\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/v0.8?urlpath=lab/tree/analysis_3d.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",
"[analysis_3d.ipynb](../_static/notebooks/analysis_3d.ipynb) |\n",
"[analysis_3d.py](../_static/notebooks/analysis_3d.py)\n",
"
\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3D analysis\n",
"\n",
"This tutorial shows how to run a 3D map-based analysis using three example observations of the Galactic center region with CTA."
]
},
{
"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 astropy.coordinates import SkyCoord\n",
"from gammapy.extern.pathlib import Path\n",
"from gammapy.data import DataStore\n",
"from gammapy.irf import EnergyDispersion\n",
"from gammapy.maps import WcsGeom, MapAxis, Map\n",
"from gammapy.cube import MapMaker, PSFKernel, MapFit\n",
"from gammapy.cube.models import SkyModel\n",
"from gammapy.spectrum.models import PowerLaw\n",
"from gammapy.image.models import SkyGaussian, SkyPointSource\n",
"from regions import CircleSkyRegion"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\r\n",
"Gammapy package:\r\n",
"\r\n",
"\tpath : /Users/jer/git/gammapy/gammapy \r\n",
"\tversion : 0.8 \r\n",
"\r\n"
]
}
],
"source": [
"!gammapy info --no-envvar --no-dependencies --no-system"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Prepare modeling input data\n",
"\n",
"### Prepare input maps\n",
"\n",
"We first use the `DataStore` object to access the CTA observations and retrieve a list of observations by passing the observations IDs to the `.obs_list()` method:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Define which data to use\n",
"data_store = DataStore.from_dir(\"$GAMMAPY_DATA/cta-1dc/index/gps/\")\n",
"obs_ids = [110380, 111140, 111159]\n",
"obs_list = data_store.obs_list(obs_ids)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we define a reference geometry for our analysis, We choose a WCS based gemoetry with a binsize of 0.02 deg and also define an energy axis: "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"energy_axis = MapAxis.from_edges(\n",
" np.logspace(-1., 1., 10), unit=\"TeV\", name=\"energy\", interp=\"log\"\n",
")\n",
"geom = WcsGeom.create(\n",
" skydir=(0, 0),\n",
" binsz=0.02,\n",
" width=(10, 8),\n",
" coordsys=\"GAL\",\n",
" proj=\"CAR\",\n",
" axes=[energy_axis],\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `MapMaker` object is initialized with this reference geometry and a field of view cut of 4 deg:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 12.8 s, sys: 2.66 s, total: 15.5 s\n",
"Wall time: 15.5 s\n"
]
}
],
"source": [
"%%time\n",
"maker = MapMaker(geom, offset_max=4. * u.deg)\n",
"maps = maker.run(obs_list)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The maps are prepare by calling the `.run()` method and passing the observation list `obs_list`. The `.run()` method returns a Python `dict` containing a `counts`, `background` and `exposure` map:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'counts': WcsNDMap\n",
"\n",
"\tgeom : WcsGeom \n",
" \taxes : lon, lat, energy\n",
"\tshape : (500, 400, 9)\n",
"\tndim : 3\n",
"\tunit : '' \n",
"\tdtype : float32 \n",
", 'exposure': WcsNDMap\n",
"\n",
"\tgeom : WcsGeom \n",
" \taxes : lon, lat, energy\n",
"\tshape : (500, 400, 9)\n",
"\tndim : 3\n",
"\tunit : 'm2 s' \n",
"\tdtype : float32 \n",
", 'background': WcsNDMap\n",
"\n",
"\tgeom : WcsGeom \n",
" \taxes : lon, lat, energy\n",
"\tshape : (500, 400, 9)\n",
"\tndim : 3\n",
"\tunit : '' \n",
"\tdtype : float32 \n",
"}\n"
]
}
],
"source": [
"print(maps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is what the summed counts image looks like:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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w2nVd1RdNwJVyDmtQ9spmYT0mHu0kYo0NAmirMqDuAFoTk/zsdkPdMUR+NjwmHQFwS40QqX+2yut1RDrZaEN7HfofZ/C8vPTZNct+NrxlJm55DFi/Z32WPIqoyAL8kRKXZWWyGDB077mXb3COkwdgbx2elQ/L4i01lzOPjJiPps1lgI7E0lUGPWBtP/1ocpKO+RUppWfp9zMO8L4m5/xrKaWPBPCTKaVfzjn/tJfYYwXMF417zIyNLUdWGOYndqDfujBka6LQY4XehJoCrOeIvuWsvmXJsLIwCBqVNvgt0Nd0mqZXjTJ69sjaQUSTgF7ZW2VQ8RhyS5TdR+oMYNFxs95YQe/q0O44FWyT1NU6fXYLqgxYt7EClo5fzSaV8Wu9o3fsEQ0diXBHstfniBradDGKXWP3oKcA6yB/oON5pLs0795ylJ9z/rX5+BsppR8B8GkAHn9gfgJ1L8tiL9sAmUHWhHtYb7WemvuwJYfpkg8dIGSSeajHZaUGqDuQeI052gWDZYsBtlhltES5B9Qiiwt3+EsNnNVCHhi3AJnF27mkt5wcPjJ1Y/VGVBaPUe4GIM+ty1QUXudj4fW6eZqz96PsPDIN9JacR3kzWEejC7vPKjlTXTBz5tHjnlg7UAMue6mz64Ncv44MODdbBs5plTHviD3knN83n38egG+Lwj9WwBzZR4Ku20vuEfUoFy2nNmkNnb2wrXAes+ZG402etUAyapAsujDF8rMORMt/HWmZwbXUEyy9oAysdxox5tZiqywKyJHayS7rN+B9E5EqpCXmvCoKX3n32wB4T1rfo04Yex2FN4qLnnEBay03zg2cS7rnZcksZyvxvwjgR1JKwIS7/13O+SeiwI8VMPPOB/oizKJCWa/1yOrUXp1x7yWe2j3z62FLDP3YjXXoUN/zKxyZq0WTP55w42jt1xcxZs9PccSeWmlZ/qqe0bCtST5P7eI5C/KAuwIO+GFYtBPzWD6bh5WVbxuAbMJqg8g5v8ZTgLR3a7pcvh4x5mEQNVvw3jW8bsVlR9VTW9wcgLK9s/2wOOw30znvM44ANbLAGLEGe/6zMOeR81ll5Jx/FcAn94Z/rIBZe0aeZBiwXhSiYuCsXq8i3xYq+p1zg3LDjz5Ysk452n3EGozHlhVAdHsiDteaUIysLlo6ZWb5QFy/yIF/j3D6Wl7t+EL2va+BVeungB11OgyMV/NOKB7Q6miHnxOv+oviAfOzHGr7YgZnr6yeeSSL2h97ViomnBbbvHOeGtdTh7E5KVDbIXufABMmA95Tt4i+OSC7CY6/LY8VMPOknemrgDWotib9TAYKqzpmSDg9N+bUYn/c+KPdQVhXeB1RMIjunbJfnl7zACtytqOgHAHzFkDxiMR+b+m7lW0bsCnrbgGkdjq60/bFfpnUa5WfwVlVFJ4qxOtgbW7CM+Gz+K6zJsnT8uAjPwuVaCuvsAMk8SZQ+V1af9ZSSQJrzW4U1lb/XbP5dMi9E6Mu8ZZnYv7NqghVUwD1stFThFkyA7ICXQ8bXDGdxhfVms3ntPS6iTYwC7MFxFF6nKe3dFzZstlHeyoSzbO3w4jKGHnsG8flA2dm502meu9VJ94Oh2WRSVQWrQOzWmXqrfdf3tVQm8CZbPkoiUYc0TfAsuWS1pPI89+5ZcACyMBihTXS/fPKPTBfSwyMB9Ss2ZNIvdGbjzUy1gl7Oj47RueRbDE6/e0xdk+frfG2mGeUJxAvp+YyMUj3iKbT6pSikUBUHhVb7WZ+kNkqI/JVopY4nvrA66TtWbecHnmfAzNuZtA9Er1zLdspoBlNevcQC81mwFIX9cHcEraD5jYfkbXzyT0wnyTMhHd0HoVR4R5WfckC0wdwlGte4/U+Vr7v6XU9AOIG03Jao/lFdtItFtpSe3hHrpfWUcNEKhMvr8hSoNXRqRplq+xbz0FtkaPOiNPTybJe8ey6j1jUFSwrcD5sW91Ez7SH8QKLhYt17tEkdAvUvVumN67KhAVUeVsqBl2T5JwrIF/Hxei23C/JPkk864oBOKsKYwXyATuze3xuv1uTgubR2xoBg7E2AA+APD3vlppCJ2lau2ZEjdu1XpD6sl52qxPT8rdUHTxa8dKMAIPfA++YbXLcAJzIjtzzj6yyBYrGplvgzOlsLTjqBeFIGJw5vy0rmtJRjVitNfBchTKoZglv5614N6e6YLnXMXdL5Myk5byexV4qv9BotV/lNrTBwPg6MzsVBRvevcLuR+B6aoPzmDmDPzMjLlNLlRFNNrEoyHnlbj3DlhqjpaJppQv4dt6VqmD0wedcEgGn5d/jq6PV8Zy6E3dLPG+ADNBHKV+5DgBjDZyeKCCzWmJEvWcgt3UPqG+ez94D86bYC1dzt1PbE7NqHT7ZOXukM7O2yDa3BWZAPCTktNQEie9HzHRLVI9aNXjU+mBPVXFKXpzPESg7fgC1G9PWkvDjBgBx2fQ9bFlt8JZWLRa/NenK4oFhr/7eu6a+jC09BfVTlumfIh7Al9HdnP5KJcHveN5OJM9xvKJw3fZ0zbzNmQqR23rkoW7EWu1xfhi9B+Yu2RrGKBvWuHbUHbDZs1y5RnbG+33cmO2aB2ItvxMeKKiqQSfQjGm3dIGWb2QmxizHfnt1i2yVvbrUFZmd2pD9LoOyB6om5sxnC2C442A1QM/oYqCytdRAJok+OgvXC8qt9PmZ830DIl0ObmFaqzyj59oqR9F3j2tTwVU681EXpFgZbXL1cEC1KIYd6gNLextRW1XYuafeuH25V2VcSwyE7ciTdQzQ3oIS3o1Ed9LeD2t9ZmuxhDJBz8HRlo8NZbXGTobRz9cu8eSVJ5Glh6kGPLbP13q8vmnZTNQRe1ENCSB5oNEDzvbsmOn1jC4YVAyg2S/ylrgjEOlQtgA/eoZADbreeyuWHnTPc1zkxYuOwPr79YTfl33z2oGUBTgbz5Tbq6kx2GLjVLkZCL0H5k3hRxTNwmbUjvRNjAXrrteYz5k9ez6D1a8yp+85IIq8dq0YXaMRtlbqcXxviKk7ZAA1aG3ZUbNEjPpUvTcvEdb0mFX35DGONXvTsFv+nXWFnaXZsjzoGS30MncFZmabLUdEvSMJPdf40cit5A8U2+tI2NUpUNt8m/DmuZqU7q6tG74OThxPRvRhw+lyb5XRJd5STV5NBExgazvnartQUGbGbB+Exwx16B85owfFPzQaeTQxxqyjpTbx0kQDCLROnv2vxm3ZCEdl4/K3dMmtiUFdwOGpexT0mClGqxK93/s5PdPFM3PeAkGPHfM3waAWqb6YZevIIdrBxISBO3JZGnne66lXa8VitJJUn1khKQ7CekWw9mhtcsscbpDrN2Myd8+YN4UffPRigQl01TbZzvnIkw9b5I9BhhlNS2caNe4W6NqHD9SqFB0aawPYYq/DsLB+L10tG//Wv002Cj9t06FH9TbxTNoUZDzQ27Iz91i6/T4MtWP7FiP2Jsn4mbTsnHXUAizhojyj6576y8riAWfR/TrfqpZxbNRBw3IcYFEP8RLzwwGLnn6Oq86IDJAvsBAwz0KDHZSBzk/Z7LVPzr4Z6w7AswD+Wc75ta2wjxUwbw1XBtQvMhL7COx86+PzpLUMGFjrPT11goWL0t5izSoeQHMakbmZVyYdBSjbbpVL0/MAYgucI2uQ3rRa5dD3pR1PBFZb78Gei4KzlpFBuVd6QLv1/vm71O+xR7fO6UadH+fl1deeRTMfLO2Tj1E0M5ljcD6vnJUx/ykA7wTw8q2AjxUwH1AvzQTqXvMKC1u22V1eFcgvGnQ02RqCt4akfN+OPBTzQCdyKM/pbgHClg6b62QWHroLt3YSnotSZducvpbbu751jRs1qxIiXWgk3nPjc32/bHetK/zsetG5DgsL3FoGzCv7NNyqDEBX+2+Bc+v7YTmO9fVIbcPfcEuikQmbJZoDKGPsXFfevcTmfIw5Zzq2GPGWU6Try1kd5b8SwBcD+C8AfMNW+McKmEfUL0CV/txrRqoOngWu7glYRh/2FhApINjw3aTHysEb7q7iO7pWjR+pRFqsPSpf73PZYoMeE+d4rR3BOc4WSLdAWeNmqqMBsKcqsXC6u4jWS8VW9lkZeoRN9HqkR53VihvJKYtuInDncpmaSi11WPWo5AqAq64YKC67Zjgvaz4bY/4rAL4ZwMt6Aj9WwOzJOXvKaMGFXl+VoRO8vWtRfsBGoxjaZk2Rq1HLMwT8IE9OQxm3SUvNwcChZfK8ulnj9VhzDwDpZJoXRztNLjfHtd/eLtnqwF7jKVjpkme7dg7x6ulNxnlWKF74KC2+roxb43tlSsMEPGpCylYZ3C/pLtq8ySuw3pX7OqZ2vpxklRFuxppSei2A38g5vz2l9Fk9iT1WwGwvJ8lv0PUhuMdpeH4w1G6ZG+gWa/A+2Oij3JIeHS7n0bq+xZCjhSMcl8Nr2npvSzWjZSrsU8pZTRhh/Sx7n6n3Xo7jGhSZwUWsz2RrZxKug5V55YtDvguv8+lZBemJqV48wD2OwPGwzq9XRRJ1ti1w1nhs8cFga+c6wTdgbaFh4TxnRxdy7dGl+wW0NmN9DYAvSSl9EYAnAbw8pfT9Oec/EiX2WAGz7j4C0AIL1C8yElWH2HnEMJuOiJxrrQ/ZC38dHepWWA+MgW2VhZdHKx8vvSiepsl67yi8Tp5pZxCZyQFrsJgu+ozW/nq8t9mf6aTDsONiAWFA1AJDj722RF2JclxvD0f2Qx2pibzttnrJhQfK3jP28in5B2kzaJvOmbeZA5ZFYh5GXF/Oo2POOb8ewOsBYGbM39QCZeAxA2YGXxOuQLQbydZ35akwoqEvH/XcY8kRkEbDTpvR91hPBHbetVOYegTkdr01YvAAWZ8fp81qi2iZe6ve1QpLKUerzjqhqKBxddje+DZSc3h5MWPmsKcyYE96mbSuQO2Jo6tVm51PB3BrR8DPWfrMAoN2DqzbsYGxtm1r8y8gYz6rPFbAbKAc6ZA84D619/RA2dsVOOr9e9QP0Uw44OsgvfRboBwJT0C1vKkpkPak3dNJeKDMYbaAQ1lxZLIYlSdiqS3QvM4oaAuwesH5FDDvKZcXJ6qz3Wf23TMR2EpzHGtQ5mCb1h/y29tD8Pymcuf3lZFz/ikAP7UV7rECZls6DcS9Ym/P2bvrAXtMa03YMLPwGrMO5bfAmaXoKoHKd8YprLhi9qjBX8vGzFbve+LFV9WDLnFvjUq8YbZnW90qR0uUxbHDpx7p6Uy80c2jsmVm33a+tXQ6dEYk5VFVR5XPfOTJOq/D5u9a/X2M46TaOYy1CoLFu+6pLgf5bU72b0bul2RvSuXPohEGFMbC8wseUZvUqXMdT7J8aCxeI4zArpRziJfScj4KqHxvawjZuleiSieh6oZesDsHKEfl7llC3ttJqQrD8y3shW11SluAq0DuxdH0bWm6F74nPtDYHFVIBJ9rxxiNRAbUpoVR+VmMKbd0yTbRF9kmD5jWK5gpXfHE10j3+nLvXa5LGJS9vf1Guqb6ZhPrcaO9/hhAW2Cs4T29qd1XBqplYdHlvgwOvMRVG4Q2XC1jVP5jAD4KgBFAt0A28rfhSTQpxaZ5ngVHSxRcIjBj3yed+L4qt+bpMf4Bdbm5fN5zjRxN6bs6BZC8Z8Fs+UB+Q7Y6nQHr75HFbLErkkIj0IgND6gn97StXmACZwbyjJtyOXQPzCeJvUDveuv8FD2UB9BVXgS4Bhpq4+utpgOwTPQBq8UHHjjbh7+1DZJXPs7fJI8IJ3a8lX+cppVxyxKjJZG+V8vhMe0tZ/vA9lZNXj5WDvY655VLwdcD56NcKyZiA1YdRgTMEev0WKrOSZw64dfStbfeq05Uc514lWExMzQnUZw+Fvgz75C2zNruMTMGahO6w/x3z5hfYKk2SJ2PvHuuhVF23dJD9TJbbhAeKLeAQz/wlm6T2YY1mmFYJmN0YYMeWzpZbYCeikCvRaZ2EXC3pDXhpOnws41W7rXSje4ruFk9xnF5tlezs3e1V1ZAVvYJ+L6R1SnQ1iinsGYK31KHmPSCstfpcFla77bVKZgY8dDNHjz3oINT3pbtsmZ5nP/OD6MvAmBOKX0MgO8D8FGYavxMzvmNKaXfAeD7AbwPwFfmnN8fpjEfFWh101W/QyDiAAAgAElEQVS2aWSA3lN465Ejh/EsOjNtRx1eXwc8CkBCAHCmDszmjG1oo+ZG5NkIKzCrHrECAgeUI5DvYcq9TFqfjbJk9dMRxe0FJq8eOtSPjpyvB8bRCEBXu+l7M6Zvf16cVt166s7v/+h8C1wuHflF+ZlpXWTtU40mnTIe5+96z981JpDgflHBd5z/Mib1xvlZ84sAmDE942/MOb8jpfQyAG9PKf0kgD8K4D8E8PEA/giA72wlwu/dU00Mcj6g1klXPpilcTIb1KFoj18Ei8tHbdS6I7YOS9nvc8XkhKVw+grKCq5az1HyZiDoAeUIpO0YeajznouWS9Pi99IrPUN4zldB2YDkcKgXuty0eC5Fb0O8b8nKAzijSKeM1Z6PJ+TDaj3DQWbGTMBMlaG6ZwNnVns8urxIHOXnnH8dwK/P5+9LKb0TwEdjMZLQ91AJA2w0AQi6z87wByeeMsQS3wGd6F7EGD0gBGr1hafXW/l9dsrBrFkbkQfKvHehxWc9qj0Hrg+DK+vNe4a2niWGxteG2QLlU2ypW3ss9giX8XBYys4TY5yuhd1aNWjS4+PYi3OqQ6NeiTYm0M5VR1xAPd9RPY/Rf1feNe/d8wShRYm0vUdMTNnAw1Qa55EXoY45pfRxAD4FwNsA/EMAbwHwzwF8RRgHDrgG4XZy7sXTBu+5fTRRfSQf+eNq7doR2Yp6+fHvTPlwOQxcT+1A7OPnYThblZgKIfLJrOXz/GXwn4FbZC6ooxNPttg2p3sY12F60udOAFgYszLnSHgTVS6rF24LnPn56QKniN16C6G28hhHnxVH5omqflC1mKrHWHo7DOuHbPk1UJvPMTs2awxTcZxfz/wiAuaU0tMA3grgT+ec3wvgvQA+cyuebQulumKVCLS9LaQ8RuDJ1sdePkhHNWH3Ioc5W3lfRzgPzyIkAm4PoFT4fmtJtjLv1TNh0KE0PNWMVwZvMi96DtE1fveen2R+Phf7eUKQ8qtUQmNdr9COmDpFDtOylIk6X33PZuXjPQ99tkDtwpTzaXXElp+Kp3/XuF5nyQShlHU+GiCzfXOJD1TWHPdbSz2CpJQuMIHyD+Scf3gj7FsAfKn9thfEL21rJaCn7vDAYhjWABaJNyveYthAzC6ivHS42Cunhgf6QdnTha+YeAOQOS6DhIKZAqXH3Dg9b2LuFLZsaam6h4f53JGzP2APoIEF7MyREY92SriDby7plcueD/vjtnIaqzeA40lED3Cj+vO597xPUZFwvhEYR9/4MAAYF9bsbdLaIyml5+jnD+ecX9dfA+BFo8pIKSUA3w3gnTnnv7wVfn6Qr5vjVnbmqmP2XpZabdjLbS182GImJh5bs6O6bBxH37OXMpge5qzAyOIxrnFcOi+vI/AYLqftdT6RZzg+Xmf14BRoXTY+T4aGVMHdABwP6/fEjb+ZpdMZ8TCfAbiqA4El2z1b3gaYZnGw6oyAAs5RuYAFdD2Q1D38eJKa0+iRzQ5anqV1XMOw1r97+Xqg3CzPfKycVUE6RqDawJVBIuf80u1cNuSU3uiMctuM+TWYgPaXUkq/OF/71pzzj/VEHlG/FNXVeWoNe3k84dejvmgxhQjgNIyJOn3vYcxArZPmPKzReB2LlimqrzecZ0DVenEYA2VveTWrOLaGw/wM9Fm4YL8PKnw4YBjGkxp+T2dh92xhSNRpW55sn8sslsF3kLgWn8HU02V735d1HKYD53DMxLfEY8ue7bEXxzoeq6v3Tbfehed/prxHxHxV55t4A9ezqTRy9p1u34LctlXGz6C9zqMp84i3GtrYNU88UzqPGV2rLA1Q9fzhKliovaeXFvvcZXCO2GjvtkVefsqUW6OILWa1ZU7YWza3bh5CDgPSjIg9PpVPFbWKaHamqNUx/J14ZfNGYz1h+H15ds5Wbg+co/x4RMS/W6NFK4M3oanqDK8eyvBLXL+IU3ocH0veZ9/7L+N6usEzyGO18s+WXVrvaItITHTPLwPvNIdls7Fetqy/e0c2ahLHf/au2RYZaC819gDZY8zqs2PXWJRh6XoNUoGZV+DZn5rhWX09ls3p8/PxxFXvVBXe1aixn49Bc9a0vEkpzjuSLcZs7LhMapJFx9Z3owDlrfjbKqe+N9Y3cxxvZOF1hgyonisALdMRa2sbL9+WjOPyFm2E7Gl6Vfds5rHRhq3Xk/yiUWU8kjyPqcBHAA/ouoG0vSCTga57Q/oIsLZUDFuiH74Hyi1Z5e0AnQd6PRNlmg+z3kj9YADPeuXdvr0ST6+rbjhhaYGR6mEF6Fook/FY3fbUNK1nAPijHBNvebV3XqkvsHiHs/ue3a/ds8lGINYRR8/I1Fred+vZdatKTePqSO7UzoqfY2QhoqLO81vBmRlb27fw1ubPJmda7ZNSehLATwN4AlMRfyjn/Gei8I8VMD8EykwtsHwA/CFYhQykS48qH5D7Qc06Qm/o5X1YLSbjgbOaR0Wz8Prb8jHGCiy+I0wiUPUm8bz8WqCsndr+hJGHAccaTMfq+brDWa+DHHZ1AKx/ekCg9fJYs2cd0QJlDacgyvMA3veg5bNrxp5PXQXYAkCPJLRUFPrceaJPw2r+yv6jMkUkxS57HeWAWm3C5nQc9yySz8qYHwL4nJzz+2fLtJ9JKf14zvnnvMCPFTDbeniTAdPIkX2zMjB7y65ZPCY1jrWJE8vWpFIEyp4vBWDNTDz9rjesZ4arddHfPTusRB0EA6vHwj1xwUsjBwrH6vmsANniUnNtzPZph6bs+9Ql3qs6YemcxnGxefYYsokHsq3nGQJXAxS3GLZd19FbNNpgYWbulUc7Wc93SNQmNM1edYRZYmyZzV5LMs42+ZdzzgDMB9AF6vnKlTxWwKzCwx5m0hVbHuphuoqCzXUmaFoA7n2kDIQR+PUy9GhovdVItd5bgOt1NmaBEKXjMmURZuxqSRA+8/HoA3SQNpenZau+AgdirRxeveuZ5MbztvxtubL3bryOf2uHEitPtDFrJDx6syfJ3+zglNNjzS1QtmtqlRSBsldsRS4vDKs2zrvI5Lw65pTSDsDbAfxuAN+Rc35bFPaxAmbdAXeQvx2Wl3QBYO8wyxJ3cEBkFmUSW6CsYbzh+aluM3X4ewpTrcqG5WM1v7maXwRWhf3N/7hx8WoxjbuyoAgK7wEVN6wqGj/oxniaF4B490wVEz0vT/fKKxS5bNHzMnFHSPt1J80mdt735rmd9b4JcwK09c1aWdztnca1NZNXV29C03POFUmPisZAWYPyZKDnSP9scppVxitSSs/S72dyzs9UyeV8BPD7UkofDuBHUkq/N+f8f3iJPVbAzEuq1SezB85bDMmun2JmdlJ5pUG3li9vmZi1PvIt0D6HsEN0ZT4uUHTqPiKQaUZrKUcp7qgASH/eQpUoS9ObdpXNkdWojO5tLaP20go0QdV97zrgx/UWKpUO2PlmzyGsP9fy8PNhANZqnY/LRnISY353zvnVXanm/J6U0k8B+AIAjz8ws4/l/fxnvjP4+gUWsFNDeeB6DUulxWL5Q/MAl1nxqaI655MALRA12/OErRZMDw8A2DsqDe11tAJU2ITRXTnn1iV66PMDr9RCdItXKu72WOz9JO10OGA3jpUTd2+47pXNI1ZajrBeiB0bDQPKApUBa2BtDB5WoxDui6L3raoq73vTlYj8rffakfN2XkVVNC5gqy49TY5yzdjziBtiz2dSZaSUPgLA1QzKTwH4QwD+qyh8FzCnlH4ngN+Tc/6f50T3