{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**This is a fixed-text formatted version of a Jupyter notebook**\n", "\n", "- Try online [![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.18.1?urlpath=lab/tree/mcmc_sampling.ipynb)\n", "- You can contribute with your own notebooks in this\n", "[GitHub repository](https://github.com/gammapy/gammapy/tree/master/docs/tutorials).\n", "- **Source files:**\n", "[mcmc_sampling.ipynb](../_static/notebooks/mcmc_sampling.ipynb) |\n", "[mcmc_sampling.py](../_static/notebooks/mcmc_sampling.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting and error estimation with MCMC\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": {}, "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.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", ")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "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": {}, "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": {}, "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": {}, "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": {}, "outputs": [], "source": [ "dataset.models = models\n", "dataset.fake()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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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": {}, "outputs": [], "source": [ "# If you want to fit the data for comparison with MCMC later\n", "\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": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MapDataset\n", "----------\n", "\n", " Name : dataset-mcmc \n", "\n", " Total counts : 247676 \n", " Total background counts : 238923.09\n", " Total excess counts : 8752.91\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)) : -1291246.34\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": {}, "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 = -1291243.6817313829\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": {}, "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 6.5 s, sys: 34.7 ms, total: 6.54 s\n", "Wall time: 6.55 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": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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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": {}, "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": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt4AAAF3CAYAAACSb0zkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdeXzcV33v/9eZfUYzmtG+77IdOwsJdRIgaUJIsxAIJQs3YWtvodD2/npLf7ckhXJ774VLC6UXegv0lqWlQNOSFm4gkLKEQkJIgpM4ie3YsR0vsRUvsraRRpp9OfcPaYaxIo1kx5Js6f18PL6PmfnqnNGZsOQ9R+d8jrHWIiIiIiIiS8ux0gMQEREREVkLFLxFRERERJaBgreIiIiIyDJQ8BYRERERWQYK3iIiIiIiy0DBW0RERERkGbhWegDLob6+3nZ3d6/0MERERERklXv66adHrLUNc/1sTQTv7u5utm7dutLDEBEREZFVzhhzeL6faamJiIiIiMgyUPAWEREREVkGCt4iIiIiIstgVQdvY8zNxpgvTUxMrPRQRERERGSNW9XB21r7PWvt+8Ph8EoPRURERETWuFUdvEVEREREzhYK3iIiIiIiy0DBW0RERERkGSh4i4iIiIgsAwVvEREREZFloOAtIiIiIrIMFLxFRERERJaBa6UHsJolEomTXhtjXtZmrntFTqdzUb+n0nss9n0Weg8REREReWUUvJdQLBY7KdDODsCzw24+nz/ptcMx9x8krLXz/k6Xq/J/pLN/Z/H1QuHcGDNvODfGLKr/fGNY7O8XEREROZcpeC+hn//851hr5wydpxIkHQ5HKYSXh/FiWC0P2+XvW+w3+/cXx+R0Ol/Wfq73Kf7M4/GUAnh5+J/9BaH43rPHtdBnLw/f5c+L7+d2u+d8j/L3nuszzBfqZ3+ZmD2uSv0qfY652oqIiIgoeC+h6r/7O5z5PBiDhVf2OPPclt3Lzzym5+lnjan4XvM9L/U71dfF8ZVdzHpdbGMcDozTWbqcbnfpOQ4HBQCHY/o9HI7pa+Y9jMMxfc0E8vIvF8Wwb4w56YtHeci21pYCusvlOul5eYAv/1k5l8uFy+XC6XS+7AtCsV/xucfjOekLSPH93G73SX3Kx14+jvJ2RXN9IZjri8d85vurh4iIiCwtBe8ldM1DD+HJZld6GKtSYXagX8RVmAnyc72e7/l8P5vv0TocZIuvHQ4mZ+4VHI7pMc88Fn9emOv1rPsLXbhcuHw+HB4P1uUClwvjduMOBHD5fOB2g9uNw+PBX12N1+8nGArh8XiAk5cKlf8lxO12l74ElP8Fw+VyvewLQbHPQn/ZmOuvMwr+IiKyVih4L6FP3X03BsDaV/64QBtj7Sn1K28/5/Mz8br8fqEwd/uy+ydd89zHWhyz25b3meO+o7xvWRvHrPbF17Pvu3K5educymPxOhtiZt7hIO90UljgsXjlHA4SZa+LV6H4fFb7vMt1cv+y+7l5Hq3HgysYxFVVhS8cprqhgapgEI/Hg8fjwe124/P5SsG/uPzI6XSW2sxeajT7LyJz7VVQ8BcRkeWyqoO3MeZm4Ob+/v4V+f35mVlBkZOUh/FiOC8G89khvVDAWf7zsmv2fWf5z/P5X96r8LzYx5nP//JnZY/F565cDm86Xbo3u03xcs3aIPxK5ZxOci5X6crPvM663eRcLpJlP8u5XOTcbrKznmfd7unnc70uuwL19dS0tODz+/H5fFRVVREMBnG5XKXAXwz55cG/uPcBOGkvRqUNybMp/IuIrA2rOnhba78HfG/z5s3vW+mxiJQ4HFiYngFe6bGcaTNfHEphPJcrBfLi65c9n3l05XLTz8vvl13OfB53Njv9frkc7mwWXyp