{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian inference for state-space models \n", "\n", "## Defining a prior distribution\n", "\n", "We have already seen that module `particles.distributions` defines various `ProbDist` objects; i.e. objects that represent probability distribution. Such objects have methods to simulate random variates, compute the log-density, and so on.\n", "\n", "This module defines in particular a class called `StructDist`, whose methods take as inputs and outputs [structured arrays](https://docs.scipy.org/doc/numpy/user/basics.rec.html). This is what we are going to use to define prior distributions. Here is a simple example:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import warnings; warnings.simplefilter('ignore') # hide warnings\n", "\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "\n", "from particles import distributions as dists\n", "\n", "prior_dict = {'mu': dists.Normal(scale=2.), \n", " 'rho': dists.Uniform(a=-1., b=1.), \n", " 'sigma':dists.Gamma()}\n", "my_prior = dists.StructDist(prior_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Object `my_prior` represents a distribution for $\\theta=(\\mu, \\rho, \\sigma)$ where $\\mu\\sim N(0,2^2)$, $\\rho \\sim \\mathcal{U}([-1,1])$, $\\sigma \\sim \\mathrm{Gamma}(1, 1)$, independently. We may now sample from this distribution, or compute its pdf, and so on. For each of the operations, the inputs and outputs must be structured arrays, with named variables `'rho'` and `'sigma'`." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = my_prior.rvs(size=500) # sample 500 theta-parameters\n", "\n", "plt.style.use('ggplot')\n", "plt.hist(theta['sigma'], 30);\n", "plt.xlabel('sigma')\n", "\n", "plt.figure()\n", "z = my_prior.logpdf(theta) \n", "plt.hist(z, 30)\n", "plt.xlabel('log-pdf');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may want to transform `sigma` into its logarithm, so that the support of the distribution is not constrained to $\\mathbb{R}^+$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "another_prior_dict = {'rho': dists.Uniform(a=-1., b=1.), \n", " 'log_sigma':dists.LogD(dists.Gamma())}\n", "another_prior = dists.StructDist(another_prior_dict)\n", "another_theta = another_prior.rvs(size=100)\n", "\n", "plt.hist(another_theta['log_sigma'], 20)\n", "plt.xlabel('log-sigma');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, `another_theta` contains two variables, `rho` and `log_sigma`, and the latter variable is distributed according to $Y=\\log(X)$, with $X\\sim \\mathrm{Gamma}(1, 1)$. (The documentation of module `distributions` has more details on transformed distributions.)\n", "\n", "We may also want to introduce dependencies between $\\rho$ and $\\sigma$. Consider this:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from collections import OrderedDict\n", "\n", "dep_prior_dict = OrderedDict()\n", "dep_prior_dict['rho'] = dists.Uniform(a=0., b=1.)\n", "dep_prior_dict['sigma'] = dists.Cond( lambda theta: dists.Gamma(b=1./theta['rho']))\n", "dep_prior = dists.StructDist(dep_prior_dict)\n", "dep_theta = dep_prior.rvs(size=2000)\n", "\n", "plt.scatter(dep_theta['rho'], dep_theta['sigma'])\n", "plt.axis([0., 1., 0., 8.])\n", "plt.xlabel('rho')\n", "plt.ylabel('sigma');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The lines above encodes a **chain rule** decomposition: first we specify the marginal distribution of $\\rho$, then we specify the distribution of $\\sigma$ given $\\rho$. A standard dictionary in Python is unordered: there is no way to make sure that the keys appear in a certain order. Thus we use instead an `OrderedDict`, and define first the distribution of $\\rho$, then the distribution of $\\sigma$ given $\\rho$; `Cond` is a particular `ProbDist` class that defines a conditional distribution, based on a function that takes an argument `theta`, and returns a `ProbDist` object.\n", "\n", "All the example above involve univariate distributions; however, the components of `StructDist` also accept multivariate distributions. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "reg_prior_dict = OrderedDict()\n", "reg_prior_dict['sigma2'] = dists.InvGamma(a=2., b=3.)\n", "reg_prior_dict['beta'] = dists.MvNormal(cov=np.eye(20))\n", "reg_prior = dists.StructDist(reg_prior_dict)\n", "reg_theta = reg_prior.rvs(size=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian inference for state-space models\n", "\n", "We return to the simplified stochastic volatility introduced in the basic tutorial: \n", "\n", "\\begin{align*}\n", "X_0 & \\sim N\\left(\\mu, \\frac{\\sigma^2}{1-\\rho^2}\\right) \\\\\n", "X_t|X_{t-1}=x_{t-1} & \\sim N\\left( \\mu + \\rho (x_{t-1}-\\mu), \\sigma^2\\right) \\\\\n", "Y_t|X_t=x_t & \\sim N\\left(0, e^{x_t}\\right)\n", "\\end{align*}\n", "\n", "which we implemented as follows (this time with default values for the parameters):" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from particles import state_space_models as ssm\n", "\n", "class StochVol(ssm.StateSpaceModel):\n", " default_parameters = {'mu':-1., 'rho':0.95, 'sigma': 0.2}\n", " def PX0(self): # Distribution of X_0\n", " return dists.Normal(loc=self.mu, scale=self.sigma / np.sqrt(1. - self.rho**2))\n", " def PX(self, t, xp): # Distribution of X_t given X_{t-1}=xp (p=past)\n", " return dists.Normal(loc=self.mu + self.rho * (xp - self.mu), scale=self.sigma)\n", " def PY(self, t, xp, x): # Distribution of Y_t given X_t=x (and possibly X_{t-1}=xp)\n", " return dists.Normal(loc=0., scale=np.exp(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We mentioned in the basic tutorial that `StochVol` represents the parameteric class of univariate stochastic volatility model. Indeed, `StochVol` will be the object we pass to Bayesian inference algorithms (such as PMMH or SMC$^2$) in order to perform inference with respect to that class of models. \n", "\n", "## PMMH (Particle marginal Metropolis-Hastings)\n", "\n", "Let's try first PMMH. This is a Metropolis-Hastings algorithm that samples from the posterior of parameter $\\theta$ (given the data). However, since the corresponding likelihood is intractable, each iteration of PMMH runs a particle filter that approximates it." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from particles import mcmc\n", "from particles import datasets as dts # real datasets available in the package\n", "\n", "# real data\n", "T = 50\n", "data = dts.GBP_vs_USD_9798().data[:T]\n", "\n", "my_pmmh = mcmc.PMMH(ssm_cls=StochVol, prior=my_prior, data=data, Nx=200, \n", " niter=1000)\n", "my_pmmh.run(); # may take several seconds..