{ "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/master?urlpath=lab/tree/spectrum_analysis.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", "[spectrum_analysis.ipynb](../_static/notebooks/spectrum_analysis.ipynb) |\n", "[spectrum_analysis.py](../_static/notebooks/spectrum_analysis.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Modeling and fitting\n", "\n", "\n", "## Prerequisites\n", "\n", "- Knowledge of spectral analysis to produce 1D On-Off datasets, [see the following tutorial](spectrum_analysis.ipynb)\n", "- Reading of pre-computed datasets [see the MWL tutorial](analysis_mwl.ipynb)\n", "- General knowledge on statistics and optimization methods\n", "\n", "## Proposed approach\n", "\n", "This is a hands-on tutorial to `~gammapy.modeling`, showing how the model, dataset and fit classes work together. As an example we are going to work with HESS data of the Crab Nebula and show in particular how to :\n", "- perform a spectral analysis\n", "- use different fitting backends\n", "- acces covariance matrix informations and parameter errors\n", "- compute likelihood profile\n", "- compute confidence contours\n", "\n", "See also: [Models gallery tutorial](models.ipynb) and `docs/modeling/index.rst`.\n", "\n", "\n", "## The setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from astropy import units as u\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as st\n", "from gammapy.modeling import Fit\n", "from gammapy.datasets import Datasets, SpectrumDatasetOnOff\n", "from gammapy.modeling.models import LogParabolaSpectralModel, SkyModel\n", "from gammapy.visualization.utils import plot_contour_line\n", "from itertools import combinations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model and dataset\n", "\n", "First we define the source model, here we need only a spectral model for which we choose a log-parabola" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "crab_spectrum = LogParabolaSpectralModel(\n", " amplitude=1e-11 / u.cm ** 2 / u.s / u.TeV,\n", " reference=1 * u.TeV,\n", " alpha=2.3,\n", " beta=0.2,\n", ")\n", "\n", "crab_spectrum.alpha.max = 3\n", "crab_spectrum.alpha.min = 1\n", "crab_model = SkyModel(spectral_model=crab_spectrum, name=\"crab\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data and background are read from pre-computed ON/OFF datasets of HESS observations, for simplicity we stack them together.\n", "Then we set the model and fit range to the resulting dataset." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "datasets = []\n", "for obs_id in [23523, 23526]:\n", " dataset = SpectrumDatasetOnOff.from_ogip_files(\n", " f\"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits\"\n", " )\n", " datasets.append(dataset)\n", "\n", "dataset_hess = Datasets(datasets).stack_reduce(name=\"HESS\")\n", "\n", "# Set model and fit range\n", "dataset_hess.models = crab_model\n", "e_min = 0.66 * u.TeV\n", "e_max = 30 * u.TeV\n", "dataset_hess.mask_fit = dataset_hess.counts.geom.energy_mask(e_min, e_max)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting options\n", "\n", "\n", "\n", "First let's create a `Fit` instance:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "fit = Fit([dataset_hess], store_trace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default the fit is performed using MINUIT, you can select alternative optimizers and set their option using the `optimize_opts` argument of the `Fit.run()` method. In addition we have specified to store the trace of parameter values of the fit.\n", "\n", "Note that, for now, covaraince matrix and errors are computed only for the fitting with MINUIT. However depending on the problem other optimizers can better perform, so somethimes it can be usefull to run a pre-fit with alternative optimization methods.\n", "\n", "For the \"scipy\" backend the available options are desribed in detail here: \n", "https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "No covariance estimate - not supported by this backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 248 ms, sys: 5.96 ms, total: 254 ms\n", "Wall time: 265 ms\n" ] } ], "source": [ "%%time\n", "scipy_opts = {\"method\": \"L-BFGS-B\", \"options\": {\"ftol\": 1e-4, \"gtol\": 1e-05}}\n", "result_scipy = fit.run(backend=\"scipy\", optimize_opts=scipy_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"sherpa\" backend you can choose the optimization algorithm between method = {\"simplex\", \"levmar\", \"moncar\", \"gridsearch\"}. \n", "Those methods are described and compared in detail on http://cxc.cfa.harvard.edu/sherpa/methods/index.html. \n", "The available options of the optimization methods are described on the following page https://cxc.cfa.harvard.edu/sherpa/methods/opt_methods.html" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "No covariance estimate - not supported by this backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 569 ms, sys: 12.4 ms, total: 581 ms\n", "Wall time: 620 ms\n" ] } ], "source": [ "%%time\n", "sherpa_opts = {\"method\": \"simplex\", \"ftol\": 1e-3, \"maxfev\": int(1e4)}\n", "results_simplex = fit.run(backend=\"sherpa\", optimize_opts=sherpa_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"minuit\" backend see https://iminuit.readthedocs.io/en/latest/reference.html for a detailed description of the available options. If there is an entry ‘migrad_opts’, those options will be passed to [iminuit.Minuit.migrad](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.migrad). Additionnaly you can set the fit tolerance using the [tol](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.tol\n", ") option. The minimization will stop when the estimated distance to the minimum is less than 0.001*tol (by default tol=0.1). The [strategy](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.strategy) option change the speed and accuracy of the optimizer: 0 fast, 1 default, 2 slow but accurate. If you want more reliable error estimates, you should run the final fit with strategy 2.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 184 ms, sys: 4.82 ms, total: 189 ms\n", "Wall time: 201 ms\n" ] } ], "source": [ "%%time\n", "minuit_opts = {\"tol\": 0.001, \"strategy\": 1}\n", "result_minuit = fit.run(backend=\"minuit\", optimize_opts=minuit_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit quality assessment\n", "\n", "There are various ways to check the convergence and quality of a fit. Among them:\n", "\n", "- Refer to the automatically-generated results dictionary" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : scipy\n", "\tmethod : L-BFGS-B\n", "\tsuccess : True\n", "\tmessage : b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", "\tnfev : 60\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(result_scipy)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : sherpa\n", "\tmethod : simplex\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully\n", "\tnfev : 135\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(results_simplex)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : minuit\n", "\tmethod : minuit\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully.\n", "\tnfev : 39\n", "\ttotal stat : 30.35\n", "\n" ] } ], "source": [ "print(result_minuit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Check the trace of the fit e.g. in case the fit did not converge properly" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Table length=39\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
total_statcrab.spectral.amplitudecrab.spectral.alphacrab.spectral.beta
float64float64float64float64
30.349530528526093.812199712807204e-112.19574697385665330.2264826943628319
30.3510341736428053.822199712807204e-112.19574697385665330.2264826943628319
30.3510022204994673.802199712807204e-112.19574697385665330.2264826943628319
30.349547240271553.813199712807204e-112.19574697385665330.2264826943628319
30.349543570065923.8111997128072045e-112.19574697385665330.2264826943628319
30.3701452638072133.812199712807204e-112.20800548935549120.2264826943628319
30.370743199655053.812199712807204e-112.18345779345805460.2264826943628319
30.349732488785483.812199712807204e-112.1969742370517340.2264826943628319
30.3497468312254673.812199712807204e-112.1945194040086120.2264826943628319
30.34953668896493.812199712807204e-112.1959790110914530.2264826943628319
............
30.349538056342043.812174134402915e-112.1957554318403510.22635139153323025
30.349530752742773.8123158974689993e-112.1957554318403510.22648880390558834
30.3495307362918473.812032371336831e-112.1957554318403510.22648880390558834
30.349530785615513.812174134402915e-112.1958018400905260.22648880390558834
30.3495307033776143.812174134402915e-112.19570902315176930.22648880390558834
30.349530717519783.812174134402915e-112.1957554318403510.22651628638005997
30.3495307714638973.812174134402915e-112.1957554318403510.22646132143111675
30.3495357927311783.812882949733337e-112.1959874687050720.22648880390558834
30.3495371367213383.812882949733337e-112.1957554318403510.22662621627794644
30.3495593445396283.812174134402915e-112.1959874687050720.22662621627794644
" ], "text/plain": [ "\n", " total_stat crab.spectral.amplitude ... crab.spectral.beta\n", " float64 float64 ... float64 \n", "------------------ ----------------------- ... -------------------\n", " 30.34953052852609 3.812199712807204e-11 ... 0.2264826943628319\n", "30.351034173642805 3.822199712807204e-11 ... 0.2264826943628319\n", "30.351002220499467 3.802199712807204e-11 ... 0.2264826943628319\n", " 30.34954724027155 3.813199712807204e-11 ... 0.2264826943628319\n", " 30.34954357006592 3.8111997128072045e-11 ... 0.2264826943628319\n", "30.370145263807213 3.812199712807204e-11 ... 0.2264826943628319\n", " 30.37074319965505 3.812199712807204e-11 ... 0.2264826943628319\n", " 30.34973248878548 3.812199712807204e-11 ... 0.2264826943628319\n", "30.349746831225467 3.812199712807204e-11 ... 0.2264826943628319\n", " 30.3495366889649 3.812199712807204e-11 ... 0.2264826943628319\n", " ... ... ... ...\n", " 30.34953805634204 3.812174134402915e-11 ... 0.22635139153323025\n", " 30.34953075274277 3.8123158974689993e-11 ... 0.22648880390558834\n", "30.349530736291847 3.812032371336831e-11 ... 0.22648880390558834\n", " 30.34953078561551 3.812174134402915e-11 ... 0.22648880390558834\n", "30.349530703377614 3.812174134402915e-11 ... 0.22648880390558834\n", " 30.34953071751978 3.812174134402915e-11 ... 0.22651628638005997\n", "30.349530771463897 3.812174134402915e-11 ... 0.22646132143111675\n", "30.349535792731178 3.812882949733337e-11 ... 0.22648880390558834\n", "30.349537136721338 3.812882949733337e-11 ... 0.22662621627794644\n", "30.349559344539628 3.812174134402915e-11 ... 0.22662621627794644" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_minuit.trace" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Check that the fitted values and errors for all parameters are reasonable, and no fitted parameter value is \"too close\" - or even outside - its allowed min-max range" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "Table length=4\n", "
\n", "\n", "\n", "\n", "\n", "\n", "\n", "
namevalueunitminmaxfrozenerror
str9float64str14float64float64boolfloat64
amplitude3.8122e-11cm-2 s-1 TeV-1nannanFalse3.546e-12
reference1.0000e+00TeVnannanTrue0.000e+00
alpha2.1958e+001.000e+003.000e+00False2.626e-01
beta2.2649e-01nannanFalse1.397e-01
" ], "text/plain": [ "\n", " name value unit min max frozen error \n", " str9 float64 str14 float64 float64 bool float64 \n", "--------- ---------- -------------- --------- --------- ------ ---------\n", "amplitude 3.8122e-11 cm-2 s-1 TeV-1 nan nan False 3.546e-12\n", "reference 1.0000e+00 TeV nan nan True 0.000e+00\n", " alpha 2.1958e+00 1.000e+00 3.000e+00 False 2.626e-01\n", " beta 2.2649e-01 nan nan False 1.397e-01" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_minuit.parameters.to_table()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Plot fit statistic profiles for all fitted prameters, using `~gammapy.modeling.Fit.stat_profile()`. For a good fit and error estimate each profile should be