{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/fonnesbeck/Bios8366/blob/master/notebooks/Section4_8-Introduction-to-Variational-Bayesian-Methods.ipynb)\n", "\n", "# Introduction to Variational Bayesian Methods\n", "\n", "### Written by D. Schleuter and C. Fonnesbeck" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Bayesian analysis, the most common strategy for computing posterior quantities is through Markov Chain Monte Carlo (MCMC). Despite recent advances in efficient sampling, MCMC methods still remain computationally intensive for more than a few thousand observations. A more scalable alternative to sampling is Variational Inference (VI), which re-frames the problem of computing the posterior distribution as a minimization of the Kullback-Leibler divergence between the true posterior and a member of some approximating family. \n", "\n", "In this lecture, we provide a basic overview of the VI framework as well as practical examples of its implementation using the Automatic Differentiation Variational Inference (ADVI) engine in PyMC." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a couple of alternatives to evaluating complex posterior distributions without using an MCMC algorithm:\n", "\n", "1. Divide and Conquer approaches: See [this paper](https://arxiv.org/abs/1311.4780) or [this paper](https://arxiv.org/abs/1508.05880) for more details\n", "\n", "2. One alternative approach is to build an approximation to the posterior $p(\\theta|X)$ using some other distribution $q(\\theta)$\n", "\n", "Let's focus on the latter option, and try to use a simple distribution to approximate a complex one." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distributional Approximations\n", "\n", "We have already seen one example of a distributional approximation: the Laplace (normal) approximation. In that scenario, we constructed a Taylor series of the posterior and threw away the terms of higher than quadratic order. \n", "\n", "Variational inference is another distribitional approximation method. Here, rather than a Taylor series approximation, we choose some class of approximating distributions, and choose the member of that class which is **closest to the posterior**.\n", "\n", "Thus, we shift from a stochastic sampling approach to approximation to a deterministic approximation that places bounds on the density of interest, then uses opimization to choose from that bounded set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Approximating a Student's t with a gaussian \n", "Let's approximate a Students-t distribution with $\\nu =3$ with a Gaussian distribution of some mean and variance.\n", "\n", "One naive approach would be to build a set of test points and minimize the MSE between the $\\log p(z)$ and $\\log q(z)$. \n", "\n", "$$\n", "{\\hat \\phi} = \\underset{\\phi}{{\\rm arg\\,min}} \\frac{\\sum_{i} q(\\theta_{i};\\phi)\\left[\\log q(\\theta_{i};\\phi) - \\log p(\\theta_{i})\\right]^{2}}{\\sum_{i} q(\\theta_{i};\\phi)}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import numpy as np\n", "import scipy as sp\n", "\n", "sns.set(style='ticks')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "nu = 3\n", "logp = sp.stats.t(nu).logpdf" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = np.linspace(-5.0, 5.0, 1000)\n", "plt.plot(z, np.exp(logp(z)), label='p(z)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementing the approximation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's weight points that have more probability in the approximation $q(z)$, the idea being that points near the bulk of $q(\\theta)$ are more important to get right. OK. \n", "\n", "How do we pick $\\theta_i$? Well, let's use the known distribution of $q(\\theta;\\phi)$ at each step of the optimization to select a grid of points which sample the regions of highest probability density. Then we will optimize the objective function that we defined in terms of MSE. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def logq(theta, mu, lnsigma):\n", " # log-Gaussian parameterized by mean and log(sigma)\n", " sigma = np.exp(lnsigma)\n", " return sp.stats.norm(mu, sigma).logpdf(theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can specify an objective function, and fit the normal distribition using `scipy.optimize`" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.034185\n", " Iterations: 107\n", " Function evaluations: 206\n", " final_simplex: (array([[-3.31217268e-09, 1.39418201e-01],\n", " [ 3.00982760e-09, 1.39418195e-01],\n", " [ 5.89924420e-09, 1.39418199e-01]]), array([0.03418518, 0.03418518, 0.03418518]))\n", " fun: 0.0341851753840014\n", " message: 'Optimization terminated successfully.'\n", " nfev: 206\n", " nit: 107\n", " status: 0\n", " success: True\n", " x: array([-3.31217268e-09, 1.39418201e-01])\n" ] } ], "source": [ "def regression_vi(logp, n, mu_start, lnsigma_start, atol=1e-6):\n", " \"\"\"use an optimizer for simple 1D VI\"\"\"\n", " phi_start = np.array([mu_start, lnsigma_start])\n", " \n", " # Objective function. Computes sum above on a grid.\n", " def obj(phi):\n", " _sigma = np.exp(phi[1]) # get sigma\n", " \n", " # This is the grid, factor of 10 is a random choice.\n", " z = np.linspace(phi[0] - 10.0*_sigma , phi[0] + 10.0*_sigma, n)\n", "\n", " # Build weights and differences.\n", " logqz = logq(z, phi[0], phi[1])\n", " w = np.exp(logqz)\n", " diff = logqz - logp(z)\n", " return np.sum(diff * diff * w) / np.sum(w)\n", "\n", " # Run the optimizer.\n", " opts = {'disp': True, 'maxiter': 5000, 'maxfev': 5000,\n", " 'fatol': atol, 'xatol': 1e-8}\n", " phi_hat = sp.optimize.minimize(obj, phi_start,\n", " method='Nelder-Mead',\n", " options=opts)\n", " print(phi_hat)\n", " return phi_hat['x'], phi_hat\n", "\n", "phi_hat, res = regression_vi(logp, 100, 100.0, -100.0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.linspace(-5.0, 5.0, 1000)\n", "ptheta = np.exp(logp(theta))\n", "qtheta = np.exp(logq(theta, phi_hat[0], phi_hat[1]))\n", "\n", "plt.plot(theta, ptheta, label='p(theta)')\n", "plt.plot(theta, qtheta, label='q(theta)')\n", "plt.xlabel('theta')\n", "plt.ylabel('PDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MSE is not an effective criterion for comparing two arbitrary distributions (its only optimal when the approximation error is normally distributed). Instead, we can adopt a more robust information-theoretic measure, such as the **Kullback-Leibler divergence**, which estimates the information distance between two densities.\n", "\n", "Hence we look to minimize the KL divergence between the approximating distribution and the truth:\n", "\n", "$$\n", "\\begin{align*}\n", "D_{\\rm KL}\\big(Q||P\\big) &=& \\int q(\\theta) \\log\\frac{q(\\theta)}{p(\\theta)}d\\theta\\\\\n", "&=& \\int q(\\theta)\\log q(\\theta)d\\theta - \\int q(\\theta)\\log p(\\theta)d\\theta\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.040695\n", " Iterations: 56\n", " Function evaluations: 108\n", " final_simplex: (array([[-4.26771590e-06, 2.31270951e-01],\n", " [ 5.19733032e-05, 2.31261077e-01],\n", " [ 5.67321110e-05, 2.31314504e-01]]), array([0.04069546, 0.04069546, 0.04069546]))\n", " fun: 0.040695455334932795\n", " message: 'Optimization terminated successfully.'\n", " nfev: 108\n", " nit: 56\n", " status: 0\n", " success: True\n", " x: array([-4.26771590e-06, 2.31270951e-01])\n" ] } ], "source": [ "def kl_vi(logp, n, mu_start, lnsigma_start):\n", " \"\"\"vi with KL divergence\"\"\"\n", " phi_start = np.array([mu_start, lnsigma_start])\n", " \n", " # Objective function. Computes the KL div of q and p.\n", " def obj(phi):\n", " # This term is -\\int q*log(q).\n", " # Also known as the differential entropy.\n", " # For a Gaussian, it can be computed exactly. \n", " # See wikipedia or something.\n", " entropy = phi[1] + 0.5*np.log(2.0 * np.pi) + 0.5 ## \n", " \n", " # now we need to evaluate the second integral in the KL divergence, let's numerically approximate it with a sum\n", " # This is the grid, factor of 20 is a random choice.\n", " _sigma = np.exp(phi[1]) # get sigma \n", " θ = np.linspace(phi[0] - 20.0*_sigma , phi[0] + 20.0*_sigma, n) #number of grid points \n", " dθ = θ[1] - θ[0] # factor needed for numerical integral\n", " \n", " # This term is \\int q*log(p)\n", " logqθ = logq(θ, phi[0], phi[1]) #just evaluate the variational density at each z on the grid and \n", " # at the current value of phi\n", " qθ = np.exp(logqθ) # back transform\n", " return -entropy - np.sum(qθ * logp(θ) * dθ) #KL divergence for this phi\n", " \n", " # Pass this objective function to a scipy optimizer\n", " phi_hat = sp.optimize.minimize(obj, phi_start,\n", " method='Nelder-Mead',\n", " options={'disp': True})\n", " print(phi_hat)\n", " return phi_hat['x'], phi_hat\n", "\n", "phi_hat, res = kl_vi(logp, 10000, 1.0, 0.0)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.linspace(-5.0, 5.0, 1000)\n", "ptheta = np.exp(logp(theta))\n", "qtheta = np.exp(logq(theta, phi_hat[0], phi_hat[1]))\n", "\n", "plt.plot(theta, ptheta, label='p(theta)')\n", "plt.plot(theta, qtheta, label='q(theta)')\n", "plt.xlabel('theta')\n", "plt.ylabel('PDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's look at a more difficult pdf to approximate:\n", "$$\n", " \\log p(\\theta) = 10^{3}\\log \\theta + \\log(1-\\theta) - c\n", "$$\n", "\n", "where the constant $c \\sim Beta(10^3+1, 2)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A naive approach here would be to fit a rescaled Gaussian to match the support of $\\theta$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.145730\n", " Iterations: 231\n", " Function evaluations: 427\n", " final_simplex: (array([[ 0.9981397 , -6.63765288],\n", " [ 0.99813979, -6.63771762],\n", " [ 0.99813975, -6.63760831]]), array([0.14572997, 0.14572997, 0.14572997]))\n", " fun: 0.14572997442662317\n", " message: 'Optimization terminated successfully.'\n", " nfev: 427\n", " nit: 231\n", " status: 0\n", " success: True\n", " x: array([ 0.9981397 , -6.63765288])\n" ] } ], "source": [ "def logq_unit(theta, mu, lnsigma):\n", " \"\"\"log of Gaussian parameterized by mean and log(sigma)\n", " has unit integral over 0,1 \n", " and value zero outside of 0,1\n", " \"\"\"\n", " val = np.zeros_like(theta)\n", " msk = (theta >= 1.0) | (theta <= 0.0)\n", " val[msk] = -np.inf\n", " if np.any(~msk):\n", " sigma = np.exp(lnsigma)\n", " a, b = (0.0 - mu) / sigma, (1.0 - mu) / sigma\n", " val[~msk] = sp.stats.truncnorm.logpdf(theta[~msk], a=a, b=b, loc=mu, scale=sigma)\n", " \n", " return val\n", "\n", "def logp_hard(theta, a=1e3, b=1):\n", " val = np.zeros_like(theta)\n", " msk = (theta >= 1.0) | (theta <= 0.0)\n", " val[msk] = -np.inf\n", " if np.any(~msk):\n", " val[~msk] = a * np.log(theta) + b * np.log(1.0 - theta) - sp.special.betaln(a + 1.0, b + 1.0)\n", " return val\n", "\n", "def kl_vi_unit(logp, n, mu_start, lnsigma_start, eps=1e-8):\n", " \"\"\"vi with KL divergence over unit integral\"\"\"\n", " phi_start = np.array([mu_start, lnsigma_start])\n", " \n", " # Objective function. Computes the KL div of q and p.\n", " def obj(phi):\n", " # This term is -\\int q*log(q).\n", " sigma = np.exp(phi[1])\n", " a, b = (0.0 - phi[0]) / sigma, (1.0 - phi[0]) / sigma\n", " entropy = sp.stats.truncnorm.entropy(a=a, b=b, loc=phi[0], scale=sigma)\n", "\n", " # This is the grid, factor of 20 is a random choice.\n", " _sigma = np.exp(phi[1]) # get sigma \n", " theta = np.linspace(eps, 1.0 - eps, n)\n", " dtheta= theta[1] - theta[0] # factor needed for numerical integral\n", " \n", " # This term is \\int q*log(p)\n", " logqtheta = logq_unit(theta, phi[0], phi[1])\n", " qtheta = np.exp(logqtheta)\n", "\n", " return -entropy - np.sum(qtheta * logp(theta) * dtheta)\n", "\n", " # Run the optimizer.\n", " phi_hat = sp.optimize.minimize(obj, phi_start,\n", " method='Nelder-Mead',\n", " options={'disp': True, 'maxfev': 10000})\n", " print(phi_hat)\n", " return phi_hat['x'], phi_hat\n", "\n", "phi_hat, res = kl_vi_unit(logp_hard, 10000, 0.0, 0.0)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "theta = np.linspace(0.5, 0.999999, 100000)\n", "ptheta = np.exp(logp_hard(theta))\n", "qtheta = np.exp(logq_unit(theta, phi_hat[0], phi_hat[1]))\n", "dtheta_dlogittheta = theta * (1.0 - theta)\n", "\n", "plt.plot(sp.special.logit(theta), ptheta * dtheta_dlogittheta, label='p(logit(theta))')\n", "plt.plot(sp.special.logit(theta), qtheta * dtheta_dlogittheta, label='q(logit(theta))')\n", "plt.xlabel('logit(theta)')\n", "plt.ylabel('PDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks a little weird and rescaling a gaussian to squeeze into the support of $\\theta$ is not really a good solution if your parameters all have different supports.\n", "\n", "Instead, let's do the reverse and transform the parameter space to that of a gaussian.\n", "A transformation $T$ that maps $[0,1] \\to R$ is the logit function. \n", "$$\n", "T(\\theta)=\\zeta = {\\rm logit}(\\theta) = \\log\\left(\\frac{\\theta}{1-\\theta}\\right)\\\\\n", "{\\rm logit}^{-1}(\\zeta) = {\\rm sigmoid}(\\zeta) = \\frac{1}{1 + \\exp\\left(-\\zeta\\right)}\\\\\n", "\\frac{d{\\rm sigmoid}(\\zeta)}{d\\zeta} = {\\rm sigmoid}(\\zeta) \\left[1 - {\\rm sigmoid}(\\zeta)\\right]\\\\\n", "$$\n", "and then our pdf in terms of the transformed parameter is given by\n", "$$\n", "\\begin{align}\n", " \\log p_{\\zeta}(\\zeta) &=& \\log p({\\rm sigmoid}(\\zeta)) + \\log\\left|\\frac{d{\\rm sigmoid}(\\zeta)}{d\\zeta}\\right|\\\\\n", "&=& \\log p({\\rm sigmoid}(\\zeta)) + \\log {\\rm sigmoid}(\\zeta) + \\log(1-{\\rm sigmoid}(\\zeta))\\ .\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 0.041045\n", " Iterations: 65\n", " Function evaluations: 126\n", " final_simplex: (array([[ 6.46509387, -0.34497398],\n", " [ 6.46518205, -0.34488247],\n", " [ 6.46511969, -0.34501641]]), array([0.04104499, 0.04104499, 0.041045 ]))\n", " fun: 0.04104499398863126\n", " message: 'Optimization terminated successfully.'\n", " nfev: 126\n", " nit: 65\n", " status: 0\n", " success: True\n", " x: array([ 6.46509387, -0.34497398])\n" ] } ], "source": [ "def logp_easy(logitθ, a=1e3, b=1):\n", " logabsjac = -1.0 * (np.log(1.0 + np.exp(-logitθ)) + np.log(1.0 + np.exp(logitθ)))\n", " return (-a * np.log(1.0 + np.exp(-logitθ)) - b * np.log(1.0 + np.exp(logitθ)) + \n", " logabsjac - \n", " sp.special.betaln(a + 1.0, b + 1.0))\n", "\n", "phi_hat, res = kl_vi(logp_easy, 10000, 1.0, 0.0)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "logit_theta = np.linspace(0.0, 14.0, 100000)\n", "plogit_theta = np.exp(logp_easy(logit_theta))\n", "qlogit_theta = np.exp(logq(logit_theta, phi_hat[0], phi_hat[1]))\n", "\n", "plt.plot(logit_theta, plogit_theta, label='p(logit(theta))')\n", "plt.plot(logit_theta, qlogit_theta, label='q(logit(theta))')\n", "plt.xlabel('logit(z)')\n", "plt.ylabel('PDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly re-casting $\\theta$ to have the same support as a Gaussian makes for nice and easy minimization and fits much better than the other way around. \n", "\n", "We will use this as a general strategy for automating variational inference.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Approximating an unknown posterior distribution\n", "\n", "Let's revisit the KL divergence and see what is available to us:\n", "\n", "\\begin{equation}\n", "\\phi^*=\\arg\\min_{\\phi\\in\\Phi}D_{\\rm KL}(q(\\theta; \\phi) || p(\\theta|X))\n", "\\end{equation}\n", "\n", "\n", "The KL divergence is given by\n", "\n", "\\begin{align}\n", "D_{\\rm KL}\\big(Q||P\\big)&=& \\int q(\\theta) \\log\\frac{q(\\theta)}{p(\\theta|x)}d\\theta\\\\\n", "&=& E_q\\left[\\log\\frac{q(\\theta)}{p(\\theta|x)}\\right]\\\\\n", "&=&E_q[\\log q(\\theta)]-E_q[\\log p(\\theta|x)]\\\\\n", "&=&-E_q[\\log p(\\theta,x)]+E_q[\\log q(\\theta)]+\\log p(x)\\\\\n", "&=& -ELBO +\\log p(x)\n", "\\end{align}\n", "\n", "Notice that the KL divergence is given by the sum of the ELBO and Model Evidence. To see why, let's revisit the model evidence. \n", "\n", "\\begin{align*}\n", "\\log p(x)&=&\\log\\int p(x,\\theta)d\\theta\\\\\n", "&=&\\log\\int p(x,\\theta)\\frac{q(\\theta)}{q(\\theta)}d\\theta\\\\\n", "&=&\\log(E_{q}\\left[\\frac{p(x,\\theta)}{q(\\theta)}\\right])\\\\\n", "&\\geq& E_q[\\log p(x,\\theta)]-E_q[\\log q(\\theta)].\n", "\\end{align*}\n", "\n", "This is due to the fact that logarithms are strictly concave, allowing us to invoke [**Jensen's inequality**](http://mathworld.wolfram.com/JensensInequality.html):\n", "\n", "> Let $f$ be a convex function (*i.e.* $f^{\\prime\\prime} \\ge 0$) of a random variable X. Then:\n", "> $f(E[X]) \\ge E[f(X)]$\n", ">\n", "> And when $f$ is *strictly* convex, then:\n", "> $$E[f(X)] = f(E[X]) \\iff X = E[X]$$\n", "> with probability 1.\n", "\n", "What this implies for a computational solution is that minimizing the KL divergence is accomplished by maximizing the evidence lower bound.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## [Automatic Differentiation Variational Inference](https://arxiv.org/abs/1603.00788): A Tale of Two Transformations\n", "With ease of computation in mind, Kucukelbir et. al. 2015 developed a way to perform VI automatically. Without going into too much detail (see reference for details), the authors proposed transforming the problem in a series of steps:\n", "\n", "1. Specify the joint model, $p(x,\\theta)$\n", "2. Transform model into surrogate containing unconstrained real-valued latent variables, $\\zeta$. $p(x,\\theta) \\to p(x,\\zeta)$\n", " - Variational inference is then performed on the transformed model. New objective: \n", " \n", "$$\n", "\\begin{equation}\n", "\\phi^*=\\arg\\min_{\\phi\\in\\Phi} KL(q(\\zeta; \\phi)||p(\\zeta|x))\n", "\\end{equation}\n", "$$\n", "\n", "all latent variables are defined on the same space. ADVI can now use a single variational family for all models\n", " \n", "3. ADVI recasts the gradient of the variational objective function as an expectation over $q$. This allows for the use of Monte Carlo integration to perform the optimization\n", "4. Next, the framework transforms the problem again and re-casts the gradient in terms of a standard Gaussian distribution. This makes MC integration very efficient since sampling is done from $N(0,1)$\n", "5. Compute noisy gradients to optimize the objective. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's get a little bit of a feel for how this happens " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember, we're first going to transform all of our parameters to have the same support in $R^k$. We next need to optimize the KL divergence on the transformed space (like in the sigmoid transformation above). \n", "\n", "To accomplish this, we need to optimize the ELBO for the transformed objective. Our objective function for the transformed variables is now given by the ELBO of the transformation:\n", "\n", "$$\n", "ELBO(\\phi) = E_{q(\\zeta;\\phi)}\\left[\\log p(x,T^{-1}(\\zeta))+\\log|\\det J_{T^{-1}}(\\zeta)|\\right] - E_q[\\log q(\\zeta;\\phi)]\n", "$$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notation is starting to get a litle hairy, so let's return to basics. Remember, the first expectation is just an expectation over a joint likelihood in terms of the approximating variational distribution. \n", "\n", "$$\n", "\\int q(z)\\log p(x,T^{-1}(\\zeta))|\\det J_{T^{-1}}(\\zeta)| dz \\approx \\frac{1}{n}\\sum_i \\log p(x|\\zeta_{i})p(\\zeta_{i})\n", "$$\n", "\n", "Problem is, we can't differentiate this MC integration with respect to the variational parameters (since they parameterize the distribution from which we draw $\\zeta_i$). So we need to transform one more time so that the expectation is in terms of a standard normal (this is called elliptic standardization), and them perform MC integration with a draw from a standard normal. \n", "\n", "$$\\begin{align}\n", "\\int q(\\zeta) \\log p(x|\\zeta)p(\\zeta) d\\zeta &= \\int N(\\zeta) \\log p(x|\\zeta\\sigma+\\mu)p(\\zeta\\sigma+\\mu) dz \\\\\n", "&\\approx \\frac{1}{n}\\sum_i \\log p(x|\\zeta_{i}\\sigma+\\mu)p(\\zeta_{i}\\sigma+\\mu)\\ .\n", "\\end{align}$$\n", "\n", "Now, since this integral is explicitly in terms of the variational parameters, we can optimize our objective. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](images/advi.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Above is something we can take derivatives of using a computational backend. We'll use PyMC in a moment. But let's return to our weird pdf.\n", "\n", "We can now implement a really crude version of advi on our weird pdf:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter, mu, lnsigma: 0| 3.3518e-01|-2.3741e-01\n", "iter, mu, lnsigma: 4000| 6.3373e+00|-4.7391e-01\n", "iter, mu, lnsigma: 8000| 6.4378e+00|-3.4406e-01\n", "iter, mu, lnsigma: 12000| 6.4592e+00|-3.5437e-01\n", "iter, mu, lnsigma: 16000| 6.4571e+00|-3.4403e-01\n", "iter, mu, lnsigma: 20000| 6.4656e+00|-3.5536e-01\n", "iter, mu, lnsigma: 24000| 6.4663e+00|-3.6306e-01\n", "iter, mu, lnsigma: 28000| 6.4572e+00|-3.5847e-01\n", "iter, mu, lnsigma: 32000| 6.4657e+00|-3.5701e-01\n", "iter, mu, lnsigma: 36000| 6.4643e+00|-3.5113e-01\n", "iter, mu, lnsigma: 40000| 6.4556e+00|-3.4125e-01\n", "iter, mu, lnsigma: 44000| 6.4647e+00|-3.4658e-01\n", "iter, mu, lnsigma: 48000| 6.4712e+00|-3.4985e-01\n", "iter, mu, lnsigma: 52000| 6.4660e+00|-3.4201e-01\n", "iter, mu, lnsigma: 56000| 6.4645e+00|-3.4355e-01\n", "iter, mu, lnsigma: 60000| 6.4649e+00|-3.4346e-01\n", "iter, mu, lnsigma: 64000| 6.4657e+00|-3.4193e-01\n", "iter, mu, lnsigma: 68000| 6.4624e+00|-3.4012e-01\n", "iter, mu, lnsigma: 72000| 6.4602e+00|-3.3670e-01\n", "iter, mu, lnsigma: 76000| 6.4618e+00|-3.3571e-01\n", "iter, mu, lnsigma: 80000| 6.4613e+00|-3.3416e-01\n", "iter, mu, lnsigma: 84000| 6.4601e+00|-3.3384e-01\n", "iter, mu, lnsigma: 88000| 6.4607e+00|-3.3474e-01\n", "iter, mu, lnsigma: 92000| 6.4619e+00|-3.3621e-01\n", "iter, mu, lnsigma: 96000| 6.4618e+00|-3.3613e-01\n" ] } ], "source": [ "def dlogp_easy_dzeta(zeta):\n", " theta = sp.special.expit(zeta)\n", " return (1e3 + 1.0) * (1.0 - theta) - 2 * theta\n", "\n", "def kl_vi_with_sgd(dlogp, mu, lnsigma, rng, n_iter=100000, n_draw=1, eta=5e-4, eta_decay=5e-5):\n", " for i in range(n_iter):\n", " # Draw the points and convert back to draws from the variational approximation.\n", " zeta_standard = rng.normal(size=n_draw)\n", " sigma = np.exp(lnsigma)\n", " zeta = zeta_standard*sigma + mu\n", " \n", " # Compute the derivs.\n", " dkl_dmu = -np.mean(dlogp(zeta))\n", " dkl_dlnsigma = -np.mean(dlogp(zeta) * zeta_standard * sigma) - 1\n", " \n", " # Now do SGD with the KL divergence.\n", " lnsigma -= dkl_dlnsigma * eta\n", " mu -= dkl_dmu * eta\n", " \n", " # Decay the learning rate.\n", " eta *= 1.0 - eta_decay\n", " \n", " if not (i % (n_iter // 25)):\n", " print(\"iter, mu, lnsigma: % 7d|% 10.4e|% 10.4e\" % \n", " (i, mu, lnsigma))\n", " \n", " return np.array([mu, lnsigma])\n", "\n", "rng = np.random.RandomState(seed=5678)\n", "phi_hat = kl_vi_with_sgd(dlogp_easy_dzeta, 0.0, 0.0, rng)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "logit_theta = np.linspace(0.0, 14.0, 100000)\n", "plogit_theta = np.exp(logp_easy(logit_theta))\n", "qlogit_theta = np.exp(logq(logit_theta, phi_hat[0], phi_hat[1]))\n", "\n", "plt.plot(logit_theta, plogit_theta, label='p(logit(theta))')\n", "plt.plot(logit_theta, qlogit_theta, label='q(logit(theta))')\n", "plt.xlabel('logit(theta)')\n", "plt.ylabel('PDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But we certainly don't want to have to compute derivatives all by hand!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variational Inference in PyMC\n", "\n", "Aesara, PyTorch, and Tensorflow are all computational backends to compute derivatives symbolically so we don't have to hand code anything. PyMC uses Aesara which is what we will be working in.\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "import pymc as pm\n", "import arviz as az\n", "import aesara.tensor as at\n", "\n", "size = 50\n", "true_intercept = 1\n", "true_slope = 2\n", "x = np.linspace(0, 1, size)\n", "\n", "# y = a + b*x\n", "true_regression_line = true_intercept + true_slope * x\n", "\n", "# add noise\n", "y = true_regression_line + np.random.normal(scale=.5, size=size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay let's plot this:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(7, 7))\n", "ax = fig.add_subplot(111, xlabel='x', ylabel='y', title='Generated data and underlying model')\n", "#plt.plot(x, y,\"bo\", label='sampled data', alpha =0.01)\n", "ax.plot(x, y,\"bo\", label='sampled data',alpha =0.5)\n", "ax.plot(x, true_regression_line, label='true regression line', lw=2.,color = \"red\")\n", "plt.legend(loc=0);" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (4 chains in 4 jobs)\n", "NUTS: [sigma, Intercept, x]\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [12000/12000 00:05<00:00 Sampling 4 chains, 2 divergences]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 2_000 tune and 1_000 draw iterations (8_000 + 4_000 draws total) took 6 seconds.\n", "The acceptance probability does not match the target. It is 0.8814, but should be close to 0.8. Try to increase the number of tuning steps.\n", "There were 2 divergences after tuning. Increase `target_accept` or reparameterize.\n", "The acceptance probability does not match the target. It is 0.6312, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "with pm.Model() as model:\n", " \n", " # Define priors\n", " sigma = pm.HalfCauchy('sigma', beta=10)\n", " intercept = pm.Normal('Intercept', 0, sigma=20)\n", " x_coeff = pm.Normal('x', 0, sigma=20)\n", " \n", " # Define likelihood\n", " likelihood = pm.Normal('y', mu=intercept + x_coeff * x,\n", " sigma=sigma, observed=y)\n", " \n", " trace = pm.sample(1000, tune=2000) \n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_trace(trace);" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [20000/20000 00:01<00:00 Average Loss = 41.356]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 41.369\n" ] } ], "source": [ "with model:\n", " approx = pm.fit(n=20_000)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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1StPn/WsvkEJd9oQQwA2TvTnJrbvWej9dVInia5olHiipdz8pH/+M3BNXnR0G8RBul+wdOiRpZoa19A5Ce2rouk9PYsmWo3Y9J7G/Xy9KkZ591tlhEA/hhsnedPrm17tKI9maUsjayxJSy58Qz+bRyV6pOyTCeal5Ju2naskzyoeqrP9wF0pq8MY/j6K9Q25wv/8c/gNxS3LQ3iGz+pyEENtyu2RvSeLuDl0d0rrbRvYwUvLYis/44b/P4OLVOlTWNhncb/fhywCA5hY3Xh+AkG7K6hLH3Zm+Vq8rrGO7+L0jKLmhmHJpWqJm2L9z/kchhLgAt2vZW0Imd17TvrGZvf6+MtGbS/s6RbmeEAK4YcvekuS25pMTNo8DAM5ckmp8rz0gfOXGLWz+6jejx5F3h34mQohLc7+WvRldMGc7H1qy+FRGXt+Uedrg63t+vGLSeb7O1V9hVJvyuuDM64O15y6tuIXmFuvXJSCEdHG/ZO+GxDWGB0YVdOpeKrY6cPzBFqeSyRm8tvkIUj+1fsUxQkgXSvYOdLLAMQups3GBMWeTKMs9FJbWODkSQtyL0WSflpaGmJgYREZGori4WLW9tLQUQqEQsbGxEAqFKCsrM+k1e3NWUvtcdMHoPvZe7tDeaOiAkO7LaLKfMmUKsrKyMGjQII3tycnJSExMRG5uLhITE7F69WqTXnMVJhUqM0L9wqKcY+5oX+VeVDzIJDP8wJN1HH8FpesKIbZlNNlHR0cjNDRUY1tNTQ0KCwshEAgAAAKBAIWFhaitrTX4WnfRXbo8AEB0rAQA0Nqm+SCTUwdorUjV3ehHT0i3YtHUS7FYjODgYHC5XAAAl8tFUFAQxGIxGIbR+1pAQIDOserr61FfX6+xTSKxvG/blZKFK3V72DKW00WVuGt4IHr5aP76dNcqooR4AqfPs8/IyEB6errNjudKrXJn5np7LUFbUd2INZ+cwCNjw7D8hQdse3A1cjmDi2W1GDVMt4FACDGfRck+NDQUlZWVkMlk4HK5kMlkkEqlCA0NBcMwel9jM2fOHMyYMUNjm0QiwcyZMy0JzcFc58qi03Jn7DP18nZn3Rtxle50UGu6b1TU4n3jw5+wb3OC9cckhFg29TIwMBB8Ph8ikQgAIBKJwOfzERAQYPA1NjweD+Hh4Rr/QkJCLPw4gCslYEdS5kjtlapsw7xj2rI7p71DDrkTy1kQ4i6MJvvU1FRMnDgREokEc+fOxdNPPw0ASElJQWZmJmJjY5GZmYk1a9ao3mPoNfuzPjEYypf5p6/ht4tS/TtY6ZcLErzzufkPFOlLsPZJ/obZpIXf6Zll+/CZCdNaCSGGGe3GSUpKQlJSks72iIgIZGdns77H0GvdgaGej/e/PgMAduteWPfpSYveZyzB6vtMR367jlFD+yMksLehd5sUg70GaHNPlGFe/Bg0NrfhL6u+x4IZd+PpCcPtci5C3JXbPUF7u9X6hTNMSVpHfi3HmWL7tfBNp6dFb+K7N2f9iv9774jNorGn6lstAIDvfy5zbiCEdENOn43TXZlSrZKNLbtVPs45jwatEslaC1WZpMmCxUZs2VWjeWC243rmOAwhtuR2LXtb+OHUNdsciCVx5Z200bEB7D1aovraUQuxuMLCLjRcS4j5KNk72Oki+xRDs1tL2xJ2CsVWl5n2DplTBq4JcSZK9nbU2m7PejXs7N3uVk+Sf007hJffPmj3k9vyZqKuoQXPLBMh56hpawkQ4i4o2dtRh12Lk7G7cuMWa5E3WzdkOeDgurTRKZU8rfksVZ0Lt/945oaNoiGke6Bk72An7FzT/tjZCqvev/foFcQtyYFM7ULF1rJ2ZLcRR+cLx6qrb9G7VjAh3QUlew9haldI5oEiAEBrO/sUVlcYoHX0EO0La3IxOyXXoeckxNYo2bsJ5WwcV8jF9krFjhiP+Pl8BWv3mzO65AixJUr2bkLZrXLyAns30VVxg91jsFsy7ryC2bs9/+tFKd75/BT+lWf6Au+EdBeU7F2IPQp+3WxoBQB8tOe8xccwdUC0W01mZPlQyp9V1c3bjo6GELujZO9ClP3lljC1Ls1VcT3iluRg308lKK/sau3X1bdYfG7dWOzDFsd1hW4uQpyByiW4kOxDf1j83puNrSbtd/jXcgC6Lf1yaQP683xV3zc2t8PPt4fe47jKM0lFpbXg9emJQQP7AACmv7EXggnD8XLCGACKEsnNLe3o18fHhKO5yIcixA6oZe9h9CXpT3IKNB6Ymqf+sJQaU1rG1qRMUyrjqH+GN9N/woINh1Tfy+SMxgNT6zN+wazkA2bFQK1/4o4o2bs5UxNXaUU9bjWyzyVXP4ahFr1yt0Wb8k07qZksmfZ5qrDS6D41txR99K5yt0KIPVCyd3PXpY2qr+saWlAmqde7r3Yube/QP93QUN5taG5HRVWj/h2cSDuh/3y+Ai+uzcNvl6Rd6/ZSlU3ihijZe5BX3vnB4CpbF8tqNdYDkNTorjOrVFqh/6IBAH/ffMTs+PTRvrCY0gJPXPU9pGqlHPQVPrt0tQ4AUHLjlt7zEeIOrE72hw8fxvTp05GQkIC4uDjk5eUBAEpLSyEUChEbGwuhUIiysjJrT0Ws1NpmeGGX1M80l0O0pjJkW7sMJwvE+PJ7y2cYWaOhuQ1Hz3bVv8k9cRWA4UTuiG6c5I9+Zq1dRIi9WZXsGYbBm2++iY0bNyInJwebNm3CsmXLIJfLkZycjMTEROTm5iIxMRGrV6+2VczEQbRzX3uHHIvNWNUq9bNf8O8fim0QiWaGljMMtu0+Z7QIm/rU0gulNTaIw3q/XXKF1c2IJ7J66qWXlxcaGhR/VA0NDQgKCkJdXR0KCwvx2WefAQAEAgHWrVuH2tpaBAQEaLy/vr4e9fWaXQISiX2LhRHTNN/uwHVpV8LUXhVLm75WM8MwNq2pI65ugri6CVfFXb83B34uw/BB/TT2yz9drhaEKUemEVrivqxK9hwOBx988AEWLlwIPz8/NDU1YefOnRCLxQgODgaXywUAcLlcBAUFQSwW6yT7jIwMpKenWxMGsZM3038CAIQH9bHqOHt+vIIZk0ZY/H79F5Gur7d+e87i4+uejzrtifuxqhuno6MDO3fuxLZt23D48GFs374dr7/+OpqbTa9xPmfOHBw6dEjjX1ZWljVhERuzNvcVdnahyOQMPs45r5rqyOaog+vMd9fplj/8ctWmTz0T92dVy76oqAhSqRRRUVEAgKioKPTq1Qs+Pj6orKyETCYDl8uFTCaDVCpFaGiozjF4PB54PJ41YZBu4twfVdh7tAQVVU1Ifvkh1n3e/1r/Qu66s3JMz9Tau2q/k8Oyj6mqb95GW7sMYQOtuwMyVV19C7Z8cxYjwvvh/dcnOeScpPuzqmUfEhICiUSCkhLFwtdXrlxBdXU1hg4dCj6fD5FIBAAQiUTg8/k6XTike1AmQWtb+MpCb3Izs6q+817snDZp1rFMmENv7uecuy4Pr6o9xWsLre0y7P3pCmtxvA6ZYpuycBshprCqZT9w4ECkpKRg8eLFqn7O9evXw9/fHykpKVi+fDm2bdsGHo+HtLQ0mwRMnEdfoly+9RheE96r933K3L7vWEnncRQ6ZHJcKKnB2DsH2jBKPTEYGXxlYNnw7IWSrlk+WQcu4tmYEfDtaX3Jqa9zL2L34cvg9fbBpPvDrT4eIVb/VsbHxyM+Pl5ne0REBLKzs609POkGLpTU4NX1+lu2v16U4vfLVaoHupQNg8zvi7D78GVs+vujGDXM+F2fPQZONQ5pQT/O8q3HVF//6+AlMAyDWU/xrY6r8XY7AKCltUPvPvqi/fViJTL2F+K9/3sM3lz2m/fjv1dgQ8YpfJ06DX166S94R9wHPUFLjLrVWVGzrsGyAcEOmRxvbf+f6ntlglWWcjC1YqctmLJ2rjUXFX3LOVqKtTCckfD++c1ZlFbUo9pAXf5v8xUVVl21rAWxPUr2xKiGZkUrc1PmrzY5npeZydQetWqUR1RvzHfTiTk6ajtn6Xy674KTIyGuhJI98QxGMjlH6+tvDl5yjbIGVswNLTNQv4ieJPA8lOyJw528IOns31Z8LzVS9sAelCm0Vm2uunpezTxw0bEBaXHUg13W1D8i3QutVEWcIkstmX6cU4D4iRH6d+Zo/MciR8/ewB/lNyHWquR55LfrABTjBiE9udafyEaUD6LZKxXTQ8Keh1r2xCX8fF5s93OoJ/or129pvGbK3P+4JTm4XH7T5PP9dOYGjv9eYfL+SiU3buGapMHofrZolFO73nNQsicu4Z3Pf9G7WIpDGqEmZr0fz1w3+ZAbM09jQ8Yps0O5pTY7iS2hU6ucWIKSPXEZzyzbp/e1s8VSvGZGeWVzqedU9Vy6O9/yReCVThZYcddisPlu7EExareTLpTsicvjcIBVO382uviKubRn27Clxq8PXtKKxXCzmi03ay8KYw679dm7wsAEcShK9oQA2PdTiWpmjnpCd/uUSI1/j0HJnrg8uf51z20q+5Ciy0Zjzr1WS95WUxUNHUf9lHabGen2VzGijZI9cXmOLKcAAAVqxc20e232/HjF4HtN7Se/dM38ip3mMqWrhqbZew5K9oRoKVNb7tBQITJrsJUuZqN+8aiqu21wwZK6hhaIq5v0vq7O0GWgpbUD6dln0dzSbtKxLFVz67bdfr5EFyV7QgwwMSd3MXF/7Vb3japGVaVLfV5KzcMLa3K7TqV1rhdScjF//Q9qoTBo75Dhtc2H8fvlKj3h6gYsOl6K3BNXVcXS7OXFtXlYse2Y8R2JTVCyJ8RMHTLFIIJ6LXul9g45Pt13AbeNtFi1u4cWbDiE198/orsj6zx70zrcJTXN+Pu7h1FaUY/tu3836T1A13iCI7p4Lms93GYvHTK5x5eGoHIJhJjpi++KEBUZhKSd/9N5LfdEGeQM4GUsH7O8LqnRrRFkbXq6UWVat45Sc