{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# MCMC sampling using the emcee package\n",
"\n",
"## Introduction\n",
"\n",
"The goal of Markov Chain Monte Carlo (MCMC) algorithms is to approximate the posterior distribution of your model parameters by random sampling in a probabilistic space. For most readers this sentence was probably not very helpful so here we'll start straight with and example but you should read the more detailed mathematical approaches of the method [here](https://www.pas.rochester.edu/~sybenzvi/courses/phy403/2015s/p403_17_mcmc.pdf) and [here](https://github.com/jakevdp/BayesianAstronomy/blob/master/03-Bayesian-Modeling-With-MCMC.ipynb).\n",
"\n",
"### How does it work ?\n",
"\n",
"The idea is that we use a number of walkers that will sample the posterior distribution (i.e. sample the Likelihood profile).\n",
"\n",
"The goal is to produce a \"chain\", i.e. a list of $\\theta$ values, where each $\\theta$ is a vector of parameters for your model. \n",
"If you start far away from the truth value, the chain will take some time to converge until it reaches a stationary state. Once it has reached this stage, each successive elements of the chain are samples of the target posterior distribution. \n",
"This means that, once we have obtained the chain of samples, we have everything we need. We can compute the distribution of each parameter by simply approximating it with the histogram of the samples projected into the parameter space. This will provide the errors and correlations between parameters.\n",
"\n",
"\n",
"Now let's try to put a picture on the ideas described above. With this notebook, we have simulated and carried out a MCMC analysis for a source with the following parameters: \n",
"$Index=2.0$, $Norm=5\\times10^{-12}$ cm$^{-2}$ s$^{-1}$ TeV$^{-1}$, $Lambda =(1/Ecut) = 0.02$ TeV$^{-1}$ (50 TeV) for 20 hours.\n",
"\n",
"The results that you can get from a MCMC analysis will look like this :\n",
"\n",
" \n",
"\n",
"On the first two top panels, we show the pseudo-random walk of one walker from an offset starting value to see it evolve to a better solution.\n",
"In the bottom right panel, we show the trace of each 16 walkers for 500 runs (the chain described previsouly). For the first 100 runs, the parameter evolve towards a solution (can be viewed as a fitting step). Then they explore the local minimum for 400 runs which will be used to estimate the parameters correlations and errors.\n",
"The choice of the Nburn value (when walkers have reached a stationary stage) can be done by eye but you can also look at the autocorrelation time.\n",
"\n",
"### Why should I use it ?\n",
"\n",
"When it comes to evaluate errors and investigate parameter correlation, one typically estimate the Likelihood in a gridded search (2D Likelihood profiles). Each point of the grid implies a new model fitting. If we use 10 steps for each parameters, we will need to carry out 100 fitting procedures. \n",
"\n",
"Now let's say that I have a model with $N$ parameters, we need to carry out that gridded analysis $N*(N-1)$ times. \n",
"So for 5 free parameters you need 20 gridded search, resulting in 2000 individual fit. \n",
"Clearly this strategy doesn't scale well to high-dimensional models.\n",
"\n",
"Just for fun: if each fit procedure takes 10s, we're talking about 5h of computing time to estimate the correlation plots. \n",
"\n",
"There are many MCMC packages in the python ecosystem but here we will focus on [emcee](https://emcee.readthedocs.io), a lightweight Python package. A description is provided here : [Foreman-Mackey, Hogg, Lang & Goodman (2012)](https://arxiv.org/abs/1202.3665)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:47.005415Z",
"iopub.status.busy": "2021-01-29T12:57:47.004770Z",
"iopub.status.idle": "2021-01-29T12:57:47.290062Z",
"shell.execute_reply": "2021-01-29T12:57:47.289399Z"
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import warnings\n",
"\n",
"warnings.filterwarnings(\"ignore\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:47.296334Z",
"iopub.status.busy": "2021-01-29T12:57:47.295724Z",
"iopub.status.idle": "2021-01-29T12:57:48.298632Z",
"shell.execute_reply": "2021-01-29T12:57:48.298169Z"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import astropy.units as u\n",
"from astropy.coordinates import SkyCoord\n",
"from gammapy.irf import load_cta_irfs\n",
"from gammapy.maps import WcsGeom, MapAxis\n",
"from gammapy.modeling.models import (\n",
" ExpCutoffPowerLawSpectralModel,\n",
" GaussianSpatialModel,\n",
" SkyModel,\n",
" Models,\n",
" FoVBackgroundModel,\n",
")\n",
"from gammapy.datasets import MapDataset\n",
"from gammapy.makers import MapDatasetMaker\n",
"from gammapy.data import Observation\n",
"from gammapy.modeling.sampling import (\n",
" run_mcmc,\n",
" par_to_model,\n",
" plot_corner,\n",
" plot_trace,\n",
")\n",
"from gammapy.modeling import Fit"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:48.303713Z",
"iopub.status.busy": "2021-01-29T12:57:48.302450Z",
"iopub.status.idle": "2021-01-29T12:57:48.304208Z",
"shell.execute_reply": "2021-01-29T12:57:48.304699Z"
}
},
"outputs": [],
"source": [
"import logging\n",
"\n",
"logging.basicConfig(level=logging.INFO)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate an observation\n",
"\n",
"Here we will start by simulating an observation using the `simulate_dataset` method."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:48.309341Z",
"iopub.status.busy": "2021-01-29T12:57:48.308731Z",
"iopub.status.idle": "2021-01-29T12:57:48.392070Z",
"shell.execute_reply": "2021-01-29T12:57:48.391269Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:gammapy.irf.background:Invalid unit found in background table! Assuming (s-1 MeV-1 sr-1)\n"
]
}
],
"source": [
"irfs = load_cta_irfs(\n",
" \"$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits\"\n",
")\n",
"\n",
"observation = Observation.create(\n",
" pointing=SkyCoord(0 * u.deg, 0 * u.deg, frame=\"galactic\"),\n",
" livetime=20 * u.h,\n",
" irfs=irfs,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:48.402319Z",
"iopub.status.busy": "2021-01-29T12:57:48.399754Z",