parabolic" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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tq7rftwb7pNZkvADTjcIpuVT8Pl8CJ/gMn+C3fX2FkwD2utNdXMW8Z+HXYg/ngLjGnX4W7oHOHZaMc7AqdNf1pT7DLsG57lLo/s7/ATr4zfuXOGfU+TgHvtSa7J/uOCk4J8zd/T6Pwrl4v9vdrlbhnKiJ3/f0X28VyTce+Kcb816cVq/jfLavL92Y9uK0ZrvGZ773uvPy3a73V/Jbn0jglpwf4ZSGAk1zmbvMvTgnTC9UsS5PDPAdZ/lsQ4pzEuEb6/FVbXviThwS4tyYlquqvwvZQo0xxngqbHsGMMYYExks0RhjjAmqkFadGWOMaXysRGOMMSaoqryPxktt2rTRjIwMr8MwxpgGZf78+TtVta3XcfgK20STkZFBVlZl3YcZY4wJREQ2Vj9WaFnVmTHGmKCyRGOMMSaoLNEYY4wJKks0xhhjgsoSjTHGmKCyRGOMMSaoLNEYY4wJqohLNAty8nnso5Veh2GMMcYVeYlmYz7/+GINP2zZW/3Ixhhjgi7iEs35QzsTFxPFK3PD7uZYY4xplCIu0SQ1i+WMAZ14Z+Fm9heXeh2OMcY0ehGXaAAmjkyjsKSM/y7c7HUoxhjT6EVkohmUmsRRnVoy5buN2PN2jDHGWxGZaESECSPSWbFtHwty8r0OxxhjGrWITDQAZw3qRPO4GF75LsfrUIwxplGL2ESTEBfDuUNS+GDJVnYXlngdjjHGNFohSzQicquILBeRZSLymojEB3uZE0akU1JWzrT5m4K9KGOMMZUISaIRkRTgJiBTVfsB0cDFwV5urw4tGJbRiilzcygvt0YBxhjjhVBWncUATUUkBmgGbAnFQieOTGfjrgPMWbMzFIszxhjjJySJRlU3A48BOcBWoEBVP/YfT0SuFZEsEcnKy8url2WP69eB5IRYplhPAcYY44lQVZ21As4CugCdgAQRmeg/nqpOVtVMVc1s27ZtvSw7LiaaCzI782n2DrYVFNXLPI0xxtRcqKrORgPrVTVPVQ8B04FjQrRsJgxPp1yV1+ZZU2djjAm1UCWaHGCkiDQTEQFOAbJDtGzSWjfjhB5tef37HErLykO1WGOMMYTuGs1cYBqwAFjqLndyKJZdYcKINLbvLebT7B2hXKwxxjR6IWt1pqr3qmpvVe2nqpepanGolg1wcu92dEyMt0YBxhgTYhHbM4C/mOgoLhmexlerd7JhZ6HX4RhjTKPRaBINwEXDUomOEl61RgHGGBMyjSrRtG8Zz6l92/Nm1iaKDpV5HY4xxjQKjSrRgNNTQP6BQ8xcttXrUIwxplFodInm6K6t6dImwR4fYIwxIdLoEk1UlDBhRBrzN+aTvXWv1+EYY0zEa3SJBuD8oZ2JjYmyps7GGBMCjTLRJDWL5YwBHfnvgs3sLy71OhxjjIlojTLRgNMooLCkjLcXbvY6FGOMiWiNNtEMTk2ib8eWTJmbg6o9FM0YY4Kl0SYaEWHCyDSyt+5lQc4er8MxxpiI1WgTDcDZg1JoHhfDlO+sUYAxxgRLo040CXExnDM4hfeXbiW/sMTrcIwxJiI16kQDMGFkGiWl5Uybn+t1KMYYE5EafaLp3aElmemtmDJ3I+Xl1ijAGGPqW6NPNOA0dd6w6wDfrN3ldSjGGBNxLNEA4/t3IDkhllesUYAxxtQ7SzRAXEw0FwztzCfZ29lWUOR1OMYYE1Es0bguHZFGWbky9ftNXodijDERxRKNK711Aif0bMtr83IoLSv3OhxjjIkYlmh8TBiRxra9RXy2YofXoRhjTMSwROPjlN7t6JgYz5S59lA0Y4ypL5ZofMRER3HxsDRmr8pj465Cr8MxxjRCkVh1b4nGz0XDUomOEl61Uo0xJsTyC0sY9ZdZzFi61etQ6pUlGj8dEuMZ06c9b2Rtori0zOtwjDGNyKTPV7O14CDd2jb3OpR6ZYkmgIkj08k/cIiZS7d5HYoxppFYv7OQl7/dyEXDUunVoYXX4dQrSzQBHNOtNRmtm1lPAcaYkHlkZjZxMVHcOqan16HUO0s0AURFCRNGpJO1MZ8V2/Z6HY4xJsLNXbeLj5Zv5/pR3WjXIt7rcOqdJZpKnD+0M7ExUUz5zhoFGGOCp7xceXBGNh0T47n6+K5ehxMUlmgq0SohljP6d+S/CzdTWFzqdTjGmAj17uItLMkt4PaxvWgaG+11OEFhiaYKE0ams7+4lHcWbfE6FGNMBCo6VMajH66gf0oiZw9K8TqcoLFEU4UhaUn06diSV77biKo9FM0YU7+en7OeLQVF3HN6H6KixOtwgsYSTRVEhAkj0vhh614WbtrjdTjGmAiyc38xT89ay5i+7RnZtbXX4QSVJZpqnD04hYTYaGsUYIypV49/soqiQ2XcNb6316EEnSWaajSPi+GcISm8v2QLew6UeB2OMSYCrNq+j9fm5TBxZDpdI6wXgEAs0dTAhBHpFJeWM21+rtehGGMiwEMzskmIi+GmU3p4HUpIWKKpgT4dWzI0vRVT5uZQXm6NAowxdffV6jxmrczjxpO7k5wQ63U4IWGJpoYmjkxj/c5Cvl23y+tQjDENVFm58uAH2aQmN+WKYzK8DidkQpZoRCRJRKaJyAoRyRaRo0O17Powvl9HWjVrYv2fGWPqbNr8TazYto87xvUmLiYyb84MJJQlmieBD1W1NzAQyA7hso9YfJNoLshM5eMftrN9b5HX4RhjGpjC4lIe+3gVQ9KSOL1/R6/DCamQJBoRaQmcADwPoKolqtrgbky5dHgaZeXK1O83eR2KMaaBeXb2OvL2FXPP6X0RidybMwMJVYmmK5AHvCgiC0XkORFJ8B9JRK4VkSwRycrLywtRaDWX0SaB43u04bV5ORH5uFVjTHBsKyhi8uy1nD6gI0PTW3kdTsiFKtHEAEOAp1V1MFAI3Ok/kqpOVtVMVc1s27ZtiEKrnQkj0tlaUMTnK3Z4HYoxpoF47OOVlJfDneMi/+bMQEKVaHKBXFWd676fhpN4GpzRfdrRoWU8U+ZaTwHGmOot31LAWwtyufLYDFKTm3kdjidCkmhUdRuwSUR6uR+dAvwQimXXt5joKC4ensrs1Xnk7DrgdTjGmDCm6jRnTmrahF+f1N3rcDwTylZnNwJTRGQJMAh4KITLrlcXD0sjSoQp86ypszGmcp+v2ME3a3dxy+ieJDZt4nU4nglZolHVRe71lwGqeraq5odq2fWtQ2I8o/u0482sXIpLy7wOxxgThg6VlfPQjGy6tk3g0hFpXofjKesZoI4mjkxnd2EJHy7b5nUoxpgw9Pq8HNbmFXLX+D40iW7ch9rG/e2PwLHd2pDeupn1FGCMOczeokM8/ulqRnZNZnSfdl6H4zlLNHUUFeU8FO37Dfms3LbP63CMMWHkqS/Wkn+ghN81wpszA7FEcwTOH5pKbEwUU+ZaqcYY49i0+wAvzFnPOYNT6JeS6HU4YcESzRFITojl9P4dmb5gM4XFpV6HY4wJA49+tJKoKLh9bK/qR24kLNEcoYkj09hfXMq7i7d4HYoxxmMLc/J5b/EWrjm+Kx0Tm3odTtiwRHOEhqS1oneHFrzy3UZU7aFoxjRWqsoDH2TTpnkc143q5nU4YcUSzRESESaMTGf5lr0s2tTgOqQ2xtSTmcu2MX9jPr85tSfN42K8DiesWKKpB+cMTiEhNtr6PzOmkSouLeORmSvo1b4FF2ameh1O2LFEUw+ax8Vw9uAU3lu8hT0HSrwOxxgTYi9/u5Gc3Qe4+/Q+REdZc2Z/lmjqyYQR6RSXlvPqPCvVGNOY5BeWMOmz1ZzQsy2jeobn4028ZommnvTt1JKTerXl6VlryS+0Uo0xjcWkz1ezv7iUe07r43UoYcsSTT26c3wfCotL+ecXa7wOxRgTAut3FvLytxu5aFgqvTq08DqcsGWJph716tCCC4am8p9vN7Jptz2rxphI98jMbOJiorh1TE+vQwlrlmjq2a1jehIV5Ty61RgTueau28VHy7dz/ahutGsR73U4Yc0STT3rkBjP1cd15Z1FW1iaW+B1OMaYICgvVx6ckU3HxHiuPr6r1+GEvRonGhFJF5FEn/cniciTInKbiMQGJ7yG6bpRXUlOiOWhGdnWW4AxEejdxVtYklvA7WN70TQ22utwwl5tSjRvAAkAIjIIeBPIAQYCT9V/aA1Xi/gm3HxKD75dt4tZq/K8DscYU4+KDpXx6Icr6J+SyNmDUrwOp0GoTaJpqqoVPUdOBF5Q1b8CPweG13tkDdwlw9PIaN2MR2asoKzcSjXGRIrn56xnS0ER95zehyi7ObNGapNofH/Rk4HPAFS1vF4jihCxMVH8dlxvVm7fx1sLcr0OxxhTD/L2FfPUF2sY07c9I7u29jqcBqM2ieYLEXlDRJ4EWgGfA4hIR8DuUAxgfL8ODEpN4m8fr+JgSZnX4RhjjtDjn66iuLScu8b39jqUBqU2ieZmYDqwAThOVQ+5n3cA7qnnuCKCiHD3aX3YtreIF75e73U4xpgjsGr7Pl6fl8PEkel0bdvc63AalNr0Zf2Rqp7q/6GqLqzHeCLO8C7JjOnbnqdnreXiYam0bh7ndUjGmDp4aEY2CXEx3HRKD69DaXBqU6Kx3uLq6I5xvTl4qIy/f25d0xjTEH21Oo9ZK/O48eTuJCfY3Ry1VZsSTaKInFvZQFWdXg/xRKTu7Zpz0bBUXvluI1cek0FGmwSvQzLG1FBZufLgB9mkJjflimMyvA6nQapNiSYROAM4M8DrjPoPLbLcMroHsTFR/MW6pjGmQZk2fxMrtu3jjnG9iYuxmzProjYlmo2q+ougRRLh2rWI55rju/LkZ6u5+rh8Bqe18jokY0w1CotLeezjVQxJS+L0/h29DqfBqut9NKYOrjmhK22ax/HwzBXWNY0xDcCzs9eRt6+Ye07vi4gdAuuqNonmsqBF0Ug0j4vhltE9mLd+N59l7/A6HGNMFbYVFDF59lpOH9CRoelWA3EkapxoVHVZMANpLC4alkrXtgk88uEKSsusUwVjwtVjH6+kvBzuHGc3Zx4pe0xAiDWJjuKOcb1Zs2M/b863rmmMCUfLtxTw1oJcrjw2g9TkZl6H0+BZovHAqX3bk5neir99sooDJaVeh2OM8XGorJy7pi+lVbNYfn1Sd6/DiQi1TjQi0kNEponIDyKyruIVjOAilYhw12l9yNtXzL9mW9c0xoSTv3+2miW5BTx0Tj8SmzbxOpyIUJcSzYvA00ApcBLwH+Dl+gyqMRia3orx/Trw7Oy15O0r9jocYwwwf2M+//hiDecN6cy4ftacub7UJdE0VdXPAFHVjap6H85jA0wt3T62FyWl5Tz52SqvQzGm0SssLuW2NxbRMbEp9/2sr9fhRJS6JJoiEYkCVovIDSJyDtCunuNqFLq2bc6lI9J4bd4m1ubt9zocYxq1Bz74gZzdB3j8okG0iLcqs/pUl0RzC9AMuAkYivO0zcvrM6jG5KZTehAfE8WjH67wOhRjGq1Pf9jOa/M2cd0J3RjeJdnrcCJOXRJNhqruV9VcVf25qp4HpNVkQhGJFpGFIvJ+HZYbkdo0j+P6Ud34aPl2sjbs9jocYxqdnfuLuXP6Evp0bMmtY+wRAMFQl0RzVw0/C+RmILsOy4xoVx3fhXYt4nhoRrZ1TWNMCKkqd761hL1FpTxx0SDrNDNIapxoRGS8iPwdSBGRST6vl3BaoFU3fWfgdOC5OkcboZrFxnDbmJ4syNnDR8u3eR2OMY3G1O838Wn2Dn47the9OrTwOpyIVZsSzRZgPlDk/q14vQuMrcH0TwC/BazflQDOH9qZHu2a8+cPV3LIuqYxJug27Czkj+//wDHdWvOLY7t4HU5Eq01fZ4tV9SWgm6r+2+c1XVXzq5pWRM4Adqjq/GrGu1ZEskQkKy8vr6ahRYSY6CjuHN+b9TsLeX1ejtfhGBPRSsvKue2NRcRECY9dMJCoKOuZOZhq/DwaEVkKqPv/YcNVdUAVkx8L/ExETgPigZYi8oqqTvSbx2RgMkBmZmaju1hxcu92jOiSzBOfruacIZ1pHlebxwUZY2rq6VlrWZCzhycvHkSnpKZehxPxanMkq/NTNFX1LtwGAyJyIvB//knG/K9rmrP/+TWTv1zLbaf28jokYyLOktw9PPnZas4c2EuShqkAABwISURBVImzBqV4HU6jUJuqs40VL/ejHu7/OwBrl1tPBqUmccaAjvzrq/Vs31vkdTjGRJSDJWXcMnURbZrH8cBZ/bwOp9GoS6ea1wDTgGfdjzoDb9d0elWdpap1Lh01BreP7UVpeTlPfGpd0xhTnx6Zmc26vEL+euFAEpvZ3f+hUpf7aH6Nc81lL4Cqrsa6oKlX6a0TmDgynanfb2L19n1eh2NMRPhyVR7//nYjvzi2C8d2b+N1OI1KXRJNsaqWVLwRkRjcRgKm/tx4cg8SYmP4s3VNY8wRyy8s4fY3F9OjXXN+O86ufYZaXRLNlyJyN9BURMYAbwLv1W9YJjkhll+e1I1Ps3fw3bpdXodjTIOlqtzz9lLyD5Tw+EWDiG9id/+HWl0SzZ1AHrAUuA6YAfyuPoMyjl8c24WOifE8bF3TGFNn/124mRlLt3HrmJ70S0n0OpxGqdaJRlXLcS7+/0pVz1fVf6kdBYMivkk0t43pyeLcAj5YutXrcIxpcHLzD3DvO8sZltGK607o5nU4jVZt+joTEblPRHYCK4CVIpInIn8IXnjm3CGd6d2hBY9+uJKSUuuaxpiaKitXbntjMQr87cJBRNvd/56pTYnmFpzWZsNUtbWqJgMjgGNF5NagRGeIjhLuHN+bnN0HmDJ3Y/UTGGMAeO6rdcxbv5t7z+xLanIzr8Np1GqTaC4HLlHV9RUfqOo67MFnQTeqZ1uO7d6aSZ+tZm/RIa/DMSbs/bBlL499vJKxR7Xn/KGdvQ6n0atNommiqjv9P1TVPMDufAoiEeGu8X3IP3CIZ2at9TocY8Ja0aEybp26iMSmsTx87oCAfTOa0KpNoimp4zBTD/qlJHL2oE48P2c9WwsOeh2OMWHrrx+vZOX2ffzl/AEkJ8R6HY6hdolmoIjsDfDaB/QPVoDmf35zai9U4W8fW9c0xgTyzdqdPDdnPRNHpnFSb+uwJFzUplPNaFVtGeDVQlWt6iwEUpObccUx6UxbkMuKbXu9DseYsFJw8BD/98ZiMloncPdpfbwOx/ioyw2bxkO/Pqk7LeJieGSmdU1jjK9731nG9n3FPH7RIJrF2rOcwoklmgYmqVksN5zcnVkr8/h6zWFtM4xplN5bvIW3F23hxpO7Myg1yetwjB9LNA3Q5UdnkJLUlIdnZlNebp0ymMZtW0ERv3t7GQNTk7jhpO5eh2MCsETTAMU3ieb/xvZk2ea9vLdki9fhGOOZ8nLl9mmLKSkt54mLBhETbYe0cGRrpYE6a2AKfTu25NEPV1JcWuZ1OMZ44t/fbuCr1Tv53Rl96NImwetwTCUs0TRQUVHC3af1YfOeg7z8rXVNYxqf1dv38cjMFZzcux2XDk/zOhxTBUs0DdhxPdpwQs+2/P3zNRQcsK5pTONRUlrOLVMXkRAXwyPn9be7/8OcJZoG7s5xvdlbdIh/zlrjdSjGhMyTn61i+Za9PHxuf9q1iPc6HFMNSzQNXN9OLTl/SGeen7Oeb9fakzhN5MvasJunZ63lwszOjD2qg9fhmBqwRBMB/nBmXzJaN+OGVxewZY/1g2Yi1/7iUm59YxEprZryhzOP8jocU0OWaCJAi/gmTL48k+LScq5/ZT5Fh6wVmolMf3xvOZvzD/L4hYNoHmd3/zcUlmgiRLe2zfnbhQNZklvA799ehj1d20Saj5Zv442sXK4f1Y3MjGSvwzG1YIkmgpx6VAduOrk7b87P5ZW5OV6HY0y92bGviLumL+WoTi25ZXRPr8MxtWSJJsLcMronJ/Vqy/3vLidrw26vwzHmiKkqd0xbQmFxKU9cNIjYGDtsNTS2xiJMVJTwxMWD6dyqKb+csoDte4u8DsmYI/LqvBy+WJnHneN706N9C6/DMXVgiSYCJTZtwrOXZVJYXMovX5lvXdSYBmtd3n4eeD+b47q34YqjM7wOx9SRJZoI1atDCx67YCALcvZw/3s/eB2OMbV2sKSMW6cuIjYmiscuGEhUlN3931BZoolgp/XvyPWjuvHq3Bxen2eNA0zDUVJazi+nzGfJ5gL+fF5/OiTa3f8NmSWaCHf72F4c36MNf3hnOQtz8r0Ox5hqlZaVc/PrC5m1Mo+HzunPuH4dvQ7JHCFLNBEuOkqYdPFg2rWM45evLCBvX7HXIRlTqfJy5c7pS5m5bBu/O70Pl1ivzBHBEk0j0CohlmcvG8qegyX8esoCDpWVex2SMYdRVf74/g9Mm5/LLaN7cPXxXb0OydQTSzSNxFGdEvnzeQOYt2E3D36Q7XU4xhzmsY9X8tI3G7j6uC7cfEoPr8Mx9cg6C2pEzhqUwpLcAp6fs54BnRM5d0hnr0MyBoCnZq3hn1+s5ZLhqdxzeh97vkyEsRJNI3PX+N6M7JrMXdOXsmxzgdfhGMPL327g0Q9X8rOBnXjgbHuIWSSyRNPIxERH8c9Lh9A6IZbrXp7P7sISr0Myjdhb83P5/TvLGd2nHX+9cCDRdq9MRLJE0wi1bh7HM5cNJW9/MTe+toBSaxxgPDBz6VZun7aYY7u35h+XDqFJtB2OIlVI1qyIpIrIFyKSLSLLReTmUCzXVG5A5yQePLsfX6/ZxaMfrfQ6HNPIfLkqj5teX8ig1CQmX5ZJfJNor0MyQRSqxgClwG9UdYGItADmi8gnqmp9o3jogsxUlm4uYPLsdfRLSeRnAzt5HZJpBOau28V1L2fRo10LXvz5cBLsAWYRLyQlGlXdqqoL3P/3AdlASiiWbar2u9P7kpneijumLSF7616vwzERbknuHq76dxYpSU35z1XDSWzaxOuQTAiEvFJURDKAwcDcAMOuFZEsEcnKy8sLdWiNUmxMFE9NHELLpjFc9/J89hywxgEmOFZu28flL8wjqVkTXrl6BG2ax3kdkgmRkCYaEWkOvAXcoqqHnT6r6mRVzVTVzLZt24YytEatXYt4np44lK0FB7n59UWUldtjoE392rCzkInPzyU2OoopV4+gY2JTr0MyIRSyRCMiTXCSzBRVnR6q5ZqaGZLWivt/1o8vV+Xxt0+scYCpP1v2HGTCc3MpLStnytUjSG+d4HVIJsRC1epMgOeBbFX9WyiWaWrv0hFpXDI8lX9+sZYPl231OhwTAXbuL2bic3PZe/AQ//nFCHtCZiMVqhLNscBlwMkissh9nRaiZZtauO9nRzEoNYnfvLGY1dv3eR2OacAKDhzisufnsaXgIC/8fBj9Oyd6HZLxSKhanc1RVVHVAao6yH3NCMWyTe3ExUTzzMShNI11GgfsLTrkdUimAdpfXMqVL81j7Y79TL4sk2EZyV6HZDxkt+Kaw3RIjOepCUPI2X2A26YuotwaB5haKDpUxjX/zmJJbgGTLhnMCT2tYU9jZ4nGBDS8SzK/P6Mvn2bvYNLnq70OxzQQh8rK+fWUBXy7bhePXTCAcf06eB2SCQOWaEylLj86nXOHpPDEp6v5LHu71+GYMFdWrtw6dRGfrdjBn87uxzmD7TEUxmGJxlRKRHjonP70S2nJLa8vYl3efq9DMmFKVbl7+lLeX7KVO8f35rKR6V6HZMKIJRpTpfgmTuOAJjFRXPfyfPYXl3odkgkzqsqf3s9matYmbjy5O9eP6uZ1SCbMWKIx1ercqhn/uGQwa/P2c/ubi1G1xgHmfx7/dDUvfL2eK4/J4LYxPb0Ox4QhSzSmRo7p3oa7T+vDzGXbePrLtV6HY8LE5NlrmfTZai4Y2pk/nNHXno5pArJEY2rsquO6cObATvzlo5V8uco6PW3sXp2bw0MzVnB6/448ct4AouzpmKYSlmhMjYkIfz6vP73at+Cm1xaSs+uA1yEZj7yzaDP3vL2Uk3q15fGLBtkjmE2VLNGYWmkWG8PkyzIBuPblLA6UWOOAxubj5du47Y3FjOiSzNMThxIbY4cRUzXbQkytpbVuxqRLBrNy+z7ufGupNQ5oROas3skNry6kX0oiz10xzB7BbGrEEo2pk1E923L72F68u3gLN7++iH3WJ1rEm79xN9f8J4uubRP498+H0dwewWxqyLYUU2e/HNWNsjLlic9Ws2jTHiZdMphBqUleh2WCYNnmAq588Xs6JMbz8lUjSGoW63VIpgGxEo2pMxHhxlN6MPXakZSVK+c//Q3PfLnWOuGMMIs37eHyF+bRMt55BHPbFvYIZlM7lmjMEcvMSGbGTcdz6lHteWTmCq54cR479hV5HZY5QkWHynh4ZjbnPPU1cTFRvHL1CFKS7BHMpvYs0Zh6kdisCf+8dAgPn9uf7zfsZvwTX/HFyh1eh2Xq6PsNuzntya949st1XJiZyoe3nECXNvYIZlM3lmhMvRERLhmexns3HEfbFnH8/MXveeD9HyguLfM6NFNDhcWl3PvOMi589ltKysp55aoRPHLeABKbNvE6NNOAWWMAU+96tG/B278+lodmZPPcnPV8t34Xky4eTNe2zb0OzVRhzuqd3Dl9CZv3HOSKozO4fWwvEqxlmakHVqIxQRHfJJo/ntWPyZcNJTf/IGf8fQ5vzc/1OiwTQMHBQ9wxbQkTn59LbHQUb153NPf97ChLMqbe2JZkgurUozrQv3Mit7y+iN+8uZg5a3byx7OOokW8VcWEg09+2M7v3l5K3r5irh/VjVtG97CbME29s0Rjgq5jYlNevWYk//xiDU98uooFOflMungwA+2eG8/sLizhvneX8+7iLfTu0IJ/XZ7JgM62PkxwWNWZCYnoKOGmU3ow9bqjOVRaznlPf8Ozds9NyKkq7y3ewpi/fcnMZVu5dXRP3r3hOEsyJqgs0ZiQGpaRzMybT2BM3/Y8bPfchNSOvUVc+/J8bnxtIZ1bNeX9G4/n5tE9rFNME3QSrh0iZmZmalZWltdhmCBRVV6bt4n731tOi/gY/nrhIEb1bOt1WBFJVXlzfq7b1Lyc28b05KrjuhATbQkmEonIfFXN9DoOX7alGU+ICJeOSOO9G4+jdUIcV7wwj4dmZFNSWu51aBElN/8Al78wj99OW0LvDi2ZefPxXDeqmyUZE1LWGMB4qmf7Frxzw7E8+EE2k2ev49u1u5h0yWC7C/0IlZcrU+Zu5JGZK1Dgj2cdxcQR6fYUTOMJO60xnotvEs2fzu7HMxOHkrP7AGdM+orpC+yem7pav7OQi//1Hb9/ZzlD0lvx0S0ncPnRGZZkjGesRGPCxrh+HRjg3nNz2xuL+Wr1Tv50dj977kkNlZUrz89Zx18/XkVsTBSPnj+AC4Z2RsQSjPGW7cEmrHRKasqr14zgH1+sYdJnq1mYk8+kSwZb89tqrNy2j99OW8zi3AJG92nPg+f0o33LeK/DMgawqjMThmKio7hldE9ev/ZoStx7bv41e53dcxNASWk5T366mjP+/hWb8g8y6ZLB/OvyoZZkTFixEo0JW8O7JDPj5uO5460lPDgjm6/W7OSvFwy0B2+5luYWcPu0xazYto8zB3bivjP70rq5/TYm/FiJxoS1pGaxPDNxKA+c3Y+563Yx/snZzF6V53VYnio6VMafP1zB2U99ze7CEv51eSZ/v2SwJRkTtizRmLAnIkwcmc67NxxHckIsl78wj4cb6T03WRt2c9qkr3h61lrOG5LCJ7eNYkzf9l6HZUyVrGcA06AcLCnjgQ9+YMrcHNq2iGN4l2SGpbciMyOZPh1bEh1hTXhVlbV5hSzIyeebNTt5Z/EWOiU25eFz+3OC9aRgAgjHngHsGo1pUJrGRvPgOf05pU873lm0hawN+XywZCsAzeNiGJLe6sfEMyg1iaaxDavL+8LiUhZv2sOCnHzmb8xn4aY97DlwCIDEpk244ugM/m9sL2vybRoUK9GYBm/znoNkbdjN9xt2k7Uhn5Xb96EKMVFCv5REhmW0YlhGMpkZySQnxHod7o9UlU27DzI/ZzcLNu5h/sZ8VmzbS0Xjuh7tmjMkrRVD01sxJD2Jrm2a202XplrhWKKxRGMiTsGBQyzIyWfeht1kbdjN4k0FlJQ513O6tU1gWEbyj6/U5KYhu6Gx6FAZSzcXMH9jPgs25rMgJ5+d+0sASIiNZnBaK4akJTEkvRWDU1uR2MweDmdqzxJNLViiMfWl6FAZyzYX8P2GfLI27CZrYz4FB53qqHYt4tzSjlPqqc/rPFv2HPyxCmxBzh5+2FLAoTJnf8to3Ywh6a1+LLH0bN8i4q4vGW806kQjIuOAJ4Fo4DlVfaSq8S3RmGApL1dW79jvVrXt5vsN+WzecxBwrvMMTkv6MfkMTm1Vo+s8JaXlLN9SwIKcPT+WVrYWOM/ZiW8SxYDOSU4VmFtqsabIJlgabaIRkWhgFTAGyAW+By5R1R8qm8YSjQmlLXsOkrUxn+/XO9d6Al3nycxIJjO9Fa2bx7FjXxELNu5hoVtiWbq5gGK3uXVKUlOGpLdiqFsN1qdjS5pYt/wmRBpzojkauE9Vx7rv7wJQ1Ycrm8YSjfFSwUHnOk/Wht18vz6fRbl7frxvp3VCLLsKnWsrsdFR9Etp6XPRvpV1/2I8FY6JJlRtJFOATT7vc4ER/iOJyLXAtQBpaWmhicyYABKbNuGkXu04qVc7AIpL/3edZ82O/fRq34Ih6a3ol9KSuJiG1YTamFALVaIJdJXzsKKUqk4GJoNTogl2UMbUVFxMNEPTkxmanux1KMY0OKGqOM4FUn3edwa2hGjZxhhjPBSqRPM90ENEuohILHAx8G6Ilm2MMcZDIak6U9VSEbkB+AinefMLqro8FMs2xhjjrZB1mKSqM4AZoVqeMcaY8GCN+40xxgSVJRpjjDFBZYnGGGNMUFmiMcYYE1Rh23uziOQBG72Ow0cbYKfXQdSQxRocFmtwWKz1K11Vw+rxq2GbaMKNiGSFW/9BlbFYg8NiDQ6LNfJZ1ZkxxpigskRjjDEmqCzR1NxkrwOoBYs1OCzW4LBYI5xdozHGGBNUVqIxxhgTVJZojDHGBJUlGh8iEi8i80RksYgsF5H7A4wzQUSWuK9vRGRguMbqM+4wESkTkfNDGaPP8msUq4icKCKL3HG+DHWcbgw12QYSReQ9n3F+7kWsbizRIrJQRN4PMExEZJKIrHG31yFexOgTT1WxhsV+5RNPpbH6jOPpftWQhKz35gaiGDhZVfeLSBNgjojMVNXvfMZZD4xS1XwRGY9zcfCwx1KHSayISDTwZ5xHNHil2lhFJAl4Chinqjki0i5cYwV+DfygqmeKSFtgpYhMUdUSD+K9GcgGWgYYNh7o4b5GAE/jzbZaoapYw2W/qlBVrOGyXzUYVqLxoY797tsm7kv9xvlGVfPdt9/hPC005GoSq+tG4C1gR6hi81fDWC8FpqtqjjuNJ/HWMFYFWoiIAM2B3UBp6KJ0iEhn4HTguUpGOQv4j/udvgOSRKRjyAL0UV2s4bJfQY1+VwiD/aohsUTjxy0yL8LZgD5R1blVjH4VMDM0kR2uulhFJAU4B3jGi/j8Yqnud+0JtBKRWSIyX0QuD32UjhrE+g+gD87jyJcCN6tqeYjDBHgC+C1Q2bJTgE0+73Pdz7xQXay+PN2vqCbWcNqvGgpLNH5UtUxVB+GcUQ0XkX6BxhORk3B2iDtCGZ+vGsT6BHCHqpaFPrqfqkGsMcBQnDPJscDvRaRniMMEahTrWGAR0AkYBPxDRAJWsQSLiJwB7FDV+VWNFuCzkN/PUMNYK8b1dL+qYaxhs181FJZoKqGqe4BZwDj/YSIyAKdYfZaq7gpxaIepItZM4HUR2QCcDzwlImeHNrqfqiLWXOBDVS1U1Z3AbMDTC8JVxPpznGo+VdU1ONcXeoc4vGOBn7nr9nXgZBF5xW+cXCDV531nnFJYqNUk1nDZr2oSa9jtV2FPVe3lvoC2QJL7f1PgK+AMv3HSgDXAMeEeq9/4LwHnh2usOFVRn+GUbJoBy4B+YRrr08B97v/tgc1AGw+3hROB9wN8fjpOFZQAI4F5XsVYg1jDYr+qSax+43i2XzWkl7U6+6mOwL/dFiVRwBuq+r6IXA+gqs8AfwBa45zFAJSqN7251iTWcFFtrKqaLSIfAktw6safU9Vl4Rgr8CfgJRFZinMQv0OdUpjn/OKcAZyGcwA/gFMSCxthul8FFKb7VYNhXdAYY4wJKrtGY4wxJqgs0RhjjAkqSzTGGGOCyhKNMcaYoLJEY4wx9UREXhCRHSJSLy0mReRDEdnj37mniNzgdpaqItKmPpYVTJZoTNir6c4rIh1F5OMAnzcVkS/dJstHEkeqiHwhItlur80312Ee/cXpoXqRiOwWkfXu/58GGPc+EXnY77NBIpLt/v+piLSq+zcyQfASAW7yPgJ/AS4L8PnXwGhgYz0uK2gs0ZiG4CVqtvOOI3Bvur/AuZP/SLsMKQV+o6p9cG6A/LWI9K3NDFR1qaoOUqeLm3eB2933owOM/hpwkd9nFwOvuv+/DPyqVt/ABJWqzsbpZPVHItLNLZnMF5GvRKTGvUio6mfAvgCfL1TVDUcccIhYojFhL9DOW4lxBO6McQLwTsUbEfmtiCwV53kyj7ifzRKRx0VktltiGSYi00VktYg84MaxVVUXuP/vw+lG/rBOKkXkAhFZ5s5/dk2+o4icKiLfisgCEXlTRJqr6kpgj4j4dpd/IU7XKOAkqktqMn/jqcnAjao6FPg/nMdhNCrWM4CJCG61WC9V/cHv81iga8XZnzjPOjkbGKGqB0Qk2Wf0ElU9wa0Sewenk8/dwFoReVx9+t8SkQxgMBCod+8/AGNVdbM4z9mpLvY2wO+A0apaKCJ3ALcBf8Qp1VwMzBWRkcAuVV0NoM6zW+JEpLWGQZ975nAi0hw4BnjT7fEAIM4ddi7OOva3WVXHhibC0LBEYyLFCAIf9NsAe3zejwZeVNUDAKrqW1J61/27FFiuqlsBRGQdTueUu9z3zXGeRXKLqu4NsMyvcbqoeQOYXoPYRwJ9ga/dg1Es8K077HXgGxH5DU7Cec1v2h04vUhboglPUcAet6r0J1R1OjXbPho8SzQmUowHPgzw+UEg3ue9UHlX+cXu33Kf/yvexwCI89TNt4Ap7oHiMKp6vVvddTqwSEQGVVPiEJzn3hxWDaaqm9xegkcB5wFH+40Sj/MdTRhS1b1ug48LVPVNcc4kBqjqYq9jCyW7RmMixSk4vT//hDpPbYwWkYpk8zHwCxFpBuBXdVYl9yDxPJCtqn+rYrxuqjpXVf8A7OSnXfUH8h1wrIh0d6dvJj99Fs9rwOPAWlXN9YunA7Chpt/BBJeIvIZTGu0lIrkichXONcKrRGQxsBznyac1nd9XwJvAKe78xrqf3yQiuTiPflgiIlU9DdRzVqIxYc/deU8E2rg7172q+rzP8LZAUSXVWOAkl+OAT1X1QxEZBGSJSAlOD8d31zCUY3Gami4V5wmcAHer6gy/8f4iIj1wSiqfAVWevapqnohcCbwmInHux78DVrn/vwk8ifP4YF9Dge9UNeSPkTaBBSqVuurU5FlVj6/k80nApLrM0wvWe7Np8ERkItBZVR+pZPhg4DZVDXQ/QoMlIk8C77pNYI0JW1aiMQ2eqh72tEa/4QvdGy2j6+FemnCyzJKMaQisRGOMMSaorDGAMcaYoLJEY4wxJqgs0RhjjAkqSzTGGGOCyhKNMcaYoPp/Q+nv6K3wQtQAAAAASUVORK5CYII=\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "total_stat = result_minuit.total_stat\n", "\n", "for par in dataset_hess.models.parameters:\n", " if par.frozen is False:\n", " profile = fit.stat_profile(parameter=par)\n", " plt.plot(\n", " profile[f\"{par.name}_scan\"], profile[\"stat_scan\"] - total_stat\n", " )\n", " plt.xlabel(f\"{par.unit}\")\n", " plt.ylabel(\"Delta TS\")\n", " plt.title(f\"{par.name}: {par.value} +- {par.error}\")\n", " plt.show()\n", " plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Inspect model residuals. Those can always be accessed using `~Dataset.residuals()`, that will return an array in case a the fitted `Dataset` is a `SpectrumDataset` and a full cube in case of a `MapDataset`. For more details, we refer here to the dedicated fitting tutorials: [analysis_3d.ipynb](analysis_3d.ipynb) (for `MapDataset` fitting) and [spectrum_analysis.ipynb](spectrum_analysis.ipynb) (for `SpectrumDataset` fitting)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance and parameters errors\n", "\n", "After the fit the covariance matrix is attached to the model. You can get the error on a specific parameter by accessing the `.error` attribute:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.2625818166100611" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crab_model.spectral_model.alpha.error" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, this step is needed to produce a butterfly plot showing the envelope of the model taking into account parameter uncertainties." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "energy_range = [1, 10] * u.TeV\n", "crab_spectrum.plot(energy_range=energy_range, energy_power=2)\n", "ax = crab_spectrum.plot_error(energy_range=energy_range, energy_power=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confidence contours\n", "\n", "\n", "In most studies, one wishes to estimate parameters distribution using observed sample data.\n", "A 1-dimensional confidence interval gives an estimated range of values which is likely to include an unknown parameter.\n", "A confidence contour is a 2-dimensional generalization of a confidence interval, often represented as an ellipsoid around the best-fit value.\n", "\n", "Gammapy offers two ways of computing confidence contours, in the dedicated methods `Fit.minos_contour()` and `Fit.stat_profile()`. In the following sections we will describe them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important point to keep in mind is: *what does a $N\\sigma$ confidence contour really mean?* The answer is it represents the points of the parameter space for which the model likelihood is $N\\sigma$ above the minimum. But one always has to keep in mind that **1 standard deviation in two dimensions has a smaller coverage probability than 68%**, and similarly for all other levels. In particular, in 2-dimensions the probability enclosed by the $N\\sigma$ confidence contour is $P(N)=1-e^{-N^2/2}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.minos_contour()` " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After the fit, MINUIT offers the possibility to compute the confidence confours.\n", "gammapy provides an interface to this functionnality throught the `Fit` object using the `minos_contour` method.\n", "Here we defined a function to automatize the contour production for the differents parameterer and confidence levels (expressed in term of sigma):" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def make_contours(fit, result, npoints, sigmas):\n", " cts_sigma = []\n", " for sigma in sigmas:\n", " contours = dict()\n", " for par_1, par_2 in combinations([\"alpha\", \"beta\", \"amplitude\"], r=2):\n", " contour = fit.minos_contour(\n", " result.parameters[par_1],\n", " result.parameters[par_2],\n", " numpoints=npoints,\n", " sigma=sigma,\n", " )\n", " contours[f\"contour_{par_1}_{par_2}\"] = {\n", " par_1: contour[par_1].tolist(),\n", " par_2: contour[par_2].tolist(),\n", " }\n", " cts_sigma.append(contours)\n", " return cts_sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compute few contours." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 15.9 s, sys: 212 ms, total: 16.1 s\n", "Wall time: 17 s\n" ] } ], "source": [ "%%time\n", "sigma = [1, 2]\n", "cts_sigma = make_contours(fit, result_minuit, 10, sigma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we prepare some aliases and annotations in order to make the plotting nicer." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "pars = {\n", " \"phi\": r\"$\\phi_0 \\,/\\,(10^{-11}\\,{\\rm TeV}^{-1} \\, {\\rm cm}^{-2} {\\rm s}^{-1})$\",\n", " \"alpha\": r\"$\\alpha$\",\n", " \"beta\": r\"$\\beta$\",\n", "}\n", "\n", "panels = [\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_amplitude\"][\"alpha\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_alpha_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"beta\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_beta_amplitude\"][\"beta\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_beta_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"beta\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_beta\"][\"alpha\"]),\n", " \"cy\": (lambda ct: ct[\"contour_alpha_beta\"][\"beta\"]),\n", " },\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we produce the confidence contours figures." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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e3KxceKEkBYYPl6WJ4N45ZdYsqfy7/36oWtWxkNUxtGwpS+RmzJD+HyBJ/kGDpKn+O+9Afr6zMSoVLH7/XfrQgCR1Jk0qW1WMxsj7wl9/yfUnyGRYp07yvqJjjVKBTRM8Sjlk2TIpkz37bLn5Allydd99sHy5JHsuv1z7YXhKXJzsBrR4sdwEg/Q16tHDXS2lVCAZNkx2S6ldW5Zv/u9/7qq0tm0lKbB5s8zUduiglX+BoHNnSfpPmCA9eQA2bZJGzS1aSCJPKw+VOnVpadJrLDdXrq/Gj4dWrZyOyhn168uy/+efl35ghYXyvtKxozZ9VyqQaYJHKR/LyIBbbpEZ2wkT5LnISOm5kJ4uy7POOsvREINas2ayK1m7dnI+darcVK1f72xcSpVWZibcfrscv/wybN8ux5Uryw5NixbBnDkwYID26QpExkhF5+LFsgNg3bryfFqaJPJSU2HKFEdDVCogZWbKpM6OHXL+7ruyNL4sCw2FRx6BuXMliQwwb54s2XrrLU0oK3W6NmzYQPfu3WnatCnNmzfntdde8/rP1ASPUj6yc6ckcRo3lua/RUXS/+KWW6Q09rnn4IwznI6ybIiLk8TOZZfJ+dKl0L69u6G1Uv4oL0+WYVWrBm+/XfJzl18ulR6vvy7NQlXgCw2VZaRpadI7KTZWnp83T/onXXABzJ/vbIxKBYoDB6RyZ80aOX/iCfjXvxwNya8kJkqS56GHJMl84IAsa+/RQ95blFKnJiwsjJdffpnly5cze/Zs3nrrLZYtW+bVn6kJHqW8LCcHXnoJGjaUxpmu7YkvvVR2M3jvPWnwp3yrfHlZ7nDffXK+ebMsl/vxR2fjUupofvhBqv7+97+Szy9ZIjOs48dDVJQzsSnvioiQ3klr1shNaYUK8vzPP0NKiuyI5tohTSl1pMJCuO46qd4F2bku2HbI8oTISLlenTrVXTn400+yhM31u1NKnZyaNWuSnJwMQMWKFWnatCkbN24EYPHixXTp0oVmzZoREhKCMYYhQ4ac9s/U7h5KeUlhofR4eeIJ2LDB/XzHjrLe2dXYTjknNFSWxNWvL1vT79snSyNGjoSBA52OTinpx/XggzB5svu5Jk3glVdk1yVXnxYV/GJipD/GnXfCU09JFVd+PowbJwm+W2+VHdS0Ib9SJT38sOwcBXDOObI0S3uSHVu3btKA+d57YcwYyMqS39u4ce7d/pQKNPffL0vYPS0pSe4lSiM9PZ2FCxfSrl07cnJy6NevH2PGjCE1NZXBgweTk5PDUA9knzXBo5SHWSs7Mjz2mCz9cWnaFJ59VkqE9cLCv9x3n8xWXXutVFjddpv0Q3rqKd1GWjlj5065mX/rLfc255UqyQ38XXdBeLgcq7KnenVpGP/AA7LD4mefyYTC22/LzdiDD8L//Z/MxitV1jVqJLtogiTEx4+X8VMdX6VK8NFHMhl5++2yZOvSS2WcufVWp6NT6uQtWgTTpzv387Ozs7niiisYMWIEMTExTJw4keTkZFJTUwFo1aoVkydPxnjgJlETPEp50B9/SJ+dGTPcz9WuLTdqN96oO2L5s8sug19/lQqe7dslGZeeDh98IEsklPKFggLZ/eqJJ2TWFCTJOGAAPPmk9I9y0SUGZVuDBvDpp/Dvf8Pjj8vy0gMH4OmnpYH/Z5+5m6YqVRZ9+607uVOjhky+Va7sbEyBZsAA+d316yfjy4ABsHGjvEfpZKUKJElJzn3f/Px8rrjiCq677jouv/xyAJYsWULLli0PvWbBggWHlnKdLr3dVMoDVqyQC2xXCTDI7MegQbKrTfnyzsWmSq99e1ln3qOH9LT4/HNpLvjNN9oAW3nflClSQrxkifu5bt2k9FcbJ6tjSUqSHk3Tp0uD1Pnzpb9bSor0fbvnHr0RU2VPnz7w3XdyXKGCJHfq1XM2pkDVu7f05enVSyYehg6VJM/IkTpxqQJHaZdReZq1lltuuYWmTZvy4IMPHno+NjaWqVOnApCWlsbXX3/NrFmzPPIzdfGBUqdhyxZZztOihTu5ExEh673XrJFqHk3uBJaGDWHWLOmVBHLT1LEjrF3rbFwqeK1eLTcj553nTu7Ury9LCaZO1eSOKp2uXaWKdPBgqfrKzZXlpxdfLO9VSpUVXbu6kzsg/fXatJGEuTo17dvD779DQoKcv/uu7N64f7+jYSnl937//Xc+/vhjpk6dSlJSEklJSfzwww9cc801ZGdn06JFCwYOHMjnn39OrGu7zNOkeVelToG1MHq0lMbv2iXPGSPLsIYNc+8+oAJT1arwyy/y3/PLL6VCq317mQFMSXE6OhUs9uyR5TQjRsgW6CAzzf/5j/RX0R4q6mSVKwfDh8sW6tdfD+vWSYPuli3lPeuSS5yOUCnvmz4dOnWSyRqQazZ1+s48U36nF18s/Uy+/x7OPVc+Vq3qdHRK+afOnTtjjzEIff/99175mVrBo9RJSkuD7t1lHbIrudOzJyxeLP1aNLkTHKKiYOxYqcYC2LZNZgV1q1B1uoqK4P33ZTesF15wJ3f+9S9ZGjhokCZ31Onp3Fnek667Ts63b5cGqXfcoTPuqmwo1tpCeVDNmpJAO+88OZ89W5Jp6emOhqWUKkYTPEqVUl6ezLa3auXuwh4fL80sJ07Ui4lgFBICL74Ib74px/v3S0ny5s1OR6YC1fz50LYt3HILbN0qz3XsCHPmSIJYt7hWnlKpEnzyiTRijomR50aNguRkWLDA2diU8jZX3yntEeN5MTFS0XzttXKelgYdOsDChc7GpZQSjiR4jDGhxpiFxpiJx3lNW2NMoTGmry9jU+po/vxT1m//3/9JXwNj4O67ZRv03r2djk552113ybbEIMmdK690V12oE9MxX4wdK5UVrpvr+HjZ6WjmTEn6KOUN114Lf/0FZ58t5ytXypLTF16Q7dWVCkauBI/umuUd4eHw8cfSqgCkz1fXrrK8XSl/cqzlUYHkZP8NTlXw3AcsP9YnjTGhwPPATz6LSKmj2LsX7r1XZiZczU+bN5dGc2+84Z4VVcHvjjvgppvk+PffpUeKKrUyPeZbK7uOXHMN5ORAaKhsMbtihTynOxwpb6tXD379VapQw8IgP182ATjvPNiwwenoVLAwxlxkjFlpjFltjHnsKJ/vZozZbYxZdPDxhPdikY9FRd76CSokRBLFI0bI73vvXunP8+mnTkemlIiMjCQrKyugkzzWWrKysog8ibX7Pi9cNMbEAz2Bp4EHj/Gye4DxgM5pKsdMnAh33um++A0Pl91JHnlEjlXZYoxsCfr33zBvnhynpLiTPuroyvqYf+CA9NYZN07OK1eWxt2u/gVK+UpoKDz+OJx/vvTmWbUKpk2TZcfvvCOViUqdqoOJ+reA84EMYK4xZoK1dtlhL51hre3l/XjkYwDf1wWM++6T5cX9+0t18/XXS0XPQw85HZkq6+Lj48nIyCAzM9PpUE5LZGQk8fHxpX69EytTRwCPABWP9kljTG3gMuAcgvBiX/m/rVvlzeqLL9zPnX22XACfdZZzcSnnRUbC11/Lcr3MTKnqadFCl9ecQJkd8zdvlsa2c+fKeaNGkjg+80xn41JlW9u2skzwgQfgvfdks4CrrpJdA994Ayoe9S9VqRNKBVZba9cAGGPGApcChyd4fEITPL511VVQrZq85+3ZIxtUhIRotbNyVrly5ahfv77TYficT5doGWN6AdustfOP87IRwKPW2hOuDDfGDDTGzDPGzAv0zJxy3pAhsrNN06bu5E6lSvD22zLLqckdBVCnjlRghIZKP6bLL5cdttSRPDnmB9p4v3AhpKa6kzvdusluI5rcUf4gOhrefVcS1lWqyHMffQRJSbpToDpltYHiC/4yDj53uA7GmMXGmB+NMc2P9c1Od8zXBI/vdesGM2ZIogfgwQdlclQp5Vu+7sHTCbjEGJMOjAXOMcZ8cthrUoCxB1/TFxhpjOlztG9mrX3HWptirU2Ji4vzYtgq2K1aBcOHy842O3fKc1dcAcuXw8CBMguhlEvXrvDyy3KckSEzV/n5zsbkpzw25gfSeP/NN9JMOSNDzgcMgJ9+gthYZ+NS6nCXXSbLTl1LBteskf93hw+HggJnY1MB52jdxA5PrywA6llrE4E3gG+P9c1Od8x3Xbdpgse3WrWCn3+GM86Q89tvl938lFK+49PbVmvtIGttvLU2AbgamGqtvf6w19S31iYcfM1XwJ3W2mO+ASh1OvLz4dln5Q3JpVYt+PZb+Oor3bJYHdu998o6c4Dp06U3kyqprI351sJzz0lV1/79coPx6qtSBah9u5S/qlVLEpCvvCL/nxYWSkVr166S8Bk61OkIVYDIAOoUO48HNhV/gbV2j7U2++DxD0A5Y0xVbwSjFTzOadUKJk+WSkFrpQ/d1187HZVSZYdf1CUYY243xtzudByqbJk3T7Ypfvxx2dnGZdMmWV6h1PEYIzfurVvL+YgROktVWsE45ufmykXsoEFyXrEiTJgA99+vu2Qp/+fqlTFnDjRrJs/NmiVLtoYNczY2FTDmAo2NMfWNMeFIUn9C8RcYY2oYIyOiMSYVuQ/J8kYwmuBxVmoqTJoEUVGSNL76akn6KKW8z7EEj7V2mquLvrV2lLV21FFe8y9r7Ve+j04Fs6IimWXv0MHdO6VpU/lorXtLY6VOpHx5mZVyLb0ZMECTg8cSzGP+tm1w7rkwZoycJyTIzXHPno6GpdRJS0yUyY+775bzvXvl4yOP6JItdXzW2gLgbuAnYDkwzlq79LCEfl9giTFmMfA6cLX10v7FmuBxXpcusmQ5PFwq5i+7TCqelVLe5RcVPEr5ysaNskXsoEFysVqunCRz9KZcnaqEBBg7VmbAc3LkAmb7dqejUr6yZAm0awe//y7nnTrBn3/K7mpKBaKoqCP7Rb34orxf6lJUdTzW2h+stU2stQ2ttU8ffO5QQt9a+6a1trm1NtFa295aO8tbsWiCxz9ceKFsXBIaKtdIvXppI3elvE0TPKrMmDBBZienTpXzJk3kTWbIEIiIkI9KnYrzzoPnn5fjdeukFFlnu4PfpElSCZieLuf9+8OUKe4dRJQKVEOHyo3x6tUlnx83TrZYV8rfaYLHf/TpIxWuxkB2NvToAYsWOR2VUsFLEzwq6B04IOXml14KWQdXet90E8yfD8nJ7tfpsix1Oh56CPr1k+MpU6S3kwpeX34Jl1wiF6sgzdo/+kiSxUoFi4YN5ePVV8vHdeukSs21HFEpf6UJHv9y7bXuLdN37YILLpCdapVSnqcJHhXUliyRRm9vvSXnMTGynOb996W7v1KeYgyMHg0tW8r5iy9KWbIKPkuXSpK4qMjdh+mxx7SZsgpOQ4bAZ5/Byy+7l1nceKNMnOTlOR2dUkfn2iY9Px/27XM2FiVuvVU2pADIzJTq5zVrnI1JqWCkCR4VlKyFkSOhbVtJ8oAspVi82F1loZSnVaggDQUrV5bz227TfjzBZvdu2QZ93z5J6IwfL32XlApWQ4fK/+sPPgg//wxVD25q/dZb0lx8yxZHw1PqqNq2lY+FhXI9qPzDfffB00/L8aZNMoZkZDgbk1LBRhM8KuhkZckN1113yUxjSAgMHgy//SYNcZXypoYN4YMP5Hj3bhg+3Nl4lOcUFclW6Glpcj5sGFx0kaMhKeVT3bvL8uaUFDmfOVOWOv/xh7NxKXW4Pn2gWTM5fuEF93Ja5bzHH5fNTkB62J17Lmzd6mhISgUVTfCooPLrr9CqFXz3nZzHx8tzw4dDWJizsamy49JL5YIF4L//hZUrnY1HecYLL8C338pxr17wn/84G49STqhbF2bMkGWKAJs3Q9euMGqU9jtR/iM01L15xvbt7qX6yj88/TTcc48cp6XJDrc7djgbk1LBQhM8Kijk58vN1rnnSsknyDKKxYuhSxdnY1NljzHSr8IY2U1LtxYOfL/84k7oNGwIH3/s7vGgVFkTGSk9x0aOlO3T8/Phjjukx0ZOjtPRKSX69oXmzeX4xRdh715n41Fuxkg/nptvlvO//5aqq9xcZ+NSKhjo5akKeGvWwNlnwzPPyOxhVJTMJH71FVSp4nR0qqxKTHTPcE+YAFOnOhuPOnXr18suQkVFMr58/bW7z5JSZZUxkurmIcgAACAASURBVNSZNg1q1pTn3n9fJlU2bHA0NKUAScK7qniysuDNN52NR5UUEiI7a111lZy7KgOLipyNS6lApwkeFdA++wySkuDPP+W8ZUuYN0+a2+qONsppTz4pjZdBtlEvLHQ2HnXycnLgiivk5gDkYrRVK2djUsqfdOwofXk6dZLzuXOhTRtJ/CjltCuucO9u+dJLsGePs/GokkJD4aOP3OPH55/DE084G5NSgU4TPCog5efLFq3XXecuub3nHpgzx91UTymn1aoFjz4qx4sWybIeFVjuvVeSxiBjzvXXOxuPUv6oZk2pUrzrLjl3bYH86qval0c5q3gVz44d8MYbzsajjhQZKf3tGjeW86eflmpApdSp0QSPCjjbt8OFF7ob5lWtCt9/D6+/Lm8SSvmThx6C2rXl+PHHZXttFRhGj4Z335Xjjh2lr5JS6ujCw2UJzIcfQkSEVCw++CDceCPk5TkdnSrLLrvMXXn58suyw6XyL1Wrwg8/QGysnN92G/z8s7MxKRWoNMGjAsrff0NqquyMBdC6tZSG9+rlbFxKHUv58tIfCmS3mRdfdDYeVTrz5rmrEapXhy+/lBtYpdTx3Xgj/P677LYFUrl44YWwc6ezcamyKyQEhg6V4507ZUJQ+Z9GjWQX3IgI2aCib1+57ldKnRxN8KiA8e230KEDrF0r5/36wcyZ7otIpfzV9ddDcrIcv/ACbNzobDzq+LZvl74NubnSH2DcOFlup5QqnTZtJEnaoYOcT5smPTbS052MSpVlffpIz0aAV16BXbucjUcdXadOMGaMHO/ZAz17unfHVUqVjiZ4lN+zVprVXnaZLG8xRtbnfv65VEco5e9CQuSCEuDAAfd228r/WAv9+8vOWSAVV126OBuTUoEoLg6mTJFkKcDy5dC+vbunlVK+ZIy7imfXLnjtNUfDUcdx1VXw3HNyvGED9O4N2dnOxqRUINEEj/Jr+/bJQO/qqB8dLeWbjz+uu2SpwNK1q8wggsxOLVjgbDzq6KZNg8mT5bhfP7j/fkfDUSqgRUVJBdzDD8v51q0yFn7/vbNxqbLpkkvc1bSvvqpVPP7skUdg4EA5XrAArr5alm0ppU5MEzzKb61bJ6WaX30l5w0bwuzZkslXKhC98AKEhUmVyEMP6e4y/ujZZ+VjVJTstqKJZKVOT0iIVMK99ZYc798vye4333Q6MlXWFK/i2b0bRoxwNBx1HMbImHHRRXI+aZJMuOh1k1Inpgke5ZdmzIC2bWHxYjk/91zZAr15c2fjUup0NG7sbtw7bRpMmOBoOOow8+e7d+0YMECWmCilPOPOO6WXXvnyUFQE99wjie6iIqcjU2VJr16QkiLHr76qzb/9WViYVAAmJsr5W29pUk6p0tAEj/I7774rCZ3MTDm/915ZMlGlirNxKeUJTzwBZ5whx//+t24f7E9ca/7DwuTGUynlWb17w2+/QY0acv7KK7IM+8ABZ+NSZUfxKp49eyTJo/xXxYowcaJ7o4OHHoKvv3Y2JqX8nSZ4lN/Iz4e775Y1t/n5UK4cjB4tjfDCwpyOTinPqFLF3VNq1SoYNcrZeJRYuRLGj5fj667T3fmU8pY2bWS5dbNmcj5+PJxzjntSRylvu/hiSE2V4xEjYMcOZ+NRxxcfL0u0oqNlidZ118GffzodlVL+SxM8yi9s3w4XXijllwDVqsGvv8LNNzsbl1LecOed0KiRHD/1lFbx+IMXXnCv7X/0UWdjUSrY1asHv/8O3bvL+ezZsqV6WpqzcamyoXgVz9697l0ulf9KSpLlWqGhkJMj1YBr1zodlVL+SRM8ynGrVslMyq+/ynlysmyj2qmTs3Ep5S3h4TB4sBxnZsKPPzobT1mXkQEffyzHffpA06bOxqNUWVC5siy/7t9fzv/5R5I8M2c6G5cqGy66CNq1k+PXXoONG52NR51Yjx4wcqQcZ2ZKkmfPHmdjUsofaYJHOWrhQujc2Z2Fv/pqabBcp46zcSnlbVdcIeXGAB995GwsZd0rr8iyUIBBg5yNRamyJDxcxj/XstUdO+C88+CLL5yNSwU/Y2D4cDnOzoZrrtFtuAPBwIHw8MNyvHSpLNcqLHQ2JqX8jSZ4lGN++w26dYNt2+R88GD47DPZYUOpYFehAvTtK8cTJ0JWlrPxlFVZWfDOO3J8zjnuvgxKKd8wBoYNg/ffl357ubky2eOaqVfKWy64AG65RY5nzHBX1ir/9txz0LOnHE+cqBMzSh1OEzzKEd9/Lz13XKWVr70mMynGOBuXUr50443yMT8fPv/c2VjKqjfegH375FgvEpVyzk03yXLVmBg5v+sueP11Z2NSwe+NN6BlSzl+7jn44Qdn41EnFhoqE8LNm8v5iy9qJbRSxWmCR/ncxx/DZZdJk7TQUDm/916no1LK97p0kWajoBcnTsjOdt9AtmkD557rbDxKlXXnnQdTp8IZZ8j5ffdpA1zlXVFR8OWX7iXT/fvDhg3OxqROLCYGJkyA2Fg5HzgQZs1yNial/IUmeJRPvfYa3HCDrJeNjIRvv4Xrr3c6KqWcERIifw8gjcWXLXM2nrLm3Xdh5045HjRIKwiV8gdt2sCUKe4bt4ceguefdzYmFdzOPNO9VHfHDujXz92XTfmvBg1g/HhZ2pmXJ5PH69Y5HZVSztMEj/IJa2HIELj/fjmPiYGffoJevZyNSymnuRI8oFU8vlRU5K4MOPNMuTBUSvmH1q2lkqdqVTl/7DF46