0u7qvR0U0s7blQ1QlLThKhRwVZG4jzNLe0QvvUdEmNH4S9TI50djtNY3bJvbW1FcnIypk6diri4OKxatQoAUFpaCqFQiNjYWAiFQpSVlVl7KkJcwn+PXMa1SvZyBspun92HL9vkXMrG6FWJ/gqWltB3d/DW9uPIP10OAPj+f2VYsOEQUj4+obHPrcZW1UI03UF9UxsA4IdT15wciXNZ3bLftGkTfHx8kJubCw6Hg+rqagBAcnIyEhMTkZCQgJycHKxevRpffPGF1QET4go+2nPebsdW789vbetAS1sHFm06bJdzafdsmNKtsvqjn1Fy4xb+kyZAD2+uSedZ88kJ+Pl6441Z0ZaEaRse3o1jVcu+qakJe/bs0ViDdsCAAaipqUFhYSEEAgEAQCAQoLCwELW1tdZHTEg3pN1frF4HqOaW/hWlMg9cxKzkAxrb5nQO0jbebtc78GpP1zvvamRao9dnLkmR8MZe1oHm00WVOHrmhsnnKLlxC8U2mp6qzE3dIdXL5YzdxhasSvbl5eXw9/dHeno6nnnmGcyePRunT5+GWCxGcHAwuFzFVZ/L5SIoKAhisW6NkPr6ely/fl3jn0QisSYsQlzOvw8VaySvlduOq75Wdpvoo69MRHuHYrnHlrYOjeJp9qCRgJRdQFo56ZsfiiGXMyitsH7QdfF7R7Bky1GrjwOwr0rmihpvtyPhjb347xHbdAFqs6obp6OjA+Xl5Rg9ejSWLVuGc+fOYcGCBdiyZYvJx8jIyEB6ero1YRDi8jK/v4jM79kXRLE2CTGM8T7969JGyOQMuJ0jx+ZWztx9+DKei7lT4731zW2QyRn0dvUFy7vJ08LKZygO/nINz0y+0+bHt6plHxYWBm9vb1V3zdixY9G/f3/4+vqisrISMpmiRSKTySCVShEaGqpzjDlz5uDQoUMa/7KysqwJi5Bu5cvvi1RfnyqUQGLmyl2mJu58KwYoj/yqe/cxL/UgEld9pxuPxWcxT/G1OsQtycFVsW0Hr53NXncgViX7gIAAjBs3DsePK25JS0tLUVNTg2HDhoHP50MkEgEARCIR+Hw+AgICdI7B4/EQHh6u8S8kJMSasAjpttbuOon07LNmvUda24yWVuMVQW+3Keb+t7XLUFhq3viZvhLQbA+d1dxqwYINP0BaZ9/lJo+dUywMc7qo0rQ3aGXR+KU5yNhfaJNYLpbV4pOcApscy16jC1ZPvVyzZg127tyJuLg4/OMf/8DGjRvB4/GQkpKCzMxMxMbGIjMzE2vWrLFFvIQQLX/bdBjrPj1pfEcGKK9swNk/ugZ11fviaw2UYjBGWtusesjsh1+u4UZVE/JOXDXpvQxj+qBk8bU67NpbAIZhuvrijbxHX40ghoHNnhJ+48OfkHPUcN0kY+y9KI3VUy8HDx6ML7/8Umd7REQEsrOzrT08IcSGFm7M1/taUZn+1n5zS9cTwWxJafVHP3d9wz5+q1f80r14dcbdEEwYbnRf5aBt3KPDccrUFj3Mi8dduXW5hL3vxjs7BEJcxscs3QzKBNghkxvsa6++qZgeelVcj9ssXUbqRdMudl40GIZB6qcndRaJYXPIzPGEeakHUd45BdTYXYFq8lA3yfYu2Wfvyjgc9qcEV774oBOiIcR1tXfIMePNfUb7r08XVWLRu7oPd7W2y9Ah68pQLZ1TRWvrW3DyguY06svXb7Ie29T8ZklXh6nvKblxy7olJE1gqNidqTWPLOW+yV7P9gfv6hr8vWfEAMcEQ4irYrrW/q0wUh55zScnWLc/t1yEhuY2ne3XJLolJV5//0fcbu3QaY0zJi5QY12rl/3NX+deRNySHCx+74hVS0gaUyaux1+SvjN6F2OvGxC3Tfa2GO0QPj7SBoEQ4rpa2227rq86fUnr+ZX7se+nEpOO8eaHP+G6tAEFV6r1PlGr7wLQ3iFDpQnTWP9jp4eYtCmniOqrK2TvKavum+xZjBraX6Ma4fi7def9q4vmG6/098Bo21cDHBbKs/kxCWGjr7VuC61t+ss8/++8ZneJvhW+ispqkfn9RazYdlzvE7XK9xZfq8Px3ytU2zd/9RtefvugqovJ1LuCkhuaTwDLZHIc/71C79jAsvSfumIxcBJTW+zi6iaTF7cxh9sme7ar5Ksz7gGHw8H9o4IAACGBvVWv/e25sWaf42/PjUXk0P4m7csfpvuMgT7eXM3ov90gwIJn7jErNkKcrbyy0eR95XJGb4IzutRj58tLthzFhoxTqs3K+fcymWYfkfYKXNpHX/zeERw9c131/e7Dl7Eh4xT+9zt7f76xZxYYRv9n00duh1Fat0v2Pb0VH4mrVVD8uZg7MWKwv/739dCs3hfVeUEAoDehxz401OS4Bg3sg32bE/Dua48a3XfC2EEa33tzvbrPVAJCLHBV0oCEN/YaLApnLu0GX11DK5ZvPQbhW99pdAmx1R7alPmr6uuqzplIG744ZXRRGrY/0w//fRYJb+w1/iwBh/VLm3G7ZP/mbEUJ1SEhfTW2Ky8CgPEf5JKZUUh5Zbyq5kd4UB/W/QyNnt8doTn4a+pC1ADw6L2DkDAxQvU914tjcHm8Af69TD42Ia7sxbV5qimVptL+02hsboNUra/+1Q2HVF8rH/wyp8haYWnXimTKKajmOPiLYkDWHl0z5nC7ZH/nEEUr/JHO1nHqqw8DAJ6J6SosxPYj9+nZ1bJXpvDBwX2x7tXx+Ouz5nfxvLPwEbwwjW/y/up3D0EBfpgXfxeenTwC6UsnG3zff9LisGDG3QCAgf0p6ZPuob5Jf5VO7Qe/9HWfKJ0trsKpwq4pni+l5mGeWl+9pZZs+RF19S2ss4r0MeWMRVfZu330PelrK26X7AN4vvj3O0/j2ckjAABjRw7Evs0J8Omhf5GF4YP6YfyYrsFa9Qb7vSODDL43uL+fzrZ+fXoCAP40pWs2j/IOLoDHnpDnxY3R+J7D4eBFwV0Y2jlYq+/OoIe3F4ICFDH09u2hMwlp8+KJemPX544wGiAm9mVOf74xF0pqsHZXV7kI5UNfHTIT53PqUXztJnb8V3Pt3oqqRsQtycE7n5s2RbNMrUjbB/86AwCoqrvtlJW+3C7ZA0AvH2+TH1DYviwG6xc+Ai8vDiZFhQMAvFgWEH33tUc1ZsmM6myJP3Z/uGrbk+OH4W/PjUXmmqdU25bMjALQNSYwsH8vfLZqqs7x+XcYGcA10GRQflY5w2h87j2b4jFySH/Mix+j762s1nXeDRHi6bTvKpTz8H/unE2k0+XU2aprvN2OtnYZPtt3gfW4xorE2aPDx+MXHA8P6urbfzl+DPr19sFDY3SnZEYODUBAP1+Uieux8sUH8WDnlEv15Mo2o+fRsWG4XtmAGZNGqLbZuo9d/dI0Znggfr9cjWkPD1MNUk9/LAK79haozm2s37FfHx+9r8U+NBS5Jha4IsTdsdUaWr71GC6U1KCHt5feWXhbvz2HljYZnnhwCE4VSvBLYaVZM/Ys4fHJXl2/Pj54OUF/K/jPj0fij2t1uDsiEFyuaTdFXK4XZj1luO/elL52Q1f6sIF9cHfEALwwjQ9vrhfe2nEcf5k6SmOfL1OehEwux9Zvz1k0yKTUxwYLVYwI72fSWqeEuDK2mj8MugaB2zvk+P1ytd7379pboGqEAcBPZ01fttESbtmNY8wDnQ9LhQ3obWRPTfw7AvDVumno49fTZrHseusJfLhEMQi78sUH8NZc9to9ymlbbNM9e3h74Z2Fj2DUsACMGOyPb95+Gv59NVvn/n19ENivF5bOjFKNKRhi7s/GLHaqAULPIhBny/nRujLHSvaYae2Ryf7pR+7AV+ueQthA9imVjrBzxRS8938TERTgp5riOf7uMNYuJHW+Pa27GfPz7cF6uxgR3k/je3N+17LfeRqvds4IYvPJW09ofP/8FMuWXFs7fzyy33la7xPGj903iHW79oWPEHv53EaLodiDRyZ7DoeDvjZsnVsibEAf3DnYtKdvAdte6dkGr/lDNS8AEYMUyf+luLtU22Y/xdd579Y3JsPXxxuCCcMheOQO1fbNiydicLDiYhocoDljafzdYdi3OUEnhn2bEzBI7QK8Z1NXieq978bjvsgg+Pp440Ot6ajKaatsd1yL/jQWy194QGe7kvrnI8Sd2SzZp6enIzIyEsXFxQAUSxQKhULExsZCKBSirKzMVqdyOfYeWAG6kj2HA9X8/Z3Lp9js+LHjhwEABg1UdN8s/vN92LjoUY2B5edZCsMNCelqZc9Xa92PHNIf/1wyGbs3CPSeU9lVtHb+eGx7MwYAsGP5FEQO6Q/hEyM1noLWvsgo74aGh/XD2vnjsUPPzyL2oWGqLjC2gfG+fo5dLFv7yW5C2LlouYQLFy7g7NmzCAsLU21LTk5GYmIicnNzkZiYiNWrV9viVC4p5ZWHkP6G4YefbOlPU0Zi3+YEm3ZD9eh8wliZRH17erNOBzXU3a6dkL25XjplKNRz3fDOu4eQwN4YHNw1K+rdxRMx60nFBS1t0QRs+ccknXMN6dz/pfi74OfbQ3VH0MtH95kI5YUyJFD3mYgRRu6uTH1O4elH7jCpZHbUKNsXziPEFFYn+7a2NqxduxbJycmqP/aamhoUFhZCIFC06gQCAQoLC1Fba94ix92Fn28PDA2x74NIylo9j4wNM7Kn6SaoHStsQG/MFYzGijmGF3d57L5wg68DXRcMNhnJT6q+fk14H9a8Mh6hBgaDR98RqLoosOnhrfkrvCtpqqo0hrJ0RkR4PwT174XZT/F17sLU+/9zNumubDZySNfFIGvtU/giOZY1Dj9fb0x7uKsbS7tch9LLCWMwL566jojjWZ3st2zZgvj4eAwePFi1TSwWIzg4GFyuopXF5XIRFBQEsVj3sef6+npcv35d459EItHZz9MNDeVh3+YEjBpqfZeRsgGufuHgcDh4ZvKdRp8BUMahzz+XTML2ZTF6X1cfLO3l462qQGou5YNvXlp3E339emJ3Whz2bU7Ao/cqBmz9fHtgV9JUjL4jkPVYyvEb9UP19euhUwKb17sn+vN8WY/x2P3hGHunomXv05OLpZ0P06lfTPz7+mCAvy+mPzaC9RiAomCftq0OvGskrsL23X1WTe04c+YMzp8/j6VLl1p8jIyMDKSnp1sTBjFTj86LsD2WQbsjjL0VvnnxRJvOivnHX+7H3p9KNFrelvpo5eOoqGrU+Hl8tW6a3v0jwvvhitZzAkNDeGjvUDye//wUzbGNGZNGoK9fD43yGYDiDsi3Jxcjwv1Vy/fdPyoI0fxgSOua8d5Xv2H0HQEa4yL67H03HnI5g+ff+g5t7TL09evJunqUpdIWTcCy9GM2Ox4xTPuO1RasSvanTp1CSUkJpkxRDI5JJBLMmzcPK1asQGVlJWQyGbhcLmQyGaRSKUJDdacVzpkzBzNmzNDYJpFIMHPmTGtCIwa8Mn0M+vN88NBdIdjwtwkGi1IpKVvJlrJFUlYXFOBn8AE4fdjqhPfp1cNgfM9OHgFvtT++9Qsn4PmV+1XfzxUoumV6eHup7npKK7ouBmwzfj5fPRW9fLzh56vo8nopNQ9VdYqH3e4aHoghzYpuIOUA+ccrH8cr7/ygN0YOhwMul6MaoNBeE+Gdvz6ClduP630/m359euJWo+KCMfqOQPz12XuwfffvOvtlrnkSL6UehH9fH41qk64g/tHh2GtgVawPl07G31nW1XUmez3jYtXlY/78+Th27Bjy8/ORn5+PkJAQ7Nq1C9OmTQOfz4dIJAIAiEQi8Pl8BATodkHweDyEh4dr/AsJCdHZj9hOvz4+mBc/BlyuF+4aHojxdxseB8jZFI83ZkU5KDr7smQVsBcFd6kGjAFF95PS3nfjMWNSBNvbDArs10uV6AFgYGf3mTJF9/XriX2bE1TPXYQE9sZnq6bitefvVb0nNLA3Xv/LfawDw9prMNw9YoDBmVFsUl4erzGuo91lptSvjw92bxDgwyWTMOfp0cjZFI/evobbkXMFo1VfPzl+GN6a+yA+X61bMypr7VOY9vAwk+LdxLJWBFsjRXmHueFvEwz+PrwxK8qk1erUJb/8kE4357OTRyAowA/v/99j8NdTimTBM/fgzVmKMSZDY1jWsFu5hJSUFCxfvhzbtm0Dj8dDWlqavU5F7IytMBwA3B9pWX+7M82ffjcmRw2Gn6+30QW2DXnsvnC0tnfYrCssJLA3CktrDQ5uD/DvhSfGDcU//30WADDxvkGIiR6CmOghqn0WPHMPdu27gCWJUbhe1YiQAD/VYIT2zCgA+CI5FpV1zai51YIxwwMxd12eqjtqcEhfLJ0ZhcXC+wDo/z1Q8vPtoRpz+HLNU2i83QaulxfkcgZf5V1EQ1Mbjp2rwCsJYxA/MQKfiRQPIKnXlMpa+xR69vBCwZUaBPbzBa93T1XlV3X8YQF4Ke4uvPFh15KAPK3nLOYKRmPUsADs25yAuCU54A8LwIJn7sH23edws6FVZ2bZn5+IBAMG3xwsxsP3hGLifeGYqDYh4bq0AX9NU9TCmXR/OI781rWalb5xrC+SY9Gf54sXO+/+Pl75OI6dq0DeyasoKqvVeC/DMJDU8vHEg6YvimQOmyb7/PyuokARERHIzs625eGJC/l45eN6BytdWc8eXNw1XDFQq298wRRLTbzTMbo6Uae/PnsPHr471KSYkl9+CH+U32QdzH1i3FA8MU6RLEaE++u8Pv7uUFXFRgDoz/PV+P+4efFEfL6/ECteeEBV2ltZB+oBfjD8fL2xfuEE/O/3CnzzQ7HeGHt4e6F/367jLnx2LD7ac14nlju1Vo/j9VYkbPUW9ZMPDUO/PooChbvz/8CX3xdh1LAARGh9vrCBffDnJyLxr4OX8OasaDyq9kT1txsE8PbigMv1Us1gV96pfLh0Mnp6eyFsYB/camyF6Fgpnp2s+7NVFk28d+RALJkZBXFNEy5drcOk+/XPUNP+G/H18cbjDw7B4w8OQdySHI0uGw6HozOuY0tUCI1YRH39Xney5R+TcF1q3kpJbMxt8fv29MY4I6UylKL5wWZ3Lygt+tO9GBHujy+/L0IAT7dL4Y6wfljzynjW9/bn+eKbt5/u3I+Hb34oxri7zO9yVSbblS8anuar5OXFwSP3KLqTxt45AF9+r5iK3MPbC/9KnYZbja2qrrWZT47CY/cP0qhmC0BjTQrlg23K/0XqXTn9+vjgX6n6B+cz1zwJv84uKuHjI7F210mLazIpx20chZI9IWqGD+pncF5/d8fr3RPPPz4SE+4Ns6pkCIfDMTgFl/U9Fp+tS+TQAORsild1KfXu1UOn60s70WtbMjMKomOlZpUrUVIv//3A6BCDPwNluRB9Avs5dmU5SvaE2IGysqilLXB7CxvgvCKA1jI2dmBMUH8/u9dE+u/GOLtMbbYGJXtC7KB/X19kJMcaXAjGU9mjfK+r8TZxvQtHcr2ICHETATxfKnymZuydAwEAI4f4OzcQD0Ute0KIQzx4Vwi+eXuaxvMFxHGoZU8IcRhK9M5DyZ4QQjwAJXtCCPEAlOwJIcQDULInhBAPQMmeEEI8ACV7QgjxAC45z14mkwEALU9ICCFmUOZMZQ5V55LJvqqqCgBotSpCCLFAVVUVhg7VrIvPYUwtuO1ALS0tKCgowMCBA1WLlptKuaRhVlaWy6545eoxunp8gOvH6OrxAa4fo6vHB7hejDKZDFVVVRgzZgx8fTVr6btky97X1xfR0dFWHSMkJATh4foXFXAFrh6jq8cHuH6Mrh4f4Poxunp8gGvFqN2iV6IBWkII8QCU7AkhxANQsieEEA/gdsmex+Nh0aJF4PF0V6R3Fa4eo6vHB7h+jK4eH+D6Mbp6fED3iFHJJWfjEEIIsS23a9kTQgjRRcmeEEI8gFsl+9LSUgiFQsTGxkIoFKKsrMzu56yrq8Mrr7yC2NhYxMXFYdGiRaitrTUaj6WvWSs9PR2RkZEoLi52qRhbW1uRnJyMqVOnIi4uDqtWrXKp+ADg8OHDmD59OhISEhAXF4e8vDynx5iWloaYmBiN/6f2ismSeNniM/Q34+j4DP0MlbT/ZpwRo00wbmT27NnMnj17GIZhmD179jCzZ8+2+znr6uqYEydOqL7fsGEDs2LFCqPxWPqaNQoKCph58+YxkyZNYi5duuRSMa5bt455++23GblczjAMw1RVVblUfHK5nImOjlb93IqKiph7772XkclkTo3x1KlTTEVFBTN58mRVbNac19bxssVn6G/G0fHpi1GJ7W/GGTHagtsk++rqaiYqKorp6OhgGIZhOjo6mKioKKampsahcRw4cICZM2eOwXgsfc0ara2tzPPPP89cu3ZN9UvtKjE2NjYyUVFRTGNjo8Z2V4mPYRTJ/sEHH2ROnz7NMAzD/PLLL8zUqVNdJkb1RGWPmKyNly2RKin/ZuwVuyU/Q4Zh/5txdozWcMlyCZYQi8UIDg5W1dLhcrkICgqCWCxGQECAQ2KQy+X4+uuvERMTYzAehmEses2az7FlyxbEx8dj8ODBqm2uEmN5eTn8/f2Rnp6OkydPonfv3li8eDF8fX1dIj4A4HA4+OCDD7Bw4UL4+fmhqakJO3fudJmfoTp7xGSveNX/ZuwVu6Xxsf3NuFqM5nCrPntnW7duHfz8/DBr1ixnh6LhzJkzOH/+PBITE50dCquOjg6Ul5dj9OjR+M9//oOlS5fi73//O5qbm50dmkpHRwd27tyJbdu24fDhw9i+fTtef/11l4qxO6K/Gcdxm5Z9aGgoKisrIZPJwOVyIZPJIJVKERoa6pDzp6Wl4erVq9ixYwe8vLwMxsMwjEWvWerUqVMoKSnBlClTACgq9c2bNw8rVqxwiRjDwsLg7e0NgUAAABg7diz69+8PX19fl4gPAIqKiiCVShEVFQUAiIqKQq9eveDj4+MyMSrZ43fPHvFq/83YK3ZL6PubWb9+Pfh8vkvEaC63adkHBgaCz+dDJBIBAEQiEfh8vkNuj95//30UFBRg69at6Nmzp9F4LH3NUvPnz8exY8eQn5+P/Px8hISEYNeuXZg2bZpLxBgQEIBx48bh+PHjABQzFmpqajBs2DCXiA9QVDWUSCQoKSkBAFy5cgXV1dUYOnSoy8SoZI/fPVvHy/Y3Y6/YLaHvb2bChAkuE6PZHDEw4CiXL19mnnvuOWbq1KnMc889x1y5csXu5ywuLmZGjhzJTJ06lYmPj2fi4+OZhQsXGo3H0tdsQX2wyVVivHbtGjNr1ixGIBAw06dPZ44cOeJS8TEMw+Tk5DACgYCJi4tj4uLimIMHDzo9xnXr1jGPPvoow+fzmYcffpiZNm2a3WKyJF62+Az9zTjj56nvZ6hOe/DWlX4vTUXlEgghxAO4TTcOIYQQ/SjZE0KIB6BkTwghHoCSPSGEeABK9oQQ4gEo2RNCiAegZE8IIR6Akj0hhHiA/wcYCZdPqxqg4wAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(approx.hist[5000:]);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trace_vi = approx.sample() \n", "az.plot_trace(trace_vi);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, `trace_vi` acts exactly like a trace from mcmc. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean field variational inference\n", "\n", "By default, `fit` employs a mean field assumption regarding the model parameters. This assumes the variational distribution factors independently: \n", "\n", "$$q(\\theta_1, \\ldots, \\theta_n) = q(\\theta_1) \\cdots q(\\theta_n)$$\n", "\n", "We can generalize this to use a full-rank covariance matrix for our approximation, which carries an associated tradeoff in performance." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:01<00:00 Average Loss = 76.876]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 76.813\n" ] } ], "source": [ "with model:\n", " approx_fr = pm.fit(n=10_000, method='fullrank_advi')" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trace_fullrank = approx_fr.sample() \n", "az.plot_trace(trace_fullrank);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Drug trial analysis\n", "\n", "To illustrate how variational inference works in practice, we will use a fictitious example from Kruschke (2012) concerning the evaluation of a clinical trial for drug evaluation. The trial aims to evaluate the efficacy of a \"smart drug\" that is supposed to increase intelligence by comparing IQ scores of individuals in a treatment arm (those receiving the drug) to those in a control arm (those recieving a placebo). There are 47 individuals and 42 individuals in the treatment and control arms, respectively.\n", "\n", "Construct a model for estimating the effect size of the drug. Fit this model using both MCMC and ADVI, and compare the resulting estimates." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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DgIEIfwAwEOEPAAYi/AHAQIQ/ABiI8AcAA/Ua/m63W3l5eRo3bpw++uijwPADBw5o9uzZuummmzR79mx98sknkawTABBGvYb/1KlTVV1drVGjRgUNd7lcKioq0s6dO1VUVKTly5dHrEgAQHj1Gv65ublyOp1Bw44dO6b6+nrl5+dLkvLz81VfX6/W1tbIVAkACKsBPc+/qalJ6enpstlskiSbzaYRI0aoqalJaWlp3ab3er3yer1Bwzwez0AWDQAIg6j8mEtVVZUqKyujsSggotxut3bu3KnGxkbV1tZq7Nixkk5fAysrK1N7e7tSU1PldruVlZUV22KBrzGg8Hc6nWpubpbP55PNZpPP51NLS0u300NnlJSUqLCwMGiYx+NRcXHxQBYPxMzUqVM1b968btvumWtgBQUFqqmp0fLly7V58+YYVQn0bkDhP3z4cOXk5Kiurk4FBQWqq6tTTk5Oj6d8JMnhcMjhcIRUKBAPcnNzuw07cw1s06ZNkk5fA1u1apVaW1u7tQlOgSJe9Br+jz76qHbt2qWjR49q/vz5Sk1N1fbt27VixQqVlZVp3bp1cjgccrvd0agXiDv9uQbGKVDEi17Dv7y8XOXl5d2GZ2dn64UXXohIUcBgxSlQxIuoXPAFBrP+XAPjFCjiBY93AEJ09jUwSb1eAwPiAXv+QD9wDQyDBeEP9APXwDBYcNoHAAxE+AOAgQh/ADAQ4Q8ABiL8AcBAhD8AGIjwBwADEf4AYCDCHwAMRPgDgIEIfwAwEOEPAAYi/AHAQIQ/ABiI8AcAAxH+AGAgwj8EnV2+WJcAAAPCL3mFwD7EppuX1vRrntpfF0SoGgDoO/b8AcBAhD8AGIjwBwADEf4AYCDCHwAMRPgDgIEIfwAwEOEPAAYi/AHAQIQ/AITZQB/9Es1HxvB4BwAIs4E8+kWK7uNf2PMHAAOFvOefl5cnu92uoUOHSpJKS0t17bXXhlwYACBywnLa59lnn9XYsWPD8VYAgCiIyjl/r9crr9cbNMzj8URj0UDUcBSMRBKW8C8tLZVlWZo4caKWLFkih8MRNL6qqkqVlZXhWBQQ1zgKRqIIOfyrq6vldDrV2dmpxx57TBUVFVq9enXQNCUlJSosLAwa5vF4VFxcHOrigYTCUTDiRcjh73Q6JUl2u11FRUVauHBht2kcDke3owFgMOIoOH51dvlkH2KLdRlxI6Tw7+jokM/n0/nnny/LsrRjxw7l5OSEqzYgoXAUHN/42dVgIYX/sWPHtHjxYvl8Pvn9fmVnZ8vlcoWrNiChcBSMRBJS+GdmZmrbtm1hKgVIXBwFI9HweAcgDDgKRqIh/IEw4CgYiYZn+wCAgQh/ADAQ4Q8ABiL8AcBAhD8AGIjwBwADEf4AYCDCHwAMRPgDgIEIfwAwEOEPAAYi/AEgTnR2+aIyj8SD3QAgbkTzB2fY8wcAAxH+AGAgwh8ADET4A4CBCH8AMBDhj5gaaDe1gc4H4DS6eiKmBtK1TRp49zYkvs4un+xDbLEuI+ER/gASCjsM4cFpHwAwEOEPAAYi/AHAQIQ/ABiI8AcAAxH+AGCguA3/aD7XerDiBqrBgf9HRELc9vOP5nOtByv6Qw8O/D8iEuJ2zx8AEDmEPwAYiPAHAAOFHP4HDhzQ7NmzddNNN2n27Nn65JNPwlAWkHhoC0gkIYe/y+VSUVGRdu7cqaKiIi1fvjwcdQEJh7aARBJSb59jx46pvr5emzZtkiTl5+dr1apVam1tVVpaWmA6r9crr9cbNG9jY6MkyePxnPP9uzpa+1XPZ5991q/pw2EgNfZ3noHOF8qyoimcNZ7Znny+6HZzjLe2IMWmPURLIrShaNbYk97aQpJlWVb/yvvKnj179NBDD2n79u2BYTNnztRTTz2lyy+/PDBs7dq1qqysHOhigH6rrq5Wbm5u1JZHW0C8OldbiEo//5KSEhUWFgYNO3TokObPn6/Nmzdr1KhR0Sgj7ng8HhUXF6u6ulojR46MdTkxEe514PP5dOTIEV1xxRVhqC78emoLnZ2d+vTTT5WVlSWbLbw/UhLv2xj1hebr6uutLYQU/k6nU83NzfL5fLLZbPL5fGppaZHT6QyazuFwyOFw9Pgeo0aNUkZGRihlJLyRI0eyDsK4DkaPHh2W9+mPUNvCd77znYjWF+/bGPWF5lz1fV1bCOmC7/Dhw5WTk6O6ujpJUl1dnXJycoLOcQImoC0g0YR82mfFihUqKyvTunXr5HA45Ha7w1EXkHBoC0gkIYd/dna2XnjhhXDUAiQ02gISSczu8HU4HFq0aNE5rwWYgHXAOoi0eF+/1BeaUOoLqasnACAx8WwfADAQ4Q8ABiL8AcBAhD8AGIjwBwADRf03fNva2gJPmxs5cqQuuOCCaJcADHq0M/QmauF/6NAh/fKXv1R9fb1GjBghSWppadF3v/tdrVy5UllZWdEqJeZomKyDSIn3dvbGG29oypQpkqQTJ06ooqJC//rXv5STkyOXy6Vvf/vbMa3vDBO2z6j1858zZ46KioqUn5+v5OTTZ5v8fr9qa2u1ZcsW/fGPf4xGGTEV7w0zGlgHkRXv7aywsFAvvfSSJKmiokJ+v19FRUXavn27Dh48qGeeeSam9SXC9hm2L1ArSm666aYBjRtMZs+ebdXU1Fg+ny8wzOfzWdu2bbPuuOOOGFYWPayDyIr3dlZQUBB4fcstt1idnZ2Bv/Pz82NQUbBE2D5vvfXWwOuVK1daLpfL2rdvn/X0009bP/3pT/v8PlG74Juamqq6ujpZZx1oWJall19+OW5vnQ639vZ23XLLLYE9MklKTk5WQUGBjh8/HsPKood1EFnx3s46OzvV0NCgjz/+WElJSRoyZEhg3NnbRKwkwvZ59v/tO++8o0ceeURjx47Vz372MzU0NPT5faJ2zv+JJ56Qy+XSypUrAz860NzcrMsuu0xPPPFEtMqIqTMNc9asWUpKSpJ0+j+ytrY2LhpmNLAOIut/25llWWpublZOTk5ctLOTJ0/q3nvvDfzd3Nys9PR0ff7553ER/omwfZ75ArUsK6Qv0Kg/26e1tVVNTU3q6OjQ0KFDlZWVFTcrNdI++eQTuVwuffjhh0pPT5f01RfgihUrIv6DHvGAdRAdZ7ezjIyMbj8qE2tnLqimpKQoMzNTknTkyJHA61hJhO0zLy9PSUlJgSOArVu3Br5A586dG7im0puohf/u3bv10EMPacSIEXK73XrwwQc1bNgwHTt2TL/61a+Ul5cXjTLiwpmGKZ3+BSgTf/CDdRAZjY2NcrlceuONNySdfurjyZMndeedd2rJkiWy2+3U1weJuH1+8cUXOnr0aJ+/QKMW/gUFBXryySfl9Xq1aNEirV+/XhMmTFBDQ4OWLl2qbdu2RaOMuGBCNzLExty5c3X77bfruuuu08svv6y2tjYVFxfr6aeflt1ul8vlor4+SIQ2GnKNoV977puzr/Jff/315xw3mB08eNCaN2+elZuba82cOdOaOXOmlZuba82bN886cOBArMuLitbWVusXv/iFNX/+fOsPf/hD0LhFixbFqKrB4+abbw76+7bbbrMs63SPlWnTpsWipCDxXl8itNFw1Ri1C75JSUlqaGiQ1+tVR0eH/v3vf+uqq67SgQMH5PP5olVGTC1btkxFRUXatGlTtz7YDz30UMz7YEeDy+VSRkaGrrvuOm3dulV///vf9cwzzyglJUWffvpprMtLeCkpKTp06JAuvvhi7dmzJ3AaJTk5WSkpUb+hv5t4ry8R2mjYaozc91OwV1991Zo0aZI1efJk680337Tuvvtua9asWdbEiROt2traaJURU/HeBzsabrnllsBrv99vrVixwlqwYIF18uRJY44AI+m1116zJk+ebOXn5wfammVZ1pEjR6xHHnkkxtXFf32J0EbDVWPUwv9/nTp1ynr//fetI0eOxKqEqJs9e7ZVW1tr+f3+wDC/32/V1NRYt99+ewwri57p06d3G/bEE09Y8+bN63Ec+u/48ePWe++9Z504cSLWpfQonutLhDYarhr5GccoSoRuZJF233336d5779WkSZOChq9Zs0bPP/+89u7dG6PKgMRoo+GqkfCPgUTsRhYu7e3tSkpK0re+9a1u4z7++GONGTMmBlUBwRKhjYZaI+EfJ26++WbV1tbGuoyYYh0gniXC9tmfGmN/ed0gH3/8cY/DLctSW1tblKuJjXOtA0nGrAPEr0Roo+GqkfCPovz8fI0aNUo9HWy1t7dHv6AYYB0gniXC9hmuGgn/KBo1apS2bNkSuEhztuuuuy4GFUUf6wDxLBG2z3DVGPvH6BnkxhtvVGNjY4/jpk2bFuVqYoN1gHiWCNtnuGrkgi8AGIg9fwAwEOEPAAYi/AHAQIQ/ABjo/wARJCwGNBzl9wAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "drug = (101,100,102,104,102,97,105,105,98,101,100,123,105,103,100,95,102,106,\n", " 109,102,82,102,100,102,102,101,102,102,103,103,97,97,103,101,97,104,\n", " 96,103,124,101,101,100,101,101,104,100,101)\n", "placebo = (99,101,100,101,102,100,97,101,104,101,102,102,100,105,88,101,100,\n", " 104,100,100,100,101,102,103,97,101,101,100,101,99,101,100,100,\n", " 101,100,99,101,100,102,99,100,99)\n", "\n", "y1 = np.array(drug)\n", "y2 = np.array(placebo)\n", "y = pd.DataFrame(dict(value=np.r_[y1, y2], group=np.r_[['drug']*len(drug), ['placebo']*len(placebo)]))\n", "\n", "y.hist('value', by='group');" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# Write your answer here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Mixture model\n", "\n", "Let's look at using VI to estimate a simple, but less straightforward model: a mixture model that features a bimodal posterior distribution. Mixture models can be specified easily in PyMC with the `Mixture` class, that accepts a set of densities and an associated set of weights. " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[0;31mInit signature:\u001b[0m\n", "\u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNormalMixture\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mmu\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0msigma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mtau\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mcomp_shape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mDocstring:\u001b[0m \n", "Normal mixture log-likelihood\n", "\n", ".. math::\n", "\n", " f(x \\mid w, \\mu, \\sigma^2) = \\sum_{i = 1}^n w_i N(x \\mid \\mu_i, \\sigma^2_i)\n", "\n", "======== =======================================\n", "Support :math:`x \\in \\mathbb{R}`\n", "Mean :math:`\\sum_{i = 1}^n w_i \\mu_i`\n", "Variance :math:`\\sum_{i = 1}^n w_i^2 \\sigma^2_i`\n", "======== =======================================\n", "\n", "Parameters\n", "----------\n", "w : tensor_like of float\n", " w >= 0 and w <= 1\n", " the mixture weights\n", "mu : tensor_like of float\n", " the component means\n", "sigma : tensor_like of float\n", " the component standard deviations\n", "tau : tensor_like of float\n", " the component precisions\n", "comp_shape : shape of the Normal component\n", " notice that it should be different than the shape\n", " of the mixture distribution, with the last axis representing\n", " the number of components.\n", "\n", "Notes\n", "-----\n", "You only have to pass in sigma or tau, but not both.\n", "\n", "Examples\n", "--------\n", ".. code-block:: python\n", "\n", " n_components = 3\n", "\n", " with pm.Model() as gauss_mix:\n", " μ = pm.Normal(\n", " \"μ\",\n", " mu=data.mean(),\n", " sigma=10,\n", " shape=n_components,\n", " transform=pm.transforms.ordered,\n", " initval=[1, 2, 3],\n", " )\n", " σ = pm.HalfNormal(\"σ\", sigma=10, shape=n_components)\n", " weights = pm.Dirichlet(\"w\", np.ones(n_components))\n", "\n", " y = pm.NormalMixture(\"y\", w=weights, mu=μ, sigma=σ, observed=data)\n", "\u001b[0;31mFile:\u001b[0m ~/pymc/pymc/distributions/mixture.py\n", "\u001b[0;31mType:\u001b[0m type\n", "\u001b[0;31mSubclasses:\u001b[0m \n" ] } ], "source": [ "pm.NormalMixture?" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "w = np.array([.2, .8])\n", "mu = np.array([-.3, .5])\n", "sd = np.array([.1, .1])\n", "\n", "with pm.Model() as mixture_model:\n", " x = pm.NormalMixture('x', w=w, mu=mu, sigma=sd)\n", " x2 = pm.Deterministic('x2', x ** 2)\n", " sin_x = pm.Deterministic('sin_x', pm.math.sin(x))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [x]\n", "/home/fonnesbeck/pymc/pymc/aesaraf.py:369: UserWarning: No value variable found for normal_rv{0, (0, 0), floatX, False}.out; the random variable will not be replaced.\n", " warnings.warn(\n", "/home/fonnesbeck/pymc/pymc/aesaraf.py:369: UserWarning: No value variable found for normal_rv{0, (0, 0), floatX, False}.out; the random variable will not be replaced.\n", " warnings.warn(\n" ] }, { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 2 chains for 5_000 tune and 10_000 draw iterations (10_000 + 20_000 draws total) took 26 seconds.\n", "We recommend running at least 4 chains for robust computation of convergence diagnostics\n" ] } ], "source": [ "with mixture_model:\n", " mixture_trace = pm.sample(10000, tune=5000, cores=2, random_seed=(1, 42))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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CkbQc2Jy76Ec4mkYwmsKyegsGhqNY1Ty6HUAyncWhMy5o1BzWLrGPKzyxpqUCSgWL/uEodGoOLn8C6QwPlZJFIsUXrC3qc0fQ1hOAxaSGw6qDzawBADAsg2Q6C7cvDp1GgVgiA5NehUanEcfOSx1ZlmEwti+TTEkdUJcvDgYMahwGeAJxGHVKVJilWTmzXg3ryFrGbFbAkDcGhgG4ke+zL5TA6U4f7GO+e25fDIPeGOrsBixvKEzFMWiV6HNHwI4MpuRSdbLZxZ3y1+uOoHswjOvW18jpSunM5O/ZE0jg7EUfrl7rRCYryOlcQ94YwlEpkOAFASw7OsM/4ImiwqxBMsVDrSyc+Q9FU6gayRQQBBHpkY50jtSJl2ZALEY1OJaBWsnBatLANJI2mkhlEYmloVJy8AYTONMlBf5atQL1VQZE4mn0uyOosRtwvjuAfl3xoPFCbwCrm22IJzKjHW1Ruj4IInCsbRhKBYt4MlswU3uhN4BEKgteEHFxMASOHd9Jz828+UJJeEMJKJQsaioMsBo1UHAsEsksGIZBz5A0O8yyDKor9AjH0vjrwZ682QjpuYORFF4+2o9oPIMVjdLnNZMVcKrDC2eFDo1OEw6ecWFVkw1Wk1pKSQtL5wRRFJFI8ejsDxWkpbEsg9dPDQEQodOqEI6mpNS1Bgs0KgUOnXEhEE4hGk8XZHewLINYIoMKsxZ7jw9AEEXUV02cxjbsj6N/WPobtOfNAr9+ahChaAXae4NQq1gMeGJodJrQ644gEs/A5YtDr1XixAWPPDBS5zBg++Y6DAfiUCpY+ENJnOv2I8sLUHAsXjnWjwanERoVh2gig2vXVUsBnSDiuvU14AUBItiCv1k6w+N0p7fgbywIojwg0FRtkiuUipDOqUoFh3SGB4PRlNaxywkAoMKsweEzLniDCVRatPCPFOdJpLJywMuyDIw6FWKJjPRZC8TRXGvCyS4//OEktGoF+oajiE9RXZUCKkLInOAFEU/84Qw2r3Bg43JHwe8YhsEH7ls/o+d1WHXgeQGvnRzETZtqwbIMPnjvOri8MfzLk4fxn39/i1zMgpCZYBjAadMhGEnDG0qg1q5HMJJCa4cXSgWLdJYvWKeQm2X4y4Ee+MNSBy53AY/GMxBFYNATQ3ONRQ6o4smM3AHwh5Nw++PymqtVTTakMwISqSy6BoJYWm8FxzJyEHO+O4Aqmw6JZBaNTiP8oST+tL8bNpMGW1Y64PZLs1RHzw/Li9QtRjVsJg0sRrXcgfaFEnJHad+pQTQ6TRgOxMHzAta0VIBjWTRVG2E1aeT3eqE3ALtFi1SaR3tfAOe7AzDolLjQG8DAcBQrm2ywGtV4/mAPHDYdTHoVznX7UVOph9kgfS87+4PQqDi5kxhLZsAx0izVYpabgQhFU7iYt14ufy1QTjyZAcex8u/cvvi4dUS5Tn88mYXZMBo4NVWbEE1k5MAjJ5MVcOK8B9WVemhUCnQNhsAxDLK8NIPk8sXkjmulRYtMVgDLMmipNeP11iGAAe6/ZSkOn3WhazCElY02eWbEbtWCGWknMJJCKIrwhZPwh5PQaZRQcAw4lsHB0y5YjWpYTGocbXOjrScAu1WLSrMW6SyPvccH0D8cRSSeRqVFml0QRFHe/Lp/OAqlgoXbH4cvlMDNm+sKjsuAJwJPIAGOZeAdmckZHI4hkxHQNTLTUTEyGJHK8Lg4GILNpEEgkoJWzaFrMIyWWjP6hyPIZAU015gRiqXltEy1iitI0QxF0/LsWCyZwfqlduxvHZJ/H4ikxqUM+kNJ/OrFdvlnm1EDs1ENfziJg6dd2LxSumYadcqCQhoqJYcldWY4rDrEkxkEIkmYdCpUmDQYGAmaBr1RZHkRg54oauyGcTN6AOCwasGxUlpeOsMjleFRZdPJa0P1GgWqK/TwBBJwWHUIx1JIpnkwDIPhQEKeVTxyzg1eEJFKZ2EzacCPzCDFExn0DUuZJMvqLRAEEX3DESRSUvroG7Y1oMZuAAAYdCocv+CBWjn6/VcpWVzoDaK60iCfF3hBlM+R6QwPk04FYWRwts4hBfJj0zaPtQ2j2xVBLJGBQacEyzBQKTkM++M41+1H95D0t2ZZacCDYxlsXG5HMsXj0DTXZy/usxchpGxeOtKLXncEf//gloLbv//bVixvsOKWLfUzfu4LvUF8+/+OodZhwNI6CziOxSfesQUf/deX8INnTuGT79x6qc0nV7hcEBGIJBGKpmHUqRBPZWBglAhGUtAXKXGe6/Rc6A3CMhI8xFNZdA4EcePGWthMakTiaSSS2ZH0GamjpdcoUD3SucjX746gzx3BxaEwmpwmXBhJ1wtEUjjd4YNKyaFnJLXHYlRDFEWc6w7Io9EAYNSpEImn4fbH5Zkwu1WL5/ZdxHAgDq1KAWeFDtmsgP7hCOLJLGrseoRGZj9EUUr5Wt5ghSCIYFkGJzs88u8BoNZugMsXR6VZi0NnXeB5EQ6rDhVmrZw6M+iNIZ3hYdSp5MIDyVQWeq1STk/KrdtZrHLj52PTs/Irs01U+nmydMgTFzy4aVMtmJFZSFGU9jdLZ3g4K0YrnzEMoFazeL11SAoKMjxCsTREUUoLy3+NSrNGTg816pTgWBbBaArReAbbVjuRyvDy5yGZzsrvIZrIoKHKiFgyg9daB+ENJtBQZZQ76hajlCLmDSURiadhH8k28AQS8AQSaK4xQaNSIDJSac4bTMCkU2HQE4MgRrG83iKliKo4LKu3yJ3sjv4QljdYkNbwuNATHLfGLxhNQa0aDToFQQTHMXIhmNy2AgzDyJ/DyJjtCWrtBgx5Y/CHkiPff+mznUhl5fTHV08M4PBISe8ltWYkUtmi6+PGFrXxR5LQ65SIJ0XoNAr0u6MQRVH+fjtVOvCCgERKwLmLfrS2e5DhBbh8cUTiGQwHexBPZFBjNyCWyEKt4hCIpFBh0RYcC7NBhXgii+GRv5d4XoROq4DbH5ePOQDEklm5UMjyegt8oQSaqk1w++No7w2g3mHAcCABlmWQSGdh1Ksw4IkilsxKs+cmNdIZKU0ynspIGSlZARVmrTxbLq0BFeWAr6M/iKZqE3yhJALhJOqrjAhGUjjX7QfLMGiqKdy7MhxPQzPyN/WHU/J5r8cVxpFzbph0Kug0CgiCCINWiYuD0jG/arUT1ZV6vHysH3qNNLCQW/snFb+Ij5vNLwUFVISQWZflBTz1/Hls31yH5hqzfLuUow05n3qmVjXb8IPP7CooFmA2qPHB+9bjn588jO1b6nDVauclvQa5kjEFa5eiiQyQyECtZDGYkdKhYokMznX74bDqYNQpEYln5NLKaiUHBSd9xk+2e5DlpcIMLx3th1LBwqhTIRBOyuv3FRwrF2Soc4wGVpUWLTzBBPpcEQTCSahUHDAy0N2ZN8NRZdPJo8M9Q4WVAvM7SbkOhyCIYBipEIKUeiuAF0TERzpQQ94YTHoVfKEkQrGU1AEOJuAJJrC83iKnClZX6mHSqeT0R2/euip/OIm+4Yic4uSw6jAciCMriKip1GPQG0OvO4IltaPnhywvIJnKLtqZKuESMhojY8p2j12f0z0UBscyOHzWLVfaC0Sk9L5kWppRTaZ5WI1qqJRcweebZRm4/XEsrbPIZctzwZRKwSISz0CvUaLRaYQ7EMeSWjOyWRGdrgBsJg2MutHBhUQyO26dXq87AotBjWDe2iwGQCojoH84Kv8OkNLTLMbRGdFKs7SdQK69nqA0O6JSsFhSZ4GCg/y7U50+pNP8uMGO3NUmneGxpNYsrR0SgXBkNIDUaRSIJ7MIRKSKeLV2AypMGvjCSSTTUlCUSGUhiiKCkRR63RE0Vo9Ps4sns/L3KPcdzQ2uACNrgDxR+MJJLG+wFlQCHfREYTaooVVz6B5TwMHlj8M1Msu1qsmGjryCDLl1eSzLyMU2HHotfKEEzvf45eBJwbEFAyGAlGbrDU2+dnE4mEA6K8jvJ+mKwGbSoKXWDP9I+fr8QYH8taWhaBqhaBoMAL1OiVSGR3WlHsfOexBNDMJp00E1kpaaqxw4eiwzONnugUrBjqu2qlUrkEhlkUzz8IeTBeX2z3T5kMlKazXBSIFw/u9dvhiW1Jnk2duxhSzCsTR8oSQanSYwjPTzRAU88i3OsxYhpKxePtoPTzCBB96wvOB2lmXwwRmm+o1VaZFGv1893o+bNtWBZRlct74G21ZX4Yk/nMGWFQ45RYqQ2ZAqst5lOBBHIqUsGIXWqhXQaaTOw9iKXKIowh9OwqxXQatWIDXS0c3pH45iVZNNKoYhiGAZZiSlhi/oDCk4FlleQKVFC7c/Dl4QYbdoYTaop+wgReMZeUQeGF9yWhTH7/OjGykq0TUYQnZkBkqnVuDiYAgVY6ogskyuYydiaKQcdK6DpVFy8hodAHJHWqlgkUhlcfCMC9vHpHAtFpMVMJmuscUtel0RDHlj48pYn+8JFBTeK9YxzD2m2O/SWQEVZg18oSRirgx6XBHswWgxP384WbAucKJVsWPb1VRtwqA3Bo2Kg1GnlH8vzYyMzrB6Q4mCQD2XapbOCnIgpVZKs23pDI9+TxS1doM8yJHfJilgCklr9zQKufIbAFiNGpj1o5/X/GIhuZmN3PHJbVvQ3htE50AIVTYd1Equ6FouAOC40dsPnXXhxAUP6hwGeAKFa8t4QZQLOOTec26GufB+hechjpXOEYIgyrNRg94YgpFUwbqf/OIjuWM2FZtJM65cfpYXMByIIxhJjitzD0D+vOQTMVqAJ1+VVTtunV99lRHxRAZ6rTRY01JrBsMwBXuB5aeyjk2nFEWgemRmNhBOyoFoTq87AuWZifsGnSVuXzEW9TYIIbOKF0T8+sULuG59DeocoyN4zx/skTfwnS1dA0H8xy+OF1RPetebVqN/OIqXjvbN6muRK0uVTYdi3SM2ryJVjkalQH5M4g0lEIqliu4rleVFqJQcQrE0XP44ApHUuOpe/cNRBKPSSHlunUxyTNpQrnOUGFkz4A0mEEtkiu4vk5ObSRjbkRr7+gDgHlPyPff6uUIyw4E4OgdCSI8UqsiXX144OKaC29hjp9NIbcpkpdmKmexTs1Bc4sT8lHId30qzRs4CKPVojq206sjbZLpY5zinukJfEPAAkNOwJtM3HJVTDvuGp650mP+81pH1gDm5z3NuBnbAEx2XrgeMfvYEURyXEjjgicrB1FQZFLkZ2lzH2+2Po3ckNXeshiqjfH8Acmogg/Hfw5xwLAXTyHqxscEUIG3UnN9EQRTlYC6/snc8lS2Y8c6XykjV/kyGydcb+8PJontwqRRs0WAKkAZHJqIaEzwlUryc8pd7S33uCHzhJFRKFi5fHG09gZEiEqVtLZBMZdHrCiMQGR9M5Uy2N9tMUUBFCJlV+1sHMeCJ4a07C2en+oej6C1x75pSLau34oeP7cKKxtG1F03VJty0sQ7/99cLs7ZZJrmyMIzUSSr26cntW5LPE0yMK209thOab7INcqXRWhG6EtPeYsksWIZBrd2AXnekoFwyALlcOTB+Tch0TGcfnskMjgm+xj5vrnLbYjR2JH625QIGhYKVg9qqInv/je1k5woT5Ct27lQpWDRUGaHM62CnMvy4jWvHBv/FzGQT52Sah06jQCCSQjyZQUuNWa48WIr8gYPJthSaar+hDC8V67AY1VIFukn0uiNIZYoMWAQm3nZAo1agwqKZ8PdZXixovygW/3txLIP4yPmhmEg8IxeymEyxwC+XVpmruJsvf+ZvrLGfs2A0KRcKGfsO8jcO7h4Ky6mLU/EEE4gls3D54gWBd6ltnCkKqAghs+q3L3dg66oqtOStjQCA9965Bu+9c82sv15u4ftLR/vki8qbdy6D2x/HgdNDUzyakLmh08wsoz6V4RGJZ8aNoE+UTgRIHcCx1a1yYsnJS/1eqtoixTSmY2wHi2WZcUHhYuGs1E99p0uQm2XK7ywWC4T7x3Sig5HUuA55sQGBdFZArztSMAvqz1sLWOp+gpcitz4pmebhCcYL0sBm22TzVIIgraUaW3mxGI1q/HGZbFAlHEvLaYaXIpdCOFmAWEraXzG51MtLTWMdu6Zrtk10XpwLFFARQmZNe18A7X1B3Hlji3zbuYt+vHCoZ2Qh/NzkvPS6wvjPX5xA20hOfVO1CRuX2/HsK51z8nqkfPbu3YvbbrsNu3btwuOPPz7u9wcPHsSWLVtw99134+6778Z3vvOdMrQScsrOTI3tAk012zrR5qhzrZSNafPpNeOrI+bLbZI6047e5WyOM/7mfAZsKsVSR+fSpcy4lmI28htsJk3RFLhS0iLJzOXSFEuZLZ0tFFARQmbNn/Z3o7pCj43L7PJtpzq9eOFw35yuH2iuMeOHj70Ba1pGNxa9Z/sSnOv243yPf5JHkoWE53l8+ctfxg9/+EM899xz+MMf/oCOjo5x99u6dSueffZZPPvss/jIRz5ShpZiwtz9K91UaxdyaWuuMamBi8FcDSjlTFZafbpUk6yDKbeJ0rguR/5wclxBDmB+O/pTKWcgbpliDddMzSSl9FJdvt8YQsiCEo2n8crxAbzx2qaChedvfcNyfOUD1815Z6LCrIUgiHh5JPVv8woH6quMeHZv15y+Lpk/ra2taGxsRH19PVQqFXbv3o09e/bM+utMVtihXMYu5l6scmeJ2VqzRWZmooIDxQoUzHWxjbFKKWE9H2wmTUmzjlMsyZpzUwVM5ZwNLhZsLlQUUBFCZsWeI30QRRFvuKoBgFSu9MUjvRBFcdKqP7Op1x3Bt//vONq6/WAYBnfd2IL9rYPwhUpbzEoub263G07n6P5iVVVVcLvd4+534sQJ3HXXXXj44YfR3t5e9LnC4TD6+/sL/nO5XHPW9ks12ZqLxYQf6X0upFmIUo2tcDjbpkqnnA3FRv5zAcNi+5tZjGpUmseX9c7JXz92OVuM6bOXI9qHihByyURRxJ/2d+PGjbVy1aVDZ134+V/O45q11XJp5LnWVG3C/3x2FyrMUsnfmzfX4Yk/nMFfDvTgb25bOS9tIHNHLDLUO3bmc82aNXjxxReh1+vxyiuv4MMf/jCef/75cY978sknS15fxWB21lOQqWWzAlQKbu4XHJXBXL+lqarTzbXpzBxZjeqyrfsr1diS/4RMhmaoCCGXrLXDiwFPFLdf1yTfdts1TfivT94yb8FUTq7q35kuHzRqBXZua8CfX+9GZoIUFrJwOJ3Oglkkt9sNh8NRcB+DwQC9Xqqmtn37dmSzWfj949fRvfvd78aePXsK/vvZz35W9HWv9GDKapybdQ7FlDs9aiGbzaIQy+stcBYpuT5bLvdgarGaqBiGfczm3GT6KKAihFyyP+6/iJZaM1Y0WJHO8Nh3chCiKMJwiZXOZurVEwN47Hv74Asl8KbrmxGIpHDgFJVQX+jWrVuH7u5u9PX1IZ1O47nnnsOOHTsK7uPxeOSZrNbWVgiCAKvVOu65TCYT6urqCv7LTycko+az88txi3BqasRcx4qKWTx2F/qCC6KwSm4/pMtdblPtS1U/wUa9pZqoGIYnSGnxU5lqLRql/BFCLokvlMCB0y586P71YBgGR9uG8W9PHcOKxp2oLNOo140batBUbZJT/zYtt+MP+7pw46basrSHzA6FQoHPf/7zePjhh8HzPO6//34sW7YMTz31FADg7W9/O/7yl7/gqaeeAsdx0Gg0+Ld/+7c5L4iSbyGkMl2OTDoVwvE0Yols0X17FgNlkYIOs8mgVS2qRf6liCXmZ58hpYK9pCyHUkq8M4z0GckvCKJSFP7cV8JGvKXgWGbCrRh0GoW839diNvbYTmWqtWiL86xFCJk3zx/shUbFYfumOgDAteuq8b1P7ShbMAUAHMeiqdoEQZA2PN19fTO++qNDuDgYQnONeeonIJet7du3Y/v27QW3vf3tb5f//Y53vAPveMc75rtZMgqmZiYclzb4zKUkTbaRMSluNoOpyTrcl5tau2Ha+6FNRKdWQK9TwhMonLGZj5RxURxfXXGiDj/LMDNaM5cLIsb+bZc3WOELJeALJRdsMGXQKpHOCiUX8JlOMFUKSvkjhMwYzwv4y4Fu7NhaDxFSqp0oinDMYe79dPzbz4/hWz8/hq2rnXBYtXhu38VyN4ksAgwjVTRzWOfuc16sPPV0TXcvoWJBzLJ6C5Y3jKZM6rVKaNVzNxabzkqdIYO2POnCi02t3TDtTaa1agVq7AboNLP3dzbMQWoew0iBQK4Q0mzQqBXjgqmS2zODx8w0FXAmwZRBq5ywxn1nfxC+UHLWNhxWKTlUjKn6ONfrtKKJTFmroVJARQiZsUNnXfCFkrj92iYcOD2E7/zqBELRdLmbJbv9uia8/dYV4FgGt1/XjJeP9SM6TykiZGGbLKARRakAwHBg/BoTjmVmJRgaW546ly5WU6kv+TmmMwJr1quKzki09wURiaXlktixRGZWix/k5J4/EKYZvpkqllI44InKs3+l0msU6HNHSpqpmCiYsRjUBet9xp53Z7KVRq3dUBC0OG36cYMAGhU35UDCZOXrY4nRY5VfjKVyJH28yqZDc7Wp6GMnC3Fq7YaCACPX7vxUQAZTr4NTKdgJA+SpApbJAo7cd7/RaUJNpR4VZg2aq03y4Ml0Ay2VgoVuTBBtM2lgM2mmLO8/9nNcaZ55Of4Gp7Gk+83G5sYUUBFCZuyP+7uxbkklGpwm3LKlHt/79E5Y5rEi2FTWtFTIo+u7rmqAIIjYc7i3zK0il7uldRY5oMld/NkxI7v5HUmbSSMHUWaDGrn+WimdEK1aMe5+Zr1K7sDlGEZGsge9sWm8k/HyU17zOzaVFi1qKvVorhntLKqVHBQcC6NehUqLtqAAQP5jzQYVzHnHY2yHtpTZiVzJ7XKX/l7I9JPMdoz9jI1NyS4265gLPIw66e+fP1OZE46ND9acFToEo6lJ1/tYjOppz6AOeKIFQctEgVGxgYTc+7dbteAYBi21xVO/VzTY5GMRiKTkf+u00v/d/jguDoWl92CQPvMTvY/qCj2aRoKveDIDX15ZeV4QsbKp8HhWWLRYVm8t2M9r7N5e6awAMMCSvPbnrrmeYAJv2NZQtC1j5Z4391iLQY0VDVYEoymEYmkkUzwuDoXl45ZM81ApOWjVCiyts4x7rvzbtGoFTHoVGEYKSvVaJVpqzTjfG4BaySGWnHhQU6Vg0VRjKqgwGYlnxgWkxVgMavk8zLEMHFZtwXnKpFPJQadOrUBLrVlu92zs1UUBFSFkRvrcEZy44MFNm2qx93g/gMtzY8dAJIlP/udeeIIJ3LixFn/cdxHCAlkbQMojFBudJcmlPeV39C1GNQw6JexWLeocBkAcnVHyh5OorpRG5pNpviClx2nTgWUYWAyjgw6JVBbJNA+OZeQR8SwvwGQYDVBqKvUTrs0yT5LuVF9lREuNuWCk/br11VjVZBs3Its5EIKCY3FxMCzf1lRtwrJ6C7atroJGxaGmUi+/n6q8Dk84loZRr0JztQl1DgNsJk3BKH6FWVN0lLnCpCl4ntxrkpkptk/bqiYb7BbtuJkk35iqbvkzRhajBlq1Qu7URuNprG2pAMcyWFpngVrJFQwwWI1qqPI+TxaDGirl6PPVVOqxrN5S8HqeQGLCGVSdRiF9r6aQP8ZRazdAwbETVrGzmqTvgErBwaBTYmVTYeCi0yiweaUDZqMKzorRz2QilUWNXY9eV2Tccxr10nPm1leZ9Sp50MGgVUKvVSKd4WExqOGw6lBp1sKgVWLrKgfeeG0T1EquYAAjN2tVZdPJz5MbaNCpFdCqFGBG3ms8mZUDudx+WQxGAz8AaKgywmpUy6nJJr0Ky+otqDBp5OfVqhRY1WRDdaUeLMtAEERksoIc9OSfd9IZHolUFh39QTmg02uVCEVTSGd5eXYtkcoinREQT2QRjKTQUGXEyiYrLEY1BFFEo3P0Pa8Yk7K5pM4CBcdClTcAkMrwiCUycNh0RdMqc8ctkcrKbeAFEVlelP8WlWYt0lle/lvFU1l0DYTQ0R+EUsEWTXfmWAZGnQo1lfqS0mYpoCKEzMjvX+tCpVmDTFbA//zuDOKTjDqVk1mvRn2VEQyA3dc3Y9Abw4kLnnI3i1zG4vGMPNJZLKUpGElBpeBQadaOW29RXaGHSsmiuiKXmjd6oZbWpugLigfkgh29VomqkY6cQaeCWsnJr61SclhSJ3VgzHoV7t+xDA1VRlgMaoRiaRh1yoKOhl6rREOVEWuXVECt4mDPW+t1rG0Y2zfX4V27V6PBKXVaq2w6OCt06HVLncYKswZLas0FMxQbl9uh4Fg4rDpYjWo57c9m0kAUAaNehUFvDNFEBlqNQh7Fz7XfG5I6cJUWLVY12QAAkXgadQ4DzAYVGpxGrGqyzUq65JUq95nLdSorzRrwgohKixZvur4ZDU4jdGoF6quMEDGaPlplk/6mRp0KWrUCLbUmJFJZeTaUZRmsHPmbOSt1qLHrYRsJkHVqBYKRFNIZHjqNAvUOAxiGwfZNdVhaZ4FOo8CgNwYFx6LRaYJayUE9ZrZsRaNVHrhodBpR5zBCo1IULWyUHwTlp68NB+Lj0mRzltVbClLRBUGERqUoSJFrrjajbqTtKgWH+iqjHASaRwKnSosWm5bb8fDda7FtVRWW1pmxpNaMllqzFDTZtLhpYy2W1plRX2VAnzuCQW9Mbue2NVWorzJi6yonmqpNMOnV2LyiCmtaKgAUVizM/Vs/clxUKg4Omxa1I4HmkC82LiBdu6QC7b1BANJ5K8MLCERS8AYT0KoVMGiVUHCsnAJq0quKzlwuqTXDpFPBYlAX/P769dUApM9X7jkyWR68ICIYScFZoYfDqoXNpEGlRQOWHd0GodZuxL03L4XNpIFKyULBMdBpFIgmMgWzQ6mRgFivUWJ1s/SZUys5rFtWCUD6LOaCH4NWiaX1FtTYDahzGJDK8AUBde61Ky1aiKIIUZQ+603VJnlASatWIJMVxhWrqq8yosqmQzKdhdmgBsNgyqCKqvwRQqYtEk/jxSN9eNuuFbjzxhbctKl23jfwLRXLMnj0gU3yz8vqLXhu30VsXumY5FHkSlbnMEJnMkKt4pDJCvLodyiaGldJzW7VYkmdBQdPDyGZ5nHd+hr0D0eQyQowaJVodBph1Kvw+qkhxFNZ6DVKcCwDhgGyvCh1chQsLAY1lAoOq5qs8v4/OrVC7uQCUge5sdoE+0j6XSKVhU6jQCSeGZlBMkAURVy1xglBFOV1Kw1VRnAsgz736Cg7xzLYttqJaDwDlZLDDRtqsPfEAIKRFHyhJPRaZcGsQ47LH0cskYHFMLI+YaSTolUpkMrwqHUYsLTOXDDTxTIM6h0GqJRcwXNmsgJqRkbbAakDFEtkFm3Z9JwKswa+UHLc7XqtUjq2RjWqK/U4d3H8htQTqa7UQ6dWoK0ngEqLFi5fHFlBxIXegBzA5u6nUnJoqTVDreRg1KkgAuh3RxBPSbMeHDsa1DLMaOB148ZapLM8fMEkXL44ltaZYTFq0NUfgj+SxKbldiytt+LQGResJg0MWiVYlsGF3gAAaRaouUaa9WzrCUAUgWQ6i43L7Kip1GPQGwPLMPCFkhgOxKFVK7CiwQqXLwaHTYdUhi+YKTKOBAQbltuh0yggAhjyxMAwUmqsUadCJJ6GgmOxvN6KUDQFTS4dDQxYlkFTtQndQ2EIooj23iDsVi1YloFeo4AgiGipMcNu1SKeNKHHFcbalgr4w0lEExnU2KVjyQsiDDolrltfC61agcaRCrPrlqbw6vEBDPliEEURDFAw+2U1qqFRcxAEETqNYtxsLQCoVQrEktJMj1LBghkZOllWb0F7XxAA5EBQqWCxqtmKroEQwrG0nI4piCISqSw0Kg5mgxqVZi1q7XqAYcALApIpHssaLKiu0OPIOTfiyawcuIVjaQx4ojBolXBW6uXP0nAgDotBBZZh4c8kYbdo5e927nO8abkdVRV66DRKCIKISCwNXhDl2aMsn0W9QwmTXoVz3dJnPZXhoVZxiCUyGPRKKaM1lXpoRp670qKFe+T8WF2plyr7ZXgYtCo0VBkRjqURjKZgMaqxabkDiVQWPUNh2MwaOb1REEQ0Oo3gRgZvjDplQeqqbeSzG46lIQgiet0RxBKZKdciLu6zFiFkTjx/oAeCIMoj6GbD5bNuaiLne/xo7fDijhua8e3/Ow63P170AkaIUa9ChVUHg04JlVJKg6swa/DGaxvx/d+eKryvTgWjXoksL4ABYDGqoNVY5c6FgmOwbkkFBEFAMJIGyzJ40/XNeL11EIFICmlewOYVDpj0Koji6NqWAU8UHSMdpuvWV2N/6xDCsTTiySz2tw5iSZ0ZTdVG9LqjaOv2o6bSgK7BEADgqjVOVJi1iI4seK+0aDHgiaK+yojtm+vktus0Snmdi7NCj9uuacILh3qlDt5IEHfjxsK92wRBhLNCB7NejTUtNpzrljrLm1Y4EI6loVSwcFZIHa8BTxSVZi2EIpt8r2iwYnmDFbV2A2rtUuetrcePlloL2kc64ItNLiFvTUsF9h4fKPgdyzJYu6SiIJhs7wsiW0JhkY3L7TDoVDh81gWzXgrALQY1qqy6gpTQXlcEWrUCTdUmOKxahKJp9LjC0uyFTgWlgkWN3SAv5M+VI8/NVOZSwgDg1qsbwbEMznX7sXZpBXqGwqiwaKFVK+TPWFuPHxzLFKwxYhgG1ZUGdPRLn9Uhbwpufxwrm2xY0WhDIJzEyXYPBFFEJJ7GiiYrzvcGIGJ0vRYzciytRjVaai3QqBTYtlralPuVY/1w+aSZtUg8Lc/catVSwJ/bYymXuporImO3SrPNS+ss4FgGva4IOgdCqDRr4AlwiCbS0KoVqKrQwWqUCivk0oCrbFp4gwwyWQFa9ejfU63koNcq5XS6PncEWV7EikYpKOkeCsszIwqOlSrjjQTb1RV6eEMJ3LK1Hr95sR2AFJCyDCvfPz+44VgGa5dUQqdRoqnGhPM9ATTXmJBIZuENJZDlRVRX6iGK0npMTygJnVoh/20qzVowDIPNK6sgiiL2nRwEIM1ixZPS3nrdg7m1Y2okU1lkBRE2k1qeWc9prhndAzInneXR2uGFJxCHw6rDhmWVSKR43LCxFvtbpddyWEdTU/PL1F8cCsNslG7PXxPFsQyuXluNV471w2xQocKsQY8rgshIimpLrRmvHOuH1aRG/3AU0XgGzgo9et0R1FTq5X7L5pVViCcz4AURsURGPleZ9Cq88domPP1SO+IMMMGSPRnNrRNCpoXnBfxh30U015jw25c75mV/jtnQ547i4GkXrl7jhFGnwp/2Uwl1MrF0lseAJwqHTYctKx1Y2WQDwzBodJpQX1VYOerIWTeyvAirUSpOYdAqUWnRonsoDFEEWJbFphVVcsdUqWBRYdFCwbHSaLonhnPd/nFrQnKUCik4a6w2YXVzBda0VKDOYYTZoEGt3SClcI107qor9DCOdEpyqVW59TG8II5bfL15hQNrWirk20WIAIOCAhT5HFYdbtpUh62rq+Cw6XHd+mpct74GSgWLW7bUYdMKhzxbbTGowXEMRBFYWm8pWKfDssy4ogIrG21XzCBHfvWx+iojbtxYO25m7po1Tlw3kmaVs25p5bjnMhvU4FgGJr0KoVgaeq1SnkldOpK2puBYOe0LkCpVAtKefQqOxdI6s5wyxzAMVjXZ4LBJneL8Cn1qlQLrl1ai0qKFWsXJAUqPKyKv5ZHbpZfWVm3fXIe1Syrk2/P/7teury4odmE1acAwDOwWLVpqzHJAmVtj2FxtkgcdVjdXjFu3e8OGGmhU0vusrtBjSZ0FG5fb5bVFuU2+1SpOnmFaVm/BikYbrllXDZVSSvdTKTlsXVmFphozLEY1fKEkKswaWI3S6+m1o2m2apUCDU7juO+MVi2tBbMY1GAYRv7u5giiCFEUUWPXY8NSOwCpDLzdqoXFqMa6pZWwW7S4+6YlqHMY0OAwYtVIIYuugZA8q5OrvKnTKKXgQq/GG7Y1wGbWwhNMYFm9Fbde3SAf50FvTB4wsYw5frkA8/oNNfLaq9w6quUNVmzfXAebWQONWoGNy+3YuqoKY+XOV/lUCg51DgNu2VKHq9c6ce26GuzYWg+lgsVVa6RgeDgvfVqrVsBq1Mhtdlj1I8+dv9ZvdCCXY1msXVIpp+jlgk29VgmHVYcKsxYMIw1wKTgGKiWHNS0V8vdLp1Fi03I7Br0x8Lwgv/dc+7asdKCmcvJ1fTRDRQiZltdPD8EbTOBL778GFWbtjMrflsOOrfXYua0eDMPgtmsa8cf93Xhg14o53VOHLFwqBQcwUkc0v6PLsoCCKfzMr262waCV1j3lOmxmvbQGoVglMpVCGrlucEp5+umMgEg8jbbuAK7fMHHp49xIek4olkKfOwKXL4ZauwF2qxY6rUJeh+Ss0MuL4wHA5Y3hwKmhglmqXGcmv21L6izQqBUFZbPVI8fguvXVBTPS+Z0njmML1pxpVBy2rKqCgmOlTv7Ieo6csVviCIIoz4CIkxahXviaa8xy+tpE51COY8EB2LqqCud7AoiMpBxV2XTQahTyjEFOLtBQsCzUSg5NNSY015jRXGOGYmSz87EaqoxyQCyKo5sDX7e+GizDoLMvNK5wgnWkE242qLFttRN/2t8NYHxRjOpKPaonKPO/aYUDoijCqFNNWK1Pr1Xi4qA0g1Y5MgABSB1vtZIrmmbOcSwyvABBFHHjplowjNROo06F6koD2kaCEIZhsKzeikGPNJsVjCTh9sexurlCDjYtJrVcBc4TSCAazyAQScpBVe67zrFM0Q3jc2vPcilqOq0SYl5BpOUNVhi0SrT3BaHgWPl7ubq5Aq8E+guO4xuvbYKCY+W0XWeFTh7MzH/tGrseJr0aWrUCCoX0vQvFUmhgpHNNlhewvMECgEF1pR5ZXoBZrxqX3qvgWCkIDUjl2LUahfy9zwUyFWYNlAoOjdUm9Iysmdy43F503SnLMkWrRALSuk6VgoXFqMG6pZVQcCzauv2wmTXod0ewrN6CxmoTqiv16BoIgWUZeAIJ+by8onG0wAjLMGA4yOl8uYDPoFOh0qzBiiYbXN4YuofCUHBswflLpeRg0EhpqisarWiuNcnHt7nGjL6+wlnlsagnQQgpmSiK+PlfzqO5xoQG58KqxpW7aHf0BXHN2mr89uVOPH+wB3fftKTMLSOXGxEi1CoOG5vt435nNWmQSGaxcbkd8WQWmSyPOocRQ9446qpGRzA1agWqK/VypyufXquASskhEkujyqZDS60ZJ9s9k25QuqzeMq4DWWXTIRrPoGsgBJWSwz03LRm3l1QufWXzSgc2r3QUbU++CrM066UaqeSW+95wLFMQiJWC49iC4Ku5xiSlXakVcicz35E297hUocUst8ZnKnqtVFEyl8KWKxBh0CoLZo/iyQxaas1orDbhmnWjM1u5QOSaddWIxtMQBOm+uRS63CJ/k0ElB1S5juYDt66YMNUpFE3hdJcP65dVYjgQlwOtUkz2WW+pNaNrQEoJXLukQkpRCyTk91Fh0Uy6ie4br2nEmS4fzvf4ce26GgDS+b9Y+f5VTTYk01mk0rxUYKZZmh0x6lUFe77dsqUOr50chCeQKJilaqk1l7w3XNtFP8KxNG7cJKXROqw6OQjVayfvjufee43dgK6BEHQaaRY8nZHOP7wgBVfL6q24OBhCW7cfzSMBtVLBIprIgGEY1DmM4563xl585iVX+Cad5XGm04chbwzVlXoYdaqCc0FTXkA1Ufp/lhdw+KwbKxut4z4nFqMad97YAotRIw8uNNWYcO6iH4FIEumsgEgsDYtRjTUtFTjb5cNw3vnDWTF6/CeqNFxl043Ofk/w4WFZBhtW2FHvMIBlmXEzxu19k6ciU0BFCCnZ0bZh9LkjqLUbwAti0VKjlzOeF/C1Jw7hli11uGVLHZ7d24nd1zdTZTEyzkRxx1WrR2d08jsPEwYbRZ4nFE0jEE7Ki5zVKk5eBzORYp0ejUqB1c02eYG19F/xxxtLKPsLAGuXjKaU5acnzQadRonNKxxw++NFA6qlIyWT+/OKZyxGuaC2sdqI052+CT9r+XIVy/JncyrM2oIAtH84Cm8wMeF5Wa3koJbvr4UvnEQkbzF+U7Vp3OdssnO8gmMh8CKqbDq8e/fqqd9EieqrjOgaCMFqVKPCrMXpTl9BGXajVjXpfmUGnQpNNWZESwhWHSOdbFEU5WqYLMtg84rCokUcx2Lb6qpxMzlj038n01RjGleJkGEYsAyDKltpQVluYEMQxAln9qpsOmhUChh1SigVXEEhjOlgGAZmgxqvHOsHw1zahuWCICKd4eEPJ8cFVMXOM1ajGrUOA7atdmJf6wDCsZQ8M7a03gJPMIFJPgKTyn2mx37vdBol1i0Zn1I79nEToYCKEFISURTxf8+fx7ollfjc+65ecMEUIF0U//lD18Nh1WHAE8VfD/XitRMDuHlLfbmbRhap/D2ntq2uAsNIdboqzFK5cYZh0DUQgjeYGKmQZ5nW8zMMM2kgdjmaqJiNzaS5ovaIy3XOVUXWnIxVXaGHgmUnLQB01WonmqrNBWmhkxnbsWQYZtz+ZJPRa5XybEsp1i+rLLq+ppjrN9TI7du6qgr9w1G4fDF5lmIqBTMSJZCq5E1+TbvUSrYT/e2u31AzrnNv1KkK1tmNNVEwBUjt1GmU6HNH0OeOTJh2WarGahOsRvUlFZ9SKTlct76m5H6DUsHJ58KbNtVBmRfMKRXS9g1NNeOzZJY3WOH2T775eU2lNAM13feztK54ymIOBVSEkJL89VAvzvcG8NUPXrug1x3l0gNMehWuXuPE0y93YPvmuilToQiZruvWVxeM6uZ3yNYtqcTe4wOoHCmB7g8nx+3l1lxjktcCLERj97jJya8El2/YHy+YiVjsjDoV1i+rLAi6J8IwjDybMhGVkitpQ1yZOPrc8yGXKleK/O+NXqtEc40JDCOlvl5Ke5WX4ffpaJsbzTXmgn23ZmNbjzqHoaC4zUyVstl2pUVbsD6ymJmutx4b5DMMg1XNtqL3nWzdXg7LMlMWmChm9QSvmbNwe0WEkHkjiiKeer4NKiWL1c2zmwZUDofOuPD1Hx/GJ9+xBV974jCOX/CMS/Eg5FJNNhrPMIVrkm7YUDPuPgttnWI+adR9eh3fvuHIhGsgFqvpBBlT6XNHwHEz6yxe7lRKbsKiBtOxqtlWsMnvfNCqFfJG2MXkF3+ZTQzDlJROOhummjXMZHnsbx1akOuvc7SaKda5zVM7CCEL2MEzLniDSXzx4WtKTtm4nK1fWokPvXkDrlpTjZWNVvz2pQ4KqEhZLbYZ0pmst9iyskraSNO1ONdQja2CN9uyvABRLP1zVGzj5sVOpeRKTomcLVtWOjBZJut0i70sREoFhxWNVtgti7fozOU390kIuazEU1l8/7ensGWlA1uK7DmxEGnUCuzc1gCWZXD3TUtwot2Djv5guZtFLhNz3O8lpaC/wbQ115inNfq/rMFSdF8rMrs4jl0w24vMJWeFfkGnME9l8b4zQsis+NHvz8AbTOCe7YuvvPjv9nbi6Zc7UFOpw29f7ih3c8jlZHFNGC0IZ7p8GPBEy92MBUsc2Si2VAqOveJSLAmZK5TyRwiZUDrD42ibG1evcWLj8sWXErempQJKJQdAxH8/fQrvvD1WsKcFIWT+GHXKCQtZkKm1dnihVnFY2Tj54nlCyOyjGSpCyIR+uecCAuEkHr57bbmbMieW1Flw+7VN2Lm1ASadkmapFoC9e/fitttuw65du/D444+P+70oivjqV7+KXbt24c4778SZM2fK0EoyEw1OU0GlMzI9DU4jqmlAiJCyoICKEFKU2x/DL/56AWuaKxb9rM1z+y5Co1bg+YM98IUmL/1KyofneXz5y1/GD3/4Qzz33HP4wx/+gI6OwiB479696O7uxvPPP4+vfOUr+OIXvzij16KMv/kXT2aQyvDlbsaCZTVqLmmvIELIzFFARQgp6q8He6FUsPjbN68vd1Pm3KomG950XTM0KgWeplmqy1ZraysaGxtRX18PlUqF3bt3Y8+ePQX32bNnD+655x4wDIONGzciHA5jeHh4ei9EBRHK4uxFP/qHy7eGKpnOIssLBbelMjzSsxjkzWUxR18ogUAkOXcvQAiZEK2hIoSM4w8l8ezeTtx3y1LU2iferX2xWNlkw8omGzJZAf/31/N4y47lsBhppPdy43a74XQ65Z+rqqrQ2to66X2cTifcbjccjsI1gOFwGOFwuOA2l8s1B60mpVrdbAPHMhgYjs5KTCuKIpJpvuhG5IlUFizLFGwaevC0C3artmCvvQOnhgAsjNLWg54Y1CpuVve2IoSUhgIqQsg4X/3RQWR5EfduX1rupswrhgF4QcRvX27HQ3cuznVjC1mxCmZj928q5T4A8OSTT+I73/nO7DWOXDKdRol0Zvws0Uz1uSO4OBjGjRtrwbKFn4HzPX7oNMqCzWJXNFqhUU3dLeroC6KqQgejTjUr7QSkdEcFx17S3lBUAp2Q8qGAihBSwOWLoXMgiGvXVkOvVZa7OfNqwzI7Tnf68Mf9F3HfLctoPcJlxul0FswiFZt5Gnsfl8s17j4A8O53vxv33ntvwW0ulwsPPvggwvH0LLeclKLXFUbXYAjtfUGsai6tUt2AJ4JMVkC9wwiWZeTg2R9OwmxQY93SSjCMlM7HMKMzUnUOY0H63YXeAIa8MVy/oabg+YsF6AOeKAKRJLatdo77XT5eEMHlBXLJVBbRRKbofQ+fdUOvVWLrItnrj5ArDa2hIoQU+Plf2mAzafHxv9lS7qbMu+UNVnzyHVvAcRx++cKFcjeHjLFu3Tp0d3ejr68P6XQazz33HHbs2FFwnx07duCZZ56BKIo4ceIEjEZj0YDKZDKhrq6u4L/8VEEy/+LJrPxvUZRmmDLZwtmqaCKDV471I57MIBpP4/evXkRruxevnRzE3uMDiCUySKayONXhxYkLHthMGjAMg4OnXThwagj+cBLxZAbtfUGc7vQBAI6dH8bpLi8AYN/JwYJ1SF2DYVwclFJDBUHEsD9e0J5MVigIujJZac1VKsNj77F+eIOj9+8cCKHPFSn63vVaJezW0iscZrICzl704UyXT77tQm8APa7wJI8ihMwVmqEihMjOdfvw0tF+PHTH6ktKPVnIDDoV1rTY8PtXu3DnjS2LvsLhQqJQKPD5z38eDz/8MHiex/33349ly5bhqaeeAgC8/e1vx/bt2/HKK69g165d0Gq1+Kd/+qcZvVaxNEEyt1Y22dDgNMIXTIIXBFwcCCOWzKChyohUmofVpEE4lgIAxBJZqJQs9Fol1EoOVTYd3P44eEGUKwV6Qwn899OteO+dqwFIAdHB00PQaZRIpXlwnPQ3jsTSqDBpkUzzyGR59LujUCk4HDnnhs2kRiiaxqsnBtBSa8Kew31QsCxUKhYrm2w41jaM+iojWmrNAID9rdKaq00rHDjfG4BSweKGjToAgMOqhdsfK/reNyyrLAgopxIIJ+EJSBVJczNhOo0CKsWVed4mpNwooCKEyJ587hyUChY3bbr8F2DPpbfuXI5THV78as8FfPStm8rdHJJn+/bt2L59e8Ftb3/72+V/MwyDL3zhC/PdLDJLjrYNwxNMFKTuuX3SLE9+YQgRIly+GGwmDXhRhNsfR4VZA62aw/5WqapjbuIoFEvLz+UJJrCy0YquwRAA4MaNtQCkTczTGR6eQBybVzrk1DxRlFL1BEGEVqUcDXriwLE26XV8oQSyvAB/OCnPWA0MR+Gs0MFiVCORykKpYGG36lDnKF7kJxeIrWqywWbWQMFNnkCkztsA+XSnFxuW2Sd8bkLI3KOUP0IIAOBMl5Q+8okHt1zxm2uuaLTh3bvX4IXDfZRCQ8g8OX5+GIIgRUHCSGGKfncUHMfg2nXVAAAmb4ewPncEfe4IAiOBTGd/CHuPD8i/t1u0WNVkkx9jNarRXG1C1+Dod/r1kSp+g94YBjxRpLMC2nuDiCcz8IUScPvjECEFc60dHlSYNWipNWNl42gxi3gyixeP9CGV5uENJTDojSErCLAaNdCqFTh0xoVTHV74Qkmcu+jPC9ZEdPYH0dbtl5/rXLcf5/J+nkh+4Y5gJIV0hkc8mUEyXfosFyFk9tAMFSEEoijiv359As3VJrnjcqW79epG/OzP5/Dp/+81/ORLb4RSQeNPhMwlu1WL8MhsUiYrgBdEJNNZKBUcsrwApYKV0/k6+oLo6JdmmSLxDCLxIACgXmGEQSt9V+PJDHpdEWg1CmR5AQqOBcsyRfeVctp0uDgkBVoNTiO6B0MYDhRu8u0LJeELJRGNZ2DUqyAIItRKDuFYCg6rFhuX2+E/koQgiDh2bhiJdBa5mhThWFp+3XA0BYNWieFAoui+W/5QEqkMD+VIe3PHY3/rIEx6FUQR49Zbnb3oAy+IMOpUBZULCSHzg3oIhBDsax1EnzuKqgodrR0ZoVSweMvO5YglMzibt/CbEDI37FYddBoF7FYtTnZ4EY2nEU9mcfz8MA6fdWP/qSF09AURjqWRyQoodqZS5qXKuXzS7NKxtmHwgpQW2NYTKJhd6h4KI5rIQKNWQKeRxpgVHDsu0HnhUI+8rjSV4eENJqSgR8FCq5aCo/2nBpFIZZHO8EiMzBR1DYblwhqVFml/qPa+II7lzcaNZTGqceDUEC70BeTbvEEpuDPpVVAqWHiChcFeKJqGWa9Gg5PS/ggpB5qhIuQKl8kK+PEfz+Gq1VX42Ns2l7s5l5V7ti/BobMu/PB3p/Gvj94IdQl71BBCZiYUTSGezMITSECtZAsGd8amwZn0tnGb/1bZdFApWbnqnsmgkgs3BCMp+MNS9b78SuiJVBZ97sLKe6+dHIDJoEYsr0hEbjas4PWsOqSzvJxm1zMkPY/dqkWDU4NYIoMBTxQuXwzxkXVYOZFYGpGR2bjGahN6hkbTEIORFNYuqYCCY+EJJGC3auU1Uxq1ouisloJjEUtkStpHixAy+2iGipAr3O9f7YLbF8N771p7xe07NRWGYfDIPevQMxTG3379xXElnMniJRTZf4jMrc7+oPzvdEZAMj0+NS+n2Dqj3AxU7j9PXspeauS59BolzvcGxj02nyAAQ97i1fjydQ2GMOSNjZtpCkXTuNAbwIAnikqzFnaLFtZJ9rTLD6ZyDDoVIvE0zl70odcVloPBjr4g9FolxiYSZHkBwWhqXFl3Qsj8oICKkCtYNJHBz//SBpZlUWHSlLs5l6XmGjNu2FCDUDSF2ASbcpLFJ1dZjsyfVU0V8r+nE86Wsn9TLJkp+P9Yzgqd/O/INDZ25gUR8VRhIQg+r2CEN5RAVhCRzk4cHBZz4NQQekb2rLo4GMZA3qxULJHBRPF+KQUtCCGzjwIqQq5gv95zAQwD/MO7tkKjplSRiXzw/g1QqxR48rmzBZ0lQsjsKTZTU4pQJDWt+1dXjt9bzhdMFqy/uhQV5sIAr88dQSQ+/cGY7AxmxLesqpr2Ywghl44CKkKuUMOBOJ7d24m37FyOq9dSZb/JmPQqvP+etXjhcC8+/M2XCkoWE0JmRyg2vcAoJz3NwKNYWlyGF5CZpe/1cKB8s5sGStsmpCwooFqAOvqD+M2L7fLP+1oHcarTC2Ak/WCClAZC8n3/6VbwvIhVTVRitxQ3b67DqiYbgtEkkina64WQ2eaw6qa+0yzgJ6iuN1dWNdnmLdB55Vj/vLwOIaQQBVQLAM8L+If/eg0vj5wo3b44/rDvolzJ6M/7u+XNCfuHI3jgsT+irUfKo77QGxhXwYiQjr4gDp1148ZNtVjVXDH1AwgYhsEn3rEFggD87+/PUOofIbNMW8a049lK9yvmXPfoZr6EkMWJAqrLVCrD43evdkIURXAci7UtFag0S0UDrt9Qgx997la5pOxXPngdHrlnHQApd/sf3rUNLTVmAMDTL3Xgh8+eBiBt3kqpSkQQRHzvNyextM6Mj//NFijmsCOx2DisOnzo/vX466FefOgbL9L3iZBZFE+Wb+Z3ttL9ym375rpyN4GQKxL1pC5TXf0h/PiP5+TSre+4fRXWLqmc8nEGrRLXb6iRNyD8xDu24NEHNgIAWju8eOSfXyhrfjcpvz+81oULfUHcuLEWHEub+E7XzVvqsW11FTzBBNz+qUsrE0JKI06rth8Zy6hTlbsJhFyxKKC6jIRjaTz9UjtEUcSqZhv+97O3osZuuKTnVHCsXHGoyqbDm65rht2ilV+PXFki8TT+76/n0VJrxs5tDeVuzoL1yXdshd2ixb///Pike+UQQkp3JW/9pdNcerpjJJ5GG5VNJ6QsKKC6jPS4wvjNSx1wjex/YtLP7miTs0KPN+9YBoZhcKrTi/d99XlaX3WF+e+nWwEw+PIj18I8yUaTZHJatQKfeudWdPQH8f6v/RXpDAVVhJTDYpljT83SOWQ2AjNCyPRRQFVmw/44fvrncxBFEeuWVOJ/HttVdI+M2bas3oL33bUWdQ5pBmw6GxmShekvB7qx9/gA3nhtIwVTs2BJnQV/88aVCEZTeP5QT7mbQ8iCV2HWYEXj9KqOLpZJLZ6X3om+SDXAZQ2Wkp9nviolEkIKUUBVZm5/HC8f7Yc/nASAcZurpjI8vMEE+ocjGPbHEYgkEUtkkMnyEEURgiAik+WRTGURS2QQjqURjqXlCoAT0agUeOO1TWAYBqc7vXjvV2i2ajELRJL48R/PosFpxP23LCt3cxaNt+5cjvtuXoofPnMaR9vc5W4OIQtaOJaGy1fedYl2ixYqxcRdI/XI+uSxJnvMdMTGVANsrjGhvTco/2w1TT4YFqJUfkLKguaGy+BomxuvnRjEow9sxLqllfjep3dCOXIyHvREceisG+d7/GjvC8JdZAPCUpj0Kiyts2Db6ipcv74GVpNmwvsurbfgvXmzVa+fGsK6JRUw0ALXRSGTFfCV/zkIlYLDP/3t9UVHQMnMvWv3apzs8OBLPziAr3/0RqxqspW7SYQsSM4KPXhewIHTrkt8Hh1C0TQSk+wXx7EMLAY1fCODmTn+cHLCfao4loFOoyianlfq5sL5KYq1dgMGPFEAwNolFTjd6Su4r0rJjssmCIQn3/yY0o8JKQ8KqOZJMp1FPJmFzaQBAwapDI9UhodGpYDLF8NLR/tw4PQQ+txRaFQcVjRacePGWjRVm2AxqKFRc8hkBaQzAtJZHpmMgAzPg2UYcCwLlmPAsdJ/giCi1x1BW3cA//v7M3j8mVNY21KJGzfW4Lr1NeNO0BqVArdf2wRA2uH9mz89gk++YwuuXVeDaCIDnVoBlqrBLVhf+9FBtPcF8dhDV1Gq3xzgWAaPvecqfOzfX8G3nzqGbz5606yvfyTkSjCT743FoEYwOhpkVFfqwTKYNJhiACxvsMqZIflq7Qb0TpCtoeBYOCv0iMTTyPKXnmyYC6YAyMEUw4wW50hnBAh5wd2SOjMyWQG9romzSSrMEw+eEkLmDgVU8+RrPzoEpYLF5993DTavdGDDcjv2tw7iuX0XcabLB4tRjWvWVuO9d67FhmWVUCqKpxWU6uq11QCAeDKDg2dcePXEAB5/5hT++7ensLzegtXNFWisNqHKpkOVTQebSQOWZeCw6vCjz90qz2L8169OIJMV8Nn3Xn3Jx4DMv//763kcbRvG7dc24ZqRzwSZfXarDv/2se345H/uxWe/tw//8pEboNPQTOBsCwaD+Lu/+zsMDAygtrYW3/72t2E2m8fdb8eOHdDr9WBZFhzH4emnny5Da8lMVdl0YBkGQyPpfzq1AvG8AIllGAiiCJZhEIymwLGMPKs05I1hVZMNA57C1EEGgE6jRCyZgQjg4mAIGtX4LhDHMWhwGosGLbmZqWX1Vpwbqaa3stGKroEQzAY1PMFE0fejUrCwW3UY8ERhNkweNIoioNUokBjZk0urUeCGDTVgGAYsyyAcS08aUBFCyoMCqjniDyfxlf89iA/fvwFL6y14z+7VMOnVEEURB8+48NM/nUOPK4LNKxz4zHuuwlWrq8DNwQarOo0St2ypxy1b6hGNp3HgtAunOr14/dQQfvtKhzwSplSwqLLp0OA0Ym1LJbasdKDGbsB9tyxFMiVdRLqHwvjvp1vxiQe3oHKk9Dq5PImiiP/85XG8cKgP77trLe7ZvqTcTVr0qmw6fOIdW/DY9/bj0995Df/+d9tp0+RZ9vjjj+Paa6/FI488gscffxyPP/44PvnJTxa975NPPgmbjdIvFyLbSIp6PJlBKJYuCKYAQBi5cFXZdMhkeRh1KgQiqYKZqkanEXqtEmcvSoGPCMBZqcOwP45IPINkmkdzjVl+jF6jRI1dDwXHyluKVNl08AYT0GkUMOhUMOSlS1sMaqQyPHrdEaSzAvRaJTJZAcFoCuxIpgggzWoxLCPPRjkr9Vi3tBIqBQtfOInuwbB0PwWL7EjaYGLMBse5vsErx/ov8cgSQuYKBVSzqNcVRmuHF3fc0AKLQY0ltWZwnJQqt6TOgtYOD77+k8M43xPAlpUO/N3bN2NJnWXe2mfQqfCGqxrwhquk/YcyWQGeYBxuXxwufxwubwydA0E88dxZPP7MKaxstGLntgbctKkWACAIIqpsOliNUtpYW7cfyxuslA54mUmms/jeb1rx4pE+NNeYKJiaR+uX2vHwXWvwxHNn8fUfH8an3rlNXh9JLt2ePXvwk5/8BABwzz334J3vfOeEARVZ+GrsBoRifiypM6Om0gB/OIkzXaPrjIZ8MXnNonok6GpwGmEZuUbp1AroNArERwKUzv4QAKDCpJFT4yrMGvhCSRj1SnkAZO2SCgx4ovCHkljeYMX5ngDUKkXBAEmuGm8gnIRJr0L3UFjeKD0/TW95gwVVNh1eOioFQwykYCvDCwXrqewWLTyBBNYvq4RGxUnp/GMGZGrsesQSGYSio4UnrCa1vK7KZtbQzDghZUIB1SUSBBHJdBY6jRId/SE8u7cTu65uhFrJ4SNv2QgAON3pxc//ch6nOr1Y1WTDv3z4BqxpqShvwyHNStVUGlBTWbh5cCbL41jbMPYc6cN/P92KH/7uNG7cUIvbrm3Ex962CQzDIBRN4R+/+xoefWATbtlSX6Z3QMa6OBjCt352FMOBOP7ubZtx3XpK85tvd29fisZqE770w4N45J9fwL9/7CZYjLSuYTb4fD44HA4AgMPhgN8/8Sam73vf+8AwDB544AE88MAD434fDocRDocLbnO5Lq0YApldoihCr1Gg1m7A6uYKhGNpMAzQ64rAYdWBF0YLQZgNaiypM8OoU6HXFQHLMrBbdWhMZpHlBfS5I/Im3A6bTg5Ebr26EU89fx5uXxzWke+p3apFQ5VRHhDN7e2UyQpQKlhsXVWFI+fcI7drEIhIa7EYhoFKwcgFKmrtBiyps4BjGWxd5YAoAvVVRhi0SvS6IxjyxtBUbUL3UBhDXilF0ThJMahl9VYkUlkcOjP6Oc0vUjFblQYJIdNHAdUl+tqPDsGoV+Jjb9uM7ZtqcfPmOrAsg2Q6i/2tQ/jz69041+3H8gYLvvj+a7B5hQMMc3nP6CgVHK5eW42r11YjGEnhxSN9+MuBbrxwuBeNTiNuu6YJt2ypwzcfvQlN1SYAwItH+rC62QZnxdzvoUXGiycz+OULF/D0yx3gWAb//KEbsJKqzZXNxuUO/M1tK/CzP7fhH7/7Gj773mtQazdM/UCC97znPfB6veNu/9jHPlbyczz11FOoqqqCz+fDQw89hJaWFmzbtq3gPk8++SS+853vXGpzyRxSKTk4K/Woskl7K7l8MfC8KH+X6mwGuRIuxzLQqRVyMYr1SyvBsQwSqSyGvDGYDWpUKlisbq5AnzsizzZxLIMlteaC63IwksKAJ4rlDdKeWFU2HZRKFjwvrdvSa5XYvrkOyXQWB0+7YNSpIIqAUa/ClpUOHGsbRiIlDbSKogiWZVFdaYBJr0I6w0OjVkCt5KDXKuW1X+uXVSKVnrpCX3Lk/eXPTFWYNXS+J6TMKKCaJp4XsPfEANa2VMJu1eJN1zfJI0rBaAqHzrpx+KwLJy94kOEFbFlZhS88fA22rLz8A6liLEY17rtlKe69eQlOd/rwlwM9+N/fn8ETfziD6zbU4A1bG7CyyYpf/PU83nhtE+69eWm5m3xFSaaz+OO+i/jVnnZkeAEPvGEF9FrFtDfHJLPvLTuX47r11fjnJw7j/33rJdy0qQ4fectGSpGdwhNPPDHh7yoqKjA8PAyHw4Hh4eEJ10hVVVXJ99+1axdaW1vHBVTvfve7ce+99xbc5nK58OCDD17aGyCz5rr1NQiEk/K2H1q1Aioli3RGmgFa2WRDOCaVRw9GUvAE4rBbdVjVbIPZoEaWF1BfZUSVTYfOgRBWNlrhDUmzSTWVBtgtOhh0KliMajktEJAyT/LT9hiGQYVJC384iU0r7PLtGpUC2zfXYdgfRzrLo6bSAJZlEImn4fLFYTWqsbzBgkQqi2QqC28ggWA0he2b69BYbUJjtQmpDA+HVVvyNiV9w1JBilwwpVCwqK8y0npNQsqMAqoSiaIIhmGQFUQ88Ycz+JvbVuK2a5rQUmPGqycH8PhvT+F8bwAKjsHaJZV4zx1rcM3aatiti6N4A8MwWLe0EuuWVuKR2Dq8dLQPzx/swWeP7kelRYubNtbIF5pf7bkAq1GNN1zVWOZWL17hWBp/ev0i/vDaRYRjaWjVCnz777ajzmEsd9NInlq7Ef/66E147Hv78NdDvegZCuM9d67BuiWV5W7agrRjxw4888wzeOSRR/DMM89g586d4+4Tj8chCAIMBgPi8Tj27duHD33oQ+PuZzKZYDKZ5qPZ5BLk76FYYzfAWaHD/tYh+baNy+14/dQQOI5Bhpf2iTKNBCf+UBLnuv24bn0Ntq6SguxcQMUwkK/PnkACnmBCzrjQaZSodRhQY9cjEEkh4o8jneGxrMFSNPDJVfyzW3VQsxy2ra7CmU4/srwAq1EjV83leUEuqNHnjsATSGDzSseEmwUXs6TWgiNhNww6JQRBhFGnou0wCLkMUEBVgq6BEP7t50fxlQ9eB6tRg28+ehNOXvDgs/+9D6c6vFBwLLatduKem5dg8wrHol8UatKrcPdNS3DXjS3oHAjhpSN92HOkD0+/3InlDRZoVAqsbpbWiEXjaSRS/KIJLMvN5Yvh2Vc68fyhHkAE3nhtE27aVItj5z1UefEypVEr8K2PbUdrhwc/+eM5fOa7+1Bh0uAD963H1WucNGM1DY888gg+9rGP4de//jWqq6vxH//xHwAAt9uNz372s/jBD34An8+HD3/4wwAAnudxxx134Kabbipns8k0bVlVVXSDWmmvRU6uqAdIaYGrmm2IxjNocBbO1OSCl3zmkb2u1KrRIGZlkxVc3+j3sNKixR03tMg/pzM8hnyxceuN5ec0qGAzaeTASK9RobHaiBWNhTOoHMci96rcDL/3uXRDQAoEo4n0FI8ghMwHRhSLnHEm0d/fj507d2LPnj2oq6ubq3aV3cXBEAY9MVy/oQbxZAbf/+0pLKkzo7Xdi6NtwxBEERuX27F9Ux2uWetc9EHUVLK8gGNtw3jxSB8OnnEBELFttRNKBYtjbcP4yZfeCAXHwh9OwmpUL8j0x3IRRRHnewJ4+pUOHGgdgsWoht2qRSKZxX99agcdywVEFEX85E/n8Kf93YgmMqip1GN1SwXu3b4EDc6FP1uy0K8Pufb/32/+gJamBhr5X+AyWR7RRAYWQ+E1J5dxkpMr9LCswQK7RTvtfSDPdPngsOrmZeCwoy+IAU9UDqoIIfNjqusbzVCN4HkBpzq9qLUboFYp8Kf93TjS5saFXj/O9wZxrtuPl4/2YVVzBR6+ey1u2FBDF9s8Co7FVWucuGqNE5F4Gq+dGMCLR/rQ1hOARs3hq/97EEtqzfjNSx2475aluPumJYjE0/AGE9iwzE5BQRFufxx7DvdiX+ugVLWKYbBjaz0+/JYNCMfSUKsUdNwWGIZh8K43rca73rQaHX1B/PrFC3jhUC9eONSLllozmmvMWF5vxvUbaun8UkZ2i5aO/yKgVHCwGscHR2PPm1q1Ateuq4ZqGql3+fRaJRSK+TkXV1fqoVTSeilCLjeLPqASBBFZXgDHMvCGEjjaNgyjToVkKosT7R4MeKJwWHXwhRJo7w2CGdmBPWf/qSEsb7Diw2/egKtWO+X9LcjEjDoVbr+uGbdf14xBTxT7Tw2hrduPFw73ghdE/GpPO361px0swwAMsLzeAqtJg66BEJbVW7BlZRVYlsFwII6dW+tRaZEWAys4dlF1ckRRlBdTByIpeIJxHD7jRprn0e+Oon9Y2ghy++ZafPDe9RgOxLG6uQJKBYcKM6X3LXRL6y34h3dfhX53BD2uMA6fc2PfyQHsOdyL7z19CjaTGizLYtNyOzYtd8Bu1cJh08mbnhJCZs9MgykACEVSUrrfPCxh1WuV8posQsjlo6wBVTCSglYjlQ9NprOIJTJyRzEQToLjWJj0KmR5AcOBOCrNWqiUHAY8UQTCSaxdUok/vd6Nl4/2wWrSwKhTwe2Lob0/iCU1ZkSTGfS6IhAEUS5NmsOyDLRqTq7e01xjxurmCtRU6lFh1sJqUsNh1S2qDnw51NgNePOOZfLPqQwPty8Glz8OXzCBIV8M8WQW/nASyXQWJ9s92N86iNyf62d/boOCY8AwDNQqDmtbKqDTKPHK8X686bpmrGqyoaMviM7+ID5w33ooOBa/f7ULKxqlwCwYSeFEuwfXb6iBVqXAkC8GlmVQXaEHICLLi1ApOWmDRYYBI/1v3AimKIoQxJHqT6IoV4HiR/4fS2bAMgwYRqr26A0koBkp4ds9FEIskQUviPD44+jzRCAIUmGJYusEau0GbF7pwN03taDSosWWlVU0E7WI1VUZUVdlxPUbavG3929A92AI/nASbd1+PH+wF0fOufHXQ72j93cYUF2px5A3hhUNVmxc4QAgwu2LY8sqB3RqJUKxFFQKDg6bDqIIhKMpmI1q5MaKcpne8s8QoVUpoFEv+jE2QmZdPJVBlhemviMhZNEq69Xz3V/+Cz76lg14w1WN2HdyEP/xi+P43b/eDQD4+k+OoKZSj0cf2IRhfxwf+Jc9+OZHb8TKJhv+erAHh8668N1P7cRrJwbQ0R+E2aBGhUmDLC91DExGFRqqTWh0mmDQKbG0zgK9RgmlgkV9lQFWk3bGi0LJzKmVHBqcpknXi/C8gGA0BV8oiWA0hUA4iYuDYYRjKaQzAnqGwtCoFPjz6934/atd8uM+9I0X5X///rXC5/z+b0/NuM0sAwjTWmlYiGEAjUp631oVB18wiZ3b6rGkzoIhbwyJVBb337IMVqMaIqT0E3JlUis5eSH7tetq8NCdawFI+4ydaPfgfHcADAMMemMIRlN47eQA9hzpkx//0z+3zfi1bSY1nvzCGy/tDRByBVpWb5U3/yWEXJnKegb4wvuuQYNTmiPftMKBrzxynfy7R+5ZJ1fhqbBo8Y2P3Cjf961vWI63vmE5AOBrf3v9PLeazDWOY1Fh1paU1pbK8IjE0ogmMshkeWSzUopnhheQzQrgBRGiKEgj8QyDSCwNXhBg0quRzQq40BdATaUBRr0KvmAcw4EEVjTaIIoiOvqDMGiVcFh1SKaz6HFFsLzeCp1WgUFPDOkMj+WNVnAsg/M9AdTaDai0aJHJ8ghF09iwrBI6jRLhWApqlULer4yQ6dJplLhuXQ2uW1cz7neZrIBIPI1AJAmBl2ZNXf4YsrwIk14FPivAHYijxm4YmYEdHUiSsm6lnystlEpIyExQhVVCSFkDqs0rHfK/bSZNwdqAllqz/G/1SFnUnCu9oh4ZpVZyUFu0M76g3bK1fsLf7dzWUPLzbFlZNeHvKi26abWJkOlQKthx58+VTcU3vCWEEELI7KNSMYQQQgghhBAyQ9OeoeJ5aRG9y+Wa9cYQQghZuHLXhdx1YqGh6xshhJBiprq+TTug8ng8AIAHH3zwEppFCCFksfJ4PGhsbCx3M6atu7sbAF3fCCGEFDfR9W3aAdXatWvxs5/9DHa7HRw3830bZsrlcuHBBx/Ez372Mzidznl//ZlYiG0GFma7F2KbgYXZ7oXYZmBhtnuhtJnneXg8Hqxdu7bcTZmR+nppTeWPf/xj1NbWlrk1C8tC+Yxebui4zRwdu5mh4zYzU13fph1QaTQabN269ZIbdqmcTifq6urK3YxpWYhtBhZmuxdim4GF2e6F2GZgYbZ7IbR5Ic5M5ahUUiXO2tray/44X64Wwmf0ckTHbebo2M0MHbfpm+z6RkUpCCGEEEIIIWSGKKAihBBCCCGEkBmigIoQQgghhBBCZmjBBVQmkwkf+chHYDKZyt2Uki3ENgMLs90Lsc3Awmz3QmwzsDDbvRDbvBDRcZ45OnYzQ8dt5ujYzQwdt7nBiKIolrsRhBBCCCGEELIQLbgZKkIIIYQQQgi5XFBARQghhBBCCCEztCACqmAwiIceegi33norHnroIYRCoaL3C4fDePTRR/HGN74Rt99+O44fPz7PLR1VapsBabOwe+65Bx/4wAfmsYXFldLuoaEhvPOd78Ttt9+O3bt348knnyxDS4G9e/fitttuw65du/D444+P+70oivjqV7+KXbt24c4778SZM2fK0MpCU7X5d7/7He68807ceeedeNvb3oa2trYytHK8qdqd09railWrVuHPf/7zPLauuFLafPDgQdx9993YvXs33vGOd8xzC4ubqt2RSAQf/OAHcdddd2H37t34zW9+U4ZWLk6lfs6vFBOd6ye7Tnz/+9/Hrl27cNttt+HVV1+Vbz99+jTuvPNO7Nq1C1/96ldxJaw2GHttp+NWmmJ9OTp2U3viiSewe/du3HHHHfj4xz+OVCpFx20+iQvA17/+dfH73/++KIqi+P3vf1/8xje+UfR+n/rUp8Rf/vKXoiiKYiqVEkOh0Ly1caxS2yyKovi///u/4sc//nHxkUcema/mTaiUdrvdbvH06dOiKIpiJBIRb731VrG9vX1e25nNZsWdO3eKvb29YiqVEu+8885xbXj55ZfF973vfaIgCOLx48fFN7/5zfPaxrFKafPRo0fFYDAoiqLU/nK3WRRLa3fufu985zvFhx9+WPzTn/5UhpYWtmWqNodCIfH2228XBwYGRFEURa/XW46mFiil3d/73vfk76XP5xO3bdsmplKpcjR3USn1c34lmehcP9F1or29XbzzzjvFVCol9vb2ijt37hSz2awoiqJ4//33i8eOHRMFQRDf9773iS+//HJ53tQ8Gnttp+NWmmJ9OTp2k3O5XOItt9wiJhIJURRF8dFHHxV/85vf0HGbRwtihmrPnj245557AAD33HMPXnjhhXH3iUajOHz4MN785jcDkHa8L2cFk1LaDAAulwsvv/yy3O5yK6XdDocDa9asAQAYDAa0tLTA7XbPZzPR2tqKxsZG1NfXQ6VSYffu3dizZ0/BfXLvhWEYbNy4EeFwGMPDw/PaznyltHnz5s0wm80AgI0bN8LlcpWjqQVKaTcA/OQnP8Ftt92GioqKMrSyUClt/v3vf49du3ahpqYGABZMuxmGQSwWgyiKiMViMJvNUCgUZWrx4lHq5/xKMtG5fqLrxJ49e7B7926oVCrU19ejsbERra2tGB4eRjQaxaZNm8AwDO65555Ff2yLXdvpuE1tor4cHbup8TyPZDKJbDaLZDIJh8NBx20eLYiAyufzweFwAJBO8H6/f9x9+vr6YLPZ8I//+I+455578NhjjyEej893U2WltBkA/umf/gmf/OQnwbKXx5+i1Hbn9Pf349y5c9iwYcN8NE/mdrvhdDrln6uqqsYFdWPv43Q65z3wm6w9xdqc79e//jVuuumm+WjapEo91i+88ALe9ra3zXfziiqlzd3d3QiHw3jnO9+J++67D88888w8t3K8Utr94IMPorOzEzfeeCPuuusuPPbYY5fN+WMhm+7380qTf66f6Dox0TG83M7F86HYtZ2O29Qm6svRsZtcVVUV3vve9+KWW27BDTfcAIPBgBtuuIGO2zy6bIY13/Oe98Dr9Y67/WMf+1hJj89mszh79iw+97nPYcOGDfjqV7+Kxx9/vOTHz8Sltvmll16CzWbD2rVrcfDgwVlu3cQutd05sVgMjz76KD7zmc/AYDDMUutKIxbJ6WUYZtr3mU/Tac+BAwfw61//Gj//+c/nullTKqXdX/va1/CJT3wCHMfNV7MmVUqbeZ7HmTNn8MQTTyCZTOJtb3sbNmzYgObm5vlq5jiltPu1117DqlWr8OMf/xi9vb146KGHsHXr1nn/Di42l9v54nJS6rl+omN4pR3b6V7b6biNmqgvNxE6dpJQKIQ9e/Zgz549MBqN+H//7//h2WefnfD+dNxm32UTUD3xxBMT/q6iogLDw8NwOBwYHh6GzWYbdx+n0wmn0ynPlLzxjW+c80XFl9rmY8eO4cUXX8TevXuRSqUQjUbxiU98Av/6r/86h62+9HYDQCaTwaOPPoo777wTt9566xy1dGJOp7MgHc7tdsujMBPdx+VyjbvPfCqlzQDQ1taGz372s/jBD34Aq9U6n00sqpR2nz59Gh//+McBAIFAAK+88goUCgXe8IY3zGtbc0r9fFitVuh0Ouh0OmzduhVtbW1lDahKaffTTz+NRx55BAzDoLGxEXV1dejq6sL69evnu7mLSqnfzytNsXP9RNeJiY7h5XYunmsTXdvpuE1tor4cHbvJ7d+/H3V1dfJxufXWW3H8+HE6bvNoQeSJ7NixQ07HeeaZZ7Bz585x97Hb7XA6nejq6gIAvP7661iyZMl8NrNAKW3++7//e+zduxcvvvgi/u3f/g3XXHPNnAdTUyml3aIo4rHHHkNLSwseeuiheW6hZN26deju7kZfXx/S6TSee+457Nixo+A+ufciiiJOnDgBo9FY1hNDKW0eHBzERz/6UXzjG98oa8c+XyntfvHFF+X/brvtNnzhC18oWzAFlNbmnTt34siRI8hms0gkEmhtbS3rOQMord3V1dV4/fXXAQBerxcXL15EXV1dOZq7qJRy7K80E53rJ7pO7NixA8899xzS6TT6+vrQ3d2N9evXw+FwQK/X48SJExBFccJry2Ix0bWdjtvUJurL0bGbXE1NDU6ePIlEIgFRFOm4lcP81b+YOb/fL77rXe8Sd+3aJb7rXe8SA4GAKIpSVZOHH35Yvt/Zs2fFe++9V7zjjjvEv/3bv5WrpZVDqW3OOXDgwGVR5a+Udh8+fFhcvny5eMcdd4h33XWXeNddd5WlCszLL78s3nrrreLOnTvF7373u6IoiuLPf/5z8ec//7koiqIoCIL4xS9+Udy5c6d4xx13iK2trfPexrGmavNnPvMZcevWrfJxvffee8vZXNlU7c736U9/uuxV/kSxtDb/4Ac/EG+//XZx9+7d4o9+9KMytbTQVO12uVziQw89JN5xxx3i7t27xWeeeaaczV1Uih37K9lE5/qJrhOiKIrf/e53xZ07d4q33nprwXWhtbVV3L17t7hz507xS1/6kigIQhne0fzLv7bTcStNsb4cHbup/cd//Id42223ibt37xY/8YlPiKlUio7bPGJEkQrME0IIIYQQQshMLIiUP0IIIYQQQgi5HFFARQghhBBCCCEzRAEVIYQQQgghhMwQBVSEEEIIIYQQMkMUUBFCCCGEEELIDFFARQghhBBCCCEzRAEVIYQQQgghhMwQBVSEEEIIIYQQMkMUUBFCCCGEEELIDFFARQghhBBCCCEzRAEVIYQQQgghhMwQBVSEEEIIIYQQMkMUUBFCCCGEEELIDFFARQghhBBCCCEzpCh3AwhZ6H75y1/ipz/9KURRBMuy+MAHPoA3velN5W4WIYQQckno+kZIaSigIuQSNTU14ac//SlMJhNcLhfuvfdebN68GU6ns9xNI4QQQmaMrm+ElIZS/ggpUWdnJ26++Wa4XC4AwNe//nV85jOfwVVXXQWTyQQAcDqdqKyslO9DCCGEXO7o+kbIpaEZKkJKtGTJEnz0ox/F3//93+Phhx/Gq6++il/96lcF9zl8+DCi0ShWrVpVplYSQggh00PXN0IuDSOKoljuRhCykHz84x/HSy+9hF/84hdYvny5fHtnZyfe//7341//9V+xefPmMraQEEIImT66vhEyM5TyR8g0pFIpdHZ2Qq/Xw+fzybd3d3fj/e9/P7785S/TxYYQQsiCQ9c3QmaOZqgImYYvfvGLUCgUuO+++/CRj3wEv/rVrxCPx/Ge97wHjz32GHbs2FHuJhJCCCHTRtc3QmaOAipCSvT888/je9/7Hn7xi19ApVLhxz/+Mfbu3QudTod9+/ahrq5Ovu+nP/1pXHfddWVsLSGEEFIaur4RcmkooCKEEEIIIYSQGaI1VIQQQgghhBAyQxRQEUIIIYQQQsgMUUBFCCGEEEIIITM07Y19k8kkTp8+DbvdDo7j5qJNhBBCFiCe5+HxeLB27VpoNJpyN2fa6PpGCCGkmKmub9MOqE6fPo0HH3xwVhpHCCFk8fnZz36GrVu3lrsZ00bXN0IIIZOZ6Po27YDKbrfLT+h0Oi+9ZYQQQhYFl8uFBx98UL5OLDR0fSOEEFLMVNe3aQdUuTQIp9NZsC8BIYQQAmDBpsvR9Y0QQshkJrq+TTugIouHKIrI8iJ4QYBKwYFlmXI3iRBCCCGEkAWFAqorgCiK6HVFcKrTi/a+IHrdEfiCCYSiKQh52zqrlByMOiUcVh3sVi2qbDo0VBnRXGtGnd0AjqOikISQ+bF371587WtfgyAIeMtb3oJHHnmk4Pc//OEP8fvf/x6AtFi4s7MTr7/+OiwWC3bs2AG9Xg+WZcFxHJ5++ulyvAVCZlV7XwCDnhi2b6bZU0IuNxRQLWKhaAp/3HcRLx3rx5A3BpWSw5JaM5bVW3DdumqY9CooFRxUShbReBp9w1HoVAr4Iyl0DQTR2uFFKJqCKAIsA9RVGbFtVRW0agXO9wTw2HuvBscyONXhhcWoRn2VsdxvmRCyCPA8jy9/+cv40Y9+hKqqKrz5zW/Gjh07sHTpUvk+Dz/8MB5++GEAwIsvvognnngCFotF/v2TTz4Jm802300vi1SGBwColQsz1ZKUZtATK3cTCCEToIBqERr2x/GrF9vx4uFecByLm7fU4cP3b4DJoMKZLh/uuKEFAPB3//4y1i6pxPvuWouO/iD+69et+M4nbkFjtQk/eOYUuofC+Nw/vgHdrjD+9adHYdar8eqJAQwHEgCAz/33fly1xom/HurB+iWV+MB96xFPZuD2x9FcYy7nISCELGCtra1obGxEfX09AGD37t3Ys2dPQUCV77nnnsMdd9wxrdcIh8MIh8MFt7lcrpk1uMw6+oIQRRFrl1SWuymEEHJFooBqEeF5Ac/u7cLPn2+DQavE39y2Eiolh+YaE9YuqcS+k4P4xV8vYNfVjVArObz91pWwmtQAgEanEf/z2V2wmaTa+u+/Z538vCsbbfjhY7vkn93+OFrbPTh01oWf/vkcUmkegiDiqefPQ8Ex+Plf2vDjL74RRp1qfg8AIWRRcLvdBVX2qqqq0NraWvS+iUQCr776Kj73uc8V3P6+970PDMPggQcewAMPPDDucU8++SS+853vzG7DJ8ALItr7AlhaZ4FiDlKnayr1EKe+GyGEFBWIJAERsJoW3v6BlwsKqBaJC70B/NevTuLiUAjXrq3G3/3NZmhUCnzyP/ciy9dg7ZJKXLuuGtetrwbDSMUnrloz2mFRKjg4rLqSXqvKpsOuqxux6+pGpDI8Wts9OHDahWf3diKWyKCl1owDp4Zw3foa/ORP5/DWNyyXAzVCCJmKKI4PD3LnrbFeeuklbN68uSDd76mnnkJVVRV8Ph8eeughtLS0YNu2bQWPe/e7341777234LZcWdzZFggn4fbFYdKpUGM3TPvxiVQW6QwPs0Fd9PeD3hhEUaTzLCFkRnqHIhBEkQKqS0AB1QIXT2bw4z+exXP7urGiwYq/vW89vvubVrw7nERNpQH/8uEb5GISc1HFT63ksG21E9tWO/GBe9fh8Fk3XjzSh+/8+iR+9IczEAHcsqWOLvSEkJI5nc6C9Du32w2Hw1H0vs899xx2795dcFtVVRUAoKKiArt27UJra+u4gMpkMsFkMs1yy+fG4bMuiCImLEZg0ClBU1SEkJlqrjUXHcgipaOAaoESRRGvnxrC9397CqFoCo1OI77+0RsBUcSWlVVw2KTZpvmszKdScrh+Qw2u31ADtz+O3+3txF8OdOMLj7+ON+9YhkAkhQd2rYBJT6mAhJCJrVu3Dt3d3ejr60NVVRWee+45fOtb3xp3v0gkgsOHD+Ob3/ymfFs8HocgCDAYDIjH49i3bx8+9KEPzWfzZ91U/ZxMVqCAihAyY/FkBqKICWfBydQooFqA2vsC+MLjryMSz+D6DTW4ZXMdKsxacCwDgJGDqXKqsunw/nvW4W23rsAvX7iAn/75HAAGLbVm7NzWUO7mEUIuYwqFAp///Ofx8MMPg+d53H///Vi2bBmeeuopAMDb3/52AMBf//pXXH/99dDpRs95Pp8PH/7whwFI1QLvuOMO3HTTTfP/JuaRQauEIFBERQiZmf7hKARBRHWlvtxNWbAooFog4skMDp9xIRBN46d/OguGYfDwXWtw9/biVa8uF0adCu+7ay1uv7YJ/98vT+A/fnEcnf0hrGmpwPUbasrdPELIZWr79u3Yvn17wW25QCrnvvvuw3333VdwW319PX73u9/NefsuJ4lUFjwFVGXxyrF+rGyyoeoyGMgk5cHzAl47OYhVzbaS16Jfbgw6JUSh3K1Y2CigWiCe3duJp54/DwC4Z/tS/M2tK6BRL5w/X43dgK/97fX40/6L+OGzp/GHfV34puVGrGi8MvaJIYSQuZLK8POS8scLIoa8UdQ5aM/BfG5/jAKqIo6ccyOT5XHtusU9eJodGczwh5ILNqBaSX2xS7ZweuRXoFMdXhw770Y6I+D3r3ahqcaEj71tM1pqF+YeTyzLYPcNLVjVXIGv/M8BfOV/D+KzD12NpmrTggoOCSHkcmK3aOfldbzBBDr7Q7AaNdBrlfPymotNJJ5GMJJCfdXiD0pjiUy5mzAvZr/c1/xr6/ZDEEWsbq4od1MWrPmrWECm7bXWATy7twvPH+zBI/euw7//3c0LNpjK11Jrxv/3iVtQX2XEP/zXa/jYv79C6SqEEDJDnkACLl98zl+nyqbD+qWVOHLOjWAkNeevtxjFEhm4fLFLfp5DZ1w4cs49Cy2aX4Igzks1uSwv4Mg5N5Lp7Jy/1mIQTWQQnSAAHvLGcPaib55btPDQtMBlpqM/iNdPDaLPHcXrp4ZwzVonPnjfelSY52cEcr4YdCp86f3X4qs/OogTFzw4cHoI169f3GkBhBAyF3QaxZSVAGcDzwuIJaVO1wTbgpEpKBUsdJpLn91LpEoPFHyhBKxGzZxsnTJdr54YQHWlHssbrHP6OpFYGrFEBp5AYs5nA3Pfhcu16vihsy7UOQyoqZx4D7w6x8S/u9AbkP7RPNstu3ylMjxYhoFSUfq8EwVUlxFRFPG7vZ145Vg/rEY1HnvoKlyztrrczZozKiWHLz58Lf7zl8fxzZ8cwYGNtbjrphYsq5/bEy0hhCwmkfj8pFYN+WLo7A9h80oHjLrybn8RTWSgUrBQKbmytmO6WIYBx81fYJPJCjjd6cO6pZVT7gfJ88Kcb7XSWG2CfhYCyoWuvS8AlZJDo3Pu98IzaJVQcpN/T7S07KLAgVNDUCnZaa3/oyN4GQhFU3jlWD9aO7w4eMaF265txHvvWDMro1iXO5Zl8NG3bgLPi3j5WD/UKo4CKkIImYaaSj2EeRgeNxvU0KoViCUy0KoVUMzjPodjHT3nhlrFlXXQcSapa6kMj+g8BcAAwDJAjV0P9RSBZyCcRGuHF1etcc5p57qp+vLcTFsURWSywrwF6IMeKe1zPgKqYCQ15QBIR38QvCDiqtXOOW/PQpHOTK/sIa2hugz831/P44e/O422Hj+++P5r8JE3b7wigqkcjmXwsbdvxs1b6rDncC9OXBjGoDda7mYRQsiC4PLF5Q7aXDLqVLAY1Th01oVAuPxrqFJpvmyvHYgkZ5TipVEpYDHO7+apCo6dMkUzEk8DwJyvOTpweginOjzzso5qOvqHpWUWpRr0RnGhx494MoNcWQpxFkptZnkBZ7p88t9jNrTUmmGdYnZSreTGBdKhaAonLgzPWjuKuTgYwoHTpR/3uXSy3XNJ75dmqMqE5wWcuODBmYs+/OG1i7hqdRX+39s2w6QvbxpFuXAsg489sAmJZBZf+d+DyGQFfOv/3USzVYSQBS2Zzs55tTOddn4u5dFEBvtODkKt4mAyzO21iucFMAxzWaz7GSuZyqK13YummunPLsSTGQx5Y1hSawYzDwvReEFErysCk1416UDtfIU38WQW53sCMOnVaJyH2apSAzebaXprzDIZASfbvRjyxXHdLK7/zmYFeIMJGLTKWUur7RwIodFphGGSypxL6y3jbrs4GEIoOnuBXTG9rkjR2y/0BqBUsGiumVkhtmQ6C41qeufFSy20QzNUZfL8wV586YcH8JsX2/HIPevw2fdefcUGUzkcx+KT79yKpXUWaNUK6CinlxCywA15Y+joD87pa7AMA3YeOueBcBKpDA+bSTNlCtmleu3k4KxVFstkeYSiszejlkuvTGemP0Om1yohCCI6B0IQRRHCHFe4nW7QxsxxEfCNy+2otRuQuMyq7+m1StTaJy7MMJZGrZiT9ECVksPKJhuclfpZe06rUQ21crQ/FY2npb3r8rj9cQx5536Wu1RD3tiEwdZU+ocjOHjahSw/ecre3uP9uDgYmtFrFEMB1TwSBBFnL/pw9qIPTz3fBpNBhX/58I2488aWeRmpWgjUSg6fe981cFh1+MIPDuCFQ734/m9bqaw6IWRB4nlxygv7pcqt/5hr1ZV6OCt06HGF53zWbWWTDfVVRkTj6UtOQ2vrCeDEBc8stax4hT1RFBFLZKb8W+dKUxu0SvS4Ijh01jVr7SpGwTHYvNIBk37u0wyT6SxePT4w6d8rywtSQHqZXdJ7XWG8cqy/5PvHEpk5SY9kGGm2TFnC+kSXLwZ/OAlBEHFxMDRhcM6AKUj5PNo2jENnCj93nkACnkDiktp+uaiy6bBhmR1c3oyjKIo43+Mv+JuJItDnnlnQVgwFVPPo9VOD+If/eg3/+F+vob7KiO98YgdWNdPu1GMZtEp88f3XQBRF/Pwv5xCJpRfFxnmEkMXnlWP9clnheDKD/uEIRFFEOJZGKJqCRs0hkxUKAh5eEGc0uzFR+hLDMPNSxlzBseBYFqKIcSPcs63KpoPZoMbRtmEcPF3Y+ct/7UNnXVN2hNc0V+D6DePTsoSRv8N01/Oc7pRmzvIflsrwOHLOLY+qdw+FkSwSeOk10kyIs0IPBcfAPMeBTq7K33xsshuKpiGI4qRpYqc6vBgYLn2NtCCII+uUJMfOD6N/uIRO8DS/D9MdkEileaTnYBAjleGxv3UQbv/U+8qd7wngVIcX3mACva4IhgMTP2bs+WFs8KVRcbCa5ndt31xRKjhYjOqCiYpkmofLFy9p1qt/OCLvFSeKYsmBMwVUcyw3KxVPZvDqiQGIInD/jmX48geum/eFqQtJhVmLLz1yLZJpAf5wCrwgoL0vMK29NwghZLYMeqPwhYqP4A55Y8hkBfQPR3FxMAxRBAaGo+h1ReANSo/h82Yuzl30TWsBfE7vBKOp4Vga8eTcnBvPdPmwr3UQgDQiPuCJoqHKCL1GOafpavtaB0f3v8kTiCRxIO/Y6TXKCde+dA+F0dkfBMsyRSsSRuJpvH5qCMlZKG6h4FgY9SpUmDUQRRE9Q2Fc6Bvf/lSGx4Anis7+INp7g1CrWHQPhSdMPXL5YnjlWD8y2Zm1kWGk1EReKN75d/vjM5ppEUVpVoSf5uyrxaCGcRrLG9r7Ajh8VtrAOJnKIhJLo2tAOlaBcHLWZn+ba8y4oUjQPZEaux4VUxR6mIlc6u50Bkim+haKEKcsoBIIp8Z9R+Y6/XOuDHqjI9+ZmX02elwRBEbWUw14ouMGdCZCi1Tm2P5Tg/jmT4/CbtEiGk/jc++9GletobKUpahzGPGFh6/GY/+9H9/86VF09gdx48ZavOeONeVuGiHkCjPkjUGnVk64ybrbH8OQNzYyMgo4K3QQRBG+UBIAoFaNrrdorjGjZhrrNXLCE4z811TqIULqOE+1rkMQRISiKRh0SigVU68ByQWEAOQOF8syeP3UIJwVeqxsmlmWRSrDo3swhAanqaC6GC+IeO3EAKKJNFRFNtUcO6i2pqViwteIJTLgBQEnL3gQjKawfXNdwe9VSg4NTuOslH9XcCw2r3AAKD6TmOUF7Ds5iLoq6e8ejWfgCyUwHIhjdXPFhBXicp3CmRbFYxgGeq0SHFv8PV7oCaC5dvrFIVJpHr2uCKxGzbQGh9ctrZTTHqcSiafh8o3OuoRiaZzr9st/x9YOLxqrTbNSij2d5RFPZqfcqytnyBdDMJqCPq/Qw2wULlQpuXGf02KmU0ChWNn0eDKDTJaXzwGCKBUvKbUIxKA3Cq1aAatx9oPKmRBH2l9XZURWDqRm9gdZ3WSDb+S8ZzGUXjyFZqjmgCiKaB8ZmcpmBShYBnqNEt/++M0UTE3TikYb/uFd23DwjAurm214260rAMxs/w9CCJmplY22Sau6WUY6Frn0pCFfDIPeGBQci3A0XbCniV6rLLnjNtagJzpuRsHtj6OrP4jXTw1NmvYDSAFLa4cX4dj0q3dVWrSocxjQPRRGLJmFL5yc9nPI7eAF+MPJcTMcuZ+bq83YsrJq3OPGjprHEhkEIylE42nsOzkIly8mF6BY01KB9UvtE1YkzAUFE83eTEcqw+PkBU9B8Yv80vK5wMgXTILjGCyptyCVEZDK8Fi3tBLrl9qLPm99lRHbN9fNuAACwzBoqTVDP0ElyCV1ZlgMhQFRKsNPuW5ZqWCxotEKnWb0eUu5Lnf2B0suEDJ2TY9ayWJpnQVKhfQZWL+0EtWzVLzh4kAYpzq8Jd9fpeAK1uiUQhRFBCKTf2d4XkCfO1I0XTQnGEnhZHvpawKLlU3vcUXQPRQu+TnG6ndHcXEgXDBrf77HD3/eOeFY27Ccuuj2x2clTTiezBRNlw5GUugeCmPIG0WD04Ttm+tKGjAqxqBTyoGyTqNEnaO0wS8KqObA/lND+MR/vop/f+oovvXzY9i+uQ7fePRGOCtmr2rLlWTrqio8+taNePnYAH7/ahf63BH843f3TZh+Qwghs204EC/oLIxl0CqxbmkllAoOoijt2WTQKqFWcQjH0+jKS+lq6/ZPawF8vva+IM5d9BfcptUooB0piT12rczYNrMsgzqHYdolhQFpBiwxklpYyqJ5QEoZPN/jL/q7dEaYcAw5neWRKSGd68g5N062eyCI0izQ+bwCFC5fDIPeKJprzEVH/dUqDjV2/bQ7xsUcODWEYDRVMKNXjCCK4HkRgXASlWYNaux6DPvj8pqNsTJZAeFYGv5wEt4i17ypXi/LCzjV4Z1wViiWzIxLjTpwamjCv1nOoTMu7D3eP+11RIPeGLzBBNz+OARBxJkuH850lVbNkeNYdIykSuZ+nq2kNGeFblpriNIZftxxmypNb8gXQ2v7xH8LQApmuwZCcE8yMDLdNMfOgdC4ILa+yjiuqmH+TKMoinD7YxMWqljdbIMgivJ6QkDaD+/cRT/OdPnQ2uFBhVkDzcjMfFu3H2fz/s6ReBpnunzTLjh2+Ky76L5VuWcRxZmvjcw53elDe18QANA3HMG+k4MlPY5S/maJKIroHgqjucaM5hoT6hwGvHpiEB9960bcenVjuZu34O3c1oBAJIUnnzsLjmVhMaihnkGHgBBCZsLli01aWjkaT+NMpw92qxYMI+2tJ4gM3HkpS4fOuqQUKcOlrZ8d208Ix9IIFAn2hgNSB2f9sko5NUcQRLj9cdhMmoJ0pVIM+WLwhZNoqjYVpDBOJtfhX9FYmBqoVimweaVjwu0xznX7EctbFxaKpmA2qMd1WjcutyOV5qHgGFiMaqxosEIz8pzne6RMEZNejXgiA4dNV/DYLC/A5YujeyiMa9dWwzDNfX+KlZlucE6eHqRWckileZzp8kIUgUxKwLluKXgpNuja6wqjfziKBqdRWic3JiPrTJevaLAYCCchjBRHAf5/9t47Tq67vPf/nDq9z+7O9pVWba3qbtwEMrYxRrbBJOBrHK7BF7iQEELLjws4mARCIDEhF5IQIMRJiC+BEGMw1TaWm2RLlqVVr9un9376748z5+zMzmxTW5Xv+/Xyy9rdMzPPfOecM8/n+zS926RBVZRh4RhQFIVwotQkrjesDM7bFr9YlZDOC7XaLv08Wki34tV9PjNSEU2X5hWE9eRrokCuvZfXj8TR1eZomFeZL4lgmYXJrEMjaQS8VrT77PC5rfMOv62nM+hoSv+dz3+XalHquerOLDyr12d5bBgJ52DlGXQGF58ebPikoYADPpcF/IxoDUNTYBgaqqqZYx3qBWK2ICCaLqNcldHma05zPjKegayoTcOAAcBuZaGoGhLZCiw8A0/tflcvntQFNuYplMWmdMViWcKxicysc0qPT2YRSZZw3frOUxrvUB+9X4wmIxGqM8SO/VF87NHn8MS2E/iTr2+DLKv46h/dRMTUGeTeN63A1puW47FfHMQtV/fCaeOQzFZm3dkjEAiEM4XPZZ2z9XSupHc4M1JcRFmFqmrmfMGAx4o2rw2dQQckRcXltXqbM0E0VWpILzMwagnqnWmK0neiuRb1SfPR4bPD57IgXxJPuxlAVZCx+3Ac5VlSmzwOC/o6XObP+ZLYlAYlySosPIN2vx0cy6Ar6ARb977WLg/gsmUB7D2WMEVLPTRFwcLRYCjKLEJfCFPxopnWb3Dd+k5cuy4077oaKaEuO49MXkA4WcTa5QGsG2xdCxb02hDwWGG3crAu0DnctnsSP3z6qBk94DnGFM+KouKV/VFM1jrtsQytN/WonSK5ooDDo2kwNNXQXa8VFLDo+Wd+jxW2moBr1dQkU6jOmrbK1kRBX8e0wHDMGFb8+pG42cRiNvTokoJ4ZjoymMpVsHdGa31V1QVpq+YGk/HZm9ScDgxNYWWvD04bh3i6jFcPxBrqBquCDHEBDUrS+Spe2R/Fy8NhFCtS02OMhi0agD2166M+uu128FjZ48WqvmbRksxWsOtQDIqitixjWdblMeeJzlafqNTWdrYokiG45Lq1N8R3uSohnJjd7+vw2xHwWKEo6pzRwGxBaIr2GxiivKfdiWsXWKpDBNVpYrTvXD8YwIaVQXzvyf24YUMX/vbjb8SKHu/SGneRQVEUHrprHW7Y0IWv/OsuHBxJ4R9/Moz/+597lto0AoFwkbOi1ztnLn27z45lXW4EvfpuLk3p9yyrRXcCFVUzHY1SRWrpjCmqdkoz93JFcU7nd6bPoqgaihUJJ6dyqAjygufPWC0srDyLdL46a1fBeKaMnQuYrURRAM/NnrLVF3KhUBZNp3s0nMdIuLHmI5Yu4ecvjuCpl0ZQEWQcHEnhpb1hM50y6LWhzWfD5avaWgoWTdPMaMdicNi4pijjjn0RvLI/2jTXpr47XyRZQkWQ0d3uRFebEzxHg+eYmmhq3ezE47Rg3WCwZuvCRGwoYDdr9GRFhSgp5joaQ4mLZf18uW5dCJ11kbHJeBF7jyWxfV8Ew8eTkBW1ZSSOY2is6PU2RA8M53iubrzb90UwlWhum25EbYaPJXFoJF2r41LN95DMVpDMVvQuirXHbL6iZ1HNXaqCDElWcGg0jZNTOVMsbNs9iXi6guyMtLiqKOP1I3GMR5trjexWtkG8A7qjb1y/mUIVrx6Yf7jsTERJwbbdk8jkq9AAsCzdEMl55UDUTHmcC03TN3H6Qy50BR3mxo4BRen1QcB05M8gVxRQERVUBKVlzVdVlEFTFMpVGYdbbFSMR/MYjeSRLQqzdpB02DgMDfjNdNtyVcLw8YR5fFVUcGIq11B3ZaSGBjw2XL+h0/y9oqgIJ6fPKeOamYwXcXSsudOmAcNQsLeoLbTwjFmrWRWVlqm2rSCC6jR49WAUH/na7/Di3in8yd9uw7GJHP70D67CR991ecswKOH0oWkKf3Lf5bhsmR9f+M4OvOUN/fjYu69YarMIBMIZ5vnnn8ftt9+OW2+9Ff/0T//U9PdXXnkFV155Je6++27cfffd+OY3v7ngx54KB06kcKKWGpPKVcw0GQOWocBzDJLZClQNKFdl5EuCOZMnWxAQTZXMHfHxqF54Xr9Lv2NfBC/tnVqwTZlCFWORPDRNM1uHS7LaJNYm4gWoqoaj4xmUqhJ2Hozh6EQWE7ECho8ncHBkYTUsmUIVkVQJHX57Q7pgvZg7NJJeUAt3iqLAscysaWInp3JIZCqmM9nb4UJvyNVwvCTrjna9iPG6LOiuCd/dh+PYvi8Cu3X27oxVQW4pYsejeYxF803OdFWQ4XVZ0OazNz1Gg9YUdXl5eLreo1gRkcpVMRUvIp4po81nx2C3Fy/umcKPnjna0r5sQcBrh/UoxUKL+lf3+9FRS280HMPZ0qt2HIg2OKP19veH3BgJ53B0PNP0eFnRcGwii1ypObI3Nk+zg1YS1hBZVw51YNOqNuzYFzGjEIlMBQdOpjAVLyKVq+LYeBaFsojndk/M2+Ci/rVeORDFzoOxWgTDBlVTzQjK8h4PBns8DRETC8egM+hAR4tUTJuFhYVjkMpVTSFWrsqmA09TVM0xn5sTU1nsPZYwr6FK7Z5Qqkoolls3YJiPfceTyBSqSOWrODKWQThRaqqtXNPvx0CnGxRgim+j6c6eowm8diiGyUSh5WZLJFmComrgOQaxdBnbdk823A9HwnmMRfJwWjmzWQ+gN4ExxHaxrHdsNM43iqLA1+4HuaKAfO28ahXAKlUljEWmr/l0XsBYpGBGEmOpEn69YxQuO98yXdHAZefR3yJFV1U1s34znCjixGTrkQYzIYLqFDC+ENcuD+DatSF87d92IeCx4e8+8UbcuLF7ia27+OFYBp998Bqs7PXia//+GrLFKgplEY/+x2sL7h5EIBDOXxRFwRe/+EV897vfxVNPPYWf//znOH78eNNxV111FX7605/ipz/9Kf7wD/9wUY9dLKWqZDq0+0+kmoaTxtJlHBnLoN1nB03paSfdbc6GlKjxWMEsdgYAQZLxwp4p02mRFVWvq5EVjEfzECRlTodq+FgSo5E87FbW3MSLJEsNheIAUCjpEaxIsoRYqgyHlUWb14r1K4INx1UFGQdOpmadL2U0pLBbWHNnOZmtYOfB2LyDY7ftnmyIdLAMje5alKYeQ9wYdQwjkTwm4wWMRnKYiBYaHNRQwIH+kAs2C4vJeAGr+n1o89qwoscLRdUQSRUhSgpOTGZbNgFhGRoBj7XlHKuRcL4pKhbPlPHKgSgS2UrT52+I6dFIfta6i5W9PqysRUXSuSrS+SrGo3mMRHJI56pIZCpNs7dSuQqKZQlOG9/QojpfEhFNlVrW44xH82ZNXbEiNqzrTGRZbbBX1TQMDfhx5VAHHDbOTBdNZCvYeyxhrqMhPKqCsqihwdev70TPjKiSJKvYczQBWVbhtHFmzY1BKGDHjRu7sGZAX7uA14r9J1I4PJqZNfVrthlKkqwilipjLJrHz14YQbagt9OnKeDEZA6JupouhqGxqk9Pv5tJJl+FqmqIZ8oNUZpSTRhJsopsQY/0zMWLe8LYvi9ipim+fiQOhqHQ7rOjKsqIpct4eV94UZHrTEGPINO1VNZsUUA4UWwQPbG03mSnIkjm/We0dq63++xm90TrjFrJTKGKZFY/tyqCbLYUr68VvWFjF1b3+5AtCg21nUcnMnj1gB69rr8PAsYAZxmaqiGSLCFTEOBzWVrWw+VLYkOU0+vicdkyv3nszoMxjITztSh4o/2CqHfjLFf17qBHxjPIFgTTLqCxlizotcHntiCcKM7bGZUIqkWy61AMH/rKM3hm5zg+9uhz2H0kjvffvQ5f+t83oL3FjhXh7GDlWXz+fddiWZcHn//2dhwaTWMiXiSCikC4CBgeHkZ/fz96e3vB8zzuvPNOPPPMM2f9sXOxoseL3nbXrPNf9CYUmln/EU6WEE2VQdO6476824PLV7XjuvXTqSqSrKIiyE33rXJVxkg4j0JJaBoArKoa9h1PNkQBKoKMQrm5u199CpPTzuPatSFIsopMQYCm6TvT1AzBl8xWZk3TCQUc6Gl3YiSSN6NQXpcFm1a1mcLl2nUhbFzZhp0How0iRpQVRFLTTpAoKTg+kYVQczhf2DOFo+PTDpfbwZtpSoWyhGiqDI6jUe8nC6KCsWgBPpcFQY8Ne48m8MKeKRyfzOLwaApWnsXlq9twfDJrRhfrKVUlTNUcckFUsH1fBIXy7E6TMVA2ma0gP+O4DSv0xh+ipCBXFFqK0nxJNOtAOoMOlKsyihUJ6waDWNXngyjLpmg16O904+rLOmrRLf2xkWQRU4kiMgUBiqY1RAhzRQHP7JpAtFbL19Puwqo+36xt+q0WBjQFc16asRYHTqYaaoqOT2Th91hNAUzTehOQ/SeS2HUo1hDlmo1wsojdR+JN51cyW0E4WYIgKxg+lmiK0qoazIhBu89mOvttXps512sx+D3TDVkkWUWplv4KoEE8SbKK516baJn2dmg0DVlR0dfhwsaVjS3vVVUzu2DuP9Hcil2WVYiygtFI3ozY2KwsDpxM4fBYBgdH0hgJ59DT7kLQa4OF0z+jhXLz5T21zRz9c7JwDKKpcsMmQDpfxWg4j50HY2YzFiNaN7TMj1V9Pmxc2dY0l6pSlWGMNNM0DaGA7veqdaqcZWhz7lm9oAn5HWZTGeO6Nx5FUbVUO5oyzw+aplpGsF12Hh2BaX9bVvQUZsOEzqADq/t8yBaEpggzRdXOeZqCIClQFQ3jsTwKZbEhxdjA77Ziw4o2vbtqi/TGekhe2gIxOgx1tTmwut+Hv/1/r2PTqjb8xYduMEPrhHOL1cLizx66Dn/2T9vx6H/sxuffdw36Qm5Isj5D41TaAhMIhKUnFoshFJouBO7o6MDw8HDTcXv27MFdd92F9vZ2/Omf/ilWrly54Mfm83nk841fttHo9C5lRZCRzFbQ1eY0ozGyomHH/inE0uWmDlMnpnIQRAUWjsHuI3EEPDZomoYjY7rjdXIqh3XLA6ajpWka4mk9ohH02nBoJA1N00BRFCRZgcvOz3kPG43kkSlU4XNZwTGM0WjNZOZMHUXVsH1/BKqqwe+2IlsQsG33pC5SZjBbGp6G6ZbNRn0Ly9AQJRW/fXUM3W1OxNJlSLKKNp8NxYpkRuh4lkGhJKEqyLBaWFA1Z89wX9TazrQBw9DIl0QzJUnVtKb25kYDkHBSb4+eLVSRLYoYDeeQzgkQZAXFigQrz2KwxwtFUcHUFcnbLCw6AnbkCgI0aFBUtaUQCieL8LmsphO4pr/xs09mK8jkBUSSJUiyCo6lURF0sZTOV3H9hi4A02ltV1/WAbuVg9vBw2ZhIIoKhFoBfqVObFSqErJFAR1+Bxy26dk441E93cnCMZBlfW6R0UVxz9EE+jpcpu4cjeRRqkiwW1lYeKYpehZLlZHMVFGsiOjw20FRlNni34gIGXQGHOhtd6EiyHrKZt1a5otiQ9vtRKaCfEk0RfG23ZNI5irwOi2YSpSwomfaUQ96bcgWBRwbz2LXoSgYmsLybq/596lEEa/sj0KUFMQzFXicJditHIJeW1MHuIUwGs4hWxSwsteLqihj16EYlnd7zPPNIJIs4vBYBu1+u/75SwqUWme7qqhAVlSEbFxDiYemaRg+nsBkvAiXnce6wWDT60fTJYxHCqBoCm21piOVaqOYFiQFkZpIvXJNx4I6KBoYmwdOO28O8p5JWy3ykisK5iaC0VDl8GgaNitrttsfqhveXSiLZtQ2mirjlf3N9ZLP7Z6EXBsaXG+1z2XB2sEAimURVgsLte56kxUNyWwFy7rcZlfDVK7asgbNZeca7r+5ooDRcA5WC4toqgSG1hutRNOlpnuGqmmoCDI0Td8MstVqXCuCjMl4EYM9HvD0tAiMZ8rm9TYfxONcAAdOpvBn/7QdN1/ejed2T8LjtOCT91+Jmy/vXtRJTjjz2CwsHvnAG/Dlf3kVD397O/70vVfjd7smoKga/s//vGapzSMQCKdAq85PM++1a9euxbPPPguHw4Ft27bhIx/5CH7zm98s6LEA8NhjjzXUXc18/cl4AeFECaGAHQzN4MRU1hwUaTQyqK9pKZb1RhOipGKg043JeBGren2Ip6dTiHYeiplNKyYTRVQEBYPdHkiSgnhFgqpqYBgKB06msfmKnpbvhaYprF8RhKppZqqOntY1+3eRqmp4cc8Ujo5lEPDakM5X4fdYdCE2433r69X6eSLJIqKpMtx2HpPxIniOwe7Dcbx6MGo6Lka6zGXLAg31F4dG0/A6LRg+kcQ1l4Wganox+Vgkj6FlgSaxMxErYGjADw36LrcGDRaOQa4oIFcUIEgKXA7OrFHja23A+0NuvGF9F7bvi+D4ZBYHTqTAMjRUTcOJukYExucYS5XBsjRoioJS2+memXJ2bDzbUDM283xy2DhUBf1cCHpt0KBHLI1UQuPwvg4XqqKCcKIEu1WAzcLCyjE4NpFFsSLh5su74XFazXXcsT+CI+NZDA340Rl0mB3LKIqCzcKiIsiIpMpY3q2Lk0JZRCSpn7OGjT6XBaWKBFlRsWd/oqnrWrhOxLb77GYXSCvHoCvoQP3M41xRr1VJZMvQND0N0GZhoaoaDo2kccWa6c6VRycyCCeLcDumnXGv0wK3g4esTEdJgWlHvlyVWrbCtnIMVE2DpzagOVOowm7lcGg0jYEud8s6mJkYDQ2qomwKAr/bCpqi0NvhQihgx1SiiJf3RXDL1X0AdOd7Va8XIb8eEdtRixZfv6HTTP86NJo2r2n9PeiiyLge+LrGFclsRU+9TagIBR1w2jiMxwpIjGUwNOBHqSoh6LEhlatgIlpApiCApij88uVRXL+hc9aW/DMjfpPxIhiGQrYgQJQVtPvsTcIk6LWhKioYi+bR7rMjnimb57ixUaG2uP/UP0/D5kPdP/MlAeFECUMDfkzGi5BrJ9GhsbR5z8zkq/C6LbV7DgUrz2CwxwOOZZDMTm90GSbUp7Yms1VsHw7jxk3dqIoyKArmNVyuyihVJYxHC+jrcJmNQ0oVCYdG07h8VZs5VqF2dYICZW78zEwVnYwVEU+XFzRiggiqOaiKMjiWwXg0D5qm8MKeSbz71tW4e/PgKfW2J5wdbBYWD7//Ovzt47vxpe+/ine8cQWuvqxjqc0iEAinSCgUaogWxWIxtLc3thl3OqdTfTZv3oxHHnkE6XR6QY8FgPe+9714+9vf3vC7aDSK+++/H+FECUciBbM+ANDTjI30ld5aO+90LU1KVlTE0iUUylKDIx3wWGGzsCgLMuxWFgxFmak7pbKEkN8BjqXB8wwGe7xmSokoKXj1YBSX1e0M11OqSLh2XcisXfG5rA3iy3B06muDbBYWdisLrfa3/pAbK3t9ePVgFJKkpz1pgJkSGPI3N4wwxKGFZxCy2mtpZ/oa2K0coqkS1i4PwGXnUSyLKFX1CJWxg58tChiP5BFJFOF1WTAaKaAqKbBbORydyDbshAPTxfKRWt2yUV+kqhpkWUUo4ICFY5EtVFGqSBjs8aBYlhBOFsGxNNq8NvR2OPHycASirJqpYqKk4PBYGmpNGHMMbaYx5YsiutuAkXAObT67mQJW7zweGcuYtUYAEE6U4LBy6Ao6wDA0btzUjRf3TAHUdDMISdIL8uvbqqdyFeSKIgY63bBZRCQyeurb+hVBvHYoBqmuA6GVZxD06GJYUaZ39kVJMYc3T8QKyBb1mhmW0dtvR1NlVEXFTAucq+scRel+j7NWOxVLV9BWJxYOj6Uhy3pnRCOaaEQaLTzTIMRtPAuPQxdzuw7FoKoabBYWa5cHcHg03VBbaIiTdp8d47ECNE1rEH7F2rlpq113nrrxBcZsp5m0SisE0FATl85X4bBxuGxZwDyP6x13UdJFPkUDL+8NI5Yuw+uyYCLWmN7Yak0rgn5eb98XwdWXdWDb7kmMRwsIeG2gICNT0NNC60VLNFlCV5sTyVwFhYo+cNkQICencrMKKiOVz7BjoNMNRdUQTpRAUxRKFalpk+TQaBqZQhVVUYEglhvWaO3yAH724knYLGxDqmi5dj07rJx+bdMUNq4MYu+xpPk+ZEVFb7truhmKrLSMkkXTZVA0ZV5fgqTgxGQOThuHk1NZAHr6ZThZRGfQgdfr0k8lZXqoshEh27iyzex+aKSljtc1qzHWUZAUVEUFlaqETEFAOl9FX4cLqqahK+hoqtlK5SoL7tRIBNUsjIRz+My3XoTbaUE0VcKt1/TjPW9Zs6jBb4RzB8fS+MT9V8Lt5PHjZ4+BZ2ms7PXhpb1T2HxFD4kkEggXEOvXr8fo6CgmJibQ0dGBp556Cn/zN3/TcEwikUAwGARFURgeHoaqqvD5fHC73fM+FgDcbjfc7tYOSq4kwOVwwMozoCkKz78+iaGBAPweXbgcGknDaeNwdDwDRVEbCqyN4vGKICNfFk1R43VacMWadnQEHLqzDd2hS+eroKA7RW4HD4qiICuangIkyEhkynr6n2V6ds9oNA9V01CqSHDYOORLIkRZMWshYpkyckUBa+qG6VYEGQG3DWVhuptYriiYQmz7vgjsFhbHJ7OgKH3m1MzbpiHgEtkKQn47ZFnvktbT7kQ8XYZEU4imSth/IolscbrGaEWPFx4nD1nRwLEMFFWFIKmQZGXWduD9IbcpFDiWNp1LRdEgySqqooLxWMGsQSlXZUSSRWSLIsLJEvIlETxLoy/kxpHxLPIlXbBg2fTcLpeDgygrsNZSuACYaWuCqECSFMDGQVU1FMqi6eQ77VzDTCyOpVERZRRKImxWFkfG0hBlBYWSaM7aSeerSGQroKBHtFb3e5HIVEDRes2HJc+gUBtYauUZjEbyGOh0o82np8ONhPNI56sQJAU8S0OsK5yPpsqoCBJGpqa7kRmCRVZUjIRzYGiq5Ywsn8sCSdbn9VRFBYlM2RyoLMpKg6CqCgqGlvnx+pEEKEp33HmOgSgpyBYFyIpmpq0WyiI6gw5EkvpAbIrSU8mGjyfhdVrgtE/v+Buic/eRuPmZ14trm5VFqSJh+EQSAbfVDMau6PFiWVfra7hVO29AF+npfFVPI61dq4//5jAGa2NujCh0Jl/FWDSPE5M5uOw8hmu1UDYLa3aVtFtY9He6cdmyAF4eDje8jsPKmq+382AMqZzeBt0Y7NzqnBdlFaO12siqIKPDbwdNU7VBttlZW8TPnJPV3+lGMluBw8bByjNo89laNlSIpcpwO3hommbWYFZFGXuPJSCICtq9toao8c6DMbT7bKY4pyjg2V2TCHga/eL6jpSSpIKmKYSTJfAsDZedN1MMBUEBaql3DE0h6LVhLJpHujZTr1iRMBkrYsOKtobGJ0GPDZctnx6DUKpK2HcsCZalwTI0fC4rhgaYhponr9OClb1eBDx6imW1dh1RlL5hY8xlc9o4RNP6ZoFaGy+x0Jl9RFDNQKsNZvy3Xx5CqSpjoMuNz7z36qbCPML5B01T+MA969HmteNfnjqA4eNJHB7LoL/TTT4/AuECgmVZPPzww3jooYegKAruvfderFy5Eo8//jgA4L777sOvf/1rPP7442AYBlarFY8++igoipr1sYulVHMwVU1PNTs6nkG734aRcA6pfBVtPhsyBcGsEeEY2iycV1RN77BV1+EqnCyhKsq6k17DSAfSan+38iyqogwLz2Cw2wOnnUcyV0UyV4WFY2C36bVHRivgiXgBa/r9YFm64Ut/Zuc2WVHRE3Dh+dFJ9IZc8Coa4ukyMnkBLKt7p8cns02zamZy5VA7Do6koEHfYWZoqiGtz2HlEE6WUK7K6A+5UK7KUGst3SlQKFVEc1ivICk1B1x3zHvanWZ9FaC3VbbXnFKfy2p2q1M1fViy3cY1zUcSZziWoqziyFgGXqfFnBtV38BBEBXkiiKcNh5TiSKyeQGyokey1tQ59JmC3sZ5WZcHiqqZjQIMJFk1hXMiU4HfXYYoKqZjqKgaxmp1GBp0R7Fclc2hvdGU3tUsU6iCgp62pKi60DTWN+ixwWZhsbzbg3CyCLEmWP1uK3wuC57dNQGnnYfTxsFp45o2fyVZaekY1g80tnAMuttdZiRwZqMtlqFh4fS6GLuVRTihRw84lkF3mxP7TiQRSZawqs+HREZPCzQiF+Va3RWgRyrra/eCXpveXa92zvpcjSmX9Y1gUvkqChUJK3r0midBUmBvMTw2mipDlBQs62787u/w26HWBG5fh8uMYqRqneskRcXxiQz2HE2YLb85lkJ/yAWWoU3hDeiCoiLIZufnelRNb56wZsCPl4fD6O1wIZwoQlFVs/7Q4+DBsUzL1Dq7lUMsXYbTxiFVu4+0mgdWTyRZwvZ9YbT7HCiURX0wrqJhMl4Ey9ANNZmD3R6omj73zrhPuR0cJFlFtNaxb6ImMtb0+8zPrizIZnYfQ9OIZ8pNgurYRBYVQcaVa9qRzOhjDdb0+1CsSHDaWRTKop6+SU1H1VRV3yAyIsvRVAmirMJqYRBJFnVBRemRT0XVN1WMxjySpEICYGem045b1Y2pqgZBUvDinik47Ty8Lgt8bivsVlYfPwH9nmGIz/pB7TOj560ggqqOaLKEz/zDS8gWqgh6bfjsg9fg2rUhEt24gKAoCu940wr0hVz42r/vQlfQsaDcVwKBcH6xefNmbN68ueF39913n/nv97znPXjPe96z4McuhkJZgqpxtbQhCteu68S23ZOYiBVMB7Qi6C2N8yURPMfAxjPIlUR4nRbQVM3hTJYaHLDt+6LoaXfqkRnoO+99IRfGa53qjGYAVp6BomroaXMiFLBDEBVkCgJeOxTH0IAfoYADdhuLQ6NpfXdfA7S6r6mOgB1tdeliyVzFTFeMJEqQFBUrej1wWHnkSgIKQqPz0R9yNbUSNwrdG1y/GV+NLEMhV9IFi93KwcKzECUFNAWz42CmUEWhJKKrzYmBTjcsHIPjk1m9JoulsazLg5FIHqKkoL3W8KlUnZ7HY7ewSOWrKJYltPls5i6yzcKCAoXOoKNhN3vfiaQpyDr8Dsg10aVpGjI1wSPK+homc1VUJb2RRSJbgbPWcKBQFmFk/Bl1Sj3tTrMhgt3CoiopqIoy2nw29LS7MBbJ12qrZDA0BVHSG5Z0BOwYjxYQTpagqhqqomy2oR7odCNbEHBsIoPBbk/DgFyvy4LJeKF2frCgnBSyRT1lyWbRox6qCnNHXZQV8Oy06CuUJZQFGcHaPK54powjY41RHK32+bgdPDr89qaGW4ZzCcCsXdPb/Kv6XC2vDV6XxRRkFKWL7EOjaQQ8Vizv9qBclTEWzZvt2A38bqvema2FI+yy85BkxbyWeJbGRKyAQlnCaCSPy5Y1D22WFL2THgCzy2N9Wi0wnRLmtHFmiuDJqZx5Llh4FkMDfoxG8piq1QRRFIWuNgcOjaZRqsooRfKYShQx0OlGuaqnS9I0hXxJgCgpZpQ3nCgiV9KbMdgsLDIFAVVRQa7mvBubJCG/HbmSCJuFhVCL/AHTacZzkSkISOUEtPv01FZZ0SBKCtp8NoiSimxRMNMDK4KMUkVCriTCXtvE2HkwjstXz10ukazVzVUE2UwPNZ4vk6+iM6iPMphKFDEeLZjr3RlwmJGgoQE/FEUDQ08LKpal4XdbUazo4x0kRa11N6QaPqs2nw2CoHehlBW9zb7dqqcmGkIoli4hkiw32J0rCjgxlYMoKSgLMlL5KjiWAcfS2LgiiLZaHdloXffUxQ5ZJ23Ta+w7nsRn//ElpPNV3P6GfnzrU1tw3bpOIqYuUK4a6sBff/RmSIqKjz36HL76bzvx9KtjS20WgUC4QLDyLBRF7/y2Y79ejB5NlVGuyujr0GcftftsqAiy3iq79mWeLQqgKAr5koiKIJv5/J1BB/pCTqzq8+H4ZA4sQ+t1BprerCDotaHDr9fsuB08xqOFmshgGqIImqbhwMlUQ9thltWfJ1cUkMxVIMta4056nfKx1aI+xYqEoWV+0PR0QbaxU27UsdQzGS/i6Z3j5s8dfjug6c6t28Ej6LXpKY6155qMF3F0PIPRSL4hJSmdq6JUlRFOFDFaE06TtZoUUVZBUXoXL6eNM6NSelMFDdFkGaqmRwOtPAOWpnQnX5tOM6rfmbZweqQvni4jVxQxGsnjlVpbdqku5ao6I8rw2qEYktkKErUW+BVBbmguYLw/g4qo/70/5IbPacGyThc4lkahLJqvs6zLDUFSkK8JEVHU/53MVjHQ6cayLnfNSdWFQzJbaYgoVUUZiqLhxGQWsXS5QXhkCgIGutzme88UBHMYaa6k11PRFGVGYQA9pS2abnQ6q4Jsduc7NpHF9n2NaWwzzwkLx4ChKbAMZUYAjffndVnQFXSaaXUOK2c2DAh6bGZzCmB6JlKpKmEiVkAkVcKh0bT5mVAAnDYeAY8VLEOj3W83G3Romj5MeiYWjkGb147JWAFT8WJT9NLA7eDNzREDntPnT0VSJYzHCuZQ6EOjaQii3NBoxuPk0e6zQ5RUTCWKkBUVpap+vkZSJbMZhnF/MIQM0NjUJpYqgar93RAnNst03eZErKA/9xwzv4yIDcfRiGcqer1drU5L0zSkc1UM17p/hpMl0yYjlZWiYK4rAHQFHQ3RKcN+Q+hzLG0KPT11V484e5wWeJwWU5C4HbxZB2lgvI7dqgsyRdGQL+lty42zTJAUnJjKQZIVDA340VVr5GGzshAl2Uy9ZGgKNEOZ6XuZvIDOumHM49E8LLx+ruqdSvW29qKkz1AbixbMcRfL6yKaM1uuz8clH6EqVUR8/tvbcWwii02r2vCXH7mRzJO6SOjtcOHRP74Zj/7HbrywJ4yqqGDLVX0thzgSCARCPYbzWN8WeHm3G3uOJjEeK2B1n2/WDTdjDhHPMaZTHE2WdPFitmBX9aYEM2obVvV6Iasa4hm9I1gy1zgDR5T1hgTj0Txcdg4sTUFV9eej6Fq0oFxGRZDNeiCjXsXCM3DZeeRLIrKF2owrStObTPjtpoMdS5dRqkhNdRccM127E6ul/ImyCkXVjw16rKa9M+c59XW4kC+L8LutCCeKsNZ24AGYM4w4lgZFURAlvfW4UfzvdVqQLQqoiLozJ9fqqIwOdaW6hguyopqpi0YB+rJuDxRVhSSrWLs8AFlRwbMMOgOOWiSKh9PG42Q4h2JZMnfVO+qcMsMBtHAM7BYWfo8VxbIeSWBofV2MtD6K0mfpUNAF786DMRysOf3Zoj6w1Oe2QtWqZvdCDYCmTUekEtkKAh4r3HYe+Vr6Fs3oDT5EeXpt7VYWVUHBa4fiYFla7xzIM2aEI5PXa5uStRlWoqSA5xj0d7qh1mpnWIbS/98iJdB4nCApsFn0iM2uQzEE3PosJ5aloShaLdoimKLcaePMzxNA07lst7FmO2qnnUM6X8VkrNjg0BtiYubMr0pVj/rJiu58G+earKg4MZVDwKPXSbntuiNvpGuVqpKZ5mfhGHhdFlNIeV0WZAuC3llS0yBJClx2vYvkyalcTeBLULXpqIrdwqKr1uK7XJXRGdCbzEwliuaGRm+7LjiM2qF8SWxqfEBTFARJhYZp4UXRFBRFhddpMQVMOFFEqSpjsBbpM7JvjHvMqj4f8iURw8emRyZ0Bh16MxSGhiApiKfLGOhyw23nwbE0bFbW3BxQVA0vD4fN95cviShVJHS1ORFOFEHTFFx1acFVUcFIOIeBTjcACgyti5rRSB6pWot84/0Z17B3RgfNclWCy85B1TQzquqycw2bSLrgqSBbENDusyPgsWJ1vw+u2nVarEg4OpHFih4vsgUBPEvD67KYIu7kVA7XruvEqj4fJFmFy87pa8Ix4Fm6oZ6tvs2612U1G3UshEtaUIUTRXz5X17FeKyAW67qxR+/+3ISkbrIcNp5fO591+K/nzuOf/3FQTzyvR14/9Z16AvNHz4nEAiXJtFkCU6vHc4Ze2t7jk47KuXarraFY/Q6jlo3P2C6FbWqaWZsSIPeeOKJ+HHzOTwuS21He9qRPjqRRWdtgG59FMRgMlbAil4fjk1kIMkqCuWs+TeeY+CwsuZrGsX3RnqVICrI1rqZpXNVVAQZfSEXIqlSQ51Kriji+GS2Lq1L7+o22y6/sRNd7zCv6PHWnN6aAKztJhupfBQoVEU9pakr6ESxIumDduNFVAW5IYJk4RkzZYirFZ7zHI1cUTTFVD2FOiFoNAzpbnNiKlHE5st7cHwyi2MTGWQKNtP+sbrdaJ/LglCdmHLYuIYZQUaUbyJeRIffDp5jzI6BgD4nqs1vg93GoVSREM+UTafNSPdiaAptPjsAqyngBjrdCHps+ntkaRTKkikmqoKCbEFvtR5wW826mnKdXT6XBfFMBQ4rC5edx5Fa6h2g12AlcxWMRfNY2euDoqjI5IWGdTYGUBtDbkVJr1PpaXdhMlbQxbymARSQLlSRylfN89TvtprnCwCzbsft4Gsd4Wh0BR3TIrgiwVGLThj/l1V9UK6VZyDXampaEcuUzciXIiu4stau/bVDMYiSYtYE5csi2mqzqhiaapgnJEhKg9Nu41lkIWAiVoDfYzWPDXptplM9NOBv2CgoCzIOjaYRCtjNuiMj/cx4nxaehiDpdXmFcdE8B0RJn9U2GS+as5GMv1UEGS47h2JZAkNPR7GM+4TRnQ6YboxhYMw6A/SNiFiqBIrShzAbUdapRBGhWmpsriiajTp8LgtoijJtMcRtZ1AzhV79zC1AF1XHJrKgacpMMTVEarq2vjRNIeCxmh0oFVVDu88GWdHM1Mc2nx2dQQeyBaFB2He3OcGxtHl/YhkKh0bTyJUEOK0cMGModcBtRVWSG1I7q6KCbbsnEM9UEHBbUShLtRlwLCwcg4DXini6DA1oaDBktyxOIl2yKX///dxx/PGjz0ED8M1Pvgkfu+8KIqYuUmiawr1bVuIv/vcNODyaxh9+7VkzhYdAIBBmUqxKqAgy4ukS1i7zI5Ismd3xAL3GyXBOjCiLIaZcdt4UNF6nxewaZlCfNMWzjBkFcdbVesYzZVNM1aeuAEAo6ABFNXb2Mpo32C0sWJZGZ5v+GMOxKVUlRFMlaJh2yrranFjd50OuKDaIKYNCSY+K6M0RtKZIGqALkZmDMwE9RYtj9SYdqVpTDYNyVcZ4tICxqD5wNlMQcDKcQzxTi4rVpckZg2Nj6bK52zwaySOZ1dOZQkG7uT4WnkFPu7NpjQ0MR3N7bZaQ3cqZTqmRWmiQKQg4NJo204BKFQk0rUdCBFFBKlfVZ/3QFFy14alGwwCv0wKapmDj2ZaCYLo5hp5ed2IyC56lYbewEEQFyVwFkVQJNp5BuM45zpdEMLTu7Kby1abnBYB4rYFFMldFNFVCd11XOKNGKOi1QZQU7DocbxBTgF60b4gpY56WMXPNqGd7/WgcoqSYTU8oSk8oTeer6A+5GhpK8CyNYtmYE0bDWotw8bXIVSxdxlg0j0ptrECH3w6HjQPD0Agniub5a7OwcDt4MzWtvgnC8akcjtfq+wa6PHDYOLPxCctQsFpYZItVs5lIPWJdyp1xfhUrEniWMaM/Vn76+q0KMqw82xTJy+QFsxviialcw2yvoxNZHBpNm3VlgF7PJkhKyw2TYO29RVNlFCvTUT2HlTPrrOo7TJYFGVPxIhRVaxARFKbTjwVJgSgp4DgGfo8ViqrpqZCJIgpl0bwOMgUBNN04sNlom24Ms5ZktaF5TWfQYTaJKFUlHK7N1NJnmOknSTpfNc8r/f2LZkqi8ZwvDU9h79EEYumymZqqR8CVhno7Y/MmnCjh6EQWkqQPxfY4eT311GVpugGMRvIYjRT0ay5b0UcN5KqYjBdwfDKLZKbS8p4xEV/YQF+DS05QaZqG//ebw/jnnx2Ax2nBX3/05ll7+xMuLtYPBvGNT7wRXe1OfOWxV/HUiydbDs4kEAiXNkYHN0FS8fTOCWSLAkq1tsIcS8PrtIDnmKb0FaAx1S1fmm6b3jbDmTOONRwNYzd4oNNt1hX43dam2oPxaMGsyzBqWMpVGXYLC5qmUCiJyNaaLayuDbGlKaphNx5ArRW41LIbFgCMRPI4MZXDsfFMQ2e8mSiqBq/T0jA3SINeb3JyKodsUZi3e2A9ThuH/pALXTXh2IpSVYIg6nNrjPXZczTR0kHt7Wh08jXoM3HqI04cSzd1lgN0R9lIezS6pdXbpKgaOJZGvaZkGQouB9fUuc1oo23Ya7dySOYqEGUVgz3ehigDoDviRtML43HqIorkcyWxIVphnF/RVHnWNKZ6YW0cY+EZfehybVDXWKSAaKoMCnodnYVjMNDlBk1RSOeFhvOsp90JS02QpHO6U20Mwg16rMgVBZSrMkYjeZSrMo7VxMeh0XRDDaDTzqFQEiErKvxua4OIVxTNjA51+O21mUL632RFw0SsgJNTeTA01RRxoGc5wURJQU9NjE7Gi+a5MRLJYyySNxubUNA79fEc05BqWs9iXYyJFucwoJ/zRsdHY/PG67KAovRIXKkiweeywGHl0B9ymwJBlBQEPTZ9dlRF0s8JTTOfA0BDCqIgNkaHO/zTQ6J5lkY6XzWvCWPjpK9Fw4z60gqGpmZt8NDT7gTP0lBVPZJEU5Rpj6Lqw8vHakN6jVTWvpALDK2nGPKcHr3WZ3rpgrZUlc3rzcDvtiLotZkbURxLm5/NWF3ksn4Dy/g7Q+spvELdmrXikkr5E0QZf/fDPXh+zxR+/5ZVeNetq8wcXcKlQcjvwLc++Sb82y8P4R//ex92H0ngUw9c2dBOlEAgXNoIkgJjD9wo/jecDElWEU2XYeHZlh3JgOkNUq6unXmi5qDSNDWdrqQ0OxnRVAlOG4cCYO7gzmWnQUWQ4Xby4FmLWQtlpHx1Bhymrca/swWhYfDlbAQ8toYd91YYz13fOt7AbmWhqhrsVhblqmzu+Nc7zCyj1zGE/HZ4nBYcncg0OKLGHKp6+Fqq5XxMxApw1ETaWLSAVX0+HDiRAsvStdQmFe0+e0O6moGqaXDZG7vEzqwr05thTNtmRBRmOpD1aZ36z7rA6fDbUax1EZy5dqGAvaF+aD7f3MozsPIsnHYOVp41Izf1OG1cy2ijbnNzSme2IKBYlpo2D9r99lrkjjKjczPr5jJFwfwc6x14o8Phsi6POYttJi47h0JZQipXbWjNP/PYdL6KDr8dh0fT8Ln19EnnjM6+RrrlzPO9XvQa16WttjExEs6ZaaaZggC7lYXTxiNTGyIN6GJz5lrWp0wC+udb3zmuFUZ91kIx0oyrggyaoqBomt4cJlDrPhjVn8uYVxZJlRCq69hYqtV7WXgGVp7B4bHp6NnM9T00yzwvAAClb/AEPTbz2udYuukxdisLhmlM2zMin0akl6Jgph12Bp2IJKcbiTisrPnZVUUZ5YoMm4VFsSLVoqX65lB73flrs3LmNWflGbOmLui1IZbWZ/s5aiMdWJoy75mtRgsoqoaRcB65TGuxa3DJRKiqgowP/dWzeH7PFD51/5V44K1DRExdojAMjffcMYR2nx27j8Twqb97Yd75DgQC4dKEZ2lwDN3kcI8toANUpiA0dA8D0BBlSOYqaPc1Rq6qotLUiGIhaNCjD+l8tWkuTH2UK5IqmS2P56PDb0ebzwa3fWERppmCoCvoQNBrMyMRgP7+FEVDu88OT21HX6k9Lpou48h4xoyGmM/bonZLkJQFR75KFcl05nYdjCFfFhtakpcFqeFnAGj32dAfckFWtIbXmen4pnJVMzWwnnSu2pA6BcAcggygYSDxRLyIqUQRHidv1qj0dbhMEb5QFEVDtig0zMWayWx1cIA+d6q/Vl9cH83hOdpsTmEQS5fNFtezkchUGqJA9ZEQww69G6AeFfA6LegMOLC8y2P6Z6KkNKTdtXxPkoJYumwO860/fmaa32wY12VFkKGqmilEetunm04EaoO9p537ZkFfnXEeGWmbnjnO1fpzykixm6sAxdhIqIqKKdwFSWkS+8Ya2y26oKkXVUaL8MNjGbOGDYA54Lee+rqp+vPC0KPJXMW89u1WtmkTolCWYK3zt2VFa/C/FVXvDtjht9eazUyLqeW1NM568mWxlppJYySSN8WQpukDwZ02riEKa3xOxuaE3cqiWNFTHZPZSkO5z1ybTAPzZLNdEoKqXJXwZ9/ZjlJZxIfevh43X9Gz1CYRlhiWofGNT7wR3/jEG6GoGj729eew82B0/gcSCIRLilDA0SQUOvz2BifkdGBbDCWdC4am5hQSoqzC67K0TEesx++xzumo0hSFbEFAriiY9TNz0cqmcLKE8WihIToB6MIrnimbu/szIy+G4z1fWfNiPgPjtRLZSlPNmNoiUhivpRodn8w2Oar11KeND3S69Z1/Tp8jVh/VdNn1NuFGWqLfbQVNUQ1RnViqbAqtSLLUFPGZD+P1YulyQ81OPRQwa1OmI+MZM/2p/jOTZbVJpM+EZ2ms6PE2CYH6CJtct865ooCRcA4n62qO3A4eDEPVusTpmwrG8NmZbevrOTGVQyxVRqEsYkWPtyE6uJgubQaR5HT9WX0K3smpXMN7aMXMaK4hDGaLCtbDszTyJf3cXGwxwswUTwO9K6Ra67I4vRb1a9SqsYtBf8gNrvbZAvp5UZ9yOTAjVTVXFFuKspkt+sUW0eVYuozxWKFhA+VkONcQia5v/T9zc+DkVA6pXGXOaF8srY++qBfDxrwyYPY0UEBvhjIXF72g2nssgQf//DcYj+bx5Y/ciDtvXL7UJhHOE5w2Dn0dbnzw7euhqBq++L1X8B+/PryoPHUCgXBxU79jaez6J7IVsxX5XMy3s+5x8vOm081EUbU5HXxAn0eTLQroC+nzslo5o9FUGUydmJu5g16s6IXz4WSpZerYTPIlER7nwmulZsOI4ADz15/MrC+bi7lEqNPOm1GSxVLvvI1G8oikSk2piOWKDKnOaaMogKamU84MH67el5MUddFieyEIktLQ7W4hiLIKQVRa1pnVH3N8MrtgIaCoWlNa5HisYHa9M8iXREiyOmdkDdC7Dlo4BuOxwoJGo1DArJFXSVEhyc2RMUFS5owcnS6irM4r2Opp89rMjRO9ayLbNIxZqA3WzhSEls8918aLzcJiLJpHviQ23APqP7fRSL7lcyz03GWZ6Sl5MyNbBslsxTz3Zm5u1Uc9HVbWvB5bbbbM7FBoUH8/ne0YAE1R7Jlc1IIqVxTwjz8ZhiSp+Pz7rzMVNoFQz2C3B3devwzvfesQfvj0UXzxezvMzkQEAoFgYGy2qKrWlMrXilYpQfW0qts5ExiO03i0oA8ensUZre9Ct5Ad9Pk41ffTH3Kh3WeDz2WBLKvzrtupMFc0S1bUJmHbqonIqSIpSsN70rTpWqvOgMOs4Z25sz+fiJhJcJ4o0ulQrHVkPJ8ZixYgSkpDG+3Z0NA836qeeKbSJOjX9PvMJhuz4XVZzKY2Z5tEttJQx+m08y1TjOc6j2arAwXmFxBzPYc8Q/jMtqFRL/KM839mlCjosbU89xiaahBz9XWK9RsYxmu3ej8eJ9+wmbSQVOjZuGgr8Xfsj+AHvz6MclXCNz7xRnOaM4EwE6edx4Nb19b+zeH7Pz+IT3zjeXz+/deip52cNwTCpYzPZUGxLDXtjF7sWHnGFAFzdek6E4wtMmJyKswVzWqVKrXY+qW5mCvqMJddi82WOJXauzNN/Ty2Vnic/JzC2xgAa9DmtaFUlRrmbc2G4Ycbs5xOF0HSo3KGMz+VKM0r9luNIDhXzLbJ47DpA8BPZ9PEaBJyqsyZNjvj55kdMueaf1d/zgc9NnhdFiTq0olnvvbMBiAzz8XTuc9dlBGqRKaMv/yXnYgmS/iLD91AxBRhwUzEinobT47GJ7/xPHYfji+1SQQCYQlR62phDOrn+5yPzGyGMBtzNWaqdxw989RjGQNcCTrz1a8tNd45UvdO63mdljnFFDB/FHNmtCORrSxITAG6Qw0sPLKyEOojI4utaTtfKFWk045AzyamGJpqSLs7G4iSMu9rcCyNTKGqDyQvibPWQi2mm+JiuegiVJKs4O/+cw8sHI0vf5iIKcLieP9d61AVZVAUhb987FV84Tvb8b671uHum5eTwc8EwiVIK0ekVUTjfMIQgDRFNe321tOqMLwV87VvlxUV+ZLYENW6lJkrjWox1LfYP5OcrSjKmXrfp8pCaqcIZ5azGbk2kJX5a8tmdgK18sy84t7AGOlwulxUEaod+yP40FeewcGRFB75wPVY0etbapMIFxg0TcFu5WDhGCSzVQz2ePG9J/fj7364pyEnl0AgEM5XDLdyLjF1NjgdMeVaYGv2c8WyzrlbJJ8p5mr0sBQNki5kUXK2NzoC7vlr1OzWhccpWkVRLtzVP3ucynUwm5hqtb5nQkwBF1mE6jc7xpDIVPBn/+s6DC3zL7U5hAsYmqbwqfdcCaeNx+GxNL7++G5MJYr4zP+8Gj7X2Sv8JRAIhNPlTLvh9XUkZ4tTSadqNfD3TDEyzzDWM8VSNHqgMPs5Qrrczk5qnkgtsDjnvNWGB32W6xXPNEGv7ZRa0y+GxTZnmYuzubIXRYSqVJHw6x2j2Hkoho/83iZcuaZjqU0iXAQs6/KgzWfDdes64XFaMBbJ4+N/+3zDFHQCgUC42Dlfu7udLTF1sXPhuOuXHudaTM032mE+zraYMmAugMjpBS+oREnBH37tWXzrx3txz+ZB3H5d/1KbRLjI4FgaH3z7evz5B9+AgMeKT/3f5/H87smlNotAIBAIBMI54ly1Qz+XXCg1jxdC1O6CF1TJbAWFsoR1y4P4n29bu9TmEC5SrlvXiVX9fvz5B68Hy9D42g9ewz//7ACUS6yVMoFAIBAIlyIzBzYTLjwctvkHsp8qF3QN1YGTKfzf/9yDUMCOz73vmgsiJEi4sLFZWHzuwWuw/2QK//n0URwaSeFP/+BqBM/gEEgCgUAgEAiXFn63dd6OmoTTo0TapjdzZCyN/+9bL8JhY/GNj78J9jmmoBMIZ5L1K9qwfkUbNqwI4rP/8DI++JVn8PD7r8XGlW1LbRqBcNHw/PPP40tf+hJUVcXv/d7v4QMf+EDD35988kl85zvfAQA4HA584QtfwJo1awAAW7ZsgcPhAE3TYBgGP/nJT865/QQCgbAYiJi6sLlgBdXvXpsETVP4/PuuRYffvtTmEC5B1i4P4i8/cgP+9amD+Py3X8abr+7F/7h9iESrCITTRFEUfPGLX8T3v/99dHR04J3vfCe2bNmCFStWmMf09PTg3//93+HxeLBt2zZ8/vOfx49+9CPz74899hj8ftLtlUAgEAhnnwtOUOVLIv71qYP49Stj+JP7rsDa5cGlNolwCTM0EMCXP3wjfvbiSXz3if14aTiCv/zwjVje7Vlq0wiEC5bh4WH09/ejt7cXAHDnnXfimWeeaRBUV1xxhfnvTZs2IRqNLuo18vk88vnG1tiLfQ4CgUAgEIALUFD96y90MXXP5kFsuap3qc0hEEBRFO66aRDLuzz4+/8axp/87TZsvrwHd920jAyXJhBOgVgshlAoZP7c0dGB4eHhWY//8Y9/jJtvvrnhd+9///tBURTe9a534V3velfTYx577DF885vfPHNGEwgEAuGS5YISVBOxAl54fRJXrmnHg6SjH+E8Y91gEP/3E2/Ez14cwfd/fgAv7p3Cp95zJa5b1wmqxUR0AoHQGq3FwMvZrqEdO3bgxz/+Mf7jP/7D/N3jjz+Ojo4OpFIpPPjgg1i+fDmuvvrqhse9973vxdvf/vaG30WjUdx///1n4B0QCAQC4VLighFUv3h5BP/vN0cQCjrx//3B1aBJRz/CeQjD0Lhn8yCuuawD3/7vYXz5X3ZisNuDe7esxE2bupfaPALhgiAUCjWk38ViMbS3tzcdd/jwYXzuc5/Dd77zHfh809Hgjg59uHsgEMCtt96K4eHhJkHldrvhdrvP0jsgEAgEwqXEBTGHSpQU/MevD6NclfH5910Lq+WC0YGES5SuNice+cD1+PL/vgGxdBlf/bdd+Nq/70IsXV5q0wiE857169djdHQUExMTEEURTz31FLZs2dJwTDgcxh/90R/hq1/9KpYtW2b+vlwuo1gsmv9+6aWXsHLlynNqP4FAIBAuLc57ZSLLKr7++G5UBRlf/vCNpIMa4YJi/Yog/uXh2/HbV8fwk+eO44N/+TS2XNWL921dC6edX2rzCITzEpZl8fDDD+Ohhx6Coii49957sXLlSjz++OMAgPvuuw/f+ta3kM1m8cgjjwCA2R49lUrhIx/5CAC9W+Db3va2pvoqAoFAIBDOJOe1oMoWqvijv34OuaKAhx+6Dqv6SIE/4cLDwjN4243Lceu1/fjE327DM7smsH1fBL93yyq87cZl4DlmqU0kEM47Nm/ejM2bNzf87r777jP//aUvfQlf+tKXmh7X29uLJ5988qzbRyAQCASCwXktqH72wklkiwIeeOsQrhrqWGpzCITTwsIxePRjmzGVKOLpneP4118cwE+fP4733nkZNl/RC4bUBRIIBAKBQCBccJyXNVSxVAn/8JO9+M9njuGhu9fh929ZtdQmEQhnBJ5jsKzLg/9193psXNkGRQW+/vjr+Nijz+G1w7GW3c0IBAKBQCAQCOcv512ESpJVfO7bLyOaKuN9Wy/D3TcPLrVJBMJZ4TPvvQb5soh8ScQ//tcwvvCdHdiwIogH37YWK3q9S20egUAgEAgEAmEBnDeCqirIODyexg9/exTJbAUfvncj7rh+YKnNIhDOGlYLC6uFRbvPjs6gA2VBRqEk4k/+dhtu3tSN99wxhM6gY6nNJBAIhEsOjqEhKepSm0EgEC4QllRQCZICCnpb9M/948s4Gc4h6LXhKx+5Eav7/UtpGoFwTvnjd1+OXFGAz2XFj549iiefP4mXhqdwx/XL8O5bV8PjtCy1iQQCgXDRQQFolWhNxBSBQFgMSyaoDo6k8KfffBG97U5EUiXQNIU73jCAB9+2lsyZIlxysAyNgEcfCSDLGoJeG965ZQV+9MwxPLNzAnfdvBx33rAMPpd1iS0lEAiEiwe/x4pUrnpOX9PCMRAk5Zy+JoFAOLssmXKJpkroDNrR4bfjrpsHcf2GLrgdZC4PgXD/W9bgns2DcNg4rOrz45s/2oMnnz+B/3r2ON50ZQ/eev0yDPZ4QFGkKyCBQCCcDudaTAEgYopAuAhZMkG15ao+bLmqb6lenkA4r3HYOACAqmrobnPia390E57ZNYGfPHccv311HP0hF7Zc1YfrN3QiFCB1VgTCxY7DyqJUlZfaDAKBQCC0gOTWEQjnMetXBLF+RRAAcPVlHfjek/vx3juHMB4t4D9+cxjf//kB9Ha4cNVQB9YNBjA04IfLTiK9BMLFBhFTc0PTFFR18WMnutucmEoUz4JFs7PUDS9sFhYV4eyfT7PVpxEIC4GhKSincE0vFURQEQgXCJ0BBx5+/3XYsCIInmPA/PB1VKoSXA4LXhoO47+fOw4A6A+5sGbAj6EBP9YM+NEVdJD0QAKBAOD0nRQrz6Aqnn8pa6cipgAgVxRO+7UdVhYMTSNfFhd0fCsx5XbwyJeaH98fcmMsmj9tG+vp63Ahli4ju8j3vliBdOG4wueGrjYHwonSUptxxlnseTHQ6cZoZP5z+kISUwARVATCBQNFUbhqqMP8eU2/D3YLh5su78ZIOIe/+cFreMsbBjARK+DQaBq/fWUMqga47DzWDPiwpt+PNQM+rOz1wUYavxAIZ4zFiAyOodHd7mxyKNp8NiQylbNhXgPzOSmBeZo0LIWY8jh55IoLEyuLpViRWv6eY2lI8sKiSKcbPezw25EptBY3Z1pMAcCR8cysf3PYOJRmWZMLy72dn8EeDzJ5AcWyCLH2WZ/NqFr9tqbdwqJ8DqKE54LFrtfMe9/ZbNLS1+HCeKxwVp57JsSrIhAuUG6/bsD8N0NTGFoWwFveMACWofHId3dgaFkAN2zoxMGTaRwYSeGJbcdR+KUEmqYw0OnGmn6fGcXq8NtJFItAmIGRDkYB4DgG4ixf+gsVGTzHgAKQzjcLlmx+7mhB0GNF8hw0UFiKJg2zYQhVt2N+QWXlGdAUtWgntTPgQCRVQshvRzRdNn+/UDF1Ksx0IGPp8oI3uc52uuBsYupUORsRtplYeAbCjGvQZeehatqc76dckZHOV8HQFEIBO6KpcpM4YBka8hlcbwp6hCaVrwKnGBzt7XBh4hyJhHPBbGLK77ZClJSWmx4L/VxONcrltHENrxvwWJGbfR9Ct+mUXolAIJxX9IXc+Mg7N5o/v/maPtgtLDasaANNUfiP3xzGP/zpFgAUXto7hYl4EQdH0vjl9lFoGuB1Wswo1tAyP1b1+cAy9NK9IQJhiaEowGXXm8NoQJOYOpXUN+M5WjkQcznJHgd/SmKKgu581e/Q8ixt7sYDQJvXhkR24ZGxlb1eHJvIzvp3hqZg4ZgzsvturC9Dz38vmk1MzRdxoGl9I8kQUxQFaAv0wUIBuznKQpAUnJzKLehxrRzBDr+9ZRpUV9CBcHI6TexMiKn+kAtj0XPjkJ9pMWW3sOA42hTYve1O8DyDE5ONa+9x8ogk506vi6RK8LksyBQERFPlhr/ZLCw8Tr7p96dKZ1BvHqUBGGnxOden4s4VsfG7rTiVrU+fywJNQ8s0z9lez2XnUVhgGisAhPx2xNLNotTA2AyYKwpqEPRYkS2Kpy1mW9VHzrwHtmKmiFtISjERVATCRcgNG7rMf/d3uvHJ+69EV9AJiqKw61AcHX47/u8n34RktoyfvzgCmqZwYiqHHz17DKWKBCvPYO3yADasaMOGlUEs6/KAoUkEi3DpMJ9TXS+mhgb8KFWkBaeWtOrY19vhQqUqwWZhMRFvdAJyLWprFoIGNNmkqFrD7q7hYNE0BU3VwNWcjd52Z5Mdg90esAyNnnYnJuOtGzkoqnZGU5mCHhuuXRuat+ai1Wt6nZZ564SSM8TkQsUUAGTyArxOCyiKaohodbc5UKrKyM6SxhcKOJocPXqWDIF6e5w2DqKktHQG50sZrXeaZ0Zz6j/PudZsLqe8HivPwGZhzTTG+iYYrSJsC22SYV43dS8/ES9iaMDfdOzM87OVsG732RHwWKFqWkMElKKAiiDPa5OFY9BZE7yzRa8NOJaGMoc4qI+kzJX+ls5XW0a452O2lFIDvhaBpwC4aym2HmejoOqoCaaZWDgGoYADDENhebcHJ1psLDhsHEJ+OybjRbT7bBipCZbuNidommqIuLEMhWSuCp5jgNpS2CwsaIpCqSqZIng+GJoCTVNN0eb5xFSrdMyFbOoQQUUgXOS47DxuvrzH/PmzD15jOoPRVBk/ee44vvfZ29Dms+HZXRMolEVQAIaPJ/HDp4/g+z8/AKeNw/oVQWyo/dfb4SIpgoSLnnJN9MxXV1SqTospv9va5PDUp484rCzcDgu0uucHdEczIypzRqJYhoKsNHv8i2k0QVFUw66v4WwYO7CDPV4cHk1jIl6EzcLCyjNNzouzNtZhLuay6eqhDuRKIo6OZzA04EdVlDESbhRMAbcVDEOD5xaX4mY4hk4bt6CmC1ZeFxr19lp5Bm1eG6K1VLxWzSIA3fFVVQ0MM+0Q8iwNt8MCt8Myq6CqF3HdbU6IkoJ0Yfpz97r0x7IMbTrXThsHt4MHxzINUR9DAM1Xf0fTlHke+txW5MsiqqJuvyE+7Ba2Yc04ltbTXVkaAGWeB0GvDel8dc5d+1ZiCgA8TguSuUZb5xMuQwN+HBpNo1SV4XHyqApKg+jobnMilasinpl29mmKAsfRpnh01N67w8qhVJUQ9NgQ8FhxfDKLoNcGTQPyJXFR0TtBUpArChAlBV1BB1iGNu8DLjsHC89Of9a1peI5BgG3FYqqNdg7G6GAHQxNNwhwI03VoL/ThaqooFASzXtKh98OCmhIY20FQ1OQFNX8LC08A1HSr7epGaK0lZgCdDE4XySyVJEahJaxYZPJV9Hf6YbHwZsbR8Y9TlWnr/v6c0TTFtadU1G1lpsX81EWZLNJjMPKmWNs5oPk9BAIlxgepwUdfjsAYN1gEI//+VvR5rMBAPYeSyCaKuGumwfxoXdsQF+HC59+4Cq8400rkC8J+OefHcBHvvY7/MEjv8bX/n0Xfr1jDNFUCdpitnUJhAsAnmNgt+p7jjYLi9V9PrjtPPpDLgDTqWIAMF7ngBliqis4PR/OyrPm70pVGclcxdzRNiK/J8M5SLIKu4U1h9x7HDy4Wuqty86ZjoaFY9Dus6GvZstCxdTQgN+0vx67lUXAY8VApxuA4UDrmzGtRAFFUWZKMF871uuymH/nGNoUXTa+ed9WlNWGiLeV19OrAJjvKZ2voirKmIwXsftwvOX7cdo4+NwW+FwWdAYcoKjptMrZmk20efV7ncOq2xf02rCsy22+d0CPPk7Ei5BkdVYxpQsn3jwPBjrd6Otw6bvqM4/laPjdVjhq55PxmJ52JwC902D9PdRY86uGOkxnrliRoKoaFLVRXBr37pkYr+GrfS6aps807Aw4MNDlRsBjNdfCwus2zxSukqyC4xiUqjKqomw+r6ZpDWKKZaiGNDTjs7dwDAIeq/l7/ZjGc7XNZ8PyLo/5s8+lfz+t7PUC0FPleI4xz7euoBNB7/R77gvpHQvjmbL5vQboUcK7Nw+atWnG+RDw6vYkcxWcmMzqn3FRwE2bujE04IfdOu08exw8+jqarxfjvQF1wtHKNkSDWYZGMlsxPz+Oo0HTFERJQSRVQr7UWmw7rBzW9PvM91KuyA2CwO+2mp+XYRvL0FBVDeWqDJqmsKbfh1i6jGi6DGPf07i+gh597YzxKj63xbwWAP3cZxkaVp4B1+JcNqiv+Wvz2uC0ceY1HfLb56wJtPIs7DWhUhb09+epu38A+j3kho3d5jlaT7YooCLI5vVjnOPdbU70tjvhdVnMz2cuPE4eq/t85nsYGvCb7yHg1s+TUlWCIMn6hsY8I2lIhIpAuMSp3335k/uuML/YZUVFT7sL6weDuGlTNybjRWga8MAdQ9h7LIFfbh/FS3unoKh6vvPKPh/esL4TG1YEEfC0/pInEC4E7BYWQY/VjMIWKxJiqTJ4nsFYtAAKwIoeL47WuqV5nDzyRbHBVQx4bZAUFYlMBW4nj2SuYtbCWDgGxYrUsMvqtHGoijI8TisYmkalKiPgtaGLY5DIVpDJV+G28xBlBVVRQTxTwdCA36xHmNm0wsrrTmiH345EpmK29J5KFBvSv5Z1umG1sJisRaQAwG7l4OVo+FwW8BwNp52Dqmhg6uoqV/Z6kS+JoCj9/Ri7z04bB6/LApqizB1njqWhaYDfbUE8U9HTCmu7+gY3bOjG8PGEKSY1oLZDzGJVnw/lqgRF1RoihcWKhH6PEVGYdlD12jcK5aoejamPCLkdPBLZCgRJQWdAd9aPTWRgs7DoaXdCUTRz99+YbWWkK/EcA0lWIcoKimUJThtnniM2C4sTk9mW6UQDnW4cHc+izWfDtes6ceBkCpKs4so17Tg6noXbwcPvtuLl4TA06KloiUwZFk4Xppct88Pv1qOkM2ta6sV0fTqdIXhESYWFZ2C3cjgynoHLzqE/5EZ/yI1tuyfBsjSCtQhsqSLB47Q0pFdKtfPEeJ0On70hOgLoDn1vhwORZAmSrOLy1e347avjECQFk/EiOvx2CKKCbFFAm8+OoNeGk1M5SIoKr9PSUK/Lsrr4BPRrrCLICAXsSGQrCCeK2LSqDTv2RQDomxE2noXTzsFl52GzsGaEuFyVIUlKQ2SDY+iGzQ9RVjE04Mc1a0N4/vVJxNNl9IXcWN3nA0UBiqoimdXPN56lwTC0+XyipGDTqjbsP5FCZ9CBmzZ1o1ASEa9FCkMBBwplETYLi1JFAs8y4NlpJ39m/aVR1yMrKg6PZeB28PC6LAh69PuI8bptXpspjiVFhdvBg2cZU9CqqtYQSaIoXQB7nRYwNG1GB3s7nGBZGt1BJ14/GkepKqGnzQlJVqFBQ1Wg0Bl04MRUDqKkoLfdCQvPolgRIcsq/B6bef/jWBq9NXFnpAX63FZk8lVE02Us7/JgMlFEf8hlCpYj4xl0Bh0oVfTryG5hccOGTpycyiOWKaMz6AAFmPWdThsHSVYhSAo8TgvcDt68XxkbQFOJInwuCwolER1+ey3KSzXURRppmqORPEoVyVyPRLaC69aFIMn6Whv3LpqmUKrIsPHSrJs05rk7518JBMIlh+EghAIO/PG7Lzd/f99tq1ERZCzr8mBZlweHRzO4d8sKqBrwo6eP4tUDUbyyPwJVA2wWBr3tLlyzLoSA24p8ScQtV/XB47KgKsrgWaZhh59AOJ8QJdW8Dlb1eiEpKrIFAX0BF0pl/YvVcAzafTYEPDa0eVUcn8yaTi1NAelcFTYL2+QE+9xWeJwWM92OpvUaKmMzI1MQYOEZc5e1WHs8x9HgOLrBGetuc0JWVLMhgpGqYrdyUDUNJ6ZyDdEDWVHR2+7CptVt+O/nTmAkkscNG7oaakA664SOy85jRa8Xx2c0ojgxlUOb1wYrzyKc1EXhdGqWhKuHQnDYOIyG85AVFZoGM5XIZW8uSh8J53DH9csAAKWyhHimjIqoYOtNg/C6LPA4eew/kWqKGlktukNdLOvPZ6+lVBrC7MRkFl1tDqSyVThsLK6+LISqqMBlnxZD7T47OJbGVKIEn9uC1f0+yIpqRgevWNOB14/oUbJcaTq9Lp2vYnWfD+1+O5LZivl5rl8RhNdpgSAqkBUVnQEnjo5nkchUUBFk9IVcYBkanUH998Zna0gjhqHgcvBQVc2MVnW36bvxDiuH5d0ehBNFM5pgNCpI1aKjAbfV/HdZkMBzDKx1UY2dB6PmZzE04IPHYQXH5jEayTecBwxNwe2wQJQU5MsilnW5G2pJVvR4EU4WIUoKrDyLqqigt6M5FYumqIbPTNOm61gESX8PhtMb9Npw2UAAB0dSOD6ZRWfAAVFS4HNaYOUYeJwWDC3zg6Yp09nu63BBUzXsOBA1X6PDb0eH34HOgAOJbAUbBoOoiDJi6TI8Th7rVwRx4EQKgC6Gl3V7oNQiwLKqQhAVuOy60M0UBN3ems1tPhtu2tSNdp/dPM7Ks7jt2n78+68OA9Cje70dLvicVvP6BfQIU7EsQlano3z1n9f0GmlgaBocS+MN6zoxGsnDwjPYsCIIiqKw91gCh0fT2LiqDYKowOuywmnjYeEZHJ/IwuuygKEpPQpU0WszDZEw0OnG8m4PxqMF9IVcECQFly3TkMkL0/eWWmCuP+RCLFXGRLyIFT1e+FxWbL6iB5KsYCScQ7vP3jIlLpIqgaVpdAYdeOOVPdi+L4J8STTva4PdHvjcVsiKiuvWdaIiyOhqc6K3w43jk1nsOhSDKE+fiwGP1Ywe+twWZPICDo2mzQg5oN/7JFmFomoIJ0vwuizgWKahDlGQFNgsLGwWFpqmb9AYIxJyRRGT8QJ4ljE3oFiGNq8JdZ5MHCKoCATCgggFpp0sh43Dn3/oevPnFT1epHIVtPnsOHAiiR8+fRSSrOLnL46YDsH3f34QLjsHRdW/KNavCMDGs9h3IoWrhtrR3+lGOldFKlfBG6/shc3CYiyaR2fAgWVdHlA0hXxRQJvX1rBTTrg4ef755/GlL30Jqqri937v9/CBD3yg4e+apuFLX/oStm3bBqvViq985StYu3btgh47H047awomhtF3pv/grUPYeTCGzl4H1g0GMRLOQVFUXLOuE2ORPJZ3e7BhRdCs5XjD+i6s6PFh95GY6Wj3hVyw8SwUVcPxySwAvaZKkBVk8lX4ajvzPMeY4spp57Csy4NiRURfyI0DJ1No89lw1VAHRsN5vdugoJnPtarPh3CyCCvHwsIz5vUXrKVeeV16ytDh0Qx8LgtW9fmQzldxxZp22CwsihUJsqziyRdOorvNiVuv6UNFbK5xMSIXLEMh4LYi4KEw2ONBOl8FRQEdAbspJJd1enAynDPrc1b1+RBNleGckUJjrPlgrxfW2u5zKldBNF1CrNZtrd4xd9k5rOz1osOn74onshWs6PE2CFhRVrG8y4MtV/WBZShY+emUSoO7bh7Ett2TGOz2gKL0z7y+SYSVZ0znrbfDBZrSd++PTWRB0xS62hxIZitYM+DHiakcckUBfrcVpaoEu4XF0DI/rBYGxZoY97stuGyZ3khhZa8XDhuHSLJkRilu2NgFRdEgKwpYVk8VG+zxYjJeRKnWuGTrTcvxq+1joCmgUBIhKapZW1Moi7BbWaiqpkfVJBWZgoChAT9uurwHLw+HISsqNl/Rg3S+in3HkxjodCOWKjVENxRVA00Dt17bD6+Lx/eePICuoKOhCcTybo8pMB02DgOdHvR2uBBJlWDjWXQGHXitlrLJMjTesL4TPKc3PfrJc8dRrtU1XbYsAI+Tx4YVbQCAIfhRrEiwcIw+yJ6hcDKcw86DUfR3uuF1WXDL1X1Qao1UOI7BzkMxKKqGwR4PbtzUXTvfLWjz2bBxdRs0TTPTbwHg2HgWh0bTCHr19NlIbejuickcaIrC6n4eA11unJzKQcN09GVVrw9Bjw0vDYdRKItm+ly+LKK/04WxSAFVUcaVazr06HVZP+83rWqD3cripb1hlKoyFFVFOFEyxZTLzsPnsoBjaVy3vhMUgNcOx2HhGVPAXL+hy4zIrOj14vLV7dixL4Kg14rjE1kIEoMVvV5kClVA0wW4w8qhL+SCpKigACzrcsPnsuqRLYrCqlra20g4h/FoATYri0qtFotlaLT59Xqz+jRdltFFyMx0f8O2bEFAT7sTmqZh+74IRsI5U6wNDfjBcwwqgox8UQRFUeivpdx6XRZcsbodDK1HmEsVCYWy1JCKadDhs2NomR8cS2PPsQRu2tiFvceSUJIlKLVNMKeNg41nMdDlRrYowGXjcGg0DUAXtzzHYGWvB6WKjOXdHrywZwpVUUFfhws0TYFnaagaZk3RrIcIKgKBcNq4HbzppFy7rhPXrus0/5YrChiPFZDJV5HKVXF0IoNyRYYsa5jMFlAsi3hx7xSe2TVhFhA/vXNiztdy2DgUSiJAAWv6/bBwDPYeS2D9iiD6Q26k81WMRvJ48zV94BgKR8Yy8LmtWF7bhUxkyujvdMNuZaFpAM/TsPIsOIYBz+m7ghxL13ZOSSTtXKMoCr74xS/i+9//Pjo6OvDOd74TW7ZswYoVK8xjnn/+eYyOjuI3v/kN9u7diy984Qv40Y9+tKDHzsft1w1gLKU7BhtWBM2Iz7rBANwOPV9/WZcH3W1O0zkE9J3udr8dawZqefk+m76LnyghyVfgqUUdyoIMnqWhqBqCXjsm4nlE02VsvlJvHlMVFByfzEJVNVy5pgN7jyVgt3KwWVhQ0GtR+kNudAWdKFZEDB9LYlWfz3R4gh4bnHYOmbyAFT1e5IoCPE4LNl/Rg4lYASdqYq4z6EB/pxv7jidRKEsIeGywWzlomoagxwqnjYPVwpripp4NK4NmlOOqy0I4PJpGT7vLbF/d7rPj+EQWDjtn1nF0tzkRz5QxEs5jZZ8X+aKI1f0+RJIleJzTNRQrerzoCjqgaXoajyyruGJNO3YfjoPnGPhcFtA0Ba/TAp/LimiqjK42XUx4XXpnMiPi8XtbVmL/yRRW9HgbnGkA2LiyzXQAAT29p91nB8/RmIwXsbLXC1ftvsaztF4n1elGtiAg4LGa9yuulsqlqhrW9PvMyGIsXTYjQ8vq6oTq6apFnuxWDrKsIpWvmnUu5aqeDnXlmnbzeJ5j4Hdb4XNZsW4wAI/TAo/Dgv0jSVyztgP5kmju1I+E87pjbdUd3FxRH2J7fV0XWJedR1/IhVxJwLoVQVxj4fD0zjHYrbrI6w+5G+q0VE1DsSLi5k3dYFk98vXScBiKosHK606y28HjXW9ejeHjCVg5FgOdblRFGQ4bZ9aYtfvtsPIMLDxbSyvlG6JjPMvAadOvuYDHpqe4ySqqggJF0VAR9HohI9PBaePwvrvW4eBICqqqmb/ffMV0Q6aZdAYdiKXLDfV/nUEHxiJ5dLU5zcdOxPSIm7GJ4Hbw0DQNsqyakVFAF2h2C4cr1rRjdZ/PPKeN88PCMdixL4qxaAGyouLmy7sRTZXNSJWi6NGV1d0eU6St7veh3WfHnqMJaIApYDqDeoqlEdZs9+kpboWyhO52J0bCOaiqZm7SLOvyIJWrgmcZrO7XBfHMyFJnwIFcUcD6FW3YeTAKQdQFvcfJY91gEK/sj8Jq0d8LRVHoaXea11R3uxM+lwVelxWT8SLafDZcszYEp41DIlvBRLwAB00j6J2uqQt6bRBEueF3gH4dXr66HfF0GeFkCSE/h81X6BsBkqyiu81pCu/nX5+E1cLi7psH9dRRKglZVnHHDQM4VkunXTPgQ0VQzOfu8Ntr42J4MAyN8WgRfo8VVguLVf0+ZAtCw9owAAIeG7Qe76znEkAEFYFAOMt4nBasd1rmPxD6jmi11q62IsjIFKqoCgpUTUOmUMVUvGimoEzECigLMiw8o+eocwzGo3mMhHPIl0QIooLRcK4hteJUoCjdUdbrPlRwtS8YTdPFYtCrO6HFsghRVtHT7gTL0JiMFxDw2OB3W1GuSoilyxjs9oJhKMTSZTA0hc6AA4qqYiJWRGfQAYeNQ74oolAW0d/pBkXpnZacdh5BjxVVSUE0WUJfyA2eo5HIlKEoQG/ICVUDjo5n0BV0wOO0IJ2vIpoqYWhAd/aPT2Rht7LoanNCUZWmNrBtPntDu/2lZHh4GP39/ejt7QUA3HnnnXjmmWcaRNEzzzyDe+65BxRFYdOmTcjn84jH45iampr3sQCQz+eRzzd2popG9ZShvUeT4Ow+OGwcfG6r6ZTMrA1s1YAAQIMIH+zxwm7lkC/p9SORZAlXrWnHUy+NoLfDhTes78TL+zSoKsyZRnDp6WRG7c/GlW3m8wU9NrCM/vwcS5uP0etGJPzBWy8DAEzECsjkBVyxph1TiSLStdqj3g4XejtcqIoyLJy+Q90ZdDQU9FMUhTbf9M8AcMPGLiSzFSSzFaRyVXQGnWj36d3RHDbOfLwhZIzN7P6QC5evbset1/ZjKlHEa4disFoYdAWd6Arqxxiioh5jR9rYPQf0Hflr14ZwYiqHZLZSiyZR8Lks6Ao6UBFkBDw2LO/2Qqx14FM1PUrD1gmnjoAdsVSjI71xZRt4jobdymG81rHMZmXhsvOQFRWDPV70driwvFsXRpKsQlE0hAJ2OG0cLDyDPUcTWN3nMyPoXUFHSzHaCo6lsXYw0NCB0W7lmgRBZ9CB9YNB02aDW67q01PcgvpavnY4hnCiCJtVv3dtvXkQw0cTmEoUTYfaeN16sVeuSugKOqGoKlx9vobIQMBthYVjYOVZVEQF7bXNBSuv1wm1eW24fPW0+KOgd5B7yxsGsG33pCkSDC5bFkBFkMFzDEJ+R0PDDa/LgivWtJuP4TnGXAtFUeFzN3+nTMUL6PDZ0e63N/2tFav6fOb5ZUQ1OZbGe+4YAkUBe48mYLUw5kaF3WmBy86jM+gAw9DYfEUPtu2eNG25Yk07eI5paohwxRo94sIwNGhGb+jC0BRW9vrgtPFgGMqsfQondOfewMgM2XJ1Lwpl0dwAGOz2IOi16RFMSk/tu2FjN+hay/dlXR5cuy7U0L3y8tXtmIoXceBkytwEqsdqYbFplf756Wn9aVy3rtN8/9dv6Gw43vhsbtzY1ZA1MtjjgcPGob12D+kPcei9zYXt+yOQa9F6u5XF0IC/Zct7ADg5lYPTrkfWvDX/QY/UqQ334asvC4Gmp5vkeJ0W5F0ifC4rhgb8cDt5vHYoDr/biu42J9p8Nuw5msD1G7ogSErtfsSawpChKbOGz6hxXd3vg8vO41eJKOaCCCoCgXDeYOR8G7tDvbN0WFosiqpBUfSC30pVRiJXMb8MTk7lUCyLGOj0QJBk/GrHGFb1+tDmtWEkksO+E0lsvrwHkqxix/4IrBYWy7s8yJcEvHY4bu7SjUaUWuSBgayoyOQFUJT+RZkviQgniuZNeypRBEXp6UuSrGA8WkAqV9VTtGq7yJFUCZoGxNIlWHkWDhsHQZSRLYo4NJoGRVEolkWomqbXy6gqihVZ785USx0SRQX7jidhFOgzNAULr+eOz6xh6ww6zhtBFYvFEAqFzJ87OjowPDw85zGhUAixWGxBjwWAxx57DN/85jdbvr4GDetWBOB3WVv+fbEEvTb0hnRnfLDHC4amsG5FEN1tTnicFly/vqupLfuafh8qLTryeV3NjuTmK3rw2uEYqsL0Dr+xO263sLhsWaBpBk59tKZetBhcfVlHw88sQyMUcCAUcCCeKSPosbWsg7xyTQdKFQkMQ5uOpOHsdLc5zVqgU8F4bJvPhmS2ghs3dpvpcABMZxBoFLtvWN/oCK7p92NNf6Mj1xilcKIqKvDUBAPL0Ni0qq1BEHAsjRW1TnSA7qz6XBb0d7rNtR3oci9qM4eiKDOa0YrZoi31HQoNjDqyGzZ2m+/tDRs653x+QBdxN27qRrEiYc+ReENHvTde2Qu7VW+lX+9AD3TqqagURTWkha1fETT/vbrf13TuXrM2hEy+2hC5qmemADMw0nBnMhYtwO+2LlhQ1WOzsGBZGu0+u3leWy26eOztcCGVq2DTqnYs6/Y02HrDxi7zPc9mb/3vb9jQhcHuaQFbX68YCjgaRPLM56h/HoaZbt5x0+XdDcfOFOKGJGZqHRpn61xZj16D1riOM7M11g0GdHE447PoaXehp73x3kXTFN6wrhPZop6GN9tmlMFErIDOoANXrO4wN2fWDwabWuzP7Ca4aVUb+jvdZp0UoEfTjdRRYPo64lgaVw51NIyBuGJ1O14/moCFZzDY40FfaLpz57VrQ5gLIqgIBMJFD0NTYGim1gqbQ6DOSZjp4NU7ZTO/qN7+xoWnjZ1NNE27qFMRW7Xhn/l+ZztmIY8FgPe+9714+9vf3vC7aDSK+++/H1cNdaCno9lJPVU4ljZTVAyuuWz6y9njtDSkvAG6wzSzxmgurlzTKIDcDr7BqWLo+dsI19OqZsGg3Te7w1q/ITKbg3m6tPvsc9pwunAs3SQyZ34+M7FwTEPkB0DTZ34uWdnrNVuPG8xMeZwNhqbgmXH+ALO3aA96bXOm1gGNNbj1GNHfM8FNm7rnP2gWWIZu2lCq/zyNyORMkcGeQj3vbGtxLujvdJv1SqfLYrv50nXRn/lodT7xdaJoNjiWabo3zHUfmjlTz2nnG86j+V6vHiKoCAQC4QLjYhZTgB5tMtLvAD0a1d7ePucx0WgU7e3tkCRp3scCgNvthtt95kQTgUAgEC5dSKssAoFAIJxXrF+/HqOjo5iYmIAoinjqqaewZcuWhmO2bNmCJ554ApqmYc+ePXC5XGhvb1/QYwkEAoFAOJMsOkKlKHqOdv0OIIFAIBAIxveC8T1xqrAsi4cffhgPPfQQFEXBvffei5UrV+Lxxx8HANx3333YvHkztm3bhltvvRU2mw1f/vKX53zsQiDfbwQCgUBoxXzfb5TWKuF8Dnbt2oX777//9C0jEAgEwkXJD37wA1x11VVLbcai2bZt26JnVhEIBALh0mG277dFR6jWrVuHH/zgB2hrawPDLK7ItR6j+PcHP/hBQ0em8x1i97mF2H1uIXafWy42uxVFQSKRwLp165bQulPHaLX+r//6r+juPvUC90uRC/VcXmrIup06ZO1ODbJup8Z832+LFlRWq/WM7jyGQiH09MzdHeZ8hNh9biF2n1uI3eeWi8nu/v7+JbLm9OF5vRtUd3f3Bfl5nA9cqOfyUkPW7dQha3dqkHVbPHN9v5GmFAQCgUAgEAgEAoFwihBBRSAQCAQCgUAgEAinCBFUBAKBQCAQCAQCgXCKLJmgcrvd+MM//MMLbrAisfvcQuw+txC7zy3E7vOLi/V9nQvI2p0aZN1OHbJ2pwZZt7PDotumEwgEAoFAIBAIBAJBh6T8EQgEAoFAIBAIBMIpQgQVgUAgEAgEAoFAIJwiZ11QPf/887j99ttx66234p/+6Z+a/q5pGv7iL/4Ct956K7Zu3YoDBw6cbZMWxHx2nzhxAu9617uwbt06fO9731sCC1szn91PPvkktm7diq1bt+Ld7343Dh8+vARWNjOf3U8//TS2bt2Ku+++G+94xzuwa9euJbCyNfPZbjA8PIyhoSH86le/OofWzc58dr/yyiu48sorcffdd+Puu+/GN7/5zSWwspmFrPcrr7yCu+++G3feeSfe8573nGMLWzOf3d/97nfNtX7b296GoaEhZLPZc2/oDOazu1Ao4EMf+hDuuusu3Hnnnfiv//qvJbDyzLDQa/lSIRKJ4IEHHsAdd9yBO++8E4899hgAIJvN4sEHH8Rtt92GBx98ELlcznzMt7/9bdx66624/fbb8cILL5i/379/P7Zu3Ypbb70Vf/EXf4FLodpAURTcc889+OAHPwiArNtCyefz+OhHP4q3vOUtuOOOO/D666+TtVsA//Iv/4I777wTb3vb2/Dxj38cgiCQdTuXaGcRWZa1W265RRsfH9cEQdC2bt2qHTt2rOGY5557Tnv/+9+vqaqqvf7669o73/nOs2nSgliI3clkUtu7d6/26KOPat/97neXyNJGFmL3a6+9pmWzWU3T9LW/UNa7WCxqqqpqmqZphw4d0m6//falMLWJhdhuHPfAAw9oDz30kPbLX/5yCSxttmc+u3fs2KF94AMfWCILW7MQu3O5nHbHHXdoU1NTmqbp1+pSs9DzxOCZZ57RHnjggXNoYWsWYvc//MM/aF/96lc1TdO0VCqlXX311ZogCEth7mmx2M/oUiAWi2n79+/XNE3TCoWCdtttt2nHjh3T/uqv/kr79re/rWmapn372982P/9jx45pW7du1QRB0MbHx7VbbrlFk2VZ0zRNu/fee7Xdu3drqqpq73//+7Xnnntuad7UOeSf//mftY9//OPmfZSs28L49Kc/rf3nf/6npmmaJgiClsvlyNrNQzQa1d70pjdplUpF0zRN++hHP6r913/9F1m3c8hZjVANDw+jv78fvb294Hked955J5555pmGY5555hncc889oCgKmzZtQj6fRzweP5tmzctC7A4EAtiwYQNYll0iK5tZiN1XXHEFPB4PAGDTpk2IRqNLYWoDC7Hb4XCAoigAQKVSMf+91CzEdgD4t3/7N9x+++0IBAJLYGUzC7X7fGMhdv/sZz/Drbfeiq6uLgA4L9Z8sev91FNP4W1ve9s5tLA1C7GboiiUSiVomoZSqQSPx3Ne3RcXyoV6TZxN2tvbsXbtWgCA0+nE8uXLEYvFzO9tALjnnnvw9NNPA9C/z++8807wPI/e3l709/djeHgY8XgcxWIRl19+OSiKwj333HPRr200GsVzzz2Hd77znebvyLrNT7FYxM6dO81143kebrebrN0CUBQF1WoVsiyjWq2ivb2drNs55KwKqlgshlAoZP7c0dGBWCw25zGhUKjpmHPNQuw+H1ms3T/+8Y9x8803nwvT5mShdv/2t7/FW97yFnzwgx/El7/85XNp4qws9Bx/+umn8e53v/tcmzcrC13zPXv24K677sJDDz2EY8eOnUsTW7IQu0dHR5HP5/HAAw/gHe94B5544olzbGUzi7k2K5UKXnjhBdx2223nyrxZWYjd999/P06cOIGbbroJd911Fz772c+Cpi+88twL9b5/rpicnMShQ4ewceNGpFIptLe3A9BFVzqdBjD7Gp6P3/Nnmy9/+cv41Kc+1XAtkHWbn4mJCfj9fnzmM5/BPffcg89+9rMol8tk7eaho6MD73vf+/CmN70JN954I5xOJ2688UaybueQs/qtp7XIu5wZWVjIMeea89GmhbAYu3fs2IEf//jH+OQnP3m2zZqXhdp966234le/+hW+9a1v4Rvf+Ma5MG1eFmL7l770JXzyk58EwzDnyqx5WYjda9euxbPPPosnn3wSDzzwAD7ykY+cK/NmZSF2K4qCAwcO4Nvf/ja++93v4u///u8xMjJyrkxsyWKuzd/97ne44oor4PV6z7JV87MQu1988UUMDQ3hhRdewBNPPIEvfvGLKBaL58rEM8aFet8/F5RKJXz0ox/F//k//wdOp3PW42Zbw0ttbX/3u9/B7/dj3bp1CzqerNs0sizj4MGDuO+++/DEE0/AZrPNWc9I1k4nl8vhmWeewTPPPIMXXngBlUoFP/3pT2c9nqzbmeesCqpQKNSQUhaLxUylPNsx0Wi06ZhzzULsPh9ZqN2HDx/G5z73Ofz93/89fD7fuTSxJYtd76uvvhrj4+PmTstSshDb9+/fj49//OPYsmULfv3rX+ORRx4xw+5LxULsdjqdcDgcAIDNmzdDluUlX/OF3lNuuukm2O12+P1+XHXVVUvefGUx5/hTTz2FO++881yZNicLsfsnP/kJbrvtNlAUhf7+fvT09ODkyZPn2tTT5kK9759tJEnCRz/6UWzdutWMmgYCATM1Px6Pw+/3A5h9Dc/H7/mzye7du/Hss89iy5Yt+PjHP44dO3bgk5/8JFm3BRAKhRAKhbBx40YAwFve8hYcPHiQrN08vPzyy+jp6YHf7wfHcbjtttvw+uuvk3U7h5xVQbV+/XqMjo5iYmICoijiqaeewpYtWxqO2bJlC5544glomoY9e/bA5XIt+Ye3ELvPRxZidzgcxh/90R/hq1/9KpYtW7ZEljayELvHxsbMnZMDBw5AkqTzQgwuxPZnn33W/O/222/Hn/3Zn+HNb37zElmssxC7E4mEuebDw8NQVXXJ13whdt9yyy3YtWsXZFlGpVLB8PAwBgcHl8hinYXeUwqFAnbu3IlbbrllCaxsZiF2d3Z2Yvv27QCAZDKJkZER9PT0LIW5p8WFet8/m2iahs9+9rNYvnw5HnzwQfP3xvc2ADzxxBPm+bplyxY89dRTEEURExMTGB0dxYYNG9De3g6Hw4E9e/ZA07SGx1yMfOITn8Dzzz+PZ599Fo8++iiuu+46/PVf/zVZtwXQ1taGUChkbsps374dg4ODZO3moaurC3v37kWlUoGmaWTdloCzWjnMsiwefvhhPPTQQ1AUBffeey9WrlyJxx9/HABw3333YfPmzdi2bRtuvfVW2Gy286I2ZiF2JxIJ3HvvvSgWi6BpGo899hh+8YtfzJkOcT7Y/a1vfQvZbBaPPPIIAIBhGPzkJz9ZMpuBhdn961//Gj/96U/BsiysViu+/vWvnxdh6IXYfj6y0DV//PHHwTAMrFYrHn300SVf84XYPTg4aNbz0DSNd77znVi1atV5bzeg1wnecMMNsNvtS2muyULs/vCHP4zPfOYz2Lp1KzRNwyc/+UlzF/RCYrb3einz2muv4ac//SlWrVqFu+++GwDw8Y9/HB/4wAfwsY99DD/+8Y/R2dlppmCvXLkSd9xxB9761reCYRg8/PDDZqrzF77wBXzmM59BtVrFzTfffF7U755ryLotjM9//vP45Cc/CUmS0Nvbi7/8y7+Eqqpk7eZg48aNuP322/H2t78dLMtiaGgI73rXu1Aqlci6nSMorVXCJIFAIBAIBAKBQCAQ5uXCa8VEIBAIBAKBQCAQCOcJRFARCAQCgUAgEAgEwilCBBWBQCAQCAQCgUAgnCJEUBEIBAKBQCAQCATCKUIEFYFAIBAIBAKBQCCcIkRQEQgEAoFAIBAIBMIpQgQVgUAgEAgEAoFAIJwiRFARCAQCgUAgEAgEwilCBBWBQCAQCAQCgUAgnCJEUBEIBAKBQCAQCATCKUIEFYFAIBAIBAKBQCCcIkRQEQgEAoFAIBAIBMIpQgQVgUAgEAgEAoFAIJwiRFARCAQCgUAgEAgEwilCBBWBMA/79u3Dpz/96aU2g0AgEAiEMwr5fiMQzgyUpmnaUhtBIBAIBAKBQCAQCBciJEJFINRRrVbx0Y9+FG9961tx11134ROf+AReeeUV/P7v/z4A4JVXXsE73vEOfP7zn8fWrVtxzz33YGRkZM7n27p1K7Zt2wYAeO6557B161ZUq9Vz8n4IBAKBQADI9xuBcDYhgopAqOOFF15ALpfDL37xCzz55JN4+OGHm445evQo/sf/+B/42c9+httuuw3/+I//OOvzWa1WPProo/jCF76A4eFhPPLII/j6178Oq9V6Nt8GgUAgEAgNkO83AuHsQQQVgVDHmjVrMDIygi984Qv41a9+BZ7nm44ZHBzE0NAQAODyyy/H+Pj4nM+5cuVKfPCDH8S73/1ufPjDH8aKFSvOiu0EAoFAIMwG+X4jEM4eRFARCHX09vbiF7/4BW688Ua8/PLLuOeeeyBJUsMxFovF/DdN01AUZd7nPXjwIPx+P6LR6Bm3mUAgEAiE+SDfbwTC2YMIKgKhjmg0CoZh8OY3vxmf+cxnkEqlkM/nT+s5f/nLX+LAgQN48skn8fOf/xyvvvrqutzHJQAAdD9JREFUGbKWQCAQCISFQb7fCISzB7vUBhAI5xNHjhzB3/zN3wAAVFXFBz/4QQQCgVN+vomJCfzVX/0VHnvsMfj9fvz1X/81Pvaxj+FHP/oR/H7/mTKbQCAQCIQ5Id9vBMLZg7RNJxAIBAKBQCAQCIRThKT8EQgEAoFAIBAIBMIpQlL+CIQzwLZt2/Doo482/f4zn/kMrrvuuiWwiEAgEAiE04d8vxEI80NS/ggEAoFAIBAIBALhFFl0hKparWL//v1oa2sDwzBnwyYCgUAgXIAoioJEIoF169ZdkMM9yfcbgUAgEFox3/fbogXV/v37cf/9958R4wgEAoFw8fGDH/wAV1111VKbsWjI9xuBQCAQ5mK277dFC6q2tjbzCUOh0OlbRiAQCISLgmg0ivvvv9/8nrjQIN9vBAKBQGjFfN9vixZURhpEKBRCT0/P6VlHIBAIhIuOCzVdjny/EQgEAmEuZvt+I23TCQTCRYmmaSiWRfNnRSX9dwgXJ6qqQSXn90WPJKsoV6WlNoNAILSACCoCgXBR8rf/73V84hvP4+BICtlCFf/7K8/gwMnUUptFuARRVQ0j4dwpi3pRUlCqzO5IH5vI4Oh45lTNI1wgvH40jp0HY0ttBoFAaAGZQ0UgEC4aNE3DS3vD+PlLIzh4MgUNwJ9+80VQANp8NnAs2UMinHvS+SrGowVYOAZdbc5FP37XoRgkWcXmK1qnIdI0hXM5AKVclWC3cufuBc9jJuMFtPvs4LmFpbmqqgZJUWFZ4PH1VKryoh+zlFQEGZqmXRLnyng0j86gAxx7YaY7E04f4l0QCISLgkiyhA995Rn81b/tAkUBH7vvCvz9p7fg7z+9BX/4+5vAMDQe/qft+N1rE/jOT/dBVtSlNplAWBCSPPe52tvhQl+H65zYki0I2HkwhlxROCevNxtVUT4vruETkzkcWUR0MJwsYse+yGm/7oGTKRweTS/o2EiytKDoqCApp2tWA68eiC5ZRE2SVbw0HEZFOPsiVJQUjITzODmVW/BjylUJVfHcCOSdB6OIp8tzHrNt9yS27Z5s+bepRBH7jifPhmnnLbmisOj0WiKoCATCBc8r+yP440efg6KqePvmQfzlh2/Elqt60dvhQm+HC7dd24+//ZPN2LAiiG/88HVs3xdZcoeQcGmQyFQwEl64o3UqnJzK4dhk9qy+BqCLqWd3jYNnaThtSxt1eGV/FHuPJSDJ6jlxmutRVQ17jyZMh0tbRHjQYePQ1eY4bRuS2Qpi8zjJgC6Sjo5n5nWoU7kKduyLnHaNljKPyK2KMl4/Gj/rtWDFsghZVpHMVs7aa5ycyiGcKIKi9J/VRej7nQdjeGV/9LRef6HnnaahYfNBkJSmzQi/2wqvy9Lwu1Sugu37wjg+kUU6Xz0tW2djLJrHrkPNojuZrSBzhl9z5nrligLEuk2EQyNpHDiZgqJqeO3w4tNriaAiEAgXLJqm4YdPH8FffP9VXL66Dd/81Ba87651LY+1Wzl8+oGrcPmqdpTK4ry7/gTCQnjtcAzj0TwAfac6W2gU6olsGbF0+YxEU2YTDrKiQlW0sxKxyRUF0xmvijLimQoKZQnFigRJPrMRjfrXrAp6BOrl4TAOjUxHYhRFNevFimUJ+08k8eoB3TGd6YBlCwIy+SoUVTuj1/vL+8LIFgVMJYrm72RFxYGTKRRqjXBeO9wcxcsWBDhtHIIeG0RJwbGJDFK5CjKFKjKF1s5jKlfBtt2T8wqV2eBZGtesDaHdb2/590SmAkFSUKzV6J1OlKpQFvHi3rC5Bq14aW8Yuw7GMB4tzPt8mqYhnCzi+EQWgP7Zj0XyZ+W8K1clRFOlBR9/dDyDHfsjOFaz7UwhySp2How23UdmIkgKXtgzhb1HEyhWJGzbPWl+hjO5Zm2oIdV4x74Idh+JNxyzfkUQG1c2tgOfiBUgSmf3e3I0nG9ZH3rgZArDi4yKGSJdkBQkMpUGASUrKp5/fQrxzPTGwp6jCew5ljB/jmfKSGYr2Hc8cUo1qURQEQiECxJN0/AvPz+If//lYTjtupNi5ecuC2UZGp9+4Cp4XVZ89d924f/8w0sYi+TPkcWEC5nxaL6lw1UsSxgJ51GuSnjlgB410TS9CcXR8Qy6gk5MJYo4NpHF/hNJ7DkaR7bQ6IwvlOMTWWzbPYlIstGONq8NVguLl/aGG3bkFVXDyalcyw6AmqYtKEqw52gCh2qpZQGPFX63FSfDObw8HMG+4/M3eRmN5E3BWY+s6NGDmUJHklXsOZrAz188iSNjGUiyinimDEHUd9VjmbL5/kVZQV/IhU2r2pDJVzF8PIl8adqZPzSaxv4TKYQTRew61BwNKFUk7D2WwGi49RrNhqLox0ZTunNGgTLXXlW1WodRCXuOTjtrgqRg77EEdh+OY/h4EodG09h7NIFf7xjDwZE0Dp5snb7HcwzafLZZbZlNBJSruuiNZyqYShQb3l+xLJrO5sGRFEZmpKotJBXt6FgGz+4abziHDMe4PEetl8dpgc9lNTcZxiJ5jM5yDw4nSzg2njWvlXS+il9uH8WOOSI7pYqeSreQT/P1I3Fzs+DoeAZHxhbuRCuKZqZRGn67EamaDUP4zCUIFUVFuSojV9IFVbGFOC1VJOzYF4GmAdmiYK77zGMnYnnkioIp3Osx6vE0TcOh0TQOjqSa7itVQWn6nUGr6NG23ZMN0fgTk1lzo2Db7kmEk9P3vFxRwLbdkw3n5cxNg4ogN/5d1bDnaBwHR1NNr1+sSNh5MIZktoJcQcDBkVTDY437zEyhWm2xSUVRlBmBj6ZKeGk43HINZkKaUhAIhAsOTdPwvScP4KfPn8BH3rkRm1a1we3gF/RYm4XFJ+6/Ep/6u+fR3+mGdB7UYRDOf0RJBVXzmLIFAYKkoKNu179c1b/8V/Z5AejOiCgrtcJ8IOS3I+CxIei1IV4TBd1tTqTzVXidFtA0hWiqBFXTEPI7MB4roLfD1TKtJ5IsoTPoQKkioVSRcGAkhWJJgs9tRTpfhappaPfZEUuXMBErgGEo9HW4MBEroM1rw89eGMHyHjdKFRlrBnyIJEvYtKodmqahVJHgtM9/LWnQUGnheOdLIpLZCpZ3ewDA3LDoC7kbjqsKMg6cTGHDyiB8Lis0TQNFUaZTJdYcoFxRAMcy2LE/gqDXhoDHaj7HaDiPRKaCq4Y6MNjtwZVr2lEoiVBUFT6XFesHA7BZWIxE8i132kVZQThRRDxNg+MYdNft4qdyFaiqLvw6g3qKnqpqDWl2M0WYqmoolMWGe1E4UURXm9N8X2VBBk1RSGYrYBgamqzi8tXtSGRaO64uO4/LlgUwGS9gLJJHf2fjOh4ZyyAUaEwhPDqewd5jCbT7ps9PC8egt8MFWVHx2uE4+kIuLOvymI1Oxmqi99h4FhPxAm7a1I12nx3FsoiDI2msXxGsbR7kcM3aEMZjBUwlirhyjQpJVhqaMaRz1YZrw6AiyBjs9pgCIJoqYTSSh6yomIgVcMOGLuRLevZAriggW5wWFXuOxpHM6U50viSiIsj4zStjWLc8gMEer/kaRvrY+hXBptcfCedgs7Bw2DjQFIVIqgS/Wz+fVvf7myJriqohkSnD67I0bdZxHA2epTEayWNZl/6ZxNJldAYd8DgbU+cMUrXNjnrB+fqROMJJ3Y6NK4OoCgrWDPjgd9twZCyN0UgeN2zoMq/Jl4bDkBcQbc0UqvjtK+Ow8Cy62hzIl0Q4rBysFv19HJ/MYnm3B+1+O55/fRKaBgwN+M1z3Rg7ki0K5u+M3+86HMNrh+Lo7XCizWdHh98On0tfx3CiBK/TglJVwmS8CJe9/loooSvorD2Pnv6aLwoAKJQqEnYdiuHadSHkSyLGonmUqzISmTI6auf3i3umAADjsQL6OlzmuauoGvIlAZqmoSLIoChdaLZSuJqmYSpRRFfde1JVDaW6jQFF1UxB7nbwWNbpRlWU561DJIKKQCBccPznM0fx0+dP4M1X92LzFT2wWRZ3K1vV58Pdm1fgV9tHEXBb538A4ZJC0zQksxUcOJnCjRu7wDC0nm5H6WlNe2tpIobTKIgKYqkSYuky8iURPe1OMDQFnmXwygG9AYHbwSMUdKAz4MALe6YgygqOT2QwlShhoMuN/pDb3CGvCgomYgU4bRyGjyXAMHSDbUfG0tCgIZoqw2njEE2WoagafG4rIskSJuNFOGw5VAV9J3w0nIfPZcWuQzHQFIV0oYoBzY0NK4M4Op4xjxuPFXBiMocbN3a17FqXylWRzlexvNtjdqnL5KvYeyyB7jYnwskSLlsWMCNw4boo3K93jIJlaFw11AG3g4dSc2KKZQkWjsFvXxmH32M1RUrQY4PHySOcLMHKM7BwDHiOaajdGuh042Q4h2d3TaCn3YlkroJfbR/Dqj4vejtcODGZw5VDHUjndbtnOv40RdU6f1KQZRXj0Ty8LivcDh77T0xH32RFRcBjNWsqYukyBFE2RaKkqLhyTTt+9uJJFCsSrDwLRdUgSgqee20S/+Mta/TPIZKHhWNw06YuFCsSDo9mwDEUDhxPIpWvos1rhyip8LosKFclKKqGcKKIfElEW504Gg3nMBLOIeCxwWXnkMpVEPDoUazDtWiD0dH0ho1d2H04DmftOIamzXMMAF4engLPsXjtcAyr+3yoCDISmQp++dIobtzYBUnRa9RePRDFYI8XgqjgyFgaqqa/v5eHI7BbWazq85n+azxTxtAyv3m+5ooCIskSRsI58ByDiiA3ONqFkohouoxQwI5dh2Lwu60NAkaUVfPzA4DOoAP7jicRSZawoYVwakWxLJpphqqqgeNoOKwcxmMFjEbyuPnybkwlRNgsrGlboSTgZy+cxF03D8LqZ1EoixAlBQGPDaPhHDIFATxLN2zK7TmaAM/REEQFFEXhDes7m64lQ1DKiopDI2nkyyKcNg6v7I8ili7D77Fi/YogXjscR74kolASsfWm5bDwbEsxpajNkR1BVDDQ5YGmabBZWCQzFbxSjpoiRJJV5IsCTk7lsKbfj8NjabO27/UjcYiyinCq1CDKAV3Av3ZITxdM5apw2niMhvMYp6dTOHcfiaNYkeB1WkwBB+hCOJWroCLISOWqWNHjNe+lgH6PhKafD1VBgd3CmkKnPnpVL6YkWUE6X8XrRxKw8vo6j0zlEEmWsH04DI6jce3azunzoCIhmirDbmWRLQiIZ8roCjoxEStAVlRwLI1CSTQ/o3RBwMhUDscmsijm505BJIKKQCBcUDz96jj+/ZeH8fu3rMTPXxrB1ZeFcP2GrkU/z7tvXYXfvTaBf3piHyqCjA+9Y0PTTi/h0mQyUURmQkab1wZVA4SqhDafDZFkCUfHM6BAwW5l8YuXR2DlWZwM53AynENPuxPxdBkuOwdJVnHFmnacmNId2KMTWfA8Y35Rj0XyKJYlxNJlZIv6l7YRAZuIFXD9hk7QFKU/jmPQFXSYjpPXZUGxLGEiVsCaft2RZZnp3dhktoLjkwJW9/kA6OlfxyYycDstkCQVbV4bQgF9V9l4zW27JyDKKk5M5nDVUEeTE6iqmhkxKFUkCKICmqbwYi3VLV8S4XFasPtIHBVBQiqn/y7o1R39kbAeAZFkFTSlp7JxDI3jE1lURSciqVJDUXwkVYKl5iC5HDzSuSrKVQmHRtNgaAqyosHCM2a61c6DMUzGiwh6bPC6LHh5OIJKLRqk1g56eTiCmy/vRr4kYs/RBIYG/OjwO5DKVZDIVhDPlGGzsHjTlb1mZJCiKBwaTUMQFTPyNLNAfypeRCxdgqLoImPfiSQkSUG+JCJfFqEoKjRNjxJRFPDzF0dw7boQWJaGqjI4NJZGuSrDYeNw4GQKv//mVdh3PAlV1XB8Mos2nw0epwWKqtfJTcb1FL6pRBFWnkGb1waWobF9XwTpXNV0DH0u3enVoEeeZtbgaZqG4VraphGpMSJVlVrziHWD04JlPJrHYI8Hrx9NYCKmt4vnWBqyouLYRBbLu6ejZ0+9eBLlmuOsahqgAU47b84CHBrwm8f63Fbdyc5W9M2JdBltXjusPAOapiCICnJF0Yz8RJMl+NxWDA34sazLg1YYqWeGyHvtsC4CEpkKkrkKOIaGx2lBriRAVTW47DxePRhFZ9CBmzZ1I5EpYypeNKMfuw/HzXUd6HTj+KT+/Mu7PejwOzAZm948ECUVE/Ei+jpceO1wDAGPDQdOphBLl9Hd5sT2/REz9czjsKDDb4fHyZupjNmaAFVUDQ4bh7Ig4z+fPootV/e1fK9Tcf21K4KM0UgOY5ECOJaGpmnQNP1+MTO1rcNvRzhZQqEswW5lsbLHa24QJHMVjEV0gSHLqhkV1pvAKOA5BgMhFyRZhaJqYGjK3AiRFRWqqumv57Rg16Go+bxHx/UUXivP4NCoHn1z2jiwDA2bhcXa5YHaBk0SqqahLMh49WAMPe0ubJ/RGVNWVFQFGa8djkNRVKxdHsBoOAdFUZGqXZ/7a+fatWs7oaoaBFFBu9+O/pAb5aqEQlmEomooCxIqgozxWAHLOt0Nkco9R+JIZitY1uUxNyFmgwgqAoFwwXDgZArf/NEebL1pOd5zxxDuunlw1vSK+bBbObz3rZfhGz98HUMDfhTLEhA4wwYTLkim4kXkRQUMTUMQZdMZS+UqiGf0tJ1lnW6MRwvoC7lgs7CoCDIma44NRVFIZCv4xcujCNWlPk3ECqgKMqLpMmRFA8vQsHAMIskSIskSVvZ6MR4twO+24rnXJuH3WGHhGAiSgtFIHoL0/7f35mFylWX+9/esdWpfu6p6X9PZF0JCAAnBhBBjCIuIyg9REV7cRnQcHWfcx0FfdUZHf5ejL+go4AiOooMLikgQIvuShBCyL71v1dVd+37Oef84dU5XdVd1V3eqq7o7z+e6cl2drtNVz/Ocpe77ue/7e4uwmXRIZyTU2PU41qU4KF6nEQO+KDKiBJahYRBY0PSEgzU4GoVB4HCmLwCXVQ9fII5X3hzG2T4lYqAaxGpU45kDfdh9WTMSOWlyf3zuHPSCYjKoaW8MTUHHK+MbGI1iIKfewmrkEU1k4AvEsazRpv1ekSPOoMlrxtBYDG6bHkPZvxsei0HgGS2KodZ9JFOKIdPvi8DrNKLfF0EiNdW4CcdSMDgMON41rjkPGUlCJJbGWCgBi5FXUsnCiiTy0XN+9AyH4XUaMRqIo2coDIPA4vd/O4N+X1RzOofHYojG07AYFSegs8kOUVIMR5qmEE9moJMZZVferINBUCIJ6jl4+egQeocimkMKAG+c9sNk4BBJpJU0NIHDcLYe6vHnu+B2GJDKiBAlJRLZ3mCD22FA30gkzzFKpEQ8+7pS46EmJFEU4LAqqVUvvzmIfl8U7fVWUBSFVFqEUc9BkmX8+cXunPfJICPKWjpaS60FVhOvCR1E42kMjEbgthtAQUlF9GUd0FRaRDQRQ99IGDRFweMwYHgsBkmW4bQKGPBF0egxQ5JkNHst6B4KZft36TUhFY5jMJJNiXPbDegaDKHGrofLqkcilUEgktSuu6Gssx2OptA1EEQqI6GzyY6xUALnBoJo9JjxytFh6HVKVKlvJIKB0QjqXCbNwUqLEkaz11eD26SJE8iyjNeODeNMfxA2sw5ehwHjoSR840oUWJ2byvHucfizabtquixDKzU4x7rG0NFgRSotaTU8as2Z+n91DAyTn54WT2awssWBUDSl1ZAdOzeW3TyhkUhmwLE0GIbWztlrx0YwGozDZtbBauTRnY3IDYxGwHMMWIbGr/96Ci6r0pOxbySSJ0JyqjeAPW9pxchYHBlRgtXII5hTk6g6gd7sGtgtAhJJZSMglRU2sZp0cNn0SKZFxBJpdA+FcbInAFv2e/rcQFBzppMpUdngsesRiadx8MQIWIbOqwO1GHitTlDd5DjbH0QsmcaAL4qOBhsG/TH0jkTQ4Dbh6QN9U+rnRFGCPxjH2YEgook0ungGAs+iMdtqIpHMoC+7xt3DYc05lCRZe6aXAnGoCATComA8lMA3H3wFq9ucMAockilxzs6UyvZNjXjs+XNgGArtDYV3OgkXHmf6g7DadegbCePQSRbHusbQ3mDVnCmepcGxNGrsei2NyKjntOjTmb4AUhmleWvPsPK6zaTTCsgzWVEDhqamGDQAEEumMeiPwhdQFNjMBg7hWBqDo4rTFI6m8MrRYfAsjTM5ggL+YAJ6HZs1SiIYDcSxotmO5loL+kYikGXAlzVWxkIJxJMZ7TVgwsjr90Vwsi8A35hybEaUNIMjF1GSiwoQqLUMZoOSoifwDBIpERlRRjItot8XQSyRwbkcha/cyA/L0KCz1q8qNBFLZNA9GIJex4JjJ5T76lxGrG13YngsNkVK3KBjEct+xqneAFiGBkUB3UNh2LMRMQrQnMFYIqPNKZWWtLqymmykbdAfzStsb6+3wiCw2hr2jUTQNxJBe4NVMwx9gTjGssX5Jj2HSDwNGUo9Fs8xWg8xWZbBcwwGRqMIxVLozEYYAUUdrxiTDUhZVtbMbODR71PmlXudOK0CTvSM5cl8xxIZpDMS2uqtODcQVBwamx4sS8Nm0iGSvW6PdvmzUvVpmAwcaFpZk1xUx7HGptQMHusa04RNVBiaxvNvDCKdkeC0CFpUAVCe9fU1Jgg6JUI52XnW61jtXjlwYgQehxFNHrOiDpkStetI3eQQeAbBSApOi6hd/8DEPavW+uh1DIb8MbTVW1Fj02vHDuVcU9FEGsZJLQN843FE42nEEhm017PoG44ilsyAoSkMjkYRzblHxsNJFNKuGMieJ6NeiW6n0uKUNTudbY2wvMmOc5OEPNrqrRAlCQxNIRxN5V2jsUQGOo5R6vZoCr7xiTUQeAYMQyMaT0OGEoVSIzTBaAp8dpNlPJTA0Fgsz6FUnS2nVYA/W982PBaD0yogEE5qNUdGgdWuCYGfeCaOhRJKhNWux7FzfkTiaTA0Bb2O0dYsHEvhVG9AO982kw6pjIQhfwzpjCLgkRtRKrTR8st9J2HQcTDqOVCA5mjyHIP2eqsSEcsZaziWzs5vYg0zojSj0iZR+SMQCAseUZTwzZ+9CoahcdNbO/D4i115X4xzhaYp3LZ7JY6c8ePJl3vwX787Miu1L8LSJp2RtOvsTN+EQdrktYCeZJjkSv+qggpWE68ZFerOtOpMKb/LaHn/bE6dVDCiGAiqI6F+wQOK8ZZIKWIXqUn1FGOhBPp9EQzmqGn5gwmlDmNSwX19jQmiJOPNs34t4sHkRLWePdSP491j6B0OF5VjzsVs4GHJqYtJZZRd+XAsjYHRqGboqOMo5oipET2epQv2WRIlGamMlFcoPzAaxS/3nSrYK+d49zgCkZRWhK46tbVOI8bDSU1MJFVALnwslNDOgS8QR9dgSHPOVHqHw4UlrnMeI7k1nqIkY2WLA3y2lstpEeAbV3pKqWulzj/3PKqG7XT1oh6HAfU1JjgsAkRRmmKQA0Cj26Sk4RWwDePJDM72B7U0Sl8gjsHRKI51jSGUNS4HfFH4xuPIiDLCsTS6BkJgGTpP0EPFF4gXHAOgnIembEPqydoBwaiiQjjkVyKDkx2Q3PYAI+NxROIpPPt6P2wmHRo9ZjgsQt791JNNxzs7qR9c7j0ripJ23/UOh8HQFGoLpID7gwn0Dk+VfFev5zP9QcSy95NSJzj1Op/uGyYaTxe8FnNRG0lbJwkxqed/snhCW51Vq/fMfY3nGFiMOgg56b29kyIyDouAIX9Ucyon35M8S0+RPfcHE3mfk7sGiZSYd3wipTiOB0/6kMlI4Fkaupz6ufFJiqiyLMNpEaDPHtM9FILZwGvnu6XWoj1TVYKRFAb9UUTj6TxVUdVpVQU1ACX9VEVV8QSUzZjJTuxkSISKQCAseH7919M43jWGb/7dFVje7MCPP79TK4o/Xy7qrMHqNid+8/RpAMAN29q1Am8CoZBR3zMcLqkv0EiOwzXZ+QEm0n2AfCOxXBgFruDGg45jNEWsXHKNINXgjsTTJTlU4VgKzV4LQjmOm82kA8fSs9r8ECUZPEtrRmkhUmkRvUNhWAx83ucVIyNKmvxzIRno6fom5aYxFuoDlspIBc9t7nUzMJL/Hse6xrS6lNzojiHHWWJZOs+RVj9juibGo4F4USUys4FHOJbC+DT9jSLx4uugbgRwTL4Igwxlfft9ETR7zdru/2TsZt2Uz1bWndLU+1RyI4bReFpLe3XbDRgZj01xUtT6vHC2JtFq4vPup5kcFAB511s6I+VFpVQsRr7k+2EuUJje2ZqMGiFiGVprQ5DbNsBs4BFPphFNpJERGRgFLk/NLpUW8/oyTR6LQc8VXAeeVVQxaYpSIl/B89/cBJTrqGc4PCXKxLMMYlDOj9Wkw1gokXcO1PuXpigM+CIF70cVf4FNFzUSCmBKfzSOpTUnjGemj0GRCBWBQFjQdA+G8PATx3H9tna88MYgEqlM2ZwpQKl3uW33SvSNRPC+t68kzhRhRlJpcUYJ3WqiCk1Ei/SZSqbFKTvR5aB7Ur+pQCQ560iyLxCf1iBSkYGSnKnc44sx2aAvB7kGXyF5eX+Bz8w16qfr5VSM6a5J1eiczhko5TOnazNRzJkCoDlTjpwIwMh4vKBBP3kWalpsMeNfRUtFi5R+XcyGUDQFk8DNfOAcmesTJSNK6BkK5zlTgHLOM6KSWtozHC76PCg2ltxIUoN7IgKZykiIxhVRh3I5U4By7xdK2WPZ3Ghj8Yj5iZ7xkp4duViM/LSbWXkRLZLyRyAQFiuiKOG7/3MQjR4z1i+rwbOvD0y7QztXVrc5sXGFGw/9+QR6hkI43l04TYVQffbv349du3Zh586duO+++6a8/tJLL+Hiiy/G9ddfj+uvvx7f//73yz4Gk37+jKpykCxhR342qD2lCITzpVBa5mJiNk78QofnmJI3J2cjzlBuRsuQ3l+MUDSVl9p3PpCUPwKBsGB57LlzONsfxH98chva6q2495925PXkKSe3vW0l/v67z+A7Dx2AwyrgS3dcOi+fQ5g7oijiq1/9Kn7605/C4/Hgne98J7Zv346Ojo684zZt2oR777133sYxXyk/C5Wz/cGZDyIQCIuKUlIhFxo8xyzYcROHikAgLEhC0RQeeuIEdl/WjDfP+uF1GmCYx3SLjkYbLltbi7P9QXzz766Yt88hzJ3Dhw+jubkZjY2NAIA9e/Zg3759UxyqUgiFQgiF8lPUhoaGyjJOAoFAIJSfhepMAcShIhAIC5SH/3wcFICrNjbiS/e9gPYGK1a1zm+jqFvftgIf//e/4m+H+rFppTev0Sih+gwPD8Pr9Wr/93g8OHz48JTjDh06hOuuuw5utxuf/exnsWzZsinHPPDAA/OSDkggEAiECw/iUBEIhAVH73AYf3yhC3dctxorWhz46RevmdL7Yz5o9lqwdUM9HvzTcXz/V6/jWx/fmtcLhlBd1MaOuVCTNJdXr16Np556CkajEc888ww+9rGP4Yknnpjyd+9///tx44035v1uaGgIt956a3kHTSAQCIQlDxGlIBAIC45f/OUEPHYDPA4D4tlO7JXilmuWIxBK4KqLG9DkNVfscwkz4/V689LyhoeH4Xa7844xmUwwGpX+Mdu2bUMmk8HY2FSREYvFgoaGhrx/udEvAoFAIBBKhThUBAJhQTEwGsGzh/qxd2sbvvvwQfzl5e6Kfn6D24y3bmrE6yd9oCd3nCRUlbVr16Krqwu9vb1IpVJ47LHHsH379rxjfD6fFsk6fPgwJEmC3U6ijAQCgUCYP0jKH4FAWFD8+qnTcFgEvO2yFly+rhYWY+XrmG65ZjmeOdCHe37yEla3OfHuncsrPgbCVFiWxZe+9CXceeedEEURN910E5YtW4aHH34YAHDLLbfgz3/+Mx5++GEwDANBEPCd73xnSloggUAgEAjlhDhUBAJhwTAaiOOpV3tw/ZXtEEWpak12vU4jrr6kCfsP9mHjCvfMf0CoGNu2bcO2bdvyfnfLLbdoP7/3ve/Fe9/73koPi0AgEAgXMCTlj0AgLBj+95nT0OtYvHx0CD/+3ZGqjuVdV3cinZFRQAeBQFi0tNRaqj0EAoFAWHKQCBWBQFgQBCNJPP5CN959dSeuurih6vVLbrsBuy5txq/2nYQoybjprR0kdYyw6OkaDM18EIFAIBBmBYlQEQiEBcHv/nYWDA3svKQJbrsBLlt10v1yuXnHMsSTGTz85+MYHotVezgEAoFAICx6jELllHsrBXGoCARC1YnG03js2bNw2fT4t/9+rdrD0XBa9Xj75a3gORoWI1/t4RAIs2JyPJUCYDGQ65hAIFSXaCJd7SGUHeJQEQiEqvPH588hLcr41C0bcdvuldUeTh437+hEWpTxq32nEI6lqj0cAqFkJpf/yQAspukdKp6tjFnAMcT8IBAISwdSQ0UgEKpKIpXBo8+cxs5LGtHRuPD6BdnMOuy5vAW//uspJFMZ3HXjumoPiUCYM30jkWlfT2WkiowjLVbmc2ZCxzFIpsVqD4NAIMwDJj2HSLwy0TCyRUQgEKrKEy91IxJL48BxH9IVMuZmy03bO8GxNCiaiFIQFg+1TmO1h7DgqYQzZRDI3jWBkIvLKlTkcyrlTAHEoSIQCFUknZHwv389jcvX1eHdOxWnZSFiMfK48aoO/OWlbgQjyWoPh0AoiUF/dMrv2husVRjJhU0skSnbexEnmbAUGA0mqj2EsrMwrRcCgXBB8NfXeuEPJnDb21dix+amag9nWm7Y1gFJkvGp7z4DmTSnIixSzvQFqz2EBYXZsLjUxgo5yQSAIdkDhCpDHCoCgVAVRFHCw08ch6BjwdIL/1Fk0nO48qIGjIUSGA+TKBXhwmUpma7h2NJTG7sQIS0CFxc2k64in+O2GyryOQBxqAgEQpV47vAARgMJbFnthXMB9JwqhffvWQWaprHvlZ5qD4WwxCmHfei0lK9OgecY7WcSn50dupy1W0jwC3RccyEjkqtyMRGKVkYxd2S8cv0jiUNFIBAqjiwrMuRbVnvxD7devGjSNawmHXZc3IBf7TuJft/0amkEwvlQDvPQH5pap9DZNL2SZo1NX9ABSC1RJbxKPHvKKXxRTln7pXpOCQsfaQmmzROHikAgVJzn3xhA12AIl6z2VHsos2bvle2IJ0X85q+nqz0UAmHWnOwZn/Z1XyA+owNg1C+uuqPpWGwNuysla7/YWGy1cISlB3GoCARCRZFlGb/4y0lYjDxWNDuqPZxZ0+gxY+v6erxxZhSitPR22QhLB4NufuS6oxWUIp5vSD1k9SmHhDaphVtcVEpt1ChUztEmDhWBQKgoB06MoGsghM994BI0eS3VHs6cuPnqZRgcjeJ3+89UeygEQlFiyXy5boam4HVWrkibUH5qFkm96WyYLwlteoGnklfS2F9oVEptNJogfagIBMISRJZl/Pi3R9Bca8bqNme1hzNnWuus8DgMePCPR5ERSQoOYXEgSjKSqenT+fTzFNVaqCy2+foC8WoPYdEgLfAMgkoa+4T5hzhUBAKhYhw+PYq+kQjs5sp0SZ9Pbr92FTKijDfP+qs9FAKhZGZKcYsnZ25CazEsrrqj6RDJhkjVKYca5VK6Ji8EKhVprXNVrhE2cagIBELF+J+/nMTyZju+cPsl1R7KeXP5ujp0Ntnwq30nSS0VYUFSX2Oal/cNxSojeVwJKiHyUI4aoaVMuAzX01K6Ji8EKhUZHhitXCNs4lARCISK8PopH944M4r37FwOHb+40mwKQVEU9l7RhtdPjeI3T52q9nAIhCkUkvZfPoNsukFgQZMuqWWlnDVCziXonBHlwguPnuFwtYdQdohDRSAQKsJ//e4IAKDJMz+75tXgyosaYDXxeOPsaLWHQiCUxIkZZNNjicyS7BFTjMWWKuafJwGHxQ5Xxv5cBMJcIFcggUCYd072jOPcQAh3XLcGbkflcprnG5qm8IE9q3HopI80+iUQFiEkVaz61NjPv54mTaJci4omj7kin1PJdFviUBEIhHnn548fR0utBddtbav2UMrOto0NMBt4/Ot/vVTtoRCWEOWoMSj0HnN9X5YhaYALAWaBS4HPBd84US680KhUyt98SfIXgjhUBAJhXjnVM44DJ0bQWmdZ8H1B5gLH0rh8XS0GfBEM+JZeXvhCY//+/di1axd27tyJ++67b8rrsizjnnvuwc6dO7F37168+eabVRjl+VOK2t5c3sM9QzTAaREKpk9lxNmlAc50py8Ux0DHMVX77LmUqhEBHAJhYUIcKgKBMK/8ct9JOCwCbt7RWe2hzBt37F0Dk4HHn17orvZQljSiKOKrX/0qfvzjH+Oxxx7DH/7wB5w+fTrvmP3796OrqwtPPPEE/vVf/xVf+cpXqjPYBUr30PROvz+UmDF9ylGCzPVMZv9CcQyq2YfqAipVm5ZyOLU2k64MIyFUikptp3BM5dwc4lARCIR543RvAC8eGcId161GY4VypquBoGOxd2srHnvuHI6eI32p5ovDhw+jubkZjY2N4Hkee/bswb59+/KO2bdvH2644QZQFIUNGzYgFAphZGSkSiOuLvPV62UstHSEEQKR6ftylYNKGnWLEUF3/g5VJc4joXy01Vsr8jnpCvaZI3c5gUCYN773PwdhFFhcvrau2kOZd/Zc3oqMKOFnfzpW7aEsWYaHh+H1erX/ezweDA8PT3uM1+udcgwAhEIh9PX15f0bGhqav8FXAV9gam1KS62lCiO5sCmnUVfrXDqiPirByPwIgyyUtNJiGAWu2kOoGmf6g9UeQtlZ/M1gCATCguTYuTF0DYZw+bpasBeApK3FpMPbL2/F/oN9iCXSMFzAX5bzhVwgR4qaVIhSyjEA8MADD+D73/9++Qa3SOgeCk37OoWZ0/WWEnodW5Z6tUox6K9co9KFBkNTRVNFKWpqCuVCSSstRjSRrvYQCGVk6Vs5BAKhKvz348fQ0WjDP71vc7WHUjHefXUnkmkJD//5RLWHsiTxer15UaTh4WG43e5pjxkaGppyDAC8//3vx759+/L+/fznP5+/wedQzZ3zmep2SjFBqynkUG4WkzO1VClV2no6B4lnl841eSHgdRoq8jmVjOgSh4pAIJSdl48M4fDpUdxwZXvB6MBSxW4RsL7DhUf3n0HvEuwEX23Wrl2Lrq4u9Pb2IpVK4bHHHsP27dvzjtm+fTseffRRyLKMQ4cOwWw2F3SoLBYLGhoa8v7lpgrOJ6XsnPNliOqWs4Yq1wlMpsWyve+FwEJtHlyOa6wclEPamlyTi4tMpjLRw0pGdBfG3UQgEJYMoiTjv/5wBDxHY027s9rDqTgffsc6cCyNvx3sq/ZQlhwsy+JLX/oS7rzzTrz97W/H7t27sWzZMjz88MN4+OGHAQDbtm1DY2Mjdu7ciS9+8Yv48pe/XOVRz41UGRqVFqqh6my0Tfs3TqtQMAK10NOnFjLlbB5s0pcvlbgc1xiBMBdGg0uv9xipoSIQCGVl3ys9GByN4tufuBJO6/yojC1k3A4Drr+yHb/921nsuaINViLnW1a2bduGbdu25f3ulltu0X6mKGrROlGV4GRvYNrX/SVEC3iWXjLGuNnAI1xGh2e+icRJ3U0hjAKLaIKkbxKqB4lQEQiEshFLpPHj376BrRvqsazRXu3hVI0br+pAMiXiaz99qdpDIVzA0POUbrtUnCkAi8qZWqq4yrDxRpypxUV7hWTTSQ0VgUBYlDzw2FHEkyIu6pxas3IhYTHy2LjcjVN9QfiXYGoDYf5hy9C7SJqkQEEBqLFfeFHjpYTdPPeI90IVE5mv9K+FXr1bzabS1aZSsumkhopAICw6zvQF8PiL3Xjf21fi6kuaqj2cqvOZ2zbBYuDw4B9JXyrC7MnMQ0NKGQA1g5lp1HNlUSGkZ3iPcjiM5WChOhnFGA/PvYHthSbcsNCr/ojC5NJiYTzRCATCokaUZHz9/pfR5DHhHVd1VHs4CwK9jsX1V7bhqVd7cfSsv9rDISwgBL56RvzIeGza16Px9IwCFKVESaQZ3mM+HMa5cAGJkC5YbGWoM7UaF6aSIqEwtvOItM6GSqUWAsShIhAIZeDXT53EyHgcW1bXglkgO88LgbesbwDH0rjvt28UbDhLuDBJpCoTKah1zU/9wPlESRYalTgX55OmdyGQKkPkLBgltXCLiUrdE5VKLQSIQ0UgEM6TM30BPPzESVx/ZRv+z64V1R7OgsLjMOArd16KM31BPP/GYLWHQ7jAGBydWj8wk2w6RzZEys5kB/R8jMkmr3nB1wbNlhhJfbvgODcQqvYQyg55chIIhDkTT6TxpfteQLPXhA9cu3rGuokLkXXLarChswY/eOR1xBJE8phQXQrJpuemS6UXSCpepTCWsa9TqZxPhK9nKLzga4Pmi+lSZVmm/N895VbJJN+O1cU8zw22iUNFIBDmzPd/9TpC0RT2vKVtwRSZL0QEnkEknsb9fzha7aEQFgCGBabudSGnS0Ur0NfpQlZzKwWXrTTlyenSMzNi+d3MySqZ58uF6ggXosFtqsjntNZZtJ95bn5tFGIBEQiEObH/YB/2H+rHx9+1Hju3NFd7OAuaj7/rItx1w1r86YUuHDkzWu3hECoIP0lFziCwJaU41dfMj8GRq+A3G4W76TZMDAJxGHKZvK7ipKjf+TjUs4lyOCxC3v8nR3HKoeY4WwqlO44GSGuJC42+kci8vr8azcxNLZypafn5BiSJQ7XICEaSpFM6oeqc7BnHdx46gKs21uOaLS3VHs6Cx2Lk8fbLW7Ci2Y5vP3SA3MMXEJML7mMlNiDt982PwdHsndixLSSjXWPXF+xVNZ0qX6lzWmhwDD0vamOT13VyI+R4MgOGpuYU1Rd0LJxWYeYDAYyF8g3IyVGcmdQccykWZZttpMFcQTU+nmPAs3M3c00zpINa5jmFrNJM3vxRqaYqae5nl2sDqBjnG5AkDtUC50xfAN956DXtwfeNB1/Bt3/+Kt4868fx7jE89uxZUpdBqCjhWApf/+nLoCjg+m1EIr1UJEnGyHgcoUgS3//VIaL6R5gVpchCl5JadnZgetUr33gcsRkc/kpJHpfC+URZ0qIEm0mHZq+5jCOaGRmKMzMX6fh4MgN/MDGv4iF6HQuWofN27Iv1TJpLpMFm1sFsmHBWGJpCS61lmr+YuUaqkPR6Ki1qzuxc1it346tQFDYUm12qbDnT4jsabFq00us0lOU9i6ktVkqVdKbPnk0fNfXc5a550zzf5yROvwD5zV9PwWERcNXFjciIEroGQ/jp79/E6b4Ajnf5IUrAq8dGtOP/8Nw5bFrpwUWdbmzodIGmiZ9MmB9ESca//exViJKMH352B7zO+ZFlXoowDI3P334JfONxfOPBV/D4sm7svqyl2sMizCM6jinZCGAZSosgeBwGyLLigKvwPANMFe3LY7aNQnmOKWhERWeIOAUmiSrMZp7lRscz5xUh6xqcX7Uxg46FzazDQAHFxfNhsngIRQFs9rt/8mtWE49gpHTj32kV5jUla/L1YzXpZjwPOo5FRpxwcCjk1yQFItMLfZyv2MpcrjGjnsur0Stn77XTfQHt52H/RG+5tnorxkKJKWu80Givt2qS5nqeBcfRCM1DLadRYLUa0Z6hcNnfPxfiUFWJSDyNTEaCzazD6yd9+L+/PISvf/RyjIzF8dKbQ5Bl4C8v9+B41xhSGQnj4STWtbvw4XesR0ejDUaBQzyZwcnecZztC2L/wT48+swZmPQc9m5tw7aL6lHvruyuG2Hp85+/OoRDJ334yv9zKXGm5kBnkx2dTXZcvbkJ9/7mMFq8FqxsdVR7WIQyw7E00hkJHEuDZSiwLD2jQZubjjU8NrX5rm+8eJ2JUWBndIJUmjxm9AwrhgVNKTv7MxmjuRQ6nmVozaGabETON3azgFhiqvHvdRow5J++ifF8wLM0vE6jtsaxZGaKs+m0CkilJQg6ZtrzWojOJjt847EpSoGyrDgNDougpfqp50q99liGLsmon40zlft5c8Fs4Ir+fe57Rydl4thn+FybSYd4gbU/X0q9vu1mHSKxwsfxHIOMKMGk50pyImqdRgz6S3PIz55H36UGtwmDo9GiqaAGgYXAs+BZGkMFnlGzIbc/lKBjtOu5lOfRZGe6EOqana/gjsXAlxyJJA5VFUhnRHzsW0+h2WtGjd2AM30BjIcTuPNrTwJQvozra0xw2cz44N7VWNvhQqPHDKpAxVxbtgv0h27MFryf9eP3fzuLh584AYFn8N7dK3HVxgZYy9CJnHBh87eD/fjLyz2ocxmxqs1Z7eEsWlJpEa8eG4bbrsfX738Z3/7klXDby5OyQZh/3HYDRsanGhO5xqoqtzyXWrlSjd5cSnWmgPy6mkRKRCIlwmXTa8IAbrseTqsex7rGCv69auxYjLxmDOYau6qx6XEYCjqGKjRFgefoKelEFADPLJwhi5FHv2/q74f8MXgcBvjG49OqtdW5jMiIUl40sBht9Vac7Q+CoorXW6QyknZ98CyNVEaCKMnaz8BEcXw4O0WDwCKWyMBl1WM0OP04ugdDaKu3wus0Fj1HasRwsmE6m+vKYREQiiaREWXUuYxahI1naTR4zJrh7nEYkEqLedd6schnLg1uE4b8MYSLOB3A1Bowo8AhkcrAZtbBatJN61CpczcbeIRjKfAcA5uJL+k8qxQy7qPxNIwCB7ORQyyRKeoQTSeNr65N7t9yDF00ilbImeposCEaTyMjSmAZumSHazqKOdIttRZ0DYYQS2TmpV4y17YtZXPHnfNsKXatTV6PBrcJ0Xg677wUi6x7HQbNYcx1pmZKuyYOVYXo90XwHw8fgM2kwxtnRhFLZBCMJNHeYEVbvRVXXtSABo8JjW4z3A7DrPPCGYbGtVe04dor2pDOiHj0mTN4+rU+PPDYUfzX747AYuSx+9IW3Hx1Z9HCQwKhGMfO+fGdh1/Dzkua8Hc3rydppecBzzH4x/dtQq3TiM/98Dnc85OX8K2/2wqBSCsvGBrdJoSK2HnFHs0ttRYtDSeZFmEx8qApqqiBMHln3yhwiCYUA6nWZcxrysuzNNqzBpQa+ShEg9uEZEqEbxrVtMlOnssqwChwGIXyNyxL4+xAEEY9B0mSC6YRumx6BHMMk9x0RZWZlOwkWUYiJeY5GsDspKVr7HptPk1eM4b9sTwDaWQsBhmY8hm5O9yyXHqq5LmsE9FSa8W5bC0aBaC9wYbe4TAsRh6+QFxzElmWhl7HIp4Sp3UwGj1mnOgen9GZAorXuajodWxRR4OhKUiSnLfGOo5GMi3lrYlJr0SNWmotCISTeemKqYyESI6R2T0YQjyZAcfQYBgKiWnmqoo8OK0CEklRc/C8DgM4lkbvNJExvY7VHHd/MDFFoMCk5wpuYISzY22ttWBgNAKeo+FxGNFb4D5qrbMgGs9oDnGuMa3Xsdp1Ek2ktbFMvrZU5xhQ0tpGxhWn0Zm9zwrdv3azbtYpeqIkaU7DyhZHngOhjsFk4IpGyUrFKLBIpMrvRBXbmFKZLo1YdaZKSWVd3mQHTSvP4clBidz3z71+LEYeybQ4xSmeKdpFvsHnme6hEB5/oQtPvtyDREpEs9eMm3d0Yv0yF1pqreDOQ4GmGBzL4OYdnbh5Ryci8TSefrUHv3jyJH7x5En8/tmzWNniwLplNbjxKiIoQJiZIX8UX7zvBZj0PD5y0zriTJWBte0uAEpk+RsPvIL/+MUBfPa2zaQx8gKhdySChnqbZozlUizqMnlHNBRNwaTn8gwsQHFGzAYOAs9CxzOa45T75R6JpbGs0YZT2Sa8qYyE/pEIHEXU3ZxWAf5gAn0jkYKqZrnGSUeDDQOjEcQSGQg8gxq7Ic+hUK/AaDwNr3PiNYFnkEiJcFgExRCmADproLus+ikpQOcGQ3k7vcVQjdHcY4v1FHJZ9QBkjAYTMOo5OMwC+kYUA3VoNJpn2Na7jOgfjcJu1sFp1WtzBvKdtkF/VJszTVFTolm50Sj1FY6duE9lAL6A4sglU2JeNEcUZTR7TYglMugemqgRmmwsTr7raZpSDNmkmBe1qK8xTRttW9nigD/HKVvWaMN4KInRYBytdRYkU2Kec1TnMoJl6SnNglmGht2sgyhKM0YM1BYAaVHCTNl1yxpt8IcSefLVbrsBeoHFuYGQFqXhWRoCz8LtMKB7MIS0KGnXYSHnHZjYKChmiJ/oGQdNU2AZaop6n3pt+8bjeU5ZrdOAfp+yXoWc7snOFDBRa7VxhRvjwYT2d/7gxLz1OhYWI4/hsRi2b2rE8a4xjIeTWbEOHr3DYTR7zfAF4rCbBRgEFuFoKu9e6hrIrzlz2/UYGY+jvsYEHc/gbH9QixYXczYnUyi9LZWWtGixxcBDL7AYHouho8GK031T0wsnbwYV/BwjD+M0rRZMem5KimchBJ5FEFOf0er9JEM5752NthnHFImnNaf5ZG8AtU4jgNk5ucShmieG/FH85yOv49BJH+xmHW7avgxXb24quYFduTDpOVy7tR3Xbm3H8FgMT7/Wi0f+ehqvHh/B4dOjuH5bG9rqrLAYSUogYSrhWApf+dGLMBt47L6sBRxLopvlQpZlPPzECXQ22fHiG4P42Z+O4f17VlV7WIQshb7QOxqsiMYziMRTiOfssAP5DWI3rfQgEkuheyiMeDIDp1VAMJJCRpQwGoijxqZEVnK/5DOipBmD4VhqijMXiqWK5vLbzYJmrE2uf5i8i8uxNBwWpe4okRIxHkrAZtblGapuuwG9w2EM+WOakaFGXcKxFNIZCStbHAiEkxj0R/MMPbtZh3AshYwo5/0+d4e/EFaTDkNjMZj0HEx6TktBzE2BNOo5bV1sJh1kAHU1JpzqDeQZtjaTDptWedHgj8I3HsfpvgBMek5zjiwGHi6bHrFkWjmfsRQoKFGz3HUoltpn0vMwG3jwHA1/MKGtbyiWQr3bhHRGgi8QB0UB4+EEEsl8A59lFbl2i5EvuCaSJEOUZBj1XJ5DEwgnpk3fD8dSkLLnX1V+84eUdVzWaJ9SX9Nab4WvQJRA/UyPw4C2Oiu6hkLa5kA4moKgY7F9UyOeerUXrbUWnCtB2KPWacTyZgeef2NA+53LKoCmJ3oFqc6j1axTasIy0pQ0uIwow27WQa9jYTfrtCiC1cgjmsjApOeQTItor7cinsyApimkMxLGQgk4LIJ2/PJmO/zBBASeQb8vgga3CTzHwJzIaJsjFy13o993Lu/z7WYdBB2rfE5KnBJxUlPQMhkJNE2BZxlkxIlzXOcyQscxEHQsbCYdDp8eRTrrAAbCSTgtAtx2A2QozpkkxRGNs7CYeCxvsuNEzziMAot6txkne8a193Va9eA5Ji9tj2VoSJKspNcWcP5ysRh4pT4skc57hqRFCTU2PTKiBIFnMeiPotZp1GwBs4FHg9uEcCyFvpFI3jPNYRGg4xiMBuJ55zEUTWnpjl6nAan0xGsWAw+GoTTnmmPzU/p4lgbPMYjE00gWUB+0mXRw2fQQJWniusrWs1qNPEZznPnJaZa59+LQWFR7v1JrTMlWc5k5csaPbzz4Cj76rafQOxzGltVe/OdntuM9O5dX3JmajMdhwLt3LsfD