{ "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://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.15?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/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", ")\n", "from gammapy.cube.simulate import simulate_dataset\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": [], "source": [ "irfs = load_cta_irfs(\n", " \"$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits\"\n", ")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SkyModel\n", "\n", " name value error unit min max frozen\n", "--------- --------- ----- -------------- ---------- --------- ------\n", " lon_0 0.000e+00 nan deg nan nan False\n", " lat_0 0.000e+00 nan deg -9.000e+01 9.000e+01 False\n", " sigma 2.000e-01 nan deg 0.000e+00 nan False\n", " e 0.000e+00 nan 0.000e+00 1.000e+00 True\n", " phi 0.000e+00 nan deg nan nan True\n", " index 2.000e+00 nan nan nan False\n", "amplitude 3.000e-12 nan cm-2 s-1 TeV-1 nan nan False\n", "reference 1.000e+00 nan TeV nan nan True\n", " lambda_ 5.000e-02 nan TeV-1 nan nan False\n", " alpha 1.000e+00 nan nan nan True\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\n", ")\n", "print(sky_model_simu)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Define map geometry\n", "axis = MapAxis.from_edges(\n", " np.logspace(-1, 2, 30), unit=\"TeV\", name=\"energy\", interp=\"log\"\n", ")\n", "geom = WcsGeom.create(\n", " skydir=(0, 0), binsz=0.05, width=(2, 2), coordsys=\"GAL\", axes=[axis]\n", ")\n", "\n", "# Define some observation parameters\n", "pointing = SkyCoord(0 * u.deg, 0 * u.deg, frame=\"galactic\")\n", "\n", "\n", "dataset = simulate_dataset(\n", " sky_model_simu, geom, pointing, irfs, livetime=20 * u.h, random_state=42\n", ")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dataset.counts.sum_over_axes().plot(add_cbar=True);" ] }, { "cell_type": "code", "execution_count": 8, "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": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SkyModels\n", "\n", "Component 0: SkyModel\n", "\n", " name value error unit min max frozen\n", "--------- --------- ----- -------------- ---------- --------- ------\n", " lon_0 0.000e+00 nan deg nan nan True\n", " lat_0 0.000e+00 nan deg -9.000e+01 9.000e+01 True\n", " sigma 2.000e-01 nan deg 5.000e-02 1.000e+00 True\n", " e 0.000e+00 nan 0.000e+00 1.000e+00 True\n", " phi 0.000e+00 nan deg nan nan True\n", " index 2.000e+00 nan 1.000e+00 5.000e+00 False\n", "amplitude 3.200e-12 nan cm-2 s-1 TeV-1 3.000e-14 3.000e-10 False\n", "reference 1.000e+00 nan TeV nan nan True\n", " lambda_ 5.000e-02 nan TeV-1 1.000e-03 1.000e+00 False\n", " alpha 1.000e+00 nan nan nan True\n", "\n", "\t\n", "\n", "\n", "stat = -939572.3185210546\n" ] } ], "source": [ "# Define the free parameters and min, max values\n", "\n", "dataset.parameters[\"sigma\"].frozen = True\n", "dataset.parameters[\"lon_0\"].frozen = True\n", "dataset.parameters[\"lat_0\"].frozen = True\n", "dataset.parameters[\"amplitude\"].frozen = False\n", "dataset.parameters[\"index\"].frozen = False\n", "dataset.parameters[\"lambda_\"].frozen = False\n", "\n", "\n", "dataset.background_model.parameters[\"norm\"].frozen = True\n", "dataset.background_model.parameters[\"tilt\"].frozen = True\n", "\n", "dataset.background_model.parameters[\"norm\"].min = 0.5\n", "dataset.background_model.parameters[\"norm\"].max = 2\n", "\n", "dataset.parameters[\"index\"].min = 1\n", "dataset.parameters[\"index\"].max = 5\n", "dataset.parameters[\"lambda_\"].min = 1e-3\n", "dataset.parameters[\"lambda_\"].max = 1\n", "\n", "dataset.parameters[\"amplitude\"].min = (\n", " 0.01 * dataset.parameters[\"amplitude\"].value\n", ")\n", "dataset.parameters[\"amplitude\"].max = (\n", " 100 * dataset.parameters[\"amplitude\"].value\n", ")\n", "\n", "dataset.parameters[\"sigma\"].min = 0.05\n", "dataset.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", "dataset.parameters[\"index\"].value = 2.0\n", "dataset.parameters[\"amplitude\"].value = 3.2e-12\n", "dataset.parameters[\"lambda_\"].value = 0.05\n", "\n", "print(dataset.models)\n", "print(\"stat =\", dataset.stat_sum())" ] }, { "cell_type": "code", "execution_count": 10, "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 20.7 s, sys: 532 ms, total: 21.2 s\n", "Wall time: 22.6 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": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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IWL3sJB6mXq9Tr9eVVtLFH+fo6IhSqcSHH36ovId4PK5i+cO7Upl/mLRoBAIBzs7O+MEPfqAWI1nWarPZ2NnZGVmkpFRGIBBA0zT8fr/6HNFolLOzs5EeBE3T2N7eVuGyxcXFa11V2eAnv69SqcTR0RE2m41QKITVaqVQKOByubhz5w7lcpmtrS2azSZTU1Mkk0m+//3vMz8/P3E3J29zOp1MTU0xOzurciTJZFI1tsmLZxIzMzO43W52dnZ49OgRwWCQg4ODG5Wtms1mpqen6XQ65PN5YrHYyHcy3I8yfF7ICjV5sfd6PRKJhDL8uVyOJ0+ecHR0xOLi4sTf2+12E4/Hrz1Gg5vR7/ep1WoEAgGEEBSLRRWOkTmzSeXgr5tsNovJZFKRAFlGLvNv6XR6RLOt3+9TLBYJhUKUSiXK5TKxWIxkMqlKYp1OJzMzM9TrdbV+3YZ3ZBgIzhf0iztx6d71+31V3gnnIYaf/OQnZDIZXC6XajKTi0iv11MLaLVaVTH1SCSiavCHDUStVpuo0trr9SgUCqqxZhiz2Uyv16Pdbquu7Xa7TavVUp2a6XSau3fvcnZ2pha109NTgsGg6rA+PDyk2Wy+kMREJpMZqWCSGk4yZiqJx+Ok02ngPPQ0NzeHx+NR3sBlhkheuC6Xi9XV1ZH75HHruk673abf76vfTV4gMoSzvb2Nw+FgaWlJGZdms3njzxmPx8nn85ydnU3sR5Fe0zAul4tKpUKhUMBsNo90xNdqNaanp0mlUuzt7bG8vDwSbtI0jUqlgtVqJRwO0+/3aTabV+aYPq9Uq1WSySQLCwvK0ywWizQaDbrdLtPT0zcqB5WbiVgshsVioVgsKs2w3d1der3eC4tTXketViOfz9Nut+n1eui6Tr/fJxwOY7FYaLVa1Go15ubmcLlcRKNRTk5OaDabJBIJGo0GxWIRXdeJxWJomka5XCaRSKhmzqOjIxKJBIFAAJPJRC6XU5WIr5sbGQghhEPX9faF28K6rucve877xMWTRNM0UqkUu7u7ZLNZ4Dz+f3Z2RqlUUmWmjx494tmzZ6TTaTV4J5/Pq9KzcrmsdgYmk4lAIEAulyOVSqnaZ6mmOkyz2WR7extN0/jyl788ttuU5W2y9FQIQSAQwOPx4Pf7OTk54fd///fpdrtUKhVarRarq6ucnp6qmd3tdptaraZOtFqtNrYrt9lsY3X9hUIBj8fD0tKSGlA0NzdHNBpVTYUXq76EEMprkfpQc3NzYzv6TqdDt9ulXq+rHILVaqXdbmO325VnMBxug3NF2Vwup76nRqOB2WxmZWVlpJxXLsDDSGmTi1itViKRiAq9DX/3Mr9w8XdzuVwUCgVKpZK6eOEzYcREIsHDhw/Z2NhQFVzDCf/t7W2Oj4/xer1kMhlyuRwffvjhG9nl3gbyuxr+nWVOa3hDJM9lTdNoNptkMhk0TePo6IgPPviAQqHA0dGRKnFuNpvcv3//2p4Z+XvL88Ln86nwoww7NZvNVwr56brOYDCgXC5TKBSo1+tYLBYVJpbzWWToVkYd5CYxGo2yu7vLycmJWjPksTocDvx+P6VSiWazyerqqirLdjgcdDodtUGsVqtvz0AAPxBC/Ge6rn8fQAjx7wF/A1h/7Uf0Ftja2lI7Ub/fz9zcHMvLy7TbbSwWi+odKJfL3Llzh/n5eTweD3a7nXA4TC6XIx6PY7PZyOVyat6z3AnIk2N6epp2u006nVa7a2BkNyQlvGW/wFUhn8uSxlNTU3z00Ufcu3ePfr/P/v4+NpuNr3/963zyySdsbGwoVdV4PE6r1WJ3dxchhFqMNE2j1+vhdrvVLq5Wq9HpdJiZmcFms5FKpXA4HMTjccxm840SsD6fT/V3DC8SuVyO4+NjZfyk93T//n3Vq7G5uakWF7vdTiQSwel0ksvlVFe4pmnMzc0RCoWwWCx0u110XafZbLK3tzeWgwHGEtaSWCw2otcEn4UtrkpUa5o28tvIMKPL5cJut7O8vMzOzg5bW1v4/X7liQSDQer1OoeHh6q8UYZIXpTBYMDh4SH9fh8hBHNzc5fmzG4LWSJ98bjg3GCvrq7S7/c5Pj4eEY1cXFzk/v377O3tcXBwQKVSYWpqitXVVVV0cHR0NKI1dhFd1ymXy5hMJuXxdrtdTk9PSafTWK1Wut0uGxsbE4sRrqNcLnNwcDASebDb7SQSiYlaahJ57lutVs7OzrDb7aoE/dGjR+p58lyamppCCEEqlcLj8eBwOPjwww85ODhgY2ODSCRCs9lkf3//VqQ6bmog/hzwW0KIbwMzQAj4U6/9aN4Sfr9f7QQKhYLKE2iaxszMDNFolHK5jN/vZ21tbcTtj8Vi5PN5kskkNpuNXq/HwsKCqiKCzwyAzWZjbW2NXq9HrVZjMBio5jLJ4eGhSi5fZRzkCTMpBNFqtbDb7Xi9XnRdZ2pqitPTUxYWFlSHtM1mw2azkc/nSafTmM1m7t27p3bYuq7z5MkTUqkUU1NT9Pt9njx5QjqdVvFcWT3xIt3PUg8qm82qap9qtUq1WmVqakoZUzkTIxgMEo/H0TSNbDZLq9VC13XVKCe7yh88eDBmoE5OTlQJa7FYxGKxsLa2poyJrus8ffqUYrE40UDIEtxhjo+PVS7pIvKiliXCEmkg5Pv6fD4WFhbGwnVw7oE+ffoUm82myoWHDUSz2VQxbLPZzOrq6kQPI5vNqsWo0WiQzWbHEu43RXoCnU5nLNzpdDovNTz1eh2bzaY6h4vFIslkkm63S7FYZG9vj0QioUo4z87OMJvNBINB/H4/4XCYfD6P1WpVHrrM08iqnlgshtlsVrLxZrMZk8lEvV5na2uLeDyujlmKNGqaxvz8vOo7gvMFf2FhgWKxyMnJCbquq+O66GHIsmq5w5fl5td5ItLznJubo1qtcnp6Cpx7VdFodOI5aDablRchhUHl+56cnPD48WNVin0beYgbGQhd1x8LIf4X4B8BNeDndV0/ueZp7w3DjV3T09McHh6q0IJMLJXLZcxm85gbZ7VamZ6e5uzsjEajgdvtVotwo9FA07SxeKls9rpIo9FQOkFXxVjloi6PVwrpyQshm83i9/vp9Xpsb2/TaDTY399ne3ubcrlMv9/H6/WSSqV4+vQpwWCQX/qlXxorb43H4xweHlIul8nlchwcHBCPxwmFQsrVfdHqCdlYN7yztNlsY9pIXq+XRqNBKpWi3+8zMzPD1NQUdrudVquF0+mk3++zu7uL2+3m6OhIeTFy5y/LbL1eL7FYjLOzM4ARgyZFBoery+TuU178w0QiEex2+9hz4DxcJWd8DD+v0WiocmNJOBwmHA4zGAzodrsAymOTVWq9Xo/Dw8ORhV1Wp3m9XsrlMsVicUwJdzAYkMlk1K5bSpskEomX6rodrgS6iNVq5eHDhxMXpkajgdfrVUUTx8fHxONx1TyZTqfx+XysrKzQ7XZpNpssLCzQarXQNI3Z2VkGgwHT09MjRjAWi9Futzk7O1MGpFAo4PV61UIpCyU+/PDDEQM7Pz+vwqL5fJ7Dw0OCwaBKBsvSaa/XS61WY39/n5WVlZF8UyaTUZ7gi/QfyPBRIBBgb28Pm83G9PS0qvi7jOXlZRWmK5fL6nM7HA6cTifT09OYzea3l6QWQvxDYAV4xHlY6XeFEH9H1/XfeO1H9JZxuVxKCkKi67pycyf9CDMzM2OxeplEdjqdN44hy7DFVSGFfr/P6emp6pGQO2QpJz4YDNjZ2WF9fZ2dnR263S4LCwvMzs6qnaxka2tLqbzK1xzehYdCIc7Oztjc3CSZTBIMBvn4449HduAvelKazWY++OAD1e9gs9ku/X6Wlpaw2WxKAFAihFAXjAwPyFh3sVhUu0SXy8XCwoJS4D07OxtL/AaDQbXblrkIGRqZ1DHtcDgIh8Ps7u7SbDbHNgyTQliy9PWy70PuwOVu/OnTp8RiMYQQHB4e0m63cTgcKtYt5UJkqDASiYzE+TOZDL1eTyU5ZR+KLKgYDmFdROqBSWQHvdQaG/6tarWa6uYd3tBUKhU1b31ubo7T01MKhQL5fJ47d+6g6zp+vx+z2Uyz2VSLs8lkYn19nYODAzXAaXl5eewYpWSMXFx//OMfMxgMRhSQ5cbg4rU0XMbt9/s5PDzEbrezvr5OKpXC5XIxNzdHMBik1WqxsbHBj3/847FjmJ+fp1wuY7PZ0HV9rFhCbhwsFgtWq1XNb3E6nTSbTZrNpjq/biJ1Lz9XIBB4o5L0Nw0xPQH+on5+Fh4IIb4O/O3bO6x3i3q9fiNZC4mu6ySTSaamptSgn5vEf6XUxVWx/FQqxWAwYH5+XjXRyaStrGY6OjqiWq2qEMRllTB2u51SqcTa2ho7Ozvs7u5y7949JW7XbDaZnZ3lj/7oj1ReY3gC3svuWGR46zpk7Nzr9dJqtbDZbDgcDhwOhyoFlP0gkkajoWLvS0tL6hjNZjN2u13N6JC43W4cDgeFQoFwOEy73VZhn0ajMWYg4Lwqa2Njg+985zs4HA6CwaBS6Lz4XXc6Hfr9vvrepNjhVcqv3W4Xq9XK8vKy8vzW19fJ5XK0Wi08Hg/tdhur1crTp08plUqYzWY1wbBareJyuZS3oOs6rVZLhU9lk+VF+v0+R0dH9Pt9VW6bSqVUgcDF39tqtXJ8fEyhUFB6WIVCgVwuR6PRoFKp4Pf76Xa77O7u4nA4lBcH5557LpcjmUwC55VjgUBAlYlfpy8m1QHm5+eJRCJjxvq6pK3FYsHr9aqcYDabVX1P09PTWK1WVlZWlGz98PdUKBRU9dHR0dFYwYUUgxwMBgwGA1qtllIE6Ha76ryB8w2E9CJl39C7wk1DTP+bEMIphJjXdX1L1/UK8Gu3fGzvDHJ3c9ORlNlslkajwQcffMDJyQmFQuFGc5c7nQ42m+3ShVeqjwaDQXZ3d1WCazj22W63mZmZIRwOEwwGr7xI5PwHTdNYWFhgf39fDc05PDykWCyqCoyL87Bflm63y+bmpjrGmzAsByKRoaSLuN1u7t27x2AwGLvQnE7nxORyMBgklUqp3bA0uBeNiSQajTI7O0u9Xlc77EQiQTKZ5MGDByNhnOH8g6ZpbG1t0W63CQQCYyGsfr9PtVpVSr2hUIhgMMjR0RG9Xo9kMqlG2MrHN5tNrFarkpG3WCyq+1aeF4VCgXK5TKlUQghx6XAaXdc5PDwklUrRbDZVX8ewoR2m1+tRrVbZ3d0d8ZzC4TAOhwNN01haWiKfz7O2tsbS0hJ2ux2bzcaTJ0+U7lCtVlNlwHIQ13CD6GXIpLPsen8ZEokE5XJZiT16PB6y2Sy5XE7NgJl03YfDYTqdDp988on6nSRnZ2dks1mVN5HerM/nw2az0W63VZjs5ORE5Rbg/Ly+Lv/4JrlpiOnfBv4WYAOWhBBfAv4nXdf/zG0e3LuAruuUSiUVO7+OVqvF6ekpfr+faDSqBN/ksKGruNh8dRG5YMkO78FgwObmJtPT08oAyQXwJvHm4RK52dlZHA6HqvCQjToybDVpJ/0yJJNJer0e2Wz2tRici8jPP2mH7nK51CS84e8mEomo+nM541sKFU5apIQQfPOb3wTOf5PNzU114Z+dnY2EMWQjpMPh4PT0lFarpTrkJ4n7SQVcuSNdX19XvSyBQEAVTcBnKqCNRgOHw8Hdu3cn/k7SU6xWqxPDocPvvbi4qCq++v2+koC5iCzF1nUdl8tFPB5XUi6FQoGtrS10XVd5hsXFxRGvxePxqIXR6/WObGRkOfgf/MEfqJ6i4TCOw+HAZrMpifuPP/544ue5CTKsVygUiEQirK2tYbfb1SJfr9dZXl5GCEGr1aJcLqt8jOxJmJmZGclFeb1e5b1fFj7qdDo8e/ZsxEvu9/scHBywtbWlPDabzaYq/uQ5Ic/HWq1Gt9t9bdfmJG7qy/yPwMfAtwF0Xf+JEOJKky2ESAC/DcQADfhNXdd//cJjBPDrwL8JNIH/RNf1Hz2/75ef32cG/oGu63/zhsf6WpEiWzdZzDRN4+DgAIvFohKLwWBQnVTXNT11Op0rk9Ny8avX67hcLtbX1zk9PSWTyaDrOolEQlUw3cSYmc1mPB4P5XJZJYmTySR7e3tYrVbm5+dfSUr4YhJXSmLLBOCr1qVqBw0AACAASURBVKBf5ODgQC26FouFR48ejSzuw3pJw9+zxWJhdXVVNTVZrVa1MLVarSuPUS6OqVSKXC7H1tYWKysrI96Lx+OhXq+TyWSIRCLMz8+rbuxhZP9IqVTi4OBAeRqylyUYDI5VLfX7fRqNBtPT05cuFDJuXS6XxyYVXqTb7dJutwmFQjSbzZHkZ6fTodlsomkaJycnmM1mPv74YzY3NwHUTlsu/I8ePWJxcXGisZZ5r+HO/k6nw9bWlpJ/kRsT6dnIBHQ+n6fX6+FwOPjyl7+sdvsvo3PVaDQ4OTmhXq+ryj/ZV1QsFtne3mZ7exur1YrNZlNVh7LpbWVlha9+9auUSiXS6bSqFHz69CmFQuFSAyErHO/fvz9y3DJ3ONx0Kue4t1otOp0Od+/eZTAYsLe3h6ZpKuR60wjHi3BTA9HXdb1y4cS6TregD/x3uq7/SAjhBT4RQvy+ruvPhh7zK8Da839fA/4u8DUhhBn4DeCXgBPO+zD+2YXnvhHkGM3hxf34+HgkaXqR4YtYJuOG5zVPQsYrr3Itm82mSu7K3gO5iGcyGRUuummuBFAxX7kApVIput0ui4uLE42DjL9GIpErjUen0+Hp06csLCwQCoXodDqcnJzg9/tZXFzk008/VZUmrwNZ0ROJRBBCqHjyRZkMQMXxLzLc0DdsTK47RhkukN6f2WweCSn6fD729/ex2+3qdpPJdGleavi9pdjh8CyMYcLhMHa7/drO4ng8TrvdplqtXrnjlEUPDx8+pFarkUwmqdfruN1ufvSjH9Fut1WfjwyFeDwezs7O1Ozyx48f0+v18Pv9l+ZapIGo1WoqPCO1t6RwYyAQwOl0srGxQSgUUiEoODdCcjpbo9Hg2bNnatzvTTdIcpGF87xSOBxWHrU0VIlEglqtptQCZIWa9PZlh7OU09jf3+fOnTvE43GSySQ/+tGP1PtJD00IQaVSYW5ubsyoOZ1OHjx4oHS8ZO7o9PRUCYdK5QeZz/rpT3+K2+0eC2++Dm6cpBZC/DnALIRYA/4r4HtXPUHX9TSQfv7/NSHEBjALDC/y/w7w28+T398XQviFEHFgEdjVdX0fQAjxfz9/7Bs1ELLbeDhBJxNxspz1Ii6Xa8SSy91IPp9Xc5Dv3bs3Fh+/bDCRRM4yaLVaTE1NjcQ85+bmcDgc6jVepOknEAioROPc3ByJRIJKpXLpIiIvBhmbvoxqtYqu68oonJycIIRgfn4es9msdmhSwOwqOp0O5XKZVqulDKTVasXj8ahk7NHRES6Xi0QiQbPZJJvNqg5siayYuiy3MIzdbsdsNtNoNK71HmVVDZzvojOZDB6PRyWmK5UK7XZbyX7c5L1lSEOWNEvdIDn/YpibdNDKsI38niYZp36/Tz6fJxgMqjG6R0dHFAoFWq0WBwcHTE9Pq2Yw2Y8yNTVFp9NRkva1Wg2LxUK5XL60DNrlcqk5HvJ8PT095fDwEI/HQygUotfrkclkaLfbrK+vj3zOaDRKOBxmf39fhcSOj4+JRqPKaEmD7XA4VDHHMMfHx5TLZaLRqMoHyOPIZrPE43F0XVchNnnuDRcaSIMajUaZnp5ma2uLvb091tbWlMw9nBv7ra0t9vf3WVxcxOl0XupdDM+ZkVWGsmfmS1/6klI8iMfjfPrpp3S7Xb75zW/eyuCgmxqI/xL4q0AH+CfA/wf89Zu+iRBiEfgy8McX7poFjof+Pnl+26Tbv3bJa38L+BYwNif5VdA0Tc1cGF4gms2mqs1+EV0fi8Wimr0KhcKYauplo03hPBn4+PFjnj17RjgcZnl5eaw57WXj+RaLhampKTU03e/3X+qByDJSmaOQ1S2TqNVqmM1m+v0+e3t71Go1Zmdn1Y4yFApRLBbZ3d0dUWUNBoMjBlYmtWXoRz5fTqGTCCHUNDr5HUpjOsxVyeeLuN3uGz9WEo/HKRaLHB4eqoqwbDaL1Wq98fkik+TFYlH1RjidTtVg+DJjTYU4V9rd2NhQDWoXkfkZmfw3mUwEg0GKxSL7+/uq50carEwmMyLPLiuZfD4f09PTSj79stCH1+tV4SiZhPf7/QwGg5HBUfF4fKIR9Pv93Lt3j06nQyqVUpuCVqvFd7/7XeA8vxSLxfB6vdhsNorFIt1uFyGEyofl8/mRxVUm1xcWFuh2u2NyIdL7k70tMscE59GDra0ttra2WFxcxGKxqPxPJBIhm82iaZrKawwGA1KplKpgjEQiYxtP2V8jdc8qlQqDwUB9Vw6H49ZGld60iqnJuYH4qy/6BkIID/D/Av+1ruvVi3dPersrbp90bL8J/CbARx999GJT5p8j5xrLjtFGo6G0YWSiViI7aF9E90Q2gsG5gcnlchMNxGUlrvl8nmazSTgcZmlp6bUrfoZCIcrlsupmvgzZZLe2tkaxWFQNPpNCMHJnKYSgUChgt9tHPrPX61U7T8lgMKBUKrG0tKTCKvv7+2iapiQ3hmm1Wkq0z+FwqOMwm81Kw+kiLpfr0uTzpMdKXSCTyaRKYOWiGAgExnbIZrOZRCLB/v4+JycnBAIBVQTwImXBLpeLfD6P1+tldXUVk8nEYDAgm80SjUZfqhRSls5ub2+rDuKLBIPBkU1KKBQik8mQTqe5c+cOa2trbGxsqOqh6enpkUVSGp+7d++ysbFBMpnk/v37qjN5GCm7Igs7Wq0WX/va19RcEfm9X1W4IRdqv9/P0tKSGofrdrux2+1qgyEXeNltLf++e/fuWK5NXq8vohAwfDz37t1jb29v5DsOhUIkEgkODg5U2XylUuH4+Jhut6sGBtXrdR48eDD23sN9HtPT06oMPZFIKGWGN56DEEL8LlfkGq6rYhJCWDk3Dv+Xruv/dMJDToDhrcwckOK8WmrS7beCLB+USJd0WC5bUq1WcbvdIxdotVodq0ix2+0TF/JIJMLBwYFqWpJcVuIqy++keNxlSb9XQTZAnZ2d0W63GQwGamgRnC8ssvPUZrPh9Xpxu90Ui0Xy+fyY5yaVLKV4oNRvGv5scsc/zGAwYHd3l4ODA1Uc0Gg0WF5enhgSuUrmwel0XmogpBrsdb0pbrcbXdc5PT1VyVG5e5S73GKxqBr6JIFAQHULy9j0i3p4Mjk7vHjF43FKpdJLexGDwQCXy8XDhw/Vb3uR4e+k1+uphcxisXD37l3VVNbtdsc8TRkGlbF86bF897vfxev1jsnU+Hw+lSSWQ5rkRko2Bsru/eH+m8twOp2srKzQ6/UIBoPcu3dPydEXi0U1sMflcjEYDPB4PBP7O14Vu93O3bt3VZe31F6C83Dws2fP2NraAj4ra/V4PDSbTTY2Ntjf3x9Z7FutFtVqlTt37oydR7qu8+mnn96ob+RluG4b8ree//fPcl6N9H8+//s/BJJXPfF5hdI/BDZ0Xb+sqe6fAX/5eY7ha0BF1/W0ECIHrD2vlDoF/gPO9aBuBY/HowyEVGG82DUKn1WMDC/8tVpNhUmGpRoKhQL9fn/MlZcxfznIRlYhXIyXS+RCKaXHb6M+WobRzs7O1AAjWa8uhKBWq7GxscFgMCAej6tO0eE8wvAOTL6G1+tVqqU3wWw2s7a2pnZZ8Fnz1IvicDhGQlCS4UT1dQbC4/FgNptVQUIoFGJubk6dF4VCgcPDQ87OzsaM5MLCApFIhLOzs7ENxXUMhxGGQxuy1FVWrU1NTSntoevOi0qlwt7enjJs09PTPHz4UOUCJi2S29vbSlJ+YWFBLdLyGrmIrHCS4Q4Z+nj69CnRaBRN07h79y4Wi4VGo6EEC7e3t3E6nXz5y18eOY5SqUSlUqHb7apw3XU0Gg0ajYYq85b9MnL6oqx2kknnVzUOcv6H9EhdLpdSb56UY3A4HNy/f195zvIcg8/yl3/yJ39CIpFQ54z07mU5r6ZpavNjNpvx+Xw36ht5Ga48a3Vd/1cAQoi/ruv6zw/d9btCiD+85rV/FvjzwGMhxE+e3/ZXgPnnr/33gH/OeYnrLudlrn/h+X19IcRf5jzXYQZ+S9f1py/ywV6ETqejDESj0VBDgu7duzey8B0cHHB0dITFYlG6TLJD9M6dOyNuoRSKkyfNMFIJVeop3b17V5WaSmRVk6yiuqla6ssyrIV0sVqm0+lwcHCgqmokMo9QqVRGFnFZn35VaOAyTCbTRLmKF0Ua3263O/K9ycl3wyNj+/0+JycnaJqG2WxmZmYGq9WKxWLhww8/VM+9ePGFQiHy+fxI810mk8HpdCrxtklSEZMolUqqy1iGV4QQ7O3tqRAToBKfmUxmpCv57t27Y7tsOY+gXq+rmd1SRfT4+JhSqaQM/kVkgn5lZWUszCqRZcAyTCS9EmmcpUcRiURwu91sb2+roTftdhuTyYTP56Ner7OwsDBW9CA7tGWy/jrdr1arRTqdVsN5NE1TRnH4NSUy5h+LxW7slctrstlsqvkUF5HFBJed/1INYBJCnMuDy8mKgLr+Zff87