\n",
"\n",
"**This is a fixed-text formatted version of a Jupyter notebook**\n",
"\n",
"- Try online [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.13?urlpath=lab/tree/source_population_model.ipynb)\n",
"- You can contribute with your own notebooks in this\n",
"[GitHub repository](https://github.com/gammapy/gammapy/tree/master/tutorials).\n",
"- **Source files:**\n",
"[source_population_model.ipynb](../_static/notebooks/source_population_model.ipynb) |\n",
"[source_population_model.py](../_static/notebooks/source_population_model.py)\n",
"
\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Astrophysical source population modeling with Gammapy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"The [gammapy.astro.population](..\/astro/population/index.rst) package contains some simple Galactic source population models.\n",
"\n",
"Here we provide some Python code to compute observable parameter distributions for Galactic gamma-ray source populations.\n",
"\n",
"* Observables: Flux, GLON, GLAT\n",
"* Source classes: Pulsar (PSR), Supernova remnant (SNR), pulsar wind nebula (PWN)\n",
"\n",
"References:\n",
"\n",
"* Section 6.2 in the Fermi-LAT collaboration paper [\"The First Fermi-LAT Catalog of Sources Above 10 GeV\"](https://ui.adsabs.harvard.edu/abs/2013ApJS..209...34A)\n",
"* Axel Donath's bachelor thesis [\"Modelling Galactic gamma-ray source populations\"](http://pubman.mpdl.mpg.de/pubman/item/escidoc:912132:1/component/escidoc:912131/BScThesis_ddonath.pdf), specifically Chapter 4.\n",
"* Casanova & Dingus (2008), [\"Constraints on the TeV source population and its contribution to the galactic diffuse TeV emission\"](https://ui.adsabs.harvard.edu/abs/2008APh....29...63C)\n",
"* Strong (2007), [\"Source population synthesis and the Galactic diffuse gamma-ray emission\"](https://ui.adsabs.harvard.edu/abs/2007Ap%26SS.309...35S)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import astropy.units as u\n",
"from gammapy.utils.random import sample_powerlaw\n",
"from gammapy.astro import population"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate positions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Spatial distribution using Lorimer (2006) model\n",
"n_sources = int(1e5)\n",
"\n",
"table = population.make_base_catalog_galactic(\n",
" n_sources=n_sources,\n",
" rad_dis=\"L06\",\n",
" vel_dis=\"F06B\",\n",
" max_age=1e6 * u.yr,\n",