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The arguments we set when instantiating class `PMMH` requires little explanation; just in case:\n", "\n", " * `Nx` is the number of particles (for the particle filter run at each iteration);\n", " * `niter` is the number of MCMC iterations. \n", " \n", "Upon completion, object `my_pmmh.chain` is a `ThetaParticles` object, with the following attributes:\n", "\n", " * `my_pmmh.chain.theta` is a structured array of size 10 (the number of iterations) with keys ``'mu'``, ``'rho'`` and ``'sigma'``; \n", " * `my_pmmh.chain.lpost` is an array of length 10, contanining the (estimated) log-posterior density for each simulated $\\theta$.\n", " \n", "Let's plot the mcmc traces. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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h2EBmUuu3q/lbx2UmmgnVbTd2/+9CMjZBncvfH1MyYY9vAf3dLwXNhdM/6IX/Cvq1S8B++N9gP7/OSbvzSYfqk94slL3vjJ/Em6sBcFalVc2uwc5vJg7WFppcGWXNM3fXW8991WbCV6f85L+o+jdy2/LZxpmYaGk2M+HJa1Fz+UaT+C9o5JDTMaYQZkK/8lnnx6FHOrYQvthw9+oD4DsgMBtIp0EOF/YVTGwm+xmYsCq1NGouPljnPWrXBZkDA3wLMc05Af/Gns0kppqLNGIIzjbOpFE2vWZJJho1XpxFhycdN1Iy0dQxlprLXWzqJFfPEYEGJVWqqXuLImEmjQCfSCxDBDwVJppWEFsFNQZ76snoALt60HQVSYuBCn2gpvSNsJmgPvsAf7U6GdYrHQp9W7cTeAAsJjOhGjVXLGaivKcR0I3fODaiqmKAFyHamtT+I3qN1eIWPQ9ImEkj4K1K1TgT/rzqP28lA3xxN+j6T4P94L/rLoL+ZGNwQzrAq2f8w8Bae6BEol7JpFEG+HqYkk4NK9JkqAMrTYM+cBfYH+9TdvwV0seRdnjyiXGwmZBYE52qpybJpAkGePHW9RvA/vRoeL5qVTbASwVwZmJrJJPEAL9/wZtI1DgTRc2VSrXWCtzdbJA9vT0ioRns1z8F/ep/Bh/wFVzUIPtrAf/GcTctbOTeXGCz2zbeaL8xMJMH7gL71uWgX18vf18x+YvPx3ixIMn84jpzMq1rcIypqxljzcRgd0XUl7sGayRXhjDJRKfmas0FV8JMGgEqSCa67VTEiaaVmAnvuFERyHWhTmPsvgqxDwCIqpAXk9GQOBPUp+byVDZKniiSRLVoWTiIS1i105uvjX4/Y/54EQ3SunT+hUtjjHajwiTdKJg0C1HNbldBUikQrZrL/RslmbT4IEm8uRoBLtJbho0eRTVYKzAT9QCvWnZtjQvGfIZak1G4NVddkQiouaLSN1LdWadkEqUGMhUlpGfVqs976ol3ybVH25nqtpnwfI1Uc9VZVjXEAO85ItjBttDWvT4Smo1EMmkEuL63rS3aAN8SNhNFYmqGZEKZ855UzC7WCkx2NqjVZtJIfT5jgtqnFsnEQEMkYxLuiwsRnr6nL169KEWsTSXrjYD3bBHNM8CTd76Pvyw8H2cUOmYiSlCqZMI0dW9RJMykEeCTcboNRBMBz/54n3OvVSQTDs7kmiKZUIehxvVu8tCiy64o1Kjm8u0UDWIm3ABfS3G8L9Z60qJ429YY4GO7OzPfthg2LmIa4NnuF8GeeNg35hvrNwuoi8GevnjvsGdcyUSnDBIM8Cqz0THCFpXeE2bSCLidl7RllKBF9/mzO53rgUJrMBNV/WY3yWZCSPyIcD6gxkfBHrwHbOv9TaCpiQgwk6j0DfY0qmdTQ5MtIXI/dZNkwvPH2ISRp48zL0qxFsI71GT/71OgX/4M2D3OCa0YHlQyNQABKS7mFMrPO9ItrkTXYLc869LvuM8Sm0nN2Lp1KzZu3AhKKVatWoW1a9dKzx9//HF86UtfwgEHHAAAOPHEE3H66afHytt0cIMkj34GZAM8AOtzV4NtvttZOTEGMp+rC9XLbGb2kgn7430gr13h36Cu6iWuZMLHyfQk6De+BABIfevmWdM1Z3BtICSVcqoSNe4breaqSzKp02YiuQALCxFvi5i4fVvgJmF0x3UNnnSPQC5NO/FTd/3KzdI8yYTkcvG+N9+3LWRxxQTJhAwUgnFprc1LWoOZUEqxYcMGXHzxxcjn87jwwguxfPlyHHTQQVK6V77ylbjgggvqyttUVAWbCe/kliV3+I5OOfKc1Kr+aQKEo4TZxBhIV0/dRbEXnvaYCStNOYdEEQR0wKxadSS1Aw8GyXWIT+QCOzrrpqXRoL/7JVDcDev0s717jNpgm34OTLteSHwVXKuaqyETRJ02k0aoubSSScydHriTBiHh6Wu1mTAGjI/q888W4uTe3QuIW59EwbJiBC0K44UQaIMWWxQtwUx27tyJRYsWYeHChQCAFStWYPPmzbEYwmzyNgwzvs3EG4iKZAICfwBQ1hoKRjG+YPtjwLIV5rQmWJYzCKanAACsUgb99DnOdUdXYPCwe34D9sP/BlmxCuT9HxUeKAMlk6udliaB/dAN6hSYCf7yHNiPXVUE/67ZdqCw0M0UMfBpgz2N6vLmMjCTqLLE1bnETITNK+OqucT3RdEZNw9jssdZI89oF74XedUyYfKPUV9SIzOxLMN2Kq1pM2kJZjI0NIR83j/iNJ/PY8eOHYF027dvx6c+9Sn09/fjrLPOwpIlS2LnBYBNmzZh0ybn6Mz169ejUCjURW86nZbyltpzGAXQt+AATOWyKAFoy2TQM9APrrXND+Qx3dWFCQCFfB6krU1T8txgOJNFBUC2rQ0l9153ZxdyIe2h1pljt/s3C4beQgF0ZAh7p6eQO3kN2v9uLUa/8jnwqadQKGCCVTEJIGPPoE8orzo56rUVAFgWqfv7NAq8zryOIj2V4i4MA+j7zJeRXfY6737pnk0Y/QXQ39eHdEh7tVkEMwDaczl0z7Kee0BA0mlQAH29vWiLWd5eABRAV1cnOtw86XQa2VwOJQDdXd1o15Q12dGBCfd3RyaDLjfNVGcnxgGk0mmk2trQH0HHWC6Lsrs5ajabRY8hfbm7CyPu786OdkwASLdlwNkY/y68bTs6OpDu6gKXTbLpNqmvqTD1bR0qL/VgmJfb2YnufAF7AXR1dHhtKGK38Lu9owPt+YLUzwEg47bVcDoFmski75azx0qhPZf1+odtV1AEAIJZj41a6hy7zIaWVid0+/ioNoVDDz0U11xzDXK5HB566CFcdtlluOqqq2Ll5Vi9ejVWr17tXReLxbroLRQKUl46NAQAGJmYBKs49pOZahXDIyNemsHhYbDpafe9ex1j/TzBdiWp8qQfKDY2OoKJkPZQ6+zBbf/Sjm0ovWMFrP/jqCHLhxyOmQMOgng6drFYBB11hnh5ZkYqjw0PQwS1ad3fp1FQ6yzRO+j8HpuaAhH7wrgzzQ4Pj4B0mOmfKZcBANPT0yjPsp6MUm/ROjI8DNIdrzzqemJNjE9gyqWhUCigXHaWGOPjY5jU0EaFfjM1PoaSm4ZOOHW3KYNdqUR+Pzo97YxfBpRKJVQM6dmIr7KadN9dFSQi9T1Tk5MgY36ecmk6lBZj39bRIvTT8kwVFXfsT0xOem1owvT0NEpj44H7lUoZxWIR9nQJoH6/Z4RgenLK6x/MfRdQ/9zFUUudVSxevFh7vxWULcjn8xgc9Pn14OAg+vv7pTQdHR3I5RzVx7Jly2DbNsbGxmLlbTq4Ab5NVHNZkMVRMe6kRXSf0qFdddLE8z33Z6fI39/hXHPDu+rtorpt+gXV9/75gqTa9OGvY+YwzkQMWqwnziSQJ6baKZWanZoLkL0eI+kU3h12DgxjYOIYa2gEvFCuFEMVo76WwbvRUzfqbCZJnElNOOyww7Br1y7s2bMH1WoV9913H5YvXy6lGRkZ8aSQnTt3glKK7u7uWHmbDiHOJMA/xN+ex00rBC4qumTNgGPbHwP92bVgf3k2fqF8sHBm0qcw9qqBmQTGSWsPHMnpQkRc20UjXYMZ/EmoDpsJe+BusEf/6Ev5kTYTPqGnwJ4VVMpxbSAcYtBi7DgT/TskDQVjcp5G2kwkZpKu0XxhYibuX1uJM+H2yEDCxGZiRCqVwjnnnIN169aBUoqVK1diyZIluO02x198zZo1uP/++3HbbbchlUohk8ngYx/7GAghxrxzCu9gpBTMBnhS3+qR53hkM+h3r4K1/tvyGdH1QHfCnmbA0hu/Bzz1JDC0Fzj2tUGa+MA66hhvwz+SSju1cweF9f6PgV74r8CCRU5aIzNR3t/iqzBpAaHFXBrgWYABsJEhIJsDae8IyebSsHMb6FWfg/W5rwELFtTGDHZsA9v1PMjLltQhmbh0M4Snj+PNpe7fJV43a28uceKPU11j3JVggBefE6tlFp5x0BLMBHBUV8uWLZPurVmzxvv9lre8BW95y1ti551TiAcdaU5adG/4Kp861Fz0xxsdd8fibmDxwbOjl8MOl0y856aVnTtgyQEv87fgdiUSvqEdKSx0vMT4rqpcPaS+L6D1am1mwozMJO5E3EDXYHE7FT4vfeps4IDFSK37eggNyssrZbVg8/sAkHedA3bdNz1PPj95rUGLNXhzmeJMVI+vZk3CqmQSR7LyQKK3oBfPf1clk1olvzlGyzCTfRqiHteo5hJ0w/VMlI3sQJ6Lst5mwoYHQb9/NfCM3itOyOSWJ2hLuR5ZDFYUSTdJJq2u1lJhsJmEhWiwJx72L176izlhrWAQAgWF8va8GJGvXmnQZSaFhW7AnqDzB+IHLTLOTRjC2oFpz/SIkEx00kwjIDJgcWPXODBtLxQaZ6JzDY4G2/MiMD0t3+zschZ3TULCTBoBPohE1ZZWzVXHlhfNhEkyeWYH8OiD/nVUhLQ4APjKSxDXCYinEvP3TVLaQF0lt6BkIu1cwA3PbeoQMq9U6e0/1xXaCMoEqZdqPRy1UNtcPWPFVIz33dUJ3f1b695cYOE8NY4ROmAziZ6E2XNPAYtqjEczqbni6bmMBnj6hzudwFe+1xfgSia1By2yF58D/eyHNa8nsL60EaRvIFY5tSJhJo2ATs0FRc0lBi3OZv5o5BxrsplEqaC8+xqVg6UY4L3nbtrYkknrMRNJp21Sc4XZxdQ6d/c2Ts0lMvS4u0AHJBPl9MeoiTtgqBck9FqCFqPUXDojtJqFKdJLhJ2EjQ2DXvJxkNetBP59XXja0WGgp89ZSMzGAE+gZybVGbBvX+EkedkbhfRq0KJQThgmHRdt8vfvBTl4qZN1xzaw237qqCSbxExawptrn4ek5uLbqahffJaSySyM98ayxB1fJbVAXPqEenPwwZJSxXX3t9EAr167fybGwJ57Sjkedp4grhKjDPBxPpPVKAOrYoAvTYcn97Kpkklchq6qNwU1DeD2hxoM8JG7BmsmVPHxxFhQzRUlmbgTLnsm/JRResv1oJ/8F7A7f+mWJUomQh+PJZhoIuAJ8dqNrD0T1unv958F+kdtY58c/gqQ404EOe5E4OVHODcb6YygIGEmjYD2CFZVMpmlzaQZoHpphAU6XISaS1Rr6HbPFf3lqyYDvP4d9IqLQS/5ONivb9TTMJcQmS//rRpUw1aNxj2wagcb2uu7djPIi424zMT0DaLIUlfIgWrFNcCzeIukiNMG6Zc/E67m0pVt+n4qiZvczUZHhvyyOUQDfKztVACi2kxEI7vmYCx2/+8EYmKKJpp0xGq+ij1hJo2AuCKL4801mw/aSEZkG4IWY070vmQi1NPWDQxhcvE2OIySTNzrCTdieHQI8w7JxqRR8Tk33L/xJpd6vicb3AP67x8Au/l/3RvMb2/KwB64K2ZBqt1KOUrYSJoyWQUM8FZMwYTFeJdCJ88jpn/+aY1kEmFnqcZjJn6QraasVI0GeB0TEBdi6uO+AZm+2F1F0zc9p5vmMZPEZtIIeCs6XdS78HM2NpNGenN5E7tJzRWTQKnekMu0DIPE9ncq9ooZGwa96vNq4fJlqYR5h/YgKOW71LThYswVvAp3lcy2bQXWngm5rZjfxq94TXg5xkVDBEPkE7oqVUiSqlktyV58Duy+3zpML5OVjc4A6N23gf3mZ/4N8Xx4JtInFqrYTCJUY4GTMaPgMloWkEz4O+IsHnTMRJDalefk8FeCPf9n4Y5pAaNAR0o9Qa01IpFMGgFRzeXZ34nCV4TBNytRs4GdwWQnibt64aRIkolmkIpqDz4hi67Iv/6pv5W7Wrb7g5VbgJlURUnO+RPcBy5kwaAO5Kit101QJwYm3hNeXuspl1HSoncf8oSmrtoj1Fzsd7/01ZZebIuQ/vEtwFARWLzE+Xf4K5z7HZ1OOt1cKjEPGqkai6vm8sYFl9rcvfcAuO1bwyJPy0wQEndGDLsGR0GTTvD2axYSyaQR4EFclgUmqrlUKaWebcID76o/q18GN5gaXIPVIMUoNZd4NosnmRjUXNptRLSzg5yuHNMOUAPYU0+C/uyHsD7yWZB0jKFg1+IEoOUm8mWdvCTobaXYHrzbNU4c3qIoKqH7PnuH8NgAACAASURBVHX7dVN0eiA7BbI5gC8QFObDwICBAlIf9M8uov/7TbD77xBUY0LDBeIxEK3m4osew3dnD90H+p2v+MzObRv23a861929IIceIb8zCtp2ESQTteEtUweJycAkL8vEZrJvQDhuU1ZtqQb4WawOmq3mqic4yvNi82ljWslEyMPfKbZB2ErTYyaNl0zoxq8CTzwM7H0pXoY4njU1faY61VyqI4foGkypT1tIP9PGogRchY2ZXSJUPTwz9lNm22BPPuJImJSFS02q5AMIdhL+bumhzIye/zOwOyJgkzuCGNRc7PGtcp8T7WULD4R1xfdAFh8skDIbNRdnwoGHSv+oVf08tzaThJk0Aoz6E2ocNVerwDaotmo1wOtsJqlaDPA6Hbjy7l0vgP78uvgBeXHAJbCwHWil9BpDsIow6bNRai7dqYo6WmzDNjiAfoUa12bCVU3qK6k70evUXI8/BHrFxWC3/MjJn1LaXJozqYGZUJ+XBFRyQn2eeBjsd7/U1EsAN6yb1Fyqaz/1F0nktSt89WYtY9pNa132XfGmeXwRJV4ntpZL/Y5IbCb7DBgLSiaBCHjMctfgBqjIOLSSiTnOhEW5BosDb88u954haFHHTMK23xA8hdjN18rG2NlC69IdIz0AoyE47DvF0HzFAn8t16cz+O1t21KbGWEHn7HxUZS3PhCtjuVMQ6tucwlU8jLXXZnt2eU8U13HETFpcgblSUXiM4TYHfT1YPzYCKN6U2Um3Haik4z07zCWKe40TWBWc6lMczZjP5FM9hFQUTIR/jZwo8eaxGkN2BMPg37zMrDpKQSMioAimdQqTgvdiG/o2Nnl3xPnCs8AL3bqEJsJGMjKU0HWnhmkebbwJoi4DgeKyiGEl8RCwyQT5tggAOdsHa+tQ9pKd+TA//wXRj73sRgqRab0b0HdRix9G6iLCHVsBMpXpiZvla6RCOPGtYhwXYOJaesXlSSvLZmy+KnDAK+qn0xu5oF6mdRhpvcJv/liI7GZtDgYhWeElrZTEdJI3i/NEzVNoD/+Dtjmu4G/PCtMNgYjJVMN8KZSuc1E6Ub5A0A6u4UbwqCQVnj8cchKj68ExZV3o8BpiVtmHDWX+Dx4U76sZxIEtDYT4jITJu78G8Yk1W8swgt6DJFIRcFbVEkS6OslevGJ55hAyCv+1phFHMlE+C0+DGtH9xn9wTWg7rYlJndcv0ilT1PbUbGavnstrsFS2USgRZ/eU+3ORs2VSCb7CBjTSCbef+5tEvR+qetddeaTJgg+UZskkxoj4FVm0t4pX4vba+gkE+2AFlbdliUYmBvJTGyZpsj0arvUKJrEVX1FgWj03/yMm0rZLzSUmYQ84gwpdBGhUXN56l4dMxG33FcmZPX76yZs72wPg5orBjNhd/4K7A93BmnWQX0/pXpJvCZJ1FC2kXaNGlGXPwBNusRmso+AigZD4v6vqrngG+0oA/3VDfKW5FGYrfFeXN2oUgKAUFfKSAO8ZnCb3q+zmWhXekq+VBMkE7fObPPdYMOD+iRq/EKAQAWC6odNjIHefK1mexox7WwWFsynT2QmOtfvQN4QRsPVXMY4kzA1F/TfU1xEqPwgoOXSqbmI33cDkg8Jr4+pDoDZHqhCtEWFquhCwOukMiOdJAEEjxWI7WWpe3fzJZOWiTPZunUrNm7cCEopVq1ahbVr10rP7777bvzsZ05UbC6Xw7nnnouXv/zlAIAPfehDyOVysCwLqVQK69evn1vixbObpdWHZnXlpmc3/A8YgNS3bq71ZXXSqOmQJmmkVhuCKpmE6X5pXG8uZbXrbRfSwMHAYwd+dQPYc39G6uOfC6Z58pFAeicTwgUTBrBrvwG2+W6QQ48CjgmeVBnw1okLsW34b24z0UgmjFLnSIGBBSBLDvXpNyFqby8GSJVn4g/D5Kpu3RNQ9ShqLhWiN1etBvAwzzqjUCD3aUZtkDDVWC0GeNHmIvYBUwAsZc6ynyn3Y77OeWfzbSYtwUwopdiwYQMuvvhi5PN5XHjhhVi+fDkOOsg/a+CAAw7Af/7nf6KrqwtbtmzBN7/5TXzxi1/0nn/2s59FT0/PfJAvx5lIBnglnarrrgmqyFsvhAnIJI3E3oKek6Yxlso3/FW0ZjsV/dhQVrtcMmmQmovZtrxVu+ac+5mndzibCHqZ1AkvhJsw5quLRHuBeBRrlHrGTL1Ag/u7zT2hT4zQ5t/x+T+Dfu0LQCqN1NdvlMvQIcpm4rkG6yQTgzpFbINIt2mdmov49dXZFkLbUfc+an4GaFyDqdDfQ1R0YdCpucIkE7V940LrGryf2Ex27tyJRYsWYeHChUin01ixYgU2b94spTnqqKPQ1eV4CB1xxBEYHNSrJeYFjAmr85COphlo9N7b472jUTEqoppLROgW9DWquVTwxyaPMZ1HjajmIpa/22qD1Fz0Cx+XJ15NFapP/UnJpKi5QuttUoMpF3VJJvwv839bxFF1Vcr+Pc54ywpT43lNqFbk9wTer6i5JCkSevWdpN5k4ROy0WbCDM8i6hPJvHRQ3mHbwiJAN23G+I6KKhwAkMmZpYWAizYfb1Ev0oxLE5NvIFpCMhkaGkI+n/eu8/k8duwwHxn729/+Fscff7x0b90654CbN7/5zVi9erU236ZNm7Bp0yYAwPr161EoFOqiN51OS3nHMhmUUykUCgWMd3RgCkC2vR3d+Tz2umkKhQJKvb0YBdDX2wu+B27qd7ci/w9nRL5zMJ1G1c3bVgfdey0CCqC3twcT6TTU45Ny2Sx63HIncjmI0RzZTCZQZwCgaQt7AXR1dWNcuJ9ua0NebJ/2dpQIQaGvD3vceymLeOVNdHYiED1CnDbbDYb2jg609fU5bdfTXVf9Vewp7gFLt3nSieV+PxHltBwd3dvdjYybZjzXjilCgnn6+jACoLe3F5OZDCoAuru7kSsUMJROY0YY4Kl0GulMBn011mdmbBBDAFIpC/l8HnsAdHR2Yqotg1xbCiSTxRQc/lIoFFB5qRvDbl5OL82kvb6pwiJOX+ns6ECnhraxXA4lYqGvrw9DAHq6e5AtFDCey2HaSqEtmwVNpaQ+MJHNYBJApq0NViaDmVQKfFmgtsNwOg3W1oYBMX+X00dyuSxKxELKHQ8AAGKhv68XgeVlug3Z40+EvXc38oUCdgttMNXRgXEA2TZ93+bjmCOTstA3MIA9ADq7urx2YbbttH97B7o0bbVb+N3V3Y2OQsHLAwDZI47GzPbHQAF0dXehQyhjsqsLEwAKA3mQbBYzQ7sxBIAQK3TuKnf3OH2wr8/rrzMTIxgC0N3ViVyhoK3zbNESzEQX1RzcQM/BY489hjvuuAOf/7y/y+wll1yCgYEBjI6O4gtf+AIWL16Mo48+OpB39erVEqMpFot10VsoFKS8dHoKjDnlUffc5XK5jMqQv216sVgEG3cO5BkZHnIOVarOoFqtxqLDdv3iR0ZGQOqgm7orw9GREdCZivyQWChNTaLilksnJqTH5XJZSycbc6aoiUmZFVRtW26fUhmM2iju8YeWPTPjpaFTUwiAMec5ZZgulVBy3zEyOATSU993k4unwNKjgO2POTRQFqhfp6ISGB0Z9tqef+dAm4yOumlHQV3JZ3x8DBPFIuyZGWm1aNs27HK55n7Ihkec/NUqikWHJUxNTYMxhtLUtLchJZ1xvhkbHvby8nex8VFj+dTta5MTE5jW0Eanp8HAMOLWdWxsFKRYBJ2aAgNDpVIBZuT+Qsed5UZlegoknZHGvF2tSu1gVyqA2oemnPYuue+ozsjLoeEhzREFhKA8MwNUZ6SyisWiR0+5ou/bVNmlulIqeW09OTXltQt3rpiamkIp4jtOTExiqliU6l6eqXgxLxOTznO/zlMuvXtBsjnvOzJGQ/sMG+N90J8r2OgYAGB8dBQTxWJgDqsFixcv1t5vCTVXPp+X1FaDg4Po7+8PpHv22WfxjW98A5/61KfQ3e3HMQwMOMdQ9vb24oQTTsDOnTubT7QIKqi5pMAkg5cTY9E6WxWz9uYS3628M6Vu21Cj10gUaVzrQRUjrPdc9WIR6OGqE6uxNhMwKp+SqK2DRm/uF6AvN1LPrap3wtvavnod6B23yDd53xHVXLryvFMtw7ZOCYGprbm9SKfm8u4bbCbVGZeeiHbQ9QkA7I5b9bsgmIz2RlVilAFeTU5DzrABMFMBvf3nzsmMt1wP9sIzBnqUhXKYvWe2qinJNdj5bfQsbABagpkcdthh2LVrF/bs2YNqtYr77rsPy5cvl9IUi0Vcfvnl+PCHPyxxxlKphGl3lVgqlfDII4/g4IMPnlP6JT2u9/1IsNOJnUO7e27Md9VLo/dbeWalZufNZTQcwn/OmFlnr9WPi8SSxrsGM8hbaej04LpYAy+/wWYStTeXFXMi4dj6B7Brv6GUI5Qn6sf5nMyfT4yB3n2bYUeDGP3I2NYM8mJJ0Olbhgmcl8UPpQqzmWiCGsnrVoKc+m6BBImLGpiJIRofENok5niybT+t+g0BsD//Cey6b4Hd9APn3y3Xa+gR8g0sADnrQ04IgXEccRKZ/Ddq9abzDttfbCapVArnnHMO1q1bB0opVq5ciSVLluC2224DAKxZswY/+clPMDExgW9/+9tenvXr12N0dBSXX345AEdtcNJJJ+G4446b2wpo4kykCGEO0ddb56obhoYZ4MXZxi+b3fMbsNPPdiLXa97oMYKZ8JWnbTDy61ahfFVMHQN84yUTFrIvE6dLk8f7rUsQltb9oTKtesa2JJmI30DlJnB2z+0b0JQRUn7UzgAuf9dGwKs7P3CIu0VzaVMqU+2TymV+Acg7zoR9q26Shl764iefhroGx/wATz3pH9glfENPynDrZ33iC6DXfgNMFwgr2ssu3QAAoE88LHzDQAaFxhDJSIRXpbn15moJZgIAy5Ytw7Jly6R7a9as8X5/8IMfxAc/+MFAvoULF+Kyyy5rOn2hYNSf7CSmok6SvOMZ1D1NhdAh1XcuORTY+YTjHnvkq4MD00RjbDUXcdKKBxKFxZmIai7uCsp3mW0gMyHpNmHc6SoRoeaKUo1FlVlv0KIUZyKUK06c2Zy/Hb1OMgnrd96WNyGSiTECnugncNElPBBnArkZdM/DQIi+jmFqrqh4CzHLsX8DPPwA2IP3COWq6d0M6XT8Y4t5WaHnmQjExO4qGubUiCPDI9ASaq59HlrJRKPm4s9qOmRJQd1qLuGvUob11tOdH3zAN1rN5Ukm/ECitvDzTMQgSD6xuMya7XwSbKQRbuFMs3OtgoDLqhp4p8sT9kqVAYWruUT9Nr3r12Cjw3453l9l4hC/ryeo6JhCSD/ypIgQm4kxAl4nkkOSTAION4F21mxBHwpDO1oGKYnTGgZh0iXHvw7kb072jkvW0kYNDEGixzDdhp20CASlqHqUFMl2KvsGmBhnIvEUwyRbj2QyazWXuJpV3sknVc2RurHKNDFN8Zoyf3JKK5KJbusMwJ90CDybCfv5/4L+R1BCrRmx1FyqZKK2S4jkoXNoYJDrGvVJhUUH+/7VoF/nOztovqU3uXNpRVB76SarsJ2hvT3LwtRcwkQtqrlMNiOu4uTSUqDPKGrBSFWO2H+U/N59S7FJCIiyWUqCMwF6+v1gzjDaxO8QfKil0bjpZL12Dq3NpPlqroSZNALiSsr7qzH+cYYjSSZzpOZS9a4i+KQqDXhdXrVMw7u0vIX59U63aSYDMb0ikos2E0A4N3wWYIghmah5YgxEabUeUWaUAV5xf8XEuF+090OQDtUocS/QT0d3mGQStZuyKoGI39IgDYiTd0CqU9ohlmSiqElNqjzTxB45QQvPLQvoFDYv1e4bptCjdQjQvEZkhKY1WWDsxm0b0WaSqLn2DeiO7dWpubSSSY3vmq03l0bNFZBMYq9eDJKJ7poxf5JKp5VOrbGZAIIrJsKPea0HqmuwZoCqZ12wgDdXWPlikcJkELYnlYqqEg+UUvZXCuRVVqLEScO0E20I7VG7KXuGdmXl7HphaaUBJixUVMljtkK3WL6Irh549rpgBvePaaGkSs6aVb5/Qy8NqDB5DJqkRLV9a1QYaG0miWTS4hgZCh7bG7zwrpkp3iIMkfELcRGi5nLPbGDbtgTzaIuqQc0VKpkYmJEomajHvDYC6RptJmJ8A5O4hZBH8x6dGkhrU1Mwo0zm3upSKE+cOAi/J3yXeiQTjzmE2UwgaPQEZmkZ1DyeZEKhjzNRy4/43mr/0Ywj64xzg2k9eiLGkZiHe4WZ6BXTC0w8AO3nFmlXx4FKS8yxr7UfJTaTlgZ79inQX90APLvT32hPGiRKBs+baxZqrlnzErOai9k28PzTQHF3dB7pfpRkAoduW7CZSHtzKeWqkgnQUMnEm/wkZqJLKd9kP7hGvDIwA8FmEMqgiHES9FBV1Fzqzq+S/cud3dVrQL8ajTOpGG0mXDJxy9+2Ffa/fwDs3tv9+6pgwhQVKgHIW/8R5NR3BemJkvpUmCZvjwmEqLlMah+hPKIyfm3/jjqfhydUbxHEtpkINLGhvbA/dTboXb82vEt5X2IzaW3QDV8Gu+F/AADW2939tVRdsAjeOWbjGix2qJFBsD89Vls+huAASgtqLm6PWLAoPk0BQcSgBqCCNxcLUfV5qyjbv25UnA3g119iUDGlDK8Mw/MoCdKTTCBPJDqoW8F7ai5xpSquiIWJUyepSPTPgpkoNhP29HZgaK9Ph658vjDw4kwIrHf+C6x3nIVAQ5oYsREGphzHNTjOEdVElUxCNiYNMHWVHs0907dQJRNR+inuBkaGwG7/uSajRmMwBzaTlokz2ScxMQbyulNA3nMeCD/zXOIlhhV7Pa7BmkmKrvsEMDIU80wUYQIKqLnE6HL3mXhaomm81ewazNVcSrdTOzhRJZMGMhLAoFOOoeYKFBLyXNdmkprLMqfjyXlcA4elMBPKhJW+QIv4XRirezXKXGZiX70O2P0iUp+/2qdZEHyk/mzyZlKlKcmrTZlQY6m5hN8mpmylzJ+Iv2/bFsw89STQq2x6KLZZlJpLki40z035eHojYzcwZiBcQ5HYTPYtMMYcHXpf3mckAELVXB4zMZwjEuvFwm/X7123UaYxn3fAkICUa4i2baEjisQbuYkmrQaemsutdyolF6nSr+p3PT18g+Ct8CK6f+TzKGaj++3mMahg2K7n/TgazuR7+uRrcWFQFexQvDiuhrLcG3H25kpp1Ihcktz6B2DX80pegZu4NJBT3w3rPf8K7QxOFTVXGOrR65dLwXtCBHxgjAhtUv3Lczoi/J+qmks