{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## A Crash Course in Bayesian Statistics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes Rule\n", "\n", "Recall that Bayes Rule is \n", "$$\n", "Prob(A|B) = \\frac{Prob(B|A)Prob(A)}{Prob(B)}\n", "$$ \n", "\n", "![conditional probability](../site_pics/conditional.png)\n", "\n", "Based on the definition of conditional probability, \n", "\n", "$$\n", "Pr(A | B) = \\frac{Pr(A \\cap B)}{Pr(B)}\n", "$$\n", "\n", "Since $Pr(A\\cap B) = Pr(B\\cap A)$, \n", "\n", "$$\n", "Pr(A|B)Pr(B) = Pr(B|A)Pr(A)\n", "$$\n", "giving us the Bayes Rule result:\n", "\n", "$$\n", "Pr(A|B) = \\frac{Pr(B|A)Pr(A)}{Pr(B)}\n", "$$\n", "\n", "#### The Monty Hall Problem\n", "\n", "The following example- one made famous for many university professors ridiculing a journalist for what they perceivied to be faulty reasoning (in fact, the journalist was correct [[see this link for some info on how often people get this wrong]](http://www.wired.com/2014/11/monty-hall-erdos-limited-minds/))- shows how we might apply Bayes Rule for cases where prior beliefs are updated with new information. It should be noted that expositions like this- of which there are many- don't really illuminate the econometric use of Bayes Rule very much, but help with understanding Bayes Rule.\n", "\n", "**The Problem**\n", "\n", ">Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, \"Do you want to pick door No. 2?\" Is it to your advantage to switch your choice? (Whitaker, 1990, as quoted by vos Savant 1990a)\n", "\n", "##### The probablility that the car is behind door 2\n", "Denote C,G as the value actually behind each door (a car and a goat respectively). Let Y and M represent Your and Monte's choices, respectively and the numbers 1,2,3 represent the 3 doors. We can solve this in a variety of ways (not necessarily involving Bayes Rule). Using Bayes Rule, let's consider that person 1 having chosen door 1 (Y1) and Monty having chosen door 3 (M3), that the probability that the car is actually behind door 2 (C2):\n", "$$\n", "Pr(C2|Y1,M3) = \\frac{Pr(M3|Y1,C2)Pr(C2|Y1)}{P(M3|Y1)}\n", "$$\n", "\n", "Let's start with the numerator:\n", "$$\n", "Pr(M3|Y1,C2)Pr(C2|Y1) = 1 \\times \\frac{1}{3} = \\frac{1}{3} \n", "$$\n", "\n", "Note that your **priors** when you choose Y=1 are:\n", "$$\n", "Pr(C1|Y1) = \\frac{1}{3} \\\\\n", "Pr(C2|Y1) = \\frac{1}{3} \\\\ \n", "Pr(C3|Y1) = \\frac{1}{3}\n", "$$\n", "Since your choice reveals no information about where the car is, your best guess about the probability that the car is behind any given door is $\\frac{1}{3}$ On the other hand, if the contestant having chosen door 1 and the car actually being behind door 2, means that Monte has to open door 3 with probability 1, since he will never reveal the actual location of the car until the contestant has had the opportunity to switch or not.\n", "\n", "The denominator, is\n", "$$\n", "P(M3|Y1) = P(M3 | Y1, C1) Pr(C1| Y1) + P(M3 | Y1, C2) Pr(C2| Y1) + P(M3 | Y1, C3) Pr(C3| Y1)\n", "$$\n", "which is equal to\n", "$$\n", "\\frac{1}{2} \\times \\frac{1}{3} + 1 \\times \\frac{1}{3} + 0 \\times \\frac{1}{3} = \\frac{1}{2} \n", "$$\n", "Note that the denominator \"integrates out\" all possible values of our parameter (where the car actually is), while holding constant Monte's choice and the contestant's initial choice.\n", "\n", "The expected probability that the car is behind door #2 from Bayes Rule is then\n", "$$\n", "\\frac{\\frac{1}{3}}{\\frac{1}{2}} = \\frac{2}{3}\n", "$$\n", "\n", "##### The probability that the car is behind door 1\n", "\n", "I'll let you solve for this, and the number you should get is $\\frac{1}{3}$. Therefore, you should always switch doors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayes Rule for Econometric Analysis\n", "\n", "Replacing the generic A and B (or You and Monte) with data and parameters, starts us down the path of operationalizing Bayesian Econometrics:\n", "\n", "![bayes formula](../site_pics/bayesrule2.png)\n", "\n", "For example, in an OLS setting $\\theta$ is comprised of the parameters $(\\beta,\\sigma)$ and we have data (usually comprised of what we call $\\mathbf{y}$ and $\\mathbf{x}$).\n", "\n", "One can see from the Monte Hall Problem that you must \"integrate out\" all possible values for where the car might be. For statistical models like OLS, the denominator ($Pr(y)$) is calculated as\n", "\n", "$$\n", "Prob(\\mathbf{y}|\\mathbf{x}) = \\int_{\\theta} Pr(\\mathbf{y}|\\theta,\\mathbf{x})Pr(\\theta|\\mathbf{x})d\\theta\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we use this idea for econometric inference? A very good book on this topic is by John Geweke, \"Contemporary Bayesian Econometrics and Statistics\". Consider the following definitions for getting us started:\n", "\n", "- Parameters we are trying to estimate (like $\\beta$): $\\theta$\n", "- Prior distribution of parameters (what we believe a priori about model parameters): $Prob(\\theta)$. Note, the prior distribution depends on additional parameters that Geweke calls \"Hyper Parameters\". These are not parameters we try to estimate. \n", "- Sampling distribution of dependent variable $\\mathbf{y}$: $Prob(\\mathbf{y}|\\theta,\\mathbf{x})$. This is also called the likelihood function (exactly equivalent to what we did in MLE).\n", "- Marginal likelihood (the evidence):\n", "$$\n", "Prob(\\mathbf{y}|\\mathbf{x})=\\int_{\\theta}Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x})d\\theta = \\text{Normalizing Constant}\n", "$$\n", "- Posterior Distribution (this is the link to Bayes Rule): \n", "$$\n", "Prob(\\theta |\\mathbf{y}) = \\frac{Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))}{Prob(\\mathbf{y}|\\mathbf{x})} \\propto Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__An example__\n", "\n", "Let's examine the posterior, $Prob(\\mathbf{y}|\\theta,\\mathbf{x})Prob(\\theta|\\mathbf{x}))$ and see how priors influence the posterior probabilities. Suppose we have an ultra-simple model: we have no independent variables (there is no $\\mathbf{x}$) and only have 1 observation on y (the number of ice-cream cones Rob consumed during a long hot summer): \n", "\n", "* You observe y=7 and know that Rob's standard deviation for y is 1.\n", "* You also have strong beliefs based on people similar to Rob, that people consume 5 ice-cream cones with a standard deviation of 2. Denote these beliefs (hyperparameters) as $\\mu_0$ and $\\sigma_0$.\n", "\n", "Letting both $Prob(\\mathbf{y}|\\theta,\\mathbf{x})$ and $Prob(\\theta|\\mathbf{x}))$ be normal pdf's, we have the likelihood:\n", "$$\n", "Prob(\\mathbf{y}|\\mu) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(y - \\mu)^2}{2\\sigma^2}} = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{(y - \\mu)^2}{2}}\n", "$$\n", "\n", "and the prior:\n", "$$\n", "P(\\mu) = \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} e^{-\\frac{(\\mu - \\mu_0)^2}{2 \\sigma_0^2}} = \\frac{1}{\\sqrt{2\\pi 4}} e^{-\\frac{(\\mu - 5)^2}{2 \\times 4}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy.stats import norm,uniform\n", "import matplotlib.pyplot as plt\n", "import seaborn as sbn\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "sbn.set_style('white')\n", "sbn.set_context('talk')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# observed data\n", "y = 7\n", "# std deviation of y\n", "sigma = 1\n", "\n", "# prior hyperparameters\n", "mu_0 = 5\n", "sigma_0 = 2 #(this is our prior on std dev of mu_0)\n", "\n", "bayes_guess = 6.5\n", "\n", "# gen some data along the support of mu and plot likelihood:\n", "\n", "mu_plot = np.arange(4,8,.05)\n", "\n", "likelihood = norm(mu_plot,sigma).pdf(y)\n", "prior = norm(mu_0,sigma_0).pdf(mu_plot)\n", "\n", "plt.figure(figsize=(14,7))\n", "plt.plot(mu_plot,likelihood,label='likelihood')\n", "plt.plot(mu_plot,prior,label='prior')\n", "plt.plot(mu_plot,likelihood*prior,label='likelihood $\\\\times$ prior')\n", "\n", "# plot the mle estimate\n", "plt.axvline(7,c='b',linestyle='--', label='mle')\n", "plt.plot([5,5],[0,norm(mu_0,sigma_0).pdf(mu_0)],c='g',linestyle='--', label='prior mean')\n", "plt.plot([bayes_guess,bayes_guess],[0,norm(bayes_guess,sigma).pdf(y)],c='k',linestyle='--')\n", "plt.legend(loc='upper left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Approaches for using the posterior\n", "\n", "1. Analytically solving it (Analytical Bayes and Conjugate Priors)\n", "2. Taking random draws of $\\theta$ from the posterior distribution using simulation (Monte Carlo Markov Chains, Gibbs Sampling): What we will be using." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytical Bayes\n", "\n", "For many years (prior to approximately 1990), these properties were used to derive the posterior **analytically**, since simulation methods were in their infancy and computers were only just gaining sufficient capability for simulation methods such as Monte Carlo Markov Chains. \n", "\n", "In the analytical Bayes approach the focus on the research was to write down forms for $Prob(\\mathbf{y}|\\theta,\\mathbf{x})$ and $Prob(\\theta|\\mathbf{x}))$ allowing for closed form solutions for the posterior distribution of our parameters. These approaches required alot of creativity for selecting models and corresponding statistical distributions but limited the analyst to a relatively small universe of models (e.g. simple OLS). Since most of us don't enjoy these types of mental gymnastics, Bayesian Statistics wasn't widely adopted. Currently, they are generally out of favor- even these simple models are often now estimated using sampling methods described below.\n", "\n", "### Conjugate Priors\n", "\n", "To think about applying Bayesian to a very simple model using analytical Bayes, we need to specify the distribution for the likelihood and the prior. Choosing **conjugate distributions** ensures that we can find closed for solutions for our model parameters (referred to as **MAP**, or Maximum a Posteriori estimates for $\\theta$). For example, assume\n", "$$\n", "Prob(\\mathbf{x}|\\mu) = \\prod_{i=1}^N \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(y_i - \\mu)^2}{2\\sigma^2}}\n", "$$\n", "\n", "Consider the case of known and fixed variance of x (denoted as $\\sigma^2$).\n", "\n", "__Conjugate Prior__\n", "\n", "A natural choice is a normal with mean $\\mu_0$ and $\\sigma_0^2$ (describing our prior beliefs about the mean of x):\n", "\n", "$$\n", "P(\\mu) = \\frac{1}{\\sqrt{2\\pi\\sigma_0^2}} e^{-\\frac{(\\mu - \\mu_0)^2}{2\\sigma_0^2}}\n", "$$\n", "\n", "So in this problem, we have\n", "\n", "| Parameter | Parameter Type |\n", "|:-----------:|----------------|\n", "|$\\mu$ | Model Parameter for mean of $\\mathbf{y}$ (What we are trying to Estimate) |\n", "|$\\sigma^2$ | Variance of $\\mathbf{y}$ (assumed known)\n", "|$\\mu_0$ | Hyper-parameter (Describing priors on $\\mu$) |\n", "|$\\sigma^2_0$ | Hyper-parameter (Describing priors on $\\mu$) | \n", "\n", "We call our choice of prior- a conjugate prior- because we have carefully chosen a set of probability forms allowing us to derive close formed solutions for $\\mu$. [More on this here](https://en.wikipedia.org/wiki/Conjugate_prior).