"iopub.status.idle": "2021-01-29T12:57:48.965520Z",
"shell.execute_reply": "2021-01-29T12:57:48.965034Z"
}
},
"outputs": [],
"source": [
"# Define map geometry\n",
"axis = MapAxis.from_edges(\n",
" np.logspace(-1, 2, 15), unit=\"TeV\", name=\"energy\", interp=\"log\"\n",
")\n",
"\n",
"geom = WcsGeom.create(\n",
" skydir=(0, 0), binsz=0.05, width=(2, 2), frame=\"galactic\", axes=[axis]\n",
")\n",
"\n",
"empty_dataset = MapDataset.create(geom=geom, name=\"dataset-mcmc\")\n",
"maker = MapDatasetMaker(selection=[\"background\", \"edisp\", \"psf\", \"exposure\"])\n",
"dataset = maker.run(empty_dataset, observation)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:48.984479Z",
"iopub.status.busy": "2021-01-29T12:57:48.978257Z",
"iopub.status.idle": "2021-01-29T12:57:48.987775Z",
"shell.execute_reply": "2021-01-29T12:57:48.987325Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Models\n",
"\n",
"Component 0: SkyModel\n",
"\n",
" Name : source\n",
" Datasets names : None\n",
" Spectral model type : ExpCutoffPowerLawSpectralModel\n",
" Spatial model type : GaussianSpatialModel\n",
" Temporal model type : \n",
" Parameters:\n",
" index : 2.000 \n",
" amplitude : 3.00e-12 1 / (cm2 s TeV)\n",
" reference (frozen) : 1.000 TeV \n",
" lambda_ : 0.050 1 / TeV \n",
" alpha (frozen) : 1.000 \n",
" lon_0 : 0.000 deg \n",
" lat_0 : 0.000 deg \n",
" sigma : 0.200 deg \n",
" e (frozen) : 0.000 \n",
" phi (frozen) : 0.000 deg \n",
"\n",
"Component 1: FoVBackgroundModel\n",
"\n",
" Name : dataset-mcmc-bkg\n",
" Datasets names : ['dataset-mcmc']\n",
" Spectral model type : PowerLawNormSpectralModel\n",
" Parameters:\n",
" norm : 1.000 \n",
" tilt (frozen) : 0.000 \n",
" reference (frozen) : 1.000 TeV \n",
"\n",
"\n"
]
}
],
"source": [
"# Define sky model to simulate the data\n",
"spatial_model = GaussianSpatialModel(\n",
" lon_0=\"0 deg\", lat_0=\"0 deg\", sigma=\"0.2 deg\", frame=\"galactic\"\n",
")\n",
"\n",
"spectral_model = ExpCutoffPowerLawSpectralModel(\n",
" index=2,\n",
" amplitude=\"3e-12 cm-2 s-1 TeV-1\",\n",
" reference=\"1 TeV\",\n",
" lambda_=\"0.05 TeV-1\",\n",
")\n",
"\n",
"sky_model_simu = SkyModel(\n",
" spatial_model=spatial_model, spectral_model=spectral_model, name=\"source\"\n",
")\n",
"\n",
"bkg_model = FoVBackgroundModel(dataset_name=\"dataset-mcmc\")\n",
"models = Models([sky_model_simu, bkg_model])\n",
"print(models)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:48.993626Z",
"iopub.status.busy": "2021-01-29T12:57:48.992820Z",
"iopub.status.idle": "2021-01-29T12:57:49.105859Z",
"shell.execute_reply": "2021-01-29T12:57:49.105063Z"
}
},
"outputs": [],
"source": [
"dataset.models = models\n",
"dataset.fake()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:49.110623Z",
"iopub.status.busy": "2021-01-29T12:57:49.109513Z",
"iopub.status.idle": "2021-01-29T12:57:49.722134Z",
"shell.execute_reply": "2021-01-29T12:57:49.721648Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"(,\n",
" ,\n",
" )"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"dataset.counts.sum_over_axes().plot(add_cbar=True);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:49.725615Z",
"iopub.status.busy": "2021-01-29T12:57:49.725093Z",
"iopub.status.idle": "2021-01-29T12:57:49.728500Z",
"shell.execute_reply": "2021-01-29T12:57:49.727932Z"
}
},
"outputs": [],
"source": [
"# If you want to fit the data for comparison with MCMC later\n",
"# fit = Fit(dataset)\n",
"# result = fit.run(optimize_opts={\"print_level\": 1})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimate parameter correlations with MCMC\n",
"\n",
"Now let's analyse the simulated data.\n",
"Here we just fit it again with the same model we had before as a starting point.\n",
"The data that would be needed are the following: \n",
"- counts cube, psf cube, exposure cube and background model\n",
"\n",
"Luckily all those maps are already in the Dataset object.\n",
"\n",
"We will need to define a Likelihood function and define priors on parameters. \n",
"Here we will assume a uniform prior reading the min, max parameters from the sky model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Define priors\n",
"\n",
"This steps is a bit manual for the moment until we find a better API to define priors. \n",
"Note the you **need** to define priors for each parameter otherwise your walkers can explore uncharted territories (e.g. negative norms)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:49.731966Z",
"iopub.status.busy": "2021-01-29T12:57:49.731467Z",
"iopub.status.idle": "2021-01-29T12:57:49.749902Z",
"shell.execute_reply": "2021-01-29T12:57:49.749476Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MapDataset\n",
"----------\n",
"\n",
" Name : dataset-mcmc \n",
"\n",
" Total counts : 248102 \n",
" Total background counts : 238923.09\n",
" Total excess counts : 9178.91\n",
"\n",
" Predicted counts : 248096.18\n",
" Predicted background counts : 238923.09\n",
" Predicted excess counts : 9173.09\n",
"\n",
" Exposure min : 1.14e+10 m2 s\n",
" Exposure max : 3.45e+11 m2 s\n",
"\n",
" Number of total bins : 22400 \n",
" Number of fit bins : 22400 \n",
"\n",
" Fit statistic type : cash\n",
" Fit statistic value (-2 log(L)) : -1296274.80\n",
"\n",
" Number of models : 2 \n",
" Number of parameters : 13\n",
" Number of free parameters : 7\n",
"\n",
" Component 0: SkyModel\n",
" \n",
" Name : source\n",
" Datasets names : None\n",
" Spectral model type : ExpCutoffPowerLawSpectralModel\n",
" Spatial model type : GaussianSpatialModel\n",
" Temporal model type : \n",
" Parameters:\n",
" index : 2.000 \n",
" amplitude : 3.00e-12 1 / (cm2 s TeV)\n",
" reference (frozen) : 1.000 TeV \n",
" lambda_ : 0.050 1 / TeV \n",
" alpha (frozen) : 1.000 \n",
" lon_0 : 0.000 deg \n",
" lat_0 : 0.000 deg \n",
" sigma : 0.200 deg \n",
" e (frozen) : 0.000 \n",
" phi (frozen) : 0.000 deg \n",
" \n",
" Component 1: FoVBackgroundModel\n",
" \n",
" Name : dataset-mcmc-bkg\n",
" Datasets names : ['dataset-mcmc']\n",
" Spectral model type : PowerLawNormSpectralModel\n",
" Parameters:\n",
" norm : 1.000 \n",
" tilt (frozen) : 0.000 \n",
" reference (frozen) : 1.000 TeV \n",
" \n",
" \n"
]
}
],
"source": [
