{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/me-manu/gammaALPs/blob/master/docs/tutorials/mixing_HelicalTangled_jet.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Mixing in the AGN jet with helical and tangled component \n", "\n", "This tutorial demonstrates the basic usage of the `JetHelicalTangled` magnetic field class, for a blazar jet magnetic field comprised of a helical and a tangled component. Values used for the jet properties come from the best fit of the Potter & Cotter model (Potter & Cotter 2015). The model in the case of ALP mixing is discussed in Davies et al. (2021)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you haven't installed `gammaALPs` already, you can do so using `pip`. Just uncomment the line below:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#!pip install gammaALPs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start with importing the necessary modules and classes:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from gammaALPs.core import Source, ALP, ModuleList\n", "from gammaALPs.base import environs, transfer\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from astropy import constants as c\n", "from matplotlib.patheffects import withStroke\n", "from astropy import units as u\n", "\n", "effect = dict(path_effects=[withStroke(foreground=\"w\", linewidth=2)]) # used for plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use Markarian 501 as the example source.\n", "In addition to the redshift and sky coordinates, we also provide \n", "the bulk Lorentz factor $\\Gamma_\\mathrm{L}$ which we assume for the jet through the `bLorentz` key word. \n", "This will be used later in the `JetHelicalTangled` class. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "src = Source(z=0.034 , ra='16h53m52.2s', dec='+39d45m37s', bLorentz=9.) # Mrk501" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set up the module list with arbitrary ALP parameters. The energy range roughly corresponds to CTA energies." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "EGeV = np.logspace(0.,5.,2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use an unpolarised initial beam." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "pin = np.diag((1.,1.,0.)) * 0.5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "ml = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Add the jet module. We will ignore any other magnetic fields. Here we use a field with 70% magnetic energy density in the tangled component, and a helical component which is a purely toroidal field. Values come from Potter & Cotter best fit. For the tangled field coherence length, we use a uniform distribution between 0.1 and 1. times the jet width at each point. This is chosen with the `l_tcor='jetwidth'` and `jwf_dist = 'Uniform'` options. `l_tcor` can also be given as a constant in parsecs, or the keyword `'jetdom'` can be used to used the jet field domains as the tangled domains." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m jet.py:\u001b[0;35m 569\u001b[0;0m --- \u001b[1;31mWARNING\u001b[1;0m: Not resolving tangled field: min z step is 0.009857915102843562pc but min tangled length is 0.0011253320407637601 pc\n", "\u001b[0;36m jet.py:\u001b[0;35m 572\u001b[0;0m --- \u001b[1;31mWARNING\u001b[1;0m: # of z doms is 399 but # tangled doms is 161\n", "\u001b[0;36m jet.py:\u001b[0;35m 585\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: rerunning with 641 domains. new min z step is 0.0002813330101908984 pc\n", "\u001b[0;36menvirons.py:\u001b[0;35m1001\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Using inputted chi\n", "\u001b[0;36menvirons.py:\u001b[0;35m1008\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Using inputted chi\n" ] } ], "source": [ "ml.add_propagation(\"JetHelicalTangled\", \n", " 0, # position of module counted from the source. \n", " ndom=400,\n", " ft=0.7, # fraction of magnetic field energy density in tangled field \n", " Bt_exp=-1., # exponent of the transverse component of the helical field\n", " r_T=0.3, # radius at which helical field becomes toroidal in pc\n", " r0=0.3, # radius where B field is equal to b0 in pc\n", " B0=0.8, # Bfield strength in G\n", " n0=1.e4, # electron density at r0 in cm**-3\n", " rjet=98.3e+3, # jet length in pc\n", " rvhe=0.3, # distance of gamma-ray emission region from BH in pc\n", " alpha=1.68, # power-law index of electron energy distribution function\n", " l_tcor='jetwidth', # tangled field coherence average length in pc if a constant, or keyword\n", " #jwf = 1., # jet width factor used when calculating l_tcor = jwf*jetwidth\n", " jwf_dist='Uniform' # type of distribution for jet width factors (jwf) \n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default number of log-spaced field domains is `ndom=400` (this is enough to resolve the field for ALPs). In this case, however, this was not enough to resolve the tangled field. Therefore the number of domains was increased until the resolution was right and the module was re-run with 641 field domains, making sure that the edges line up with the 161 tangled component domains." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Peek at the electron density and the magnetic field" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The overall shape of the magnetic field strength in the jet comes from the Potter & Cotter model" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Transverse B field [$\\\\mu$G]')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(ml.modules[\"JetHelicalTangled\"].r, ml.modules[\"JetHelicalTangled\"].B)\n", "plt.grid(True)\n", "plt.xlabel('Distance from BH [pc]')\n", "plt.ylabel('Transverse B field [$\\mu$G]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The electron density used to propagate the ALP-photon beam is not the actual electron density, but rather the effective electron density of a cold plasma that would give the save effective photon mass as the non-thermal plasma of the jet. That is why it appears lower here than the actual electron density inputted." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Effective Electron dentity [cm$^{-3}$]')" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(ml.modules[\"JetHelicalTangled\"].r, ml.modules[\"JetHelicalTangled\"].nel)\n", "plt.grid(True)\n", "plt.ylabel('Effective Electron dentity [cm$^{-3}$]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the photon-ALP mixing probability\n", "\n", "Now we compute the mixing probability and plot the output. First we chance the ALP parameters:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "ml.alp.m = 40.\n", "ml.alp.g = 0.6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then run the calculation to compute the mixing probabilities into the different photon polarzation states and the ALP state ($P_x, P_y$, and $P_a$)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: \n", "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:799: UserWarning: Not all values of linear polarization are real values!\n", " warnings.warn(\"Not all values of linear polarization are real values!\")\n", "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:802: UserWarning: Not all values of circular polarization are real values!\n", " warnings.warn(\"Not all values of circular polarization are real values!\")\n" ] } ], "source": [ "px, py, pa = ml.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the output. Note that we access the module list by the index (an integer), rather then the name, simply for brevity. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1, 2000)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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CiA1SqhnsvZQFuVyO8Z39m3Susiolpn5zGgUVcrTxc8FfiwYb5DU2hw6Bbjj00jDd7etZZXj4ixM4l1KM1MJKhHk747vj9xHi5YTRsYGtsmpx6/uJHhQsCxQUcBeadGvQt99+i5EjR6Jbt25YuXKltYdDCLFBSjWDl3dfxRt/3IFS3bS/qx/tv420Iin83BzwzYy4FglqjOkc4oEh7bn6WxuPJOHPq9lY/fdtLPzpEqZ8dQrqFirI2pIosCEPhMWLF6O4uBi7du0yqKdDCCEA11IhvoMfBrf1blKOTblMib2XsgAAqyd3QVt/N0sNsVEWDedKUOy6kInFOy7r7r+WVYafzqZZaVTNhwIbQgghBFxLhS1z+uCrJ7o0aVfUjnPpkCrUaOfvihExTVvSsoRekd6Y0C1Yd1ss4GNER25c2t1arQnl2BBCCCEWwrIsfjqbDgB4ZlBUvQ0tW9KqiZ0AAFcySvHf2b3g7eKA3u8fxI3scqQVVSLUyxllVUp4u4itPNKmo8CGEEJIi1KqGeRXyBHo7tisXbSt4XZuBVKLpHAU8fVmSazNy0WML57UL1fRP9oHJ5IK8de1HGQUV2H7OS4gG9LeD6891BEdAy27W6mlUGBDCCGkxeSWyTD1m9NIL5YixNMJ387shdhg2/gArVKoMe7zY2AYFr/MjWtUS4UrGaUAgJ7hXnBxsO2P2Ie6BOFEUiE+3n9H7/5jdwtw7G4BEt8YCR9XByuNrvEox4YQQkiL+Xj/baQXSwEAWaVVePHnKzbTL40Fi9QiKdJLqhq92fRaVhkAoEuohwVH1jzGdQ6s9/GP9t9uoZFYFgU2hBBCWkSlXIW/r3MtR76d2QtiIR+3cspxK6fCyiPjOAgF2D2vP7bN6t7o5GFdYBNi+4GNl4sYrz3UETweEBvkjjvvjUXqh+Px/uTOALhdVKeTi6w8SvNRYEMIIaRFHLiZhyqlGpE+zhgZ44/BbbnecSeTCq08Mo6Az0OvSG/0DPNoVO6PQsXgtiZI6xriaeHRNY+5Q9rg7Gsj8PvCgbomyk/1jcC0XmEAuNo39oYCG2Jxs2fPBo/HM7iMHTvW2kMzkJqaCh6Ph8uXL5v8nGHDhmHJkiUmHaf92fl8PgICAvD4448jLa311Y0gxBR7L3O1XSZ2DwGPxwURAHAxvcSaw7KYQ7fzoVAz8HERI8y7eVsnWJK/myOEtfpXLRzeFnwecPxeIe7mccFaVmkVRn92FM9tuwDGhgv7UWBDmsXYsWORk5Ojd9m+fbu1h9XinnvuOeTk5CArKwu//fYbMjIy8J///MfawyKkxRVJ5Lq+RY9053YL9Qz3BGA7gY1KzeCvqzlIuFkAlZkf3BK5Cu/+eRMA8FivUJvZ5t1YYd7OGNOJy8H574kUAMAH+27hbp4EB27m6YJUW0SBDWkWDg4OCAwM1Lt4eXnpHufxePjmm2/w8MMPw9nZGTExMTh9+jSSkpIwbNgwuLi4oH///khOTtY9Jzk5GZMmTUJAQABcXV3Ru3dvHDx4UPf47du34ezsjJ9++kl336+//goXFxdcu3bN5LHfvHkTDz30EFxdXREQEIAZM2agsJD7gzx79mwcPXoUn3/+uW42JjU1tc5zOTs7IzAwEEFBQejXrx8WLFiAixcv6h5Xq9V45plnEBUVBScnJ3To0AGff/653jmOHDmCPn36wMXFBZ6enhg4cKDerM8ff/yBuLg4ODo6Ijo6Gu+88w5UKpXJPy8hLeHInQKoGRadgt0R7cftN+oa6gkBn4e8cjnyymVWHiGgUDNY8NNFvPjrTShUjMnPyyiWYuKXJ5BVWoUQTycsHtGuGUfZcp4eFAWAK+L38s9X8NfVHN1jr++5jpyyKmsNrV4U2NijykpAKgUEAu4ilXL31Xep+UGnUnH3VVUZnrf2pRm9++67mDlzJi5fvoyOHTti+vTpeP7557FixQpcuHABALBw4ULd8RKJBA899BAOHjyIS5cuYcyYMZgwYQLS07naCx07dsSnn36K+fPnIy0tDdnZ2XjuuefwwQcfoEuXLiaNKScnB0OHDkX37t1x4cIF7N+/H3l5eZg6dSoA4PPPP0f//v11MzE5OTkICwsz6dzFxcX4+eef0bdvX919DMMgNDQUu3btws2bN7Fy5Uq89tpr2LVrFwBApVLhkUcewdChQ3H16lWcPn0ac+fO1X0bTEhIwH/+8x8sWrQIN2/exDfffIOtW7fi/fffN2lMhLSU4/cKAADDOvjp7nMSC9DOnwtyrmaWWWVcNfF5PPSN8kavcA+Yk2LzxaF7uF9QiQB3B3w5vQecxba9zdtUvSK80DuS+0L6c2ImAC7JuK2/K6qUagz48JA1h1c3llhNWVkZC4AtKyszeKyqqoq9efMmW1VVZfhEru2leZddu6qfv2sXd9/Qofrn9fU1fF4jzJo1ixUIBKyLi4veZdWqVTV+BLBvvPGG7vbp06dZAOzmzZt1923fvp11dHSs97ViY2PZL774Qu++8ePHs4MHD2ZHjBjBjho1ilUqlaxKpTL6/JSUFBYAe+nSJZZlWfbNN99kR48erXdMRkYGC4C9c+cOy7IsO3ToUHbx4sUNvg9Dhw5lRSIR6+Liwjo7O7MA2Pbt27MpKSn1Pm/+/PnslClTWJZl2aKiIhYAe+TIEaPHDh48mP3ggw/07vvhhx/YoKAgo8fX+3vVBBUVFWxFRYVFz0kM2fP73Of9A2zEK3+yp5IK9e5/cddlNuKVP9k1/9yx0sgMmfs+D1j9Lxvxyp/s4dt5zTgq68gtq2Lj3uX+7Tqt3M+eTi5k917KZCNe+ZONeOVPNrVQ0qjzZmVl1fn511StI6wkNic+Ph5fffWV3n21m0927dpVdz0gIAAA9GZWAgICIJPJUF5eDnd3d1RWVuKdd97Bn3/+iezsbKhUKlRVVelmbLT++9//on379uDz+bh+/bpZa92JiYk4fPgwXF0NS3MlJyejffv2Jp8LAJ566im8/vrrAIC8vDx88MEHGD16NBITE+HmxjXG+/rrr/Hdd98hLS0NVVVVUCgU6N69OwDuPZs9ezbGjBmDUaNGYeTIkZg6dSqCgoJ04z1//rzeDI1arYZMJoNUKoWzs7NZ4yWkOZRUKpBXLgdgWN+lS4gHdidm4nqW9WdsGqNIIkdWKTf73Tuy9TXYDXB3xIU3RqJUqoCDUAAnsQAMw+qaaR67V4gZPi7WHWQtFNjYI4nE/Oc41KgeOXkydw5+rZXIenJFzOXi4oK2bdvWe4xIJNJd1wYfxu5jGG6t++WXX0ZCQgI+/fRTtG3bFk5OTnjsscegUCj0znvlyhVUVlaCz+cjNzdXFzSZgmEYTJgwAR999JHBY9pgwhweHh6696Ft27bYvHkzgoKCsHPnTjz77LPYtWsXli5dijVr1qB///5wc3PDJ598grNnz+rOsWXLFixatAj79+/Hzp078cYbb+DAgQPo168fGIbBO++8g0cffdTgtR0dHc0eLyHNIamA+5sV4ukE11rVeDtr6r1cyyoDy7J2l3R7N4/72cK8nWy+0nBTeDpX95Di83l4cVR7rDlwFz+eTsN/+obb1L9b6/1XaM1cXAC1GtAmxHbpwuXamEoo5C7GzmvDjh8/jtmzZ2Py5MkAuJyb2om7xcXFmD17Nl5//XXk5ubiqaeewvnz5+HkZNrWy549e+KXX35BZGQkhMbeIwBisRhqtbpRP4NA8+9UpclvOn78OAYMGID58+frjqmZMK3Vo0cP9OjRAytWrED//v3x008/oV+/fujZsyfu3LnTYBBJiDVptwu3CzCcCY0NcgefBxRUyJFXLkegh/UCcplSjckbT4Fh1Pjf7B4mtVS4l8/9bO393Zp3cDbm8V5hWHPgLu7kVWD57qv45PFu1h6SDiUP2zOVSj8p2IbI5XLk5ubqXbQ7ixqrbdu2+PXXX3H58mVcuXIF06dP183maM2bNw9hYWF44403sHbtWrAsi+XLl5v8GgsWLEBxcTGefPJJnDt3Dvfv38c///yDp59+WhfMREZG4uzZs0hNTUVhYaHBGGqSSqW6n//KlSuYP38+HB0dMXr0aN3PdOHCBSQkJODu3bt48803cf78ed3zU1JSsGLFCpw+fRppaWn4559/cPfuXcTExAAAVq5ciW3btuHtt9/GjRs3cOvWLd2sDiG24p5mVkObKFyTk1iA9gFcUHDNystRDMviVk457uRVwtTd3tVB24MV2AR6OOLJPuEAuMTi5IJGrCQ0Ewps7BWfD3TqxF1qLynZgP379yMoKEjvMmjQoCad87PPPoOXlxcGDBiACRMmYMyYMejZs6fu8W3btmHfvn344YcfIBQK4ezsjP/973/YvHkz9u3bZ/Sc2qBEOzsTHByMkydPQq1WY8yYMejcuTMWL14MDw8P8DXv80svvQSBQIDY2Fj4+fkZ5PjU9O233+p+/vj4eBQUFGDfvn3o0KEDAC4Qe/TRRzFt2jT07dsXRUVFerM3zs7OuH37NqZMmYL27dtj7ty5WLhwIZ5//nkAwJgxY/Dnn3/iwIED6N27N/r164e1a9ciIiKiCe80IZaVlK8NbIx/+NdcjrImB6EAPzzTB5umdzG5pYJ2Kaq9kdmo1m75mA6666v+uGnFkejjsayNdB97AJWXl8PDwwNlZWVwd9fvbiuTyZCSkoKoqCjKlWgi7UyLwMhy3ZkzZ9C/f38UFBTA19e3pYfW4prr90qiyfsylnRNLMde3+c+7x9EfoUce+YPQI9wL4PHvz+Vird+v4H4Dn7YMqePFUaoz9T3mWVZ9Hj3AEqlSvz5f4N0AdqDJKWwEvGfHgEAXFk5Gh7OovqfoJGdnY2QkBCjn39NZXtf9QlpASqVCklJSfjkk0/QrVu3ByKoIcQayqRK5FdwO6LaGlmKAmrO2JTbTKdvU2SVVqFUqoSQzzOaP/QgiPJ1QbQvl59pKxWkKbCxVwwDZGdzl3pyPIhx169fR9euXZGTk4Nt27ZZeziEtFpJBVwOSpCHI9wcjX+b1yYQF0rkum3h1qBSMzh0Ow9H7xWZ1FLhSga3dNYuwE3XQPJB1DOCm4W7ZCOBDe2KslcsywU1AGDGdmbC6d69O6RSqbWHQUirp81BqWu2BuASiNv6u+JungQ3c8qstjNKoWbw9Fau6vm55Q3nBB66nQ8A6B/t06zjsnXdwjyxOzETl22gejRAMzaEEEKa0Z1czXboBnYNaR/X7qCyBj6Ph66hHugU5NZgSwWGYXHodh4AYFTsg/3lspum6OK1zFIUSuSQKRtXDsNSaMaGEEJIs7mZUw4AiAmqP0GU2zGVo5vhsQZHkQC/LxykSx6uT0pRJUqkSjiK+OgVaZgQ/SBpH+AGAZ+HEqkSvd47iGhfF+ya1x++rg4NP7kZ0IyNBU2ePBleXl547LHHLHZOe0qkI7aPfp9IS2I1dWEALo+mPtrt0kmagne2TtsCIibIHSLBg/1R6igSIMK7un3L/cJKfHv8vtXG82D/a1jYokWLLJaIqm0tQHkgxJK0v081W1cQ0lyySqtQIVNBJODVm2MDAO0DuaWo27kVUKhsf0PEjWwuYOsc/OBt8TYmJlg/cN11PsNqS1K0FGVB8fHxOHLkiEXOJRAI4Onpifx8LjnN2dlZvxdHzZL+Mpl5LRUeMPXVsXlQsCwLqVSK/Px8eHp6PtDvBWk5t3K42Zc2fq4QN1DwLtrXBd4uYhRXKnAtqxRxES3fUFKmVOOp785CrVbju6e61ttSQTtj0znEsjVY7NWzg6JQKlXgsbhQfJpwF1mlVej45n4sGdkOC+PbQtiCs1pWD2wqKirw5ptvYs+ePcjPz0ePHj3w+eefo3fv3hZ7jWPHjuGTTz5BYmIicnJysGfPHjzyyCMGx23cuBGffPIJcnJy0KlTJ6xbtw6DBw+22DjMFRgYCAC64EYPwwDaFgWpqTZZfdhWaKsL8+k9gqenp+73ipDmZuoyFMA1ve0d6YWEG3k4m1JslcCGYVkkppVortd9HMuyNQIbmrEBgB7hXvjfs/0AAGoGeOnnKwCAdQfvAQCWjGzfYmOxemDz7LPP4vr16/jhhx8QHByMH3/8ESNHjsTNmzcREhJicPzJkyfRp08fg6n027dv1/lHu7KyEt26dcOcOXMwZcoUo+PYuXMnlixZgo0bN2LgwIH45ptvMG7cONy8eRPh4Vw/jLi4OMjlhjUW/vnnHwQHBzfmx68Xj8dDUFAQ/P39oVQq9R+USoHx47nrFy8Czs6GJyAAuH9/gOs4/iATiUQ0U0Na1C0TE4e1+kT5IOFGHs6nFAPDmnFgdRAL+PhmRhxkMlm9M0z3CytRLlNBLODX2SbiQfZYXChSCiXYcJhr6Pv3tdwHJ7CpqqrCL7/8gt9++w1DhgwBALz99tvYu3cvvvrqK7z33nt6xzMMgwULFqBdu3bYsWOH7o/03bt3ER8fj6VLlxpteDhu3DiMGzeu3rGsXbsWzzzzDJ599lkAwLp165CQkICvvvoKq1evBgAkJiY2+Wc2RiKRmD+boFTCNS2Ne75SabPNMG2BdilK9YC/R83581MuWMuwt/f5hmZWI9JTZNJOo84BXP2aC6nFKK+oAJ/XwJ7rZjAwwhVSKR8KWRUkdez5/udqJgCgR5g7FDIpFC05QDvxwsBQTOvujyGfncadvAqk5hbD11Wse7yqqqrZXtuqc/MqlQpqtdqgZ42TkxNOnDhhcDyfz8e+fftw6dIlzJw5EwzDIDk5GcOHD8fEiRPN6uJck0KhQGJioq7jstbo0aNx6tSpRp2zPhs2bEBsbKxFl9sIIcSWSBVqZJRwH17tA0ybLe0Q4AqRgIcKuRrZpbLmHF6THE8uBgAMadvyy2X2xNtFjA6af/uEWwUokSobeIZlWHXGxs3NDf3798e7776LmJgYBAQEYPv27Th79izatWtn9DnBwcE4dOgQhgwZgunTp+P06dMYMWIEvv7660aPo7CwEGq1GgG1KvgGBAQgNzfX5POMGTMGFy9eRGVlJUJDQ7Fnzx6jwcuCBQuwYMECXRNMV1dX85va1fgm4+rqCjzgyyymsLfGgfaI3uOWYQ/v8930ErAA/NwcEBFgegAQ7euKO3kVyJGy6BjWsj+nmmFxLqUYVVUKxIV71Pk+38njlreHdAy2i38LaxraIQB38u5jdUISNhxNRcLSIQjycEJ5eXmzvabVsyl/+OEHsCyLkJAQODg4YP369Zg+fXq9uQDh4eHYtm0bdu7cCaFQiM2bN+vvGGqk2udgWdas8yYkJKCgoABSqRSZmZk0I0MIeWClFHAf/u0a2OZdm3ZbeHJ+yxfqk6vUePLbM3j6xyuQ17HlvFSqQFElt/gU7UdfKBvy7KAohHk7AQDKZSrM/9/FZn9Nqwc2bdq0wdGjRyGRSJCRkYFz585BqVQiKiqqzufk5eVh7ty5mDBhAqRSKZYuXdqkMfj6+kIgEBjMzuTn5xvM4tgMHg+IjeUuVliHJoSQ+qQVc/lAET7mbWwI1XwIZpU2Xw5GXXjgoZ2/K9r4Otf5ZzVZE7AFujvCxcHq+29snr+7IxKWDMGqSZ0AAJfSS1Fc2bxZSVYPbLRcXFwQFBSEkpISJCQkYNKkSUaPKywsxIgRIxATE4Nff/0Vhw4dwq5du/DSSy81+rXFYjHi4uJw4MABvfsPHDiAAQMGNPq8zcrZGbhxg7vQjihCiI3J0AQ2Yd7m/X0KcudyLvPKWz7HxkkswIFlQ/HbvN5wEhlfNbhfwM0ktfGn2RpTOYuFmNk/Ujcb19xdwK0ebiYkJIBlWXTo0AFJSUl4+eWX0aFDB8yZM8fgWIZhMHbsWEREROiWoWJiYnDw4EHEx8cjJCTE6OyNRCJBUlKS7nZKSgouX74Mb29v3VbuZcuWYcaMGejVqxf69++PTZs2IT09HfPmzWu+H54QQlqptCJuZiPC27wAQNvZO7fMNpOH7xdyP1e0L+XWmKtnuCeS8iU4c78IMT08m+11rB7YlJWVYcWKFcjMzIS3tzemTJmC999/32jJdz6fj9WrV2Pw4MEQi6u3jXXp0gUHDx6Ej4/x1vEXLlxAfHy87vayZcsAALNmzcLWrVsBANOmTUNRURFWrVqFnJwcdO7cGfv27UNERIQFf1pCCHkwpBdzS0nhZs7YBOhmbAxrhtkC7YwN5deYb2h7f+y6kIl/b+djTmsObKZOnYqpU6eafPyoUaOM3t+9e/c6nzNs2DCTmv/Nnz8f8+fPN3ksViWVAtrk5PPnaTmKEGIzKuUqFEq4wCTczBwb7YxNXrkMDMOCX0ctmeYgU6rx7PcXoFKr8OXUzkZbKmhzbNr40YyNuQa394WQz8P9gkpd4NscrB7YkEZiWeDmzerrhBBiIzJKuPwaDycRPJzMa7jq5+oAPg9QMSwKK+Xwd3Ns+EkWwrAsTiQVaq4bPq5SM7olNpqxMZ+7owj92/jg+L1CJNwqaLbXocDGXjk6AocPV18nhBAbkV7EBTbmLkMBgFDAh6+rA/Ir5Mgvb9nARizgY9207nW2VEgrlkKpZuEo4iPYw6nFxtWajIoNwPF7hdh8KqPZXsNmdkURMwkEwLBh3IX6/xBCbEh6ceMDG4Ar6gcABZKWzbMRCvh4pEcIHu4SAKGRJbALqVzF4a4hni26RNaajIxp/hIqFNgQQgixqExNKwVtTRpz6QKbCttKID6bwgU2faKolUJjBXs6oVuYZ7O+BgU29kqpBDZs4C61O38TQoiFsCyLv67m4NOEO7ida1oZ/Iymzti4WiewUTMsrmSU4lp2OdRGkmyuZJQCAHpFerXouFqbj6d0xfjO/s12fgps7JVCASxcyF0U1FuWENI8dl3IwIKfLuLLw0l46PPj2HW+4dwI7VJUmFfjAhtfK83YyFVqTNpwEk/+95JBSwWWZXXVkKN8KXG4KToEuuHNccb7QVoCBTaEEEKMYlkWXxziipsGuDuAYYHX9lzD3byKep+j3RXV1BmbwhbOseGBhxBPJwR7OBi0VCiuVECmZMDjVW9JJ7aJAhtCCCFG3cwpR2ZJFRxFfBx5KR4jY/yhYlh8d/x+nc8pkMh1AUCwp33l2DiJBTj56nD883/9DFoqZJdylZD9XB3gIKQNG7aMAhtCCCFGXUwvBQD0jfKBk1iA5wZHAwD2X881moMCABmawmvBHk5Gt0ybwlq7ouqjXYZqbLBGWg4FNoQQQoy6kVUGAOgS4gEAiIvwgrujEOUyFa5mlhp9Toqml1Jjl6EA29wVpQ1sQrwosLF1FNgQQggx6no2F9h0DnEHwNV5GdjWFwBw4l6h0ecka3opaTs5N4Y2sKmQqSBTqht9HnPJlGo8t+0CFu26bpA8rP25mhKwkZZBgQ0hhBADDMPibi73YR4b5KG7v6+mhsv5tBKjz0vO557TpgktB9wchHDQLGO15KwNw7I4cDMPh+4W6S21MQyLfddyAABdQzzqejqxEdRSgRBCiIECiRwKNQMBn4dgz+pdQL0iucDmUlqJ0SaVSZqZjTZNmLHh8Xjwc3NAZkkVCiRyhLXQLIlIwMfqR7tALpNDJKj+udYcuINSqRIuYgGGdvBrkbGQxqPAhhBCiAFtTkmguyOEgurJ/Y6BbnAWC1AhV+FufgU6BrrrHlOqGV2fqKYsRQGoDmxacMZGJODjyT7hkEgkuvtYlsXeS9kAgMk9Q+Aspo9NW0dLUYQQQgxklWh3AenXbBEK+OgR7gkAuJCqvxyVVlQJFcPCWSxAoHvTar34Wqn6cG03c8qRVcpteX/9oVirjoWYhgIbQgghBnS7gIxsb46L4JajEmvl2STlczui2vi5gle7wp2ZrLEzimFY3M2rQFJBJRiWy7HZczELADCknR+cxFS/xh7QnBohhBAD2fVsb+4VwfVKupBWrHe/JXZEaVmj+rBMpcboz44BAM4tHwS2SomfzqUDAJ7oE9Zi4yBNQ4GNPfP1tfYICCGtVPVSlGFg0z3cEzweV4wvv1wGf82ykyV2RGlZq5aNt4sYrGa2ZtupVEgVanQMdEN8h+Zr2kgsiwIbe+XiAhQUWHsUhJBWqr6lKHdHEToEuOF2bgUS00owrksQgOoZmzZ+FpixsUL1YWexEBffHAWJRAKpQo3/nkwBALwwrE2Tl9ZIy6EcG0IIIQa0MzahdVTa7RWpXY7i8mxYlkVyAZdjY5GlKCtXH957JRclUiUifZzxcNdgq4yBNA4FNoQQQvSUy5SokKsA1N0bqbemns3hO/lgWRY5ZTJI5CoI+DyE+zS97oxfjV1R2qWhlnQurRQAMK13OAR8mq2xJ7QUZa+qqoBx47jrf/8NOFH/EkKIZWhna7ycRXXWbRne0R9OIgHuF1QiMa0EJVIlAKCdv6tFul9rZ2zkKgYVchXcHUVNPmdDZEo1XvnlKlRKFa5nlQMAuod5NvvrEsuiwMZeMQxw9Gj1dUIIsRBtYFNfw0c3RxHGdw3C7sRM7DifocvF6RRsmZYDjiIB3ByFqJCpUFAhb5HAhmFZ/HY5W+++TiHudRxNbBUtRdkrBwdg1y7u4uBg7dEQQlqR+hKHa3qiN7cF+o8r2Th+j9vM0CnYcoGAXwsX6RMJ+Hjz4Vg8Ecfl1IR6ObVIQEUsiwIbeyUUAo8/zl2ENPFGCLEcbQ2buvJrtOIivNA5xB1yFYOL6aUAqnNvLMFXsxyV34KBzTODohDgzr1uzXYRxH5QYGMD/m/7Rfx1NcfawyCEEABApokzNjweD88NjtbdDvF0QmcLLt0Ee3D1cTJLpBY7pykSNUHa4HZUK8we0Vd9G3D4dgFOpkkxulMARAK+bgdAvXUTVCpgzx7u+uTJNGtDCLGYhrZ61zShazDOpxbj8O0CvD2xk0XrvWjr4STlSxo40jIYhkVWaRXuF3CBVPsAtxZ5XWJZ9GloI1QMi5vZ5egY5IbJG05BKOBh+3P94OLA/RMVSeRYd/Aewr2dMWdgJIRyOTB1KvdkiYQCG0JIgyrlXCJupG/9lYGzTFyKAgA+n4f3HulikfHVpq2Hk9xCgY1Mpcbgjw/rbkc18D4R20SfhjbA302MQgWw9sBdzBoQgZs53DbDny9kYPbAKDAMi2mbzui+tfB4wLM9A6w5ZEKInSmTKvHQ+uPIKq3CK2M74oVhbYweJ1epdcm6DS1FNTddYFNQCZZlW6T6r6OQD5mKgYOAB3832phhj8zOsRk2bBi2bduGqqqq5hjPA+mLJ3sCAI7eLcCrv1zT3f/j2XSwLIsTSYV6U7G7EzNbfIyEEPv235MpupmYLw/dQ4VMafS4nFIZAMBRxIe3i7jFxmdMhI8LRAIeJHIVMoqb/zPHWSzEVzPiAADhPs7gU2E+u2R2YBMXF4fly5cjMDAQzz33HM6cOdMc43qgdArxgIuYK2hVM/s/KV+C/ddzcfhOPgBgbKdAAMDt3ApUaqqCEkKIKfZdq96gUKlQ42RSodHjai5DWbs/kljIR6ymLs6ljJIWec3UQq4tRLgJ+UXENpkd2KxZswZZWVnYtm0bCgoKMGTIEMTGxuLTTz9FXl5ec4zxgVB7WvjRHiEAgJ0XMvC7pmDUhG7BugDoVB1/lAghpLYiiRz3NLO+j/bk/racaCCwsfYylFYPTeXfS5qdSs1NOzse4W0bPz8xX6O2ewsEAkyaNAl79+5FVlYWpk+fjjfffBNhYWF45JFHcOjQIUuPs9VbOLwdVozrCLGAj9ce6oinB0UBAI7cKUBRpQJiIR8jYvwR5s31YPn+dKoVR0sIsSdXs8oAANG+Lojv4A8AupYBtZmzI6ol9Aj3BABcSm/+GRu5So2/r3MzW+38mt7vilhHk5KHz507hy1btmD79u3w9/fH7NmzkZOTgwkTJuCFF17Ap59+aqlxPhCeH9oGswdG6vqs9InyxrmUYgBA70gvOIoEGNreD7dzK1BcqbDmUAkhduRqBhfYdAvzRKymMvDt3HKoGdagwaOtzdj0DOe6iN/ILodMqYajqOl9qOoiV6pRXMnlHnUMbHqHcmIdZs/Y5OfnY82aNejcuTMGDx6MgoIC7NixA6mpqXjnnXewadMm/Pbbb/j666+bY7ytXs3mcbMHRAIARAIelo3qAACY0T8CAJDeAol0hJDW4XYuNzvTKdgdUT4ucBYLIFMyuF9guI1aO2NjylbvlhDq5QRfVzFUDIsb2WXN+lqFEu4Lo4AHhNNSlN0ye8YmNDQUbdq0wdNPP43Zs2fDz8/P4Jg+ffqgd+/eFhngg+yhLkH48/8GwdNZhFAvblo0xNMJET7OyM+RWXl0hBB7kaJJiG3j7wo+n4f2AW64nFGKe/kStKtVhC67zLZmbHg8HrqFeuLf2/m4kV2OuAjLtWyoLVuzIyzCx9kiHcqJdZgd2Pz7778YPHhwvce4u7vj8OHD9R5DTNM5RL9TLo/Hw+jYAPyYU2ylERFC7AnDsLrAJlpTcC7K1wWXM0qRWlRpcKx2u3d9nb1bmjbfJ6+8eb/Qad+PMC/HZn0d0rzMXop66623UFpaanB/eXk5hg8fbokxkQbMG2q8sBYhhNSWUy6DXMVAJODpZmEifbgAR7u1WatAIodCzYDPAwLcbefD3V8zlrzy5m2GmaYJbPxcxbrWNsT+mB3YHD16FAqFYeKqTCbD8ePHLTIoUj8fVwcsGdnO2sMghNiBlALNLIS3M4QC7k9+pC+3tJ1apN9cUttsMsjDCSKB7fRIDtAFNs07Y5Osea92X8pFlZJp1tcizcfkpairV68CAFiWxc2bN5Gbm6t7TK1WY//+/QgJCbH8CIlR4zoH6q5nFEnx4W93MKFrEMZ2DrLiqAghtiarlAtWwryqty/XNWOTqUkctqVlKAAIcOdaGzR3YHO/sGV6UpHmZXJg0717d/B4PPB4PKNLTk5OTvjiiy8sOjhSt/Bwfwz56BDSi6XAxnMAgL+u5uCfpUOoIy0hRCenjAsGgj2rl5a0gU1+hRxShQrOYu6jINPGatho+Wl6NhVUNN9SlELF6No2HFzUD85iSh62VyYHNikpKWBZFtHR0Th37pzebiixWAx/f38IBPSL0JKGtPfFj2fS9e47c78IB27moUiiwOvjYwxqVBBCHizaZOAgj+pgxcNZBC9nEUqkSqQWSnW1baoDG9sqTufnygU2JVIllGrG4stkSjWDqd+chpph4e4oRICbdXtkkaYxObCJiODqpzAMrTvailGxgQaBzcrfbuiu94v2xuhOgbWfRgh5gGi3bwd66CcDR/i4oERairSiyhqBDbdsZWszNl7OYgj4PKgZFsWVCosnNp+4V4jLGaUAgPFdg6zeI4s0jUmBze+//45x48ZBJBLh999/r/fYiRMnWmRgpAEyGYa+Ph8XJHLc/mQDrhbK8fH+O3qHzP0hEQCwdU5vDNOUUSeEPFh0S1Ee+sGKdst3So0t37bWTkGLz+fB20WMggo5CirkFg9sLmraNbg6CCAS8PHhP0lYNjzaoq9BWo5Jgc0jjzyC3Nxc+Pv745FHHqnzOB6PB7Vabamxkfqo1cDu3fAFMGj3diiEdSe9zd5yHm9PiMXsgVEtNz5CiE3I1QQ2QZ61Z2y45aa0Qm6WhmFYZGraKYTZ2FIUAPi6OqCgQo5CieXzbM7cLwIAvDS6I97+g5v1XjSM/l7aK5MCm5rLT7QUZSPEYuDLL3XX4zv4Y8nIdricUYrPpnbHc9su4EJaddO4DUeSKbAh5AFTLlNCIlcBAIJqLUXpdkZpZmwKJXIoVFwNm9rLVrbA15XLe7F0AnFJpQKJmr+VQzv4YoGkDRQKJUQCWo6yV01qgkmsSCQCFizQ3eQBWDKyve725tm9cTunHAo1gxmbz6GgQo4yqRIeziIrDJYQYg3axGEPJ5Fu55NWpK9+YJNhozVstLQ7o7T9nCzlyN18MCzQMdANUb6ueHlMR0gktO3bnpkU2Kxfv97kEy5atKjRgyGW4+EkQt9oHwDcN51CiQIZJVJ4OHs08ExCSGuRo0kcrj1bAwCRmqWovHJuy7e2OF2UJuCxNdqdUZZeijqXwrWnoTzE1sOkwOazzz4z6WQ8Ho8Cm5aiVgPaSs+DBwP1bLUP93ZGoUSBtCKpQe8pQkjrVV3DxjAZ2NNZDE9nEUqlSqQVSZGs6fTdxs82AxvfZgps0ou5map2/q5gWRZVSjWkCjWcRLY3a0VMY1Jgk5KS0tzjaBUmT56MI0eOYMSIEdi9e3fzvphMBsTHc9clEsCl7j9GbfxccTG9FF8eTsL4rlSZmJAHRU5p3TM2ALflu1Sz5fu+ZsYm2s+1xcZnDl9NbRlLBzY1ixJWKdWIXZkAADi3fBCo1Kl9opDUghYtWoRt27ZZexgGhrTniineyinHhVTqCk7Ig0I7Y1NXYKNdjrpfWKmbsYm29RmbCsvl2KgZFtnanWDetrcTjDSOSTM2y5Ytw7vvvgsXFxcsW7as3mPXrl1rkYHZo/j4eBw5csTawzDwcNcg/N/2SwCAp747i1urxoJPFYkJafVyyw2rDtfUMdAdvyEbZ+4X6/pGdQi0zXkKXVsFC87Y5JXLoFSzEPJ5CHB3BJ8H3Fw1BhJJJS1F2TGT/uUuXboEpVKpu17X5fLly2YPQKVS4Y033kBUVBScnJwQHR2NVatWWXRb+bFjxzBhwgQEBweDx+Nh7969Ro/buHEjoqKi4OjoiLi4uFbTrZzH4+GN8TEAALmKwdWsskadJym/Atcb+VxCSMtraMamZ7gnAODY3QIwLHecv5vtbfUGoBtXcaUCcpVl6qVpl6GCPZ0g4HO9EJ3FQjiLBVR92I6ZNGNz+PBho9ct4aOPPsLXX3+N77//Hp06dcKFCxcwZ84ceHh4YPHixQbHnzx5En369IFIpL9t+fbt2/D09ERgoGELgcrKSnTr1g1z5szBlClTjI5j586dWLJkCTZu3IiBAwfim2++wbhx43Dz5k2Eh4cDAOLi4iCXG35b+OeffxAcHNyYH7/FPDs4Gu/9dQsA8MiGk7jxzhi4OJi+2/9kUiGe+u4sxEI+zq4YAS8X6qVCiK3TFuerqy5Nl1APXasCAOgZ4dViYzOXl7MIjiI+ZEoGuWUyRPg0fclM20IizNu2Ki2TpmlSHZuMjAzweDyEhoY2+hynT5/GpEmTMH78eABAZGQktm/fjgsXLhgcyzAMFixYgHbt2mHHjh26ppt3795FfHw8li5diuXLlxs8b9y4cRg3bly941i7di2eeeYZPPvsswCAdevWISEhAV999RVWr14NAEhMTGz0z1kfiUQCPt/Mac/KSmhT/CQSCcCyDT7lka4B2Hs1DwAw6cvj2DO3l0nfSo4nFeGFHdcBcB1wL6fmo3eEp3njtSKpVGrtIbR69B63DGPv84FbBbibX4n/9AmBh1P1Fz6JXKUrzucqUNdZm6VvpCdO3ecK1A1r42nTNVyC3B2QUlSF5Jxi+Dg0/DevIcm5pQAAfxcRJBIJlGoGG4+lQalU4rn+tv1l1d5VVVU127nNXkRUqVR488034eHhgcjISERERMDDwwNvvPGGbrnKHIMGDcK///6Lu3fvAgCuXLmCEydO4KGHHjIcLJ+Pffv24dKlS5g5cyYYhkFycjKGDx+OiRMnGg1qTKFQKJCYmIjRo0fr3T969GicOnWqUeesz4YNGxAbG4vevXtb/Nz1eW9iR4yN5RKJkwqk2HAsrcHnsCyLj/5J1rvvfiF9iBFiC65nV2DpLzfx1fE0vL8/Se+xvHJudtndkVtaqcuy4dHwdxNjSFtvjOzo26zjbSrtklp2mWXybLI0BQxDNe0mlGoW355Mx9ZzOVAxTQ+ciHWYPWOzcOFC7NmzBx9//DH69+8PgJt1efvtt1FYWIivv/7arPO98sorKCsrQ8eOHSEQCKBWq/H+++/jySefNHp8cHAwDh06hCFDhmD69Ok4ffo0RowYYfbr1lRYWAi1Wo2AgAC9+wMCApCbm2vyecaMGYOLFy+isrISoaGh2LNnj9HgZcGCBViwYAHKy8vh4eEBV1dXuLqaucWyxkyLq6trvdu9a1o/vRfav/E3AODr42m4liPBnAFRGBkbYPT4/AoZUou5yLqtvyuS8iX4+VIunhna3ujxtszs95iYjd7jlqF9n/deu6+778DtAih53XTLxGXZ1fkj9f279GrrinOvGy7h26JwH1ecul+CwirGIr9rORXcl/E2gZ5wdXWFSKXGnIGRUCqVcHNxod/nZlReXt5s5zY7sNm+fTt27Niht7TTtWtXhIeH44knnjA7wNi5cyd+/PFH/PTTT+jUqRMuX76MJUuWIDg4GLNmzTL6nPDwcGzbtg1Dhw5FdHQ0Nm/ebJFEr9rnYFnWrPMmJCQ0eQzNTSzk49aqsYhZuR8AcDKpCBdSS+rcKZVWVL0GPX9YGyzbdQW3cytwK6ccMUHuLTp2Qoi+k8mFuutKNYtzqcUY04kLUrT5NZbuhG1NIZpCg9ot2k2lTR7W5tg4CAV4a0Inm16OIw0zeynK0dERkZGRBvdHRkZCLDY/ofTll1/Gq6++iieeeAJdunTBjBkzsHTpUl1eizF5eXmYO3cuJkyYAKlUiqVLl5r9ujX5+vpCIBAYzM7k5+cbzOK0Bk5iAbY/1093W65icDPHePS863wGAK5h3oiY6vfirKYbLiHEOvLLZcgorgKPB0zsxuWD1KxT1dCOKHsU4sUFIFkWCGyUakbXcsIWu5mTxjM7sFmwYAHeffddvd1Bcrkc77//PhYuXGj2AKRSqUHirEAgqHO7d2FhIUaMGIGYmBj8+uuvOHToEHbt2oWXXnrJ7NfWEovFiIuLw4EDB/TuP3DgAAYMGNDo89qy/m188Of/DdLdXvPPHYNjWJbF7ouZALjqxR5OIiwe0Q4AcC2r+aYRCSENu5jOJfx2CHBDfEcud+5caonu8dxy7kPbFjt1N5a2NURWSdMDm+zSKjAs4CDk62rkkNbBpKWoRx99VO/2wYMHERoaim7dugHgEn4VCgVGjBhh9gAmTJiA999/H+Hh4ejUqRMuXbqEtWvX4umnnzY4lmEYjB07FhEREdi5cyeEQiFiYmJw8OBBxMfHIyQkxOjsjUQiQVJSdWJdSkoKLl++DG9vb91W7mXLlmHGjBno1asX+vfvj02bNiE9PR3z5s0z+2eyF51DPPD1f3pi3o8XcSG1BGqGhaDGclRakVS32WpBfFsAQLsAV81jlS0+XkJag+QCCdYdvIfZAyIR14Tt1RfTSwFwW7R7hnPnuZVdDoWKgVjIb50zNtqlqDIZGIZtUqHRjOLqVgralAOpQqXXUoEybOyTSYGNh4d+48TatWDCwsIaPYAvvvgCb775JubPn4/8/HwEBwfj+eefx8qVKw2O5fP5WL16NQYPHqy37NWlSxccPHgQPj4+Rl/jwoULiNf2VQJ01ZNnzZqFrVu3AgCmTZuGoqIirFq1Cjk5OejcuTP27duHiIiIRv9s9mBkTABcxAJUyFW4m1ehlzejLeTXPcxT941GO2WrbRxHCDHP6n23cPBWPg7czMWtVWMbnR+YmMbNzsSFeyHc21nX0PJ2bjm6hnrqFZ9rLQI9uOrAChWDwkp5k4oJZuhq2NAyVGtjUmCzZcuWZhuAm5sb1q1bh3Xr1pl0/KhRo4ze37179zqfM2zYMLAm1HmZP38+5s+fb9I4rM7ZGcjPr77eSEIBH93DPbkk4rQSvcDmXl4FAOjdp/0jkF8hh0yphqOo7m2khBB9SjWDg7e4/7cyJYOiSoWuB5I55Co1rmVyXzziIrzA4/HQJcQDx+8V4kpmGToFeyBdk/gfaYFCdrZCJOAjwN0ROWUy5JTKmhbYaL6c1cyvcRIJkPjGSFRWUksFe0b/cvaKxwP8/LhLE3eExUV4AwD+vpajd/+9PG5nQDv/6glZL2cRXDQ1MTItsM5NyINEu8tQKym/cbtvrmeVQaFm4OMiRoSmkWW3UE8AwNWMUuSWy6BQMxAJeK1qxgaonoFq6s6ou5q/b5G+1YEfj8eDj6sDvF3E1FLBjjUqsNm9ezemTp2Kfv36oWfPnnoXYn9Ga2rYnE0p1vVgKalU4EQSt5W0Y1B1Uzwej6ebtbmRTX2jyINHoWKgVJvey+74vQIs330FmSVSJOVX6D2m7ajdkIxiKZ7cdAZv/H4bMqUa5zVJwtrZGgDoGsqlDFzNLEOapqFlmLezXt5ca6BLIG5CYMOyLC5ncO9h9zBPSwyL2BCzA5v169djzpw58Pf3x6VLl9CnTx/4+Pjg/v37DbYtIBYklwMLFnAXI/2rzNEp2B0eTiKoGVY3S3MyuRASuQohnk7oG6Wfu6TtJ3P0TkGTXpcQe1OlUCP+0yPo+8G/KDKhyzTDsFi84zJ2XcjEe3/eMpih0daaacg7f9zA6ftF2Hs1D2v/vY9zKdy27t6R3rpjumk+oO/lV+jKN7SmZSitYE2V4OxS0947YzJLqlAoUUAk4KFTcPVSu0LF4MtD9/DNiTSzgldiW8wObDZu3IhNmzbhyy+/hFgsxvLly3HgwAEsWrQIZWX0Db7FqFTAxo3cRaVq0ql4PB5iNXk0lzRbSG9p/jAOae9r8I1vZIw/AOBKZmmTXpcQe3MpvQRZpVUorlTgiAmBfWpRJYorFQCAE0mFuuUPJ01uWkFFw8GRVKHCsbvVhfh+upCNQ7e5PJ1B7apbIAS4OyLQ3REMC+y6wNWfqrmM3FoEezR9KepSRikAIDbIXS9PUMUw+PSfu/jiSCqUamqpYK/MDmzS09N1tV2cnJxQUcFNrc6YMQPbt2+37OhI3UQi4K23uEutTueNof0DeeY+903wVo5h4rBWV81afnJBpclT6YS0BtqdNABwt9aykjGpNcoiSOQq7L/BFQEd2JabBc03IbC5nFEKhZpBsIcjHulaXSSzQ4AbOga66R2rXY7SBlDa/6utSbhmKfxOXsPvf120X+B6hOtvtxfweXiidximdA+EsJUt4T1IzA5sAgMDUVTEVZ2NiIjAmTNnAHC1YUzZeUQsRCwG3n6buzSi4nNtPTTT2IlpJfjtcpbuG6GxwMbX1QG9I710xxPyoCiVVjf6vV9QicS0YpxKKqzzeG0jSi2FilveGNiW+yKRX9HwcsptzZeMTiEeeHlUG7Tzd4GzWIBVkzoZJLh2q5Uv0pQ6ObYqLtILQj4PKYWVuJnduEKhp5O5z7Ae4Z569zsIBfhwSle883AHiIW0t8Zemf0vN3z4cPzxxx8AgGeeeQZLly7FqFGjMG3aNEyePNniAyQto3OoB4R8HnLLZVi84zIAwM1RqAt4ausSwt3/45mGO4QT0lqU1Ahsjt8rwLRvzuCpzWfr3N2UV24YuLg5CnUBhylLUXc1MxMdA93g4STC7mfjcHnlaPSNNqzbNal7sG7puG+Ud6uqOqzl7ijCCM1y+Pp/75n9/LSiStzOrQCPBwxu52fp4REbYHYTzE2bNunaHcybNw/e3t44ceIEJkyY0Kqr9NochgFu3eKux8QA/KZ9u3B3FOGpvuH4/nR1oDKlZyiEAuPn1Sbc3cuTNLkCKCH2oqxKobsuU1Ynl55LKUZbI/ks2hmbrqEeuKqpO9M52AM+mto1xZWKBpvtape/tInAAj6vztmEUC9nfP5Edxy+XYCFw9ua86PZlcUj2iPhRh4O3clHpVwFFwfTP8o+P8gFQ4Pa+sLbpemz3cT2mP1pyOfzIRRW/xJNnToV69evx6JFixrVBJM0UlUV0Lkzd6myTD2ZJ/uG664/1Tccb0/sVOexE7tzTfeqlOo6G2gS0trUXIqqKaXQ+IxNvmbG5pHuIQhw54KZSd2D4aP5QFWqWVTI60/+1+6cCvI0bfbl4a7BWDO1G6J8W9+OKK2YIDeEeTtBoWJwxoyGvIlpxfj1UhZ4PODF0R0MHpcqVIh5cz96f3QcUoXakkMmLcjsGRsAKCkpwebNm3Hr1i3weDzExMRgzpw58Pb2bvjJxGZ1DHTHiI7+SCmsxGsPxdR7rEjAx7AOfjhypwCJaSXoHOJR7/GEtAYlUoXR+4skxu/P0+TQRPo6Y++CgUgtlKJftDd4PB5cxAJUKtQokijg7mh8AwDLsjV6PjkBoDxGgNvJObidH346m44FP13Es4Oi8fSgqAZnYL49lgIAmBoXVmf9miolBTT2zuwZm6NHjyIqKgrr169HSUkJiouLsX79ekRFReHo0aPNMUbSgjbP7o1DLw0zaWpXu5W0djVVQlor7YxN7aWgoso6AhvNUpS/myOCPJzQv42PbtnJ25X7EC6urDvPpkKu0s0cBLq3vnyZphiiyY+RKRl8eTgJC/53scHnXNWUqJgSF2r0cUehAMeXxyNhYV84UksFu2X2v9yCBQswdepUpKSk4Ndff8Wvv/6K+/fv44knnsCCBQuaY4zERoVr1vxTqdM3eUCUVXGBzZSe+h+MRUaCE5ZldTVsjPWD8nbh7qtrtgeoXobydBbBSUx92WoaEeOPx+JCdVveT98vqre2TYVMiWzN+9khwM3oMXw+V1k9xNMRfGqpYLfMDmySk5Px4osvQiCo/k8mEAiwbNkyJCcnW3RwxLZpZ2xO3CtEThn1jSKtn3bG5oWhbfDTc32xZXZvAECxkeCkvEoFNcMtHXm5GC41afNsiuuY7QGgW4ai2RpDIgEfnz7eDfuXDNEtK52sZ+u9trZPgLsDPJybXvuL2C6zA5uePXvilnY3Tg23bt2qt8M2aX36RHqjrb8rFGoGF9NKrT0cQpqVTKnW5V94uogwoI2vbieUsaWoYk0+jquDEA5Cw9kWbT5IXctYAJCr+cLQGrdtW1L/NtzW99P1JBLf02ybb1/HbA3AdV/ffCIFP5zNpJYKdsyk5OGrV6/qri9atAiLFy9GUlIS+vXrBwA4c+YMNmzYgA8//LB5RklsEp/PQ5cQDyTlS2g5ijSaXKXGvTwJ2vq76pW317qZXY6HvzgOhgW2zO6N+I7+Vhhl9TKUgM+DmyYHzVPzzV+uYiBTqvXGr82dMTZbA5g3YxNEgU29+kZ546sjyfj1YhakcjW++k9Pgy302hmbhgKbd/+8CQCY0iOo+QZMmpVJgU337t3B4/H0KgsvX77c4Ljp06dj2rRplhsdsXna8uZpFNiQRpCr1Ojwxn4AwPiuQdgwvafBMVtOpkCzooMFP13EzVVjW3KIOtplKE8nke5D00UsBJ8HMCxQLlPWCmy447W5NLX5uDYc2OTqlqKcmv4DtGJ9o3zg6+qAQokc+2/k4npWObqE6u/U1HbzNlZNXYvP42FS92ColKpW1xX9QWJSYJOSktLc4yB2Spu4dzKpqMFCY4TUpi1aBwB/Xc3BhumGx5TLqmvHWLO2iHard838DD6fBzdHEcqqlCivUsG/xmSAdsbGp44tyNqAp7CeLuE0Y2MaJ7EAv74wACPWHoFSzeJcarFeYCNTqnEti/td6xNZd1kSR5EAnz/RAxIJ9cCzZyYFNhEREc09DmKn4jv6Q8jnIau0ClmlVQj1crb2kIgdqb2LRalmIKpV7Vr74Q6Amx2xUqXrmjM2Nbk7CbnARqZfvE87Y+PlbDywMWUpStuSgXJsGhbu44wlI9vjk4Q7uJhegmcQpXvsUnoplGoWAe4OCPOm2a/WrlEF+pKTk7Fu3Tq9An2LFy9GmzZtLD0+YuMcRQLEBrvjamYZLqaXUmBD6sWyLEqlSjz/YyLiIrwMZjPKqpQGW6NrBjYMC0gUqjoL2jUnbTuF2oEKN5YqXQ6Olm7GxrWuGRvKsbE0bW+7v67m4GLavxAJ+BgdGwBXR+6jrnekN80qPwDMDmwSEhIwceJEdO/eHQMHDgTLsjh16hQ6deqEP/74A6NGjWqOcRIb1jPcC1czy3ApvQQTuwVbezjERpVVKTHxyxO6go7nUooxd0i03jGlUv3ARqFiDJZqyqTKFg1srmaW4tVfrunqyHjUnrHRjKW8SomMYime3noewzr4NThjU3NXlLFlXKlCpQuWAiiwMUmPcC94u4hRXKnQBYXfnahOpegTVX91fKlChUEfHQbLskhY2BeG3b+IPTA7sHn11VexdOlSgx1Qr776Kl555RUKbB5AMUFcYkFdHY4JAYBfL2YaVKnedOy+3u2aTSYB4NN/7kC7Z8HfzQH5FXKUSpUIa8HuLR/vv6PXD83XTX9Gyd2J+zNaLlPhhzNpuJcvwb18Cbpo2ozUlWOjnclRqBhUKtRwrVXtW5s47CIW6HZhkfo5iQXY9Xx/7L2UhTP3i3A1qwwKVfW27d715Ndo1TeDRuyD2f9bbt26hV27dhnc//TTT2PdunWWGBMxhZMTcP169XUrivbjvtekFNLOKFI3iaz+Zo+AYZPJmoGPl7MY+RVygyWf5qZNOtXyq7VUVnPG5nqNY7XP86ojsHEWC+EkEqBKqUaxRFFnYBPo4UjLJ2Zo6++Kl8ZwDS6rFGrErNyve6yuisNajkIB/lk6BFKplFoq2DGz/+X8/Pxw+fJlg/svX74Mf3/r1Jd4IPH5QKdO3IVv3f+A2i7CWaVVkFEDOVIHmaru3w3tFty6umevf7KHbjdSaVXLfaNmWRbyWuP2M5ix0QQ2MqUuGKlJ29XbmOrlKMOdUfrNL0ljOIkFeGtCLABgYXzbBpPO+Xwe2ge4oa2fC7VUsGNmz9g899xzmDt3Lu7fv48BAwaAx+PhxIkT+Oijj/Diiy82xxiJjfNxEcPNUYgKmQppRVJ0CKz/WxF5MJXUCFra+rsiwN0BF1JLsHveAGw6fh+3cspRWmM2hmFY8HgAywL9o33w55VsAGjRGRupQg2ZUr8CrUFgU2PGJrfcMLAJqyeh3sdVjKzSKqP9orRtSgKonUKTzBkYhcfiQg1mxEjrZfa/9Jtvvgk3NzesWbMGK1asAAAEBwfj7bffxqJFiyw+QFIHhQL44APu+muvAWLj090tgcfjIdrXBVcyy5BaVEmBDTHqp7PpALjKvb8vHAixgA+5ioGLg1C3hfpiWgmeGcRt05UoVLr8GjdHoS5pt65ZneZgLOCoPQOjzbHJKpUZ1NlxdRDqqhMbU9/OqCzNVvgQL5qxaSo3E5PNlWoGuxMzIZfJMalbQDOPijQXs9YwVCoVtm3bhieffBKZmZkoKytDWVkZMjMzsXjxYloHbklKJfDOO9xF2bI5B8aEaioQZxRzyaFbT6Zg4pcnUFBRd/Ex8uDIr6ieyfjxmb5wFgshFPDhovkWrQ1a/rqWo1vOrNDk5IgFfDiKBLoAoeaMTVJ+Bbqv+gdfHrrXLOMurLVEFODugChf/b0y2hkbbS8iB2H1n1U3R2G9fxfr6xeVVcq9Z6GeFNi0FKWawYpfr+HtfXehVLMNP4HYJLMCG6FQiBdeeAFyOfef3c3NDW5u9O3cKoRCYP587iK0/hSrdro9s4T7lvn2HzdxNbMMm45Rx3cCvd1Qxrbcju0cqLuu/R2q0BS8c3PU9mXigoBSaXUQsOnYfZRKlfj0n7tNHiPDsLiRXabXOkY7Y9Mt1AM75vbDT8/1Myi1r82x0ebEhHs7Y5zm53l6YBTqU12kz/ALQFYJ957RjE3L4fN4GBUbgOHtfailgh0z+xOxb9++uHTpElUjtjYHB2DDBmuPQkdbzTOjWKqXQJxfIadWC0SXVNsnytvoB0bnEA90CHDDnbwK5JRVoa2/q27GRhvYaGd1as7Y1AyYPjtwF88OjjJ52aG2Lw8nYe2Bu/i/4W3x4mhuV02RRFtkzwH9on2MPs/dUf/PaKCHI9ZO7Y75wyToHFJ3XyKguq1C7RkblmWrl6JoxqbFOIoE+HZmL2qpYOfMDmzmz5+PF198EZmZmYiLi4OLi4ve4127drXY4Ij90M7YZJRI9Wp+/HY5G79dzsazg6LwxsOx1hoesTJtMFK7HUFNtfNNqmdsuOdoAxttEnJmiRRnU4p1z//833u4llWG/87ubdbYGIaFQs1g7QFu1ueLQ0nVgY1mLHXVogGqZ2y0Atwd4SQWGDRhNKauRpjFlQpd0nKQJyUPE2IOswMbbffumonC2s7fPB4PajVt920RLAsUFnLXfX0BK8+IRPpwAe7dPAke3XjK4PHvTqTglXEdDfoAkQeDto9S7SCgJi8XTeCiC2z0Z2y0QYC2ErE2EKnp0O18s8bFMCzGf3FClx+jpe1ZpV2K8nGte8t27UrE9W3vrq2uflHJBVxNqBBPJzgIBQbPI4TUzezAhjp92wipFNDWDZJIgFozZy0tzNsJIZ5OuulzY/66moNHeoS04KiIrfjviVQAqLcVgjaHRjsjU14rsAnW1HPJKZWBZVmDKsaNcTOnHLdqzDBqZRRLkVpUiaQCbknCt45+T4BhsBZoRt0Z7SxVoSbJPrNECh8XB9zJ5cZEOwxbVpVCjZFrj4JlGfw2rze1VLBTZgc2lFtDjOHxeIjyddELbP59cShSCiqx60IG/rmZh92JmRTYPICU6up+TxJ53Tv4vLQF+KTGl6K0Ha6rlGqUSpW6/BdfVwfd+cVC82YEj98rNHr/4h2X9SoO11ckz0Us4LqOa3KOQ8xYOtLOdGaXyfDBvlvYdOw+gjwcdUu7FNi0LBbVuU0sbYqyW41aF7hz5w4WLlyIESNGYOTIkVi4cCHu3Llj6bERO1OzBPmVlaPRxs8VI2MDML1vOADgRFIh/ryaba3hESupucwyMqbu2iDaZpHfn06DSs3olqK0szyOIoFu5iS7rEqX/1Kz8zXLsnq7muqTUSzFR/tvG32sdhuFQI+6l5d4PJ5e4GNOpWAvFzGCNePXto/IKZPhXCqXOzSwja/J5yJN5yAU4LcFA7H96R562/aJfTH7X2737t3o3LkzEhMT0a1bN3Tt2hUXL15E586d8fPPPzfHGImdGB3LbXHtFeGlK38PAAPa+Oqqfv5+mQKbB03N7tyjOwXWeVzNir7nUoqRX67dkVS9DKQNGjKKpbrAZ/GIdroPIaWahUTecE8qlmXxzPfndben9w3HyBh/DGprPJBoaHmpZl5NsJm7mHqEe+mu9470gr/mffB3c2iwGzWxLAGfh25hnugS7E7bve2Y2UtRy5cvx4oVK7Bq1Sq9+9966y288sorePzxxy02OGJfHu8Viig/F0T76uf7iIV8fDerF57YdEavSSB5MGgTcDs2sKyiDYwBIKWoEnc1Cb3BNZZ2gjwccS2rDNezuBwUAZ+H4R39cfvdsYhdmYAqpRoHbubh0Z6h9b5WQYUcd/O4/JkF8W3w8piOAIDV+27hRJLh8pS/W/0Jwf5u1WOsvf27Ic8MjsKJpEL4uzlg41NxqJApsedSFsZ3DTJ7aY0Q0ogZm9zcXMycOdPg/v/85z/Izc21yKCIfeLxeOgd6W10B0lsMFfPI7tMpsudALhkvfav/402r+3T+2ZP7ItSzeBGTgUYxnAZSNvg0aeeBFyAa1j4eBwXkNzNrcC1rDLweECfqOr6MdplpxvZms7ZzmLw+TzweDxdIu6yXVdwIbUY9bmv6UQf4eOsC2qA6jyemiZ0C25wN9+8YW0QE+SOdyd1MrtmU89wL5x9bQQSlgyBn5sDov1c8eLoDugYWH8NHGJ5KjWDvZey8Oe1PKiM/C4T+2B2YDNs2DAcP37c4P4TJ05g8ODBFhkUaX3cHUW6kvg1E4x3nk+HQs1AzbD4+1qOtYZHmuiDhCRM23wRW06lGjym2zLt0vA2aO3vyMFb3LbtaF8XvQJ1AZrAQ1srqWZ9mZqzG//czKv3dbQJyn61gvCa+TrjuwYh8Y2RWDete4Pj7h7mib8XD8aM/pENHmuMo0jQYOdp0vwUagZLdl7Gq7/dhkLFNPwEYpPMXoqaOHEiXnnlFSQmJqJfv34AgDNnzuDnn3/GO++8g99//13vWEK0wrycUSotQ0ZxFToGumPD4SR8klCddH4vn6p92qufL3JB6Ud/39Y1sdT64UwagOqtzfXR1oTRBr++tQKPAM2ST54m/6bmOWu2WlA38G1bu6W8doPKmvkxbXxd6q1fQ1ofPo+HQW19oVKrQHGm/WpU5WEA2LhxIzZu3Gj0MQBUrI8YCPVy4irDnkjBmn/u4HauflG0bafT8FhcKLqGelpngMRs17PK8HGN4FSh1v+WW1Ah19WbySmru8aRloezfvBTe/kqwF1/qahmwnG4jwtKpKUAAIms/gRibYdwDyf983cMdIePixhFlQrEd/RvcLykdXEUCfDjs32ppYKdM3spimEYky4U1JDatPkLp+8XGQQ1Wm/uvd6SQyJN9PAXJ3DsboHefTV7hdXMm5plwjJN7ZYLtWd5Qms1hPSqMeOy/onuuusN7YwqreJmd2rP2IiFfPw8rz9+XzhQb7cSIcR+UMo9aTE1d45offFkD9x+d6zu9pXMMlrbtnMX00t018s1PaKcxQIMqGMrdU21Aw3vWjM4ET7OerVwOtRIsI3wccGax7sBACoaCGzKpHX3ror2c6VZQ0LsGAU2pMVE1doG/tm0bpjQLRiOIgEurxwFkYBb1D6ZbLwaLLEtVQrjs7Ipmh1HQHVbhPYBplXQjQ3S3wnkINLvk8Tj8fDdrF745YUBWPlwLKb1DtN73FWz1Voiq7vCMQCUaPJxPE3I+yEPjiqFGqPWHsWkr8+jSkmrDvaKAhvSYvrWKDb2weQumNyjutaIp7MYT/bhKhTT7ij7UNf2/Nf3XMeF1GLIVWrdjI2bibVdfFwdcGDpEN3tuurHxEV44elBUQZF1Nw0hSAbXIqqZ8aGPLhYsLiXL0FyoZRaKtgxs5OHiY1wdAQOH66+bge8XMToGuqBzJIqjO1sWIF2SDs/bDudpiu+RmxbfXWHHvv6NBaNaKfLgamvq3dt7QLcsGh4W1xML8WEbsFmjal6xqaBpagq47uiyIPNQSjA9uf6oaqqiloq2DEKbOyVQAAMG2btUZhtx9x+UKgYXSfnmsK8ucZ/2SbsniHWl1sm07s9p38otpzO1N3++kiybpeUU60lpYYsG92hUWPSNsxsKMemesaGlqJINQGfh/5tfGhXlJ0zKbApLzf9G7S7O1XLJHVzFgthJKYBUF06v1SqRKVcBRcHirtt2Y1s7u9C11APDGnjhaf7h+kFNjW3frfUtL5rjaUohmHrLHqny7GhGRtCWh2TPjk8PT0bLBPOsizVrmlJSiWwaRN3fe5cQGT/f6DdHEVwcxSiQqZCdmkV2pmYcEqso1gTHAzv6I9n+3FLRh8+2gWv/nrN4NinB0W2yJi0uTwsy83aeBhZApMp1ZBrdt5RYENqUqkZ/Hs7HzKZDEPb+TT8BGKTTApsDmtzOYjtUCiAhQu567Nnt4rABgAifVxwLasMyQWVFNjYOG1isLtj9e/eE33C8VhcKF7430Uc0LQ1CPN2QqdgjxYZk6NIAAchH3IVg/IqpdHARrsMJeDzdDM8hADcLOPzPyQCAM4tH2Tl0ZDGMul/9dChQ5t7HMRcAgHw2GPV11uJdgGuuJZVhrt5FUYTjIntqNAk6NZODBYK+Ijv4K8LbEor6996bWkeTiLkV8hRXseWb21TTi9nkdkNK0nrxufxEBfhBbVaTS0V7Fijv65IpVKkp6dDoVDo3d+1a9cmD4qYwNER+Plna4/C4jpoZmnu5hmvTExshzZwMLaVe2gHP931hhJ5Lc1dE9jsTsxEbJC7QfBSqGnKWbsPFSGOIgF+eWEAJQ/bObMDm4KCAsyZMwd///230ccpx4Y0RXsKbOyGbsbG0XC5J8TTCa+O64gP/76Nl8c0bodTY7lrAq0tJ1PRP9oHozvpz/wVabapU2BDSOtk9kb9JUuWoKSkBGfOnIGTkxP279+P77//Hu3atdPr7E1IY7QLcAUA3M2TIL9C1sDRxJp0OTZOxr8fzRvaBkdeGoa5Q6JbclhQqqu3YJ1IMqxira2/U7vBJiGkdTB7xubQoUP47bff0Lt3b/D5fERERGDUqFFwd3fH6tWrMX78+OYYJ6mtshJw5YIASCSAi0v9x9uJEM/qJoeHbuXjCU01YmJb5Co1iiu5JR1uxsZ4f69I35b/vRQKqpee1IzhPnNaiiJ1kSnVmPrNaajVDL6f2Q2u1h4QaRSzZ2wqKyvh7+8PAPD29kZBAdfZt0uXLrh48aJlR0ceODweD4/2DAHAzdoQ23Q9qxwqhoWHkwhBHrZV+fqjKdV5fkUShcHjmSVSALC5cRPrY1gWVzPLcCOnAkZiYmInzA5sOnTogDt37gAAunfvjm+++QZZWVn4+uuvERQUZPEBkgePtqfUtaxSo49/d/w+er57AOdSiltwVKSmAs0yYVt/VwgFtlV6vn2AGzY+1RNA9Q6omrQtO6icAKlNLODjv7N7YcO0zhBTSwW71agcm5wcrknhW2+9hf379yM8PBzr16/HBx98YPEBkgdP3yiuMNb51BL8fiVb7zGVmsF7f91CcaUCU785DRl14LWKggouYPCz0eUcH03X7sJaMzYZxVKkF0sh4HPbegmpSSjgY3jHAAxt5wMh7fe2W2bn2Dz11FO66z169EBqaipu376N8PBw+Pr6WnRw5MEU4eOsu75o+yWEezuje5gnAOBevv7y1J3cCnTTPEZaji6wqaP7trX5aAIubaLwqaRCbDudhvaa5PROwe5UnI+QVsrsGZujR4/q3XZ2dkbPnj0pqAEwefJkeHl54TFt4TzSKLXrjtzILoNSzeBqZikyiqV6j13LKmvJoRGNAhvfMu2r2fFUIVNBrlJjyc7L2H8jF+sPJQEAoq2Q1Exsn5phcfxeAU7dLzaaeE7sg9mBzahRoxAeHo5XX30V169fb44x2a1FixZh27Zt1h5Gq/DNjDjd9fxyOT76+zYmfnkS6w/d0zvuzP2ilh4age3P2Lg7inRLCc9tS0R+hX6ujTV2axHbJ1epMWPzOcz96ZqunxixP2YHNtnZ2Vi+fDmOHz+Orl27omvXrvj444+RmZnZ8JNbufj4eLi5UUKiJYzpFIjlY7nCbj+dS8d3J1IAVCd+dg7husj/eTUH1zJp1qal2Xpgw+fz4KXJszl2t8Dg8SgKbIgRfB4PMUHu6BDgQi0V7JjZgY2vry8WLlyIkydPIjk5GdOmTcO2bdsQGRmJ4cOHmz2AyMhI8Hg8g8uCBQvMPlddjh07hgkTJiA4OBg8Hg979+41etzGjRsRFRUFR0dHxMXF4fjx4xYbAzHfsPZcWYGCCsOdLZO6heiuT/jyRIuNiXBsPbABUG9ieaQPBTbEkKNIgL8XD8Yvz/WCo6j19OB70DRpP1tUVBReffVVfPjhh+jSpYtB/o0pzp8/j5ycHN3lwIEDAIDHH3/c6PEnT56EUmnY3O727dvIzc01+pzKykp069YNX375ZZ3j2LlzJ5YsWYLXX38dly5dwuDBgzFu3Dikp6frjomLi0Pnzp0NLtnZ2XWelzRebLA7YoLcjT7WJ8obNVNxbmTTrE1LYVlWl2Njy4GNXFn3UgItRRHSejV6W8DJkyfxv//9D7t374ZMJsPEiRMbtd3bz89P7/aHH36INm3aGO0ozjAMFixYgHbt2mHHjh0QaLpa3717F/Hx8Vi6dCmWL19u8Lxx48Zh3Lhx9Y5j7dq1eOaZZ/Dss88CANatW4eEhAR89dVXWL16NQAgMTHR7J/PFBKJBHy+mTFmZaWuKqZEIgHY1pnotnJsG/xwLguP9wzC2n/v41o210PK15HFsaUDMHjtKQDA1uPJeGt8e6PnkEqlRu8njVNWpdS1LXCCEhKJ2ibf40ndAvDzxRyjjwnUckgkhjOBts4W3+fWiN7n5ldVVdVs5zZ7xua1115DVFQUhg8fjrS0NKxbtw65ubn48ccfGwweGqJQKPDjjz/i6aefNtgZAwB8Ph/79u3DpUuXMHPmTDAMg+TkZAwfPhwTJ040GtSY+rqJiYkYPXq03v2jR4/GqVOnGnXO+mzYsAGxsbHo3bu3xc/d2nQJccfHk2PQO8ITjqLqX1cPJxG8nEUI0VSPzShtvv8kD7IDtwpwKUN/NkxbG8bdUWjTRcwWDInEG+PaGdw/vIOPFUZD7IFMqcbsbZcxb9dtyOqZ8SO2zewZmyNHjuCll17CtGnTLL7Fe+/evSgtLcXs2bPrPCY4OBiHDh3CkCFDMH36dJw+fRojRozA119/3ejXLSwshFqtRkBAgN79AQEBdS5vGTNmzBhcvHgRlZWVCA0NxZ49e4wGLwsWLMCCBQtQXl4ODw8PuLq6wtXVzK4kNQI/V1fXVtMrqj7T+kTifNoVDG3vp3u/Nv4nDpM2nMSZlFLIIKp3+7HZ7/ED7nxqMZb+chMAkLL6Id2Xjd+PcMuzaoY1eE9t6T12dQWeDfTG2n/vQ6pQ49GeIRja3g8D2vjC1Ua3qZvKlt7n1oSvUOFCOhfIOzo50fvcjMrLy5vt3GYHNs0xg6G1efNmjBs3DsHBwfUeFx4ejm3btmHo0KGIjo7G5s2bjc7wmKv2OViWNeu8CQkJTR6DyRwcgF27qq8/AKb0DEHHQDdE+1UHcTVzcA7dzsfUXmHWGFqrdPBWnu56gUQOfzdHSBUqbNbsUAuu0bDUlr0+PgZH7hRg5cOx8HSmjt6kbmIBHxum94RMJrPp2UhSP5MCm99//x3jxo2DSCTC77//Xu+xEydObNRA0tLScPDgQfz6668NHpuXl4e5c+diwoQJOH/+PJYuXYovvviiUa8LcDu9BAKBwexMfn6+wSyOzRAKgToSrFsrHo+HziEeeveJhXzM6h+B70+n4X5BpZVGZv9kSjUchHy9QD67VKa7fjq5CJO6h2Dfter/I9/N6tWiY2ysp/pG4Km+EdYeBrEDQgEf47sGcXmLxG6ZFNg88sgjyM3Nhb+/Px555JE6j+PxeFCrG9e7Z8uWLfD398f48ePrPa6wsBAjRoxATEwMfv75Z9y7dw/Dhg2Dg4MDPv3000a9tlgsRlxcHA4cOIDJkyfr7j9w4AAmTZrUqHOSlhPmzbVgyCihhL/GOJVciKe+O4uHOgfh/cmd8cvFLEzsFqxrdAkAWZocppW/cUU5o/1cEEFbpgkhNsikwIZhGKPXLYVhGGzZsgWzZs2CUFj3kBiGwdixYxEREYGdO3dCKBQiJiYGBw8eRHx8PEJCQrB06VKD50kkEiQlJelup6Sk4PLly/D29kZ4eDgAYNmyZZgxYwZ69eqF/v37Y9OmTUhPT8e8efMs/vNahEoF7NnDXZ88mZvBeUCFenGBzV9Xc/BYz3zEd/S38ojsy9xtiWBZ4K9rOSiXKXH8XiESbuSiqMauocIKBTafSIFUwX1xebJ3uLWGS0izUTMsLqWXQFpVhW4hxktNENtn9qdhamoqIiMjLTqIgwcPIj09HU8//XS9x/H5fKxevRqDBw+GWFy9Vt6lSxccPHgQPj7GdztcuHAB8fHxutvLli0DAMyaNQtbt24FAEybNg1FRUVYtWoVcnJy0LlzZ+zbtw8RETY6hS2XA1Onctclkgc6sOkYWF3t+eOEOxTYmCGjWAqJXKW7ffxeIQDgXEox3B2rf6d2XcjQO+6pfhTYkNZHrlLjsa9PAwDOLR9k5dGQxjL70zA6OhoDBgzAjBkz8Pjjj8Pb27vJgxg9ejRYE+uwjBo1yuj93bt3r/M5w4YNM+n88+fPx/z5800ah9Xx+YC21o+5NXBamUhfF7w0uj0+/ecubuWUQ6VmIBQ82O+Jqa7W046iXFYdyNQMagDAWfzgBtKk9eKBh0gfZzAMCwvsRyFWYvZf/wsXLqB///547733EBwcjEmTJuHnn3+GXG5/xa7smpMTcOQId3Gyj90pzWn+sLZwEXMFG1OLKNfGFGVVSpy+X2jtYRBiM5zEAhx5OR77FvSBE7VUsFtmBzY9e/bEJ598gvT0dPz999/w9/fH888/D39//waXkghpLnw+D20DuCWpkWuPIvLVv/Ds9+ehoA69der3wb/48QxXk8ahjq2tr4ztaHDfT8/1bdZxEUJIUzR6vp7H4yE+Ph7ffvstDh48iOjoaHz//feWHBshZukUrJ/sd/BWPk4l04xEXapqNImsq+fTwLY+ekUPf184EAPaWLYwJyGEWFKjA5uMjAx8/PHH6N69O3r37g0XF5d6m0wSC6usBPz8uEsl1W8BgOEdDJOGT9xrnYHN5YxS/HPD9KrYtWXW2ho/d0i00ePCvZ2xY25ffDSlC5LeH4euoZ6Nfk1CbJ1MqcacLefwwo5rkNNsr90yOwNw06ZN+N///oeTJ0+iQ4cOeOqpp7B3716L75QiJihsnR/ajTWkvR+GtPfDsbsF6BzijutZ5civaJ25X499dQoqhsXWOb0xzEhA1xDtEpTWjH4ROJdSjOP3ClFWpdTd7+kshqezGG393WqfgpBWh2FZHL5TAIDb+k3sk9mBzbvvvosnnngCn3/+eb07kQhpaWIhH9ue7gMA2J2YiZd+voISqcLKo7I8hYqBSvNH90JqSaMCm6+PJuuua/tAffFkDyjUDFIKKzF23XF8+ng3i42ZEHsgEvDxyWNdIZfLIRLQtih7ZVZgo1KpMGfOHDz33HMIC6OePMR2ebuIAAAFrXDGpqiy+mf68nASJvcMgYtYCJGABx8zmzv6uIh1bRR4PB4chAJ0DHRH6of1VwAnpDUSCfh4vFcYtVSwc2bl2AiFQnz22WeNbptASEtpp1k6SS6QtLq18sIK/VmoBf+7iGGfHkbceweRlF9h1rnWTKVZGUJI62J28vCIESNw5MiRZhgKIZYT6uUEL2cRlGoWd/Nb17evwkr9WajbuRWQKbngbdvptAafz7IsxJoChu0CKHeGEC01w+JGdhlu50oox8aOmZ1jM27cOKxYsQLXr19HXFwcXFz0G+E1trs3IZbE4/HQJdQTx+4W4EaOBF2CW0/fl8J6ltfSTChOKFMyUKi5QMjNkSoIE6IlV6kxfv0JANRSwZ6Z/VfthRdeAACsXbvW4LGmdPcmxNK6hnhwgU12BRBn7dHUbfu5dHxzNBmbZ/dGGz/XBo8vlNSdEH30bgH+upqD8V2D6jymtIp7vpDPg5sDBTaEaPHAQ4C7A1iWWirYM7OXohiGqfNCQQ2xJV1DPQAA13PMyztpaSt+vYbUIine+/OmSccXSupPiP70nzv1Pl5SyW3n9nQW6RKHCSFcS4Wzr43EocX9qaWCHaNOgaTV6hTCBTYphVIo1bafQGxqzZ0iTWAzuJ0vwr2ddfd7OXM7wVIKKyFT1v0lo1SzBd7TWdzYoRJCiM0yex561apV9T6+cuXKRg+GEEsKcneEs1gAqUKNzFIZvDxsL8+mZtdskYkdybVLUZN7hKBjoDse//oUPJxEOPnqcHR+KwGVCjXSi6VobyQx+F5eBZ7/MREA4OkkssBPQAghtsXswGbPnj16t5VKJVJSUiAUCtGmTRsKbIjN4PN5iPZzwfWscuxKzIbIwREdA20ruLmeVaa7XlkjyKlPbrkMAODr6oDYYHeceW0EnEQC8Hg8dA/3xMmkInx9JBkzB0Sie5in3nP/b/slVMi416EZG0L0yZRqLNt1GSqVCqsnxaDhjDdii8xeirp06ZLe5fr168jJycGIESOwdOnS5hgjIY3WVpOM+8O5LIxdd1zX7VuuUuPPq9korrReZWKVmsETm87obueUyRp8TpVCjfsF3PZ17YyMm6MIQs1sz8RuwQCAXy9l4ZENJ5GYVqz3/Nu51flGvq4U2BBSE8Oy2HctF//cKqTt3nbMIlsi3N3dsWrVKjz88MOYMWOGJU5JGiIWA9qmo2L6gKpLiJeT3u1Ob+3HV0/F4efEDCTcyIOAz0PyBw9ZZWxZpVV6tyVyFQoq5HV22gaAmznlYFhutibA3fC4UC9nvdszNp/DzVVjdbfdHYUo18zYRPjol2og5EEnEvCxalInaqlg5yyWPFxaWoqysrKGDySWIRIBCxZwFxHlStRlet8IvdtKNYtnt11Awo08AFxBrtoBRkvJKuFet42fiy6Y+f5Uar3PuZHN/R/rEuJudEdTTJD+UptUoUZGcXVtGwG/+jljOgU0atyEtFYiAR8z+0fiyV4hJue8Edtj9ozN+vXr9W6zLIucnBz88MMPGDt2bB3PIsQ6QjydML6TP/66kV/nMSfuFWBa7/AWHBWnVNNF29tFDGexEAUVcl3+TF0ydcGQ8dV/bxcx/N0c9HZYrfnnDtY90QMKFYMSKfeau57vj2gTauYQQoi9MTuw+eyzz/Ru8/l8+Pn5YdasWVixYoXFBkYaoFYDx49z1wcPBgRUc6EuH02OwfODI7D0l5tILqg0ePx6Vjmm9QZOJRUi4UYuXh0XAydx87+f5ZrAxt1RhKf6BmPJzst6syvGaKsO+9azXPXLCwOw/t97+DkxEwDA18zsFGi2iYsEPPSO9Gry+AlpbRiGRVqxFFKpFGG1lrGJ/TA7sElJSWmOcRBzyWRAfDx3XSIBXChfoj7Rvs7498VhOHAzD89tuwAAGBnjj4O38nEtqwxlUiWmf3cWABDg4Yj5w9o2+5i0u5PcnUQI8+b+iGpnZOqinYnxcak7ryrM2xmfPN4NPq4O+PpoMqo0NW3yNLNB/m6OVJiPECNkKjXiPz0CgGupYFt7KImpmryIWF5ejr179+LWrVuWGA8xFY8HxMZyF/qQMlmvCC+IhXyIBXw8MygaAJeQ+/6+6qq/SXkt0zTz44TbALh+TWGapN+csqp6iwmmFHIzTpG+DQeyvSK4WZmMEm4WKFez6yrQw7HxgyaklXNzFMLNgWbA7ZnZMzZTp07FkCFDsHDhQlRVVaFXr15ITU0Fy7LYsWMHpkyZ0hzjJLU5OwM3blh7FHbHy0WM3xYMhELFoGuoB8K9nZFeLMWuC5m6YypMrCfTFCo1A6Wa205aXqWEn5sDHIR8yFUMckplCPdxNniOTKlGdhk3oxNlQmATpqlKfD2rHGlFlcjWJEkHUWBDiFHOYiGuvT0GEknLfLkhzcPsGZtjx45h8ODBALhifSzLorS0FOvXr8d7771n8QESYmkxQe7oFuYJHo+HkTGGO4NyTagn01TZpdWvsXhke/B4PIRq1vS1Myy1pRRWgmW5Ldv1LUVp1Wy38H/bLyG1iJvtCfak3AFCSOtldmBTVlYGb29vAMD+/fsxZcoUODs7Y/z48bh3757FB0hIcxrQxkd33VmTMHwjuwxyVfM2dNUGGe38XXWzL9oaNMkFxr8tapehov1cTcqRcRIL8FCXQADA1cwy/HgmHQDN2BBCWjezA5uwsDCcPn0alZWV2L9/P0aPHg0AKCkpgaMj/cFsMVIp0KkTd5HWv5OG1K13lLfu+oA2PuDzAIYFyjTbopuLNkk4rMasirYq8srfDJcYlWoG8/93EQAQ7Wd6ovgXT/Y0uG9AG1+zxkrIg0KuUuPFXVfw+u+3df8fif0xO7BZsmQJnnrqKYSGhiI4OBjDhg0DwC1RdenSxdLjI3VhWeDmTe7CUunvxnJ3rE4zG9rBH64O3O0TSYXN+rolmg7bNdsajIjx111PuJGrt/W7ZuG+UDOWkmoW5AOASB9ndAg0bI5JCOEKdv5yMRO/Xc2Diloq2C2zA5v58+fjzJkz+O9//4sTJ06Az+dOER0dTTk2xO7weDz8tmAgFo1oh2m9wqD9U7bhcFKzvq62R5VXjUaUswZE6q4//0MiBn98WJfvU3N5akb/6uNM8eGj1V84fFzrrn9DyINOyOdjxbiOWDYimloq2LFG9YqKi4tDXFyc3n3jx4+3yIAIaWndwjzRTdMFe97QNvgk4Y4un6W5lGgDmxpJwCIBH91CPXAls7o1Sb/V/+Le++N0DTJXP9ql3l5SxvSpsdw2s39EPUcS8mATC/l4fmgb2hVl56gZBiE1aD/4GRaobMZt39qlKG9n/d1NYqHhf8mrmaW4nFEKAGjrb34bhGg/V3wwuQueHRSFh7sGmz9YQgixIxbp7k1Ia+HmKIKXswglUiXu5UvQXTOTk1EshVLNWKy/UrEmOdnLhG3bf1zJQalUCV9XMbqGejTq9ab3bfleWITYG4ZhkV8hR2WlHH5uDf/fJLaJZmwIqaVLqCcA4FZOOQDgYnoJBn98GMPXHEVSvmWmqHVLUc76ndnfe6QLXMQCPDMoCsM7csnE/zubBgAY2NYXDkKqiEpIc5Gp1Oi3+l+MWH8GMiXtirJXFNgQUkugO5fDok3wfXLTGd1jJy20W0q7FFV7xqZDoBuuvzMGbz4cqyuwp61QPLAtbdMmpLkJ+TwI+ZQ4bM8atRRVWlqKc+fOIT8/HwyjH9XOnDnTIgMjxFq0O4fyy2VgGBbyGvUsvjychJn9I5rURFKpZnQNMGvn2ADQnVu7DKb1aI+QRr8mIaRhzmIhkj54iJKH7ZzZgc0ff/yBp556CpWVlXBzc9P7A8/j8SiwIXYvWlMJ+Hp2OS5llOg9VlAhx3PbLuC7Wb0bfX7tbA2Px3X2rkv/GlWRAUAooAlWQghpiNl/KV988UU8/fTTqKioQGlpKUpKSnSX4uLi5hgjIS1Kuz06Ma0El9JLAVS3WwCAg7fyIVM2vuVCqSZx2NNJZFBAr6YAd6rkTQgh5jI7sMnKysKiRYvg7GzYfZiQ1iDc21lXK+a9v24BALqFemL7c/10x2gTixuj2EgNm7rM1hTtm9IztNGvRwgxjVylxpt7r+O9v+9RSwU7ZnZgM2bMGFy4cKE5xkKITeDxeOhYq+1AgLsD+rfx0e1UmrzxFBLTSow9vUFZmj5R/iYU2nt1XEd8/kR3vD+5c6NeixBiOjXD4oczadiRmE0tFeyY2Tk248ePx8svv4ybN2+iS5cuEIn0cwQmTpxoscGReohEwFtvVV8nFvV4rzAcv1e9A2rRiHYAgB5hnjh0Ox8AsGTnJRxfPtzsc98v5BITTamJ4ygSYFJ3ShompCUI+XwsHtEOCoWCWirYMbMDm+eeew4AsGrVKoPHeDwe1OrG5x4QM4jFwNtvW3sUrZY2gRgAvF3EiNLcHhETgDUH7gIAMoqrIFepza4tc7+g0uA1CCHWJxbysXRUe9oVZefMXopiGKbOCwU1pLWICXLHIE3dmFn9I3W7/2KD3XWzNwCQnG9+TyltYNPGQlWMCSGEVKOWCvaKYYBbXGIrYmIAPm0FtiQBn4cfnumDsiolPGvVmlk2qj3OJBfhXGoxHlp/HJdXjjI4pi4MwyKlSDNj40czNoTYEpZlUS5ToVKmgpsDVfm2V436NDx69CgmTJiAtm3bol27dpg4cSKOHz9u6bGR+lRVAZ07c5eqKmuPplXi8Xh1BixRNZaRdpzPMPmcT2w6A4WKgVjAR6gX7SwkxJZUKdXo9s4/GPDpSVRRSwW7ZXZg8+OPP2LkyJFwdnbGokWLsHDhQjg5OWHEiBH46aefmmOMpC6+vtyFtDhHUfV/nQ//vm3Sc3LKqnAulav11D3Ms94aNoQQQhrH7KWo999/Hx9//DGWLl2qu2/x4sVYu3Yt3n33XUyfPt2iAyR1cHEBCgqsPYoH1jODovH96TTdbZZlIVMyOJtShMHt/IwGLdpt3gDw+ZPdW2KYhBAzOIkEuPf+OEgkEuoXZcfMnrG5f/8+JkyYYHD/xIkTkZKSYpFBEWLrwn2ccf2dMbrb5TIVYlbux+wt57H2wB2jz8kukwEA+kR6I8jDqUXGSQgxHY/Hg0jAh0jAb1I/OGJdZgc2YWFh+Pfffw3u//fffxEWFmaRQRFiD1zEAjgIuf9C/z1RHdRvOJxs9PicUm7GJtiTWiUQQkhzMXsp6sUXX8SiRYtw+fJlDBgwADweDydOnMDWrVvx+eefN8cYiTFVVcC4cdz1v/8GnGgGoKXxeDx4u4iRUybDzxf0E4hzyqoMZmWO3OGWDtv60zZvQmyRQsXg03/uQKFQYHF8lLWHQxrJ7MDmhRdeQGBgINasWYNdu3YBAGJiYrBz505MmjTJ4gMkdWAY4OjR6uvEKrSBjXaZSWvNP3fx6ePddLeVai7/BgAmdAtu0TESQkyjYhhsOnYfADB/SKR1B0MarVF1bCZPnozJkydbeiyE2J1Ad0fcyK5uiDl7QCS2nkrFuZRiRL76FwBg65zeaOPnCoYFxAI+wmibNyE2ScjnY+6QaGqpYOfMzrGJjo5GUVGRwf2lpaWIjo62yKAIsRcPdQmqcT0Qc4dw/wfSi6W6+2dvOY/BHx8GAAR6OIJPuy0IsUliIR+vPRSDl0a2gUhARU/tldn/cqmpqUZbJ8jlcmRlZVlkUITYiylxobrrI2MCEOThCA+nupuSBnlQ4jAhhDQnk5eifv/9d931hIQEeHh46G6r1Wr8+++/iIyMtOjgCLEHW+b0RmJqCR7pHgIej4eyKmWdx7o5Uid2QmwVy7JQMSyUaobq2NgxkwObRx55BAC3E2TWrFl6j4lEIkRGRmLNmjUWHRwh9iC+gz/iO/jrbr88pgM+STBey+ahLoEtNSxCiJmqlGrErkwAAJxbPghuVh4PaRyTAxtGs/MmKioK58+fhy+V8ifEqAXxbfHFoXuQKRl0CnZHbpkMvy0ciNwyGXqGe1l7eIQQ0qqZvSuKqgsT0rCjL8ejrEqJdv6uUDEsRNT0khCb5yQS4Mpbo1FZWQknESUP2yvq7k1IMwhwd0T7ADddiXZCiO3j8XjwcBLB3VFILRXsGHX3JoQQQkirwWNZljXnCTExMZg7d65ed28AWLt2Lb799lvcunXLogNszcrLy+Hh4YGysjK4u7ub9+TKSsBVU5pfIuG6fROjJBIJAMDVlVoZNBd6j1sGvc/NS6FisOFwEhQKBeYOCoeXh5l/l4nJsrOzERIS0rjPvwZQd29CCCEEXEuFz/+9h6+Op0GpNus7P7EhZicPa7t7t23bVu9+6u7dwoRCYP786uuEEEKaRMDnYUa/CCiVSqpjY8eou7e9cnAANmyw9igIIaTVcBAK8O4jnXVLfsQ+UXdvQgghhLQa1N3bXrEsUFjIXff1BWhrIiGEENK4wAYAFAoF8vPzdRWJtcLDw5s8KGICqRTw15Txp11RhBDSZFKFCl3f/gcAcOqlgaC9Z/bJ7MDm3r17ePrpp3Hq1Cm9+1mWBY/HM9r5mxBCCLEHKoZ2Q9k7swOb2bNnQygU4s8//0RQUBBVZ7QWFxduOYoQQohFOAoFOLNiBCorK+FILRXsltmBzeXLl5GYmIiOHTs2x3gIIYQQq+DzeQj0cIREoLL2UEgTmB2SxsbGolCbtEr0TJ48GV5eXnjsscesPRRCCCHkgWRSYFNeXq67fPTRR1i+fDmOHDmCoqIivcfKy8ube7w2bdGiRdi2bVvLvJhMBjz+OHeRyVrmNQkhpBVTqBh8czQZ/z2dAaWaafgJxCaZtBTl6empl0vDsixGjBihdwwlDwPx8fE4cuRIy7yYWg3s3s1d37q1ZV6TEEJaMRXDYPXftwEAT8QFW3k0pLFMCmwOHz7crIPIysrCK6+8gr///htVVVVo3749Nm/ejLi4OIuc/9ixY/jkk0+QmJiInJwc7NmzB4888ojBcRs3bsQnn3yCnJwcdOrUCevWrcPgwYMtMgZCCCG2TcDnYUrPUKhU1FLBnpkU2AwdOrTZBlBSUoKBAwciPj4ef//9N/z9/ZGcnAxPT0+jx588eRJ9+vSBSCTSu//27dvw9PREYGCgwXMqKyvRrVs3zJkzB1OmTDF63p07d2LJkiXYuHEjBg4ciG+++Qbjxo3DzZs3dbV54uLiIJfLDZ77zz//IDiYontCCLFnDkIB1kztRi0V7JzJu6KkUilefvll7N27F0qlEiNHjsT69evh6+vbpAF89NFHCAsLw5YtW3T3RUZGGj2WYRgsWLAA7dq1w44dOyAQCAAAd+/eRXx8PJYuXYrly5cbPG/cuHEYN25cveNYu3YtnnnmGTz77LMAgHXr1iEhIQFfffUVVq9eDQBITExszI/YIIlEAj7fzDzuykpd8SiJREJbv+shlUqtPYRWj97jlkHvc8ug97n5VVVVNdu5Tf40feutt7B161aMHz8eTzzxBA4cOIAXXnihyQP4/fff0atXLzz++OPw9/dHjx498O233xofLJ+Pffv24dKlS5g5cyYYhkFycjKGDx+OiRMnGg1qTKFQKJCYmIjRo0fr3T969GiDQoSWsGHDBsTGxqJ3794WPzchhBDyQGNNFB0dzW7fvl13++zZs6xQKGRVKpWppzDKwcGBdXBwYFesWMFevHiR/frrr1lHR0f2+++/r/M5aWlpbEREBDtt2jQ2PDycnTlzJsswjEmvB4Dds2eP3n1ZWVksAPbkyZN697///vts+/btTf5ZRo8ezfr6+rJOTk5sSEgIe+7cuXqPLysrYwGwZWVlJr+GjkTCstw8DXed1KmiooKtqKiw9jBaNXqPWwa9z82rUq5kO7+1n+288m82r6jU2sNp1bSfu436/GuAyUtRGRkZeom0ffr0gVAoRHZ2NsLCwhodWDEMg169euGDDz4AAPTo0QM3btzAV199hZkzZxp9Tnh4OLZt24ahQ4ciOjoamzdvtkgF5NrnYDU7vUyVkJDQ5DEQQgixngoZFeezdyYvRanVaojFYr37hEIhVKqm/RIEBQUhNjZW776YmBikp6fX+Zy8vDzMnTsXEyZMgFQqxdKlS5s0Bl9fXwgEAuTm5urdn5+fj4CAgCadmxBCiH1wFApw+KVh+Gt+b2qpYMdMnrFhWRazZ8+Gg4OD7j6ZTIZ58+bBpUZn6V9//dWsAQwcOBB37tzRu+/u3buIiIgwenxhYSFGjBiBmJgY/Pzzz7h37x6GDRsGBwcHfPrpp2a9tpZYLEZcXBwOHDiAyZMn6+4/cOAAJk2a1KhzEkIIsS98Pg9Rvi6QSGgzhj0zObCZNWuWwX3/+c9/mjyApUuXYsCAAfjggw8wdepUnDt3Dps2bcKmTZsMjmUYBmPHjkVERAR27twJoVCImJgYHDx4EPHx8QgJCTE6eyORSJCUlKS7nZKSgsuXL8Pb21u3lXvZsmWYMWMGevXqhf79+2PTpk1IT0/HvHnzmvwzEkIIIaSFWDxrpxH++OMPtnPnzqyDgwPbsWNHdtOmTXUe+88//7BVVVUG91+6dIlNT083+pzDhw+zAAwus2bN0jtuw4YNbEREBCsWi9mePXuyR48ebdLP1RBKHm4ZlHDZ/Og9bhn0PjcvhUrNfn8qhd10+DZbXGr5pFZSrTmTh3ksSwVQrKW8vBweHh4oKyuDu7u7eU+urARcNZVsJBKgxnIg0acttuWqfb+IxdF73DLofW5eUoUKsSu5TSDnlg+Cv7eHlUfUemVnZyMkJKRxn38NMHkpitgYgQDQdhHXFCokhBDSeHweDw91CYRKpYKAWirYLQps7JWjI/Dzz9YeBSGEtBqOIgE2PhVHLRXsHO1nI4QQQkirQYENIYQQQloNCmzsVWUlwONxl8pKa4+GEELsXpVCjb4fHMTwz0+jSqm29nBII1GODSGEEAKABYu8cjl3nfYL2y0KbOyVszOQn199nRBCSJM4CAX4a9EgVEmr4CCkBQ17RYGNveLxAD8/a4+CEEJaDQGfh07BHpBIqISGPaOQlBBCCCGtBgU29kouBxYs4C5yubVHQwghdk+pZvDzhQzsvZILpZqx9nBII9FSlL1SqYCNG7nrH38M1Oi6TgghxHxKNYOXd18FAIyOoaV+e0WBDSGEEAKupUJ8Bz+o1GpqqWDHKLAhhBBCwLVU2DKnD7VUsHOUY0MIIYSQVoMCG0IIIYS0GhTYEEIIIeBaKgz75DAe2nCOWirYMcqxIYQQQsC1VEgtknLXqaWC3aLAhhBCCAHXUmH3vP6QVlFLBXtGgQ0hhBACrqVCr0hv2hVl5ygkJYQQQkirQYENIYQQAkClZvDX1Rwk3CyAiqEkG3tFS1GEEEIIAIWawYKfLgIAzi0fZOXRkMaiwMZe8fnA0KHV1wkhhDQJn8dD3yhvqNVqUEcF+0WBjb1ycgKOHLH2KAghpNVwFAmw8/n+lDxs5+irPiGEEEJaDQpsCCGEENJqUGBjryorAT8/7lJZae3REEKI3ZMp1Rj3+XFM+fYCZNRSwW5Rjo09Kyy09ggIIaTVYFgWt3LKNdetPBjSaBTY2CsnJ+D69errhBBCmsRBKMAPz/RBFbVUsGsU2NgrPh/o1MnaoyCEkFZDwOdhcDs/2hVl5ygkJYQQQkirQTM29kqhAD74gLv+2muAWGzd8RBCiJ1TqRkcu1eAqioZBrbxtvZwSCNRYGOvlErgnXe46y+/TIENIYQ0kULN4OmtFwBQSwV7RoENIYQQAq6lQtdQD6jVDLVUsGMU2BBCCCHgWir8vnAQJQ/bOUoeJoQQQkirQYENIYQQQloNCmwIIaSVUygUWL58OYYPH47Y2Fikp6frPf7bb7/hiSeeQNeuXfHhhx9aaZTN49ChQ5gxYwa6d++Ol19+ud5jZUo1pnx1Cv/ZeolaKtgxyrEhhBA7wefzwTCM2c9jGAYODg74v//7Pzz66KNQKpV6j1dWVmLEiBGQyWTIy8uz1HBtgkQiQf/+/cHn85GVlVXvsQzLIjGtRHO9JUZHmgMFNsSmVVVVoaSkBCKRCH5+fkaPyc7OxqVLl+Dt7Y1+/fqBxzNvO0Nqaipu3LiBwMBA9OzZ0+znN1ZlZSXKysrg5eUFpzraYrAsi5ycHDg4OMDHx6dFxmVNDMPgzJkzKC0tRY8ePRAUFGT2OcrKynDu3DnI5XK0a9cO7du3N/pvmpubi4sXL8LDw0P3wddSGIZBXl4eeDweAgMD6z326tWrSE9PR8eOHdG2bVuoVCqzX8/R0RHvvvsuWNb4p/X06dMBAFeuXDHrvCqVChcuXEBBQQEcHR3RoUMHhIWFmf1/yNTf85KSElRVVSEgIAACgcCkc0+cOBEAUFhYiNu3b9d7rFjAxzcz4iCTySCmlgr2iyVWU1ZWxgJgy8rKzH+yRMKyAHeRSCw/OBvAMAz78MMPswDYAQMGGDyuUqnYF198kXVwcGABsADYnj17somJiXrHVVRUsBUVFQbPl0ql7DPPPMMKBALd84cMGcLevXu32X6mmq5evcoCYF9++eU6jzl79iwLgH3rrbdaZEyNVdd7bI4LFy6wPXr00P1bODg4sC+99BKrUqlMer5MJmNfffVV1t3dXXcOAOy8efP0jlOr1eyrr77KOjo66o7p1q0be/bs2SaN3xRbtmxhhw4dyrq5ubEAWH9//zqPTU9PZ8eMGaMbI4/HY5988snG/b3QYBiGBcAmJSUZfXzBggXskiVLGjxPaWkpu3z5cjYoKEjvvQbAxsbGslu2bDF7bHFxcWxgYCCrVCrrHHunTp3YiIgIVq1Wm33+d955h33yySdNOtYSv8+kfllZWY3//GsAzdgQm7V9+3acPHkS3t7GK4B++OGHWLNmDd555x0sX74cN27cwPTp0zF+/HjcvXsXbm5u9Z7/5ZdfxpYtW7B+/XrMnTsXJ0+exPTp0zFp0iRcvXoVQmHz/vfo0qULevXqhR9++AEffPCB0dfbunUrAGD27NnNOhZrKy8vx/jx4+Hh4YHExETExsbio48+wttvvw1vb2+sWLGiwXPMnj0bu3fvxiuvvILZs2fD1dUVN27cQGFhod5xa9euxYcffojXX38dr7/+Ou7evYsnn3wS48ePx7179+Dp6dlMPyVw9uxZAMBzzz2Hffv2obi42OhxLMviscceQ1JSEvbt24eRI0di+/bteO6558Dj8fC///1Pd+xXX32F0tJSo+cZOXIkevfubdGfoby8HIMGDcLt27cxd+5czJgxAzExMaiqqsLFixfx3Xff6f4NzPH0009jwYIFSEhIwPjx4w0ev3DhAm7cuIG33noLfD4f169fxx9//GH0XGKxGC+++GJjfjzSCtBcWyvHMAxKSkogl8vBsiyuXbuGI0eOoKysTO+Yixcv4sSJE6isrLTiaKvl5eXh//7v//Dpp5/Cw8PD4HGGYfDZZ59h6NChWLlyJRwdHREXF4f169cjNzcXO3bsqPf8EokE33zzDaZOnYoFCxZAJBJh2LBheP/993Hr1i3s37/f6PPKysp0NS6ys7Px77//4t69e/W+VnJyMg4ePIgbN24YPPb0008jNzcXCQkJBo/JZDJs374dw4cPR2RkZL2vYUxlZSWOHz+Os2fPQqVSQa1Wo6SkBAqFwuxzNbft27cjLy8PX3zxBXr27AlHR0e89dZbGDx4MD777LM6l1C0jh49ih07duCjjz7Ce++9h7Zt2yIwMBAjRozAtGnTdMexLIvPPvsM/fr1w3vvvQcnJyd069YNGzduRGFhIX788cc6X6OiogIzZsyoM09j27Zt+PLLL+sd51dffYUjR45gzZo1iIiIqPO4U6dO4dy5c3j99dcxbtw4iEQizJw5E8888wx++ukn5Obm6o5VKBR1XtRqyyfAvvXWW7h+/Tq2b9+ODRs2oF+/fvDw8EBgYCAeeugh/Prrr9i9e7fR51ZUVODo0aM4fvw4ZDKZ3mNPPvkkHBwcsGXLFqPPrR3kMwxT78/eGGqGxenkIpxLLYWakmzsl8XngIjJWmIpSruUsXbtWrZ79+666WIvLy/28uXL7MmTJ9m2bdvq7g8LC2MzMzOb8FNZxuOPP84OHz6cZRiGjYqKMliKunHjhu7nqkkul7Nubm7szJkzdfcZm1Y+ePAgC4Ddvn273v0FBQUsj8djX3nlFaPj6tixIztlyhT25ZdfZnk8nu59e/jhh9mqqiq9Y69evcoOGTJEb5q+V69e7LVr13THFBcXsw4ODuxjjz1m8Fo7duxgAbA//vhjPe+UcRs3btQtdwBgY2Ji2O+//54FwB4/ftzs8zVErVY3anlA66mnnmLd3NxYuVyud/+aNWtYAOzt27frff6SJUtYgUDAlpSU1HtccnIyC4BdvXq13v1KpZL19vZmp02bVudz09PT2YiICLZdu3ZsVlaW3mPff/89y+Px2Hnz5rEMw9Q7Bq0xY8bUuRS1evVqo0tGCQkJLAB29+7dJr1GbU1dilKpVGxAQADbtWtXs15XJpOxixYtYl1cXHS/kz4+PuwXX3yhd9wTTzzBikQitrCwUO/+qqoq1tPTkx0xYoRZr1uTKUtRlXIlG/HKn2zEK3+yeUWljX4t0jBaiiKGeDwgNrb6eh0uXrwIAPj888+xevVqjBkzBufPn8fDDz+MefPmoaysDGvXrsXgwYPx999/Y/r06di0aRPe0fahMsOv/9/evYdFVa1/AP/ODBcFEQUURQRBQFNABMRQQbAOomleorKOBIGoR8rUPGiZpmnaxa5HSa2UoFI0Q9NTlnbwhuQFRQHvhT9AEOQmN7nO+/uDwxy2MwPDbcYZ38/z7Odh1qy199rvDDPv7L3W3j/+iJSUlFbrWVpaYuHChUqf37t3Lw4cOIC0tDSlgxDPnDkDAHB0dBSUGxgYYNCgQbLnlVHW3sLCAmZmZi22P3ToEHx8fJCWlob+/ftj69atePPNN7Fjxw784x//AAAUFBTgiSeewMCBA3H69Gm4urri6tWrCA0NlZ0qMzQ0RO/evTFz5kzs3bsXRUVFgoGTO3bsgKmpKWbOnNnivjxo+/btWLBgAVatWoXFixdDIpFg2bJlWLBgAUQiEUaMGNGm9bUmMTERR44cabWeoaEhVq1apfC5M2fOYNCgQTB44J5nTa/PmTNnMGTIEKXrPnToEDw9PXHo0CGsW7cOf/75J+zt7fHyyy/jtddeg76+vmw9zdfbRE9PD/b29i2+7gMHDkRiYiL8/Pzg5+eHo0ePwsrKCrGxsQgNDUVERAQ2b97cKYPPz5w5A7FYDDs7O0F583g888wzbVrnkSNHUFVVBQD4/fffcfnyZTz11FMQi8W4efMmrly5gszMTOjp6eHAgQMYPnw47O3tBetITk5Gfn4+wsPD27Ttf/zjH9i5cyc2bdqEZ555BvX19Xjvvffw6quvwt7eHpMnTwbQeARz165d2LlzJ1555RVZ+59++gmlpaV4+eWX27RdAMjOzkZqaiquXr2KnJwcHDhwAA4ODnjsscfk6ooggmPfHpBKpS19rLKHXaenSkxlHTpio6KIiAgCQMeOHROUu7q6koGBAaWnpwvKLSwsKCwsrF3beuONN8jJyanVZcqUKUrXUVhYSJaWlvT+++/LyhQdsWn6JX/q1Cm5dfj5+VGfPn1kjxUdsVm6dCkBoMzMTLn2Tk5OSn+RDh06lMzMzASvmVQqJXt7e5o2bZqsbOPGjSSRSCgrK0vQPjU1lQDQwYMHZWWHDx8mAIJfrzk5OSQWi2nevHkK+6FMYWEh9ejRgyIiIgTllZWVJBaLycnJqU3rU8XmzZtVet1HjhypdB3m5ubk5+cnV56UlEQA6JNPPmmxDyYmJmRhYUGGhob0xhtvUExMDM2aNYsAUEhIiKzepk2bCAAlJibKrWPixInUs2fPVvf3zz//pIEDB5KjoyN99NFHJBKJaM6cOW0+YtXSEZvx48eThYWFXHnTZ0Z4eHibtkVENH/+fAoKChIsTQOz9+3bJ/dc8/dok2+//ZYA0Pbt2wXl1dXV9NNPPwmWoqIiIiLKz88nsVhM7777rqCNVCold3d3mjlzpqysvr6ebGxsyN3dXVA3MDCQTE1Nqaqqqs37nZiYKLdvrR0F5cHDXY+P2LB2O3/+PLy9veHr6ysov3v3LqZMmYLhw4fLympra1FaWooBAwa0a1vr16/H+vXrO9TfxYsXw8rKCkuWLFGpPikYe0FEKv9qbk97Dw8P9OzZU/ZYJBLBwcEBubm5srL9+/fDysoK586dw9mzZ2XrJSLo6enhxIkTsgGSEyZMgI2NDWJiYmS/UmNjYyGVShEWFqbSfjSJiYlBRUWF3JERIyMjmJqawt3dvU3rU8WCBQuwYMGCDq9H2WsBoNXXUyqVorCwEF999ZXsaEJISAikUiliY2Oxfv16WFlZydbTkfeNvb09EhMT4e3tjddffx2zZ8/G1q1bO326eEfiocgXX3yh9Llp06Zh2rRpra5D2XZLS0tl06qbnDp1Ct7e3vj3v/8NqVQKfX19/PjjjwD+tx9mZmY4ceKErI1EIkFISAjWrl2LS5cuwdXVFbdv38Zvv/2GiIgIpZdFaEnTETb26ODERofV1tYiLS0NUVFRgvK8vDzk5eXhiSeeEJRnZGSgvr6+3V9+t27dQlFRUav1unfvjmFNp9GaOXHiBOLi4vD1118LBtrW1NSgsrISFy9ehKWlJfr16wcLCwsAUDirpLi4uNVrvjRv/+Dh/uLiYgwcOFBpW0WDmQ0MDAQXTrtz5w6KioqwfPlyubr29vYwMjKSPRaLxQgNDcU777yDtLQ0ODs7IyYmBsOGDWvzjJb//Oc/eOyxx2BtbS23T6WlpV2S2OTl5QmSOmXEYjFGjhyp8DkLCwulryUAlV7PyspKPPvss4LyoKAg7N69G7///juCg4M7/L5pkpSUhMLCQnTv3h2nT5/GnTt3YGVlpVJbVVhYWKCkpARSqVSQMKkaj67SNIj92rVrgvI+ffqgrKwMQOOp0EWLFsmeaxrovGXLFoUz/x68VlFoaCjWrl2LmJgYfPzxx4iLi2tXks8eXZzYaKuqKqDpS+/sWaDZF2WTy5cvo7a2Fh4eHoLyCxcuAIDS8uZfPhkZGYiOjsaNGzdgamqKBQsWwN/fX2GX1q5di+3bt7fadRcXF1y6dEmuPDs7GwAUnr/Pzc2Fm5sbVq1ahTVr1sDLywsAcPXqVUyZMkVWr6amBpmZmQgKCpKVSSQSuV+azds3j0NBQQGKi4sxevToVvejJebm5jAwMEB6erpK9ZsSm5iYGDzzzDO4fv06Nm7c2OZf5vn5+Qq/9H755RcQkSCxKSwsxMcff4zU1FRIJBJMnz5dFvu33noLkydPxpgxY2T1m2YTeXt7C9b91VdfKR0705yJiYnsy+9BXl5eSEhIQE1NDQwNDWXlTRdUa+31ePzxx5GVlYVu3boJypsSyJqaGtl2mq+3SX19PW7evIlJkya1uh9NY2rmzp2LqKgo+Pv7C8bcdAYvLy/s3bsXN2/ehJOTk6xc1Xh0ldGjR8PKygoHDx4U3HpBLBbLLq/w4GvQ9H7ctWuXSom6vb09/P398e233+K9997Djh072pXkt0d1XQPmfHMO9Q312PScM3p0+RZZV+Dp3tqKCLh8uXFRMhW2aeDwg7/Sz58/D4lEAldXV0F509V7bWxsZGXZ2dl46qmn8Pnnn8sOVzcNQHzQ6tWrkZqa2uqyZ88ehe0nTZqksL6VlRVGjBiB1NRU2eDcIUOGoE+fPti3b59gHUeOHEFFRQV8fHxkZd26dYNEIhFMffXy8oKBgYFc+/3794OIBO3bY8aMGbh8+TJSU1NVqm9nZ4cJEybg22+/xZdffgk9PT3Mnj1brh4Roa6uTuk03n79+uHGjRuC6a7l5eVYt24dAGHSmpubCxcXF2zcuBGLFi3CypUrkZycDKAxIQgODpbVTU5OxubNmxUecZk7d65Kr3tSUpLS/ffx8UFFRQV+//13wb4mJCTA0tISDg4OsvL6+nrU1dUJTtX4+fmBiPDHH38I1tu0P00Jja2tLaytrbFv3z5B+6NHj6K0tLTV1z0uLk6W1ERHR8Pe3h5Hjx5FTU0N/Pz8VDpypYqmfjz4/kxISIBIJBIknOokkUjw97//HRkZGYJr6bRk6tSpEIvF2Llzp8rbCQsLw927d/H222/j+vXrCAsLU8sVwaVEOHmzEH9klvItFbRZp4/aYSrr0ODh+nqixMTGRcmVWSMjI8nc3Fxu+umMGTPI2dlZrv6YMWPoySeflCvPysqipKQkOnr0KJmbm9OtW7fa3t8OUDR4mIjo/fffJwC0bNkyKikpoRMnTpCdnR1ZW1tTRbMp8BcvXlR4hd9FixYRAPrwww/p3r179PPPP1Pfvn3JxcVF6dVuhw4dqnBq9pQpU8jDw0P2OD8/nywtLWnQoEF04MABKi0tperqakpNTaWVK1fSxYsX5dYRFxcnmwrbfCByc037EhUVpfD57du3EwCaNWsWHTlyhOLi4mjIkCFkZmZGtra2cvXv3r1Lp0+fpqNHj5Kvr69s+ntdXR1169aNKioqqL6+ntzd3enAgQMKt0nUOM3+wanabVFeXk5WVlZkb29PJ0+epJKSEoqKipK9Ps09//zzBEAwtbusrIwGDBhAQ4YMoVOnTlFRURF99913ZGRkRGPHjhW0//TTTwkALVmyhIqLiyk5OZkcHR2pX79+Lf4vZmRkyAZ0PzhQ+K+//iIbGxvy9fVtcbr3zZs3KT4+nuLj48nV1ZV69uwpe3z27FlZPalUSmPHjiVTU1Pau3cvlZWV0ZYtW0hPT08wGFoTysvLyd3dncRiMYWGhtLvv/9OeXl5lJ2dTb/99hs9+eSTBICSk5NlbcLCwkgsFtPbb79NWVlZVF9fTzk5ORQbGys35ZuocbB70xWkJRIJ3blzRy37VlffQAnnc2jnqZtUcq9MLdt8VHXl4GFObDSoq2dFeXt7U0BAgFy5ra2t3IdjfX09GRsbC778c3JyaPz48TR+/HiaM2cOzZ49m4yMjFS+xH1nUZbYNDQ00MqVK8nIyEiWEIwdO5YuXbokqKcssamurqZXX32V9PX1Ze0DAwPpr7/+UtoXVRMbIqKrV6/SxIkTSSwWC65l4+TkpPC2Dc0/zPfv369w+ydPnlR4/Z4m9fX1FBUVRSYmJiQSicjV1ZX27NlDw4cPpxdffFFWr6amhoKDg8nNzY1CQ0MpMjKSDA0N6cKFC7I6w4cPp5SUFIqOjqapU6cqjQlR58wiuXjxInl7e8viZGxsTKtWrZJLIhQlNkRE6enp5OfnJ7gFQWBgIOXm5grqSaVSWrNmDfXo0UNWd/To0YJ9V+aXX35ROvvpr7/+osuXL7fYfsuWLXK3IGhaHpwBl5ubSzNmzJA9L5FIKDw8XJC0a0pFRQWtXr2a7Ozs5PbD09OTdu7cKUjwampqaPny5WRmZiaoa2JiQp9//rnCbcydO7fFJL8r8ayorteViY2IqJVLerIuU1ZWBlNTU9y7d08wy6azVFZWQiKRyJ3zrqiogL6+vmAsAxGhsrISBgYGsmuJzJ07F/3795dd0+bLL79ETExMi6cUukJlZSVEIpFgwG1zhYWFSEtLQ+/evTFixAi5Q9YNDQ24f/++3D43ycvLw5UrV9CvXz+Fg5of7ItYLJabnXH//n0QkcI+Nq1fIpFg8ODBcgN7m6uqqoJUKoWRkZHCWTZNt5HIzMxEjx7KRwBIpVI0NDRAX18fp0+fxuOPP45ff/0VAQEBABqvkbNr1y4cOnQIIpEIaWlp8PT0RHl5uez1DwoKgo+PDz744AOcOHFC7pomzTVdjbmlPqmCiHDx4kWUlJTAxcVFNti3uerqatTX18PY2Fjh6Yn09HTk5+fDycmpxUHgRUVFuHTpEnr16gU3Nze1nOqoq6uTjfd5kJ6entz/KgBcv34dOTk5cHR0xMCBA1FXVye7Lo+mSaVSpKeno6CgAN27d8eQIUMUvmZNamtrkZKSgoqKClhaWuKxxx5Tui9NsWr+maQunfV+Zsrl5uZiwIABXfL9x4OHtVVdHbBtW+Pfc+cCCj4cjI2NFTZV9M8qEonkyu/evQszMzNIpVKcPHkSb731Fp577rmO972NlO1HEwsLC6UDmoHGD1NlSQ3QOCtD1btIK+tLS9NQ27J+Zclbk2PHjmH58uVKP3BTU1MxYsQIiMViiMVinDt3Ds8//zzGjRuHv/3tb7J6d+/eRUNDA+rq6pCdnY2wsDC4uLgIvkCGDh2KN998E//85z9bTGo6k0gkgpubW4t1FH35N+fs7AxnZ+dWt2Vubt7i+6Yr6OvrtzkpcXJykg0gbkp8H5bERiwWy43Va4mBgYHc4HNl2hOrjmqQEtJv30PV/SoM69fyvebYw4uP2GhQh47YVFYCTV9uFRVAK1/+7XHhwgWEhoaipKQETz31FIyNjTF27FjMmDGj07fVlR6VX19SqRSmpqbo1asXHBwckJeXh2vXrmHs2LHYs2ePILkqKirCrFmzkJGRAU9PT/j4+KC6uhorV66U1YmNjcXKlStx9erVVq8f8qjEWNM4zl2rqrYew1Y13rftTNQ49DWTv7QD6xx8xIZpxMiRI3Hx4kVNd4OpSCQS4ciRI/jjjz9QXFyMXr16ISAgQHARxibm5uY4fPhwi+srKCjApEmT2nVRNMa0kQgiDOjVHUR8SwVtxokNYzpCJBJh9OjRnXaNk/Pnz/MVW9kjpbuBBEnLJ8iOjDHtxIkNY0yhlStXdurVdBljTB04sWGMKaTo7seMMfaw4ysPM8YYY2i8pUJE7Dks3J2Omnpp6w3YQ4mP2DDGGGNovKXC4cv5ABqnfjPtxIkNY4wxBkBfIsaGmS6oqa6BvoSnRWkrTmwYY4wxNCY2L3jZ8KwoLcdjbBhjjDGmMzixYYwxxgBIpYTr+eW4ebcSUr4ov9biU1GMMcYYgOr6BgR8chxA4y0VOv/WxEwdOLHRZi3cRZcxxljbmRkbgG+hqN04sdFWxsbA3bua7gVjjOkMIwM9nF/5Nx48rOV4jA1jjDHGdAYnNowxxhjTGZzYaKv79wE/v8bl/n1N94YxxrRedV0DXtt1AcsSrvAtFbQYj7HRVlIpcOzY//5mjDHWIVIi7E/NBQC8/ZSThnvD2osTG21laAjs3v2/vxljjHWIvkSMlVOGobaGb6mgzTix0VZ6esCzz2q6F4wxpjP0JWKEj7PjWVFajsfYMMYYY0xn8BEbbVVfDyQkNP49Y0bjERzGGGPtJpUSbpfeR1VVNfqb8il+bcXfhtqqpgZ47rnGvysqOLFhjLEOqq5vgM8HiQD4lgrajL8NGWOMsf/qri8BwLdU0Gac2DDGGGNovKXClbWBPHhYy/HgYcYYY4zpDE5sGGOMMaYz+FQUY4wxBqCmvgFv789AXV0dVgQ6aro7rJ34iA1jjDEGoEFK2HU2G3tT76BeygOItRUnNp1oxowZ6N27N4KCgjTdFcYYY22kJxZjaYATXvUbxLdU0GKc2HSihQsXIjY2VtPdYIwx1g4GemK8MsER88bZQl/CX4/ail+5TuTv7w8TExNNd4Mxxhh7ZGk8sVm9ejVEIpFg6devX6du4/jx45g6dSqsrKwgEomwb98+hfWio6NhZ2eHbt26wcPDAydOnOjUfjDGGHt4ERGKKmpQXFkLIh5jo600ntgAwPDhw5GXlydb0tLSlNZNSkpCXV2dXPnVq1dx584dhW0qKysxYsQIbNq0Sel64+PjsWjRIqxYsQIXLlyAj48PJk2ahKysLFkdDw8PODs7yy25ublt2FvGGGMPo/t1DfBYdwS+nyTjfp1U091h7fRQTPfW09NT6SiNVCpFZGQkHB0dsWvXLkgkEgDA9evX4e/vj8WLFyMqKkqu3aRJkzBp0qQW1/3xxx8jPDwcc+bMAQB8+umn+PXXX/HFF19gw4YNAICUlJS27lqLmn4R5OXltf1Kl1VV6PHfPyvy8gAjo07tmy65f/8+AKCsrEzDPdFdHGP14Dh3rfu1DZDWVAEACgryUV9dqeEe6a6CggIA6JIjYw9FYnPjxg1YWVnB0NAQo0ePxvr162Fvby9XTywW4+eff4avry9eeuklxMXFITMzExMmTMDTTz+tMKlRRW1tLVJSUrB8+XJBeUBAAE6dOtWudbZk8+bN2Lx5M2pqagAAQ4cO7dgKHfl6C4wx1plcPtV0Dx4NRUVFMDU17dR1ajyxGT16NGJjY+Hk5IT8/HysW7cOY8aMQUZGBszNzeXqW1lZ4T//+Q98fX3x4osvIjk5GU888QS2bNnS7j4UFhaioaEBlpaWgnJLS0ulp7cUmThxIs6fP4/KykpYW1sjISEBo0aNkqsXGRmJyMhIlJaWonfv3sjKyur0F1aRUaNG4ezZs2ppr0rdluooe05ReWtlZWVlGDhwILKzs9GzZ9ffr7cjcW5r29bqd1aMFZVra4zb2p7fy7of5wcfa1OctSXGD5bdu3cPNjY2MDMzU6nvbaHxxKb5KSIXFxd4e3tj8ODB+Oabb7BkyRKFbWxsbBAbG4vx48fD3t4eX3/9NUSijl9z4MF1EFGb1vvrr7+2aXticeMQJ1NTU7X880gkkg5tpy3tVanbUh1lzykqV7WsZ8+eD32c29q2tfqdFWNF5doa47a25/ey7sdZWVttiLO2xFhZWdP3YGd6KAYPN2dsbAwXFxfcuHFDaZ38/HzMnTsXU6dORVVVFRYvXtyhbVpYWEAikcgdnSkoKJA7iqPNIiMj1dZelbot1VH2nKJyVcvUpSPbbmvb1up3VowVlWtrjNvant/L6mmvyThrMsYd3b62xFjV7XcGET1kc9pqamowePBgzJ07F6tWrZJ7vrCwEH5+fnB0dMSePXtw48YN+Pn5ITg4GBs3bmx1/SKRCAkJCZg+fbqgfPTo0fDw8EB0dLSsbNiwYZg2bZps8HBnKysrg6mpKe7du6eWXwWPKo5z1+MYqwfHWT04zl2vK2Os8VNRS5cuxdSpU2FjY4OCggKsW7cOZWVlCAkJkasrlUoRGBgIW1tbxMfHQ09PD4899hiOHDkCf39/DBgwQOHRm4qKCty8eVP2ODMzE6mpqTAzM4ONjQ0AYMmSJQgODoanpye8vb2xbds2ZGVlYf78+V2274aGhnj77bdhaGjYZdtgHGd14BirB8dZPTjOXa8rY6zxIzazZs3C8ePHUVhYiD59+uDxxx/H2rVrMWzYMIX1Dx8+DB8fH3Tr1k1QnpqaCnNzcwwcOFCuzdGjR+Hv7y9XHhISgpiYGNnj6OhofPDBB8jLy4OzszM++eQT+Pr6dmwHGWOMMaY2Gk9sGGOMMcY6y0M3eJgxxhhjrL04sWGMMcaYzuDEhjHGGGM6gxMbxhhjjOkMTmweUgcPHsSQIUPg6OiIr776StPd0VkzZsxA7969ERQUpOmu6Kzs7Gz4+flh2LBhcHV1xZ49ezTdJZ1TXl6OUaNGwc3NDS4uLvjyyy813SWdVlVVBVtbWyxdulTTXdFZenp6cHNzg5ubm+zm1KriWVEPofr6egwbNgyJiYno2bMn3N3dcfr06S65p8ajLjExERUVFfjmm2/www8/aLo7OikvLw/5+flwc3NDQUEB3N3dce3aNRgbG2u6azqjoaEBNTU1MDIyQlVVFZydnXH27FmF99tjHbdixQrcuHEDNjY2Kl0YlrWdhYUFCgsL29WWj9g8hM6cOYPhw4djwIABMDExweTJk9t8HyqmGn9/f5iYmGi6Gzqtf//+cHNzAwD07dsXZmZmKC4u1myndIxEIoGRkREAoLq6Gg0NDeDfrF3jxo0buHr1KiZPnqzprjAlOLHpAsePH8fUqVNhZWUFkUiEffv2ydWJjo6GnZ0dunXrBg8PD5w4cUL2XG5uLgYMGCB7bG1tjdu3b6uj61qlo3FmqunMOJ87dw5SqVThhTQfZZ0R49LSUowYMQLW1taIioqChYWFmnqvPTojzkuXLu2y2+zois6Ic1lZGTw8PDBu3DgcO3asTdvnxKYLVFZWYsSIEdi0aZPC5+Pj47Fo0SKsWLECFy5cgI+PDyZNmoSsrCwAUPhLqzPuXq5rOhpnpprOinNRURFeeuklbNu2TR3d1iqdEeNevXrh4sWLyMzMxPfff4/8/Hx1dV9rdDTO+/fvh5OTE5ycnNTZba3TGe/nW7duISUlBVu2bMFLL72EsrIy1TtArEsBoISEBEGZl5cXzZ8/X1A2dOhQWr58ORERJSUl0fTp02XPLVy4kL777rsu76s2a0+cmyQmJtIzzzzT1V3UCe2Nc3V1Nfn4+FBsbKw6uqnVOvJebjJ//nzavXt3V3VRJ7QnzsuXLydra2uytbUlc3Nz6tmzJ61Zs0ZdXdZKnfF+DgwMpLNnz6q8TT5io2a1tbVISUlBQECAoDwgIACnTp0CAHh5eSE9PR23b99GeXk5fv75Z0ycOFET3dVaqsSZdZwqcSYihIaGYsKECQgODtZEN7WaKjHOz8+X/aItKyvD8ePHMWTIELX3VZupEucNGzYgOzsbt27dwsaNGxEREYFVq1ZportaS5U4l5SUoKamBgCQk5ODy5cvw97eXuVtaPzu3o+awsJCNDQ0wNLSUlBuaWmJO3fuAGic5vbRRx/B398fUqkUUVFRPLuhjVSJMwBMnDgR58+fR2VlJaytrZGQkIBRo0apu7taS5U4JyUlIT4+Hq6urrJz7XFxcXBxcVF3d7WSKjHOyclBeHg4iAhEhFdeeQWurq6a6K7WUvUzg3WMKnG+cuUK5s2bB7FYDJFIhM8++6xNs4I5sdGQB8fMEJGg7Omnn8bTTz+t7m7pnNbizLPNOkdLcR43bhykUqkmuqVTWoqxh4cHUlNTNdAr3dPaZ0aT0NBQNfVIN7UU5zFjxiAtLa3d6+ZTUWpmYWEBiUQi9wugoKBALoNl7cdxVg+Oc9fjGKsHx1k91BFnTmzUzMDAAB4eHjh8+LCg/PDhwxgzZoyGeqV7OM7qwXHuehxj9eA4q4c64synorpARUUFbt68KXucmZmJ1NRUmJmZwcbGBkuWLEFwcDA8PT3h7e2Nbdu2ISsrC/Pnz9dgr7UPx1k9OM5dj2OsHhxn9dB4nFWeP8VUlpiYSADklpCQEFmdzZs3k62tLRkYGJC7uzsdO3ZMcx3WUhxn9eA4dz2OsXpwnNVD03Hme0UxxhhjTGfwGBvGGGOM6QxObBhjjDGmMzixYYwxxpjO4MSGMcYYYzqDExvGGGOM6QxObBhjjDGmMzixYYwxxpjO4MSGMcYYYzqDExvGGGtBUVER+vbti1u3bmmsD5s2bcLTTz+tse0zpk04sWGMdYrQ0FCIRCK5JTAwUNNd65ANGzZg6tSpGDRokKB87969mDBhAnr37g0jIyMMGTIEYWFhuHDhgkrrra2thYWFBdatW6d0uxYWFqitrUVERATOnj2LkydPdnR3GNN5nNgwxjpNYGAg8vLyBMvOnTu7dJu1tbVdtu779+/j66+/xpw5cwTly5Ytw/PPPw83Nzf89NNPyMjIwLZt2zB48GC8+eabKq3bwMAAs2fPRkxMDBTd2WbHjh0IDg6GgYEBDA0N8eKLL+Jf//pXp+wXYzqt0+46xRh7pIWEhNC0adNarAOAvvzyS5o+fTp1796dHBwcaP/+/YI6GRkZNGnSJDI2Nqa+ffvS7Nmz6e7du7Lnx48fT5GRkbR48WIyNzcnX19fIiLav38/OTg4ULdu3cjPz49iYmIIAJWUlFBFRQWZmJjQnj17BNv66aefyMjIiMrKyhT2d+/evWRhYSEoS05OJgD02WefKWwjlUrltuHu7k6GhoZkZ2dHq1evprq6OiIiunTpEgGgo0ePCtocP36cAFBaWpqs7OjRo2RgYEBVVVUKt8sYa8RHbBhjarVmzRo899xzuHTpEiZPnoy///3vKC4uBgDk5eVh/PjxcHNzw7lz53Do0CHk5+fjueeeE6zjm2++gZ6eHpKSkrB161bcunULQUFBmD59OlJTUzFv3jysWLFCVt/Y2BizZs3Cjh07BOvZsWMHgoKCYGJiorCvx48fh6enp6Bs586d6NGjBxYsWKCwjUgkkv3966+/Yvbs2Vi4cCEuX76MrVu3IiYmBu+++y4AwMXFBaNGjZLr1/bt2+Hl5QVnZ2dZmaenJ+rq6nDmzBmF22WM/ZemMyvGmG4ICQkhiURCxsbGguWdd96R1QFAb731luxxRUUFiUQi+uWXX4iIaOXKlRQQECBYb3Z2NgGga9euEVHjERs3NzdBnWXLlpGzs7OgbMWKFbIjNkREp0+fJolEQrdv3yYiort375K+vr7c0ZLmpk2bRmFhYYKywMBAcnV1FZR99NFHgn0uLS0lIiIfHx9av369oG5cXBz1799f9viLL74gY2NjKi8vJyKi8vJyMjY2pq1bt8r1p3fv3hQTE6O0v4wxPmLDGOtE/v7+SE1NFSyRkZGCOq6urrK/jY2NYWJigoKCAgBASkoKEhMT0aNHD9kydOhQAMCff/4pa/fgUZRr165h1KhRgjIvLy+5x8OHD0dsbCwAIC4uDjY2NvD19VW6P/fv30e3bt3kypsflQGAsLAwpKamYuvWraisrJSNmUlJScE777wj2J+IiAjk5eWhqqoKAPDCCy9AKpUiPj4eABAfHw8iwqxZs+S22717d1k7xphiepruAGNMdxgbG8PBwaHFOvr6+oLHIpEIUqkUACCVSjF16lS8//77cu369+8v2E5zRCSXbJCCAblz5szBpk2bsHz5cuzYsQMvv/yyXLvmLCwsUFJSIihzdHTEyZMnUVdXJ9uXXr16oVevXsjJyRHUlUqlWLNmDWbOnCm37qaEydTUFEFBQdixYwfCw8Nlp8d69uwp16a4uBh9+vRR2l/GGM+KYow9RNzd3ZGRkYFBgwbBwcFBsDyYzDQ3dOhQnD17VlB27tw5uXqzZ89GVlYWPv/8c2RkZCAkJKTF/owcORKXL18WlL3wwguoqKhAdHS0Svtz7do1uX1xcHCAWPy/j9/w8HAkJSXh4MGDSEpKQnh4uNy6/vzzT1RXV2PkyJGtbpexRxknNoyxTlNTU4M7d+4IlsLCQpXbR0ZGori4GC+88ALOnDmDv/76C7/99hvCwsLQ0NCgtN28efNw9epVLFu2DNevX8fu3bsRExMDQHjaqHfv3pg5cyb++c9/IiAgANbW1i32Z+LEicjIyBActfH29sbrr7+O119/HUuWLMHJkyfxf//3f/jjjz/w9ddfQyQSyZKWVatWITY2FqtXr0ZGRgauXLmC+Ph4vPXWW4LtjB8/Hg4ODnjppZfg4OCg8PTYiRMnYG9vj8GDB7caR8YeZZzYMMY6zaFDh9C/f3/BMm7cOJXbW1lZISkpCQ0NDZg4cSKcnZ3x2muvwdTUVHCE40F2dnb44Ycf8OOPP8LV1RVffPGFbFaUoaGhoG54eDhqa2sRFhbWan9cXFzg6emJ3bt3C8o3btyI77//HhcuXMCUKVPg6OiIZ599FlKpFMnJybLTSBMnTsTBgwdx+PBhjBo1Co8//jg+/vhj2Nraym0rLCwMJSUlSvu1c+dOREREtNpnxh51IlJ0IpoxxrTcu+++iy1btiA7O1tQ/t133+G1115Dbm4uDAwMWl3Pzz//jKVLlyI9Pb3F5Korpaen44knnsD169dhamqqkT4wpi148DBjTCdER0dj1KhRMDc3R1JSEj788EO88sorsuerqqqQmZmJDRs2YN68eSolNQAwefJk3LhxA7dv38bAgQO7qvstys3NRWxsLCc1jKmAj9gwxnTC4sWLER8fj+LiYtjY2CA4OBhvvPEG9PQaf7+tXr0a7777Lnx9fbF//3706NFDwz1mjHUFTmwYY4wxpjN48DBjjDHGdAYnNowxxhjTGZzYMMYYY0xncGLDGGOMMZ3BiQ1jjDHGdAYnNowxxhjTGZzYMMYYY0xncGLDGGOMMZ3BiQ1jjDHGdMb/A2wZ+Sibp26BAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pgg = px + py # the total photon survival probability\n", "\n", "print (pgg.shape)\n", "\n", "plt.plot(ml.EGeV, pgg[0])\n", "\n", "plt.grid(True, lw = 0.2)\n", "plt.grid(True, which = 'minor', axis = 'y', lw = 0.2)\n", "\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel(r'Photon survival probability')\n", "\n", "plt.gca().set_xscale('log')\n", "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}} = {1:.2f}'\\\n", " r' \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n", " xy=(0.05,0.1),\n", " size='large',\n", " xycoords='axes fraction',\n", " ha='left',**effect)\n", "\n", "plt.axvline(transfer.EminGeV(ml.alp.m, ml.alp.g, ml.modules[0].nel[-1], ml.modules[0].B[-1]),\n", " ls=':',\n", " label='Emin Jet End')\n", "plt.axvline(transfer.EmaxGeV(ml.alp.g, ml.modules[0].B[0]), \n", " ls='-.',\n", " color='red',\n", " label='Emax Jet Base')\n", "\n", "plt.gca().set_ylim(0.5,1.)\n", "plt.gca().set_xlim(min(ml.EGeV),max(ml.EGeV))\n", "plt.gca().set_yscale('log')\n", "plt.subplots_adjust(left = 0.2)\n", "plt.legend(loc = 'upper left', fontsize = 'medium')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 4 }