{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multivariate Gaussians\n", "\n", "Modeling Uncertainty in Multiple Dimensions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from __future__ import division, print_function\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "import book_format\n", "book_format.set_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The techniques in the last chapter are very powerful, but they only work with one variable or dimension. They provide no way to represent multidimensional data, such as the position and velocity of a dog in a field. Position and velocity are related to each other, and as we learned in the g-h chapter we should never throw away information. In this chapter we learn how to describe this relationship probabilistically. Through this key insight we will achieve markedly better filter performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distributions\n", "\n", "We've been using Gaussians for a scalar random variable, expressed as $\\mathcal{N}(\\mu, \\sigma^2)$. A more formal term for this is *univariate normal*, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the *univariate normal distribution*.\n", "\n", "What might a *multivariate normal distribution* be? *Multivariate* means multiple variables. Our goal is to be able to represent a normal distribution with multiple dimensions. I don't necessarily mean spatial dimensions - if we track the position, velocity, and acceleration of an aircraft in (x, y, z) that gives us a nine dimensional problem. Consider a two dimensional case. It might be the *x* and *y* coordinates of a robot, it might be the position and velocity of a dog on the x-axis, or milk production and feed rate at a dairy. It doesn't really matter. We can see that for $N$ dimensions, we need $N$ means, which we will arrange in a column matrix (vector) like so:\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n", "$$\n", "\n", "Let's say we believe that $x = 2$ and $y = 17$. We would have\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}2\\\\17\\end{bmatrix} \n", "$$\n", "\n", "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 4, like so. \n", "\n", "$$\\sigma^2 = \\begin{bmatrix}10\\\\4\\end{bmatrix}$$ \n", "\n", "This is incomplete because it does not consider the more general case. In the **Gaussians** chapter we computed the variance in the heights of students. That is a measure of how the heights vary relative to each other. If all students are the same height, then the variance is 0, and if their heights are wildly different, then the variance will be large. \n", "\n", "There is also a relationship between height and weight. In general, a taller person weighs more than a shorter person. Height and weight are *correlated*. We want a way to express not only what we think the variance is in the height and the weight, but also the degree to which they are correlated. In other words, we want to know how weight varies compared to the heights. We call that the *covariance*. \n", "\n", "Before we can understand multivariate normal distributions we need to understand the mathematics behind correlations and covariances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation and Covariance\n", "\n", "*Covariance* describes how much two variables vary together. Covariance is short for *correlated variances*. In other words, *variance* is a measure for how a population vary amongst themselves, and *covariance* is a measure for how much two variables change in relation to each other. For example, as height increases weight also generally increases. These variables are *correlated*. They are *positively correlated* because as one variable gets larger so does the other. As the outdoor temperature decreases home heating bills increase. These are *inversely correlated* or *negatively correlated* because as one variable gets larger the other variable lowers. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are *uncorrelated* or *independent*- each can change independent of the other.\n", "\n", "Correlation allows prediction. If you are significantly taller than me I can predict that you also weigh more than me. As winter comes I predict that I will be spending more to heat my house. If my dog wags his tail more I don't conclude that tea prices will be changing.\n", "\n", "For example, here is a plot of height and weight of students on the school's track team. If a student is 68 inches tall I can predict they weigh roughly 160 pounds. Since the correlation is not perfect neither is my prediction. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.gaussian_internal import plot_correlated_data\n", "\n", "height = [60, 62, 63, 65, 65.1, 68, 69, 70, 72, 74]\n", "weight = [95, 120, 127, 119, 151, 143, 173, 171, 180, 210]\n", "plot_correlated_data(height, weight, 'Height (in)', 'Weight (lbs)', False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this book we only consider *linear correlation*. We assume that the relationship between variables is linear. That is, a straight line is a good fit for the data. I've fit a straight line through the data in the above chart. The concept of *nonlinear correlation* exists, but we will not be using it.\n", "\n", "The equation for the covariance between $X$ and $Y$ is\n", "\n", "$$ COV(X, Y) = \\sigma_{xy} = \\mathbb E\\big[(X-\\mu_x)(Y-\\mu_y)\\big]$$\n", "\n", "Where $\\mathbb E[X]$ is the *expected value* of X, defined as\n", "\n", "$$\\mathbb E[X] = \\begin{cases} \\sum_{i=1}^n p_ix_i & \\mbox{discrete}\\\\ \\int_{-\\infty}^\\infty f(x)\\, x & \\mbox{continuous}\\end{cases}$$\n", "\n", "We assume each data point is equally likely, so the probability of each is $\\frac{1}{N}$, giving\n", "\n", "$$\\mathbb E[X] = \\frac{1}{N}\\sum_{i=1}^n x_i$$\n", "\n", "for the discrete case we will be considering.\n", "\n", "Compare the covariance equation to the equation for the variance. As you can see they are very similar:\n", "\n", "$$\\begin{aligned}VAR(X) = \\sigma_x^2 &= \\mathbb E[(X - \\mu)^2]\\\\\n", "COV(X, Y) = \\sigma_{xy} &= \\mathbb E\\big[(X-\\mu_x)(Y-\\mu_y)\\big]\\end{aligned}$$\n", "\n", "In particular, if you compute $COV(X, X)$ you get the equation for $VAR(X)$, which supports my statement that the variance computes how a random variable varies amongst itself." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use a *covariance matrix* to denote covariances of a multivariate normal distribution, and it looks like this:\n", "$$\n", "\\Sigma = \\begin{bmatrix}\n", " \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n", " \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n", " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n", " \\end{bmatrix}\n", "$$\n", "\n", "The diagonal contains the variance for each variable, and the off-diagonal elements contain the covariance between the $i^{th}$ and $j^{th}$ variables. So $\\sigma_3^2$ is the variance of the third variable, and $\\sigma_{13}$ is the covariance between the first and third variables.\n", "\n", "A covariance of 0 indicates no correlation. If the variance for $x$ is 10, the variance for $y$ is 4, and there is no linear correlation between $x$ and $y$, then we would write\n", "\n", "$$\\Sigma = \\begin{bmatrix}10&0\\\\0&4\\end{bmatrix}$$\n", "\n", "If there was a small amount of positive correlation between $x$ and $y$ we might have\n", "\n", "$$\\Sigma = \\begin{bmatrix}10&1.2\\\\1.2&4\\end{bmatrix}$$\n", "\n", "where 1.2 is the covariance between $x$ and $y$. I say the correlation is \"small\" because the covariance of 1.2 is small relative to the variances of 10. \n", "\n", "If there was a large amount of negative correlation between between $x$ and $y$ we might have\n", "$$\\Sigma = \\begin{bmatrix}10&-9.7\\\\-9.7&4\\end{bmatrix}$$\n", "\n", "The covariance matrix is symmetric. After all, the covariance between $x$ and $y$ is always equal to the covariance between $y$ and $x$. That is, $\\sigma_{xy}=\\sigma_{yx}$ for any $x$ and $y$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I fear I might be losing you, so let's work an example. In the **Gaussians** chapter we had a class of students with heights H=[1.8, 2.0, 1.7, 1.9, 1.6] meters. We computed:\n", "\n", "$$\\begin{aligned}\n", "\\mathit{VAR}(H) &= E[(H - \\mu_H)^2] \\\\\n", "&= \\frac{1}{N}\\sum_{i=1}^n (H_i - \\mu_H)^2 \\\\\n", "&= \\frac{1}{5}\\left[(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2\\right] \\\\\n", "&= 0.02\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Easy, right? If we weigh the students we might find their weights to be W = [70.1, 91.2, 59.5, 93.2, 53.5]. Can we use the covariance equation to create the covariance matrix? Sure. It will look like:\n", "\n", "$$\\Sigma = \\begin{bmatrix}\\sigma_H^2 & \\sigma_{H,W} \\\\\n", "\\sigma_{W,H} & \\sigma_{W}^2\\end{bmatrix}$$\n", "\n", "We just computed the variance of the height, and it will go in the upper left hand corner of the matrix. The lower right corner contains the variance in weights. Using the same equation we get:\n", "\n", "$$\\begin{aligned}\n", "\\mu_W &= \\frac{1}{5}(70.1 + 91.2 + 59.5 + 93.2 + 53.5) = 73.5 \\\\\n", "\\sigma_W^2 &= \\frac{1}{5}\\left[(70.1-73.5)^2 + (91.2-73.5)^2 + (59.5-73.5)^2 + (93.2-73.5)^2 + (53.5-73.5)^2\\right] \\\\\n", "&= 261.8\n", "\\end{aligned}$$\n", "\n", "Now the covariances. Using the formula above, we compute:\n", "\n", "$$\\begin{aligned}\n", "\\sigma_{H,W} &= \\mathbb E\\big[(H-\\mu_H)(W-\\mu_W)\\big] \\\\\n", "&= \\frac{1}{N}\\sum_{i=1}^n (H_i-\\mu_H)(W_i-\\mu_W) \\\\\n", "&= \\frac{1}{5}[(1.8-1.8)(70.1-73.5) + (2-1.8)(91.2-73.5) + (1.7-1.8)(59.5-73.5)\\, +\\\\\n", "&\\, \\, \\, \\, \\, (1.9-1.8)(93.2-73.5) + (1.6-1.8)(53.5-73.5)] \\\\\n", "&= 2.18\n", "\\end{aligned}$$\n", "\n", "That was tedious, but easy enough. We will never do that again because, of course, NumPy will compute it for you. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.025, 2.727],\n", " [ 2.727, 327.235]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "\n", "W = [70.1, 91.2, 59.5, 93.2, 53.5]\n", "H = [1.8, 2.0, 1.7, 1.9, 1.6]\n", "np.cov(H, W)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That doesn't agree with our calculation! What went wrong? Nothing. NumPy applies a correction for small sample sizes; it uses $\\frac{1}{N-1}$ as the normalization term instead of $\\frac{1}{N}$.\n", "\n", "This is a bit beyond the scope of this book. Briefly, suppose the actual class size is 200 students, and we took a sample of 5 students to perform this computation because we couldn't afford to measure and weigh all 200 students. It is nearly certain that there will be some error in our estimator because the sample is unlikely to perfectly represent the class. As our sample size approaches 200 the error will approach 0. We say there is no *bias* in the latter, and that we have an *unbiased estimator*. In contrast, when we take a small sample there is bias (error is nonzero), and we have a *biased estimator*.\n", "\n", "If the error is zero it makes sense to divide by $N$. I will not prove why, but for biased estimators we use $\\frac{1}{N-1}$ to correct for the small sample size. NumPy does this by default because in practice we are almost always working from data samples from a larger collection. If you want the unbiased estimator, which we computed above, use `bias=1` in the call to `np.cov'." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.02 , 2.182],\n", " [ 2.182, 261.788]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.cov(H, W, bias=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This agrees with our computation. We will not use `bias=1` again in this book since we are using *random variables* which are sampling from the infinite set of positions of the objects we are tracking. Here we are computing the variance and covariance for the entire population, so `bias=1` is correct.\n", "\n", "What does this matrix tell us? It tells us the variance in heights is 0.02 $m^2$ and the variance in weights is 261.788 $kg^2$. Furthermore, it tells us the weights and heights are positively correlated - as heights increase so do the weights.\n", "\n", "Let's create perfectly correlated data. By this I mean that the data perfectly fits on a line - there is no variance from the line." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[6.956, 6.956],\n", " [6.956, 6.956]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = np.linspace(1, 10, 100)\n", "Y = np.linspace(1, 10, 100)\n", "np.cov(X, Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the covariance matrix that the covariance is equal to the variance in x and in y. \n", "\n", "Now let's add some noise to one of the variables so that they are no longer perfectly correlated. I will make $Y$ negative to create a negative correlation." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[ 6.956 -3.084]\n", " [-3.084 1.387]]\n" ] } ], "source": [ "X = np.linspace(1, 10, 100)\n", "Y = -(np.linspace(1, 5, 100) + np.sin(X)*.2)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data no longer forms a straight line. The covariance is $\\sigma_{xy}=-3.08$. It is not close to zero compared to the magnitudes of $\\sigma_x^2$ and $\\sigma_y^2$, and so we know there is still a high degree of correlation. We can verify this by looking at the chart. The data forms nearly a straight line.\n", "\n", "Now I will add random noise to a straight line." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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8GAAwatQojBgRWTTpyy+/hCiKyM3NxaRJkyKOHT16FKdOnQIAVFRUICcnJ3TM7XajsbERAFBSUoKzzjor4tp9+/aFAomqqqoijh0/fhzt7e0AgPLycrhcrtAxj8eD+vpgga6hQ4dizJgxEdc2NDRgYGAAHMfhvPPOizjW0dERiqcZN24chgwZEjrG8zxqamoAAIWFhTj77LMjrj148GBo22zq1KmwWq2hY52dnThyJOhvPHr0aAwfPjzi2j179gAA8vLycM4550QcO3LkCDo7OwEAkydPjih209PTg0OHDgEASktLY1YTampqwPM8nE4nJk+eHHGspaUFHR3Bj/fEiRORn58fOtbf34/9+/cDAIYNG4aysrKIa+vr6+HxeGC1WjF16tSIY+3t7Th+/DgAYPz48SgqKgod8/l8qK2tBQAUFRVh/PjxEdc2NjbC7Q6uSJ977rkRW44nT55Ec3MzAKCsrAzDhg0LHRMEAV999RUAwOVyoby8PKLdpqYmdHd3AwAqKyvhcDgABD9Uv177JT6oawcviHDabaieOipiJWzv3r0IBALIyclBRUVkVpvm5macPHkSAHDOOecgLy8vdKyvrw8HDhwAAIwYMQKjRo2KuLaurg5erxc2mw1TpkSusre2tqKtLagYn3322TRHQH6O+Nkb8jsY0fj4QMSqazbOEeePsKClExBk7t8C4PwRFrS2tqbdHDFu3DhduzBmzxEA0N3djaamJgDAWWedhZKSkohrzZgjqqqqmDJwhdPY3odlf/0MT982PeLvanPE4ZY2PLW+Fp8e80DkrHDaraHdgUAggOuf24qjPTzCeyLFgTw7bzR4T3BHyug5gjUGSdIjvjnOih2NrliXSgBlhTbcefnoiHaycY7IZD0CAB577DE8/fTTEec9++yzuPHGG3HVVVeF/paKOYIVXUaGIAjweDxYtmwZHnzwQQDArFmz4HA4sHjxYnzwwQeYPXu24vU8z8esFIiiCL/fHzoud410XK4/0jFBiP3UsLYb3afwdgOBgGy7oijCbrfHHAsEAgm1q3Sv4e1G32u4DOXale5VzgBkbTddno3Wvfr9fvA8L+sfqPZsWNr1+/2yx9Tala7ValcOVhnKXR/eJ4mQf3Ob+4xiNuCLCZz0+XwQBCFisme5V1YZysmItd10GYepmiM+Odof8zc5bJbIVfxsnCNurczDnlYPjvUGYuJSRhdYcWtlXlrOEQB07cKovTfJniMktO7VjDmCZbcqGgHA9kOxXhVK49Dt5fFvr+3FoZOe00ZEsE/SnHjR2OIYAwM4o9j/flcbflDllL3XZM8RLEU6l90wJSRDux0xCQ8gBnBhqQ3fm+JCrj1y/GfjHJHI/J2KOWL37t148sknQ4aKHHPmzMEVV1wh264cRs0RrOgyMoYNG4b9+/ejuro64u9z587F4sWL8fnnn6saGTabTb5Y0umXLHwVIPwauZcQACwWS+iY3GBgbTe6T+Htyk2idrsdoijKtmu1WhXblVaG1NoN/7dSu9H3Gi5DuXale5WbHFjbTZdno3WvdrsdPM/D6/WipqYmYsVc7dmwtCsFeUWj1m74vSq1m6gMtcaLRGglLOrc6JUwh8OBQCCg2q7f70dDQwMcDkdIxiwyFARB93uTjuPQqDkiut2amjOpVauqqhCQW7aPwgLg6knDIv6WjXNEYZ4TT84pxbqjVvyj4UQoa9SV5cW4fjyQZ7coPpvwfgMIyTn8d42cI1jTFLu9PP7P7pPY3tQLXhCR98FWzK4644Of7DmC9V5Z5gipnXCk1WOldqPnCDU5KcGLsbE4SuNw1YZ6NIUMjDNIc+KxroGYY+HnfHK0D/82LehVYOQcoScGSVK4eZ6Pie1qbW0NeUQMNj0iPJ7F5w8AYgBfG52De0tiLpWdI6Lv1e/3Y//+/bq/geFzxMDAAJ566iksW7ZM9v4lbrvtNsyfPx+lpaUoKiqKkYWZeoRedGWX+vGPf4yXX34Zn3/+OS644ILQ3+vr6zF58mQ89dRTWLp0KQDKLiXHnj17KK+yCZCc5Yk3G48cJGNziJaz1jMEgEmlgyO7VDSJBOWaPZ5ZsoMByJoMYtKz0Stn1uxS4eiZx7TeJwsH1d81M0MT6/xNc3MsRmTji1fOe/bswU9/+lN8+OGHiufk5+fj+eefx/z589NOZ9ar2+vq/be//W0AwPvvvx/x93Xr1gEApk+fHnMNcQan0xn6hzAOknMselbCWCAZm0O0nNWCOQGgcmRBRimfySQRRc/s8SzV7lgwYzzKinMxsjAHZcW5WDBjfOj5sfjgpzNyAdN//FcPAhY7s5zl5JRnV1ZbOLAHNLNWXVfDzOQCrIHcNDfHYsS7xCpnv9+P3/zmN+C44Fg5//zzZQ2M66+/Hg0NDRBFEW63G3fccUfaGRjxoOtLNGfOHFx//fX45S9/CUEQMH36dHz22Wd49NFH8c1vfhMzZ840qp9ZQXQAEWEMJOdYkp2Nh2RsDtFyVirUxwE4p9SFvyy8bFAaGImSivGslqYYYPfBT0eUVo5bugZQe0oI7dSw4HLasKS6AiKAzfva4MqxwxfwgZcRjtXCYcO+NoiAZlFKljkx127FgD+g6dZmBqxFOmlujsWId0lNzgcOHMB9992Hv//976pt/OY3v8HChQsTdklKZ3SbSW+++SYWL16Ml19+GXPnzsWLL76Ie++9F3/961+N6B9BEEmCUhpmPkor4HdcNn7Q7mBkA9EGRrJ3Hs0mmSvHEalbuwbQ3usNGRhWLmhYSPCCiJYu5bSu0WjNiTdfMBoTS1wx50Qr9mbAsvtFxGLGuyQIAl555RW4XC5wHIdzzjlH1sC46qqr8MUXX0A8HTf0k5/8JKsNDEBnTIYeKCaDINILqhKdfaS6OFimke7yCu9fMmOozCaZfV++tkZ38DfAVgWcNTYmPEOTzcrh2srSiMJ/qRhX6T6W0wkj3qVjx47hgQcewGuvvaZ63qOPPor7778fubm5utpPVwyt+E0QROYirYRpfTCJzIGUDG1YqiTrIdnKnVL/rpo0Am98esR0V51E7y+Rauxy6CnIFw6LGwzrnCjn1ibFnCRrXOmF3n12WLO5qSGKIt555x0sWrQoVM9CjgsuuAC//e1vKXzgNLSTYSItLS2h9GXRRYiI5EFyZiMRZYJkbA7ZIudUrbqy7t5pyTnZhgpL/yYMzwc44GBHH/POY7xyTvb9aa0cjyxw4JOHr9VsRxRFTF+xBW09Ht19APRnf2KVXzrvCmfLnJFM4n1eJ0+exLJly7B69WrV9pcsWYJf/OIXEYV4sxXayUhjOjo6QinP6OU3DpIzG4kofSRjc8hkORulmGsRriiyVklWk7OSghJdxDIe1Pp38EQfvv+1sbhi4gjVVfZE5WzE/amuHAO4+Cw2P/R4CvKFozf7E+u5rONKL8kwxjN5zjAKPbv4mzdvxqJFi0LVz+WYMGEC7rvvPlx66aWUKlgDMjIIgiCIpGKkYq70e3KK9sZ9rQlnlTFKoQS0s95sbejAtgeuUcxAlQw5G3F/ipmQAIwutOK289hXfOMpyAcY61KWzGxFqTLGBxtK2dzcbjd+9ujjWLFiher1P/rRj/CrX/0KJSXB6n1SnQxCHRrBJjJx4kQK1jIBkrPxkIzNIRPlLIqioYp5NGqKtpbcpNgANTnHo1CyPDO9sQty7SVDzkak91RaOZ41cSjumTUerpwzOxlaslJL3arlUmZE9qdkxpwYYYxn4pxhNrt378ZPfvIT7Nq1S/GcYcOG4fnnn8ett94qK0uSMxtkZJhIfn5+qrswKCA5Gw/J2BwyRc7hq7E+XsDJPl/CiivrB1xN0YZGyKHttCuOkpz1KJR9voCuFelk1K5J1EDo9fhx0u1V7YOcwszybNTqgOgJms53WFVdXQDt7E/JJJk1h1iNRD3KbKbMGWbi9Xrx3HPP4cEHH1Q975ZbbsGTTz6JcePGabZJcmaDjAyCIAgibtxeHjc9vw0HOvqYr1Fa6Y3HdSTe7EMA0NXvw/QVWxR/p88XgNuj7hJhs3Lo8wXiWpFOJOtNoivqbi+Pb7+4AwN+QbUNSWFOxK0n2sDQkhUA2d9av/hK5DusMfez7IYpeOT6qpjfMopEsxVJz0TLSPzvz45iE7lRxcW+ffuwePFibNq0SfEcu92O559/Hj/84Q9htVpN7N3ggUYqQRAEETcr1tXqMjAA+ZXeeFxHWBRtNdzeANzegOzvSP3p8wUUr5cUynjdllirOMuR6Iq61Gc1pPtLpluPlqyeWFeLT5tOMf2W28tj1fo6bK5rN1URj+e5RRtpNgvQ2a9uwPb5AujzncnSZVRMUzYQCATw+9//HosWLUIgoPzOVldX45lnnkFVVZWJvRu8DN58simgv78ffX196O/vT3VXshqSs/GQjM0hE+T87hfHdJ2vtNKrp0q0lHldb/ahPIcV+Q75Fcvo32FRwiWFksVtSY5EqzhrVaxWW1Fn2QGS7i9ZFbz7+/uxqea4qqze+eKY5m+5vTwefucrnP/oRryy8zCaOwfQ1uNBcyd7te9E0PvcIqqWn+7rsS4P+lUMWDlY5J0Jc0ayaGpqwne+8x1wHAebzYaFCxfKGhhPPfUUPB4PRFHE+vXrk2JgDCY5JwKZwiayf//+UGo5SnlmHCRn4yEZm0O6y1kURQz42RUltZVeLUV9w75WiKfP8wcE2K0WzaJ10RTn2cFxXMTqcPTvSHEMWkq4pGjmO6wJuS2pxS5oEe9OCMsOUJ7DircWXgaX0xZ37Ee4MQgADQ0NGPBqr94rIYjAxn1t2N54Ag1t8gagEckF5NDz3JSMtHjQirVJ9zkjEURRxBtvvIFFixahs7NT8bwZM2bgN7/5DS655BLD+pLNck4mZGQQBEEYBGUfCTKy0Amb1RITkCvJh0Xpbevx4pUdTRF/e2VHEyYMz8OEEflobO+Dlg7HB0SA0zYIBEHQ7I/LaQvFByQrEFjvWNGT/z/6d7T6PDTfgYIcu+7YD7eXx4p1tfjbv46FVupz7VbcdMFofHOMCGuC/hOd/T60dKkbtvFmxYr3fdW6JpG4ITn0VEzPdNra2vDwww/jD3/4g+p5Dz/8MB588EG4XC6TekawQEaGiQwbNixUiZMwDpKz8ZCMlUlm3vt0lzPHcchzWENxDXK4nFbsfOjrZ/LSK2QW0lI+Awpa2sET/chzWJHrsGq6n9ht2hquzcrBYrHoMhwSDQROhHh3Qlj7zGREWc4Eh9+0ehsOtEfG6PT5Anht1xFsa3Bgxvgi/E9tZ9xKt5cXNI1JQF8aWSPrVLAYabl2C4a5nCEjsavfp/pOqRmt6T5nsPDee+/h7rvvxuHDhxXPqaqqwvPPP4+rr77axJ6dIRvkbAZkZJhIWVlZqrswKCA5Gw/JWJ5k5703Us7JWgm98fzReG3XEdXj4QaGknwKc+zgACYFMhoW33ZJcRZP/56Wcq3HcEgkgFsiGc8jGa5WHGL7rFUQ72SfFzNXbkGB0xZjYIRzuNOHKyaNxMQSf1zuQxYOcFg5DDBcyLJ7ZEbRSBYjbZjLiW0PXBMaA8vX1sRttGbi3NzV1YVf/vKXePbZZ1XPu+eee7B8+XIMHTrUpJ4pk4lyTgUU+E0QBJEkkhUgaxTSLsLMlVswfcUWzFy5BcvX1iQUJPvQvEpMLJHPGT+xJB8PzasM/b+afHo8fhTl2mICmZPhEBKu7C+trsDEElfM70QbBKzniaIYdwB3Mp+HFP/ASnifRw3JQa7dAquFQ+7pnalVpwOs1WQhMeAX0Nw5gNrWXs3f3drQgbfvuhzzp49TbE8OSe5FeXamc1l2j8x6X1kD9CWjiHXsZTIff/wxzj//fHAch+LiYlkDY/To0XjnnXcgCAJEUcRvf/vbtDAwCHY4Ue/MxIggCOjtjZxwCgoKYLGQXUMQRHYQvfo8c+UWNHfKBxUDQFlxLrY9cI0ZXYtBadVWUlwSWbV1e/mwuABBNv4C0JbP6CG5mFNVGhFfMLuyBGt2Hta96m21cBjhcsrGKET2VzmOQem8O2eV48WtjYouNkrF68L/noznkQxXH9Z+hMviVJ9Pd2YkidICJz75WdB9Tms8yD3D7764Q9OYmVTKJj+z3vYQu64AACAASURBVNd4njXrGM0U+vv78eSTT+LRRx9VPW/BggV4/PHHMWrUKJN6RuhBr25PRgZBEFmLEcGRkmK3aV8reAEhxW7JnEmY/cxHaOvxKF47sjAHOx+6JiUBm1ouGAtmjE9KNh4lmYuiiOkrtjDLJ7yKdnTANwsjC3Ow48GrNb85rGMkPLCZVSlftaEeG/e1oavfBy8vwGHlUJzvwJyqkfAHBLy+64isexjL89CjuKrdYzzj4vInPsCxLuXnqEa44v7wO1+putrddulY/OqmqRF9v+yJLWjpUjYM8h1W7Hp4tqYirnc8JkoiRkOmBnl/8cUX+OlPf4qPP/5Y8ZyCggI8//zz+MEPfkD6YQagV7fPPHM4g6mvrw+lPKuoyPztznSF5Gw86SxjIwM523o8qH72Q3QNRLqz/GlH0IfbquH/IecnrqZAJFPO8aYh1SK6/0r3ojcLU3gV7XiQAri14DiOSc5Sv1hcbJZUV8gaAAOCiIEuj6bRxPI8tPqxYl0t7FaL5nugd1yIoghevUi4KheUWFFfX880njkgZkdIKQGAREGOXbEWSkTbScwKxoJSgD7LOq+ePqRybvb7/Vi9ejXuvfde1fNuvPFGrFq1ChMnTjSpZ8knnb+B6QQZGSbi8Xjg9/tVq1ESiUNyNp50lbGRgZxuL4/qZz+KMTCAYLDy/jY3Jo8sQCsHzYBNVkMoWXLWm4ZUi3gNOT3B1InUFpDzyVe7Nz1yZlHKRSDhughaz0OrH2/uPgpBFFXfg3jGhd4CiOGUFVpxy+RceDzB3YMPGzpUz98adTzZhoGe8ZjM3QRph86IhRCz5+b9+/fj3nvvxXvvvad63u9+9zv8+Mc/ht2uHVOTCaTrNzDdICPDRKxWK6U8MwGSs/Gkq4xZVpnjdQlataEeXQPKhcREAN0ePyaWuFSzDOkxhJIl52QqZ4kYcnqyMGnVFrBwQGGOHT0ev6qsWZQ5VjmzKuWb9yVeF0HteTD1Q6YD0e9BvONCK9tUOBYuWCfj5gtG44bxImwiD6vVGrfhm8x0wVrj8c5Z5bLpllmMASWjxOiMVkbPzYIg4JVXXsGiRYswMKDstnb11Vfjueeew3nnnWdIP1JNun4D0w0yMkxk6tSpqe7CoIDkbDzpKmOjXIIAYPO+Ns1zBAF4a+FleGZjg6Lv9fK1NcyGUDLlnCzlLBFDjrV4HIsCWlKQg033XYlnNjZg4742dIbFPUgF4XYdOomDHX2ayhyrnFmUcqsF8CdoYWg9j0R2E6Lfg3jGhaSc729za6Ycnj99HJbfGCtfURTjMnCSkS5YQmk8zq4swcJZE3H7H3bpMgZ6PX48vbFB1SgxciEEMGZubm5uxoMPPojXXntN9bzHHnsMS5YsQW5ubtL7kG6k6zcw3SAjgyCIrCDZLkExbTMojlZL0CdcrTiakYaQGslSzhLtP0vxONYV9oIcO5ZUV2B74wm0dAUg4kzcg1JAcaLKnJZSPqdqJDbVahukSsjVqdDbDy3C34N4xoWknLNketpc147lNwb/O3pnye3xKV6nZODEW+VcCWk8LqmuwFPr6/BBXTve39uGv3zWjD6ZDFrR4yc8wL+9xxOzgxRtlKTq/deDKIp4++23cffdd6OtTXksX3jhhfjd736Hyy67zMTeEZkEGRkEQWQFRgZysq4cz6kaGXNdOEYaQlokQzkzs/+sK+zSyrAeXTsRZY5FKVcr+KeG1cJh/vRxss8jWqZq/bBwnKy7lET4exDvuHA5bej1aNfz8PgDoUxh33phO9Puh5bhG2+VcyWUXJiUkMaPUoB/9LmSUfLI9VUpe/+1OHHiBB555BG8+OKLqufdf//9+PnPf47CwkKTekZkMmRkEASRNSTTX1tP2wAwJNemufpsdkabaBJVzuLpf/TvsMZJsK6wa8VuKBGvMseilCv1XQ0LF3QtCjd8tGSl1A9fQMAbnx5hfg/0jIvwFM7Hu7XT2J5w+9De68WLWxtVDQwOwIgCJxw2+RorSiTjXYknyQAfELFqfR3TdeFGbSrf/2g2bdqEe+65B/X1ykUHy8vL8bvf/Q5z5841pU9EdkFGhom0t7eHAoVKSkpS3Z2sheRsPOkq42T6a7O2DQBDcu3YcO+VTEqRHkPISDnHq8iw9F9JOV44q5zZz51FmWfZWVEiXJnTK2eX0xbasdi0rxX+gBjKKhVtAITHi9gtAC/EBmXLjU/WAGE546DX48fuplNxvQdaBoaeFX+JO/74KXq9vOoOhghg3rkjsfyG+HzdE1n9j8dQtVk5bK5rZ75OMmqNXAgB1Mdyb28vlv3yMTy76inVNn784x/jsccew4gRIxLqSzaTrt/AdIOMDBM5fvx4KK8yDUrjIDkbT7rKONn+2ka0rccQSkc5s2TkUVKO3/3iGLoH/DHKpiAGUwBHx0lorbDHGwAdrczplXO8BoDkNsQyhp5SWCVXiimJTotqtXCoKC1At8cPQUBS3oN40wrXt/ViREGO5nmba9ux/Ab2dpNREyceQ9XCAbMnl+D9GvbYG8moNXIhBIgdy7t27cI999yD3bt3K15jySvClO8sxvb/8zAKcrIjxazRpOPcnI6QkUEQRFaRbH/t6LYfub4qobaNNITMQK3/d84qxx1//BQNbbEF9AQRmimA13xyOGI3IHRMRdZ6A6CTocyxZAh65PqqiNoS0r/VxqeUFetv/zoGt1c5/350TImS0dN6+l7fWnhZUpTHeF3TAMDG8KrordWSjFSweg1VafwsvW4yNte1M183a1JwV8Do99/r9WLNmjVYvXq16nl5lVeieNYdsBUGFWQ3BzyzsSHlQedEdsGJLOUm40Bv6fHBQHd3d2gCLSoqSnV3shaSs/EMNhkbWUVcTanKBDlL/ZOUPjkDQw+SEvfqDy/Fi1sbNWWupGxaOGDC8HxcOmEYPmzogI8X0O8LBiHnOW1w2iyh9gKevgg5aym6M1duQXOnco0Aq4XDcJcz1OclcyZpKvluL4+bVm/DgfY+JjmNLMzBzoeuAcdxWL62RtUFZ8GM8SHlMV7jWBRFTF+xBW092nEY0VgtHG6fPk6z0nlZcS62PXANU5t67jmRtoCgYeBy2iKMgXyHFY/+fR+zgTuxJB/v3j0T+Q6rasxSPNTU1OCnP/0pPvjgA8VzHA4HxnxzEfzlV4GzyNd20CP/aFIRrJ5KMmFuNgK9uj0ZGQRBEFGEfzDVlNiJJa6Ei2dlC8vX1uBPO5p0ZXlSIlhoz4YeD88kc7eXV10Zdnt53Lx6GxqjamaEtwcAq9bXYXNd+xmjZnIJll43OWZXRa+ybbVwKC10Yk7VSFnD1O3lmdLBhiMphKIo4oon/6Fq9Iwekotrq0rjNpIlI/vVTw4jEMdWxuRSF/561+WY+cQH6BqQz0il1zDQMvT0KMws73i+wyrrktbv9aN7QD3eRCLfYYUrx57wIgXP83j55ZexaNEiqKlwc+fOxTPPPIPJkyczjdtww5UFIxdfiPSEjAyCIIg4UPpg+jUy9ehRjLIZLaUvWXAA7rhMWeZyK6pqK9UcgHNKXDh4ok827avNwuHWS8bgoXmVIcUp3nuVM5Li2QGycEBFaQF6vTx8vIATbq/qarrNwiEgiBGKMKuRHG+wdzi7fvZ1lBbmoK3Hg+pnP4pxm9NrsBulMGsZqkqGSGGOHXlOK1q7Pbrd9ljv+dChQ7j//vvx1ltvqZ63atUq3HPPPXA4HDHHzDbMyNDIPvTq9qTxEwQx6JE+mGt2NqG5cwBtPR40dw5gzc4mvLn7qGbxrHTCoHUjzd9kDZ5N1KFCit1YvrYGbm/sqricUqkWSyACaGh3K9aV4AURr+06gm+9sD30e7MrS2GJ40bCYzYkVm2ox36dBobNwqGutRfNnQNo71U3MKR7kAu2j+6LHPEGe0vk2i14cWsj3F4epYU52PbgNfi3y8ajrDgXIwtzUFaciwUzxutSSo1IBS3Fymx74BrsfOgabHvgGiy7YQpTpe4ejx9zqkox3OVk/j1BBBra3Fixrlb2uCiK+POf/4whQ4aA4zhMmDBB1sC4/PLL8dlnn0EUg/EsS5YskTUwAPVxqzezFUtcEkGQkWEiPp8v9A9hHCRn48k2Gat9MNWKmgFnglWNgFXObi+P5WtrMHPlFkxfsQUzV25RVMKNgOM4WBm/JqVFOfi3y8bDGo+WfpqAIGLNzqYIxV+JRNLchhOuOC2trsDEElfchka4Ybr5dOpbFqxcMGOUPxBrNMQDi5GcSLA3AAz4hdCzOtXbDwcn4KHrzsHH/3m1rDLPyuzKUkWDlUNiqWD1GqqCGMyM5bDpV6ne3H00NIZbW1vx7//+7+A4DhaLBbfffju6u7tjrim67H9h3H1/xbXPbMX6D7bioosuCh1TmzOUxm08yRBYKpdnM9n2DTQK2ssykdra2lDKs2nTpqW6O1kLydl4sk3GCWXN0VgxTSQgkkXOWll2pMxCRgdmFuXY0QL1OAUOwNwpI4OZlRBfVWwJpUxOMb8ZZ5pbud+TMjrJZQjqcHuZ4xXCDVM9BtCkUpdmvQm9qGV0SpaBJj2rn725CxxE/PO4D5w1/tgEt5dHv09ZDnYrhztnlSfcbwnWSvfVU0rx6ieHmce0KIroafgUZWP+A90dxxXPsw8fi6HX3omcsedF/F0ulbHanJGszFas8sjmYPBs+wYaBRkZBEEMahJRpJRcDMwMiFTbhWloc+OCX26CCMBh5VCc74gIPk6mEtDt0d41Oaf0zGqpWr2Awhy7bD2NaAQx6Dq1bm+rqoxnV5ZqZjZiIVxxik5FqyfTULhhqscA6hrwQRDVz7dwQI7Nin6/cgpcpb5Ew3Ec7AnsOIUjiMCmxn4IIk4/12D/5FLOqo1LlhgWXhDx0tbGpMVKsbpn3X/dZOw8eFLVvUzwuNG17XX0/nOtansFF92AopnfhzXHpXhOdCpjFpKR4tsIdzUiOyEjw0SKiopCFSIJ4yA5G082yZjpg2nhIIgiU/GsZOXvB4Jy5nkeNpvy+Vq7MJK714AgYqDLgz/tCBbFy3NaERCQFANIFEXNVfw8hxVvLbyMqaL3j6+agPl//BT729yahkZAEEMBwEoyXjJnEv78yWFN1zctlBQntSJr0UQbpnrqfIiittI/akguRFFEf5e2kcHihz+7KjkGGgDI2fLSLseK9/bBbrNqGuaSUa1GPMo3EH89FkmOcmPa7fXjxIE9OLXpJfg7mhR/21E0AlO/cy9ODT8Xoo7IpegdAz1zcyJGgNGVy9OdbPoGGglllyIIYtDS6/Hj6Y0N+Os/jyoWP7NwwPe/NhZ2q4XJxSAZ+ftZd0ISqV0Q3a94MsKEKzcstSNunz5O0ZiRnsWZ9KBBF6yGNjcCOj5TSjK+7IktaOmKP/sVy7OTium9+8Ux9Plix5NadimW4Oqy4lxN5W7+jHF4f2+b5pjQk11q5hNbVAspGoVcH1mfI2t2KdZ3TU82pf7+fjz55JN49NFHVX87f+psDLlqPmyuoZr3o0QitS0SgbJLDU4ohS1BEIQKklKxcV8b2ns8qqvbch/MRAu1aSkFej/eyUodm6gBpJbqV+se1NODxtbL0EJOxonU8WAdB2oGg1wq3PDrnt5Qj7/8s1kxkF16PkuqKzTHx3XPfaRp8M2fPo7ZDz+YevZDxRoXRhI+LkVRxJRlG9AvY8BFo/aehReQ1KqfwlqPpaHmS/zkJz/B9u3bFfvEOfIwdM5C5FddBY5LXBdKdQptrbS/RPZBRgZBEIQCelaN8x1W3HLxGN0BkYnm79e7E6JVrVgPiRhAE4bnAxxwMEphS/QeOABFuXb0ePzM9ygnYz31KBxWDkNdDkDkIhQnAKqr3onuYrEqvXLK3ezKEiytnqzZD606I0oo1bgAgKJcG6qnjMS2AyfQ3uNN2C0tmvBxWf6zdZqueXKyDjeOvbyA/tM1RvwKbWk9L6/Xi9WrV2PJkiWqfcmdNAPFV/8Q9iEjVc/TS7rtGGRzkDdxBqqTQRAEoYCenP/F+Q5dqTWlj2yiAZF6U0Mmkk41Gq10vFJNB7kg84Mn+jD97GFYMEM9Pa3cPWjVschzWrFgxpnaClrpb+VkLPnLV45UDqSV8AVE9A7wuG5KKdYvvjKkaCrVUpFS6Saa1tPltOGdu2dG3KtcHQkpeHf94itRPSXo+/7+3jZc99xHWL62BgtnlSumKg0PvtfDi1sb0eORd5nq9fDId9iw48Gv44tHrkW+I7l+6tK4FEURDoZA+fIR+RH3GF0Hp6PXiz5fQNHAAOSfV0NDA775zW+C4zjk5OQoGhhz//fDGP+ff8O4B/4HJTc/nDQDI99hjbu2iNGQgUHIkR6jc5DQ2NgYSnlWXp689HpEJCRn48lUGetJVcuSglHOdajAaYOFQ1wBkaypIQVBCK0cRQebnnR7MeAX2G4yCjnlXBRF9PkCWLWhHq9+cljR3UgQga0NHfj4P6/Gur2tqrs5Pl4IyZblngUBeOT6KqZMTnIyjl7Ftlk4zdX2Pl8Aaz45jB0HT+Ltuy7XLD62akNdUtJ6upy2iHvVyrKklGDg1R9eipe2NibNlYXFgJKMMS8f3/hTInxcFuc7MNClPLbyHRa8c/dM2WBxvRssfj+P3//+97jnnnvg9XoVzzv7vOl4448v4NKLLgAQdGEUk+DCKBG+a5HvsKqOn0ydmzMNkjMbZGSYiNvtDg1KwjhIzsaTbjJm2arXm6pWa8dBScnjEMzYxAts2ajCYdkJ6XB7MeOJf8S46khpKXs9fnz7xR26lapw5TxcKffxAk71+ZhcYPjT8tW6h1N9PvT5AnA5bbp3f9QyOcnJWI+LXDThtThYirFp3Uevxx+672j0pj3WMnpe2trIZKywIIqipuEgGVBPb2zQHCvSDgvL84g2GudUluJPO+WNXQ7ALRePjZGXrsWFng50bn0F/bUf4jCATxXOG3LlfBRechM4mwPggF981IO3p/LId1gTri1SObIAvV4+LuMw3ebmbIXkzAYZGQRBZCR6lTI9RdlYUjAqKXkiggXWJsepKGilNNVK2VqQYw/tbGzc14bOfh+8vACHlcOQPAcGfDy6ByILmYUr54ko5ZIxoFWXghfEiCJiavcsV71ZT1GxeFexJaRVepZdijlVJfjzLuXg9z5fAN96YTtz4Lta2uNN+1pVjR6W+iGs9PkC6OxTr2wsPfvNDJWe552Tj+HDhmONRuE6aVzeOascy9fWhHairDI7UUpGvNbigiiK6K/fjlObXoLQ36V43sUXX4xpt9yLLaeKFA07aUwnUvxxSK4Nfzmd6pniHIhMhwK/TUQQzqwEDWY5GA3J2XhSLeN40yeyBEmzBlSyZpHSqyi4vTxuWr0NB9r7mM7XClANd0uSMuqoKefxBpKH98Pt5XH+oxtVV7TDg3m1sjKVFOZgTpWyoqwm42Rk3xpZmAMLJ6KlW9llxmrhMCzfwbTrc9ulY/Hrm88N/T9rwHjIsN7XhpbuAeZnlGiQ8PK1NZq1MlxOK75zYRne29uKjl51OX3+86/DarWqPvPS08/8zlnluP0PuxTPG5rvgMNmUTXio8dAoL8bXR+/Cve/1qve071L78fyX/wchYWFsu1EI43peBMZDMm1Y8O9V6K0MEe1X2qYNTcPdgMo1d/AVKFXt6edDBMZTAMxlZCcjSfVMtZyFQlfJQ9HrWBaUJl1orpqpOaOA2vsRDwfYpfThkvPHsZsZGgVHgt3M5LaV6v4q8e1JPQbiFxFzndYMTTfgXYVZTO6era0M7FhX2tEhiJeENHSNaC6qi8nY2n9LFHXFSDooua0qY/5gCCq3m84b+4+GpHKliXeQSl1LQta7wWgrjSy7E64vcEYFovGeC8tdKIozwkAirtR982ZhIKcoBvK8rU1ivcsiCLmTR2J5TdOVf3N2ZWleOn1t3Fy40vgO1sUz7MVj8KouXfh32+9KWYO0PPOa7nzJTteJhwj52a9u8fZTKq/gZnC4BoVBEFkBXqCUMNRc7MJV2y0SEYWKSVEUcSHDR26ronXoJEL8tarlMvVXOA4Dg4NpTxaPpLxIyLoJhQNi6IcqQQJsFstcCtkRNJDQBCZajOwwgsiVq2vw/IbpzIrr6vW1yXF7UuSXXhAv5rSqGdMCGJQ8VfCwgHVVWcyLWkZvID2u765rh3Lb4w91tvbi1//+tdYuXKlap9d58/FkCt+AHt+kepuj553nsWdT+u+0414XPoIgkYEQRAZRaK7CMn6wGtVXtaK6QgnOtD6hJttRVwiXoMmGj1xK8DpCtPTx8kq/fHIx+3l8ZfPjqoqla9+0oQ7Z5XHuJTodTNLlFy7Bb6AqFmzQQlJOWZVXjfXtSdcC8XHC1j+t73YXNcOLy/glNuL6FcpWmnUOyaA4K6gIOpLfKC0G6XnXf/kk0+waNEi/POf/1Q83+4qxthvLoJj4gxYLBbkOaya7lYSesY06zyTCQYGEP/uMTG4ISPDRE6ePBlKPTls2LBUdydrITkbTyplnMxdhEQ+8AtnlePdL47FFCdjySIVrnQkEmgt/Z4eg0YLrcBziWgXqWj0ZIACTsth9Xb0aewY8AJwxcot+PiBayIMjRXrak0zMABgmMsJf0BUTdWrRrhyrKW8zp5cgvdrtF2WtDjV51PMzCQhpzSyjgmJofkOzJ1Sig/qOyJW8f/tkhEY6OmEl3He0HrXRd6H4x+9DcvDs1Xb+d73voeVK1dizJgxwevC3j89Cw16x3T4fZiFUXNzvLvH2QrpGWyQkWEizc3NoZRnNCiNg+RsPKmWcTJ3EeLB7eVx+x92oVum+nFhjg2v/vDSmBVRJX9mf0BIyMDQMmi0iFaylsyZJGs8hcMByHVY4fYG3W3kfLJdThveWngZntnYoOgyEv7bqzbU40CHdjVuIFgs744/for3F18Zuoe//euYzjtPDD4gQsMjTBVLWKU8LeV16XWTsbmuPYHeBmGtxB2tNKrFMslxss+H9fuCKX2rq0pw/9xg/MmePXvQrnPeiH7XfR1N6PzgZXgOf6l4TU5ODlavXo0FCxbAao0tDBg+3vUYAHqymqUKI+ZmI2PQMpVUfwMzhdS/EQRBEDqJd0UxWUiuA3Kf3R4Pj5e2Nkas6qn5M1s4TpeBwZpRR41og8dqAYpy7Oj28AgIIno14hhEAP2+APp9sQHZSsbUktMxL0rHN+7TF3Be39YbSmvq4wW4vYnFTFgAcBxi3IeUsFnVdyC06OjxYPqKLaH71woGZv0tJVclC6ddgDCcaKVxWlkR9rexGYHhaZb/9MkRvPbpUdx6yRh8c4wAvVUFFn+9HG/+6feoe/s3qud94xvfwNNPP42KCmPf/UyMp0gU1vo9j/5936AMAieUoRS2JkLba+ZAcjaedJCxVipWI9FKZZnvsGLXw7ND/Yg3LSwQVBCH5dvhtNtC96dV9VeNRN2zlPq4YMZ4xQxI4Vl15NKRcoBs7QOW303kHiwcUFLghIUTccWEIdjccAon+3im69TuN55+hAcdyymv0nNrUFH0LRzwva+NhcNqiXgvZk8uwbq9rczZr4BgOtb1i6/EinW1eHP3Ud3PRo4Jw3Lxx+9XoSBHffX34MGDWLp0Kd555x3V9h5f+SSWLP4pHA5Hwn3LFoyam5OZ/jsbSIdvYCrQq9uTkUEQRMZj5oqiKIqYvmKLpi/+pBIX3r47+LFNpFZDWXEuPv7Pq5N2f4kYPGqUFedqurFVlBagvq036b8dL5JsgeBqLctzilakwo3dli722hVy7arVOwGChsYT62rx/2SUfjkFL/y9uPyJD3Csiy1+xMIB3//aWHzadErVqNGL0j0KgoDXX38dd999N3p6ehSvnzlzJp577jlcdNFFiudIKs1g2GEwg/D6OiwGNcs4JjIXMjIIgiAMhlUZXTBjPB65vorJKFFrI5kf7GQUp5NjZGEOrBaoKrJWCxd3NqZkwwGhquyS21aB04a61l7FwGiX04bvXlSmuFs2Y8UHON4dXyA4EFmgUI2gy1kdNte2M+/isRTUA84YK5eMH4o3PlWuXh4v0j0eP34cP/vZz/DKK6+onl90+fcwZPq3MWn0cMUVcreXx4p1tfjbv46FUg3n2q246YLREfVIohks7k56UXJpXDirHC9tbcSaTw6rvses45jIPKgYH0EQWUk6KQRXTRqB13YdUT1HCp595Poq3SlAAWPiS+Kpg8GKzcLBr6GRaq1pWXXERCQCB8Bu5WJ2VSxc8O/+gBhhaFg4oHxEPt65e6aiwur28hjwabtaqcEaPOty2rD8hqlYfgP7e7G0ugLvftGMrgHlPuY7rLjl