{ "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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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[10.888 2.922]\n", " [ 2.922 2.259]]\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 1.003]]\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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oDIyyUQE+QYwXEiMEMWUk2e+GVx4ty4KmaVhfX4eqquKBXygUhBjhtSF+wv0LThv/A3sS+4wcB8uycHh4CKD3PZEYCSLLsrCDjmvmR0wnsiz3NbSYnZ3F7OxsbERCkiQUi8XYYnwgGHEJT/A7nY6IBqdSqYAYcRwHb775JhRFQS6Xi0ROeF+YuFRWKsAniNFAYoQgpoC49KtBD61arSYEx+rqaiDKkUqlMDMzg2w2O5EOT+l0Gqurq5AkKTb1Y9wcZ7Lgfw31GYmiKMrYRTAxHuLuJ03TsLS01Pc11Wo1ED3xk1THYlmW+BM3tjx48ACdTgeyLGN9fT1wbqZpijoWTdOOLViA4Qrw/WlhPNJCURbiLEJihCAmEH/6VTiXOfwQcl0XrVZLOF1x/IXnuq4HUjsYY4m9DMaNoigTlYpyEqRSKVy8eLFvfwmCIIbHbyseZm5uDqVSCa1WSzR6LJfLmJ2dFf1ZXNfta3HMCU/2dV3H3t4egF7Bv38hx3Ec7O3tiRqWQSmux4myxIkWKsAnzgL0RCSICWFQ9/M4dnd3sb29Ddd1cfny5UDqTy6XQzabRT6fT3xwE0fnOJENWZbPjfUxMTq4OxVjDMVikYRtDDw1jEeS/TUr2WwW165d61uwnslkYFlWbGpZUlNJy7JETVipVIqIkYcPHwoDkYWFhciCUlyk4zhRljDhAnwuVOIiLQQxLmgUI4gxcpT0q263C03TAtsURREPWV3XA2KEMYb19XXYti1yqFOpFOXjE8QU02w2Re1RNpslMZIAtzJ2XTciLvrZmydZHBcKhb4F94Msjg3DgG3bkGU54hS3v78voipLS0sBIeO6LjqdDhRF6WvLPqzNcdyzxn+MpAJ8irIQo4RGMYI4RY6SfsXZ399HrVaDaZq4du1aQEzwh2M+n+9b+2EYhrDIrFarU2GZyj8j/vn0641wmoQf3rwPws7OjnDtCReln6b96rTT7XaFtW+xWKT6kT6ExwyiP9lsFleuXDmx4yVZHGcyGayursZaHPPxDIgXKlzI8OJ5P6ZpYmNjA0C85TWPxqiqmmiKEVeTEsewBfhhm2MqwCceBxIjBDFijpJ+xfOZwz/jTc50XQ+IEVmW8VM/9VOJg3+cte+k43keXnnlFQC9CcX6+vrYzqXRaODw8BDNZhM3btwINGAzTRPtdhtAr+A2PBm4ffs2GGNIp9NYXFyEaZqiwzVfqY1zAzqP8HQaYHqu03FQLpeRy+VEjw1iMpBluW+dCGNMpIbFXdu8yedxIi57e3twHAeyLOPq1auBbfV6Hc1mE4qiYGZmJiCS+i2UjMLmmArwiUHQSEYQI+Co7leHh4c4ODhAq9XCjRs3ApGAYrGIzc1N5HK5WPeXQQO6pmmoVqtTVbMwSc5T9XpdpMU0Gg2USiVxfkkTBf/kmuevv/nmmwB6ES1JkoT96NraWsB+1LZttNtt4dpzHiad/sL+fik0RM9pjlItpw+e+hRXizI3NxexV+eoqoqZmZlYi2N/xCUuemwYBprNJoBos9put4t79+5BVVWUSiVhq+3fLkkSFEU5tmhJirLw15LNMQGQGCGIE4ELDh4BCQuQ8OQ6zhefPzQajUbgwaBpGp588sm+Xv2D4E0MpwlenAtgYMOyk8A0TdTrdbRaLVy6dCnw/RSLRRwcHECSpIjTTrlcFr0Qwt+P4zjQNE2sdoavAb8taVhsGIYhmj7Ozc1FeiHs7OxAlmVomjaR1szHIZVKjTUCRhCTSCqVwvz8fN/tKysrsG07dtKetFhi27ZINfVHa7a3t9FqtcT4pChK5L5st9uwLEs4h/V7Np2kzfEgwUKiZbohMUIQx2RQ+lV4cOSFp81mE9evXw+s/haLRdRqtb61EccVItPMpUuXTu29Hj58iEajAaD3oPXnhefzeaytrSGXy0VW7JNWOxVFweXLlwE8EqvlchmMMZGSwRiD4ziR4yZNIlzXFXni6XQ6IkZ2d3dFwevc3Fzg9eF0CoI4y+i6jk6nA0mSUC6Xz1yEkTHWt4YFAJaXl2Hbduxiied5UFU1khrGe7Bw4j4zXddFVPfSpUuBY3e7XVGMn8/nB1oc89/D/3ccPAo0jM0xFeBPH2frziSIERNOv+IMM8DV63UxiWw2mwG73Uwmg2vXriGVStFgOSI8z0Or1UK73Y6sNBaLRSFGWq1W4AEvSdJjRx/4A3JhYWGo/TOZDKrVKmzbjkSGhnHt4XUs4SLwZrOJzc1NIVTCls9cxFAdy+TCV7T5hIu+p/60Wi3oug7gkdnHeYK7icUtchUKBRQKhUgaLB+rPM/rmxqcNAaZpinG0rg6mjt37gTq6MLH9RfHh8/L/3c/qAB/OjlfdyZBHBF/+tXGxga63S4YY5FUHk6n04Gu62i1WlhbWwvsUygUsL+/D8aYKEjn8MH5NH6f8zrQ3r17N5A/7Z/kF4tFOI6DQqEwEfn4SXUBiqLg4sWLsaudwKPCUv9qIIdPZC3LikxCXNcVNS2ZTAYXL14MbG+1WqJRXDqdPrfX0bjhHcIB4Pr162M+m8nGH7GmOqR4wvfx8vIygORnRaVSQS6Xix2DBtXR8Wdf3LF3d3dRr9fFM/Y4dXSjKMDnwp8v1BAnD4kRggjBByd/oyygt6rMxUi/gW57e1usxBmGEVgVyufzuHTpEvL5/Kk/GF9//XWYpinct84ytm3DMIxINCOfzwsxout6IGqgKMrUWMlKkpRoRHDp0iURvYtbXdQ0TeR7+xkUcdnf3xcRl6tXrwYeyoZhQNd1kZpxnDofy7KEUUAmk0m0KT3PkLXv8MzPz6NSqcT2GSGSSbq2stls3/SrUqmEXC4Hy7IiURXHcfr2aQEg0sM8z4t8X8PU0UmSBE3ThmryO2wBPr/f+LlJkhSbsks8HiRGCAKP0q/irBf5YMUHR8/zsL+/j06nE2mQVSgUhBhpt9uBAVuSpLF1Que/1zRNXjY3N2EYBlzXxfr6+lDnvrGxISa04aL/YrEIwzBQLBbPTNF3HNyVKu5hXy6XUS6XAURdyhhjKJVKsa49wCOxEhdx6XQ64nPnNqUc13Vx7949KIqCbDYbce3h16Vt29jf3xfnSWIknlwuNxF9d6aBfilKxOjggiAuvYsXw/ujEX74Igu3KvYzKOLir6MLP2drtRoMw4CiKJifnw+8nj/vk5pJ+s912p6j0wKJEeLcwifow9rvXrx4EYwxvPnmm3jw4AEAYHZ2NpLu43keCoVC7GA8Lnjn9mlaHex0Omi1WgAQWdnkkavwRMP/kNF1HTMzM+L/qVQqknp02ty5cwee50HTNKysrIz1XMLX+SDXtbm5OdEnJfxaf8Fr+DuxbRvdbldYhYZ58OABDMMIfL9+62S+ikr1ET2mJYJHEP3o95ztZ28M9ITK3NzcseroOp0ODMMAgEjdXqvVwsOHDyFJEqrVqlis8W/nFsfnreboNKFPljg3hNOv/JOqOPvddruNTqcjwsF8klUoFES6SqPRCAyMiqJEwseTAHd1mib69RrZ3t7G4eEhbNvGE088EXEl03UdxWJxInuq8FqNaZxUJ0WTKpUKCoVC7ESB52YD/btP88jkyspKoN+Iruuo1WoAgMXFxUCvBNd1Ua/XRQ75aVhAE8RZhkcnZVlGOp1OdOo6bQbV0V26dCm2gz0QdBHs51wYF/H467/+a3z7299GtVrFysoKnn76aSwvL0d6tjwO3/nOd/D1r38dL7/8MjY2NlAul/Gud70Lzz//PN75zncmvvarX/0qfv3Xfz122+bm5lRZ+pMYIc40SelXSTmft27dEisp5XI5sGpbKpXgOA6KxeJQtoXE8VhdXQWAiLOKaZqiCLLVagUmydlsFtevX5/Yyb4sy7H50NNO0qphJpPB9evXA6LEj6qqoit9ePLjX/GMi7js7OwA6AmlcMrk7u4uHMcRTeMm9ZogRodhGCIiTOlag7EsS6Q7lcvliRIjSQwygLl48aLIggiPA7wZcFykvV6v45VXXsHf/d3fYXd3F7VaDaZpolwuY3l5GRcuXMDy8jL+4A/+4NgC5Stf+Qr29vbw0Y9+FE8++SRqtRpefPFFPPPMM/jWt76FZ599duAx/uiP/ihSCzqJi6JJkBghzhxH6X5umia63W5k1TeXywkx0mg0AqHbVCqFpaWl0f4S55zDw0PU63V0u11cu3YtsK1YLOLw8BC5XK6v/eNpcJz3Oq9N/fzRjjBJ6WqZTAau68ZOFAalZui6DsuywBgLpOsBvevr8PBQRDL9UTQ+ZlCB6vSzsbEBz/OQSqWwtrY27tOZePwLBmdtwYRb94YpFot9azl/5Vd+BT/3cz8n6uh45P3g4AAPHjzAw4cP8eDBg8eKwn/pS1+KWM0/99xzuHr1Kn73d393KDHy1FNP4V3vetexz2ESIDFCTD188sAFiJ+kGpDbt2+LfNC4dB/LslAoFEQhrWmaMAwDjuMgm81OhAXsWeXg4EA4X3U6ncBgXygU8MQTT1D+7jmA90KIQ9M0LC4uxhbc83RMoBdRCY8BfBGi2+1GCuoty8KdO3cgSRJKpVJkosBX21VVje2HMGo2NjYADK7xOe/4i6RJWA5HJpPB6uoqHMeZqJrHcRGXdl2tVnHx4kU8/fTTJ/Ie4fEF6Dk/Pvnkk+JePw/Q05yYSgZ1P/fjui5M04xMWPhKq+u6aLfbAfeeXC4XCVG3Wi3cv38fALC0tDRVYkTXdTQaDbiui2q1OhHnznuymKYZWR0vFotoNpuQZRmmaQbESL8VrtNmWms/JhXXdUUhPPf0T0JRlMTUiMuXLwcK6/34a5D6WRyHxxXO5uYmLMuCJEmRqF273Ua32xXOYaNYXeb1alQjk4zneZiZmYHrujSxHpK4JoVEkNMY8+v1On7wgx8MFRUBehGcWq2GUqmE9773vfid3/kdPPXUUyM+y5OFxAgxNRwl/Yrvf+/ePTQaDSiKghs3bgT2LRaL6Ha7KBaLQz2s/BOLfvnvk4phGAHb1EkQIxsbG6J528LCQiANp1QqBRyVTNOcuAkFCZGTpdPpiJXAmZmZ2BXDYUnqPA30rrf5+flYC1EAfXPI/RGXOLHUbDZFzv3q6mpgYmdZFmq1mhAqx7Euph4jwyNJ0mNdQwQRx2kshH34wx9Gq9XCJz7xicT9FhcX8YlPfALPPPMMisUifvjDH+Lzn/88nnnmGXz3u989sejNaUBihJhY/OlX/uZDQLz7FW+o5N+Hv86yrEi6T6lUOlLRWTqdxuLioih4myb8A+hpCinXddFqtWCaZiTcXSwWhRhptVqBuhzeGGt7extArwBxksTIcSeC3AUMSLaxJEZPvzqWbDabaAFdqVRim0YCyXUspmmi0WiI/4fFyL1798QqfrgYnxfeSpKE69evx/ZoIAhi9Ix6EeBTn/oUvvGNb+CLX/ziQDet5557Ds8995z4/3ve8x584AMfwNvf/nY8//zz+LM/+7ORnutJQmKEmCiOkn7F99/c3BTdn69evRrYzie8hULhsVc0NE2bWo9/7owiSdKpusq88cYbomt92JWM/79fZMr/fZ2VydfBwQFM0wRjjMRICH/a1aSK/UHf28zMDHK5XGyH6SRnMM/z0Ol0+jaD29vbw8HBASRJwurqaiCy6TgOOp0OFEURdSwEcRy63S6AXhYA9fWJf+6M8v564YUX8NnPfhaf+9zn8JGPfORYx1hbW8PP//zP43vf+94Jn91oITFCjJ2jpF+F8/QZY2i1WrAsS/zxP+hnZmZQqVTO/aA66k7ElmXBNM1InU0ul0O324XneWg2m4FIVCqVSsx7z+VyuHDhAiRJOjN5zHEdfYkevCB9mslkMn2FVKFQSEz/kmU5VsQAwTqW8GSo0+mIWrZKpRJZMNnf3wdjDJqmTY1VKzEetre3hYvktWvXzv1zM45RfSYvvPACbt68iZs3b+LjH//4Yx1rGt0ASYwQp85R0q+A3gN4b28PjUYDsizj0qVLge289iOXy4m+ApxpuyGnDc/zcPfuXVFs/sQTTwS+v1KpBNd1USwWj5wjnzSxmwQYY0cWFfPz87HNtYizjyRJ0DStbxRwfX1dRIbDaJomhExSxCW8zfM87O7uwvM8aJoWaX56cHAAwzCgKGLNlU0AACAASURBVAoqlcqZcqhrNpvY3t6GJEmYnZ3ta99KPIKn8MY1ByR6jGLs/sxnPoObN2/ik5/8JD796U8/1rHu3LmD7373u3j/+99/Qmd3OpydkYeYaDzPg2EYaLfbsCwL+XxeiIZBNzdjDLu7u7BtW9SB+AfK2dlZzM3NnZovelx9ynmAF+/6xZ7/oeU4DtrtdmD1NZ/PH6tQdxo4TnTjrER4iNHAG/SF4alhjuOgXq+LdMtsNotUKoVKpQLbtiORRv9iT9x41W63hYV2uBdLq9XC1tYWFEVBuVyO1NdZlgVZlid20uo4jhBq02Y4Mi6KxaJoKEtESTLMOS4vvvginn/+eTz33HP4wAc+EEmveuaZZwAAH/rQh/C1r30Nt27dEguy73//+/Ge97wH73jHO0QB+xe+8AUwxvCZz3zmRM9z1Jyv2RRxqoTTr2q1Gmq1GoBeXqN/hdB1XTQaDVH74W8qyBhDsVjE/v4+VFWN2PSepih49dVXYZomFEXBE088cWrv+7i4rotOpwPXdY9cgO+vy+EFtH78rmTU5ZggRoe/63yxWBT9jvq54zHGsLKyAtu2Y0VOUlTFtm3xJxyt8TwPd+7cged5yGQykYJ/wzDgui4URYGmaWOLBMqyHJvaRsQzbV27T5tRXEff/OY3AQAvvfQSXnrppch2vpjgn0tx3v72t+NP/uRP8Hu/93swDAPz8/N49tln8alPfSrynJ50SIwQJwZPv+IF6OH6D//Dzv8Q5Ny/f19MlhcXFwMPsLm5OczNzY3dW5+f07SttFmWhVu3bgHoFY6vrq723TeuLscwDNGzodvtBr6HcrkcWVU9Kfj1RGkDZx/DMIR7WqlUGtk1Nc0c1dpXkqTEOpHV1VUhOMLH43UscVFg/6Qo7r7c398XEZcrV64EFim63a6wW89kMiMb0/1uiVSjRZwEoxDVf/M3fzPUfl/96lfx1a9+NfCz3//93z/x8xkXJEaIx2KQ+5X/5s1ms5iZmYFlWcK1gyNJEvL5PHRdh+d5ME0z8JAatwjhZDIZ4TQyTU3vBln7ep6Hg4MD8fmHc8uLxSIMw0AulxvK5ewkaLfbQkDNzs5G7E7HzXFqRvgqM8/hn5br5zRwXVeMC3GLFcSjruv8+nlckupYyuUyyuVy32u8UCjEpoYByRGXTqeDvb09AL0aKv/rPc/D/fv3RfQ2LEiPO+bSfUYch/C1Twtio4PECHFk/MXn/onpoAFf0zTREMyyrIhzTrVaRaVSERa0k0hSRGGSkWUZlUoFsiz3FXa1Wk3kC4cLZSuVinj9aeG/Bvp1w542tre3xYrx+vr6uas7SsK/eEGTx3hkWT5Sb6STIO67UBQlcXGgXC7DNM1YswYeYeXH8cPrzoDePR8WI5ubm6LgfmVlJdKIlkdxJvX5QUw3NC6NDnoSEgMZlH4VxrIsEYb3O5jwzsPtdhvdbjfSVZuKe0eHJEm4cOECOp0OdF3H1tZWQAzyupzd3V0oioJutxuYKJymCPGfczabBWNsYiJjj0u4USdxF6r6EiTp+9C0q8hm/ysAZ+O7Ps8kCaZSqYR0Og3btiO1LkkRFaD3bOFpZWHB0Ww2sbW1BQBYWFgINFH1PE/UI6qqOlENVCeFdruNra0tyLIca1hAkBgZJSRGiFi44PCnlfhXLfvdlKZp4tVXXwXQ6xMRtlOcm5uD4zgoFApU7DwG7ty5A8dxIEkS5ufnI65kvCh2EgZdTdOwvr4+7tM4UbhxwChcWSYbC5L0t1CUv4Is/ztI0i0wtg/GgimDmvb7cJx/D93uZ+C67xrTuRKjJKnnUTqdxrVr1/qm6fmb8Q2KuNTrdViWJVKAuVDJ5XJYWVkJvPbg4EBEVYrF4rmMrNi2LXp1TVtN5GlxHq+L04LECCHol34FRG9C13XRbrcjDel4/rFpmmi1WpF0n1Kp1NdLnzgZXNdFs9mE67qB1UHGGAqFAg4PD+G6rqgB4fTLHSfi4TbTRxEVMzMz56ww24Mm/zNomT8GY4PrQBgzoSjfhSw/C8+rwjR/A5b1MQC0cAEgEJUGzuZKLa9jiYOLiLiooqZpyOfzwn784OBApHz5I6txERdd19HpdABEozqNRgOHh4fC4tjvRMjP4yx8D7xRHjeROe/EXWNn4XueVEiMnHOO0v2c0+l0cOvWLdHMLtyEcHZ2FrZto1gsRgY1bo2raRpu3Lgxkt9plDSbTbGKNjs7i0KhMO5TCuC6Ln7yk5+I5o+lUinwXVYqFWSzWbLhJU6BLeSUX4KkvQkc8RnOGMBYDen0f4dU6vfgOD/3VrTkZ0ZzqlNCo9HA5uYmgF7x9/kSto+Iez4Vi8VAJN6/4KVpGubn52NTw4BHURVFUSLH7na7QtSEx3vHcXDr1i0oioJCoYD5+fnAdtM0hZPkpE9kufsYpY/2hyIjo4PEyDnjqOlX3W4XjLHASlUqlRL78RV4/03KG3QlMa1uOZZl4fDwEECvod84xQgPqfsjU5IkIZPJoNlswrIsdDodsZJ37949tNttOI6DSqUyrtOeejzPE7U3kiRRbnUMCv5XpJV/CiZbwGMusjLmQFH+DjJ7L0zzozDt3zmZk5xCjmrte55ZWFgQkX5VVROFG+/FEjcR96csxfVi4X/HRfs3NzdFxOX69euB76zT6aDb7UJVVaRSqYmJRtB11R/6bEYHiZFzwFHSrzidTgf37t1Dt9tFpVLB8vKy2MYYQ7lcFrUfRyGdTkOWZSiKMlXWuJywe8s4cF0Xt2/fhmEYIsfaz8zMDFRVRbFYDKQnOI4jVgCnJRR///59kcvtvwbHia7ruHfvHoBe/nlYjGxtbYnGmIuLi4F77CyldcTjIS3/EyjsT8EYTiy7yvMAZnnQ2B+AqTvoWv/yZA48ZciyjGw2C8/zyIltAP0aQR5134WFBczNzYn0Lz+e5yGVSkXSkTlJEZdmsyksjpeXl5HP58U2x3FQq9VEL5akXjHE6XD+6vxOFxrNzihHSb/i+/gHU97pHOilBoSFw3F7PoRTuqaNXC6H69evi0LKUcO/R/9345/cdjqdiCsZ7w8QRlEUYXs5LaF4XdfhOM5Yalk8z0O73YamaYFJSD6fFz1G4lLd+IonACwtLQW2bW5uotFogDGGubm5QITK8zzhYsaLdKeLu8gpvwyJ9QqFoaBvepbnAZ6XhSS1Bx/WA9CRAeaAAdDwP4OpNXSs/6X/G5xR8vl8YNJKnA79xvtMJoO1tTUA0RoDz/NQLBZFEX2YJOcwy7JQr9cB9NKnwmLkwYMHIuKzsLAQ69I3fePHZEOf52ghMXJG4IKDCxA//URIp9PB5uYmWq0WqtUqFhYWxDZZlpHP5+E4DorF4lRGMUbBaYkQ13WxubkJXdeRTqdjmxDyh92w38s09kiRJCm2oeaoaTQauH//PmzbxsLCQiAXXJZlzM3NQZKk2BVVfq6qqvZ1/OH3qx/btvHmm28C6E06w5Eg3p9EUZRAquQkoLCvIS3/s0fuWAyJ6VmelYakDSFEAMBExHVLwV8ioz0Lw/w3oOJ2YhII34+MsUgNiZ9isQhN02IjLn5nsLgFD8MwxCJV+H339vawv78PRVGwtLQUKLjnjUX5wpT/tfv7+/A8T1j7EkGoXmS0kBiZYgZ1Pw/vy90yOLIsiwmOrusBMQL0ohiTNOE5y4TFHmMMjUYDtm2j1WrBcZyACKpWq4kPurPClStXwBgb6YOA3zv+9+CpF0Dv3gh/1ouLi3AcJ7b26cqVK+K+DBO+//wM6rHgb0p5/fr1wLZWq4V2uw1FUZDP50/VnCCF34Iqfx2BoUJFNGjhAp6TA7otSHKnl3o1YHjxnN7rwvsxALL775Bh74XhvgSwyTKSIMYLjzJKknRqC0hHJZvN9u2tlcvlcOnSpb6pYXzMihsneO2LZVmxNaA8xbRcLgee+YeHh+I1mqad+75f4cUimguNFhIjU8ZR3a+63S52d3fFhGp2dlZsU1UV6XQajuMgl8vFToiJ0eG6Lg4ODqDrOlRVDXjf8yaE+/v7KBQKETFyXr6bUaZnGYaBWq2GRqOBpaWlQMoUfxjzvgNHjQxKkhQroPh3HHcsXgzfz/GHi5W4iEu73cb+/r44d/8ExrZtbG5uQlGU2N4/j4PqfAFqKiREJPRSq0wADgAL8GyAeQBDC3B7+zADcNMZSCkjPoriAcxE30wsxgBF+SGy3WfQxt8ArHpivxcx3TiOI6KMcX1FJp1+UVegN3Zcu3YttgYU6AkUHnHpV3DP94vb5nkeNjc3Iz2edF1Hu90W9YjnzY2RIiOjhcTIhMMFB/dMtyxLFMUOU1Dluq6YpOi6HhAjAHD58uVTzU83DAN7e3uwbRszMzNT6UTUbDbFqvfjnv/W1pYoJg9PeOfn5yMF0MTJ4XmeyMvWdT3iMMajMidJ0vFSqRQWFxdjt3meh/n5+djVTiB5kmGaprAmlSQpIkbefPNNkX8enrTx6zxuZVm2/xIp9XeFEPE8BrgyWCsaLQqcsffob8kwAAO9SEoKgObbOUGIBM4jtYFc999HC98B2OXBL5hi6vU6ms2mqDmivkDx+CfpZ3H8ZIz1jfjMzc31dbRUVRXlchm2bQfMTYBeEf39+/cBxEdcWq0WdF0H0BN4fjHCU7754k34ucgb7U7zIto0n/s0QGJkAolLv9rb2xMDQbVaDQxCpmni8PAQuq6jWq0GBoJ0Og1VVWHbtihc9t9Up+3IYts2Dg4OxLlNoxjZ2NgQ4fNB5+95HgzDgK7rUBQl8JCQJAmFQgH1eh2SJME0zYHNuR4HwzBQr9fhum5sUeRZxLZt6LqOer2Oubm5gPtbJpOBqqpiIj7JkUHGWOK1Njs7K4plwyuWfqESt5ppmqaw+Q6zv7+P/f19SJKE5eXlR6kb7l2k8Y/BlLcmfQ7AGm/VwQyaH8fNDa23/jA8EiUuhq5Pl1J7yHV/Hob3Elzp7cO9aArpdrsitfa89hgZBh5ldF03UDNx3kmn030jLplMBktLS7BtO1bkJI0jlmXBNE2Yphmb3nXnzh24rot0Oo2LFy8GtnW7XTEGT7Jxx6Se11mBxMiEMCj9Kpx24V8R63a72N7eBtBb4fVPWhhjuHTpElKp1ESsEPkn2OOyxn1cZFmGbdtDnT9vigX00mdmZ2cDg1q1WkW1WkU6nR75YNfpdFCr1QD0VuGnQYwYhgHTNEWx/lGv4Xa7jQcPHgDo3UN+McIYw+XLl6Fp2rE++0l6OGma1neVvFAoIJfLxU4yXNeFoiiwLKtv/jnfT7zW7SJn/hKkfKsX5egCaPU2MWXAPfFWilZfPAAdAG0AaRypNl1KNZBp/xIM71/Dld8z/AunCOozMhzcVpsYnrioqR8uVOLcwVzXFQ6D4XHEXz/Xb8GDL7Sura0FFuQsy0Kj0YCiKEin02ONBE7C/OksQ2JkArBtWxSdcQESftDwQaLT6UQmwblcDpIkwXXdgAsHZ5JWhlKpFK5evSrcPKaR2dnZSGqV4zgifcI/oPM8/VarBdM0YVlWYEA9ze/GP5ietjvVcanVaiKV6saNG30fRqZpQtd15PP5wMpfPp8X94ZhGJHoRzhV4Sgcxx7Z3805m80+1vsPS1JKhyRJuHz5cqy7F/CodsYfccl23w8pu90TDk30IhrigANOZtiPzAGgA8ijFykZBguQzDYy0j9ER/sf4cj/YMgXTg/ValWMP9M6fhLTCX9mx0VWSqUSisWiECV+XNdFNpuNTQ0DklNM/Qtoc3NzkTTzhw8fQpZlpFKpE3UAixsLSfyPFhrNJoB+AsSPZVmiQVImkwms8EqShNXV1bGvHAwD7xA+zYQHRMuy8Oqrr8LzPGSz2cjq0tzcHMrlMgqFwliL/rLZLNbW1iDL8tQUHw4joOr1unCIqVargRVRSZJw4cIFpFIpZDKZsT9QOp0OdnZ2APSaqZ2GGBmGfuPP7Oxs4HpPdT8MWf1/exEOHRFx4bET6PzhoSdGgJ7Y8dCLkiS9xJPADBdggOR2kel+EB3ti7CVf/y4ZzNR9DNGIIjHgUf6+aLFcSPFcQseiqIk2srz5yKvKwmfl/84flzXRaPRANCbE4XFyPb2tii4X1xcDLyep6UepY6F7rvRQmJkAuA3A2+yxotp/RMVv/hotVqRY5ykQw7RH55f718dUlUVmqaJVe9w3v6kfDeqqk6NCOFwL35u0dnpdCJRNX+6Wb1ejzQBG2Vu/eP035mWxpMcxfojqM4f9/4T0yLEkxkYS/idPAyOnMTR6r3WSydYAXckwHtLrDKAuR7S3Y+g6+7C0v6LY7wpQZwfms2mSPVeWFg41T4jSe+Vy+VEelh4EXOQFTqvYTFNMzJGt1otPHz4UPSCCZ9Ds9mELMuBZ824F7LOOiRGJgB+ke/t7WFzcxNA7+aqVh9ZVfIGRul0eipy/c8almXh7t276HQ6KBaLkU7yMzMzME0TxWKR0idOkGKxiGKxiGazidu3b8M0TSwtLQWMABRFQaVSEZaTk/zQyGQyWFxcBGOsbyHpJCI5/zfS5n8O5gCImmUBADzkwNDsf5BhxUhcAKwNeF4BLNOIhl4cgJmhk5IA5gIp6ybgNWGlnodlWTAMQ1if0n16dqnX6zg4OIAkSZibmzv3PTMG4U/9nqSeLEm1cKqq4sqVK7Btu++Yz38ejmr4m8+GX/u3f/u3eOmllzA/P4/V1VU8/fTTWF5ePjGzne985zv4+te/jpdffhkbGxsol8t417veheeffx7vfOc7B75+Z2cHH/vYx/Dnf/7naLfbePrpp/HZz34W73vf+07k/MYFjcYTRKFQEGKk0WgExIjnecKSr9PpTHWqU6fTgWmawt530iaP3M3MPyjzIl+g9934c2MZY4Hving8eMQg7PrGG/5xZyw/4W7lp8Fxrtukh+vE4u4h2/2VXhpUwqlLLEGIAEerF4k7vtHoCZUcHgkSD6J4PsJbKWMp+/fhSL8Ew3ibGF+r1WrEynlnZ0cIlXw+P+TJni7tdhuO44AxhlwuN3Fj56Rg2za63S6A6amPGyepVErUfExL9JwxlhjtX11dFc/y8H2iKIqoYwm/vtFo4PXXX8fLL7+MWq2GnZ0dmKaJSqWClZUVLC8vY2VlBV/+8pePtaDxla98BXt7e/joRz+KJ598ErVaDS+++CKeeeYZfOtb38Kzzz7b97Xdbhfve9/7cHh4iD/8wz/E/Pw8vvSlL+G5557Dt7/9bfziL/7ikc9nUmDetOUKnFH4wPnw4UNRE+K/0D3Pw49+9CMAPXu+a9eujeU8T4K7d++KXM8nnnhiYlYoLcvC9va2cCQLT3Dv37+PTqcDVVXRaDTgeR5WV1dPNaT9OHieJ9LMJnFlvtPpCAvrpaWlyOf62muvQVEUlEolVCqVsU/E/F2ezyyeh1znbZA693uuWf0WmN2Ebf59hilw7w7YR0OvsJ2h16PEHHA8BnhOCW92v4/dvd64s7S0FEifdBwHb7zxBoBe9CpsP7q7u4tutwtVVTE7Ozu21eN79+7BMAwAwLVr1872tfcY7O7uYn9/X4zRFBkhhoW3H+DNZ7n9/sHBAe7fv4/79+9je3sbN2/ePNbxd3Z2MD8/H/hZs9nE1atX8dRTT+Hb3/5239d++ctfxoc//GG8/PLL+Nmf/Vlxvk8//TTy+Ty+//3vH+ucJoHJmAUSwhbvwoULfberqgrLsgK5ktOIX3zEdYk9LcIhWlmWcXh4CM/zoOs6Lly4ENi+vLwMxpjomg5Mnz3xa6+9BqBXzB7usDtubNsWDTrr9XpEjKyvr09UCgFw9vOIU61/Ajh6L/qQNJ8b9DF4Q+zD9xuEiV7xfBbJQoSflwswuY4L6q+DVf9VrKvPoF4s7XZbiIBwVE7XddRqNSiKgtnZ2UhUhdsmn8S1Qta+w8Eb/9FaK3FU+H3sZ2FhAWtra/iZn/mZxz5+WIgAPdfHJ598EhsbG4mv/dM//VPcuHFDCBF+vh/84Afx8Y9/HA8ePBhLlsBJQGJkQuBiJAkeRlUU5bEKZ8cNL0rmBWKnieM4QkzkcjksLCyIbZIkIZ/Po9VqIZfLRVK1+OetKApSqVRfu9RJhTsm8Z4244A7oNTrdczOzgbqn3K5HGRZDnjWHx4e4uHDh3BdF8vLy5HUmmmDW+jy+3eSV7al7v8B1frfwZpOL7ogK2D9CkaGiXgct14kDhvAIQY3WAR65+6pUJX/Cwup/w1W+jcju6iqitXV1b6LI1ysxLlZ8QUibs/ux3Ec3L59G0AvDTe82MQFzrAN32ZmZmBZ1lSP/6cJfUbESTDqcbper+MHP/hBYooWAPzoRz/CL/zCL0R+/o53vAMA8OMf/5jECDF6+kVNpg1elDwOXNcVeeOO4wTECNCLfsiynDj4FAqFgLvZNMGdpcaVF6zrulj9kWU5IEYYY6LplV/k8Zzvs7DKaRiG+P1nZmZiV8kmAreBjPGfCSHSi1gkRGQHPUmG/Oo8WwIbQpF4HgOaHlAE2KD3ZgC8Xr1Xyv6vYTm/DMjBNCxJkhJTeS5fvpzY6FSWZTiOExEy/ohL3MS4VqsF0q78+3Q6HVFwn8lkoCjKxDjzEcR5YtSi9sMf/jBarRY+8YlPJO63t7cXuyDHf8bbP0wjJEYmBFrBOTn8Fslh/3FVVZHJZGAYhugM65/4Tkvx3nE5rVUT27bRaDSQy+UCBduFQkFEPeIsqsMTQh6F4ta+08603Ofp5n8MqVl7lFqlJNjqugAGfDUeY2ADFInnpMAGFoz0YGbvWF4d8MpZMDnGa9i/PwNcpwBJbiDXeg6two8TfqG41/cvluW9WOIKZYFeCka42SknKeLSarWwu7sLoLcQ5V8AcRwH29vbUFVV5LUTxHG5e/cuGGPQNA1LS0vjPp2JY5SRkU996lP4xje+gS9+8YtDuWklPUOm5fkSB4mRCWGaL6JJo9PpiNSIfD4fqT1YWloSXVvpcz95/E0I5+fnA9EnWZaxuLiIVCo1lEX1NEeh4pBlGdlsVjz4JxGl/S+gNL8b/GGS2Bh0C7kAkvqP8MMY3eGfSG91fWcMQL0NlDBQEDGpCdiApNxHqv3b6Ob+xZBvNhxxE5ZUKpW4AFAul4VLX5ikPgpc7AO9SHP4Hnn48KFIOVtaWgqMc3FudWeNw8NDkWZ7UpasZxVuxEH0OM3u6y+88AI++9nP4nOf+xw+8pGPDNx/dnY2NvrBay2nOY2ZxAgxNnju/HFXHRzHga7r0DQtMLFNp9Oi2L/VasF13cB7UJ+Wk8M0zUjtjN92Wtf1SCpcuAD4PKFpWmI34rFj3UJK/wKYG0rJSgoYDgpYOQAbJuB4lCy8cCZXA8AAUzvGvF6ExvOg4n+CZf0HcNX3HuFNT56kyUOpVEI6nYZt2xHhOqjhm2EYsG07tg5lf38fe3t7UBQFi4uLgWik67owTROqqh6pO/WkcXBwIJrdkRhJhou2uA7oRI9R3AcvvPACbt68iZs3b+LjH//4UK95+9vfjh/+8IeRn/OfPfXUUyd6jqcJiZEJYZiL3TAMPHjwALZto1KpTG6++QAsy8Lrr78Ox3FQKpUiNprDYBiGsOIsl8uR2gM+AS4UCiMZYPnKoyzLU1sw9ji0Wi1sbm7CMAxcuHAh4D6iaRpKpZJoQkhMCZ6H7N4/gmQfRrf1ExweTqZeZIhUL3E4Oybly0XP8WvgOkMGqLfBCkC28x+hKd8BpMns2ZROpyP222+88QZc14Wmabh8+TIsy4qkjvFFHiBeqPBCe8uyIs8dy7Lw5ptvAuiJocXFxcD2RqMhUtbCjmSTBK8zo8n1YGRZxtWrVwPXDRHkpMXIZz7zGdy8eROf/OQn8elPf3ro1/3qr/4qfuu3fgvf//738e53vxtA737++te/jne/+91TXVdMYmRCGPZi58WO/UL704AkSaIQdBib4k6nA0mSAquDvI7AdV3ouh5xl+GF2qOiXq/HNkyadLa3t1Gv1+G6Lq5cuTJ0qlD485UkSVyLuq5HrBCPIzCJ8aLt/beQ7deiG5KeEsO4ZA0zH+wOuR8e1YtE6KDnrtXvlvQA1M1eU8UDgBXbyLT+AYxCf1//ScN1XTFp7NdAkzGGq1evipq4MLIsQ9O0WOcw/3MlrkZrZ2dHLMJcvXo1sK3ZbKLT6UBRFOTz+bH2j1pcXJw62/Vxw90WiSAn/bm8+OKLeP755/Hcc8/hAx/4AL73ve8Ftj/zzDMAgA996EP42te+hlu3buHSpUsAgN/4jd/Al770Jfzar/0aPv/5z2N+fh5f/vKX8eqrryb2J5kGSIxMEXxwH8YCcpKRJEmIiaTVNe481O12MTs7G1D9kiShUqnA87yxrL7LspzorjOpWJYl8oMHnbtpmtjf3xepVv50B54KF3bEOmls28b29jY8z0Mmk4mIHuJkkDo/hmr86/j6j6SnRJyA8NCLVNhv/RlGrw+7H9C3QzsYgCZ66Vpxv0cbYI796BzrgJz5t1DlL8PK/taQbz5eUqmUiIwMIq4oHnjUgwOI5sfzpqKWZUWiMp7nicWjOKHRarVweHgoztO/j2maouA+l8uNvA6MUnGJk+Kko2vf/OY3AQAvvfQSXnrppch2fk86jgPHcQL3aCqVwl/91V/hYx/7GH77t38b7XYbP/3TP42/+Iu/mOru6wB1YJ8oTNNMDJM+bo3FJMNX/PyrcY7j4O///u8B9Fyubty4MTEirNPpgDE2ll4pj8Pm5ib29vYgyzIuXbqUaGeq67pI2SiXy5Fah7AT2SiwLAs/+clPAPQKdfkK0STAU12OguM42Nragud5SKfTk1E/43nI3X0KTL4PJoXGHw/wCgDrIzpcNwPJNXoF5fyPiUepWRIAF/BUFch4YCU7vjdIE8MtjXnoNTxMGgYUAKH1Ca+lgLXjo7CerKC58P8A6uRcW5OI53kiIizLciT6fP/+feGQt76+HhgXm80mHjx4T7fuEgAAIABJREFUAKBXhBu+7u/cuQOgN9kKp5o4jjPxPXmIswNP8eMoikLi9hSYnlkUcSbDqN1uF9vb22g0Gpifn0e1WhXbZFlGPp+H67oTV4QYXjWcFhYXFwPWjdxiV9d1zMzMBIrP8/m8SIXrl+4xavzXe/ghMQkctfmc53loNpsjPKOjk6r9N2DdTbB8zEKI3EeIGAB2ASYlu/BwS19mWYDVs+JlKQCFt/7I6EU6hr2UTAx277IAr5sGS3XEa1jL7vs65tjI7P4mjKW/HPIkzieMsYgzoZ/5+XmYpinEip+kgnvP82CapniPMLu7uzg8PIQkSbh48WIgmu44DjqdDlRVhaIoJFiOQbvdhmEYounvtKUejxq6pk4HEiMTxDBd2M8ajDHU63UAvToMvxgBgLW1tTMnwMZJ+LM8PDzE/fv3xTa/GJEkCZcuXUIqlRrbA4rnpvMo1KRx1GszzmJ1nLDua1Dr/wOY3CdqoGbAYDz6gQ1gH71icQBMGyAQnQyARz1AGENPUOwB2AWQBZB+6+9hGCYQxQA0O/CUt4TUoEgKANn8t5CafwU3/74hT4QI06+GBegVwxcKBViWFREjrutCVdXYGhbgUR0Ld33yw01dgEcRF55OJkkS6vU6ZFmGqqqJUeDzTKvVEtawmqaRGAlB84/TgcTIBHFWL3rLsnB4eAhd11GpVALhfU3TkE6nYZomUqlUZKX5rH4mp43rumg2m8hkMoGHjT93u9FoRBpe5fP5UzvHOMICaZI4zrUpSRLW19cnJsqZ2fyHYG2rvy0u89VY6OgJEbFt8PGZ0+4f9WDoRVgaAPIAKkMc0xnyfRngNVIA6w7l5sXgIbP3YbTyPxm8M3Fk+GJC3IKCLMu4cuVKXzendDoN13WHjrh0u12RXspJpVJYW1sL/Izb/yqKgnK5PJGLHaeBP+p9Xj+DJCgycjqQGJkyWq0WWq0WLMtCtVqd2MZpfizLwtbWFgCIXGNd16HrOmzbxsLCgujMPS3wQnDHcZDJZCb6e9B1HRsbG3BdF4uLi4Hok6IomJ+fRyqVOlPNBScVxtjE1BhptU9Dbr/Z1xHLgwymWj2Xql1EoxLDNDsc5jnOhY4FYD7hNfYQ7+nHsXtiZ0gHWgkPoe69CGv2vzzCm5wetm2jVqsJgT5pqauPSz+BnlRXlUqlUKlUYFmWSN+KS+eMW+3nz1IAkc+y1WqhVqtBVVWUSqXIosxR0zMnmZmZGeTzeTiOQ1GRGM7K9zzpTMZTkQAw3EXfaDRQq9UA9Ap6J2US7K89KBaLgcE7k8lAURTYti087judDg4ODgD0BsNpu+Hr9To2NzcBAKurqxPzPcQVe3IHHgDC7cZ1XWSzWRQKhUhTQuLo8Fx5nrs+8dezeQfawZcAE/C0FBiLqf1wnZ4IaSBeBAwSGi6GL0oHesLhIYAFxDtrmUMcy39YJwNmNHsF80N+HSn987BmPgJIk9dDg9uY83+fNTFyHDKZTCRyKssyCoUCHMcRqWP9+q34X+OHLzZ1u91I8bLneXjttdeEk2A4msybLU7FOIDe82GSe8acJnGROYqMnA4kRiaIYQYu/8rFJPUaaTQaIjTuum5AjDDGsLKyAk3TxKDnfzhMmz0ugIjr17hpt9vY3t5Gq9XC8vJyIBUulUohl8uJz59Hqebm5qYiGmIYhviMx5k25jgOGo0GHMeJWAzruo69vT0AwPLycuA8HceBrutQFAWpVGoihGv2wX8I1n6raFiOChHPlcH2nd4kvt+wNGi4GqYkJryPBeAh4M0DLJydN7glUQDWNXvH7wAYMtOPSV2kt/8TdJa+erQ3OwX8EyWaIPUnzpErjpWVFViWJRZw/PjH9HC0gIsYx3FiozA7Ozt9XcVM0xS9WFKpFKVFTQHTICjPAiRGpoxCoYCLFy+OrQOubdtoNBrIZDIBR6l8Pi8K8JvNZiSMHZ70FotFZLPZqbPG5aTTaVSrVciyPBGFkX6XJu6M5efKlSsAHjXNBCbTnSqOe/fuwTRNSJKEt73tbWM5B74aygtjZ2ZmAhNC/8JAePJimiZ2dnYA9CySs9mssOjO5/PY3d0VrzuN1W619s8hN1599IPQMOJ5GtiWGW/BK3bC0VKmko4TxgXYFuDNZ8ByxqP9jvKeHsA6b4VSeDPEhHmf/9BK508B8yagrQ35ZqeDqqpYW1s7s/bup42iKH2fPbOzs6hUKrF1KtyWu1/T26SIC180AoCFhYWAO5nneajVakKokJ3sZEBi5HSYvlngGWaYiz7JsWTU+PtOVKtVLC4uim2SJGFhYQGqqg5V/5H0IJgG4tIDRo3fCGB+fj4g8LLZrEgLSBKpmqbh4sWLkY72kwyfeJ2W+5TjOJGmb4wx5PN5HB4ewnVdtFqtwOefz+chy3KsW1C4yHZra0s0ruPHdBxHNJzzc3BwgFarBVVVMTMz8/jfmXkPqa0XeylUQC/Vyne6niMBW24vCpH0VsPMhYfZJ0EPsx0DKAGYwXCWvn5sBIWOgV6RfL/38v9b8pDd+iDaF//PI7zh6BnUJJY4WRhjsWJD0zTR7yhuTPLb44afg0mLFrZti9TlfD4fESM7OzvCcWxubu5EBCm3VZZluW+TzPPMpBiNnAemdzZIjAxe08Hz3zn+ybeu6wExAiBiy0ucLO12W6RY1ev1wGSYMYb19XWoqpo4eMqyPHW55jMzM7BtW0TeRvVw8DwPGxsb0HUdqqri+vXrgfcql8uQJAmlUikyUSgUCn1T3tLpNBYXF2HbNrLZrJhweJ4X6OESN/HpdDoi5SPc44HbmvKISni74ziQJCnwO2Tu/CMwx1d84X9LB8C2Amab8BQNjCUUaQyTojVs8XoSdfSEyFEXicOnzhsyJtTnepDA3lJHkvv/QW7+Gzj5Xz7iGxPniaMW3PsXLcILC0m9WIDe+N/t9lIqw8/aw8ND7O3tCaHiH588zxMNasPn63ke7t69C6C3oBVubHveISFyepAYmSC4Ch9n/4FGo4EHDx7AsiwsLS0FBlZVVVEul6EoCorF4plyFJkUuBDUdR2lUimwOs8jTv4mYX6mJdJxVEbVpTzORpobLPDcbr8AjxMcw9yv4fSr2dlZeJ4nJgdra2uwLCv2XkqaoNi2Dcdx4DhObC3NnTt34Lou0ul0L7Vz87+HYvw4uBNfaHcAb1sFs3rXlccUsKSK8WEseI9SvJ6EgV6q1cwQ78uJ68VovHVO/ZofwoXHMmCeAcaA9O5/ilb+9pBvSEwKBwcHaDQakCQJ1Wp1oqJJSRH1VCqF1dXVgelfcQtOlmUJg5i4192+3buOS6VSYBExXO9Iz/QgFCk6PUiMTCG2bYvCu8cp6OU1A/4bTlVVEUrWdT0yETzJlZNWqyUGz2lbrfdzkgO4vwmh53mRVLjV1VWk0+mJesBOE57noV6vo16vw3VdXL58ObC9VCqh0+mgVCqN7EEUrudJcrNZWVkRaWNxueuyLMdacvojLgAAu4HU1j+PTsRVvCVE0OuS/haS20Yigz6a4xSvJ9FA72lVHGJfB/HpXw56EZOkW8c13hJiNiS2C3XvC7BmP3aEEx0dtm0Lp6Zw1Jp4RLfbFbVxo1rIGAWSJCXWH165cgW2bfet9eNjQVKaaPg5xZ0XXddFux295w3DEAX33BXzLBNeWCJhdnqc7StrChlmpfX27dvodrtgjOFtb3vbkW+YdruNWq2GRqOBlZWVQHoHnxipqopicZgn//G5d++eWAWaRjHy6quvwrZtaJqGa9euHem1nueh3W4jlUoFBni/uIxLhTuJz4k/0Piq+XmCMYadnR2R7mCaZiCiNDMzg0qlMjEPIW4RGjcJKBaLKBaLsZMT13WRy+VEOkj6td9EJFygojdp3wZY2JgvyeRnlMXrSRygV8cy6JJNsgA2kGj1yxjgmhqgAozZSOlfgDXz24A0/sabhmHg4cOHAHppOpVKZcxnNJmcVdexpDq/arWKarUK13VjBUculxPPKj/+cSUu4tJsNkV39pWVlcD+vO+NoijIZrNnsuD+LF0/kw6JkQljWHvfbrcrcs6Pag/o96vXdT0gRhhjuHbt2qlMxmRZDvQemZQJ4LBwa8ejWvvquo4HDx7Atu3YVLjZ2VmkUqmRicE33nhDFFo/8cQTI3mPceO6LhqNBkzTjORXl0ol7OzsQJbliBiZxodP3DkrioKVlZXe9uaPodz7Flh4HiMD2Ea0maGH5CfDMLfpEPt4LgMbRpH4d9kGcAGJtR+xKVr+YxkA+i1AW4C024abyoFlbbC0ifTWP0Xnwh8PPs8R459kT9tYeZosLi5iYWHhWM/GaSduLEin02IsCON5nmgaGffapDRR0zQDfW/CYuT+/fvwPA+qqkYW1fi1POnX8aSf31mCxMgUwt06kkKmpmkK56XFxcXAinsulxODdNwxTusGnJ2djQ0rTwupVGpg19p+qXB8kI9LhRvGI/9x4OcyLda+29vbODg4EGlVg1zMPM/D66+/LlJaKpVKYFIyMzODXC6HXC431ofNaQnwzCsfBBQZgdwlF73i8LjeHQyJaViOpEKOKBgfHpIjK+J9UugVgwwgrPW5IIk7RxeD+5F00UvVCp+jC2D/rVPrtnv7aYBS+nPAvANolzFONE1DpVKB53mUppkAr72cxoWF04YxFumZ5GdmZgbZbBaWZfXttwLEm28YhgHXdWO37e7u4uDgAIqi4MKFC4EIveu6YrEsbMBx2tA1dHpM5yzwDDPMjTeMa5Xfz1zX9UgTwvX1dWiaNtYbPWkQnAbW19f7bjMMI5AK50+vSqfTSKfT0DRtLOlphUIB6XQasixPRUSK10wAUQHlui663W5AoHAb3v39fXieh0ajEYj+naQ9NmMsNjUiiXv37omc9hs3bpzIefRD2fpXkOxb8MLzgRb6C44Bvwpzkx/QnguwYcTIkBFFzw6dkgN4uxmg2gFjocjKsH1g46x+6xDCh8GDhzSY2QGrOcjYvwHjp/56yIOPBj5uEMT/z96bB0mSnud9vy+zsq6urr6v6enpnmNnZ4ldLEzTxkKCQIBAINYEQgbogHkESBGETQrWQUkU15QgwjBJhdYkI2Q6DNoCQYGgRMLEwoQgkVoKF2WSC+LgQhR2Aexid7DTc/b0WfeVx+c/sjM7syozK7unj6qefCJmd6by+ior8/ve5z2e97gQ9cwVCgVWVlYCC+6983SQs9HJhggS7mi1Wty4cQOwydDs7KxvuyNO4PRjOSwEpccP+tp4mpCQkQHDfh5+p99BpVJhampqX8pLiWftaGEYBuVyGbBleL2kQwjBpUuXTmyiW1hYOJHrHhROzYTXSyWl5NatW5RKJVRV5cqVKz0yvECgDO9Jw7voHSkZlJLsKz+Dlcqj4ClObRHdR6SPM1ARUXlQIMkj6FMAb4GIwRykVEC3egiSaDbhDnaExLt/TYt13h6p3zo2QfFdJOWmiKk7zyIqX0UW/6v+506QYEiwublJrVZDVVXm5ub25aRx+t4E2RKKovDAAw+EdqlXVZV0Ot034hJEZJw+TZqmuc18HVSrVdrtNqlUitHR0XtO00siI8eHhIwMMba3t7lz5w5gh0m9ZERVVZaWlsjlcqdW8vWkYRgGlUqFSqXCzMyMz+h19OThZFPhTgNmZ2eZmZnpkeE1TRMpJYZhUK/Xe1IRB42EOEin08cSkcq8/LMIaqB6jAUT2MRuJhiGqPXbIlqNCoi1rMQssxKtXiLiQsf+Lk6WowHC0uMX1zeAIkgriyi1eo+TNTsqk7I35a79Axqv/tOYJ09wUnCcQKqq3pPa5P2ATqfjinkcBVRVDSQETrQjaB50WgcEFdw7wivOft2oVqtUq1XAllH2XrvVarG5uekSlTjrQ7JOHx8S2jdgCHr4dV1na2urR0PcW+DsvIBejI2NDQURcQrxhw1OT5ZqteougA6EEFy4cIGHHnroyGtATjPK5TLXr1/n6tWrPdvGxsZQVZWJiYmhqjtaWFhgZWWF5eXlo1vsOhtoG7+JNFWEE8mQ2MY7IMNm/n7F6yYx0rhi1IHEfd371X/UsGV/nb/v53ZaQAvklhl4nAC8WWBK/esopS/u4wIJTgLr6+usra2xsbFx0kMZKpxEsX/Q/JfP51lYWGBpaSmQTM7NzTE5ORko8BJVx9LpdKjX65TL5R4CVi6X+cpXvsIrr7zipreHje+gqFarPPHEE7z1rW91nWsf/OAHYx37W7/1W24tVPcfpxHysGN4VvD7FFtbW66co1OMq+s6q6urGIZBJpNhbm4utPvzIKNarXLjxg1M02R+fn5gO7g7qiHFYjFUecnpku1Fkt9979jc3HT171utlu+ejo2NMTY2lnivApD71o8hMLHUHELs5h+VsaMJUS6oPsXrccSvhBKlrbtP9GueKIBtsDJplE5n/+61KoiARnEOZAqEYY9BIMle+4c0XvPFE6m12traolQqIYRgYWGhr5DD/QivYytJsemPM2fOuPdsGO6Xoii++r9uzM3NuQ0gu79PVPrX7//+7/PTP/3TaJrG3NwcS0tLnD17lgsXLnD27FmWlpZYWlriNa95zYHv09bWFh/+8Id59NFHecc73sFHPvKRfZ/jox/9KFeuXPF9Nuy1tw4SMjJg6O7C7l1wyuWyqwzkFMCOjIwMZY8O2Eu1AQI7xw4CdnZ23CaElmX5ium8tTjD1FxrZ2eH7e1tLMvizJkzJ57O5MjwttvtnmLFsbExGo2GK8PrJSMJCQmGUv4Kav0ZaILI21EK2dYQNbuWQmZURFieVL9b2m8d3jXcDw0xf2KxLqLlfsNQB5GWkX1HvARMaX4DZedPaI08xurqqptS0m0QOMbQYRp4pmm682S/XlT3MxYWFobGuB4ECCFOjQRyVAPZiYkJN/2rO2ry7ne/m9e+9rXcvn2bSqVCq9Xi9u3bbGxs8B/+w3/g5s2bbGxsuIX1B8Hy8jI7OzsIIdjc3DwQGXn44Yf5nu/5ngOPYZCRkJEBRy6Xo1AokMvlXNLhLHKKogz1JJJKpUin06iqGimPexyQUtJut9E0zXdPvYZ6uVz2Gcve/YYpzUzXdTfaMAgk8OrVq7RattE8OTnp81o5kY9Op0OtVkMIMVBRwEEkRLkXfxzR3lWhykq7MHtzr5ZCankEvWmdQH+y0W/FiENGLOKRDJN4EsEAbcOuAdlHH0BJBtFuQwfkqIIIyx1L7Y1FIMle/ftUH/oTLMui0+kEvvvXr193i3O7i2w7nY4rCa6qauxnyFEQGgYFvJOCEOLIm/UmGE5ENZDVNI0rV67w4IMPIqVEURQ0TSOfD2tIdLDrJwhHQkYGEN7IiBCC8+d79e2/67u+a+gf7mw2e+TSpnFQrVa5ffs2nU6HxcVFX2fjdDrN+Ph4YBPCYrHoSuSeNJnaDxyPofc5Ow5YlkWr1eqZ4EdHR10yUqlUfPdf0zQ0TXNTFVVVHSgychCUSiU3sjkzM3Oo9S7arQ+jNG9CB4TTYX1n18O/CyEiCGiE8S8lvY0TuxGDk0srhtoWRDcv7ILomMgWiDz9O7Q7x5Q8tTQUgErIjtjfa/feKPpLaDtfQNNehWEYPb+fI6oAwQZIqVRiZ2cHgKWlJd/7YBgGtVrNlS31zivT09NDFYFNkGDY4GSmOH8fNLz97W9nY2ODsbEx3vjGN/ILv/ALPPzwwyc9rENBQkYGEHFegkF8UYYBQZ1fnRQg2EuF82JpaSnwXGFelkHH5OQkk5OTx5rG4MjwAjz00EO+a4+NjWEYBmNjY4EFi92SvsOOZrPpdi4+1HxfSyfzyi/t9RHMYhes9xCEECu/X/G6rkKmjwxWjEdK1BrhHdC9MOKdDwBzl3DtAPPEi7x4S1uqNZuPhB3ni47AxO1/RPq/fj7weZRSUigU0HU9UEDE6ZkDvUW27XbbLaCdnJzsqaPb2NhwvbZJBCDBvcA0TXZ2dlBVlUwmc6hRgNOAQUrzm5+f5/3vfz+PPfYYxWKR5557jieffJLHHnuMZ555hkcfffSkh3jPGD5LKkGCA6DVarG1tUWlUmFxcdG3kOdyOTRNI51O3xcL/FFPskFpJF5Jxlqt1nP/z549G3q+XC7H+fPnEUIMhTrcfnCY5Crzwj9A1Et7H7TpbQIoQSgh4Ys+xevCiKHHe5grisW+yIj7/zIQXuNqo42vFkRIC8saRVFD0te6oiPCvI66+TTm9H/Ts6uiKJEKeoVCgVQq5XaZ9iKqyFZKyc7ODlLKwLlqe3ubZrOJpmk96Y73C7zF2InDLhqGYbC1tQXYUf6EjPgxSM/P448/zuOPP+7++w1veANve9vbeOSRR/jABz7Apz/96RMc3eHg/puthgCD9BKcFnQ6Hba3twFcZSwHQgguX748UJ6QYUSlUqFUKtFqtXjggQd8z/HY2BjVapVisbjvlLZB7hdwkHd1enqayclJhBCHl97XuI12/bf3PPsmwVK3/ZS09gtr91omdiQjTi/VuKtO3PGY+FW+qtiRlyjeGpAlJmpV5FgKEaYn3BUdyX7nH1APICP94KjABSGXyzE3N4dhGD1qWU5fHeiNqIAdcavVaoBdrOtFo9FgbW2NVCrF+Ph4D5GxLMuXojKsqNfr3Lp1C7Dfs9OiNHQUcMRj4GRkfQcdg24PrKys8PrXv54vfelLJz2UQ0FCRgYQcRaEVqtFuVzGMAzGx8dPXBHpoNja2qLZbGIYBufOnbunCcBRZapUKkxPT/sW80KhgKIooZ7og1xXSkmr1XIn9UE1mI8LW1tbrjHUbDZ9nrbR0VGuXLky8BP8fnGQyMZR1Bfl/tNPIpymGBI7BSlodo+yOaJ+mhpQBlnNIIy2TTwMgqV+s9jNBIsqIt0VTTGIp3ql9xlr975e7Mr9Mkc4oQlQHxYCZNkIbwjZHR0xbqFufBpz5r+NOdD+SKfTodE/J6IopezbY6E7KqLruvunu+ZKSsnLL7+MEIJ8Ps/i4qJvu5PCmkqlBv799YoJDDuxOmpkMhkWFxcxTfPURZz3i6B5fBieH6fY/jQgISNDimazyfr6OmBPKsNKRmq1mps/H9RxdT8olUquV0zTNB8ZURSFlZUVt+D8sPDyyy8DdjH+Aw88cGjnPUqYpkm5XMY0zcDC/ChYlkWtVqPRaDA/P+/bNjY2Rq1Wc2twvGTkNHhdBxXK5tdQS3+6N5vXCI8KRBGB7tdCYtd0b2KnNWnsNVAMgiOD27L/iHUTmVIRedM28Au72+K84vtpVRIUyDCwIyRBj3ZET0YhcbuuB8IbHRGQ/c7PUj9EMhKFarXqquDNzc31bD937hyGYWAYRmCapKIoWJbVQ4adiIvzpxsbGxuuk+HChQu+43Vdp9Vq+ZQRTxKqqpLP5wO/ZwI/BjniPAgYdCP/lVde4ZlnnuEtb3nLSQ/lUJCQkQFEHKOte0EYVng9eN6wcRQMw6BarVIoFHz3oVgsumTEWTy9OGzC5uizm6YZe+yDANM03ftULBb3RUZeeeUV1yCanJz0kcexsTE0TWNkZORQJ3IppSuhKoQYuGaSJy21mv2Ln0Sou0akji3lG3SLJOFEQO42+ANXgYst9gx9yYHSuIRh2oSmsnt8Bligf9TDiLGPg7BXrwLk6CVgUUJeCog68aMj5hqpu5/AmPvvYw724PAShaDnzUn7CzLCJyYmmJiYCJQhllKSz+djFdx3R1zq9bpbcD87O+tLD5NSsrm56SqDHUdNwsjIyNA65hKcfjz99NPU63WqVbs27Zvf/Caf/OQnAfj+7/9+8vk8733ve/nYxz7G1atXWV5eBuAtb3kLb3jDG3j1q1/tFrD/8i//MkIIfvEXf/HEvs9hIiEjA4g4hk02m2V5edn1SA0rZmZmmJqaIpVKxfKqeZsQLiws+KQuU6kU8/PzZLPZY1uQpqamkFIOlRcuTn+UKBleh4yUy2Wf2s9Rye5KKfn2t78N2MZGd9+Gk8RBSIiTLiOlJJPJ3FOhcWr1Uyidb9tGvgRKREcewjiiAIQCG5ad4nQU3NoZXx04A0Q9KnGz3yT2WMN+Biddy9ldguhE7O9AJzyKlMLtpyIEZF75R8dCRmZnZ12nx0HJb5CTQNO0UMVAsN/5dDodSLq9qWFBERenTm9kZKRnLtna2nKL+I9b3S9BgigclQDC+973PlZXV91/P/XUUzz11FOA7ehbWVlxnZte58MjjzzC7/3e7/Grv/qrNJtNZmdn+b7v+z5+/ud/nsuXLx/6OE8CQp4GrcxTiE6ncypkTO8FnU6nJ0+51Wrx0ksvAZDP57l48eJJDW9o4ajyOBKh3cTtzp07bG9vI6XkoYce8pGXdrvNxsYGxWLRrcM5jvE+//zzgF3ge+nSpSO/Zlw4zTL3cx82NzddFZvFxcWDp0pIyci/WUHJ7Nie+hp7qUlBhEQQqjJltUYQG3VE1JRzGD6PFjYhksAEtgxv962T2N8jzi3tYJObKIzhEh+pZxHbEXla3jGERUfq2IpdIyALGkLVaa78OsbCu2MM+HSh2WzSaDQwDIOJiQmfY6zZbHL9+nXAjpp2p3Veu3aNdttO+7t8+bLP+KtUKmxvb6NpGhMTEz4iEyTPnmD/cCJeqqre90SwO0UxSWE7fiSRkQHFcTekGyTUajXW1tZoNpssLS0xPr5nQWWzWQqFAtlsNlSRJkE0hBBuL5WwPglOxKRSqfhSLzKZTKQM71FACMHExMSpkfY9LCNK+8avoMhdIuLUSED4rB70uQXyroLQZXSw4DBsFW/ndcFelOQsdjqVA30f14vo3+iivHv+FFDfR8inQy8Ba2OPG2zyV9OROY00v3RfkpFcLtej+uUgnU5z9uzZ0PQvJ6qSSqV63olOp0O73abdbvfM86ZpcvXqVTRNY3R0tKcXi67rKIqSyPv2wfr6upvOfPHixftSCtpB9zqYPDfHj/v36UswMAgK/zsdqsvlso+MAIEd6RPsD9Vk+/xMAAAgAElEQVRqlVKpRKPR6PFKjo2NsbOzQ7FYJJOJo9V69DhuArQf7HfhyuVy9y7ta+lkXvgVyICUArGzu5gKwlOQuu3BDnALRMdC5kV0alSfr2gpBRSrt07Lv1PAeXTgFWAa5Mxu48J7LV4PwjYwA6Ids75OYNeWeO6ZtLKIrZZvHyGBpo5y6zap1Y9iLL8n5oBOP1RVjUyXXVlZwTCMwFRR72dBymDO/7tr9ba2ttje3nYL9i9duuR7PzudDrquu7U197PRmUj7huN+jxSdBBIyMqCIM0kahoGu6xiGcehFw0eNdrvNzs4O5XKZqakpNE0jlUq5BYiqqqJpWtKI6Yjg3HuwI1HeWo98Pt/TJT1BMEzTpNPpoGla7PuVz+fv+bnOfOXvImgj0yqiZu4Z5RmCiYPEXwNRA+6w153daoUTDknfSIXSrPXvMRLSaxGATZDtPGKu4apVxULcQEcHm5DsBw4xSmOTpi3TT9jkXl2/ADLf+GdHSkaclCYnvXLYkUqlQr3xs7OzzMzMYBhG4D6ZTMYlFV40m02XyAQp+FUqldAUSUdl0Cm4HxRHzFEhn8+jqqorDJJgD8n9OH4kZGSIcevWLVcW98EHHxyqFJZms8nGxgZg1yiArew0MjLiNiEchrDx5uYmGxsbmKbJysrKQOWZOjK89Xqd+fl53wRbLBYpl8soitKjxpbI8MbD5uam++wG5cRXKhU3+nGoCmCtDbQbH0dqgKVA1WORh9mojsUssY3yTc82C4ToY9UfxuPQR5FLqTbstK0JII7+RNyoiIPS7nnjfhcnOpICNkFYvVEV4dxTQGmskbrxcYylH97nwOLhxo0bmKZJKpW6L2rlwiKHuVyOlZUVoDe9xuvtD0ofi1IG63Q67poU9D472zRN64nWDyO84i8J/EgcccePwbf27lMcRN530MiIlJJ6vU6lUmFyctJnkI2OjvbUxUQ17RpUSCndcQ+avO/q6qqbEzw+Pu5bnB3voGVZp2JhPWoEdaj2Ps9BRtP6+nqo8Vir1Wi1Wq6AwH6e99wX34MQFlZ2FLHT1fcj7DQqdhRhDTsq4kW/0rQ4xnuctTuOPLAJ3MKuI+kXPNovGXGK5/cTlBLAXcKjOtL/tTLP/9MjIyNJ4XYvuu/F0tISlmWF9hkpFAqoqophGD3bo5TBALc3k9PF3oudnR1qtRqapvVInicYPiTv2PFjOCy++xBxXoaRkRF30h3EsP329ja3b98G7JxUr/Gmqirnzp0jl8uxtbWFoihDGRZ3Ug1UVT2xCcyyLJrNZk9+drFYdMlIpVLxkZFued9B9wTdvHmTRqOBlLKnxuUo0Wg02NzcpFqtsry87It8jYyMkMvlUBSlJ/JhWZZLToOIRq1Wc9PkHIluB+12m62tLV/aogNl5xuoW3+ClClEueWrgZBCgBpSiC6B6wTXY/S7lf22S+KtJDF+MikEQkq4CSzhL2zvxn7IiMROtSqDzKn9I0EOTOxoTdQ41BSY9mBE/Tqpm/8vxtn/bh+Di4disYhlWUPjqDkJOIXrYRgdHQ2VH89msywsLKDrek8aZb/3udVquZLn3USl2Wxy69Ytl8R0bzcM40TXj/sdQSIug74enkYks9oQY2xsbCAUpZx0oHw+75uoi8WiS0aq1WpP12Cn2V53OHyY4DQTOyncvXuXzc1NLMviypUrPU0gG40GY2NjPeljuVwOKeXQFC466jpwvE0GO52OSxrK5bLvPgohuHjxIp1OJ3A8jmHTfY+r1aqbXgm9XthOp+M2xeouAs7++Y8jDDBkjlS76jPwRViIQ8duYhiGfutuv1ttEN3ZHZBSQYioohEbFhlUWjZ5uEE0IdkPGfFyj4oZLtvbjcbudSLqWIRp+GtHnv/FIyEjQV3XExweopx6QgjOnz8f2mDYGxUPirg4vSOCoufXrl3DNE23d5gXTrNXpyYtISzHg+Q+Hz8SMjKgGJaXoVQqcevWLSzL4syZM0xNTbnbNE1jZmaGbDZ7JM3w7jcEGeHdMrzd9z+smdmwGTbOQqwoyqFHcqSUNBoNSqUS09PTvgidk07oXHs/4w3rbO/VtA/q1RKWrqjefBql/CKyBapV7TGOZSaDoCttS8cuVI8qWenHR/t97f4cA6wUcWSyhNCw86nYIyTn6B2/RbA6Vxg8NqRogCxkEGo7fH/n+g32CtkjoiMyVUAYdhRS1L6DevsPMM+8PebgEgw6HFnxsPSrxcVFLMtyZYW9kFKSSqUCi/G9EZcgbG1tuY6L5eVlXwRW13UajYZbcL+fiFmr1WJtbQ1VVSkWiwPh1BwkDIv9dZqQkJEBxSC+DKZp9hhlmUwm1BiG4Y56DApqtRqlUolarcbly5d99398fJytrS2KxeLhFkkPGJyC1aOAN50wlUr5iJqqqly8eJFMJnNoBEhRFLe3giPY4MX4+DgjIyMYhuEzfrJf/VlEG3RzFC1V7T4tpLvGZwC3iSYT3SpbQdvjpGn1Q7sTb7UxugwzJ72si5BIfbd4PC66eVBF2A0go87RYu+79YuOyD0CKYDMf/55GgkZOVZIKalUKu77Fdb/5CgghEBV1cBIc7FYpFgsBqYDWZZFoVBA1/XANOWoOhaHUIBdjN699m5sbKCqKul0uicybhiGG2k+zvs0DEgEXE4GCRkZYOyn8eFRpq7U63XW19ep1+ssLS35vCjZbJZcLncoTQiTAs1glEoldnbsPJtqteq7z5lMJpHh3QeconGv0eBNJ6xUKj1Ro36L9X6f10KhEKm6FuSF1Z77EEr5OtJSSbWq0HW4BITa3Pt3B1hTEIYVXe8Qh2zc63aI7uzu3a/T6P1QgrwBrKQR2i6rqBB79ZKooJu+YYpWyyYbUfem6fl7n+iIMFtIE8TuY6XUrqLc/gzWmbfGG2SCe4aU0jXO8/l8aFT4pBA0T6RSKRYXF0OPKRQKaJqGYRg9c3yUMphlWWxv21rWuVyuZ77xpokm660fyVp6MkjIyAAjDhm5evWq2+fg0qVLRzIOpyYE7EnMaww7efP3MqFtbGywvr6OZVmcP39+oORx+0FKyd27dzFNE03TmJ2dPdB5LMuiXq9TrVZZWFgIbEKYyPAeHLVajdu3b9Nut1lcXHQ70MNeOmEmkwlNrTpRmDqZZ39pN20ojdCavfsoKVB3vag6iFuA0zguKg3rEJS0pKYi+jX8iPOIyvDdhAVc7cAiMAqIDHSnpIUdWwkZWxm7N0qA7SFlCtEy/AMysFPDwmyVVBaknWImBGS/9g9pnPl6rDH2g2EY3Lhxw42mdXcdT+BvlHhaDMqoekQnqmoYRk9UvJ8ypTc1rHvOq9VqbGxskEqlmJiY6FmPh0Hw5F6QrKcng4SMDDmcpodxIyhR5ymVSlQqFebn531Fs05DRSfk243DeHmdhcQ7iQ4LHP35bDZ7YDJy8+ZNt1B6bGzMd/8LhYKr5HRYi0CtVnML36empk59zrCqqm5aQqlU8pERuLd0wqMuqE9/4e8hZB1pZhGNJgS0B3DThAxsaVxvHUfU0O61eN0ElD5EJMqA796v31huYxMSJWYndQgvVZEgmxpipPdcUs8jRMX/oRMdCcmGFLLlS+VSmtdQr/4+5sUfiD/WsKFKSadjf5FENjYYQghmZ2exLOu+uEdRjRlTqRTnzp1D1/VAMuI4tYQQgf1WnD/d64JlWbz00kuoqkqhUOiZNx0xDycNdRjQbTsNy7hPGxIyMsCI22tESun+/6AvUq1Wc0PclUrFLyeqKDzwwANomnYkL6qTkqKq6tB5XJxc4TCllG44xdLdMryjo6M+1SbvdiHEoXvsDcNwFZsGMhrQhUajQb1ed/uihOVXl0olyuUyMzMzvu+VzWZJp9OkUqlDJ15HunhVb5O+9nu2gVvq2PUdQa9Imj0i4nkM+2Zh9Slel6mAongvdBD9SpVMYpERS+RRCEjT6sY1YE6FVJzKeaLJUFlH5rIIpeX7WFQDok8AOsishiCYDHnvtxCQef5/oXHhnfsscAk47+7cfpxKcsMGVVVPVNlwkKAoCrlcLjTFdGVlxVX5ChJFcZ61bqLi7anljUQ5uHv3ritxfOnSJV86rENwUqkU6XR6YNf6QR3XaUdCRgYYcRadCxcuxF6cpJS0Wi0qlQoTExM+75FX7crxIHtxlJ6mQZEoPiiWl5cDPUzdWF9fZ3NzE9M0uXz5ss+gLhaLjI+PUywWj0V5zDvhDlqzxiDUajXu3r0L2DnQQWSk0Wi4HdFLpZKPjAgheOCBBw59oTmIYehEIaWU5HK5yN8794d/A5HqYLXyKFYjvMYhjR016Aos9h1evxXA6kQTljiPjkF/xS52O7DHmWZ04I7cjZDEuHbEPRACWGvBGf/5RSck8iKAjgwfp4qP/Cj6dbSv/Qr6f/lEn4FGI51Oc/nyZSC4L0KCBPuBoiiha/rU1BSTk5Nuo1cvnDlL1/VAGWQn4uJkUnjhpH+BLXvunZ+dGhdN00in0ydaVJ+Q/ZNBQkaGHPt5cbyqQYqi+PKOU6kUZ8+eJZ/PD2XzwZNEd5QDglN3hBCu4V8ul30pXaqqHmvBZaFQcAvfh2Hy9Y7RMAx2dnZc4QQHTndl0zTpdDo9v8GgeLxM03SLS6WUoWREufFnqDtfQaq7hjoEG8EWsA5BznqpiPD+IxaRJEFKFaH2YRtx7OI+13ER9+cx7d4e1l2BstBnAI40bxQEdv3Irj/E6hRQetrUe3ZvG8iUglB6PcMCkMpeNEkgSb/4a+iP/jSkDmdeHYb3NcFgo1wuY1kWqqq68uVeOBH/bmQyGc6dOxd6XkcZLAhRdSyGYbC1tQXYjtFuMuI48VKpFJOTk0f6DgzKOnG/ISEjA4yDvnBOKlA2m/VNKN5CNCeVxYskxH3vqNfr7OzsUK1WeeCBB3yT7tjYGOvr64yOjvZ0+D1u9OtUPGgoFouk02na7Ta3b99GSsn09DQLCwvuPoqisLi4SCaTGRqZ4ygvd+7p9yLSEllJ4xY+dM/YEtuQDvkpZXYEEWZY97HjpcwiqEfvdFg9MyNkc3uwG3lQGhK2gcmIffu3NrFRwy6Mt0Ap1aKJkQBp5hFK2H1tIyWI3XMIrUbmz36G9hv/z5iDSXAQJGqM8bGzs+NmQBxmJD6qZtKpPe2WLAe/MlhQxKVSqbg9XLrr/crlMuVy2SUq3rm/3zMRNP8mz8/JICEjA4yDvBTlcpnbt29jGAZnz571EYxMJsPExAS5XG4o6gSGEZVKxZXhrVQqvokznU4nMrz7gJOTrCiKW6xpGAbr6+uA/azPz8/3KI8NOtLptBsFC0vt0579v1D0O0hdIPRdizpDr5e/gp2KFJI2JIxaeEpR387qMXKw+nReB+JFPNoxxgO9RTDb2PelNzhp727tkYJIKMDW7rlj7C/au4QlgEAJAZY1gTB3QAUhJNqN/4d24wOQP5jARYL+KJfL3L17FyEE8/PzyRoXASdCr6rqsRnfIyMjgVkEYNf0LS4uout6jyNJSulGVYIK49vtNs2mXeM1Pj7u26brOteuXUPTNIrFYk8vFofgeNfkZH0+GSR3fYhhWRbtdpu7d+9y69YtSqWS2+kVcAuivTh79ixTU1OB3oeTxNraGjdu3ODWrVsnPZS+kFJSrVbdzvOGYdBsNqnVam70SVGUwFqMZKLrj3a7zc2bN/nWt77lhu4dpFIpxsfHmZqaGrg+AnGhKAr5fJ58Ph+ct23qZJ75oG3o1j2eu+5dG0CJ0IiClAIR9Zr3eRQVoxW9g0F/d1bM4vXuWpdQ6PjJiCA0Ra1n3zjnDqlb74YAt1F8N2RVIG7vINdUWAfZ0hBKh+wf/+Q+BuNHp9Nha2uLnZ0d1/BK4IfjvEiK/Ptjfn6e+fn5gZGIdtS5HGdpN86fP8+5c+d6ekCBv+ax267Rdd1VousuuN/Y2OC3f/u3+YM/+AOeffbZI4msVatVnnjiCd761rcyMzODEIIPfvCDsY9fX1/nx3/8x5meniafz/O6172Oz3/+84c2vkFCEhkZYIS9FI1Gg83NTarVKnNzc66nWErJ4uIi6XT6UJoQHidKpRK6rqOqamQTqEHArVu33OjH6OgojUbDLcxbWVk5dBneo4DTrdg0TVRVHbhnxbm/QemEZ8+ePYkhHRsyn/17CJrIZle9h3ed7QAbu38PecyEFdG4A/qnRfXzV+jEIyNxIx5xEEQ6LOAOsNR1reY+RaxMoArEzFaVFoju9LImUJYIAVIq0DERm/agUzt/jLL5DazpV+1jUDY6nQ6bm5uA3W076ZrdC