\n", "\n", "Our posterior distribution is\n", "$$\n", "Prob(\\mu|\\mathbf{y}) \\propto Prob(\\mathbf{y}|\\mu)Prob(\\mathbf{\\mu})\n", "$$\n", "\n", "\n", "Given our conjugate prior and the likelihood function, the **MAP** estimate for our mean conditional on x is \n", "\n", "$$\n", "E(\\mu|x_i) = \\frac{\\sigma^2_0}{\\sigma^2 + \\sigma^2_0}y_i + \\frac{\\sigma^2}{\\sigma^2 + \\sigma^2_0} \\mu_0 \n", "$$\n", "\n", "Or, for our entire sample, we have\n", "$$\n", "E(\\mu|\\mathbf{x}) = \\frac{\\sigma_0^2}{\\frac{\\sigma^2}{n} + \\sigma^2_0}\\frac{\\sum y_i}{n} + \\frac{\\frac{\\sigma^2}{n}}{\\frac{\\sigma^2}{n} + \\sigma^2_0} \\mu_0 \n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is an extremely intuitive result, it is simply a weighted average between our prior belief about $\\mu$ and the maximum likelihood estimate. This weight depends on the relative uncertainty across the two measures. As the variance of our prior beliefs get larger, the MAP estimate for $\\mu$ places **more** weight on the MLE estimator rather than our priors. MLE estimates with low precision, relative to our priors, are downweighted.\n", "\n", "The posterior distribution, $Prob(\\theta|\\mathbf{x})$, can then be solved analytically and is distributed as:\n", "\n", "$$\n", "N \\left (\\frac{\\sigma_0^2}{\\frac{\\sigma^2}{n} + \\sigma^2_0}\\frac{\\sum y_i}{n} + \\frac{\\sigma^2/n}{\\frac{\\sigma^2}{n} + \\sigma^2_0} \\mu_0,\\left ( {\\frac{1}{\\sigma_0^2} + \\frac{n}{\\sigma^2}} \\right )^{-1} \\right ) \n", "$$\n", "\n", "Let's visualize this in code:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def calc_posterior_analytical(data, x, sigma, mu_0, sigma_0):\n", " n = data.shape[0]\n", " # posterior parameter\n", " mu_post = ( mu_0/(sigma_0**2) + data.sum()/(sigma**2) )*(1. / sigma_0**2 + n / sigma**2)**(-1)\n", " sigma_post = np.sqrt((1. / sigma_0**2 + n / sigma**2)**(-1))\n", " # probabilities\n", " posterior = norm(mu_post,sigma_post).pdf(x)\n", " prior = norm(mu_0,sigma_0).pdf(x)\n", " return posterior,prior,mu_post,sigma_post \n", "\n", "def calc_like(mu_trial,sigma,data):\n", " like = np.zeros(mu_trial.shape[0])\n", " count = 0\n", " for i in mu_trial:\n", " like[count] = norm(i,sigma).pdf(data).prod()\n", " count += 1\n", " return like" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = norm(10,3).rvs(10)\n", "ax = plt.subplot()\n", "sbn.distplot(data, kde=False, ax=ax,bins=5)\n", "_ = ax.set(title='Histogram of observed data', xlabel='y', ylabel='# observations');" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "sigma = 3 # Note this the KNOWN std dev of y\n", "mu_prior = 8\n", "sigma_prior = 2 # Note this is our prior on the std of mu" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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8Ofb29mmazUsIIYQQQgghhBDCGFLgMRNfX182btxIiRIlmDRpEsWLF1c7JCGEEEIIIYQQQmRSMgaPEEIIIYQQQgghRAYnY/AIIYQQQgghhBBCZHBS4BFCCCGEEEIIIYTI4Iwu8Fy9epWKFSty6NAhc8YjLKRnz554e3vHWzd69Gjc3NxSfa779+/j5ubGjBkzTBWesKAlS5bg5eVFcHCw2qEIK3Ps2DHc3NxYv359suvMcZ3E8oq15xpzvDZCCPXJ37YQOmr8LaTnHjSxeNevX4+bmxvHjh0zWYzGvl8yx7VNzdvbm549e6odRrqY+/d09+7duLu7c/v2bbOcP72MLvBMnDiRt99+m7p165oznhStX7+eJUuWqBqDEOkxY8YMdu/ebdFrHjt2jBkzZhASEpJgW7du3ciWLRuzZ8+2aExCXfp/fgsXLlQ7FCGEMBt9rov7qFq1Ku3bt2fp0qXExMSoHaIQIhmJ3YPKe5jMKaPk6yZNmqDVapk0aZLaoSTKqFm0Tp8+zaFDh5g1a5a540nRhg0bePDggUw7bgbff/893333XaqPK1asGOfOncPW1tYMUWU+M2fOpF27djRp0sRi1zx+/Ljhurlz5463LXv27HTp0oXff/8dHx8f8ubNa7G4hHWrUaMG586dw87O8hMuSl4RQpjSe++9R/369VEUhadPn7JhwwZ+/PFHrl+/zvfff5/ssWrmQiGysvTeg6r5tyt5I+3Sk6/BMq99r169GDVqFNeuXaNcuXJmu05aGNWCZ+XKlTg7O9OgQQNzx5OlvHz5kujoaLXDMLC3tyd79uypPk6j0ZA9e3ZJYBlYmzZtePXqFRs2bFA7FGFFbGxsyJ49uypFFskrQghTqlixIm3atKFt27Z88sknrF27loIFC7J27VqePXuW6DEvXrwAzJMLFUUhLCzMZOcTIjNK7z2omu9j1Ly2pSiKwtq1a5NtWePn50dUVFSqzpuWfA0QExNDRESEWV57/bn1mjZtioODA6tWrTLZNUwlxQJPdHQ0u3fvpm7dutjb28fbNmPGDNzc3Lh//36C4xLrv+fm5sbo0aM5fPgwnTt3pkqVKtStW5cJEyYQHh6eYrDe3t4cP36cBw8exGu6Fbcf47///svHH39MtWrVqFy5Mu3atWPt2rUpnvvNGE+fPk2PHj3w9PTEy8uLMWPGJPqP+PLlywwcOBAvLy88PDxo2bIl8+fPT/CLrh/fJjAwkC+//JI6derg6enJ48ePDa/j9evX+eGHH6hXrx6enp58+OGH3Lx5E4CdO3fSrl07KleujLe3N6tXr04Qy7Zt2/Dx8aFhw4a4u7vj5eXFp59+yuXLl4167m+OwZNYM7m4D32/xpTGyti3bx8dOnTAw8ODevXq8fPPPyda2NqxYwfvv/8+Hh4eNGzYkJkzZ3L48OFU9aH09/dnwoQJNG7cGHd3d2rXrs3HH3+coN+usb8n+rGKnjx5wvDhw6lRowaenp706dOHW7duxds3MjKSGTNm0Lx5c6pUqUL16tVp3bo1P//8c7zXBHQt0eK+lnqp+Rnq/8Zu3LjBJ598QtWqValWrRpDhgzB39/fsN/o0aOZOXMmAI0bNzZcM+7Pq0SJEri6urJ9+3ajXmeRNaSmD/OGDRuoVKkSQ4YM4dWrVwCEhoby66+/0rRpU9zd3alVqxbDhw/n3r17KZ4vpfF2jM0rqfmfkJp9d+/eTdu2bfHw8KBBgwZMmzbNqgr2QojkOTo6UrVqVRRF4d69e4b/qRcvXqRPnz5Uq1aN999/H0g6F4aHhzN58mSaNGmCu7s7devWZeTIkTx48CDefnGP/+OPP2jZsiUeHh4sWrTIYs9XCHMKDAzku+++o0GDBri7u9OgQQO+++47nj9/nmDf+/fvM3jwYN5++22qVavGgAED4v0N6iV3D2qs1LyPmTNnDm5ubnz//ffExsYC8OrVK+bOnUurVq3w8PCgevXq+Pj4cPHixXRdOzY2loULFxpyR/PmzZP8kDU1r21q9n306BGfffYZ1apV4+2338bHx4e7d++m+LziOnToEF9//TUjR45MtMgzYcIExowZw59//pmq877pzXwNr8czOnz4MLNmzaJJkyZUrlyZv/76K8nX3tjXJ7lz6+XKlYtq1apZ5b1Tih+NXrhwgfDwcCpXrmySC164cIEdO3bQqVMn2rRpw7Fjx1i+fDnXrl1j8eLF2NgkXXP66quvmDx5Ms+fP+fLL780rC9TpgwAe/fuZdCgQeTPn5+PP/4YR0dH/vzzT77++mvu37/PsGHDjIrx0qVL+Pj40L59e9577z2OHz+On58fNjY28ZqF/ffff/Ts2RM7Ozu6d+9O/vz52bdvH5MmTeLy5ctMnjw5wbk//vhj8ufPz6effkp4eDg5c+Y0bBs1ahQ5c+akf//+BAYGsnjxYvr27cuQIUOYNGkSXbt2pUOHDvj5+fHNN99QpkwZqlevbjh+xYoV5MmTh86dO1OgQAHu3r3LmjVr6NatGxs2bKB06dJGPf+4r+svv/ySYP2iRYu4fPky+fLlS/Ec+/fvZ+XKlYbY9+zZw6JFi8iTJw8+Pj6G/bZt28bw4cMpWbIkgwYNwtbWlo0bN7J3716j471//z7dunUjICCANm3a4O7uTkREBGfPnuXw4cOGvrup/T0JDw+nR48eVKlShWHDhnH//n2WLVvGp59+ytatWw3V4e+++45169bRtm1bPD09iY2N5fbt24YCpIuLC7/88gsjR46kevXqdO7cOcFzSO3P8MmTJ/Tq1YsmTZowcuRILl++zOrVq3nx4oXhjWOXLl148eIFu3bt4ssvvzR0wXpzQO2qVauyefNmwsLCyJUrl9GvuxBz585l6tSpdO/ena+//hobGxtCQ0Pp2rUrDx8+pEOHDpQrVw5/f39WrlxJp06dWLduHcWKFUvT9YzNK6n5W0/Nvrt27WLw4MEUK1aMgQMHYmtry/r16/n777/T/BoKISxLURTu3LkDYPi/+PDhQz788ENatGhBs2bNkv3wMTo6mj59+nDq1CmaN2/Oxx9/zJ07d/D19eXQoUOsW7eOwoULxztm6dKlBAUF0alTJwoUKJBguxAZUWhoKN26dePOnTt06NCBihUrcunSJXx9fTl69Chr167F0dERgOfPn9O9e3cCAgLo2rUrb731FidPnuTDDz9M8Pdm6nvQpMTGxjJ+/Hh8fX35/PPP+eSTTwCIioqiT58+nD59mjZt2tC9e3devHhheF++YsUKPDw80nTNqVOn8vLlS7p06UK2bNnw9fVl9OjRlCxZkmrVqhn2S81rm5p9Q0JC6N69O48fP6Zr166UKVOGf//9l169evHy5Uujn0e9evX48ssv+emnn1AUhV9//dVwX/T999+zYsUK+vfvT9u2bdP0Oukllq/19B/wde7cmVy5cuHq6mr4oDGu1Lw+yZ07rqpVq3Lw4EFu3LhhqEdYBSUFfn5+ilarVXbv3p1g2/Tp0xWtVqvcu3cvwbZGjRopPXr0iLdOq9UqWq1W2bVrV7z133//vaLVapWtW7emFI7So0cPpVGjRgnWR0dHKw0bNlSqVaumPH782LA+MjJS6dKli1K+fHnl1q1bKZ5fq9Uqbm5uyunTp+Ot79evn1KxYkXlxYsXhnVdunRRKlSooFy6dMmwLjY2VhkyZIii1WqVw4cPG9aPGjVK0Wq1yueff57gmvrXsX///kpsbKxh/dKlSxWtVqt4enoqDx48MKwPCAhQ3N3dlWHDhsU7T1hYWIJzX79+XalUqZLy7bffxluf2OuojzE5f/zxh6LVapUJEyYY1t27d0/RarXK9OnTE6yrUqVKvN+P2NhYpVWrVkrdunUN66KiopR69eoptWvXVoKCggzrX7x4oXh7eytarVZZt25dsnEpiqL07dtX0Wq1yoEDBxJsi4mJURQl9b8nPXr0ULRarTJv3rx455s/f36Ca9WoUUPp27dvinFqtVpl1KhRiW5Lzc+wUaNGilarVf78889468eNG6dotVrl+vXrhnXJ/a3qzZo1S9Fqtcp///2X4nMQGd/Ro0cVrVarLFiwIMV94v79xV0XExNj+H2bM2dOvGO///57xcPDI15+VBRFuX//vlK1atV4fwOJXSe9eSU1f+up3bdBgwZKzZo1lYCAAMO+ISEhSsOGDY3OV0IIy9DnlxkzZigBAQFKQECAcunSJWXMmDGKVqtVOnfurCjK6/+pa9asSfIccf+2V69erWi1WuXnn3+Ot+++ffsUrVarjBgxIsHxNWrUUJ49e2amZyqE+SX2tzBlyhRFq9UqK1asiLfvihUrFK1Wq0ydOtWw7ueff1a0Wq2yadOmePvq18e9d0zuHtSY9zBJxbtu3TpFq9UqR48eVSIiIpRPP/1UqVSpkrJhw4Z4xy5evDjR+4rQ0FClQYMG8WJN6f3Sm9du06aNEhkZaVj/+PFjpVKlSgnu7VLz2qZm38mTJytarVbx8/OLt++ECRMS/ByMsWTJEkWr1SqfffaZ8urVK8N7wylTpqTqPMbma0V5/Vo2a9ZMCQ8PT/Q8af09Te7ccW3cuFHRarXK9u3bU/U8zS3FLlqBgYEA5MmTxyQFJVdX1wSDy+orpbt27UrzeS9cuGD4pLhQoUKG9dmyZaNv377ExsayZ88eo87l6emJp6dnvHW1atUiOjra0Ow2ICCA06dP4+3tTfny5Q37aTQawyfIiT2fPn36JHndnj17otFoDN/rW+c0btyYokWLGta7uLjg6uqaYGo2fWsgRVF48eIFgYGB5M2bF1dXV86dO2fEM0/eP//8w4QJE2jYsGG8FlTJady4McWLFzd8r9Fo8PLywt/f39Dl7cKFCzx9+pR27drF+z3LlSsXXbt2Neo6QUFB/PPPP7zzzju88847CbbrW4al5ffExsaGXr16xVtXq1YtAEM1GXTNB69fv87Vq1eNijkxqf0ZFixYkJYtWyYaW2qbWTo7OwO6320hUhIZGcmQIUNYs2YNEydOjNdyRlEUtmzZQo0aNShYsCCBgYGGh4ODA56enhw8eDDN1zY2rxj7t57afR89ekT79u1xcXEx7Ovk5GR0vhJCWN6MGTOoXbs2tWvXpk2bNqxbtw5vb+94g7c6OzvTvn17o863a9cubGxs6N+/f7z1DRs2pEKFCuzZs8fQzUOvTZs2RrV+FiIj2bVrFy4uLnTp0iXe+i5dupA3b954M8fu27ePAgUK8N5778XbN7H7I1Pfg74pODiYjz/+mMOHDzNnzpwErUw2b97MW2+9RaVKleK9j3n16hV16tTh5MmTqWrtEtcHH3xAtmzZDN8XKlQo0Xu71Ly2qdl39+7d5M+fP8Fz7tevX5qez4cffsiYMWP466+/aNGiBStXrsTHx8fo3jNvMiZf63Xr1g0HB4cUz5ma18fYc1vrvVOKXbTiFhxMIbHmSwULFiR37txGjcuQFP04QGXLlk2wTT+ytbHnL1GiRIJ1+h9gUFBQitcrU6YMNjY2iV4vuW5Sb15XP9tR3BsZvTx58iTo433x4kWmTZvG8ePHEzRzTOwcqXHlyhWGDh1KuXLlmDJlSrJd6eJK6bXMlSuX4bV8s9lbUusSc/fuXRRFoWLFisnul5bfk4IFCyYYfPrN3wfQdSEcOXIkrVu3pkSJEnh5edGoUSO8vb2Nfr1S+zM05nfVWIqiAKb/mxeZ06+//kpYWBiTJk2idevW8bYFBgYSFBTEwYMHqV27dqLHG/s3kZjU5BVj/tZTs6/+61tvvZVgX6tqniuEiKdLly60aNECjUaDg4MDpUuXNuQNvRIlShg9KOf9+/cpWLBgojefZcuW5dKlSzx//jxeQSe1XeWFyAju37+Pu7t7gkkR7OzscHV1jTdezf3796lcuXKC9wD58uVLMMurud+Pjh49mvDwcFasWBFvyAu9Gzdu8PLlyyTfx4Cuy1mRIkVSfe2k3se8eW+X2tfW2H3v3buHh4dHgnynvydPi549e/LXX39x6tQpSpcuzaBBg9J0HjAuX+sZe6+Ymtcntee2tnunFAs8+k8oE7tZTO7JJDXYZFLH6G8u0yq9x8eV3D93/XXSer3kqoBJ3fAY82bj4cOHdO/eHUdHRwYMGMBbb72Fg4MDGo2GH3/80ahBrJPi7++Pj48PDg4OzJ07N1Xjs5jztUzsXCn9gaXlWsY8B4AmTZqwd+9e9u/fz7///svhw4fx8/OjevXqLF68OF6lPjFp+RkaG5sxgoODAeK1ShAiKU2aNGHnzp0sXLiQevXqxesTrf/dq1OnTpo/DUqOqfNKWva1tn/mQojklSpVijp16iS7jzGfAuul5f1Eas4vRFaX3D2oKbRs2ZL169cze/ZsZs+eTY4cOeJtVxQFrVabbK+FtL5nTs+HXKZiyntyRVH4+uuvOXXqFA0bNmT//v0MHTqU3377LU0DZBuTr/Xe/LmZUkrn1v9uWtu9U4oFHv2nl3G7oujpP7UIDg6O17ogMjISf39/SpUqleCY69evJ1j39OlTQkNDE61mGkt/bGLn169Lz/lTc72bN28SGxtr0uulZNeuXYSHhzNnzhxDFx29oKCgFIsLSYmIiGDAgAE8f/6c5cuXp6lKnRL9786bs1IltS4xpUqVQqPRpDiqvbl/T5ydnWnTpg1t2rRBURQmTZrEggUL2LNnD++++26yx5rrZwjG3YzevXvXUMUWIiW1atWiY8eO9O/fn169erFkyRLDJ9UuLi7kzp2bFy9eGP0P2tRS87eemn1LliwJ6D7Ze1Ni64QQmVPJkiX5559/CAkJSfCJ940bN3B0dEwwGKgQmVGJEiW4desW0dHR8VpHREdHc/v27Xjvq4sVK8adO3eIjY2NV+QICAggJCQk3nmTuwc1hdatW1O7dm1GjhxJ//79mTt3brwibKlSpXj+/Dm1atVSrSCTmtc2tfvevn2bmJiYeB+a6e/JUyM2NpYxY8awfv16hgwZwsCBA1m1ahXjxo1jyJAhTJs2LV33MKaSmtfHWPrhMPS/q9Yixd/WihUr4ujoyNmzZxNs0zc1PXz4cLz1S5YsSdDvWO/WrVsJ+rjNnz8fIMHYPInJlSsXwcHBCaqLlSpVomjRoqxfvz7eFNFRUVEsXLgQjUZD48aNUzy/sfLly0fVqlXZt29fvDFXFEVh3rx5ADRt2tRk10uJ/o/zzddlzZo18V6P1FAUhZEjR3L+/Hl++eWXNI8UnxJ3d3cKFCjAhg0bDK1IAMLCwli1apVR53B2dqZ+/focOHAgwe8jvH5dzPV7EhMTk+Afk0ajMXQZi/u8cubMmeinEeb4Gca95ptxvOnMmTNUqlRJZtASRqtZsybz58/nwYMH9OzZ0/B7amNjQ+vWrTl37lyS00eau79yav7WU7tv4cKFWb9+vWF8AIAXL14Yna+EEBlfkyZNiI2NNbzn09u/fz8XL15MVfdsITKyJk2aEBgYyNq1a+OtX7NmDYGBgfHu7xo1aoS/vz9bt26Nt+/ChQsTnDe5e1BTadWqFZMnT+bkyZP069fPMI4fQNu2bfH392fx4sWJHvvs2TOzxaWXmtc2Nfs2btyYZ8+esXHjxnj76u/JjRW3uDN06FAGDhwIQNeuXRk/fjz79u1jyJAhic5qZWmpeX2MdebMGfLnz59ot301pdiCx9bWlmbNmrFnzx5evXoVrwJXp04d3nrrLaZPn05QUBDFixfn5MmTnD17NslPLbRaLV988QWdOnWiVKlSHDt2jB07dlCzZs0Eg8UmpkqVKuzbt4/x48dTtWpVbG1tqVWrFvny5WPs2LEMGjSIjh07GqYz++uvvzhz5gw+Pj4m7/s8ZswYevbsSffu3fnggw8oUKAA+/bt4+DBg7z33nvJ9tk0tfr16+Pg4MDIkSPp0aMHuXPn5tSpUxw4cICSJUsSExOT6nP6+vqyc+dOatasSUREBJs2bYq3/e233zZJKyU7OztGjRrFiBEj6NSpEx07dsTW1pYNGzbg7OzM/fv3jWqBMnbsWC5evEi/fv1o27YtlSpVIjIykrNnz1KsWDG++OILbG1tzfJ7EhYWRr169fD29qZixYq4uLhw//59fH19yZMnD40aNTLs6+npyZEjR5g3bx5FixZFo9HQqlUrs/wM9apUqQJgGC8le/bslCtXDq1WC+gq0Ldu3WLUqFFpvobImI4cOUJkZGSC9Xnz5jXqH1b16tVZtGgRffv2pWfPnixdupRChQoxbNgwTp06xdChQ3n33XepUqUK9vb2PHz4kAMHDlCpUiUmTpxojqcEkKq/9dTu++WXXzJ06FA6depE586dsbW1Zd26dTg7O/Pw4UOzPSchhPVo164dGzZsMBS5q1evzt27d1m5ciX58+dn+PDhaocohEX07duX7du3M378eC5evEiFChW4dOkSfn5+uLq60rdvX8O+/fr1Y+vWrXz11VecO3fOME366dOnE9w7JncPqpfce5hu3boZFX+LFi2ws7Nj6NCh9OnThwULFuDo6EivXr04fPgwv/zyC0ePHqVWrVo4Ojry8OFDjh49SrZs2Vi+fHkqX63USc1rm9p9t27dytixY7lw4QJly5bl+PHjnDlzJlUtDw8fPsz69esZPnx4ggHnO3fujEajYezYsWzbti3dU6WnV2peH2OEhYVx8uRJOnToYKaI0y7FAg/oRpBev349+/bto3nz5ob1tra2zJ49mwkTJrBixQrs7e2pW7cuK1asSPKPqlKlSnz55ZdMnTqVVatW4ejoSI8ePRg2bJhRn3R8+OGH3Lt3jx07drBq1SpiY2NZtmwZ+fLlw9vbmyVLljBnzhwWLlxIVFQUZcqUYcKECXTq1MnIl8R4Hh4erFq1iunTp+Pr60t4eDglSpRgxIgR9O7d2+TXS07JkiWZP38+U6ZMYe7cudja2vL222+zfPlyvv/++wSDdhlD/wn78ePHOX78eILtP/30k8m6obVu3RpbW1vmzJnD9OnTyZ8/Px07dsTNzY1BgwYlGOQ4MSVKlGDdunXMmjWLAwcOsGnTJnLnzk358uXjjZhujt+THDly8OGHH3LkyBGOHDlCWFgYBQsWxNvbm/79+8ebmefbb79l/PjxzJ071/BJQatWrczyM9SrVq0aI0aMYNWqVYwdO5bo6GgGDRpkKPBs3ryZbNmy0a5duzRfQ2RM//zzD//880+C9a6urnz33XdGncPT05PFixfTp08fQ5GnSJEi+Pr6smjRIrZv386ePXuwtbWlcOHCVKtWzSw5+U2p+VtPzb4tWrRg+vTpzJo1ixkzZpAvXz7atWtHjRo1LJ77hRDqsLe3Z+HChcyZM4dt27axa9cunJycaNGiBUOHDjVLl3YhrJGTkxO+vr5Mnz6dvXv3sn79evLly0fXrl0ZPHgwjo6Ohn1dXFxYuXIlP//8M+vWrTPMgrl06VI6duyYYMyTpO5B9ZJ7D2NsgQd0rTtmzpzJ4MGD6d27NwsWLCB37tz8/vvvrFy5kk2bNjFjxgxANxCxh4eHRd4zp+a1Tc2+efLk4Y8//mDixIls3LgRRVHw8vJi2bJlfPTRR0bHV69ePfz8/JLs5dGpUyfKly9vtl4gqZGa18cYO3fuJCIiIsGsXNZAoxg5klKfPn2IiIhg5cqVab6Ym5sb7dq1M+untiJzWbRoET///DOrV69OMHW9MI3IyEgaN25Mq1atkh1ITgghhBBCCFPTj3XTpUsXxo8fH2+bKe5BhTC19u3bU7RoUWbOnKl2KAkY3Tl49OjRnDlzhoMHD5ozHpFFvXr1KkEXpLCwMP744w+cnZ1TnP5cpJ2vry+vXr3i008/VTsUIYQQQgiRib18+TLBOv3YL3Xr1k2wTe5BhbXZvXs3V69eZcSIEWqHkiijW/CYgrTgEUm5ceMG/fr1o1WrVhQvXhx/f382bNjA/fv3GTduXKqaWYqs6fHjxyxYsIALFy5w+fJlwsPDWbZsGV5eXhaNY+PGjezbt48LFy5w7949atasmWgf7VOnTjFr1iyuXr1KUFAQuXLlQqvV0qdPHxo0aGDRmIUQQgghLKFnz54ULVoUd3d3YmJiOHr0KPv27aNq1ar88ccf8WZ1EkKknlFj8Ahhbi4uLnh6erJlyxYCAgKws7NDq9Xy+eefGzX4thB37tzhzz//pGLFitSqVYu9e/eqEsemTZsICAigRo0aREREJLlfSEgIrq6utG/fnvz58xMSEsLq1av55JNPmDJlCq1atbJg1EIIIYQQ5teoUSM2btzI7t27iYyMpFChQvTu3ZuBAwdKcUcIE7BoCx4hhDCX2NhYw0Dtu3fvZuDAgaq04IkbR5s2bcidO7fRsyxER0fTuHFjSpUqxbJly8wZphBCCCGEECKTMXoMHiGEsGbGzMIHugLMkiVLaN26NR4eHnh5eTFy5Ej8/f0tGkdi7OzscHJywt7e3iSxCCGEEEIIIbIO6aIlhMhSvvzyS7Zt20bv3r2pWbMmT548Ydq0afTs2ZP169eTM2dOi8YTGxtLbGwsAQEBrF69mtu3bzNy5EiLxiCEEEIIIYTI+KTAI4TIMk6dOsXGjRv55ptv6N69u2F9hQoVaNeuHRs2bIi33hKGDh3Kjh07AHB0dOS3336jfv36Fo1BCCGEEEIIkfFJgUcIkWXs378fGxsbWrVqRXR0tGF9uXLlKFSoEMePHzcUeEaPHs2GDRtSPGfDhg35/fff0xzTF198Qd++fXn27Blbt25l6NChTJw4kffeey/N5xRCCCGEEEJkPVLgEUJkGQEBAcTGxiY58PLz588Nyx07dqRmzZopnrNIkSLpiqlEiRKUKFECAG9vb3x8fBg/fjwtW7ZM13g+QgghhBBCiKxFCjxCiCwjb9682NjYsHLlSuzsEqa/XLlyGZarV69O9erVLRkeAB4eHuzbt4/AwEDy589v8esLIYQQQgghMiYp8Aghsoz69eszb948nj17RtOmTdUOJwFFUTh+/Di5c+fG2dlZ7XCEEEIIIYQQGYgUeIQQmcb27dsB+O+//wD4999/ef78OQ4ODjRo0IAaNWrQvn17Ro4cSc+ePalWrRrZsmXjyZMnHDt2jAYNGtCiRYt0xXD9+nWuX78OQGhoKNHR0Ya4PDw8KFasGACff/45xYoVo1KlSuTNmxd/f382bNjA0aNHGTt2bKItjIQQQgghhBAiKRpFURS1gxBCCFNwc3NLdH2xYsXYu3cvoGsls3r1atasWcONGzewsbGhYMGC1KxZk969e+Pq6pquGGbMmMHMmTMT3fbTTz/Rvn17AFasWMGWLVu4ffs2oaGhODk54e7uTvfu3fH29k5XDEIIIYQQQoisRwo8QgghhBBCCGECe/bsYcmSJdy8eZPg4GCcnZ1xd3fHx8cHT0/PBPtv2bKF+fPnc+vWLfLmzcv777/P4MGDyZ49u+WDF0JkeGkq8DRq1AiAffv2mTwgIYQwluQiIYQ1kFwkhNDz8/Pj5s2bVK5cGRcXF/z9/Vm6dCkXLlxg6dKl8SZw2LRpEyNHjqRbt260aNGCGzduMGnSJBo2bMjUqVNTfW3JRUKINA3yEBoaauo4hBAi1SQXCSGsgeQiIYRex44dE6xr0KABtWrVYt26dYYCT0xMDL/++ive3t6MGzcOgFq1amFvb8/YsWP56KOPqFKlSqquLblICGGjdgDW7mnYUzqs6UCHNR14GvZUpSCeQocOusfTp8ZuEkJkIpKLhBDWQHKREKmXM2dOsmXLhr29vWHdmTNn8Pf3p127dvH2bd26Nfb29uzYscPSYWYo1p6LjNgshFlIgScF4VHhrL+0nvWX1hMeFa5SEOGwfr3uER5u7CYhRCYiuUgIYQ0kFwlhnJiYGKKiorh//z7jxo1DURQ++OADw/Zr164BUK5cuXjHOTg4UKJECcN2kThrz0VGbBbCLGQeXiGEEEIIIYQwoU6dOnHhwgUAChQowIIFCyhfvrxhe1BQEAB58uRJcGyePHkM24UQIjWkwCOEEEIIIYQQbzh27Bi9evUyat8jR47g4uJi+P7XX38lLCyMx48fs2rVKvr168ecOXPw8vKKd5xGo0n0fEmtF0KI5EiBRwghhBBCCCHe8NZbb/HTTz8Zta+jo2O878uUKQNA5cqVady4Me3bt+eHH35g8+bNADg7OwO6ljx58+aNd2xwcDDFixdPZ/RCiKxICjxCCCGEEEII8YYCBQrQvn37dJ/H1taWSpUqsXXrVsO6smXLArqxeFxdXQ3rIyIiuHfvnmHKcyGESA0ZZFkIIYQQViEsLIwJEyZQr149KleuTPv27dmzZ0+Kx61duxYfHx8aNWpE5cqVadasGRMmTCAwMDDR/ZctW0bz5s1xd3enSZMmzJ8/n9jYWFM/HSGEAODVq1ecPn2aUqVKGdZ5enpSoEABNm3aFG/frVu3EhUVRbNmzSwdphAiE5AWPEIIIYSwCoMGDeLixYuMGDGC4sWLs2HDBgYNGsTcuXNp0KBBksdNnz4dLy8vhg8fTqFChbh+/TqzZs1i7969bNy4kdy5cxv2nT17NjNmzMDHx4datWpx+vRpfvvtN4KDgxkxYoQlnqYQIhP7+OOPqVGjBlqtFicnJx4+fMiqVau4ffs2M2bMMOxnZ2fH559/zujRoxk/fjzNmzfnxo0bTJo0iebNm+Pp6anekxBCZFhS4ElBLvtcdHPvZlhWJ4hc0K3b62XjNgkhMhHJRSKz279/P4cPH2bmzJk0bdoUgFq1anHv3j0mTpyYbIFn48aN5MuXz/B9zZo1KVu2LD179mTTpk307NkTgOfPnzN37ly6d+/OZ599BoCXlxcREREsWLCAHj16ULhwYTM+y4xPcpEQyatatSq7du1i8eLFhIeH4+zsjKenJ8uXL6d69erx9m3Xrh02NjYsWLCANWvWkDdvXrp27cqQIUNUij7jsPZcZMRmIcxCoyiKktqD9MnpxIkTJg9ICCGMJblIiMzj66+/Zvv27Rw/fhwbm9c9yNesWcPYsWP5888/DWNWGCMiIgJPT0/69u3LF198AcDmzZv54osvWL9+PZUqVTLse/v2bZo3b84333xD9+7dUx275CIhhDWQXCSEkBY81k5R4Nw5WLMG7t2D8eOhdGm1oxJCiHhCQ+Hnn+HhQ/j4Y6hXD2SGV5Ea165do2zZsvGKOwBubm4AXL16NVUFnqNHjwJQrly5eNfQaDTx1gGULl2aHDlycO3atbSGn+kFRgSy+cpmLjy9wN2Qu0RGR1IidwnKuJThPe17lHUx/mcjhBAZSXR0NFevXuXq1avcvHmTBw8eEBgYSFBQEFFRUURHR5M9e3Zy5cqFi4sLRYoUoWTJkri5uVG+fPl43YSFMDcp8FizyEho1QriDjC5ezfs2AEeHurFJYQQcaxdC0OH6oo7AIsXg6enri79xn20EEkKCgqidCIfYOTJk8ewPTXnmjBhAqVLl6Zly5bx1js4OJAtW7YEx+TOnTtV18gq/n3wL+MPjGf79e1Ex0Ynus+wHcOoXrQ6w2oNo5t7NzRS3RVCZGAvXrzg77//Zv/+/fzzzz+cPXuWly9fpvl8bm5ueHl50bBhQ5o2bUrx4sVNGK0Q8UmBJwWPXzymq19XAFZ1XEVhRwv2zZ848XVxJ0cOiIqCR4/gnXdg1y6oUYPHj6GrLjxWrQIZOkCIzEnVXGQIImHC2boVOnfWrbKxAQcHCAuDM2egSxc4ehQSuZcWIlHJFQaMLRpEREQwcOBAgoODWbFiRaLFnPReIyt48uIJI3ePZNnZZYZ1uexz8XaRt7kWeA0bbHAv5M75p+d5GPqQEw9P0H19d2Ycn8GMd2dQvWj1ZM6eTsm8+ZH3RUJkDaZ+XxQcHMz69etZu3Yte/fuJTIyMsE+Dg4OvPXWW5QsWZL8+fNTwt6e3jt3gkbD4mbNeAw8e/aMhw8fcvv2bfz9bYBVXLkCV650ZdkyXT6tXLkyHTt2pHPnzoZWqkKYihR4UvAy+iX77+w3LFvMpUvw44+65b59YcEC3XKBAuDvDwMGwL//8vKlhv37/x+rBcMTQliWarkoXhAviZtwXryAgQN133p66oo6YWGwZAn07g2nT8PYsbquW0KkxNnZOdEWNMHBwcDrljzJefnyJQMGDODixYssXLiQ8uXLJ7hGREQEr169SlD4CQkJMeoaWcGRe0fosKYDj148AqByocp8Ve8rWru15mnYU1ynuQJwqM8hSuYpycG7B5l2bBrrL63n6P2j1FlYh+nvTqd/tf7mKZq9kYuM3CSEyERM8b5IURQOHTrE7Nmz2bBhQ7xWOnZ2dtSoUYP69evj5eWFp6cnpUuXjp/Tbt+GRYsAmPD11wmG0ThzJoiqVZ0BaNr0fY4dW01ISAjnzp3j3LlzfPPNN9SuXZu+ffvSrVs3HBwc0vQ8hIjLJuVdhMXFxkK/fvDqFbz1Fgwf/nrbnDm6rydPxu+6JYQQFjZuHNy9C9mzw9Spr9c3aABffqlb/vVX+PtvNaITGU3ZsmW5ceMGsbGx8dZfvXoVAK1Wm+zxkZGRfPrpp5w5c4bff/+dt99+O9FrKIqSYKydO3fu8PLlywRj82RFi04vosGSBjx68QinbE7Me28epz45RRf3LuS0z5lgfxuNDfVL1Wdd53X8/eHflM9fnqjYKAb8OYBPtnySZLcuIYRQS3R0NCtXrqRq1aq88847+Pr68vLlS3LkyEHnzp1ZtWoV/v7+HD58mIkTJ9KuXTtcXV1TXbB2dnY2LM+bN4+AgAD++ecfhg0bRsmSJQE4cuQIffr0oWTJkowdOxZ/f39TPlWRBUmBxxpt2QKHDumWf/9d1+dBr1o13d0TwE8/WT42IYQALl6E337TLY8dm3Ds92+/herVdePEjxpl6ehERtS0aVNCQkLYu3dvvPUbN27E1dU12QGWX716xaeffsqJEyeYPXs2NWvWTHS/+vXrky1bNjZt2hRv/YYNG7Czs8Pb2zv9TyQD+/3E7/TZ3Ieo2CjK5y/Pv/3+pV+1ftja2Bp1fIPSDTje9zjtK7QHYMHpBfTc0FOKPEIIqxATE8PSpUtxc3Oje/funD17FoCaNWuyaNEinjx5wurVq+nSpUu84oyp2NnZUa9ePaZMmcKtW7fYs2cPH3zwAfb29jx79swwdtyoUaOk0CPSTAo81uj//TNp1gyaNEm4Xf/R+N69uj4RQghhYQsWQEwMlC8P/5+BOh57e5gyRbd8/Dj8+69l4xMZT4MGDfDy8mLMmDH4+flx9OhRRo8ezcmTJxk5cqRhv549eyYYs2DIkCEcPHiQvn37kjNnTs6cOWN43L1717Bf3rx56d+/PytWrGDGjBkcP36cefPmsWDBAnr16kWRIkUs9nytzfyT8/H50weAhqUbcqzvMdzyp35sCKfsTvh18mN03dEArDq/ig83fkhMbIxJ4xVCiNT466+/qFKlCh999BE3b95Eo9HQsWNHjh8/zrFjx/j4448tOtuVjY0N3t7e/PHHH9y5c4evv/6avHnzEh4ezi+//ELZsmX5+eef0zW4s8iapMBjbZ4/h61bdcu9eiW+T7NmULWqbnnuXMvEJYQQcfz5p+7r558nPYhyvXqvJ/ybNcsycYmMS6PRMHv2bFq1asXUqVPp168fV65cYebMmSm2rNm3bx8As2bNokuXLvEes2fPjrfvwIEDGTlyJFu2bKF3796sWrWKwYMH80VilcosYtu1bfTf2h+ABqUasLXbVnJnT/uNjkaj4cfGPzKqrq753sr/VjJqtzTlE0JY3o0bN2jdujUtW7bkwoULAHTr1o1Lly6xdu1aatSooXKEUKRIEb7//ntu377NDz/8QN68eQkJCWH06NFUqFCBrfp7QyGMIIMsW5s1a3Rj7+TKBW3bJr6PRgMjRkD37jIOjxBCFZH/T1NduiS9j0ajG4TZx0c3m82kSZA/v+ViFBmPo6Mj33zzDd98802S+yxfvjzBuitXrhh9DY1Gw0cffcRHH32UlhAznUv+l+i2rhsKCjWL1WTrB1vJlS1Xus+r0Wj4qfFPRERFMP34dCYfmUzlQpXpVSWJD6+EEMKEoqOjmTJlCt9++62hFYy3tzeTJ0/G09NT3eCSkDt3br766it8fHyYMGECM2fO5Pbt27Ru3Zq2bdsya9YsihYtqnaYwspJCx5ro++e1aGD7u4pKa1b6z42j46yTFxCCPGGrl3BySn5fbp3hzx5IDLSMNGEEMJKBL0M4v1V7xMSGUJRp6Js7LIRx2yOJju/RqNhSvMpNC/THIBPtnzC8QfHTXZ+IYRIzKVLl6hVqxajRo3i5cuXlChRAj8/P3bv3m21xZ24XFxcmDJlCufPn6fJ/4fr2LhxI+7u7vzxxx8oiqJyhMKaSQueFDhlc2JQjUGGZbO6cQMOH9Yt9+wZJwgnGDTo9bL+a+PGOP11jEHandCsWYo3WkKIjMuiuSjJIJx42nkQq9dAKE707RtvU4I0BeDoCB99BNOm6caM/+ILXcseIYT6Pv3zU64HXie7bXY2dtlIEaeUxyBKbS6ytbHFt4MvXgu8uBZ4jW7runGm/xmcsqcjjyWVcJLfJITIRBLLRYqiMHv2bEaMGMHLly/RaDQMHDiQH3/8ESdzJIQUEk5685FWq2Xnzp34+voyePBgAgMD6dGjB1u2bOH3338nT5486QheZFYaJQ0lwOrVqwNw4sQJkweUpf34I4wZA0WL6uYetk1h1oq5c2HAAHB2hqdPdaOaCpGFSC6yvE8/hTlzoFIl+O8/44o1Z8+C/gOzc+dej8sjRGaREXPRyv9W0n19dwDmtppL/+r9zXq980/PU31edSJjIunt2ZuFbRaa9XpCZEUZMReZSlBQEL1792bDhg0AlCpVimXLllG/fn2VIzONx48f4+PjY5gFsnTp0qxevTrJWSNF1iVdtKzJzp26r23bplzcAV03LYCgIDh40FxRCSEEoJvyXD+7dK9exrfEqVwZSpXSLW/ebJ7YhBDGuxt8l0///BSA97Tv8Um1T8x+TfeC7kxsMhGARWcWsfHyRrNfUwiRNZw5c4Zq1aoZijs9evTg7Nmzmaa4A1C4cGE2bNjA77//To4cObh9+zbvvPMOv//+u3TZEvFIgcdahIfDkSO65cSmRk9MsWLw/0q93DUJIczt3Dl4+FC3rK8vG0Ojgfff1y1v2WL6uIQQxlMUhQF/DiA4MpgCOQuwoPUCNBbqNznEawiNXRsD0H9rf55HPLfIdYUQmdfatWupU6cON2/eJEeOHCxcuJDly5dnyu5LGo2GTz75hBMnTlC+fHlevXqFj48Pffv25dWrV2qHJ6yEFHhS8CDkAR5zPPCY48GDkAfmu9ChQ7rZszQaaNDgjSAe6Po0eHjoluNuatgdD87hMcuHB/eleitEZmWxXJSM/SsfcA4PLtl7UN7pjVyUdJoCXhd4jh2Dx48tEKwQIlHrL61n27VtAMxuNZtCjoVSdXx6cpGNxobFbRbjmM2Rp2FPGbN3TKqOfx1EMu+LUshFQojM4X7wfQqNK0TnfZ2JsIugdOnSHD16lN69e1suiBQSjrnyUaVKlTh+/Djt27cHYNGiRTRt2pSAgADTXURkWFLgSUFUbBTnn57n/NPzRMWaccYq/XTnb78NLi5vBBEF58/rHlHxY4hq1IzzeHA+yo2oa7fNF58QQlUWy0XJOLAnCg/OUz7qPJo3ZvBLJk0BUL8+5M6tW9661QLBCiESCI0M5bPtnwHQslxLOlTokOpzpDcXlchTgvENxwMw98TctM2qldz7ohRykRAi43v16hVDhg3hqeYpFAKvul78+++/VKlSxbKBpJBwzJmPnJyc8PPz4/vvvwfgwIED1KpVi+vXr5v2QiLDkQKPtdAXeBo3Tt1x5cu/Xj550nTxCCFEHIGBcOpU2o/Plg3efVe3LD1KhVDHuL/H8SD0ATnscjDz3ZkW65r1psFeg6lSqAoKCj5bfYiJjVElDiFExhMaGkrLli0N4+0ALF+2nPz586sYlTo0Gg1ff/01a9asIUeOHFy/fp26detyUu4JszQp8FiD589fF2dSW+CxifMj/Pdf08UkhBBx7NwJsensBarvprVrl27YMSGE5VwPvM7049MBGFt/LK55XVWLxc7GjrnvzQXg9OPTLD27VLVYhBAZx7Nnz/D29maP/oPx/7PP4jMJd+rUib179+Li4sLTp09p2LAhe/fuVTssoRIp8FiDv//WTU9jbw/16qX9PFlwSkQhhGX8+Wf6z9GihW6YsZcv4fDh9J9PCGG8L/d8SXRsNKXylGJ47eFqh0Ot4rXo7qGbpn3svrGEvQpTOSIhhDV7+PAh9evX58SJE9jY2PDLL7+oHZJVqV27NgcPHqRkyZK8ePGCli1bsm3bNrXDEiqQAo810Feha9eGnDnTfp6bN8Df3zQxCfGGI0eOMHr0aJo3b06VKlWoX78+gwYN4sqVKykeO2PGDNzc3BI86tata4HIRXopCuzYkf7zuLiAvnv8gQPpP58QwjhH7h3B76IfAD82/pEcdjlUjkjnB+8fyG6bnYehD5l6dKra4QghrNSDBw9o2LAhly5dIlu2bPj5+dGpUye1w7I6FSpU4NChQ2i1WiIjI2nbtm28rmwia5ACjzU4eFD3tVGj9J9LPhYXZuLr68vDhw/56KOPmD9/PqNHj+bhw4d07NiRM2fOGHWOxYsXs3r1asNj3rx55g1amMSVK6arHdevr/u6f79pzieESJ6iKIzYNQKAakWq0dW9q8oRvVbKuRRDvIYA8POhn3ny4onKEQkhrM39+/dp2LAh165dI0eOHGzZsoV27dqpHZbVKl68OAcOHMDd3Z2oqCg6d+7Mpk2b1A5LWJAUeNQWHq4bWh2gVq30n+/QofSfQ4hEfPvttyxbtoxu3bpRs2ZNWrZsyZIlS8iRIwcLFy406hzu7u54enoaHpUqVTJz1MIU9DVol7zpP1eDBrqvx47pumoJIczrr+t/cfie7sOfSc0mYaOxrrd+X73zFS4OLrx49YKfD/2sdjhCCCvy5MkTGjduzPXr13FwcGDLli00a9ZM7bCsXqFChfj777+pXLky0dHRdOrUia0yhWmWYad2ANbOOYcz3zb41rBscqdPQ8z/Z4+oUSOJIJzh229fLye2adcunA8Hvb4TE8LE8uXLl2Bd7ty5KVWqFI8fP1YhoqzF7LkoGf/8o/taobYz1EghFyXcFM877+i+RkbqxoXXfy+EMD1FUfj2b90fZpO3mtCwdMN0n9PUucg5hzNf1PmCL/d8yZwTc/iizhcUcSqSwkHOKb8vSrhJCJGBBAQE0LRpU65evUr27NnZsmULjeNMRqPm+6LXQTgnm3DUzEf58uVj9+7dNGrUiAsXLtCxY0f++usvGpmix4iwahpFUVI9L0r16tUBOCGD+qbfb7/BsGHw1ltw40baz7N5M7RpoxuoOTgYHBxMFqIQSQkMDKRRo0a0atWKH3/8Mcn9ZsyYwcyZMylQoAABAQHky5ePhg0bMmzYsEQLR8aSXGQZZcrAzZswaRJ8/nn6z1exIly6BN9/D19/nf7zCaE2a81Ff179k/d83wPgUO9D1ClRR+WIEvfi1Qtcp7nyLPwZQ72GMrWFjMcjRFpYay5KrbCwMLy9vTl+/Dj29vZs2LCBVq1aqR1WhvTkyRMaNGjAlStXcHR0ZO/evdRIqlGByBSsq51uVqSf2jy9f2h1/v+mLSpKZtMSFqEoCmPHjiU2NpY+ffoku2+JEiUYPnw4P/74I4sWLaJbt278+eefdO7cmeDgYAtFLNLi4UNdcQdM19pG301LBloWwnwURWHc/nEANCvTzGqLOwCO2Rz5os4XAMw9OZdHoY9UjkgIoZaoqCg6duzI8ePHsbGxYeXKlVLcSYdChQqxc+dOSpQowYsXL3j33XeNmiBFZFxS4FHb8eO6rzVrpu88+fNDuXK6ZSnwCAv45