Oef3naXEJ0gxfUMNzAbGzJZ5ZVoknt5wazmrx/CicC05Fex709WwW5NdLTbYarzlOYzyewXOuy4qyABdXQ/Ran1tGMbSIZtNLasvCig/eKLuNAR9E51zmbzheTRkZ1C07zECeZND8O3t5w0TFJyjdDS+PX7bTYQ95mld7KgdpYLzbh/n3es9r8QflmXrpkrRKTcPcI9yHqk+ri0Z53SO/S8BePOsZx4A/A855x+NAm8Cc0rpqwF8DYDfDuBfBvBKTI7s/+BZinuC6O4jtnBEVRlM1pgYRYxH3R1yeO8Dvw4Qt6QwlI30ozJrWhr/lLCalx09HxzMfjjs8vAv6oRUaa50bByXfCJEKL9FE7rfI+GAPWozPItagfJ+DwyJytSmkWlGDGb2XER9dnzOnuS8UYHOR3jf21y9snjF8wvdKoOF47KzzXXU2RzHZe2OprkbgGPjm6g8B1K99b3w74OBM6Y2zWDMOxTZfoDATbuxP9+S7Jzz38fk5rhLehjz1wL4NEx+k5Fz/pWU0kder3iPJupNjlf6uX4ynPbmfci6PJp9FOtEkMdUNJ+IzTQb9Abz8rQDW52BsmG+riCv6TPbtjBROU5egh31QN4Y3Y2/8+/P4Lwbx8mMakRtGVKce6R1/B6EG0ck+LpoVgdpH2SgaC5DOUsGK88CRKqHcfQdI3lFr0B5WFRQ6YT35Y6G6keyal8aThm0Vy6r/wC4jvKB2jezCu+W/QgcqZbz2jGfJD3A/DDnfDk5hgNSSnvc4ERoSzwXntd1vBG1f55Z1n3MWkxZATMC8dZ71sbdyqO3bqYbZv0fW2do2rzpqeav4Qy8OY3mRKoHvB4zbo3PDZS30Av0bZSeZLfOd8w1imqFHUnzYHmgKKw+iSbyWn4teFFJVeW5OOykaByxqDY2vgm9ZyPI1gj9UUZ/UTpl+XTj9dozLCwdi+4YWHbPVgf6Jf55il3LHQbmv5NS+lYAT6WUPhfAfwDgb9xssXzxvhdzkM2LTLxhExAz1gHLy18ZvM+NTE2Loo83YrPKvO3cY55brDhyUaniqRvsPAJbz2Oc1mtFQLWM+gKiIURUwV5kGHhr3kZ8U3uUchCvKGXttICVulTPxVQATqnsXej+gZycN7pRp0gm5uBe/VJ4wK+MFvA92HH4YViXp9WuIl0756/PRb9bDjfMf1afFhM8G0NWybjTwPwtAL4KwC8B+JMAfgzAm26yUNcRA+UBsw7qsICHDpmUzRqzLGk5uDIMk3F9ywTPfnusxwvHKoMt50Qm0dLyJjgHaVjeBsjeCj/v2PKrUWd+XD/4RxFmy0MwVmLdszfsKGVjXcNxu2xOHdRXM0thv9IhF1bYmHxTURC1tKJJvCgt/p6Nvfd8wzriM/3zKa9T2bOJ6e21LgXErSNBfVylT+fXdl+5knyKHfNZZROYc84jgO+a/+6UbLn/LPq9od2jK1BHTBuWh4A6g5O3oKVlCpWGyRmQ/VZAvo4rz6j8HtBHi2/0qPXb6kCqzCvKdjMbAK2kNeQoZWkw5daYm+57/iy8UYoWhbetirKJ4nvan6j/a1Uh0mkrKG89Cs6nRxvkzedYHtGz65HzAfIsOQPHO+aPOaX0S2iMIHLOn3QjJbqGMFu+mo/DCKRZF3eKDs5N32FDXtzW0m/TP5p4q9AUAAEfODXvLeyJtAURC+b7do/LrPe5vM2C6HlViV0btLd0y2HlqLmaCkN7X288zeehDmy6b6Z+ZiIQJWe/bTJwNywM8UBxPefxTrZVVfXReJokvQ6035uqv7wy9ZAdr9x8jevMKwqLWhH15qslLmo3nzfiL+MOqjJeOx+/dj6+ZT5+JYAP3FiJGkIjwyLGlDOdHzCb0JmHI4vf2aar9CO1R/DR6VE/UG1I6iUOuJ6DHc3DyxdYq2J6nokCsuZXlb8CxV0dIVRCOtM2XIEeFQbnX87V+mKs9cteXC2LqWO28hxH7PZjZb/FHbiH8Wr2Ngr4bQG8HVkFlSgfHjFWVZrT3VoQYsCoemtVCeoxkohM2GQm+xqx+h+mW6sdsM2cTrM7KyjfRauMnPM/AYCU0mtyzq+hW9+SUvrfAHzbTRfOk9aDN9bMk4HDuLDV6CPlj8qAK1ouCtQNwcJEumdO266zT2N1n9lSx3oftsdsdXjq6aWjBtQairbAuVnY1r1KJzyfGxgqsCvQBgy2CrvqIcd1784dwKp8jQ7FrdoSlv1RrNRb8o4YpNXXhILeYus9f0fDPFKUR3Nl+loqvpbDUysoS9+a1OPf2sG0OpQordIGsIDxFdYO86MdS84KzncNmElemlL6A/O2UEgpfQaAR9/k8BpiXCljrU8yEsvHESiTX6pKqOISKMPCEZvg1WitnZ+933xNWTI7nufGFzmzidKzNDX/CNwZyCOQ1mfSAuXVJrAMqm7iM1xF9shuD+TYHpcw0kQZlJWxr4ZAwpBbvdaWugVA2gO7meppUtX5/G72c5GiSbxSTAJlY7pcxeh7UYdJbDJ5XekB5Fac1iMGlolFVWHY41lZSM3HUY5nkTsMzF8F4HtSSh82/34PgD9xc0WKxfRJESgDtGwVC3OOxGPQCrqjqC20vffKFigrsbPvQRtSxJS3yqUs5tTya94q3g7dIehGwNuTucmKLac6fesc3HTkpTI1NbZdR2qXDVhAe0bXYRir3Uy8KtjqOXuH3nJpHm0pKYi6iBZIRj6/S3nG2sGQho3mPmxlY4tURN8PjxKZLduRVRi2iIStNG7Ou9zdtsp4O4BPTim9HEDKOf/zmy/W9WTEaUbm+oGY7rhSb3Ywxigu5xM1rlZ5WoxZ0/NAXtNRkIgcLDVJ4xZGtRJYZSYsmHsnT6oJu1wDqLJjZewFfKnJD7ta5xzRW8jLbaHtvDoi4YAhWE3idZIG0gbmbIoHBJPEh/WyaH0UPFI8pUOOVDCWDh8LicDyeHrz0W9zHGdVDtYdD/vDuJUVbnd5l+yU0n8mvwEAOedvu6EybYq36kc40LVFl2ezXJdpeumcEq7XYxeDNQvrzKN4raGtltfbemnlRrNEnt+STroxKHu9g4mCdLU4JPvg3lKjaNqRGsStxwbqSDnSsNZnR52k9iuev+TVSK4hvYRCy2Zp6/cQ9ln0m/Xmp2gAWvMqQK3OsCBRNc7Ob8/nxOgk6VFlPEfnT2Ky1njnzRSnLV7fdcTpSzG9j7MQKixLsbd8OWtczzOdgmbLKX2UT+SnYoVHw9ou2tJWMyxvz75WPaN7rvrCVSE02K0nK0AeUZm7adyoMluVGm02YiNerwK1XJte6G4/riws+H1wVYwlGztmstZ65/ynzLv1qL2Jut5+h9Mw4SXnPQDN+Xsb1apLzyqulYnOvXCPLHdVx5xzfgP/Tin9JQB//cZK1BD7Tgc6bhmVj/O/FgNQ8x+7byv9NHwk5pciYhSRzag3Qua4W6DN6UeAO846wJU6dajLtTWjHjJjYK1PYb2vJuoBuE2sbbXm64j3QCzPlkK0N78hrdUicxrm+IiTsq2dGIh0VSB7RvQGAPY+2L20Hb1OmMU6hsh51pY2KbrvLTn3+tittHijZWbLypgZuM/v9vMOmss15CUAPv7cBekRs08G1kOZga55sOHZHqu47RMz2Ha+n9YuJb15rsrgMCMF1BbL8XTmXpwtttTcw68UzNQIjqqCwdjrGaPzqLfQSbqVxcVG5TkMW4qU9IR/aXmi52Bi3njGycfzcBhd5uyBc9S5axUu9tPiNAPkBw/a1W7lzeLty+dN0nF6JgrOej+KZ2UdmAZz2ODcQDli148kdxWYZQXgDsBHAPhzN1moSAxbzfJC9wAE/fbwpWenDnd+B5NN6IU8rR4WbeG8ST/9cL3GqA2Mwyg79nxJh5i20WF45Q/H0+VcQJnBmsPqQyjguEHHSj7CxFtj7G5w3ug5vYUpVUcQTSLuCitPOGBw6vYog4BhmOzh91SU3V50/yQKtFuAySsTW8BsUjacQAzO0WCk+pZRqy6jR8Sg7Nk6P5Lcccb8Wjo/APh/c84vyFSlAbO6/zS2zA70OQ4kPEuLQZY0xgWcGQxZh+fh1TAs5nEXjd1UPHKnZdKjmsjxfQXlqGxby77t3qCgzGCrhfNAOeoFvN6jRcV6ABmYgHDY+S2f0wFQLDMULU5pkNGLK2kuHQ8vQPH6Il3ur2o2r0q7Acj7dVruoxyWCW7zWQ34AM6mb0fJXyekPXXJgcrRw55NzPlTr+8LA2VTe5yNMWcsq3RuWXqA+c/nnF/HF1JKb9FrtyGDHBWgW5OA47h2fB+RKAt/UtmGGoAZ/C5km6vej9QDU6Bm36Zf1G20vNE2l2nLuf0K9EtPcxE8uMCOuLLzEr8VHtJsSUTzV6BP4LxZUdADIxO6nrJ5QxJ+FuM4pXnA5Mj/cIDNeaip25b1TVQVfqdaLA8UPZt4PlqcNExqksM8WnxUA4UedUYpC2qAnbG6SHHTO1+343lh9G4z5k/kH7Oj/FfdTHG2Zcv9H4sOPlnPrMDFoIcl2KZUw6+hvmZspkUYOW9OM8ojOXl4K/iiYSLbPbfqxHk1A3kslplyCa9gJZNlPdIzvGExcD4lPa8hngLQ3ssTVcrQO2FB0Tkbrz/j1YAegEffQ2vwEem7Ob9e6cW3R8FB3aj1LHLXzOVSSq8HYA7y32uXAVwCeOYWyrYS2xG7BzQNg7XX3fIMx4Ej3wElCH3czFpt48/dUDPa1ooqTVPDROC/27cZOYfl8tm1SAfIncpKvzwMWPmiKMddnQiHZYlAWQvV6qV6hCfwrCyaLj+4YcDiq4P+NJ1CSWnSsJSb8inh/QE2J8UbArPPltbAQq+3HOBrvvxdaJr2t5u3DVECEPVfrVezNcno3WfvcQNq0DWWzCsDzwvK52PMKaWPAfB9AD4KUzGfyTm/MQrfcmL07QC+PaX07Tnn15+ldI8oW6BsEw6ZzhmcTVesVhYt1mDpAjX7Zd8Uqk4wsOR7xccB1WELc7zOQ/O8kLy9uTRuVKr2UEzywlcsGEBzck8r4FlO8LmCcKt1K/if27dzi83zAhMOa7Iqywwj+jIoK2WtfI9F9brF61swbq+sdZx0vLw0jjfpzEvIhyF2C+r99q57E5Fcxh0m3TFQj5D5SZsag8t+VjmfKuMA4Btzzu9IKb0MwNtTSj+Zc/4/vcAtxvwJOedfBvCDKaVP1fs553ecq8S9YkDrWWMYQybOUp0XQCRdc8RYAf/+ijQOa9NdZbAGcsaGDJw9B+XaSL0VfJwudwi7/RJGtxuyRqVl0rT53NJf2S2vCq0e4IKmUYGYWDCwfrclkdOjcwJ0SX9cOh01APfyV5DeX6B8hY7OWhloVAx+PAbEVwdUmN8Sm0jjfLw4PT6WtSNhf9ImvEVbZL3B7NibAAWW9mtt3vb5syDeeOvse/6dcUl2zvnXAfz6fP6+lNI7AXw0gNOAGcA3APgaAG9w7mUAn/NoRT1dFJQ9CDgG5zssL7osBKEPwtqe1yAUd3QjUgZHBWWv0SlzLvVz2AvH0Q6A8/HUMNbYor38vEU3/Jf2VNn9xbpQK3ZsD6oxA+CBcmv82+oUVmm3HO13cCktz5DloUCQxpCOFsZU6EIdyeGqXGZrmOx8I963w+Bl8fhaS9/bAvBRvntmrofDWsXAozbX+iMA+NUAY1wfWaWTh8kEkF34AkubYbg0a6yON3y63IATo5TSxwH4FABvi8K0VBlfM59+Yc75eUn4yTOU75EkegmsxuCVQL0vTcG5ypMazGqR27AGT2Wm/PFH4NyacOO8d04eyoh0ojDKQwF/6W0u6GanqZqrT44oWEJlrqYgvXoBqhYRNInEe5F6rj3yMMCWVU/WJViXbxyBMfm073BY4nMZx7GMlrhz1+LZHAUwT+o51diqtvcYPBBWkLW/aF8/j3BcZ8TvzYXwtzsA2I2o1i2YqFe5G9kt+zQd8ytSSs/S72dyzqu5uJTS0wDeCuBP55zfq/dNeqwyfhaAqjK8azcuI+qH3gJbBuNTetIeYsVho41MI2ZaEUtqAOo2U9ksqy2UAe+ooal420Fx+gz2acC0dGx/MWfScgbkqDC8CUFt+ZpUhQoyYabh+FghSQLbCofxotWImp+ViWfFxmGdtrn53O9rdQYfBQVXu7A7WXvmjNEuIp5Eju5dlcGw3kkFqEdcPHJkll86lo4yWXxv8p0/EbvuEVVVZwB+2z6lvW9KPzC/O+f86laAlNIFJlD+gZzzD7fCtnTMH4VJB/JUSulTsHRKL8e0LPsFkS0Dq2jJtsqWo/Bo+BexHM9Hhcbz8MpEdw7WuJq3x8hLWjQk1DS8MpV02GxjbzbIgV7Xq1jP9ahiKwDfAGaOc7DNh4JyAOtOw0sTQFmpVwF6azuqWQ82yFq1FYiPq8tRHxIJM9lziVceBmVPIv8xCra94r3+cg9rtmzZ8Ijz/AqHWc5kLpcmt5zfDeCdOee/vBW+xZg/H8AfA/BKAJzQ+zCZ0d26XAG4wNoEzsRenjeU8bSeCkytUbqHMxpXARTw1RsWxtPBRXmoDlsXlJi0dmYegjLt9liY8oOLNWtmabW4Sr9DgK4TY5G/jK1JPG8PQQbnwwHli/AWvHgPxdLl6/xyjDV7c0BcP8tjjlfaswCyqgp0opYnihkoOZ5XBBMztavKgPi18fWWfwzLqzDa+fxiv66LDhRYIg901cCJy811BVbbSakp3VnZ8nmXZL8GwOsA/FJK6Rfna9+ac/4xL3BLx/xmAG9OKX1Zzvmt5yrdo0jUbPllMIwwGJ+ylGFLXbnlYL4Fyt6IWSdgNIyB58V+cVLDQ14WM/yPnKOrzruA8oMnpgt2vt9RZo5jn2hcbHrpPYFd9UAv1pW0dEZnXTGLpVta9DwVfHComoWJWL+GG4YFzIvOe5gm7YZhYsXa7BmQnZ67NcHlsdJo9BPZ+HJfUKrDeaBN+LgswFp1oXmpykGrzCBp6ShAt9g+d1hH6QhNjXGBeX9DusfqjbMy5/NaZfwM+leZd7n9fGtK6YsxrQB8kq5/27VK+AhyibjAg5xHPecpvWo0qq7yHXyVQY+XOYdoVWkw+LJuGajtqL0y6e/wmk3ymeqiAOt+Yc2smx1HVOZfHqVS3bTulee5+yw9VEK4XFsfpMXhj4JfWlkSLuUHANikozBrTsd03gVhDLnyEqe8xARvlMCPiNUQWyNkXXjBj2I3ANjXvgNvApwAACAASURBVC48Rm4gzdtUbUnEyCNVAws7MJoircvmHbncV2YJMkfXnbGBZdEJvZGbk/Mx5pNkE5hTSt+JSaf82QDeBODfBvDzN1wuV+xFRTg5YG0iZ/FA96yB8KS5Xe8VVUs0wQ/bAOqxWrYntmPL57LWIepQCuM2czidTawmyRLdI4BlBGCAY/M676GojCOA/ey+7Finqws6qoUtu6U8h8P6S+bw3tK2Vdios8hTXRhNWsvJ5/ry7iWM3yYtpU0LlHkgoFVilYJ5g1N1CIffAloVD0i5XPabl2trp3Q8rONyenmcVB1mXHjqFlJnXXKUcXeBGcBn5Jw/KaX093POfzal9AYAzRnFmxJju3qMdM5mOrej36s0iV1U6QRAqhN/kXmbB5pempGHt2okTqDMu5NEwN/zLQ0DFkAqrJFVFoQqFcjul/vjuGbChW07XuVCqjQz5IImx2VCT73YWXmqa7tF5aBhW2qM8iCwLqepMfbkCKmUP3ByJPm0Ok5reN4j8dQcUUdcFZkA2RwQMQjm/cKeFZTZWqL1/RjAVv0ntuMY6Go8N12s/Svrb3akD7oOnHM/wDu8GSuAD87HD6SUfgeA3wTwu26uSLF4GKjgbOctnjZiGeat2ui+rYbYckrkseYt0a2gVFQ9omXy8vQwo+lVTkFJ7xXWTHpY7wGablonDw2AK6YtKowCzsTOOf3Krlp6oujBez2WC+Ds+Y5BeFw6A62vhzKUb8K4ngOg860lyVFxgfWCIQPcy0tRix6WMEoq7Dux8N6KVK+6unJPRXdnYdDldDQ+b8LqgTL7W9Z7JY11ca4vd5wx/2hK6cMB/EUA78BU3O+60VI1RNfMM3PGfM4ff8vY3CbJCmseag90SqZaiz+uA8qn7CsY5eWVa8vxTZzwMQAtAq+BnvSwq0F8SGLd8USd3uFqRgID5GFhusaQbbM6u6+gx6qJ0kkIHbWwVd3koVQvVxbFrJwYiR462o6KRSmy04OmuZ4D+pNTl68m9th2+3ZarX7KLDq29N8Ry++RCNCj+AzEWyz6rE7yLfe75l3OJOdsu5W8NaX0o5gmAD/hRksVCH/WBsAj3VOmzDbNA2pQH8eaaTM4A3W7ZN2ut9ya2/w4xow7rJdDAFnst61lsLw4jnomUy92qpt2dyQJnRQNE9CaaqAUTDR6BshPPgU8+cQC0qyeuLyaad2VPHBiyOWPVAYMoKymUPG2gxrH2tzNA1t+mbzKj9UzbtrqvU7KpB+UU7Z0OJR9/kwO9E3x+wNoUdN+SXM3jsizHdrxUFfHxHOixYz5Yj9NvnngfEonr2w5Ult4eTAAG3NmJ/hmsQ46KiifDUozzmaVcar0MOYiOeeHAB6mlH4QwMfeTJFiUVuTnmGLfYSRnYoxZP6AGJCrUXwDZD3G3JIeZ/XcWVg5DodF18wdgee1y+oCOCqYVaVYP8yWGjPYsrVGJMaSX/IU8PTTE0AzA37+g8DzD6fj5VyZ4WopqI51FQjNysJb/FJ6r6sF1AsoXy1heEcVwPcB4n0IHNebYjImHTH1sCOZ7ieMVVUMHL1RWOlY7T0BwHhEGg7Yj4cSJ3IkpJ7kOF/7lnqYsxcvCqd66UodguXIu5CwE3xTYxxQP312u8BAfR65247yPem2x1tFTOkLALwRE+F9U875v0wpfSImi49/COCP53y98YO5BdWj3uePUf1J8G/zV7Aa0VOi5hAJIKBEnaanbogk0sMVHNmjDH0LcI/rRQX8Pa1WCxrTYvA1oDZwLccHtdXG3plMAybQefBgYspPPw08/TIgPQXgYnJ4sDsCFw+A/XNzOg8n9nww0CPwLBWXrtfK+uSTtaqEqd/lw0lVcnk5Xbt8uIAiA/2e7Kl5uANg8Qk7LqC830/pFrZt8Zgx0/KH4qc5ePGOOoTJNbBehr0KXFhDKrbcu/2hfAvKWHVFaGsxEt9T9QM/MvvtgbPH2lnfrFzUwFivGTgfnDAeez6rPGbAfC0de0ppB+A7AHwugHcB+Hsppb+OyZPdlwD4cgCfB+AnokzdFXxAtd+fHoEYlL3JPAXfiCmzXpq91UWG+tEycP1w7agNRxsZT2AOWKfB+VobLkxrBb5kx2yr/x48WNiyATJvLaUPyNQYL3npDMovBfAAyzz6DniK4gAopmfaipkxM5t/8okp/aefBnZPYaq5LTu4Ah5+APjAByZWbrqfy4fAgbaMsny5HmNakKJ6+XkZJTygB24b4nlmdlZm78VuCIOesVZP7bYrz8XUO7NZ33CJXWOHlAiUe0XN7ljdUsAZWOkTmGrxJF+5ZnVDrc7QpFSP7AHy2SYA8x20ykgp/Q34dUwA/oVr5vdpAP5RzvlX5zz+GoA/jNo/SZONq0ep/Xy8mBPhozUvz8G+TrzZHy+HNRM6darfUlt4+jQF+VY8ZTcaRkmdN1TlvJgtV8NfA+ICvgzKTwgoO7bJq54rLWqG3R7Lm9jPf6YdvJrA2wp9+XB+SGlRP3gPb7+bQf8p4KUfDuDDAXwYlrd9BeCDwBPvAR68F3j/bmLkwwfXjJjLrWqTA2qwrRavHIH9cQnLHYqV13tpnJfec8plj3fFWkdyE2plHuch1JBWYOiJqrx0ZNYrPXG0epXe2crA4YFKnTGiDbI3CsolkzsGzAD+0jXvteSjAfxT+v0uAJ+OSbXxNwH8CoDvjCKPWAB2wNQkzT/z4BzZdzPHZfFwpvqg5vdysa/jsHiLPq7zkQOBVy1h9QayzFS0bKxbLr85gRVA2zLsJ2o9rq6cUzFQNva4CscVmtltOk75jCMwyuKNstou12mb7vqlHwbgtwP4iPn4BBbgfw+AB9PDeRoTaza1CS9/45dkncHl5dzbOZYppSojsD9MZbbfdjwAxaERhvUHsMp3QSz1aaF9kyZ1dZiKsTscpnd4WAf0RngskU3xFtBGy8OZUHhhWgQCqEG5Ba42Eo6SuraO1ZOc12vDb0lavjL+zg3k5z23nHP+BUwA3RQFVwZpVWFE8e0kUivwhpbMTpn4lPyH7Uk8S2fLm53lrRI5QeL0Ixa/8gKmqF0S5SFxkNHJMtIfUFuap3U+OiZmqwmekMQFJjA2VckTWFxbHTGZ3V8Aae5sDgSkVfEorwP8cgBYTOdGeT675XpvJ+wgU6T2av2273E3jvMiGLJ8Cdg3X/ZA+TrEMBrlKUM+lzZgwA3okLfkDjLmm5B3AfgY+v1KAL8WBU4pvQXAl9pvb+HIllPs0PGRoLy1xTxOjMQDUpsHAmpGWuZgWGVAwmoRjluVc06X/TJ7aXtkTsmYpx+vzeMcEHb/Gk+3AlFZMXg8ALuHWJqScRwC6qhCSv/N+sIWruApLKD89Hz+BCZVxgjgufneB6eP4wEtddPyG7C1dq3W/Qz3F4vuulwXd58tL3mEWqeqEuz+4QA8vASGYcRufH5m8VNCV5fL6j9PPFM2zn9rJ5SoTN4y8lZ97MtQh/dA3Z1bWGV02t3v5DcApJSeo58/nHN+XVwiRzKQT93J/Uxy28D89wD8npTS7wLwzzBN9n1FFHh+kK8DgJRSeUK83Yx6tAKWlzbIb2D6CPaYZryTNIgyn2PpHmr27PnXYELnMWhOe78/rcf30gb6/CyvmHxhhLv6GCVUAIaWYGv4As7z9MB4nC0iHgJPDnNr0k9snls/u32olZ+neakD2gOhf4vexsdqIO6h+dkdrmo7aA91BZQVxDxHRxyOs5s2/T2UMJeXy+o/9pfhrcbTvNW22ANWm7Pw1GjeikBP/WHxzBkR4KsxoraioGznSiNyzi8NkuiWF4gw3y4w55wPKaWvA/C3MD3H78k5/4Pu+FjUGfYiC+5gcXxi4j1Tu7bHROzynMCe8Ke0NXELMcgH5pnaeUxbgT8HIMtpqgrDU5moZoLP3aXjXgQuJPdCtmWSAah9KWptsOQ8V3AHXNpDJWbJ+RhTvbyq0aP82cKS45L3OLtgvLgE8BATMzam/ASmr+E5AM9j8kM4W74WhBD/Fp7TpBZ9ZXVGMbWTRTLjOKsV5g5KN3KVdDlLZapb7jrtsR336+uHQw3O6tBIq+vtVuIUF0C9g4kHzl4cvu5OaludgUrXrPdZFMQTTiM9PZIzmoOfm5RNYE4p/SSAfyfn/J75928D8Ndyzp9/nQxnx9Cuc+ge0WXYEfhGHEiHRMOIYialKs8e2QoX9rjzR+29d2XEkUe5KH/XNpv1olrAApaHBXjLVk3H+Xx+2uboXsGmpPtwubY/+AW0JdmHw7L443DAypeGDjvM8iPZZ2tbJzyF6SV+ANME4PunclxdLnbNVV2PC1qZzfPhCiv/H6sFLsMyfKlUOWyDPXcg+8P6GcF30+kJL/AISDeGYb0tFIOxAXTU5yiTjsrDgwOP+UZi6euIwIuj/jGA2jSOF5uMcg9YCNpZJ/+A7sHUuaWHMb/CQBkAcs6/lVL6yBssUygMxrpLrr2sPWpQ9nCT75taA6I2BHzWyjijQ8OiAhFpfcAD+hafnNpprJhyFKmA76wcOsi4g1m0a21ANS77342kGHdW5zEwrhwbjes0TV1i4V9yAC4eYgLgHSbGPGJiy88Bx+dmO2ZbaEKTYofDdL0As/rvaIAyMLP32d6HzfuMLRsg84dDoKys9TpirFP1uqV6h2me5ChsmfOLXIu22K7dS8M2KFselr6ViUcCurpPrwG146KjHO2cVRidfKpLcl43h9uSHmAeU0ofm3P+vwEgpfQ7cQPmgj1iwHxEDYJDUKBW72lpHLCoBM0iQ2UT18YFP+zvMK53C7Hw/JvF0x2P4+wTZGyXI5IQ9MswPi1MuQCJsWQCyuIoKFErlqc+kHpguFpM7ap88/LAGIRVjcFpGgowDXzyg/XKP2C69/zztS8OD/xNjeIhVsnX0cEraJd6zH40htkhk61QPEGP7qnAvIUa0fZP/B2WPofOI1WJp+LwhK9HJnMcjo9WhtIJrKsFqyp7koP8ZoDm+7R86exy3c7zUaUHmP9jAD+TUjLzuc8E8DU3V6RYDIht4g9YVgN6L8WsW5OEBdY964i1OlCFGw8zFKAG5YIVY6yuiNL1hP15WF69Uu2+rSDIhS9bKAkd0jHoAXUa6o95f1xUGLpKsIC8ACanx+WsOosZUM0R0gcc+2pWkXjM15ixLd3mPKuXR5YYfCyTfuwBb6zDrf52WC8+9sV7r1leB7AGVWbFCsysrlBpMeXourrvjOJUQDySSgN1263SxhqEDYjtni1T4pWCQDxafRTJec0Tbkt6vMv9RErpUwH8fky49vU553ffeMm8stA5vwRl0QWHsGbTPc95q5e0tsjgzN7nSrkcda7HnCvw7Cxfj665hFMAKQxytrrg+xFt0koryBbWagWi7Zc4DY/BAvBscKt4wNzTXqGoQrwHbEx5lQYxdQN47hj2UlbvAdv2UdXSbgFzFa+z25CeoMqUK/Cjx9pjaeGlrWF7t8TyyujF2wJRBmVPlWFhVM7NnO8cY04pfULO+ZdnUAYWe+OPnVUb77j54q1F1RfGlo1FDxSOmxb3rJ6cqptSIjkME7s5jmbCVP+ZJYb5gGaAbjFgbnSlrMOaqPGRyzeOU92SgZJZFqjVhc0klck/A0qa6FsN4WUJtQ3jbdHDYVgXasWaLW0nrWqvvuPk70L1OdpR6MvhB1ZoJeu458lMPJjCPnhAD45fIm+3BRTfGhWYi9pGXmwa0OV7maN6HXZVFdLdKnuOGG30W+95HgujtPW+dhLKlsN8UXuT81gz5DjQ7wG945NteQH95DcZ8zdgUlm8wbmXAXzOjZSoIfYSWmy51/6vZ6WgCuugI1K5n33aXtAcmN2zuAbS7LrTyq9b15dzU4ZLWt6RPd4ZsdxjXIwZeEZjGDA5rD8uoM12up7/CgM2MzkDFrXDuCeQD4CZ0/WYM6sSXDtGfjCWrlpUjPWDMbEys7qDV/DY/oFseeL1fMAyKijlCcZjAWNW8LOgHmO1sKweYFBuAbJKz/2IaXtMncMUYBYb6lPEwHlEvGuJgTGDMuT8keUumsvlnE2P/IU55+f5XkrpSSfKjYv2iua8yF6Ot3NJ74sahj51grZV/cjNMMFWD+qIu9JBk+z3tdvEHTXQstCMwNkbdfM1Bmcr527VuoaaMZsi+3CYme9c+AMm0Ga/Ejy5xhUztrxF40s51JY4o1qZeLiaQPLgPLhVfY7rPPghcR4eOlUPVXphA2ovf8BvwUEZIp2xhwE80eYtEPEm4jT9Ht/KVtwWq44AXZ0teb6XPfFW/QELCDNAGyhzPAZltms+FzjnvFha3rb0EMyfBfCpHdduRfiha2/JoqqMSDzPc13lcAC6OsdimdHa0aTa2ooqo1YdZfcSwh1PxcpiZSh+3kcggUFMVBo2ZC++h2dmzax1HBfbYLY64CE/90YhkAlIWplKers6zahHW4GzMGcuXwkn+mzzpXH5kMKPVO95VAGv/A0K6dQ7