ilnY1LB7Zpr4Lbb5PiPP+Dxx52NR5VO167w3//K8bZtcMklUp2rVFmmCR7ldUVFcM897t0KqlWD6dNleYpSZV2jRtCpkxx/8onuBuEry5bJ9ugAd98t1VRKKf/RqhVMmwbVq8v54MEwdKhMGCnlDSNGQFKSHL/0kvSLVP7v1ltlOSfAX3/JMruiImdjUspJekmrvCovT5ZgvfWWnNerBzNnut9AlVLuZsubNsEvvzgbS1kxY4b7WHvvKOWfmjeXJE/NmnI+bJgkejTJo7whMlL68VSsKOc33qhLfgLFSy/J5i0g7R90RzRVljmS4DHGhBpjFhpjJh7lc9cZY/46+JhljEl0IkZ1+vbvhz593LsDNW8Ov/8OjRs7G5dS/uaqq+TCEoJzmZY/jvmuBE9sLJx1li9+olLqVJx1liR5ateW86efliVbmuRR3tCoEYweLcc7d8r7c16eszGpEwsLg7FjZck1wDPPyE5bQ4c6GpZSjnCqguc+YPkxPrcW6GqtbQU8Cbzjs6iUx+zcCeefL1ueArRrB7/95r5AU0q5VaokyVCAb76BPXucjccL/GrMt9ad4OncWZsrK+XvmjSRpd116sj5Cy9I82VN8ihvuPJKWboLMGcOPPqos/Go0qlcWZbVuXbhu/lmqfpTqqzxeYLHGBMP9ATeO9rnrbWzrLUH9zVhNhDvq9iUZ2zeLE3PXNsVnn++LDupUsXZuJTyZ65lWjk5UiIeLPxxzF+/3t1/5+yzvf3TlFKe0LChJHnq1ZPzV1+Vvhua5FHe8NJLkJIixyNGyOSL8n+NG8s1VGgo5ObKc673e6XKCicqeEYAjwClaX91C/DjsT5pjBlojJlnjJmXmZnpqfjUadi6Fbp3h7//lvMrr5RsenS0s3Ep5e/OP9/dZyLIlml5ZMz35HhfvP9O586n9a2UUj5Uv74keRo0kPM33oC77tKGqsrzIiJg3DipsAW46SZYs8bZmFTpzJhRcsOKOnWkUleXa6mywqcJHmNML2CbtXZ+KV7bHbnYP2ZhpLX2HWttirU2JS4uzoORqlORlSU3qStXyvmtt0r/nYgIZ+NSKhCEhkpDcpCLk2C4kPTkmO/J8d6V4ClfHpKTT+tbKaV8rF49SfI0aiTn//2vJHm0kkd5Wv368MEHcrx7t/TjcVWFKP/l2m3vzjvdz11+uTZeVmWHryt4OgGXGGPSgbHAOcaYTw5/kTGmFVLOf6m1Nsu3IapTsWuXdK93Ve7cfDO8/bbctCr/tXboWqdDUMW4lmkBjBnjXBwe5Jdj/syZ8rF9eyhXzts/TXmbjmNlT3y8JHlcDVVHjZLmy0p52mWXwf33y/H8+fDww87Go0pvxAj38ddfw+23ayJYlQ0+TfBYawdZa+OttQnA1cBUa+31xV9jjKkLfA30t9am+TI+dWqys+Hii+WND+Daa+GddyDEqRbeqgR7nHezdcN0/09/0rw5tGkjx2PGBP6yA38c87OyYNkyOdblWcGh+DhmraVgd8Fxxz0VHGrVgl9/dffkGTwYPvzQ0ZBUkHr+eUhNleM33wyuPnnBrFw5eOQRaNVKzt97Txpm69uDCnZhTgcAYIy5HcBaOwp4AogFRhrZ2qTAWpviYHjqOPbvh9694Y8/5Pzyy6V/iFbu+J61lpz0HLIXZLN3/l72LthL9oJs8jPzMeUMIZEhhESEYCLcxwALOi4gtEIoMZ1iqHppVaKTojG6rZBjbrhBkqVr18KKFdCsmdMReZ6TY76rege0wXIgskWWvK155KzLISddHgCLL1pMTnoOuetyKcopwkQYIutFHnpE1ItwnydEEl4rnJAwnYUIdDVrym6dnTrJ7p0DBkji54ILnI6sbDLGXAS8BoQC71lrnzvG69oiTfX7WWu/8mGIpyQ8XPrxtG4t/5/dcoscu5YJKv/1/PPwwAMyofPPP/Dii7Lpy2OPOR2ZUt5jgmWWKyUlxc6bN8/pMMqU3Fy49FL46Sc5v/hi2WUgPNzZuMoCay0H0g4cSuK4PhbsKjjt7x0RH0HsJbFUvbQqlbtVJiRcb4J8acECdxXPp59KRdzpMMbMD7Yk+emM9//+t+yOEhoqS0u1Abz/yduWx4HVBySBUyyR4zq3uR64bgmVsa54EigyIZKoJlFU6lgJE6pJ7kAycyacd55cl0RHw2+/yQ14WePkeG+MCQXSgPOBDGAucI21dtlRXvczkAO8X5oEj79c43//PVxyiRwnJcnkZmSkszGp0lm7VpI8mzbJ+ahRcNttzsak1Ok61pjvFxU8KvDk50O/fu7kzrnnwvjxmtzxtgP/HGDrJ1vZ+slWDqw+cOwXhkD5s8pTMbkikfUjsfmWotwiinKKSnzcPn47Z5x3Bnlb8ti3ZB8AuRm5bBq5iU0jNxFaMZQqPapQ9ZKqVOlRhXJVtGGJtzVvDmFhUFAAixadfoJHleRqsJycrMkdf2GLLHvm7CFrYhZZ32ex7699J/09opOj3dU5NcIPVfnkrsslZ10O+Zn5Jb+gEHLX5ZK7Lpfd7C7xqfDa4dS4sQY1bqpB+UblT+efpnykc2f45BNpgutaNj57tnv5lvKJVGC1tXYNgDFmLHApsOyw190DjAfa+ja809e7t/TgeekleX9+4AFp8q38X/368L//QZcusGMH3HGH7JB29dVOR6aU52mCR520wkLZ7ee77+S8c2c51lkM78jfmU/muEy2fLyFPb/vOeLzJsxQvrkkcyq2qUh0cjTRraIJrXDidXLTzDQSf04EIGd9DtsnbCdrQha7ft2FLbAU7i0kc1wmmeMyMeUM8ffFU++JeoRV1KHDWyIiZFnWX3/JBaTynP373b3CtP+OswqyC9j5806yvs8ia1IW+dvyj/nasNgwIhMkeeNK4hQ/n1lpJinzj1+0ULi/kJz1OYeWceWsyzn0yF2XS+7GXDhYGJS3MY/1z6xn/TPrqXR2JWrcXIO4vnGEReu458/69oVXXpGb7i1boEcPqeypUsXpyMqM2sCGYucZQLviLzDG1AYuA84hABM8AM88A7NmyWPUKJksGDDA6ahUaTRvLks6zz1XEsH9+0NMjCSElQomp3S1YoypAORYaws9HI/yc0VFskPWuHFy3rYtTJoEFSo4G1ewKcorIuuHLLZ+vJWsiVnYvJJLEqJbR1P9uupU6lqJCi0qEBp5ak2P6g1xT29G1o0k/u544u+Op2B3ATsm72D7d9vJ+iGLwt2F2HzLhpc2sPXTrTR8qSHVrqmmvXq8JCnJneCxFpz8NQfTeL9hg1RGQdlcvuG0nHU5ZE3MYvv32yWJnHfkUqvoNtHE9oqlYkrFQwmcEyWUi49jxxJaPpQKZ1WgwllHf7MqyisiNyOXnVN3suX9Lez5Q5Lpu2fsZveM3ay+ZzVx/eKoeXNNYjrE6Njnp+6/H9avh1dfheXLoU8fmbXXCSifONofxeF/5COAR621hSf6GzLGDAQGAtStW9cjAXpCuXIwdiykpMC2bbIVd4MGkjRQ/i81VSalL75YlnT27SurEbQnnwomperBY4wJQXZAuQ7JuOcCEUAm8APwjrV2lRfjPCF/WZ8bzKyVksa335bzxESYOlVnxzxpf9p+Ml7PYNvYbRRkleynE147nOrXVad6/+pEt/Dd2pKi/CJ2TdtF+pD0Qzc9AJXOrkTjNxsT3UrXuXjaq6/Cgw/K8caN0jT0VJ1sT4ZgHu9nz4YOHeR40iSdtfO2Q0uvvs8ia+LRl16FRIVwxnlnENs7ltiesUTUinAg0iPtW76PLR9sYcuYLeRvLVldFHVmFDVvrkn1/tWJqOkf8Sq3oiJZduHa6ejKK6FpUxg2zNm4fMHhHjwdgKHW2gsPng8CsNY+W+w1a3EngqoC+4GB1tpvj/e9/fEa/48/oHt3SRJUrizvL2ee6XRUqrS++w6uuEJWJcTEwLRpOvGjAs+xxvzSJnimA78A3wFLrLVFB5+vAnQHrgW+sdZ+4tGoT4I/Dv7BxFq54RwxQs6bNoXp0yEuztm4gsW+5ftY9/Q6tn2+DYptjR1SIYS4vnHU6F+Dyt0qO9r40xZZtn6ylX8e+cd9wxMCte+qTcKwBMqdof15POXXX+Gcc+T4dBMRp5DgCdrx/scf3b/LWbPcyR7lWWsGryGqQRTrn1/PgZVH9goLrxUuCZ1esZxxzhmElvffbReL8ovY8eMOtnywRaopC4pdM4VCbI9Yat9dmyoX6kyHP8nJkZ20XD23oGxsjexwgicMabJ8LrARabJ8rbV26TFe/yEwMZCaLB/u88/dffIaNZIkT2ysszGp0hszBm68UY7j4mRJZ5Mmzsak1Mk43SbL51lrj1ggb63dgTRKG2+M0bu7IPZ//+dO7jRqBFOmaHLHE/Yt3ce6p9ax7YttJQqZz7jgDGrcUIOqfaqWqpeOL5gQIzFdWpX0YelkvJ4BhbDxjY1s+3wbDZ5rQI2ba+jSBQ9ITHQfL1rk80qToB3vd+50H1eu7FwcwapwXyGb39vM+qfWH/G5iikVie0VS2zvWKJbRwfMOBFSLoSql1Sl6iVVyduax9ZPtrJ59Gb2L98PhUhj6IlZxPaKpdFrjYhqEOV0yApZkvXtt9Jra/lyeW7ECFnCpbzDWltgjLkb+AnZJv19a+1SY8ztBz8/ytEAveCaa2DlSqkOW71aKkL+9z/dcCRQ3HCDXBfcfz9kZsL550uSp04dpyNT6vSUav/jo13sn8prVGB6/XVpKgeyI8WUKVCzprMxBbrsxdksvXIpc1vMZdvYg8kdA3H94kj5O4XEnxKpfl11v0nuFBdWKYxGrzSi7eK2VO4ud8n52/NZeetKVt6ykqKCohN8B3UiVaqAq+WArxstB/N4v2uX+/iMM5yLI9jk78wn/cl0/qj3B6vvX33o+fBa4TR8qSEdNnagzdw2JAxJoGJyxYBJ7hwuvHo4dR6qQ9ulbUmenUzNgTUJrShjdNbELOY0m8PaoWspPBDw7aqCwuuvu5M7IM2XjYGhQx0LKehZa3+w1jax1ja01j598LlRR0vuWGv/VZrqHX83ZIh7J6bp0+H228tGtViwuO8++W8I0r/rggsk2aNUICtVgqc4Y8yj3ghE+afvvnPPeNWoIckdP+p1F3D2LtjLksuWMC9pHplfHXwHCYFq11Wj7dK2NB/b3Kf9dU5HheYVSJySSLMvmhFeW6artnywhaWXL6Vwv97gnK6kJPno5E5awTbeF6/g0QTP6cvdlMs///6H2XVnk/5E+hF9w/I25VGwt8Bv+up4ijGGmHYxnPn2mbRb3Y4a/6oBgM21rBu2jrnN57L9++0OR6mGDpUb7QUL3M9VqAD9+jkWkgpCxsAHH0D79nL+wQfw4ovOxqROzpAhcO+9crxihezAt+fITWuVChgnXKJljBlX/BRIAp73WkTKb8ydK+Wn1kL58jBxIjRs6HRUgenAmgP889A/bP+22EV/KFS/vjr1Hq9H+SblnQvuNBhjqHZVNSp3rcxfPf4ie2E2Wd9nsfiCxbT8vqX25TkNSUkwYYKUfe/dCxUrev9nBvt470rwREXJdvTq1Bz45wDrX1jPlg+3lNgJKzopmrqD6rKs3zK62W7OBehD4dXCOeuDs6g5oCar7lpF9qJsctbmsOSSJVTpWYXGrzUmqqEu23JS8cap+/ZJ0+U//9TdP5XnuJYEpqZKFchjj0HjxrB4cdmsGLPWsm/JPnLW5pC7IZecDfLx0GNTLuHVw4lOipZHa/kYmRDpSIWnMbK5xc6d8PHHMH++VPJMmqQ9lVRgKk0Pnj3W2ltdJ8aY/3oxHuUn0tOhd284cABCQmRLyDZtnI4q8BTuL2T9c+tZ/8J6bK7cCJkwQ/Ubq1NvUL2gufAPrx5O0rQklly2hF1Td7Hn9z0sPHshiT8lElFb76RPhauCx1qpohs92ic/NqjHe1eCR/vvnJqigiLWP7Oe9OHpUKxIr1KXStQdVJcqF1bBGMOyfssci9EplTpWos28NmwatYk1/1lD4e5CdkzawZxf5lD3kbrUfayuXzeTDnZDhkBBATz9NCxdKltbf/ih3Ngp5QnVq8tEaMeOkJ0N110n19BlIcGzduha6g+tT1FuEVs/3cqGVzawf+n+436NK9mT9X3WoedCK4USnRRNbM9Yag2sRVil0raKPX0hIXKdtWePrF7480/o0kV6KtWu7bMwlPKIE+6iZYypb61da4ypaq3dboypcrDZpl/x1w77gWjXLnmDcq1df/NNuOsuZ2MKNNZatn+9ndUPriZ3fe6h56vfUJ2EYQlEJQRHYudwRblFLO+/nMwvZflZRN0IWv3Uigpn6VTpyVq7Fho0cJ+f6pr+k9lVJdjH+8svh2++gWbN5CZPld7+1ftZ0X8Fe2a769Zje8dS97G6VOpYqcRrXRf7ZVXetjzWPLaGLR9sOfRcZEIkjUY0IvaS2IDtQRToCgqkieq0aXI+ejTcfLOjIXmck7toeVMgXeP/8INMkBYdbEeYkRH8CYJpZhoJTyaw8c2N7l1WizFhhvDa4UTWiSSiTgThNcPJzcgle2E2B1YfKLHJiEtoxVBqDqhJ/P3xRNaJ9MG/QuTlyc5aY8fKeb16kuTR3bWUPzrlXbSstWsPHr4PXOKPF/vKc/LypJw5PV3OH3xQkzsnY+3QtVS7qhqr7l3Frinujq7RydE0frMxlTpUOs5XB76QiBCafd6MVXGr2DRyE7nrc1nYeSGtfmhFTGqM0+EFlIQEiInx7TrwYB/vXU2Wtf9O6Vlr2Tx6M6vvX03RPrljKd+sPGd9dBYxKUf/my7LyR04uGzr/WLLthZmk5Oew5I+S4i7Mo4m7zShXGVdvuprYWGyrXVSEmzdKtc2KSnQqpXTkalgMmeOO7kDEB8vH4cMCb5qnv2r95PxagYA6YPTDz0fXjuc+HviqdytsiR0qodjQo+e2C7YW8C+v/eRvSib7EXZ7Jq+iwNpByjcW0jGKxlsfH0j1a6uRp2H6xCd6P0eleHh8OmnsjTrrbdg3TrZjW/yZEhO9vqPV8ojTqbJsk45BTlrYcAAd3Ln8su1UdzJKNhTwLph65iXOO9QcicsNowmbzehzZw2QZ/ccTGhhsZvNiZheAIABVkFLDpnEXvn73U2sAAzbFjJ5I4xPt0BJijHe9cSLU3wlE7etjyW9FlC2oC0Q8md2vfVps28NsdM7ii3Sh0q0WZuGxq/1ZiwyjKflvllJvNbz2f37N2ATAoo36lRQ5I8ISGQkwN9+2ozVeVZQ4dKgueOO9zP9ekDTzzhWEgeV1RQxLw285jTeA6bRm4q8bnYPrG0X9Oeuo/WJaZdDBG1Io6Z3AEIqxhGpY6VqH1nbc5850xSV6TSclLLQ7u02gLL1k+2Mi9pHosvWMyeed7/gw0JgTfecO+ulZkJ3bq5q/+U8ncnk+DRTf+C3PDhMGaMHLdrJ43GQk56n7Wyx1rL1s+38meTP+W8wEII1LqzFu3S2lFrYK3jvrkFI2MMCYMTaDKqCYRA0b4ilvZdSv7OgNxd2xFDh7p3dQDIz5ckrI8SPEE53muCp/SyJmUxt+VcsiZIf4TwWuG0+l8rGo9oTGiU9pIpLRNqqH1nbVJXplKlZxUActJzWHT2ItY/v551w9Y5HGHZ0727XO8ArFoFAwfqttbKs4yB115zn3/7LTz+uHPxeJIttKz41wqyF2SXeD7xl0S6FnWl5TctCQk/9ZsHYwyxF8eSNDWJ5LnJxPWLO3S3uvPnnSxov4C1T6ylKL/o+N/oNLkm1N54Q8737oWLLpL/lkr5O63gUYDMLhS/cXTtMBFs5aSelrc1jznN5rD82uUl1x0XQbm4cpSrUrbL8GvdVosGz0sjmZz0HFbcsAJbpFfSpZWY6D5evdqnPzoox3ttsnxiRQVFpN2Vxt+9/iZ/m4xpcVfG0fbvtlQ5v4rD0QWu8GrhtPy+JQ1faYgpZ7AFljWPrQHkfUT51qBBcOGFcvzFF/DfoGonr/xBuXLw6KPQtKmcP/+8bKEeyGyRZeXAlWz7dBsgOye2XdIWgDPOPcPj/cViUmJoPrY57Va3o/a9tTHlDBTCuifXsaD9AvYt3efRn3c0d98tS7bCwiA3F664IvD/O6rgdzIJnkFei0I5aupU2QoQ3DPb1vq0WiAgbRu3jTnN53BgxQFAEjoAXYu60s12K/N9KFzqPFSHqn2qApA1MYv1L6x3OKLAUaXY/XROjk9/o623jwAAIABJREFUdFCO9/sOXgtGe38Zf0CyRZaVt648VHIfWjGUs8acRbMvmpX5ZLUnGGOo80AdavyrRonnZ9WYxTQzTZdr+VBICHzyibv57QMPQID08FUB5LnnZGct11bbAwcG7jIfay2r7l7FlveleXyFFhVo9XMrKjSvQL0h9bz6s6PqR9H4tca0mduGCi1l047sBdnMazOPDS9vwBZ6d+Lw2mthwgSIipLldzffrC0slH8rdYLHWrvEm4EoZyxbJr12CgqksZiWHp5YXmYeS69ayrJ+yyjIKgAg7qo42i6VWQzdIaUkYwxnfnAmkQ1lF4S1/1nLzl93OhxVYCjeqNGXyyWDdbyvcHAzt/3H3721TLLWsvrB1Wz9aCsgM7Mpf6VQo38NHdM87Mx3zqTz7s5Uu7ZaieeLcoq8vuxAuVWtCuPGycx8Xh5ceaW7yk8pT2nQQK6tw8PlWvuKK2RpYCCx1vJHnT/Y9F9J/pc/qzyJvyQSXjUc8F1j/ejEaNrMbUPdx+pCCNhcyz8P/8Oi7os4sOaAV392jx4wZYp7IvyRR6RCS5d3Kn90UrcMxpgrjTEVDx7/nzHma2OM9hQPUFu2wMUXw27p9cgHH0CXLu6mYupImV9nMrf53EPbgIfFhtHsi2Y0/6I54XHhXp/FCFTlKpejxfgWhESGQBEsu3oZuZtyT/yFZZxTCR4IzvG+YkX5qE1Vj7TuyXVsfG0jAFFnRtHqf62ISohyOKrgFRYTRtNPZO1GSHn5497w/AYWdVlEznrfluuVZR07ytIZkA0mbrpJb9iU53XuDO+9J8c7dkCvXvIxEBRkF5B2Rxp5G2UpaVSjKBKnJBJePdyReEIiQmjwbANaz2h9aOJw94zdzEucR9akLK/+7A4d4LffoGZNOX/hBdmcpqDAqz9WqZN2srcMg621e40xnYELgY8AXbkcgHJzpe/OuoP9HZ96SkoQQZdlHU3+jnyWXbuMpVcsJT9T+lJUvawqqUtTqXaVexZWl2UdW3RiNI1HNgYgf1s+y/ot09nqEyh+o+FAEUXQjfcxBzd+2qsbupWQ8UYG6UPSAYioE0Hi/xIJj3Pm4r0sMcZQb0g9UhakUCFRysv2zN7D/JT57Jq5y+Hoyo4HHoBLL5Xj775zN1VVypP694f//EeO09KkkicvANpvzaw4k81vbwYgMiGSxKmJRNSKcDgqqNSxEm0Xt6XWnbUAKMwu5O9L/mbT25tO8JWnp0UL+P13aNRIzkePhquu8vkyeqWO62QTPIUHP/YE/mut/Q7Qq8AAdPfd0kgZZC1psHT394bdf8jMwLbPpalc2BlhNP2sKc3HN3dsBiNQ1bypJjVulv4Tu2fuZu1/tOfE8ThZwUMQjveuCh5N8Lht+XgLq++VDt7l4sqR+EsikXUjHY6q7Kg/tD7lzyxP8uzkQzcq+Zn5LD5nMZtHb3Y4urLBGPjwQ6h/cH5m0CBYq29NyguGD5elgCC9ePx9B7cFZy8ocZ6TnsPsurNZ2G2hQxGVFFohlCZvNaH5N80JiZIK8bTb01gzaI1XN/SoXx9mzoSkJDn/5htZwqVLPJW/ONlbho3GmLeBq4AfjDERp/A9lMPeecddKtqhg+weoS0WjmStZcOrUjKfmyHLiWJ7x9J2aVuqX1Nd+1KcosZvNiY6Sbrcbnh5A/uWeX8XhEDlcIIn6MZ7XaJVUtakLFbctAKA0JhQWv3UivJNyjscVdkUGik3Kk3ebSK7bOVLw+tV962iqEArHb2tcmWZiQfp0XXbbf59460CU0gIfPQRtGsn5x99BE8/7WxMx5M8I5mYDjGHzrvZbnSz3Wg9rbWDUR0prk8cSb8mHdrsZP1z61l+/XKKcr03dlavLkm6Ll3kfNo0aN9eqrOUctrJXqxfBfwEXGSt3QVUAf7t8aiU18yeLdU7ADVqwFdfSeM3VVLB7gKW9l3KPw/+gy2wmHKGxm82psV3LYio6XxpaiALjQqV3hMGKIK1g3Wq9FgcTvAE3XivS7TcCvYWsOKWFVAIIZEhtJzYkoqtKzodVplX69ZaJE5NPHSjsvH1jfzd42/yd+Q7HFnw694dbr1Vjn/+GcaMcTYeFZyiomRHpoQEOR88GD77zNGQjiusSpjTIZRKTLsYkv9IJqqx9I7b9vk2Fl+4mPyd3hs7K1WCyZOhb185T0uT5N0vv3jtRypVKie8ZTDGnG+MedcYk2St3Q9UtdauArDWbrbW/s/rUSqP2LJF1vzm58uuEV9+CbVqOR2V/9m7cC/z2sxj+9fbAYioF0Hr31tT+67aWrXjIRWaV6B6/+oAbP96O3vmaknF0fg6wRPs471W8Litf249+VvlwrfJ202ofHZlhyNSLpU7V6bNvDaHKh13/rKT+anztdrRB1580d1A9YEHYOtWZ+NRwalaNfjhB0kQgDT3njnT2ZiO6eB1SEi0/xfwRjWMovWs1sR0lNmc3dN3s7DTQnLWea9BTlQUfPGFJOoAdu2Ciy6CkSO99iOVOqHS/LXeiczaXm+MOQdI8m5IyhtcW4BuOth7bMQI6eqv3Ky1bHpnEws6LCDnH3kziO0VS8qCFGLaxpzgq9XJShiWgCknCbO1j2sVz9E4UMET1OO9VvCInHU5bHh5AwAVUytS/frqDkekDhdZN5LWM1sT1zcOgJx/cljQfgFZP3h3l5iyrnJleOstOd65E+6919l4VPBq2hS+/lomXPPyZOMTf9w+3dXLpkLzCg5HUjrhVcNJ/CXx0Ni5f/l+FnZd6NXdCUNCpL/SZ59BRAQUFsJdd8kjX4svlQNKc8uQaa3dZa19GLgAaOvlmJQXPPSQe3bgxhvhzjudjcffFOUWseKmFaTdlobNtRAKDZ5rQIvvWlCuSjmnwwtKUQlR1LpNSsh2/rKTnVO1O93hHEjwBPV4X7yCpyz311jz2BoZ54BGrzbChGhloj8KrRBKs3HNSBieAEDhXtklZuunWlbiTZddJtXOAOPGyc5aSnnDOedIX0yArCzo2VM++pWD1yGB9D4RGhVKsy+aEX9/PAC563JZ1H0RORne3erqmmtkG/UaspcII0dq82XljNLcMkxyHVhrHwN0VXKAGTMG3nxTjpOTtany4fJ35LP4gsVs/UgumsNrhpM0NYm6j9YNqDe0QFTv/+oRUl6GoTWD1mDL8l33UTiQ4Anq8d5VwVNYWHa3NN09azfbxsqOgHH94qjUsZLDEanjMcaQMDiB5uObExIZAoWwvP9yNv53o9OhBbU335RqHpAJsd27nY1HBa+bbnJvn75qlSQYc3Odjam4Q7tR+f8KrRJMiKHhKw2Jf1CSPDlrclh8zmJyN3v3l5uaCnPnyv0WwJQp0pdn5Uqv/lilSjjhn+vBrXExxlQ9eP6Gt4NSnrNggewGAVD1/9k77/CoqvSPf86kN5LQgkAIIbQAiQRQV91VFGw/C5ZV7F3X3nsj9ord1RXFtay9ICqWdTV2kR4IHQIEQkkoIZWUOb8/3plMQJBEMvfO3Hs+zzPPnJPMcL6a5My973nf79tZ0kHj4uzVFErULqtl5v4zqfhert46HNiBEbNGkHKQ8aOwgui06OYTlsrfKin/uNxmRaFFywCPFUFZp+/3SS08hN1YpqW9mqXXSkt0FaPIejjLZkWG1tLlxC7kfpFLRFIEaFhy2RJWPrTSblmOpVs3GD9exqWlcNNN9uoxOJt775XsD4AffoDzzw+hLNMmedL1oSKo9SilyHosix5X9ACgdkktcw6dQ/36+qCu27OnZPL4zZeXLJEOW//9b1CXNRiaaUs8dmLQVBiCQnm5nATU1cnp/zvvQEaG3apCh4pfKpj5l5nULq4FoOupXdn7672JTjNtxawk/cZ0IlOlS0Px7cXopvC7iAgWNnbRcuR+3zLA40aj5U1fbqLyN4lspV+fTmxGrM2KDG0h5eAU9v5m7+auNsW3FpvMxyBy3nkwapSMX3wRvvvOXj0G56IUTJwIBx4o8zffhPx8WyU1EzdAToUrp1VSOSv8TkaUUvR9ui97/UPc02sW1jBn9Bzqy4Mb5ElI+L358lFHBTy+DIZg0pZbBlOrEkY0NsKpp8KqVTJ/+GGp9TUIG97bwOxDZtNQLu5nvW7tRfZ/somIjbBZmfuISomi1829AKiZX0PFjyYX3k/L+zaLAzyO3O87tPBKd2OAx58hp6IVvW7qZbMaw5+hw4gO5H2fR/RechCx6qFVLLl8SaCMwtBuKCWBHX/W84UXQm2tvZoMziU2FiZNgixfYuU994jFgt30urEXKtLXEOOO8GyIoZSi/z/70+18McepnlfNnNFzaNgUXAfknZkvX3GFMV82BJ+23DKYq4cw4rbbpO4TYOxYMVk2SKesVY+sYv4p85vNlPtP6E+fB/oYvx0b6XZBt+bdqHySKdPyY2MGjyP3+65dA2N/R0G3oLVm46fi3plySAqRyZE2KzL8WRIGJ5D3Yx6xfSQDq/T5Uhaeu9AEeYJAnz5SPgOwdCncfbe9egzOpnNnaZ+emirzCy+EggJbJRGXFdccGNk0ZRMVP4fnIZzyKAa8OIC0s6RrZPWcagqPLKSpuinoaxvzZYPV2JLBo5SKUErNUkp9upPvKaXU00qppUqpQqXUsPZa1y28+y48+qiMhwyBl182psogNzjLrl/G8puXAxCRFEHuZ7l0v7C7zcoM0Z2jSf6bmL2WTyo3JQc+ysoC4/h4S5du1x0jVPb83r0D45Uusy+pml1F/RpJSe98bGeb1Rj2lLg+ceT9kEf8INkY1r++nqXXLjV7ZxC4+moYMULGjz0Gc+faq8fgbPr3l0yeqCjJ8jjhBFi40F5NGXdmoGLksmD5beFbFqoiFANfGUjXU+W0p3JaJUWnFOFt8O7mnXvOzsyX990XioqCvrTBhbQlwHNrO657NbBgF987Cujne1wMPN+O6zqexYvFnA2kA8RHH0kdqNvRWrP0qqWsfmI1ADE9Y8j7MY+OR3S0WZnBT+fj5aazbkUd1YXVNqsJDWbNkuesLEhMtHTp9tzvIUT2/G7dINpnseW2AI8/eweg49Fm33MCMd1jGPrdUOKzJciz5uk1rHpolc2qnEdkpByURURIicUtt9ityOB0DjpIPHlAvFuOPnr7Ax+rie0ZS4/LxKi44rsKNn8dvqknKkIx8LWBpB4haVKbpmxi8SWLLQla7Wi+vHSpmC9/+GHQlza4jFYHeLTW89pjQaVUT+Bo4KVdvGQM8JoWfgVSlFJ7tcfaTmfbNvHdqfbdG7/xBvTta6+mUEB7NYsvXcyaZ6WtbGxWLHk/5ZGYa+0ds+GP6TwmkFVgyrSEmTPleZjFeYzttd9DaO35Hg+kp8t4xYpgrBC6+AM8CUMSiOttWik6hejO0eR+mUtMzxgAim8rZu3La21W5TxycwOHZ1Om2F82Y3A+Z54ZMFpevhzGjLHXA6rXLb3wJMhtY/HtxWGbxQPgifIw+L3BJA6X+4B1E9exIn+FJWv7zZfvuUfmVVVw0klwxx3bl+UbDHtCm1wdlFIjlFIfKaVm+lLp5yqlCtu45pPATcCufo17ACUt5qt9X9uZnouVUtOVUtPL7Axthwg33xw48b/hBon4ux3dpFl00SLW/ksueOP6xZH3XR6xvUz3mFAjLjOOhL0l3cwEeKQLXolvJ7Q6wAPttt9DO+357bXf+zsJuimDp359fXP3rE7HdLJZjaG9iU2PJffL3ObuWosuXkT5ZLOHtjf5+QHD5ZtvDqE21gbHctddEugB+OUXOOssySKzg+iu0fS8picgpU0bJ2/czTtCm8ikSHI/yyU2U+4HVt6zktIXrTHn83iku9YnnwSaP9x/Pxx7rGRsGQx7SlttO/8DvAKcBBwLHON7bhVKqWOADVrrGX/0sp18bacfo1rrF7XWI7TWI7p06dJaGY5k8mR46ikZ77uvbBRuRzdpFp63kHUT1wEQPzCeod8NJaZHjM3KDLuiywnyd1w1u4raFe5uV+IP1gLk5dkiYY/2e2jfPb+99ns3BngqZwRa2/rT0g3OImFQAjmf5uCJ84AX5o+dz5Yft1CcH55db0KR7t3h2mtl/Ntv8MEH9uoxOB+l4KWX4OCDZf7BB/I7aFdwMf2GdCJTJJBcfEdx2Bu7R6dJBmRU5ygAFl+6mPJPrAuOH3OM7CUDB8p8yhS5h5s/3zIJBofS1gBPmdZ6sta6WGu90v9ow/sPBI5TSq0A3gYOVUq9scNrVgPpLeY9AZf1O2kbJSVw3nky7tAB3nor4DPhVryNXhactYD1r68HpCxhaMFQYvYywZ1Qxu/DA7D4ksU2KrEff3kW2Bbg2dP9HkJwz/cHeNavh7q6YK0SWmxbs615HNfHlGc5leT9kxn83mCIAG+dl3nHzmPl3S6KZFrATTdBJ18S3G23mVbHhuATEyOmy4MHy/yZZ8Ts2w6iUqJIv1E+rqvnVbP66dX2CGlH4vvF/y44XvGrdZ3CBgyAqVOlBA9gyRLYbz/xUDUY/ixtDfCMU0q9pJQ6TSl1ov/R2jdrrW/VWvfUWvcGTgW+0VqfucPLJgNn+zqr/AWo0FqbgvJd0NgIZ5wBmzbJ/MUXpa2nm9Fas+jCRWx4awMACbkJ7P3N3kSnuTzqFQYk5CYQ00uCcJu/DF8Tv/bAH+Dp2XP79t4Wskf7PYTmnu8P8ACscokfbX1pffM4upvZB51Mp6M7MfBlOQ5u3NIIQFOdTTUdDiQ5WbwyQG7EXtqVs5jB0I6kpMDnn0MPX/HyTTfBm2/ao6XHVT2ar9OW37icip/Cs216Szrs14FB7w6S4HitBMdrl1uXRd6hgxgt3323zKuq4MQTpUTP+PIY/gxtDfCcBwwFjkRS9f1p+3uEUuoSpdQlvukUYDmwFJgAXLan/76Tufde+OEHGV90EYwda6+eUGD5rctZ/6pk7iTmJTL0m6FEdzE3NeGAUor4gdb2Aw9V7DJYbkFQ9nuwd89v2SrdLUbL20olgyeqSxSe6LZ+7BvCjdri7W9Mfoj7gQJVYMq12olLLw3sI3ffLTdjBkOwSU+XII/fs+Xcc6XVttVEJkYy+L3BqGiFbtQUnVzEtnXbdv/GEKfzMZ3p/3x/ABrKG5h79FwaNluXoufxSEBn8uTAz/jeeyWzpyL8Y2gGi2nrld7ePg+Ec7TW5/ke5/+ZhbXWBVrrY3zjF7TWL/jGWmt9udY6S2udo7We/mf+fTfw7bfyxw8waBA8+aS9ekKBOUfOoeRh8WuN6xtH7he5RHWKslmVobUU5xez+atA5k6BKnDljUlFhbTPBFsDPO2230Po7PktM3jc4sPjz+CJ7m4C3W4gMz+Tg+oPosMBHZq/NvC1gWTmZ9qoyjnExMB998l4/Xp4/HF79RjcQ06OlGtFR0t54Iknwpw51uvosG8H+j4lbXrr19Yz/9T5eBvDP9Wk+0XdSb9JStBqFtZQ9PcivPXW/ncde6z48gwYIPNPPxVfngULLJVhCHPaGuD5VSk1KChKDG2irExKs7SG2FhpuRfv8sSH9W+tby7rie4WTe5XuUR3NTc04URmfibpNwTsWA72HsxIPdJ1NyazZwfGNgZ4HLnf9+wpJ2UQuElzOv4MnpjuxoPMLXiiPAx6J/Dnu/iSxVTNM6km7cVpp8HQoTJ+9FHYsMFePQb3cMgh8OqrMt66Ff7v/+wpN+7+j+6knZMGQMV3FRTf6oyDuD4P9qHzSeIHueWbLSy+dDHF46z9b/P78hx3nMwXLxZfnkmTLJVhCGPaGuD5KzBbKbVoD9vmGvYArxfOOQfW+lwqnn4ahgyxV5PdbPpqEwvPWQhARIcIcj7PIS7TmImGIy09QhorGm1UYh8tO2jZGOBx5H4fFSXdcMB9Hjwmg8ddxPaMpeuZXUGBt8ZL0d+LaKx0557a3ng88PDDMq6qCmRTGwxWcOqpAaPl0lI48kjYbLFtoVKK/v/sT8LeCQCUPFZC2Qdl1ooIAsqjyH4tm6R9kwBYN3EdK++xPt03OVmMlvPzZV5ZCSecIGWhxpfHsDvaGuA5EugHHM6fbJtr2HOefFLqcAFOOQUuvNBePXaz8KKFFB5RiG6Qdo1NW5uYkTfDdWU9TiEqLVBS17DenS1K/P47XboEghE24Nj9fnX4N/5oE946uRqMiIuwWYnBaga9Poje43oDULuolmXXL7NXkIM4/HAYPVrGL7wAy8z/WoOFXHcdXHONjBcsEK8WqztDRsRHMOSDIUQky2fLwnMXUr2w2loRQSAiPoIhHw9pNpMG2PCe9Wl6Hg+MGwcffwxJEm8iP1/u/arD/3+zIYi0KcDTslXuHrTNNewB06bBLbfIuHdv6ZqllK2SbKVuVR0bJ2+Uie//w0g90pVlPU6hZQZP/fr6P3ilc2lpsGzX37dT9/uRI7efKyWPHb/uJDxx8lHvD/QY3EXGHRmkHJoCwNoJa9ny3RabFTmHhx6S58bGQHctg8EKlILx4+Hkk2X+ww9w1lnWZ3fEZcWR/UY2AE1VTRSdWERjVfhnCpa+UMq2VQHz6PmnzLfNE/K446Rkq6/YHvHBB3Dgge7xETS0nTYFeJRSryqlUlrMU5VSE9tflmFnVFRIWmZDA0RGwttvSwqfW2mqaWLe8fNo2CBZHv2e7WezIkN70LKdff069wV4amoCZno2lmc5dr8vKIDs7MB861bxMisosEtR8PHEmgCPm1ERigETBjQH+hZdtMi0Tm8nhg8XPx4QL0STxWOwEo8HXnsNDjpI5u+/L5k9Wluro/Mxncm4QzoY1CyoYdGFi9BWi2hnMvMzGalHkvtlbvPXIpIi6HR0J1v0ZGeL+fJhh8l8zhzYZ59AJ2WDoSVtLdHK1Vo3H/1orTcDee0rybArrrwSli+X8QMPiOGWW9Fas+iCRVTNEtPIHlf0oMdlPcgYl7GbdxpCHf9NCEgQz23MmhU4gbMzwIOD9/u77w6MFy2yT4dV+P+mmmrd9/dkEOL6xJF5r2S11i6pZeW95ui3vbj1VnnWWjwR3YxS6kifb9tSpdQtO/n+GJ+n22yl1HSl1F/t0OkkYmPFfHfwYJk/9ZQ9nd165/cm9fBUAMreKWPVw84wuet4eMfmcVNlE4VHFFJVaI9hfWoqTJkSKM0rK4NRo2DCBFvkGEKYtgZ4PEqpVP9EKdURiGxfSYad8cEH8PrrMj78cLj+env12E3JIyVseFvqYVMOSSHr8SwAU5blAFqmxMamx9qoxB7ef1+elYIDDrBVimP3+4EDA2NXBHhMBo8B6HF1DxKHJwLyGVo1x3TVag9ycgKn6i+/DFtcWgGnlIoAngOOAgYBp+2kE+P/gL211kOB84GXrFXpTFJTxZvT79l3ww3w1lvWalARiuz/ZDf71hTfWsz6t9dbKyJIZIzLoP8L/QFo3NzInNFzbPMaioyEJ56QvSYqSqo6Lr5YkgAa3GlbadgJbQ3wjAd+Vkrdq5S6B/gZeKT9ZRlasnYt/OMfMk5NhVdeCbT5dSMbp2xk+a2SyhTbO5ZB7w7CE+Xi/yEOo25FwCUwtre7AjyNjYGLskMPtdVgGRy83/ftG/A2WrjQXi1WYDx4DACeSA8DXhoAEaAbNYsuXIS30fxOtAfXXSfP1dWuPk3fF1iqtV6uta4H3gbGtHyB1rpKB2p3EoDwruMJIdLTJcjToYPMzz5bsj2sJLpzNDmf5RDRwWe6fM5CtvwQ/hHPzPxMuv+jO1lPyGFyQ1kDc0bNoXZZrW2azj8fvv0WunaV+bPPSje1jRttk2QIIdpqsvwacBKwHigDTtRavx4MYQZBa+mS5f+Dff5522/6bKVmUQ3zT5sPGjzxHoZ8PITozqb1r5OoW+kL8CiISY/54xc7jK+/hvW+A68zz7RXi5P3+7g4MakHd2Tw+LtneWvMzbzbSRqaRK8bewFQOb2SdRPX2azIGRxxBAzy5ao8/bRrT9J7ACUt5qt9X9sOpdQJSqmFwGdIFs9OUUpd7Cvjml5WFv7tt60gN1fKtWJi5MDopJPgu++s1ZA4JJEhHw5BRSp0vWbemHnULKpxRGfb9GvSybxfKgXqS+uZPWo2dassbl3WggMPlOY7eb7i+W++EfuO+fNtk2QIEdqc9qC1nq+1flZr/YzW2vwKBZkJEwIR+NNOg7Fj7dVjJ42VjcwdM5emreIjkf1aNom5iTarMrQ3/gye6O7ReKLdlZn1xhvyHBsLJ55orxZw9n7vL9NyQwZPVNcoAOrXus+03PB7Mu7KaC6jWHH3Cld6nbU3SsG118p49epAqa3L2FnPx99l6GitP9JaDwSOB+7d1T+mtX5Raz1Caz2iS5cu7SjT2RxyiBh+R0RI2/Rjj4Xp063VkDoqVbIFkZKmwqMKWXm3M3y/Mm7LoNdtEiTftnIbc0bNsTXI06sX/PijtE4HMXr/y1/g009tk2QIAdx19xRmLFsWSPvt0QOee85ePXaitWbxJYupXSTpkBl3ZdDlJPOB70T8AR63lWdVVcFHH8l4zJhAmrUhOAyQa08WL4Ymh9/f+jPhtq3ehm4yFRFuJyIugsx7AqfQa55dY7MiZ3DGGeCPQzz+uPWdjEKA1UB6i3lPoHRXL9Zafw9kKaU6B1uY2xgzBl59VQKPlZVSumN1Vke3c7rRO783AHXFcl3nlGBy5n2Z9LymJwC1S2uZuf9M24yXAeLjpbPyvb5waWWltFZ/+GFX7kMG/kSARyl1czCEGLanqUnqZ6t9Hl6vvCL+O25l3Svr2PCmmCqnHp5K73G97RVkCBpuDfBMmiQt0sH+8iw/Tt7v/Rk827bBKmc0+9glsb3kb0k3aurXmyweA6SdmUb84HgAVj24iobN7qwpak/i4uCyy2Q8fbqcqruMaUA/pVSmUioaOBWY3PIFSqm+SokDmlJqGBANGNeQIHDGGYGD4Y0bYfToQCdeq9De7aMLPyT8QIEqCPtyLaUUWY9n0fM6CfLUl9Yz62+z2FxG5T4OAAAgAElEQVSw2UZNcMcd8OGHkJAggZ1bboHzznNtyair2W2ARyn1bovHe8CFFuhyPY88Aj//LOMrrwx0aHAj1fOrWXLFEgCiu0WT/Xo2yrOzTGBDuNNY1ci21dJFKzbDXQEef3lWp07i52AHbtrv/Rk84PwyrZZeVttKtv3BKw1uQUUo+jzQB4DGLY2UPFKym3cYWsOll4r/CdjTqtpOtNaNwBXAl8AC4F2tdZFS6hKl1CW+l50EzFNKzUY6bo1tYbpsaGcuvRQefFDGa9dKkGeNhQl7mXdnctC2g0gZldL8tR5X93BEx1ulFH3H9yXrMTFebtoqLdQ3vLvBVl0nnAC//BLwGXz1Vcnoqran6ZfBJlqTwbNVa32K73Ey8HWwRbmd2bNh3DgZDxgADz1krx47aappouiUIry1XlCQ/UY20V2NqbJT2fzlZvD5wHbY3z01SuvWwX//K+NTT5XWlzbhmv3eTa3SWwZ47PQKMIQWnY7t1LzPrn5qNdtKTfBvT0lLC2RgfvwxLF1qrx6r0VpP0Vr311pnaa3v933tBa31C77xw1rrwVrroVrr/bXW7stzsphbbpEHQHExHH44lJdbt74n2sOQD4Y0z9c8tYbVT622TkCQSb8+nez/ZKOixFR6/qnzbf/vy8mBqVNhxAiZf/65dGa18udusJfWBHju32F+ezCEGIS6Ork4aGgQg7TXX5faSrey9Jql1BRJ3UrG7RmkjnJxnZoLKJ8knz6eBI+rftZvvw1eX2DL5vIs1+z3aWmQnCxjp2fwRKZENo9X3LXCPiGGkEIpRZ+HJIvHW+tl1cMOr1W0CL/Zstbw1FP2ajEYAB54QLJ5QLx4jjwStm61bv3I5Eh6XNOD6L3kgHbptUsp+8A5ndHSTk8j9/NcIpIiQMu9y7Kblv2uRM1KunaVNur+jPDffpOuWytW2CbJYCG7DfBorYsB/CZoWutNwRblZu64A4qKZHznnbDPPvbqsZMN72xg7YS1ACT/LZmMcRk2KzIEE2+Dl42fSSl+xyM7Nrd2dgP+8qysLGlxaRdu2u+VCpRpOTmDZ9bIWUzNnNo8r1lYQ4EqYNbIWTaqMoQKKQelkDpagunrJq6jsaLRZkXhz+DBgZuqiRNhk2N3UUO4oBQ8+6z48gDMmCHdtfy+f1bQ74l+5EzJISJRgiALzlxAxc8V1gkIMqmjUhn6/VCiu0kQq+TREopOLqKxyr49NTERJk8OHBwuXgwHHACFhbZJMlhEW0yWJwZNhQGA774L1Gzvsw/cdpu9euykrqSORRfLXVdkp0iy38zGE2mavjmZih8qaNwsH4Sdx7inqcaCBXKxBfIhrELDXsoV+72/TKuoyLmdJvIK8hipR273tZF6JHkFefYIMoQcPa8Vo9CmqibWTlxrsxpncP318lxTI0Eeg8FuPB5p2DJmjMy//x7+/neot9B3P2loEoPfHwwR4K3zMve4udQstjDKFGSShiaR93Mecf3jACj/sJxZB8yidnmtbZqio8WH54YbZL52Lfztb1BQAPn5tskyBJm23DGHxm2HQ9m6Fc45R24y4uKkNMtGHw5b0Vqz6PxFNG2VdooDXxlIbE93Ge66kfKPfcXBEdDp6E72irEQf/YOBE7XQgBX7Pe5ufJcViYXPU6m62ldAYjpFbObVxrcRscjOzbfkKx5eg26yaHRTgsZPTqQIdhyjzcY7CQqSkrCDz1U5p9/DmedJZ17raLjER0Z8KL8cTRubKTwqELqNzinu2NcZhzDfh1G6hGSGVk9t5oZ+8xg8//s67Dl8cCjj8L48TLfulWyDO++2zZJhiDTlgCP+cQPItdeCytXyviRR7bv8OI2Sl8oZfPXshF2u6AbnY91TzaHW9FaN/vvpBycQlRHd0Q3vV74z39k/Je/QL9+9uppgSv2+7wWSSyzHF6xFD9QzNy2rdpGU7WFV/OGkEd5FD2vliyeuhV1lE82Tpx7ilKBgP2cOTBvnr16DAY/sbFiAO4vB3/3XbjgAmuDPHudvxcZd4ntQt3yOuYeO9dRn0tRqVHkfpZL+o3pADRuamTOEXNY/dRq7Gwad911EnCOjAxkbv3zn7bJMQQRk8ETAnzxRSCF97DD4LLL7NVjJzVLa1h2wzJATpr7Pt7XZkUGK6j8rZJtq6SDi5vKs77/PhDYtdlceUdcsd8PHRoYuyXAA1CzyDkp8Yb2Ie3stGYz7tVPOqfDjZ2cfnpg7A/kGwyhQGIiTJki3ZZASnjOPRcaLbSL6Z3fm27ndgPkGnD+6fMdlT2oIhRZj2SR/UY2nlgPNIn58sLzFtJUZ18wa8mS7X/Ol18uAWl/92aDM2hLgOfWoKlwMVu3wkUXyTgpCV5+WVLp3Ihu0iw8dyHeGmknNPDfA4nsELmbdxmcQMnjJQCoSEWXk7rYrMY6HnxQnmNi4JRT7NWyA67Y7zt2hN69ZeyqAM9CE+AxbE9kYiR7XbgXABXfV1A5u9JmReFPVhbsv7+M33wz0CnRYAgFOnaEr78OBHneeEPKtawK8iil6P9if1IPk1KmjZM3suSqJbZmuASDtDPSyPsxj5ieUh69/tX1zP7bbOpW1tmiJz9f7ECmTdv+66Wl1gb4DMGlVaEEpdSzQHKQtbiSG2+E1b7Dssceg/R0e/XYSckTJWz9Sfo29riqB6mHuKdNtpupXV5L2fvSLrPraV2J6eEOj5CpU+Grr2R80UXQJUTiWm7b7/1lWjNn2qsj2MT1i2vOy6pZYAI8ht/T/fLuzeP1b6y3UYlz8JdprVoFP/5orxaDYUe6doVvvglks779Npx6KjQ0WLO+J8rD4PcHk7B3AgCl/yxl1UOrrFncQpKGJzF8+nA6HNgBgMrplUwfPp1NX9nXYm/ECHnOzJTnl16Ck0+21nTbEDxamyuyBHhMKbVCKfWwUmrobt9h2C3/+x+8+KKMR40KZPK4ker51RTfUQzIjUifB/vYrMhgFSWPl4DvZDP9BvdEOO+9V56jo+Hmm+3VsgOu2u/9AZ4VK2CzfR6IQSciLoLYPmJWX1VYZbMaQygS1zuO5IMktrvhrQ2OKpewi1NOEb8LMGVahtCkc2e5Hxk+XOYffCA3+tu2WbN+ZIdIcj/LJSZdDveKbytm3avrrFncQqLTohn6zVB6XNED8BlMH1nIivtWoL327LXjxsHPPwcCfJMmwWmnWRfgMwSPVgV4tNZPaa33Bw4GNgGvKKUWKKXuUkr1D6pCh1JVBRdeKOOEBImchkh7ZMvRXs2iCxeht2nwwMBXBxIRH2G3LIMF1JfXs26ifJCnHpFKYm6izYqsYcYM+OwzGZ9/PvTsaa+elrhtv29ptDx7tn06rCBpWBIAlTNM+Y1h56SdkQZAfWk9W77bYrOa8KdLF+lWA2Jma9VNs8HQFvzlWvvuK/OPP4aTToI6i6qIYnrEkPtFLpGpEg1deMFCNn6x0ZrFLcQT7aHfM/3ElyfeAxpW3LmCeWPm0bDZ+qhKfj506wbffSeNPgA+/BDOPtuUa4U7bXJ70Vqv1Fo/rLXOA04HTgAWBEWZw7nlFjkxBnj44YAPhBspfb6Urb9IaVbPa3uSvL9rqkNcT+k/S/HWSvpOrxt72azGOvzZO5GRsheEIm7Z793USStpuAR46tfUU7/e5GEbfk+Xv3dBRclp0/o3TZlWe+A30N+yRdpShyJKqQuVUp8qpc5TSsUqpW5TSt2plMqxW5vBGlJSpGzc7xv12Wdw/PFQW2vN+gmDEhgyeUizIXHR34vYOm2rNYtbTNoZaQz7dRhxfeMA2PjpRmaMmGGb91mHDrI3+cu23n4bzjvP2s5qhvalTQEepVSUUupYpdR/gM+BxcBJQVHmYL77Dp57TsYHHwyXXmqvHjupW13H8luXAxDbO5bMuzNtVmSwiqbaJtY8uwaAxGGJpByaYrMia5g9W07HQLpWZGTYKmeXuGW/79494H/k9ABP4vBAhlzlTJPFY/g9UR2j6HhURwDK3i+ztduLUzjuOOlaBCFdpnUDcAuwHzAN6A+sB55RSp1jpzCDdSQnw5dfwt/+JvMvv5Tf3xqLbNtS/ppC9pvZ4AFvtZe5R8+lZqkzPeMScxIZPn04nY+XzrF1y+uYtf8s1r1hT3laSor8vP3lWm+8IdYhxhw+PGmtyfJhSqmJwGrgYmAKkKW1Hqu1nhRMgU6julpKMgDi4qQ0y7Vds7RmyRVLaKqUC8j+L/QnIsGUZrmFtS+upaFMUlLTb0xHuaRG8b775DkiAm4NwV5VbtvvlXKP0bK/RAtMmZZh1/jLtJoqmtg0xT4TUKcQHw8nnCDjTz6Bigp79eyCeq31POAaIBP4h9b6ReAI4HJblRksJSlJsjlGjpT511/D0UeLtYQVdDmhC/2e7QdAQ1kDhUcUOjbjNDI5ksEfDqbPw30kqFXnZeFZC1ly9RK8DdZHVjp2hP/+F4YMkfkrr0gSgsMam7mC1oYWbgN+AbK11sdqrf+jta4Ooi7HcvvtsFwSVnjgAejb1149dlL+YTkbP5Ya265ndKXjER1tVmSwiobNDay4ZwUAcX3j6PL3EGkhFWTmzRMDQ5B2pH1C00vcdfv9sGHyvHChdSeVdhDVMYrYTJ/R8gxjtGzYOZ2O7UREohy2lE8qt1mNM/CXaW3bFvgMCDE+Ukp9DBwFXKa19rsFNQCd7ZNlsIOEBCnRGj1a5gUFcNRRUGnRuUCPS3uQcYekN9ctr6Pw/wpprHCmKYxSil439WLvr/YmspN4EK15eg1zRs+xJbDlN93Ozpb5iy/CVVeZIE+40VqT5UO01hOAzUqpM5VSdwEopXoppfYNqkIH8dNP8PTTMj7gALjySnv12EnDlgaWXLEEgMhOkfR9wsWRLhey6oFVNG6SD+s+j/TBE+mONDZ/9o7HA7fdZq+WXeHG/d6fweP1wty59moJNn4fnq2/bUWbKzbDToiIiyB1dCoAm77cZFuHFydx6KGQJolRvPGGvVp2htZ6HPAcMAq4VCm1Sin1P+B75LMgWynljg9qAyCZZ5Mnw5FHyvzHH8UwfItF3uu97+lNt/O7AVA1s4q5x86lqca5JaOpo1IZMWMEicOknrPi+wqmD5/O1qnW+xB17SpBnv6+thrPPgvXX2+CPOFEWzfrfwL7A6f55pXIB0Kr8Zm3/aaUmqOUKlJK3b2T1yQrpT5p8Zrz2qgz5KitldIsrSE2FiZOlBINt7L8luXUr5PIdN/H+xLdJdpmRQarqC2uldboQPJfk5vrj53OggXSRQXg9NOhXz979bSCPd7vw4WWRsvTp9unwwo6HNgBkC5Jtcsscs80hB0dj5SM2oYNDVTNNtlee0pkpLQfBsmG2LDBVjk7RWv9ldb6Cl8XxQykNOs54GvgKaDYTn0G64mLk9bZxxwj819+EX+e1auDv7ZSiv7/6t98jVjxQwVFfy/CW+9cU5jYjFjyfswj7WxfN8M19cw6aBalL5VarmWvveCbbyArS+ZPPCFNQUyQJzxoa4BnP6315UAdgNZ6M9DWO/NtwKFa672BocCRSqm/7PCay4H5vteMBMYrpcI6AnDXXbB4sYzvuQcGDLBXj51snb6Vtf9aC0DKqBTSzkqzWZHBSpbfuhx8n89Z47Nc471z//3ywaiUlGqGAXu834dLQL9vX0lLBvjhB6tXt5aUkQEz8y3fmjbYhp2TekRq83jTF8aHpz3w+/BoLT4XoYwWFmqt39Ja36y1PlxrHaItAQzBJCZGygpP8rVYmDdPOm0VFQV/bU+kh+y3skkZJZ9bmz7fxIKzF6CbnBtliIiLYOC/B9L3mb6oSIWu1yy+aDFLb1hqeTZljx4S5PF3en7kERg3zlIJhj9JWwM8DUqpCEADKKW60Hyr1jp8Hxr+46Ao32PH31gNJCm580sENgFhW3w5dSo8/riM990XrrvOXj12or2aJZdLaZaKUvT/Z3/X3OAboOLXCsreKQOg62ld6bBvB5sVWcPixfDWWzI+5RQYONBePa1kj/d7wiSgrxQcdJCMv/vO2SdUibmJRHaUOn8T4DHsirjeccQPjAdMgKe92H//QDetr76yV4vB0Baio+Gdd+Byn9326tXw17/K52WwiYiNYMikISTtJ+XFZe+UsfjSxY4uMVZK0fOKnuz97d5EdY0CYPX41RSdXERTTRPF+dYl0/XqJUGenj1lfu+98jCENm0N8DwNfAR0VUrdD/wIPNDWRZVSEUqp2cAG4L9a66k7vORZIBsoBeYCV2utwzInr74eLrhAvB2io8WR3M2lWWsnrqXyN3FpS78hnfj+8TYrMlhF8bhiZu0f6EO94a0NFKgCSz+o7OKBBwKtJu+4w14tbWCP9/twCuj7Azzr1sHSpVavbh3Ko0g5WE5Dt3y7xdEXyYY9w1+mVfFzhWMNTq0kKkq8eEACPOZPzxBORETAM8/AQw/JfMsWOPxwKT3Pzw/u2pGJkeROySUhJwGAtRPWsvym5Y7//Er5awrDpg4jPlvulco/LGf2obNZefdKS3VkZsK330rZFkhVylNPWSrB0EZa2yY9EkBr/R/gJuBBYC1wvNb6vbYuqrVu0loPBXoC+yqlhuzwkiOA2UB35NT3WaXU7476lVIXK6WmK6Wml5WVtVWGJTz8cCCN8a67YNAge/XYybKbl7H4osXN81UPrnLNDb4B4vrFbTcfqUcyUo8kMz/TJkXWsGBBwFTzpJMC7SdDlfbe79sroB/s/f7ggwNjK04l7cRfplW/rp7axcaHx7Bz/AEemmDzN5vtFeMQDj9cntetk1IXgyGcUApuvhlef118perr4dRT4e7fFV+3P1Edo8j9KpfYLOkEWfJYCSvuWuH4IE9c7zjyfs4j5VD53K6cKofk1QutbW7at68Eefxm8ddcA2+/bakEQxtobQbPb/6Bryb3Oa31s1rrBXuyuNZ6C1AAHLnDt84DPvSd/i5FjN1+V9SgtX5Raz1Caz2iS5fQa7O8cGEgqp2TAzfdZKsc22mq3N793i03+AZo2NTAsuuWARCVFmWzGuvQWtpLNjVJ56y77rJbUato1/2+vQL6wd7vc3IgOVnG33/f7v98SJFySMCHx9y4G3ZF8t+SwZdxvPUX6zu5OJEjjgiMv/zSPh0Gw55w5pkwZQokJQUy0W64IZCpHCxiusWw99d7E9MzBoCV962k+M5ixwd5olKi6HDA9pdF07KnWX5IPmAAfP65/NwBzj5byrcMoUdrAzztZpKilOqilErxjeOA0cDCHV62CmnViFIqDRgALG8vDVbg9cLFF8uzUjBhgqTnupXKmZWUviAu8P72qwb3sPyW5TSUNQDQ94m+ZIxzh1fjxx/D11/L+B//gNxce/W0kqCYYu1pQD/YRERIdxBwfgZPwuCE5kDrxk832qzGEKpExEeQuLeYxmz91QR42oOsLCl3AOPDYwhvfvoJKisD8/Hj5XM02GXocb3j2PvbQJBn1f2rKL7d+UGePvf24WDvwfS+p3fz1zyxHpIPSLZUR16edFaLioKGBjj+eJg921IJhlbQ2gBPF6XUdbt6tHHNvYBvlVKFwDQkZf9TpdQlSqlLfK+5FzhAKTUX+B9ws9a6vI3r2MrLLwe6sVxxBey3n7167ERrzZIrl4AWY+W+z7jnBt8AFT9VsHaCdE1LPSyVrqd2dUXWVl1dwFA9NTWsTOnabb8Pt4C+v0xr1SpYaW2Ju6Uoj6LzcdI2bPPXm2ncavxVDDunw1/k1LhyeiXehrC0QgwplAqUaX3/PdSaCklDmJKfL9k7xTskkPz0k/jzBJP4vvEMLRhKTLovyPPgKpbf6nxPHqUUve/sLZMI8NZ5mXvcXDZOsfag5tBDpUwPJMh31FG//z0w2EtrAzwRiPll0i4erUZrXai1ztNa52qth2it7/F9/QWt9Qu+camvJWOO7zVvtGUNu7n+esne8fPMM/KhHmwTslBl4ycb2fqznP71vKYnCQMTXHGDbwBvg5fFl4jvkifWQ//n3dM1bfz4wAfeffdBp0726mkD7bbfE2YBfb/RMjg/i6fziRLg0fXa8otDQ/jQYT8J8HhrvVTPtdbzwan4y7S2bXN+OajB+fhbaB94oDwXFEg27OrVwV03LitOgjy9JMhT8nAJy29xfpAHIGNcBoPfGSxt1Ldp5h0/j/LJ1l42jR0LTz4p43XrZF8LUTtcVxLZytet9QdiDLunpGT7uQv2ml2ivZriO+QuNzIlkl639bJZkcFKVj++mup5clOQcUcGcVlxu3mHM7j22sAHH0hr0csvh3HjwiLQ2277vda6EMjbyddfaDEuBQ5vj/X2lGHDICEBqqvlxuvss+1WFDxSD00lokMETVubKP+wnLRT0+yWZAhB/Bk8AFunbiVpWFtjvIYdOeQQKWVpapIyrZa+PAZDODJunJgvn3EGfPSRGIjvv7/49OTkBG/duD4S5Jl9yGy2rdxGySMleGu99H2yL8rj3MNE/yH54PcHU3RyEbpBU3RSEYPeGUSXE63zpL36aigthUcegSVL4OijxZMnMdEyCYZdYLkHj9P55BN4z9dn5pRT7NUSCmx4Z0PzqV/6jelEpbjYiMhl1BbXsuLuFQDEZ8eTfmO6vYIsZN267edayyMMgjvg4v0+MjJwCun0DB5PtIdOx0ha2abPN9FU17SbdxjcSFy/OCJT5SzQ+PC0DykpgbJ948NjcAL5+RAXJ/c/l18uX1u9WoI8H30U3LXjMn2ZPBmSybPmmTXMP30+3m1ex3fp7TymM0M+GoKKVuhGTdEpRWx4Z4OlGh58EM46S8bTpsm9b0ODpRIMO6G1AZ5RQVXhELZuhcsuk3FKCjz1lES13Yq30cuKcSsAiOoaRY+retgryGAZukmz8JyFeGvFs6H/C/3xRLd2uwlvvv8+0Dpy7Fh7tfxJXL3f+314li6Vkykn0/kEKdNqqmpi89emm5bh9yilmsu0KqdX7ubVhtbiz9qZN8/5+4zBPUREiC3FI4+INUV1NZx4ItxzT3A7bMX1jiPvhzziB8UDUPZOGYVHF7Lybgeb6fnodHQncibn4In1QBPMP2M+5R9bV67l8YjvrH9P+/xzuOgid1evhAKtuuPSWm8KthAncMcdgZrTRx+Fbt3C5sQ+KKx/dT21S8RBMOO2DCITW1sRaAh3SsaXUPFDBQDdL+1OykEpu3mHM2hshCuvlHFcnOwD4Rbkdft+39KHx+n+GB2P7CgXhcD6N9bbrMYQqiTkJABQu6TWGC23E4e3KEo1WTwGJ6EU3HgjTJ4caKc9bpxkdlQH0cYrNj2WvB/ymtuJb/mfOD3Xr68P3qIhQscjOpLzaSDIUzS2iM3fWndoExUF778PI0bI/NVX4fbbLVvesBPafKSulLo5GELCnV9/hWeflfHBB8MFF9irx26827zN5Tkx6THs9Y+97BVksIyqOVXNvktx/eLIejTLZkXWMWECFBbK+LbbID09vIO8btzv99kHYmNl7G9x71QiEyPp8nep1y//qJz6MudfCBvajv9UXDdoapeZtk/twYgRkukNzt9nDO7kmGPk3qhvX5l/8IGUQAezQ2VUxyhSRm5/oPhzt58pUAWOL9dKHZXK4PdbGC8fN4+t060rq01MhM8+C/y8H3xQsrkM9rDbAI9S6t0Wj/eACy3QFVbU1wfS0WJi4F//kgi2mymdUMq2km0AZNyVQURshM2KDFbQVNfEgjMXoBs0RED269lEJLjjZ79xo2TxAWRmwg032Kvnz2D2e9nDR4+W8SefiBGqk9nrIgm+63rN+tdMFo/h9yQMSmge18yvsVGJc4iMhAMOkPH06fZqMRiCxaBBMHVq4DN1zhwJbgYzO7bP/X04qOEgup3frflrUV2i6HhYx+AtGiJ0OroTA18bCEpKrwuPLKR6gXXdD7t2hS+/hDRfz4arr4Z337VseUMLWpPBs1VrfYrvcTJgzhp24LHHpI4a5AZvwAB79diN1prS56WoPLZPLN3O6babdxicQvEdxdt1zfJ7N7iBu+6CTb7ipscfD2SBhBlmvweOP16eN2yAX36xV0uwSf5bMnEDpLtd6Yulrmgxa2gb8dnxzePq+aZVensxfLg8L14MlcbeyOBQOnYUX5ZrrpF5eTmMGiWH4cHCE+lhwEuBm7GGsgZmHzqbda+t+4N3OYO009Lo91w/ABo3NjLnsDnUrayzbP0+feTnnZQkiQ9nnQU//mjZ8gYfrQnw3L/D3FTVtWDxYjEPAxg8GG66yV49oUDltMrmU77uF3fHE+UOc123s/nbzax+XEyokvZNIuP2DJsVWcecOfCCr/H3YYfBmDH26tkDzH4PHHtsIAtz0iR7tQQbpRTdL+4OQO3iWiq+r7BZkSHUiEyKJCZdOtRY3aHFyQwbJs9aw+zZ9moxGIJJZCQ88QRMnAjR0eJXeMkl0pgmWB2XlFJkjMug/4T+UrZUL80/lt28DN3k7IOMHpf2IPN+aaVev6aeOaPnUL/BuhLsvDz48EP5udfXyzXxokWWLW+gFQEerXXxDnNXG3DuyNVXw7ZtcjMwYYJsXG5n3Su+CLkH0s5Ks1eMwRLqy+tZeM5C0OCJ85D9erZrAntaw1VXSYeIyEjpnheuJZpmvxe6dg20S580yfndINLOTkNFyy9t6YumpY/h9/h9eGrmmRKt9sKfwQMwY4Z9OgwGqzjvPCgoCJTwPP+8GI6XB6npU2Z+Jt0v7E7uf3OJ7CiNXkoeKWHeCfNorGwMzqIhQq9be9Hz+p4A1C6tZe4xc2mqtq7mfPRoeOklGW/aBEcdJVnRBmswJst7wBdfyAPg4oth//3t1RMKNNU1sf4t8XHoeERHYrrH2KzIEGx0k2bBaQuaPZeyHssivn/8bt7lHCZMCNSTX3klZGfbq6c9cfN+7y/TWrYMiors1RJsojtH0+UkMVsue7+MbWu22azIEGrE93PPnm4VPXtC584ynjnTXi0Gg1Xsv7pn0QMAACAASURBVL/4TvkDnAUF0txg7tzgrZk6MpXhvw1vLjfd+MlGZh04i9oVzjWNV0qR9WgWaedINK1yWiVFpxThbbSuE+I55wQajRQXS3Z0jTkjsARjsvwnaWyE66+XcYcOgTItt1M+qZymCokQdzvPeO+4geI7itn8tbRj7DK2C90v7W6zIutYsSKwD6Snh19L9B0x+32AlmV2Ti/TAuhxZQ9AzJZXPbrKZjWGUKI4v5g1z65pnheoAld0pQk2SgVuck0Gj8FN9OwpB2OnnirzFSsk8BNMQ964rDiG/TKMjkeJ2XL13GpmjJjB5m+sayduNUopBkwYQOrhqQBsmrKJJZcusdRr76674NxzZfzbb3D66c5vXhEKGJPlP8lLL8H8+TK+/XZJ6TcEyrMiO0bS+bjONqsxBJuyD8tY9ZDcDMYPjmfASwNQ4Vqf1Ea8XrjgAqiqkvnLL0Nysr2a2gGz3/vo2xeGDJGxGwI8yfsnkzJK2suu/ddatq0zWTwGITM/k+w3A6mJ+8zbh5F6JJn5mTaqcgb+AM/ChVBt/KsNLiI+Ht58U9ppKyW//2PHyqFZsHx5IpMjyfkkh57XSumS34S4ZHyJYxsMeKI8DH5/MIl5iQCsfWktK+8JYq/6HVBKDLVHjZL5xx/Dtdc6v/TdbozJ8p+gokIikgC9e4v/hgHqVtex+b8SCU87PQ1PjDs8WNxK9cJq8d0BIjpEMOSjIUQmRtqsyjpeeAG++UbG//iHmCs7ALPft8BfpjVjBpSU2KvFCnrf2RsAb52X1eNX2yvGEFLE9AyUW9eVWNeRxen4jZa9XjHrNxjchFJwyy3w6aeQIucLPP64+LesC1LDKxWh6Pt4Xwa+NhBPrAe8sOyGZSw4fYGlHjVWEpkUSc6UHGJ7S3vXFfkrWPvyWsvWj46GDz4IHJo98ww8+aRly7uSVpssK6U6++auNN1syQMPQFmZjB9+OGzbIbc7W/63BXwRWWOu7GwatzZSdEIRTVXyYZj9RrarPBqWL4cbb5RxRgY8+qi9etoLs99vjz/AA3Lq5HRSDk4h+W+Shrbm+TXUl1vXdcMQ2vi7aAFsW22yu9qLlkbLTvDhUUodqZRapJRaqpS6ZSffP0MpVeh7/KyU2tsOnYbQ4v/+Tw5Shg6V+fffS/Dzp5+Ct2a3s7qR91MeMb18HQLf3sDMA2ZSu9yZvjwx3WLI/SJgNr3oH4vYOGWjZesnJ8OUKdDd5+Jw/fUS9DEEh7akWEwMmooworg4EHU84AA4+WR79YQS1fMkv1hFqeZUQIPz0F7NwvMWUrNQnNIy7syg87HuKcfzeqUThN8obuJESEqyV1MQMPs9coHZUzK5XVGmBfL3DOCt9rL6CZPFYxBiuseAr/rWb6hv2HMyMiBV7DHC3odHKRUBPAccBQwCTlNKDdrhZcXAwVrrXOBe4EVrVRpClT59JKBzzjkyX7sWRo6UbI9glfMkDUti+IzhzeXJ1YXiy7PpS2eebcUPiCfnkxzJXGqCopOL2Dptq2Xrp6fDZ59BYqL8TM88E375xbLlXUVbAjzuMNbYDbfcAvW+Q83HHw/fdsjBoGqumJHED4x3TYtsN7LsxmWUfyg9LTse1ZHe43rbK8hinn020DXr8svh0EPt1RMkzM6G7O/+LJ6CAtjsXC/GZlJHp9LhLx0AWPP0GratNTfzBvBEe4hOiwZMBk974jCj5X2BpVrr5VrreuBtYEzLF2itf9Za+3fSX4GeFms0hDDx8fDKK1ICHxUlDW2uukoCAcHyqIruHE3uF7mk35AOQOPmRgqPKmTl/SvRXucZxSQfkEz2W9ngAW+Nl7lHz6V2mXVZS0OHwvvvQ0QE1NXBccfB0qWWLe8a2nIX7rzf8jby888Bh/fTT4f99rNXT6jhz+BJGJJgsxJDsCgZX8Lqx+VUP25AHNlvZKMi3BMLWLJEgrwgp00PPWSvniDi+v3ejz/A09QkPgFORylF73t6A9BU1cTym5bbK8gQMkQkRgDgrbWuza4b8PvwzJ8PteFdHdIDaOlWttr3tV1xAfD5rr6plLpYKTVdKTW9zO+LYHA8Somv4Q8/BDJo33wT/vIXuQYLBp5ID1mPZpH9VjaeeA9o6RA778R5NFY0BmdRG+lyfBf6PdMPgIayBgqPKqS+zLqS7COOkCAeQHk5HHWUPBvaD5PB00q8XnH9BvHcefBBe/WEGg2bG6hfI5tDQo4J8DiRdW+sY9kNywCI3iuavb/cm6iOUTarso6mJinN8l+Av/KKpJk6FFfv9y056CDoKF1Vee01e7VYRcfDOtL5eCm7XP/Gerb8sMVmRYaQQOI76CYT/21P/Bk8TU1QWGivlj1kZ58bO/1lUUodggR4bt7VP6a1flFrPUJrPaJLly7tJNEQLuy3n2S1+bOk582DESNg8uTgrZl2ahrDfh1GXN84ADZ+vJEZ+8ygush5Le56XNaDXrf0AqB2SS1zj51LU411JtMXXihdqEEyeI47LuwD3CFFWwI8twZNRRjw9tvw228yvu466NXLXj2hhj97B0wGjxPZ9NUmFp23CJCOWblf5BKb4S538aeeChj+XX213Pg7GFfv9y2JipL0cICvv4Zly+zVYxVZT2RJnT6w5IoleBtN1obb8WdrmgBP+5KTExgvXmyfjnZgNZDeYt4TKN3xRUqpXOAlYIzW2jqXV0PY0bUrfPllIHN661YYMwbuuEMCosEgMSeRYdOG0emYToAEP2bsN4MN724IzoI2knl/Jl3P6ApA5dRK5p8239LP+nvvhTPOkPEvv8BZZwXv5+o22hLgaVRK3ayUelop9ZRvnB00ZSFEbW1gc0lLC4wNAUyAx7lsnb6VeSfOQzdqVLRiyMdDSMx1burKzli4MHDS0LevdNJzOK7d73fGRRcFxi+/bJ8OK4nrHUevW+Uko7qwmtIXfnefZnAZzeW45gK8XendOzBescIuFe3CNKCfUipTKRUNnApsl2+hlOoFfAicpbUO73CWwRIiI6Vq4sMPAw0t7r8/uGU9USlRDPl4iJQrK2k6MH/sfJbesNRRhx3Koxg4cWCzyfTGyRtZetVSdLBcrXdcX8k11ciRMv/gA0misGh5R9OqAI9S6mbELE0BvyGbuALe2lkbRKfxxBNQ4qsqvu8+R3bM2WNqF0tenSfW47rMDiez+KrFzP2/uXirvaAg+z/ZpI5MtVuWpTQ2wrnnihmcUvDvf4sRoFNx+36/M4YMka6JIF3TGhrs1WMV6TelE9tH9vMVd66gfoNpm+5mTAZPcIiLg27dZBzOAR6tdSNwBfAlsAB4V2tdpJS6RCl1ie9ldwGdgH8qpWYrpabbJNcQZpxwAkybBoN8fdn++1/xr/JXV7Q3yqPofWdvcj7LITJFWouvHr+auUfNpWGjcy4CPNEehnwwhIRcOZwvfb6UVQ+usmz9mBj46CMYPFjmTz8N48dbtrxjaW0GzwXAPlrrh7TWb/geDyGO+RcET579rFsX8NvJyREPDsPv8cTLr5K33mvsWR1CzaIaSp8ppaFMPsj6PdOPrn/varMq6xk/HqZOlfF118GBB9qrxwJcu9//ERdfLM/r18Mnn9irxSoiYiPo+2RfABq3NLLkyiWWnewZQhDjwRM0/Fk8xcW2ythjtNZTtNb9tdZZWuv7fV97QWv9gm98odY6VWs91PcYYa9iQzgxYIBcj40dK/OSEvjrX+H554OX9dHpqE4MnzG8OQCy+evNzNhnBlWFVcFZ0AYikyPJ/TyXmPQYAIpvL2btxLWWrZ+SAp9/Dj18luw33ijG2oY/T2sDPF6g+06+vpfve47lwQehyvc3/Pjj0tbN8Hv87VPxQsMm50S23UrV3CpmHTSreZ5xZwY9Lv+jZhjOZMYMuOsuGQ8YIPXCLsC1+/0fcfLJkJws4xdftFeLlXQ6phOdjhMvgrJ3y1j/2nqbFRlsw5RmBQ1/gCecM3gMBitITIS33hJfxMhIyai97DI45xyoqQnOmnF94hj28zC6nCJm33XFdczcfyYb3nOOL09M9xhyv8glMlWylRZdtIjyyda1tkpPlyBPhw4yP/dc+OYby5Z3HK0N8FwD/E8p9blS6kXf4wvgf8DVwZNnL1VVUo4BMGoUjB5tq5yQJqproJtS/XqTxh/OLLp4EdNzp9OwIRCoW3nvSorzw/xosY1s2gQnnQT19RLY/fe/JZXeBbhyv98d8fFiAAjw1Vfhf9LeWpRSDJgwgKg02eMXX76YmqVBuoo2hCxaa2qXSil2bG9Tht3e+AM8JSVSFmwwGHaNUnDVVVBQAN19x1Gvvx7cVuoRCREMensQfR7qI748NV7mnzKf5bctd0xWY8KgBHI+zcET5wEvzB8739Iumjk5MGkSREdL4O6EE8K+s6BttCrAo7X+AugP3I3U1n4F5AMDfN9zJP/5jzi2g2wkhl3TnMED2wUGDOFFxc8VbHhn+xOJkXokI/VIMvMzbVJlPV6vdE5auVLmjzwiFw5uwK37fWvwl2lp7R6zZYDortEM/PdAQMwmF5y+AG+Da5O5XEl9aT1NVZLCEz/QwSZkNuEP8DQ2QqnxMzcYWsWBB8LMmXDIITKfO1daqU+aFJz1lFL0urkXOZ/lEJEsJR2rHlzF3GPn0rDFGfc+yQckM/i9wRAB3jovc4+da2k52iGHwKuvynjrVjHTXmWdJZBjaHUXLa21V2v9q9b6A631+76xYxN2tYZ//lPGvXrB0UfbqyfUie4aCPAYI87wZPO3m5lz+Byatsqfdb/n+tmsyD7uu09SRQH+/ne49lp79ViN2/b71pKTA/vtJ2M3mS0DdDqyEz2v6QlA5bRKVuSvcF1Wn5upWRjI2jIBnvbHQZ20DAZLSUuTrNqWrdRPOAFuvjl42XCdjurE8GnDic+WvXDT55uYdcAsapfXBmdBi+l0dCcGviyHOk0VTRQeWciSq4OUGrUTTj0VHntMxqWlEuTZvNmy5R1BW9qk7xSllCNth3/+OZAWdsklxntnd7Qs0apd5IwNzk1s/Gzjdt2yBkwcQI/LepAxLsNuaZbz5ZeQny/jAQMkU0MpWyWFDE7d79uCP4tn7Vr47DN7tVhN5oOZzUaTqx5cxcq7V9qsyGAVJsATXEyAx2D48/hbqU+aFPBweeQROOwwaZYTDOL7xTNs6jA6jRGPupoFNczcbyYVP1UEZ0GL6XZON/o82geA+rX1rHl6jaUH+NddB1f7TAHmz4fjj5dutobWsccBHiSN33H4s3eiouAC1/aNaT1NlYHD/dVPrrZRiaEtaK0pebKEucfNxVvnhQhphb7XeXsBuKosC6Qk6/TTJYMvPh4++CBwsWAAHLrft4WxYyEpScZuMlsG6ao16K1BeGI9zd0Sa4tNQN8N+AM8ngQPMT1ibFbjPHr1CoxNgMdg+HOMGSPNMXJzZV5QIK3Uf/opOOtFJkUy5MMhpN+YDkBDeQOzD53N+jed0Yyg1w29SL8hvXle+H+FNFZaYxKmlDQ3OvlkmX//PZx9tlgoGHZPqwI8SqnCXTzmAmlB1mg5GzbAe+/J+OSToav7OkO3iVkjZzE1a2rzvHFLIwWqgFkjZ/3Buwx24633suiiRSy7dhl4wRPnYfD7g0k7zXF/0q1i2zb5e9+0SeYTJsDgwfZqsgO37fdtJSFB/JkAvvgi4NPkFja8u0GCwT6m9plKgSow5VoOp3pBNQDxA+JRHpPS2N7ExUG3bjL+6CN7tRgM4UzfvvDLLxIMAMm2HTkSnnwyOK3UlUeR9UgW/Sf0R0UqdL1mwRkLWHH3CnSwerdbRHF+MSWPlTTPq2ZU8WOHH1l+53JL1vd44LXX4KCDZP7ee3D99ZYsHfa0NoMnDTgbOHYnj43BkWYfL70U8Fa47DJ7tYQDeQV5jNQjt+usMXzWcPIK8mxUZfgj6svqmTN6DuteltzV6B7R5P2YR5fju9iszD6uuQamTZPxFVdIJo9LcdV+/2doabbsz/Z0C5n5mYzUI7c71UsZmULGbe4r53QL9Rvqqfheyg4ShybarMa5+Mu0Zs+2VYbBEPbEx0vn03/9SzoyNTaKl+LYsdIhORh0v7A7uV/kNpsvr8hfwYIzF9BUF772hf7P+4PqD9ru63XL69Bea4JXsbFSejdokMyffFIyewx/TGsDPJ8CiVrrlTs8VgAFbVlQKRWrlPpNKTVHKVWklNppyr9SaqRSarbvNd+1ZY09oakJXnhBxrm5cMABVq0c/gwtGNo8XjcxSEWvhj2mal4VM/edScUPcsGetG8Sw6cNJ2lYks3K7OO11wJ/9/vtB+PH26vHZtptv3cqQ4dK9w6A556D8nJ79dhBn4f7NI+3FGxh0YWLwv600rBz1v17HbpBfrbdzutmsxrn0tKHx2Aw7BlKyWHMTz9Bhu/84b335BovWK3UU0elMuzXYcT2kQPvDW9uoPCwwrDvsOWJknBBh7+IZ8GGNzew/GZrsngAUlMlY7p7d5lffz28/bZly4clrW2TfoHW+sddfK+t59zbgEO11nsDQ4EjlVLbNSBWSqUA/wSO01oPBk5u4xp/ms8+gxJfNtpllxlz1bYQmxFLRIpErte/sT6so9ZOpfyTcmbtP4u6FeJU1vWMrgwtGErMXu71VCgsFCN1gM6d5QIgOvqP3+Nk2nO/D/WA/p4wbpw8V1cHuj24CeVR9LqtV/MF3/rX17PyHpfVq7kA7dWU/kv6dscPiif5wGSbFTmT/Pztb1iUkoff8N9gMPw5RowQX54jjpD5/Pmwzz7w6afBWS9hYALDpg4j+a+yV1b8WMHsg2ezbe224CxoERnjMhjyyRDi+scBUPJYCSVPluzmXe1Herp0t/X7Yp5zDnz7rWXLhx2t9eDZbZijNa8B0II/QS7K99jx2O904EOt9Srfeza05t9uD/zp9klJcMYZVq3qHPo/3x+Axs2NbJxsqjlCBW+Dl+W3L2femHk0VUngLfOBTLJfzyYizr0t4ioq4KSToLZWan3ffls+RNxMe+73hHhAf08YPTqQ4fnss1D2/+zdd3hU1dbA4d9ObySE0Kv0HloAFaWKICrNXhD1U8TevRYUsN9r91rRa++9YkVRkRo60ntLCCFACCF9f3+sDEMJEGBmzpT1Ps88c85kzOwxzJlz1l57ra3OjscJTR5pQruv2+2drVw7bi0Zb2Y4PCrlSdt/3U7BapkQqDu6LpX/6KujMW6cdAFyyc+XJaAa4FHq+KWkyAT+vffK/s6dcPbZMH68d4r2RlWPosOvHah+TnUAdi/YzdxT5rJn1Z6ArVfXeFxjoqpHkfpTKlG1ZRZ01W2ryPrEZ5fopKbKcq3ISCgqks5aro7Xan+VXaL1uzHmRmNMw30fNMZEGWP6GmPeBkZW9kWNMeHGmHlAFvCLtXbGAU9pASQbYyYbY2YbYy47xO8ZZYxJN8akb/XA2fXKldIiGSQymKBLzY9a9aHViUiOACDjf3qi7w/2rNrD3FPmsv7R9WClC0rbL9vS6J5GIX2ybi1cfrl87gEeegj69XN0SP7CY8d7fw/oHw9j5OQQJIsnVJf1RdWMInVi6t7j/rIrl7Hxee2kGCxc2TthsWHUGhHyNda9at9zTm/VCVEqVIWHwyOPSHdU12dt3DgJEuz0QmfzsOgw2n7cljqjpCttweoC5vSYw7rxgZ3pGntCLO1/aE94lXCwsGTEErZP3u6z1+/TB95+W7ZzcyUza9Uqn718wKhsgGcgUAp8aIzZbIxZbIxZDawALgKesda+VdkXtdaWWms7AvWBbsaYdgc8JQLoApwJDADuN8a0qOD3TLDWpllr02rUOP7isC+/7N7W4srHJjwmnFqXyEng9l+2U7C+wOERhbbMdzNJ75jOrpm7AIhPjafLzC4hXUzZ5YknZCYA4Kyz4O67nR2PH/Ho8d5fA/qe0K+fuxZPqGbxgHRWav9t+QkfsPLmlawes1pr8gS4ws2FZH8tBaZqXliTyKqRDo8ouMXHu7d373ZuHEoFs+HDYcYMaFF+Vfntt9Ctmyzd8jQTbmjxSgsa3ifzZcVbpBbPjr92eP7FfKhKxyq0/aItJlK6hi0auoi8hb6LSl90kXtSLTMT+veHzZt99vIBobI1eAqstS9Za3sAjYB+QGdrbSNr7dXW2mOq+W+t3YEU7Rx4wI82Aj9aa3dba7OBP4EOx/IalZWfD2++Kdt9+kDr1t58teBW+8ryIowW1j0a2JHqQFWys4TFly5m6WVL9y7JqndzPTrP6Ex8m/gj/NfB7/vv4Z57ZLtxYymyHFbZcHeQ8/Tx3l8D+p6wb42MUK3F45LUI4mOf3QksqYEAdY/sp7l1yzHlmqQJxBZa1lx4woJ9SLLs5R3aYBHKd9o0wZmzpRlWgDLl0vx5c8/9/xrGWMwEftny8/rOY/JZnLALtcCqHZaNVq91QqA0p2lLBi4wKeT+rfd5l5yt2YNnH465OT47OX93lFf0lhri621GeXBmaNmjKlRXnMBY0wscBqw9ICnfQ2caoyJMMbEAd2BJcfyepX1ySewvTzDTLN3jk+VTlWo2qcqABmvZpDzi37ifGnn9J2kd0on631Z6RJZI5L237en+bPNCY8J3Xo7LjNmwHnnybrrmBj5Qk9OdnpU/ul4j/cH/C6/Ceh7kmbxuFXpVIVOf3ciprHU5Ml4LYN/zvtHC+4HoE3/3UT2F5K9kzI4hSpdQ7fLoq9ogEcp30lKkizu8eNlsiYvD849Vyb/Sj38leVqN97qnVbuB8MhrlWcZ1/Ix2pdXIsmT0hHzaLNRSw4YwHFOb7rGPbww3DttbL9zz8waJAub3WpbJHlk46iqOaR1EFqPCwAZiEp+98ZY0YbY0YDWGuXAD8CC4CZwOvW2kUeev0K/fij3FevDkOGePOVQkPL11sSFi//vJZduYySnSUOjyj4le4pZfWY1cw9ZS4FaySKnjwgmbQFaaQMSnF4dP5h2TI488z9iyp36uT0qPyLJ4/3/hrQ96R9a/Hk54d2Fg9AXLM4Ov3difgOcrWa/WU2CwYu0O+AAJI7M5dVd0hRg+hG0bR6s1VI12vzlX0DPHqRopT3hYXBAw/IMq2k8gaBjz8ugQJvZIPUHiErHMJiw6AUllyyhMz3Mj3/Qj7U4PYG1L+lPgD5i/NZNHQRZcVeqFxdAWNkYu2ii2R/xgypqVQY2A3LPKKyGTwjgdnGmI+MMZcbY2of6wtaaxdYaztZa1Otte2stQ+WP/6KtfaVfZ73hLW2Tflznj3W16usuXPlvnt3qc6tjk9sk1iaPdUMgMKNhay8ZaXDIwpu2ydtJz01nfWPrIdSMFGGps80JXViKtG1Q7cF+r42b5ZibNvKm7u9/LIGcw/BY8d7/DSg72l9+8Ipp8h2qGfxAETXiabj5I4k9SxvE/vHTub2nEv+snyHR6aOpHh7Mf+c/w+22GIiDW0/bktkNT0p8oV9iyxrBo9SvnPmmTBrlizdAvj5Z2mvPn++51+r0dhGtJ/YnrC4MCiDpZctDejuk8YYmj7VlBrny9L5nX/tZO34tT57/bAwKbo8aJDsT5oEF18MJSE+p1TZGjyjrbWdgXFAMvCWMWaaMeZRY0xPY0xAr/vYtUvWXwJ07uzsWIJJnVF1SD5d1r5kvpVJ9rfZDo8o+BRlF7Fk5BLmnzafPSv3AJDQOYHOMzrT4JYGmDCddQXpkDBoEKwrLwk1bhyMGuXokPyWJ4/3/hrQ97R9a/Hk50sB71AXWTWS1B9TqT7U3SY2vXM6myds1uLLfspay9IrllK4TqY/m/ynCYndEx0eVejQJVpKOad5c8kAOfdc2V+zBk46CT74wLOv03hcY5J7J5P6YyrhCdKJatmVy9j8WuBWCTZhhlZvtyI+VQ5i6x9dz44/fFdIOjISPv0UTj1V9r/4Qs7xy3yTSOSXjqoGj7V2qbX2GWvtQKAvMAU4DziwK0pA2TdCq8s1PMcYQ8vXWxKeJNeDy65eRvE2363NDGbWWjLfzmRmq5lseWcLIO3Pmz7dlM4zOlOlo9ZLcCkshGHD3J/zUaMkJVcdXrAe771l3yyeF1+ErIBo9u5d4bHhtPm0DQ3ubABAWX4Zy69ZzqJhiyjaWuTw6NSBNj69kW1fS4pj9aHVqX9zfYdHFFo0wKOUsxISpCbrv/8tmSF79sAll0gxX08HC6qeWpXUn1IJT5RrpOWjlrPppU2efREfCo8Jp82HbQiLCZP26Zcu8Wk9nrg4WWrXsaPsv/km3HEHhOp80jH3jbHW7rHWTrTW3mitTfPkoHzNtTwLNIPH02IaxND8+eaAtAdcccMKh0cU+PJX5DP/tPksvXwpJdskBzHlrBS6Le5Gg1sbEBah7aBcysrgssvg999lf8gQufjWchJHJ5iO995yYC2exx93djz+IiwijKb/aUqHXzsQVS8KgG1fbyM9NZ2cn7QAvz+wZZbV963eW3cn5oQYWr7RUuvu+JjW4FHKecbAXXdJbdZq1eSxxx6T5hyeDrwmnZxEh186EFE1AoAV169g43MbPfsiPhTfJp6mzzQFpDzHsquX+TRjNykJfvoJWpT3YX3mGXj0UXeGdSjRK0Fgzhy5T06Ghg2dHUswqjWiFimDpchv1kdZbHoxcCPUTirJLWH1fauZ1X4WO36T1MeoOlG0+bQN7b5pR0zDGIdH6F+shVtvldkYgJNPhg8/hIgIZ8elglefPtCzp2w//zwsWODsePxJcr9kui7oSo1zZZ1+UWYRCwYuYMUtK7TLloNKdpawcPBC1j+6HoDwpHDaftaWyGStu+NrWoNHKf/Rv78s2WrZUva/+EK+3zd5+BImsVsiHSZ1ICJZTk5X3rKS9U+u9+yL+FDda+qSMkSu+bK/yCbjf76tL1SzptRQql+egDpmjHvyLZQcc4DHGHNxeRHO940xHxhjLvLkwHzJlcHTqZPO7HuDMYYWr7YgsrqcMK64YQUbXwjc4W4eSwAAIABJREFUCLWvlZWUsemVTcxoPoP1j67HFlowUPfaunRb0o2a59bUmdYKPPGEXGQDtG4tqZuxsc6OKVAF0/Hem4yRf3Ph4dJm9ZprQnsN+IEiq0XS5pM2tHyzpdQeADY9t4k5XeeQt1BTFnwtf1k+s7vPJud7yaSKax1Hl1ldqNJFl/g6ISpKjh2gAR6l/EGzZjBtGpx2muzPmQNdu0J6umdfp0rnKnT8vSMRKRLkWX3natY9ts6zL+IjrvIcUXUlY3flzSt93mChUSP45RfpjO3y/vs+HYLjjieDp5e19kJr7SXW2ouBUzw1KF8qLIR//pFtXZ7lPdG1o2n/Q/u9aYgrb1zJhmc3ODwq/2atJfu7bNLbp7Pi2hUUZ8la1ipdq9Dp7060eKkFEUmajlKRd96Bf/1LtuvV2z/VVh2ToDje+0KHDpI5BjB9OkyY4Ox4/I0xhjqX1yFtXhpVuksgYfei3cxOm83KO1ZSvL2YNePWODzK4Lft+23M7jabPcukOH/K4BQ6T+9MXPM4h0cWuoxxL9PSAI9S/iE5GSZOhGuvlf2MDMnk+ewzz75OQocEOk7uSGQNmQxfc+8a1j641rMv4iNR1aNo/U5rMFJ7b/FFiykr9O1s10cfQfY+vX0uvXT/hhjB7ngCPNHGmDONManGmEFAQM6NL1rkbqWmBZa9KzGtPA2xmgQlVt26KqDTEL1p2TXLmN9vPovOXkT+Uol8x5wQQ+sPW9N5emeSTkpyeIT+68cf4f/+T7aTkmRfl14et6A43vvKuHHuf3N33w2ZmY4Oxy/FNo2l01+daPRAIwgDW2TZ+NRGZjSdwbrx63x+MhgqrLWse3QdC89eSGmuLI1r9EAj2n3ZjohEnTDwF5r5p5T/iIyU+o3PP+8uvnzeefDII54t4pvQrjzIU0uCPGvHrmXNA2sCsvNkcr9kGtwlDRby5uaxZoxvJ27GjZO/zeTJ7sdiYmQpfSg46gCPMSbKGBMLXIu00B1Ufn+Dh8fmE1pg2beqdK5Cx98OSEN8PDDTEL2hYEMBSy5bQsaEDHb8LnV2wpPCafJEE7ot7UatC2tp6/PDSE+XFpclJRAdDd98A+3aOT2qwBVsx3tfiY+HF16Q7Z074bbbnB2PvwqLDKPx+MZ0ntGZpJ4StC7ZLjMuM1vPJOuTrIA8sfVX+SvzWTRsEWvuWwNWOi+2/bwtjcc31