u7uiDaW7Mx+3cYBbp6kjgghloeqipaAK38tXde/w+RcwvBjdOAvXXLfP+fcgNw6Dx48GH5f1R2aTCbVBS6lgfv9PmazmZOTE1Xyt7a2NhYznJubU1UY+XxeXTBwfpI1m01mZmao1Wo0Gg018N5isdDv95ULCp+VKN5GY9kwl8Vc7Xa7GpQ+fCHJztB8Pj9iIOT4xLeJ9A7a7fbYbIqLiep8Pq/mBHQ6HXq9ngp/3SRPIT0VOZTpMpXdq8jn82oOudvtJhqN0mw2OTg4YHt7G7PZPLIYmc1mWq0WQgjS6bTqhZANZcObHjgPl62tranw1PT0NHt7eyqcOuypaJrGs2fPyOVyqg/D7XYzMzODpmns7++PLFDDUi/SEx3uR/n5n/952u22GpgkPQvpdW1sbKjKHomMx8/MzFAoFPjjP/5jtZDL38TtdqtCAlmKCp+VgGezWQaDAXfu3MHtdtPtdpWopcVioVarkcvlKJVKI0rGl6Hruiq4sNlsqgdGenKDwYB6vc7+/r4yvi9Cu92mUqnw0UcfjVQiyv4qOepWdp17PB76/b7aUNwGNzUQ/w3wbSGEnBK/CPznt3JEb5ler6caUzKZDAcHB/j9fp48eUK1WuUb3/gGS0tLfPrppySTSb7xjW9cemJJaYFut0sikVDxb03TyOVy9Pt9PB4PJpNJVWqk02kKhQLZbJZYLKZ2UBdlwd80wz0Cw4RCIdLpNE+ffubgdbvdiTIYb5LhSqaLi7XsqIbziz6TyWCz2VhdXeXs7Iz9/X3a7baSOZdS1zabDbfbTSwWU0ZneASp3LE3Gg21kbjJrk7u8qUI3/Bn6Pf7nJ2dKfnvYbxerxLwq1Qq6nyRGkMOh0N5g3JAVa1WU4J07XabRqOhhAGHj0cKy8l54plMRslK9/t99V5WqxW/36/CId1ulydPnhCJRNRCLfM2gUBgLO8E5xuQWq024iHInb7L5eL4+Fh5QTLsJicPytG0Ho+H6elpZmdnlYBeNpvF4/GozYrdbh8JxclckSw/lX0Ul3F0dEStVmNxgogjoIaCyfklN0WKSEqvamlpaSwk2el0VJWWTKLfhsdwkZtWMf3L5/0Pd5/ftKnr+mQ5yPeQZrNJpVJRU6uk6xuNRsnn8+RyOU5PT7l3757yKKTUbj6fp16vqx3URWRPwdra2sj9iUSCzc1N9vf36Xa7PHr0SA1U39raIhaLqVkE8nkvU1Vx20QiETVJTuJ2u9+o4uQkpC7RZYnqfD7PJ598QqvVIplMEo/H1Q5ddsXKnaHsOxkMBqTTaeXNyT4MGBVc0zSNn/zkJ7jdbtbX16/93aS89SSvKxqNEo1G1QLhdruV9IKmadTrddrttpqfLe+bdC4OJ5Hla+/s7IyNwZUx9QcPHqjfUTbNAdy5c+fS5kG5y5VidzdhamqKUqmkdKu63S7f+9731GdwOBz86q/+6sjrSQkcWTYK59IXstpPNrNdp4HmcrlYXFxkf39feVRSYUDmEgClRhuLxa6VtvB6vSpicN0ins/nOT09Vb0vw7mHYcLhMJlMhlarpZrt3gQvUiv3r3HuOViAD59rg/z2rRzVG0TTNL797W+rKgc5ZU3q1szNzalSSykD3mq1aDQafPWrX1XjCyctRHB+8k/6QWX1gqzblmEqmYB62VLGN83wMJd3jeHmwWHkYi8b+eLxOA8fPlTf98rKCul0WjVE9Xo9tSM8PT3l6OhI1bHL15IltxaLhXq9rkT/Dg4OJspbnJ2dqYFUcmG8KiwnZwBMQkrAdzodtQuXg5aGY91yPon0ROUs9cePH/PgwQMlky67toerYrxeLw8ePFD3TULTNPL5PH6/f2LSXHo7w+EsOc0vn88ryQ5ZTffw4UM1N2NS/s3pdKpqrmGDIRve7Hb7jSp7pMZVJpNR5e3y2GRS/eTkBI/Hc6OpbVLwr9lsXll91el01IjZ9fWrh3M6HA6l1/Si0+9ehZuK9f0jzudB/ASQGR+dc62l9x7ZXyAHiMvYpNTx39zcxOFwsLOzA6Dqs2UD3IsOzZFIgbWdnR0ajYZK2MlmI4NXQ4qwHRwcqNusViszMzNqVkImk2F5eXms4mS4hLPT6VCv15WSaj6fZ3V1lUqlQj6fp1wuEwwG1ayJYrFIq9ViZmaGVCrF3t4es7OzKkQ0LNUihy9JrZ9JaJpGqVRSswOkQRFCqHp/q9VKvV5ndnZWNX/JEly5oMi8wbAhkotUNptlZWVF5Wcmjc0UQtDv90mn0xMbCAeDAf1+f6zHR77P7u7uRIM9NzfH+vq6ko9oNpvMz8/z4MGDG++UpbEOBoNqFrucCX0T4vG4yhkMBgPlMe3t7akKwknNhZOQ36+UKJmEruscHBwo+Y2bIIs33pT3ADf3ID4C7usXRc8/B5hMJj766CN1MXi9Xg4ODtQYQxnHvChxIAW7XhV5AkkDUa1WMZlMbz3J+3nA7/erIgCJnM+wuLioZmtcl/wfjl273W41enN+fh4hBKenp2o2hdvtVt5JPB5XM5GfPXs2kq+QFWAyRHnV710ul5Vw3WUlpnNzc2o3Ksdy7u3tcXh4qPpF6vU6DoeDarVKv9+n1WoxGAyYmppSWlyLi4tqoT48PByp0JJVS1LBddJCJUNvw7RaLba2thBCsLa2NpJLkfLi9+/fx263k81mVfXXyy6ENpvtpTdt8NmYTzk7vNVqEQ6Hb6wbZrVaVV5lkrGE802CrBK7aXXi2wgxv8jAoBjPtZU+b1zsorxz5w4rKys8fvwYIQR37959qZLNm2A2m3E4HGoRq1arKnFt8Gr4fD4++OCDkdvS6bSSNqjX60Sj0RdK/svErdQQkto/UihQ9o7IRj2psirnacN53mZ6elqVTErplssoFAqqQfEygsEgmUyG7e1tVlZWlMT29773PX7v936PcDjM6empmqcM5zvR2dlZfvEXf5GTkxPK5bLS+zo9PWUwGIy9ZyQSUZ/5pkgD9+DBg7HnLSws8PTpU5LJJLFYTG3IbtIYd9v4fD7m5+fJ5XI3Ci0N4/V6lUKDpNfrqYFOUk3hRYQ13wY3NRBh4JkQ4k8412MCru+kfp+xWCwqwXhbxkHidrupVCpKkO429d2/6MTjcZrNJuVymXA4fOOwgUQIoeTK4dy7iEajbGxsqIS9rFar1Wo4HA4sFsvEzudIJKKqqSYtiLKTuVqtXlsyKePlOzs77OzsqHyW1WpF0zTS6bSaCT01NaXO6X6/z8bGBmazWSmywnlc/t69ezeahHgd3W4Xi8Uy0ahYrVY1bElKU7zoYnybRCKRl/JGPB4P+XyeVCqFyWRSxlcy3DX+LvMi8yC+cLypXYzH46FQKKhB5m+7AujzztLS0itp10gNISnxvbCwwJMnT8jn81gsFiXlcLE/5GJI0ufz4XA4lFEZZriREm6m0Cu71jOZDIPBQCkJy1zMzs4ODx8+HPEKms0m1WqVarWK0+lUulYygX9xYuHL0Ov1rgyjhEIhFZq7Sgb9fcLr9WIymdRv6HQ6VQmuEAKfz/dGcwkvy03LXP/VbR/IFxkZK5+amiIQCLwXJ877zIuMj52EXGA3NzdVKLDZbCr56HA4rMbDZjIZ9XiPx8Pa2praUVYqFdXfMvyby05pn89HIBBQs7hvguwEn4Tdbh97HZnTiMVirK6uqvxJsVhUIatXDbFenMsxidv20t80NpuNDz/8UFVsvYsl6jfhOrG+7+i6/nNCiBqjon2C80Zoo9TmNWCxWF56pq7Bm0cO/hlWov3lX/5l1aQmZa+3t7fp9/vMzMyo8ZsHBwf4fD6Ojo7UotFsNikWi8pLkCWwiUTitS2csgnrqt4E2QME50OQAoEAm5ub7O7uqnLPl0F2iH/R+DzkEa/TYvq55/99ey28BgbvIFcllSUej4fNzU0Gg4ES+ZNextTUlKrU2dnZIZlMYrFYsFqt5HI5QqHQa91VdzqdFxZ6tNvtrKyssL29zeHh4UtpZMmKqNvUETO4Pd79TiwDg/cU2VEup/VFo1EGgwG9Xo9EIqHCSsvLy2xubqo+GyHEa5/50el0Xiq27/F41MztRqPxwnk52V1uGIj3E8NAGBjcIn6/X8lIyP6Ei0j1Tzld7aJm0KsiB2G9bEllNBolm82SSqWUHMxNGZ4pYvD+8f4HyQwM3mHkVD1ZznoZVquVUChEKBR67fH6breLrusvbXTMZrMaITosQndycsL29vaVz+31eoDhQbyvGAbCwOAWkcJv1xmI20Qm01/FK5HaYHIGhRyKVavVRuYtXMQIMb3fGAbCwOCW8fv9tNvtkaqnN4l831dJeptMJiKRCJVKRY2ClfMXJukySWSTnFG6/X5iGAgDg1tG9lwUCgU18/tN0ul0ri1xvQmyDFdOEZSL/nCH8EWua5IzeLcxktQGBreM3W7H6XSSTqdJp9Oqw1l209rt9lvt2r9s3vmL4nA4cLvdFAoFdF3H6/XS6XSu9SBuY466wZvBMBAGBm+AlZUVms2mGtpTKBTUWE44l5uYmZmZ2HErZ1JIEcAXpdPpvLaeimAwyPHxMXCuU9RoNK6cnvZFbZL7vGAYCAODN8Bw6WowGFRzG2SyN5PJKKG8q4hGo8zNzU2M6TebzbHZxK9a4nqRYDDIyckJuq7j9/uVLEev1xsLYRlNcu8/hoEwMHgLmEwmZTBmZ2cJhUKqD+Iich54rVYjm81Sq9Ww2+2q/NThcHB0dHTpxDl4fVpHcgJct9tVM7rh3Dhd1LcyKpjefwwDYWDwDuBwOK5dxP1+Px6Ph7OzMzqdDt1ul2KxiMPhoNVqEYvFJk4ilJPnXhdLS0tKhE4ODmo0GoaB+BxiGAgDg/eIQCCgJMT7/T6pVIpCocDCwsK1k/FeF0IIFeIymUw4HA4qlcqYgZO5CaOL+v3l1gyEEOK3gH8LyOq6/mDC/QHgtzifdd0G/lNd1588vy8J1Diff93Xdf2j2zpOA4P3FYvFwvz8PPPz82/1OLxeL9lsdmT2t8RsNhsexHvMbXoQ/wfwd4DfvuT+vwL8RNf1f1cIcRf4DeAXh+7/pq7rlwdVDQwM3gnm5uYunbpmNMm939yagdB1/Q+FEItXPOQ+8DeeP3ZTCLEohJjWdT1zW8dkYGDw+hFCfO4G/hic8zZzEJ8Cfxb4jhDiY2ABmAMynA8n+j0hhA78fV3Xf/OyFxFCfAv41vM/60KIrZc8njDwrnssxjG+Ou/68YFxjK8L4xhvxsJld7xNA/E3gV8XQvwEeAz8GOg/v+9ndV1PCSGiwO8LITZ1Xf/DSS/y3HhcakBuihDih+96rsM4xlfnXT8+MI7xdWEc46vz1gyErutV4C8AiPMg5cHzf+i6nnr+36wQ4neAj4GJBsLAwMDA4HZ4a2J9Qgi/EEKWN/xF4A91Xa8KIdxCCO/zx7iBfwN48raO08DAwOCLym2Wuf4T4F8HwkKIE+CvAVYAXdf/HnAP+G0hxAB4Bvza86dOA7/zvPLBAvxjXdf/5W0d5xCvHKZ6AxjH+Oq868cHxjG+LoxjfEWE7Ig0MDAwMDAYxpgHYWBgYGAwEcNAGBgYGBhMxDAQBgYGBgYTMQyEgYGBgcFEDANhYGBgYDARw0AYGBgYGEzEMBAGBgYGBhP5XA0MCofD+uLi4ts+DAMDA4P3hk8++SSv6/pEvfbPlYFYXFzkhz/84ds+DAMDA4P3BiHE4WX3fa4MxJumWCxeOije4XCQSCSMYSkGBgbvLUYO4iVptVokk0m63S66ro/80zSNXC7H6enp2z5MAwMDg5fG8CCAXq83dttVoxJ1XSeZTGI2m7l79y4Wy/jXeHx8TCaTweFw4PV6MZlMxvB2AwOD9wrDQABPnjxB07SR24QQOJ3OiYt6v9+n2WyyvLw80TjA+ZzeZrPJ4eFn4T2z2YzL5SIajeL3+1/vh7gGaQQNI2VgYHBTDAMBJBIJhlVte70ejUaDVquFpmmYTOORuHg8TiAQuPQ1hRCsrq5SqVTQdZ3BYEC73aZarbK3t4fdbleLtfRUhBCYzWZmZ2ex2+2v7fPpus7W1hY2m4319fXX9roGBgafbwwDARQKBcxmM3a7nWazSb1eV/e5XC5WV1df6nXNZjPBYJBms0mxWCQej5NIJCgWi5RKJeW1SOOkaRqNRoN2u82dO3cwm80TX1fXdc7Ozuh0OmP3CSEIBAL4fD51Wy6Xo9Pp0Ov10HXdSJwbGBjciC+8gdB1HavVSrvdplarYbfbmZmZwel0UiqVyOfzNBoN3G73S71+t9tlZ2eHfr9PPp9ndnYWl8vF3Nwcuq5jMplGvIVarcbOzg4HBwesrKxMXMwPDw8pFArYbLax+waDAYVCgZWVFaamphgMBqTTaUwmE5qm0el0cDgcL/VZDAwMvlh84Q2EEILl5eWx2/P5PKVSiWQyiaZpPHr0iEajgaZpWK1WPB4PcL7rvywcNBgM2N3dRdd1VldXOTs74+joaOxx9+7dw2azYbFY8Hq9JBIJFexAUAAAIABJREFUjo6OePz4MeFweOT16/U6hUKBeDzOzMzMxPfc3t5mb2+PSCRCp9Oh3++ztLTEwcEBjUbDMBAGBgY34pUMhBBiHfi7wLSu6w+EEI+AP6Pr+v98xXMcwB8C9ufv///ouv7XLjzmPwL+h+d/1oH/Qtf1T1/lWK/ixz/+sQr3mEwmTCYT/X4fr9dLPB5nZ2eHbrc7slBXq1VcLhd2u51gMEg0GlW7fU3T6Pf7pNNp2u02q6urOBwOFhYWVFnsYDBACMHOzg6ffPIJLpcLs9mMx+Nhbm6OtbU1MpkM6XR67HgjkchE4wDnYa319XV2d3dVj8b09DSBQIDDw0OazSahUOh1f4UGBgafQ17Vg/jfgf8e+PsAuq7/VAjxj4FLDQTQAf6Urut1IYQV+I4Q4l/ouv79occcAL+g63pJCPErnM9t/dorHuulxONxlQcYDAb0+308Hg/hcJiVlRX6/T6lUgmHw4HZbKbb7XJ2dobT6WRhYYHNzU0+/fRTGo0GtVqNXC5HtVrlm9/8Jl//+tfJZrNUKhX1fuFwmHA4rEJY1WqVn/3Zn0XTNMrlMpubm6ysrLC2tka/3x+psBJCXFuJZDabuXPnztjtLpeLRqPxmr41AwODzzuvaiBcuq7/yYU4ef+qJ+jnK7HMAluf/9MvPOZ7Q39+H5h7xeO8klgsdul9uq7jdDrpdrvAuQExm83Mz8+Tz+fZ29tTFUo2mw1N03C5XNTrdU5OTtjb28NsNjMzM4PNZqPZbJLL5cjn8wghmJubUzmOYDBILBZjd3eXnZ0dzGYzQghCoRCxWOzSpPVNcbvd5HI5I1FtYGBwI17VQOSFECs8X+CFEP8+MB4TuYAQwgx8AqwCv6Hr+h9f8fBfA/7FFa/1LeBbAPPz8zc/8iGKxSJ2ux2XyzW2cB4fH2O1Wvn444/Vzv34+Jh8Pk88HleVRGazWeURAoEAuVyOw8NDjo6OmJ+fp1gsqsdFo1GsVivBYBCr1cqTJ0/I5/NMTU0BsLS0xNnZGf1+n36/z+HhIalUCp/PhxCCWCw2UqV0U1wuF5qm0W63cTqdL/VdGRgYfHF4VQPxlzgP/9wVQpxyHhr6j697kq7rA+BLQgg/8DtCiAe6rj+5+DghxDc5NxA/d8Vr/ebzY+Cjjz7SL3vcZWiaxtOnT9E0TZW6mkwmIpEINpuNYrHIzMwMfr+fdDpNsVhkc3MTj8dDNBpldnZ2ZLF1OBwEg0FVnRQOh0d6LDqdDplMBoCTkxPgPCF+dnZ2aWWSpmmkUim63S4+n4/d3V2V1yiVSng8nhtVWcnHNBoNw0AYGBhcyysZCF3X94E/LYRwAyZd12sv+PyyEOLbwC8DIwbiecL7HwC/out64VWO8ypMJhONRoN6vU6r1aLValGr1XC73XzlK1/B5/MRi8XI5XKkUin6/b7qb5A5A4vFQiwWUw11vV4Pt9tNsVjE5/PR6/VoNpsA2O121e8QCARwOBw0m02q1Srtdls1sl30ZIrFItVqlcXFRU5OTtjc3KRUKlEul3G5XHzlK19hdnb2ys9qt9sxm81Uq9WRSqbhpj0DAwMDyUsZCCHEf3vJ7QDouv63r3huBOg9Nw5O4E8D/+uFx8wD/xT487qub7/MMb4IXq9X7a5lT0QymcTv97O2tka9Xuf4+JipqSnMZjMOh4NHjx4xGAw4Ozsjm82Oqbr2+312dnYol8uqVHV40bfZbFSr/z97bxobabbe9/1O7fvCIotFFvelye6e7pm5M1eJhJsAjmMjSrzAhh3Yn2IFgmLAcoQEiBF/iGLZMZAgSGAncCJcGEnswHAiW1ZiKLJjC9dyrJE0Gt2rnuludnNfqoq17/v2vvnAPmeqyCKbzaWbPfP+AKKbxVpOvct5znmW/1OhVqvhdrtZWVlR8YHx8fEzY/T5fGxsbPD06VOcTicHBwfYbDZWV1d58eIFv/RLv0QwGMTlcjExMcHExAThcJhwODz0Pm63m2KxSLFYHBrLo0ePbvKQGhgYfAO46g7C++rfNeC7wD9+9fsf5SSF9SKmgL/zKg5hAn5J1/VfFUL8eQBd138R+HkgBPxPrybVnq7rn15xrK/lx3/8x9X/TSYT5XKZSqVCKpXC7XaTTqex2+3Mz8/z7NkzxsbGEEJgsViYmZlhfHycavXs5kmmu45y/1itVtxuN61Wi0gkwuzsLJ999hkvX74kFArh9/vx+Xy43W71WW63m6+++gqr1YrP58Pv96PrOgsLC+i6TqfToVKp4HQ6CYVCFIvFMwZicXGRZrOpfq/VahwfH1+rGNDAwOCbyZUMhK7rvwAghPhnwHeka0kI8VeAf/Ca134FfDzi8V8c+P9PAz99lbFdhdNaSz6fj+npaRKJBMfHx1QqFSYnJ8lms2iadkaDyeFwjCw+M5lMxGIxVVw3SK1WQ9M07t27h8lkwuFwMDMzgxACk8lEKpVSFdBms5lWq8X+/j42m425uTm8Xi+hUAghBC6Xi5/4iZ8gn8/z1VdfUS6XcTqdyq01iCzGk7hcLpLJJMVi0TAQBgYGQ1w3SD0HdAZ+7wAL13zPd44QgqmpKWq1GmazmUAgoCQrTk+wFxEKhc4tSiuVSuzu7rK/v08gEFD1DTI2IY1Cq9VSEhl+v5+VlRX6/T71ep1ut8vs7Kx6z/Hxcebm5vj888/pdDoqC+o8xVk4yaryer2USiVmZkZnExtpsQYG306uayD+d+B3hRC/wkmq658A/u61R3UHGB8fJ5VKoes60WiUcDhMJpPBZrPdyGQZCASYmZkhHo9TKpUAVKxjb29PBZRlVpUQgsnJSfr9PuPj4wghhkQFJZOTk1gsFgqFAi6Xi2az+VqDJqusm83mmeymeDxOOp3GbDbjdrtZXl4eqW77JkjjBagdkhEkf78wFg3fDq6bxfTXhRD/BPg3Xj30U7qu//71h/XukSmqZrNZFdJdVFB3FSYnJ1U2lJTfWF5exuFwYDKZVFbVYCV1r9fj4OCAVquFxWJRhXsSj8eD1+ulUCjgdDpptVqvNRCBQIDDw0OKxeKQgUgmk6TTabWjyeVyFAqFkUH0y9Lv91Va8SDRaPTGj6/BzaNpGjs7OwCGdPy3gOtqMc0BOeBXBh/Tdf2sIt17yPz8/K1/xumV82XiAJlMhs3NTQqFArVaTRXYwYl7bHp6mhcvXtBut2m1Wq99P4vFgsfjIZ1Oq4I+GfQOhUIsLCwAJ/UT2Wz2jQyEpmkkk0nVsKhSqRCPx4lEIirlV0qRtFotQqHQpV14Bm8XXdfZ29tTCRnftsSGb+Ou6boupv+Hr2UynMAisAk8vOb7GlxAOBwml8uRzWapVqtDBgJgenqaZ8+eUa1WzxgI2Q1PBsZlfCIajZ5J1bXb7UOr+vHxcWKxGI1GA5fLdamxxuNxstmsKgBMp9M0m02V9ivlRHK5HMFgkGKxyL17975VE8/7gKZpHBwcUC6XmZmZIZlMks1mcbvdKntuFHa7/Rth8GWP+ZWVFaXk/G3gui6moeR5IcR3gP/oWiMyuBRSdmNUeq1che/u7lKpVBBCoOs63W5XdZaLRCI4nU4ePHgAoKqxC4UC3W6XycnJM6ulUChEIpEgm81eandVKpXIZrNMTk6qALjJZGJhYYHV1VX1vGg0qvpfHB0dsbOzw/r6+o121TO4Oq1Wi93dXVqtFjMzM0xOTtJut8nlcoTDYXZ3d5VW2SjW19ffa4PfbreJx+Nomsbu7u636tq80X4Quq7/SAjx3Zt8T4PRuN1unE4nhULhTFtUs9nMxx9/TLlc5vDwkMXFRbxeL+l0mnw+j8/nIxAIUCqV6Ha7WK1WyuUyR0dH6kZvNpssLCwMGQlZQZ7P50caJjipIpepvd1uF7vdjsPhIBAIYLfbabVaZ1xUcvJot9usrKywubnJzs4Oa2trF2ZgfRNotVp0u923ssrudDpq13bZRIN2u83m5iZwEnOQ45yYmCCbzaqKfpfLhdVqVVlxLpcLXdc5PDwkFouxvr5+a9/rtjk8PETXdVZXV9nb22Nzc1MpOy8sLFxbRPMuc90YxGBFtQn4DpC91ogMLoXH41G1DrVa7Yx439zcHD/5kz/JD37wA9rtNoFAAJvNxsTEBNVqlWKxiBCCSqWC2+1WmVMrKys0m00SiQS6rrO4uDhkJCKRCLquD+lLDSJ1poLBICaTiXA4TLvd5vDwULmrTk+Gdrsdi8VCvV5nYmKC5eVl1fRodXX12llTdxVN09je3qbb7fLgwYMbbeTU7XZJp9P0+300TaNWqw2t8ufn518bS+p2u2xvbwOwtrY2ND6n06nSo+12O4FAALfbTbfbpVqtKnn7ZrNJuVymWCxe2MP9LqLrOs+fP+fJkydEIhG2t7dpNpsUCgVmZ2fRNI1CocDExMS7Huqtcd3l2eCd3uMkJvHL13xPg0tgtVpV9tH+/r5qWjS49fV6vSwsLOB2u6nValQqFWZnZ8lms+zt7bGwsEC5XCadTmMymVhZWcFms+H3+xFCEI/HsdlsQ/URdrtdBa1Po+s6lUqFBw8eDPXxLpfL7OzsEI/HsVgsI+MXbrdb9arweDwsLi6yt7dHIpEYqvX4JiEFGE0mE/F4/Nze56d3iKf/VqvVlMFut9scHByoRlN+v59AIIDX61Vuw1gsxsbGBvfv38disajXSp0xye7uLrqu88EHH+BwOFSigUysWFpaUnGJxcVFZUB0XafX61Gv19nZ2aHf75NIJFS9z/tAv99nb2+Pg4MDxsbGePjw67Cqz+dTLXwNA3ExG7quD1VOCyH+NK+ppja4GbxeL+FwGK/XSzabVb2o5QpdivB5vV6cTie9Xo9oNMrMzAy//uu/rnpfr6yssLq6qvpZ9Ho9gsEg1WpVGYnTkh2jKBaL9Hq9M8/1+/34/X7K5fK5q0i32025XFZpu8FgULmzZIX5N4lms0kmk2F8fByHw0E8HqdSqZzZCR4eHpLL5XA6nXg8nqHj0Ov1KJVKKmW4XC6r6vtAIEAkElEp1GNjYwSDQVqtFs1mk6OjI2q1GpOTkwDKv261Wpmbm0PXdba2tohGo9hsNo6Pj9XuUNYF6bpOtVolFAoN7S5k0aecSN1uN41Gg2KxyNjY2JljoWkauVxOnfvx8fF3vmuMx+NUq1V1HKemptTffD4fm5ubNJtNkskk5XKZjz/++BtZy3NdA/GXOWsMRj1mcAt4PB6KxSIzMzNEo1HVaGhpaUmt1pxOp8pOcjqdavJeWVnh8PCQfD6vCvT6/b5aJcLJSvD4+Jjd3V1+7Md+jKWlpQv9rdlsFrvdPrJXxezsLLVajUAgMPK1g1Lk8vXBYJBCoUC1Wr1S/4u7TCKRwGw2E41GMZvNZLNZdnZ2MJlMWK1WJiYmaLVa5HI5xsbG6Ha7KgVZYjKZzkz8Dx48YGlpSWW2NRoNjo6OODg4wOFwkE6ncblcfPLJJxSLRWZnZ/F4PCoeBSfnolKp8PTpU46OjnC73cpo9/t9YrEYyWSSfD5PPp9Xbkm5IBFCqEWF0+lUApeZTGakgUgmk6RSKfV7p9M5t6r/bdBut8nn84yNjaHr+pkAu9vtZnZ2Vt1v8rHBXcY3hauquf4k8O8CUSHE/zDwJx+v6ShncHMMTqrBYJD19XWeP39OoVBQE/HS0pIS5xtcgd67dw+fz8fW1hYulwuXy4XJZMJmsw2thGw2G5999hm//Mu/rCYTWU1uMpmGVnv9fv/cG9tut/Phhx+euxOQ3yUej6vAtt/vx2QyUSqVzhiI0wWC7xP9fp9KpUI4HFZB+OXlZfL5PLqu02g0iMViwEnM53Uy7vB1j/THjx8PHReXy8Xy8jIvXrzgxYsX9Ho9pqamiEQiPH/+nFgsptxOnU6HsbEx9vf3yeVyeL1e/H4/zWaT73znO2pnWigUyGQyNJtNotEofr+ffr9Po9Gg1+uh67qStHe73eTzeaLRKLFYjFqtNpQm2mq1SKfTqt7m8PCQTCZDKBR6Zz1LkskkQgi8Xi/5fH5kWuvExIRqDLa5ucne3h5LS0vKQN7mtSl3hW/j+r/qDuIY+D3gj3HSGU5SBf6T6w7K4HK4XC7MZrOaVF0uF3a7XclYwMnEPColLxAIEAgE6PV6OJ1OFhcX1d9kEPr4+Jhut8v3vvc9dnZ2aDabdDodut2uMhAyJmEymVSjpfO4yE0kXQv1ep1Wq0WpVFJS6jJVVhbWbW9vK52s09t6l8t1JvvqrlEqldB1fcjd5nQ6h4xrrVaj3W6fq+Ul6XQ6qj+IxWJhb29v5PPcbjcbGxuYzWY++ugjrFYrDx8+pFarUSqVSCaTRKNRJicn1cQ3MTGhgs2ZTEYZiGAwSDqdZnZ2lgcPHozMNEulUiQSCXq9npKoSafTNBoNPvnkE1UXE4vFMJlMyghGo1GKxSKxWIzl5WV1nUkuisdclsH7YxDZbTGfz6tUXuDcmh9d13G5XASDQZ49e6Y03OBySQBXRSopyBT12+Sqaq5fAl8KIf6eruvGjuEdIYTg3r177O7usrm5SSAQIJfL0el0hlY9gUDg3Ivc7/eTzWbVyi4Wi5HJZNTfw+Ews7OzzM/PE4vFhgrvpIZUp9NRLg3ZazsUCr3xjTxYWyH967qus7m5ydOnT/n00085PDykVqsRiUTo9/tDN7sMGjqdzluT7ZB1IoAyyt1uV2XzOBwO5VY5j2KxiM1mu7A2wOPxXKogKx6Pk8vlaDabKuZwGk3TlLKvruvqvFitVoLBII1Gg0gkwuPHj7FarUxNTfHll18yOTmpVqqlUolyuYzf7yeVStFoNFhaWjo3DVn2UI/H4zQaDXK5HDabjaOjI46OjpiYmFDGb3Z2Vhl6s9mMxWLhiy++4Msvv8TtdjM1NYXJZFLnWiZSTE1NvZHfv9vtsrOzM1LleBCz2czk5CQHBwcXnkt5PD755BOePXum1Aeq1SrtdlvtzG+Sfr+v7ou3Ucl+VRfTL+m6/u8Dvy+EOJPvqOv642uPzOBSuFwu7t+/r4KO5XL5jEsmk8lw//79kTuJ6elpyuUy+/v7hEIhNjc3EULw8OFDbDab8hn7fD4ePnyIpml0Oh36/T4HBwfk83nVP2MQ6cq4KhaLhfHxcYLBoBqfzWaj2+0yPT197nvv7e1xfHyM3++/lotCbuMHkVk5p5FBX7l7CQQCLC8vj3zfQffSdanVaqoGYWFhgYcPH56bKtvtdolEIsTjcTKZDNPT0wCq4M3v96vJVopA+v1+ZfharRbxeJxut8vx8bGKfVyEbFwlayPm5uZIpVIqIG82m5mfn1fu0F6vpybwUChEs9lkf3+fdDrN2tqact9UKhUlUX///v2RbXrh5FiXy2V6vR4mk4lkMqkSNUZN+jK47nQ6h5SVz6NUKuFwOLh//766J0KhEDabjYODAxWXuMlankqloq7LfD6P2+2m3+/T7/fPPQ7X4aoj/7lX//6RmxqIwdWxWCwsLS0BJzdlIpHg448/xmQy0el02NjYYH9/n7W1tTOuF7PZzOLiIpubm8TjcdrtNpFIhEAgcG6PC/n43NwcrVaLycnJoQlb3tThcPjaflKz2czq6iq/+7u/SzqdZn19/ULDMzc3R7VaZXt7e8ggymwal8ul3BZOp/PMzSu1o9Lp9BkDkUgkqNVqyvXR6XRU5tDg6rZUKpHP54feW67s2+22yiqCk0lGGlep3itjPNKXfd4EE4/HsVqtamK4qI5CZhz1ej2SySSTk5P0ej1evHhBuVxmYmKCdruN1WqlUqkMHa9arcbc3Bw7OzscHh7i8/mGUp11XVc7S+mmsVgsalcpU5hlUF7GIzKZDO12W1X67+3tKeMkDYvH4yGbzQ65E2Vc6tmzZ7RaLaxWKxaLRQlctlqtkSrBFouFtbW1S63qW60W/X7/3F2cpmlUKhUmJiawWCwEAgHV30W2Lz44OKDdbjMzMzPU+GvwHnQ4HJd2h8ZiMZ4/f06v1yMQCPDixQtcLhflcpl6vc4HH3xw49lfV3UxJV/9e3ijozG4NvKG6PV62Gw2bDYbCwsL7O7u8uLFC8xms5qIgsGgktiYm5tjd3dXrWxP960ehWxalMlkVKtUp9OpxAJl1opsjiSEUMqwb8Lc3ByaplEsFl8bsJXGUkq1S3q9HkdHR9TrdVU8JjOG3G63ysDp9Xp0u11VOyApFApqV+T1epVBcDqdLC8vMzs7yw9/+EP29/dptVocHx8zPT2tfPyyVkEIoaTeU6kUxWJR6VH1+/1zCxBH0Ww28Xg8bG5unltDAScr6Z2dHWWctre3lXSEzBhKJpOqdgK+lnJxuVwUCgXcbrfKppIGUnJ0dHRGxwvgww8/VP1TSqUSL168UOff4XCg6zpPnz5lf38fIYQqprPZbCwuLhIMBul2uzx9+pRwOHwmRvPkyRM8Ho+KpZVKJY6Pj9Vz/H4/09PTNJtN5ZbZ3d1VRlj+nL4epTGFr5Mnut0u5XJZSdYUi0V0XVe7H7/fTyKRUO7de/fusb29TSwWY2vr667JQggcDgdWqxWr1UooFOKjjz7CYrHQaDSw2+1KuHKQwRiOx+NB13VyuRy/