960SnToormYTZjtSymKlPqdBwE2/BmDCT1sNMxVmRtXfI98PEYZ1kEnvghKhPatmvimnK8NRcwpkNpgCrQFkwM03/BiTJRI2AV9tANcCjScxEhK6+obwiQo2lK4AxZ2uTzm6QU0/Xqjjo//0Q6KfeL7+DCkwYEHgJ8+0qbW3w1SuCGsoomSj0H3NCMEmUmosIzCTdBusdZ4Ic+zcy7V7FxAj4KNffOGoupd3+57+CSSzXC2ty3D/73csQ0v/U4lVvrjBmGTJOtTuhR0k8UllCmTqJNAyex6Z6+ETjkDCTevH8087fjk5jkkDn8WwmwqQaF7wo3cSgupCGQadDF08x5I/UKHRTWRJxKrH80p3U+OSUSkMaGAFmoojkUkxDIxBToopRRABhK1MA6OpG6is/hPX298R4B2cm3HakMcBLkolqMyH6762jP7DaRnjQIn8H4PTnVIQzg8gYVZuIVs1Vw7chxHk/l+A4LDfWa3oKbMOXDZWA4VsJ9yLVXMrvmtRcIfU0uQZHtY3Oy5LXoVEbpWqQMJM6QX/yXQAAyR8gPxBdP1WIKzkguPV7reCdTXUh1SHMvVA0wHuTUZyuYZiUdZIKg+8SnU7LZKgMkjMyfpQud7dsFHRqrigVRLCQ8DwmNV7YJGqi02PCqmQCTzIh/Bsy9d2I582lq4vRtidIPoDTn0U1ma5eoppLW+VZMBP+2le/Vrkh0JjNOVui6Fxko1yHA2ounQFeSa/9rlHMxDCOanSg8B/55RFCnG9UncVWThGIvTSuVqu48cYbceedd2JkZAT9/f04+eST8c53vhPpqG0p/irBgANeBnKMvFV++ErDfcYHlpVCuO5T91ohfVvaOXpWPexKn9H/E5BMRDWXYKeIWWQAJgPlzifc9yn6eYPNxDt/3a6iodzEYyYSkcF0Yd/S6PrrJQgWGZgA4jITdwJQPXIY9dVckmTi2jT4dQybCSFW8HP+6VEw3eTD6+6pbWeAbHt4vaTtS5g8Ieskk6jvLabvywPjo8EsokRhWY6HIs8WpeYSW6O9Q/rWQXWVSL9mMQH5kfFmoFiDa7DYXto+quvfcGyjs9kXMAKxucAPfvADPPXUUzjvvPOwYMEC7N27FzfccAOmpqZw9tlnN43AlgVjgCqVAAgdBKrNxErpO11YXjFDus1hJnHUXEz4oRorRW8u3ardOOGZOrRevcd++wvnsi8PZjRQwxn0XCrhj5tigA8ZyHAm2HDUSJM6SUaaBVw6uYE7JUgf/Ieq5hLrxq/j2ExMNrJp3SmYynW1CnREqLkkySRGp4+zmOHo6QXGRoLSNFdzcaLcfbAYUxmsYeVPLFgXXwEsWQo8IxwjHradSphruDYC3nghSSZs++OgP/6OTJ8JJkbTZMkktprr/vvvx6c//Wkce+yxWLx4MY499lh88pOfxO9///umEdfyCF2Z6tIrcSapVA1qLi7VCOn55KLu4aSFk4+NjwGDe6QnxEo5tIn61FpsJkbDoXv5+pX+xcGHOduji2Uqvv5kyVK5PGo3Vs2lY4JR3/KVxwKFhebnajlC/aTmq0XNFZjwFZsJZYJkIqq5lPrFUZOYmLVpx2FRMqFUkTY19RKlKZ1UF1B71iCZeO7Gaj9M+WOOQFZxRam5GAN6+0AOPsyVRCIWAaprsNabS5Mvps2EPfEw8KLrdfayJfAbrIaBkU63hs0klvvp/gRThw/rHGoEfB1qLjY+CvbsTicGoM116VUjpcPy/+YmwwMKduv1/pYhcWwmGt2sDmTBIj8IMpVy0ptsCkBwlRxH7VELtPErEXXo6omegKRyGEgkzVwtFQSrlIMBdZ4LumA00am5xO9CqcFmopJSw/bo/HuIfT2waWaYzUSV0DTpa/ncXNIISCYijcJvVTIxMlvRTiLSq0omYhkkZA6ImC+MDJ2rLgEc9HIg125Q1YrpNQ9T6aZ6c8VWc73+9a/HpZdeitNPP907jP6GG27A61//+oYQsnXrVmzcuBGUUqxatQpr166VnjPGsHHjRmzZsgXZbBbnn38+li5dGitv06AVxUNFE+eP6KUUl0m7HY1950pH6/OP/+JvVFjcDRxyeHh+/p49u7Tl4tWvBR77I9ioe2aDWLfnnsKef14D1tUD63P/BeJtkMj8aujKFMFXrum02wzixEzlttAxk0aquQTJhPzT/+cei6ubUITf6uaUJgYXouUIpiXGuAvnVD+lEB5Iyid41ZtLdQ0Os5kEJm9D+5riQtTVumSADynHcz0PmUQZi6FilNM7fUSlUbHLiJKUtC4w2ExMxnFdW4XaMDT0aMtVHnnjQJS8SFCyMr5PuW4VyeTMM8/EMcccgw0bNuCCCy7Ahg0b8KpXvQr//M//PGsiKKXYsGEDLrroIlx55ZW499578cILL0hptmzZgpdeeglXXXUVzjvvPO/43jh5mwKjZBKSJ2CAt1CrZOJhatI7jpVtezg6vfE1Dk2eKkp3yM/0FNjUBLDnRXmLj5hqLgD+yjWV1qs4pBWaykxoY9Vc3sKNwFr5NuC4E6PtCqm0EvBlYnDC6lfVn8dx0eWoVs2qIrE8Uc2lrnL5gj+Omsud3NteeazhnUpehZcE3NzVV3quwZy5BRmIXL7+g5O3vds5+VCr5tLZTNxyJDUXRbRkArPUEGAKCtNplJpLVG0zpYBQ7ahJMmkRb650Oo0zzjgDZ5xxRsOJ2LlzJxYtWoSFCx2d9IoVK7B582YcdNBBXpoHH3wQJ598MgghOPLIIzE5OYnh4WHs3bs3Mm/ToNWzh/Bn7xxmYc+par3qQway8ECw7Y/HNFYa3uNpART9ulHk1l3EYSYp+a80GXAVBQ/OU9owjg69Fqgb6xkGv7RitVLyLrq1aN5Et2zVxfRPj4K99IIjdairxgBNTPoDSkF/dq3z24uAZ/JkEtcA79kWlEoZ3YpDJJNQby5XzRUWFBuy6rbWngkAsP/vh+T0OgbEgxY5TTXZTJTASum7afp7gPFrou4j40xI4JFTApc2xSQxJCEVqbT+bPoGoSaf3hdffBHPPPMMSiXZG+hNb3rTrIgYGhpCPp/3rvP5PHbs2BFIUygUpDRDQ0Ox8nJs2rQJmzZtAgCsX79eKq8WpNNppFMWrGwW/UoZk11dmACQy+XQUyiA779bKBRQrZYxCCCXyWAaQKqtDbRSjkXHcCYD0WerPZcDm6lgGkAunUZPRBm71RuW5R03XCgUUOrpxSiAzvZ2TADIKO/jyA/0w+rtBwDMjA9jCEB3Tw9GhTTZbBZ9Cj2D2RyqADLtHWjr6MQk4NV7PJfDlGUB7lza2dWNCSFvRy6Hjnwee4V79X47AKCZNPYC6OrqQkehgJFcDlXLCpQ584w/4eU6OlAS3juazaKSSgXz8Dbp7kYpl0UZQE93N3KFAgbTaanPTBx7AiafeBjZu2/D9G2yLaujswOUViFu9diea0d3oYBSV5ff3sWXkD1pFXqPfCUGU2mkMxlY2SzKVgpIpZDJZpFqb8ck4H1rkU6xftMAiOK23d/XB35IMs87ksmgmk6jP59H0X3WlsthgLdNezsqFpHaZtAi4NNYWyoFpNu89ENtGZC2Nq9diikLbe3t6A35xsVUincXtKXTqAp14BgoFDDZ3u7Uy7LQ6Y7N/EA/JjIZTLtMIKXQvIXhCAAAIABJREFUCgS/71R3F9yjydDT04uskH4PISCEgALoH+jHWFsGSKXQn89DdHXp6e2T8gHAeHs7uL9cd08P2oXnpV5nTPb19aHU3o4pQpBOp2FlMmh3+0A63Ya8UuZ0VxfGAPQPDCAtfoNsDpZlob9QQDqdntUY0iE2M7nxxhtxww034JBDDkE2m5WezZaZ6HSWqi+3KU2cvByrV6/G6tWrvetisahNF4VCoYDqzAwwMxMog046BuxSqYSK8KxYLIINO2d4l6ac7mO7G/XFocNWPLamp6YAl6mXJiekd2mh2ym4UgFAHNrcU/wm3b8Vg4fY4OAgyIwzjHl9xsfHpTTlSiVQJ9v9ThVKMeO6m+7du9cZhOI5IQAmleupqUlMDw1L9+r9dgDAxp2peGJqClPFIuhMFUzzLbsElUBpZgbMrnppaKkERlkgDxsdAQCMj42BlR12PDY+joli0fmGQtuw418PXPdtTKt2LABTU1PAlOyWOz01iXKxCDo25t/s7Eb1Xz6KwdFR2JTCLpdAUmkwVwIol0r+CY3utwb8b+fVr6w/vXJ4UO7DAGCXywClGBr22dEM89uClstgttyvxf47Uy4DxPLLc9tZvKblcug3tgUpbqZSBqgdWOQODY+AuW7wjDFMTjmsZnDvXrDpaWdBZduwbTs4jkslMLFOk/63GBsfBxHSMwZvxT88MgJanXHH9V6pzLGxMSmf8x6/3cfHxzEpluuOq5GhITB3TFRtG6hUUHX7QLVaDdLu5hseGQbJ+PE/NgBMT6NYLHp273qwePFi7f3YzOTWW2/FF7/4RRxyyCF1ERCGfD6PwcFB73pwcBD9/f2BNGLleZpqtRqZtykw6XVDvbmUICSdF0vs9/vlsN/fAXvL/cDLliB10eXx8vMYFY/cmGouXXxIDTYTJ1ZCsSuo+mlVf0Q1xtXZgCl2IZOOW7xHrKDNRAuNBd4LOlOTao4kkAnQX0adnSEFt5niOgxqLlX9ZFKRqQb4dnVbIZO9B/r6xrSZGNObbCbiN1bVXFbKoUXnsRa2Nb1OrewlF2wmge+tyRem7hODFkWbiaimC/v+OpvJti1gf7wP+LvTzO+tE7EN8JlMBgceeGDDCQCAww47DLt27cKePXtQrVZx3333YflyObJ8+fLluOuuu8AYw/bt29HR0YH+/v5YeZsCY4cP8+ZQDPCCGxRjDPS6b4H+4Br5JEY1r/d+Cqm3lqaBp7fLR8tK6ZVrzyNLGGwqbTpIkcNyEQKxwXyizURXl7CtTWKdCV4DVLrdYDZzQjiDPuwMFo6w2A7xufhb971nZgBVWtAe16txZhA9zRgEhqD5dhymUxV1/YkGJzLrLMGGUS4Do8OwL7vIP29HLIfaSjso5dfqvecxB43NRLQJWgLzZlT2lgoWGrRvefRqXIOlqHN3kRjHZpIK6ffeuoQzS+FmnPgkNd7rhDcAAOgDd4bkrR+hkgkVOsAZZ5yB73znO3jXu96F3t5eKZ0VZ4fZEKRSKZxzzjlYt24dKKVYuXIllixZgttuuw0AsGbNGhx//PF46KGH8JGPfASZTAbnn39+aN6mwyiZhORRNzC0hL25KhXvoBuy+h+ARRGM27XJBUCpfrWjdj7OTEQjtEhbLZKJKXJXhOjNJeRnMzNgT6s2Lo1k0kh4qzq+Go8hmVgWUKmA/uI6kGUrEJhs4r1YvrSUNhdT/uoGc3aJLpU5cWMt8a7ZYw8F86nMc9KxUpFueWyHSiZC/Umvrw1gu//i/Nj+GNgjD4Ac9WqFmSgOFRrX4JpEUS/OJMIAn3HV85Wy00xhR9kGJJ2IRaIqDTDNANVKJinzcyIyO3GBYBr84bBWvg32nb+KYET1I5SZvPe97w3cu/322wP3fvSjH82akGXLlmHZsmXSvTVr1ni/CSE499xzY+dtOupRc3krDXHCZvI9APSbX4L1yXUgHV0wg+lX08aT1EzMRKE7iplIvMSwAgqVTNJCOwDslz8Bdm4z0MzTNdqbS1xFwqF/dAj09l+AvOltvs1NrKs76NnPrgXb8QRId0+oZKrXLCmTZKSaK1CA8hcISHRS3YhjC5uUbVpqEc6lcyPzmuUo37NJodn9OTnhnN3D6xEaZOeCb92jSiaqFCE1WBxGrai5qIYBiQyPACSbc3KVS65kovEsFMs0aV7jbPSoKA6MCD2Omo9JV80l1ieMIYS916TSbQBCmcnXvvY1AI6x6xOf+AS+9KUvIZPJhGXZf8BMEc5hzESztbputfn8086miK8RzpjQrd5MkomWXuW6zaDmUu0JgXJ0qhICsvo0sE0362kFFNdgYUDoJjo1O60vzoRRG3j2KWDJoUKgpVgHXndH6mDXfRPk2BOEbVMUyYRjehLo6tG/1KMzhuQapubSQWd70cXs8OeVMrBti1IEc5mlUEhvv68ZUTfhFPoT/cpnkfqPK4R6mFShQh/kzETsN7YN80wNf+KMC75S16q5BMmEb0ZZmobonqwNWjQxfuhoE5m4+EyVRDVMSHWpltILqy7uGuyRF2IzCXMbbiIzCdVPLViwAAsWLMCiRYuwePFitLe3e/fEf/snoiYLs9TCPMlECFp075ET3+heh3zwjk6zqBv3WE5PMlHiCzxGZ8qoUXMRgJz+fv+2pl2INmiR6c+Dma3ag+PhzaBf/CTYr25UHiiDTXyf2H6qmosjm4P5+8fRafO0NUomTO4r0vu838xvL11MgVeG85ec+wlY677pl6mulEVGxzc75FK5URPq08e0kokuhkNRwUUa4IW8JgM8UVRIOZeZlKdlzYIuxkj9vhLvC5FMCJTvIEB3fpHQ3sEqC2NSHQNxDPBzzExie3OddNJJuPTSS/HWt74V+Xxecr999atf3RTiWhrUJIrXKpkwMGqD/f53zj11Mz9ducTyB1CArphqLj45qmouPsmA6KVlk5oraq5XgxaVMsh7/hXsum9xYpQ0wcnFX2G718ODQLrNUT/xe1NutMrel7Tv9MqUVowsmE5Nk83p6RTvGVUn6iSK+AsArWSi6PX5IkOxaQiFSGWRji6QbNYvWw0YNW5fX6uaS2BKg3uAxQeb88SRTHh6ywKe3en81tlMBDWX991KJde2GKbmUsqTJBMlLYEs0aveXAceArL6NODQI4PvCTXAi8wD8hiNxRB0zGSWZyiFIDYz4cbwH//4x9J9QoinDtu/EEevq4AnlwzwALvjl2DXfdO/BwSNzqpWoGY1l4mZCGoAALI9R1eObuVOZAI1eXkcC/rz/pYsDJ66wVr197A5M1Gzq/prToe78mTjY6CfdiSj1Ldu1tPNs01NgF5wrkynOmi9n+6Ee+IbJWZCsu36Sdb4Umn29396G3/OQjKRDPAh781kHFdwtc8QOS2xlCnB5Pygugbr3ptOy2quo44B/vSoS7fKtJSLuDaT9g4/jkZtR9UAn3OYCd1wBTBwQIQBPkQ60m2nEqLmIq87BdZJb9aXFWYzkVTPCgMPtZlEMIv5ZiZXX311UwjYZ1Gr+yIAyW8c8MXhET9OJtxd0SsInh41QFfEUascnnFfmVAjDfCad5rEc/FOb78zHF5+BBifULgqIHSvI06TRq/OMTWB2BAC7bw6SvYUkVm6yd5+BtjjW/37KQuoGiYbYrwItp0nqdZogDcxJ3VFLCLb7jITtQxlcgpIjibJBLrPLOdp7wSeehL2eWsBRkF6+vS9Wm3HGragJ//0f8DuuQ3YtjW4kBIlZkKAvGsLq1SAl15w9vga2muWTESIzE/LAAySKH+3CWE2E0EbLD82jH0Vutfu2QU8uxMzTz0J9M5TBHwCBXUxEz5h2/41Y/Ig0O1dpStHFXXbMs6Ji8qAYuOjUDe2Iyf/nbN5IxBUc0W6BouFC73cpF/mt979AZC/XQ0sPQrY/pifXyd1BGwmmombUQD87PoIKUH1FFIJFe02WjWeBbLiTUBnJ9iGK30dtraJhMlZfT41qUiYSn+IAtUwE6ldFDWXmC6bc04jVD3CVPVmiAHeB+/7hj7i0kn+/r0A34WaEJBXLQPbfLeGboEejpiHY5GubuDo48C2bQ2UQSwLTHRfTqUcVdPT20FOORXk9LNBP/zu4Ls5PSbXYN3eXOoxvyaGr0JyDVYrpwRZSt5cwrsCpAe4j49pJ5Kejo0kzKRlUA8z4Z2Q6/C5AV6cTLgLKmXKIle3AhU6LN/6Qxj8zLZB/+0s9zAdAd7ZF4BRMonjzSVMSNIWNhoDJWnvAA5/pZtLGBBaw6mSWef2KZFhYCbaTQo1xmvJBZsF0xKHfvK6lbB//iOh7XVcU11OOr/p5rudifWZnULaBrgGq8ffSr+FdAe93DmqQC1CUXPppQSVDGViCzx3nUlefgTIoUf4tyeEbWB0EpWUP55kIjE1Va0nvke1j4nBszFcg0XHy3ADvEsPY6CX/0d4HUR6wqCTImM5eIS0YS1b/MdE40vcX1CPhxFXp/C9mCy3h+pOOAw1wGuYiXf6nhocBmDX83JRkmFS+RulwpCNCvq0Uc0iqZVjMOVce7BMpqmnCq2DgmZVLzITXYS/uiqlNOjtoyZlQvkMwBPuMQHiKZf1GuB1dRDTKPUm7/swiGf8Nai5vIVBjO1UQha+UtmBFbyoKgr55nGGls75Q6h26uqfyDTyduKSlzgGYjlLhNBOAMnWSNz8nmNASD1CXYNd1+XhYlDSDVWhzZLR1ImEmdQNZhgQ5g9J0m3e6ty5wb2yRINqiFHQy0fcNzE/qpcjzsSkerkIZXr5D16qzytNtsqsoko7kWB6FZaY/5XHgrzzfZpJU6QpgplojKLifdLpMxN2/x2gd/0aTDxPRJlUjFvWmGD6lnUY4OltPwW75zcCPRppJCB9EM3EqdSNGhiATurb/li4mosZGJOqktPeh15aNUGSTHTfRZ2gU8LfCGYi0SgWqdpMJLHF+SP1kbhqLiVdrsMh5foNMj3M+0+PKGYPwLQZ7myQqLnqhU71IsLwiPQXhH7nDn47qOYKGmuVgchPi8sfAPLyw4FcO9gdt+rVUAEilGAusXyuonjNCSBvejvoNf8PePRBQ5nqZOvWJ6qjSi6Oat3ka+vv3gmSawdTdzGWDOWCak90GQ4zHot4xTGOq+qLz3nbmJC+AWjbz+L7eJkmO90EFfIdgJqCFtlNP3TsY14ZOnWRYjMhglcT88uS8pu8+FQb3EzFOZBrcsL8nb2YlRBmEpA0lUVKVB8S6xaqzlHVXME94oxHkseVTABJJeq0fcRmnBzSccfKs4OXAgceAkxPITCuYnlzhTGxRM3VQmDxPshhrwB6B/xrL0YB8BSxGptJtGTiTxrWOR8HDj/aeSapuUwrYssfHCpTETqiFDXOETZHxhZMBL1EVICaKkHpXk71jCXouQStiojkOmD9wz/JpW++2yiZOO8zqbkkPVfw/VJSvoqNyUxmKsBMBWTNWpDT/kmfRloha1RBqporwMgj1FxuICR5wxoYP7Qn5ZiZibx7RICz6MvVpREFpFBPQ0XNFWkzUQMrxTI19ZLancjtFta91bgeqVgCcvBhfvmcUYkBkWFqrjjjqoFIJJN6EdNXO3XBl+QbEjPhBnjRm8tkMxHAO5ewgiOW5XQhafCHMJO08ulVNZdRp+2UyXY9D3r5RXLeuGoucb6V8mmuTWVSEzMxpNElkALR5EHNtv4B09xgLNLDDxWzIlbEEtMNWxioW9uHFMnPeeno8t2hdZ5dHhPlNJMgrerq1eTFp/ZDTmsqZf7MzMRMTM4CSj3iqLk88oWFUZiaS62XJdAfx2YCpQ8E0os2E1Kfmsvk0CHGmYj0RSFsGDbBAJ8wk3pRi15XhMhM+G61WgN8iJqLdzBRReTlE7dJD2EmXFWiMgLVm8swCbHf/My/d4ByWE7kqkd4rospUCdvXZkvPufbn0xboOhiboS0prkC6TagNI0ZvtuuOpGYYjmkQnW2JQ0sEl8y4Qyko9Nz8QzSIa5KNbaLQL8KvQT9+qXKDZdW3VEC3jsMaq7ADscGGN2uNe+QbCaA9eGL5W1kTJKtuEecNkZEoTF0by5NEXHtaqkQmwngC5iiBx1XZXoJImjRIVFztRDidHgdRIM5cSLgJWaiBjZyqIFSDJBcKL3I+biSSZ1b0PMiK/5ZG2SA+6sbGJAJfFAEpCDNpKMKJpf+OxjfJNJUZ825G6ExGhxtymamUjISU80VE4To99DS4c9/crJ0dOqDWyU7iUqTMnEG3E0NDEAF76uiAVtFHAO86TfPH7cdFRUeOfZv3CMCvATKXxfWLNRc6liUGLd7T1wghH3f0F2D3QJ1ixeq+c4eYthMmqDmSphJvTBIJuRl7p5DRxr2KxPdUC1HzcVE8dwQtEhEtZQlbBDpjRVNAJ9xKwxLM2Eqk4p6nyNU/WZ+pC+T637DOj1vY00a3b5PkeolAzORDKwhEfmeAd5Ak/hur5phbRZfzeXhkMOjz+IQ/xJLswhXGG2oDl4Ab2vx4KnA+w2bRhrPByFKPWIwE1FFalqAia9Ry0tZgs0qjsooSjIRJnCi1GemYi7XMrWJ+C5REvFeaC4zxrdshjdXwkzqhUEyIUe9GtY3fgrrb07WZiPHKtvKG9VcygSjGsMpk1dw2oOWwtRcbnl81RRXMvFWtrpnMSUTcWLTrUIDq2pDmd6kaaiz7mRCaeIwrTxD1DPcZmJUXWlWu2Fzler5EwGyYhVIT59eguD9iTNoj5eIqiDl+3nfwiBNqLAFNdcsDPCh3lxRnpKAYqPQlKF7pwjuRSVKFSo9ps0dQ+tFBOlVl1nBooPCk4nfVJKwNe8OZg55lDCT1kGIzYSEia46v3Kx45k2ehQlE8mjg0+2GjWXaRITbSYzMjMJPychpEwpT1RHVSSTwLuCKhDtSorX1WgzCVm1S/RCkUw0cQRiOtENVIXuXpQBvhZwyZXoJFhn4vEDKoVvqdpyAmqu4Hcna9YG308FqaNWm0lsG0QcyUSkN0RdFWaA5/eNBnhNOUB4wKWn5vL3JyMnrTYn78/7DMWkNmXKd5Ri03SLLPMjD02wmcy7AX5iYgJXXnkl9u7diwULFuDjH/84urrkEwaLxSKuvvpqjIyMgBCC1atX49RTTwUAXH/99bj99tvR0+NsPf7e9753bk5drEWvK0I0uHmMQ+MaLMzajFI5UA0kOPgVmwl7/mnQz3/UQEPaZ05VHr+hqrkMgzB0YlT+GtOJKywNUw7Tp+toEWmamgB77ing0KPM+0pp3yMkCZsELctpM+P3Fye2sEmOl1djH+K06dRcptV+nWou613nwH7o9842LBxxDPA6WxXcBQGfDMOqzYJ5jYiMM/FeLt8XHDuMh2NJ313sKyGLDU/N5cZrveMskL58WA2ipQtR2vToCyswjtqu8ZLJvDOTm266CccccwzWrl2Lm266CTfddBPOPPNMKU0qlcJZZ52FpUuXYnp6GhdccAFe85rX4KCDHI7+tre9DaeddtocU14nM5EOw7GCway6OBO+ZbuXRjNJKeoxtvUPRhLIcSeCPfmIc8HVXKqazChlhIomSt4IeOK7vhjnd8gKitdfPA1w41XAti0g7/+YXn0k+f8rkwBHgJlAfqYb3LoydZ5doektPc0iuHpGy0z4xMNvaFbvJjWlq0YNSNXqt3TVXCRMMuGFh6ni1LaTJMqI2CMxPRFoDJNMVHiLuqBkwhhzovwlu2eIZKJ7RS0bpoYVJKrwiHTDXEwc+9df495cmzdvxhvf+EYAwBvf+EZs3rw5kKa/vx9Llzrbe7S3t+PAAw/E0NBQIN2cIo5eV4eww3CAgJqLfv9q0I++V0nEdbIsuFLlnbga5kGiMcBHxRtwqBOVVESNai7PZhJm8A6TTDRqLr5L7fSk3rCqqoV07wkzwIv68NCJIkLd5pUXZvjXwNsOROPN5fuRupO28I7AhCtP+NYH/g3k1HcjffgrzPQBgmQiGLBVhHmG6douIP3yuoRBlLpCmImJRk/NpcnHvQSN3mch34kzbhrSBiYatYKuxuFDVHNp6xdDz/XXqOYaHR1Ff38/AIdpjI2Nhabfs2cPnn76aRx++OHevV//+te46667sHTpUrzvfe8LqMk4Nm3ahE2bNgEA1q9fj0Khvi2Y0+k0CAHaOzvQXWMZrFwG3+ov296OEoBMWxrc36O7pxdjALo62tFRKGD3Xb8OlJFKp5HOZMDsGbC2NgwUCqjsHcAwgJ7uLmQLBYxn2jBloGGgUMDMYB6j7nWhUMDM+BCGAGTSDi0D+QGkBgoYyWZRFvL29fagrVDASCbj3eftuIc4pzPmOjrQE9IuU91dGAeQH+jHeDaDSiqFQqEArkzp7ukB7wV9/f1oc8varZTT39uHdKGAUlenV5d0KoUqgM72djBqYxJANptFr1tGuacbI27anr5eZPn93j7vfqotAzHyI5/Pw+p1+uhwLgdamoaVaQNtSyOv1NO2GIoAujq7MJPLoQSgq6MD1WwWXL4U+92eVMpnBykLiAg5ae/qQnehgOlup41SbtsBwFAmA1AbViYLO51Glfj1tEsTbpsPwOrpQ7nLaYe+vj6nfQsF4MhXIJ1OI3/N9WDjY2grFFBsS0sk9XV3YwhAT18/ssI3E+u0261QfsECWO3yscw8fa6n1+sjw9ksaDrlteVuMHR0dqIrpA/tgdPX+gcGMLO3G2OQvzPHRGcnJuH0i3yhgOFMGyoAevr7kSsUsNuyYFlEot+2gCKA7lPegg73fqWvD8MQ69Xhpd+bSoFP9/l8HmPZLCrMOVqtu6cH7RFzxGA6jSqAnh6/P3KMtbejBIJsNotKKoVUpg2wUsh2dGICQJs7/kVMdnZhAkC+kIfV2S094+2fTqfrnv9MmBNmcskll2BkZCRw/z3veU9N5ZRKJVxxxRU4++yz0dHhfMw1a9bg9NNPBwD86Ec/wve+9z2cf/752vyrV6/G6tW+MaxYLNb0fo5CoQBGbUxPl1CusQwmSAzlisNCKsK+U+NTDguYmJjAlKFsm1LY5bJzyE+1imKxCOYy4bHhEZBiEXTczJSHRkaBKZ/VFItFsBFnOq6UHRYxNDQMQglsxa1xhJdfLkv5AX+BVyqVUAlpFzrpBNwNDg6CTZfAGJO+xfj4uP++0TEQQ1nDQ0Mg7V2gI6PevarbvpPj415gX7k07dMopB0bG/fKZsIixlZWqoNDwyAzzpRqV20nxqZcAWaqgT7ERpwpZ2J83HNdnpiYADTtBUDR10dLutOVCsrFIqgbDW9Xba88e2bGUUOVS85fVzIbGx8HE9qcVKpgY047jIyOSu1bKBQw0pYDBnJAsQhbke5GXI3A2MSklE9qB3dVPjg0ApJVVLQuyke8yqe7UgFmZvwyGMPU9DRKIX2Ib7Y5PDICNuEEc5ZLpcD3oG4/r9pOO9kVZ6yNT05iwk1LhTYEAObu7DxRLntjUOwfg0PDIFl//FDBtXtwaAh0puKpA8cnJzEZMUfYbtqxsWBfp6USGKUol0pgjILOzAAWRdWt84zYbjyP+2xwcBBkugwdbMowUuf8t3jxYu39OWEmn/nMZ4zPent7MTw8jP7+fgwPD3uGdBXVahVXXHEF3vCGN+DEE0/07vf19Xm/V61ahUsvvVSXvfGoU8ulPX9CnFBiH45FZSMhPwflhadBjnltRKCUZQi8QoT4DITr/5WyIhMi2pEh1ADP1VyGSHfPpmJQOUkmk5g2E0/nb6Cbe8U9shmkp5e/1FwHzxAcU+2gqrkC3mk6m4lGFRQ3rsRgM5EcSfqVFW6cAEjDsb1MtIWEQvRwCoszUZwAOrucnN4Gi1w1KIAv+FKqB6WB9oA6jMDbfSGOzSTM/V313Ixjh1M99bTvjCarVsy7mmv58uW48847sXbtWtx555044YQTAmkYY/j617+OAw88EG9/+9ulZ5wRAcADDzyAJUuWBPI3BYzWZcQiEjPR5I+zBT0Q7Et5d0DvesH5G2UzUTeYC8SZeA+U98Y0JscCk42t/MyNuPppXZyJx0Bsvy6GHYaN7qlR3lxUYeQiut3FkG0IpFThLQZitl1KYT7q7rQio2PC/YDhNo7/KIJ1/P/bO/cwKYp773+rZ/YKe5ndWUBuEfBCCAga8IIXYlgxXoPGEDS8Bk1CFJGEDR7B80JyjiGSKFmPCT5wTkzi5XnOG/I+Yd/XvJf4IAbeI+a4CgaCinjBYBRhr7DsfabeP/oy1dXV3dXdszuzS32eZ5+ZnamururuqV/9LvWrNLsCHtDuXwdMmGwvY94DWWHCR/cB/r8