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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# automatically reflect changes in imported modules\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"from pathlib import Path\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import astropy.units as u\n",
"\n",
"import utils\n",
"import utils.logging_config\n",
"utils.logging_config.set_log_level(\"info\")\n",
"import logging\n",
"logger = logging.getLogger(\"task1\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"DATA_ROOT = Path('data')\n",
"DATA_NAME = 'data.txt'\n",
"NBINS = 30\n",
"CACHE_ROOT = Path('.cache')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"17:34:01 - utils.load - Loaded 50010 rows and 10 columns from data/data.txt\n"
]
}
],
"source": [
"points, columns = utils.load_data(DATA_ROOT / DATA_NAME)\n",
"logger.debug(f\"Fetched {points.shape[0]} points, columns: {columns}\")\n",
"# reorder the columns to match the expected order (x, y, z, mass)\n",
"particles = points[:, [2, 3, 4, 1]]\n",
"\n",
"# particles = particles[::10, ...]\n",
"# particles = particles[:5000, ...]\n",
"# particles = utils.remove_outliers(particles)\n",
"# logger.warning(f\"Reduced selection to {particles.shape[0]} particles\")\n",
"# TODO: make sure this is not executed in the final version"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Q0BDGx8fR0NCA0tLSqF+GdKXUAoEAzp07B4/HEzGSigTx80ZLHVmtVkxMTAAIntwJAcVqnryUkWxxnqIoGAwGGAwGVFZWguM4rKyshEiwVSpVCAGRmUbxrAnIvBrOehBOOBIhIGkc90VIhLNBiNVbs56E4/V60d7ejkAggObmZuj1+jWvkY6Umt/vx/z8PPLz8wUxQizEMgMNTx1Fap4k5JOTkxP3xvlmgnjIHBBM6xIJ9uTkJHp6eqDVakMIKFodLVNTahtBOOGIl4De7LOAJMLZAMTTW7NeKbXFxUV0dHQItZN4aiCJjpgWg+d5jI6OCo13e/bsiftLlUhkFX5yZ1lWOLlPT0+jt7cXWq1WIKDs7Ox1HR+w3lgv+bFMJkNubi5yc3MBBCXYhIAi1dFI5z5ZU6ZFN8BF94PN3MzFBCQeRmez2TA4OIi9e/e+KQno0v0GXiKIt7cm3REOx3EYHBzExMQEtm/fjtLS0rivkWyEEwgE0NHRAYfDgfz8/IQNKoHkZdFEXp2TkyOshYwPGB4ehsfjETbOnJwcGI3GjNwso2Gj+l0UCgXy8/ORn58PILSO1t/fD5/PJ7hgJ1v7WW8kqlBbb4g94MgcK/F/v5nGcUuEs04gvTUMw8RlT5NOwvF4PBgYGADDMHGl0CJdI9GNf2VlBWazGXq9Hi0tLRgaGlrzGtEUV+lC+MYpHh/Q3d0NhmEE5VZOTk5S5LjR2Iz1ietoAEIk2NPT0+A4Dm1tbSHv42Zv9plGOGIQF5DwCCjWNFRCRpl+j8aCRDjrgGTsadJFOCzLoqenByUlJaivr09KRpxIaovneUxMTGBgYAA1NTWorq4W0hmJklY6zUfDET4+wO12w2q1ChM8iUKOpOAyrQE1U9aj0Wig0WhQUlKClZUVdHR0ID8/HzabTXCoENd/0iXBTgSZTDgk0yFGNCds8Sygd7zjHbj77rtx1113bfSS0wqJcNIMcW9Noj5oqRAOx3Ho7++H1+tFVVUV6uvrk75WvBs/wzDo6uqCzWZDY2OjkM5K5Brh2IiNlaIo6HQ66HS6EPdmq9WK+fl5DAwMCCOm5+bmkJOTE3WU9kYhUy1kaJpGWVkZysrKwPM8nE6noCQcGRkJESmQNNx6v45Im3qmgGXZmIfASATkcrmg0+k2YonrColw0gRxb00y9jSpEI7b7UZ7ezt4noder09qnECia3E4HGhra4NarUZLS8sqRVisOtB6p9QSgdi9ubq6WrC3d7lcmJiYQE9PD/R6fUgD6mYIEDKNcMIblSmKQlZWFrKyslBRUQGO4wQXbELkSqUyhIDUavW6rOtSJpxIkAhHggCO48AwTFIOzwTJEs7c3By6urpQUlKCbdu24dy5c+tuvDk9PY2enh5UVVWhtrY2KnlkaoQTCzKZDBqNBnK5HPX19fD7/YIAYWBgQCick/TbRniXZcL7Eo5YKjWSpjSZTAKRi5WEfX190Gg0IUSejkgykwknGSd3IEg48fSxZTokwkkB8Y5+jgeJdvdzHIe+vj7MzMxg586dQlE3HbWgaGRBTv7z8/PYu3evUJBP5BrJPO9mQ6lUoqCgAAUFBQAQ0oAaPj46Jydn3eoWmR7hxEK4klA8hmF0dBQulystkWQmE06y6T4pwnmTgxSeJycnhfHLqWwIiRCFy+VCe3s7AKClpQVarTap6ySyFpfLBbPZDJlMhpaWlpiS2HjII/znmbahRoO4cC6uW9hsNoyMjKTNOkaMTCTiVOtK4WMY/H6/8D4ODg7C6/Wu6gGKJzrIdMJJZlaV2+1OWG2aiZAIJwmQqIbIj6urq1O+ZrxEMTs7i+7ubpSWlmLbtm0RFS/pjnBI2q6srAxbt26N68sci3Ai/SxTI5y1EK1uYbVaQ6Z3ihtQk3HAzkTRQLobP5VKJQoLC1FYWAggVMre29uLQCAg9ADl5ORE9dK73AjH7/eDYRgppfZmQ3hvjUKhENJqqd7gsQiHZVn09fVhbm4Ou3btEr6Uka6TrhqOOG231nOudY1EcakRTjjEdQtgddpI3LlPGlDj2YAykXBSdTePhXApe/gYBnEqMzs7W+ilymTC4Tgu4TqV0+kEACnCeTMhUm8N2SjWm3CcTifa29tB03TMdFa6ajgMw+DMmTPgeX5V2i7eayRTw7ncEJ42Enfui0/tl6ID9kaSYCQvPXEqc3R0FBRFITs7W7j/M5Gkk4lwXC6X8PovdUiEEweIBUV4b00iA89igaZpYVyBGDMzM+ju7kZ5eXlc6ax0pKXsdjs8Hg/y8vI2pHk0ld+51BDJAZs0oK7lgJ2Jm+dmeqlFSmUSM9eZmRl4vV68/vrrQvSTk5OzLhLsRJGMaIAIBjLt808GEuGsgVijn8mNk+rsGHItMXGJFWF79uwRFFKJXicRkBEGY2NjUCgU2LFjR1LXAd68KbVEID61k8bJcAdsMl46E8l4vVNqiUDcS0VaFAoKCmC1WjEzMyPU0sRijs1o5k0mwnE6nRLhXO6Ix54mnXNsiJkfELzBzGYz5HI5jhw5ktDJLNn1kBEGfr8fO3bswMDAQMLXECPWBrm8vAyn04nc3FyhafRy+EKlgrUcsOfn5+H1enH69OmMccDOxKgLuNjrIh7DIK6ljY+Po7u7GzqdLkSCvRHjzJPpw7lcJNGARDirkGhvjUwmS2uEMzU1hd7eXlRWVqK2tjbh8DuZk7DFYkF7eztyc3PR2NgIl8u1bs2jPM9jZGQEw8PD0Gq16Ovrg06nQ05OTkjzrITQvhWVSoXFxUWUlZVljAN2Jo8nCCfiSBJsQkDDw8Nwu91JiTkSRbI1HCnCuQwRPvo5nt6adEU4AIQvQKymyljrITPXY4Fs/iMjI6ivr0dZWVnSxpvhiHSNQCCAzs5OOBwOHDx4EGq1WpgRYrVa4fV60dvbi5mZGWGjzcrKuiy+aOmATCaL6IBttVo3xQE7k1JqYsQj4glv5vX5fEItrbe3VxhnTiKgdLlJpFLDuRwgEc4FhI9+jvemSNQhIBIcDgdGR0fBsiyuuOKKlIqb8RKg3+9HR0cHXC4XDh06FOK/th69PHa7HWazGVqtFs3NzZDJZPD7/VAoFMIX3+VyIT8/HzKZLGSMNNlAc3JyMnYGy3oj0gEgHgfs9TTOzOSUWqKbukqlWlOCzbJsiAQ72YNQKjWcywFvesKJNfo5FsS1l2See2pqCn19fcjNzYXf709ZSRNPdLK8vAyz2Qyj0YiWlpZVuet09vIAF73XqqurUVNTA4qiopK0UqlEUVERSktLI7o4q1QqgXySbaKMd/2ZhFibezwO2CqVSiDvdBTNMzmllsq6IkmwXS6XQEBjY2OgKCokmiRqwnjWlkxK7XLowQHe5ISTzNyacCSbUmMYBt3d3bBYLNi/fz8CgQBGR0cTvk4i6+F5HuPj4xgYGEBdXR2qqqrSarwZfg2O49Dd3Y25ublVacJ4njfcxZkUfq1Wq9BEKe48v9SmeCaKRN3Hwx2ww4vmqfqWXcoptURAURT0ej30er1A5k6nE1arFUtLSxgeHo7LzoioXhMlHLfbLUU4lzriHf0cC8mIBkh6SaPR4MiRI1CpVFhYWEjriOlwBAIBdHV1YWVlBQcPHhTUO9GuQQZAJfu+BAIBOJ1O8DyP5ubmiE1rkVR/ayFSE6XVahVqGCTtQU7wl0uhFUhdLi6TyZCbm4vc3FwAob5lyTpgX04ptURA07SgJqyqqgLHcYKakNgZkWiS/FGpVAmn6wmcTqcU4VyqiNVbkygSiXB4nsfk5CT6+/tD0kuJXmctRIpOxPWTlpaWmKkUsqZkN5SlpSX09/eDpmkcPnw4oRNdIhtreN7d5XIFPcym5vDb7zyBgddGwXhY1B2sxq3/cAO2N21L+LVkCtK9uYf7lkVzwF6LvC/XlFqiENfKgGD2ghDQ5OQkenp6oNVqhTppot9zl8uV8oyrTMGbinBICq21tVXo9k71SxyvaCAQCKC7uzvidExynXRHOOIa0ZYtW7Bly5a4Xq+YcBIBz/MYHh7G6OioIN9NhGxSSeWRtIdGo8X/fvHP6Hy1L/g6aB4dL/Wi9/QQ3vV/j2FnSz1ycnJgMpnWRfa6nljPaCKaA7bFYlmVMiJd+8nOdllvbLaXmlwuD4kmA4EAlpeXsbi4CAA4efLkKhfstdKZbrcbpaWlG7L29cabhnDEo59Jv0c6vsDxiAZWVlZgNpuh0+lw5MiRiBFGugmHYRj09PRgaWkJ+/fvF27+eK8BJEY4gUAAHR0dcDqdOHz4MHw+HywWS0JrT8fn0flKL7pPDECtU0GhCgoKeJ6Hw+pE99NDqD9Ui/7+fvh8PhiNxktGfr2RLgORbGPCU0ZqtVoQKgQCgQ1pmowXm0044VAoFMjPz4dWq8Xi4iKampqEdCa5F0ktkhCQeP0ul+uy8FED3gSEE95bQ0w309VgGE+RfnBwEDU1Naiuro66qaWTcAKBAE6fPg2FQoGWlpaElW9kjfGux263o62tDXq9XlC9LS4uboqX2uD5EfA8L5ANua5CpcCYeRLbtm0DRVGCh5nVasX4+DgoihLSR+HRZyZgM+slkVJGy8vLGBoawvLyMl577bUNaZqMF8kOOVtvkHWJ/fQAhEiwZ2ZmwDAMjEYj7HY7gNRqOA8//DAefvhhjI2NAQB27NiBBx54ADfccAOAYC/XZz/7Wfz2t7+Fz+fDsWPH8B//8R8hzvATExO455578NJLL0Gv1+POO+/Et7/97aRcLi5rwgnvrSFNjekknGjXEhfpDxw4sGaRHkgf4dhsNjidTlRXV6Ouri6pL14iKTXijBCesktWWp0q4ai1KvBYLXjgWA4qo1a4B8QeZmIJ8dzcHAYGBiCTyaBUKrGwsLCu8utEkCkRGBFvzM3NISsrC0VFRascsEnT5GZEj5kW4RBEU6iFpzPdbjdsNhueeeYZ/PjHPxYIiWEYXHvttdi5c2fc72dZWRm+853voK6uDjzP49e//jVuueUWtLW1YceOHfjMZz6DJ598Eo899hiMRiPuu+8+vOtd78Lrr78urPmmm25CUVERTp48idnZWXz4wx+GQqHAt771rYTfg8uScGL11qx3hEP6XLKysuIq0ke7TiIg83JmZmagVquxbVvyBfJ4Ihyxuei+ffsE5ZgYmzGe4OANe/GnHz0N14obugsEE/Az4FgOV9x2KOJzRJJf9/X1weVyYWRkRLCQIRHQZsivM824E7goGkjWAXu9cKkRjhjifqovfvGL+Kd/+iccPHgQO3bswDPPPIMvfelLaGpqwgsvvBDXc77jHe8I+fs3v/lNPPzwwzh9+jTKysrw85//HI8++iiuvfZaAMAvf/lLNDQ04PTp02hqasJzzz2Hnp4ePP/88ygsLMTevXvxjW98A5///Ofx1a9+NeFersuOcOLprUk34ZB0Hc/zGBsbw9DQEGpra6P2uUS7TrJSZLfbDbPZDIqisGPHDgwNDSX8OsSIZW8jfr5o83mSiXDSkVIr2lKADzzwLvzma3+A0+YS3sutB2tw833H4rqGXC6HVquFXC5HfX19iIXM9PR0iIIrkaa/VJCJEuRIa4rmgG21Wlc5YJMIiJi3pguZSjjJiCzI4z/wgQ/g+uuvh9/vx+zsbFLPz7IsHnvsMbhcLjQ3N+P8+fMIBAI4evSo8Jj6+npUVFTg1KlTaGpqwqlTp1YNXzx27BjuuecedHd3Y9++fQmt4bIinHh7a9JhR0NALFr8fn+ITxiZ+BgvxLN1Erkp5+fn0dnZiZKSEtTX12N5eTktp+Fom//i4iI6OjpQVFSEhoaGNb/YmzWe4K0fvBLbm7fizJNt8Dg8qGusxt637oRckdztHm4hE67gIhsoIaD1sr3PNMKJp/FT7IBdVVUV4oBN0rFi1+ZUHbDJoS0TCSfZ2pLT6RTGSyuVSlRWVib0+52dnWhubobX64Ver8ef/vQnbN++HWazGUqlctVeVVhYiLm5OQDB8fLhk37J38ljEsFlQTjho59j9dYQkkgHaJqGx+PByZMnYTAYcOTIkaTy/YkSDsdxGBgYwOTkJHbu3Ini4mLhOunq5xFfh+d5YVbO9u3bY8o0k60dpSt1VFxTiFv/4fq4Huvz+MExLFQ61ap1+zx+MD4GWqNGiPzECi6ygVqtVqHngnTwp1N+nakptURJUOyAXVNTI0iGwx2wk01fJttcuRFIxmUACGYUUmn83LZtG8xmM1ZWVvD444/jzjvvxCuvvJL09VLBJU84ydjTpCulxvO8kGqpr69HZWVl0qdQ8TC3WITl9XphNpvBMAyam5tDbsZ0qt3IJkeMPt1uN5qamoTTViwkuo6NPsF7nF6MtI9jdmQBXICFscCALXsqkV+eC6fVhVcfPYOp9sfBMizKG0px7KPXYNvBmpBriDdQ4GIHv9VqRV9fX9oK6JmYUktH6opIhiM5YBPFViIO2Jcb4ZCG5lSsbZRKJWprawEAjY2NOHv2LH70ox/hve99rzCmQRzlzM/PCwq6oqIivPHGGyHXm5+fF36WKC5pwhH31iTiGJAOwiGb8MrKCoxGI6qqqlK6XrzjqpeWltDe3o6CggJs37591Q2criiBXGdlZQVtbW0wGAxobm6OO3pL9gu/USd5lmHR9WofpgZmYMw3QKFXYWFiCStLduy+ajue+N6zmOiahjHXCJlchr4zQ5jqn8UnHvwwavZGT2mIO/jFBXQivyYSY3KCT8T9OtMIZz1IMDx9GW6aKZZoR3IPv9wIx+PxgOO4uA958YDjOPh8PjQ2NkKhUOCFF17AbbfdBgDo7+/HxMQEmpubAQDNzc345je/iYWFBWGUw/Hjx2EwGLB9+/aEn/uSJBxxb00y9jSpEo7VakV7eztMJhO2bt2KmZmZpK8lRqyeHpLSamhoQFlZWcLXSBRzc3OYmJiI2UMUDclEOBtFOJZpG+ZGF1BYXQCFMvg10GZpMDM8jxN/eAPTvXMwFhpgzDYAAHQmLeZGF/DKb0+uSThirCW/FjdQit2vo9UvMjWltp4beyTTzFgO2KSulImEk6xTNICkU2pf/OIXccMNN6CiogIOhwOPPvooXn75ZTz77LMwGo346Ec/ivvvvx85OTkwGAz41Kc+hebmZjQ1NQEArrvuOmzfvh0f+tCH8L3vfQ9zc3P4yle+gnvvvTcpscclRzhipwAgOYfnZAlHPLBs27ZtKC8vx/z8fNo2eJlMFnFj8fl86OjogMfjiZnSSgfhsCwLlmUxOTmZsEsBQaadxsPhdnjAspxANgTaLDW62sfB8zzkop9RFAWNXo2RjvGknzOS/Jqc3sPrF2QDELs+ZNp7utFriscBm3TkWyyWmJYxG41kp33SNJ302JKFhQV8+MMfxuzsLIxGI3bv3o1nn30Wb3vb2wAADz74IGiaxm233RbS+Ekgk8nwt7/9Dffccw+am5uh0+lw55134utf/3pS68mcTyMGEh39vBaS2ZTFm/7hw4dhMBiEa6VTYh1+LZvNBrPZjOzsbOzbty/mFyhV40232422tjbwPI+dO3cmRTZkHZkc4Sg1yuAaWQ607OJp2Of2w5ibBR4Az4VNLPUxMOSmL7Uhl8tX1S9I+o3Ir0n6KNPsY4DNH08QyQF7dnYWIyMjIZYxiThgrydYlk1YwZjqeOmf//zna/5crVbjoYcewkMPPRT1MZWVlXjqqaeSev5wXBKEk8zo57WQaIRjsVjQ0dGBnJycVZt+KgPYwiHepMU9PVu3bkVFRUVcrzlZeTUQPA11dHSgpKQELMumdDpca608z2NiYgKzs7NCP4vRaNzQzSuvNAfZRUbMjy8irzQHMoUM9iUnKADNtzSi40QPVubt0Gg0oGU0XMtu8ByHppsb121NarUaJSUlIQaaZOaKzWYT1JUkhbRe8ut4kWnyYyLxVSqVaGlpCWlAjdcBez2R7LTP9R4VvpHIeMIhUc3rr7+O+vr6pE/cYsRLOOK6SX19PcrKylZ98OmsmZBrBQIBdHZ2wm63J9zTkwzhiF/njh07UFJSgtdffz2laINEK+GRFsuy6O7uxtLSEioqKuB0OoVZNgqFAhqNBm63O+3jkMOhVCuw+6oG9J4ahGXGBpbhoDdpsf3INlTtKsf1f38Vnn3kFSxNWcHzPNQ6Fa5492EceefBdVuTGGL5dWVlJbq7u4OecAoFJiYmBPk1Sb9thn/ZZkc4kSBWzmk0GpSWlgpTO+NxwF7vtSWTUrtchq8BGUw44b01ANbd/0wMr9eLjo4O+Hy+Nesm6fZlIxswMcJM9BSb6GgBv9+P9vb2VfWhVNNbkTYikq6TyWRobm4WirtkMxgYGIDb7caZM2c2ZJS0qcCIQ2/fj5WFFbAMh6wcPdS6YCF0a9MWFNTkgrVS8Ln9qNpVjtK61MdZJAuKoqDRaFBdXQ0g+LmR07vYv4y8ZxtxKs7EulI0qXa8DtjkfluPey6Zxk+3270hThYbhYwknEi9NTKZTEippYpYJLG0tISOjg7k5eVh//79a6aW0hXhkNc8MDCA2trapFRhZD1AfAox4vlmNBrR0tIS8jrTRThkUyJy7uLiYtTX1wOA0HxLNgPSkb5ly5aQUdLd3d3IyspCbm6u0MuSrlSOTEYjpziysarGoEbD4Ya0PE+qCN/clUpliH8ZMXy0Wq0h8mFCQOtxes+0lBoQf29QNAds8fjydDtgp5JSu1yQcYTDcRz8fv+q3pp0+58REYL45uQ4DkNDQxgfH0dDQwNKS0tjbvqk0J/KaY9hGHR1dcHn86G6uhpbtmxJ6jrAxfrWWoQjnjwazfMtVSIVG4COjY1heHg4xKEg0rXJusOLweJi+uTkJACEbKaJ9LJcqljr/hIbPhL5td1uD5FfazSakNN7OtRbmZ5SSwSRxpcTAk+XA3ayKjWJcNYBsUY/y+XytKaugNCb0+v1or29HYFAYFX3fjzXSpZwHA4HzGYzVCoVTCZTWgYtrUU44hpKpMmj4mukI8Lp6OiA3W7HoUOH4hqTG+k5w4vp4b0YZDMlVjKZJIVNJxIxgjWZTELtj8ivxfYxRL2VSsR4KaXUEsV6OGAnSzhSDSfN2GiHZ/KhEyUWMaSM1r2/FsQprERv9OnpafT09KCqqgq1tbVobW1Nuy2NGC6XC2azGTKZLOZgtlQJx+12AwjOBYpWi4rkNBwL4WaQJBVisVgwODgIr9d7SU3yjBepfBZrya+Jeis8YoznPbuUU2qJIBEHbEJAkZoiJdFABhCOOKpZS+6c7pQaRVEIBAIYGxvDxMSEoM5KFOHkFQ/Es2T27t0rbATpHjMtBnGVLi0txbZt22J+KVNZC3kuANizZ8+awgfxKTkZkgtPhYitZCYmJkBRlLAR5Obmpt0Kf6OQzmgimvxavHmKBRuRPr9kR2msNzZiNMFaDtjEwDWSA3YyogEppZYmJNpbk07RAHm+9vZ28DyfUAot0nWA+BV04VGGuP6wHk7PHMdhcHAQExMTIa7S8Vwj0c0/XF7d0dERsx8n/OepNn6KpbDECsVisWBmZgb9/f3QarUh6bfNHIWcKNZjcw+XX0fq3o8kvyafU6ZFOJsxXjqSA3YkBwmO4+B0OoO9XXGu0el0pqUVJFOwKYQTKYUWCzKZDIFAIC3Pv7CwAI7joNVqsXv37pQ2HYqi4m7+nJubQ1dXV9QoI91Ozz6fD+3t7fD5fAmTaqJOAYFAAO3t7YKjtF6vR0dHR0IEkm6nAbEVypYtW4SNwGq1or+/H36/X0i/5ebmbngjYCLYKAeGSN37JGIML55nIjJh+JpCoUBBQYFgdun1erG0tAS73Y6BgQH09vaG1H/WkrB7PB4ppZYqxCmUeL/g6RANcByH/v5+TE9PQ6FQoLKyMi0n3FhEIX7enTt3RrX1Tifh2O12tLe3Izs7O6a0O9o14t3kHA4HWltbodfrVzlKJ0o46wnxRhDu5Dw2NhZyUk1X+jad2AwyjCS/tlqtsFgsAIAzZ84IG+dGNE/GQiYQTjjUajUKCgowMDAgOCCQCGh0dHRNB2yn0ykRTjqQ6AjiVGs4brc7JIXW1ta2rh5oBB6PB2azGTzPo6WlZU0VWjTCCfgZnH2qDeaXuuB1+rD1YA2a3tGIvNLVCjNxP8/WrVuTntETb7QxOzuLrq4uVFdXo6amJuS5kk3LbQQiOTmLB6k5HA7I5XKhnmEymTZ1I8sEt2ix/LqwsBAnTpzA9u3bsbKyIqQsN1sxmImEAwRTfaTROR4H7Lm5OUEMk2y6/9vf/jb++Mc/oq+vDxqNBi0tLfjud7+Lbdu2CY/xer347Gc/i9/+9rch5p3iKZ8TExO455578NJLL0Gv1+POO+/Et7/97aQ+200XDcSLVAiHpLJKSkqwbds2yGSytKveIhEFUb8VFhaioaEhZjQVibhYlsPvv/dnnH3aHGyAVcgw1jWBrtd68bHvfgB5ZRfzuwzDoLu7G4FAQOivSRaxUmpk4ujU1BT27NkjpA/Cr7GZKbVEID5l1tTUYHBwEA6HA36/Hz09PWAYJkTJtdHd35lWoCefE0lHkpQlaZ4kisF0yK8TAcdxGWdyClysLUXqd4vkgN3Z2YlHHnkEw8PDmJ6extDQEI4ePYorr7wybgJ65ZVXcO+99+LgwYNgGAZf+tKXcN111wmiBgD4zGc+gyeffBKPPfYYjEYj7rvvPrzrXe/C66+/Lqz7pptuQlFREU6ePInZ2Vl8+MMfhkKhwLe+9a2E34dLinASFQ1wHIe+vj7MzMysSmWtp8uzuIE0EfUbTdOr6lRDraNoe74TpkIjdIZgdMSxHKYGZnDij2/g1n+4AUBQjNDW1gaFQoGsrKyU+3nWikBJbcjv9wuW5ZGwFoFE2jwzaUOVyWTQaDRoaGgQBoGRVNLw8HCIkisnJ2fdN7lMIxxyGBGvKXx6p7h3hTTsktpFIvLrRNeVqRFOPOl7UkP7xCc+gU984hM4ePAgbrrpJjgcDtx7772oqqrCiy++GNdzPvPMMyF//9WvfoWCggKcP38eb3nLW7CysoKf//znePTRR3HttdcCAH75y1+ioaEBp0+fRlNTE5577jn09PTg+eefR2FhIfbu3YtvfOMb+PznP4+vfvWrCVtvbRrhrPcMG5fLhfb2dgCImMparwhHXKhPZBwzEDmlNt49Cb+XEcgGAGgZDa1Bi55TA7j1H24QIriysjJs3boVZ8+eTTlSiEYWxA7HZDLFrA3Filgi3QOZkDoKh3gQWEVFhSCDJVM8u7u7Q07ym22DvxGIpwcn3DxT3LsyODgYMjwtXaSdqYSTTA8Oz/Pw+/24/vrrhfk1Docj6TWsrKwAgNDsff78eQQCARw9elR4TH19PSoqKnDq1Ck0NTXh1KlT2LVrV0iK7dixY7jnnnvQ3d2Nffv2JbSGSybCSUQ0MDs7i+7u7jV7TtI5VoAQhcViQXt7O3Jzc5Mu1IevSaaQAVjd88AxLBQquTASdteuXUIElw7xQaSU2tTUFHp7e6Pa4US6RiaJBtIFsbgACB4yiPigs7NzVSNlOtwjMi3CSXQ9kXpXSPqNkDYZPpednZ10zSxTCScZlwFgdR9OsqOmOY7Dpz/9aRw5cgQ7d+4EECw1kJEOYhQWFmJubk54jJhsyM/JzxLFJUM48UQkLMuir68Pc3Nzq1g5mevFC4qiMDc3B4vFIkwCTdZ4M3yTrz9Ui+eNWlhnl5FTbAJFUfC5ffC6fTBW67C4uLhK8pwOwhGnCTmOQ29vL+bm5hKaAJoI4XAch94Tgzj/XCdO57aj8fo92HvtjozcPMKhUqlQXFyM4uLiVY2U5CRPjEdT8THLJMJJ1UctXH4t9i4jNTNx+i1eyXomE04y63K73WlRqd17773o6urCiRMnUr5WKrikUmpr1XCcTifa29tB0/Sqhspo10sH4fj9fjidTvA8H7dfWDREIorSumJcd9dVePaXL2OqfwYAwINHdnUW9l63A/sPrp4Cmq4Ih+d5eL1eYQJorPeVZVh0vNKDzld74XX5EFB7UFe1NeZ7wjIsHvzYz3Dmr+eBC1L55371CppvOYB//OnHIJNfWs2Z4Y2Ua/mYGQyGuG1kMolw0r2ecO8yIr8m7s0ymSwkaozmGJHJhJNohMNxXFqcBu677z787W9/w6uvvoqysjLh34uKiuD3+7G8vBwS5czPzwvZkqKiIrzxxhsh15ufnxd+liguqQgnksMzAMzMzKC7uxsVFRWoq6uL2548VcIh9QyKolBeXp4S2ay1pqvvOIIte6rQe2oAc7PzYNUBXHXLEdTUbolafE9HDcfr9eLkyZPIz8+P6THHcRz+9KOncOrP58CyHGQyGjbrMhwTXnzyB3fCVBD9vXnld6dw5q+toGgq+IeiwLHAqSfOovG63bjqvc0pvZbNhEwmC7HeieZ8TSKgaH0smVbbWk8fNbH8mkiHiXXM9PQ0+vr6oNVqBQISy6+TqZVsBJJZl9vtBs/zSafReJ7Hpz71KfzpT3/Cyy+/LMxSImhsbIRCocALL7yA2267DQCEFH1zc/A719zcjG9+85tYWFgQlKjHjx+HwWDA9u3bE17TJUM45IYSh6ZiT7Jo0txoION6kwHP8xgfH8fg4CBqa2vhcDjSctqLFplQFIXSrUWw+ZegslHYu3fvmp3eqUY4PM/DbrdjaWkJDQ0NcaUIR9rHcebJVuhzdMjKDp7IeDWPiZ5pnHziLG78+NGov/vqY6eD65bRwslZJqfA+Hm89viZS5pwwhHJ+dpisawaIxCpjyWTIpyNHE0glqyLHSNsNluIYWt2djYCgUBGvU8EyTpFA0g6wrn33nvx6KOP4s9//jOysrKEmovRaIRGo4HRaMRHP/pR3H///UK0/alPfQrNzc1oamoCAFx33XXYvn07PvShD+F73/se5ubm8JWvfAX33ntvUr6El1RKDYAwitjpdMJsNkMul+PIkSMJdzgnKxoIBALo6urC8vIyDhw4gOzsbGFEcqqIJkV2Op1oa2uDSqVCS0tLzA86FcIh4wusVitycnJQUVER1++NtI/D7wmgsDJf+De5goZap0Lnib5VhMOyLObm5qDX6+Fz+SK+bp7n4XP5knodlwLEhfTq6uqQMQLhztcMw2RUlLOZTtHh1jFixwiPx4Oenp4Q89F0iDZSRbLTPuVyedKGsw8//DAA4Oqrrw7591/+8pe46667AAAPPvggaJrGbbfdFtL4SSCTyfC3v/0N99xzj9ACceedd+LrX/96Umu6ZCIc0qXLsqyglqqsrERtbW1SN34yNRy73Q6z2QyNRoMjR44IGvR0WtKEr2lubg6dnZ0JpQuTTamJR0BXVVUJJ6x4QNGhEz4JIm1MHo8HbW1tCAQC8Pv9yK7JAtUKcBwP8qs8x4OmKey6OjMmbm4EwscIiOsYHo8Hvb29WFxcjFnH2AhkUk1JLL9+/fXXUVVVhUAgENK5v97jymMh2Wmfqfj7xbMHqNVqPPTQQ3jooYeiPqayshJPPfVUUmsIxyVDOEBwQ+7r68PKykqIrX8ySIRweJ7H9PQ0ent7I1q4pMtYVExcYv+13bt3r6m4W+s68SJ8BPTExERC16hr3AK1XoWVJQdM+QYAABtg4fMEsOeaHcLjrFYrzGYzCgoKUFNTAwCoLK5G/yujWFlwBDcysKBoGjnFJrztrqsSeh2XE8TWO6dPn0ZxcTFYlhXuRZ1Ot2nO15k47ROAUPOIJL8Wj44Wu19vRKTGcVzC6sTLzUcNuIRSag6HAyzLwuv1xhweFg/iJRyGYdDT04OlpaWokuB0uRYQogifPproTZfIeniex8jICEZGRkJGQCfqdVe5vQxXvrsZr/zudUz2TYOiKDhdLtQfrEXLLQfA8zwmJiYwMDAgSMdJDa1qawW++/w/43/+5TGcf7oDMpkM9W+pwZ6bt6Gzrx3Z87GL6m8G6PX6EBsZm80Gi8WCvr4+BAKBpGTEySITh68Bq1VqkeTXxP2gu7s7afl1omBZNuGI1O12X1azcIBLIMLheR5TU1Po6+uDXC5HXV1dWjadeKIAUidSKBRrkly6mkhpmgbDMDh16hRyc3PR2NiYVM9GvCk1hmHQ2dmJlZWVVZLuZJo2b/r4W1G3rwrdpwbgd/vhVbhwzbuuhNagQXd3NxYWFoS6V/i180pz8L6v3oorPtqIAwcOAEDEojqZZ5ObmyvMZnkzIDyFFe58LU6/jYyMQC6Xh1jvJGpBEguZGuHEkkWH90wRyyKbzSa8b/HIrxNFssPXNtqzb72xqYQTa1MjZpQWiwX79+/HwMBA2twBYkU4xAU5ntpJOiIcnucxOzsLlmVTah4l64mHTNva2qBWqyOOgE50Hg75nW2HarHtUC0A4NSpU6AVFM6cOQMAq0g7/POPNHJaXFQXn+rJbBbxNM/18ObKJER7bdFkxER63dPTk/Y0UibVcAiitU1EQ7hlkfh9C09bEpVcsgecZGs4UoSzQQgv0KtUqrT7n0W6Fumqn52djVtqnWqEQyINm80GAHErw6IhFuGQEdDl5eXYunVrxI0j0ZRaJLAsi/7+fhQUFGDHjh1xfeHWes5Ip3qLxYKlpSUMDw9DqVSmpaM/E5HIZxHufC0eokYUleI0UjKn6EwlHCD5KaTi9w1AyMC+gYEB+Hw+QTVI3K/jfQ+SlUVLNZx1Bs/zmJycRH9//6oCfTrHTEciHLfbDbPZDCCy4Wc0pKJSE0caBw4cwMmTJ1P+MkeLHHmex+DgIMbHx0O816JdIxUSnZqagtPpRElJCXbt2hXX60kkjSc+1RNDTTI/hHT0i6d5rjVV8VJAKvdE+BA1kkYiRK1QKEKIOh4VVyZ29JP7NV3rWkt+PTExAQAh6be1XDiSafyUCCfNCN9gAoEAuru7YbPZ0NjYKJgjEqxnhLOwsICOjg6UlJSgvr4+oZs22ZQaSdtVVlairq5OULql2i0diQD9fj86OjrgdrvjGjedbIRDRkLMzs4iKysLubm5cW+U6fTmIpuDxWLB+Ph4iOHmetQ0NgLpIMxIztfhKq54nK8zMcJJN+GEI5r7dTzy62RrOFJKbZ2wsrICs9kMnU4X0uMiRjrGTBOQTZllWQwNDWFiYgI7d+5EcXFxwtdKNKUmljyL03bkhkw34djtdrS1tSErK2vVCOhoSKaXx+fzwWw2g2EYNDc3o7u7e9Mmfoo3B3FufmJiQqhpkFP9pTBOYL2aPqOpuMTO12KiJqf4TFSpkb1hI4gw3P2aYRgsLy8LY6MJcZMIiGEYKcJBBhCO2CampqYG1dXVUW+YdEc4PM/j7NmzwgaZ7GkikQjH6/XCbDaDZdlVaTsx4aQCMVkQn7lI/UPxXiMerKysoK2tDSaTSVDXZcp4gkg1DYvFImyqPM/H5WcmxvLCCnpODiLgD6B6VwXK60vWXYa8ERtpJOdri8UinOLVanVGOh8AF9N8mxF5yeXyEM88MXF3d3fD7/djeHgYBQUFyM7Ojkt+7XK5Uuo1zERsKuEwDIP29nasrKwIctm1kK4GSyBovAkET8I7d+5MKaKIN8Ih83KimWGSGzBdowV6e3sxPT2dVJNsInUpQmrhB4ZMHTGtVCpDNlWSGhFLr2UymRBRh39ObzzVhj/+25NwWINODCqNEodu2ofbP/eOdXW23uiNVOx8LT7Fk400EAjg/PnzQp0skSL6eiCT6krhxP3yyy/DZDIJNUaxbD07Ozui/Nrlcq0y3LzUsamE093dDY7jIspyI0Emk8Hj8aT0nDzPY3h4GKOjowCAbdu2pdzLEWtz5nkeo6OjGB4eRn19PcrKyqK6PKfDJodlWTgcDiFySyYsj2fz5zgOAwMDmJqaikhqyRDIRp+aw1MjRJk0NjaG5eVlvPbaazCZTEL0Y19w4fHv/xU+tx8FFbmgaAquZTde/+MbKNtajCvefXhd1pkJ0YT4FC+Xy+F2u5GdnR3ifC1Ov210k24mEU44eJ5HWVkZVCpVRNl6JNeIdM3CySRs6qezY8cO7N+/P+4CbqopNb/fj3PnzmFmZgaHDx9Oq0NAtOsEAgG0tbVhYmIChw4ditlfkyrhLC8vY2BgABRFoampKekbNhZZ+P1+nD9/HktLS2hubo4YQWVqhLMWiDIpLy8PBQUFOHjwIHJycmCxWHD27Fk88fO/wrawjKx8nTBKQZ+tAygKZ582J/28rmU33Pboh6lMK9JzHAeFQoHS0lLs2rULV155Jfbs2QOdTofZ2VmcOnUKp0+fxuDgICwWS9pS4bHWlImEQ147WRtJ8dbU1ODgwYO48sorUV1dLbQRPPDAA3jLW96Cjo4OLC0tJfXevfrqq3jHO96BkpJgqveJJ54I+TnP83jggQdQXFwMjUaDo0ePYnBwMOQxVqsVH/jAB2AwGGAymfDRj34UTqczuTfhAjY1wlEqlQnJnFMRDdhsNpjNZphMJrS0tEAul6fNIYBcJ3xTcDgcaGtrg1arjTuKS4VwJicn0dfXh+LiYthstpT6UNZah8PhQGtrK7KystDU1BT1eeIhEPF7lkkbKhBZej1z2gJQFDweL5wuFxRyORQKBWgZBbs18S/jsHkcv//OnzFwbhgAhZ1XbMN7v3QryrauFq9k0vsTfq9TFAWj0Qij0Sg06ZL0W39/P3w+X0jvz3rI1DOdcKJlUsL7y/Lz85GdnY0f/vCH+PGPf4yf/exnuPbaa3HbbbfhjjvuiOs5XS4X9uzZg4985CN417vetern3/ve9/DjH/8Yv/71r1FdXY1//ud/xrFjx9DT0yNEph/4wAcwOzuL48ePIxAI4O/+7u/w8Y9/HI8++miS70QGiAYSQTIRDs/zGBsbw9DQELZu3YqKigrhRk9XhENuJLG6jNQ1qqqqUFtbG/eXKxnC4TgOPT09WFhYwP79+wEETyepIBpZEPfqeEQIl2KEsxZkMhnq9tTg5GPnoNNoQctlguO13WZH0c5cdHd3C+m3WAeMmeF5fP9DD8FudUKlVoDnebQe78Ro1yS+/rfPIafIJDw2096XWCo1hUIhOF/zPB/SwzI2NgaapkPSb+mwkMlkwiHp8ligKAp1dXX4P//n/+Dxxx/H17/+dZSVleH48eMYHh6O+zlvuOEG3HDDDRF/xvM8fvjDH+IrX/kKbrnlFgDAf/3Xf6GwsBBPPPEE7rjjDvT29uKZZ57B2bNnBaupn/zkJ7jxxhvxgx/8ACUlJXGvRYzLmnACgQA6Oztht9tx8ODBkDGqyVwvGsTqMoqihD6U9S7WAwgZAd3c3AyNRgOr1ZpWpRsQvEmHhoYwPj4et3v1pVDDSRS7r96O6j2VGD4/Co1BA5mchtPmRlFFIW7++A1QqxWr7GRyc3MjSq+f//UrcNicyMq+qFhSahSwzS3j5Udfx7vuv0l4bCam1OKtfVIUFeJ8zXEc7HY7LBaLMGpEr9eHWO8kU1fNVMJJps2BNOiaTCYcPnwYhw+nrzY4OjqKubk5HD16cUaV0WjE4cOHcerUKdxxxx04deoUTCaTQDYAcPToUdA0jTNnzuCd73xnUs99yRFOvCk40tej1+ujprPSTTgulwu9vb3C5p/M4KdECIdY/Yer3tJhSyN2GggEAujo6IDL5UJTU1Pc8vFMkUWnEyqNEh/73vvx3C9fQdvzXWACDPZeswPX/d3VqN4dtCQS28lYLJao/SwD50ZAUVTI66ZpGuCBkY7xVc+dSe9PKgRI0zRMJhNMJhNqamoQCASE6Id45CXj4JyphJNM0yewfm7RZPJn+KGxsLBQ+Nnc3NwqWy+irCOPSQab7jSQCOKp4YitcbZs2YItW7ase18PuZnOnz+PwsJCNDQ0JK18i4dwxL1LkYw+06F0I6RFrHc0Gk3cTaMEl2OEAwDGPANu/6d34G13XYWXH30dna/24n++9jj2Hd2Fa95/BDqjdpWdDOlnmZubw8DAADQaDeTaC7U/8KBwcYAdKMCQGzrHPtPel3Q2fioUChQWFqKwsDCi87VCoQiREEdLVabaML1eSMZHDZAaPzcdsQiCuEtbrdaI1jiJXi8ekHkyAIQJpKkgFlmwLIuuri5YrdaovUup+qCRa/A8j9OnT69p8hnPNdbr8ZsJt92DH3/i/2HEPA4ypnS4bQytz3fin351DzRZF321IvWz2Gw27H7bIvpPDcNhc0KlVYKW0fC7A5Ar5LjitospFPKeZFKEs17jCcKdr1mWFSTE4+Pj6O7ujup8nckRTqKEw7LsukU4xENxfn4+xFllfn4ee/fuFR6zsLAQ8nsMw8Bqta7pwRgLlyThRArnHQ4HzGYzVCoVWlpa4ipCphoJkBqRw+EQxgOnirWEDGQEtFwuX/M1pppSI8PSAGD79u1JFwhjEYjL5YJMJhNUMZm0ocbCa4+fwYh5HPpsHeTK4NeI8TMYaRvDiT+8seakUnKvvPPjb4ffyuLp//cifC5/MGqQ0zj07l2gczgsLCwgJydH2Kwy6f3ZKGsbsQceEOzgJw7OxPma2Md4vd6Meo8IknWKBoCsrKwYj0wc1dXVKCoqwgsvvCAQjN1ux5kzZ3DPPfcAAJqbm7G8vIzz58+jsbERAPDiiy+C47iU6kmXVEotkhoMAKanp9HT0yOYYMZ73VQiHDI+QafTobm5GSdPnkzbELZI11lcXERHR4cwAjrWfJ5IMu14IB7KBqzO8yaCtVyrR0ZGMDw8DI7jhBOrVqtNy3vIcRwGz4/CYXGgamcF8srWjnSTQddrvQAgkA35bx5A56u9cY3GpigKd3zxVrzlPc3ofKUXNE1h19UNUGTJBDPN7u5uGAzBkd1OpxNKpTIjNtXNEjGoVKpVqUqr1YrFxUUsLy8LY+gTcb5ebyQTebndbgBIOsJxOp0YGhoS/j46Ogqz2YycnBxUVFTg05/+NP7lX/4FdXV1giy6pKQEt956KwCgoaEB119/Pe6++2488sgjCAQCuO+++3DHHXckfQAFLsEIB4BghEfsW0gomGiEkSzhEIITS4PTPWaaINoI6LVANoJENwW3240TL76OhSErSopKYHUsp5QXj0Q4LMuis7MTy8vLOHDgAORyuTBWYHp6GhzHoaurS1B3JSqXneqfwYMf/RmmBmbB8zxkchpX39GCj3z3/VAo03e7y+RBclkFHpApEnu/SmoKUVITSuzETNPr9WJpaQkrKyvo6uoS5MTxSq/XC5kw8VOcqqysrMTg4CDcbjdkMplA1mKT1qysrE1JuSUb4SiVyqQJ89y5c7jmmmuEv99///0AgDvvvBO/+tWv8LnPfQ4ulwsf//jHsby8jCuuuALPPPNMiDvEb37zG9x3331461vfCpqmcdttt+HHP/5xUushuKQIhxjzsSwLl8sFs9kMmqbR0tKy5iyKaEiUcMhwtrm5uVUEl84x02STJtGG3W7H4cOHhZNuPNcAEis0Ly0t4S+/egq9z46A8XA4x3fB43dDvqzBbZ95e1IeYeG1JK/Xi9bWVtA0jebmZoGkyYnV5XLhjTfegE6nw8zMDPr6+qDX6wU341iuzn5vAN+648ewTFtByWiA5cH4GRz/r1chk8vwse9/IOHXEA37r9sF84tdcK24QctoKJSKC2okCvvftittz6NWq1FcXIyBgQE0NTUJ/SzrNckzXmSaTJtAq9Wirq4OQPB+I+KDqakpwaQ1nvk16USy0z7jVedFwtVXX73m95+iKHz961/H17/+9aiPycnJSanJMxIuqZQaRVGQyWSYn5/H8PAwSktLsW3btqS/ZIkQjsfjgdlsBs/zEQkuHcowch2WZUMGszU3Nyd0kk1kzAFpjG09ZUb/8TFQHI3SugKAAkYHxnHqL+dRvq0UzTcfWPM6kSCOcJaXl9Ha2oqCggJs374dNE2vMmIl90N1dTWqq6tXSYvFrs6Rop9zz7RjacoKWk6D8THgOV54jc/+4iXsv2532sigdn81FCo5rLPLAA+AAhQqBQ6/fR+a3tGYlucgEE+yJHLiLVu2hEzy7OrqAsdxIa7X67mhZuJ4Ao7jQlwv1Go1SkpKUFJSEnF+jVqtFt4rk8m0bhNiUyGcyw2XVIRD6hJDQ0MxJ1bGg0ibXiQsLS2hvb0dRUVFaGhoiPhFS6fE2uFwYGxsLGl1WLxjDsSKN63fAJ8zgPJtJaDo4POps1SAm0Lr850pEQ5JQYY7PUR6vBjh0mKHwwGLxYKZmRn09/cLhoe5ubkwGo1YmFgCRVNgAyx4jhdeB3iAZTk89r2/YMeRrVBpU+tq5zgOv/jC/yLgY5BdaETAx4AJsKBooKAyDwpVeusG0VRq0aTXZEPVaDTC+0MMIdOFTEiphWOtWkm0+TUWiwWDg4Pwer1Jj4+OZ12JvvfEuDPT3uNUsemEE68UlkQYHMdh586dKZMNEJskxM7Sseon6YhweJ6H3W6Hw+HAnj17kn6N4hpONHg8HrS1tQkpyZdGTwabEOnQG1yuUsBpS96wb3l5GfPz89i3b58wKyR8neK/R1uzeMMgXl0k+iGn+4DCC47lwDLB1BYBz/OQy2VYXrRjqG0MO45sS/r1AMDguRGMd0/CkKuHUn0x8nTYnDjzl1a88x9vhNaQ/ugilo1QJOk18TLz+/0wGo1CdKjValPazDI1wol3TeHza8LHR1MUJaTfkqklisGybMK1mMuxBwfIAMKJB0ShVVhYCJZl0xb6rkU4fr8fnZ2dcDqdcdVP0uFkTUZAk1NrsiDd69EIkDgUkCZVmqZRUlsIWkbD5/FDpSGbKA+33Y2Dx/YkvIZAIIDZ2Vn4/f64RyQkInYIbxZ0OByYL17AMz95BbbpFXAcD4riAZ4CBQo5xdkAD3BM6mlP6+wyGD+zKpJRqpXwefywLznSSjjJSNyJ9FrsZUaGzombKXNzc5NSc2ViDSeVPpzwCbHh0bRWq101PiBesCyb8KgGp9N52Y2XBjKccHiex+DgIMbHx4UI48yZM2md+hnpWmQkM7HFiefLmEqEIx4BXVZWlpCDdiLrIf01AwMD2LZtGyoqKoSfNRyuQ11jNfpOD0Fr1EAml8E2ZUd5bSmabzmY0HO7XC60traCoijk5uZGJZtoG2mim5k4+vmXJ7+Iz13zDbhsrmBphQZ0OVqwYKDP0qGkPnmZN0FBZT4UKgV8bj/UuosnX5/bB51Ri+wiY8rPEQnJbvBiLzNxM6XFYgmRXicySO1SS6klApqmBefrLVu2CDOSwqNF8n7FSn0lU8O5HGfhABlAONHSKD6fD+3t7fD5fGhqahIaoNI5ZjqSlJmYCcayxYnnWvGAuEqT5xsZGYHf70/4OuEIf1/FjtKRHAoUKgU++MC78crvT6Ht+U4wfgZVjWW4/b5bUFobf7S1uLiI9vZ2lJeXQ6FQwG63J7TmVFFcXYDP//e9+On9/w3XshsavQpMgAEtp7Hn7Q3o6GmHdkwbUixOdJPasqcC9Ydr0flqLziWhUKlgNflAxtgcfX7WlKuEYUj3e4L4c2URM1lsVgwOTkJiqJiOjlnYoSTrGdZLISPDwh3vha/n5Gk6snUcKSU2gbCarWivb0dOTk52L9/f0gKLZ2EI5Yyi3t6ItUbErlWPOA4Dv39/atGQKdT7UauQxylAaClpSVqeK836XDTx4/i+o9eC47l8NqJV1FSF19EIPZ327FjB0pKSjA2NpaUeWeqG+zOK+tx/y8+gdf/+AYm+2aQX5aL5lsPYMeRbcJp1WKxoKenR+hUJ7WNeFIfFEXh7h98EI9+448wv9gNt8MDjV6D6z5yNd5+z9tSWnskrLe1jVjNJU4nTU9PC07OhKCJ9DoTbWQ2Yk2RnK/Dp3eKna9NJlNSRCil1DYA4ibHSKaUQPoJh3gWmc1mUBSVdE9PIkTh8/lgNpsRCATQ0tIS4iqdbsJZXl5GW1sbcnNzsWPHjrhOWjIZDZmMjlvQwXEcuru7sbS0tGoMRDLkkY4TffWuClTvqlj17+Gn1XBTTZKr9/v9a27wWTl6fOLBD8MyY4Pd4kBBeR50psTdwePBRnqphaeTxNJrsZUMwzBpicTTic0gQTK9k0zw9Pv9Qvqtp6cHDMOAoijYbDZkZWXFLdaQIpx1AnnzxUX6Q4cOwWiMnAdPZERBLMhkMvj9fpw6dSouy5hY1/L5fDEfRwggJycHjY2NqwQQ6SIciqKwsLCAiYkJ1NXVobKyMqm+p1hr8fl8IfN4xBFCop5uyWyo1lkb+s4Mg2UY1OyrXtWxH+v5xMoucfSztLQEjuPAMMyafS25JdnILVltoJpubFb6KpL0mqTfuru7MTw8LLw/2dnZm+rWnAlRl1KpDBGzuFwutLW1wel04uzZsyHO1zk5OVHrw263OyVbqUzFphMOENyEzWYzDAZDzCJ9KmOmxSD9IYFAALt3707JHwiIjyjICOi1CCAdhMNxHAKBACYnJ7F//37BJiVRxCKMlZUVtLW1ITs7Gzt37oy42axnhHPi8TP468PH4VoOGh2q9Wpc+e7DaDy2Gy/8zwn0nxmG3qRF082NuPL2ppjWNuLoR6lUwuVywWg0Cn0tKqUKeflBKW0ytZ9kkSkO2mKCHh8fx549e4QIaGBgQBgjTQhoo/tIMoFwxKAoCnq9HjRNY+vWrdDr9aucr4lYIycnJ8RJw+VySSm19cDk5CS6u7tRW1uLqqqqmDcoiUpSAZEgO51OUBSVMtkAa4sGwkdAr0UAqRIOSddxHIeGhoakyQZYuy9mdnYWXV1dqKmpQXV1dVTyjGWvEenv8Wyw491T+PNPngHDcCioygdFUXBYnHj2Fy8H3Zc9fiiUcsyPLWDYPIbhtjF89Hvvj3tDoigKCoUClZWVsI+7cfw7z2Dw/CgUKjnqr96CQ+/bjeLyIqH2s942KZlWoCdd/Uajcd2k18msKZMIh4Co1CI5X5N0JRnSt7CwgLGxMczNzaG5uXld1/XQQw/h+9//Pubm5rBnzx785Cc/waFDh9b1OTedcLRabdS5LpGQag2HnMoNBgMaGxvx+uuvp0VxE000IC7YkxHQayEVwiGvzWQyQafTpWzsGCmlRqTqExMT2LNnz6qpgOFYr5Ra+0vdcNs9KKopFH7PkJeFmaE5MH4GZVuLhSZWj9OLs0+bcdUdzdh6oCbi9WaG59F7cgCggF1XNgj/3n2iH//y7h+CYy9MP/UG0PnsAFYmnfj7X9yJ+bl59Pf1Q6fXhSjf0playkRFWHjjZ7j0mtQPxa7XxEgzXul1oshkwom0LpVKheLiYhQXFwvpyqeffhpPPvkk2tra0NfXh4GBARw7dgzXXntt1DJDMvjd736H+++/H4888ggOHz6MH/7whzh27Bj6+/tjfqdTwaYTTl5eXkI1mWQJh+d5TE1Noa+vTziVE1ubdEwKjEQUpMGyoKAg7imgyRIOkVeT13bmzJm0Tf0kYBhGiAzjGTWd7FyeeH7HbfcAVChJ8TwPvzcAmZwOcUxQ61RwO7wYODuyinB4nscfH3wKx3/5Cnwe/4XHK9FyxwEcuHUXfvedP4NjOdCyi6OgOY7DeNc0fvulv2BudBE8x2Fr0xY03roTCwsLCAQCIZ5myYwaT/T92EjwPB+TBImrdU5ODmpra0OMNCcnJwEgxPU6lU5+gkwkHGLHFeu7T9KV73nPe/Ce97wHb3nLW/C2t70Nfr8fX/rSl1BaWornn38+bev6t3/7N9x99934u7/7OwDAI488gieffBK/+MUv8IUvfCFtzxOOTSecRJGMaIBlWfT09GBxcTEkpUVugmRHwIavixChWCJcX1+P8vLyuK+TKOFwHIeBgQFMTU2lXV4tTqm53W60trZCpVKhqakp7uhpvVJqpVuLQFEUmAADuSJ4GwdfLx8yo0a0kIg1nNbjnXj6Zy+Alsmg1l1wCrC48NxPX4WhSI/+N4ZA3DkZhgXPBkdA8xyPzld6YcwPOlC0PtOFye5ZfP5/7oXapBJmtAwODgomkal4mmVShJOMai4e6bXYFy9R4uB5PmMJB0DCn7nX68UVV1yBm2++GUDQeidd8Pv9OH/+PL74xS8K/0bTNI4ePYpTp06l7XkiYdMJJ9EvUqKiATIlUyaTrepBITdnOufYiA0xwyXCiVwnHvj9frS3t8Pr9a6yj0nHuGaSUrNYLDCbzQkr+dZTpbb/6G6c/NM5jPdMQWvQgpZRcNpcyC40wev2gfEzwYFoPA+HxQm1To3dV29fdZ3Tfz4HJsBCDsBt912wBQK8Th9e+sVJqPVquJZdYPzsxddC/o8HdKagzFVr0GBpyoJXf38a77r/JtimVjB1ahE+jx8lDTowRhZ9fX2YG1qAc9aLnPxsNN14APnFsfu9MjHCAZD05h6pk1+sfBNP8Yw3QiRr2kyVXCSQvSWR94qo28TTPtNZI1xaWgLLsqtUcIWFhejr60vb80TCphNOokgkpbawsICOjo6oYwzIuIN0EU4gEMDp06djjoCOdZ14CMfhcKC1tRVZWVlobm5eF3k1TdNYWlrC/Px8wpEaQaKbZbxEqTNpcfcPPoBnf/EyOl7pBc9xOHD9HjTfcgCPf/+vGOucvOCnBqg0Ktz6j9ejOIJkesXiAMdxcDv84DkeHMeDpoOkszLnwM4r6nH6L+cQaUksy8Lj9EKbpQEto0HRNPreGMLfHj6Ov/z7c/B7/aAogJbJsP9tuyBTyHD26Tb4PQHwPIcn/u0ZvPWeIzhw3Z41o59Mq+GQ+ypdawr3xXO5XLBYLKsixLWk12RNmRbhsCwrDGhMBJK1TYYgHoIQe7CRrvdoSNekTofDAY/Hg8rKypRm9MRDFHNzc+js7AyZOJrMddYCx3FwuVxYWVlBY2OjoKxJBLEiHJfLBY/HA5PJtKoWEw9yirPxvi+/E++6/0YMnB3B9MAcFict+OQPP4z+M8MY7ZyAJkuDxut2o3r36iZQAKjZW4XOl3vh9wYA8GS0DXgeoOU0jHnRZ8rzPA+/xw9tVvD0yXM8eJbHn3/yLAAepsJgus3n9uP1P50FBUCfrYO+WAee42FfcuDV//cG6vZWY2lpCX6/X5AVE+UbeV8yiXDWsxGVSIn1ej0qKysjjhEwmUyrfMwymXCSibrWUxadl5cnzBUTY35+Pi0u/GvhsiMckmbyeDwhHmxrXS+VjZm4IwwPD0Mul6OhoSH2L62BtYiCzAIaGxvD7t2712wMSyWl5vf7YTabwTAMqqurkyIbgmhrICIH4mxNNpBE4XX58LP7/xtdJ/rABIL3hSFXj7v+5b340Nduj/n7V723GX/41yeD67wgQuC54H+7bG7Mjy2AltPg2QvzdS6sl/EzwXrOhdfotntAy2io9SoEvH6YiozChqzWqbA0aQFFU9BkBVO6lIyCIT8L9kUHrANOXPd3V8HtdgtNp0NDQ1CpVALxZFJaLdWUWiIIHyPgdruF9BvxMSOqNyCziBlITpDEMAy8Xu+6EY5SqURjYyNeeOEF3HrrrQCC63zhhRdw3333rctzEmw64SR6g6wlGiANpEajES0tLXGNMUglpUZUWw6HA7t27UJ3d3dS1xGDEE54GiUQCKCjowMulwvNzc1xKcSSIVKSqjMYDCn3TkQiPUKa4+Pj2LVrFwwGA1wuF5aWljAxMQGe59HV1YWCggLk5uZCr9eveY889dPnYX6xCzqTFgaNEjzHY3nBjl99+Xf42p4KGPPWHivBMixUWiU4lhPWqlApQMsoMAEWfj8DmqbBMAx4DsEUmZwSXhvjZ2CbX4FSpcBbP3QFfG5fMEqiKHAMB7fdA6/bB5blIEPoBk1GpjuswX4wnU4HnU6HiooKsCwruB5MTEwgEAjAbDaHKN82a3NNd0otEYT7mBHp9dTUFADg/PnzwntkMBg2nYCSnfYJIOZhORXcf//9uPPOO3HgwAEcOnQIP/zhD+FyuQTV2nph0wknUcjl8lWKFJ7nMTk5if7+/rgbSAmSJZzwEdCBQCBtHmhAaN6ePJdGo0Fzc/O6jUuYn59HR0eHkKojI7XFcC67MHh+BDND81DrlKjeVYmqXeURT7vhhMOyLDo6OmC323H48GFoNBp4vV5kZWXBaDSipqYGL7/8MvLz8+FwODA+Pi6cYMkmIj5EcByH1/90FnKlHOoLDs2UjIKpwADbgh1tz3fh6jta1nzNLMNBoVKAomkEvH6AByhZ8L2TyWnwHA+WucA0fLDGw7EcQAF1jdW4+n0t4Hlge8tWVO4ow2uPn8ErvzsNn9sP29wKGH8g+B7wweeyWxww5AY3EsbPgAdQ0bB6sJ9MJhNO9gUFBeju7kZubi4sFguGh4ehVCqF92WjLWUyZfiaWHpdVFSE8+fPo7S0VHC9BiD8PNUhaskiGeNOt9sNAOvqNPDe974Xi4uLeOCBBzA3N4e9e/fimWeeWXc7nUuOcMRSZlJ/6e7uhsViSarWkAzhzM/Po7OzExUVFairqxNyyJEik0QhHg9N07QgfEh03HQihCM2TRWP7g4nDLvFgWd+/iKmBmahVCvBBhj0nB7Ewev3ountjauuK/59r9eL1tZWyGQyNDU1QaFQCH1QJGKlaRo0TSM/Px/V1dWCE+/S0hJGRkbQ3d0No9GIvLw85ObmQk4HxwLIFaGbLS0Lvodue2wpaUFlHuQKGexLjmBKDRTkFC6kx5QXajRqeN0+cAwX8n4wARZ55bnY/7bdkF14zkM37sNLvzmB3lODCPiZ4Fp4QK6kwbE8VhYdoGUyUBTg9/hRvasC+47ujLlOmqZRXl4uzLMhBpHiuka6pnnGQqaJGICLqStxI6XdbofVag0ZopbKWIpkkEyE43K5oFar1/0Qcd999617Ci0cm044yaTUgOAH6ff70dbWBoVCsco4Ml4kujETMUJ4DUVMFKncKGKp9vj4OEZGRrBz504UFxcndJ14azgsy6KzsxPLy8urJpuGvzddJ/ow2T+DioYyyOTB17iyaIf5xS5s2V2JgorVI6R5nsfKygpaW1uRl5eH7du3C89L0zSUSqVA1g6HAyzLgmEYBAIBQT6bnZ2Nuro6wTrFYrFgZGQESqUS2eUGTHXNQmPQgL5wL/ncfshkNCq3l8V8/a/89pSgTCPvl98bgFwhw46rd2KqYw5bD9dirHMStrnloOJIQYPiKUwNzOJf73oYVTvKce0Hr8C1H7wCap0K//DTj+HTzQ+AYzlQNAWtUQtToQF+bwCLk1b43X7oTFocvHEfbv+nt2NmeB7dJ/rBcxy2t2xD1a5Ql/TwDV4c/QAQaj/i90Ws6krXhFyCS2H4GkVRgvRaPJJc7OKczubcaEg2pbbRPnQbhU0nHCCxAjeRGM7Pz2NwcDCq5DlexBvhhPe8hIe7YqJIB+F0dXXB4XDENd462nVivS6PxyP0KDU3N69KOYR/LiPmcWRl6wWyAQBjvgHj3ZOYG1uISDgMw+CNN95AbW0tKisrhShQ/FqJYqa7uxvV1dXQ6/XgeT5k/TRNQ6VSoaysDGVlZWBZFsvLy1h+jxOP9T+JufGF4PRNHuACHHa9pQH1zXVrvn6/N4DX//gGDDk65JflwDpjg+dCxETJKBTV5WOmex622WX4PX7IlXJodCp43X4EvAHIaRlYlsfM8Dz++6t/wKuPncb1H70We67ZDmOeATqjFnrTxWhDoVLA4/Ti5r+/Dsc+eg3UejX+8K9P4vn/evWCSg7460PHcdUdzXjvF29ZtYFGQ/g0T6LqGhoaWpfoJ1MjnLX2gEjS6/DmXJJ6M5lMaSNpafhaKDKCcBIBOXEPDAyEpH+SRTyEIx4BHannhVxHvL5kQTqK/X4/WlpakvZDI31B0WCz2dDW1oaCggJs3749rhoMLaPAcatFAJFy+sSNm2EY7N+/H/n5+UIkQ4rl5HFjY2MYHR3Fzp07BR8nQkziVCVJvZFDR3Z2Nm78wHUoKy3DX/7jWUz0ToOWU6h6Syka37MdIyPDwgYS6fW5Vtxw2z1Q69TQGjTQGS+ecif6p7EyZ4dldhnuZTcYhgX4oJea8P7QFLgAK9js9J8ZwvzoIrbsrcTWg1vQ+lwHdMaL0mbXigcqrQr7rtsNtV6N1uOdePYXL0GukCHnwlhqt92DF//nBOoaq3Hg+r3CexQvxDUv4GL0IzbUFNd+ktlYM6WGI0YiLgNi6bVYoCFOURqNRiH6iSVcWQvJ1HAI4WQaqacDlxThkLHTPM9jx44dadGMxyKc8BHQ0W4CIu9NhXCWlpbQ3t4OiqKwffv2lMw314oayRjtrVu3oqKiIuprCk+p1TVuwauPn0HAF4BCFRQuWGdtyMrWh8yhIWk6m80GuVyO/Px8sCy7imyIi7bVasWBAwdWpfOAUCJnWVYgIfFntv2Krdhx5TYEvAwUKjl48LDZbFhaWlo11TMvL0+I5PTZOuizdVhZtENruNjJ7XX5QMsodL00AKVagYBKIUiuxfB7guTD4+L7zHEcek8PonJnBTRZGixMWACOh9/PQCajcfgdjZgdnscvPv+/GGwdgd8TgDZLDddK8KCh0avBBBi88WQbimsKsTBugUwbfA6H1Qm1Xi1Y9LhW3Oh8tRcOqwsltYWoP1wbEn0CgNvmxYn/PofOl3tBy2nsuGor9EezMGQbCtlYxT0tsXAppNQSQaQUZaQR0oSAElFuJlvDkSKcTYbNZoPZbEZ2dja0Wm3KTsgE0QiHjICemZkJ8ShL5lqxQE75Q0ND2L59e1rsJSLVpsSvKZ4x2uGktePINkwPzWG0cxK4ENloszRovuUAcoqDbt/EHZuiKFQUVeGp/3kOyx0e5BSZsPetu4RGSpKi5DgOhw4dill/I4IC8jpIyo0QEADQCgocH9x4cnNzBdv88KmeOp1O2GSP3HYIf/nJs7DNr0Bn1MLv9cNucUJn0mJx3AKO4eFxeuN+321zKwCA7ld7g5sydSEFRVNQKBU4/dfzOPH4GcjkNDiWA8dycC67LzgS0HCvuMFTwNmn29Hxci/8Xj9YhgVP8cgpzIbOGJzvs2VPJX7ztT/AMmsDBYCWy1DXuAV3f/8D0GcHNyvrrA0PfuSnmBtdgEIlB8fxmP3FPMbbp/GZ//w4WLBCT8vo6Gjc0U8mRjjJRBLREGmEtMViWTXDhvT/rPW8ydZwLsdZOECGEM5ap3Ge5zExMYGBgQFhcNnp06fTNmY6Uq2DzJRhGAbNzc1xFxSTkSJH8l4bHBxMi/Gm+BqBQCCkITaeE1T4NbQGLW742Fsx2jGBhcklqNQKlDeUoqQmGGna7Xa0trYiJycH6oAO//mZRzE1PAO5vBsymQwv/fYkPvad98NUaoDZbEZWVlbUwW1rId7oh0SdOp0uZKon2WQ7OzuhKOew9+0N6H15GMuLdihVCpTVFWOofRQumzuipU28IHJoAODZoCsBLgjnWCbUhYG/IJsmWFm0w5Crh1qnhmXWFpRicxR4Hnjy4efBMixoGY3c0mzI5DL43D70nhrAn//9WXzgn98FAHj5f09ibnQB2cUmQUUX8AUw1DqKs0+344rbDgkbK6n9WK1WDA8Pw+PxRI1+LsUaTrIQj5AGLs6wIcajPM+vKb1mWTZhObbb7V43EcNmIyMIJxoYhkF3d7eQciEf+nqMmSYQj4DesWNHQjnuRG1ySNGepukQ77V0+aCRDc3pdKK1tRU6nS5qDSraNcJfj0qjRP3hWtQfrg35d2K3U1NTg7LSMnz/zv/A8vwKKuvLEGAC8Hq8GOsdxyNf+hWuvucQiouL0dDQkJZNIlr0Q+o/YtsTIrsmxWO73Y6KygpsfUsVZkfmQbM0nn/4FJgAmxLZxAQFIMZH7HZ44PME/dhkcho+tx+aLDUYfwCWWRsqGkqFFJpKq4JGr0br8Q686zM3QqNXo/v1fsgUMoFsgKBwgWM5DLWO4IrbLg7bEtd+whWBJPohmyrHBSOzN55sw+zIPIq3FKLx2O5V6byNxEY5RYfPsCGu17OzsxGl18ms63Kd9glkMOGQWeAKhWKVEWa6DDfDrxXPCOhY14qXKMSzcsKL9ukiHI7jsLi4iPb29oT7eID41IPiHp7du3ejoKAAQ22jmBtdQE5xNlRqFVRQBQuvHIX54SUE7Czm6XlYLBYhdx7e1JksokU/YhECeW00TQtNp1u2bIH/iB//8y+Pw+PwQpujgsvqWjfS4ZjYny/H8eD9DGQKWVCcwfFgfAzkSgV4jkfAHwBwsfYkV8rB+Bj43D5o9GqotCphcFwIKApK9dopaY1GE6IIJGmlkZERzAzP4y9ffQH2BScoOmgFVFCZh68+8X9QtGX9hnethc1I81EUBYPBAIPBIEiviTtEb28vAoGAsCe43e4Qb7y1IBHOOiP8Q5ibm0NXVxfKy8tRV1e36kZKdETBWiDRUldXFxYWFpI2qgTiIwpxinDbtm2oqFhtKpkOwgGCN67ZbI5pYBoNsUQQJB1os9lw+PBhZGVlgWVZeD0+cCwH2YWGTFJH8QcC0Kg12Ll9F0q3FgmF/YGBAXi9XuTk5AgElK6UwlrRD7mH3HYPul/rh8PqwtzAIuQyGZwLHsFdYLPAc7ywoZMNValWAAj+e8DLwDa3guWFFTABFjRNoWpXBQwX6mQHb9iLgXMj8Lp8UOtUQTnwihtKlQJ73xq72ZRAPBq5trYWn/qHL8Gx5BLWCABLUxZ8630/wg9e+79pq68mgnTWcJKFQqFAQUEBCgoKBOl1Z2cnXC4Xzpw5I3jjxeqPkkQDGwTxMLGdO3dGVaGlM8Ihkki9Xr9qXk6iiLUuospaWFhYc6x2qoTDsixmZmbg9XrR1NSU9GjatdyefT4fWltbAUCw2yEbeWVDGYz5BqwsrCCnJBt2ux0swwJ+CoVV+SiqzhcK+7m5udi2bZvgp7a4uIiBgQFoNBqBfLKzs8EyHObHFqHSKJFXlhPxpMgEGPSeGoRtbhmF1QWoa6xeFTkCoZHokHkU//XPj2Fp0hI07FzxwLXsBo+gtQ3jT899lgx4jodMrQDjYwDwMOQZQMtoOJddyCkyYWXRDp/bf8HeOvg7k71TGDg7gvrDtbjitkPoPT0I8wtdcC4HCUKhUuDaD12Bhhg9StEw2jGBmf75Vf/OsTym+mbx0//7K/A+HgaTAc1vP4Ct+2o3pN6TacPXiPRaoVCgvLwceXl5gvRaXCMjaUqx9NrlcqG0dLXd0eWAjCEcUqgPBAIxxxenq4ZDfKlomsbhw4dTvmHXquEQ9RbP8zGJLRXCIc8TCASg1+tTmoMeLaVGxAHZ2dnYsWNHyOumaRo6oxbX3XU1/vDg3zDSPQ6VRgGal0GbpcH1H7tGkFSLQYwriSU9acrr6urC0Olx9D4/DLfFC4VKgdp9VXj3Z98RMt9mbnQB//EPv8TUwCw4hoNcKUdd4xbc88M7hRO/GDRNI+Bn8Ltv/RlLU1bkV+RBJqfhXHZjqHU0OBsHm0c2BIwvmFKTKWjQMhrz44vIytaj5Z0H8PgP/gaKDgojZHIaSo0SAV8Av/v2n/F/n/gsFCoFPvFvH0L3iX70vTEEmUyG3Vc3oHZ/ddIksLywsubPX//l+WCdiOPwwq9ex6Hbd+PoXVcKEVIqZrBrIdMIh4A0foZLrz0ejyA+IJ6BTqcTU1NTWFpawrZt29K2hm9+85t48sknYTaboVQqsby8vOoxExMTuOeee/DSSy9Br9fjzjvvxLe//e2QKOzll1/G/fffj+7ubpSXl+MrX/kK7rrrroTWkhGEY7PZcP78eeTk5KCxsTFmLj+80J8oxCOgS0tLYbPZ0nKzRqvhECFCbm4uduzYEVOVlSzhEAuZ3NxcFBQUYHh4OOFriBGJcBYWFtDe3o4tW7YIfmfhqjAA2HFtHcZmtmOmfREBB4vS2iI033JwldggEuRyuZCa6H69H3/403PwOL1QZing8Xlw7ng7pkdm8Y//724UlQWL/z/77H9jvHsaxvwsyJVy+D1+9Jzsx6Pf/CM++eCdEZ9nqHUU86OLyC3JFvzYdEYtFGo5/O7oTbMbAgrQ6NRQahUo3JKHfTfvQOsfe7A4sYTlhRX8+cfPIuALerXRNAWFSi4Q+bB5DK4VN3RGLWRyGXZfvT3itNNkULp1bYulgI9Bfnmw6dS17Ebbn3qw+8rtsNvt6OnpgcFgECLbVBoqw5GqpdR6IVqqT6PRoLS0FKWlpYL0+umnn8ZDDz2E4eFhdHd3w+fz4frrr8ehQ4dSqm/6/X7cfvvtaG5uxs9//vOIa7zppptQVFSEkydPYnZ2Fh/+8IehUCjwrW99CwAwOjqKm266CZ/85Cfxm9/8Bi+88AI+9rGPobi4GMeOHYt7LRlBOD6fD1u2bFmzCVGMVEcKEOXbwYMHwbIslpaWkrpWOCIRBWmyTESIkAzhzM7OoqurS3DLXlpaSnmGingdPM9jdHQUw8PD2LVrFwoLCyM2cwLBZtne3l5c/c4rUP4PiU8JFePVx07D7wmgtLboQk2Jh8ftwcK4BX/51dOof8sWeOb9GO2agD5HJ2y6Kq0KTICF+YUuWOeWkVNkWnVtr8sLJsDAbnHCbnGADTCQqWVQapTwuwOQyekQqfKGggeM+VlQ69VYWXSi47k+LE5akJWrh1whw2TfTNDJmmPB0RdGKfgYKFVy0HLZuinGul7rAyWjhFlAq5bN8eCYYP1OZ9LCvujAXJcF7/3CLfB6vYLrATnVJ9tQGQ6O49YtekoF8fThEOn1+9//frz//e/H0aNHsWPHDgwNDeHmm2/G3r178fzzzye9hq997WsAgF/96lcRf/7cc8+hp6cHzz//PAoLC7F371584xvfwOc//3l89atfhVKpxCOPPILq6mr867/+KwCgoaEBJ06cwIMPPnjpEU5xcXFCKbJkRQNutxttbW0hI6CXl5fXpaeH4zj09fVhdnYW+/fvT2i4WDKGohMTEyENqukQHpAIh+M4dHV1wWKx4NChQzAYDBHJhsy6mZqawt69e5MaqBaOmcE5qHUq4TlomoJOr4VD6USBoRC7du3CiZEz8Hl9kKlpsDwDuVwOhVwOhUoOj8MLh8UZkXDKtpXA4/RicdoKmYwGx/OAiw9O+5TRm6kXAAAsTlqQX54HHjxm+xegN+qg1qqwvLACVqQ+o6jg/wR8AYDn0XLr3qCv3DrgzF9boVCtHQFS9MUppTwAn8sHAFCr1atO9WSQGol+xA2ViUQ/mZpSS6bxk2EYHDt2DO9973vBsiwWFxfXaXVBnDp1SjhEEhw7dgz33HMPuru7sW/fPpw6dQpHjx4N+b1jx47h05/+dELPlRGEk4z8OFGSIPLgcLPPdEusOY5LunGUIF6yIAPgnE7nqrpXugiHZVm88cYb4DgOzc3NUCqVEcmGKNYcDgcOHTqUNpVNXnkOlmasIf/GsRx4AKaCYNH18DUH8OS/vQggqBRimAB8Ph88di/kcjke/9Ffwfl4bNlTgSPvPISi6qB01za3LIwkYDnuQlTAg2VYmPINWLHYsZllHJbhsDi5hIYr6jDePQ2FOniCd9u9QVm3nA66EHAAEGwyVWqUeN9X3rlua3I7PFCqlQh4AhEJWa1TCeMhGD8DiqJQs69q1ePEDZW1tbXwer1CTWNiYkIQlRACihW9ZGJKjRzWknWLBoJ7ynqPfZ6bm1s1B4f8fW5ubs3H2O12eDweaDQaxIPMOxLEgUREAzzPY3h4GGazGdu3b1/VbJhOwqFpGm63G6dOnYJKpcLhw4eTkvfGQxZut1twXIgkskhlxDSB3+/HysoK1Go1Dh06JJANkegSsvF6vTh79iz8fn9ayQYAjtx6EHK5DNa5ZbAMC7/Xj4XxJeSWZGPfW3cBAAqr8nHopn3wuXzwOnygeTlYDw/Gw4LxMeh6rRe95wfw5P87jn/92H9goC1Y2xrrnIRCLYe+QBMUEXgCYFkO6iw1aKUMFLX5Xw+W4TDRPQ2P3RskSOACSQYjCblcBn22DjqTFmqdCodu3CfUUNYD21u2gec4ZOXrEX5OpGU0aBkF14obTpsLzmU3tuypwIEb9sa8rlqtRklJCXbt2oUrr7wSO3fuhEqlwsTEBE6cOIFz585hdHQUdrs94n2diREOMbZNhHCInDrWtM8vfOELQs002p90WGSlGxkR4SSKeEkiEAigs7NzTZt/Iv1Nxw3r8XiwtLSEuro6VFcnrwSKRTgWiwVmsxklJSVRRzOkGuEsLCxgaGgISqUSu3fvDhkXIBYH2O12YfRxupwDxGg8tge2+RUc//UrWJqygpbRKKkrwh1feidMBRc/zw999d0w5GbhtcdPw+vyQW/SgpZRMOUbYMwPpgB9Xh/mRhfw39/5HW789DWYnJ6E3xcAx/AAx0OhkoOiKHgcXgQ8AaizVHBa0uNokQrcDi9YhsHyoh0cx0OlVcJj94DnWWTlZMGYnwXb3DICfgZ9p4fw0H2/xNvuugrbDtakfS1HP3wlXv/zG1iZX4GxwAifyweWYVFYnY+P/+uH8PL/vo6u1/qhVCvQfMsB3PTJo1BpEuvLEUc/NTU18Pl8guvB5OQkKIoKqf2QmUqZRjhi5WYiiMfa5rOf/WxMhdiWLVvier6ioiK88cYbIf82Pz8v/Iz8P/k38WMMBkPc0Q2QIYSzHik1Yuei1WqFVFC0awGpnZBI/5DFYkFOTk7cH3Q0rEUWExMT6O/vR319PcrLoxfkkyUcsZFoeXk5bDabYA9DuvMJyAybLVu2JOXMEA8oisLb7rwKh9/eiImeKSjUCmzZUyk4JhMo1Urc/k/vwM33XgeHzYWekwP47befgDE/ONdeLpdDrpcjvyQPnvkAGB+LnBpD8ES57IZSrQim1HgeLHPBzXqzBANhYLwXSc9uccCYFxQTEPPP2eF5sAwHnVEDrVGNnpMDmOidxt3f/yDqGqvTupaCijx8+HvvwonfncVE2wyyC404/Pb9uOHua5GVo8eOI9vS7rWmUqlQUlKCkpIScBwHu90upN5I7cfn88Hr9WaUzxvZo5Jxi44V4eTn58dlKBwPmpub8c1vfhMLCwvCeJDjx4/DYDAIAxObm5vx1FNPhfze8ePH0dzcnNBzZQThJIpYogHi61VZWSmMgI4G8QTRZKSH4sFs5eXlKcm1CSLNsuE4Dr29vZifn1+zaZQgmVEJpDF1cXERhw4dgtfrxcLCgpCjjTXDZj1hyNVj55X1MR+n0qqg0qoudORf6NaXXfz8WYaD1+8BRQE3vut6mH87gK7XesEGWDCB4Mau1qkgk8uE8QMZBR7weX145xeuh8FogPmZbnSf6Ed2sQm5JdmgKApZOXrMjS7ipUdPpJ1wACCnzIR33H8UW7dujfjz9dzwaZqGyWSCyWQKiX6GhoYwPj6OqampVdHPZoFIohN5PwKBAPx+f0zCSQQTExOwWq2YmJgAy7Iwm80AgNraWuj1elx33XXYvn07PvShD+F73/se5ubm8JWvfAX33nuvYCn2yU9+Ev/+7/+Oz33uc/jIRz6CF198Eb///e/x5JNPJrSWS5JwokU4PM9jYGAAk5OTq0ZARwO5IZKp4zgcDrS2tgqD2aampuD1xm9lv9aaxGRBRmkTEUI8ISxJFcZ74iPPwbKsMP2TpmkoFAqcPHkSWVlZyMvLQ25uLiYnJ2Gz2VbNsMkk1B+qhSFHD+usDbmlQWcCn9cPy7wFu47Wo/mKZshkMmzZXYHJ3mmodWpwLAulVgmlVoHFSQuyKwzwdKf+eaYbbICH+dkevOPL10LTpYRSr4QuRysUqCmKgtagwUj7+Lqc+DNpPAGJfiYnJ1FTUwO5XC6k3np6epCVlSX0/RgMhg2NfpIVDABIq5faAw88gF//+tfC3/ft2wcAeOmll3D11VdDJpPhb3/7G+655x40NzdDp9PhzjvvxNe//nXhd6qrq/Hkk0/iM5/5DH70ox+hrKwM//mf/5mQJBq4xAlH/GUSRxqxnAqiXS8RkCiqqqoKtbW1QropHQIEMeEQUjMYDHE1xYqvAcRnJe90OnH+/HkYDAZhXACxVT906BACgQCWlpawsLCAkZERUBSFwsJCeL1e6HS6jFMHAYCp0Iib7zuGPz74FGaG58GxHHx+H0rqCvHhL94hrHnPtTtx+q+tUGmU0F0YB72y5IBcJsfbP3Idfv/9v2B5zr7JryYUFAVMtE9j4KkJGJTGC64Jfng8blA0DZqnsDS9DJVGiT//+BkcuGEvymI0bCaCTEpbEZDNPTz6Icq3qakpofZDIqD1jn6SnfYJIK3Cm1/96ldRe3AIKisrV6XMwnH11Vejra0tpbVkBOEkU8MBLqbByAhog8GQkP0+QaJ9L0NDQxgbG1sVRSXiFh3Peubn59HR0YHq6mrU1NQk7PQMxK5NEbl4RUUFamtrQ8QBJPpTKpUwGAwYGRlBfn4+SktLYbVaMTAwAJ/Ph+zsbOTn5yMvLy+hAuJ6o+XWgyjbVoITfzmNsaFx1O/fiuvedw30potf5t1XNeCq9zbjtcfPwDG2ANeKG35vAGqtCs/8/CUoVUpoDGp47JkT6fg9ATB+Fi/+5nXI5MHP1rPsQ25pLlx2F6Z6ZxDwMfBpFHji35/G8//zKj7wf29D89sPpOX5L5WJn+JRAhzHCaMESDP2ekc/yU771Gq1GRNBphsZQThAYjJeQigsy2JhYSGuEdBrIRHVW0dHB1wuF5qamlblWdMV4VAUBYfDgY6ODuzatSspHb44wokEsb3Pjh07UFxcLESN4t8HgqOvOzs7UV5eLhBffn4+tm7dCrfbjcXFRczPz6O/vx86nU4gH6PRuPkbk45F0cFsvPWuKyKmWGmaxnu/cAsar9uNR//ljxg4N4K8khyYCgzwun3wOn0AB8gUsmC/DssKDsmbCVpGI7ckG16XF06bGzRNB21v5lfABliYCo3IL8tBgAnAOruM//ra7xHQe1BcWoTc3FyYTKaENzWvy4eAL5CRirBYa6JpGkaj8eIoCr9fUL5NTU0BgBD5pCv6SXbaZ7yjvi9FZAzhJALyYfT392NxcTHuEdDREK/qra2tDRqNRnBHjnSdVCMclmUxPT0tpAaTrZGILfnDIRYgHDx4EEajMSRFKb7ZJycnMTg4iIaGBhQXh6ZlyDRNnU4nTNO0WCxYXFwUCpN5eXnIz89PybpkYWLpgikni/zyPJRtK45p3ULqecTpwWQyRX0sRVEorCrA8oIdOcXZwhhshUoRTLEtOgAK8Ln8oGkK7HoTjsj9ORpYhkHAG4AmSwO3w4v6plpU7S7HH77/JLKLjDAVBE1b5Qo5CsuVwR6eFTmYQgY9PT1gWTZkg11rKqVlxoZffOF/cfapNnAcj7yqHNxy/3WoqqpK20tOFYmSoFKpDBmkRpRv4uiHvD8GgyEpgk2mhnM5T/sELlHCIUqwlZWVpDr5wxGLcBYWFtDR0RFziFmqvS9kAijLssjKykqpIC9WlInh9/sFV+7m5mao1eqIZEOk3nNzczE3bAKFQoGioiIUFRUJ1iVLS0sYHh5GZ2cnsrOzBQKK9zNrf6kbZ55shWvZHZQ3K2WoP1yHq+5oWSWNJiCuB06nE4cOHYrruayzNnjdPmRlX6z98TwPNsDCYXWAltFBD7E0pExjgaKje5WJHgUmwEJFUaAAyORyNB7dg6ceeRFKtVz43HmeB6jg6Ia2p7ph/y8H9CYt9l63A7oynTCpUqfThaSXyAbrdfnwlRu/g6VJa/C1U8DiqAU//8ffoqy8FLuualjfNyNOpBJ1URS1KvoRjyEnY6SJ8i3ekdFShLMaGUM48abUbDYbzGYzaJpGQ0NDWk4D0VJh4mmWO3fuXHXCj/c68cBms6GtrQ0FBQXIycnB2NhYUtchIOQhJkDSm6TX67Fv3z6BaMNtakjDrNfrxeHDh5Oqy4ib9+rq6uB2u7G0tISlpSUMDg5Co9EIqbdo6Z3FSQvOPNkKWkajalew58jt8KD79T4U1xRix5HVFu6EUCmKwsGDB+NOjWQXGqHSKOF1eaFUK8DzPObHFmGdDTocyJUyyBVyKJRy+Lz+C75lF36ZRCTiyITsF0kEQ7HJJphSk8lpBHwBUBSF7S1bUVRdgJLaQox1TkKjv/iZWWctcNpcOPe0+YJHHI/2l3twzQeO4MNfux0MwwjppfANtv2pXiyML4GmKcGyhuU4gAce+/5fM4JwyGC9dKX5lEqlcHASRz/T09Po7e2FXq+PSM7hSFY0cLlO+wQyiHBiged5TE5Oor+/H3V1dRgfH0/btSNFOAzDoLOzEysrK1FdCiJdJ5kIh4TxW7duRUVFBRYXF9MqPgCCdRiz2SxMUY0kDgCCIb3ZbBbsbNIx9hkAtFotKioqUFFRETLvprOzExzHITc3F/n5+SH588n+GbiW3QLZAIA2SwO5Uo5h89gqwiFjyQ0GQ1xjIMQw5htw8Ia9ePl/T4KmaTAMi+VFO1iWBUWTkcw83E4PKFCQyWUw5RsACvA4vajZW4U9V2+Hx+mDz+2HQiXDySfOwTa3DJblwAbSbMpGASuLDlA0hYbmOjS9vRE0TeNd/3gjfvZ//gcLExYolHIwAQZuuxe0jIYhP+vCBsjD4/Tild+eQsutB1CztyriBjs1NYXXnzktmHESTqWo4BTSodbR9L6mJBGp7pguxBP9ZGdnR0xNJisauFynfQKXCOGwLCs0JJIR0DMzM2k33SRwu91obW2FUqlES0tL3KfkRCMcjuPQ39+PmZmZEEfpdI2YJr04xJ1g+/btKCkpiSoOsNlsaG9vR3FxccTR3umCeN4N2eAWFxcxPj6O7u5uGI1G5OXlweVwXYwURJDJZQh4Q5syl5eXBbufWM2+0XDb/W9HwMeg9XgHLNNWgSR4PrhBUzQlWO/TNA2ZQoaCijwsL65gsm8GlmkrvC4f6pvq8NYPXoHTf21FTnE2nCsuuGzumBG82qCE1x67cViploPnAJ/HD41eDZVWCcbPADoVdlxRj8/85yfw6mOnMNk7g5zibJz523mAokI2P41ejZVFB7pP9KNyZxkACNL+rKwsYYPt3TGKvhdHLqboyAV4HvrszNgYyXdlI4QM4dEPUb7NzMygr69PiH5ycnIkwomAjCccUtegKCpkUma6XZ7JtZaWltDe3r6mT9la14mXKAKBAMxmM3w+36o6VLrk1QAwNDQkNGmaTKaYM2y2bt26pmVOuiE+QRLXYDJqenZ5GhabBbJRCrkFOdBoNeBYDh6HFxU7yoRrEIudurq6lNau1qlw17+8Fzd94ige/NhP0XdmELSMDlrcUEGXagDgeQ6ggu/fzPAcVhbsYBkObrsHKq0Sbcc70XtyAEqNAjQtQ3F1AeawCKfNFZV0lBo5KhrKMHR+DHKlDIyfXWWtQ1EXogyZDBUNJVCo5PC6fOg5OYDff/8v+Mi33gcAqNpZjqqdwfeBZTm0vdAJfwhBXxwfIJfLIZfLBT9B8XeKpmlc874r8Nd/Pw6e40FfeH6e4wGKQu1byoWBf7m5uZtWe9hIwhGDoigYDAYYDAZUV1cLohmr1Yquri4wDAO1Wo2ZmZmYwgwCKaW2QYh0oxKTysLCQmzfvn2Vy3M6xkyLrzU6OoqhoSE0NDSgrKws9i+GId7uflJL0el0aGpqWpW2SkeEEwgEwLIs7HY7mpqaoNFoNmyGTSpQq9UoKytDWVkZduzYCYXnOXS82ouFqSWA4kFxNCobyrFlb4Ug7R4ZGcGuXbvS5i2VX54L7oISTaVWwufxBzfZC1zBs4BCp4DD6kTAzwhD2jiWA01R0Ofo4LS6oMnSwOP0QKlRwJCXBdeKW6jP0DJaIDBKRiGnJBueFS+qdpRjfnwRFCj4mNBoR6VXCko5Yt2j0auDgoDnu2C/37FqnLZMRuPA9Xvwym9PgdNzQh3G4/BAoZJj77U7BfUgqYWQCJjjOBRW5+HuH3wA//lPj4JjuQszbnjsvrYBf//dj2LFEZxpMzo6CoVCgdzcXOTl5SE7O3vDGoJZll2lrtwMiEUzPM+jo6MDLMtiZmYG/f390Gq1AjkbjcaIBCkRziZAbCAZzaQynREOEFSiMQyDgwcPxqXIigRyA63ly0YaLddSvKVKOC6XC62trQCCk/mIEm2jZtikC0qlAm//2DFs3VOL4bYxOB1OZBXrYCjToq2rFfI+OTiOQ0NDgzArPl1g/AEoNUqwDAuZQgaOYcGxwXtTppQFFVscQIbCyBUyUBTgcfmg1CihUMmDRpv5WZgbXQjO8OF5aPRqFNUUgAcHl90FxsOB8bOo3bsFar0K2UUm9J0awOD5UYAK3gtyhQw5pSYE/Ax8Tj8gAxxOBxQKBeRyBRQqRbAfZ9m1inAA4J3/eCP63xjG/NiCMMNGrpDjpk++FZWiSFE8IwqAEPG89UNXYu9bd+L0X8/D6/RBUQA0HTsIrV4LvUGP0tJSsCyL5eVlWCwWDA4Owuv1htQ21lPqm4l9QdSFFKbJZEJlZSUCgYBQ++nu7hZk6UScQTI3Ukptg8EwDLq6urC8vLzm5p8uwvF4PILt9pEjR+KWPEZbExC590VMojt27EBJSUnU6yRjvElAosLS0lIsLCwAQERxgNfrhdlshkwmE2bdZCIUSjl2HNkWIhAgBoROpxMmkwm9vb0YHBwM6flJ9XRdtrUES9M2qHUquO0eAIBar4LP7UdRVT5GOiZA0xSoC39oeZBwOIa7MLcnAMbPQK1TQW/SwWV3g2U45BSbQMmAQIBBblEu7AsO0AYaM8Nz8DiCbga0jEbtvipMD84h4GeQUxxU8XmddtAyGbKMOiiVSgQCAXi9XrhtHmTl6sEp2Yh1g/zyXDzwh/vx6mOnMXh+BDqTDoffvh97rt6+5ntA07SwkRdW5OPmvz+GiYkJjI6OQqPRCBkGcl8RggGCdVCifBsaGoJarRbIx2QypTX6yUTCAUL7cBQKBQoLC1FYWAie5+F0OmGxWDA3N4eBgQHMz8/jxIkTGB8fR1NTU1qef2xsDN/4xjfw4osvYm5uDiUlJfjgBz+IL3/5yyHf946ODtx77704e/Ys8vPz8alPfQqf+9znQq712GOP4Z//+Z8xNjaGuro6fPe738WNN96Y8JoyhnAoihKK9QqFQjCQjIZkx0yLYbVaBUWWTqdLiWyA0AhHDJZl0d3dLYxoNhqNa16H1HAS9ayanJxEX18fGhoaUFpaKsiQtVptiLR5vWfYrCd8Pl/ImHCn1YUx2yRcyy54lF70W/vh8/mQk5MjEBA5PSaCa95/BL1nBsH4A8gpNoFjOdgtThRU5OHuH3wIP73/15DJZVDr1Og60QeOYUHJ6As9L0HC0WSpUVRdEDSHZVgMnh/F/Pgi8qqzYco2wWP3wucNgJbRkKsUKK4pBEVR8HsDWJqy4NBN+zDaOQnrjC2ohio0YsueSkz0TMGz4oNKo4TPHYBcrsDBm/dgbGIUnR2dmHhjDuPnpyGn5Wi8bg+u/cAVMOYb8I6/vy7p952iKIyNjWF8fByNjY3IysoSomaSfiOPo2kaarUa5eXlKC8vB8MwsNlssFgs6OvrQyAQCGk6TebzESNTCSeaLJqiKGRlZSErK0tomD5z5gwsFgtOnTqFU6dOob+/HzfccANuuOGGpOuSfX194DgOP/3pT1FbW4uuri7cfffdcLlc+MEPfgAguBdcd911OHr0KB555BF0dnbiIx/5CEwmEz7+8Y8DAE6ePIn3ve99+Pa3v423v/3tePTRR3HrrbeitbUVO3fuTGhNFJ/qWMg0YW5uDufPn181Ajoa+vv7wbKsMK8hERDl1sDAALZt2waO42Cz2QQX1VTw3HPP4ciRI0JY7PV6BcO7ffv2xfXl8vl8eOmll3DdddfF9UUSq9327duH7OxscByH6elpTE9Pw263IysrC/n5+aBpGsPDw6ipqVm3GTbrBeL2kJ2djYaGBpz+63mc+MMbcFqDajZDrh7XvP8K1B+pEYQHKysrgt1Ofn5+Qp5Zrz1+Bn956FksL6yApmmUN5Tggw+8G5U7yvCzz/43+s4MobimEEtTFoy0j4MJsJDJaMiVcnAcj8rtpVDrgp83z/NYmFqEbXYFhtygPFmTpUbxlkJM9E6jeEuhID8Ggo2o+mwdHvjD/RhpnwDLsNiypxK0jMZf/+NZnPzTOXjdPhhys3D0Q1fi2g9eAb83gO/d+e/oOz0EnuPBXxg7XbK1EJ/5xcdRWlWS1MbM8zwGBwcF14ZwSydx7Yf8NwGJksRWSy6XS4h+VlZW4qptrAXi65euyCBdOHfuHMrLy+NyrSe47bbbsH//fhiNRjz99NOQyWR46aWX0ram73//+3j44YcxMjICAHj44Yfx5S9/GXNzc0LU84UvfAFPPPGEMDH0ve99L1wuF/72t78J12lqasLevXvxyCOPJPT8GRPhKBQKQbYbD2QyGXw+X8LPQ2a+LCwsCHNlJicn0zpmmpz2VlZWBBVPIn0hYluaWF++QCAguGST0QXki19SUoLS0lL4/X5BduxyuaBQKODxeISBcZl4OgyH1WoVal81NTUYNo/hpd+8DrlShvL6EvA8j6VpK47/6hUUVuajqr5KOD2SSK+1tRU0TSMvL08YtbBWn9GV7z6MQzftw/TALBQqBUq3Fgnv1c33HYPD6sTMcDAdW7ylEJSMRkNTHYq3FOCZ/3wRtCjF6nQ6IFfJkV+eizu+8E7os7Uo21aCjpd7MNk/s0r+TctoMD4GMoUc9YdrQ3727s++A2//5HVwrbhgyDMIjgun/3oeg2dHYczJgkIVbF71+fyYHVrA4z/5C/be3CAU9fPy8uJKo/I8j56eHlitVhw8eDBiLUZc+yH3vph8SOqNRD9arRZ6vV6obdhsNiwtLaGrqyuprv5MjnCSsbbZunUrPvKRj+CLX/xiWuvUQHBPysnJEf5+6tQpvOUtbwm5F44dO4bvfve7sNlsyM7OxqlTp3D//feHXOfYsWN44oknEn7+jCGc7OzsdR8pQKINnufXXWI9MzOD7u5u1NbWoqqqKqFIYi0fNDHcbjfOnz8PjUaDw4cPR3UOkMvlsNlsgiiCYRgsLi6ip6cHDMMITZfxbkIbjdnZWfT09KC+vh6lpaUAgJ5Tg/B5/CisCv6dAoX88lxM9Eyh741BlNcHDy4KhSLEMXhlZQWLi4shdjvktUfaTFUaJbbsqVz178VbCvH3P/47dL/eD9vcMowFBuw4sg16kw4BXwDnn+3A/PgickpMcLmckMnkYNx+VGwvxRXvPgzZBbVYzd4qqNQKuFfc0F1wseY4Dq4VN/bcckB4HAHP82AZFiqtEmpd6GbcfaIfPMdDoQqqziiKglqtglfuhWPCg/3792NpaQmTk5Po7u6GwWAQ0o5ZWVmr7lGO4wSLoIMHD8YVnZN7V3wPi/+Ey65lMllITxbpayFd/fE4Ol9OhON0OkMiyHTWuoaGhvCTn/xESKcBwcxSdXXokD4Skc3NzSE7Oxtzc3OrorTCwkLMzc0lvIaMIZxEkShJLC8vo62tLWK0ka5GSyD4JR8fH0/JVDQewrFarWhra0NJSYmgdoskDiBzgjiOw+HDh4UTY15eHurr6+F0OrGwsCAMrDIYDEL6abM9nXiex+joKMbHx1dJtl02F+SK0C8jRVGgZTK4VzwRrye22yFO1yT1NjAwAK1WK2zA8aR2tAYNDt6wd9W/K1QK3P5P78B/fuE3mB6ahVwug0wuhynfiNv/6eYQEqneXYEDN+zDqT+fhXPZDblSBp/Lj/yyXBz98FXC4ziOw/O/fhVP/+eLsM4tI78sFzd+/K245v1HhM+IjCqI9D7KFXKh34nMiiGR3/j4OGQyWUjkR1EU2tvb4ff7ceDAgaQPIuJ0mrjeEy360ev1Ql9LuKMzmWeTl5cXYgabqYSTqHknz/Nwu90xVWpf+MIX8N3vfnfNx/T29qK+/uKE3OnpaVx//fW4/fbbcffdd8e9pnTjkiWcREQDxDqmrq4uYt0iXREOwzCC/DHRIXBiRPJBE4O8nm3btqG8vFyIasS/CwRPS2azOarVi7h4WVNTE9J0OTIyApVKJZBPMnb2qYA4WlssFhw4cGBV3aCkrgjdJ/qCvS/E4ysQfB+KtsQ38jrcbsdisQiNvzzPCxtwXl5ewk7XpbsKcdXfH8DykAuMi0NRdQEO37QfRdWha6MoCnd88RZU7yzH2WfMcC27UXdgC95ye1PIYx/7/l/x5x8/A54PRjDTg7P4+ed/A+eyCzffG5y6uO+tu3DyiWBtR60NHiz83gBAUThw/Z6Q51WpVCgtLUVpaSk4jsPy8jIWFxcxNDSEzs5OyGQyKBQK7N69O21RbzTZdbSmU7lcHhKdEsud8fFx4XCUm5ubkfN5gPXzUvvsZz+Lu+66a83HbNmyRfjvmZkZXHPNNWhpacHPfvazkMcVFRUJKl0C8ncyFiXaY5IZm5IxhJPMELZYJMFxHPr6+oRiZ7SmxnQQDlHYAcDWrVtTbt6KFHXxPI/+/n5MT09j//79yMnJEU6L4c4BkWbYxIK46ZJlWWEDDvc7S2YDTgQMw6CjowM+nw+HDh2KmMrZc9V2dL7Sg4neaRjzDQDPY2XJgYqG0oimnrEgl8tDZKuR7HbIa48V+ZEUYMvbmlD84diTNuUKOY686xCOvOtQxJ+vLNov1IToYBqNCroiuFbc+OtDz+GtH7wSOqMWB67fg8M37cOZJ9sEKTdNU9h1ZT2uek9z1OenaVroCamursa5c+cABEnpjTfegFqtFl57dnZ22g4ekaIfcngif8jjSFe/eJoniX6WlpZAURR6e3uFNabLAzBZkNeyHtY25BAYD6anp3HNNdegsbERv/zlL1d9ds3Nzfjyl7+MQCAgfKePHz+Obdu2ITs7W3jMCy+8gE9/+tPC7x0/fhzNzdHvqWjIGMJJFLGcBnw+H8xmMxiGiTnCIFXCIb0vJSUlWF5eTstpK5xwGIZBe3s73G43mpqaoNVqo9rUrDXDJl6E59bJBjw2Nobu7m6YTCbhxk9nUx+ps6lUKhw8eDDqxmEqNOI9n78Fr//pDQy3jQEUjcPvaMSRdx4MmeiZDCLZ7SwuLgqjFkjkF2kDHh8fx/DwcFpdG0a7JoM9OjQFhzU4816ulEOhksNtd2Oybwb1h2shk8vwyR/eiYM37oP5xS5wLIddVzbg0E37hLrOWvB6vcKo8R07dgjegGRT7+7uBsMwQlorLy8vZUkzQbToJ5rsWqFQoKSkBCUlJRgfH4fFYoFcLsfw8DA8Hg9MJlNI0+lGR0BkvYmm1Fwu16poPllMT0/j6quvRmVlJX7wgx9gcXFR+BmJTt7//vfja1/7Gj760Y/i85//