha=0.5, label=\"low_lim\")\n", "plt.plot(z, bns_density_up_det, color='C2', linestyle='-.', alpha=0.5, label=\"up_lim\")\n", "plt.fill_between(z, bns_density_low_det, bns_density_up_det, color='C2', alpha=0.2)\n", "\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"$\\frac{dR}{dz} (Mpc^{-3} yr^{-1})$\")\n", "#plt.yscale(\"log\")\n", "plt.xlim(0, 5)\n", "plt.legend() \n", "plt.grid(alpha=0.5)\n", "plt.title(\"Merger rate density (detector frame)\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Redshift distribution (BBH)\n", "\n", "* The redshift distribution of the BBH merger should follow the merger rate density distribution.\n", "* The redshift distribution (source frame) of the BBH merger is given by the merger rate density distribution multiplied by the differential comoving volume and the time dilation factor.\n", "* It is then normalized to unity in the redshift range $z_{min}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the merger rate density\n", "plt.figure(figsize=(4,4))\n", "plt.plot(z, rate1_det, color='C0', linestyle='-', alpha=0.5, label=\"detector frame\")\n", "plt.plot(z, rate1_src, color='C1', linestyle='-', alpha=0.5, label=\"source frame\")\n", "plt.xlim(0, 5)\n", "# labels\n", "plt.xlabel(\"z\")\n", "plt.ylabel(r\"pdf\")\n", "plt.legend()\n", "plt.grid(alpha=0.5)\n", "plt.title(\"Source redshift distribution \\n(Source Frame)\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "ler", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 2 }