1Uht3Nlt6dFSo/jPv8KEUxDMez8uepzweoh4PWY+HzBxXuvjc6/3la68X4/fj8Xrx+XzU1NTQ0NBAKBQiGAzidDrxer2l/QD+meA/18boShugZ1OYFxE5+6zq4C1rV3E2EnjZ5kZjDIVC4aT21tpSpZbZgWchlco7zlYoFE5qXz6O8k2fc72/tZZcLvey+7M/y4oyhsLMEpSV3t3gKAvormwW9+znmUzpnjubnX6dzeKZ/XrmMTQ5WXpdvBYb7vMOx3QQLwZyr5eUzzf96PUyMfOY9vlOekz5fNPPZ17bmbX4tbW1BAIBamtrqa6uJhKJEAgE8Hg8+Hy+UqAvr3xUqfLPbArtIiJLQ8F7Ca1fv/5l/wIr35RWvqmtGPbcZctTZv8Lsvh6rk1pizkkp1AonNR3ds3vYkWOSsrHMVdILH//udpVOkSo0r/sZ1ctKTdXffTFVPcoN7t98XWlCiKzf3aqAXh2YF8owM+u8178fbPvLyQ7a8Nv+ZeO4nsVCoU5v5wUCgUymcycYy4fR7HN7M+UyWRedm/278rlcmSzWbLZbOnLRvn4stks6XS69CXGWks+nyeRSJz0xaTgdJJxOsl4vYv8J3OKrMWZy50UxL1lzz3p9PTrdBrv7OfpNIFEgppotPR6MRux0x7PdAifuZJ+P0m/n5TPx4TfT8rvJ1m8HwiQmHlMe70w899bj8dDR0cHfr+f6upq6uvr8Xq9RCIRqqqqSv/fUPzfUXmFoCKtkxcROT0K3kvoiiuumPP+Qv/Smn0gzXwBtlK4XKj/6SpuVpvtTL23nNvm+vKw0BeD2QG/PPwXg3Xxy0LxZ3P91aD8XjqdLgXyYnAvD+W5XO6kLy6FQqF0r9guk8mQzWbJZDJkMhlyuRyJRIJEIkGhUCCZTJI3hqTbTbKqanH/gCow+TzedBpfOo03lcKXTuNLpfClUtOvZ13+ZJLI+Dgtx49Ptyn7QjRbwRiSfj+JQKB0JWceh2ce41VVxGceE1VV5MomCaqrqwkGg9TW1tLa2ko4HCYSiZQ2uhZLbBYnFMqDukK6iMgvKXgvoZaWlgXbnEpgVTCVs91CJQTPFvPN1MPcXwTS6XSpX3n78tn4VCpFJpMp9S+G9Xw+/7IvAKOjo6TTaeLxOKlUinQ6TTKZJBUIkAoETuszOXK5UiD3J5MEkkn8icTLnycS1I6NEThyhEAigXOev9SkPR4SgQBTweB0KA8GmaqqYqyqioFgkKlgkKlQiKlgkOxMaUqAcDhcCunNzc20traWlsAUK88Uy0/O3oxapHAuIqvV2fdvxFXEraomImel8mC3mC8Gfr//tH/XXCG/OJtfXDpTbFOcbS8uvxkfHy/NwufzeZLJJOPj46RSKZLJJMlkkng8TiaTmZ6NDwZJBIOnMjg86TRV8ThViQSBmceqeHz6+cxVE43SfuQIVfH4nOUw0x4PkzMhfDIUKl3HqqvZO/M8FgqdVOmpvr6eQCBAV1cXkUiE+vp6/H4/Xq+39Je18v8PnWu5nYjIuUbBW0RkCZ1qyC/X3Nz8snuz1+MXZ9SLAb58hj2RSDA1NcXIyAjZbLYU1JPJJIlEgnQ6TcoYMj4f0bq6hT9LoUAgkSA4NfXLa3Ky9Dw0OUnb0aPTG1HLlvYUxQMBYtXVJ13j4TCHw2EmwmEmq6splP1lr6Ojg5qaGtra2giHwwQCAYIztd2LM+flYVzBXETOdgreIiLnkNkbjU9nKU9xyUtxDXtxBj6TyTA8PMzExASTk5Ok02kmJydLs+sTExPEg0HiwSAnKv8CvKkUoclJQpOTVMdiVM88hmIxqmOx6Rn0ROLkbsBkKMREOMx4JFK69kYijNfUMBEOk5/5vB6Ph7a2Nurq6mhsbCQSiRAOh/F6vaV153DyMhYt1xORlabgLSKyxhQrKLndbgKz1pTPtzfFWks6nSabzTI1NUUqlSIWixGLxZiYmCCdTjM6OkoikZh+7feT9vsZaWycdxyubJbqiQnCExNEZh6rJyaIjI/TfuQI5+/adVLJRgvEqquJ1tRMX7W1RGtq2FZTw1htbWl9vMvloqOjg+rqalpaWgiHw9TW1pbqpRcD+OyqUiIiS03BW0REFmSMwefz4fP5CIVC87YrLoGZnJxkamqKeDxOLBYjmUwyNjbG5OQkg4OD0+Uf3W7G6usZq6+f+3fm84QmJ4mMjxMZH6dmfJxINErt2Bj9+/cTmpo6qX3C72estpbRujrGamsZq6tje10dI3V1ZGfKSoZCIbq6ugiFQrS0tJTqoBdPJYVfBvLTKU0qIlKJgreIiJwxxdAaiUSIRCJztsnn86UNovF4nGg0SiKRIBqNEovFGBwcJBaLYZ1OYpEIsUiEgTnex5XJUDM+Ts3YGHVjY9SOjlI7Nkb3oUO8aseOk9pOVFczWlfHSH09I/X1DDY08FxDA1PBIBhDTU0N9fX1VFVV0d3dXRq/1+t9WV1/LVkRkdNlTuXUvXPV5s2b7datW1d6GCIisgjFYJ5IJEpVXIaGhhgdHWViYoITJ04sWB/elc1OB/LRUepHRqgfGSk9982UhwRI+nwMNzSUrqHGRoaamojPVIepr6+nsbGRxsZGGhoaqK6uprq6Gp/PB/Cyg4ZERIwxT1trN8/5MwVvERE5VxRDeTqdZmxsjEQiwcjICKOjowwNDTEyMlL5DawlODVF/fAwjcPDNAwP0zA0RMPwMIFkstQsHghwoqmJoaYmTsxcQ42N5F0uqqqqaG5uJhgM0tPTQ01NTSmMF0N4+fpxEVlbFLwVvEVEVr3iqaLRaLS0vjwajXLkyBEGBwfJVDjdE2upisdpHBqi8cQJmmYeG4eGSqUR8w4Hww0NDDY3T18tLQw2N5P2+fB6vaVTPXt7e0trx8vrkmtWXGRtqBS8tcZbRERWhWKFluCsQ4SK1ViKgXxiYoKJiQmOHTvGwMDM6nFjiAeDvBgM8mJvb6mvKRSoGRuj+cQJmo8fp3lwkL4DB7h4+/ZSm9HaWo61tk5fbW3sam4m6/USCATo6OigqamJ5uZmampqCAaDeGc2empWXGTt0Yy3iIisSeWBvHiNjo5y5MgRotFoxb5Vk5M0Dw7Sevw4LceO0XrsGOFYDJguezjc0MDR9naOzFzDDQ0Yl4va2lra29vp6ekhHA5TV1eH2+0uHQgECuIi5zotNVHwFhGRRUin0+RyOWKxGOPj44yPjzM0NMTRo0cZHh6u2LdqcpLW48dpPXaM1qNHaT9ypLRuPO3xcLStjaPt7Qx0dPBSRwdpv5/a2lra2tro7OykpqaGxsbGk07mBAVxkXONgreCt4iInKZ0Ok0+n2diYoKpqSmGhoYYGhriyJEjjI2Nzd/RWmrGxmg/cqR0NQ8O4rAWCww1NjLQ2Vm6YpEI1dXVdHV10dnZSV1dHXV1dTidzpPKGiqIi5zdFLwVvEVE5AwqX6YSi8U4ceIEQ0ND7N27t2I/dyZD29GjdA4M0DEwQMdLL+Gd2fQZjUQ41N3N4e5uDnV3MxGJUFNTQ1tbG93d3TQ2NhKJRHA4HKUgrhAucvZR8FbwFhGRJZZOp5mammJqaooTJ04wPDzMtm3byM1URZmLyedpGhqi6/Bhug4douvw4dLylGIQf7G3l4M9PaRraohEIvT29tLZ2TnnIT8K4iIrb80Gb2PMzcDN/f3979u3b99KD0dERNaQdDqNtZbh4WGGh4cZHR3lhRdeqFxrvFCgcWiI7kOHSpc/lQLgRGMjB/v6ONDby0BXFyYYpKuri97eXtrb2wmHw5oNFzkLrNngXaQZbxERWWnFID4+Ps7IyAjHjx/n2WefJVl2cM9splCg+fhxeg8epPfgQToHBnDl8+ScTgY6O9m3bh371q1jvKmJhsZG1q1bR0NDAw0NDYRCIYVwkRWg4K3gLSIiZ5l0Ok2hUGB8fJzh4WGOHTvGE088UbGPK5Ohc2CAvgMH6N+/n8aZSivRSIT969axr7+fF3t6qG5uprOzk7a2Ntrb2wkGg7hcrlLFFBFZOgreCt4iInKWS6fTZDIZRkZGGBkZYf/+/bzwwgsV+4THx+nft4/+/fvpPXgQTzZL1uXiQF8fezds4IX16zFNTXR1ddHd3U1LSwuRSEQhXGQJKXgreIuIyDkmnU6TSCQ4fvw4Q0NDPPnkkxWXpThzOboOH2bD3r1s2LOHcCyGBV7q6GDveeex+7zzSHd