4jFYUl2BOc9+lFQDQxRFDBz4FLs/eAncg8p1YOwjxmPotXciZ0xkgb3ojFfhK+xyqYv7fAG8tusIdh08iXcXnXluVFBOHa16GG8tvAzr9raqLpoMtiBwQhl6o0xksJahNxuSs/GYJeN0VAjcXh67Dp1kOrelawCXPv4B+rxsymd0UPe9156DPLsl5PubKPHUPGDBwgHXVpViw75W9d/XaEfLwJB2H7oG/HHtGEhV3Yty7LJuW4IYzMAk7XDoifVZtaEe3SoKPFP/4qh3wnq+y2nDhnuvQvWzHymmXQ6PCenq9+nqhxyC34ueT99G97bXVM+79Prbcbz8G+CcLuW2RGDjvjaIQMR8UOC0qaYuPtDRFzJOBkNBuUTnZq16GM9sbDCsEGkmQXoGG5n9NmUYX331VSjl2bRp01LdnayF5Gw8Zsg4XRWCVRvqcbCDrR6DIEJXsK0giph37kgsvyG4irtnz56kyZmlJkM8SArqnbPK8c4XGmlkOUC1SIMGo4tz8f7iK+OOKxFEEdVVI7FJI+d/r5fHtgeu0bUau7m2LZFbSzj1slJfw/9eWpiDbQ9eo5kwgeM4eHkhpi0W+O42DDR+hoGDn8Fz+EuIfOz4P+uss/Dyyy/jG9/4RigW06VPNAAAIABJREFUhmNw4Wvr8TC5fEUjpeNVU6Ab2tx4Yl0tfnXzubrbTycSnZtZ6mGkOoV4OkB6BhtkZBAEkZaka4VZtY8wC2p6tiACm2vbsfyG+NsPR24n6KpJIzBheD4OnuhLOCPSqCG5IQV11YZ69KjU1gCAQHx6awjJDUMthbFaqtbgangrtPRnve4eibqhabnGKfVFzXf+xa2N2HT6XqN3ALVSsIqiCIeVwwDDABEDfnibazFw8DMMNO6G/+RR2fPyz52N4isX4Lpzz8Ki6cNDipke2cWb4crPCxBFUfPd/X+7j+JBlRiObIe1HsaSOZNSmkI8EciNy1wG55uUIlwuV8jyJYyD5Gw8Zsg4HSvMJiOmgeMAtdCEcAU3ETkr7QS98ekRTBiRj+9/bSy2NnTgpNuLAb8+7Z8DMH/6OCy/cWpI0X31k8NI0IbQxGYJumEoFUWbXVmC975qRYfK7lFAEGHXcG9we/3o8wWYlc143dBsFg6lhTmYUxXrjqXlKqi20ye3yvynHbE7gErKFsdxKM53YEAhiJ/vPYmBg/+E5+BnGGj6AqIvbBeCs8A5uhK55Rcjt/wS2IePi/idD5o8+LKjDXMP14TuxQgXvnDsp6smairQgohVG+qw7PoppiiiRii8icwZLOPYZuVQkGNP+6KE4Rjhdkt6BhvpNRKynPLy8lR3YVBQXl5OqxUGY+RYloKDE60wG+8YULvOqJiGcML9mRORs9pO0MGOPlwxcQS2PXANZj6xBc1d+rJNWS0cNta2wy98hV0HT6Kxoy8hVyFWrq0644ahtCK/uVa9MnZ7rxe59tgq0OG4vQF864Xtulzy4nFDCwgi5lSVxhjLLK6Cas9XDhHA/jb2HcA5VSPxpx1NEAGIQgDeloagC9TBz+Bra4w415I3BLkTLkLuhIuRc/YFsOaox1a0uf0R95JsF75orq0sZX53X/3kCN7f22ZY/JfRcWaJzs2srlCZUpTQKLdb0ufYICODyBrSMUg4WaTzJJ4M5J6dW6PqtFxwYbxjQM91LJml1Mi1WzDgFwz3Z2bZCXrk+irNjFB5DiuKcm3o6PWF3FV4QURL10BCctDLkFy7ohtG+DjQUlgFMZh5SAu9LnlKLlxqiJDfkdNyFXxiXS3e/dcx3Uq50u/JccdFw/DWf7+BQ19sw8DBzyF4wtJWchxGTZwC67iLEBg9DbbSieA4fcGv4W6P8ciOlYkj8kPj5uuTS/CnnYdVzw+vVp7s+K90jTMLR80VUckVKp2/TenqdjtYoJB4IiuQJu81O5vQ3DmAth4PmjsHsGZnE771wna4GbP76MGgEjMh3F4ey9fWYObKLZi+YgtmrtyC5WtrDLmXVKL07NQUQTllPN4xoOc6PZmllOj3CbLuUsn0Z2b1rQagubo7NN+B6ilnQTB4vKsxJNeGDfdeqaqASe/j0uoKTCxxwZKg3iMZYmq/FY7kwvW9S8bo+h1pRy4cLQPxjU+PwO3VNpRYfw8IZsv5/PPP8dhjj2HGjBmYMGYU9r72a/Tt+xCCpxfWHBeGnzcLN/301zh4uBnN9V/iyKZX8B83XwtrnNl1JBlLsvv+18bCluiDC6Mox4rXfjQ9NG7uv26yrvbDFdFkwKLwphqX04a3Fl6GBTPGo6w4FyMLc1BWnIsFM8anhRGkF5bFFsI4Eh4t//Vf/4Uf/ehHyM/Ph9udvMqgBKEHs1YrzNotyYQVr2Sh9OyUUFLG4x0Deq7Tk1lKifCfsXLAMJczlLI2Wf7MrL7VWtmmJGNOLRtTsrBwwITh+bh0wjB82NABf0CAzcJhTtVIRbkovY+v/vBSvLS1MeEq3OEueSzvvstpg92m7ooVTfSOHIuBmEhYkNVyZuW5u7sbmzZtwrp16/D++++jtTUyBfG0adMwb948zJs3D5deeim8AodVG+px++t18Adqk5JIgA+I6PX48fTGBrzzxbG4g7vl6PUG8NLWxtD7m++w4tZLxujagUtm/Fc6xplJKI3vJXMmoSAnM+MOWBdbst1TIJUk9DU7duwYli5dilGjRqG7uztZfcpampqaEAgEYLVaMX78+FR3J6swY/I2U/FP9y3eZI5lrYwvLqcNQ/LsmsGF8Y4BPdclmlkqmoAIzJs6EstvnCp7PBE5s/pWL62uwLYDHbK1BiaMyMd9cyZh3V71+hdKWDmgIMeG7gE+prhdYY4deU4rBAGh53r7jHG4+7XPcbzbA0EQYbFw+OTgSfR5+ZjnzfI+PnJ9FS59/ANdaYTDkQwAPe/+Zh0ro3I7ckbG/YiiiPNdbjz11FN47733sH37dvD8mZ06iyMHQyZehMuuvhar7l2AivLxoWNGJRKwWDjcvHo7DsRpvNssUMwWJojAhn2tEbU1rJag612Px8/8Lp/q86HX409I2TZL4Y1nzsjWRS09iy16SZU+l2kGUUKj5s4778SVV16JoUOH4q9//Wuy+pS1dHd3UzYCAzBr8jZT8U/nFS8geWOZ5dm5nDZ8/J9XA1D2/Y13DOi5DtAORo/GauEQ0NBkNte1Y/mN8scSkbMu32qlLorxK70cgEmlBej2+OHlBfgCIpw2C4rzHBHZlKRn0tbjwRUrt8AXJuOAIKK2tRdXrNyCjx+4BiUFztDzY30fHbb4vYJnTRrB9FurNtRh+Q1TdWUfU3OPS2YgtODzwHNkT6h2xQs9kdW280rGwDbuQuRMuAQ5ZVPA2eyo4YB71h7G23eVhZRLIxIJWDjA5bCioV2/F4Qkv85+v2o2sfYeb4wsOQBFuTbkO+0ICCI63F7V97TfF8C3X9yRkLJtpMIbTjxzRrovaiWCUTU9zNTnMjneNO7e/fnPf8aHH36Iffv24ec//3ky+0QQujBr8jZL8R9MW7zJenbxtqP3Oj3KNgfAabOgXyPIWMrhn/RUlgppXqN3glZtqMfBE/KryAdPBKsl61V6LVwwPWtda2+E/TLgC6Cs2BpT+A0A7vjjpxEGRji+gIjLn/gAw1w5oQ/sxn1s7+PsytK4CrgBwCeHTsLt5TXf/T/tOIyN+9oxp6oUVg2ffw7BooJq7nHx1gGR8He2nCmId+QrIHAmiYLN4cS1X78G8+bNQ4O9HP/TFJuEQE651JLBhn2tEEQRLd3sBsbEEheaO/uZzgeCRvsIlzNiHF/33Eeq18jJSgTQ4+Fx8wVleOT6Kjz6932a4zsZyna6FrFL90WtRIgnkD2dyPRdprh61t7ejsWLF+OJJ55AWVkZ83U1NTUYN24cCgsLQ3/zer2oq6sDABQXF2Ps2LER1+zfvx/9/cFJKLqq4okTJ3DsWLDC7NixY1FcXBw6FggEsHfvXgBAQUEBJkyYEHHtoUOH0NPTAwCYMmUKbLYzoujq6sLhw8EMFKNGjcKIESMirv3yyy8hiiJyc3MxadKkiGNHjx7FqVOnAAAVFRXIyckJHRs7diyOHAn6gh4/fhxnnXVWxLX79u0LWcZVVVURx44fP4729mBqxvLycrhcZ1IEejwe1NcHA8aGDh2KMWMiAw8bGhowMDAAjuNw3nnnRRzr6OhAS0sLAGDcuHEYMmRI6BjP86ipqQEAFBYW4uyzz4649uDBg+jtDWYcmTp1KqzWM77InZ2doXsdPXo0hg8fHnHtnj17AAB5eXk455xzIo4dOXIEnZ2dAIDJkyfD6XSGjvX09ODQoUMAgNLSUowcORIA2+Td0tKCjo7gKt7EiRORn58fOqe/vx/79+8HAAwbNixmXNfV1aHfo+5yMeDxoqurK0KGPp8PtbW1AICioqKYbdXGxsZQLNO5554Li8XCpvhaOHz55ZcAgvm6o9PpNTU1hVwYKysr4XA4Qse6u7vR1NQEIFh5t6SkJOLavXv3IhAIICcnBxUVkRNwc3MzTp4MBj6fc845yM3NDR3r6+vDgQMHAAAjRozAqFGjIq6tq6uD1+uFzWbDlClnPlhaCuzM8qGh8aI2R5w/woKWLvkUnhYAV0woAnBmu1maI6YNt6ClE7I1HiwAzh9hAc/zsNlszMq2BUBZkQ0eHuj3qZ9rt1lCirbb7UZjYzA9aElJCSorKyPO1TtHSGkmH5hTjrq6OnAch6FDCyM+SprK494W/OrqofgzJy9bmwWYNT4Xezt4gLMG8+g7bTEGBhBU7iRl7SdXjIqYI7RWs3kBoaw/LEZD/4AHx48fx9LqCvz5k8Nx+fof7OjDqvV1mka/CKClawBrdjQhz8HBoiArC4D/ddFZePy7F4b+JjdHhBuI7395DP5AAFYLh3nnlcEviHjj0yMR7Yu8H56jezHQuBueg5/B39kS8bvWwhLkll+C3PKLUX7e17DuF/PQ1NSEW16tU3327+05ioXTR2DEiBGaMmjv8QZrpWi9GxwwPM+KqyYW45GbL8S0RzeqXxDG3Il5+I8Lh2DChAkhPSLeXR9Jeb77slJUj/JhS4ENR3qUk2rIKdt69QhWhVdNj4ieI6L1CKkP4X2RkJsjWBe16uvr4fF4MlKPeOOHF+P5rU2hxRYLJ+LCUhtuO68Q7s4TcJ3WIyRqamrA8zycTicmT54ccSxaj8jLywsd09IjJBlarVZMnRrpItve3o7jx48DAMaPH4+iouD3imWX6QdTcmL0CImTJ0+iubkZAFBWVoZhw4adaUMQ8NVXXwHQr0ewEpeRcdddd6GiogILFy7UdR3P8zFZLURRhN/vDx2Xu0Y6Ho0gCKFjghCrIrC2G92n8HYDgdhVSL/fD1EUZbfJAoGAYrtWq1WzXaV7DW83+l7DZSjXrnSvciulrO0a+WyiV3HVno3SvYYm7zZ3hLIYPnl3th/X3W54n7QWsZUWMON55lpG0+zKEvj9noj2wwl/rtFo3avP54MgCBGTvVy7NpstYtLRatfv98Pn88XIfml1Bf5RexyHO+WNuE+bOvGN0fnItVtUx+GtlXlo6OZiP+AAziqwwMcLmLlyy2m/bA6FTis6evogCMECedEasQXA6EIrbq3Mi8hcpJRq02bhMDTfAYfNgvOGAd+b4sJf6j1YW9cLNcJXL6PnnuhJPZ45QhSDu16S7MKfDYuC4RdE/PfeLkW/94AAOCzAq7ecjYkTJ4LjOMxcuUW1qvmm2jYsunxkzDyQTLq9wYDiUrsFxfkOVZcaJQQx6M7GuoMlAOjziSiS8fmXxtPdV46NuU7uvZEMxFsnWdHb2wuO43DhhVXo9wvY3XQKtfsPof/gZxho/Ayew3sg+sMK51mscJZNQe6Ei5FXfglsw8pCc6xodYbGA8+gXPI8z7TwwWLEWTigekIufnhBIUpLS3WtwNoswK2VeTFjZWl1Bbbt78DBjj7dxSD5gIhAIACbyONXs4bgf687CQ+vfB/RO8h69Yhw4/G9fx0JVmO3WTDvvLKIXS01PUJLP1H7LsvNEay7udK16apHqLWb77BG1PTo6ek5bQwEFL9VPM9HKOty9xrPN9Dv98seU3rmLLtMt04albAM9eoRrOg2Mt566y38/e9/xxdffKF7e99ms8m7K5xW1uUsb5vNpujzZrFYQsfkBgNru9F9Cm9XTtGy2+0QRVG2XavVmlC74f9Wajf6XsNlKNeudK9yz4u1XTUZyikHWs/GDyte+7Ibu1tOApaWCB9DtWejdK/S5P2z13fgk+Z+BEQg1+mIcEnoUXk2WjK02+24tCwX6xrkP2QWAJeW5crKWKtduee9tLoCH9W3oenkgKzRdN+cSTjUUBvRfjjhzzUarXt1OBwIBAKa7bLKUPInff/LllDGoHlHzlT7dTltuLCsQNHIaDrZjzdrOfzHhUNUx6HdDrx914UR7kEWCDivxIa97T68s6c9QpYtMS1FGgpfG52D707ORZ79zE6DNM4eX/slNte1IyCIcNptqJ46CkuqK5DvsILjuNBu579fUoh9pwTZoGoAmDA0N2K7nmUchv87nPBnM+AX8MzampAPr80CXFBixW3nFUW0y7pr9nmr8odGBPDZcV9ofmcxXE66vej3CRHzC6dVCl0nARG46f/WoCBnP071aWwnqeDxBzCnqhSvf3qU6XwRQPeA/3RwMQ/xtLk1tsiGR64aDpdM8LDWM3c4HPD7/fjoo4+wfv16tLz3HppP79RLWF1DkTvh4mBBvPHnw+LMi2kLADrcXjz69324ZXIObAzKpfTOJRonEswelof5FwyB3W6B1Rp8V/IcVqZ0vEW5NhTkOsBxkW6PLqcNb/7oEiz76258cLAPAzoyfPd4/LjpD1/C6+dhs3CwWGRWG8KIdrmMR4+QjMebxwcgCALy8vJiPCLM1iNYPAGM1iPkMELHk8aPlgzDzwknnm9geLtSsDhLu6y7TMmQoV49ghVO1LF85Ha7MXHiRPzgBz+IiMO46667sHbtWjQ3N8NutyM/Px+CIIS2wCQKCgpkb5LIPBIJRFLyMZQU6GT4GBrh425Gv6N/T8ufPt1hldnMlVvQ3Knsy221cBjucgbH2eQSLL1usqYMpDGwfG0Ns3Jk4YD508cpZntS+g013F4eK9bV4m//akG/jw/9jtNmQb7TDpuVQ1GOHd0eHgEh8aA+veNUTT4WDpg/Yxze39sWclWSY2RhDnY+dE1IFpc98QFaupTPB4BJpZF9mfvcR6htVd/1SRU3XzAK73whZ5ayE8880dbWhvXr1+O9997Dxo0bI7M4chY4R1UEDYvyi2EvmcA850l9OX/MEPz3Z82K5yyYMT7kHuT28rhp9TZFg1nr9+bPGIel1bHv7cPvfMWUUrasOBfbHrhG9RyteSQRouWRTZj9bSPY0RrTLO9FMtGr2+syMpqammL86aK58cYb8e6775KRIUN3d3dIKZH87TKRRCckLaUm0YncSDmnSvFPtyBvVhmzPOtHrq/C9BVbVJXYaGwWDrdeMgYPzavUlLtexcPISbvX48e3X9iBAx3qdUGkd+mV26Yi7/TuCMtYFkVRNYhV7v1q6/Gg+tmP0DXgjzlXep+ve+4jXR+66mc/RH2beoxFeF/aejz4we8/wf4Ea5AYhVqaVD1ozW+CIGD37t1Yt24d1q1bh88++yzi+LBhwzB37lzMnTsXq/bl4BTvlG2HtS8FTiu6PfK7CBNL8vHu3TMj3i9WgyAaaXzIzRssxgvLd0EURd3zCCuZpGzH+/3LhkUtMzFLnzNaX9KLXt1e18gZOXIk/vGPf8T8/YknnsCHH36I999/PyYwhzhDU1NTKGgzOog9k0g03Z3RmSyMlLO01S35dpql+KeTgQGwy5j1WetNkcoLIl7bdQS7m06pfvj1pBQNta2RuSuR5/70xgZNAwM48y49/j9f4Y7zXKpyjt5VPOH2Mr9fbi+P2/+wC90Dse5QhTk2vPrDS+Fyqge8y2XFYTHqpL7cOas8JnWtWdgs2pmagOQYGID8/Hbq1Cls3LgR69atw/r160NBpRIXXXQR5s2bh//P3pcGRnFd6X5V1au6JSRAC2IXIITAxhgwGOMNMMLyeJ1JZpyMnUw8b14c500cm4mXJLacSWKcYMeZLPa8N/bDxk7GkxfHy1gGAQJjzGIw3oQ2kEAgQAtCW+9dy/vRqlZ1dy23qhct1PfHRt1969ate2+dc88533fzzTfjqquuiqZa/P6ZWlxM4tSeF6DoYADA0hl5Cevqg+ZuhW8rQzo/5PYNt92Ctx5YjaerG/DG4TMJz4OUBSiV+iKk2jyjEUbffyP1bhuryJQ9N9bZsXStGIfDgRtuuCHh71u2bAHDMLKfmRh/SMZJGE/0rKO9fyMNPc/aaL63llNrxPCQo7pNFU+5HjE/XgA+PhvANy93K35HKaqoBpYTwPM8aJqOHhjI/XQgwOLFPS144tZyXS86QRDgD2vn2It9+cZLh1QdDCsdqa9IpQiiCC0Nk3QgGObw2WefRaMVBw4ciCnIzMnJwfr161FZWYlrb1yH174YwM6GTmzf7YN17wfReZdKLQ05/PnoWfz41oXR+W3EYadAZgi57Rb87M7L8FjlAmze1oidjV2GDPxUjQmJNs94xqV4z6MVpFTkoxWju3fjDFOmTFEs+hkrSNZJyISmhdY4jwUHZrSDZC7redZqrE1qIIl86TE8aApYVxZL6ZsKnnJPkMUvtzXiHKFImQiBolFcXCxb2AgoRxXV0O0J4upNu2FlKPR6Q6oHBq8ebEN1XQesDIXrS/OxfNZEfNDcnbIXXbcnqJneEuYBt52BIABOG4M+X9gQHa0cMuVi8EEfAm2fwd9yBO2tn2DJj3tiPl+4cCFuueUWVFZWYtWqVbBarZrzbut9KwytGVKwvICnq+vxszsjdKVGHPYJTms0Ggao7xuCIMBtt6Dq9kWout3YPm10H4lHKnSVRgrjwc4YC8jkOI/lKFNKnIwtW7Zgy5YtqWhqXCNej2AsIhVOQroFieTGWekk+uH1pciWYXsxoQ5xjLVKukiftdxpjZYKr4hzfX5cs2kXbiovko0siIZHs0aNQKRPFKrrOrCzsSt6Yvx0dYPsb+XSA8UXgPRFYCTaIMJutWDKlCmK60lPZEQExwvEeevS7/7x49OYk+/Ctgevi7JoyYGiKDitDLwaIoRi+yTwBDnQFDA114n3/vlavLinBa8ebEs6EkEhQiqQjNMiR4olCALYi+3DgnhnjgH8MO2R1e7EhvXromlQM2fOTGhXKy31xT0tePM712Dz9ka8ekBbn8II3v7sfNTJAPRHCgYCYby4pyW6PuL35lQrGcvtI54gC0+QnHJqJEXxUoHxYGeMBYzUOI8lBwPQWfitB2bh9/hFsoVII8HSpGTkMTSFwhw71isYqCYSoccwMPqstQqY5aDWpifIYsXPdhIZvtL2SvJdOHXBp2qETs114qbyQtTUd6DXG0KIE2BjKOS57FhfXogwxyeIp5HCZWPgdlhlxzidha5qcNsZ/M3S6arrxWiBsBaSIQuQQ5aVhtthRZcBDQ0Rk1w2DATCCAYCCJ7+Ev7Ww/C3HAHb3xnzPUvuFDjnRChm51x+Ffb/aINqu3pYZfSSG0SKvi3oD6gb3zQFtPy8MimHWYlIIVMsg94QR9znsVTgbcLESECvbc9UVVVVpaMjgiAgFIrlJrfb7WPOCzORiGWzJmJHfSd6faGYdANxg/713Utgsyg7kzYLjTuvnAZfkMMFTxBZtkiR3V1LpuHXdy9J+eb+8+oG7G7qkn3BCAIwGGDxRXsfdtR34s4rp6n2/VKHaBjsbupCv5+FN8hiQGX8jD5riqKi86yHUONAANDrC8EX5HDD/NhTJitD4dWDp+HVcaIpALjoDWsaJv4Qh6On+zAYYMHyAgQhkmoyGGDx2Zk+1J/rN3zKHOaE6Bh/fqYPOxuGx5iiKLyy/xQGVAxFhqZQmO2AP8ylTIIixAma62VFySTUHOvARV9yQk7xEABc8ARx3+oSzXsnwVeXTUN7n1+1HRrKaVXhvg4M1O1G9wev42LN7+Gt24XQ+ePgg16AscAxczGyl96Kiev+J3Kv/TqcJctgzSuGy2HHfatnq5IL/O+9J1Xna5bNEm3j9EUfvmjvk+0nBWBBUTYcViZm/T3/d1fgP/adVGwfiERpvrd2XrSf8evZaWUic0ulDWk/RXiCLL7ywn40dSbWA6mtY72gKEpxD7ptcTEumzYBvb5Q2t9BJkyMF+i17c1IhglDSCXdXbpzDElP+cYzD3qqUPV2HV49KJ+aQUozKX3WWs9e1JiQY51RgtLJaTo59JMBBaCsyI2BAAeO107vWFCUjT/dvyqSp/t2HbZqPI8f/9UCXL1pd8ojHlrP2xNksfLnO4mE1vRA1OTQG+mKh4WmkJdlQ68vqMgeRVPA/MJsNHUOghcAgQsj0F6PwFAaVLgnVqCPyZ48FK1YDsfMy0HbnLLtpkLzQdoGaVQgfr2VP7ENPpXonsvG4NhPlCMugiDg2l/s1kVvLPZVK30xXVTScnvOWMtzN2FipJBWClsTyaGurg6hUAg2mw2LFpGJfY1WpLIQKdWbu3ScFy5cSMyIkgr63PEIaXrUuT5/UvTDFEXpSreSY51R6wMwTDwgXk9Eutl4jGJqnhPvP3g9gGGjTc3JaOgYxOpNtciyMxFVc4oCH3dWJGV9ommaQNUbEBCpJdHDfqX2vF02Bi67ldjJEPugVWeRLFmAWEPB8pG6H/XvUujsPIdw/ce42HgQ/lOfQQgNG9QUTcM9YyGYmUsjgniTZ2ruZ6Q5/3pq19QYaB5aXxpdV/F9u3PJVNW0tjuXTFXtI0VRuvpZV1eH3x/sRnOnT7VdIH0sg0qEJCQYC87IeLIzRjPMcSaD6WRkEBzHged5cFxqT/ZGGqNt05WOs15GlLFCn5sp6M3B1ho/o0xNUtaZazbtwlkVNenBQBjX/mJ3ggOTKuaZVELO4CRxivv84QTxPAtNYaLLBpuFTogqajlYkZN8/YMSYnlZh078N+naoyngnpWRqIhWdEaJLEDL+ZyW68S6BQV49WCb6p0KPIfguSb4W4/A33IErV2tMZ9bXLmYWLYC169dj+ceuhd/t+ULXRGyHIeViNteLz++9OBnwB/CczuOY0dDZ5QdTM6Rf6xyAQ619uCEjAgiTQG1TV2oeueYav2Nnn5yHIfD58giaqOF4SnVxenpxni1M0YbzHEmw+hbIeMYDocDDMPAajXZjNKJ+HHWc4I9Wl5sJMiEM6SXIlVr/JIVcgSAm8qLVJ+nN8TBKzltljowcqe9Hf1+w2JrWVYavjDZjylAtoZJaoQlIyjGCwIqLytC1W2Jp2rpcrC6B4O45placDxkja91CwqxZf8pzXak4/AvG8pwoLWHyGiVGtaazkl5IXYosHFxvn74Tx6Fv+UIAiePgg9I0wEo2KaUImvOMnzljlvxwoN/A4ZhouuP9B5FZNkZRbID6drRy48vGsM19Z3oGggkpBfKOfJuuwVvfXc1nh36XUe/H6KPywvAub6A6gGAeE1PkIXdQiPECbBbaORl2bC+PLGfdrspvotsAAAgAElEQVQdvKA9v0cLw1Mq6KszDdPOyAzMcSaDWZNhYtyD9DR+LNRkpONUTc1Z0VPHQDJ+evLMlWCE4Uaub+LWd9XPd6FbJ7uQaPAunzWRiDnKZWPw1WXTUVPfAY6HqrFY9c4xXUarFHLjJz5fuTqqPl9INZ0p3jHSgrQGwGVj4AmyuOInO1RToLJsDA49vjaGStpIzZdWXcKf71+Fdc/tRedAAILAI9TZCn9LhAkqdL455k5phxuO2VfCWbIMzpKlYLImAACKcx24aUEhdjV2Rdff9aX5ONDSg9YLidEAOYg1JXpTB41ECOOhtkar3jmGV/afkn3ecr9TuiYFYF6hMkMTyZ5SqvL7dEBpbJNlUjRhYrxBr21vOhkmLgmIRktNfSc6ZU75xgJ1YSopH0mMGz0UqSR9IGlPaoBp9V+vwZxsQThNAQXZdliY4XQkAERFrPML3fCGuMhY0xTWlSs7hp4giyueqjGk3SCOnzfEJT7fsgJs3FAWLQAGoPk8CrLtuOgN6e6LlHq31xuEN6Qc7SnOdWL/o8qOpZ6InZpzwgW8WPGd59D+xX74Tx4B7+2L+a21oCRKMWsvng+KJhPZoimgZLILS2fm4b0vOzQ1GcT7TeV6VjOG42F0HcT/zqgBrtVXKbFBOkGyB6biUMSEifEEs/DbhAkZSNMqBgNhPFfTnBJmrEwiFalGAHkKAEnqDk1FjCZx/Fy25BXASRBPPABEDGY1J0OpXoQ0na4414kPf3Bjwu/f/M412FTdgP9UYMCyMhSO60i3cNkY5GZZccFDRt0rhYWhFHUBthxow2uHTuNvl0/HY5UL4LZbNJ+HlYnUeejVkYikrJHlKvuCYXiCrCqdMSmk84LnedTX16O6+j381XMPYN++fTH505TNCcesK6LRCkv2ZOLrSMELQOsFL66dl4+6pyqw4fkP0Nih7HROcETu0+h6lpvDekQZ5daBIAiatUDxv1O7phopwMaK+dh/4gJOdMtHQDLlYGjtgS4bo3tMTJgwEYvRa1GZMJEmZDusKWPGyiSMvtTjoce40TLA714+HY/dUo7N25uw4fm9mikfWu31ekNY+XStrjQw8flpOkS0fL0IiSI4BWBdWYHs7912C35652V4tHIBNm9vxM6GLrAcDwtDI9tuidKfSqFmSFIUBb8O0cDo/Q3lsavV0bC8gNcPncbhUxfx5neu0WQGWl9ehB0NnYkfphD9fpbYQdaC1+tFbW0t3nvvPVRXV+PMmViK2dL5ZQgUXY7QlMthm7YQFJOafGrp+tPS7ugPRAr29axntVN3EmNYCrm6KdIDAPF3RpwS6T0EWR5Oa0Q1PsvGwMpQWF9elLGDHtI9UM+YmDBhIhFm7lIG0d7ejra2NrS3t490V8Y19IzzWHlBRF7q6gXGUupWNZAYNyI2VsxHyWSXYlt7mztxx+/24dUDp9De60fnQADtvX68euAU7vr9RwmpIxsr5mNugRu0wrB7Q5xmG0pYt6BQsV1g+MQ8HmKB7ddXzIBFoQEBwKsH27DoyW344V++VGyn6rZF2PfIGhx4bC32PbIGgwGWeKyl0DstpUXRJKfaoiGl9Dyk7WmNa7IQoDwOJDh+/Dh+/etfo6KiAhMnTsRtt92Gf//3f8eZM2fgcDhQWVmJ3/72t2hpaUFjQz2ObX8d3777DkyfnIOCbDvcdgucVgoTsxgUuq3IdVpg5HZZTsCAP4Q+DQFCno+kHJAa6eKpu9Ia84Y4XSxeSgXVas85/nd6nZLoPeyP3EP3YBDeEAdPkMVFbwhhTsCOhs5oEXm6QboH6hmT0QLTzsgMzHEmg+lkZBA9PT3o7u5GT09Pxq+dptKbUYmRHOdUwxNkUfXOMVz7i92axckkp2p6TiCBiOG8omSS4nfP9IVwosureiIohWjQf+PqWZiW50RRjkPx5FKpDSVsrJiPHIfyybR4Yi5CuiZEPY7PnlyPb149E8W5DsTbULwAeIIcXj90Gnf8bp+iMeQJsnjq3Xpcs2kXzvWr13rIOYaCIMBh1a4HyLLSKMpxYFqeE9+4ehZxiod4LzsaOmWfh7Q9t92i6RimAqQOMgAEAgHU1NTgwQcfRGlpKUpLS/Hggw+ipqYGoVAIs2bNwgMPPID33nsPPT09eOPNt9E9/Qbc+6dTWPl0LTY8vxcCgG0PXodDj6/FwcfXYu3sLNACjzDHIctuQVlRNqbmOlGYbSe+b5oG/ubFA6ridpHvUWTaJUPrmeTUncQRVKK+FUHicEpBaoALgjB8DzLfZXkBXYNBQwcLRqBnD9Q7JqMB4+n9N5phjjMZzHSpcYyxxu9tIhZ6WJRIT9X0nkACwAfN3UT9jYdSCld8PYWa+JyeNDC33YIsO5OgHyFCALC9vgMCoLgmRD0OUJQqw9OJLi82b2uMfFcCvcxXco6hN8RpnoYDkRqRvzxwTQwrE6CdNiZCNKS0hDXddgv+fP+qmDomhqbgDYbR72cNqGskQstBPn36NKqrq1FdXY1du3bB5xsWc7NYLLjuuutQWVmJW265BfPnz084QVfKvd963wrc89IhHO/0Dt2HAPgD6KACQ4xU1+LmX3+oSQxAU8AEhxVNnYOq3wOGazJIRey0Tt1r6jtxw/x8WVFGIKKfUpBjR4VGOpJeylw1fYySyS6EOB6rn6lFmBNwwRMkWg9668uMQM8eqHdMTJgwEQtzhWQQ8+bNy1gNwFjk904VMjnO6QSpRkX8qZrWvetR6CU59VODNC9bqV+pKq4UBAEaGWXoGggm3LvcmthJkL7z6sE27GzsinFSfrmtkdjBUHIMN29vImJzar3gxXM1zQnGGGkhu1JuvgilQ4qH15ci22FF50AAFb/6AH3+5E6d5cYhFArhwIEDUceirq4u5vPi4mJUVlaisrISa9euRU5OjmzbWlGAb778MU50eRIcJfHz52qaicZzboEb/SqpcVKINRkkInYk669zIIA/HDot6+zNL3TjlW9dhaIJTu2OIfEAQG7NiX9XMsBvKM3HwZM9RNTOctBzsBDfJ1LoVVMfSzV84+X9N9phjjMZxqeVOUqRlZWVsWulioloLCKT45xOkOTWF+c6UFFehG/fMIc4aqVHoTcZcTggkhry1Lv1iv1KJeMUSVtyxnv8mhAEASECdT5eQDTF461Pz8Jpo9E5QHZiq5ZuQeLgiNeXM8ZICtm1Il8khxQv7GnRLHIWr1WS7wKGWJiU5lxLWzsefu4V7Nu9A33Hj4ALDOtO0DSNq6++OupYLF68mOjlrhUFaFZxCMXx3fbgdYpChhaawt8tn45Hbi7Duuf2avYHiNRkiBEkklNyI3NaRFOnB/e+/LGhQyUSh3NjxfwEA7zqnWNo7U5ModQDkoOFZCL1etXURYwFg3K8vP9GO8xxJoPpZIxTpIqJyMTIQBAEBAkMXVFVV84gfGW/fNRKbwqAHsV0KWgqUmytFTnQar/PR844ZbSv0jVBURRsFvJyNV4A+vxh9BFoFsZT/soJrumJHMlFisTn+3R1A96QodUlyScnOaTQcoIpAFPznDGaItI5x1A8yi0XMKn7AK5b9RA+PXo0tp/OHDhLlmL2ktV47xffxYwpBcTjAgCDgTAuetVpgLXqQFhOgMvGyK6XdQsKsLGijNgZkPbLG+Ki6Xlap+RG57SIZA+V9FBeA/rodJWglD4nPi8lmmbSSL2ZBmXCRGZgivGNQ6RS9MzEyGAwEMaSn+zQTJuZlufUNEK0xK1ITgyV6gwYCnA7LAksSjQF5Dis6PeHNRWE9daeqAmVqakQMzSlOp7SNZGM6rYapuY68NGja1W/o0dlvTjXgfXlRYqnuZ4gi83bGrGjoQu9vhCCLA8bQyHPZcP68iJFh23VplqcU/GapuY6wPLQFGr82lXT8fgt5dFrXLx4Edu3b0d1dTW2bduGCxcuxHzfVjQvolsxZxlsRXNB0YyisBuJAraWSCJDU6pq5GoK6vHQI4inR9FaTbSPotT7L0JLNE5tLPWI7ukR8FRCfJueIIunqxvw1qdn4Q9HiuoZikJY4b6NKHGbaS8mTJDBVPwexfB6vdHNzOVSpgVNBUazUmm6N/RMjnMqIQ3/93iC8Ie1IxlFOQ5YaArtGsfoeowapb4pnYxTACY4LXDZreD44RPB7fUdONenbGxI52C8UrN42isHLSMivi2GxlB/OnG+n7w/d/x2H050exW/rxekxo8eYzXXacVAIKyqGC0aqcc7Y2sPlBw2QRCw8MntqixJWTYGeVlWnFV5vmJbxVwH1ud0YFfNNhw4cAA8PzyvGXsWckuXwz57KejpS8C482TbEZ/NYCCMZ2uaNVNkSMaQpoD5hdmyOibi53qMVb3Ost625U7dtdaYCLlDJdJ0I73vEq3vMxSQ57Kiz8cqRtmkc9fIOtTjHI43jNX331jDpTrOpuL3KMaJEycQDodhtVqxePHitF5LT2FbJpBJpqtMjnOqoJeVSMSAPwS3Cm2riGRTJiLq0LQse40AYCDA4s4l0/DEreXR1J3qug7VNqWpPnKMU96QvKGile7ntlvwcMV8hDg+evr5yoE2VRYkmgLWLSiIaeOt767GpuoG/GWojWRTQEomu/DQ+lLN74mKyM1d6qfwFCAbKYqvMdm8vSnBwRC/d7wzcV5QFKWZqhdkedxUXiQb7eGDPgTaPoO/5Qj8rUdw2nMRByWfu4tmg5l5JRxzlsNeXAaK0V7/PZ4Qrn56J7oGQwkn90qF+1rPa26BG1u+dRXueekQTnTG0qsaoSiVpuDU1HfiXJ9fcc7pTVlVSqsSAENF/qQpUEZE97QiqzaGwoopNjzxlevw4p4W1XSlzdubDDn6Yp+8Ie6SY1gci++/sQhznMkwPleZCcOFbenApcx0RQpSJql4+MI8Qpx63jmQmjqcHfUdxHU+RqhypdBj2MSfUBo5/RQAvPdlB3Y2xLJF/fTOy/DTOy+DIAh46p1jePVgm2Fn41SPD2ue/QB2Cy1r6Egdrq3/uALXbNoFNVtfrRvS51EzRNur1Mb2+o6YeSEIAmwMBb/KjdoYCv/zutl4Zf8p8IIAtqcd/tbD8LceQeBMPcAPF4RTVjvy5i7Fz793Lxotc/D2CbLieCn8YQ7+fvnIilzhvtb8cVpp/Pn+Vch2WPHmd67Bo6/vw8ftfnAC4HTYDefmi87AE7eWY+XTu9A5oKxtQ8qaFg/p940W+ZMSgxhZx0rvHhF+VsD7x704/tIhvPmda1TrUUhJEOT6lGzdhgkTJpKHucIyiPz8fHAcB4bRFtpKFqOpsC3TTFeZHOdUIZliSRK6U8CYURONQGmkGknbF08Pe1WKbtWiaSSGDU0DT71zDDsbuxJOKI2cfgoComKHckYIRVHYuKEM+1t7DDmDQOQ5xV9j630r8MKelpiT1utL83GotUfVwSC6HieA53nV5wAAvd5QzLygqEjNhl8lDcdt4VD5L79Bz9EP4W85ArY/1hi05BVHaysc0xdhysQc/NM/rcG1v9iddERIDvGF+1rzZ5LbHtUXcdsteHxDKTiOA03TmDp1alKpNWIGspVRTw0mEc/UgrjPb6puwH/qKPLXQwyiNyoufff815EzsmmPPBKdmXiQsrwp9elSZVgci++/sQhznMlgOhkZRHFxcUavN1r4vTPNdJXpcU4WyWpRABEqTS1nQ69RY0RYTun0UAqSaJpWysX5/gC2HGiL+ZtouCerFqxkhMQ77he9IU11Z7VrHO/0oOJXexNqKl4/dDqp/ouwMBFl6ZDG3ApxiXvD+vIivLL/VEwEJNzXAX/LYQRaj+DMmS/BhyXOC2OBY/plcM5ZDmfJUlgnTk3oC6AdoUoG5/r8ePLtOvzLhjKsLSvAVoWok5xhXFxcPOxQv9ZEnFoj7qtizdLbn52Nzgk1Be5UpqyKEbdHKxdg8/ZG7GzoUj1U0psCpRUVl0sBFN89Oxo6Dac96mV5k/bp4Yr52PD83kuSYXGsvf/GKsxxJoPpZFwiGCkHw0hO76WIZLQoAGCiy4ZJLisaOuTTJkiNGulz0JPCpXV6KMJtt+ArS6cp0reK19ZKuZCjqxCdA7tOw0QOUiNE2i+p4z4YCOOvX9hvOLIhAIrq5MlCfB6CIMBuoVWdIbuFTlh/GyvmY1/TeRw7egjeliORaMXF9pjfMdn5cM4ZilbMWAza5lDtS7KaK1rgBeCVA2145UAbHBYKcldScnD1pHTG15cxNOAJsAmaIck42UbgtltQddsiVN2mXuSsNwVKLipO0xGF8/4Ai3XP7ZV1yFKx969bUKjJ8uayMch2WGOcKpeNMd87JkyMAphOhom0Itnc/PGKeEPFG1Q3Nimo5+DbLDT+dP81ilSXakaNUlF+TT1ZChfp6SEA5GZZY04P1QgB4g0bNcYpEbwAzZN7Ulz0hqJ1EXJGlJjPv3l7I17Zr15YnklIT5gpikJulg0+hdNkAMjNskXX39mzZ/H++++juroah3bsgMcjcVppGjPLr8R9f3cX/qsrHwOOIs11Gz/3ktV8IEWAHb6AhaYw0WWDzUIrpouSptYYJWgQNTEylbKq9VyMpEDFO9fxrFxyuhnJ7v0bK+Zj3/FuxfTHuQUuvPXAarhsTEI75nvHhImRh+lkmEg7RhvT1UjDiC7Espl5+M/DZ1THUE8djjTNQ47e9JX9p8Co5XsMXXfKhIhOg5HTQ5LTY1LGKSlsDA0/byyNSQpfiIuJAMidarvtFmysKMOW/W0KrYwABGDAH46eME9wWHAe8k4qJXBYQJ3F448/jurqanz++ecxnxcWFuLmm29GZWUlbrrpJuTm5gIAtj9Ti0ENLY+puc6oWKQ4XmqpN4Kg7kgbBS8IqLysCFW3LVL8DmlKp1GChtwsKz78wY0jGlEmKc4mibI8W9NMXOuQ7N4vx/IGAFk2C26/ohiPVS4wJMx5Kb53TJgYCZhORgbR2NgYpTwrKysb6e5kDJlmusrUOBsNtWsZKnLhfwA40tarOYZqdThyaR7+IIdemZQdAdoF5ZOzGLx0x9SYMdZzeqi3MJM0n1/DN4p+x2llNCMjWv3yBFnc9buPiNvIBHgAHSqsRpyvH/7WTxBoPYLgqU/xsn+Y85yiKKxYsQKVlZWorKzEkiVLZPnPSdJY1pcXJuS8qznC3hCL/zrSrtCacfACsLOhC1W3yX8uCAL8QfXieNE5NkrQEE62it8AlKKED68vjUbhjBCD6KmxU9z7Qb73x7O8AWTpv6OJYTGTuFTtjEzDHGcymE5GBhEMBhEOh2PEqC4FZJrpKp3jnAq9Dy1DJc9lkz311DuGJLz4RkEDWDbFhmAw1pjVc3qox1ghzeePnIhr32BBth07Hrped02FtF+eIIuvvLBfU88iVaCpiNYGKOBElw56XoFHqKMF/tZIbUXofDOkMYO8vDxs2LABlZWVqKioQH5+vmabGyvm47WDbaqOqFJhrZIj7AmyONrWK5saM8FhgdsxLPbY5wvBEyR3ENXy7ymKgtbUSrZwXU9qTirqBJTW+5b9p7D1YBsKc+xRxXc9xCB66yzi935/IAiGAq6a5sSmr+unkNUzLqOJYTGTuFTtjEzDHGcyjM9VNkphsUTEjSyWS2/Y3XYLnri1PCNMV+ka51TofZC+pOWQDFuY0TQPC02BF4SEk8DpOVbcszg3YYxJTw/TIfIFADlDESBfWP1k2kLTiqe5WmrrYn3Inb//SJexTwqaAkryXVg5exJ21J1DmOdhpWlULo4UzAuCgKt+tlO1j3zAA//JTyOOResn4H19MZ/bCkqw4vp12PTgN3DVVVfpXisuG4M8ly1KySsHksJa6Wdiaoz4PMIsDwtDRdPxRHE4iqJ0qaID2kb+imlZeK9pEEoj2usN4al362F021pfXqT6earFStXWO8cLONcXMKQXYaTOQrpv1dXVgWVZWK3WjBj5o4VhMZO4lO2MTMIcZzKYo5NBLFw4/ujytJBJpW8R6Rpnvek9ci+1VBXC631ZkhZxx6Mgx46K8iLik0DS00OScRALvbXy+aXo94c1a0kA4Kbywmh/442Q1c/Uol2l3sDCUNj0fiOxgzHBwWAwKK8YTlPA/MJsDAZZ2bESU0Tin/dElw1nJToWgiAgfKEtqrIdbK8HhGGTmbI54Zy1BI6SZXCWXAlL9mRwuQ6sWrWK6B7iQaploneeimrtAoCd9Z0I8wJ2NHRCAGL2DBIRumhfoZ1///TXVqFJJdLnDXF4Zf8pQ07GBAejmpqTDrFSkrQuo3oRydQ6LFqkXBeTblwKDgZwadoZIwFznMlACSS5BQbA8zwGBwdj/padnS2b32tifELp5Smeao81xVUt43NanhPbHrxO06lSO4WlKeAbV88ieumTnswNBsJY8pMdxKJ9IigA31w1K2qAA/pf1Eqq3ABQ9XadpoJ2aaE7gT5UTeSLBLlOK/Y9uka2EB4gez5/+uQMUbqO285g18M34J6XDmmuAz0pKz96qw5bP2xCoO2LiNJ2yyfgBrtjvmedNB3OkmVwzFkGx7RyUIw14V6KJzixrlze6dfqz83P70VDx6Di5wuKsvH+g9dp3o8UevYMUZviDRkROilsDIUPH1mDwhx5il3ptZOdW/GY4LCg5qHrVa9Nuh/omR8rn65F54C6eKaIaXlO7HtkDdF3gczs65dK1MGEibEGvbb92LHwTKhiNG7K40lxlSS9J8TyuPN3+9DS7VU9kUymINFIZOjZmmbdDgYAzClwIcTxWP1MraEolFxfry+N5Pt/0NyNIMuDpiLpWEo40eXB5m2NqLp9+ARUABDQKKS10BQ4XkhgK8p1WrD9+9fBbbcojuX9N8zRFB975cApzfsHIoxJL+xpwdb7VuDFPS0x0Z11ZQXYuKEsJrqjBLGv7374CbrrD+JC/UH4z3wJcMPaDJTFBseMy+GcsxyOkqWw5qqn6PAC0N7nj5mfAIjnV39AXfRwIMCmLK1Pbs9w2y342Z2X4bHKBfjKCx8pasSwvIAX97Ro7jViFGXrwdQwhblsDD56bK3mWtGqTfrTJ+2R9DHCNahXj0SvXkS6ah1GIuptwoSJ9MKMZIxhjPZNmeTkX88JWqYR/+LVuh+3nYEvpJwWI41QiKemel7SRk8Qtfoth/mFbnC8gNYLXkOnlaksNKcpoDjXietL83GotQct3V5NqtOCbDsqLyuKqh8zNGJy+7XGUs4pkAp9zXm8mvi+pGMGAJu3NWJnYxfRmg0EAti2sxb//IuXcb5uP9je8zGfWyYUDqlsL4N9xmWgrXayTsn08e6rZuDwqYtE84vktJymgMluO2wWmnhfMrpnGP1d/BqversuQUneKIpyHDjw2BpF41189eqJOgBka1BPzUqy+3A6C9XHatTbhInxCjOSMYrR0dEBjuPAMAyKitRPGbWQjjzeVGIklb6TGWc1x00rF1kQlFV+49mSjBQkGokM8TyvixEnqssxayL++PFpxWv95C9H8b1rpyqOsdFCcznwAtDe68frh04T/8YXYrGzIWLIW2jgJomDodY/8f7Ek2+l56OH/pYXgOOdHjz9Xj0Oy9AQx6/Ztra2qCDezp074fdLjGfaAsf0hXCWRJS2LROnpWT98ALw9mfn4AuxRPOL5LScF4CuocJwkn2JZM841+fHNZt24aYhZiQxzSykEdmK12eJX+OrZrrxjyuKsP3YedV29ECutkru2p6APtV3kkgwSf0SkBq9CD3zT2lvHk9R75FGKu0ME8owx5kMppORQXR2dkZ5lZOdlKN9Ux5JpW+j46zluG29b4VqGk2vT12RWsmpIh0DUsrXeEPmgkeZAQgAGArIz3bEnNarKXfzArDn+EV8dS6tOMZG9QRSBU+Qgyc4bJyLz/DP969CtsOqmz43HncsmarL6REAvP7xGdnPOJbFl4f3o+LuV9Df/DGOHTsW87k1exLss5dG0qBmLgZtzyK+rh7IORgieAH4ryNnYhw1PerdJPsSqeNyNo4ZCYios6tB3GuU1vj/6/XjQOtFBEKpoaOUM95TGd2Ln6PxkKY01dR3onMgkJAyORJ6EUp7s571aEIdqbQzTCjDHGcymE7GGMVY2JTHmuIqyem2Wi7yhuf3qrafjFNFGhkaDIR1aT/QFHDv1bPwxK3l0b6RXIvjBUU9CpLfZxq8ADR3erDi57uQ67Sgz69eT6AVZXuscgEOtfbIajqQgPP0DtHLHoH/5KcQQj50DH1G0zRWrVqFyspKlJSU4On6bPQFyceTGapHSTW8IQ53/e4jvPmAem2REkj2JVLHReq0CNAWjhT3GsU1DuDsAIdUBH+VjPenqxuI2LBIoTVHpdHSwUAYz9U0j6heRDL7Rbqi3iZMmEgvLjknYyQ3qtmzZ6fk+mNlUx4pxVWj40zquCml0aTTqSKNDD1b06zLwRCfg/Q+SK5lt1lRWlqqKG6mp/A0VSBR8faFOPgI0py0HEJBELCiZBLO9weI0qYEnkPo/PGoYxHqOBHbd2cOJs6/Cv/2g2+hoqICEydOBACc6+rBDz8/pNm+FHMmu3CiW99pOakC+onu4WhEYgEwj67BoOp1tfYlPY6LuCa1YKGp6F6jusYB0DQDmpKvq1IDQwGThupP5Ix3T5DFG4flI1kiKECz1kgKPYcW2Q7riOhFxEdVGUrA9XMn4p9vmB79zkhGvccjUmVnmFCHOc5kuCScjNFSIJ2Tk5OSdsbKpjxSiqtGxtmI4yZVKt68vQk19R2Rv8Wd2KXKqSJxYnZopCkxNIV8t13zOawrK1Ckl6UpoGLhFEyYMCHhM3Eser3qKVrxoACUFUX0Is71+Q2lk+Q4rLBa6KTpR6UOYbwi9eah9JMumfSTeHD+AQROHo1oV5w8Ct4/EPO5rWgenHOWwVmyDLaiuch22nDrXesARAp3dzZ04qInpJsZbGFxNjoHA+jXiNZI73dugRvLFepwpFBLy7PQlKajorUvxe8ZWnOB5bEMDgkAACAASURBVHjNucLxAjb8ai/WLijQrN1w2S0oznXguIYGCkNTmOyywSpxKlw2RvHefrmtUfM5ymwdikjm0CKTDoZcetgbR8/jk/bBmPqcsRb1Hs1IlZ1hQh3mOJNh3DsZo71A2ijGyqY8VhRXjTpuannWFppCYY4D68tT41RpRYYeWl+K6roO5QYA5Lvt+OiRG8AwTMJnUqNRiV5WzWESx+J4p0fXiazY5p/uXwW33UKknyGHgUAYTmvifenFrElZCdS9IrNVPNuWFIIgINzVOiyId64pVhDP7oJz9pWRou2SK8G48mJ+7wlyuOO3+8ALQOsF40ri737RQeSYiKxdopEMAB+f7NE0sEMsrzstT7weyb4k3TOu2bQrRnQwHhZGm61QQISqd+vBNtAa+4/NQuO1f1yJa5+pRUjh0IGmgHtXzoxJMdTCrsYuze/IHVAoXT/TtRRGoKducKSi3iZMmEgvxp51rROjvUDaKMbipjwSDoYex8aI46bGosTxAtaXF6ZsfpFEhrQcpW5PEKue2ZMQzVNzECw0hYkuW0wqiMuWaMyLY6FlJs0vdMMb4hQjWxs3lGF/a4/s3KYpStGA5oXIHNObdhKPHm8o4URfqcibD/oQOPVZNA2K81yM+dyaPyvKBGUvLgPFqG+5Rms8pCB1MO5dOTNGfwQA/vLAalzx1HaoHfh7g6yutDzxekb2pZvKizTXpAAQ13GoabKI7b2wp0U1qpnjsCakGKqBtEaptMCFpk7lMXVaaUxy2zNeS2EUeuoGRyrqbcKEifRi3K/cVBdIJ3MaHwwGo7+3243x2YswN2Vl9Ax48fzOE6htvgCWB3F6nBHHTW1+CUh9Ab5WZEircJbjhSgnv5Q165svf6xYlMoLAioXFWHjhjJs3t6EDc/vRZjlYWEorJmfj0cqy+G2W4gZpQaDLPY/ulZxLSnN7XULCvDelx3oHlROxfKFWNA0wCVBEqSWZiQIAtiedvhaDkeiFe3HAH44PYiy2uGYecWQdsVSWHLyjXckTaAQmc8bN5QlfOayMXBYGVU1c4qiNJ+1225BbpY16X1pY8V87DveLet8lUx2RdekngJ0Cx2J0MWv8ZLJLnz3hlm4/YVDqk5qlp3RdR8kUVKKAnr9YdV0S5EZbSzASPrpWIl6j3ak0s4woQxznMkwri3RVBVIp6qmo7GxMUp5tnjxYuLfKcHclBPhCbK487f7cGaAjTEUSNLj9DpugiAgqJHjHWL5tD0buTb1Fs4e7/Sg4ld70edX5urnBaCmoVM2uvD6oTM4dKoXf75/FTGjVNdAEIOBsKrBpDS3dzaop53wAmLCGMlGNQCADwcQOP1lNA2K648tNrZMnDqUArUMjumLQFlGtyE4v9CN/ydZB9L9LcTymoXxWTZGs7bBbbfgwx/cCCAFEUyln1PD1xqma+3A+f6A6tyf6LJFhRrF++U4Fj0DPtz86w8xGFKfMTyv/7BJy/kXBKCjP9Z5TnW6ZSaRbN2g+S4zjlTbGSbkYY4zGcbOrmUAqSiQHis1HeamHMHm7U0JDgZAnh6nx3GjKAq+oHpxrTfIZvTZyDlK3Z6gIqWpAKg6GCJ6vSF0yBhvPCLj+lxNMzGjFMsLeK6m2VCER482A6CvmFaKcF8H/GK04vSXEFiJDgNjhWPGZdE0KGtesa62nRYKfnbkKH49IS7GwdCr3WCzaNdBpIp4YvP2JrQqpJC1dntjmK7Edbt6Uy3a+5TVv20WGlW3LcLGChZ3/m4fLngijFh+VgBUIjgiSJjH4j/XS/cLpD7dMtNQTT/F6KkbNGHCRPow8tZxmpFsgXQqazry8vLAsiwslnE/7COGnQ2diifXetPjSIwkra+MhPMnNbh4nsfVm3ZHU6SMIsQJmmmHehwAreegFD28/4Y5urUZsqw0fGH1k3eBDSPQfmzIsfgE7MX2mM+ZnPyhFKhlcMy4HLTNoX1xGUzLc+p2lOTa6BkMGHZUpNFbvcrsJHUQqSSe0JPuKt7TunKyPX/z9ia0dCsX8stBi3lMKdqtFCXt9YYU2bjSkW6ZSSimnwKYmWcflXWD4wGmnZEZmONMhnE/OskWSKeypmPGjBmk3TZhAJnWDxEEAVk2i2r+epaNAc/zoGnt0990gKbplGhW2C20ahrNRW8I376+BPtOdOOEBjsRoP4cSJTXX9zTglcPthGJzgmgMHuiEycvxp5uswMXogXbgbbPIYQkn9MM7NPKo2lQ1skzkp4zooH6sMqepHU7WVYaH/7gRqx8uhZ+g46j9CRejzJ7/J6ZbuIJkvUcYnlUvV2HnY1dMUxgJZNdCUxg8X3Tq0ov1m2QMo/FR7vjo6QAsPLpWlXK39Ggd2QUZt3gyMC0MzIDc5zJMO5XeTIb3VgRvTMRQab1QyiK0kwd6fGGcPWm3SOmzSIIQtIn56WFbniCHHwh5RQUX4jDvS9/jCtn5BE5GWrPgUR5/Ylby1Fd10EUofGHOdAMDTvNo/90Q7S2Itx1MuZ7jCsPjpKlEcdi9hLQdlf0M9HAbO/1IWAggiA1cNUK2//7i/O44AkptuMeqmMx6jjGn8Rr7W80BRRk22FhEkXm0mVAivspyXruHgwm0B3/8ePTKMl34WtXzcCe5m7ZvpHce5aNQV6WFRwfma83lObj4MkecuYxIaIy/3R1A35252Uxn4lzfyzoHSUDs27QhIlLG+PeyQCMb3RjRfTuUoPaM0y3fogelW9Ans0p3XU8CSq7NIVshwUD/sRaFS3YLDS23rcCL+w+oaldcaLLg7O9yo6IiPjnED+mpNFDEkOb8/bBf/ITHGo9Av/JT8EHpAxaFOzF8+EQBfEKS0BRdIwwYLyBuuH5vWgnuMf4+7336pl4eP2w8a20J+2oV1ewtg7tN1rzTi4qIrJKiSf5JPtbca4TH/7gRkUWsFQZkErpRteX5qsKBApIrLnhhUi9xrVz87HvkTUJfRP/rXXvE122mN9XvXMMrTrTqwDgjcNn8FjlAnnRyzGid5QKmO9JEyYuPVwSToYUeje6S+klkAzSfUpFyvClJz2OtM9q11aj2IxHJrRZ1Ap5KQpgABCSQAGIpKOsfXYPnDaLrDifFLwQiRpoYW6BG9++YU5U1TqiFh3RRHh4fSlx9HBdWQG2HGiL+UwQeIQ6TkSjFaHzxyHll6Id2XCUDAnizb4STFaiavmcfFdUGFCvUykHp5XBzoYuvF/XKTtvvSEuOr96fepF+L2+MFY/U6uYEkQh4oiwMmM4wWnF1vtWxKwXkv2NrDYpOQdDKT2uJN+Fksku3fohojMqCubJreFsu0UxRU26t3tDHDZva8TWQ+pq6EpgeQGbtzUmaJIAmdU7MiMJJkyYyDQoQVCxGpIAz/MYHByM+Vt2dvaI5aYbhdILUHwJ6DmVPn78eLRQaN68eWnqceaQKmpfEgphPc/g82NNePlwFw62+0DRlpiTaAC6+kxy7aerGxRTJuQwLc+JfY+sIf5+PKTjFT92Ve8cSyo1Kllo1RW4bAxqN96Ae146JCv8l+u0wGmz4Hy/chqUOH6eIIsrnqpB0DeIwMlPh+orPgHv64v5vq1wDhwlyzD1slUonrcQJy6op1h9fcWMhPQWEUbYmOIhnTsADLVHU0BJvgsrZ0+KSQnKtlvQ1DmoaDh/4+pZMQ6uJ8jijt/ukzXi5+a78NZ3V6c9vU9rzrpsDHwhTncUjqaAye5IqpcvGEZ/XCQv6pDxiZoZcwvc2HrfCvzbruN44/AZIoFDNaiteU+QTVvdQqr26FRhvL0DRyPMMc4MLtVx1mvbX3KRDL1IZfGaz+eL8iqPdSRL7avn5aeb4YsN4J5FTnxrSQ4uv/zyGAYYvX0mufYHzd1awxUDI3U80vEKshx8QQ4UBWTZLLBZ6OjY6S1mTTWyhgxCJSP3q8um44U9LbIOBgD0+Vn4Qpyqs9LrDeL+f3sTRQONCL39Z7Q3fAYIw+xRlM0J56wlcM5ZBsfspbBkTwIATMxz4q3/dR1W/nynarH+B83duoQCGZqCV8aIVYJ07giAqoNBI0ITLNeGXErQ6mdq9RNVaOhQpBtac1atMFoNvAB0qQg3CgDCnICyomz0DPqie/sti6fj2zfMwT0vHVIUqNQLtTUvpp09cWs5gNSkFQmCAG+IG3X06+PpHThaYY5xZmCOMxlMJ4MAZvFaIpKh9tVr7CfD8CV9Vkb6THJtUhE6EXrreDxBFnf8bp9sQbVoLL964BT2n7igKQ6YTtAUcPsVU3H41EXV9I8Nz+9VNcZDnIBcpxUDgXC0DT7kR6Dtc/hbjqC99QjqBy/E/MY6aQacQ7UV9mkLQDGxG7+Y/uKyMXDZrapOxrk+P1Y+vQtWhpZ1fOX2A/E0uqa+I1oo3OcLKV5HnDvi/ytCRU1QOvcpijJEVEGqQ5EukPQ5nRAQUaD/P7dNQSgUgs1mw+LFC1H1zjGc6EqNgwEor/lURhri2/IGw7LzL36/M99pJkyYSBdMJ0MnktmMx5MqZDKGvx5j34jhpDTOevtMem2aIjeSjNTxPF3doMnYxAvAiW4PnFZGV9upguhEPFa5AAAUI38uG0NkVPb7Q5hO96P56F70Nx9G4MyXADcsfEhZ7HDMvBw3rqtA1QN/j//xZpuiqKDUwSEp+OUFoHMgcgKudeobn+/P8oCVprCurADv1XWoOjMsxycddZLOfSNEFTX1qaPoNgKSPqcbLCfERDwB/dS+2Q4L+v3ywpw0BawrK0j4e6qEXtWiFkrgBeC/jpyJHpJkKo1qPL0DRyvMMc4MzHEmg+lkmNCNZKl99Rj7qWL4MtJn0mtn260436+cliHCaDHn25+dJfoeL0T6TKK3kCzcdga5WTbF9EG1yJ8S66/AhhA4/WWktqLlCE71nY/9XW5RVBDPPn0RaKsd/XlOLL9sPvaVzsGz25uwvb4Dvd4QQpwAu4VGXpYN68tj+6aneFsrMqdoKB5sA60xJy1M8vVp8XNfD1HFYCCMLg0K4ExQdCdDsSzWVYSSiIbEj6EgCAgRRgQZmsK9K2dG06vkjHyaolBd14GdjV0xhnyy0WBp1MITCOtOK/OGOHgltNQjmUZlwoSJ8QlzJzGhG8kY/kaM/VQwfBntM8m1t2vQjtJUhArUSB2PIAiqInjxyLIxmDLBjuMEWhVKoKkII5KS0UJTwFeWTidKtZD77KbyImzZfwoAwPZ3DTkVhxFo+wICK3HWaAsc0xdF06AsE6cmtCfOFbkUJqW+KTH6KEHtRF/NUFRj4iJRzqYQcUTUDN74ua+HrejZmmbNguZ0U3QLgqD7eYhw2y24/Ypi7G7qxrk+fbTCIuT2D2+Iw0WvslaJFPeunBmdF9JanRDL46I3BJYXwPJCtDZEasgbjQangnxA6ZrpZr8zYcLEpYWxRfVkYtRg3YJC0Aq2h5rhb8TY31gxH3ML3AnX0xsZUOszAPT5Qqh65xg8weG0B61rP7S+VFN1Ot9tx4c/uBFP3rYw7SeENguNvzywGl9fMQNGs1DuvXomDv1wHeYWuGQ/L8l3xWgt6EE4HMYKRwd8H27Buf/4Ds6++C1crPk9/C2HIbBBMO5JcC+uQP5dP8L0f/4DCv/up8hZfgesk6bJXkvOCJZGouQgFm/ffdUMWNQmhASiMxMPrbQaC02pzlu1+TXBaQGr4mBQALbXd8bMWem9uYcoWkWncfmsiQl910I6KLo9QRZV7xzD6mdqsfLpWmx4fi+Wz5qIu6+agam5TmTZyFL+fCEWH5/sAcsZq0NS2j82b28iYpOy0BQeWl8a/bfo6O57ZA0qFxXJOpmiIb95WyPxYUs8lBzbVEBaKzTSSBPxpQmYY2siczAjGRnEhQsXwPM8aJrG5MmTR7o7SSEZfne9kQm9DF9K43z/DXPwh0NtiqkVniCXkDJAcm0tp8lqoQ2fBlMUpRpVkEJa3CxSsOqh1gUihtPGirLIP5TeQwLQ09MDn4VKGGO56MH58+fx/vvvo7q6Gjt27MDAwIDkBmnYpy6IRius+bN0jdX1pfnE35Ui8txo1WiDFHLODM/zmobiRJcNlYuKsLOxS3HeKs2v7fWd6FPI8wcij+dcnz9hznqDLN774nyMs+wNcfjjx6dx+NRFvPmda4hqY+KN6FRA6RReVOl2WmmcI4zc8QLQ0u0lckpoCshxWJFlZ8APFeZLn4N0zyBxvgCgIMeObIc8s8zOxi7VKMXOxi7D0eB0M8ilM0VO6x042ih3xyKUxtgc29RiPNlz6YQ5szKIs2fPRinPxvqkTIba14iDoofhS2mcX9jTomlYyaUMaF073YKNdyyZSuQsCAKw7VgHqus6YGUo9BKmfEgx0WWDy8bgqXfr0XpBgXXoghe/3NaAb17uhtVqhSM7N+blZaF4lDFdmNxbj50123D06NGY3+fn5+Pmm2/GgfB0+AsuA+Nw6+6nCCNmkPgMd9R3EBlr0mcY/6K+4FGvxbFZaFTdvghVtyvrwSilelXXdRDdj3TOPlwxHxW/+kDWOYmf21pGrpoRbRTqdQj6U/x4ITLv1eqQXDYGX102PbovyT0Hcc+wWCzEbFc3zk8s5gbIU0I3LCzEqwfbdO0bRtm4XDYG2Q6rJusZkN4UObV3oCfI4q7ffYQT3aOHcncsQm6MU0UyYGIY48meSyfMWWXCMIxS+yarPWL0BbizoZNYx0ApH1pPjn+qVHsfq1yAAycuoLXHp/o9AVAVsSOBbSjqopUvfqg9gG9e7oYvzOOu33+EprZz8LUejShtnzyK/f6BmN8sX74clZWVuOWWW7B06VLQNJ0S4cA9hBolonNQU9+JPl8IwTAPjiCKIX2GenPh4w1FPcrZelmXxDkrAKrRD+nc1nKOK8qLiK9PinScwrvsFkzNdSYYp0pinUrPwR/m8cYXfZqOo4hDrT3wBNmE/Yo0JXTjhjLsb+3RtW/onRfSMXDZGFAUpbruUnEoohfi2vzTkTOyEVuzViR5JEMyYMJEMjCdjAxixowZ0fDaeEP8i1vL6Uin9ojcOOs9ASRJGRA/T6VgoxLoDNB8RouRCcaqx8+is6cXz7z8Jj7+aA+C55pjBPFouwvOkitx0/oNePGx+1BYmGi4iM6ZkjAfCUiek9FCWZE5SHyGonYCqYOh5WAq9Vs0ui4SGrsiWE7AjmPa0Q9xzNLtHMcjXZoYNguNNx9Ibv1NKpyK72/9Aqd6/LLih3JovaCsI0IS3TS6b2ixcYlpnkptZfq5SxG/N5OuzUzQKY8XyL3/kqGcNyGP8WzPpRKmk5FB5OXljXQX0gqjOZ+pDs3LjbPeE0Aj4lnpcprUBNNSBRItCT7ohf/UZ/C3HEHg5Cf4q00XYz635s8aFsSbugAUzeBzCvjrLcewtqwb/7KhLEHUTjSyROrZIKtPO0KOfjR+7I0Wyt69fHrMi1frFJ6hKeS77Qm6IFJorZHOgYBiupMWGBogYV610