tmz+IO9YDcvMdevqf86dnjuePMyIcbQuFBeHqoq+cvkeZMcLLZ2LeR+Z5swJABG2BUdb1O7PeYegzWbhwIerr67Fz504kk0nU1dUBAFpaWrB161asXbsWhw4dwu7duzFx4kQ88MADADIhwM899xyOHDkCQghqamqwbNmywWl4WM2ERXCziWbY0F2iesg360D/uB3WbMVch1Ge0GeI5qDkKUxi7msp+FkN30TPH6zHDEtQzFrYa5SPPfQYAOi7Elpt9ahLtM6E/U7koHezKtkEhnvoJzH3M3G5DESL6TnD2FQ3nhFakteMb5tMGg7b7N34OKAscQiEVMYBDwDkAufkD7GY/vx5ChM+wSGvMfm0y5YBwmO2zmlkpGYMyE2MeV3kgDd/O7asE14BGuz5uDqlNBOv70wrBFdYKmLLo97h6IAvKyvD+vXrHZ9XVVVh7dq1AICpU6di27ZtwuPvv//+AW2fKyE1ExsiLcRHM9Eu/QJSL2xnZifcjMn8TfaKbaXWOfjByBEaHKJvbtqMW0ErKoUv7zELZBEJCxPGzGXzS9gGdiJ+LxMa7BUarmk2zYS+fcDYH0VU1hQmktfbML1YWaKFocHcwKxpcAxCMqYQUbvMgdZDmGkPbQL9y3+6R3tZbWII2i7bGhqBudjEfDY+/pu4HtGiRXPtlS3rhNczyZnSQDIbqEWhHOcYAAAgAElEQVQNDYZAM7GZMgXwgkd4quzbuXIeGjxkkQpf9MErNNjXZ2IOFLwwMR7ivXvcj9c0brtQwDGLthQT3swlSFHC1+ErS7iZJK999DMbYQVcZ2ITMKavRGQGs7WDe++ZOl3TTT1evh4tpp/f3If8VLu4HFu37I/bNHMJnxMifAtzsaB+gP01oM+ENhvxQI7nhzlkwiRoN/oE19jMXLYzyLXL1m3i/Mz8auoM73ogWLSY8vaZeOe1Itzv00+DhPczQACbFYL3bQqRMPeprMH5BA2+eplHNKOS2hzLXDjHzepZO7kXIjOXw2fiYn6xxiIPk0KQWY8oBX03E9TsVZfIzGVqBDQlFnzse7cdC/00kxPH9J0G3dAMgWMe6JXoz7pmPiu5rbr5dSYcrPlD6FfgXgOauazFsDKDpGe9LqnXpc1DjNblNcCOrHB+xiKrmcgGidgEN4y8aD741W1biAq79ilCygSmNJP8wW0FdBBEs26ZzbHM8/OzY1Yz4WEGBSLjgHez5Us4Of1NJ2ZdYPJIMXRJChNROhVWwIi+N23nN90OTD5PfB6v3Fymuepv77m3y9RMzBGAz2Bgq9qoW9oB77UCHtxn7KDC1x/MAU+uXACUlAKHD9rPHxY/M5evZiJZzu+6CoWJwGciO/g6LGBZmHBKRA/akDJzKc0kL/BNhiiL8OGwr4B3P05gNzVmo9QtVJYl5rLTolcSQ72AR7u4V7+CIoEIyGsm5n1gB3ZTM0mnXRJBGjmTPn+5PXWIZDQXueW/+LfN1EzMS2WmyhcR1Mzl2CzMzWdCxANuhNBg8uWvAxfM0QXLaPFaA2ncUq9bMk5SMwEB+Yy+gJl8fq6zmN+gSeAhTCQ1E0eFAc7P1i08B3dPAb3rMtsgeDU5qlVFQM4d8EOSUM41AUIHPJfoUZSvyXW2Ymgm3R6Dl+M8TJ0AI8Rc+uapmEhKE5sjUaSZMDN5T59JGvTNffYkmKzPxDJzZa6fq3/XMxyZNVsY/qZUCq795DWTXo/7YXPAS+y4GOPXmXDtFAkJ2xbDZlACnOVEMMJOm38TMP8m/zbKYBPkTIN81zkZmO3XCMiYcdC2Noj9AFL9y1xESinoO3/V/5HVTDzMXHLRXB7CxJw48t97/g5lJgrKzJUnDKRmQuyqt9++FbZBQ39P/98L/ufmzVwm/I/Z0UZjMPIKwwxyXUTChE2w56OZ0HY9swIx948RmblsixbdotWY8/DOZb4JbF4nEVw0F3p7bSvg7XUHdcCb+3C4LVoUnUMwCMkO2tbzl+XBx9VMFiKaC3B3KMtoBuzz8e5boC8+r79nN7IL1H+viUlATFlCqf7eskrQzPc8MqZo5YDPE1xSbAdGlKxPM4SJ1zlEdl79C9CWE6D7XpE4Nx8abJrXfAYZmb2tZS+L9SOxH6DNuQIoMxynjoSUXFtMk15ytP5qOeBZn4kgmovvn9c6Ar6staeIuKMkFnNsoEVf3SXuQxABnBwNMm6i0UbnVgX6vwLnLHFqJvKhwUSqWGBYH14UM5dfMSkzHnO9DP8WWfpdECMfGwCftSWcdYD9N5A5yc3MJdiMTcYB73FxBmKnRWXmCkWWNRN+9z/WtOWlulNqn/kc+yjzftJ5wAfvuJ/bddGiXwp6A6EsY002HviZuQBoax8FTnwCUiZOr6MfTp3pPWyhwR6bZznOKWfm0hsXE39ufc/4TGIxkFu/Afq7X4nLmsKyoFDXYFwgc66EtuwB+zkA+32wBkZBYAb7zACCTAcuBE33Igvvrwpr5vJrV1AHvOlTG8tl0jhrAsj1i4Ca0T718f9LXDfrGovq02AFqtjCjs3rFaAtjnZJmFUDoDSTMGRLMxE9aITYbcjCGRFhUnq41B33mSc4TDmmYOOjubjjIs6IbOeyTHXOPpKaMSDTLhQfPu9LmePZnf+AzP8pNp2KM5rLce/Yfx2RblwDPNZY6G3RMj6TkeXQRDsWmkWX3g/yjfuh3fOgd50OTUqg1XqaP+3ChP75Jf3/giK58w6gZmLTDmQ1E1mhIzGxsS9qFZ+fxOPQblkC7YprfOsTmZ5DQ5hGiQIpwkoT5YDPF7LtM2HNXBps+YKEAsc8TDyrB+DcM57HNdGjn/nA/SEmC5cARw5n/BeucMIkKOM+o7+yZi7Tl8BGc5l1s9kA3AYh5jpbKW349ppo3mYuywHvtRbH/Hf8JJDxk8T1eLaBM0uaCDVGzXE4KRmhz3Wra3xO66OhhsV1nUxQzURy4uJeQKiZBPpt82auoD4Tr2tsTRC4z71+NjK/qeGYm2soEi5VggBXzYR5wIVmLo0ZiF3a4OVrACQSPbrY8i1Z4nxgtauuBa661vu8ANdkGtwZqDEmrbSLmau/D/T1l/X3Rw6DvvUXkM/OdB+EbOMB1x5+FucWvGCV1zLt8koVEwS+Deb9HX82U7Uxw+dvDRFoJpQCYyf6nzdogIAs/GTGMUeR9ZlE10zsz3LEiSInS+Tq8bRHGa/cxNEzE4VEH5Rmki9kywHPaQNmnTI+E3Owyrpmwsev88LEfIi9q5cm7aFducGGVJt7ScTtmgk9fNA2a6dNnxoWA5doLs8dDwNqJqwDPowsSY6277suOnDcZ0CW/QPIlPPtZUQh40IHfFruuoeJ0JOBN3PxZhvpwc6nnIzPhH2Y/ULjpdoQVDMx33hosubvhPeZiJDqQvaFifKZBIQe3IfO//Hvxn9ZMnPx+5KzPhPXhniXIX7CxC381fIHeZwXgGPtSyBYM5fkoMZimrSowMxl0qFvsKWt+K+ZsuY5AcE5WTu3TzSXnzAhRmhwyCwJpPZm4KLLXJunn5pAm3MFSFWNuIzDAW+8Z8dsmes+ACGk4nr5yDs/M5ek0JExg9kCYIIKM/4cjhslf7xXUAv/e5OazLmfW+XmygPoG/+J07/9FUAISM2YaJWJ7N6E85m4HieYgbIUBBUmXBoXy7zBH8hFA4WBnyUHFiams511wHOPsplfyVwrYCV9lHHA26+NI4zSzwEfixlCTnB/vPpKmDeO6ys5KLF+qOpR+qswa7CsZjIYZi7WfOP8yBNfM5bMECcI0Ag7UYzkgBdpJsZr2rxfJDMJA8TjRI5ycykzV0DI176FmnsfQFNLi//s37cyU5gwIXq8z8QNt1QkJj7RXESLgSx7AKTCTI3O+0wA7k3mvOxrGFhZIkr06AebDDPlopmYlJQYZX00Ez4zsBey0VzhFBO7ZmrWJWt7Z+6Lds+DoIf+CtSMYcLEmfsnpZkMhpkLzudK2kEcUTPRuIlb4PNzTXD4TGTMXIIFqHzlvJbr4buUUluUAz73kHgcpLAouiABGBWW85loxNuM5BYCyiLI6kpuvRMoz2xzrM25kinPm9xc6s2mmYs/t+zRMWYDsXRK/2G41VEyQn/ld13ky7P/+pkApKK53MxckhoGG/KcTssJJUtI688FOftckLPP1T8yy7CDUOS8URHwzXosW4+fMJHoI7u4NOj5nSe0HxzEnOQV/UfT9qq9LAPWfMmjE8PRAd/R0YH6+nqcOHECNTU1WLVqFUaOHOkod99996G4uBiapiEWi2Hjxo2Bjs9LiMjMRfzNXDZzhstDIZipa9fd5tUY/UUynUokzcTkVDtw9H1AKjSWwegbpVQftGOMGYenmNdMzC88BnkZM5awDgM2N5eXOc0VZjIROp2Jm3ktmGZCiLEJV9ZDg31S0Muez1fzkNBcomomNoc7Z+YK4jPx+o6/X5EmcxiemklDQwNmzJiBhQsXoqGhAQ0NDViyZImw7A9+8AOUl5eHPj7vMENMzV3gYnGgzNAc/LIG+82g/MJXRXUClmCzZjUOWeIVkhjsXOmf/zPQeVr/C0KMEcKpNJfIkKGoxLmY0S2ay7bJmEToL+B+7VkzVxgIMvffkSXY6zBjAZ7nDDdsNJd/USnKK4GTbc6swXw0l7QmFNHMFS+w70oaRjNhzkEI4XJvZkszMSaO5v9W2iAXM1fk9TfBybkDvrGxEfPmzQMAzJs3D42NjYN6fC4hsy7J/DP5fGibf6enD9FiPjMPCTOXmw/BtUqByU0APdkOeqo9mgPexBQiXQGFCeszSaedJr3xZ4Nc/1WQb6xwBjm4RgEFME345ObKCLuUoIyMU1SgmUgP/G6DoXl/kXkN4oDPkjTRHnoM2vp/cUYTOXwmkueLauaqrEKqpcnZjigzd7btMpM6Xmu0f6m/sH4zNvOD6BiJKMJhmZurvb0diYSeUC2RSODkyZOuZTds2AAAuOaaa1BbWxv4+B07dmDHjh0AgI0bNyKZTIZqczweD30sAJgrCKo/MwntF8xG7/7XUFBUjKrRet6fE/E4CgsKUJFM4jg300kmk2gtKkK6Kw6aTiFeVIRKoy3syoTSkWXgh2ivNqe7OnECsGasZtn24hKwCdTps5tBn90sXa+I7vJysBvZkr5eqTrM/lVUVaMVQNnIEegrKkB3PI5yps7SCy9B2d3f1dvb24PjAEaUlGBEMonO0lKcAlCdTEIbUWbVnUr1whxSSkaMALOjiqNtrUXF6AVQWFiEhKDdpyur0AGgEBT9sRiSyWTm3jDXlse81yPLytAdi6EPAInFQQEUFxej3OcatRUXoV+LQSsoANIxVDHlzWueSFQinkyitSAOmi60lQGcz3Z7qX7/S0pLURbhmbcQ1NFeXIxe4zql0n1oAlBWVoYSj/OZ1zNZM8pzYKTpNI5bpxace8w4dO/8X6gZUQKtZAS6Ro7ASQCJqirEJfvbFI9bWa6SySROFhfD3EQhUVXtW09rYSF6AZSXl6OIK3t65Ah0ACiIxUAL4tAKi5COd6GgsABdAAriccc97CgpwWki7q953aKOYSIGRZg8/PDDaGtrc3y+eLHPPtFcHVVVVWhvb8ePfvQjjB07FtOmTQvUjtraWksIAUBTU5NHaXeSyWToY1mam1ssa0Zff59VZxpAT1cnmpqawO9P3dTUhFRfn74VbH8/Ur29wrZ0MinPyfWLQGZf7tlmapZP6bNpqy2i1OmcnTnotUh32Le8pT3dgepoN9aQnGo/CZw+DUo0nGTq7OrpQY9RHzVChE93dKCrqck6d3NzC0hXpm+0tdV2PAvftpQxK+x1ufZp46b2tLUC6bS9DKWufTXvdcfpDlAj6SM1Bsrunh70+lyjdE8vqPFMAPbz0FP6JKu1tRWktAmpnh6gv9/RFv7ZTvfo7ejq7rauabZJ9/SAplL6897cDAA4dfo0Tkucr9ko7wb1eU7TpfqEornxFZBps5A+qT9brW1tIAXFUu1PmZtpGb8b9jfTevIkiE8/Un36M3qyrd1RNt2pi6W+3l6gP6UnA+3rQ8rYjbSvr8/Rr3Rnp2t/TfoF916WsWPFG6MNijBZt26d63cVFRVobW1FIpFAa2urwydiUlVVZZWfM2cO3n33XUybNk36+LyEkEwIL78CO+VhRmIc8MRNHY/FrHLknKkgE3yc3KY6nkrJhb6msphxtNdlrw/X8zOpU1IpQIvZbdVEYLLyjeZij/HuP5l0PujbB2BGSjkwI8g6Twsc8JJhWY71M0HMXAIzh8NnkuPQYBZCgJ5u0AOvA8lR5odZqtrH3DP9ItA//LdMeH4YXyBrnrS9Qi6ay8vMZX2Vtjv303xAiVuddrR71yD98ov+bQpBzn0ms2fPxq5duwAAu3btwpw5cxxluru70WXsvtfd3Y39+/dj4sSJ0sfnLQSZEGObndXHZ0KI8RB5+UxiTO4lmUGDc4iy5xKdPxLc8UF/wDHWZ5JyOuBtaxh4YcJ9bpWTHwC0L9+B2JbfQ/vyHcLvSUmp/qbrNJyDumfVmbY4fCYSx3n60kTRXAHWQAxA+g2L0pFAx0mkn/gn0Fd3G6cbwPOxmM9SivNBBAnp9QpS8JmY2I73WmfC+yhD+kzIRXMRu999ch+FnPtMFi5ciPr6euzcuRPJZBJ1dXUAgJaWFmzduhVr165Fe3s7HnvsMQBAKpXCFVdcgVmzZnkePzQgmRxatnBCDdRz5k+Anq7MXtWiEuPPBnVdxS46wCs3lUfZEFiyMCxsUsd02r7CG7C1jxih1vS9t5D+zb+AfvSh+Q3fqszbqKkmTGHS3gJUjfIu6wbvCJZylkt8d9IwN1NB4IIIM4NAqs+/bEjIV+4EuWA20j9bZ21O5dvf8ZOAjz6IfnIr2o/JNq03IHhdIqEi9SxJBGVQaq9LtL2CRRbC9kOQc2FSVlaG9evXOz6vqqrC2rVrAQCjR4/Go48+Guj4IQEhmbQnvGbiES1FSkpATxzT/zEHLgZt09Mg5QlAe9o8QqIp+qCrDzISmVajwB1P2MWTMhgDAN39gr5WJR63d5Fvn0aAt/6iC9dENXD+DGe6mQCaiS9njQcmTgE6O0CmX2T/zvN3zpiUzPvvt6bFdripmQi+S+jOVnrooL5PjOw6k6kXgL6wPWO6GwBIvADUzH4smZFbW70BaDoW/eSWZsJNzKI84wFMpjb8QoOF0VzM4S1NQG+3npdukBQ7lpwLkzMaQjKpxPnBLO2umZDF3waZO1//5zPnCApo3KtsmKXhq3FbUMbXHxqjzqJiPYz3W98PdnhZJTD1AqCtGSgsBJk+G7Zfz5hx3Ok0ACkgUY3YT55yaVL2hAkpHYnYuvoIFTABDkHNXE2f6n9TL7B/Zfp32IzLMs/F9Iug/fNmYJTY6Zo1eF+AX/ERI4ERgmc/KObEJJXSL3GY/UwyreJeEcxnIrRyiU1glDOD0w/fRfpHjFVmAIW/G0qY5BKbA56bzaTTrqYuUjrSOVjw9Ype/dA0fSdPW2y84NhspWJIp4GS0uAZTAsKEPv+j2wf0X1/1t9MmQrt0qvt5c36vQILws4mBwTGZxLEZ+GhnVmaJ2sekZgUEEKAsyb4losM79saqGzFPDF+UavZngDPOG/eYg/1C2axnUvCZ2IGWfBmrlN6YDy5+Q5g1FkgAy38BShhklNcfCaaBvz1daTvuSVktZxGEkSYsMczFF0+Hz1mFEhkM5fxmk6H03K8dp8U/XjN8l4LObNp5vJCahc8OAdVqcgriSg8NoNBDkwhrljPhNumYgNEjPOZhNJMRFLE/CjqCnjzOy5jAS9MjFcy/SKQSefJnzOL5Dya64yGICNM2PQpUWfG5kMXeAdDwQze+HERdufGbJm5pLPhcgg1I1NwCtoWWDMZyJ+FjHNUZOaSuE5+WQ9YX4xsNNdgwWkmgxXMZf3WrPQkZnsiOOCD5HmzHSeZTkXkM7H2IcrdDCGPnqYzEcYBzzoAow5mYc1c5g+aPb+xoIoUFjnrj9q+MBtjuZ3fS4BqEpqJzc6dYzMXO+gHaUvMx9fl0EzySDXhfSaDJejY1DdAOM2ElyFBJyZW3/0c8MznvDBxyzk3iChhkksIY+ZihYnMbMavXtGrH+aDzw5gRrtIIauZZMnMBYR7+N22MmZfRd95XVct4AAQFi/FhBmUyJUL9PeJauOzoJqJizCxNgkLKcgHCt5nMtiayYljoH190TQTk6z63wRaPAUcCVeD5jQbAJTPJJewZi52zUjU2QUfzSW7KFBzaiZmOhKwZi7z+4mTod0fMSw7jDNf6DPxECZme702DCsdCXLj1/Qfv5m2fkCQM3Np13wZtPZm0N88IZ8C3m8SQvJYMzGfA9lte7N2XiOa64UGoLUZmHy+cfoQDng3Ae5fgfHqpZlwm8g5fCYumR0GEaWZ5JQB0kz4FBiBhQlzfkPIxaqSQLwA5AvXWfWSsyaAVFbxtUjAPPAhBjRhigyvbK8SZi5CCLQvfx3aTYsxaAOZe2OsNnn5dh2wwlJUng05zzufid5garZvsAZF5rdGD7wWcobvMpEhmvhZ5bEEqXvVlvC3orm4SM9sZDuOiNJMcgkbGsyGAWfLZ6JF10zMvdRJRSW0X2wDNA30L0aa/7APLvMDc80tFhTeYW07n4QDni0ejw/cGuLAuZ8CmCpZYenqM2HTqQRsyoBiNCaVG83Eeh9pUObulfSeQl6aCWf+M+H+p3nggFfCJIcQYwU8BexmrsjChIsAkh3AiEAzMX0m8QIQfh+P0O2MppkI8Vo5LeWAZ5g2KzttCoyX4Aho5nJbTW1ep7Bh2QMFb+YarEGRHfBZYRtIMTHvm/VBpj6Zw0efpY8BIyvcC1k+Li6aizdzKc3kDEZk5sp2NJfsFp9CzcQUJgIHfNgffEgHvPbdH4B2uOxX49jmlj0woGZSJJd6PBQecp1c/1XQN/4McjazstsxUHnACkvRgldzB0ir6jxSTRwO+MFpG2EnTrEYrBsUav0Td68kne/k5q+DnDsd5Pzp7nWmOR+XI5pLaSYKgTAhWiyamcV6qIOauYyHnx10LQc8k8tKJHTCEsA2TqZ/3n1M9TJPGJ+RoLtPDgju90K79hbgWm6hqpdzlyfm1CjtJ2Ad8PkVzWUJNtMXkIu2aTEmPDfM+blJlqxmEo8DMz7v8iVnXbAsYlzWYOWAVwijuaLmhuI1B6/95FkEQoKc+zn9I9bRHlkzyb6Zi/J717OYP7AAgQ1a3cPZaFb2COozEWkmbDoVfqabD7Dty4kw0ZBJQR8mmouvLxvrlRjrgtcK+HTuHfBKmOQaa9Ei64DP0qI5ywEf3sxFFt0NbeNTKLCZXgImkHTACpMsPYJeOZ1k0qnwlOXJJmtBzFxMNBf53IXO721mrjyL5gL0ATxKCvjI59dCnZ8k9e22Mxt7ZRG/FfDmPFGZuc5MyPWLQP/3Nv0fU5iUV2YKZGvRXBZCg4kWA6prxPWGjuYS1BUVLwekuUaGXXjpywD9KMPs5AcgiJmLzL4C2s2CjbtIPkdzwQgQyL6Zi3zr+yBVNa7fF1+1AN27XwDYMgHOT769GuTOFYCRJYL+7X39C8kMyN6Vs5oJQIgG+vHfnOWUA/7MRLtlCXDLEv2fsyaCXPcVkAsuzhSoztYMJ6gD3hAisvuZZEMzyZbgTLubJ7Q7vgP6wSGQWZfK15cvs/aJU/QFleZiOi/8NC925p9v0VwAwG5XnEVhol0yz/P7ilU/RPeH7+uTjhDRZETT7PsKGRl8tXseDNxWZ+XGq2GWJNd/FRirZ3Gmr7yEjM9EaSZnPCQWA7n1G/bPbvyavjiwvQX0P3aAvvi8/nntzcEq18JqJj6DTDYd8Fl7+N1/TGTKVJApU4NVlyezdm3el4B5X5IsbEwGClw0MKJZviX9/zzppIk2MMJEioICPdgkG+lUujr118rqyM3KTAh1MxeZOBlk4mQAQOroEeDEJ8b3uXfA51yYdHR0oL6+HidOnEBNTQ1WrVqFkSNH2sp8/PHHqK/PbDZ0/PhxLFq0CDfccAO2bduGF198EeXluo379ttvx0UXcbvbDTEIIUBZhf73laUZYfL5ywPWoxlpfKjc2ChaAS+u2HiNvmgx++tMsmwiHEKQqTOAL1wHcvUN4gJ8NFcOBx4hrAN+sInFgZYToLv/r9GWCNem2xAmgl1QAyObFHWwE2QKyLkwaWhowIwZM7Bw4UI0NDSgoaEBS5YssZUZO3astW1vOp3Gd77zHVx8ccYsdMMNN+DmmwPO2ocKUQbeoA54UdZgrzaFHYxCrjPxxGsFfCgGZqAlty8bkHoBgJRVgHz9Xo8CXDRXvqhfJoR4rxcayFNXjwI9dIBpShTNxNjHPhu7HfLZlG3fMe/zwMyVc6NpY2Mj5s3TbZrz5s1DY2OjZ/kDBw5gzJgxqKlxd6gNK6IIk6AO+JhgnYmw3mxGcw3CCvgwDNBvUvvijQNTsdTJuWiuQR6wfSEaE9U4uIMi+cYKaI/+OjuVXTBbfw0U8OGC12/YjOwC8iI0OOeaSXt7OxKJBAAgkUjg5EmXFc4GL7/8Mi6/3G7u+eMf/4jdu3dj8uTJuPPOOx1mMpMdO3Zgx44dAICNGzcimUyGanM8Hg99bFBoOo3jxvvKygQKPM77qfFqtq1/6QqcPNWOyqu/BK3Uf5bUvfAO9LzyEoqvvg5F3HnYPjcXFqAfQEnpCJSFuA49lZVoM96XjAhXB0/niFKcAlBcOgLlWaivv6cTzcb7bNxr/t7kgubCQmgFBUgkkzhBCIpKShzXajCfbZ7jMQ2apiEFoKKyAoWD1I54PI6aUaOBUaOzcp/oQz9B+tRJxPgoyBB0l5ejHQBS/SgsKkKCaVdbURH6YzEkk0l0lpbgFIDqmiS0kf5h7QNxnwdFmDz88MNoa2tzfL548eJA9fT39+P111/HHXdkwh4XLFiA2267DQDw29/+Fs888wyWL18uPL62tha1tbXW/01NTYHOb5JMJkMfGxTKzEja2ttBJM5rta2gGKh7GC2dXUBnl//JzvkccM7n0AfgFHcets8pIxlfV3c3ekJcB9rebr3v6u4JVQdP+tQpAEB3Tw96s1AfZZ7XbNxrcuUC0Nf+Y9CeGxGpVAro7kZTUxPS/f3o7nZeq8F8tnloxymkOvT72N5+UupZzwaiPke/BgTIxnNYWq77Tvt60XfWRFu7Uj29QH+/fj87OgAAzS2tIN29vvVGuc9jx4r3lx8UYbJu3TrX7yoqKtDa2opEIoHW1lbLkS5i3759mDRpEiorM2sy2Pfz58/HT37yk+w0Ok+w2W7zxcQdOdEjQ7acwFk3c2X3Ymt3rgDuXJHVOoM3gtvPJN8c8AbkygWAEbF0pkMmTELsZ8+6fMm8z4NorpwbTWfPno1du3YBAHbt2oU5c+a4lhWZuFpbW633r776KiZMmDAwDc0HfOyh5GLvePrstSP/ornIrEv016sWZKW+oRjN5YtjBXx+9lG7cwXIgG5QNjwgYHwmaj8TYOHChaivr8fOnTuRTCZRV1cHAGhpacHWrVuxdu1aAEBPTw/279+PZcvs0TDPPfccjhw5AkIIampqHN8PK3x++9q3vw98+/uD0I5s5ubKzsNPqkch9m//Myt1DVvYnRbzMZpLEQxzoyyAccCfwetMysrKsH69c3le36UAAAtVSURBVOvXqqoqS5AAQFFREX71q185yt1///0D2r78Is9+/NlQqfN0dpy37YqCpmWyQNM8jOZSBMfKzZX7dSbqaRpK5NsAF/rBHYBEj9km3651NmA3f8pjM5dCEvb+qXUmikDk248/G5tj5akTOO+0wGxACNDSpEcIKjPX8IDfafFMdsArApAvwiSqs489Ll/6xJOv7YpCQRHQ2gT65z/lZzoVRQjUokVFGPItwiWszb0ikXmfr2auigSKr7wGPecJtlIdomhf+ybSb/wZ9Jmf65ux5eu1V8ghMHPlcitmJUyGANqP/xXo7gLJWmr6LBH2wWU3EcpTJzCJxVBR9085XWSYbUhyNLT7/hH07f16OvPL5+e6SYpIELuZK8eTAyVMhgCkZkyumyAmpJmEaDGQb68G/v43kEuvznKjFF6QWZdYa3IUQxw+0WOOzZZKmCjCE2EmpF18VRYbolBkB3LrnaCv78l1M+SxaSZKmCiGGubmS26bMCkUQxTtutuA627LdTPkYIVHmiozl2LoodXeDDpmHMicK3PdFIXiDIZLp6I0E8VQg8y8GGTmxf4FFQrFwEEAnD6F9P/573rOtRxrJvkZSqNQKBQKb84+F6AU9PfPgDYdy7kDXgkThUKhGIJoX7wR2j1r9H9amnJu5lLCRKFQKIYqiWr99dO/59zMpXwmCoVCMVSpGaObu9pbQc75bE6booSJQqHIC7Tv/ANQlGcpg/IcUliE2D9uynUzAChholAo8gQy+4pcN0ERgZwLk1deeQW/+93v8Pe//x0//vGPMWXKFGG5N954A7/+9a+RTqcxf/58LFy4EADQ0dGB+vp6nDhxAjU1NVi1ahVGjhw5mF1QKBSKM56cO+AnTJiA1atX47Ofdbf3pdNpPPXUU3jooYdQX1+Pl19+GR999BEAoKGhATNmzMATTzyBGTNmoKGhYbCarlAoFAqDnAuT8ePHY+zYsZ5l3n33XYwZMwajR49GPB7H3Llz0djYCABobGzEvHnzAADz5s2zPlcoFArF4JFzM5cMLS0tqK6utv6vrq7G4cOHAQDt7e1IJPT9MRKJBE6ePOlaz44dO7Bjxw4AwMaNG5FMJkO1Jx6Phz52qKL6fGag+nxmMBB9HhRh8vDDD6Otrc3x+eLFizFnzhzf46m1b3WGMJvA1NbWora21vo/7F4VyWRyWO1zIYPq85mB6vOZQZQ+u1mSBkWYrFu3LtLx1dXVaG5utv5vbm62tJGKigq0trYikUigtbUV5eXlkc6lUCgUiuDk3Gciw5QpU/DJJ5/g+PHj6O/vx549ezB79mwAwOzZs7Fr1y4AwK5du6Q0HYVCoVBkl5wLk1dffRX33HMP3nnnHWzcuBEbNmwAoPtJHnnkEQBALBbD3XffjQ0bNmDVqlW47LLLMGHCBADAwoULsX//fqxcuRL79++3QoYVCoVCMXgQKnJIKBQKhUIRgJxrJkORNWvW5LoJg47q85mB6vOZwUD0WQkThUKhUERGCROFQqFQRCb2wx/+8Ie5bsRQZPLkybluwqCj+nxmoPp8ZpDtPisHvEKhUCgio8xcCoVCoYiMEiYKhUKhiMyQSPSYT7jtqzKUaWpqwubNm9HW1gZCCGpra3H99dd77hWzfft27Ny5E5qm4a677sKsWbNy3ItwpNNprFmzBlVVVVizZs2w7/Pp06exZcsWHD16FIQQ3HvvvRg7duyw7vMf/vAH7Ny5E4QQTJgwAcuXL0dvb++w6vOTTz6JvXv3oqKiAps26TsvhnmW33//fWzevBm9vb248MILcdddd8nnQaQKaVKpFF2xYgU9duwY7evro6tXr6ZHjx7NdbMi09LSQt977z1KKaWdnZ105cqV9OjRo/TZZ5+l27dvp5RSun37dvrss89SSik9evQoXb16Ne3t7aWffvopXbFiBU2lUjlrfxSef/55+vjjj9NHHnmEUkqHfZ9//vOf0x07dlBKKe3r66MdHR3Dus/Nzc10+fLltKenh1JK6aZNm+hLL7007Pp88OBB+t5779G6ujrrszB9XLNmDT106BBNp9N0w4YNdO/evdJtUGauAHjtqzKUSSQSVmRHSUkJxo0bh5aWFte9YhobGzF37lwUFBRg1KhRGDNmDN59992ctT8szc3N2Lt3L+bPn299Npz73NnZibfeegtf/OIXAehpyEeMGDGs+wzo2mdvby9SqRR6e3uRSCSGXZ+nTZvm2GE2aB9bW1vR1dWF8847D4QQXHXVVYHGN2XmCoDXvirDhePHj+ODDz7AOeec47pXTEtLC84991zrmKqqKrS0tOSkvVH4zW9+gyVLlqCrq8v6bDj3+fjx4ygvL8eTTz6JDz/8EJMnT8bSpUuHdZ+rqqpw00034d5770VhYSFmzpyJmTNnDus+mwTtYywWc4xvQfquNJMA0Cztq5KvdHd3Y9OmTVi6dClKS0tdy4muw1Dj9ddfR0VFhXSs/XDocyqVwgcffIAFCxbgpz/9KYqKijy3uR4Ofe7o6EBjYyM2b96MrVu3oru7G7t373YtPxz67IdbH6P2XWkmAfDaV2Wo09/fj02bNuHKK6/EJZdcAsB9rxj+OrS0tKCqqion7Q7LoUOH8Nprr2Hfvn3o7e1FV1cXnnjiiWHd5+rqalRXV1uz0ksvvRQNDQ3Dus8HDhzAqFGjrD5dcskleOedd4Z1n02C9lE0vgXpu9JMAuC1r8pQhlKKLVu2YNy4cbjxxhutz932ipk9ezb27NmDvr4+HD9+HJ988gnOOeecnLQ9LHfccQe2bNmCzZs343vf+x6mT5+OlStXDus+V1ZWorq6Gh9//DEAfaAdP378sO5zMpnE4cOH0dPTA0opDhw4gHHjxg3rPpsE7WMikUBJSQneeecdUEqxe/fuQOObWgEfkL179+Lpp59GOp3G1VdfjVtvvTXXTYrM22+/jfXr12PixImW2e7222/Hueeei/r6ejQ1NSGZTKKurs5y8v3+97/HSy+9BE3TsHTpUlx44YW57EIkDh48iOeffx5r1qzBqVOnhnWfjxw5gi1btqC/vx+jRo3C8uXLQSkd1n3etm0b9uzZg1gshrPPPhv33HMPuru7h1WfH3/8cbz55ps4deoUKioqsGjRIsyZMydwH9977z08+eST6O3txaxZs3D33XdLm/KVMFEoFApFZJSZS6FQKBSRUcJEoVAoFJFRwkShUCgUkVHCRKFQKBSRUcJEoVAoFJFRwkShGETq6upw8ODBXDdDocg6KjRYocgB27Ztw7Fjx7By5cpcN0WhyApKM1EohiCpVCrXTVAobCjNRKEYRO677z7cfffdeOyxxwDoaeDHjBmDRx99FJ2dnXj66aexb98+EEJw9dVXY9GiRdA0DX/605/w4osvYsqUKdi1axeuvfZaLF68OMe9USgyqESPCsUgU1BQgFtuucVh5vrFL36ByspKPPHEE+jp6cHGjRtRXV2Na665BgBw+PBhzJ07F7/85S+VZqLIO5SZS6HIA9ra2vDGG29g6dKlKC4uRkVFBW644Qbs2bPHKpNIJHDdddchFouhsLAwh61VKJwozUShyAOampqQSqWwbNky6zNKqW2zomQymYumKRRSKGGiUOQAPhNrdXU14vE4nnrqKcRisRy1SqEIjzJzKRQ5oKKiAidOnEA6nQagm7BmzpyJZ555Bp2dnUin0zh27BjefPPNHLdUoZBDCROFIgdcdtllAIBvfvObePDBBwEAK1asQH9/P+rq6nDXXXfhZz/7GVpbW3PZTIVCGhUarFAoFIrIKM1EoVAoFJFRwkShUCgUkVHCRKFQKBSRUcJEoVAoFJFRwkShUCgUkVHCRKFQKBSRUcJEoVAoFJFRwkShUCgUkfn/DP8wAS3g+CMAAAAASUVORK5CYII=\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for p in prior_dict.keys(): # loop over mu, theta, rho\n", " plt.figure()\n", " plt.plot(my_pmmh.chain.theta[p]) \n", " plt.xlabel('iter')\n", " plt.ylabel(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You might wonder what type of Metropolis sampler is really implemented here: \n", "\n", " * the starting point of the chain is sampled from the prior; you may instead set it to a specific value using option `starting_point` (when instantiating `PMMH`); \n", " * the proposal is an **adaptative** Gaussian random walk: this means that the covariance matrix of the random step is calibrated on the fly on past simulations (using vanishing adaptation). This may be disabled by setting option `adaptive=False`; \n", " * a bootstrap filter is run to approximate the log-likelihood; you may use a different filter (e.g. a guided filter) by passing a `FeynmanKac` class to option `fk_cls`;\n", " * you may also want to pass various parameters to each call to ` SMC` through (dict) argument `smc_options`; e.g. `smc_options={'qmc': True}` will make each particle filter a SQMC algorithm. \n", " \n", "Thus, by and large, quite a lot of flexibility is hidden behind this default behaviour." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Particle Gibbs\n", "PMMH is just a particular instance of the general family of PMCMC samplers; that is MCMC samplers that run some particle filter at each iteration. Another instance is Particle Gibbs (PG), where one simulate alternatively: \n", "1. from the distribution of $\\theta$ given the states and the data; \n", "2. renew the state trajectory through a CSMC (conditional SMC step). \n", "\n", "Since Step 1 is model- (and user-)dependent, you need to define it for the model you are considering. This is done by sub-classing `ParticleGibbs` and defining method `update_theta` as follows:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "class PGStochVol(mcmc.ParticleGibbs):\n", " def update_theta(self, theta, x):\n", " new_theta = theta.copy()\n", " sigma, rho = 0.2, 0.95 # fixed values\n", " xlag = np.array(x[1:] + [0.,])\n", " dx = (x - rho * xlag) / (1. - rho)\n", " s = sigma / (1. - rho)**2\n", " new_theta['mu'] = self.prior.laws['mu'].posterior(dx, sigma=s).rvs() \n", " return new_theta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For simplicity $\\rho$ and $\\sigma$ are kept constant; only $\\mu$ is updated. This means we are actually sampling from the posterior of $\\mu$ given the data, while these other parameters are kept constant. Let's run our PG algorithm:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "pg = PGStochVol(ssm_cls=StochVol, data=data, prior=my_prior, Nx=200, niter=1000)\n", "pg.run() # may take several seconds..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the results:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(pg.chain.theta['mu']) \n", "plt.xlabel('iter')\n", "plt.ylabel(r'$\\mu$')\n", "\n", "plt.figure()\n", "plt.hist(pg.chain.theta['mu'][20:], 50)\n", "plt.xlabel(r'$\\mu$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SMC^2\n", "\n", "Finally, we consider SMC$^2$, a SMC algorithm that makes it possible to approximate:\n", "\n", " * all the partial posteriors (of $\\theta$ given $y_{0:t}$, for $t=0, 1, ..., T$) rather than only the final posterior;\n", " \n", " * the marginal likelihoods of the data. \n", " \n", " SMC$^2$ is a two-level SMC sampler: \n", " \n", " 1. it simulates many $\\theta$-values from the prior, and update their weights recursively, according to the likelihood of each new datapoint; \n", " \n", " 2. however, since these likelihood factors are intractable, for each $\\theta$, a particle filter is run to approximate it; hence a number $N_x$ of $x$-particles are generated for, and attached to, each $\\theta$. \n", " \n", " The class `SMC2` is defined inside module `smc_samplers`. It is run in the same way as the other SMC algorithms. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import particles\n", "from particles import smc_samplers as ssp\n", "\n", "fk_smc2 = ssp.SMC2(ssm_cls=StochVol, data=data, prior=my_prior,init_Nx=50, \n", " ar_to_increase_Nx=0.1)\n", "alg_smc2 = particles.SMC(fk=fk_smc2, N=500)\n", "alg_smc2.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, a few choices are made for you by default: \n", "\n", "* A bootstrap filter is run for each $\\theta-$particle; this may be changed by setting option `fk_class` while instantiating `SMC2`; e.g. ``fk_class=ssm.GuidedPF`` will run instead a guided filter. \n", "* Option `init_Nx` determines the **initial** number of $x-$particles; the algorithm automatically increases $N_x$ each time the acceptance rate drops below $10%$ (as specified through option ``ar_to_increase=0.1``. Set this this option to `0.` if you do not want to increase $N_x$ in the course of t he algorithm.\n", "* The particle filters (in the $x-$dimension) are run with the default options of class `SMC`; e.g. resampling is set to `systematic` and so on; other options may be set by using option `smc_options`." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(alg_smc2.X.theta['mu'], alg_smc2.X.theta['rho'])\n", "plt.xlabel(r'$\\mu$')\n", "plt.ylabel(r'$\\rho$');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 1 }