Zdf2L17N9999x1lypRJdt+2bdvSv39/6tevT+3atRk4cCAzZ87k/v37/PHHHxaKWKSFvtengwNUrWqac+oHWj58WFeTFkKY3l/X/+LEQ937ge8afqdyNCkbWGMgBXIW4GX0S349/Kva4QghVKAoCn379mX79u0AzJ49m44dO6ocVcZXsmRJdu/ebWhJ/+6778rwCpmYFHhScC/4HkUnF6Xo5KLcC75n2pM/fw7Xr+uWk2vBc+8eFC2qe9y7l/Sm8k11K0+fNm2cQrxh6tSpLFq0iDFjxtC+ffs0naNu3boUKFDA6Bm4sjqz5qJk6As8tWqB/WMjc1EK4ekLPGFhcOqUGYIWQjDx4ERAN/ZOreImmMTh/8yVi3Jly8XntXV9QOednEdgRGAyQZgmFwkhrMt3333HsmXLABg3bhz9+/dPcl+13hfFDyL5hGNN+Uir1bJ161Zy5szJrVu3eO+993jx4oW6QQmzkAJPCmKUGB69eMSjF4+IUWJMe3J9SxsbG3j77WSCiIFHj3SPmJikN1Vw162UOyZhRtOmTWPu3Ll88cUX9OrVK13nUhQFGxtJQ8Yway5Khn6A5XfewfhclEJ4xYrphh0DXSseIYRpHbl3hH/u6v54R9cdbdJzmzMX+VT3IXf23IRFhTH739nJBGGaXCSEsB7Lli3ju+90rQ379OnDN998k+z+ar0vih9E8gnH2vJRzZo1Wb16NTY2Npw8eZLu3bsTYw2BCZOSOys16cffqVQJcuVK//n0U05fvgwREek/nxBvmDlzJrNnz+azzz6jb9++6TrXwYMHefbsGVWqVDFRdMLUQkLg3Dndcr16pj23vleqPg0KIUxHP914tSLV8Hb1Vjka4+XJkQefaj4ATD82nYgoeS8jRFbwzz//GN5XNmnShDlz5qDRaFSOKnN67733mDVrFgCbN2/myy+/VDkiYWpS4FGTqQZY1tMXeGJi4L//THNOIf5v0aJFzJgxg0aNGlGnTh3OnDljeFy8eNGwX8+ePXFzc4t3bNu2bVmyZAn79+/n0KFDzJw5k8GDB1OqVCm6d+9u6acijHTiBMTGgkaj66JlSvq0JwUeIUzrkv8lNl3ZBMCouqMy3E3S0FpDyWabDf9wfxafWax2OEIIM7tz5w4dOnQgKiqKihUr4ufnh729vdphZWo+Pj589tlnAPz6668sXiy5NjOxUzuALM3UBZ58+XR9Hx480I3Dk96Bm4WIY9++fYav+mW9YsWKsXfv3iSPfeutt1i5ciVPnz4lOjqawoUL06lTJz799FNy585t1rhF2ul7kVaoAE5OQIDpzq1Pe9evQ2AguLiY7txCZGVTj+qmGC+TtwztK6RtjDQ1FXEqQq/KvVhwegFTjkzBp7oPNhr5PFKIzCgsLIw2bdrg7++Pi4sLmzdvJk+ePGqHlSVMnjyZa9eusW3bNnx8fKhYsSJeXl5qhyVMQAo8avH31xViAKpVM915q1bVnVfG4REmtnz58jTvN2XKFFOHIyxAX+CpXt305377bd3wY7Gxuus0a2b6awiR1QSEB7D8nC4HD601FFsbW5UjSpthtYex4PQCbjy/wbZr23hP+57aIQkhTEw/Y9bZs2extbVl7dq1Kc7KKkzH1taWlStX4uXlxZUrV2jfvj0nT56kcOHCaocm0kk+ElGLvguVRvO6a5Up6Adrlpm0hBDpZM4CT65cr1OfdNMSwjTmn5rPy+iX5Mmeh488P1I7nDSrWKAizcroqr7Tjk1TORohhDlMmzaNVatWAboPAr29M854YZlFnjx52LhxI05OTjx8+JBOnToRFRWldlginaTAoxb9yKXlykHOnKY7b9Wquq///QfR0aY7rxAiSwkIgFu3dMvmKPCAjMMjhClFxUQx8/hMAPpU7YNjNkeVI0qfz7x040Psvrmb80/PqxyNEMKUDhw4wIgRIwDo3r07gwcPVjmirKt8+fKsWLEC0E2AIoMuZ3zSRSsFLg4uTG8x3bBsMvoWPB4eRgThAtOnv15ObpO+wPPypW42LXd308QrhFCV2XJREk6e1H21tQXDRGepyUVGqFkTFi2SAo8QprD+0noehD7ARmPDoJqDzHYdS+WiFmVboM2n5WrAVaYfm8681vPiBGHaXCSEsJynT5/StWtXYmJi8PDw4Pfff0/TYPCWfl+UeBDJJ5yMko/ef/99Ro8ezcSJE5k8eTJ16tShffuMN4ab0NEoiqKk9qDq//8494S+/b5IvRo1dP0fvvsOvvnGdOdVFN1gy8+fw9Kl0KuX6c4thJWRXGQ+P/4IY8ZA5cpw9qx5rnHq1OshyO7f140RL0RGZA25qN6iehy6d4i25duyocsG1eIwpVnHZzHor0E42DnwYPgD8jrkVTskIayaNeSi5MTGxtKiRQt27dqFk5MTJ0+epFy5cmqHJYDo6GiaNWvGvn37yJ07N6dPn+att95SOyyRBtJFSw0xMXDhgm7ZmBY8qaHRvG7Fc+aMac8thMgyzDn+jp6HB2TPrluWVjxCpN1/T/7j0L1DAAyqYb7WO5bWq0ovnLI5EREdwdKzS9UORwiRTj/99BO7du0CYMGCBVLcsSJ2dnb4+vpSuHBhQkJC6Nq1K69evVI7LJEGUuBRw40bEBGhW65c2fTn1xeN9EUkIYRIJUsUeOztwdNTtywFHiHSbu6JuQBo82nxds08A5U6ZXeiR+UegO45pqHRuRDCShw+fJhvv/0WgE8//ZTOnTurHJF4U6FChVixYgUajYZ///2XMWPGqB2SSAMp8KTgdtBtsn2fjWzfZ+N20G3TnFQ/wHKuXODqakQQtyFbNt3j9u2UN+mnppECjxCZhllyURKePoV793TL+i5UuiBupy4XGUFfQJKJ/4RImxevXhimRvep5pOmsSxSw5K5CMCnug8AVwKusO/2vv8HcdvkuUgIYT7BwcF0796dmJgYKleuzOTJk9N9TkvnosSDuJ1swsmI+ahx48Z89dVXAEyaNIkdO3aoHJFILSnwGCEqNoqoWBNOGacfYNndHWyM/BFERekexmzSF3gePICgoDSHKYSwLibPRUnQD7BsZ5dII8PU5CIj6AdwNtc4P0Jkdn+c+4PQV6HksMvBh54fWuSalspFAJULVaZOiToAzDkxJ04Qps1FQgjzUBSFAQMGcPv2bXLkyIGvry85cuQwybktmYuSDiL5hJMR89G4ceOoU0eXdz/66COePXumckQiNaTAowZ9Cx5zdM+C1wUekFY8QohU07emqVQJTPQeLEn6LloPH4K/v3mvJURmoygKc0/qumd1de+q3kwyZjag+gAANl7eyKPQRypHI4RIDV9fX3x9fQGYOnUqFStWVDkikRI7OztWrFiBk5MTjx8/pl+/ftJFNgORAo8aUjNFelrkyQPFi+uWpcAjhEglfWsaffHFnOI2ZJRWPEKkzslHJznz+Ayg656VWXWs2JF8DvmIjo2WwZaFyEDu37/PwIEDAWjdujX9+/dXOSJhLFdXV2bOnAnAxo0bWbx4scoRCWNJgcfSXrzQDbIM5mvBAzIOjxAizfSFFnOmKD0HB9Bqdcsy8Z8QqbPw1EIAPAp6ULNYTZWjMZ8cdjnoWbknAAtPL5RPkoXIAGJjY/n4448JCgqiQIECzJ8/3+xjhAnT6tmzp2Ew7KFDh3Lnzh2VIxLGkAKPpcUtuJirBQ9IgUcIkSbh4XDtmm5ZPz6OuelbCkkLHiGMF/YqjJXnVwLQp2qfTH/j1OftPgBcD7zOsQfHVI5GCJGSuXPnsnv3bgDmzZtHoUKFVI5IpJZGo2H27NkUKlSI0NBQevfuTWxsrNphiRRIgcfSLl3SfS1UCFzM2FdeCjxCiDS4cAH0/7st0YIHZKBlIdLC76IfIZEhZLPNZphKPDNzL+iOVzEvAFZfWK1yNEIkbc+ePfTs2ZO6devi7u5OvXr18PHx4UwizVS9vb1xc3NL8Jg0aZLlAzehW7duMXLkSAA+/PBD2rZtq25AIs3y5cvH/PnzAdi7dy9z5sxJ4QihNju1A8hy9AWeChXMex19gefxYwgMNG8xSQiRaejHgC9SBAoUsMw19QWeS5cgMhKyZ7fMdYXIyBae1nXPale+Hfly5lM5Gsvo+3Zfjj04xrZr25iqdjBCJOH58+d4eHjQvXt3XFxc8Pf3Z+nSpXTv3p2lS5dSvXr1ePvXqFGDESNGxFuXkVu7xMbG0qdPH8LCwihatChTp8pfa0bXunVrPvzwQ5YuXcqoUaNo1aoVpUuXVjsskQQp8KQgf878/NH+D8NyuqWlwJM/P/zxx+tlYzbFHaH+wgV4553UxyqEsBomz0VJ0LeiSbR7VlpykRH0XbSio+HiRahaNXXHC5HVXA24yj93/wF0RQ9LslQuSkyXSl0Yun0oD7KFsWv8RzQt09SkuUgIU+jYsWOCdQ0aNKBWrVqsW7cuQYEnd+7ceFpiVgMLmT9/Pvv27QN0XbPy5s1rluuomYteB5F8wslM+ei3335j586dPHr0iE8++YQdO3Zk+q7BGZUUeFLgmM2RDzw+MN0J9QWe8uVTEYQjfJB4DElucnKCUqXgzh0p8AiRCZg8FyUh2QGW05KLjFC4sK61kL+/7vpS4BEieUvP6GaSKpmnJN6u3ha9tqVyUWKcsjvRuVJnFp9ZzNdFLtL0g4SzuqQnFwlhLjlz5iRbtmzY29urHYpZPXjwgC+++ALQDdDbqlUrs11LzVz0OojkE05mykfOzs7MnTuXNm3asGvXLhYvXkzv3r3VDkskQsbgsaTISLh5U7ds7i5aIOPwCCFSRVFed9Gy1ADLABrN61Y8MpOWEMmLiY1h2bllAHxY5UNsNFnrrdxHnh8BcPzBcS75X1I3GCGSERMTQ1RUFPfv32fcuHEoisIHidztHz16lKpVq+Lu7k7r1q1ZuXJlhpwpTlEUBg4cSGhoKAUKFJCuWZnQ+++/T9euXQEYPnw4jx8/VjkikZis9a4gDWKVWEIjQwmNDCVWSeeo4deuvR69NDUFnthYCA3VPd4YuTyZTVLgESITMWkuSsK9exAUpFtOtAVPWnOREWSgZSGMs/fWXu6H3AegV5VeFr++JXJRcuqVrMdbuUvjGAm+R+aZPBcJYSqdOnXC3d2dxo0bs3fvXhYsWED5N1rwN2zYkK+//pp58+YxdepUSpcuzXfffcdPP/2kUtRpt379ejZt2gTA9OnTyZfPvGODqZ2LdEEkn3AyYz7S/2yDg4MZOnSo2uGIREiBJwV3g++Se2Juck/Mzd3gu+k7mb57lpMTFCuWiiDuQu7cusfdu8Zuel1Eunw57TELIayCSXNREvStd7JlAze3xIJIYy4ygr6g9N9/upZEQojELT2r655Vr2Q9yrqUtfj1LZGLkmOjsWFwkTaE/gTj2/xGzO1b8eNLZy4SIq5jx44lOstVYo/AwMB4x/7666+sXbuWGTNmoNVq6devH8eOHYu3zzfffEP79u2pUaMGTZs2ZcaMGbz33nssX76cBw8eWPKppktwcDCDBw8GoFWrVnTp0sXs11Q7F+mCSD7hZMZ8VKBAAcMsb6tXr+avv/5SOSLxJhmDx5Lijr9jiUGp9J8SPHoEISG67CKEEEnQt56pWBEsPUyAu7vua0AAPHmiG5dHCBFf8Mtg1l9aD+i6Z2VVHSp0AKYBcPDuQRq8VUbdgESm9dZbbxndmsbR0THe92XK6H4vK1euTOPGjWnfvj0//PADmzdvTvY87dq1Y+vWrZw7d45iqflAWEVff/01jx49ImfOnMyePVsG383kPvzwQ5YtW8a+ffsYMGAAFy5cIFeuXGqHJf5PCjyWlJYBltMj7kfwV65AjRqWua4QIkP67z/d10S7Z5lZ+fJgY6NrwnzhghR4hEiM30U/IqIjcLBzoFPFTmqHo5oSeUoYlv0u+dGgYdYtdgnzKlCgAO3bt0/3eWxtbalUqRJbt25Ncd/Y//flsbHJGB0tTpw4waxZswD47rvvKFmypMoRCXPTaDTMnTuXypUrc+fOHX744Qd+/PFHtcMS/5cxMkdmkZYp0tPDxUU3NQ3oCjxCCJGM8+d1X/WtaSzJwQH+/2GnIQ4hRHwr/lsBQNvybcmTI4/K0ViHXTd2ERoZqnYYQiTr1atXnD59mlKlSqW476ZNm7CxscHDw8MCkaVPTEwMPj4+KIqCh4cHn332mdohCQvRarWMGjUKgEmTJnHpkgx6by2kBY+lxMS8LrJYqsADulY8/v4yDo8QIllRUXD1qm5ZPz67pbm768ailwKPEAndDb7L37f/BqBn5Z7qBmNFXkZHsv7Sej70lFY8wjp8/PHH1KhRA61Wi5OTEw8fPmTVqlXcvn2bGTNmGPbbunUre/bsoUGDBhQuXJjg4GA2b97M7t276dOnD0WLFlXxWRhn3rx5nDx5EoC5c+dm+mngRXyjR49mxYoV3Lx5k4EDB7Jnzx7pnmcFpMBjKXfuwMuXumVLF3gOHpQWPEKIZF27pivygLoFng0bZOI/IRLj+58vAAVyFqBpmaYqR2NdVvy3Qgo8wmpUrVqVXbt2sXjxYsLDw3F2dsbT05Ply5dTvXp1w37Fixfn+fPnTJo0iaCgIOzt7XFzc2PixIm0a9dOxWdgnGfPnjFmzBgAevfuTZ06dVSOSFiag4MDM2bMoFWrVuzbt49Vq1bRrVs3tcPK8qTAYyn6FjT29q/7IViCfrwfKfAIIZKhL6o4OoJa3ef1XcPOn9fNpCUfAgmhoygKy88tB6CbezfsbOTtW1x7bu7hYehDijpZf4sHkfkNGTKEIUOGpLifp6cnS5YsMX9AZvLll1/y/PlznJ2dM+S07sI0WrZsSdu2bdm4cSNffPEFrVu3TjDguLAsGYPHUvQFnrJlwc6Cb8z0Ay1fvarrJiaEEInQF3gqVVKvsKJvORQaCvfuqRODENbo7JOzXPDX/ZH2rCLds+LKm8MZBYWV/61UOxQhsowTJ06wcOFCAL7//nsKFiyockRCTVOmTCFHjhw8ePBAin1WQD4CSkGhXIXY0WOHYTnN9INbxJ3ZyuggCsGOHa+XjdsU/3qRkXD3Lri6pv76QgjVmSwXJUE/7k2y3bPSk4uMUK6crpFjVJQuHpmII+sJCwtj6tSpbN++nZCQEMqWLcvAgQNp3LhxssedOHGCdevWcfHiRa5fv050dDRXkmi56pbE/+Fx48ZZbdPyFed0gyu75XOjWpFqqsZi7lxkXBCvE06DF+s48988VpxbwYg6I0ySi4QQSVMUhSFDhqAoCpUrV8bHx0eVOKwtFyWWcLJKPnJ1dWXkyJGMHz+eSZMm0bt3b8pYsseKiEcKPClwsHegWZlm6T+RvsCj1aYhCAdolngMyWzScXV9fcd0+bIUeITIoEyWi5IQtwVP0kGkIxcZIVs2XU36/HldPC1bpu98IuMZNGgQFy9eZMSIERQvXpwNGzYwaNAg5s6dS4MGDZI87ujRoxw/fpxKlSphZ2fH+RRG6m7ZsiUffhh/zJYSJUoksbe6YpVYVp1fBUB3j+6qD2Bp7lxkXBCvE06Xe05M+28eZ5+c5aL/RSoWqJjuXCSESJqvry9HjhwBYNq0adhZsmdCHNaWi9KwOVMZNWoUS5Ys4e7duwwfPpxNmzapHVKWJV20LCU9BZ70iDvmj4zDI4RIRGSkbpBlUG+AZT399WUmraxn//79HD58mAkTJtCpUydq167Nzz//jKenJxMnTkz22E8//ZQ9e/Ywffp03n777RSvlT9/fjw9PeM98uXLZ6qnYlL/3PmHB6EPAOjmYZ0tjNRUq3gtSjuXBl4PRC2EMI+wsDDD1NgdOnSgYcOG6gYkrEbOnDmZNGkSAJs3b2bv3r0qR5R1SYEnBdGx0dwOus3toNtEx0an7SQvXsAD3ZuzNBV4oqPh9m3dIzra2E2vyUDLQmR4JslFSYg7RJd+oOPEg0hnLjJC3IGWRdaya9cunJyc4nXH0mg0tGvXjps3b3L9+vUkj7WxybxvZ/Rjy9QsVpOyLmVVjsa8ucj4IF4nHE1MDN3cdYWvledXEhWlmCQXCSES+vXXX7l//z7Zs2fn119/VTUWa8tFiSUcU703yig6duxIvXr1ABg2bBgxMv6rKjLvOyITuR9yH9dprrhOc+V+yP20nSTum9K0FHju39d1rXJ11S0bt+k1/XgD+oGehRAZjklyURL03bPy5IGiyU1Ck95cZAR9gefSJRkXPqu5du0aZcuWTVCs0Y+Zc1XfEtYENm3aROXKlfHw8KBTp05s27bNZOc2pVcxr/C75AdgKGKozZy5yPgg4icc/Wtz8/lN/jx51iS5SAgR38OHDw1FnWHDhuGq8rAP1piLUrk509FoNEydOhWAc+fOsWjRIpUjypqkwGMJ+jelefKAGqPM6ws80oJHCJEIa5hBS0/fRSsiQveJl8g6goKCyJMnT4L1+nVBQUEmuU7r1q0ZO3YsixYt4ueffyZHjhwMGzaMpUuXmuT8prTzxk4CIwLRoKFLpS5qh2O1PAp54F5QVx3efGWzytEIkTl9/fXXhIeHU7BgQb788ku1wxFWqnr16vTq1QvQ/c6EhoaqHFHWIwUeS4g7/o4ad0/6LlqPHkFIiOWvLzKFI0eOMHr0aJo3b06VKlWoX78+gwYNSnKmmjfdvXuXTz/9lGrVqlG1alX69euXbJcLYTlGzaBlIa6uusGWQdeKR2QtyQ0gbKrBhSdNmkTr1q2pXr06LVu2ZOnSpVSvXp3ffvuNly9fmuQapuJ7XjemTCPXRhRxKqJyNNZN34pny9UtKkciROZz5swZlixZAsB3331H7ty51Q1IWLUff/wRBwcHnj59qnpXvqxICjyWoNYAy3rlyr1elhtqkUa+vr48fPiQjz76iPnz5zN69GgePnxIx44dOXPmTLLHBgQE8MEHH/DgwQN+/vlnpkyZQnBwMD169ODx48eWeQIiSRcv6r5aQ4HHzu51o0N9XCJrcHZ2TrSVTnBwMECirXtMwcbGhvfff5/w8HCTdgNLr/CocDZd1s1CYi3ds6yZ/jV6FuavciRCZD4jR45EURQqVKhA37591Q5HWLlixYoxbNgwACZPnszDhw9VjihrkQKPJahd4MmXD5yddcv6qXKESKVvv/2WZcuW0a1bN2rWrEnLli1ZsmQJOXLkYOHChckeu3DhQkJCQpg3bx5NmjShUaNG/P7777x69Yo5c+ZY6BmIxERGvq77Vqyobix6FSrovkoLnqylbNmy3Lhxg9jY2Hjr9UUXrRn/h+qvaU2DNf959U/CosKws7GjfYX2aodj9VzzulKzWE21wxAi09m1axe7du0C4JdfflFtWnSRsYwaNYoCBQoQHh7Ot99+q3Y4WYr1vJPJrBTl9dg3ahV4NJrXrXikwCPSKLEphHPnzk2pUqVSbIWze/du6tSpQ6FChQzr8ubNS6NGjQxvGoQ6rl0D/f20vrCiNn0c0oIna2natCkhISEJplbduHEjrq6ulC1rnhmkYmNj2bJlC7ly5aJc3BavKlt9YTUAzcs0x8XBReVoMoaulbqqHYIQmUpsbKxhWvT69evTqlUrlSMSGUXu3LkNhZ1FixZxUd7UWYwUeMwtIAD0Tc7VKvDA6wKPFTU/FxlfYGAg165dS/am6OXLl9y9ezfRT9/d3NwICAggICDAnGGKZOhbyTg5QbFi6saip29JdOmSrkYusoYGDRrg5eXFmDFj8PPz4+jRo4wePZqTJ08ycuRIw349e/Y0zKylFxgYyPbt29m+fTt3794FMHz/33//GfZbuHAhX3/9NVu3buXYsWP8+eef9OrVi5MnT/L555+TPXt2yzzZFIRGhvLntT8BZHDlVOhUqZPaIQiRqaxevZrTp08DutY7phoLTWQNn3zyCWXLliU2NpYxY8aoHU6WIW3szC1uQUXNTwalBY8wMUVRGDt2LLGxsfTp0yfJ/YKDg1EUJdHxM5z/33UwKCgo0RZCwvz0BZ7y5dWfQUtP34InNBQePrSewpMwL41Gw+zZs5kyZQpTp04lJCSEsmXLMnPmTLy9vZM99tq1a3z22Wfx1um/b9euHRMnTgTA1dWVPXv2sHv3bkJDQ3FwcKBSpUrMmTMnxWtY0uYrm3kZ/ZLsttlpU76N2uFkGMVzF6dGsZr8q3YgQmQCr169MtyUd+zYES8vL5UjEhmNvb09EyZMoGvXrmzcuJGjR49Sq1YttcPK9KTAk4IijkU40e+EYTnV9AWeIkV0H5GnKYgicOLE62XjNsWnbz0hBR5hIr/88gu7d+/mp59+okyZMinuL5/6pE+6c1ES9AUeo7pnmSIXGUGrBRsbXdexixelwJOVODo68s033/DNN98kuc/y5csTrPPy8jJqRj9vb2+rKuQkZdWFVQC0LNeS3Nmta7Yac+Wi1AWRdML5oHYj/v2kGo7ZHHEpsBOwjlZZQmQ0CxYs4NatW9ja2vLDDz+oHU4C1p6LjNicJXTq1IlffvmFU6dOMXr0aPbt2yf3BGYmBZ4UZLfLTrWi1dJ+AlMMsJw9O1RLPIZkNsWnb8ETEADPn0PevGmPR2R5U6dOZdGiRYwZM4b27ZMf/DNPnjxoNJpEZ8fRr9O35BFJS3cuSkKqCjymyEVGXqZMGV09+tIlaNrUNOcVIiN4HvGcHdd3ANbZPctcuSh1QSSdcLp5tufzvYN4ocTy9/0dvO/2voWDEyLjCw8P5/vvvwegd+/eZh3kPq2sPRcZsTlLsLGxYeLEiTRr1oz9+/ezY8cOWrRooXZYmZqMwWNu+gKP2gM3xr2+tOIR6TBt2jTmzp3LF198Qa9evVLcP0eOHJQoUSLR6YevXr2Ki4uLdM9SSUwMXL6sW7aWAZb1ZKBlkVVturKJqNgoctrn5D3te2qHk+EUcixEw9INAVhzYY26wQiRQc2cOZPHjx+TPXv2ZFtUCmEM/Qy6AF9//TWKDLBoVlLgSUFkdCQnH57k5MOTREZHpv4E+mJKego8kZFw8qTuERlp7Kb4nJ0hf37dsgy0LNJo5syZzJ49m88++4y+ffsafVyTJk04fPgw/v7+hnVBQUHs27ePptI8wyjpzkWJuH37dd4waop0U+QiI8UdaFmIrERflGhVrhW5suVSOZqEzJGLUh9E8rnIS/MpPHybjRf+IiIqQp0YhciggoODDeOWDRw4kOLFi6scUeKsPRcZsTnL0Gg0hm5+J0+eZOPGjeoGlMlJgScFj148ovr86lSfX51HLx6l7mBFgevXdcvpKfA8egTVq+sejx4ZuykhGWhZpMOiRYuYMWMGjRo1ok6dOpw5c8bwiDv1YWIz3PTp0wcnJyc++eQTdu/ezd9//03//v2xs7PDx8fH0k8lQ0pXLkqCvniSLRu4uhoThIlykRH0LXikwCOyksCIQHbd3AVA50qdVY4mcebIRakPIvlc9FOvDjDvJGEBTuy4sUOdGIXIoKZOncrz589xdHRk9OjRaoeTJGvPRUZszlJq165Nq1atABg7diwxMTEqR5R5SYHHnB49gvBw3XLZsurGAlLgEemyb98+w9cuXbrEewwaNCjZY/Pnz88ff/xB4cKFGTlyJMOGDcPJyYkVK1ZQtGhRS4QvEqEvnmi1YGdlI7LpW/D4+8OzZ+rGIoSlbLq8iejYaHLa56RluZZqh5MprL24Vu0QhMgwAgMDmTp1KqCbibBAgQIqRyQyE/24ThcuXGD16tUqR5N5Wdlb+kxG33oHdCOGqk1m0hLpkNjMNanZr3Tp0syZM8eUIYl0StUAyxZWvvzr5YsXoX599WIRwlLWXNR1z2qtbU1O+5wqR5M5bL6ymYioCBzsHdQORQirN3nyZEJCQsidOzfDhw9XOxyRyVStWpWOHTvi5+fH+PHj6dKlC7a2tmqHlelICx5z0hdSihWDnFbwRi1uCx4Z3EqILM+aCzyOjlCihG7ZiNmvhcjwAsID2H1zN2C93bMyGhuNLS9evWD79e1qhyKE1Xv27BnTpk0DYPjw4bi4uKgckciMvv32WzQaDVeuXMHX11ftcDIlKfCYkynG3zElfRzBwbp+D0KILEtRrLvAA69b8cg4PCIr2Hh5I9Gx0eSyz8W7Zd9VO5xMoW7JusDrllFCiKRNmjSJsLAwnJ2dGTp0qNrhiEzK3d2dTp06ATB+/Hiio6NVjijzkQKPOelb8FjD+DsgU6ULIQweP9bVesH6Czz6qdyFyMz0Y8W0dmst3YlMRD+O0darW2U2LSGS8ezZM2bOnAnoWu/kyZNH5YhEZqZvxXPt2jVpxWMGUuAxJ2trwePoCIUL65Zv3FA3FiGEqvRFE43m9fBc1kYKPCKrCIwIZM+tPQB0rNBR5Wgyj2ZlmmH7/25aMpuWEEmbMmWKofXOkCFD1A5HZHIVK1akS5cugG7gZZlRy7SkwGMucadIt5YWPPA6FmnBI0SWpi+alC4NDlbaWEDfsuj2bYiQD99FJhZ39qx3y0n3LFNxcXChkWsjQGbTEiIpAQEBzJgxA4ChQ4dK6x1hEWPHjjW04lmzRrrRmpLMopWC4rmLc+uzW4Zloz1+DGFhuuX0tuApXhxu3Xq9bNymxJUtCwcPxp/hSwhh9dKci5KgL/DEna0q5SBMmIuMoI9NUXQ16cqVTXNeIayNvvjwnvY9q589y9S5KG1BGJ+LOlXsxO6bu9lyZQsvo1+Swy6HhYMVwrr99ttvvHjxgty5c2eo1jvWnouM2JylVaxYkQ4dOuDn58cPP/xAly5dsLGRtiemIK9iCuxs7CjtXJrSzqWxs0lFPSxuC5n0TpFuZ6f7mL10ad2ycZsSp2/BIwUeITKUNOeiJKSpwGPKXGSEwoUhd27dsnTTEpnV84jnhtmzMkL3LFPnorQFYXwualu+LTYaG0JfhbLzxk4VghXCegUHBxta7wwZMoS8efOqHJHxrD0XGbE5yxszZgwAFy5cYMOGDSpHk3lIgcdc9AUUa5kiXS9uFy2ZKl2ILCtNBR4L02hkHB6R+W2+spmo2Cgc7BwMgwIL0ymYqyANSzcEpJuWEG+aNWsWwcHB5MqVS2bOEhbn6elJ69atAZgwYQKK3JuahBR4UhARFcHOGzvZeWNn6mZg0LfgMcUAyxERsHOn7vHGQBTJbEqcvsATHAyBgemPTQhhEWnORYkIC4O7d3XLqSrwmDIXGUkKPCKz87vkB+hmfMqVLZfK0aTMlLko7UGkLhd1qqibknfLlS1ERkdaOlohrFJYWBhTp04FYMCAAeTLl0/liFLH2nOREZsFurF4AM6cOcNff/2lcjSZgxR4UvAk7AnNVzSn+YrmPAl7YvyBphxg+ckTaN5c93jyxNhNiYvbXUy6aQmRYaQ5FyXi6tXXy6kq8JgyFxlJCjwiMwt+GWzoNqQvQlg7U+aitAeRulzUrnw7NGgIjgw2zFYmRFY3f/58nj17Rvbs2Rk+fLja4aSateciIzYLoEaNGjRp0gSAH374QVrxmIAUeMzFlC14TMnZGfLn1y1LgUeILElfLMmbFwoUUDeWlOgLPFeuQGysurEIYWpbr27lVcwrctjlkO5ZZlTIsRD1S9UHwO+in8rRCGEd9DMX9enThyJFiqgcjcjKvvrqKwAOHz7MP//8o3I0GZ8UeMwh7hTp6R1g2Rz0RScp8AiRJcUdf0ejUTeWlOgLPOHhcO+eurEIYWr67lktyrbAKbuTytFkbh0r6gaw3nh5I1ExUSpHI4T6fHx86NKlC+PGjVM7FJHFNWzYkFq1agHw008/qRxNxicFHnN48sR0U6Sbg8ykJUSWlhEGWNYrW/b1zBPSTUtkJqGRofx1TTfeQEaYPSuja1+hPQDPXz5n3+19KkcjhPp69erFqlWrKGDtTXlFpqfRaAyteLZv386pU6dUjihjkwKPOcQtnFhjCx4p8AiRpV25ovuaEQo89vav0+ilS+rGIoQpbbu2jciYSLLZZuM97Xtqh5PpFXUqSt0SdQHppiWEENamVatWuLu7A/DLL7+oHE3GJgUec7hxQ/e1SBHIZYUzYkiBR4gsKzY2YxV4IP44PEJkFusurQOgWZlm5MmRR+VosgZ9N60NlzcQHRutcjRCCCH0bGxs+OKLLwBYu3YtN2/eVDmijEsKPOZgyhm0zEEf17NnEBSkaihCCMu6exdevtQtZ7QCj3TREplFeFQ4f177E4AOFTqoHE3Woe+m9Sz8GQfuHFA5GiGEEHF169aNEiVKEBsby+TJk9UOJ8OSAo85ZJQCD0grHiGyGH2RxM4OXF3VjcVYbm66r9KCR2QW269vJzwqHDsbO953e1/tcLKMknlKUrNYTUC6aQkhhLWxt7dn2LBhACxatAh/f3+VI8qYpMCTgpJ5ShIyOoSQ0SGUzFPSuINMXeApWRJCQnSPkiWN3ZQ0Fxfd/MhxYxVCWLU05aJE6As8ZcvqxrdJXRAmzkVG0rfgefQIgoNNe24h1KAvLni7euPi4KJyNKljqlyUviDSnov0LaY2XN5ATGyMJaIVQpiBteciIzaLRPTr14+8efPy8uVLZs6cqXY4GZIUeFJgo7HBKbsTTtmdsNEY8XIpCly7pls2VYHHxgacnHQPGxtjNyVPH5s+ViGEVUt1LkpCumbQMkcuMoK+BQ9IKx6R8b2MfsnWq1uBjDl7lqlyUfqCSHsu0hd4Hr94zOF7hy0RrRDCDKw9FxmxWSTC0dGRAQMGADB79mwiIiJUjijjkV81UwsMfP0RszXOoKWnL/DoB4QWQmQJGWmKdD0XFyhYULcs4/CIjG7XjV2EvgrFRmND2/Jt1Q4nyynjUgbPwp7A64GuhRBCWI9BgwaRLVs2nj17xrJly9QOJ8ORAk8KXrx6wcr/VrLyv5W8ePUi5QPMMUX6ixewcqXu8eKFsZuSJzNpCZGhpDoXJUFfIInbKsb4IMyQi4wkAy2LzMLvkq57VoNSDSiQq4DK0aSeqXJR+oJIXy7St5xad2kdsUqsuaMVQpiBteciIzaLJBQpUoTu3bsDMGXKFGJjJU+nhp3aAVi7Z+HP6L5e9wt267NbOGZzTP4AfcEkf35wdjZREM/g/7/k3LoFjo7GbEqeFHiEyFBSnYsSERQET57oltPUgsccuchIbm5w4IB00RIZ384bO4HXU3ZnNKbIRekPIn25qGPFjny972vuh9zn+IPj1CpeywJBCyFMydpzkRGbRTI+//xzFi9ezNWrV9m6dSvvvy8TEhhLWvCYmrXPoKWnj+/JEwgNVTcWIYRFxC2OpKkFj4qkBY/ILJqXaY5XMS+6uXdTO5Qsyy2/G5UKVAJg3UXppiWEENamUqVKtGjRAkCmTE8lKfCYmn5Mm4xS4AEZh0eILEJfHClU6PVEehmFvsBz7RpER6sbixDpsaTtEo72PUpehwz2R5jJ6FtQ+V3yQ1EUlaMRmdno0aNxc3Pj008/TXT7li1beP/99/Hw8KB+/fpMmjSJyMhIC0cphPUZPnw4AAcOHOD06dMqR5NxSIHH1DJKC54CBXRDuoN00xIii0jX+Dsq0xd4oqJ0zZyFECI99AWe20G3Of1YbhyEeRw6dIgdO3bgmETfnE2bNjFixAjefvtt5s+fT//+/fnjjz8YPXq0hSMVwvo0adKESpV0rS1/++03dYPJQKTAY2oZpcCj0cg4PEJkMRlxBi29UqUge3bdsozDI4RIr0oFKqHNpwXA76KfytGIzCgsLIyxY8cyePBg8uTJk2B7TEwMv/76K97e3owbN45atWrRvXt3vvzyS7Zt28bZs2dViFoI66HRaBg6dCgAvr6+PH78WN2AMggp8JhScDD4++uWrb3AAzJVuhBZjL4wkhELPLa2UK6cblnG4RFCpJdGozHMpuV3UbppCdObMmUKefLk4cMPP0x0+5kzZ/D396ddu3bx1rdu3Rp7e3t27NhhiTCFsGrdu3cnf/78REVFMWfOHLXDyRCkwGNKcQslppoi3ZykBY8QWUZU1Os/9YzYRQtkoGUhhGnpu2ldC7zG+afnVY5GZCanTp1i9erVfP/999ja2ia6z7Vr1wAop//04v8cHBwoUaKEYbsQWZmDgwM+Pj4AzJkzh5cvX6ockfWTAo8R7G3ssbexT3lH/d2TszPky2fiIOx1j9RtSp6+CCUFHiEyBKNzUSJu3dIVeSCdLXjMkYuMpI/70iXzXUMIkbL05CLTBZH+XORZ2JO38r4FSDctYTqvXr1izJgxdO/eHXd39yT3CwoKAki0+1aePHkM20XSrD0XGbFZGGHAgAHY2dnh7+/P6tWr1Q7H6tmpHYC1K+1cmldjXxm3s77SXrasbowbkwVRGl4lHkMym1Kmb8Fz/z5ERICDQxpPJIQwt1TlokToW71kz64bzyZtQZQ2Ty4ykr7AI2PwCKGe9OYi0wRR2iS5SKPR0KFCB349/CvrLq3ju0bfmSxEkTkcO3aMXr16GbXvkSNHcHFxYebMmURGRvLZZ58ZdZwmiXuGpNYLHWvPRUZsFkYqWrQonTp1wtfXl2nTptGrVy/5+0iGFHhMKaMMsKwXN86bN+H/o5QLITIffYFHq9WNZ5MR6Qs8AQHw7Bnkz69uPEKIjK9jxY78evhXLvhf4JL/JSoUqKB2SMKKvPXWW/z0009G7evo6MiNGzdYuHAhEydOJDo6mpCQEABiY2MN3+fIkYNs2bLh7OwM6Fry5M2bN965goODKV68uEmfixAZ2ZAhQ/D19eX06dMcPnyYunXrqh2S1ZICjylltAJPkSK6VjsREbrYpcAjRKaVkadI14sb++XLUK+eerEIITKHGkVrUCJ3Ce6F3GPdpXV8XeBrtUMSVqRAgQK0b9/e6P1v3bpFdHQ0I0aMSLDt0aNH1KhRg3HjxtGtWzfK/v9+4dq1a7i6uhr2i4iI4N69ezRq1Cj9T0CITMLLy4vq1atz4sQJZsyYIQWeZEiBJwUhkSEsPbMUgA89PyR39txJ72yuAk9ICCzVxcCHH0Lu3MZsSpmNjW4cnvPnZRweYZTHjx+zYMECLly4wOXLlwkPD2fZsmV4eXmleOyMGTOYOXNmgvX58+fn0KFD5gg3U0lVLkqEvsBTIT0fTpsrFxnJ0RGKF9f1KpUCjxDqSG8uMk0QpstFGo2GjhU7MvXoVPwu+vF1fSnwiLR7++23WbZsWYL1w4cPp2TJkgwdOpTSpUsD4OnpSYECBdi0aRPNmjUz7Lt161aioqLirRMJWXsuMmKzSAWNRsOQIUPo1asXfn5+PHjwgGLFiqkdllWSAk8KAiMCGbJ9CACt3VonnTxevIDHj3XLb4yGn/4gAmGILgZat46XHZLZZJyyZaXAI4x2584d/vzzTypWrEitWrXYu3dvqs+xePFicubMafjeXkaeM4rRuSgRivK6wJOuAZbNmYuMVL786wKPEMLy0pOLTBeEaXORvsBz9slZrgVco1w+E7+PE1mGi4tLoh96Zc+enbx588bbZmdnx+eff87o0aMZP348zZs358aNG0yaNInmzZvj6elpwcgzHmvPRUZsFqnUuXNnRowYwdOnT/n9998ZP3682iFZJZlFy1TiTpGeUbpowetYZSpGYYQaNWpw5MgRFi5cSIcOHdJ0Dnd3dzw9PQ2PStI10Oz8/eH5c91yugo8VkCmShdCmFqt4rUo6lQUgHWX1qkcjchK2rVrxy+//MK///5Lnz59mDNnDl27duWXX35ROzQhrE727Nnp27cvAPPmzeOVjGCdKCnwmIq+QOLkBAUKqBtLaugLPNKCRxjBxkZSRkYUd1rxjDwGD0iBRwhhejYaGzpU0H1osfbiWpWjEZnR3r17mT17dqLb2rRpw5YtWzh//jz//PMPI0eOJEeOHBaOUIiMoX///tjY2PDkyRPWr1+vdjhWSe7WTCXu+DsZado2fXeyu3fh5Ut1YxFZQsuWLalQoQL16tXj66+/JiAgQO2QMj19MaRkSciVS91Y0ktf4Ll1S1KWEMJ0OlbsCMCpR6e4+fymytEIIYRITMmSJWnTpg0As2bNUjka6yQFHlPJaDNo6ekLPIqiu2MSwkxKlCjB8OHD+fHHH1m0aBHdunXjzz//pHPnzgQHB6sdXqZmkvF3rIT+OcTGSsNDIYTp1C1Rl0K5CgGw7qJ00xJCCGs1cOBAAA4ePMi5c+dUjsb6SIHHVDJqgadYMdA3A5VxeIQZtW3blv79+1O/fn1q167NwIEDmTlzJvfv3+ePP/5QO7xMLTMVeIoW1c2mBdJNSwhhOrY2ttJNSwghMgBvb2/K//9N7Zw5c1SOxvpIgcdU9AUeU8+gZW76qdJBCjzC4urWrUuBAgU4c+aM2qFkaiaZIt1KaDSvC1VxxxYSQoj06lSpEwD/PvyX20G31Q1GCCFEojQaDT4+PgCsWLGC0NBQlSOyLlLgSYGtxpYijkUo4lgEW41t4juFh8ODB7plc7TgsbWFIkV0D1tbYzcZTwZaFipSFEUGbzaCUbkoEeHhcOeObjndLXjMnYuMpC9USQseISwvrbnItEGYJxe9U/IdCuYqCEg3LSGsnbXnIiM2i3To1asXDg4OvHjxQnoCvMFO7QCsXYk8JXj4+cPkdzL3FOklSsDDxGNIZpPx9K2OpAWPsLCDBw/y7NkzqlSponYoVs+oXJSIq1d1Q2yBCQo85s5FRpKZtIRQT1pzkWmDME8usrWxpX359sw9OZe1F9fyeZ3P0xGkEMKcrD0XGbFZpEPevHnp2rUrixcvZs6cOfTv3x9NRproyIzkY3NT0Ld8yZkTChdWN5a0kBY8IhW2b9/O9u3bOX36NAD//vsv27dvZ//+/YZ9evbsidsb83G3bduWJUuWsH//fg4dOsTMmTMZPHgwpUqVonv37hZ9DlmJvgiSJw8UKqRuLKYSt8ATG6tuLEKIzEXfTevYg2PcDb6rcjRCCCGSMmDAAADOnTvH0aNHVY7GekgLHlPQt3wpVy5jTZGu9+ZU6fpBl4VIxGeffRbv+xkzZgBQrFgx9u7dm+Rxb731FitXruTp06dER0dTuHBhOnXqxKeffkru3LnNGnNWFneA5YyYnhKjL/CEh8P9+7rp30XmEBYWxtSpU9m+fTshISGULVuWgQMH0rhx42SPO3HiBOvWrePixYtcv36d6Ohorly5kuT+y5Yt448//uDBgwcULlyYLl260KdPH+kuKqhfqj4FchbAP9wfv4t+DK89XO2QhBBCJKJ69eq8/fbbnDp1ijlz5lC7dm21Q7IKUuBJQdDLIH47+hsAQ2sNxTmHc8Kd4hZ4zBJEEPymi4GhQ8HZ2ZhNxntzqvTMMBKrMJvkbpr0li9fnmDdlClTzBFOlmFULkqESQdYNncuMlLZsrq+7DExuoGWpcCTeQwaNIiLFy8yYsQIihcvzoYNGxg0aBBz586lQYMGSR539OhRjh8/TqVKlbCzs+P8+fNJ7jt79mxmzJiBj48PtWrV4vTp0/z2228EBwczYsQIczytTCWtuci0QQSZLRfZ2djRoUIH5p6cy5oLa6TAI4SVsvZcZMRmkU76wZY/+eQT1q5dy7Rp08ibN6/aYalPSYNq1aop1apVS8uhGc6t57cUxqEwDuXW81uJ71S/vqKAonz5pZmCuKU7P+iWjdtkvJgYRcmRQ3eSTZvSF6sQFiS5KGWVK+v+tCdONEUQt8ybi1LBzU13ralTzX8tYRl///23otVqlZ07dxrWxcbGKl27dlVatGiR7LExMTGG5QkTJiharTbR/QIDAxUPDw/l+++/j7d+ypQpSsWKFZVHjx6lKXbJRZYO4pZZc9Hem3sNz/H289vpDFYIy5FcZOkgbiWbcCz93igrCgkJURwdHRVAmT59utrhWAVpi2wK5m7BY25xp0qXcXiEyDRiYkDf4CqzNczTP5+LF9WNQ5jOrl27cHJyitcdS6PR0K5dO27evMn1ZP4/Gdu16p9//iEyMpJ27drFW9+uXTuio6PZs2dP2oIXmUr9UvUNs2n5XfRTORohhBBJcXJy4oMPPgBg3rx5KPqZRbIwKfCk14sX8OiRbjmjFnjg9UDLMpOWEJnGrVsQGalbrlhR3VhMTV/guXRJ3TiE6Vy7do2yZcsmKNboB2y/evWqSa6h0Wgo98b/69KlS5MjRw6uyf9AgW42rQ4VOgCw5uIalaMRQgiRnP79+wNw/vx5jhw5onI06pMCT3rF/URRq1UvjvSSqdKFyHT0xY/s2cHVVd1YTE1fsJICT+YRFBREnjx5EqzXrwsKCjLJNRwcHMiWLVuCbblz5zbJNUTm0Kmibjat4w+OczvotrrBCCGESNLbb79NtWrVAF0rnqxOCjzppS+I5M4NBQqoG0t6SIFHiExH331Jq9UNSpyZ6FvwBASAv7+6sQjT0SQz1Vty2yxxfZG11C9Vn0K5CgGw5oK04hFCCGv2ySefALBmzRqCg4NVjkZdUuBJL32T8Yw6RbqevsBz755uqnQhRIanb92S2bpnweup0kFa8WQWzs7Oibag0b9RS6x1T1quERERwatXrxJsCwkJMck1ROZga2NLx4odASnwCCGEtevWrRu5cuUiIiICX19ftcNRlRR40iujD7Csp+9epihw44a6sQghTEJf+MhsAywD5Mr1enp0KfBkDmXLluXGjRvExsbGW68fe0drgm7QZcuWRVGUBGPt3Llzh5cvXyYYm0dkbV0qdQHg5KOTXA+USSiEEMJaOTk50blzZwAWLFigcjTqkgJPCuxt7HEv6I57QXfsbewT7qB/k2jO8Xfs7cHdXfewtzd2U+oULQo5c+qWTTCQpRDCtFLMRW9QFDMUeCyRi1JBBlrOXJo2bUpISAh79+6Nt37jxo24urpSVj8ZQDrUr1+fbNmysWnTpnjrN2zYgJ2dHd7e3um+RmaX2lxkniAsk4vqlqxLUaeigLTiEcLaWHsuMmKzMLG+ffsCcPLkSU6fPq1yNOqxUzsAa1csdzH+G/Bf0jtYogVPsWLwX+IxJLMpdTQaXZHqzBkp8AhhhVLMRW948ABCQ3XLJivwWCIXpUKFCrBjhxR4MosGDRrg5eXFmDFjCAoKonjx4mzcuJGTJ08ye/Zsw349e/bk+PHjXLlyxbAuMDCQ48ePA3D37l0Atm/fDkCxYsXw8PAAIG/evPTv35/Zs2fj5OSEl5cXZ86cYcGCBfTq1YsiRYpY6ulmWKnNReYJwjK5yEZjQ6eKnZh2bBqrL6zmq3e+Ms2JhRDpZu25yIjNwsRq165NhQoVuHTpEgsXLmTmzJlqh6QKKfCkR1DQ69E9M0OzbinwCJFp6IseNjYZe4K/5EgLnsxFo9Ewe/ZspkyZwtSpUwkJCaFs2bLMnDkzxZY1165d47PPPou3Tv99u3btmDhxomH9wIEDcXR0ZOXKlfz+++8ULFiQwYMH069fP9M/KZHhdanUhWnHpnHuyTkuP7tM+fzlUz5ICCGExWk0Gvr27cvnn3/OihUr+PXXX3FwcFA7LIuTAk96xO3Dn1kKPCAFHiEyAf0MWmXK6KZJz4z0BZ579+DFC3B0VDcekX6Ojo588803fPPNN0nus3z58gTrvLy84rXoSY5Go+Gjjz7io48+SmuYIgupVbwWJfOU5G7wXVadX8W4huPUDkkIIUQSevbsyahRowgODmbDhg188MEHaodkcTIGTwoCwgMYvG0wg7cNJiA8IP5GfYEnXz5wcTFjEAEweLDuERBg7KbU0xeppMAjhNVJNhclwiwDLFsqFxkp7uxg0opHCMtIbS4yTxCWy0UajcYw2PKq86tQFCX9JxVCpJu15yIjNgszKFCgAO+//z4AixYtUjkadUiBJwWhr0KZ+e9MZv47k9BXofE3WmoGrdBQmDlT9wgNNXZT6ulb8Dx9qut+JoSwGsnmokToW/CYdIp0S+UiI+XLBwUL6pYvXLDMNYXI6lKbi8wThGVzUTf3bgBcCbjCmcdnTHNSIUS6WHsuMmKzMJPevXsDsGfPHm7fvq1uMCqQAk966Fu6ZIbuWRB/oI43ppAVQmQsmXmK9LgqVdJ91Re0hBDC1DwLe6LNp3uPtOr8KpWjEUIIkZzmzZsbJk1YunSpytFYnhR40kPf39/NTd04TMXFRfeROEg3LSEysKdP4dkz3bJJW/BYIX2BR1rwCCHMRaPRGFrxrLqwilglVuWIhBBCJMXOzo5evXoBsHjxYmJjs1bOlgJPWilK5ivwgAy0LEQmELfYkdlb8OgLWFLgEUKYU1f3rgDcDb7LkXtHVI5GCCFEcj7++GMA7ty5w969e1WOxrKkwJNWjx7ppm0BKfAIIayKvtjh6gq5cqkbi7npW/DcufM6JQshhKmVz18ez8KeAPie91U3GCGEEMlyc3OjTp06QNbrpiUFnrTSt97RaKBsWXVjMSUp8AiR4ekLPO7u6sZhCfoCD8g4PEII89J301pzYQ1RMVEqRyOEECI5H330EQDr1q0jJCRE3WAsSAo8aaUv8JQqBQ4O6sZiSnELPDIVqBAZkr7AE7f4kVnlyweFCumWpcAjhDAnfTct/3B/9tzao3I0QgghktO5c2dy5MhBREQEfn5+aodjMXZqB2DtctjloEGpBoZlA0uOv5MjBzRo8HrZuE1poy/wvHih64ZWtKgJTiqESK8kc9EbFAXOn9ctm7zAY8lclAoVK8KTJzIOjxCWYGwuMm8Q6uSiknlKUr9UfQ7cOcAf//1Bi7ItTHsBIYTRrD0XGbFZmFmePHlo164dvr6+LF261DB9emanUZTUN9OoXr06ACdOnDB5QBlGy5bw118wZAhMm6Z2NKYTHg6Ojrq7xH37oGFDtSMSIkmSixKKW5c9dQqqVlU3HksYPBhmzoR334Vt29SORmRFkouyjt9P/I7Pnz7kss/F0y+ektM+p9ohCWEguUiI+Hbs2EGLFrpi/PXr1ylTpozKEZmfdNFKq8w4gxZAzpy6bmcAly+rG4sQItX0rVhsbKB8eXVjsRSZKl0IYSkdK3bE3saesKgwNl/ZrHY4QgghktGkSROK/v+Tz2XLlqkcjWVIgSctIiPh9m3dcmYr8MDru0Ip8AiR4eiLHGXKZK7hwZKjL/DcvQuhoerGIoTI3PLlzGfomvXHf3+oHI0QQojk2Nra0rNnTwCWL19OGjovZThS4EmBf5g/H6z7gA/WfYB/mL9u5fXrEBurW7ZEgcffHz74QPfw9zd2U9rpCzyXLpnohEKI9Eo0FyXCrAMsWzoXGalixdfLMtCyEOZlbC4ybxDq5qLuHt0B2H59u3qvgRBZnLXnIiM2CwvRF3hu3brFoUOHVI7G/KTAk4KwqDB8z/vie96XsKgw3Up996xcuaBYMQsEEQa+vrpHWJixm9JOWvAIYXUSzUWJMNsAy2D5XGSkuDNpSTctIczL2Fxk3iDUzUXvu72PUzYnomOjWX1htXkuIoRIlrXnIiM2CwupVKkSb7/9NqBrxZPZSYEnLfQFHq0WNBp1YzEHfYHn7l3JRkJkIIryusDh7q5uLJamf776ApcQQpiLg70DHSt2BGDFuRUqRyOEECIlvXr1AmD16tW8fPlS5WjMSwo8aZFZB1jWizsy69Wr6sUhhEiVBw8gJES3bJYWPFascmXd13Pn1I1DCJE19Kysa/J/7MExrgbIeyUhhLBm3bp1w9bWluDgYLZs2aJ2OGYlBZ60yOwFnoIFwdlZtyzdtITIMPStV+zsdA0MsxIPD93X//5TNw4hRNbQoHQDSuQuAUgrHiGEsHYFCxY0TJee2btpSYEntRTl9SieFSqoG4u5aDQyDo8QGZC+9YqbG2TPrm4slqYv8Dx9qnsIIYQ52WhsDIMtrzi3IkvMzCKEEBmZfrDlv/76i2fPnqkcjflIgSe1Hj163Qci7tQtmY2+eCUFHiEyDH2BR99dKSupWPH1kGjSikcIYQk9q/x/ZpagWxy8e1DlaIQQQiSndevWODk5ER0dzdq1a9UOx2ykwJNa+tY7NjaZuw+EtOARIsPRFzayYoEnZ04oV063LOPwCCEsoWKBilQvWh2ApWeXqhyNEEKI5OTMmZMOHToAsGJF5u1aa6d2ANYup31O2ldob1g2FHjKlLFcH4icOaF9+9fLxm1KH32B58oViIkBW1sTnlxkVI8fP2bBggVcuHCBy5cvEx4ezrJly/Dy8jLq+Lt37zJx4kSOHTtGbGws1atXZ9SoUZQtW9bMkWd8CXLRG169gkuXdMtmK/CokYtSwcNDNy68tOARwnxSykWWCcJ6ctFHVT7ixMMTrLmwhmktppErWy7zX1QIYfW5yIjNQgU9evRgyZIlHD58mJs3b/LWW2+pHZLJaZQ0dBquXl33acWJEydMHpDVGzAA5s6F99+HTZvUjsZ8rl59PYj0jRuQCX/5ReodO3aMoUOHUrFiRbJly8bevXuNLvAEBATQpk0b8uXLx+DBg7G1tWXOnDncvXuXjRs3Urhw4VTHk6Vz0Rv+1959xzdV738cf6W7tKUtBQEBLVipKEILhSKiDNkblKGAi6sM8bq4/nChIg6uXMcFWYJeVFBU9hBki+wNArJlb2gLpaUrvz+OaSl0pNDmJM37+XjkkdMzcj6HJB+ST75j+/asws6RI1CxornxmOHdd+GddyAmBtavNzsacSfKRe7r3OVz3PrJraSkp/Btp2/pWaOn2SGJG1MuEslbeno6lSpV4sSJE7z33nu8+eabZodU6NRFq6BsLXiK8/g7AJUrg7e3sWxrFiBur06dOqxevZoJEyZkNnG014QJE0hISGDcuHE0bdqUxo0bM3bsWFJSUhg9enQRRew+bN2SQkKgQgVTQzGNrcC1Y4fR8FBEpKiFlQijXdV2gLppiYg4O09PTx577DHA6KZVHAfIV4GnoNylwOPtnTWghQo88jcPjxtPGYsWLaJ+/fqULVs2c11oaCiNGzdm4cKFhRGeW7t6/B3bYMPuxjaTVlKS0fBQRMQRnox6EoDFBxZzOP6wucGIiEieevQwZkDcvXs3mzdvNjmawqcCTz5OXjpJ82+b0/zb5pw89AfYplRz5BTpJ09C8+bG7eRJezfdPFsRa8eOQn5gcTfJyckcPnyYqjkMTB4ZGcm5c+c4d+6cCZG5jmy56NL1b3aHzKBlVi6yU5UqWX3cNQ6PSNHILxc5JgjnykUt7mhB2YCyWLHyzdZvHHNScRmDBg0iMjKS/v37X7etSZMmREZGXncbPny4CZG6FmfPRXZsFpNERUVx19/jzU6ePNnkaAqfBlnOR3JaMgsPGK0Lkm+5qtBhG4TYIUEkg62FQ3KyvZtuXvXq8PPPKvDITYuPj8dqtRIcHHzdtpCQEADi4uIICwtzcGSuI1suSrv+ze6QAo9ZuchOHh5wzz3G+Dvbt0MBexGKiB3yy0WOCcK5cpG3pze9avRi+OrhfLX5K15/4HU8LPoNVWDlypUsWLCAwMDAXPepU6cOAwcOzLbu6tbOkjNnz0V2bBaTWCwWHnvsMQYPHswPP/zAv//975vqpeBsis+VOMK+fcb97bdDHom62LjnHuN+507IyDA3FikWLO7ad6iInT8Px44Zy+44RfrVbNe/dau5cYiIe+ldqzcAB+MOsuyvZeYGI04hMTGRt956i+effz7HH7hsSpYsSVRUVLZb+fLlHRipiPt59NFHATh27BgrVqwwOZrCpQJPQdgKPI7snmUmW4EnMREOq0+53Ljg4GAsFgtxcXHXbbOts7XkkYK7ujuS7W3rrqKijPstW8yMQkTczV2l76J+pfoATNg8weRoxBl88sknBAcH88QTT5gdiohcIyIigrp16wLFr5uWCjwFsXevcV/cB1i2iYjImklL3bTkJvj5+VGpUiX27Nlz3bY9e/ZQqlQpdc+6CbbWKlWquEfjwrzYCjx//QU51BNFRIrM01FPAzB151QuJF0wORox06ZNm5gyZQrvvfcenp6eee67Zs0aoqOjqV69Ou3atWPy5MnFcmYfEWdja8Xz008/kZKSYnI0hUcFnoJwtwKPtzdERhrLKvDITWratCmrVq3izJkzmevi4uJYunQpzZo1MzEy12ebACA62tw4nEHNmlnLasUjIo7U9Z6uBHgHcCX9CpO3F69fhMV+KSkpvPHGG/To0YPq1avnuW+jRo148803GTduHJ9++inh4eG8++67fPjhhw6KVsR9devWDQ8PDy5cuMCCBQvMDqfQqMBTEKdPG/fu0kULsvp7/PGHuXGI05g/fz7z58/PnFZw/fr1zJ8/n+XLl2fu06tXLyJtxcG/9e7dm6CgIJ599lkWLVrEsmXL6NOnD15eXvTt29eh11DcqMCTJSjIaHwIKvCIiGMF+QbR7Z5uAHy56Uu1wigG1q5dm+MsVzndzp8/D8DIkSO5cuUKL7zwQr6PP3jwYDp37kydOnVo1qwZI0aMoG3btnz77bccsw2uJyJFonz58jRq1AiAKVOmmBtMIdIsWjcin2p8sVK9OkyZohY8kunaDywjRowAoEKFCixZsiTX40qXLs2kSZMYNmwYr776Klarldq1a/Pdd99x6623FmnMxdmVK1lvTxV4DNHRxpBptsKXiIijPFv7Wb7a8hVbT21l/fH11K1Q1+yQ5CZUqVLF7tY0gYGB7N+/nwkTJvDRRx+RlpZGQkICABkZGZl/+/n54ePjk+vjdOrUiTlz5rBt2zYqVKhQKNchIjnr3r07S5YsYebMmVy+fJkSJUqYHdJNU4EnH4E+gTxT6xnYuZPAlJXGDFolSzo4iEB45pmsZfs2FQ5bC55du4yZtIrRFHJyY3bv3p3vPt9++22O68PDwxk9enRhh+QWMnPR38s2f/wBaWnGcq1aRR2EibmoAKKi4Kef1IJHpCjkloscG4Tz5qK6FepSo2wNtp3axriN41TgcXFlypShc+fOdu9/8OBB0tLSrpv2HODEiRPUqVOHd955J3Psj5xk/D1zbXGatrkoOHsusmOzOIHOnTvTv39/Ll26xLx583jkkUfMDummWaw30H40JiYGgA0bNhR6QE6rXz8YMwbatoXZs82OxnH27Mkah2ffPrjjDnPjEbmKW+aia4wfb3x4KFcOTpwwOxrn8Msv0Lo1eHnBpUvg62t2RFLcKRfJ1b5Y9wUDfhlACe8SnHjlBCV9HfzDoJjm/Pnz7LWN2XmVl19+mdtuu40XX3yR8PBwypYtm+tjvPLKK8ybN4/FixcXuIWzcpFIwbVp04Z58+bx8MMP8/PPP5sdzk1TCx572eYhvvdec+NwtDvuML4d2fqBqMAj4lQ0/s71bDNppaUZaavIWzaJiFylR40e/Gvhv7icepnJ2yfTN0bjzLmLUqVKERsbe916X19fQkNDs22bM2cOixcvpmHDhpQrV474+HhmzZrFokWL6N27t7qvizhI9+7dmTdvHnPnziUhIYGSju6tU8jU9s8eVmtWgadGDXNjcTRPT7jrLmNZ4/CIOJ1Nm4x7FXiylC8Pth9HNQ6PiDhaiF8I3at3B2DMhjEabFlyVLFiRS5cuMDw4cP5xz/+waBBgzh37hwfffQRr776qtnhibiNDh064OfnR3JyMjNnzjQ7nJumAk8+jl88Tu0valC7ewLHgzCnBc/x41C7tnE7ftzeTYXHNqi0rcglIg53/OJxao+rTe1xtTl+0Xizp6fDtm3Gdoe0UjE7FxWAreClcXhECldOucjxQTh/LupTuw8AW09tZc3RNeYFIk5hyZIljBo1Ktu6qKgo/ve///H777/zxx9/sHnzZn744Qc6depkUpSuxdlzkR2bxUmULFmS1q1bA/Djjz+aHM3NUxetfKSkp7Dp3B9wK6T4ekHVqiYEkZL1M31Kir2bCk+NGjBpEmzdWkQnEJH8pKSnsOnEpsxlMIbIunzZ2O6QFjxm56ICiIqC+fPVgkeksOWUixwfhPPnoroV6lK7fG02ntjIqA2juK/SfeYFI1IMOXsusmOzOJGuXbsybdo0FixYwIULFwgNDTU7pBumFjwFEREB3t5mR+F4tgEtdu+G5GRTQxGRLLbiRXAwVK5sbizOxtaiacsWo6WTiIgjWSwW+tfpD8CPO37kTOIZkyMSEZHctG3bFn9/f1JTU12+m5YKPAVhm03K3dSsadynp2scHhEnYvtVKCoKLBZTQ3E6f08kQmIi/PmnubGIiHvqXr07IX4hpKSn8NXmr8wOR0REchEQEEDbtm0B1++mpQJPQdgGG3Y3ZctmjViqbloiTmPjRuNes0RdLzwcwsKM5fXrTQ1FRNxUCe8SPBX1FABjNo4hPUPNCUVEnFW3bt0AWLhwIefOnTM5mhunAk9+ru4w6a4FHshqxaMRS0WcQnp6VoGnTh1zY3FGFktWKx4VeETELP1i+gHwV9xfzNkzx+RoREQkN61atSIgIIC0tDRmzJhhdjg3TAWe/Ozfn7Xsrl20IKvAoxY8Ik5h9264eNFYrlvX3Ficla3wtWGDuXGIiPu6M+xOWt9pzM7y+drPTY5GRERyU6JECdq3bw/AlClTTI7mxqnAk5+dO7OWy5UzLw6zXV3gsVrNjUVEWLfOuC9VCqpUMTcWZ2VrwbNli2avEBHz/LPuPwFY+tdStp3aZnI0IiKSmy5dugCwZMkSl+2mpWnS8xH8x15e2w6EhxPsF2JSEMHw2mtZy/ZtKly2mbTi4+HwYbj99iI8mYhcK9g3mNcavJa5bOt2VLeuAwdYdoZcVAC2FjwpKbB9O9SubW48IsXBtbnInCBcKxc1v6M5d5W+iz/P/smItSP4sv2XZock4vKcPRfZsVmcUMuWLQkICCAxMZEZM2bQu3dvs0MqMIvVWvDmGDF//yy6wR3avT/4IKxYAa++CsOGmR2NedLSIDAQrlyBGTOgQwezIxJxr1x0jTp1jK5Hb70FQ4aYHY3zqlABjh+H0aOhb1+zo5Hiyp1zkdhn1PpRPDfvOfy8/Djy0hFKlyhtdkhSDCkXidy87t27M2XKFFq0aMH8+fPNDqfA1EUrLxkZsHmzsezu09R4ecE99xjLGodHxFRXrmS9DTX+Tt40Do+IOIPHaz5OsG8wyWnJjNkwxuxwREQkF7ZuWosXL+b8+fMmR1NwKvDkZd8+uHTJWI6ONjcWZ6CBlkWcwtatkJpqLGsGrbxpJi0RcQaBPoH0qd0HgJHrRpKclmxyRCIikpNWrVpRokQJ0tLSmDlzptnhFJgKPHnZtImjJSH8JQvh85pzNOGoOXEcPQrh4cbt6FF7NxU+2zg8tlZNIuIwRxOOEv5ZOOGfhbNgtfFmv+02KFvWkUE4SS4qAFsBbMcOuHzZ3FhEioOrc5Hbfy4qoOdjn8fLw4tTiaeYtG2S2eGIuDRnz0V2bBYnVaJECdq2bQvATz/9ZHI0BacCT142bybNAw4FWzkUf4i0jDRz4khLg0OHjFtamr2bCp9thNKDB8FFRxUXcVVpGWkcij/EofhDbNlmvNkd3j3LWXJRAdgKPOnp6qblChITExk6dCgNGjSgRo0adO7cmcWLF9t17OHDh+nfvz+1a9cmOjqaZ555hn379l23X2RkZI6377//vrAvp1i6Ohe5/eeiAqpYsiKPVn8UgP+s/g8Z1gyTIxJxXc6ei+zYLE7skUceAWDRokXExcWZG0wBqcCTl02bzI7AuURHg8ffLxl9UxIxzRaNv2O3UqWgWjVjedUqc2OR/A0YMIDZs2fzwgsvMHbsWCIiIhgwYADLly/P87hz587x2GOPcezYMYYNG8Ynn3xCfHw8PXv25OTJk9ft37p1a6ZMmZLt1rx586K6LJFMr9z3CgC7zu7il72/mByNiIjkpHXr1vj7+5Oamsrs2bPNDqdAVODJjdWqAs+1SpTIGmhZBR4R0xzYb9zHxpobh6uoX9+4V4HHuS1fvpxVq1YxdOhQunTpwn333cewYcOIiorio48+yvPYCRMmkJCQwLhx42jatCmNGzdm7NixpKSkMHr06Ov2L126NFFRUdluYWFhRXVpIplqlqtJ0ypNARi20o1nZxURcWIBAQG0bNkSgKlTp5ocTcGowJObw4fBBUfNLnKakkbEKXh7a4Ble11d4LFazY1Fcrdw4UKCgoJ46KGHMtdZLBY6derEgQMHcuxuZbNo0SLq169P2asGpQoNDaVx48YsXLiwSOMWKahB9w8CYMXhFaw8vNLkaEREJCcPP/wwAPPnz+fixYsmR2M/FXhyY2u94+tjbhzORlPSiDiFWrXA39/sKFyDrcBz7hzs3WtuLJK7vXv3EhERgYdH9o8mkZGRAOzZsyfH45KTkzl8+DBVq1a9bltkZCTnzp3j3DXjxs2cOZMaNWpw77330qVLF+bNm1dIVyGSvyaVm1DnVqNC/+HvH5ocjYiI5KRt27Z4e3tz5coVl/qcoAJPbmwtVKrdbW4czsbWZODYMThxwtxYRNzY/febHYHrqFrVGIsH1E3LmcXFxREcHHzdetu63AY5jI+Px2q15nhsSEjIdce2a9eOt956i6+++ophw4bh5+fHSy+9xMSJE2/6GkTsYbFYeK3BawDM3TuXbae2mRyRiIhcKzg4mGbNmgGu1U1LBZ7crF1r3NumBhfDvfcafUNA3bRETKQCj/08POC++4xlFXicm8ViuaFt9my3GT58OO3atSMmJobWrVszceJEYmJi+Oyzz0hOTi5QvCI3qsNdHahW2hgB/oMVH5gcjYiI5MQ2m9a8efNISkoyORr7eJkdgFNKT4d16wAIrXU/w++obiz7hZoTT2goDB+etWzfpqLh6ws1axrFnQ0boF07B5xUREL9QhlQdTgjRwBJoeYUeJwpFxVQ/fowd64KPM4sJCQkx1Y68fHxADm20LGtt1gsOR5rW2dryZMTDw8P2rdvz4YNG9izZw81atQoaOhuJdQvlOHNhmcumxOE6+YiGw+LB4MaDOKJGU/w444febvh21QrU83ssERchrPnIjs2iwto3749np6eJCYm8uuvv9KhQwezQ8qXCjw52bUL/h5IKfj+JrxSpYq58QQHwyuvFHRT0YmJMYo7GodHxGGC/YK57egrsBruuAOuGkvWgUE4WS4qANs4PDt2wIUL+qDljCIiIvj111/JyMjINg6PbeydnMbYAfDz86NSpUo5jtGzZ88eSpUqle8MWRkZGQDXjf8j1wv2C+aV+ia/2V04F13tsXsf473f3mPf+X0MXTGUSZ0nmR2SiMtw9lxkx2ZxAWFhYTRs2JAlS5Ywffp0lyjw6JNMTtasMe7LlIHKlc2NxRnZBlresEFT0og40Mq/J1tp0MDcOFxRnTrg6Wksr15tbiySs2bNmpGQkMCSJUuyrZ8xYwaVK1cmIiIi12ObNm3KqlWrOHPmTOa6uLg4li5dmtl/PjcZGRnMnj2bgIAA7rzzzpu7CJEC8PLw4o0H3gDghz9+YPfZ3SZHJCIi1+rcuTMAs2bNIjU11eRo8qcCT05sBZ569cDOPv1upW5d4/7MGTh40NxYRNyE1ZrVvUjj7xRcQADUrm0sL19ubiySs4YNGxIbG8sbb7zBzz//zJo1axg0aBAbN27k1VdfzdyvV69emTNr2fTu3ZugoCCeffZZFi1axLJly+jTpw9eXl707ds3c78JEybw5ptvMmfOHNauXcvcuXN5/PHH2bhxI6+88gq+vr4Ou14RgJ41elIltAoZ1gze++09s8MREZFrdOzYEYALFy6w3AU+RKrAk5OrCjyH4g4R9GEQQR8GcSjukDnxHDoEQUHG7dAhezcVnbvvhpIljWVbkwIRKVJLNh3izD+C4LUgKkcpF92IRo2M+6VLTQ1DcmGxWBg1ahRt2rTh008/5ZlnnmH37t2MHDmSJk2a5Hls6dKlmTRpEuXKlePVV1/lpZdeIigoiO+++45bb701c7/KlStz4MABhg4dytNPP83bb7+Np6cno0ePpkePHkV9icWCPhcVLi8PL9584E0AJm+fzM4zO02OSMQ1OHsusmOzuIgKFSoQGxsLwPTp002OJn8ag+daCQmw8+//XOvVw4qVSymXALBiUnckqxUuXcpatm9T0fH0NKakWbDAKPD06uWgE4u4r1WrrOBrvNnviFAuuhGNG8O//w0bN0J8vNE3XpxLYGAggwcPZvDgwbnu8+233+a4Pjw8nNGjR+f5+E2aNMm3WCR50+eiwtezRk8+/P1D9p7fy+Clg/m5689mhyTi9Jw9F9mxWVxI586dWbt2LdOnT2fEiBFOPWaf80ZmlvXrjXegxWIM2iA5s/URUQseEYe4evYn9Ry9MQ0aGPXpjAxYscLsaEREDN6e3gxpPASAqbumsuH4BpMjEhGRq3Xq1AmAEydOsHbtWpOjyZsKPNeydc+qXt1oTyc5sxV4duyAHKamFZHCk5GhgYELQ2BgVt1+2TJTQxERyabrPV2pUbYGAG8uedPkaERE5Gp33nkn99xzD2BM/uDMVOC5lu1b1N/97CQXsbHGT+FWq755ihSxbduMLkVy8xo3Nu41Do+IOBMPiwfvN3kfgAX7F7Dk4JJ8jhAREUeyteKZPn06Vifuc6cCz9XS07Pa7Wse4rwFBEBUlLGsblpuIzExkaFDh9KgQQNq1KhB586dWbx4cb7HjRgxgsjIyOtu92s6KLss0ef8QmMr8GzeDBcumBuLiMjV2tzZhga3GZ8/B/46kAxrhskRiYiIjW02rb179/Lnn3+aG0weVOC52pYtxiDLAA0bmhqKS7AVwX7/3dw4xGEGDBjA7NmzeeGFFxg7diwREREMGDDA7ikDv/76a6ZMmZJ5GzduXBFHXDyowFN46tcHb2+j8eFvv5kdjYhIFovFwvBmwwHYfHIzk7dPNjkiERGxqVWrFpUqVQKcu5uWCjxXsw3KcPvtEB5uZiSuwdb6Yt06SE01NxYpcsuXL2fVqlUMHTqULl26cN999zFs2DCioqL46KOP7HqM6tWrExUVlXmz9WWV3KWmgp31M7FDQADUrWss29H4TETEoWIrxtLtnm4AvL74dZJSk0yOSEREwCjC21rxOHOBR9OkX832LapRo8xVpUuU5usOX2cum6J0afj666xl+zYVPVuBJykJNm3SuEXF3MKFCwkKCuKhhx7KXGexWOjUqRNvvfUW+/btIyIiwsQIi6eNG/+eYtOnNJ88+DWhocpFN6tZM6Nn6fz5Zkci4nr0uajoffDQB0zbNY0jCUf4z+r/8OaDGnRZ5FrOnovs2CwuqGPHjowYMYJ169Zx7NgxKlSoYHZI17FYb2CEoJiYGAA2bChG0zimp0NYmDGS6VdfwVNPmR2Ra4iIgP374cMPYdAgs6ORItStWzcsFgs//PBDtvVbt26la9eufPrpp7Ru3TrHY0eMGMHIkSMpU6YM586dIywsjEaNGvHSSy8RFhZ2wzEVy1x0jXfegXffhbvugl27zI6meFi3LqsevW8f3HGHufGI63OHXCSO9erCV/l41ceU8C7B7gG7qViyotkhiQtQLhIpWqmpqZQtW5YLFy7wxRdf0L9/f7NDuo66aNlcPU3NVS14JB+21hyLFpkbhxS5uLg4goODr1tvWxcXF5frsZUqVeLll1/mgw8+4KuvvuLRRx9l7ty5dO3alXhND5WnuXON+1xqZ3IDYmKyfkn75RdzYxERycmbD75J2YCyXE69zKsLXzU7HBERAby9vWnbti0AM2fONDmanKnAY2Mbf6dSpWzj71itVlLSU0hJTzFvOjSrFVJSjNs1MeSxyTGaNjXuf//d6KolxZrFYrmhbR07dqRPnz48+OCD3HfffTz33HOMHDmSo0ePMmnSpKIItVg4eRJsP8K1aqVcVFg8PKBFC2NZBR6RgtHnIsco6VuSYU2HAfD9H9/z2yGNCi9yNWfPRXZsFhfVoUMHAJYuXeqUP1SrwGNz9fg7V31RPRR/CN+hvvgO9eVQ/CFzYjt0CHx9jduhQ/ZucozGjY1/rytXYNUqEwIQRwkJCcmxlY4tseXUuicv999/P2XKlGHLli2FEF3xZCs+BAXBbTWUiwpTq1bG/dKlkJxsbiwirkSfixynV81exFYw+pM+