FTGnGMp0qGJITXYk1l///FxJ05dJHcwAHXjjNSQN9JvrbalUQs5ZPq5SxG/N+tZm5mgUx4PiB/jZCnnTchjvNtzqYKu3aS2thavvfYa9u/fjzNnziA3NxfLli3DE088gaVLl6arjybGAEZjzmf8prluQSFe2X+K6NR83QLj4lmp3qjTkWJCU0BhjgOCkFgEC0TG6v9+dBLhnjORFKjWwwi21wP8cDoDbXMgZ86VoGdcGaGYzUnMS+UFoL3Xj1cOtOH1Q6fxt8un49Gby6LjJGdkrd5Ui3YCSlLRwBwMhPFsTbOi4W50/N794hz+19p5Q+Ok/aLOd9ux/9Eb4Qvz2Ly9CRue3xvTn/sVtBTE+bP1vhWo+NVeQw4GTQHry4uImIFuKh+OKqUzoiiHZDQx4qF08m7kHozOESXjzIghn6l0U7GNTD53JegZ93TTKY9XpEpryoQJI9Bl9b3wwgvo6enB9773PZSXl6O7uxvPPvssVq5cie3bt2PNmjXp6qeJUY7RkvOpdlIsngA2d3pU24hhWJJgJO4xXSkmvACsKSvAT+9YFPNy8fl8qK2tRft7/41zb/wFbH9XzO8sE6fBWbIUzjnLMbP8SthsdiKHAABYXsDrh07j9UOno7SqdyyZikdvLkO2wzqsi1KubYhSAHIcFmw71oGtB9sSKEdFw/3P968yPH79fhYVv/oA+x5dC7fdAkaD7pamqWiNipwj8dan7RgIsIrz55svf6yoWi7CQlOy9Ko0RSHE8bi+NB9/OHRa0ZHOdVpjjPJ48UmjSMUpfEm+CxAiaUgJn012YUXJJHzQ3B1jVD+0vjTpw4tk1piacZZOQz6VbZOkhKYDesZ9JGpFxhPSTU5iwoQSKEEHYXJXVxcKCmJPeD0eD+bOnYtFixZh586d0b/zPI/BwcGY72ZnZ1/S+WscN3wKzDBkXPBjBaufqUV7r7KxOS3PiX2PpNcJVYo0SNMIAOArL+xHQ8egQivA36+YgZ8OUcBKMVL3qHVdo3DbLah7qgItLS2orq5GdXU1du/ejWBQUgvAWOGYcflQGtRSWPOKox9NzXViXVk+th46ndTJNE0BRRMcWF9ehI1DBrBSnraFpjA524ZAiMdAIKx6XZoCvnH1LOxo6Exq/P5h1Sw8edtC3Pz8XtV5s6AoGytKJhk+qWdoSlNzhaEAJbtMNMZBAS1d3gRHI9dpwfbvXw/XkNp0slSWRtMjPUFW8RQegOYJvVbkygiu2VSLszoF/cT5Nd5y2dNJdRr/DiTZ25QK+E3IQ87OIHk3mmOrD+PZnlODXttel5OhhDVr1uDs2bNoamoy3JFLAZ9//nmU8mzx4sUj3Z2UQRAErHy6Fp0DysxGRTkOHHhsTVpDslqsKaJBYGTDHcl7rHrnWFQhOxUQ2DAC7ccQaD2Mov4GNDc3x3w+c+ZMVFZWom/yIuz3FQIWR0IbNIANc52454o8PPnhQErEweKdwc3bG7GzoSvh5PrZmmZiQ35anjPpFJ2puQ589OharNq0C+f6lJ9/ca4DFICzKt9RgxoNq542vnbVDFgZOmqoM3QklephFQdOr7GRKqNF7aRc7rN0GUvffXkPqpu9xDUZ49U4S7cxGv8O1GKYc9st+MrSaWmvFRlPULIz1Jx7c2z1Y7zac1rQa9snPbP6+/tx9OhRolSpY8eOYebMmcjJyYn+LRgMorGxEUCkkGbGjBkxvzl+/Dh8vgh1Z/yDvHDhAs6ePQsgUukvLcThOA51dXUAIgNQUlIS89uTJ09GRcEWLlwIi2V4KPr6+tDW1gYAKC4uRn5+rODXF198AUEQ4HQ6UVoaK1Z15swZXLwYKYidP38+HI5hA43nI6+wcDiMc+fOobi4OOa39fX10UlbXl4e89n58+fR1RVJXZkzZw7c7mFtgUAgEHXwJk6ciOnTp8f8trm5GX6/HxRF4fLLL4/5rLu7G+fOnQMQMS5zc3Ojn7Esi2PHjgEAcnJyMHv27Jjftra2RieblnJyfFrB559/DgDIysrCvHnzYr57+vRp9Pb2AgDKyspgt9ujnw0MDODkyZMAgMLCQhQVDdNsajFobPvyHO6YGcl3f+0bV+CFfe0xhtiSAgZfvzwHfd0dcE+bFv2tJ8jih/95EN2D6sYjz4UxMDCACRMmRP8WCoXQ0NAAAJgwYQJmzZoV/UwQBLS2tsLjiaRvXXbZZTELtaenB+3t7Vg/hcNWlRNsErADF+BvPQJ/6xEETn0GIRy5lwEAFosF1157LSorK1FZWQmO48DzPHjGhkd2dCUaHACm5jC4e6EbWVY6mh9ec6wD5/sDuopnpeAF4HinB3f97kP4wsLwKWrZZNwyg0eWlUVv13ldedzn+vx499M2ZFkp+MKCISM+EAwhFApBS1i6oz+AZI5sKIpCUg0gMoY1dWdR+/3VMak0gUAATY3H8H8+6cWJzkRjmheAE50ePPr6R/jtt66P+Uxuj9i8vUmWFUx8hs9ub8ITt5bj5MmT0T1i0aJFMSd+vb29OH06ov8yderUBK75L774AkBkj5g7dy4oiiJKWfz+DdMV9wgg8h5iWRZ2ux1lZZG0yK9fPgGfdwRwdoCLGRsxjWvl7EnY3dSFQDAEhqZw3ZxcVP31shjjrKmpCYFAAAzDYNGiRTHX7Orqwvnz5wEAs2bNQk5OTnQ/VNsjAKClpQWDg4OgKEpxjwCAadOmYdKkScNjwvP48ssvAQButxtz5syJaffUqVPo7+8HACxYsAA2m404JbSurg4cx8HhcGD+/NiamPb2dvT09AAA5s2bh6ysrOhn4pmm+A5UTJ8DMKfAhb88sDo6xh0dHejsjNQczZ49+5K1IzweD1paWgAABQUFmDJlSsxvWZaN+a8It92Cf1o+EXfMZCEIAubOnTvq7Ai9e0Q67AhAfo8Qce7cOXR3dyMcTkxt9fl8OH78OABg0qRJmCaxIwB9ewSpHQFE9ggtOwJIzR6hF0k7GQ888AC8Xi9++MMfan6XZdkEOXtBEKIPK35RiH+Te5jAkOLu0GeiAS8FabvxfZK2Kw2JSdsVBAFWa6JQFcdxiu3C6sBLn5zHkXNBCFQPHLbGmDB0OBxWvFdpu/H3Kh1Duf6K9yp3YhjfrvT0UM+zUUubkcv5NPpslO6VJL83zPMIhUKgKApZNiYmp9nn8w0tYi7ariAI8IY43PX7jzRpVmkAy6bYEp+55F45jktIRQDP4soiK762MFGQTpyHVgjId9vQMUgurifwHIJnGyKORcsRhLtPxXzOuPLgmrsMN9y4Bp255fBaXXiLo+A5IeCmwiDsDOBgmIQCUwgcriy04O6FbkzOzYbdbo/mhz+8ZiY2/vEQalqMOxoCgOauWD2QPxxuxweNDH5+40S43WFd+fO8APT4BVAAsu0MXA4r+v1h+EMcMW0uTZEVTyYThaAAlBa40NSZfESI5YToHI5fy4falRmUeAAftydqsUjXo7j31NR3qAnC45UDpyJiggTzW9quFAO+Wfkj6AAAIABJREFUIP5wzIOj5zsA5jSsQ0JyWlScD14/TXP/Zlk25kVcOHECfnO7Ey993IlDZ3xgecBpt2H9wqLoSa/X60V9fT0oikJ+fn7C6a+4fyvtweL9fF7dDU6gomlI/3zjbNn+invF+1+0I8zyYGig8hQTw9JG+g6Ue69I934RpFSnoVAIPM/LpomovQOdTmfUoOQ4LqGI3R8IgaEEXDXViU1/vzpmjNXavZTsCK121ZApO0Kp3dHybLTuVW6PECG916ysrBgHkKRdpT1C1XYEiNqVQ6r3CL1Iysn48Y9/jNdffx2/+c1viNilLJZE5h2KoqKLTHoKIP2N3CIEAJqmo5/JTQbSduP7JG1XbhO1Wq0QBEG2XYZhZNv1BFn8y7YOtFzwD72cecDLxjATib+Tu19pu/H3Kh1Duf6K9yq3OTAMgzAYvP5FP47uOBrz8ntw7RziMXxofSkOnLwoeyI1a6IzgQHG6LNRuleKosBoZOLRFBX1xKXtUhQVbdcX5vGbj87j4B9bEOYFeAJhWYGo2HaBaTkW3HNFnuwYi/0NcvKpKttPsDjWFcZ/X8EixxnpnyfI4tndbahtugCWFxAgIBzivH3wn/xkiGL2KPiglPaWgr14PpxzlsM5ZxmsBbPhttH4MgzwfgD+SGTj1QOnUJtjxTM35SPbak0oMD179mz0lHLmzJkxp5QUReGri3Kx73QnPOHUFavzAnB2gMMbDT78YGqRIRpUAYAnxOGvl07HE7eW49pf7Caq06AArJjmBEVRSaddUQAmOK2ytSQCgIYOj6KC+QSnBZ4ASxTNsjBUwj5AURQsFovm7zmBijrXojMcDLOgBB5XTXXgsemRgwgtNXleQDS1UJzf7y5mMSFruF9q+7cnyOKHu3txZoAd2i/JGLfYoRvU2r+l+wiA6An1Y3k56O7uhiAImDdvHlwuV/Q7lGT/UGqX47iYPHhxDP2hMPp8ic/v1QOn8NGJbvzkugnIstKaOfRbD7bhQGtPNG2J9B2o9U4B9FGd2mw2cByn2K74ro/fD6dNm4YTJ05EvwfEFrE3NDQgFArBYrEkOHFK71bx35eCHUHSrtPpjGZEqLWbajuCpN3R8my07lVujxAhvdeZM2cm7BFa7Ur3CKV21ewIpXaTHUOSPcIIDNdkPPXUU6iqqsLPfvYzPP744wmfmzUZsSCtF8g0UpmDO9I5nySFue8/eJ3i5xGNgr2aDD9SxAu2qSHZmpF4CDwHz2fvg+3rRKC9DqHzJwDJ+TLtzIFz9pVwzlkGx6wlYLKGw68THAwGg5xiX+5dORNVty9K/FAFRkXvSCEW1iejFD4tz4kPf3CjZn0NEHEK5hUOr4Fk76+00I2t963Ai3tasL2+A50DQcVCbwtNYaLLBpuFxk0LChHieLx+6LTmNbT2EhLygm0PXqe5Jyx+qkazSF1Pv+Jh9BlngmCCBHrmitzYjNT7Ihlyi3QWjJswYWJ0ICM1GaKDUVVVJetgmEjEaFXcTCUt60hzr/drHPcPqHzuCbKGRNDy3XY8cWs50b2SzgE1gapwXwcGP3gZg437ZduxFc6Bs2QZnHOWwTalFBSdeOqxoCgbvf4w+gPyERpeAF492IadjV26jASjonek0FKqJm0DgGY0RM55TNQn4NE1GCTqg/hbcY0IgGoxP8sLuGlBAX52VyT3efUztZrXEJ2Ah9aXKn6HhMpSa0/YvK0RdgsNn0aEL/63eva4HfUdhubRDaX52l/KAPSsBbmxGan3hVGq09Gok2TChImRh+6wwr/+67+iqqoKP/rRj/Dkk0+mo0/jDnrC0JkGycvMCDLtYAiCoHmyyvHKY7x5e5MhETRSESM9c0D6TASBh+fYbpz+1VfR9sxf4dy//6OsgzHp5u9h6gOvYso3f43c6+6JKm7Hw8ZQ+O3XlqB7MJjwmRSiiN6rB07hrt9/BE9QfWw8QRZ/OnJG1ajKstGRFA+DU0Mca5ctUivyjatnYVqeE0U5DkzLc+IfVs3ClAl2ojbWLShU7AeFSCTnydsWJhhGopOw75E1OPDYWhTnOon67rZbYtS/dxKsq7c+ixRSkswdmgJKC9zwBDmse24vVj9Ti6p3jiU8t40V8zG3wJ1w71JhO609YWdjF3Kz9BcAau1xniCLqneOYfWmWpzvN8bQdfBkj+ZcNQK9e7NecT/p2Izk+4JkfsiB5LDKhAkTlx50HS08++yzeOKJJ7BhwwbccsstOHjwYMznK1euTGnnxgtGq+KmnpfZaFcDJRnj7sEgnnq3XvZkfkd9h+5rkooYieNHMgcAwNt7ARfe+9/w1u1S/X7h9X8P+9I7QFkTKWaVEOYEfPcPnxKnuihFtE6ePAmWZWGxWJBfPB13/e4jzdqVHIcNOx4SU3ESdRy0kG23YPUztTGpGNsevA4uGzNc4AwQncSqicKpGVNS6KnTkK7vyLrTLo33hzm0traCZVlQvFZdEIVmglNkLbVol40h2hM2LCzElgNtmvcghdoel6pUu9ZuryFRTOl8FtlvjKb/GBH3k47NSL4vjKqJk0Ze5MY5ExgL77BUYaTG+FKDOc5k0OVkvPvuuwCAbdu2Ydu2bQmfj8RJ/FjBugWFeHX/KVlml5FS3DTyMhvNm7WWwccJArbsP4W3Pj2L7d+/DoU5EeNcEASwOumQtIxROQMle+gUP6HoVxDgP/ExPqn9d9CPdsm2BwDW/FmYeNO34Ziur1Yi5loAmrvUFc/jIZeeMTAwEC0ufOXLJpzo1m7TwlB4tqYZLd36HQwAaOwYjPmdnBG9sWI+9p+4gBPd6s6DUWNKCk+QRZjjFYu1pdeWrm+KojQpn4EIm+3fvtYEjgf8GhNUTgVcyUHUSmvU2hNoGti4oQyvHTote13Z32jscalKtTOaSiSdz0By6T8k+6oUcmMzkgrNetNe9RxWxY9zOnGp1ohkcowvZZjjTAZdK23Pnj1p6sb4x8aK+aita0f7AJvAw056cpoOkLzMxspmHT2d7vSoUqj2+cOo+NUH2PfoWrjtFmKjwG2PMJ5oGaNKBgqFiAEX5gSwAQ/6972OwU/eVb1m9rLbkXvN3aAdiRSgRmHkMEAtokWSGiLOpR0600ikiP+Z1Ih+uGL+MBsSy8NpZaJUxWLxdPzzijemAPI0vwhJgHYNj9L6vqm8SFNgUQDQ7VN3LmgqEsVQMvalRrfcPcrd77oFhXhl/ylFR9AX5CAIAvJcNs20O7GPWnscaXoRhUi9jJpzk4roa7K1aqQRLqWxSUWkLRUgGcPRGKk3a0RMmBgdSInitxxMdqlE9HkDeG5HM2obI7Sko0FxU4tdaut9K3DPS4fSpgCbaniCLH75fgNeO3Rak67zH1YNM7RUvXNM1bDKdVqx79E1Mak5SlBihgmc/gIXd7yI8AVlliBLTgHu/O6P0TtpkaGUIhIwNKWLGQhIZJWRat6s/uVeTaameQUuvPmda7DuOe3v6sXUXCeybDRaur0Jc3ROfqygVzyMONCeIIvVm2pVWciybAwmumyK69sTZHHNpl3oN1AHRAFw2hjkZdn+f3tnHh9Fle79X/WS7qwkQAIkbAKyBBB8R9aLgmxBXMNcx9FRcZt5xxdG9IKCFxe8owPM4KjjenWcURRxZBRRhzGIgA4IiMuwr4EAYUkCSUg6dJbuPu8foZteajlVXVXdnX6+n08+H6iu5dRTp049zznPgkmFefjHztOyyn6q3QKLRYD7gjtbqt2Kmy4vwKNTB0gayWMWfSlpQPmzG32xt0I2E5FFAPKzUxXHOMaYYrYviwB0aefE5MLOKNlTgZO12jIgSeHvz/5Uv9FkWQKU3b8sApCWYsONQ/Nln0OiVGjmzYYVLudYt6ctYpaMk51klbPpFb8JfrLTnfifmy7D/yB+3I6U3Eb0zD5lBhkOGxbcOAif76lUVGbX7DkdaLt/5lCs6F52qg0lD13F/WH3z8r6mhtRt/XvOPfN+7L7pw+ehJyr7oQ1o7XS7MmsVHw+YwyeLdmPpVuOqjYI5PAHCMul+hU7Jtw9wz+oupo8aGiST/mb4bAGFH0tNS7EXMyCOVnrFjXGfAwolfHR1zrb2ZokQP6ec9Lsiqk+U1OsqHN7VBuSDIC72YuCbAvmFPXH2r3SLnYA4G4JXQ1paPZi2dZj2Hr4LD6eGWmAZThsSHPYJY0M/+qI0ironaN6YMENyq59PDPh+e1SsXFeqzx5427UEKwk6BGrFjyurtlTgYq6xpDVFx8Dzjd7sK2sWvIasc7WpwbelRezlLF4zeZoBsmk8MYSkjMfybusEGPi6YMRmjFnPDbOHR/IrGNU9ikjEQQBdg6fd6/vouuQXymYPrpHIGNRQbYTd4/uiY3zJgTiN5T4/vvvsf2VB3B08XU4/tx/ihoYFmcGOl4/B90f+RQ95n6GjlNnBQwMoFWBSb9QkfyOkT00Z2OKuO6FD/5b9wznignwk+W0B5SE4IVPv5LuapIOSrYIwM0/6RZQZCcO6KQYwxBMhsOKzu3kZS+nDsr1Ua0ZcdbuUe7zwX0rGL/Mlm4uw+lzTSFtt1qAgmwnUu3KwzIDcLCyASN/txaZDpsqmfo5dMEAC2/fk6t24fQ5+UKFHi/D7Ml9ZTMRzSnqz90WuWxfFgGYVHjRcNCaAYkXvdx//OPqpMJOohMFajIvxdP3QozA+BmW8W36qJ6mr3bHczZHgkg2yBQjQggP8tYr+1Q0M3Fajp1Y2EnR592vKIS7zNgsQNHATnh4Sn9kOGyyH6Pm5mb86U9/wsMPPyx7rbS+o5F99T2wZ3dWdFcKVmD8M4QHKuQDqwXIK9sCgNuGd8dvJlyKV9Yfgk/FB9aZYhF1KWrx+nBIIYg8XOmbU9QPGw9W4VBVg8xRrfgNFLmZax6k+qiW2U7GGFo4GmK1iCuGS0r2i66WAa2GyeTCzopuSMG4mryqVqXCCb5HNRmebFYBmU571MHzftTEIOgRtK+EnoHXa/dWSL6bbWlWPV5WXuIxRoQgkhUyMkyktrYWPp8PFosF2dnZsW6OItEO1tEEjEdzbG1tLe4dloePfiiXLMAn4GJQ+7RXNkUofm9vPorl3x5D+4wUMCaEXP9EWSkeeugh/POf/5RphYD2k+9HxpCikHoVfnel/RX1XApMhsOGD+8fjRG/+1K2+FlupgNNLV7FgoRi8TVKnKlvjlC4lm4ug0UQZM/jr2cR8bw4v+3ByqXW4nuAeB/VakDzJgmYXNhZdPuaPadljcGSPacxubBzVEaVzSIgL9OBWneLYsG8Fo8vcI+8GZ6C+6heiqVaw0FvhTZ8bNYr8DpeJmrMRqqdZn0DY5mdK9Ykmp6RqJCc+SAjw0SOHj0aSHmWKJ0yFhVgo80M4pfz80Ud8V9rzkT4lgsALu2UEYg5kZpZbvayVpcWnxeunWuxaf6reMorrcRPmjQJzz33HHr06ScbTP/WPcNlg+nDFZhMpx3t01Nwvll6djvFaoHNKkgaGQzAyh9PwN3iVV8lW8LVQ2k1JNNpDylAB7TO5B/mWMXIctrwzr0jAs85WAFt8fhQ5eKrtC3VR6MxoJUyB2Wn2kSVUMYYahqaZa9Z09CM2ZP7RmVUeX0MRQNbV0Tk+gwA2G2WwD3yZgmTUrKjVYC1Gg56KN7hY7NeqyWxnKiJR8z6BsZLdq5YkIh6RiJCcuaDYjIIWeYU9UOv3HTR33rlphtSAVav6rEd0mzYOG8C7h7dEwXZzoCf8F2jL/oJS7kyeOoqUbVqMY4uvg7H/nAjqj9/ERAxMBYuXAi32w3GGNasWYOBAwcq+id3ynKq9l+W81kHgPJaN07Wyge6azEwokFMeeJNVVrX6MH4JRuwYNUuuJo8IXFDW/6br9K2kkKhGAcgYUBLxQQArVnISh4aK/oMBUFAs8KsdrOXBdyQpo/qiVQNeiTDxcBsJTJSrHA1ebirit85qocpPvZSSne466KRfvVysWpq0NrPguN3ymvcqKhrRHmNG0s3l12IhdK/snlbIZ5iRAgimaEUtiZSVVUFr9cLq9WK3NzcWDeHC1eTBze9tFHUh75PbrpodhoAUaWAjDZ9pJScw2dHg1NnMsZwft9GVK99Db7z5yTPndLlUvQvnoXtL8+Q3CccpVlZud/9v+lREVkpS1M4PDUJ5Lh9RHc8XTw48H+eVKVi2CwCbhnWLSTVp1yKSqDVVetnV3STnXVWSt+stNqmdpabMYaBT5bIujClpVix+6miQH8oO3Eady/bjaM1jaqeXV6mA1/OHoviC9XV5fDLd/3+SllDVUtqWD0In823WgS0c9pwrrEFXh90md03cmzW2s/UpGFNFFeqWH0DE0U+epCIekYikqxyphS2cUwidsQlJftx+Iy4knL4jHh60Gj8kPXwYZaSc/j+Z86cwdFVz6Pi289kr5c18ma0G3kzLI40AEBqllNXd47w36VcJN65dwRe21CKFd+Xq57FbM3Lb5XNBBW+/52jemDNnkrZmgRWAZL1SLYcORtYhQDUV0L24/ExLNt6DNvKqgMK2f3jeuO9rUdFVwZSrALWzRkXkhFM7HllOFpdsu76y7c4UOkK7NP3gkubnMKqxbVHEARkp8m7vWWnpYScq2dBZ3w6qyOeLdmPD747jgaFGAs/1Q3NEAQBH88Yg4Wr9+KDbcclA9b98s1OtUsmENDDj12LoieloJ8M2y/aImtGjs1aXa+UEhOUXIjvSSRXqlh9A5PFwAASU89IREjOfCTvsgLBhZYUttH4IRudGeTzzz9Hnz59IAgC8vLyRA0MW/uuyPvZb9Fj7mfoMfcz5IydHjAwor2+EnIuEne8uRWzi/ohO82u+rwWQUBBdip3qtP87FQsuGEQJhfKu3r0yZOuRH5YJEWqktuXHMGucq9uKJU0Rlu8DK9tKIWryYMFn+zGmMXrMHLhOoxZvA4LPtkdMNBcTR7c8eZW7K+oh9fH4GOt8Qz7K+pxx5tbuQ05NX1BSZ5FhZGKvN+g2Tp/IrJT+Z69x8fwbMl+ZDhseKZ4MDoppAEGgLrGFrRLtemaGlbpGYQTvrDOG4yu1pXSbNS6XvFMtlTWNZErFUEQcQ0ZGYQk0eQb1+qHHO2x4dTV1eGRRx6BILQaBtdccw1KS0sj9su4/Fp0feA99Jj7GQp++RpSL7lcl+urRSkeZUnJPjR5+Gazg/H4GA5WumC3CoqGRvA9KtUkqJdZGREzQucU9UOvjuIxPkoEn08uLShD6yyvkj+7XrE/auCp8SBVX2NJyX7UNcoXAQzGLyue9xhove90h103P3bemAI5Q4Q3hsff/mjq9phVN4F31UtpssVzwTAOJt6NLYIgkov4XFMl4oJoVhWiye4RbWaQzZs3Y+bMmfjhhx8k9+nSpQteeuklFBcXo7K+CVcuXqcYlGtGZhKllaO1eytxntPlSex4j4+hf+dM1DV6IqoQA5H3KOfq8V+T+2LiH7+Wvaaoa1sUi0DNHh+eXLVL1oULaM3SdPpcZBxDsBIWi6rAUvIc27d16X3K81+HuL7MntwXgiBoisdpDkpPy+um5vUxPHF9oS6pYf/w+T5FI252kXgmtqWby7DpUBWawqqVK8GbDtZPPGdvUspiJoW/7z5xfWFSuQkRBBF/kJFhIjt27AikPLvsssti3RwutKawjSYFpNpj3W43nn32WTz++OOy9/KLX/wCixYtQteuXUO2d8pyomOmUz72wCLgzpE9dCv2Fa4IuZo8+MPn+xSVZ4+XRaWk+xhQ3+TBpnnjUd/Ygj+uOaAoY7H4gx07duDA7h1gXvmZ9XAjlDeFrRTVDc14Z8tRRcWr2Rs5y+vHx1rrVXgU9Fe1Cisv4fJsaPaKKtpvfVOGdzaXwW4BGjXYlQ1NnkDbeRXW4Oel5b6DlfaTtW5FI44BkoZIaVWDbE0RpfbztDWaVNlGIzXZwpOQ4WStGyMXfgm71RI3RhOQmN/ARINkbA4kZz5iP+okEYyxwF+iEM2qQjQFs5SO3blzJ2bNmoX169dLnkOwOdB+0q+RedkEXNopC69JKA2MMdkK3ACQm+GIemYwdNbUF1AA7h/Xm7tIntUCpKfY0KBxNQO4qDxnOu2agpeBi315eIETqw82cBuhatxfRNvOcbAAwGGzyGZx8voAu0JwiBlVgZWK4HkZ4NX4qJs9vkDgPU/l+GhdAdVmQPN4Gb7Yc1rWEFGD2vbzuMvFshK33GRLyZ4K2QkJHwMq6poAxI/RBCTmNzDRIBmbA8mZDzIyTCQ1NRV2ux02W+KIXc+iVFoRBAEejwevvfYafvOb38jum9pnOHKuvhf29gWBbf7ZUimlwehgc+BCKuCXN0akE33rmzKs/LEc9Y0eLqWq9nwL3C3aDQxA/F7U3pu/L983IgMHzlWIKmsWQUCz96KiyxsbIIZFaD2fkpHhN35dTV7ZLE62C24x8VAVOFrDS4oWH0PxyxuxcsaYwHu8aPVevL/tuKKbnBZ4g7T92CyCZMYrLYT3NyVi4S6nFqnJFgZwu1LFi9EEJOY3MNEgGZsDyZkPko6J9O3bN9ZN0EQ0KxLRUFpaitmzZ2PVqlWy+/W/aSbO95kIwSrdnZWUBh6FM5p7X7h6r2S9gnNu/kwwvClMpZBSntXeW3Bf/rB3byz+574I5dXjY1j+bWjqWbUpbFPtFnTIcGBi/zys3nUalfVNkvtaBODOkT0wZ0p/LCnZr/g8ZxtUFViNLKMxvHgorbqYZjrDYcPTxYMxb+oALCnZh7V7KzVPGoihxliyCMCkwk5RBWqHI9bfpNAjVbbZBLdDaoVZingxmhL1G5hIkIzNgeTMBxkZhCqM/OD6fD68++67mDlzZkSxl2DGjh2L559/Hn0GDMK0VzbhQIWLK0xBTmmYU9QPGw9ViRoCmU4bSvacxupdpzUHhq769wnufcORql2glnDlOZqg1/BjXY0toqsM4bOoE/vnYSlHTIW/rR/ePxqZzta0rWv3Vcoek5+digU3DgLA5+an1yqdmDx4Zam1dggvYsplhsOGBTcMwoIb9CtSpsZYCsmkBf4ZeR54Z+3NWL00kvC+2+LxocrVJCvHeDOaCIJo+5CRQcSUU6dO4dFHH8Xbb78tu99TTz2FOXPmIC3tYr2KBZ/sxkEZH/NwFJUGiQ/0ObcnZLVBrY8zY0w2PkAJi0VQjBkJRwDwsyu6YlPpWVHlOZqgV7W+9z4GrPi+HCV7KlAtowjZLALap6cgxWYRVfTVuDfxGhB6rNJFG0CsNYsQLydr3Xhy1S48PKV/RDv0UjgFQVCMcbEIrYZg8DNQOyPPA++sfby4y2klvO9e+fv1KK+RdxEkA4MgCDMhIyMMmukxFsYYVq1ahZkzZ+LECenZ/SFDhuDFF1/ElVdeKbmPXK2EcJSUBrnK5uGY6eNsEVorWLtVamAMwI7yc/j8wauQnmKN6NPRBL2q9b0HWhVxuQJh7VJtWPPQWORlOiTfP7VJCNQaEFrf+2gDiOcU9cOmQ1UorRIPoA8mPcWKJo+PKwA+uB3vbDmKzYfP6h78G7yCc7ZBwZVtVA8suGFQyPZgY1BNRXMlWoLS90oRbarseEIQ4ifGiCAIwg8V44P6qrRaOX78OMrKynD8+HFdzxvvVFdX44EHHoAgCLBYLCguLhY1MGbPno3a2lowxvDvf/9b1sBQ68uupDSoDb6VKvwllmlCEASk2q2y5xMAyQJtOekp/A0LYu/pekx7ZZOo4qalkrv/3owIVD7n9uC1DaWySqFfIb1YLM7BXSzOqIkDxpgmWQIXx50pz3+Nc24P0lKsSE2RHpJTrAKuvayL6lUtfzv0LtIWXmzPLVHTwt+P5xT1F/3dbwxq7ediVLmacOXv18uO48H9qXOmHR3TbeicaddcfDDW8BR6jDXJ+g00E5KxOZCc+UisUdQAzMyVXl1dHcir3K1bN13OGa+sX78eM2fOxJ49eyT3ueSSS/DSSy9h6tSpqs/P68tuswj4+bBumDd1gORz1Bp86/dxbmj2Kvrj33R5AZZtPSZ5rp9d0RVpKTZR1x65IGYlxGbSee7XX8gt4t4sguyMdTTwBqb6W+6Xh9kJBP2z92v2nEZNQ7Okcu1HzBdercsZ0BrY/I8dpzTfr97Bv0orWmkpVrRPT+GKcdE7AN7HEKguLjeO+w2cm3p40NzcjJSUFAwZEtvgaK3oGWNkFMn0DYwVJGNzIDnzEftRJ8bEe670RKGhoQELFy7EM888I7vfvffei2eeeQadOkW/dK/ky96znRWf/ddExY+r1uBbm1WQLKQWrtw8OnUANpeeweEz5yPO06tjGh6/fmBA4QlXSKPxW/cxYOmWo2AXzpPhsHHdb3VDMyrrm7jrd+iBxyvv4hIPxdNcTR7c9NJGHFJRUFDMF16Ly5mPIer0xXoG/yqtaOWk2bFx7niucxkVAK9mHJeSSSK50MYqEyBBEIQYSW9kmJkrvV+/fm1q4P/uu+/wwAMPYPPmzZL7dOjQAS+99BJuueUW3e9briJu79x0vH/fFdxKp9rgW7+Psxoj1SJx/+Hbw+UkNUOZ6bBh3+l6xZltr4/hrW/KsPFgFT6e2VozYeKATnjrmzLJYzw+hrv+8q0mAyPDYUOGwwabVUBNQzO3n73NapHtI/EwIbBw9V5VBoaUL7xRtTGsCkkC9Ar+5Vl58PrUKehGBcDzjOPhY3M0mdfihXj8zrS1b2A8QjI2B5IzH0kdk6EmV7oeOJ1OpKamwul06nI+s2lubsaSJUsgCK2KyrBhw0QNjPaDrsJPHlmGJ1ftQtmJ0/j5z39uyIsY6aPvRNecVNw1uic+njkGHdtlcJ9Lyp9ZjGAfZ15/fLnAcn8tAzn8M5Qb547H5kfHY+Pc8Vhx/2hc2on/Hg9VNWDR6r0AWu/XpnCzByrUGRgWAejbKQNb/ntCoI03X9GNS6aAcmCqkqw/+O647nFU4Xz8I38qYilf+Ghcg9JSrJLytAhAX5k+rGcX+1bnAAAgAElEQVTwrxEpYNW8g2pRGseDx+bwWJOKusaA69W0VzYZ3sfaMon+DUwESMbmQHLmIzGmZAwi0XOlm8HevXvx0EMPoaSkRHIfq9WKS4sfQGOvcWBCa4DzGZjjxuJXvp+4vhCA9tk7qdWCsX1zIQDYcKAqwsc5PcXKbaTKKcgMkS5NIb+HzZb4/+1v882vfoO9p6XrigSz8scTeLp4MNJTrLBbLfD4pFcZvArGdardivbpdnh9kPT95nX16pOXLhuYyqOYNzR7Me3lTfhohjH9jTHG7a4UXBhQLG2sVtegguxUeH0Mh8+EZqLyGzRv3TNc1MXNiOBfvbMZib2D9Y0tumSc4h3HGWNxsWJGEATRFkhqIwPQ/qFsq8tkXq8Xb775JmbOnImWlhbJ/YqKivDHP/4RhYWFWPDJbizdXIZwndToj7LeLg1K/sxi23iMVAAcriUsxCgDwHVvGQ4bVtw/mjuI2N3iDdxHs1c+YFmJFq8PJQ+NFU2RG9w+v+K4Zk8Fqhua0djiBUOrW1u6w4Ybh+bjUZnAfIBfMT9UxdffjH5/gwsDiqHVNehgpQu9ctNx2/Duooav1uBfLfIwIgVs+DsoFfOkBiWDJ3wcOSNTyyVeKmcTBEEkAgLTyxcoDJ/PF1G1OTMzExZLfHloSQWT+j+UwbPw0Sq1LpcLPp8PFosFGRn8bi5Gc+zYMTz88MP44IMPZPdbvHgxZs2aBYfDEbJ9zOJ1skWguuakcgeA8iL33Hp1SMM704cgMzXFcDn7DSwpI3X6qJ548oaBijIK5pYruuLH47VcfdJPa9/ch7e+OSp7bosAlP6uNZvXgMc/R6NH2tCwCFBU7H4xLB/P/PRy+Z2C8Cuz/mFHjWIrJ+tgpPqbHkbpoCc/h6tJfmY9+LlLIdt/c9NhgYADleKFJoPPr2QcKAXSRysPV5PH8GxGYtcIX2G0WIDzTV7UNbZwvzP+c097ZRMOVbjAa3J3znJi86Pj2+Qkk9HE6zewLUEyNodklbNa3T7pjQyA70OpxhiRYvv27YGUZ0OGDDHylmRhjOFvf/sbZs6cibNnz0ruN2LECPzpT3/C8OHDZc81cuE6VNQ1Su5jxEdZVrkHMKVPKv7vsA6Gy5m3X/AqyEDrDL8go+DfPqI7ni4eLPqbkhKc4bBi11NT4GryYNCT0i5wfmwWQbbwW166Fd8+PkXxPHrgavKg+OWNOFgpH3gt1t+0vr/hSvr8lTtlUxEDrTK7ZVg3xdUZuXFnyvNfG2q4q5UHz0oH7+pfNMhdQ4vBo+a99GPEpEmyEC/fwLYMydgcklXOanX7pHeXAvjS/iW6n25lZSUee+wxvPHGG7L7zZ8/H/PmzeO2zGMV1yIbBAzgu5NN+L+6XlEcXvcUv2vJwQqXYjYoBkS4ngXz/rbjknU/bhwqX4/jxqEFAFr7Mw82CyCz2AGvT7+UqHIwxpDhsGHljDEY+bu1soaUmpSxYu+v3Az/o1MHYOuRszgkY+h4fAzLvz2GbWXVspMPUuOOmoQURlYp99do4V3pMCMzk9j9BscoqU3fqjbLF1XOJgiC4IeMjDCkPkx6pLrNy8uD1+uF1Spf/VkvPv/8c8yYMQOHDx+W3GfAgAF48cUXMWHCBM3X0TsAVAkeJcwnWJCbm6vrdaVQUm78SperyQOn3aJYvE0Jj49hSck+LLgh0udfTgnuk5eOR6cOAACs3SNehTocJTmn2G2GGRhSyuqNQwuw/Ntjqvob7/vLU4vj4xljAkZltasZ50WCwdVOPoQH9httuCvJY82eCmwSibdQSuYQD7VMAD43PLVZvuKpcnaiYvY3MBkhGZsDyZmP+PNdikP0SnXbpUsXdO3aFV26dNGzeQHOnTuHOXPmBFLMXnPNNaIGxowZM3DmzBkwxrBnz56oDAxAOvWkUR9lHiXMmWJHfn6+rtflQczA8KfDPFnbGLWB4Wft3krR7RkOGz6eMQZ3j/an9XWga04q7h7dEx/PaK2RwRhDC+f0rcNuhZSkBQBTBukn4+D3Ry6N6NYjZ9GrYzp3f/P5fNwVznlm+IPTCeek2yXPGZzCWC0TB3QyLBUtz3hWc74ZB0VSGAfLQQwe+cULPOOI1SIEUmNPH9XTNCOprWL0N5AgGZsFyZkPGi05iOdUt5s2bcJvfvMb/Pjjj5L7FBQU4KWXXsKNN95oaL0KowNAgzF79UQrWio78xDsLhO+epLhsOGJ6wslV1bUpFDNTktB1xyr6D1YLQJK9lRIpt7lQWq1osXrk1RWD1c14Nbh3XHlpbmS/U0sY5Ac/grnK747zr1iyRiTdSUDtLs1GZG5Cbgo7zP18vJo8vgk3frkVm7NLG6qB2P75sq6F946rBt+e9MgCvImCILQABkZnMSLUut2u7FkyRI88cQTsvvdcccdWLhwIQoKCkxpV4bDhtlF/cAAfLHnNFq8DF/sjU4BlcMoJUxvjKrsbLEIeOrTPSHK+di+re5hXx2oUvSF50mhahGAosJWxf3Zkv0o2XMalXVNgUBwj4/hZK1bsyuMnGuNRRBkldWvDlRh49zxooaU1Hnl8PgYip77WrEmQ7DRwGOsVbma8NSne1S/A5GGuw82qyUqw51XLhYBSLEKcMvsJGY8mRFLYjYM8Vk5myAIIhEgdylOzHYJCmb79u0YN24cBEFAWlqaqIGRnp6Ot956C15vax2EpUuXmmZgAKHuLSdqGw2vkitV7VvJpcGgZGqS19Ja2VkOiwCcb2qJcCVatvUYlm09xlWlWKm6soCL/drvHjS5sDN8IvLT6goj51ojl9EKCHVP5A3yVqLWLV0Xxk/4iqWcWxNwsf6J1nfAfwv+e4mmN/HKJctpR056iuw+Yiu38bziK4aryYNV/5av4P7VgSqTWkMQBNH2oJUMTvRwCdqzZ08g5VlhYaHkfi0tLXj11Vcxa9Ys2fPdeOONWLJkCfr06aP6fvQmFtm3pAKuw+VsRLYbntlYHqUrzW5Bs5cpKtV+LEKrEnjO3cKlcErJP7xIXs35ZjR5fEixCshJT0FRYeeIfq23K0w0qzx+ZVXsORi2eiSyYslT0VzLO+A32sOzkSmtGsn1S165pDmsmFzYWdPKbbys+CrhT4esVPMk0VZe4h3ebyChHZKxOZCc+SAjQwVaUiQG09LSIllFu7S0FLNnz8aqVatkz/HCCy/g/vvvh90uHXAaC2Ltix38LILlrGe2Gy3GipLS1aNDOvZX1Ef+KLJvfnYqJg3ohJI9p7lm3f34GLDi+/IIo0GsP0vVIQCUM02pUciiWeWxCECmw4Yxi9dFPIf0FKshq0cA0KtjWsSKZbCxtnTLUXglXgK174DfaA8/m9qUu/7nrUbePh8we3JfTe6IieLGuKRkP0qr5OutAPG18tIWkPsGEvpAMjYHkjMfZGRoRMuHx28Y2O12+Hw+LF26FDNnzkRDg/THbuzYsXjhhRfiuthLvPliB8tZrxUWrcaKktJ1rtGjOLtsEYA7R/XAghsGgTGG1btOK7ZXrP3FL2/EygsZpsLxPxe5WgeuRvkBVY1CJggCbBqcNS1Ca7G7fafrJWf4eYPa1SAAqGv0YsrzX0co8P5A+9W7TssWpVTzDuiZcjfDYVMV7G+zCsh02jWt3MYiCYQWeFZ14mnlpa0QPDYTxkAyNgeSMx/xMeInCdnZ2Zg3bx7eeecd2f1++9vfYvbs2UhNTTWpZdERb77YwUuXaz9dp8sKi1ZjRU7p+q/JfTHxj18rXrt3bjrmFPUHoC4zVDilVQ1cRpWWwGlehSzYeKk5zz8LlJZiRfv0FGQ6bBEGBhD6HHiC2sPbnuW0oU7G4GMAKi9kZBIzLPV8B9QY7Wr6JW+wv/85al25jXbF12h4V3XiaeWlrUBuJcZDMjYHkjMfFPhtIIwxfPzxxygoKIAgCCgoKBA1MC6//HL861//AmOtisNjjz2WMAaGHyPz+mtFr/omAN/MshT+me6Nc8dj86PjA1mRMp12RcVUANDQ7A0U82OMKQYbS8Fbt0Ft4DSvK0x9Y0tI7YvzCpmcgslJs2Pj3PGob/IoplaVT9KQjttHdI9IFlDy0FjZQPjw64gFuuv1DqgxWNT0SzXB/mJt0kK8GRgAn3zTU6xUE4MgCCJKaATVmbNnz+LJJ5/Eyy+/LLvfww8/jPnz56Ndu3YmtcxYovXFNmLGU6/ZZa3uYDy+8kqzywzAydpGvPVNGd7dchQ56SmwWy3Ictpwzi2tcKtpZzhKriR2i4C8LCe8PmVXmGAZnHU1aS5G2Ozx4YmPd+JEjVtxP7+CqOSyEy6H8GOqXE2qYiz0jEfgCaBW2y+1BPu3VZTk+7MruiWFHAiCIIyERlEdWLduHWbOnIm9e/dK7tO7d2+8+OKLuOaaa0xsmXlo8cU2IutTOHpku9FirPD6yvNkJ/Lj8TFUXXDZsQhAu1Q70hxW+Hyt1x/XNxcf/XhCdoVAyajiUVxbfAxpKRZ89P/+A5lOaX9ULW5XUlS5mrF0i3TRND8NTZ6AQq3kshO+LfgYn8+HUYvWq4qxCH8HWjw+2G2htS14jWkeg0VLv+QN9m/rJEqAOkEQRCJDRoYGXC4XFi1ahGeeeUZ2v1/+8pd4+umnkZeXBwA4deoUysvLYbVa22QpejW+2HpmfQrn1KlT8Hq9sFqtuikTao0VXl/5cMX0ZK2bSyH3MaCusQXFlxfgiesLA7K2WS1RGVW8MR+lVQ146qPvMfvqHpJ92ahq53LwGBM8WCwWzatggdu98FOz14eFq/dyFUn04+8X//PRD/j6cC28PsCRYosw2qMxosOD/ZOJ8PeuqdkDqwW4qlc2npj2f2gVwyCCx+a2+A2MB0jG5kBy5oNiMjjZtm0bRo4cCUEQkJmZKWpgdOzYEX/729/g8/nAGMPrr78eMDAAoLKyEqdPn0ZlZaWZTY8JSooLjxKulWA5ay3aF47aYoxqfOX9xtm/HrkaHTMc3PfpP0+wrPUoGskT8+FjwNeHamT7slH1KuRIS7HqVnBRbYxFcEHK1oKITaqLJAaT4bDhF4UOvFTUHm9cnxeI5Qnus7EsEpro+N+7jXPH443r8/BSUXv8otBBBoaBJNM3MFaQjM2B5MwHjaYSNDU14YUXXsDcuXNl97vllluwePFi9OjRw6SWtQ3MrKuhR7YbNe5gWmM4BEFAisq8rkouO1pSiM4p6odvDp3BgUqX/LV90hXUtdbBSE+xIic9hXtFJ5wUm0W3mXm1q2BqVm7UplAWuye/u6GryQOHrbWoo8NmQU5aCiYXxlfK2HgnGVdzCIIgjIa+QEHs3bsXDz74INasWSO5j91ux0svvYR7770XVqtV1fl79+4Nn88HiyW5F5CMrqshJ+dolAleYyWagHO16VfFzhOtUZXhsOGjGf+BEc+sRYNMfIfTYZesNq811W6m046vHx6HUYvWoaKuSdWxemcxU2uwqV254TGmpfqylLuhu9mLrjlWMjBUQmOzOZCcjYdkbA4kZz6S+ivk9XrxxhtvYObMmfB6pZWpKVOm4LnnnkP//v2jul5GRkZUx7cVjK6rYYac/W2TyihVe75Z8lg5ZVhNIDhvjIUYUsZHcCaim6/oJuvvXzSwi6ys1RpMQOtzb42HUDdwG+UexGuwaV25UTKmpeQrtWrCoG6FhGiFxmZzIDkbD8nYHEjOfCSdkXH06FE8/PDDWLFihex+f/jDH/Cb3/wGDocjKbOvGI0eWZ9ihVRWrPvH9cYdb26VNRCUlOEMhw0f3j8az5bsx9p9lWj2+FDd0AxP2Am1KNVy7X51Q6no9miC5tUYTH7G9c0FwG+g2CwCOmU5VbsHaXmn5fbXunKj1Zg2090QMCbFNEEQBNG2SSojQ+4jOWrUKLzwwgsYNmwYgFaFbKHB6VWTmURNISmXFevjH8tlq0anp1jxsyu6iSrDriYPFq7ei49/PAF3S+uqWlqKFTcMycesiX3x2oZSzTEWSu1+b+tRtHhZSM0Nf5avd+4dofnaoXUZTuPUuUZFo2Hz4bNwNXlkDRSbRUBelgNFhZ3xX5P7yqbRDZeBkSmTtVQa12JMG+1u6MeMFNMEQRBE20VgeqViCcPn86G+vj5kW2ZmZkz918I/uI8//jjmzp2L9PT0kO1SCplfAdaaXrWxsTHw4Xc6nZruoS3havJEFaAshZFyXvDJbtUuQH665qRi49zxAEJnhl1NHtz00kYcqmoQPa5PXjo+njFGVZ0FPdptEYDpo3oGZsSDr61FxmMWrUN5rXwxveBrSvUPNYaFH6V3+sP7R6s+ZzCMMTQ0e7nrgvCOJVJyHrN4HcplChMG9zUtGDUGxis0NpsDydl4SMbmkKxyVqvbJ5WRUVlZiePHj+MnP/mJ7H5yClm44qWG7du3o6WlBXa7HUOGDFF9fFtGT3cMI+WspNzJkZfpwDWDOuPLfZUhM8MtXh+WbZUvNHf3aG19zo/Wdkspq1pkzGvoiF0z2v6hdO20FCvap6eomqkXm+kf2zcXAoANB6oChtG4vrlgAL4K2sZrTEvJ2agxyqzz6020/YPGZnMgORsPydgcklXOanX7tjMVxUFeXl5I3QopzPZ3JhIjhaTW4F4/1Q3NeGfL0Qh3JZ47j6bPMcbQ7PFpOlYPtxugVSFv8fq47lUqvW80KGV+Ot/sxflmN3cxSKmZ/uXfHkOfvAx8/uBVSE+xRrRbqyzD54KMdjdMhDGQ3LkIgiDiGxqJwzDS37l9+/aBCpGEcRglZ63BvX7Cg7cBcLsvebw+zQpqQ7MX1Q3S2a7kkApMViNjKYVc7TW1osY45K1fwVvRPRw19+Vq8mDpbjc2Ha6DhzE4S9aFKNHR1kORwqyYj2iQizHiMRLDobHZHEjOxkMyNgeSMx9kZIRhZHrVbt26aW0WoQIeOWtVkOSCewUA7VLtqGtsiZhdtgiCqJHBi80qXWRO6V6WlOzXdG0B0oHJavqymiJ1RmQWU2sc8szUGz3TL6pEN3gilOhoi0yKYXSKaT3QauRJQWOzOZCcjYdkbA4kZz6oiogIEwd0gkXi+xnv6VUJaVxNHiz4ZDfGLF6HkQvXYczidVjwyW64mjzc55hT1A+9OqaL/tY7Nx0lD12F6aN6omtOKjpnOdE1JxV3juqBnPSUqNoe3ufU3MvavRWarmm3Cvj1uN6ajg2/Pq+BYVRmMbl3Wgz/TL0Yamb6tcKjRAejt8If72OgkpG34vtyVe81QRAEoT9kZIgwp6gf+uRlRHxk4z29KiGNf2Z46eYylNe4UVHXiPKaVh/8aa9sUqeQSOlzApB+YXZ549zx2PzoeGycOx4LbhgEh037q9YnLz2kz6m5l2jiSDw+htc2lGpuN+/1LUJrsPf0UT0Ny1ok9U5LITdTb8ZMP89KiR8jcnfE8xjI06dcTR4Uv7yRDA2CIIgYQkaGCH5/5/AZaSOVIMJY1M4My53nsESq2cNVDSHnCVYy1c6kC2jth78Y0T2QvlbLvUQTRxKuzGqB5/pd2jmxce54PHnDQMPerfB3OtUuPfTxzNQbOdPPo0Q3e3x4ctWuqFbl5IjnMZC3T5eGvY8EQRCEuSRVClut6OXvfODAAXg8HthsNvTt21eHlhFiiMlZr7oCWs+jJvi5a3Yq/jX3ask+p7YN0dT26JzlxOZHx0e0RU1fjsd0qPWNLfjpq99orgNhdB0JpWdsswjwMWZaDYt4q/gdTTpkMWhsNgeSs/GQjM0hWeWsVrdPPI0/Buj1cXW73Th//jzcbm11Fgg+wuXMMzN8staNJ1ftkp0JjsYXP3hmOD1FOhuFRQAmFXaSDfJW2wa1rkLBSLn98PZlf+pai8g5Yul6k+m0q5qpD3+mRs/0K618eXws6lU5NcSTgQFc6NO5GYr78cbG0NhsDiRn4yEZmwPJmQ/y+zERQRACf4RxhMuZx73Cx4B3thzF5sNnJZXEaH3x/dmAZhf1w7SXN+FQlfoaB1raEJ7utNnjQ3VDs2LGKTm3H56+LLd6Y7MIuGVYNzw6dUDMXG+UsjMp1WEwKrsTEFQHo8KF4AonSpnK4qWGhdFkOGz4aMZ/YMQza9HQ7JXcjzc2hsZmcyA5Gw/J2BxIznyo/rq7XC489thj+OCDD1BdXY3+/ftj3rx5+PnPf25E+9oUl112WaybkBSIyVku9awfnvSXcufh9cX3K0haaxxoaUO4QtzQ7MWzJfuxZk8FKuoaI5RWJYOHpy/Lpa71MYYUqyVu4pvEDAw1dRj0/tBI1cGY0D8Xq3dVoKq+SfLYWNewMIsMhw03X9Et6vcRoLHZLEjOxkMyNgeSMx+qYzImT56Mbdu2YdGiRejbty/ee+89/PnPf8ayZctw2223BfZrSzEZROKjKiZCxo/bCF98n88X8l4oKYh6t6HO3Yznvjioe1E3veJgYkE8xZG4mjxY8vk+rN1XiRYvwxlXE7wynTie5ao3RsfGEARBEBdRq9urMjJWr16Na6+9Fu+99x5uvfXWwPbJkydj9+7dOHbsWKD6IRkZRLzR6v6yD0s3H5U1NKSCnYPPE22l5XBXHKtFQDunDecaW+D1IcI1R+82SLkCzZ7cF5lOO9c9yMEYw8iF61BR1yi5j5KcY0m8GEhqq6XHKpA+lujxPhIEQRDKGGpk/PKXv8T777+Pmpoa2GwXB+/ly5fjtttuw6ZNmzB69GhNDSH0IxlcJaJBTwVSi6x5FUfe2Vi1bTBr9jdeFHW1xJOBpCYzGM3e09hHEARhJGp1e1Vfol27dmHAgAEhBgZw0Tdt165dASNDjN27d6NHjx7IysoKbGtqasK+ffsAADk5OejevXvIMQcPHsT58+cBAEOGDAn57cyZMzhx4gQAoHv37sjJyQn85vV6sWvXLgCtAujVq1fIsUeOHEFdXR0AYODAgSH3VFtbi6NHjwIA8vPzkZubG3Lsjh07wBhDampqROqy48ePo7q6GgDQr18/OJ3OwG/l5eWoqqoCAHTu3BldunQJOXbPnj1oaWmB3W5HYWFhyG+nTp1CZWUlAKB3797IyLiYWaWxsRE/7tqLZTvO4btTzWCCNWQm/OTRw3C73RAEIcKPsKqqCidPngQA9OjRA9nZ2YHfPB4Pdu/eDQDIysrCJZdcEnLs4cOHA51t0KBBgVUsAKipqcGxY8cAAAUFBejYsWPIsdu3bwcApKWl4dJLLw357dixY6ipqQEA9O/fHw6HI/BbXV0djhw5AgDo1KkTOnfuHHLs7t270dzcDKvVii5duoQ8u5MnT6KqqgpDcy04WQtxVxgAI7ulRWzfv38/GhsbYbVaMWjQoMB2QRBQWVmJU6dOAQB69uyJdu3aBX5vbm7G3r17AQDt2rVDz549ZWMVgvEx4FCFC/OWbcRTNw5Ghw4dLv7m82Hnzp0AgIyMDPTuHVqZu6ysDOfOnQMADBgwACkpFyuOP/PJDhyscCH88v6YlEff24T7/k82nE4n+vULjckoLy/H2bNn4fP50LFjRzidzoCMGxoacOjQIQBAbm6uqtiR06dPo6KitSbHJZdcEtMxgie43iIw7NixA4C+Y4TL5UJpaWsBxLy8PJTsOinbT6wWAbkZDtisAkZ3z0DxpXaU7tstOkbs39+adap9+/bo1q1byHkOHDjQJsYIQRC4xgiPxwOHw4H+/fsH7tHr9aK+vj7Ql/r06YP09PTAcefPn8fBgwcBAB06dEDXrl1Dzis1RgBQPUYEU1paCpfLBQAYPHhwyMf87NmzKC8vBwB07dpVtzHi3LlzKCsrAwB06dIFeXl5Icfu2rULXq9XdowAgEsvvRRpaWkhv/m/gZ06dUJ+fn7Isfv27UNTUxNsNhsGDgxdjYunMcJPLPSI8DEiXI/YsWMHvF4vrFZrxLuspEckwxgB8OkR4WOEH78e4fP50KFDB6SmpgaebTKNEbyoMjLOnj0b8ZIBrR3S/7scHo8nIp0gYwwtLS2B38WO8f8ejs/nC/zm8/kifuc9b3ibgs/r9UZmLmlpaQFjDHZ7pFuJ1+uVPK//QyZ3Xql7DT5v+L26GlvwyJoKlNd5LyiOrfv5g1R/N74D0NIiOsMnd954fDbBbZKSodfrhdfrxcmTJ0MGdv+93jIgDfuqGQ6fPR86kw+gIMuKe4fliZ7Xf+5w5J558L36j5Wr5hyOD8C35W5ZGYo9g+A2hfPVoeoIAyNwPQZsLT+P6YPTQwZ7sfNWVFTAbrcHZBz+bAIZksJXTBAZVC4nw1j0w4kDOmHpN2WIPKLVQBrbO8eQMSK4vR6PB00t8sX1cjMc+Gbe1bBYLCgvL8fp06fR0uKVfZfF2uuXYbKMER6PJ+RDfPLkSbS0tMBisQTaouW8eo0RYucVg1eGascIpXttbm6Gz+dTHCO0fgPFZBRvY0T4ec3SI5TO29zcLPkb77tMY0TkGOEn+F4rKytlv4Fi520rYwQvqtfU5ZailZapbTZbxD6CIAResvAVEv82sZcQACwWS+A3sc7Ae97wNgWfV2wQtdvtYIyJntdqtUqeN3w/qfaK3W/wecPv9YV1h4MMjIv4Z6bf3W7F3UMyRdsjd954fDbBbZKSodiA49/fbrfDbgfeu6cfXt1YHvDjtlqAy/Os+MVl7ZCZGmmt2+32wOyQ1HnF2ht8r1arlavORTheJn9epf4SDGMMHoXre32C5LP1n1ds4Al/NuEZktxNzbAKwMiuafjdbaNDXHrkZBiLfjinqB827D2FYzVNESlk++RlYObYHjhz+kSg7WLn1TJGBLfXZrMp1jaxWYXAffG+y2Lt9cswWcaI4H2krqvlvHqMEWK/RStDNWOEv41ybUpJSYHX61U8r5gMg/cTa6/P51P93sRjPzRKj1A6ryAIkm6DNEZEtkntGKHmGyh23rYyRvCiKiZj1KhR8Hq9+Pbbb0O27969G4MGDcL//u//4le/+hUAiskQo7a2NpBJKHg5MVoS1ffdKNTK2Ww/bqXnFY7ez2YUYIoAABb0SURBVE+P/qKlLyeav3ysA4pdTR6MXvgl6hrFjWYBwF2jkyvI2yiMGpuJUEjOxkMyNodklbOhMRmDBw/G8uXLA6XU/fh9usJ9zIhQjOiIaipAJ5KCFw1q5Wy2XHhqdvhRk+tfj+vzXk9LX060/mdksT0elpTsl61A3y7VFpNq6W2RZFISYgnJ2XhIxuZAcuZD1bJCcXExXC4XPvzww5Dtb7/9NvLz8zFixAhdG0coo6UCtMrSKITOzCnqhz55GYquMBYB6J2brrsiKXV9norjyUosDCSl2J10hz1ps0gRBEEQ8Y+qL9Q111yDSZMm4f7770ddXR369OmD5cuX4/PPP8e7774r6itGGA/PzLRUXQSpOgyEcYhVc7ZaBGRdqJPh8TI0NHkgCMA5twdTnv9a12clVU2aagvEDzwrlF5fcq1QEgRBEImF6orfLpcL8+fPxwcffIDq6mr0798fjz76KH7+85+H7EcxGZH4s2sJgiAaqKQVpboH79w7Ane8uTVpquIaJWejCFYUXU0eTHt5Ew5VmfestCiqiSbjRIRircyD+rM5kJyNh2RsDskqZ0OL8RnZkGRg+/btgToY4bm6o0UuSHVJyX7ZlY62ViHYSDkbjVzxtXh6Voks40RhwSe7ZdPoxktfaAtQfzYHkrPxkIzNIVnlbGjgNxG/yAWpyvl2+xjwxd4KUlbiBHpWbRe1K0Zzivph3a5ylNd5RNPoUuwMQRAEEc+QkWEiWVlZEZm5jCA8yDvZsk+ZJWe9SaRnZaSM4+H+9CKaWKgMhw2v/rQ33thagS3HGwDBSrEzBsAYS9gxI9EgORsPydgcSM58kHRM5JJLLjH9mlqyTyU6sZBzMFqV5ER6VnrLuC0mJpCKlVq6uQzflJ7hiq8Z2K8Pnu/XB0DbMr5ijXR/i+3Y0daJ9dicDJCMzYHkzEdifr0JVehRF4GQRy8lORmflR7KeDyypGR/xD0BrW5vhypdeLZkvyrXN60GBhknobTV/kYQBBFvJG8UdhJBdRGMxa+0LN1chvIaNyrqGlFe48bSzWWY9som2YJq4STjs+JRxhMRnvgao3A1ebDgk90Ys3gdRi5chzGL12HBJ7tV9cW2SlvtbwRBEPEGGRlJgL8uwvRRPdE1JxWds5zompOK6aN60qydDuiptCTjs4qlMm4UauJr9EZPo7ct0hb7G0EQRDzS9jSWOObw4cOBQKFevXqZeu0Mhw2zi/qBAfhiz2m0eBm+2FsBBiS037sYZstZ74xQcpnC4gW9ZJxIwe5q0Cu+Rouc9XbTaku01f6WKMTyG5gskIzNgeTMR9vRLBOA+vr6QF5ls0kmP2Qz5Wy00hKvio5eMk6kYHe16BFfo0XOlAZZmrbc3xKBWH4DkwWSsTmQnPkgd6kkgfyQjYGUluiZOKBTRAyKn0QOdo9FfE0s3bQSBdn+hsTtbwRBEPFG25i6ThAGDRoUs2sn0+ymX85mKVLJmBFKz748p6gfvik9E2EEJ3qwuz++5tmS/fhibwU8Xqa6zoVaOZPRq4xcf+udm7j9LRGI5TcwWSAZmwPJmQ8yMkzEarXG5LrJ5Icci3oLbVVJlkPPvqyHMh6vRBtfo0XOyWj0qqEt97d4J1bfwGSCZGwOJGc+BGbQdK/P50N9fX3ItszMTFgs5KEVC8YsXofyGrfk711zUrFx7ngTW6Q/UnEnfmXfyLgTV5OHlBadaAvGbiyJ5XuQiFB/IwiC4EOtbk9GRpKw4JPdsrOb00f1THh3qXi5R1JaiFhDRi9BEAShN2RkxDE1NTXw+XywWCzIyckx9drJMLuZDKs18UIs+3IyoYecyehVhvqzOZCcjYdkbA7JKme1un1ia5UJxrFjxwIpz8zulG3dDzmZ4k7igVj25WRCDzlTf1eG+rM5kJyNh2RsDiRnPhJbsyRUkQhF3rRCWXUIgiAIgiDiBzIyTKSgoCCwvBZr2qKyrSWrTlsztswinvpyW4bkbA4kZ3MgORsPydgcSM58UEwG0WbgjTuJRZpbgiAIgiCIRIYCv4mkRimrTjIEwEtBqzYEQRAEQWiFjAyCuICYUh0vaW7NglZtCIIgCILQA7W6PWn8RJtFbNZ+7d4KUQMDAHwM+GJvhcGtMg//qs3SzWUor3Gjoq4R5TVuLN1chmmvbIKryRPrJhIEQRAE0UahqUwT2b59eyDl2ZAhQ2LdnDaLlJyTLc3tkpL9EW5hQKsxdajShWdL9mtetaG+bA4kZ3MgOZsDydl4SMbmQHLmg1YyiKQh2dLcJtOqDUEQBEEQ8QWtZJhIWloaPB4PbDYSu5HIyVlLmttExOhVG+rL5kByNgeSszmQnI2HZGwOJGc+KPCbSCqSKbvUmMXrUF7jlvy9a04qNs4db2KLCIIgCIJIVCjwmyBkyHDY8NH/+w9MH9UTXXNS0TnLia45qZg+qmebMjCA1lUbi8QiRVtatSEIgiAIIv6glQwiqWkrQd5iJNOqDUEQBEEQxkJ1MgiCCKBUnJAgCIIgCIIHMjLimGPHjgUChbp37x7r5rRZSM7i6LlqQzI2B5KzOZCczYHkbDwkY3NIVjlTTEYcU1NTg+rqatTU1MS6KW0akrM4erqFkYzNgeRsDiRncyA5Gw/J2BxIznyQkUEQBEEQBEEQhK6Qu5SJNDU1BVxWHA5HrJvTZiE5Gw/J2BxIzuZAcjYHkrPxkIzNIVnlrFa3p8hPE0mmjhhLSM7GQzI2B5KzOZCczYHkbDwkY3MgOfORvMsKBEEQBEEQBEEYAhkZBEEQBEEQBEHoimHuUmKhHj6fz6jLJQTBfmyZmZkxbEnbhuRsPCRjcyA5mwPJ2RxIzsZDMjaHZJWzmB4vF9ptWOC3x+NBQ0ODEacmCIIgCIIgCCLGpKenw2YTX7MgdymCIAiCIAiCIHSFjAyCIAiCIAiCIHSFjAyCIAiCIAiCIHTF0GJ84QEigiBAEAQjLkcQBEEQBEEQhEEwxiICvS0Wi2QxPsOMDIIgCIIgCIIgkhNylyIIgiAIgiAIQlfIyCAIgiAIgiAIQlfIyDCIdevW4Z577kH//v2Rnp6OgoIC3Hjjjfj++++5jn/rrbcCMSzhf6dPnza49fGJy+XCgw8+iPz8fDidTgwdOhTvv/8+17GVlZW466670LFjR6SlpWHUqFH48ssvDW5xYhFNn6X+ys+GDRskZbVlyxbF4w8fPoxp06YhOzsbGRkZmDRpEn744QcTWp5Y3HXXXZJyVpI19Wdx6uvr8cgjj2Dy5MnIzc2FIAhYsGCB6L4//PADJk6ciIyMDGRnZ2PatGk4fPgw97XWrl2LUaNGIS0tDR07dsRdd92FyspKne4kvuGRs9frxR//+EdMmTIFXbt2RVpaGgYMGIB58+ahtraW6zrjxo0T7eNTpkwx4K7iD97+LDWW9O/fn/ta77//PoYOHQqn04n8/Hw8+OCDcLlcOt5NfGJYxe9k59VXX8XZs2cxa9YsFBYWoqqqCs8++yxGjhyJkpISjB8/nus8f/3rXyM6cocOHYxoctwzbdo0bNu2DYsWLULfvn3x3nvv4dZbb4XP58Ntt90meVxTUxMmTJiA2tpavPDCC8jLy8PLL7+MKVOmYO3atRg7dqyJdxG/6NFnqb/y87vf/Q5XX311yLZBgwbJHlNVVYUrr7wSOTk5+Mtf/gKn04mFCxdi3Lhx2LZtG/r162dkkxOKxx9/HL/+9a8jtl9//fVwOBwYNmyY4jmoP4dy9uxZvP766xgyZAhuuukm/PnPfxbdb9++fRg3bhyGDh2KDz74AI2NjXjiiSdw5ZVX4t///jdyc3Nlr/PVV1/hmmuuwbXXXotVq1ahsrISc+fOxYQJE/Ddd9/B4XAYcXtxA4+c3W43FixYgFtvvRX33XcfOnbsiB9++AFPP/00Pv30U3z33XdITU1VvFavXr2wbNmykG3Z2dm63Us8w9ufASA1NRXr1q2L2MbDsmXLcPvtt+O+++7Dc889hwMHDmDu3LnYs2cP1qxZE9U9xD2MMISKioqIbfX19axTp05swoQJisf/9a9/ZQDYtm3bjGhewvGPf/yDAWDvvfdeyPZJkyax/Px85vF4JI99+eWXGQD2zTffBLa1tLSwwsJCNnz4cMPanGhE02epv/Kzfv16BoCtWLFC9bEPP/wws9vtrKysLLDt3LlzrGPHjuxnP/uZns1sk2zYsIEBYI899pjsftSfxfH5fMzn8zHGGKuqqmIA2JNPPhmx380338w6duzIzp07F9hWVlbG7HY7e+SRRxSvM2zYMFZYWMhaWloC2zZt2sQAsFdeeSX6G4lzeOTs8XjYmTNnIo5dsWIFA8DeeecdxeuMHTuWDRw4UJc2JyK8/Xn69OksPT1d0zU8Hg/r0qULmzx5csj2ZcuWMQBs9erVms6bKJC7lEHk5eVFbMvIyEBhYSGOHz8egxYlNitXrkRGRgZuvvnmkO133303Tp48ia1bt8oe269fP4waNSqwzWaz4fbbb8e3336LEydOGNbuRIL6bPyzcuVKjB8/Hj169Ahsy8rKwrRp0/Dpp5/C4/HEsHXxz5tvvglBEHDPPffEuikJCU8aeo/Hg88++ww//elPkZWVFdjeo0cPXH311Vi5cqXs8SdOnMC2bdtwxx13wGa76GwxevRo9O3bV/H4tgCPnK1Wq+iq2vDhwwGAxmwOzCirsGXLFpw6dQp33313yPabb74ZGRkZbb4/k5FhIufOncMPP/yAgQMHch9z3XXXwWq1on379pg2bRp27dplYAvjl127dmHAgAEhHx0AuOyyywK/yx3r30/s2N27d+vY0raF2j5L/ZWfGTNmwGazISsrC0VFRdi4caPs/m63G6WlpZJ92e12q/J5TzbOnTuHv//975gwYQIuueQSrmOoP6untLQUbrdbsp8eOnQIjY2Nksf7ZSx1PD0DefwuPbxjdmlpKdq3bw+bzYbevXtj/vz5cLvdRjYxIXG73ejcuTOsViu6du2KmTNnorq6WvE4qf5st9vRv3//Nt+fKSbDRGbMmIGGhgbMnz9fcd/OnTtj/vz5GDlyJLKysrBz504sWrQII0eOxKZNmzBkyBATWhw/nD17Fr169YrY3r59+8Dvcsf691N7bLLD22epv/LTrl07zJo1C+PGjUOHDh1w6NAh/OEPf8C4cePwj3/8A0VFRaLH1dTUgDFGfVkjy5cvh9vtxr333qu4L/Vn7fj7oFQ/ZYyhpqYGXbp00XQ89XFpTpw4gXnz5uGKK67Addddp7j/mDFjcMstt6B///5wu9345z//id///vfYuHEj1q9fL1lgLdkYMmQIhgwZEoiZ++qrr/Dcc8/hyy+/xLZt25CRkSF5rFJ/LisrM6TN8QIZGRxs2LAhIkBTih9//BFDhw6N2P74449j2bJlePHFF/GTn/xE8TxTpkwJyfBw1VVX4dprr8XgwYPxxBNPYNWqVfw30EaQW9ZUWvKM5thkRU2fpf7Kz+WXX47LL7888P8rr7wSxcXFGDx4MB555BFJI8MP9WVtvPnmm+jQoQOKi4sV96X+HD3R9lOpfaiPi1NdXY2pU6eCMYa//e1vXAbC008/HfL/qVOnomfPnpgzZw5WrVrF9a4kAw899FDI/ydNmoTLL78c//mf/4k33ngj4ncxkrU/k5HBQb9+/fDGG29w7du9e/eIbU899RSefvppPPPMM5g5c6bmdvTs2RNjxozhSnPZ1ujQoYPoDJZ/uVJslkCPY5MVPfpsMvdXtWRnZ+O6667Da6+9BrfbLZq1JCcnB4IgUF/WwI4dO/Ddd99h1qxZmjMTUX/mwx8nINVPBUGQzV6kdDz18UhqamowadIknDhxAuvWrRNd9efl9ttvx5w5c7BlyxYyMmQoLi5Genq64ngQ3J87deoU8lsy9GcyMjjo0qUL7rvvPk3HPvXUU1iwYAEWLFiA//7v/466LYyxpFzCHDx4MJYvXw6PxxMSl7Fz504A8qk/Bw8eHNgvGJ5jkxE9+2yy9lctMMYASM9spaamok+fPpJ9OTU1NSrloi3z5ptvAoDmcdwP9WdlevfujdTUVMl+2qdPHzidTsnj/ePxzp07MXXq1IjjabwOpaamBhMnTsSRI0fw5ZdfisayaIH6uTI848HgwYMBtPbdwsLCwHaPx4N9+/bh1ltvNbSNsYZ6kYH89re/xYIFC/DYY4/hySefjPp8R44cwaZNmzBy5EgdWpdYFBcXw+Vy4cMPPwzZ/vbbbyM/Px8jRoyQPXbfvn0hGag8Hg/effddjBgxAvn5+Ya1O9HQs88mc39VS01NDT777LNAsSYpiouLsW7dupDMMfX19fjoo49www03RCRGIFrr5Lz77rsYPnx4VAoq9Wc+bDYbrr/+enz00Ueor68PbD927BjWr1+PadOmyR5fUFCA4cOH491334XX6w1s37JlC/bv3694fDLhNzAOHz6MNWvWhLhhauXtt98GAOrnCvz973/H+fPnFeU0YsQIdOnSBW+99VbE8S6Xq+3359hlz23bLFmyhAFgU6ZMYZs3b474C+aee+5hVqs1JPf9hAkT2FNPPcVWrlzJvvzyS/b888+z/Px8lpmZyXbu3Gn27cQFkyZNYjk5Oez1119n69atY7/85S8ZAPbuu+8G9hGTZWNjIxs4cCDr1q0bW7ZsGfviiy9YcXExs9lsbMOGDbG4lbiEt89Sf42OW2+9lc2dO5etWLGCrV+/nr3++uusX79+zGazsS+++CKw3/jx45nVag05trKyknXp0oUNHjyYrVy5kq1evZpdddVVLDMzk+3du9fsW0kI3n//fQaAvf7666K/U39Wx+rVq9mKFSvYX/7yFwaA3XzzzWzFihVsxYoVrKGhgTHG2N69e1lGRga76qqr2OrVq9lHH33EBg0axPLz81llZWXI+axWKxs/fnzItvXr1zObzcaKi4vZF198wZYtW8a6devGBg0axBobG02711iiJOfz58+zYcOGMUEQ2AsvvBAxXh86dCjkfOFy/vrrr1lRURF77bXX2Jo1a9gnn3zC7r///sB+Xq/X7FuOCUpyLisrY6NHj2Z/+tOf2OrVq9k///lPNm/ePOZ0OtnAgQOZy+UKnKusrIxZrVZ2zz33hFzjnXfeYQDYr371q8CYn52dzSZNmmT27ZoOGRkGMXbsWAZA8i+Y6dOnMwDsyJEjgW0PPvggKywsZJmZmcxms7H8/Hx2++23s/3795t8J/FDfX09e+CBB1jnzp1ZSkoKu+yyy9jy5ctD9hGTJWOMnT59mt15552sffv2zOl0spEjR4YodAR/n6X+Gh0LFy5kQ4cOZe3atWNWq5Xl5uay4uJi9u2334bs538e4Rw6dIjddNNNLCsri6WlpbEJEyaw77//3qzmJxyTJk1i6enprK6uTvR36s/q6NGjh+QYESzD7777jk2YMIGlpaWxrKwsdtNNN0UovowxBoCNHTs2YvuaNWvYyJEjmdPpZO3bt2d33nmnaMHQtoqSnI8cOSI7Xk+fPj3kfOFyPnjwIJs6dSorKChgDoeDOZ1ONnjwYPbMM88kjSHHmLKcq6urWXFxMevZsydLTU1lKSkp7NJLL2WPPPIIq62tDTmX/5mEy54xxt577z122WWXsZSUFNa5c2f2wAMPsPr6epPuMnYIjF1wBCYIgiAIgiAIgtABiskgCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJXyMggCIIgCIIgCEJX/j8PE9fceQ+UXgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[10.691 3.098]\n", " [ 3.098 2.392]]\n" ] } ], "source": [ "from numpy.random import randn\n", "X = np.linspace(1, 10, 1000) + randn(1000)*2\n", "Y = np.linspace(1, 5, 1000) + randn(1000)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the covariance is smaller in relation to the variances, reflecting the lower correlation between $X$ and $Y$. We can still fit a straight line through this data, but there is much greater variation in the data.