/7ob//B/NiIYSeKL/98LeO+XH8e+V3qIjDMhj2g8jc//4DlE4yl842NX4F1Xd1Z7SEsKiqLw6VsvxudvvwR33bAWjzx1Cn96oavawyIAcFoEzTBtrbNokskcy0DgGdjNwpR6FLW/k5JCJaLebYLAMzAKLCKxNCw5+ffnBoLITDJubCYd0hlJ+57I3cE1ZI3HyTR5FOEhXyAGgWfQWmfR6rcAwOPQo8410SfImN2ZzzWYwvE0Eikxb9ff4zAU/FnPs0hnJNQ6jVi/rKZgiloy+16TGxOr3y/unB5XuX18KEoxwCLxtBaFMQgsJFmGjmPA0BS6h0IYCyVgN+vQ74tgNBAHyygGlsMioLPRho4GGwKRJEbGYrCadFoWSCSe1mqOJVlGKiMikRTR4DZh00q3Ng51HQwCm42IKXQ02NCe/ft4MoNwLIW6GpN2DgAlUnisa0xLuWQZGsNjMc0gq3UpQj7ReBrDYzGc6g3AbOBhzzbgXdFsx8oWB+pcRsQSGQQiSe06YGgKkpzfKyi3NIChKfSNRCADWNXqwMh4HKd6A5pDOB5OYEWrHa11E/LkuQ6Wen1yDI1al1FrCqzjGVyzpRmhaApD/hhMBh7NXjM6GpS1BiauKzXy0+iZKojltAlIpDKgKQouq4BljTbEkyLiiQyaPOa83mcOiwCaAnhOqSdXJdUZmoLFqNREqWJdANDZZENLnQUehwFGPQe9TrlOjXpOu3duuWZ51hmVtfO585ImJNMizAYeHENDxzF5LQHsZsU4NwgTvb8MAotwLIVILK31ijPnXMft9VaYDTyG/FF4HAaYDByaPGZQUKPDUWQkGYlkRnOIDHpOO88cRyMcS0HMXoeJlFIL1zMUBk1T6GiwoclrAUNTcNv1cGXHFUukNWfKbtah1mmEwDEQJTnvnuJZGk0eM6wmXotmq/dZPJmBy6bPe1bVuYywmXWQJFlzNHMl7N12PSRJVjYYWBp6XpnHug4XmrxmMAwFq2ni/epr8sWsaJqCxzFx7kPZTYH2BhtkeSLF1Za9l1MZSbs2g9Fk3j3Q5DEjEEnidF8A5wZCaKuzosauh6Bj0dFgw45LmtDgNmFZoyI5r0YEDTpWu8YcFgErmu3wOpRxhmMptNZZ4LIK2vVeDOJQlYGMKCGVFvHmWT++fv9LeP71Ady8fRl+9Lmr8YUPbqloI7tSYBkaV13ciG9/4kp8/gOXoMFtwnd/cRB3f/uv+Op/vZgnx0m4MIkl0vjivc+jazCE7Zub8owqQvnwOo0wCBw2rfJiRbMdP3zkdbx6bLjaw7rgUQ1cQNk9N+gmUoQMAlewnwzPTfwuk5GQSktZ45xCMi3CILCasUZRFAwCm2cMUJRi6McSaVy6xptnlNa7TfA6jVjeZM/7TDW1iWeVlCVRlLW0QI/DgBXNiniM6tyoDoycdaj0OhZNHnNezyEhaxCtbHFgZYsD+qzsNwVAx9NoqbXAZtbBZtZp4zcKnGZUcywNl02POpcRbrsB79zeAV02pQpQDBajngVFKcYTxyhKiLKsGP1WEw8dx2j/JElGMi1ClGR4HQY0uE1aWpVJz2HQH0UqLWJ5kx0MQ2NgNJJdM8UgomkKyxptaK2zgMomAymGmoRgJIm6GiPCsbR2/tR12NBZoxjaLI06lxGn+wJ5ymSrWh24dLUXRj2nnZfJvY5Yhkajxwxv9vkp8CzqXMa8fmFNXjOMgrJ2UrY3ldWkQ2ej4sBRFIUVzXaIkgy9js3rh1RfY9Ia6/IcA4/DAIPA4Wx/EFL2eOX8sKh1GtFQY9bO72Ta620AlIgEBSVKpTpj3YMhzRFTUl4p0DQFjqUxEogjGk/DbOC167FvUtTGpOcgijJC0RT0OhajwQR6h8MwGzmYjUpkRHXQ1DtiebMdLEPDpOc0R8ppFVBfY0JGlPM2gBmaxqAvin6f4lDGkxn0DIdxqjeAvqzTEwgnIWaV9ZCd36GTPvjG4xCzdWXLGpU1UK9lhqY15+TqzU1Y1eqAxahDo9uMWE4kRz0H6v1d6zJi16UtWNnqwKVramHUc7CadFrUVU29lKE8NziGRjSRQY1NDwoU4skMDAKLBrcJHQ02eJ0GvGVdnXKNsTRM2R5eI+NxLeKibgDVuYywWwREE2ntOUbTlPYMo2kKRj2HOpcJbfVWeBwG1LmMSGVESLIMgWe16JHTImjjDkZT2LqhHgCQydmQOdMfhD+UgJh1gnZsboTNrINB4LB5lRcbV7jB5WwC7L68FSuaFbXbzkZbtuYvqTkrNTa9Zm/kpi8HIkk0us14987lWlSw0WPO2xwy6rk8h03HM3mbIhQomA08WIYGl40Sh2MpxLKO5MoWB2gKiCdFdDbbwNAUKEq5b2mamrF+kThU54koSvjIN/bhcz98Dv/0n8+iwW3G9z/zVtyya8WCT4+iKAqXrq3FD/5xB/7t7q2wmwW8cnQYX/vJS3jy5W4Mjkaq1luEUD3GQgl87ofPYXA0ijtvWIN3k8jUvHO2P4hoIoPNq7345oOv4HS2doZQHU73BeC26yHwDFiG1pwU1ZDR8QxWtji0XWKGprR6Jx3PYt0yF5prLXDZBHhdBjR6zEgkRUiSjJUtDrTUWkBRFDwOg2aEJVIiWmotaKm1aCktKixDY027E6vb89U1dRyj7aIDQM9wGMNjMTitAtIZCR6nAeuWubCuwwWXTQ8dr3wnubMGC8vQ2LzKA46l0VZnxcoWR0HRolqnEStaHLjq4kbodSxO9wZwpi8Aj8MAvY6FyyaAZ2ms63DBbOQxGogjEEli55YmcCyTJ1BBURSaPBasaFbaBaRFCXUuEyhKmY/VqIOOZ5AWJQg6xfFSHZVdl7UglRaVCGCNCe0NVixvUqI6FhOPY11jiCUyuKizBi6bAU6rEmnsHQ4rRnPWCLdbdHBYdHj/tasw4IuCoihsXOHBskYb6rJRJFlSzvPqNmdemp3ZwIOiFBEShlHk8dVIiS8Q184voBiBuREoQEltbHCb0Oy1YGWLsgZqHdjJ3oB2HTEMDYOeQ7N3QuG3xqbH6hyF1WRahJA9p2JWMj2dEbVazJZai6JulpgQWrCZdRB0DCgK2LLaq73Xmf6A9jPHMjAbOM25vGxtLa6+pBlGQWn4q94HTV4z9DwLHaccL0kyrCYeMqBF8wBlQ2BNuxN1OVHLREpEMKKktqqfE4omtVouKRvADcdSONMfhMAzaPJatFRGpXZPSRkEAFN241p1yPZubcPGFW7U2PSQZeBUbwCiJKOt3gaP06CJWjR6zBBFCZIsQ591ViVJSStkGBqJpCIgFoqlcOVFDdi2sQGbV3lQV2NCW93EHNW/8wcTONkzDo5VFCzV8xmIJBGIJNHkMcNu1qHRY0aTx4x1HTXgWBoMTU1JL5VlZJ8xBqzIXis1dj3WdbgwGZ5XorSRmNKSR31mWI08Wuss2j2vXotmA4/xcBKReAosS6OzyQ6TnsPyZjuavRaYDRwuXVs78f6c8sxr9pq1a85s4NFaq0RvxkIJ9I6EYTby2HlJE1IZUdmE4Zi8iBbL0Bjyx3CyZxz1HsVhNBs4ZSPGqodRz4HJ3u/LmuxKNIlSNnh0vPK862hQ1p2laWxdX6e99+ZVHrTWWeGy6tGYlYBXU1r7RsJ4ISfdtLnWghqbHjazDvU1igLgppUecByD7qEQLEYdREnWNiDcdsO0gkAAqaGaE6OBOH67/wze+7YVeOHIEELRFILRFD7+rg24enPToiwsX9HswFc/dDnO9gfwq32n8H9/eQgso+zMffuT26Yo6hCWJl2DIXzx3ueRESV86+NbC6ZuEMrPZWtrsXmVB5Ik45/+81n8y49fwL9/YhuJDFaJ+hojxkNJWEw8nBZBi8REYmktpU5Ng3Fkd3EDkSR843F4nQbYzQLePOuHP5hAfY0JPMsgnkiDgpLupdZ1DIxGYcsa6xSUiJHVqMPwWAyJZAbLm+xIpUU4rQIcFiErCqEDQCGVUWq41MhPS60FqbSIkfEYeFZJXXrj9Kg2J72OQTIlQq9jsbbDhbP9QXAsDUM2OuILKAXtnU12xYjtC2A8rOwcD/mjkGUZgUhSEQzQsYoKoCwjk5HQXGtB73AYl6+rwzMH+tDZaMPWi+rx/OFB7fMtRl4p/BZYSJKMVa1OBMJJLTVLlpWICpNNa4onMxgLJmDS81oE4PApHyKxNFiGQr8vgq0b6jWHNCNKWrNQUzYSZzXpsHGFGyd6xhGOprT2BJGYElEReBar25xgaApHzvq1iFI4lgab3R1XjdzOJjsSyQyavGYsb7ZrG6aBcAKjwQQMAotmrxmyLGt1XrU5vfqavGZsXunBL/edhN2sy+vj11ZvxfHucXgdBog5VvXla2tx9JwfowGlzm0snMCZHCEAjqU1Z8ti5JFMiaixG7B9UxMOnhgBAC11TDXI1y+rAcfQOHxmFLKsRBVO9gRA0xQYmkKTx4xlTTaEoilNeU51spu8FoyFEloaZWudFa11VjxzoA+AIrgSiipRR7VeZ0WLHRuWuWEz6xDLqUv0OAyQZDkvSpsrad7kNcPjNODgcWUeZgOv1ee11VvBZ3u7qVHHGrseOm6ir5fTKiCezCCeyIBjaaxpd8Gk5/C3Q/3ZKHAtamx6HDrpg8CzYChKixTGkxk0uE1KdLLGhGAkP7VMvWd0PANnjrNcX2OCJMlgGAp8Nrpqy1Hwsxp5CDwDmp6I8KnrazXpMB5OoMaux/ImO+LJDPp9EbTVW9HbF9aiZrmYDTxMesWM51kGTqtSIxZPZsCzyntyHIOeobCWspibEjw8FtOc+kaPGd2DYQQjSQg8g2girW1AeJ1G1LqMeOP0KLqHwqivMUHgFSdeVae1mngkxjI4dNKHi1e44bQIoCjl8ww6DjV2vXavqimwFCg0esxIpUUM+WPYuaUJqbSEo+f82hgVgRQBGzprcKJ7HK8eG8aqNieSaQlyVqBG5Xj3OMZDCWRECX2+uPZspSkKHocRbXVW9GY3LxIpETUOA9ZmazTXtDnBMDTqa4x5yohqBCwQSRLZ9HIhyzLGQgk4rUpx3jMH+vDmWT9O9QZw1cUNuGPvmrzc28VKW70Nn33fZvT7IvjvPx3D84cHcOfX/oKt6+tgNetw01uXFUx3ISxuZFnGH5/vwk9+dwQWEw+vw6Tl+xMqA8vQkGkZFEUhlZHwLz9+Af/vR68gPeSqwFUbG/HEwSBCkZRS85GNANW6jBjOKl5RlCKIAAqoc5lAUxRCkZRmaPMcjbXtThw9N4aMKMNi5OGyczjepdRNLG+yo9ZpRDyVgcXI4x1v7UBGlBVjJp4GRSmpP4OjEaxpn9iRtpp08I3H4cjKMKvXh17HQq9jkUiJsGa/i/QCi3g2Pe4t6+rx+imlYdPwWAyNHrMWaQCUVKHL19WCYxl4JAPMBg5HzvpB05TmBNYKLAAKDdkURLOBh6mRn/KsYBgaHMtgRYtDE+Iw6pV1YWkaJhOHkfGY9p3Z6FFSqFTngKKUYn6WpTEejiMUS6Ela8wLOgZ6HQt/KJGneMcyNK6+pAlr/DEtigEojsbOLU0wCBxOdo9PSbVU6juonJQpE4LZ866+7huPYyyUwK5Lm2E28Dh2bgw6nkFbvRV2iwC7RcBVGxtA0xT2H+zXnIfc9TUKHEwGDqvaHIjH84Uo1GJ4m1mXJ+1MURQyGVn7+0Qqo23YMgyFrRvqIUqyFn2xW3RY0+7C4GgUfSMRzSnQ61jwORkzvkAcTquAkz0BZc41Rly+rg6/3ncK0UQGbdn0P9VRUukdDiNaQAygrd4Ko57D8a4x7TocCyVg1LO4amOjdpySBuaBLCvPuZ6hMDiWhtthQDKlCEmo4i49w2HUuYwQdCx2XtIEnmNg0nMIRlPZVCwqrz2Aev6cVgGxRBpvnB7Vam2WN9vz6oJkWUl94zlG2yi4bF2t5jiuaLZj28YGAMo9r6YqFmL75kYcOePH7sua0TWo1DmphrwM5bu10WPGyhZHXt8w33gMo8EEmrPRTLtFhzVtTmQkCV0DIViMvKLYxzHgWBqBcAKT9SANAouLV3ogSjK6BkKgKQqNHhNGx+OwGBVHTuAZ+IOilsanpq3JkNFeb8WW1V7oeAaBSFJJJ8w2G1acKJMm7NDZZMd4KIFBfxRr253oG4lomw6A4tDpOAY8xyCWzKBvJILWOiv8wQRomkIwnNRGv+vSZoyFEpqS6Zm+oBaZqjHpgKwOiMXIIxBOIppQ+kc1uBWVS2WjhcvrdWfJ1sEx9ESrCq/TiCavGTRNoWsgBIdV0BwqfzCOk93jaKu3IppIa1GxVa1OROMZmLMObDqTbVgucKiZoV8kcahK5Gd/Oob9B/vx/j2r8MRL3RgPJ+GwCrjnQ5djfWdNtYdXduprTPjs+zZjZDyG//3rafzx+S4t7/z6K9vzHk6Exc3gaBQ//M3rOHjChxu2teO23StA0zRxnKsARVG447rViCcz+L//cwj//INn8bWPvAV2c2G57AuNQCCAv//7v0d/fz/q6+vx3e9+F1ardcpx27dvh9FoBE3TYBgGv/nNb2b9WS6bgAFfFL5AHC6bHrVOI+pyHCpASY81GxXngKYptNVbNSNO3aFWaoY4uLPy5DW2BHhO2aW2mXUIDCqGzLFzY7houSKOYDUp0a+DJ0bQ5J2IEut1LDYu9+C3+88gmRa1HXVA6bkUT2XgtAiIxtO4ZksT0hkJb571Y1WrM2+H22ER0D8SmWK8q84gTVOodZngdhjx7KF+bFzhxmggjjXtLpzonlAWU7GbBe0aXdfh0lIL1Qjr2g7FyG+rs6LBY9aiJ75AHMlURjNeVQNeHevl6+oQi2eQSGXgcRiwtsOFYCSJh584ASBfDEB9v0QqM2Vean2QLCupXF05qnQvHhmCjmOwtsMFmpqok8idg288jtFAHAeOj2BDZw1GxmNKmmS9FSxDw6jn4AvEQdNUNsVPh2AkhWRKEScZ9scgSjK6h0K4ckPDFEdF3RGf3CcHUJwsMdsPrMlrx7oOFw6cGEFLrUVzptUow+ZVSgpf73AY4ZjiBGxZ40UomsrLnFm/rEaLSL16bBhWow7haAoyALNxaiRERV2byX0yczMZRgNx+AJx7N3aCqMw1U545egwTvUGcNnaWmzb2ABJkkFRwOHTo+CzBnmD26Sl/qUyIobGYti80gNJlmE2cJpzUF9jQjCqGM/q9xVFKVLusUQGNXbld7l1Y6vbnIjE0+gfiaBrMASzkYfLKqAmRzSMoijtXHidxrxoosryZjvGQ0nt/JsMhW0inmOQzohIi0rUx+tUnEeTgYcoyaApaI21V7U58dzrA6irMSIaz2h21obOGnQ22vHa8RE0uCfWWhRlRZq/1oKeIcVR2LjcjWcO9KPfF4HNooguKPVnekT6g5rMvTq2RErEWCiBuhoTlmdr9QDlGcGxNFa3ObV7waDn0OQ1w24RYDLwWZXIuHbeV7U6sbrNiUQqg5WtDlCUklpnMfIYHI1q761GNgGlniyZFgtG4Na0u/DsoX6tX4GaMqoqCS5rtIFlaU3FTy+w4KKMloqsot7D5pwNDq/DgCbv1JpCg8Bh28YGyLIMg45FKutQLWuy4ReHTxY8xyrEoSqCLMv44a8Pw+NUGs6d7BlHMJLEt372Kla3OfG5D1yCS9d4Cz4AlxJuuwEfesc6vGtnJx59+jR+/7ezePTp0zAbeXz2tk1Y2eqc+U0IC5JoPI3/ffo0fvP0aZgEpfB379Y28Bx5LFSTVdl76p4PX4a7v/0MPvGdp/FvH7+SpP8BuO+++3DZZZfhrrvuwn333Yf77rsPn/nMZwoe+8ADD8DhcMz5s/Ze0YbfPnNGS12ymXVTjKZUWoTTIoCmaa3gfEWzIlCgCirwHAO33QCHVUAmK9+cS5PHjGRKzMtwyBUmmdyrsMaux2VrvYrRmBPpaK41w2TgYTby6BkMYzychMXIa0Z2LmoKt1rrUwyGprBtYwNGxmJ5vbQmM+SP4kT3OLZtbMirF8qdYyotYkWLQ5Oy7myyY+Rgn5aSlotJz+HKi+oLfr+qRtkl2dqvXMZDCQz5Y5qxBig7zM8fHkRbvRWNHjPqXKa8hp0MTYFhKM0RHsnueBsEFpeurdXWqr3eCpdNqfFY2+HSnIpwLIWzAxM9f1RjTHUUWuusWNHswDMH+vIcVimnmL6t3lqw0SygXHddgyE015rR2eQARVG4eIWn4LG57yfoWGzorEEgnMSxrjFF8CAnXVVlXYcL8VRGi0RMdpZyaW+woWc4jGi8+LVg0nNIZyTU15g1x1F1mAElErNzSxMaPRZtLQDFERocjSIQScLjNEDO1lCJogzfeAwZUYIkyRjwRSFKEliazipb1qCzya5EQoNxnOsPwWUVcOnaWrCMckyuse6y6eGy6bXIxtp2FyLxdFYIgtOc5JlQHa1EKoNoPJ3X30tFlmWk0xJ8kSTgj8EocFjR7IDAs/AF4siIkuKsyTLi2Y2Ty9fVZv9WqeUcHI0inZaQkWRckq15U6MmqbSo3ZdbVnuRSGXw7KF+7Vr0OoxwWfUIx1LwOAw42x+E1cjDZtaBZxlEYmkMj0Ux5I9pipU0TWF4LKalq+aqU9PURJqp6sy77QaIooRnA3HIsiI8YjHymqNCUTJAKdEmi2mq01nvNiGRykx5vpgMnHYtOm1Cnspp7jPNNx7D6b4AVrY40NFg04RdchF4FptW5t8zHocRrXVW9AyFCl7PGVFGLJlBR6MNm1d5wDK0tjFTDGI55eAbj+MPz55Fo8eEAyd8eOnNQaTSEniOwaoWB27e0Ykr1tflFVZeKNjNAm7fuwY37+jEg386hr+81IN//P6zWN5sx+Vra3HlRQ1Vl4UnlEYilcEfnzuHX+07iWRaws3bl+HGqzrQOxLWagwI1afWZcI1W5rwytEh/P1/PI1PvGdjXhH5hci+ffvws5/9DABwww034LbbbivqUJ0vFEVpzsFFy91T2krIsnKMJEPrIwNASx2JxNNI5OwGqwb7n1/shqBjtHuNpik011rynIBc47wQq9tcCEVTOHhiBG31VpztD8JuEbCs0a6kZCVFHDs3BoFX+t0sa7TBICh9hIx6RZFv64Z6zZhd3ebUCs0Loe5Q64ocI/BswR1m7XUdq6UtslnZZodFh52XNCNdpDdOsc1Kh0XAu67uxMi4EvXJdQCWNzuwvDnfieZYBh2NtqIbEpeuqS34ewB5tcM8x2iCEDxLa2snijIoAB6nARYjj5M943DZ9GifJLFc7FwCSqRzaCyGtgYr6lwmmAycllanNgTWcWxBZ0epo8vAYZn4/m30mLWokcmgpEYVW0+7RYAdwHgoCZdNr8n/F8NjN6C5tnhtraBjUZuNDtjMurwoKgCs6yie0WMx8ljebFf6MMkTSpRrO1wwCEp/qUaPWRMHSGVEDI/FkBYlrGp1os5lgsdhxPBYFGw2/WtydKl7KITxUAIbOt3wOJTP2bzKq13/s60bznVexoL5myUGgcP6zhrNsVy/rEZTjMu/Hilts2Yi7VWJwMQTGaWmMiVqDpXq8FnNOniy6a08pwiNyFA2HeprTDAbOQz4ojDqOaxpc2qpquuX1UAUJTR4TDAInPbs6R0Jg2eZoteqKMkIR9NTet0xDI2LV7jx6vFh+IOJvL+PJzM4dm4MY6HElJ5iQLZVgsOAcwMhqJf3hs6aPDVLu1komvpuMwl5DrDdLEzbxPct6+vQPRjS7HiDwBXVPehssoOm1Og9jc2rp9/IuOAdqoMnRtA/GkEklsazh/rRPRQGBWBlqwPv3N6JdR0udDbZFrxiX6UwGXh89Kb1+H+uX4tXjw3jj8+fxU//cBQ//cNRdDTacOlqL7asqc1TJiIsDCKxFP78Yjd+u/80wrEM1nY4ceSMH9dc2pw1uuwzvwmhYrAMjY/ctB7ve/sqfOeh13DPT15CR6MV//qht2jSvxcafr8fbreSFud2uzE2Nlb02DvuuAMUReHd73433v3ud095PRQKIRTKb0g6NDSU9//B0SjiyUxRA6PRY8KqVgc4lsHzhwfynIOOBhtiibTWcFclmkgjkcrAbTfg8nW1ecINKmqUYzyUgFHPFVTesxh5vGV9HVJpMa+fkGJQSWips8Ck53DkzESBd+7Obq4RMdNmmNWkw+ZVHhgEDssabXkRHkAxnCfvABdDFCV0DYbQNRiasq56gS3qYOUSjCQx7I8pSntFZMBzmdwTa1mTTYsQ+QJx0BSV1wdpJg6fHoVBYLGhUxFbWLfMpRmlzxzoQyCc1IxfleGxGMwGDgZB6ZOU2wi6Kav4RuXU66k7/PU1JlhNOniKbHbRlKIC15LTXyo3MmQQOE2QYjpWNNvR3mCdVoDKYuQRQkoTZZiM2cDnRWDXLyu9HMLjUIRgLlruxvHuMa0XEQAtOpFOi+jN1lYNjkY1G2MsmMg6YEoa46meAE71BAret3R2E0SFoqjzep4as7U8uW0TJnPF+jqt99RsoCgK6ztrEI2nweQo5VEUhfXLFKcjvy8ZjRXNDoyFEoglMkilJbjtSh8tJttfbKIGj9ZSZhlaeY9VM2QcCTyLjSvcBV8zGXisbnVN2XgyG3isbHVgZCw2JXKk0uA2Kz3DstfVZOcpVyVwMitbHZqCJaBE8LfZGxCOpXAgK2iS/1503mZHsWcfTU1Ea19+cwhb1sy8mXnBOVShaAp/eakbNXZF3eWZA31IZSSYDRw2Lnfjprcuw6ZVnim52YR8OJbGZWtrcdHyGjzxYjesJh1ePT6M/3nyJP778ePwOAy4dE0ttqzxYlWLQ9u1JVQWWZZxpj+IJ1/uwb5XepDKSKivMeLfP7ENDougCa0QFi5GPYfPfeAS/Ocjr+Nvh/rx4W88ibesq0d9jRF7t7YtuY2LD3zgAxgdHZ3y+09+8pMlv8fDDz8Mj8cDv9+P22+/HW1tbdi8eXPeMQ888AC+//3vT/s+iVSmaOsIm1mHl98cwsi4oo538UpPSQbTu67uLPhFn4skyZBkGYdPj6K1zoKmIlEDlqGn9EYRRQmJpIj2BhtYhp42MjIbVGOnrsZ0Xlka06ngbi7RKat1GqHjmTyhhdmQ2+z4eFYoYJtdWSc1LWk6MZhVrU7NyLtifR1omsLrJ33gOBqXrq0tGEk63jUGm0mH9Z01WL/MledIM9k6nEI4rXqMjMUxxiZQp5u67jRNabV358Prp0dhNnDTbqyt7XBN6/CuanXg3GBoSipmKXgcBi1qwzI0JEpp6Jx7/eoFDhevcCOdkTA4GsWyRhscFiUikate1+Q157UdyCU3elcOBJ7FihaHpuxYEIrCeCiOE93j2LLaqynjlUqha6OQCBpNU6irMcHtMODcQBAsQ8Eg5Nd3FRPXAHDeddPFNiXcdgMMeg62Ail/6riL2SGrWp154i6TCUVTqHebyq5EzTA0mrxm+IMJxBJpMPTMa3NBOFTPHurXQsQvvzmkNedrqbXg2itasWVNLZY3O6bNHSYURuBZXHdlOwBlN0wpTFYKJfcf6sNv95+BSc/hktVeeJ0GtNVbsWV1LSRJybU1G3my7mUmGEngdG8QZwcUR2pgNAqbWYebd3RqO1pquhFJ8VscMAyNu999Ed739lV46Inj+POLXZBkGaf6AtiyyguWpbBxuadgJGOxcf/99xd9zel0YmRkBG63GyMjI0VrpDwej3b8zp07cfjw4SkO1fvf/37ceOONeb8bGhrCrbfeqv2/1mWckt7icRowOBpFk8eMm3d0wpiVLVYb0eaiGpa5zd1Neg5GgdVqswrxt0P9AIBL19bmNbcshPoZqtFlzRrtzxzow/Jme8GC+moi8GxRJ6/UzQFBxxZ0LuZCa50lz5Ccbnwqucasullo1Cu9dIoZdq11Fi2FdLYZL2PhRF6EYibm4kTHE5kp11qT15znQLHM9GJFDENrDVrPB4uBz1Nw1N6fVlLjglkVt0gsDb2OnRKBa62bKlQz35gNSr+n7qFwXn0coNiggCIeMltnai6wDF3QMd64wj1tau/5cvScH6IoY22BPll73tI6p/ecKXJ8ui+AcDRVto2jXHLFM0ph0TpUoighEk9ru0iHT/vAZIsU3zgziseeO4fWOiv6RsLoHVY6ZVtNPNYvq8HbLmvGppVeUvMzD3xw72rt56svacLPHz+O1jorXjk2hKde7QUAuKwC6t0mvH5qFNdsacbqNgdOdI/jTF8Qf/9/NsJs4HHw5Aja6qykD1IJDPmjePSZ02jyWHC6L4BnDvYhlZZgEJRCzPZ6K2592wrUu8laLnZsZh0+etN63LprBZ54sRsvHBnEN197FYCSNrRppQdOq4CWWgtWt7uW3GbF9u3b8eijj+Kuu+7Co48+ih07dkw5JhaLQZIkmEwmxGIxPPfcc/joRz865TiLxQKLZfp6kckKUICSV680m6RmbJXBsQwuX1eXt2P/whuDGPBFUFdjmpDmNufv3F6y2qs1up0JjmWwZY13yljNBn7a3WiCQrHo32zpaLQBUNLtal1GdDblG7STP2fjCveMkUoVq3F25zKWSINl6FltsLQ3WKccXw3HBFDqDyVJBopkoFmyzWqD0RROdI8vmE2DJq8FMoCugfxU4o0r3OedWlgO5jvzSq9jC4rMzCcbltVMSTMEJp6dtvNsOxJLpDE8FivpOVH1p+2QPwqeY2Az6RCMJnHs3Bja6q2QZBkvvzkEfzCB9ctqEI2l8bPHj2Fdhws1dgOOnvXj9dM+rGlzIhBJot8XzdsV4FgaFiOPjcs9uHlHJzqzPT8WY9PdxUprnRVf+OAWAMCtb1uBYCSJo+fGcLovgO6hEGqdBjx3eABPvNSt/c2Hv7FP+5nnaDgtetA0MBpMYPNKD+wWAYFQAlazDsubHTAKLJJpEc1eRZpTlV1dTIakJMlIpRXp0FRaQiojIpUWEQgnkExJWuFt33AETpuAWCKDV48Pg82GoIf8EYiSkvPb3mDD1g31uHiFB5dlVY4ISw+rSYebr+7EzVd3wh+M4y8v9aDPF8YLbwxi0K8U5CpNKY3KjmG7E821Vuh1iuKV12FU+sUIrNJoklIaTS709MG77roLn/zkJ/HII4+gtrYW3/ve9wAAw8PD+MIXvoAf/ehH8Pv9+NjHPgYAEEUR1157La688so5fd6WNd4pu81A6ZEUYKpK37plLjR6TOgfiYJhaLxlfd2U+3S2jlAhx69YrUM5YRgamRJqnhY7Rj0HsUj9RyEK2Rn7D/aho9GmpRuqR9AlXEu5fchK4ZWjw7AY+VmlAi4UpwRQFBYL2MgaFEWhyWuBKCrqdwuJZq9lirDHhVJCUg0HXLnXpt5DPFdcXGM2ROJp9AyFS9rcp+RCrt009PX1YceOHdi3bx8aGuY+2N/tP4OH/nwcsUQGpQ6AogA9z8Bo4LUGYk0eE5xWPYx6Hh6HHvU1SkPSYkWThIWHKMmIxFIIx1KIxNIIxVIIR5MIRFKIJ5Ru4d1DYTjMOoTjafQNhyFK8pRUnFxYhoaOo5FIKf0NbGYdMqIEfzCBFc126HUseobDoCkKTV4zMqKEk93jaPIq0sP+YAKBcBLtDcoD4lx/CGYjB6dVj1hC6WHR5LWAY2kMZ4st61wmSLKEM31BuB0GmLOpCb7xGOrdZiTTIob8UVBQjKx4UtQaOs4EQ1MQJRm1LgNMeh7RuNI0cm27C7UuIxo9ZrQ32MqeR0xYfAyPxXCyewyReBonusfx7OsDsBg5hGJTG3LmUusy4r5/vvq8Prtc3w/VYrGPv9LEEmlE4mmSOlwCrx0fRludNU9Wvm8kjFqXCRSUNE+HVcDaWTpPhYgl0uBYmohpEQhlQG1EPdP3Q9UiVOruWTiWgkFgYTcLoGggnZZgMfEw6Xmt47Zex8IgsOThsERhaKWnwXRFwIVIZySMBeM43j0Gs0EHSZZxbiAIfzCB1joLkmkRB46PwG4WYDHyGA3EwTIhmA08MqIEjqFBU5TWHI9haMjyRLM8UZIgijJkWZGmzYiyViyeFiVQVLafiKz8jmNpyDIFZHs1CDyDBK84/nUuI3QcAzY7V7WB3vGuMVy8wg2HVY8hfxSJVAabVii1MCd7Amivt6C51qr0NZHlgjvRBEIuucXduy9vxSdv2QhA+VLoGQqh3xdVmsymMnjpzSHYTTo4bXo4raR5MGF2KFLsZPOyFAr1jspt0up1GsqW4k7OCYFQPkrNSKiaddbgNuc9TAiE2cKxNDxOIzw5qQqTpXuv29pe6WGVjWrlrxOWJhRFobnWiubaieuqHLvhBALh/JncP4tAICwuSIEFgUAgEAgEAoFAIMyRWUeoRFHJwZ/cAJFAIBAIFzbq94L6PbHYIN9vBAKBQCjETN9vs3aofD4fAOT16iAQCAQCQcXn86G5ubnaw5g1XV1dAMj3G4FAIBAKU+z7bdYO1Zo1a/Dzn/8cNTU1YJjSRSLUhok///nP4fV6Z/uxC46lNh+AzGkxsNTmA5A5LQZKnY8oivD5fFizZk0FR1c+GhsbAQAPPvgg6uvrqzyaxcVSu+YrBVm3uUPWbm6QdZsbM32/zdqhEgQBmzZtmvOAvF7vkpKjXWrzAcicFgNLbT4AmdNioJT5LMbIlArPK/1i6uvrl9R5qyRL7ZqvFGTd5g5Zu7lB1m32TPf9RkQpCAQCgUAgEAgEAmGOEIeKQCAQCAQCgUAgEOYIcagIBAKBQCAQCAQCYY5UzKGyWCz4u7/7O1gslkp95Lyy1OYDkDktBpbafAAyp8XAUptPMS6Uec4HZO3mBlm3uUPWbm6QdZsfKFmW5WoPgkAgEAgEAoFAIBAWIyTlj0AgEAgEAoFAIBDmCHGoCAQCgUAgEAgEAmGOzKtDFQgEcPvtt+Oaa67B7bffjmAwWPC4UCiEu+++G29729uwe/duHDx4cD6HNWdKnQ+gNAC74YYb8KEPfaiCI5w9pcxpcHAQt912G3bv3o09e/bggQceqMJIp2f//v3YtWsXdu7cifvuu2/K67Is45577sHOnTuxd+9evPnmm1UY5eyYaU6/+93vsHfvXuzduxfvec97cPz48SqMcnbMNCeVw4cPY+XKlXj88ccrOLrZU8p8XnrpJVx//fXYs2cP3vve91Z4hLNnpjmFw2F8+MMfxnXXXYc9e/bg17/+dRVGOT+Uen1eKBR79k/3vXHvvfdi586d2LVrF/72t79pvz9y5Aj27t2LnTt34p577sGFUG0w2Q4g61YahWxCsnYzc//992PPnj249tpr8alPfQrJZJKsWyWR55FvfvOb8r333ivLsizfe++98re+9a2Cx/3jP/6j/Mtf/lKWZVlOJpNyMBicz2HNmVLnI8uy/JOf/ET+1Kc+Jd91112VGt6cKGVOw8PD8pEjR2RZluVwOCxfc8018qlTpyo6zunIZDLyjh075J6eHjmZTMp79+6dMr6nn35avuOOO2RJkuSDBw/K73znO6s02tIoZU6vvfaaHAgEZFlW5rcU5qQed9ttt8l33nmn/Kc//akKIy2NUuYTDAbl3bt3y/39/bIsy/Lo6Gg1hloypczphz/8ofac8Pv98ubNm+VkMlmN4ZaVUq/PC4liz/5i3xunTp2S9+7dKyeTSbmnp0fesWOHnMlkZFmW5Ztuukk+cOCALEmSfMcdd8hPP/10dSZVQSbbAWTdSqOQTUjWbnqGhobkt771rXI8HpdlWZbvvvtu+de//jVZtwoyrxGqffv24YYbbgAA3HDDDXjyySenHBOJRPDKK6/gne98JwClU/1CVR4pZT4AMDQ0hKefflqb00KmlDm53W6sXr0aAGAymdDW1obh4eFKDnNaDh8+jObmZjQ2NoLneezZswf79u3LO0adJ0VR2LBhA0KhEEZGRqo04pkpZU4bN26E1WoFAGzYsAFDQ0PVGGrJlDInAPjZz36GXbt2wel0VmGUpVPKfH7/+99j586dqKurA4AlMSeKohCNRiHLMqLRKKxWK1iWrdKIy0ep1+eFRLFnf7HvjX379mHPnj3geR6NjY1obm7G4cOHMTIygkgkgosuuggUReGGG25Y8mtbyA4g6zYzxWxCsnYzI4oiEokEMpkMEokE3G43WbcKMq8Old/vh9vtBqA8mMfGxqYc09vbC4fDgX/+53/GDTfcgM9//vOIxWLzOaw5U8p8AODrX/86PvOZz4CmF36JWqlzUunr68OxY8ewfv36SgyvJIaHh+H1erX/ezyeKQ7f5GO8Xu+CcgonU8qccnnkkUdw5ZVXVmJoc6bU8/Tkk0/iPe95T6WHN2tKmU9XVxdCoRBuu+02vOMd78Cjjz5a4VHOjlLmdOutt+LMmTPYunUrrrvuOnz+859fFM+6mZjtPXehkfvsL/a9UWwNF9vztxwUsgPIus1MMZuQrN30eDwefPCDH8Rb3/pWXHHFFTCZTLjiiivIulWQ895W/MAHPoDR0dEpv//kJz9Z0t9nMhkcPXoUX/ziF7F+/Xrcc889uO+++0r++3JzvvP561//CofDgTVr1uCll14q8+jmxvnOSSUajeLuu+/G5z73OZhMpjKN7vyRC+T3UhQ162MWErMZ74svvohHHnkEDz300HwP67woZU5f+9rX8OlPfxoMw1RqWHOmlPmIoog333wT999/PxKJBN7znvdg/fr1aG1trdQwZ0Upc3r22WexcuVKPPjgg+jp6cHtt9+OTZs2LahnwlxYbM+ISlLqs7/YGl5oaztbO4Cs2wTFbMJikLVTCAaD2LdvH/bt2wez2YxPfOIT+O1vf1v0eLJu5ee8Har777+/6GtOpxMjIyNwu90YGRmBw+GYcozX64XX69UiHm9729uqWgx8vvM5cOAAnnrqKezfvx/JZBKRSASf/vSn8e///u/zOOrpOd85AUA6ncbdd9+NvXv34pprrpmnkc4Nr9ebl+42PDys7cgUO2ZoaGjKMQuJUuYEAMePH8cXvvAF/OhHP4Ldbq/kEGdNKXM6cuQIPvWpTwEAxsfH8cwzz4BlWVx99dUVHWsplHrd2e12GAwGGAwGbNq0CcePH1+wDlUpc/rNb36Du+66CxRFobm5GQ0NDTh79izWrVtX6eGWlVLvuQuNQs/+Yt8bxdZwsT1/z5didgBZt5kpZhOStZue559/Hg0NDdq6XHPNNTh48CBZtwoyr3ka27dv11JcHn30UezYsWPKMTU1NfB6vTh79iwA4IUXXkB7e/t8DmvOlDKff/iHf8D+/fvx1FNP4Tvf+Q4uvfTSqjpTM1HKnGRZxuc//3m0tbXh9ttvr/AIZ2bt2rXo6upCb28vUqkUHnvsMWzfvj3vGHWesizj0KFDMJvNC/ohUcqcBgYG8PGPfxzf+ta3FqyBnkspc3rqqae0f7t27cKXv/zlBelMAaXNZ8eOHXj11VeRyWQQj8dx+PDhBft8A0qbU21tLV544QUAwOjoKM6dO4eGhoZqDLeslDL3C41iz/5i3xvbt2/HY489hlQqhd7eXnR1dWHdunVwu90wGo04dOgQZFku+l2zVChmB5B1m5liNiFZu+mpq6vD66+/jng8DlmWybpVg/lUvBgbG5Pf9773yTt37pTf9773yePj47IsK2okd955p3bc0aNH5RtvvFG+9tpr5Y985COactlCo9T5qLz44osLXuWvlDm98sorcmdnp3zttdfK1113nXzdddctONWXp59+Wr7mmmvkHTt2yD/4wQ9kWZblhx56SH7ooYdkWZZlSZLkr3zlK/KOHTvka6+9Vj58+HA1h1sSM83pc5/7nLxp0ybtnNx4443VHG5JzDSnXD772c8uaJU/WS5tPj/60Y/k3bt3y3v27JF/+tOfVmmkpTPTnIaGhuTbb79dvvbaa+U9e/bIjz76aDWHW1YKzf1Cptizv9j3hizL8g9+8AN5x44d8jXXXJP3PXH48GF5z5498o4dO+R/+Zd/kSVJqsKMKk+uHUDWrTQK2YRk7Wbme9/7nrxr1y55z5498qc//Wk5mUySdasglCwTgXkCgUAgEAgEAoFAmAuLX5qJQCAQCAQCgUAgEKoEcagIBAKBQCAQCAQCYY4Qh4pAIBAIBAKBQCAQ5ghxqAgEAoFAIBAIBAJhjhCHikAgEAgEAoFAIBDmCHGoCAQCgUAgEAgEAmGOEIeKQCAQCAQCgUAgEOYIcagIBAKBQCAQCAQCYY78/67fYG1F7B7RAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "az.plot_trace(mixture_trace)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The NUTS algorithm is easily able to sample from the distribution. Let's try to replicate the analysis with mean-field VI:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:00<00:00 Average Loss = 2.0949]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 2.0842\n" ] } ], "source": [ "with mixture_model:\n", " mean_field = pm.fit()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:369: UserWarning: No value variable found for normal_rv{0, (0, 0), floatX, False}.out; the random variable will not be replaced.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "meanfield_trace = mean_field.sample(500)\n", "az.plot_trace(meanfield_trace, var_names=['x']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that ADVI has failed to approximate the multimodal distribution, since it uses a Gaussian distribution that has a single mode.\n", "\n", "## Checking convergence\n", "\n", "The `fit` function supports the use of \"callbacks\", which are functions that are passed as arguments to other functions, and executed at a specified time within that function. For example, the `CheckParametersConvergence` callback will monitor the model parameter trajectories, and stop the VI algoithm when convergence is achieved." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:00<00:00 Average Loss = 2.2717]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 2.2555\n" ] } ], "source": [ "from pymc.variational.callbacks import CheckParametersConvergence\n", "\n", "with mixture_model:\n", " mean_field = pm.fit(callbacks=[CheckParametersConvergence()])" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(mean_field.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that the model did not converge, despite the fact that we ran many iterations. In this case, this is because the mean of the ADVI approximation is close to zero, so taking the relative difference (the default method) is an unstable convergence check.\n", "\n", "Let's try again, using absolute difference as the criterion:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 52.84% [5284/10000 00:00<00:00 Average Loss = 2.9555]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Convergence achieved at 8100\n", "Interrupted at 8,099 [80%]: Average Loss = 3.7981\n" ] } ], "source": [ "with mixture_model:\n", " mean_field = pm.fit(method='advi', callbacks=[pm.callbacks.CheckParametersConvergence(diff='absolute')])" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(mean_field.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's much better! We've reached convergence after approximately 5000 iterations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another useful callback allows users to track parameters directly during the fitting procedure. To do this we need to use the object-oriented (OO) API, which allows direct access to the approximation before inference is performed." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "with mixture_model:\n", " advi = pm.ADVI()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Different approximations have different hyperparameters. In mean-field ADVI, we have $\\rho$ and $\\mu$ (inspired by [Bayes by BackProp](https://arxiv.org/abs/1505.05424))." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'mu': mu, 'rho': rho}" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx.shared_params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are convenient shortcuts to relevant statistics associated with the approximation. This can be useful, for example, when specifying a mass matrix for NUTS sampling:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.34]), array([0.69314718]))" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "advi.approx.mean.eval(), advi.approx.std.eval()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can roll these statistics into the `Tracker` callback." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [], "source": [ "tracker = pm.callbacks.Tracker(\n", " mean=advi.approx.mean.eval, # callable that returns mean\n", " std=advi.approx.std.eval # callable that returns std\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, calling `advi.fit` will record the mean and standard deviation of the approximation as it runs." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [20000/20000 00:01<00:00 Average Loss = 2.0623]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 2.0509\n" ] } ], "source": [ "approx = advi.fit(20_000, callbacks=[tracker])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now plot both the evidence lower bound and parameter traces:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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R8+lIzszDsk0n8WInTklARESmTZexLwBg4sSJWvc3hvEtcu7cR0TsFZy6lInPp70oaixERGS82EILwMHWUuwQiIiIqBxXx3oAgITk21CpVCJHQ0RExooJLYCWTR4+V3QhseJ5+oiIiMhw3hjwDIDSnlRERETaMKF9xKpf/hE7BCIiIgLQ77kmAIDF646JHAkRERkrJrQPLP+/XgCAa+l3RI6EiIiIAMC2ngWe8mgAAMi6fU/kaIiIyBgxoX3gaU8HsUMgIiKiR8wc7QMA2Hs0SeRIiIjIGDGh1YLT9xARERkH94Y2aN3cCX+cuC52KEREZISY0GqxbNNJsUMgIiKiB7o844q0rLu4eI0DNxIRkTomtOWsnNFbWJ614qCIkRAREVGZZ59xAwB88XOcyJEQEZGxYUJbThO5nbB84Wo2snMLRIyGiIiIAMDT1RYAkJyZh9t590WOhoiIjAkT2keUjXYMAHGXMkWMhIiIiMrMHNUZAKfwISIidUxoH1F+tOO4SzdEjISIiIjK9OzQCEBpDyqVSiVyNEREZCyY0GoR8tZzAIA/4zjaMRERkTGQSCR41a8FAOC7yHMiR0NERMaCCa0WHVu6iB0CERERPWKo79MAgB0H/0OxskTkaIiIyBgwodVCJpUIy3+c5Lx3RERExsDKwgxBL3gBAM4l3BQ5GiIiMgY6JbSJiYkYNmwY/P39MWzYMFy9elWjztatWxEYGAiFQoHAwEBs2LBB2LZq1SoMGDAAAwcOxODBg3Hw4MMpcVasWIFu3bpBoVBAoVAgNDT0yc9KjziROxERkfEY9ZI3LC1kOHI2TexQiIjICJjpUikkJAQjRoyAQqFAZGQk5s2bp5awAoC/vz8GDx4MiUSCvLw8BAYGokuXLmjVqhXatWuHcePGwdraGhcvXsSoUaNw6NAhWFlZAQCCgoIwe/Zs/Z/dE9gY2h+jQnbDx9tV7FCIiIjoAUtzGdo/5YxdR67i9ZefgY21udghERGRiKpsoc3KykJ8fDwCAgIAAAEBAYiPj0d2drZaPRsbG0gkpV11CwoKUFRUJKz37NkT1tbWAICWLVtCpVIhJydHn+ehdzb1LAAAayLPoahYKXI0REREVKZf18YAgE83nhA5EiIiEluVCW1aWhpcXV0hk8kAADKZDC4uLkhL0+zqExsbiwEDBqB3795466230LJlS40627dvR+PGjeHm5iaU7dy5E4GBgRg3bhzi4uK0xpGbm4vk5GS1V3p6us4nWl3ln6P9ae+lGnsfIiIiqp4urUt/QyQk54gbCBERiU6nLse68vX1ha+vL1JTUzF58mT06tULzZs3F7YfO3YMX3zxBdauXSuUDR8+HBMmTIC5uTkOHz6MSZMmISYmBg4ODmrHXr9+PVauXKnPcHWWdbtAlPclIiIiTRKJBKNf8saPuy4gMfU2mrk3EDskIiISSZUttHK5HBkZGVAqS7vdKpVKZGZmQi6XV7iPu7s72rZti/379wtlcXFxmDlzJlatWqWW5Do7O8PcvPT5l+7du0Mul+PKlSsaxxwzZgxiY2PVXps2bdL5RJ+EvGF9g7wPERER6ebFzh4AgC37LoscCRERianKhNbJyQne3t6Ijo4GAERHR8Pb2xuOjo5q9RISEoTl7OxsHD16FC1alE6AfubMGUybNg1ffvklWrdurbZfRkaGsHzhwgWkpKSgWbNmGnHY2dnBw8ND7VW+23JNiFqmAABs2n2xRt+HiIiIqsfFoR6cGljh8OlUHI+vuUeQiIjIuOnU5Xj+/PkIDg7G6tWrYWdnh7CwMADA+PHjMXXqVLRt2xZbtmzB4cOHYWZmBpVKhVGjRqFHjx4AgNDQUBQUFGDevHnCMcPDw9GyZUssX74c58+fh1Qqhbm5OcLDw+Hs7FwDp0pERES1yZsD2yD8xxNYsv44toYFih0OERGJQKeE1svLCxERERrla9asEZY/+OCDCvffunVrhdvKkmNjZWUhQ0GhEkplCWQynabtJSIiElViYiKCg4ORk5MDe3t7hIWFoWnTphr1YmJi8NVXX0GlUkEikWDdunVo2LAhVqxYgc2bN8PFxQUA0KlTJ4SEhBj4LKrWs0MjfBd5Dtm5BSgqVsLcTCZ2SEREZGB6HRSqNurt44ldR67iSnIOWjVxrHoHIiIikekyf/zZs2excuVKrF+/Hs7Ozrhz5w4sLCyE7cY4R7w2Lz/fFBt3X8Rvx5Lw8vOajywREVHtxibHKjzr7QoASMnMEzkSIiKiquk6f/wPP/yAcePGCY/52NrawtLS0uDxPqkhfZ4GAPx5KlnkSIiISAxsoa2Cbf3Su9Wf/xwHLw97NJXbiRwRERFRxSqbP778gI4JCQnw8PDAyJEjkZ+fj759+2LixImQSErnYd+5cycOHToEZ2dnTJkyBR07dtR4r9zcXOTm5qqV1eQc8dqYyaRo0dge6Vl3UawsgRkfDyIiqlOY0FahidvDBPbw6VQmtEREVCsolUpcunQJ69atQ2FhId566y24u7sjKCjIJOaIL2+obwssXncMod/9jYXvPC92OEREZEC8jVkFK4uHA0z8/NslESMhIiKqmq7zx7u7u6N///6wsLCAjY0NfH19cebMGQCmMUd8eV1bl07j98/lG8gvKDL4+xMRkXiY0FahrOsVERGRKdB1/viAgAAcOnQIKpUKRUVF+Pvvv9GqVSsAxj1HvDYSiQTjFW0AAJv38OYzEVFdwi7H1ZSRnQ9Xx3pih0FERFQhXeaPHzBgAM6dO4eXX34ZUqkUPXr0wCuvvAIAJjlH/IAezbEm8hz2HU/CWw+SWyIiqv2Y0Orgs2kv4Jffr+Dw6VTcyS9kQktEREZNl/njpVIp5syZgzlz5mjUM/Y54rWRSSV4pc/T+OX3K0jOvAMPF1uxQyIiIgNgl2MdPOVhj5efbwoA+PtcmrjBEBERkVYvdvIAACz47qjIkRARkaEwodVR2bO0W367LHIkREREpE0TuR2kEiAt6y4KCovFDoeIiAyACa2O2jR3EjsEIiIiqsKcN7oAAE5eyBQ5EiIiMgQmtDriaMdERETGr1NLF8ikEmz781+xQyEiIgNgQvsYAqdHck5aIiIiI2RhLkPQC164dO0WTl++IXY4RERUw5jQPqZNuy/i/H9ZYodBREREj/Dr0hgAMPebIyJHQkRENY0JbTW8OVB9XrtzCTdFioSIiIgq4uFii6c97QEAWbfviRsMERHVKCa01RDYs7naemJarkiREBERUWVGv+QNAPj4h2MiR0JERDWJCW01yKQSRC1T4P0RnQAAh0+nihwRERERadOxpQsA4HJSDpTKEpGjISKimsKE9jH07uwpLF9IzBYxEiIiIqrIK32eBgBEHvhP5EiIiKim6JTQJiYmYtiwYfD398ewYcNw9epVjTpbt25FYGAgFAoFAgMDsWHDBmGbUqlEaGgo/Pz80LdvX0REROi0zZjZWJsDAFJv5okcCREREWkz1Lc0oV0XfR4qlUrkaIiIqCbolNCGhIRgxIgR2LNnD0aMGIF58+Zp1PH398eOHTsQGRmJn376CevWrcPFixcBAFFRUUhKSsLevXuxZcsWrFixAsnJyVVuM2afTO4BAPj9xHWRIyEiIiJt6lmZo3t7dwDAJ+uPixwNERHVhCoT2qysLMTHxyMgIAAAEBAQgPj4eGRnq3e1tbGxgUQiAQAUFBSgqKhIWI+JicHQoUMhlUrh6OgIPz8/7N69u8ptxszNsR4A4My/HOmYiIjIWL03rCMA4K+zaWylJSKqhapMaNPS0uDq6gqZTAYAkMlkcHFxQVpamkbd2NhYDBgwAL1798Zbb72Fli1bCsdwd3cX6snlcqSnp1e5rbzc3FwkJyervbTVMxQrSzNhubBIKVocREREVDFrSzOMeqkVAOCfyzdEjoaIiPTNrOoquvP19YWvry9SU1MxefJk9OrVC82bN696Rx2sX78eK1eu1Mux9C0jOx+errZih0FERERa9O7siY27LmLVL6fx3Yd9xQ6HiIj0qMoWWrlcjoyMDCiVpa2QSqUSmZmZkMvlFe7j7u6Otm3bYv/+/cIxUlMfTnGTlpYGNze3KreVN2bMGMTGxqq9Nm3apNtZ1pCeHRoBAPYdSxI1DiIiIqqYi0M9tGzsgIzsfPxzOVPscIiISI+qTGidnJzg7e2N6OhoAEB0dDS8vb3h6OioVi8hIUFYzs7OxtGjR9GiRQsAQP/+/REREYGSkhJkZ2dj37598Pf3r3JbeXZ2dvDw8FB7aUt8DWlcYGsAwK/7/xU1DiIiIqrc24PaAgA++uYvkSMhIiJ90qnL8fz58xEcHIzVq1fDzs4OYWFhAIDx48dj6tSpaNu2LbZs2YLDhw/DzMwMKpUKo0aNQo8epSMBKxQKnD59Gv369QMATJ48GZ6enlVuM3aOdlZih0BEREQ6aNHYAV1bu+Ho+XRcuX4LT3s6iB0SERHpgU4JrZeXl9b5YdesWSMsf/DBBxXuL5PJEBoaWu1txk4qlQjLd+8Vof6DuWmJiIjI+Ch6eeHo+XS8//kBRC1TiB0OERHpgU7z0FLV0m7eFTsEIiIiqkQbLydh+e69IhEjISIifWFC+4TmjHkWALD36DWRIyEiIqLKSCQSzHuzKwBg6vL94gZDRER6wYT2CTk7WAMAdv11VdxAiIiIqEo+3q4AgMzsfNzMuSdyNERE9KSY0D6hskElej2YwoeIiEhsiYmJGDZsGPz9/TFs2DBcvXpVa72YmBgEBgYiICAAgYGBuHnzJoDSKfpCQ0Ph5+eHvn37ah1Hw1RJJBJ8M8cXABBzJFHkaIiI6EnpNCgUVc7FwRoXrmWLHQYREREAICQkBCNGjIBCoUBkZCTmzZuHDRs2qNU5e/YsVq5cifXr18PZ2Rl37tyBhYUFACAqKgpJSUnYu3cvcnJyEBQUhG7dusHDw0OM09E794Y26NDCGRGxVzCwpxfsbS3FDomIiB4TW2j1IPPWPdy4dQ/LNp8UOxQiIqrjsrKyEB8fj4CAAABAQEAA4uPjkZ2tfuP1hx9+wLhx4+Ds7AwAsLW1haVlaWIXExODoUOHQiqVwtHREX5+fti9e7dhT6SGDejeDAAwKfx3kSMhIqInwYRWj/afTEZSeq7YYRARUR2WlpYGV1dXyGQyAKXT47m4uCAtLU2tXkJCAq5fv46RI0di0KBBWL16NVQqlXAMd3d3oa5cLkd6errGe+Xm5iI5OVntpa2eMera2g0AcCe/EP9ezxE3GCIiemxMaPUg6AUvYXnyp3+IGAkREZFulEolLl26hHXr1uHHH3/EgQMHEBkZWa1jrF+/Hr6+vmqvkSNH1lDE+iWRSLB6Vh8AwAdfHRY5GiIielxMaPXg9Ze9xQ6BiIgIQGlrakZGBpRKJYDSxDUzMxNyuVytnru7O/r37w8LCwvY2NjA19cXZ86cEY6Rmpoq1E1LS4Obm5vGe40ZMwaxsbFqr02bNtXg2emXp6stpFIJ7t0vRmLqbbHDISKix8CEVg/MzWT4OthX7DCIiIjg5OQEb29vREdHAwCio6Ph7e0NR0dHtXoBAQE4dOgQVCoVioqK8Pfff6NVq1YAgP79+yMiIgIlJSXIzs7Gvn374O/vr/FednZ28PDwUHtpS3yN2bL3egEA1u+MFzkSIiJ6HBzlWE8aOduIHQIREREAYP78+QgODsbq1athZ2eHsLAwAMD48eMxdepUtG3bFgMGDMC5c+fw8ssvQyqVokePHnjllVcAAAqFAqdPn0a/fv0AAJMnT4anp6do51OTnvKwRyNnG5y8mImSEhWkUonYIRERUTUwoa0BhUVKWJjLxA6DiIjqKC8vL61zx65Zs0ZYlkqlmDNnDubMmaNRTyaTITQ0tEZjNCb9ujbBuujzOJtwE+2fdhY7HCIiqgZ2Odajdwa1BQBcTeNIx0RERKbi5e5NYW0pw96j18QOhYiIqokJrR7FJ5bO8Tf9iwMiR0JERES6srIwg4+3Gw7EpeBy0i2xwyEiompgQqtHbwe1FTsEIiIiegx9fEqfET58OrWKmkREZEyY0OqRva2l2CEQERHRY/DxdkVz9wb4df+/KCxSih0OERHpiAltDfm/z/aLHQIRERFVwyu+TwMAhgRHQ6VSiRwNERHpggltDUlI5gTtREREpqRHe3dheV0056UlIjIFOiW0iYmJGDZsGPz9/TFs2DBcvXpVo86qVaswYMAADBw4EIMHD8bBgweFbbNmzYJCoRBerVq1QmxsLABgxYoV6Natm7DN1KcJGPTiU8JycuYdESMhIiKi6pBIJPhmji8AYNv+f0WOhoiIdKHTPLQhISEYMWIEFAoFIiMjMW/ePGzYsEGtTrt27TBu3DhYW1vj4sWLGDVqFA4dOgQrKyuEh4cL9S5evIgxY8agZ8+eQllQUBBmz56tp1MS17jA1jh8OgWZt+5hYtjv+GVJACw5Jy0REZFJcG9oAx9vV5y4kIFTFzPRqZWL2CEREVElqmyhzcrKQnx8PAICAgAAAQEBiI+PR3Z2tlq9nj17wtraGgDQsmVLqFQq5OTkaBzvl19+QWBgICwsLKoVaG5uLpKTk9Ve6enp1TqGoWTeuicsvxIcjesZbKklIiIyFRMGtwMARPx+WeRIiIioKlUmtGlpaXB1dYVMVtrKKJPJ4OLigrS0tAr32b59Oxo3bgw3Nze18sLCQkRFRWHIkCFq5Tt37kRgYCDGjRuHuLg4rcdcv349fH191V4jR46s8gTF8ObANmrr7y3fj2JliUjREBERUXW4OtZDp1YuOJeQhT9PJYsdDhERVUKnLsfVcezYMXzxxRdYu3atxrZ9+/bB3d0d3t7eQtnw4cMxYcIEmJub4/Dhw5g0aRJiYmLg4OCgtu+YMWMwaNAgtbL09HSjTGofnb6nqLgEh0+n4oVOHiJFRERERNUx0r8VTl3MxNJNJ3n9JiIyYlW20MrlcmRkZECpLJ2TTalUIjMzE3K5XKNuXFwcZs6ciVWrVqF58+Ya27du3arROuvs7Axzc3MAQPfu3SGXy3HlyhWNfe3s7ODh4aH2erQF2FgU3C/WKOPg/0RERKajRWMHvNi5NJG9lpYrcjRERFSRKhNaJycneHt7Izo6GgAQHR0Nb29vODo6qtU7c+YMpk2bhi+//BKtW7fWOE56ejpOnjwpPItbJiMjQ1i+cOECUlJS0KxZs8c6GWPRx8cTADDplfZCmYUZZ0giIiIyJW8NbAMzmRQf/3BM7FCIiKgCOnU5nj9/PoKDg7F69WrY2dkhLCwMADB+/HhMnToVbdu2RWhoKAoKCjBv3jxhv/DwcLRs2RIAsG3bNvTu3Rv29vZqx16+fDnOnz8PqVQKc3NzhIeHw9nZWU+nJw4LcxmilikAAKt/OQ0AuH23UMyQiIiIqJoa2Fiiaxs3HD6ditOXb6B9C9P+fUJEVBvplNB6eXkhIiJCo3zNmjXC8tatWys9xsSJE7WWlyXHtdX28EAMnh2FrNv3qq5MRERERmXSkPY4fDoVc785gohPBsDKQu/DjxAR0RNgP9gaJpNJUaICtu1PEDsUIiIiqia7+hZ42tMeAPDa3F3iBkNERBqY0BpIYZFS7BCIiIjoMSyd2gsAUKwswbTP/xQ5GiIiKo8JrQG82NkDLg7WYodBREREj0EqlSDi4wEAgH+v5+Cjb46gpITzFxARGQMmtAbQsIE1Mm/dw4Lv/0ZBoeaUPkRERGTcrCzNMGuUDwDgn8s3cO6/myJHREREABNag2jYwAoAcDw+A28u+k3kaIiIiOhx9OzYCO+P6AQACPn2b5GjISIigAmtQdy8XSAs53L6HiIiIpPVu7MnbOtZoFhZgt9PXBc7HCKiOo8JrQG82NlD7BCIiIhIT74O9gUAHItPFzkSIiLiZGoG0MTNDp1bueDkxUwAQMH9YlhZ8qMnIqKakZiYiODgYOTk5MDe3h5hYWFo2rSpWp0VK1Zg8+bNcHFxAQB06tQJISEhVW6j0ql8+vh44vcT1/Hv9Rw89WBaHyIiMjxmVQYyf3w3/HHyOpZvPoWbt+/Bw8VW7JCIiKiWCgkJwYgRI6BQKBAZGYl58+Zhw4YNGvWCgoIwe/ZsrceobBsBQ32fxu8nriNkzV/YtOAlscMhIqqz2OXYgBral07dczPnnsiREBFRbZWVlYX4