00NPTQ1tbGx0dHVRVVeH3+xXCRc4gBW8FbxEROYcVZ8OLR91v27aN48ePz9/BWpoHB9mwZw8b9u6lZXAQgOPNzTy/aRPPb9pEqrOTrq4uWltb6e7uVggXOUMUvBW8RURkFUmlUqW14Tt37lzUkpSNu3ezadcuOo4cAWCwqYndmzax8/zzYf162tvbaW1tpa2tjZqaGpxOp0K4yGlQ8FbwFhGRVSqVSpVqhx87dozHH3+8YvvQxASbdu9m4/PP0zkwgAGOtbTw3EUXsfP88wn099M5MxteU1NDbW3tSbXCRaQyBW8FbxERWQNSqRTxeJzR0VH279/PU089VbF9KBbj/F27uHDHDlqPH8cCL/b08NyFF7L3ggto3biR5uZmurq6CIfDVFdXaxZcZAEK3greIiKyxpSH8F27drFjx46K7euGh7lw504u3LGD2miUrMvF7o0b2XbxxYxdfDFdPT20trbS2NhIOBwmGAzi8XiW6dOInDsUvBW8RURkDUulUsRiMY4fP86ePXvYs2fP/I2tpe3oUV61bRsX7NyJP5ViPBxm+6texbaLLyb0qlfR1tZGT08PwWCQ6upqAoGAZsFFZih4K3iLiIgA0yF8dHSUwcFBnnzySYaGhuZt68xmOW/PHi7eto2+AwcwwIvd3Ty9eTNDV1xBa3c37e3t1NbWEolENAsugoK3greIiMgs1loSiQQjIyPs2bOHLVu2VGwfmpjgVdu38+pnnqFmfJypqiq2XXIJ2y67jPpLL6Wuro7W1lZqa2sJh8MEAoFl+iQiZxcFbwVvERGReZUvRdm2bRuHDh2av3GhQN/Bg/zK1q1s2LsXYy37+/t5evNmMtdfT1NZScJiANcyFFlLFLwVvEVERBZUnAUfHBzkyJEjPPzwwxXbhyYmePWzz/Lqp5+menKSaCTCk5dfzrEbb6Smu7u0DjwYDBIKhTQLLmuCgreCt4iIyClJpVKkUikOHTrEo48+yujo6LxtTT7PeXv2cPkTT9A1MEDa42HbxRfzzBVX0HLVVbS0tBAOh4lEIqXNmCKrlYK3greIiMhpsdYyNTXF0aNHOXToEE888UTF9i3HjnH5li1csHMnjkKBF9av5xdXXkn4TW+io7OTqqoqampqFMBl1VLwVvAWERF5RYrLUMbGxnjxxRd5+OGHqZQhqiYn2bx1K5c+9RRViQQvtbfz2JVXYt7yFto7O4lEIoRCIcLhMFVVVbhcrmX8NCJLR8FbwVtEROSMKRQKjI+Pc+DAAR599FFisdi8bV2ZDJds28ZrH3+cmvFxhuvreeyKK0jfdhvtvb2EQiEikYgCuKwaCt4K3iIiImectZbJyUkOHjzI448/zvDw8LxtTT7P+bt2ccVjj9F84gQT1dU8euWVxN72NjrXrSudhllTU6MALuc0BW8FbxERkSVTDOCHDh3iscceq3goD9bSt38/Vz3yCJ0vvUQsFOLRX/1V4nfeSdeGDQQCAYLBIHV1dfj9fgVwOecoeCt4i4iILLnyAL5z50727dtXqTE9L77I1Q8/TNfAQCmAp9/1Ltr6+giFQgSDQSKRiAK4nFMUvBW8RURElo21lmQyycDAAM8888yCAbz7xRd5fVkA/9nVV5P/zd+kZ906qqqq8Hq9CuByzlDwVvAWERFZdsUAvm/fvoVPxLSW7kOHuOanP6XzpZcYqavj8ZtuwvP2t9PZ1YXH41EAl3OCgreCt4iIyIopliJ84YUXeOyxxyoexoO1rN+7l2t/8hMah4c52trK1ttuo/qWW2hqasLpdJYO4nG73QrgctZR8FbwFhERWXHWWiYmJti/fz9btmypfBpmocBF27dzzUMPEY7FONDby7PvfCetN95YmvUOh8P4/X4FcDmrKHgreIuIiJw1inXAd+/ezWOPPUYymZy3rTOb5dKtW/nVRx7Bl0rx7KtfzfH/9J/ovuwyfD4fbrebUCiE3+/H7/cv46cQmZuCt4K3iIjIWSefzzM8PMyuXbv4xS9+QT6fn7etL5Hg6p/9jEufeoqs283j116L/f3fp723F4fDgd/vJxAIEAqFcLvdy/gpRE6m4K3gLSIiclay1pLL5Th27BjPPvss27dvr9i+bniY6x98kPX79jFaW8uW227Df8cdNDU3EwgEqK6uxu/34/F4tPxEVoSCt4K3iIjIWa1YAeXQoUNs2bKFl156qWL7vn37uOFHP6JhZIR9/f08/3u/R8frX084HCYQCODxeAgEAlr/LctOwVvBW0RE5JxQXP+9c+dOtmzZUnH9tyOf59Inn+Sahx7CUSjw+OtfT+YDH6Cjvx+/34/T6SxVP9H6b1kuCt4K3iIiIueM4vKTEydOsHXrVnbs2EGlvBKKxbjhhz/k/OefZ6Sujl+8+9003nkn9fX1uN1uqqqqtPxElo2Ct4K3iIjIOadY//vFF1/kqaeeYmBgoGL7vn37uOn736c2GmXHhRdy/IMfpPHCC4lEIvh8vtISFC0/kaV0zgdvY0wv8BEgbK29febeW4E3AY3A31hrH5yvv4K3iIjIuSufzxONRtmxYwePP/54xeonrmyWKx99lCsefZSMx8PP3/Y2Qu9/P03NzaXygz6fr1T/W+RMW9HgbYz5CvBmYMhae0HZ/RuBvwacwN9Zaz+5iPf6VjF4l92rAf6Xtfa98/VT8BYRETm3WWvJZDIcOnSIJ598koMHD1ZsXz88zFvuv5+OI0fYu349h/74j2m4+OLS8hPNfstSWengfRUwBXy9GLyNMU7gBeA64AjwFPB2pkP4J2a9xXustUMz/eYK3p8G/sla+8x8Y1DwFhERWR3KD9959NFHSaVS87Y1hQKXb9nCG376U/JOJ0/ccQeZd76T7p4eAoEAfr8fl8ulzZdyRq34UhNjTDfwQFnwfi3wP6y1N8y8/jCAtXZ26J79Pt8qW2pigE8CP7bW/vscbd8PvB+gs7PzVw4fPnzGPo+IiIisHGst6XSao0ePsn37dp577rmK7WtHR7n5u9+l+/BhDvT28sLdd9N06aXU19fj8/nwer243W5tvpQzolLwdiz3YGa0AeUFOo/M3JuTMabOGPMF4JJiSAf+M/BrwO3GmN+d3cda+yVr7WZr7eaGhoYzOHQRERFZScYYfD4fvb29XH311bzxjW8kEAjM236sro6v/eZv8m833UTHSy9xzQc+wNSXvsTAwABTU1OkUilSqRSJRKJi+UKRV2qlvtaZOe7NO/VurR0FfnfWvc8Cnz3D4xIREZFzhDGG2tpavF4v4XCYXbt2zT/77XCw9bLL2N/fz6333cdVX/wiO7ds4cBHPkLLxo3U1NTg8Xiw1mKt1ey3LImVmvE+AnSUvW4Hjq3QWEREROQcZYwhGAzS19fHa17zGq6++mq8Xu+87cdra/mH3/otHrrmGjbt2MGl73sfw9/6FocPHy7NfmcyGRKJBNlsdhk/iawFKxW8nwLWGWN6jDEe4E7guys0FhERETnHuVwuWlpaePWrX81b3vIWent7521rnU4eufpqvvLe95J3Onn9Rz+K/2Mf49ALLzA+Pk4ymSSfz5NIJEgkEuRyuWX8JLKaLXnwNsZ8A/gFsMEYc8QY815rbQ74feBHwG7gX621u5Z6LCIiIrJ6GWOorq6mv7+fK664giuuuKJire6j7e188Xd+h2de/Wou+dGP2PCe9/DiT3/K8PBwacY7m81q9lvOmHPiAJ3TZYy5Gbi5v7//ffv27Vvp4YiIiMgyKR66s2/fPh577DHi8XjF9uft3s2vf+c7WGN46vd+D9ftt9PW1lYqOeh0OvF4PCo7KAta8XKCK011vEVERNYeay2xWIxjx46xZ88eduzYUbF9ZGyMt33zm7QeP86Oa69l/EMforG9nXA4TDAYpFAoqOygLKhS8NZ/a0RERGRVMsYQDofxer14PB4ikQhPPPEE6XR6zvbjtbV85b3v5foHH+Syn/yEY/v28dx//a+0XH45hUKBqqoqrLUkEgkdOS+nZaU2V4qIiIgsC5/PR1dXF5s2beLaa68lGAzO2zbvcvGDm27im297G3WDg1z1B3/A6Ne/ztGjR4nFYmQyGQDV/JbTohlvERERWfVcLlfppEqfz8eBAwfYvn37vO2fP/98jjc387ZvfpPXf/rTbD1wgJf+6I9obGqipqYGr9dLJpNRzW85JZrxFhERkTXB6XQSDofp7+9n06ZNXHrppTidznnbR+vq+Mp73sNzF17Ipd/5Dk1/8Acc3buXkZER4vE41lpVPZFTsqqDtzHmZmPMlyYmJlZ6KCIiInKW8Pv9dHZ2snHjRt7whjfg8XjmbZvzePj2rbfy4HXX0bttG+f/zu9w9NFHeemll5icnATA4XBo6YksiqqaiIiIyJqUyWSIRqMcPnyYrVu3Mjw8XLF93/793Patb2EdDp784AcJvOlNNDU1EQ6HcTqdFAoFlRyUilVNVvWMt4iIiMh8PB4P9fX19PX18drXvpZXvepVFdsf6O/ny+97H1NVVVz18Y9jPvc5Tpw4wfDwMNlsFo/HUzpuXqddyly0E0BERETWLKfTSSQSwel04vf7Mcawbdu2edtH6+r4+9/+bW657z4uvecenjt6lMH/9t8oFArU19cTCATIZDLkcjmVHJSXUfAWERGRNc3pdBIKhUrVSaqqqnjiiSfmnbXOeL386x13cN2Pf8xrH3qIF0dGOPyJT2Ctpba2Fq/XW1r3HQgEFL6lREtNREREZM1zOp34fD7a2tro7e3lda97XcXAbB0OHrzhBr5/00107dzJpt/7PY498wwDAwPEYjGMMbhcLm26lJMoeIuIiIgwXZ3E6/XS1tbGxo0bueaaayoetgPw1GWXce+ddxIZHORXfv/3mXziCYaGhhgdHQWm64dnMhmFbwFWefBWOUERERE5FQ6HA7fbTU1NDX19fVx11VV0dHRU7LNvwwa++lu/hSOb5XV33cXU/fdz4sQJRkZGAE7adClr26oO3tba71lr3x8Oh1d6KCIiInKOKM58RyIRenp6uPDCC+nv76/Y59aeAHIAACAASURBVHhrK3//27/NRDDIlX/+5+TuvZfh4WEGBwfJ5XJ4PJ7SYTuqeLJ2rergLSIiInK6PB4P1dXV9Pb2snHjRi644IKK7SciEb7ynvdwtLWVy//qr+Dv/74UvovlBhW+1zYFbxEREZF5eDweQqEQXV1dXHjhhfzKr/xKxfZpv5973v1uDvT1sfkLX8D32c8yOjrK8ePHicfjeDwenE6njplfo1ROUERERKSCYvh2Op04HA4cDgfbt28nk8nM2T7r8XDvnXdyy7e/zcXf+AbPx+OM3HUXxdPCq6qqAFRucA1S8BYRERFZgMfjAaClpQWn04kxhu3bt5NOp+dsX3C5uO+220j5/Wz+7nfZF4sx/LGPlcJ3OBzGGKPwvcYoeIuIiIgsQjF8NzY2AmCM4bnnnpu3Wol1OPi3N72JhN/PVQ8/jOeDH+SlT34SgHw+T21tLdZahe81RMFbREREZJE8Hg/GGJqamkr3KoVvjOGha68l5fdz/YMPYu66i4FPfar045qaGkDLTtaKisHbGPNfFvEecWvtF8/QeM4oY8zNwM0LlQASERERWSy32421dvHhG/jF615H3uHgjT/8Idx9NwOf+hSFQgGASCQCTIdvj8eD3+9f2g8gK2ahqiZ3AUEgVOH6o6Uc4CuhOt4iIiKyFDweDy6Xi6amJjZs2MBFF11EIBCo2OfJ17yGH7zxjXQ+/TRdd91F9MQJhoaGiEajuFwunXK5Biy01OQfrbUfq9TAGFN1BscjIiIick4orvluamrCGAPAjh07Ks58P3n55VhjuOn734cPfpBDf/mXpeooxWUnxdea+V59KgZva+3dC73BYtqIiIiIrEYu13SUKm64hIXD91OXXYYF3vT978Ndd3HoU5/i6MzPFL5Xt0VtrjTGbAZ+FWgFksBO4N+ttWNLODYRERGRs5rD4cDlclEoFGhubgamK5Y899xzpFKpefttvewyMIY3/du/wV13cfjTn2bY48HtdhMMBgGF79Wo4hpvY8x/NMY8A3wY8AN7gSHgSuDHxpivGWM6l36YIiIiImcnh8NRWnbS3NzMpk2buOCCCxasULL10kt54E1vomPbNjr+5E+YGBvj+PHjTE1Nac33KrXQjHcVcIW1ds7/xI0xFwPrgIEzPTARERGRc0UxfGcymdKyk2w2y65du8jlcvP2e/rSS/Fks1z/4IPkP/pRTnz848D0QT3lM98ul0ulBleBhdZ4/80CP992ZocjIiIicm4qD98NDQ1cdNFFWGvZu3fvvCdcwnSpQV8qxVUPPUT2E59g6K67MMbQ3NxMsTKb6nyvDguVEwTAGPMpY0y1McZtjPmJMWbEGPOupR6ciIiIyLnE4XDgdrtxOBzU19dz0UUXsX79+tJSlPk8dM01PHnZZWx44AFq//ZvGRsbY3BwkImJCbxeL263m0QiQTabXaZPIkthUcEbuN5aGwPeDBwB1jNd41tEREREyjidztLSkKamJtatW8e6desqh29j+MGNN7Lj4os5/957qfvnf2ZsbIyRkRFisRiemY2XCt/ntsUeGV/8u8ZNwDestWPFepVnM51cKSIiIiuhfElId3c3uVyOQqHA7t275+/kcPCdm2/Gm06z6QtfYHtVFSO33IIxBqfTSVXV9NEpWnZy7lrsjPf3jDF7gM3AT4wxDcD8NXLOEjq5UkRERFaK2+0uVSfp6+ujr6+PhSYDrdPJN2+7jcPr1nHhZz6D79//neHhYYaHh0mn05r5PsctKnhbaz8EvBbYbK3NAgng15dyYCIiIiLnOrfbjdPpxO1209vbS09PDz09PRX75F0u/un22xlua+NVn/gErm3biEajnDhxgkwmg9vtVvg+Ry12xhtrbdRam595HrfWDi7dsERERERWB5fLhTGGQCDApk2baG9vp6urq2KfrNfLP95xB/FAgIs+8hEyL7xANBpldHSUfD5fOqI+m81WLFcoZ5dFB28REREROXXFMoPWWvx+Pxs2bKC1tXXB8B0Phbjn7W/HZDJc+Md/TGZwkOHhYYaGhjDG4Pf7yWazpRMu5eyn4C0iIiKyxIplBguFAvX19WzcuJGmpiY6OysfAD7S2Mi9d9xB1YkTrLv7bhIzs96Tk5MUCoVS+E4kEsv0SeSVWGwd75dtmzXG1J/54YiIiIisTsUyg4VCgcbGRjZu3EgkEilVK5nP4e5u7n/rW6l//nl6PvYxpmIxjhw5wuTkZGkWXeH73FAxeBtjrjHGHAGOGWMeNMZ0l/34waUcmIiIiMhqU6x0UigUaGlp4YILLqC7u3vBfs9dcAE/vf562h55hJbPf55EIsHw8DDxeBxjDD6fT+H7HLBQHe9PATdYa3cZY24HfmyMebe1dgtw9hfyFhERETnLOJ1O8vk8AO3t7cRiMTKZDPv27avY7+evfS01sRiXfOtbJNvbid5+Ow6Ho1Tj2+12k81myWazqvF9llooeHustbsArLXfMsbsBu4zxnwIsEs+OhEREZFVprjZMpPJ4HA4WLduHel0GqBy+DaG7113HbVjY5z/uc+xtbOT0csuK9UK93q9gA7YOZsttMY7a4xpLr6YCeHXAv8dWLeUAxMRERFZrco3W/p8PjZt2kRTU9OCy06s08m9t9zCRE0NF330ozAwQDQaJR6Pk8vldMDOWW6h4P0hoKn8hrX2CPB64JNLNKYzxhhzszHmSxMTEys9FBEREZGTFDdb5vN5AoEAGzZsoK6ubsEDdlJ+P/98xx040mku+NM/JTM+zpEjRxgfHyeXy+FyTS9oUPA++1QM3tbaf7fWbp/j/ri19s+Wblhnho6MFxERkbNZcbNlPp8vVToJBoMslF1GGhq4/847qT54kJ6Pf5zJWIzjx48Ti8VUZvAstthygm82xjxrjBkzxsSMMZPGmNhSD05ERERktXM6nRhjsNbS1tbG+vXraWtrK63Zns/z3d08csMNtD7yCC1f+xrJZJKRkREymcxJB+wofJ89FtpcWfS/gVuB56y12lQpIiIicobM3mzZ1dXF1NQU6XSaAwcOVOz78OWX03TiBBu+9jUSvb1E3/AGHA4HLS0tqnRyFlrsyZUvATsVukVERETOvGJZwHw+XzpWvrm5mb6+vsodjeH/3nQTwx0dnP+JT2D27GF8fJzx8XHS6bQ2W55lFhu87wa+b4z5sDHmvxSvpRyYiIiIyFpSXO+dzWYJBoNs2LCBUCi0YKWTnNvNv9x5JzmXiws++lHSY2OlY+VzuRw+n6808y0ra7HB+8+ABOADQmWXiIiIiJwhxfXexZMtN23aRFVVFX6/v2K/sUCA7955J6EjR1j3mc8Qm5jgxIkTJBIJMplMKdBrvffKWuwa71pr7fVLOhIRERGRNa58vXc+n6etrY2xsTHS6TSHDh0il8vN23dPWxuPXXcdVz74IGObNhG7805OnDhBW1sbfr8fv99PMpkkk8ng8XiW8VNJ0WJnvP/dGKPgLSIiIrLEiuu9C4UCHo+HDRs20NraSl9fX6lG93x+8prXcOi889j4hS/g3L6daDTKyMgIiUSidGhPMpnUspMVstjg/f8BPzTGJFVOUERERGRpla/3DoVC9Pf3EwwGF1zvjcPBt2+9lVQwyIUf+xiOWIxoNEosFjtpvbc2W66MRQVva23IWuuw1vqttdUzr6uXenAiIiIia1VxvXcul6O1tZUNGzbg9/sJhSpvs4t5PHznHe/ANzxMz//8n0zGYqXNlsX13qCTLVfCYg/QucUYEy57HTHGvHXphiUiIiKythXXexcKhdLhOj09PTQ2NuJwVI5w+xsaePQtb6Hp8cdp+5d/KR2uk0qldLjOClrsUpP/bq2dKL6w1o4D/31phiQiIiIiMB2+i0tOPB4PPT09tLW1sW7dugX7PrZ5MwcvuYS+L38Z5xNPEI1GSxs1i6G+eLiOLI/FBu+52i22IoqIiIiInKbikpN8Pk8oFKK3t5dAIEB/f3/FfplslgduuYWpujou/OQnsTMH60SjUXK5HF6vV+u9l9lig/dWY8xnjDF9xpheY8xfAU8v5cBERERE5JdLTqy15HI5Ojo6WL9+PT6fj2AwWLFvtFDgB+94B97hYXo+/WlisRhjY2Mn1fcGrfdeLosN3v8ZyAD/AvwrkGS60slZzRhzszHmSxMTEws3FhERETlLlZcYLBQKtLa20tLSQltb24I1uffW1rLluuto/elPqX/wQZLJJIODg6TTaa33XmaLrWoSt9Z+yFq7eeb6E2ttfKkH90pZa79nrX1/OBxeuLGIiIjIWaxYYjCfz1NVVUV/fz+RSISenh6cTue8/ay1PPy61zHY38+Gv/5rOHSI2Eylk+J67+KR8pr5XloVg7cx5kvGmAvn+VmVMeY9xph3Ls3QRERERKSc0+ksLTmpr6+nv78fn89He3t7xX5Za7n/9tux1nLen/0Z6Xic8fFxEonESfW9M5kM1tpl+jRrz0Iz3v8H+FNjzG5jzDeNMf/HGPMVY8zPgceBEPCtJR+liIiIiLxsyUn5cpNAIFCx76DPx0O3305k507a77mHRCLBiRMnSuHb5XKRy+VIJpPL9GnWnoqVSay124D/YIwJApuBFqbXd++21u5dhvGJiIiISBm32w1APp8nEAjQ3d3N5OQkDoeD/fv3k8/n5+37zMaN9F1+Ob1f/zqjl1zC1KWXMjExgcvlIhAIEAgESlVOir9HzpzFrvGestY+bK39hrX2OwrdIiIiIiunuOQkk8lQV1dHT08PgUCAzs7Oiv0ymQw/ePObSdTWcsEnP0l+prxgPB4nk8ngdDpVYnAJLbaqiYiIiIicJWYvOWlvb6e3txe/34/f76/Ydyyf50fvfje+wUG6P/tZYrFY6VTLTCaD2+3GGKPgvQQUvEVERETOQeVVTlwuF62trdTV1dHZ2VmxygnA4fZ2dt54I+0//CHVW7YQn9lsmU6nAfD5fGSzWTKZzHJ8lDVjoaomHzbGXLJcgxERERGRxSuvchKJROju7iYQCNDV1VWx3+TkJA9dfTUTra1s/MxnyEejjI6OkkqlyGazuFwu3G43yWRSM99n0EIz3i8CHzDGPGuM+aox5g5jTM1yDExEREREKisuOcnlchQKBTo6Oujq6lrUqZbjqRQ/fsc78I6M0Pm5z5FMJhkaGiqdaun3+7Xk5AyrGLyttfdaa/+jtfYS4K+BXuA+Y8wjxpj/Zoy5bFlGKSIiIiJzKq7JLi45aWtro66ujo6OjgVPtTzY0MCuG2+k4wc/ILJ1K/F4nGg0WtpcqSUnZ9ai13hba5+11n7CWnsN8GZgF/DbSzYyEREREVkUj8eDtZZ8Pk9tbS0dHR2LOlgnmUzy4yuvZKK1lXV/8RfYiQnGx8eJx+Ol2t5acnLmnNbmSmttzFr7f6217z/TAxIRERGRU1NccpLNZktLTjo6OvD7/QsuOZnMZvnJO9+Jb3iY9s9+lmQyWTrVsrjkpHiqpbwyqmoiIiIisgo4nc7SkhO3201HRwd1dXW0t7cvWOXkYGMju264gY7vf5+ap58mkUgQjUZJp9Olw3RyuRyJRGKZPs3qpOAtIiIisgo4HA48Hg+FQgFrLTU1NaVZ74WqnMTjcX5+3XXEWlro/4u/oDAxQTQaJZVKkcvlSgfrZLNZLTl5BRYqJ/i8MeYjxpi+5RqQiIiIiJweh8NRqu3tcDhob2+nubkZr9dLVVVVxb6Tudz0kpOhIdo+/3lSqRSjo6OqcnIGLTTj/XYgCDxojHnCGPOHxpjWZRiXiIiIiJyG8treHo+H7u5uIpEIbW1tFZecJJNJBtrbeeH66+l44AFCu3czNTVFLBYrLTnx+/2qcvIKLFROcLu19sPW2j7gA0AXsMUY81NjzPuWZYQiIiIismiza3vX1NTQ3d2N1+ultbXy/Onk5CSP3nADyUiE/r/8S7LJJBMTEyQSiZOWnKjKyek5lXKCW6y1/z/wG0AN8PklG5WIiIiInLbyjZYul4uGhgZaWlqorq4mEAjM2y+fzzNhLVve/nZCBw5Qf++9JBKJ0qx3Lpcr1Q1X8D51iwrexphLjTGfMcYcBj4KfAloW9KRiYiIiMhpKW60LNb2rq6uprOzk0AgQEtLS8W+k5OTPNvTw9GLL6bva1/DHD1KLBZjcnKSZDKJMaa05ETh+9QstLnyz40xB4C/BY4BV1hrr7bW/q21dmRZRigiIiIip6y45KS40bKuro6mpiZ8Pt+CVU7SmQw/ueUWyOfp++xnKRQKpdre2Wy2tOQkkUhgrV2mT3TuW2jGOw280Vq72Vr7v6y1R5ZjUGeKMeZmY8yXJiYmVnooIiIiIsuuuNEyk8ng8Xjo6Oigra0Nn89X8Tj5bDbLaCjEc7feStNjj1H105+STqdJJBIkk8nSkhOY3pQpi7PQ5sqPWmtfMMYEjDF/aoz5MoAxZp0x5s3LM8TTZ639nrX2/eFweKWHIiIiIrLsirPehUKBQqFAXV0dDQ0NVFVVLbjRMhaL8eQVVzDR3k7f//7fpMfGGB0dLR0n73Q68Xg8WnJyCha7ufIfmJ79fu3M6yPAx5dkRCIiIiJyxpRvtHQ4HDQ3N9PY2EggEKC6urpi36l0msd/8zfxDw3R+nd/RyqVYnJykqmpKTKZDD6fT8fJn4LFBu8+a+2ngCyAtTYJmCUblYiIiIicEcVDdQqFAvl8Hr/fT3t7O9XV1TQ0NFTsOzU1xd76eg5eey3d992Hd+9epqamSCaTLztOXuF7YYsN3hljjB+wADMnWaaXbFQiIiIicsa4XC4cDsdJGy2bm5vx+Xz09PRU7JtOp3nohhvIBoOs/+u/xhYKxGKxOWt7a6NlZQtVNXlw5un/AH4IdBhj/gn4CXD30g5NRERERM4Ut9tdKi/o8XhobW2ltbUVr9eLy+Wat18qlWLK42HHnXdSs2sXVQ88QCqVIpFIkEqltNHyFCw0490AYK19ELgV+I/AN4DN1tqHl3RkIiIiInLGlJcXNMYQiUSor68nEAjQ1lb5eJZEIsH2V7+aaHc3fV/8IulolImJCaampkrlBbXRcmELBe+wMeZWY8ytwNWAF/AAV83cExEREZFzRLG8YHGWur6+noaGBkKhUMUTLTOZDKPj4zzxznfiHxmh+etfZ2pqing8TjweJ51Oa6PlIsz/d4VpYeDNzL2R0gL3nfERiYiIiMiSKM5653I5jDGEw2Ha29uJRqO0tLRw5MgR0um5t/GlUin2Nzcz8LrX0fPNbzL21rcy6fMRCATwer0nHapTrBsuJ1soeB+21r5nWUYiIiIiIkuuuNykuNY7EonQ2NhIMpmkra2NgwcPzts3lUrxi7e+ldu3bqXz859n4FOfYnJyEo/Hg9vtLs16J5NJ3G43xqgIXrmFlpron5aIiIjIKjJXecHm5mbC4fCCYTkej3PC62X3W95C889+hvOxx0ilUqTTaW20XISFgve7l2UUIiIiIrJsZpcXjEQiNDU14fV6FywvGI/H+cWVV5Kor2f93/wNmWSSaDRKJpPRiZYLWCh4f3KhNzDGPHCGxiIiIiIiy6S8vKDf76e+vp6WlhY8Hk/F9dmZTIakMWx/17sIHThA5L77SKfTRKNRkskkuVwOn8+HMUYbLWdZaI33lcaY71b4uQE2ncHxiIiIiMgyKC8v6HQ6qampIR6PMzY2RktLC4cPH563bzqd5vnzz6fvvPPo/4d/4MlrryXl9RKPx0t1wf1+P4lEonS6pSwcvH99Ee+hrzIiIiIi56DyjZZer5e6ujoaGhqIx+MEAgESicSc/Yr3n3vve3nD3XfT+dWvMvCHf4jH48Hn8+F0Ok8qL+hyubTRkgWCt7X2Z8s1EBERERFZXrNnvUOhEM3NzYyMjNDY2MjAwACFQmHOvolEgv3NzfS94Q103n8/g297Gwmvl2Qy+bLygtlsVuUFWXiNt4iIiIisYuWH6hSXnDQ2NlJVVUV7e3vFvuPj4zz15jdjHQ7av/hFrLVMTk6SSCRKYb5YXtBau0yf6Oyl4C0iIiKyhhVnvQuFAtbak8oLGmPw+/3z9k2lUoz6fLzwxjfS+tBD2GeeIZ1Ok06nSxstVV7wlxYVvI0xjXPc23DmhyMiIiIiy232rHc4HKa+vp5wOExLS0vFvlNTUzx7/fVkQiH6vvxlstks8Xhc5QXnsNgZ758bY/5D8YUx5o+Aby/NkERERERkOZUfJV8oFPD7/TQ2NhKJRDDG4HLNvy0wHo8zms+z59ZbqX/mGTyPPEIymSSVSpFIJMjlcqXNlQrei/N64N3GmG8aYx4B1gOXLdmoRERERGRZOZ3OUjguHqoTiUQIBoN0dnZW7JtOp9lx5ZUkGhro//KXSSeTjI+Pk8lkyGazpbXea33We1HB21p7HPgh8FqgG/i6tXZqCcclIiIiIsto9lpvn89Hc3MzDQ0NeDwenE7nvH3j8TgT6TS73/EOqvfvJ/SDH5DJZIjH48TjcR2qM2Oxa7x/DFwOXADcBPyVMeZ/LeXARERERGR5zZ71rq6uJhgM4vf76e7urth3cnKS3ZdcQqy7m/6vfpXsTOhOpVLkcrnSxs1cLrdmw/dil5r8jbX2N6y149bancDrgIklHJeIiIiILLO5Zr2bmpqor6/H4/HgcMwfHdPpNNFYjJ3veheB48dp/Pa3S2u9p6amyGazuFyu0pKTtWixS02+M+t1zlr7P5dmSCIiIiKyUuaa9a6pqSEQCCy41ntycpL9/f2MXHQRXV/7GvlolEQiQSqVIpVKUSgUcLvda3bWe7FLTSaNMbGZK2WMyRtjNOMtIiIissrMnvX2er3U1NTQ0NCA3++vWOEkm80yFo2y813vwhOL0frP/1xabpJOp0vHxxdnvdfaoTqLnfEOWWurZy4fcBvwN0s7NBERERFZCXPNetfW1uLz+RY8zTKdTnO4sZHjV15J5333YYeHS7PemUzmpFnvtbbk5LROrpxZevKGMzwWERERETkLzDXrXVtbS1NTE36/H4/HM2/fVCpFNBpl9x134EylaLv33tJSk2L4Xquz3otdanJr2XW7MeaTwNr5pyQiIiKyxsye9fb7/dTW1hIMBmlra6vYN5VK8aLfz9Ff/VU67r8fhodLS06Ktb09Hs+am/Ve7Iz3zWXXDcAk8OtLNSgRERERWVnzrfWuq6sjEAgQCATm7ZtOp4nFYjx/2204Mxma77mHTCZDMpkkmUySz+dLh+okk8k1M+s9/+r4Mtba31rqgYiIiIjI2cXpdJLP50sz1IFAgLq6OqLRKE1NTQwMDJDP5+fsm0wmGWhs5NjVV9N+//0cf8c7yPj9pFIpfD4fTqcTj8dTOs2y0vKV1aJi8DbGfI4KS0qstX9wxkckIiIiImeF4qx38QAcr9dLJBKhtraWyclJGhoaGBwcnLNvNptlfHyc5976Vlp/9jNa77mHkQ99iHg8jsfjwev14na78Xg8JJNJ3G43xphl/oTLa6EZ763LMgoREREROSvNNetdW1tLLBYjmUyWfj6XdDrNQHU1x17/etq/+12Ov/OduHp6SKfTpb5ut/ukdd+r2ULB+5+stbllGck8jDG9wEeAsLX29pl7G4EPAPXAT6y1f7uCQxQRERFZteab9a6urmZ8fLzirHculyMWi7HzlltoefhhWu65h5EPf5ipqSm8Xi9+v39NzXovtLnyyeKTmWUnp8QY8xVjzJAxZues+zcaY/YaY/YbYz5U6T2stQette+ddW+3tfZ3gf8AbD7VcYmIiIjI4hUrnBQ3RRZnvWtqavD7/QseJX+sqorjb3gD7d/7HtmBAQqFQulQnWw2i9vtBqbXha9mCwXv8q8cV5zG+38VuPGkNzTGyfThO28ENgFvN8ZsMsZcaIx5YNbVOO/AjHkL8Cjwk9MYl4iIiIgsUvmsd6FQOGmtt9/vp6qqat6+uVyO8fFxdt16KyaXo/Uf/5FcLkc6nSaRSJTCfHGj5WqucLJQ8H5Fn9xa+wgwNuv2ZcD+mZnsDHAv8OvW2uestW+edQ1VeO/vWmtfB7zzlYxRRERERBY216x3dXV1KYBXkk6nOeb3c/zXfo22Bx4gc+gQmUyGdDq9pma9Fwre5xljdhhjnit7vsMY85wxZsdp/s424KWy10dm7s3JGFNnjPkCcIkx5sMz915vjPmsMeaLwPfn6fd+Y8xWY8zW4eHh0xyqiIiIiMDcdb3D4TChUAi/34/X6523bzqdnp71vuUWTKFA2z33kMvlSKVSa2rWe6HNlRuX4HfOtWK+UsnCUeB3Z917GHi40i+x1n4J+BLA5s2bV+d/eiIiIiLLqFjBJJ/P43K58Pv9NDQ0MDo6SmtrK4cOHZo3NCeTSQZrazl23XW0/du/cfQ3fgNPf39p1nstVDipOONtrT1c6TrN33kE6Ch73Q4cO833EhEREZFlUpz1zufzWGvx+XxUVVVRV1e3YEWSTCZDLBZj71vfiiOfp/lf/oVkMjnnrPdqPc1ysUfGn0lPAeuMMT3GGA9wJ/DdFRiHiIiIiJwip9OJtbYUlEOhEFVVVQSDQbq7u0trtecSj8c5XlXFiSuvpP173yM3OlraaJlOp8nn86X+2Wx2uT7SslnS4G2M+QbwC2CDMeaIMea9M3XBfx/4EbAb+Fdr7a6lHIeIiIj8v/buPsix6rzz+O+RdPXe3eru6Z7Bw7txiE2Z2EBwsYsLxx67gHiwDTixk1StEypsNmVX7R+7G3udfcm6dp0qbyW7rs3LkthhN1WBMJgMHjOA8bhSJOs3IHEwmEAmxjADM8x0z/S7pKsrnf1jpBuNRupWz7SkK833U9XVaumeq0cNh3449ZznAFsjFouFmywbq97T09NdrXqXSiUtLi7qpdtvl7e2ppkHH1SxWFSlUlGpVFKlUglLTkax1nvDxNvMrq5/f/tmb+6c+7hz7gLnnOecu9A596X68/udcz/hnHuzc+6/bj7s7pjZN5NbCwAAGhhJREFUbjO7Z3FxsVdvAQAAcN7xPO+0Ve/x8XHl83nlcjnt3Llz3Y2WS0tLOrRtm+auvVYXP/SQguVl+b6vYrEo3/dVrVaVTCYVBMHIrXp3s+L9K2b2Fkl3bXhlxDjn9jnn7p6YmBh0KAAAACOjddU7k8loampKU1NT8jxP8Xi841jf90+tet9xh1ILC5p8+OFwtbtYLIbJ/Ciueq+beJvZf6pf8x1JMTP7j32JCgAAAJHWaC3YXOudzWaVzWa1ffv2dVe9FxYWdPjyy7X41rfqkj17VFxeVqlUCjdb1mq1kVz13qiryW9J+oakP5f0Defcf+lLVAAAAIi0WCymWCx22qr39PS0CoWCnHPrHiMfBIHm5uf10u23K3v0qApPPKFKpaJKpaJyuawgCEZy1bubUpN3Oed+XdJP9zoYAAAADIfWA3U8z1MulwtPstyxY0fHsc45LS0t6ZWrr9bKJZfo0vvvV6m+2t2o9a7VavI8b6RWvTdMvJ1zn61//w+9DwcAAADDornW28yUyWRUKBQ0MTERnm7ZSRAEWlha0ssf/ajGXn5ZqQMHVCqVwo2WQRAokUiEq96jYBB9vPuGriYAAAC901j1DoJAtVpNmUxG+Xxek5OTmpiY0OzsbMex1WpVx48f149vuEHF2Vm9ec8eBUEQJt2NezZWvX3f7+Mn642RTrzpagIAANBb8Xj8jFXviYkJbdu2TWa2bl9v55wWVlf14zvv1OTzzyvxne+oVqvJ932VSqVw1dvMRmLVe6QTbwAAAPRWa613KpVSNptVoVBQNpvVzMxMx7GVSkVHjx7VSzfeKH9iQpfVj5FfW1uT7/sKgiDcuDkKtd4btROMm9m/NLPPmdk/b3ntN3sbGgAAAIZB6zHymUxGY2NjKhQKymQySiQSHccGQaAF39ehj3xEM9/7nhIvvihJ4UbLSqUyMqveG614/29JN0mal/RFM/udptdu71lUAAAAGBrtjpFvbLRMpVIqFAodxzbKSg7u2qVqMqkL9uwJV7wrlUq46j0KrQU3Sryvd879gnPuf0h6l6S8mT1kZilJnQt2AAAAcF5pPVAnnU5rfHxcY2Nj4eE6nZw4cUILiYSO7NqlC77xDZVfey3caNnYbOl5nsxMxWKxj59qa22UeCcbD5xzgXPubknfl/RNSfleBgYAAIDh0W7Ve2xsTNPT0zKzdVeqfd/XyZMn9dLNNyvu+5p9+GFVKhX5vi/f90fmGPmNEu+nzezm5ifqp1f+iaRLexXUVqGdIAAAQH90OlCnUXKyfft2xePxjuOXlpY0t3275q+7Thc9/LCKi4sKgkDlclnFYlHValWe50nS0NZ6b3Rk/C855x5r8/wfO+e83oW1NWgnCAAA0D/tWgtOT09rcnJSzjklk8mOY33f1+Liol758IeVPnFCY489pmq1Gq58j8Kq90ZdTf5d0+OPtrz233oVFAAAAIZPp9aCjQN1pqenO46tVquam5vT4auu0upFF+nir3xFa6urKpVKKpfL4THyyWRyaFsLblRq8rGmx59pee1mAQAAAE2aWws2Vr0btd6NFev1zJ88qcN33KHxf/gHJb77XVWr1dOOkW9e9R42GyXe1uFxu58BAABwnmvdZJlKpZROp5XL5ZROpzdsLTg3N6e/v/56+fm8Ln7oIZXLZVUqlbC1YPMx8sOWfG+UeLsOj9v9DAAAALRtLZjL5TQ1NaVsNqtUKtVxrO/7KsVien33bs1+61uKvfKKnHOnrXo3DtTxfb+Pn+rcbZR4/5SZLZnZsqSr648bP7+9D/EBAABgyLRrLZjP5zU+Pq5UKrVuuUkQBHrjjTf00q5dcmbavmePisVi2Fqw+UCdYVv13qirSdw5N+6cG3POJeqPGz9HvqsJAAAA+q9da8FMJqNsNquxsTFt27ZNZp2rlovFohbHxnT8Pe/Rmx59VP78vKrVqsrlssrlclhuMmzHyG+04j3U6OMNAAAwGO1aC05OTmpmZkaS1l31LpfLWl5e1qsf+Yi8tTVN7t2rtbW1oW8tONKJN328AQAABqNTa8F8Pq9CoRAm4O0453Ts2DEdvfhiLV51lS7Zu1fLCwtha8FSqRSuekvDc6DOSCfeAAAAGJzm1oKNTZZjY2OanJyU53mKxTqnos45zc3N6bU771T26FGNfetbqtVqpzZflkpD2VqQxBsAAAA909paMJlMht/XW/WuVqtaWlrSq9deq/LUlC7Zv1+lUilsKziMrQVJvAEAANATreUmzavehUIh3HDZTrVa1erqqpZLJb1+663a9r3vyV59VbFY7LRV70ZrQRJvAAAAnNeaWwua2WnlJrFYTOl0uuPYSqWi48eP65UPfEAy08zevSoWi+Emy+bWgsOwyZLEGwAAAD3TaZNl86p3IpHoOH5lZUUncjnN33CDdj76qFZPnlQQBOFGy2FqLUjiDQAAgJ5q3mTZaC3YWPVOJBLrthasVqs6efKkDv3szyq1sKDxAwfk+/5QthYk8QYAAEDPNW+yTCaTSiaTyuVy8jxP4+PjHcdVKhWtrKzotauuUnHHDl34ta9pZWUl3GDZ3Fow6pssSbwBAADQU+ttspyZmVEmk1Eul2s71jmnYrGolbU1vb57t6aefVapf/xHVatVVSoVFYvFsLVg1MtNRjrx5uRKAACAaGi3yTKdToebLCcnJzuOLZfLOnbsmF7dtUs1z9P2vXtVLpfDpHtYWguOdOLNyZUAAADR0G6TZaOdYKFQUDweX3f86uqqTsTjOn7TTbrg619XUF9YbSTgje4mUV71HunEGwAAANHRusmyUW4yPT0tScpkMh3H1mo1LSws6PXbbpO3tqbxRx4JD9MZlk2WJN4AAADoi+Zyk+aTLMfHx8MWg50EQaDl5WUdufxyrVx2mS7ct08nT5xQrVZTpVI5bZNlLBZTtVrt4yfrDok3AAAA+qbdJstMJqOZmRmlUql1D9RZWVnR8sqKXr/tNo0fPKj0D36gtbW1006yjMfjG/YGHxQSbwAAAPRNu02W2WxW4+Pj8jxPhUKh49hqtapjx47p0E03KUinddEjj4SnVzZvsoxi0i2ReAMAAKCPGol38ybLZDKpTCYTbrJcL3EulUpaicV0/P3v146//EvV5ufDft7FYlG1Wq2Pn2ZzSLwBAADQV83lJs2bLKempsINkp1UKhXNzc3ptd27Ffd9FfbvP62tYKN+PIpIvAEAANBXzeUmkpRKpeR5nrLZrJLJ5LrlJpK0vLysYzt3avmKK7Tz8cfDjZVBEKhcLkd21ZvEGwAAAH213kmWs7Oz8jyvY2vBRgeT5eVlHb3lFo0fPKjUCy+Edd6NFoNRXPUm8QYAAEDftevpnU6nwzrv9U6yrFarWlhY0KF3v1s1z9PsI4/I9335vq9yuRzZchMSbwAAAPRdp57ejU2WtVpNZtZ2bKOn93Iyqbkbb9SOAwdUXFiQpDD57jR2kEY68Taz3WZ2z2L9SFEAAABER7tNluPj45qYmFA6nVYqleo41vd9LS0t6Y1bb1VyeVnZAwe0trYWbrJkxbvPnHP7nHN3T0xMDDoUAAAAtGjdZJlMJsOTLGOxWHiUfCcnTpzQkauuUmlmRm96/PEw8W5stIyakU68AQAAEF3tenp7nqdcLqepqSklEomOJ1lWKhWVy2WdXFrS0Ztv1rZnnlH8yBGZmSqVCiveAAAAQLPGJsvmcpPGEfKSlM/nO46tVCo6efKkDr33vbJaTdP1TZae5ymZTPbrI3SNxBsAAAADE4udSkdbe3onk8nwcSdBEKhYLGp5dlYL73iHLnjsMS0vLcn3fVUqlb7Evxkk3gAAABiYTj29x8fHtWPHDiUSCWWz2Y7jS6WSlpaWdPTWW5U7ckSZp5+O7NHxJN4AAAAYqHY9vTOZjPL5vBKJhNZrlOH7vhYXF/XyNdcoyGa1Y/9+BUFAqQkAAADQqrWndzKZVDweDzdZ1mo1xePxjuOXlpbkJxI6/r73afbJJ1U+fpxSEwAAAKCd1p7eyWRS+XxeU1NTymaz69Z6+76v+fl5Hb3lFiXKZWX27dPq6mofo+8OiTcAAAAGrrm1YKPcJJlMKpfLycw0NTXVcaxzTsvLy1q48kqtXnKJLnziiY5tCAeJxBsAAAAD1+4Iec/zlM1mw6S70ybLarWqUqmkkwsLeuPWW5V/9ll5Bw/2M/yukHgDAAAgEtqVm6TTac3OzsrzvHUPxalWq5qbm9Pr73uflq+5Rv78fB8j7w6JNwAAACKh9Qj5VCoVHiPveZ4KhULHsbVaTcViUaWJCR360z9V6t3v7lfYXSPxBgAAQCS0HiHveZ5SqZTGxsY0OzurRCKhVCrVdmy1WlW5XNb8/Lycc/TxBgAAANbTWm7SqPWemJhQPB4Pj5JvJwgCLSwsqFKpyMz6GHV3RjrxNrPdZnbP4uLioEMBAABAF1rLTTzPk+d5yuVyymQyCoKg49ggCFQul7WysrLudYMy0om3c26fc+7u9U47AgAAQHR0OkI+m81qZmZGnucpk8m0Heuc09ramo4cOUKpCQAAALARM5Nz7rRyk3Q6HR4hv23bto5jK5UKNd4AAABAN2KxUylqc7mJmSmTyWhqakq+7yuZTLYdW6vVtLa2piiWGpN4AwAAIFI6lZuMj4+rUCiEp1p24vt+mLRHCYk3AAAAIicej8s5p2q1Gh4h3zjJMpFIqNMevkYNeKe2g4NE4g0AAIBIaq71TiaTMjNls1lNTk4qCIK2q96VSkVBELDiDQAAAHQjFospFouFmyQbq965XE6Tk5PKZrNhLXirZDLZsfPJIJF4AwAAIJI6lZvkcjmZmaanp9uOc871OdLukHgDAAAgslrLTeLxeNjTOwiCtivb8/PzKpfLA4h2fSTeAAAAiKTW7iZmJs/zlE6nNT09rWw2q3g8fsa4hYUFarwBAACAzYjFYuGBOK3dTSQpn88POMLukXgDAAAgsmKxmMxM1Wo1LDdJJBLK5XKamZlRtVptW25CqQkAAACwSc3dSxrlJvF4XNu2bVM+n2+beFNqAgAAAGxSa3eTVCp1WrlJu8NyOrUaHKToRQQAAAC0aO5ukkqllEwmlc1mNTs7q1qtFibhDYuLiwOKtDMSbwAAAERa62E60qmj4ROJhKampsLTLJu1JuJRQOINAACAyGstN/E8LzxMR9JpSblEjTcAAABw1tqVm2QymbDcpJGES1KhUBhgpO2ReAMAACDy2pWbxONxeZ4XHqbTnGwXi8VBhLkuEm8AAAAMhfW6m5hZeF0ikVAikRhgpO2NdOJtZrvN7J4o7moFAADA5jWXmzQO02l0NwmCIDxYZ3V1ddChnmGkE2/n3D7n3N0TExODDgUAAADnqLXcxMzC1e3m7iYzMzOanp4ecLRnGunEGwAAAKOlUW7inJOZKZ1On1Zu4pxTPp/X2NjYoEM9A4k3AAAAhoqZqVqthuUmZhZ2NwmCIJKtBCUSbwAAAAyRduUmjU2WjXKTcrmseDw+4EjPROINAACAodK8wbI58c5kMjIzlUoljowHAAAAzlUsFgvLTSQplUqdVm6STqdPay8YFdFrcAgAAACso7ncpHnVOwgCTU1NaXl5WZlMZtBhnoHEGwAAAEOnudwkFosplUqpVCopnU4rFovJ87xBh3gGEm8AAAAMnVjsVMV0tVoNE29JymazisfjlJoAAAAAW6FR591cbpJOp+WcUzqdpqsJAAAAsFXi8fgZdd5mpnw+r0QieuvLJN4AAAAYSq3dTTzPC1fBoyh6/ysAAAAAdKG13CQej4e13lHEijcAAACGVqOWu7ncpFKpqFKpDDiyM5F4AwAAYGjFYjE558LykiivelNqAgAAgKHW3NPb8zzF4/Gw3WCURC8iAAAAoEvNp1g2RLGHt0TiDQAAgCEXj8fDFW8zCzddRg2JNwAAAEZCo61gVJF4AwAAYKjFYrHTDtOJKhJvAAAADL3mDZZRReINAACAodfoYhLlchMSbwAAAAy91lMso4jEGwAAACOh+RTLKCLxBgAAwEhonGIZ1XITEm8AAACMhKiXm5B4AwAAYGTE4/FIHp4jkXgDAABghDS6m7DiDQAAAJynEoMOAAAAANgqsVhMyWRy0GG0xYo3AAAA0Ack3gAAAEAfRD7xNrPLzexLZvZgy/M5M3vGzD44qNgAAACAbvU08TazL5vZMTN7ruX5m83sRTM7aGafXu8ezrkfOefuavPSb0h6YCvjBQAAAHql15sr75X0vyT938YTZhaX9HuS3i/psKSnzOyrkuKSPt8y/lecc8dab2pmuyT9UFK6N2EDAAAAW6unibdz7kkzu7Tl6eslHXTO/UiSzOx+SR9yzn1eUrdlIz8jKSfpbZKKZrbfOVdrvsDM7pZ0tyRdfPHFZ/0ZAAAAgK0wiBrvnZIONf18uP5cW2Y2bWZ/KOmdZvYZSXLOfdY5968l/ZmkP2pNuuvX3OOcu845d93MzMzWfgIAAABgkwbRx7vdGZ4djxZyzs1L+rUOr927RTEBAAAAPTWIFe/Dki5q+vlCSa8PIA4AAACgbwaReD8l6S1mdpmZJSV9TNJXBxAHAAAA0De9bid4n6RvS7rSzA6b2V3OuUDSJyU9LukFSQ84557vZRwAAADAoPW6q8nHOzy/X9L+Xr63JJnZbkm7r7jiil6/FQAAALCuyJ9ceS6cc/ucc3dPTEwMOhQAAACc58y5jg1FRoaZHZf0SpeXT0ha3MJrt0ma6/J+o2Izv8N+6Ec8W/0e53q/sxm/2THdXt/tdcyVwWOu9GYMc+XcRWmu9CuWrXyfrbgXc6V7lzjn2veyds7x1fQl6Z6tvFbS04P+TFH+HY5KPFv9Hud6v7MZv9kx3V6/ieuYK+dBPMyVLbmOuXIexLKV77MV92KubM3XSJeanKV9Pbr2fBK130s/4tnq9zjX+53N+M2O6fb6qP37ECVR+90wV3ozhrly7qL0u+lXLFv5PltxL+bKFjgvSk0Gycyeds5dN+g4gKhjrgDdYa4A3YniXGHFu/fuGXQAwJBgrgDdYa4A3YncXGHFGwAAAOgDVrwBAACAPiDxBgAAAPqAxBsAAADoAxLvATKzy83sS2b24KBjAaLEzHJm9n/M7I/M7BcHHQ8QVfwdAbpjZh+u/0152Mw+MKg4SLzPkpl92cyOmdlzLc/fbGYvmtlBM/v0evdwzv3IOXdXbyMFomGTc+Z2SQ86535V0m19DxYYoM3MFf6O4Hy2ybmyt/435ROSfn4A4Uoi8T4X90q6ufkJM4tL+j1Jt0h6m6SPm9nbzOztZva1lq/Z/ocMDNS96nLOSLpQ0qH6ZdU+xghEwb3qfq4A57N7tfm58pv11wciMag3HnbOuSfN7NKWp6+XdNA59yNJMrP7JX3IOfd5SR/sb4RAtGxmzkg6rFPJ9/fFAgHOM5ucKz/sb3RAdGxmrpjZC5J+W9Kjzrm/6WugTfiDtrV26p9W6aRTycPOTheb2bSZ/aGkd5rZZ3odHBBBnebMQ5LuMLM/0BAfDQxsobZzhb8jwBk6/V35lKRdku40s18bRGASK95bzdo81/GEIufcvKSB/cMHIqDtnHHOrUr65X4HA0RYp7nC3xHgdJ3myhclfbHfwbRixXtrHZZ0UdPPF0p6fUCxAMOAOQN0h7kCdCfSc4XEe2s9JektZnaZmSUlfUzSVwccExBlzBmgO8wVoDuRnisk3mfJzO6T9G1JV5rZYTO7yzkXSPqkpMclvSDpAefc84OME4gK5gzQHeYK0J1hnCvmXMcSZAAAAABbhBVvAAAAoA9IvAEAAIA+IPEGAAAA+oDEGwAAAOgDEm8AAACgD0i8AQAAgD4g8QaAiDOzqpl9v+nr04OOSTotrjeZ2Xfrj181s+NNsV7aMuY9ZvbtlucSZvaGmV1gZl8ws6Nm9m/6+VkAoB8Sgw4AALChonPuHVt5QzNL1A+aOBfNcb2rft9PSLrOOffJDmOelHShmV3qnPtx/bldkp5zzh2R9G/NbPUc4wKASGLFGwCGlJn92Mx+y8z+xsx+YGY/WX8+Z2ZfNrOnzOxvzexD9ec/YWZ7zGyfpK+bWdbMHjCzZ83sz+ur1teZ2V1m9rtN7/OrZvY7ZxHfm83sMTN7xsz+ysx+0jlXk7RH0s83XfoxSfed0y8DAIYAiTcARF+mpdSkOWmdc85dI+kPJDXKMz4r6ZvOuZ+W9DOSvmBmufprN0j6F86590r6dUknnXNXS/qcpGvr19wv6TYz8+o//7KkPzmLuO+R9Cnn3LX12H6//vx9OpVsy8xSkm6V9JWzuD8ADBVKTQAg+tYrNXmo/v0ZSbfXH39ApxLnRiKelnRx/fETzrkT9cc3SvqfkuSce87Mnq0/XjWzb0r6oJm9IMlzzv1gMwGbWV7SP5O0x8waT6fq93/KzPJmdqWkt0r6jnPu5GbuDwDDiMQbAIZbuf69qn/6b7pJusM592LzhWb2LknN9dOmzv5Y0r+X9Pc6u9XumKSFdf6H4X6dWvV+qygzAXCeoNQEAEbP45I+ZfWlZjN7Z4fr/lrSz9WveZuktzdecM59V9JFkn5BZ5EYO+eWJL1sZh+t39/M7KeaLrlP0i9Jeq+kr272/gAwjEi8ASD6Wmu8f3uD6z8nyZP0rJk9V/+5nd+XNFMvMfkNSc9KWmx6/QFJ/+8cykB+UdJdZvZ3kp6X9KHGC865H0pa06ladLqYADgvmHNu0DEAAAbAzOI6Vb9dMrM3Szog6Secc3799a9J+l3n3IEO41ecc/kexPWfJa045/77Vt8bAAaJFW8AOH9lJf11fUX6LyT9K+ecb2YFM3tJpzZ1tk2665YaB+hsVUBm9gWdKkFhFRzAyGHFGwAAAOgDVrwBAACAPiDxBgAAAPqAxBsAAADoAxJvAAAAoA9IvAEAAIA+IPEGAAAA+uD/A4PVuSbH7gwnAAAAAElFTkSuQmCC\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": {}, "outputs": [ { "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": {}, "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": "3.7.0" }, "nbsphinx": { "orphan": true } }, "nbformat": 4, "nbformat_minor": 4 }