Akn9ZoD2Sr2IbUt2Kx/JUb+lEtk2R9Xka95ilV6wZJUFTwaq8CS+pc2Afi65c4w5pfRRmLzBPZVS+hQsz+LlAF5yC2VbyYh6CNMTXkXjGYCfAs4KwoA7Ui35VUtHx1rHzKPcFrBaXhEgtyb/bCn56iazZp4YNF2zhWPVR7EDvloXqBzFqiESlzGPNQhbGhULJw90nBaXt4U8yvRZtOy8A4t9fdXuKA3HFFyuhvDIaBD8VwuLCBh13sHSjSwyvPw9wHcHOXTuOcbnBU7lMdfVAlCz5XH+bX+ejTMQ+8ywsAes87mu5GBgdRvSYsyfD+CPYXI09AYsz+S9AL71ZosVC4OyZ/rGPaY61uc9AjmtEQtjMT01f3QFL7AwGt0NwgPHolOWl3vEoq/WD11la2KwpfM2qcqIeSIQWADX9qzS4TtvXVQyPdYosVXQLXAu7jgJ7DymXHUAshuJldeO1UPNCG2pAQDEnodh2fEEwGK7zXbclIe3WlB76KD+Vi39xvQ9mh5ZwZkBNwJl79GobH1/XtkUkHUrs90AZJpjOXKjxNqqgheM2J9aYpT0tWxB/HPJnTOXyzm/GcCbU0pflnN+6y2W6STxPntdtq3XdZKwqD3GWrfr7QfIeSpARyRMxTOP24obXW8BcliOqtWSSgNY7Jlt4YnX4s0io0ozGvPZ5GCw3MfSYX/JSw3gNrMISRSQSxgHsapn0Oghrf6r8bxjWVKKHahdThAuiuqRvcm0qIOO1CaReLvm2NHOW6ZzXG17bOZfg/NlfbAxZAZVBuiqPE6ZWQ99TrmrVhkmr0op/W3xlfGNOef/5GaLthZuYgMcb1JYv5yy/x5qsB4x6a5Yx7wDoH4zGC90yTafH+fzos+lMLofX6kPsR9VNfCw0BvZnzLTzVtQLYR0RKq2QbmodSatCbzSWsmCQsXbSFUrx2l6cabAKG91Na7WzqEB2Pp7Vb6ZnR/2mFYtmo/j5MQPQFlRyQPocZy+h1afIszUU2Gcuitmiy0z4LZWBEZO8FmsutwO9HWrxcWBjraqz5hwKauTF6s7boQx3/El2V+Ycy6qi9lXxhcBuHVgNgmJIGiJ9RzOmq5V1NgxL+lkXxvAlMhBVIy7xocGrK+Xyb09Tf4FKhDPLaIdXS9xqK0utlQgZejJqmSry3iYNmcFZsC5qHskTUwz1Er36GW8B8WF0t2mi1tRZ2GKJ61OgUHV8rdRwn5cLFJKuKBO47juGCyvcURZjFIWpVB+HTRMgXCryiV75xFrtl4RIg9zDMpHR4MV5aHlKflgAWVezacr+lqiFhgW99zAnOG/4utISul7ALwWwG/knH/vVvgeYN6llJ7IOT+cMzDP5LcuIx0VG1lvZfd52ykDbGbNzJj1+Q8OUzb7Y11CzRN641hv+1TSCzCJGXDPyLf68EcUt6UspmK5IAJsD8DKyvkP44jdeLluvaWgjbVUVcVk+fNKjks43qFklZaTHzsZ2prc0/Lxy1CUsxd8OCwLWA42NKIJ0P2uTq9Ki+utnQL1qg1Ui1QRUZSWaedA2dqiFi06p3+KtDoJroOnOzcWfEVHY8oHLEy5hYUtlnwTjPmMqoz/FsBfBfB9PYF7gPn7AfztlNL3YnomfwLAm69bukcRZsM81FF2zKsBK4uIORxbYhwoPCi+eZzjBrDfL/GBmmGYKgOYHYztFzaMBstmUTDXe95vF9fm37bQpbKDxgLmax/PM0CHCTcq4YEpLz7hgg/D/NKMHeuKOQlvR1tKbSCtZQDWafWIgevhOPXIlw+x7Os3q2tGR49VOgqzVGFHFUeszPJmUY9uVdUp+WjxSWujBP4WWTOlI7VhXL4LGxwd57L1kHpm9EDtR9yus68OZrYGygbQDNKWrVWLV/EpKJey0N+5Vv3B8jqTuVzO+adTSh/XG77HV8ZfSCn9EoA/iAmz/lzO+W9du4SPIAcsjNdejIIxUAOynfP36/lyVdAGpo93QN3+DJyBGjNMbKPMq/kL8XxnKOa19g1k/XOkJwwnDFGDMxO3YWZSZmUyjvU9e0J2Xnw6Vxm4EZ1Cin0yPzgG6aJLdloDOzBauSZlNktls7RWVhljPUaNFoeM4+yUabeoOzg/s1CxXVsuL1H7mqZl6x1s2bJtSdRfcket8xWj8w0dQcY49u0d+sCZQVkd6B1pYFCA+TABLzPjIxagZuasFhstYRx4DBjzSdK1gjnn/OMAfvyGy7IpBswm6h/D9MWDhMsUzp6zNsVBwhibZkf6vFLZRNubuehUz1q8lyfQJqGctoGr54EuIrCMkbyHoU5MegC9c8pnYayii7e6AIxbysaVmZss6d5jWRa98oYn9tMlbacc1ZAiYOYcTqnW4bjswDIMWC14YWuSy4d1p1Gx6Nq96NYu072i35I+crOEYPBd6ZWxMGt+lQbOXhntz0BZjWlYY2N6aZvcMzA2XxgGxFnOvTYaseWqfDg/az5Bx/yKlNKz9PuZnPMz1823ZweT3w/gvwbwr2Ly9LID8FzO+eXXzfS6or2iAimHi/DOGLF9KCZe+Nbk2jmkR6dsokNRoE1SvfvaeBSgdRl3VGZutEmbSUS1osKsws1vtFr0IozTzldgLMyc8xmGdSvjMowjVqsguU6lZ5WJxLJdyHFh9UWVMa7KrqOs1gq7Hq9wWkyurll/tCb+WvdYtra60jqwmkNtkUesF5cAMfC2mt+AddrnkpzXI4KGvDvn/Opz5d3DmP8qpk1TfxDAqwH8UQC/+1wFOEWYMRuj1Qq0llgra7ZwqsZgHXS5NrPelq53cFQSyp4trN1bMVMnPteHgbO1uIXF85uhjVDLxvsSajlNTPswmd5BbjjiZahj8PE4m+pJ1+k5H9LeJcqLVRCtzuEAFNWDPSD20VF5uxuXsMaYi9e69SIcb6cQd4KM2OaGBmTzERhr5rC9JEP7QFZP6J+3unAcF5DlFXwta3cLX+Zw0AZdbssj/Z2LMd/pPf8AIOf8j1JKu5zzEcD3ppR+9obL5Qo/8AFrVQbDgXqN4+fLE34DfP+tlm5ZgXSoF5GoDMNkGmdtOEmDMHM13ZsU2F6coqoJTdtT/ep9A2fNy8MzZtTsrtTKqnktf+TBriXU6pfJo3FJyGXDDZRqsXEF/q1hCrNx3ZZGJzhZx1z5eV6rLCJGyfOFNi/RMpHTTjXqYLeqqKZ4HDdy4WkgrB2Ip55RkLVrJtw+I5WFxuHRsQfI/HcuOaO53H8P4LMwqTzeBeDP5Jy/Owrf04w+kFJ6AOAXU0p/AcCvA3jkbcGvI7O9QGGzHvv1wDaap7cPQl+4pcXnQG0LrEwXWPS4ypzHccKEI1DAucISov4RQLfAOZIeDIquMz5yOmx9AtQTl/s9MBwInBts1h9FjAv7jnqoVgWV5oGZHKWrlVpVXPTexpa1TsKY82Hc7D+AGJSPpK/11BtaZe5DPACPGHnkd8OLowDe7DSkvjyRp2rDHRZ1xk7CKLhqXA+UD/J3LukdYWxJzvnfPSV8DzC/DtOz+zoAXw/gYwB82elFe3QxVYb+9Yi3ShBYv3RVZ4x0XsBVRNUQzJxNxnFJ18Bdgc+GnbyfqaVf0mCQHGMGrOAJ+BOIWwCg9fB0lKz2KOBcerc64ahhrzuDdotYTUAKKK82ymVWPzgPl+IuwoxZnBuNI4o53AzK6ssCqJ+5twEqg3IE6JZtdG9lGdF4dK4D+wCEnX7OLWOxlR7XTFcJp220NWBhzTv47UqveW5CPVB+Uagycs7/ZD79IIA/e7PFaYuqMuxPbZsLAGJRRxyx9tHM9wYsqwGNdY+o2fNhnMBZF5ps9aoVkM35MahaozOs0EUgnnjDwIhtA2tQ9liS6gmZDXvkl8s9oDYRHCSwdgAtEIqEO6apYa9poucqk0GyjGh07X2rUBHLtk5gBmUb6gPLqMbbBFXL56kUPJ0+Z8vHyKEQh7FzdbSv719BWdPT0aJJMTMlcI4m82wE6wEyOy9S0QlDBePL+e/EzyqUDNw9f8yz7XKoYck5f9KNlKghBswDphfAjJmB2gD1KPdA9yw9u8egbPmw97rq/YwoJmaezrgEI6D0Gp0u9LAGsd8v91ojbysbUDPxsqAEcTwdVnvAwGw4srOuWDqWBs/qYs3TzhlQtjak9Z4f3/Q2KFX9J2/9xczcfIZ4Cz8W9j666iMvjpVFVU5bfiY4Tz3Xeisot8zwXLUDdVqsQvGOUfkqj6iYv0E6t+imN47O1WqDw6zqgxiQ7fe5gPmu2jG/9tZK0Slj559aVZgYa+Znbec7CmPfP7NpF5wDMLFG4g0/3WuUNn/oDLAc1zuC4kfzZxwGaA9dWXqsP+yeN4yOwFnTtzpu6cZNDPi8/ehUV1rSx7Lohq+1mHwBcacMFTCNbbOyU6WlQmLpBXwTVV3YNb4XvTPPAZOVk13ZlrhYn1s79awutBre756/c8mdA2ZSYdwZYcbMrNl7drbYxIZLO7neEtaDcfoeOAP1x8yMzfOroSyauo1yJQAAIABJREFUh+bGeu26gbKnUljJSLpemmAE1rtYAP6QlssHzO6YZUsrK7tbhHGtqjHR/HeDD8iebr5KX/L2QNmG7BzfrvMEKlC/I1XpsG6+1Vn0NF61Se7psL08esLoNQZifUbRuweW8FxGz6cLf2eHcQFdE1ZPsEN7W1RypPOSpnNuoMsqi+dRs+VzMuY7rWO+iwtMGDQvsTgnUnWFgcQwh2GwZhWIWmfwxB9QfzCcJjB9qHs65y30VBUQgTJX0FZrAUta+/32wo9V+UZi3LJWw46R43WVBw/6LUHG+SUNcyP1hNNRneWWMUbE2iO2zPeA5Znqe9K8uEw8uQmsgbslXgfRKx5rvY66gt8vs/vWSIk7t6g8mqcCubWlKg2sQZSdFymoj/KnqotL+W3hziV3zlE+yZ1ZYGIvBqiHldq7MjBbuD2mjVsvUAO0paUqDMi1zbKNExheSYNXgG6JAbaxbdOFGsBGFiEMVsZa1YGRN1TVBssNjYHJA8MeAI3qOADA4INya787Lg+XoRfsFLhZWvsyTpH9um11JltH7UT0nMut0vKfzHG3rC28eJ6pnTon0nu2/NoAUhmwbqzKjFl9MI909EBZgZnzPRcw33VH+XdmgQm/LAVobUN83divfRx7un/EBNasY7aHEjm71OusEhiG6eMtLhaIAXOeW5NdmdIsds8gdh+AQQFSrFmiV94t1nTFFmNciUYZot/VLL4D9lxvKzcDmLF29fvRYoZaFt0Vy9K4Qt057AZ/YrenoXodStQhKNBxHgreW/4rOA2No/e95d5q3cH7DbJJn7fiz1QYrKLwdq22iT7d16+qEx05zQiYFZTPhqV33FH+nVlgYqLArC+CmbICs8VntsxAHomlw06SIl0oULNez0oi0tUxQ+UwHmv1hNOoQF3YZWsLIT4y8EUmXBHba4GYjS54Ek6ZnGcxYqMP3dTWA2WP1TE4az25IzV10FZ9VbjT85jqlhpmC1i1PF4dNZ7Gj55zVI9xrBfEFJDG0qYYGD09LwMynPuefXILlC/l/ih/55CccadVGa/DhEMv+AITr2c1fTNfUzWGAjNfA2qdMgO2HU0nXak/AlC2xrc342o44Iy2M/2qjo0GHcXj8LoIpZWGskjO387ZU57myUc99+plKheWaJmwMm8zKfTM0TS+/XkOgyJmbSMOtYDhtL14BsjHgz8i4Tpo3MhKIiqn1i9cHh3UUZ+LvjsGZwVlnWgbsaglPFCOvMa5daK/CJRVT31uUC5lOXeCnXLKApPn8QIvMDEx8OUXYS8RWCpl4YD1y7MPCYDLlqP3wYCvVhcKaKbW4IYNLNcR6G+r/DpYsiclL8SqE1uxtQUalt6W+V0PiFj6I7047RS8c5XS0TmdiJfG1h6JHhvtEQUzBmVewFF55HPy8Ni+5qGdk1eGVvm4jJxv1HlwWAZxU1Vw+2PwbS0a4fbqiTfxtwXCNwHIVpY7B8wppT8M4JU55++Yf78NwEfMt7855/xDt1C+lTAoAz5jtjAt5mxhdOk1Ed2SnokxZ56kArYbiTowMl20p86w355v5Ei8PDkOOzAqdZnzt81ee2Qca/36Fni00lGgj4bynrAKY2U3O/q6aS8PEzXta5U5AjBgyvfysmaZUedyHPwOxcuXj9F9T+2zVZ/DYelENA+PTR/HSZfMzJgBWX9X+dH11uIROx6CP9UpK2s/q9xRc7lvxmSNYfIEgH8Nk375ewG8IMAM+C/djuxxbkA90adgzfpnA2gz2dUdtEHnnn1yVR4poDow4usMUjzxBCzXVI7SgHqA1TohYEnfjt6+gZa/1olHAHrPY6a9/jkYUFvsdRho5t4pC09YaV6nDPGBRW2j9yKdrAFzz8alXv25rJ55o8Zl9coWKHuqiy2TOc/umQF2C5TtaNdV/aEAfUQMxi0VBud1brmLOuYHOed/Sr9/Juf8mwB+M6X0gk7+AesXwczZY8rKlvmlGijbYhQD5wJkWB5UjyWCSrHWcAA3DXPnQaCsZmScj/20RRxAvLuJmn0NWDP9caw37PTqw3pla9D822OnVjdlox7oMNtjCxIFXbY4sck5Tw0S6XY9kO5VcTAgtzoW7Rii9Lzrmp5ObJpsLd7hdHREwXm1PMVFJnZAmxlrGKBm16Pc4+u8+MSzurhtUM531Crjt/GPnPPX0c+PwB0Q74UYQBtb5pengKzCrNnAeUDNChgYWHoXHfCKQNZBj+PM0AVMAX8irjI9kzw8kK8mJPfbQ3fLD1iYffGBIeAU+WvgTgTwnT55S6e5jnruMXXuIFqMWeNtgbKpgFogxWn2qBC0M2uF88pjslq44