"print(dataset)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:49.757714Z",
"iopub.status.busy": "2021-01-29T12:57:49.756987Z",
"iopub.status.idle": "2021-01-29T12:57:49.769824Z",
"shell.execute_reply": "2021-01-29T12:57:49.769403Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"DatasetModels\n",
"\n",
"Component 0: SkyModel\n",
"\n",
" Name : source\n",
" Datasets names : None\n",
" Spectral model type : ExpCutoffPowerLawSpectralModel\n",
" Spatial model type : GaussianSpatialModel\n",
" Temporal model type : \n",
" Parameters:\n",
" index : 2.000 \n",
" amplitude : 3.20e-12 1 / (cm2 s TeV)\n",
" reference (frozen) : 1.000 TeV \n",
" lambda_ : 0.050 1 / TeV \n",
" alpha (frozen) : 1.000 \n",
" lon_0 (frozen) : 0.000 deg \n",
" lat_0 (frozen) : 0.000 deg \n",
" sigma (frozen) : 0.200 deg \n",
" e (frozen) : 0.000 \n",
" phi (frozen) : 0.000 deg \n",
"\n",
"Component 1: FoVBackgroundModel\n",
"\n",
" Name : dataset-mcmc-bkg\n",
" Datasets names : ['dataset-mcmc']\n",
" Spectral model type : PowerLawNormSpectralModel\n",
" Parameters:\n",
" norm (frozen) : 1.000 \n",
" tilt (frozen) : 0.000 \n",
" reference (frozen) : 1.000 TeV \n",
"\n",
"\n",
"stat = -1296269.9292261866\n"
]
}
],
"source": [
"# Define the free parameters and min, max values\n",
"parameters = dataset.models.parameters\n",
"\n",
"parameters[\"sigma\"].frozen = True\n",
"parameters[\"lon_0\"].frozen = True\n",
"parameters[\"lat_0\"].frozen = True\n",
"parameters[\"amplitude\"].frozen = False\n",
"parameters[\"index\"].frozen = False\n",
"parameters[\"lambda_\"].frozen = False\n",
"\n",
"\n",
"parameters[\"norm\"].frozen = True\n",
"parameters[\"tilt\"].frozen = True\n",
"\n",
"parameters[\"norm\"].min = 0.5\n",
"parameters[\"norm\"].max = 2\n",
"\n",
"parameters[\"index\"].min = 1\n",
"parameters[\"index\"].max = 5\n",
"parameters[\"lambda_\"].min = 1e-3\n",
"parameters[\"lambda_\"].max = 1\n",
"\n",
"parameters[\"amplitude\"].min = 0.01 * parameters[\"amplitude\"].value\n",
"parameters[\"amplitude\"].max = 100 * parameters[\"amplitude\"].value\n",
"\n",
"parameters[\"sigma\"].min = 0.05\n",
"parameters[\"sigma\"].max = 1\n",
"\n",
"# Setting amplitude init values a bit offset to see evolution\n",
"# Here starting close to the real value\n",
"parameters[\"index\"].value = 2.0\n",
"parameters[\"amplitude\"].value = 3.2e-12\n",
"parameters[\"lambda_\"].value = 0.05\n",
"\n",
"print(dataset.models)\n",
"print(\"stat =\", dataset.stat_sum())"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:49.773906Z",
"iopub.status.busy": "2021-01-29T12:57:49.773410Z",
"iopub.status.idle": "2021-01-29T12:57:57.839428Z",
"shell.execute_reply": "2021-01-29T12:57:57.840016Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"INFO:gammapy.modeling.sampling:Free parameters: ['index', 'amplitude', 'lambda_']\n",
"INFO:gammapy.modeling.sampling:Starting MCMC sampling: nwalkers=6, nrun=150\n",
"INFO:gammapy.modeling.sampling: 0%\n",
"INFO:gammapy.modeling.sampling: 50%\n",
"INFO:gammapy.modeling.sampling:100% => sampling completed\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 8.06 s, sys: 1.74 ms, total: 8.07 s\n",
"Wall time: 8.06 s\n"
]
}
],
"source": [
"%%time\n",
"# Now let's define a function to init parameters and run the MCMC with emcee\n",
"# Depending on your number of walkers, Nrun and dimensionality, this can take a while (> minutes)\n",
"sampler = run_mcmc(dataset, nwalkers=6, nrun=150) # to speedup the notebook\n",
"# sampler=run_mcmc(dataset,nwalkers=12,nrun=1000) # more accurate contours"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the results\n",
"\n",
"The MCMC will return a sampler object containing the trace of all walkers. \n",
"The most important part is the chain attribute which is an array of shape: \n",
"_(nwalkers, nrun, nfreeparam)_\n",
"\n",
"The chain is then used to plot the trace of the walkers and estimate the burnin period (the time for the walkers to reach a stationary stage)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:57.859509Z",
"iopub.status.busy": "2021-01-29T12:57:57.854039Z",
"iopub.status.idle": "2021-01-29T12:57:58.120308Z",
"shell.execute_reply": "2021-01-29T12:57:58.119483Z"
},
"scrolled": true
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_trace(sampler, dataset)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:58.129702Z",
"iopub.status.busy": "2021-01-29T12:57:58.123692Z",
"iopub.status.idle": "2021-01-29T12:57:58.939935Z",
"shell.execute_reply": "2021-01-29T12:57:58.939479Z"
},
"tags": [
"nbsphinx-thumbnail"
]
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_corner(sampler, dataset, nburn=50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the model dispersion\n",
"\n",
"Using the samples from the chain after the burn period, we can plot the different models compared to the truth model. To do this we need to the spectral models for each parameter state in the sample."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:57:58.957354Z",
"iopub.status.busy": "2021-01-29T12:57:58.955789Z",
"iopub.status.idle": "2021-01-29T12:58:01.862792Z",
"shell.execute_reply": "2021-01-29T12:58:01.862261Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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9CuEiM0DBW8FbRETmoUqlQqFQYOerr7Lva19j7Z49rH3rLVYcPoxjLaV0mj2XXsqeyy7jrXXrqJ2jdeH111/PtddeS09PD/F4HDPJDYBEZPIUvBW8RURkngtnw3ft2sW2J58k/9xzXLZ7N+v37iVdqeA7DgdXrWLXhg28uWEDw+3tZ73eTTfdxMaNG1m0aBGJREIhXGSKKHgreIuIyAJTqVR4++232b51K7Wf/pTLdu/msl27WHTyJABHly7lzSuu4I0NG+jr6TnrAs2bb76Z66+/nmw2S3KSG/6IyMQUvBW8RURkAatWq+zfv5/XX3+dIz/9KVe8+SYb3niDlYcPA9DX1cUbGzfy2pVX0rt48VlD+D333MOGDRtob2/XLLjIBVDwVvAWEZGLRL1eHy1H2baNvldeYcOuXVyxcyeX7N+PYy0nu7t5/coref2qq0Znws8gHo9z//33s3r1arLZrEK4yCQpeCt4i4jIRWh4eJg33niD7du3U3z7ba7YuZOrXnuN1QcOYIDjixfz2lVX8eo11zCSz5/xOuvXr+fOO+9k8eLFOI6jEC5yFgreCt4iInKRO3nyJC+//DI7duzAHDvGxrEQvvLwYSyw/5JL2LFpE29s3Ej9LG0H77vvPq644gqy2SzOJLa6F7nYKHgreIuIiACjpSjHjh3jueeeY+/evbSdPMk1r7zCNTt20Dk4SCMW480NG3j52mvZt3btGbevb29v58EHH2Tp0qW4rqtZcJExCt4K3iIiIqcpFArs2LGDbdu2MTgwwIpDh9j0yitc+dprpKpVhvJ5tm/ezMubN5+1FOXDH/4wV155JYlEQrPgctFT8FbwFhEROSPf99mzZw/btm1j//79BJUKG958k83btrFu3z4ssHf9erZddx27L7uMIBab8Drr1q3jQx/6EPl8Htd1