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{
"cells": [
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The autoreload extension is already loaded. To reload it, use:\n",
" %reload_ext autoreload\n"
]
}
],
"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",
"from astropy.visualization import quantity_support\n",
"quantity_support()\n",
"\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\")\n"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [],
"source": [
"DATA_ROOT = Path('data')\n",
"DATA_NAME = 'data.txt'\n",
"CACHE_ROOT = Path('.cache')"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"20:14:58 - 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]]"
]
},
{
"cell_type": "code",
"execution_count": 111,
"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": 112,
"metadata": {
"tags": [
"plot_particle_distribution"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"20:15:00 - task1 - Considering a globular cluster - total mass of particles: 4622219.258999999, maximum radius of particles: 724.689657812915\n",
"20:15:00 - utils.units - Set scales: M_SCALE = 0.011 solMass, R_SCALE = 0.014 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 = 5* 1e4 * u.M_sun\n",
"R_TOT = 10 * 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",
"utils.particles_plot_3d(positions, masses, title=\"Particle distribution\")\n"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {
"tags": [
"plot_density_distribution"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"NBINS = 25\n",
"all_r = utils.r_distribution(particles)\n",
"rbins = np.logspace(np.log10(np.min(2*all_r)), np.log10(np.max(all_r)), NBINS, endpoint=True)\n",
"\n",
"\n",
"## Using the Hernquist model with parameters M and a\n",
"a = utils.half_mass_radius(particles) / (1 + np.sqrt(2))\n",
"logger.debug(f\"Scale length: {a=:.2g}, total mass: {M_particles=:.2g}\")\n",
"rho_t = utils.model_density_distribution(rbins, M_particles, a)\n",
"\n",
"## Numerical density distribution\n",
"rho, err = utils.density_distribution(rbins, particles, ret_error=True)\n",
"# since we are using a logarithmic scale, the error should be scaled accordingly:\n",
"# the error of log(rho) is delta=dlog/drho * err\n",
"err = err * 1 / rho * np.log(10)\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(f'Density distribution {NBINS=}')\n",
"plt.xscale('log')\n",
"# plt.yscale('log')\n",
"plt.xlabel(\"R\")\n",
"plt.xlabel(f'r [{rbins.unit:latex}]')\n",
"plt.ylabel(f'$\\\\rho$ [log {rho.unit:latex}]')\n",
"\n",
"plt.plot(rbins, np.log(rho_t.value), 'o', label=\"Analytic model\", color=\"black\", zorder=10)\n",
"\n",
"# since we used the value between the bins we should shift the values to the center of the bins\n",
"rbins = rbins.value\n",
"rbins -= np.diff(rbins, prepend=0) / 2\n",
"plt.fill_between(rbins, np.log(rho.value) - err, np.log(rho.value) + err, alpha=0.3, label=\"Particle data\", color=plt.cm.Blues(0.6))\n",
"\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"20:15:05 - 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": 115,
"metadata": {
"tags": [
"plot_force_radial"
]
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"SKIP_N = 1\n",
"\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",
"\n",
"plt.plot(r[::SKIP_N], f_analytical[::SKIP_N], '.', label=\"Analytical\", zorder=10, alpha=0.5, color='black')\n",
"\n",
"colors = plt.cm.Blues(np.linspace(0.3,1,len(epsilon_range)))\n",
"for e, f, c in zip(epsilon_range, n_squared_forces, colors):\n",
" # print((np.log(e)+10) * 10)\n",
" f_abs = np.linalg.norm(f, axis=1)\n",
" f_abs = utils.apply_units(f_abs, \"force\")\n",
" plt.plot(r[::SKIP_N], f_abs[::SKIP_N], '.', label=f\"$N^2$ - {e:.1g} * $\\\\epsilon$\", color=c)\n",
"\n",
"\n",
"plt.title('Radial force')\n",
"plt.xscale('log')\n",
"plt.yscale('log')\n",
"plt.xlabel(f'$r$ [{r.unit:latex}]')\n",
"plt.ylabel(f'$|F(r)|$ [{f_analytical.unit:latex}]')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'\\nparticles = utils.remove_outliers(particles)\\nr = np.linalg.norm(particles[:,:3], axis=1)\\nr = utils.apply_units(r, \"position\")\\n\\nplt.figure()\\nf_nsquare = utils.analytical_forces(particles)\\nf_abs = np.linalg.norm(f_nsquare, axis=1)\\nf_abs = utils.apply_units(f_abs, \"force\")\\nplt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], \\'.\\', label=\"N^2\")\\n\\nf_mesh = utils.mesh_forces(particles, G, 405, utils.particle_to_cells_nn)\\nf_abs = np.linalg.norm(f_mesh, axis=1)\\nf_abs = utils.apply_units(f_abs, \"force\")\\nplt.plot(r.value[::SKIP_N], f_abs.value[::SKIP_N], \\'.\\', label=\"Mesh\")\\n\\nplt.title(\\'Radial force\\')\\nplt.xscale(\\'log\\')\\nplt.yscale(\\'log\\')\\nplt.xlabel(f\\'$r$ [{r.unit}]\\')\\nplt.ylabel(f\\'$F_r(r) [{f_analytical.unit}]$\\')\\nplt.legend()\\nplt.show()\\n'"