" spiralarms=True,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate luminosities"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Several source population models, e.g. the 1FHL paper or Strong (2007), use power-law luminosity functions.\n",
"\n",
"Here we implement the \"reference model\" from the 1FHL catalog paper section 6.2."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Source luminosity (ph s^-1)\n",
"\n",
"luminosity = sample_powerlaw(x_min=1e34, x_max=1e37, gamma=1.5, size=n_sources)\n",
"table[\"luminosity\"] = luminosity"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Compute observable parameters"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"
\n",
" name dtype unit description \n",
"---------- ------- --------- --------------------------------------\n",
" age float64 yr Age of the source\n",
" n_ISM float64 1 / cm3 Interstellar medium density\n",
" spiralarm str18 Which spiralarm?\n",
" x_birth float64 kpc Galactocentric x coordinate at birth\n",
" y_birth float64 kpc Galactocentric y coordinate at birth\n",
" z_birth float64 kpc Galactocentric z coordinate at birth\n",
" x float64 kpc Galactocentric x coordinate\n",
" y float64 kpc Galactocentric y coordinate\n",
" z float64 kpc Galactocentric z coordinate\n",
" vx float64 km / s Galactocentric velocity in x direction\n",
" vy float64 km / s Galactocentric velocity in y direction\n",
" vz float64 km / s Galactocentric velocity in z direction\n",
" v_abs float64 km / s Galactocentric velocity (absolute)\n",
"luminosity float64 \n",
" distance float64 pc Distance observer to source center\n",
" GLON float64 deg Galactic longitude\n",
" GLAT float64 deg Galactic latitude\n",
" VGLON float64 deg / Myr Velocity in Galactic longitude\n",
" VGLAT float64 deg / Myr Velocity in Galactic latitude\n",
" RA float64 deg Right ascension\n",
" DEC float64 deg Declination\n",
" flux float64 1 / kpc2 Source flux\n"
]
}
],
"source": [
"table = population.add_observed_parameters(table)\n",
"table.info()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Check output"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simulation is done, you could save the simulated catalog to a file.\n",
"\n",