Z/ZDiMwRCt4K3iIiIpNy8uRJXn/9dV555RUGBwdpHxxk8/btXLt9O22FAsVMhpeuv56Xtmyh0NY24TUcx+FXfuVXWLFiBbFYTGUoclFR8FbwFhEROS+VSoXXXnuNnTt3sn//fkwQsH7vXra8+CKX7tmDNYY3rriCF2+4gQOXXHLG3uB33303mzdvJh6PaxZcLgoK3greIiIiF6RWq7F371727t3Lrl27qFQqtA8McMPWrWzeto1UtUpvTw8/v/FGdmzaRDMen/A6N954I7fddhvpdFoBXBY0BW8FbxERkXfF932OHTvGq6++yltvvUV/fz+xep2rXnuNG158kWXHjlFOpdh6ww38/MYbKWWzE15n48aN3HPPPWQyGWJnqBUXmc8UvBW8RUREpoTv+/T19fHqq6+yZ88eent7wVpWHTjALc89x+W7duG7Lq9ecw3P3XILJxctmvA6K1as4GMf+xjt7e0K4LKgKHgreIuIiEypMIDv3LmTvXv3cvToUQA6+/q4+fnnufbll/GaTXZfeinP3HYbh1avnvA6K1as4KMf/WgUwLUQU+Y7BW8FbxERkWkRBAH9/f289tpr7N+/n4MHDwKQKpXYsnUrN73wAplymf2rV/P0e987uinPBOF60aJFPPjgg3R2diqAy7ym4K3gLSIiMq1836e/v5/XX3+d/fv3c+jQIay1xOp1rt+2jff87Ge0FQocWbaMp9/7XnZddtmEu2L29PTwwAMP0NPTowAu85KCt4K3iIjIjPB9n0OHDrFv3z4OHz7M/v37sdbiNptsevllbnvmGTqGhjixaBE/ufNO3tywYcIZ8NWrV3PffffR1dWlAC7zioK3greIiMiM8n2fAwcO8NZbb3HkyBEOHDgAgPF9rnrtNd771FN09/dzdOlSfnzXXexdv37CAL5x40buuOMO1YDLvKHgreAtIiIyK2q1GgcOHOC1117j5MmTHD9+HBgN4Ne88grv++lP6Rga4uDKlTx5110cWLNmwuts3ryZW2+9lXw+ry4oMqcpeCt4i4iIzKpyuczrr7/OwYMHOXToEMPDwwA4zSabt2/nvU89RVuhwL41a/jR3XdzbNmyCa/zvve9j82bN5PNZrURj8xJCt4K3iIiIrMuCAKGhobYtWsXBw8eZN++fdTrdQBijQbXb93K7U8/TaZc5pWrr+bJ97+f4fb2064Tj8e55557uOyyy8hkMjgTLNIUmS0K3greIiIic4bv+9HCyyNHjnDw4EFqtRoAiWqVW595hpuffx5jLc/ffDPP3H47tWTytOusXLmSW2+9ldWrVxOPxxXAZU5Q8FbwFhERmXOq1Sp79+6NtqDv7e2NAnjb8DB3Pvkkm3bsoJJK8dM77mDrli0EE5SXXHbZZdx55510d3fjuq4WYMqsUvBW8BYREZmzBgYG2LVrF8ePH+fo0aP09/cT5pMlx45x9+OPs/btt+nt6eEHH/wgb69dO+F13vve97Jp0yby+bzqv2XWKHgreIuIiMxpYf/vt956ixMnTnD8+HEKhcLok9Zy2a5d3PeDH9AxNMTrGzfy+L33MpLPn3adpUuXcuutt7Jy5Uqy2azKT2TGKXgreIuIiMwLxWKRt956i7fffpuBgQEGBgYolUoAuI0Gtz77LLc9/TTWGJ6+/Xaee8978CdoL3j55Zdz++23093dTTweV/mJzBgFbwVvERGRecP3fXp7e9mzZw+9vb0cP36coaEhfN8HID84yD2PP87GN96gv7OTxz78YfatW3fadbLZLDfccANXXXWVyk9kxsz74G2MWQv8AZC31n587NgDwIeBRcCfWGsfP9P5Ct4iIiLzT7VaZdeuXRw5coS+vj76+vool8tRAF/71lt88LHH6O7vZ8c11/DDe++lksmcdp3Vq1dzyy23sHLlSpLJpMpPZFrNavA2xvwl8BGg11p7Vcvx+4D/BLjAn1tr/3gS13okDN4txzqAf2+t/cKZzlPwFhERmZ9836evr4/du3dz4sQJTp48yfDwcNT9xG00uP3pp7ntmWeoJRL88L77eOWaa07bfj4Wi3HDDTdw9dVXs2jRIs1+y7SZ7eD9XqAI/FUYvI0xLrAbuBs4DLwIfJrREP5Hp1zi1621vWPnTRS8///A31prt51pDAreIiIi81u5XGbPnj0cPXqUvr4+hoaGKJVKUQDv6e3l/kcfZeXhw+xdt45/+PCHGersPO06y5cv54YbbmDNmjVafCnTYtZLTYwxlwDfawnetwD/ylp779jj3wew1p4auk+9ziMtpSYG+GPgCWvtjyZ47ReBLwKsWrXq+gMHDkzdBxIREZEZ5/s+J06cYO/evRw7doyRkREqlQojIyOj5SdBwA1bt/L+H/0IJwj4x/e/nxduuglOCdfGGG666SauueYaenp6iE2wOFPkQp0teM/Wr3nLgUMtjw+PHZuQMabLGPOnwOYwpAO/A3wA+Lgx5jdPPcda+5C1dou1dktPT88UDl1ERERmg+u6LFu2jM2bN3PZZZexZMkSOjs7aW9vx/M8cBxevPFG/uSf/3P2rV3LfT/8Ib/6la/QPjg47jrWWp5//nm+//3vs3PnTkqlEkEQzNKnkovJbM14fwK411r7T8Yefxa40Vr7O9Px/io1ERERWVh832ffvn28/fbb9Pf3UyqVKJVKDA8Pj26+Yy3Xvvwy933/+wA8fu+9bLvuutNqvzOZDJs3b+bKK6+ks7OTeDw+Gx9HFpCzzXjP1r+tHAZWtjxeARydpbGIiIjIPOO6LuvWraOrq4u9e/dy8OBBMpkMrutSLBap1Wq8vHkzb69Zw0e/8x3u/+532fDGGzz60Y9SbGuLrlMqlXjmmWfo6+tj48aNrF+/nkQiodpvmRazNeMdY3Rx5fuBI4wurvxla+3r0/H+mvEWERFZuMKFl8ePH2dwcJBSqcTQ0BDVapVmszla+/3ii9z9xBM0YzG+95GPsPOqq067TldXF9dffz1r1qyhp6dHnU/kgsxqjbcx5mHgOeByY8xhY8wXrLVN4LeBHwJvAF+frtAtIiIiC1s6neaqq67i0ksvpbOzk2w2y6pVq2hvbyeRSIzWft90E3/6z/4Z/V1dfOKRR7j/0Ufx6vVx1+nv7+fJJ5/k5Zdf5siRI1QqFebDficyf8yLDXQulDHmfuD+9evX/8aePXtmezgiIiIyjYIgYGRkhN27d3Po0CFqtRojIyOUy2UKhQIAju9zx49/zG3PPENfdzePfPzj9C5Zctq1li9fznXXXcfq1avp6OhQ6YlM2qy3E5xtKjURERG5eJRKpXEtB8vlMoNjnU1GRkYAWLNvH7/w939PqlLh8Xvv5cUbbjht4WV3dzcbN25kw4YNtLe3k0qlZvyzyPyj4K3gLSIiclHxfZ+3336bffv2MTg4SBAEUe13qVQCIF0s8sC3v82le/fyxoYNPPrRj1JNp8ddx/M8rr76ajZs2MCKFSu08FLOScFbwVtEROSiE264c+DAAQ4ePIjruhQKBYaGhqKZb4KAm59/ng/86EcUcjm+/ku/xLFly0671tq1a7nyyitZu3YtbW1tCt9yRnOxnaCIiIjItHJdlyVLlpBOp4nFYpw4cYJms4njOLiuS6PRoFgs8vx73sPB1av55Ne+xq//xV/wDx/+MC9fd924a+3bt49CoUC1WmXNmjUqPZELol/XREREZMFyHIf29vaoVKS9vZ1sNkt3dzexWIzOzk4Aji5fzkP/9J9ycNUqPvboo3zk0UdxG41x1zp58iQvvPACr776KsePH6dSqczGR5J5bEGXmqiriYiIiIRqtRqHDh3irbfeolQq0Wg0osWXQ0NDAJgg4M4nn+T2Z57hyLJlfP2Tn2SkvX3cdWKxGFdeeSXr1q1j9erVZLNZlZ5IRDXeqvEWERERRuu+Dx8+zIEDB+jt7QVGu6AMDAxQLpdHN9wBNrzxBg9861v4rssjn/gEb69dO+46nuexcuVKLrvsMi6//HLVfUtkVjfQEREREZkrXNdlxYoVrF+/nuXLlwOQyWTo7u6mq6uLZDIJwJtXXMFDX/wixWyWX/nrv2bLz38+7jqNRoN9+/axc+dOXnvtNY4fP061Wp3xzyPzixZXioiIyEWlddGl67r09vZijIm2iE+lUgwODjLQ3c1ffOEL/OI3v8mHH3uMnr4+fnDvvdiWreQPHjxIuVwmCAJWrlzJkiVLtOhSzkjBW0RERC464aLLK664glgsRm9vL9ZaOjo6KBQKuK5Lf38/9WSSr37609z9xBPc8txzdPb388gnPkFtbGYcoK+vj+3bt1Mul/F9n0WLFpHL5TCnbMgjolITERERuWjlcjkuvfRSli9fTjabJRaL0dHRQSKRYMmSJTiOg3UcHr/3Xh69/37WvP02X/jzP6djYGDcdYaGhti5cydvvPEGBw4cYGRkhCAIZulTyVy1oIO3MeZ+Y8xDw8PDsz0UERERmaNyuVzUoSSTyWCMIZ/P47ouixcvJpFIALD9+uv5689+lkypxD/5sz9j1f79465TKBTYtWsX+/fv580332RkZCRarCkC6moiIiIiAkC5XObo0aO89dZbVKtVgiBgeHiYer3OyMhItNV8R38/v/x3f0f70BDfevBBdl555bjrJBIJ1q1bFy3ibGtri8K7LHzqaiIiIiJyDul0mjVr1rBu3bpoxjufz5PL5chms7S1tRGLxRjs6uIvvvAFji5bxse/8Q1ueOGFcdep1Wrs3r2bPXv2sHv3bk6cOKGOJwJocaWIiIhIxHVd1qxZg+d5HDx4kIGBAZLJJK7rMjw8/M5W88Bff+5z/OIjj/Ch73+fXLHIk3fdBWMLKpvNJocPH8Zai+/7BEHA4sWL1fHkIqfgLSIiItIi7PUNo91P+vr6SCQStLe34zgOpVKJbDZLsVjk65/8JB9+7DFuf/ppsoUC37v/foKxdoONRoMDBw5grSUIAqy19PT0kM1mZ/PjySxS8BYRERE5RRi+HcfBGEN/fz/xeJx8Po/jONEul9Vqle995CMUcjnu+MlPyBaLfOOTn6QRjwNgreXo0aP4vo8xJmo32NbWNsufUGaDgreIiIjIBFzXZdmyZdHjMHyHtd7hFvHVapWf3nEHhWyWD//DP/C5r3yFv/2VX6E6VlbSaDTo7e3F933q9XrUZlC9vi8+Ct4iIiIiZ3Bq+B4cHARGF2K2qlarbNuyhVImw8cfeYTPfeUr/M1nP0s5kwGgXq/T29sbvT4IApYtW6bwfZFZ0F1N1MdbRERE3q0wfK9cuZKOjg5isRie55FOp8lms3R0dJAc28ly1xVX8NVPfYruvj5+9ctfJlsoRNfxfZ/e3l4OHDjAoUOHOHjwICMjI/i+P1sfTWbYgg7e1trvWmu/mM/nZ3soIiIiMo+1hu/29nY8z8PzPDKZDKlUis7OTpLJJMYY3rr0Uv7uM5+hfWiIz3/pS7S1TAC2hu9jx45x4MABisWiNtq5SCzo4C0iIiIyVcLwvXr1avL5/Gnhu6enJ9ooZ/+aNdEul5//0pdob9livtFocPLkSQ4ePMiJEyeiLeYVvhc+BW8RERGRSXJdlyVLlrBy5Ura2tpwXZd4PE46nSYej7No0aIofB9etYq/+tznSFar/NqXvkRXX190nXq9zsmTJzlw4AAnTpzg8OHDCt8XAQVvERERkfMQznyvWLGCtrY2jDEkk8kofPf09EQ138eWL+fLn/88ru/z+VPCd61WY2BgIArfR44cUfhe4M7a1cQY8z9O4hola+3/M0XjEREREZnzWjfZARgeHo46nVhr6e7uZnBwkHK5TO+SJXz5136Nz3/pS3zuK1/hy7/2awx2dgJQqVQYHByMWhO6rou1lnw+Tyym5nMLzblmvP9nIAvkznL7n6ZzgCIiIiJzURi+V65cSS6Xo9FokEqlSKVSJJNJ8vl8tFFOX08Pf/W5zxFrNvncV75Cfmgouk65XGZgYIBDhw5x/PhxTpw4wfDwsGa+F6Bz/Sr119ba/+NsLzDGZKZwPCIiIiLzRlh2ErYEHB4exvM8fN8nm81ircVxHAYHB+ldsoS//uxn+dWvfCWa+S6MBfNSqYTruhw+fBhjTNTbWzPfC8tZZ7yttb97rgtM5jUiIiIiC5XneSxevJhFixZFG+JkMhlc1yWbzZJOp+kcKy05vmwZfzPW7eRzX/kKmWIxus7IyAiDg4McOXKE48eP09vbq5nvBWZSv0IZY7YAtwPLgArwGvAja+3AWU8UERERuQhkMhlWrlyJtZZms0m9XiedTlOr1bDWEgQBXV1d9Pf3c2TFCv7uM5/hM3/zN3z2r/6Kr/zqr1IZ2+FyaGgIY0xU822MiQK8Zr7nv7POeBtjPm+M2Qb8PpACdgG9wG3AE8aYrxhjVk3/MC+Mdq4UERGRmZLJZFixYgVLliyJjiUSCdLpNJlMhkQiQU9PDwAHV6/m4U9/ms6BAT77139NolqNzhkcHKSvr48TJ05w/Phxjh8/TrlcJgiCGf9MMrWMtfbMTxrzz4G/tNZWzvD8tUCXtfYfp2d4U2PLli1269atsz0MERERuQgUCgV27drFiRMnotnrSqVCqVSi0WhQLpfpG2sruH7PHj718MMcXLWKv/3MZ/A9L7pOV1cXixYtYunSpSxevJglS5aQzWaj2XCZm4wxL1lrt0z03LlqvP/kTKF77PmX53roFhEREZlJmUyGdevWsXTpUowxNBoNXNclk8mQTCZJJBLkcjkA9l56Kd954AHW7N/PL3zrW5iWWe1isUhvby99fX2cPHmS3t5eSqXSbH0smQKT+pXJGPNvjTFtxhjPGPOPxpg+Y8yvTPfgREREROYbx3Foa2tj6dKldHZ2kk6nicViUejOZDLkcjlSqRQAr15zDY/fcw9X7tzJfd//PoxVI9RqNQqFAn19feNuhUJhNj+evAuTrdK/x1r7u8aYXwAOA58Afgz8zbSNTERERGSecl2XRYsW0Ww2OXjwIEEQ4Ps+iUQCay2ZTIZGo4ExhnK5zHPveQ/ZYpH3PPssxWyWp9/3PuCdreUB4vE4juNEt0xGHZ3nm8kG77Dg6EPAw9bagbC/pIiIiIicLuzxHQQBhw4dolAoEIvFcF2XZDJJW1sbzWYT3/ep1Wo88YEPkCkWuevHP6aYzbL9+usBaDQa43a3DK9hjIl2y5T5YbLB+7vGmDcZbSX4W8aYHqB6jnNERERELmqu67JkyRIajQbNZpNisYjneTQaDRKJBB0dHdE28fV6nUc/9jHS5TIf+d73KGUy7N6wARjdWr5YLHL8+HFc1yUIgqi9oML3/DGpGm9r7e8BtwBbrLUNoAx8bDoHJiIiIrIQJBIJli5dSk9PD8lkEs/zovaCyWSSTCZDe3s7AIHr8o1PfIJjS5fy8UceYfnhw9F1hoaGKBaL9PX1Ua1WOXr0KKVSiXq9PkufTM7XpPvRWGsHrbX+2P2Stfb49A1LREREZOHIZDKsWrWK9vZ2Go0GjUaDeDxOLBbD8zza2tpYvHgxAI1Egr/7zGco5HJ86uGHaRsaiq4zNDTE4OAgR48epVwuc/LkSQqFgsL3PKFGkCIiIiIzIJ1Os3z5chYvXkwymYzKRTKZDLFYjFwuR3d3NwDlTIaHf/mXiTWbfPrhh4nXagAEQUClUqG/v59jx44xODjIyZMnKRaL+L4/mx9PJkHBW0RERGQGhJ1OFi9eTCKRwPM84vE48Xgcz/OiloPZbBaAvp4evvGJT7Cot5cHv/nNqMd3qVSiUChQrVajdoP9/f0UCgWF7zlusn28vQmOdU/9cKaWtowXERGRuSRcbLlixQo8z8P3fVzXxXVd4vE4qVRqXI/vfevX8/0PfpDLd+/m7ieeiK4Tznr39vYyODhIf38/g4ODlMvl2fpoMglnDd7GmDuNMYeBo8aYx40xl7Q8/fi0jmwKWGu/a639Yj6fn+2hiIiIiADgeR7d3d0sWrSIeDyOMYZUKoXruiQSCVKpFO3t7Xhj28dvvfFGXrjxRm557jmu27o1us7w8DBDQ0PRbPfg4CAjIyMK33PYudoJ/lvgXmvt68aYjwNPGGM+a619HlAjbxEREZELkMlkWLlyJY1Gg5MnTxIEAalUiiAIoo4nxhiOHj0KwA/vvZfOgQE+9NhjDHZ28vbatQAMDg4CRN1SYLTPdxjmZW45V6lJ3Fr7OoC19hHgAeArYztY2mkem4iIiMiClU6nWblyZTS77ft+tDkOQDabpaenBwDrunzz4x+nv6uLT3z963T290fXqVarDA0NcfLkSarVKr29vRSLRXU6mYPOFbwbxpgl4YOxEP5+4F8Cl07nwEREREQWMtd1yefzLF68OArc8XicZDJJOp2OtoUPt4avJZM8/Mu/jDWGX/rqV/HGOp1UKhWq1WpU9z0yMkJ/fz+lUkmLLeeYcwXv3wMWtx6w1h4G7gD+eJrGJCIiInJRaF1sGdZ7h7ew3jubzUalJ0MdHXzz4x+nu6+Pjz76KNjRAoTh4eHoFtZ6Dw0NqdPJHHPW4G2t/ZG1dscEx4estf9m+oYlIiIicnEIF1t2dHTgOA6O4xCPx3FdN+rz3d3djTGjy+v2rVvHk3fdxVWvv87Nzz0XXWdgYCCa8Q4DeKlU0mLLOeRciysBMMZ8BPhDYPXYOQaw1tq2aRybiIiIyEWhdbHlyMgIzWYTx3HGdToBOHbsGEEQ8LPbbmP5kSPc/cQTHFu6lANr1gCjO1vGYjESiQTxeDy6RiwW02LLOWCyG+j8X8CvAl3W2jZrbU6hW0RERGRqOI5DW1sbixYtwvM8HMfB8zySySTJZBLf90mn03R2do6eYAzffuABBjo7+cQ3vkGuZc+SSqXC4OAgQ0NDVCqVaGfLarU6S59OQpMN3oeA16y16mQiIiIiMg1a673DloDGGFzXjdoFZrPZaLFlPZnka5/6FLFmk09+/eu4zSYwurNlpVKhWCxSKBQoFAr09/dTqVRU7z3LJhu8fxd4zBjz+8aY/zG8TefARERERC42nufR1dVFZ2cnruviOA6JRCKq+06n07S3t+M4oxGur6eH7zzwACuOHOG+H/wgus7AwAClUinaXKdcLjMyMkKhUCAY23peZt6karyBfwMUgSQQn77hiIiIiFzcMpkMK1asoF6vMzg4iO/7OI5DEATEYjHa29sJgoBjx44B8MbGjfzs1lu59Wc/49DKlbyyaRNAdK7nedEMeiKRGFczLjNrssG701p7z7SORERERETG1XsXi0WstSQSiWhjnZGREbLZLJ2dnQwNDREEAf94110sP3yYD3/vexxevpyB7m6q1SqpVIqRkZGoJ3hvb290HYXvmTfZUpMfGWMUvEVERERmgOu6dHZ2smjRomhznVgsRhAEJBIJYrEY+XyeZDIJjO5s+fcPPkgzFuPjjzwS1XsPDg5SLpcpl8sMDw9Hm+xUq1XVe8+CyQbvfw78wBhTMcaMGGMKxpiR6RyYiIiIyMUsLDnp6urCWosxJupykk6nyWQy9PT0EIuNFjAU8nm+88ADLD1+nLufeCK6Tn9/P+VymVKpRKFQoFKpRPXeCt8za1LBe6x9oGOtTc2ndoLGmPuNMQ8Nt7TYEREREZkv0uk0XV1dUSeT1nrvIAjIZrP09PREr999+eU8f9NN3PTCC1z25pvR8aGhIY4fP06hUIg216nX69Tr9Rn/TBezSQVvY8wvGGPyLY/bjTEPTNuopoi19rvW2i/m8/lzv1hERERkjnFdl0WLFkX9vcMdLcOabYBsNkt3d3d0zo/uvptjS5bwse98h7axycdKpUK9XqdUKlEqlajVahw/fpyRkREqlcqsfLaL0WRLTf6ltTaaNrbWDgH/clpGJCIiIiKR1i3lw5nuRCIRlZ6kUim6urqiRZN+LMYjn/gEru/z4De/iRkrJxkeHqZQKERbypdKpWhjHZWczIzJBu+JXjfZjigiIiIi8i6k02m6u7vJZrMAUc13EARYa0mn0yxbtix6/UBXF//wkY+w+uBB3vfUU9HxQqFAqVSiWq1SrVajWu9isaj+3jNgsuF5qzHmPwB/Aljgd4CXpm1UIiIiIhIJS06azSaVSgVrLdZaHMfBGEOtViOTyYxrMfjqNdewZt8+3vvTn/L2mjUcuOQSKpUK5XKZ/v7+qC+4MYZ4PE48HleLwWk22Rnv3wHqwNeArwMVRjudiIiIiMgMCFsM9vT04Pt+tNCytUykq6sr2tUS4Psf/CADnZ088K1vEa9WgdEWg+G28tVqlVqtFu1uWavVZvxzXUwm29WkZK39PWvtlrHb/2qtLU334ERERETkHalUiiVLlpDNZrHWEgQBxhistaRSKbLZLMuXL4/CdyOR4Nu/8Au0jYxw3w9/GF1neHiYWq0WtRgsFovRQkvVe0+fswZvY8xDxpirz/Bcxhjz68aYz0zP0ERERESkVbir5ZIlS4jH41Ff77BMxPd9UqkUnZ2dUfg+vHIlP7v1VjZv385lu3YB0Gw2GR4e5sSJEzSbTUZGRiiVSjQaDbUYnEbnmvH+r8C/MMa8YYz5hjHmvxpj/tIY8zTwLJADHpn2UYqIiIgIMFpy0tXVRWdnJ77vEwQBrusSBEEUtjs7O6PWgwA/ueMOji9ezP2PPkqqNFq0MDQ0RKPRYGhoiGazSalU4tixY1EZiky9swZva+3L1tpPAjcwurDyaeBR4J9YazdZa/+TtVbFQCIiIiIzKJlMsnTpUjKZDJ7n4ThOdEsmk+RyOZYuXRq9PojF+NYv/AKpSoUP/8M/gLUA0fbxYX/vZrNJoVBQi8FpMtka76K19ifW2oettd+21u6a7oGJiIiIyMRc16W9vZ3FixcTBEG0uU48HiedThMEAblcjq6uruic3iVL+PFdd3Hlzp1c9eqr0fGRkRFOnDgRbbBTLpej+zK1JtvVRERERETmENd16e7upru7O9pYx3Ecms0mrutirR3X+xvg2fe8h4MrV/Khxx4jNzICEG0fPzIyQrVapVgscuLECcrlskpOppiCt4iIiMg8lUwmyefzUckJENV5u65LNptlyZIl0THrOHz7gQdwfZ+Pfuc7UcnJ8PAwlUol6vPdaDSiTXZUcjJ1ztXV5PeNMZtnajAiIiIiMnnhxjo9PT3RVvLxeJxYLEY6ncb3feLxOJ2dndE5g11dPHHPPax/6y2u37oVgEajwfDwcFTzXSwWKRaLUcmJdrWcGuea8X4b+O+NMduNMV82xvySMaZjJgYmIiIiIufmeR6dnZ1RlxPHcaIFl67r4jgOixYtinapBNi6ZQv71qzh7ieeGFdyUi6XKRaL0YLLEydOUK1W1WJwipyrq8lXrbWft9ZuBv4TsBb4e2PMU8aY/90Yc+OMjFJEREREziidTtPR0UEymaTZbGLHSkjCbeHDLihhe0GM4Xv3348TBHyopctJWGoSbq7TbDajWm+VnLx7k67xttZut9b+kbX2TuAjwOvAP5m2kYmIiIjIpLiuS09PD11dXcRiMVKpFI7jYIwhmUxGO1u2t7dHteCDnZ385M472bBrF1e88QYApVKJkZERBgYGojrvYrEY9flWycm7c0GLK621I9bab1prvzjVAxIRERGR8xePx1m0aBEdHR1Rh5N0Oj2uzWBnZ2dUbgLw3M03c2zJEj742GMkxzqYDAwMUCqVKBaLVCqVaGOder2ukpN3SV1NRERERBaIXC5HPp/HWhuVlYQlIsYYurq66OnpiV5vXZdHP/pRMqUSdz/xRHS80WgwMjJCo9GgXC5jrVXJyRRQ8BYRERFZIMLe3l1dXQRBgDEmmuFOJBKUy2Wy2SxdXV3R8ePLlvHce97Dddu2ccnbbwOj7QWr1Sr9/f04jkOxWGRkZIRms0m1Wp21zzffnaud4E5jzB8YY9bN1ICmkjHmfmPMQ8PDw7M9FBEREZEZ0drb23VdYrEYjuPQaDTwPI9cLkdHR0fU2xvgJ+97HwMdHXzku98l1mgA0NvbS7Va5eTJk1FbwcHBwai/t5y/c814fxrIAo8bY14wxvwPxphlMzCuKWGt/a619ov5fH62hyIiIiIyI8KFlt3d3fi+TywWIx6P43le1FIwm82OKzlpxuN87/776RoY4L0//Wl0PKz1bjab0QY7YbtBlZycv3O1E9xhrf19a+064L8HVgPPG2OeNMb8xoyMUERERETOSzweJ5/P09Exuv2K67pR+HZdF9d16erqIpFIROe8vXYt26+9llt/9jMWHzsGjAbvWq3G4OAgzWaTQqFAoVCg0WhooeUFOJ92gs9ba/8/wOeADuC/TNuoRERERORdyeVytLe3Y4whCAKstVhro