\n", "\n", "Finally, here is the covariance between completely random data." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[1.004 0.001]\n", " [0.001 1.004]]\n" ] } ], "source": [ "X = randn(100000)\n", "Y = randn(100000)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the covariances are very near zero. As you can see with the plot, there is no clear way to draw a line to fit the data. A vertical line would be as unconvincing as the horizontal line I've shown." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distribution Equation\n", "\n", "Recall the equation for the normal distribution from the **Gaussians** chapter:\n", "\n", "$$ \n", "f(x, \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp \\Big [{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 \\Big ]\n", "$$\n", "\n", "\n", "Here is the multivariate normal distribution in $n$ dimensions.\n", "\n", "$$\n", "f(\\mathbf{x},\\, \\mu,\\,\\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^n|\\Sigma|}}\\, \\exp \\Big [{ -\\frac{1}{2}(\\mathbf{x}-\\mu)^\\mathsf{T}\\Sigma^{-1}(\\mathbf{x}-\\mu) \\Big ]}\n", "$$\n", "\n", "The multivariate version merely replaces the scalars of the univariate equations with matrices. If you are reasonably well-versed in linear algebra this equation should look quite manageable. If not, don't worry, both FilterPy and SciPy provide functions to compute it for you. Let's ignore the computation for a moment and plot it to see what it looks like." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.mkf_internal as mkf_internal\n", "\n", "mean = [2., 17.]\n", "cov = [[10., 0.], \n", " [0., 4.]]\n", "\n", "mkf_internal.plot_3d_covariance(mean, cov)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a plot of multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}10&0\\\\0&4\\end{smallmatrix}]$. The three dimensional shape shows the probability density for any value of $(X, Y)$ in the z-axis. I have projected the variance for x and y onto the walls of the chart - you can see that they take on the Gaussian bell curve shape. The curve for $X$ is wider than the curve for $Y$, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. The highest point of the 3D surface is at the the means for $X$ and $Y$. \n", "\n", "All multivariate Gaussians have this shape. If we think of this as the Gaussian for the position of a dog, the z-value at each point of ($X, Y$) is the probability density of the dog being at that position. Strictly speaking this is the *joint probability density function*, which I will define soon. So, the dog has the highest probability of being near (2, 17), a modest probability of being near (5, 14), and a very low probability of being near (10, 10). As with the univariate case this is a *probability density*, not a *probability*. Continuous distributions have an infinite range, and so the probability of being exactly at (2, 17), or any other point, is 0%. We can compute the probability of being within a given range by computing the volume under the surface with an integral." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FilterPy [2] implements the equation with the function `multivariate_gaussian()` in the `filterpy.stats.` module. SciPy's `stats` module implements the multivariate normal equation with `multivariate_normal()`. It implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability density for any number of values for x over any arbitrary number of calls. I named my function `multivariate_gaussian()` to ensure it is never confused with the SciPy version.\n", "\n", "> The tutorial[1] for the `scipy.stats` module explains 'freezing' distributions and other very useful features." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import gaussian, multivariate_gaussian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll demonstrate using it, and then move on to more interesting things.\n", "\n", "First, let's find the probability density for our dog being at (2.5, 7.3) if we believe he is at (2, 7) with a variance of 8 for $x$ and a variance of 3 for $y$.\n", "\n", "Start by setting $x$ to (2.5, 7.3). You can use a tuple, list, or NumPy array." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "x = [2.5, 7.3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we set the mean of our belief:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "mu = [2.0, 7.0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. I will use the variable name `P`. Kalman filters use the name $\\textbf{P}$ for the covariance matrix, and we need to become familiar with the conventions." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "P = [[8., 0.], \n", " [0., 3.]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now call the function" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0315" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%precision 4\n", "multivariate_gaussian(x, mu, P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get the same result from the `scipy.stats` module." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0315\n" ] } ], "source": [ "import scipy\n", "try:\n", " print('{:.4f}'.format(scipy.stats.multivariate_normal(mu, P).pdf(x)))\n", "except:\n", " print('you have an old version of scipy, upgrade it now!')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's time to define some terms. The *joint probability*, denoted $P(x,y)$, is the probability of both $x$ and $y$ happening. For example, if you roll two die $P(2,5)$ is the probability of the first die rolling a 2 and the second die rolling a 5. Assuming the die are six sided and fair, the probability $P(2,5) = \\frac{1}{6}\\times \\frac{1}{6}=\\frac{1}{36}$. The 3D chart above shows the *joint probability density function*.\n", "\n", "The *marginal probability* is the probability of an event happening without regard of any other event. In the chart above the Gaussian curve drawn to the left is the marginal for $Y$. This is the probability for the dog being at any position in $Y$ disregarding the value for $X$. Earlier I wrote \"I have projected the variance for x and y onto the walls of the chart\"; these are the marginal probabilities for $x$ and $y$. Another computational benefit of Gaussians is that the marginal of a multivariate Gaussian is another Gaussian!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at this in a slightly different way. Instead of plotting a surface showing the probability distribution I will generate 1,000 points with the distribution of $[\\begin{smallmatrix}8&0\\\\0&3\\end{smallmatrix}]$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_3d_sampled_covariance(mu, P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can think of the sampled points as being possible locations for our dog given those particular mean and covariances. The contours on the side show the marginal probability for $X$ and $Y$. We can see that he is far more likely to be at (2, 7) where there are many points, than at (-5, 5) where there are few." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As beautiful as these plots are, it is hard to get useful information from them. For example, it is not easy to tell if $X$ and $Y$ both have the same variance, and how much they are correlated. In most of the book I'll display Gaussians as contour plots.\n", "\n", "The contour plots display the range of values that the multivariate Gaussian takes for a specific standard deviation. This is like taking a horizontal slice out of the 3D plot.\n", "\n", "These plots show the shape of the slice for 3 standard deviations." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_3_covariances()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For those of you viewing this online or in Juptyer Notebook on your computer, here is an animation of varying the covariance while holding the variance constant.\n", "\n", "\n", "\n", "(source: http://git.io/vqxLS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These plots look like circles and ellipses. Indeed, it turns out that any slice through the multivariate Gaussian is an ellipse. Hence, in statistics we do not call these 'contour plots', but either *error ellipses* or *confidence ellipses*; the terms are interchangable.\n", "\n", "This code uses the function `plot_covariance_ellipse()` from `filterpy.stats`. By default the function displays one standard deviation, but you can use either the `variance` or `std` parameter to control what is displayed. For example, `variance=3**2` or `std=3` would display the 3rd standard deviation, and `variance=[1,4,9]` or `std=[1,2,3]` would display the 1st, 2nd, and 3rd standard deviations. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "import matplotlib.pyplot as plt\n", "\n", "P = [[2, 0], [0, 6]]\n", "plot_covariance_ellipse((2, 7), P, fc='g', alpha=0.2, \n", " std=[1, 2, 3],\n", " title='|2 0|\\n|0 6|')\n", "plt.gca().grid(b=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solid colors may suggest to you that the probability distribution is constant between the standard deviations. This is not true, as you can tell from the 3D plot of the Gaussian. Here is a 2D shaded representation of the probability distribution for the covariance ($\\begin{smallmatrix}2&1.2\\\\1.2&1.3\\end{smallmatrix})$. Darker gray corresponds to higher probability density." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.nonlinear_plots import plot_cov_ellipse_colormap\n", "plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 1.3]]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thinking about the physical interpretation of these plots clarifies their meaning. The mean and covariance of the first plot is\n", "\n", "$$\n", "\\mathbf{\\mu} =\\begin{bmatrix}2\\\\7\\end{bmatrix},\\, \\,\n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&2 \\end{bmatrix}\n", "$$ " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 0], [0, 2]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 0|\\n|0 2|')\n", "plt.gca().grid(b=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Bayesian way of thinking about this is that the ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. The shape of the ellipse shows us the geometric relationship of the errors in $X$ and $Y$. Here we have a circle so errors in $X$ and $Y$ are equally likely." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and covariance of the second plot are\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&6\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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UqdYK9JQtFVlsBAAAfY8gAwAbXBgl+tm+WTWDQIcaB9UIGxore9o8npNpDu9sSM6zdOr2sg7P+jrYPKBm1FSSbVUnjHX6jnE59vAFPAAYJHzlBAAbWCeMdd/eGTU6vvZU96gdt7Rjc1FTk/mhDjGLTNPQ1k0Fbd9cUCtsaE91jxq+r/v2zioI416XBwB4EgQZANig2p1I9z38SIiREWvntqLKxcE6F2Y9jBRdnbK9pEyR9lT3qO63dd/eWflB1OvSAABPgCADABtQ0w91/75ZNYKWHqo+JMvKtHNrSa7Dcqkn4jqWnrKtJMNK9VD1ITU6Ld23d1YtP+x1aQCAx0GQAYANptbs6Gf7ZlXrNPRQ9WG5rvSUbRt3a+VucmxTT9lalOtKD9UeViNo6f59s6q3gl6XBgD4JdzVAGADma219YsD86r6de2r7VUxb+nkqaIs5mGWzLZMnTxVVD5n6OHqw6p3Gvr5/jnNN/xelwYAeBSCDABsENPzLe05VNW8P6/9jX0qFx3t2FJgqH8FTNPQSVuKKhUt7avv07xf1QMH5nWk2up1aQCAo9h+GQA2gLm6r73TNc36c5puHdbYiKepiXyvyxpohmFo+6aCDhkL2zOnSqXDCx2bsTL/bwGg1wgyADDgmn6oPYeqqnZqmm4d1uRoTpvGcr0ua0MwjIXtmU3T0OH6IVmGpT2HDLm2pWLe7XV5ADDUlr207Lvf/a4uvvhilctllUolXXjhhfrOd76zFrUBAE6gE8b6+f45NcOWDjUParTkEmLWwJaJvColVwcbB9QM2/r5/jnOmQGAHltWkPne976n888/X77v6+abb9bNN9+sTqej5z3vebrjjjvWqkYAwOOIk1Q/3z+nVuBrX32fCnlLU5MseVorWyfzyucs7avtUzsM9PP9c4qTtNdlAcDQMrIsy5b6wy984Qt1zz336IEHHlChUJAkNRoNnXrqqfqVX/mV4zozaZqq0Wgc9/vlclmmyf4CALBaaZrp/n2zqrXa2lPdI9NK9ZRtJXYnW2NJmmnPgaay1NLO0Z0aLeT1KydNyDD4/w4Aq7GS7LCsVPGd73xHF1xwwbEQs/gfOP/883X77bfr4MGDyywZALASew5V1fAD7a3vVWYkOoktlteFZRo6eaqoNIu1r7ZPdT/QnkPVXpcFAENpWUEmDEN5nveYxxcf+/GPf9ydqgAAT2jfkbrmG74O1PcrSAKdtKUoh8Mu141jmzppS0GdxNeBxgHN1X0dmGmc+BcBAF21rF3LzjzzTN15551K0/RYmyeOY911112SpNnZ2e5XCAA45ki1pcNzTR1qHlYzbGrHloJyntXrsoZOPmdr+6aC9k3XNW0u7F7mOZYmKoUT/CYAoFuW9RXe5Zdfrvvvv19/9Ed/pP3792vv3r3atWuXHnrooYUXY/4FANZMuxNp73Rdc515zXfmtGUip1LB6XVZQ6tcdLRlPK9Zf0bVTlUPHa7JD6JelwUAQ2NZyeOyyy7TBz/4Qd18883asWOHTj75ZN177716xzveIUnavn37mhQJAMMuTTM9eHBefuRrunlY4yOexkYeu9QX62u84mms7OlQ87D8qKMHD1a1jD10AACrsOwWyjvf+U7NzMzoxz/+sfbs2aPbb79d8/PzKhaL+o3f+I21qBEAht6+I3W1w0j7GwfkuaY2j3NWTL/YPJ6T6xg60DygdhBqP/MyALAuljUjs8jzPJ111lmSpIcfflhf+MIX9Ad/8AfK5zm/AAC6rdbs6Ei1penmYUVpqFOmSmz320dM09C2zQXt2d/UdOuIDBmqFD2VC3TMAGAtLSvI/OQnP9Ett9yis88+W57n6Yc//KE++MEP6vTTT9d11123VjUCwNCKk1R7DlXVDJua78xraiIvz2W4v9/kXEubxnOanptVyS3pwYOWzty5SbbF7CgArJVlBRnXdfX1r39df/M3f6Nms6mTTz5Zu3bt0rve9S4Vi8W1qhEAhtZDh6rqxJEONg+qlHeYi+ljExVPzXakg40Dytmn6uHDNZ26bazXZQHAhmVkazSVuJLTOQEAj5iptfXQoar21vfKj9s6dXtJNufF9LUoTvXAvoaKblk7ytu1c2qULZkBYAlWkh24IwJAH+qEsfZO1zTfmVczbGrbpjwhZgA4tqmtm/JqBHVVOzXtPVJXEMa9LgsANiTuigDQZ7Is055DVflRoMPNaY2VPc6LGSAjRVeVkqvDrcPyw0B7DrElMwCsBYIMAPSZw/MtNf1ABxr75TgGWy0PoC0TeVlWpgONA2r4gabnW70uCQA2HIIMAPSRMEp0cLahOX9enbijbZN5mSZbLQ8ayzS0bVNBftxWtVPVwbmmojjpdVkAsKEQZACgj+w7UlcYR5ppz2hsxFM+t6LjvtAHCjlboyVX060jCuJI+47Ue10SAGwoBBkA6BP1VqD5hq/DrWkZRqZNYywpG3SbxnMyjExHWtOaq/tq+mGvSwKADYMgAwB9IMsy7Z2uqRW1VQ9q2jyek8WSsoFnW6Y2jXmqdqryY18PH64x+A8AXUKQAYA+MD3fkh9GOtw6rLxna7Ts9rokdMlo2VXOtXSoeUh+EGmm1u51SQCwIRBkAKDH4iTVwbmmqp2qgrijqYl8r0tCFxmGoamJvDpxR9VOVQdmGkqStNdlAcDAI8gAQI8dnG0ojGMdac2oUnKV86xel4Quy+dsjRRdHWkfUZgkOjTX7HVJADDwCDIA0EOdMNaRaluz7VmlSrSZAf8Na/N4TkmaaLY9o8PzLQVh3OuSAGCgEWQAoIf2H6krTELN+bOaqHiybS7LG5VjmxqvuJptzylKIu2fafS6JAAYaNwxAaBHmn6oarOj6dYRWZahiYrX65KwxiZGczJNabp9RPMNXy22YwaAFSPIAECPHJxtqBN3VA9q2jSWk8l2yxueZRraNOap1qkqSEIdZFYGAFaMIAMAPdDuRKq3As34s3JsU5WS0+uSsE5Gy64cy9SsP6tasyM/iHpdEgAMJIIMAPTAwdmGwiRSI6hrouLJMOjGDAvDMDRe8VTv1BSlETuYAcAKEWQAYJ11wljVZkez/oxsy1SlxOGXw2a07Mo0Dc22ZzVX99nBDABWgCADAOvs0FxTcRqr1qlpvOIxGzOETNPQ+IiraqemOEt0eL7V65IAYOAQZABgHYVRorm6r1l/Toax8M08htNYxZOMTHPtOc3U2oripNclAcBAIcgAwDo6PN9UlMaa9+c1XvFk0Y0ZWpZpaKzsar4zrzhNNE1XBgCWhSADAOskTlLN1Nqa9+ckI9PYCN2YYTdR8ZRlqeY78zpSaytJ0l6XBAADgyADAOtker6lOE0171c1WnZlW1yCh51tmxotu5r35xQliaardGUAYKm4iwLAOkiSVNPVlub9eaVZoomK1+uS0CfGK+7RzR+qmp5vKU2zXpcEAAOBIAMA62Cm1lacJJrzZzVScuTYXH6xwHUsjRRdzbZnFSWJZmrtXpcEAAOBOykArIPpaku1Tl1xGtONwWNMjHqK0kj1oKEjLC8DgCUhyADAGqu3AoVRompnXqW8I8+1el0S+kzOtVTI2ap2quqEsZp+2OuSAKDvEWQAYI3N1tsKklB+7KtSdnpdDvrUaNlVO2opTCKWlwHAEhBkAGANxUmq+UZH1U5VlmmqXCDI4PGVC45Mw1AtqGq+4bMVMwCcAEEGANbQXN1XmqWqdWqqlBwZBgdg4vGZpqFKyVWtU1OaZppvdnpdEgD0NYIMAKyh2XpbzbCpJItVKXMAJp7caNlVlEZqhk2WlwHACRBkAGCNtDuR2p1I1U5Vec9WjiF/nEDOs+Q5lqpBTS0/VCeMe10SAPQtggwArJGZWltxGqsVtlQpMRuDpRktu2oGDcUZZ8oAwJMhyADAGkjTTHMNX9WgJhnSSIllZViakaOht9apabbWVpZlPa4IAPoTQQYA1kC12VGSpKp2qhopOrJMhvyxNLZlqlS0VQtqipNUtVbQ65IAoC8RZABgDczU2mrHvqIkVIVuDJZptOQqiDvyY5/lZQDwBAgyANBlYZSo0Q5U7VTl2KaKebvXJWHAFPO2HMtUrVNTrdlRFCe9LgkA+g5BBgC6bK7hK1WmeqeuUboxWAHDMFQpu6oFdWXKNN/gTBkA+GUEGQDosmqzo1bYVKb02OA2sFzloqM0S9QKW6pyOCYAPAZBBgC6KIoTtfxQjbApz7HkOpwdg5XJuZYc21QzbKrph4qTtNclAUBfIcgAQBfVWoEyZWoGTZUKzMZgdcoFR42woSzLVGf3MgA4DkEGALqo2uzIjztKsljlAsvKsDrloqM4jeXHPsvLAOCXEGQAoEvSdOFb80bQkG2ZyufoyGB18p4lyzTVCJqqtTocjgkAj0KQAYAuqbcDZVmmRtigG4OuMAxDpYKtZtRUmmZqtMNelwQAfYMgAwBdUm12FCShoiRkPgZdUy44CuKOwiRieRkAPApBBgC6IMsy1ZodNcKGDMNQgWVl6JJi3pYhQ42wQZABgEchyABAF7Q6keIkVTNoqFSwZZpGr0vCBmGahop5W82weWx7bwAAQQYAuqLa7BzbXaqUZz4G3VUuOvKjtuIsUY1tmAFA0gqCzP/8z//opS99qbZt26ZCoaBf/dVf1fve9z612+21qA8ABkK12VEzbMqQwXwMuq6Ut4+dT8TyMgBYsKy77b333qvnPOc5OuOMM/TRj35Uk5OTuu222/S+971P3//+9/XFL35xreoEgL7VCWMFYaxG2FA+Z8m2aHaju2zbVN6z1Qwb8oOKgjCW5xKYAQy3ZV0FP/e5z6nT6eiWW27RaaedJkm66KKLdPDgQX3qU5/S/Py8xsbG1qRQAOhX9VagTJlaYVubxr1el4MNqlSwNVttK1Omhh8SZAAMvWV9beg4C+u+K5XKcY+Pjo7KNE25rtu9ygBgQDT9UH7cUaZURXYrwxop5GylWaIgDtRk4B8Alhdk3vCGN2h0dFRvfetb9cADD6jRaOhLX/qSPvnJT+ptb3ubisXiWtUJAH2r6YdqR22ZhiHPZVkZ1kbes2QYhlpRW402A/8AsKyvDnfu3Kk77rhDL3vZy44tLZOkK664Qh/96Ee7XhwA9LsgjBXFifyorXxu4YMmsBYMw1Des+RHbYVRojBK5DpWr8sCgJ5ZVpDZs2ePLr30Um3ZskW7d+/Wpk2bdNddd+n973+/ms2mbrzxxrWqEwD6UuPoEp925GuiyLbLWFuFnK35mi9poRM47uR7XBEA9M6ygsy73vUu1et13XPPPceWkZ1//vmanJzUZZddpt/93d/V//t//29NCgWAftT0Q3XijtIsUSHHh0qsrbxnaSbrKEjChSAzwnsOwPBa1mLue+65R2eeeeZjZmHOOeccSdJPfvKT7lUGAAOg6Ydqx74MGcq5LPPB2irkbBky5EdtBv4BDL1lBZlt27bppz/9qZrN5nGP33HHHZKkHTt2dK8yAOhzUZwoCGO1o7ZyniXTZD4Ga8s0DeU8S62oLT+IFCdpr0sCgJ5ZVpC56qqrNDMzoxe84AX653/+Z33961/XBz7wAf3xH/+xzjzzTF1yySVrVScA9J3Fb8T9qK1Cjm4M1sfiwL8kujIAhtqygsxLXvISfe1rX9PIyIiuvPJKvfjFL9ZnP/tZveUtb9Ftt93GOTIAhkqjHSpIQsVprALnx2CdFHK2ojRSlEYEGQBDbdl33gsvvFAXXnjhWtQCAAOl6YfHvhnPE2SwTvJHu3/tyFfT5/w2AMOLk9sAYAWSJJUfRGrHvnKuJYv5GKwT2zLlOgvLy9qdSGma9bokAOgJggwArEDz2PkxbboxWHfFnK1W1FaWZWp1WF4GYDgRZABgBVqdSHEaK0pCBv2x7vI5S2ESKMlS5mQADC2CDACsgB9E6iSBJHF+DNbd4nuuE3fkB3GPqwGA3iDIAMAK+GGsIA5kGIZchyCD9eU6pgwZCpJAfhD1uhwA6AmCDAAsU5pmCsJYQRLQjUFPLARoU2EcKIgSZRkD/wCGD0EGAJZp8RvwIO7Ic7iMojc811InDpRlmTohy8sADB/uwACwTH4YK1OmIA7l0ZFBj3iuqeDonBZzMgCGEUEGAJbJDyKFSaRMKUEGPZNzLZw0NaEAACAASURBVKVZoiiNmJMBMJQIMgCwTH6wMOgvLXwrDvTCYogO4kA+S8sADCHuwACwTH4QKUg6si1TtsVlFL3h2KZMw1CHncsADCnuwACwDFGcKE5SBXFANwY957mWgjhQGCVKkrTX5QDAuuIuDADLsDhU3UkCeZwfgx7LudYjA/8sLwMwZAgyALAMfhApVaYoYccy9J7nLpwlkyljeRmAoUOQAYBl8MNYQdyRJA7DRM95rnVsK3C2YAYwbAgyALAMfhAd27HM5TBM9NixncsY+AcwhLgLA8AyBFGiIAkXdowyjV6XgyFnmYZsy1SYBOowIwNgyBBkAGCJkiRVkqSK0kiOzeUT/cGxTUVprDhJlaZZr8sBgHXDnRgAliiME0lSnBBk0D9s21CULCwri46+RwFgGHAnBoAlCqOFD4l0ZNBPHMtUlC4EmZAgA2CIcCcGgCUK40SZMsVpTJBB33BsU3GyMB+zGLYBYBhwJwaAJQqjRHG68IHRthj0R39wbFOZUsVZQkcGwFAhyADAEoVxouhokKEjg36x+F6Mk4iODIChwp0YAJYoitNjQ9U2QQZ9wrYXuoNRGtGRATBUuBMDwBItdGQimYYhizNk0Cdsy5RhGIrSmI4MgKFCkAGAJQqjhK2X0Zdsa2ELZjoyAIYJd2MAWIIoTpRlGVsvoy8tHIoZKU0zJUna63IAYF1wNwaAJXjkDBm2Xkb/WdiCmbNkAAwX7sYAsASLHw6jJDo2XA30i8WOjMRZMgCGB0EGAJYgjBKlypRmCR0Z9B3HNhWnsTJldGQADA3uxgCwBFHyqK2XLS6d6C+LB7TGaawoZkYGwHDgbgwAS5AkqdJs4Ztuy2JpGfrL4nbgSZoqSQkyAIYDQQYAliBJMyXZwgdEzpBBvzGPvidTpUrSrMfVAMD6IMgAwBIkaar06DfdBjkGfWYxXKdpwvbLAIYGQQYAliBJs0eWltGRQZ9Z7MgkGR0ZAMODIAMAS5AkqVJlMgxDBi0Z9BnTNGTIUJolzMgAGBoEGQBYgjTLlKYJ3Rj0LcOgIwNguBBkAGAJFof9TYIM+pRlGkrTlBkZAEODIAMAJ5Bl2bHtl+nIoF+Z5uLSMjoyAIYDQQYATiA9+sFwoSPT42KAJ2CahpIsVZZlyjLCDICNj1syAJzA4jfcacrSMvQv62hHRhJdGQBDgSADACewuAtUmiWy2LEMfWphadnR7iFzMgCGAEEGAE4gOW5pGUEG/YmODIBhQ5ABgBNY/HabYX/0M9NcCNuSOEsGwFAgyADACRzryKSpDIIM+pR5dPtliY4MgOFAkAGAE3hkB6hM5Bj0K8MwlB7tyLBrGYBhQJABgCXKxIdD9K9HZ2xyDIBhsKwg88Y3vlGGYTzhnzvvvHOt6gSAnnn0Z0KDXcvQ10gwAIaHvZwffs973qNdu3Y95vFLL71UnufpnHPO6VphAICNyw8i/X9X/L0k6b//5veU95weVzT4Hp2xWVoGYBgsK8icdtppOu2004577Fvf+pZmZmb07ne/W5ZldbU4AOgHWZaxrAwDgfcpgGGyrCDzeG688UYZhqHLLrusG/UAADYwP4gW/hnGjzz2qH+nM7Nyj172SJwBMAxWFWRqtZp2796t5z3veTrllFO6VRMA9JUse+SDISMyq7O4nOzRfvMdNx/797s/+eb1LAcAMMBWtWvZP/3TP8n3ff3+7/9+t+oBAAAAgBNaVUfmxhtv1MTEhF72spd1qx4A6Dt0Ybrnv//m9yQtLCdb7MT8x/WvV95d9UpnAMCQWfGd40c/+pHuvvtuXXnllfI8r5s1AUDfWcwybAa1Oo83A5N3bWZjuuDRO5WRvQEMgxUvLbvxxhslSW9605u6VgwAAFg5gwgDYIisqCMTBIH+4R/+Qc985jN11llndbsmAOgrhmHwAbHL8p7DYH+XPbpbyMGtAIbBijoy//qv/6q5uTm6MQAA9BUCDIDhsaIgc+ONN6pYLOrVr351t+sBgL5jHPunwYnp6FuPfmfSkAEwDFa0tOw//uM/ul0HAPStR5bpGAz7o6+xpAzAMFnVOTIAMAxMc+HDoWmYSlOSDPpTmmayjIXbumVyewew8XGlA4ATsBaDjGkqIcigTyVpJtO0JD3yngWAjYwgAwAnsPjttmWYLC1D30rTTObR27plcXsHsPFxpQOAEzjWkTEsOjLoW2maPRK66cgAGAIEGQA4gcVvty1mZNDHkjSTaSwuLeP2DmDj40oHACfwyIwMHRn0r8Vhf8Mwjm1QAQAbGUEGAE5g8YOhKToy6F9JmskwTEIMgKFBkAGAJbBMU5ZJkEH/StOF5Y/MxwAYFgQZAFgCyzQY9kdfS49uv8x8DIBhwdUOAJbAssyFYX/2X0YfyrJMmRa2X6YjA2BYEGQAYAkWOzKS6Mqg7yy+Jy3T5AwZAEODqx0ALIFpGDKPLtlhTgb9ZvE9aRoWHRkAQ4MgAwBLYFmmTGPhkklHBv0mTRf+uTDsz60dwHDgagcAS2Ad3X5ZoiOD/pPQkQEwhAgyALAEjm3JtmxJUpykPa4GON7ie9K2bNnMyAAYElztAGAJXNuSbVgyZCqK6cigv0RxKtOwZMqQ61i9LgcA1gVBBgCWwLEXLpeO5SiO6cigv8RxJsdyJC2EbgAYBgQZAFiCxQ+HjukoYmkZ+kwUp3LMhaWPdGQADAuCDAAsweKHQ8eyFbO0DH1mIcg4MgxDDh0ZAEOCIAMAS7D4AdE2bUUsLUOfieJUtuXQjQEwVAgyALBErmPJMR3FSaosoyuD/pCkmdIsk2M6zMcAGCoEGQBYIte2ZB8dqKYrg36xuPmEQ0cGwJAhyADAEi12ZCSxBTP6xmKodkxbDmfIABgiXPEAYIlc2zq2xS2HYqJfxEkmQ4Zs06YjA2CoEGQAYIkc25QpQ5bBwD/6RxSnsk1bhgxmZAAMFYIMACzRsbNk2IIZfWQxyEicIQNguBBkAGCJjp0lYzp0ZNA3FrdelkRHBsBQIcgAwBI5tiXDMDhLBn1l8TBMyzJlMewPYIhwxQOAZfAcS67tKYw5Swa9l2WZ4jiTZ7l0YwAMHYIMACxD3nPkWZ6yLFMY0ZVBbwVhqkyZPNtT3rN7XQ4ArCuCDAAsQ96z5dmeJCmIkh5Xg2HXCRfeg67lKe85Pa4GANYXQQYAliHvObINS7ZpKwjpyKC3gjBZmI8xTOVdOjIAhgtBBgCWYfHDomflFIR0ZNBbQZQc6xDSkQEwbAgyALAMrmPJNA15tndsWQ/QK2GYyrNysiyTM2QADB2CDAAsg2EYyrm2PMtTFKdKU3YuQ28kaaYoSRcG/VlWBmAIEWQAYJnynqPc4sA/XRn0yOJ7z2PQH8CQIsgAwDLlXVvusZ3LGPhHbwRhIkOGPNtl62UAQ4kgAwDLlPccmTLkWC5zMuiZIEzl2p4MGXRkAAwlggwALNPit985y2NpGXqmEybyrKM7ljEjA2AIEWQAYJkc25JtmfJsj7Nk0DNBuLD1sutYsixu5wCGD1c+AFiBvOfIs3JK0lRxQpjB+oriVGmWKcegP4AhRpABgBXIe/axgwg7AcvLsL6O7VjG1ssAhhhBBgBWoJhz5VmuLMMmyGDdtTuxbNOWYzoq5OjIABhOBBkAWIFS3pUkFZy8Wp24x9Vg2LQ7ifJOQdIj70UAGDYEGQBYAdex5DqW8k5BfpAoy7Jel4QhkaaZOkGiglOQ59pybKvXJQFATxBkAGCFSnlXBSevLMtYXoZ14weJMmUq2AWV6cYAGGIEGQBYoVLeVc7OyZCpNkEG68TvxDINSznbY1kZgKG2oiDz7W9/Wy960Ys0NjamfD6v008/Xdddd123awOAvlbKuwunqjt5+czJYJ20g1gFJy+J+RgAw23ZezZ+7nOf0+tf/3r99m//tm666SaVSiX94he/0IEDB9aiPgDoW3nPkW2ZKjoFzfrtXpeDIZBlmdqdRJOFghzbksfWywCG2LKugPv379eb3/xmveUtb9HHP/7xY49feOGFXS8MAAZBKe8q3ykobWfqhIlyLoPXWDtBmCrLMhWcAt0YAENvWUvLbrjhBrVaLb3zne9cq3oAYKCU8q7yTl6GDJaXYc21OrEMmcrbOZULBBkAw21ZQea2227T+Pi4/u///k/PeMYzZNu2Nm/erF27dqler69VjQDQt0p5V6YM5eyc2h0G/rG2/E58LDjTkQEw7JYVZPbv3692u63f+q3f0qte9Sr913/9l/7kT/5EN910k170ohdxjgKAoVPIOTJNQ3mnoDYdGayxdidRwcnLskzlPafX5QBATy1rRiZNU3U6Hf3FX/yF3vWud0mSLrjgArmuq6uuukpf+9rX9PznP39NCgWAfmQYhoo5V8VOQXP+rMIokeswJ4PuC8JESZoqz3wMAEhaZkdmYmJCknTxxRcf9/gll1wiSfrBD37QpbIAYHCUC67yTkGSWF6GNdPuxDJkqOBwECYASMsMMk972tMe9/HFJWWmyfmaAIZPueDJMkzl7byaftTrcrBBtfxYOTsvk/kYAJC0zCDzile8QpL0la985bjHv/zlL0uSzj333C6VBQCDo5hzZFmmSm5JrXbMvCC6Lk0zNf1YZa8sx7ZUJMgAwPJmZH7zN39Tl156qd73vvcpTVOde+65uvvuu3XttdfqxS9+sc4777y1qhMA+pZhGKoUPbWCso60j6jlxyoVGMRG97T8hYBcdsuqFL1elwMAfWHZa8G+8IUv6KqrrtKnPvUpXXLJJfrEJz6hq6++Wrt3716L+gBgIIyWcsrZnhzLVbPN7mXorkY7kmt5ci1Ho6Vcr8sBgL5gZGu0BiJNUzUajeMeK5fLzNEA2JCSJNUPf3FYBxuH1IiqOv3kkV6XhA0iyzL97OGGRr1xTZU36+mnTck0jV6XBQBdtZLsQKoAgC6wLFMjRU9lr6w4SdUJ2L0M3eEHC9sul72SRgoeIQYAjiLIAECXVIrewmGFhq1Gm93L0B2NViTbtJW38ywrA4BHIcgAQJeMlnIyZKjoFtVoEWTQHU0/VsktLWwqQZABgGMIMgDQJYvb4pbdsoIoURixvAyrE4QL76OyW1Yp78q2uG0DwCKuiADQRZWip5JXkiGD3cuwao12JEOmCm6RbZcB4JcQZACgi0ZLOZmLy8uYk8EqNduxSm5RpgzmYwDglxBkAKCL8p4jz7VVckvyO4niJO11SRhQcZzKD2KV3PKx9xUA4BEEGQDostFSTmW3rEwZy8uwYgvLygyVvBLLygDgcRBkAKDLxko52aatolNStRH2uhwMqFozUtEtyjYsjZXzvS4HAPoOQQYAuqyYd5VzbVVyFflBzO5lWLZOmMgPYo3mRlXIOSrknF6XBAB9hyADAGtgslJQ2SvLNCy6Mli2WiOUZSzMWk2MFHpdDgD0JYIMAKyB8ZG8LMNUxRtRrRkpy7Jel4QBkWWZas1IlVxFpmFqfIRlZQDweAgyALAGHNtSpehpNDeqOEnV8hn6x9I02pGSNNVoblRj5RyHYALAE+DqCABrZLJSUM7OKWfnWF6GJas1IuXtvDzLZVkZADwJggwArJGRorfQmcmNqtmOOVMGJxTFqZp+pNHcqFzH0gjbLgPAEyLIAMAaMQxDEyN5VbyKpIXtdIEnU2uEMmSq7I1oskI3BgCeDEEGANbQRKUgy1j4YMryMpxItRlqJDciyzBZVgYAJ0CQAYA1lHNtlfKuKrmKwiiR32HoH4+v5ceK4oUh/5GiJ9exel0SAPQ1ggwArLHJSkElpyjHdOjK4AlVG6Fcy1PBztONAYAlIMgAwBobK+dlmoZGc6OqtSIlKWfK4HhxkqrRXjg7xrJMjZZyvS4JAPoeQQYA1phpGpoYKWg0PyZlhuZrQa9LQp+Zr4dSZmgsN6bJSkGmafS6JADoewQZAFgHW8aKsg1Lo7mK5uqhUroyOCpJM83VAo3lx2SbljaPFntdEgAMBIIMAKwDz7U1PpLXRGFCaZoxK4Nj5uuBskyayI9rYiTPkD8ALBFBBgDWydR4SY7paCRX0VwtUJbRlRl2aZppvh6qkqvINm1tGS/1uiQAGBgEGQBYJ3nPUaWU00R+QlGSckAmVGuGSpJME/lJjZXzyrl2r0sCgIFBkAGAdTQ1XpJnuSq7Zc3SlRlqWZZpthao7I3ItRxN0Y0BgGUhyADAOirlXZULniYKEwqjRI02XZlhVW9FiuJUE/kJjRQ9FXJOr0sCgIFCkAGAdTY1XlLezqvgFDVbZSvmYTVbDVRyS8rZHt0YAFgBggwArLPFb98nChPqhImadGWGTrMdKYgSTRQmVTzapQMALA9BBgB6YGq8pJJTVM7OaZYDMofOTDVQ3i6oYOe1lW4MAKwIQQYAemC0lFPOtTVZmFS7E6vdiXtdEtZJsx3JD2JNFiaO7WQHAFg+ggwA9IBhGJoaL6nslpWzc5qe6/S6JKyDLMt0ZL6jvJ1XyS0xGwMAq0CQAYAeGR/JK+852lzcIj+IVWuGvS4Ja6zWjNQJE20pbVEh52h8JN/rkgBgYBFkAKBHDMPQjk0jKjoFld2yjsx1lKacK7NRpelCN6bsjShv57Vj00ivSwKAgUaQAYAeGil6Gil62lTcrDjJNFdn8H+jmqsFSpJMW4qbNVrKsVMZAKwSQQYAemzHphF5lqvR3Jhmq4HiJO11SeiyOE41Uws0lh+Xa7naTjcGAFaNIAMAPZb3HE1WCposTsqQpSMM/m84h+c6MmVpsjCpyUpBOdfudUkAMPAIMgDQB7ZNluXZjjYVJ1VthvLZjnnDaPmx6q1Qm4ub5dm2tk2We10SAGwIBBkA6AOObWnbRFljuTHl7JwOzfrKMgb/B12WZTo86ytv5zWaq2jbZFm2xa0XALqBqykA9IlNowXlPUdTpSl1wkTVBtsxD7r5eqggSjRVmlIht7CEEADQHQQZAOgThmHo5C0V5e28KrlRTc91GPwfYHGc6sh851iX7eTNFRmG0euyAGDDIMgAQB8p5V2Nj+S1ubhZhiwdPOL3uiSs0IGZtkzD0qbiZk1WCirm3V6XBAAbCkEGAPrMjk0jytmOtpan1PQjlpgNoLlaoJYfa2t5m3KOw3bLALAGCDIA0Gcc29LOqVGV3bJGc6M6NOsrCJNel4Ul6oSJpuc6GsuNq+QUtXNqlAF/AFgDXFkBoA9VSjltGi1qS2lKjunq4Ay7mA2CLMt0YLot1/a0ubRZm8eKGil6vS4LADYkggwA9Kkdm0ZUcB1tK29VJ0g0Uw16XRJOYHquozBKta20TUXP1fZJlpQBwFohyABAnzJNQ6dsHVPBKWiyMKmZakdtDsrsWy0/1lw90KbiZuWdnE7ZOirTZJcyAFgrywoy3/zmN2UYxuP+ufPOO9eqRgAYWoWco60TJU0UJpS3Czow3VaSssSs3yRppoNH2io4RU3kx7V9sqy85/S6LADY0OyV/NIHPvABXXjhhcc9dtZZZ3WlIADA8abGS6q3Am1LtunB6oM6POtr2yYOVuwnB2faSlJDT6lsVbngact4qdclAcCGt6Igc/rpp+vcc8/tdi0AgMdhGIZ2To3KfzjWluIWHWweUKlga6TIuST9oNoI1WhF2l7eoZzjaefUaK9LAoChsKIgAwBYX55r66RNI0qSVK2opQNH6nIsU/kcl/FeandiHZrxVcmNasQr6ylbKnIdq9dlAcBQWNGw/9ve9jbZtq2RkRFdfPHF+va3v93tugAAv2SiUtBEpaCt5a3KWTntm24ritNelzW0wijRvsNt5Z2CtpamNFkpaKyc73VZADA0lhVkKpWKrrzySn3yk5/UN77xDf31X/+19u7dqwsuuED//u//vlY1AgCOesqWikbynnZUTpIhWw8fajH83wNxkurhQy1ZhqMdIztUKeZ08pZKr8sCgKFiZKs8Ya1arerXf/3XNT4+rh/+8IfHHk/TVI1G47ifLZfLMk12fAaA1YiTVPc9PKOa39ZD1YfkedLJU0UZBlv9roc0zfTwoZbCUNo5ulOVQkFnnDQhy+L+BgArtZLssOqr7ujoqF784hfrRz/6kXzfX+3LAQBOwLZMPXX7uIpuTjsqO+R3Eh2c4fq7Xg7O+OoEqU6q7FDRy+mp28cJMQDQA1258i42dfg2EADWh+faeur2cZXcgraWt6nWDDUz3+l1WRve9JyveivU9pFtKroFPXX7OMP9ANAjq97uZn5+Xl/60pf0jGc8Q7lcrhs1AQCWoJh3tXNqVOmBTFES6kj1iBzHVKXEtsxrodoINVsLtLm4RWW3rFO3jqmQ49BLAOiVZQWZ1772tTr55JN19tlna3JyUj/72c/04Q9/WIcPH9ZnPvOZNSoRAPBExsp57diUSEekKI108EhNlmmoVOADdjc125EOzfgay41pIj+ukzZXVCnx5R0A9NKygszTnvY0feELX9Df/u3fqtlsanx8XOedd55uvvlmnXPOOWtVIwDgSWwZLymIEmWaUpzG2ne4pe2bCyoXCTPdUG+FOjDtq+SWtKW0RVvGS9o8Vux1WQAw9Fa9a9kTYdcyAFg/WZbpgQPzmm/62t84oEZQ19bJgkbLLDNbjfl6oEOzCwdebi1Nabxc0ClbR5kJBYAuW0l24EhoANgADMPQqdvG9NBhU4a265Bh6eDMvJI000TF63V5A2lmvqMj1Y7GcuOaKm3RZKWgk7dUCDEA0CcIMgCwQRiGoZ1To7JMQ9KULNPS9NyMkiTV5nFOnF+Ow7O+5uqBNhU2abIwqanxkrZvGul1WQCARyHIAMAGc9LmimzLlGYk07A0XTusJMk0NZmnm3ACWZbp4IyvWjPUVGlKY7kx7dg0oi3jpV6XBgD4JQQZANiAtk6UF8LMYckyLB1qHlSSZdq+qUCYeQJpmunAkbaa7VjbyttV8Ub0lKlRTVYKvS4NAPA4CDIAsEFtGi3KMk3tOWTIMk3trx/QQ/HCjmaOzcYrjxbFqfZPt9UJUu2onKSyW9Kp28Y0yhbLANC3CDIAsIGNj+RlW6Z+cUCyTFsH6vv1wL6Gtm1ie+ZF9Vaog0f+//buPrSq8oED+Pe83HPu++7b5rzasp/mlkYs/EP/qhWySlkasSwlLaEXW8GCIs3Vtpy0CP+IIsitPwqdEUqUoRSWTQqT1ha1QqhMqk2du9fd3fe3c35/mKM1LXWbx3Pv9wMiPLvsfGF77rMvzznPTUISZFzrqYBDsWPeLB9cdh6SQER0NWORISIqcG6Hivmz/Th2QoQiXYeT0RP4cygKj1PBDL8Nolict5rlNR2nQmefh3Gpbsx0zoRNsWBu0Ae7lSWPiOhqxyJDRFQEHDYFN1xbit9PRSALszGSGsHJ2Ckk0jHMKrXDqkpGR7yikqkcBk4nkMsBM51BeKwl8LltqCgrgSTxtjsiIjNgkSEiKhKyJOJ/QS+GIyrEIQE2ix2D0QEcH4yh1Gctis+b0XUdoUgaw2fSsMpWVHhnwWpRUFFWAj8f6iciMhUWGSKiIhMoscNpU/DbiTNQpDkYip/GUDiEeDKLcr8NiqUwd2cy2TxODCeRSOXgtwVQ6gjAaVNxXbkHqsLlkIjIbPjOTURUhKyKjKqKAAaGoxAgwKE4cCI6iGN/xuBxKwiUqJAL5GSzXE7D8EgaI9EMZFFGRcm1cFjsmOl3YabfyeOoiYhMikWGiKhICYKA2aVuuO0qjp+UYLfYEU6GEYqGMBLNwOdW4PdYIZn0MIBcXkNoJI0z0QxESCh1lMFr88JqkTGn3MNTyYiITI5FhoioyLkdKhbOKcWpM3HIZ0R4rV6EEiGEI2GcGc3A71Hhc6umOd1M03SEI2mEImnougC/3Q+fzQ+LJGGG14kZXgcf6CciKgAsMkREBEkSEQy4UOqx42Q4BlmU4LN5MZwYxvCZEZwZzSDgUeF2KlftDk1e0xGJZjA8koam6fBYvQg4ArCIMsq8DpT7nJBZYIiICgaLDBERjbHIEq4pK8EMrxODoShkUYbP5sdwchgnQyM4FU7BaZdR4lDgsMmG79Jomo5YMovRWBaxRA4AUGItQcAegCIp8LttmOl3FewBBkRExYxFhoiIJlAsEuaUe1Duc2Lg9CgUyYJSewCj6ShG0xH8GY9DFAS4HBa4HRY4bPIVe2he13XEkzlEYllEE1noug6rbEWpwwe36oJFtMDrsiEYcMHK08iIiAoW3+GJiOiCrIqMubN8SKSyGI4kYIuq8Nt8SOcziKZHEUmOIhKLQxJFuB0WWFUJVkWCYhGnbLdG03RkshpSmTySqRyiiRzymgZFUhGwBeBWS6BIFlhkCV6XFX63HXarZUquTUREVy9B13V9Or6xpmmIRqPjxlwuF0SR9ycTEZmVruuIJjIIR5MYiaWQz2tI5VJnd2oyo8jmM2OvtcgirIoEVZGgKiIUiwRZEiAIAkQBYzs4uq5D08/+n8vryGTzSGc0pDN5pDJ5ZHPa2PdUJBUuxQW36oZVViFJIrxOK7wuG1x2hUcpExGZ1OV0B+7IEBHRRRMEAW6HCrdDhabpGE2kER5Nwh63oUwrhQYd6VwK6Vwa6XwG6WwaI6kUclrukq4jizJUyQqXRYVqVaHKClTZChECRFGA56/yUuJQWV6IiIoUiwwREV2Wc4XC47Qin9cQT2WRTGeRzDiQTGeRyuSgaWc3/XN6Hpl8BnktB10HNF0DcO6GAAGiIEIQAEmUoUoqJEEcu4ZNtcCqyLApMmyqBU6bYvghA0REZDwWGSIimjRJEsd2as7R9bO3iSUzubFik9f0s7eSafrfaszZwiIIAqR/FBeVD+sTEdEFcIUgIqJpIQgC1L/KiMdpNToOEREVGD55T0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpsMiQ0REREREpiNP1zfWdX3CmKZp03U5IiIiIiIy0XBMtAAAB1BJREFUqfP1hPP1ib+7okUmHo9P1+WIiIiIiKiA/FeR4a1lRERERERkOiwyRERERERkOiwyRERERERkOoL+XzefXSZN0yY8tCMIAgRBmI7LERERERGRSem6PuGZGFEUIYoX3neZtiJDREREREQ0XXhrGRERERERmQ6LDBERERERmU5RF5nOzk4IggCn02l0FJoCn3/+OdavX4+qqio4HA7MmjULK1aswLfffmt0NLpEsVgMjY2NCAaDsFqtqK6uxnvvvWd0LJoCnKfFh2tt4fnyyy+xbNkyeL1e2Gw2XH/99diyZYvRsWiK9PX1YeXKlQgGg7Db7aiqqsJLL72ERCJhdLQJivYZmYGBASxcuBAOhwORSASxWMzoSDRJ9fX1CIVCqK+vx4IFC3D69Gls27YNPT09+OSTT3D77bcbHZEuUm1tLb755hu0t7dj/vz56OrqQmdnJ3bu3InVq1cbHY8mgfO0uHCtLTxdXV148MEHcd9992H16tVwOp349ddfMTg4iBdffNHoeDRJP/30ExYtWoTKyko8//zzCAQCOHToENra2rB8+XJ8+OGHRkccp2iLTF1dHQRBgM/nw+7du/nmWgCGhoZQVlY2biwWi2HevHm48cYbceDAAYOS0aXYt28fli9fjq6uLjzwwANj47W1tfjxxx/x+++/Q5IkAxPSZHCeFheutYVlYGAAlZWVWLt2Ld58802j49A0aGpqwtatW/HLL79g7ty5Y+OPPfYYtm/fjnA4DK/Xa2DC8Yry1rIdO3agu7ubk7DA/POPIwBwOp1YsGAB/vjjDwMS0eX44IMP4HQ6UV9fP2784YcfxuDgII4cOWJQMpoKnKfFg2tt4ens7EQ8Hsdzzz1ndBSaJhaLBQBQUlIybtzj8UAURSiKYkSsCyq6IjM0NITGxka0t7dj9uzZRsehaRaJRNDb24uFCxcaHYUuUn9/P2644QbIsjxu/Kabbhr7OhUWztPCw7W2MB06dAg+nw9Hjx5FdXU1ZFlGWVkZHn/8cYyOjhodj6bAunXr4PF4sGHDBhw7dgzRaBQff/wx3nrrLTQ0NMDhcBgdcZyiKzJPPPEEKisrsWHDBqOj0BXQ0NCAeDyOzZs3Gx2FLlIoFILP55swfm4sFApd6Ug0zThPCw/X2sI0MDCARCKB+vp6rFq1CgcOHMCzzz6Ld999F8uWLZvwYYZkPnPmzMHhw4fR39+PuXPnwu12o66uDuvWrcNrr71mdLwJ5P9+ydXpiy++wG233XZRr+3r60N1dTX27NmDvXv3oq+vD4IgTHNCmozL+fn+0wsvvICdO3fi9ddfx6JFi6Y6Ik2jf5ufnLuFhfO08HCtLVyapiGVSqG5uRkbN24EANTU1EBRFDQ2NuKzzz7D0qVLDU5Jk3H8+HHU1dVhxowZ2L17N0pLS3HkyBG0tbUhFovh7bffNjriOKYtMpWVlejo6Lio11ZUVCAWi6GhoQFPPfUUgsEgRkZGAACZTAYAMDIyAovFctVtmRWrS/35/lNrayva2tqwdetWPPnkk1Mdj6aR3+8/765LOBwGgPPu1pA5cZ4WHq61hc3v9+Pnn3/GHXfcMW78rrvuQmNjI3p7e1lkTG7jxo0YHR3Fd999NzZPb7nlFgQCAaxfvx5r167FrbfeanDKv9GLxG+//aYD+Nd/K1asMDomTYGWlhYdgN7S0mJ0FLoMjzzyiO50OvVsNjtufNeuXToA/auvvjIoGU0lztPCxLW2sD366KM6AL23t3fc+NGjR3UA+quvvmpQMpoqlZWVek1NzYTxH374QQegv/HGGwakujDT7shcqvLychw8eHDCeHt7O7q7u7F//34EAgEDktFU2rJlC1paWtDU1ITm5maj49BluOeee9DR0YE9e/Zg1apVY+PvvPMOgsEgFi9ebGA6mgqcp4WLa21hu/fee7F9+3bs378fN99889j4vn37AABLliwxKhpNkWAwiP7+fsRisXEfYnv48GEAuOoO7yjaz5E556GHHuLZ9gVi27ZteOaZZ3DnnXee948jvsGaR21tLXp6evDKK69g3rx52LVrFzo6OrBjxw6sWbPG6Hg0CZynxYlrbeG4++678emnn6KpqQlLlixBT08PWltbsXTpUuzdu9foeDRJH330EVauXInFixfj6aefRiAQwNdff42XX34ZFRUV6Ovru6qOYGaR4ZtrwaipqUF3d/cFv17kv+qmEovFsHnzZrz//vsIh8OoqqrCpk2bcP/99xsdjSaJ87Q4ca0tHMlkEq2trejq6sKJEycQDAaxZs0aNDc3Q1VVo+PRFDh48CDa29vx/fffIxKJ4JprrkFdXR02bdoEv99vdLxxir7IEBERERGR+RTd58gQEREREZH5scgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHpsMgQEREREZHp/B/bN5gAtBQXsAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 