+Zu/STQaZX5+/lZSg6/qYqrytUgfgHj1uwB0Xde/WTmJ7xFytdntdtXKUk5IMuAo/aT5fJ7Hjx9jMpkIBoM4HA7VBrVarZ5xg4xSs5yZmUHTNFKpFF999RVLS0s4HA6KxSJ7e3tD/mU4mdSuUvg2Pj5OPp9Xq85yuaxiAefdGLVajVqthsViUTd1q9Wi3W7T7XbV4z6fj2AwyMzMjEptjMViTE9Ps7y8TKvV4kc/+hGNRoOpqSmVFSb7f09OTqossKdPnzIxMaHSI2VLWflZchX/5MkTTCYTkUiEsbExFfyXP/J4V6tVZexkEoCmaZTLZTKZDG63G5PJRCaTwWq1jnQjysC/rEq32+00Gg10XWd6eppoNIoQQhlPec3I7wgn6bKDiQySfr9PoVDA7/eruJOmaezt7VGpVBgbG2NiYkIJMiYSiaHXa5rG/v6+2lU5nU7m5uaUa0cWhB4fH6u6Crm7crlcVKtVlSmVyWRYWVlhZWWF7e1tNjY2cDgceDweIpEIVquVdrutrv96vT40GUuD2e12cTgczM/PU6lU2N7eplqtKhcXnBjQSCQyFLhPJpPs7+9z7949leK7vr6uzrncabXbbdrtNs1mU9UiBYNBVWAYiUSGrmld10kkEgghiEajrK+v4/P5+O3f/m329vYuXad0Fa66g3j/5Rm/ocjJeLCeAU56T8iiKDiZNF6+fEk+n2diYoJMJqNWyLlcTq2Q5A0h1SzX19eHdhZyxe50Otnc3CSVSqkApJQBmZqaUqv6XC7H1NTUpfyyzWZzKAjd6/X47LPPaDabuFwubDabyp6Sk4bJZMLlctHr9YjFYlSr1aHdSyQSUa6b2dlZzGYzqVSKarVKIpGg0Wgo1008Hmdzc5NKpUKhUGB1dZVgMMj09DRer3eksSyVSthsNmWcZFvYTCaj5NnlRCAfl+dNrmg9Ho+64QuFAhaLRcmq+Hw+QqEQW1tbhEIhlpeXcblctNttMpnMyCZSQggWFhbUZPbd746WSxt0vUgjJM+T/OzTFItFNE1jampKrbZ1XcdisSgDIYRQ8Qg5UQ6ODVCy9aePab/fp9lssrW1RSqVUg2xdF3n4OCAly9fEgwG1Xfzer08efJEyYoEg0HW1taG3rNSqZBOp1WXRpltJHfWsoOjrut89tln1Ot1/H4/Y2NjWCwWdc0PXsOyZ/3+/j5HR0fMz8+rMZ2XiaZpGul0mmfPnintsmazSTAYVAZSqh7H43GVhi6vveXlZUql0q2qy147evJKwfV7nOwgfvOb0jDofeU8A3Ea6V/OZrP4fD5SqZTS0+l0OuRyORqNhgqCHR8f0+/3OTw8PHPDwYnPVq7+ZID2wYMH5HI5UqkU5XKZqakplUMvg6SDxONxJbfRbDbValaiaRqhUIiZmRn8fr/Kt5eumV6vpybhUqlEOBzm008/HQremUwmPB6PynVfW1tjenqa4+Nj9vb2yGQyzMzM8NFHH5HNZnn69KnK0x8fH6fZbKpjdhqbzcbs7CzxeJxWq6VcR91ul06nw9zcHKFQCLvdTrfbVd9PGjhZSyBX63a7nU6nw9LSEouLizx//hyTyYTFYmFsbOyMSupNZG7J3VM+n0fTNOUzl+flNPl8Xu08JbKGYJQE+HkLg1EFlMVikXg8TqfTYW1tjWazSbfbxWw20+12CYVCrK6uKp0xk8mksugCgQChUOjMNfRbv/VbqkAwGo2qoPKo4yBjcrOzs3i9XiWsKA3x6TGPjY3RbDZJpVIIIZidnT03vlAqlTg8PETTNLWD6/f7PHv2jGfPng25UuXOYWJiQnWYhJNF3wcffKDO1Z1xMUmEED8P/GngH7166H8TQvwDXdf/q2uPzOBKDLqYXkc4HObg4IDt7W2EEMzNzQFfi+lJIT+5u5AKnvl8/syqqFKpMDk5ObSCtdlsRKNRSqWSWoVZrVYODw/PuDSkIYlEIkxMTKgYwGmXicPhoN1uU61W1WoOUHpG0rUjs2YuqiM4ODhQmSjSHVAul9WEIMc7Pz/Po0ePsFqtJBIJUqkU7XZ7pDtHjj2VSqFpGi6Xi0QigdvtVtpHF9HpdHj69KnKRJMuMDiZgDY2NigUCkSj0RtPcez3++zu7ir5DJ/PRywWo1QqKdfH4Ge2Wi1qtdrIuJDP56NYLI5sY3seMk4kK/objQaVSoXFxUVmZ2fp9XqkUim63a5yuUnXkWzDC1/vfra3tykUCmoMOzs77O3tEQwGWVlZGRms7na7qmBRypkPukQ1TSObzVKv10catWg0iq7rqu/J5OQkDoeDVqtFvV5XbqxSqYTb7VZuSDnBLyws0G63WV5eVq7AcrmMy+VSi7d8Po/L5cLpdKqalYtkbK7DdXcQfxb4WNf1FoA3EwPOAAAgAElEQVQQ4r8GfgQYBuIdITMlzisGkrTbbdUwqN1uMzc3p3YfUlCvXC4rmfBgMMjc3BzNZpNYLIbZbFY3iKygnZiYUAVeQgiePXumsnrS6TSlUolGo8Hh4SG7u7vYbDaCwSB+v59MJoPH48HhcGC329Wqqt1uU6/XEULg8XhoNBpK3kCiaRpHRydNDB89ekSv11OTST6fZ3Z29swkNTY2RjKZ5OjoSLl75OR9cHDA0dGRWqlOTEyoYxMOh0mn02Sz2XOrxqVURj6fV/GD5eXlS7nVbDYbLpdLufjS6bT6ft1ul1QqRSgUulR19Wl6vR65XE7pHsljJwuvNE1jfHyc7373uyrLymaz0el02NvbI5VKsbKyoiZiedxGGWFp1CqVyrkGQp6j6elpTCYT+XyeYrE4JO0BJ262QqEwtBqXbiqbzUaj0aDZbDI3N4ff76fT6ajuiOVyWe2EXr58qWJGmUxmpOjkYCaVzWY70/dEZr9dVEsxMzODy+VS17lksMI6EokwPT19Zochg/KHh4dqVwQnhYe9Xk/FzzRNY2lpSakm35Za7nUNxAHgAGTI3Q7snvtsg7eC1Wq9cAchM1mk71jKbA8i3U6yF4B0CS0sLLCzs8Pu7i4+n4+lpSXlSohEIuzs7FCv11WKrdlsplqt0u12CQaDLC0tIYRQcQEpPT4+Ps7jx4/J5/MkEgmVcy9dHHLllUqlsNlszM3NYTKZlGtJ1j1Uq1UVmASoVqu8ePGC6elpwuGwuuFka1aphDs7O6t821KuWo5xMK3WarXicrn4/PPPyWQyKsA/MzOjbv56vc7W1ha6risV1TcpmAoEAhwcHLC1tUWr1VINakwmEz6fj3q9rjLSZPzndfR6PZUiKcUbAXU8o9GoqhwejDF5PB7u37+Pw+FQEhyyINDtdhMOh0cWq9lsNhwOh9pZjqJQKJBOp7FarUxOTlIoFHC5XKp3xM7OjpKgl0KOErlg8Pl8VKtV1WgqEAionenCwgJffPEFL1++BE6uhYWFBZrNJl9++aWKV/X7fSYnJymXy9RqNWZnZ9X9MMpFJBtrXcTY2BiBQECl3drtdpXqehFWq5WlpSW1a5Pp0XKnIN2Wx8fHKl05m83S6/WUosFNcl0D0QaeCyH+OScxiD8E/KbUZ9J1/T8+/QIhhAP4/zgxJhbgH+q6/l+eeo4A/iYnek8N4M/puv6ja471W8PrDITMBIKTwOSoDAiZzqnrOlarVU0adrudBw8ekM1micfjHBwc0O/3cTqdKsukXq/TbDbZ3d1Vmk/5fJ6DgwPi8TjJZBKn06l2CIVCAYfDoVIUZdaNlKNYWlpSBicajaoAodwlyZ7aXq8XTdOG0hZ7vR6Hh4ckEgn29vbodDpDq3mphySPifQJn5dp1Wq1KJfLdDodMpkMmqbx4sULrFYr4XBYVRqbTCYWFxexWq1vlLoKJy6+o6MjNE3j8ePHqsYFTrK55K6kVCqxvb3N+vq6KniT31+6OuQuyuFw0Ov1WFtbU8ZTxlMePnzIwsKC8oHHYrGhOJPH4+HRo0c4nU6VCSclWi7KnpE7w06nM9LPL1fq6XQar9dLo9FQx12mlU5NTeF0Oi80gl6vlwcPHpBKpUgmk9hsNu7du6cmZXmta5rG2NgY1WqVZDLJv/pX/4qpqSn8fj/tdptarYbdbldZV+chY3etVuvCVHBZS/I6V2AymVQ7klAopGRwBikUCuRyObVL+vDDD9ne3qZcLuN0OlWyxk1zXQPxK69+JL9xide0gX9L1/WaEMLKiUH5J7qu/87Ac34SWH31868B//Orfw0ugdVqPZNHLel2uySTSbxer6rEHZUFIVeroxBCqIlBisrJXgNut5tqtcrh4SEul4vV1VV0Xaff7ytZB7fbzdramgrOygwOuXWWRU71ep12u836+rqqWRgM0o3idE67xWJheXmZarXKZ599pmQpRk1sNptN+eHX19dpNBrKAEo0TcPhcPDjP/7j6rOkuJ6sErZarSwsLFCv15Uve3l5+Vwl20FkSqPUJzrtxrJarWoSnZiYYHNzk42NDfr9PhaLRZ17uXKVvvqNjQ0++OAD3G43iUSCdrutepPLz5CG5fDwkEKhcEZ5dWVlRWUhSQXWer3O6urqyAlVxqykrpJUlpVutEqlgt1up91us7u7ixBCfWY+nwfOzwA6jdzpjY+PD3XMk+cRUK4rOFnhf/XVV1gsFrU6B840yBqFnPAbjcalmzzJ+gm5K5XFkJlMhuPjYxwOh5LRWFhYGPre/X6feDyOy+UaSu748MMPVVHibXVevG5P6r9zhdfogIxkWl/9nF5i/XHg77567u8IIQJCiClZoGdwMRftIJLJJJqmMT8/Tzwep1QqXbkhTzgcptFoqDamcHLzyLTRe/fuqUkxEomo2ozHjx+rgPhFZLNZjo6OcDqd1+4B3O/3mZiYIBqN0uv1ePTo0cibSlZhb21tKQnrwYldCKF6OAyytram3FODAomaprG1tcXe3h7T09MXFglKkcJOp8PDhw/pdDoXtiKVAn+///u/z/3795UvP5lM8uTJE9xuNz/2Yz+mAqYykJ/JZHA4HCooOngcxsfHVWvaUdLc8rlzc3PKzx6Px0deQ3a7nampKRKJBKVSiWq1quJVqVSKWq3GRx99RDKZZHt7m5WVFVUjIFVU3/S8n3Z3WSyWkQudubk5IpEIGxsbdLtdotEozWZz5Hc+jTx29Xr93OfLxYUsvDyNrKGJx+NKmkXTNHZ2dlTyhDRUsjbjtHyLlPO/Ta6bxfRHgL8GzL96r0sVygkhzJyowK4Af0vX9c9PPSUKxAZ+j796zDAQl0D60k9LYuu6roJZspJaZhhdNSNmbm6OQCCgbkJZ5SlvAIk0HHD5VaHc2cit/5siazemp6fJ5/PY7XaWl5fZ2NgglUqNDDJ7vV5mZmaIxWIqxnLZym8hxJnJyGQysbq6ytbW1pkisfNePzs7qyS0X+c2KJVKjI2NDaU5SsMtabfbascodaAuWhTIfhCvQ6b9yiI9acgHjaeMLcjAv81mY21tjf39fV68eIHT6VQZS/l8fmgyHRVEvklsNhuRSIREIsHi4uKltYxkkV69Xiefz5PNZlXN0NjYGC6Xi93dXVWUGIvFCAQCrKysqGr9VCqlAtEyEC67Oh4eHp4Jgk9PT9+6MN8orrsv+RvAnwSe6m/gaNV1vQ98JIQIAL8ihPhA1/VnA08Ztccb+f5CiJ8Bfga41Kr028BgLcTg5Fav15WOC6AKk2TmyFWQ3cskPp+P8fFxNE0bWt3I9z+dM38RUklTFpy9CdL/LvP64WTCcTqdjI2NkclkKBaL6rmD32d5eZn79++rOMmbkM1mR2a4OJ1OlQJ7Hqf9yKN0ogb/LoPpVquVXC5HJBJRRXqyQO358+cA3L9/n2q1isfjeW0zHqfTST6fp9frvdZ1MTMzQ6PRUMbPZDIN7c6EECwuLnJ0dKSkKWR/bKmhtLi4yOLi4tA5lkHo2yYQCJBIJJQe1WUxmUx89dVXTE5OKsMomykBKg4iK/Klq1F2bgyFQmSzWfx+/9AxlrGru8J1DUQMePYmxmEQXddLQojfAP4dYNBAxIHBJc4MJz0oRr3H94HvA3z66adXGsc3jUEDMbiaK5fLQ6tcs9msAsjhcPhSKyhZjHZeIE++fz6fHzIQslnRm/bvHexVLel0OmSzWVVlvL6+fmYslUpFFZkJIdSkCSe56jIDSo5ZUigUSKVSI29SKQsxMTEx0m0hVV1PC7LBiYurWq1euUeADPLL3uNms5lYLIbNZmN1dVXtiubm5lQXuqWlJdW7w+/3U6vVlFjhRcjz1mw2L3RxwdeS87JXyO7uruqnMPh+ssBRKs5KmQ+pMQQnBvFtt5eVadWlUunS16aMG8gCSKfTqQLhoVAIs9lMOBxWYo4y7XVnZ0edI7PZfGuS9DfJdQ3EXwJ+TQjxLzkJPgOg6/p/f94LhBATQPeVcXAC/zbw35x62j8GflYI8X9wEpwuG/GHy3NeNXW5XMbj8QztKmZmZnj58iU7Ozusra2dcUnB8ASaSqWUT/t0jrik1WohhBhyC1ksFlVs9iZ4PB5VxS0D1zs7O/T7/aFt/vj4uEp5tVqtZLNZpeMjK2slo/LbJWazmUwmo3oxD5JMJpVL7uHDh2dcT8fHx5jN5pESzzKe8rrMl/OQbpxSqTSUYrm4uIjD4WB8fJxcLqeK12Sv8kEu27b1TQwEfO1ycblceL1eMpkM4XB46LqpVCoq9VXm8i8vL6vEgHq9TiaTUUHvt9ktMBAIkMlkLtWlUAbdZaabEEI12Mrn8+zt7bGyskKtVlONkiYmJtROu1AoMDMz8857bl+W6xqIv85JwNkBXFaMfAr4O6/iECbgl3Rd/1UhxJ8H0HX9F4Ff4yTFdYeTNNefuuY4v1WMMhCdTodms3nGveBwOFhaWmJnZ4cXL16oG7bdbqvsHdl9zGw2K/XRXC53bpqjDO6evgmu0tR9MA4hi7qsVquqDdjc3OT4+Biv18ve3p7SspEpkm+6Gg2Hw2QyGdUxTSJbY0pffjweHzIy9XqdUqnE9PT0SLfMYOHYmxoIKb8xOzur0jRl+rGcwKempuh0OmiahtfrvZZ4m3T9vK6xzijC4TC7u7sq2C61muQCRNM05Ybx+XzqWIRCIXUOU6nUlQoBr4rf7yedTlOtVi90AUq3pdvtxuPxjIwpZbNZZSA9Hg8rKyvqPgiFQhQKBRU3uiqyOnxUod1Nc10DMabr+h9+kxfouv4V8PGIx39x4P868BeuObZvLbKYZrCaWuavS43+QXw+H4uLiyrVz2Kx4Ha7VQ5/MplULSc7nQ4LCwuUSiVisZjSBRpEiundBLK4SGaEuN1uVlZW1CQsd0AbGxvASfqirLp9U3cWoKq7B0UFZRxD+oczmYyqbJU3aKPRwGKxnDsxy8ymqzQLGuzSN1hhPIjVar1Q8vtNcblcSrX2TfD7/dhsNtX6VEpJ1Ot1JT/SaDSYm5s7YyilSJ1sMXtbqZunkbtq2Y3QYrGM3EkUCgVVi3N0dITf7z8T7L937x47OztKDuTg4IDDw0OWl5fx+XzYbLZzM8Quy/HxsVIYWF5evtXd1nXPwK8LIf6wruv