9KTU7eTB3j8nnsop9N8+B/+AYKAer0eLaqs1+s0m00ajQalUinaWl4mb1LB2xhzgzHmPxhjDgD/GngIWD6tIxMRERGRCxbOaufzeYwxUf/uIAhIp9M0Gg2SyeS47eSr6TQ/uvtuVh4+zLU7dgDvbKrT39+PtTZqMRgEgbqcnKdzLa78P40xbwH/DTgK3GqtfZ+19r9Za/tmZIQiIiIickGSySTt7e0kk0lgNIwbY6Kt5TOZDPl8/p0dLYEd11zDwZUr+cATT5CsVGg0Gpw8eZJqtcrQ0FBU593X10etVtOs93k414x3DfigtXaLtfbfW2sPz8SgREREROTdCxdatre3EwQBiUSCeDyO7/vE4/EofHd1db0Tvh2H73/oQ6QqFe788Y+j69TrdYaHh6NdLOv1etThRLPek3OuxZX/2lq72xiTNsb8C2PMnwEYYy41xnxkZoYoIiIiIhcqHo/T09NDPp+PtnyPx+PEYjFc18XzPHp6ekilUtE5x5cu5aUtW9jy4ossPn6cZrNJsViMwrfrupRKJYaHh2k0GlTGdr2Us5vs4sovMTr7fcvY48PA/29aRiQiIiIiU6qtrW3cVvKO4xAEAa7rEgQBbW1tdHZ2jis5efKuu6ikUnzwscfAWqrVKqVSKWor2LrQslarqbf3JEw2eK+z1v5boAFgra0AZtpGJSIiIiJTxnVdOjs7o/aCnufhOA7WWjKZDI1Gg2w2S3t7e3RONZXiHz/wAVYfPMg1r7wCQLFYpFwuMzQ0RCwWo16vMzIyQrVapV6vq+TkHCYbvOvGmBRgAcZ2sqxN26hEREREZEql02na2tqiTXQAHMehVqthjCGfz5+20HL7tddyePly7n78cRLVKkEQMDQ0RKlUoq+vj2q1SqVSoVAoUBlbiClndq6uJo+P3f1XwA+AlcaYvwX+Efjd6R2aiIiIiEyVsL1gW1sbvu+TSqWiAJ5Op2k2m+RyObq7u985yXF47EMfIlMuc8dPfgJAo9GgWq0yMjJCo9Gg0WhQq9WixZaa9T6zc8149wBYax8HHgQ+DzwMbLHW/mRaRyYiIiIiUyqZTNLW1kY8HqfZbJJIJPA8L6r9DhdaxuPx6Jxjy5ez7brruPGFF+g5cQJrLYODg1SrVYaHh7HWUigUoo4nqvU+s3MF77wx5kFjzIPA+4AEEAfeO3ZMREREROYJ13VZtGgRnZ2dUdiOx+PUarVo0WUsFqOjo2Ncyck/vv/9VJNJ7vvBD8BagKifd6VSIRjb5bJYLKq391nEzvF8HvgIEy+ktMDfT/mIRERERGTaxGIxOjs7KRQKFItFrLWkUik8z6NQKEQLMUulEsViEYBKOs1P77iDD37/+1y6Zw97LruMarVKMpmkWCySSqWirieZTIZKpYLjOOPCu5w7eB+w1v76jIxERERERKad4zhks1k6OjoYGRmJNtSpVqtRiUnYfrB1S/it11/PjS+8wN2PP87edeuiFoLFYpFMJkMqlYq6nLS3t9NoNBS8T3GuUhO1DBQRERFZYDzPi7qYWGsxxkTbyYf13+3t7bS1tUXnBLEYT953Hz19fVy3bVsU1qvVKv39/dHulpVKhXq9Tq1W00LLU5wreH92RkYhIiIiIjMql8vR3t4eheNwUx1rLY7jkE6nT6v13nnppexfvZo7f/xj4tUq5XI5aiU4MDAQzYIXCoWo44m841zB+4/PdQFjzPemaCwiIiIiMkNc16WjoyPasTKRSEQ7WaZSKVzXJZvN0tnZ+c5JxvDEvfeSKZe57ZlnAKKAPTw8DBBtphOGcM16v+NcNd63GWMePcvzBtg4heMRERERkRmSyWTI5XKMjIwQBAHGGGKxGL7v02w2yWaztLW1MTg4SLPZBODosmW8cvXV3Pz882zdsoWR9nYKhQKe5zEwMBAt3HQch0QiQbVaJZPJzPInnRvOFbw/Nolr1KdiICIiIiIys1zXpbu7m2KxyMjICOl0elynk1qtRjabpaurixMnTkTn/fjuu9m4cyd3Pfkk337wwWhTnXq9Tr1ej3bELBaLUctCz/Nm8ZPODWcN3tban87UQERERERk5iWTSXK5HMViMZr1ttYSBAFBEJBMJlm0aBH9/f3RrPdQWxvP33ILtz3zDC/cfDPHli1jaGgoKlfJZDJRe8FsNkulUsF1XRznXFXOC9vF/elFRERELnLhVvLZbJZqtUo2m8XzPBqNBul0miAIoo13wi3mAZ593/soZTLc88MfwlhnlOrYgstyuYzv+9GmOs1mMwrtFzMFbxEREZGLXDKZJJ/Pk06nqdfrxGKjRRHWWmKxGIlEgq6urnFbyVc8j5+8731ccuAAl+3aRaPRoFarUavVKJVKJJNJKpUKpVIp2kr+Yl9oOangbYxZNMGxy6d+OCIiIiIy08IOJ21tbVhricfjJBIJarUa8Xgcay2e59Hd3T2uXOSl66+nr7ubD/zoR5iWvt7FYpGhoSGazSb1ep1yuUyz2bzo2wtOdsb7aWPMJ8MHxpj/CfjW9AxJRERERGZaWOsdj8dpNBrEYrFoUx3P8zDG0NXVRTKZfOekWIyffOAD9PT1cc2rr0Yz2+VymWKxSCKRGBe86/X6RT3rPdngfQfwWWPMN4wxTwGXATdO26hEREREZEaFHU7C3So9z8PzPCqVCo7j4LousVgs6vsNo6Uor19+OceWLeN9P/kJTrOJ7/vUajUKhUI06x0+9n3/op71nlTwttYeA34A3AJcAvyVtbY4jeMSERERkRnmui5tbW3RrHcYtmOxGPF4PJr1bt1K3nFdfnzXXXQMDXHd9u1Uq1VqtRr1ej3aVCfcSj587mKd9Z5sjfcTwE3AVcCHgP9ojPn30zkwEREREZlZYYeTfD6PMYZEIkEikcD3/ajkJNzRMuzLHQQBe9at49Dq1dz+1FPEGg1836dcLlOpVMZ1NSkUChd1rfdkS03+xFr7OWvtkLX2NeA9wPA0jktEREREZkHrrHetVovKSlprvru6usjlctE5xnF46p57aCsUuOHFF6Oa7mazydDQEAClUinaYOdinfWebKnJt0953LTW/uG0jEhEREREZk04693e3g68U+vt+z6O4+B5Ho7jkMlkSCQSwGit976VK9m3fj23PvMM8VqNIAgoFArUajWq1Squ6+L7PoVCIWo9eLGZbKlJwRgzMnarGmN8Y4xmvEVEREQWoHD3yUQiEdV6G2Oieu9w1jufz0fnWGt5+t57yZTL3Pz88xSLRRqNBo1Gg5MnT9JsNqNZ71qtRmOsJOViMtkZ75y1tm3slgR+EfiT6R3aKGPMWmPMXxhjHmk5doUx5k+NMY8YY/7ZTIxDRERE5GIRdjhpb28nCAJisVg06x3WejuOQyqVijbVsdZycPFi3rziCm559lmS5XI06x2Gbdd1aTQaDA8PX5Sz3he0c+VY6cld53qdMeYvjTG9xpjXTjl+nzFmlzFmrzHm987xXvustV845dgb1trfBD4JbDn/TyAiIiIiZ3PqrHe4cU7rrHdHR0dUkhL62b33kqjVuPXZZ6lWq9Gsd39/P41Gg3q9ThAEF+Wsd2wyLzLGPNjy0GE07NpJnPpl4L8Af9VyLZfR2fK7gcPAi8aYRwEX+KNTzv91a23vGcb0UeD3xq4vIiIiIlPIdV3a29splUr09vYSj8ejcpF4PB5tqpNKpfA8j0ajQRAEnOjp4fVrruHGF17g+Ztuou55FItFPM+jVqvhjT12XZdEIkG1WiWTycz2x50Rk53xvr/ldi9QAD52rpOstU8BA6ccvhHYOzaTXQe+CnzMWvuqtfYjp9wmDN1j137UWvse4DOT/AwiIiIich4SiURUTlKv16O+3uGCS2MMnZ2d4/p6B0HAz+65h1izye3PPBPNcrfOehtjoo12mmOb7lwMJjXjba39tSl8z+XAoZbHhxntET4hY0wX8G+AzcaY37fW/pEx5g7gQSABPHaG874IfBFg1apVUzJwERERkYuJ67p0dnZSqVQ4fvw4iUQCz/Mol8vE43Fc18VxHNLpdFTL7fs+/R0dvHLddVy/dSvP3HYbZLPROeGsd7lcxvO8i2rW+6zB2xjzf3OWkhJr7X93Ae9pJrrUWd6jH/jNU479BPjJ2d7EWvsQ8BDAli1bJlMWIyIiIiKnCGe9k8lkVOsddjgJgoBqtUpXVxfDw8PU63VgdNb7+bvu4ppt27jl2Wd54t57yefz1Ot1+vv7owAfLrAM74eb8ixU55rx3joN73kYWNnyeAVwdBreR0RERETeJdd16ejooFQqceLECdLpNM1mk2q1Gi20DIKAfD5PtVqNZr2HOjt5bdMmtmzdys9uu40gl6NSqeB5HtVqFcdxqNfrFItFEokE9Xr9og/ef2utbU7xe74IXGqMWQMcAT4F/PIUv4eIiIiITJFkMkkmkyGVSuH7PvF4HN/3o9Dt+z7d3d1RuQlAvV7nhTvv5OqXX+bm55/nyfe/n3w+T6PRYGBggGQySbVaHVd+Uq/Xo/aEC9G5Flf+PLwzVnZyXowxDwPPAZcbYw4bY74wFuR/G/gh8AbwdWvt6+d7bRERERGZGeGsdy6Xo1arkUgkcF032pEyrPXOZDLj+noPLlnCG1deyY0vvECyUgGgWq1GN9d1qdfrlMvlqO3gQnau4N1aj33r+V7cWvtpa+1Sa61nrV1hrf2LseOPWWsvs9aus9b+m/O97mQZY+43xjw0PKxNNkVERETejWQySSqVIpVKYa0lmUxGm+mE3U56enpIp9PROZVKhaduv51Evc6NP/95tHFOOOvdaDSoVqvUarWow8lCDt/nCt7zelGitfa71tovtm5nKiIiIiLnz3Vdurq6yGQy43azDGu9HcfBcRyy2Syx2DvVzMOXXMKuDRu46fnniddqWGujoF0qlaJylXDWOyxVWYjOFbw3GGNeMca82nL/FWPMq8aYV2ZigCIiIiIyN6RSKdLpdLR1PBAFbgDP8+jp6SGbzUbnVKtVnrrtNtKVCltefJGRkZFoEWahUMBaS7FYHDfrvVD7ep9rceUVMzIKEREREZnzwt0si8UilUqFXC5HqVSiVqsRj8dpNBpYa8lkMgwPD2PtaPFE/7p17Lv0Um557jl+fuON+L4fzW4XCgXa2tqiWe9w0eVC7Ot91hlva+2Bs91mapAiIiIiMjdkMhnS6TSVSiUK1uHiSmst6XSanp4eUqlUdE6tVuOp228nWypx3bZtlMvlaFFlpVLBcZwowNfr9QU76z3ZLeNFRERERPA8j/b2dtrb22k2m6TT6agnd7iNvDGGXC437ryTGzZw8JJLuPVnP8NtNqlUKjQaDUqlEoVCgVgsRrPZpFAoRDPiC82CDt7qaiIiIiIy9XK5HNlsFt/3sdaSSCSA0VAeBAHpdJqurq5xiyzL5TLP3nUXbYUC1778MtVqFd/3qVQqlMtlHMeJwrjv+9RqtQU3633O4G2MuWbs59XTP5yppa4mIiIiIlPPdV3a2tqIx+PU6/WoraDv+1G7wUQiQWdn57jzjm7cyOHly7n1mWcwY6E7rO0Og3aj0WBkZGRBznpPZsb7140xlwJfmO7BiIiIiMjc5zgObW1ttLe3Y63FGEMsFosWV4ab6WSz2XHbwDd9n+fvvJOOoSGueOMNKpUKpVKJSqXC8PBwtItlGMIX2qz3WYO3MeZfjr3mecAxxvzvMzIqEREREZnTXNclk8mQTCaj9oKO42CMIZFI0Gw2aW9vJ6w8MMbQaDQ4cPXV9Hd28p5nn8UGAdZagiCIFmvW63VqtVr0eCHNep+rq8m/Bn4EfA34kbX2/5iRUYmIiIjInOa6Lvl8PmoFGG4jH3Yl8TyPZDJJJpMhFothrR3dmTIIeO6WW1h+9CirDhyg0WhQLpcpFouMjIyQTqepVqtRGUq9Xl8ws96TKTW5yVr7W8AN0z0YEREREZk/EokEqVQqmuEOF1fGYjHi8TjNZpPOzk7a2tqic5rNJrtvvplSOs17nn2WUqkUbRVfKBSo1Wq4rkutVqNQKBAEwYKZ9T5n8LbW/sHYz38x/cMRERERkfnCdV06OjpIp9PRgkrP86Jab8/zSCQSpNPpqNbb9338RIKXbrqJy3fvpquvjyAIqFarFItFSqVS1Ne7Wq0uqFlvtRMUERERkQuWTCZJp9PR