TxHr3ye3TSXC1i/k+pdO2VtVYXZdaT+4K2mlBl7bPk2QBmYrTJuMoOGtID5bSmlr845fxdfTCn9SQA/f7PF6pcRtc7ZfqsKgsHawo0UjtM50h8zbfagpV+E/TQWx8uSlb2aORZ/+MxgPJa4qndHwzY9ppnt2fVhruwWmzThFYgGztbBtPS3pc7z71PVdcoaK6Cm9BhQlDFrehYukhXwO/XTd7QlOkLoDc+SNe9xsUpRSw4+b11L9E3y890N65HLcaxZrXqOs3cROcBXx0XcpmwyUQE5Ysm3Acomd1GV8fUA/seU0lcAeMd87VWYdM3/5k0X7BSJXpC+RH2xdp3B2SYAM5YP6IrCbPna2GEG5wZAAzO4zb93tMIvESON9Lg9wvl4fp11MYECDzfUPZXP0uEGrWXzym5gEgHaVgfkmfOxesiuexuEsmyxZM3Xzj32yO+zxUC9dLUD46NXZu/dFOseJw99x0A9otHvQ+tmzorsmumXAV8l0SMK6DyBFzHkSwl3m6B8J60ycs6/AeAzUkqfA+AT58t/M+f8v9xKyc4gXu/qgXMrLltqqHmd144896Dsl3eLDWnjaTGfXhlHrPYrZN8XHgiVeAK+x3Fdpq0yRiDVa/LVc98ru0oPKHssOwI6k1OtZrZ+q+oqmtjrYe7eCj876p6ALFFd+bJ960wqI9LC7cfOuS229MjaXm8NK++oKgMAMAPxYwHG3jNkQDa9MX8MpuJgnTLHsd+6ln9A7fAblFblI2Cs2TM7FDKnR2p+Zw1ua5JHhb2k6cSgxzg9D3MKQOa/mDeOfoj1qjuvfN4oQTudCFi2RgheulsAuiVRB+Mt3FDrEGBtLaNpe+BqaXlhLc0obusZtha38DWb+LW0WrtC6ySdN8r3rjGAm9rC/GOYCsNbQMKA7QH0Tctdnfx7rGWUowEvD5kMSAGyukDNlgcsTvTto+MVgGa9wX6eFZytIHa9NLrDWp8HLI3N9MSecGOMJhxt8so6gx3tK8ggpECglhUrJnyImRYD72GM7bEjqxMFV4/xsUVLtHUTl98TVQEUC4KxDtMCRVOleLp2Li8fPdeikQ8NYBtgPXUSd7Zs081lZ9Z8pPxaVhzlNxaQjoTbH0/uqdpixOK6M5rkeyFA2eQu6pgfWxlR643taAz5ksIygwZqH85sE812zQawBsbKmE3Uu9Z+rJdHW0M1NYPtJNEymdPJMPvtLR4BlhWGds6TjnDOS3mtoUo9eHeSljCI8k4tLJ5lSGSSpmyVJ8CifAFfB+uFX03mBh2XlsFjuxyPr7nMO4ireTOo23PjUQynwSz76rB+Bi3LIU99whN/Wz4vTNgKw4D8gGm0xRYY43z0wHmk4wshGbiTC0wea9GXaS9ZxZj0g/m3ARGb9gxYe5RjMGbABtZ6NlZ/rEzNvELt12oMBelBgNiTqAFGDMsDjnEM1DMbwGxlrDoQeSnRN99inZbuVufQqxuMVCYt9q4O9CNduao4Ihtozk/LxO/FhEciHjCzTbg5H2KJOhQGc/aNYRN/DMjA0j5A13nDVGtzV/Pfw/lPHRFFC0gsDT7eqtxlHfPjLvZcPfwzMsmgrEOogY4m7GGOnfQrIOukyIi6oVtD8CbmgBq4omXDpiuOllyrLlhtiRV8WHioPKAGBO+D9Rp7y1RMwdYDNQY3r6PiMp4qrZFC1FFNN6eDbsprEqkmPNZteUWjmMjDHo8WIh/WRydd1Uurfv7hJXB1OYHyw0usHBYZGNsx2nBVyY2Bs7JjA2a1wOD0XiBsnPL+UAfmlNJXAviP5p/vB/Dv55z/9/nel2NaAv59Oee/cq48GViBGpxHTIBsbcpA2f6OFD6h1kGzt7ktUB4pnrFvW6I9OA2nUgHIR+EtJPFUDrzkWtmRx4hP8WpmAO0JM/SeJeutj97TF/f4sY7SjfLyOgCTSMdcqZZArNEB+Egi9RSLB8orgHbqw2zZGxmp3TIz5avLaVn55eX0nq+wXk7Nk3/WRrRtMXAz8D6PNTC/EKv6eiQDLwod8/8F4N/IOf9WSukLATwD4NPne1+OyQ/HD6SUns45v/9cmXrgPKIGWjvy5KD19mzJYXpnA+LIkb6CMoPziIWBKrvhl+GxK2XGHmgCPoBxIzbw2RpiMwC07nP6Rbc71OZ4kS7UE2/BBECd27BOM7Kp9srqAaCXr8c2e8rrxfFUUMx0uQ6RtDpNvebtMsJ14rzM9aqB8tVhAmUDVGBpNzpvEvnLsDhGcKLVfAzMI/2Bji+UvCisMnLOvOvJzwF4Jf02wtmzV+rJYuDM5/oB2Acywv9ARixAzOcmVvAIlLvKeY0vUcGTTfFa7LIXlDUP/q1hdHhsQLqTsvXUU/OwNHsY81ZagL/4IgrbA85RXhHT9vT/0fOJANsrY8tUMHq/KxXIof5u2f7Yjqsl4fBB2oBZAViPdw2UAbwodcxfBeDH6fcPA3gWwPfnnN93Exny8zXrDGBRRagZjzHjHerJvQMWFYa3uWuUp53zsm72XqZqCwUAnnAC1oDFM/QD2hN/cBroKUzNzj0AsaP96V6F0aSldhRR+t6y9Z7yevm06uada1la+UcqB6/+Zen/uDw3i2umeJ4OnsFY1SjeX2unEvuGzALD0yOv6kn3PF8YzJijPwVnwM/rhZIXgyoDAJBS+mxMwPwH7FrO+c0A3nzTeY+o1Rp29EDZ7Jz38FUWBsq8uSuCsBrP8jVQ9gBIgditj4BzlUb55+dh17zrHnPTc9VLq22xmvsNc8+2BapHwO04qjAj3GXrveLpXjmvKE1PLaHqCC539Mxb6WsZwhV4Y3vUE4HyVjiuhxET9XlhgAwsgMq+MFgNyKqLFiALX7gTku+oP+ZHlpTS1wL46vnnFwF4BYA3AfjC2YXoVvy3APjSc5aJwZkBWkHZ9M3AAtI8wWF2zHY01hzpYiLAbjHVi33diCMm6KkJhgErR/wR4/LUEFGeHrPVfNVawXx19FhWbDm1j+rjiQLgMGDZydxhlD3So8poqUzKc0JsLnhK+i2bbw+UvXfG4axs9m1bdZU1GzOGXFPXnQzQt622SP9/e9caq81VlZ815/2gQLkJ1RRKUwgCgoZaW8rN2HBL8catCEGrrQGDAUWMAeQH2hgDGGNBylUubRQCKBWwmgrKVeVWakspxYoUsLERCJpglX7fObP9MXvNPLPetfbM+fp9533fc/aTvGdue+/ZM2fm2WuevfbaIrfS5uUppfN3W8a+lDLy7Cc6A8qp6CSL81NKN87Mfz66OQchIsfso4LJGRgPzbYWc4vliFktOo+OIzmtBj3iDsWSLzM/8H2d6AHwrE5OV9IcI+LwSHlu7AfPOotImT/HscDIFbCfMAB+A2BDUtrjffkThO1dD5+PY0Ts9sWzFu3U5K+pHRMYD9CJBqfM6QScGohjZQ6WK7x0in6IdrtMvCxVMAnbUYA8sCSSLywpHw/+SyndrrjxaxnE6DjgFQDuBeANIgIA2ymlM/fw/CPY+80PkrWY+f25A61bLmACt52BStQthhGDkeWiL7M36Wl/7kLn0ei6HIvNvtRNMyZMTuvJFpGVaRuN3jqlcq3mrLCzfjCB7MajwyPsUIKYqn/QKOp6RMjAeCh0g+VBIV69IrK05wDmDVbx6mfrDpQ7DAGfiFk7tumA4V2y5Nya37rDG/+wF9hLr4znAnjuXp1vLloMljG7xvFDpxZxiyFuBtDpy2r98hBuYJA1FAm+paxuckpG3GmmL9DU53NEyFqvkm+u12FoX1omASbMiMBsHZgQ+vkOnbQR6XuEyUHsvRFwFlFDFkk3Jas1IsKSFds04/+HjR8SSTReZLm5jZLmt/VkRKFBlYiP0JLJ1g65XqoLLaMfEOdfB5RmaDne2Pcj/+bAe1Ci35bJ15jtvofdnKPEG541w7GZS5gipCjso31J51rbtr5z6qIvv85sbS1PWycvSp1XD5aXSpiSBjxEDaJH3JaULTGPGhVTZyVpez6+D5FlfDTXxeWELoMYll5gfGtB6/WoIeK5jHqkvAmoxLwCMLHyQ2M/u9SStoGNmIR5qQGPgKFzEJTG6wjkz3erP3odZnbdK28usZbKiYLoc94pXZs/5T0iiVzYes+EoGw+r43Cx14iNu2RbfQxSizp2ZCnHnhI+lTHmldvW8cdjOsLlDtBbUQ4ex1zyNp+RfV50f0OYzkinO6zrnFAPDS7DZZ2fR1RLeYVQm+8kqYlaGAgY9bYGsqjnYfcwccyhhI768+jOtCLoeQshnRUF40+3T1t2DuHrttybMwHTRMRsp6zRMz2vGjHJBtpqbZ8tBg9qRHx2EZLf3aWk0hv9cjKgzYymm6KlKeuk+vu6drevVdynmIOT0tXLMkcGJ5njm2hZGyX+k5oNdia9izk1qTdBFRiXjE8UrbbbC3rP8yL2ewF0LdaNMfNUMZmHbdpukhcau0tFgPReAM2PJ000hM5SFJJKpmKFeERs3fuaH0KvTbbABoDmhusiDxtDOjI+8Elu3Y65oVq3LwdpWdr3Yu7DfhuhN7/lY97MslceAH9+Tm3Q6nVgtb91jsDtO1Zzh5J87F1BccC2WtUYiZEFrOSMo8YjMaN8yhAJV8xx5jkrZbIZNdmklBdlskZi2XC0TJY85wL69ZVspa5jnP8eu36bvRpTW/vi1c+l7VDxAz4A0G8QTwlmcDWk8uc6/pmJRDdx14xcwYXhZHvnHN6GHVSYky0ajGrcWIlDY+A7b6IiBHsW1dUi3nFYEvYI2j2dQYGucLeQDvAZAtjTw/FSDd1rMH+kJE2+olV2/HLDyyTcunl9KQPlmPYdW1KOog68nifXbdB360O7OWZIvlI3vF0eZVIdFYXm9eSswWTJ0tYfB2RpBG5HyqhagPEkolFNA/gbi1oJV5gkClaDF5EKlt4Lm/c4WfflxbLX52bRMhA1ZhXjoiUWWO2xAwMMZa5M48tZpYw7CdRg06qUCwMMY7q1w4vPROSN6rM8w4A5ncU8nmmZAxeenlKBFGKfhfV0V5jCdbqtPKLrvMML7Yu7N7IhGsD5QPD/8KznD2ytNNR8XJUF8QdglEeRqmB1uecXUGT2W9ntY4sZs+QseQMWm4KKjGvMTwrmsmclyPryTmmJC3OOlr/81Vfbg565KUpbc/FbvPNSW+t4ynMkWhKckib/0HW6pwi/zl1aoiUGVv5XF6+SMu2aSyJN4aQgd2RMiNKa32RW2cfaNuTLGC2vWObikrMa4ToIfMeOmsRW4nDkrUesxZzn2d7yGzlBv5UbjNJW13YnRpqpnXKZU9ZvJGMwj9r0UexMry6eR1qdnSgzeNJHazJe+fRcqN7xJHforpqGd5x7z6V4FnYvO19kUQNmddPwOWwl4WdwZr1Zt7WdCVCnjPSz26vI6qUsUawrbz9x3gPGTAeBVgqW3/MFVxWA4xmOLHYyU9+T84gX9IJ8uDtaPbqOSjpvtayZZTc/UrwOtDmNBqjMvSmY0yS3vocRFNxRY2DXS+5u9m6WFK1M197dddGzAbM120lXHWLY0uYdeUdOmZjYlir2CPlTR2KDVSvjLUDP2xTRKtWMEM7/zivF4lLkWyadiBlG1tB3eW0U3CxwK6f9KmYDSVEpMzbpZlJSjM0axmRh8NuMNfat42b7i/WL69zg1j6yphjJU/l875G7OSwCi/uiKbX6aJ2MA7FqYTM5KzEzGQa3ZoGCEm6BZa05k1BtZjXACUibswPhbQw6YDlASfsucER6xQC4BB5a7CVuTCDLeZKFW49Z5KgNwdfX9fgfNzBNYUpIm2JiKLr9bRXlgZKYVAtOZfq2N/zgDin8gKx7KTXY2UlYGiMrcXcYKxvKxn31rFjJW+jk9I8KYPn+GOyBsbzXLIFbJ/3iJQ3zWquxLxiWFKO/iEeQYs57k075VnhifJYbOXjR1rgUNu9MOra1bYDiXtyhPUvti96Qye1ZOBpmWydLZECnd/zwbVuZ9ZfmuENfLDHpqx7T6PV69Bod4dIw7cEp3Xm+rIc0KcNGrQpYo7Cp059ifD/YU767e1h6Lm1YHU0H/snWylDydnqrPxs27gw3nITyVhRNeY1QukBapx1yw9eXi2z9xHOS33IvcEqqu0pQQuAO2aLqQ9A344HUlg3rpLlHAVw53WPDCxJNc3Ygt9qYu+LPg/oHjR+J6EHS/q7mZW6J+dC2pIlXGqQ+Pxe2d7Xhr2XNp9tKOfG5PC0ZLZYLSnfhuUARdzxx/t5JGt/bVh+B0D5ot+moBLzBqD0T2oxDlxk3u+RMz5MOk2rSyt1qBXeYtwxuPQyc7nGSu7TEKlFPtN9/RwyYOuNy7OSSjTirU+LoTMwgqdJ95Z4u+zfOwWto+eqVsqjJDcVtzjS2L1Zv+2XiebzZkCPXAQ9Qtd6snShZKhEqx15ahFrBxc/o/psaPEeKc/BJpKxolrMa4pSK89EytIE71ewbqdQQj6C5bjOetxiFHK0HWJqAGMLebHoPmM5Cpol0MVi0CY9LdiSiJLTke1xpxOX3zS+x4W18vrjROaRHs3n4rKZUEOrzSFCDT26Q/ujRsyTEPp6NX6nm623R8D2nkxFtLPyhf1qsefdbsdEzNKEjYVhZQzQcg6iYdjee7OJ5Fy9MtYI0QPmjf5TEmZibTD+h7aURrGDjpA1v5KuDa7Px9y6mqeddWTtEPLc1JjUp8qMPrf1fFZf1jzWO4BJakkHL1xjNNXWlHxR0oG5UYoGwET113oowbMcExGyJz2UrPDdznrdlw/fLxmIJYqSZRj9XzRv9J5EBL1J5Fwt5jVCi3GPM1sZC4wfMkUD9LM8KCyZWilDh3PbBz8KjmQbhLD