u8VP7BnD+TmynatWs6ORSm1P2Pgxhvh++8hMVEeGzMGRoyAggLPvU58m3g6/dFp7xKndQ+tY829gRnkafxgY6qkSabuhic3sPPvnT4fQ69ech8eLn+ns892194NZkcV4DHG3AxkACuBOUBVa+3j1tr3rbW+XWDnIa4/clwcNG/u7FhCRUKHBDr+vk8a4j1rWPvwWmcH5bA9a/ew/LrlzGg2gy3vSttzE2mod3M9Tlx1Ig3vaEhYtNZEP5xly2DQIEltDwuTgsqugrfq6AXj8d6Xzj4bhg+X7Q8/lKJ/qmKJaYlU7V11v8cK1hSw+ILFTGswjR1Tdjg0suBQsLGAZdcsY2armXvboMc0iaHztM7UGF7D4dEply1b3Nu1azs3DqXUoQ0cKHV5GjeW/fffh7599//8Hq+4lnF0/KMj0fWjAVj/+HpW3bkq4II8YVFhtP6gNSZaJhB8XXDZZexYeOst2d61CwYMgKVLHRmKz1TqitEY86wx5jLgZqC1tbYe0BNoY4x50JsD9DZXBk/Hju7idsr7EtofkIZ4/1pWj1mNLQusg9fxyl+Rz9IrlzKz+Uw2v7wZW+R+/7bYsum5TWz8rxakPpIFCyRKv3Wr7L/4Igwb5uyYAlUwH+997bnn3J1xrr1WZuhVxRqPb0xv25ueRRKVdU0AFG0qYt6p81g0fBH5yzWueDSKthax8vaVzGg2g4wJGVDerKzmRTXpMqsLCe0TDv8LlE9l7HPtU6eOc+NQSh1emzbSYeuU8mqE06ZBt26wcKHnXiOuWXmQp6EEeTY+tZGVN60MuOukuOZxVBsoRTCzv86mrMT360/HjZMaPP/9r+xnZ8Ppp8P6IK4SUtmUgD+AZkB1YKoxZg7wBLAKuMgYU/Vw/7G/Ki2F+fNlW+vv+F58m3g6Tu5IVB1JQ1z/yHrm9pwbEifxeYvyWHzxYma2mknmm5nYEjlgVxtUjU5T5R9jb9ub3rY3jcc1dnKofm/mTOjd2z178tBDMHq0o0MKdEF5vHdC/frw8MOyvXq1rNdXhxcWKacl3Vd2p+G9DQmLkf3sL7OZ1XYWK25cQWFmoZND9HsluSWsGbuGGU1msPHpjdJ5EUg5K4W0eWm0+aANkdW0Dbq/2bdWl2bwKOXfatSAX3+FkSNlf/16OPlkWcLlKbFNYun0ZydiGscAsOmFTSy5bAllxYFVpMuVKVqSU8LOP32/TMvlhhvgwfJpyg0bJMjjmhgONpUK8Fhrv7TWPgBMB4YApwFvAyVANWCyMWal10bpJcuWuWdUtf6OM+JbSZAnpokcvHL/ziW9Qzobnt6ALQ2sKHVl7Jq9i0XDF5HePp2sD7Og/BhdfXh1uqR3IfX7VC2gfBT++AP69YPt22X/6adlTbQ6dsF6vHfKDTdAly6y/Z//wOLFzo4nEDQa24iIxAiaPNKEbsu7UWtkLTBgSyybXtjE9AbT+eeCf9j++/aAS1n3ptI9pax/cj3TG09n3YPrKM2TlJ2kXkl0+rsT7b9tT0IHzdrxVxrgUSqwREfDm2/C449LjZ68PBg8GJ55xnPFl2MaxdDxz47EtZIOh1nvZ7FoyCJKd5d65gV8IOWsFEyELNPa+oWzEZUxY+CWW2TbVdph1y5Hh+QVR1vU43rgPeApoBPQDlhore0ItPHw2LxuwQL3dseOzo0j1MW1iKPrgq7Uu6keAGUFZay6fRVzT51L/rLAz+axpZZtP2xjwaAFzE6bTfaX5X37wqDmxTVJW5hGu8/bUaVLlb3/TaOxjRwabeD44QdZC52XJ1+sEya421Mrjwiq471TwsPh1VelLlRxsWSXaYecw9s3azGmQQyt32pNlzldqNpPksdsiWXrJ1uZ33c+M1vNZMMzGyjOKXZquI5beftKNjyzgRnNZrD6ztWU5Eih6ippVUj9OZWOv3ck6WSdOPB3riVaxkDNms6ORSlVOcbAv/4FX3wh9VzLyqSxwh13eO67PqZ+DB3/6kiVbnKdkPNDDvP7zw+Y773IapFU7SPf39lfZju6zMwYeOopWbIF0pxl2DAoDLLE4KMK8FhrVwDdgc+QNrkLgGHlPyvy+Oi8zOzTNCJSs5UdFR4fTvPnmtPxz47ENpMOzLnTcknvmM76J9cHZDbPnjV7WPPAGqafMJ2FgxaS80MOACbCUPvK2nRb2o0277chod3BM6q6LOvwPv8chgyRivjh4fDee3D11U6PKrgE2/HeSV26SPcNgL/+chf7U5VXpWMVOvzSgU5/d6LWiFp7izbuWb6HVbetYmrdqSwZuYSd03aGRFZP8bZiNr+2mXl957Hx6Y2sum0VRZvlYxnXOo62n7el88zOVOtfDWO0Q1YgcGXw1KgBEdqxXqmAMnQoTJkCdevK/tNPw+WXy8SOJ0RVj6LDpA4k908G5Bppbs+5FG4KjMhE9eHVASjaXETuzFxHxxIWBm+8AWeeKfuTJsEll0jplmBhguVEKC0tzaanpx/Vf/Pnn+72aT/+KFW1lfNK80tZM2YNG5/dCOX/PKt0r0Kr/7Uivm28s4M7gtKCUrK/yibzf5ls/3X7fj8Liw2j9uW1afivhsQ0inFohIHv7bfhyitlZiQqCj75RII9qmLGmNnW2jSnx+FJx3K8d9quXdC6NWzaBNWqwaJFWkj1eBRvKybz7Uw2v7KZPSv2r14dnxpP3dF1qXVJLSISg+dKuSS3hOyvs8n6KIvtP2/fW7vNJbZZLI3ub0StS2phwjWoE2gGD4Zvv4XUVHd9yKMVjMd7CMxjvgpN69ZJbZfly2V/0CA5T4330OVLWVEZSy5bwtaPZalTdKNoOvzcgbgWcZ55AS8pzChkWr1pYKHBnQ1o+p+mTg+J/Hz5W/39t+yPGgWvvLJ/Aoi/O9QxP6T7LruirLB/9wLlrPC4cJo93YxOUzoR20KyeXbN2MWsdrOYf/p8sj7NoqzIv9Y45C3IY8XNK5hWbxpLLlqyX3CnStcqtHilBSdnnEyLl1pocOc4vPSSzIiUlUkq7HffaXBHBYYqVdwdHHJy4KKLoKTE2TEFssiUSBrc1oBuy7rRYVIHapxXY+8a/90LdrPiuhVMrTuVZaOWkZueG7BZPaV7Ssn6LItF5y5iaq2pLL1sKTkTcw4K7gDsWbmHPav3aHAnQLnOQzXwq1TgatRIMnm6dpX9iRPhtNPke98TwqLCaPN+G+peJxexhesKmdtjLtsnbz/Cf+ms6DrRJJ6cCOAuVeGwuDgJqrdvL/sTJsD99zs7Jk8JnqmtY7Dvl6gGePxP0slJpM1LY+0Da9nw9AYog+2/bGf7L9uJrBFJ7ctrU+eqOo5ErUsLSsmdnsuO33awbeI28mbn7ffziOQIao2oRZ3/q0NCqha19ITTTpM0SoDERPnS7NHD2TEpdTSGDZMA5VtvSYHw+++Hxx5zelSBzRhDct9kkvsmU5hZSOYbmWyesJnCdYWU7S4j47UMMl7LILJ6JEmnJJF0ahJJpySR0Clhb8cuf1NWVMb2X7az5cMtbPt6295iyS4RKRHUOLcGtS6qRdIpSfwR8Qe9bW9nBqs8xrVESwssKxXYatSA336D4cPhl19g+nQ49VT46Sfprnm8TLih+QvNiaoZxdpxaynOLmb+afNp+kRT6t9S3y+X5VprsUUyMeFPBaKTk+Xv0qMHrFkj3U6rV3cXYg5UIR3giY+XC8XcXNi82enRqIqEx4bT9Imm1L6yNptf3cyWd7ZQsr2E4q3FbHhiAxue2EDV3lWpc3Udqg+vTnhMuFfGUVZSRt7sPLb/tp0dv+1g55SdlBUcnEWUfFoytf+vNtWHem8socZauRB2BXdSUuRg7OpMpFQgefFFmD0bFi6Uzhs9esBZZzk9quAQXTuaRvc2ouG/GpLzcw6bX9nMtu+2QRkUZxeT/VU22V/JzGFYXBiJJybuDfgknphIRILvT4mKtxWTtyCP3Qt2y/3C3exetJuyPft/v4RXCaf6sOrUvKgmyf2S/TY4pY5NWRls2SLbGuBRKvAlJEiW+ciR8NFH0kHz5JPl/PXjj2HcuOP7/cYYThh7AtGNolk+ejm20LLqtlXsSt9FywktCY/3r2uQbd9tY9csaVdV5//8K02xTh34+Wc45RQ5Dt96q1xrjBjh9MiOXUgHeED+qLm5msHj7+Jbx9P82eY0eawJ2V9ks3nCZnb+uROAHZN3sGPyDiKqRZBydgpxLeOIbRa797bhqQ1HVbTYllqKc4op3FDIjj93sOO3Hez4YweluRVHnONT46k+pDq1r6hNbONYj7xfJcrK5ED7/POyX6eOzIa0bevsuJQ6VnFx8NlnkJYmdXlGjIA5c6Cx1lX3GBNuSDkjhZQzUijYUMC2b7exc8pOdv61k8KNUpCyLL9Mju2/7ZD/KByqdKqyN+CTdEoSUTWjjup114xbc8jvmrKiMvKX5bsDOeX3rsLIFQmLDSPl7BRqXliTamdUO+SkgXZdDHw5Oe5irLpES6ngEBUF778vGT3//S9s2CBBhJyc4w/wuNS5vA7x7eL5Z/g/FG4oJOuDLHYv2k27L9oR29Q/rklsmWXN/Wv27te/3QNpTB7WrJnU4+3VS+ICV1wh9RJdhZgDTUgXWQbo0wcmT5aoqqvIkgoMu5fuJuP1DLa8vYXi7MOXqU/skegO+jSOpXRPKcVZxRRlFe1/v6VIftdhSvzENo+lat+qJPdNpmqfqkTVOLqLAFU5paVyETxv3sE/GzvWc1+OwS4Yi24GQ8HNTz+F88+X7bQ0WbMfHe3smIKdtZbC9YXs+GsHO//ayc4pO8lfnH/I58c2jyWqdhRhMWEH36IPfmzVHato+XpLwmLCMFGGgrUFewM5+UvyscWHP9+KSI4goUMC8anxJJ6YSMrZKY5kFSnfmzsXOneW7Q8/hAsvPLbfE4zHewiOY74KXdbCo4/CmDHux374AQYO9NxrFG0tYvGFi/dOWkRUjaD1B61JOSPFcy9yjLI+zWLx+Yv37vvzkuI//pCmS4WFEBsrk8r+XA7iUMf8kD9zcBVa1iVagSe+VTzNnmxGk0eakP1VNhlvZpA3J4/irQcHe3L/ziX372NryxdVL4rkflLjoWrfqsQ00CLJ3rZ7t6S1uoI7LVpIR4IgiUcrxXnnwU03SXZaejrcdpss31LeY4whplEMtRvVpvalsg6mKLuI3Km5ewM+u9J37S1gvGfFnoM6dB3JsquWHXkcEYa4VnHEp8aTkJqw9z6qbpRf1k5Q3vfTT+7tTp2cG8fxMsYMBJ4DwoHXrbWPH/DzVsCbQGfgPmvtk74fpVK+ZczB7dLPOEPuPTVhGVUjitSfUllzzxo2PLmBkh0lLDxzIfVuqkfjBxs71lHSllqWX7t8v8cmm8mAZJ8ezQoLX+jVS7qeDR8Oe/bIEvo//3QXYg4UIR/gcaXCZmTIxaOeWwWesOgwal5Qk5oX1ASgZGcJq+5aRcaEI6+7C68STmTNSKJqRu29j6rl3k7onEBss1g96fah1ath6FCpUQLSMvbnn7UugQo+TzwBM2bI7aWXZJbo4oudHlVoiaoeRfXB1ak+uDoApfml5M6UgM+uWbso3VVKWUGZ+1ZYtv/+nsN3dIysFUlCasLezJyE1ATiWsURFq01dJTb11/LfatW0LKls2M5VsaYcOBFoD+wEZhljPnGWrt4n6flADcBQx0YolKOGTdObl98Aeec4348OdlzrxEWEUbTJ5pSJa0KS69cSll+GZue28TWT7bS9Omm1Lygps+vZza/tpmSbdIytOlTTVl1+yq/zuABGDwYXn9dlmnt2CEZPVOmQJMmTo+s8jTAUx7gKSyUP6InP2jKGRFJEbR8tSUtX5WzpMlm8t6DSUleCYXrCwlPCCeyRiThsf5VhCzU/forXHCBu51k//5SjC45WWY5lAomUVEyU9S5M2zbBqNGyex969ZOjyx0hceFk9w7meTelTsZsNZiiy1lBWVMSZrCietO3BsEck0YKHU4GRnSZQdgyBBnx3KcugErrbWrAYwxHwFDgL0BHmttFpBljAnQyhZKHZ/hw+Xe1eTnlluksO8jj3guyaDmBTWJT41n+TXL2fnXTooyilhy0RIyXs+gxYstiGvp3e7Da8atofZltVl15yqyv5DGBlF1oqh7bV1W3b7Kq6/tKZdfDtnZcOedcow+/XQJ8gTKZHPITyG5lmiBLtMKBREJEcS3iSemYYwGd/yItfDUUxIldwV37rhDWqG7gq5ac0cFo4YN4b335MRu924491y4916nR6UqyxhDWFTY3vT3mIYxxDWPI6F9ggZ3VKV8+617e2hg57XUAzbss7+x/LFjYowZZYxJN8akb9269bgHp5S/GDtWar3UqiX7jz0GV18ttSc9Jb51PB3/6Eirt1oRWSMSgB2TdjCr/SxW37ea0nzvtCov2VXCuvHrmNlm5t7gTlh8GC1ebUF4bHhANQW44w646y7ZXrVKaibt3OnsmCor5AM8+3Yr0E5awSmQDiahKD8fLr1UDqRlZRATI10HnngCIkI+x1CFgoED3cUXFy+Wkz2tNxV49LtGHYuvvpL72rWhWzdnx3KcKso/OOYjmbV2grU2zVqbVqNGjeMYllL+Zdw46NhRmvs0bSqP/e9/cNllUFLiudcxxlB7ZG26LetG3WvrggFbbFn/6HqmnzCdlbeuJG9+nkdey5ZZMt/JZGbLmbJfKB/9WiNq0X1Zd6qfLcug/a3mzpE8/jhceaVsz58vy7f2HF1pPkdogEcDPEEv0A4moWTdOmkZ+cEHst+woXzhaR0SFWrGjoV+/dz7EyY4NxZ1bPS7Rh2tXbtg0iTZHjwYwgL7rHwj0GCf/fqA5sYrdQhNm8o5r6uA7wcfyPnvgQWZj1dkciQtXmpB5xmdSeiSAEDx1mI2PruR9I7pzOo4iw3PbqAoq+iofq+1lvyV+WS+m8m0BtNYOnIpRRn7/46YJjFE1wvcFqHGwKuvurMr//xTuhx6MhDnDSE/P56yT/e4H36AESOcG4tSoWTyZOkklC0ZnPTuLfVIdKJOhaKHHnJf6AGMHi03T3XYUEr5nx9/hKLy66EAr78DMAtoboxpDGwCLgR0ukapw6hVC37/XWq8zJkDn34qx4SPP4ZoD8dFErsm0mVGF7I+yiLjjYy9LdV3z9/NqltXsfrO1VQbWI341Hiiake5b3XkHgu7Zu0id1ouudPlVpy9fzQqqk4URRlF9CrthQkLjgY1ERHw4YfS+WzyZPjmG1lS98Yb/tucydggyQNPS0uz6enpR/3frV0LjfeZdAuS/x1K+S1r4YUX4NZb3euNb7oJnnwSIiOdHVswMsbMttamOT0OTzrW430gmDIFTj1VtqtUgd9+g7Sg+usppVwuvVSWJCckwNatskT5eDh9vDfGDAKeRdqkv2GtfcQYMxrAWvuKMaY2kA4kAmVAHtDGWpt7uN8bzMd8pcDdrWmmrHBi0CD4/PPjPyYcTsG6AjLfzSTzrUwKVhUc1+8Kiw+j/s31aXhPQ6ZUmeL3nbKORW6uTEbPnSv7Y8bI5JyTDnXMD+kAT+/eUuTqQL16SYROKeVZBQVw7bXw1luyHx0Nr7wi1eqVdzh9wu8NwX6yv++MUEqKfE+1bevceJRSnldcDDVryoXduefKzP3xCsbjPQT/MV8pkADCoEGybAvgtNPg668hzrtNr7DWkjs1l8y3Mtn2wzaKMovgCDWYY5rGkHhiIkknJZF4YiLxqfGERcoa0zXj1gTtkuWsLCktsWKFnKv99JN0/HXKoY75Ib1EyxXEmToVevSQ7QcegPHjHRuSUkFr40ZpDzlrluzXqwdffBHwRSWV8rixY+XC7/rrpX16//7w11/uYoxKqcD3558S3IGA756llPKAxERZtnn22XKN+uuvcOaZ0mkvIcF7r2uMIalHEkk9kgCwpZbibcUUZRbJLUPuywrKSOicQGL3RKJqHrpLZLAGd0DOzb75Brp0cTeJmT/f/9qn+7ycmzEmxhgz0xgz3xjzjzHmkOEUY0xXY0ypMeZcb47ppJPc2y+/LFkGSinPmTJFDoau4E6PHpCersGdYOePx/tAMG4cXHeddG8AaQDQr58ESZVSwcHVPSs8XGbtlVIqIQG+/96dFTJ5snTazD3sIkbPMuGGqJpRJKQmUO30atQeWZuG/2rICWNPoPrZ1Q8b3AkFrVrBSy/JdlaWBHk82eLeE5yo118I9LXWdgA6AgONMSce+CRjTDjwb+Anbw/IGPljgayBfv99b7+iUqGhtFTanfftKwdBkMKxv/3mf9Fu5RV+d7wPJP/6F9x7r2yvWyfp2q7PkVIqcFkrSy9AygUkJzs6HKWUH4mLkywRV+D3778l4LN9u7PjUm4jR7obM02a5J6Q8xc+D/BYkVe+G1l+q6gQ0I3A54BPTmcXLID69WX7mWe02LJSx2v1ajlxvesuqTUQGSmtBl9+GaJCO/gfMvz1eB9IHn4YbrxRtpctk04bepKnVGCbOhU2bJDtIOiepZTysJgYKWPgOj7MnCmZvNu2OTsu5fbSS9CihWw/8IAspfcXTmTwYIwJN8bMQ07mf7HWzjjg5/WAYcArR/g9o4wx6caY9K1btx7XmCIj4YYbZPuff2Tdo1Lq6FkLr78OHTrI0iyAZs3kwDdqlLNjU77nqeN9qDIGnn3WXYh8/nyZ1cvLO+x/ppTyU6WlcPPNsh0ZCcOGOTsepZR/io6W4uvnnSf7c+dCnz6ayesvEhLc7ezLyuDii/0nAOdIgMdaW2qt7QjUB7oZY9od8JRngX9Zaw+7os1aO8Fam2atTatRo8Zxj2vUKHel8meeOe5fp1TIycyEwYPh6qvdF6DXXQfz5kH37s6OTTnDU8d7Twb0A01YGLz2mnTaAZg+XWb1tF6cUoHnxRdh9mzZvvNOd/a4UkodKDISPvgALrlE9hculOz4jAxHh6XKdewITz8t2xs3ymScP6wCciTA42Kt3QFMBgYe8KM04CNjzFrgXOAlY4zXewwkJ7tnSX/4AZYs8fYrKhU8Pv8c2rWD776T/bp1pRvAiy9CfLyzY1POO97jvacD+oEmIkLqw51xhuz/9hucf74sf1RKBYZNm2DMGNlu0sS9rZRShxIRAW+/DVdcIftLlkCvXtp4wV9cey2cc45sf/cdPPecs+MBZ7po1TDGVC3fjgVOA5bu+xxrbWNr7QnW2hOAz4DrrLVf+WJ8rrRZ8I8/kFL+bscOuOwyyS5wpSZedJHMMgwY4OzYlLP8/XgfaKKiJJDaq5fsf/utFPrzt+4NSqmK3Xwz7Nol2y+9BLGxzo5HKRUYwsOl/MHo0bK/YgX07Alr1zo6LIUspX/9dTjhBNm/6y7pFOwkJzJ46gC/G2MWALOQmgzfGWNGG2NGOzCe/bRoAWedJdvvvOM/a+mU8keTJkH79vDuu7KfnAwffSTppNWqOTs25Rf8+ngfiGJjpbtG166y/+GHcsLnDynBSqlD++47CdACXHCBToAopY5OWJgEhm+6SfbXrJEJn1WrnB2XgqpV5fonIkIyqy+4AHbudG48TnTRWmCt7WStTbXWtrPWPlj++CvW2oOKbFprL7fWfubLMd5yi9zv2QMTJvjylZUKDPn5MhN52mnuFNGBA2HRIjmoKQWBcbwPRImJsoy4XXk1o9dfl+Vau3c7Oy6lVMV274brr5ftpCSt86iUOjauxgt33in769dLkGf5cmfHpaTW6KOPyvbq1VLb16nJN0dr8Pirvn0hNVW2X3hOfZm0AAAgAElEQVQBioqcHY9S/mTWLOjcGZ5/Xvbj4qT1+cSJUndHKeV9KSnwyy/uFp2ffQYnn6zp2kr5o/Hj5UIM4LHHoE4dZ8ejlApcxsC//w333Sf7mzZJkGfxYmfHpeD22921Ej/5RBpkOEEDPBUwxp3Fs3mztKhTKtQVF8O4cXDSSbBsmTx20knStnn0aPncKKV8p3ZtmDYN+veX/QULZOnWH384Oy6llNuCBe4uK927wzXXODsepVTgMwYefhgefFD2MzOlu9bChY4OK+SFhUlBbNeE9803O/M30QDPIVx0EdSsKdtPP631DVRomzNHgjnjx0tB18hISUP86y9o1szp0SkVuqpVk+y5W2+V/exsWTr58svOjkspBWVlEtApLZUiqa++KhcASinlCfffL1mBAFu3Qp8+MHeus2MKdTVqSNfTsDAoKHBmCb1+zRxCTAxcd51sz5kjqXBKhZqcHPkcpKXB7NnyWLt2MHMm3HOPnLAqpZwVESETEW+9JZ22Skrkczt6tC4xVspJr70G06fL9i23QIcOzo5HKRV87r7bnSW4bZuUGpk509kxhbreveGBB2R76VK48Ubfvr4GeA7j5puhSRPZvu8++PVXZ8ejlK+UlUnh1hYtJBPAWrmIvPtuaf3XsaPTI1RKHWjkSPjzT3d9j1dflWyerCxnx6VUKNqyRb4zARo0kCXOSinlDbfeKnVjAXbskO/+qVOdHVOoGzNGAj0Ab74J773nu9fWAM9hVK0KX3whbWnLyuDCC2HdOqdHpZR3pafLcqyrr5aZAJAvioULJQ00OtrZ8SmlDq17d/kMd+sm+3/9JXV5NGVbKd+67Ta50AK58EpIcHY8Sqngdv31MrFjDOzaBaefLpM+yhnh4bJUq3p12R892nfdzjTAcwQdOrhbpW/bBuecI+vplAo227ZJrYBu3dypnQ0aSJHxn3+GVq2cHZ9SqnLq1pVCyyNGyP769dCjB3z8sbPjUioUWCuZOx98IPtDh8Lgwc6OSSkVGkaNgjfekCDP7t0wcCBMmuT0qEJX3brwzjuyvXs33HGHb15XAzyVcOmlcMMNsj17tntbqWBQWioR/xYtJJhprRRRvuceWLIEzj1XO2QpFWhiYqSTw1NPSaG/PXskC/W++yQjVSnleWVlUv/KVbexbl3473+dHZNSKrRcfjm8+677u/+ss+Cnn5weVeg64wxZQg/w44+wc6f3X1MDPJX01FNw8smy/b//OdfXXilPmjFDlnSMHi0FlQEGDIBFi6RLVny8s+NTSh07Y2SZyMSJsuQY5HM9dCjk5jo7NqWCTXGxZM298orsN2kCU6ZA/frOjkspFXouuQQ++kiWCRUUSBbhd985ParQdfHFcl9cDN984/3X0wBPJUVFyVKV2rVl/4YbtEK5Clxbt8JVV8GJJ7q7YzVsKDWnfvhBsnmUUsFhwAD5vmrdWva//VY++ytWODsupYJFQYFku7qWZbVpI/WvGjd2dlxKqdB13nnw2WeSlV9UBMOHw+efOz2q0NSnD1SrJtuffeb919MAz1GoW1eCPBER8kE55xztTqICS2kpvPQStGwpmWggwcv77pPlWMOG6XIspYJR8+bSrvmss2R/yRKpt/X++7IsUyl1bHbtgjPPdM/KpqVJDay6dZ0dl1JKDR0KX34pDVKKi+H883UVihMiI+VvAbJczttZ1BrgOUqnnCLLtQA2bpSaBiUlzo5JqcqYPl0u6K6/HrZvl8fOOEOWYz38MMTFOTs+pZR3JSbCV19JfS2QDj+XXgr9+/uus4NSwSQnRz4/v/0m+z17SkFTV9cUpZRy2plnSuZuXJzUCRs1SpZr6+SOb517rtwXFsL333v3tTTAcwxuvNG9lu733+Hee50dj1KHs2yZROxPOgnmzJHHTjgBvv5aDjDNmzs6PKWUD4WHy4ndZ59BzZry2KRJ0L49jB+vXSKVqqzMTOjdW2rZAQwaJAU0ExMdHZZSSh3EFYh2LRO67z649VZtuuBL/fq56yF6e5mWBniOgTHSbah9e9l/4gnfrKdT6mhs2CB1dtq2laWFICmaDzwAixdLwTVdjqVUaDrnHFi6VAqsGyPLjseNg9RU+PVXp0enlH9btw5OPRUWLpT988+XZRCxsc6OSymlDqV79/0Lvz/3nBSGLypydlyhIioKhgyR7YkTIS/Pe6+lAZ5jFB8vBWmTkmT/iiukpoFSTtu6VaLyzZpJnZ3SUrmAu/RS+Tc6fryehCqlIDkZXn4Zpk6FDh3ksRUrZKbv0kthyxZnx6eUP1q2TJbrr1wp+1ddJcWVo6KcHZdSSh1J69bynd+qlex/8IEEHXbvdnZcocK1TKugQII83qIBnuPQrJkUqASJwg0bpq1nlXNyc2HsWGnN+uyz7oj8kCEwfz68+6529FBKHezEEyE9XerLxcfLY++/LyeAr76qKdxKucybJ5k7GzfK/m23SUZ3eLiz41JKqcpq0EAyebp3l/0ff5TlQ9u2OTuuUNC/P1SpItveXP2jAZ7jdOaZclENMqszcqRUKVfKV/bskQuzJk3gwQfdKX+9e8O0aVJU1bWcUCmlKhIRIRerS5a4Oz3s2CFLuHr0kCCxUqFs6lT5Xt26VfbHj4cnn9SlzkqpwJOSIsuxBwyQ/RkzJHi9YYOz4wp20dFSIgOkDmp+vndeRwM8HvDAA1JcD+RietAgd5cipbylpERaHTZvDnfc4Y68d+kCP/8sxdROPNHZMSqlAkuDBlJL5OuvoWFDeWz6dDmu3HGHd9eMK+WPrJWMtv79YedOeezZZ+XcT4M7SqlAlZAA33wDF10k+0uWwMkna8kRb3Mt08rPl+wpb9AAjweEhcF778kJMEhE9KST3OuzlfKksjL4+GNo00ZaHW7aJI+3aiXpfrNmyYmonngqpY7V4MFSjP3OO2X5SWmpZAq2bi0TGUqFgvnzJWvn0kvlZDwsTGrb3Xyz0yNTSqnjFxUl17A33ij7GzdKjTFXd0DleQMGSHAN3E1wPE0DPB6SnAx//imdSUCWa3XvDn/84ey4VPCwVgpydekCF14oxVBBZtnfeEO6eZxzjgZ2lFKeER8P//kPzJ0rs3ogJ3/Dhkltr3XrnB2fUt6SkwM33ACdO8u5HUDNmvD553Dllc6OTSmlPCksTDpqPfyw7OfkQN++8NNPzo4rWMXGwllnyfZ330mpDU/TAI8HxcXBJ5/AvffKfk6OZFK88Yaz41KBb8oU6NlTaj7NmyeP1aghaeLLl0sXt4gIZ8eolApO7dvDX3/JktDkZHnsm28ki/CJJ6Tu3Lhxjg5RKY8oLZXC4i1awIsvSsZseLh0ply+3F2fSimlgokxcN99UjQ+LEwyFs8+Gz780OmRBSfXMq28PCmr4Wka4PGwsDB45BF45x1Jeysuhv/7P0lzLy11enQqkFgLv/8Op58uhc+mTJHHExOlmPKqVZImHh3t7DiVUsEvLEzaQS9dCiNGyGP5+XDXXZJVOH68HLOUClRTp0K3blJY3FXTrl8/WLAAnn4akpKcHZ9SSnnb1VfLsiHXNezFF8O//63f7552xhmSGALe6aalAR4vGTFCitxWry77Tz4Jw4drgUp1ZGVlcMEFUiC5b1/45Rd5PCZGAoWrV8P997vb7CmllK/UrCkTGL/9Bi1bymMLF8p9t25yoqKTGSqQZGTAZZdJt7g5c+Sxhg3l3/Ivv0immlJKhYrhw6X4r+s64+675bpEr2E9Jy4OevWS7d9+8/zv1wCPF/XoATNnuk8OvvlGCldpCzpVkaIiePNN+ffyySfybwdkreaNN0rR7v/8R1obKqWUk/r0cacYu6Snw3nnSRDotdegoMCZsSlVGUVFMvnWsiW8+648Fh0t3bGWLNGadkqp0NWnjyzNPuEE2f/0U6ktu3y5o8MKGlu2uOu7NW/u+d+vAR4va9xY0n4HDpT9+fNlltN18a5UXp6kfzdpIsUbly2Tx5OT5URz3Tp4/nmoV8/ZcSql1L4efljStrOyZL9aNbnPyZEOf40bS2q3q7W0Uv7ip58gNVWyYnftkseGDpXAzvjx7tR5pZQKVR06yMTN6afL/uLF0LUrfPuts+MKBo89Brt3y/bYsZ7//Rrg8YGkJPkw3HST7GdmSlrWxx87Oy7lrOxs+VA3bAi33+5ud+6yfbvU2nnxRWfGp5RSlVGjhtyvWwfPPAMNGsh+ZqakdjdsKPcZGc6NUSmANWskkDNwoHsypWVLCfh8+aUEJZVSSomUFOnge889sp+bC4MHy/VLWZmzYwtU69fDyy/Ldr9+ki3laRrg8ZGICGlB99JL0pGhoEBaXT/4oBauCjXr1klx5IYN5e+/fbs83