0], [0, 6]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 0|\\n|0 6|')\n", "plt.gca().grid(b=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time we use a different variance for $X$ ($\\sigma_x^2=2$) vs $Y$ ($\\sigma^2_y=6$). The result is a tall and narrow ellipse. We can see that a lot more uncertainty in $Y$ vs $X$. In both cases we believe the dog is at (2, 7), but the uncertainties are different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The third plot shows the mean and covariance\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 1.2], [1.2, 2]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 1.2|\\n|1.2 2|')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the first contour that has values in the off-diagonal elements of the covariance, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling us the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow correlated. The off-diagonal elements in the covariance matrix are non-zero, indicating that a correlation exists.\n", "\n", "Recall the plot for height versus weight. It formed a slanted grouping of points. We can use NumPy's `cov()` function to compute the covariance of two or more variables by placing them into a 2D array. Let's do that, then plot the $2\\sigma$ covariance ellipse on top of the data. We will need to use `bias=1` because the data represents the entire population; it is not a sample." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 18.5249, 135.701 ],\n", " [ 135.701 , 1092.29 ]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov_hw = np.cov(np.vstack((height, weight)), bias=1)\n", "cov_hw" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(height, weight, s=120, marker='s')\n", "plt.title('Track Team Height vs. Weight')\n", "plt.xlabel('Height (in)'); plt.ylabel('Weight (lbs)')\n", "plot_covariance_ellipse((np.mean(height), np.mean(weight)), cov_hw, fc='g', \n", " alpha=0.2, axis_equal=False, std=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should help you form a strong intuition on the meaning and use of covariances. The covariance ellipse shows you how the data is 'scattered' in relation to each other. A narrow ellipse like this tells you that the data is very correlated. There is only a narrow range of weights for any given height. The ellipse leans towards the right, telling us there is a positive correlation - as x increases y also increases. If the ellipse leaned towards the left then the correlation would be negative - as x increases y decreases. We can see this in the following plot:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_temp = [200, 250, 300, 400, 450, 500]\n", "lifespan = [10, 9.7, 5, 5.4, 4.3, 0.3]\n", "\n", "plt.scatter(max_temp, lifespan, s=80)\n", "cov = np.cov(np.vstack((max_temp, lifespan)))\n", "plot_covariance_ellipse((np.mean(max_temp), np.mean(lifespan)), cov, fc='g', \n", " alpha=0.2, axis_equal=False, std=2)\n", "plt.title('Engine Temperature vs Lifespan')\n", "plt.xlabel('Temperature (C)'); plt.ylabel('Years');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The relationships between variances and covariances can be hard to puzzle out by inspection, so here is an interactive plot. (If you are reading this in a static form instructions to run this online are here: https://git.io/vza7b)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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+tHd04aufivDhwTx8+8uFXlvxySPCMD0jDtPGxSFj1HAkx4TB08M+CUbdqUX+xXocOFuOb38pxdGcCqvlmJo2Ao8smojbbhwDL0/6cS5WjsyHA0743S+XSCRoaGiAQqGw2sJvaWlBWFiY2bqZmZlYtmwZ3nvvPdxzzz3c85TwibOdKa7Ftk9P4ONDeVb74eOHB2POpERMHx+PGzPiEBkW4LSyqTq1OHROia9/LsLu/blQdWrNlidEBuPvD87Ckmmj6WIjEXJkPhxwM8GWA0wmk/VI9gAwefJkAEBlZeVA35aQITMYGHz1cxG2Zp7AkfMXeyyPDg/Ab2ek4Y6b0jExJYq3ZOrv44kF1yZjwbXJ+MfDs/H+9+fxxpenkFteBwAor23BbRs+wbRxcdj62BxMSIrkpZxEeJz6u/DAgQMAgLS0tH5fm5eXh7i4OAQGBnLPdXV1obCwEAAQEhKC2NhYs3VKSkrQ0dEBAD3O1jc0NKC6uhoAEBsbi5CQEG6ZwWBAbm4uAOM36ciRI83WLS8vR1tbG1d2ufzKbmtpacHFi8bkERUVBYVCYbbu+fPnwbIsfHx8kJycbLassrISTU1NAICUlBR4e3tzy1QqFUpLSwEAERERiIw0/1Dn5+dzIxPGjBljtqy2thZ1dcbkkJiYCH9/f26ZRqNBUVERACA0NBQjRowwW7e4uBidnZ2QSCQYN26c2bL6+nrU1NQAAOLi4szOxej1euTl5QEAAgMDkZCQYLZuWVkZ12pJT083629tbm5GRUUFACA6Ohrh4eFm62ZnZwMAfH19kZSUZLasoqICzc3NAIDU1FR4eV05wdnW1oby8nJ0dOnxXW4j3v6+AMpLLWbrB/p6YP7EODy89Hpclx4LqdSY5GtqalBfXw8AGDVqFPz8/Lh1Ojo6UFJSAgAICwtDTEyM2TaLioqg0Wggk8mQnp5utqyurg61tbUAjFMCBAUFccu0Wi0KCgoAGPul4+PjEeDrhYcXTcJDv5mIj/Ydx9YvzuJEsbFcR85fxNUPbsf9t0zAs3dMQmuTsc5jYmLMGlwMwyAnJwcA4O/vj8TERLMyKZVKtLYazyOMHj3abGhja2srlEolACAyMrLH5GS5ubkwGAzw9vbucQPxqqoqNDY2AgCSkpLg6+vLLVOr1bhw4QIAQKFQICoqymzdwsJCdHV1QS6X98gXly5dwuXLlwEACQkJos4R9ua0hF9dXY21a9di4sSJWLBgQb+v1+v1sOxtYlkWOp2OW25tne7llhiG4ZYxTM/+UVu3a1km0+1au4myTqcDy7IwGAwoLS01+7AZDIYhbbe3WE23axmr6T60tt3uWK21bi23W1payn3pxMbGulzddGn1+OBQCd78oQRNKvNukdTYcCy9Jhpzxg9HcIAfxo6N45aVlpZCpVL1ut3+9mF33Vhb1ledm8Zqua5EIsH4hBD864FJ+LGgDv/5rgwl1U1gWeDNvWdx6Gw5nr9jLJKiAvvch62trX0eh5b6i1Wr1YJhGKsnTPuK1dZ9aG0fWW7X9DiMjo52uePQ1hzh4eFhtVz25JSE39TUhHnz5oFlWXz00Uc29UXJ5fIeSUcikXA7xfQb1HSd3naaVCrllll7f1u3a1km0+1aO+g9PDy4D4VKpTJbJpPJhrRd0/97265lrKb70Np2u2O1lvAtt9udFLtf7yp1wzAs/rc/B395cz8uXm4ze/3cyaPw+NJrMGtiIgoK8qHX63uUyzTZW9sX/e1DDw+PXkeN9FXnprH2tl1PT0/cnBGDR347G//+6hQ2vHMYbeoulNa24Hev/YR1t2XgMYtfV93r6nS6fo9DS/3F6unpCYPB0O9xOJh9yDCM1Tq33K6rHofWtttbrCzLWt2uvQ1p8rTeTtqaam5uxsyZM3Hx4kUcOHCgRzcBIP6TttnZ2aK8MMQV48o6UYK12/fjfNlls+dvn56G9ctvxJh4RS9rXuGKcfWmrKYZt234GGdLLnHP3X/LePz7iQU9RhEJKa6BEFtcLnXSdiC6k315eTn2799vNdm7g7Fjx/JdBIdwpbiq69vw2D+z8MXRQrPnZ00cic0P3IyrU6J6WbMnV4qrPyOjQvDza7/H46/tw3+/Pg0A2JV1DrVNKny68Xb4eF1pzQoproEQa1yO4LAmdHeyLysrw3fffYcJEyY46q1cnlQq5f6JiSvExTAs3vjiF4xe8bpZsp+UGoUf/nEvvvv7vQNK9oBrxDUQ3p5y/OfPC/DeM7fCx8vYhss6cQHz1+1Gh+ZKf7XQ4rKVWONyhEG18LOysqBWq7mfHfn5+cjMzAQAzJs3DxKJBHPmzMHZs2exdetW6PV6HD9+nFtfoVD0GClAyEDllddh5ctf41heFffcsBA/vProHNxxU7rbjVG/Z9Y4xEYEYf663VB1anHwrBJLnvsIX75wB12oRQAMsg8/Pj6eG2Zkqby8HAB6DMsztXz5crz99tvc32Lvwyf2ZTAweOH9I/i/9380uyL1gfkTsOXBWQgJ8OljbfE7kV+FWU+/h/YO48ik26en4cPnlrrdF6BQudSVto4g9oTf2NgIhmEglUqtXpAmVHzEVdPQjrte+BSHs680OJJHhOG/f16A6ePj7fIeYqivozkVmLP6fa5LZ+ujc3DPjCTBx2WNGOrLlGBP2hKjqqoqbhSBGA7Ibs6Oa9/JC7j3b5+jodV44YxMKsHau67Hs/dOg7cduyzEUF/Xj43F/55dikXPfggAeOo/3yPUoxOjowMEHZc1YqgvZxFHE5qImk5vwLodP+CWNR9wyT5GEYhDW1fghd/fZNdkLya/uS4Fq++YCgDQGxisfvsXtKi1/axFxIw+KU4QExPD/eQUE2fEdalJhdvWf4yfcq/Mv7Tg2mS8vWYRwoJ8+1hz8MRUX//3wM04ll+FH89X4FJLJ/7xdQk+WNf/le5CIqb6cjTqwycuK6+8DvPX7cbFX+eLl8ukeGnVTDyxbAqdgByAmoZ2TFj1X9Q1qwEA32y+C/OmJPWzFuGLI/MhZVTikvafLsN1f9jFJfsREYE4+s/f4c+3X0vJfoCiwgPwz8fmcn//+Y1vodP3nNOFiB8lfOJy3so6i7lrPkCr2ngT8KuSInHijQdwzZiYftYkvbl9RhquSzfOjFpU2Yh/f3mK5xIRPlDCdwKGYbh/YmLvuFiWxV93HcD9W76C3mDc5sKpyTiybYVTb0AixvqSSCR45ZHZ3N8b3jmExl9PgAudGOvLUeikrRPk5OSIanKnbvaMi2FYPPTKHuz45gz33B+XTMYrj8yBTObcdolY68tL24j5V8fgm9NVaG7X4F+fn8SGFdP5LtaQibW+HIFa+IR3BgOD+7d8ySV7icR4odC2P9zi9GQvdg/NTYbs15u87PjmDPXluxn6NDmBv78/909M7BGXwcBg+Ytf4J1vjXe1kkkl2P3sUvzptin2KuaAibm+RsUocHOG8VxITUM7vvqpiOdSDZ1Y68sRaFgm4Q3DsPj937/C2/vOATAOu/zouduwZNponksmbj+cLsOsp94DANw0IQH7X7mP5xIRUzQsk4gOyxr77E2T/acbb6dk7wQ3TUhA8gjjFAQHzpaj4GI9zyUizkIJn/Dir7sOcn32MqkEHz13G35zXUo/axF7kEoleGjh1dzfnx4p4LE0xJko4ROn27X3LP7v/R8BGE/Qvv+XJdSyd7IlN1zZ3/tOXuCxJMSZaFimEyiVSu6m1vHx8XwXx24GE9cPp8vw4Ct7uL9ffcR4sxJX4i71lTIiDEWVjTieX4VWlQZB/t58F3FQxFpfjkAJ3wlaW1u5ccJiMtC4csvrsHT9x9xFVX9cMpnX0Ti9cZf6mjMpEUWVjTAwLPafKRfsryyx1pcjUJcOcYraxnbMX7cbbb9Ol/CbqSl45ZE5PJfKvc2ZNIp7/O0v1K3jDqiF7wSjRwuz5dQfW+PS6Q24bf0nqPh1IrSrkyOx+9klLntRlbvU1/Tx8fCQS6HTM2bTTwuNWOvLESjhO4GnpyffRXAIW+N69s0D+DnPmFBGRATi67/dCT8f190n7lJfvt4eSI4JQ56yHiXVTdAbGMhd9Eu4L2KtL0cQXu0SQck6UYItH/4MAPCQS5G54XanToRG+pYaGw4A0OoMUF5q4bk0xNEo4ROHqa5vw32bv+D+fmnVTEweHc1jiYil0XHh3GO6AEv8qEvHCVpbW8GyLCQSCYKCgvgujt30FZfewODOFz7l7kH7m6kpeNwFR+RY4071lTriSsIvrGjAwqnCu/hNrPXlCJTwnUCpVIpy+ta+4nr+3cP48XwFAGO//VtrFgnmTlXuVF/dXToAUFzVyFfRhkSs9eUI1KVD7O586WX87YOjAIzTJnz419sQGujDc6mINREhftzjFlUXjyUhzkAtfCeIjIzkrgQUE2txGQwMVr38NXdx1V/uuQFTf721nlC4U30F+Hpxj1WdWj6KNWRirS9HoITvBBEREXwXwSGsxfXGl7/gREE1AGN3wTN33+DsYg2ZO9WXn/eVq1PbO4TZwhdrfTkCdekQu6msa8UzOw9wf29/cgG8PKlN4co85DJ4eRhbxkJt4RPbUcIndsGyLB7dtpdLGqsWXIUbxsXxXCpiC/9fL4KjhC9+lPCJXXxzvARf/1wMABge6o+XHpzFc4mIrTzkxha+lu5vK3r0e9sJcnNzodVq4enpifR015oKeCi645LJPbB2+4/c89sem4tggU61C4i/vizj6u67DzQ5gSskYq0vR6CE7wQGgwEMw8BgEFcLqjuuvSeUyFMar9K8ZnQ0lk0fw3PJhkbs9WUal8HAQK3RAQAC/YSZ8MVaX45ACd8JvL29IZPJRDdft7e3NwwM8O99hdxzL66aKZgLrHoj5vqyjKvdpN9eqC18sdaXI1DCd4KUFOFdrm6LlJQUbM08jpom4/QJcyePwvTx8fwWyg7EXF+Wuu9PAAg34Yu1vhyBTtqSQWtTd3H3pgWAzStv5rE0ZDDaTMbeC7VLh9iOEj4ZtP9+fYqbHO3Om9IxftRwnktEBqq6vo17rAj25bEkxBko4ZNB0RsY/Ovzk9zfG1ZM568wZNBKa5q5x4lRoTyWhDgD9eE7QVVVFTfXR0xMDN/FsYvPfyxAZZ2xdThz/AgkjwjjuUT2I8b6AqzHdaG6iVueGBXCV9GGRKz15QiU8J2gsbGRm75VLAfk1swT3ONlU2N5LIn9ibG+AOtxFVQ0cMuTY4T5pS3W+nIE6tIhA3ayoJq7R23i8ABMTgrvZw3iqvKUdQCAYH9vRIXTrSfFjlr4TpCUlMTdkUcMtn16pXX/59unIjk5mcfS2J/Y6qubZVwtKg3XLZcWrxBsvGKtL0eghO8Evr7iGf3QotIg80g+ACAs0Ae/m3c1fLzEdcGLmOrLlGVcP+dWco+vSop0dnHsRqz15QgD7tJpb2/H6tWrMXv2bCgUxlbBhg0brL72zJkzmDlzJvz9/REcHIwlS5agrKxsqGUmPPriaCG0OuMl7PfMGie6ZO9ODp1Tco9vzKCZTd3BgBN+Y2Mjtm/fjq6uLixevLjX1xUWFmL69OnQarX4+OOPsWvXLhQXF+OGG25AfX39kApN+PPhgVzu8R03iW+iKnWnFpIZGyGZsRFqkU8XfDj7Ivd4GiV8tzDgLp24uDg0NzdDIpGgoaEBO3futPq65557Dl5eXtizZw8CAwMBAFdffTWSkpLwj3/8Ay+99NLQSi4garWa62P08/PrfwUXVd+ixg+njb/Q4oYFIT02GCqVSvBx9UbdoYbfr3PFi4HpcWiAHKeLawAA6QkRUAQLt/7E8vlyhgEnfFtOjOj1euzZswf33Xcfl+wB45fFjBkz8Pnnn7tVwr9w4QI3bCwjI4Pv4gzaZ0cKYGBYAMBvZ6ShtLRUFHEB4Frz3TNHAkBeQQn8rh4PAKJI/KbHYY3Gl6vL6eOF3boXy+fLGRxy0ra0tBSdnZ0YN25cj2Xjxo3D999/D41GA2/v3udMz8vLQ1xcnNkXRldXFwoLjTMzhoSEIDbWfPx3SUkJOjqMl/pbVnxDQwOqq433Wo2NjUVIyJWLTAwGA3JzjV0VAQEBGDlypNm65eXlaGv7dTRDWhrk8iu7raWlBRcvGn8aR0VFQdV4JF8AACAASURBVKFQmK17/vx56HQ6WFNZWYmmJuOFLykpKWb7Q6VSobS0FIDxnp2RkeYn1fLz87mDfMwY8+mIa2trUVdnHG6XmJgIf39/bplGo0FRUREAIDQ0FCNGmN9gvLi4GJ2dnZBIJD3q773vznKP50+KA9DJ/a3X65GXlwcACAwMREJCgtm6ZWVlaG9vBwCkp6eb3XC6ubkZFRUVAIDo6GiEh5sP88zOzgZgPDmXlJRktqyiogLNzcarRVNTU+HldWU+mLa2NpSXlwMAhg0bhuHDzad+yMvLg16vh5eXF0Y//BEAwFOixzJFKb7umohZm36AQZcFAGAPrufW6+joQElJCQAgLCysx9jvoqIiaDQayGSyHvOz19XVoba2FgAQHx+PoKAgbplWq0VBQQEAICgoCPHx8WbrlpaWQqVSAQDGjh0LqfRKj2xjYyOqqqoAADExMQgLuzKmnmEY5OTkmB2H+8+Uc49HR/py+3j06NHw9Lzy5dba2gqlUgnAeLNwy/vH5ubmwmAwwNvbu8ckZlVVVWhsbARgHEljenJVrVbjwoULAACFQoGoqCizdQsLC9HV1QW5XI60tDSzZZcuXcLly5cBoMdxJtQcwbIsfHx8HD7izSEJv7uSQ0N7XqodGhoKlmXR3NzcI4mZ0uv1YFnW7DmWZbmDVq/XW12nt+TKMAy3jGGYHstt3a5lmUy3a20+7u5lcrm8R0UbDIYhbbe3WE23axmr6T60tt3uWC1/ybWqNDiWb0xUseF+SIsLQ1dXF3eFoyvWTX+x6nQ66PV6LnF6SvT4NO1rLAgrx9+0AXhdPRuXC4pgsCi3LdvV6XRWl/VV56axDrTObd2HHh4eCA8PR+bhgwAAmVSCyckR0Ok6rG63v1i1Wi0YhjH7Au/WV6y27kNr+8hyuwqFwqWPQ1s+yyzLOmV6Z4cOy+yr+6e/riG5XN7jNRKJhNsppt+gpuv0ttOkUim3zLRl1M3W7VqWyXS71g56Dw8P7tvbshVjOof3YLZr+n9v27WM1XQfWttud6yW5TmaUwHm1wN56ugIyGQys3j0er3L1U1/sXbH6eHhAdVXf4bXF7+DvLQcnYwc2doR8PDxxqRpV2HnvRMGvN3uBGSprzo3jbW37Q51H/r7+6OylcXFy60AgFkTExEe5IvWVutJsL9YPT09YTAY+j0OB1M3DMNYrXPL7Zoeh11dXS53HNqaI6xt194krLWvUBs1NDRAoVBg/fr1ZkMzi4qKkJqaitdffx2PPPKI2TpPP/00Xn75ZXR0dHBdGAzDcD/3uwUEBFjd6YQfT//nO/zjo2MAgMwNy7D0RmHf1cqMvgv46F6g5Fuwcm/MPL0AhztGYfL0yahp1WBkuB/+t2oKhgUK97aNph5/bR938dzbaxZh+dzxPJeImHJkPnRIRk1MTISPjw9ycnJ6LMvJycGoUaP67L8nrke0Q/hMkj3k3tAs/QAHWmJh0Grx9oqJiA72QVmDGnduP47LbRq+SztkBgODjw8Zz7V4esiw+PpUnktEnMkhCV8ul2PhwoX47LPPzL6pKioqcPDgQSxZssQRb0scpE3dhdPFxv77tHiFoIfwmbFI9rjrI/iMngn24HqwB9cjOTIIH66aIqqk/2NOBWobjSd+b5k8CkECvtk8GbhBdRplZWVBrVZzyTw/Px+ZmZkAgHnz5sHX1xcbN27EpEmTsGDBAqxduxYajQbPPfccwsPD8eSTT9ovAgEoLCzkRtSkpgqvRXU0pwIMN4Qvnnte0HFZSfYYOR1Az7g+XDUFd2w/ziV9oXbvFBYW4p8fHef+FsuFc4I+Dp1sUC38hx9+GMuWLcP9998PAPjkk0+wbNkyLFu2jBsOmJqaikOHDsHDwwO33XYbVqxYgVGjRuHIkSM9RquIXVdXF/dPiE4WVnOPp4270p0j2Lj6SPZAz7hGhPqKoqVf29iGb04Z588J8vPCwmvFMemdYI9DHgyqhd89Lrc/V199NX744YfBvIWoyOVyp52Fd4Tc8jruseltDAUZVz/JHrAeV3fSF3JL//PjFdDqjcMNH5h/lSguJgMEehzyZEijdOyFRum4ttHLX0dhRQO8PGRQZz0DmUyg9WJDsu9PZVMH7th+HNUtnYIavaPVGRB3x1ZcalJBKpWg9IM/In54MN/FIlYIbpQOEQ+9geFug5cyItytkz0g3O6djw/l4VKT8WTtrdenUrJ3UwL99BJnqbjcCr3B2A2QFCPQm1zbKdl3E1rSZ1kWr35y5WTt47dN4bE0hE+U8EmfSmsEfpNrOyf7bkJK+t/+UoozJcZhtVcnR+K69BH9rEHEihK+E1y6dAnV1dW4dOkS30UZsOqGK32JccPMuwFcPq5BJntb4xJC0mcYFut27Of+fmD2aG7iMbFw+ePQhVDCd4LLly+jtrZWkB+0NvWVoW7BFhfpuHRcQ2jZDyQuV0/6Hx3MxbkLxkQ4OiYIV43wds36GgKXPg5dDCV80qe2jisJP9DPq49XuhAHdeP0xlWTvlZnwLO7DnJ//3FhGqRSutG3O6OBq06QkJDA3ZFHaExb+IG+5gnfJeOyQ7IfTFyuOE5/5zdnUFZjvFfAzVcl4K6517hefdmBSx6HLopa+E4QGBiIoKAgs5u5CEVfLXyXi8tOLfvBxuVKLf32ji5sevcw9/fmlTe7Xn3ZiVjjcgRK+KRPfbXwXYqTu3F6Y5n0fyjgp1/52TcP4HKzGgBw241jMCk1mpdyENdCXTqkT4zJhdgu+4vZRZJ9t+6kf7CoDndf4/yppE/kV+Ffn58EAPh4yfHSqplOLwNxTZTwnaCrq4vrYzS956oQ+JvMt6L69Ubf3VwiLgcke3vENSLUF/ddGz+kcgyGTm/Aype/Rvf39KbfzcDIX6+fcIn6cgCxxuUIlPCdwHT6VssbJ7u6vhI+73E5qGXPe1xD8PcPf0ZOmXGyuwlJw82uqhVyXH0Ra1yOQH34pE8Bvr0nfF65WDeOKyipauRO1EqlEux4ciHkQp37iDgEtfCdICQkBHq9XpDTt/bVwuctLgcneyHWl05vwIoXv0SXzgAAeHzpNbg6JcrsNUKMyxZijcsRaA85QWxsLN9FGLQAnyt9os3t5kMMeYvr8wcd2rIXYn0999ZB/JxnvLlJQmQwNv1uRo/XCDEuW4g1Lkeg33ukTwmRV+bPKa5q5LEkJib+HvANo26cX+07eQEv7v4JACCXSfG/Z5eK5uYmxL6ohU/6lBobzj0urGjgsSQmEm4A/nQe8PLnuyS8q2lox71/+5z7+8VVN+OaMTE8loi4Mmrhkz7FDQuGt6exXVDgKgkfoGQP481p7nrhUzS0dgAAFlybjD8vu5bnUhFXRi18JygpKeFOKiUlJfFdnAGRSiVIGRGG7NLLKK1uglZngKeHDICw4+qLUOL6664DOJx9EQAQowjE22sW9TmfjFDiGiixxuUI1MJ3go6ODqjVanR0dPBdlEHp7tYxMCyKKq+08oUeV2+EENeuvWe5fnuZVIIP/7oUYUG+fa4jhLgGQ6xxOQIlfNKvq5MjuccHzyr5KwgBAPxwugwPvrKH+/uVR+bgurE0UoX0T8KyJpOl8MSRd2knQ3e+9DIyHvgPAGDeNUn45sW7eC6R+8otr8N1f9jFTWr3xyWTse0Pt/BcKmJPjsyHlFFJv8aOjEBkmPEk6aFsJbq0ep5L5J5qG9sxf91uLtn/ZmoKXnlkDs+lIkJCCZ/0SyKRYPbERABAh0aHozkVPJfI/bSpu7Dwmf+h4nIrAGM32+5nl0BGUyeQAaCjhdhk7uRR3OM9x4t5LIn7UXVqccuaD3C6uBYAEDssCHs230UXV5EBo2GZTtDQ0ACGYSCVShEeHt7/Ci5o9sREeHrIoNUZ8O535/G3B26Gur1V8HFZ40r1pe7UYv7a3dy0CWGBPti7+S4MDx34dQiuFJc9iTUuR6CE7wTV1dXc9K1CPSBDA31w+/Q0vP/9eTS1deLjg3kYHykRfFzWuEp9qTq1WLBuN46cN461Dwnwxg8v34e0hIhBbc9V4rI3scblCNSlQ2z2yKKJ3OM3vjzFY0nEr1WlwZyn3+curAr088J3f78X40cN57lkRMiohe8EsbGx3E9OIZsyJgbjRw3HuQuXcLKwGo3a65ExMkbwcVniu74uNamwYN1urs8+2N8b3//jXky0mO54oPiOy1HEGpcj0Dh8MiA79pzGqpeNF/0sui4FX7xwB88lEpe88jrMW7ebG40TFuiDH16+j1r2boTG4ROXcdfNY7kx+V/+VIT9p8t4LpF4/HC6DFP/sItL9iMiAnF46wpK9sRuKOGTAfHz8cTmB27m/n7ijW9hMDA8lkgc3so6i1vWfMBdVHVVUiROvPHAoE/QEmINJXwnMBgM3D8xuHd2Bje/Tk5ZHXbsOc1ziezLmfVlMDD4y879uH/LV9D/+sW5cGoyjmxbgciwADu/l7iOw25ijcsRqA/fCbKzs7lhYxkZGXwXxy6O5lTghj++BQAI9vNE7luPIloRyHOp7MNZ9VXT0I67/+8zHDqn5J7745LJeOWROQ65glaMxyEgvrioD5+4nOvHxmLuhGgAQItai99uyoROTy0sW333SynGr/wPl+ylUgm2PjoH2/5wC02XQByGjiwnCAgIQGBgIAIC7PsTnW8vrLgOUaHGOdh/yq3EMzv381wi+3Bkfel/7cKZu+Z91LcY52+PDg/AoVeX40+3TbH7+5kS63Eo1rgcgbp0yJCcyK/CDX96Czq9sf/5i+d/i0XXp/JcKtdUWt2EFS99aTb53LxrkvDOusUI7+fmJcR9UJcOcVnXjInBPx6azf197+bPcaqohscSuR6d3oAt//sJY3//by7Zy2VS/P2hWfj6b3dSsidOQy18MmQsy+K3GzPxyeF8AMZ5dw6+shzjEofxXDL+/VJYjZX/+BrZpZe55+KGBeHD527DlDExPJaMuCpq4ROXJpFI8PbaxZg2Lg4A0NTWiZv+/A5Ou3FLX9WpxROv78OUR9/kkr1UKsHjt12D3LceoWRPeOHQFv7Zs2exceNGnDx5Ei0tLYiNjcVdd92Fp556Cr6+V37Gir2FX15eDr1eD7lcjoSEBL6LYzeWcbV3dGHWU+/hREE1AOOEX59tvB03Xz2S55IOzFDqS6c3YNfes9j47mHUNqq45zMSh2HHUwsxKTXa3sW1mbsch0LnyHzosMnT8vPzMXXqVKSkpGDr1q0IDw/HkSNHsGnTJpw+fRpffvmlo97a5bS1tXHjhMXEMq4AX+OMjvPX7cbRnAq0qbswe/X72LhiOp65+wZIpRKeS2ybwdQXw7DIPJyPZ3cdQElVE/e8t6ccG1bciD8vuxYecpkjimszdzkOSe8clvB3794NjUaDTz/9FImJxtvj3XTTTaitrcX27dvR3NyMkJAQR7094Umgnxf2vXQ3bt+Yib0nSsAwLP666yB+yq3Ee8/cKsoTlN+fKsW6Hfu52S273XpDKrY8OAujokN5Khkh5hyW8Lu/bYOCgsyeDw4OhlQqhaen+9yeLS0tDSzLQiIRRgvXVr3F5efjia//dif+9sGPWP/2ITAMi30nL2DCyv/i30/Mx/wpSS69L2ypL53egE+PFGBr5nGuC6vbjRlxeHHVTJfrp3e345D05LA+fKVSiQkTJmDmzJl46aWXoFAocPjwYdxzzz2477778M9//pN7rbU+q4qKCsTFxSEw8Mrl+l1dXSgsLAQAhISEIDY21mydkpISdHQYL2axvMS6oaEB1dXGD2ZsbKzZrwuDwYDc3FwAxr6ykSPN+5zLy8vR1tYGwHhwyeVXvidbWlpw8aLxJhVRUVFQKBRm654/fx4sy8LHxwfJyclmyyorK9HUZPz5n5KSAm9vb26ZSqVCaWkpACAiIgKRkZFm6+bn53M/Y8eMGWO2rLa2FnV1dQCAxMRE+PtfuR2eRqNBUVERACA0NBQjRowwW7e4uBidnZ2QSCQYN26c2bL6+nrU1BhPxMbFxSE4OJhbptfrkZeXBwAIDAzk+lIPnCnHnS98irpmNffaWVePxKuPzuEmBmtubkZFhXG4YnR0dI+7FmVnZwMAfH19kZSUZLasoqICzc3NAIDU1FR4eXlxy9ra2lBeXg4AGDZsGIYPN591Mi8vD3q9Hl5eXkhNNb92oKamBvX19QCAUaNGwc/PDwDQ2NqB1z8/gde/OIm6Vo3ZOuNHDcfmlTcjPlCPrq4uyGQypKenm72mrq4OtbXGXwLx8fFmDSKtVouCggIAxoZSfHy82bqlpaVQqYznBcaOHWvWp9vY2IiqqioAQExMDMLCwrhlDMMgJycHAODv78/94u6mVCrR2mqcoXP06NFmjbHW1lYolUoAQGRkJCIizCdzy83NhcFggLe3N1JSUsyWVVVVobGxEQCQlJRkdt5OrVbjwoULAACFQoGoKPO5/gsLC9HV1QW5XI60tDSzZZcuXcLly8YT4QkJCaLLEYLsw4+Pj8exY8dw6623mh1gf/zjH7F169Z+19fr9bD8LmJZFjqdjltubZ3u5ZYYhuGWMUzP2R1t3a5lmUy3a23yJp1OB5ZlrfYvGgyGIW23t1hNt2sZq+k+tLbd7littZZs3a7pPrzpqgSc3f4gljz7Pk4UGb+Evj9dhowH/oMHF16N5+67EXLWMXXTX6w6nQ56vd7qB8k0VoOBwU85FXj3u2y89/15dHaZlyMjcRjW3HkdfjsjHVKpBLm5udDpdFbfs686N411oHVu6/FtbX3TMlnqbx9qtVowDAOZrOf5ib5itaVuuj87g92uGHKEvTks4SuVSixcuBDDhg1DZmYmFAoFTpw4gRdeeAEqlQpvvvlm3wWTy3skHYlEwu0U029Q03V622lSqZRbZu0Dbut2Lctkul1rB72HhwdYlrW6XZlMNqTtmv7f23YtYzXdh9a22x2rtYRv63YtY40KD8AHT8/GZ0eL8OqXuaht7oSBYfHGl6ewc+9ZLLp2FOZPiEBGfKhd66a/WLvjtLYPpVIpimtV+PZsNfa/dATVDeYtLokEuDFtOB75zVW4beZEs/f28PCAwWCw+p591blprL2Vd6jHd3/Hi6X+9qGnpycMBkO/2x1M3TAMM+DPjdhyhL05rEvnjjvuwMGDB1FWVsb9HAaAt956C/fffz8OHTqEG2+8EYD4h2W2tLRwt2Az7QYRusHE1dmlw6ufHMffPvgRao15SysjcRge/s1ELL4+FcNC/XvZguOoO7U4ll+Fb34uwJc/l6D8UmuP1wT4euL38ybgscWTkSiwk7F0HAqDILt0zp07hzFjxpglewCYNGkSAGPfX3fCF7uLFy9y/e1iOCC7DSYuHy8PPHPPDfjdLeOxNfM43tx7Fo1tnQCA7NLLeOjVb/DQq99g/KjhmDMpEXMmJeK69Fh4eth/SKOqU4tjeZU4dE6JQ+cu4peiam5OIFNymRSzJybijpvSsOi6VAT6eVnZmuuj45A4LOFHRUUhNzcXKpXK7KThsWPHABhPLBH3FRkWgJcenIWNv5uBTw7l4Y0vT+F4fhW3/NyFSzh34RJe+t9P8PX2wOjYcKTGhmN0XDhSRxgfR4T4wd/HE96ePbv/WJaFRqtHm7oLreouVDe04UJ1E0prmlFwsQF5yjqU1Tajt9+3UgkwKUmBB34zBbden4owEQ4nJe7HYV06X331FRYvXoxrrrkGTzzxBMLDw3H8+HFs3rwZsbGxOHv2LDcaQOxdOvX19VyfruUZeiGzd1xnimvx6ZF87DtZijMltf2v8CupVAJ/H08E+HhCLpOivVOLNnUXdwcpWyWPCMON4+JwVWIorhsdieFhAVRfAiC2uByZDx06tcLBgwfx4osv4vz582htbcWIESOwcOFCrFu3rsewMTEnfDJwdc1qfHeqFN/+Uoqf8ypR3kdrfDB8vT2QFq/AhFHDMX18PG7MiEdUOM2nTvgn2IRvK0r4pD8arR4lVY0ouNiAwooGFFc1olXdBVWnFqpOLdo7jI91BgaBvl7Gf35eCPIzPlYE+yIxKhSJUSFIHhGGuGHBgpnqgbgXSviEEOImaHpkQgghQ+b4kf4E58+f54aNWU5XIGQUl7BQXIRa+E7Asiz3T0woLmGhuAi18J3Ax8cHHh4eTrl02pkoLmGhuAidtCWEEBdCJ20JIYQMGSV8QghxE5TwCSHETdBZDieorKzk5vqwvMOUkFFcwkJxEWrhO0FTUxMaGhq42xmKBcUlLBQXoYRPCCFugoZlOoFGowHLspBIJGY3Khc6iktYKC5hEOQdr8gVYjgIraG4hIXiIuJoQhNCCOkXJXxCCHET1KXjBCqVCgzDQCqVmt3fV+goLmGhuAglfCcoLS3lpm/NyMjguzh2Q3EJC8VFqEuHEELcBLXwnSAiIoK7ElBMKC5hobgIjcMnhBAXQtMjE0IIGTJK+IQQ4iYo4RNCiJugk7ZOkJ+fzw0bGzNmDN/FsRuKS1goLkIJ3wl0Oh10Oh3fxbA7iktYKC5CCd8JPDw8zP4XC4pLWCguQsMyCSHEhdCwTEIIIUNGCZ8QQtwEJXxCCHETdNLWCWpra7m5PiIjI/kujt1QXMJCcRFK+E5QV1fHjRMW0wFJcQkLxUWoS4cQQtwEtfCdIDExkbsjj5hQXMJCcRFK+E4g1tuuUVzCQnER+kokhBA3QQmfEELcBHXpOIFGowHLspBIJPD29ua7OHZDcQkLxUUo4TtBUVERN2wsIyOD7+LYDcUlLBQXoS4dQghxEw5P+EePHsW8efMQEhICHx8fJCUl4fnnn3f027qU0NBQhIeHIzQ0lO+i2BXFJSwUF3Fol87u3btx77334vbbb8e7774Lf39/lJaWoqamxpFv63JGjBjBdxEcguISFoqLOGw+/OrqaqSkpOC+++7DG2+80edraT58QggxEuR8+Dt37oRarcaaNWsc9RaEEEIGwGFdOkeOHEFoaCgKCwuxaNEi5ObmIjQ0FEuWLMGWLVsQGBjY5/p5eXmIi4sze11XVxcKCwsBACEhIYiNjTVbp6SkBB0dHQDQ42x9Q0MDqqurAQCxsbEICQnhlhkMBuTm5gIwfpOOHDnSbN3y8nK0tbUBANLS0iCXX9ltLS0tuHjxIgAgKioKCoXCbN3z58+DZVn4+PggOTnZbFllZSWampoAACkpKWZDylQqFUpLSwEAERERPSaF6uvGzbW1tairqwNgvOzc9EpEjUaDoqIiAMa+T8ufw8XFxejs7IREIsG4cePMltXX13PdcXFxcQgODuaW6fV65OXlAQACAwORkJBgtm5ZWRnXaklPT4dMJuOWNTc3o6KiAgAQHR2N8PBws3Wzs7MBAL6+vkhKSjJbVlFRgebmZgBAamoqvLy8uGVtbW0oLy8HAAwbNgzDhw83WzcvLw96vR5eXl5ITU01W1ZTU4P6+noAwKhRo+Dn58ct6+joQElJCQAgLCwMMTExZusWFRVBo9FAJpMhPT3dbFldXR1qa2sBAPHx8QgKCuKWabVaFBQUAACCgoIQHx9vtm5paSlUKhUAYOzYsWYtvsbGRlRVVQEAYmJiEBYWxi1jGAY5OTkAjFelJiYmmm1XqVSitbUVADB69Gh4enpyy1pbW6FUKgEAkZGRiIiIMFs3NzcXBoMB3t7eSElJMVtWVVWFxsZGAEBSUhJ8fX25ZWq1GhcuXAAAKBQKREVFma1bWFiIrq4uyOVypKWlmS27dOkSLl++DABISEgQdY6wN4cl/OrqanR0dGDZsmVYt24dtm7dil9++QXr169Hbm4ufvzxR0gkkl7X1+v1sOxtYlmWu1mxXq+3uk5vNzNmGIZbxjBMj+W2bteyTKbbNRgMVrfLsiz0ej2Ki4vNKtRgMAxpu73Farpdy1hN96G17XbHaq1uLLdbXFwMvV4PuVyOhIQEl6ub/mLV6XTQ6/U9fioXFxejo6ODe7/BbFen01ld1ledm8Y60Dq3dR+2trb2eRxa6i9WrVYLhmHMvsCtbXew+9DaPrLcrulxGBsb63LHoa05whn35HVYwmcYBhqNBuvXr8fatWsBANOnT4enpycef/xx7N+/HzNnzuy9YHJ5j6QjkUi4nWL6DWq6Tm87TSqVcsus9YXZul3LMplu19pB7+HhAa1WC5Zl0dnZabZMJpMNabum//e2XctYTfehte12x2ot4Vtut7Ozk/uV4Yp101+sluXu1tnZyX2ore0LW7bbPT+7pb7q3DTW3rY7lH2o0+nAMEyfx6Gl/mL19PSEwWDo9zgczD5kGMZqnVtu19WPQ1s+yyzLWt2uvTnspO21116L48eP48yZM5gwYQL3fHFxMVJSUvDSSy9h9erVAMR/0vb8+fPcAWnZTSJkFJewUFzC4Mh86LCvlHHjxuH48eM9nu/+fhFLMreFGA5CayguYaG4iMOy7tKlSwEAWVlZZs/v3bsXADBlyhRHvTUhhBArHNbCnz17NhYuXIhNmzaBYRhMmTIFp06dwsaNG7FgwQJcf/31jnprQgghVjisDx8wnvzauHEjdu/ejdraWkRFReHuu+/G+vXrzYbPib0PnxBCbOXIfOjQhG8rsSf8+vp6btSG5RhcIaO4hIXiEgZBnrQlV9TU1HCjCMRwQHajuISF4iLiaEITQgjpF7XwnSAuLg4Mw4imi6obxSUsFBehPnxCCHEhgpwtkxBCiGuhhE8IIW6C+vCdoHvmT4lE4pQJkpyF4hIWiovQ3nGCvLw8btiY5RzcQkZxCQvFRahLhxBC3AS18J0gMDCQu0GDmFBcwkJxERqWSQghLoSGZRJCCBkySviEEOImKOETQoiboLMcTlBWVsadVBo5ciTfxbEbiktYKC5CCd8J2tvbuXHCYkJxCQvFRahLhxBC3AQNy3QCg8HAPZbJZDyWxL4oLmGhuISB7nglcGI4CK2huISF4iLiaEITQgjpFyV8QghxE9Sl4wTNzc3cLdhCUjlr8QAACrpJREFUQkL4Lo7dUFzCQnERSvhOUFFRwQ0bE9MBSXEJC8VFqEuHEELcBLXwnSA6Opr7ySkmFJewUFyExuETQogLoemRCSGEDBklfEIIcROU8AkhxE3QSVsnyM7O5oaNZWRk8F0cu6G4hIXiItTCJ4QQN0EtfCfw9fXlbtAgJhSXsFBchIZlEkKIC6FhmYQQQoaMEj4hhLgJSviEEOIm6CyHE1RUVHAnlWJjY/kujt1QXMJCcRFq4TtBc3Mzmpqa0NzczHdR7IriEhaKi1DCJ4QQN0HDMp2gq6sLLMtCIpHAy8uL7+LYDcUlLBSXMDgyH1IfvhOI4SC0huISFoqLOLUJvXPnTkgkEvj7+zvzbQkhhMCJCb+6uhpPPfUUoqKinPWWhBBCTDitD3/hwoWQSCQIDQ1FZmYmVCoVt8xgMJj9DQB+fn6i6cM37Y8LCAjgsST2RXEJC8UlDAzDQK1Wmz3n7+8PmUw25G07pQ///fffx+HDh5Gfn49nn322x3Jr3zmWAYuF5ckYsaC4hIXiEhZ7tcsd3oSuq6vD448/jhdffBExMTGOfjtCCCG9cHjCf+SRR5CSkoKHH37Y0W9FCCGkDw7t0vn000/x9ddf4+zZs5BIJI58K0IIIf1wWMJXqVR49NFH8Yc//AFRUVFoaWkBAGi1WgBAS0sLPDw8uJOzfn5+ZutLJBL6kiCEuB2WZXv02dtrAIvDRukolUokJCT0+ZpFixbhiy++cMTbE0IIseCwFv7w4cNx8ODBHs+/+OKLOHz4MLKyshAeHu6otyeEEGLB6XPprFixosc4fEIIIY7nklc2iWkKhqNHj2LevHkICQmBj48PkpKS8Pzzz/NdrCE5e/YsFi9ejKioKPj6+iI1NRWbNm1CR0cH30WzSXt7O1avXo3Zs2dDoVBAIpFgw4YNVl975swZzJw5E/7+/ggODsaSJUtQVlbm3ALbyJa4DAYDXnnlFcydOxcxMTHw9fXF6NGjsXbtWu48m6sZSH11Y1kW06ZNg0QiwWOPPeacgg7QQOLS6XR45ZVXMHbsWPj4+CA4OBhTp07Fzz//PKD3dHrCf/vtt/ts3YtpCobdu3fjxhtvRFBQEN59913s3bsXa9assdtFFHzIz8/H1KlToVQqsXXrVuzZswd33HEHNm3ahDvvvJPv4tmksbER27dvR1dXFxYvXtzr6woLCzF9+nRotVp8/PHH2LVrF4qLi3HDDTegvr7eiSW2jS1xdXZ2YsOGDYiLi8PWrVuxd+9erFy5Etu3b8d1112Hzs5OJ5e6f7bWl6nXX38dFy5ccHDJhsbWuAwGA2699VbuM5aVlYUPPvgAc+fOHfgFqqyLWbBgAbtw4UJ2+fLlrJ+fH9/FGbSqqirWz8+Pffjhh/kuil395S9/YQGwFy5cMHt+1apVLAC2qamJp5LZjmEYlmEYlmVZtr6+ngXArl+/vsfrli1bxoaHh7Otra3cc0qlkvXw8GBXr17trOLazJa49Ho929DQ0GPdTz75hAXAvvfee84o6oDYWl/dysvLWX9/f/azzz5jAbCPPvqok0o6MLbG9eqrr7JSqZQ9duzYkN/Tpbp0uqdgeOONN/guypDt3LkTarUaa9as4bsoduXh4QEACAoKMns+ODgYUqkUnp6efBRrQGwZ8qvX67Fnzx4sXboUgYGB3PNxcXGYMWMGPv/8c0cXc8BsiUsmkyEsLKzH85MnTwYAVFZWOqRsQzHQIdqrVq3CrFmzcOuttzqwVENna1zbtm3DtGnTMGXKlCG/p8skfLFNwXDkyBGEhoaisLAQ48ePh1wuR0REBB566CG0tbXxXbxBW758OYKDg/Hwww+jrKwM7e3t2LNnD/773//i0Ucf7XE9hVCVlpais7MT48aN67Fs3LhxuHDhAjQaDQ8lc4wDBw4AANLS0nguydDs3LkTJ0+exGuvvcZ3UeyisrISSqUSY8eOxTPPPINhw4ZBLpcjLS0N77zzzoC35zIJX2xTMFRXV6OjowPLli3Db3/7W/zwww94+umn8e6772LevHmC7cePj4/HsWPHkJubi8TERAQGBmLhwoVYvnw5tm3bxnfx7KaxsREAEBoa2mNZaGgoWJYVzT1Uq6ursXbtWkycOBELFizguziD1n3+b8uWLaI4BwgYYwKAd955B19++SVee+017N27F2PGjMGKFSuwY8eOAW3PJe54JcYpGBiGgUajwfr167F27VoAwPTp0+Hp6YnHH38c+/fvx8yZM3ku5cAplUosXLgQw4YNQ2ZmJhQKBU6cOIEXXngBKpUKb775Jt9FtKu+jkcxHKtNTU1cA+Sjjz4S9JTkDz30EDIyMrBy5Uq+i2I3DMMAADQaDfbu3Yu4uDgAwKxZszBx4kRs2rRpQPHyXrvWpmBoaWkxm4JBiFMld/eTzpkzx+z5W265BYBxuJ8QrV27Fm1tbfj222+xdOlSTJs2DU8//TS2bt2KXbt24fDhw3wX0S6666+7pW+qqakJEokEwcHBzi6WXTU3N2PWrFmorq7G999/j5EjR/JdpEHLzMzEvn37sGXLFrS2tnJ5BDBO59LS0gKdTsdzKQeu+zhMTU3lkj1gbGzMmTMHVVVVqKurs3l7vCf8hoYGXL58GS+//DJCQkK4f//73/+gVqsREhKCu+++m+9iDpi1vl/gyrzWQm1JnTt3DmPGjOnRVz9p0iQAQG5uLh/FsrvExET4+PggJyenx7KcnByMGjUK3t7ePJTMPpqbmzFz5kyUl5fj+++/7/V4FYrc3Fzo9XpMmTLFLI8AwI4dOxASEoJvvvmG51IOXGJiInx9fa0uG0wu4b1LR6xTMCxduhTbt29HVlYWJkyYwD2/d+9eALDLGXc+REVFITc3FyqVyuzCuGPHjgGAKE64A4BcLsfChQvx2WefYcuWLdydlCoqKnDw4EE88cQTPJdw8LqTfVlZGb7//nuz41OoVqxYgenTp/d4fsaMGVi8eDH+9Kc/IT093fkFGyK5XI5FixYhMzMTSqUS8fHxAIzJft++fUhMTBxQfuQ94Xt7e1utqLfffhsymczqMiGYPXs2Fi5ciE2bNoFhGEyZMgWnTp3Cxo0bsWDBAlx//fV8F3FQHn/8cSxevBizZs3CE088gfDwcBw/fhybN2/GmDFjuC4rV5eVlQW1Ws3dISk/Px+ZmZkAgHnz5sHX1xcbN27EpEmTsGDBAqxduxYajQbPPfccwsPD8eSTT/JZ/F71F1d3V8DZs2exdetW6PV6HD9+nFtfoVAgMTGRl7L3pb+44uPjuWRoKTo62mXziC3H4fPPP4+srCzMnTsXGzZsQGBgIHbu3Ins7Gx8/PHHA3vDIY/kdxChX3jFsizb0dHBrlmzhh0xYgQrl8vZ2NhYdt26daxGo+G7aENy4MABdvbs2ezw4cNZHx8fNjk5mX3yySetXtDjquLi4lgAVv+Vl5dzrzt16hR78803s76+vmxgYCC7ePHiHheduZL+4iovL+91OQB2+fLlfIdgla31ZQkufOEVy9oeV05ODjt//nw2ICCA9fb2ZqdMmcJ+/fXXA34/p0+eRgghhB/CPHNICCFkwCjhE0KIm6CETwghboISPiGEuAlK+IQQ4iYo4RNCiJughE8IIW6CEj4hhLgJSviEEOImKOETQoiboIRPCCFu4v8BJCKwzRHz10YAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ipywidgets import interact\n", "from kf_book.book_plots import figsize, FloatSlider\n", "\n", "fig = None\n", "def plot_covariance(var_x, var_y, cov_xy):\n", " global fig\n", " if fig: plt.close(fig)\n", " fig = plt.figure(figsize=(4,4))\n", " P1 = [[var_x, cov_xy], [cov_xy, var_y]]\n", "\n", " plot_covariance_ellipse((10, 10), P1, axis_equal=False,\n", " show_semiaxis=True)\n", "\n", " plt.xlim(4, 16)\n", " plt.gca().set_aspect('equal')\n", " plt.ylim(4, 16)\n", "\n", " \n", "with figsize(y=6):\n", " interact (plot_covariance, \n", " var_x=FloatSlider(5, min=0, max=20), \n", " var_y=FloatSlider(5, min=0, max=20), \n", " cov_xy=FloatSlider(1.5, min=0, max=50, step=.2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pearson's Correlation Coefficient\n", "\n", "We will not be using this coefficient in this book, but you may see it elsewhere. You can safely skip this section if uninterested.\n", "\n", "The correlation between two variables can be given a numerical value with *Pearson's Correlation Coefficient*. It is defined as\n", "\n", "$$\\rho_{xy} = \\frac{COV(X, Y)}{\\sigma_x \\sigma_y}$$\n", "\n", "This value can range in value from -1 to 1. If the covariance is 0 than $\\rho=0$. A value greater than 0 indicates that the relationship is a positive correlation, and a negative value indicates that there is a negative correlation. Values near -1 or 1 indicate a very strong correlation, and values near 0 indicate a very weak correlation.\n", "\n", "Correlation and covariance are very closely related. Covariance has units associated with it, and correlation is a unitless ratio. For example, for our dog $\\sigma_{xy}$ has units of meters squared.