+HgEBAQAAAICAhAfH4/s7GyRI6tdPFxsIZNKkHu3EOuizosdDhFRncWE1oDsbSwBAL8dTRI5EiIiqq3S0tLg6uoKmUwGAJDJZHBxcUFaWppG3Z07dyIwMBDjxo1DXFycztvK5ObmIjk5We2Vnl53nitdPasPAODX/f+KHAkRUd3FLscGZGVR+nEf+CcFM0f7iBwNERHVZcOHD8eECRNgbm6Ow4cPY9KkSYiJiYGDg0Ol28pbv349Vq5cKdIZiM/d2Qbd2srx19k0fP7zKfzf8E5ih0REVOewhdaAnB2sxQ6BiIhqOblcjoyMDCiVSgCAUqlEZmYm5HK5Wj1nZ2eYm5sDALp37w65XI4rV65Uua28MWPGIDY2Vu21adOmmjw9ozP6JW8AQOzx6zh0OkXkaIiI6h4mtCJRqVRih0BERLWQk5MTvL29ER0dDQCIjo6Gt7c3HB0d1eplZGQIyxcuXEBKSgqaNWtW5bby7Ozs4OHhofZyc3OridMyWp6uthgb8AwAYNmmUyJHQ0RU97DLsYFJJUCJCriWfgdN5XZih0NERLXQ/PnzERwcjNWrV8POzg5hYWEAgPHjx2Pq1Klo27Ytli9fjvPnz0MqlcLc3Bzh4eFwdnYGgEq3kabBvZ/G7r+vIe3mXSRn3uFMBkREBsSE1sAaudjiesYdhHx7BOtD+osdDhER1UJeXl6IiIjQKF+zZo2wXJbkalPZNtJu/lvP4Z0lsfj1j38xdVhHscMhIqoz2OXYwKYM7QAAyM69L24gREREpDdlA0T9diwJaTfvih0OEVGdoVNCm5iYiGHDhsHf3x/Dhg3D1atXNeqsWrUKAwYMwMCBAzF48GAcPHhQ2LZixQp069YNCoUCCoUCoaGhwjalUonQ0FD4+fmhb9++Wu8o1yYtmjhUXYmIiIhMTt8ujQEAb3+yT+RIiIjqDp26HIeEhGDEiBFQKBSIjIzEvHnzsGHDBrU67dq1w7hx42BtbY2LFy9i1KhROHToEKysrAAAQUFBmD17tsaxo6KikJSUhL179yInJwdBQUHo1q0bPDw89HB6xkcmlaCRsw1SbuQhL78QNvUsxA6JiIiI9ODZZx4OiBU4PRLbwwMhk7EzHBFRTaryr2xWVhbi4+MREBAAAAgICEB8fDyys7PV6vXs2RPW1qXT0rRs2RIqlQo5OTlVBhATE4OhQ4dCKpXC0dERfn5+2L1792OciulIuZEHAHg9dI/IkRAREZE+fRPsKywHzYpCwf1iEaMhIqr9qkxo09LS4OrqCplMBgCQyWRwcXFBWlpahfts374djRs3Vhu6f+fOnQgMDMS4ceMQFxendnx3d3dhXS6XIz09XeOYubm5SE5OVntpq2dKiopLxA6BiIiI9Mjd2QazRvkI6/+LvSxiNEREtZ/eRzk+duwYvvjiC6xdu1YoGz58OCZMmABzc3McPnwYkyZNQkxMDBwcdH+edP369Vi5cqW+wxXFZ//3AqZ9/ifqW5ujoLAYVhYcbJqIiKi26NmxEZ5v746gmTsQEXsFI/1bsesxEVENqfKvq1wuR0ZGBpRKJYDSQZwyMzMhl8s16sbFxWHmzJlYtWoVmjdvLpQ7OzvD3NwcANC9e3fI5XJcuXJFOH5qaqpQNy0tTeuk7GPGjEFsbKzaa9OmTdU8XePwlKc9AODuvSIMnbMTW/ZdEjcgIiIi0iuZVII3BjwDoLTrMRER1YwqE1onJyd4e3sjOjoaABAdHQ1vb284Ojqq1Ttz5gymTZuGL7/8Eq1bt1bblpGRISxfuHABKSkpaNasGQCgf//+iIiIQElJCbKzs7Fv3z74+/trxGFnZwcPDw+1l7bE1xRt3HVR7BCIiIhIz4JefEpYPv9floiREBHVXjr1dZ0/fz6Cg4OxevVq2NnZCROujx8/HlOnTkXbtm0RGhqKgoICzJs3T9gvPDwcLVu2xPLly3H+/HlIpVKYm5sjPDwczs7OAACFQoHTp0+jX79+AIDJkyfD09NT3+dJREREZFAyqQRfB/tiwpJYBK86hDcHtkHQC15ih0VEVKtIVCqVSuwgHldycjJ8fX0RGxtrctP8HD6diiUbjgvr7Z5qiMUTu4sYERERmfJ1xVjwM9S0eutp7DpyFQDg1MAKP8zT7IlGRETaVXVd4QgFIune3h2rZ/UR1s/8exO38+6LGBERERHVhImD2wnLWbcL8EP0eRGjISKqXZjQisjT1RZeHg2E9bMJN0WMhoiIiGqCRCJB1DIFlkzuAQDY+se/nJ+WiEhPmNCK7N2hHYTlsA0nxAuEiIiIalTr5k4Y9VIrAMBH3xyBCT/1RURkNJjQisyrUQMEdG8mrCtLeHEjIiKqrV71bQEAuHjtFhatPSZyNEREpo8JrcgkEgneKfdszb2CIhGjISIiopokkUjw1ezSMTSOxadj7MK9uMfux0REj40JrZGY/Ep7AMA5zlNHRERUq3m42GJsQGsAwM2ce3j1g53I5w1tIqLHwoTWSFy4mg0AWLzuGL759QwCp0fir7OpIkdFRERENWFw76fw/ohOwvqwD2OQdvOuiBEREZkmJrRGovyQ/tGHEwEAH/9wvKLqREREZOJ6d/ZE1DKFsP72J/sQOD2Sg0UREVUDE1ojYWVpprX8ctItA0dCREREhhS1TAELs4c/ycJ/5KwHRES6YkJr5KZ/cYB3aomIiGq5rWGBeDuoLQDg0OlUPlNLRKQjJrRGZPunA2FbzwLWlmb4OthXKM+8dU/EqIiIiMgQAns2x4RBpUntsA9jOJUfEZEOmNAaEZlUgs0LX8L/Ph4A94b1hfICDudPRERUJwzo0VxYnrPqkIiREBGZBia0RkoikWB8UBsAQN49djsiIiLdJSYmYtiwYfD398ewYcNw9epVjTorVqxAt27doFAooFAoEBoaKmxTKpUIDQ2Fn58f+vbti4iICANGT5sXvgSgdAaEwOmRKFaWiBwREZHxYkJrxFo1cQQA5OUXInB6JAKnR+Jcwk2RoyIiImMXEhKCESNGYM+ePRgxYgTmzZuntV5QUBAiIyMRGRmJkJAQoTwqKgpJSUnYu3cvtmzZghUrViA5OdlQ4dd5tvUs8Eqfp4X19z//U8RoiIiMGxNaE7Bo3TFh+cSFDBEjISIiY5eVlYX4+HgEBAQAAAICAhAfH4/s7GydjxETE4OhQ4dCKpXC0dERfn5+2L17d02FTFqMGfAMZr/uAwBITM3FkNlRuJ13X+SoiIiMDxNaI+bVqIFGWVLGHREiISIiU5GWlgZXV1fIZDIAgEwmg4uLC9LS0jTq7ty5E4GBgRg3bhzi4uLUjuHu7i6sy+VypKena+yfm5uL5ORktZe2evR4erRvhElDSuepLywuwaiQ3Zz5gIjoEdonPyWjIJNp3m84Hs8WWiIienLDhw/HhAkTYG5ujsOHD2PSpEmIiYmBg4ODzsdYv349Vq5cWYNR0kvPN4ODnRUWP+itNXDGDkQtU4gcFRGR8WALrZFbOrWn2CEQEZEJkcvlyMjIgFKpBFA6wFNmZibkcrlaPWdnZ5ibmwMAunfvDrlcjitXrgjHSE1NFeqmpaXBzc1N473GjBmD2NhYtdemTZtq6tTqrOfayPFrWICwHp+YJWI0RETGRaeEVpfREletWoUBAwZg4MCBGDx4MA4ePKjTtspGWSSg5YOBoWzrWcDCrPSf6/x/vJAREZF2Tk5O8Pb2RnR0NAAgOjoa3t7ecHR0VKuXkfGwx8+FCxeQkpKCZs2aAQD69++PiIgIlJSUIDs7G/v27YO/v7/Ge9nZ2cHDw0PtpS3xpSdnbibD2rn9AACzVx5CetZdkSMiIjIOOnU5LhstUaFQIDIyEvPmzcOGDRvU6rRr1w7jxo2DtbU1Ll68iFGjRuHQoUOwsrKqdBtQOsri7Nmz9X92tURZ16KPfziGv86mISk9F62bO4kcFRERGav58+cjODgYq1evhp2dHcLCwgAA48ePx9SpU9G2bVssX74c58+fh1Qqhbm5OcLDw+Hs7AwAUCgUOH36NPr1K02gJk+eDE9PT9HOh0o5O1jD09UW1zPuYPzH+7D904GQSSVih0VEJKoqE9qy0RLXrVsHoHS0xIULFyI7O1vtbm/Png+7xrZs2RIqlQo5OTlwc3OrdBvpbqjv0/jrbBpWbz2DFo0d4OVhL3ZIRERkhLy8vLTOHbtmzRphuSzJ1UYmk7HHlJFaMf1FBM2KAgAEzdyBHUsHQiJhUktEdVeVXY6rM1pime3bt6Nx48ZaE1Zt2yoaZbE8jqQIeLjYCssrIv4RLxAiIiIShUwmxbbwQGGdg0USUV2n91GOjx07hi+++AJr167VaZuuoyxyJEXA2vLhP1dC8m0RIyEiIiKxmMmk2LokAEOCo7Fw7VGsntUHnq62Ve9IRFQLVdlCq+toiQAQFxeHmTNnYtWqVWjevLlO2yobZbE8jqRIREREVMrCXIbxijYAgEnhvyMzO1/kiIiIxFFlQqvraIlnzpzBtGnT8OWXX6J169Y6b6tslMXyOJJiqe3luhldupYtYiREREQkpoG9vNCrYyMAwMK1R0WOhohIHDp1OdZltMTQ0FAUFBRg3rx5wn7h4eFo2bJlpdsqG2WRNMlkD+9BzPjyICdXJyIiqsNmjvKBuZkUscevI3B6JEc+JqI6R6eEVpfRErdu3Vrh/pVtq2yURdJu0TvPY+43R8QOg4iM1L/JOXCwtYRTA2ucTbgJTxdb2Ntaih0WEdWQqa92ROzx6wBKRz7+do4f5A3rixwVEZFhVNnlmIxP+xZswSYi7UpKVJj22Z94Y8Fe3LpTgA9WH8bo+bvFDouIapBUKlEb+fjtT/bhnU/24X6RUsSoiIgMgwmtierbpTEAQKVSiRwJERkTxcwdwvLr8/eIGAkRGZKZTIrt4YEo622cevMuXgmOFjcoIiIDYEJron47lgQAGDhjRxU1iaiuKCkx3RtcyhIVb9ARPSGZTIrIpQqEvPWcUPbT3ksiRkREVPOY0Jqo+lZ6n0KYiEzcnfzCCrd98XOcASPRXVFxCQKnRyJo5g7eoCPSEx9vV/y08CUAwOY9F7HrSCJvGBFRrcWE1kRtXviysBw4PZIXKqI6bM/fV/Fd5DmMCil9VnbCoLYadfYdT6pw/7SbdxE4PRK37hTUWIwVGTw7yuDvSVQX2NSzgO+zngCA1VvP8IYREdVaTGhNlPSRIflX/XJapEiISEx38guxMuI0Ig8kCGVJGXe01k27eVdr+duf7ANguGdukzPvIHB6JAKnRxrk/Yjqqv8b3gmDXnxKWL+QyPnriaj2YUJrwmyszYXlI2dSRYyEiMSSe1ezm/GYAc9gY2h/AEDwmGeF8rLE9Un9EH0egdMjMXBGJOasPqSWmKpUKq0jqy74/m98/esZAMDEsN/1EgcRVW1cYGt88f6LAIBZKw/ibMJNcQMiItIzJrQmbPXsPgh6wQsAcCe/CEplCa6m5bL7MVEdcq+gWG29j48n6lmZo4GNJaKWKdC9nbva9mJlCZZtPol/k3MAAP/bd1lt+7X0XLX1/1Ju4+69IrWyrX/8CwBQqYBzCVkAgH3HrgEoHajuleBotUT7dt59HI/PwM7DiVWeT+D0SOz+6yqKikuqrEtEumneqAFaNXEAAHyw+rBJDyBHRPQoJrQmzMHWCm8ObCOsB82KwpSlf/A5GSIjduPWPb0e79790oS2vrU5ZozsjGmvddKoE7VMAQtzGQBg0Kwo7D+ZjGmf/QkA+HHXBbW6py5mAijtmpiceQfvLd+P4XNjqrxR9sWWf9TWR87bJfxo/utsWqX7tvFyUltf9ctpzFl1qNJ9iKh6Pp3aCz3al97g+m7HOZGjISLSHya0tdSfp5LFDoGIHrH/VDLGLdqL345e09sxyxLahe90wwudPCqsV6ilG3DMkUS80LF0n/FBpTfHftx1Af9czsSslQfVugbfyS+CskSFg/+kVPgee/6+qrY+/Ys/cePWPbVn/MviGNm/Fb6a3QefTu2JTyb1ELpElrmUdKvC9yGixzNzlA8AIOrgf0jO1P6sPRGRqWFCWws0ldtplC3ddFKESIioMsse/L/88n//6O2YuXfvAwBs61lUe9+vtp6BuZkUTg2shMS2qLgEH33zl0bdkfN2IWjmDoT/eEIo+3F+f9jVf/i+KyPUB6f7N/k2xi3aq1b22U+nAAAOtpbwcLFFqyaOALT/HQtmKy2RXkmlEsx58Fz9xLDf8T1baomoFmBCWwusmNEb/s81ETsMIqqG05dvPNH+SmUJ4hOzhK6+jnZWldb/Zo6v1vK7BUWwsTaHTTUT4p4dGsHe1hKbFrwERS8vnfc7dLp0ADt7G0u1cqlUgvUh/lg04Xmh7Px/Wbidd79acRFR5Z5v545nmpXeSNr+Z4LWgeWIiEwJE9pa4t2hHTDCvxXeH6H+/Nyt3ALk3OEPQiJD27LvEmatOCisn7yYobZ97jdHkJ6lfRodXcxZfRizVz5swSx7RrYi7g1tsGPpQI3yv86moZ6VOWSPTAVWlRc6NhKWH72h9lq/lhr1PV1t1Na1xetoZ4X2TzvjVb8WQlnod39XON0QET2esHd7YtIr7QEAn6w/JnI0RERPhgltLfJav5bo3dkT9a3MAABDZkfh9dA9GD1/N4qKNZ+fIyL9KigsxoG4ZKhUKmzcdREXrmZj119XEXs8CfPX/K1Rf/zH1ZtGp6REhcDpkThyJhUXrlZ/PkmJRIKF73TDdx/2VSuv/2AKsAY22ltpX36+qUZZ1zZyYbnBI62tnVq54KVu6vusnqXeQmxbv+IW4dEveQvLV67n6G26ISJ6qOz/6LmELGHUcyIiU2QmdgCkf3cfTONRWG7ai4tXb6GBjQWuXM+B77ONxQqNqFb7IToeOw8n4n7hwxtIq385XckeQNbte3BqYK3T8TftuQgA+GT9cbXyjyd21znGDi1cAAAL3u6Ged+WPitrJittnX13aAcsXqfeWjNzVGf06uiBiUPaC/PNRi1TqNUpPyc2ADjbW+Odwe0wsn8rtWQ3apkCefeKcPrKDTzlYV9pnBtD+2NUyG5hvaREha1/XEFE7BX8vOhlSKvZokxEmpZM7oHgVYeEUc8Bzf/fRETGjgltLfRiZw/sP6k+yvFnP58Spgv5/Oc4tPVqiI8n6f4jmIiqVjbPamWDPs0a7YPfjl5D3INnaO/kF6kltBt3X8D+k8n47sO+CJweiX5dm2DKqx0AAKevaH/u9nHmlGz3tLOw/Pe5dADAc23k2P7pQMT/lwXHBlZo5Gyjsd/z7eQaZVKpBIsnPo8PvzoCAML5PNpyC5Qmv4/OjavNo4NcDZq1A2WnufWPK/BqZI/kG3cwsKfuz+8SkbrWzZ3g+6wnYo9fF8oCp0fi0yk90bKJAyQS3jgiIuPHhLYWKngwjUd5j859eTbhJlQqFS9WRAa0Y+lASCQSPN/OHa8ER6FYqcK1tFy1EX63/HYZAITW0L1Hr+Gl55viKQ97XLqmPpWNUwMr9O/WFG2ealjtWGRSCQJ6NEP0oUQ85WmvVt62guNt/3QgKmoYbfeUMyI+GYAqpqvVmVQqwcCezbHj4H8AgPI5+4aYh3PnvtStGczN+PTMoxITExEcHIycnBzY29sjLCwMTZs21Vr3v//+w6BBgzBixAjMnj0bALBixQps3rwZLi6lLfqdOnVCSEiIocInA/q/4Z3g4lAPEbFXUKws7dk188Hz/7+GBfL/FxEZPf6VqoVG9veuuhKAI2fSajgSIioT/m5P4QaSTCrBtNdKB3BbEfGPUGf/yevadsW0z/7Ed5Ga02us+aAvhvdtWe0Bncq8HdQWoW93Q/i7PXWqL5NKKr0JZmVhBmtL/d0nHR/UFtvDAyutM3h2FE5dzNTbe9YWISEhGDFiBPbs2YMRI0Zg3rx5WusplUqEhITAz89PY1tQUBAiIyMRGRnJZLaWG+HfCtvCA7HmA/XvwUffHIHyMXqAEBEZkk4JbWJiIoYNGwZ/f38MGzYMV69e1aizatUqDBgwAAMHDsTgwYNx8ODD0T2VSiVCQ0Ph5+eHvn37IiIiQqdt9Hiayu0QtUyBHUsH4vtHBn8p70bOvQq3EdGTC3nrOWHZ+8E0GWXKBlUa0vtpAMC5hJtYtvlUhceKPJAgLL/q1wLfBPs+ccuJRCJBp5YuRt0CI5NJ4eJQ+TPGIWv+4o/ucrKyshAfH4+AgAAAQEBAAOLj45GdrTmQ2LfffosXX3yxwtZbqlvcnOoLvx8szGU4/18Wgmbu4P8vIjJqOv2K0eVOb7t27fDLL79gx44d+PjjjzFt2jQUFBQAAKKiopCUlIS9e/diy5YtWLFiBZKTk6vcRk9GIpHAxbEe1nzgJ4x8XB4nVCfSn+zcArX1Ls+4wcfbFVHLFFoHWbE0l8HaUobNey5i37EkzFl9WOf3Gv2SN9y1PN9aWy1+MOiVhZkUW5cEaK1zJemW1vK6KC0tDa6urpDJSqdGkslkcHFxQVqaeq+cixcv4tChQ3jjjTe0Hmfnzp0IDAzEuHHjEBcXp7VObm4ukpOT1V7p6el6PR8yPIlEgq9m9xHWg2buQN69IhEjIiKqWJUJra53env27Alr69K76C1btoRKpUJOTg4AICYmBkOHDoVUKoWjoyP8/Pywe/fuKreRfrg51cfPiwcgapkCA3s2R8smDmKHRCS6zFv5SEy9rbfjxTwYEKpM6+ZOOu/7xRb1ZGH++OcqqAm8O7R99QKrBcpajbaGBcLCXIZfwwLxTbD6NEDp2fkiRWeaioqK8NFHHyE0NFRIfMsbPnw4YmNjERUVhTfffBOTJk3CrVuaNw3Wr18PX19ftdfIkSMNcQpUw1wc6iHy04dzV782NwaFRZwCkIiMT5UPO1V2p9fR0VHrPtu3b0fjxo3h5uYmHMPd/eGolnK5XLiDW9m28nJzc5Gbm6tWxrvA1Tc+qC2AhwPOfLrxBGaO8hEzJCKDu1+kxJuLfgMAfDbthSqnkKlM4PRItGhsj8tJOQCAdwa1xTfbzqJrG7cq9713X/PH4YRBbdGppYvQqnvj1j2MW7QXABA85lmdRgiu7czNpHB3tkHUMgV+P3Edn/10Css2nUTP9u6QyYy3+7ShyOVyZGRkQKlUQiaTQalUIjMzE3L5wxGqb9y4gaSkJLz99tsASq+xKpUKeXl5WLhwIZydH46C3b17d8jlcly5cgVdunRRe68xY8Zg0KBBamXp6elMamsJqVSCqGUK4TfDkOBobP904GM/t09EVBP0PsrxsWPH8MUXX2Dt2rV6Pe769euxcuVKvR6zLrOtZ4E7+YU4EJeClk0cNKa+uHuvCPUfmVuSqLbIyLorLJfNv1jR3Ivb9v+LpPQ7eG94R41tKx8M6FSWzAJAt7ZyBPRo/lhxvTesI/y6qM8T7exgjTcHtoFKpWIyq8ULnTzw2U+lzx6n3rwLT1dbkSMSn5OTE7y9vREdHQ2FQoHo6Gh4e3ur3YR2d3fH0aNHhfUVK1YgPz9fGOU4IyMDrq6uAIALFy4gJSUFzZo103gvOzs72NnZaZRT7RLxyQAMnbMTADBu4V58Pu0FONhZiRwVEVGpKm9ll7/TC0Drnd4ycXFxmDlzJlatWoXmzZurHSM1NVVYT0tLE1pvK9tW3pgxYxAbG6v22rRpUzVOlcq7k18oLK/Zfg6B0yORc+c+AOB4fDqGz43B8Xi2gFPtcPhMKgKnR+KrracBAEfPa363y/+fKHPqYibWRp3HvuNJuJx0C4HTI9Xq7fn7msY+5eeUrUofH0+19d6PrJcJesELg158Sufj1iXlW4oenbu2Lps/fz42btwIf39/bNy4EaGhoQCA8ePH4+zZs1Xuv3z5cgQEBGDgwIGYO3cuwsPD1VptqW6xsjATRhzPzi3A66F7UFRcInJURESlqmyh1eVOLwCcOXMG06ZNw5dffonWrVurbevfvz8iIiLQr18/5OTkYN++fUIyWtm28ngXWL9e6tYUu/66qlZ25fotPPuMm1C+4PujFbZaEZmSJeuPAwBijlxFzJGrWuuM+GgXmrjZYuXM0oFQsnMLELLmL2H79C8OCPWililwNuEmrC1lWrsN62raa50w7bVOKCxSokSlYje+J9TAhgltGS8vL62zBqxZs0Zr/SlTpqith4WF1UhcZLpkMik+GtcVC9eWtuwPnh2FLYtfRj0r9uYiInHp9LCRLnd6Q0NDUVBQgHnz5kGhUEChUODSpUsAAIVCAQ8PD/Tr1w+vvvoqJk+eDE9Pzyq3Uc2ZOKQdwt7toVZW8mBY/hIOz0911LX0O0i9mQcAGBO6p8J6efmF+GD1YY1k9sOxXSrYo3IW5jJYWej9CZA6o8PTzqhvZVbpHLlE9OS6tHZD1DKFMJXWsA9jMHROtMhREVFdp9MvKF3u9G7durXC/WUymZAEV2cb1RyJRIJnmjnh82kv4P8ePEOYe7e0K+XJi5lCvSUbjiP49WdFiZFIHxKSc6pV/51PYhH+bs9K69wtKNZa/qy3a7Xei/Rj4YTnxQ6BqE5Z80FfzF55EBev3UJBoRInL2agcyv+/SMicXA4yDrOy8MeP87vDwD48n//IPrQf2rbD59O5YTqpCYvvxCh3/2NG7fuiR2Khty7hQicHimMyAlAuGGjTdkcsVHLFOjW9uG4ALNWHhSWp77aAWaPjJy7+sGzuOV1buXCEXaJqE6QSiX4dGovLHuvFwBg/pq/cebfGyJHRUR1FX99kdpzZ99s0xws5PI1zbkHqe7Izi1A8KpDyLp9D6ev3MCWfZdx4kIGNu+5KHZoGr759YywnHPnPgqLlHC0swQAvNDRQ63u8L4t1dYrmr7q2Wfc8GtYABZPfB6DHwzMdKpcL4YN8/0RtUyB+eO76eUciIhMRYvGDpj2WicAwIdfHUFBofbeK0RENYkPbVGVz53NWnmQg0PVYWXPkv6095LaqL6FxY8/GFJNOfBPirA8ev5udGrlguzc0tG7pw7rgGmvlU69o60l1dxMih1LB2LgjB1C2UfjusLetjQhbveUM9p6NcSv+/8Vtgf2bA4HW05dQUR1Vx8fT/wYE4+btwswdM5O/DCvX7VGeycielJsoSWtPpnUHd/M8RXWOTx/7TUpPFati26ZK9dvYW3UeWH90SlqjPE74elqo7ZeviXVwlwGmUxaabdgiUSCqa92AAC0auKALq3dNLaX9+bANk8YMRGR6Vs3z19YfmPBXoRtOA6Vio8rEZFhMKElAMCQ3qVdKWeN8sHiic+jjVdDuDd8mBzcyi0QKzSqYdczSkf1Tc+6K5TduHUP739+ANvKtUY+ysWhXo3HVl1l5/IkWjUtnZKsU0uXKutymh0iolLbHsxTCwCHTqdi4Iwd+L/P9osXEBHVGUxoCQDw+svP4KdFL6Nnx0Zo95SzUG4mK/3BXjYCMtUut/PuC8vjP96HouISnE24iXGL9la5b+SBhAq3qVQqFBY9WZfkM//eQNrNu1VXfOC/lNsVbhvZv5XOx/F0tcWqmb0xvF9LrdujlinQvZ071nzgp/MxiYhqOzOZFFHLFAjs2VwoS0i+jcDpkbwpTkQ1igktASgdsdDGWnNy9LKBbqIeGf2Yaoc/Tl5XWx88OwofrD6sUa/+g+/GK32exoRBbYXyiuYsnrP6MIYER2NiWKxa+alLmWrdmCtSUqLCh18dwduf7Kuybpn3lu+vcJt3E0edjwMAjd3sKn22PHjMs3Bzql+tYxIR1QVvB7XFtvBAtZHjXw/dg33HkgCAMycQkd5xUCiqlPODydN/P3Edx+Mz8GNof3azrEW+31F5ctmwgRW+n9sP0kf+zb9+MBr2O0v2Yc0HfTX2O/9fFgAgOVO9C3DIt38BAN4Y8IzGMcsrPy1OQWExrCwq/1NVPrEuazk1N5PixIVMNLS3QvsWzhXtSkREemYmk+KDN7pAWaJC0MzSgfa+2BKHL7bECXWG922J+tZmiDqUiMzsfHRo4YyF73BOaSKqPrbQUqVcHR+2Qt3JL8RZzjNXa+QXFFVZ5+btAq2JZx8fTwCAg60VAqdHYtdfV4Uuxvfuq0/b8L99lzXuyA8Jjq70fcsPQLVOhxbdGzkP58R1c6oPN6f6cGpgDf/nmqBzK9cq9yciIv2TSSWIWqbA8+3kGtt+/u0Svt9xHpnZ+QCAfy7fQOD0SE79Q0TVxoSWKvVoa2xhkfGNbEuPZ/UvD+ds/X6uZisrAHh5NNBa/s6DbscXrmY/ONZpDAmOxuDZUXj1g51qdX/cdUG4Q1+mWFmCcwk3tR777CPlMUeuVnwSD6TcKG0JnjVa+1yyREQknjljumDDfH8seud5rJjRG880U38MJOgFL2F56JyduJqWa+gQiciEscsxVWn7pwMxMSwWaTfvQlnChLa2+DMuGUDpD4mKRiz+dEpPreXWltr/dFQ1lY9tPQvcyS8dYGzO6sNoKrfDx5O6w7aeBYDSrsPanuGdvfIgwt7VHgvwsCuzUwPOCUtEZIwcbK2Eebu1/T0fG9Aaigc3P6cs/QOj+rfCq34tKh3PgIgIYAst6UAmlWDB26WDQyWm8q5pbdP+afXnSzfM98c3c3zxyaTuMDeTad1Hlx8Ya+f2U1vPvVsoJLNlrqblYsRHu4R1RbmW3EbOD6eNik/MrvL9AAg/loiIyLRIpRL8GhYgrG/cfREDZ+yodPo4IiKACS3pyN7WEgDw095LIkdC+tLhaWfUtzaHj3fpM6bbwwPxa1gAHGyt4N7QBm28Gla6f8smDhVua+7eAM4O1mpdgEPW/FVh/YL7xUjOvKNW9tXsPnhvWEdhXaV6+Bzuxl0XEDg9EulZdxE4PVIod7CzrDRmIiIyXuZmMkQtU+CjcV2FsrVR5/lcLRFVigkt6aT8KLMXdGwtI+OWe7dQ7TkmmUxaYYusNvPfeg6WFjKNZ6EA4C1FGwBAzw6NMNT3aQDAv9dzAAATh7TDhhB/tfpDP9iJiWG/C+vbwwMhkUjg16WxUPbRN0dw9Fwahs+NwZZ9lwGUzp1bXlWjIRMRkfHr0toNUcsUmDGyM4DS52qPxaeLHBURGSsmtFRts1YeRLGSz9Kautt376NB/cdv0bSpZ4FfPgnA2MDWAIDAns2xelYftG7uhLZPPWzd7dmhkdp+DraWQot/RWSyh3+aZr9e2sp7+spNLFp3DHfvaR+dufych0REZPpe6OQBu/qlYyws/P4ovt9xTq23DhERwISWqqGp3E5YHjQrihcVE5aYehtZtwvQwMbiiY/VqokjtoUH4u2gtvB0tcWSyT3UtjdzVx8puUtrOSQSCaa82kHr8ZZOVR8sRCbV7c/UxMHtdA+aiIhMwo/z+8P/uSYAgO1/JmDgjB3453Im0m7eRVGxUuToiMgYsH8e6ezL6S9i4IyHg/Ys+P4oQt56TsSIHp9KpUJ2bgGcGlgLZSUlKkgkug14ZMqKlSWYumw/AODkxUy8EdD6iY9pJqs86XRxrIfM7Hx88EYXYSqofl2b4I+T13EuIUutbssm6l2YO7dyqfTY7w7tgC6tXTkgFBFRLSSVSvDu0A4wl0kRfTgRAPDRNxWPybByZm80cbOrcDsR1T5soSWdSSQSONo9TBpOXMhAYuptXM+4gylL/0BJiem02C7ddBJvLNiLpPSHozYrZu5QS9hrq5krDgrLhrrolyWlzdzV3+/DN7pg3ptd0enB9haN7TX2tTAvHSREm6hlCvg/14TJLBFRLffO4HbY/unAKuu9++kfGPFRDJR8NIqoztCphTYxMRHBwcHIycmBvb09wsLC0LRpU7U6hw4dwvLly3H58mWMHj0as2fPFrbNmjULly49HB330qVLWLVqFXx9fbFixQps3rwZLi6lP2g7deqEkJAQPZwa1YT1If5qo8qWtfQBwMK1ptFiqyxR4UBcCgDgyNk02Na3wOvz9wjbzybcxNOe9rV2gKGywZkA4J3BbQ3ynuMVbeD3bGO4OdVXK7epZ4Fnn3HDs8+46XwsecP6SLt5F2P10LJMRESmQyaVqN3gPH35Bs4k3MRI/1ZIy7qLCUtiAQB38osQNCtKqDfCvxWG9+WctkS1lU6/2ENCQjBixAgoFApERkZi3rx52LBhg1odT09PLFq0CHv27EFhofpck+Hh4cLyxYsXMWbMGPTs+fA5uaCgILUEmIxb1DKFWlJb5sSFDBGiqb6V//tHWN60+yI27b6otv2D1Yfh6WqD1bN8DRyZYb0d1Ba29Z78GVpdmJvJ0KJxxdP86GJbeCCAqrs3ExFR3dC+hTPatyidS72Rsw2ililw49Y9jFu0V63e5j0XsXnPRWwLD+Q1hKgWqvJ/dVZWFuLj4xEQUDrZdUBAAOLj45GdrT51S5MmTfDMM8/AzKzyHPmXX35BYGAgLCwM80OaDGvP31fFDqFK+44nVVnnekYeAqdHCq/aNABW3y6N4WhnicCezcUOpVrMZFL+ECEioko5O1gjapkCn0zqjqVTe+Kr2X2EbYNmRSEzO1/E6IioJlT56zAtLQ2urq6QyUrnp5TJZHBxcUFaWlq136ywsBBRUVEYMmSIWvnOnTsRGBiIcePGIS4uTuu+ubm5SE5OVnulp3NOMrEEveCltXxlxGkDR1I9jzvd0JVy3XRNwStzohGyRvugGbfzCmH3BNP1EJHxS0xMxLBhw+Dv749hw4bh6tWrFdb977//0L59e4SFhQllSqUSoaGh8PPzQ9++fREREWGAqIn0p41XQ7Rs4ggPF1u1Z2/fXPwbCu4XixgZEembQR8S3LdvH9zd3eHt7S2UDR8+HBMmTIC5uTkOHz6MSZMmISYmBg4O6t0T169fj5UrVxoyXKrEmwPb4JU+T+PStVvo0tpNaxdkY/TJD8cr3DayfyuN7sdlpn9xoMKBiYzNpWvZuF+oxKmLmTh6Lg1d2zycn7WkRIVj8emob1U7nw8molK6PCoElCauISEh8PPzUyuPiopCUlIS9u7di5ycHAQFBaFbt27w8PAw1CkQ6U3Zs7eTwmNxPSMPQz/YCQB46fmmUPTyQiNnG5EjJKInUWULrVwuR0ZGBpTK0rm+lEolMjMzIZfLq9hT09atWzVaZ52dnWFubg4A6N69O+RyOa5cuaKx75gxYxAbG6v22rRpU7VjIP1pYGOJLq11H8zHGByLL23Vb93cCZGPjJY4sGdz/LzoZTHC0ovCIiVSb+Rh3rcPW2YXrTumVue/lNsAgLsFvDtNVFvp+qgQAHz77bd48cUXNQZ6jImJwdChQyGVSuHo6Ag/Pz/s3r1bY3/2niJTsnqWr9po+7uOXMWEJbFqjxh9uvGEiBES0eOoMqF1cnKCt7c3oqOjAQDR0dHw9vaGo6NjFXuqS09Px8mTJ4ULbJmMjIcDCV24cAEpKSlo1qyZxv52dnbw8PBQe7m5mVYyVZutD/EXlk3heVNrSzNIpRIsmdxDKKtnZY761ubYsXSgWnmZ3X9dNWCE1TckOBrvLIlF/iPJavl/j2mf/wmgNKEnotpJ10eFLl68iEOHDuGNN97Qegx3d3dhXS6Xa01U169fD19fX7XXyJEj9XtCRHr05fTeCHnrOUil2kc8PhCXgglLYpFz576BIyOix6VTv8P58+cjODgYq1evhp2dnfCczfjx4zF16lS0bdsWJ06cwPvvv4+8vDyoVCrs3LkTixcvFkYz3rZtG3r37g17e3u1Yy9fvhznz5+HVCqFubk5wsPD4ezsrN+zpBrnaGeF7u3ccfhMKu4XKmFladxdWgN6lN40ad3cCR+80QV5+Q9H5pZIJGjd3AmOdlbIzi0Qylf9chr9uzXFjVv3MCEsFp9O6YnmjRpg/c54yBvWR7+uTQx+Hrr45/INdGzpolbWsIG1SNEQkTEoKirCRx99hE8++URIfB/HmDFjMGjQILWy9PR0JrVk1Hy8XYVeWkplCe4WFOOfy5nILyjGql9OI+VGHkbP1+yR4OZUDyum9zb63zhEdY1O/yO9vLy0DgixZs0aYdnHxwcHDhyo8BgTJ07UWl5+EAoybd7NHHH4TCr+S72NZ5oZrgWwqFgJmVRa4d3WMuWT1s6tXIXlbm21d59fNasPMrPz8d7y/ULZjgMJWBN5DgCweN1RfPdhX/zye2kXeTES2nMJNyGTSrEi4p8K68z79i+N538NNf8sERle+UeFZDKZ1keFbty4gaSkJLz99tsASrsOq1Qq5OXlYeHChZDL5UhNTUW7du0AaLbYlrGzs4OdnZ1GOZGpkMmksKtvgV4dS58Pb+xmi9krD2mtm56VLzx/W6Z5owZY/n8vQFbuN0h+QRGsLEp7gpWUqFBYpISlhQwf/3AM/6Xcxvdz+9XcCRHVQbzFRHpT1rX1r7NpBk1oB8+ORh8fT0x7rVOl9W7fLU1oW+o4H6qNtTlsGjVAfWtz3L1XBABCMgsAmbfu4XbewyRZpVIZfNL2OasPay3/cX5/ABDuMAdOj8Tz7R7+mDXU/LNEZHjlHxVSKBRaHxVyd3fH0aNHhfUVK1YgPz9fmBO+f//+iIiIQL9+/ZCTk4N9+/Zx3AqqE55p5iTcBL5x6x5+/eMKbt6+h75dmmDh2qMa9f9LuY2gmTuq9R6B0yPx+sve6N+tKa/HRHrASR1Jb154cHfTwvzxu69V1+280mdcfj9xHQAwct4uTFn6h0a9rNv3MGFJLABgeL+W1XqPTyZ1r3BbYurtcu9RUGG9mrB+Z7zW8g3z/WFvawm7+uoXySNnqj/VFhGZpvnz52Pjxo3w9/fHxo0bERoaCqD0UaGzZ89Wub9CoYCHhwf69euHV199FZMnT4anp2dNh01kVJwdrPHO4Hb4cGxXdGnthqhlCkQtU2DJ5B54b1gHdG+n2WtBVxtiLmDER7s4hRCRHrCFlvTG9kEC9b99lzH6Je8qauvHT3svCctlUwfl3i1EsbIEZrKH92veWLBXWLasZsLdzL0BVs/qg0nhv2tsKz+i8NiFe7FyZm80cTNM97uyrs7l9WjvDgdbKwCosAt2qya6tVATkenS5VGh8qZMmaK2LpPJhCSYiNS1bu6E1s2d4NelCVQqFc4m3IS1pRniE7PxXeQ5THm1Aw6fTsWpS5n4/sO+cGpghT/jUtC1tRusLc2w6pfT2Hv0GgAIXZinvdYJL3TyUOu6TES6YQst6U35BNJQ89LuPJyotXzQrChh+eg59ZbJtk81rPb7eLraCssvPd8Ubw5srbXe3K+PVPvYj1IqS/DX2bTHGi161mgftfXt4YEadRa+8/xjx0ZEREQPSSQStHvKGU97OkDRywtRyxTo17UJQt/uhqhlCrg41oNMJkUfH0/UtzaHVCrBlFc7YMdS9akDP/vpFIJm7kDg9EgcjEvBjVv3RDojItPDFlqqMef/y6rR6WGKiksq3R44PRKN3WyRlH5HKLN+gpEJNy98CckZefBu5oi0m3fx/Y7zGnVy7txH4PRIrA/xh0QCobW0Ol79YCcKH5ybh4sNVs/qo/Fs7r1yXZQ2zPfHvfvFyLpdoFFPJpMiapkCW367BL8ujWEmk3J0RiIiIpFJJBJELVMg714RIvZdxq/7/xW2hT8yF+6Ewe0woLvmlJamqKCwGFYWT/Y7RKksgUzGNjl6iL9sSa9aNLbH5aQcAEDwqkMao+s+iX8uZ+LuvWL8/NslXE3L1Wmf8slsHx9PTH6l/WO/v209C3g3Kx1URd6wvlAetUyBi1ezMXPFQaFsTOgeYVt1FZZL1JMz85CcmafWQgwAM758OKK4g60VHGwB94Y2FR5zWN/qPTdMRERENc/G2hxjA1uje3t3mJtJceh0Kv6377Jana9/PYM/TlzHpaRb6NulMd4e1PaJk0J9U6lUKClRYfXWM6hnZYY3B7YBANwvUiL2eBK6tZXj9fl7hPplv48SknMgkUjQzN0OEokEU5b+IfzG+zUsEOZm6onrsk0nsf9UcoXbqW4yrv8NZPI+mdQDQ4KjhfWSEhWupuViyYbjmP/Wc8jJu4/ZKw+hRWN7LHvvBZ2P++32s4g6+F+F26eP7Ixlm05WeoyqRkGurrB3e8DexhIA0Kqpo9Y6m3ZfxMj+rZ7ofZQl6l2P8/ILhUS9R/vHH5CCiIiIjEOLBzMwNHNvgNEveSPt5l2kZd3F1dTbWBcdj0tJtwAAvx1Lwm/HkoT9enZohIP/pAjraz7wg5tTfRhKUnouJn+qORjn9j8T1Na/2npGbV2XR9MGz374+FhA92ZQAUIyW7b93aEd4P+c4adNJOPC2xqkVxbmMswd20VYV8zcgfeW70fazbt4Z0msMLfb5aQcqFQqFBQWY1L472qjBT+qqFhZaTLr3dQRL3byqDQuV8d61TyTqj3TzAnuzg9bRb+f21ejzs+/XdIoq8yh0ykaZXfuFqqtv/bRLmH50WdmiYiIyPTJG9ZHp5YuGNz7aaz7qHTe2kbOmolq+WQWAMZ/vA+B0yOxLuo80rPuIjH1tsaN8cdRrCyBSqXCfym3ETg9UnhpS2Yr8nw7OdbqMAdvc/cGGmXRhxOFcVOG9H5KKF8Z8Q8Cp0eiqFgJANh56D8ETo/Egu//1jkuMn1soSW969pGji7PuOFYfHql9f5LuY0fdsbjesYdTF22H+tD/LHn72sY5tdCbYTewbOjKzkK8OGDBPr/hnfE7bz7WBddOp1N+e7PiydWPPWOvjw6TU51pd28i7ANpc/NvNLnaWEU433HkyocyMrQ894SERGRYTW0t1Z7hCm/oAiJqbkIXnVIKAsd3w0bdsUjIbm0geDX/f+qPZdbZtRLrTDMT/tjSCqVCrfu3MfqX07j6PnKf8OV5/dsY4wPagNrSzNIJBKUlKhwOekW5q/5C4sndoeXhz3uFylhYSaFRCJB5KcDkXIjD2YyKdyc6kEikWBd1Hn8uv9fhI7vhk6tXIRj37h1D+MWPZypIugFL7wR0Bqvv/wMglcdwoWr2QA0fysej88QWoE7tHBGrw6N0MfHk8/e1lIS1eMMpWokkpOT4evri9jYWHh4VN5CR4aVeSsfby767bH393S1xeiXWiE79z6+/vVMhfUiPh6gMcjR9j8T8P2Oc9iy+GVk5xbAvaFNhVPY6Nu19Fw421tjy28PB3j4dGpPfB95DuFTelaYgD7a9cbB1hIfT+qOiWGlUwWVXcgKCosxdE7pEP+G7lZEVBfwuvLk+BkSiUOlUiHnzn0kpd/B3G8qnnXBxtocPy16WaNc1xkqBvZqjvZPOaOp3A71rM1hY23+2DE/qbx7RXhtboxaWR8fT/x+4nql+7VobI8Px3aFo131B+8kw6vqusIWWqoRLg4Pu/ja21iijZcTDp1O1Xn/6xl38PEPx9XK3h3aHof+ScU/V24geMyzFU5oHvSCF4Je8AIA1LMy7B/Zsjloxwa2FhLamV+WDhZVfnAnlUolJLfa7im9PagtPFzUB4IqKVEJySwAJrNEREQkkEgkcLCzgoOdlXAjvGywptz8QsxZdRgpN/KQd69ISF4HdG+mdQrEKa92QPSh/9C/W1M0kzeAdzNHpGfdRQMbyyeaMULfbKzNEbVMgfP/ZSF41SGEv9sT3s0cMe21TriecQdnrtzA19vOaux3OSlHGMCzDBsKTJfxfCOp1rG2lOHefSW+meOLelbmCEzMEp6hra5OrVzg/1xT9OvaBPkFxagv4t1AXXVv547DZx4m8Zv3XMTs158VLiKfTu0JZ3trHI/PUNtvxsjOGsm6skSFoJk7aj5oIiIiqjUkEglkMgkcbK3wdbAvCu4XY+gHD2+OP5rMfjPHV5g1oV9X9cGWjDnZa93cSWNmCU9XW3i62mJAj+YAShsG0rPvYv/JZOw6chU5effV6o//eB+8mzoifEpPg8VdXXn5hcjJu485qw7jKU97zHuzK4qVKpibSVFSosKd/EI0eDBgaV3ChJZqzOaFL+NW7n2hlfSZZk6I/HQg8u4V4autp4UW24hPBqi1PGrj9KBLiEQiMYlkFigdebl8QnvodCpmKB9OyVPWcvuoF8oNcDVhcDt8/esZtZH+AGDem131HC0RERHVdlaWZvj+w774etsZHI/PQH0rMzR1bwC7+haY/fqzkBnoES0xSKUSuDe0wQj/Vhjh3woqlQonLmTA1bGeMLjVhavZCJweqdO0i3+dTcXHPxzHxxO7VzjWiT4pS1RqA4OeuJCBgTO0N3a8MeAZDOnztF7fX6VSQaVCtR7jKylRGeSxPya0VGPMZFI4O1irlUmlEtjVt8Cs0T6Y/XrlX3BPVxtcz8gDAKPq3qIrbXOjnfsvq8L6iyc+j8audmplyRml0/OUPDJC4bPPuOkhQiIiIqprXBzrYd6bz4kdhugkEonweypqmQLJmXeEsUvKetPNGNkZHVo44/x/WejWVo6kjDvIyy9SG5Drg68OA9A+rosuVCoVipUlkEmlWpO/z38+hdjjlT8T/Kgfdsbjh53x+N/HA1BQWAxLc1m1HsO7lpaLj745gjljuuApT3v8fTYN4RtPCNuDXvAS5hrW5uy/NzF/zV8oLC7BlsUv1/gjgKaXJVCtUNnovN/P7YvYY0l4zb8VrqXn4t1P/0CP9o0MGJ3+fD+3r9rgWHO/rniQhqc87DX+w7d5qiGiH+kOtOYDP/0GSURERFTHebjY4utgX0xYEiuULd10stJ9yg9AVb4rd5kR/VriNf9WWve9X6TEou+P4p8rNzS2zRjZGUfPp2tMy9S8UQMsf6+X2mjNp6/cQFFxCTxcbODiUA/TPvsT/z2YDvPVR2L6aeFLsKlXOitHUbESN27dg7uzDXLvFuLEhXT0aN8I2bkFeHdpaYv1rJXaexNu/zMBx+MzsGpmbxy/kIHUG3exLvo8Jgxuh11HEnEt/Y5Q18JcpvUY+sRRjskolD3T8e0cP8gbGu8zGo+jWFmCQbOiqqynrXvL7bz7GBWyu8p6RKQfvK48OX6GRFQbbNp9ET//dknrti7PuGHuuC5CA01lI0SbyaRY84EfrCxk2HHwP/y0V/sxK+Pj7Qo3p3oYr2irUxfe3LuFGDlvl9ZtrZs7QaVSIT4xu1oxDOzVHG8MaI0/T13HF1v+0WkffQ20xVGOySRYWZrV2kTNTCbFUN+nERF7RSjzbuqIC1ezsTG0P2Z+eRBThnXQum/ZXTT/55qgS2s3dGrporUeEREREenPyP6tMLK/9tbVR20LD0Ts8euwq28BH29X/HU2FZ9uLG3dLVaWYOzCvRXuO+XVDujXtQlKSlT4cdcFnEu4iYvXbgEAxgY8g0EvPlVpz0Zt7OpbIGqZAhti4nE1LRd9uzQWZg85X8njb2V8vF0R8lZpt/R794thZSETYvDr0gRN3Rtg2md/qu3TsrEDLiWVxr0hxB8OBpwSiS20RAagUqlwKemWMBBUbU3eiUwdrytPjp8hEVGp6xl3MCn8d7WypVN74ilPB6Rk3kFjN7sK9qwZKTfysOC7v+HubIOBPZuj/dPOyMjOh5WFDA52VlAqS1BcooKlAboJV4deWmgTExMRHByMnJwc2NvbIywsDE2bNlWrc+jQISxfvhyXL1/G6NGjMXv2bGHbihUrsHnzZri4lLYuderUCSEhIQAApVKJRYsW4eDBg5BIJHj77bcxdOjQxz1fIqMkkUjQqokjopYptM47S0RERES1i6errdCIoSxRASqV8PyroZNZAGjkbINv5qiPxVL+UT+ZTAqZceWyOtEpoQ0JCcGIESOgUCgQGRmJefPmYcOGDWp1PD09sWjRIuzZsweFhYUaxwgKClJLcstERUUhKSkJe/fuRU5ODoKCgtCtWzfe1aVaq7rdRoiIiIjItJVOicTfgDVBc16RR2RlZSE+Ph4BAQEAgICAAMTHxyM7W/1B4iZNmuCZZ56BmVn1HsuNiYnB0KFDIZVK4ejoCD8/P+zevbvqHYmIiIiIiKhOqzL7TEtLg6urK2QP2p9lMhlcXFyQlpYGR0dHnd9o586dOHToEJydnTFlyhR07NhROL67u7tQTy6XIz09XWP/3Nxc5ObmqpVpq0dERERERER1g0FGOR4+fDgmTJgAc3NzHD58GJMmTUJMTAwcHBx0Psb69euxcuXKGoySiIiIiIiITEmVCa1cLkdGRgaUSiVkMhmUSiUyMzMhl8t1fhNnZ2dhuXv37pDL5bhy5Qq6dOkCuVyO1NRUtGvXDoBmi22ZMWPGYNCgQWpl6enpGDlypM5xEBERERERUe1R5TO0Tk5O8Pb2RnR0NAAgOjoa3t7e1epunJGRISxfuHABKSkpaNasGQCgf//+iIiIQElJCbKzs7Fv3z74+/trHMPOzg4eHh5qLzc3N51jICIiIiIiotpFpy7H8+fPR3BwMFavXg07OzuEhYUBAMaPH4+pU6eibdu2OHHiBN5//33k5eVBpVJh586dWLx4MXr27Inly5fj/PnzkEqlMDc3R3h4uNBqq1AocPr0afTr1w8AMHnyZHh6etbQ6RIREREREVFtoVNC6+XlhYiICI3yNWvWCMs+Pj44cOCA1v3LEmBtZDIZQkNDdQlDg1KpBMDBoYiISD/Kridl1xeqPl6biYhIn6q6NhtkUKiacuPGDQDgc7RERKRXN27cQJMmTcQOwyTx2kxERDWhomuzRKVSqUSIRy8KCgpw7tw5ODs7C9MKPa6yAaY2bdpkUs/mMm7DYtyGxbgNi3GX3v29ceMG2rRpAysrKz1FWLfw2sy4DY1xGxbjNizGXfW12aRbaK2srODj46PXY7q5ucHDw0OvxzQExm1YjNuwGLdh1fW42TL7ZHhtfohxGxbjNizGbVh1Pe7Krs1VjnJMREREREREZIyY0BIREREREZFJYkJLREREREREJokJ7QN2dnZ49913YWdnJ3Yo1cK4DYtxGxbjNizGTcbGVP9tGbdhMW7DYtyGxbirZtKjHBMREREREVHdxRZaIiIiIiIiMklMaImIiIiIiMgkmfQ8tPqSmJiI4OBg5OTkwN7eHmFhYWjatKnB47h16xZmzZqFpKQkWFhYoEmTJliwYAEcHR3Rp08fWFhYwNLSEgAwY8YM9OzZs8r4DXluFcX4uPEZIvbk5GRMnjxZWL9z5w7y8vJw7Ngxo/vMw8LCsGfPHqSkpCAqKgotWrR4olgMdQ7a4q7suw5U/F0SO+6aiq2m467se15T51RdlX0njP07TjXDWP6NeG3mtbkyvDbz2vy4cfParMfYVaQaPXq0avv27SqVSqXavn27avTo0aLEcevWLdXff/8trC9ZskQ1Z84clUqlUvXu3Vt16dIlrftVFr8hz62iGB83PjH+XRYtWqQKDQ1VqVTG95kfP35clZqaqhFXTXy++jwHbXFX9l1XqYzjs6/o866J2AwRd3nlv+c1dU7VVdl3wti/41QzjOXfiNdm8f/v8Nqs/3Pgtdk44i6P1+bHj73OJ7Q3b95Ude7cWVVcXKxSqVSq4uJiVefOnVVZWVkiR6ZS7d69WzVmzBiVSlXxl7qy+A19btpifNz4xPh3uX//vqpr166qc+fOVXg+T3JO+lI+rpr4fGvqHCr7w1z+u15ZXWOIW9+xGfrzfvR7XhPnpA9l3wlT+o6T/hjzvxGvzbw2a8NrM6/NjxN3GV6bnyz2Ot/lOC0tDa6urpDJZAAAmUwGFxcXpKWlCV0sxFBSUoKffvoJffr0EcpmzJgBlUqFzp074/3334ednV2l8atUKoOf26MxPm58YsT++++/w9XVFa1bt67wfIztM6+Jz9fQ56Dtuw4Y92evz9gM/Xlr+57r+5yeNO7y34na8B2n6uO1Wb94bea1ubp4bea1+VHGfG3moFBGauHChahXrx5GjRoFANi0aRN27NiBrVu3QqVSYcGCBSJHqMkUYqzM1q1bMWTIEGHd1M/HVDz6XQeM+7M35th08ej3HDC+c9L2nSAyBrw2Gx6vzeLgtdmweG1+MnU+oZXL5cjIyIBSqQQAKJVKZGZmQi6XixZTWFgYrl27hs8//xxSqVSIEwAsLCwwYsQInDp1SiivKH5Dn5u2GB83PkPHnpGRgePHjyMwMLDS8ykrN5a4a+LzNeQ5aPuul50XYJyfvb5jM+Tnre17XhPn9CQe/U6Y+necHo8x/hvx2sxrs65M/e8Wr828Nj/K2K/NdT6hdXJygre3N6KjowEA0dHR8Pb2Fq1L02effYZz585h1apVsLCwAADk5+fjzp07AACVSoWYmBh4e3tXGb8hz62iGB83PkP/u2zbtg0vvPACHBwcKj0fwHg+8yeJxRjOQdt3HTDuz74mYjPkd+bR73lNndPj0vadMOXvOD0+Y/s34rWZ1+bqMOW/W7w289r8KFO4NktUKpXqsc+wlkhISEBwcDByc3NhZ2eHsLAwNG/e3OBxXLlyBQEBAWjatCmsrKwAAB4eHggODsaUKVOgVCpRUlICLy8vzJ07Fy4uLlXGb6hzu379eoUxPm58hvx38ff3x4cffohevXpVeT5ixb1o0SLs3bsXN2/ehIODA+zt7bFz584a+Xz1eQ7a4v7888+1ftdXrVplNJ+9tri//vrrGomtpuPeuXMnAM3vOWA83/WK/v6tWrXK6L/jVDOM5d+I12ZemyvDazOvzY8bN6/N+oudCS0RERERERGZpDrf5ZiIiIiIiIhMExNaIiIiIiIiMklMaImIiIiIiMgkMaElIiIiIiIik8SEloiIiIiIiEwSE1oiIiIiIiIySUxoiYiIiIiIyCQxoSUiIiIiIiKTxISWiIiIiIiITBITWiIiIiIiIjJJTGiJiIj05K233sK2bdvEDsOk9enTB0eOHBE7DCIiMhFmYgdARET0uPr06YOCggLs27cP9erVAwBERERgx44d+PHHH2v0vVesWIFr165h6dKlQtl3331XI+/VsmVLWFtbQyKRCGWTJk3C+PHjtcZRpk+fPrh58yZkMhnMzMzQsWNHhIaGQi6XC3V+/fVXrFu3DklJSbCxsYGfnx+mT58OOzs7rbEEBwfD1dUV06ZN0/+JEhERVRNbaImIyKQplUps2LBB7DBqXGRkJOLi4oTX+PHjddrv66+/RlxcHA4dOgQnJycsXLhQ2LZ27VosXboUM2fOxIkTJ7BlyxakpqZi7NixKCwsfKw4i4uLH2s/IiKix8GEloiITNqbb76JtWvXIjc3V+v2hIQEjB07Fl26dIG/vz9iYmKEbbdu3cKECRPQqVMnDBkyBJ999hlee+01YfuiRYvwwgsvoFOnThg8eDBOnDgBADhw4AC++eYb7Nq1Cx07dsTAgQMBAKNHj0ZERAQKCwvh4+ODy5cvC8fKzs5Gu3btkJWVBQD4448/oFAo4OPjg+HDh+PixYt6/2zKs7S0RP/+/ZGQkAAAyMvLw4oVKzB37lz06tUL5ubm8PDwwOeff47U1FTs2LFD4xhbtmxBVFQUvv/+e3Ts2BETJkwAUNoS/O233yIwMBAdOnRAcXExvv32W/j5+aFjx454+eWX8dtvv6kd63//+x9eeuklYfv58+c13i8hIQF9+vTBzp07a+ATISKi2oBdjomIyKS1adMGXbp0wffff6/RDTY/Px/jxo3D1KlTsWbNGly6dAnjxo3D008/jaeffhoLFiyAtbU1Dh8+jJSUFLz55ptwd3cX9m/bti0mT54MW1tbbNiwAe+99x5+//139OrVC++8806FXX0tLCzQt29f7Ny5Ey1atAAA7Nq1C88++yycnJxw/vx5fPDBB/j666/Rpk0b7NixA5MmTcLu3bthYWFRI5/TvXv3EBMTg/bt2wMATp06hfv376Nfv35q9erXr49evXrhyJEjeOWVV9S2DRs2DHFxcVq7HO/cuRPffvstHBwcYGZmBk9PT2zatAnOzs7YvXs3Zs6cib1798LFxQW7du3CihUrsGrVKrRt2xZJSUkwM1P/SXL+/HlMnjwZISEh6N27dw18IkREVBuwhZaIiEze1KlTsXHjRmRnZ6uV79+/H40aNcKQIUNgZmaG1q1bw9/fH3v27IFSqcTevXsxZcoUWFtb46mnnkJQUJDa/gqFQkjQxo0bh8LCQiQmJuoUU2BgIKKjo4X1qKgoBAYGAihtnRw2bBjat28PmUyGQYMGwdzcHP/880+Fxxs0aBB8fHyE18GDB3WKY/LkyfDx8UHnzp1x+PBhvPnmmwBKW6fLzu1Rzs7OuHXrlk7HLzN69GjI5XJYWVkBAF566SW4urpCKpXi5ZdfRpMmTXDmzBkAwC+//IK33noL7dq1g0QiQZMmTdCoUSPhWCdOnMDEiROxZMkSJrNERFQpttASEZHJa9GiBV588UV8++238PLyEspTUlJw5swZ+Pj4CGVKpRIDBw5EdnY2iouL1QZIKr8MlD5jGhERgczMTEgkEuTl5emc6D333HO4f/8+Tp8+jYYNG+LixYvw8/MDAKSmpmL79u3YuHGjUL+oqAiZmZkVHm/btm1o0qSJTu9d3qpVq/D8889DqVQiNjYWo0ePxs6dO+Hg4IBbt26huLhYI6m9ceMGHBwcqvU+j35227dvx7p165CSkgKgtLW87LNLS0tD48aNKzzWzz//jGeffRbPPfdctWIgIqK6hy20RERUK0ydOhX/+9//kJGRIZTJ5XI8++yzOHHihPCKi4tDaGgoHB0dYWZmhvT0dKF+WlqasHzixAmsWbMGn3/+OY4fP44TJ07A1tYWKpUKANRGHNZGKpWif//+iI6ORnR0NF588UXY2NgIcU2YMEEtrtOnTyMgIECfH4kamUyGfv36QSqV4uTJk+jYsSMsLCywd+9etXr5+fk4cOAAunXrpvU4FZ13+fKUlBTMnTsXH330EY4ePYoTJ07g6aefFrbL5XIkJSVVGGtoaCjS0tLw8ccfV+cUiYioDmJCS0REtUKTJk3w8ssvq03X8+KLL+Lq1avYvn07ioqKUFRUhDNnziAhIQEymQx9+/bFypUrce/ePSQkJCAyMlLY9+7du5DJZHB0dERxcTFWrlyJvLw8YbuTkxNSUlJQUlJSYUyBgYHYtWsXoqKi1JLVoUOH4ueff8bp06ehUqmQn5+P/fv3qx2/OlQqFe7fvy+8tI1QrFKpsG/fPuTm5sLLywu2traYPHkyFi1ahAMHDqCoqAjJycl477334ObmBoVCofW9nJyckJycXGk89+7dg0QigaOjIwBg69atuHLlirD9lVdewdq1a3Hu3DmoVCpcu3ZNaMkFSp/j/e6773DixAmtzygTERGVYZdjIiKqNSZPnqyWlNrY2OD777/HkiVLsGTJEqhUKrRs2RJz5swBAMybNw/BwcHo3r07mjVrhgEDBuDcuXMAgB49eqBXr17w9/dHvXr1MGbMGLVutf3798eOHTvQtWtXeHh4YNu2bRrxtG/fHtbW1sjMzESvXr2E8rZt22LhwoVYsGABrl27BisrK3Tq1Emta/SjFAqFWivoK6+8gg8//BAAhFbgMq6urjhw4AAAYMKECZDJZACARo0aYcmSJUJr6fjx42Fvb4/w8HC1eWiXLl1a4eBUr7zyCt577z34+PigS5cuWL16tUadp556CuPGjcPw4cMhkUgQFBSETp06Cdtfeukl5OTkYPr06cjMzESjRo0QHh6u9hytnZ0d1q5di9dffx1mZmb4v//7vwo/GyIiqrskqrK+U0RERHXcp59+ips3byIsLEzsUIiIiEgH7HJMRER1VkJCAi5evAiVSoUzZ87gl19+Qd++fcUOi4iIiHTELsdERFRn3b17V+j26uTkhHHjxsHX11fssIiIiEhH7HJMREREREREJkmvLbRhYWHYs2cPUlJSEBUVhRYtWiA5ORmTJ08W6ty5cwd5eXk4duwYAKBPnz6wsLCApaUlAGDGjBno2bOnPsMiIiIiIiKiWkivCa2vry9ef/11jBw5Uijz8PBQG3Fy8eLFUCqVavt9+eWXaNGiRbXfr6CgAOfOnYOzs7MwgiMRERERERHVDkqlEjdu3ECbNm1gZWWlsV2vCW1l0w0AQGFhIaKiovD999/r5f3OnTunljwTERERERFR7bNp0yat+aZBB4X6/fff4erqitatW6uVz5gxAyqVCp07d8b7778POzs7jX1zc3ORm5urVlbW0rtp0ya4ubnVXOBERERERERkcOnp6Rg5ciScnZ21bjdoQrt161YMGTJErWzTpk2Qy+UoLCzE4sWLsWDBAixdulRj3/Xr12PlypVaj+vm5gYPD48aiZmIiIiIiIjEVdEjpgZLaDMyMnD8+HGEh4erlcvlcgCAhYUFRowYgYkTJ2rdf8yYMRg0aJBaWVm2TkRERERERHWPwRLabdu24YUXXoCDg4NQlp+fD6VSCVtbW6hUKsTExMDb21vr/nZ2dlq7IhMREREREVHdpNeEdtGiRdi7dy9u3ryJsWPHwt7eHjt37gRQmtB++OGHavWzsrIwZcoUKJVKlJSUwMvLCyEhIfoMiYiIiIiIiGopiUqlUokdxONKTk6Gr68vYmNj+QwtERERERFRLVNVzicVISYiIiIiIiKiJ8aEloiIiIiIiEwSE1oDijmSiBMXMsQOg4iIiIiIqFYw6Dy0dd1XW88AAKKWKUSOhIiIiIiIyPSxhZaIiIiIiIhMEhNaIiIiIiIiMklMaImIiIiIiMgkMaElIiIiIiIik8SEloiIiIiIiEwSE1oiIiIiIiIySUxoTdhXW09j6JxoscMgIiIiIiISBeehNWExR66KHQIREREREZFo2EJLREREREREJokJLREREREREZkkJrRERERERERkkpjQEhERERERkUliQktEREREREQmiQktERERERERmSQmtERERERERGSSmNASERERERGRSWJCS0RERERERCbJTJ8HCwsLw549e5CSkoKoqCi0aNECANCnTx9YWFjA0tISADBjxgz07NkTAJCYmIjg4GDk5OTA3t4eYWFhaNq0qT7DIiIiIiIiolpIrwmtr68vXn/9dYwcOVJj25dffikkuOWFhIRgxIgRUCgUiIyMxLx587BhwwZ9hkVERERERES1kF4TWh8fn2rVz8rKQnx8PNatWwcACAgIwMKFC5GdnQ1HR0e1urm5ucjNzVUrS09Pf7KAiYiIiIiIyGTpNaGtzIwZM6BSqdC5c2e8//77sLOzQ1paGlxdXSGTyQAAMpkMLi4uSEtL00ho169fj5UrVxoqXCIiIiIiIjJyBkloN23aBLlcjsLCQixevBgLFizA0qVLq3WMMWPGYNCgQWpl6enpWrs3ExERERERUe1nkIRWLpcDACwsLDBixAhMnDhRKM/IyIBSqYRMJoNSqURmZqZQvzw7OzvY2dkZIlwiIiIiIiIyATU+bU9+fj7u3LkDAFCpVIiJiYG3tzcAwMnJCd7e3oiOjgYAREdHw9vbW6O7MREREREREdGj9NpCu2jRIuzduxc3b97E2LFjYW9vj6+//hpTpkyBUqlESUkJvLy8EBISIuwzf/58BAcHY/Xq1bCzs0NYWJg+QyIiIiIiIqJaSq8J7dy5czF37lyN8u3bt1e4j5eXFyIiIvQZBhEREREREdUBNd7lmIiIiIiIiKgmMKElIiIiIiIik8SEloiIiIiIiEwSE1oiIiIiIiIySUxoiYiIiIiIyCQxoSUiIiIiIiKTxISWiIiIiIiITBITWiIiIiIiIjJJTGhNQPCqQ9jy2yWxwyAiIiIiIjIqTGhNwPn/srBx90WxwyAiIiIiIjIqTGiJiIiIiIjIJDGhJSIiIiIiIpPEhJaIiIiIiIhMEhNaIiIiIiIiMklMaImIiIiIiMgkMaElIiIiIiIik8SEloiIiIiIiEwSE1oiIiIiIiIySUxoqUo3bt2DSqUSOwwiIiIiIiI1TGipUhevZWPcor3YdyxJ7FCIiIiIiIjUmOnzYGFhYdizZw9SUlIQFRWFFi1a4NatW5g1axaSkpJgYWGBJk2aYMGCBXB0dAQA9OnTBxYWFrC0tAQAzJgxAz179tRnWPQEktLvAAAuXM1G365NRI6GiIiIiIjoIb220Pr6+mLTpk1o1KiRUCaRSPDWW29hz549iIqKgqenJ5YuXaq235dffonIyEhERkYymSUiIiIiIiKd6DWh9fHxgVwuVyuzt7dH165dhfUOHTogNTVVn29LREREREREdZBeuxxXpaSkBD/99BP69OmjVj5jxgyoVCp07twZ77//Puzs7DT2zc3NRW5urlpZenp6jcZLRERERERExsugCe3ChQtRr149jBo1SijbtGkT5HI5CgsLsXjxYixYsECjSzIArF+/HitXrjRkuERERERERGTEDJbQhoWF4dq1a/j6668hlT7s6VzWRdnCwgIjRozAxIkTte4/ZswYDBo0SK0sPT0dI0eOrLmgiYiIiIiIyGgZJKH97LPPcO7cOXz77bewsLAQyvPz86FUKmFrawuVSoWYmBh4e3trPYadnZ3WrshERERERERUN+k1oV20aBH27t2LmzdvYuzYsbC3t8fnn3+Or7/+Gk2bNsXw4cMBAB4eHli1ahWysrIwZcoUKJVKlJSUwMvLCyEhIfoMiYiIiIiIiGopvSa0c+fOxdy5czXKL126pLW+p6cntm/frs8QiIiIiIiIqI7Q67Q9RERERERERIbChJaIiIiIiIhMEhNaE1JSohI7BCIiIiIiIqPBhNaE/C/2stghEBERERERGQ0mtCYkITlHtPdWsXGYiIiIiIiMDBNaIiIiIiIiMklMaEknEonYERAREREREaljQktEREREREQmiQktERERERERmSQmtERERERERGSSmNAauTv5hWKHQEREREREZJTMxA6AKnY24SY+WH1Y7DCIiIiIiIiMEltojdiVpFtih0BERERERGS0mNCSTtKz8nHyYobYYRAREREREQmY0Ios81Y+AqdHGn2yeDbhJuav+VvsMIiIiIiIiARMaEV2+UG34t+OJokcCRERERERkWnhoFAGUHC/GIXFJU98HJVKD8EQERERERHVEkxoDWDy0j+QmZ0vdhhERERERES1CrscG4C+klmJRC+HISIiIiIiqhWY0FKlmEMTEREREZGxYkJLleJju0REREREZKz0mtCGhYWhT58+aNmyJS5fviyUJyYmYtiwYfD398ewYcNw9epVnbYRERERERERVUSvCa2vry82bdqERo0aqZWHhIRgxIgR2LNnD0aMGIF58+bptI3Y4ZeIiIiIiKgiek1ofXx8IJfL1cqysrIQHx+PgIAAAEBAQADi4+ORnZ1d6TYC2OGXiIiIiIioYjU+bU9aWhpcXV0hk8kAADKZDC4uLkhLS4NKpapwm6Ojo9pxcnNzkZubq1aWnp5e0+ETERERERGRkTKZeWjXr1+PlStXih2G3qnKNcKujPgH3k0d4ftsY/ECIiIiIiIiMhE1ntDK5XJkZGRAqVRCJpNBqVQiMzMTcrkcKpWqwm2PGjNmDAYNGqRWlp6ejpEjR9b0KRiGBNjz9zXs+ftanUloVSoVSlSATMpnhYmIiIiIqPpqfNoeJycneHt7Izo6GgAQHR0Nb29vODo6VrrtUXZ2dvDw8FB7ubm51XT4hlMHH5fd/ddVBM3cgezcgirrBk6PxIaYeANERUREREREpkKvCe2iRYvQq1cvpKenY+zYsRgwYAAAYP78+di4cSP8/f2xceNGhIaGCvtUtq0ukFSjcVJVy5LeP04mAwDSs+7qVD8i9kpNhkNERERERCZGr12O586di7lz52qUe3l5ISIiQus+lW0jIiIiIiIiqkiNdzkmIiIiIiIiqglMaKlWOPhPCvYduyZ2GEREREREZEAmM21P3aT+gG11nreta8J/PAEA8OvSRORIiIiIiIjIUNhCS5ViDk1ERERERMaKCa1Rq2XDGhMREREREekRE1qqFFNqIiIiIiIyVkxoRVbb5pYlIiIiIiIyFCa0xoIPqxIREREREVULE1oSHVupiYiIiIjocTChJSIiIiIiIpPEhJZEx/l1iYiIiIjocZiJHQA9UK7brbJEhStJtzSrsGsuERERERGRgAmtyLS1Tm757RJ+2nsJ3drKDR8QERERERGRiWCXYyN0NS0XAJCdWyByJERERERERMaLCS0RERERERGZJCa0Ihi3aC9u5txDyo083L5zX+f9jp5Px7UHrbdERERERER1HZ+hFcGNW/ew/1Qy1u+Mr7yilkGgpiz7AzuWKmomMC04ADERERERERkrJrQmRqUCFq87ikbONmKHQkREREREJComtEZMpa2JFsDf59INHEnN4nRERERERET0OPgMrbFg314iIiIiIqJqYUJrxCRGkOU+2niqUqlw5EwqiopLRImHiIiIiIiojEG6HCcnJ2Py5MnC+p07d/D/7d15eFTV/T/wdwgGXAibLJEgFJSaYuuCFrXiAv2JtaRWrfoVRLTVWqt2EUQWlVUFhUIRELWoKBEBEQIhECDs+xK2AElYQkjIvidkn7m/PyYzmeXeO3dm7jbJ+/U8PA+Z5d4z99ztc885n1NZWYmDBw9i8ODBCAsLQ5s2bQAAY8aMwaBBg/QoFvnhWFoBPlpyCE89fBNeHNbf6OIQEREREVELpktAGxkZidjYWMffH3zwASwWi+PvefPmoV+/fnoUhQJUfqUOgC1Ts1pCjG+IJiIiIiKiIKR7l+O6ujqsW7cOTz31lN6rDj4M9IiIiIiIiCTpnuV469at6NatG/r3b+quOmbMGAiCgAEDBuCtt95CeHi4x/fKy8tRXl7u8lpubvBm+xXcU/uKZfpl9l+frd5+DlsOXcKCtwcbXRQiIiIiItKY7gHtqlWrXFpnY2JiEBERgbq6OnzwwQeYOnUqZs2a5fG9JUuWYP78+XoWlYLQV+tOGV0EIiIiIiLSia5djvPy8nDo0CFER0c7XouIiAAAhIWFYfjw4UhKShL97qhRo5CYmOjyLyYmRpdyayFEycDRFtLl+J35u40uApFqBEFAbb3F+weJiIiIKGC6ttCuXr0aDz74IDp27AgAqKqqgsViQbt27SAIAuLj4xEVFSX63fDwcNGuyM0auxwTBZ3V28/h67jT+G7yo+jQro3RxSEiIiJq1nQPaCdOnOj4u6ioCG+++SYsFgusViv69u2LSZMm6VkkU7I33gqMaImCzo6kywCAorJqBrREREREGtM1oE1ISHD5u2fPnlizZo2eRQgK7vmizMTERSMiIiIiohZG92l7SFxBaZXHayEaD6KN2ZiCFVvSZD/TQobxEhERERFRENI9yzGJS7tUqvs6f9icCgB45rf9FH+HAS4REREREZkFW2iJiIiIiIgoKDGgNTM2hxIREREREUliQGsQQUnmJ2ZgIiIiIiIiksSAtpmJHh2L6V8dMLoYkqxWAVar90j9bGYJqmrqdSgREREREREFKwa0BgkJUdCfWGGX4zPpxUjYn+H4+8CpXD9L5UntRuIXpmzEqCkJsp9psFjx1tydmLrY2MC8rt6Cv364BUdT8w0tR0shCAKWbjiD3KIrRheFiIiIiIIEA1ozUxhNjp2/C/NXHtO0KGopq6xDaWWt7Gfs3bFTM0r0KJKknKIryCm6gi9jk3363rYjmaiubdCoVM3X5YJKLN+Shg++Pmh0UYiIiIgoSDCgNSEljbdG4bBeeWfSi/Gf75Pw+eoTRhcl6NiHlTdYrMYWhIiIiIiCBgNaE1KSL6o5qqyqw+EzeUYXIyD2ltnishqDS0JERERE1PwxoDUxwYTtoVo2Hn/4zSFM+d9+lFXWabgWIiIiIiJqLhjQmpCZuxxr6XJBJQB2OTWDL9acRPToWKOLQUREREQkiwGtCdm7HIdo2h5KRmmwWHHwtHqZqLWwbtcFo4tAREREROQVA1qDCDoOlBUEASsT01DmJbuws437LjpaTJuTmroG/Gl8HPadzDGsDDEbUzBt8QEcTyswrAxmpOcxQURERETNAwNajRWVVfv8HbW7HJ9OL8a38Wfw3+VHFX9nwY/H8a//bPe7jbiqph4Wq/kClIKSatTWWfBt/GnDymCfZ7X8CscKExEREREFggGthqpq6vHi1E0+f0/thiqL1TYm1de5UWvqLH6tTxAEPDsxHp+uUB5ANzdH2frqs5CWOniciIiIiPzGgFZDcgGk1jfvxeU1jhZA+1hcQQDqG6z4Ju4UqmrqNV0/ACQeyvTre+x5SkRqKiipRmW19uc8IiIi0l9rowtAntSIdUdNSQAArJv9uMtcO1sPZ2LVtnOoa/AvkzBjTSIKNn+evgkd27XBt5MfNbooREREpDK20LYA9nhWEARH9+MGPwNaj4VqQM+ep9W1DagPdFsQkemVVChPikdERETBgwGtiaVeKlFlOWLdmzfsuyj5+U0HMrwv1KCm2qz8CkSPjkVSar4qy3tmwnqMmbdTlWUREREREZG+GNCSB7lgV9+0PZ5R8+n0YgDA7mOXVVvLhctlqi2L/Mdpe4iIiIjIV7qNoR08eDDCwsLQpk0bAMCYMWMwaNAgpKenY9y4cSgtLUWHDh0wc+ZM9O7dW69iacps9+f+lMf9Kyb7SdpqUT+2+RIEAVYBCG3FLMpERKSPf8/dgS4drsaEF39tdFGImj1dk0LNmzcP/fr1c3lt0qRJGD58OB5//HHExsbi/fffx7fffqtnsQwRrK1RRxV09VXvp6kfgKzefk71ZUqxWGxjc0ND2RFCCa0yf/+wOQ3fJ6Rg5Ye/R9s2zIMXqIyccpRU1OD2fl2NLgoRkWmdyyzFucxSo4tB1CIYeqddVFSE06dPY9iwYQCAYcOG4fTp0yguLjayWKoxy7Sa9nKoEURXVmk/9YVWsX59gxWbD15y/J146JLMpxFwPD1ycgKGv78hsIVQwDY2dqG/osNUVS3BG7O24b3P9xldDCIiIiIAOrfQjhkzBoIgYMCAAXjrrbeQk5ODbt26ITQ0FAAQGhqKrl27IicnB506dXL5bnl5OcrLy11ey83N1a3swepMenHTPLQGl8UbrR8ArNnh2jo794ejmq6voqpO0+UTERG1FHnFVXj9k62Y868H0bNbO6OLQ0QmolsLbUxMDNauXYtVq1ZBEARMnTrVp+8vWbIEQ4YMcfk3YsQIjUrbfGxPyjRNS7E3WvfC/jb+jLYrUEjLn5mVX4GismqX1/aeyMZbc3cEbTd3ErfopxN4ZsJ6o4tBRKSLPccvo7bO4tLTiogI0LGFNiIiAgAQFhaG4cOH47XXXsP48eORl5cHi8WC0NBQWCwW5OfnOz7rbNSoUXjiiSdcXsvNzQ3aoFar8YLNATeN/16buRUAsG72447XPv7uMCxWARargNah5t24DLh9s35PutFFICIiIjKcLi20VVVVqKioAGC7aY2Pj0dUVBQ6d+6MqKgoxMXFAQDi4uIQFRXl0d0YAMLDwxEZGenyr3v37noU3296359LBQRW++sqlEewL0SXuKh5BjjOm2755lRk5JZLfrYl4gMNIiIiIlJKl4C2qKgII0eORHR0NIYNG4b09HRMmjQJADB58mQsXboUQ4cOxdKlSzFlyhQ9itQs/WHMWtHXYzamAABKKmp8XqZ7bGEfj+sea16prseGvemmaWWrqW3AsoQUNDRmGjaj2noLlm5MwdhPdzley8gpR32DxcBSGc/oXSi36ArSLpUYWwgiIiIiUkSXLsc9e/bEmjVrRN/r27cvVq5cqUcxdGeWlqYT5woBAKUVtV4/KwiCbJp5qWBrwY/HsevYZfSKCMeN3cN9LqPVKhbF+L8Bl21KxU/bz6FT+6sx9J5e/i3En8DKjyI3NNiC7uLyGrwxaxv+369vxD+evcOPlQc3s3TDf+XDLQBcu20TEZE5mOXBORGZByfIbEGUXALi916Uff9oWoHo62WVtmD54KlcPPduvOP1DfsuInp0LMqvyGf8Xb45tamcKlyrauoaAAANQdTaeaXaNq3MmYvNY9oqat5SuJ8SERGRCTCgNYhZnzBeCnA8Z/L5Ipe/NzYGyAUlVbLfO3m+yDQt2g4i5Tl4KhfLt6R6vmGnoFrNUvOCIJh2PyTze/vTXUhKzTe6GETUwpilNw8RmQcD2hakwWLFhctlku8nny9ERm6FjiVypWds5e+6pn11AEs3pKhbGIOMX7hHctw1kRLeHlQRERERaU23aXtaIrmgqbZO/66wggAk7M+QfH/8wj06lkaa0oevdfUWXNW6VdA9rTVLaU9dKPL+IR1p11rMVmgiIiKi5oottAZZviXN6CLo4kK2rUU4u/AKTjYmp1JOOhApv1KHp8bFYWXiWb/KZcYYmN1/bdSqm/oGK6JHx6K43HsyNCIiMtbZzBLkF3vv9cFrJRG5YwttM6dZF2KpoEPi9Y+/O6zq6s83dp3enpSFZ37bT9Vl+8NqFVDvZYogQRBw8FQuLKIZnclOrXuV2sbEYEREZH5vzd0JgBnmich3bKHVkBlaAQPtVrph30V1CuIDJQFNYWm1DgVR/tGlG8/gT+PiUFsvHUQdPJWL6V8fxL6TOaLv+9p12mIVcDEnsCReZhJsXceJiEh/vFYQkTsGtISftkl32z0rMSdtcXmN6uWwX6MERyQZPBetLQcvAQCqaqQD2tJKdbu+rticijdnbZNN9KWl/3x/BGt2nDNk3VoRnw+ZiIiIiMyKAS3h67jTPn/HfXoeX+07mR3Q93XhRzyt59CetMaHDUVlOrRWi9h2JAuL157y67tFZdX4/KcTsHjpph0QP57iv/3pTg0KQkRERERaYUCrIX+Dm70nxLukBgOlIcSH3xzCuaxSx9+CRplog6m9TY9EF3X1FuQWXdF8Pd7MX3kccXvScTStQLuVKNieSSn5iB4di8w821jztEul2pXHQOnZZfh63SkmUyGioMfzGBG5Y0BLqjjhcwZjWxZaZ1pdo6pq6hE9OlabhStgVAuqmI+/O4xXPtyCBi1bRhWwulX2ysQ0VbpO1zdYUeZD1+7dxy8DAM5cLA543Wb2zvzd+Gn7OVTXMlEWEQWfmroG1DUYe90iIvNiQEuq8jcmDXFq2236v/elFZdVY/MB6bl1QwAUKEgg9ePWs6iqqff6OX+8OHUTTpzz3hKpR6KLIyn5AMz3hPvb+DOYFXMEQGDJ1D7+7hCen7RRpVI1J+aqbzKn6NGxqmekJ1LD0+PXI2ZjitHFICKTYkCroZaYiE/vKWmu1DRg3opjAS9nyfrTeHZiPK5UaxPUTvxsb1DOh+prkC8IgmiL9MlzhY5uvd6X4dMqXexPzm36w4cD0GTxPZFhdh27bHQRmj2LVUANe0v4zZeHv5dyyzW7rhOReTCgJVWdk8iKLEbqmqTVeFolvlhz0rkgPpO7ztbVW0Rf9/fX+ppp2ha0+bY2X9cRv/ciXpy6CenZrt2HJ3y2B3//eKuiZVRW1ePk+UK8NG1TYDfXjFKJyITmLT+KpyesN7oYLcLrn2zDxEV7jC4GEWmMAS0ZxvkpqwChKRh0xCGBN3H7GsOJtUiq1dLu3s3Xfbm+dgP2Nua0oqrOp+Wp4fhZW9fq7EL/E0+VVtZiwsI9KCytxmerjqtVNFnNoTfFxn0XsWJLmtHF8NmpC0U4mppvdDGIdLP1cKbRRQhqvl4rz2cZM7UdEemHAa2G2EAkr5WGQURWfqXj/1sOXQpoWVL1mF9chZKKGkWflVuu+2ZQI7jaczwbw9/bgBSPZEfNIHJTqoV1OV7w43F8t+GMzmsNgcUqoFai94ES4xbsxvtf7FOxTERERNSSMKAlwzi30IYoDLSWb05V9DnnrMtrdpz3q0zeivSXDzbjhckJ/i1bhhrBlT0J1XmnqZEalx74whVYsFJ5y6pZElSZoRw1dQ34/KcTmiUoU5+AT747jD+NizO6IERERNRCMaAlw7iHd0riifwS36bACab2SD2yHDutzadP5xdX4bgPc8b60t1Zrt71jDE3yWTL1svGfRcRtyc9qLoO7zmRbXQRiKgF0fdaSVqpqqnH5C/3oVDBTBQEXC6o1D3xajBhQEuGkZxTznGtal4HrtQcoFr+SrWW/drMRLz7+V6VlubKLLWcmlFidBFgbbxY8ZoVmOzCSrzy4WaUeElqVlPXwLl5iYgMsOPoZRxJyccPCnvetWTZhZX424xELNV9WFHwYECrIT5EVE6rzMZmigvW70kXfb2+wYrUjGIdurwKEv+3jWN8b5F0wGrUhPbBdAzll1Qht8j/ZFjByZwVtG7nBeQWVWH3cfnW41FTEvAMs80SGeZKdT3mrzzWrKcxSrtk/MNSCm4ljdM+nk4vMrgk5tVaj5WUlJRg7NixuHTpEsLCwtCrVy9MnToVnTp1wuDBgxEWFoY2bdoAAMaMGYNBgwbpUSxyErf7gtFFaKJiXLc9KUu9hWnov8uPolf3cADiQdzw9zbgrqiueGv4AJ+X7dxFpcEivnFPXfDtJPnB1wd8LockE4xdVWOn+8v0zQCAPje0D3hZekrPLsOmAxn46x9/GVBXvn/P2Y5Z/3gAoaHB85y0qsaYm2iLVYAgCGgdRNuqObFYBdTVW3B1G11ugUjGj1vPImF/Brp3vlbxd8yQ78AXWfmV6HdjR0PW/dS4OPz+Nz/Dn6P7G7J+Ir3ocjUNCQnByy+/jISEBKxbtw49e/bErFmzHO/PmzcPsbGxiI2NbVbBbDCdcz9ffdL7hzSUfL4INXW2m0s1N5tUN1JFdaNj/WXmVTpak8TKVlFVh21H5INz+/ZztvmAVIbnwFrW9ifnBvR9Z3KbOZBjyJxth+bz/uf7ELc7HaWVtX58u6mCzmWV+bkM9al56FbXNqh+A/3O/F14Yuw6VZfZUlSqMB3Zwh+P45kJ6x1d/I0mCAKOpOQFXaCmhkB/c0l5DUorzHHeMaO6egtWbz9ndDEMVVPb4PNDewo+ugS0HTp0wMCBAx1/33777cjOZiIRcuXZWhICQRCQkVOu+rqKypQnIfCl0crILrJirU0Xss01/16OyPy0Wt3DuS92/Z50JEpO4aRexWnVfV4rwVZePRWX1+CZCetVvyE0w3jtYLQ9KQvPvbcB5zyyt/tmy0FbAjiz7PlbDl7C5C/3y5yfgpv79HZqemFKAkZO3qjZ8tXhfU87nlaAXccu61AWbVyprscrH27G2Uzzndvm/JCEcQt2+3TfR8FH9/5OVqsVy5Ytw+DBgx2vjRkzBtHR0Zg8eTLKy8WDl/LycmRlZbn8y81Vr5WIzKfBYsX3Cal4Y9Y21ZddUyc+b2ZtvcVjLI8/c8uqobKqDss3p6rWivBlbLLTX8qW6evvySuukn3/rx9tQUqG+9y40itR8wHBysSzmPvDUYl3/d/G+05mq55YyFurxaylR1RdX3Oj1m5TUGLbn5nJ2RyOpeUDANIvm+tBXaDs2fsLfMziHwy2HcnEC5MTRM77/muOWY7f/XwvPv7usNHFwNnMEkSPjvW5IeF0ehFyi6rwfYKxCZ4EQcCeE9mod8r7kZ5t+y21Evd91DzoHtBOmzYN11xzDZ5//nkAQExMDNauXYtVq1ZBEARMnTpV9HtLlizBkCFDXP6NGDFCz6KTAfTOfpeUko+n7UlifLhmljR2efIlKdDek/I3yYt+OomlG1OQlJov+zmlF/cNey8qLZqk6NGxyC6slHz/SrX3+VOzC6S/r6eyytqAA5WMnHJ8+M0hzF9xzPGa0jmVA7HjqLZjw7+JO4Up/9uv4JPmvLE0S8tbMGiwWDU9Jq1WARaLOknl9Di2jKBWL4n6BqtoLxgjJZ+3dfXUoqcVqW9P49CnQ2fyfPqeWc65San5mLHkEGI2OmUDNkvhSFO6BrQzZ85ERkYG5s6di1atbKuOiIgAAISFhWH48OFISkoS/e6oUaOQmJjo8i8mJka3spN+gvmW5WxmqeLPHjotfsGwx6f2MbGXvdxs7k/OwdhPd7k8kfRXZl4FokfHepTF2d4TOaLfFQRbohVv3BsflcxDm3Kx2Ke5bQHv+9EHXx/0OynQnuPZOHwmz9Eym1ci3zLtKyNaIJyDhVXbzuGwjzc0WhAEAdGjYzmtg0qyCys95nxcvDYZr85IFO2Ol5Saj+jRscjKr/B7nXOWJeGPKo8X5v2puM9Xn8BfP9qC8iuBjzNWW8L+DEewFKiWONZYL8G+aSsa9/3CUu26uZtBbtEVfJ+QwmPBiW4B7Zw5c5CcnIwFCxYgLCwMAFBVVYWKCtuFUhAExMfHIyoqSvT74eHhiIyMdPnXvXt3vYrvl2bYK0YXQX14qljn9vPUul2uGairaxsw+ct9jr8T9mfgzMViXMpV/gT8aFqB6Ou7AxjDE5OQ4mip9oWS+n77012Y+Nke3wsloyCAIHTGt4cw5X/7tRv/G8CCGxS2hlXV1Kswts21nGpvD3tv+2UJKT59T69Tb8rF4qCa6P7VjxLx0rRNLq+dPFcIAKio8uxdsbOxJ0DKRVt30W1HMnEkxbcHHUoyzecVVykKmlW/phpwM+icnEbsOH9tZqLfWeTt5/WqGu89ZfR2NrMUM749ZHQxHHIKr6BWwQNYb5LPF6JSQc8kIjVN/+oAlm1KRU6LmypQmi4B7dmzZ7Fo0SLk5+fj//7v//D444/j9ddfR1FREUaOHIno6GgMGzYM6enpmDRpkh5F0kVzf3By6LRtDLNYdt2WSo37LW/7zYHkHBxJke+G7M20xcpumJTuw5l5FVi+Oc2vssgFb843sPZxMGZi7ypopmdXSuepe/WjRLwwOaFZnqf0+Eln0ovx9qe7sELH1uN35u/SbJydkoco//k+CZO/VNIV3Tcvf7AZr83cqvjz7kW9lFtuGw5hkuEMcsYt2C39ZkgIsvIr/c8i76UOrVYBe45nmya7s7PtRzJ1W5fVKuCvH23BjCWBBdg1dQ0Yv3APpn+l4jR2KvKnRdzvh0bm26U8melC7Sf7IV5n75EXDNtdJ7pMwnbzzTcjNVX8or9mzRo9ikAaOHAqF3f/ojueHr9e1eWapguFQcXIype/KZMqll7dVMXq5x+z1U/cBQDVtcGRxEHJtn9xagIirr8WH/39flWWp1R6dpnodnSfYse/Vbp+qSX1Sikqt3XRzcj1vzuur06n21pKx468S7d12q3ZYd6pP+xTmu05kY2nh/QzuDQB0Pjal3joEuatOIa/PfFL/P7+Ppquy1e+HEeBnh/tWznJx94G7iyN87qnm2w2AcD2YNOIFnGzXANEx6Wb5NaStMFZ3clvZok7tWbECdo5gYbS9TsHmvEqJICSWveyTZ4PpxosyncGj/1G5qvu3WcnfbEPZRrMdVpQUu3X/iz2HanxtEVlNY4EKd5UqDgG7h+zt6u2LG/Mck7Q45A1y2+9XFApm6hNLYvXntJ8HUpdqa7HhIV7HIGEvw9BGwxuqVR9H/JysShuHGJQVN68xxeq4at1p/DXD7cYXQy/KUnQqCY1s1iTNLM8MDAjBrTkt6z8Cp/GbbYEat2fyHXj1vRG2u1sKQhAhlsdK00+JfXU2v11X35OUmo+4nan+/ANZZZvSYNVpQ0byI2EvXV+SzOdj9Jdibcbaz/rxJ9vXcot1yUwVMv5rFJYrQL+NiMRr36U6PdylLR2GRG8l5TX4LzEfLO7jl/GyfOF+Mfs7T4ni3P27znbPV7Lyq/AMxPW43xWKaJHx2Kfl2z0qgr0blWHirJYrI4x1UYJuBeXgu+v3n6uRY5P9GfTTl28HysTz6pfGLU1g2BQEIC5PySZLpu5GTCgJb+dTi/G65+o39W0rNJcGRrFTvBmzCKphfi96XjDzzq+JNGFbK1bkitfb04CneKiuLzGtA9iNh8MPJD1tjnds9wq3fwnzhV4ncrHl/vxK9X1eGFKgvIvqGB7UpZkUqPXP9kWUGCop7RLJfjXnB1YmejfuHVneg3xcN/vvHnt463415wdou8572YVV+r87oKamef5AGPTgUuorm1wzKe5Zsd5v5bdXH234Qze/nQXzkk8bGiJzNJbwyhSMzYYQuRc4Os9gyAIphlnXltvwYlzTUk8LVYrEg/pN948mDCgJdORTZqhk7p6i0dLpHOXmhHvb3D8P79Y3SlbvJVLbHoNrZzPMn5skNo33KOmJGjyICYYHEnJx0vTNmHfSc+pl7ILpJ/4VtXUY+Jne71O5eNLVfk7ZZK7unqLI0GdnVR4MzvmiPpJjQx46l/QGByev9x0fH4TZ54uwWLcsyt7I9bTQWr/kjtHbD2c6VeyKF9vgusbLH48nAs+9uR8Wgz9UKqwtNoxZZo/xLa7IAjYsO+iR4botEsliB4di7RLJR7fOZpmS87orSxGBLzBuG+pQoWNPemLfXj87bUqFCZwi1adwMTP9joewstdp8Vk5NgS5rlfI+2sVgExG1O895YKAgxoiUQ89248/j23qXWgqqYeb8/bJfrZiYvUnU7G7qDICejDbw7i2/gzIp/WRqA94HYdu+wyr63dWZGbAyne5uE1g2AZ12Lvwnk203P7j51v27/FxkL5MkZ6zY5zOJbmmoW7qqber3pUstbFa5MxdfEBlxtOtW/mgqEFZtU2/5I2ybVumuGBljNHVvEQ59c81TdYHfv6nGVJeFPBOPKnxsV5zXpbUVUnenNYW2/Bk+/EYcn6017XIyoI9i87e9AeYmD/zd3Hs/HOfPHrsbNnJ3omrBQEAQdEskifuViMhT8ex4Ifj7u8bn+IJ/YwL2ajsunE5v5wFBdzzNkrSG1G7hdqkZrWUEvp2WWwiEy5dynPtt8sXHUCAHyeIsp+PZcaqpWSUYwfNqdizrIkn5ZrRgxoiUTUubXOyo0b1bP7caDT9Yj5/KcTku8Fmk3yR4lxNc5zXnoLFnyZzsMXhWWuTyTdW1fqG6yoUdgKoNWYsncX7UHC/gzVlpcr2pvA9XdvEEkodvCUZ4suYOu+7SwkxJY86L3P96HOaY7Hdxftxd9m2LrzHj6Th+jRscgrVmcMkH0sUaXIPKpKd988HXtZ6G3bkUxEj471uctvVU295E34hctlouNbz2WVIkmDc5Q7qZtmQbC13n2++gT+NWcH8hsTtNUpmG+0rt6CPSfkx8vax///tN314YH9PKHGkAG9NFisiB4di598fBCiJPaO35uueYuP3DRuecVVOJ9VKtoL5GhqgWj239o62z7i3vJs39MCzbFw8JSfUzEpkHapxDyzQ5iYWYPtzLwK/GP2dny3QbvGiqRU8fOyvWu1GnMyG40BLVGAXK4jGlxTGhQmYfJ31XF7pJMs6dHyaJbLsHs5xi/cjacnyE9JZb+J0Gq4zfGzhZi/8phqy/M2L2FxeQ22HvYcn3MxR3w89PcJri0UzsfCc+81dcs/m1nq+L99+WJd+HyRkVOO+gb5i7DSe7yXP9gs+77S46CkokZx0jS9bG0cb5WZ59v0QnK/45//2S46vvXfc3Zg0pf7IAgCdh7NgkXlA8Nbfa7ZcR4vTduELY2BpdqZXu03xGaPHZQ8iLQH4V/HnUL8Xh8S7dl/u9MqLFYBGTnlWJmYhr0nsvHZqhP44JuDAIBNB1wfyEWPjtV82MzLH2yWHH9ddqUpYLUKwPGzttY4qU0W0sr2xtnM0oDKHci1dNriA3jynXWi7x1Ly8fo/+70yE0RKHOGfs1TaYVtn0wVuSZqHYTbzxVmP6cpwYCWSIFTF6SnW3EZP6PBuce9JVFPrQKe70/BWVKjM2mgS03NCCzgcuaehMpqFbD1cKbHtERS9BqvJpX0yZ/dQKpVzL6o4nLvv0lq1ygur8Ebs7bhs1VNvQucE2eofRgq3UVfmJyAj7/Tf+5Hs9l2JAufLD2CWJ0TKtkzHtsDadXn5tZ4x1KruL621v24VXmGWke3b6fXliWk4I1Z2/Bt/Bl81NhtW67nkprnVjul51L3Tfzuor0ApI9x++eTUvLx6gxts4mLSblYjIOnc1HfYBWt19wiWy8E9ySMxQbdNxg+/MbwAvihscj+3AqlOT0sbukY0BJ5YbVaHRdpb4w8lWoxuXugAa1ctzB/NUh0BXa+2MdsTEGarzdNEheTgpJqZBdWoqauAdGjY/3qAuyehOqb9acxZ1kSXv9YWXfq6V8d8Hmd/nDvQqyJxl0qdqf3YOdijvg+bU/ccjq96UGT8xhSb/cFw9/bENB0L3Ir2S8yPk9Og8WKT1cc87lLsK/sU0Lpwd7iUFIR+P5ULDN9DyD/sDGQs5f9dOIciIQ43tPoIZzWrSQqLL9puzS9JhqgBrCukvIan4fyKO4Z4eM1ba9TAj17t2R/tPJzZ3R+mOnL/mGGniKCIPjdqi0IAnJVnjbpwKlcfa5xPpLdNbzsN7NjjgS2bkcwHfxNtAxoibzwpddcmYHT+SzdoCxBhRz3a70e4yp8PY2u2nZOtCvwpgNN49d+2JyKSV/u82m525OyRF//8/RNePWjRMdN+gqnqVL8vQTYA7FshXPJNZcxnn98ey12Hr2s+PNvzd0p+rpzNynnrsvRo2M9spSKqaiqwxmJcc9vztrm0VLtfFwUllaLdnX294bgWFoBNh3IULVruZjzl0s9XktKzQ84Wc2h07nIyvetO7Mv/vrRFs/uo0718emKY46sz+6c623D3vSAu7pq3T0vXmb4hy9Ub5l2Yq9rbw8rA5le7YUpCS4zCahh3ILdqG+wSMYHUpvswmXpB8Xu30nYfxH//M92qU97K6JXclt004EMzFt+FBMW7sGRlDzZuP1Aco5s7gxv63ImlsjIbsvBS3hx6iaP4SWCIHidOi9253m88uEW2e3vq8VrkzFhYVMSz5raBl2y+67efs7LfmQ/rzRt9bLKWizfnKpJI0napRJsP2IbimJvtAj+cJYBLZGqzjWz7h9SN/1KKD1BBnJzuP1IpmNsoFpJhrxxucD4UfbDZ/IUfa8y0BZEFUnN3eorv8dUut2dOVrKAFxxS/ySV1yl6CZAqvfBxZxyR0ZT+0OS6lpbAGuxCnhp2iY8+U4cLFbXGzl/92PnVmZ3Ut0MlVi9/Rw2SIyNtFoFXLhchh82pSpa1rwVxyTfm7r4gGqJ25LPF2KhW5ZZJa1iUtOmOAd2C1edwPSvbeM65baoI4uvyO6hdpzoXo5Sp9a46V8dwAuTN/q1XIu1Kcvz+t0X8GHjeFYlB4YgCPhuwxlHsjV39qECu441PZgSC17N1uBz6kIRJn+5X7QOnZPxBFLu+SuPSwYu9vVuOpCBr9b5OcWWl8JtPngJJ88XYvKX+2UTSE7/+qBs7gxfyM0lfvJ8IQDP8fvxe9Lx+ifbcFqmd8XpdNu9R45MK21JeQ2+jT8tPmesxKZyXt4783cHNBd6VU09jrolWyoqq3Yko7P7at0pmQcdTZyr9/lJG7F0YwpSNOieP/q/OzH7+8asxs4X0yDHgJbIC7NMsG1WYtO8+CKQri6zv0/C3z/eiqqaes3ryZ9i7j2R7bF9lHb9nLpYeTfjghL/W56U/K7MPGVlTpa5QQmIeyG9dJOyv+oedPrKntCmtLHrrPP67F367Dc0YmXZcyLbYwojdysbM4G7f7vBYsWT76zD4rXKb36dxy1/te4UFq464Zj2wdnjb6/FP/+zXTQJiZHGL9yDDfsuSr7fNGWMfyoC7EHTlBRK/qA5frYAX/sQtIgt7cCpXJRU+Dd2PmZDCv41ZwcycsqxaPVJ0XmnpeQVV2HFljRMXRzYfM1y28ioK+qJc4WiSXZWbEkT+bS67A9XPl1xDKu3+zfFlth2k3rIIjbNkNUqKO7K7e0YK6mowacrjvk1y8PZxoct2YXS1xWprrAXc8qxfIvtQdzc5UexMvEsTsk8FASAfIkeThcah2lN/+qA14et6dllHnkhZsUcwftf7HPp+fHi1E34y3T5JIPuAn1QFj06VrJ7ttypymKxOsWzwX+fy4CWyAsjunteqfZ/0ni9Sc3P+6lMq44azqQ3BYrPTozXLNOwO9c5MOVX+tGSQ6LbR8nFw7l1vKSiFhkyXbT+PH2T1+XpIdDxPEpUVNWhvt4WTHobdyoXDLrPN+nOWyIu+35QVdOAIyl5ojU6Y8khvPe5b13fAduNxneN802LBXj2hC/uLZOfrz7p+VmZ5FvOD4G2HNJnypn84iqsD7B1SOl44zdnuY5dbxUSgqqa+oBbD719/d1Fez2m9vFXVU09dh9X1k3fXi57wODPeEH7trEnWfr8pxPYedRzOEYgN+FWq+DzfJpKeXvY8PHSw5qs19t4T3/H0DoT+2m+7MvLt6T53JVbEATRbfq/2GSPDNbupLq+t1LQdV8qo/ibs7Zh6YYURI+OdZwHJR9sCgI2H8jwem9w4FSu46GlmJKKGvxj9naPa4a95TnQoVn23xrI1FCnLhRBEAQs35Kq+J418XAmsxwTkbZ8Hf+plrwi9YJ3JXM/BiLxsOsNeKCtcd40ZfcM7M5k8dpkvxL0vPHJNhSWVnuMtfRomXb609dEYaV+tgipQTZLaUgIMvMqUFZZi+HvbcA/Zm9r/I74VVhJDXkLiuKd5uO1X+ylLvol5bWqJtVYsSVNNiCyz2l5LK3A5fULMvXtrXhrd6o77YeUv3ywGYt+OoGS8hr8bUYiJouc67y1vLtnfpc6Jt1bXUJCgL0nlLVWihUhROXuefZ1yHWrnrf8GGZ+e9hlzGGDxYrZ3x9BdoH4ecQeMHjcIPtR7rg96fhkqeeDKotVwPakLK91JWZ2zBE8926812m3fPHMhPXIyCmXHE/tjT/ndeef/r/YZPnlyzwBEEvgtG7XBUSPjnUbUhHYjndAYj5xOX8Ysxb/sXdPdS6JVFZo5we+Xk46RTKZmMWOtf3JruX3Nv7/8Jk8z+ESfpynqxvrwPkhOtC0z5w6XyRah+eyShE9Otbr8tUaypBXXIWlG1IUJ5F0Pu80g3iWAS0RNdGrlcaZv3GAe7ZhzW/I7eV0uvhUVEm3Msi1QFTV+NcCv3DVcY/fLTfOWUlLmJYXsrfn7VScTXjusqPIL6nCF2tOeiYaEQT8/eOtjmkzvD1xd35bSZIo0WU47ZiV1fWSScPsAu4h0Pj94vIafO80trWu3qK4S6TZJ6xwrlerIOByQaXoWD9fzwlyvRec2W4c5RfuHni4ZFG2d4P086iRSkAjl/HbnhugxunmMzWjBNuPZGHuD0cB2G7cD5/Jc9R/U3fNpuVEj451PAAShADGszc6n1WG2TFHJJO8CTLLt6977g9HZY8bufHlYlIySgy7Mz9wSj67uVzQIjbHbNxu2/VszrKmYDLQc4y/11pv5z5f5JdUYXPjPNFyPQhCRB7K/JjofXopR2K1EPHrrFXwo0XVqe6cc1vY63TeimP4Js6zN9D2Iwq3m0oPyuwPty/mlCN6dKyi39n04CD4Q9rWRheAiFq2YBm7YS+lc7KUGTLTOa1ROAdndkElIq6/VlFmUrFWhHELdrt/yCdyT9ErquoCyjKZklHikjxGzo6jWdjR2LXx9pu74Nf9u3t85oof3RSfnRjv83cAz+v77Jgj+M2vIpxecd3QfxoX5/h/Zl4FenZrJ7pc5wDJ+WbVXg/uGUEBW9Ial26fEnUstwt5yyrqrKCkGq18fNztfKO372S26GfGO2UYlSO5R0q8oXxYSIjX+7b1u6UfjNk3b9qlUkVrEwTB5bj2p/VQrLhNXTZt79qzcnfpeDWApnH67se2/Qb3x61nXRKGBXIvW1FVh7JKz4dWSha58+hl9I1sL/n+O/N3Y93sxxWXRY1uvSfOFcq+n11YiRuuv87n5fpaNLHtp+XUKss2pWLb4Uzc+8sI7x+WKYsg2AKrVq1CHPt+fnEVLFYBoa1CMF9kKFJ2QdM19et1p1BYWu0R4+05kY1MiWzqDQ1NZXE84BWkz4eZuRW4qWcHl9dCQkJQVFaN8GvDHK99uuIYfnZDOHp2tZ3Lc4qu4Ln3NuCdF+7C/bf1cFm++zzAH393WPG1z3kc69KNZxw9cHzlXiPuOQOOpxXgtn5dHH/vT85xDFsJjrsweSFCEE8+lJWVhSFDhiAxMRGRkZFGF8dDYWk1XppmjrFtRGb00J2RqKiqk83IaBadwttqNofd8KG34PsE79Mudet0jdeb9z492uPmnh3w1MM3Y+z8XQF1I47q3SmgTNcA8PSQmx2Jj3yx8qPf4+nxntMzedOnR3tVp3rwx0N3Rrq0ajz/6C1YutFWv7+66XrRm+bb+3XBzT07+LWtnL370q+xLzkHiYcyA1qOkdpdExb4PMEK3dSzA9567k78XWZO6PGj7vaYi3xg/+5eW+VeeCwKv+x7Pd7/Yi8+e2cIPlpySHzOVoU6t2+LqN6dsPu47YFB74hwPHBHD3wbf8bLN72b8OKv0aXj1YjbfUF033n3pV/jqqtCMekLZcNhrrv6Kiyb/piiLpdyFo4dLFs37q5u01oy67WcB+7ooXhKsQfviMRDAyLxv9hkXBbp9v3n6P6imYxH/i7KkVF55hv34535uz0+84cH+mD/yRzkiyT6e+jOSDx6b2+MW7Ab/3z2DiRfKERWfmVA+1SPLtfislNAOeTuno76f+Pp2zB/pW3c6NfvPYKQEGD55jRs2HcRndu3le0y/Jc/3IrFa+W7YTvrFN5Gcrz/P5+9A/9dflTxsuwG3NJV9N7CHswGMivFY/f1dhmWosSDd0Ti1Sd/iXOZpdh6OBN3RXVDp/Zt8dE3B2V7eynlfqw8PCASrUNbOVrEAds5Sep88cbTt2PoPb0CLodWvMV8DGg1xICWiIiIWqJxL9yNGd9K92IhInNZ83E0QkPNORrVW8xnzlITERERUdBiMEsUXOrlkjOaHANaIiIiIiKiFkxJLg+zYkBLRERERETUgqmRWM0opgho09PT8eyzz2Lo0KF49tlncfHiRaOLpIogftBBREREREQtRvAGLqYIaCdNmoThw4cjISEBw4cPx/vvv290kVTR4bo2RheBiIiIiIhIVjA3xBke0BYVFeH06dMYNmwYAGDYsGE4ffo0iosDmyrCDMyaKYyIiIiIiMguiONZtDa6ADk5OejWrRtCQ0MBAKGhoejatStycnLQqVMnx+fKy8tRXu46MXxurn+TDxMREREREZFNMCeFMjygVWrJkiWYP3++0cUgIiIiIiJqVoI4njU+oI2IiEBeXh4sFgtCQ0NhsViQn5+PiIgIl8+NGjUKTzzxhMtrubm5GDFihJ7FJSIiIiIialaCuYXW8EGenTt3RlRUFOLi4gAAcXFxiIqKculuDADh4eGIjIx0+de9e3cjiuyT3hHhPn3+rqhuHq89dl9v0c/ef9sN/hRJkff+MtDv70Z2vQ6PDOzl8fr4UXeLfr5nt3a459buuPbqq2SX27NbO5e/o3p3Qvi1YRgnsVwlHrwj0utnOrTzTO7VsV0b3BTZHp3C2wIAQt1ynfeOCMdDA5qWPeLRWySXb/9q69AQPDQgEgP7d0fXTtcAAH53X2/c1LODy+fDrgpF74hw3HNr0/7fN7I9AGDY/T/z+nucPf+7pnLZ99U+Pdrjd/f2dvmc1D7YJizU5e9/P3cnhtzdEy8N+4XjtYjrr0WncPUSpPXv0xm39+uC4UNvwSt/vBVvPH2bx2c6t7fVS0Tnaz3esx9j0YP64KrW3k+BYvXveM8t8VuY2/IeGdgLrRvH0vfq7rr/KjHp5Xsc/4/sep3jd4mZ8OLdHvU29vm7JD/f/rowl787hbdFx3aev+cPg/o4/h72m5859sfWoa3wzfuP4KO//wZ/e/JXLmX11YQX7/Y4n/Xo0lR3Tz18E/7wQFM5Wocqv+i6/07AdlzddvP1Lq8N+430sTPglq6O/3fpeDXaXxeGq9vYngff1LMD+vRoj1/8rJOjfiK7Xoe/PfkryeXZ95s+Pdo7Xnvgjh6OZf7iZ03Xvxuud92H7cf9rX07I7LrdS7vvfBYFADgvl/ZHgi3DQt1rOv+225wOWc4G3qP7Xw9sL/0NfV39/bGe38eiAin8lzdpjXefOZ2ALbj3L7/9+nR3nEOA4A/Db7Zcf7u0eVajHvhbvw4Yxh6dLkWo37fdK6wl/3hxnOn83ln8F09Hf8fM2IAvnr3Efzf//u547XnH70Fwx9p+rt752tczjsD+3d37N/O19nf3dvbY793FtXb9V5k8F098exv+wEA3nlB/Piyb+enh9yMGa/fD8B2fA3s3x0vP36rx74HANe2tdV9/z6d8f9+faNsGeRc53QdHdi/O6a9eq/L+9e0bY1Xn/gl2oaFopXbdUvqGvyHB1zPlX1uaC/6OcB2rAK28+u80Q/hjn5dMOWVex3b/N2Xfu1Y1tB7eqHdNWH4dMzDju8PvaeXR33Yt83wobfgz9H9XY7pqN6d0LXTNXh6yM2O12a8fj8mvXwPfnPbDbi1b2dc3cZ2nfrNr27AvNEPuZyr+vRoj5t6dvDYxv1u7IDH7uuN6ztc7fJ69KA+mP7qfS7n/sF39cQLj0W57KPOn//gtfscZQWAq1q3Qr8bO+BOp/NKZNfr8PMbO6J1aIjLuejJh27CPbd2dxyjN/XsgLt/YduWA27pilf+eKvL9njlj7c66gCw1VWv7u3wyh9vxex/PoBWIbbr0s9uCMfwR36Ox+7rjSmv3IuHB0SiS0fbb213zVVYOuVRl/sD+73F2OfvwhMP2ZZ/TWO9vPL4rejfpzMAOO6JHruvN76f9ju8+PtfuJwLnLeZmN/efSNuv7kLANu+7HwfZWe/3wq/1va7e3RpOg9e07Y1Irteh/t+FYHBd/XEUw/fhL//6Tbc+XPbtn5pWH+P/bdHl2sd5xwAuPOWrnh6yM0u19NHBvbCnT/vint/GYFHG1+/tm1r9OhynaMcgO28A9iOmZG/i8Izv+3ncQ4HbPvXUw/fhN/ebTvWr736KnQKb4uf9+qIIXf3xIev/cbx2f59OuOhO23le+6Rn+PJh25ynCOct8+fBt+M5x+9xXG8vPaU7Rr04B2RuP3mLujToz0G3d7DUd6o3p0wb/RDGDvyLtzYvR0+eXOQRzmDSYggCILRhTh//jzGjRuH8vJyhIeHY+bMmejTp4/X72VlZWHIkCFITExEZKT3wISIiIiIiIiCh7eYz/AuxwDQt29frFy50uhiEBERERERURAxvMsxERERERERkT8Y0BIREREREVFQYkBLREREREREQYkBLREREREREQUlBrREREREREQUlBjQEhERERERUVAyxbQ9/rJYLACA3Nxcg0tCREREREREarPHevbYz11QB7QFBQUAgBEjRhhcEiIiIiIiItJKQUEBevXq5fF6iCAIggHlUUVNTQ2Sk5PRpUsXhIaGGl0cUbm5uRgxYgRiYmLQvXt3o4tDYJ2YFevFfFgn5sM6MSfWi/mwTsyJ9WI+wVAnFosFBQUFuPXWW9G2bVuP94O6hbZt27a46667jC6GIt27d0dkZKTRxSAnrBNzYr2YD+vEfFgn5sR6MR/WiTmxXszH7HUi1jJrx6RQREREREREFJQY0BIREREREVFQYkBLREREREREQYkBrcbCw8PxxhtvIDw83OiiUCPWiTmxXsyHdWI+rBNzYr2YD+vEnFgv5tMc6iSosxwTERERERFRy8UWWiIiIiIiIgpKDGiJiIiIiIgoKAX1PLRml56ejnHjxqG0tBQdOnTAzJkz0bt3b6OL1eyUlJRg7NixuHTpEsLCwtCrVy9MnToVnTp1wuDBgxEWFoY2bdoAAMaMGYNBgwYBkK8f1l3gpLa9v9uddRK4rKwsvP76646/KyoqUFlZiYMHD/JY0dHMmTORkJCAy5cvY926dejXrx8A/7cz60cdYvUid30BpM9zAOtFDVLHihbbnXWinFi9yF1fAB4rWpM7V7WIa4tAmhk5cqSwZs0aQRAEYc2aNcLIkSMNLlHzVFJSIuzfv9/x94wZM4Tx48cLgiAIDz/8sJCamir6Pbn6Yd0FTmrb+7vdWSfqmz59ujBlyhRBEHis6OnQoUNCdna2xzbX4thg/SgnVi9y1xdB4HGjNaljRYvtzjpRTqpenDlfXwSBx4rW5M5VLeHawoBWI4WFhcKAAQOEhoYGQRAEoaGhQRgwYIBQVFRkcMmav40bNwqjRo0SBEH6BCpXP6w7dYhte3+3O+tEfbW1tcLAgQOF5ORkQRB4rBjBeZtrcWywfvwjd+PtfH2R+yzrRV1KA1oeK/qSqgf364vcZ1kv2rCfq1rKtYVdjjWSk5ODbt26ITQ0FAAQGhqKrl27Iicnx9FVidRntVqxbNkyDB482PHamDFjIAgCBgwYgLfeegvh4eGy9SMIAutOJe7b3t/tzjpR39atW9GtWzf079/f8RqPFeNocWywftQldn0BeNwYRc3tzjpRl9j1BeCxohfnc1VLubYwKRQ1K9OmTcM111yD559/HgAQExODtWvXYtWqVRAEAVOnTjW4hC0Ht725rVq1Ck899ZTjb9YXkTz36wvA48Yo3O7m5n59AVhnehI7VzV3DGg1EhERgby8PFgsFgCAxWJBfn4+IiIiDC5Z8zVz5kxkZGRg7ty5aNXKtmvbt3dYWBiGDx+OpKQkx+tS9cO6U4fYtvd3u7NO1JWXl4dDhw4hOjra8RqPFWNpcWywftQjdn0BeNwYRe3tzjpRj9j1BeCxohf3c1VLubYwoNVI586dERUVhbi4OABAXFwcoqKi2EVCI3PmzEFycjIWLFiAsLAwAEBVVRUqKioAAIIgID4+HlFRUQDk64d1Fzipbe/vdmedqGv16tV48MEH0bFjRwA8VsxAi2OD9aMOsesLwOPGKFpsd9aJetyvLwCPFb2InatayrUlRBAEwbC1N3Pnz5/HuHHjUF5ejvDwcMycORN9+vQxuljNztmzZzFs2DD07t0bbdu2BQBERkZi3LhxePPNN2GxWGC1WtG3b1+8++676Nq1KwD5+mHdBSYzM1Ny2/u73Vkn6hk6dCgmTpyIBx54AIB8fQGsF7VNnz4dmzZtQmFhITp27IgOHTpg/fr1mhwbrB/lxOpl7ty5oteXBQsW8LjRgVidLFq0SJPtzjpRTuocBnheXwBeY/QgdS+8YMGCFnFtYUBLREREREREQYldjomIiIiIiCgoMaAlIiIiIiKioMSAloiIiIiIiIISA1oiIiIiIiIKSgxoiYiIiIiIKCgxoCUiIiIiIqKgxICWiIiIiIiIghIDWiIiIiIiIgpK/x9/AxKLVlNN4AAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16, 9))\n", "mu_ax = fig.add_subplot(221)\n", "std_ax = fig.add_subplot(222)\n", "hist_ax = fig.add_subplot(212)\n", "mu_ax.plot(tracker['mean'])\n", "mu_ax.set_title('Mean track')\n", "std_ax.plot(tracker['std'])\n", "std_ax.set_title('Std track')\n", "hist_ax.plot(advi.hist)\n", "hist_ax.set_title('Negative ELBO track');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that there are convergence issues with the mean, and that lack of convergence does not seem to change the ELBO trajectory significantly. As we are using the OO API, we can run the approximation longer until convergence is achieved." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:00<00:00 Average Loss = 1.8632]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 1.8388\n" ] } ], "source": [ "advi.refine(10_000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(16, 9))\n", "mu_ax = fig.add_subplot(221)\n", "std_ax = fig.add_subplot(222)\n", "hist_ax = fig.add_subplot(212)\n", "mu_ax.plot(tracker['mean'])\n", "mu_ax.set_title('Mean track')\n", "std_ax.plot(tracker['std'])\n", "std_ax.set_title('Std track')\n", "hist_ax.plot(advi.hist)\n", "hist_ax.set_title('Negative ELBO track');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We still see evidence for lack of convergence, as the mean has devolved into a random walk. This could be the result of choosing a poor algorithm for inference. At any rate, it is unstable and can produce very different results even using different random seeds.\n", "\n", "Let's compare results with the NUTS output:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:369: UserWarning: No value variable found for normal_rv{0, (0, 0), floatX, False}.out; the random variable will not be replaced.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "ax = sns.kdeplot(mixture_trace.posterior['x'].values.ravel(), label='NUTS');\n", "sns.kdeplot(approx.sample(10_000).posterior['x'].values.ravel(), label='ADVI');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stein Variational Gradient Descent (SVGD)\n", "\n", "SVGD is a general VI algorithm that iteratively shifts a set of particles to match a target posterior. This is done via a form of functional gradient descent that minimizes the KL divergence.\n", "\n", "1. Sample particles from prior distribution of parameters\n", "2. Formulate bijective (i.e. reversible) transformation of particles\n", "3. Iteratively apply transformation until convergence\n", "\n", "SVGD directly minimizes $KL(\\{x_i\\} || p)$ by iteratively moving points $\\{x_i\\}_{i=1}^n$ towards the target p by updates of form:\n", "\n", "$$x_i^{\\prime} \\leftarrow x_i + \\epsilon\\phi(xi)$$\n", "\n", "where $\\phi$ is a *perturbation direction* chosen to optimally decrease the KL divergence:\n", "\n", "$$\\phi = \\text{argmax}_{\\phi}\\left\\{-\\frac{\\partial}{\\partial \\epsilon} KL(q_{[\\epsilon \\phi]} || p)|_{\\epsilon=0}\\right\\}$$\n", "\n", "where $q_{[\\epsilon \\phi]}$ is the density of $x^{\\prime}$ when the density of $x$ is $q$.\n", "\n", "The name of the procedure reflects the fadt that this direction is related to the **Stein operator**:\n", "\n", "$$-\\frac{\\partial}{\\partial \\epsilon} KL(q_{[\\epsilon \\phi]} || p)|_{\\epsilon=0} = E_{x \\sim q}[\\mathcal{T}_p \\phi(x)]$$\n", "\n", "[SVGD visualization](https://chi-feng.github.io/mcmc-demo/app.html#SVGD,multimodal)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with mixture_model:\n", " svgd_approx = pm.fit(300, method='svgd', inf_kwargs=dict(n_particles=1000), \n", " obj_optimizer=pm.sgd(learning_rate=0.01))" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:369: UserWarning: No value variable found for normal_rv{0, (0, 0), floatX, False}.out; the random variable will not be replaced.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = sns.kdeplot(mixture_trace.posterior['x'].values.ravel(), label='NUTS');\n", "sns.kdeplot(svgd_approx.sample(2000).posterior['x'].values.squeeze(), label='SVGD');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Minibatches\n", "When dealing with large datasets, using minibatch training can drastically speed up and improve approximation performance. Large datasets impose a hefty cost on the computation of gradients. \n", "\n", "Minibatch gradient descent is a variation of the gradient descent algorithm that divides a large dataset into (much) smaller batches, each of which are used to calculate gradients, model error and updated model coefficients. These \"noisy\" gradients are more robust to the presence of local minima, and avoid having to ever use the entire dataset to calculate a gradient.\n", "\n", "There is a nice API in PyMC to handle these cases, which is avaliable through the `pm.Minibatch` class. The minibatch is just a highly specialized Aesara tensor:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "issubclass(pm.Minibatch, at.TensorVariable)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To demonstrate, let's simulate a large quantity of data:" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Raw values\n", "data = np.random.rand(400_000, 100) \n", "# Scaled values\n", "data *= np.random.randint(1, 5, size=(100,))\n", "# Shifted values\n", "data += np.random.rand(100) * 2 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, let's fit a model without minibatch processing:" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": true }, "outputs": [], "source": [ "with pm.Model() as model:\n", " mu = pm.Flat('mu', shape=(100,))\n", " sd = pm.HalfNormal('sd', shape=(100,))\n", " like = pm.Normal('like', mu, sd, observed=data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, let's create a custom special purpose callback to halt slow optimization. Here we define a callback that causes a hard stop when approximation runs too slowly:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def stop_after_10(approx, loss_history, i):\n", " if (i > 0) and (i % 10) == 0:\n", " raise StopIteration('I was slow, sorry')" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/pymc/pymc/aesaraf.py:996: UserWarning: The parameter 'updates' of aesara.function() expects an OrderedDict, got . Using a standard dictionary here results in non-deterministic behavior. You should use an OrderedDict if you are using Python 2.7 (collections.OrderedDict for older python), or use a list of (shared, update) pairs. Do not just convert your dictionary to this type before the call as the conversion will still be non-deterministic.\n", " aesara_function = aesara.function(\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 0.09% [9/10000 00:08<2:31:25 Average Loss = 4.3686e+08]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "I was slow, sorry\n", "Interrupted at 9 [0%]: Average Loss = 3.4257e+08\n" ] } ], "source": [ "with model:\n", " advifit = pm.fit(callbacks=[stop_after_10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inference is too slow, taking several seconds per iteration; fitting the approximation would have taken hours!\n", "\n", "Instead, let's use minibatches. At every iteration, we will draw 500 random values. Since PyMC variables are just Aesara variables, we can swap data in and out of the likelihood at each iteration. However, we need to provide the total size of the dataset in order for the model to be properly specified." ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X = pm.Minibatch(data, batch_size=(1000, 100))\n", "\n", "with pm.Model() as model:\n", " \n", " mu = pm.Normal('mu', mu=0., sigma=1.e5, shape=(100,))\n", " sd = pm.HalfNormal('sd', shape=(100,))\n", " likelihood = pm.Normal('likelihood', mu, sd, observed=X, total_size=data.size)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 100.00% [10000/10000 00:27<00:00 Average Loss = 1.7121e+05]\n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Finished [100%]: Average Loss = 1.7118e+05\n" ] } ], "source": [ "with model:\n", " advifit = pm.fit()" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(advifit.hist);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Minibatch inference is dramatically faster. Multidimensional minibatches may be needed for some corner cases where you do matrix factorization or model is very wide.\n", "\n", "Here is the docstring for `Minibatch` to illustrate how it can be customized." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Minibatch ADVI\n", "\n", "Try using minibatch ADVI on the regression model:\n", "\n", "1. Simulate a dataset of size n=50,000\n", "2. Set up the model to fit to this data using minibatch" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Write your answer here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## References: \n", "\n", "1. [Variational Inference from the ground up](https://www.civisanalytics.com/blog/variational-inference-ground/)\n", "2. [Automatic Differentiation Variational Inference. Kucukelbir, A., Tran D., Ranganath, R., Gelman, A., and Blei, D. M. (2016)](https://arxiv.org/abs/1603.00788)\n", "2. [Variational Inference: A Review for Statisticians, David M. Blei, Alp Kucukelbir, Jon D. McAuliffe (2016)](https://arxiv.org/abs/1601.00670)" ] } ], "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": "3.9.9" } }, "nbformat": 4, "nbformat_minor": 2 }