PLq6uvCjH/0IDz74oPDYf/zHf8RVV12Ff/3Xf8VNN92E3/72tzh37tyqaCkeXNKEE40kVlZW0NbWBpPJhMbGxpinnWQJR+xgTexwzp49m3anZxI9qVQqNDU1RRUHJDPDJh6Eb8Aej0dIvQ0ODkKr1YaMGkj2y+1wOIQ6Wzz9QQUVeXjnP94In9sHUBRUmvURPIh7SliWFZyuyQZMlF92ux3z8/M4cOBASrOMwuF1ehHwMwAVjIbA8/B7giMSlGoFtFkXN32ZXIZDN+7DoRsTk/gTdwpS2xPqQmEHD6fTiaWlpRCzSkI+6Zzwulb0E5564zgOKpUKdXV1qKurExSYFosFIyMjUCqVwmeU7qbTaEiGcPx+PxiGSRvhHD9+HENDQxgaGlpl1UWk60ajEc899xzuvfdeNDY2Ii8vDw888IDQgwMALS0tePTRR/GVr3wFX/rSl1BXV4cnnngi4R4cIIMIJ9EbNVoNh6jDampqUF1dHdd1yU2bSKOleGomkVeLr5UqyHXInJyioiJs27YtqjggHTNs4oVGowlp6iNTPtvb2wFcnPIZS3YshsViQUdHByorK+P+3AhU2tQadhOBTCYTIjuiqiLEGwgEkJWVJaR49Hp9WjbgFYsDSrUCfq8/OB5ARgMUBb/Hj+KaQpQ3lKZ0fYfDgdbWVpSUlKC2tjbqmsU1P1LUX1xYxNTYNMbHxiGThwoP0pV2XSv6CUrOnZDJZAgEAqBpGiqVKiQ1TJpO+/v74ff7Qyx31ut7Iv6OxguXywUAabO2ueuuu2LWegBg9+7deO2119Z8zO23347bb7895TVlDOEkivCohJzuiQllIuowmUwWl+kmgd/vR1tbm5CuE9+0qQxhE4OmaUE9RubkRBMHrNcMm3gQXvtYXl4OmfIp7viP9uWenp5GX18ftm/fnnQKcDNAURS0Wi1WVlagVqvR2NgIu92OpaUljI2NQS6XC5FfPHY7UwOzaHu+Ex6nF1U7y7H32h1QqpWYG1lAzb4qjHVOwOP0BV2jeUCpUeDK2w6nRGpEvVlVVbVKHrsWWJbD8796Dc//16uwLzmgz9HhyO0HUXxDMUZHR9HV1SWMmUi34pFEP6SmabfbsXv37gvrYlc9jpAgUYGRAxIZBCi23ElXfYoIBhJ5zU6nU7inLldkFOHEO/UTuEgSHMcJ9Q3S/JjoCYFsBPGoSshp0Gg0RkzXpWO0AM/zCAQCmJycxL59+5CbmyuQDclhE2zUDJt4QPy0xFM+FxcXsbCwgIGBgVUd/wAwPDwsvE5xQ9qlAHLwkMvlOHDgAORyObKysgTll81mw+LiIvr6+uD3+5GTkyMQUHjt49Xfn8Lvv/eXYK2GCo6Zrtu/BX//47tgyjdAoZLjLe9pxtzoAtx2D7QGDXzeANQ6NeZGF1BYlZ/whm6xWNDe3p7UWIc/Pfgk/vLQs6AoCkqNEra5Ffz1x8+B83F47xduFdKuS0tLQlqLbPzp8LrjeR59fX1YWlrCgQMHoNVq45JdazSaVYMALRYLenp6BEPNSMPUEkUqgoFMlHinCxlFOImAfJjLy8vo7OxEVlYWmpubkzrdiwlnrTTA/Pw8Ojo6UF1dHVX5lWqEQxRaDMNg69atIWSTKTNs4oVWq0VlZaXQUU7qPqTjnwg/iJVHKnA7PLDO2GDMNyArZ/3t3T0eD1pbW5GVlYWdO3eu2iRomhY2rm3btsHlcmFpaQmzs7MhtY/8/Hz4VgJ47Ad/RcDHIL882APj9wXQf3YIT//ni9h3dBd6Tw1gedGO0rqgRHjg7DBmBucwfH4Uv/mXP6BqRzk+8p33o25/fFHK/Pw8urq6kooqHVYnjv/Xq5DJ5ci6MIRNo1PDuezCC/9zAsc+ci1MBYaQuhdxExCTLyGgRNNaxP2AzHkivx8p9bZW0ylN06vqUxaLBbOzs+jv74dOpwux3EmE0FMhnEyUeKcLlzzhnD9/HlVVVWvmnmOBnH6iEQXP8xgeHsbo6Ch27969pjdSKhEO2cQUCgWysrKgUCguiRk28UDc8e/z+dDa2gqfzweZTIZz586tefpfC0yAwR8ffAov/s9r8Dh9UKjlaL75AN735XdCm7U++XkS5RYWFgp1tbVA6jl6vR5VVVVCQyMh354XhrBisSOvNFewuFGqFFCplXjjyVbc9tmb8NYPvQWv/+kNTPXPwO3wYLRjAqAoqLWq4P1pHsN33vdjfOf5ryC/fO37YXp6Gv39/di9e3dSjclT/7+98w6Pqkzb+D3pvWeSUEISAqmQSSFUKYoESEjCqqirggjsioiIKKCA6K4rTVdclaK7iquiLi00AWmhiyG9F9LblPSZZPr5/sj3HmdSJ5PJzATO77q8Lpk5mZwzmTnP+z7lvovqIBaKYeuonvqxtrNCW5MINUW1cGL/0TShOlSqGny5XC7tE0P+9v0N3BJpqpaWFkRFRfX5Wemt8YCkz7vufmxtbdUENUnjAbGSJsHHxcWl39mkgQ59Ap0B50FOpwFGFnA0TamRGy7QOfMyZkx36ZGB0lugULVLmDJlSr8dJNrucJqbm5GWlgY2m42goCCkpaVBKBTCzc0Npqamw8bDpj+Ig6u1tTWio6NhYmICkUjU6fD5/6t/e3v7PiVXVDn60Rmc2X8RpmYmsLC2gFwix5UfbkLU0o7X9q/U+fkTTTcfH58BSxYRLCws1AYaGzLbwAILYkkH2jvaYW5uBjMzc8CEBZlEDlDApAUcBE72R21JPY58dBompqawtrf6Q77I3AzCZhGuHr6JJZsSev3dxLCOw+FoncK0c7KFqZkp5DJFZ9fc/yOXymFqZkJL9PRE1+BLBqVJ0wm5sfek96YqtRMVFTWglNdAh05NTU3VzNTI0GlVVVU3yZ2ePqPaDH0KhUJmh2NsyGQyZGVlQSQSwczMTGetvz0FCnJzNDU1xbRp0zSauDYxMYFU2r8vvSqks27cuHHw9vamv3Tl5eWoqqpSk5rJyckxeg+b3mhpaUFGRgbYbLaaIji5AZHOJ5J6q6iogLm5OR18urpICptFuPLDTZiamcLOqXNlaGFpDpaIhbSL2aguqsOo8bprQiBpqKCgII1FZvvDxMQEE2eE4NLXN2DOsoClQ6fPjVQqRUtjK/ynjEFpWWnn6t/JEQHR/mioaer04VG5MbFMWFAqKVTk1fT4eyiKQmlpKaqqqgadwhwV4AX/CF/k3S6CqZkpzC3MIJPKIWptx/hJ/mqmbv3R1SeGNF1UVlbSagKk662srAwdHR2DktohDHTo1N7eHo6OjvDz81MbOq2srISpqama5A7poNVmh/Mgu30CwyzgEHl6a2trTJ06Fbdv39a56CaBtCOz2exu9tb9vY6mKTUi+15ZWQkOhwM3Nzf6Qz969Gh4e3vTYpNFRUUQi8WwtLSEj4+PzrTf9AWfz0d2djb8/Pz6tEWwsLCgB/qUSiW9+s3Pz4dMJlNTO+BXNUAsknQTsbS0tkRrQxvq7nN1FnAqKytRUlKidRqqL/wjfBE1Pwy/nU5De2sHzCzMIGmXwGOUOxJemQ+JREK3nLu6usKBbYea4jq116AoCiYmLLiNdO72+qSbiyikD/amxmKxsGLXn/HpX79CdWEd3d05OnAk/vLR84NKbfek90akloDOgcXm5mb6xq4LBjN0SgRhic02UaUwMzMbUOcrwKTU9E5ffxgej4esrCw1a+b+1AYGgmrA6apVNlClZ02CoFwuR3Z2NlpbWzFlyhTY2tr2WK9xcnKCRCJBVVUVxowZAwsLC3C5XBQVFdEeN+7u7jqb+RgKiPJBSEjIgLxBura0CoVC8Pl8WmjURG4KmABSiZSW6Ac67aHNzE3h7Dm4RgTgj/pddXW1TodpVTExMcGyD56BzwRv3Dl5D6LmdgREc/DYCzPh/f8zNhRFoaWlBQKBAGMfGY28m0UQtYpgaW0JFosFSUfnezD72elqr01qHsRBV1dzJx5j3PH+qY3IvpYHXmUD3Ea5IGx2sEaKBppiaWlJ63iR2Z+mpiYUFxejo6MDzs7O9OdDl6nlgQydmpiYwNHREc7OzvRQdGNjI6qqqtDe3o7bt2/TO7SuO/SuMDscI4CkAkpLSxEaGqrWUaNrWwG5XI78/HzU1tb2qb3W3+v0t/sQi8VIS0uDqakppk6d2mdzQHl5OcrKyhAaGgo2u1PMkRSeyeqvrKwMFhYWcHd3B5vN1rvQZm+QHRx5Pwdzs1YdOiRpDT6fD//J3si5UgS5XAErGwtQCgodQinGRfpiLMdnUOdPhnsbGxt1sjPoC3MLM8x9YSbmvjCzx+dZLBacnJw6tcTWj4U1ZYukvecgFopBAbC0tUD8m3PhMMKW/hwplUpkZ2ejvb0dkyZNGrSjbU/nHPH4RK1+llvBx+2kFHS0iRE0dRzC5oR0+8wqFAraToSMIJB0rKrSN5mnIcFH13pvQO+7n66NB0QUVSqVor29HZ6enmhoaEBxcTEkEkk3yR1VHoaAYzSOn0Dnql81gJBdQEtLCyIiIrrJhaSkpMDLy6ubbIM23L17F1KpFCwWCxEREVpvbWtqalBdXY3Jkyf3+DwZtHNzc0NwcDCtCt2TTA0xvuJwOH1KpajKrfD5fCiVSrru4ebmZhAhQ2Kr3draivDw8CFrbhA2ibDvtW+QfbMAUrG0M63k64Kn3o3FuAljtRYaVSgUyMrKglgs1tipVd80c1uQe6sQLFMWRoZ6QCQR0n9/Z2dntLe3g8ViISoqakjFVgfKxW+v4d8bf4BCrvz/IVYKoY8E4u3Dr9GqEXK5HOnp6WCxWAgPD+9zZ0Dmacjcj6rckJubm84DLaFr27XqrbS8vBxKpVLNIoAMnQoEAjQ3N8PKyooeOLWzs8OOHTvQ0dGBgwcP6uT84uPjkZGRAR6PB2dnZ8ydOxe7du1Sqz9mZWVhzZo1SElJgbu7O9auXYuNGzeqvc6RI0ewbds2lJeXY9y4cdi1axcWLlyo1TkZbcAh+mEWFhbgcDg9FgmJm+Zgu9SEQiHu3LkDa2trTJkyZVA36Pr6epSVlfWopFpXV4ecnBz4+/tjzJgx3fLDPXnYcDicAX1hSOGVx+OBz+ejvb2dbjl2d3fXy41TKpUiIyMDAHr92+kSiqJQnlOFuvtcuHg5wWO8G912LBKJaKFRTVMv5PxZLBY4HI5R3az7g6IoNDU1IScnB3K5HEqlkvY4cnNzM3jqtaa4HuunvwulXAFzq//3s1EooZArsHjdQjz37hOQyWT0QG1YWNiABTDb2tro4NPa2qo28zQQi/GBoFrvId9fNzc3OiVPFpNkxySXy2nJneTkZGzbtg0uLi4ICgrCN998A29v70Gf0yeffIKpU6fCy8sLNTU1ePPNNwEAt2/fBgC0trZi/PjxmDt3Lt5++21kZ2fjpZdewt69e2kttdu3b2PmzJnYsWMH4uLicPjwYezatQtpaWlaaakZVcBRKBSQy+W0J8mIESPUupm6kpmZSadYtIW0Y5Kt8GBeC+isNRUXF2P69D9y6aSNu7y8HGFhYXB3d6dbMgF1vaX+PGwGCpn25/P5aG5uhp2dHZ16G4qbT3t7O9LT02FnZ4fQ0FC9CCX2harQaGNjY78mayTdaWtraxTnP1DIjJO1tTUmTJhAf5/I9ffV9acP/rfrJP635zTMLczUPntSsRRObEfsz9qF1NRUWFpaYuLEiYM+P9WZp4aGBrBYrCHReyPI5XKkpaXBzMwMISEhdAZD9TZLaj+qdaLU1FSsXbsWQqEQNTU1CAoKwtNPP42tW7fq7NxOnTqFxMRESCQSmJubY//+/diyZQvq6+vpReHmzZuRlJSEgoICAMDTTz8NkUiEM2fO0K8zZcoUcDgcHDhwYMDnYFQ1HOLwWFJSQqsv98VgmgZIfaSkpAQhISFoaGjQSedX17qSQqGg04LElK035QBtPGz6Q3Xav6eWY7Lz0UXeu7m5GRkZGfDy8qIbOwzNQIRGSbBxc3NDUFCQUZz/QOjo6EBqaiqcnJzozkpTU1PaaE114j8/Px9SqVQt9aSP3a+wub1TgLTLe8tisSBsFuHevXuwsbHBhAkTdFKH6TrzRBoviN6bk5OTWuPBYP7mqsFGdWemydBpZGQk/P39MW3aNPz1r3/Fr7/+2s30bDA0Njbihx9+wLRp0+gge+fOHcycOVMtAxETE4Ndu3ahqakJzs7OuHPnDt544w2114qJiUFSUpJW52FUAaeqqgrl5eWYNGmSRgVmbZsGSH2hoaEB0dHRcHR0RHNzs85EN0ngIjcwExMTTJkyBRYWFvQHbSg8bPpDteWY3Hx4PB5ycnLU6j7arPy4XC5yc3Ph7++vk3TAUNBVaJS0nBOhUQBwcXHReqDTkIhEIqSmptJF9Z7Ov6eJf9WBW7L7dXNzG7LUU8CksTh78BIUCiVttd2ZiqIwcrwbvbMciqYXVYtxYmNAUm/379+nG29I48FAdlek5mRqatotDajp0GlVVRWUSiWcnJywZMkSnVzzpk2b8Pnnn9M+Wqo7lfr6+m6CraSLtL6+Hs7Ozqivr+/WWerh4YH6+nqtzseoAs6oUaMGJJpnZmYGiUQyoN9BDL6ATic7sqrTVccbaYtuaWmha0xka00+ZPrwsOkP1ZuPqsEaWfk5OzvTu5++WmkpikJlZSXu37+v1kln7Kh2fTk6OiI7Oxvu7u6QyWS4fft2N6FRYw5Ara2tSEtLw6hRozTeGatO/JOBW7L7q6yspFvS3d3ddTrzEh0bDr+J3ijLroJCpugcWFUowDI1wdxVj2DChAl6e69Vd7+k8UZ196ep3hvppjMxMQGHw+k3UPXUdn327FlkZ2cjMTGxz5/dvHkzdu3a1ecx+fn5dLPCW2+9hRUrVqCiogLvv/8+li5dijNnzhjs82xUAcfU1HRABfKBBomuQaDrKkQmkw3ofPs6p99//x1jx46Fj48PvZ0mv8cQHjZ90dVgravKM1n5dpWaIQOFXC4XkZGRgxbgNATV1dUoKirChAkT6GBJdLRUhUZVd3/GVNdpampCRkYGfH194ePjo/XrdE09NTc30y3HYrGYXoBoI7apirmlObYd24AfPzyO6//7DTKJDF6BbMS8PAuxz8UY7EbY1eeI6L3V19fTQp6qRnMkYJBgQxpMBvrZMDExwa+//oqVK1fiu+++wzPPPNPn8Rs2bOjX40a1Dk3Oefz48QgKCsLo0aPx22+/YerUqfSMkyrk38QRtLdjyPMDxagCzkAZSMAh8jH+/v49pkx0scMhDqBKpRLh4eFgs9m9NgcY0sOmP3pTeVat+7i6uqK6uhrt7e2Ijo42WLDUFlIvrKioQHh4OG2gB3TKrRAdLdWbb1FRESQSidZCo7pGIBAgKysL48eP18loAMHExAQuLi5wcXFRE9vk8XhqN1/SeDHQIOHgaoe/frwUz733J6T8fg+eIzzUXEYNTU96b6SdWVXvzdXVFbW1tQCAiIgIrRYiV69exfPPP499+/bh6aef7vd4EhS1gaT6SVZo6tSp2LJlC2QyGZ1Cv3jxIgICAujvw9SpU3H58mW8/vrr9OtcvHixxy5cTTCqLjWKogakQ1ZdXY3a2lpER0f3+ZpFRUWoqqqiO8R6gviiR0REDPi8gT9ENRsbGyGRSPD444/Tj3et1xiTh81AIFIz9fX1qK+vB0VRcHd3h4eHh9bzLoaAeKnw+XxERERoPGxHDLxI119LS0uvu7+hpr6+Hrm5uQgJCdF6takNqjdfgUAAAFp1fZGak4eHh9E0mGiCau2vqqoKCoWCbjsfqOLHjRs38OSTT+KTTz7BihUrdPoe3L17FykpKZgxYwacnZ1x//59bNu2ja61WlpaoqWlBQEBAZg3bx42bdqEnJwcvPTSS/jkk0/U2qJnzZqFnTt3IjY2Fj/99BM+/PDDB6MteqABp6+ZFwC0MZtIJOr3xlJdXY26ujpMmjRpwOdNWlEBYMKECbh58yZmz55N52qHk4dNf4hEIqSnp8PBwQHe3t707kckEmlc9zEkZGEgEokQHh4+qPNU7fpraGigHT6HuuWYpAEnTpwINze3IfkdmqB68xUIBBrPPAmFQqSmpvZraW2sKBQKZGZmQi6XIyQkhO78a2xshJmZmZrRXG+Zizt37mDx4sXYsWMHXnnlFZ2/B9nZ2Vi3bh19//Py8sL8+fOxdetWjBz5hyW56uCnm5sb1q5di02bNqm91pEjR7B161Z68HP37t0PxuDnQAMOn89HYWEhZsyY0e05MjhqaWmp0fBebW0tKisrMWXKlAGdMynYOjs7IzQ0FBRF4dKlS2Cz2fTKnwj5EQ+biRMnDgsPm66QesGoUaO63Sg6OjrolX9TUxNddGez2Xpd+ROUSiUk7VJYWFvQ3VAymUxtoFaXA6mqDp98Pp8WGiWpJ139LiJ1xOFw1NKAxkDXmSciN+Pu7k7LLbW1tSE1NRWjR4+Gn5/fsAs2SqUSmZmZkMlkiIiIUAso5DNAdn8dHR1qjQdEveTevXuIj4/H+++/j9dee23YvQeDwagCDoABdZ01NjYiOzsbs2bNUnu8oaEBGRkZ/Q6OqsLlcnH//n1MmzZN499PHED9/Pzo9kKFQkF3fPH5fFpkUCqV0h/S4eZhA3SqJOTl5SEgIKDfeoFq3UcgEKit/F1cXIY0hUhRFFIvZOLGsbtoqGmCvbMtpiREIXLBRGTnZMHKykonA4X9nQMRGuXz+Whra1NLu2gz79FVRLQvqSNjQFVuhsjtODg4oKWlBd7e3vD39zf0KQ4YEmykUikiIiL6XcSS2pdAIEBGRgZ2796NiRMn4tq1a9iyZQs2b978UAUbYJgHnJaWFqSmpuLRRx8F8EeLblFRkUaDo6qQdshHHnmk32NJwfn+/fuYMGECPDw8em0OIEFRoVBAoVDQKQc2mz0spMhVBUS1SeGQVR+R2pHL5Wo6b7qu+9xOSsGJvb9AoVDCzskWHUIxpGIpfKeNxOMvzURQUJDea2ZEaFQgEKChoQGWlpZq0/79nY9qzSkyMnLYLVgoiqJTyRYWFpBKpXB0dKTfg+FgOqZUKpGVlQWJRKJRsOlKS0sL9u3bh127dtGNJvPmzcOiRYuwbNmyoThlo8R4WqP+H01dPwF1pQEidkk8PwaabtC0S424DpKhUQcHhx7FN4HOdFtOTg49uS6Tyeh245KSEoOnnfpDqVSioKAAAoEAkyZN6tfttCdMTEzojp7AwEC0tbXRHW+5ublwcnICm83WSd1HKpYi+afbAIsFL7/OYTUre0vUlNWiMrUOnm+OMEiDhqWlJUaNGoVRo0apCa2SgVtVj5+uNzJVS2Vd2gtQFAW5VA6zLhIzQ0FzczOKioowfvx4eHt7QywW0yv/0tLSQQ1c6gOiui0WixEZGanVIqm2thYHDx7E5s2bsX37dmRmZuLs2bO4cePGQxVwjG6HI5VKNQ44YrEYycnJmDNnDjIyMqBQKLQuBLe2tiIlJQWPPfZYr8dIJBJaLj08PByWlpa9ytSQbpDeDMdUNa4EAgFMTU3pG68u5dW1RS6X0yu6oVJL7q3uo+2wZV0pF3tXfQk7J1tY2VlBIpGgpaUZNtY2aK0XYeWe5xAyPUDn16Etqg6XfD4fQqGQllohQqvZ2dno6OhARESETlSPKYpC6q9ZuHr4JrjlfNi72uORJyZj1tNTYWqm+xt9Y2MjMjIyem3dJooX5Hsgk8nU2s6HSulZU0iw6ejo0DrYFBUVYcGCBVi6dCl27Nhh8O+2ITG6Hc5AICuhO3fuwMnJCRMmTNB6ddSfcRopdpLfQ5QDNPWw6YqZmZnarEdPMjNsNhuurq56n9ERi8XIyMiAubn5kErbW1tbw9vbG97e3mp1H+IVNNC6j7WdNcwszCCVyECZdt7MHR0dAIUJzCzFsHEwrs65rg6XYrGYDsAlJSVgsVgwMzNDcHCwzv4Gv51KxY8fnoBMIoONgw34lQIc2XMajfXNeHJDnE5+B6GhoQGZmZkIDAzs1ZK7q+KFUCiEQCBATU0N8vPzYW9vTwdgfWcBSDajvb1d62BTWlqKuLg4PPPMMw99sAGMcIcjk8k0FtGsq6tDZmYmfH19B93L39HRgWvXriEmpvu0M4/Ho38PmeIlwUnVVmAgHja90dVegHS6kJvvUK/42trakJ6eDldXV4PUO4DeO77Ie9DXF//7vx3DraS7sHQ0h7unO1gUC9xyPsZyxmDNFyvojjVjRiqVIi0tDRRFwc7ODg0NDQDUhUa1WYTIpHL8Y8le8KsEcB/9Ry2uVdAGgMLbP62D+yjddE8SS/HBaAOStnNS+1INTkOt+KBUKpGbmwuhUIjIyEitugwrKiowf/58xMXF4bPPPnvogw0wTHc4pGOnrKwMAAZsA90TqsJ65P9VFaVDQ0Ph6emp1hzQm4fN5MmTtQ4MqqvecePG0QKLtbW1KCgogKOj45A1HTQ0NCArKwve3t4GbVlVrfsEBARAKBSCx+OhsrISeXl5dOOFu7u72ntAURSC5/mhILsQwroO8CsaYGLCwuigEXhqY/ywCDaq9ghEMbknoVFtZp4aahrRVN8MO2f1eTQ7F1vwyvmoKqjVScDh8XjIzs5GaGjogCzFu6IqNtuT4oOu5Ha6QlEUcnNz0dbWhqioKK2CTU1NDWJjYxETE8MEGxWGXcAhLqCtra2YMmUK7t69q7VFgSokyCgUCtomOjc3FwKBgG4O6K1eo2sPG1VsbW1ha2sLHx8futuJNB3Y2NjQdZ/BCkySLqKgoKBe0x+GQNVaumvaqbi4mK77uLq6orKyEu1yETb9Zy1qC7gQVDfC3tUegZPHwsJqaE3gdAGZHXN2dlbbXaoKjY4bN07NXrmoqIh+D4jOV2+fAytbK5iam0IuVf++yKVymJqbwsZ+8DdtooCgqk2nC3qS2+Hz+eByubTcjibvQX+oBhttdzb19fVYuHAhZs6cif379zPBRgWjS6l1tZlWpaOjg/abCA8Ph4WFBZKTkxEWFjboITiKonDhwgXMmjULpqamSE9Ph0KhoIu1+vSw0QRdNR1QFIXS0lJUVlYOu4FUIrPC4/HA4/EAdIoNenh4wMXFxei6nfqCTN97enoOKD2sKjQqEAj6FRr9z9uHcfdMGtxGusDCygJymQL8KgFGB4zA5sNrYWau/Rq0rq4O+fn5eldA6E1uZ6DpR4qikJeXh+bmZkRFRWmVpeDxeFiwYAHCw8Px3//+16g0Eo2BYRNwmpqakJ6eDg8PD7XV340bNxAUFKSTD/jFixcRFhaG/Px8ODg4YOLEibRjX0/BRh8eNprQddZFoVBo1HRAak5NTU0IDw/XWFPMmCCdg2ZmZvD29qZbjlXrPm5ubkNucz0YWlpakJ6ePujpe9W0k0AggFgspifdSddbE7cZ/954GGXZFVAqKLAAuI9xw0sfPgufUO2llmpqalBYWIiwsDCDLlpUTdaIxbqzszP9HvSWhlYNNpGRkVp1ZQoEAsTGxiIgIAA//vjjsNEW1CfDIuBUV1cjPz8fAQEB3cy9bt++jbFjxw4qV0y4ePEiAMDHxwdjx44F0HtzAPGw4XA4evOw0QRVbxsej9dr04FMJkNWVhZkMhk4HI5BVY+1haSgHB0dERISQi9CSLcTCcBCoRCOjo70DtCYBm4bGxuRmZmJsWPH6ty4jqSdugqNOjs6oyqnDvzKBji42WPCzCBY22n/9ycLLw6HAxcXFx1eweAhrfdE68za2ppehBC5HYqikJ+fj8bGRkRFRWn1XWhqakJcXBy8vb1x5MgRo17gGBKjCzgKhUJtmLOwsBC1tbXgcDg9rpzu3r2L0aNHD6ruQFEUKioqUFBQgLFjx8Lf35/e1QDqwUbVw2aw4o/6gNx0eDweWltb4eDgAGdnZ3C5XLowPRy3/a2trUhPT9coBaVa92lsbISNjQ0dgAeT7x8spJOrr7ZhXaHa8aUqN0REJrVNPxLzvfDwcKNaePUEkdshAYgM3cpkMrS3t2PSpElaBZuWlhbEx8fDzc0NSUlJBp8dMmaMNuCQri8iJdHbqvTevXtgs9larw5VFQpMTEwQEhICZ2dnKJVK2m+coOphM3HixGF3o5ZIJLSNN0VRsLW11VnTgT4h8x1+fn4DNh2Ty+V03YfUPFTnffRV9yHadIPt5NKGrm3nUqlULf2o6Q2TzJtFREQMO/M90vlXWFiItrY2UBTVTelak+9DW1sbEhMTYWdnh1OnThn9AtTQGGXAaW5uRlpaGuzs7Pq9sWdkZMDR0bGbN7cmSKVSZGRk0KKa6enp8PHxgZub2wPjYaMKWVH7+flh5MiRaGxspG+8ZNCSzWYbhdJBb5AuKF1006nWPHg8HqRSqZrO21ClRUgKytD1DkBdaFQgENC74P6ERkmjyXAQEu0J4lbL5/MRFRUFFoulpnStid6dSCTCE088ARMTE5w9e3bYadwZAqMLODweDykpKfD29sa4ceP6XWVkZ2fD2tp6wOqzQqFQLaiZmpoiLS0NbW1t8PT0BJvNplf9w93DBuisgxUWFvZo2KVt04G+qaiowP3794ekC6onhWcy80RuvLqgrKwM5eXlRpuCkkgkah4/ROeM3HhZLBbu37+PmpoaREREaKWvZ2iIKSPRXey6KyF6dyT9qGo14ejoCDs7O3R0dOCpp56CVCrFuXPnhuX7YAiMLuC0tbWhoaFB466vvLw8mJqaIiBAc40sIheuKpOuVCrpdItqq7GFhQVEIhHCwsIManalLcSHp6amRqP28a5NB+3t7WpT/obIT6teQ3h4uF7SN7qu+5BrqK2tHTY3alWhUYFAALlcDktLS1pfz9j8eDSBoigUFxejvr4eUVFR/TaQdN0Brlu3DmKxGFKpFHZ2drhx44ZRLhyMFaMLOEqlEjKZTOPjCwsLoVAoEBwcrNHxFRUVKCoqQnBwMD3B3FtzQHp6OoRCIb2dJjecoZbV0BVEC6q1tRXh4eFardK7djo5ODjQdR99pBBUW7cN5SWkuhDh8/n0rAubzdao7kO6oIiF+XBMvZDPkkAggJWVFdrb24dkBziUkKBfV1enUbDpidLSUixZsgS1tbVQKBRwdHREbGwsXn31VUyYMGEIzvrBwjhyJYPA1NRUIw8dIrVPVjZOTk69etgQ8UpTU1PMmDED5ubmaGlpAY/HQ1FREV1kZbPZQ+LpogtkMhkyMjKgVCoRHR2tdT2iJ6UDIrFCWkxV04+6hFj5SiQSREdHG6z7x8zMDB4eHvDw8FCr+xQWFkIikajtALu+z+RG3dbWpnUXlKEhfjwtLS2YOnUqrK2t1XaA9+/fh5WVldoO0NhqgEQOq7a2VutgI5PJsHXrVpibm6OkpAT29va4ceMGzpw5g7a2tiE46wcPo9vhDNRmury8nB5c7A1y85VIJPRQFwk2qrsaoLPdNiMjo1fxStUZDx6PB5FIBBcXF3rVbwwtke3t7UhPT6fbnodiN9a120vXTQekocPExARhYWFGGdQpilJrO+9a97GyslIz7RqOsxlkILKpqQmRkZE9dmGpthvz+XwAUBPZNIa/HUnJRkVFabUbk8vlWLFiBfLy8nD16lWdyvY8TAz7gFNVVQUul4uoqKgenxeJREhNTYWtrS3CwsJoo7Wegk1/HjY90d7eTgefTjn8zgFDNpttkBZJMrXu6emJgIAAvbQ6q7bZ8ng8uumAdHsNtOmASBjZ2dnRApbDAWIsRuo+AGBubo7g4GC4uroOm7ZzAtETbG1t1Xj6XlVoVCAQQCQSaSU0qkuINXdkZKRWahoKhQKrV6/GvXv3cPXqVYOqigx3hn3Aqa2tRVVVFSZPntztuYaGBmRkZGDUqFEYN24cAPQoU6Oph01/SCQSutOrsbGRnnNhs9mws7Mb8hsO8dPx9/fX+dS6pvTUdDCQHWBbWxvS0tLg4eGht4Cpa6RSKVJTUwFAzV5gONUASSqQyPNru3PvyWSPLEb0MXRL2rejoqK0DjavvfYabty4geTk5AHZ1g+EmpoabNq0CefOnUN7ezv8/f3xzTff0AtpiqKwfft2fPXVV2hubsb06dOxf/9++r4GdKpWrF27FqdPn4aJiQmeeOIJfPrpp0YlWWV0AQeARjUZApfLxf379zFt2jS1xysrK1FYWIigoCCMHDmy1+YAXXjY9AQxFCMpJ0tLSzr4DMUXrbKykrZRMKbt/kCaDojMy5gxY+Dr6zssgw2xF7Czs0NoaChMTExofS+yGJFIJHQQNgZXy64olUpkZWVBLBbrNBU4UKHRwVJWVoaKigpERkZq1RWoVCrxxhtv4OLFi7h69eqAh4w1hZQE5syZg9WrV8Pd3R3FxcUYO3YsLbG1a9cu7NixA99++y18fX2xbds2ZGdnIy8vj955LliwAHV1dTh48CBkMhmWL1+OSZMm4fDhw0Ny3tow7AOOQCBAXl4eZs6cCeCP5oC6ujq6dbO35gBVDxsOhzNkX3yFQkHXO0iXEwk+g613kJkCcr3GPPFNZjx4PJ6arhWbzUZHRwfy8vIQEBCAkSNHGvpUtaK9vR2pqal0/a+ngKla9+Hz+WqDlsTjyJCBVqFQICsrC1KpFBEREUNWfyFBmLwPYrFYLfU22OaK8vJylJeXDyrYbN68GSdPnkRycjJ94x8KNm/ejFu3buHGjRs9Pk9RFEaMGIENGzbgzTffBNCZOvfw8MChQ4fwzDPPID8/H8HBwUhJSaF3RefPn8fChQtRXV1tNJYjRhlwpFIpND2t5uZmpKenY86cOWrNAREREbC2tjaIh01f9FTvIDebga7yFAoFnfYIDw83KlHK/lBtNeZyubSulbe3t8aW0sYESQUSJQpNg4Zq519jY6Nat5eTk5Neg49CoUBGRgYUCgXCw8P1WuzvTWhUG2tpXQSbd999Fz/99BOSk5Mxfvz4Ab/GQAgODkZMTAyqq6tx7do1jBw5Eq+88gpWrVoFoDMtOHbsWKSnp4PD4dA/N2vWLHA4HHz66af4+uuvsWHDBjQ1NdHPy+VyWFlZ4ciRI1i8ePGQXoOmPBBt0QqFAiKRCGlpabC2tsaUKVPox43Jwwbo7mZJ7KSLi4uRnZ1Nt1v3Z6VMurhYLBYmTZo07DqgzMzMwGaz0dbWBhaLhYCAALS3tyMvLw8KhUKt7dxYlA56gyx6fHx84OPjM6DPk6WlJUaNGoVRo0bRO2E+n4/MzEwA+qv7yOVyZGRkgKIoRERE6P09V22/l0ql9PtQUVEBMzMzOvXW39xTRUUFysrKtA42FEXhH//4B3744QdcvXp1yIMN0BlQ9u/fjzfeeAPvvPMOUlJS8Nprr8HCwgLLli1DfX09AHTT3PPw8KCfq6+v75ZKNzMzg4uLC32MMWDc32QNMDU1hVwux2+//YYRI0YgMDAQFEX1GmyMxcMGULeT9vf3h0gkUrNSdnZ2poOPaopBJBIhPT1d77szXUJSn8RRlRQ2AwIC0NbWBh6Ph7KyMuTk5Bhd27kqREh03Lhxg5Y9IiZ6bDYbFEXR8z5kMdKTzYQukMvlSE9Ph4mJCcLDww3+ebKwsICXlxe8vLzUMgIFBQV9Co1WVlaitLRUa303iqKwe/dufPXVV7hy5YrGw+SDRalUIioqCh9++CEAIDw8HDk5OThw4ACWLVuml3PQF0YZcFgslsYpNS6XCwD0F161OUA12Kh62ERERBidHAWLxYKdnR3s7Ozg5+eHjo4O8Hg81NfXo7CwkC62W1paorCwECNHjoS/v/+wLKwrFApkZ2ejvb0d0dHRasGUxWLBwcEBDg4O8Pf3p9vO6+rqUFBQoFbvMPR0O+kKHIrFC4vFgrOzM5ydnWlbaR6Ph9raWrX3oS+BTU2QyWRIS0uDubk5PTZgTHTNCJDUW01NDW2U6O7uDrlcjqqqKkRGRmpVx6QoCnv37sVnn32GixcvYuLEiUNwNT3j5eXVLbgFBQXh2LFjAEBrH3K5XLXPGZfLpVNsnp6etOstgcxHddVONCRGGXA0gUw/19bWAujcXvbWHKDqYTN58uRhISFubW2NMWPGYMyYMZBKpeDxeKiqqoJQKISlpSVYLBaEQqFe2q11CamzAcCkSZP6rRPY2NjQqSqpVErXvkpLS4dc6aAvyI1fH12BLBYLtra28PX1ha+vr5rAZmlpKSwtLen3YSBT/lKpFGlpabC0tERYWJjR181UF2Wq70NlZSWEQiEsLCxQV1cHuVw+YJv1L774Ah999BEuXLiAyMjIIb4SdaZPn47CwkK1x4qKijBmzBgAgK+vLzw9PXH58mU6wLS2tuLu3btYvXo1AGDq1Klobm5Gamoqff5XrlyBUqnscWTEUBhl04BMJqN3KT0hl8uRmZmJ9vZ2hIeH4+bNm5gxYwYsLCy6pdCGu4cN8IdBXGlpKb0SIu3W5ubmdBpG30XmgUJahm1sbAatgNCTvhlJuw110wFpQTcGh0vVuo/qlD+p+/T2eSezQuRvYezBpjeqq6tRVFQEDocDhUJBB2K5XE6rHfRlNUFRFL766its374dv/zyC6ZPn67nKwBSUlIwbdo0vP/++1iyZAl+//13rFq1Cl9++SWee+45AJ1t0Tt37lRri87KyurWFs3lcnHgwAG6LToqKoppi+6PnmymCcRW2NLSEhwOB2ZmZrh8+TLYbDZGjBihdtN9EDxsiOspj8dDeHi4Wm6aqPmSdmsWi0WvdI2t00soFCI9PR2urq4IDAzU6bkRfTPyPsjlcrrpQJfSKhRF0bMdxmg6pjrlz+PxIBaLe6z7SCQSpKamwt7eXs2ae7hRU1ODwsLCbsrVFEWhra2NDsLEYryr0ChFUfj222+xadMmnDlzBrNmzTLUpeDMmTN4++23UVxcDF9fX7zxxht0lxo51+3bt+PLL79Ec3MzZsyYgX379qk1NTQ2NuLVV19VG/z817/+xQx+9kdvAaepqYluPQ0MDATQebNpbGxEXV0d+Hw+XXg1MTFBZWUlAgICdO5ho5ArcO98JtIvZUMmlSN42nhMTYiCjb1uU3VyuRzZ2dno6Ojo1866p5uusXjakC4ufXQFkpsNeR+I1t1g5zvIvFN9fb3WEin6pmursb29PW0v7uTkhNDQUKPeEfcFSWlqYpPQVXLo1KlT9NzP119/jZMnT+Kxxx7T05k/3AybgFNdXY38/Hw6gJBONOAP5QASfEpKStDW1ka33np4eOhsxa9QKPH15sP47XQqlHIlwALAYsGf44N1X66CnZNuCtkSiQTp6ekwMzMbsHhlV3mZjo4OtU4vfbZQE5dRXXRxaUN7ezv9PhClg4E2HagKWPZld27MSKVS1NbW4v79+6Aoqtu8z3Da5ZBgo01KU6FQ4OTJk9i7dy9SU1NhZ2eH+Ph4xMfHY/78+Ua3a33QMMqAo1AoIJfLAfyxsqyqqgKHw4Grq6tac4CqTA0ZhGxrawOHw4FMJqOFNcmK38PDY1AzDRlXcvD5mq9hZWcFa7vO1bJMKkcLrwV/Wh+LRa/MG/T1k/STs7MzgoODB30zIO3WRNHYycmJrvsMpVw+SXmEhIR0myEwBKpNB2TIkgTh3uSGlEolsrOzIRKJEBERMSztBYA/VBDc3d3h7+9PO7wKBAIolUq1eR9jrnPW1dUhPz9/UPbcSUlJWLVqFX744Qd4enri1KlTOH36NJ544gm89957uj1hBjWMOuDI5XJkZWVBKBTSxlVKpRIKhaJbc4Cqh01YWJjaKp6s+Hk8HrhcLiQSCZ1ucnd3H9AX7Pv3j+LSdzfgPlr9w95Y1wTvoJHYfuLNQV070RMbqvSTWCymg09zczPs7e3p4KOrNmPVWkdYWJjBC+s90VPTQdf6F/HjkclkCA8PH3bDtQSimO7h4YHx48erfaZU6z58Pp8WW9WVxIwuqa+vR15e3qCCzZkzZ7B8+XL897//xRNPPKH2nEKhMLq28AcNow04RCrE3NwcHA4H5ubmvQ5z9udho0pPfjaq0/393VS+e+8oLn9/He6j1e2mG+ub4R04YlABp7a2Fvn5+QgMDNSLnljXFb+1tTX9PmjbZkxRFAoLC8HlcoeNlXLX+pdMJoOLiwtEIhEsLCwQHh5u1Kv+vhAKhUhNTcXIkSM1WsD0VPchwceQLfjEOmTixIlaW71fuHABzz//PP7zn//gmWee0fEZMmiCUQachoYG/P777/Dw8EBQUBCAnm0FAO08bFTpmm4i0/1kyLIraZey8cWrX8PGwRpWtp2rP7lUjmbu/6fU1gw8paa6I5g4caLWq7fB0NVQzczMjF7xa5rjJ+knsiMdDvNOXaEoCo2NjcjJyaEXOMa64u+PtrY2pKamYvTo0fDz8xvwd0MqldLFdqJ4boi6jy6CzdWrV/H0009j3759eOGFF/QSOHfu3Im3334b69atw969ewF0Zhg2bNiAn376CRKJBDExMdi3b59ayrmyshKrV6/G1atXYWdnh2XLlmHHjh3DdtGjilEGHCLlTrwnujYHALrzsFGFTPeTAnNPZmoKuQJfbvgOKeczQSmVAIsFUBR8J3pj/Vd/hb3LwLqXlEol7XcfHh5uFDsC0nxBVvwURamlm3pKO8hkMmRmZtLCj8M1/UTM34hsELFSJp8JkoIc7IT/UNPS0oK0tDT4+PjA19d30K9HWvDJ7kepVA7KZE9TeDwesrOzMXHiRLi7u2v1Gjdu3MCTTz6JvXv34qWXXtLL3ywlJQVLliyBg4MD5syZQwec1atX4+zZszh06BAcHR3x6quvwsTEBLdu3QLQ+T5zOBx4enpiz549qKurw9KlS7Fq1Spa+mY4Y5QBR6lUQiqV9tocMFQeNqoQMzUej4empibY2dnBw8Ojc+djYYm7p9OQdikbMokMoTMCMW3xpAF3qJEBVqlUivDwcKNcPRNNL/JeyGQyuv5FbjQSiURtYn245sGJAKybmxsCAwO73ZhICpLP56OhoUGjpgNDQNrQya5f16jWRIey7kOCzYQJE7ReUN65cweLFy/Gzp07sXr1ar38jcgOf9++ffjggw/A4XCwd+9etLS0wN3dHYcPH8aTTz4JACgoKEBQUBDu3LmDKVOm4Ny5c4iLi0NtbS296zlw4AA2bdoEPp8/bBdyBKMMOO3t7VAqlbQNtCE8bFSRyWS0jH5DQ4NOnDzFYjHS09NhaWk5bBQQSP2Ly+XSMy6Ojo4QCoVwcXEZ1hPrJP2kqUZdTx5HxjB029TUhPT0dL22oXdtPSfWAoP5fvD5fGRlZQ0q2KSkpCAhIQHvv/8+XnvtNb0tCJYtWwYXFxd88sknmD17Nh1wrly5gsceewxNTU1qWo5jxozB66+/jvXr1+Pdd9/FqVOnaPknoNNIzs/PD2lpaQgPD9fLNQwVRnmXe+mll5CdnY2EhAQsXryYbgRIS0tDTU0NxowZo1eVZHNzc4wYMQIjRoyAXC6HQCAAl8tFeXk5LC0t6Z2PpoX2trY2pKen0yvp4XKTZrFYsLe3h729Pfz9/cHlcpGTkwNzc3Pw+XykpqZ2S0EOB1TtBTRNP6kqO6s2HeTn59O7QJJu0pevDFGuHj9+/JBZIfeEjY2Nmu4fqftUVFTA3Nyc3vloqm9Ggs1gUuXp6elITEzEli1b9BpsfvrpJ6SlpSElJaXbc/X19bCwsOgmHNzVZqAnGwLy3HDHKAPOwYMHcerUKRw7dgx79+7F6NGjERgYiIsXL2Ljxo2Ii4szWPrCzMwMnp6e8PT0VFvlpqWl0YOmfemaCQQCZGVlwdfXd8DeKcaEQCBAbm4u/P39MWbMGLVaR3FxMezs7NTarY31OsnfYzA3aRMTE7i4uMDFxYW2V+Dz+SgvL0dubq5emg7IdQQGBhrU3dHCwoJenKnWfXJyctTqPr1JDhGvqsHMbmVnZyM+Ph5vvvkm3nzzTb199qqqqrBu3TpcvHjRKNPjxoBRptRUaWtrw7p16/Df//4XZmZmGDFiBOLj47F48WJERkYaze5AtdDO4/FoXTMPDw96ZVddXY3CwkIEBwcb3ItnMNTV1SEvL6/X6yApSB6Pp1brMISqc1+QHdpQ/j1IIwqfz1ebe9Jl0wHZEYSEhBiVFL0qquoXJB1LOkLd3NxgbW1N79CCg4O1vo78/HwsWLAAq1evxnvvvafXz1pSUhIWL16slnlRKBR0WeDChQuYO3fuQ51SM+qAo1QqsW7dOvz8889ISkpCWFgYzp8/j+PHj+Ps2bNwcHBAfHw8EhMTMXnyZKMpVqumWIiNtJWVFdrb2xEWFqZ1a6cxUF5ejtLSUo2H77rWOkxNTen8/kAk5HUNUUGYMGGC1t1PA4Wkm1QDsaqtgDY3RxI0Q0NDjULNQVNI3YcEYisrK4jFYvj5+cHX11er96KoqAgLFiyg24j1vbBpa2tDRUWF2mPLly9HYGAgNm3ahNGjR8Pd3R0//vgjPXRaWFiIwMDAbk0DdXV1dDrxyy+/xFtvvQUej2d0BoQDxagDDgB89NFHePLJJ+Hj46P2eEdHBy5evIjjx4/j1KlTsLKywqJFi5CYmIjp06cbTRGe+MS3tLTAzMysm8SOsZxnf6iKV3ZVrdYU4t5IAjGRVCECo/paMBCrB0OqIKgGYoFAQO+INbFRJtTX19PzKfoKmkMBj8dDVlYW7O3tIRKJtKr7lJaWYv78+Xjqqafw8ccfG03mQ7VpAOhsi/7ll19w6NAhODg4YO3atQCA27dvA/ijLXrEiBHYvXs36uvr8cILL2DlypVMW7SxIJVKcfXqVRw9ehQnT54EAMTGxmLx4sWYOXOmwVoJVWdTOBwOLCwsaCVjIqqpqnKgr+LyQFEqlcjNzUVLS4vOxCuJpAp5L1Tlhoaq0E5RFO7fv4/q6mqEh4cbjVAj2RGTNKQmTQdEwHIww5DGQGNjIzIyMujaE0lNk92PQqFQs5Tu6b2oqKjA/PnzERcXh88++8xogg3QPeCQwc8ff/xRbfBTNYVYUVGB1atXIzk5Gba2tli2bBl27tw5bBanffFABBxV5HI5rl+/jiNHjuDkyZMQi8WIjY1FYmIi5syZo7diXkdHB9LT02FtbY2JEyf2uGJVldghrcWk1mEs/fZEz47MCg3Flr4nuSFSaO9N8UGb30F8hSIiIozWXqCn94LUOkjTgarpmDHq1GkKaeEOCAjoUcqpt7oPWZx5eXmhpqYG8+bNw+OPP44DBw4YVbBh6M4DF3BUUSgUuHXrFo4ePYqkpCS0tLRgwYIFSExMxNy5c4dMZr6lpQUZGRnw8PBAQECARrlk4lnP4/HQ2tqqN0XnvpBKpWoWCfpaYfVkKUDeC23+ZmRQuLm5GZGRkcOqZbtr04GlpSUkEgnd6GAsDRgDpbm5GWlpaQPqDuzo6KDn4RISEuDk5ISWlhbMmDEDJ06ceCB2AA86D3TAUUWpVOLu3bt08OFyuYiJiUFiYiJiYmJ0tuIl/i9jx46Ft7e31kOhqorOg73hagNxVnVwcEBoaKjBVo4SiURNYHSgQ7cKhYI2sYuIiBjWRdfS0lKUlZXBwcEBra2tOmk6MARk7snf31/r4dT8/HzExsbCwsICzc3NcHR0RHx8PNavXw9/f38dnzGDrnhoAo4qSqUSaWlpOHbsGI4fP46qqirMnTsXCQkJWLhwodatu1VVVSguLtap/4tUKqWDT2Njo9p8y1ClhVpbW5Geng5PT89ucvaGRCaT0V1eREySvBc93XCJdBDRdzPWGpkmlJWVoby8nLa2Jk0HJN2kTdOBISAab4MJNgKBALGxsQgMDMThw4dBURSSk5Nx6tQpvPrqq7QbMIPx8VAGHFUoikJOTg6OHDmC48ePo6SkBI8++iji4+MRFxcHZ2fnfm+4FEWhuLgYtbW14HA43SaJdQW54RKJHWInwGazYW9vr5PAQPx4fHx8jHowtbcbLpGWUSgUSE9Pp/2Rhmu6haIolJaWoqqqCpGRkT2Ku/bUdECaUfSpdNAfJNiQ3b82NDU1IS4uDt7e3jhy5IjR1DoZNOOhDziqUBSFgoICHD16FCdOnEBOTg5mzpyJxMRELFq0CG5ubt1uwKouo+Hh4TozMesPhUJBBx+BQABzc3PaTlvb9Appsw0KCjLotPpA6Tr3JJfLwWKxYGNjM6yVqymKQklJCWpraxEZGanRjla16YDP50MoFHZrOjAEra2tSE1NHZSgaEtLCxYtWgQ2m40TJ04M6/TowwoTcHqBtNCS4JOWloZp06YhMTER8fHx8PT0RH19Pb777ju69dFQNzYiIUJuuCYmJnTw0dS3pLKyEiUlJXodhBwK2tvbce/ePZiZmYGiKIjF4mHRet4VMvfE5XIRGRmp9UKGFNpVHV7JTlBfkkNEGJXsmrV9jYSEBNjb2+P06dNDFjh37NiB48ePo6CgANbW1pg2bRp27dqFgIAA+piH3dNmMDABRwMoikJFRQWOHTuGEydO4LfffsOECRNQVlaGCRMm4MyZM0ZzI+s6XKnqZePq6tot+JBVdE1NjVHNpmiDUChEWloa2Gw23R3YtfXcGFb7/UFauPl8PiIjI3XWKNJV6aC/Gpgu0EWwEYlEeOKJJ2BiYoKzZ88OaRZh/vz5eOaZZzBp0iTI5XK88847yMnJQV5eHv17H3ZPm8HABJwBQlEUTp06heeeew6Ojo60lXJCQgISEhK0luUYCrp62RCVA5LbZ7FYyM/PR2NjIyIiIvSWDhwKWltbkZaWhlGjRvVqpdx1te/g4KC22jcGKIqi/yZD2cKtj6YDoVCIe/fuYcyYMVqbwHV0dODJJ5+ETCbDuXPn9G5QyOfzwWazce3aNcycOZPxtBkkTMAZIGfPnsXTTz+NXbt24ZVXXgGXy0VSUhKOHTuGa9euISQkhA4+xtThpWqaxePxIBaLYWZmBhaLZdSDkJrQ1NSEjIwMWoFbE4iZGlnt29jY6LwBY6BQFEUrOkRGRuptB6ZUKtVUH3TRdECCjbe3N/z8/LQ6L7FYjGeeeQatra24cOGCQXbfJSUlGDduHLKzsxEaGsp42gwSJuAMkIKCAhQXF2PRokVqj1MUhcbGRjr4XL58GePGjVPz9DGW4EMcOmUyGczMzNDe3q5W5xhOKzAy99TbtLomEI8j0m5NGjD6spnQNUQ+qK2tDZGRkQYriPfWdEB2gpoEQaFQiNTUVHq3qQ0SiQTPP/886uvrcenSJTg7O2v1OoNBqVQiPj4ezc3NuHnzJgDg8OHDWL58OSQSidqx0dHRmDNnDnbt2oW//OUvqKiowIULF+jn29vbYWtri19++QULFizQ63UYEw93BUsLAgMDe+zzZ7FYcHV1xYoVK/DSSy+hpaUFp06dwvHjx/HPf/4T3t7edPAxpDMmkdyxtbVFaGgoTE1NIRKJwOPxUF1djfz8fLrOoStZmaGCdNUNVilZ1eNIqVTSopqZmZkA0GcNTBcolUpkZ2ejvb0dUVFRBg34qiZ7Y8eOVUtDFhUV9etzJBKJaOdUbYONTCbDiy++iOrqaly5csUgwQYA1qxZg5ycHDrYMAweJuAMASwWC05OTli6dCmWLl2K1tZWnD17FsePH8fjjz8ONpuNhIQEJCYm6tXThxTV3d3dERgYSN8sbG1t4evrC19fX1pKpb6+HoWFhXB0dDRKF0+iJ6ZruwdiFe3u7q5WAysoKKBFNUmqSRcdR0qlEpmZmZBIJIiMjDS63aW1tTW8vb3h7e2t5uZZVlZGNx24u7vDycmJ7hAcTLCRy+VYuXIlSkpKcPXqVY0sMIaCV199FWfOnMH169fVpHc8PT0hlUrR3NysllLjcrm0AKenpyd+//13tdfjcrn0cw8zTEpNz4hEIpw7d4729HFyckJ8fDwSEhKG1NOH1DlITl2TNJFEIqHz+k1NTbCzs6PttA1ZZC8vL0dZWRk4HI7eVr8URXVT+iZiq9qmIRUKBTIzMyGTyRAREWE0nY6a0LXpgDzm5uaGkJAQrYKxQqHAyy+/jNTUVCQnJxvk5kxRFNauXYsTJ04gOTkZ48aNU3ueNA08zJ42g4EJOAaEePocO3aMni1YtGgRFi9ejGnTpumsZ5/H4yEnJ2dQNsrExZOoHNjY2NDBRxNNM12g2sIdERGhlSePriBpSB6Ph7a2Nlps1d3dXaOdIPFJUigUiIiIGNbzGSKRCCkpKbCysoJcLodUKh1w04FCocDatWtx69YtJCcna12PGyyvvPIKDh8+jJMnT6rN3jg6OtJ/14fd02YwMAHHSJBKpbh8+TKOHTuGkydPgsViIS4uDosXL8YjjzyidaqFpJ5CQ0Pp1dZgIUV2onJgaWlJB5+hspAmKhACgcDoWrjFYjFd51DdCbq7u/fY/SeXy5Geng4WiwUOhzOsg01HRwfu3bsHNpuN8ePHA+hM3ZL3Q7XpoLdgrFQqsX79ely6dAnJyclaKxHogt4+u9988w1efPFFAIynzWBgAo4RIpfLce3aNdrTRyKRIC4uDgkJCXj00Uc12pITDa7KysohTT31ZCGtqnKgi+BDOrhaW1sRERFhVLWkrvRkI01qYA4ODnSwMTU1BYfDMVqRTU3oGmz6mn3i8/l0MCYpWaJosWnTJpw+fRpXr17VuvbDMDxgAo6Ro1AocPPmTdpWoa2tDQsWLEBCQkKvnj5keJDsBvQ1Y0PcGkmqiQwTenh4aGwV3BWFQoGsrCyIxeJhZy9A9O5Iu7WpqSmUSiWsra2HXc2mKyTYuLu7a+z5RNKyfD4ff/vb35CZmQkXFxfU19fjxo0bCAoK0sOZMxgSJuAMI5RKJX777Tc6+PD5fMTExCAhIYH29BGJRPjhhx8QGhqK8PBwg+0GugpqKhQKtfZiTVb2crkcGRkZUCqVw95eQCwW4969e6AoCkqlkpYccnd31/j9MBbItbi6uqp1Ow6EtrY2rFy5EpcuXYK1tTXMzMywaNEiPPfcc3j00UeH4KwZjAEm4AxTlEolUlNTaU+f6upqzJ49G7m5ubCzs8O1a9f0ZtbWHxRFqU2yS6XSftuLiduoubk5wsLChtUNuSsSiQSpqamws7NDaGgoWCxWt/fDGO0EeoIEGxcXF62HmSmKwq5du7B//35cuXIFwcHBuH37NpKSkuDq6op33nlnCM6cwRjQW8CJj49HRkYGeDwenJ2dMXfuXOzatUtNBj8rKwtr1qxBSkoK3N3dsXbtWmzcuFHtdY4cOYJt27ahvLwc48aNw65du7Bw4UJ9XILRolQqcfnyZTz//PMQiUSQyWR47LHHkJCQgNjYWI08ffRFT+3FXdWcxWIx0tLSYGtra9AhWV1ArsXe3h4hISE9iqeqCoyKRCK1dmtjSiGKxWKkpqbC2dl5UMFm7969+Pjjj3H58uWHWublYURvAeeTTz7B1KlT4eXlhZqaGrz55psA/mglbG1txfjx4zF37ly8/fbbyM7OxksvvYS9e/fiL3/5C33szJkzsWPHDsTFxeHw4cPYtWsX0tLSEBoaqo/LMEoKCgoQExODuXPn4sCBAyguLqZtFXJzczFr1iwkJiYiLi6uR08fQ9JVzdnR0ZG+6RrS2loXdHR00Dfo4OBgjd739vZ2+v1obW01msFbiUSCe/fuwcnJSeNr6QpFUfjiiy+wY8cOXLhwAdHR0UNwpgzGjMFSaqdOnUJiYiIkEgnMzc2xf/9+bNmyBfX19XQL8ObNm5GUlISCggIAwNNPPw2RSIQzZ87QrzNlyhRwOBwcOHDAEJdhFOTm5uL48ePYunWr2o2AzK2Q4JOeno7p06cjISGB9vQxpuAjEAiQlZUFU1NTyGQyerZFUw0vY4IU1V1dXbXeDZDBWz6fT9uLkzqYvmafyHmkpqbCwcEBISEhWgebr776Ctu3b8e5c+cwbdq0ITjTgfPFF19gz549qK+vR1hYGD777DMmEA4hBgk4jY2NWL16NWpqamidIiIBk5SURB939epVPProo2hsbISzszO8vb3xxhtv4PXXX6eP2b59O5KSkmjdK4aeUfX0OX78OO7evYspU6bQKgejRo0yaPBpaWlBeno6Ro8eDT8/PzWVA2IlQIKPsdSmeoPoian68gwWYi9OOt704WUDdNbS7t27N+hg8+2332Lz5s04ffo0Zs2aNQRnOnB+/vlnLF26FAcOHMDkyZOxd+9eHDlyBIWFhTqbWWNQR6/5ik2bNsHW1haurq6orKzEyZMn6efq6+u7CTCSf9fX1/d5DHmeoXdYLBZ8fHywYcMG3Lx5E+Xl5ViyZAnOnj2LkJAQzJkzB3v37kVZWRn0vQZpbGyk7YeJl42VlRW8vb0RFRWFmTNnYsSIEWhsbMTt27dx584dlJaWQigU6v1c+4PI8nt6euos2ACAubk5vLy8EBYWhtmzZ2P8+PF0Y8X169eRn5+PhoYGKJVKnfw+oDPYpKam0vUnbYPNDz/8gI0bNyIpKclogg0A/POf/8SqVauwfPlyBAcH48CBA7CxscHXX39t6FN7YBlUwNm8eTNYLFaf/5F0GAC89dZbSE9Px6+//gpTU1MsXbrU6G4YDwMsFgujRo3Ca6+9huTkZFRVVWH58uW4cuUKOBwOZsyYgT179qCoqGjI/z48Hg8ZGRkIDAyEt7d3j8dYWFhg1KhRiIiIwKxZs+Dj44O2tjbcvXsXt2/fRklJCVpbWw3+WSKy/CNHjsS4ceOGbNdBhmtDQ0Mxa9Ysun6Zm5uLa9euIScnh25F1xYSbGxtbQcVbI4cOYI33ngDR48eNap2Z3J9c+fOpR8zMTHB3LlzcefOHQOe2YPNoHQWNmzYQMs99Iaq+ZKbmxvc3Nwwfvx4BAUFYfTo0fjtt98wdepUeHp60oqqhK4Kq70d87ArsA4GFosFLy8vrF69Gi+//DIaGhpw8uRJHD16FB9++CHGjx9PK1vr2tOnrq4OeXl5A7IXICt9Ly8verCSy+Xi3r17tI+Nh4fHkKaZeoI4jg7GcEwbTExM4OrqSs/EEJO94uJiZGdnw83NjZ730bTdWiaTIS0tDTY2NoNq3EhKSsKaNWvw008/Yf78+Vq9xlAhEAigUCh6zJioLpIZdMugAg75IGsD2foTI6OpU6diy5YtkMlk9Bfj4sWLCAgIoGVZpk6disuXL6vVcC5evIipU6cO4ioYCCwWC25ubrSnT3NzM+3p8/HHH2PMmDF08Blsu3JVVRWKi4vB4XC0lqA3NTWFh4cHPDw8oFAoaJWD9PR0mJiYqEnsDGW3W0tLC9LS0gbkODoUsFgsODo6wtHREf7+/rTAaGVlJfLy8mifI3d3916bMGQyGVJTU2FtbT2ov/GZM2fwl7/8Bd999103s0KGhxe9NA3cvXsXKSkpmDFjBpydnXH//n1s27YNXC4Xubm5sLS0REtLCwICAjBv3jxs2rQJOTk5eOmll/DJJ5+otUXPmjULO3fuRGxsLH766Sd8+OGHD31btD5obW3FmTNncPz4cZw7dw6enp6Ij4/H4sWLERERofGNiaIolJeXo7y8HOHh4WqeIrpCqVSiqamJbjogU/1DYaLW3NyM9PR0+Pn5GVR0sj+IzxGPx0NLS0uPTRhkZ2NpaYmJEydq/T6dP38eL7zwAr7++ms8/fTTurwMnSGVSmFjY4OjR48iMTGRfnzZsmVobm5Wqy8z6A69BJzs7GysW7cOmZmZEIlE8PLywvz587F161Y1GXLVwU83NzesXbsWmzZtUnutI0eOYOvWrfTg5+7dux/6wU99IxQK1Tx9nJ2dER8fj8TERERHR/eqCkBRFIqLi1FXV4eIiAjY29sP+bmqmqjxeDzI5XI1lYPBKBg0NjYiIyMD48aNw+jRo3V41kOLRCKh1ZwbGxvpRh6BQAArKytwOBytg82VK1fwzDPPYP/+/Xj++eeNqu2+K5MnT0Z0dDQ+++wzAJ0LFW9vb7z66qvYvHmzgc/uwYSRtmEYFB0dHfj1119x7NgxnDlzBtbW1li0aBESExPVPH3kcjkyMzPR3t5uMHsBiqLoGgePx4NYLKaDj7u7+4Ck4xsaGpCZmYmAgACDebfoArlcDi6Xi+LiYshkMjV164GqfV+/fh1PPfUUPv30Uyxfvtyogw3Q2Ra9bNkyHDx4ENHR0di7dy/+97//oaCgYFCW5Qy9wwQcBp0hkUjUPH1MTEywaNEiLFiwAPv374elpSW+//57oxjipCgKIpEIXC6XlpRRldjpy3+IDKgGBQXBy8tLj2ete+RyOdLS0mBmZobQ0FBa443P59Nq32w2Gy4uLn3ueu7cuYPFixdj165dePnll40+2BA+//xzevCTw+HgX//6FyZPnmzo03pgeSgDTnl5Of7+97/jypUrqK+vx4gRI/D8889jy5YtajcaRttNe2QyGa5du4Yff/wR33//PeRyORYvXow///nPmDNnjlFphAHdHTxJgZ3NZqudK4/HQ3Z2NkJCQoZ9dyTx5jExMenmzaOq9s3n89VSka6urmq7wZSUFCQkJOBvf/sb1q5dO2yCDYP+eSgDzvnz5/Hzzz/j2Wefhb+/P3JycrBq1Sq88MIL+OijjwAw2m66oKWlBYsWLQJFUdi0aRMuXLiAEydOQCgUYsGCBUhMTMTcuXONzlCNmIZxuVy0tLTQemYmJiYoKirChAkThv0kukKhQFpaWo/BpiskFUnqPh0dHUhJSYGtrS2CgoKwbNkybNmyBRs2bGCCDUOfPJQBpyf27NmD/fv3o7S0FAAYbTcd8Pe//x137tzB0aNH6U4ohUKB3377DceOHcOJEycgEAgQExODxMREzJs3T29mcZpCJHaqqqogEolgbW2NkSNH0q6VwxGFQoH09HQAQHh4+IAbJ0QiEfbv349vvvkG5eXl8PPzw7p167B48eJh1TzBoH+GrxSvjmlpaYGLiwv97zt37mDmzJlqKbaYmBgUFhaiqamJPkZ1Upkcw0wqd/L2228jKSlJTfvM1NQU06dPxz//+U/cv38fly9fxtixY/G3v/0NPj4+ePbZZ/Hzzz+jtbXVgGf+B5aWljA1NYVYLMbEiRPh5+eH5uZm/Pbbb7h9+zbu37+PtrY2g6scaIpCoUBGRgYA7YINANja2mLhwoUQCoV47bXXsG7dOpw4cQJ+fn5Yv369js+Y4UFiUIOfDwolJSX47LPP6HQa0Knb5uvrq3acqrabs7Mzo+3WD/11fZmYmCA6OhrR0dHYsWMHsrKycPToUezZswerV69W8/QZaMeUrqiurkZRURE4HA69IBkxYgTkcjmtclBeXg5LS0t4eHiAzWbDwcHBKFNLJNgQB1VtW8ILCwsRFxeHlStX4sMPPwSLxcJrr70GgUCAxsZGHZ81w4PEA7XDGai2GwDU1NRg/vz5eOqpp7Bq1SoDnTkDqSV88MEHyM3NRWpqKqKjo7Fv3z74+vpi8eLF+Oabb8Dn8/W2m6isrERxcTHCw8PVdr9AZzD19PRUE9OUSCRIS0vDjRs3UFBQgKamJqPZ+SgUCmRmZtLBZiAt4Krcv38fcXFx+POf/4x//OMfaoGVyFYxMPTGAxVwNmzYgPz8/D7/U9W5qq2txZw5czBt2jR8+eWXaq/FaLsZDhaLhZCQEGzfvh3p6enIycnB7NmzcejQIfj7+yMuLg5ffvkl6uvrh+yGXl5ejvv37yMiIoKWVuqNrmKawcHBUCqVyMzMxPXr15GXl6dzJeeBoFQqkZWVBblcPqhgU15ejri4OCxevBgfffSR3s3xysvLsWLFCvj6+sLa2hpjx47F9u3bIZVK1Y7LysrCI488AisrK4wePRq7d+/u9lpHjhxBYGAgrKysMGHCBPzyyy/6uoyHmoe2aaCmpgZz5sxBZGQkvv/++27pBdI0wOVyaW23d955B8ePH1drGmhvb8fp06fpn5s2bRomTpzINA0MAUQWh3j6/P7775gyZQoSEhKQkJCAkSNH6iSVVVpaisrKSkRERMDBwUHr11FtLSbqzaoSO4NRORjIOWRmZkIqlSIiIkJjAc+uVFdXIyYmBvPmzcP+/fsN4sTKdJcOfx7KgFNTU4PZs2djzJgx+Pbbb9W++GR3wmi7GTcURaG6uhrHjx/H8ePHcevWLURGRiIxMREJCQkYM2bMgIMPRVEoLS1FVVUVIiMjdSq9Q1EUPVTJ4/EglUrVJHa03XX0BdnZSCSSQQWburo6zJ8/HzNmzMC///1vvQRKTWG6S4cXD1RKTVMuXryIkpISXL58GaNGjaLl7lWnxh0dHfHrr7+irKwMkZGR2LBhA95991062ACdu5nDhw/jyy+/RFhYGI4ePYqkpCQm2OgBFouF0aNHY926dbSnz7Jly3Dp0iWEhYXhkUcewZ49e1BcXKxR2o3YcVdXVyMqKkrnOm8sFgtOTk4YP348pk+fjkmTJsHGxgalpaW4du0aMjIyUFtbC5lMppPfp1QqkZ2dDbFYPKhgw+VyERcXh+joaKMLNgDTXTrceCh3OAwPLhRFQSAQ0J4+V69eRUBAAC0u2pOnD0VRKCoqApfLRWRkpN7na4RCIb3zEQqFcHFxoVUO+pLY6Q0SbDo6OhAZGal1sBEIBFi4cCGCgoJw+PBhrV9nqCgpKUFkZCQ++ugjuuFn3rx58PX1xcGDB+nj8vLyEBISgry8PAQFBcHCwgLffvstnn32WfqYffv24f333+9Wk2XQLQ/lDofhwYXof61cuRLnzp1DXV0d3njjDWRlZWHGjBmIiorC+++/j6ysLCiVSigUCnzwwQf0zsYQw5x2dnbw8/PDlClTMG3aNLi4uKC2thbXr1/HvXv3UFlZCbFYrNFrKZVK5OTk0CKp2gaJxsZGxMfHw9/fHz/88MOQBhumu/ThgQk4RsQ//vEPTJs2DTY2Nr36xFRWViI2NhY2NjZgs9l46623IJfL1Y5JTk5GREQELC0t4e/vj0OHDg39yRshLBYLLi4uePHFF3Hq1ClwuVxs3boVJSUleOyxxxAWFoaoqCj8+9//ho+Pj9qAqqGwsbGBj48PoqOjMWPGDHh4eIDH4+HmzZv4/fffUV5ejvb29h5/lgQbkUiEyMhIrXZHQGeaKjExESNHjsTPP/+s9etoCtNd+vDADH4aEVKpFE899RSmTp2K//znP92eVygUiI2NhaenJ27fvo26ujosXboU5ubm+PDDDwEAZWVliI2Nxcsvv4wffvgBly9fxsqVK+Hl5YWYmBh9X5JR4ejoiOeeew7PPfccWlpaEB8fj7S0NCiVSixatIi2VejL00efkLbe0aNHQyqV0vpuJSUlsLW1pQdNya4sNzcXQqEQUVFRWgeJtrY2LF68GC4uLjh27JheRFYH4hys2l36zTffdOuWY5yDjRumhmOEHDp0CK+//jqam5vVHj937hzi4uJQW1tLKxwcOHAAmzZtAp/Ph4WFBTZt2oSzZ88iJyeH/rlnnnkGzc3NOH/+vD4vw2iRyWRYunQpsrKycPnyZTg4OKh5+tjY2CA+Ph4JCQlqnj7Ggkwmg0AgAI/Ho03TWCwWFAoFJk2apLX9g0gkwp/+9CeYmZnhzJkzRqcVx3SXDn+YlNow4s6dO5gwYYKanE5MTAxaW1uRm5tLH8N04PTPyJEjkZycDE9PT9jY2CAxMRHfffcd6urq8OWXX0IikeD555/HuHHjsHbtWly5ckVnHWSDxdzcHF5eXggLC8OsWbNgaWkJsVgMmUyGlJQUFBYWorm5eUBDse3t7ViyZAkA4NSpU0YXbACmu/RBwLiWbgx90pt2G3mur2NaW1vR0dFhdFYAhsDc3FxNN08VKysrxMbGIjY2FjKZDMnJyTh69ChWrlwJmUyGuLg4JCYmYvbs2Qb39KEoCoWFhZBIJJg+fTrMzMzQ2NgIHo9H+9yw2Wx4eHjAycmp12FNsViMZ599Fh0dHbhw4YJerL+14cUXX8SLL77Y73ETJ07EjRs3+jzmqaeewlNPPaWjM2PQFGaHM8Ro04HDYByYm5vj8ccfx8GDB1FdXY1jx47B3t4ea9euha+vL1auXIkzZ86go6ND7+dGURTy8/PR1NSEyMhIWtXa3d0dISEhmDVrFr1iz87OxvXr15Gbmws+n68msUN2ck1NTTh37hwcHR31fi0MDw/MDmeI2bBhQ7+rMtUOnL7w9PTE77//rvaYph04Dg4OzO5mEJiZmWH27NmYPXs2Pv30U9y5cwfHjh3Dxo0b0dDQgPnz5yMhIQExMTFDno6iKAoFBQVobGxEVFRUjzUbExMTuLq6wtXVFYGBgbTEDhEVPXToEOLi4vDLL7+gtrYWly9f7lczjoFhsDABZ4gZSAdOf0ydOhX/+Mc/wOPxaMfJixcvwsHBAcHBwfQxXYUImQ4c3WJqaooZM2ZgxowZ+Pjjj5GSkoJjx47h/fffx1//+lc8/vjjSEhIwIIFCwalxdYTJI3W0NDQa7DpCovFgrOzM5ydnTF+/HiUlZXBy8sLGzduhFgsxsKFC3HhwgXExcXp/HwZGFRhUmpGRGVlJTIyMlBZWUl7l2RkZEAoFALonKIODg7GCy+8gMzMTFy4cAFbt27FmjVr6HrCyy+/jNLSUmzcuBEFBQXYt28f/ve//zHGWEOEiYkJJk+ejN27d6OwsBA3b95ESEgIdu/eDR8fHyxZsgTff/+9TqwKSLDh8/mIjIzUqhuNxWJhzJgxkEgkGD16NK5cuYJJkyZh586dcHd3R3Z29qDOkYGhL5i2aCPixRdfxLffftvt8atXr2L27NkAgIqKCqxevRrJycmwtbXFsmXLsHPnTrXW3eTkZKxfvx55eXkYNWoUtm3bplGxlUF3UBSF3NxcHD16FCdOnEB+fj5mz56NxMRExMXFwdXVdUDiokR+h8fjISoqSuv0qEKhwNq1a3Hr1i0kJydj5MiR9HPFxcXw8/MzihkkhgcTJuAwMAwxJFgQW4XMzEzMmDEDiYmJWLRoETw8PPoMPhRFobi4mNZ601YRQalUYv369bh8+TKuXr2KMWPGaHtJDAxawaTUGBiGGBaLhYCAALzzzjv0nMzChQvx008/Yfz48Zg/fz727duH6urqbmk3omJdX18/6GCzadMmXLhwAZcuXTJ4sJFIJOBwOGCxWMjIyFB7jjFQe3BhAg4Dgx5hsVjw8/PDW2+9hdu3b6O0tBRPPPEETp06heDgYDz22GP49NNPUV5eDoVCgbfeegsXL14cdLDZunUrkpKScOnSJY27IoeSjRs3YsSIEd0eb21txbx58zBmzBikpqZiz549eO+999Q0027fvo1nn30WK1asQHp6OhITE5GYmKimrsFgpFAMDFrw+eefU2PGjKEsLS2p6Oho6u7du4Y+pWGNUqmkampqqM8//5yaM2cOZWpqSrHZbMra2pr68ccfKaFQSIlEogH/JxQKqY0bN1IeHh5UXl6eoS+ToiiK+uWXX6jAwEAqNzeXAkClp6fTz+3bt49ydnamJBIJ/dimTZuogIAA+t9LliyhYmNj1V5z8uTJ1F//+tchP3eGwcHscBgGzM8//4w33ngD27dvR1paGsLCwhATEwMej2foUxu2sFgsjBgxAmvWrMHly5exfv16dHR0gMPhYOnSpZg6dSp27NiBvLw8jbvdKIrCzp078fXXX+PixYsICgoa4qvoHy6Xi1WrVuG7777rccfGGKg92DABh2HA/POf/8SqVauwfPlyBAcH48CBA7CxscHXX39t6FN7INixYwe+/fZb3LlzB7du3UJ9fT3Wr1+PjIwM2tPnb3/7G7Kzs9VUA1ShKAqffPIJvvjiC/z666+YMGGCnq+i53N68cUX8fLLLyMqKqrHYwYj30SeZzBemIDDMCCkUilSU1PVVpgmJiaYO3cus8LUEREREbh8+TJCQkJoT5/ly5fj9OnT4HK52LJlC4qKivDoo4+Cw+Fg27ZtSE1NpYMPRVH4/PPP8fHHH+P8+fMIDw8f0vPVVL7ps88+Q1tbG95+++0hPR8G44VRGmAYEAKBAAqFoscVJqMJpxvmz5/f63OOjo54/vnn8fzzz0MoFOKXX37BsWPHsHDhQri6uiI+Ph4sFguHDh3CuXPnEB0dPeTnq6l805UrV3Dnzp1uoqdRUVF47rnn8O233zIGag84TMBhYBim2NnZYcmSJViyZAna29tx4cIFHD58GMePH8eJEycwbdo0vZyHpvJN//rXv/DBBx/Q/66trUVMTAx+/vlnTJ48GQBjoPbAY9CWBYZhh0QioUxNTakTJ06oPb506VIqPj7eMCfFoIZQKDT0KWhEWVlZty615uZmysPDg3rhhReonJwc6qeffqJsbGyogwcP0sfcunWLMjMzoz766CMqPz+f2r59O2Vubk5lZ2cb4CoYBgJTw2EYEBYWFoiMjMTly5fpx5RKJS5fvsysMI0EYzRP0xTGQO3BhpG2YRgwP//8M5YtW4aDBw8iOjoae/fuxf/+9z8UFBR0q+0wMDAwEJgaDsOAefrpp8Hn8/Huu++ivr4eHA4H58+fZ4INAwNDnzA7HAYGBgYGvcDUcBgYGBgY9AITcBgYGBgY9AITcBiGDdevX8eiRYswYsQIsFgsJCUlqT1PURTeffddeHl5wdraGnPnzkVxcbHaMY2NjXjuuefg4OAAJycnrFixgnZUZWBgGFqYgMMwbBCJRAgLC8MXX3zR4/O7d+/Gv/71Lxw4cAB3796Fra0tYmJiIBaL6WOee+455Obm4uLFizhz5gyuX7+u1nLLwMAwhBh0CoiBQUsAqA2fKpVKytPTk9qzZw/9WHNzM2VpaUn9+OOPFEVRVF5eHgWASklJoY85d+4cxWKxqJqaGr2d+3DmzJkzVHR0NGVlZUU5OTlRCQkJas9XVFRQCxcupKytrSl3d3fqzTffpGQymdoxV69epcLDwykLCwtq7Nix1DfffKO/C2AwKMwOh+GBoKysDPX19Wqioo6Ojpg8eTItKnrnzh04OTmpKRXPnTsXJiYmuHv3rt7Pebhx7NgxvPDCC1i+fDkyMzNx69Yt/PnPf6afVygUiI2NhVQqxe3bt/Htt9/i0KFDePfdd+ljysrKEBsbizlz5iAjIwOvv/46Vq5ciQsXLhjikhj0DDOHw/BAQKTp+5Ktr6+vB5vNVnvezMwMLi4ujLR9P8jlcqxbtw579uzBihUr6MeDg4Pp///111+Rl5eHS5cuwcPDAxwOB3//+9+xadMmvPfee7CwsMCBAwfg6+uLjz/+GAAQFBSEmzdv4pNPPkFMTIzer4tBvzA7HAYGhn5JS0tDTU0NTExMEB4eDi8vLyxYsEDN1vnOnTuYMGGCWtCPiYlBa2srcnNz6WMY87SHFybgMDwQEGn6vmTrPT09u7mSyuVyNDY2MtL2/VBaWgoAeO+997B161acOXMGzs7OmD17NhobGwEMzjyttbUVHR0dQ30ZDAaGCTgMDwS+vr7w9PRUExVtbW3F3bt3aVHRqVOnorm5GampqfQxV65cgVKppOXxHzY0NU8j5m5btmzBE088gcjISHzzzTdgsVg4cuSIga+CYbjA1HAYhg1CoRAlJSX0v8vKypCRkQEXFxd4e3vj9ddfxwcffIBx48bB19cX27Ztw4gRI5CYmAigs14wf/58rFq1CgcOHIBMJsOrr76KZ555BiNGjDDQVRkWTc3T6urqAKjXbCwtLeHn54fKykoAnTvI33//Xe1nNTVPc3BwgLW19aCuhWEYYOg2OQYGTbl69SoFoNt/y5YtoyiqszV627ZtlIeHB2VpaUk99thjVGFhodprNDQ0UM8++yxlZ2dHOTg4UMuXL6fa2toMcDXDi5aWFsrS0pL697//TT8mlUopNptNe9X88ssvlImJCcXlculjDh48SDk4OFBisZiiKIrauHEjFRoaqvbazz77LBUTE6OHq2AwNEzAYWBg0Ih169ZRI0eOpC5cuEAVFBRQK1asoNhsNtXY2EhRFEXJ5XIqNDSUmjdvHpWRkUGdP3+ecnd3p95++236NUpLSykbGxvqrbfeovLz86kvvviCMjU1pc6fP2+oy2LQI0zAYWBg0AipVEpt2LCBYrPZlL29PTV37lwqJydH7Zjy8nJqwYIFlLW1NeXm5kZt2LChx8FPDodDWVhYUH5+fszg50MEY0/AwMDAwKAXmC41BoZBsmPHDkyaNAn29vZgs9lITExEYWGh2jFisRhr1qyBq6sr7Ozs8MQTT3QrnldWViI2NhY2NjZgs9l46623IJfL9XkpDAxDChNwGBgGybVr17BmzRr89ttvuHjxImQyGebNmweRSEQfs379epw+fRpHjhzBtWvXUFtbiz/96U/085rIwjAwDHeYlBoDg47h8/lgs9m4du0aZs6ciZaWFri7u+Pw4cN48sknAQAFBQUICgrCnTt3MGXKFJw7dw5xcXGora2lByMPHDiATZs2gc/nw8LCwpCXxMCgE5gdDgODjmlpaQEAuLi4AABSU1Mhk8nUJF0CAwPh7e2tJizanywMA8Nwhwk4DAw6RKlU4vXXX8f06dMRGhoKoFPOxcLCAk5OTmrHdhUW7U8WhoFhuMMoDTAw6JA1a9YgJycHN2/eNPSpMDAYHcwOh4FBR7z66qs4c+YMrl69ilGjRtGPe3p6QiqVorm5We34rsKiPUm+kOcYGB4EmIDDwDBIKIrCq6++ihMnTuDKlSvw9fVVez4yMhLm5uZqwqKFhYWorKxUExbNzs5WU7O+ePEiHBwc1PTLGBiGM0yXGgPDIHnllVdw+PBhnDx5EgEBAfTjjo6OtCDl6tWr8csvv+DQoUNwcHDA2rVrAQC3b98G0NkWzeFwMGLECOzevRv19fV44YUXsHLlSnz44Yf6vygGhiGACTgMDIOExWL1+Pg333xDKzGLxWJs2LABP/74IyQSCWJiYrBv3z61dFlFRQVWr16N5ORk2NraYtmyZdi5cyfMzJhSK8ODARNwGBgYGBj0AlPDYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC0zAYWBgYGDQC/8HcJrCReoizEMAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot the distribution of the particles\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(particles[:,0], particles[:,1], particles[:,2], cmap='viridis', c=particles[:,3])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choice of units\n",
"Recap of the particle properties:\n",
"- $\\sim 10^4$ particles\n",
"- spherical distribution\n",
"\n",
"$\\implies$ this seems to be a **globular cluster**"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": [
"plot_particle_distribution"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"17:34:05 - task1 - Considering a globular cluster - total mass of particles: 4622219.258999999, maximum radius of particles: 724.689657812915\n",
"17:34:05 - utils.units - Set scales: M_SCALE = 0.022 solMass, R_SCALE = 0.028 pc\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Set G = 1\n",
"G = 1\n",
"\n",
"\n",
"# Since we have a globular cluster, we can use typical values\n",
"M_TOT = 1e5 * u.M_sun\n",
"R_TOT = 20 * u.pc\n",
"\n",
"# Rescale the units of the particles\n",
"M_particles = particles[:,3].sum()\n",
"R_particles = np.max(np.linalg.norm(particles[:, :3], axis=1))\n",
"logger.info(f\"Considering a globular cluster - total mass of particles: {M_particles}, maximum radius of particles: {R_particles}\")\n",
"m_scale = M_TOT / M_particles\n",
"r_scale = R_TOT / R_particles\n",
"utils.seed_scales(r_scale, m_scale)\n",
"\n",
"\n",
"\n",
"### Plot again with scales\n",
"reduced = utils.remove_outliers(particles.copy())\n",
"positions = utils.apply_units(reduced[:, :3], \"position\")\n",
"masses = utils.apply_units(reduced[:, 3], \"mass\")\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"sc = ax.scatter(positions[:,0], positions[:,1], positions[:,2], cmap='viridis', c=masses)\n",
"\n",
"ax.set_xlabel(f'x [{positions.unit}]')\n",
"ax.set_ylabel(f'y [{positions.unit}]')\n",
"ax.set_zlabel(f'z [{positions.unit}]')\n",
"cbar = plt.colorbar(sc, ax=ax, pad=0.1)\n",
"cbar.set_label(f'Mass [{masses.unit}]')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"all_r = utils.r_distribution(particles)\n",
"rbins = np.logspace(np.log10(np.min(all_r)), np.log10(np.max(all_r)), NBINS, endpoint=True)\n",
"\n",
"## Using the Hernquist model with parameters M and a\n",
"m = M_particles\n",
"a = utils.half_mass_radius(particles) / (1 + np.sqrt(2))\n",
"logger.debug(f\"Scale length: {a=:.2g}, total mass: {m=:.2g}\")\n",
"rho_t = utils.model_density_distribution(rbins, m, a)\n",
"\n",
"## Numerical density distribution\n",
"rho, err = utils.density_distribution(rbins, particles, ret_error=True)\n",
"\n",
"## Add the units\n",
"rho = utils.apply_units(rho, \"density\")\n",
"err = utils.apply_units(err, \"density\")\n",
"rho_t = utils.apply_units(rho_t, \"density\")\n",
"rbins = utils.apply_units(rbins, \"position\")\n",
"\n",
"\n",
"plt.figure()\n",
"plt.title('Density distribution')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel(f'r [{rbins.unit}]')\n",
"plt.ylabel(f'$\\\\rho$ [{rho.unit}]')\n",
"plt.errorbar(rbins.value, rho.value, yerr=err.value, fmt='o', label=\"Particle data\")\n",
"plt.plot(rbins.value, rho_t.value, 'o', label=\"Analytic model\")\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"## Note that by construction, the first shell contains no particles\n",
"## => the numerical density is zero there\n",
"## Having more bins means to have shells that are nearly empty\n",
"## => the error is large, NBINS = 30 is a good compromise"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"tags": [
"plotting"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"21:30:11 - utils.particles - Found mean interparticle distance: 0.010402746349924056\n"
]
}
],
"source": [
"### Direct N body force computation and comparison with analytical model\n",
"epsilon = utils.mean_interparticle_distance(particles)\n",
"\n",
"\n",
"epsilon_range = np.logspace(-3, 3, 7)\n",
"n_squared_forces = []\n",
"for e in epsilon_range:\n",
" n_particles = particles.shape[0]\n",
" cache_file = CACHE_ROOT / f\"n_squared_forces__n_{n_particles}__softening_multiplier_{e:.0f}.npy\"\n",
" try:\n",
" f = np.load(cache_file)\n",
" except FileNotFoundError:\n",
" f = utils.n_body_forces(particles, G, e * epsilon)\n",
" np.save(cache_file, f)\n",
" logger.debug(f\"Saved forces to {cache_file}\")\n",
" n_squared_forces.append(f)\n",
"\n",
"analytical_force = utils.analytical_forces(particles)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"SKIP_N = 20\n",
"## Plot the radial force behaviour\n",
"r = np.linalg.norm(particles[:,:3], axis=1)\n",
"r = utils.apply_units(r, \"position\")\n",
"\n",
"plt.figure()\n",
"f_analytical = np.linalg.norm(analytical_force, axis=1)\n",
"f_analytical = utils.apply_units(f_analytical, \"force\")\n",
"plt.plot(r.value[::SKIP_N], f_analytical.value[::SKIP_N], '.', label=\"Analytical\", zorder=10, alpha=0.5)\n",
"\n",
"for e, f in zip(epsilon_range, n_squared_forces):\n",
" f_abs = np.linalg.norm(f, axis=1)\n",
" f_abs = utils.apply_units(f_abs, \"force\")\n",
" plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=f\"$N^2$ - {e:.1g} * $\\\\epsilon$\")\n",
"\n",
"\n",
"plt.title('Radial force')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel(f'$r$ [{r.unit}]')\n",
"plt.ylabel(f'$F_r(r) [{f_analytical.unit}]$')\n",
"plt.legend()\n",
"plt.show()\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## For fun, do this with the mesh solver as well:\n",
"particles = utils.remove_outliers(particles)\n",
"r = np.linalg.norm(particles[:,:3], axis=1)\n",
"r = utils.apply_units(r, \"position\")\n",
"\n",
"plt.figure()\n",
"f_nsquare = utils.analytical_forces(particles)\n",
"f_abs = np.linalg.norm(f_nsquare, axis=1)\n",
"f_abs = utils.apply_units(f_abs, \"force\")\n",
"plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=\"N^2\")\n",
"\n",
"f_mesh = utils.mesh_forces(particles, G, 405, utils.particle_to_cells_nn)\n",
"f_abs = np.linalg.norm(f_mesh, axis=1)\n",
"f_abs = utils.apply_units(f_abs, \"force\")\n",
"plt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], '.', label=\"Mesh\")\n",
"\n",
"plt.title('Radial force')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel(f'$r$ [{r.unit}]')\n",
"plt.ylabel(f'$F_r(r) [{f_analytical.unit}]$')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Discussion\n",
"- basic $N^2$ matches analytical solution without dropoff. but: noisy data from \"bad\" samples\n",
"- $N^2$ with softening matches analytical solution but has a dropoff. No noisy data.\n",
" - softening $\\approx 1 \\varepsilon$ is a sweet spot since the dropoff is \"late\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Relaxation time\n",
"\n",
"For an estimate of the crossing time we use the half mass radius and the circular velocity at the half mass radius.\n",
"\n",
"$\\implies$ the crossing time is of order radius / velocity"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"21:31:32 - task1 - Central velocity @ HM 3106.1056463446503 solMass(1/2) / pc(1/2)\n",
"21:31:32 - task1 - Crossing time for half mass system: 1.7e-06 pc(3/2) / solMass(1/2)\n",
"21:31:32 - task1 - Direct estimate of the relaxation timescale: 0.00076 pc(3/2) / solMass(1/2)\n"
]
}
],
"source": [
"## Computes the relaxation timescale of a set of particles using the velocity at the half mass radius.\n",
"\n",
"# enclosed mass at half mass radius\n",
"m_half = np.sum(particles[:, 3]) / 2\n",
"r_half = utils.half_mass_radius(particles)\n",
"# set the units\n",
"m_half = utils.apply_units(m_half, \"mass\")\n",
"r_half = utils.apply_units(r_half, \"position\")\n",
"\n",
"v_c = np.sqrt(G * m_half / r_half)\n",
"logger.info(f\"Central velocity @ HM {v_c}\")\n",
"\n",
"t_c = r_half / v_c\n",
"logger.info(f\"Crossing time for half mass system: {t_c:.2g}\")\n",
"# TODO: how to treat this unit?\n",
"\n",
"## Using the derived formula for the relaxation timescale\n",
"# Compute the relaxation timescale through the estimate\n",
"# t_relax = t_c *n_relax = t_c * N / (10 * log(N))\n",
"n = particles.shape[0]\n",
"n_relax = n / (10 * np.log(n))\n",
"t_rel = t_c * n_relax\n",
"logger.info(f\"Direct estimate of the relaxation timescale: {t_rel:.2g}\")\n"
]
},
{
"attachments": {
"Pasted image 20250118155501.png": {
"image/png": 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"
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"#### Discussion\n",
"\n",
"\n",
"The estimate for $n_{relax}$ comes from the contribution of each star-star encounter to the velocity dispersion. This depends on the perpendicular force\n",
"\n",
"![Pasted image 20250118155501.png](<attachment:Pasted image 20250118155501.png>)\n",
"\n",
"The full integration of the force along the path of the star reduces to the main contribution at the closest approach (distance $b$):\n",
"$$\n",
"\\delta v \\approx \\frac{2 G m}{b} \\to \\delta v \\approx \\frac{2 G m}{b + \\varepsilon}\n",
"$$\n",
"$\\implies$ a bigger softening length leads to a smaller $\\delta v$.\n",
"\n",
"Using $n_{relax} = \\frac{\\delta v^2}{v^2}$, and knowing that the value of $v^2$ is derived from the Virial theorem (i.e. unaffected by the softening length), we can see that $n_{relax}$ scales like $\\varepsilon^{-2}$.\n",
"\n",
"##### Effect\n",
"- The relaxation time decreases with increasing softening length\n",
"- From the integration over all impact parameters $b$ even $b_{min}$ is chosen to be larger than $\\varepsilon$ $\\implies$ expect only a small effect on the relaxation time\n",
"\n",
"#TODO : The softening dampens the change of velocity => time to relax is longer"
]
}
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