\n", "\n", "We can use `scipy.stats.pearsonr` function to compute the Pearson coefficient. It returns a tuple of the Pearson coefficient and of the 2 tailed p-value. The latter is not used in this book. Here we compute $\\rho$ for height vs weight of student athletes:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9539731096080194" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import pearsonr\n", "pearsonr(height, weight)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we compute the correlation between engine temperature and lifespan." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.9178223453527254" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pearsonr(max_temp, lifespan)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Correlations to Improve Estimates\n", "\n", "Suppose we believe our dog is at position (5, 10) with some given covariance. If the standard deviation in x and y is each 2 meters, but they are strongly correlated, the covariance contour would look something like this." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = [[4, 3.9], [3.9, 4]]\n", "\n", "plot_covariance_ellipse((5, 10), P, ec='k', std=[1, 2, 3])\n", "plt.xlabel('X')\n", "plt.ylabel('Y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose I were to tell you that we know that $x=7.5$. What can we infer about the value for $y$? The position is extremely likely to lie within the 3$\\sigma$ covariance ellipse. We can infer the position in *y* based on the covariance matrix because there is a correlation between *x* and *y*. I've illustrated the likely range of values for y as a blue filled circle." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_correlation_covariance()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The circle not mathematically correct, but it gets the idea across. We will tackle the mathematics in the next section. For now recognize that we can predict that $y$ is likely near 12. A value of $y=-10$ is extremely improbable.\n", "\n", "A word about *correlation* and *independence*. If variables are *independent* they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also *uncorrelated*. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, $y$ is dependent on $x$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiplying Multidimensional Gaussians" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous chapter we incorporated an uncertain measurement with an uncertain estimate by multiplying their Gaussians together. The result was another Gaussian with a smaller variance. If two pieces of uncertain information corroborate each other we should be more certain in our conclusion. The graphs look like this:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_gaussian_multiply()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The combination of measurements 1 and 2 yields more certainty, so the new Gaussian is taller and narrower - the variance became smaller. The same happens in multiple dimensions with multivariate Gaussians.\n", "\n", "Here are the equations for multiplying multivariate Gaussians. The capital sigma ($\\Sigma$) indicates that these are matrices, not scalars. Specifically, they are covariance matrices:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\Sigma_2(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_1 + \\Sigma_1(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_2 \\\\\n", "\\Sigma &= \\Sigma_1(\\Sigma_1+\\Sigma_2)^{-1}\\Sigma_2\n", "\\end{aligned}$$\n", "\n", "\n", "They are generated by plugging the multivariate Gaussians for the prior and the estimate into Bayes Theorem. I gave you the algebra for the univariate case in the **Gaussians** chapter. \n", "\n", "You will not need to remember these equations as they are computed by Kalman filter equations that will be presented shortly. This computation is also available in FilterPy using the `multivariate_multiply()` method, which you can import from `filterpy.stats`. \n", "\n", "To give you some intuition about this, recall the equations for multiplying univariate Gaussians:\n", "\n", "$$\\begin{aligned}\n", "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", "\\sigma^2 &= \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n", "\\end{aligned}$$\n", "\n", "This looks similar to the equations for the multivariate equations. This will be more obvious if you recognize that matrix inversion, denoted by the -1 power, is *like* a reciprocal since $AA^{-1} =I$. I will rewrite the inversions as divisions - this is not a mathematically correct thing to do as division for matrices is not defined, but it does help us compare the equations.\n", "\n", "$$\\begin{aligned}\n", "\\mu &\\approx \\frac{\\Sigma_2\\mu_1 + \\Sigma_1\\mu_2}{\\Sigma_1 + \\Sigma_2} \\\\ \\\\\n", "\\Sigma &\\approx \\frac{\\Sigma_1\\Sigma_2}{(\\Sigma_1+\\Sigma_2)}\n", "\\end{aligned}$$\n", "\n", "In this form the relationship between the univariate and multivariate equations is clear.\n", "\n", "Now let's explore multivariate Gaussians in terms of a concrete example. Suppose that we are tracking an aircraft with two radar systems. I will ignore altitude so I can use two dimensional plots. Radar provides the range and bearing to a target. We start out being uncertain about the position of the aircraft, so the covariance, which is our uncertainty about the position, might look like this. In the language of Bayesian statistics this is our *prior*. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P0 = [[6, 0], [0, 6]]\n", "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose that there is a radar to the lower left of the aircraft. Further suppose that the radar's bearing measurement is accurate, but the range measurement is inaccurate. The covariance for the error in the measurement might look like this (plotted in green on top of the yellow prior):" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 1.9], [1.9, 2]]\n", "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P1, fc='g', alpha=0.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that Bayesian statistics calls this the *evidence*. The ellipse points towards the radar. It is very long because the range measurement is inaccurate, and the aircraft could be within a considerable distance of the measured range. It is very narrow because the bearing estimate is very accurate and thus the aircraft must be very close to the bearing estimate.\n", "\n", "We want to find the *posterior* - the mean and covariance that results from incorporating the evidence into the prior. As in every other chapter we combine evidence by multiplying them together. " ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import multivariate_multiply\n", "\n", "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.9)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have plotted the original estimate (prior) in a very transparent yellow, the radar reading in green (evidence), and the finale estimate (posterior) in blue.\n", "\n", "The posterior retained the same shape and position as the radar measurement, but is smaller. We've seen this with one dimensional Gaussians. Multiplying two Gaussians makes the variance smaller because we are incorporating more information, hence we are less uncertain. Another point to recognize is that the covariance shape reflects the physical layout of the aircraft and the radar system. The importance of this will become clear in the next step.\n", "\n", "Now let's say we get a measurement from a second radar, this one to the lower right. The posterior from the last step becomes our new prior, which I plot in yellow. The new measurement is plotted in green." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P3 = [[2, -1.9], [-1.9, 2.2]]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We incorporate this information by multiplying the Gaussians:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The only likely place for the aircraft is where the two ellipses intersect. The intersection, formed by multiplying the prior and measurement, is a new Gaussian. The shapes reflects the geometry of the problem. This allows us to *triangulate* on the aircraft, resulting in a very accurate estimate. We didn't explicitly write any code to perform triangulation; it was a natural outcome of multiplying the Gaussians of each measurement together.\n", "\n", "Think back to the **g-h Filter** chapter where we displayed the error bars of two weighings on a scale. The estimate must fall somewhere within the region where the error bars overlap. Here the estimate must fall between 161 to 163 pounds." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.book_plots as book_plots\n", "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's consider a different layout. Suppose the first radar is directly to the left of the aircraft. I can model the measurement error with\n", "$$\\Sigma = \\begin{bmatrix}2&0\\\\0&0.2\\end{bmatrix}$$\n", "\n", "Here we see the result of multiplying the prior with the measurement." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 0], [0, .2]]\n", "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can incorporate the measurement from the second radar system, which we will leave in the same position as before." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P3 = [[2, -1.9], [-1.9, 2.2]]\n", "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our estimate is not as accurate as the previous example. The two radar stations are no longer orthogonal to each other relative to the aircraft's position so the triangulation is not optimal.\n", "\n", "For a final example, imagine taking two measurements from the same radar a short time apart. The covariance ellipses will nearly overlap, leaving a very large error in our new estimate:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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u3ACScrj+Pb916xaO4wBs+DxWq9X0czM5OTnw3ROGYfp5zOWyHD48+J7PzMykzY5Pnz6Fpq19RzQajfQ9Hxsb2zAD/bvvvkscx5imyejoOLVag0ajRavVYWZmhuXlVTodl2w2j+f53QDkUKvVWVqqEMcxmYw18P0RxTErtVWCMCAiwspmCKIQPwoJooCO28HxXIIoRDU0IiKCKCSKo3QuKqA71Pnac1EUhTAOQAVVV8lmbRRdQdNVVE1N9hMHqJpKJmthWiaqpqDqKoqm0HE7qLqaNBErZFF1BVVLHuv4DiERqqZQHiqh6RqqlpzEe76ffrfbto21rjlXtVt+dU0b+L4DaHc6aXktFApofZ8bPwjS9y2TschYg/+n1et1ojhGVVTyuRxREBOFEVEQ0W51cNoOURiTsWzUWCEMkm2+F9BqtIjDGFXRMFSdKIyJgrXHhkFIHMQYhknkR8n2MMJ3fTzXhzgJDgMBIY7xuu+NrunYZmYgRIV+gBoraIpGKV/E0HQ0tfv3gwjf9VBQyGbtgc+5oih4nottWxSLeaamJvuCVoZOpw1E2LbF2bOPMTo6nNZmNZvN9P+F0dFRhoeHB17Dq1ffw3U9QGFiYhLHcXEcD89rMTd3Nf1/YXJyikym0K2JsqhWQ+bmlgCD4eERLl26BJA28bt9+zaKopDP53n++ecHXqf5+XkWFhYAOHnypJxHsHfnEevPI+/leUTvfdusy4icRyT24jyiVqul/y9PTU0xPj4+8Ni33nqLMAzJZDI89thjA9ump6epVCoAPProo2Sz2XRb7/3eqXsSmHoHt/6Lr3dbHMesrq5u+PD1u3DhAl/+8pf56le/Si6X23VgCoL1HVEZ+I98/RDBvdvWz6PSE0VRuq3XLKjfTve7/pj697vZRJa+7xPHMYax8ZfUMAw/0H63eq79+13/XPtfw83223uum/3auNP97pf35k7PtTcZ6Wa/WG733uxkv77vb7ptu/32Hnun/W5mp6/hZo/vHVMYhjQaDYIgoNPp0G63WVpa4tatW8RxzNhYmeHhIlHkpv2KXPdqtwmdgevG3cEVTCwrg6qWyedNDEPnscc2ftE1GtXu8W5eDjf7DkiON0rLwvrNcRyn28JwY3npTTy7mWTOnN5+N76GvW2bzZ3Tv9/1x9R7b9pth07H5/btRarVBtVqnVqtweXL71Gvt7qhKDvw2GazRdvtEMQhdtYmUmKCbg2Q67s02i3COERpJ4EkCUUBUZyMLNiryjE7yX9euqWhWzpxLoJCcj1fymFlTfSMjmFpKIaC4ztohoqVtcgXcqjdQKRqCvVGgzAIQYGhdRPPOq5Dp50E0lwuO/CfZhTH1KrJf6iGoW8INnEzIvCT11Az19WgxDFx1OurtLFM9LZF6mbbonT7himy4rXHbvKWE3X/bqzF3ecPkJykRUaE0j03LRTyAyfAQRjSqCcnXZZlbnhf6/U6YRihKGyYvNdxkqaRcRRj21l0RUuDlu8GrC7XCN0QIgVDMQicgMAN8Z2AVt3B7/gEbshStTr4XLqfG1VRyDQzWIaJruoYqoam6rgdB13RsHSD4sx0GsJ0VcfrOPjd96ZU+g6qqmKaJqVSAds2CUOfQiHLsWOHOX78KOVygVKpQD6fTR9nWQYjI4PPtVSyWVxcwvN8JiZGUVWtWzNVw3Ub+P5s9zVZpdNppU382m2TxcVpPG8tVGYyGbLZLNlsllqtlp5synmEnEeAnEes3+9m7sZ5xGbu9Fw9zyOKok2nZbjTa7gb97Tecbsq+u22BUHAb/zGb/BLv/RL/NRP/dT7+tu6vnHUqmS0KyPdvtljNvtCAbqddo10fb2d7nf9MfXvd7M32zAM4jjedL+apn2g/fYvt9rv+ufa/xputt/ec93s/d3pfvfLe3On59p7nnd6Dd/PfsMw3HTbdvvtPXa7/X7Q17C39Lu/2Lfbbaanp1leXsbzvG5Z1bqhyMH3K6jqAnHsE4YNXLeEpqlkMhamaTA1NYymaRQKOR599JGB415YUKnV9E2PSVGU9P1U1c3L4VZfoL05kJL9DG7r329/Lc/aY7Utm2v016asnwS0d0zJcvCYoiii2ewwP1+h2WwzP1+jXm+loWhxscL8/CJhGCW1I5ZJFMd4oY8beqzUVvEjn4AItaPhhh5+GBBEAa7vpf9xGZ21z6VuaqimQlSI0CwNO6dj5zPoGT0JRRkdN3RRdQXD1hkaLaObGkp3YAPHcXBcF4B8LjfwmoRhRKOZPH/TNDHtwTKnKAqKqgz080m3oaZ/Y7OOPEo6sMLG11ft7ndTfds2+9z0tm3WTE1R+49pwwGv7XeTll6qohCpSRO7jYek7Oi5br5NRYnjTY8XJal1QwPDTPoW9URRRJztlgfDILc+YLda6QlhIVck8gN8JyRwAzoNh2a9TeiGaGgQKmnY6jgeLb9F6IbELuju8sB+gyBAiUFTNPJeDks3sTQTs2KgxSqhF2CoOoULV7D7ajg0TSeOffL5LMPDJU6fvkW5XKRUylMuF/F9h0zGIpu1mZgYGagdabVa5HI6nudj2znyebPb1K+B70coyjyqGqAoGVy3iO9naDYtNC1DpbLCysoKhpE0652YmCCbzWLb9r78v0rOIzbud7+8N3IesXG/d3qu693puZqmSRiG7+s13A0l3m3E6rO8vMzY2NiGYcUvX77M448/zt/+7d/y27/92wOP+dznPsdf//Vf0263t2yS9/LLL/MXf/EX/PCHP0ybV926dYvz58/zxS9+kd/93d9NmkZ0X7jdztYrhNg513XTcNRut+l0On2/2ISEoUMcO+my179IURQyGbPbJyJDJmNh2w9Xh+wgCKjVmmn4qVYb1Gpr69VqnXq9OfBLVxhF3TDk44UebujhhX4akLzQJ4iCgcoO3dIwcwZWzsTMGRhZHSOjJwHI1LrrWlpDtGWwEOIDisKYwE2CVOAGBE5SexW4IYET4LV9vJaP1/RxWx6hv/ZLtAIYqoGpG5iaiaUlS1MzuusGlmqmIxJCcmJWKhUolwvdMLW2vnZbfuB8IAgCHMej03HodNx02fscJoNLZFBVC1XNdC+9Hzz0tCaqF6Lu1L1ACLH/7DY73JMzl9OnT2Pbdtpesd+bb77JI488su0XzFtvvUWtVtvQThSSIcb/+I//mNdee41nnnnmrh63uDtu3bqVdpxc375b7F9xHHeb8wyGo14VeBT5ac1R7xLHvb4qSneUrRzZbGZXI27Nz88ThgGapm9o373fxXFMq9VhcXGFpaUKS0urLC5WqFSqVKsNms3B6RCCKBwIPmuhKFkmYWiwyYGR0THzSRgq5HJJMMobmDmzuzTQjI2/uj2o2p0OcRShqCrZrUYQEHtG1RTMrIGZ3X5ADkg+P6EX4bU83KafhKmmh9fycVs+9WYTt+URuIOfCV3V1wKUZmJWDazpJFj1btNUNWmaGEeoqsrk5DilUoGRkTLj48OMjY10l8Nks5l0AJQkPCWXdruB7ychKpk/KglRjpOhWs2kA02oqjoQoPpro8TBIecuYjv3JDDpus7P/dzP8c///M98+ctfplAoAElh/Na3vsVnP/vZbR//+c9/nl//9V8fuG1+fp5f/uVf5jd/8zf5pV/6JR555JF7cejiLlhdXU07gsqXzv4URVHaz6g/HPV+YQ1DtztMd384Sk5adF3rhqJCWnu0k1GytlKv19P/pPZrYHJdj6WllW4wWknXFxcrdDpJn5s4Bjf0cAIXJ3DXAlHk4QY+XuQTRv1DJ/fCkImVMyjlC1i5JAD1ApKZM1B1qSnv53kecRSjqIoEpgNOUZRuradNdnjr9zL0wyRE9YUqt1tL1Wi18Fo+fn2wb4muakR+hKFomJrBkl/FmjXJaBYZ3cLS1wJdPp9jbGyI8fERxsdH0vUTJ44QhmEapJJ+hKvpEOiKonVH7MvgeRlqtQyaZqXPzbbtNED1QtRmTYrE/iDnLmI77yswff3rX6fVaqVVWZcuXeKf/umfAPjUpz5FNpvlz/7sz/jwhz/Mpz/9aT7/+c+nE9eOjo7y+7//+4MHoev82I/9GP/+7/8OJKOMrB8tpDdCxunTp/nEJz7xfg5biIeW53k0m02azSaNRiMd6S2Zz8jtC0VJ07pe73bTNMjnM9j2UBqOTPPOvxwfRGEYsrJSS4NQfziqVuvp/bwwSENRJ3DodJdO4BF1e/4rioKZ1TELSRjK5u1uk7kkDJm55Bd4VZMwJMSdaIaGXdawy1u3TImCCK/dDVUtD6/ps7pUw2v5dDoublDBb/jpoCqaopLRLWw9g12zyCxY2EYGW7fQu/0iFUVhaKjE2Ngw4+PDaZgaGxvGspI+UUmIauC6K90jUdJmfJ6XodHIdENV8oNSJpMhn8+nl/4R1YQQ+9f7Cky/9Vu/lQ5hCfCVr3yFr3zlK0Ay9OWJEyd4/PHH+Y//+A/+6I/+iJ//+Z9H13VeeuklXn755Q1DNoZhuOnIF+Jgevzxx4njWJoj7CHHcdJw1Gw202GRw9AhijqEYadbg+TSC0dr/Y0K3Y7UmfvS3+jEiRP3rbzEcUyt1mRpqdINRmu1RZXKajpAQhhFdPpCUbJM1vubzFl5E3vEolTKM1HOYJcs7LKFlTeln9A9UigU0tH7hOhRdZVM0SJTXAsgk9FYWlY0VSUKI9yGR6fq0qm5OFWHTs2lXmvira6N0GWoOrZukemGKXsmCVYZ3UoH2tA0ndHRMhMTI4yNDTM8XKJYzJPPZ1EUBcdp4Tir3T0qab8o37dptWyWl5PwZ5rmQICypdZ0z8i5i9jOBxr0Yb+QQR/Ewyxpe99Jw1Gz2UyH1E5qjtqEYYcoahPHYbepiJXWGPX6Gz1InxfX9ZifX077FvVqjZaWVtPwGMfghC4d38VJa4qSUOSHfjqogpHRscsWmZKFXbLI9IJRyZLmckI8IAIvxKm7ON0w1ak6ODWXTtUl8LpN8ABLN5MgpfdClImtZ7A0Mx3QMJPJMD4+zOjoEKVSnkIhTz5vUyjk8LzedAcqmpZFVW00LYeqZtJROvsDVDablRN4Ie6B3WYHCUxCHDBRFHXnIVoLSFEUEcdRNxh1uiGpDcSoajLRZD6fJZ/PksvZD9Rno9FoMTOzwPT0AtPT80xPL7C8vJL2x3IDf9Ng5IR9o2JpKna5F4gs7HIGu5isG5mHZ1Q/IcSgOI4JnCCtlUqClEenlgSqKOx+hygqGc3ENjLdpn5rtVKmtjY9wtjYMGNjQwwPlymXi+TzvUmAFTTNRlWzqGoWTbNRFBVVVcnlchQKBfL5PLlc7oH6/hZir0hg6pLAJB4UYRimwajZbNJqtYjjuDukdxKOkoCU9D3SNJVcLks+b5PPJ6PWPQi/UMZxzMpKjenp+YGAVKsln/0gimj5bVp+h5bXoR106PgOYV+/okzRTGqKurVEmW4TOjO3+ZwfQgixlTiKcVteUiu1rmbKbXppfyld1bD1DFnDJm/Y5MwsOd1GVRXiGIrFPKOjZYaGSpRKeYaHy+TzuW6AstG0LJqWRVE0FEUhm82mASqfz8tAEkK8DxKYuiQw7Z16vZ62Ay4Wi3t9OAeO7/sDAandbgMQRUFac5SEpGTiUMPQyeWS5h65nI1tH6w5QVqtJnGcjBqXy+WB5DO9uLjC7dvzzMzMp+GoNyKdFwZJOPI6tPwOTb+NG7jEJMMaZ4dtciM29lBfv6KCKYMsPAD8IEj7pRgP0ZxeYvf2sqxEQYRTT4KUU3Nprzq0Kh3aK07y/yMKtm4l4cmwyRlZ8qaNrmoEQYhlmYyMJLVQw8MlJiZGGB4eQ9N6QSqXzg1l2zb5fD4NUVtNACq2J+cuD5d9MQ+TeLhdv349HZrz/Pnze304+57neQPN63oj2EWRl/Y/CsNWOueRZRkUi1ny+WHy+SyWZe7l4X9gN2/eYnZ2iUqlBhjMzCwwM7NAECTDBDuBl4ajZrcGyQuT10I3NXKjNsMjRXJj2SQklTOomtQWPaharVY6rHi5VNrrwxH72F6WFVVXyQ5vHC49CiPaK0l4ai21aVU6rCxXCYOkJjyjm2SNJEQtNVfJzdroiobvB6iqyvBwieHhEuPjw0xMTDI2dgjfL9Bs2iwtJQNeWJaV1hG11VcAACAASURBVD4VCgUZiW+H5NxFbEcCkxD3WRzHNJtNarUatVotDUhrI9i1iKIOcZwEBtu2GBrKd5vZZTGMg/ux7XQcpqcXuk3qkpqjy5ffIwwjFAXMXIam36HltdPmdb1R6cysQW7cZnx0mNxolvyojVV4//M/CSHE/aZqKvmxLPmxLDw+AiRN+zo1dyBEzS8t4teT7z5D1dOaqPpik4WVZa5cuUEQhMRxTLlcYGxshMnJcSYnDzE5eZR2u0ylkrQ2yGQylEolisUihUJBvjOFeB+kSZ646+bn5wnDEE3T9u1EpPeb7/tpQGo0GoRhSBQFhGGze2kBUbd9eqY7OEPSD+mgtk/3/YCbN2e5du12NxzNU6lUAYiimFaQBKNqu07L79AJHZTuZzZTtMiN2uRHbXKjWXKjNmZWmpkIcFyHOAJFhYx1sJqfivvrIJeVOI7xWj6t5Q6t5TbN5Q6t5Q5uMxnlU1PUpCmfmSWrZ8goFnqsEYYRQRBSLheZmBjl0KEjHDt2mkOHTmIYGVRVpVgspgEqGXBCgJy7PGykD1OXBCaxl+I4ptVqUa/XqdVqaT+kIGgTRS3CsEkUJTVLuZxNsZgnl7MP9Ah2juNy/fo0V6/e5urVW9y8OUcYBslgDN0ao6bfoeW36fguMUlb8exwhtyITa4XjkZsdOtghkQhhLiXfCdIQ1SrG6I6NYc4Tkbqs3WLnGGTUS0sxcSIdcIgQtd1Dh+e4vjxkxw79ihHj57CNE1s26ZUKlEqlcjlclL7JB4aEpi6JDCJ+y0IgjQg1et1giDoDtTQIgiaRFGLOA7RdY1CIUexmKdYzN2XyWHvhUajxdWrt7l2LQlIMzMLya+iYUDdbVL3mtTdJm2/Qwxoukq2G4zyoza5kSzZ4YzMZSSEEB9A6Ie0Kw7NXoiqdGivdIjC5EepnG6T1WxsxcKMDVRUVFVjaupQN0A9wvHjJ8nlcgO1TzJ4hHiQSWDqksAk7od2u502tWu1WkDSF6nX1C6KOgBks5luQMofyGG+e0N692qPrl69zdJSBUgGZVgLSC06QVJzlilaFKdyFKfyFCZy2CULRT1Yz1sIIQ6iKIzpVB0a8y3qc03qc03clp9MvqtZZNWkGV8GC0PVUVWd8fFJjh49xYkTpzl27Bjj4+Np7ZNMoCseNBKYuiQwiXshiiLq9TrVapV6vY7v+935kPprkQI0Te2rRcofuIEa4jhmfn45rT26evU21WqdOIZO4FBzmzS8JjW3iRf6KApkh22Kk92ANJXDyknbeCGE2A/iOMZtetTnWjTmmtRmm3RqydQUOno3QJlkNRtLtVAUg+HhUY4dO8Xx4yc4efIkx48fZ2hoiFKpJOdX4sCTwNQlgWnvXLx4MR2a88knn9zrw/nAwjCkVqtRrVap1WpEUZTWIkVRM50w1rYtisU8hUKOfP5g/RoXRRG3b8+n4ejatdu02x2iOKbld5IaJLdJ3WsRRAGqqpAbyyY1SJN5ilM5dOv9hcJ6vU4Ux6gy94XYASkvYqekrGzP7/jU53o1UC2alTZRGKGhYasWtpIhp2fJ6lkUxaBQGOo24TvGE088wdmzZymXywd2YKL1HrRzF7E9mYdJ7LkgCAiC4EAFhvXCMKRaraYhKY7jbkiqEwR14thHVRUKhTzF4gTFYh7TPDjtvX0/4MaNmbSJ3Y0bM3ieRxhFNLw2da9B3W3R8FpEcYSmqxQmchyaGqU4lSc/nkMz7s4PElEcE0cxkfy+IXZAyovYKSkr2zNsg5FTZUZOlQEIvHCtCd98i5WFGovOCkoMGcUi27aZq1znjTeLfP3rX8O2cxw9epTHH3+cp556inPnzpHJHKzRCPs9COcu4t6RwCTuOsuyUFX1wHUYDYKAarXK6uoqjUaDOI4JgjZh2CAMG8Sxj65rDA8XKJUKFArZA1OLGccxMzMLXLp0lbffvsqNG7NEUUgQhdTdFnW3Qd1r0fTbxHGMYWkUpvIcm5ykeChPbiR7zyaD1VSNSIlQlYPxWoq9JeVF7JSUld3RTY2hY0WGjiW1cVEQ0Vhs05hvUptrUZttsOysELfBVi1yrRzztdu8ffkiX/3qVzEMg9OnT/Pcc8/xIz/yIxw5cuRAhY+Deu4i7g9pkiceakEQsLq6OhCSwrA/JAUYhk6pVKBcLhyopnaO43L58nUuXnyPd965Rq3WIIgiam6dmtug5rbodEewM3MGpak8xamkeZ09dPAGphBCCHHvxFFMq9KhNtekOl2nOtvAbXkQg61nyOtFimaJglFGVVTGx8d59tlneeGFFzh37pwEEbGvSB+mLglMYitRFFGtVqlUKjQajW6fpFZfSAoxTYNSKU+5XCSfz+71Ie9IHMcsLFS4dOk9Ll26ytWrt4mikLbvsOrUWXVq1L0WcRxjl6wkHB3KU5zMYRVMCUhCCCF2LI5jOlWX1ek6q9M1qjMN3KaPqijk9QIlc4iyNYypmmSzWc6dO8eHP/xhzp8/z+jo6F4fvnjISWDqksAk+sVxTL1eZ2VlhWq1ShRF3eZ2dcKwThyHWJZBuVykVCqQy9l7fcg74nk+7757Mw1JKytVwiii5jZZdWpU3TpO4KFqKqXD+bS5RaZo7fWhCyGEeIDEcUyz0mbp2iqVG1Ua8y3iCDJahpI5RMkcIm/kyVgZjh07xvPPP8/TTz/NI488cmDnIxQHlwSmLglMAqDVarGyssLKygpBEGwYuME0DYaGigwNFbHtg9FZdXl5lUuXrnLx4nu8++5NwjDACTxWnBqrTp262ySKIzIFk6HjJYaOFSkdyssEsUIIIe4bt+OxfKPK8vVVatNN/HaApuoUjBJlc4iSVaJgFygWi5w/f55z585x7tw5yuXyXh+6eAhIYOqSwLR3ZmdnCcMQTdM4dOjQff/7nuexsrJCpVLBcRyiKCAMawRBjShy0XWNcjkJSQehuV0QBFy9ejsNSUtLFaI4pu42WXXqrDg1nMBF1RSKU321SCXrQDSz6zgOcZzMSG8f4BGWxP0h5UXslJSV/cPzA6rzDSrXVqnNNGkvOYBKVs9RNEoMZYYYyY+QyWQ4fvx4OureqVOn7tu53F6fu4j7S4YVF3tuaWkpncvgfn3pxHFMtVpleXmZer1OHEeEYYMgqBGGLRRFoVTKMzw8TrGY2/dBwvN83n77Km+8cZk333wX13VxA5/Vbi1SzW0QxhFWzmDo0SJDxw9TOpxHMw7efBiu6xJHMYoqJzXizqS8iJ2SsrJ/mIbO+NEhxo4O4fsBrVqHlZur1GZaLM/Ns7A6h1YzKBpFbizf4O0rb/Ov//qvFAoFnnnmGZ577jkee+yxe9p0by/OXcTBIYFJHGiu67K8vEylUsH3fYKgTRBUCcM6EJPP2wwPT1EuF/b95HqO43Lp0lUuXHibS5eu4vs+La9DxalS6dRo+x0URaEwmePosUnKx4pkh2U0O/HwiaOYKIjwnQDimDhOfjRhYEm6rbdUFEBR1i1JPkPd5do2Bc1QUVT5fAlxtygk4ckcLVAayeOd83E6LvWFJo3ZFo2ZJldXVrhavUrOyDGeG2d+eZ7vfOc7ZLNZnn76aZ577jmeeOIJGXVP3FfSJE/cda1WK20Gkcvl7vr+e7VJS0tL3aHAQ4KgRhBUiSIX0zQYGSkzPFza95PJttsOb731Lq+//g5vv32NMAxoeG0qnSqVThUncNEtjeHjJYaOFykfKaBbD9bvHEEY0jub1fd5qBV3FnghbsPDbXoEbkjohgReSOiFyXVv7XroRQRuQOBF3et99+3bHnrRwO2RH92356MZKpqpoZkautVdmhqaqXaX2tpy3fYtt1kaRkbHyhuYeRPdlHJ/L8h3y8ERRhGu6+E6Hm7bozHboTHj0JhpEYUxOTPHRH6CqdIUOTOHZVk89dRTPP/88zz55JNY1gcfyOhen7uI/UX6MHVJYHrwOI6T1iYlM3K3CYJVwrCBokCplGdkpEyxmN/rQ91Wo9Hirbfe5cKFd7hy5TphGNHwWlQ6VVacKk7gYWR0hk+UGDlVpnQ4j6pJWRb3V+iHuE0/CT/dADS49De9LfTCvT70A0e3NMy8iZU3sAomVt5cW252W3epGfK9IB48nh8kwcnziIKI5pxL/XaH+nSTyI/IWTkmChNMFCbIm3kMw+DcuXM8++yzPP3009j2wRjlVuwtCUxdEpgeDL3apMXFRZrNZt8ADlWiyMOyerVJZQxj/9a8OI7LG29c4ZVXLqYhqe42qTirVDo1vNDHtHVGTpUZPlmmdCgvTYHEXRVHMU7dpVXp0F5xkmWl0w073fDTF4ACZz8EHwWw112y3WUG0Lr3UXe4jIFoh8sQcIA20Nnksvf/deoZbV246q4XTLLDGXIjNtkRm9yITaZgyneKOFCiOMZ1PBzXJQwjohDaCz61W21qt2vEQbfmqTjBWHYsDU9PPfUUL7zwAk899ZQ02xNbksDUJYHpYAuCgOXlZZaWlvA8jyBodWuTmigKlMsFRkbKFAr7t9o8CALefvsar7xykTffvILvB9S9JsvtVSqdKn4UYOUMRk6VGTldpjCx/wejEPtTFMZ0qg7tSodW95KsO7RXutdXOkTBvfq6N4ERYLh7GQGGgAKDIWer8LPV7SZJ0NlvYsBl8yC1VcBaf3sDWOm7VLoX/54csaqraYjqD1LZkbXbMqUMqrYfX2/xsPP9AMf18Fwv+aki1pPwdLuZhCc/JmtlGc+NM5Ydo2AVyGQyPPfcc7zwwgs89thjck4oBkhg6pLAtHfa7XbaDjib3d2w3Y7jsLi4SKVSIQwDgqBOEKwQRS6ZjJn2Tdqvk9zFccz16zP84Adv8tprl+h0HFpeh6XOKsvtVdzQI1MwGTldZuRUmfxY9qEPSUG4VpMh/Qw2ioIoqRFa6Q9Cnb5w5NBZdYiju/FVbrAWePqXW633lln2Z7A5aGKgxWCIWr++1W3BB/7riqqQHc4kYWrYJjeSrPfCVW7YJjucOTBzusl3y4MniuO0r1MQhiiogEV72aN2s0ZjukHsJzVPY7kxxrPj2IZNsVjkhRde4CMf+QhHjhzZdN8f5NxFHDwSmLokMO2d119/PR2a8/z58zt6TL1eZ3FxkVqtRhQFBMEqQbBKHIeUSgXGxob2dW3S8vIqP/jBW/zgB29SqaziBj5L7RWWOiu0fQcjozN6uszoo0NSk7ROtVZLh/4tl0p7fTh7Io5iWisd6rNN6rNNanPd5WyT5mL7LoShEeBI3+Vw33KMtfCTQ4LPQRQDTdbC0xIwC0xvcln5QH9JURUKE1mKh/KUpvIUDxWS9UP5fTdqp3y3PNh8P6DjuHieDyioqoUSmzQWmjRuNZLwFMYUzALjuXHGc+MYmsHhw4f50R/9UV544YWBSXLfz7mLOLhkHiZxYERRxMrKCgsLCziOQxg6+P4KYVhHVWF0tMzY2DCWZe71oW7KdT0uXHib//7vC1y/Pk0QRax0qiy2K9TdJqquMnyixIkzhykdLkhTF4Hb8AbCUH22SX0uuQTu++0zNMFgGFp/OUzSvE08uBSS5o8F4Pgd7tsGZtg8TPUui1s+Oo5i6nMt6nMtplkY2KZbGsVDeYpTSYBKl4fyWPn9+T0uDi7D0DEMnTCKcDoujusSxQ65CZPC1CTxh6ZozjVp3G5wbeYa11avMWwPs9Ra4vb0bf75n/+Zs2fP8uKLL0pAEnckNUzirpuenk5ny96s6jsMQxYXF1lcXOyOdtcgCCqEYQfTNBgbG2JkpLxv502anp7ne9+7wA9/+BaO41JzGyy2K1Q6NWIiSocKjD02zMjJ0oGcSPZ+a3c66dC/2QdgdKPADbonlGuhqBeS3Ia3y73lgDPAKTYPQ4dI+vkIcTe5rNVQ9Yer28A14ApJ8No5q2h2a6T6wtThAoWJHLp1b74nH7TvFrG9XnM9p+MSRhEKelLrpBpEXkRrtkXtRo3GQgNd1RnNjjKZn6RoFSkUCpw5c4bnnnuOycnJLZvtiQeHNMnrksC0/wRBwMLCAktLSwSBTxBU8f0V4tgnn7cZHR2mXC7sqyYdPY7j8uqrl/jv/77ArVuzuIHPYrvCYruCE3hkhzKMnxlm9NEh+SX1IRFHMY2FFpXrNVauV6lcr1G9Xae13NnlnnTgNEkwWn+ZQprIif0nJglUVza5XGNX/akUyI9mKR0pMHKy1B0ptCRNl8X7FgO+F9DpOPhBAKioqpWEJ0VBcRXqt+osvbuEU3fIGlmm8lNpk70zZ87w8Y9/nGeeeUZG2XuASWDqksC0f/i+nwalZCCHVXx/BQgplwuMj4+QzWb2+jA3iOOY27fn+d73XuOVVy7iuh6rTp2F1jKrTh1VVxh9ZIiJsyPkx2XwhgdZFERUpxtUrlXTgLRyo4bf2U1H+yOsBaHH+tZPIK2jxYPDB24Al9kYpmZ2vBcjqzNyMglPvWX5SEHmpBO7EoQhnY6L63r0+jklwUnFsiy8FY/FtxepXKtADKPZUabyU5QyJXK5HB/5yEd48cUXmZqa2uunIu4yCUxdEpj2nud5zM/Ps7y8TBQF+P4qQbACRAwPl5iYGNmX/ZMcx+WHP3yL733vNWZmFnADn4X2MoutFdzQIzdqM3l2lNFHh9BNaXL3oPGdgNWbtYGao9WbdaIg2sGjy8DjbKwpeoSkeZ0QD7Mm8B4bg9Q7QO2Oj9YMlaFjRYZPlhk5WWL4VJnh40V0S35wENsLo4hOx8VxXNLgpHSDU8ZCV3QqVyrMX5qnXW2TNbJM5ieZyE1gaAaPPPIIH/vYx3j++eel1ukBIYGpSwLT3nFdl/n5+e7Q4H5ao6QoMaOjZcbHRzDN/feFs7y8yn/91w/5/vdfx3FcVp0a861lqk4d1VAZe2SIibOj5MdluNEHhdNwWblWo3K9ysr1ZFmfaxLvJBtxFHgWeK67fJakFklqGoXYnRi4Bby27jJ9x0cqKpQOFRg+1Q1R3TAlTaPFZqIoptNxcByXGFAVC1XNpMHJzti0FlvMXZxj+eoyRDBijzCZn6ScKVMoFPj4xz/OJz7xCUoy8uKBJoGpSwLT/ef7PrOzs7zyyiv4fgdVbTExkeuOeDfE+PgIhrG/fgmM45j33rvFf/zH/3Lx4rt4gc98a5n51jJe6FMYzzJxdoTRR4ZkAId7pNFsEkcRiqpSyOfv2d+Jwpjq7Trzl5ZZuFRh6d2VHfY3Ukia0D277jJyz45VCAHJ8OgXSMLTq93luyQBa3v5sSzlUwVGHy0x9vgwhx+bRFHlxwyRiOI4rXGK4xhVsWi3faIYMpkMk5OTRF7E4uVF5i7O0V5tY+s2hwqHmMxPYhomH/rQh/iJn/gJjh+/08iUYj+SwNQlgen+CcOQ+fn57qh3Hleu/IAgqGIYGh/60LOMjQ3tu4lmgyDglVcu8Z//+b/MzCzQ9h1mm4sstVdBhfEzQ0yeGyM3IiMr3Wv3aq6U0I9YvrrKwtsVFi4ts/jOCl7bv8OjTOAcgzVHTyPN6YTYL5rA6wzWRL1F0ndqa2beYOKxESaeGGHiiVFGTpbRDDlHeNhFcYzjuHQ6Lo1GgzjSUdUM5fIQtm1jZ20UFBrzDWbfnGXpvSU0RWMyP8mhwiEyeoZHH32Un/iJn+D8+fNy3nmASGDqksB070VRxNLSEvPz8/i+h++v4PsV5uZuUyzmGB8f4cyZM3t9mAMajRbf+c6rfPe7r1KvN6m6dWabi1SdBmbOYOrJUSaeGMXI7K+A9yCr1+tEUYSqqhSLxfe9H78TsHhlhYVLyyy8ndQghd52bevybKw1OosM0y3EQeMBl1irhXqNpGaqteUjNFNj7MwQk0+MMnF2hLEzw/K9/xCL4pjlpQrtjoOCQqE40u3npGFnbWw7CU5u02XurTnmLs4ROAEj2REOFw5TypQYGRnhpZde4qMf/Si2DGO/70lg6pLAdO/EcczKygqzs7O4rtsdHnwZCBkbG2JiYmTf1SjNzy/z7//+fV555SKe77HYXmGuuUQncCiMZ5l6epyRk2WZXPYAcepuUnvUvVSuVYmj7b7OxoCPAx/rXs4D0sxSiAdTQBKavt13Wd7y3oqmMHqqzMTZpAZq4vERrIL8ePKwSZvqdRxiFFQ10x1ZTyWXzWFlLBQUQj9k8coiM6/P0F5tkzfzHC4eZiw7hp2x+ehHP8onP/lJRkak6fZ+JYGpSwLTvVGr1ZiZmaHT6RAEdXx/iSjyGB4uMTU1tu8Gc5iZWeAb3/gOb7xxGcf3mGsustCuEMYhIyfLHHp6nPyEDAl+EDSX22nzuoVLFarTjTs84gSDAekMMiCDEA+rmGQ0vl54+i+SgSa2Vj5WZLIXoM6OSBPth0gUxbTbHRzXA1Q0NYOimuiaTjaXxTItIPkBuXq7yswbM6zcXMHUTA4VDjGVn8IyLD7ykY/w0z/904yPj+/tExIbSGDqksB0dzmOw61bt2g0GgRBqxuUOhSLeQ4dGsO299c8SjdvzvKNb3yHixffxQk8phvzLLZX0AyVibMjTJ4bJVOw9vowxTaiIGLx8gq3X5nn9ivz1O4YkJ4kCUa9kCQztQshtnOLtfD0beDtbe9dPlbk6HMTHHl+kvHHhmVOqIdAEEa02x08z0dBQ1VtFFXHMAzy+Ty6ttaapr3SZuaNGRbeWUCJFabyUxwpHsHSLV544QV+5md+RuZz2kckMHVJYLo7oihibm6OhYUFwtDF8xYIwya5nM3U1BiFwv7qDP/ee7f4t3/7LpcvX6PtO0w3Flhur2LYGofOjzPxxKjMnbSPOXWX6VcXmH51npnXFrcZpEEDnmet9uhFZNQ6IcQHswR8h7VaqNeAcNN7mnmDI88k4enws+PyA9wDzvcD2m0HPwhQFB1VzaIoKrZtk8vmBlqp+I7PzOszzL4xS+RHTOYnOVo8SsbI8Oyzz/KpT32Ko0eP7uGzESCBKSWB6YNbXV3l9u3beJ6L71fw/QqmqXPo0DhDQ1t3zl9ZWUk78Q8PD9/z44zjmCtXbvCNb3yHq1dv0fI6TDfmqXSqmDmDw89MMHF2BFWX8rDfxHHM/JVlZl9bYPbCEsvvVbcYMVgFfhT4JElA+lGSQRuEEOJeaQD/TRKe/i/wP2z2BaWoMHZmmKPPT3Lk+UmGjhWlmfcB5LguxDEoChlr8wDseQGtdpswjJI5nDQ76d+Uy5GxBlvaBG7A7FuzzFyYIXRDxnPjHC0exTZsnn76aT71qU9x8uTJ+/HUxCYkMHVJYHr/BpvfNfC8BSBgYmKEiYmRO76uV65cIQgCdF2/56PkXb58na997T+5eXOGhtdmuj7PqlPDKpgcfnZCmk3sQ74TMPfmErdfmWf61QXala3mQioDPw18uruUGiQhxF5aAr4OfA34BlDb9F65UZsjz01y9EOTTJ0bRbf21yBIYnM7neIiBjodh07bIe7r37RZMz2A0A+Ze2uO6QvT+G0/CU6lo2SNLGfPnuUzn/kMJ06cuLdPTmwggalLAtPubdX8rljMc+TIBJa1sxGD7kdgunVrjq9+9VtcuXKdutvidmOeqlPHLlkceX6SsUeGZJLCfaSx0EoD0vxbS4T+VsN9Pwn8LElI+gggJxpCiP3IB75LEp6+xlb9nzRTZercWFr7lB/L3sdjFLux2zkBwyii1er2b+o201MVjYyd2dBMD5J+ufOX5rn92m28psdodpRjpWPkzBzPPfccn/nMZ5iYmLhXT0+sI4GpSwLT7tRqNW7duoXrOgPN7w4fnqBcLuxqX81mkziOURSFfP7uNptaXl7la1/7T1599SJt3+FmbZYVp0Zu2ObIcxOMnCpLUNoH4jhm9Wad69+d5tb/zm0zop0FvEQSkn6WZGQ7IYQ4aK6xFp6+RTI31EblY0WOfXiKUy8eYejY+593Ttx9vh8QE6OgYBg7/7HO8wNazTZhNNhML5/Pp6Pp9YvCiMXLi9x65RZu3WU8N87x8nGyZpYXX3yRT3/605Tu4iTuYnP3PDA1Gg2++MUvcuHCBV577TWWl5f5kz/5E/70T/90w31fffVV/vAP/5Dvf//76LrOSy+9xMsvv8ypU6e2/Rv1ep2/+Zu/4Zvf/CbvvPMOzWaTkydP8iu/8iv83u/9HpnMYDtRCUzvXxiG3L59m0qlQhA08bx5dtP87n6p15v82799l+9+91U6nsvtxhyLrRWsgsGxHznE6OmytBnfB+pzTa59d5rr357eJiQdYa0W6SVAfnEVQjxImsC/sxagZje919CxIqc+doSTHz1CYWJ/DaAkdmdjMz0bRTXIWBly+RyqsvFcKgoj5t+e59YPbhF0Ag4VDnG0eJScneOTn/wkP/mTPykT4N5D9zww3bhxg2eeeYbz589z5swZ/v7v/37TwPTOO+/wwgsv8Mwzz/D5z38ex3H4whe+wOrqKhcuXGBsbGzLv/HWW2/x4z/+4/zqr/4qn/jEJ8jn83z729/mL//yL/noRz/KN7/5zYGTYwlM70+9XufmzZu4bgfPWyQIqhQKOY4endxx87t7zXFcvvWt/+H//b//oe10mK7PM9daRsuoHH1ukoknRqSP0h5rVTpc/+401787w/J7q5vcozdgQy8kPYXMhySEeDjEJBPo9sLT5gNHjD06xMkXk/CUHdpf03SInRtspmeiqTaqpm1Z2wRJH6eZ12eYfm0aAjhaPMqh4iGK+SI/+7M/y4/92I+h69I8/W6754Gpd3dFUVheXmZsbGzTwPSLv/iLfOtb3+Lq1asUi0m1882bN3n00Uf57Gc/y5e+9KUt/0ar1QIglxv8xeXll1/mc5/7HN/+9rd58cUX09slMO1OGIZMT0+zvLyc1iqpasjhwxOMjJT3+vCA5D393vde4+tf/zb1epPZ1hIzjXliLebQ0+McOj8uw4PvIa/tc+N7M1z9r9vMX1reYmS7jwK/DPwCIJP2CSEEzANfAf4/khH4BikqTD45xumPH+XER/5/9u47c+eJegAAIABJREFUzpKrPPD+r6pujp3T9HSYmZ6sOJKMkIRGCVlCYyFAYNbGFuy7sGi9BtYm2N7lxWm9gNjX2MB6QfBZgpecZYRQGklIo4AGafL0TE/n6Z7ON8eqev+43bdvd9+eeEP37ef7+eijuVVdVc+9Heo8dc55TgtW58paDF6cn3giSSQSwzQVNNWFolpwOBx43J5lR8Mko0kG9w8ycnAEq2Klzd9Gk6eJuro67rvvPq655hoZSVNAF5o7XHDKej7frHQ6zSOPPMIf/dEfZZMlgPb2dm655RZ+/OMfnzVhWpwozbnuuusAGBwcvMCoxZxQKERfXx+JRHy2V2kar9dNW1szNlth/jCnUvNr51itF37O3t4hfvCDxxgcHGU8OsVAcISkkaJpey2tu5qwueQGUg6GbjJycIyTewfof2kEPZlvfZIrySRJvw+0lTZAIYRY8ZqA/zz7Xx/wHTLJ0wEATANGDo4zcnCcFx9+nfY3tLBpdxvNO+tlfm6RGcZ8MaJLfeDusNuwWa2Ew1GSqTCKaSMeN0kmk3g9Xmy2paN4bC4bG2/cyLrL19H3Uh8nT5xkODRMZ6yThx9+mOeee453v/vdsvhtmRSlj6+np4dYLMbll1++ZN/ll1/O448/TjweXzIX6VyeeuopAHbs2HHOrz18+DDt7e0LErZEIsGxY8cAqK6upq1tYYPuxIkTRKNRAK644ooF+yYmJhgeHgagra2N6urq7D5d1zl06BCQyU4Xz9Hq7e0lGAxmY8/tWp2ZmaG/vx+AlpaWJUMVDxw4gGmaOJ3OJRXnBgcHmZqaAmDLli0LPs9wOExPTw8ADQ0NNDY2MjQ0xPj4OOl0hN7eV9D1JC0tDWzatG3Je507b2trKy7X/ByTRCKRjdfv99HY2LTg2P7+/mwP4eIqedPT04yPjwPQ3NyM1ztfTELX0xw4cJinn36FI0d6Ma1wamaIUDJC3cYq6nb60Vwa0VQUi+lDzUnck6lU9vvmdDqxL/pDNBPIlH61zHaL54rGYiSTmcm5Xq8XLeePZCqdzr4Xh8O+ZI2FYDCIYZpoqobXu/C8sXicRCIBMFtmdL43LK3rhMNhAGw2G65FY5RD4TC6rqMqyoKfX8isExGPxwFwu9wLJqYahkFw9mmJ1WrF7Vo4NygciZBOpwHw+/zkPvtIJpNEY5ny3i6nc8Ef8+nBIIcfO8Hgi2eITydYqotMkvRuYGue/UIIIZbqAD4x+98RMonT/yVTQALSCZ2eZwbpeWYQV42D1usbabuhmXWbm5a/BzqcS4bUBwJBTEw0TcN7tnugx4uWM8Q9nU4TnrsH2u1L2mzBUCi75qLPu7A4VDwez6xrBHjc7gXtHl03CIUz96qz3QMVFPz+hffARCJJLD57r3K5sOU8lDVMM9vWslqsuN0L74GRSITU7D3Q51vajoiEM+9VUaHKv3C0zcW0I1RVwemyE5+OEYuGsdrsOB3VBIKBTG+Tx8PM9AyGaaCpGlVVmWs6fA623rGVmi019O7rZf/Qfhq8DcRSMU78zQluv/12brnllmznQW1tLa2trQtiOn78OPF4HE3T2Llz54J9Y2NjjIyMANDR0bGgwEQymeTo0UzFR7/fv6TceU9PT7b9ctllly1ILCcnJxkaGgIybcfa2vmlQAzD4ODBg0CmTbRx48YF5+3r6yMw+xlv27ZtQRskEAjQ19cHZNqODQ0LR6wcOnQIXddxOBxs2bJlwb6hoSEmJycB6OrqWtCenfudOV9FSZjmgsu3aGlNTU2mgtb09AVlyQcOHOAzn/kM9913X95EbLF0Os3i0YamaWZ7P+YajouPye0dyWUYRnZf7lOIOed73sUx5Z5X15c+sU+lUpimmbenRtf18zpvNBrl2LFjRKORbK+SzaZQX9+Iy7V0QqGu69n3YZqL36uZ3afrSz+HfO9hPqb58+Z+hoZh8Otf7+df//WnRGIxziSnCKTDuGqdXHZjF75mD6FwmHRq6Wc7GySmYeb9HIDsPkPNt8/I7l8yrMycP3bJx0Dmj7NpmBjK0p1mTkycJab8+4zZ8+YZ55b7XvOMgzvX55C97tLT5hybWXCv55lBup/qZ+JEvnlJNWQSpD8CrkXmJAkhxKXYDvwt8Ddk5jl9nUzv0wwA0ak43f/WT/e/9VO/uZrNt3Ww4ab1WOzaovvC0vuRYRqZ+1m+e2DuvWrRPcUk5/6Z555izN2r8l4zN6YlVz37vWr2WDPPPdDEOK9769K2y8KY8lw09yLLnvdi2hFWiwXN40I3THQjjGraiMchnUqTTCVRVRUlzz3UVetiw20bCAwGmDgwwasjr9Lqa+XRxx7l+eef58orr2Tbtm3Lth1TqVTefWdrO84dO/d1y503n/NtJ+c7PjemxXLb7vliSiaTGIaBpi2dpnG293qhRcKLOovsbMP3LmQcZl9fH/fccw/r16/n4YcfPq9jLBbLkmsoipJNPPJNoLNYLMsOIVNVNbsvX1ft+Z53cUy55833zbZarZimmfe8mqad87zBYJDp6Wn8fjfJ5DCQpLW1Eb/fnl0rKd9557YrSyq7KNl9Wp5iC5qmZT+fxU9hVHX+vHNf09c3zPe//0sGBk5zOjjO6dg4ilVhww1tNO+oyw5BUBVl+eEIOfvy/VzlnmPpPnX+vIt3K/PH5ilwg6ooGCp5q98oufGeJab8+1QU08wb74L3mucP7Lk+h+U+Q2X2vcam4nT/bICTTw2QDC/+42UB7gIeIFPAIf8EViGEEBdLIVMk5w3A/wf8HPg/ZBbKzTQWx7unGe+e5jffOsyWN3ey8bb1KI65+8LS+5GqqJiKmf++sODeuqjNxNnvn6qqYmDkbROpC+5VS9/jWe9Vs8fmvcehnte9dWnb5TzaEUom39G0pe2iS21HaKqG22EH1EwJ8nQa03QTiURxOpx556opioKqqlS3V7N+23pGD44y+OogY5Ex2n3tDPxsgAMHDvDud7+b9vb2BcdarVZ0Xc/brjxb23Hu2Lmvy7fvUtvJ+Y7PjWmx3LZ7vphsNhu6rp/zvPlyggtxSeswLVf04fjx42zdupUvfvGLPPjggwuO+ehHP8rnPvc5otHoeQ3J6+/vZ/fu3SiKwrPPPruk2xGk6EM+pmkyNDTE2NgY6XSQRGIEh8NCR8c6nM7yV+CJRGL87GdP8eKLrxFOxjg1M0goGaFhcw3tb2iReUolNt49xeFHeujbN5znCdyVwB8D/w4p3iCEEOUwCvwrmZ6ngwv2qBaFzje2sv2ejdRtrM53sFhBdN0gFIqQ1vXZghC27BC9fElirngwTs9zPUz2TVLjrGFj9Ubc9kwZ8j179uSdGyXyK3rRh/OxceNGnE5ndrxiroMHD7Jp06YLSpZM02Tv3r15kyWxVDKZ5NSpU4TDYZLJM6TT01RX+2hra14RSeShQyf4znd+wXQgQH/gNGciE7hqnOy8sQt/S2EXuhXLM3SD/hdPc/jfehg/PrVor5XMkLsPAVeXPjghhBA5moA/A/4L8Bvg88B3gTRG2qTn2UF6nh2kcVst29+ykbbrWlA1GSq9Emmait/vJRKJEk9EUcx0ZoheOo3P50NTl68A7PA52PGWHUz2TtLz657sML1fPvZLXnvtNR544IEl84NEYRQlYbJYLOzZs4cf/ehHfOYzn8lO7h8YGODpp5/mIx/5yDnPMTAwwO7du9F1nb179y7pbhT5BQIBent7SaXiJBLDmGac9eubqKsr/1OnaDTOj3/8OC+/fICpWJCemQF01aDjjeukAlAJJcJJup/o4+ijp4hMxBbtrQc+OPtf09KDhRBClJFCZt7ot4BPA18C/gXIPPQ6c3SSM0cn8TS42HbXBjbf1oHNLSM2VhpFAY/HhcVqmR2ip2OabmamZ/B4l1+zaU5tZy3V66sZ3D/I4P5BxiPjbElu4bOf/Sy33347995770VVKRbLu6gheY8++iiRSIRQKMT73vc+7r//ft75zncCcPfdd+NyuTh27BjXXnstV1999YKFa6emppYsXGuxWLj55pt58skngUwFj+uvv57h4WG++tWvLsmWW1tbF/Q2yZC8jNHRUYaHh0mnwyQSw9jtGh0drbhc5R+Cd/RoD9/+9r8xOT1D78wwY9FJqtt8bLx5PXa3dCGXQmA4xJFf9HDy6QHSicUTJy8DPkKmV6n8Py9CCCHOV5TMcL1/JFNtb57FYaHr1ja2370RX7OM4FiJ0rpOKBRB183ZIXpWXC4Xblf+JXYWi05H6X6qm9BoiHW+dXRUddDS3MIDDzxAZ2dnkaNfvYq+cC1kyhDOlZZerLe3N1uG8NVXX+XjH/84+/btw2KxcOutt/LQQw8tSYAUReHmm29m7969AOzdu5dbbrll2esvnjO11hMm0zQZGBhgYmKCZHKCVGocv99Le3tz3glyxTY0NJQtKFFXV89PfvIk+/b9lul4kJ7pQdKqTucN62jYUiOLsBWZaZqcPjDOkUdOMrT/zKK9CnAP8GHgFqTSnRBCrGYm8DiZxOnRhbsUWH9NEzvesommnXVy780jHIlgGiaKquBZZj3QYjFMk0g4RiKZRFXsqJoTh92Bx3vueU2QqeI3/PowfS/14VAdbKndgs/h484772TPnj15C3ytdSVJmFaatZww6brOqVOnCAQCJBIj6HqAlpZ6GhvryhZTd3c36XSaoaEzvPDCYcYnp+kLDHMmMkFVq5dNN7dh90qvUjGZpsnQq6O8+n+PMN0fXLTXDbwX+FMyaygJIYSoLMeAfyJTYW/h0OuaTj+7/mAH665skMQpx0wgkE2YqnLWJiqlWDxBJBJDUaxomhur1Tq7ZtT5tWejU1GOP3mc8FiY9f71tPnbaF3XygMPPCBTWxaRhGnWWkiYkskkJ0+eJBoNk0gMYRgx2tqaqakpzy/6nGPHjvHkky/x8suHwaHRM9NPSknTcf06GrfVyh/oIhs7PslvvnmYM0cnF+1pI5Mk/XugaumBQgghKswU8BXgC8DQgj1NO+u45j07qd9U/jnOK8FKSJgAEskU4VAEsKBpbiwWKz7/2YtB5DINk8HfDjLw8gBOzcmWukxv09vf/nZuu+02aYPNkoRpVqUnTNFolJMnT5JIREkkBlBVnc7OVjwe17kPLqKZmRBf//qPOXlygP7gaUbCY/haPGy6pQ2HV9btKaaZoRCv/t/DDLw0smjPtcDHgLdS5KXXhBBCrEgp4EfAZ4D9C/Z0XL+Oq//d9jVfpTa3NVzunCKVzsxrMgzQNA+aZsHn82G1nH8hh8hkhONPHCcyEaGjqoNWXytXXXUVf/zHf4zLVd624kogCdOsSk6YgsEgPT09pFIREokhbDaFDRvW43CUNyE5fryXb3zjp0zOzNA91UsoFaXjDS00X14vTzSKKDIZ47XvHePEU30sXNx8M/APwH3I/CQhhBBgAN8H/groyW5VNIUtt3dwxf1bcVVL4Z+VQDcMgsHwbDEIN6pmxev1nrOCXi5DN+h/uZ/B/YPUOmvZUreFpoYm3v/+96/5IXqSMM2q1IQpEAjMJkshEokh3G4HGza0lnVCn2EYPPbY8zz22HNMx4J0T/WhOhW23NGJt6m0EyfXkkQkycEfn+DIv/WgJ3Or3jUDnwLeh/QoCSGEWCpJZqje3wBj2a0Wu8aOPZvYeW+XLCC/AhimSSgYIZVOZ5Im1YbXd2FJE8BU3xTHnjiGRbewrW4b1e5q3vWud3HTTTet2QfakjDNqsSEaT5ZCpJIDOP3e+joaCnr+wyFInzzmz/j2LFTDIZGGAqOUtXmo+uWdqxOaawXQzqpc+yXp3j9h8dJhlM5e3zAJ8gsNivd7UIIIc4lDPxP4LOz/86w+2xc+Y6tbHlzB5q19NV2xTwTCIeiJJJJNNWFqtovKmmKB+Mc+9UxwmNhNlRvoMXbwnXXXccf/uEfYrevvSkTkjDNqrSEaXGyVF3tpb29paxPBvr7T/PVr/6A8alpuqf6CCZDtF3bTP2OakBBUcBmk2p4hWLoJj3PDvDb7xxdtOCsDfgT4C+B2vIEJ4QQYhUbA/6OzCK48w/iPA0urn73djbc2Frxi8snk0lMkxXbdgmHo8QTl5Y0GbpB775ehl8fpt5Vz+bazaxrWceDDz5IY2NjkSJfmSRhmlVJCdNKTJYOHDjO17/+E6YiAY5P9YLNZPPtHfjXeVdMpZlKMnZ8khf+5TWmB3JLhCvAe8gMqVjbY5GFEEIUQg/w34BvL9ha0+nnhv94FXUVXFFvNbRdCpE0AUz0TND9VDc208b2+u3UV9XzwQ9+kK6utbPUiCRMsyolYQoGg5w8eTKbLFVVeejoWFfWZGnv3pf5yU+eYDwyzYnpfjxNLrbc0ZEd77wa/uisFulEmv3fPsrhR05m+uWz7iZT0OHy8gQmhBCigu0nM8T78ewWRYWdv9fFle/ahsVWecP0VkvbJRSOkihA0hSbiXHkl0dITCfYXr+dOk8dDzzwANdee20Rol55JGGaVQkJUygU4sSJEysmWTIMgx//+AmeffYVhkJjDASGqeuqZtPuNlRt/rNe6d3aq8XokQl+/cX9hEYjOVuvBj4H7C5PUEIIIdaQx4E/Bw5kt/jXebjxP11Nw5bKGgK+mtoui5Mmn893UTGnk2mO/vIogaEAXbVdNLobue+++7jzzjsrvhiEJEyzVnvCFI/HOXbsGIlEgERiqOzJUiKR5Bvf+CkHD3ZzamaQ0cgE63c1sf6apor/pSq1VDzNq/96mKOPnsrpVbKTGXr3X5DKd0IIIUonBXyazD1odn6TAjvu2cTV796GxS73pFIzyQzPyyRNblTNRlVVFRbtwr8Xhm5w8tmTjB4Zpb2qnXZ/OzfddBPvfve70bTK60mcIwnTrNWcMKXTaY4dO0Y0GiAe78fnc7FhQ2vZEpNgMMyXv/w9+vqHOT7Vy0wixMab19O4tbKeLq0EIwfH+fWX9hMei+ZsvR74GrC1TFEJIYQQh4D3Ar/JbvE2ubnxP11N0/a6skW1VplkKhUnkyk0zYtlNmm6mLavaZoM7h+k78U+Gj2NbK7ZzM6dO3n/+9+Pw1GZ63JJwjRrtSZMpmnS3d1NMDhDPN6Hw6HS1dVetix/ejrIP//ztzh9Zoyjkz3ESbL1zg6qWn1liadSpWIpXvnGYY7/qjdnqxP4e+BPgcp9yiOEEGK1SJMZFv7/AonMJgW23bWBXX+wA6tDeptKyTQhEAyTThtYNC9Wqw1/lR/lIherHzsxRveT3fisPrbXb2dj50Y+/OEP43JV3lIlkjDNWq0JU19fHxMTEyQS/ahqis2bO7DZyrN43FyyNHzmDIcnTmDaTba/ZSOuGudZj8v9iZLReuc2eWqGpz/38qK5SjcBXwXWTsUaIYQQq8VRMoujv5jd4m/xsPvPr6OmfeUWTDib1dp2MQyTmUAI01DQLF7sdjs+78U/1A6cDnDk0SPYDTuXNVzGpg2bKjJpkoRp1mpMmEZHRxkeHiYeH8Y0Q2za1I7bffbkpFgWJ0uKW2HHnk3YPeeeVLhaKs2Um2madD/ex0tfO4CeMma3uoH/ATwIrK6fXyGEEGuJDnwe+CsgDoBm07j+/VfQdcvqW+piNbdd0rpOYCYEihVNc+NyuXC73Bd9vuhUlAM/OYBNt1Vs0nShuYO0yFaIYDDI8PAwyeQEuh6kra2lbMnSzEyIL3zhX7PJEq7zT5bE+UnF0zz3z6/ywv9+LSdZuoZMJaI/QX41hRBCrGwamUJErwNXAKAndX79hf38+kv7SSf0cga3plg0Da/Xg2mmMPQY0WiURDJx0edz1bi4/K2Xk9SSHBw7yMlTJ/n85z9PNBo998EVSlplK0A6naavr490OkwqNU5zcz3V1eWZIzQzE+Kf//lbDI2OZpOlnb93YcmSxWLJ/ieWmhkK8sjH99LzzGDO1j8Bfg1sKFNUQgghxMXYDOwD/kN2y4kn+3nkL/YSOB1a9qiVZrW3XWw2C263E8NMYBopwuEwhmGc+8BluGpcXHbvZdmk6UTPiTWdNMmQvBWgp6eHqakJ4vFevF4HGzeuL0scS5IlJ+y8t0t6lgro9OtjPPXQS6Si6dktHuBh4F1ljEoIIYQohG8C/xHINKptbiu3ffwNNO2QKnqlEgxFSCbTWDQfNrsdv+/ShhdGJiMc/OnB7PC8ro1dfPjDH8bpLM8oqEKRIXmrzOTkJDMzMySTo2iaSVtbc1niSCSSfPnL32V49IwkS0XS/WQfv/r7F3KSpcuAV5FkSQghRGV4D/AysA2AZCTFY3/za3qeHTzrUaJwPB4XqqqgGxGSySSxeOySzueudS/oaTp56iRf/vKXL6n3ajWShKmMEokEAwMDpFIz6HqI9eubsVpL3xVsmibf/ObP6B8c4ehkTyZZ+j1JlgrFNE32f/sIz3/pt5j6XIfuvWSGMGwuY2RCCCFEoe0AXgLuAsBImzz7+d/w2g+OUQGDmlY8VVHweFyYZhrDSBCJRND1S5tPNpc0JdQER8aPcPjwYb773e+uqe+nJExlYprm7LylOMnkKLW1VVRVecsSy89+9hQHDhyne6qXOEm23b0Ru1eSpULQUwbP/tOrvP6D4zlb/xT4IZmKeEIIIUSl8QI/Az6Q3fLbbx/l+S/tx0ivrZ6JcrBZLTgcdgwjhmHoBENBTC4tuXHXutl+13aCySAnp06yd+9e9u7dW5iAVwFJmMpkfHycUChEMnkau93CunUNZYlj377XeOqpF+kLDDOTCLH1zR24qi9tVedINEo4EiGyRicGztFTBk8/9BKnskMRFOAfyZRhlYVohRBCVDIL8L+AT2e3nHhqgGf+8ZUVmTRVWtvF7XKiaSqGHiGdThOLXtrQPAB/i5+uW7oYCY8wFBziu9/9LocOHSpAtCufJExloOs6p0+fJp2eQddjtLW1oGmlb0CfONHH9773KKPhCU6Hx9hwYytV6y+9Ol8qlSKVTJFKpQoQ5eo0lywN/mZ0dosD+BHwoTJGJYQQQpSSAnwM+C5gB6Bv3+kVmTRVWttFUcDrcWOiYxgJorFoQeYdNW5tpG1XG73TvUxEJvjKV77C8PBwASJe2SRhKoORkRHS6RSp1AQ1NX48ntIvBDY+PsVXv/pDpqIBTs0M0XJZvVSxKRA9ZfD053KTJSfwb8BbyxiVEEIIUS7vBH7CwqTpNysuaao0Fos2OzQvjmkYRKKRgpy3/Xfaqd1Yy7HJY0wEJ/jCF76wpOJcpZGEqcQSiQRjY2OkUpMoik5zc33JYzAMg29+82dMhQIcn+qlqs1Lx/XrCnZ+n9eL3+/D5y3PnKxy0lMGez/3MoOv5CZLjwC3ljEqIYQQotx+l4VJ03AmadJXRtJUqW0Xl8uBooBhxInH46T19LkPOgdFUdhy2xZctS4Ojx/mzPgZvvWtb1V0EQhJmEpseHgYXU+RSk1SX1+DzWYteQyPPfY8fX3DdE/1YfVa2Hx7B4qqFOz8qqpm/1tLTNNk35d/y8ArI7NbHMDPkWRJCCGEgPmkKVNYqm/fMC999cCKaGhXattFVRScTjuGmQDTIBIpTC+TZtXYfvd2DItB91Q3r732Gi+88EJBzr0SVdZPxQoXiUSYnp4mmRzDYlFpbKwteQx9fcP86le/ZjA0QiQVo+u2diw2KUBQCId+eoITTw3MvrKT6Vm6rYwRCSGEECvNXNKUeWB87LFejv7iVFkjqnROhwNVVdGNGMlkkmQqWZDz2j12Nt+6mcnoJKPhUb773e8yPj5ekHOvNJIwlVCmdymOrgdobq4veaGHRCLJN7/5MwLxMEPBM6zf1Yi3QUpbF0L/S6f5zbcO52z5BpIsCSGEEPncBTycffXy/znA4Kujy3+5uCSKkhmaZ5opTCNNNFK4SoC1nbU0bWuiZ7qHmfAMX/va1ypyUVtJmEokHo8TCoVIpSax263U1laVPIaf/ORJzoxN0D3Vh6fBSevVTUW5TiqVJplKkUpd+jjZ1WCiZ5pn/vE3zC9x8DdkJrgKIYQQIr8/Av4SANOAvf/zFab6A2WLptLbLg67DYumYZgJUukU6XTh3ueGGzdg9Vg5Pnmcnp4efvnLXxbs3CuFJEwlMj4+jmGk0fUQdXXVKErh5gydj6NHe3jhhf30BoZJKSm6bivsvKVckWiESDhSsGosK1kykuKpz7yEnpxbRfsPgP9azpCEEEKIVeJvgXcAkI6neeozL5GKlSdhWQttF4fTjmmmwDSIxS99XaY5FpuFrXdsJZQMMRgc5Oc//zmDg4PnPnAVkYSpBAzDYHJyknR6BlWFmhp/Sa+v6zo//OHjzMRDnIlM0HH9Opx+e0ljqFQvPvw6kYm5PzrXkxliUNpkWAghhFidVODrwDUAhEYjvPx/DpQ1okpmt9lQFAXDTJJIJDDMwg2d8zX5WL9rPf0z/YQSIb73ve+tiGIehSIJUwlMTU2RTqdJp2eorvZjsVhKev0XXvgtY2OT9AWG8TW5adxW3GITDocDp9OBw+Eo6nXKrff5IXqenXuC4gO+TaYynhBCCCHOjwv4DpCZU939RH9OtdnSWQttF0UBu92GYSQwTZNEPFHQ87dd04bD76B3upfu7m4OHKic5FcSphIYGxtD18OYZoq6uuqSXjsWi/Poo88xFp0kkorR8cZ1RR8O6LDbcTgcOOyV24sVmYzxwpdfy9nyRaC9XOEIIYQQq9hG4B+zr57/0n5iM/GSRrAW2i4ADocdMDGNZEGH5QGomkrn9Z1MxaaYjk3zwx/+EF3Xz33gKiAJU5FFo1FisRjp9DRutxOXq7RPLh5//AWCoTADwRHqN1VLVbwC2fe/XyMZTs2+eheZuUtCCCGEuDj/HrgXgHgwyb6vvF7ecCqURVOxWi0YZhJd10mlUuc+6ALUbqjF3+Knd6aX0dFRnnvuuYKev1wkYSqyQCCAaeroerTkc5cmJ2fYu/cVhsNjpEnT9jvNJb1+pTqIZwDYAAAgAElEQVT9+lhO+dMW4EvIvCUhhBDiUijAV4AGAPpfPM2ZoxNljahS2e02TDMNplmwNZnmKIrChjduIJwMcyZyhp///OfEYoXtySoHSZiKLBgMoutRwMTn85T02o8++iyxZJzToTM0X1aPw1vZ3cylYOgmr3zjUM6W/wHUlCscIYQQooLUA3+XffXy1w9VVOGAlcJmyywabJopksnCJkwA3kYvDV0N9M/0EwgGeOyxxwp+jVKThKmIdF0nEomg6xEcDlv2B7QUAoEwr756mOHQGVSbQutVjSW7djAYZGZmhmAwWLJrlkrPMwNM9c2tE3E1MhRPCCGEKKT3ATsBmDgxTe/zwyW5aiW3XRZTFQWLRcMw06TT6aIsNNvxhg5SpBgJj/DMM88UfOhfqUnCVEShUAjTNNH1MF5vaecO7dv3Gql0mrHoJI3b67DYS1eZzzBNTDPz/0qSTurs//aRnC2fQ36FhBBCiELSgM9mX736r4cx0oVv0C9WqW2X5Vit1syaTFDwYXkADp+D+k31nA6dJhKJ8MorrxT8GqUkrb0iygzHS2CaKbze0g3HMwyDF17Yz3h0Gt3UadpeV7JrA2iahqapaJpW0usWW98Lw0Sn5qr27AF2lzEaIYQQolL9LnAHAOGxKP0vF7/MeKW2XZZjtVoAE9PUSSWL0/vTvLOZeDrOdHyavXv3FuUapSIJUxEFg0EMI4KiKHi9rpJd9+DBbgKBEKORcarb/di9tpJdG8Dr8eDz+fB6Sjtnq9iOPXYq59XHyhaHEEIIUfnm77PHfnnqLF9XGJXadlmO1WpBYXYeUxF6mCAzl8lT72EkNEJ/fz99fX1FuU4pSMJUJKZpZlZRNhI4nXZUtXQf9XPPvUowESGSitG8o7S9S5Vq4tQM493Ts68uB24oZzhCCCFEhbsN2ALA6OEJpgcqf25RKSmAxWLBNHUMwyhKcQ1FUWjZ2cJUbIp4Or6qe5kkYSqSRCKzerJpJkta7GFsbJITJ/oYjYzj9Nvxt3pLdu1KtvDp1oNIGXEhhBCimBTgg9lXC0d5iELQNBXMzPywYi0wW99Vj2bXGAmN8MorrxCJRIpynWKThKlI5hImw0hht5duSNyBA93ohsFkLEDjtloURRr2l8rQDfr3nZ595UMq4wkhhBCl8MdAZkpD7wvDmMbaKMhQKqqmYjKbMBnFSZg0q0bj1kbORM6QSqU4fPhwUa5TbJIwFUkikcA0DUyztAnTsWOnCCTCGKZBTUdpF8qdE43FiEajRCtgoTKA8RPTJKNzEyLvAtbG+GYhhBCivKqYK/6QCCaZ7J0p2pUqre1yPjRVA0wwzaL1MAHUdtSS1JNEU1GOHDly7gNWoAtOmEKhEB/72Md485vfTH19PYqi8KlPfSrv1+7fv5/bb78dj8dDVVUVb3vb2zh16vy7VJ944gmuv/56XC4XdXV1PPDAA4yNjV1oyGWRmb+UaWSXKmFKJJKcOjXETCKIw2vD4S/PQrXJZJJEIlmUxdDK4fRruT9zd5YtDiGEEGLtmb/vnn69eG3ASmu7nA9Ny6QBJkZREyZfsw/NojEdn+bIkSOrcjHiC06YJicn+fKXv0wikeCtb33rsl937Ngxdu/eTTKZ5Hvf+x5f+9rX6O7u5qabbmJ8fPyc13nmmWe46667aGxs5Kc//Smf//zneeKJJ7jtttuyw91WskwPU2kTpp6eAXQ9zUw8RNV6nwzHK5Dh187kvLqjbHEIIYQQa8+bs/8afm11PDRfLdTZhAlTL2rCpGoq/nV+pmJTBAIBhodLsxhxIV3waqbt7e1MT0+jKAoTExM8/PDDeb/uk5/8JHa7nUceeQSfzwfArl276Orq4qGHHuLTn/70Wa/z0Y9+lM2bN/ODH/wAiyUTZmdnJzfccANf+9rX+OAHP3jW48st84OXBsBiKU1N/6NHTxFPJ4ml47S3Npfkmvl4KqgkZyqWZqJnrjreDqC1nOEIIYQQa8zG2f96OHNsEj2lo1kL366qpLbL+VJnH6ybUPRen+r11fQO9KKbOkeOHKG1dXW1py64h0lRlHP2XKTTaR555BHe/va3Z5MlyCRbt9xyCz/+8Y/Pevzw8DCvvPIK73nPe7LJEsAb3/hGNm/efM7jVwJzdsVooGQ9PUePnmImHkJRFPzrylcdz6Jp2f9Wu9CZyFwBGeCacoYihBBCrFGZ+6+pm4THokW5QiW1XS7EfMpUXNVt1RimQSAeWJXzmC64h+l89PT0EIvFuPzyy5fsu/zyy3n88ceJx+M4HI68xx86dCj7tfmOf/75588Zw+HDh2lvb1+QsCUSCY4dOwZAdXU1bW1tC445ceIE0WjmF/GKK65YsG9iYiLbhdjW1kZ1dXV2n67r2Zi9Xi8bNmyYzdRNFEVheHg4W0Zx48YNaNr8xx4KhRgZyaxgXV9fv+C8czGZpondbqe9vX3BvjNnRgkEMusSNDU1Mz4+SSgZxlPvBM1kJhAAwGG3L/msg6EQhmGgqio+78LkKh6PE58d9uhxuxckrbpuEAqHALDZbLiczgXHhsJhdF1HQcHv9y3Yl0gkicUzkyldLhc263y5dcM0CQYz78VqseJ2L1zoNxKJkEpneux8Pl/2qQhAMpXKft+cTid228IhkHOfg0XTljxBisZi2fHKXq8XLWe9rFQ6zcip3O7/jQghhBCi1ObvvyOnxjA9xqppR8y1/xwOOw77orZYMIhhmmiqhte78LyxeDw7BcXj8SxI5NK6TjgcBs7eFlMVZUE7GCCeSBCPxwFwu9yzD/VNTNNEN3RmZmay5/V6FrYPg8EgqXRmuklNTQ1KzhIr8UQ8+17dbveC92piEjWiGJrB6PQoAwMDC87b19dHYPYz3rZtG7aczz8QCGQXvG1ubqahoWHBsYcOHULXdRwOB1u2bFmwb2hoiMnJSQC6urpwueZ/Jua+3+erKAnTXHA1NTVL9tXU1GCaJtPT0zQ35x82dq7j5/afTTqdXtK9aJomqVQquz/fMXP7FzMMI7vPMIwl+892Xl3Xs9sX93gahpHdZ+Qp6Tj3PnKTlvnzzh87OZkZNhZLJ3BWOTLdq7PlN4083ayGYWAaJgZL34thmtljlx6Zsy/Pec3ZY00l35HGfEnQfMdmz3v2mPJc9OwxzX0Oar59uTEtCZjImdxqOZvyX18IIYQQRTR//w2fiWXu26ukHZE979KQsjEZytKdZm68Z4kp/77ZNl6ettiC94qJycKVJefauPk+K8Mw8raB5+LNHrtM+9DmtRELxIhEIkSj0WwCo+v6su3v3LZ7vnlWyWQSwzDQ8vQM5p43X05wIYqSMM0521C08xmmttzXnM+xFotlydcpioJ19mlEvgTEYrFk9y+mqmp2n6ouHcm4+LyZayuYpommaTnbl553bp+qLv1mZ1ZhNvP+IGja/LETE5nMPJ5OUO33oQCKmrmYmufzUlUVAyPve1EVJXvs0iNz9uU5r5JzbFrXFzwRUVCz+5Z8EDnxKsrZY8pz0bPHdJbPQVFzY1q8EyITuQmT9DAJIYQQpTd//42OxzL37SK1I/IlCpfSjsjGlGcSjKooGCqoeXbmtqfO9l7z71NRTDNvvAvaTCiZhCtnus1cuzDfZ6Wqat5241y82WOXaXc6/U7i05nerfHx8ezIKU3Tlm1/57bd87WFbTYbuq7nPT73vPlyggtRlISptrYWIG9P0NTUFIqiUFVVddHH5+t5WmzHjh1Lvql2u33JULtcXV1dy+6rq6ujrq4u7z5N05acNzPXK/PvlpaWZb8xXq8Xr3f5+UZni6mxsYnGxiYAnnzyRdKGQcpI4/DZsFgsVPmXX4dp8TC8XA6HY9nhkpqmnvW8Xo+HmUAA0zAJh8MLvtZuty1bMVBVlLOe1+12L7vPZrViO8uxZzuvy+lc0pU9x2qxQDL3+9a47HmEEEIIUSxN8/9M528vXGo7IkomWUokEzidC9tAl9KOOGtbbNFwuVxOhwPnMm0xi6adsy22HIfdjsM+v+xMpocp09bRVI3amtqLitdhdywZcjhHQaG2ppZoS5TBwUFgYcLU0dGx7Hn9fv9Z2+47d+5cdl9ra+uyxSVcLhehUGjZYxcrysK1GzduxOl0cvDgwSX7Dh48yKZNm5ZtkMP8m1/u+LN9OCtFpucnk4+mUkuH6RXaxMQ08XRmrKvDV571lyqRkcrtepbPVQghhCi9+YetRmr1reGzUs1N2VBQ8vZyFZrT7yRtpEnpqVWzruqconw6FouFPXv28KMf/WhB9jYwMMDTTz/N2972trMev27dOq677jq+9a1vLRiv+OKLL3L8+PFzHr8S2O12VDXzC55IFH8RtAUJU5kWrJ1jt9uxO+zY7as/wTBLUDlGCCGEEGczP9qjWOWvK6ntcr50ffahsKLOr8lURA5fprMkno6f15qsK8lFDcl79NFHiUQi2WToyJEj/OAHPwDg7rvvxuVy8dd//ddce+213HPPPXziE58gHo/zyU9+krq6Ov7sz/5sYRAWCzfffDNPPvlkdtunP/1p7rjjDu6//34efPBBxsbG+MQnPsHOnTt573vfe7Hvt2TsdjuKYgUUksn8E9kKKRgMkzRSqJqKxV7ekpjLdSGvRpol9w9I8b+PQgghhFhs/sHzwvty4VRS2+V8zXVKKIqad35Qodm9mWQ0oSeyVfFWi4tKmD74wQ/S39+fff3973+f73//+wD09vbS0dHB1q1b2bt3Lx//+Md5xzvegcVi4dZbb+Whhx6ivr5+wfl0fekKw7t37+YXv/gFn/zkJ9mzZw8ul4t77rmHz372s6si+88kTAqKYilJD1M6rWdKU1rOvU6WOH8We+6vyAywvlyhCCGEEGvUfOPa4lhb6yQVU6aqXaZIWSkSprleLMM08laVXskuKmGaq4d+Lrt27eKJJ54459ct1716xx13cMcdd1xIaCvGXFKnqtaSJEyGYWCaxvIVYMRF8TTmruNwCrisXKEIIYQQa1RP9l+ehuWLN4gLo+sGCplEqZQJk2maqy5hKv6AxTXKZrPN9jDZS5cwAUjCVFC+xtw/zCfLFocQQgixds3ff31NkjAViqEb2XrnWp6lbQputolqzi6Uu5oUdR2mtUxRFOx2O8mkg3h8Bl3Xi5q9a5qKQv71A0otFApjmAaqoi5ZuXq18Tbnxt+z7NcJIYQQoljm77/eIiVMldR2OR+mCel0GkV1oqlaSaZzzLVRFaU0QwALSXqYisjn86FpbkzTJBSKFvVaqqqhKuqKSJh0Q8fQDXRj6YrMq83CJ1mHyhaHEEIIsXbN33+9jcVJmCqp7XI+Uul0Zg0mxYLVln/R2EKba6OqqLPL76wekjAVkc/nQ1WtqKqNYDBc1GvZbBY0RUVPGmVPmuZW0867wvQq4/DZc55m7QPOf5EzIYQQQlyqKeBVAKrafNhcxWncV1Lb5XykkilARVE0bDbbOb++ENKJzLwlVVWxWkuTpBWKJExF5PV6URQFVXUTCkWKeq2amirsFhumaZKIFH/O1Nn4fD6q/P6zrgi9mqy7smH2X2ng6XKGIoQQQqwxTwCZ9YLWXdFw9i+9BJXWdjmXVCqNomR6eUqVvMSDcQAcFge1tbUluWahSMJURKqq4vF40DQPyWSKeDxRtGvV1VXhsGQq88UD5U2YKs26KxtzXv2qbHEIIYQQa8/8fXf+Aaa4FIZhktZ1VMWK1WJFVUqTDsQCMRQUnBbnkiWGVjpJmIrM7/ejaS5AKWovU319DXbNhoJCPFi8xGwtatpRh6LNddE/wtyTLiGEEEIUUxr4BQCaTaVxW115w6kQyVQKKO38JYB4II5Ns6EqKg0Nqyv5lYSpyHw+3+wKyh4mJ2eKdp26umpURcFusRIPSMJUSDaXlZbL5p6E9AOPlTMcIYQQYo34OTACQMsVDVjsq6uy2koVjyczw/EUpWTzlyAzJM9pdQJID5NYyOl04na7sViqiMUShMPFqZZXV1cNgMNiJx4s75C8eCJOLBYnnoiXNY5C2nJnZ86rL5YtDiGEEGLtmL/fbrtzQ1GvVIltl3zSaZ10Oo2q2LFYLFgtpethigViOCwOFEWhrm519RZKwlQCDQ0NWCweVNXG+PhUUa5RXe1D0yw4LQ4iE8UtYX4u8XiCeDxe1DlbpbZ+VxPuOufsq18AveUMRwghhKhwx4AngczaSy1FLPgAldl2ySfz/lQU1YrD4SjZdQ3dIDodxWV1UVNTI2XFxVLV1dVYLBYslmoCgTCpVLrg11BVlc7OdVTZvcRDSRmWV2CqprLlzXO9TCbwz+UMRwghhKhw/5T919Y7O1HUtVHuu5gM0ySRSKKqmXlEpUyYgqNB9JROlaOKrq6ukl23UCRhKoG5rkeLxY9pUrS5TFu2dOKzZ0qZTw8Gi3KN8+F2u/F4PLjdxVlcrlw2396BZp37lfki0FfGaIQQQohK1Q18BQCLXaPrlvaiX7FS2y65EokkJqAqduwOOwqlS0KnB6axaTbcVjfbt28v2XULRRKmEqmvr0dRNCwWPxMT0xhG4Sutbdu2EYuq4rW5mRkq3wKrVosFq9WCdZV1t56L029n+z2bZl8lgb8oZzhCCCFEhfo4mQp5sPOtXdi9xS9MUKltlzkmEI8lUBQbKApOh/OcxxTS9OA01Y5qFEWRhEksz2azUVVVhdVaSyqlF2UuU2trIx6Pm2q7j8BwGEM3C36Nte7y+zZj98394f4O8FI5wxFCCCEqzLPATwBwVjvY+Xurb/jWSpSIJ9ENA1W1Y7Pa0LTSVRxMRpOEx8NUOatYv349Xq+3ZNcuFEmYSqilpQVVtWGxVHHmzCTpdGHnMimKwtatnVQ5vOgpndCZ4q37tFbZ3Faueue2nC0fAfRyhSOEEEJUkDTwX7Kvrv79bVgdldnjU0qGaRKNxlAUG4qi4XK7Snr9mcEZFBSqHdWrsncJJGEqKafTSV1dHVZrHboOo6MTBb/Gli0bcFtd2DQrEz3TBT//+dANA1030Isw7HAl2HJHB/4Wz+yrfcBD5QxHCCGEqBB/D7wKQFWbj00lmLs0p5LbLrFYAsM00VQndru9pKXEAcZPjuOxebBpNnbs2FHSaxeKJEwl1tLSgsViw2arY2JipuDlKy+7rAu73Uaju5bx7inSydL3foRCIYLBIKFQ+eZRFZNqUXnjf7yK+bmS/w34bRkjEkIIIVa7l4C/BUBRFW744FWoWumKElRq20U3DOKxOKrqQFHUkhe1iAfjTPVP0extprq6elVWyANJmErOarXS1NSExVIDWDh9eryg53c6HVxzzU4aXXUYKZPx7uKs+7TWNe2o47J7537pU8AfArEyRiSEEEKsVhHgPcwNcb/iHVto2FxT1ogqRTQSx0RFVR04nU40tXRzlwBGDo+gKRr17nre9KY3oaqrM/VYnVGvco2NjdhsNmy2egKBEIFAuKDnv/HGq7FbrNQ4/YwensA0S1v8IfPerNhsxa9qU05X/f52ajr9s6+OAH9eznCEEEKIVcgEPgScAKCuq5or3r6l5FFUYtsllUqTSCZRVQeqquJylXbukpE2GD0ySqOnEZvFxo033ljS6xeSJExloKoq69atw2Lxo2keBgdHCloAYt26RjZsWE+Tu57odJzgSGETsnNxOZ243W5cztKWrCw1zarypj+9Jmdtpi8B/1LOkIQQQohV5vPAV4HMmktv+tNrUC2lb55WWtvFME1C4SiKYkFVbbhcLhSltIv/TvRMkI6nafG0cPXVV+Pz+Up6/UKShKlMamtr8fv92GzNpNMmAwOjBT3/jTfuosrhwWVxMHqo8MUlREZ1m483/D9X5Gz5E+BX5QpHCCGEWEUeIbcq3hs/cGVOUSVxKSKRGIZhoqkubFYbDoejpNc3TZPTh05T5ajCaXWye/fukl6/0CRhKqP29nZsNgc2WzOBQIjJyZmCnfuKK7bg8bhp9tQz2TtDZFLm1xTL5ts72Pl7cwva6sD9ZIboCSGEECK/14HfJzMkLzNvaePNbWWNqFIkEikSiSSa6kRVLXi8HhRK27s0PTBNcDTIOt86Wltb2bhxY0mvX2iSMJWR1Wqlvb0di8WLxVLF0NAoiUSyIOe2WCzceusbaHTX4dAc9O0bLvlcprVk1x/uZP21TbOvgsA9wOkyRiSEEEKsVAPAHjLFHqDj+nVc9a5tZz1CnB/DMAlHoiiKFUW14fF4Sl7owTRMTj1/iipHFTXOGu66666SDwcsNEmYyqyqqoq6ujpstkZM08LAwOmCJTY333wNtbVVdPhbmBkKMTNYmlKZ4XCYYChEOFzauVPlpGoKN3/o2pwiEL3ALUjSJIQQQuQaJHN/HAQyRR5u+s+7UNTyNqgrpe0SCkcwTQVNc2G327Hb7SWPYfToKLHpGJ1VnXR2drJr166Sx1BokjCtAK2trTgcTuz2dYTDcYaHzxTkvBaLhT17bqHG6cdv92R6mYzi9zKldR09rZPWS78GVDlZnRZu/4vr8TTMVaHpJnNTGCljVEIIIcRKMQjsBk4B4Gt2c9vH34DFXtoekHwqoe0SjcZJpdJoqgtV1fB4Sj8fLJ1M0/9yPw3uBrx2L/fff/+q710CSZhWBE3T6OzsxGJxYbM1Mj4+zcTEdEHOfdVV22hvX0eHfx2x6Thnjk0W5LwiP3etk7v++iZJmoQQQogFhsjcD+eTpd/965twVZe2GEGliieSROcWqFUteL1eVKX0zfyh/UOkY2k6qjq4+uqrV/3cpTmSMK0QbrebtrY2rNZqLJZqhobOEAxeerewoii89a2347G5qHPVMPDKCOlE4UqY51Pl91NdXUWV33/uL65AngbXoqTpOJmbRH8ZoxJCCCHKpYdMz1IPAN6mTLLkrl05JbxXc9sllUoTDkdRFRuq6sDj8WCzln49qXgoztBrQ7T6WnHZXdx3330lj6FYJGFaQerq6mhsbMRub0JV3fT1DROPJy75vBs2tHLFFVtp97VgJkxO/XqoANGKs8mfNL0B+E0ZoxJCCCFKbR+Z+998snTX36ysZGk103WDUCiSWW9Jc+F0OHE6Sv/ZmqZJ9xPdWBUr633r2b17Nw0NDSWPo1gkYVphWltbqaqqwm5vwTStnDo1WJBFbd/61tvxe7x0Vq1n/MQ0EycLM+RPLG8uafJl15QYBW4Gfl7GqIQQQohS+SFwK5BZD7Kq1SvJUgEZpkkwFJ4t8uDGZrPh9rjLEsvwa8METgfYWruVuto67rnnnrLEUSySMK1AnZ2duN1e7Pb1JJMmvb1DGIZxSeesqfHzjnfcSYOrmjpnNT3PDZIIF6aEuViep8HFW/77m2jcVju7JQq8FfhCGaMSQgghiskEHiKzLmEcgObL6rn7v79JkqUCMYFQKIKum2iaB4tmxef1lXy9JYDwRJi+l/po9bVS5azive99Ly6X69wHriKSMK1AqqqyadMm7HYXdnsr4XCcnp7BS06arrlmB1dfvYON1evR0honnx4oytpMiWSSeCJBIikJGYDDa+fNn7yBzhtaZ7cYwH8GHgQufcilEEIIsXLEgP8AfJS5RWk37W7jjr96I3Z36efVnK/V1HYxgVAwMlsRz42qWfD5fWWpRmekDY4/fhyX5qK9qp077riDLVu2lDyOYpOEaYWyWq1s2rQJm82D3d5GOBy75KRJURTuv/93qaupZlN1O4HhECMHxwsYdUYsFiMWjRGLxQp+7tXKYtO4+cPXcPnbNuds/V/AjWTWbBJCCCFWuxPA9cBXs1uuetc2bvyTq9GsK7vJuVraLnPJUjKVQlM9qJoVn89X8sVp5/S92EdsOsaWui20rW/j3nvvLUscxbayf3rXOJfLRVdXF3a7t2BJk8vl4A/+YA9VDg/Nngb6XzpNaCxSwKjFchRVYdcf7ODG/5R74/gNcDXwszJGJoQQQlyqHwC7gNcB0Gwab/rQNVz5zq0VsQ7PSpAvWfL7/Fgt1rLEM9U3xdDrQ3RWdeJ3+nnf+96HxWIpSyzFJgnTCud2u5ckTadOXdqcps2bO9i9+3do97fg1lwce/RUQeczuVwu3G5XxY1fLZSuW9t5yz/cjLdpbmLmDHAv8DEgVb7AhBBCiAuWBD5EZr5SCAD/Og97Pr2bjW9aX87ALshKb7ssmyxZy5MsRSYjHP3VUWpdtbR4W7jvvvtYt25dWWIpBUmYVoHFSVMoFL3kpGnPnt10bWpna+0G1JTK0UdPoacKs7q1zWrFZrNhK9Mv8WpQ21nF733mFtrf0JKz9bPAG4FDZYpKCCGEuBCvAb8D/FN2y4YbW9nz6VuobvOVLaqLsZLbListWUpGkxx+5DBOxcnW2q3s2rWL2267rSyxlIokTKtEvqSpp2cQXb+4JMdisfC+972d5oZ6ttVuJD6dpPuJfkyj8EUgRH42t5Vb/vw6fud9l6Na5oYrzA3R+zukt0kIIcTKlAQ+CVxLJmkC1aJy/fuv5E0fvgarszKHZZWDYZoEg+EVkywZaYMjvziCGTPZ0bCDjRs28t73vrfih11KwrSKLE6aIpEE3d19JBIXN5zO43HxgQ+8kxpvFVtqOpjuD9L34ukCRy3ORlEUtr9lI3f//c34W72zW1PAfwOuY+5GJIQQQqwMvyEzV+lvgcw6kdVtPu75h5vZemdnxTecS0k3DIKBMKmUviKSJdM0Of7kcSJjEbbXb6eprokHH3wQm23lVj8sFO1Tn/rUp8odxKUyTZPkojKQdru9In9pbTYbXq+XYDCCorhJJAJMT0/j8biw2S78F8jjcdHW1syR10+iKRoD/SPYXFY89Rc/htcwTUwyXciV+D0oBneNk67b2sE0GTs+NVuJdZRMpaE0cANQngo4QgghRGY9pf8KvBc4A4CiKVz5jq286UPX4K5b3esrrbS2SzqtEwxG0A3QNA+aZsPvL1+yBDDwygAjh0bYWr+VpqomPvKRj9DQ0FC2eC7FheYOkoKVZlEAACAASURBVDCtQjabjerqakKhCKbpQtcjTE1N4nDYcTjsF3y+urpqfD4P/SeGSRs6gydHcVbZcdVc3B+/QDBIPBYnmUzicDgu6hxrkaqptFzeQOuuRsaPTxEPJMis2fQs8BMyPU4tZz2HEEIIUXj7gLuBnzK3tlJNp587/vJ6Nty0HlVb/e2tldR2SabSBINhMFUsmheLxUqVv6qsFeiGXx+m98VeOqs6afG18IEPfICurq6yxXOpJGGaVckJE2TmINXW1hKNxtB1J7qeYGpqAotFw+2+8ERn/fpm4vEkMyMhEukEg90XnzTFEwkwM09oyv1HZzVy1Tjpuq0DRVE4c3xy9t40BnwNiJCZYHvhibEQQghxYaaBvwTeD0wAoFoUrnzXNt70J7tw167uXqVcK6XtEk8kCYUiKIoVzeLBarXhr/KXbZ0lyCRLPb/uYb1vPe1V7dx///1cf/31ZYunECRhmlXpCROAqqrU1NSQTCZJpayAyczMOLqu4/W6L/j9b93aSSAQIjoRn0+aqi88adJ1HUVVsWjamhjXWgyqptC8s5711zQxfmKa2EyCTOb0PPAwmYTpKkAm1gohhCi0OPCPZEqF781urdtYxR3/9QY6r1+HolZWG6vcbRcTiEbjRKMxVMWOprmw2+z4/D5UpXwlB3KTpc7qTu655x7uuuuussVTKBeaOyimaa76smiGYRAKhRZs83q9qOraqWlx+vRpRkZGSKVmSCZH8XgctLevu+B5TaZp8p3v/IJ9+17jxHQ/E7Fp/n/23jw4squ++/7cpfdNUmsfSTOaTZ7Nu8c2XrAxi+0xMSYxkJCAHb+YJIXf90mRVJGQFMkbKCBPXkjeShVFJcUL5YcAD5g4EJOQAMaAGXu8zoxmxiPNql1qdav35a7vH7e71S21NBp7ZiTNnE9VV0t9+p4+9/bpe8/3/n7ne7a/cyOtW5ovUssF58IyLA49PcTB776BZdT+XDfhuOn9NsK/RSAQCARvHRN4EscBb7T6quKSufaDO9j9G1uRFXG9udBYlk0mk0M3DGTZhyx78Pv8BAKBc298EZk4NMGJX56oE0vvfe97V7VNF4rz1Q5CMF1GxONxzp49i2HkKZXGURSLjRu7CYeD51WPEE1rk8xUjle/fZRTvxxbUHIN8AXgPcDldcdPIBAIBJcCG3gG+BRwZP5lCba+vY/rPriDYPvaXNB1vaPrBplsHssCRfYjyy4CwQA+7+qmO17OYgnOXztcVEVx4MAB3vOe9xAKhQgGg9x99908//zzK97+qaee4rbbbqOlpYWmpib27t3Lk08+eRFbvL6JRqMMDAzg80Xwejdh2z5OnhxlcjLG+ehiSZL40Ifu55ZbrmFb80Zafc0M/eQssRNzF7H1gnMR6gzw9v9xE7/xP+9mw7W1rjQHgfuAe4CXVqdxAoFAIFin/Bq4E3gvtWKp54YOHvx/3sEdT9wgxNJFIl8okkpnscvmDorqzFdabbE0fnB8kVh64IEHVrVNq81FE0wvvfQSd955J4VCgSeffJInn3ySYrHIPffcw/79+8+5/de+9jV+67d+i66uLr75zW/y7W9/my1btvCRj3yEL3/5yxer2eueQCDAjh07aG6O4vX24nK1MTUV58SJEXTdWHE9kiTx27+9ryqa2nzNDP3kDOOvTZ+X+BJceKKbm3j3X97Gez5zG9EtTTUlz+I46X0AGF6dxgkEAoFgnXAMeAhn2YpfVV9t29bMff/3Hbzrz99Gy8bIajXussZZjDZHPl9Elr0oShC320NzczMudfVsw23L5uSvTtbNWdq3bx8PPPDAZe8LcC4uWkrevffey+uvv86pU6fw+507E5lMhs2bN7N9+/ZzRppuv/12xsbGOHXqVDU8Zts2O3fuxO12c/Dgwep7RUpeY6amppiYmEDXs2jaBKoKmzZtIBhc+Z0i27b5znf+g/37X2MkPcloeorOna1svr1nyQmfuVwe27aQJJlAQNyVupjYls2Z/eO88i9HyUzlakpU4GM4eeidq9M4gUAgEKxBxoG/wnFetaqvhruD3PDhnWy8ufuKHBxfqrGLbphkMjksy0aRA0iyit/vx+/3I61iWr2pmxz/7+PET8fZ2rKVrlBXNbJ0OfaH89UOF81i6/nnn2ffvn1VsVRpyJ133sn3v/99Jicn6erqWnJ7l8tFMBisa7gkSYTD4YvV5MuOzs5OgsFgWXR60LRxhofP0tERpaurbUU/AEmS+OAH76O5OcyPfvQcXsXDiWMjlDIa29+1CdW92OZSN3Rsy77sHHTWIpIs0X9bD317uxn66Rle/99vlNdvMoCvAN8A/hj4P4H1ubicQCAQCC4EUzjOd/+A44Ln4Gv2ct0HrmLbPRuvaEOHiz12sYFCoUg+X0RCRVX8yIpKKBTC7VpdR2Etr3HkmSPkZ/Psat9Fa6CVD3/4w9x+++2r2q61xEUTTJqm4fEsXium8trhw4eXFUxPPPEEDz/8MJ/73Od4/PHHkSSJr3/967zyyit861vfOufnHzlyhI0bN9YJrFKpxBtvvAFAc3MzfX19ddsMDw+Tz+cBuOaaa+rKZmdnGR8fB6Cvr4/m5nkDBNM0GRwcBBxRuHnz5rptT58+TTqdBmDXrl11C48lk0nOnj0LQHd3N21tbXXbHjp0CNu28fl8bN++va5sdHSURCIBwMDAQN26AdlslpMnT1b3tVj0kk4r6Hqc6elZjhx5g46OZoLBwKL2zs7OVuvt6enB7/fznvfcTktLE//rf/0ArVDk1Klxct/Lc/WDA3gC8z/0TDaLbTUOWpZKGoViAQC/34+7ZrVqJzztHCOX6lp0dyeXc9xjAMLhMHKN2NN0vfq9+Xw+PAvsQJOpFACqohAM1htg5AuFqq1kKBRCqRHoumGQyzlRG6/Xg9dTvy5DOp3Gsm0UWSEUqq+3UCxSKpUACAaDqMq8sDRMk2w2CziLEPt99bnKmWwW0zSRG9wgKJZKFIvOhS7gD+ByOX1JcckMvHsTbddFOPFfowz/5whG0QTywOeAvwN+B/gfwNUIBAKB4ErhNRyh9C1Ar77q8qtcta+fTe/oRvUoLLxyG4ZBtnIN9HgWrU2UzmSwLAtZlgmHQnVlxWLRWdcICAYCdeMe07TIZJ07+8tdAyUkIpH6a+DFHEfMj10Wj2He6jjCNC1Mw0RWVGTZiyx7cblcmIZJJpNBkRWamprq6s3lc9XrfTgcrkvVMwyDVNppk9fjXeSml0wlnWMoSbQ0t9SVFYqF6pgpFAxhZA0G/30QO2+zp20Pki7xrne9i56enkXH4eTJk9Xxy549e+qCGvF4nLExx5Sqp6eHaDRaLbMsi8OHDwPOmGjLli119Z45c4ZU+Rjv2LGjztY9lUpx5swZALq6umhvr7/5Ozg4iGmaeL1eBgYG6srGxsaIx+MAbNu2rS6IUzkGK+WiCaadO3fywgsvVH9M4HzBL774IkB1B5bi/e9/P9///vf56Ec/yl/8xV8AzmD4G9/4Bg8//PA5P98wjEVzbWzbRtf1anmjbSrlC7Esq1pmWdai8pXWu7BNtfWaptmwXtu2cbkW57SaprmiemVZZtu2bUxPTzMxIaMoQQqFSU6cGKWjI0p/f39dtMk0zep+2Pb8vt50024CATd///ffQEbhbHKSQ98fYuf9W6qL11XbIbFosG9jzZ+QGmSCVspqP7O6P7a9pBCjpqxRhmmlzJIbldW2aWFhTZsWN6naJktaXGjXtneZNjUus8r1Ntjf2n1tcFJX3AoDD2xi6zv7OPGjUY7/1+myFXkJ+P/Kj3fgCKd9CDtygUAguBwxgR8CXwZ+UVciqzI77u3n6t8cwFRNtJJWvq4sGDNRc/1scK2yKtcqlr9mN7jKLX/NLm9rN7gGXsxxRIWFN0dr6z3fcYRt2xQKRYoFDbfHh98dQpZUfH4ffr+fRDyBZVkNU/Fs22443nQ+Zr7MarSvlrV0vdb8tsmJJCd+cgKP7WF3527aWtq4++67aW9vX3JM+lbHyY22rx3PLmpvzdi9UZs0TcOyLBRlccbTcuPk852RdNEE0xNPPMFjjz3GJz7xCT796U9jWRZ//dd/XY2mnGt+0X/+53/yu7/7uzz88MN84AMfQFVVfvCDH/DII4+gaRqPPvrosturqroo5UySpKrwqL3bUbtNI2FSaW+lrFHbV1rvwjbV1tvoy3a5XNi23bBeRVFWXK8kSXR2dhKJRDhz5gwuVx8wy9xchuPHT7NxYzc+n7f6/srnSQsWS9uyZSOPPPIg3/nOjwlkfZzJT3L46SG2vL2Ptq3NSJKEJEtISHV3bwAk5PlQd4N0wErZws8EkMv1NqSmrFGaYaVsYXucsto2LSysaVOD7ipLEpZMwwXlpNr2LtOmxmUykm03bG/dvjY4EVbKfBEvtzx2Dbt/YxvHfnSSoZ+cRctXTkY/Kz+2Av8X8AhwftbzAoFAIFiLpHHmJv2/wOm6EldA5ap3b2bHfZurNznzhULNtXXhNXv566csy1hYDcdEct21aiHnuGbXjCMWb3kJxhEN9ufNjCMM0yKdzlIq6UiyB0UJ4lI9hEKh6hhLlmWwG48rJUlaek0g5ssajUFkWca27SXHRJIkETsWY+b1GVp8Lexs38mmjZt4/PHHmZycBJYek77VcXKj7WvHs4vaWzN2b9Qmt9uNaZrnrLeRJjgfLuo6TF/84hf57Gc/Ww3f3Xrrrdx555188Ytf5Je//OWSuZG2bbNhwwauu+46nnnmmbqyj370ozz11FNMT09XQ5DC9OH8sG2bqakpJicnMYwCmjaBbWt0drbS0RFdUSfKZHL80z99l1OnRzmVHGUmn6BzVyv9t25AVsVxX2voBYMTPx/h6DMnSE/mFpRGgP8DeALYeOkbJxAIBIK3yCkckfQ1oH48FNkQZOe+rWx5ey8u70W7Ty4oYwPFQolcvoCEjKwEkCRlTRg7ABglg6Fnh5g9OUtPuIf+pn727NnDxz72sUVpl5cza27h2lKpxPDwMKFQiI0bN/Lxj3+cb37zm8RiMXy+xj7zU1NTdHV18Vd/9Vd85jOfqSv7x3/8R5544gkGBwfZtWsXIATTmyWfz3PmzBny+Ty6Pouux/H7PfT0dBIInHsNAE3T+e53f8yBAweZysY5nRrDH/Uy8O5NeMOL568JVh/bshl7bZojPzzB5OHYglIZeD9Out7bEIvgCgQCwVrGxkm3+3vg31iYD7bh2nZ2PrCVDde0CxOmS4RhmGRzBQzDQJY8yIoPVVEJhoKrahdeIRvLcuzHx9AzOgPRAaL+KO9+97t56KGHrrgx85oTTLWMjIxw9dVX8+ijjy67llKpVKKpqYm77rqL//iP/6gr+/CHP8y3v/1tYrEYLS3ORDYhmN48tm0zOTnJ1NRUOdo0iWUViUab6O5ua5gKuJAXXnid7373xyTzGY4nTlNCY/OdG2jpb6qbkClYWyTOpjj6zElO/WIUU1+Yb3wjjrvebwGr694jEAgEglpKwHdwhNJrdSWKW2bL2/vYtW8LTb3CVfh80HTdmcskSec9drFsm3y+SLFYQkJBln2OXbjPjz+w+lEl27aZOjrFyV+exK/42dm2k5ZwC4888sgik7MrhTUjmAYHB3nqqae48cYb8Xg8HDx4kC984Qts2rSJZ599ts5l5J577uG5556rM0z45Cc/yZe+9CV+7/d+jw9+8IMoisLTTz/NV7/6VR577DH++Z//ufpeIZjeOrlcjrNnz1IoFND1OTRtBkWB7u52otGmc6bpjY9P87WvfZ+pmVkOT7xBspShfVcLO+7eiqyIO1trmWKqxBv/dZo3/vMUhWRpQWkX8HvAR4Gdl75xAoFAICgziLNUxJPAdF2Jv8XLjvs2s/1dm/CGRIbHmyGZSlVtxZsiK1+wt1jSyOcKWDZlBzzPmooqmbrJiedOMH18mq5gF1tattC/qZ/HH3+c1tbW1W7eqrFmBNPQ0BAf+9jHGBwcJJvN0tfXx4c+9CE+9alPLbI/vOuuu3juuefqHCssy+JrX/saX/3qVzlx4gSWZbFlyxYee+wxHn/88brJXUIwXRhs2yYWi5UXuy2h6zEMI4nf711Rml6xWOJb33qGn//8BWYKcSYKs7T0NrHtHRvxRcQJfK1j6iannx/nyL+fIHE61eAdN+EIpw8B0QblAoFAILiwxHDswL8BvLqotHVrM7se2MImMX/4LXO+gskwTHK5ArphIEluFNmHJMv4/X58Pt+qR5XAScF747/foJQqsa1lG+2Bdu666y4efvjhFWUQXc6sGcF0KRGC6cKi6zrj4+PE43FMs4CmTa04Tc+2bX70o5/zzDPPkS7lOJMdR7MNNt3STefu1stytejLDdu2mT4W5+i/n2Tk5Ulsc+EpwgU8gCOe7i//LxAIBIILgwY8gyOSnsFZiHweWZXou6mbnQ9soX2gRVxXLxClkoaNhYSMx7N0KvpS6Xcej4dAIIAiL3Zyu9RYpsXoK6OMvDxCwBXgqtaraA4285GPfIQbb7xxtZu3JhCCqYwQTG+dbDbLyMjIojS9rq42Wlublz1Jnz07wTe+8a/MxBKcTY8zlZ0l3B1k6119whBiHVFMlTj5y1FO/HxkiahTG/AB4LeBWxHrOgkEAsGbwQKex4km/W9g8VqVrVua2HJXH5vv6BFpd6uAjSOqGqXfBYIB3K61Md83O5tl6KdD5GZz9EX66Iv00dvby+OPP05HR8dqN2/NIARTGSGYLgyN0/RSeDwqnZ1ttLQsHbYulTR+8IOf8atfvUKymOVk8iy6ZLDplg107FyZfblg7ZA4m+LEz0c49YvRBnOdAPpw0vV+G7gG4bInEAgEy2HjmDZ8C/g2MLboHf4WL5vv7GXbXX3CxGEVKWk6+XwB07TWbPqdbdmMvjrKyEsj+FQfA9EBwt4w9913H/fff/8Vn4K3ECGYygjBdGHRdZ2xsTESiQSm6Qgn08zg93vp6mojHF564dOhoTP8y7/8O7H4HGdS40znZmnqCbH17X14Qmvjjoxg5VimxfjrM5z4+QijL002cNgDuAr4HRzxtPXSNlAgEAjWNMdxRNK3gKFFpYpbpu+mbrbd3UfX1e3COGkV0XSDfL6IYRhIkuqk30nKmkq/A8gn8hz/yXGysSy9kV76In30bOjhkUceYeNGsb5iI4RgKiME08Uhn88zPj5OOp3GMPIYxgymWSAY9LNhQwd+f+NFz4rFEk8//VP273+NZDHDibkRDNlk063ddOwQ0ab1ipbTOXtggtO/GmPiUAzbanQ6uR74DWBf+W/xuxQIBFcSFvAyznykHwCvL3qHpEhsuKadzbf30Le3C5dPzA1dTQzTJJ8rouk6Eiqy7EWSVVwuF4FAYE2430H5BubBcc4eOItX9lajSvfeey8PPPCAiCotgxBMZYRgurik02nGx8fJ5/MYRgZdn8GyNJqaQuTzaWRZQlVVtm3bVrfdsWMn+da3niE+l+JMaozpXJxQu5/Nd/QSbPOv0t4ILgTFVIkz+8c59asxpo8tzr936MQxitgHvAsIXbL2CQQCwaUjDfwXjkj6ETCz+C0SdO5spf/2Hjbd0i3m964yqVQawzQolXTcbg8gl1PvXKiqSsAfwO1eO1kxybEkJ35xgsJcgZ5wDxubNtLV2cWjjz5Kf3//ajdvzSMEUxkhmC4NiUSCiYkJisUihpFC12cZGTlJMOijo6OVXbsWr92Tzxf513/9CQcOHCRVynIqOUbBKNC5s5W+vV2oHnFHZL2Tnc1z+vlxTv9qjPip5BLvcgFvxxFPDyBS9wQCwfrFxkmve6b8+AUL3e0qtG5tZvPtPWx62wYC0eWX6xBcGizLZno65jjfyTLhcBuy7EaRFfwBPx6PZ03MUwIoZUuc/vVpZoZniHgibG3ZStAT5J3vfCcPPvhg3bI7gqURgqmMEEyXjooxxOTkJLqucebMYXQ9jqJI7Nw5QGdna0OLzuPHT/O97/0X09OzTOZijKQnkd0SG2/pFlaplxHZ2Txjr04z9soUE4dimJq5xDu3My+ebgfWzp08gUAgWEwJRxhVRNKJhu9SvQrde9rpvbGTnus78LcIkbRWMC2LQqFEsVginy8ALmTJSzgcxu/34/V514xQskyLiUMTnH3pLIql0N/cT7u/nf7+fn7nd35HzFU6T4RgKiME06XHNE2mp6eZnp7GNA0MYw5dT2DbBs3NYTo6ovh89XOcDMPg5z9/iR//+FdkC3nOpMaJ5ROEOgJsvr1HpOldZhglk6kjMUZfmWbs1SmyM/kl3hkC3o0jnu4DhBWqQCBYC0zipNg9A/w3kG34rlBHgJ4bOui9oZPOXa0orrVhDiBwMEyLQqFIqaQBErLsQZY9SJKMz+fD7/OvqZu2tel33aFuNjZtJBKK8P73v5/bbrttTbV1vSAEUxkhmFYPwzCYmZlhZmYGwzAwjCS6Hse2dSKREJ2drYvMIebm0vzbv/2U1147uihNr/emLlxekaZ3uWHbNsnRDGOvTjH6yhQzbySWMI0AuAkn+vRO4EZA5PoLBIJLQRF4CfgJjkh6peG7JEWi46ooPTd00ntDJ5ENQTGIXYMYpkkhX6KkaYBcI5QkfD4fPp8PWVo7Y8fa9LuwJ8y2lm0EPUHuuOMO3ve+9xEIBFa7iesWIZjKCMG0+pimSSwWY3p6Gl3Xq3OcbFsnHA7S2dlKIFCfmtAoTU9SYcN1HXTtbkNxie/0cqWU1Rh/fYbRV6YYf3WKUlZf4p1eYC9wJ3AHzoK5wjxCIBBcCNLAr4Ff4qTbHQC0hu/0hN30XN9B7/WddF/bjicg0ojXKoZhki8U0TQdRyh5kWU3siTj9XnXnFAySgajr44yfnAcFZX+pn7aAyL97kIiBFMZIZjWDpZlVYWTpmmYZhpdn8WyNIJBP21tLTQ1zQ94F6bpjWWmmM7FUf0KfTd20j4QRZLFnbvLGcu0iQ0nGHvFiT7NnU0v824FuA5HPN2BM/+p7VI0UyAQrHtmcMRR5fE6jg14Y1r6I/Te0EnPDZ20bmkWayStcTTdoFAoousGjuudF0l2I8tO6p3P61tTkUDLsJg4PMHIKyPYuk1PqIeecA/hUFik311ghGAqIwTT6jE6OoppmiiKQm9vb/V1y7KIx+NMTU2haRqGkUbXE1hWAY/HRVtbCy0tERTFyfVOJjP86EfPceDAIQp6iZH0BLP5OXxNXvpu7qJlU0ScOC4D8oUCtm0jSRJ+X+PJ0NlYnomDM0wdm2X6aHyZuU8VduCIp0oUqu/CNlogEKxDbOAs89GjX+IsIrs0oY4AHTujdOyIsuHaDuFqtw6wbSiVNArFIqZpIaE4aXdloeT3NTZzyOay1WtRMBC8tG22bGaGZjjz4hm0rEZXqIu+SB9+j5+77rqL+++/X6TfXWCEYCojBNPqcfDgQXRdx+Vycc011ywqt227KpxKpRKmWUDXE5hmBkWRiEabaGtrwe12rDGnpmb54Q+fZXBwiKxW4Gx6gmQxTagjwKZbugl3XdoTm+DCkkylsC0bSZZoikRWtE0uXmD66CxTR+NMH5slOZo5xxZ9zIunO4CrYI04HwkEgouFBRxjPnr0C2Bs2S2a+8KOQNrZSueOqHC0W0eYlkWxqFEqlrBsG0lyIUseJFlFkRV8fh9e79Kud/FEHMuykGWZaEv0krTZtm3mzs5xev9p8ok8rf5WNjVtwu/2c8stt/De976XaPTStOVKQwimMkIwrR7nEky1pFIppqenyWQyWJaOYcxhGEls26SpKURbWwvBoOOUd+rUGD/4wU85fXqMZDHL2fQ4WS1Py8YIfXu7xJ2/dcqbEUwLKWZKTB+LVx/xk8llDCQAWnFS927ASee7DuhCiCiBYL1iAxPAq8BrOOYMzwNLLaLtGDW0bmmiY0crHTuidFwVxRMS85DWG7phUixUjBwkZMmNLHtAknG5XPh8Ptxu9zntwS+1YEpPpjn9wmlSEymavE30N/UT8oTYs2cPDz30EBs2bLjobbiSEYKpjBBMq0exWKyGtb1e77k3AAqFAjMzM8TjcSzLxDBSGEYCy9Lw+720tbXQ3BwGYHBwmB/+8FmmpmaJF5KcTU9QNEpEN0Xoub6TYLuwIl9PmKaFM9iRUJQL85vVCwaxoQTTx+JMHZslNpTA1Jael+DQzrx4ug64HtgMiPOIQLC2sHDWPHptwSO27FaqR6Fte0s5xa6Vtm3NwoF1nWIDWkmnUCxhGM78pKrjHRIerwef14eqrvz7NU0TGxsJqTo14IK327ZJjacYeWWE5FiSoDtIf1M/zb5m+vv7ef/738/27dsvymcL6hGCqYwQTOsTwzCIxWLEYrGys14Ww0hgmjlUVaGlJUI02oTb7eLAgUP86Ee/IJnMEMsnGMtMUzCKNPeG6bmhg3CnSNUTOJi6RfzUnCOgjs4y80YCLbeUC18tIeBa6oXUTkCspC4QXBo04Aj1wuggS61/VIs76KLjqvn0uujmJmRVjAvWM6ZpUSxplEoalmUhSWo57c6FLMt4vV58Xt+aG//Zts3c6BwjL42QnkoTdAfpi/QR9UXp7OzkoYce4tprrxXzsi8hQjCVEYJpfWPbNolEgpmZGfL5PKZZwjCSmGYK2zYJBv1Eo00EAj7273+dn/3sBZLJDLOFOcYyU+T1IpHuID3Xi/UwBIuxLZvURJbE6STx0ynip5IkTieXsTKvxQ3spl5EXQOICbkCwVsjiyOGasXRIHDu36Un7Cba30RLf4RofxPR/gjhrqBwVL0MqESTiqVS2e3OSbuTZDeSpKCqKj6vD4/Xc860u0uNbdvET8cZfXmUTCxD2BOmL9JHi6+F9vZ27r33Xm699VYxXl0FhGAqIwTT5UM2myUWizE3N4dlWZhmuiye8qiqQnNzmEgkyKFDQ/zkJ/uJx5MkiinGMlNktTyhjgC9N3TS1BsSwkmweB4ndQAAIABJREFUJLZtk5stED+dJHE6VX3OzRZWsLUEDOAIpwFge83jzc3LEgguX5LAUM3jOI6d9zDO8Hh5gm3+qjBq6Y8Q3dyEv8Urzu+XGYZpUSqWnGiSbZejSWWhhITb48bn9eFyrb2Iv23ZxE7GGH15lFwiR5O3ib5IH03eJrq7u7n//vu54YYbxDh1FRGCqYwQTKtHNputTpwMBi9cWpxhGMTjcWZnZykWi1iWhmEkqyYRwaCPSCTEyZOj/OQn+5mdTTBXTDOWniKt5Qi0+ui5roNof5O467iGMAyjPIOJ88o3v1QU06U6ARU/nSQ1kV3JuK5MO/UCajuOqNoCeC5KmwWC1aeIM89oqMFj+blGFSQZwt0hov0RWvqbiG5uIropsmJjhrV+bhEsxrahpGmUihq6URtN8iBJMoqi4PV68Xq8F3yMpxt6df61S31zIswyLGaGZhh7bYx8Mk+Lr4W+SB9hT5je3l727dsnUu/WCEIwlRGCafU4H5e8N8viqFOmHHXKoSgykUiIsbEpfvGLl5maipEqZhnNTJEqZfAE3XTtdlyRVI+4iK42F8Il71KjFw3mzqaIn05V0/rmzqaxjHMZS9QiAZtYLKa2A704C/IKBGsZExhhsSA6Xn595cMLxSXT3Bd2hFF/hJbNTbRsDL+lc/R6PLdcqRiGSbGkoa1iNOmtuORpeY3JwUkmByfRCzpRf5TecC8hT4jNmzezb98+du3aJYTSGkIIpjJCMK0el0IwVTAMg0QiwezsLIVCoRx1SmEYKWxbx+1WmZ6O8+KLh5iaipHVCkxmZ5gtJJFUaB+I0rWnDV9E3OlfLS6XQY1lWGSmc6QmsqQmsqQnsqQnnb8Lc8XzrM0DbGVeQG0GemoezQgLdMHFxwbmcNYuqjxOMi+MTuCYMqwcf4uXcFeQcHeQSPkR7g4Sag9ccEOGy+XccrliWhalsoGD45YqI8tuZMkNkoyqqHi9XjxeD7J08cdzb0YwZWNZxg+NExuOIdkSnYFOukPd+Fw+tm/fzr59+xgYGBBCaQ0iBFMZIZhWj8nJSUzTRFEUurq6Ltnn5nK5uqiTYeQwjBSmmcG2TWZnEwwOnuD06TEM22QqF2MqO4thGzT3Reja0yYMIlaBYrGIZdvI52FDv97QCzqpyZwjoiaypCbLzxMZ9LzxJmr0US+gGj1aEZbogqWxcFLjxpZ5jAMrmcNXj9vvIrwhSKQsjMLd5b+7grh8ly6qfyWcW9Yblm2jaXpNyh1IkrscTVIdS3CPB6/P+6bT4t4s+Xy+mpLn9y+9PIlt2cTPxJk4OEFyIolX9dId6qYz2IlbdXP99ddzzz33sHnz5kvYesH5IgRTGSGYrlxM0ySZTBKPx8lkMth2JWUvhWnmmZtLcezYSd544xQ2NvFCkonsDDm9QKDFR9fVbbRtbRb2s4KLjm3bFNMaqfFMnZBKT2RJT+XOM8VvIW5gA43FVOX1TkTq3+WIAUxzbjG0ElfIxigumVBnoBwpClUjRZGuIJ6wW9x4ElSxbdB0nVJJQ9OcPlebcgfgcrnwerx4PJ4123cMzWD62DTjh8YppouEPWF6wj1EfVECgQB33HEHd999N83NzavdVMEKEIKpjBBMAgBN00gkEsTj8bJRhFF22UuTzycZHBzmyJETlEoaeavAZDbGXDGF6lNpH2ihY0erSNcTrAqWaZObzZOeyJKN5cnFC+QTBXLxovN3vIBeeDPRqVpkoKX8iDb4u9FrLUAYkRJ4KbCBNJAA4guel/o7jpNG91bENrj8KoEWH/6oj0D54Y96Cbb6CW8IEoj6kRXRBwSNsQFdN9BKGiWtbKaAglRNuXMWh/V6nJQ7RV67N26ys1mmjkwxMzSDpVu0+lvZENpAyBOio6ODd77zndx88814PGKssJ4QgqmMEEyCheTzeRKJBIlEAl3Xy/Od0uj6HG+8McRrrx1jdnYOS7GIa0li+TkMyyDSHaRjZyvR/giyIvqUYO2g5fWqiMrHC+TKj3zN88rWljpfFJYXVJW/gzjpg/7yc6PH5fibsnBS2Wof+QX/Z1la8CRqHuYFb50n6KoKoXpB5CMQ9eJv8eH2rz2rZsHaxgZ0zaCkOZEkZ3jpzEuSJDeSJCPLMh6PB4/Hc8lT7s4HUzeJDceYPDJJZiaDW3HTGeykK9SFR/Gwc+dO7rnnHmHksI4RgqmMEEyCpbBtm2w2SyKRYG5uDtM0Mc0ipplhdPQkL7/8GsPDZ5AUmZyVJ6GlSGtZXB6FtoEoHTui+JtFPrxgfWCUjDpB5Qisyt9FShmNUlZ7k3OpLgQeGguppURW5XUvjnCTcETXSp5tHDGzkmcTxxp7odBZSgDVvn5+RggXCpdfxRN04wm58bd454VQS70gEu6gggtFJd1OK+loeiWSJJcXlXUhSQqSJM2LJJdrzS0uW0tmJuNEk4adaFKzr5muYBctvhbcbje33HIL73jHO+ju7l7tpgreIkIwlRGCafU4evRo1SVv586dq92cZbEsi3Q6zdzcHKlUqiyeSqTT0xw69CoHDx4mmUxjyjYpM01CS2NYBuGuIJ07okQ3N4m5Tm+RdCZTdSYKh0Kr3ZwrFsuwKOX0qoAqZbT5v7Pzr2tZjWJGQ8vqFDMaRnG1hNbli8s3L3w8QRfuoBtvyF3z7KopLz8HXOJctABxbrk4VIwbNE1H1/TyWlcKkuyqE0lutxuPx4Pb7V7TIsnQDGJDMU6/eprcbA634mZTdBOdwU48qofe3l7uuOMO9u7di8/nW+3mCi4QQjCVEYJp9biUtuIXEtu2SafTJJNJkskkhmFgmiXOnHmDV199mePHhzBMk5xdIGmkyZkFVI9C27YWOnZECUTFifTNIKx/1zembqHlGosro2hiaCZGycTUnIex8LlU+d+qe895LOGzekiguhWU8kP1KOX/Zef/yutuBcVT/7/qVepEUVX8BN1C+FwgxLnlwlErkqrGDWWRVLEBlyUZt8eN2+1e8yLJtm0y0xmmjk4RG45hGRYey0OLu4UmbxMbujewd+9e7rjjDvr6+kTa3WXI+WoHEZcXXHAqC8tdzAXmLgaSJBGJRIhEIvT19ZHJZEgmk3i9QbZsuYZcLs3Bgy/x2msvMzs7S0nRSOoZpg7NMn5ohlCbn7btLbRtbcYdWF/7vprIsoyFJW5wrFMUl4yvyYuv6cKlqdq2jWVYjqgqVcSV8386mcEoGdiGjc/rw7YcZWVbtqOxap9tpy7Kz5IkgeT81iUJkMtDuvKzJDuDIkl23qe6ymKoLHYqwkdxy6huBVmVxUBqDSPOLW8NwzCddDvNwKhagKvIsg9ZcjkiSZarkaS1nm4HUEwXmT4+zczxGQqpAl7VS2+wl45gB/l0no6ODvbu3cvDDz8srOgFdYgIk0BwDmzbJpfLMTc3RzKZpFQqMTJyhtdee5GjR4+i6QUyepakniZj5ZFliZa+CO3bW2jpj6C41q77j0AgEAgE4ESRdM1A03V03cCyLEAqW4A76XZIkmPc4HbmJKkudc2LJKNkEDsRY+b4DKnJFIqs0OpvpSPQQcQTwefzcfPNN3PHHXfQ29u72s0VXCJESl4ZIZgEF4tcLkcymSSdTpNIJBgcHOTQodcYHx/BsIrMaUnmtDRFq4jqUWnd3EzHQJTIhpCw4RUIBALBmsEwzfJcJGN+IdnKfCRUJNlJRFJVtZpqt5bd7SpYhkXibIKZoRkSZxPYpk2zr5n2QDtRfxRVVhkYGODmm2/mhhtuEJbgVyBCMJURgklwKdB1nVQqRSqV4syZMxw8eJDDhw8xNzdLycyTKMVJ6mlKlobH76Z1azMdV7US6QyIVB6BQCAQXFIqrna6bqBpejmKRNmswYUsqSA5qaZulxuX24Xb7V7T6yRVsC2b5HiS2FCM2VOzGJpByB2iPdBOW6ANt+Kmq6uLW265hZtvvlksMHuFIwRTGSGYBJeail15Mpnk8OHDvPLKKxw7doxCIUtOzzCnxUlqKTTLwBty07q5mfbtUZq6g0I8CQQCgeCiYJgWul52tdMrrpZyNc2uGkVS1KpAWg/zkQAs0yI1kWL25Czx03G0vIZP9dEeaKc90I7P5SMcDnPTTTdx8803CwMHQRUhmMoIwbR6TE5OYpomiqLQ1dW12s1ZNUqlEolEgpdffpkDBw5w/PhxdF0jqyeZ0xIktRS6ZeD2q0T7m2jd0kxLXwRVXft38i4kxWIRy7aRJUlMshWcE9FfBCvlSu0rlmWj606Kna7pmNUoklqOIjmGDRJSVSCtlygSOCIpOZp0RNKZOHpRx6t6afO30epvJeQJ4fV6uf7669m7dy8DAwMrGg+KscuVhRBMZYRgWj3Wq634xcSyLGZnZ9m/fz8vvPACJ06cwDQNsnqauVKCpJZEszRUr0JTX4jo5mZa+sK4PW5U5fLux8L6V3A+iP4iWClXSl8xTcsRR7qBoRvzAgm5mmpXiSIpsjI/F8m9PqJIAKZuMjcyx+zJWRJnExiagd/lp9XfSqu/laA7iMvlYvfu3ezdu5c9e/act1OvGLtcWQhbcYFgDSLLMu3t7Tz44IM8+OCDJBIJXnjhBQ4cOMDRo0cxDIO8kXMiTyfniA+dQXZLhHuCNG8M0dwXweNz41JVFFVZJ5c4gUAgEFxIbMA0TSeCpBsYhjk/DwkFSXKhyCqSpIIkOVEkV00USVkfUSRwFpRNnE0we3KWubNzmIZJ0B1kg38Dra2tBFwBPB4PV199Nddffz27du0S5g2Ci4aIMAkuONlstrq6ejAYXO3mrHny+TwHDhzgxRdfZHBwkHw+T97Ik9SSJEsJCmYBWYVgp4/QhgDhDUH8ES8ul4pLVVFVlfWckm0YRnmleMeJSSBYDtFfBCvlcugrNmCU0+sM3UQ3DCrDNifFTi272SmAI5BUl4rL5XIeqmtdzdkppArMnZ0jcTZBcjyJZVqE3KFqJMnn8uH3+6siaefOnRdszUcxdrmyECl5ZYRgEqxHNE1jcHCQF198kVdeeYVsNku2mGVOmyOtpckaGWzbwtvsJtTtJ9TtJ9Dmw+12lS+SKqqqIK+jC6RAIBAIHGybsjiqRJAc0QcLBZIjAGVJrhNIqrr210WqpWLakDibYO7sHPlkHlmSiXgitPhaiPqjeFUvwWCQa6+9luuvv56BgYF1K4AFawchmMoIwSRY7xiGwbFjx3j11Vd57bXXSCQSFLUi8XycZClJWk9jWDqySyLU5SfY7Se8wYfqdUSTqjoRKJdbFQJKIBAI1iCWbVfnHumGiWFUXOykeYEkqUiSk0ony3Jd9MhJ0V5f5/dipuhEkUYSJMeSmLqJR/XQ4m2hxddCk7cJRVZobm7mmmuu4brrrmP79u1iTCe4oAjBVEYIJsHlhG3bnD17lsOHDzM4OMjJkyfRdZ1kPkk8H2euNEfeyAM2vqi3HH3y4Yu6kSQJRZGd9L1yFEoRvw2BQCC45JiWVZ17pOs6pmmVS+QFAsk5RyuygsvtiCOXy7Wu5iBVsEyL9FS6mmqXS+SQkAh7w1WRFHAHkGWZLVu2sGfPHnbv3k13d/e6SicUrC+EYCojBNPqUSwWsW0b6Qqzcr2UpNNpjh49yuHDhzl69CjZbJZ8Kc9sdrYagTJtE9WjlsVTgGCXF6U8H1aWZVRFQVUVlOrz6vxenAGDM9NgtdogWD+I/iJYKavdV0zLwjBMTMPEMEwMs9agoeJgp5QNGpz2OZkB5fQ6l7purL4XouW1aprd3OgchmbgVtw0+5pp8bbQ7GtGlVVCoVBVIO3YsQO/379qbRZjlysLIZjKCMG0eghrzkuLZVmcOnWKwcFBDh8+zNjYGJZlkcglmM3NEi/EyWk5kCDQGiC8IUCw24+3yQWSBVTW6JBQFQVFVcopfY6Yutj3964U61/BhUH0F8FKuVR9peJct1AczQ+v5LIwUspOdvMOdqqqVsWRy+VCltbnuMUyLbIzWRIjjkjKxDJISIQ8oapICrqDyLLMpk2b2L17N3v27FlTC8mKscuVxZqyFT9w4AB/+Zd/ya9//Wts2+amm27is5/9LLfddtuKtrdtm69//et85Stf4ciRIyiKwtatW/nMZz7Dgw8+eDGbLhCsG2RZZuvWrWzdupX3ve99zM3NceTIEQ4fPsyxY8colUqUjBIzmRni+Tizh+eYej2G7JIJtAUItPsJtPvwRV0Y2OiGDpSq9auqUo5GOZbmqqKsa1c+gUAgeLPYNhimWRVIjkiaN2aYF0ce5Mrco/IJU5Zk1GpqtBNFWm/zjyqYukl6Kk1qIkV6Ik16Oo1lWrhkF82+Zja0bqDZ24xLceH3+9m1axd79uxh586dhEKh1W6+QHDeXDTB9NJLL3HnnXeyd+9ennzySWzb5m//9m+55557ePbZZ7n11lvPWccf/uEf8vWvf50//uM/5vOf/zyGYXD48GHy+fzFarbgAtDS0lJdLVtw6Wlubub222/n9ttvxzAMTpw4UZ37NDU1hWVbZLUsc/k55jJzJGJzTB+aAQl8UR/BjiDBjgD+Vi+yy7lzahomxZJW/QxFkVEVx1yiEpF6s8YSbre7mgYhEJwL0V8EK+Wt9hXLtuejRub8cwUJBSQFSfYho1StvaGc9lxe9qHyWK/pdQB6USc96Qik1ESKbCyLbdu4ZBcRb4T+cD9hT5igO4gkSfT29lZT7fr7+9dFxo8YuwiW46Kl5N177728/vrrnDp1qpqTmslk2Lx5M9u3b+f5559fdvunn36ahx56iO985zt84AMfWPa9IiVPIFgZs7OzDA4OMjQ0xPDwMOl0Gtu2yek5UqUUyUKSZCFJyShh2za+Zh++NkdEBdoDqF4Z2zbBNrFtExujWrczQCin8ykqiioLcwmBQLAusCy7nEpnVEWSaVnVcolKtEipptdVUMoR+OpDUdf9+KOULVXFUXoyTS6RA8CjemjyNBH2hIl4I/hUH5IkEY1G2bp1KwMDA+zatYumpqZV3gOBYHnWzBymUCjEvn37+Pa3v133+m/+5m/y/e9/n4mJCbq6upbc/u677+bMmTOcPn36nJ8lBJNAcP7Ytk0sFmN4eJgTJ04wPDxMLBYDoKAXSJVSpIopUqUUeS2Pbdu4Q24C7QH8rX78HX7cATdgg22UBZQjpCgnqMiSVI5AqeWoVHlelAgOCASCVcC2wbRMTMPCMB0bb9O0qmYMjp13Za6RAjWOdRLz57NacbTeo522bVNIFuoiSMVMEQC/y0/EEyHijRD2hPGqjhlCV1cX27ZtY+vWrWzbto2WlpbV3AWB4LxZM3OYNE3D4/Eser3y2uHDh5cUTIZhsH//fu6//36+9KUv8Q//8A+MjY2xceNG/uiP/ohPfvKT6/4EJRCsNpIk0d7eTnt7e3VeYTKZrIqnEydOMD4+jm3blMwS6WLaEVHjKabOTGFbNqpfJdAeINAewBv14okEnN+mbVUFlGOfq1ExlwAnGqXIMoqqOM+K49InK/I6zegXCARrBRvHhMA0LUccmVY1YmTVRI3m5xu5UeSKQCqLI0kqpx3XpNStwzWPGmFbNrl4zhFHk84cJK2gISERdAeJeqNE2iJEPBFcigtZlunr66uKo61btxIMBld7NwSCS8pFE0w7d+7khRdewLKsqlozDIMXX3wRgHg8vuS2s7OzlEolfvrTn/LSSy/xuc99jp6eHr773e/yp3/6p8zNzfG5z31u2c8/cuQIGzduJBwOV18rlUq88cYbgDPPo6+vr26b4eHh6vyohQ4ps7OzjI+PA9DX10dzc3O1zDRNBgcHAUedbt68uW7b06dPk06nAdi1a1fdCtXJZJKzZ88C0N3dTVtbW922hw4dclKjfD62b99eVzY6OkoikQBgYGCgzgYzm81y8uRJANrb2xeJ06NHj1bdYHbu3FlXNjk5yczMDABbtmypOzEWi0WOHz8OOPm+vb29ddsODQ1RKBSQJImrr766riwWizExMQHAxo0b60L2hmFw5MgRAMLhMP39/XXbnjp1qnonYPfu3XU5xnNzc4yMjACwYcMGWltb67Y9ePAgAH6/n23bttWVjYyMMDc3B8BVV11VJ/LT6XQ1wtnR0UFnZ2fdtkeOHMEwDDweD1dddVVd2cTERDVas3XrVgKBQLUsn88zPDwMQDQapaenp27b48ePUywWURSF3bt315XNzMwwOTkJwKZNm4jUOD9pmsaxY8cAiEQibNq0qW7bkydPks1mAdizZ0/dXZR4PM7Y2BgA/f393HjjjdW2Dg0N8bOf/YyRkRFisRhbW7aimzrpUpp0Kc3MyAyzw7PY2PiCPkKdIScK1eZH8qnkCo6BhNfjxe1xOel8OHd3k8kkNiayLOH3O8dIUWQUWUHTNSzTRFZkwuEwbtf878Ywzeq+eDwefAssYDOZLKZlIktS3TkAoFgqUiw6bQoEArhqfo9mzR0nt9uN3+er2zabzVbnMCx03SppGoVCAXD6mtvlqpZZtl09B7hUta4/AORy+bLZhtP/a+eDabpePS/5vD48HnfdtqlUGhsbRVEILRjE5AsFNM2ZexYKhuqslQ3DIJtz0my8Hs8iG910JlM9f4cXTNIuFosUS84xDAYCdec007TIZJc+hplsFtM0kZCIROq/m1JJo1BcyTF0EQjU2w/ncjn08qKfyx5Dnw+Pu/4YJlMpAFRFWTQQrDuGoVBdmqluGOQqx9DrwetZcAzTaSzbRpEVQqH6egvFIqXKMQwGUWvOabX9e7lj2Lh/lygWnehAwB/AVfO7sSyLdLl/u1wuAgssnLO5XHXh1Eg4UhcJ1jSNfKV/+3y4a46hbUMqXT6GqkpwYf/O59H1cv9ecAdX1w1y+cox9OJdcKO1egwb9O9sLk+xWMSyrHL/lZw5l6aFaZoUCnlAwu3y4vH6ysJIBmSyuTyWZSNJJk1NoWq0SFVVNF1DK2mYlonf48ftmt9X03LOWwAet2dRf0mlU9VjGG2J1pUVi8XqvgaDQTzu+X21bZvEnHM9d7lchEP132smk0HTnX7Y3Nxc56ZX0krV/uL3+/F56/tLLBYjP5unECtgpAzSU2kMzUCWZDx4CEgBOtwddLd243F5cLlc9Pf309PTg9vtpqenh56eHjGOQIwjVjqO6OnpIRqd7/+WZXH48GHA6ftbtmypq/fMmTOkyufhHTt21J1fUqkUZ86cAZzIZnt7e922g4ODmKaJ1+tlYGCgrmxsbKyqN7Zt21ZnW3++fggXTTA98cQTPPbYY3ziE5/g05/+NJZl8dd//ddVcbBculzlDlA6nebHP/4xt9xyCwDveMc7mJqa4ktf+hJ/9md/tuwdDsMwWJhtaNt29aQ9v5p2/TaV8kZtqpTV36FyWGm9C9tUW69ZM5m0tl7btnHVDBwqmKb5lupdal9r6124r7XHsFG9tfs6NDRUJ/JWWu9a+W7Ota+6rmMYRsO+vNx3s5J6nQUNF5ctV29l23PV24iljqHf7+fqq6+uHju3243H42F4eJjh4WFOnTpFVIlSKBbIGTkkn0QmlmFqzDGXQAY1rOJt8SJ1RvB2+FD8HqzynV4bHWznbnCxAP6AH9sy0S2LYlFH10qAjWnaVctz53jblIoasiI3/G1YtoVt2VgNTjO25dxhdf5ZWDhfZjfoS5Ztz2+7cNPasgbfTaXMalRWbu8SFc+3iUZtspx2y43qrW3vgn54jjZZVvkYNvzM2jYt+tT5sob76pTbUqMtrRUdQ93QyGStugH0ct9N3TFc7rtpdAwta4X9ZfHHVtpkSYsLV9pfGpeVv5sGx7C+vyxd71LHYen+Xbttg/LqcThXP1xQxvLHwTAtLNPE0A0UWZ2PGhkmhWIRXdMACWwFRXUh4UKWlXKUW0JCxjBk/EoAWSpHs1UF3bCQkHC5XIuEjWEa1d9Vo++8co60Gnzp1qIoVv2+VsoaHf9qWYNjZdk19TpLSzVuk2WRn8uTm82RjWVJT6eZOTPjZATIKu2Rdnr9vYRbwoTcIXLZHLZt09PTw+23387u3bvZuHEjqqqSTqcZGhoCVmcc0SiT6FKMI6amphYJJjGOqK+3ESsdizXavrZNCznXvmqahmVZDc06znUMz4eLJph+//d/n1gsxmc/+1m+8pWvAHDrrbfyJ3/yJ3zxi19kw4YNS27b3NyMJEmEQqGqWKpw33338fTTT3P06FH27t27ZB2qujivWJKk6uCq9o5o7TaNBl/gCLxKWaOOvdJ6F7aptt5GX7bL5cK27Yb1KoryluqtfV6q3oX7WnsMG9Vb287K3fbzrXetfDfn2leXy1X3nlqW+25WUu9STj3L1VvZdrl63+oxDAQCbNmypXoXxzRN9u/fz+HDhxkdHSWXy1UX/8toGeLZOLFEjNRMitRwypkc7VEJtgbxt/oxXSauoAtX0AMSuN1+zPL6JYoiY8oewEKRfUiyhFW5e2zoFMp30TXNoFTUURQFWZFRFBnDcE6qKov3RZJBksvHbuEhlObLpAbHQZYkLLlxSo4kSTX1Ln5PpayRm6AkyfPbLi6cb1OD/ZElGVtq7ARW16YFOyudo02yLGNhNewPcl2bFn3qfNkybWqU2iQhn/MYOoN6MKm/cMp1+7roQ5dv03LfjSyvsL8s/linv9BwbZ2V9pfGZTKSbTd2pqz7bpaud6njsNQxlGr3tdHHVo/DufrhgrJyf7FMC003sOxiTTqdRSadxcZ2+qHkcn4rKEiyG1mWkWUPIKOowfL8SAlFUZxBluFE9xRVIRqN1n0PToqeueR3U+33Db7zSlmjbZ02LTFpnPl6Gx3/almDYyVL8qI2WaZFPpFnbnKO+FicfCKPntaRbOcNHtVD2B2mx99DUA0S8oRoamoiHA6zbdu26h13t9s5lgszVVZzHFG5vr7Zet/MOKJCo4G7GEfMl73VccS59nUh59pXt9uNaZpv6hieDxd94dpSqcTw8DChUIiNGzfy8Y9/nG+DS3jUAAAaOUlEQVR+85vEYjF8C9IMahkYGGBqaqoaoqvw1a9+lT/4gz/gpZdeqqYNCdOHtcWhQ4eqYfqF4XTB5Y1t20xOTlYjUMPDw9X0Fc3UyGpZslqWnJYjo2UoGk5akiRL+Fp8tPe1E2wN4ov68DX5sCQLy7QwTAPTNLFMq+6uedWxDwvbCR1hM286AfPzpWSl/Fx5KM7g5c3aoQtWh1QqjWVbyJK8KKVPsDaxbCeyYpm2EykpmyyYlvO3WXc32okKOW50ct3ftepFKRvILHrUWHfHE/FqWunCKNJ6w9TNatQoO5slG8uST+SxLCdS5nP5CLqDBFwBgu4gQXcQl+IMFNva2uoMGtra2sQ88AaIscuVxZpxyWvEyMgIV199NY8++ihf/vKXl33vn//5n/P5z3+e559/nre97W3V1x988EF+9rOfMTMzUxVcQjAJBGsT27ZJJBKMjIwwMjLC6Ogoo6OjVRFlWAY5LVcVUlk96zjy4URM/M1+Aq0Bgm1Bgm1BAq0BZFUuz1OYfximUZ8CYNtl0wkLsMrCyq7+X4vE/F1huUZYSbJUI7DE4EIgaIRl21XRY1t21VihIoqc1NuFVIRQjTgqGzDUhq9k2VnvTVYWP18O5gtLoeU1RxyVhVFuNkchVcC2bWRJxu/yV0VRRSRVhGI0GqW3t5fe3l76+vro6+sTFt8CQQPWjGAaHBzkqaee4sYbb8Tj8XDw4EG+8IUvsGnTJp599tm6+Uf33HMPzz33XF1uaCKR4LrrrsMwDP7mb/6Gnp4evve97/FP//RP/N3f/R2f/OQnq+8VgkkgWF+k02lGR0frRFRlgrBlW3UiKqc7f1fmC3jDXoKtjoAKtjoiyh1wgzSfZmMa9YJq0VyDiniyrZpnGyqRqgbzdqqRqrKAkhXZSZNRyv/LwuFPcPlQmeNWFUBVEWRX/zcbzFNwnOecaJAjhuSaZ2lR7mLlN6Qq6qJo0eUeBbFtm1KmVCeMsrEspZxjBqLKKgF3gKBrXhz5XX4nxVGS6OzspK+vryqQent7FxnKCASCxqwZwTQ0NMTHPvYxBgcHyWaz9PX18aEPfYhPfepTi37Qd911F88999yiCVijo6P/f3v3GyNHWccB/Dt/9u/t/e1d78zBHWkbUhFoFEugkV7riSgJpq0BfQFEURNjNPEFVhKMoLFJU97IG17wgkTrG0mEEEyKWCxFSmspaFNiKJRaz1C4P7299rr/Z+bxxew8O7O7s7fT2729vf1+ks3Ozs7szh4/pvvd55nnwd69e/GXv/wFqVQKmzdvxk9/+lN897vf9WzHwETU/rLZrAxPTpi6ePGi/Qu1EMgYmVJLVPFmWMXBKGJh2QLlhKlob1R+4RJCwLRM+aVPLru/CNYMVd4wVStUyUClllqq5LritUpr+2sgrWZOEJIDo5QFIPfjSk4Y8gtFZdfSKqVWW+f/DU3VvOuqXfy1BgnLnutIdqkrhiQjVzyHaeGKLnVR3T6H6bqO0dFR2WJ0/fXXY3R01DOSGBEFs2oC00piYCJamwzDwMWLFytao5xhnrNG1tulL38VOdP+dVYLaYj1xRDviyPWF0Os174uKtYXgx6pvHBXFK+zcAcrz+NqXyJlqBKu7n/FMCWDVuUp1h5wwb5+yrkg3h60QJWDFyiKIpcZtKhcKfgICMuy751R+YrLzkiH9uhs9nZ+/+A7wccTijzd5ioHFnLfNFWTIcgJRWu9haiaQraAzEJG3tILaWQXskgvpGGZxVZyPertUhfuQkSzh6KOxWKeLnXXX389RkZGql7sTkTXjoGpiIGpdWZnZ+XoLOXzShGVC1ovlmVhZmbGE6KmpqbkfDgFsyC78mUKGaSNNDKFDPJmXr5GOB6uCFHxvjiivVGomv95wxkWuCJMlbVaVewlisFJFFuqUHrstF6VlquHLMAVtIqjzDmtV+5wVVp2ha8l/6rtI5fLQ8CCArViTqp2JOCE9WKgEaVh8YUQcsCEeoNPsUqK3d+cZdW1rADux8V7N7/WIHcoaoeqymTt634URamYm2g5zIKJzOUMspftIOQOSIWsPcKaAgVhPYyYHkNMjyEeitvd68IJ6Kr9g01vb68nGI2NjWHdunUdGTRXA3536SxBs0PThhWnznXx4kU50gxPOrSUoPWiqipGRkYwMjKCrVu3ArC/cC4sLHgC1Mcff4xLly7Jrr6mZSJdSCNrZO0QdTmD1FwKc8ac7NqnKAoi3REZnuL9pdapSHfEHrJY9Y7EVU6GqvKL350uUMKq+PW/+gsVn5NdBUtByzKLLVqmAISxdNByWrKKy/AsF79G2yvkdvb3bUV+ebPXK671zn5lr9FkmWwGwhJQVKWpgUmI4jxGojiPEIS9TpTmMaq+XNxGiCqvgeJ6IYOS/2+W1YKPJocNV53gA7iuD6o9dLfTUll+7w5C7RKG6pFOp+UoeUEDk7AEsleyyFz2thZlFjLIXc3J7XRVRzwUR0yPYSA6gFjCDkfRUBSaYp8nVFXF0NBQRbe68kmHqbX43YVqYWAioranKAr6+/vR39+PLVu2yPWGYWBubg7T09OYnp7GzMwMPv30U0xPT+PKlStyu7yZR6aQQcbI2K1Sc2ksfLKAT41P5bVNqqZ6WqTcrVKhWGnOEAVLhyo3J2CVWhQsed2W51qTsvtrCVqlyWqdvYXcpvht3vW6/gGsluqhzBXCnC/jNb6Te76wly2m01kIy4KiqtCKwya7D9P37+LaToYYwBNgPMuBlVpqFGdZcT+nymfhCqGqbOFRAgcfZ74gVVFLXTurPF4rAajRhBAopAulViJXOMpezsrWYlVREQvFENfj6An12NMehOyWI2fobsCeQ3J4eNhzW79+PQYHB9njhajNsUseNdzCwoL8VY/DmdJSWlUv2WxWhignUDm3bHFSXCEEcmbODlGFtAxUGSODnJGTX871iF66VqovhmhvFJGuCCKJCMJd4Zrd/K6VE66qtlr5BC9nv2s67YtSkJKRQnjDlXAte/crD2hV36COYwAKRqG4bfXJHr1qBQWlIsCU9nE9JwNeWRhyrQvC3VK3VPCxA5WrNYhdtQLJ5XOwChZy6RyQB/JX8zIUOSHJLNgTICtQENEjdmtRMQw5XenCWlj+7ePxOEZGRrB+/fqKYMRBGNobv7t0Fl7DVMTARETXQgiBxcXFihA1MzODmZkZmKb9BcsSlqdVKmMUQ1Uhg4LlnSk+HA8j3BVGJBFBpCuCcCIsA5UTqrTQyl7ULZxrq0RpWT6WrVTu7mhVuqAF2XaVquxqqFTpauh9Xu5Xx7ae12ZLT0OZBRO5qzl5y6fypeWreeRSOXlNkSOshWVrkQxGoRiielSO2BcKhTyBaP369RgZGcHw8DCH7SZaIxiYihiYiKjRLMvC/Py87Nbnbp2an5+X25mWiZyZQ87IIW/m5XLOLD42chWhKhQNVYSpcMIbsvRw+/aiLnWD8/Sf8z5ffceK16kIHj45xL9rXyng0OojhICZL4ahVDH8VAlFRr40d6MCBSEthLAWRkSLIKJHENEiCOvFx1oEYS0su8oqioJ169ZheHi4osWov7+frXlEaxwDUxEDExGtpHw+j9nZWUxPT2Nubg4LCwtIJpOee/fp1hKWDFE5M4e8kZfLTtAqmAVPkNDDeqmlytU65b7XIzq/7NGqJYRAIVMoBR93IEqVWoacrnJAccQ5LWyHIb0UfpzliG4/ds/ppKoq+vv70dfXJ69v7Ovrw9DQENavX4+hoSHoevv+AEFEy8PAVMTA1DqGYcihXPkPEi2lU+rFsixcuXIFyWRS3pww5X7sdPkD7FDltFC5A5VcLgYrd6hSNRXhrjBC0RBC0RD0iA49qsvlUDQEPap7l8M6FLU9QpYlLOcSpo6Z9HS1EpZAIVuAkTNgZA25XMgWYGQNz3IhZ9/n03k5HxFg/zeUYcjdMlQWjtw/AoRCoYog5Cw7t+7ubpim2RHnFmqMTvm3iGwMTEUMTK1z+vRpOTSne8QyompYLyXO9VPuIFUeqpLJJAqFgmcfGaqK3f3yZh6GZcCwDBSsgrwvmAU5+IOboijQwppvqKoavGIhaGFtxVuzLs1fkhdmrxtYt6LvvVYJS8DIGyhkgoUfd5c4N03VEFJD0FUduqrLZafLnDschdSQp4YikYgn+FQLQ/F4vK6647mFgmC9dBbOw0RE1KYURUFPTw96enowNjZWdRshBNLptG+YWlhYwJUrV5BOp6sOtmAJyw5RZlmgMu17I22gcLWAvJVHykrBMO1t/IKWHtGrhiwtpEEN2ZOearoGVS9OgKqr9nPFZfd6Vbe3bZfWrlYQloBpmLAMq3Qz7Xv3etMw5XrnZuQNb/hx3VejKRp0zRV41BCiatRe7gpB7y49596uWsufqqqIx+Po7e2tCEPuUBSNRtmllIhWHQYmarienh4YhsEmbaoL6yUYRVHQ1dWFrq4uXHfddb7bCSGQyWSQSqWq3q5evYp0Ol2xXDNomYXqIcsyUEgVYCwayFk5pMwUTGHCEpZ9b1n+gzpUoarVw5SqqSiYBSiaAk3XcClxybtNlYDmCV/F0eqcv2NpuiTF81xp1PDSvvJvIkqPPevKJrX1DGjhhJyyAOMXbGTwMb2hyCyYgUYcdOYEUxV7yHJ3y09CTdhBJ6YjlCgFIl0rtQpVCz7u+gtya0UQ4rmFgmC9UC3skkdERJJlWTWDlt8tnU7XfF1nbignSFnCgmmZsGDPF+WsK9/Gs+0S21xrQFsp5QHGfdMU13q17HH588VtVKgVr+ferlZAURQF8Xg8cPCJxWJsASKitscueUREdM1UVZVfjoOwLEu2UqVSKeRyOeTzeRQKhSXvneWl1ltWZbdAP3JiX7hafZzn5DS6pZYgd8Aq39Y9/Lg7LMj1riHKq22rIPjEs6qqIhwOIxwOIxQKyXv3svv5etZHo1H537be64CIiIiBiYiIGkBVVSQSCSQSiaa9h2maFYGrPFyVBy6n61ytGwAZxqo9Lyeh9bk5nx+A7zZBAw97SBARrR4MTERE1BY0TYOmaYhGo60+FCIi6iAMTNRw58+flxdObtiwodWHQ6sc64WCYL1QvVgrFATrhWphYKKGW1xclHMZEC2F9UJBsF6oXqwVCoL1QrWwkzQREREREZEPDitODWeaplzWNK2FR0LtgPVCQbBeqF6sFQqC9dJZOKw4tRxPNBQE64WCYL1QvVgrFATrhWphEwwREREREZEPBiYiIiIiIiIf7JJHDZdMJmFZFlRVRX9/f6sPh1Y51gsFwXqherFWKAjWC9XCwEQNNzU1JYfm5EmHlsJ6oSBYL1Qv1goFwXqhWtglj4iIiIiIyAdbmKjhRkdHZbM20VJYLxQE64XqxVqhIFgvVAvnYSIiIiIioo4RNDswURAREREREflgYCIiIiIiIvLBwEREREREROSDgz5Qw50+fVoOzblly5ZWHw6tcqwXCoL1QvVirVAQrBeqhS1MREREREREPtjCRA0Xj8dhGAZ0neVFS2O9UBCsF6oXa4WCYL1QLRxWnIiIiIiIOgaHFSciIiIiImoQBiYiIiIiIiIfDExEREREREQ+eGUbNdzU1JS8cHJsbKzVh0OrHOuFgmC9UL1YKxQE64VqYQsTNVwymcT8/DySyWSrD4XaAOuFgmC9UL1YKxQE64VqYWAiIiIiIiLywWHFqeFyuRyEEFAUBZFIpNWHQ6sc64WCYL1QvVgrFATrpbMEzQ68hokajicaCoL1QkGwXqherBUKgvVCtbAJhoiIiIiIyAcDExERERERkY810SWv2mVYlmW14EgIgKdPaHd3dwuPhNoB64WCYL1QvVgrFATrpbNUywm1hnVYE4M+GIaBVCrV6sMgIiIiIqI21NXVBV2v3pbELnlEREREREQ+GJiIiIiIiIh8MDARERERERH5WBPXMFmWVXHxlqIoUBSlRUdERERERESrkRCiYpAHVVV9J65dE4GJiIiIiIioGdglj4iIiIiIyAcDExERERERkQ8GJqrbyZMncc8996C7uxuJRAI7d+7EsWPH6t7//Pnz2LNnD/r6+pBIJHD33Xfj3XffbeIRUystp16efPJJeR2i+xaNRpt81NRsi4uL2Lt3L7761a9iaGgIiqLgySefrLrtu+++i6985StIJBLo6+vDnj17cP78+brf6/Dhw7jzzjsRj8cxODiI73znO5iZmWnQJ6GVsFL1smPHjqrnnK997WsN/DTUTPXWyptvvonvf//7uO222xCJRKAoCi5cuBDovXhu6TwMTFSXt99+G9u3b0cmk8HBgwdx8OBBZLNZTE5O4vjx40vuPzs7i7vuugsffPABnnvuOTz//PPIZrPYsWMHzp49uwKfgFbScuvF8corr+D48ePy9sYbbzTxqGklXLp0Cc8++yxyuRx27drlu93777+PHTt2IJ/P4/nnn8dzzz2HDz74AHfddRdmZ2eXfJ+jR4/i61//OoaHh/HSSy/h6aefxuHDhzE5OYlcLtfIj0RNtFL1AgAbNmzwnG+OHz+O3/72t436KNRk9dbKa6+9hsOHD2NsbAzbtm0L/D48t3QoQVSHe+65RwwPD4tUKiXXXblyRQwODopt27Ytuf/PfvYzEQqFxIULF+S6y5cvi8HBQfHAAw805ZipdZZbL0888YQAIGZnZ5t5mNQClmUJy7KEEELMzs4KAOKJJ56o2O7+++8Xg4OD4vLly3LdhQsXRCgUEnv37l3yfbZu3SpuuukmUSgU5Lpjx44JAOKZZ55Z/gehFbFS9TIxMSE+97nPNey4aeXVWyumacrlp556SgAQ//nPf+p+H55bOhNbmKgux44dw44dOxCPx+W67u5ubN++HW+99RY++eSTmvu/+OKL+PKXv4zx8XG5rqenB3v27MHLL78MwzCaduy08pZbL7R21TPlg2EY+POf/4xvfvOb6OnpkevHx8exc+dOvPjiizX3//jjj/H222/joYcegq7rcv22bdtw4403Lrk/rR4rUS+0NtQ7nYzfsNH14LmlczEwUV3y+TwikUjFemfdmTNnfPfNZDL46KOPcOutt1Y8d+uttyKTyQS6LoFWv+XUi9stt9wCTdMwPDyMhx9+GFNTUw09TlqdPvroI2QyGd9zxrlz55DNZn33f++99+S21fZ3nqe1Ybn14n6dgYEB6LqOjRs34vHHH0cmk2nGIVOb4rmlc+lLb0IE3HTTTThx4gQsy5K/zhiGgX/84x8A7L7DfpLJJIQQGBgYqHjOWVdrf2o/y6kXANi4cSP27duHz3/+84hGozh58iQOHDiAV199Fe+88w5GR0eb/hmodZz68DtnCCGQTCbxmc985pr25/lmbVluvQDAl770JXzrW9/C5s2bkclkcOjQIRw4cABvvvkmjhw5sqxWCVo7eG7pXAxMVJef/OQn+N73vocf//jHePzxx2FZFn71q1/hv//9L4D6mrhrNZXX04xO7WO59fLQQw95Hu/cuRM7d+7EnXfeiQMHDuDpp59u2rHT6rHcc4bfNjzfrE3LqZff/OY3nsf33nsvbrjhBjz66KN46aWXsHv37oYcI60NPLd0Hv5kQnV55JFHsH//fhw8eBDXXXcdxsbG8O9//xuPPvooANT8xb+/vx+KolT95WV+fh5A9V9rqH0tp1783H777bjxxhtx4sSJRh8urTLr1q0DUL0lcn5+HoqioK+v75r35/lmbVluvfh58MEHAYDnHJJ4bulcDExUt5///OeYm5vDmTNncOHCBbz11ltIJpPo6urCbbfd5rtfLBbDpk2bql63cubMGcRiMWzYsKGZh04tcK31UosQgl1jOsDGjRsRi8V8zxmbNm2qOSfXzTffLLettr/zPK0Ny62XpfCcQw6eWzoXzwIUSCQSwc0334zx8XFMTU3hj3/8I37wgx8gFovV3G/37t3429/+hv/9739y3eLiIl544QV84xvf8Iw2Q2vHtdZLNSdOnMCHH36IO+64owlHSquJruu477778MILL2BxcVGun5qawpEjR7Bnz56a+4+OjuL222/HH/7wB5imKdefOHECZ8+eXXJ/ai/LrRc/v/vd7wCA5xySeG7pXIoQQrT6IGj1e++99/CnP/0JX/ziFxGJRHD69Gns378fN9xwA44cOYJEIiG3nZycxNGjRz1Dhc/OzmLLli0YHBzEr3/9a0QiEezfvx///Oc/cfLkSWzevLkVH4uaZLn1smXLFjz44IP47Gc/Kwd9eOqppxCPx3Hq1KmaF2/T6nfo0CGkUiksLi7ikUcewf33348HHngAgH3tSDwex/vvv4+tW7fiC1/4Ah577DFks1n88pe/xPz8PP71r39haGhIvp6u65iYmMBrr70m173++uu4++67cd999+FHP/oRZmZm8Nhjj6G3txenTp2qOoojrU7Nrpe///3v2LdvH3bv3o0NGzYgm83i0KFDePbZZzExMYG//vWvbGVqE/XUyuzsLI4ePQoAePnll/H73/8ezzzzDIaGhjA0NISJiQn5ejy3kNTKSaCofZw9e1Zs375dDAwMiHA4LDZt2iR+8YtfiKtXr1ZsOzExIaqV1rlz58SuXbtET0+PiMfjYnJyUrzzzjsrcfi0wpZbL9/+9rfFpk2bRFdXlwiFQmJ8fFz88Ic/FBcvXlypj0BNND4+LgBUvbknkDx16pSYnJwU8Xhc9PT0iF27dolz585VvB4AMTExUbH+1VdfFXfccYeIRqNiYGBAPPzww2J6erqJn4yaodn18uGHH4p7771XjI6OikgkIqLRqLjlllvEvn37RDabXYFPSI1ST60cOXLEd5vy8wjPLeRgCxMREREREZEPtjETERERERH5YGAiIiIiIiLywcBERERERETkg4GJiIiIiIjIBwMTERERERGRDwYmIiIiIiIiHwxMREREREREPhiYiIiIiIiIfDAwERERERER+WBgIiIiIiIi8sHARERERERE5OP/AkWQyhipF3UAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P5 = multivariate_multiply((10,10), P2, (10.1, 9.97), P2)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10.1, 9.97), P2, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse(P5[0], P5[1], ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hidden Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can already see why a multivariate Kalman filter can perform better than a univariate one. Correlations between variables can significantly improve our estimates. We can take this much further. **This section contains the key insight to this chapter, so read carefully**.\n", "\n", "Let's say we are tracking an aircraft and we get the following data for the $x$ and $y$ coordinates at time $t$=1, 2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_position_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that the aircraft is flying in a straight line and we know that aircraft cannot turn on a dime. The most reasonable guess is that at $t$=4 the aircraft is at (4,4). I will depict that with a green arrow." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_position_prediction_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You made this inference because you *inferred* a constant velocity for the airplane. The reasonable\n", "assumption is that the aircraft is moving one unit each in *x* and *y* per time step.\n", "\n", "Think back to the **g-h Filter** chapter when we were trying to improve the weight predictions of a noisy scale. We incorporated *weight gain* into the equations because it allowed us to make a better prediction of the weight the next day. The g-h filter uses the $g$ parameter to scale the amount of significance given to the current weight measurement, and the $h$ parameter scaled the amount of significance given to the weight gain.\n", "\n", "We are going to do the same thing with our Kalman filter. After all, the Kalman filter is a form of a g-h filter. In this case we are tracking an airplane, so instead of weight and weight gain we need to track position and velocity. Weight gain is the *derivative* of weight, and of course velocity is the derivative of position. It's impossible to plot and understand the 4D chart that would be needed to plot *x* and *y* and their respective velocities so let's do it for $x$, knowing that the math generalizes to more dimensions.\n", "\n", "At time 1 we might be fairly certain about the position (x=0) but have no idea about the velocity. We can plot that with a covariance matrix like this. The narrow width expresses our relative certainty about position, and the tall height expresses our lack of knowledge about velocity." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now after one second we get a position update of x=5." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This implies that our velocity is roughly 5 m/s. But of course position and velocity are correlated. If the velocity is 5 m/s the position would be 5, but if the velocity was 10 m/s the position would be 10. So let's draw a covariance matrix in red showing the relationship between the position and velocity." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It won't be clear until the next chapter how I calculate this covariance. Ignore the calculation, and think about what this implies. We have no easy way to say where the object really is because we are so uncertain about the velocity. Hence the ellipse stretches very far in the x-axis. Our uncertainty in velocity of course means it is also very spread in the y-axis. But as I said in the last paragraph, position is correlated to velocity. If the velocity is 5 m/s the next position would be 5, and if the velocity is 10 the next position would be 10. They are very correlated, so the ellipse must be very narrow. \n", "\n", "This superposition of the two covariances is where the magic happens. The only reasonable estimate at time t=1 (where position=5) is roughly the intersection between the two covariance matrices! More exactly, we can use the math from the last section and multiply the two covariances together. From a Bayesian point of view we multiply the prior with the probability of the evidence (the *likelihood*) to get the posterior. If we multiply the position covariance with the velocity covariance using the Bayesian equations we get this result:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The new covariance (the posterior) lies at the intersection of the position covariance and the velocity covariance. It is slightly tilted, showing that there is some correlation between the position and velocity. Far more importantly, it is much smaller than either the position or velocity covariances. In the previous chapter our variance would get smaller each time we performed an `update()` because the previous estimate was multiplied by the new measurement. The same happens here. However, here the improvement is markedly better. This is because we are using two different pieces of information which are nevertheless correlated. Knowing the velocity approximately and their correlation and the position approximately allows us to make a very accurate estimate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a key point, so read carefully! The radar is only detecting the position of the aircraft. This is called an *observed variable*. Based on the position estimates we can compute velocity. We call the velocity a *hidden variable*. Hidden means what it sounds like - there is no sensor that is measuring velocity, thus its value is hidden from us. We are able to use the correlation between position and velocity to infer its value very accurately.\n", "\n", "To round out the terminology there are also *unobserved variables*. For example, the aircraft's state includes things such as as heading, engine RPM, weight, color, the first name of the pilot, and so on. We cannot sense these directly using the position sensor so they are not *observed*. There is no way to *infer* them from the sensor measurements and correlations (red planes don't go faster than white planes), so they are not *hidden*. Instead, they are *unobservable*. If you include an unobserved variable in your filter state the estimate for that variable will be nonsense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What makes this possible? Imagine for a moment that we superimposed the velocity from a different airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the measurement of the position is not in the direction of the velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. \n", "\n", "It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurements, and use Bayes theorem to produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you do not understand this you will quickly find it impossible to reason about what you will learn in the following chapters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Higher Dimensions\n", "\n", "So far I have shown you two dimensional Gaussians, but the math does not limit you to two dimensions. In later chapters we will be working in 9, or even 12 dimensions. If you work in areas such as weather prediction, you can end up with thousands of dimensions.\n", "\n", "What do these higher dimensions 'look like? Well, a two dimensional Gaussian can be represented by an error ellipse, so it stands to reason a three dimensional Gaussian could be represented by a 3D error ellipsoid. We won't delve into the math here, but this turns out to be true. `FilterPy` provides a function to plot this ellipse.\n", "\n", "First, let's make some noisy data with a given covariance, just so we can plot it inside the ellipsoid." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import plot_3d_covariance\n", "\n", "mu = [0.3, 5., 10.]\n", "C = np.array([[1.0, .03, .2],\n", " [.03, 4.0, .0],\n", " [.2, .0, 16.1]])\n", "\n", "sample = np.random.multivariate_normal(mu, C, size=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the ellipsoid with the `FilterPy` function `plot_3d_covariance`, and then scatter plot the samples." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plot_3d_covariance(mu, C, alpha=.4, std=3, limit_xyz=True)\n", "ax.scatter(sample[:, 0], sample[:, 1], zs=sample[:, 2],);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Theory states that roughly 99% of a distribution will fall withing 3 standard deviations, and this appears to be the case.\n", "\n", "Nine dimensions? I haven't quite figured out how to plot a 9D ellipsoid on a 2D screen, so there will be no graphs. The concept is the same; the standard deviation error of the distribution can be described by a 9D ellipsoid." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "We have taken advantage of the geometry and correlations of the system to produce a very accurate estimate. The math does not care whether we are working with two positions, or a position and a correlated velocity, or if these are spatial dimensions. If floor space is correlated to house price you can write a Kalman filter to track house prices. If age is correlated to disease incidence you can write a Kalman filter to track diseases. If the zombie population is inversely correlated with the number of shotguns then you can write a Kalman filter to track zombie populations. I showed you this in terms of geometry and talked about *triangulation*. That was just to build your intuition. You can write a Kalman filter for state variables that have no geometric representation, such as filters for stock prices or milk production of cows (I received an email from someone tracking milk production!) Get used to thinking of these as Gaussians with correlations. If we can express our uncertainties as a multidimensional Gaussian we can then multiply the prior with the likelihood and get a much more accurate result. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n", "\n", "- [2] `FilterPy` library. Roger Labbe.\n", "https://github.com/rlabbe/filterpy" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.6" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "085fcd724d9847049501c96196f0fde6": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "1.2.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "1.2.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border": null, "bottom": null, "display": null, "flex": null, 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