+hvy6DfRudlP55mwrAR9ajAMr8Wd45EcLxA2Ct59H7c0h5SkvE/7SUD25b6yCtFx/b9CP9SO3RBw1bJF1zOWXCJnJWJdMtDaWhQ1sD4zzK1hes2XY81h/ZeuJ4ZW/SajEvAawpKz/FH7o9KH1btwWlVH6BLJ+zrvV7SLYz3FLhGrZlUbKRdvWquzlEMdaZlJW74ASIh1c4c1gElmMtkxPQ57atudRP2C9tkOLcb7G5LH5I9nBg0o6Ni+7v80hvDZY98D112cz6g9p6ThbxttYJudNtZQV1WJeQ+jDZucAbOinYI0ZlM6C95U8MqL6FF/EgIQYW5gfrwKISSQi5X4Qw/b4t0S6DtEykSqsNMJLLrdkPXPZnt7O2x5GurI5X6RPe41EqZ4lMCmrdlz68rFkwus8WfAWBk8LLs+6w3nro/phepTfJpNzJeY1gX2omYwtMfOsJArrEgeMe7QFQwS6BmX9WMHWi34+o2AJ2iHAvNR1j5w84vDiF1si4zQeKc8lQI+UuSFRyzsKSbqbEYy3Bxw/u9QgeoTsuQfqfi2bZx3RLwMdsQcsS2Jw9nteQDaPnoafQb51OyaN9+HDpGut5yljYt2xyiHZx/kR3h/gBy6yAJR0PVjXo7nntHltwKIwb+uvA2XSmiK0SDbQfVYH9XTVqSHZEXopYXv5XKVfVF/F1DVPHfeu0WsEPb9yzwvFTu9l01mL2JsAdc5z5slodt+U0eCRsnfuTSZnz/qPvgiOJarFHMASsFrLKm+wzOEh0uiAuDVsMXQmsV6tpNyfr122vEpDpW0wpDlkw2WyxasatUf+JSuW16PBL54mzlBSZkuc74F1p/NQGiFp68Hp2G86SsflR/KF9d6Yih/S31PEFrA3754dNMLpFF5Ml6gqVtawlz5FWptIzlVjXjMwIQIDKfNn2hQp22MjH2QMLwD7LfOAE9tr3tA6MCbb0CJsh2HcnNb7/PYIxPMtLgZeN8fsuYHdadzeeVUi8aLXTcW6sA3D1OhIRdtO19tKMVEaYHwPm2YY7ON1cu60y19Lmow76vRWsLeElTMiouyfKbPfC7ylDYSul3TlTSRji0rMawj+pyg5s8vcnAdQSZUHn3DZTMILDANOGKz18cAIW0cPOkKwbQcCmEPqapFL4+joJr8lpLmEx+e3lqZav56XQzQSrun/lGFJ2VqstoiSm57Xocjr9isinBIKg7sefxW4X0J5aTvumDTZf9mSrZU/OL99Pu3z7Y0kjLa9/JuEajGvIdhq1iVbCGxFa/o5HXnAWKoAfHLeov3cGFhr2pbJaEBWl1rKiK1mi96CczqseEg2k1FJSrCSh0VElB6sZ4StV1QHu8+d+FQlm7y5WGBphuuoTtY7w9PdOX309dK2XWenyhiAP/s6sPw8aFhPJWjPat4x6xY2n5KUHUF4mJZMzqDlJqMS8xrDknNE0pYHSv/UiJwbDJZQY9JEUsdSPGeDpjWDKlAmP6vDRiS+NHqvoN9qXus+F52X80zNDjIHkQXPGu9SmmaobyT9WA8Yj5Sn5ii0pM9fODZbKWYFa7/WguU0nNbqz9GIVV0yIeuv5L+8yaiB8tcUU4QMjIkZtLQPJvuQKiw5c4cfjwzUl4J1be/F1JdLLSuWPdhaU8t55NIXWLxTXhyRbFHKxx1g1le5bdEHauIOTraMeX69OZJJ1HhEujBLERJIKraM3UgujMh7xFrXo/qZ7chTAxieV5g0kTVt17kjUZeWmFssB93fL1ZztZjXFEqOuj7186CWL7D8ObrbunidQBYaJnRFSpB0AAATl0lEQVQpvyGABvMsZ89q3m0H2lIdHXJmK5MbDvYOmfIZZpQ65EaeI/lcfC26nBqpV6rXaNh0Oyb8Un2mLGzbYJfAOrNnOcPsb81xG9zIGiieZb5fSLlqzBsAaz2XLGbmgoXZ7xEy5ymRrcILK1rK2wKjMKFMJErOc7RZzWd/TO5ReEpd9p/ohg1stDY7ZZZtVLxOSZ7HUOvsWf4eMXqR+DyU5BXezwH2OW/UMRi5PlrytQOYbFwMr1r2mYVJZwnbi43hxcSw2jJbzPsFlZjXHNZS0Hf3MK23GEYDMtkKLUvGpbWqPc2aZQ6bpjXbPMJw6XqIJKK54yysu9nWwvE1zuezRGo7wDzy1nCl9nycn8H1jaQYu87ljZB9IK1O7MEjUbbuta7ecPSS5GHrp7tKlhuniaDEba3m0TWZc1nL2SPlkq68X8i5EvMag61l5Q22WK2ubIdqK0FG8oWSLZflTeETxR32yivB+6xmf9pRWQ7BMSnPcSWLvDDsPo2VrKS2CJ7OqE5Tx+w52StisUA/9RQPjy5JCnbKLC6T41crPF/oUiAmtlSPIMacqHFexDkrd0WDUlrzs6S8Hzv+gNr5tzGwn3ZqjR6mNNZCPQr51SVwbRyOYNwzzw+OnfXEg6cV6349UWrGpDhntFwE27nlhca09eDRhZ6P9Jw6eQRdahzUM6JpuuuPUNKe7TVZ2UZ1bGB58I5Hymrl2glRPVhrlYmV5Q/2p4/6IhTeQBJPV7a//YKqMW8AWCbgB5AJujQaEHCs0UJaS/Ds58wjD20joMc0z6iMdllLjT7X1WL1XNhK0kA0gCLyapgql1HyoJjyDGFN2qub16lpyyp5V0yhb/f0PKZhtGmZjHkkn8JrvD0PCl6HWS5p9Bh/CTIBe/LFfghUNIVKzBsA/ifZDj8mZc96UaLdxtidzfql8vTwrmcFnV8wvKw2FrTKKS1lbDB+uXkWE2u9LhbZcjUkzp2GO4g7rbTMqIPLg5av5F5yc+N9kc+0QrVoJWcm2R3zT/U6N0sNGdfTu5ejSHF6LXAa1Vw2kykToW3US2E4eaaSIxiXqWms1MZlNlQGW8yRzzLM+n5CJeYNgj7YpU85a5nwaD7Qcsds67qGB+U0Ni1/inovLjcEW+hItmnHUsWSCx2Rizfhq+eZ4ZVTsi7n6NK2UZjC0VrhwNAQqGeIaucs57BVXZphXMH3Jo1ayHw8p/EmlOUBHZwtCkLExzxr+YjZF0FDe3IZus0j/ParpmxRpYwNApNyY/Z7BM15mFi9T8kINibCbusKm7/trGUloUgvBcZ6L1D+pN8NOZfyW6t5qhxLwLZzs8F4ZhAvf3/u/MfKGxZzZubWuosh5rn/d0UUW9mLdcF5vOfQG7rPeTgtW8uR8bFfSVlRiXkDYR9Wb4g2689WSgDt2+3L6oFfOO70sRY2W8+2PmpN9x4LGJOZ1WJ13R73trea+Fo9D46dfFPnaM+Rht0fM+Xrz07jxJ1zNtiT17nnXTOfO7Ka1VpWTw2eb9DqxBYlslBCTmbdknZ0S+1zzCP7PClD8+xHgq5eGRsGfQj1XbMeGlau4EEmC/jkrNYMd+pF1g2fX+HFUNCX05bj9cb3+VtA2rGModY1MIzU41m351jGms4j54jMueHwPDhKiEhTyfXI9ngQSCTpHFqUr69EzlZr1kbO1r8fdk4/G4TIWr4ebBzmyLfZmyhYl0cQD7lmcrbW835FtZg3EGwxeO5zlj+YdIXyKgmrx4VatbwdnZ/Lsg0CMA5wZAmaJRU9T4NgCLTDDHa0noX1c+b1ktVmO/O8yHY8oMRKF7xksCW+sz3siyxh69eseaNOTu982unpDc9Wv/HeaseyxhsN+LDgIERMnDY993PYvJqereXSoBJQvv2IqjFvIJTQdJ29NBTetuZTazaaWZuJVAlf91uUrGpbl2gAQvhpO2EtRtZr05CUEpAok7PVse2oRHu+UcwQR8rwOuosOdqfvWb1WplqgLwy9NxMuqP73eZrp2NKeDbyG6/b4dIw25HUACw33Nzg83kjKSPyXd7PqMS8gbD/NKtHeTqzPsy241Dz79BxlT22sEzQbElbnTp6YbhBAGbM6TbjqZzUVxfDdgRPq/bib7AO7On1XCdvRN3czknXy6JwruI54Vuu/PWiEsQ2rVtSRWE/l2GJ3coZ/IXFZap1XvJXPijeGIpqMW8w+B/HxGw1Zx4YYmGtY9WAWwwvL3fccfnsI22H7XpDb7n8Ug/9HF01wki+yK3MXA8NG7i+5JrWoOs0s9ZsRMh23YM3oEaX3jFPrrBkHGm9+rxweiYDlqGm3N00rQbJnzNasL8ODBKGtYYjn+WDgkrM+wTWmvC2I9iQni0tdV/UcajrgumANp71VwoTGpY106JmTXhOvmh+vcjS7T/NmzjuRJ82aCSiIdxLA2ua5XqMiN+UO4ccLRHvFix5eOVG8CLTlVzjvOV+RvXK2HB4LwR3BvKnYemGs8xgyxQMcwFago7yKNgTRPnHemawld62gyeGJdX+nPlk0ezcW83gdte0g2WrftORT7FemzcxKS95vTQs2+4vkW0pvgafy6vLSL/G8BXEl+jJV1Hc46PxW+eyPS3aNvZ6Hh0dGA0iOQhDryOs6poLyt/xgYicJSI7InIe7XuxiFwtIs/a6/ocK0Sff94QVvuQ23CfwLizTl80fYFUi+TOoqgH3fNrbYN9icrdbjvPBXUp22mH33bev5Ndzbbpp77BGt5TZ7XW/ZqXj3Eazl8icJYRNK91ffPgDbm2+21UOz7P4cPj+h7Z9gfo2PjZoPuscsO2uece+dlt7sDb7cvLz+cRWrIr3Pew7LNsn9uDQtBeZL3od6yxpxaziGwBeDWAv6V9JwI4C8AjALwPwHv2sk7HGmz1qNUcxRfgF8u6saksofvV0rGWVOROx52FOvN2Q+lZq7YSytIwbiyTgGqpFm3+06AjrUMLLM03CPgkqqToxb6Y8hNmWA8PXtr8npXsndtrJLxAR3pT7P/EdsSxxeqhJIE0Zt02rnr+yEJn2YIt5MPO7yBby8DqrnuvpYxfQ0e+Z9E+fYaPVmJbGyh56jowyBfWetZ9XiCjLVpaF6epiVcVKk0oIXOsDkvGTP58DVyGfULnkEZqB3K2JKhWOJPdVk7nRbXryw80YuvL7K1HZUXkbKWKbdMY9Y1WQxO6AkDb3VPbkcdkzFID33OYdcB/MViOKMHrq7Ck7A0iOajucRarut49kzJE5L4AngbgTbw/pfRdANcBuAobbi0D/oM8x0mfCVjd43g2FA9sKR0xP7We2JLikV2qgYKOeddgP+dKGFloObGSs5Uetrc7KWS7He7HkUDaWOrsm/HUcr4peYPL9WSOvgyM750Wqdr5ViborUX3v+sH7GD4H7EMdRvGkoL37Ez1H4DKt5q2NxNOFGPZezZbLJPzQYLnPhj9piAi54rIv4jIV0TkZVPp99Jifg2Al6aUdkTGH3oppVcCeOVUAWecccZxqtqxhcoQSrKH8u8OAE4AcMe8/w4YCFhMPl33IogpomNahv5zeUi4Hl9QGj2Xdx1blF73eS9oX3Ze4emqRJzRcykvMfar3sp5Flt5GDNVbMm32dyQRvyBII0MJGvrZ6UJe47tHeC227qlasKKRa5vszWQcq+v7wwNoWrKnsavp+f/gZUgPFmjoWORq1t/HXmp6biBVqtZLWavvtGglnXG1VdffbvLOFZ+zFnCfT2AJwK4GcDnROSDKaUvRXmOKzGLyAsAPC9v3h3AuzMp3xvAT4rIdkrp/YX8fwrg6bp9LG52RUXFwYCI3Eqbl6eUzt9tGceoMXoEgK+klL6a6/VuAE8BEBKzpLT30q6IXArgipTSX+z5yWdARG5NKd1l1fU41tiP17UfrwnYn9e1adckIleiMyLn4AR0Ti2Kt6SU3pLLOQ/AuSml5+bt8wGcnVJ6YVRY9WOuqKiocJBSOvcYFeUphUWLeCXEnFK6YBXnraioqFgBbgZwP9o+BcB/lDLs+QCTDcHlq67AccJ+vK79eE3A/ryu/XhNc/A5AD8oIvcXkTsAeDaAD5YyVGLOEJEtEflnEbkipXS+iDxMRD4lIpeJlII+ridE5H4i8lERuUFErheRF+Xruo+IfEREPpAH92wUrNvRJv2vROQEEfmsiFyb/ycX5f2XishNInJN/p2er+vuIvJXlP5CKmstRsvu9prysXPyvutF5ONU1rPzNf3Gqq7neCCltA3ghegG1t0A4L0ppeunMtVf1wH6mwDeha5TEgDeBuAkdINizl11/Y7iek4GcEZevyuAGwE8FMCrADwMwM8AeP6q67nLa9oC8G8AHoDO2/DafE0b8b9CpzWemNcPAfgMgEcCuBTAeU76lwN4dV4/CcB38nWfmJ/VBYAPbNg13QOdN8Kpefv76dj78//43VrmQf2trXWxlxCRUwD8FIC30m4evBVNIrK2SCndklK6Oq9/F11LfV8Msfk38bp6t6OU0mF0L/BTsCH/q9Thf/KmureXOoESgLtK52N6Ijpi5lH4Kx8texTX9Bx0rmvfyPm/Scf4utb2/7gXqMTc4TUAXoKx2+JrAfw1gEcB+NAqKnWsICKnAfhRdNbMJQDeDOD5AP5sdbU6KtwXwL/T9s1538b8r7Jkdg2AbwL4cErpM/nQ74vIF0TkYhG5Y953CYAfQtdRdB2AF6WU2rRmo2V3eU0PAnBPEfmYiHxeRH6Riroc3TVdla/x4GLVJvuqfwB+GsAb8vo5yFLGfvmhs7Q+D+Dpq67LMbiWZwJ4K22fD+B1q67XUV7LPQB8FMAPo5OdBN2g0MsAvCKnOQ/AxfnYAwHcBOBuq6777bymSwB8GsBd0PkI/yuAB6267uv2qxYz8BgAPysiX0P3afw4Edk0S9KFiBxCFzTqnSml/dAjvmu3o3VFSum/AXwMnSZ+S+pwG4B3oJNsAOBCdJ/9KaX0FXTE/JCVVHgGZl7TzQCuTCndmlL6NoBPAHj4Siq8xjjwxJxS+u2U0ikppdPQubF8JKX0Cyuu1u1G1iXfBuCGlNIfrbo+xwi7djtaJ4jISSJyj7x+JwBPAPBlETk57xMATwXwxZzlGwAen4/9AIAHA/jqXte7hKO4pg8A+HERWYjInQGcja7/o4JQR/7tXzwG3af+dVn/A4CXp5T+ZoV1ul1IKW2LiLodbQF4e5pyO1ovnAzgshzUpkHnNnVFdl88Cd2n/zXo9H8A+D0Al4rIdfnYS7OVuU7Y1TWllG7IQ52/gK5P560ppS8GZR9YrCRWRkVFRUVFjAMvZVRUVFSsGyoxV1RUVKwZKjFXVFRUrBkqMVdUVFSsGSoxV1RUVKwZKjFXVFRUrBkqMVcA6AYwiMi7ROSrOYbBp0TkaRN5ThORo/JBFZELROQ+tP1WEXnozLzniMgVR3PeuRCRf8rL00TkOUeR/wIRueTY16ziIKASc4WOzno/gE+klB6QUvoxdKPqTjmOp70AQE/MKaXnpsKswXuNlNKj8+pp6CKiVVTsGSoxVwDA4wAcTim9SXeklL6eUnod0FuNn8xBzK8WkUfbAkppROQlInJdDqb+KukmpzwTwDtzwPQ75WhjZ+b05+YyrhWRv597ESLyeOkmO7hORN6uEc1E5GsiclEu8zoReUjef5KIfDjvf7OIfF1E7p2PaSjLV6EbQnyNdMHpR5awiFwhIufk9QtF5MYc/P0xlOYkEXmfiHwu//pjFRUeKjFXAF3g/KsLx78J4IkppTMAPAvAH89NIyJPRhcr4eyU0sMB/EHqZke/CsDPp5ROTyn9nxaSh/H+CYBn5PTPnHMBInICuuDsz0op/Qi6cAO/Skm+nev2RgC/lff9DrrYKGcA+EsApzpFvwzAJ3M9Ly6c/2QAF6Ej5CeiC+CveC2Ai1NKZwF4BsZxvysqllBjZVQsQUReD+Cx6Kzos9AFP79ERE4HsIMupq5FlOYJAN6RUvpfAEgpfWfi9I9EJ6ncNDO94sEAbkop3Zi3LwPwAnSxtoFhvrnPA3h6Xn8sgKfl81wpIv8181wezgbwsZTStwBARN6D8T14aKcYAQDuJiJ3TQc95nBFiErMFQBwPTpLDgCQUnpB/qS/Ku96MYD/RBeesQHwPaeMKI1gdzNt7DY95yvhtrzcwfDcH80sGdsYf2meQOtRvRsAj+Ivg4qKEqqUUQEAHwFwgojwp/+daf3uAG5JKbXoItZtOWVEaT4E4JdziEeIyPfl/d9FNxehxacA/ISI3N+kn8KXAZwmIg/M2+cD+HghPQD8A4Cfy+d5EoB7OmlsPb8G4HQRaUTkfhjiDH8GwDkici/p4mCzBPMhdJNxIp/r9FlXVHFgUYm5AqkLMfhUdIR4k4h8Fp0U8NKc5A0AfklEPo3u8/xWpxg3TUrpSnQxk6/K4UdV370UwJu084/q8i0AvwLgchG5FvHUSY8XkZv1h27qrAsB/HkOk9kCeFOQV3ERgCeJyNUAngzgFnREzPgCgO3cEfliAP+ILmD9dQD+EFmbTyndAuB30TUsf4exZv/rAM6UbpqlL2EI61lR4aKG/aw4sMheGzs5zvOjALwxpVSt2YqVo2rMFQcZpwJ4r4g0AA4DeN6K61NRAaBazBUVFRVrh6oxV1RUVKwZKjFXVFRUrBkqMVdUVFSsGSoxV1RUVKwZKjFXVFRUrBkqMVdUVFSsGf4flp35SCeQGY4AAAAASUVORK5CYII=\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"background = maps[\"background\"].sum_over_axes()\n",
"background.smooth(width=0.1 * u.deg).plot(\n",
" stretch=\"sqrt\", add_cbar=True, vmax=6\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also compute an excess image just with a few lines of code:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"excess = Map.from_geom(geom.to_image())\n",
"excess.data = counts.data - background.data\n",
"excess.smooth(5).plot(stretch=\"sqrt\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Prepare IRFs\n",
"\n",
"To estimate the mean PSF across all observations at a given source position `src_pos`, we use the `obs_list.make_mean_psf()` method:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# mean PSF\n",
"src_pos = SkyCoord(0, 0, unit=\"deg\", frame=\"galactic\")\n",
"table_psf = obs_list.make_mean_psf(src_pos)\n",
"\n",
"# PSF kernel used for the model convolution\n",
"psf_kernel = PSFKernel.from_table_psf(table_psf, geom, max_radius=\"0.3 deg\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To estimate the mean energy dispersion across all observations at a given source position `src_pos`, we use the `obs_list.make_mean_edisp()` method:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# define energy grid\n",
"energy = energy_axis.edges * energy_axis.unit\n",
"\n",
"# mean edisp\n",
"edisp = obs_list.make_mean_edisp(\n",
" position=src_pos, e_true=energy, e_reco=energy\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Save maps and IRFs to disk\n",
"\n",
"It is common to run the preparation step independent of the likelihood fit, because often the preparation of maps, PSF and energy dispersion is slow if you have a lot of data. We first create a folder:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"path = Path(\"analysis_3d\")\n",
"path.mkdir(exist_ok=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the write the maps and IRFs to disk by calling the dedicated `.write()` methods:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# write maps\n",
"maps[\"counts\"].write(str(path / \"counts.fits\"), overwrite=True)\n",
"maps[\"background\"].write(str(path / \"background.fits\"), overwrite=True)\n",
"maps[\"exposure\"].write(str(path / \"exposure.fits\"), overwrite=True)\n",
"\n",
"# write IRFs\n",
"psf_kernel.write(str(path / \"psf.fits\"), overwrite=True)\n",
"edisp.write(str(path / \"edisp.fits\"), overwrite=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Likelihood fit\n",
"\n",
"### Reading maps and IRFs\n",
"As first step we read in the maps and IRFs that we have saved to disk again:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# read maps\n",
"maps = {\n",
" \"counts\": Map.read(str(path / \"counts.fits\")),\n",
" \"background\": Map.read(str(path / \"background.fits\")),\n",
" \"exposure\": Map.read(str(path / \"exposure.fits\")),\n",
"}\n",
"\n",
"# read IRFs\n",
"psf_kernel = PSFKernel.read(str(path / \"psf.fits\"))\n",
"edisp = EnergyDispersion.read(str(path / \"edisp.fits\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's cut out only part of the maps, so that we the fitting step does not take so long:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmaps = {\n",
" name: m.cutout(SkyCoord(0, 0, unit=\"deg\", frame=\"galactic\"), 2 * u.deg)\n",
" for name, m in maps.items()\n",
"}\n",
"cmaps[\"counts\"].sum_over_axes().plot(stretch=\"sqrt\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Fit mask\n",
"\n",
"To select a certain spatial region and/or energy range for the fit we can create a fit mask:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mask = Map.from_geom(cmaps[\"counts\"].geom)\n",
"\n",
"region = CircleSkyRegion(center=src_pos, radius=0.6 * u.deg)\n",
"mask.data = mask.geom.region_mask([region])\n",
"\n",
"mask.get_image_by_idx((0,)).plot();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In addition we also exclude the range below 0.3 TeV for the fit:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"coords = mask.geom.get_coord()\n",
"mask.data &= coords[\"energy\"] > 0.3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Model fit\n",
"\n",
"No we are ready for the actual likelihood fit. We first define the model as a combination of a point source with a powerlaw:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"spatial_model = SkyPointSource(lon_0=\"0.01 deg\", lat_0=\"0.01 deg\")\n",
"spectral_model = PowerLaw(\n",
" index=2.2, amplitude=\"3e-12 cm-2 s-1 TeV-1\", reference=\"1 TeV\"\n",
")\n",
"model = SkyModel(spatial_model=spatial_model, spectral_model=spectral_model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we set up the `MapFit` object by passing the prepared maps, IRFs as well as the model:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"fit = MapFit(\n",
" model=model,\n",
" counts=cmaps[\"counts\"],\n",
" exposure=cmaps[\"exposure\"],\n",
" background=cmaps[\"background\"],\n",
" mask=mask,\n",
" psf=psf_kernel,\n",
" edisp=edisp,\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"No we run the model fit:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"