"Here we just plot a few distributions to check if the results look OK."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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mYolKAS7Yd/0ma5TJ7P2szjwhgK7aL0mFFZyuNzC4zC5mvdEU2PHsEWVtGm+xMq8QMS0UJ383qcUjoM6OledPutiZThkaGnRwttFbliHN5ycpE2w//HdLMrqmH9uurG/tNt3/fOjkIZXGHhShESWKxyaypCUgzDXssAxHCGEcdEqoNxaNFqChQQfTf3C99TnunTqMr+2PljvglAm7fnNjYvPWb04A2SqwposgixrZY1vTR0eq0TVE9GMA/wagCWBBN5B+0a/Il6w1RpiarmH7M0e0mpspFaeEB2+9wvoB9NOE5OvH5+qdQmJz843OsXWRJV5B75QJp+cbsBHvYWLynTJh7XvDC3mTQmiSU/ONUBq19HnozFomNJoCd++ewYE3Tgb6T8IQtDvJ0vOTlAm2H/67xDX5tpAfE0L8NOi9/dDk41o5s4rcQbhrzQ8NOtbCT4etdueOd9bhJ2iDHJzuyJ0z5xasFrHhtplEF3+tYmjQwY1XXhRZS7Yhjrm5NqJvolwiND11fLIYX58USZVK7ocmv+TKGqQZ+ZJ03Q13eQHgQnmBUzEJeKCl3ZnWOpEmAz8BXyby1aSDBPxLk9d1yg7YCHhp433x6KyxgC8RcOOVF+GxGEoo2BDH3HR3xgpD0+O8SbrmTdZq1NiUZbChH53X+uF4FQCeJyIB4C+FEI+6XySiuwDcBQAjIyOJDyatyJd+mIlUZo2w+GnQOqHj9UOcOO0vnMKYStzU5uq4ZucLHaelKe4koG2uMNEgFgX6qsFLwtTz8ZLEhj0pxSiryYRJmGD70XmtH0L+GiHEcSJ6P4DvENFRIcT35Ittof8o0DLXJD2YtCJfonjnTZ24cT50AuiYe7y4F0S3eci9MATZq8OYSlTU5urW5hb3NjjOGjBJEVDU04jTEX0xKpJSjPKUTBgHSfvvEjfXCCGOt/9/G8DTAK5O+px+JLXtCiKsmUjVYFpXeS/Oh264WsFDt2/03Up6zUOmgrZMhJcmr7Mylfhhc4w5jxPSrzF6VvCOOQxR50bZU/IyScUoT8mEeSBRIU9EK4no3fJnANcDeCXJc5owvmm4Y8t9afI6Zfu6uO2BQfXYdQRFpbiZ2LIetkqfo5gBTok6uwW/BTGseeiOj10CIJ2H1nu/vde4fCB7bioBRJ6HOtvvnZtH4ATULL5z8wgeum1j3xSjsM8KoyZpc80HADxNrf3mAICvCyH+NuFzRiIpe2BYM5FtbZnPbh7pMV8QWlEx5xUNoJ1yCSDR3Rza9cz7bSXDCmlZM8XPVKIrkxAF3f12X+Nl9zwX70ljIuo89LP9jl26uquEhZev7X8TLx6dDbQVx5UbMrFlfU/ZCql4MPYsyWQoP5IMsQzzEOjGU3FKAMg4kcQkA9KNyfWGqRJZrThYuVzfYi9OnDJh5bIBnK43jO931FDDfpBE9cjL7nkusBSCX8hgnCGGU9M1TDx5qFvxQHdRNaYbLjVsQZL2QKkxSmG/zaCxtUqrAaDM6JRmHJUJyrY+u7s5tq55hdfZGoRTIpw5fyGW/dR8A06ZUPUpVWzDoFPCuQWBphAgap3PRsADemdzlkgi2sTkmv2cnzbO0iBlZ9e+Yz0CHmjV2hm7dHUhna9Jkj0DZMokbQ+0caQCrYfYr5SvF10fTJ1NVhc/fXG1ohzr3btn8MXdM13OVjm64WoFd24e6dhuhwYdVCtOx477rhUDPQ9voymwcvmAtS/Bi1MmNJqiI6yEaGWW2raJk/6CrBN3nLppHL0MW/XeS1PlSDf/75063JmzOmVEAH3pR1s0WJP3kHSIZZDGo9JybNLgB5eVlT6FB2+9olOOQGbD1htNLB8odQSk93p1jlXvaGTN+CDzjq4iZNR2dgRgoES+9WrqjSa2P3MkUAt8YPwKvD77Dl567WSosfSTOIuI2WxeVDsJ0/wT3fw3DYPlCBt7WJP3kHSIZZAjVaXl2HDmfG89bvciIjV6qfHO1RuAaGly8no/fdVwaPOOH367pCihjAJq85WXuXoDm+5/3jdqamq6hh+8firUONLg7t0z2HT/85EjwGzj6N07ianpGs6cW+h5j0o50s0T0zWGI2zsYU1eQZLJCX4aj07LIYqesSgfLtU5GosCP6sv4OGtowDQs5MxweTh89sl2dRCj4Is1lWbq2Nbu/iW25m3a9+xxBzBSXFqvhHZRh9mJ+VWTLzzZWjQwX03begZT5QdW9rlhvMKa/J9xq9WhVbLEeixy3uTU4KQQlj3gDWFwD1PHcaOZ49YC3jTh0+1S5K7hnWTe7Fr37G+Oj0FWuGB904dxuiO57HWxx6cdaLa6Ce2rA+Ml/eiU0wAYHDZgHLBUc1/3VmHBp2+Jy0WEdbk+4xfvLKfiaTRFJ3Ij+GAioveiBcphKema77RMH6t19yECU0EeqMqVI0ybNvqxUEc9WjKJcK7lw/EEiUUlij26vFNwzjwxkmreyHLUtiMRTX/vfMAaM1Z1U6AsYfj5DPC1HTNqPa3jD32i3u/c/MIXjw627OIhIlr1+GO1TaJ/7dp/JFHZCOQi6sVnDxzLrVG4/J7AcyKXrm/u5Jl+Oiwz+7QNq9EpQDsfflE53moVhxsv5mFvg6/OHkW8hnApgEz4P9w+XUS0nW3CUvFKePTVw0rtTDv1jrOBSbrOGUCBFKz7TslAgg9EVPe78R23nkhAA9vHY29zrouGcopEXbdllynqjzD9eQzjm0NmONzda1t/76bNmg/F3dkQr3RxOPf/4lRbZ2lFPrWaAq8a8VAZzHu+/kXRY+AVH0nUUtTy/m0wlUAqVpxItvOdclQjUXzXgbMBVjIZ4CwXettQz2TqLio2957rymroW+EZB6CufkGXpq8LjVBr8L7nURZeCtOGddevgb3PHW4y8R4bsHfTGVS/M9vXEtJWYgLdrymiLRD2mzq3ZEspqGebntnddDB8oFSx2k6+29nlYXLTDGpOQ+0nHRpNNwIYlXFwSc3XoSnDr5llXQWRIkI6yb3YlXF6Uk2SwvvdxI2nFHa/W3rvpsW//MbV1aVhSzDmnxKeGuxmxAmjMybYHVqvoFzC4t4eOsoXpq8Drf/Uvg0/opTxh0fuySwfdnUdA2Pf/8noc8TJyV0h6PO1RvYc7CGP7r1SjyydRRlww4dQaUmmkJAoDfZbFBV2zlmStQ7PlWYq83OruKU8MjWUfzYVZ7bts6TadnsiS3rlfeXK1GGo9CavLuJdJkId3zsksxUsQtjDw1TeVD3YO149gi2P3MkVMgfAV0RG2OXrtZGcshFJgtFv6oVB0ToiWByF3YDzJLBVi4bUB5LRWNRYHDZAO67aYN1BnMY3rOiFYkSFF0jf/crMyxZvXK5cWKTTtu2KZu99ZcuyXx0TVyllZOmsEJeNpGWNIXo/J4FQR/Gthgmq1G3UzARTircpYKlBuZnNoqz72wQg04JZxcWlXXoqxUHM/dd71s/B+iO4/bbZZ2uN1C1aI4t71c/7sXpesPYlDe+adgoy1h1L2zrPOkWheqg02PG2XOwlunkp6z2oVVRWHONzjyQFbNBGNtimKxGU/ODCbJUsGkFzanpWl/DJodWLteWf5irNzA1XTOqMio7h925Wd9YvuKUrBbKi6uV/jkNCVZdzUx2WQT0OExtnf+6iDAhYNz9LCvYdGxLm8IKed3EzYLZAAgf6WIrKOK63jKRslSwbmLfO3XYyAwQJ0ELiqzdH+RDkPgpBDZOWnn8fjkNhYBViWWTCCB5PO9xg1pputEtCrriaFmOpMlTH9rCCnmdBhunZhsF74Q3HZetoIgjhK/ilPHQ7Ru1DaVVNcPTiqTxW9JqLpOJvN8q7VOG+YVdIAedklK7DVMfJipB2uXUdA3z53srSEY9rg7VopC3nq5T0zWUNM9rFsecuJAnohuI6BgRvUpEk0mfT6Jr/pClphDuCf/Q7RsDNXvbKnxhH2A3ZaKOkDJ9GO956uVI50wKwgVtvylETwVMIFzUk5sSAbde9UEArQXn/50+i7t3z+CanS8AAN61ov9uMJ12Ka81rH8mLq3VZneVNn6BBFkdc6JCnojKAP4MwK8D+CiAO4joo3GfR5Vg8cD4Fbhz80hHYysTZbpHpNTsq5ULzrxBp9RV593GERX1AZYsCtE5p8nDODVdS61uix+qOjlJZIGWCdhzsNa1mAAXTBxRv48wyJh9r43e71rdOx2/7mFxkHQPhzjR3TO3MpQ1klYrrgbwqhDiRwBARN8AcAuAH8Z1Aj8v9wPjV2RWqOt6p7ozBlvt6wgPbx2NJXQyDF6HpDy2X3/OrOHXtzXOLFAAaCwCjUX1fa83migRlNE/SeJeaCa+eQgAfOPc5WdkVuu3D53oeT1urTXJHg5xortnbmUoayRtrhkG4PZevdX+WwciuouIDhDRgdnZWesT5MnLLVF1gNq2ewZ3756J7VpMhFWJ0OnJCvTW9VY9yEGOtiSjaVYuK3fG7WZo0MGdm0eU9m6nTHjo9o1a30SJqEu7TdqmmoSAJ6j7C6isxo1Fge3PHAEQfK2yLZ83l2JoMHp9mrySN/8BkLwmr5pnXdNcCPEogEeBVhVK2xPkycstUS1Mfhce5lpMUtYXRXfOQNTkjqB69VFYPlDCkftv8H3P2KWrexK8Vi5rTXFVTDdwoVkKgI5zNEplRhOcUkvjV7FyWRlOuWSVpCbQ0tbeM+hgbv5CjX9ddJM8tsm1qr5LXUOQOMlqolHSPaCTIGkh/xYAt6fzgwCOx3kC26y7LGCr7Ya5FlNhddk9z3UakUxsWY+XJq/rPGDbds90wg5NHjDbOjw2nPcUvpJjlE3J5TV8cuNFXaWP5+qNrkbmqsSfeqOJLz1xwYwhr0XW+nnn7EKsZYP9XBbz55t4fecNmJquWYWgyqxad5npoM+bJn55iapA6UyV8m+rKg7OnF/ohOtmKdHIxGSZNZIW8v8E4MNEtA5ADcBnAPyHOE+Ql5XVPbFtCHstctIFlS7wOgYPvHGyp1uT6QOW5O7JvdB5/TDua1CFbkqT18SW9b75E+7r9Ebc2ArCsMgs2jhMdEODjtLR63akymv1Zoj7EUWBUvnQ7t490+WrUM1Xv8Jn/SYv/gNJokJeCLFARF8AsA9AGcBXhBBH4jxHHlbWsM0ZhmO4lqDSr25kfXiVpmvygEVp0uwHAVj73kpn1xEG92KlQ9b0Uc0l2QEr6e5Wc/OtzNywJjo39920oaf5RrlEEKKVESs7ML14dNb4e4uqQOkCAkw2Slk2wWaZxIN2hRDPAXguyXNkfWW1jXSJo7NOWM3TNApFRRL2bALwofevxEuvnYx0nDKR0bhOzTc62q93F6PrT/rY/jdjE/QCrRpFVY0WrkPnJJfjrc3VUSKguSg6mrJu56MjDqUjiqDOsgk2yxS2QFmWsJnYQ4NOpAbGUVu6mdSHV/XjlD1lq4MOzjaaRkIvSAuW7eWkvTwKYXcA3l2MSqHwE5RD7fthkztQbzRBlsuGTimQf4u6+Nr2bNURdreXRRNsXihsWYMsYaOBRI1ciBIfb1IfXhX++bX9b3bVqx8IqLUOtKpCPrx11LfswkCZcOCNk7HU39El9JgQtEjrrmG4Wmm3Y7QvZWBTG6dM5Dtn4siZiMsMN7FlvdHdcEoUOhEwK5h0weoHrMknhFvbtekOFNXuGPbz7nrdfvXhTQRGoymMkn627Z7BqoqjdRA2miKWGjglAt45G768g8wYVfl7dKUjZAmFfhRpC1oE47BlE9ApSBaF8U3DOPDGSV8TV5ny37A7S6WIWcgngPcLnqs3OprJ3HyrDvncfEM5yaPaHcNuh2WTiW27Z3yd16YCI0jAS7twmKYltiwfKEUqteCNQJL4RS71M6nVbzcki2lF3Q0JILboFpmb8dj33+wpDR3VH5UVbFsjJgkL+QRQfcHeOGaV7TwOu+PElvXYtnvGSshUK71NG3Rah+kiMlytYP78Qiq1WtzcuXkEj8VYEbPeaPa9hLIfujkzNV0L3flLR1zRLVPTNew5WOsR8G5/VFaToUzJUpIm2+QTQCcE3X9PqijT+KZh68bgROZNG0zq4DvlVi/O+27aENgLNSkqThmPbB3FA+NXFDYqQ1cUSyoQce+S4rqPOpOf9Eep/D4mdfGzRFpU36gAABj6SURBVJbKH7CQTwDTWvY2DRdssKkh/+mrhrV14mvt3ptu5OLk68gUF94rywokjcpRB7S6GdXm6iFcn9lHVxQriTaDcUa3BGm5eaxH5SVL5ZPZXJMAaXelmtiyHl/cPQMTK/SLR2d9TTATT3an+8ufd+07pjXFNBZFx/ao6/oTJ6r4ba85LBv9wOJFpxXGnZDmvb82phTVe4NKkWTJ1BGWLCVpspBPgGHNJI6jS5Mppm7G43N1PLx1VGvHbzSF0lkU9MDV5upYN7kXRND2XY2Kn5Ounw3Ek4IIePj2UQC9ce46rfDeKf+sXusxAF3x8TZRI1PTta6MWxltREBP9JX7evJYj0pFVpI02VyTAGlv1XY8a1454uJqJdCOrxLoJg+cQHK104OaNORJ61NRQkvAS0Gh89/IWOy1k3vx8/fsjb3tovd7tjGl7Hj2iDJsWM6LQaek9Eel/fwUDdbkEyDNrdrUdM04osX94Oh2H4BaoPejJK+OilPGp68a9g35TKqOTj+oOCU8eOuVPeYRWXGzNlfHl5441BPlE/eCqhKsNqaUoHl4bkHg9Z039vw9S6aOIsBCPiFMt2pxh4oFOaeGPDXHgQvOSRUyUsaLty6KX/elOBlul1EIqpTZj0VoaNDB4LKBTjkHXe6DCQR0CTypoUunsTyuvMdJ32tdnZo4TSlNIbQJVlkxdRQBFvIpkkRWnJ+ZwtvjNqjOTVAdHdWD6LdgREUKHl1NeK/vYIVTSkzIO2XCO2cv5AGcmm8YZzWr8Cul3G+ncbXiaOvU2JT2rlacwDBOdztCJhlYyPcZt+auykSMmhWn07SqFadHwKuEJWBfjMp9TdVBB06JYm2yIVn73gomnlSPGbiwwEUp0ha0IyG07vGZcws9Asy0nIMXb20g3fcSN+USoekZrFMibL95g/YzNqaU7TdvwMQ3D/nOBXckFpMMLOT7iK7ZhZcoTkOVpiUTktZN7sWqioNGcxFnzusFoM35vdckNdpqxcHpenjzhYqgcsMCwOiO55XJXaY0hdBWx3Qvfusm9yo/vyhaQtv0/G6ziIxG6Veo7UO3bQSgFth+lUZNzYqmnafy7iTPOizk+4hpWF+UUDFd+zqbWjE251eWcGgKrFw+gJn7ro/U6CMMcWR5qkbr9U3odkxSaJvU8x8a7DaL6KJRkmC4HVUFqEMfvWZEd9SOjVlRmvT8zHh5C43MGxxCmSDeUqMmtuq4Q8V+VrfvT1qbqxuXRg2KtuingE+SRlNg+zNHOvfEL8xPZjIH5UUI0T1H+lXnJ2iOmSgjsouWJKis7sSW9coSF05J7dhn4oM1+YRQaUM6M0CZCItCxBJdY2oSCiJIW5Pbed3RpXbmF5qZN+bqDUw8eQjbnzmC0/UGVlUcrHBKXdFK7rDHM+f8yxvLJuO2pqVHfJLXVJRLhHcvH8Dpeu84VZiaT061WxUCCAwgkP/vePZIZzFzl7dmkiMxIU9E2wH8JwCz7T/913YrwCWBShsS6O2GFHdp1TgzPXVO4CDHpltTTDOePgkaTdFj+hoadHoEvOk1h70vpgKe0LK9+80vr/3dpvWgDNk1KavLYZHpkLQm/7AQ4r8nfI5MotOGBC5EcJSJ8Omr4p34cTuxVMfzW0i88dWmzresEKYx96n5RpfmmnRJhXueOqxttOKmRMCqioNtu2ewa98xpQav2nE6JYqlyU3aDtW8lyuOC7bJJ4TOmUToTmjZc7AWawlV3XnLRKEqMaqOp3t4ZZ0T74MkbdS66pzuMaZNWA+CO7U/6cWs3mhCCP+mghWnhHKJcKqdoKUr17v9mSPK3gcrlw10lVGoOGpRUR10UNJ8b2k6VItQrjgukhbyXyCil4noK0Q0pHoDEd1FRAeI6MDs7KzqLblE5ZhTaYlxl1DVOQQfun0jXt95o1WRNGofz0vYWtlB/oGg17OwCPhxvF2auR+jPF1v4JcvW619/WxjsUcT9861qemaNhpprt5Ard26cmLLejx465U980omhKm+t7RrzRShXHFcRBLyRPRdInpF8e8WAH8O4DIAowBOAHhIdQwhxKNCiDEhxNiaNWuiDCdTqIpK6URYnNvaoGYkNg+egNrpGraAVJQqnE6ZlE3Gs8TF1YqvMzpOVjgl/INP3oDJXDMReHP1Ricr1TuvVi4bUEZuBRWP6wdFKFccF5Fs8kKIT5i8j4j+CsC3o5wrb6jsgTq7dNzbWj8H1/im4a4IBz90Qtkk61F1/VGcsCuXDeCB8Ss6TcbDmkTC2NxNkIvcthCtAQedEgSo6774jdMpUeiete65ZirwZFaq1xSnTwhTNzPpJ0UpVxwHiZlriOgi16+fAvBKUufKGjp74LWXr8lECdX7btpgZFI4c25Ba8P062qlu36gWxu0Mb/I5iPyvGGRju84cWuutkLEKRH+6NYru+5LteJgcJl6x1KtOFg2EO6xdcqEM+cWOrHsqyo+3b082AjMLAhSLld8gSRt8n9MRIeJ6GUA1wLYluC5MoXOHvji0dlE+rraYtoHVsZx2zqrgjrVy8Xhods3Kv0WKryCQ+MHNCJs7kC14mj9HW5zWNASIp3gw9UKdrXDG+V9eXjrKM4t9JadqFYcPLJ1FDP3Xe9bksLNoFPqzLWhQQcQre9ULrxnzi/AKZkteAQoE5yyKkiT6qGcRxILoRRC/Mekjp11/OyBWYkVNk1ScjurTMPRTO2hKrOPt4ww0FvAa9e+YwhprehCJqHJ0g9+mcEE4JMbL8K3D53ojM1bpTMoQUxei5+w0YVfrlw+YD1v6o1F/LC967lm5ws9JrpGU2Bo0MHP6mrnqRvRHps37l2OOYthill51tKGM14TIA/2QBv7uDS3uGOpt+2ewd27Z5R1x22uX/UgSru7qmhWnIlVTSHwyNbRzrH9qj9+6P0r8dj+N7sE+DtnF7Dj2SPYtntGuVBIu7o7L8K9aKoEkMkCaVLCFzCzv8/NN/Dw1lGj+6o6RpqClOPgzeA4+QTI8jZW4t3O+lFSVHWUokwVfxz1+nX2/iSSjCaePIR7pw5j175jnQqUbgjANZetxqtvn+nR0BuLohOHfmq+0bMTkAJeRgXJBUQukmsVdV5M7Nzbb94Q+OB6w1/9juudCzqfRZaUFI6DN4c1+QTI+jZW4tbC/AqoBdU386awJ3X9SYS/NZqiq8Ki+1KlgH7x6GzoiJymEMq+q95FUqKqd0MArr18Te8ffQb12c0jXfdbt3OTznX3XFDtmLKmpAT5fZgLkMhQlcCxsTFx4MCBWI/JWzozVA82QXZXCjaAe9vXJUGSXad02NSGj4qf3JZ9bfe+fCIw/HVo0MH0H1zf8/ep6Zo2fNZbLCzrz826yb3Ke9WPeZhFiOigEGJM9VqhNfkk2usVFZ32bRr33Y+tfBrFzvp5Lj91q95o9vgEdMxpFgFZV0cl5GUklXxf1m3tefB7ZYVC2+Q5tdkOlS3c5KHp11bebTvWYRgRGAvlfp4M5klcft+Zn8krC8+Gqa09D36vrFBoIV+01OagxgxJoHqY3PQ7hV0uRD/eeSPu3DzScRKWiXDn5hH8ye2jrZjwBCG0mqLfcfUlfalTY0OQoAtatGtz9b7OLy+mihnHwZtTaHNNkbZ0aZme5LG3P3OkJ2wv7lr4tjwwfkVXc3KJt0epnwZ85+YR7P7BT6y6ZwkALx6d7fycNtKWrwpn9WJi8vJmKffz+7VRzDgO3oxCC3nVhM7rli7NaAL5