/7EZGY3BjWK1W5Q6Ck9XP6QyTQQYVJE/TaDRUIZmsHA4Gg0qqWNM0ZXikEuZ1boBBZLGR3P2cdl3IPgXlcpmVlRU8Hg/T09PK1XQVIpEIxWKR58+fE4lEyOfzSqZctuSUss2D45yamrrwZvX7/aqY7bIuBtlG9Sp9NK6D0+lUfT7eZJUqUy9lrMZsNqPrOisrK7jdbhqNxoX9mqempigWi+cKOp4mnU6rniZXRcZoCoUCxWIRk8mkKu/ld5e7B2k4+/0+0Wj0THad3W7nk08+UTpSuq4rJV+pxJtMJoeKBzudzpm6JZfLNdJAyusuEAhQLpf58ssvlRLwKBHN63JdA/EXgL8khGgDXYx+EHeGubm5M9LPl/VBnyYSibC5uUk+n1faLwCrq6uqy9hpbrIXr1wZnzdBLiwsDPValrLZV0UK9x0dHanCN6l7A19nOr0pPp9PKYG+7lyUy2USiYRSq71qcPuqOJ1OdF1Xml2XpV6vU6lUWFlZURW+UhJD1udcZLidTqeKCUgtokAgMNKg9no94vE4Ho/n2pOjVAiGr1VkS6USi4uLlEolSqUSiUSC+fl51QjrvBoEWTAqjVar1VJpw9JASBdmu91mY2PjTC9xv9+vrvtKpaIaGMld3ezsrFrIDO5kb5rrFsp5hRBjnFQ8v3nkzeDW8Pv9I91JV8Hj8eDxeIYygeDrvO1SqTR0gcsV2U3xupWzEOLGbxCXy8Xa2ppqSHMTq3ep4y93djLLTKYGS2S/b7PZjMvlwu/3XypYfJNIA99sNs8YiG63O7JSX7pU5Gp21DG7zK5uamqKcrmsFh6zs7Mj3XIyu61Wq9FoNK61KLFareraHhsbI51O8/LlSwqFAjabjXg8rgrpzGbzG/Vb9/v9Q8q24+PjZDIZ1WRICKGaOcGJKyubzdLpdLBYLOzt7dHv95WrdWpqSi2Cbrs24rqFcj/NSX/qGeAJ8K8DvwX8wesPzeAuMTMzQzqdPjPxm0ymG3Mn3TVGFb5dB5PJpPokyPTKRqOhVoEy7TGRSNDr9VhdXb3RndibIHsll0olNdFL/Scphz0KWRh4HYPqcrl4/PixqkIf1d0QTgyDXBxks9lzM9MuQz6fJ5lMqu+laRrxeJzJyUkeP36MruuEQiElEvkmCxJ5DUndpJmZGSqVisrGm5ubG7rObDYb2WyWXC6H2Wym3++zvr6OzWbj4OCAcrlMOp1WMjVwsoi6SsztdVzXxfRzwHeB39F1/Q8IIdaBX7j+sAzuGm63e0g0zuBqLC0t0e/3lQtMrroTiYRSr81ms4TD4XdmHODr1FUptT34+Pj4OMFgcOQkeV33nkT6371e75nuhpJ6va76Isj00asYpm63y9HREXa7feiYy/a5Ur5e6jy9KbLKvFKpEIlEMJvNLCwssLW1hcfjOTOx22w2Fa8S4qT5ktvtplgsqhTZeDx+5jPuooFo6breemXF7bquvxRC3HykxMDgG4LZbB6aZIQQSlJCth+12+2XCtDeNlIbaRC73f7WsovgZPU92N1Qous69Xqd8fFxQqEQuVyO58+fo2maWlUHAoFLSWDLnYM0CBK/38/e3h6JRAKr1Xqtym4Zf5IJCl6vl3v37g3FMWKxmIobVioVlQ48Pz/PixcvhrTMpErCbddTXPdMx1/JZfxfwD8XQhQ5p+LZwMBgNFKOQrpIbiOmchVuUyX0spzubihpNptomobH48HlchGJRGi321itVkwmE/1+n2w2q5phnXc8u90uuVyOiYmJM7EWv9+vZOZfJwH+OmStRaVSUbUWg3GlUqmkmmZZLBZCoRD5fH7IhSt3FlLj6W1w3SD1n3j1378ihPgXgB/4p9celYHBt5D3pbr2bWKxWFQjqMHAsFxpS6MxqrBO7gBkw6DzOC/oPFj9fN1ubR6PB5vNRiwWUzVGEinx7nA4uHfvnjJEslL7Jlx2V+XGlge6rv/Lm3ovAwMDA8lp9wycxB9eF+/w+/08ePDgtQV/59UcwEmKt2xIdR2EECwvL7O5ucne3t5Q34lCoUCr1WJ5eXlol/K2dgkX8W73jwYGBgavQfZF39/fVxN5pVK5VOrvYG+Oq+B0Oq/cL+U0LpeL+fl59vf3efr06dDfPB7PpRpKvW0MA2FgYHCn8Xq9SphRMth97n1ibGwMq9V6Jvh/F40DGAbCwMDgjmMymbh///67HsaN4fV633rh41UxomIGBgYGBiMRV+z1cycRQmSBs8JAl2McyN3gcG4DY4zX566PD4wx3hTGGC/HvK7rI6vsvlEG4joIIX5P1/VP3/U4LsIY4/W56+MDY4w3hTHG62O4mAwMDAwMRmIYCAMDAwODkRgG4mu+/64HcAmMMV6fuz4+MMZ4UxhjvCZGDMLAwMDAYCTGDsLAwMDAYCSGgTAwMDAwGIlhIAwMDAwMRmIYCAMDAwODkRgGwsDAwMBgJIaBMDAwMDAYiWEgDAwMDAxGcmflvoUQa8D/OfDQEvDzuq7/jfNeMz4+rssG8AYGBgYGr+eHP/xh7jyxvjtrIHRd3wQ+AhBCmIEE8CsXvWZhYYHf+73fewujMzAwMPhmIIQ4VwH7zhqIU/xBYFfX9atKeRsYGNwS6XSaeDw+8m92u52HDx8O9Vo2eH94XwzEnwH+/rsehIGBwVnK5TI2m41QKDT0eLPZpFQq0e12sdls72h0BtfhzhsIIYQN+GPAXz7n7z8D/AzA3NzcWxyZgYEBQKvVwufzMT09PfR4pVKhVCrRbrcNA/Ge8j5kMf0k8CNd19Oj/qjr+vd1Xf9U1/VPJyZGxlkMDAxuiV6vR7fbxel0nvmb3W4HoNPpvO1hGdwQ74OB+LMY7iUDgztJq9UCwOFwnPmb3DUYBuL95U4bCCGEC/hDwD9612MxMDA4odPpKMPQbDYBRu4ghBBYrVba7fZbHZ/BzXGnDYSu6w1d10O6rpff9VgMDAxOODg4YHt7GzjZQZhMpnNjDDabzdhBvMfc+SC1gYHB3aHX61GtVgFoNBo0m82RuweJ3W6nXq+/reEZ3DB3egdhYGBwtyiXy0P/b7VaI+MPErmDMDpXvp8YBsLAwODSlEolbDYbbrebfD5/bgaTxGazoes63W73LY7S4KYwDISBgcGl0DSNSqWC3+8nEAio4PNFOwgj1fX95k4YCCHEf/Cux2BgYHAx1WoVTdMIBAIEAgH1+Ot2EGAYiPeVO2EggJ971wMwMDC4mFKphNlsxuv14nA4cDgcF2YwwdcGwkh1fT+5K1lMhpKXgcEdRtM0isUifr9fCe9FIpHXTvwmkwmr1WrsIN5T7oqBMFIcDAzuMIVCgX6/z6CczWlxvvMwaiHeX+6Ki8nYQRgY3GFyuRwOhwOPx/PGr7XZbIaL6T3lrhiIz971AAwMrkO320XTtLf+uTKzaLDOoNvt0mw2b2xSbjQa1Ot1riqGabfbjR3Ee8pbczEJIf494CGgcuJ0Xf+rr/792bc1DgODm0bXdTY2NhgfHycajd765/X7fQDq9TpHR0e0222CwSCLi4tUKhV2dnbUc4PBIPPz85jN5it/XiaTwWQyXdqldBqHw4Gu61QqFXw+38jn9Pt9NE1DCIHFclc83wZv5UwIIX4RcAF/APjbwJ8CfvdtfLaBwW1Tq9Xo9XpKuO4q9Pt9JYB3GiEEZrOZbrdLMpmkUqmov9ntdsLhMJlMhna7TSqVwmw2Mzk5SavVYnd3l3g8zqefforL5XrjcaVSKfL5POFw+MpGZmxsjOPjY46Pj0caiEKhwMHBgdoFra2tXcmVZXDzvC1T/RO6rj8WQnyl6/ovCCH+OwyFVoNvCFJ+4rIunX6/T6PRUG6Xer1OPp+/lIvKYrEwNTWFxWLBZDIxNjaGyWTC6XTyO7/zO5TLZRYWFqjVasCJAZHtQL/3ve9hMl3eq5zJZEgkEoyNjTEzM3Pp151GCMHU1BSHh4eUSqWhGopms8nh4SEul4uxsTFisRi5XA6Xy/VGY72LdLtd+v0+QghVMPi+8bYMhFxaNYQQ00AeWHxLn21gcKtIA3GRnz0ej5PP54ETwbtBhBCMjY0RCARGToqapim3UjAYHPkcl8tFJBLho48+OtPZ7Uc/+hH7+/vE4/FLd13UNE2t+BcWFq7dUzoUCpFKpYjH4zQaDfV4oVCg0+nQ6XSo1+vE43F2dnbI5/Pcu3cPr9d7rc99V3Q6HZ49e6Z2RW63m2g0isvlQgjx3hi/t2UgflUIEQD+W+BHnKS1/u3XvejVa/428MGr1/yHuq7/9m0O1MDgIqT+EJy4TuBE8tput9Nut+l2u1it1qHX6LpONpvF4XDgdruxWCx4PB61qrRYLNeKEcBJIFkIQTgcPjP5zM7Oqt1AIBA4Nw6g67oyBOVymX6/z+Tk5LWNA5wYwZmZGfb29kgmk+pxi8XC2NgY1WqV6elpXC4XsViMdrtNqVRSBiKdTp/RcxofH79Q5uNd0mg00HWdaDSKyWQinU6ztbWl/j4xMcHs7OyNHNvb5K0YCF3X/9qr//6yEOJXAcclezz8TeCf6rr+p171pn5zJ6rBO6der59ZNY9CCIHH47mzq6tms8nBwYH6PZfLKSMRDofVxHbaQEiJiunpafx+/62N7byq5mAwSDgcplgsUqlUcDgcZybbfr/Py5cvcbvdrKysUCgUsFqtN7qCDwQCfOc73znz+MbGBh6Ph0gkwvj4uJIRl7LitVqNeDyOyWRSE6qmaRQKBdbX1+9kv2sZj5IGe3x8nGKxSK/Xo9Vqkc1m6ff7I3dn7Xb7TDzL5XKd+z07nQ4mk+lWgvu3aiCEEH/ygr+h6/q5cQghhA/4N4E/B6Dregf4RubKNRoNdnd3mZ+fP3d1977SaDR4+fLlpZ/vdrtZW1u7kyurQqGAEIJHjx7R6XTY2toimUxit9vVeRvlZqpUKgghbtVdclFfBqm+mslkqFarZLPZM/GORCJBtVpFCMGzZ89UrMBut3Pv3r1bOx+dTodms6liHHJ3Va/XaTabdLtdSqUSQggeP36sdlrNZpPNzU22t7eJRqP0ej31EwgE0DQNh8PxzoxHs9nEbrerxc7pLDC73U4ikUAIwcLCwtBrt7a2zlxHXq+XYDCIpmlMTk4O/S2VSlEoFPjwww9v/Dzd9g7ij776Nwz8BPCDV7//AeA3uDhQvQRkgf9VCPEh8EPg53RdH+o+IoT4GeBngEv7V+8auVyOTqfD3t4ea2trF4qfvW9ks1lMJhOrq6uvvXgbjQZHR0ckk8kzfvS7QKFQwOfzYbVasVqtLC8vs7OzQzAYvFBzqFwu4/V6b3Vn1Gw2h4K/pwkGg+zu7pJKpfD5fMzMzCj3TKlUolarqWvviy++oNFo4PF4ePLkCQCLi4u3MtnK+M3gzsrv95PL5cjlcuzv79NoNPD5fENuOKfTyfz8PD/4wQ/48ssvgRPjYrPZMJlMRKNRfD4fq6urNz7my/C6PhmRSARN00gmk7hcLsLhsHpdp9MZ2m1mMhmKxSKNRgNN04auNzjZoXo8nlsx4rdqIHRd/ymAV26lB7quJ1/9PgX8rUuM7TvAX9R1/XMhxN8E/nPgvzj1Gd8Hvg/w6aefvneSHbquUywW8Xq9tFotdnZ2WF9fP+OmeB/p9/sUCgXGxsYulbbodrtpNBokk0m8Xu+dClBWq1U6nc5QnYPP5+PRo0dYLJZz+y+3221ardaVi8wug1w5XzQhBYNB7HY7W1tbPHjwgHA4jBCCYrHIkydPEEIQCoXo9/usrKywvr7O5OQkX375pdo53bt378bHXi6XsdvtQ2MPBoM4HA4ODw/V5AfCSvAAACAASURBVPfd73536HX9fp9UKsXs7CyBQACz2Yyu68RiMSqVCm63m1qtNhRXeVvouk6r1XqtO3F6eppms0ksFlMxJLmzGxsbUzEqn89HPB5HCIHD4SCdTjM7OwucZEq1Wi3Gx8dv5bu8rSD1gjQOr0gDr7va4kBc1/XPX/3+DzkxEN8oqtUqvV6PcDiMzWbj5cuXJBKJM9vO9xGZuvkmk+Ps7CzVapWjoyMePHhwZ1xNhUIBk8l0ZpU+aMhHVQzLmoXbdB1Kf/XrWn/eu3ePJ0+eEIvFeP78uRLga7VarK+vqzoJu91OKBTC4/EQDAbp9/vU6/Uzk221WlXfT2ZayWwrh8Px2qJBWQV++vqw2+18/PHHeL1eNjY2KJfL+Hw+dF0nHo/TbrfVz9ra2tBEHIlE2NzcxGazKTfVVeo/rkOr1ULX9Ut5AhYXF9nd3aVSqdDv98lkMkxPTw+lxbpcLmq1GjabjUgkQi6XU6nOtVqNVqt1bg3NdXlbBuI3hBD/L/D3OclG+jPAv7joBbqup4QQMSHEmq7rm8AfBDZuf6hvl0KhgNlsViqZk5OTpFIpxsfH39tiIZkBk8lkcLvdb3SDSvfA3t4exWJRBYHfBXJC6nQ6VCqVc9NQJTabTdUfSEql0pkV8iCtVotut3ut3dJlDATA5OQk4XCYiYkJ3G63jAPi8/l4/PjxSGPs8XjI5XKYTCYajQZutxs48XtLH7r8MZvNmM1m+v0+pVKJiYmJC91SUiJk1ErbZDIRDAYJBoMUCgVqtRrtdptMJoPT6cRkMrG4uHjmtW63G7PZrJIiarXaOzEQ8PrzASj3K5wsqF6+fHnGvepwOKjX69jtdqLRKJubm5RKJT744ANevnzJ0dERbreb2dnZG3djvq0spp8VQvwJToLOAN/Xdf1XLvHSvwj8vVcZTHvAT93WGN8FmqapYKC8OaempigUChwdHTE3N4fJZHrtBd7v9zk6OlIX5uTk5DubWGu12pDUw1ViCcFgEKfTyfHxMcFg8MzE1el06Ha7arK6Ler1OplMBrvdjtPpPBMcPI3dbqdQKKiVtlxhX3QM9vf3aTabPHr06MpuxVarhdlsfu3rm80mDoeD6elpFhcX0XWdL7/8Uh1jTdPOTDDBYFDtMur1Om63m3g8TjqdZmxsjPn5eVqtltpJyMDwixcvqNfrFxqIwf4So/D5fHg8HsxmM8lkklarRTAYZGlp6dz3FELg9/upVqvYbDaq1ary778tpMF+0+I4p9OJEOJMBlOn01EuTJvNRr/fJ5FIYDKZyOVyLC4u8ujRo1uJcb1N0ZPfBrRXP19c5gW6rj8BPr3NQb1L8vk8/X5/aDI3mUwqX3xzcxM4yfeen58f+R79fp/t7W0VyKvX60Ppl28bmZp4//59zGbzlStIp6en2d3dpVAonNEAOjg4UBPA6V2W0+kkEolcbfCnkAVda2trr518j4+PSSQSJBIJZmdnmZiY4OjoCLvdfq5hqVQq6jOkP/0qXJTBdPrzBp8n3RrSjfT8+XOcTicrKyvKKAcCASwWC9VqlRcvXlAoFMhms8rIpFIpjo+PVUGYEIKPPvoIk8lErVYjGAyOHIuu62cWR6ex2+08evSIQqFAIpHAbDZf6hj5fD4KhYJyzdwE7Xaber2O3+9/bc2KNMSjJmx5v7ZaLVUgOTMzoxYUMlNpMMhdLpdxOByYzWaKxSJTU1NMTk5is9lwuVzMzs5eu47mPN6WFtNPAz/PSRaTAP5HIcRf1XX9f3kbn38XabfbxONxvF7vGf90MBjkwYMHdLtdKpUK6XQaq9V6ZiWq67oyDktLSwQCAY6Ojsjn8+8kOAcnOwin03ntbX0gEMDpdJLJZIYMRK/Xo1arKddCvf51UpvMjfd4PDfinms0Gipj6SKazSbJZBJN02g0GsRiMRWoXF5ePndlJ8+rz+cjm82qm36QTCZDPB7HYrGMLMDr9XpsbGzg8/loNBqq6E4GrrvdLqlUik8++YRqtUooFKLdbqvkCLPZjM/nIxaL0e126Xa7xONxZmdn0TQNTdOwWq3s7u6qTKLDw0M1wcPJ9To3N0elUmF/f59Wq4XH41GLBUmlUmFvbw8hBN1uV6WkXoTNZmN8fJxsNks0Gr3ULkteGzIj6LyMona7rWJL5xnxXq/H0dERxWIROFnASSNhNpuZnp4+c34vymBKpVJKGbfX65HJZKjVaoyPj1MoFJicnETTNDY2vvamSzeczWbj+PgYu92upEtMJtOtJnO8rR3EfwZ8rOt6HkAIEQJ+C/hWGghd19nf3x+ZAy1xOp04nU58Ph/9fp9kMkkymUQIwfz8PKFQiEKhwLNnz1hcXMTtdivBuEajQavVeuvpsrquq4v9JgiFQiooKXci0m89NTV1xsWkaRrPnj0jkUiwtrZ27c9vNBqXMnS5XE7VRxSLReLxuEpHPG8CbDQaVCoVotEoY2NjFAoFYrEYPp8Pm82G3++n0WgQj8dxu90ji9u63S4WiwWfz0c0GiUUCtHr9ej3+2rce3t7tNttfu3Xfo3Hjx8zMTFBtVollUpRLBYJBoM0Gg1loHRdJ5PJoGka5XKZbrersoEcDodyRy0unijlOJ1OtUuQRrler+PxeDg+Pqbf76vVrTxOwWCQZ8+e0W63z2QnjcJisfDo0aPXPm/w+cFgkFQqxd7eHr1ej6mpKRwOBy6Xi263q+IacLKq7/V62Gw2dF1XP0IIMpkM2WxWZUsVi0VVRNjr9bBarUPGRa7+R+2c2u026XSaUCikUvJLpRKHh4ccHR0BJ+5hWQcyiN1u5/DwkE6nQyQSIRQKkUwm6fV6txpjeVsGIg4MLieqQOwtffadI5PJUK/XWVpaulRu+dzcnLqwK5UKsVgMr9fL5uam2tpL3RdZpVmv19+6gZB52jcVXA8Gg8TjcQqFAlNTU8DJdttisYyMP5hMJqampjg6OrpQWvoyyBv9dStcTdPI5/MqbuJ2u9VEKCdRiczwKZVKJJNJzGYzExMTmM1mtUqWq3Kfz0en08FisbC8vKyqZKVsRy6Xo9lsomkaFotFidvJ60nTNLa3t+n1ekxMTKiivgcPHlAsFtnb21OFaFtbW/T7fRWEz+VyHBwcsL6+zvT0NEIInE4ne3t7NBoNFhYWRsZVbDYbFouFSqWCzWaj1WqpDKR+v6/iFjMzMxwcHNDtdslkMsoleBM7XumvX1paIhKJUCwW2dra4vPPP1c7G7vdjs1mY2JiAr/fz8HBAVtbW0PnS6Ysf/HFF6pewW63qziAEIJcLseTJ09YWVlhcXERk8mkzp/T6aRUKg0Z9WKxiBBiKLtLSp/Ia0PukEZdd/F4nH6/TygUUt9Rft/b4rYrqf/TV/9NAJ8LIf5vTrKY/jjfYLnvXq9Hu90eOYl1u12Oj4/x+/3n+mdPI4RQqYChUIiNjQ02NzdJp///9s48tvXsuu/fy33fREqiFmp52t+8ybyZwczYMQqPnbZ2aoyL9h8bDmC0BQIUBZoaCdoYBtqm/ato3KZ/uEvgtnFbN0GbxI0RwMG47hhjG7A9dt549J5WaiMlUlzFneKm2z+oc4aUSElPK9/M/QDC06Mk6oj8/e659yzfE8PQ0BDu37+PaDQKnU6HarWKcDj81Dt5KlG8SjMU7ciuy0FQjoHirlJKZLPZMxdtr9eL/f19bG9vtzlIo9H4VNo35XIZUspzd2etozhJCymTycDr9fLO+eDgAHt7e209EhaLpW1OQyAQYCeYyWT4FDI9Pd0mobC9vY10Os1VK7FYDAaDAblcrk0GnJzQ6Ogo7HY7XnrpJWQyGfz4xz/G5uYmarUa3G43UqkUDAYD/H4/50O0Wi1MJhNmZ2f5dxsMBqyvryMajfIppFNoQ6vV4vHjxxgaGuJcEX0/VYQVCgVYrVY4HA6EQiFsbW1Bo9HghRdeuJK20uHhIVZWVvg6Pjg4wP7+PjKZDJ+0crkcCoUC9Ho9h3QsFgtSqRS/b1SVRRIZs7OzfLKqVCrI5XKoVCooFApIpVJIp9Mol8vo7++H3W7nJrhWWRZidHT0VJhMo9FcKMFst9tRq9X4NbJarTdeqHHTJwi6gjaOP4g/u+Hfe6eQcufCwsKpXfzu7i6klJdOSFL8cXt7G/V6HRMTEzCZTLz7OTg4gMFgQDKZvHAvxeHhIdbX19FoNPDgwYNLJ7zy+Tzvsq4Lt9uNcDjM5aC00+2GEAKBQADRaJR3ZUCzo5vqyKvVKiqVypmxW1osTzoIKSWKxSKHX/L5PMxmMzvFqakp1Ot17O3twWKxYHt7m5OMY2NjXBHV6XRDr5vP54PZbEYsFmtbMBOJBNLpNIaGhuD3+1GtVrG7u4vx8fFT7/XKygoGBwdx//59AE2H99Of/hS1Wo17B3w+H9xu9ymHPjY21lb4ADQXJ7/fj4ODA6RSKaRSKUxMTMDj8SCTySCfz0NKiUgkgsPDQ0xNTXFvxOjoKMLhMAKBAB48eIBSqYR6vQ6z2Yxf/OIXaDQaSCaT8Pl8uHfvXtf3pBMUUms0GlhdXUW9XocQAqurqzg6OsLMzAxGRkZ44afNm5SSnYfJZOITQb1eh8fjgZQSqVQKlUqFN192ux0ulwt6vZ43d2trawgGg0gmk5zcJwfv8XgwPz/Ptl51GNLJE+ltcNOd1L9zk8/fi1DzEdB0BtPT08jlctjf3+cYvd/vv5I+/MDAAMLhMPx+/6lTgs1mg9ls5ia183YmhUIBGxsbkFKi0WjwcJjLcFbVymUhB0E76otoGjmdTjidThQKBUSjUU7IhsNhTExMcI382NhY11NWqVSCVqtFPp9HsVjkWDa9ThTa0Wg0GBwcxP7+PjQaDd59911sbm4ikUjgnXfe4coUp9OJSCSCV155pWNClEJaQDOGTjvaTCbDAob5fB5Op5NPGtSHcDLcUy6XUSwW22Y4mM1mvPrqq10F/Voh2YZ8Pt/myD7+8Y/ze7CxsYGtrS0Ol9IumEImBoMBw8PDiMViCIVCWFtbg91uRygUwvj4OEwmE5aWlhAIBODz+fDWW29ha2vrwg6C4vnJZBJHR0fcjUzh2JdffhlDQ0Nn/q2Dg4OIx+NcTZVIJJBKpRCPx9FoNBCJRFCv1zE0NASbzca9I0BThI/KfI+OjrCysoKNjQ0+1VHVFd2n1xHuvQsRy9uqYnoZwFcAjLX+Tinl87fx+2+Tg4MDTlBSwjIej0Ov13OH6lXLMEkIzOVynboB9Ho9XC4XotEoisXimYtpPp9HMBiEXq/H9PQ0tre3EY/HOVxCfw8tsmdBC+d1N/fRbo2crsfjudAJp9FoYHNzEwC41JSE6gKBAEsc2O32js66VCohn89jY2MD29vbaDQa3MxoMpnYWdDitLW1he3tbTidTjz//PP8nrtcLgQCAU6g/+hHP+JFkhq+SqVS28AgIQTS6TQCgQDq9TqCwSAajQY0Gg30ej2WlpYgpUS5XIZer8fa2hr8fj9Xe1EO5GR58EXDN9R7c7JEtDUUMjU1hWAwiHK5jEAgwDv0arWKxcVFlEolDAwMcA+DVqvF9PQ0pJQIBoMcxyeNp0AggK2tLXaIGxsbbSdAQkqJarXKjsrr9XKeY2FhgTvAL/q39vf384Zobm4OtVoNxWIRjUYDy8vLCAQCnFBuNBps/+7uLpxOJ8xmM9544w1+H6kPY3BwEA6Hg3WUKD9lsVjaTpy9zm0lqb+JZiXTIpp9EB9YUqkUjEYjJiYmUCqVEIvFYLVaMT09fS21yuFwmBefbg1Y/f39CAaDHePEkUgEuVwORqMRBwcHMJlMmJ6ehl6vR39/PzY3NznOn81msbW1BZPJdKEdkM1mOzepexnOaozqRjgcRr1eb5OQ8Hq92NzcRDwe55LOxcVFrswhpyilxDvvvINyuYyBgQFuzqKbmkJy9H7qdDrUajVotVr09fXB5/Ph4OCAY9hWqxUejwejo6N49OgRwuEwO5xarYZqtQqXy4X+/n5YrVZEo1Hs7++jXC6zE9BoNGg0Gtjd3eWEdK1W48WQQlkWiwXpdJr7Fy6L3W5HLBbregpt7QBuzetQJRCVwlKSmEpJnU4nX2OtRRrUPR8OhzE0NMSlzPS7qbIIACeabTYbyuUyEokEpqenr0Wsk5w6Leqt1zO936Ojo1hZWcH+/j7Pe3jxxRfx6NEjxGIxng9uMpkwMDCAZDKJfD6Pg4MDJJNJAM3Ty0Xnl1O4Kx6P82t1U7LxJ7ktB5GQUn77ln7XnVGtVnnwCZWwplIpjIyMXItzyOfziMfj8Hq9Zz4n1bW/9dZb+MxnPgMAXHceDodhMplQrVZhs9kwOTnJCwnFvcPhMObm5rgBa2ZmpuvvIq1+2v2urq6yXMZF6rPL5TIikQg8Hs+Vw1N0QqAafb/fz86BKmpoMaNKL/r+VhKJBNbW1jA4OAir1QqbzcbhHgAcu251+k6nE/Pz89DpdKhUKpwQPzw85LGdtJCQfITRaGSRPepX0Gq1KJfL3CvQ19eHyclJPm3k83keRkN1+C6XC/v7+4hGo1wpc9XuYbvdjv39fRQKha7VYJ0S/ul0Gjs7O0ilUlheXubrn5rqXC4X7t27h1qt1nb6tdls8Pl8iEajPFypr6+PnRTpGwHNBTOfz8NisXBu4LI5PQBcaVSv11EqlXBwcIBsNgu9Xt9xp2+1WnlCXiKR4NyCy+XieQ9LS0swm83QarXQaDQYGhqC1WrlvFE8HsfAwEBHJ046U/R3plIpLmc9OjriE1i5XIZWq8X8/PyNlbreloP4Z0KIrwP4HgAu5ThrHsSzRCQSQTqdblNiBHDhhi0qlTwZPqHKCbqAqXzTZrOx2FonqPnmZz/7GTKZDGZmZriprlwu4+HDh1hYWADQXAzNZjNKpRL29/f588XFRYyOjsLr9XIp4skFgUJUVGZJlMtl1ukvl8u8ow0EAtDpdIhGo6hWq2g0Ghw6oi5VjUbDDVpAc9d2kcqjarWKjY0Nvlmp7PTJkycclqAwB4U0Njc3MTw8DK/Xy4tPNpvF97//fbz++uv49Kc/zfLRre9Vo9HAzMxMW2K4WwIylUphe3ubeyoorCKlRKlUwujoKBwOB4dnstksotEoHA4H7t+/31bpBKDrwu/3+zE4OMj1+1ctfaR4eywWa6vJp47i1vLNYrHIzrNcLnMpslarxcjICAYHB9lhZDIZLCwscI4oHo/zqSORSLBD9fv9XPVEpb4Uxtrb20O1WuXQ6Fnd2OcRCoWQSCTaHtPpdBgaGoLP5+sa9x8ZGWHZC7q+XC4XDg8PUSqVkM1mUa1WIaVErVZDLBbDiy++CLPZjKGhIa6wGhkZ4SFTdO2vrq7y6yuEgMvlgs/ng91uh5QSyWQSkUgEkUgEhUIBuVwOfX19ePDgwTM3D4L4OwDmAOjxfohJ4ux5ED0PlbIdHBzA4XBAp9PBbDY/dQKadn+JRAJTU1MAmotvJpNBPB5nAbSNjQ14PB4OLXSqFqJj/fPPP49EIsGLDe1srVYrHj9+zM1MANj+qakpPHjwgOOs5XIZ+/v7qFQqSCaTfJJIJpMoFoscqqIQFUHxf5oC5nK5uNLF7Xbzrj2RSMBiscButyMYDLIgXms5qNFoxNDQ0JnSIdR4CDTjyKSqurS0BL1ez3HfQCDAdjqdThweHp6Ks4dCIVgsFnziE5/oeAJKJpO8c79oVy/JapMTFUJ0TMZarVY4nU6k02n09/e3JZkvwnU4BoIEJDOZTFv5LPWgtJ4qcrkc50fcbjc+9rGPwWazwWAwQKvVolKpcMgtl8thZWWF80p6vZ51oMxmM4aHh2EwGGC32+H1ehEIBHB4eMgNavQ6jY+PIxaL8fPSTBWgGf6i3pKzTqW0MXM4HCwZbrFYYDQaz30dyYmchBwkdbIDzVPV1tYWlpeX2cE3Gg2sra1xrqu/vx+jo6NIJpOo1WqcyDcajW0bD7KrXq9jdnaWT8Yej+fZmwfRwi9JKS/eCtmjUMel0WhEoVBAKBTiaVjnCbl1gpKc8XgcFosFlUqFy/4ajQZ2dnZgNBoxPj7O4RGXy4V8Po+lpSUMDAzglVdegdls5h0wXfAPHz6E0WjEd77zHRQKBdRqNYyNjXEJIyXTqGyTjrM0N/fo6AiVSoU7ftfW1vDo0SPodDpuMOrr68PY2NipnbNWq8XU1BQnHPV6PY/rfPToEYQQvLOkRdNutyOZTKK/vx99fX3Q6XS8W9ra2kIoFILZbObHW18/6vb1eDwcpyXJh4mJCZZULxaLsFgsKJVKyGQyXAlDpxW6qV977bWu1U104rpo/TlNSMtkMheKOVO5KC3A9XqdpVP0ev2pxPNNcpGKIoqPj4+Pd80BWCwWfp9Jr2p9fR12ux1DQ0OYmZmB1WqF2+1GKBTC1NQUhoeH4fP52AmXy2UudabiDL1ej3A4jEwmw7pEAFjyhMQeW6EEt8lk4oISv99/bUljUkBoxefz4fDwkOdqAGB1hIODA0xOTvJY2r29PZhMprYcAzkaKSX29vaQSqXgdDoxOTmJYrGIt99+GysrKxgeHn5mTxA/FkIsSCmfWbnuZDLJnYx0FDQYDJiamrpwwqhQKHAHKS1KqVSKwz6k+0JNPNQIFw6HWTOGShidTid2d3c5rksXkRACfr+fk2tvvPEGLzpmsxkmkwk+nw/xeBxzc3PQarUYHx/HT37yE7z33ntt9goh4HA44Ha7odPpsLu7i3w+z7LLGxsbiEQi595c5BAmJiYQCoUgpYTNZuO+AKBZcvrkyRMUCgWuBqFmJeoWNRqNyGaziMfjXBJK32c2m6HX61EsFvnGGxwcRKFQgMvlgtVqRS6XY+19muHbekogR9ftZBYKhVAqlboKJ54klUohEolwySydWMrlMjwezyknQ/0TWq2WX9N4PI5o9P1RKnQaumlqtRpSqRQsFsuZHemHh4cXrl4bHBzkDQ/NaUgkEtje3sbCwgKsVisODg7gcrlO7c47Lbw071mn0/FJjYjH4zwjvPVEHwwGUalUMD8/j2QyCZPJdOMVRdTUGI/HMT09DZvNBiklxsbGsLu7y30hP/jBDxAOhzE6OnrmfIehoSEO+drtds5b3YT+2m05iI8B+KIQYgvNHIQAIM8rcxVCbKMpy9EAUJdS3rqya7FY5Hm9NpsNHo8Hh4eHXPWj0WjadrT00Wg0eNdDCpihUIi1/+k4m8lkUK/Xsb6+Dp1OB7/fz7FFj8fDC9jAwAB8Ph8SiQQKhQIePnwIh8OBn//856