43D7+LDeG6Cnp2fcayqVCi9cfz1N1+WW555jeHg4Wkw5PDxMtVolFotFtd4LZUOdBR281U5QREREZHqFtd6pVIpms0kul8N13Sg8hwG8dQt4ay22p4cdmzez6eWXSReLBEFAs9mkXC7TbDYxxtBsNqPWgguhw8mCDt4iIiIiMv2y2Sy5XC7a/CYej+M4Dq7rYq0lmUzS1dV12jbyW2+/nZjvc+OLLzI8PBzVeg8NDUVBPKzxXgiz3udqJ+gaY/6pMeYPjTG3nvLc/za9QxMRERGR+SDcUCeZTEaLLF3XJQgCPM/DWkssFqO1CiEIAsorV/Lm5Zdzw89/Tqxep1qt0mg0qFarlEolYLQmvFQqLYhFluea8f5/gPcB/cB/Nsb8h5bnHpy2UYmIiIjIvBFuqNPW1ja6eNL3o9aC4ex3Op0ml8sRj8ej88rlMs/feivpSoVrd+yIdrAsl8tUq1Vc16VUKlGr1aI2hfN51vtcwftGa+0vW2v/L+AmIGuM+XtjTAIw0z46EREREZkXXNeNWguGj2F0ZjvcRr69vZ2urq7onGazSWHTJg4vX87Nzz2HCQKCIIhqxJvNJo7jRLXfYa33fHWu4B39SmKtbVprvwi8DDwJZKdxXCIiIiIyj7iuS2dnJ7lcDgDP84jFYtFMteu6UXvBsPMJQLVW44Vbb6VrYIDLdu0aDeOFAoVCgWKxGG1FHy6uDOvI56NzBe+txpj7Wg+M7V75JeCS6RqUiIiIiMw/yWQymvE2xhCPx6MNdYwxBEEwLpzDaGvBvddcw2B7O+959lnK5XJUz10sFqO67vpYDfh83kb+XFvG/4q19gcTHP9za603fcOaGurjLSIiIjJzTm0tmEwmicfjVKtVHMchHo9jjCGbzUaz3tZanHicrbfeyqpDh1h65EgUroeHh6nX6yQSCcrl8rhQPh9nvc/V1eR3W+5/4pTn/s/pGtRUUR9vERERkZmVzWbJZDJRfXYYtj3Pw/d9YrHYaRvq1Go1dt54I3XP44YXX2RoaAjf96nX6wwMDFCpVKJt5OfzhjrnKjX5VMv93z/lufsQEREREWnR2lownOl2XZdGo0EqlYp2s8xm31kuGAQBQS7Hjk2buPrVV0mXStTrdRzHiTqahNcoFosA83LW+1zB25zh/kSPRUREROQiF7YWzGaz+L6PMQbHcaLZbs/zSCaT5PP5qLWgtZZqtcpLt9xCzPfZvG0bhUIhmuEeGRkhCIJooWaj0aBery+44G3PcH+ixyIiIiIip7UWjMVi+L5Ps9mMZr0zmQydnZ3AaFhvNBpU165l35o1bNm6FZrNaNa7Wq3i+34U4IvF4rxcZHmu4L3JGDNijCkA14zdDx9fPQPjExEREZF5xnVd2tvbSSaTWGtJJBIkEgkajUa0m2U48x3ucBkG6RdvvJH24WEu272bRqNBqVSiVCpRLBbxPI9arUatVou2lJ9Ps97n6mriWmvbrLU5a21s7H74eM53NRERERGR2ZFOp6MFlOGW8UBUemKMOa21YLVaZf/VVzPc1saNP/85pVIpmg0vjdV9A9GGOvNt1vtcM94iIiIiIuctXGQZj8fxfZ9EIoHrujSbTYwx0S2TyUTnBEGAm0iw9YYbWPv223SfPBntYDk8PEytVos21KlUKgRBEG2sMx8oeIuIiIjItGhrayOTyUQdSDzPo9Fo4Hke1lqSySQdHR3jZr193+fVm26i6brc8POfMzIyQrPZpNlsMjg4SBAE0dbxYV9vBe85QBvoiIiIiMwe13XH7WYJ7yykzGaz0WLL1p7e1WoVenp47aqr2LRjB7FyedzulY1GI2otWCqVonKT+RC+F3Tw1gY6IiIiIrPHdV06OjqicpJwM51wBjuRSOB5HrlcDs97Z/lgrVbjxZtuIlGvs2nHDprNJtVqlWq1elprwfCm4C0iIiIiF7V0Oj1uxjuTyURlJ2FHk/b29nHlJvV6neKGDRxevnx0keVYT+9GoxGVl7iui+/7lEolfN+fF4ssFbxFREREZNq0LrJsNpvE43GSySSVSiV63nEcstlstKtlEAQEQcBLt9xCd38/a99+G2MMvu8zMjJCvV4nHo9Hu1qGPcLn+qy3greIiIiITKvWRZbNZhPXdbHWRossw5KUtra26JwgCNi7eTOldHrcIstGo8HQ0BDNZhMYrQmfL60FFbxFREREZFq17mQZBAEw2s87XGTpui6xWIxkMhmdU6vV8LJZtm3ZwuW7dpEfGor6eFcqFer1erTIslqtzotFlgreIiIiIjKtXNcln89Hiyxbe3qHO1kmEglyuVy00Y7v+9TrdbZdfz0Am7dvp1arRZvnhIssw1n0+bDIUsFbRERERKZduMjSWhs9hnd2soR3SlJCtVoNd+1a9q5fz7Xbt1Mrl6NZ73DjHMdx8H2fYrE458tNFLxFREREZNqFiywTiQSNRoNYLBbtQhkEQfS4tc47rOl+5cYbyY+MsH7vXprNJrVajZGREcrlMolEIlpkaa2d07PeCt4iIiIiMiPCGe1wt8mw3CQejwOjs9+dnZ2n7WS5d8MGipkM1730EiMjI1EZSmGszaAxhnq9PucXWSp4i4iIiMiMcF2XeDyO53kYY3BdFxgN18lkklgsFi3EDNVqNVL5PDuuvZbLdu8mWyhEHU0qlUpUblKr1eb8IssFHby1ZbyIiIjI3DHRTpae51Gr1aJyk0QiQTqdjsJ5WFqy/frrcazl2u3bowWVlUqF4eHhaJFlvV6nVqvhOE4U6ueSBR28tWW8iIiIyNySTqdJJpNUq1Ucx8HzPBzHiRZZWmujcB72+K7X6/hr1/L2JZeweft2CmNhG0ZnvVt3sqxUKlhro+fnkgUdvEVERERkbjHG0NbWRjqdpl6vR8G70WhE4dt1XbLZbNSxJFxkue266+gcHGTN/v3UajWstRSLRarVKqlUatxOlnORgreIiIiIzBjHcWhrayObzdJoNHAcJwrY8XicWCyG53m0t7ePay3o+z77rr2WcirFdS+9RKVSoVqtRjtZhsE9XGQ5Fyl4i4iIiMiMal1kCZDJZKJOJYlEAsdxSCaTJBKJ6JxqtYqXy/HKNdew4c03cQcHx4XtMMTXajUqlcpsfbSzUvAWERERkRnlui65XI5EIkGz2cR1XZLJJI1GA2ttNAsebidvjAFGZ71f3rKFmO+zaceOaDFlpVKhUChE29CH28jPNQreIiIiIjLjcrkcmUwmCtvhTLfrulH4bm9vJ5/PR7td+r5Pdf16Dq1YwXXbtlEqFqNFlaVSCd/3SSQSBEEQnTOXKHiLiIiIyIwLZ7nDWW+AIAiihZJhn+/WOu+whGTbddfR09fHyoMHKZfL+L5PuVymVqvhed5pW8/PFQreIiIiIjLjXNcln8+TTqcBiMViOI4TtQZMpVIkEgkymQyxWCw6r9ls8uamTdTi8dFZ71KJWq1GrVajUCjQaDQoFApzss5bwVtEREREZkUymYxqu40xZDKZaNMcxxmNqZlMJpq9Dmu4s4sX8+rVV3Pl66/jju1kGYvFoi3jrbVRXfhcouAtIiIiIrPCdV3a2tpIJBJRVxLXdWk2mxhjolnwjo4OAKy11Ot1KpUKr954I16zyZU7d0a7VpbLZQqFAslkcpY/2cQUvEVERERkVjiOQyqVIpPJRHXexhh8348204nH4+TzeXK5XHReEASMXHYZJ7u72fTyyxSLxajcpFgsRrtXzjUK3iIiIiIya5LJZLRxjjGGVCoV7VbpeR7GGBKJBPF4PDqnUqngxmLs2LSJVYcO0TEwQKPRAIi2om99/Vyh4C0iIiIisybcHj6RSOD7Pp7nkUwm8X2fIAiiQN7W1jbuvHq9zqubNmGBa3bsiPp3VyoVhoaGqNfrs/OBzkLBW0RERERmVdj+LwzPYW/ueDwe9eTO5XLjyk1838ddvZp9a9eyaceOcT29R0ZGVGoy04wx9xtjHhoeHp7toYiIiIjIGbRuIR8uqgy3gk+lUnieRywWGxe86/U61lpe2bSJjqEhVhw4QK1WA1CN92yw1n7XWvvFfD4/20MRERERkTMIe3rH43GstcTjcRzHibaTD/t6x+PxaGOdcDHm7iuvpO55XLtjB7VajWq1SrPZpFQqzfKnOt2CDt4iIiIiMj+k02lyuRzVahVjTLQ40hiD53n4vh9tIe/7Po7jUC6XSXZ3s3PjRja+/jrVwcFot0vP82b5E51OwVtEREREZl24hXy4oU64W2W1Wo02xHEch7a2tmhznXq9Tq1W45VNm0jWaly+axflchnXdcftdjlXKHiLiIiIyKxzHIdcLhdtfhNuntNoNEgmk8RiMeLxeLSVfBAEwOiM+JFLL2W4rY1rduzA933VeIuIiIiInE0ymSSdTkf12+EW8o1Gg3Q6jeM4ZLPZcT26a7Ua6VyOV665hvV79xIcPUqj0SCRSMzWxzgjBW8RERERmRNaF1GGddzhQsrwsbWWjo6OqIbb9/3Rnt7XXotjLVe/+irDw8MMDQ3N7oeZgIK3iIiIiMwJYblJJpPBWhuVizSbTRzHIRaLkUgkaG9vJ5VKRef5vk91zRqOLFvGph07qFQqGGNm62OckYK3iIiIiMwZYd/ucEFlOp0mCAKCICCRSOA4DolEYlwpie/7uK7Ljk2bWHLiBLm331bwFhERERE5G2MMuVyOeDxOs9nE8zzi8XjUnzsWi2GtpXWflmazSbPZ5M1rr8V3HNY/+yzlcnkWP8XEFLxFREREZM5wHIdUKkUmkyEIgqi2O+zn7bouMLrwsq2tLTrPWou3dCl7Lr2Uq199lZo20BERERERObtUKhVtGx+Wm/i+H+1kGY/HSSQS4+q8S6USxhh23nADuWKRzLPPzuInmJiCt4iIiIjMKa7r0tbWRiKRoNFoRGG7VqsBEI/Hox0qw3AOoxvqvHX55Tz1yU9S37RpNj/ChBS8RURERGTOyeVypNNpGo0Gvu9HM+BhqUkQBORyObLZbNT9xPd9Em1tHP7Yx0ivWjWbw5+QgreIiIiIzDmxWAzP8/A8D2MMiUSCZrNJvV7HdV0SiQSe55FOp6Nzwh0rM5mMtowXEREREZkM13WjXSp934+6m4RtBo0xxONx0ul0VGrSOvPtOHMv5s69EYmIiIiIQFRKUq/XgdFZ8LBndywWo9lsks/nyeVy0Tm1Wi3qgDLXKHiLiIiIyJwUi8VwXRfP8wiCgGQySbPZjBZcep6H4zjjyk2azSZBEFCtVmdx5BNT8BYRERGROcl13WgzndZyk7CUxPO8qK2g4zi4rkuj0aDRaMz20Cek4C0iIiIic1bY3aRer2OMiUpMYrEYjuPg+35UbhIG8kajoS3jZ5ox5n5jzEPDw8OzPRQRERERuQBhSUkYuNPpNNZaqtVq9Fy4EDNULBZVajLTrLXftdZ+MZ/Pz/ZQREREROQChOUmiURi3MLK1vvhTpau6xIEAalUing8PttDP82CDt4iIiIiMv9ls1lSqVRUbtJa8x2G8Hw+H816JxIJtRMUERERETlf4ax2GLKTySRBEFCpVKJFluE288aYqBRlrlHwFhEREZE5LazhDnevbC03CbuZeJ5HMpnE8zyq1eq43t5zhYK3iIiIiMx5p3Y3SSaTUfeSMIRns9loJ8u52FJQwVtERERE5rxwM50wZCcSCYIgiGbAw8WVuVyOZrNJpVKZ7SGfRsFbREREROa81u4mQRDgOE60yNJ13Wib+GQySTKZxFo720M+jYK3iIiIiMwLbW1tpFIpqtXquBKTMHT7vk8ul2Px4sWkUqnZHu5pFLxFREREZF6IxWLRzfd90uk0zWaTer2O4zgkk0lc1yWTyZBOp2d7uKdR8BYRERGReeHUcpOwm0mz2YxaCoblJnORgreIiIiIzBu5XI5UKoXv+wB4noe1liAIom3lw+fmGgVvEREREZk3wt0qrbX4vh+F8GazCTBnF1aCgreIiIiIzCPGGHK5HPF4PArbiUSCRqOB67q4rjsnt4sHBW8RERERmUccxyGVSpFKpcbNbFtroxrveDyO67qzOMqJKXiLiIiIyLySSqXwPI8gCDDGRFvJh4/DWu+5RsFbREREROaVsNwkDNye55FKpajValGpiTFmtod5GgVvEREREZlXwnKTsK1gGLKbzSbGGOLxOPF