N+85UtM1oYWIjbPnIjs2i4tq0aIFPj4+pKamMt8JB3RUgQcgLS2rwKPp0QumdGmIjjaW1U2rWIuIiGD//v1kZGRkW79nzx4AqlatWuDHtFqteHgoDeXG1j2rWTPw8TE3luKmRQujNp2UpOnSRcQ5eVg8GNVmFB4WD/44/Qf/Wf0fs0MSEXF7gYGBmZPOOGM3LX2zAli7FmwtE5o1MzUUl2TrpqUCT7HWrFkzEhISWLJkSbb1M2bMoHLlygWeQev333/n7Nmz1KxZszDDLDZSU+HXX43lNm3MjaU4Kl0a6tQxltVNS0ScVa3ytXi+7vMADFk+hIMXDpockYiI2LppzZs3j9RU52pdqQIPZH26v+ceuO02c2NxRbaBljduhPPnzY1FikzDhg2JjY3ljTfe4Oeff2bNmjUMGjSIjRs38uqrWQNA9urVi8jIyGzHduzYkf/9738sX76clStXMnLkSJ5//nluv/12evTo4ehLcQm//w4XLxrLtu5EUrhsA1fPnq2+8SLivN5r/B4VgiqQlJZEv7n9zBtvREREAGjXrh1gDFXxm5M1BVeBB7IKPPoWdWMaNDD6j1itWYNVS7FjsVgYNWoUbdq04dNPP+WZZ55h9+7djBw5kiZNmuR5bJUqVZg8eTIvvPACffr0YcaMGXTp0oUff/yRkiVLOugKXMucOcZ9rVpQvry5sRRXHTsa9/v3GxMpiog4oyDfIEa0GgHAgv0LmLh1oskRiYi4t1tvvZW6desCztdNy8vsAEx38iRs2mQsax7iG1OiBNx/vzFa6bx50Lmz2RFJEQkMDGTw4MEMHjw4132+/fbb69Z98sknRRlWsWO1ws8/G8t/twCVIlCjBtxxh1Hg+flnUG9BEXFWnap1osvdXfhp50+8OP9FmlVpRoWSFcwOS0TEbbVv355169Yxc+ZMPv/88zxnFHYkteCxjXwdGGgUKeTGtG1r3M+ZA9cMwisiBbNuHRw+bCx36WJuLMWZxQKPPGIsT51qbiwiIvkZ2XokpUuUJv5KPH3m9FFXLRERE7Vv3x6Aw4cPs337dpOjyaICz7x5xr2mqbk5tmYGp04Zg1aLyA378Ufjvnp1qFbN3FiKu4cfNu537YKdO82NRUQkL7cE3MLIViMBmLt3Ll9u+tLkiERE3Ff16tUJDw8HYPbs2eYGcxX37qKVlgYLFxrLuYy/c0vALczqPitz2RS33AKzZmUt27fJse64wxikescOI6D77jMxGBHXZbXCTz8Zy1e33lEuKhoxMcbY+ocPG6147r7b7IhEnJtykbm63tOV6X9OZ8qOKby04CUahTeialhVs8MScThnz0V2bBYXZ7FYaNeuHSNGjGDWrFm88cYbZocEgMV6A+07Y2JiANiwYUOhB+RQS5eCbXDYI0egYkVz43F1b7wBH3xgNDnQT+HiAMUmF11lzZqs+ujOnWrB4wgvvwyffmqMybN1q9nRiCsqjrlInNeFpAvUHFOTIwlHiLk1hpVPr8THU63QncW0adN47bXXcty2bds2fH19s62bPXs2X375JQcPHiQ0NJT27dvz/PPPX7efPZSLRBxr0aJFNGvWDIATJ05Qrlw5kyNy9y5atn4QsbEq7hSGv/shsmsX7N1rbiwiLsrWekfdsxzHNg7Ptm3wxx/mxiIikp9Q/1C+6fQNFixsOL6B1xblXEwQcw0bNowpU6Zku/lcMxzEzJkzGThwILVq1eLLL7+kT58+TJo0iUGDBpkUtYgUxIMPPpg5I/DcuXNNjsbgvgWetLSsUTXzGMU0LSON4xePc/zicdIy0hwU3LVBpMHx48YtLc3eTY5Xp07WfM629ogiYre0NPjhB2P52rSkXFR07rvP6GUKMFGzD4vkSbnIOTQKb8TrD7wOwCdrPmHmn841Ta9AZGQkUVFR2W5Xz7KTnp7Oxx9/TJMmTXjnnXeoV68ePXr04LXXXmPevHlsVZPSPDl7LrJjsxQDPj4+tGjRAoBZTvL9130LPMuXw5kzxrLt59scHE04SoVPKlDhkwocTTjqoOCuDeIoVKhg3I4etXeT43l4QLt2xrKmpBEpsAULjA8BAL16Zd+mXFR0LBZ48klj+dtv9SFMJC/KRc7jnUbv0Ci8EQBPzHiCAxcOmBuQFMiWLVs4c+YMnTp1yra+Xbt2eHt7s2DBApMicw3Onovs2CzFhG02rYULF5KUlGRyNO5c4LF1z6pXD26/3dxYipOuXY371ath/35zYxFxMRMmGPcPPQSVK5sbi7t5/HGj0HPqlFFoExFxdl4eXkzuPJmyAWWJvxJPpymduJRyyeyw5G//+Mc/qFatGrGxsbz00kscOnQo2/a9fw9ncOedd2Zb7+/vT6VKlTK3i4hza9WqFR4eHiQlJbF06VKzw3HTAs/V3bNsBQkpHI0aGWVqgO++MzUUEVdy6hTYZljs3dvcWNzRbbcZhTWAr782NxYREXuVDyrPlEem4OXhxbZT23hyxpPcwPwpUohKly5N3759GTp0KBMnTqRfv36sWbOGrl27cuTIkcz94uLiAAgODr7uMYKDgzO3i4hzCwsLo379+gDMmTPH5GjctcCzZAmcO2cs59E9S26Apyf06GEsf/utMeeziOTL1jUoNBSuaa0tDmLrpjVrFpw9a2ooIiJ2axjekM9bfg7A1F1TGbJ8iMkRFR9r164lMjLSrtv58+cBY9DVl156icaNG1O3bl2efPJJJk6cSGJiImPGjLnuHFePy2PPehFxPm3btgWMAo/ZRXYvU89ulq++Mu4bNIBKlcyNpTjq1Qv+/W+ji9batUY3OBHJldWa1T2rRw/w8zM3HnfVqRMEB0N8PIwfD5rERERcRb+Yfmw5uYUvN33JO8vfoUpoFXrV7JX/gZKnKlWq8OGHH9q1b2BgYK7bqlatSvXq1dmyZUvmupCQEMBoyRMaGppt//j4eCpqhl8Rl9G2bVsGDRrEkSNH2L59OzVq1DAtFvcr8Jw5A9OmGcvPPGNuLMVV9epQsyZs3Wo0S1CBRyRPCxfCn38ay//4h7mxuLMSJYzucZ98AiNHwiuvgLe32VGJiOTPYrEwsvVIDlw4wOKDi+k9qzcVSlagSeUmZofm0sqUKUPnzp0L5bEyMjLw8MjqPBEREQEYY/FUvmrgvaSkJI4cOULjxo0L5bwiUvTuvvtuwsPD+euvv5gzZ46pBR7366L1zTeQmgohIXlOjy43yTYF0PffgxOMJi7izIYPN+4bNzZqo2Ke5583JgQ8dgx+/tnsaERE7Ofj6cPUrlOpfkt1UjNS6fhDRzYe32h2WALs2bOHnTt3UvOq/+SjoqIoU6YMM2dmn+J+zpw5pKam0rx5c0eHKSI3yGKxZOumZSb3KvBYrTBunLHcqxf4+5sbT3HWsyf4+MCFCzBpktnRiDitrVuNFjxgtBgRc4WHZ42B9OmnGkZMRFxLsF8w8x6bR8WSFbmYcpEW37Vg55mdZoflVp566inGjh3L4sWLWb16NV999RVPPPEEQUFB9O3bN3M/Ly8vXnnlFRYtWsSQIUNYu3YtkydP5sMPP6RFixZERUWZdxEiUmDt2rUDYM2aNZw5c8a0ONyri9Zvv8GePcaynd2zygWWY+XTKzOXTVGuHKxcmbVs3yZzlS0L3bsbLaY+/9zo96DB4kSu88knxn21atCqVe77KRc5zosvGhMtrl8Pq1bB/febHZGI81Aucn6VgiuxsNdCHvz6Qc5cPkPTb5qy7MllVA2ranZobuHOO+9k1qxZnDhxgitXrlCmTBmaNGnCc889x6233ppt306dOuHh4cH48eP58ccfCQ0NpXv37vzzn/80KXrX4ey5yI7NUsw0bNiQgIAAEhMT+eWXX3j88cdNicNivYFhnmNiYgDYsGFDoQdUpB55xPjUft99xqd2KVqbNkHt2sby4sXQRP3ApXC5bC7625EjUKWKMXvW+PGaHt1ZWK1Qty5s2ADNm8OCBWZHJM7O1XORFE9bTm6h0f8aEX8lnnKB5Vjy+BKqlalmdlhShJSLRMzVsWNHZs6cSdeuXZkyZYopMbhPF61du7IGV37+eXNjcRe1ahkzlYHRikdEsnn3XaO4U66cMXuWOAeLBd5+21j+9Vej8aeIiKuJKhfFoscXEeIXwslLJ2k0sRFbT241OywRkWKrTZs2ACxYsIC0tDRTYnCfAs9HHxk/y0ZEQNeudh+Wkp7C9lPb2X5qOynpKUUYYF5BpMD27cYtJcXeTc7B1sR09uys7nEiwq5d8PXXxvLgwflPja5c5Fht2mRNAPjmmxqLR8RGuci1xNwaw5LHl1DKvxSnE0/z4P8eZNlfy8wOS+SmOXsusmOzFEOtW7cGID4+nlUm9RhyjwLPwYNZA/0OGgSennYfevzicWqMqUGNMTU4fvF4EQWYXxDHoUYN43b8uL2bnEOnTlC5svHtyPaTuIjwxhuQkWHUnO2ZGl25yLEsFhg61FhescJoySMiykWuKLp8NMufXM6tQbeScCWBFt+1YMof5nQdECkszp6L7NgsxVCFChUyB0ifO3euKTG4R4Hn3/+G9HSoWDFr+m5xDC8vox8KwA8/wJYtpoYj4gxWr4bp043loUPB29vceCRnDz1kTF0PxgxnqanmxiMicqOq31KdVU+vIjIskpT0FLpP7c47y97hBobiFBGRPNi6aanAU1R27jRGLwX417+MqbvFsR57DO65x1h+801zYxExWWoq2GZJrVULunQxNx7J2/Dh4OEBO3ZkzXgmIuKKbg+5nZVPr6RReCMA3l3+Ll1+6kLClQRzAxMRKUZs3bR27NjBoUOHHH7+4l3gsVrhhReMUUwjIqBPH7Mjck+enll9HebO1Yil4taGD4dt24wuQKNHG8UDcV61asGAAcbyu+/CX3+ZGo6IyE0JKxHGgp4LeLbWswBM3TWVmHExbDu1zeTIRESKh9jYWMLCwgBzWvEU768WM2fCokXG8mefga+vqeG4tQ4dIDbWWO7bF65cMTceERPs2ZPVY/GFF4ypuMX5vfce3HorJCVBv34acFlEXJuPpw9j2o5hbNux+Hj6sPf8Xup+WZfP13xOhjXD7PBERFyap6cnLVu2BOCXX35x+PmLb4Hn4kV46SVjuXVrY0oUMY+tuYKnpzF90Pvvmx2RiENduWIMAXblCtx+u1E0ENdQsiR8/rmxPH8+fPqpufGIiNwsi8XCs7WfZXXv1VQJrcKV9Cu8uOBFWnzXgkNxju9SICJSnLRq1QqAxYsXk5yc7NBzF98Cz/PPG23pfXz0adxZREfDwIHG8ocfGnMGiriJl1+GdeuMWuf48RAYaHZEUhCPPAJPPmks/9//wdq1poYjIlIoapWvxZY+W3g66mkAFh1YxD2j7uGzNZ+RnpFucnQiIq6pRYsWWCwWkpKSWL58uUPPXTwLPN9/DxMnGsv//jdUrWpuPJLl7bfhzjuNcZG6dzdaWokUc999B6NGGcvvvANNm5oajtygkSPh7ruN9NWtG5w6ZXZEIiI3L8g3iAkdJjC923TKB5YnMTWRlxa8RO1xtVn+l2O/mIiIFAelS5cm9u/hSRzdTctivYH5EWNiYgDYsGFDoQd003bvNga2SEgwumbNmWP8ZH6DUtNTORh3EIDKIZXx9jRhPuPUVDhoxEDlytnmVM5jk/NavRoaNjSC79wZfv75pp4jcV9OnYv+tmiR0UM0JQVatTJS0o0MrKxc5Bx27DD+i7l8GaKiYNkyCA42OyoxmyvkosKiXFS8xSXH8X8L/49xm8Zlrut0Vyfeb/I+1cpUMzEysYdykaODyDvhKB+5tyFDhvD2229z5513smfPHoedt3gVeI4fh/r14dAhKFcOtm6FW24xOyrJyZgxxmilYIw6O3iwufGIS3LaXPS3VaugWTOjGHDXXfD77/D3oPriwubONcaNT083atW//AL+/mZHJWZy9lwkUlDrj63nn/P/yZqjawDwsHjQq0YvXmvwGpGlI02OTnKjXCTiPDZs2ECdOnUA2Lt3LxEREQ45b/HponXhArRsaRR3AgJg1iwVd5xZnz7wj38Yy2+/bXSlEylGFi82Wuxcvmz8arNokYo7xUWbNvDVV8by8uVGl7vz582NSUSkMNWpUIeVT6/k+4e/J6JUBBnWDCZunUi1L6rR9aeurD6ymhv4jVhExG3UqlWLW/6uRziym1bxKPAcPgwPPGAM2uvlBdOmwd/VspuVnJbMsr+WseyvZSSnOXYE7Kwgko1+AMuWGcv2bXJuFosxoEXr1sbf//d/8MEHmn9YioXx4416c0KCMb32okVQocLNPaZykXN5/HEjhVksRkut+++H/fvNjkqk6CkXuQ8Piwfdq3dnZ/+djGs7jiqhVbBi5aedP1H/q/rEjo9lwqYJXEq5ZHao4oacPRfZsVmKOQ8Pj8zp0ufNm+ew87p+F63164228idOGB0bv/sOunYttIf/K+4vKn9eGYCDLxwkPCS80B7b/iD+MpoAgNGRMzzcnk2u4coVY3qaOXOMv3v0gLFjjVZYIvlwqlwExMXBCy/AN98Yf9eoYby0K1W6+cdWLnJOP/0EPXsaYywFBRlFn169NKyYu3G2XFSUlIvcV1pGGlP+mMKnaz5l44mNmesDfQJ5uNrD9Li3B40rN8bLw8vEKN2bcpGjg/grz4SjfCQ//PADjz76KH5+fpw/fx5/B/Tpd90WPCkpRtee++4zijvBwbBgQaEWd8QBfH2NQZa7dzf+njQJ6tUz5pMWcRFWq9Fw8N57s4o7bdoYY+4URnFHnFeXLkYLrfLljUkBn3gCOnaEffvMjkxEpHB5eXjRo0YP1j+znt+f+p2eNXri5+XHpZRLTNw6kebfNaf8f8rTe2ZvZu2epZY9IuL2mjVrhoeHB8nJyfz2228OOafrFXisVpgxA6KjYcgQY5TLatVg5Upo3Njs6ORG+PrC5Mnw2WdGF7s//jCKPM8+awycLU4jMTGRoUOH0qBBA2rUqEHnzp1ZvHixXccePnyY/v37U7t2baKjo3nmmWfY5+Lfgq1WWLjQ6J7z8MNw9CiUKAFffAGzZxstOqT4e+AB2LbNaEwKxhBwd99ttOb66y9TQxMRKXQWi4X7b7ufbzt9y/GXjzOq9Sga3NYAgLOXz/LVlq/o8EMHwv4dxkPfPMT7v73PqiOruJJ2xeTIRUQcKywsjLp16wKOG4fHdQo8Fy/Cl19C7drQqRPs3Gm0gf/Xv2DTJrjnHrMjlJthsRjfhn7/HWrWNL45f/ml0Zbx6aeNrngan8d0AwYMYPbs2bzwwguMHTuWiIgIBgwYwPLly/M87ty5czz22GMcO3aMYcOG8cknnxAfH0/Pnj05efKkg6IvPEePGvXIu++G5s1h9Wpjfdu2sGUL9O+vLjrupnRpmD4dfvgBbr/dmBr1v/+FO+4win8zZhg9UiVvjioif/PNN7Ro0YLq1avTtGlTvvzySzIyMgrzUkTcQqh/KP3q9GPFUys49OIhPm/5OY3CG+Fp8SQlPYUlB5fw5tI3uf+r+wn+KJgGXzXg5QUvM3n7ZHad2UVaRprZlyAiUqRs4/DMnz/fIedz3k6yVqsxYuXy5cactL/+ComJWdvbtIH33jNa8kjxERsLGzbA6NEwdCicPg1ff23cIiKM4t5DDxlNJgIDzY7WrSxfvpxVq1YxcuRImjVrBkC9evU4cuQIH330EQ0bNsz12AkTJpCQkMDUqVMpW7YsAFFRUTz00EOMHj2ad9991yHXcKMuXDBelsuWGbNjrV2bfXvDhvDuu8a9uC+LBbp1g/btjVZcn30Gx44Z3femTYOSJaFJE2PWrfvvN36X8PY2O2rnMmDAAHbu3MnAgQOpWLEi06dPZ8CAAYwZMybPHGMrIoeFhTFs2DA8PT0ZPXo0PXv2ZMaMGZQrVy5z31GjRjFixAj69u1LvXr12Lx5M5999hnx8fEMHDjQEZcpUizdFnwb/4z9J/+M/SfxyfEsPriYhfsXsvSvpew+t5sr6VdYeWQlK4+szDzG19OXu8vcTbUy1bgr7C7uDLuTO0LvoHJoZcL8w7Do1xIRcXEtW7bknXfeYffu3Rw8eJDKtoGZioh5BR6rFZKS4MwZ40v8sWPGbFh798KuXbB1K5w9m/0YX19jwIPnnjO68Ejx5OUFzz9vTKP+zTfGz+A7dxqDWnz8sXHz8ICqVY3WPnfeafxMXrGiMWVRmTIQGmo8jhSahQsXEhQUxEMPPZS5zmKx0KlTJ9566y327dtHREREjscuWrSI+vXrZxZ3AEJDQ2ncuDELFy40tcCTlgbx8XDunJGOTpww0tHBg0Y62rkz5242pUoZ6ah/f2MwZREbf38YONBolPjTTzBxolEYTEgwWvLMmGHs5+trtAKLjDTq15UqGWmsbFkjjZUqZYw37y7fbxxRRL5w4QJjxoyhR48evPDCCwDExsaSlJTE+PHj6dmzZ7ZikIjcmGC/YDpX60znap0BOHnpJKuPrGbVkVVsPLGRjSc2knAlgSvpV9h8cjObT26+7jECvAO4Lfg2KpasSIWSFSgXUI5ygeUoE1CGMiXKEFYijDD/MEL9QwnyCVIxSEScUkxMDGFhYZw7d4758+fTr1+/Ij1f0X4DTk01ijF//GG0TU9ONlrhXLpkfNJNTc3/MYKDoVkzo+9Du3bGJ15xD/7+0KePMRbP9u0wZYox4MnGjZCRAX/+adxyExBgDIISGGg8lr8/+PgYN29vowDk6WkUi2z3FkvONxvbcm4fIpzhw0VoKAwaBIX8JWXv3r1ERETg4ZG9Z2dkZCQAe/bsybHAk5yczOHDhzObJ1577Jw5czh37hxhYWGFGu+1Bg6EpUuNNJSUlJWKLl+273iLxagnNm4MrVpBo0ZqfSF58/aGxx4zbqdPGzOqLVpkvA5PnjT+W9y82bjlxtPTSGEBAcb4Tv7+4OeXlca8vY19rr55eOSezsBxKa1ECXj5ZaMGbw9HFJFXrFjBlStX6NSpU7bjO3XqxJgxY1i8eDE9evQo4JWKSH7KBZajU7VOdKpmvPcyrBkcijvEtlPb2HFmB7vO7uLPs3+y7/w+4pLjAEhMTWTX2V3sOrsr38f3tHgS7BdMSd+SBPkEEegTSKBPIAE+AQT7BvNcneeoU6FOUV6iiEiOPD09ad68Od9//30xKPDs32+Mo2KPEiXgttuMueTuvttoux4bC3fdZXxSFfdlsRhNJGrUgPffN+ai3rjR+Fa0fbvxOjtwAE6dMgo/NomJ2bv1uZPwcHjxxUJ9yLi4OMJzmN8xODg4c3tO4uPjsVqtmftdLSQkJPPYoizwXLpkNASzp6ZcsqTRkuK224wvplWrQlSU8fLToMlyo265xRhO7OmnjQasx44Z3f527YLdu40UduSIsf7q12l6utHCLD7evNhvho8PfP65ffs6ooi8d+9eLBYLd15TdQoPD8fPz4+9e/faeWUicjM8LB5UDq1M5dDKdLirQ7Zt55POcyjuEH/F/cXRhKMcSTjCiUsnOHHxBKcST3Em8QxnLp8hw5r1mS/dms75pPOcTzqf4/nOJZ1j9qOzi/SaRERy06ZNG77//nt2795d5Ocq2gLPXXcZI07u22f85Ojra/wMGRBgtMwJDjZGpixTxvhW5QytH65RqWQlzv7L6CoW4hdiUhCVsrqrhYTYu6n4CgkxxuG56ldewPgmdPq08Q9y/rzxjejiRePbfXKycUtJMX42T0szvkVlZBjHpacb37oyMoz7q282tuXcBnt2lkGgS5WCRx8tkofOq/lzfk2jzWw6HRhoNP5av95oAZFbKgoLM7Y7I+Wi4sNiMbpiVaxoTKl+NavVSF1nzxq17AsXjBR26ZLR8iwpyUhlqalGOrs2lWVkZC3nlMocmdICAozetvZyRBE5Li4Of39/fHx8rtu3ZMmSuZ5DsigXSVEr5V+KUv6liC6f+zibGdYM4pPjOZd0jrjkOC4kXSD+SjwXr1wk4UoCF1MucinlEokpiaRlpNG7Vm8HXoE4grPnIjs2ixvp3r07R44cIdoB4wcX/SAl3boV+SmKkqeHJ2ElirbrSP5BeBrfPAu2yf14ekL58sZNCl1ISEiOX37i/25akNOXK9t6i8WS47G2dSEO+F+vYUPXHgRZucg9WCzGh0B3/SBodhFZY3jkT7lInIGHxYNQ/1BC/UPNDkVM4uy5yI7N4kY8PT0ZNGiQQ86lvk8iYpeIiAj2799/3VTCe/bsAaBq1ao5Hufn50elSpUy97v22FKlShX5+Dsi4vwcUUQOCQkhKSmJlJSU6/ZNSEjI9RwiIiIirkAFnnwkpiQydedUpu6cSmKKSeO5JCbC1KnG7ZoxZfLYJFKomjVrRkJCAkuWLMm2fsaMGVSuXDnXwU8BmjZtyqpVqzhz5kzmuri4OJYuXZo5W47kTblIijtHFJEjIiKwWq3XjbVz6NAhkpOTrxubR66nXCQizsDZc5Edm0WKhOaRzseZy2d45KdHADj4wkECfAJMCOIMPGLEwMGDxsAG+W8SKVQNGzYkNjaWN954g7i4OCpWrMiMGTPYuHEjo0aNytyvV69erFu3LtsgYr1792bWrFk8++yzPPfcc3h5eTF69Gi8vLzo27evGZfjcpSLpLhr1qwZP//8M0uWLKFp06aZ6+0tIk+aNIkzZ85QpkwZIKuI3KZNm8z9HnzwQXx8fJg5cyb33HNP5vrp06fj5eVFkyZNiuDKihflIhFxBs6ei+zYLFIkVOAREbtYLBZGjRrFJ598wqeffkpCQgIRERGMHDky3y9FpUuXZtKkSQwbNoxXX30Vq9VK7dq1+e6777j11lsddAUi4swcUUQODQ2lT58+jBo1iqCgIGJjY9myZQvjx4/n8ccfp7zGcBMREREXpgKPiNgtMDCQwYMHM3jw4Fz3+fbbb3NcHx4ezujRo4sqNBFxcY4qIj/33HMEBgYyefJkxo4dyy233MLzzz/PM888U5SXJyIiIlLkVOARERERp+CIIrLFYuHJJ5/kySefvNEwRURERJySBlkWEREREREREXFxKvCIiIiIiIiIiLg4FXhERERERERERFycxWq1Wgt60F133YXVaiUoKKgoYnIqGdYMEq4kAFDStyQeFhNqYhkZkGDEQMmS4OFhzyaRfAUFBbF06VKzw7hhykWODkK5SIqOK+cj5SJHB6FcJEVHucg1OHsusmOzSJ5uNBfd0CDLHh4eZGRk3MihLsfD4kGIX4jJQXhASM4x5LFJpNhTLnJ0EMpFIjlRLnJ0EMpFIjlRLnJ0EHknHOUjMcMNteARERERERERERHnoYZiIiIiIiIiIiIuTgUeEREREREREREXpwKPiIiIiIiIiIiLU4FHRERERERERMTFqcAjIiIiIiIiIuLiVOAREREREREREXFxKvCIiIiIiIiIiLg4FXhERERERERERFycCjwiIiIiIiIiIi5OBR4RERERERERERenAo+IiIiIiIiIiIvzMjuAwjJo0CCmT5+e6/bff/+dMmXK5LhtxIgRjBw58rr1pUuXZuXKlYUW4804efIk48ePZ8eOHfz5559cvnyZb775htjY2Ov2XblyJZ9//jl//vknAQEBNGvWjIEDB1KyZEm7zvXNN98wadIkjh07Rrly5ejWrRu9e/fGw8Px9UB7rvvSpUt88803rFq1igMHDpCUlESlSpXo3Lkzjz32GD4+PvmeJzIyMsf177zzDo8++mihXY897H2ue/Xqxbp16647vnXr1nz66ad2ncuZnuviQrkoi3KRcpFykXmKey4C98xHykXKRa5GuSg75SLlInvczPNcbAo8/fv3p3v37tnWpaWl0bt3byIjI3NNHFf7+uuvKVGiRObf3t7ehR7njTp06BBz587l7rvvpl69eixZsiTH/dauXcuzzz7LQw89xIsvvsjp06cZPnw4e/bsYfLkyfm+KEaNGsWIESPo27cv9erVY/PmzXz22WfEx8czcODAori0PNlz3cePH+ebb76hQ4cOPPXUU5QoUYI1a9YwfPhw1q1bx6hRo+w6V+vWrXniiSeyratUqVKhXEdB2PtcA4SHhzNs2LBs60JDQ+06j7M918WFcpFBuUi5SLnIXMU9F4F75iPlIuUiV6NclEW5SLnIHjf9PFuLsQULFlirVq1qnTJlSp77/fe//7VWrVrVGh8f76DICi49PT1zeeHChdaqVata16xZc91+Dz/8sLVDhw7Z9v/999+tVatWtc6dOzfPc5w/f9567733Wt97771s6z/55BPr3XffbT1x4sRNXkXB2XPdiYmJ1sTExOuOHTFihLVq1arWP//8M9/zVK1a1Tp06NCbD7gQ2Ptc9+zZ09q+ffsbOoczPtfFmXKRQblIuehazvhcF2fFKRdZre6Zj5SLlIuKA+Ui5SLlopwVxvNcrNsbTp06FX9/f1q3bm12KDfNnuZYp06dYvv27XTo0CHb/vfffz9ly5ZlwYIFeR6/YsUKrly5QqdOnbKt79SpE2lpaSxevPjGgr8J9lx3iRIlslX1be69917AaE7nShzRxNIZn+viTLnIoFykXHQtZ3yui7PilIvAPfORclHRcLbnubhTLlIuAuWinBTG81xsCzynT59mxYoVtGjRgsDAQLuOad26NdWqVaNBgwa8+eabnDt3roijLFx79uwB4M4777xuW9WqVdm7d2+ex+/duxeLxXLd8eHh4fj5+eV7vLNZs2YNFouFiIgIu/afOXMmNWrU4N5776VLly7MmzeviCO8eQcPHqROnTrcfffdNG/enFGjRpGamprvccXtuXZmykXZKRflT7nIdZ9rZ+aOuQiUj66mXJS74vQ8OzvlIuUi5aLcFcbzXGzG4LnWjBkzSE9P55FHHsl330qVKvHyyy9TrVo1vL292bRpE+PHj2f16tVMmzaN4OBgB0R88+Li4gByjDc4OJidO3fme7y/v3+OA16VLFky8/FdwbZt2/j222/p0KEDFSpUyHf/du3a0bBhQ8qXL8/p06f5/vvveemllzhz5sx1fT6dRe3atWndujVVqlTh8uXLLFq0iP/+97/s2LGDL774Is9ji9Nz7eyUi7JTLsqbclEWV3uunZ075iJQPrJRLlIuchbKRcpFykW5K4znudgWeKZNm8btt99OnTp18t23Y8eO2f6+7777iIqK4umnn2bSpEn079+/iKIsGhaLpUDrb/Zxnc2hQ4fo168fVapU4a233rLrmOHDh2f7u2XLlvTq1YvPPvuMbt264efnVxSh3pQXX3wx29+NGzemdOnSjBkzhg0bNhATE3PDj+0qz7UrUC6yf/3NPq6zUS5SLnIm7pyLwL3zkXKRcpEzUS5SLlIuKtpcVCy7aG3YsIGDBw/SuXPnG36M+++/nzJlyrBly5bCC6yIhYSEAORY2YuPj8+3yh0SEkJSUhIpKSnXbUtISHCJKvmRI0d4/PHHKVmyJF9//bXdTT+v5eHhQfv27bl8+XJmk0pXYPuPML/XbXF4rl2BclHcdduUiwpGucj5n2tX4K65CJSPlIs6AspFzkK5SLlIuWhLnvsVxvNcLAs8U6dOxdPT87rBiQrKarU6ZDClwmLrq5dT37w9e/bk2OfzahEREVit1uuOP3ToEMnJyfkebzZb4vD19eV///sfYWFhN/V4GRkZgGMG1Cos9sbs6s+1q1AuUi5SLlIucgbumovAvfORcpFykbNRLlIuUi4q+lzkOv8qdrp8+TLz58+nQYMGlC1b9oYf5/fff+fs2bPUrFmzEKMrWuXKlaN69erMnj0780UEsHr1ak6dOkXz5s3zPP7BBx/Ex8eHmTNnZls/ffp0vLy8aNKkSZHEXRiOHTvGE088gYeHBxMnTryp5x6MN+Hs2bMJCAhw6oR5Ldtzl9/r1pWfa1ehXKRcpFykXOQM3DkXgfvmI+Uig3KR81AuUi5SLnJMLip2Y/DMmzePy5cv8/DDD+e4vVevXqxbt47du3dnruvYsSMdO3akcuXKeHl5sXnzZiZMmMDtt99Ojx49HBV6vubPnw/A9u3bAVi/fj0XLlzA39+fhg0bAjBw4EB69+7Nyy+/TLdu3Th16hTDhw+nZs2atGzZMvOx1q5dy+OPP86AAQN4/vnnAQgNDaVPnz6MGjWKoKAgYmNj2bJlC+PHj+fxxx+nfPnyDr5iQ37Xfe7cOZ544gnOnTvHBx98wKlTpzh16lTm8bfddhulSpUCcr7uCRMmcPDgQerVq0eZMmU4e/Ys33//PRs3bmTw4MH4+vo6+Irzv+YNGzYwbtw4mjdvToUKFbh8+TKLFy9m2rRptGzZktq1a2c+lis918WJcpFykXKRcpEzKM65CNwzHykXKRe5IuUi5SLlIsfkomJX4Jk2bRqhoaEFqmJWqVKFyZMnc/r0adLS0ihXrhxdunShf//+lCxZsgijLZgXXngh298jRowAoEKFCixZsgQwBh8bM2YMI0aM4NlnnyUgIICmTZvyr3/9C09Pz3zP8dxzzxEYGMjkyZMZO3Yst9xyC88//zzPPPNM4V+QnfK77n379nHkyBEAXn755euO//DDD/Ps61u5cmUWL17MokWLuHjxIv7+/txzzz2MHj3atGp4ftdcpkwZAP773/9y4cIFPDw8qFy5MoMGDaJXr152ncMZn+viRLlIuehaykU5c8bnujgpzrkI3DMfKRcpF7ki5SLlomspF+XsZp9ni9VqtRbgmkRERERERERExMkUuzF4RERERERERETcjQo8IiIiIiIiIiIuTgUeEREREREREREXpwKPiIiIiIiIiIiLU4FHRERERERERMTFqcAjIiIiIiIiIuLiVOAREREREREREXFxKvCIiIiIiIiIiLg4FXhERERERERERFycCjwiIiIiIiIiIi5OBR4RERERERERERenAo+IiIiIiIiIiIvzMjsAERFxvIsXL3LmzBlSU1PNDkVERAqJt7c3ZcqUISgoyOxQRETEBGrBIyLiZtLS0jhw4AAXL140OxQRESlEFy9e5MCBA6SlpZkdioiImMBitVqtZgchIiKOc+TIEc6cOUO1atXw9/c3OxwRESkkly9fZteuXXh7e3P33Xfj5aXG+iIi7kQteERE3ExycjL+/v4q7oiIFDMlSpTAz8+PkydPsnTpUrXkERFxMyrwiIi4mYyMDDw8lP5FRIojLy8vvL292bx5Mzt37jQ7HBERcSB9whcRERERKUa8vLxISUnRWGsiIm5GBR4RERERkWLGYrGgoTZFRNyLCjwiIiL5SElJoXXr1pw5c8Yh5/vzzz/p3r27Q87l6qKjozly5IjZYQDQpEkTVq1aBcCYMWN444037Dru7Nmz9OjRg+joaD766KOiDFEK0T/+8Q+mT59udhgiIiKZVOARERGn0qRJE6pXr8758+ezre/QoQORkZEcPXrU4TFNmTKFmJgYypQpA8CgQYOIjIxk8eLF2fZ7//33iYyMZNq0aQBMmzaNRx99NMfH7NWrF/feey/R0dGZt759+wJw1113ERQUxJIlS4rwqpxTkyZNqFGjBtHR0dSvX5/XXnuNxMTEXPffvHkzlSpVKpRzjxgxgnvuuSfz+WjVqhULFiy4ocfq27cv77//vl37TpkyhdDQUDZt2sSgQYNu6HyuqKDv9REjRhAZGcm2bduyrZ82bRrVqlUjOjqaWrVq0aFDB5YuXZrjOa/e9+rbqVOn8ox1xIgRDBw4MNu68ePH06lTJ3sv125Hjx4lMjJSAySLiEiBqcAjIiJOp0KFCsydOzfz7927d5OcnGxaPFOmTKFDhw7Z1oWHhzNjxozMv9PS0pg/fz633Xab3Y87ePBgNm/enHkbM2ZM5rZ27doxZcqUm47dFY0ZM4bNmzczffp0tm/fzujRo6/b52a//OZ2fKtWrTKfj9dff51//etfnD179qbOlZ/jx49zxx13YLFYivQ8zsje97rVamXmzJmEhITk2GomKiqKzZs3s2HDBh555BFefPFF4uLicjynbd+rb2XLli20axIRETGLCjwiIgLAX3/lfbu6EUV6ev77X/0dLTW1YLF06NAhW/FkxowZdOzYMds+KSkpDBs2jEaNGlG/fn0GDx6c+cUwPj6ePn36UK9ePerUqUOfPn04efJk5rG9evXis88+o3v37kRHR/P0009f14rA5vjx4xw+fJiaNWtmW9+kSRM2bdpEfHw8ACtWrCAyMpLSpUsX7GJzERsby+rVq0lJSSmUx8vPX3F/5XlLTMl6AaRnpOe7f3Ja1gsgNb2AL4C/lS1blgceeIC9e/cCEBkZyaRJk2jevDnNmzfPXHfo0CEALl68yKuvvkq9evVo3Lgxo0aNIiMjAzBabnTv3p0PPviAunXrMmLEiHzP/8ADDxAQEMDhw4cz1y1dupQOHToQExND9+7d+fPPP3M89toWH1u2bKF79+7ExMTQvn171q5dCxitwWbMmMGECROIjo7O7OJVpJzozW7Pex1gw4YNnD59mtdff5158+bl+r7w8PDg4YcfJjk5+Ya67o0bN44HHniA6OhoWrRowerVq/ntt98YO3Ysv/zyC9HR0bRv3x4w8shPP/0EZH99xcTE8NBDD7Fp0yamTZtGw4YNue+++7IVppYtW0bHjh2pVasWDRs2zPZ67NmzJwB16tQhOjqazZs3A/Dzzz/TqlUr6tSpQ+/evTl27FiBr09ERIo3FXhERASAypXzvs2fn7VvXFz++69Zk7X/wYMFiyUqKopLly6xf/9+0tPTmTdvXuaXKpuPP/6YgwcPMmPGDH799VdOnz7NF198ARhTwXfu3JmlS5eydOlSfH19GTJkSLbj58yZw4cffsjq1atJTU3lq6++yjGWPXv2UKlSJby8vLKt9/HxoUmTJpmtD3L7YnqjypYti5eXFwcOHCi0x8xL5c8r53mbvy/rBRCXHJfv/muOZr0ADsYV8AXwtxMnTvDbb79RrVq1zHWLFi3ixx9/ZN68edft/95773Hx4kUWLVrEt99+y8yZM5k6dWrm9m3btlGpUiVWrVpFv3798jy31Wpl2bJlpKamEhERAcCOHTt4/fXXGTJkCGvXrqVbt270798/3yLcqVOn6NOnD/369WPdunX83//9H//85z85f/48H330Ee3ataN3795s3ryZ+vXrF+Sf6MY40Zvdnvc6wPTp02ncuDGtW7cGjAJJTtLS0vjpp58oUaIE4eHhBYrlwIEDTJo0iZ9//pnNmzczYcIEKlSowIMPPkifPn0yW3fNmjUrx+O3bdtGZGQka9eupW3btrz88sts376dhQsX8vHHHzNkyJDM7ob+/v4MGzaMDRs2MHbsWL7//nsWLVoEwHfffQfA+vXr2bx5M9HR0SxatIixY8cycuRIVq9eTe3atXnllVcKdH0iIlL8qcAjIiJOyfbL/sqVK6lSpUq2LhRWq5WffvqJ119/nZCQEAIDA+nTp09msSU0NJQWLVrg7+9PYGAg/fr1Y/369dkev3PnzlSuXBk/Pz9atmzJrl27cowjISGBgICAXGOcOXMmFy9eZP369TRt2rRA1zh06FBiYmIyb5999lm27QEBAW45zfFzzz1HTEwMjz32GHXq1Mkcmwjg2WefJSQkBD8/v2zH2IoDr7zyCoGBgVSsWJGnnnoq25fxW265hV69euHl5XXd8Tbz588nJiaGqKgo+vXrR58+fShZsiQAP/74I926daNmzZp4enrSqVMnvL292bJlS57XM3PmTB588EEaNmyIh4cH999/P9WrV2f58uU3+C9UvOT1XgdISkpi/vz5tGvXDm9vb1q0aHFdN62tW7cSExPD/fffz9y5c/niiy8ICgrK8Xy2fW032/vW09OTlJQU9u/fT2pqKhUrVixQl8uKFSvy8MMP4+npSevWrTlx4gTPPfccPj4+NGjQAB8fn8zWYLGxsURGRuLh4cFdd91FmzZtWLduXa6P/cMPP/Dss89yxx134OXlRd++fdm1a5da8YiISDZe+e8iIiLuIL8f3v8eXxiAkJD89y9XLmu5cuWCx9OhQwd69uzJ0aNHrxv/5vz58yQlJdG5c+fMdVarNbM7TlJSEh9++CErVqzI7EKVmJhIeno6np6ef19P1gX5+/tz+fLlHOMIDg7OdZDfmJgYzp8/z6hRo2jUqFGuRYPcvPnmm3Tp0iXX7YmJibl+SS1sB1/I+wktUyLr3yvELyTf/csFZr0AKocU7AXwxRdf5NqSpXz58jmuv3DhAqmpqdx6662Z62699dZsg+eWu/pFmYuWLVsyfPhwwBjstm/fvgQFBdG9e3eOHz/OjBkzMltYAKSmpnL69Ok8H/P48ePMnz8/28C/aWlpxMbG5htPkXCyN3te73WAhQsX4uXlxYMPPggY41M99dRTnD9/nlKlSgFQs2ZNvv/+e7vOl9u+t99+O6+//jojRoxg3759NGjQgEGDBtk9Pk9YWFjmsi0XXN1l09fXNzOXbN26leHDh7N3715SU1NJSUmhZcuWuT728ePH+eCDDxg2bFjmOqvVyqlTp6hQoYJd8YmISPGnAo+IiABQkN4Mnp4F29/bu6DRGIOvVqxYkeXLl183G1FoaCh+fn7MnTs3xy9fX331FQcPHuTHH3+kTJky7Nq1i44dO2K1WgscR2RkJEeOHCEtLe26bloA7du354svvuCbb74p8GPn5dSpU6SmplKlSpVCfdzchIeE272vp4dngfb39ryBF0AuchuIODQ0FG9vb44fP57ZperEiRPZXh8FHcS4YsWKPPDAAyxdupTu3btTvnx5+vbtm2/3rmuVL1+eDh06MHTo0AIdV2Sc7M2e13sdjO6Ply9fpnHjxoBR2EhNTWXOnDk8/vjjBT5fXtq1a0e7du24dOkSgwcPZvjw4Xz88ceFPgD2K6+8Qs+ePRk/fjy+vr68//77XLhwAcj5dWp77eXUfU1ERMRGXbRERMRpvf/++0ycOJESJUpkW+/h4UGXLl344IMPOHfuHGAURFasWAEYLV98fX0pWbIkcXFxjBw58oZjKFeuHLfffvt1UzPb9OrVi6+//po6derkuN1qtXLlypVsN3usW7eOevXq4ePjc8OxuxNPT09atmzJp59+yqVLlzh27Bhff/31TX0hPnnyJL///ntmwahLly788MMPbN26FavVyuXLl1m2bBmXLl3K83Hat2/P0qVLWbFiBenp6Vy5coW1a9dmG/jb3eX2Xj916hSrV69mzJgxzJgxgxkzZjBz5kyeeeaZbIMzF4YDBw5kDmzu4+ODr69vZou/sLAwjh07ltlK8GYlJiYSHByMr68v27ZtY86cOZnbSpUqhYeHR7ZBort37864ceMyBxy/ePEiv/zyS6HEIiIixYda8IiIiNPKa/yLf/3rX3zxxRd07dqVCxcuULZsWR599FEeeOABnnjiCQYOHEi9evW45ZZbeOqppzIHML0R3bt3Z+bMmdSqVeu6bSEhIdx33325Hrt582Zq1KiRbd2OHTsAGDJkCB988EHm+sqVKzNt2jQAZs+eTffu3W84Znf01ltv8d5779G0aVN8fX3p0qULDz/8cIEe45dffmHx4sWAMQZSkyZNGDBgAAD33nsv7733HkOGDOHQoUP4+flRq1YtYmJi8nzM8uXLM2rUKD7++GNeeeUVPDw8qFGjBu+8884NXWdxlNt7febMmVSrVo0GDRpkW28rrO7Zs6fA59qyZQvR0dHZ1k2cOBEfHx/+85//sH//fry9vYmOjs4cnL1ly5bMmjWL2NhYKlasmONU7QXx9ttvM2zYMIYMGULdunVp1aoVCQkJgNFltG/fvjz66KOkpaUxfvx4mjVrRmJiIi+//DLHjh0jKCiI+vXr06pVq5uKQ0REiheL9Ubaq4uIiMvavXs3YHQ9EvukpKTQsWNH/ve//3HLLbcU+fl2797N4MGDmTJlSpGfS0SKl927d3P69Gl+++03GjZseF1xTEREii+14BEREcmHj49PjtNyF5XIyEgVd0RERESkQDQGj4iIiIiIiIiIi1OBR0RERERERETExanAIyLiZjw8PAptJhgREXEuaWlpyvEiIm5KBR4RETfj5+dHUlISSUlJZociIiKF6PLlyyQnJ5OSkmJ2KCIiYgINsiwi4mbKly/P+fPn2b17N/7+/maHIyIihSQpKYn09HTOnz+P1WrFYrGYHZKIiDiQCjwiIm7Gy8uLKlWqsGfPHg4fPoyXlxdeXvrvQETE1aWlpREXF8fZs2fx8fEhKCjI7JBERMSBLFar1Wp2ECIi4ngpKSksXryYP/74Q835RUSKEV9fX2rWrEnjxo1VwBcRcSMq8IiIuLGUlBQOHjzI5cuX0X8HIiKuz2KxEBgYSOXKlVXcERFxMyrwiIiIiIiIiIi4OM2iJSIiIiIiIiLi4lTgERERERERERFxcSrwiIiIiIiIiIi4uP8HzFZ8DRLGsFcAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_trial = np.linspace(6, 15, 100)\n", "\n", "plt.figure(figsize=(20,5))\n", "ax1 = plt.subplot(141)\n", "ax1.set_title('Analytical Posterior \\n(up to normalizing constant)', y=1.04)\n", "posterior, prior,mu_post,sigma_post = calc_posterior_analytical(data, mu_trial, sigma, mu_prior, sigma_prior)\n", "\n", "ax1.plot(mu_trial, posterior,c='r')\n", "\n", "# plot prior,mle, and posterior on x-axis\n", "MLE_opt = data.sum()/len(data) #MLE estimate is the mean\n", "\n", "ax1.axvline(MLE_opt,c='b',linestyle='--',label='Mean (MLE)')\n", "ax1.axvline(mu_prior,c='g',linestyle='--',label='Prior Belief')\n", "ax1.axvline(mu_post,c='r',linestyle='--',label='MAP Estimate')\n", "ax1.axes.get_yaxis().set_ticks([])\n", "\n", "ax2 = plt.subplot(1,4,2)\n", "ax2.set_title('Likelihood', y=1.04)\n", "like = calc_like(mu_trial,sigma,data)\n", "ax2.plot(mu_trial,like,c='b')\n", "ax2.axvline(MLE_opt,c='b',linestyle='--',label='Mean (MLE)')\n", "ax2.axvline(mu_prior,c='g',linestyle='--',label='Prior Belief')\n", "ax2.axvline(mu_post,c='r',linestyle='--',label='MAP Estimate')\n", "\n", "\n", "ax3 = plt.subplot(1,4,3)\n", "ax3.set_title('Prior', y=1.04)\n", "ax3.plot(mu_trial,prior,c='g',label='Prior')\n", "ax3.axvline(MLE_opt,c='b',linestyle='--',label='Mean (MLE)')\n", "ax3.axvline(mu_prior,c='g',linestyle='--',label='Prior Belief')\n", "ax3.axvline(mu_post,c='r',linestyle='--',label='MAP Estimate')\n", "\n", "# sanity check: plot ln(like) + ln(prior) and check that map estimate is at max\n", "\n", "ax4 = plt.subplot(1,4,4)\n", "ax4.set_title('log(Likelihood $\\\\times$ Prior)', y=1.04)\n", "like = calc_like(mu_trial,sigma,data)\n", "ax4.plot(mu_trial,(np.log(like)+np.log(prior)),c='k')\n", "ax4.axvline(MLE_opt,c='b',linestyle='--',label='Mean (MLE)')\n", "ax4.axvline(mu_prior,c='g',linestyle='--',label='Prior Belief')\n", "ax4.axvline(mu_post,c='r',linestyle='--',label='MAP Estimate')\n", "\n", "ax2.legend(loc='lower right', bbox_to_anchor=(1.9, -.25),\n", " ncol=4, fancybox=True, shadow=True,fontsize=12)\n", "\n", "\n", "sbn.despine()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" } }, "nbformat": 4, "nbformat_minor": 4 }