hUKlw2SDFyqj6heHwrbrcbwWAQKysrMJlMKBQKCAQC+OhHP8o7dLrQqHqmWq1yg9nW1hYLnaVSKQwODp65aBWLRezs7MBqtcLn82F+fv7U99OAGdot0wcNZE8mk0ilUqySSa8LDbKnmHc+n4dWq8Xs7CyGhobanqdUKsFkMuG5556D3+/vGF+m9ykWi/Gp8OjoCDs7Oyz5cZEO9WAwyNPSgKazWFtb45wLidadXNRqtRpmZmbYtlKpxAqri4uLyGazl3YQFLc/bxEJh8McBjQYDGfqID1N9zyFfVqx2+1YXl7G5uYmTxSkJPxFFrtu74XL5eLTBb2PpVKJpbTX19dPTQi8KXK5HAYGBrijnmauU5hyaWkJi4uLXBlG+cFOWCyWto1FtVqF2+3maqrr5rYcxKeu8LOvSymT12ZJB4LBIOvp04tcq9VQKpVQKBSg0+n4yAu8H+f/4Q9/yBUGJxPG5CSKxSLvEGKxGJxOJ4xGI0qlEh93+/v7WfJACAGLxYJ79+6xvgupdubzeU5GJpNJuFwufPKTn2z7vYVCAaurq4hGo6cufup0jcfjSKfTnCC0WCzQarXcN9CJ1hLQ/v5+1hEKBoNYXl6GwWDggeperxc+nw8Wi4VLNYUQKBaLnDw+SSaTaZONboV2iOl0GtVqFZlMpmONPNnp9/shhGBxQyEEJ+n1ej2cTid3zJ6c5evz+ZDL5bC3t4ejoyPY7XZuwhoeHr5QD0s2m0U2m+WO583NTezt7WFxcREmkwkjIyM8AKf177VYLCzTQDtfOi3S+5TNZk/ZUKvVzs2H1Ot1PHnyBFarFVNTU10XE7o+vF4vTCYTdnd3z9S1ItmKy0q0mEwmBAIBbG9vo1AosODgxsYGJ5/dbvdTL34Gg4H1kMhBtGpk0bV+0yE7KlLQ6XS8GWstP6cN0/LyMtxuN1599dWnqkjK5XLQ6XQ39nfc1sCgHQAQQvQDuLzYyg0gpcTXv/51XnBo102161SpQGEh2pFSqIUarWguMQDeydPNPzAwgMPDQ/T19WFiYgLFYrFtt0/zdOn3u1wumEwmHqhCi9zAwAAGBweh0WiwsrKCnZ0d3L9/v+3msdlsXB5ot9t54Tg6OsLu7i6fTF5//XU0Go02m4larcY7X7Lz8PAQ5XKZy/XoOfv6+rC8vAygGVcNBoOIx+PweDzcxES5Akrih0Ihfr3ptaP6/kAgwCWeOzs7MJlMmJychFarZdG0nZ0dTE5O8qLVutvU6/Vt7wVRKpVQq9XaZjEnk0kOE7Y6rbGxMWxtbSESiQBoOqiLhhIpTmw0GnkhHxsbQy6XQ7VaPXO2hMFgQK1Ww9LSEgqFAjQaTZtap8PhQCwWa1NIpQQoJXS77boLhQKOjo44z9QpZ0ayEjR/hOQoEolEVwdBJ+ur0NfXB7vdzs1vJEiZzWYBNK+ry5TtUsNovV6HRqNBOp3mKXXj4+MXcqxXgXTR6H7J5XIIhULIZDL4yEc+cmrE69jYWFfnQFVv9JrQzPZcLge9Xn9jYcfb6qR+A8BXAQwBiKPZUb0M4P45PyoBvCmEkAD+k5Ty9zs8968D+HUAl2qUadVnaV3UDw4OWAgNAA/soJCLXq/H1NQU7HY7Sy4AOBWOoTePGoV8Ph9mZmbO3BXRgtd6ojlJIBDA6uoqIpHIqWqXkZERZDIZrK+vtz1OYxrPqgiiJqb5E0GFFAAAD9dJREFU+fm2btStrS3kcrm22Dk9H2nE0OIYiUSQSCSws7MDt9uNgYEBxONxZLNZRCIRdoBHR0dceUKTzo6Ojrhfg5rIEokEx1zT6TQ7bcrXTE5OnhuOoIqZ0dFR6HQ6lrMOh8NYX1/H3Nwcy16PjIxgenqahdloB38RSLit1SatVsthmvP6YShURidX4H09KKfTif39feRyObjdbn69dTodkskkjwQlVdvW30V5nfHxcWxvb3c9Ldrtdr6PqBubQl8nF1Oa7HcdMfzW19fn88Hj8XClTy6Xu5KDyGQyfN/STvuqO26aPdLtJAs0rzkpJXeLU3hxfX0db775JrxeL1wuF09HJBuB9uuEJE02NzdhsVgwMjKC/f19zM3NsfzKTXFbIaZ/CeA1AP9XSvlQCPE6gM9f4Od+WUoZOT55fFcIsSKlfLv1G46dxu8DwMsvv3y2HkQXPv/5z/Oi3Gg0WDK7UCjAaDRyWGRwcJBDRRT3pvg2JYmpJ8BqtcLr9XLVjJTyzKP902Kz2bhHwePxtO08dDodFhYWWHCOsFgspxa6XC7HHcOFQoEv4q2tLczNzbH4WDqdhk6n42qikzudcrmMra0tPpVYrVZIKWG321moLp/Ps0wIANYFooXmrbfeYodhsVgwPz+PbDaL5eVlXhjD4TBr/NApi5qOTkJ/z8DAANLpNJf70u92u90wmUxYXV3F0tIS35wbGxtcLkthxYtASWaqyGnlaRolrVZr27hOeq1p3nI2m+Vy4Wq1iunpae6yPjg44NkGrYsqyb97PB44HI5TsyUIEq4jvF4vYrEY9vf34ff72yrWrlu9txUayONwOM4cgEV9Ep3uK4vFAr1ej52dHQDg8tnrgLrdz4IcMl3v1AzqcDiwu7vLM16A5j27srKCSqUCk8nEZa/U9FkqlWC32/n0s7e3h2AwiHq9fiVZ+/O4LQdRk1KmhBAaIYRGSvmWEOJfnfdDUsrI8b9xIcS3ALwC4O2zf+rpeemllzo+ns1mUalUoNVqkUqleELW+Ph41yQnhahug+HhYWSzWayvr+PevXttN6rBYDh311utVrG5uYlGo8ElrXq9HsPDw9je3uYBNjs7O7BYLJiamsLKygqCwSAvNHRxUgLe5XLBbrfD5/OxJPLR0RGsVivMZjO8Xi8qlQo7EgonbW5u8s1Dj1MZIklXk5LtCy+8wIn+1kqqUqmERqMBr9fLchhHR0eccO1Ut242m3Hv3j3s7OzwEKK1tTVsbW21jd68CDs7O6jX69zLcllo2A7JbtN1RlVl2WwWqVQK0Wi0bSIhOaUnT54gm82echB0ctTpdBe+Rk0mE1wuF+LxOOLxeNvPHR0dQavV3mhVFU3bKxQKpxZ3yqv4fL6uPSOTk5PsyOx2+7VU+VSrVd6YnRW1oCq8k4/Nzs5idnYW1WoV5XKZ/11ZWYFer2fFXJfLhaOjI7b/+eef5wmTgUAAGxtNgewPgoPICCFsaC7u3xRCxAHUz/oBIYQVgEZKmT/+/K8B+Bc3b+r7tB7d+vr6uBfhJt+Qp0Gn02F2dhbBYBBra2tc6tf6AbyflzgJlZzSsBqg6fz6+vpYtoKkBMbHxzmsFgqFEI/HEYvF4PP5YLVaUSgUOqqjptNp7jRvNBrI5XKYm5vjG6darWJ1dRUGgwHz8/Ntry31JbRW0ZzsbA4EAnjy5AlWVlb4MdqVGQwGbqgqFotddaLsdjuee+65tufc2dlBJpPp2mhFw3YI6iYeGRm5suwBOXrKF7VCDWY0a6BTFY7T6eSpcBqNhktRL2vX5OQkN3TRCa/V1pto0CJoUe+kK0Z/Y2sj30mua/xsKyReOTw8fCUJnZObOBowpNfrsbu7i8XFRe42n5ubY/kaGtxExS5UAn9dkxxbuS0H8VkAhwC+BOALAJw4f7EfAPCt44tPB+B/Sin/4iaNPI/bEsh6GoxGI2ZnZxEKhViv5uRHMplEIpHgHSU1EmWzWYyOjqK/vx96vR6Hh4e8II2Pj/MIyta5zGazGbOzs5wwpiQmhdRO4vF4+DlzuRzW19dZzbR1mhk1S7VykZ0u5SCoS1uj0SASiaBSqeDevXswGAxPLfbX19eHcDjMz3kSUvo8WXHlcDgu1TB5EpK5kB0GFrndbu52p+7lkzidTsRiMe5MJ6mMyw6XoZDhTQ+n6YRWq+UeltYTIJ0MhRAol8uo1+s3cnLP5/NIJpNt7zWFLa8yXKsTc3Nz/Hvee+89OJ1O6HQ6GI1GPPfcc9BqtXC73SzoCIAlxfV6/bPrIKSUrQNWv3HBn9kE8Es3Y9EHC51Od+YimEqlsLu7y3IUBA2NAdA1/NINEuQzGAzY39+/UIGAw+GA3+9HNBpFLpfjooBOzuFpaA11AZdTf21FCAGbzXZKhoOgxsOxsTFO5FN58nWg0WhYE6vTc15kngPlKlwuF0qlEjQazZWmtd0ldrudq5HICdBwHxpG1M2ZPw2URySSySQXAbQ6H5oad920vq9U2GI0GtHf39/23k1NTXEv1nWIgJ7FTY8czaNZiXTqS2g2yvVGrOYDTl9fH9xud5tWzUUapi6Cz+d7qkQu9ShUKhXW87+Lnel5UB6gtaSUoE5smg18E9jt9q4O4jxacxVAM/zVOuzmWcPhcCAajWJ5ebktNEkKsJFI5MoOIhKJtHWsE263+5Rg4m3gcDj45HIyREbyLbfBTU+Uu56SAcWV6ZUdJDWy9TqteYCTocVcLndtCc9uDA4Owul0XnphcjqdODg4wMbGBg/veVaxWq3o7+9vy/lYLBYMDAzwaY8KSC5LKpXi3ifCYDDcyHyTi2C32zkveJfDhW4rB6FQPFPQjvukg6D+lqvOWziPkzpRT4vT6eROdpo++KwihDhz3oPdbmd57cvkBYrFIqrVKoaGhm5VDPEs6L2nDuy7QjkIhaID3cZuUsXMddXT3xQ6nQ7z8/N3bcatQO8FlQZTPwuVYp8HDVnqJSeq0+l4tved2nGnv12h6GE6jd28aWkDxdNDDXGpVIr7kGgY1dzc3LnvFc1Due08w3nQSNe7RDkIhaILNpsN+/v72NjYaHMQV62WUVw/CwsLXJINgDWtSBGgm4IBiWZ2m+/+YUc5CIWiCzabDXa7vS05ajKZbqTeXHE1TvZA6PV6TExMYH19HY8fP+7qIKijvxd7nHoB5SAUii5otVrMzMzctRmKS+JwODA+Pn5mpzXQLEi4LXmcZw31qigUig8sfX19PVOZ9Cxy/SOIFAqFQvGBQHSa4PWsIoRIANi55I97Adzo5LprQNl4dXrdPkDZeF0oGy/GmJSyoxzCB8pBXAUhxM/uYub106BsvDq9bh+gbLwulI1XR4WYFAqFQtER5SAUCoVC0RHlIN7n1LzrHkTZeHV63T5A2XhdKBuviMpBKBQKhaIj6gShUCgUio4oB6FQKBSKjnzoHYQQ4lNCiFUhRFAI8dt3bQ8ACCFGhRBvCSGWhRBPhBC/cfy4RwjxXSHE+vG/d64aJ4TQCiEeCSH+vBdtFEK4hBB/LIRYOX49P9JLNgohvnT8Hj8WQvyhEMLUC/YJIf6LECIuhHjc8lhXu4QQXz6+h1aFEH/9juz718fv83tCiG8JIVwtX7tV+7rZ2PK13xJCSCGEt+WxW7fxPD7UDkIIoQXwNQCfBrAA4PNCiIW7tQoAUAfwm1LKeQCvAfgHx3b9NoDvSSmnAXzv+P93zW8AWG75f6/Z+O8A/IWUcg7NGefL6BEbhRDDAP4hgJellM8B0AL4XI/Y9wcAPnXisY52HV+bnwNw//hn/v3xvXXb9n0XwHNSyucBrAH48h3a181GCCFGAfxVAKGWx+7KxjP5UDsIAK8ACEopN6WUVQB/BOCzd2wTpJRRKeVfHn+eR3NRG0bTtm8cf9s3APzNu7GwiRBiBMDfAPD1lod7xkYhhAPAXwHwnwFASlmVUmbQQzaiqYdmFkLoAFgARNAD9kkp3waQPvFwN7s+C+CPpJQVKeUWgCCa99at2ielfFNKWT/+748BjNyVfd1sPObfAvjHAForhO7ExvP4sDuIYQDhlv/vHj/WMwghxgE8BPATAANSyijQdCIAbnbu5fn8HpoX+lHLY71k4ySABID/ehwG+7oQwtorNkop9wD8Lpo7ySiArJTyzV6xrwPd7OrF++jvAvjO8ec9Y58Q4g0Ae1LKX5z4Us/Y2MqH3UF0mjrfM3W/QggbgD8B8I+klGdrFt8yQojPAIhLKX9+17acgQ7AiwD+g5TyIYAi7j7kxRzH8D8LYALAEACrEOLX7taqS9FT95EQ4itohmm/SQ91+LZbt08IYQHwFQD/tNOXOzx252vRh91B7AJonYY+guYR/84RQujRdA7flFL+6fHDMSGE//jrfgDxu7IPwC8DeEMIsY1maO4TQoj/gd6ycRfArpTyJ8f//2M0HUav2PgrALaklAkpZQ3AnwL4aA/Zd5JudvXMfSSE+CKAzwD4gny/yatX7LuH5mbgF8f3zQiAvxRCDKJ3bGzjw+4g3gEwLYSYEEIY0EwSffuObYIQQqAZN1+WUv6bli99G8AXjz//IoA/u23bCCnll6WUI1LKcTRft/8npfw19JaN+wDCQojZ44c+CWAJvWNjCMBrQgjL8Xv+STTzTb1i30m62fVtAJ8TQhiFEBMApgH89LaNE0J8CsA/AfCGlLLU8qWesE9KuSil7JdSjh/fN7sAXjy+TnvCxlNIKT/UHwB+Fc2Khw0AX7lre45t+hiax8v3ALx7/PGrAPrQrB5ZP/7Xc9e2Htv7cQB/fvx5T9kI4AUAPzt+Lf8PAHcv2QjgdwCsAHgM4L8DMPaCfQD+EM28SA3NhezvnWUXmqGTDQCrAD59R/YF0Yzj0z3zH+/Kvm42nvj6NgDvXdp43oeS2lAoFApFRz7sISaFQqFQdEE5CIVCoVB0RDkIhUKhUHREOQiFQqFQdEQ5CIVCoVB0RDkIheKSHKtxfrXl/78lhPjnd2iSQnGtKAehUFyeCoC/1SrZ3IljIT6F4plDXbgKxeWpozlT+EtoNjkxQog/QFPJ8yGacgp5AAUp5e8ef/0xmpIQQFNU7odoymzsAfislLJ8G3+AQnEW6gShUFyNrwH4ghDC2eFrMwB+RUr5m+c8xzSAr0kp7wPIAPjb12yjQnEplINQKK6AbKrs/jc0B/+c5H9LKRsXeJotKeW7x5//HMD4NZmnUFwJ5SAUiqvze2hqAVlPPF5s+byO9vvN1PJ5peXzBlToV9EjKAehUFwRKWUawP9C00l0YxtNqXEIIV5EU/ZZoehplINQKK6HrwI4q5rpTwB4hBDvAvj7aCoIKxQ9jVJzVSgUCkVH1AlCoVAoFB1RDkKhUCgUHVEOQqFQKBQdUQ5CoVAoFB1RDkKhUCgUHVEOQqFQKBQdUQ5CoVAoFB35/ykMfCI50MrqAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, "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": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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[0].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": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": 15, "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 }