MPnZSrPmqDOJHBquVrrq4RxvV108fbaBoHiErOwGbbsrqTo06UgjWqVIillW4OianJDlaAJVZI5TIrxrxYCyNV4Wxue3CzFJupJ+gTijfYYGHZyeb8AvlinuVpFBu51+zy/b74ppsWSja4BsbemiLDhZ1nBUuwyZKATYbf3d96g66EAIGPcm1WEbt+/tZqVq2Sh3g6rFYGjQwY1XXoTHv/8Tozo5biEmr1933jiFnclup9/zKy85Jnmi8Jp8VoiqoaSp4QQtTrpdhpfhakVbQXJquqa0+7tJS6MLa6YyuS9+dvR+7kJ1eRKf3Tyi9Hsw2cJPk2ch3yf87MKmpXPTMD2ZLC6jO543qqWi2/rb1KTx3q8sm+Pi+M77yb1Th3ti8dlUkg+WtLkmK8QRzpmG6cnE4Wtanl239bepSeO+X34RR/K4aQr/vDn+VeUbuFRA/mEh3yeybFP3w2Rx0mVYulGVC5YC2MZ5WXXFwOsWoB3PHsHZxmLqmc55sy8XLa+EacFCvk/EqdX100Rhsjjp3qOKBFFp3zacrjcwuuN5nG43v1ChCg1MSyPNkuM/CN33KACsndxrFIfPZI9CZ7xmibgy9PpdYtUkfVz3nodu3xh7ueBFV3cjW5aSRhomOzoou5nL+eYT1uT7SBxaXb+TokxMDjZmiaQFbcUpY/lASekIzrppLC7CZEfL3WHQAsw2+vwRScgT0W0AtgP4dwCuFkIccL12D4DfBtAE8J+FEPuinItpkYbd1GRxMl3AbG3wplD72Lr4dWVN9oJiqwjYdtxaSjuiIhBVk38FwK0A/tL9RyL6KIDPANgA4GIA3yWijwgh+le3taDk1YErSaJcsDskUaeRCgB7DtYwdunqwmuhOiEsi4+tqjggQicb+cy5BavvIy9zjWkRySYvhPhnIYSqNuktAL4hhDgnhHgdwKsAro5yLqZF3kusen0T1YoDp9wdg2lT2dEbtSP9FSrCltJNo/pnlPP7CWGBlk9Dti2szdWNchwkeZprTIukbPLDAPa7fn+r/bceiOguAHcBwMjISELDKQ55C8tT4TXteKOFrr18jbJlnmS4WlFeu4lN2avlBkUqha3+GVcE1NR0DRNPHkKjeaE/7MSTh3zPH9duyd2AvCkER9fklMCMVyL6LoCfU7z0+0KIb7Xf8/cA/ou0yRPRnwH4RyHE19q//zWA54QQe/zOVeSMV8aOTfc/rwyF9MsWNS0j4DbtBGXz6rJWvS323EJ9VcXBmfMLHcHs/sx9N5lXjAT090HX4k81njCRSJzpmi/8Ml4DzTVCiE8IIX5B8e9bPh97C8Alrt8/COC43bCZpcx9N22wNksF2Yq9nzdpUKGzb5+ab3TMJt6w1rl6o0fAy8/YhiDqygEHlQl2d/ny66QlGRp0uAFHQUnKXPMMgK8T0Z+g5Xj9MIAfJHQupoCEMUupzBR+DTX8HJTX7HwBx+fqKLVNFSpktIpN7H8aIYhB5puKU7beYTD5IWoI5acAfBnAGgB7iWhGCLFFCHGEiJ4A8EMACwB+lyNrGFts8wpsFwZdpBLhQiauX6lguRjYhoTahCBWK47SMVqtmLc49N4Xb3QN29mLDVehZJYsuvK6tk+E7WdsK49OfPNQV3tCp0TYddtGFsxMB65CyTAKVJp/mEQtgV5B75QITpkw3+ju82QbgliEaComXViTZxgXYcwvElVoZ5br3TPFgTV5JhRLUUCFjTHXmWDyVIWSKSYs5Bkl3i5BadVk7zcq88j8+QXfkEXOAmWyDAv5JYhJlqe3DRywdCoQqjJybUIzGSZLsJBfYpik6e/ad0wbLVKbq2NqurakhBo7P5k8w0I+BvJkuzYpQxsUx70UzDZe2LbO5BXuDBWRfndqiopJPfqg8gBhqzkyDNN/WMhHxKT+SZbQCXD33ye2rA8s98uNIxgmH7CQj0jeOtyb1KMf3zQcmMEZpXFE2vXZGWYpwTZ5F2Fs63nr1GTqRBz2yf6MEjIYtj47wzDhYCHfJqzwUSXPZD1u2sSJqEsKClMT3U2/G5EzzFKHhXybsMInrvC6rEXoJHVdut2BjXlL1UnqxaOzmbl3DJMlWMi3iWJbjxpel1UTRhLXpavYaGreUh3T3SowK/eOYbICO17bmESdJEXeInRMUV2XrNjoxsa8ZdKgw3vv2NGbD/h7SgYW8m1Mok6SIm8ROqboxi/LAYRpNWd6T+T78pbHsFTh7yk52FzTJs3U9bxF6Jiiuy6bphmmx1S9D2BHb17g7yk5WJN34W5+/NLkdX2bXGnuIpIkietSHdOL+xx+fVzZLJAdirqbzQKRhDwR3UZER4hokYjGXH9fS0R1Ippp//uL6EMtLuObhvHgrVeENmFkFZPrsrXDymOWSZ2TWybqOoffbojNAtkhTZ9Y0YlqrnkFwK0A/lLx2mtCiNGIx18yFLUAlt91RYkqeveKgZ4G1xWn3LOImDQBYbNA+uQx3yQvRNLkhRD/LITIdwgIkxphoorkwuAV8EODjnL3491N6GCzQLoUdTebBZJ0vK4jomkAPwNwrxDi/6jeRER3AbgLAEZGRhIcDpM1wthhdSGUg8sGtALBvZvQ9XD1mgWylpy2FCjqbjZtAjV5IvouEb2i+HeLz8dOABgRQmwC8EUAXyei96jeKIR4VAgxJoQYW7NmTbirYHJJGDtsVAediTOYw/mYIhGoyQshPmF7UCHEOQDn2j8fJKLXAHwEwAHrETKFJYwdNmq4qUmorEk4H2v6TF5IxFxDRGsAnBRCNIno5wF8GMCPkjgXk1/C5CbE4aALMgsE7RayWoaCYVREEvJE9CkAXwawBsBeIpoRQmwB8CsA7ieiBQBNAJ8XQpyMPFqmcNjaYfuRtBa0W+DEHSZPRBLyQoinATyt+PseAHuiHJthdCTtoAvaLXDiDpMnOOOVYTwEhfNx4g6TJ7h2DcMo8NstcOIOkydYyDOMJWkWs2MYW1jIM0wIOHGHyQtsk2cYhikwLOQZhmEKDAt5hmGYAsNCnmEYpsCwkGcYhikwLOQZhmEKDAt5hmGYAsNCnmEYpsCwkGcYhikwLOQZhmEKDAt5hmGYAsNCnmEYpsBwgTImMbgPKsOkDwt5JhG4DyrDZINI5hoi2kVER4noZSJ6moiqrtfuIaJXiegYEW2JPlQmT/j1QWUYpn9Etcl/B8AvCCGuBPB/AdwDAET0UQCfAbABwA0A/gcRlSOei8kR3AeVYbJBJCEvhHheCLHQ/nU/gA+2f74FwDeEEOeEEK8DeBXA1VHOxeQL7oPKMNkgzuia3wLwv9o/DwP4ieu1t9p/64GI7iKiA0R0YHZ2NsbhMGkysWU9Kk735o37oDJM/wl0vBLRdwH8nOKl3xdCfKv9nt8HsADgMfkxxfuF6vhCiEcBPAoAY2Njyvcw+YP7oDJMNggU8kKIT/i9TkSfA/BJAL8qhJBC+i0Al7je9kEAx8MOkskn3AeVYdInanTNDQB+D8DNQoh510vPAPgMES0nonUAPgzgB1HOxTAMw9gTNU7+TwEsB/AdIgKA/UKIzwshjhDREwB+iJYZ53eFEE2f4zAMwzAJEEnICyE+5PPaHwL4wyjHZxiGYaLBtWsYhmEKDAt5hmGYAkMXAmLSh4hmAbwR4RDvA/DTmIaTBjz+dOHxp0uex5/22C8VQqxRvZApIR8VIjoghBhLexxh4fGnC48/XfI8/iyPnc01DMMwBYaFPMMwTIEpmpB/NO0BRITHny48/nTJ8/gzO/ZC2eQZhmGYboqmyTMMwzAuWMgzDMMUmEIIeSK6jYiOENEiEY25/r6WiOpENNP+9xdpjlOHbvzt13LVRpGIthNRzXXPfyPtMQVBRDe07++rRDSZ9nhsIaIfE9Hh9v0+kPZ4giCirxDR20T0iutvq4noO0T0L+3/h9Icox+a8Wd23hdCyAN4BcCtAL6neO01IcRo+9/n+zwuU5Tjz3EbxYdd9/y5tAfjR/t+/hmAXwfwUQB3tO973ri2fb8zGavt4atozWc3kwD+TgjxYQB/1/49q3wVveMHMjrvCyHkhRD/LITIbYdon/FzG8XkuRrAq0KIHwkhzgP4Blr3nUkIIcT3AJz0/PkWAH/T/vlvAIz3dVAWaMafWQoh5ANYR0TTRPS/iejfpz0YS4zbKGaMLxDRy+1tbWa33W3yeo/dCADPE9FBIror7cGE5ANCiBMA0P7//SmPJwyZnPe5EfJE9F0iekXxz0/rOgFgRAixCcAXAXydiN7TnxF3E3L8xm0U+0nAtfw5gMsAjKJ1/x9KdbDBZPIeW3KNEOIX0TI5/S4R/UraA1qCZHbeR20a0jeC2hBqPnMOwLn2zweJ6DUAHwHQd+dUmPEjo20UTa+FiP4KwLcTHk5UMnmPbRBCHG///zYRPY2WCUrln8oy/0pEFwkhThDRRQDeTntANggh/lX+nLV5nxtNPgxEtEY6Kono59FqQ/ijdEdlRe7aKLYfUMmn0HIqZ5l/AvBhIlpHRMvQcnQ/k/KYjCGilUT0bvkzgOuR/Xuu4hkAn2v//DkA30pxLNZked7nRpP3g4g+BeDLANYA2EtEM0KILQB+BcD9RLQAoAng80KIzDlMdOPPaRvFPyaiUbRMHj8G8DvpDscfIcQCEX0BwD4AZQBfEUIcSXlYNnwAwNPt9psDAL4uhPjbdIfkDxE9DuDjAN5HRG8BuA/ATgBPENFvA3gTwG3pjdAfzfg/ntV5z2UNGIZhCkyhzTUMwzBLHRbyDMMwBYaFPMMwTIFhIc8wDFNgWMgzDMMUGBbyDMMwBYaFPMMwTIH5/zGE3tEAgyWvAAAAAElFTkSuQmCC\n",
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