]
},
"execution_count": 116,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## For fun, do this with the mesh solver as well:\n",
"\"\"\"\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": 117,
"metadata": {
"tags": [
"compute_relaxation_time"
]
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"20:22:42 - task1 - Circular velocity @ HM 203.1824123982491 km / s\n",
"20:22:42 - task1 - Crossing time for half mass system: 0.048 Myr\n",
"20:22:42 - task1 - Relaxation timescale: 28 Myr\n"
]
}
],
"source": [
"## Relaxation timescale (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",
"\n",
"# set the units\n",
"m_half = utils.apply_units(m_half, \"mass\")\n",
"r_half = utils.apply_units(r_half, \"position\")\n",
"# finally add a unit to G\n",
"true_G = 4.3e-3 * (u.pc / u.M_sun) * (u.km / u.s)**2\n",
"\n",
"# crossing time\n",
"v_c = np.sqrt(true_G * m_half / r_half)\n",
"logger.info(f\"Circular velocity @ HM {v_c}\")\n",
"r_tot = np.max(np.linalg.norm(particles[:, :3], axis=1))\n",
"r_tot = utils.apply_units(r_tot, \"position\")\n",
"t_c = r_tot / v_c\n",
"t_c = t_c.to(u.Myr)\n",
"logger.info(f\"Crossing time for half mass system: {t_c:.2g}\")\n",
"\n",
"## Using the relaxation timescale formula\n",
"n = particles.shape[0]\n",
"n_relax = n / (8 * np.log(n))\n",
"t_rel = t_c * n_relax\n",
"t_rel = t_rel.to(u.Myr)\n",
"\n",
"logger.info(f\"Relaxation timescale: {t_rel:.2g}\")\n"
]
},
{
"attachments": {
"Pasted image 20250118155501.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 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 $n_{relax} = \\frac{v^2}{\\delta v^2}$, 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 $n_{relax}$ should increase with $\\varepsilon$.\n",
"\n",
"##### Effect\n",
"- The relaxation time **increases** 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",
"**In other words:**\n",
"The softening dampens the change of velocity => time to relax is longer"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [],
"source": [
"import inspect\n"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {
"tags": [
"function_apply_units"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def apply_units(columns: np.array, quantity: str):\n",
" if quantity == \"mass\":\n",
" return columns * M_SCALE\n",
" elif quantity == \"position\":\n",
" return columns * R_SCALE\n",
" elif quantity == \"volume\":\n",
" return columns * R_SCALE**3\n",
" elif quantity == \"density\":\n",
" return columns * M_SCALE / R_SCALE**3\n",
" \n",
" ## Derived quantities\n",
" elif quantity == \"force\":\n",
" # using F = GMm/R^2 => F = M_SCALE**2 / R_SCALE**2 (G = 1)\n",
" return columns * M_SCALE**2 / R_SCALE**2\n",
" elif quantity == \"velocity\":\n",
" # using the Virial theorem: v^2 = GM/R => v = sqrt(GM/R) => v = sqrt(M_SCALE / R_SCALE) (G = 1)\n",
" return columns * np.sqrt(M_SCALE / R_SCALE)\n",
" elif quantity == \"time\":\n",
" # using the dynamical time: t_dyn = 1/sqrt(G*rho) => t_dyn = sqrt(4/3 * pi * R_SCALE**3 / M_SCALE) (G = 1)\n",
" return columns * np.sqrt(4/3 * np.pi * R_SCALE**3 / M_SCALE)\n",
" else:\n",
" raise ValueError(f\"Unknown quantity: {quantity}\")\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(utils.apply_units))"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {
"tags": [
"function_density_distribution"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def density_distribution(r_bins: np.ndarray, particles: np.ndarray, ret_error: bool = False):\n",
" \"\"\"\n",
" Computes the radial density distribution of a set of particles.\n",
" Assumes that the particles array has the following columns: x, y, z, m.\n",
" If ret_error is True, it will return the absolute error of the density.\n",
" \"\"\"\n",
" if particles.shape[1] != 4:\n",
" raise ValueError(\"Particles array must have 4 columns: x, y, z, m\")\n",
"\n",
" m = particles[:, 3]\n",
" r = np.linalg.norm(particles[:, :3], axis=1)\n",
"\n",
" m_shells = np.zeros_like(r_bins)\n",
" v_shells = np.zeros_like(r_bins)\n",
" error_relative = np.zeros_like(r_bins)\n",
" r_bins = np.insert(r_bins, 0, 0)\n",
"\n",
" for i in range(len(r_bins) - 1):\n",
" mask = (r >= r_bins[i]) & (r < r_bins[i + 1])\n",
" m_shells[i] = np.sum(m[mask])\n",
" v_shells[i] = 4/3 * np.pi * (r_bins[i + 1]**3 - r_bins[i]**3)\n",
" if ret_error:\n",
" count = np.count_nonzero(mask)\n",
" if count > 0:\n",
" # the absolute error is the square root of the number of particles\n",
" error_relative[i] = 1 / np.sqrt(count)\n",
" else:\n",
" error_relative[i] = 0\n",
"\n",
" density = m_shells / v_shells\n",
"\n",
" if ret_error:\n",
" return density, density * error_relative\n",
" else:\n",
" return density\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(utils.density_distribution))"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"tags": [
"function_analytical_forces"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def analytical_forces(particles: np.ndarray):\n",
" \"\"\"\n",
" Computes the interparticle forces without computing the n^2 interactions.\n",
" This is done by using newton's second theorem for a spherical mass distribution.\n",
" The force on a particle at radius r is simply the force exerted by a point mass with the enclosed mass.\n",
" Assumes that the particles array has the following columns: x, y, z, m.\n",
" \"\"\"\n",
"\n",
" n = particles.shape[0]\n",
" forces = np.zeros((n, 3))\n",
"\n",
" logger.debug(f\"Computing forces for {n} particles using spherical approximation\")\n",
"\n",
" r_particles = np.linalg.norm(particles[:, :3], axis=1)\n",
" for i in range(n):\n",
" r_current = np.linalg.norm(particles[i, 0:3])\n",
" m_current = particles[i, 3]\n",
"\n",
" m_enclosed = np.sum(particles[r_particles < r_current, 3])\n",
"\n",
" # the force is the same as the force exerted by a point mass at the center\n",
" f = - m_current * m_enclosed / r_current**2\n",
" forces[i] = f\n",
"\n",
" if i % 5000 == 0:\n",
" logger.debug(f\"Particle {i} done\")\n",
"\n",
" return forces\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(utils.analytical_forces))"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {
"tags": [
"function_n2_forces"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def n_body_forces(particles: np.ndarray, G: float = 1, softening: float = 0):\n",
" \"\"\"\n",
" Computes the gravitational forces between a set of particles.\n",
" Assumes that the particles array has the following columns: x, y, z, m.\n",
" \"\"\"\n",
" if particles.shape[1] != 4:\n",
" raise ValueError(\"Particles array must have 4 columns: x, y, z, m\")\n",
"\n",
" x_vec = particles[:, 0:3]\n",
" masses = particles[:, 3]\n",
"\n",
" n = particles.shape[0]\n",
" forces = np.zeros((n, 3))\n",
" logger.debug(f\"Computing forces for {n} particles using n^2 algorithm (using {softening=:.2g})\")\n",
"\n",
" for i in range(n):\n",
" # the current particle is at x_current\n",
" x_current = x_vec[i, :]\n",
" m_current = masses[i]\n",
"\n",
" # first compute the displacement to all other particles (and its magnitude)\n",
" r_vec = x_vec - x_current\n",
" r = np.linalg.norm(r_vec, axis=1)\n",
"\n",
" # add softening to the denominator\n",
" r_adjusted = r**2 + softening**2\n",
" # usually with a square root: r' = sqrt(r^2 + softening^2)\n",
" # and then cubed, but we combine that below\n",
"\n",
" # the numerator is tricky:\n",
" # m is a list of scalars and r_vec is a list of vectors (2D array)\n",
" # we only want row_wise multiplication\n",
" num = G * (masses * r_vec.T).T\n",
" # a zero value is expected where we have the same particle\n",
" r_adjusted[i] = 1\n",
" num[i] = 0\n",
"\n",
" f = - np.sum((num.T / r_adjusted**1.5).T, axis=0) * m_current\n",
" forces[i] = f\n",
"\n",
" if i!= 0 and i % 5000 == 0:\n",
" logger.debug(f\"Particle {i} done\")\n",
"\n",
" return forces\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(utils.n_body_forces))"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {
"tags": [
"function_interparticle_distance"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def mean_interparticle_distance(particles: np.ndarray):\n",
" \"\"\"\n",
" Computes the mean interparticle distance of a set of particles.\n",
" Assumes that the particles array has the following columns: x, y, z ...\n",
" \"\"\"\n",
" if particles.shape[1] < 3:\n",
" raise ValueError(\"Particles array must have at least 3 columns: x, y, z\")\n",
" \n",
"\n",
" r_half_mass = half_mass_radius(particles)\n",
" r = np.linalg.norm(particles[:, :3], axis=1)\n",
"\n",
" n_half_mass = np.sum(r < r_half_mass)\n",
" logger.debug(f\"Number of particles within half mass radius: {n_half_mass} of {particles.shape[0]}\")\n",
"\n",
" rho = n_half_mass / (4/3 * np.pi * r_half_mass**3)\n",
" # the mean distance between particles is the inverse of the density\n",
"\n",
" epsilon = (1 / rho)**(1/3)\n",
" logger.info(f\"Found mean interparticle distance: {epsilon}\")\n",
" return epsilon\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(utils.mean_interparticle_distance))"
]
}
],
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"kernelspec": {
"display_name": "projects-X-9bmgL6",
"language": "python",
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