rKldFwrLJR9a+Wm3WmUUv5u7FhISIBbbpEC8G+/DW3bys9ycyWT54QTJLNnxQpHh6pCUH6+ZMS2bg1ffy2PVakiS7QWLHDPUKvjY4wZaIxZZoxZaYy5u4KfG2PM8+U/X2CM6ezEOJVSlRceDo8+Cp9/Lt/zINcvZ58NO3Y4O7ZA9OCDskQYpDGTN2iAx8euvRZ++MHdjWHsWLjkEq1VEAr++QdGjoRmzWTJ1Z498njXrvDFF5L6eMUVUrleKaUCyb6B6MhIKVq7YIFkr/boIY8XFUltnpYtpVZPerojQ1UhxFoplty6NTz0kHsC5bLLJIPn9tv1O9dTjDHhwIvAGUAb4CJjzIElqs8AmpffRgEv+3SQSqljNny4lBhxNViYOBHS0tyNFtSRLVsGb70l2y1bSl0jb9AAjwP694fp06FpU9n/8EPo3VvT14PV1KmSztiunXSfKSmRx08/XSqnz5gBw4ZJG2IXb6zHVEopXwoLg7POgilT5Hb22fK466K7a1dJT/75Z81kVZ61dassF+zQQYKJ69fL4507w99/S4ZZnTrOjjEIdQNWWmtXW2uLgI+AIQc8ZwjwjhXTgarGGP1LKBUgWreWIM+Q8k/2qlXS9VfLjlTO2LHSadQY9zJhb9AAj0NatZIL+549ZX/GDHns8cfdmR0qcJWVSWS7Z0+ZvXYVJAsLg/PPh9mzZc1/nz4Vd+nQZVlKqWDSo4d0kly0SLInIiLk8d9+gwEDoEsXOUF0BcCVOlrFxfJvbNgwqFsXbrvNPbOckgITJsiFycknOzvOIFYP2LdP7Mbyx472OQAYY0YZY9KNMelbt2716ECVUscuMVFWHjz8sFzD5OdL2ZE77tDv8MOZN88dCLv4Yu++ls8DPMaYGGPMTGPMfGPMP8aY8RU855LytbkLjDFTjTEdfD1OX0hJgV9+kc5JIHUK7rlHUrbee0+LVwWiTZtkPWWzZnDmmdJiECQFfNQoWLpUPtydddW5CgF6vFcHattWsidWrZJ6PfHx8vjcuXKC2LKlFB/UiQ5VWYsWyVKr+vVlVvmrr9wXGc2ayUXI8uVw9dVSS0J5TUVN5Q/MzavMc+RBaydYa9OstWk1XJXclVJ+ISwM7rtPJrOTk+Wxp56S1Qkaj63YmDHu7fffl3tj5ObpiX0nMngKgb7W2g5AR2CgMebEA56zBuhlrU0FHgIm+HiMPhMVBf/7H/z4oyzhAdiwAUaMkHbqkyc7OjxVCSUlMms4eLAUTh4zRjp1gBRxvOsuWLsWXn0Vmjd3dKhK+Zoe71WFGjaUJTTr1klb6urV5fHVq+G666Qg86OPagFHVbGcHGla0bUrtG8PTz8NWVnys4QEmTj76y8J7Nx3H1Sr5ux4Q8RGoME++/WBzcfwHKVUgBg4UOrppabK/u+/S0buH384Oy5/M3UqfP+9bF9zjXtZurca6vg8wFO+7javfDey/GYPeM5Ua215byGmI18AQW3AAEndeu01qF1bHps9W5bwDBkimR/Kv6xaBffeKxcqQ4bIMixX1lVqKvz3v7Lu/9//1rX+KjTp8V4dSUqKdDdat06OmY0ayeNZWXJh3qCBdB38+2/Nag11Dzwgk2EXXCDfqddfv3+h7l69pHhlRoZMnJ1ySsVLoJXXzAKaG2MaG2OigAuBbw54zjfAZeXdtE4EdlprtQKlUgGsSRMJYLiWHW3YILVlR450B95DmbVyvQgQHb1/Jo+3OFKDxxgTboyZB2QBv1hrZxzm6f8H/HCI3xNU63PDw+Gqq6SF7NixEBcnj3/zjWT3XH+9flCcVlAgRbH79ZPU78cecxfHTkiQZVizZkmw7oYboGpVZ8erlNP0eK8qIy5OjpkrVsgS5fbt5fG8POk6eMopUlflmmvkIt/VYlQFv+XLZfn6Qw/BGWfAJ5+4//4NG0rgZ9UqyXgeOdLdxlf5lrW2BLgB+AlYAnxirf3HGDPaGDO6/GkTgdXASuA14DpHBquU8qj4ePnufv55iI2Vx955x73surTU2fE56ddf3RlN118vy4nBuw11jHWwdYUxpirwJXCjtXZRBT/vA7wEnGKt3Xa435WWlmbTg6zn6ubNcuLyxhvuVK4qVeRE55Zb3B8g5X0LF8Lrr8O778L27fv/7OSTJTB33nl6Yqn8jzFmtrU2zQ/Gocd7VWnWSiDnyScl5fvAU5XERKlzNmyYXPTrsTe45OZKIOfNN2VmeF8xMXDOOXDFFZLlHKbtQvbyl+O9p+kxX6nAsW6dZN5+/bX7sa5dJdDTpYtz43JCQQGceqpkmyYkyDJ0T5YUO9Qx39GvRWvtDmAyMPDAnxljUoHXgSFHOtkPVnXrSlBh3jwpWgWwa5ekebVsKcEGTVn3nl275P//iSfKkqvnn3cHd1JS4NZb4Z9/ZOnAFVfoBYZSh6PHe3U0jJHAzaRJkiU5YYLsR0bKz3NzJZvy/POlfs/gwRIMyM52dtzq2JWVSVe1ESNkqfrVVx8c3AE5YW7WTDJpNbijlFL+pVEjKXb/zTfuZdezZklt2RtvDI3aetbCl19CmzbupcS33ebZ4M7hONFFq0b5TC7GmFjgNGDpAc9pCHwBjLDWLvf1GP1Naqq01D6wEPNll0FamsxuKs+wVlrWX3WVrPG/+mrZd+nfX7pgbdokRR3btHFurEr5Oz3eK0+oVUuOxRMnSneODz7YP2OysFBqoF15pTy3Tx8JyK9f7+y4VeWsWSMFJps2laDNe++5u6jVrQt33+2uQ+itgpRKKaU86+yzYfFiWXkSGSlB/BdegFatpIuUg4uIvGrRIrleHD7c3XQnLU26PfqKz5dolc/Uvg2EIwGmT6y1D7rW51prXzHGvA6cA6wr/89KjpRyGirpm6WlUkRwzBjIzHQ/ftZZ8J//QOvWjg0tYFkrJ48TJ8r/20UHLB6pW1cuHK68Eho3dmSISh0zJ1P29XivvKmgQNa2f/mlzBRWlL3TpYss4xo+XL8f/UVODkyfDtOmSV2Cv/7a/+dRUdK44Ior5CQ5IkIeNyZ4Lwg8RZdoKaX80ZIlUn9m36SEPn2kG2KrVs6Ny5NycqS0yssvu1fYVKsm9eNGjXJ/l3nSoY75jtbg8aRQO/jn5cFTT0lQJz9fHgsPh0svlQ4TfftKpW5VsZ07JfX/xx8lO+rAmd7wcAmaXXWVtAD0xodSKV8IxhP+UDveqyMrKZHlsl9+KbeKsndatpRgz7BhMpumy3u8r6xMZnCnTXPfDtUVtEsXCepcdFHFbc3HjdPMnSMJxuM96DFfqWBgrWTg3nabu2lQZCTcead0zXQ1Fwo0JSXw6qtwxx0y8QRyHXnttTB+fMXfZ56iAZ4gVVEhZpDU9TPOgKFDYdAg7eZUVgZz5riXuk2bVnFF96ZNJagzcqS2NlfBIRhP+EP1eK8qx1qYO1cCPV98IQGGA9WrJ9+Pw4ZBz57u2j7q+OzYIcuaXcGcGTNkQuVQ2rSBAQMksOPqnKaOXTAe70GP+UoFkx07ZCXKSy+5r10bNZIgzwUXSBOFQDFpkhSU/ucf92P9+sGzz7rLqniTBniC3MKFEuiZOPHg9rEREZIGN3SoFKJ0tWcLdlu2wM8/S0Dn558rTt+PjoZevSRLZ8AASeE3xvdjVcpbgvGEP9SP9+roLF/uzuzZt6aaS3Ky1AoYNkwaGgTqLKKvlZXBsmX7Z+csXnzoZVSJidC9u3SePOkk2Q71ySdPC8bjPegxX6lglJ4uWS77frRjY91dEnv39t9M29WrJWPnyy/3f/zLL2WJsa+uJTXAEyJycyWg8dVX8P33sn+gtDQJ9gwdKrNnwRLQKCqSE0zXsqu5cyt+XqtW7oBOz556Mq+CWzCe8OvxXh2rTZukdeuXX8LkyZJava/YWMkkad4cWrSQW/PmcgukWUVvyM2FmTPdwZzp092dJSvSqpUEcly31q0lbV15TzAe70GP+UoFq9JSWd70yCOyKmVfjRrJiorLL/efGqh5efDYY1ImpbDw0M8bO9Y3S4o1wBOCioqkgOFXX8ntwA8OSKvRoUMl2njSSYF38rVmjTugM2mSfPAOlJgIp50mAZ0BA9wt+5QKBcF4wq/He+UJ27fDd99JsOfHH92dmw6ldu2DAz8tWsjS3pgY34zZV6yFFSvcwZypU6UBwaFOGRMSJCPHFcw58UTv1h1QFQvG4z3oMV+pYFdaCr/8Am++KdesB65G6d1bsnrOOQfi430/vqwsOV8YMwYyMtyPX3aZBHzq1nWmEYAGeEJcWRnMni0fmq+/3n+toEuNGrKEa+hQWT8YG3vwc3xd5NBaOQlfswbWrt3/fulSSZGrSFqaBHMGDpSTTq2voEJVMJ7w6/FeeVp+vizl/eknWXa0fLlk+1SGMdCw4cGBnxYtZELB34v0Wwu7dsk5giuYM306bNt26P+meXN3MOfkk6Ft28CbIApGwXi8Bz3mKxVKcnLgo48k2HPgxz4hAc4/X4I9PXp4ZxVKURHMny/fg67bgdeb3brB88/LNaaLBni8QA/+R2fFCgn0fPWVnMwd+M8gPl4+OLVqQUqK+3bdddKWdt/HjneJ065dErCpKIizdm3Fy8wOVKuW1E4YOFDaqtaocXxjUipYBOMJvx7vlS/s3g0rV0qwZ/ly+d50bR8u+LGvyEho0uTgwE/z5lLo+VhOTseNg3vuke9O1y0vb//9o7nl5VXcdMAlLk5OZl21c048EapXP/pxK+8LxuM96DFfqVC1aJEEet57z915y6VZM+l4XK+eNMapW1fu69SR1RuV/X7duNEdyJk2TSY7DrX8qk4dePxx6Vp9YH0gJzo9aoBHHdKWLZJ29tVXkh53uDWFFYmJkUBPtWr7B34OvIWFwbp1BwdzcnKO7vWqVJG1mI0by4nmgAHQoYP/FuJSyknBeMKvx3vltJwcd8Bn38DPihUVLxWuSFycu75Pixby3VaZgMzRfmcerSZN3MGck06SmkT+noWkRDAe70GP+UqFuuJi+OEHCfZ8993B9fMOFBfnDvYcGPxJSYElS9xBncNl69aoIdearttJJ1W8wsUpGuBRlZKXJ2nqX30lUdNt22StYXGx78YQGwsnnOAO4ri2XffJycFTGFopbwvGE3493it/ZS1kZlYc+Fm58uC6At4WGSmBo8rcWreWE9hatXw7RuU5wXi8Bz3mK6XcsrLggw/g3Xelc2NBgWd+b0QEdOq0f0CncWP/vuY81DFf52TUfhISYPhwue2rsFBmDevWlc4j27Yd+ZaTU3Had1SU1CU4VBCnZk3//jAppZRSFTHGPUvYq9f+PysthfXrDw78LF8uGa1lZZKJWlHwZeNGqQ10oMGDYcQI+e6u6L+LjvbJ21ZKKaV8omZNuOUWuVkLO3dKMsLmzXJ/qO3du/f/PfXr7x/M6dzZv7JzjocGeFSlREfLCSscfNJ6KGVlUj/HFfApKZHATp06upxKKaVUaAkPd09qnH76/j8rKpLvyNjYI09wOFHIUSmllPI3xkDVqnJr3frwz921SwI9WVmSUFC/vk+G6AgN8KijMnZs5Z8bFub+0DVt6r0xKaWUUoEsKkpuSimllPI8V2ZrixZOj8T7NI9CHRVfVwdXSimllNvRTLQopZRSKrRogEcppZRSKkDoRItSSimlDkUDPEoppZRSSimllFIBTgM8SimllFJKKaWUUgFOAzxKKaWUUkoppZRSAU4DPEoppZRSSimllFIBTgM8SimllFJKKaWUUgFOAzxKKaWUUkoppZRSAU4DPEoppZRSSimllFIBTgM8SimllFJKKaWUUgFOAzxKKaWUUkoppZRSAc5Ya50eg0cYY7YC647wtOpAtg+G45Rgfn/63gJXML+/QHhvjay1NZwehCdV8njvDYHw964sfS/+KZjeCwTX+wmE9xJ0x3uo1DE/EP42x0rfW2AK5vcGwf3+Aum9VXjMD5oAT2UYY9KttWlOj8Nbgvn96XsLXMH8/oL5vamDBdPfW9+Lfwqm9wLB9X6C6b0Em2D+2+h7C0zB/N4guN9fMLw3XaKllFJKKaWUUkopFeA0wKOUUkoppZRSSikV4EItwDPB6QF4WTC/P31vgSuY318wvzd1sGD6e+t78U/B9F4guN5PML2XYBPMfxt9b4EpmN8bBPf7C/j3FlI1eJRSSimllFJKKaWCUahl8CillFJKKaWUUkoFHQ3wKKWUUkoppZRSSgW4oAvwGGPeMMZkGWMWHeY5vY0x84wx/xhj/vDl+I7Xkd6fMSbJGPOtMWZ++fu7wtdjPFbGmAbGmN+NMUvKx35zBc8xxpjnjTErjTELjDGdnRjr0arke7uk/D0tMMZMNcZ0cGKsR6sy722f53Y1xpQaY8715RiPR2XfXyAfV9T+jDEDjTHLyo8zd1fw84A5DlXivbQyxkwzxhQaY+5wYoyVVYn3EjDH0Eq8lyHl72OeMSbdGHOKE+OsjCO9l32e5/fH/0r8XXobY3aW/13mGWMecGKcoSiYz+/13D5wvlP3pef2e5/r98f2AwX9ub21NqhuQE+gM7DoED+vCiwGGpbv13R6zB5+f/cC/y7frgH8f3v3H2p3Xcdx/Plu2y3LRdIobcu2zCwF8+aP7IGvcN8AAAc0SURBVJf0QxD3RyEZiTChgqiwkgiEoIIiqj8KoRgSFiMohXJa1CyKiIU5W1uuJVtrLtBLgkyjmkl527s/vmd5t93r/Zy7c+73+/me5wMunLtzBq83n3vf3/f9fL/fc54AptrOXVjbWcDrB49XAweA8094zUbgHiCAy4H72849wtreBJwxeHx1n2obPLcC+CWwDbi27dwjXruq+4pfx63lCuAh4JXAFLCn1j5UWMtLgEuBLwKfajvzKdZSRQ8trOV0nnmfxAuB/W3nXmotc17X6f5fuC5vA37cdtZJ/KLH831Bbc72HfwqrK2K49JSahs81/nefgprV21P6d0VPJm5nabxLeR6YGtmPjx4/WPLEmxECupLYHVEBM2A+AQwuxzZTlVmPpqZuweP/wnsA9ae8LJ3A9/Jxg7gRRFx1jJHHVpJbZn5m8z82+DbHcC65U25NIXrBvAx4E6gtt+5kvqq7is6zmXAwcw8lJn/Ae6g6Ttz1dKHFq0lMx/LzJ3A020EHEJJLbX00JJajuRgogReQHNs76KS3xeoo/+X1qIW9Hm+d7av5ph6HGd7oI7efpK+z/a92+Ap8GrgjIj4VUTsiogb2g40Yt8AXgv8FdgLfCIzj7YbaXgRsR6YBu4/4am1wCNzvp9h/obTWc9S21wfpDmbUZWFaouItcA1wK3Ln2p0nmXt+t5XJklJj6mlD9WSs8SwtXS5hxbVEhHXRMR+4CfAB5Yp27AWraWi/l/6M/bGwa0y90TEBcsTTQX6fBx2tu84Z/t69XG2X9l2gBasBC4G3gmcBtwXETsy80C7sUbmKuAB4B3AOcDPI+LXmfmPdmOVi4jTaXaDb5ond8zzX7p6ZvMki9R27DVvpzkIdPY9F+azSG23ADdn5n+bE1D1WaS+vveVSVLSY2rpQ7XkLFFcSwU9tKiWzLwLuCsirgC+AFw57mBLUFJLLf2/pJbdwCsy80hEbATuBs4dezKV6PNx2Nm+w5ztO9/bF9TX2X4SN3hmgMOZ+STwZERsB15Hc+9dH7wf+PLg0u6DEfEX4DXAb9uNVSYiVtH8on03M7fO85IZ4OVzvl9Hc0aj8wpqIyIuBG4Drs7Mx5cz36koqO0S4I7BAWANsDEiZjPz7mWMuWSFP5d97iuTpKTH1NKHaslZoqiWSnroUOuSmdsj4pyIWJOZh8eebjgltdTS/xetZe4fAJm5LSI2d3RdJlGfj8PO9h3lbF9Fb59Xn2f7SbxF64fAWyNiZUQ8H3gDzX13ffEwzU4jEfFS4DzgUKuJCg3uLf4WsC8zv7bAy34E3DB4x/3Lgb9n5qPLFnKJSmqLiLOBrcCmGnaHjympLTM3ZOb6zFwP/AD4aEUHgJKfy773lUmyEzg3IjZExBRwHU3fmauWPlRSSy0WraWiHlpSy6sGvYdoPlFmCujiHwaL1lJR/y9ZlzPnrMtlNHN0F9dlEvX5OOxs30HO9tX09pP0fbbv3RU8EXE7zaccrImIGeBzwCqAzLw1M/dFxE+BPwBHgdsyc8GPXOyaxeqjuYx7S0Tspbnk8eaKziy9GdgE7I2IBwb/9mngbPh/fdto3m3/IPAvmrMaNSip7bPAi4HNg/lxNjMvaSHrsEpqq9mi9dXeV/SMzJyNiBuBn9F8OsS3M/PBiPjw4Plq+lBJLRFxJvA74IXA0Yi4ieaTJDp16X/hulTRQwtreQ/NHzxPA08B7xucve+UwlqqUFjLtcBHImKWZl2u6+K69FGf53tn+zqOqfNwtq9Xr2f78LgkSZIkSZJUt0m8RUuSJEmSJKlX3OCRJEmSJEmqnBs8kiRJkiRJlXODR5IkSZIkqXJu8EiSJEmSJFXODR5JkiRJkqTKucEjSZIkSZJUOTd4pBGJiAsi4hcRcSAiPhMRX4+IS9vOJUkaj4j4fETsHfT9D7WdR5I0es74qsnKtgNIfRARzwO+D7wXOATsB3Zl5s5Wg0mSxiIirgKmgYuA84GvAN9sNZQkaaSc8VUbN3ik0bgS+H1mPggQEVPAV9uNJEkao3cBW4BVwI3Ana2mkSSNgzO+quItWtJoTAO7ASLiZcCRzLy33UiSpDG6GFgNPA68Bbi93TiSpDFwxldV3OCRRuPfwLrB4y8BUy1mkSSNUUQ8B1iXmVuANcAu4JOthpIkjYMzvqriBo80Gt8DroiIPwF7gPsi4paWM0mSxuM84M8AmfkUcC+wotVEkqRxcMZXVXwPHmkEMnOG5nJ9SVL/TQPPjYgVNLPU9cDH240kSRo1Z3zVxg0eSZKk4VwEnAY8BBwGNmfmnnYjSZKkSecGjyRJ0nCmgU2Z+ce2g0iSJB0Tmdl2BkmSpGpExCPAhsycbTuLJEnSMW7wSJIkSZIkVc5P0ZIkSZIkSaqcGzySJEmSJEmVc4NHkiRJkiSpcm7wSJIkSZIkVc4NHkmSJEmSpMq5wSNJkiRJklQ5N3gkSZIkSZIq9z9Dttn7Ag4vyQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n", "colors = [\"m\", \"b\", \"c\"]\n", "for p, ax in zip(panels, axes):\n", " xlabel = pars[p[\"x\"]]\n", " ylabel = pars[p[\"y\"]]\n", " for ks in range(len(cts_sigma)):\n", " plot_contour_line(\n", " ax,\n", " p[\"cx\"](cts_sigma[ks]),\n", " p[\"cy\"](cts_sigma[ks]),\n", " lw=2.5,\n", " color=colors[ks],\n", " label=f\"{sigma[ks]}\" + r\"$\\sigma$\",\n", " )\n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", "plt.legend()\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.stat_surface()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This alternative method for the computation of confidence contours, although more time consuming than `Fit.minos_contour()`, is expected to be more stable. It consists of a generalization of `Fit.stat_profile()` to a 2-dimensional parameter space. The algorithm is very simple:\n", "- First, passing two arrays of parameters values, a 2-dimensional discrete parameter space is defined;\n", "- For each node of the parameter space, the two parameters of interest are frozen. This way, a likelihood value ($-2\\mathrm{ln}\\,\\mathcal{L}$, actually) is computed, by either freezing (default) or fitting all nuisance parameters;\n", "- Finally, a 2-dimensional surface of $-2\\mathrm{ln}(\\mathcal{L})$ values is returned.\n", "Using that surface, one can easily compute a surface of $TS = -2\\Delta\\mathrm{ln}(\\mathcal{L})$ and compute confidence contours.\n", "\n", "Let's see it step by step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all, we can notice that this method is \"backend-agnostic\", meaning that it can be run with MINUIT, sherpa or scipy as fitting tools. Here we will stick with MINUIT, which is the default choice:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "optimize_opts = {\"backend\": \"minuit\", \"print_level\": 0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, we can compute the confidence contour for the `alpha` and `beta` parameters of the `dataset_hess`. Here we define the parameter space:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "result = result_minuit\n", "par_1 = result.parameters[\"alpha\"]\n", "par_2 = result.parameters[\"beta\"]\n", "\n", "x = par_1\n", "y = par_2\n", "x_values = np.linspace(1.55, 2.7, 20)\n", "y_values = np.linspace(-0.05, 0.55, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we run the algorithm, by choosing `reoptimize=False` for the sake of time saving. In real life applications, we strongly recommend to use `reoptimize=True`, so that all free nuisance parameters will be fit at each grid node. This is the correct way, statistically speaking, of computing confidence contours, but is expected to be time consuming." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "stat_surface = fit.stat_surface(\n", " x, y, x_values, y_values, reoptimize=False, **optimize_opts\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to easily inspect the results, we can convert the $-2\\mathrm{ln}(\\mathcal{L})$ surface to a surface of statistical significance (in units of Gaussian standard deviations from the surface minimum):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# Compute TS\n", "TS = stat_surface[\"stat_scan\"] - result.total_stat" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "gaussian_sigmas = np.sqrt(TS.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, as explained before, $1\\sigma$ contour obtained this way will not contain 68% of the probability, but rather " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "# p_value = 1 - st.chi2(df=1).cdf(TS)\n", "# gaussian_sigmas = st.norm.isf(p_value / 2).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the surface values together with contours:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# We choose to plot 1 and 2 sigma confidence contours\n", "levels = [1, 2]\n", "\n", "contours = plt.contour(gaussian_sigmas, levels=levels, colors=\"white\")\n", "plt.clabel(contours, fmt=\"%.0f$\\,\\sigma$\", inline=3, fontsize=15)\n", "\n", "im = plt.imshow(\n", " gaussian_sigmas,\n", " extent=[0, len(x_values) - 1, 0, len(y_values) - 1],\n", " origin=\"lower\",\n", ")\n", "fig.colorbar(im)\n", "\n", "plt.xticks(range(len(x_values)), np.around(x_values, decimals=2), rotation=45)\n", "plt.yticks(range(len(y_values)), np.around(y_values, decimals=2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, if computed with `reoptimize=True`, this plot would be completely consistent with the third panel of the plot produced with `Fit.minos_contour` (try!)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, it is always remember that confidence contours are approximations. In particular, when the parameter range boundaries are close to the contours lines, it is expected that the statistical meaning of the countours is not well defined. That's why we advise to always choose a parameter space that com contain the contours you're interested in." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }