{ "cells": [ { "cell_type": "markdown", "id": "20bb9c44", "metadata": {}, "source": [ "# AstronomyCalc tutorial\n", "This is a tutorial to show an usage of the [AstronomyCalc](https://github.com/sambit-giri/AstronomyCalc) package. Corresponding notebooks can be found [here](https://github.com/sambit-giri/AstronomyCalc/tree/main/notebooks)." ] }, { "cell_type": "code", "execution_count": 1, "id": "6d5c776e", "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "\n", "from astropy import units" ] }, { "cell_type": "code", "execution_count": 2, "id": "4bee9a11", "metadata": {}, "outputs": [], "source": [ "try:\n", " import AstronomyCalc\n", "except:\n", " !pip install git+https://github.com/sambit-giri/AstronomyCalc.git\n", " import AstronomyCalc\n", "from AstronomyCalc import create_data" ] }, { "cell_type": "markdown", "id": "50370ffa", "metadata": {}, "source": [ "# Model universes\n", "Here simulation of a few model universes are shown." ] }, { "cell_type": "code", "execution_count": 3, "id": "721839b0", "metadata": {}, "outputs": [], "source": [ "code_param_dict = {'zmin': 0.01, 'zmax': 11.0, 'Nz': 100, 'verbose': True}" ] }, { "cell_type": "markdown", "id": "26cc9e31", "metadata": {}, "source": [ "### Einsten-de Sitter universe\n", "\n", "In this model, the universe is assumed to be dominated by matter." ] }, { "cell_type": "code", "execution_count": 4, "id": "bb3d1a53", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cosmo_dict = {'Om': 1.0, 'Or': 0, 'Ok': 0, 'Ode': 0, 'h': 0.68}\n", "param_EdS = AstronomyCalc.param(cosmo=cosmo_dict, code=code_param_dict)\n", "\n", "AstronomyCalc.plot_universe_pie(cosmo_dict, title=\"Content of Einsten-de Sitter universe\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "dae78111", "metadata": {}, "outputs": [], "source": [ "D_EdS = AstronomyCalc.CosmoDistances(param_EdS)" ] }, { "cell_type": "markdown", "id": "22d3aa44", "metadata": {}, "source": [ "### de Sitter universe\n", "\n", "In this model, the universe is assumed to be dominated by dark energy." ] }, { "cell_type": "code", "execution_count": 6, "id": "3c07ddb6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cosmo_dict = {'Om': 0.0, 'Or': 0, 'Ok': 0, 'Ode': 1.0, 'h': 0.68}\n", "param_dS = AstronomyCalc.param(cosmo=cosmo_dict, code=code_param_dict)\n", "\n", "AstronomyCalc.plot_universe_pie(cosmo_dict, title=\"Content of de Sitter universe\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "92ce5202", "metadata": {}, "outputs": [], "source": [ "D_dS = AstronomyCalc.CosmoDistances(param_dS)" ] }, { "cell_type": "markdown", "id": "e2ea37b6", "metadata": {}, "source": [ "### Benchmark model or flat $\\Lambda$-cold dark matter ($\\Lambda$CDM) universe\n", "\n", "In this model, the universe is flat ($\\Omega_m+\\Omega_r+\\Omega_{DE}=1$ or $\\Omega_\\kappa=0$) universe containing cold dark matter and constant dark energy. This model best explains the Cosmic Microwave Background (CMB) observations from WMAP and Planck. " ] }, { "cell_type": "code", "execution_count": 8, "id": "d18c19b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cosmo_dict = {'Om': 0.31, 'Or': 0.0, 'Ok': 0.0, 'Ode': 0.69, 'h': 0.68}\n", "param = AstronomyCalc.param(cosmo=cosmo_dict, code=code_param_dict)\n", "\n", "AstronomyCalc.plot_universe_pie(cosmo_dict, title=\"Content of the Benchmark universe\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "5a921cfc", "metadata": {}, "outputs": [], "source": [ "D = AstronomyCalc.CosmoDistances(param)" ] }, { "cell_type": "markdown", "id": "7f52b8db", "metadata": {}, "source": [ "## Plot distances in model universes" ] }, { "cell_type": "code", "execution_count": 10, "id": "87c14e7e", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zs = np.linspace(param.code.zmin,param.code.zmax,param.code.Nz)\n", "\n", "fig, axs = plt.subplots(1,2,figsize=(10,4))\n", "axs[0].loglog(zs, D_dS.comoving_dist(zs), ls='-.', label='de Sitter')\n", "axs[0].loglog(zs, D.comoving_dist(zs), ls='-', label='Planck')\n", "axs[0].loglog(zs, D_EdS.comoving_dist(zs), ls='--', label='Einstein-de Sitter')\n", "axs[0].legend(loc=2, fontsize=14)\n", "axs[0].set_xlabel('Redshift', fontsize=15)\n", "axs[0].set_ylabel('Comoving distance', fontsize=15)\n", "axs[0].axis([0.01,10,40,5e4])\n", "\n", "axs[1].loglog(zs, D_dS.proper_dist(zs), ls='-.', label='de Sitter')\n", "axs[1].loglog(zs, D.proper_dist(zs), ls='-', label='Planck')\n", "axs[1].loglog(zs, D_EdS.proper_dist(zs), ls='--', label='Einstein-de Sitter')\n", "axs[1].legend(loc=2, fontsize=14)\n", "axs[1].set_xlabel('Redshift', fontsize=15)\n", "axs[1].set_ylabel('Proper distance', fontsize=15)\n", "axs[1].axis([0.01,10,40,5e4])\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c2cb230f", "metadata": {}, "source": [ "# Hubble diagram" ] }, { "cell_type": "markdown", "id": "4a0a766e", "metadata": {}, "source": [ "### Original data used in Hubble (1929)\n", "Edwin Hubble measured the recession velocity ($v$) of the galaxies at different distances ($d$). To explain this data, he fitted a line $v=H_0 d$, where $H_0$ is a constant. This constant tells us how fast objects are moving away from us, which is a fundamental aspect of cosmology." ] }, { "cell_type": "code", "execution_count": 11, "id": "ff9e65c2", "metadata": {}, "outputs": [], "source": [ "dist_Hubble1929, vel_Hubble1929 = create_data.Hubble1929_data()" ] }, { "cell_type": "code", "execution_count": 12, "id": "edc8396d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v_func = lambda r,H0: H0*r\n", "rr = np.linspace(0,2.2)\n", "\n", "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(dist_Hubble1929, vel_Hubble1929,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Hubble (1929)', zorder=5)\n", "ax.plot(rr, v_func(rr,500), c='C0') # 500 km/s/Mpc is the value of Hubble constant estimated in Hubble (1929).\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Distance ($10^6$ parsecs)', fontsize=16)\n", "ax.set_ylabel(r'Recessional Velocity (km/s)', fontsize=16)\n", "ax.set_xticks([0,1,2])\n", "ax.set_yticks([0,500,1000])\n", "ax.axis([-0.5,2.5,-400,1300])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d38c918b", "metadata": {}, "source": [ "### Least Square Fit\n", "To find the best fit model, we require a loss or cost function that describes how far the model is from the data. For the above data, we can find the best fit model by minimising the total squared error between the model and the observed data, which can be give as,\n", "\n", "$r^2 = \\sum_i \\left[y_i-f(x_i|\\theta)\\right]^2$,\n", "\n", "where $(x_i,y_i)$ are the data and $\\theta$ represents the model parameters." ] }, { "cell_type": "code", "execution_count": 13, "id": "315911f3", "metadata": {}, "outputs": [], "source": [ "least_sq = lambda y,f: np.vectorize(lambda f: np.sum((y-f)**2))" ] }, { "cell_type": "code", "execution_count": 14, "id": "a958151f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v_func = lambda r,H0: H0*r\n", "rr = np.linspace(0,2.2)\n", "\n", "fig, axs = plt.subplots(1,2,figsize=(15,6))\n", "ax = axs[0]\n", "ax.errorbar(dist_Hubble1929, vel_Hubble1929,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Hubble (1929)', zorder=5)\n", "ax.plot(rr, v_func(rr,500), c='C0') # 500 km/s/Mpc is the value of Hubble constant estimated in Hubble (1929).\n", "# Plot vertical lines from every data point to the line\n", "for dist, vel in zip(dist_Hubble1929, vel_Hubble1929):\n", " ax.plot([dist, dist], [vel, v_func(dist, 500)], c='gray', linestyle='--', linewidth=1)\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Distance ($10^6$ parsecs)', fontsize=16)\n", "ax.set_ylabel(r'Recessional Velocity (km/s)', fontsize=16)\n", "ax.set_xticks([0,1,2])\n", "ax.set_yticks([0,500,1000])\n", "ax.axis([-0.5,2.5,-400,1300])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "ax.grid()\n", "\n", "least_sq = lambda y,f: np.sum((y-f)**2)\n", "H0_array = np.linspace(60,800)\n", "least_sq_array = np.array([least_sq(vel_Hubble1929,v_func(dist_Hubble1929,Hi)) for Hi in H0_array])\n", "\n", "ax = axs[1]\n", "\n", "ax.plot(H0_array, least_sq_array/1e6, c='C0')\n", "# ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'$H_0$ (km/s/Mpc)', fontsize=16)\n", "ax.set_ylabel(r'Total squared error ($10^6$ km/s)', fontsize=16)\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "ax.grid()\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4d060ca5", "metadata": {}, "source": [ "### Generate synthetic supernova data\n", "\n", "We generate distance modulus data $\\mu(z)$ given as,\n", "\n", "$\\mu(z) = 5\\log_{10}\\left(\\frac{d_L(z)}{1~\\mathrm{Mpc}}\\right)+25$ ,\n", "\n", "where $d_L$ is the luminosity distance estimated by observing supernova. This distance is related to the comoving distance $d_c(z)$ as,\n", "\n", "$d_L(z) = (1+z) d_c(z) = (1+z)\\frac{c}{H_0}\\int\\frac{dz}{\\left[\\Omega_m(1+z)^3+\\Omega_\\Lambda\\right]^{1/2}}$ ." ] }, { "cell_type": "code", "execution_count": 15, "id": "909f0d04", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Cosmological parameters\n", "{'Om': 0.3, 'Or': 0, 'Ok': 0, 'Ode': 0.7, 'h': 0.7, 'Tcmb': 2.725}\n", "Code parameters\n", "{'zmin': 0.001, 'zmax': 3.0, 'Nz': 100, 'verbose': True}\n" ] } ], "source": [ "code_param_dict = {'zmin': 0.001, 'zmax': 3.0, 'Nz': 100, 'verbose': True}\n", "cosmo_dict = {'Om': 0.30, 'Or': 0, 'Ok': 0, 'Ode': 0.70, 'h': 0.70}\n", "param = AstronomyCalc.param(cosmo=cosmo_dict, code=code_param_dict)\n", "\n", "print('Cosmological parameters')\n", "print(param.cosmo.__dict__)\n", "print('Code parameters')\n", "print(param.code.__dict__)" ] }, { "cell_type": "code", "execution_count": 16, "id": "81fc6806", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100,) (100,) (100,)\n" ] } ], "source": [ "z_true = np.linspace(0.01, 2, 1000)\n", "mu_true = AstronomyCalc.distance_modulus(param, z=z_true)\n", "\n", "z_sample, mu_sample, dmu = create_data.generate_distance_modulus()\n", "print(z_sample.shape, mu_sample.shape, dmu.shape)" ] }, { "cell_type": "code", "execution_count": 17, "id": "4d97489c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(z_true, mu_true, c='k', alpha=0.8, lw=3, ls='--', label='Truth')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e7cb68a6", "metadata": {}, "source": [ "### Posterior distribution\n", "\n", "To find a model for a dataset with errorbar, we can define the loss function using the posterior distribution defined by the [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) as,\n", "\n", "$p(\\theta|{x_i,y_i})\\propto p({x_i,y_i}|\\theta) p(\\theta)$ ,\n", "\n", "where $p({x_i,y_i}|\\theta)$ and $p(\\theta)$ are the data likelihood and the prior distribution, respectively." ] }, { "cell_type": "markdown", "id": "2b0ffc94", "metadata": {}, "source": [ "Based on the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem), the each supernova data point can be assumed to be well defined by Gaussian distribution and, therefore, the likelihood can be given as,\n", "\n", "$p({x_i,y_i}|\\theta) = \\frac{1}{\\sqrt{2\\pi\\sigma^2_i}} \\mathrm{exp}\\left(-\\frac{[y_i-f(x_i|\\theta)]^2}{2\\sigma^2_i}\\right)$ ,\n", "\n", "where $\\sigma_i$ is the standard deviation of the $i^\\mathrm{th}$ data point. If we assume no prior knowledge, then $p(\\theta)=1$. Instead of likelihood ($L$), it is more convenient to work with log-likelihood:\n", "\n", "$\\log(L) \\propto - \\sum^N_i \\left(\\frac{[y_i-f(x_i|\\theta)]^2}{2\\sigma^2_i}\\right)$, \n", "\n", "which should maximize for the best-fit. Therefore the loss function should be:\n", "\n", "$_{~~\\theta}^\\mathrm{min}\\sum^N_i \\left(\\frac{[y_i-f(x_i|\\theta)]^2}{2\\sigma^2_i}\\right)$" ] }, { "cell_type": "markdown", "id": "7f6d932a", "metadata": {}, "source": [ "### Linear Regression\n", "This regression finds a parametric model where $f(x|\\theta)=\\sum^k_p\\theta_p g_p(x)$, where the functions $g_p(x)$ can be nonlinear functions of x.\n", "\n", "For a straight-line, $f(x|\\theta)=\\theta_0 + \\theta_1 x$." ] }, { "cell_type": "code", "execution_count": 18, "id": "7ee175c8", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/sambit/miniconda3/envs/py3/lib/python3.10/site-packages/astroML/linear_model/linear_regression_errors.py:10: UserWarning: LinearRegressionwithErrors requires PyMC3 to be installed\n", " warnings.warn('LinearRegressionwithErrors requires PyMC3 to be installed')\n" ] } ], "source": [ "from astroML.linear_model import LinearRegression" ] }, { "cell_type": "code", "execution_count": 19, "id": "cf338c8c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(50,)\n" ] } ], "source": [ "model = LinearRegression()\n", "model.fit(z_sample[:,None], mu_sample, dmu)\n", "\n", "zz = np.linspace(0,2)\n", "mu_line = model.predict(zz[:,None])\n", "print(mu_line.shape)" ] }, { "cell_type": "code", "execution_count": 20, "id": "d889993a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(zz, mu_line, c='C2', alpha=0.8, lw=3, label='Straight-line Regression')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b8fe4fb4", "metadata": {}, "source": [ "### Polynomial Regression\n", "This is also a linear regression, but higher order dependence on the independent variable is explored, which means $g_p(x)$ is could be higher order polynomial." ] }, { "cell_type": "code", "execution_count": 21, "id": "40822e2c", "metadata": {}, "outputs": [], "source": [ "from astroML.linear_model import PolynomialRegression" ] }, { "cell_type": "markdown", "id": "e7614e4d", "metadata": {}, "source": [ "For a third-order polynomial, $f(x|\\theta)=\\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3$." ] }, { "cell_type": "code", "execution_count": 22, "id": "511f4ada", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(50,)\n" ] } ], "source": [ "model = PolynomialRegression(degree=3)\n", "model.fit(z_sample[:,None], mu_sample, dmu)\n", "\n", "zz = np.linspace(0,2)\n", "mu_poly3 = model.predict(zz[:,None])\n", "print(mu_poly3.shape)" ] }, { "cell_type": "markdown", "id": "088290a2", "metadata": {}, "source": [ "For a fifth-order polynomial, $f(x|\\theta)=\\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 + \\theta_4 x^4 + \\theta_5 x^5$." ] }, { "cell_type": "code", "execution_count": 23, "id": "638a6110", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(50,)\n" ] } ], "source": [ "model = PolynomialRegression(degree=5)\n", "model.fit(z_sample[:,None], mu_sample, dmu)\n", "\n", "zz = np.linspace(0,2)\n", "mu_poly5 = model.predict(zz[:,None])\n", "print(mu_poly5.shape)" ] }, { "cell_type": "code", "execution_count": 24, "id": "6b7d3d16", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(zz, mu_line, c='C2', alpha=0.8, lw=3, label='Straight-line Regression')\n", "ax.plot(zz, mu_poly3, c='C3', alpha=0.8, lw=3, label='Third-order polynomial Regression')\n", "ax.plot(zz, mu_poly5, c='C4', alpha=0.8, lw=3, label='Fifth-order polynomial Regression')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3dd635e2", "metadata": {}, "source": [ "### Underfitting vs overfitting\n", "\n", "To illustrate this effect, we consider a simple example $y=x \\sin(x)$ with some scatter." ] }, { "cell_type": "code", "execution_count": 25, "id": "cc6385eb", "metadata": {}, "outputs": [], "source": [ "x_simple = np.linspace(0,3,20)\n", "yerr_simple = 0.01*np.ones_like(x_simple)\n", "y_simple = 0.2+x_simple*np.sin(x_simple)+0.1*np.random.randn(len(x_simple))" ] }, { "cell_type": "code", "execution_count": 26, "id": "e75085f7", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1,3,figsize=(17,5))\n", "\n", "for i,deg in enumerate([1,3,20]):\n", " ax = axs[i]\n", " model = PolynomialRegression(degree=deg)\n", " model.fit(x_simple[:,None], y_simple, yerr_simple)\n", " xx = np.linspace(0,3)\n", " yy = model.predict(xx[:,None])\n", " \n", " ax.errorbar(x_simple, y_simple,\n", " ls=' ',\n", " color='C0',\n", " marker='^', markeredgecolor='k', markersize=10, \n", " label='Observation', zorder=5)\n", " ax.plot(xx, yy, c=f'C{i+2}', lw=3, alpha=0.8, label=f'degree={deg}')\n", " ax.legend(loc=4, facecolor='white', framealpha=1)\n", " ax.set_xlabel(r'$x$', fontsize=16)\n", " ax.set_ylabel(r'$y$', fontsize=16)\n", " ax.axis([-0.1,3.1,-0.3,2.4])\n", " ax.tick_params(axis='both', which='major', labelsize=15) \n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "728645cd", "metadata": {}, "source": [ "### Cross-Validation\n", "\n", "We divide the data into three sets: training, validation and testing set. In this method, the model is fit on the training set and validated using the validation set for different complexity of the model." ] }, { "cell_type": "code", "execution_count": 27, "id": "29f47afe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Full data: (20,) (20,)\n", "Training data: (14,) (14,)\n", "Validation data: (3,) (3,)\n", "Testing data: (3,) (3,)\n" ] } ], "source": [ "from sklearn.model_selection import train_test_split\n", "\n", "X, y = x_simple.copy(), y_simple.copy()\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1)\n", "X_test, X_val, y_test, y_val = train_test_split(X_test, y_test, test_size=0.5, random_state=1)\n", "yerr_train, yerr_val, yerr_test = yerr_simple[:len(y_train)], yerr_simple[:len(y_val)], yerr_simple[:len(y_test)]\n", "\n", "print('Full data:', X.shape, y.shape)\n", "print('Training data:', X_train.shape, y_train.shape)\n", "print('Validation data:', X_val.shape, y_val.shape)\n", "print('Testing data:', X_test.shape, y_test.shape)" ] }, { "cell_type": "markdown", "id": "8b91ae80", "metadata": {}, "source": [ "We can define the \"Goodness of fit\" using mean squared error (MSE):\n", "\n", "$\\mathrm{MSE} = \\frac{1}{N}\\sum^N_i \\left[y_i-f(x_i|\\theta)\\right]^2$" ] }, { "cell_type": "code", "execution_count": 28, "id": "e055a031", "metadata": {}, "outputs": [], "source": [ "from sklearn.metrics import mean_squared_error" ] }, { "cell_type": "code", "execution_count": 29, "id": "646dce7f", "metadata": {}, "outputs": [], "source": [ "degree_list = np.arange(15)\n", "mse_train = np.zeros_like(degree_list, dtype=float)\n", "mse_val = np.zeros_like(degree_list, dtype=float)\n", "\n", "for i,deg in enumerate(degree_list):\n", " model = PolynomialRegression(degree=deg)\n", " model.fit(X_train[:,None], y_train, yerr_train)\n", " y_pred = model.predict(X_val[:,None])\n", " mse_val[i] = mean_squared_error(y_val,y_pred)\n", " y_pred = model.predict(X_train[:,None])\n", " mse_train[i] = mean_squared_error(y_train,y_pred)" ] }, { "cell_type": "code", "execution_count": 30, "id": "2aaa20f3", "metadata": {}, "outputs": [ { "data": { "image/png": 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NGjVSOd+nTx8AwIEDB4rt601zS1/n5ORUspBERERUrhjobEt6A4MsZK9fvw4AaNy4sdrzBe03btwotq9mzZrB3t4ex48fx6lTp5TOnT59GiEhIfD19UVAQEApUxMREVF5whFZw2eQhWzBTk7VqlVTe76gvfAao+rIZDJs3rwZUqkUbdu2RevWrdG/f3+0bt0abdq0QdOmTRESEgJzc3PdfQNEREREpHcGuY5sWloagKLXTi3YevTly5ca9de7d28cPnwYffv2xblz5xTtdnZ26NSpE6pWrVpsH9nZ2cjOzlYcp6amvvF67hBV/vAjJyKi8o3/zhsfgxyR1bWVK1eiQ4cOePfdd3Hjxg2kpaXhxo0baNeuHebMmYPevXsX28fixYshk8kUXx4eHmqvKxjZLSjGqfwoeCNjamqQ7/+IiEjHOLXA8Bnkb+SCVQoyMjLUni/YerRSpUrF9nXy5ElMmjQJjRs3xu7duyGVvqrd69Wrhz179qBJkyY4ePAgDh8+jK5duxbZz/Tp0zFx4kTFcWpqqtpi1tTUFM7OzopNG2xtbRXPScZLLpfjyZMnsLW1hZmZmdhxiIiICAZayHp6egIAHj9+rPZ8QbuXl1exff38888AgF69eqkUlCYmJujduzeuXbuG06dPv7GQtbCw0HgFhIL82uxARoZLKpXCz8+P79CJiMqp4OBgDB48WDHFwMTEROREVByDLGQbNGgAAIiIiFB7vqC9fv36xfZVUPTKZDK15wvak5KSSpyzKBKJBF5eXqhatSpycnJ01i+JRyKRwMLCgqPrRETlmLm5OW/+NjIGWci2atUKMpkM9+7dw7Vr19CwYUOl83v27AEAdOvWrdi+3NzcAKDIDQ8uX74MAKhevbr2gYtgamrK+ZREREREemKQw0vm5uYYM2YMAGD06NGKObEAsGrVKty4cQOBgYHw9/dXtG/YsAG1a9fG9OnTlfrq2bMnAGD79u3466+/lM798ccf2LFjB6RSKXr16qWn74aIiIiI9MFghwtnzZqFsLAwnD9/XrFhQUxMDC5evAgXFxds2bJF6frnz5/j7t27iI+PV2rv2bMnPvroI+zevRvdunVDkyZNUKNGDTx48EAxSvvVV1+hVq1aZfa9EREREVHpGeSILABYWlrixIkTmD17NqytrbF//37ExMQgKCgIERER8Pb21qgfiUSCX3/9FZs3b8a7776L6Oho7Nu3Dw8fPsR7772Hw4cPY8aMGXr+boiIiIhI1yQCV//VSmpqKmQyGVJSUmBnZyd2HCIiIiqlR48eKW4Sl0gkcHZ2hq+vr8ipjJu+6yWDnVpAREREVJYOHDiArVu3Ko67dOmChQsXipiIimOwUwuIiIiIiN6EhSwRERERAM62ND4sZImIiIjU4E6Oho+FLBERERE4ImuMWMgSERERqcERWcPHQpaIiIiIjBILWSIiIiJwaoExYiFLREREREaJhSwRERERGSUWskRERERklFjIEhEREanBVQsMHwtZIiIiIvBmL2PEQpaIiIhIDY7IGj4WskRERERklCQCx9G1kpqaCplMhpSUFNjZ2Ykdh4iIiEopOTkZaWlpimNra2s4OjqKmMj46bteMtV5j0RERERGyN7eHvb29mLHoBLg1AIiIiIiMkosZImIiIjIKLGQJSIiIiKjxEKWiIiIiIwSb/YiIiIiAvD06VMkJiYCeLWGrEwmQ5UqVURORW/CQpaIiIgIwPbt27Fjxw7FcY8ePTB79mwRE1FxOLWAiIiIiIwSC1kiIiIiANwjyviwkCUiIiJSQyKRiB2BisFCloiIiAgckTVGLGSJiIiI1OCIrOFjIUtERERERomFLBERERE4tcAYsZAlIiIiUoNTCwwfC1kiIiIiMkosZImIiIjAqQXGiIUsERERERklFrJEREREZJRYyBIRERGpwZu9DB8LWSIiIiIySqZiByAiIiIyBIMGDULXrl0VN305OTmJnIiKw0KWiIiICIC7uzvc3d3FjkElwKkFRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJd7sRURERAQgNTUVmZmZimMrKyvY2dmJmIiKw0KWiIiICMCGDRvw+++/K4779u2LKVOmiJiIisOpBURERERklFjIEhEREZFRYiFLREREpIZEIhE7AhWDhSwRERERGSUWskREREQABEEQOwKVEAtZIiIiIjU4tcDwsZAlIiIiAkdkjRELWSIiIiI1OCJr+Eq1IUJcXBwiIiLw9OlTJCUlwcHBAZUrV4a/vz+qVKmiq4xERERERCpKXMg+evQI33zzDfbv34/IyMgir/Pz80OvXr0wcuRIeHp6liokERERkb5xaoHx0biQvXfvHqZOnYo//vgD+fn5AAB7e3vUqVMHTk5OsLOzQ0pKCl68eIHbt2/j7t27WLJkCZYvX46ePXti6dKl8Pb21ts3QkRERKRLnFpg+DQqZKdNm4a1a9ciOzsbDRo0QFBQEDp27Ii6deuqvV4QBNy8eROhoaH48ccfsXfvXvz1118YP348Fi9erNNvgIiIiEgXOCJrfDS62WvZsmXo0KEDrly5gqtXr2LcuHFFFrHAq3cwb7/9NiZMmIBr167h8uXLaNeuHZYtW6az4ERERERUsWk0InvmzBm0atVK6yfx9/fHwYMHce7cOa37ICIiIiJ6nUTgOLpWUlNTIZPJkJKSAjs7O7HjEBERUSlFRkbiv//+UxxXrVoVPj4+IiYyfvqul0q1/BYRERFReeHn5wc/Pz+xY1AJaDRH9tGjR0hMTCxx59euXcOff/5Z4scRERERERVHo0K2Ro0amDx5stpzjRs3xpdffqn23Nq1a9GrVy/t0xERERERFUGjQlYQhCKXpLh27RpiYmJ0GoqIiIiIqDgaFbJERERERIaGN3sRERERAcjNzVX6BNrExAQmJiYiJqLisJAlIiIiArBw4UIcPHhQcTx48GCMHTtWxERUHE4tICIiIiKjxEKWiIiICCjyxnYyXBpPLUhLS8OjR49KdC4tLU37ZEREREREb6BxIbt3717s3btXpV0ikRR5joiIiIhIXzQuZLUdbpdIJFo9joiIiIjoTTQqZB88eKDvHEREREQGhYNxhk+jQtbLy0vfOYiIiIhExZu9jA9XLSAiIiJSgyOyhk9nGyLExcXh8OHDeP78OapVq4auXbvC0dFRV90TERERESnRqJC9desWtm3bhkaNGmHAgAEq57ds2YLRo0cjJydH0SaTyfDTTz/hgw8+0F1aIiIiIj3h1ALjo9HUgt9//x0rV66EmZmZyrkrV65gxIgRyM7OhpWVFfz9/eHm5obk5GT0798fsbGxOg9NREREpG+cWmD4NCpkz507BysrK7Wjq0uWLEF+fj78/PwQGRmJS5cuITY2Fp999hkyMjLwzTff6Dw0ERERka5xRNb4aFTIRkdHo1GjRrC0tFRqz83NxaFDhyCRSLBo0SK4u7u/6lQqxfLly2FjY4OwsDDdpyYiIiLSM47IGj6NCtlnz57B09NTpf3q1avIysqCubk5unbtqnROJpOhadOmiI6O1k1SIiIiIqLXaHSzV2ZmJjIzM1XaIyIiAAD169eHlZWVynk3NzekpaWVMiIRERGR/vXq1QvNmjVTHPv6+oqYhjShUSHr7OysdmT1/PnzkEgkaNKkidrHZWVlwd7evlQBiYiIiMpCkyZNiqxpyDBpNLXA398fN2/exOnTpxVtqampOHDgAACgbdu2ah939+5duLm56SAmEREREZEyjQrZ4OBgCIKA7t27Y/bs2Vi3bh3atGmDlJQUODk5qV3NID4+Hnfu3EHdunV1HpqIiIiISKOpBT179kT//v2xa9cuLFq0CMD/LVGxbNkyldUMAODnn38GALRr105XWYmIiIiIFDQakQWAX375BevXr0erVq1Qs2ZNtG/fHvv27UNQUJDa60+fPo369eujY8eOWofLzMzEnDlz4OfnB0tLS7i7uyM4OBhPnjzRqr+HDx9i5MiRqFGjBiwsLODs7IwWLVpg+fLlWmckIiIiInFIBANd/TcrKwtt27ZFeHg4qlSpgoCAADx8+BCXLl2Ci4sLwsPD4e3trXF/hw8fRp8+fZCZmYnGjRvD19cXL168wD///AMbG5sSLxOWmpoKmUyGlJQU2NnZlfTbIyIiIir39F0vaTS1QAwLFy5EeHg4WrRogaNHj8LW1hYAsGrVKvzvf/9DcHAwTp48qVFfd+7cQe/evVGpUiWEhoaiZcuWinNyuVyxjBgRERFVXHPnzsWJEycUx0FBQQgODhYxERVH46kFZSknJwcbNmwAAHz99deKIhYAJk6ciPr16+PUqVP4+++/Nepv4sSJyMrKwrZt25SKWODVLmRcaoOIiIiys7ORkZGh+MrNzRU7EhVDoxHZghu8tDVjxowSXX/u3DmkpKTAx8cHjRo1Ujnfp08f3LhxAwcOHIC/v/8b+4qNjUVISAi8vb3x3nvvlSgHERERVRwGOtuS3kCjQnbWrFmK/YYFQdB47+GCa0tayF6/fh0A0LhxY7XnC9pv3LhRbF8nT56EXC5Hy5YtkZeXh99//x3nzp1Dfn4+3n77bfTr1w8ODg4lykdERETln6b1DomnRHNkmzZtijp16ugri8KjR48AANWqVVN7vqA9Jiam2L5u3boFALC1tUVAQADCw8OVzs+cORN79uwpclMHIiIiIjJMGhWyDg4OSEpKwuXLlyGVShEcHIz+/fsrzV3VpbS0NACAtbW12vM2NjYAgJcvXxbbV1JSEgDghx9+gK2tLXbs2IEuXbrg2bNnWLBgAX755Rf06tULN2/eRNWqVYvsJzs7G9nZ2Yrj1NRUjb8fIiIiMnycWmB8NLrZKz4+Hjt27ED79u1x6dIljBgxAlWqVEFwcDDOnj2r74ylIpfLAQB5eXnYtGkTBgwYAAcHB/j5+eHnn39G06ZNkZKSgo0bN76xn8WLF0Mmkym+PDw8yiI+ERERERVBo0LW3Nwc/fv3x9GjR/HgwQPMmTMHTk5O2LZtGwIDA+Hn54clS5YgLi5OJ6EKRnozMjLUnk9PTwcAVKpUSeO+bG1t8dFHH6mc//TTTwEAp06demM/06dPR0pKiuIrNja22OcmIiIiIv0p8fJbHh4emDt3Lh4+fIijR4+ib9++ePz4MWbMmAEvLy+8//772L9/f6lCeXp6AgAeP36s9nxBu5eXV7F9FVzj6empdtJ29erVAQAJCQlv7MfCwgJ2dnZKX0RERFR+8WYvw1eqdWQ7dOiAnTt3Ii4uDhs2bEC9evVw+PBhjBgxolShGjRoAABFblRQ0F6/fv1i+ypYvqtgrmxhiYmJAKC3+b5EREREpB862RAhOTkZT58+VRSFpZ0s3apVK8hkMty7dw/Xrl1TOb9nzx4AQLdu3Yrtq2XLlnBycsJ///2Hu3fvqpwvmFKgbr1aIiIiqjh4s5fx0bqQzc7Oxvbt29G+fXvUrFkTCxYsQFJSEoYOHYoDBw6UKpS5uTnGjBkDABg9erRiTizwaovaGzduIDAwUGkzhA0bNqB27dqYPn26Ul+mpqaYOHEiBEHA6NGjlVYbCAsLw7Zt2yCRSEo9ikxERETlC6cWGL4SrSMLAJcvX8aWLVuwa9cupKamQhAEBAQEIDg4GB999FGRS2aV1KxZsxAWFobz58/D19cXAQEBiImJwcWLF+Hi4oItW7YoXf/8+XPcvXsX8fHxKn1NnjwZJ06cQFhYGPz8/NC8eXM8f/4c4eHhyM/Px1dffYVmzZrpJDcREREZJ47IGh+NCtnnz5/j559/xtatW3Hz5k0IggB3d3d8/vnn+PTTT1GzZk2dB7O0tMSJEyewePFi7NixA/v374ejoyOCgoKwYMGCIjdLUMfMzAyHDh3C6tWr8dNPPyEkJATm5uYIDAzEhAkT8MEHH+g8PxERERk3jsgaPomgwdsPCwsL5OXlwdTUFN27d0dwcDC6dOlSof+CU1NTIZPJkJKSwhUMiIiIyoFJkybh5MmTiuNRo0Zh6NCh4gUqB/RdL2lUyEqlUkgkEtSvXx8uLi4lewKJBCEhIVoHNFQsZImIiMqX48eP49GjR4opBo0bN1aspETa0Xe9pPEcWUEQcP369RI/QUUetSUiIiLj0a5dO7EjUAlpVMhu3bpV3zmIiIiIiEpEo0J2yJAh+s5BRERERFQiOtkQgYiIiIiorLGQJSIiIiKjpFEhu3r1auTk5JTqiXJycrBq1apS9UFEREREVEDj5be8vLwwbdo0DBw4EJUqVdL4CVJSUvDLL79g2bJlePz4MfLz80sV2FBw+S0iIqLy5auvvsKlS5cUx4MHD8aHH34oYiLjp+96SaMR2X379kEqlWLUqFFwc3PDoEGDsHXrVty5c0dlOzdBEHD79m1s2bIFAwYMgLu7O8aOHQszMzPs27dP598AERERkS68ePECT548UXy9fPlS7EhUDI1WLejRowe6du2KdevWYf369dixYwd27twJ4NVorUwmg52dHVJTU5GcnKwobgVBgKenJ7744gt88cUXMDc31993QkRERFQKGnxITQZG4w0RzM3NMWnSJEycOBF//PEH9u/fj5MnTyI2NhaJiYlITExUXOvh4YG2bduiZ8+e6N69O6RS3lNGRERExoWbOhk+jQvZAlKpFL169UKvXr0AvBqGf/r0KVJSUmBvbw9XV1c4OTnpPCgRERGRPnFE1viUuJAtzMnJiYUrEREREZU5fuZPREREBNURWU4tMHwsZImIiIjIKLGQJSIiIgLnyBojFrJEREREZJRYyBIRERGRUWIhS0RERKQGb/YyfCxkiYiIiMgoaVXIBgcHY8qUKbrOQkRERCQaLr9lfLQqZH/55Rc8ePBA11mIiIiIiDSm1c5ebm5ufJdCRERE5Urbtm3h7e2tGJmtXbu2yImoOFoVsh07dsSRI0eQm5sLMzMzXWciIiIiKnO9e/cWOwKVkFZTC+bNm4fs7GwMGzYML1++1HUmIiIiIqJiaTUiu3XrVnTp0gU//fQTDh48iA4dOqB69eqwsrJSuVYikWD27NmlDkpERERE9DqJoMV+bFKpFBKJ5I1buRWcl0gkyM/PL1VIQ5SamgqZTIaUlBTY2dmJHYeIiIjI4Oi7XtJqRHbOnDm82YuIiIiIRKXViCxxRJaIiIioOAY5IktERERU3ixfvhw3b94E8GqK5IABA9CpUyeRU9Gb6KSQ/e+///D48WMAQNWqVVGlShVddEtERERUZh48eIB///1Xccwi1vBptfxWgc2bN6N27dqoWrUq3nnnHbzzzjuoVq0a6tSpgy1btugqIxERERGRCq0L2WHDhmH48OGIjIyEIAhwcHCAg4MDBEHA3bt3MWzYMAwbNkyXWYmIiIjKDG9sN3xaFbK7d+/G5s2bYW9vjxUrViApKQnPnz/H8+fPkZycjJUrV8LBwQFbtmzBnj17dJ2ZiIiISOd4/7vx0aqQ3bRpE0xNTREaGoqJEydCJpMpztnZ2WHChAkIDQ2FiYkJNm3apLOwREREREQFtCpkr169isDAQDRu3LjIaxo1aoTAwEBERERoHY6IiIiorBQekeXUAsOnVSGbnp4OV1fXYq9zdXVFenq6Nk9BRERERPRGWhWybm5uuHr1arHXXb16FZUrV9bmKYiIiIhExRFZw6dVIdu2bVvcvXsXS5YsKfKaxYsX4+7du2jfvr3W4YiIiIjKCm/2Mj5abYgwbdo0/Prrr5g5cyb27duHwYMHo0aNGgCA+/fv48cff0RERAQsLS0xdepUnQYmIiIiIgK0LGRr1aqF3bt34+OPP8bly5dx5coVpfOCIMDOzg7bt29HrVq1dBKUiIiISJ84Imt8tN6i9v3330dkZCS+++47nDp1Ck+ePAHwaovaNm3aYNiwYRrdEEZEREREpA2tCtnTp0/DxMQErVq1wqxZszBr1ixd5yIiIiIieiOtbvZq06YNZs+eressRERERAaDqxYYPq1GZB0cHODu7q7rLERERESiad68Odzc3BTHXl5eIqYhTWhVyDZs2BBRUVG6zkJEREQkmuDgYLEjUAlpNbVg7NixuHz5Mg4ePKjrPEREREREGtFqRLZRo0YYM2YMevXqhaCgIHz44YeoXr06rKys1F7v6elZqpBERERERIVJBC0WTTMxMQHwar214iZCSyQS5OXlaZfOgKWmpkImkyElJQV2dnZixyEiIiIyOPqul7QakfXw8OCdfEREREQkKq0K2YcPH+o4BhERERFRyWhVyP7000+wsLBAv379dJ2HiIiISBTr1q3DgwcPALyaGtmnTx+0bNlS5FT0JloVsp9++ik6derEQpaIiIjKjWvXruHGjRuK49atW4uYhjSh1fJbTk5OcHR01HUWIiIiIiKNaVXIvvPOO0rvWIiIiIiMXXlcZam806qQnTJlCm7fvo1NmzbpOg8RERFRmRMEAY8ePVJqc3Z2FikNaUqrObKCIGDkyJH4/PPPsXfv3mI3RHj33XdLFZKIiIhIn/777z+kpaUptfn5+YmUhjSlVSHbpk0bSCQSCIKAsLAwHDt2rMhry+uGCERERFR+REVFKR1XqlQJlStXFikNaUqrQvbdd9/lhghERERUbhQuZH19fVnrGAGtCtmTJ0/qOAYRERGReCIjI5WOfX19RUpCJaHVzV5ERERE5UnhEVnOjzUOLGSJiIioQsvMzERsbKxSG0dkjYNGhWxwcDC2bNmi9tyff/6Ja9euqT03d+5c+Pv7ax2OiIiISN/u3bsHQRAUx1KpFD4+PiImIk1pVMhu27YNZ8+eVXuuZ8+eWLdundpzjx49KrLIJSIiIjIEhefHenp6wsLCQqQ0VBKcWkBEREQVGufHGi8WskRERFShqVt6i4yDVstvEREREZUXEydOxO3btxEZGYmoqCjUrVtX7EikIRayREREVKHVrVuXxauR4tQCIiIiIjJKLGSJiIiIyChpPLXg7NmzCA4OLtG5opbsIiIiIiIqLYnw+grARZBKpZBIJNDg0v/r+P9fL5FIkJ+fX6qQhig1NRUymQwpKSmws7MTOw4RERGRwdF3vaTRiOyQIUN0/sREREREYsrJycHDhw9RvXp1mJubix2HtKBRIbt161Z95yAiIiIqU3fu3EFwcDBMTExQo0YN1KlTB3PmzIFEIhE7GmmIy28RERFRhRQdHQ0AyM/PR3R0NORyOYtYI8NVC4iIiKhCioyMVDquWbOmSElIWyxkiYiIqEIqXMj6+fmJlIS0xUKWiIiIKhy5XK6YWlCAhazxYSFLREREFU58fDwyMjKU2ji1wPiwkCUiIqIKp/C0AplMBhcXF5HSkLZYyBIREVGFExUVpXTs5+fHFQuMEAtZIiIiqnAKF7K+vr4iJaHSYCFLREREFU7hqQUsZI2TRhsiPHr0qFRP4unpWarHG4OjR4/Cz88P1atXFzsKERERvUFGRgaePHmi1MYVC4yTRoVs9erVtZ43IpFIkJeXp9VjjYEgCNiyZQs2btwId3d3bNu2DY6OjmLHIiIioiIUXnZLKpWiRo0aIqWh0tCokPX09FRbyMbExCj+LJPJAAApKSkAXhWwFWEkdunSpTh69CgAIC4uDv/73//w7bffwsLCQuRkREREpE7haQXVq1eHubm5SGmoNDSaI/vw4UM8ePBA8XXv3j00adIEzs7OWL16NRITE5GUlKT4WrNmDZydndGkSRPcu3dP63CZmZmYM2cO/Pz8YGlpCXd3dwQHB6t8HFBSUVFRsLKygkQiQYcOHUrV1/3795WO//nnH8yePRtyubxU/RIREZF+qFuxgIyTVjd7rV69GgcOHMDx48cxbtw42NvbK87JZDKMHTsWx44dw59//omVK1dqFSwrKwvt2rXDggULkJaWhh49esDDwwNbt25Fo0aNVArIkhg+fDiys7O1fvzrlixZgipVqii1HT9+HOvXr9dJ/0RERKRbsbGxSscsZI2XVoXstm3bEBgYiLfffrvIa95++220adMGP/74o1bBFi5ciPDwcLRo0QKRkZH49ddfcfHiRaxcuRLPnj1DcHCwVv1u3rwZJ0+exLBhw7R6fGGOjo5Yu3YtbG1tldp//vln7N27VyfPQURERLrz9ddf48CBA1i1ahVGjRqFd955R+xIpCWtCtl79+7B2dm52OucnJy0GjnNycnBhg0bALz6YXu9SJw4cSLq16+PU6dO4e+//y5Rv0+fPsXkyZPRsWNHDBgwoMS5iuLt7Y1ly5bBxMREqX3p0qU4f/68zp6HiIiISk8ikaBKlSp49913MXToUNSqVUvsSKQlrQpZGxsbXLp0CYIgFHmNIAi4fPkybGxsStz/uXPnkJKSAh8fHzRq1EjlfJ8+fQAABw4cKFG/48aNQ2ZmJjZu3FjiTMVp1qwZZs6cqdQml8sxbdo0lUnlRERERFR6WhWybdq0wf379zF58mTk5+ernM/Pz8eUKVNw7949tGnTpsT9X79+HQDQuHFjtecL2m/cuKFxn4cOHcKvv/6KGTNmoGbNmiXOpInu3btj6NChSm0ZGRkYP348EhIS9PKcRERERBWVRstvFTZ//nwcOXIEq1evxp49e9C3b1/F+msPHz7Eb7/9hkePHsHGxgZffvllifsv2IChWrVqas8XtL++/NebpKen4/PPP0etWrUwderUEucpiZEjR+LJkyc4cuSIoi0hIQHjx4/HDz/8AGtra70+PxEREVFFoVUhW6dOHRw+fBgDBw7Eo0ePVFYmEAQBVatWxfbt21G3bt0S95+WlgYARRZ9BdMVXr58qVF/s2bNQkxMDE6cOKH1OnHZ2dlKKx2kpqaqvU4ikWDOnDl4+vQprl69qmiPjIzEtGnTsHr1apW5tERERERUclpNLQCA1q1bIyoqCr/88guGDh2Kzp07o3PnzggODsZPP/2EqKgovPvuu7rMqpUrV65g3bp1GDx4sFbTHAosXrwYMplM8eXh4VHktebm5lixYoXKhhDnz5/HsmXL3ji3mIiIiPQjPT0d27Ztw/nz5/Hs2TP+Pi4HtBqRLWBhYYGBAwdi4MCBusoDAIpVCjIyMtSeT09PBwBUqlTpjf3k5eVh2LBhsLe3x4oVK0qVafr06Zg4caLiODU19Y3FrEwmw9q1a/Hpp58iOTlZ0b53715Uq1YNn3zySanyEBERUclERUUpVkUCAGdnZxw6dAhSqdbjeiSyUhWy+lIwkvn48WO15wvavby83tjP48ePce3aNbi5ueGjjz5SOldQXP7999+KkdqTJ08W2ZeFhUWJt5318PDAqlWrMHLkSOTk5Cja165di6pVq6Jdu3Yl6o+IiIi0V3gVIXt7exaxRq5Uhey9e/ewadMmxRB9jx49sGzZMgDAxYsXcf36dfTr1w8ymaxE/TZo0AAAEBERofZ8QXv9+vU16u+///7Df//9p/ZccnIyTp06VaJ8JVG/fn3Mnz8f06ZNU2qfNWsWNm3ahHr16untuYmIiOj/FN6a1tfXV6QkpCtavw358ccf8fbbb2PFihU4f/48oqOj8fz5c8X5jIwMjBo1Cvv27Stx361atYJMJsO9e/dw7do1lfN79uwBAHTr1u2N/VSvXh2CIKj9OnHiBACgffv2ijZ96dChA7744gultpycHEycOBFPnjzR2/MSERHR/2EhW/5oVciGh4fjs88+g7m5OZYtW4aLFy+qFIKBgYGQyWQl3rQAeHWz1JgxYwAAo0ePVsyJBYBVq1bhxo0bCAwMhL+/v6J9w4YNqF27NqZPn67Nt6R3gwcPRq9evZTakpKSMHbs2CJXQCAiIiLdkMvliI6OVmrz8/MTKQ3pilZTCwruvD948CBat26t9hqpVIqGDRvi1q1bWgWbNWsWwsLCcP78efj6+iIgIAAxMTG4ePEiXFxcsGXLFqXrnz9/jrt37yI+Pl6r59M3iUSCqVOnIj4+HuHh4Yr2mJgYTJo0CRs2bNB6aTAiIiJ6s8ePHyMrK0upjSOyxk+rEdlz586hWbNmRRaxBdzc3LQuLC0tLXHixAnMnj0b1tbW2L9/P2JiYhAUFISIiAh4e3tr1a+YTE1NsXTpUpWdxSIiIrBw4UIuA0JERKQnhacVODo6wsnJSaQ0pCtaFbLJyckqa6Sqk5mZqXS3fklZWVlh/vz5iI6ORnZ2NuLj47F161a1O37NmzcPgiBg27ZtGvXdpk0bCIKAsLAwrfNpw8bGBmvXroWzs7NS+6FDh/D999+XaRYiIqKKovCKBRyNLR+0KmSdnJw02h42Ojoabm5u2jxFuVa5cmWsXbsWVlZWSu3fffcdDh48KFIqIiKi8os3epVPWhWyzZs3x5UrV3Dz5s0irzl37hxu3rxZ7PSDiqpWrVpYvHixyvp1CxYswJUrV0RKRUREVD4VHpHljV7lg1aF7OjRo5Gfn48PP/xQ7fJYt2/fRnBwMCQSCT7//PPSZiy3WrdujUmTJim15eXlYdKkSXjw4IFIqYiIiMqXly9fqqwnzxHZ8kGrQrZ9+/aYOHEiIiMj4e/vDz8/P0gkEoSEhKB+/fqoV68eoqKiMHnyZDRv3lzXmcuVvn37qmzxm5aWhnHjxiExMVGkVEREROVH4WkFpqamqF69ujhhSKe03hBhxYoV2LRpE9zc3BAdHQ1BEBAfH49///0Xjo6OWL9+PZYsWaLLrOXW+PHj0bZtW6W2uLg4TJgwQWWpECIiIiqZwoVsjRo1YGZmJlIa0qVSbTA8bNgwPH78GFeuXMFvv/2GXbt24dy5c4iLi8Po0aN1lbHck0qlWLBgAd566y2l9ps3b2LOnDmQy+UiJSMiIjJ+vNGr/NKqkG3Xrh0GDx4M4NVC/40bN0afPn3Qt29ftGjRAqamWu2zUKFZWlpi9erVcHd3V2o/fvw41q1bJ1IqIiIi4+fo6AgvLy/FDdYsZMsPiaDFKvyWlpbo2bMndu3apY9MRiE1NRUymQwpKSmws7PTWb/3799HcHAw0tLSlNqnTp2Kjz76SGfPQ0REVNFkZWXh/v37cHZ2hqurq9hxKgR91UsFtBqRrVatGrKzs3WdhQB4e3tj+fLlMDExUWpfvnw5zp49K1IqIiIi42dpaYm6deuyiC1HtCpkP/jgA5w5cwbp6em6zkMAmjZtitmzZyu1yeVyTJ8+HXfv3hUpFREREZFh0aqQnTt3LmQyGXr37q3RDl9Uch988AGGDRum1JaZmYnx48cjISFBpFREREREhkOrObLBwcF4/vw5/vrrL5ibm6NRo0aoXr26yparwKubwTZv3qyTsIZE33M+AEAQBMydOxeHDh1Savf19cUPP/wAGxsbvTwvERERkS7ou17SqpCVSqWQSCTQ5KESiQT5+flahTNkZVHIAkBOTg7GjBmDiIgIpfaWLVti9erVKnNpiYiIiAyFvuslrdbJ2rp1q65zUBHMzc2xYsUKfPrpp0rTOM6fP4+lS5di+vTpkEgkIiYkIiIyTKmpqZg8eTJ8fX3h5+eHmjVronbt2opluMj4aTUiS2U3IlvgyZMnCAoKQlJSklL72LFjFWv6EhER0f+JiIjA8OHDFcdmZmY4c+YM17svQwa5/BaVvapVq2LVqlUwNzdXal+3bh3CwsJESkVERGS4IiMjlY5r1KjBIracYSFrROrVq4cFCxaotM+ZMwc3btwQIREREZHhKlzI+vn5iZSE9KVUb0vi4+Pxxx9/4O7du0hNTVV781d5XbVALO3bt8fYsWOVtq3NycnBxIkTsW3bNlSrVk3EdERERIYjOjpa6ZiFbPmjdSG7fv16TJ48Gbm5uYq2gkK24OYjQRBYyOrBJ598gsePH+P3339XtCUnJ2PcuHHYunVrmczZJSIiMmT5+fkqhWzNmjVFSkP6otXUgmPHjmHcuHGwtLTEtGnT0KJFCwDApk2b8L///Q/Vq1cHAIwfPx5btmzRWVh6RSKRYOrUqWjZsqVSe0xMDCZNmoScnByRkhERERmGR48eqfw+5Ihs+aNVIbt27VpIJBKEhITgq6++gq+vLwBg2LBhWL58OW7duoUhQ4Zgy5YtCAgI0GlgesXExARLlixR+Z8yIiIC8+fP12iNXyIiovIqKipK6djFxQX29vbihCG90aqQvXTpEho3box33nlH7XkLCwt88803sLS0xPz580sVkIpmbW2NNWvWwMXFRan9yJEj2LRpk0ipiIiIxFe4kC0YdKPyRatCNikpCT4+PopjMzMzAEBmZqaizcLCAgEBATh27FgpI9KbuLq6Yu3atbC2tlZq/+GHH3DgwAGRUhEREYmr8IoFLGTLJ60KWUdHR6SnpyuOHRwcALyaj/K6/Px8vHjxohTxSBN+fn5YvHixyk4lCxcuxOXLl0VKRUREJJ7CI7KcH1s+aVXIenp6IjY2VnH89ttvQxAE/PXXX4q2tLQ0nDlzhstBlZFWrVphypQpSm35+fmYPHky7t+/L1IqIiKispeamoqEhASlNo7Ilk9aFbKBgYG4efMmnj59CgB4//33YWNjgxkzZmDy5MlYv3492rRpg8TERHTu3Fmngaloffr0wSeffKLUlpaWhnHjxnFknIiIKozC0wrMzc3h5eUlUhrSJ60K2Y8++ght2rTBtWvXALyaarBq1Srk5eVh1apVGD9+PCIiIuDl5YUvv/xSl3mpGF988QXatWun1BYfH48JEyYgKytLpFRERERlp/C0Am9vb5iYmIiUhvRJqw0RmjZtitDQUKW2YcOGwd/fH7t370ZiYiLq1KmDTz/9FDKZTCdBSTNSqRQLFixAQkIC/v33X0X7rVu3MGvWLCxbtkxlLi0REVF5whULKo5SbVFbWOPGjdG4cWNddklasLCwwKpVqxAUFIS4uDhF+8mTJ7FmzRpMnDhRxHRERET61bZtW9ja2iIyMhKRkZEsZMsxicCV87WSmpoKmUyGlJQUg90S9sGDBwgODsbLly+V2qdMmYK+ffuKlIqIiKjsCIKA/Px8mJrqdOyONKTveomfMZdjNWrUwIoVK1T+512xYgXu3LkjUioiIqKyI5FIWMSWY1oVsiYmJhp/8YdHXP7+/pgzZ45Sm1wux+7du0VKRERERKQbWhWygiBo/CWXy3WdmUrovffeU1mW6/jx48jNzRUpEREREVHpaVXIyuVytV/5+fm4f/8+1q1bBwcHB8ydO5eFrIHo16+f0vHLly8RHh4uUhoiIiKi0tPpHFmJRILq1atjzJgx2Lt3LxYsWIC9e/fq8ilIS25ubmjQoIFS29GjR0VKQ0REpB9cM71i0dvNXm3atEGjRo2watUqfT0FlVDhXdZOnTrF/+GJiKjcSE5ORkBAAHr37o2pU6di8+bNyMzMFDsW6ZFeVy3w9vbGP//8o8+nMAiCICAyMhIbN27E1KlTxY5TpPbt2ytthpCRkYFz586JmIiIiEh3oqKiIAgCHj16hGPHjmHz5s0wNzcXOxbpkV6XFCj4gSrP4uPjMXjwYDx+/FjRFhsbCw8PDxFTqefk5IQmTZrg0qVLiraQkBC0b99exFRERES6UXhHLx8fH25NW87pZUQ2Ly8PX331Fa5du4ZGjRrp4ykMRuXKlZGenq7Udvz4cZHSFK9Tp05Kx2fPnkVGRoZIaYiIiHQnMjJS6Zg7epV/Wo3ItmvXrshzL1++xP3795GcnAypVIoZM2ZoHc4YSKVStG3bFr///rui7dixYxgyZIiIqYrWrl07LF68GPn5+QCAnJwcnDp1Cl27dhU5GRERUekULmT9/PxESkJlRatC9uTJk8Ve4+vriyVLlqBLly7aPIVR6dChg1Ihe+vWLcTFxcHd3V3EVOrZ2dmhRYsWOHv2rKLt6NGjLGSJiMio5eXl4cGDB0ptHJEt/7QqZE+cOFHkOXNzc1StWhWenp5ahzI2/v7+in2ECxw/fhyDBg0SMVXROnXqpFTIXrhwAampqXrZA5mIiKgsxMTEqGz0w0K2/NOqkA0MDNR1DqNmYmKCtm3bYv/+/Yq2Y8eOGWwhGxgYCHNzc+Tk5AB49S72xIkT6NGjh8jJiIiItFN4WkHlypU5QFMB6HX5rYqk8J3///zzD54+fSpSmjezsbFB69atldpCQkJESkNERFR6hVcs4GhsxcBCVkeaNm2q8s7PmFYvuHLlChITE0VKQ0REVDqFC1ne6FUxaDW1wNvbW+snlEgkuHfvntaPN1SmpqYIDAzEgQMHFG1hYWEYMGCAiKmK1rp1a1hZWSl2PJHL5QgLC0Pfvn1FTkZERFRyXHqrYtKqkH348CGAV0VpURseFHVOIpFo85RGoX379kqF7PXr15GQkABXV1cRU6lnaWmJwMBAHDlyRNF29OhRFrJERGR0EhMT8eLFC6U2FrIVg1ZTCx48eICJEycCAHr06IHff/8dV69exdWrV7Fv3z707NkTADBx4kQ8ePBA6ev+/fs6C29omjVrBhsbG6U2TZYqE0vh6QXXrl0z2Hm9RERERYmOjlY6trCwqFCrJ1VkWhWy169fx+rVq/HLL78oCtcGDRqgQYMGisJ2+/btWL16Na5evQovLy+lr/LK3NxcZUWHsLAwkdIUr3nz5qhUqZJSW2hoqEhpiIiItFN4WoGPjw+kUt4GVBFo9be8YsUKNGnS5I3zP/v3748mTZpg5cqVWoczRoVXL7h69arB3kRlbm6Otm3bKrUdPXpUpDRERETa4fzYikurQvbGjRsa/ZD4+vrixo0b2jyF0WrevDmsra0VxxKJxKBfg86dOysd37p1C7GxsSKlISIiKrnx48dj/fr1GDt2LLp27Yp33nlH7EhURrS62Usul2u08sC9e/eKvBmsvLKwsECbNm3w4sULtG/fHm3atIGjo6PYsYrUpEkTODg4ICkpSdEWGhqK4OBgEVMRERFpztHRES1atECLFi3EjkJlTKsR2UaNGuHSpUvYt29fkdfs378fFy9eRKNGjbQOZ6y+/PJLfP311+jdu7dBF7HAq13JOnTooNTGzRGIiIjIGGhVyE6ePBmCIKBv3774+OOPcejQIdy+fRu3b9/G4cOHMWjQIPTt2xcSiQSTJ0/WdWaDZ2xLjBVeveDevXvlenUJIiIiKh8kgpaf/a9evRpTpkyBXC5XOScIAkxMTLB48WJMmjSp1CENUWpqKmQyGVJSUox+L2e5XI4PPvgACQkJirbPPvsMI0eOFDEVERERGTt910tar00xYcIEREREIDg4GD4+PrCwsICFhQW8vb0RHByMK1eulNsitryRSqXo2LGjUtvRo0cr3PxmIiIiMi5aj8hWdOVpRBZ4tVrB4MGDldp++eUX1K5dW6RERERExTtz5gx8fHxQpUoVo5vaVxHou17SatUC0pxcLse1a9dw7NgxZGVlYfbs2WJHUqtOnTqoWrUqnjx5omg7evQoC1kiIjJYiYmJmDBhAgDA2toavr6+WLFiBRwcHERORmVFZ9texMXFYfPmzVi6dCm2b99usJsAlKVbt26hS5cuGD58OH799VccPHgQL1++FDuWWhKJROWmr6NHj6qdA01ERGQIXt8IISMjA3fu3IFMJhMxEZU1jQrZW7duYcqUKdi5c6fa81u2bIGPjw+GDx+OGTNmYPDgwahZsyb++usvnYY1Nl5eXkqFa15eHs6cOSNiojcrXMj+999/+Pfff0VKQ0RE9GaFd/SqWbMmt6atYDT62/7999+xcuVKmJmZqZy7cuUKRowYgezsbFhZWcHf3x9ubm5ITk5G//79K/QuUTY2NiqLM4eFhYmUpng1a9ZEjRo1lNq4piwRERmq6OhopWM/Pz+RkpBYNCpkz507BysrK3zwwQcq55YsWYL8/Hz4+fkhMjISly5dQmxsLD777DNkZGTgm2++0XloY9K+fXul4/DwcKSnp4uU5s3UTS8IDQ3l9AIiIjJIhUdkfX19RUpCYtGokI2OjkajRo1gaWmp1J6bm4tDhw5BIpFg0aJFcHd3f9WpVIrly5fDxsbGoEcgy0JAQABMTf/vnrqcnBycPXtWxERvVriQTUxMxN9//y1SGiIiIvVycnLw4MEDpTYWshWPRoXss2fP4OnpqdJ+9epVZGVlwdzcHF27dlU6J5PJ0LRpU5Vh/4rGzs4OzZo1U2o7duyYSGmK5+XlhVq1aim1HT16VKQ0RERE6j18+BD5+flKbSxkKx6NCtnMzExkZmaqtEdERAAA6tevDysrK5Xzbm5uSEtLK2VE49ehQwel47NnzyIjI0OkNMXr3Lmz0vGxY8eQm5srUhoiIiJVUVFRSsfu7u6wtbUVKQ2JRaNC1tnZWe3I6vnz5yGRSNCkSRO1j8vKyoK9vX2pApYHgYGBSndR5uTk4Pz58yImerPChXdqaiouXbokUhoiIiJVnB9LgIaFrL+/P27evInTp08r2lJTU3HgwAEAQNu2bdU+7u7du3Bzc9NBTONWMM3idYY8vcDd3R3169dXauPqBUREZEgKj8iykK2YNCpkg4ODIQgCunfvjtmzZ2PdunVo06YNUlJS4OTkpHY1g/j4eNy5cwd169bVeWhjpG56QVZWlkhpilf4pq+TJ08iJydHpDRERET/RxAElUKWS29VTBoVsj179kT//v2RmpqKRYsWYcKECbh27RoAYNmyZSqrGQDAzz//DABo166d7tIasTZt2ihNL8jMzMSFCxdETPRmHTp0UNqzOiMjA+fOnRMxERER0SsvXrxAUlKSUhtHZCsmjbe/+OWXX7B+/Xq0atUKNWvWRPv27bFv3z4EBQWpvf706dOoX78+OnbsqKusRs3BwQH+/v5KbYY8vcDZ2VklL1cvICIiQ1B4fqyVlRWqVq0qUhoSk2nxl7wilUoxevRojB49WqPrK/r2tOq0b98ely9fVhyfPn0aOTk5MDc3FzFV0Tp16oQrV64ojk+fPo2MjAxYW1uLmIqIiCq6wjegc2vaiot/62Wobdu2Sh/X5+XlqczxMSTt2rWDiYmJ4jg7OxtnzpwRMREREdGrG85f32yI0woqLo1HZKn0nJyc0KJFC1haWqJDhw5o3bq1QY9u2tvb45133lFaKiwkJERlnVkiIqKyNGbMGIwYMQIPHz5EVFQUqlWrJnYkEgkL2TK2du1apVFZQ9epUyelQvb8+fNITU2FnZ2diKmIiKiiMzMzg6+vL0djKzhOLShjxlTEAq9WWzAzM1Mc5+Xl4eTJk+IFIiIiIvr/WMjSG9na2qJVq1ZKbVy9gIiIiAwBC1kqVuHNES5duoTExESR0hARERG9wkKWihUQEKC06YVcLsfx48dFTERERETEQlZUOTk5OHPmDObNm4e1a9eKHadIVlZWePfdd5XaOL2AiIjKmiAIWLVqFXbv3o3r168jIyND7EgkMq5aIJIzZ85g1qxZSE9PB/BqqasxY8YordtqSDp37qxUvF69ehUJCQlwdXUVMRUREVUkz58/x44dO5TaDhw4gCpVqoiUiMRWqkL24sWLCAsLw5MnT5CVlaX2GolEgs2bN5fmacolb29vRRELAMnJyYiIiEDTpk1FTFW0Fi1awNbWFmlpaQBevSsOCwvDwIEDRU5GREQVReFNhKytrVG5cmWR0pAh0KqQzcnJwYABA7B//34Ar4qaorCQVa9q1aqoXbs27ty5o2g7duyYwRay5ubmaNu2LQ4cOKBoCwkJYSFLRERlJjIyUumYW9OSVoXsggULsG/fPtjY2OCTTz5BnTp1uEC+Ftq3b69UyB4/fhxTpkwx2P8pO3XqpFTI3rx5E0+ePEHVqlVFTEVERBVF4RFZPz8/kZKQodCqkN25cyesra1x8eJF1K1bV9eZKoz27dvj66+/VhwnJibi2rVraNy4sYipita0aVPY29sjOTlZ0RYaGoqgoCDRMhERUcVRuJDlrl6k1dDf48eP0apVKxaxpeTp6anyP2FYWJhIaYpnamqK9u3bK7Vx9QIiIioLOTk5ePjwoVIbC1nSqpB1cHCAo6OjrrNUSIULw+PHj0Mul4uUpnidO3dWOo6MjMSDBw9ESkNERBXF/fv3VX4/1qxZU6Q0ZCi0KmQ7dOiAixcvvvEmL13IzMzEnDlz4OfnB0tLS7i7uyM4OBhPnjzRuI/k5GTs2LEDAwYMQI0aNWBubo5KlSrhnXfewdq1a5Gbm6vH76B4hQvZ58+f459//hEpTfEaNmwIZ2dnpbbQ0FCR0hARUUVR+EavatWqwdraWqQ0ZCi0KmQXLFiAxMREzJs3T8dx/k9WVhbatWuHBQsWIC0tDT169ICHhwe2bt2KRo0a4f79+xr1s2LFCnz88cf49ddf4eDggN69e6NZs2a4fv06xo8fj3bt2om6oHKNGjXg7e2t1Hbs2DGR0hRPKpWiY8eOSm0hISF6f1NDREQVG2/0InW0utnr9OnT+PTTT7Fw4UIcOXIE77//Pjw9PYu8237w4MElfo6FCxciPDwcLVq0wNGjR2FrawsAWLVqFf73v/8hODgYJ0+eLLYfGxsbTJkyBaNHj4anp6eiPSoqCh06dMDZs2excOFCLFq0qMQZdaV9+/ZKhXlYWBjGjx9v0KsX7Ny5U3EcExODqKgo/qNCRER6wxu9SB2JoMVQmlQqhUQiUYzCSSSSN16fn59fov5zcnLg6uqKlJQUREREoFGjRkrnGzRogBs3buDKlSvw9/cvWfjX7Ny5EwMHDkT16tVLPM8zNTUVMpkMKSkppV567N69e+jXr59S27Zt2/D222+Xql99EQQB3bt3R3x8vKJtyJAh+OKLL0RMRURE5ZUgCGjfvj1SU1MVbStWrECbNm3EC0Ua0WW9pI5WI7KDBw8utngtjXPnziElJQU+Pj4qRSwA9OnTBzdu3MCBAwdKVcg2aNAAABAXF6d1H7rg7e0NLy8vxMTEKNqOHTtmsIWsRCJBp06d8OOPPyrajh49ijFjxuj154KIiCqmZ8+eKRWxAKcW0CtaFbLbtm3TcQxl169fB4Ai11MtaL9x40apnqfg43w3N7dS9VNaEokE7du3x5YtWxRtx44dw9ixYw22MOzcubNSIRsfH49///0X9erVEzEVERGVR+q2pq1SpYpIaciQGOQkzEePHgF4dUeiOgXtr49gamPt2rUAgB49epSqH13o0KGD0nFqair+++8/kdIUz9fXF15eXkptXFOWiIj0ofCKBb6+vgY70ENlyyAL2bS0NAAoclkNGxsbAMDLly+1fo5vv/0WYWFhsLe3x7Rp04q9Pjs7G6mpqUpfuuTr64u33noL3bt3x7p16xAaGmrQ7zYlEonKmrKhoaEGvQYuEREZJ3d3d7Rs2RIuLi4AOK2A/o9WUwted+fOHdy9exepqalFLsGkzaoF+nTmzBmMGzcOEokEW7Zsgbu7e7GPWbx4Mb788ku9ZZJIJNi2bZtRvcPs2LEjvvvuO8Xx8+fPcfXq1VLNWyYiIiqsc+fOisGT5ORk0deAJ8OhdSEbHh6O4cOH4+bNm0VeIwgCJBJJiQvZgqW2ilrfNT09HQBQqVKlEvULAP/++y969OiBnJwcrFu3Dr169dLocdOnT8fEiRMVx6mpqfDw8Cjx87+JMRWxwKs1cP38/JQ+8gkJCWEhS0REemNvby92BDIgWk0tiIyMRMeOHfHvv/+iefPmqFGjBgCgf//+8Pf3h4mJCQCgV69eWo3GFqz3+vjxY7XnC9oLz9EszoMHD9CpUyckJSVh3rx5JVouysLCAnZ2dkpf9GpN2dcdO3YMeXl5IqUhIiKiikSrQnbp0qVIT0/Hxo0bce7cOQQEBAAAtm/fjkuXLuHq1ato2LAhoqKisGHDhhL3X7AsVkREhNrzBe3169fXuM/4+Hh07NgR8fHxGDduHObOnVviXKSqcCGbkpKCS5cuiZSGiIiIKhKtCtkTJ07Ax8cHI0eOVHv+rbfewl9//YV79+7hq6++KnH/rVq1gkwmw71793Dt2jWV83v27AEAdOvWTaP+kpKS0LlzZ9y7dw+ffvopVq9eXeJMpJ67u7vKerehoaEipSEiIqKKRKtCNj4+Xql4KZhKkJOTo2irUqUKAgMD8fvvv5e4f3Nzc4wZMwYAMHr0aMWcWODVFrU3btxAYGCg0lzMDRs2oHbt2pg+fbpSXxkZGXj//ffxzz//oG/fvvj++++NYi5qeno6jhw5gsmTJyut12qICo/KHj9+XOlngYiIiEgftLrZy8rKCqam//fQgpuunj59qnQDlJ2dHWJjY7UKNmvWLISFheH8+fPw9fVFQEAAYmJicPHiRbi4uChtHgC8umP+7t27StumAsDMmTNx4cIFmJiYwNTUFEOHDlX7fPre5KEk9u3bh2XLlinuynz06BGGDBkicqqidejQAatXr1asWpGeno4LFy4gMDBQ5GRERGTMBEHAwIEDUaVKFfj6+sLX1xctW7YscnlOqni0KmSrVq2q2LQAAGrWrAkAuHDhgqKQFQQBERERcHBw0CqYpaUlTpw4gcWLF2PHjh3Yv38/HB0dERQUhAULFhS5WUJhSUlJAID8/Hzs2LGjyOsMqZD19vZWWlrk3r17ePjwIapXry5eqDdwdXVFo0aNlOY0h4SEsJAlIqJSefr0KaKiohAVFYXTp08DAP78808WsqSg1dSCd955B7du3UJmZiYAoEuXLgCACRMm4ODBg/jnn38watQo3Lt3D02bNtU6nJWVFebPn4/o6GhkZ2cjPj4eW7duVVvEzps3D4IgqBSk27ZtgyAIxX4Zknr16sHZ2Vmp7fjx4yKl0Uzh6QWnT59W/HwQERFpo/COXra2tga9WRCVPa0K2ffeew9ZWVn466+/AAA+Pj4YPnw44uPj0b17dzRs2BDfffcdzM3NsXDhQp0GrgikUinatWun1BYWFiZSGs20a9cOUun//ThlZWXhzJkzIiYiIiJjFx0drXTMrWmpMK0K2d69eyM3NxcfffSRou3rr7/GihUr0KxZM9SsWRPdu3fHqVOn8NZbb+ksbEXSoUMHpePIyEit5xuXBUdHRzRr1kyp7ejRoyKlISKi8qDwiKyvr69ISchQaVXIqu1IKsXEiRNx4cIF3L17F/v371cpbEhzDRs2hKOjo1LbsWPHREqjmcLTC86dO4e0tDSR0hARkbFjIUvF0VkhS7ollUrRtm1bpTZDL2Tbtm2rtJpFbm4uTp48KV4gIiIyWllZWSqfRPr5+YmUhgxVqQpZQRBw6NAhzJo1CyNGjFBaEuvZs2eIjIxEfn5+qUNWVO3bt1c6vn37NuLi4kRKU7xKlSqhZcuWSm2cXkBERNq4d++e0s3YEokE3t7eIiYiQ6R1IXv9+nXUqVMH3bp1w6JFi/DDDz/g7NmzivOhoaGoU6cODh06pJOgFZG/vz9kMplSm6GPynbu3FnpODw8HMnJyeKEISIio1V4WoGHhwesrKxESkOGSqtC9vHjx+jQoQMiIyPRtWtXLFu2TGUJq549e8LMzAx//PGHToJWRCYmJkY3vSAgIAAWFhaKY7lcbvBLhxERkeGJiopSOua0AlJHq0J20aJFePHiBdasWYO//voLkyZNUrnG2toaDRo0wOXLl0sdsiIrPL3g33//xX///SdSmuJZW1vj3XffVWoLCQkRKQ0RERkrFrKkCa0K2SNHjqB27doYO3bsG6+rXr26ypaxVDJNmzaFnZ2dUpuhj3AWXr0gIiICz549EykNEREZG0EQVArZgl1EiV6nVSEbFxeHevXqFXudRCJBamqqNk9B/5+pqanKVq+GPr2gVatWStsHCoJg8Bs6EBGR4fjvv/9Ulm/kiCypo1Uha2Njo9EI24MHD1TWQqWSKzy9IC4uzqC3fzU3N1eZ2xsaGipSGiIiMjaFR2MrVaqEypUri5SGDJlWhWy9evXw999/4/nz50VeExMTg+vXr8Pf31/rcPRKs2bN4OPjg4EDB+KHH37AwYMHDf7OzcLTC27cuGHQS4cREZHhULcRAremJXVMi79E1aBBg3D69Gl89tln2LFjh9LHyACQk5ODzz//HLm5uRg0aJBOglZk5ubm+PXXX8WOUSLNmjWDnZ2d0tSSsLAwDB48WMRURERkDNq2bQsbGxtERUUhKioKb7/9ttiRyEBJhMLrZmkgPz8fHTp0wKlTp1CtWjV06dIFP/zwAxo1aoRWrVrhzz//xKNHj9ChQ4dyuyB+amoqZDIZUlJSVG7Gole++uor7Nu3T3Fcq1YtbN++XcREREREVJb0XS9pVcgCQFpaGkaMGIFdu3aprCELAB9++CG2bt0KW1vbUoc0RCxki3f58mWMGjVKqW3v3r3w8vISKRERERGVJYMtZAvcuXMHhw4dwv379yGXy+Hh4YGuXbuiYcOGOopomFjIFk8ul6NLly5ITExUtI0YMQLDhg0TMRURERGVFX3XS1rNkX1d7dq1Ubt2bV1koXJGKpWiY8eOSvN7Q0JC8Nlnn3HSPhEREZWaVqsWkLgSExOxd+9efP755/jzzz/FjvNGnTt3Vjp++PAhoqOjRUpDRERE5UmpR2SpbH333Xf4/vvvFfOSpVIpunfvLnKqor399ttwc3NT2lb36NGj8PX1FTEVEREZqvj4eLi6usLExETsKGQENBqRNTc31/rLwsJC399DhVKjRg2lm+suXbqElJQUERO9mVQqVVlTNiQkRO0NgkREVLEJgoB+/fohICAAn3zyCebPn8+t7umNNCpk8/LytP7Kzc3V9/dQobRq1Qrm5uaKY7lcjlOnTomYqHiFC9m4uDjcunVLpDREROXDixcvkJ2dLXYMnYqPj0dGRgZycnJw+/Zt/PnnnxyZpTfSeGqBRCJB06ZNERwcjE6dOvFmHZFYW1ujVatWOHHihKLt2LFjBj29oFatWvD09MSjR48UbSEhIXjrrbdETEVEZLxycnIwceJE5ObmYtmyZahWrZrYkXSi8I5ednZ2cHFxESkNGQONRmSXLl2KWrVq4dKlSxg1ahTatGmDLVu2QBAEeHl5FftFutW+fXul44sXL+Lly5cipSmeRCJRGZUNDQ2FXC4XKRERkXFbs2YNbt68icjISAwaNEjlk7m4uDhERUWJlE57hTP7+flx4IzeSKNCdvLkybh16xbOnj2LoKAgJCYmYsGCBahZsyY6dOiAHTt2lLuPNwxZQECA0vSCvLw8nDlzRsRExStcyD579gzXrl0TJwwRkRELCQnBb7/9pjhOS0vD2rVrFVP5jh49igEDBmDKlCnIyMgQK6ZWCheyvDGYilOi5bdatmyJzZs3Iz4+Hj/88AOaN2+O48eP45NPPoGbmxs+//xzXL58WV9Z6f+zsbFB8+bNldrCwsJESqMZb29v1KxZU6mtvG5fTESkL/fv38fChQuV2szNzbFkyRLI5XLMnz8fM2bMQHp6OmJjY7F06VKRkmqn8NQCFrJUHK3WkbWxsUFwcDDOnj2LO3fuYNKkSbC0tMS3336L5s2bo3Xr1rrOSYV06NBB6Tg8PBzp6ekipdFM4VHZY8eOIT8/X6Q0RETGJSMjA1OnTkVmZqZS+/Tp0+Hn5wcTExM8ePBA6dzBgwdx6NChsoyptYyMDDx+/Fipzc/PT6Q0ZCxKvSGCn58fli5ditu3b6Nbt24QBEHlHRXpXkBAAExN/+9evZycHIOfXtCxY0el46SkJFy5ckWkNERExkMQBCxcuFClUO3Zsye6desGADA1NcVXX30FGxsbpWuWLFmC2NjYMsuqrcKb5UilUnh7e4uUhoxFqQvZM2fO4NNPP4WHhwf++usvSKVSvPvuu7rIRm9QqVIlvPPOO0ptx44dEymNZjw8PFC3bl2ltpCQEJHSEBEZj927d6tMx/Lz88PkyZOV2tzd3TFz5kyltoyMDMycOdPgl8MsPD+2evXqSveDEKmjVSEbHx+PxYsXo1atWmjTpg1+/PFHuLq6Yt68eXjw4AH27Nmj65ykRuHVC86dO2fwE/sLTy84ceIEcnJyREpDRGT4/v33X6xatUqpzdbWFsuXL1e76VCnTp3Qo0cPpbZbt27hm2++0WvO0uKNXqQNjQvZvLw87N27F++//z48PT0xc+ZMPH78GAMHDsSxY8dw7949zJ49Gx4eHvrMS69p06aN0kLROTk5OHfunIiJild4esHLly8RHh4uUhoiIsOWnJyMqVOnIi8vT6l9/vz5qFq1apGPmzRpksrylz/99JNB/3vLG71IGxoVshMmTIC7uzv69u2Lw4cPo1GjRti4cSPi4+Px888/o23btvrOSWrY2dmhadOmSm2GPr2gcuXKaNiwoVIbVy8gIlIll8sxe/ZsPH36VKl9yJAhxU7hs7KywuLFi2FmZqbUPmfOHCQmJuo8a2nJ5XKVObK80Ys0odHOXmvXroVEIkGTJk0QHByMevXqAXj1cYcmWrZsqX1CeqP27dsrvcN+9OgR5HI5pNJST3/Wm06dOimtIXvq1ClkZWXB0tJSvFBERAbmhx9+wIULF5Ta/P398fnnn2v0eD8/P4wbNw4rVqxQtCUmJmLu3LlYu3atQf2eKNia9nUckSVNaLxFLQBcuXKlxHeZSyQSlY9ESHfatGmDX3/9FW3btkX79u3h4+Nj8LugdOjQAStWrFDs7JWZmYmzZ8+qLClGRFRRXb58Gd9//71Sm7OzMxYtWqQ0paw4/fr1Q3h4OM6ePatou3DhAnbs2IFBgwbpLG9pFZ5WIJPJ4OzsLFIaMiYaFbKenp4GXxxVVA4ODti1a5fYMUrE0dERTZo0waVLlxRtR48eZSFLRPT/1a5dG4GBgTh58iSAV0tRLVq0CE5OTiXqRyKRYO7cuRgwYACeP3+uaN+wYQMaN26sspKMWNRNK2DdQZqQCIIgiB3CGKWmpkImkyElJQV2dnZixzE6f/zxBxYsWKA4Njc3R2hoqMr6h0REFZUgCPj555+xYcMGjBkzBoMHD9a6r8uXL+Pzzz/H67/yPTw8sH37dlhbW+sibqnI5XLExsYiKioKkZGRqFq1qsrKC2Sc9F0vsZDVEgvZ0klNTUWnTp2Upp3Mnz8f7733noipiIgMT1RUFGrWrFnqEcqNGzdiy5YtAF5tnjBmzBgMHDjQoObKUvmj73qJP70kCjs7O7Ro0UKpjZsjEBGp8vX11cnH7MOHD0e9evXg4eGBLVu2YNCgQSxiyeiV6GYvIl3q1KmT0ra64eHhSElJgUwmEzEVEVH5ZGpqiqVLl8LW1tYgphMQ6QLfipUzjx8/xo8//ojBgwcb/OYIgYGBStsP5ufn4/jx4yImIiIqexkZGVi0aFGZrO/q6urKIpbKFRay5cj8+fPRs2dPrF+/Hrdu3TL4zRGsra0REBCg1MbNEYioIhEEAV999RV+//13fPzxx7h+/brYkYiMCgvZcqRmzZpKxydPnjT4NXw7deqkdPz333/jxYsXIqUhIipbu3fvVtwf8OzZMwwfPhxHjhwRJcu1a9dKvFa8LoSEhODy5ctITk4u8+cm48dCthxp166d0nFqaqoo/yiVRKtWrZQ+5pLL5QY/kkxEpAs3b97EqlWrlNqsrKzw9ttvl2kOuVyO77//HsOHD8eMGTPKdAtbuVyOhQsXYtSoUejQoQO6du2KW7duldnzk/FjIVuOuLm5qfwDaOhFoaWlJQIDA5XauHoBEZV3KSkpmDp1qsqnZl9++SWqVatWZjnS09MxcuRIbNq0CXK5HImJiZg3b55i50V9e/LkCTIzMxXHz549g6ura5k8N5UPLGTLmfbt2ysdnzhxAvn5+SKl0Uzh6QXXr1/Hf//9J1IaIiL9ksvlmD17tsq/c4MHD1Z5Y69v1tbWKhvRnD9/Hjt37iyT54+KilI6dnBwKPHuZVSxsZAtZwoXssnJyYiIiBApjWaaN2+OSpUqKbWFhoaKlIaISL82b96M8+fPK7U1btwYo0ePLvMsBVvYOjs7K7WvX78et2/f1vvzFy5kdbVmLlUcLGTLGXd3d9SpU0epzdCnF5iZmanM7+XqBURUHl28eBHfffedUpujoyMWLVoEExMTUTLZ29tjwYIFSgVkXl4eZsyYgYyMDL0+d2RkpNKxr6+vXp+Pyh8WsuVQ4VHZ48ePl9l8J2117txZ6fj27dt49OiRSGmIiHTv6dOnmDlzJl7fGV4qlWLJkiUqI6JlrWnTpvj000+V2mJjY7F06VK9Pm/hEVk/Pz+9Ph+VPyxky6HCo5uJiYm4du2aOGE05O/vD0dHR6U2Ti8govIiNzcX06ZNU1liasyYMWjcuLE4oQop2ML2dQcPHsShQ4f08nxpaWmIi4tTauOILJUUC9lyyNPTU+VdbVhYmEhpNGNiYoIOHTootYWEhBj8SDIRkSbWrl2Lf/75R6ktMDAQn3zyiUiJVJmamuKrr75SuflryZIlePz4sc6fLzo6WunYxMQE1atX1/nzUPnGQracMsbpBYVXL7h//z4WLlxo8LmJiN4kNDQUu3btUmqrVq0a5s2bZ3A3Nrm7u2PmzJlKbRkZGZgxYwZyc3N1+lyF58fWqFFDadtyIk2wkC2nCheyz58/VxkNMDT169eHu7u7Utuff/6JuXPnGvwSYkRE6giCgAMHDii1mZubY9myZSqrtRiKTp06oXv37kptt27dwjfffKPT5+H8WNIFFrLlVPXq1eHt7a3UZuirF0ilUsyYMQOmpqZK7YcPH8bs2bMNfrtdIqLCJBIJVq1ahY8//ljRNnXqVIMv2iZPngwvLy+ltp9++gnh4eE6e47ChWzhbdaJNMFCthwrPOf0yZMnIiXRXPPmzbFs2TKYmZkptR89elQvH20REembqakpJkyYgGXLlqF///7o0aOH2JGKZWVlhcWLF6v8WzxnzhydLMkll8tV5sgaenFPhomFbDnWvn17vP322xg3bhz+/PNPrFy5UuxIGnn33XexcuVKlblSx48fx9SpU5GTkyNSMiIi7bVr1w6TJk0SO4bG/Pz8MG7cOMWxTCbDrFmzYG1tXeq+Hz9+jKysLJXnIyopifD6gnaksdTUVMhkMqSkpMDOzk7sOOXSpUuXMGHCBGRnZyu1t2zZEsuXL4eFhYVIyYiIKgZBEDBhwgRkZmZiwYIFcHV11Um/YWFhmDZtmuLY0dGRG+GUU/qulzgiSwarWbNmWL9+PaysrJTaz58/jwkTJqi8myciEltqaqred8MqSxKJBIsWLcI333yjsyIWeLWu7us393L9WNIWR2S1xBHZsnP9+nV88cUXKr8c/P39sXr1ap18zEVEVFpyuRzjx49HXFwcli1bpnLDLalKS0tDdHQ0pFIp6tevL3Yc0gOOyFKF16BBA3z99dewtbVVav/777/xxRdfID09XaRkRET/Z8uWLTh//jwePnyIIUOGICQkROxIBs/W1hYNGzZkEUtaYyFbwWRkZODWrVt49uyZUW00UK9ePWzcuFHl3dz169cxZswYvHz5UqRkRESv5vRv2rRJcZyZmYmVK1eW6zfagiDg4MGDnNtKouLUAi0Z29QCQRAQGRmJsLAwbN26FcCrdVudnZ3h4uICFxcXuLq6Kv3Z2dkZrq6usLGxMZjdZyIjIzFq1CikpKQotdetWxcbNmwwir8LIipfEhISMHDgQCQnJyvapFIpvvnmG/j7+4sXTI/S09OxZMkSHD58GNbW1tixYweqVasmdiwyQPqul1jIasnYCtnPP/8cly5d0uqxVlZWaN++PebNm6f2fGpqKiwtLctsa8F79+5h1KhRSExMVGr38/PDxo0bYW9vXyY5iIhyc3MxYsQI3LhxQ6n9iy++wJAhQ0RKpV8vX77EJ598gsePHyva6tati82bN6usO0uk73rJtPhLqDzw9/fXupDNzMzEm97vLFy4EMePH4e9vb3SSO7rfy4Y6bW3t4dUWroZLT4+Pti0aRNGjhyJFy9eKNojIyMxYsQIfPPNN3B0dCzVcxARaWLdunUqRey7776LTz75RKRE+lepUiU0btxYqZAt2MJ27NixIiajioiFbAUxePBgJCcn4/jx41rNj33TsivPnj0DACQnJyM5ORmRkZFFXmtqaqoobp2dndGsWTP06dOnRFkAoEaNGvj+++8xcuRIJCQkKNrv3bunKGadnZ1L3C8RkabCwsKwc+dOpTZ3d3fMmzev1G/YDd3kyZNx/fp1xMTEKNp++uknNGvWDM2bN3/jYwvWAff19YWvry+qV6+usjU5kaY4tUBLxja14HVyuRxJSUlISEjAs2fPFF+vHyckJCA1NVXxmClTpqBv375q+3v//ffx9OlTrbJ069YNc+fOfWPWN/1CePz4MUaOHIn//vtPqd3T0xPffvutTtc9JCIqEBMTg08++URpWUBzc3Ns3boVtWrVEjFZ2bl79y6CgoKUtg53dHTErl27ivxUTC6XIyAgQGmjm40bN6JZs2Z6z0vi4NQC0jmpVAonJyc4OTmhTp06RV6Xk5OjKGqrVq2q9hq5XI7nz59rncXFxaXIcxcuXMDq1asxa9asIpdmqVatGr777juMHDkScXFxivZHjx5h2LBh+Pbbb1GlShWt8xERFZaZmYnJkyerrG09ZcqUClPEAkCtWrUwduxYpe3PExMTMW/ePKxZs0btIERsbKzKbo3cDIFKg4UsFcnc3BxVq1YtsogFXu36EhoaWuSo7vPnz5GQkIDExES10xmKGjHNzMzE4sWLERcXh6FDh6JPnz4YPXq0ylqywKuP8gqmGcTGxiranzx5guHDh2PTpk1KO8gQEWlLEAQsXrwY9+/fV2r/4IMP0KNHD5FSiad///64ePEizp49q2g7f/48du7ciY8//ljl+sJTz5ydneHg4KD3nFR+sZClUpFIJLCzs4OdnR18fHyKvC4/Px8vXrxQKXjffvtttdd///33ihFWQRCwe/dunDx5ElOmTEHbtm1Vrq9cubJiZPb1OVvx8fH47LPPsGnTJnh4eJTyuyWiim7fvn04dOiQUpuvry+mTZtmMMsUliWJRIK5c+diwIABSp/OrV+/Ho0bN1b51C8qKkrpmKOxVFrlezY6GQwTExO4urrirbfeQps2bdC3b1+MHj0atWvXVrk2Ly8Pf//9t0r7s2fPMHnyZEyaNEnpBq8CLi4u+P7771W2hUxISMCwYcPw8OFDnX0/RFTx3L17F8uXL1dqs7GxwdKlS2FpaSlSKvE5ODhg/vz5SoV8Xl4eZsyYoTL9ovCILAtZKi0WsmRwTE1NsWXLFowfP17tL4eTJ0+iT58++O2331SmKzg6OmLTpk0q/zg+f/4cw4cPV/k4kIhIUx4eHmjfvr1S29y5c+Hp6SlSIsPRrFkzBAUFKbXFxsZi6dKlSm2FR2T9/Pz0HY3KORayZJBMTEwwaNAg/Pbbb2jZsqXK+YyMDCxbtgxDhw5FdHS00jkHBwd8++23KqO9iYmJGD58+BuXByMiKoq1tTUWLFiAadOmwczMDB9//DHatWsndiyDMWLECJXpYgcPHlRMxUhNTVVZ4YYjslRaXH5LS8a8/JaxEQQBR48exYoVK5CUlKRy3sTEBEOGDMHQoUNhYWGhaH/58iXGjBmDmzdvKl1vZ2eHjRs3qp3WQESkiaioKNSoUYPrnxYSFxeHAQMGID09XdFmb2+Pv/76Czdv3sSIESMU7WZmZjhz5gxfw3JO3/USR2TJ4EkkEnTu3Bl79+5F9+7dVc7n5+djy5Yt6N+/Py5fvqxor1SpEr7++muVpbtSU1MxatQolQKXiEhTvr6+LMDUcHd3x4wZMxTH1atXx8aNG2FpaakyrcDb25uvIZUaC1kyGnZ2dpgzZw6+/fZbtXPSYmNjsWDBAuTl5SnabG1tsWHDBjRu3Fjp2pcvX2LUqFEqW0sSERW4f/8+59VroXPnzujevTt69uyJn3/+WTEPljd6kT6wkCWj06RJE+zatQtDhw6FiYmJ0rnp06ervMO3trbG2rVr0bRpU6X2jIwMjBkzBhEREXrPTETGQRAEnD9/HmPGjEHfvn3x9ddfix3JKM2aNQuzZs2ClZWVoo03epE+sJAlo2Rubo5Ro0Zhx44dqFevHgCga9euaNGihdrrrayssGbNGpXzGRkZGDt2rNKUBCKqeLKysvD777+jb9++GDt2LMLDwwEAp0+fxuPHj0VOZ3wK7+qVn5+Pe/fuKbVxRJZ0gYUsGTUfHx9s3rwZ06dPx4QJE4q8Ljk5Gaampli5ciUCAgKUzmVlZWHcuHGKX1xEVHEkJCTg66+/xnvvvYdFixbhwYMHSucFQcCuXbtESld+PHr0CDk5OUptLGRJF1jIktGTSqX48MMP4ejoqPa8IAiYMWMGPvnkE0RHR2PZsmUqu4Pl5ORgwoQJStssElH5devWLcyaNQvdunXD1q1bkZqaqvY6mUwGJyenMk5X/kRFRcHR0RHvvvsuzM3NYW1tDXt7e7FjUTnA2wWp3Dt06BAuXboEAAgKCkL//v0xe/ZsmJiYICwsTHFdbm4uJk2ahKVLlyIwMFCsuESkJ/n5+Th16hS2b9+O69evv/Fab29vDBgwAO+9957Ssn6knTZt2uDtt9/GrFmzkJOTgyZNmogdicoJFrJUriUlJWHVqlWKY7lcjh07duDEiROYPHkyTE1NceTIEcX5vLw8TJkyBYsWLVLZwYeIjNf+/fuxefNmxMfHv/G6li1bYuDAgXjnnXeUtlyl0snKykJQUBASExMBAD179hQ3EJUbnFpA5VpSUpLajwXj4+MxceJE5OfnqxSs+fn5mD59OkJCQsoqJhHpWVxcXJFFrIWFBXr37o3du3dj3bp1aN68OYtYHbOzs8O6deswYsQIrF+/njuikc5wZy8tcWcv45Gbm4uff/4ZP/zwg8rNBsCrjRPc3d1x584dpV9eUqkUc+fOxfvvv1+WcYlID549e4YPPvgA+fn5ijZXV1f07dsXvXr1gkwmEzEdUfnFnb2ISsnMzAzBwcHYtWsX/P39Vc6/fPkSd+/ehampqVKhK5fLMW/ePPzxxx9lGZeItJCTk4ODBw8iISFB7XkXFxd06tQJAFC3bl0sXLgQf/75J4KCgljEEhkxjshqiSOyxkkQBBw4cABr1qxRe5fy8+fPAQBOTk5Ko7PTp0/Hhx9+WGY5iUgzSUlJ2Lt3L3bv3o0XL17g008/xejRo9VeGxMTg+TkZNSvX59TB4jKiL7rJRayWmIha9wSExOxcuVKtfNgExISkJaWBjc3N1hbWyvaJ02ahP79+5dlTCIqQnR0NHbu3InDhw8rfZJiZ2eHQ4cOwdLSUsR0RFSAUwuI9MDR0RFfffUV1q1bhypVqiidc3V1RaVKlZCZmanUvmLFCvzyyy9lGZOIXiOXy3H27Fl8/vnn6N+/P/744w+Vee+pqak4dOiQSAmJqKyxkKUKrWXLlvjtt98waNAgpS0VAwICMG3aNJXr16xZg61bt5ZlRKIKLzMzE7t370afPn0wfvx4xbrQ6jRp0gSenp5lmI6IxGTQhWxmZibmzJkDPz8/WFpawt3dHcHBwXjy5EmJ+0pKSsK4cePg5eUFCwsLeHl5Yfz48UhOTtZ9cDIqVlZWGD9+PH788UfUrl0bUqkUs2bNwogRI9TOtfv666/x3XffgbNyiPTr6dOnWLduHd577z0sXboUjx49UnudmZkZunXrhh07duDbb7/lYvtEFYjBzpHNyspC27ZtER4ejipVqiAgIAAPHz7EpUuX4OLigvDwcHh7e2vU1/Pnz9GiRQtER0fD29sbTZo0wc2bN3Hz5k34+fnhwoULRW5vWhTOkS2f8vPzcf36dTRu3FjR9ssvv2DNmjWK44yMDFhZWWHo0KEYNWoUbxoh0jG5XI45c+bg6NGjkMvlRV7n4OCAjz76CB9++CG3kSUyUPqulwx2Z6+FCxciPDwcLVq0wNGjR2FrawsAWLVqFf73v/8hODgYJ0+e1Kiv8ePHIzo6Gr1798avv/4KU9NX3/bYsWOxfv16TJw4Edu2bdPTd0LGxMTERKmIBYBBgwbBzMwMy5cvR2ZmJmJiYmBlZYWNGzciNTVV5XqJRKIobgv/V13b69frsg9BEJCfnw+5XA5zc3NYWFjAxMQEUqkUpqamkEqlMDExUbSp+7O6cyzcSd+kUimysrKKLGJr1qyJgQMHokuXLjA3Ny/jdERkSAxyRDYnJweurq5ISUlBREQEGjVqpHS+QYMGuHHjBq5cuaJ2XdDXxcfHo1q1ajA1NcWjR49QuXJlxbns7Gx4eHggMTERcXFxcHV11TgjR2Qrnt9++w0jR45Edna2ok0mkynm1hb8r1TUf93d3ZXm4RbIzMzE06dPVa4vqq/C52vUqKH2l3lmZiYePnyo1FZQiEokkmL/7OjoqPbOb4lEgpcvX8LExASmpqaK/5qZmcHExARmZmYwNTWFqakpzM3NFde8qTh+vUguTVFfmjcOpe0DgKLwksvlEARB8d+CP7/ebmNjo3iDXriv2NhYZGVlKfXx+n8L9/X6f6tUqYLatWurzf7gwQO8fPlS8ffz+t9fUV8Ff69F/R2oe700vU4ikcDCwkLxRqvgy9zcHPfu3cOXX36p9DPZunVrDBo0CM2aNeMbKiIjUSFHZM+dO4eUlBT4+PioFLEA0KdPH9y4cQMHDhwotpA9cuQI5HI5AgIClIpY4NW2hN26dcOWLVtw6NAhBAUF6fLboHImKysLjo6OSttcpqSkaPz4ot4z5ufnq6yQoAtvKrQ0UdQi8Xl5eYiNjS1xloJixM3NDZUqVVKbLS4uTu3rpEmbk5OTojAs7OHDhypvAjTt28nJCQ4ODmr7jY6ORl5enlbzpZ2cnIp883z//n2lN0wlYW9vr7ISR4HHjx/j5cuXWvVrY2NT5E1UL168QFpamtKbEXVvkgp/FQxaqPtZFQQBcXFxyM7Ohr29PRwdHXHhwgVcuHABZmZmaotfS0tLpXZ112jzGHNzc0ilUsVXQWHPYppIfAZZyF6/fh0AVD6yLVDQfuPGDZ30tWXLFo36oortrbfeUiykHhcXp7N+S/vLUF8fqhSVqyTFcIGCaQ4Ffy6KtkUWUHThDUAxuqmNN32/RRXHpVWan4k35dHm704T2dnZyMjI0OqxlpaWav/uJBIJ3N3dFaPGr8vNzUVubi7S09O1ek5dKSjUCz5RUPdV+Jy6awsKY22uLeqxRWV507Wvn9emT037Lvwavv7fN/25LB9T+I2Yuk+tCrcV9SkX6ZdBFrIFd6ZWq1ZN7fmC9piYmDLtiyo2f39/7Nq1C5s3b8aGDRuQkJCgtG97YYULiqpVqyqmALw+VSApKUlplFfT/go4OjrCyspKcU3BdRkZGUq/NIqanlAUddMg3pRDU0X1a4z0VXDq65dfaf7u3vT3Vpp+ExMTYWdnp/Z7trCw0LrfslDwBu1N/w4QFVfsFjfNq+BxAFT6MIZiOTc3V6/9G2Qhm5aWBgBKuyq9zsbGBoBmoze66is7O1vpoz5125tS+Wdubo5Ro0ahS5cuOHLkCJ49e6Yyz/P1P7/eNmjQILU/h8+ePcOZM2dUHvP6HNKi+jQxMUGtWrXUzmXNzc1FQkICJBIJcnNzFT/DOTk5ij9nZWUpvjIyMpCdnY3MzExkZ2fjww8/hL29veKGsYJf2E+ePMHSpUsVfb3+9frH7EXN7/3ss89Qo0YNlX6zs7Px1VdfafT3oK5w6tixIxo0aKB2rvGqVatUFs7XtN933nkHzZo1U/tG4Mcff9RoCb/C/UokErz99tto1aqV2rxhYWF4/vy5yi+6ov77+i8+V1dX1KpVS+3zX7hwAc+fP1e85gVfr/89FJXf09MTrVu3Vuqv4L9nzpxRO9pbXIFb8FpWrlwZNjY2Kj+jmvydERm61+fJV0T6fqNnkIWsIVq8eDG+/PJLsWOQgahRowZGjRqlk75cXFzQu3dvnfT1OjMzM1StWlXn/Xp7eyMgIEDtOblcrlIsv/7n7Oxs1K1bV+2E//z8fLXzKAtGIoqbb9mkSRPUqFGjyMyF+1fXLwCV56hevTo8PDzU9tujRw/k5+cr3TD1+k1tr99M9Xp7cSMoc+bMeeN5fREEAXl5eYo3Pq//t2Atb3XOnz+PmJgYtY8r/Gbn9S+pVIrGjRujX79+cHFxUelXLpcjLy8PWVlZKj9Hb/oZy8nJUXlMSR6fnZ3NdaKJjIRBFrIFN2wUNeeqYF6UuhtG9NXX9OnTMXHiRMVxampqkb/ciCoqqVQKKysrxVSHkjAxMcFnn32mh1RAly5d9NKvn5+fXvoVi0QigZmZGczMzIr8FEudli1bomXLljrPI5VKFTdblaWCgr6gwM3NzUV+fr7SknavfxVuK801rz9HSZ+zqGuL+nr9MYX/q+n1mj7X6328/joXft2LOkdUFIMsZAvujH38+LHa8wXtXl5eZdZXwR2sRERUvr1e0BdMPyPxqZuGU/hcUddpUjQXbnt9SoC65fSKO//6cnyaXK9tf4YuPT0dPXv21Fv/BlnINmjQAAAQERGh9nxBe/369cu0LyIiIhJHUWsWk2HT9z1FBnn7cKtWrSCTyXDv3j1cu3ZN5fyePXsAAN26dSu2ry5dukAqleLMmTNISEhQOpednY0DBw7AxMQE7733nk6yExEREVHZMMhC1tzcHGPGjAEAjB49WmmtwFWrVuHGjRsIDAxU2gxhw4YNqF27NqZPn67UV5UqVTBgwADk5OTg888/R15enuLclClT8OzZMwwaNKhEu3oRERERkfgMcmoBAMyaNQthYWE4f/48fH19ERAQgJiYGFy8eBEuLi7YsmWL0vXPnz/H3bt31a7HuWbNGoSHh2Pv3r2oXbs2mjRpgps3b+Lff/+Fr68vVq1aVVbfFhERERHpiEGOyAKvdns5ceIEZs+eDWtra+zfvx8xMTEICgpCREQEvL29Ne7L2dkZly5dwhdffIGcnBzs27cPKSkpGDt2LC5dugRHR0c9fidEREREpA8SwRhueTNAqampkMlkSElJUbsmJhEREVFFp+96yWBHZImIiIiI3oSFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJRayRERERGSUWMgSERERkVFiIUtERERERomFLBEREREZJVOxAxgrQRAAAKmpqSInISIiIjJMBXVSQd2kayxktfTy5UsAgIeHh8hJiIiIiAzbixcvIJPJdN6vRNBXiVzOyeVyxMXFoVKlSpBIJEhNTYWHhwdiY2NhZ2cndjyjxtdSt/h66g5fS93ha6lbfD11h6+lbqWkpMDT0xNJSUmwt7fXef8ckdWSVCpFtWrVVNrt7Oz4g68jfC11i6+n7vC11B2+lrrF11N3+FrqllSqn9uyeLMXERERERklFrJEREREZJRYyOqIhYUF5s6dCwsLC7GjGD2+lrrF11N3+FrqDl9L3eLrqTt8LXVL368nb/YiIiIiIqPEEVkiIiIiMkosZImIiIjIKLGQLYXMzEzMmTMHfn5+sLS0hLu7O4KDg/HkyROxoxmVjIwM7N+/H0OHDkWtWrVgaWkJGxsbNGjQAPPnz0daWprYEY3aixcv4OrqColEgpo1a4odx2g9e/YMkyZNQq1atWBlZQVHR0c0btwYkydPFjuaUbl8+TL69u0Ld3d3mJmZwd7eHgEBAdi6davedv4xZn///TeWLFmC3r17o1q1apBIJJBIJMU+btu2bWjWrBlsbW3h6OiI9957D+fPny+DxIarJK+lXC7HmTNnMGXKFPj7+6NSpUqwsLCAj48PRo4ciQcPHpRxesOj7c/m6zp06KB43OPHj7ULIpBWMjMzhebNmwsAhCpVqgh9+/YVmjVrJgAQXFxchHv37okd0Wh8//33AgABgFCnTh3ho48+Ejp37ixUqlRJACDUrl1bePr0qdgxjdaQIUMEiUQiABB8fHzEjmOUrly5Ijg5OQkAhLfeekvo16+f0LVrV8HLy0swMTERO57R2LNnj2BiYiIAEBo3biz07dtXaNu2rWBqaioAEAYOHCh2RIPTo0cPxb+Pr3+9ybhx4wQAgpWVldCjRw+hc+fOgqmpqWBiYiLs27evbIIboJK8llFRUYrzbm5uQvfu3YVevXoJVatWFQAIlSpVEs6cOVPG34Fh0eZn83Vbt24VACh+P8XGxmqVg4WslmbOnCkAEFq0aCG8fPlS0b5y5UoBgBAYGCheOCOzbds2Yfjw4cKtW7eU2uPi4oRGjRoJAIQBAwaIlM64hYWFCQCE4cOHs5DVUkJCguDs7CxYW1sLf/zxh8r5ixcvipDK+OTm5gqurq4CAGH79u1K527duiU4OjoKAITjx4+LlNAwLVmyRJg9e7bw559/CvHx8YKFhcUbi4XQ0FABgODk5CRERkYq2s+fPy+Ym5sL9vb2QlJSUhkkNzwleS2jo6OFjh07CseOHRPkcrmiPSsrSwgKChIACJ6enkJOTk5ZxTc4Jf3ZfF1CQoLg6OgodOrUSfDy8mIhW9ays7MFmUwmABAiIiJUztevX18AIFy5ckWEdOXL+fPnBQCChYWFkJ2dLXYco5KRkSH4+PgIdevWFSIjI1nIamnUqFECAOHrr78WO4pR++effwQAQq1atdSeHzt2rABAWLp0aRknMy7FFQtdu3YVAAirV69WOVfwGq9YsUKPCY1HSQqv12VkZChqgJMnT+ohmXEqyes5cOBAwdLSUoiOji51Ics5slo4d+4cUlJS4OPjg0aNGqmc79OnDwDgwIEDZR2t3GnQoAEAIDs7Gy9evBA5jXH58ssvcf/+fXz77bcwMzMTO45RyszMxC+//AIbGxt8+umnYscxapquIenk5KTnJOVXZmYmjh8/DuD/fg+9jr+bdMPKygp+fn4AgLi4OJHTGJ8jR45gx44dmDlzJnx8fErdHwtZLVy/fh0A0LhxY7XnC9pv3LhRZpnKq/v37wMAzMzM4OjoKHIa43Hjxg2sXLkSn376KQICAsSOY7SuXLmCly9folGjRrCyssLhw4cxceJEfP7551izZg1/iZWAt7c3fHx8cPfuXezYsUPp3O3bt/HLL7/AwcEBvXr1Eimh8bt79y6ys7Ph4uKCatWqqZzn7ybdkMvliImJAQC4ubmJnMa4pKenY9SoUahduzamTJmikz5NddJLBfPo0SMAUPsPxevtBT/opL21a9cCALp06cJdVjQkl8vx2Wefwd7eHsuWLRM7jlG7desWAMDV1RU9e/bEH3/8oXR+xowZ2Lx5MwYMGCBGPKNiYmKCH3/8ER988AE+/vhjrFy5Er6+vkhISMCZM2dQt25dbNu2jW9YS6G43002Njawt7dHUlISXr58iUqVKpVlvHJj586dSEhIgIuLC1q2bCl2HKMyZ84cPHz4ECdPnoS5ublO+uSIrBYKloOytrZWe97GxgYA8PLlyzLLVB4dOnQImzdvhpmZGRYsWCB2HKOxfv16XL58GcuXL+fHtKWUlJQEAPjzzz9x5MgRfP3110hISMDDhw8xadIkZGZmYsiQIbh27Zq4QY1Eq1atcOrUKXh7eyMiIgK//vorTpw4AalUio4dO8Lb21vsiEatuN9NAH8/lVZsbCzGjx8PAJg/fz4HWEogIiICa9euxZAhQxAYGKizflnIkkG6c+cOBg0aBEEQsHz5csVcWXqzR48eYdasWQgMDERQUJDYcYyeXC4HAOTl5WH+/Pn4/PPP4eLiAi8vLyxfvhwfffQRcnNzsXz5cpGTGoedO3eiWbNm8PDwwMWLF5GWlobIyEgEBQVh5cqVaNeuHbKzs8WOSaRWeno6evfujefPn6Nnz54YOXKk2JGMRn5+vuKTwhUrVui0bxayWrC1tQXwaiF/ddLT0wGAH9to6cmTJ+jSpQuSkpIwceJEjBs3TuxIRmP06NHIycnBt99+K3aUcqHg/3UAam/2Kmg7depUmWUyVlFRURgyZAicnZ3x119/oVmzZrCxsYGvry82bdqEDz74ABEREdiyZYvYUY1Wcb+bAP5+0lZubi4++ugjXLlyBa1bt1aZ501vtmbNGly9ehXLli2Ds7OzTvvmHFkteHp6AkCRu1AUtHt5eZVZpvIiMTERnTp1QkxMDD799FOdv3Mr7/766y/Y29urjBRkZWUBePUmoU2bNgCAXbt28UaFYhT8P2xtbQ0XFxeV89WrVwcAJCQklGUso7Rr1y7k5uaiS5cuSm8QCvTt2xd//fUXTp8+jVGjRomQ0PgV97spPT0dycnJcHBwYCFbAnK5HEOGDMHhw4fRsGFDHDhwAFZWVmLHMioHDhyARCLBjz/+iJ9++knp3H///QcA+Oijj2BhYYFp06ahS5cuGvfNQlYLBR9zR0REqD1f0F6/fv0yy1QepKWloWvXrrh16xZ69+6N77//vsTb3RGQnJxc5AhhVlaW4lxBcUtFK1heLzMzE9nZ2Srz4RITEwFAbWFGygqKK5lMpvZ8QXvBvGQquVq1asHCwgLPnj3DkydPULVqVaXz/N2knS+++AI7d+6En58fQkJCYG9vL3YkoyQIAk6fPl3k+fDwcAAo8bQ4Ti3QQqtWrSCTyXDv3j21N3ns2bMHANCtW7cyTma8srOz0aNHD1y6dAmdO3fGzp07YWJiInYsoyO82uRE5atgX3AfHx9FW8FoIhXN09MTDRo0gCAIat8cFLSpW0+alBWM/l+5ckXt+cuXLwMAfy5LwcrKCu3atQMA7N69W+U8fzeV3KxZs7Bx40Z4enoiNDQUrq6uYkcySidPnizy91PBJ1+xsbEQBKHk93dotY0CKbaobdmypZCWlqZo5xa1JZeXlyf06tVLACAEBAQI6enpYkcqdx48eMCdvbS0fft2AYBQr149IS4uTtF+9epVxbaqv/32m4gJjcPff/+t2It948aNSucuXLgg2NjYCACE0NBQkRIah9JsUWthYVGht6gtrLjXctWqVQIAwc3NTem1JPW03SmttDt7SQRBEHRQbFc4WVlZaNOmDS5evIgqVaogICAAMTExuHjxIlxcXBAeHs6lZDS0du1axXImvXr1gp2dndrrVqxYofNJ4hXFw4cPUaNGDfj4+CA6OlrsOEYnKCgIP/74I+zt7dGyZUtkZmbi/PnzyM7OxrBhw/Ddd9+JHdEoTJ48WTHv/a233kLdunURFxeHCxcuQC6XY/jw4di0aZPIKQ3LwYMHlZYfvHTpEgRBwDvvvKNomz17Nt5//33F8fjx47F27VpYW1ujY8eOyMnJQWhoKARBwJ49e9CzZ8+y/BYMRkley2vXrqFx48YQBAEtWrRQ7ORV2GeffYbWrVvrPbsh0uZnU53q1asjJiYGsbGxRa6B/EZalb8kCMKr/ZZnz54t+Pj4CObm5oKbm5sQFBSk9buKimru3LmKkZo3fT148EDsqEaLI7KlI5fLhe+++07w9/cXrK2tBRsbG6FFixbCtm3bxI5mdH7//XehU6dOgpOTk2Bqaio4ODgIbdu2FXbs2CF2NIO0devWYv9t3Lp1q9rHFfy82tvbC126dBHOnTtX9t+AASnJa3nixAmNfi+pe+0rCm1/NgvjiCwRERERVUi82YuIiIiIjBILWSIiIiIySixkiYiIiMgosZAlIiIiIqPEQpaIiIiIjBILWSIiIiIySixkiYiIiMgosZAlIiIiIqPEQpaIiIiIjBILWSLSWvXq1SGRSJS+LCws4OnpiX79+uHMmTM6eZ6goCBIJBJs27ZNJ/2VBwWv/cOHD3XSX8Hfny7x742I9M1U7ABEZPxatWqFmjVrAgCSk5Nx5coV/Pbbb9i9ezdWrFiBiRMnipyQiIjKIxayRFRqn332GYKCghTHWVlZGDFiBH766SdMmTIFH3zwAfz8/MQLWA4dO3YMubm5qFq1qthRiIhEw6kFRKRzlpaW+Prrr2FjY4P8/Hz8/vvvYkcqd3x8fFC7dm2YmZmJHYWISDQsZIlIL2xtbVGrVi0AUJnHGRISgg8++ACurq4wNzeHu7s7+vXrhytXrmjc/5AhQyCRSLB48eIir/ntt98gkUjQrFkzRdu2bdsgkUgQFBSE9PR0TJ8+HTVr1oSFhQXc3NwwZMgQPHnypMg+L126hL59+8Ld3R3m5uZwdXVFt27dEBoaqvb61+eJ3r17F/369YOrqytsbGzQtGlT/PHHH4prL168iO7du8PFxQVWVlZo0aIFjh07prbfoubIxsTEYOnSpWjXrh08PT1hYWEBe3t7tG7dGps2bYJcLi/ye9NGYmIixo8fDy8vL8X86DFjxiAxMbHYxx47dgy9e/dGlSpVFK9lr169cOHChSIf8++//+LDDz+Es7MzrK2tUa9ePaxZswZyubzI1+T19j/++APt2rWDo6MjJBIJTp48qbguKSkJc+fORcOGDVGpUiVF/wsXLkRGRkaRmf7++298/PHHitfb0dERnTt3xqFDh4p9DYiolAQiIi15eXkJAIStW7eqPV+zZk0BgDB27FhF26xZswQAgkQiEVq1aiUMGDBAaNiwoQBAMDExETZv3qzSz5AhQ1Se5++//xYACJ6enkLe/2vv3mOqrP84gL8P53C4E3AIARGEIzJBEARvBSIQNwXkOjidURHDwDBb5JplZeZ0g62VgyxilIy1ktZFByibCngZWtO4GeqA5oLJEAJPIBDw+f3Bzvl1fM7hJuH4/T6vP7/f53t5Hg7w5uH7fJ/xcZ3jb926lQDQiRMnNGVffvklAaD4+Hjy8fEhKysrio2NpZ07d5KdnR0BIBcXFxoYGBD0V1xcTAYGBgSA/Pz8SKFQ0DPPPEMACAAdPHhQ79z37NlDZmZm5OHhQWlpabRlyxbNdaioqKAffviBDA0Nyc/Pj1JTU2ndunUEgCQSCV28eFHvte/s7NQq//DDDwkAubq6UlhYGKWlpVFwcDBJpVICQImJiTQ5OSnoT30Oc3Hv3j1yd3cnAGRtbU2JiYkUHx9PVlZWJJfLKS4uTu/nIy8vjwCQgYEBbdy4kVJSUmjTpk0kEolILBZTaWmpoE1tbS2ZmJgQAJLL5ZSWlkbh4eEklUopNTVV7zVRl+fm5hIACggIIIVCQcHBwVRfX09ERK2trbRixQoCQA4ODhQVFUWxsbG0bNkyAkC+vr46PxMff/yx5jPh6+tLycnJFBgYqLneH3zwwZyuKWNsbjjIMsbmbbog29jYqPkFrw4l1dXVBICMjY2ppqZG6/iSkhICQIaGhtTS0qJVpyvIEhE9++yzBIC+//57wfjNzc0EgJ5++mkaGRnRlKuDLACKjIykwcFBTV1/f78mVB85ckSrv6amJpJIJCQSiaisrEyrrqqqShNcHj0v9dwB0OHDh7VC5LFjxwgAOTk5kbW1taDf119/nQDQc889Jzg/faHt2rVr1NzcLDi+q6tLE45PnjwpqJ9PkE1OTiYAFBQUpBXy+vr6aNOmTZo+H/26FRcXEwBatWoVNTY2atXV1dWRhYUFSaVSun37tqZ8eHiYli9fTgAoLy+PJiYmNHWtra2awDldkBWLxfTTTz8JzmN4eJjkcjkBoAMHDtDo6KimbmhoiBQKBQGgjIwMrXZnzpwhkUhEtra2VFdXp1XX1NRETk5OBIBqa2unv5CMsXnjIMsYmzddQXZgYIAqKys1wcDR0ZH++usvIiIKCwsjAPTGG2/o7C8mJoYAUFZWlla5viB78uRJAkBhYWGCvl555RUCQPv379cqVwdZMzMz6u7uFrT75ptvCACFhoZqlWdmZmruaOqivtsXHh6uc+4bN24U3An9+++/ycbGhgBQSkqKoM/79+8TAJJKpTQ2NqZVpy/ITufs2bN6x5prkL179y4ZGBiQSCSi1tZWQf2NGzd0BtmJiQlydHQkAPTLL7/o7Ds/P18TWNXKyso0d8sfvRZERIWFhTMG2ZdfflnneMePHycAFBMTo7NepVKRnZ0dSSQS6u/v15Srw/p3332ns53685mUlKSznjH2+HiNLGPssWVkZGj2IbWyssKOHTvQ3t4OuVyOqqoqmJmZYXx8HJcvXwYArR0O/ikzMxMAcOHChVmNm5CQgBUrVuDcuXNoa2vTlA8ODqK8vBxisRg5OTk62wYEBMDBwUFQvmbNGgAQrJNVr6Wcae4XL17ExMSEoD46OlqwT6tEIoGrqysAYPv27YI2MpkMNjY2GBsbQ19fn85xdRkdHcXp06fx3nvvITs7GxkZGXjppZfw+eefAwBu3bo16770qa+vx+TkJNavXw9PT09Bva+vL3x8fATlN27cQHd3N+RyOfz9/XX2vW3bNgDAlStXNGV1dXUAgJSUFJ0PuCmVyhnnnJycrLO8srISAJCamqqz3tzcHAEBARgfH8fPP/8MALh//z6uXbsGExMTxMbGzvo8GGMLi7ffYow9tn/uI6t+aGfz5s2IioqCRDL1Y6avrw8jIyMAoAlvj5LL5QCEIVIfiUSC3bt3Y//+/SgsLERhYSEA4MSJExgaGtIEXV2cnZ11lltaWgKAZq5q6jnNNPeRkRH09fXBzs5uVuOZm5tPW29hYYH+/n7BfPRpaGhAamoq7t69q/eYBw8ezKqv6fzxxx8A9F8PdV1TU5NWWUdHBwCgvb19xhcw9Pb2CsZbuXKlzmOtrKzw1FNPYXBwUG9/+tqq55Seno709PRZzamzsxNEhIcPH8LIyGhWbRhjC4+DLGPssT26j+xiysrKwqFDh1BWVoajR4/C3Nwcn376KQAgNzdXbzsDg8X9h9RM4y3EfIaHhxEfH4+enh5kZGQgJycHq1atgqWlJcRiMW7fvg0PDw8Q0WOPNV/qXRPs7e0RGRk57bG2traCsunC70zB2MTEZNo5RUVFYdmyZdP24eLiotXG3NwcSUlJ07ZhjP17OMgyxhaFTCaDkZERRkdH0dHRofPfzuo7Y3PZ5F8mk0GpVKKkpARlZWVYvXo1bt26BU9PT4SGhi7Y/JcvX4729nZ0dHRg7dq1eudubGwMGxubBRt3Lurr69HT04P169ejtLRUUH/nzp0FG0v9NZruFbm66tR3yGUy2ZxeXTvTeIODgxgYGJh1f4/Oqa2tDZmZmXqXH+hqA0yF59LS0kX/w4gxNoW/8xhji0IikSAwMBAA9AYYdfgKCQmZU9+vvfYaAKCoqEizvODVV1+d50x1U693nGnuQUFBmuUUi029d6u+ZQrl5eULNtbWrVshEolw/fp1rfXJao2NjYJlBQCwYcMG2Nra4ubNm2htbZ3TeABQUVGB8fFxQf3XX389h9lri46OBjC17/BsOTo6wsfHByqVCmfOnJn32Iyxx8NBljG2aPLy8gAAx48fF2z0/9VXX+HUqVMwNDTE3r1759Svt7c3QkND8dtvv+HUqVOwtLTECy+8sGDzBoC9e/dCIpHgxx9/FATCmpoazYNUb7755oKOOxfqB9XOnTuHmzdvatUVFxfj22+/XbCxnJ2dkZCQgMnJSeTk5Gitu/3zzz+xe/dunUsYDA0N8f7774OIkJCQgEuXLgmOmZiYwPnz59HQ0KApS0lJgYODA37//Xe88847Wi92aGtrw6FDh+Z9Lrt27YKLiwsqKirw1ltvQaVSCY65d+8evvjiC62yw4cPA5h62PH06dOCNkSEq1evoqamZt5zY4xNj4MsY2zRREdH48CBAxgZGUF4eDiCgoKgVCrh7++PjIwMiMVifPbZZ/Dy8ppz3+q7ssDUW7/UD1EtFG9vbxQVFUEkEiE9PR3+/v5QKpUIDAxEVFQURkdHcfDgQURERCzouHPh5+eHnTt3QqVSwc/PD5GRkVAoFFizZg2ys7Px9ttvL+h4RUVFkMvlqK2thaurK5KSkpCYmAg3Nzf09PQgLi5OZ7vc3Fzs27cPd+7cQVBQENauXYv4+HgoFAqEhITA1tYWYWFh+PXXXzVtTE1NUV5eDmNjY+Tn58PDwwMKhQKRkZFYt24dgoKCNHeipVLpnM7DzMwMlZWVWLlyJfLz8+Hs7Izg4GAolUokJCTAy8sLjo6OePfdd7XaxcbG4pNPPkF/fz/i4uLg7u6OmJgYKJVKREREwN7eHps3b8b58+fndmEZY7P3RDf/YowtaTO92Uuf6upq2r59O8lkMpJIJGRvb08pKSl09epVncfr20f2n1QqFYnFYhKJRNTW1qb3OPU+si+++KLO+s7OTs1+pbo0NDRQcnIy2dvbk0QiIZlMRjt27BC8CGG2cw8ODiYAdOHCBZ31M72t6tHysbExKigoIG9vbzI1NSUbGxuKiIigmpqaac8N83ghAtHUXrd79uwhJycnkkql5OTkRNnZ2dTb2zvjuV++fJmUSiW5uLiQkZERWVhY0OrVqyk+Pp5KSkq09mxVa2xspISEBLKxsSFjY2Py9PSkgoICGh0dJalUSgYGBvTw4cNZXatHPXjwgPLz82nLli1kZWVFhoaG5ODgQBs2bKB9+/bRlStXdLZrbm6mXbt2kbu7OxkbG5OpqSm5ublRZGQkHTt2jLq6umZ1LRljcycieoKPrzLG2AIpKSlBVlYWIiIicPbs2Sc9HbbI6uvrERwcDG9vb51rcxlj/5t4aQFjbMkbGhrC0aNHAfx3HS7739Pb24vOzk5BeUtLC7KysgBMrVdljP3/4DuyjLElq6CgAC0tLbh06RI6OjoQFRWF6urqJz0t9i+pra1FSEgIPD094ebmBhMTE3R2duL69euYnJxEeHg4qqqqntiuEYyxxcdBljG2ZG3btg11dXWwtbVFTEwMPvroI1hbWz/pabF/SXd3N44cOYK6ujp0dXVBpVLBwsICXl5eeP7555GVlcUhlrH/MxxkGWOMMcbYksRrZBljjDHG2JLEQZYxxhhjjC1JHGQZY4wxxtiSxEGWMcYYY4wtSRxkGWOMMcbYksRBljHGGGOMLUkcZBljjDHG2JLEQZYxxhhjjC1JHGQZY4wxxtiS9B/+HWaiFctmKQAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.plot(degree_list, mse_train, c='k', alpha=0.8, lw=3, ls='-', label='Training')\n", "ax.plot(degree_list, mse_val, c='k', alpha=0.8, lw=3, ls='--', label='Validation')\n", "ax.legend(loc=2, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Polynomial degree', fontsize=16)\n", "ax.set_ylabel(r'Mean Squared Error (MSE)', fontsize=16)\n", "ax.axis([-0.1,14,-0.1,0.9])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "23aa2b35", "metadata": {}, "source": [ "Multiple options for the degree of the polynomial is possible based on the above plot. Based on the Occam's razor, the simplest models among them should be choosen.\n", "\n", "A general metric to test this criteria is Bayesian Information Criteria (BIC) defined as,\n", "\n", "$\\mathrm{BIC} = k\\log(N)-2\\log(L_\\mathrm{max})$ ,\n", "\n", "where $k$ and $N$ are the number of degrees of freedom and data points, respectively. $L_\\mathrm{max}$ is the maximum likelihood values from the training process." ] }, { "cell_type": "code", "execution_count": 31, "id": "a7c57576", "metadata": {}, "outputs": [], "source": [ "def BIC(model, X_train, y_train, N):\n", " k = model.degree\n", " y_pred = model.predict(X_train[:,None])\n", " Lmax = np.exp(- mean_squared_error(y_train,y_pred)*N)\n", " # print(N, k*np.log(N),Lmax)\n", " bic = k*np.log(N)-2*np.log(Lmax)\n", " return bic" ] }, { "cell_type": "code", "execution_count": 32, "id": "79c0a279", "metadata": {}, "outputs": [], "source": [ "degree_list = np.arange(15)\n", "bic_train = np.zeros_like(degree_list, dtype=float)\n", "bic_val = np.zeros_like(degree_list, dtype=float)\n", "\n", "for i,deg in enumerate(degree_list):\n", " model = PolynomialRegression(degree=deg)\n", " model.fit(X_train[:,None], y_train, yerr_train)\n", " y_pred = model.predict(X_val[:,None])\n", " bic_val[i] = BIC(model,X_val,y_val,X_train.shape[0])\n", " y_pred = model.predict(X_train[:,None])\n", " bic_train[i] = BIC(model,X_train,y_train,X_train.shape[0])" ] }, { "cell_type": "code", "execution_count": 33, "id": "0a25a8ab", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.plot(degree_list, bic_train, c='k', alpha=0.8, lw=3, ls='-', label='Training')\n", "ax.plot(degree_list, bic_val, c='k', alpha=0.8, lw=3, ls='--', label='Validation')\n", "ax.legend(loc=2, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Polynomial degree', fontsize=16)\n", "ax.set_ylabel(r'Bayesian Information Criteria (BIC)', fontsize=16)\n", "ax.axis([-0.1,14,-0.1,90])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9377f599", "metadata": {}, "source": [ "### Polynomial Regression of Supernova data" ] }, { "cell_type": "code", "execution_count": 34, "id": "610bf4cb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Full data: (100,) (100, 2)\n", "Training data: (70,) (70,) (70,)\n", "Validation data: (15,) (15,) (15,)\n", "Testing data: (15,) (15,) (15,)\n" ] } ], "source": [ "from sklearn.model_selection import train_test_split\n", "\n", "X, y = z_sample.copy(), np.vstack((mu_sample,dmu)).T.copy()\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1)\n", "X_test, X_val, y_test, y_val = train_test_split(X_test, y_test, test_size=0.5, random_state=1)\n", "y_train, yerr_train = y_train[:,0], y_train[:,1]\n", "y_test, yerr_test = y_test[:,0], y_test[:,1]\n", "y_val, yerr_val = y_val[:,0], y_val[:,1]\n", "\n", "print('Full data:', X.shape, y.shape)\n", "print('Training data:', X_train.shape, y_train.shape, yerr_train.shape)\n", "print('Validation data:', X_val.shape, y_val.shape, yerr_val.shape)\n", "print('Testing data:', X_test.shape, y_test.shape, yerr_test.shape)" ] }, { "cell_type": "code", "execution_count": 35, "id": "699ff7f2", "metadata": {}, "outputs": [], "source": [ "degree_list = np.arange(15)\n", "mse_train = np.zeros_like(degree_list, dtype=float)\n", "mse_val = np.zeros_like(degree_list, dtype=float)\n", "\n", "for i,deg in enumerate(degree_list):\n", " model = PolynomialRegression(degree=deg)\n", " model.fit(X_train[:,None], y_train, yerr_train)\n", " y_pred = model.predict(X_val[:,None])\n", " mse_val[i] = mean_squared_error(y_val,y_pred)\n", " y_pred = model.predict(X_train[:,None])\n", " mse_train[i] = mean_squared_error(y_train,y_pred)" ] }, { "cell_type": "code", "execution_count": 36, "id": "6e886f68", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.plot(degree_list, mse_train, c='k', alpha=0.8, lw=3, ls='-', label='Training')\n", "ax.plot(degree_list, mse_val, c='k', alpha=0.8, lw=3, ls='--', label='Validation')\n", "ax.legend(loc=2, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Polynomial degree', fontsize=16)\n", "ax.set_ylabel(r'Mean Squared Error (MSE)', fontsize=16)\n", "ax.axis([-0.1,14,-0.1,2.9])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 37, "id": "161b1d38", "metadata": {}, "outputs": [], "source": [ "degree_list = np.arange(15)\n", "bic_train = np.zeros_like(degree_list, dtype=float)\n", "bic_val = np.zeros_like(degree_list, dtype=float)\n", "\n", "for i,deg in enumerate(degree_list):\n", " model = PolynomialRegression(degree=deg)\n", " model.fit(X_train[:,None], y_train, yerr_train)\n", " y_pred = model.predict(X_val[:,None])\n", " bic_val[i] = BIC(model,X_val,y_val,X_train.shape[0])\n", " y_pred = model.predict(X_train[:,None])\n", " bic_train[i] = BIC(model,X_train,y_train,X_train.shape[0])" ] }, { "cell_type": "code", "execution_count": 38, "id": "4815ea2f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.plot(degree_list, bic_train, c='k', alpha=0.8, lw=3, ls='-', label='Training')\n", "ax.plot(degree_list, bic_val, c='k', alpha=0.8, lw=3, ls='--', label='Validation')\n", "ax.legend(loc=2, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'Polynomial degree', fontsize=16)\n", "ax.set_ylabel(r'Bayesian Information Criteria (BIC)', fontsize=16)\n", "ax.axis([-0.1,14,-0.1,390])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 39, "id": "0635b504", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(50,)\n" ] } ], "source": [ "model = PolynomialRegression(degree=2)\n", "model.fit(z_sample[:,None], mu_sample, dmu)\n", "\n", "zz = np.linspace(0,2)\n", "mu_poly = model.predict(zz[:,None])\n", "print(mu_poly.shape)" ] }, { "cell_type": "code", "execution_count": 40, "id": "d461970c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(zz, mu_poly, c='C3', alpha=0.8, lw=3, label='Best-fit')\n", "ax.plot(z_true, mu_true, c='k', alpha=0.8, lw=3, ls='--', label='Truth')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "46a58bb3", "metadata": {}, "source": [ "### Basis Function Regression\n", "\n", "In the linear regression framework, various categories of basis functions can be used instead of polynomials. These include Gaussian functions, trigonometric functions, Fourier basis functions, and spline functions. Below we show an example with Gaussian functions, represented as: $g_p(x) = \\mathcal{N}(\\mu_1,\\sigma_1)$. These basis functions transform the input variable xx into a higher-dimensional space, allowing for more complex relationships to be captured. Gaussian functions offer a flexible approach to modeling nonlinear relationships between variables within the linear regression framework." ] }, { "cell_type": "code", "execution_count": 41, "id": "11dc7c81", "metadata": {}, "outputs": [], "source": [ "from astroML.linear_model import BasisFunctionRegression" ] }, { "cell_type": "code", "execution_count": 42, "id": "f4b595a2", "metadata": {}, "outputs": [], "source": [ "mu = np.linspace(0,1,6)[:,None]\n", "sigma = 0.1\n", "\n", "model = BasisFunctionRegression('gaussian', mu=mu, sigma=sigma)\n", "model.fit(X_train[:,None], y_train, yerr_train)\n", "zz = np.linspace(0,2)\n", "mu_basis = model.predict(zz[:,None])" ] }, { "cell_type": "code", "execution_count": 43, "id": "990bac81", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(zz, mu_basis, c='C4', alpha=0.8, lw=3, label='Gaussian Basis Function Regression')\n", "ax.plot(z_true, mu_true, c='k', alpha=0.8, lw=3, ls='--', label='Truth')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "995fdbeb", "metadata": {}, "source": [ "### Learning about cosmology\n", "\n", "Within our standard cosmological framework, we can approximate the luminosity distance of these supernovae using the following relation:\n", "\n", "$d_L\\approx \\frac{c}{H_0}z\\left(1+\\frac{1-q_0}{2}z\\right)$ ,\n", "\n", "where $q_0$ is the deceleration paremeter. This parameter is related to the scale factor $a(t)$ as\n", "\n", "$q_0=-\\left(\\frac{\\ddot{a}a}{\\dot{a}^2}\\right)_{t=t_0}=-\\left(\\frac{\\ddot{a}}{aH^2}\\right)_{t=t_0}$ .\n", "\n", "With this expression, the distance modulus becomes:\n", "\n", "$\\mu(z) \\approx 43.17 - 5\\log_{10}\\left(\\frac{H_0}{70~\\mathrm{km/s/Mpc}}\\right)+5\\log_{10}(z)+1.086(1-q_0)z$ .\n", "\n", "For more description of the above expressions, see chapter 7 (or 6) of [Introduction to cosmology, first (or second) edition, by Barbara Ryden](https://ui.adsabs.harvard.edu/abs/2016inco.book.....R/abstract)." ] }, { "cell_type": "code", "execution_count": 44, "id": "a597c5d4", "metadata": {}, "outputs": [], "source": [ "def dlum_linear(z, H0=70., q0=-0.55):\n", " c = 3e8*units.m/units.s\n", " if isinstance(H0,(int,float)):\n", " H0 = H0*units.km/units.s/units.Mpc\n", " d_hubble = (c/H0).to('Mpc')\n", " dL = d_hubble*z*(1+(1-q0)/2*z)\n", " return dL\n", "\n", "def mu_linear(z, H0=70., q0=-0.55):\n", " c = 3e8*units.m/units.s\n", " if isinstance(H0,(int,float)):\n", " H0 = H0*units.km/units.s/units.Mpc\n", " H0_70 = 70*units.km/units.s/units.Mpc\n", " mu = 43.17 - 5*np.log10((H0/H0_70).to('').value)+5*np.log10(z)+1.086*(1-q0)*z\n", " return mu" ] }, { "cell_type": "code", "execution_count": 45, "id": "322815b0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(zz, mu_poly, c='C3', alpha=0.8, lw=3, label='Best-fit')\n", "ax.plot(z_true, mu_true, c='k', alpha=0.8, lw=3, ls='--', label='Truth')\n", "ax.plot(z_true, mu_linear(z_true), c='k', alpha=0.8, lw=3, ls=':', label='Approximation')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "800e4fed", "metadata": {}, "source": [ "# Bayesian parameter inference\n", "This method is a powerful tool used to derived constraints on astrophysical and cosmological model by interpreting observations." ] }, { "cell_type": "markdown", "id": "a6872a24", "metadata": {}, "source": [ "To find a model for a dataset with errorbar, we can define the loss function using the posterior distribution defined by the [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) as,\n", "\n", "$p(\\theta|{x_i,y_i})\\propto p({x_i,y_i}|\\theta) p(\\theta)$ ,\n", "\n", "where $p({x_i,y_i}|\\theta)$ and $p(\\theta)$ are the data likelihood and the prior distribution, respectively." ] }, { "cell_type": "markdown", "id": "f2765a03", "metadata": {}, "source": [ "Based on the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem), the each supernova data point can be assumed to be well defined by Gaussian distribution and, therefore, the likelihood can be given as,\n", "\n", "$p({x_i,y_i}|\\theta) = \\frac{1}{\\sqrt{2\\pi\\sigma^2_i}} \\mathrm{exp}\\left(-\\frac{[y_i-f(x_i|\\theta)]^2}{2\\sigma^2_i}\\right)$ ,\n", "\n", "where $\\sigma_i$ is the standard deviation of the $i^\\mathrm{th}$ data point. If we assume no prior knowledge, then $p(\\theta)=1$. Instead of likelihood ($L$), it is more convenient to work with log-likelihood:\n", "\n", "$\\log(L) \\propto - \\sum^N_i \\left(\\frac{[y_i-f(x_i|\\theta)]^2}{2\\sigma^2_i}\\right)$, \n", "\n", "which should maximize for the best-fit. " ] }, { "cell_type": "markdown", "id": "cc99623d", "metadata": {}, "source": [ "### Simple example of Bayesian inference\n", "We consider a simple example of observation points scattered about a straight line given as $y(x,m,b) = mx+b$. $x$ is the vector containing the points where observations were taken." ] }, { "cell_type": "code", "execution_count": 46, "id": "66583940", "metadata": {}, "outputs": [], "source": [ "true_m = 2\n", "true_b = 1\n", "x_obs, y_obs, y_err = AstronomyCalc.line_data(true_m=true_m, true_b=true_b, sigma=2, error_sigma=0.5).T" ] }, { "cell_type": "code", "execution_count": 47, "id": "2153e268", "metadata": {}, "outputs": [], "source": [ "def model(param):\n", " m, b = param\n", " return m*x_obs+b" ] }, { "cell_type": "code", "execution_count": 48, "id": "4590d36f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "true_param = [true_m,true_b]\n", "plt.title('Observation')\n", "plt.errorbar(x_obs, y_obs, yerr=y_err, color='k', ls=' ', marker='o')\n", "plt.plot(x_obs, model(true_param), color='r', ls='--')\n", "plt.xlabel('X')\n", "plt.ylabel('Y')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2bf13880", "metadata": {}, "source": [ "As mentioned above, we assume a Gaussian likelihood for this analysis. We also define a flat prior for the parameters of the model. We restrict the explored parameter space to remain within minimum values vector `mins` and maximum values vector `maxs`. " ] }, { "cell_type": "code", "execution_count": 49, "id": "1e972560", "metadata": {}, "outputs": [], "source": [ "def log_likelihood(param):\n", " y_mod = model(param)\n", " # y_err = 0.5*y_obs\n", " logL = -np.sum((y_obs-y_mod)**2/2/y_err**2)\n", " return logL\n", "\n", "mins = np.array([-2,-3])\n", "maxs = np.array([6,5])\n", "def log_prior(param):\n", " m, b = param\n", " if mins[0]<=m<=maxs[0] and mins[1]<=b<=maxs[1]:\n", " return 0\n", " else:\n", " return -np.inf\n", "\n", "def log_probability(param):\n", " lp = log_prior(param)\n", " if np.isfinite(lp):\n", " return lp+log_likelihood(param)\n", " return -np.inf" ] }, { "cell_type": "code", "execution_count": 50, "id": "f3203add", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "logL([2, 1]) = -26.545129387851276\n", "logL([0, 1]) = -953.4748879076326\n", "logL([10, 1]) = -inf\n" ] } ], "source": [ "print(f'logL({true_param}) =', log_probability(true_param))\n", "param = [0,1]\n", "print(f'logL({param}) =', log_probability(param))\n", "param = [10,1]\n", "print(f'logL({param}) =', log_probability(param))" ] }, { "cell_type": "markdown", "id": "07872198", "metadata": {}, "source": [ "### Importance Sampling\n", "\n", "[Importance Sampling](https://en.wikipedia.org/wiki/Importance_sampling) is a Monte Carlo method used to evaluate properties of an unknown distribution by using samples generated from a different, known distribution called the proposal distribution. This technique allows us to approximate the target distribution, which in many cases is the posterior distribution of interest, using samples drawn from the proposal distribution.\n", "\n", "**Importance Sampling Algorithm Steps:**\n", "\n", "We provide the steps along with application to our example case using a implementation of this algorithm in AstronomyCalc." ] }, { "cell_type": "markdown", "id": "7f023e2d", "metadata": {}, "source": [ "1. **Define the Target Distribution:**\n", " - Let \\( p(x) \\) be the target distribution you wish to sample from. This is often the posterior distribution in a Bayesian context." ] }, { "cell_type": "code", "execution_count": 51, "id": "ffc26a32", "metadata": {}, "outputs": [], "source": [ "def target_distribution(param):\n", " if np.array(param).ndim==1: return np.exp(log_probability(param))\n", " else: return np.array([np.exp(log_probability(par)) for par in param])" ] }, { "cell_type": "markdown", "id": "dc9dc79a", "metadata": {}, "source": [ "2. **Choose a Proposal Distribution:**\n", " - Select a proposal distribution $q(x)$ from which it is easier to draw samples. The proposal distribution should be chosen so that it covers the regions where $p(x)$ has significant mass.\n", " - A commonly used proposal distribution is a multivariate Gaussian, which used in this AstronomyCalc implementation. " ] }, { "cell_type": "code", "execution_count": 52, "id": "51cf744c", "metadata": {}, "outputs": [], "source": [ "# Set up the proposal distribution mean and covariance of the Gaussian proposal distribution.\n", "proposal_mean = [2.5, 1.5]\n", "proposal_cov = [[2.0, 1.5], [1.5, 2.0]]" ] }, { "cell_type": "code", "execution_count": 53, "id": "61d4452a", "metadata": {}, "outputs": [], "source": [ "# Initialize the Importance Sampling with default Gaussian proposal\n", "is_sampler = AstronomyCalc.ImportanceSampling(target_distribution, proposal_mean=proposal_mean, proposal_cov=proposal_cov)" ] }, { "cell_type": "markdown", "id": "cd8ad472", "metadata": {}, "source": [ "3. **Generate Samples:**\n", " - Draw $N$ independent samples \\( $x_1, x_2, \\ldots, x_N$ \\) from the proposal distribution $q(x)$.\n", "\n", "4. **Compute Importance Weights:**\n", " - For each sample $x_i$, compute the importance weight:\n", "\n", " $w_i = \\frac{p(x_i)}{q(x_i)}$.\n", "\n", " These weights represent how much each sample should be \"counted\" when approximating the target distribution.\n", " - Normalize the importance weights to sum to 1:\n", "\n", " $\\tilde{w}_i = \\frac{w_i}{\\sum_{j=1}^N w_j}$ ." ] }, { "cell_type": "code", "execution_count": 54, "id": "a8aef317", "metadata": {}, "outputs": [], "source": [ "# Draw samples and compute expectation\n", "samples, weights = is_sampler.sample(n_samples=1000)" ] }, { "cell_type": "markdown", "id": "7162f51a", "metadata": {}, "source": [ "6. **Post-Processing**:\n", " - From sampler, we got the samples \\($x_1$, $x_2$, $\\ldots$, $x_N$\\) and corresponding weights \\($w_1$, $w_2$, $\\ldots$, $w_N$\\) that we can be used to approximate the posterior distribution. " ] }, { "cell_type": "code", "execution_count": 55, "id": "268ac840", "metadata": {}, "outputs": [], "source": [ "labels = ['$m$', '$b$']" ] }, { "cell_type": "code", "execution_count": 56, "id": "05e9f0f5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(samples[:, 0], samples[:, 1], c=weights, cmap='viridis', alpha=0.2)\n", "plt.scatter(true_m, true_b, marker='X', color='red')\n", "plt.xlabel('m')\n", "plt.ylabel('b')\n", "plt.colorbar(label='Importance Weights')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 57, "id": "90f1b98c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1000, 2)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "AstronomyCalc.plot_posterior_corner(samples, labels, truths=true_param, weights=weights)" ] }, { "cell_type": "markdown", "id": "433e3faf", "metadata": {}, "source": [ "**Notes on Importance Sampling**\n", "\n", "While Importance Sampling can effectively approximate the posterior distribution in simpler cases, it becomes inefficient for large and high-dimensional parameter spaces. To address these limitations, several improvements have been developed, such as [Sequential Monte Carlo](https://en.wikipedia.org/wiki/Particle_filter).\n", "\n", "In this tutorial, we will also explore another method that converges more effectively to the target distribution." ] }, { "cell_type": "markdown", "id": "c13dccbe", "metadata": {}, "source": [ "### Metropolis–Hastings Algorithm\n", "\n", "The [Metropolis–Hastings algorithm](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) is a widely used Markov chain Monte Carlo (MCMC) method for generating a sequence of random samples from a probability distribution, especially when direct sampling is challenging or impossible. This method is particularly valuable in Bayesian statistics, where we often need to sample from complex posterior distributions that cannot be sampled directly.\n", "\n", "The key idea behind the Metropolis–Hastings algorithm is to construct a Markov chain whose equilibrium distribution is the target distribution. By running the chain for a sufficient number of iterations, the samples generated will approximate the desired distribution, allowing us to estimate properties such as means, variances, and credible intervals.\n", "\n", "**Metropolis-Hastings Algorithm Steps:**\n", "\n", "We provide the steps along with application to our example case using a implementation of this algorithm in AstronomyCalc." ] }, { "cell_type": "markdown", "id": "89c5c86f", "metadata": {}, "source": [ "1. **Initialize the Chain**:\n", " - Choose an initial point \\($x_0$\\) from the state space.\n", " - Set the initial step to \\($n = 0$\\)." ] }, { "cell_type": "code", "execution_count": 58, "id": "32a0ce0a", "metadata": {}, "outputs": [], "source": [ "nwalkers = 8 #Independent walkers that will sample the distribution.\n", "ndim = 2 #Dimension of the parameter space\n", "n_samples = 1000 #Total number of samples we want to obtain from each walker\n", "\n", "# Setup a sampler\n", "mh_sampler = AstronomyCalc.MetropolisHastings(nwalkers=nwalkers, ndim=ndim, log_probability=log_probability, \n", " proposal_cov=np.eye(ndim), n_jobs=2)" ] }, { "cell_type": "code", "execution_count": 59, "id": "b07f992b", "metadata": {}, "outputs": [], "source": [ "# We randomly initialise the walkers are different locations \n", "# inside the mininum and maximun ranges of the parameter space\n", "initial_value = np.random.uniform(size=(nwalkers, ndim))*(maxs-mins)+mins \n", "mh_sampler.initialise(initial_value)" ] }, { "cell_type": "markdown", "id": "ef303571", "metadata": {}, "source": [ "2. **Proposal Step**:\n", " - Propose a new candidate point \\($x^*$\\) from a proposal distribution $q(x^* | x_n)$, which suggests a new state based on the current state \\($x_n$\\).\n", " - A commonly used proposal distribution is a multivariate Gaussian. We denote a new sample drawn from this distribution as: $x^* \\mid x_n \\sim \\mathcal{N}(x_n, \\sigma^2)$, where $\\sigma^2$ is the covariance matrix that controls the extent to which we explore from any given position in the parameter space. If $\\sigma^2$ is too small, the chain will exhibit slow mixing. This occurs because the acceptance rate might be high, but the chain's successive samples will move very slowly through the space, leading to slow convergence to the target distribution $p(x)$. Conversely, if $\\sigma^2$ is too large, the acceptance rate will be very low. This happens because the proposed samples are likely to fall in regions with much lower probability density, resulting in a very small acceptance probability $\\alpha$, and hence, slow convergence of the chain.\n", " - For a Gaussian proposal, the proposal distribution is symmetric, meaning $q(x_n \\mid x^*) = q(x^* \\mid x_n)$. Therefore, the acceptance probability simplifies to: $\\alpha = \\min\\left(1, \\frac{p(x^*)}{p(x_n)}\\right)$." ] }, { "cell_type": "code", "execution_count": 60, "id": "666845ba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Drawing new samples from the initial value.\n", "Walker Number 0: [-0.90719277 2.21311808] -> [-1.13579269 1.21876871]\n", "Walker Number 1: [ 3.90877967 -0.47498125] -> [ 1.34644601 -0.66600901]\n", "Walker Number 2: [3.15866083 0.16104726] -> [5.57127625 0.94565155]\n", "Walker Number 3: [ 3.70565507 -1.4062778 ] -> [ 3.68639469 -1.66916863]\n", "Walker Number 4: [ 5.12172002 -0.70072323] -> [ 5.14418591 -0.15360411]\n", "Walker Number 5: [ 0.9422879 -2.53526438] -> [-0.23852491 -1.42094269]\n", "Walker Number 6: [-1.1079023 1.12689522] -> [-0.39252099 1.84508095]\n", "Walker Number 7: [0.14074141 3.68384181] -> [0.57921715 3.70345846]\n" ] } ], "source": [ "#We assume the covariance of the Gaussian proposal is a diagonal matrix.\n", "proposal_cov = np.eye(ndim) \n", "\n", "print('Drawing new samples from the initial value.')\n", "new_samples = []\n", "for i in range(nwalkers):\n", " new_sample, q21, q12 = mh_sampler.draw_from_proposal(initial_value[i], proposal_cov)\n", " print(f'Walker Number {i}: {initial_value[i]} ->', new_sample)\n", " new_samples.append(new_sample)\n", "new_samples = np.array(new_samples)" ] }, { "cell_type": "code", "execution_count": 61, "id": "f60468a1", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(true_param[0], true_param[1], color='k', marker='X')\n", "for i in range(nwalkers):\n", " plt.scatter(initial_value[i,0], initial_value[i,1], color=f'C{i}', label='$x_n$' if i==0 else None)\n", " plt.annotate('', xy=(new_samples[i,0], new_samples[i,1]), xytext=(initial_value[i,0], initial_value[i,1]),\n", " arrowprops=dict(facecolor='red', edgecolor='grey', arrowstyle='->', lw=1))\n", " plt.scatter(new_samples[i,0], new_samples[i,1], color=f'C{i}', label='$x_{n+1}$' if i==0 else None)\n", "plt.axis([mins[0],maxs[0],mins[1],maxs[1]])\n", "plt.legend()\n", "plt.xlabel('$m$')\n", "plt.ylabel('$b$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fb9d2af4", "metadata": {}, "source": [ "3. **Acceptance Probability**:\n", " - Calculate the acceptance probability \\( $\\alpha$ \\) for moving from the current state \\($x_n$\\) to the proposed state \\($x^*$\\):\n", " \n", " $\\alpha = \\min\\left(1, \\frac{p(x^*) \\cdot q(x_n | x^*)}{p(x_n) \\cdot q(x^* | x_n)}\\right)$\n", " \n", " - Here, $p(x)$ is the target distribution we want to sample from, and $q(x'|x)$ is the proposal distribution.\n" ] }, { "cell_type": "code", "execution_count": 62, "id": "b510f646", "metadata": {}, "outputs": [], "source": [ "p_acc = np.array([mh_sampler.acceptance_probability(initial_value[i], new_samples[i], q21, q12) for i in range(nwalkers)])" ] }, { "cell_type": "markdown", "id": "009781fd", "metadata": {}, "source": [ "4. **Accept or Reject the Proposal**:\n", " - Generate a random number $u$ from a uniform distribution $U(0, 1)$.\n", " - If $u \\leq \\alpha$, accept the proposed state and set $x_{n+1} = x^*$.\n", " - If $u > \\alpha$, reject the proposed state and set $x_{n+1} = x_n$." ] }, { "cell_type": "code", "execution_count": 63, "id": "61e3e95d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Comparing u and a:\n", "Walker Number 0: 0.12555 > 0.00000\n", "Walker Number 1: 0.01695 <= 1.00000\n", "Walker Number 2: 0.77016 > 0.00000\n", "Walker Number 3: 0.80716 <= 1.00000\n", "Walker Number 4: 0.12021 > 0.00000\n", "Walker Number 5: 0.26558 > 0.00000\n", "Walker Number 6: 0.01755 <= 1.00000\n", "Walker Number 7: 0.29331 <= 1.00000\n" ] } ], "source": [ "u_acc = np.array([np.random.uniform(0,1) for i in range(nwalkers)])\n", "print('Comparing u and a:')\n", "accept_array = []\n", "for i in range(nwalkers):\n", " accept = (u_acc[i]<=p_acc[i])\n", " if accept: print(f'Walker Number {i}: {u_acc[i]:.5f} <= {p_acc[i]:.5f}')\n", " else: print(f'Walker Number {i}: {u_acc[i]:.5f} > {p_acc[i]:.5f}')\n", " accept_array.append(accept)" ] }, { "cell_type": "code", "execution_count": 64, "id": "73ae0288", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(true_param[0], true_param[1], color='k', marker='X')\n", "for i in range(nwalkers):\n", " plt.scatter(initial_value[i,0], initial_value[i,1], color=f'C{i}', label='$x_n$' if i==0 else None)\n", " plt.annotate('', xy=(new_samples[i,0], new_samples[i,1]), xytext=(initial_value[i,0], initial_value[i,1]),\n", " arrowprops=dict(facecolor='red', edgecolor='grey', arrowstyle='->', lw=1))\n", " plt.scatter(new_samples[i,0], new_samples[i,1], color=f'C{i}', label='$x_{n+1}$' if i==0 else None)\n", "plt.scatter(new_samples[accept_array,0], new_samples[accept_array,1], \n", " edgecolor='green', facecolor='none', s=100, linewidth=1.5, label='Accepted')\n", "plt.axis([mins[0],maxs[0],mins[1],maxs[1]])\n", "plt.legend()\n", "plt.xlabel('$m$')\n", "plt.ylabel('$b$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1235553c", "metadata": {}, "source": [ "5. **Iterate**:\n", " - Repeat steps 2 to 4 for a large number of iterations to allow the chain to converge to the target distribution.\n" ] }, { "cell_type": "code", "execution_count": 65, "id": "8db553b2", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████████████████████████████████| 1000/1000 [00:01<00:00, 788.28it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Samples shape: (8, 1000, 2)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "samples = mh_sampler.run_sampler(n_samples=n_samples, initial_value=initial_value)\n", "print(\"Samples shape:\", samples.shape)" ] }, { "cell_type": "markdown", "id": "a575ad75", "metadata": {}, "source": [ "6. **Post-Processing**:\n", " - After running the chain, the samples \\($x_1$, $x_2$, $\\ldots$, $x_N$\\) can be used to approximate the target distribution. Typically, the initial portion of the chain (referred to as the \"burn-in\" period) is discarded to reduce the impact of the initial state." ] }, { "cell_type": "code", "execution_count": 66, "id": "b3e2d8ff", "metadata": {}, "outputs": [ { "data": { "image/png": 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dHm7VUL2BhTXboGAQbN8A2zcwICubc4uqUIFA3H1dw4aR/8D96C5XbxZZCCFEPyVBOsEs3e44ZgZrAfAEQnjT06lsqKPmaDn+bbva3TewZw+Na9eSdNZZvVJWIYQQ/ZsE6QSLZNJWuEf30KPVjD9jJq9sXklI2csyv/51kmfNitmv7P77aVy/nsD+/fimTLEXahqaQ/5EQgjxSSVt0glmOZoAUOE5vHUFDlR4GZRnnsLrB07jiLuApDOnR/95Tj0VgJJf/ortEyfZ/yZN5ujf/94n70MIIUTfkyCdYJYjSKOjFpTdo1tTCt1S0fUbJn6LQFDj7b9uitkvefa54HS2OphF7fvvH/cyCyGE6J+kLjXBDHR2DVzDuCq72ltXCk01B2lUCDRnm/2SZ89m7KqPo53K6pev4PAtt2DVN/RKuYUQQvQ/EqQTTNM0/EYDhNufdcvOpHXDwDJNoP2HbegeD3g8ADgGDgTAqqs77mUWQgjRP0mQTjADDb+jOfvVlUKVbMXQ7YnHlDLRIis/+ov9/4JZMGhyzHH05CQArPr6Xii1EEKI/qhXg7Tf76e4uJiBAweSlJTUmy/da3RNx+9oRGGPdd496nMcMocQDD4DQKD2edxp38SpBeC9n9o7+bLgh7tAb+4iYITPj2TSQgjxydUrHceqqqr43Oc+R3JyMiNHjiQ1NZVRo0bx+c9/nt///vcsWrSI6urq3ijKcWdoOkd9RdGOYwFXBvXOnOYNVD2oJpJ9fpj0edCd0FAOq/8e89xpPTnZ3jwQaHfyEyGEECe3Xsmkf/jDH/Kf//wHTdPIzc2lpqaGvXv3snfvXl566aXodiNGjGDatGk8++yzvVGs40LXdCqSivC6oKHRyeg9r5AZVCwbYrTYKohjQB5c+RiUboWSTfDWD8GdApO/YB+nRU3Dnosujsmy49HcbnJ+/COSZ88+Hm9LCCFEH+iVTPqtt97C6/WycuVKDh8+TG1tLdu3b+eZZ57htttuY/bs2aSmprJnzx6ef/75bh37nnvuYdq0aaSkpJCdnc3ll1/Ojh07jtM76ZxhhKf0tOysOKWumNSK/THbKBXEDIYfXznnruYVlQeiP2oOB66RIwEIFhURPHSow3+BPXuoevmV4/a+hBBC9L5eyaTr6uqYN28eU6dOjS4bM2YMY8aM4dprr40u27NnD2vWrOnWsZcsWcL8+fOZNm0aoVCIO++8k3nz5rF169Y+affW3anQVI7pyQR/I9nf/QJZuaPQnnwSFRmKpYL4G0OUlVZB2jSY9H1Y9wxU+nEcrSVjQAoABS88j3/XLjiyBRxujvg97N62CVoO6QIChw7RuHEjzspidj/1eJsy5Y05hTFnnXO837oQfadyPyz8P/C304dDd8CM78Bw+R4Eg0F27NhBoJNmNKfTyZgxY3C73b1UMhGPplSrK/5xMGPGDHJzc3nlleOf6ZWVlZGdnc2SJUs499xzu7RPTU0NaWlpVFdXk5qaekyvf8VrV7C7ajefW5RPUpOD12cWU5EWIKXewVVL8gFwJl+N4Rza7jEODDnEzEvn8NnT8qGuDP4wCoB/Nd5A6f693S+UpnPOF/8fwyflkzO8+f0V797BG/ffS6Axdix27sgxXHnHL9F1o/WRRD9lWiZBK9ju+l3LPkBDY8J5c3uxVL1o0d2w9Hcdb1NwLtzwhv1zsBGKN7S54e2JgGnR+iiGBo5IE5XDDYNO67TJqqcaa2soO7A/Zln28BF4wv1aWlu6dCmLFi3q0rFnzZrFnDlzjrWIPfLL17ew5kBl3HW6rvHNWSO4dNIgAJRpUrdkCWZlVafH1VOSSTnvPLROHmRU3RjkwNG2o2sMXWN8Xlrnb6ATXY07vZJJf+UrX+GOO+6grq6O5HY+OIkS6YCWmZnZ7jZ+vx+/3x/9vaamJmGvf3be2eQsqSSpyT61lm5/fWuTQpSl+RlY7abSc4g0ldtmX13pGMqB+6jOLc+tt4N0dWF0fe3RMgAmzrkQb3JKdHngwAGOLlpG8aCZKE2LOabZtA5UiI/f2MzW9wu5ccpj9grDya6qCdSWl7Upx4GN66gpKyM9p20ZT3Tl5eXs2LEDpRRai3PVk5+TkpI45ZRT0CMX3/pyWPL/oKn9TpDVDjd/cQWp9qZAq79Vtjeb753xPVxG956Cdqj2ENf+91qq/FVx1xumxpfetW8KR0490/7s1B4Bwwm+9r8nPVVZWcnBgwfjrisoKGhzQQqaFot3lFHT2P5NRmcmFx5mFMCYi+GUy2JXVuyFD/4INUXNy567DvYs7PHrtdSlv9Z5d8B5twNgWRZvvvkmZWWx372CggI+9alPdeu1lVI8+9MfUHWkGMvpxnR7o+smfmpezGc2YldRif2D5iDk9KG5fQwfkITX1XxTXllZSVlZGVVVVd0qT6KU1jTx5Ef7GaEVcYPxLn8NfYZiBsRs89jSPdEgXbtgAYdv/T6abwCaKyXeIaNUqJGcH1WR8flr2t3GHzKZe98Symr9bdZlJrlY+/MLevCueqZXgvQ3v/lNnnnmGb7yla/w7LPP4jpOj2K0LItbb72VmTNnMmHChHa3u+eee/jVr351XMrw3VNu4qHDSwBwuN289qV3cft8ALy+71cUVW/l8s9PZ9SMmc07rXkK3r2DjwZcw87NX8AX8qCnHmZz2Rb0yp3gcjI0EKIxPBzrbw1jCIaab3ZGVge5ODiEMt+5WIAZjhmWDmZoN0aoEmU10NA4gMDOD3DpTRwNDmVnif0FrsqaRm3GJAAG7X0Wh9lIoKnxuJyfrqh5+20qn3mW9it5dHCmkzxzJqmXXdbONvH95+WXKC4rOfZChl0173LGFoy2f1n3H1jxXofbv5/sY0Va/LvwbcAM6xSm5ZwRs9zwGWhGkKpX38Rs8GOkZZB25ZUY4bH0G8o2tBugUeAINl+oAw31eP2l8JepYLjh+5shKQuAhmADhbXNN4V5yXmktHPBW7t2bdxAbFkWGzdubO/tk5+fzze+8Y2YZf9Zc4jbX97Uzh5d8zvHIUY5oCrrdBpyPsXu3bubPz/BJGA6VLlhyRI7e97XBExnd+A8Kvz2hd6tnJym8jCVzvamUJvsuCs0LEYnv0aBbxEOXSPDaCTVrGTN6o/42yG7Kc/RVMWAQ2vb7FtYWMhLhV5UF2/SlFIYjTWMOFKMpevUjxgfk62v2tVxrZt332ZUUyN/H3ElV40axi1zRkfXbd+0nSXvLqG6vpriuuIulSfVnUqSM7aJsbL4MK/fdy/uBhc6Xa+ZM5Xi9sYg6dShk8at+jJCzlRAofx+zJAJRRrPfdXuw6SCAdLP/hwTs7sWPBu3byOjg/X7yuspq/Vj6Bq5qZ6YdWnetjNGHk+9Ut0NdoY7ffp0UlJS+PnPf87FF1+c8GB900038fbbb7Ns2TIGDx7c7nbxMukhQ4YkpLq7vqqSv37rS3Z5Hn8GX2rzBfmV//cr9q5dxcChw0nJGti8U00RlGykQhtATVMBCsWR5P0A1CbDrqEaeU0mk9bYX8BXBn8bpTV/4IdVF3N1aTHFg2awzhXif77mjOTKolfJ9xejuSdjGDnMSP4XaxmCajiXxsatKLMIp+8iDLf9gA9/9d9QVg1XndHE8CFZ8JkHITk77nsNNDYQaGwRzDWNmvJG9m86GqcaUWvzo9ZyWfNCKp97AbO6Kv4JVjBq1LmkpOTEX98BE4snPPZc6CPMHIzwa7YsqWq1pOVPLber0uqp1OvxKhc+FdtmN9TKYkpoRLfL1x6lLA4V/4Gj+8qjy5Jnn4PvjNNxebxsHVTBfWseY1buTH429UeAnaSHNlbjX1SGpmBf7SY+Ln+LghnfxhNqgqJwkBhxPso3gLryAHuLD2KFZ8oDcCqd7KAXLCumPKYWojB7U8yfNJ7MYHrzLxpUOKpAQaoVG/gtZZ9bLbyhanFcC2jQocnjotEzgJDDSzxnl7/EJG03JQVX8NG+po4L1oHzA+MZaeWyoi7EkVDPLo1JAzw8EqrGtBQX6Kv5geM/rDLHclfoK2hAtlHJFO8uGk0PjQ3D0IHUpN3oukl51WmYpq/T19BdlRje/Qw4soPkmlL8yZkEhoxAKbBME8OMrZUY6MiOZtXVoSr8gTp8h3ZhKIuiYWcQdMe+phOTFCNIUGnUWm5q3EdZM/hd0OKfk/zqMYwtnY7X4Yt+r7O8A8itrWBgeT2nps/o/omMQ6Eo02oIaO3P3AjgD9Uz2DcInzc8lBU42liOr9HArfk4WLGQH57ffEMdNBUhs/lzbikwLQtD10lyGzh1Jz+e9mMuHXFpQt4HdL26u1eC9P79+7n44ovZuXNntJrR4/EwefJkpk2bxtSpU5k2bRrjxo3r8WvcfPPNvPbaayxdupSCgoJu7ZvINuma8jIen38juuHg+8++GrNu4T8eYf27/+3+QTUfmp6CMo+A5saTPr/dTbNm5pA5JSv6+4GX/orauRefo/335c2bQzIaZp2fitr1oGpJTTqV01JWkH92DvpEO1s1gz6qPvZhNZn46+s5sm933Gz3UP0O9tSu7/777KIrh92KU3fTZNZ3kG23td5VyBZXEQ6lc03DWdGLiYaG4dJBg1oV2z5v6AaG1rLCSRGyFCVUscyxrd3X+pw1AwOdEqoo0irCe4KlTCylcKLs2eiAkNKjNweK5tuBLCuZieZwDN3Bx2Vvsa8ufrbpykpHN7/aZvlZSQY5TvvGzlQhXtr/R1zJ16A727+B7YqQo47KrLVoloGvvrlvRboBeU4dDY2hVhbpKjaretX1MeV67TG9dnd4/NlEB7BYJrTOjZUGGOhmAE0rpD45ienBUUwyh9FQuIKmI5uxNChK9xA0utCerBvUezq/eaxOsjgyQJHUCPll9s32/kEmASekVUwi4K4g6Krq0nu0zApQQTDcWC4HTn8a6ZWxsxcawGXpzdnfuoYQBwMKf81TKLMcp+9CNEd+zD4Bdy21Wfswgh4yyiag6T7envBXStLjZ+eXr7mNjMa2zWPBhoWcnT6aPN9IGk0z+rhe3aGTlN5+hzR/0KSs1s9gvblJoDE5m311B/jIc6Dd/WLed2MVmrMMDQhaQUobyzgveBZnJ19CUc0mnnS/2KXjaAp8foMUPYmhKUNx+Xx88Rf/r0v7dqRftUl///vfZ8eOHXi9XiZMmEBtbS27du1ixYoVrFixInqHl5yczBlnnMH73Xjyk1KK7373u7zyyissXry42wE60ez5uUF3tK3aOecLN5A35hTMYKu2t7Lt8NGfAdjVOJPykP0e6hq2YFn1oBpQph08LEcK1Z5SWqYxDlORVa0wzHoeavotdWsqousmJA/mt4N/1Emhw//3Ab5BLVZMYMvqDzmw4/MADGz8NPkNX4quzfEMi3u4LHfecQvSumbg1O0v91uHHidotW0zak9jXgG4BmD563nj4INxt/nflFIqBjahgEa97Q2AK6hzwcfZJDc6MNxJKD32K2QNGgOazsuFD0MogDl8it2zOKKT7LOl/RzFrNaZ4h6B2/KRX1GDptmVFO6UELXJLsr8yYQa04hXKeXRm1/M0By4dA/lAzZQ4GnksFHJTscRPLiYGMxH16DJVcfEnAmcOuBUXtv9GkN3VjOsDJxDhtCUlUMk0TiiqvkYSNFdzE5trjRMCXrxhTw0Gn6aXEEqqcO0glRV7cMZgvGaTrUzmTbBMsznB8OCokxo9GgMDeaSqpLY5Q9SbBzFNLr6t9bwNObgaYpfA9RaXtEy6pOL2D1mdDRD8w05C9+Qs6ilkaCjGBOrw2MMtFIosGID9H69jEP60TbbKr0WqCHfOYhzs+0arFp9DcVU0ZS1Hb/VjcmLnC5atooPG5TDKZOyMF06Ia/9ufP6dVh5JLrNyAIPuQMdbF6ZQUVpOcGGd9sc1vT4IOtULGporPsbeupcrq+6how4fzqlYLupEXBVMaj4I4wWHRiLvVXUuEaCXkHD6AwaPC52rCzBgc5ln5/c9mBhq/dVcP//Cvm36zf2awDfyxnKrIp88AxGmY1Uee0ak9xK8IY/GkdTIeB04FUpmN50tKAP376teMwQKSShfH5IhuzkscwPfbfDU1sfqmF56WuEVOT9mBwt30fQ0bsPj+yVIL1kyRIyMjJYvXp1NIg2NDSwbt061qxZw+rVq1m9ejU7d+5k6dKl3Tr2/PnzefbZZ3nttddISUmhpMRub0xLS8PrjV81djxZ4VnDDEfbU+v2+TjlnPPa7hSYCf73ObRvO5NCyxmUtg6fyyBowsEqN6+btSxMsqujjmQW0uSOHaY2oEbxyEMmQQMq5zloeT1JdtoX0UatiXK9juYooQg4mqLPvY5Iq3fhMMFhZJDicNOkxnJHtp2Z31QyhPwGWJayjsN1Oxl6xMvhgY3sybd7QOro/KjoKzh0F++da1GUbLdvfmGJyZUfta5Iji+yfmc+3HW9fQ61FisHBNP43D5Qlsmn1m/jx181KBoQG/ncITdD64eiKwNdWTSGDuHX6zmlcRipFlSoXRTn271Gh1fNwmOm0GhtxBmoZ+aWYaQ5nAxUJtUOjVDrjnjBEMH6cBV/oG21at3AIMrpxm150EyNesMBSuE6WmK/gegJsH8IGdk4QkcwjXSCyflgOVGWB91bjKabBA27Y5fXdzoVWYMIqiBTN/+dldYIFmSfypn+1fhNB8p9lKMZWzDQMVDooSAvG86WZw9r9Kk4NINCjoAFIwPJaBhUUmUXpwlWHFjPigPrATia62BdLkAxhJrbJS0UaJBm+sgJtm3Zu99fy4fhPg26dz/eU15EmR7M+pFt/+At/GjNYQp2lBNpIEqdeD2+IWeTUvg/qg580OG+PaYUq745lrrgUDgCgfADcIpdFbibTFY7DnDQ0YXZEBV8uqoer+HFSkvBwmKR2kTbft/NPE4n9S77PCX7XWAQDdBOr5PR54xud9/ntz9PdaCaq7dMZHKqPYrFQCenKB2jyC6vb0oOzrwkat5diqK59sSz7C20LS8xND2ZuvwsrDidy7SgfR6U00X9mNOAcraHyqHtPYct3P+wOrN1x+AMlnEQOAiFsdv+85/r231/ABe54J98Lvr7mYchEE44/ZWNfOjOwuc2uGb/Fmbssg/+1KzT2Dg4nTPr/Xh0R7T8IctC08BvONlvdv2zFEw7HTNSWxc+T5rVjTvtBOiV6u709HQuuOACXnyx4+qFuro61q1bx6xZs7p87Hi9FwGeeOIJvvKVr3TpGIms7i47uJ+nfnQz3tQ0vvP4M93a96IHlrK9pJZ/fW06s0a3aLPe8Q7lS+8lZIUg1GT3Vk0bDF+z21Ssymqq514OgJ7fnAk3OZ2UjjkbI2UcDLDQa/8C3gyY9jVY+gcwXDA3PJnK+mfgyFY2NUymvrIet2cyk1PysVBsd5ZjqBD5ZhrJysc2xy7Kag/iqfNTl+qjIc2+GdLQubBhKg5d478pC2nwVGHoGpO2BMgvDHJ4qJOiwV3rdFGXYjBQyyBVa3Gj5a8hJZjKedWXY/qraHj7x7w3N0RZVuy+OtPRib3ATVv5MZsnTqDR5+P8hYvIDves3TT+G5QNPI1Q0zpCjV2vwTHcZ2C4J6Bh8amBH+Iy7Lvt1xhAreGEgAUocBkQtDAO2DcyKe6JGLqPYN1/UdZRNEc+KnQYwzUeZ9KF0eNXDFiD6axnQt0kznKEn4gW/qpqSqE0hdIiTYQar7tX92pVMsCY+lSGN8ZelBvNOjZWLMbqJPPsivHp5zAhY2bnGybARuMAHzt3M8rM5angML702VPw//s3FHnTsbzJlHiKmTjc7ly5v2Y/h+sOR/fNb8gnKRR/ToYmvYk9qXvaLA/pIfan7Cek28Hw52s/R1byWPapfTToTZxqDscVt6OV4mNjNauM1Zy+RzHOM5cpWfNQoUZUUzXoOrqv4xoEpazotMUx940tWFi84VnPUcPurOpSRkzfCwX4Q6HoZxJAs/xoVpA6p5cmd4iMpgYUTpKc6WjomA2lKCtEkzcHdQzzaOmWm9SqU9BV+zmmQtHoO0x9ag+GrHbCCGn8/Dd3db5hJ/pVdffpp59OQ0Pnz0VOTk7uVoAGutUm2RusUDiTNuL3ZFRKESyqR/nNNutGNikO0WJ8ZcTYi8gae5H9c00R3HcKVB6Cza+DpqFMi/qMJEKV9ViHmzOelbPOoShTAdugBuACaACWbLB/DgHvLA5vnW//8wJeaKKGpbQYmqbBEUdV8++peTSl2h+g1BZv5SP3dgBSmvJIacoDoGiQ/Q/o6EmdMZIrIaQMLvbPwhHnYqUF7YA073/hoW6axobTJlOflETZwIEE3JBZfpSKLHvYxqozp0f3TQo1gtP+3Iw8/AZus5qQ7qDaGIZFCMyOA4yGQVqjRnl2MqbDQ+2CnaTW2j2dB06bSu3IkeBq/hsOKT7E2auXo4Als+ZiGW6SG2updYPhP0zIgKyjOxi6d190n3VnDKVyQDJV5mY2uDtuwinXa6MBem5gIllW8xferC3haMlyMkddhqPVc8x37HmWwXmfIsmby679L3E4cIhGd+wlQQF+Z2xnLnuFxQEzRNzWwThXFZdSuLr5Xa3w78FUZ7bqE3B8uMKFrtAacIcOECy0qG4KolLtwLQlcysf+j+yN3aH/wFnZJ9BQ2kDvn3NHaZaGr9zH5fviPQlaD8DqxlbzRhvHmPIo7P7m4JQAb595TSEanCHJ2wKFq7Ev8GeTllzp+A65bNojuZeybrXQ8Y1l1Lz/iE0Swet+fMZr1Q6cHlwOrRomYv3/mLYTfx2+VsODgnX3te99wNUoJbdI67gcN7Mdl65a3RnCMJNE5bhim1SCksODcFblYXSLIKmhWU11+aVeWDGhcMBOFxeQ8Vrb5KlBZk6LB2UhREagMMVv+ZH6+pFLEF6JUjfdNNNfPWrX+XIkSPk5HS/V+6JpLlNOv6prf+4hKpXdsdddwc6XyQJh9HBhzc5F+XwUdv0aUKvNQfkzNmfwQzG7tfosbO5bCsVb6gc3QyPEx002Z7IAcCVYn9XAg2gTI46cqhv8uNweHAZybi1Fo2dysRUJg2heiyCWFYIt2cgDmdzb123BZ42V/TuK9GrCGomL7nWoZQdpF3KR1aoAIXG4foypvkGoIc7olRmZbJz7Njo/pppMW7VJkrzc9k8Yixl3nSGDfBxzqTRpH77NuY98AFpXicb7prHlFavbVZVUfbgg5i1HT2BrJHF9X6qLA/GOXNJddiZ+WxgaD0cDA3CQkcDknyj2DZ3LkrpWKZ9dR+Q4aO2IUAofP8xcHAGI8c3154ccOpUAofSLA7RNhOLxwgG2bvtafaFg6GRmobKSaMhp5G6/Y9S6x1J6lmf5lp/MsHiJmYVpNGoZaDwMOf223HmeKD+KPxtLrsNiyfSUqn2agS7OOLEqxST/H4yWt3keJRi7inX4uvm+G8AZf4PZXUx6xowkhdCs/ntW1u7PHxqTtn7jGjYRyA5FfKHUaHXMCW5hoNbSyCv+eZo8pDJKFfzUTM9mdw+/fbokKNATQ27L7wIs8WcC5pSGJZFV4KRp+gALWqkCZl+du57KXYjTePUkV8E4Myks9l94HUGpts1TekT3STllYInFVwO4LmYXZ3JoG95lOQsL5aKHVKkaB6MoWmxpT1Y7ebd3bHjk5OdmZw18LJo35DOaIBL30b2ZbV84NH4c8rruHiNjBY390rTaXKmR0etmCpIg1nN4GCIz4SHnurAmU1+sh1BjBZ/Cwpmww2vd1iGZ1ce5M5XYjtevrDwUPMvw89l6rAMvnPT2bDobvyL/0V54P9QtK0h0Y3OE85E6pUgfeGFF3LllVdy9dVX8/rrr5OR0dEItRObGW6T1tvJpENl4bY6nwM9ydlm3TAMygMd3ErrOoGzH6bmvay261pdTIOOD4EmzgqOIXXtVoIHVobXrGy9Z9T2QZnszW7++8TrqtPyUnvm7iUMqG/VNmu42kzUAZDy4MM4JrbfWSRCKXj46ecwagqp05vbA+upYOXAPBqdaTB0KiumNU8zm9F4mKG1W2k0kin3DaHJkcL6G+zq45rGIHvK6hmvp/K5Uyazuci+kKb74kcfIz2d3F/8otNyZjyykaoN5WxyzmCH14Ev1cXE8wZT/cFharc3z5TUOtSn5/jIn3QZ+194Orps8HXXkz+7eWani8vLWbFiBcGGAP7dlVhBCy3dzYGi+mj9pCKIGdgJgGaGcJcXU+ZqceXzH4WDzY2Iu5xuvL4UjJQkgsVNNOhXRdc5hg9CT3UDufDdt3n5n68QqvJz+5RRFAw4hgmINM2e6Ss1r2e707186wvA5TOGYlodh2lLKe59ezsl206nZmcpWjCA1lAPhgNQaC2Gok2bfR4XX3xJh8dzpaYy9p23CRQearsy1Ai1HY/NVwr8hQ1YTfYoA3d+gBxf2zkAGnY10bjTQ3bmZLIzm79LrlMn4N4YAirC/1oJT5yl070HNuRaTiym0GQ2f1cazFpeL3woZrshvipmZ+9rvTsAme4GnLp9Pk/THZRlDMLS9GgTdbOqVr9rXFnZwJWRZpzz7oDRLcZBl++GV74Jh1bB01d3+D6uBS4dGcRUirqmEKW1fmIq+jWNYZoPnnZD0Trcejl5GfOhIc659A0A4idax0OvBOnMzEzy8/M5fPgwp512GrfddhtXXnklQ4YM6Y2X71VWyL5IGo74AUCFs4ykswaRNm94zLpNdywlQ2kkry+ntrT9nqzB0lOAMhw5PpKmtl8zEVryAYTAqFqDg804ssLHHDrDbttuPc+xw82priR8KtClCh0vOvljTmm3X0BLrqFDGXTudLR2ahhau+Pb17Jr1y7McM3E8uXLKSsr42sT3BQUDGqz/aZN5axbB2dPGs1nP/vZmHW7jtRywf1L2VJUw8V/au40cqyTEmQPS2HfhnIaagI01ASoOtJA0a6q6PqplwyPO8xk8NgMvCmT8KamEmhqwpOczNizY6ewzcrK4rI4E7U01QdpqmrADI9PryotoraiDE+SA71Fb27d4UDzNGdMawprePijesytRyjG4Fs4yKWOSpJZBzx8b+vZt84EYP6k2TDw+M4SmGgeZ9cmzbj7iolwxUTgupjllmXywBevQCkLb0pqpwE6wkhLw9vORDVd0fnoaPCcZXLkL+sJHWnO5jSvA/fM2TBrFfgTN3tipEzfCgbxN7V/PdI0DW+Sr0vXgWHAu00VlPpbTPdZtB5W/63Ntm6lGB0I17cPng5nfceuKYgYOA7+mwKBWti9oMPX1SDaITETiDspc8v7KN2B9u2l0HDUfpRwS3rvTmbSK0E6JSWFQ4fsO8zCwkJuu+02brvtNnJzc5k6dWp0nPTUqVPJyoqTIZ5ArE4yacITJGhxxl0W6YoMU8OztozqtW2n62zNMy6TlFntj3kNvG+XZfi9t5Lm+h689zM47XoY1vHEAmM7XNs7fD4fkyc3ZwpFRUWUlZXxwQcf8MEH7ffOjNcBY+TAZOadmsPag1XRZYYO10w9tpvEKRcNZ8ipAzCDJiX7ati/oRzTDI9xHpzM9MsK0PT2L1yTL+jaxb8lT5ITT1IakUvOgFFdm7rVN6qRpPVLqWkKsQmTmzGxq17av/iOyEpicEbvj5Doa7pucOXtd7Fn7SpGTT2rr4sTQ3Ma5Nx6BpgtskBdC3/OxhyX13SQ2ECRG/4XNf7zcNYt0FgVf4e0weCOc6PoSoKvvdvcdJdIWWMhLd/+18d6JUhXVVVFn3C1du3a6P+Li4t54403ePPNN6PbDh06lH374lebnAjMUCRIxz+1KmRn0lqcsXZPOALMMXUuGJdDiqfjP43uMkg+u/0qxFAohBWeKcrlcoHXC599qN3t+7szzjiDkpKSDp/c4/F4mDhxYpvluq7x2Jenxtnj2Gi6Fn1gSd7oDM6YF3/ceH8wKM3L6p9dQEOg651eUjxOjA5uMk5mw0+bwvDTWvdW6B80TQPHSfZ3Scm1/3VXznj730msV4I0wMiRIxk5ciTXXNM8qfn+/ftZs2ZNNGivXr263Yn5TxTRTDrOZCbQXN0d70u2RbNYQYC5lxUwICsJ0zSj1b1xXwvaDVote9OfDI+ay8vL4+tf/3pfF+OE5nLouBzHZ958IcTx0WtBOp7hw4czfPhwrrqquQPLiR+kI23S7WXS4eruOJl0KFyF5dA1ysrK+Nvf/hYzx3hPOJ3O5qc0CSGEOKH0u6v30KHtP2f5RGB1Ut0dGYOrxRlmFemR6jA09u3bd8wBGmD06PZnLRJCCNG/9WkmfTKKVE+3O5lJB23SwXAbsqFr0ediT506lXnz5vW4PMfrsaBCCCGOPwnSCdbcJt1xdTetendblkIpyNAaeO+NVyktsSceycjIkEArhBCfUBKkE6y5d3fHHce0Vh3HIln0BEcxu3c2D6DPzu7ak3yEEEKcfCRIJ1hkMpN226Tbqe6uqaklU6snU7MnqTjrrLMYMWIEI0d2/OQgIYQQJy8J0glmhuwZchzOdmYcizOZSWVlJY/85c98xt08FeGUKVMYOHBgm/2FEEJ8ckiQTjAzaAfp1tOCWo0h/HursBrDk0m0qO4uLi7GsixMpdGEg6mnjmLAgNhJ7YUQQnzySJBOsEgmbbTKpCte3EnT1uaHHVSHTPQ6e4hVcbk9j22hlc4H5mh+//nuTxcphBDi5CNBOsFCwfhB2qy0nxRV6tb4yO/nj499hIMQY4xyhhhV5OrQoD650zAKIYRoS4J0gkWqu1u3SUd6dd9PEx+EH2pwqnGE051F0W3qlJuLJvRg/lohhBAnJQnSCWYG7bm0I23SlmWxdetWDjbuwjJCJFlBJhom3zx3JIV7QpSWQkFBAfn5+fxk5ky83k/eU4eEEELEJ0E6wUKBAA1Dx/DOpu28s+mXsSud4ce0GbBm+eHo4jlz5jB4cPuPnBRCCPHJJEE6wfzBEGZS7DONDcMg10wnKeRiCSFqUVxxej4uh86AAQPIz+/7Z5YKIYTofyRIJ1gw3CatAT/44Q8Be/7ssrtXo0ImD1PHISz+/umL8Lriz0omhBBCgATphDPNEKCh6zrJycnR5ZGOY0HsyUxccR6wIYQQQrQkkSLBQoHwEKwWz3BWSkF4prEA9vOiZaiVEEKIzkiQTrBQ5ClYLZ9yZaroj0EUbsmihRBCdIFEiwRa+coLlB08AIChN7c3R6q6wc6k3U5pixZCCNE5CdIJVF9VidLsamynq3kyk+gzpIEQSCYthBCiSyRaJNDpF13G7C9/HQCX29O8IpxJKw0spNOYEEKIrpHe3QmUMSifzNp6wB4bDfCHd3ewY0cZdwEBZWfUkkkLIYToCgnSCWaaJgAOh4PqhiB/eX83T5MEGOEZu2FIhq/PyieEEOLEIUE6wUIhu3e3YRgcrffjAoaGWxXUsBT+Nnss00dk9mEJhRBCnCgkSCdYy0y6siHA5bjQ0dB9Dk799mmM12R8tBBCiK6RxtEEa5lJV9QHmUh4uJWmoUmAFkII0Q0SpBMoFArx5ptvAnaQrqwPRKsqUs4b0ncFE0IIcUKSIJ1ApaWl0Z+zs7OpD4SiJ1j3yAQmQgghukeCdAJFqroBZs+ejWkpDMJV3FLVLYQQopskSCdQpNNYVlYWmqZhWqr5BBsSpIUQQnSPBOkEigTpyEQmplKRbmOSSAshhOg2CdIJ1DpIWy0zaXk0pRBCiG6SIJ1AbTJpi2gmLam0EEKI7pIgnUDxqrsjJ1iTMy2EEKKbJHQkUPzqbundLYQQomckSCdQRx3HpHe3EEKI7pIgnUAddRyTKUGFEEJ0lwTpBGrbcaxl7+6+KZMQQogTl4SOBOqwulsyaSGEEN0kQTqB4lV3RyczkXHSQgghukmCdALFH4IVDs4SpIUQQnSTBOkEijeZSfM4aQnSQgghukeCdAJ1OC2oxGghhBDddNIE6Yceeojhw4fj8Xg488wz+fjjj3u9DB12HJNMWgghRDedFEH6+eef57bbbuOuu+5i7dq1TJ48mQsvvJDS0tJeLccZZ5zB1Vdfzfjx44FW46QlSAshhOimkyJI33fffXzjG9/gxhtv5NRTT+Wvf/0rPp+Pf/zjH71ajkGDBjFhwgRycnKA1kOwerUoQgghTgInfJAOBAKsWbOGuXPnRpfpus7cuXNZvnx5H5YsMpmJ9O4WQgjRM46+LsCxKi8vxzTNaPYakZOTw/bt2+Pu4/f78fv90d9ramqOS9ksJeOkhRBC9NwJn0n3xD333ENaWlr035AhQ47L68RMCyozjgkhhOimEz5IZ2VlYRgGR44ciVl+5MgRcnNz4+5zxx13UF1dHf1XWFh4XMrWcpy0VHcLIYTorhM+SLtcLqZMmcLChQujyyzLYuHChcyYMSPuPm63m9TU1Jh/x4OlWvbuPi4vIYQQ4iR2wrdJA9x2223ccMMNTJ06lenTp/PAAw9QX1/PjTfe2KflCpkWjkjHManuFkII0U0nRZD+/Oc/T1lZGb/4xS8oKSnhtNNO45133mnTmay3KUs1/yLV3UIIIbrppAjSADfffDM333xzXxcjRssgLb27hRBCdJe0lB5HycGWmXTflUMIIcSJSULHcWLWB/nZITP6u2TSQgghukuC9HFiVjVPllIxNg3NaXSwtRBCCNHWSdMm3Z8ETYvSqkYADmNRd1bfdmATQghxYpIgnWCmpbjwgaWkljXxF5IIotClqlsIIUQPSHV3glU1BNhbVh+9+9EMncmD0/uySEIIIU5QEqQTzB+yAPCGs+dRg1LITHL1ZZGEEEKcoCRIJ1ggHKR9ut1RTDPkFAshhOgZiSAJFs2kDTuT1hzSHi2EEKJnJEgnWCST9ujhUyuZtBBCiB6SCJJg/pA9gYlHj2TScoqFEEL0jESQBGvOpMNB2pDqbiGEED0jQTrBIm3SnvADpCVICyGE6CkJ0gkWCdLuyAQmUt0thBCihySCJFikTdqtSXW3EEKIYyNBOsEibdKuaJCWUyyEEKJnJIIk2IZDVUBzJi3V3UIIIXpKIkgCHa5q5OkVBwGp7hZCCHHsJEgn0PbimujP47KTAQnSQgghek6CdAIdqrSfIX3h+ByyvOGHakh1txBCiB6SCJJAh6vsID04w4cy7Q5k0nFMCCFET0kESaA0r5NR2ckUZCVBuJe3PGBDCCFETzn6ugAnk/nnj2L++aMAKN+xBZBMWgghRM9JBDlOlKnsH6TjmBBCiB6SIH28RKu75RQLIYToGanuTqBQlR+zqgkj1R3NpGUIlhBCiJ6SIJ1AtYsOUv9xCalzh6LCmbQMwRJCCNFTEkESSPc5AbAaQhAdgiWZtBBCiJ6RIJ1Aus+umLAaQy2qu+UUCyGE6BmJIAmke8NBuiHYorpbMmkhhBA9I0E6gaLV3ZJJCyGESADpOJZAkeruQGEthIdJy4xjQgghekrSvARy5vjQPEY0QOtJTox0T98WSgghxAlLMukE0n1OBt1xJlZtwP491YXuMvq4VEIIIU5UEqQTTHcb6G5vXxdDCCHESUCqu4UQQoh+SoK0EEII0U9JkBZCCCH6KQnSQgghRD8lQVoIIYTopyRICyGEEP2UDMEClLJnH6mpqenjkgghhPgkiMSbSPxpjwRpoLa2FoAhQ4b0cUmEEEJ8ktTW1pKWltbuek11FsY/ASzLoqioiJSUFDSt53Nt19TUMGTIEAoLC0lNTU1gCU9Ocr66Ts5V98j56jo5V12XyHOllKK2tpa8vDx0vf2WZ8mkAV3XGTx4cMKOl5qaKh/2bpDz1XVyrrpHzlfXybnqukSdq44y6AjpOCaEEEL0UxKkhRBCiH5KgnQCud1u7rrrLtxud18X5YQg56vr5Fx1j5yvrpNz1XV9ca6k45gQQgjRT0kmLYQQQvRTEqSFEEKIfkqCtBBCCNFPSZBOoIceeojhw4fj8Xg488wz+fjjj/u6SL3unnvuYdq0aaSkpJCdnc3ll1/Ojh07YrZpampi/vz5DBgwgOTkZK666iqOHDkSs83Bgwe59NJL8fl8ZGdn86Mf/YhQKNSbb6XX3XvvvWiaxq233hpdJueq2eHDh7n++usZMGAAXq+XiRMnsnr16uh6pRS/+MUvGDRoEF6vl7lz57Jr166YY1RUVHDdddeRmppKeno6X/va16irq+vtt3LcmabJz3/+cwoKCvB6vYwcOZJf//rXMVNQflLP19KlS/n0pz9NXl4emqbx6quvxqxP1HnZuHEjs2bNwuPxMGTIEH73u9/1rMBKJMRzzz2nXC6X+sc//qG2bNmivvGNb6j09HR15MiRvi5ar7rwwgvVE088oTZv3qzWr1+vLrnkEjV06FBVV1cX3ebb3/62GjJkiFq4cKFavXq1Ouuss9TZZ58dXR8KhdSECRPU3Llz1bp169Rbb72lsrKy1B133NEXb6lXfPzxx2r48OFq0qRJ6pZbbokul3Nlq6ioUMOGDVNf+cpX1MqVK9XevXvVu+++q3bv3h3d5t5771VpaWnq1VdfVRs2bFCf+cxnVEFBgWpsbIxuc9FFF6nJkyerFStWqA8++ECNGjVKXXvttX3xlo6ru+++Ww0YMEC9+eabat++ferFF19UycnJ6k9/+lN0m0/q+XrrrbfUT3/6U/Xyyy8rQL3yyisx6xNxXqqrq1VOTo667rrr1ObNm9W///1v5fV61aOPPtrt8kqQTpDp06er+fPnR383TVPl5eWpe+65pw9L1fdKS0sVoJYsWaKUUqqqqko5nU714osvRrfZtm2bAtTy5cuVUvaXSNd1VVJSEt3mkUceUampqcrv9/fuG+gFtbW1avTo0WrBggVq9uzZ0SAt56rZT37yE3XOOee0u96yLJWbm6t+//vfR5dVVVUpt9ut/v3vfyullNq6dasC1KpVq6LbvP3220rTNHX48OHjV/g+cOmll6qvfvWrMcuuvPJKdd111yml5HxFtA7SiTovDz/8sMrIyIj5Dv7kJz9RY8eO7XYZpbo7AQKBAGvWrGHu3LnRZbquM3fuXJYvX96HJet71dXVAGRmZgKwZs0agsFgzLkaN24cQ4cOjZ6r5cuXM3HiRHJycqLbXHjhhdTU1LBly5ZeLH3vmD9/PpdeemnMOQE5Vy29/vrrTJ06lc997nNkZ2dz+umn8/jjj0fX79u3j5KSkphzlZaWxplnnhlzrtLT05k6dWp0m7lz56LrOitXruy9N9MLzj77bBYuXMjOnTsB2LBhA8uWLePiiy8G5Hy1J1HnZfny5Zx77rm4XK7oNhdeeCE7duygsrKyW2WSubsToLy8HNM0Yy6UADk5OWzfvr2PStX3LMvi1ltvZebMmUyYMAGAkpISXC4X6enpMdvm5ORQUlIS3SbeuYysO5k899xzrF27llWrVrVZJ+eq2d69e3nkkUe47bbbuPPOO1m1ahXf+973cLlc3HDDDdH3Gu9ctDxX2dnZMesdDgeZmZkn1bkCuP3226mpqWHcuHEYhoFpmtx9991cd911AHK+2pGo81JSUkJBQUGbY0TWZWRkdLlMEqTFcTN//nw2b97MsmXL+roo/VJhYSG33HILCxYswOPx9HVx+jXLspg6dSq//e1vATj99NPZvHkzf/3rX7nhhhv6uHT9zwsvvMAzzzzDs88+y/jx41m/fj233noreXl5cr5OMFLdnQBZWVkYhtGm1+2RI0fIzc3to1L1rZtvvpk333yT999/P+YJY7m5uQQCAaqqqmK2b3mucnNz457LyLqTxZo1aygtLeWMM87A4XDgcDhYsmQJDz74IA6Hg5ycHDlXYYMGDeLUU0+NWXbKKadw8OBBoPm9dvQdzM3NpbS0NGZ9KBSioqLipDpXAD/60Y+4/fbb+cIXvsDEiRP50pe+xPe//33uueceQM5XexJ1XhL5vZQgnQAul4spU6awcOHC6DLLsli4cCEzZszow5L1PqUUN998M6+88gqLFi1qU+UzZcoUnE5nzLnasWMHBw8ejJ6rGTNmsGnTppgvwoIFC0hNTW1zoT6RzZkzh02bNrF+/frov6lTp3LddddFf5ZzZZs5c2aboXw7d+5k2LBhABQUFJCbmxtzrmpqali5cmXMuaqqqmLNmjXRbRYtWoRlWZx55pm98C56T0NDQ5tnFBuGgWVZgJyv9iTqvMyYMYOlS5cSDAaj2yxYsICxY8d2q6obkCFYifLcc88pt9utnnzySbV161b1zW9+U6Wnp8f0uv0kuOmmm1RaWppavHixKi4ujv5raGiIbvPtb39bDR06VC1atEitXr1azZgxQ82YMSO6PjKsaN68eWr9+vXqnXfeUQMHDjzphhXF07J3t1JyriI+/vhj5XA41N1336127dqlnnnmGeXz+dTTTz8d3ebee+9V6enp6rXXXlMbN25Un/3sZ+MOnTn99NPVypUr1bJly9To0aNP+CFF8dxwww0qPz8/OgTr5ZdfVllZWerHP/5xdJtP6vmqra1V69atU+vWrVOAuu+++9S6devUgQMHlFKJOS9VVVUqJydHfelLX1KbN29Wzz33nPL5fDIEq6/9+c9/VkOHDlUul0tNnz5drVixoq+L1OuAuP+eeOKJ6DaNjY3qO9/5jsrIyFA+n09dccUVqri4OOY4+/fvVxdffLHyer0qKytL/eAHP1DBYLCX303vax2k5Vw1e+ONN9SECROU2+1W48aNU4899ljMesuy1M9//nOVk5Oj3G63mjNnjtqxY0fMNkePHlXXXnutSk5OVqmpqerGG29UtbW1vfk2ekVNTY265ZZb1NChQ5XH41EjRoxQP/3pT2OGBH1Sz9f7778f9xp1ww03KKUSd142bNigzjnnHOV2u1V+fr669957e1ReeQqWEEII0U9Jm7QQQgjRT0mQFkIIIfopCdJCCCFEPyVBWgghhOinJEgLIYQQ/ZQEaSGEEKKfkiAthBBC9FMSpIUQQoh+SoK0EOKkMnz4cDRNY//+/X1dFCGOmQRpIY6TxYsXo2ka5513Xl8XRQhxgpIgLYQQQvRTEqSFEEKIfkqCtBDdsGvXLr761a9SUFCA2+0mOTmZYcOGcemll/LEE09EtzvvvPM4//zzAViyZAmapkX/DR8+vM1xFy5cyJVXXsmgQYNwuVxkZ2dzxRVXsHz58rjliBwL4PHHH2fKlCkkJSWRnp7OJZdcwooVK7r93s477zw0TWPx4sWsX7+eK6+8kqysLNxuN6eeeip//OMfifc8npb7xfPLX/4STdP45S9/2e7yoqIivv71r5OXl4fX62XChAn8/e9/j267fft2vvjFL5Kbm4vH42Hy5Mk8//zznb6nV155hXPOOYfU1FRSUlI477zzeOuttzrc56WXXuKiiy5i4MCBuFwu8vPzuf7669m6dWubbffv3x/9m5qmyX333cfpp59OcnJy9O8jxLFw9HUBhDhRbN68mZkzZ1JTU8PYsWO57LLLMAyDQ4cOsXTpUg4fPsyNN94IwEUXXYTH4+Hdd98lJyeHiy66KHqcrKysmOP+8Ic/5I9//CO6rjN16lRmzZrFwYMHee2113jjjTd4/PHHo8dt7bbbbuOBBx5g5syZfPazn2XTpk28/fbbLFiwgBdeeIErrrii2+/z3Xff5b777mPkyJFccMEFFBcXs2zZMn74wx9SWFjIAw880O1jduTgwYNMmTIFl8vFrFmzKCsrY+nSpXz961+nqqqKmTNnMm/ePPLy8jj//PM5cOAAy5cv5wtf+AIAn//85+Me98EHH+T+++9n6tSpXHbZZezZs4clS5awZMkSHnzwQb773e/GbB8Khbjuuut44YUXcLvdTJkyhfz8fHbu3MkzzzzDyy+/zMsvvxzzt4xQSnHllVfyzjvvMGvWLE455RS2bNmS0PMkPqF69IBLIT6BbrzxRgWo3/zmN23WNTQ0qCVLlsQsizy3dvbs2e0e87HHHlOAGjVqlNqwYUPMuiVLlqiUlBTlcrnUzp07Y9YRfgau1+tVCxcujFn3u9/9TgEqLS1NHTlypMvvb/bs2dHj/vWvf41Zt3DhQqVpmjIMQxUWFsbd7/3334973LvuuksB6q677oq7HFDf/va3Y56B/frrrytApaSkqGHDhqnf/OY3yrKs6PoHHngget5aGzZsmAKUpmnq6aefjln33HPPKU3TlMPhUJs2bYpZd+eddypAnXnmmWrv3r0x61588UVlGIbKyMhQlZWV0eX79u2LvofBgwe3ee6wEMdKgrQQXXTJJZcoQK1du7ZL23cWpE3TVHl5eQpQq1evjrtNJOD+4Ac/iFkeCQy33npr3P2mTp2qAHX33Xd3qaxKNQfbK6+8Mu76iy66SAHqqaeeirtfT4P00KFDVWNjY5v9Jk2apAA1ffr0mACtlFLBYFBlZmYqQB04cCBmXSRIX3755XHLc9VVVylAfeMb34guO3r0qPJ6vcrj8ahDhw7F3e873/mOAtSf//zn6LKWQbr1eREiEaRNWogumj59OgA33XQT7777Lk1NTcd0vHXr1lFUVMTIkSOZMmVK3G0iw7c++uijuOtvuOGGuMu//OUvA7TbTtyRT3/603GXn3LKKQAcPny428fsyPnnn4/H42mzfPTo0QBcfPHFbdp3HQ5HtG2/qKgo7nHbOzeR5S3Pzfvvv09jYyMzZ84kPz8/7n6d/S2uuuqquMuFOBbSJi1EF/3oRz9i2bJl/O9//+Oiiy7C6XQyefJkzj33XL7whS8wbdq0bh1v7969AOzZs6fTTkZlZWVxlxcUFHS4/NChQ90qE8DQoUPjLk9NTQU45puTrr5ecnJyh+tTUlI6LE93zk3kb7Fw4cIe/S2ys7Px+Xwd7idET0iQFqKLfD4fCxYsYNWqVbzzzjt89NFHfPTRR6xevZr77ruP73znOzz00ENdPp5lWQDk5uZy4YUXdrht685mXaXi9MbujK4ntoIt8j57+nqJLk9Ey3MTKeOoUaOYOXNmh/uNGzeuzTKv15vYwgkRJkFaiG6aNm1aNGsOhUK8+uqrfPnLX+bhhx/m6quvjg696syQIUMAGDBgAE8++WSPyrJv3z5OO+20NssjU2IOHjy4R8ftDpfLBUBtbW3c9QcOHDjuZYhn3759TJ48uc3yeOcm8rcYO3Zsj/8WQhwP0iYtxDFwOBxcffXV0Ux4/fr10XWR4BUKheLuO23aNLKysti6dWuPh+v861//6nB5b0xJGmnD3bZtW5t1DQ0NvP/++8e9DPG0d26eeuopIPbczJkzB5fLxeLFiyktLe2N4gnRJRKkheiihx9+mB07drRZXlJSwurVqwEYNmxYdHkkU9u1axfBYLDNfk6nk7vuugulFFdccQXLli1rs41pmixatKjdyUkeeeSRNp3D7r//fj7++GNSUlL42te+1uX311Nz584F4KGHHorpVFZfX883v/lNCgsLj3sZ4nnllVd47rnnYpa99NJL/Oc//8HhcMSMk87JyeG73/0u9fX1fPrTn2bTpk1tjuf3+3n99dfZvn37cS+7EBFS3S1EFz322GPMnz+fgoICJkyYQGpqKmVlZXzwwQc0NjbyqU99is985jPR7YcOHcrUqVNZvXo1EydOZOrUqXg8HrKysrj33nsBuPnmmzl48CC///3vmTVrFuPHj2fUqFF4vV5KSkpYv349VVVVPPLII5x11lltyvStb32LT33qU8yaNYv8/Hw2b97Mpk2bMAyDf/zjH+Tm5h7383LNNdfwwAMPsHr1asaPH88555yDZVmsXr0al8vFV7/6Vf7xj38c93K0dsstt3Dttddy3333MXr0aPbs2cPKlSsB+MMf/sCkSZNitr/33nspLi7m2Wef5bTTTmPy5MmMGDECh8PBoUOHWL9+PfX19bz99ttx26WFOB4kkxaii+6++25uuukm0tPTWbFiBS+++CJbt27lzDPP5J///CfvvPMODkfsfe9//vMfvvjFL1JTU8Pzzz/P3//+9zbZ3e9+9zs+/PBDrrvuOurq6njnnXf473//S1FREeeddx5/+9vf2p1V6/777+fhhx+mpqaGV199lQMHDnDRRRexdOlSrr766uN2LlpyOp0sWLCAm2++mZSUFN577z02btzIFVdcwdq1a6Ptvb3tlltu4YUXXsDhcPD666+zefNmZs2axRtvvMH3v//9Nts7HA6eeeYZ3nrrLS6//HJKS0t5/fXXeffdd6moqODTn/40zz77LOeee24fvBvxSaWpnnT/FEL0qcgwIfn6CnFyk0xaCCGE6KckSAshhBD9lARpIYQQop+S3t1CnICkLVqITwbJpIUQQoh+SoK0EEII0U9JkBZCCCH6KQnSQgghRD8lQVoIIYTopyRICyGEEP2UBGkhhBCin5IgLYQQQvRTEqSFEEKIfkqCtBBCCNFPSZAWQggh+ikJ0kIIIUQ/JUFaCCGE6KfkKViAZVkUFRWRkpKCpml9XRwhhBAnOaUUtbW15OXloevt58sSpIGioiKGDBnS18UQQgjxCVNYWMjgwYPbXS9BGkhJSQHsk5WamtrHpRFCCHGyq6mpYciQIdH40x4J0hCt4k5NTZUgLYQQotd01sQqHceEEEKIfkqCtBBCCNFPSZAWQggh+ikJ0kIIIUQ/JUFaCCGE6Kekd/dxtvFQFesLq6K/a5rGnHHZ5KV7+65QQgghTggSpI8jf8jk2sdWUB8wY5a/NzqLf33tzD4qlRBCiBOFVHcfRw1+MxqgL5mYy/SCTADKav3RbWpqaigrK6O2trZPyiiEEKL/kkz6OAqYFgCGrvHwdVNYvuco1z6+gpClANi8eTMvvfRSdPvrrruO0aNH90lZhRBC9D+SSR9HgZAdpF2GfZqdhj2zTCgcvIuKimK2P3LkSC+WTgghRH8nQfo48oeDtM/QCRTXYyg7gw6a9v9DoVDM9pZl9W4BhRBC9GtS3X0cRTLpe4NuSv+0loxBPgBMS4K0EEKIzkkmfRz5Q3ansVNM+zQ7ihsACIWDcTAYjNlegrQQQoiWJEgfR5FMurVQq0zaMAxAgrQQQohYEqSPo0jv7tZCrdqkXS4XIEFaCCFELAnSx1H7mXRsdbcEaSGEEPFIx7HjoLS0lOLiYooOVTFKL6eQAPnWAHQiQ7BiM2m32w1IkBZCCBFLgnSChUIh/va3vxEIBAA4xwXvAucHxjPSykXHbpNWSkkmLYQQokNS3Z1gfr8/GqCTBuZTZ9lZ8gGjjBKtilytlmytlv0HDtDU1ARIkBZCCBGfZNIJZpr2sCtd1xk0ZR5LXl/CVNde9hql7DVKmRfe7p9Pbo/uI9XdQggh4pEgnWAtg3QgZFFupZNrpdOA/VCNw1hYwPABSWgaZGVlkZeXx7Zt2yRICyGEiCFBOsEiQdowDAKmhcLBZYEp0fWXUks1ivXfuIB0n13NvXz5ckAyaSGEELGkTTrBIoHWMAwCIavNXZAR/n9kQhOws24ApRRCCCFEhATpBIvJpEMWjvCwqwi3FjsMC5qDtGTSQgghWjrpgvS9996LpmnceuutffL6MW3SpoWz1XqXbgfpYIvZyCRICyGEiOekCtKrVq3i0UcfZdKkSX1WhtaZtNFqvTsckM041d0SpIUQQrR00gTpuro6rrvuOh5//HEyMjL6rBwt26T9caq7I5n08r1HWbyjlMU7StlxpA6A8tomKuoDvVtgIYQQ/dZJE6Tnz5/PpZdeyty5c/u0HG3bpGN5DfuU3/HyJr7yxCq+8sQqHl26D4Ath6u4+q8f9WZxhRBC9GMnxRCs5557jrVr17Jq1aoube/3+/H7/dHfa2pqElaWztqkvzBlME17y1A0V3dn+BuhDnQNDlc2JqwsQgghTmwnfJAuLCzklltuYcGCBXg8ni7tc8899/CrX/3quJQnNpM2uaBVmP70pDyuunRszLJt27bx/POb0VDIKCwhhBARJ3x195o1aygtLeWMM87A4XDgcDhYsmQJDz74IA6HIxo0W7rjjjuorq6O/issLExYeVqPk05v1Sat4jxjOtJxTEdhSZQWQggRdsJn0nPmzGHTpk0xy2688UbGjRvHT37yEwyjdf9qe67syHzZiRaTSfstfK2CNFbbIBwJ0poEaSGEEC2c8EE6JSWFCRMmxCxLSkpiwIABbZb3htZzdye3zqQ7CNJeLchIvYzDhw+Tn59//AsrhBCiXzvhq7v7m3UHKwB4f2c5qw9UktQqSDduLKdpR0XMMqfTbrdO0oLMdO7niSeeiOnYJoQQ4pPphM+k41m8eHGfvO7eIzUUrl8GQNACpYhm0rrPgdUQov7jEuo/LiH39uk40u0q9/z8fE6bMo3XP97FYL2KUChEY2PjcauSF0IIcWKQTDqBduzcEf35U5NH8MHXZ5AaDtLpnx2J74xsNGd4drH6YHRbwzA4f848FgVHEwrPURYKhXqx5EIIIfojCdIJVHRgLwCVeipfnHcB2t+2RNd5xmWSec1YdF94SFarDmJa+C9hhoO6BGkhhBASpBNo8OhT2RrKZq9rBKq2OcimnDcY3R1uWYg0UbfqP6aHn45lhv8k8YaOCSGE+GSRIJ1AmTn5fBwaRp0jPToe2shwk3ZRQfNG4bm7W/fyDi/GVJJJCyGEsEmQTiArHHh1jeh4aM2IPcVaJBqr1kE6NpOWIC2EEEKCdAKZKhKkNZQZDsJ6q8lMIr+2yqTDMRpL2qSFEEKEnZRDsPpKJDk2dA3MSCbdKkhHq7tbL26bSe/atYu6urpjKtPw4cP79NGdQgghek6CdAKZkSpuTWtuc24VpDWtk+puZQfpHTt2sHHjxmMu04ABA/jud797zMcRQgjR+yRIJ1Bk3m1DB8Idx7TW1d16dOPYxZGOY+Hq7uLiYsCe9jQnJ6fbZQkGgxw4cOCYM3EhhBB9R4J0Alnx2qRbV3eHM+bWz9HQWlV3V1VVATBhwgQuvPDCbpeloqKCBx98MPpULiGEECce6TiWQJGnUOpayzbpVqc4kjLHe9CG1pxJB4P2jGQpKSk9KosWvRmQp2oJIcSJSoJ0AjVn0rTbuzvSJN0mlcYO7o3KGbMsMzOzR2WRIC2EECc+qe5OoMg4aUPXUOFq5q727rZXaWwM5fGtCybhc0BycjJjxozpUVkij7+UIC2EECcuCdIJZEWT5w6GYLXTu9teBwEcnDr5DPLTvcdUlkgmLW3SQghx4pLq7gSKO5lJmxnHwj+00yYNicl+o0O9EnQ8IYQQvU+CdAIp1VzdHZ0WtM0QrPi9u+1V7a/rrkh1d8tyCSGEOLFIkE6g5slM6HQIVvxMOlxFLZm0EEIIJEgnVHSSMV1rnsykzYxjrTaOsy7Oqm5rGaSlXVoIIU5MEqQTqPkpWC2mBW23uvv4ZtJS3S2EECc+CdIJ1HLGsXYnM4n27m67v3QcE0II0ZIE6QQy401m0rq6u8Pe3Vp7q7pNqruFEOLEJ0E6gVq2SZs1fvvnpNgZxDqaFlSTjmNCCCFakMlMEsgyLa7EyeyiAP7w3NuOrFaTknQwzCoavxOQ+EqbtBBCnPgkSCeQpy7IbXihIkQkzjpzfDHbdNS7W4ZgCSGEaEmCdAJpATs0+3XIOn8ozlwfjgGtMunm3mFt9u9gVc/Ko2kopaRNWgghTlASpBMokrE2OTTSLhgWf6NIdXecuJnINmmwq7xN05RMWgghTlDScSyBIoG3o5CoddhxLLIqMUFVHlcphBAnNgnSCRSdwETT2t8ocsY7nMwkMeWRJ2EJIcSJTYJ0IoWjq+ogRneld3fHuXjXSSYthBAnNgnSCRSZFrSn1d2JzqQjw7AkSAshxIlJgnQCRWJhx5l0q41broqOk5ZMWgghhATpxFJdaJPuoHe3tEkLIYRoSYZgJVBzx7EONgpXd9evKKZxQ1nMqj/UaryLO2GZr1R3CyHEiU2CdAKpLnQci8xApgImZsCMWTcAjatwUZzgTFqCtBBCnJgkSCdSJBZ2UN2dNCUH19AUlD82QFuNIcr/vhk3WsKqp6W6WwghTmwSpBNIdaF3N4BzoK/NMqsp1PyzmZigKtXdQghxYpMgnUiqC23S7dAczX34tJD07haJ5Q+Z/PrNrRRVNXV5n9OGpPO9OaOPY6mEOEbv/Rz2Lk78cQdNhs/8ueNOwL1EgnQCqS5Ud7fLaPHUqlBiq7tr3nuPSl/b7L03OYcOJXnmzC5vb5omRUVFmGZzs0BqaiqZmZnHo3gnvdX7K3l6xcFu7bNoeynXTh/KwBT3cSqVEF2wZxEcWA7n3QEtHsGLvw4+evD4vGbJRpj1A8gsOD7H74YTPkjfc889vPzyy2zfvh2v18vZZ5/N//t//4+xY8f2elkKBviAOnxuo9v7appGEHACKkGZtGpsBKD8yX+il5V1svXxN/Kdt3ENH96lbf/3v/+xfPnyNsuHDh2Kx+OJu4/X62XOnDmkpqYeSzFPSk1B+2ZncIa3S9nxnS9vImQp/CGz022FOG6CjfCvK+yfh8+EEec1rzMDzT9/8cXYAH4sXrwR/DUQ8ifmeMfohA/SS5YsYf78+UybNo1QKMSdd97JvHnz2Lp1K0lJSb1almnDMqj4qJTM5J5lHkENnApIUJu0Fs5CjYwMUgoGQtEaSM6FIdMTcvyuqv/wQ6yGBkLl5V0O0keOHAEgJSUFt9tNeXk5AAcPdpwN5uTkcPbZZx9TeU9GZri/xMAUN9dMHdLp9ne9toWQZSJ9DkWfKtve/LMZil1ntfh99AWJq5p2+uwg3fImoA+d8EH6nXfeifn9ySefJDs7mzVr1nDuuef2bmEiCbDesw+LqYWPkajq7vD/naNHM3jUcjhSCVTCL1ck5PhdtffTn8G/axcqGOzyPn6/fRd76aWXMm7cOILBINu2bSMUCsXdfsOGDRw4cIBgN17jkyQSpB1d/GwaemIfmypEj7QMzKpVrU4kSOuObgXoe9/ezj8+3BfTw9fQNX580VhunFkAhit8/P5xLTnhg3Rr1dXVAH3SdtncJt2z/UOR/cwEdRyL/KBr9p1hH9Fc9oe+O0G6qcnu4BSp2nY6nUyaNKnd7YuLizlw4EBMG7ZoFgoHab2LF7NILDclSIu+1HJqRqudTFrvXhh7c2MRgdaJkAlvbyoJB+nw8UwJ0glnWRa33norM2fOZMKECe1u5/f7o5kaQE1NggJYVx5V2YFIkL7vnR1kjsxg8pD0YypOdJpw3YCmPgzSTqddjmMI0p2JDDeTMeHxRTJih9HFIB3JpBM1R60QPdEye24dNCO/685uHTIYbk584sZpjM1JYdmucn78n40EI9eOSCYt1d2JN3/+fDZv3syyZcs63O6ee+7hV7/6VeILEL4Q9rRpxOEyIGTiApbsLDv2IB2+voZ0jWBTAxDu0NbLVcKmy0XIMAg0NXW5Orq7Qdow7PfWXia9eEcpmw5VR3/XdY3LJg1i2IDE9FtQSlFd2kgwPItc6gAPbl/3Lh7HU8hszqSVUoSKa1CHNkHOKThy0tA9sZcCI8HzyPeWQ5UNPLPyIP5g5zdrbqfO9WcNIz/d2wslO3mte/dNdnz0QbvrTzlnNpMvuKRnB+8wkw5/1/XuddSNfBfy0rzkpXvJTrX7EEWCdzToSyadWDfffDNvvvkmS5cuZfDgwR1ue8cdd3DbbbdFf6+pqWHIkM4703Qq8nnqYZt0dqaXYEMdTrRob9y4tr0JO97q9Hhaow8cyfzP7eZ/zG9ecffdPSpfj40osP+tWmX/6wa3u2ud8DrKpI/W+fnaP1dH22UjVu+v4IkbE9OJbuOiQyx7cVf0d7fPwZd/ezYuT//4ikWqrR26Ru2iQmoWHAiv2Yqe7GTQ7dNjxupHMunW56y/e+j9Pfz7464PNatrCvHryyeglGLv3r1xa9Xy8/PJzs5OZDFPKh8+/y/89fXtrq84XNjzIG21uA4mqLo7EowjtUouw/7cByOjaowWQXrHO1BbFHsAhwdO+2K3XvNY9I8ryDFQSvHd736XV155hcWLF1NQ0Pm4Nrfb3eWLf3fLAvQ4ldbCH5af48Hx0VGK166Mv2GticY5ZDrvw6Xvir8NMKRyNkcGntGjsvQH9c501hfVo2kNnW5bXGM3XxRXNbBi79GYdduLazAtRbrPycUTcjlU2cgHu8qpbEjcnXJZYS0ALo9B0G/ibwhRW9HEgLzkhL3GsYgEW0PXCB6xL6gadSiSseqCWA1BjNTm70TzY89PrCBdWW9XUc4eM5Dxee0Pxdt4qJplu8upabI/A4WFhfzrX/+Ku63b7eZHP/oRDkcPL5dmCBorerZvR5xecKck/rjdFArY53zu1+fjbTH8sbGmmv/97WGCgWMYytQyk26d2UY6dhndq7GK9M9whm/sneGb02gmHanu3v8BLP9L2wP4BkiQ7o758+fz7LPP8tprr5GSkkJJSQkAaWlpeL29XI11bDEaZ66PwIEa0tAhYGEG2msTyQQyaRj0A1wTS9o93llvrmXYiy+RNnMsOVOqoXg95E2BG17vWQG76cXVh/jlG1v49abnGX9gI4XXfovycy/sdL/qxiAPLtpNqEnnxcfbuVFpZZJRxBlOWLClhP/bEL/3+rThmdxz5STe31HKB7vKCSWw/TrQaN/Vz7hyFOsXHKS6rJFAQ/ye6BH+hgbMYACn24OzVbX+0aNHWbFiRZebB5KSkjj33HPbvflsGaQj4/DTHE9SHfo6Ck+bsfnN1d0nVpBuCNdAfWZyHldNab9G7anl+1m2uzx6Ya6rqwPs5pVITZxSij179uD3+wmFQj0L0mYIHpkB5Ts73EwpjQZzDiYDgRA+430cWnnHx9Yd8MXnYdRc8NfCmiehsar7ZTxGZvgzOqrpI5J0V3R5fVOA/wFmwI/63/9FJ1eKK2kgTPt6c6etCHX8M2lnODkKRIN0OOhX7LX/78uCoWc1H6CXb4xO+CD9yCOPAHDeeefFLH/iiSf4yle+0ruFiVzQeljdnf7ZUbzjNPnHsn18amw2P5gXZ0IWM0DDo/9HnXkVZvJ4OOfa9ouz4SEc5mqcgybiPncqPH8d6Bb0pBZBKVj+EJRtg+HnwuTPd7qLqRmEMPB5XDhDIWYMSSNzVucTaSilKK4LsWp/ZZeLl+l3gx/SvQajvG2zV7dD5ytnDwea76BDCepFDxAMPzDF5TFw++yvlb+DIL1r5Ue88cC9KMvCcDr53M/uJn/cqdH1H330EWvWrOlWGY5sXs9Ab/y/bXV5IxmBPBz6IAjYFyN7+hy7jK1nuTtRq7sbA/b78bk6bqeMXJiD4c9ApJkkJyeH66+/HrD7N/z617+OWd/9AlW0CNDtXxcC6hQqQ7dGfw9Zg8l0PdDBgZUdpApX2UF6w3Pw3s96VsZjYH88ZgGgr3wYHM2fecN0ADNQCqwP7sPQOvkspeTC+Mtjl7W8SUxAm7RSKvo3j3wGnOFgHe3xHQnSTeE+LIOnwRee6fJrJNoJH6T71bzUXXmedAc0XSM0wMMuLEY5wZUfp6q0sYqQvgtMCFUGCRyqbb84jW709GEovM0f5NZjDbvq6B5476f2zxuet79Mjo6DfXP1kf0x62rvbk3TuOfK9odbxfPRRx/x3nt7mTtuII9cNbvDbSN30KEEBqBIJu30OHB5w0G6sf0gfXjnNlT4wm8Gg5Ts2RUTpAPhWpTRo0czbNiwuMeor6pkzVuvEUrNwPIkUbhzO0cqjrT7mlOTRqPrE1BmpINjCI0gijhB+kTNpMMd9zydBOnIePFQ+DMauY7oest2+eafexykI4FEM+Cu9qu8ra1H4amtzb+P+Rx85ZftH/e9n8FHf4ZguC24rtT+f84EGH5Oz8raA2bIgu3bANCn3QgtzrsRsmCnvc6c8nUMZzt/kwMf2dNw7nwXkrJi1+1b0uLFjr13d8ubTmfrNunWHccitRKuvp1S+YQP0v3JMc3dHeYJf5Ab2+s4FmzE0Owve7CogdK/rO/gaGNJOu+nWH5oPNSEF2LbeLojUNf8sxWEUFOnQTpSfaSc3R8n3V0tO44ppaioqCAUCqHrOllZWTFVba0v0IkQzaTdzZl02cFaUga07Z0+cEgKqlUvdGW1+j38YRo5ciRnnXVWzLqmrVsJHDzIkYqjbD5agu720uRJYlD+UAqG230yNJcL15AhaIZB8e6d7Fm9ApcK4tC1FgE5GM6maTM234hm0t08EX2sMRykfe0FhLBIFuU9sotHvvkgdQ43ZA+hcMsmHvzy1Wi6zvTLP4cW7g3f4yAd+b5pnUxZ2eqGUXV24p3hwBG0p/4lEA7Wo+bABf/XzUL2nNXQAE9fA4Bx8W/B1Vzd7bAsePozAITO+zmu1LT4B1nxV3hnI2x41v7X7osde3V3sMXn3BHNpGNrVZoz6Sr7/04J0iePYxyCBc1But3e3aFGXNpO3MZGQsnTOjyWWVuDCig0h4dgpcMO0lYPM+nWGXgofnu5f3819SuKUQpOL6nll3gpyDobz9QRBI4M4ui/t8fdLx7d6yBt3jD0LgxlajkEa/ny5bz33nvRddOnT+eSS5p7l0a+nMcjk3Z5HdGhVxsWFrJhYWGbbXMKUknPavU88VZBIPJ763a8wKHD7LvyKgAqfB4YnY/e1ARp4Nq8nez165tf5847yPzytWxc+C57Vq8AlD0EK5JJE0LTgqDaBoWEdhwLNsZWWx4vDk80k/a5Or60RS7MKSVbaaiuwkwbANg3S0G/Pfxv08J30LOHY5pmz2vsVNeqZFWrm6SO5u9XlgI9CZQLmvxgKrRIRu3s3amQrRYzgumO2Peo6TqGw4EZCkXbreMafzlsex3q47TBl+9o8WLtdRzrRpBu8T2LZNKRjmOB1h3HItXdrt49p61JkE6kY5wWFMAbzaTbuZMONqFpIQam3w8/2t3hsUr/+EfqVtTiGjkHFZkppccXm1b7mfF7bNa8dwD/XvvDPQQYghO8Q2HwUKxGaNzQvQd9OAZ6SZmZH3edWVUVrTIm/DARs6mJogP28CJd17EsKzoPePSY0Uz62ALH7jWlLHxqG2bAjJ4ep9tg3Fm5lB6oIRRoFXhNi5ryJiqK6knLaJ1JtxOklUbNooNYdUG8kwcSLC3G0hxoHjfOU8ZCqLp5FrG8QficToKHDxMsKiJw0L5B0MLvV1fKfu/hh2bYWbR9oWu3uvtYb2Reuanj7CiR0oeiAr8BHHg7q+4OX6CNcCY6atoMNh8uYej4iVw0/2aevv0WqkuPwEC7qaGzTFpZFodu+g6NGze2WmFCYw6gwX/bn1Nezz4NzynN/UtqNm5k1/k3t91Q0xk0YT4u3xnAy7AKtE3LyR7lwAm9XjVrRqbp1TT0ODcihtOFGQoRCnYwMUhKLtzYzpDSX7bIvlsnGNE26a6HsZbf+Wjv7vBnIWjatXBaJJOO1B5KJn0SOcYhWNCcSfs7qO4GwNF5z3VlWqjwrDnNQTp8sfnPN2DbG7E7ZBbAV98FT5yhK62/IO3MxmOFM5mk6bksPlrLh3uOcmXDHrJ3b8J35nRS5s7ttNwA/l1VNG2voGlbBbq71cdUg7pFz1Px90eii8qGD4ezzqR2+XIaTBMGDyan8BDF+Xk0HToUs3tzm/Sx1eUe2HKUkL/FozSzPKRkekjP8fH5n7Ydf91YG+AfP1pG0G+2mXSldZCOZG5maSM1H9k3HQ3bK/jvoVoCs/9krwsehLqXCCq72cE5YwbDPvc5yh99jLL777erIiF68dRQ6LrWImsORau71dZ3oDKcjTk8pGh2ZnnM04Juf/PY9u+OqoNkBwo5QkEXOo7ZnwFHwD5H3rR0OFyCy+Mlp2AkTo+XYFMjVigIutFpkA6VlFC3ZEk7a8Nl8bffEbJksIMRLX5vcLlYkd32e5jsSGeYLzdmmWoyCVSnhoN032TSRjs93w2nExrpYKRKN7QZgtX96u5IE5euNXeOjLRJK2W3WTtaD+mSNumTR7S59xiqu91O+wPTUXU3YI+R7IxpRh+31hykTfvTuOmFttuXboXiDVAwq+26LlZ3Rx4O4p2YxabtQV7aE+AcisjYu4iGwE7MIx93Xm7Ad+blgAf/7ir8u6varLcaB8T8rodPvqXrqPBNkjs8PjNYVxezrUNPTHW3FX6v0y4rYPysPDzJTgyj/bbHlhObhAKxF5x2q7tbVHua1X5ir3XhautwIN2yZQuf+9zn0MPPDrca7QCkhd+vFs6kI1WpmtaiTXrVP8FofjTo9e7LWcs1xzbjWKChec74H+zo9tAVZSmadtegGjtvoml86068oRqmW2kM1l14d1XR4Gi/U2V6SS0X4GCMkYcnKRVnbbhzo98+75/5/u385567ojfenWbS4epczeej4PnnmldUHoR/XwPOZPjG/9rdv/yf70EITBXE0Jw4nR6ycvPabJesZQDgtxp4f8eDTBr2OfJ8I5v7e/RydXckk9bbqXJ2hPujhBLRH6V1dXcPOo5FqrSdLb6nLX8OmgpH6+P18jltTYJ0IkXapI+hujtaFdvy6thQYfd8tIJQaveWxNn5dJlKWaiQ3b5mtcykW2bF314G7lT497VQusXuEBZPm0w6fnV3tL3T0KOZajDDDqjBQ4cItspq29O0fRcDvvMXrNrYmwGzIUSwsNZukwOGPP4YybNmYW3ZwooXX8QzbZqdpR4+TNbcuezfs6fNMKJEVXdb4f09SU6S0jof1mY4dQyHjhmy2gRppeJn0i2f1KOZCgMYWLKCicZGtB/fxuv3/Qe9RVV1dXV1c5AOZ9KRdm0NZXcIM5uHYEXbpPPPZME+H7sO+8EKEaKMb6h/sP6ep9jSwY1HhywLmsKd3r5/W8fbxpHvGsWU1Au6uPU3aQRuBLCg/j+7aX8OLMgG7sIH6ecDsHVvITghuLcasz7IoDGn2Bt2NUhHgpXTiXt0i2GGZRakhcCrwej2hx9qrsUQAs3lgCBk5ORxww8ea7Odf381ZX/diC/ZybTd+2kYGhlCF/5+9nLWZ4Vft71M2uGyA16H1d1df7H4v3djCFao1fCr1j8HTAtvSmxNBaltb5Z6kwTpRDrGIVjQnOXFBJZ37oCNz8Vu6G5/NqUo04pWS6tgpCeQGfthzxhuZzieVOrNdN56GhoCH2I4dWZ9fgzDxocz1ta9wtvJpKNtmw4tOqThyIwLuHDGOMzazh/yYZaXU/anB7Hqa8i8ekyb9ZGLlBY+yVr4Tr1l7+7I8CVferp9TBVuawoHK0eLNqhjYYbfq97Fh1YAuLwGjbUWZrimRNN0+2aq3Tbp2P2HuHTSPD5c3pFQYjEkaRyKVLaF56St3FhESn0KjrwpYOUSOtrYnEmHg3Q0kyYEA4ZBGVhTb2Lj+1/H/vDaF1YPfkINfjqekqUz4aykC3/71ow0+/LUGKqlOni0k617TjcMtMFuqLHPt1UXwDUwXFPVzSCNs1UW1nIIVkf7R3sWA8G2Hcmi20XGuDt1u6zhGi6r8rB9qo+hujsQsnh/Ryl1Tc1/8SnDMhie1f4xI9XduhH//Rnh72eHHce6qs3zpLveJh0yLZbtLmfzYbu/TMsHzRhmkOu2vUumv5bSX35ItWahVV+CboXQXV54bg1o66Lb6z4fObf/5NjfTxdJkE6gRAzBijuGt7bY/n/uJPuuTnfA9G92oUAWKlrd3bwsJkhHLh4OD4cDEymtNgB7n73LihgYCWQlFpjnYGhluPUd7bZJt8ykA+Fg4PC6SZ3d+UxjAIFDhyj704PtD9eK1lKEA0/4Tr1l7+5IkE4OP67U1HX2X3V19O8SNC3+VFKLBuzb9ve4L+PIySHvd7/DSO7gAhWZxcvR9b+30+OgsTbI0SK7KlbTDZRpcWBzOdZzzbNSVZbYeWDZvlrySY8un+wzYPgU+5flQc7O/iwAh6wPqdWbqHhrDw6Vhnf6twAoue9jGjLsGdgGNFUzYsV7WNbpgE7NQQeh/FognbrlzbO0fTq1nJ3BSpb6vBxNhZ2De5hJt3DR8Iv41uRvdWuf0JpqQiuqSZ6YS8anxne4beXfriAjUMybI3/BZRd2Pk/09pJavvfvdWSnuHntJ5exdsMGeHcTGnbvd03XcbWYsbCz3t0qaH+ntNYZZaSZqKtDsCK7t/NMeRXu86H5fOhKRYO0wgneDHucdA89t+ogv3htS8yynFQ3K+6Y0+5sYdHq7jiZdGD/fswi+9pV/Mc/ojm69rCcGLtbPHJ43Ufwn2/gzMsj92c/RevGtKAvrD7Ena9siv7eMnuuX7qU63csACC0nzg3pbHPGzAyMiRIn7BUIjLpOGN4I0F11m0w/oquF8dsru72FykOq+ehRIffbgD/8/ZGd6+3/x+8GS9wSaoDsL/4zn1VVOyripQMuB2AssZfE3p/GcljQow7+9zYL3D44qK1yKSd3agujT7Wsp2OJpH5zSM3F5HtI5m03++PPkHLl2b3DLV0naatW2OOE8nRm6raqX7fsoWGFcs77OgWqe7Wu/H+ktPd1JQ1Ul9l9y2wLHvfsoPVVJU3l6UuswlcUHOkERzpmEpREb7pSa4vQjkU1ZnZ6NUlaJobwh0OzVw3jpBO07btOLLGgKlT+/IbMCSdvPpyTn/pUdRlf0FzuCjb4MUdKsE5eAj1y7czJGmc/eJ7jzAWiMx391yah8rUzt+jU3dw5pgZTJrcPF/8K3te56ntz9CQrpE1JP6kLO2p2XmQGqrxpKaQ0cm+ltciS2vAm5rapdfJMKqpcB3A6Xbj9vmaay7QomPGXV5flzNpQuE26TZBOjJBRhcz6fANX3uZdKRjpu7zoKGwwjUo1lm3wsUPdzp3QUeKquzvzeAMLyMGJrN0ZxlHavzUNIVI88YPhB11HKt6+RWoroIkL41bt1Ff01EDRHtaBPaSMthhjw5JveQSkpxd7zhWFP6+RThbNEmGyuxj7kvN5YO8yTHbjc1N4dJJg2KW6Z7enW5agnQiRTt39zxKG/HapHv43FQsE6vmMGgWKB1Fkl1GvwWEM8Ro72Q3mgZODVp+LBpDddQG7clT0t05uHQ3O2rGc/idD+CdD0gdMDBmpqyWmXRzkO76+dAikyGEQijLilbVRtdHstZwZhIJ0pF5lSsqmmd18oXbZlVSEkMeezS6vN4fYv6zawH4+w3Touc8ouzPf6Fp0ybM2tgOZ61ZPajunv3FsexeU8rm/7mpLAan202wyU9OQQo73G52HbFfc7Bm4QUqDPt8rjJDvBIKkldTyFdW3M+GrJH8/bS5XFL6Hpojn0bfGDBgySAnN08awL7H/0jK5fZ7do4fDzWHqfEYbDp1IGc77HO8Z1iQ/BSLLMA9dCbRAUKtHvh0YzVQTdccgOyxQ3ANtjuJ5ZetB8DfTh+GjqjId6ALfTyscM2KQ+taE0bkxjHSRhnJlDXV3Pvd5fUR+VLXV1dBi6frWcrCDGexlRWVfLRuLdXTpqGnJLPptVfsYus6pw/2MQjsz2vrjk9x3qsKf/WUaRGMs33IH17m1tEcDlSkultzHVOAhuZpMT8zOY8fXzSO0/7vPaoagpRUN7UJ0qHKJqy6IGZJE5muXFIc2QQKYzvqmfUO0jx5aC43GV+cS15BAbsqd/OPzf/ocplOb/JzTeR7mJRF2VoHwSo/auE9kBXuLd+FNunWTVstr9FWtf3hnjTvHOb88pcA/OujAzz36g70/HTKJsfe9DmcOrHdVo8vCdKJdIxzd0PbiwfQ46e9KMtCNVbgHrqL9HNPp/7fN6O82ZROvpXF/7areTXD4Jq77iF51Z/YuqaOlWW5WMEdaEYmDUY6m3X77neQdpTrHOfg0scyLKmRA34HDjNEfVXsVIexbdJtO2l0RmvRpqeCQbTW84zr8YN0Xl4eI0aMoLLS/uIOHjyYzHB1t6VpJJ97bvNr+EOsXmjfWbtnnhMd9hZR/eqrNG3ahFXbfu9gaM6kW/bofm9LCff/b1ens5lNrW8gC6ixwAt8VFnDu6k1BLwW104fim/fLszaWgYMSoYSGDA8laljU8lbuQ99ucXgrGQuHZ+DKgU7/7PLUN3QhHvMGNKuvALTNNE0g4PzJsBLhynJVAwa9jkIv61ffwbyAu/zpbIkvCEXA6vcaLrOkFMmsKZ4B8NKqvAGQB81mmLl7nRik+x6E7cFf397B3vS7b/LoZCdpaw9WMoPX9zQ7r7DMn3MP39UdFiMfYK73hEzEqQ7nR86LFJjFbl4t8ykIzea6Tm5FFY1oICDWzcxdrxdlby9Yjs3vnMjdUE7eJxefjojakfAyPAgqnXN7/PtrSV8WDDU/uVf7T+R7lf11zAyCbZWb2Mip9Dob+SMONv/5uDNTOFU3jr0DpMMK1rdnYip4fzhTmCu8OQeuakeqhqCfOvvq/h/k4Y3T9hTHyR/h/2914AL8m8AoPSh9a2OeBpnjjoNAKtKkXrZLGoPL+YD7UmGpw7nJ9PbrzL+8PCHPL3taYx6xTdKI1lwIRVGFkFcqP0fQTB845fU+WNEA63Oz4iBzc1YZpUdpF0Z6bjDE7JohQ1c0eCGXY28vyt2AiZPspMx01t1LjuOJEgnUHObdM+PYcR7sIHZ/fGA4YPYuzlhxccBNpbbz5EO7VpNKFRlbxOC+mAV6SkhAqqRerMOM1SFwzGBKu9U/pdqfxHm6avIooImCyamV7KwzoOjsS76mDoIZyNxM+luBOkW0wqqQKDNw0Daq+52uVx8+ctfjtm2NhxkQ6FQTMexlplz0LTaBGk9yZ4z3arvOJOO13Hs6ZUH2VbceSepCeHe3U1KwwvUNPgJ+CzSfU5+ftkpPPPPFRyuhbHZKVACpw/P5PwLRlBVs4lioCA7lYHjs3nrfbvzGSo8dM/vR9N18n57N4d/8SEqYDVX1ZpuJgTstt36pIP8qvwgnD6b3w14iabSCq7cno87KYmbv/lF7n7iQX6w9EPGHoYPR/+E31QP7PQ9/Rkfp+Pg4z1HeT/csudIrcObD8W1Nby0peOe/eeOGcjkIenR33uUSdO9TDrYKpPWIfoZvmj+bWz+rf2d2VK8kcLNdrD4uPjjaIAGcFrhG8XDh9H9R3lnik5qIJWh9UNxWF37zhrh8vt1+/vkVPGzw7GNw6PbNTgsrHDnqfo167F2v93u8X3Tp5E8a5Z9A9LOuDozYOICPJqGClqcnpfK3pJacsuCrP3v/uh2o9w6+V6DkFIErBBKNQAGhiOZpPTm76tZVUVTwI/HlY7epGE1hfBb9vUky5vFOfntzzFeF6zj6W1PU9uyJu3i36GteQGOFqFOuwGmjrJnBzv1s+0eJyKS9NwwYxiXDE9i1NGD1C1dCoB/l/24XyOtxcQp9fbnN+DSGDM2M+ZYzl5+RnxCXs3v9x+X5zOfcKK9uxMxBCtOm3R3g3SLeYOPHA63HWkBzFaDUyzLBKcXU9WjWjxvsyDDx4afzbbLtcOP/4XN9mHx4NXtABgs3Q1F9tjNlvM/3/Lnf1FT38QEzSKr1glFXZtpTGuRranCtZAe24tdc4ezlVZBOh6jRY9Ty7IwDIPainL2rV/HqbX2ULati7XoFJIpmQMYNvkM9GQ7SJt1nVR3h//eeouOYw1++zzfdsEYpg3PjLsfwKZHF1J7APIHpNJQUs0Fp2Tz7cvPYuTAJHwuR3NmF/kYhG8EokNtHC220XS08EXd729RRWrogIWywNCcDDQGkBKwz9eo4UsZu6cR0sbwWONeyiy7BiIyrhUUocgcHI32hXX2mIGcNaL9ir7Bq8rhaIDLJ+UxPc9uatjXUM3bZZCf4eCqU8fF3e/vy/ZRXuenPtCqy47ZjUw6XLOidzNIB0yLV9cdprjIzqY0NHYU1TB5TAbe5BQ8ScnUB0NsLd3C8jWxE7P8YsYvuHD4hbz20mvs2bmHQUXFnOJ1c81N/2Dv7r28+sKrjE8ezm8PPA3pw+HbS9stz7qN9rOsT8s7HfZZGBgs+/yymPeuTEXt/9kzmr2bvYIhPnCE+4/4d+yiYcO/2z1+xVNPUfDa+5Q/sQ3ljz/u/GbgZlJhQQmHF5QwH5hPqt0sHKfP186GNWyvXUWwsQbNyCVt0A187fbmSXyK7vwpy7d+xOzJv0TXdAhZBMIdTt1Gx/EixWk3l9RFgrQrBc78Flr6h0ARjJwDZ17U4TFqamr44IMP8Pv9cLCSWc4GPIfL2PH+erZWVcVufNaZeGtrcb38MgDV5UfJyAqRpGlUlsd+/lwOF9BxR8ZE6nGQXrt2LT/96U9ZsmQJfr+f5ORkpk6dytVXX81Xv/rVT2bQjsS3Y+gMG5lX2lJ2ENB1refV3aZFSNc4UF5MXWUQM2AyKe1t9nqHU364xXaWBQ4vJs7mN4GGWV9DmhG0x146NQJaU/htehhnbGM72YSW3g+bi+zlygu8CMADTXeiO8JZ9vtgvd/1clv6IFAa5hNXovtaDU3KngHcgaYbWJqB0h3N56mVls//DYVCGIbB23/+I4VbNzEnvHzZE4tj9rn213/AGe7RbVZWdRiozXAnHgL+6HZWfR2+YBOTMx1Mz2n/O7DXUNQCKV4XDcBAtxbePoRZV4cVGdITNAEHmEFUKIQK16pohtFi2JaGFs6k/S1qNjSHZv81FVyUfyPJzgz7z6tr6I7wjZpu4NJdGFa4liEapO3PDihUeIzruWMG8rVzCtp9T2V7G/EfDTB3bDZJU3IA+KjoCG8vgLQkxU3njYy73+sbiiiv86NtWMfeHzyMCk/xauRfgCN7OpXPP0f5A+3N5hU+TZW17FHZDF7wN/Y8HmeinlZMpXj8aAMrc0/lVktxuqOYyQ47SP/xne38ZEw64/PSmmtflM7Fwy/GFZ7XeYB3AJ8d+Vlchgstcu5ME4fTTaorlZTIxC0WpFoKNAe42h82qanwPNJuN4pw9e4HVTG1CCpg2n8/h8ZRXw2PXWRw00F7nWvUKLyn3RDnyIqKfz6F8vvx765oN0B3V9DyU1i1kWDArjXSjExCrXukmyE0pTBVCF1zoUIWftPPtIOXcMra8/j7Ox+0e/yQCnFD4G4M4O+mZSc+P/gA0/cFmHk1+n+daAva3x+g2rWPGvdewB7ZNtIAf+lR9qanQ3h4ZuwO1dBiWteayOWjVcWDJ9jNvkHHqEdBetWqVcyePRu/3x+tJqqtreX9999n8eLF3HvvvTz++OPMmzcvoYXt9xIwLWjLqtiQpXDp2jF1HNuVk8m+tc0zSX1cD7AvdjPLguRsTHW0xXhonUATbH1lIeRPgcMO3KFs3BqUqtM5apYDfg6bk/GqmQBoyk1kTqlHS9u/q+9UuPl4cS3R9tMIxxG4NN3+eensB1l81yZ0Q+NTXz6FsWfGthO1zKQj03BWlZYAUOTJo0l3MmtUFm6nQcnunTRUV1FxuJC8FPtdVL/8MtXhO+t4mqb/Anw5HP7WN6mv3gPA3ZGV/4Wd7e4JDaPzwechsGkzJHupeu1Vdv7l8eZjX3QhpKfTsPQDyDmfo48/Run/W0nGNfZzvLWWmbSuR4N0Rt1+7rnvzwAkBQNoLqjaU09Fkl2lpzRwJDkx9g8GvggflDA8OJz8phzqhztpcrl49NFHmXY0l30T53JkDNQYlVzm2MKRj/fy6BY7SDkcDubMmcPw4cOjZY5mfS2qU73h6Wub2pskh+baI/e7b+Df3tz+506rh2wwqyoJhOdj70gAB04qCRxtf/rNlgYDg/csZddnv0x67VGotYO0EyipbgoHaXtb3dL4zTm/iQbplkLhGyrDNKO9uyOfvWjfhE6HYIU3cxsow+5hXrvwYNxNHZkenA4nu/M1VJF9XPfYU8j58hfjbl/x9DNgmljhWhbvpCwyrmo7scp3nl7Lkl1l/PozE7hyij1f/pd+/QzTd7+Gpqcyce6XGD3N/o45dbjI+BEATQ0h3n70CFar5w2oYCh2mFg4kx5XehaOoJsmf/sd6QC82DVaTWAHyvogaB57PHgQ6GTsdVD3gxuc/nRc/lZV1lYT069pf7jangUHyApYlOkwYlbsswMcHdTeHQ89CtI//elPaWpqYt68edxzzz2MHz+epqYmVqxYwT//+U9eeOEFLr30Uh599FG++tWvJrrM/ZZKwGQmLXtCR9ulI9Xd3XjaS6Q8TeGqXMOZgVLJZLkOoA8cRWmxC0KHsaxa+7GJk68ltOw9KF1G5E2YuHj/fRewHUhirOc0xnmguGEcFaFDwHr21o2n0LSDtEeDC9M6H1N6LFpeBvTw75ap+N8TW/nfE7HDrBQKws82+ONv/wxoaK5UPJQx3DUP3cjkaCEM8mzB8DmgGl75cBvejAIu8PhwNTV0WBYVrnLXW8+E1AWRqUv18LlSrT40kfVaZBy7ZWKWldO0LTzjnKNlJq1jhOxg6CGAv8ae+MNvrwITjuot7nYa7C3BA9UB3OH/LK99PouLi0nFjT/JjT8JwCKLBgI1DbRsbl+zZk1MkI5Wybdo9vAYHgxToVfWUlwY/wloSYFDpIdqUYfsrMc7/xs4zpgEGxxwENyfvRj3jzq+4S965afk+fezZdiXGT+jC2PyTZPab94KwL2fzmHlujLWfxyeykVvpLyxlCP1YIbbG1w44wZoaA7SumWhOWODtBn5G3XWAznS/O4ySL9mLP49Ve1u6jstG/cGu5bGCpev5VPMQtV+ql/fgxXu6OWbeRsqFMS/K1yl7zLazocP1Ck7h3d4HdH1mmERUgE0DDKHj2HwxCFt9musC6Bp5ViW4oa3bohe/75WfhRNgakis6IpmkJNOCy77feymyfHfZQrQJW/ihveblsz8P3FqQQtH66ZM3GNsJu+QmVlNKxcieZykjz7PDS3G0PXKSpxcvAQnDFzPO8WpbF0Vzk/yQ1RvisZwwpw9tntP/AkuABGmibrdDhnXpxpkntRj4L08uXLGTJkCK+++ioej32SXS4X8+bNY968eXz/+9/nM5/5DDfddBNTp05l0qRJCS10f5V81iA84zJxZPZg0H5YTKcmy8KL0fNM2jSjNTVJ6VMJhCYyJ/vX+K75Ks/8pYJAzdNArZ2RuZMxM8cBdrtZfeZ2e5IOd4r9FJhgE41+LzCEwW6NATkz0a3pKN0V/RTpaKAgqFk8Nu5JJuSlkZ3S/WaPz//6I3w1fl67dSoV+S3mez6yCa26BIr/AsDZK+/iqesDDN57Jw6z7bzQGhqG6cV0NGI6wlWIaRmoMpc9tjisuGk8h5JeJoskGvYuYrdjJJumzo0G0Nb8uovzr7wK5+J6qA4w/LlnGTjEvuuf95tXGGoVMaMgA5/bga7rTJsyhREFsdXEK2+/BQ4XkjrrXI6uX03FuRP4Yt4STh1wKqYyGbxFJzkEyTPPgV1gZGfBLqI9zjXDEQ3Smq7jbRiMOXEIh/3NGeslxQHSg4qlvp2c2zAGU5l4rz2VVK8TFt0NxevgrPk8VLOVI3t2cdquNDLzBnPeDd/gR//7A3OW72J8oWLN5PN51TeSb80eyYwRA9ixYwerV69u85AQzWibSbtDGn961CS7uoyq38cf439Xq9+/1/AP9u3WuLX6ei7kbJ6o+C8v7H437r5RE8EeO/YO7H6n423DntXBYcEXXrqc/NAkxjAGDY2knLf5zaaP+M0muKjxfJK0TFyq/e9ey0yacCYdaWqJBulOMulIp3TN0PFNHohvcscd9ZybwvMJhG9bWz7asnF9KY1bmmdoMzLtrDlYYjdbHKw7yId7WjwCMqxM7caRWs+W6gqM/9/eecdHVeX9/33vtEx6QkhCIEAo0kEkgIAICCrWFduq6FpW/dl27bu6+6xuc/XRXdfVx7K6lnXVxd4LIiKKQqihdwgBQgrpddo9vz9umZnMTBIwQIDzfr3ySubec+89cyZzP/d7zrdsT9XPazfb2dhQu47i7YURx2leMEM6V5euJWDT71fTqwO4yECzRFq3pO2a/rCTnpNAUox7ZToJXH/qVRQu1GtjN9jsLIlzUpaUTFmvAVBTBitDqtvlGL4S61dGnCs5LZ6GSpW69OVs95aSwsUEVCePLf4r2KN/x0d6RwAJNKilPLbsMZw2JxcNvIheSb2itj+UHJRI22w2xo8fbwl0a/Lz8/nggw+YMGECjz76KK+99tqP6uTRgiMrAUfWj0vGbg/xZgyYFsmPCcEyU3Ybf6j4cTiML7bhUWre7AM+DfORfkXaOrb0XhJ2vrENwxi9+1YcqDhsiVZxn9ZrNsWuvWhpq1jTDOby2oFwQcBPih9Wln/PNkeIhakAKXDHPg0VFYfm44tujajpD+AMRE8wYNfsJHv1tcD8ytE4hAOhqLw25iECNrhi5QM4tTh2JdjJADIa/WQQeQNrTfmaXvTQdOcRu9uJanil96OEHHste3cHA4tbPB4GDBoUdrwZzmR36cdpCPx2hZ7pfRFCWA58qplZzQgNCRge54rdFhY2pKDw8xlj6Z4bfFgpe2oVvr0NDO1WSW5DBp5AM82Ve3ULu7IaapqhvJyExjoSqxqwNyok21UGDhxI1Q8N2JtL6bFP4OjvZ29cKt1z+jBwYA9qDKebiAQfaqQlnVkj8HQ0xhrYma1QkmXHrirYjX8woQrs7ThNioAfBYFQbBGx9bFocfpJbIFEvy04zijYNQeqYkcFhKGebjX2g7cl0loAxd46A14Hp7tNS9rejsVtYDpeaaa6h1jSgTpdjOOGduM15X2mf9pAWt9gFrYfyhbz7KIo6/ZOcPeEObv0H4A8ezyC7gink4+3vsee8sjvhipsXOC4HYArsmczIDOPZwufxeduRrMlU67W0aSoLFq8lrWijBPsPdCANxatRm2jWpnTNpy7y/XPvcEex43dU6hP1KetbVodlT3099xnWwOZ+/RZr21DUmhITCShNngffmPLG6xU1uHOqWLLFo1xYhZCsfHu2g9odEX/5/xf/59ASaDBVsKrG14FoKyxjL9M/kvM/h4qDkqkx4wZY8WjxmLcuHFMmDCBr7/++qA6drxiUxUURV/etgqUH2wIlqZZ06iWSAufJdJmas1Ni/dSsWcbFbvrMe8WQoHxzS2c0XsG9J8GxUtgzZusHAD2QT9l4YfLGVJegZqdTtKofmGXfWv7drpvOo0zhmXRI6Vj2XkUpx1XbncUm0ryq09B7X5uyrqQprwotaQ3693UHA5+N+GBDg/H5vc2E/AEwG7jzil3oigKlZttaPVwttPPynFpVFSVMDZ7HGOyxkQ9x/LFS/GXbMdTUxkRJx3QBC6jqtToMeNw2hUKCgrwRVk7C2ZqMiwiwyp1qA7sqp0mjOIY5j3euHlrDYbDV4jjmKKYD1vhT0umZWs33LQDws/c554JaXECfLqEdCDd8CZwmA/eStC7WxjZtMwKbaYAtRbp4Jp0cLvapFv2jl69GPDVvIhxALjqxQK+27qfv/90FLNG98KUk8o5m2gurODO/Lt4YPLfoh5rsvZ/ZzCieRkFo/7M+Fm/aLOtydYXp+EvLeWdGa/zzZ7dFBQUoKAQKPsJ9036FZeP680/Hn+U6romesT1iHkea7o7oEWsSVtLVu1Md5uOY8qBirRpSYc8GAWMojSuvBS+KP+O/HoXaQRFOjMxi4k5kVO9K3ZV0+jxM6JXCmnxTpIrW0jbWoI/OZ2Wnhmc0AQnNEWv7V7TrVD/YymsYQ2TmMRuI8dREUbd+036XIfZtmZlYbvv818YNbb9cNo+aErVXzY2rmd+vO6wekNJgJNW6e//u14q2zJ6cEptMLxrV+MufEl6XHcC8dh9jficyVxZ+PuYS5PJTju4ADKY3ns684vnU9JY0m5/DwUduusHAoEwJ5xbb72Vyy+/nKKiovA1qVbk5eWxcmXk9IOkbeyqnggkuCZtTncf6Jp0IIol7cNhD2BXmvEYN/cdheXs2lBsHqT/UgQjPR4uTRoAgy6F+kaofxFyVJg8i1fe2UamZzXsKqFi17qw6+abf+zYzv4D6rHO7owUyEiBL1fqP604sU9/VNXFd4P60PDAqx0+r9Z/BDhduNwJ/HSw7oD1dloB5fWNjK7rRunIIRSUVDA6N51h/UZFPUfRrn2UlmxH27+XFocPBYV/ffQVIk6gCYFb0W+Qw0cMg4CfgoKCiGlhAM3YZjOcUEzBs6t24u3xNAtjCsIUaYcp0qYl7bBiZLGKi7Sa0rCZXsemSPvIyO1DcvdM2L0MmishexSb/LWUNZbRL70/4y64xOwhfjMk3XjIcBr3gNBiJqGYMeyhgmE+VJhhbdGwsuy1ToVpJTOBmpqaNg2D0kAqifSiusFLUVERPXv2xNGOg09oSU/zvajAKdhx76qnyVmOW3NTTRNJ/hQaVpVGPY+/xYht7jYYzd6HmiV7aWzWP6eAX6PBfyo05EHI8fvrqtixdR97t1QjNEFGnJ16mln/RTE7P2lfDPK1KzlJXIHPXwDx0LRzPwtv06tm9YjLJd6eyIJ3t3G2506K+6j0DTk2Y/sgRm8MLV6jz9sMCwiEEDg2qKiKgvD58GtrqEvURdbu8+PyRHcAbInrhkAhzlMFDgdVCRpJ9T4QKg5nCjbFRoNdoVlpJN6jj7s3Lvbsgl/T8PkFuWq5tU1LycVfWUlCVTUjB+Rz+rTTAEhd+Rqgz/r9bNBsSkcOZs2nQS/tK4dfyb+3VLGlrIWLe3Zj/8atlGeOQdFiX99m5vlXe3PF4IHML55PVUtVzPaHkg7d9ZOTkxkzZgzjxo1j/PjxjBs3jiuuuIILL7yQL7/8koyMjKjHrV+/ngEDBnRqh48HbIZIWzcty3HsQL27heWAJIRZU9iHIgLMTH2ML5t7UOeH3sPTyeitO4R8/YkgwQ+aAomaFrTiRbgglKUOYFftDkZ0s+NuNWW1cV8dvoBgYGZixL5oCE1Qube4w5VyNONBIsvdlyR/21nBQtmp2PEBfXuNpnmjvmaXabeh2BU2Nt1K3y/hTqbCOviK6HHdDl8mPdz9yQkkoar6nGDclkUoih5LXOjuj4bKio8+tGZCavfv56NnghZsvMNNmj+TRHcyKd5u9HD3x+ZPZVz9cPqWZZHgiKde6B5aoskP2C2HJEuko1nSrUROMTJHOUIs6ZPO+QkjTjsDXjkXijbAxffyh/q1zN+yjkEnXkKvwWb8p4bPvDuYIm2cL5ZIR3Mc0xpNkY69DGSPlsBH7zAAjf5mnn/qpagPO0GG8z3DYXs9S7a/wsCBA5k9e3Yb7Qkr6RmaFnQMdlhRRdWKKmwOBWyQFehNzZtbo57H5/KCAgnDLkYVCTR8sIMWPBCnR2hU++9FKVfAOL4RD3Nc3+tT6UZlyR3AalHOsMZ8Av52psYBFRsqNjxGAZ14ezL9E8NDvBp8GjbhQLQKTwxowkrEE4qReQAREAQQCEUloAg0h2612/c0Yi+NLlRpvWeg2JycXPAHSh027rk6jYcWbIBAN/qMvIksdx+eyH6DJc5NXL78d6AKbn1metRzgR47/6dPNlAUZ3is25xwZwUlv76P2q8XkDnmHrr11o/f65yL6c84JHkg/XtPYg1BkR7dYzRz1u8n0FiDs1sVwza8xMi03eQ89mjM6xe/sQH2NNJk08PtAMqbyvmy6EscqoNpvafFPLaz6ZBI+3w+Fi1axKJFi6y4wW7dulFZWcmQIUP4zW9+w5VXXkn37rqzg9/v5w9/+AOFhYX861//OnS9PwZZX7keR9oiAv4A727bR3qCExLdnNTiYfiPcBwTQgEFbPhA89PHtYo0l5O6Zicn5Hdn6Km6c8nHn2skoFvSCZoIPiBY4WWGRZeQwkfZ53LtLRMZ3Tst7LKj//gl1U0+5t15KgOzIh26onbV78PT1LY3tUn1kxsQDX7yMzpWWcukwlZANQ1kN/Sm8t+6J3h/oH/igcxQ5AF5+PCz3L6dZsWLx5g7EICm6E/+Y0qGU6M0sdW1HKfPyUnFI8JPk2Y8vO6D3Oy+oMGkPTPASMq101VCs+IlUN4MJKE4DSE246DtoSKtx0O39qo3LdvsOv0hOqD5sZszYlYJRRWnqq+L+wLBhySBZk13K8Z0rqsdkY4WgmVmbbMlxLakTT8MXyuRNqfvK5tqrNm8tLS0iOMBWip3EyeaaHJm0OQV7N/f/hyOalS5qvzn8zTk9QWn0yqB6vXV4bS1oAhdBMv8pdi80WPmfS59LKtaSvAY2ce8SkB3oFdgX3OR7lRpsN/ejIgTqEIhOaCPfY3Ng0fx8aS7mTJ3+7HMrux3sSduYeZ3WcRVCNz2BLYmDMah+ejbvJ3qQAsPdzuJhP6P8+u53SHpzmB/a9bjKderXeX3SWP5Ln2GQlUg0eXg1IEZKDb4qKWW+uxEMKqwbc+fRpM7egrO/MImnH7QVDupqp+e7iHYtA2IkBCsgM9vPeTbHDHmmQ3srfMemP/bxnKAldQHwivm+f0RvlIOh8NKDmUTfhQg3u6N6bQWen0venY0gEZfI3cvvJs0V1rXE+mGhgYKCwtZvnw5y5YtY/ny5WzcuBEhBJWVldxzzz3cc8899OnTh6SkJIqKimhoaODBBx88rkKwfixCCG6adxN0qyEOeNGItqFbGomaxrd6QbqOn0/TLEtaE/pat4rfKjNpJgAJu9la092QoGnBqfaQmzqA0xAAT5Qn8hYjXrJ1us22sNkdxCentN8Q0Gb0oXFFeUge1o5hr7GDH5QMJw5npGhUt1Szt2EvSc4kkpxJlDSU4FAdVqyv1dcGP3upZr09eppLh1CppZJaPcITn+KnAt0TNaD50YQg3hGPOy4Bm8NBbXkpuOzsj2siw52BQ3XgM9ISViXWU+tupGrb14S6ni0o+ZbNagaJQHPAQ5wKjZ5mIChiirGGnOTVzbWA8OMyE7yEVGcyQ4vCpvMUYU13x7U0kt5ci7OmEp/Ti6jTZy8CHg++spDpyBZ9ij5Q32ht95XqU7xtTncbFnigdf5pQ6SbvEZ1pl69uPbaa6OeY8kj53ByyyIW9f0NX21ptsqVtoW9hx7z27xqFR6HHfr1s0Q6sPJ16vetQps4EXrnssVdzRZ32344ypL/sGTEPSiqwgfuJiYZ2wcn38tWdQAPJur+E2n+Svp7QPgTsFcMYWlPlVxW4hA+krMc2G2xx8qkKl6j0VWDnTR2NuhW44cjHSQ2NzN92TK8djspfe3Uumqod4bfNQZWbqPPDiO70A44q9W5AxugMSGe+vPOs7Y5VYV//HyGVbSmNf++/3saqj1oqp1Mp5+vrvszWz5ey8aqCisE6y7b9XgcKqXuJuxOler3os9MAAwpq+dXxFHtu83YosJ7WxFiOK4T4/GWZ1nHC9soXCfqQurZk0hyq5SqDocDn1k217zXOdqWPtWYxfEKQYorhVtG3UJBaQEQzIZ2uOiQSDudTsaNG8e4ccGUb01NTaxcudIS7WXLlrF9+/awp/k//vGPvPLKK+zcuTPaaSWt8Gk+ajw1+t91I5g2KJtkp8qCnZ/ToKr8bvn/YlOTWztTx+T0qh0I4yMOBAR2FZ5KT6Rl4xxc3dJwVASw4+DdTR/whvo9AMKmT/MKIFETwfAva7pb/wI4jSfa615ZFvHU2+zT25qWV2eTeHIOiSfnHPBxcS+uhN01JM7sQ9bQoRH7Vxd9yd0LH8Wu2nGoDpr9zVw77Fruyr8rom1g2TL4dA9ZWVmMHj1a37jkWagpovcZt5Az6RJKS0v59rntqIlORv/hYgCum3sdy0qX8dipjzEzbwYbvv2ar57+D6JvGv/OK+S64dcxsvtIml5pwak5+W3mP6h31nP52kCYSG+t2862qmpOJBWf8BEHrCxdycDhwXFJnJiD1uzHs60GAIfqCtb9DalzbIr0u1vfJScxhxtH3oieFlTPOHbqjgJO3VEAc2EbUNYzByZPpmntWrb9/Qnres6hs3CdcBY1c96k7H/eDhsvNSGBQCAQ1cJ1eutJVZporquirCwoAtUtNXiVBspqjSlddwKe5ugx6d5AHB4tHtVY1vH5fDHbmqTefg+OkWOwCx9x5WVQX08jTayq3YV3Qj7ThpzN8IZ6KvfvJ9DOA2FOXBw9r/8Fa5e5cSU5qA6J6HfYBGP6pvHJNfrMz7Jly/j00y24VTeK6uav1+Tz9ic7qKio4K+zhtCvX79Yl7H4w+IFvLNlOTbNj+kAWp34H3yqHeiJIrzUxr8DwLenJnNaSC6YhFMm8Vn3ePZUN3Nyv3SW7KgiwWXjlqnBpUmH3w/7K7AB7k0rGDX9zJgCDWAzHghrk/uhiRriNlVRY8+lJU7gCRhOkHu8xAF9XXrbxqXR1/gBcoDzcdIYCEn9ubQU6IWzby+0xuDxiqM/zr56Njt/JWxcsBd3UirN9TWodjsbqzRqm/X7mM0wNkwv/FgoxgOix7jb3nzizdzMzW0ec6g46LSg8fHxnHLKKZxyStCLrra2luXLl1uivWzZMnZ1IFOQRKclEHTKaNn7U269cCrDu8HNGz9gUbybT3d9eUDnG9PsR7gMb0zDcezDJDfNVQWQnMRpNo3ewJqKFWzZqU/lna1mAy6EIugeCIRMd5seTLo4j+yZwsZ9dTR5o0/N9Ux1k5YQPfnDkSIYFhO9z4PSB2FX7Pg1P37jfY/NHhu1renRm5mZycknn6xv3PwQ1BRCsi3seqEzFaYgmqUbzXAhEeI4NqXXFL63fY+maVw/8nqcSU6yi7+Hxd9Y55nQdwrd05Jo3LYBm+FQ2OANz8nuykuh+/Uj2HOfnj7RqzXjtrWypBUbJ/c4mefX6E5Hy0qXcePIG7HbBGv7KpxVEEeiYZWaKWvNNXBNVa24YOOk+i+bI2y76naTOG0qc+bMYevWSOspBbjABWUF63m2oNVOF/qCLVC0ooZ/fRMr//WtrOVWtP1eyFyC1+PlhTsXWpZxbLqTkZtIUzegvp7taaksbkphSu4QhuT1IBk4r50zmJSWNgK7ccbbaW5GHw4FvhKn4KjKgi/0+O2SEiONrl8fI1e83RLAwsJCysrKGDZsGMnJsdOIXjboMqpbqnEEtlnbJuVMwtYYAPZhFyqTciaBAj/JPBdCRXrSBH5I68XiHZUkT87jTcdOeqTE8cBNwTViUVEBTz9tZLMTloNjLOzGrNnWgbrj4conCqHbhfgTlrK/ZhENwonTGXzMdCc7GTktdszx2r21zF1fyj12M1RMgdP+h4ZvFtJcWMi2HgP5Pk0X5tN3LSOnsRJ79ghs6f35tGA3/6Y/SYqHphYHL/036NhqFwHUpBxw9LT8UqJhMx7wPIcwMVNH6dRyHikpKUyfPp3p04MfdkVFxworSLCcQPSKRjZufHU53e2N/J+nis88Cfw9cCGaUCLqHwP0qG2k3/7w6kspdVupNnIiKIZbyNV11cxVhjJTXUatT98pGgbjr0zVG/qKAQ9XJJ/A0LLNQUtaC7ekH7loBLdM6x/p7GOQk+o+oOpXhwMrwUQMke6T3If5l86nsln/8iY5k8hOiF6SzgyrCvMgNosGGJ9jtIcCl6q38eoZIIIiHQiKtF21Y8OGhsasE2aRlpaGL/U0yqvdBOrqsSUnMeC6u3F9+xVL2YDNEN4WX3TP23dOmM+4lTlsrl3KVLsxgxBSfGVs9lgeO/Ux7v32XuvhJCPRwaaeCnP/9lv6J45lSHYSI4yCIY5t2/jutddwDR3KkCeftK5T99Uu6r4qJu2yy0ib9buIfpT+TQ+jcrvd1ro2QIPHT4svQLzTTnyIo6HW7IeAwCcEQrPhamm/EpdZaETXZo1gMH9s9u9uoK6uFtzgKPEws9kJq2tZsPoAArxDcCY6aGlRUIQDofhYoYyEOmBJeN4Bxas/sLncDpKMVLRr1qxhzZo1zJ07l9zcyOxeoYxgBHt7B2/hE0pGMGn8OD7kXhQNnp3xLIqiEGj0sY/gtRWbgt1YYjCXq1rfU4LFW/TXtnYsz1HTc1k9r4iWrfpDg+uEgXiLimjy1NOkNbIrUER6xomYJx11Wi+SJ8aeDStbuYdX1xfzxzCRfp7mpSV4t3zGSuU0Xk3LZXB2EuOXFpBRsgVsTmzp/clLdDEsNXK9OS8jgczK/XhPewAU1fJLiYb5bmMnsz18HPKaW6YzmaR9zPzGKg5AoaS2BR915MYFuL66noc9ZzC6dyrv3zIp7Djh9bLllMlodZElEndmGmuUxrft+toabp11IXz4FR8749gC/M/UCznpLN1e+M99t1O+czsTE3oZ97lW3t1WukqFPt1+XOKWw42VT9kfexo0PS6d9LjY1atMTJEOLeKB3RDpQGyRNi1pr+UXYIi0IZoONTwky3TUdOTk0PPxx8P60Nq7u9kb/ZayPWUPgYrl+vWiOI4BOIzIAZ/pg2AkyTh9SA8m9ewTdr4D8e4OxRz3a6+9lszMoAPSb95fy5sFxdw5+QRunxHMKV3+7Gq8u+pY2ujnxJ8Pp8+w2BW45j96KdO9C9g+4k7eMAynnz1yMgkJbf+PrvtuL3s2VbOt1onHAyLZyVZvgNx0N4OzY1uysbDZFNJO7Ebg/TLsdYOx22uitlOEDXdTD9zJTpxuG6eeeipOp5Pm5mY2Gqlfd+/e3f4F44Pr1zt37iQhZEpaC/ix2R3BTHDmtW1q0DGqpQWH5iVO2MIcN82/zVwp7Yn0kIk9GJTfjc0jdR+kE55dys4L/oetngY29MwgPqmW3EHBWZSqPVv4vo06KDWl9YyvLuV7e8j/3luv0VhWTHNWGjZbFeOrl3Lt0L4EutvYEkgjK07QCxjrbGBwn2aSM7oTHgjdSPmGBtIUFU14EWmxZ/o8/gDrauqordvHd28UsWb+XKssrzspmRufebnN8ehMZD3pLoQ53Z0SF8+LN01AAM76PfAu4IjjnWsnMKRH5I1Da262BDp+7FjLgxJADTSArwVz3UpVQhzHrCQYIZ6S5o3fFB9TpLXw6e6jEVM0P/nkE7Zsaav8ReRxEydODLNsTMEJs6RNkfZ7w64XCASsetatRVox2piezHZFH3ervnEb2bPMWGtVVUEDj88TtZ1fBB9KbNaatJlkwxBp4+HAtKQDxkOZGiVTVmzvbqNtrHrFZmy4rZVjT7TyrATHRBPgTnJa657REArYFD8Om6Y7Cvl8BIS/zWMARp2Wy6jTcnnzzY1Ub9yLOiCJD1q8/HRkFndffHDpjNcbZS/npqfw6sgAFDwLOWNg6n0RbTN6JaHaVDIzMzn//PMBqKqqoqysLKJtNIrWrGLT9wtJGzKKorJyvL6gw5zmDxgi3WoMbAo2VWV43Xoy3nuOmxCwC/7v2v+zmgTi4iFvKD5PMy7A1o6jFRhlY1UVNA1/eTnC58NufOaVe4qp3BO9YEgsxgFL6B3c8O4c/Xd2OjbqGVezgvWfrrC2afEqvYDaPaUsWvFu1HOekJxPWjfY07idxUUftduHk4ClReHb/N7o37NDhRTpLoS5Tum2u8k3axFX6I42NrsruK0VIuTm1vvfr4SlRbTfcyvs3oUl0gRg48f630YpwtCbbTAftCE+luNYBwsFdGFCxeFARBp0gbniimCVoTanu1tZ0hCsZ22KdF1pHZ/v/pza8lJasnLR4myMqnRSvbqaz3d/HmFJRyP4WdlAgxZ/9JuHj6BIq7ZIxzHASrtpWtLm9W1RHsras6QDNR5atkZ6QpsPNoHdjbRUBf9Hc+v85GMjY3/4caJJ74sA4hLavlUFDJ8LGxoORxw+n4833ngjfKajDaqqdM92PUQtwGfr9rGyuGPVtM4Z2YM7ZgSTg5hLQH6HQt/cJihcCd2yYET0fBKtSU9PJz29/dkcgCFDhnDWT69gzZo1FL33Hj5vMBwp4Pfr07YRlrSCXVXIbd6NEtMN1cqChCPOTe6QETHahRyhKKhxcWhNTew451wAslUF17Qz8DnbtsRbU1zZxDebK/iZPcQPZ9wNNK9eQ8u6dexMzmZdt/5cOjYX75dfEKipISVQBd2hR0I/ZvW7PWqhH5tm/D+rHnoNjV0Fq9ETYO3eWpw2hZP6pOGKT2TSpbNxxSf8qCqHB4MU6S5Es18PYXGZFhmAWeLP3kbRDnP6VlEi8hYHb6RmxrEAbJ+vb7E5AG+YyFvWmWVJt/LuPoot6VBmzpzZbkYqgPLycgoKCqivD0+aEn2625g+80eKtBnna6ZzrFleQ0GL4SWVrtdeHlCXQW1dLQXo2xVg3fwvgrHNngZY8yZ49L6UVsUBTlRPHdhgc/l6znw5/Gbat2wS2eVjAP0z/+6pD4lzLgTfpXqDNwW4V1Hv9zGp4UKS9iXyvW8bA7ZOpLtnGHvmefElbAs7Z22T/uDYVO/h+3eD+xLLG+kGeHbU4tkRvp4rEGhxRnKXOVvxEpxqnAnMJAHW1LJ/TeQ6sAa44tv+rPzWQ6hGt27daGpqOih/mJ5Z3YBy6lv81LfEriUeyj8X7ggTab9mpotVDtvDrdPIHe/1hYq0/reiKnoQtJWiVMFmU7AZMyzzM6aiDBjDh7cFnYCLi4t59T//IS07h9v+9FBwmaQdEmdMp+6jj63X8X36MuyaG1Fj1HmIxVcbylhYuZxhman8yvsMXPIK9D+NiqefZv/cbyhyDGBhxmSeuvoMKj78DO/e/Sg1G2GAhipUnMS4nnF7zMtwM/GBR2Jef1NpHX984ju6JTj539+dfkB972ykSHchTEs6zhbyD2ZaR6HC3QpLZKN8kSxrCwVFESgn36TvUO0oG+OguMASZgiujSq21tPd4ZbX0c748ePbtFJN9uzZQ0FBAY2N4Z7TUae7YziOQXCq16k6UYSCaNFvmMNPGMiWHxZGvbatuZEfNi5vtVUBwpc8nELDB/hRKFEhq74vE4ouwO1PJKWlO0JrxGOIdHlLX1RfiJ/ILgHoFuMIpgBQWFRMnpGgZd8+L/sIn6b02eshA7wtPgrnBffFKXBSvE2vgd6KQEhIUkMAvB0MJGzSBLWKgiu+PUs6KNJXXHEFe/ZEj2Fvi4SEBLKzsxk+pIHqpvbjrGubfNz8+kq8reK7TUvarqqH7Xvjcun/ex6PB9VmRwv4w77Xik2xlg9MS9pmfLc9qpMEhyOsTrL5sG+z2Tos0AA9H32UnIceCm6w2zv0PWuNGTv/neMUfnXnr4O+MMZ9yWbcp5w21UpmIhrLUe3fknHznVHOqFP18svUvPc26bN/0ub1rSx4x5p3t0RfS9zTsOegairvrd8LQFyo1RwwRbp9S1pp9WXav6cej3mzUVS9ws5Z/2vtV4v1NagwS9rMYWymII1IC3r0WtITJ06kqamJoUOHdvjGkWgk4WhsbGTt2rXWdnN6NOqatPGZqWEVzQyRtjlxGlmmFEXhgksupcAu+HLNR5Q3lXNi5mh6J8Xw6t2/BfaugMQsyNYtZleci7qGsewthunbr2TGjisRWvh7U0PK8U08zUVS5SLYvVTfMPU+6DaA7SXFvLfmQxIcCVx6wqW8s+Ud6n31nJN3Dpnx4Vmm6purWbxtFXaXyujTe4fti1X4zB/wguFM2zCupxU2BrCsqIqVxdUMy0nhlAGRU8JnnJCKrZ2Ye785UyQ03G43AwcObLN9W0Tz+4hGVaP+3QpoAk0TVnIgM52vTQ2xpA+xSFuWtNeL3a6LdCDEQVKJsyOM9WrFZcemKtgNS9qv2GN6d7flExELpQMzVO1ht/wURNj0slmAJL2ljhOqi/GvW4sWmqnQ14izZxvJYEQtoqmiVehgJKoSI1XtEUCKdCfz20W/5eMdH7ffsA3MKVEgZLo7tidiNEu6ud7L239ZTlO9uU6pYG/lRKOokXG8kY5jrdakj2JLukePHlx11VUHdIzpHRwIBHj33UhnFPPmCEQ4jimKgqqqaJpGSUmJLvh1kNGiC1F8fDx2h4NJl17JK6kLWbJvI+dMns5Z/c6N3plv/wpf/xdGj4efPGxtXv7ZTvYW7wShhCVhm3HNEOJTXCRnwL+M4gv9po0jbctW2K/HTjP8AcjNRlTVsqT2IzLcGTxx0W/4wzsLKGks4ZczL2NE9/D8++Xl5SzeBnanysSLOpabv7Gxka8NkZ500QlhN//l87eysKKCmsQACVGWYlftr4EFNW2eP8ksFIfWZrvOxBGy1uvTNFzm98ksQ6oe/unulpYW4uMTCSgqJftKaDTSZ3qmJuPZXoMtycF+VwN2zYvDEGmf4ohISPRjRLozsFki2erzNO5L48o2Ma5sE7sXPhm227NjB9Vz3ox5Xs9mvdSmNVMY6/pWNkYp0sccqytWA7rzVzSnm/awq3bOygtJ1Odv35IWUSzpxlovmiZQ0BBAZp8Uhk3pH3acFf4T4t0dtKQN8Wmq1K2uWt3KP5pF+mBwOBycfvrpbNu2LWJfYmJieAEZ8+Fq1Wuw6VMA7NoFeHHwxhtvWM1ORk9+0qg08uclfwZgR42esaPNusnGWjSucEsv/+w8hp7SEy1k2jUuwYHdiDluaQyuraqqCu4QJTT+R83rRnh3R7lJx3Qca4NAiCd663MmuPRrr95dw+rdNR0+Zyj32wE7ONTDd1MNzQPgCwiMtxFck1aVwz7d7fV68Wb3BeCtD2J4L68Gt6I7yAH41c61pDsDW6glHULilClUfvARe4tLUVDolaan7PXt1e9PLWvXUhoy4xULM297zP2KnO4+Zqn36jfS189+nYFpBz/lBlC2YxuLXv0I/76RUBoHe+9j+NTTGTalVfUY4wYYKtJmlRtF0b1jp101lMy+4bVgVVvkzdasa2ylzStZBS+GOE4caE3rY4BJkyYxadKk9htmDtF/+xr1H2Acq1jDYKtJs6JSq6oIRbDFtYUdm3eEnSLVlRr7/JZIR+YOjk+OPdOihAiEoqrgTgvdCUTx7hbte3e3XZUqHHMNv3X4FcCs0T0pq2uhtqljVdCicUJpKuyHVOqhakdkA9UOKbnBqdNNn+kPU+LgLW8Xghcceo5y51v/BuP7NLTBwwuOGlIa7LDScIQ7xA6XSUlJjBgxguLiYhqqKtECARLT0oMOoCHU1dWBCOhLCD7wKXaryInJkRZpM9lK6+lmV14ecS++xrWPLcDtsLHxT3ra0EBNDeWP/51AdfvlJNXkZJLPjTFbZWA+JMjp7mMMIYQl0knOH5+EffW8zyjavhdIgSageh11FeURIm1mqyKKSAvMMJ3IL5s53R11TbpXPvSeCPX7gge4kmBo2w4XxzVDzoVfFkJLjbVphvEDwJq3aSl4hvcGTKZmyFnkkRd2eGZ8JmOzoqchBdoU6bYJ3mgURYXUkHVkQ7A7I066LWLFSAOkJzj5zdlDOnyuqMzPhu9AKXwdCl+P3mbiL+CMPxvt/wAVm37UJRXgdPPtbA9u725u94JVUD0xevWozkJRFC666CIA/vXL66ktK+XyPz1GzgmR4/qPf/yD6upqbIr++XX2mnRnYDOuG1FjHKwSsKHLDbbUVHr88Q+ddv2Y5VOPAFKkO5Fmf7OVOCLZeeDZilpjTlOOSN1HRm5fFqz14G2O4pYTiJzuDtaLNZNiRN4cTeEO8+4216QT0uG6z3/0ezjuSM+Lva9sA3FCcMXmb2FfFGsPgAdjH2+EPh2oSNtD1s3jEhMhfQxc+C9wxFn9bW1Jm46PBxQn3QamSHc0bvmAGXgGFP43+CATiuYHfzMUhyQGbzTGctpvISl66teO8Nv31+LTBPefNYQ0I0xs7Z5a/lOwi7xuCdw8tT/Y3TBoZjtn6jzMWPiPn/hfHM7IqJCGpAywObAZ9waf2vXWpNsSSVO4D2XaYatCoMBKRHSkkCLdiZQ26lVZbIotorxhu3gboTk8eYK3Tn/dK76WXrkJLFjrweeJTP0Y1ZI2ykWa03nRLGk1iiUdTJBxfK09HxbiQ9Ja1h14iJBF1rADam6zO7jmb88ihIbDZfg2jLwkrI2VjlRoBLSAZUlHuzkFU5kK1q5dG9FGURT69euHO2Tdr63p7k6h98lw98bo+4oWwSvnBL9fQkCLMQ194mxI6Rn9uA7w4YdzafD5uWXwVNIydCfDIlsJb/2wipMT07n5pAkHfe6DJT2nJ9Ule2iojF5TO+BKBrcDFJUmWzxe1RlhSYf6EBwJYq1JA/jMPPe2QyectpD/6UmPfB32P57idvDZ7ZMP2bVbc8yI9NNPP81jjz1GaWkpo0aN4qmnngorrXk4eHyFnls5yZl0YE9e9aXwVD54w60A785RQDJONYDdcAwJ+HxoWiDcMo5iSWt+8587dnpJU4irS0vYWvCDdf5Y7SU/klCRzhoB5z8Zu20sErpDatuFF6LRrVfbx4Q6rPmFv8016VBrOJrHu4npzARBy+yQWdJtYTrKNRvrlb6mYNRCXMdqmMfCnHINTWkaFid9BDj3jvso27HNynnQmo+/+pqy/ZX80O1ktig5aIotQvC6jiUd+R78h2F8E+PsZCW7KKvzUFIbbhiZpXgPF8eESL/55pvcddddPPfcc4wfP54nnniCM888k82bN4cl8j/U9ErqhaqonNn3zAM7sHxDUKBtwalJj9CtG1dcHI4hZ8H7LwHga/HgCkmkb1m/0aa7hemtHeVma8QzFhWuoKhwRdi+9krTSQ6CrKGQ3h+qi2DM1dDzpCPdIwvTkgZ9XbqtNem4uDimTp1KUVFR1HPt27cPj8eDxxOZpjQn58DrgP9oTEe55mo9B71pRat2cP64IjFm+U6vP2jxhXl3HwHsDgc9B8Ve448vWA77K6lzpNCs6TMrti7mONYRS9pxCC1ph01l3l1T2FnRGLHvcH+ux4RIP/7449xwww1ce+21ADz33HN8+umnvPTSS9x3X2RS+0PFfePu475xbV9PaBqidbYln0c3eHNOghu+sjZ7b7kWPFU4r/8Ee99+oLwMQuD3thJpM2lBVMcxI8tQlC/boAmTKdmykZZW2bR6DBhIYnrsikOSg8SZAL9YoYfltBOnebgJtaRf3fAqPiNne6wwwqlTp8Y8l6ZpVFdH5r1WFIW0tLQoRxxi3Kn6b6HBEyOCWfTiUn50HmanIdLhlrRZdvTIrWO2hZmAx64E+9z11qSNCII2RfrQ9i05zsGo3NRDeo2O0LXuFAeB1+tlxYoV3H///dY2VVWZMWMGixcvPoI9i2Ttgi/56oVn0AL+KHsnwybg60jvab/XRkO1B7vThd/TQk1ZLZoWXO9rrvfT4kpFtQeFu7UlHU2kU7N7MOvXbTgqSTofRelyAg26GLtsLjwBD88UPmNtj2sr010MVFWlW7cu9JDncEPGINi/OdwXIPvgqlyFndqw5nwhMepH2pJuD3PJwRaS+KWreXebl41mSZuOY/YuVq/+UNH17hYHyP79+wkEAmRlZYVtz8rKYtOm6CEWrafi6qLUYT4UFK1aEUOgY6Ooabz/+FYUZQd+r/5P+d5jBaj2VnW6JzyEIgIkbashZ0AqAb9meOi2X/JQIlEUhT9O/COL9i6ytg3PGN6h2tpHBTcugIrNwdeKApkH5oAXjWjT3WaWqkPp2PRjCIp0sM9d1ZL2+jUufvaHsH21zUYFui46vp3NUS/SB8PDDz/MH/7QeTF1HUUzsg9NufI6hk2dEdyx9l347B5E3hReKvg5AKpdQUEBxWUlo1AUO0KAv+kLUEKTVwgrHeSn//iYxLQ4Gms8eOuD4Vqt83pLJK05u9/ZnN3v7CPdjUODM+GQ+AA4okx3By3prvlgfDRY0iluBwlOG43eAMt3RS8Z2jP1ACNojlKOepHOyMjAZrNFFEkvKysjOzt6/OP999/PXXfdZb2uq6sjN/fAPWYPFDMe2ZWQiDspJI7aCdj9+F0JKKr+j3f946fijAv/eN7+0zyK161GC8QuwVdXrv+E4kpIwHmApeIkEkn7OKNMdwe9u7umpWeKdA+1zrKl7eXNfPddjdXGdAo8UiLtdtr49JeT2VQafZZTVRQm9O9CSyqHkKNepJ1OJ2PGjGH+/PlccMEFgP4UOH/+fG677baox7hcrrDwkMNFMC92K6s2YFTTUYJ9ilb159w772PPxnXBurAGTatXs/W97ynJmUx8spOM3CRqy5uorWim97B0pl45GZtdemtLJJ2NOd39zILtvLtSzx+9vVxPQtRV16TjjAf2HrZ6etiMqJJ9e5m/b11E27ACMoeZvhkJ9M34cd73xwJHvUgD3HXXXVx99dXk5+czbtw4nnjiCRobGy1v766CaUnHFGk1OH2jRllvcScmMXBsZHKEuup6GmrnUtZ3IJ4W2LsVIB2bE3qc0JfUrIPPqCSRSGLTPVF/sI42Jdst8cgJXFvk5+fT0uJhR1kNHr+GTVXITXNHOGI5HA5OPvnkI9RLickxIdI//elPqaio4IEHHqC0tJQTTzyRL774IsKZ7EgjYom0UekqoOhPuKpdOaBkKCLgJ616CyO8i3FdcLm13eGyMXTSEYhLlUiOE/7wk2FMGphBIBCedCPOYeOsET2OUK/aJjk5mbPPPqv9hpIuwTEh0gC33XZbzOntrkIw1V7b093tFbiPQNNQEPRlB73P7/ej+ymRSDpGVnIcV53c50h3Q3IM0zXdD49RRJSSkkCISBvZfw5QpIVR2B279OCWSCSSYwkp0ocRMwRLbR2E79dFWkNfwzpgS9rM3R2l0pVEIpFIjl6kSB9Ggo5jrVYZAuaatDndfWBeoVYVLGlJSyQSyTHFMbMmfTSgRVuTrtgMy/4FQCCKJV378Sd4i3e1ed6WNWsBaUlLJBLJsYYU6c5k23woWQm9J0DfUyJ2B+OkQyYw5v7W+jNgT9L3GyLt2baNknvv7fDl1QQZUyiRSCTHElKkO5Mtc2HpP+HUe6OKdNQQrJYa/XfPMQRyTwW2WZZ0oEbfpyYlkXxO2+kaFaeT9Cuu+LHvQCKRSCRdCCnSnYlZe1eLXhQ8YDh4hU13GyUBmXIfgXrTu1tfkza9tu1ZmfT4/e87v78SiUQi6dJIke5MTPEV0UXatKS/f3cHDTVG/u2G23WhfsGGT9Ordllr0obYy7VmiUQiOT6RIt2ZmJa00KLuNtekS7bVodrMlIGp+q96AN3STu+hry2boi69tiUSieT4RIp0Z2JNd8cQaVN0UXEl2Dn/lyfCm1dB7W4470noMRLVptAtJxEA4Tfin1uHbEkkEonkuEDe/TuRH9b1Z33Za4zeVEL+zMj9QZFWcDhtZPZJBlcROIqgpwtyk1sdoIu90kXr0kokEonk0CLv/p1IQLPhFQn4/NGTkWha0JK2qlwZzmREWXcOpvuUz1ISiURyPCJFuhNRVb3Os9BiiLQhuoqiBmOlNVOkowix5TgmPyaJRCI5HpF3/05ENYq8ayL6/qiWtGaEYNkcEe1l4QyJRCI5vpEi3YmYM9bRwqSFpoEw1VsNCbOKbUmLgHQck0gkkuMZKdKdiDkrHYgy3V25pzj4Qgm1pA1FjzbdbRbOaF01SyKRSCTHBfLu34mY090iynR38fo1Ia8cIY5jxnS3tKQlEolE0gop0p2IKbxaFEva79VrRucMyu+445gRsqXY5Jq0RCKRHI9Ike5EVCuXSWyRtjv1bGI2m6Kb3GYK0WiOY9Z0txRpiUQiOR6RIt2JtGlJ+7xGG3uwrWlF6xsiT2hNd0uRlkgkkuMRKdKdiGVJR1mT9ns9ACiKbjGrdrWVSEdbkzYyjskQLIlEIjkukSLdiQQt6chhDXh1BzHFmNZWbUrQaQxAjTbdHTsbmUQikUiOfaRIdyKWSItoa9K6Ja0aFrPN1r4lbTmOSUtaIpFIjkukSHcipsd2W45jKB1fk7ZKVUpLWiKRSI5LpEh3IsG0oLEdx6w16VCRVu2gRMn3LUOwJBKJ5LhGZsnoRKKuSZesgu//gb+4GgClpBCYibpjHnww3zgw+sdghWDJ6W6JRCI5LpGWdCdiTXeHWtLfPwnr38ffWKW/bqjU21Zvgx0L9G2JWdFPaIZgyeluiUQiOS6RlnQn0rxhB3Ai3gYNEQjo09SeOgAC7u7Q7EVkjYJSsA+cCmNP1A/sOznq+cwqWNJxTCKRSI5PpEh3Ir6SCv13EzQuWkTilCngawZAuJKASrSU3lAKtt4nQn5em+cTZvENmbtbIpFIjkvk3b8TSRjSBwpBKDb2P/8CDQu/xbG7gvQeIIwpcGH4ilmlKtvCtKRlFSyJRCI5LpEi3YkkDO5tiLRK84oVNK9YAYD7NCfCYYi0mY67AyJd/cYbRmM53S2RSCTHI1KkOxHVyAuquB1k3HILNe+8g7+8nIBfQRgjrVkiHR5y5S0qovShv6DV1wPgKy+z9rkGDDz0nZdIJBJJl0OKdCdiTksrdpXuv/wFjT/8gL+8HDQFM523KdJqK0u69rPPaPzuu4hzuk86ieQzzziU3ZZIJBJJF0WKdCeiGJa0wLCSjWlqIfQfANMXzO4IF2lhZCRLmHIqaZdcYh0fP3bsoe20RCKRSLosUqQ7kWCctGFRm2vJoSIda03aSFzi6tuXpBkzDnlfJRKJRNL1kSLdieiWtIbQBPwpE4qTACdCU6zylZpf/6O1SFvhVor05JZIJBKJjlSETsRMOqKhQsCDgmE2J/UMrklboc/RLWlkuJVEIpFIDKQidCLWmrRQ4aSrod+p+usp9yGMeW5rutsR7t1tWtIyBahEIpFITI5qkS4qKuLnP/85eXl5uN1u+vfvz4MPPojXLAt5mFEtxzGVfb7BlLgGUdb9JIpKnfg8ehYTb4suxq29u6UlLZFIJJLWHNVr0ps2bULTNP75z38yYMAA1q1bxw033EBjYyN//etfD3t/TEcxDQfvzRusbxx2MqwDT5MPAE9TANUGDme4xSwtaYlEIpG05qgW6ZkzZzJz5kzrdb9+/di8eTPPPvvsERLp8ClsOz4Sq3fi7NuHPfV6+eisPilk9e9Jeo+E8IOlJS2RSCSSVhxzilBbW0t6evoRubbqChfeVLWWk1b/g+nDKnC69KGefu0wplw+CEWNsSYtU4BKJBKJxOCotqRbs23bNp566ql2rWiPx4PH47Fe19XVdcr1lYwBQGnwtaHDwh9AGIHSSqwQK9OSltPdEolEIjHokpb0fffdh6Iobf5s2rQp7Ji9e/cyc+ZMLrnkEm644YY2z//www+TkpJi/eTm5nZKv1tXq7KMZS2AMCprmM5lEWiy4pVEIpFIwumSlvTdd9/NNddc02abfv36WX+XlJQwbdo0Jk6cyPPPP9/u+e+//37uuusu63VdXV2nCLXaagpbUXXrWfgDaEbsVetpbhMhLWmJRCKRtKJLinT37t3p3r17h9ru3buXadOmMWbMGF5++eXYlmoILpcLl8v1Y7sZgSnAQggURbEsaRHwY6YcU2Ja0oaIS0taIpFIJAZdUqQ7yt69e5k6dSp9+vThr3/9KxUVFda+7Ozsw94fRVXQ/KV4Gz7A7p6MGpep7whoQUs6xpq00KQlLZFIJJJwjmqRnjdvHtu2bWPbtm306tUrbJ/pqHU4URTwNc4F0YS/aS5K2s/0vgSCa9IxLemAXJOWSCQSSThHtSJcc801CCGi/hwJFEUBgtcOcxyzLOkYa9LSkpZIJBJJK45qke6SKMHJCXNmW/P5Q7ZJS1oikUgkHUMqQiejqEGRthzHzNJXxBZpq420pCUSiURiIEW6k1FCLOld5fPQaGVJx5juNpOZSEtaIpFIJCZSEToZRQ2GdjU276PR5UALBEU6VoiYtKQlEolE0hop0p1OIOyVpirWejO0nxZUWtISiUQiMZGK0NkIX/hLRUELyDVpiUQikRw4UqQ7kUVz/oPfsztsm6YoCH+oSLe9Jk2s/RKJRCI57pAi3Yl4m5uMv1TACUBAUWjetNFq0/DNt1GPlaUqJRKJRNIaKdKdyNifXERqr5/jSrkRxZYG6Ja0Z+dOq03JnXeiNTdHHmxZ0vIjkUgkEonOUZ0WtKuRlJ6B051FS2OLldQk6fzzSMUG6wpACPD5CNTVobrdYcdKS1oikUgkrZFmWydjxkEr6GIbP20qGbfeYmzT0RobIw+UpSolEolE0gop0p1M0DFMH9qAzxeRSzyqSGsyLahEIpFIwpGK0MlYIq3oFnHA7wsW1zBs6WgiLaQlLZFIJJJWSJHuZBLTzIxj+pp0wO8Plqk09Dv6dLe0pCUSiUQSjnQc62ROv3YouzdWsWZeAbvWbCbg86G1sqRbNmzElpYedpzl8S0taYlEIpEYSJHuZNxJTk4Yl01RYSJgrElr+pq06VS2/+mn2f/001GPV+xSpCUSiUSiI0X6EGGzOwBY8t4cln74DgCq04lr4AA0rzfqMa6+ecQNHnzY+iiRSCSSro0U6UNEdv+BgL4mHfDrVbCyThhMv//585HslkQikUiOIqRIHyKGTZlOn5Gj8XlarG0pmVlHsEcSiUQiOdqQIn0ISWzlHCaRSCQSyYEg430kEolEIumiSJGWSCQSiaSLIkVaIpFIJJIuihRpiUQikUi6KFKkJRKJRCLpokiRlkgkEomkiyJDsMAqJVlXV3eEeyKRSCSS4wFTb1qXMm6NFGmgvr4egNzc3CPcE4lEIpEcT9TX15OSkhJzvyLak/HjAE3TKCkpISkpySqCcTDU1dWRm5vL7t27SU5O7sQeHpvI8eo4cqwODDleHUeOVcfpzLESQlBfX09OTg6qGnvlWVrSgKqq9OrVq9POl5ycLP/ZDwA5Xh1HjtWBIcer48ix6jidNVZtWdAm0nFMIpFIJJIuihRpiUQikUi6KFKkOxGXy8WDDz6Iy+U60l05KpDj1XHkWB0Ycrw6jhyrjnMkxko6jkkkEolE0kWRlrREIpFIJF0UKdISiUQikXRRpEhLJBKJRNJFkSLdiTz99NP07duXuLg4xo8fz9KlS490lw47Dz/8MGPHjiUpKYnMzEwuuOACNm/eHNampaWFW2+9lW7dupGYmMhFF11EWVlZWJvi4mLOOecc4uPjyczM5N5778Xv9x/Ot3LYeeSRR1AUhTvuuMPaJscqyN69e7nyyivp1q0bbrebESNGsHz5cmu/EIIHHniAHj164Ha7mTFjBlu3bg07R1VVFbNnzyY5OZnU1FR+/vOf09DQcLjfyiEnEAjwu9/9jry8PNxuN/379+dPf/pTWArK43W8vv32W8477zxycnJQFIUPPvggbH9njcuaNWuYPHkycXFx5Obm8uijjx5ch4WkU5gzZ45wOp3ipZdeEuvXrxc33HCDSE1NFWVlZUe6a4eVM888U7z88sti3bp1orCwUJx99tmid+/eoqGhwWpz0003idzcXDF//nyxfPlycfLJJ4uJEyda+/1+vxg+fLiYMWOGWLVqlfjss89ERkaGuP/++4/EWzosLF26VPTt21eMHDlS3H777dZ2OVY6VVVVok+fPuKaa64RBQUFYseOHWLu3Lli27ZtVptHHnlEpKSkiA8++ECsXr1anH/++SIvL080NzdbbWbOnClGjRollixZIr777jsxYMAAcfnllx+Jt3RIeeihh0S3bt3EJ598Inbu3CnefvttkZiYKP7xj39YbY7X8frss8/Eb3/7W/Hee+8JQLz//vth+ztjXGpra0VWVpaYPXu2WLdunfjvf/8r3G63+Oc//3nA/ZUi3UmMGzdO3HrrrdbrQCAgcnJyxMMPP3wEe3XkKS8vF4BYuHChEEKImpoa4XA4xNtvv2212bhxowDE4sWLhRD6l0hVVVFaWmq1efbZZ0VycrLweDyH9w0cBurr68XAgQPFvHnzxJQpUyyRlmMV5Ne//rU45ZRTYu7XNE1kZ2eLxx57zNpWU1MjXC6X+O9//yuEEGLDhg0CEMuWLbPafP7550JRFLF3795D1/kjwDnnnCOuu+66sG0XXnihmD17thBCjpdJa5HurHF55plnRFpaWth38Ne//rUYNGjQAfdRTnd3Al6vlxUrVjBjxgxrm6qqzJgxg8WLFx/Bnh15amtrAUhPTwdgxYoV+Hy+sLEaPHgwvXv3tsZq8eLFjBgxgqysLKvNmWeeSV1dHevXrz+MvT883HrrrZxzzjlhYwJyrEL56KOPyM/P55JLLiEzM5PRo0fzwgsvWPt37txJaWlp2FilpKQwfvz4sLFKTU0lPz/fajNjxgxUVaWgoODwvZnDwMSJE5k/fz5btmwBYPXq1SxatIizzjoLkOMVi84al8WLF3PqqafidDqtNmeeeSabN2+murr6gPokc3d3Avv37ycQCITdKAGysrLYtGnTEerVkUfTNO644w4mTZrE8OHDASgtLcXpdJKamhrWNisri9LSUqtNtLE09x1LzJkzh5UrV7Js2bKIfXKsguzYsYNnn32Wu+66i9/85jcsW7aMX/7ylzidTq6++mrrvUYbi9CxyszMDNtvt9tJT08/psYK4L777qOuro7Bgwdjs9kIBAI89NBDzJ49G0COVww6a1xKS0vJy8uLOIe5Ly0trcN9kiItOWTceuutrFu3jkWLFh3prnRJdu/eze233868efOIi4s70t3p0miaRn5+Pn/5y18AGD16NOvWreO5557j6quvPsK963q89dZbvP7667zxxhsMGzaMwsJC7rjjDnJycuR4HWXI6e5OICMjA5vNFuF1W1ZWRnZ29hHq1ZHltttu45NPPmHBggVhFcays7Pxer3U1NSEtQ8dq+zs7Khjae47VlixYgXl5eWcdNJJ2O127HY7Cxcu5Mknn8Rut5OVlSXHyqBHjx4MHTo0bNuQIUMoLi4Ggu+1re9gdnY25eXlYfv9fj9VVVXH1FgB3Hvvvdx3331cdtlljBgxgquuuoo777yThx9+GJDjFYvOGpfO/F5Kke4EnE4nY8aMYf78+dY2TdOYP38+EyZMOII9O/wIIbjtttt4//33+frrryOmfMaMGYPD4Qgbq82bN1NcXGyN1YQJE1i7dm3YF2HevHkkJydH3KiPZqZPn87atWspLCy0fvLz85k9e7b1txwrnUmTJkWE8m3ZsoU+ffoAkJeXR3Z2dthY1dXVUVBQEDZWNTU1rFixwmrz9ddfo2ka48ePPwzv4vDR1NQUUaPYZrOhaRogxysWnTUuEyZM4Ntvv8Xn81lt5s2bx6BBgw5oqhuQIVidxZw5c4TL5RKvvPKK2LBhg7jxxhtFampqmNft8cDNN98sUlJSxDfffCP27dtn/TQ1NVltbrrpJtG7d2/x9ddfi+XLl4sJEyaICRMmWPvNsKIzzjhDFBYWii+++EJ07979mAsrikaod7cQcqxMli5dKux2u3jooYfE1q1bxeuvvy7i4+PFa6+9ZrV55JFHRGpqqvjwww/FmjVrxE9+8pOooTOjR48WBQUFYtGiRWLgwIFHfUhRNK6++mrRs2dPKwTrvffeExkZGeJXv/qV1eZ4Ha/6+nqxatUqsWrVKgGIxx9/XKxatUrs2rVLCNE541JTUyOysrLEVVddJdatWyfmzJkj4uPjZQjWkeapp54SvXv3Fk6nU4wbN04sWbLkSHfpsANE/Xn55ZetNs3NzeKWW24RaWlpIj4+XsyaNUvs27cv7DxFRUXirLPOEm63W2RkZIi7775b+Hy+w/xuDj+tRVqOVZCPP/5YDB8+XLhcLjF48GDx/PPPh+3XNE387ne/E1lZWcLlconp06eLzZs3h7WprKwUl19+uUhMTBTJycni2muvFfX19YfzbRwW6urqxO233y569+4t4uLiRL9+/cRvf/vbsJCg43W8FixYEPUedfXVVwshOm9cVq9eLU455RThcrlEz549xSOPPHJQ/ZVVsCQSiUQi6aLINWmJRCKRSLooUqQlEolEIumiSJGWSCQSiaSLIkVaIpFIJJIuihRpiUQikUi6KFKkJRKJRCLpokiRlkgkEomkiyJFWiKRSCSSLooUaYlEckzRt29fFEWhqKjoSHdFIvnRSJGWSA4R33zzDYqiMHXq1CPdFYlEcpQiRVoikUgkki6KFGmJRCKRSLooUqQlkgNg69atXHfddeTl5eFyuUhMTKRPnz6cc845vPzyy1a7qVOnMm3aNAAWLlyIoijWT9++fSPOO3/+fC688EJ69OiB0+kkMzOTWbNmsXjx4qj9MM8F8MILLzBmzBgSEhJITU3l7LPPZsmSJQf83qZOnYqiKHzzzTcUFhZy4YUXkpGRgcvlYujQofztb38jWj2e0OOi8fvf/x5FUfj9738fc3tJSQnXX389OTk5uN1uhg8fzosvvmi13bRpE1dccQXZ2dnExcUxatQo3nzzzXbf0/vvv88pp5xCcnIySUlJTJ06lc8++6zNY9555x1mzpxJ9+7dcTqd9OzZkyuvvJINGzZEtC0qKrI+00AgwOOPP87o0aNJTEy0Ph+J5MdgP9IdkEiOFtatW8ekSZOoq6tj0KBBnHvuudhsNvbs2cO3337L3r17ufbaawGYOXMmcXFxzJ07l6ysLGbOnGmdJyMjI+y899xzD3/7299QVZX8/HwmT55McXExH374IR9//DEvvPCCdd7W3HXXXTzxxBNMmjSJn/zkJ6xdu5bPP/+cefPm8dZbbzFr1qwDfp9z587l8ccfp3///px++uns27ePRYsWcc8997B7926eeOKJAz5nWxQXFzNmzBicTieTJ0+moqKCb7/9luuvv56amhomTZrEGWecQU5ODtOmTWPXrl0sXryYyy67DICf/vSnUc/75JNP8ve//538/HzOPfdctm/fzsKFC1m4cCFPPvkkv/jFL8La+/1+Zs+ezVtvvYXL5WLMmDH07NmTLVu28Prrr/Pee+/x3nvvhX2WJkIILrzwQr744gsmT57MkCFDWL9+faeOk+Q45aAKXEokxyHXXnutAMSf//zniH1NTU1i4cKFYdvMurVTpkyJec7nn39eAGLAgAFi9erVYfsWLlwokpKShNPpFFu2bAnbh1ED1+12i/nz54fte/TRRwUgUlJSRFlZWYff35QpU6zzPvfcc2H75s+fLxRFETabTezevTvqcQsWLIh63gcffFAA4sEHH4y6HRA33XRTWA3sjz76SAAiKSlJ9OnTR/z5z38WmqZZ+5944glr3FrTp08fAQhFUcRrr70Wtm/OnDlCURRht9vF2rVrw/b95je/EYAYP3682LFjR9i+t99+W9hsNpGWliaqq6ut7Tt37rTeQ69evSLqDkskPxYp0hJJBzn77LMFIFauXNmh9u2JdCAQEDk5OQIQy5cvj9rGFNy77747bLspDHfccUfU4/Lz8wUgHnrooQ71VYig2F544YVR98+cOVMA4tVXX4163MGKdO/evUVzc3PEcSNHjhSAGDduXJhACyGEz+cT6enpAhC7du0K22eK9AUXXBC1PxdddJEAxA033GBtq6ysFG63W8TFxYk9e/ZEPe6WW24RgHjqqaesbaEi3XpcJJLOQK5JSyQdZNy4cQDcfPPNzJ07l5aWlh91vlWrVlFSUkL//v0ZM2ZM1DZm+NYPP/wQdf/VV18ddfvPfvYzgJjrxG1x3nnnRd0+ZMgQAPbu3XvA52yLadOmERcXF7F94MCBAJx11lkR67t2u91a2y8pKYl63lhjY24PHZsFCxbQ3NzMpEmT6NmzZ9Tj2vssLrrooqjbJZIfg1yTlkg6yL333suiRYv46quvmDlzJg6Hg1GjRnHqqady2WWXMXbs2AM6344dOwDYvn17u05GFRUVUbfn5eW1uX3Pnj0H1CeA3r17R92enJwM8KMfTjp6vcTExDb3JyUltdmfAxkb87OYP3/+QX0WmZmZxMfHt3mcRHIwSJGWSDpIfHw88+bNY9myZXzxxRf88MMP/PDDDyxfvpzHH3+cW265haeffrrD59M0DYDs7GzOPPPMNtu2djbrKCKKN3Z7qGrnTrCZ7/Ngr9fZ/TEJHRuzjwMGDGDSpEltHjd48OCIbW63u3M7J5EYSJGWSA6QsWPHWlaz3+/ngw8+4Gc/+xnPPPMMF198sRV61R65ubkAdOvWjVdeeeWg+rJz505OPPHEiO1mSsxevXod1HkPBKfTCUB9fX3U/bt27TrkfYjGzp07GTVqVMT2aGNjfhaDBg066M9CIjkUyDVpieRHYLfbufjiiy1LuLCw0Npnipff74967NixY8nIyGDDhg0HHa7zn//8p83thyMlqbmGu3Hjxoh9TU1NLFiw4JD3IRqxxubVV18Fwsdm+vTpOJ1OvvnmG8rLyw9H9ySSDiFFWiLpIM888wybN2+O2F5aWsry5csB6NOnj7XdtNS2bt2Kz+eLOM7hcPDggw8ihGDWrFksWrQook0gEODrr7+OmZzk2WefjXAO+/vf/87SpUtJSkri5z//eYff38EyY8YMAJ5++ukwp7LGxkZuvPFGdu/efcj7EI3333+fOXPmhG175513ePfdd7Hb7WFx0llZWfziF7+gsbGR8847j7Vr10acz+Px8NFHH7Fp06ZD3neJxEROd0skHeT555/n1ltvJS8vj+HDh5OcnExFRQXfffcdzc3NnHbaaZx//vlW+969e5Ofn8/y5csZMWIE+fn5xMXFkZGRwSOPPALAbbfdRnFxMY899hiTJ09m2LBhDBgwALfbTWlpKYWFhdTU1PDss89y8sknR/Tp//2//8dpp53G5MmT6dmzJ+vWrWPt2rXYbDZeeuklsrOzD/m4XHrppTzxxBMsX76cYcOGccopp6BpGsuXL8fpdHLdddfx0ksvHfJ+tOb222/n8ssv5/HHH2fgwIFs376dgoICAP76178ycuTIsPaPPPII+/bt44033uDEE09k1KhR9OvXD7vdzp49eygsLKSxsZHPP/886rq0RHIokJa0RNJBHnroIW6++WZSU1NZsmQJb7/9Nhs2bGD8+PH8+9//5osvvsBuD3/ufffdd7niiiuoq6vjzTff5MUXX4yw7h599FG+//57Zs+eTUNDA1988QWffvopJSUlTJ06lX/9618xs2r9/e9/55lnnqGuro4PPviAXbt2MXPmTL799lsuvvjiQzYWoTgcDubNm8dtt91GUlISX375JWvWrGHWrFmsXLnSWu893Nx+++289dZb2O12PvroI9atW8fkyZP5+OOPufPOOyPa2+12Xn/9dT777DMuuOACysvL+eijj5g7dy5VVVWcd955vPHGG5x66qlH4N1IjlcUcTDunxKJ5IhihgnJr69EcmwjLWmJRCKRSLooUqQlEolEIumiSJGWSCQSiaSLIr27JZKjELkWLZEcH0hLWiKRSCSSLooUaYlEIpFIuihSpCUSiUQi6aJIkZZIJBKJpIsiRVoikUgkki6KFGmJRCKRSLooUqQlEolEIumiSJGWSCQSiaSLIkVaIpFIJJIuyv8Hgbb+HEZXkNgAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "labels = ['$m$', '$b$']\n", "\n", "fig, axs = plt.subplots(ndim, 1, figsize=(5,ndim*3))\n", "fig.suptitle('Trace plot')\n", "for i in range(ndim):\n", " axs[i].set_ylabel(labels[i], fontsize=16)\n", " axs[i].set_xlabel('step number', fontsize=16)\n", " for j in range(nwalkers):\n", " axs[i].plot(samples[j,:,i], c=f'C{j}')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 67, "id": "a3fe1477", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Flat samples shape: (7920, 2)\n" ] } ], "source": [ "# We flatten the samples received from all the walkers after removing burn-in\n", "flat_samples = mh_sampler.get_flat_samples(burn_in=10)\n", "print('Flat samples shape:', flat_samples.shape)" ] }, { "cell_type": "code", "execution_count": 68, "id": "ca8a1256", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(7920, 2)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "AstronomyCalc.plot_posterior_corner(flat_samples, labels, truths=true_param)" ] }, { "cell_type": "markdown", "id": "3ee5de22", "metadata": {}, "source": [ "**Notes on Metropolis-Hasting Algorithm**\n", "Here we used a naive implementation of the algorithm. However, there exists sophisticated packages that employ more robust improvements to better explore the parameter space. Few examples of such open-source packages are [emcee](https://emcee.readthedocs.io/en/stable/) and [pyMC](https://www.pymc.io/projects/docs/en/stable/learn.html)." ] }, { "cell_type": "markdown", "id": "3e509bea", "metadata": {}, "source": [ "### Inferring cosmological parameters from supernova data\n", "\n", "We generate distance modulus data $\\mu(z)$ given as,\n", "\n", "$\\mu(z) = 5\\log_{10}\\left(\\frac{d_L(z)}{1~\\mathrm{Mpc}}\\right)+25$ ,\n", "\n", "where $d_L$ is the luminosity distance estimated by observing supernova. This distance is related to the comoving distance $d_c(z)$ as,\n", "\n", "$d_L(z) = (1+z) d_c(z) = (1+z)\\frac{c}{100 h_0}\\int\\frac{dz}{\\left[\\Omega_m(1+z)^3+\\Omega_\\Lambda\\right]^{1/2}}$ .\n", "\n", "For a flat universe, $\\Omega_\\Lambda = 1-\\Omega_m$. Therefore, in this model, we will infer two cosmological parameters $(h_0, \\Omega_m)$. " ] }, { "cell_type": "code", "execution_count": 69, "id": "008d5e48", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(100,) (100,) (100,)\n" ] } ], "source": [ "def model(param, zz):\n", " h0, Om0 = param\n", " param = AstronomyCalc.param()\n", " param.cosmo.Om = Om0 \n", " param.cosmo.Or = 0.0\n", " param.cosmo.Ok = 0.0\n", " param.cosmo.Ode = 1-Om0 #Flat Universe\n", " param.cosmo.h = h0\n", " return AstronomyCalc.distance_modulus(param,zz)\n", "\n", "param_true = [0.70,0.30]\n", "z_true = np.linspace(0.01, 2, 1000)\n", "mu_true = model(param_true, z_true)\n", "\n", "dmu_0=0.1\n", "dmu_1=0.001\n", "z_sample, mu_sample, dmu = AstronomyCalc.generate_distance_modulus(n_samples=100, z0=0.3, dmu_0=dmu_0, dmu_1=dmu_1)\n", "dmu_sample = dmu_0+dmu_1*mu_sample\n", "print(z_sample.shape, mu_sample.shape, dmu.shape)" ] }, { "cell_type": "code", "execution_count": 70, "id": "b99fbd0d", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(7,6))\n", "ax.errorbar(z_sample, mu_sample, yerr=dmu,\n", " ls=' ',\n", " color='C1',\n", " marker='o', markeredgecolor='k', markersize=5, \n", " label='Observation', zorder=5)\n", "ax.plot(z_true, mu_true, c='k', alpha=0.8, lw=3, ls='--', label='Truth')\n", "ax.legend(loc=4, facecolor='white', framealpha=1)\n", "ax.set_xlabel(r'z', fontsize=16)\n", "ax.set_ylabel(r'$\\mu$', fontsize=16)\n", "ax.axis([0.001,1.8,35,48])\n", "ax.tick_params(axis='both', which='major', labelsize=15) \n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cd02c75e", "metadata": {}, "source": [ "Now we will apply the MCMC method studied above to this cosmological data and infer the cosmological parameters. " ] }, { "cell_type": "code", "execution_count": 71, "id": "8e0ebad1", "metadata": {}, "outputs": [], "source": [ "def log_likelihood(param):\n", " zz_obs = z_sample\n", " mu_obs = mu_sample\n", " covinv = np.eye(len(mu_sample))*(1/dmu_sample**2)\n", " mu_mod = model(param,zz_obs)\n", " delta = (mu_obs-mu_mod)\n", " logL = -0.5*np.dot(delta.T, np.dot(covinv, delta))\n", " return logL\n", "\n", "mins = np.array([0.50,0.01])\n", "maxs = np.array([0.90,0.50])\n", "def log_prior(param):\n", " H0, Om0 = param\n", " lp = 0\n", " for i in range(len(mins)):\n", " if mins[i]<=param[i]<=maxs[i]:\n", " lp += 0\n", " else:\n", " return -np.inf\n", " return lp\n", "\n", "def log_probability(param):\n", " lp = log_prior(param)\n", " if np.isfinite(lp):\n", " return lp+log_likelihood(param)\n", " return -np.inf" ] }, { "cell_type": "code", "execution_count": 72, "id": "1b972cae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "logL([0.7, 0.3]) = -40.61810691066014\n", "logL([0.1, 0.31]) = -inf\n", "logL([0.6, 0.31]) = -316.7496238662658\n" ] } ], "source": [ "param_true = [0.70,0.30]\n", "print(f'logL({param_true}) =', log_probability(param_true))\n", "param = [0.10,0.31]\n", "print(f'logL({param}) =', log_probability(param))\n", "param = [0.60,0.31]\n", "print(f'logL({param}) =', log_probability(param))" ] }, { "cell_type": "code", "execution_count": 73, "id": "9b89324e", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████████████████████████████████████████████████████████████████| 3000/3000 [04:24<00:00, 11.35it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Samples shape: (16, 3000, 2)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "nwalkers = 16\n", "ndim = len(mins)\n", "n_samples = 3000\n", "initial_value = np.random.uniform(size=(nwalkers, ndim))*(maxs-mins)+mins\n", "\n", "# Setup a sampler\n", "mh_sampler = AstronomyCalc.MetropolisHastings(nwalkers=nwalkers, ndim=ndim, log_probability=log_probability, \n", " proposal_cov=np.eye(ndim)*0.01, n_jobs=4)\n", "\n", "samples = mh_sampler.run_sampler(n_samples=n_samples, initial_value=initial_value)\n", "print(\"Samples shape:\", samples.shape)" ] }, { "cell_type": "code", "execution_count": 74, "id": "6ef0fbca", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "labels = ['$h_0$', '$\\Omega_{m,0}$']\n", "\n", "fig, axs = plt.subplots(ndim, 1, figsize=(5,ndim*3))\n", "for i in range(ndim):\n", " axs[i].set_ylabel(labels[i], fontsize=16)\n", " axs[i].set_xlabel('step number', fontsize=16)\n", " for j in range(nwalkers):\n", " axs[i].plot(samples[j,:,i], c=f'C{j}')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 75, "id": "142e8e6a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Flat samples shape: (47200, 2)\n", "(47200, 2)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "flat_samples = mh_sampler.get_flat_samples(burn_in=50)\n", "print('Flat samples shape:', flat_samples.shape)\n", "\n", "AstronomyCalc.plot_posterior_corner(flat_samples, labels, truths=param_true)" ] }, { "cell_type": "markdown", "id": "624b2b0a", "metadata": {}, "source": [ "Though we showed the analysis with only two cosmological parameters, the framework is generic enough to test more complex theories, such as dynamical dark energy models." ] } ], "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 5 }