4fJZHeToFbxERERGZdxKJRLRhDhBtHx8EAY1GY062FFTwFhEREZF5x3Vdkskkxpio3MTzPGq1GsCcbCmo4C0iIiIi847jOFGdd1jTHfb29jxPNd4iIiIiIlMlLDdpNBpREAfG1X3PJQreIiIiIjIvua5LPB7HcRyazWa0cU6z2VQfbxERERGRqeK6LplMhng8jjEmCtuVSkU13iIiIiIiUymbzZJOp6lUKlF/73q9Tr1en+2hnSY22wMQEREREblQsVgM13WJxWL4vh/NegdBMMsjO51mvEVERERk3nJdN+puEgQBjuOQTqe1uFJEREREZKqFu1g2Gg1isRjZbBbP82Z7WKdR8BYRERGReS2VShGPx7HWUqvVcBwn6nAyl8y9EYmIiIiInAdjDMlkkkQigbWWRqMx20OakIK3iIiIiMxrrbtYWmvn5MJKUPAWERERkQUgkUhEwbvZbGpx5YUwxqw1xvyFMeaRU45njDEvGWM+MltjExEREZG5wXVdkskkjuNEtd5zzbQGb2PMXxpjeo0xr51y/D5jzC5jzF5jzO+d7RrW2n3W2i9M8NT/Anx9KscrIiIiIvOT67okEgni8Tie583JGe/p3kDny8B/Af4qPGCMcYE/Ae4GDgMvGmMeBVzgj045/9ettb2nXtQY8wFgJ5CcnmGLiIiIyHyTy+UYGhrCGEM8Hp/t4ZxmWoO3tfYpY8wlpxy+Edhrrd0HYIz5KvAxa+0fAZMtG7kTyAAbgYox5jFr7dysohcRERGRGRGLxXAcR11NWiwHDrU8Pjx2bELGmC5jzJ8Cm40xvw9grf0Da+3/APwd8GcThW5jzBeNMVuNMVtPnjw5pR9AREREROaecBdL13XnZI33dJeaTGSight7phdba/uB3zzDc18+y3kPAQ8BbNmy5YzXFxEREZGFI5fL0Ww2icVmI+ae3WzMeB8GVrY8XgEcnYVxiIiIiMgC43ke+Xwe13VneyinmY3g/SJwqTFmjTEmDnwKeHQWxiEiIiIiC4wxZk5uFw/T307wYeA54HJjzGFjzBestU3gt4EfAm8AX7fWvj6d4xARERGRi4PjOCSTyTk54z3dXU0+fYbjjwGPTed7Axhj7gfuX79+/XS/lYiIiIjIWc3NefgpYq39rrX2i/l8fraHIiIiIiIXuQUdvEVERERE5goFbxERERGRGaDgLSIiIiIyAxS8RURERERmwIIO3saY+40xDw0PD8/2UERERETkIregg7e6moiIiIjIXLGgg7eIiIiIyFyh4C0iIiIiMgMUvEVEREREZoCCt4iIiIjIDFDwFhERERGZAbHZHsB0MsbcD9wPjBhj9kzytDww2f6Dk3ltN9A3yestFOfzZzgTZmI8U/0e7/Z6F3L++Z4z2ddP9nX6rsw+fVem5xx9V969ufRdmamxTOX7TMW19F2ZvNVnfMZaq1vLDXhoKl8LbJ3tzzSX/wwXynim+j3e7fUu5PzzPWeyrz+P1+m7chGMR9+VKXmdvisXwVim8n2m4lr6rkzNTaUmp/vuNL32YjLX/lxmYjxT/R7v9noXcv75njPZ18+1/x7mkrn2Z6PvyvSco+/KuzeX/mxmaixT+T5TcS19V6aAGfuNQKaJMWartXbLbI9DZK7Td0VkcvRdEZmcufhd0Yz39HtotgcgMk/ouyIyOfquiEzOnPuuaMZbRERERGQGaMZbRERERGQGKHiLiIiIiMwABW8RERERkRmg4D2LjDFrjTF/YYx5ZLbHIjKXGGMyxpivGGP+zBjzmdkej8hcpb9HRCbHGPPA2N8p3zHG3DNb41DwvkDGmL80xvQaY1475fh9xphdxpi9xpjfO9s1rLX7rLVfmN6RiswN5/mdeRB4xFr7G8BHZ3ywIrPofL4r+ntELmbn+V359tjfKZ8HfmkWhgsoeL8bXwbuaz1gjHGBPwE+CGwEPm2M2WiMudoY871Tbotmfsgis+rLTPI7A6wADo29zJ/BMYrMBV9m8t8VkYvZlzn/78r/Nvb8rIjN1hvPd9bap4wxl5xy+EZgr7V2H4Ax5qvAx6y1fwR8ZIaHKDKnnM93BjjMaPh+GU0QyEXmPL8rO2d4eCJzxvl8V4wxbwB/DHzfWrttZkf6Dv2FNrWW884sHYyGh+VnerExpssY86fAZmPM70/34ETmoDN9Z/4e+EVjzH9jHm8NLDKFJvyu6O8RkdOc6e+V3wE+AHzcGPObszEw0Iz3VDMTHDvjDkXW2n5g1v7HF5kDJvzOWGtLwK/N9GBE5rAzfVf094jIeGf6rvxn4D/P9GBOpRnvqXUYWNnyeAVwdJbGIjIf6DsjMjn6rohMzpz+rih4T60XgUuNMWuMMXHgU8CjszwmkblM3xmRydF3RWRy5vR3RcH7AhljHgaeAy43xhw2xnzBWtsEfhv4IfAG8HVr7euzOU6RuULfGZHJ0XdFZHLm43fFWHvGEmQREREREZkimvEWEREREZkBCt4iIiIiIjNAwVtEREREZAYoeIuIiIiIzAAFbxERERGRGaDgLSIiIiIyAxS8RUTmOGOMb4x5ueX2e7M9Jhg3rmXGmBfG7h80xpxsGeslp5xzhzHmuVOOxYwxJ4wxS40x/84Yc9wY8/+d0Q8jIjIDYrM9ABEROaeKtfbaqbygMSY2ttHEu9E6rpvGrvt5YIu19rfPcM5TwApjzCXW2v1jxz4AvGatPQb8z8aY0rscl4jInKQZbxGRecoYs98Y86+NMduMMa8aYzaMHc8YY/7SGPOiMWa7MeZjY8c/b4z5hjHmu8Djxpi0MebrxphXjDFfG5u13mKM+YIx5j+2vM9vGGP+wwWMb50x5gfGmJeMMU8bYzZYawPgG8Avtbz0U8DD7+oPQ0RkHlDwFhGZ+1KnlJq0htY+a+11wH8DwvKMPwCetNbeANwJ/DtjTGbsuVuAX7XW3gX8FjBorb0G+EPg+rHXfBX4qDHGG3v8a8CXLmDcDwG/Y629fmxs/3Xs+MOMhm2MMQngQ8A3L+D6IiLzikpNRETmvrOVmvz92M+XgAfH7t/DaHAOg3gSWDV2/wlr7cDY/duA/wRgrX3NGPPK2P2SMeZJ4CPGmDcAz1r76vkM2BiTBd4DfMMYEx5OjF3/RWNM1hhzOXAF8Ly1dvB8ri8iMh8peIuIzG+1sZ8+7/x/ugF+0Vq7q/WFxpibgNb6acOZ/TnwvwJvcmGz3Q4wdJZfGL7K6Kz3FajMREQuEio1ERFZeH4I/I4Zm2o2xmw+w+ueAT459pqNwNXhE9baF4CVwC9zAcHYWjsCvG2M+cTY9Y0xZlPLSx4GfgW4C3j0fK8vIjIfKXiLiMx9p9Z4//E5Xv+HgAe8Yox5bezxRP4r0DNWYvK/AK8Awy3Pfx342bsoA/kM8AVjzA7gdeBj4RPW2p1AmdFadHUxEZGLgrHWzvYYRERkFhhjXEbrt6vGmHXAPwKXWWvrY89/D/iP1tp/PMP5RWttdhrG9a+AorX230/1tUVEZpNmvEVELl5p4JmxGelvAf/MWls3xrQbY3YzuqhzwtA9ZiTcQGeqBmSM+XeMlqBoFlxEFhzNeIuIiIiIzADNeIuIiIiIzAAFbxERERGRGaDgLSIiIiIyAxS8RURERERmgIK3iIiIiMgMUPAWEREREZkB/y849JzgMal7SAAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"emin, emax = [0.1, 100] * u.TeV\n",
"nburn = 50\n",
"\n",
"fig, ax = plt.subplots(1, 1, figsize=(12, 6))\n",
"\n",
"for nwalk in range(0, 6):\n",
" for n in range(nburn, nburn + 100):\n",
" pars = sampler.chain[nwalk, n, :]\n",
"\n",
" # set model parameters\n",
" par_to_model(dataset, pars)\n",
" spectral_model = dataset.models[\"source\"].spectral_model\n",
"\n",
" spectral_model.plot(\n",
" energy_range=(emin, emax),\n",
" ax=ax,\n",
" energy_power=2,\n",
" alpha=0.02,\n",
" color=\"grey\",\n",
" )\n",
"\n",
"\n",
"sky_model_simu.spectral_model.plot(\n",
" energy_range=(emin, emax), energy_power=2, ax=ax, color=\"red\"\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fun Zone\n",
"\n",
"Now that you have the sampler chain, you have in your hands the entire history of each walkers in the N-Dimensional parameter space. \n",
"You can for example trace the steps of each walker in any parameter space."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:58:01.885897Z",
"iopub.status.busy": "2021-01-29T12:58:01.884309Z",
"iopub.status.idle": "2021-01-29T12:58:02.007733Z",
"shell.execute_reply": "2021-01-29T12:58:02.007227Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Amplitude')"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Here we plot the trace of one walker in a given parameter space\n",
"parx, pary = 0, 1\n",
"\n",
"plt.plot(sampler.chain[0, :, parx], sampler.chain[0, :, pary], \"ko\", ms=1)\n",
"plt.plot(\n",
" sampler.chain[0, :, parx],\n",
" sampler.chain[0, :, pary],\n",
" ls=\":\",\n",
" color=\"grey\",\n",
" alpha=0.5,\n",
")\n",
"\n",
"plt.xlabel(\"Index\")\n",
"plt.ylabel(\"Amplitude\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PeVatrons in CTA ?\n",
"\n",
"Now it's your turn to play with this MCMC notebook. For example to test the CTA performance to measure a cutoff at very high energies (100 TeV ?).\n",
"\n",
"After defining your Skymodel it can be as simple as this :"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2021-01-29T12:58:02.011458Z",
"iopub.status.busy": "2021-01-29T12:58:02.010979Z",
"iopub.status.idle": "2021-01-29T12:58:02.014278Z",
"shell.execute_reply": "2021-01-29T12:58:02.013802Z"
}
},
"outputs": [],
"source": [
"# dataset = simulate_dataset(model, geom, pointing, irfs)\n",
"# sampler = run_mcmc(dataset)\n",
"# plot_trace(sampler, dataset)\n",
"# plot_corner(sampler, dataset, nburn=200)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}