1VVyWazbi1EgnCERSgGEUIINE0LdaAuLCwwNzeHYRiBkeZ0Oh0ocby6usq/+Bf/grW1NcrlshudWV5e5ty5cywtLXHu3Dl+7Md+7MACPltbW3z4wx/m0Ucf5R3veAcf+chHYh/bbrd585vfTKlU4td+7deYnZ3lQx/6EI8//jif+9zn+N7v/d4DjWlQkZCRAUdQ40Nd192ohyOjB3YRmBCCy5cvD51nKJVKoes6pmkOjGdLSkm9XnebSzkoFou+VCxvwb9lWQNn2Ifh+vXrgK1OddxjllLSbDZdGWNvSkUmkyGXy9Fut8lkMq6qi9NPR1GUvsplQ4vaGtoLv2NnI+l7771UQex+ZWkKxPruthQRnQIjriOJJhuS0H4aLmJkcVliBEX2qTuB+BGMMDVfHbgLeNsexK0XcdDaPaZDLFUvIXaPcey6FrDlkfaVOlLsNYQUukR5+ieovPPz+27s6l0DBmFuHEQMuypjgoMjTB1sZGSE8+fPB9aGfPd3fzef/vSnXbtD13Vu377N5uYmN27c4Pr163zlK1/hPe95z4HHtby8zM7ODkIINjc390VGfvM3f5Pnn3+eL37xi7zuda8D4E1vehOPPvooTzzxBF/+8pcPPK5BxCld0U8HpJSsrq4yMzPj84Q56heOUba8vEwqlXI9B8O4WDne7kExMjc3N1lfX8c0TS5duuS7/4VCwSfD22g0mJycDG0KOYhwnh/Lsk5E2rfRaPCd73wHsD1A3fndS0tLaJrmRpfq9bq7/9TUFGfOnGFQEOQwiIKTNuAQK+8zk/t3P2q73A2BN1zgvNESBdatPSIQ9br067weNU10sGsxohBjmlHKdeiXum8RfyWKGncdO23NSRuP22zRQWf33FVgqs++Dizs38IANru2CRCGuffdBGQ3v4XyytPwyLvc3aSUXL16FVVVyeVyPY3kTNMkk8lw5swZpJSJ2mGCBPtEkE2kKAoLCwu+ufuhhx461KjRvdhin/rUp3jwwQddIgK2ffTud7+bf/yP/zG3bt0a+CyS/WAwLL8EgXCMnHK57DOGFUXh4sWLZLPZoSQeQThJ9aM4Mrzd999br1AoFPbt6RwEOEbPURNAR7XFa0Tl83m3vslpZuhNa+s2uLzbhr3PgmVZXLt2DbDvg/MsKTf/HHXty8jOCIroiiakQUpgzUJ4Pf5RhKNf5CMKcWo44mTCxNnHIQH9EKfH4RY2iUqxPyIi2fvOJna6VZxMKIFNgqoh21X7d3OmFwFMfvmDtDxkxGmY6kiXdmNtbY1areZzPHmPNQzDR9wTJIiC44AaxibDh41B7r7+/PPP89f+2l/r+fzVr341AN/4xjcSMpLg+DA2Nub2JPAiyRm+dzQaDXZ2diiXy1y6dMnnoR4bG2NtbY3R0dGhyq/dD7qVRQ4b7XabGzdu0Gw2mZiY8NV6CCHcYsRisdh3UXT08J3OwsMM74LnXQyzT/9NaGYQqS6mIEHmQJazKJ2uqukwY98iOtWonw3STVas3c+k5+9xVo84Tvw4tSfOfnFshTX2oiNx0V2MXsNOU4tzvXLEfgKEzh4xFKCVb2D+p19H/y/+J8A2DjVNc0lFNxxBEsMwAhvJra2tAbasqlc9UUrpkhhN0wYm6pzgZFGr1dzmsDMzMz1SufczBomMbG1tBf42zmfd4i7DjmR2GnBMTU0lebBHhGq16hK9SqXC9PS0uy2VSiUyvPtEd4RJ0zQ3KlKpVHqiH/tZBNPpNCsrK4c21pOEEMJ9px0CnHr2X6JsXIOytPtmdClGSXMUpex3v8uUhlBCOoX3ScOSmRyiWzrKKeCuYCt13e5zLgHksWsmCjZh8q3lbeKtMHEiHhBfccvCLu7fj43V7vq3xI549Al4SjONaHZs4hf2XVX891CB9J/+M/RHfwoUO7XzwoULSCkDo36ZTMbd1m0sefszdJMN0zTdJrfeCJwD553UNI18Pj9QhthBsLm56Uq1zs7ODv33OSp403KTQn8/Bm29j3qGT9vznZCRAYcQou9DZxgGuq6j67qb/jJsME2TZrPp5kcfVtqWU4Tu9KTwTr5OE0JvSpYXgzYxDSJM06RcLlMqlRgZGfFJLyqKwujoKJ1OJyHUHjh9EFx0mmQ/848QVYlVGEURXaRDaIi1gDwgM4SIxBrE7rEGtme/Srisbdj04xjsdWB9t/t4BhhTEKOWbeAfZm/PuKSF3TGl6UsmXATdygb2+COmAVnTEHSQHRAqwfdKwS+DLEDplEl/4efovOVX3N3C5vr5+XlX2MM0TRRFcffLZDIUi0V0Xe+pV/N2vA6KuOzs7NBq2SGhy5cv+796o+FGVQqFwlDUwtVqNdf5ESQBm8CGpmkUCgVM0xw4if+TxiAZ+FNTU4HRD8eBetoiWsNntd5niPNybG1tufK+Kysrh9pR9bhQr9dZXV0F7HSDwyIjd+7ccV/okZERX1OkbDZ7KDK8lmXx8ssvY5om+Xye5eXlex73cUFK6UYsDjIRW5bl9obRdb3HI3n27NlTT+qEEK7i10GQfeq9iHYTdBDdxQcW0EkhAqzlyGZ+EQ5PqQOtDLIiEHW914CW0cdHQbSxC+zXsSMts0QXg+/nWv2K7r37Wew1ROxjb0lTQcgQplMFwni0DqJu1/YIQEoVIULEIBT841ch/bV/Seevvh9y/XPKSqWSK+27uLjo1qiNjo6GzveqqjI9PY1hGIGpjU5UJaiRnJPCCrbx6iUjTsTFiagMSnNBb5PUBOEY1hrH48AgPTuPPPIIzz33XM/nzmcPP/zwcQ/pSDE4dz5BIOIYON5IiDdsP0zoLsrcL5z86O40B+9CWalUeo6LU6/QD0II2u22G6EaFty8eZPnn3+eb37zm65HMQyWZVEul6lW/caypmm+mhqvNxYGa3IfRChX/5zU1T+EOkgBwuuAlmDVsggrJGQRZWQHbbOALZB3Coi1OqIRQESc/Q7DQWhgk5KXsVO/gtAhHhnZz5TgPIISW+GqT7G+aEaEXFogrRCfXbXrNrVMZNiNc6Ij7kVBKDrZf/dT0YPbxUGkfTVNY2pqirm5uUDCMD8/z+zsbKCHNSqqous6jUaDcrnsk5Z3cPPmTVZXV7l9+3bPfByWinYYOHfuHCsrK0PbDDXB8SLoORykyMg73/lOXnjhBZ+Er2EY/Ot//a957WtfO1CKkoeBJDJyCpDL5ZicnCSVSg1tca+maUxPTx/oO2xvb7O2toZpmpw/f97n9RkZGWFiYoJCoXBkHjwhhEumhikH10sUurvTeqHrOt/+9rexLIt8Pt/jiZ2bm0MIQS6XO9LJ/Nq1a25qwblz547sOscGKcl98r2IlgQJIoPPupU1BdHWg4mFJLxAPWhbBbuOwgDFqO31xjjo0JUUwupTxOF8Fx24ha10NY9fpUonHhnZTzd177A62GloUcGHqH4kAqjK3uiIhZ3WJvy7Wp00Ih1C7LuUtVAhde0LKGvfwJqPboSYTqcpFApIKQ9tjonyjk9PT4emf3kdLkFpPq1Wy1X56p4PnC7yqVSK+fl531wvpXQb1x1kHkmlUkOZopxgcHAUzrOnn36aer3uOvK++c1v8slPfhKA7//+7yefz/Pe976Xj33sY1y9etXNrPiJn/gJPvShD/Gud72LJ598ktnZWX7913+dF198kc997nOHPs6TRvLmDjjiTMr5fJ58/jCTs48fmqaxsLDQd7+gIk5FUXwyvN5FVghxLB27H3rooSO/xmEjnU6Tz+dRFMWdhJ28dO+i7qjxtNttGo0Guq77jJDjUhtrNBqYpjkU+ev9cOPGDab/+ElGazf3jGGv8lQTRNWKVqMKWze9/TWa2NEJr1pUv/W2z5QjUfsSESkFQunyPLaAV4BRbFKigbQEQo3hKY9bvA69UZQyyGIOoQREmCz6Eh3RMpH5FELzDKISfIyit5EpFaEEhHIUEF21I0Jpk/30/0Djp/486htRLBaPNR0qyrAvFApcunQJXdd7iJHX2xx0vGEYWJZFp9Ppmcfb7babqjsxMcHs7Kxve7PZRFGURMY4wZHhKJxp73vf+9znGuCpp57iqaeeAuCVV15hZWXFlfb2vj+ZTIbPf/7zPPHEE/ydv/N3aDQavOY1r+Hpp58+dd3XAYQcdtH++wBOg7T7Gc1mk+3tbSqVCufPn/fVlJimyYsvvuhGQQYlh3mYYJoma2trVCoVRkZGeiIPm5ubtFotxsfHezrSHxe+9a1vufKnV65cOfbrh8EwDEzT3Nc9Wf3LZ/iuT/x1FF3fSyOaxiYKOsiNXVt3hMAIiFR3i8SDYO4et45d89A9LIX+PUii3FRt+kr2SvIIszeFx4UAxkAWswilW1c3ACHGf8CF7UhI98cZDTGr9xKxJuE9QjywsnmUYmPvGmuEp3+Z2IQr8EQgFc9XkSA7aZpv+w3Mh9/ZfyBDAsuysCyrh5BsbGxQrVYxDIOLFy/6yEy1WnXVv6anp3ukx526PFVVuXTpkm9bs9l0nSSZTCYhKxG4efMmUko0TetpsHk/oTtl0BFcSXAySCIjQ4D9dng+jajX666KRLlc9pERVVW5cuVKsgDdAxRFoVwuY5omlUrFXfQdeGWPTwqXL18+cKH9UeIg47nwh38XRXqISBrbULZAbu8aqxGkQGZzCOq9n0sQNeCuM7iuHRyhbXYAACAASURBVPr1H4lTUB5D1UoaFpG3RQIlkA0VMd1nTM7+MW6zlClEQBhFtHXYobeYPipFywOl1bDvywh2D5Ko6bhbPat7m9T21MwEoFlkn/571F/1DqJv2vDAG231YmZmhpmZmcD1TFVVCoVCYGqY06gPglPDSqWSWxN45swZn1HZ6XSoVCpomkY2m73vO9g3m01X0jnBHgZtXbnfkFhvpwzDTFqcIvSbN2/2FII70rCOclE3EiISD61Wi7W1NTY2NnyfO70vhBCMjo4eSETgqKGq6qlYMFJf/lfkSi/55WQz2AbuDriCTCqhM7Ri9hIROsCddLSnv19xehyjP8ZP0NOcMWQsSrUOqxDAq/aGZIjYK5UoR+Rz1UA2u9JZY5IRwB6jI2ccOQjCZZIBYen4pmlhIMwa6S/8030MZrgRJGOcz+dZXFwMVYScnJykWCwGpoV2Ons/ZLdQSbvdZmtri7W1tR4BDrA73K+vr1MuB4TUThkc9UQYrvrGo0C3rZTYECeLJDIyBIhjgF2/fp16vY5pmrzqVa8aSqPtpZdeclWdstmszxuvaRorKyvk8/mBnERrtRq1Wg3TNJmZmRnIugbTNHn55ZeRUpJKpZienvY9J7Ozsz29WBIcMjpNsk/9TK89n8EmEd7a5xDHpXSK3b3YLVAXVgc5IhD9JKTCEOMwqamIfvJWcdZ15xQWcBOYIbhRoXTCETHPGbGqibUGnAEyIBsg9nubNonX72Q33S7wN1RBKgWEZX8nIUDm0qS//M/pvP7vQ6bX2N7c3KTZbCKEYGFh4b57RxVFYWZmJnT76Oio2zOl+95EKYM5KoFgrznd/ZCc++4VWBlmCCG4fPkylmUNtePyKDCMNtNpwnC/WfcJ4rwkjnqJ8/dBnjSdRoRO8bQDb8fucrnckxo0yPmctVrNjTaMjY2dOBnpdDoYhuETNlBVldHRUSqVCoZhuFK9pmlSLBZPXROlQUT2Y38DYbV8xrpUFWipiFqXLHTIKyy80Q2JXRviqamIJCL3WLyOBah9rHGLg3Ve38CW0p3391AR27X4zRP7jV/BTmE7t5vOtl9UgGyM6wjsgv0QQimkYUdltN19ZR1QyH7qJ2n90O/07N9qtVwZ3cSI7MXo6Kjr9e9WYywUCmiahq7rPdv6NYZsNpvufe8mQ7Vajbt375JKpZicnOxZn7obVA4KhBD3HZmNgyQycrIYXIs1wb6gaZqrehQl03rS2NnZYW1tDcMwWF5e9hWbZ7NZGo0GqVQqlrLWIME7uZ9kipNlWbzyyis0Gg2y2SwPPPCAb/vU1BQjIyOMjY2h6zqlUgngxMlTHNRqNTqdDpZlMTk5ORCLh2MAOQXsjuERNDblO39O6lufRWpZhLmXxiRMC3Ysv6wvIMJmZ+fUHeAOfjWofnZPvxm/3/EdENk+xrAe4zoQnBJWxQ6CnGXf3dulmUGo0f1y3OvepW8Upfcw4cowxxpbWHTEArZaSF0gpIQUyEIWsjlSV/8Atr8Dkxf81z5An5H7CU5PlbBtYfURmqZx4cIFdF0PfGeduVwI0bNd13UMw3AVwrxwGuEqisLIyEhPTwhHTeygMsYJDh/J73CySMjIECDOS7K4uDhwL5OzgHrHpaqq640ql8s+MrKwsDB0JMRBsVgkm82iquqxFkh2Sx0riuLe91arRavV8hX7e7vveknTIBNYB1tbW24+eLFYPDEC5dxfJ9VBSuned+eP14gBkJbF2L/6H5G6huJVj3KkZXsclQK6pXEdaNiKUUEN/aL4WT+VrH7HQ7zmg/s08rshJHAdO21riv7F7Q7a+5j/6tj3fD/jFDk7t6uFnVbXz7kcEB2RZBCbbYQBUtXA6IAJSrmFLLcgC/lP/CiNv/mM71Rnz571PWsJDgdCiEiysry8jGVZgT1TnJ4vTu8jL5w1LmxevXv3rhtxuXTpks+Z1el06HQ67riS3/t4MGj20/2GhIwMAeK8JIP0InlleJeXl32pQoVCgVQqRT6fP1USvJlM5thIiJSSUqnk5jqvrKz4to+Pj2NZFuPj45Hh+HQ67SpUDUPY3rson0SqimMMOiTEeedUVQ28f44hIqVE+/2fR7l1C7Le/CzsSEBAmxYRVswgsVOFQlRzZTqinsMkMvIhhYZQ9PAdDhGSFEJEFJsL7LStKr0KWGGHNFrxV7Q2dmQpTsrVLqS343qDcPleLxSQ1u59bYLY2YvcCLPjiw4JQFo5lLvPobz0OawH3rK3b0DBd4Kjh5PSFPR+T05OMjk5iWVZgUQln8/39GRy4JCVoIhLvV5nfX0dgPn5eV8di5SSnZ0dNE0jnU7ve81ptVo0m01UVSWXy923ilpB60dC+k4WCRlJcOhwyAjY0Q8vGVEUhStXriQL6z3i7t27ruKY07XYwdTUVCwpXkVRhkrmcmJigpGRERRFObaaKC/58CLOwiWEoF6vo936BoXPfAjRNpFFz3mCeoA4CLIRLOz6kDC5X4lHimv/kGQQ9CEjcdbrGPuImhHd6wTse7ODHV1YjHHd/UDHVS8LLJrvhgVKveHvKh9WoO6FABo6UhGIHdn7ewv8hKTTRDYh92//NvWfeSHed0lwogiaCzKZDEtLS6HHFAoFVwGsey2M6nCv67pbmzg6OtqT/rW9ve3K9haLxZ5z1+t1Njc3AVsC+X4lI0FIbJKTRUJGhgCOV2yQChellDQaDbfQ3JsyUywWuXXrVqgMb/LSx4NlWdRqNQzD8BWXOzK8m5ubbtG/1zg/rffXSS87anjlLw+aq99ut7l27Rpmp8WjH/lBRNPAmhhFcXR3G9jF2tN5hNUV5pDYHnvfmNKI253o3iNKGkVEaNX2Gb5SqcF49D59U6Ys+qcvgR2liWMHmdgyuTdBLka04TBiXtd7XkeCtwnkonenTs/9k50spFp9W4MIC2RFg6DfRtArt5zJo9y+jfZn/wf66/9un4ElAFv1amdnB0VRWFhY8DnABhFRymBOU1mnwasX3oL7IIdMuVx261G6Mw8qlYpPvngYouHHidO6bg4LEjJySmCaJpubmxiGQTqdjpzsDgObm5usra0BtvfGe71UKsX58+fJ5XL7mvBM0+Tu3buYpkk2mz3y73CYkFKi67pbyOyt0zjo+b797W+7hZXj4+M+D9zU1BTFYpF8Pp9MoocAb72H82c/qTHdtTsOOb/wqf8Zbcdupy6sXSLSwe55oQgwG8EkwfvaNICNXSISQQYUvRNtVN9rvUgn+vpAfFKw30e2BeImyLMhhKQR/5zS8qSyCaCEXQMS9f0D2qaIdgupZCDXp2i+CpAOJiPOGLzREaOBpWZJP/0k+uveB6pGpVJx60UGWVXwpOB0fA9KmRo2jIyMBPZSAXteWVhYCFQGc9YgsNfk7vvQarXc7d2Kj7quc/PmTVKpFKOjo4yP+70S3fPbaUOSBnnySMjIkKBfZEQI4eaZ5vP5QzPknQiIU5ztoFgsumSkUqn0XO8gXmwpJVtbW+7xw0RGLMvixRdfBOyxnz9/PvaxziLiXRyEEIyMjFAqldwIidfTlU6nD6WAu16vu962bo390w7nfepWP4u7MJmmSblcplQqkc/nmZ+f3zuHYXD+U/87Y1f/1C0yF2lsj7zjnBQy2LD2GsVl7EaIzpg1BRHW6CKKBPQhMhBjuxFjH7PPOBzElf713os2yJ1RxES1l3gEigAEQ5JHiKr3A9gGwjIbLUKbRYp6274nYdfuYBMpUbOPD8qKDIiOCKlDtUX2d/4mrR/7TTY2NjAMw5XnTuCHoiiukuRpzv1PpVKRtZbnzp3zRU+88KZ/TU5O+iIruq67hfNBqbvXrl3DsizS6XRP+pkzfw5zpOU0PzPDgoSMDAn6GUeKoqAoiqv8cRgol8vcvn0bwzA4e/YsExMT7rZMJsPU1BS5XO7QCtG9k9lhfYfjgncyiyvtK6VkbW2NcrnsNqPy/s6Od2psbOzIUpRu3rxJp9NBVdWBJyPdUYuDLiBBhegH9YrdvXvXJZNzs7OoX/4y6u/9HsrXvkju3Df3yEYO2+AssUdOwsp1nK+1ib+uREJkx70IoiBFn4Jxk2BD2XeSPtsBmcog6BMpaBOPOHToIQDKdtWOgix2bdtPBms74P1sY583KLun1juOvQFhE8awuhPP7yelgrCswAiMVHZVxJzoiDCx8qOknv0k4s0/g5T2j5sYTcGYnp6OVSd3mtEvIn/mzBlXjrg7/cuJ6Espe7Y581uYktvW1pabInf27FlfxMY0Tdrtttt6YFCiD92O3UEZ1/2MhIycIiwvL6Oq6oGKe4NkeFOplE+G10tGgJ7iuXuFEIKLFy8e+DucJIQQTExMIISIXRQuhPCFzpvNpi/XeXR09Mi9oM7iYprmwIfit7e3uX37NkAPOe6HMCWsOMadlJJaze6Q5/09VFW1C1G/8Q1m/+iPyH7mM6irq/bGN3lPgF0DUmFPGjckUiGlrSDLGnZqUJfBHfrzWETWYEglgyCCjLSDx+NDnEej2Q5UB/MhTuE3hKt/tbA7tp9lL6qwDxtdNANS45x0rWzAuQJStHyQ2Pev+7Vvg1cPQGDtKXgFXF4ifA0rFaOKRJD72I8z87c+e+q9/gmOFkKI0Ij66OgohULBJSVeSCnJZDKhymDO+mVZVk90pN1uc+PGDcAWIJmdnfVtr1QqqKrqqoOdFJL36uQxXBbffYw4RuJBvOetVovt7W3K5TJnz571GVv5fB5N08hmsz05pEeFQS88jMLZs2cDP2+3225hYfc+Y2Nj1Gq1E0u9mJqacjsFDzq8Y4zTF+VelLAcmKbJyy+/jGmaZDKZvd/pzh1STz3FxY9/nNTXv45MpZBzc1iPPAJzd1AKm3sGbxq7SNpbMqASbEAb2A35gnhDVDShz+1QmvVoAhAnmBdjtRBx7Im4xetRxfBtbEKyiH1v4/6knQhCB73pWib9yY7AjoB4yIiUQDOL6GYyTspX0PmE2GWju/9WADWFuvYCU8/+Lsb3vS9iEAkS9Ieu66iqGjgHOk0Yu6EoCsvLy0CwJG42m8WyLHRd7zk+ShnMyQyQUpJOp3tSm6vVqkuA8vn8kaaBDbIT7n5BQkaGBEf1srTbbbdOo1wu+4xiIQQPPvhg8qLeI1ZXV2m37dSV2dlZnwdofHycYrF4YpEgr0rXoEPTNFdpJkyS0quE5fx/P2lY3d5nVVVJp9M0m0307W2sP/szMl/9Kspf/AVibQ2xK7MpDANx6xa0b8EKfmOzO8IBgca4NEDsEJ4uFfWIHHXndZP+kZM28UhG3Omk334OIRkhvpJWvwbtbWzlLCe6Uye+nLHnOFEGWgEhFQX7eQjwuQgsrHQRRa/sfaboSCVF9o9+idpf/THI9As7JUgQDCkl3/nOdwCbQDgEYz8ImkenpqaYmgpuBpROpxkfH8cwjJ6MAScaD8HKYNVqlWrVru06f/68j4y0Wi2338rIyEhPMf9+MQzOuNOOhIzcB/DK8E5OTvrySkdHR/e6RAd4PRIiEh+6rtNsNntqaMbHx7l79y5gF4x7yYhT65OgP7zd470IU8KKe1+llG50UFVV/yKt68x/9aukP/EJCv/xPyKaTf+xmQzW3BxyYgI5WUTNfBFS5p4drRNcI5Dyp+TIDogtwmfkfgXoEca4lECmj23fj0R06C9/2wL6BWfjdIEHOzIU5+frYNd6zBGP5PQrRRNAGWReQQirf4qWF00gv5tu1ZDh4xeEFvornQpSTSOs3TCaAsIyoFUl+xs/Sutv//4+BnT/YGNjA8uySKVSoYbx/Q5vNPm41pxcLhdKFIQQzM3N9U3/gt6oSrvdplKxSbvTwNGBlJIbN264n8dxuCV2zskjISNDgrjqPu122/VCOJ6InZ0dbt26BdgvrpeMKIrC+fPne9SyTgq6rtNutzFN000TGwZcv37dLUR/6KGHfPdyfHzc7Q1yknmxpwm6rgfmKB+0GH17e3uviaSuk/6Lv7AL0Z9/noyigBBYr3oVolxGbGwgSiX7QFVFLixAu43a/FOEwp7X28A2Zrud2RJExkP8WyC2sdN3wupPPcXNgYh4rEQ74rz0ua6DOGlc/TPnkIaCUGPsGNEuxX9CbBKwAczG2LfffXSwJZET/qLyvnCK2dNZUJrh+wnsCExQRqoAGh3/75EB2RakXvoCykvPYD3wV2MO6P5BuVzGNE00TUvISAiklG5dyL1Kzx8GVFWNTP+enZ31yeV74SUq3VEVy7Jo7jqNLMvykREpJV/72tcoFotks1nm5+dRVfVQyUitVuOf/JN/wic+8Qm2t7e5cuUKP/dzP8cP/dAPRR73W7/1W7znPe8J3Hbnzh2fWuNpREJGThEqlQo3b94EYH5+3pXG9aZeVSoV5ubmfMeFaZqfBLa3t12J4uXl5YEkI0GF3o5RLKXkhRde4OLFi+6Efxx9X+4VQQIGgwgn8rGzs+NGmxYXF31KYE4kUNM0n96+U4huGIav+N1pEFZ79lnmPvMZRryF6EFjUFXMxx4DRYFOB1IpyK2BBDmya7ua2HUEYQanc64qUN6tY1AI96ZHkQEj5Dre7VHo0LfoXEpPb44wxHG2Ghoo/XKliC8R7BS5N4AtIMoObRObWIi2xKqP+iWA40AHUW/2H7vA/l0CVmCRAamD0Pb2FYoES5L+jR+l9b9d7VP4cv/Bm5KZIBipVIrFxcWTHkZsREVVJicnKRQKGIbRQ6yiIipbW1u8+c1vRgjBzMwMKysrLC0tcfHiRZaXlzl37hzLy8tcvnz5wLbHD/zAD/DVr36VJ598ksuXL/O7v/u7/PAP/zCWZfEjP/IjfY//6Ec/ypUrV3yf3Q8EOyEjQ4J+Xdir1Sp37txx/+2VxnWaEmYymUOT4T0qeL0cgybv6/SUaDabPbU04+Pjbk+Qw5RXPmpsbGywvr6OZVksLy8P5PMRpIQV5RnTdZ3VXTIxOjrK0tISUkpefvlldF13CzUzmQzprS1STz3FuY9/HOW552B6Gjkzg/na14KmgWVBo4EolZDZLExNobzwAuqXvrR3wQngEezZNIUdIXBs2KD1zIlilICax66MkqeNWhf1iG0QbYC37TGg7+7X/Wc3MiBk/9CI1Prb+iKO2hYgRTzeIFNFBLs1FlWQahYxHpxbJc08gkbgtt6Bgiwr9n3fT0ZLC/ue9ktXc6IjQSuwANFd5J8GGqC1NrH+zQfpvPN/3cegTj+Wl5djiVokOB1QFCU0upPNZrl8+bI713sxPT3Ns88+y82bN1lbW8OyLG7cuMHdu3f5y7/8S1ZXV1ldXeWFF17o6acSB//+3/97PvvZz7oEBOBNb3oTq6ur/OzP/iw/+IM/2DcD5eGHH+Z7vud79n3tYUdCRoYQQV5sTdPc/haapvWoMw1LiC+XyzE9PU0qlRo4Za1SqeTmqdbrdV/9Qj6fZ3p6mo2NjYFId9sPugu+BwHeQnQvAXdynbPZLKOjo4H5xkGeMSEE+XzeTqWr1aj9xm+gfuUrFJ1CdOcaGxtuUTqAtbSEXF6G7W3UF15ATk0hZ2exLl6EdBqsCkrq6/bOI7tpPVXClaAkdl1BSYGa5XNwy1SEAR6VVdHvcUthe+Hr2MZyZzddytj9vfs0M5TWLmFaxzaQc9jGtvf11CP6puxnrADWPmrcdyo+o13stGxiFRCIFLVG/yL8XUgESqVsn3s/QoJtwARJgJJW9zVU7KbsQWPSgB2QuQwIwyWDUkL6//sQnTf/LSj2y0u7fxBXTj3B/QFHxjgIFy5cYGVlxU3zdSLjDqKaS/fDpz71KQqFAu9617t8n7/nPe/hR37kR/jyl7/MX/krf+XA5z/NSMjIEKHT6bCxsUGlUmFhYcGXmpLJZMhms2iadqRN8o4a+Xz+REmIlJJ6vU6tVushcOPj41QqFV//FQdCCGZnZ3tS4AYdmqaRyWRQFOXESVRYIXpQ6sX4+HhgvvH29jbb29soisLIyMjes6TrzH7pS8x9/OMUvvAFlPZeqpBMp+0i9MlJOppGZ/d62Xwe7cUXUZ55xiUrYmsLsas+hwbytcJWZFVBpLCJyG4QQeaCjWq5CULvsritCGM+JJ3HRVDUxCFFFQKLwX1d3Pt4/kWbvaaN7d0/Jc+1M4AKcqpP9pAMGWv3bg3s2pu+O9JLbgR2pEfF34jQZF+rnahK+/wdsKxRFCVGulaHvU7q1TayEH0/BCDFCIJ673l27DGLVtv3nAgF5JhJ7v/+QZpP/HH8L5QgQQIXQgh3veteX+4l1e/555/noYce6onWv/rVr3a39yMjb3/729nY2GBsbIw3vvGN/MIv/AIPP/zwgcc0LEjIyBCh0+n4ZHi9ZEQIwaVLl5Kc2XvE6uqqKyc4Pj7eozx2/vx5V162G8N478OM+uNCN/lwcNBC9Gq1SqdjVz9PTU5S+PrXUT/5ScTLL5NpNqHZxFxYgI0NlLptBIpOBzY2kAsLiGaT0W9+E8XcS0uSmoY1N4c5Pk5LVTHTaTRNIad8DUWxozBiBDvy4OGoont2lSDLIaRjP4XS3efM7h0qa46s7O4HBtEqWEEGfdA+YdB3/zRBlEAWBGJaBq8srRjXwkN++g2rFUJadhWxUAFniqyxv3Sr9t7+ynrVJjb9oiqemnUhJZY1glDr4fsDwqwjRQ6R2i241TMo27tEWaG3dsYEygKV51G/9m8xv/uvx/5KCe5v7OzsUKvVUFWVqampJJq0i8NUFtva2uLChQs9nztF9I79FoT5+Xne//7389hjj1EsFnnuued48skneeyxx3jmmWd49NFHD22cg4iEjAwRRkdHUVXVTcfqLqQeRmP4pCClpNPp9EzIhULBJSPlcrlHeWxYI06DBId0eFOxIP7z6xSiN5vNno6+Y2NjmM8/z+xnP8vEH/0R6m73Xy8c205OTmK+5jVgmiAlwjRRdR1zaclPVnQdymWshQWUcpnCc/8Z8Sgwim34prC92V4FqG7D1QK2sLurByHKSI/a1t5NDSvt/j1i1yBIE0ScYut+2K0vEVWJrILIY9fSeIKcsgMijohPzCwJ0SH83gjsBoYK9u8UtwdK0PWV3XNFyQdb9NTuiEbDJlV9VlnRaCILIPUsyk5Xapey2wfRua4AYRjIbch88v00Hn0bDFla6GHDUZFUFIVUKnViPZsGHZ1Oh0bDrpkapv5Sh43uNKzDtpuizhe17fHHH+fxxx93//2GN7yBt73tbTzyyCN84AMf4NOf/vShjnPQkLy1QwSnE2ocGd5hUUeKQpBq1WFgc3OTra0tOp1OT0h1bGyMer3O+Pj4iXVFP60IKkSH/T+jq6ur7qI6Pj5OOp1G3LmD+olPMPeJTzC/sYGcmoKzZzGXl8EwoFazU6zu3kVeuoScnUV8+9ukvvAF37m9b5WcmrLJSqeDAFTTRBkZQX53GpHv7BmmJn61q92+Hi5MkNu7pCHstY3yugdskxKoqIgdM7xJIvQnEh0B6T7Wf7+IgIVvJRFgq1s1dutgCsBUDIlhB3FXpX6KWwLYBKn5e7r0RYPeKIpDSEJEbSSjCPypXEJK+1z9NCHSIG6DSAXUmDjF7N7vqdj/Ub6zivbb/xD9Pf+8zwVON1qtlqsiOTk5OfDKhScF0xPtTXpb7eEw78XU1FRg9GN7exvYPwlcWVnh9a9/PV/yCqacUiRkZIgghOgrw3vnzh1KpRKGYfDggw8OZV+Ll19+mXa7jaqqPRJ3hwHDMNxUnnK57JPN0zTtQJ1p+f/Ze7PfyLL7zvNzzo09ghEkI7gzuefK3GvLqizZHkMGxvBLezAYuxsDvxjdDfdfMIBhv/jN8ADzOrCBgdy2S2pYfmhIssouW7ZUUpWUVZX7xtxJZiZ3MoLB2O8583DujX3LyipVssQfkEhmxo0bNy4j7v19z++7YC72W1tb2LaNz+f7lV59cqsafFRXtzeAUqnUsNIZiUTIZDLIdJrS3/4tke9/H+v99xHVAnwnV8ctNTaGnpuDUAj29iCVQs/OYh85YsDK3h5iYwOxtoY6ehT6+pC3buH5l3+pPaA5YJhKk5/HgIH6pt+qenzHWdlu0ThrBaLV19Sm1plJAdsg0s6DnTwHOkwDhOzQpLcSWFdXG02LKGGmNtuY999De7pUvovXc6ubgYAAsaQrdK1uKkdzEOfQ0ZpRyMT6buvjafGccu1Sofc1O48SFBayCvEKXTCY95/+P3Jv/u/oo2+VH9NaI6Usg/yve+P5VYT57ccaGRlhaGionMdyUKa+yAXPU6dO8d577zXct65fvw7wubQf7vf5614HYORrVlrrsri6WCzuSzDi2uO+TBUKBZLJJLu7u0xNTdV8mWOxGOvr64TD4S/0oqy1ZmVlBTAN834AI6VSidXVVZRSZSezl61q+pVS6nNNQLa3t9ne3iafz3PkyJHKJLBQoP/DD+n7678m8u//jsiZ1WTd24saHETHYuD3m9FBPo8OhRDpNPLyZWQ1QKkHK5OT6NlZ8HoRySTa40EdO2YyRIpFA1ZKDxChTIXWlMM01vVvy/lI6Qw11r2trG9FpwwRDJ2KJLBbt492LlilNrQwaJzgtHr9DpcQ3Y37lUtjeoTRX/S12C7b+fWArvUnYOhhrIMY6vI5rZzQ3FBDP7WAarfDfgtNnuNWicokpkBLq1+pbLSsOs8CdCSMTO8R/X/+gMz/uwCWp8GFrtkk8usGVrxeL/39/SilXokwv1e1XNH2V21U8qrVF/n5/93f/V3+8i//ku9+97v83u/9Xvn/v/WtbzE6Ospbb73V5tmN9ejRI37605/yzW9+8ws7xle1DsDIPqpumjmv14vH49nXKx8ugLIs63NTtdbW1tje3gaMqLla7B8IBJo6XrxsVV/kq0fir3q5I2Tbtj83GGnlhPV5L/S5XI6cAzR2Uyn6b940048rVxCrq8Z+N1ehtYidnXIWiDpzBkol5LVrRu9BHVhxPl86n4dw2Th9CAAAIABJREFUGLGzg3X1KlQHHdaDlaNxRCBToRm5FrnRukZcYax70wL2dIXrr6iE2NVXu4+hBlYxAvH6r0EnoKDcoJAWVaAroXinEsUOxwG1mo0tTFM/1OT1uwA/5f112VMJG9Psr9Ne9wEGDLXbr8SEK1YxgXROIESb8yww5gbNWJ/JquPxUJm0NXld7e9B5CtUMFHIoKUHubtO4P/+Pyn8X/8DoGmz2QqgNAMrQM0CwqsOVgKBwAEIOaiuqplt7xc5Gfnt3/5tfuu3fos/+qM/IpVKMTc3x3vvvccPf/hD/uZv/qb83fzDP/xDvvWtb/HgwYMyE+Ob3/wmv/Zrv8bp06fLAvY///M/RwjBn/3Zn31hx/iq1gEY+ZrVwMDAvufMTk1Ndb1tqVRid3eX3t7emotKLBYrg5FMJtPgPPZliByFEExMTJSFlPuhqhuNF51GuRf2euDVrROWK0Tf3d1lZGSk4feXu3SJwX/+Z/rffx+rDhwAaL/fWPI62R/YNuRyiO1txMaGoV+5x+SClVAIdfo05PNY168jnG10LIaunqwAulAwYGXzNpZYNU2qB9OwFgGrCUAQoJMCUdS1TW+709Gsj1LAjpPE7WlhEduBYSVUhw26wcvdfIy7AQ/1IX428NTYHzNcJaLvti/oNqG9+hTYmKyUdu7b2TaPuaUw7lwRoORoQzoct1ZAQSCq9Dk622Qqppw/Tfp/kds1YnbnMYE2OSR7JaxPvo/8yf9AfeP/aPr63QCKaoBS/adUKjVoEOv/ftUBy0EdVKv6oj+7//AP/8Af//Ef86d/+qdsbW1x7Ngx3nvvPX7/93+/vI1t29i2XQOOTp06xXe+8x3+4i/+omzO8pu/+Zv8yZ/8CUeOHPlCj/FVLKFfJuHloH7pVSgUXiqU5+tUq6urrK2tASbIqFpPo7Uue3UfWBi2Lq012Wy2PL7vBkRVr6i69XlWl54+fUoymQRgYmKCSCSCWF7G+s53sN5/H1UoIP3+mhR08fw5wskIsY8ehYEBxMIC0vkc1Bynz4ceGkIPDKAHBgxYyecNWHHE7KIOgOloFDU/D5kM8vp1xJCCAScRPIZpVkuOw1GU2qZRY1bAW4XYNQEd2nb2W72PFGjHJliEaN3o2rSfbCja07AytE8KtzHUoHa/2lbUovpKtzkWRYW61Uw83qxc695OlacxoT5ASyE6613uV2GmI0k663bcKoLud86nAjZabFeiNlCyunI0fI5ci2NtS+z+/w01ewx96BB6YgI9OYkeGzN0w5es6ulKtQ6s2pb760oF2++llCKZTGJZFl6vl2DwCxiJ7sOqt5AHiEaj+9ro5+tSB2Bkn9WvKhhRSjXc0La3t8suKvF4nNHR0a/i0H4l6mWdsAqFQoN+KZVKsby8jEylGP/oI+I//GFNwGCzUhMTqNlZxNaWmWD4fAYZZLMGrKyuIvb20GBARW8v8vZts339e/J4DFgZHKydrOzuIrY3EdYywrXvDWGaWncl2wNUeUloG6PnCNIIHpRD52p2qvJUGuM06JTjuoXzei0M3bQ2x9DSlrdTvoi7Tbuphrv6367StG6cndK2I2Tv1I8qIEFnHUuOmjyXtq+dapFFEqYhWV0XBCL9gtfWbnJaqks5r7tKa5CpMeeqCa1Pa2eaUo0tSlSCLbeAKuMdDaizZyEeh1zOgJTJSdTEhAErzh++AG1hPVhxf66mbVbexwFY+WVWsVjk4cOHgNEzjo2NfcVH9NVUMzBSzZo4qK+u9geX5KDKJYT4lQIje3t7bG1tkUqlOHz4cE1DG41G8fl8RKPRrzS47+taL+uEBcatbHNzk1wux8zMTIXbnc3S+/77RP76rwl/+CE4Uwx17hwEg6ZzLxQglUJkMuiJCcTGBvLOHeTiYsvXU7Oz2IcOGU2Jk76uTpyAfB5SKeT6OmJrCy2lASuhEPLmTcTly1VvEJgGHcbQriygZCHK+T6Av6qXzIFwV/SbNZiqzXTBC2Qd69/6p7dpckWJ9k17kfZgpBttRjcr/t1QvXJdvJaznX4OREG08X7Qe7ROq68r0eJ96l0H9FUJ6UVKv3gwoqIGlHYsNxOmXQnKNMD64xHCASTVIZke0CWJQEEf2K/HEGsx9OQk4vFjrCtX2r6cOnwYNT2N2N1Fj42ZacrEBMoBLnpiovxdalfV14VOupVqgwswtJXPC1ZWV1dJp9NIKRkbG9uXpi1fdlVTaQ8E7JU6AMGvTh1MRvZZlUqljuLotbU1CoUCQoh9uQKSy+XY2toqu4K5VJ6hoaGGkLsvK4vk85bLBbVtG7/fv28udlprMpkMXq+3fLOqXtH8vOd4a2ur7DAWj8UYuX0b+aMf4fne9xCPHpUb/IbjcelS2Szy+nXwes0Uo6/PNEaWVXG5ymbRo6OIp0+RDx60fo8405L+fsTKCjocNvuS0uhLMhnE9goiuGbAhhM4B3UTCE15VV2nnIZXgPYLhKfJ5VTSvGEtYmhd0AhiNKaJbtU3ZGhY2a+pLG3zLXRWIMLtL/067WSEtKs9Ok9gknScnpS3c/clgFGaL5etdbm/EuY8tAsq7KUyfVqhe1thqFC0onQfqAiGCtZFhJG227ih1dO1tHFvE15Hn/IZkA5VvjOBgPmcF4uwu2sc4yYnEVtbyDt32h6HGh5GnTljnjM8XJmoTE6WAQvRTmEqnavZNKV6JbuZyF4IwcrKSjmodmZmZl+bt3xZZds26XQapRQ+n69jRMDXteonI5ZlHQQZvyJ1AEb2WXUDRu7cuUOxWMSyLE6cOPFLOrLPX24jnEwmGRoaIpPJ8PjxY8CEBG1tbSGlZGBgoAGMvGq1vLxcFs7Pzc3tC25uNpulWCyyvr5OJpNhenqaQCBQvvEXi8UyUPH7/Q0ra64QPZlMMjw8XKM7KRWLPPv7v2fgn/+Z3g8+wKoKhNKWZehR8Tg6EkH7fKZh8vuRjx4hnj5F7O3RrNTgIPrIEcTmJvL2bbSUMDBgxOyRSIW+lc9DoYDu70fevYt8/rzledC9HhjS4FMmf0OBVhLhq9OV+DFBdcmq/7Rp2vxrhaF6ydr/IyVhT7Vs9nWpAxAo0J5C1YGmpVMg2oEZ7TTD7Wbn7mWoE07dofP0QBkL3hpKlaslqWdRbNNd89+NrsSlhlkYi94uMbd2DAbKx9tLd1OVPSo5Jp0AlcKERjb5HWiHllV9vnQBcNPaM8AlKmDXKfvUKQiHkVevglIVsBIOV0B5Oo3Y2EAfOgS2jbxypUFbVXMskQjqwgVDA+vtLVPB9MREmQ5GvJVI58Wqmcjetm2ePXtGPp9nenq6vAC0nxzBDuqXU/UmLV6vl1AXU7+D+vLrgKa1z6qbFWqPx0OxWMS27aZai1etVldXWV9fByAYDNbYNGqtmZ6eJhQKvfLvA2pH4C+blfJlVvVq48bGBjs7Fe6Iz+er+Zxls1meOm5WzdzaFhcX2XNAQzAYJB6PI65fx/Pd7+K7eZPZ7W1ksYjo60OXSghn0iVsG9bWUMPDAFiffYZIp2uPMxYzAvRYDHp60JYFloVYWUE8foxwhOtCKVhdRayuAoZ6ooeGECsrSEdXpP1+1Pg49PWhQyEzbcG4IeniJtbGAghlGrwiUAARqQMiWiAsbRrsqq+i9jo0mfpybWXdSoHYA2SncA5JS56Upm2SubbN4+123xZkgKGedcDROgOiE8hwjqVjZZtYH0sM8EgDI86/M3Q/hSjRGYy4lr/+F9gvIHapBZhJiejr4vvuTmpszGes3WtKIC+g2bQNEJugLcdWWINQZr86bIwP1GsetH0OLQMmPyedRt64gchkKvtYXIQq2qOankaPjRmjiCtXDHXy5EkDViyrMkHc3ET39kI0irx6FeuDD1q+DW1ZqLffNgsEXm+DXkVNTMDQUAenBHMd2tnZQWvdoA+Mx+MUi0X8fv+BI9hBdV2vEqviV70OwMg+q26+PC41y+PxvHJftlwuh9/vrzmunp6eMhhJJpPEYjFmZmbweDx4PJ59xXENBoPEYrFXNlyqmRB9aGiIYDBIPp+nVCo1HLebVg/m81cNcJVSZSDie/oU/3//7wT++Z+Rt2+3PoZIBHX+vGk+3CmfbRthejKJWFuraZj0wICha334YdmKt2Z//f3oRMI0NbYNUprn7+1BMIiOx2FzE5HPI5aX0bsp9PETUMhj3byO6MmZhtkH2mfcibAxqeh1Xx+hdOMKugIRaNGIOv2NzgJJp99y6F/tdA9CtmlsC7Sn+eRAtAMAThZKu9L5zmBE1LtUNassnQXpYIBDs8ZcOI8tYix5M3QFbrRuI+6vL4tKdki3zylQc7xCKwNQ202bMlQ+NxJzbjw0fMaqS3h1Y4J7FgPQBIi8rj1vEkTKmahEbET6MvzMRthVlsL9/QbgR6Pg96OFKAMB6/Jl5KNHlddfXgYHzLvPVSdOGP3VnTvG/GFmBhWJgNdbAStbWyAl+tAhxMIC1ocflvfR7BTbp08bEJTPG4AyOVmZsExOooaHWVpaKlN3BwcHayaw3WoG24nsXcZBtS7zQGT/9a6D3+mrUwc0rX1WSimKxW66gFerkskkq6ur5PN5pqam6OmpdFNaa5aXl4lEIkSj0Veyid/P1UqI3i1QzWazbG9vk0qlUEoxPj5O1OGIFxYXSf3VX9H/T/+Eb3sbK5GoaDpKJQo7O4hkEu/WFkxNQTyOvH+/PMFoerzRKPbZs4hs1jQ3gYDZn0u7SqfL9rzqyBGjAXn0qDZhva7UxAT68GFIJc1+fD5ILSMzzw3nxcI0fE64oAYIVy3WairOUXWnTduOzW/DG8FoEFIYAFD9vAKtNR026FDrhWKdlYhYG7Cyi6E3tahu9CIdG2sw76sT3XqLrvQR7NIZtLjnsJtczgzdW+7aVOhMg3SmahUcEX0T1zQitAZLG032rel4DnUBCDlP3TWvX96PotHRS2HspwEsYaYrn6mGl7ZPnDBuc1ev1tAhazJ3AgFwefbBINaVK4gqqmXDsfp8xoQim0XeuAGJBDqRQPf0GLCilHG+295G7O6ijh1DrK0h791rew7U2BjZ+XlKOzsUh4YIHD2Kd26uYl88Pv6l2Be7P+93RzDXIOBl9H9fh6pnKwSDwQPDg1ekDsDIPiutdc1K9X6pZDLJokMH6OvrY3x8/Cs+oq931d9M3fq8N6J0Ol3+/cWAievX8bz3HvJf/7WlCB0gNzFBIZEg8PQp3lzONCbRKAQCFLWmkM8j83l8hQLW4CAUCiY5vcVnXFuWoY30RBAPHiAcnjo9PehAwIAMB01o24aeCGRzyMUnpuFKpRC6aJp1H+B1mjafE1ToTjI8lemCLgI5AVIggo0drrZkw2REa9DFMMLOmlXz+ucEoghSTd+jPTSFlXzc8pyq/lFk+lnrx+PjyNRy68etBFK3Crlwjk/5ELL1dUY7lKBO0wedlIhQe1Sgi7R3HCtviAENXmCYthoNvW0hvN1YfWFAZvVdsJMsbZvWgKWEAUv1x5aiMe8E53W9dARieleCUs3PUZHGCUuJCnhToHcEOn/IuGVFImZf6bQB9m7mTl0roEZH0bOziPv3a7RWuqfHgJXeXgNWhECXSoaydfcu8smTtu/FPnkSIhHktWtmcjkwYMCK30+pUMDe20OmUviTSdThwwBGt9LmOqPDYexf/3Uj0O/vr9gXu9OVQ4fMsb5k7Vew8vz5c1KpFEIIpqamfmUb8HowEg6H901A8de9Dn4L+6xe5VWNYrFIMpkkmUwyOjpaI97u6elBSkkgEDgQjH1J1Ywr/SIrYUqpshA9Ho/X/J7ClkX8Rz8i/sMf0vPTnxo6hRAQj6Pi8XIzgRBo20aEw5BK4bt1i0AVJ93ViwAQiVCcnQUB3qVFxIP7Zp99fdixGDmvD+33I4JB/BGj8SCTRaRS2E5zZNk28sljhHYoJEcOgwa5cBex0+ihquPSCNA9AiG1ccsSQKkKiGDAhdZAKQi5rBH3hqA+9VxF+xFqu+b/7blziNUkOjGIvPkxzUoPRhFrzcEIoyPQAoxoy0KUWjzPfTzXmKlSs83sNNxvDUZ0Txyx23r1G0CPHUY+bb+arTUQ6uKzlxMIf+c1MZ11tC4aeIqhbbXoqUTJ7loDovMOJc/99xqIdoBE0ZrO5aFC+aquXIvnCEe476U1uLJB5JV53Wb9tBczLak+Fx4q4EcCMY1GIz/5BNFksq69XpSbueMEhIq9PdjZMd9pKcsidrG7a2yAw2HjsrW1hVVFy9ShkHHdisXMlFQIKJXQwaBx77p6tYKbHP2JWxaQHxwkPz6ON59H3r9fsfx2pjTk82U6p04k0MPDyBs38PzgBy1OIGghsL/xDYjFjI14lV7Fna7QhcPUi9gX1/+pz2gCaq7PXyZYscu25PqVnuB8mdVs3f1V7qd+1epgMrIPq1PwoVKKXC5HqVTC4/H80pr/zc1Nnj0zK7YDAwMMO8Jkt2zb7pqClc/nKRaLlEolYrHYwUWjRbmfg3qHtc9zvnZ2dsq/v76+PkYGB5H/8i9Y//7vyE8+gdVV5OYmbG015vqNjJhV1NXVBsqFDoWMbiMWM247oaCZXGQzkM2iszmsXBaZSsHODsK2Ub297E1OIGyb0IMHyFyu8b1LSXZ6Gv/oKGJzA7a3wetDeSxKQoLXg+ztQ8Zi8Ow+1sZjs6TvByE0GgsdjCALFYCkLQs9O2F+tv1Y943tqf32u1jXPmw4BvvNb2Dd/Ik5B6OzaBHFunYZHY6Ct4jIZxueoyYPI1dbN/J6ZAix3ZzGZk8ex3reWo9jTxzDet7eqlX3JhCp1mDEnn0d68EnbfdhH3sX61bj+ajZZvQo1pO7bbcBsI++g3X9Zx23U7oXma8ATK2AWBOKXInuk9xtjIVx/baCRkAB6IxEFLrgf0kqNDeXWtWmtC0R0Sb71ZhJTLW7WbMlRE2D7kZrR9fjZJNgg/KegELABISurJS1WWp2Fj0yYjJ3HDfAmt17PGXnOzUyYuhWLijY2jL7qtNzaSFQZ86Az4e8fLkMgnQggB4aotTTgxWNGgpmoYC2LGyt8f7858h27l2hkAFBOzuIpSXjCFY1pXHzieTaGmiNOnEC8exZjRamWaljx1CnTkGxWEmwdwHL5KQBMl9ANXMEa2df7P79MiBifX2dXC6HbdtMTk7+St5PD9LXX+06mIzsw+oUfJjP53ng5C309fV94WDEtm1SqRSRSKTG0z0Wi5Wb2VyT5vFFtCDPnz8ve8eHw+F94x1fLBZZXFzEtm0ikciXlgrfbLXtRS6quVyubBDgVk9PD0IIQlevEvvgA4IffGDCA+tf2+dDDQwYykdvL5RKptEoFs1q6eHDpqHZ2jKrqVKix0ahVEJ+cgmRzzc9JjU8jH77bUjvIjY2CKXTZsX2yBFj+2t50MEgeCz2dncRSiG1Ic3reBziCbTfR6GQp5jLQbFIeOMJcjVjtglFIKAhnyNz+DSefA7fcm1jb79+ASEF8tNLSOc4dTCEfHSj8TwIEKsP0bEEavAI8tLHSNsJcTt+Es/N5g22HhiCFmBEjc8gNx42fQyA3ji0dieGWO3jWkgI9qADPRAIocL9yHwaHeqF/B4itwe53VqKjq8LOkupC91aTwLoDEbESusQy5oaTMBSBYwICTrvxx4/hbVcAU/K6kfK9tOhcjUDImCmEFs0aG/ErupekO9mgWTpKIwXlmqeeJ+iPHUTljPFaXbXdowRqApDFMJ5Xdv5WYC1dwvuAEVHm/UbvwHJZFlvoU6cMJqOZNJQt1x3u2gUPT2NeP4czz/9U8PLaymNK14igUokyhovsbmJqLPTFrkc4skTfEDp0CHE5KTRkW1u4sG5vlRbDrsuXsUiOhbD+vRTrI8+quyvzoEPjIWxOnwYefcu4ulTdF8f9jvvmAlnoWCyVjY2jO7s7FkQAnnlCp42mSs6kTDny7bN5KfOwphEN2KmzhOQan1fNXBp5gjm/txpulLvgHhQB/Wq1QEY+RpWTc5DE/ehl6mdnR2Wl5fRWjMyMkKi6gLs8XgYGxsjFArV2PN+nqp+D7Zt7xswIoQg46w2ftHH3Grc/yIrZplMhufPn5PP52tsesWdOwS+8x3mf/YzpG0jLQs1MwPDwxWHq1wO3dNjNBvZLPLTT1uHFgaDqDffNNz0zQ1EOo0OBAzdwvI4ug6FRoM/gJASNtbNdMMugc+HKJUQe3vo/jh6IIHI5RErz8CyiFiWaYA8FtoS4PcjigWgiBI22qfx5ZKoMyeQ9++aZeWgpNQ/DIuL+BduQ6Kn5vjVxCzF1TWCj2qBgjpzDuv6TxveozpyGnqiiMtXsB7WAg+ZaR2zLTZbC+314Ci0AyP5OuvjcAwdP4T2x0yDmfWhfIdNGGQ6DXsphE4iMNMffe4i8motsNJSoEPRcgik3vNgT78LoojYXUVsLDboXsR6e12AOdbmoLO6VHwc+by1vqW8Xf8wcul+w/+LQh7r559gX7iIfH4JUSqgZ45BF5MWgJIniEc1Tq9c+hSpyuRF24Cns74dMI5pKaDgWEF3U4oau1+9a/5dvcYgfBjdTDNGkUUjXcsCraX5/VmgfcBxifKfQd64g/Vv/9bycLQQ2G+/bQ6gaA5Ej4xg9/WZqcTaGsJZMEIIIyJXCusnP2m4LmghDAUskaAYiZB1vr/BZBLf8jJUAQpRKCCWlmBpyTjvOVQwubBg9uXxoEZHTT5ROFxx8cpm0b29yKUlrOvXK/vb2QEnt6p8qoeH0UePwpMnJlOlrw/11lsNWStidbUskJc3b+L5+79vfb7CYeyLF41oPxRqCIdkeLgLYdTnS7Jv5QimlMKyrPI+f1UpWs3qV13M/6rVAU1rH1an4EOtNc+ePcPr9RIIBMrORy9aSqmGL2wul+OeQ8MJhULMzs5+rn13qmQySSaTwePx0Nvbu2/AiNaaGzduIIQgEokwNTX10vt7GSes+ioUCty/b5q60M4Os5cu4f3Od0wIWqtj8PkM3UJKxMa6EcAGTHYBQho73UIBMhl0TwQCQaxrV5tqNgDU5BR64hBi5TnyfmODqf1+k5QeCCDvLyA2KpQiHYkYF6D+PkMLKeTNtMRrQSGPkBp55xr2iZOwsYLn4QJqYBA9MwWZHNatawDsnj5Nz33zsxoYQQ9Nor0ePJ/VUo+0x4MeTSA3VyrH7/FiH3kdaWusq42aEDU+hdx83PS9F4cP4d1Zanmu7ROnsR5ea37eRmbQiTEoKkjtGerJ+lrlWEMR0EVEoTUIsI+dwVpo87vuS8DOZs2kRAdDqMkpiPeBV4MuIB981lSYX34OgC+G2Eu23MYczztY1zoDB/v4O1iX229nHzmB8GxCViC3VtpuC2D7Q4hkCVlsI9SXFsS8CG8OnfYhSi9oHrJJW2ezhioAfUAeMxVp0jtqDULTekJTD0jAOKg5eSU6D9gSxRGI9JnJQ7FoAOz6Ong86JmZBuF6s7KPH0ePjBjg6/WaZjuXA2eyIlMVfVOZCnb9eq12zD3GeNwAlp4eozcRwiyErK/XUMpqngOo06chGDRUsEKhEoCaSJhrlevitbdnNGjQdiEFHA3N+fNmSrS5aSavTjYRpZI5Vw49DZ8PdfZsxzR77fejjh9HnTuH0Lo2b2VyEj0yYn4XL1mu4+bW1hbJZJLBwcFy4vqrLLL/susgff3VrgMwsg+rmxT2l6lcLsfGxgbJZJLx8XFidVzZhw8f4vf76e3tLV/kDqpSLxs0Wb3i5f79eYXo0Wi09veXSrHzV39F9HvfI/jgAcJNLA8EKquCWSMS1z0RCEeQt242bR7A4YW7qc63btVsp/1+iERMuvroKLon4jzuxEQLYcCMEKYBCgYMhatkKF8Ui6a58HrRiQQiuY1YW0H3J1B9fUhtw94uOtqDUEXkwi3U8ZNACevKJXMMfXHU/CnkLyqrtfYbF7BufozuiaFmTyE/vYQeGTMTALt2kmi//jbWbUMJ0ZaH9ORJfE+e4vH5kKmVpg1N7rULBG41F67vnXyD8P1Lzc9lIAyeYrnhVUNT6N4xyJSQ9++jRiax7n7W9LkA9um3sG7+vOXjOtQDpRyiDcXKPt0ZHJROv4P15A7q+DGw8sinNxDFWgCkhueaTjIaXm/uTaxbv+i83cxrWLc+7bzdkdMIXwm5dKvztoffwvqs9flyS/fG0SNhtLcf686VjtuXn5cFUcBMPLqLwTDlBG62o3bpkjMlabKNdj6Sos7ut4bilXNe5y6OlXTINPWZDPLuXeNw1d9fS5NypwW7u6hTp8ohiu2qEI9Tmp/HXygYKpjWZuEimUSur9foU3QsZva7stJ8kaKvz4CVaNRcs6RxGJOLi7VTmrpSw8PouTkDrlZWjElGImHeYyRiHPgcy2FyORgcNIBpqz3VT83NmWDVxUVDY+vpMe/RAT5lXU4+bxZQnIBIkW0yicNZ+Bgfx373XWMGMjSEqqKC6fFxA4a6qL29PZ44rmahUKhmUazdZMX92b3XfJ3ASr2TlsfjOehfXqE6ACP7sGzb/sLpV9WVTqd55Ij9otEok5OTX9prHZSpl3XCqq5MJsNjh5YQDoeZHB1F/OhHeP/2b7G+9z1EEz2PW2pmBj06injg3Lg9HpNYHosZSoQzEdE+Xxm8iGQSCgWzcpnNGhee3V3DHz921FkxbBRda5/PNEAeC/nwgVnRDIbQwQD4A+hoxFC49tKI7S3E5gbq2DF0OIzIZhCb6+jhQchlwOOH5BZC5ZHLj1GTc+ihMcTWM2QV7UqNjCFEDjV93DQcKQOe7LOnse7WTiS0FOjZScTqMur4m6iFh3jXzIq7feEi1pVG6paWEnuoH89Oc4F4bmqawEpzIW3p1NsIKSBrIx48RG7U6nXscxewrjcHOQD2mbewbrRuru2TnRt/+/hrWLfbN/320fNYtyugSIciqJPzEAT5/BYiu4t99F2sG+0F7loI8PUhdju4f/kChu7TBfkmAAAgAElEQVSUa97E1RzbyXeR136BevM1rHsftd928g2sG82BYcO2c/OI3U3kdueJi1sqcAi5umSmRIEgwtf5+AEzTbHoGO6o8wIRaXH7dvUq1VU0on/hhG6SA4QXO/E2+s4DvG1yegDs+XmIxZC3b6PD4TJY0Q5YES5YWVvDPnqUrM9HaGEBq0XzDc6k87XXjL7EbRarBOjVgECD0XfUCeLLj7v5KL29JszRSXwXjx8jV1ZaL6hUTUHk9esIbTRo5WBI1wY3k0EkkwaAbG+3DXYFDKX19Onye9DRqAETWpf35U58dF+fEdovL7e0RtZSokdGUKdPo2dmIBRCTUxQGhtDHTqENTNTti/WWvPgwQOKxSLRaJTR0dEXWsxy99HMIv6rcgR72aoHIz6fr8bx86C+2joAI/uwvojgQ6012Wy2nHheLXLXWnPnzh2UUsRiMcbGxg64lV9C1YsU3XpRIboQAr+/wtnQWnP//n18n31G4oc/JPHBB4itLdPsx+Mmgdm14nVWF7XfbzI+7i0Y0WmTFX81OIg+cgTx/DnSMUhoeE9+v2kYSkXkwl0z9ZAWWNK8luXBnp5G+H2IRw8QqV3YS5cbEXt+3qwgXr8K4RBqYAhiveD3INZXEPfvARr74jfAklgLtxFrq9jnziGfP0FNziH2MoiH99DHjiDvVrjj2pLYv/5N5M1ryNVKU2m/9hbWrcYm3j77hnndR0vIp1Up1NFesAqIbCNtZG/uOOGnzZuUfO8A/lwFYGgp0RPHyYoQ1vIzStE4kfvNKVra64egF5FpFOuax30Q8LV8HMA+fQHrRmswo33GjaiZA1h5m0DYNJ4tqGDa60XNn0QPj2Dd/FdEsQ3wHT2MfNzeHhjAnjuPdaP1RKhmn30TyOdGEG+/cxH56GOEavws60AYkq3fR8MxzL+LeLaM8KQRyfYZLQAqMY54/AzhGBponx99ZBa52H5io/MCMhphY6hWneIgcrQOlcxgcnRKIEpQdtyyQAcEoBHuhGQBlNdPIZHAMzCACIWM8USphO33Yz97RqhDMKGOx1HHjxvBei5HMRZDRCJIR//F3l5Zh0Ffn9l2aaltLokOhYyBxcCAmZoqVRagy7W1hgBG19VP3rvXEKxan4+ivV4DVjY3kY8eNXURK+/XWaRxKWY1wMfNNsrlzGPOAo68cqUptay63Oud2N6uXJOh1kRgd7dCR/P7DRBrshiphYCBAdTUFOqttygJARMTiOnpMh2ML4iW1MwRDGonLNVOYO7fXyVYqQcjfr//pbWtB/XF1QEY2Yf1ImCkmfsG1IYQ9vf3MzY2VvN4NpvF7/e/Eisd9Ssx+73qV5zgxTUg+Xye5eVl8vl8GTACiEePkN//PvoHP8B37ZpJOm52DIGAubkViyZksAp8aCGMDW9fX5kaIfI5ow3RGmzl6ETyzkQki46E0QMDyIcPjFbELpUdcITW6IEE6vgJSO6YlUK/34QUer3g9aEjQbAsRHoXsb2DWHmGDoXRR48gr3yKjifQI6PoaBS5+gx592b5eEu//hsIZSPv3kZsbqAtiXrtPNY147Ck+xOoqWPg92F99K+15yEYQg/EkOtVoW7hHtThM4idLeS9xuax+OY7eFtQmdInThF5dL3pY3vzrxNcvomePAm2xzj9bJtV01IwjBQlZIvmOH14nsijm00fAygdP4dn4XLLx7W0IBJBpFtrOOzjtROPptuc6DxN0L4AIMHnR52eRyQfIZuI9u3j72JdbT89AbCPNZ9C1Vd+aAr/k8e1zz15Fpl51KBd6ZaiBQ5oDAwi11dQEzMIkUSk2uew2EcuYl2qPWbdG0f3B5AbzScQWghUbA7LAWhaBsCTa+725T7HuYSIev1I1vnjiO5rqoQR6AucxQJtwMoChs4Vi6Hm502eyM2blYWCYBA1NITs74dgEFtrCqkUyqFZ9ly/3rRJLh+rlGahwuNBPHtmJq7hsKE2uWBlc9PoMHCmIFKapr7FfnUwiB4dRc3OVsBKPl9xy1pfr7n+aY8H9dprNVOQ8mOhkLEJ7uuDYNCAMcsCIbCuXWufPO/aDW9tGZpbk2BI8nkTuppMVmzQm9DRavbb24t99qx5bb+/AlYKBdjZQa+s4HHoaSoeR584gXj4ENliyqXjcfShQ9inThmNSiJRFtjryUnofRE+Yeuqp4K1Ayvuz1/2dOUgff3VrgM3rX1Y3TSum5ubrK6uYts2o6OjxGKxGoeqSCRSdtxIpVINY9yvenxZLBZ58OBB2SJ3P1HF0uk02WwW27ZJJBJ4PJ6WTlifF2R5vd4yIM08fYr8x3/E++1v11hegjOpGBiA3l5DrXDNDBxdiEilzGpZFYVBaI09NmYoGTeuIy43b1DdlVAyy1g3m3PH7TNnwO9DXr2C9ZMf1zymRsfQs1PI61dr7DnV4CD2OxeNIH13F3wBxMpz9NQU1kf/higWUWMTqLEJ8Aqsj2rde9RbbyE/+wj76Gmw/MjrV2BwD3m5iSPWufNYl01DrMZn0P0jyKtXoGA3BSLK64VHzScfqidGeHmh8TzF4qjxo/i1RKzZyOXGZr4wd5zQ7TbZHh1u0AUh2l7M1ewJrAfNQVK5urH0lZ0Ftmr2JNaNTyCbwfrJh2gpsM++BkEb+eRqpQFsM8WpLvG0fT6EW7pvGOrAiHXjCmpsAj0UR65WuZR1kxXilJo9i3XFfAfk4kPU1BxEbES6uUGD7ulHXm/8zoidTXTPDDrYg8g26hvU0QtYH1dZ1qoc9rELWAutp1nG3hhzJ3dsfEk5IncB2gJKdXbAHsDVj2ht6FsWcNJPMXACK9BjQgqlhJERWDHaKCubxXr8GB4/xj52DCseJ7C0hMe5dtjhMGJqqkyTAijs7qL39ijF40SePMH6rOq8LDe6qKmxMdTFi4jnzxGuVfiFCwasZDLlyYqwbdTYmLEbXlhoajcMzvVvaAg1NVUWsotMxtjzDg7C2lr58ygyGcSjRyitjXvW9es1Jhw6FDIAoxqsKGX0cvfuIT/6qAx83GDI6rKPHoV4HLG0hLh8GT08jH3uXCUY0p34rK+jBgfNhPjKFTxtHM8A9ubnkaEQPts2U+7paXP9TqWMLscBURqMq5fHg+fv/q7p9FvHYuhDh1CTk8b50HUFcx3BurQIfllHsGrNiru/LxqsfJ0WOL8OdTAZ2aeV72CbWR1ACDA0NMTgYG2s8OrqKl6vl2g0WgNUXoVSSnHzplkJDofDzMzMfMVH1H0tLy+z7Yz8Z2ZmCAQCNZSs6gtru6oWovv9/trfX7FI8r338P34x4QfPsS7t2emIGtrDVxqNT5ubtqPHiGbNABgbtp6dhY1NoZI7hjRquX4mGpdnnKQy0EoiO6JGkrXXgaKBUNRcFN+Y1EjRH36FPF02TQmXh/a6zF/x/uNLmUvbW7CSpmU83wBBgeQlz42kxj3+OcOo6Mh8PpBehCLjxGZPfT0BPJ2bYNd+rXfQBRLiKVF5LKZ/KmhYYQoIHZqtQlqfAKRXkfNzUOmiHXduEzpQBDiUcRGY/Dg7vxZeh40FzHbb1zEumEAj4oPo0dmYTOFvH0TNXUYa6l15oY6egL5oDmFR/mD4NHIfHPKk5YSFY1i7ba2Ey6du4jnauvpggZ03yBye631NtKCYA+izesA2PMXsK41b6DVxBR6Zgz5/Daks4hCex2FGplBPmpjdVy9be8h5EpzpzIdiqDOHMV6+CnaH4JdVfMZa1f2zOtY12uBopo5giisNnULs49/A+vjn7Te34lzyGfXauhjOtIHuyCSjVQh+7VKsGar0oTBLkCm2Oge60xC6sXuuigQ0lmxtp2ARAmsYChe7naWRTEepzg7iy8YNKvY6TSkUrC2htVkYqCjUdTJkxQ3Ngi4lrwutSkWA7+fkm1TTKWwdncRg4N4SyUzpW3TkpQnG6WSMbdwJyu2XUMDE7Zttj1/HvL5lvvVPp+ZhgwMVJLn02kj1t/cNPuqW1HXfr9xxEqlkLdu1fy/HhoyWppQqOxSpn0+RC6HvHSp/XsLh40r19paJcyxr4+clNiAVSoRsG3zHnM51MmT3YU5Dg+bbXd2DKXMCZkknTaTo7W1MojS/f1Gu/LoUdPpStmy+NAhQzEbHjbH6Yrsu7Qv7lTNwEr1/72oI1j9VATMguyLZJ8d1JdbB2Bkn1anFPZUKsXTp0/LQne/38+RI0d+WYf3hdSdO3eQUhIMBjl06NBXfThdldaalZUVNjY2iMViDAwM4PV6yxfKR48ekcvl8Pl8zMzM1FxUXYc09wJZKpVYcG7kXq+Xubk5rEuXsN57D893v9uUNqCFMCnJY2PmxpDPG5DgumTt7hpLSgcsaY8Hde6scaW5erV1bkgiYTjeDx8gq0BudanZWfToCPLWTeNMk8/X3Hzt06dN8Nr1OqG4x0K9dQF5/46x0Yz0oEbHytMc+fwp4v5CuSlQY+MQ8iAXH5t/D42gx6fRPT1YP/u3Gh2A9ljoE8eQC7UUJxUfQp06g7x1A/m89v0ULryDr4mNrBZQnBjHt9oc0NlvvgNawsoGcuGOsV91H3vjQlMbYPN+ppCrj5s+Bo4wvY1LVn76OP7F9mJaNTyOXGud52FPHcN63D653Z47jbXQXNPilvZ4wRNE7KXabmfPvwaxIHLlVlsBuz3/LtannalcauKo0Si1OzYpUBcvAkWsT7ukaPUNwfONpt8Le+4YMvO0ZsqhfUEoBBHJ9qJ8+42LWHcr4NA+/DbWpeaCe+NY9xrWQuvJmT3/DcirlnQ2XXKAR3WfpjGuXe46lG30JQiJ9ifQniHQmozfj295Gf9qIzgHp0EdHjYUoL4+ADN1XV+H58+RLXQThbk5cj09hO7fx7O7i+7tLYMV7fORzWQQ+Ty+3V0zXR4bQ96+3ZYuBaCmptBTUyazKBisgJV0upIW7/w+1eQk+tAh4wTYxD1Lezym2XZshwFDPd3aKlPK6sEKOBoT18bYsTfWXm8FrLggqlg06fO9vViffFLetlUV5+aQg4PImzcNFcy1HHYdz6qoburoUejtNRqTNqYl2ufDfuMNY92ulAETdRqf6vdonzpVsVKuNxHw+9Hj4+VpSukP/sDkt3zB9SKOYNDcjbKnp+eVoKEflKkDMLJPq1gsopTCtm2SySQ7Ozv09fXR59wM3Hrw4AFaa2KxGIlE4mA0+SWU+xVywUQ+n2dpaYm+vr6aUEiAu3fvYts2Ho+nDA611uTzeba2ttjZ2cGyLMbHxwmHwywuLlK4e5fE++8Tv3cPTy5nJgmZjLGOXF0tW0VqIYwOJBAwN8E24kl15AhqbBS5tmYmAT5vOYW5nBuSzUIwgA5HsG5ch52dhpU9LQzVCa2wrraYGJw/j8jnkLdvGXFnNIqO9Bi+d1+f0TJkM4aisPIcsbFuci3CAeRCbYNsHz+B2NtBJ4YgGEI8fYp88hj7nYtYnzQ2Yva772J94tCw4kPoiTnE9g461ov1WRPaVn8Cbe9hNXFuss+cr7HW1UKgp4+hexLoksBz6ccNzwHQff1Q3GsplrbffBfrs9YNt336daxbbRrR19prKoojU3jbgB0A+9w3sC63X323z7xbprS13ObYeaybncXm9skLWFc+RofCqDfOIZ7dRKabTAXGTmI9aG8fa/ZX+T13quLF/xXPrR8j8u3FxeCAoV+0+d0cmUfuPjZJ9jj6lp931rcA2G9dxLr9U9TkPOLazRrwWl86EEKPjSKfNmoM7JPvYv30Q+f7/2ZLRzUVHUCk6jQUGhOs6CwQa4UBKEJAViNWQQWDFBMDEO/HCofNcbrOWZubJgTV40HevNnUXlf39Zkm3LXkFcK88L17yOfPkS30IHYgQOboUXy5HL6FBaMxcax9s0qhSyVkPk8wm0VsbaGOHYNcrkEL0nguA9gXLpjro5S1k5XtbUMRc47JddoSmQzyeiPNUVuWASmJhHl/Dn1LrKxUgE8zsXmT6Yr2eLATCeTAQE2Yo727SyEQwL+3h7eTg1coVM48IZVqDIZMp817XFkBv9/oXNbW2mpXtMeDnpoyIbiZjPn8uOeryXvUsRil//SfKP3n/2yCJb+Csm27IVcEzL3WNXsJBAIH/dArVAdgZJ+WC0YymQwPHGejSCTC9PR0zXYvm3lxUK2rmQ6knutaP05eWlqiUCjg9XqZnJzEtm0eP35MPp/HsqwyoJmNxwl9//vIv/kbPL/4Rdubqz0/jz04iNzdRfj95mbv3iycFUqxt2fSjE+fRiR3augFDe+rrx81fwKx+AS5VEt70cGQoWn19aGmp82Iv1SknEtdfrsCNTaKWF9DpJKGzrW7W3agUtMz6L5oUwBjv3MRee2zspWrGhpGD42g++OInU3k3Ts1Nq/2hbeRlz9uOEf22fOIjWfoQ7NGFH/nlgkbGx1DZJOGJlb/2hdah+upU6cQTxZQs/NoGTA88XXjjmWfPoN1u3mYoH2hNdjQUsDAIGKzxapzOAo639b1SQ2PItebT6sA7PPvYl1p36irQ51zQVSi/XQFIH/sDfw3Ownc/UCtM5gOhdk9cZTQ1n08WWclOdILW6mmK88NxxYdQ661t6YF0H0DsLaFPjQN/hxyvfX70VKiQyPI1Q6Wt8dPIbcfQDGHDowhn7cOtazdv0Cdfx2xto183DmTRQ2MIkS+Rjxvz1/E+lkF/GivD3X4BNbdFgsDZxuBq0ZCQVUAiY2hdgFa+9HeQeRa0mQPSYk6cgQSCdjbQz58hI5FKyv0ANmcaXifPkXk80aEfeJEOZek+veppaw08z09RjCOAUAsLOBdXGx77csdOoR3YsLY7AqBHhigEApRBFCKgFJYqRRiZQU9NIQaH0fcvInVIpDVPSZ16pTJNspmzdShvvmumgi44YXy5s0GR66a9xcOG8csKc11+enThn1Vl5qaqmhXksnKvtxsKJ/PHFcmYxaP4nEz3e4wXSnbtz950piPkslU3mOhUJnwXK3V9dW/RwYGsN96C/t3fgf7d3/XTH5+yVV/P25VB8L1V7MOwMg+LTf4UGvN3bt3KRaL+Hw+Dh8+fAA+vsR6WSF6M2ewhw8fGoveUonEpUvE/uf/pOf5cyMsd3zp7b097I0NfFtbWJmM4WSfOmX87tsAC4DS/LxxoVpZMfsMhczNxw05LOQR6bRxt4r2ID/5xDjTNCk3QEzeaJGiLEC98SZiewv5oElwmRNsJi99XLuaZlnokVHU8WNmxVJpRHIHsbwE6V3UxXeRP/9pI+B48y3ktUvlBkf7/KiZI+j4AGJzDXnnZq1jjhSoEyewFhqdqdTUDGLtSQMlR8eHsGePI3J7hs6xt1d7DEfnsR42d7rSHgsGE031JwD2ibNYC62D9Dpmi0wdbatFAVAzx5GPW6+oqsQIcqN90rY6NId80sH5R1oofwSrjWMXQGbuNKE7zelediBE7sw8wc176PGjWFc706nUxLGGCVqrss+8i/WxAWY61os6OoXVSgM0dw7ramuHspptT5yBWAjr5+2zTeqrdPobyN1tZBfTHwA1O49YvYcoFbBPvI38+KOGiYoOhlGjh1rS7krn3sVTN+EqxRLobB6vQznTSkDRobwoDzowCD4nrT3sBA7u7SHWVhHPnjd8L136E5ksolgwzbPlMQ58qRRyZbWmcXe3F48f1+jatNdbpoDh2A1TKlEUAp3NErh6tf0UxOczQuxsFvnsGXY8Ts7nQ3u9eKTEZ9uVSUGpRP7UKUMNu3275X61ECbv4+RJQ30FtG0bAbyzr+rrZ1m7ksthXbvWsC8GByn29lLw+VBeL55AAF8kglxYMFOaFtdiVz/jTm1ca1/tALtypokTwKgHBxGOi1i7KutycjljIlAXDFkOc8xm0V4v9n/4D5T+y39BvfNO2/1+WeXej5vpQupLSkkgEMDbZXjkQf3y6gCM7NOqDj5MpVJ4PB6CjrjwoL7YarXa8iIAZHd3l2QyiRCC8fHxmsd3P/gAz7e/Te/772O1Sf3VlkX2+HE8gQCeVMrccAIBNJBNpbByOTzJJN7NTZMlcvQoYnER6Vg4N91nNErxxAms1RXjlIO5gZdXzEIhtD+ATsSNaLRUcrgd2vyttVmdUwoCJmhMpNPOhESY5kEIc6MM+BHayQkoFs2qYzqNSO6gjh9H3r3VAHB0MIg6fQrr08awPvu115GL91GHpiEQNo3Ag3smiK0vilxqzC+wL76Ldan5lMA+dw7r1mV0IIiaOQa+EOLpM8STx+hjx5D3mjf09pmzWLdaUdQ6BBGeewvrerugwnNYd1o3xPZr38C60ppepfoHEMmN9pO1Mxex2ojbAeyz38D6rAON6/AZrDvNp0PVlZ6cJ/KgtU0xgA5HKF38dTw3/g2R3Wu7bbcULS0EOjZeM7nQlkS9/Q7W7cbn27Ovl+2hu6nSuf8F696ltlkvNccTiUFGQLGAnpvpGpDYZ94GYZtFA7t5A6ZjJktIPm/8DmghUCffbPjcFYcOYaV3kSkzNdDhGKRziGIebUtQXtTAHCKdQzx+UqEy9fVhnzwJwbAxs0Agnj1FPn3aMhUdwD52HD02ZsC9ZaGVMsGJrhajzm5cnT5ttArXrpUpqDoYNGClt7fsSqWyWVQuhx2LEbx1q8YRq1m5kw2xtETesrDDYbTPR8jvN823S93K5ykODVGanMT/8CFyo3nejJvwrubmzLXIFdtnMuiNDay1NWShUHsMIyPkDh0iULffclq8CzB8PjOJ8PsNveru3fYhtsPD6MOHkXfuINbXy9oXd19oXQYYFAroqSmzz/X1lvsE43pW+m//jdJ//I8wNNR22y+rXADSTQvr9Xrx+XxYlnXQI72idQBG9ml1k8K+ublJNpulVCoxOTm5776E6XSaVCpFqVRiYGDgl2o33MzF4/MmomutuXfvHqVSCSEER44cwbO4iPXtb+P5zncQGxvGzcVxmSnfIJzQKz08jB4eNjeUFjdAAOXxUDh5Eq9lIZaXjQC8p4ec1thaI2ybEMZ2UgcCxrr3Smtxo7YsimfPIvfSeO42X33XloV64w3EygqyzlbVLfu11wy96nHj4zqRQE1PYX3W2PSpoWHoiyLvLxiKwug4Oj4AgaBptB7fRzx8UEv78PlMNsmdxsZOzc4hVhYRxdpGQFsW9rk3EV4LdlKGBpavbGO/9TbWZ81XvO2jJ7Aetp5Mqfl55L0WU5NIFFRrCpaO9kJhz6HBtdj/xDSyjfWtffYdrBaZKOVtjp5tSeupvM5R5OP2Exj79EWsJvbJ1VUKhJG5IrJUaLud7umFvSxEIqhTx5B3f46wm1/vVM9ITU5My+M7fAbrWgsq3etvIZ9dL+tIdO8ArGy1NHRoeP7Rc1ifXUbNHkHkNxHJ9iJrAPvkRayPzfnSwVDXgERNn0AH4m1BKIAaHAVdQm41OqRprw81faxsSKAjMdTYDLpnwHzeSnkoFcHymDyMpYeoaByR3EMF+qBnxCxCRJzExWQKubRczs0pv04iYa5fPVEDOPJ56IkiFxeRC4022OXneTxm+jA3V7a1Fru7lVX5JlQk18FLbG0h75ipUDnvo6/PZBuBAQXJJPT3YxUKnTUmUqLOnzfU6N1d7HAYf0+PMSdzwcrKCiKXQwtB8fRpLMsy+ShNVuu1EKj+fsTQEGpiwizM5PPlCYY7dah5DpgJj2UZ4Xg1UHPT4t3QRFcrEQxiXbrUlralAXXmDHi9yCtXwD1f0WhjAOPaGur8eUr/9b9i/87vmCnZL7m6pWKBuV/7fD58Pt8BW2Qf1AEY2afVTfDho0ePSDs8z+PHj79y9r2dan19nRUnAGtiYoJYLPalvl59omy9DqSb5+fzeQqFAlE3z8OplZUVko8eEf/xjxn5x3/Ee6k9r14NDJjJxsqKWdFyLTHdxNhCoewjr/v70UNDTTnL1WVHInDmTDlsS3s8qN5eCqEQKhTCE4ngCQQMtcjyQKlIfmUFmc9h5fJ4s1nYTRlagtdL4fx5rOUlPK3ctQ4fRodDZcvchuN5803kg3uQShrgFO1Fh8Jm2hM2lAyRTiM21hHPnpa51faFt5FXLjUIQ7UA9eabWJ81TlG0z4eePIR88gAd60MdmkYHQohkCrGyCl6JXG1saHVP1CSfbzdvLttNRdTsYeRS69Rq+7V3sK62Bgr2+fZAQo1NIVcet3wcwD5xHutOa0G5DkagVGgAaDWvEx9Grq+0fBycFdyeBGK7/Ypq/vjr+K93njbYZ2unHYXRcQrDMSJLda5ok8eRd9uLesv7PPYm1uXGz0Z5X9NzZR1JJ+F6w77H57GcIE41NgEB1VZfo0amEI+Wa6mKXQASHe1DF/3ItRXsNzqHRqqJOcTOWlN3M/voWXRkAPnoPmLxUZnupcYmoWQjny87r9mLffI8wi6CKiJWVtF4UP3joL1GC/L4MfLZM/TAoLESj8Ygn4NiCeEPmIb9/v3ywoehZY6gEwOOvkDDXgaxtmZW/8fHTTp7kwUMMHRPPTRkHLhiMRDCvMbqajmjpOn5cDUQt28jtrYq+4nFjBOUbZebb1kqmUnBwkJDmnvDuUwkSM/M4NnexopE8IRCBuC4U4dnz5AO3aoYi1E6ehT/s2etrdZdgDEwgHYAhtjeroCVJuYkurfXhFUuLdVMw3VfX8NilwGFPchnz5AtFpqqz/VXLUh/ESqWZVn4fL4aF8uDevXrAIzs09JaUyi0X12szrs4fPgwgUAXoWavUG1tbfHU8TofHR0lHo9/4a9R74Tl1otexLTWZdtey7I4cuSI2Uc+j/WDHyD/7u/wfPCBGddHIpWkX1dwnssZXm8iUXGEabMqq/v7jdXu2hpicbGy+hcKlcO93GBDHQxCJGJW6rKtcx1Khw8jEnGzXatpSTSKff48cmmRUr6AsiTa8uALhcABMTrag9IKlU4jMW6iAkDZoLRpPiQGYCSTJpXYtWQUGH1InabELfvd5toR9zHr53Vc+BVLQukAACAASURBVFAPhcQgcmYGbyaNePoMuVhLXbHfaN2k2u+0oXV1mIrYb76NdaW1hkAdOY58WNtI60AIHeuHSAw1PG6C9aTHcSDCnD9lqHEq1o/cXi9T4cp/pACEcUhDmT92wWR6ZHYR6Z1yVog9/ybWzdYNOjg0rg4TD3v2JNZCF65Xc2ex7rSfwgCo8cPIx41ALjN3mEDMg3SsjLulaJXCUWQyi+ywgKNjvahj04jVdeRKe7G+W/bh01hX6rQA8QR6qK8lGLVnzmNdawSJ7QCJFgI1dRbrWoW2Z7/+Lta1DoDk8EnE8n1EwXynVf8gengW+YuPIBRBTcw2mC/o3jgqPoTlBH+a6cA7yJ9/CL0J7FPnENsb6Gg/aC/s5SC9hxASPD7Y2kI+eGCmBR4PevyQyfHw+SCXL2dpCKXQPT2oI0cN9WjxCWJtDT06aixwg6GK7mFjA/HsGUIps9AxNIS8d68BKJSF3gMDZb2DFoYyKm/eNIClxbnSUpoJBJhJQTRaWQjy+VAOWLGcqbWamwO/30wr2qXPC0H61CnweAhaljEa+f/Ze7PgSLb8rv9zTmbtkqpU2ve1tatb3a3exyzzn/DD3wHGmIExGOzwRDiAgAdeiYAAAj+CH+CBBwKCMA8e/31tggjAGwPGc9debu+7WmpJrX1XqaRa8pz/w6lFparM0p25c+f2oF/ERN/pzkqdSlVlnt/vu2kNySROjrplHdOGOGNjhdDDSvdinXcWi0aLzdjubjE3xEVsrs6dQzc1mfPmqW75/JdYzPx+cs8jfD6cX/olst/5ztdakJ6vPBXrfRu6npWps2bkPa3TNCOpVAqlFD6f773kSmYyGdLpNLZt4/P5vlSo9fiNLl9f5PpUEqIvLi6yt2fij/vfvaPmo4+wP/gA+cY9tK3AhQ6HTQOSSJSFgwEms2NnB1Vfj8A8KN2mf5CjP42MIBYXkXNzhlvd0FDI7sDObXAzGbTPZ/I/Hj+Bne2KD2onHofxceSjhxWF60AukX0Eeec2osJnU1sW6voN5IN7lSd78Tiqt8dVNOx8oyg+Pln7l6YJZ1IQqQWEce5aWkJubpC5fgPfHRea1bUbWHcr/5vqG0Asz7k2hc7URawnldeqY3FwkiXBerq+EV3fhI7UmhTu9BGkMsbBZncPsbVZEMergSHknAeNJRiCYLBiSF5hfVfdGynts9H1DajRcUQ6CQEbsoeI7VXExlJprsC56jQu54K3PTGAjjXC9nZV6pPTM4w14z6tNSYJ1xAHS5DMIDe8URuAvcGL1D06rRj9MkTCyCcfnsrJy+mZxHpawfa1phY92Is8kXzvDE1h3XO/nm4NiXP+Z7A+LKdmOdO3kA8/dN1gAzjjl5Fvn6OGLiHv3S35/mmfHzV+Eet+qYZEB0OooQms+0UU15m8jHz9CrG/hzN6Hiw/Oh5HbGyi481oLRFpB7G+hnz+At3RYdCPbBbxbhlxmDQZQjU15L+nhEMGiT1Kmc304kK5iQSY3IzmFlhfN/khedru0ZHRmSwtFe47GuN+RyRSojEBDALS2loMJxQCnc2agc3bt8hX7mgmUAwGXFgw9+umJkNr8vvJpNM4+/tYe3v4NzcRfj/OxATO/DwBFxQkX6nmZuSFC8iDAzNg0BqVSOBsbODb3MQ61pToYBB18SJ6cxO7At3tOOJDKGRcymwbOTtrmjEXLc/7Jkg/o2L99NRZM/IeV7UU9rMqrR/VCQuMWcDOzg6ZTKYstDB5+zb6t36L+j/4A+xj6bWFULD6ekOzEgKdyZjJ15s3yJw1s1s5w8PQ2FikFuSRlViscD4yGdjfR4fDCCGqTupUdze6p7ssREz7fMbPPxo1VpR5NCqTKYYn5pLY9cGBmcApByYnkZ/fdc02ccbGEZlURYctMEFacmMNsVaccqpQyExGQ2Hz8N/eMpM7cqFcuaniUVsbtY8+r7hxdC5eQj6tHOaoOrsRe5uIZGWBtDo/WZbwXjjv0CjW7AlUozaKbmpF10ZR8Sbk7rZxE9raRqyulEw4nanLWA/vVjy3Wbe3eNq5UjlXpbAWy0I3NiPX3LUUqrUDsb5SvvELhUxwWWMDhANwuI98+xxx5JFbE/e2F4Zcw3KKAEPnwi2su9WzOpyRixCNIN8+rBqymIp1ETil5a7TYyhX6dFxRGIJ3757w5ftHcV+4k4T034/auoC1jOzodeWhY71IN96p8qfbEicc+eRDx67Ctady7eQj9wbEtU1gIp1Yn3+SUWNkhYCdflWGcpkEJEbWJ8Vfx+qvQukHzk3gw6FUeMXkffu4kxfBzsA6TTiMAWZLKSzEI7A6hry1UuorTMZQrW1kM6YgcFJ+3C/3zQx7R1G2yYkYmcb+fiJZ3ZSXtuhY7GiA1U6DTs7yJWVcnOMQAA1NWWQ6GMJ7bqmpiiKDwYNgpFKmT+DQZOkXmUQeNjXBw0NpgGJxQrNinYcRA4Fz2tD0j09pBsaCL14gXXgbtagYjH02Ji5Jo6DyGQ43NkpND7WCdTbaW/H6e3F9/x5WaDjyYGXrq1FXb1K9ld/9ScmSP+iVKxAIIBt2+/dkPWsKtdZM/IeV7UU9rPCFeb9YW9gs7OzHOZu+n19fYR3drB+//eRn32GePq0CJNXWkserVhdLZm+VYLJ9dGR4fSurBgPfY9SfX0mnTjngqJt29AU4vFi4JXWpoHwGx6t/KQ8l6OwHiihKrgeVx9HTYwjHz6ARMI8uINBM3n0+VA+H9loFLumBrm3a9aAQCmHTCoNaGQgiN3aglxaNBPOw0ND7zo8NHSMpiZ0awvW08oUoKPr1wnermx96wwNI1cWKqMwto0+N4h8Vdn+1Jm+VmYrq31+dHOrcSpqbUMc7MNRukxUq1rbEIndQqZK2bnHJrGeu9trqv5BxPyM+3WXEt3Shlxxz79wLl7Ful+FfnXFHTkpOeazH6BtCzV4DloawTmChZdYuQYg0zWEzwPFyZfqGUPOeNtQ60AQhB+R8G4uAJzhS1iP7plJ9eQo8tknlZvOvrGq9teFYwcnkI+Ln7VMLEa6q4WIi33yQfsoEReXtXxpS6Ku3sB6/CHO5E2sj70NBQqvyzUkbK0hEgqx5W5eAUaDJB9/XG5/PTyFfDGDSOyjhsYR68uuCfHOlW8gb/+g7P7lTN9C3vkIoXIb9mAYNTKJdcd8R9TwOOwmEJsbqMlLsL6FbmlFI43ubmEBubyMGjgH/oAJK501xgu6LooaGzOUquQRBAPI2TnETOl3QAthhjAtLcZeWAjjxpdMoltaDAo8627moKNRdGurEY0rZTb0x5PUK3x2DNo7WuJKqGIx0vE42XAYKxzG7/MZSuzWlmmi1tcrohUl5/X5jH3u4aGh7ubdrfL02uOieClJjo3hFwL78WP3+0IsZt5fTw9kMqT29tDJJNb+PsHt7TLqlhaCzJ/7czi//uvov/SXvvaCdKCAglg/gbWe1Y+3zpqR97jywYdnVVpfhhD96OiIw8ND4vF4yb9tbW2x9vo1jX/6p7T8yZ/g/+ijsom8DgaLSEhdnYHIfT7E27fI5WV3mlM4bChb+UldPjsjFiulbeUbi0gEsbeHdb+KE1LOw/+4G5f2+w3qUV9f9JGXEm1bCEcZCsL2dkXalhHXDxn0xWVSqWtrURcuGEqIi04lPTaOldjDWqw8sT4cGia4u+nqIJa+cRP/Z5U3dk5rG5IsYqOyoNq5Va4v0eEIOt5kxLeNDcamNJOFPbPJEmurCKUNtcuF9gXgXL5SQm05WWp41NUm+DSvdy5eK6PUlP2McyPI1+7ZGzocAWl5bvq1baOjceRGBTcmAamOTpy2FqzGRgKPP0F45Iuo5g7kUvVQQuf8dax77rkqhfO19yLevi3ZmKm+fnRLHdar0u+DM+ZOxSv7+UPlWg4tBc7NW1jPPi7ZsB629hKamTvVeQGyP/MXsB4/ROy423efLB2pxZm8iv3h/zzV8c6lG8gnxUGDc+Em8tNPEdniulV7t3HdXq5s+e1cvG6ye05szp3JaeSLJ6WBo5dvIe9+ishm0YEg6vw08pMPoTaKGp5A3n+AGho1aMnWNqqnD6G00XkIYRzjfD6z8X79unjPC4XQXd3ohjgImXPrmkfs7Bq0aXQUamoRC6ZJ0MGg0Zk0NIA/YDb1e3sGEdnYQLW1oQcGCrTVsuts28U8k0jEoA9+vzl+aakMWSi5LufOQVOTodnu71e2z805ZaG1uRefQKQrlWpuNojw5qahpLk0KwBOLAYTE2U5LSXvMU/damsjcfEi87dukertpb29nVgsVjxOa7a2tvD5fAQCgUJi+ZdZXzQbJN+EnKEgP7111oy8x1WtGdFac3h4SCaTQUpJbW3tV7i6L6eOjo7IZrNorT3Xf7L5yNcPc/Oan58vuJCdO3fOBCRlMlh/9EeI//pf4e1bZDZrnJ7W1sz/SoL1pLFL9PvNA+rEhl3X1ZXQrLRl5cSb88i5OdfNu5bS0Aps2zQreWea45B7nlaQ04KIbNagNh5fczUwYKyDK6Tsap/PICzRKKqjAwRmk5KbLOYpWyKZNMjAQQJ1+TLy+TPXB7iORlHjY1ifVN4gaoHRedz9rPK0UgoS5y9Q+6hyE5atqUU31uNbnDdNV7QeIjWkbb8JRaytJSjIUb0OTUL8xgYisW9CES9ewrpfmUKl2jsM6lEhvR3AmTLTerdyLl7BeuDRqPT2IxZnq/y+hpBv3CevzvB4xVDHkmOmvWleAIfjlwg9dn8vkGtqLBuSCdTYGMSjiNW3yNXSBtOZ+hmsO95WtABqYBL5wjuUDXI2wi7rdy5dQmS2kEtz6HANJJUrSlXys7sHEa9el4UIFs47Pok8XENsGSphqm+KwOPqYvzC6y/cMu5Ss4+QHpS343UweoXw/c9R09ex7p/O3cu5eB357DZq8gbWhy6aoVgc1dKG5WI77YxfRL55UXbdnIs3IKvNFD13b9XCBttn9FHKQYcjiHVzXwTQnX3IO5+hW9rRnd0Gpco6qKERAOTTZ8ZoIxJB9Q9AXRT2E8iZ12ZzXx9H9fYautdh0kC34RBkHdjeRi4slAWRAqiWFvTgIOzuGYQhFjPDHMcxiMrqagmKbairPYhXr0xA7PHrFYkY96/cPTuVTuNojc+yCJzQpJRd6xx9DMdBPnxo7qd5K16fz+SrHBwU3MDU8PCpRPEA2elpCIUMbSyPgCeTpvFZXkYeo4aqyUkyv/7rOH/jb7Cyv89W7v7c09ND5JhAPZ1O8/q1odPW1tbS1dVV8jO3trZQSuH3+6mtrf3CWst8WHO1sm27IEg/a0J++uusGXmPK5/C7lZKKZ48MQ+bcDjMwMDAV7W0L62ePXtGNpvFtm1GR0dL/i3/0f1RhOhKqTLh29raGhsbG6A1XfPzxP/H/8D+/d9331z7/UVP/HwmycEB7O5W5CpDrgFoa6vsBtPYWBRF+nzGCSYUQiwvG3TDQ7jujI5CfX1hSgc5pOa425ZlgVImPEsIrHv3Kj7MC+e8cAHsnL+9G0XA7zd5I3OzBlGJRNChMISChpPs85n3EouZ5kWVfm6zWQcnYx7wweYm5P4eWgiEBoUmk86Yh5Jto8IhOEhgW1bOXco0Rs7RESk0QimC25tYe3tlm4TkwCCBlXdYR5UbvuT0VcIuzlrakuiRUeRzl9yQQBDd1FiwRC1/vYXu6EQulgfR5cu57E2vcsbOYz2rnF5eOGbKu+ExCdJdyCX3MEyATM85fBUcrUp+1pXKFriqtw/d3YE43EbMPkO39CIXvHUSqrUbuei9JsCEBR5mPBsMbRuzBB20sT/631XPCeCMX8O664046fo46lwPIrmHeDnj2ricLNVzDvFqBuEo0u1dKL8iuOaNFB129BF48xaZ04k4V24hn7jnrRTWKCXZGz+L/cmfeQZG6kAQNXbBNeVeDYzA/h66qRV8ITMsWVwwmqihUaw7RQRL+3yoS9eQn99DHCZzrlRXzb0tnUI3NKGbWhCplLlvB0OInV3TGEhpBilHaXCUoYLlNGGkUlBfbwTdW1vIN2/KEsnziegFNFpp0Jj7WrXAw5YW1PnzZghjWcXN/MaGseM9iQ4ND0NDgxkGHRvcFKx4c9qQfFaUrq9HvnxZposp+11Eo6jJScTioqGd5Z3A8s6IBweGUrayAraNmppCbG56ZrWACVN0fvEXcX7hF1DXrxf+/uDggGQySSaToampqSSR/ODggLdvzT2qoaGBlhMaktevX5NOpxFCMDIyUvK83d/fJ5FI4PP5qKurw+/3f+FskDwicyZI/7+rzpqR97hOE3z49OlTHMfB7/cz/BPyCP9R6tWrVxwdHSGEYHx8HCHElyJE39/fZ3t7m2QyydDQUMmNL/PwIen/+B+pu3MHy+dD+Hzm4XhwUIaEqI4OdF+fK/wPRSREtbebh4sQZhJ/LNm37DVu+hIpjWVlPpE3b2Po95vm58EDb+F6fz+6vR35+HHJg1rX1Zlz5txX8PkKzYpcXDCN2OZmGWVLh0Koy5fMNHGtnM6TL2dqCnFwgHxdeXOrBSTOTxF6M4OdqOz0ogYGQCvkXGVeuOruBq2R71xoX319+DfWsFwE6/sTk9S6CNYBDi5PE7nvISq/WU79Kvn3azexbnvkhnT3IZbfejo4ORNTWE/cp/GqrROxtuR9jsnLWI/cxfMAzrC3rgVy1Jb6RuSat5uVc/6yEcJnEsiZx65rO5kt4nq+i97XubA+KdE9I+jWOPLZbddwSTA0MrG0UkJncj2vgOz/83PYn/zPErc09+MFqmcc61lRi6LCETLDQwReuDjHBUJkfVECJ65tsu8cvt1VfB6C/cPRK4Tu3kZ194HUyMU577VdqSBcr6lDDZ1HLCyha2qxnpRnBTkXLhua1GaRCqla2tBtnVh3c4J92zZNydwscnnZoB8TU2awMvvGNHdDI5BMFuzMdUMDqm/AoC0nMzNsG93bZxy6BLC1aRz0AgFDUXpX2uDphgZD36qtNXSvZNLo6lpbAUxT4WIEoy2LTEMDRy0tBJqbsYQwA56dHeTqasVGRwth9HZSFsIJtRDQ3Gzur3lKbO55Ahht4L17nrbrAKq31+SvvH1r6L8uzYrIZFCdnWS/+12yv/IrX1iQns1mOTg4IJ1OEw6HS1ATrTXPnz9Ha43f72dwcLDktSsrKwXEpbu7m8ePH3N4eEh3dzft7e2utrtSSgKBwFk2yP/FddaMvMd1mmZkLbdB9Pl81NfXfxXL+lJrfX0dx3GwLKuw/qOjI7TW+Hy+HxrCXVpaYif3MOno6CCaTGL/zu9gf+97yAeVQ/rypZqbzRQrkSha5Oasd8Xqaknira6pQU1MwOGhedie1JcIYfz3m5qMNiQUAssqUghWViqn+OadYNJp80DNTfAKHvsNDcUHn1Joy0I4DvLOHdeHLxQfePLRo3L3GZ+vaA/c2IgO5VxdUilD10omcynJ2wVUxgQfRrAeeGyge/tQkRC2h8jYuXkTef+ea/6JMzaOXF1yDX1U584hNtdc9TpHvX341paxXDaXh929BFYXkS7ft3RrO/buBtLFZUeHwlATQWy6hwI609ewPnefzKu+ytkbJefwsPMtHDN6CnRl0tvNC4w+4TRaDGfsIlbOVlc1N6NHhhCJDeRsUdOipUTXNiI33RtayKFLtd4uYYWfO3UdK2duoDo60L0dWI9d8mQunK7BAVDnxpGPnxhXqFgIOeMtYHcu3HClJCanrxJ6frcMKUyNXiVwt/Ja0w3N6NoQgeVyhG1v6BJ194vUOh2pQQ2PYj30Dll1pm8h738MgSBq9BLy4SPEnvmuaCFQV28iP79T1tDpuihqcKQMUXLOX0KsryNzejDt96MuXjEmGzkNmBqfRPuDBk1xHBPaNzwKh7mcpdx3Tbe0oHr6DDqyswfRmLEKXllGzM8bZKW7u5hjcpA0Ll3HqFY6GESNTxiK65MnkEqh29tRDQ1kbRutFP5Uytx3V1dBSrKTk2SEIPTsWeWB0TG6rWl2BCKTQczPl9gMl70uHDbIxsYG8uVL85luboZ8s2JZxeHXxga6s9PkVT30/s5qIVDf+haZv/f3UN/61o9FkH6c+g2UBREvLCywn7v39/b28hu/8Rt88MEHvHv3DiEEHR0ddHd3F/7X19fHzZs3C4PGs/q/t86akfe4TpPC/j7XcfrV8Y/p4uJi4YZX0HTkKpPJkEql8Pl8+Hw+UqkU+/v7NDU1ldzsDg4OWHj6tCBE9716VXwY2LZ5GBzThBAIGB2IUmbz72HtqONxnIsXjR0umHMdHhrXlhPpwBqMaD0SKeSMlJzL5zMPvMZGQ30KBIzgc30dOT/vKu4uOe+DB8WAKyFMo9LYWKQUgBGT2jbWgweeYk01MIBuaTZTP5fGAIqhXWJrCx0OQyBAWikyjoNAE7B9WE7WZBQsLpgGLpFAHCRK9Td1daiREaw7HtSlK1eRTx66rkf19SP2d4w1cKVrFW9AB/0VE9gBVCBAuqmR4LI7reZgaITIjLtgPDE1TY3H5l519iDWFj0zOJxL3s2KrqkDlKueBcDpGcR6W9leubCWjm7E0qInuqIB3dWPnPemXjmDY1gvKjeZqqsb3d+D2FxER+OeVseF801Wp1JBrmlp6EC+K6V9OSOjiLBEzhSpdjrWADsHnp/nwrFCoLqGsXIubNqSqBs3kU8rIy+6pg6UH7Hp7oR1MDBE4GAde2879x6vYn3q7YSmwhH0yCjWk+JnKjE6Tc3dyp+x1OXr+B9+htDuv9O9K3+e4Nwc/oXKNELV02828zPl1CBnaho5P1fyPnUgiJqaRt69XdjM62AINXXZ2PTubJvfU08/qqMTsbRsNB2BIARDBpm1/WbTPvumcF/S8QajIQmFjLD9zZuKIX+qr984wKXTptnb3kG+e+cpHFeDg+j2dlhbM1kowaBBHhKJ4v07/0yyLIOCaG1cB499dwtoyDG6lVbK3I/fvClzCitbR0sLemjI0LA2N4u5KJFIsVlJJAzCnk6T/aVfMgnp5865nvPHWXm2QjqdJp1Ok81mqampKTxzM5kMS0tLzM/Ps7CwwNLSEgsLC7x9+5a/+lf/Kv/wH/7Dn8i6z+rrU2fNyHtcpwk+fN/qNE5YMzMzhYyV0dHRkn/b3t5medlsKkOhUMGGt6enh3A4zN7WFuH/838IffABvj/4A09ovLChr61FrKyYzXsuJIvjXvG5B6EzMmL4xM+fuz7w8siFGhoqUKzEwYF5sLjYAqvOTnSvcQ8q8+QPhYpc6VDIaDNsGxIJrOfPPTnTqr/f6FaelYrNdThcFMSHw2DbZmMQCBiNy/qaq8bEmZgEn431uXvAnLJtji5eJDj/tiK1S4fDUFOLMzGO2FhHaEPPwGeb6WhePCslOhTO5V9o8tbBaA1aGecaKcHvy200j/075j/RoOP1iN1j1ymfYA6mSYtFjcA29xpx7N+UUiQtC3GYwJcTXB57JxweHpG1baSTJRIKFl4Hhg6RynGv7fo4/nTus6iVEQIrx2x8nCzYNmJ/zySn7+8hMuXf+9OgIqkLVwh46EnAOCRVE7c7k945KYXjjqEiXpW9+ecRVhY5+8zVdhZAdY8iX3sjEWCE1tZnHo5n01cQiVXk8ryhfX18SnH41HWsT8vdvlRvH0SDZSiJc+EW1ifVM1Oy8UZERzNidwuxc1hAJbxKC4G69g2sz/8M59I3sH7g/R6S/UP4ttfw7ZfeE1RtlIOmLmqfPMapi8K5Eax7lRu+gjbkdgUXwVg9qn+o0CzqcATd2YNqaQctEPsJOEoiEgeQSKL7+hFrRRqqlhI9Oo6urUO+eoFY3yi8Tz14Dt3UDHv7xhzj2HNPS4nu7UO1tQMC/D7kuyXE8+cVN/y6vt5Y8NbVkck6ZPf2cGpqCK+v43Oh2hZe6/ejLlxA19WZoZLjGFQ8bw984nmSDycUu7sl9tLa5yu6d+V1fKmUuUMFAsiPP64qXlcXLhhB+l//6+YcP4H6otkgfr//jIp1VhXrrBl5j+unpRnJfwRPivHdblibm5ukckLIjo6Owmsty2J1dZXNXCPQ0NBg/ltr2mZnafzDP0R+8AH2/j7ZxkaslpYiLJ7JoHZ2kOvrJjSrvR3x+nWZq8rJUh0dhgK0tWWmaHn7xfwk7Zh/fUEHsrbmKjws2AK3tZm1CWG0JRUoYIXXRCKmaTo4MOjKcWQhH+CVc9rSUpoNPWDdv+9KW4LcdO7cuYrXQdfWFjUmkYhpIKREr6+hd3cR2zvYO9tlLmPJCxcIrKxgr3iE8fX2oWPRKtSuXpNa/8yD2nXtGvJxuZtZYT0NDQblee5hs3vLe6PqTJxHvnruipSpQJB0awtBl2kzwP7EBWorcPIL6xSgJi9gPSoeo0MhY0Fck7v2NTXogB+BApWF1CFifxexvVmw783URrGODpEVGpnCeWujJoyuituTGhpHvqji2DU4ivXiFI3DxEWsh6Zh0X6fQSB9GvmiVP/k9I9hPa+eF2IsiVs8c1gAtM9G3byFWJhDvnP//RSOD4bRgTpXjcxJlOS4aP00pQMBstf/Ivaf/dGpkt/zlf2L/y/W7Y8Ru+7hjPlSjS3oxjhWrqFTw5Po5TWsEyYazsUryPk3iK3KQxU1PAaJRAnypCI16OEJtC8EBwdYdz8rEfirzi50RzfyXilVVA2NoOvjyAf3iwiuS2MCOXRleNh8/pNHCL9BT8Tr1wXUWft86N5eoz8RArW1jbW4iJ0bHOW1fqyvY70wGTI6FDJBi/F6g85kMrC3i1xahmzWUHP39gzNy6V0U5MZNrW1mb9Ip42WY33d3L8rvSYWQ01MlGSZ6FDIIOLxuEGAhDABjvv76Kkpk5B+9arrOn6c9UWzQfKC9LNskLPyqrNm5D2v06aw5ycXXyeHikpC9C86MUkkEmxtbZFIJBgcHCSTyZBIJMhkMrTs7JD67d8m/nu/h/3We7OhgEZHYQAAIABJREFUWltJdnRgr63h29hAtLcXE3gBlUzC1hb26qqhbI2Pm2mXx4MJzKbdmZ42k/mcIJxMxojN19ZKEQnbNhsxyzLUqko85Vxwl45GzfryzcrqqqEQVNgUFxCecNhQzI5tznVtbTFwMZ8OrzWEQoayte6ucdD19eY6vHmDXCpP39a2XaCEqa4uk0+QtwROpw0nem/XNG2pVDGb5NNPXKeCWgjUrVvIu3dcaTXa50NduYr1sftEWnX3AI6rJz9Ub0TUwKBBifbdxcTO1WuFYLhKlWrvwN7ecnX3Aji8fIXQvSpoxrVbWJ9Wfr86EiEdi5LqGyCQTWEF/YijA8TWhhG7HxsCuLljlfysIZNQXq2c8fLMjrK1CYHuHkDOllPHdGMjamwEsbWEXHiDM1Y9yBHAuXgTyyV/puzYy99APr6PujRlmp+DyuYJ5tifwfroFPbEOZREO1aJaP00a7E+/AHq3AiIDHJ+pvprJi4j79+HaD2qt6+qNgRy34/L10GD/PhD12ZJ18dRfYNYbu5y4TCHI5M4h0eIVJrI8WZACJxLV8i+WyS4XHpv0A2NqKFRxKMHyBJ9XS1q4rwx7Zgpfh60lDjXboDtM2ns2zvGzjd3b9LhMGpgEOrqjBD+zSxip7wxO+zuRvT04svb4KbT5t4zP1/5vikl6vwFI46fnTWWvHlqazpddEvMoc86FDJakBMoSOF8gUCRbhUOG8qt329E+ouL3oOh3l4jSP87fwcaG12P+3HWF0FBhBAFQfrXac9xVl/fOmtG3vOqlsK+v7/PwsICjuPQ2tpKU1PTV7i68voynLCO18bGRkGk39TURFM2i/3//X/Yv/3bBSG69vmM9W48TtbnQwmBnc1iJRLQ1AT7+8ZdyuMmq/x+DoaGEFoTWl9H5N2sfD50Nouzu4u9tVWgHakLFyAYNEiFh22urqkx+hLbBqXMJjwfarW8XLbhzqetV0QrTvCUdd4FJZVCzswYlMbls6I6O40r2AmPfR0OFzNR8uiHUua/nz/HevfO3R2ppgamppCvy+2LS9YdieBcuWKccAIBI+LPhTCilOFHp3I0q2DQTFDdkIj2dqirQ75w12844+PIFXexO5yiEWltQ2iFWHN/X9XOoQMBdGcX8o27hiPV0YVvcw3pMXRwJqewXDJXCscMj5oJ80lqjd9npsFNjeiaCFjSpNYvzrk2hKehaDmDI1gev4PCcZdvYN2uLoLPXruB8FnIFw+rBDX6jBD+FAJ31d2PeDtfFEpHY6gLE8ind0uC/QB0Ywts7Z8qrwSMIBylDe1srzpi4YxeQD54WEw49/lQ09eQjz5FZCvrAtXgKOL1XGkI4aWryIXXnsGKOlKD6j4HGYVI7CIX5rzXdukqcvZVyQZf1zegzo0h7n1OJt5AJhyhpoI2SEuLxOg4gc0N/CeaEicc5mBwhOD8HP68HiSnIXG6e1FKYe0nsJ4+KdGEqPYOdHePye148bJi46G6u9GdXWjbh7Is9LNnBCoMTAo/s6MD3dxi0GPlQDiCfP68qiUvYO7f0aixIbasYo7J+rq55x7/WbW1xkp4dRX5uvR7X5I/FQiYwVBTE9m/9bdQP/uzBUT7q64v0oScZYOc1Q9bZ83Ie17Vgg8PDg5488aITBsbG2nLw8dfYblBul80EX13d5empqYSuDeTyTBz/z7xjz6i8f59wv/rfyG9pvm+HA1EykJwYD6ZNltTg+PzIZTCl8kYJ5N43AgZHz40zYtHHXZ3o9vaCG5vm0Ygpy/JJhLIvT2stTXkcZpAf7+ZirlZAuceRrq311DHHMd47+cfdKurZc2Frq01kH8igXj8uJQmlRfD51KGsW3TwORCFD2vW22toSnkHGAKf593gonHC0LNrFLISAS5vGxsgd0S5+vqUOfPI5888WwMVEsLemAAefuz4sYxHEZHY1BbY5yqggF0NGZExNksqFwgYypleNzJBGJ/HzU27il2h1M0EdEoOt6AnHMXbzsXLiKfPPC22L1+E+tT9wm+9vnQPb3IGXcHLSdSg6ipQa660wl1IIBuaUPOz7keA6Xoig740T296KYGsKUxAHj3Ft3QjJj3DmWEU6IigSC6NlbVGhjAGTMNlw4GzfQ5c1AxHNG55I4QnSx1bhL5tPwcqqkJPTqEfHS7oM1xzheduaqet6MbsbyOODo0blPjE8hHn7iaE+iGJjjSFUXuqqcfXRPEmind6KuObsRWoqIpg66PowbPYd0vR+RUcxv4IgXkodD0PCxvwErOGW9A9fQj382jegeRd+6VHe+MjoOQWBWuqbZt1KUrhop0zAgiG45w1DtAsLEZoTTyo49KzquFwBkaRjQ05mx+SxFuLSV6YJBsQyPO9jbs72N1dmEdHhrtXj4Y1raN41Zzswnp3N0zgvvdvdx17kF3dZfcj7UQ5n7Z0mKeAUIUTU0OD006eoWmomR9waAZhA0MgNbm/pVIFBPUK1BIdVMT2V/5FbK/9mvonh7Xc/8464tSsfIJ6WdUrLP6YeusGXnPq1ozkkqlmJ2dxbZtYrEYjV8RxHtcgJ5f3w9DwwJj77ue2yi3tbUZi99cIrr1ve9h/ff/XiIc1OGw0VzU15sJE6AdB2pqkI8eIT2m9FDM4hAzM4i1NWMtGY+TDYXQQuATwkDxa2tov59MXx96cZFglSlatqYGpqeN7a1lgd9PNpNBJBLI7W2s1dWiviTv3uU4rtkh2u83sH9jo3Hb0tqgMJubrmGLAM7EhPG2P+HeVeAp58MRhSg6wDx9WubhX7KW4ynD9++XNkF5QXwsBuEQOhgCSyL2E4i1VcTGZkWqUz4ITN6762k0oIaGwOfz5nLnJpLyzm2jcck1izqYQ2F8tmnOaiLmmijHNDWZtDErODxEJBOQTqN7e5FP3ek3qrPbpLR7iJCd6equUM7N6sJq56q3UBvAuXGK80ycRz555NlkaClIT19HCgfht5Hb64j5N2WbbGdgBOvlKVCRq9/A+uQ0uSKVqW7GjasbMfcSubmG9gcgHEOse3+/AZypa1i3va+/au8w50/sIJ4+O1XAobIsVMcA9utSTZjq6UM3RLGelSJYWkrUwATWI3fbVi0l6uoN5IvPTaBgvBEtgsh37hRDMA5XYuVtIQdEDQzD2lbFoYNqbUd3dGDdr0zz0oEg6sIV2E9C8qDgJlbx5164iDhIVMwU0n4/zq2/CNkszvw8/tnSz49qbUP3D+DML+CfL6fWqt4+sq1tOMvLBN/O4tTHEYPncBwFb95g7+6S7u5GNjUjHIW1vORKxVTd3ajBc+aeaedpWxuI+YXKtC3LKtJoX7wwmrOGhqLjVj6HKodAF1CQtbWSrKiSczY0FMxC1OAg6lvfwvn5ny+6HH7F9UVQEClloQk5Q0HO6kets2bkPa9qKexfZZ3GCataZbNZLMsqec3h4SGzs7OgNY0vX9L+4AHWnTuG67uy4kqDKlCaZmcLG2kthMn0aGoqhgbmPN11PI5cWnJ9cBTeZ00NanLS8JNnZ1FNTTh1dTh+P7YQyFTKTL6WlkApDoaHQUrCL1645lCAmd45164hbBscB6U1TjKJlUhgbWwgT6AHhQDDCinuQGUffMdBzM25hi2CmQyroSFYWMA+HjiWp2zV13MkBMKysJVCRqPIxUVkTgjqVs7oKESjyLt3y1LkdSRifid5LYzfZ445OIDEPnJz04QuHm9y4nHUyAjyk0+8EYjL08h3C55UMdXbB37b83evWlshHkfMvoHaWtPQhPLcb+NipgMB43yVPIBsBlJHZtKbPDBuWMkDVEcXYm8H4RLuCOCMTSJfPPF+X1OXsO57ow/O8Cjy9UtPy2AdqUHX1SGXK9NY8nU4NU3o81LrWB2JoAYHUNFadDKBvTSH6hzAflQFFYnWQ9bx1NuA0RFoXwi54Z4/oi2JmrqIbmnB+tM/qupCpCM14IucqmnRto1zfhrhE8iHd1wpU/nKTN/C95E7MuNMXUbsryOXzPfKmf4ZrB9U16EAqLYOdGc77OxhvfL+rhXWXxdFjYyBk0E+fOKJfgA4Fy4hNteQy8UNvDMxhVjdLGSGADgXLyP291xROy2EQULW15Dzc6iuXnR7lwkmzJ1HjeUE6o8eVEQI0t29ZBobCS0uFqij2rZJD5wjHQxh7e4i6+uNO9P8gmtzdtwK2NnfR0VqsFdXsV0QDW1Z6M5Og6IEgmaQFQ4b2paHxqxwbc6fN7Stw8OC5pBk0gjZ370rtXaPRsn+zb9J9rvfRY+OVj33j6u01jiOcyoUxLbtgiD9rAk5qy+rzpqR97xOE3z446z8x+cknPtFb1LJZJKNjQ0SiQRdXV3U1tYW//H5c47+/b+n7r/9t5LNcWEN+elSXZ3ZIObWIZ8/99RJ6EjENBXHAgkLblZ5FxMwk/HtbbNJ9vkMvatKWq4zNgb19YjFRZxIBJWzyLW1Ni40q6uFjJBUWxuptjZqVle90YeaGhMi2NQEmQyZRAJ5dIS1t4e1slLWXHi6bJ1oyrTfb2gIgQDy6VPz0HS7bnl/faUMapNHc441K8cdYLTfjzg6wrrjHaKnurrQPd0mw6QSfcG2zXrb2tANDeb95jUlh0nE3r4RpOY2uLqxEdXfj3XbW/Ts3LxlAhU9fqfO+fMmo8DFXQiMoJ2DA6SXU1h3D4RDkMkYjUYwaMS0IucznMlA5gglLayZl8hDFwvl2lpEMIRc99ikn5qe5U0XA4P2sL6GrJLFkRgZx59MYHV1gjIi7ErXzLlyOjqVc+V06Inq6Dbfp1DIiN43lpFvK9PonMunOyfk0JuPzLGZxiYOezqJzDzHSpV/VtTACOLVq6op7trvR12+Cs6RaczV6R7B2h9A9Q+DtBGH+8hZ76FJ4T1cuYXY2kVbsmrYJeRQkEtXEAtv0M2dWJ+52PwKgbo4jdjerEhZzKeva2kjtrexnpTTtyB3X5s4DzvbWBWc7XRDA87UNE7WQb2ZITQ7W/E8qrUN1d3N4dER/uVlAnn9Xm9uKLWyUqBUpRsbkV3diHDYUDlXVkzeUe5XoRoa0SPDiNUiqlFG2wLTZKytIZJJQ9taWUHOuBsPaCnRra2omzdxfvZncX7hF36itrynpWIJIQquWGeC9LP6cdRZM/Ke10+qGTlJwcrXDzspyQvtAerq6ui0LOzf/V3k7duwvGw0ECescgtryTcVR7nk3uPhU3kqU0OD2SBblqEehULG2tYlNDBfJ7NDjB1sS0G8XhArrq0ZMXtfn8kDqdA0lay5vh41OYne2UFJiQoE8Nm2aXy2tko865XfT/b8eax84GIlytYx8brq6CBzeGiux/4+vq0tV1tJZ3gYFY9jPXuGPJZJon0+0g0NZHPWvYFw2LzXmhrkmzeeD1zIoVLt7aaxySE6BRpYXgyfs1TWjgORCNZHH5YhJiXvMR5HjY2Za1DB4rhwXEMDztSUcdvJ2y2Dyes4Oiw0LfhsVG8v1j13MbYWoG59A/nJx1UCCS8jXzz3NCtQg+cMIuKhzVH19aTrogTfzpmfHw6jGxohGjWuQbaFkAIdjSIX3iJ2NhEbaxURlFPRs84XbXXdSlsWemAIWcWmN9XQhHV0hH0C8VG9vRzEYwjlEFxdRIYjZgPnYTEMJnFezJbTwMrWJyW6fwR5QkDtDI9AcwPyxaOC6P2kaN2rnLHzFY0tsnV1OBPj+N88K+TT6GAIHWup2vgV3ltbJwgfurMT+eyBpygfcgOA8YuFhl4Lgbp8FbG5XBbsWPIerpTmjziTFyCbxnpVJTX+0lXE+ha6pRX58HOD9LmtTUrU5SsmM2R+zgjkx6eMycYxLZPq6UV3dJh7QgXROZigQt3Wjlh6h25pN7kiT5+UfAbSTc2kOjoIWxby5QtDez1Rme4enK5ufI4yjf7OjglOdLH5BnDicfaHRhDZDH4p8R8emSR3l+9rwaUwFEI+e4aOx4u0LSiGEuaCEnVNDc63v03mu99FX7zouo4fd31RKlbeFesMBTmrH2edNSPveX2VKezHpyg/jBPWcSF6LBYjmL9p5/7t9eefU//979P0x39M8KPyUC3ITcdbW82EvKUFHAdxcGBu+isrrptUt0BCHYuZ8+UtG5WCZNJQtmZnkS5TuMLro1EjGN/ZQczMFL3h89OuVKoQjkg6bTjHWhtEwWvjjcnJcHw+SKWw/H5zPVzE614uW0CJrWS2rs40sEJgLSxgr69juzykVW0temKiPLQrr8uJxYoIUipVREHuerst6Zoa1IULJQJQbduGGtHQYFADO9fsHR2h43Gse3c9he46GERNT5sQR4+UZe33o65eQbx6ZRrKaNQgankHr7x7V/IQmhuRH/6gYiOXL+fmN5CfVP68Fo45fx45N1tx45Qv1dICoTByzv0zp4VAXb+O9UlRJ1K4bvVFEwEd9JuMkbVVxHpldFDX1qHDYU/xO4Bzo7qlrbYssn2D+KrQh4z+4SZYQPYI+eZlZb0QoAfHyhqMiuu75r0+HQygLkyBSkFWYz12z3TJVzZSi/SHkR5ULh2OoC5fRL59heoe9LSSLnldbR26No7MN5y1dajzF0zTtFceUqqFQE1dqxi2qG0bNX0VsfAGuX7MBc+yUBeuYn1cWU/kTF1GHOyWWSrrSA1qeALrk+LP0rEYanwS+fxJRcF84bhoDOfyNcTGJtY9dxRUBwKo81NwmMR6XERLdDCImrhgkOpnz8gODCIbGhDvlpCzlVEubdvo4RGDxu7toeuiyIXFisdry8Lp6sZpbEQJ8O/vG5rt0DBEIoiHD5EVhgk6GkV1dJD0+dDSwk6n8Tc3I1+9Op3b1qVLZP/u38X5y38ZjiP+X2H9MNkgeUH6T6oJ+f73v89//s//mY8++oiFhQVisRjT09P803/6T7l8+XLhuF/91V/lP/2n/1T2+uHhYZ4/r65dO6uvR501I+95nSb4cGdnp5C90dHRcSIluvr58xOUH4WGlV/HUs5eMR6P09raaoTof/zHWB98gF5cRIARD+7uGirTiQRxZ3QU4nHXlPO8M1ZBJwGIbNYEYlVAVQqvi8UMzH4sO6QsJVdK01zs7ppNeL6pqHL9nfFxiMUQs7NQV1dsfPKoytZWYXpmXF26SnQuFdfr9+MMDpJtbUVmMlhalzQ+Jze9Ohg0jVA6bZCFE9chW1eHbGtDRaOktEZYFiISIfD2rdGYeEySndFRqK83qFTu5+pYrJjiHggY6tzhIWSz6GgU6949TxQBctzrQAB5716RChaPF8MWA7nPcTqDjoQNjerVK9fGwSRWX8s5+rjrI7SUqOvXkS9eGDQsn5cSq0fX1pjfnWWBNtNOOfvG5MVsbVZGn65eQz743PNzojo6ATxFyVpKk5/ymberkzM6ZlzM8r+LQADd2pZDB3MDgMMDdEMD1v/5n96N1vCosWaugiQ4N4p0Jq9KX7mB/9NjjZQlOertI1MfxT5KEFqYQ2TSONPVqWMAqd4B/HNvEc4pkI7r30C8fo0eHESsLyHn3d3QEucmqDllRogzbTI7ONitijho20YNjGE9LqdL6UgEdeEicuYZYrt4b3Ou3ML60LvR0YEA6vIV5OuncHRofoYH4gfHdB1ba8iFORNkuL3nqovQwRDq4iXE/FyJI5b2+VAXryKfFVFQ1dNrUJ8Xzz3RZ9XTi+obAKWx7tx2bdZVR6dxlkocGKQkN8hRzc3owSEz1Hj1yqCvAwPm/nx0hJybq/jz8+sTc2/B7zOIsu2DgwRidRVrebnUkte2SYyMILMO4RfGIlv7/ej2dnRjI0eAymSwDg4I7uwgDg9xfvEXyX73u+yNjLC1tYXP5yMajRL+CmlZ+SbkNLpSIURBkP51oGJ9+9vfZnNzk29/+9uMjY2xvr7Ov/pX/4o7d+7wh3/4h3zzm98ETDPyO7/zO3z/+98veX0oFOLChQs/iaWf1Q9RZ83Ie16naUaWlpYKqeT9/f1E8vkTHuf8MoToQogSqz/HcXjx4gVoTfTJE3p/8APs//JfvKfY0ajRX0QiBgVJpQxPNw9/n6RsxWImiG97uyx4qoCqNDQYzm/uhqsDgdNRtnJNhXz82DQkxwIITyavY1nonh7TVFQRPer6etTEBOzumjXlG590uthc5BAf7febpiJP2XJBV1QshmpuJtvZiVSKzNERvkQCe2en4nUDQ6dx2tvRL1/iP3Yt8va9uqmJtM+HtiyE4+CLRhGbm1gPvCfNuq7O2AKvrxdsgXVjozlnnu6WQ6TEzg6qs9MI4l0sjwvrbW9H9/ebJijnHKaDwaJzVyRS8P3XUiBUzunLK7Pj/HnEQbIkdK3icdNXEO/elTQ12uczn636eiOSDgbQkYiZ/CcTiN1dxMZ6mTbF6e1DJpOemSXaslCXp6s6QDljE8aytIoNtXPTBOzpYAjd1WnQPL8fMikThrg0Dz4/uqERueBNOXTOX0Q+vF/d7nf6mqv+IF86HMK5fMVYb68sIuZeuzeXwRDp2noCK97CewBn8iLyYanVcrqnF9nZicy5ceVrf2yK2ofeuS2F8w6PI1/PIFJGS6MGh9BNDcin9yuKxZ1LN7A+9XY/06Gw2fTPvUT3D59a4A7GAUwNTSCfPfTULpX8PJ+P7J//FnJ+Hut59TBLowWZRmxvoGMN5nvgJh63bYOCaGXygfKDLSnNOXLNBRjNlW5tI/NukcDcrPvvvaEB59IVcw+cnTWDJo/PnuroNIL0nC5Obm0jPdzLwCC3uqurMCTg4MCI75eWPJv3w8FBrL//98l+5ztGxE5pFlZHRwfR3N+DYTbMzs7i8/mIRCI0NDR4ruu09UWoWJZl4ff7v3ZUrLW1NZqbm0v+Lh9uPDExwZ/8yZ8Aphn53d/9XRJV7nln9fWus2bkp6CqBR+ur6+zkqPudHV1EYvFyo7Jv/7kBOWL3pyOjo5YXV3l4OCAlpaWkpureP6c1H/4D4R/8AMsv99MzPOWiJubJZtkHY+jRkcRm5tIF6hVW5ZpBlpbUY2NCKXMJmxrC7m8XJGypcFs/KPRQlNR+Lc8qpKf5isFh4fo+nqjk6iyOdb19QZd2d5GvHpVmumRay7yqb0kk6ipqVNRtgCcy5fRNTXGNz+/ea9w3SAvBO/JOdeUbxK0ZaFbWnDiceMOlaMn5d3J5E45VQTMpiU5MgJObjp4XLje2kq2tpZMLnHXzmaRQhg+9R33tPTC+xsbM7+TBw/g6Kgors/Rjsj7829tFQTyxxGTiuv1+1HT0+Y9vSlOwXUuFV7X1RXQFe04UFuLdf9z2Nhw3XCori50YxPW595uUercOZBWxfBFHY2Sqa8nEwySbmggbEnsbMY4bm3vINZXS1AUs/m7iHWnSgr7+CRy7k11xCnXiHiVDoVxLl82m+xgENJHiLUVxNJCybVRjU0IR3kK+wFU/yDi3VLV0EAdjaGjsQKFScUbcPr7URJ8S/PIjWLDlr50Hf8psj9SLW34E0lXq2UtJWp8EmpCsL+DnJ/31BYU3lNHF2LvoHLWR52xpRbL8wVNh3PldAnu+cre+HPmc3Cwf6omQXV2Q1YjFxdyNK2L4GQ8aWmqqRnd2FqwFlaD59DNzcbh6sB9c6f6B8E290gdjyNfPjPooEfp5haj4xES+fyFJzqZbWwy2UKplEFC0mmztsZm5ONHJfd2XRdFDfRDOGK0IS9fFr4/huI2BbbP3GdTKXP/6+oy1Ea/39xHFxcL2hAdDhsK6U55kroOhUxAYjxunhHpNGJ3l+zlyxz+7b9N6uJFavLi9lwtLy+znUOMent7S5CRVCrFTE5/F41G6ejoKHntwsICmUwGn89HZ2dnyfP4OFU6//+/KBUr74r1PtU3v/lN3r17ZwabnDUjPy111oz8FFS1ZiSTyeA4DrZtl3FAKyWi/yjTkeM312AwSH8oVJaI7la6thbnyhUzOZay4MZ0Eh2AY+LBSMSE5lVqPI41F7quzljbplKIN2+8KVv5RmhrC/nM0C4Kjc9xVCXXXBCNmqbi/v3qTUXeZetNzh72eONzcFCkbGWzJhixr8/QijwE8dqy0H19OP39xm44d90KVLcTOgttWeYBnQ9+POnCVVOD09xs1hkKGZpSIIBYXES8fIn0eI+p5mZSnZ1EVlawcpQ8HY+jmpo4CgYRfj+WENipFGJvz+hclpZKmoWK7zGPrqyuImZnjV6oocFoPXw+40KV1w6lUqjxcaMdqYZ2jY4aUf7du8WpbR5dqY+ZDY5tgdboSMRQshYWXNGVgm7lk088qU2qtpb0yAjBCg2GFsKESDY2oZub0MGg2cQfHSF2d4wO5MRG0Zk8j3z92nOzrwF14xaWh/UsmA2XGhrGelCODuhwGN3dg47XgyXRwRDW3U+9U9Fj9ehgGLnkTjuEHJ2sf7AwKa9Uqs/YWatQAPvOp54bZgAnFCYbbSDwrjq3X8cb0dF6VF2UlMoQmnuJdHFY09EYOhKrKljXQqAmz6NaWrD/7H9XpXQW1n2ttGFU/QPo1lbk00cVr7UzOoFceFc5jbynF93RaUI4j5kLOOcvIufmKzaSxhTkAmJrA3ksM0XX1KHGJpGfloY4attGTZ4Hvw/5uNxtUNfUoianDIq5s0O6pZVUWxvyMEl49o3rfVP7/ThXrhmHMilhY8PQBr2GEIEA6tJldCgC2QzyzRszaHF9Re56XJ6GmgjaUQaF39sz1E8XnZoaHSX73e+S/aVfggoDvsJ6cjSpdDpNMBgsoUAdHBwwPz+P1prGxsYyJODVq1dkMhmklIyMjJT82+bmJhsbG/h8Ppqamko0mG4lhCgI0r8OVKwvWru7u/T09PDNb36T3/u93wNMM/Jbv/VbNDU1sb6+TltbG3/lr/wV/sW/+BfE4/Gf8IrP6rR11oz8FFS14MOTlc1mkVKWNCDwxYToh4eH7O7uUlNTU2rDC7x58wbHcairq6MlmUTOzBju7uysoS3l/hT7+2Yqef48BIPmQeUGZXujAAAgAElEQVQx1dXRKM7kpNkYKwWpVNGxZGWlTECsGxpQIyMmNfxEBkYJZStP5yFH2fr8c0/qGLhQtk6iKjnkAji9y1ZdHc7kpLkOShUbn0ymrLnIh3BpyzIJ6m65Ifnmoq/PPJCVMg3e1hZiaaniRkA1N6OHhsoahXwqvGpsRNTVmZwWxzH+/8kkoXv3qgTnSVLj4/hCIeT9++a1LS2k6upQ4TDS58MPsL+PXFtDNTdDXZ2Zap7GTrmuDvnkSS4lPV783eablfV1xPq6mXxms8hHle1GC+uNRk1Y4uNHBf1SoVnIZ9UEAoBGC4nIpJHPXxRcliqu8+IlxMpSRaOBkuOuXDEbqUraqGOaHF1fb5CnxL4RrS8vlTVCGlDXb1UVWeuaWnRPD/KJt15C19Sg+gawHj4wn4n2DnR7m0FRDg8QK++Q66vm+z06ifWoyiAiZxNr3fVGfyCHAL2egWwGPTRsmsa9beTr56UbZCA5PEHEI6CycGxdFB1vKqHnKb+f9OgovlAQ+fJJofFRtk2qa4DQKbM+nOlryLt3oaYGNToGB3vIZ48rbo41oK66N4w6ZKb27G4XggedS9cMBcqDfgi5BuP8FGJzDd3Ygvzow6rUOgA1PGK+S0qbhtfDDa7wcyYmIXWEnJvFGZvEOkalLDt/JIIeHQPbNpk4m5uolhb0wLmKZhQm2+acEYPv7CBfvSwgHmrqEmSz5n5x7Hmga2rQvb3oaAycrHlmzM5Cbq1Vgwnb240Fus8H3d1kf+VXUDduVL12pymtdYHWbNt2yd/PzMwUmpj+/v6S1+URl3/7b/8tn376KT09PfT09NDd3V3yZywWw7Zt/H4/tm1/rahYX7R++Zd/me9973t88sknBRH7b/7mbwIwMTEBwJ/+6Z/ym7/5m3R3d3P79u0ypOqsvp511oz8FNRpgg+Pc0hfvHiBEIKamho6OztLjnMcByml5w0rmUwyl6Ms1dTU0N3dXbaeU7lwbGyYqf/r14ZSlG9SZmfNJjn3MFEtLehz50p84sven20bd6c8NUopxN5e0Sa3gjBSg7EErq01TcVx5OWYEL7MZWtmBvm2PB245Nx1dTgTE8i9PcTz58V1HW8udnbMhjSRMBsM2zZIRTVK0+Skydk4PCxQto62t7F3dvCtryOPbUR1Y6NpyFyunZbS0BXygYP50L537wzVzaUpK1y7XKp9XqOgQyHjCnU8pyWVwtnf57C2ltDsLP4qjZ5uaDDI1NISYmWFbGMjmdpadChkxJV5tGx1FbQ2Kcfr66cLq8w5eJFKlTYr6XTBolmsr0NjI2p0xKBdVeD/zIUp9GES/8vjE+QanKYmUqEQhMP4/H4spdB1dVif30NsuiM2OhpDDQ9X11fU1aFGx8pclvI0PN3YBDUG2dGRCHLmtWlUXChIOmqc5SpRy0qOa2hAxxsK+h+3Us3NqMnzhuqVSZsGxQUdca5XtyGGnCbmTWWLVl1TgxoehlAQvbxAsr6RuiqhkAA6HEF3dCMrZFwUjgkEzAbbZ5HIZIne9xaHF9Z79Qby00/LBiWqzeidxEpRSK+lRF26VuKU5lXq3BBO3yD23c88P08lr+nshmAElINubjZi9CpJ7qqrx7hUvXiBGp+AgN9Y6nrQsnQwSObCRXj7lnRDI8FwGGvmdXWkcmgY3dRsGrVk0jwbXOh1hfW1d5jAwHTOunt1DfF2zrPRckZGDEV1c8s0s7YNyUPz/V9cLHutOneO7K/9Gtlf/mVzb/sKK4+s2LZdwmRYX19nf3+f+fl5EokE79694+3bt8zPzxf+3NnZIRqN8p3vfId/9+/+3Ve67i+7/sk/+Sf8y3/5L/k3/+bf8A/+wT/wPPaDDz7gr/21v8a//tf/mn/0j/7RV7TCs/pR6qwZ+Skot2bkuBNW/s9sNsvr3Ka0UiOxsLBAIpHA5/PR29tbOI/P5yucQwjBq1evCgjL0NDQlw/5plKIt28Nl3dmxogU8w3L3FwJgqKFMOhKOGw285XsGevrzQYt72YFiKMjxMyMdzBiBUF8GaqSF5tvb6OiUYSUBX6yV6lz59AtLYi5OQiHvSlbTU3m+OVlfB52w1pKVGcnemTEXEOlzEZ7b8+gKhU2EM74eFFDc4LulteD6Pp6CAYNZcvnQ+zsmOM9GiddW2uoVcccylQ8bpqfvOg/pwXJrq6SaWzEsm2Cz56dju4Wi8HMDOlw2Gzyw2FsIYppx8vLiEwGNTCAbmkxv5Mqegp1znDmxdKS+X1EIoYumMnA3i5yfb3QoDmXLpHd2yPg0iAXrkN9HDU+ZjQuuU10IXMlHxCZa1C1z0Kurbk23YX3P3URubzkmSoPJmtDpFMlFtW6uQXdkjMPyDnEkUwglEK+9J72q/YOo4WpImrXdXWo3j6sh6WIiI5GTRp2ba1pUFZX0D3dVTUsAM7ouEFYq/wOAbI3voF+/oyjjg6kzyK0uY5cqqCfCgRQA8MFzYTne7JtnKnLWHfvcNg/ALEowY1V5GLla5G5ehP7k4+rog9q8JzRvUkL35/976rrAIwF79Ao1p3bZqAwNo6O1iFfvXBtTJyrNyreH9XQMLqpCfF2tqRZ1D4favoa8vbtciqnlOjRMXQshpgrvk5bFurKNXPPPvHZ1EKgBwfRzS3mfvTsaQHBcyYvAKKMGqiFQPf3F23cF+aRy0aY74yNQ6TGfK9O3C90OIzu6zPDJKVMk7G2Zu5Hm5tlSHnJa0MhdGcXurkJNTqG8/M/j/oLfyEXTPqTKS9Ben4Llx/+SSkLrlh7e3vMzc2htWZqauorXfOXWf/8n/9z/tk/+2f8xm/8Bv/4H//jqscrpairq+Pnfu7n+N73vvcVrPCsftQ6a0Z+CiqbzXJ0dFQRiTipA0mlUiwvL5PJZKitrTX2usdqZmaGVO7BEw6HSSaTxGKx/5+9Lw+S467v/fy6e+6Znd2Znb20l/bWfVm+4Tkm+OII9osxODxCAnlQhCqKF0IoB2zznBAScEJVCgIJpIoQjhAC+YOEkBBjA8+HbOuwZEmr1a72vmdnZ2fn7v793h/f7t7pOVdG0kpyf6pUljU7vd09s7O/7+9zoa2tDbFYDHNzc5BlGYFAAF6vF4FAALIsm7s3VyyXfGGBFibj47Tr/+qrG6xKmeGiqmSrsBjRSLISgiRbR49W7bYACjpMzpCJUwSDxNIUdpfocjJwTtGic3M1iwOF203eDlUFcjmkJAlCkiCpKjzZbEn0cbWhwjymz0cLn44OYgQYIxN8LEZMRBlNu9HkztbXwU6dMu9tcYu74d0QnANeL+QXXqgpreLd3RSxee4c3btCX47ufclHo1AWFyEYg7RnD927Wh4TjwfagQPIRqOQhAACATi9XhoqCrtaoOvdDx0CW183h6aKx3U6od14I7ElsgxVUZDN5yHlcnCmUnBElzeSz+rrwXfvpkb5TcQYM03biJUu2+OSAVuLQ7S0Qv7Fz6ufp6KA33QzaftrxfIevpGGn9VVkqNEIoDPS/RXMgG2OE+Sud4+SgSrIdPhbdsAp7NqXwqgbyLcchukUyfBu7qBOmNAmYNU5PHQhnaSsbwGS0U9LLeWjcLlbW0UD8sE2OQ42Moy+K59NSNwAWJPeG9/WR8N7+yE6OwEEmuQhqmgb23vQdTVCDkwnx9pAhoaIZ05jUxnF3hzE1yJNUjnh8tKuXjXdkATpsnfcp6FQ8LoOUhLi9Rj0j8E+cUjtc9lcIjCHbJZSItLZb9HOai9fUBPD5BKQ37+uU2VSgq/H9qttwMap02n8yM1NyGEwwHtttvpc4oxknNOTFYsUQT016ejA9LZYYiGevp8cTiJRVlcJA9YYWdTWxvU3/ldqL/zPqCldVPXf7lg/F7dzDJNURTTkH4tS7GKYQwijz/+OB577LFNPYdzjkAggLe//e34zne+c5nP0MalgD2MXAdQVRXJCoudQj9IOW9I8YfWzMwMMvput2GMN9iP5eVlLOs0e2dnp0WLmc/nMTIyAsYY6uvr0dpq/RA3WJQrYppLp2lI0ZkUrK1BOnaMduvGxysukIt9IAZEKGSyKmbruiHZMr5HFQivlyRN2Sw19TY1lXaXGLKjtTXw3bsh/H7Ir75atSQPoJ183tVFizRFAYSwdpcUSrb0oQLJJEmrige2ghZ3EQgAPh/F+C4sQJqaquqj4Z2dlOA1OgrJMK673WbRYqFki8Xj4M3NkKJRMyCg4r2TJBrIZBlsdFTv+6g3u0u0tTWIaJTkafk8+MAARCRCO8A17l22owPZbdugrK/DWVcHVvRaFA50aiSCdGcnfBcuQKqRGsT7+8E7Oug1MTp90ilKypqfs7z/tF27AFmG/EqNqFGXC/zwYWqvXlkp/55MroMtLxHrIADpfA3ZWjgMvr0H8ovVfRoCgPaGN0KKLm98v0wabCUKNj1leY9pO3ZCWlyo6bkSdUHwnh7Ix8q3v4u6IHh3F1BXB67IkOfnII1Ul4UJpxN8z/5NLbpFoI5S9YQAIMBmpyvH04bDEA2NNVkjgKRu6o03gSXWIE1OQKoRO6wN7QRbXIa0tFjymGhuBu/pBXJpsNOnIOXzWN+1F77R0U2xQ4Ix8F97E32GT06CjVbu4DGfE24E394H+YXnKTmuoxPI5/Sm8/IbHOm+AQhVg3eMNleExws+0E8ei+VlKKPnrZ9DkgR+w2GwxSWrH83loo6QUMhkxiU9ElfUNxBDfe6c+W+F4K2tENu26Z6lNNj0NER7O8X/Hq8eOy3cbojOTmi33QZ+193Q7rvP9BBuBS4mFetq6wa51HjiiSfw6KOP4lOf+hSeeOKJTT/ve9/7Hh566CF88YtfxEc/+tHLeIY2LhXsYeQ6QCaTMdmMi4EQAtlsFolEAk6nE6FQyDKwzMzMIJVKIRgMIhwOIx6PIx6PI5/Po6urCy6XyzxWoY+koaGhZBgZGxtDJpOBw+FAX1+fZQhS9V9UV2RHRwhiTgrM9CIep4z9I0fAyvyiM58aCFDbegFDUNhsbmldX1mhBb3HU9OYD2zsrvKpKWiSBC0QgLuuzsKqGCZ94feT3KCIqSg5X1mGaG0F37GD2BXOSVZVIWXLPI+iocI8XrFky0g84xxyjfheU0rndpNcKpOhRV5Tk3VBrbMWcLtNxqTc4sNy7Pp6aLqUjkmSGQfMs1moKyuQV1bgWFkhFsThAD9wgMofT5youkhR/X6kdu+GLAS0fB6Mczg1DY61NRr0ilgkbc8eur5akcORCPjevRD5PH1/TQXWk2DR0iAGYjhuIu18DUkWb2mh3pXjx+m+mu9JAaQzNDzMEfulHb6JdqJrDVYdnRAN9RWHJaEo1OHQGIEIh/TQhiVIM9MV3/O8t48K6Wr17wDgt91Onot8HryuDqJ7OzEoap4Gu2lKSdL8fqBzu6XRu+I19fQAObVEaiaammkAcjgoxvjCKER7B8ABaXozaVwh8G0dlt4dc0Gv5iGNjVh28LWbbqXY600kbKnBeqzv2Ak5nYZvdQXSZA3Pmj8AvnuvxQgvwmG697IEdmHU8nNFhaC3lmzEmI/LMsTAAES4EYivQho+A9HeATUQhLMMW2R5rtcLPjAABALgTII8M1tzUDag7d8P0RAiiVY8Dml6uqrvhFL39tKmUyJBEb51dYDEgMQ6pNkZy/NFIAD14d+C+nu/R9LWLcTFdINIkmSmYl1PLEghnnzySXz84x/HPffcU5YRufnmmzExMYGHH34Y73rXu8x1xTPPPIMvfvGL6O3txQsvvFCzV83G1QF7GLkOkMvlkK4hhymHtbU1fPOb38RPfvITPPbYYzh48KDlg41zbrIZxaxK8QdgOp3G0tIScrkcQqGQJVJPCIHh4WFwzuFwONDf32957uLiIpaXlyFJEjo6OiwfHpxzqKp65T50k0kaUsbHKQJYl4EBgPz00xUTYczz3b6d4mrPn4c0P08LbmMHW1E2+jIWF80IWra6WpJnXwwqCTtAjEA6veEzqNC6zru6IDo76Tzmypefibo6OremJgivlyRbS0sbhZJlpBaWoeKVjQhPi2Srrm4jwSqdhgiHIZ09W/E8zGMbHpPVVWrKLhzyihmkRIJM/07npvw52tAQREsLsRX6EJ1LJMB0079c8PPDGxuR7emBNDkJV4XEK8EY1FAIWlsblLY2QFVp8W28touLJbvQ1JJ9qKT3xPI1Dge9Jq2tNPRpGr2ua/ESWZ75nMZG8MEhSC+VavtL78MOWsxnMoDPD8j6fY3pTJrhaZFl8Ftu2VRHDO/eTkEGBYOAYIxa31uayXcjOLAWBwJBSn6q1TfS2Aje1l5WFmX5ukAdtIMHqScnlQRbqm5e1g7fRMlom+gR0W65lX5eXS4gEYc0VpmR0HbsgrS8XHVgJM9EP0RrC4TXC/nZZyuyDZZjDw6BryfhmNoYiERTM/j2bkCSICbGoBR8X23fAbC5+Zqlh7ynB1pzC4QQkFOpmuWl5vOaWyB6e4FkEsLnRzYWhWt6GkoFJlIoCvjhG8EmJiHNTJtR5CLSBDAA0Six1kUMG3w+S+S2ebzGRpKZ+nxAPg82vwAwBtHWRixIjY0fUV8P7dZbob3lLdD+5/8kJnGL8Fq6QZxO53UnxSqHO+64A88880zFx4UQiMVieP/7349jx45hYWEBmqahq6sL999/Px555BFLwaSNqxv2MHIdQFVV5HI5c1el2kuqaRp+/vOf43vf+x5+9KMfobGxEXfddRcefPBB7Nu3Dw6HY9Pft1j6VWlQ4ZxjdnYWuVwOTqezJMFrenoaa7okpre3tyLjUi6HPZvNmv0plx2ck69ibMw6sExOQtTVUWt4hYJGA0YcL2cM8rlzJDsKh0leAEBbXwePRuFcWoKUzYL3UK+CNDJSe2e8s5N295JJYiwMpsEoRix4XwhJsi7mixacha3r8Pkg9OGHJRJUKlbFR1POuC68Xlpkh0LmtSKdBovFaHjxeDYV32syN1NTgMtFJvNCX040anbICL+fvC6xWE05mBYKITk0BJHNwu1yQeTzEIkEpGgUzmi0ZEGU7uyEGg7Dd+4cpDKLH+50Ih+JQDFM6ozRon9ujoaKCgs3I1JZevXVsvfYHCDr64l5UxR9GJ2rOEACAO/rg6ivh/zSS1XvA29qAt+7j5rYudAHQN1PVHSdZqfKkSM1d/d5RwdEpAny0ZdpMdnaRkMRQLr/2Rmz70Lbf4BkRbWkXpIEfuttxJwUlkR6vRTj2tBATGh0CWx6CvzgDZsyyguPB3z/wZJ4XSFJZKZuagaERu+zyXHyvRw5UtPvAJDpmq2vQ5qYsB6Pq5QsWDBACEUBv/EWSM89W5VpA4B8SysynR1w1ddDOXu2ZsAAQCmF6eZWeE+coMV8dzdES4v5OVd8DDUQgLpjJ1zlPi8Yg+jshGhtI+ZlYR5sehr80A1gYxeqFhwCukSrpwe8swvggozqExM1h0Zt3z4KVDhzhsoIw2FiWbNZ+iyYnDR/JoQkQbv3Xqgf+hD4nXfWvD+XE8YQUisFE7j+pVg2bAD2MHJdopDuLf7z3ve+F8899xweeOABPPTQQ+jr6wPnHD6f75Iu6Dc7qADA8vIykskkcrkcent7LR+48XgcMzOU1NLU1ITGxkbLc4eHh6FpWtkc9ry+OLhi2epra7D0qIyPUwzp+DjgcJCXoUxufjF4KAShN7kDMBedUFUgkaBMfKMtWB9uoChVGQLhcJBkq7fXTIVhOjPA5ubKGoNFHenqyzE3IhAg5qLAvyE0jYzrL71U0UBvXqPREj82Bml2lhiVpqbSxvWlJbD1dRoqEglIp2p3Rmj79tFuZyJhSTsz5WkF7ALftg2ipwcYGYFciQVxOOhadaaG5/NQo1FIa2twLi9DKhcbLUlI79gBl8tFu7VFw4xaVwe0tIDp0dFCkgC3G2x4mKQoVRYpfGCA/Eovv2xZAJuRvvoACVmiMAGfD/KRF6t2nxj3jeXzFVk60dhI9yAQoLJJjUOanqRBpVJcsMcDfugGSC8eqcna5Ds6kGvvgBsgWU0yCTZPw1vJPdjeQ4N0jeEfALTBQUBWwHJZujeyRD6yqamSe6INDoGl0zWjuwHdEL+tnd5bfj8FDExPlT1f4XbTfXj22ZL3guWYLa0QXZ3EVKoamcFrmbolCfzmW2iANbpwwmHw7m5wlwvaagzO8QuQ9AFCuN3gB2+wpLuVg1Zfj3RbGzS3G8LphGdsDK4akknAYABvAJuepo0MfSjEygqkifHSQcbhoK+fm4OkbzwB+oCzbRtEi95fk8tSbO/iAvj+A+RlqxUCoijgO3dCe+ABaA8+CKEnRG4VLkaKJcsyXC7XNd8NYsPGZmAPI68zzM3NIRwOm6WHxX+uxNuh2pBS/KG7vr6OWCyGfD6PSCRiKVjUNA3DejKW1+s1o4gNzMzMIB6PgzGGnp4eC+OiaZop/7qcu02G1I1iKafALlxA8uRJ5M6cgWt2Fr6FBTinpoBkkozanJP8qVa07a5dFEFryI6EMJkGNjtrWfiZ8cTRaMXFmxl9bOy4SxINAnNzVaOPeVcXREeHKUsD9B3k5magsZGGC0OytbZG2f7x+OaGCqPH5OxZs9wPupzMvNb5ebBUivwSfX1kep2qru9XQyFo+/dDyWZpUNGjlLWFBShFPS2AHiMcDFaOjS4ovBR+PzKqCqTTcM7NwbG4WLld2uej3pPlZUtnB5dl8KYmsEjE0kujCQGJcyg12A0BgB88CGiaRXojgkEaJgw2SXAgsQ4o8uYKIAEyHq+ulnS6iGY9LtgfoMV+JgPhchJbWKvo0+lEcvceeM6ehVzu/vr95EtpqAccTgiXizpTxqt3SZB/YA+k556rOADwlhZa8Pr8gNulh1xcqDowCFmmxf/LR8vKzURjI+3wez1AOkXszMrKpgYc0RACHxqC9Pzz5A9zOiG290A06t1JS4u00aGfn7ZrN1g2W7tjR5aJeejppRjy2RnaNKnCaHGnE8mdu+AeH4cjFiOJZlsb0NYGzeFAPrYC59w8HPpAJ7xe8AMHIQ0PV0xcE7JMDEpTE4TbTcze7CzkGswloJvrd+wAGxkB/H5iWZ1OkmqtrIDNzFiGKz40BPVDH4L68MM0nG8RXosUy0jFsmHj9QJ7GLFhQTVW5WJa3n8VbJZVUVUVCwsLyOfz8Hg8aG5utjx+4cIF00szNDRUkXFpaWmxeFwA8sA4HI7XrM1NJBKIxWJIpVLo7++3/GLJ5/OYn59HMBhEIBCg48diG0xKsWdF3ymvVWBoQDBGLMiuXbRrKwQNJ2trkBYXyzIzhtelnBzMjD7W/RtCUcz4Y/no0aqpVQKwdsCkUrS4NFgVt5sGKb0bBKpKZXDj4zWHCuF0ko8mnydDvBEvXGCEZwsL5oJV7etD2u+H5/x5KBUiYo0SSNHVRfIxzmngq3LvhCzT4r9c83PRYJbnHJqqQvV4ENjE4GTItgqHPc3vBzNif/VeGrG+Dra6CtHeDml21rLDXPY6HQ7yr6ysQDp3jl7j1laSuXg8NPBl0mArMbC5WTIFr6zU7D8RjIEfPmx+LXlHWiCaIoA/QHKgdArSygodd/8BinWdKV+GWHgf+U030ftC9x4JPeRAhMO0KM3lKARgehp8/34aLGqU7AGAduNNlnMw0pVEOAwo8oaMbHmZZFaZTM0deUBPeOrohHTkCBAOg7e3AwE/kMuDLS+Rt0V/r5jsRgUDueVeeL3gBw5AuD1gqZR+rImqg4V26AYaIgteP+Fw0Ps8EgFnQH5pGa6ZGbB8DuLGm4gt3AQTku/qAhsYoJ/DFKWsYWICUoUhXGtuRr57O5ynTkEyylL9fjKb19fT5kU6RRsNs7MQvX3EKh89WpVdMz73tLe8Bdrb335VSLE2+3uTMQaXywWn02mzIDZel7CHERubRuEOj/FH07QrPqgY/y3390IsLS0hnU6Dc17CmiwvL2NR/0Xb3t6OOr0IESA246zOIPh8PnR1dVmem8lkIElSVVP93NwcYrrMqq2tDfX19a/hanXk88SqGMOKPqSYcrBC47pepFhNDia8XuqTaG4mOQhApnUjDrhc10gF4zqA8jGz6TRJic6dq52a5HIRK5TJQHr1VZLSlGFVjNJGbXAQaGzc1MKNNzeb/hXhcCCdyYBls1ASCbhWVizytMIYYen48bKMhtn/0dBACyfo5ZkzMyWMlOV5Rvt7Uc9N4fE0hwOqbvqXHQ4objcZyGt0NvCeHmRCITjPnIGcyWx4fXRWRWSzJFFbXASTJPCdO6vuXpvn5vOBH6BhgaXTG5HPxmsSj0Oan6chSFFoCJmZqc2ESBK0G26AtLpKEdmRRgiPF6qmQcnnIEWjdD91qZp2w2Gw5aWaAxZA6UssRwWVoqmJmDTO6f0zOwsW20gP04Z2gIFBOlM9PAIoSMVaT2wYntfWIM3MWI4JGK/1/prmf+HxQHR1UQmkpoEtzNPxqjWbNzaCDwxSEWGhT0ZRzMECigIk1yFNTYO3tRHrVSMgAwC4w4Hk7t2QV1fhDIXAPF6SRi0vW7wXBrRQGLneXrhOnzaHCvN8ZBm55iZojRG46uro/ZLJAH4fpBeO1HxPCwDqgQOQhKANDGPwzuWA1VW6T4U/u3V1UN/zHqgf+hCZ67cQFzOEKIoCp9NpS7FsvO5hDyM2LgnKDSpXWv4FbAwmteRfiUTCjClubW2F2zBVg4aNMT3tKBgMYtu2bZbnjo+PI6XLAXp6erC+vo5wOAzGGPL5PFRVhaqqmJqagqIoiEQiaGhouGzXjOVlWqjNzlJqldFSPzZGC+SinXpzwf3KK+WblZuaKBnL7zeN61hfh6wXE1aC8HjIv5JKmT0mJYWSjAGZDC1gnU6goYG+tobHRIRCJNFYWgI0jSRbhuyusHE9l4OQJKR27IDicMD56qtVJW8iRLIYeDy0aM1kyKuwtFS+PNPrpaGijH+lXAmkEIJYobNnaUFX5Rp5U/O0+TsAACAASURBVBPE4CAxY9PTluNxvx95ISDyecipFMlmurvBUqlNSd5SfX3QvF54JyfBIhELq6IlEpBjMRosVJV8NNu30/uj1utSX08DwPIyvb6FYQKLi3QPjetzOpHcuRPOuTm4aoQxCKcT2u2309BrsIrJJLEARe9pwBhCcrVT6RoaSP4ny2B5ldifpWWwmemyC2SKS+6FdOSFigtoEQ6Db9sGBIMQThcZ1M+fr9iEbp5zUdFlyfECAWINV1fBVqIQff01fR7msffsBQBIMzO08aBvtoj4KjA9DaWwR8njIWbv3DnIleRVikLMRWPE9HWZGyI1wgs0vflbPn4cQpaRb2pCvqEB3OWCx+MBW1uDNDcHFo2CezxIDg3BubAA12wN03skAu3QIWJCHnzwmkrFMgzpWy3Feuqpp/CP//iPePbZZzE1NYX6+nrccMMNePTRR3Ho0CHL1x49ehSf+MQn8Pzzz0NRFNx55534whe+UOLVtGHjtcAeRmxcEVxL8q9cLodoNIpcLodAIFAi4Tp37hxUVQVjzPzFY5RAFjIujY2NiEQi5vE550in01d2JyyXIwnH2BixK7OzkF59dWNgKafRL5OGZT5WLLECIPJ5wO/fVFs9j0RowT1DmvWyrIohsVpepsGJsYpMheXY27dD6+pCbm4O3O0GUxR4FMXCqpjX4fWarfKVFvOFg5SIREjuVjioVIoyDYXAd+40r9H8d49no6fFKIHMZKhYUpJot7tGuo7RWC+dPk3sk368vKKACwGWycC1vk5x1EZy28wMHLVkW4whvWsXXF6vvoNNrIqWTkNKJCAtLEAqWMDynh6IlhZql6+SgCZcLjLct7aCp1LIJJNQcjk419Ygz8+XvKZk9D5EyVIVJGzC6aQFdjgM0dgIQJAcz4ikrvB5ou3YAXi8tKAvHjIVZaN93usBwCC8HvpZqSUh089ZGrF2wYhgkPwo9UFAksnnpDeiQ6lddAkY76VdkE6cADwe8JYWem0Ako/NzVqkaNqBA2DZXMnPbTHy9fVg/f1AQwMxr7EYJWAVDI/F0IaGgEAdBSfo71MhywX3bYOFYvPzEP39YEtLNaV9AA19fHAQfGEBWacTQlHgliTIiQQNKgVDsWAM67feCsf/+T/gd99tBnKsrKwgl8vB4XCgvr7+iiz0L7YbxBhCrhYW5MEHH0Q0GsWDDz6InTt3YmlpCU8++SReeukl/OQnP8GdutTt7NmzuPHGG7F//3588pOfRCaTwaOPPopYLIbjx48jEols8ZXYuNZhDyM2thxXA6tSy1QvhDD/u7i4aDIgBkNiMCiF8qzt27fDYyw6UZtxSaVS5i+sKxbhuLBg8acgmYR8/DjY2bPVjeutrRC9vRbDuJAkWhw3NpJhVFHMFCsRDJJc5Pjx2gtuPc6YjY5S0lRxoaRhXE8mwX0+iL17aXe1xgJM+HzQDh0yTetM00pYFcvXG2zM3FzZXhBRX0/XW1dHMcN6IpZ09iwNftVSkzo6ILq7KSZZX8CKxkaSWAUCxDAYiWLRKHXGVBmcCqENDVFQwPg4UF8P1eeDJkkQuRycuZzZh8EA8HAY611dcE9Pw1mrXLKhAdqhQ6b0iKsqRDIJeWWFWJWi11UdHARraKCBpYx8rfD9Qv4MBchm6Vjz8xVZGUqDOkiDddGQJRwOc1AxvC9C0wBFoV6PzQx7bW204NbPWfj9dMyGBhqY83kgvkqvy9AQpDNnN+dNOXAATFXBzp3biKF1u2gAj8chzc6ZpYi8mQIZNsOEiPp6aDfeSIwj5xuxttPTZVmLbGMjcp2d8A0Pl8RSC6+Xzi0U0q81BwEGpqqQX3655jWKUIjCMoaHwbJZum/BIL22+TxJrAqGC23XLuoTOXq0qnRLhMPQurqwcOgQYnfdBde+fVUZ68HBQcswkkwmEYvF4HA4UFdXZ/lcfi0wYnk387tJURTTkH61DCEGFhcXS+Ly19fX0dfXh927d+OnP/0pAOCd73wnfvazn2F0dNSUNE9MTKC/vx8f+9jH8Od//udX/NxtXF+whxEbVz0qDSqb/WXwqyCXy2FtbQ3xeBydnZ1wuVzmwMI5x+TkJAKBAILBIBwOB+LxuBlT3N7eDkVRzGMlEglM6Qv3cp0pIyMjyOfzkCQJQ0VtwNlsFpqmXdnCq3Sa2JMCYz1bWaGB5amnai6STP+K3plRLg4Y6+s0DKyvE5tQJfHLgACQHhiA6vPBub4Oh7FwMlgVo3RQf2+Yxv/p6Yq+A9O43txMhnPOiTVaXa1oXAc2IoqLjf9CUTbkaUa8cD4PoSgUn/vii1WToMz719REA0gmYy2BBCyDGWSZ2KyFhdomcwD80CEaoNJpqLqcTM7noSQS5qBnIBuJINfRAf/UVPWUpJYWqJEIUj4fGOdwJJNwpFKQFxchVRgszMXosWOlLIkx7JnpXwLC46HheWSkquRNuFw0sBTszAtFIX9OY+PGPUynwVZWKKrY46EhpNbrYnTBnDoF6NdtlprmcvR+1ntZhCyTl2Z5eVMMgbZvHxAM0sJdH85YLFaSFAVsyKvYxERZX5aQJLpe3TsjFAXc5YJ0+jTkmZnqSWTGsWdmzJ8ZEYmY0c5mCWk0SibztjZiyo4erVmSKRwOaLfeSu8xRaGfXSN6W/cgWe53by/UD34Qud/6LWRdLpP98BqvoQ7j81OWZQwODloeK2Sst23bZinDMz7HHQ4HfD5fRX/fxUixrvVukDvvvBMzMzMYHh6Gqqqoq6vDe9/7XnzlK1+xfN3dd9+NCxcu4FxBGqANG68F9jBi45rG5ZR/qaqKH/3oR/j2t7+NbDaLr3/96yU9J0Apq1JJ/pXJZLC6uop8Po/6+npLTLEQAmf0eMtynSmFjEt3d7flF7GmaUilUnA6nZc9qrjghGnRWpz+NTEBEQhAGh+vHTfKGHlMXC5Ip07R4jMctsTZYnWVFijx+EXF9wqfD9qNN9LOMGM0+BSxKoXgnZ0QnZ0VyyULjebweiFkGXA4iNmYna0ekVowVBiG+8I4YMO7gWQSbHUVvL0d0tKSJe63ErTduwG/H+zCBSAUssrdirwv5lC2mRSvSAR83z6oySR1lWganNlsSUKZeR4dHUBnp6XrwnL/jOutr4fweJDnHAyAY3SUXt8qP6vanj00KBTsnpuSt1BoQ/KWSoElEuCtrZBPnarqbwL0RLGDB8HW1sCGh+l4RkeLsdiOxYg1SybpdQyHS/pdyh47GCQWaWWF5IwVmAHzGgt8FRWPqQ/LvLGRInHTaTq32dmKUjnBGMnesllLdLNwuazpacb7b32dmKGTJ8u+jiXHPnCABveFBUtoAnK5jXunG80NiaZ0tjqTJIJBiLY2aLfdBu3eey1SrGrI5/Nm+W+gyD9S7fMzm81iVE9HK8dYT09PQ9M00/9XbSNIlmXzc/hqY0E2i3g8jq6uLtx55534wQ9+gOHhYQwNDeFLX/oSPvzhD1u+9g//8A/x5JNPIpVKWXyXNmxcLJTaX2LDxtULxhhkWS6rD36t8q9Tp07hu9/9Lv75n/8ZjDHcdddduO+++yoON8Zxyh2vcDBxOp1oamoq+0tKCIFIJGLu+hUjV7DYdTqdlsdSqVRVxiWRSJipLZdMR63HaIrWVuC221AifkkmURxRbKR/IZ+HaG8HGx21LL5YMgkU6fO5w4HM7t1wMkaPZ7MQXV3ItLZCJBJwxOPkPdBfG7Ox/swZKD/7WcXTF+EwsRrNzZRklEySnMw4l+LLTaXAFYUGp+PHSzTsRtmgmTalqhAuF1giAfnoUaBoMGPxuCUJTNu9GwgEwEZGIE9PQ7S0QNu7t+xgBkUh+dj0NORC2Va5IUpfjBq77OAcoqsLWkuL3txu9b4Y8jtpZATKT39a9heEcDqRDYeRb2igxTljcKVSVPZXQWrD4nGzHVs+dgxK4f1TFDLN6yEHmhDgmQyYzwclFoNcpv+EpdP0XtI9OdrevYDLBXbhAuTRUXo99uwhs3WBXFCanycpl74oll94YeOYs7NAkWlayDL4DTfQYKL/DPKbbqLrNLxIBawZ376d3n/HjkF56qmy9wIgyRvv7KTGc1WlBXsiAREOV2bhQiEqsPzlL0tZpKYmU+KnAciurwNeLzzRaNleGpbNkoxPZz0Mhoq9+irY1BREWxt4Tw8xSEaHkc6CwOMhFm5ykt7bBubmSr4PAKiHD4O53eZ7g/f1Ac3NNIQWXauoq4P68MNQP/hBiP7+ivevHBwOR9nPTgBobm5GKBRCPp8vWTTnC+6l8fzC3x0f/vCHcfr0abS1tWHHjh3o6uqy/GlubjZZkEIm/FrF7//+7yOZTOKP//iPAQBR/TUq9k4a/yaEQCwWQ2tr6xU9TxvXF2xmxMbrFuUGlbW1NezatQtvetOb8O53vxtvfOMbkU6n4fF4LoshcrOm+tXVVaTTaaiqivb2dsvjKysrmNc7KFpbWy3JXbUYl1QqBc75ld3N45x2c8t0qkjj49TnMDCAlM9HnSBVekwAfWF38CA1rjsctIuazdJie2GhdBd6506gvp7Soso1zxu7xg0NQH09pVoxRsOUXrJY9jygd6p4PJb4YwurYiSApdNga2sQra1k1q5RiGeySA4HpNFR8lkUsyqG90VViUXq7wcbHYVUK5WosRHagQPkOQA25G7Ly3S9xclVHR1IRiLwjI7CUSZaWTQ0gDc1QQ0EwB0OSIoCxekEO3OGzq/Krxze349sfT2cr74KWb/Phd4c4XBAzWYhpdOQ19aAri7yjpTx9BTDZFjOn7fcP6F3ybBo1DTAi0Yq2Cv09FS8f4EAsXDZLL33DC+SYagv8qmYaWUnT5aNphZ+P71f9JAIIctgskw+rioGfUD3vGzbBnbixEaHhxESEQzSz4eqAokE2OIidfrEYpa46YrH7umh9+vUFL2XDQYpl9sYbPWfNeF0Euu0ulpVdmn8bPA9e6C96U3Q3vnODYP+FYSmaaZEVlEUaIZBXwg8//zzmJiYwOLiIhKJBCYmJjA5OYnx8XHMz8/D7XbjPe95D/7u7/7uip/3pcanP/1p/Mmf/An++q//Gh/5yEcAAM8++yxuu+02fPe738VDDz1k+fo/+7M/wyOPPIK5uTm0tLRsxSnbuE5gDyM2bBTBYCeudlO9gVQqhfX1deRyOYTDYYs5M5fL4byuVQ8EAujo6LB8j8nJSazri5b+/n7LzmIul0Mmk7ns2mchBHK5HFzGQj2RABsbQ/z4ceTPnoV7ZgZ10SgcU1MUj5vP08J/z56NMsVqiU719eB9fSTpUVXStCcStPgss9g2F/5OJ5UYFscfh8O0uDNKFoWAcLvJn/DKK9W9DJJE0hZJgnTsGC1c9V4Qcxc/n6ekpIUFGox6ezc3VMgysSBCEBNQ4FVBPE67+AVpZ6Y0rUZjttbcDGZImDgHW1uDFo1CqeIFMRmCItmWcDiI9WlogOZygckyFL1pnCWTkI8dq3qNAJDu7oZaXw/f8DCYqlq8Obl8HlIuBymRgKJ7BPi+fZsfWPbto/uWStF/qwy2Zmra2FjF18b0DjU2EgsnBB1rZYXeexXKN01fStFrIxwOiNZWqPX1yEoSBGNwahoUtxtMCOo2qeV50eWO0pkzG4lsoRANtoxtDLazs4Cm0aCfy20q/YsPDEB0dgLr6/ReNmKey0RlC1mGdt99UD/4QfBf+7Wax76cqJaKZZjVjU0bWZbhcrmgKAoymQwmJiagaRp27dq1BWd+6fCZz3wGjz/+OP70T/8UjzzyiPnvtkzLxpWAPYzYsPEaYPzyKix93KpOlXJ/N6CqKlZXV5HL5eDxeEr6Ts6fP49cLgfGGIaGhi6KcYnH43A4HOYv5teCxcVFrOqL1f7+fsv3z2azSKVSqKur22ClNI1SgqamwEZGLJ0q0vi4ZbEtZNkaDVxGQmQsjkU4TAtaRslBbGbGoncveZ6imHr5woQw4XaXehmyWSCZhGhqgnz2bO2ddofDbJaXRkZo8ClmVQwWJJvdGCpqaPEBWkBrhw4Ru6OnillYlSL5T6atDWprK3xjY2Vjmy3eF7cbQlGow2Z4mNivKulVvLeXTM8FPTMiGITW1ASusyqKJFGcst4uzxcX4diEETzT3Q2HkcjW0ABRV4e8JAGqCimdhmJ4hzinKOu9e8Hm52s2q4uGBhpYhKCFtZF4VoFFEsEg+O7dYFNTZcsgLdHWTifJBD0eSKdP03uwymdJvq4OucFBuGdmIOvDkCWRzfAOGSxIczOlvR09WjNVzEzFmp+n17WwgNQo0Czw5BgyuWrHNqOyt2+Heued4A89BFG0OXIlca12g1wOGIPI448/jscee8zymGFg/+3f/m38zd/8jeWxe+65B2NjY7aB3cavDHsYuQ6QSCTwxBNP4Pjx4zh27BiWl5fx2GOP4fHHHy/79XZ50eXFtdSpEovFkMvlIIQoodkXFhZMvbDRo2Ign89jRPdBlGNcErq0qlau/tTUlPm1HR0dJcbTi8bqqin9wuws5DNnKAVsfJwGmKKFkqX9/ZVXSvsnGho20pIcDnOxyKamaMFdLZHIOHY6vVECWbxYNBazi4uAHiErnTlT0TdgObYhrVJVK6uyvk4sSMFgYnpp9GSzsseUJFoYt7ZCRCJI6z4GRzJJbfUVnmceu0h2ZCRsmVHPRqKYwwGWTm8qKpb39VEi2yuv0C5+czO0UAjc44GkKJBU1fSCIJfD+uAglHgcnoJ+l0rQduwAIhFgbQ3c7UZe0yCpKpT1dcjFLIjPB75/P9jiYsVgBstg29REA4sxqJSRC5rP8/uJvSmKkBZOJ3LhMNRgEHJdHRxOJw22uRxQV0eJbLWSq4xBa3YWbG6u7KBsMoTpNN2TYLBiHHMheFOTWQAKRSFGLpUi43qZUAft0CGoH/wgtN/8zY3BegtwrXeDXGo88cQTePTRR/GpT30KTzzxRNmveeihh/D000/j/Pnz5mf05OSkGe37uc997kqeso3rEPYwch1gfHwc+/fvx759+zAwMICvfe1rFYcRu7xoa3EtdKoYSCaTSKVSyOVyaGpqski4kskkJnSfQygUKhlkRkdHkdUXM0NDQ0in00gmk2hqakI6nTalcPl8HjMzMwgEAmhsbPyV8/+rQlVJ5qWzKCIahTwyQgv08fHKi0WfjxZ0RV0mwuWyxu3q7fLIZqlZ/sSJsp4Ay7GNRvd4HGxszLpYZGyDBdEXi+bivCCZq+Kxw2HygiSTYLK8YUQ2FotFi81ax7YUXhqJYrJMbeO1EsWMYxeyIOWinpNJioFua6PSzRqN6sAGw8JGR8H9fnC990U2JEfG9aoqNJcLqaEh+LLZ2hHSwSD5TBQF2XQakqZBzmSgrK6W9YIIjwf8wAGKpy7jwbD00jidG700o6M0MFfzguhRxdLKinls0dBgYVVMr080Cng8dL9PnChbbGo5L7ebBttEgpgiI6a4QlS24R2RTpyozBwyBjQ1gbe3Q3vjG8Hvv58khFuIixlCjMCPK1ZOu0V48skn8fGPfxz33HNPCSMCADfffDMAWjccPnwYBw8etKwbVlZW7HWDjUsCexi5DmC8hIwxLC8vIxKJVBxG7PKiqxvXCquSz+extraGfD4Pn89XElN89uxZCCHgdDrhcrlM9qOnpwfxeNxkXDo6OuDxeEyZl6ZpiMfj5vMqpeNcFkSjZuKXYaYXAOTnnqNeiyr3X9TVUcJQQSRvibekYHEnGhqAUKiiid5ybH3nHPG4dbFYwKqwxUXTq6INDgLhMC38K7XEM0bsR2Mj8vX1AOfw6zv5xaxKIcyY4oKhAoDZ0wLD+2IkihksSJlEp5JjG4vcU6coWaqlBQiHrRIhPcEKqRQt/Dc7sPT1QWtrA2IxcI8HitNJDMPaWonkyGCd2NpaxWMXsj6ZYBCCc8j5PJxlvDmW5zmddOz1detgqyjg+v0rNIbn1tYgGhrgPn0aUq3hU5f3sVRqI6pYTygrZzQ3O3JOnaod4+vzQbvpJhpmJckcvFk8XpLIBgC8qwvqBz4A9bd/GwiHqx77csKWYlXHHXfcgWeeeabi44X37OWXX8Yf/dEf4bnnnrMoKnp7e6/Eqdq4zmEPI9cZqg0jdnnRtY1yrEqhZ+VKoNKQYvzd+DiJx+PI5XKQJAmSJJneEyNe0xhO+vr6LFHFtRiXWCxmZvlfUcNkLgc2MUESsIKBha2ukhn9yJGqJnpAN9Lv2kWSnakpkkMVSmYymY0elFSKUr+CQdqBrtXC3dgIbf/+DckMQAvH1VViBYrkPNrgINDYCHb8eEkLN6CnHDU30/n5fOQFkSQqvyxzvEIUSquMRWrFRLGVFWJBVlc3N1TokjA2MkKytsLjFUmEzESnRMKy8C97//x+5HfuBPd4IAsByUjEMrw0RayP2VGSSln6O8zHddZH9fuhyjKgKFD8fsjz8yTvq9JTImSZTOP5PL32QlCSmN7TYiao6XG70DRK59qMZ4gxOjZAnSI6i2R6hwpYJEA30g8Ogg0PQ9IDAcoet74eorWVukHuvhv8nntoANoiXKwUy9j4uJ5ZEBs2rmZc+6HYNjaN0dFRpNNp7N27t+SxvXv34r/+67+QyWTsVIyrFMaiv1yq1ZWSf1XqVMlms4jH40gkEti+fbvJujHGoGkaEomEWfRoRCXn8/kS5qNc5n/h915YWADnHA6HA/1FPQTr6+vI5/NwOp3weDyXNv3L6YTo74fo70fZ5c3CAhno9UHFHFguXKAUKo8H0vHjkP/f/zOfUtjzYF5jKESL3OVlMP2a+cGDlVmQXbvIP3DiBJSf/rTi6ecbGpBta4Nr2zYwPcoWq6skt0omy/eqOJ1kSn75ZYvURzBGvhejV0WX9JgsyIsvAkUmc5ZKkZlchymtWlkBm5ggSc/u3WW9L1hfJ7+GMVQYvooKQQC8uxu8uxvQ2Q7R0EC7+npCWaEfRygKyYfSaTiPHCl7PMEYeHMzeDgM3twMSWdp2PJyxXNgiQSQTILv2QORTsNb4C8SkkSJVo2NyDgc0CQJLJ+HlMnA2dYG5cwZuoeFx1tbszJRAPj+/RCRCPlpOKeI3P5+K4u0tAS2vEy9Ojt2gI2N1fTqCFmGdttt+v8ISovbvh1aOEwsUnE3SEMD1Pe8B+rv/R7EFu+SX8znnaIocLlckGXZHkJs2Nhi2MPI6wh2edH1i2qDCnB55V+qquJf//Vf8Z3vfAfhcBhf+MIXSlK72trawBiDEAJutxsej6fsAsDr9aK1tRW5XM7SkgzAZIGA0uJHgLpY1vQFW29v70ZUMCimOJFImIzKJZd/NTeDNzcDN91U+lg6TSyKUfxoJH/pf5BObzTRHz8O+Ze/rPqteEsLtN27aXGqXwcfGqrIgmQHBpDzeOAdHoZchiEQHg8tjkMhYhtkeaNX5ejRkuMxIQB9KOIDAxCNjSTbMnotClkVY2PDYEFaWzekVYXJVQsLJSljfPt2uq6REWr4DoU2FslFrI/BVCCdpgjaoiHPcr1eL/iuXcQKqCqxAA4HeE9PedaHMSrp5ByOZ54pTczyeGhYaWiAZHhpnE6wlRU4X30VUpE3h3FOKVXz8/ACSA0NgTmd8IyNgZ07R+fX04OszwfuckHS43vZ6iqwvg4xMAA2MWEtDJ2bK1s6qO3aBfT1UTxwOg3R0wNt+/ayrJlpdp+bswzN5e6faGkBP3QI2pvfDO2BBzbYvS3AxUixjPLZyxlVbsOGjYuHPYxcZXj66afxa5vMXD927Bj2799/0d+j2i6QvUN0feJyNNUPDw/jW9/6Fr773e/C4XDgnnvuwdve9raqTfWVjmW872RZRjAYNP9NCGE+JkkStm3btqmW+uLH0+k0FvTFbnNzM8JFOvbl5WVzp/SSm+g9HogdOyB27ChlVYQgVmVsbGNIKWRXdGmMACwDSyUWRDBG0pquLpIwaRrY2hqc8Th5EcrIq1g6De7xUK/Kiy9aJGFVWZBUirwgRdJOlkqhsB3dkG2ZLEgkQsOAcbyCEj62tkYsSDJJ3pHCVKwyCVm8sxNaTw/t1jMGBIPQbr5543hLSybrIySJBhZNI7anXKeE7qURTU3gkQixDJzTcRYXSc5U5v5J4+NAMEh9HMeOWWKkue4r0Xw+QFHgcTrB1teRDwbBxsbgKzLSs1QKbGwMhe9CbedO8urMzYENDyMfCiG/fz+YwwGHJEFKpUzWDF4v3cOFhbLDZzG0Awfo3PXSRtHcDM3nKzGuA+Sn0d7+duoGufHGmse+nLgYKZYh7bSlWDZsXJ2wh5GrDIODg5tucu3s7LyoYxsLsGiZ2NCVlRUwxlBfX39Rx7Rx7eO1sCqxWAxvfvOb8eY3vxlf/epXf+Wm+kryr+Jz9Pv95t8LBxWAhoxsNgtVVUuupXBQKWZVNE3Dor7o93q96O7utjwej8ehaRqcTid8Pt+lXcwwBrS0gLe0ALfeipKGhmSShpOZGfIajI8D9fX0bxMTFi+DAJDq74czGITyyitlo1mNXW3R0EDDgH6fpLExsNHRkucUsiCmMf6VV0zZVlkWJJMBi0bJ2xGLUbleoWzLWDQXgHd3QwwOAiMjpsG/IgtS5KlQyvR3mNfr8UAbGiIjdz5PQ0ImA9HVBegJZdYnCPBt2wBFgfzLX5Z00wi3e4NF8niIBVEUGp5Onizr7ZGWl+HVvRzp3l6IxkbI58/DncnQ4r6rCzAazQEaCmIx8GgUme5uOONxuAr9NOk0nEtLKOYGeU8P+G23QUxPI7eyAhEMQrn5ZiiqulHaaHh4dHlaraJJ4XKBt7SADw5C+/Vfp4b0LUxOulhDusPhMFOxbNiwcfXC/gm9ytDa2ooPfOADl+XYvb298Hg8OFnGcHny5En09fXZfhEbJSjHqng8HszPz8PtdpsDis/nu2zpX5thVQrlX8WDSl1dHRwOh7XpXUe1QQWgQT2tL1qLiyGNyGKHwwGv13vp5V8+j7DuYAAAIABJREFUH8Tu3RC7d4Pffbe1rZ5zWqCPjSF15gySFy7Ad+4cHIuLQCBAi9oisFQK3OcDHA7Izz9vkSQJfVfc0gavadSOnkhAPnq07PFqsiCVvCBra2b6k3TypFVaVY4F2bYN2sAAsSCyDLhc4DfdVNZLIxijuFqj8LJSEZ/e+8IjEdP4zxYWSPZUpiSTZTJg4+PEcjidkF9+2XIP1fp65MNhOBsbLQlqWjAIaWEBnpERizyNZbOQJyYAPbQB2EgVUxYX4ZuchIhEoN14oyW+ly8sQFleptfs0CFiZ06eNP00lX6xawMDWA+HoWQykISAs64O2t69G10jBfdJMAZ+++3UDXLvvdeMIf1qk2Jttgfsfe97H77xjW+UPH9wcBBna8RQXyq89a1vxS9/+UucPHmypDtqZWUFu3btQk9PD37xi19cFffWxvUDexh5HUFRFLztbW/DD37wA/zFX/yFpbzoZz/7GT72sY9t8RnauJZgyJkutfzrYlGNVTEGB0VRLKb6wmHF6XSio6Oj7KACbAwriqKU/AJeX1/H0tISAKC9vd0yjHDOsbS0ZPpUflX51+rqKqLRKLLZLPr7++FwOCDa2yHa2+G8/Xak43E46uqgyjJUAFhbg1EAycbGTKmRdOQI2NmzJYlOTJeMsYUFKr+rr7ckeQmvF6KtbSPRCTATrC6KBenqIi/I+fNgS0ulLEhBu7yQZRoqNI1YkJmZivdHuN3QBgepaTyXo+vLZCA6O8uzIAB4ayvg9VJ8c3FilssFbiSAeb3UC6Kbw+Xjx8v2dyirq1BWV4HR0Y2o4vFxyIkEpXt1dm7E7RrxuKurYNEo+MDAxmCmDxUMMI34lteqpQX8ttvIJ5LLQQQC0G6/HcjlwPVeGsXw8ECX+DkckI4dQ7BCYqJQFORbWpBta0Pyllvge//7IQ0ObjxeECF/pXCxUiyXy3XVdYNEo1H87d/+Lfbt24d3vOMd+NrXvlbxaz0eD5566qmSf7tS+NrXvobdu3fjAx/4AH7yk59YHvvIRz6CRCKBb3zjG/YgYuOSwx5GrhP8+Mc/RjKZNCNTT58+je9///sAgPvuu880A3/mM5/B4cOH8da3vtVSXtTY2Ig/+IM/2LLz3wpU8+c899xzZuGTjdeGrTTVF36Pwv9WOkev12tKsIpZlfb2dgt7Uohq6V+5XM6URNbX15csKqLRqNnFEggEai6gcrmcWSS5urpqKRqTJKkkNAB1dRD79kHbt6/0YJoGNj1t9aeMjxPbMjFRmQUpGDRMFuT8ebDJSWIY9uyx9oLE4xQJm0hYDeYFTEA58LY28MFBWogrCuDxgB8+XD4RC/pi2+mk5vATJ8oe0/SChELmMMXm54nZKfP6smwWbHwc3OGA8HggHz1qTRXTm9ZFXR3gcEDN5aDGYkAgAFc2C6Uw+QsAy+XAJieBAlkZb22F6O2laONz58ivUcSCGKwFOLcMFZIel10MY1uAb9tGCVrJpOl90Xbtgra4CMfSEsUXF96fXbuw+MADWLjzTnC3G0NFaXXxeBxzc3NwOBxoamoyh3vzWji/JIvU660bpKurC7FYzOwBqzaMSJK0pb93Wlpa8OUvfxkPPfQQvvrVr+KDH/wgAOCHP/whvvOd7+DLX/4y+vr6tuz8bFy/sHtGrhN0d3eb/QzFuHDhgkUHb5cXEYxh5LOf/WzJULJ79274/f4tOjMb10pTfTabRTabRS6XQygUsizG1tbWMD09DQCIRCIlLcXnzp2DqqqQZRmDBTvQqqpicXHR3On1+/1QFAW5XA7nz5+Hx+NBOBwuWQxeUqyulnSqSGNj1I+iR/JKZ87UPAzv7ITo7KQFv9db2ra+smL2WghJAt+/n6RVx45VL5n0eqmAsZAFMViVCm3w2tAQ0NBAsq0ilkS43RslgW43IEnEhHAO+aWXanbI8G3bILZvBzt9GtLKCoTTaS0dLGRBFhbA+/qot6WKhMw8t2CQhpClJRpSCkoRC0sMzXMZGIAIh6v20whZpkGqrQ3aG94A/hu/AX7jjZicnERGl50NDAxYnrO0tGRhAQvff5qmYXh4GLIso66uriSR0XifVxu4L7YbxBhCriYWpBaq9YC9733vw/e//32s1yhBvRJ497vfjR/96Ec4efIkAoEAdu7ciX379uE///M/t/rUbFynsJmR6wTjVaIsi3Ho0CH8tEonwesN/f39NgtylWGzrEph6eOVlH8Z56goChRFMY31hayK1+tFZ2cncrlcCSvCOYeqexIKfSorKytmQaSB7du3Q1EUOJ1O9Pf3QwiBlZUV5PN5+Hy+y+Pzqq+HOHCAkpaKoapgk5NWCZgxrBhRxToLIp08CamKwRwgdkDbsYNay/VBgB8+TKzK/HxJO7i2Zw/g9VZkQSzel/p6CLcbYAxsehrSuXNlBwvDC8IBiG3byKRf0HhueEtyHg9yQoBpGpyZDOS6OjBVhXTiBKQCCVk5FkSEQuA7dwKZDKTxcYjmZuo4cToppWt9naR08/NgQlBgQChEcc8//3nVeygiESq9TCZpUOEcvL9/Q/JWbMTftg3q+99PDekFQ7IRilJuIDDKAXO5XIm3ymAONU0r+/MyNTWFdDoNp9OJ3t5eywChqio455saKoyfg6tNinWpkE6n0dLSgqWlJbS2tuId73gH/u///b9l4/gvJ770pS/hmWeewe/+7u8iEokgl8vh7//+76/oOdh4fcEeRmzYsHHNoVZU8eWWfxnfp5b8y+PxwOv1lgwqjDF0d3cjn89bFlXlPCuFCz+Hw4FEIoEV3UcQiURKhpH5+XmTVbks7ImiQPT0QPT0lC+AjEZLGRVjaJmdBeOczNH79wOyDOnYMShlOjIMiLo68O3bIVpaiA3IZoFUCqKpCZibK2EWmBDggQCE0V6vS1fN4/l8ZqIYXC4IgJgLSYL8wgsU01sEtrwMtrwMNwA5FEK+vx+OxUVIw8PEqnR2kvzLGDqzWVNexXt6AL+/pEOGxWKl1+p2Q7v1VupsYQxgjAaWbHYjEauQBdEZGen0aSj/9V/l758sg7e1QUQi4DfcAH7PPdBqNKSX2wQIh8MIh8MV3/Ner7fsoAJsDCvG0CGEgKqq+PznP2+yfIcPH0ZnZ2fZIeNql2JdCuzbtw/79u3D7t27AQDPPPMM/uqv/gr//d//jRdffPGKMvWhUAhf//rXcd999wEAvvnNb6K9vf2KfX8brz/YMi0br1sYMq2mpiZEo1F4vV7ccsst+PSnP43bb799q0/PxmXA1SD/AoBkMol4PI5wOGwOKwYmJibMFnkhRMmuaDQaNTtT2traLHHcnHMzecftdqOnp8fy3FgsZva0BIPBK7+4y2YpknhmhlgKg1XRB5diU7i2YwdgDBVlGA0hyxCtreTfqKsjlkGWwSYmqJOjYOFeDN7aCtHXB+nsWSoFhN5F0tiIbDAIzeuFw+OBQwggkaB0LJeLGJki83/Jefl84Pv2EdMRi5EkKhCgY6jqBguysAAGXc7W0QHp1CkLI1P22A0N4AcPQuRyZHAv8pYUD2eioQHqb/0WNaRfAb1/sedKCIHp6Wnk83nIsoz29nZwzpFIJPDxj38cIyMjmJqawtLSEjweD7q7u9HZ2Ynt27ejr68P9957L3bu3HnZz/tKoJpMqxz+5V/+Bb/5m7+Jv/zLv9ySgJlbbrkF0WgU5yqEHtiwcalgMyM2XrcIBoP46Ec/ijvuuAPhcBjnz5/H5z//edxxxx34t3/7N9x9991bfYo2LjGuBlP97Ows/uEf/gHnzp3DZz/72RI2pL293cKgFKcYBYNBuN1u5PP5kpb6QkN9uR3qtbU1JPUFfzFrkkqlEI/H4XA44Pf7L4/8y+WCGBiAGBgALxcesbBgFj8iGoV84gTYhQvkNclkLAV8AMA0DUJRAL8f8smTJZIuEQwSCxIMmnIoIQTF8j77LKQiRoZxDnlxEV49AUwNBIB9+yjlanycWJXOTnCdVQFAiWK6V0V0dFCC1okTkJ99duO4es+I5dwkCfzmm2k40d9bfPduus5YjAaLwgJKXebFxsch//d/l729QlHA29shwmHwoSHw//E/oD34IPlWrhCKmQ3GGLZt22YO+8bPUSAQwFe/+lXEYjGkUik0NDRgamoK09PTmJqawvj4OH7xi1+gp6fnuhlGLhb3338/fD4fnn/++S35/i6Xq+zniA0blxr2MGLjusBraa4/cOAADhRo4t/whjfg/vvvx549e/CJT3zCHkZeh7jYpvpCz0o1CCHw4osv4hvf+AZ++MMforu7G+94xzuQTqfL7iRvtlPF+PrCmOKenh7kcrmy12DIZSRJKnk8nU4jpkuHFEWxDCNCCMzMzJiMjRELfsnR3Aze3AzcdBMAWEsgdV+HaayfnAQyGci//CWko0fLe0HicbB4HKKxkeKEx8chz87SNSkK8q2tQCQCye8n2ZIuh8oBQH09XKdOgRVKq5JJsIKeEAAQDgd5ZAIBYHmZWuT37NlIFFtbowQwXVonGhsp5WpkBHKNRaZobISmy3YY50A+T8xIPm+yKhbIstkNcjU0pG8mFauhoQGhUAhOpxPNzc24cYvP+2qDEMKO0rVx3cMeRmxcF7hUzfX19fV461vfiq985Stmo7gNG0B1VqWW/Ot973sfnnrqKbzzne/Ef/zHf6CrqwuKopRItGphM6Z6o3W68OuM79HV1YVcLlfWMFwtpjifz2NNlzwFAoGSYWRxcdFsqQ+FQpfHXOx2QwwNQQwNWbwqeYDSuebnTa+KYaw3Ojrkp5+2+DUAgKkqHHNz1NUBamvn+/cDkgT38DCZ37u6wA35l6ZRAphuMhdtbeTXOHMG8gsvbBy4QuSudsMNdJx8HhACorcXWmvrRgJYwf03zoVFo1Cefrrs8Yx2dBEKQWzbBn7zzVDf854tbUgHLr4bxOl0wuFwXJeG9F8V3//+95FKpeyAFRvXPexhxMZ1gUvZXL8V5V42rm3Ukn999rOfRXt7u6WxfitM9bIsW1rqjX8HyAwfDAaRy+VKJFq1WurX1taQy+XAGCvxuKytrSGRSMDpdCIYDF4e2QdjQGsrlRjeequFURFCQCSTkCcmNtK/LlxA+tQpOKanwQAo7e2QT56E/NxzG4dcXS2VfenN7qKtjaRX6+vgQ0PW6N75eTKgQzff790LNjsL+aWXKp6+kCTw1lbw/n7qVeEcLJ0mT0woZLIqFuRyEP391JBew5B+uXGx3SDGwKwor48lSK0esKWlJTz88MN417vehb6+PjDG8Mwzz+CLX/widu3adcl+t9mwcbXCNrDbsFGAWCyGPXv2IBKJ4NixY1t9OjZeB7gaTPW1OlWEEMjlcqb5vVjCdfbsWQgh4HK5SvqK5ufnzfSvrq4u+Hw+87F8Po/5+Xk4HA74fL5LKv/inGN1dRWxWAw+nw8tLS2Wx+PxOBhjCPh8ZHYvLIAsZFiWlzf8GhcuWCJ8K0E7cACoqwOy2fKm9YLXVEgSybzyeYoULvN6C7+fvC/19STT2rcP2nvfC7HF3VAXw4IwxsxUrNeb7KhWD1gwGMT73/9+HDt2DAsLC9A0DV1dXbj//vvxyCOPIBgMXuEzJtxxxx1YXl7GqVOntuT723j9wB5GbLxu8fDDD6OzsxM33HADGhsbMTIygieffBKjo6P48Y9/jF//9V/f6lO8olhfX8enPvUpfO9738PKygqGhobwyU9+Eu9617u2+tRe16g0qFTqdLgcKB5SigcVVVWRz+chhLAMGwB1TBg7wv39/RYJWDKZNBdpoVCoZGCY1f0dLpcL4XD4os5ZVVWMjIyYmvuBgYHXtgheW6N0Lp1RsQwsU1OmvEo4neAHDoAlEpBOn654OOFyQbS0gLe3UxSwEORticWoE6RCUSHfvx/5//2/ob3znRsRwluEi5ViuVyu67YbxIYNG786Xh8cqQ0bZbB371780z/9E77yla9gfX0doVAIt99+O775zW/i8OHDW316VxwPPPAAXnzxRXzuc5/DwMAAvv3tb+Pd7343OOd4+OGHt/r0Xre4VjpVXC5XWfnXtm3bTFalWJZTTf4lhEA8HocQAk6ns2QYWVlZQSqVgsPhMOONC5PJFEVBXV0d4vE4XC4XVFV9bRKxujqIPXuobLEYmgY2PU2DycwMpOFhSv9yuYhVKdMlwvv7Aa8X8pEjZSOCRThMpY2BAITHA9HTA+1//a9rxpBu4PXQDWLDho1LA5sZsWHDBv793/8db3nLW8wBxMBdd92FV199FZOTk/ai4hrDtSL/yufzyOfzppHZQD6fx8jICADA7/eXBE8UMi6SJMHhcKCnpweMMaTTaSwuLkKWZfh8PjQ0NFz2ay2LWGyjR2ViAlhdhfzSSzS8TE+XdIIY4J2dZRvStwIXw4JIkmQOITYLYsOGjc3CZkZs2LCBH/7wh/D7/XjwwQct//47v/M7ePjhh/HCCy/g1ltv3aKzs/FacDV0qmwm/ctgfYpZFYfDgcHBQQt7UojC9C/OObLZLNLpNLxeL7LZrNmnUtzFIoTAxMQEHA4HPB5PieH+kqKhAaKhgTwkOlTzLyrY5CTY2JjZrcKWlqD9xm9Au/feLTWkA3SfNisFVBTFNKTbQ4gNGzYuFvYwYsOGDZw6dQo7duwokdHs3bvXfNweRq4vXGynyuVgVTbTqWLsshvDRjAYBGMM27dvRz6fRywWw8rKCurq6sxrKRxgimOKNU1DSvdlqKpaMowsLCwgm83C6XQiEolcPkZQUSB6eiB6enDpBHW/Gi5GimUMjC6X63VnSLdhw8alhT2M2LBhA9FoFD09PSX/bizUotHolT4lG1uIzbIqhaWPl2NQMf67uLiII0eOwOv14g1veIPZSyHLMkKhEBoaGixDRyQSQSgUQi6XK2m4r9VSn0wmkclkAADNzc2Wx9bW1rCysgKn04n6+voS1uVaxcVKsVwul90NYsOGjUsGezvDhg0bAKr3qtiLDhuFMAYBp9MJt9sNr9cLv9+Puro61NXVwe/3w+v1wu12m/Kd17J7nk6n8a1vfQsPPvggPvCBD+CVV14xyxeNBbRxPqqqmqlemqaVmOqN4cbj8WBoaAi9vb1lE7pUlYRU5RbbmUwGqVQKq6ur0Ir8HpqmYWxsDFNTU2aT/dUM4/4Z963WIGLEL/v9/qvGE5JIJPCJT/z/9u4upsmzjQP4v1CEsgJdsVNYlCptdJutTEaEqElxHU4SjGJkhmTTkJmMeGBcjLKQVRcX4gcmkh2Ibi4u2yQjExPDwvwKmDgbE3U0TQyZgHxsB2xC1fJR4aF9D963fYstWhj0LvD/Jcb4PE/kXw9Mr+e67vvej7y8PGg0GshkMhw6dCjos/fu3YPZbIZSqYRKpUJhYSHa29vDG5iIgmJnhIiQnJwctPvhPR9iWufqaVaZivEvp9OJiooKnD9/Hqmpqdi5cydycnLw+uuvIzEx8aUZQhn/8q5v8D+NXiaTQa/XQ5KkgGIDwJhrz49/DQ8Pw+VyweVyITo6OmDRfHd3N9xuN+bNm4eFCxcK+zI/0VGsSD4bpLe3F2fOnMHKlSuxefNmfPPNN0Gfa2lpgclkQkZGBmpra+FyuWCxWLBu3To0NzdDI3iTAKK5jsUIEcFgMKCmpgaSJI1ZN2K32wEAK1asEBWNZpFQx79iY2Ph8Xhw4cIFrF692reYeiq+wIeyqD4qKgpRUVEBhUpKSgpee+01jIyMBIx/eTsqQPDxr8HBQYyOjuLZs2dISUkZc6+3txdPnjzxrVN5/u+eChM9G8S7u1kkdEDGk5aWBofDAZlMhkePHo1bjFgsFsTGxqK+vt5XzGZmZkKv16OyshJHjx4NZ2wiek7kveogorDbsmUL+vv7ceHChTHXv/vuO6SmpmL16tWCktFc4u2qxMXF4dSpU3j33XehVCqRkJCApKQkJCQk4JVXXoFCofAdpDfVb+z9v7SPjo6OGf+SJAkejwcxMTEB3YWEhAS88cYb0Ol0vnNPvPyfC1aoeDsqT58+DSiSXC4XWltb0dXVhSdPnkzqs0xkFEupVEbUKNaL+G8ZPR5JklBfX4+tW7eO6aqlpaUhNzcXFy9enO6YRPQS7IwQETZu3Ij33nsPpaWlePr0KXQ6HWpqavDrr7/ihx9+4BkjfpqampCbmxv0ntVqRXZ2dpgTzQ0v6qqEc/cv/9+DZfRuU+zfVYmKisKyZct8C/6f538t2PiX91ewBfPt7e2QyWRQKBS+E+wn0gXxrq2JiYmJyFGsf6utrQ1DQ0O+nQH9GY1GXL16FS6XC3FxcQLSERHAYoSI/qeurg7l5eWwWCzo6+vD8uXLUVNTg+3bt4uOFpEqKioCihKOs4kRCWeqeH/Oy06qj46ODhj/WrRoEdxuN0ZGRgIKf+94mrcj48/tdvt2/vL+/NraWgwMDGDJkiVITU2FVqsN+u8yV84G8a6FC7buTa1Ww+PxwOFwBIzOEVH4sBghIgD/PeW6qqoKVVVVL3yupKQEP/74I+7cuQODwTDm3pEjR/DZZ5/h0qVLKCgomM64wun1enZBZoiZcqaKXC4fs0MYALz66qtQqVSQJCmgqJAkCdHR0RgdHYVcLockSWhvb8eNGzfQ0dGBv/76CzExMUhLS4NWq4VWq4VOp8Nbb72F/Pz8KflcMwV3CySKXCxGiGhCTp48ievXr2PHjh24ffu2722t3W7HwYMHsXPnzllfiNDsMdmuSqink4ci1EX1AHxdFY/Hg+joaCxdunRMh2ffvn3Yt28fAKC/vx89PT3o6OjAn3/+ic7OTty6dQu3b9+eM8WId/vm8XYLlMlkAWt8iCi8WIwQ0YQkJibi7NmzyMvLw5dffokvvvgCIyMj+PDDD7FgwQKcPHlSdMSw2L17N7Zv3474+Hjk5OTg888/x9q1a0XHoin2sq6K6PEvAL7dv56nUqmwYMECvP3223P27X96ejoUCoVvZ0B/drsdOp2O60WIBGMxQkQTZjab8cknn6CiogKbNm1CXV0dbDYbrly5gqSkJNHxplVSUhL27NkDk8mE5ORktLa24vjx4zCZTPjll1+wYcMG0REpTCJh/CtYppiYGMTGxs7KBekTJZfLUVBQgLq6Ohw7dgwJCQkAgK6uLjQ2NmLv3r2CExKRzDNd/yMS0aw2MDAAo9EIt9uN7u5u7Nq1C6dOnRIdS4jHjx/DYDBArVbDZrOJjkMzwL/tqnjPQfH/s3dXrLnUBWloaMDAwACcTidKSkqwbds2FBUVAQDy8/MRHx+PlpYWZGVlYdWqVSgrK/MdetjX18dDD4kiAIsRIpq0mpoaFBcXY+HChXjw4AGUSqXoSMKUlpaiuroag4ODUCgUouPQDBZKV2XevHljzi7xbik812i1WnR2dga99/DhQ2i1WgDA3bt3ceDAAVitVsjlcqxfvx6VlZVIT08PY1oiCoZjWkQ0KW63G1999RWioqLw999/w2azYc2aNaJjCeP9YjgXvxDS1AplUb3H4wnp0L/ZrqOjI6TnMjMzce3atekNQ0STwoFSIpqUyspKWK1WnD9/Hnq9HiUlJRgaGhIdSwiHw4H6+npkZGRwMSxNO2+hMtcLESKaHViMENGE3b9/HxaLBR999BE++OADnDt3Dq2trSgvLxcdbdoVFxejrKwMP//8M5qamvD1118jJycHPT09OH78uOh4wjmdTuzfvx95eXnQaDSQyWQ4dOhQ0Gfv3bsHs9kMpVIJlUqFwsJCtLe3hzcwEREJxWKEiCZEkiTs2LED8+fP9x2QmJ2djU8//RRVVVX47bffBCecXkajEZcvX8bHH38Ms9mM8vJyvPnmm7h16xbMZrPoeML19vbizJkzePbsGTZv3jzucy0tLTCZTBgeHkZtbS2+/fZb/PHHH1i3bh3++eefMCYmIiKRuICdiCbk8OHDsFgsaGhowPvvv++77nK5kJGRAY/Hg+bmZi7inqP81848evQIGo0GBw8eDOiOFBUVobGxEW1tbUhMTAQAdHZ2Qq/XY+/evTh69Gi4oxMRkQDsjBBRyGw2Gw4fPoxdu3aNKUQAIC4ubk6Na1FwoSyqliQJ9fX12Lp1q68QAYC0tDTk5ubi4sWL0x2TiIgiBHfTIqKQrVy5EsPDw+Pez87OxujoaBgT0UzU1taGoaEhGI3GgHtGoxFXr16Fy+XiZgARoqmpCbm5uUHvWa1WZGdnhzkREc0mLEaIiCisent7AQBqtTrgnlqthsfjgcPhQEpKSrij0QtUVFQEFCUrVqwQlIaIZgsWI0REJMSLxrm4bW3k0ev17IIQ0ZTjmhEiIgqr5ORkAP/vkPjr6+uDTCaDSqUKdywiIhKAxQgREYVVeno6FAoF7HZ7wD273Q6dTsf1IhFo9+7dkMvlSExMxIYNG3Dz5k3RkYhoFmAxQkREYSWXy1FQUIC6ujo4nU7f9a6uLjQ2NqKwsFBgOnpeUlIS9uzZg9OnT6OxsRFVVVXo7u6GyWTC5cuXRccjohmO54wQEdGUamhowMDAAJxOJ0pKSrBt2zYUFRUBAPLz8xEfH4+WlhZkZWVh1apVKCsrg8vlgsViQV9fH5qbm6HRaAR/CnqRx48fw2AwQK1Ww2aziY5DRDMYixEiIppSWq0WnZ2dQe89fPgQWq0WAHD37l0cOHAAVqsVcrkc69evR2VlJdLT08OYliartLQU1dXVGBwc5CGnRDRp3E2LiIimVEdHR0jPZWZm4tq1a9MbhqaN910mdz4jon+DnREiIiKaEIfDAYPBAI1Gg99//110HCKawdgZISIionEVFxdj8eLFeOeddzB//nw8ePAAJ06cQE9PD86dOyc6HhHNcCxGiIiIaFxGoxE//fQTqqur0d/fD7VajbVr1+L7779HVlaW6HhENMNxTIuIiIiIiITgOSNERERERCQEixEiIiIiIhKCxQgREREREQnBYoSIiIiIiIRgMULAEwTbAAAAMElEQVREREREREKwGCEiIiIiIiFYjBARERERkRAsRoiIiIiISAgWI0REREREJMR/ACdxdtN9o4a+AAAAAElFTkSuQmCC\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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\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": { "application/vnd.jupyter.widget-view+json": { "model_id": "ae16868906cb4db9a9320aa237fda5da", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=5.0, continuous_update=False, description='var_x', max=20.0), FloatSli…" ] }, "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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qbdu29O3bt1DfXwhhG+ROlBBCCCGKhMFgYNGiRYwfP5709HQAKlWqxMqVK+nWrVuh1+f48eO0bNkSnU6Ho6MjJ06coEmTJoVeDyFE4ZMhzoUQQghh9RISEnj77bdZv369Wvb666+zdu1aatasWej1SUtLY/jw4WowiY8++kgSKCFEtiSJsqDw8HA1RGPz5s2LujqigEl8tU3iq20S36L1559/0rNnT06fPq2WTZo0iS+++AIHhyf/afI48f3yyy85efIkAM2aNWPy5MlPXA9hGXL+aputxFeSKCGEEEIUmqCgIAYNGkR8fDwApUuXZvXq1fTq1avI6nTu3DmmT58OQLFixVi5ciXFixcvsvoIIayfJFEW5OzsTHp6eoFcVRPWR+KrbRJfbZP4Fj69Xs+nn36qkhWARo0aERgYSOPGjQv0vfITX51Ox/Dhw0lNTQVgwoQJtGjRokDrIwqWnL/aZivxlYElhBBCCGFRd+/eZdCgQezatUst69WrF6tWraJMmTJFWDNYsGAB48aNA6B+/fqEh4dTsmTJIq2TEKLwyRDnQgghhLAaJ0+epEWLFiqBKlasGLNnz2bz5s1FnkBdunSJKVOmqNcrVqyQBEoIkSfWfZ9MCCGEEDbr+++/5+233yY5ORmAypUr88MPP9ChQ4cirhmkpqbSv39/EhMTARg5ciT/93//V8S1EkLYCrkTJYQQQogClZaWhp+fH0OGDFEJ1CuvvMKxY8esIoEC4xDmx48fB6Bhw4Z8+eWXRVwjIYQtkTtRFnTt2jX1YFzt2rWLujqigEl8tU3iq20SX8uJiYmhb9++HDhwQC3z9fXl66+/pkSJEoVSh9ziu2/fPubMmQOAo6MjGzZsoFSpUoVSN/Hk5PzVNluJr9yJsqC4uDju3r1LXFxcUVdFWIDEV9skvtom8bWMU6dO8corr6gEytHRkWXLluHv719oCRTkHN/o6GgGDx6sXs+aNYuXXnqp0Oomnpycv9pmK/GVO1FCCCGEeGKbN29m2LBh6hmjatWqsXXrVtq2bVvENfuHwWDAx8eHW7duAeDh4cHYsWOLuFZCCFskQ5xbUEpKCgaDATs7O5ycnArtfUXhkPhqm8RX2yS+BUev1/Pxxx8zY8YMtaxFixZs27YNFxeXIqlTdvFdsmQJ//3vfwGoUqUKp06donr16kVSR/H45PzVtqKKb35zB0mihBBCCPFY4uPjGTRoEEFBQWrZ4MGDWbZsmdUNFX7mzBlatGhBSkoKAMHBwXh5eRVxrYQQ1iK/uYN05xNCCCFEvl28eBFvb28uXrwIGOd/mjt3LmPHjsXOzq6Ia2cqKSmJ/v37qwRqzJgxkkAJIZ6IJFFCCCGEyJeQkBD69+/P/fv3AahQoQKbNm3Czc2tiGtm3sSJEzlz5gwAL7zwArNnzy7iGgkhbJ0kURZ0//591aezbNmyRV0dUcAkvtom8dU2ie/jMRgMzJ49mw8//JCMpwGaNm3K9u3bqVu3bhHX7h+Z4/vTTz+xZMkSAEqUKMGGDRsKdaRAUfDk/NU2W4mvJFEWFBERQVpaGo6OjjRv3ryoqyMKmMRX2yS+2ibxzb/k5GR8fHzYsGGDWtazZ0++++47SpcuXYQ1yyojvnFxcbz11ltq+fz583n++eeLsGaiIMj5q222El8ZZUEIIYQQOYqJicHNzc0kgZo+fTqbN2+2ugQqQ8aogbGxsQB0796dd955p4hrJYTQCrkTZUHVqlVDp9Nhb29f1FURFiDx1TaJr7ZJfPPu0qVLeHl5ceXKFQCcnZ1Zt24d3bt3L+KaZa9atWosWbKE33//HYCaNWsSEBBgdQNeiMcj56+22Up8i3yI8wcPHvDZZ59x8uRJTpw4QUxMDFOnTmXatGnZ7mMwGGjfvj0///wzo0aNYvHixVm2kSHOhRBCiCdz6NAhevTowd27dwGoXr06QUFBvPzyy0Vcs5z9+uuvtG/fnrS0NOzs7Ni3bx9vvPFGUVdLCGHF8ps7FHlGERsbi7+/PykpKXm+qrVkyRL+/PNPC9dMCCGEeHqtW7eOjh07qgSqWbNm/P7771afQN26dYvevXuTlpYGwPvvvy8JlBCiwBV5EuXq6kpcXBw//fQTM2fOzHX7yMhIPvjgAzXSjhBCCCEKjsFgYPr06QwaNIjU1FQAPDw8OHz4MLVr1y7i2uUsLS2Nfv36ERUVBcBrr73GZ599VsS1EkJoUZE/E5Xf/slvv/02HTt2pEePHhaqkRBCCPF0Sk1NxdfXlzVr1qhl77zzDosWLcLR0bEIa5Y377//PocOHQKgVq1abNy4EQeHIv+pI4TQIJtqWQICAvjf//7HuXPniroqeXL27Fk1RGOTJk2KujqigEl8tU3iq20S36zu3r1Lr169OHjwoFo2Z84cxo8f/0QDMty4cYPQ0FD27dtHYmIi5cqV48UXX2TMmDEF+uD4Dz/8wPz58wFwcHBgxowZREdHU7Vq1QJ7D2Ed5PzVNluJr80kUTdu3GDChAl8+eWX1KxZ87HKOHv2LK6uriYTd6WkpHDhwgXAOOP6o10VLl++TGJiIkCWsepjYmK4ceMGALVr16ZChQpqnU6nIykpSf37UREREWqm9yZNmphcKbt37x5//fUXYBxRqEqVKib7njp1CoPBQMmSJWnQoIHJur///lv1X2/YsKHJhIIPHz5UoytVrVqVGjVqmOx77tw59aV9dB6NmzdvcufOHQDq1q1rMqRtcnIyFy9eBKBixYo888wzJvteunSJpKQk7OzseOGFF0zWRUdHq24Xrq6ulC9fXq1LT0/n7NmzAJQtW5Znn33WZN+rV6+qBwCbNm1q8sc4Li6Oa9euAcarkZUrVzbZNzw8HDCOMlW/fn2TddeuXSMuLg6ARo0a4eTkpNbdv3+fiIgIwBhXvV5v8uPi7NmzpKen4+TkRKNGjUzKjYqKIjo6GoB69epRqlQptS4xMZHLly8DUKlSJVxcXEz2vXjxIsnJydjb29O0aVOTdXfu3OHmzZsA1KlTh3Llyql1qampnD9/HoBy5cpRp04dk32vXLnCw4cPAePzDpkfnoyNjeX69esAuLi4UKlSJbVOr9dz+vRpAEqXLp1lks3IyEji4+MBaNy4McWLF1fr4uPjiYyMBKBGjRpZfuCcOXMGnU5HiRIlaNiwocm669evq+GK69evj7Ozs1qXkJCgnpWsUqVKlnbiwoULpKSk4ODgkKVRvnXrFrdv3wbg2WefpWzZsqSnp5Oeng78830p6DbizJkzgPHB1eeee85kX2kjjCzVRqSmpqLT6UhPTycmJsYibUS1atWoXr26yb7W2kb8/fff+Pn5cfXqVcA4Ke3atWt58cUXOXXqFJC/NiI1NZWvvvqKtWvXmr3wuWbNGnbv3s3s2bN5/vnnn7iNOHPmDMOHD1fbTJgwgeeff16dw1DwbUQGS/6OkDbC6NE2IqN9trOzs+nfEbbURkDh/Y7IiG96ejrh4eGF9jsi4zzNK5tJokaMGEHz5s3x9fV97DLS09N5dDBCg8GgHj7N3Nhm3idj/aP0er1ap9frs31fc6N6ZC730TplLtdcApaWlobBYDDbtUKn0z1Rudkda+ZyHz3WzJ+huXIzjtXclcy8llvQsclruTl9XxwdHdV/mctNT083G/OcYpPbZ5gRG3Prcio387HmN+Z5/QzN7Z+5To/K7VhTU1PR6/Vmr1AXxGdo7jMyV66TkxPFihXD3t5eNazW8j2UNiJrufmNjYODg6qLpdqI7D5Da2sjjh49yoQJE7h37x5g/HH8448/0qpVKy5cuJCv73dCQgIrVqxg3rx56kd8dvbs2YOXl1eWH9v5bSPu3btHz5491XnapUsXevbsiaOjo8mP14JuI8yVK21E4bQRGe2zo6OjTf+OsJU2orB/Rzg5OakL1ebKtuTviPywiSRqy5Yt7N69m8OHD6ur2xlSU1O5d+8epUqVyrW/toODQ5Y/0nZ2dmo/c/2mHRwcsi034wTO+PejMtaVKVMmx3IfrVPmcs19ARwdHTEYDGbra29v/0TlZv5/duU+eqyZP0Nz5WYcq7kfSHkt11Kxya3cnL4v5q4gZRxnbp9hTuVmF5vs5kzIqdzMx5pduU/6GeZ2rI/K7ViLFy+OTqezyGeo1+vzfN5kXAHMfJXZWr6H0kZkLTe/sXFxcVFXmS3VRmT3GVpTG7F582ZGjhypBpBo3LgxwcHB6op9XtsIOzs71q5dy6RJk9QV7QyNGzemT58+eHh4UKdOHT777DO+/fZbAHXHIz/HmrmN0Ov1DBkyRF2Bb9q0KR999BHFixfPcpW5oNsIc+VKG1E4bUTmOzTR0dE2+zvCFtqIjH1zKregf0c0atTIpEfLoyz5OyI/inyeqMxiYmKoUqVKlnmipk2bxqeffprjvtu2bTMZIl3miRJCCCHMMxgMzJo1iw8//FAte+ONN9i6datJd6i8OH78OKNHj+bIkSMmyzt16sSkSZNo3769yY+T9evXM3DgQMD4zNWECRMe+zg+//xzPv74Y8DYle7YsWNZumwJIURe5Dd3sIk7UcOGDeO1117Lsvz111+ne/fu+Pn5ZenfKYQQQois0tLSePfdd1mxYoVa9tZbb/Htt9+aPHeQm5iYGKZMmcLy5ctNusF069aNzz//nGbNmpnd79ixY+rfTzJk+u7du/nkk08A4xXkDRs2SAIlhCg0VpFE7dq1i4SEBJX9nTt3ji1btgDg5eVFnTp1sjzIlqFWrVpmEywhhBBCmLp37x69e/cmLCxMLfviiy/44IMP8tyVJT09nWXLlvHxxx+rh+cBGjRowMKFC/H09Mxx/9DQUMDYvcfNze0xjsI4qMKAAQNU8jZ9+nQ8PDweqywhhHgcVpFEvfvuuyYPoG7evJnNmzcDxoYyuwTK2kVFRan+p487oqCwXhJfbZP4atvTGN/IyEg6d+6sRstzcnJi9erVvPnmm3ku4+LFiwwcONDkblLp0qWZOnUqY8aMyfVO1rlz59RoaS1btqRixYr5Po6EhAR69OihEriuXbuadEuEpzO+TxOJr7bZSnytIonKGKYwv6zocS6zoqOj1VCf1vwlEI9H4qttEl9te9ri+8cff9C1a1c1THelSpXYsWMHbdu2zdP+BoOBgIAAxo4dazIM8JAhQ5g1a1aWoa6zM3fuXPXvvn375uMI/qmHj4+PGl66Xr16rFmzJsszC09bfJ82El9ts5X4WkUSJYQQQgjL2LZtGwMHDlRzFzZo0IDg4GDq1auXp/1jYmLw9fVl+/btalnDhg1ZtWoVr776ap7rcePGDdauXQtA+fLl+c9//pOPozCaNWsWmzZtAox3wHbs2JHvgTCEEKIgSBJlQfXq1cNgMDzRTO/Cekl8tU3iq21PQ3wNBgPz5s1j4sSJqudGu3btCAwMNJn0Mid79+5l6NChJsOWv/vuu8ydO9dk+PC8WLBggZqf5d133zU7/UdOgoODmTJlinq9bt26LHNMZXga4vs0k/hqm63E16qGOC9IMsS5EEKIp1V6ejpjxozhm2++UcsGDRpEQECAyQS02UlJSeHDDz9k3rx5alnlypVZuXIlXbt2zXd9IiIiaNy4MSkpKRQvXpy//voryzx7Obl48SItW7bk/v37gHEgiYyhzYUQoiBocohzIYQQQuTNgwcP6NevH7t27VLLpk6dytSpU/N0Zffs2bMMGDCAU6dOqWXu7u6sXr06z88+PWr8+PGkpKQAMHr06HwlUPHx8Xh7e6sEqmfPniZ3pIQQoijInSghhBBCI65fv07nzp1VAuTo6MiKFSsYPHhwrvsaDAaWLl3KhAkTSE5OBqB48eJ8+eWXjB49+rH/fu7duxd3d3cAqlWrxqVLlyhbtmye9tXpdHh7exMcHAxA06ZN+fXXXylduvRj1UUIIbIjd6KsSGJiourTmd++48L6SXy1TeKrbVqM74kTJ+jSpQtRUVEAVKhQgW3bttG+fftc9719+zY+Pj6EhISoZU2aNGH9+vW88MILj12ntLQ0/Pz81OvZs2fnOYEC+OSTT1QCVbFiRXbs2JGnBEqL8RX/kPhqm63EV5IoC7p8+bIaorF58+ZFXR1RwCS+2ibx1TatxTcsLIzu3bvz8DVRM90AACAASURBVOFDAJ577jlCQkJo2LBhrvvu2rWLYcOGcefOHbVszJgxzJo1i5IlSz5RvRYvXsz58+cBaN26dZ7uiGXYvHkzM2bMAIwT827cuJHnnnsuT/tqLb7ClMRX22wlvtK3TQghhLBhmzZtwsvLSyVQr776Kr/99luuCZROp+Pjjz/Gy8tLJVDVqlUjJCSEhQsXPnECdfv2baZNmwaAnZ0dixYtynOXwPDwcIYNG6Zez507Fzc3tyeqjxBCFCS5E2VBlSpVUjMuC+2R+GqbxFfbtBLfJUuWMHr0aDWEebdu3fjhhx9yTYDu3r3LwIED2b17t1rWpUsXVqxYQdWqVQukbu+//74aDGL48OG0aNEiT/vFxMTg7e2tJvUdMmQIY8eOzdd7ayW+wjyJr7bZSnxlYAkhhBDCxhgMBqZNm8b06dPVMh8fH5YtW4aDQ87XR0+cOEGvXr2IiIgAjF3lZs2axYQJEwpsXpbt27fTo0cPAMqVK8elS5fylJylpqbi4eHBwYMHAXjllVc4dOgQJUqUKJB6CSFEdmRgCSGEEELDdDodo0aNYtmyZWrZ5MmTmTFjRq5J0Jo1a3jnnXfU6HuVK1dm48aNvPHGGwVWv6ioKP7zn/+o11999VWeEiiDwcA777yjEqhq1aoRGBgoCZQQwipJEiWEEELYiOTkZAYNGsTWrVvVsvnz5+fa3S01NZVx48axdOlStaxly5Zs2bKFZ555psDqp9frGTp0KLGxsYBxTicfH5887TtjxgxWr14NQIkSJdi+fTsuLi4FVjchhChIkkQJIYQQNuD+/ft4e3urOzUODg6sXr2agQMH5rhfVFQUvXv35tdff1XL3n77bb7++mucnJwKtI4LFixg3759ANSsWRN/f/88dRHcsGEDH330kXq9Zs0aWrduXaB1E0KIgiRJlAVdvHhRDdGYl2FmhW2R+GqbxFfbbC2+t2/fplOnTpw4cQIAZ2dntm7diqenZ477/f777/To0YObN28C4OTkxNKlS/N8dyg/Tp48yQcffKBer1mzhkqVKuW63+HDh01G4ps1axZ9+vR5orrYWnxF/kh8tc1W4itJlAUlJyeTlpaGTqcr6qoIC5D4apvEV9tsKb5Xr17F3d2dK1euAMZJZ0NCQmjVqlWO+61atYoRI0aQmpoKwDPPPENgYGCeR8nLj8TERAYMGKDea8KECXTo0CHX/S5fvkz37t3Vfr6+vkyaNOmJ62NL8RX5J/HVNluJrwxVZ0H29vYUK1bM6odoFI9H4qttEl9ts5X4njx5kjZt2qgE6plnnuHw4cM5JlBpaWn4+fnh4+OjkpN27dpx9OhRiyRQAJMmTVKT6r744ot8/vnnue4TGxtL586d1fNTHTt2ZMmSJQUyQqCtxFc8HomvttlKfGWIcyGEEMIKHTx4EG9vbzXXUuPGjQkNDc1xIIiYmBj69u3LgQMH1LKRI0eyYMECHB0dLVLPoKAgunbtChgHhDh+/DiNGzfOcZ+UlBQ6duzIzz//DECTJk345ZdfKFeunEXqKIQQuclv7iAZhRBCCGFlAgMD8fT0VAlU69at+fnnn3NMoMLDw3nllVdUAuXo6Mjy5ctZsmSJxRKo27dvmzxfNW/evFwTKIPBgI+Pj0qgqlevTnBwsCRQQgibIkmUEEIIYUWWL19Onz59SElJAaBTp07s27cvx0EatmzZQps2bYiMjASMcywdPHjQZL6mgmYwGHjrrbeIjo4GoEuXLowYMSLX/aZNm8b69esBKFmyJDt37sTV1dVi9RRCCEuQJEoIIYSwAgaDgc8//5y3334bvV4PwODBg9mxYwelSpXKdp+M0ewSExMBeOWVVzh69Cht2rSxaH2XLFnCrl27AGPStmLFijxN9jt9+nQA7OzsWL9+vcWe0xJCCEuS0fks6M6dO+h0Ouzt7fM0W7uwLRJfbZP4apu1xVev1+Pn58fixYvVsvHjx/Pll19m2x8/LS2Nd999lxUrVqhlQ4YMYdmyZZQoUcKi9T1z5gwTJkxQr1evXp3r5/jonbGvvvqK7t27W6R+1hZfUbAkvtpmK/GVJMqCbt68qca5t+YvgXg8El9tk/hqmzXFNzU1laFDh/LDDz+oZV9++SUTJ07Mdp/4+Hh69+6tJrYFmDFjBpMnTy6Q0e1yEh8fT8+ePVV3wzFjxuQ6X9WFCxfo0aMHaWlpgHGwi7Fjx1qsjtYUX1HwJL7aZivxlSRKCCGEKCIPHjygV69e7N27FzAO7RsQEGAy+eyj/vrrL7y8vDh37hxgnED3u+++o1+/fhavr16vZ+jQoVy+fBkwDmc+e/bsHPeJjo7Gy8uLe/fuAeDl5cXChQstnuwJIYQlSRJlQXXq1MFgMMgfCo2S+GqbxFfbrCG+GcnF0aNHAePw4Js2bVLDhZvzxx9/0LVrV27fvg1ApUqV2LFjB23bti2UOs+cOZMdO3YAUKFCBQIDA3PsOpiUlES3bt2IiIgAoHnz5vzwww84OFj254c1xFdYjsRX22wlvjJPlBBCCFHIIiMj8fDw4NKlSwCUL1+eoKCgHJOhbdu2MXDgQJKSkgBo0KABwcHB1KtXr1DqHBoaSqdOndSPm5CQkBy78en1et588002b94MQM2aNfn9999xcXEplPoKIUR+yDxRQgghhBU7ffo0bdu2VQlUzZo1+fnnn7NNoAwGA/PmzaNXr14qgWrXrh2//vproSVQkZGRDBgwgIzrrp9++mmuz0FNmTJFJVClSpUiKChIEighhGZIEiWEEEIUksOHD9OuXTuioqIA492kI0eO0LRpU7Pbp6enM2rUKMaPH68SmEGDBrFnzx4qVqxYKHVOSkqiZ8+e3L17F4CuXbsyZcqUHPcJCAhg1qxZABQrVoyNGzfy0ksvWbyuQghRWOSZKAtKTU1V/y5evHgR1kRYgsRX2yS+2lYU8d25cyd9+/YlOTkZMM7nFBwcTJUqVcxu/+DBA/r166fmYgLjRLWffPJJoT0rYDAYGDlyJCdOnACgXr16rFmzJseu8Xv37jWZdPfrr7+mc+fOFq9rZnL+apvEV9tsJb6SRFnQ+fPn1RCNzZs3L+rqiAIm8dU2ia+2FXZ8V61aha+vLzqdDoCOHTsSGBhI6dKlzW5//fp1OnfuzKlTpwBwdHRkxYoVDB482OJ1zWzJkiWsXr0aAGdnZwIDAylfvny22585c4bevXur4xw7diyjRo0qjKqakPNX2yS+2mYr8ZXufEIIIYSFGAwGvvzyS3x8fFRi8eabbxIUFJRtAnXixAlatWqlEqgKFSqwd+/eQk+gDh48aDKXU0BAAM2aNct2+1u3btG5c2fu378PgLe3N3PnzrV4PYUQoijInSgLKleunJpxWWiPxFfbJL7aVhjxNRgMTJw4ka+++kotGz16NAsWLMi2O1xQUBBvvvkmCQkJADz33HOEhITQsGFDi9XTnL/++os+ffqoxG/ixIn0798/2+0TExPp2rUr165dA+Dll19m3bp1RXb+yPmrbRJfbbOV+MoQ50IIIUQB0+v1jBw5kmXLlqllX3zxBR988EG2zzMtXrwYPz8/9Ho9AG3atGH79u3ZPjNlKYmJibRt25aTJ08C4OnpSVBQULY/aHQ6Hb1792b79u0APPPMM/z+++/UqFGj0OoshBBPKr+5g9yJEkIIIQpQeno6Pj4+fP/99wDY2dnx7bff8vbbb5vdXqfTMX78eBYuXKiW9evXj9WrV+c4ka0lGAwGfHx8VAJVr1491q9fn+MV4UmTJqkEqkyZMgQHB0sCJYTQPEmihBBCiAKSmprKgAED2Lp1KwD29vasWbOGAQMGmN0+OTmZgQMHEhgYqJZ9+OGHfPbZZ0XSc2L27Nls3LgRgNKlS7Njxw4qVKiQ7fZLly5l3rx5gPFYt2zZkuNzU0IIoRWSRAkhhBAFICkpid69exMSEgIYh+bduHEj3bt3N7t9fHw83t7e/PTTTwA4ODiwbNkyfHx8Cq3OmYWEhPDhhx+q12vXruX555/PdvugoCBGjx6tXn/zzTe4u7tbtI5CCGEtijyJevDgAZ999hknT57kxIkTxMTEMHXqVKZNm6a20el0LFy4kD179nDmzBnu3r2Lq6sr3t7eTJ48OcfhVovSlStX1BCNdevWLerqiAIm8dU2ia+2FXR8Hz58SLdu3Thw4AAAJUqUYPv27Xh4eJjd/tatW3h6ehIeHg5AqVKlCAwMLLIk5MKFCwwYMEBN6Dt9+nS8vb2z3f7IkSP07dtXPb81adIkfH19C6WueSHnr7ZJfLXNVuJb5KMsxMbG4u/vT0pKSrZX65KSkpg2bRqurq4sWLCAkJAQfH198ff3p23btiQlJRVyrfPm4cOH6j+hPRJfbZP4altBxvfevXt4eHioBKp06dLs3r072wTqypUrtG3bViVQlStX5sCBA0WWQEVHR9O5c2fi4+MB6NmzJ1OmTMl2+7Nnz9KlSxf1t7dfv37MnDmzUOqaV3L+apvEV9tsJb5FfifK1dWVuLg47OzsiImJISAgIMs2JUuWJCIigkqVKqllr732GrVr16ZPnz5s3bqVQYMGFWa1hRBCCGJiYvDw8OD48eMAlC9fnl27dtG6dWuz2584cQJPT0/u3LkDGP8GhoaGFvoQ5hmSkpLw9vbm6tWrADRv3pzvvvsu2+exrl27hoeHB3FxcQC4ubnluL0QQmhVkSdR2Q31mpm9vb1JApWhZcuWAPz9998FXq+CIA/XapvEV9skvtpWEPG9efMmHTt25OzZs4DxjtLevXt58cUXzW5/4MABvL291RC6TZs2Zffu3dSqVeuJ6/I49Ho9w4YN49dffwWgVq1aBAcHZzsJcExMDO7u7ty4cQOAFi1aEBgYiJOTU6HVOa/k/NU2ia+22Up8izyJehL79+8HoEmTJkVcE/Pkypy2SXy1TeKrbU8a32vXrtGhQwf+/PNPAGrUqEFYWBiNGzc2u/3WrVsZMGAAqampALRt25adO3fmOPJdZgaDgfDwcLZt28ahQ4dwdnbGx8eHXr16PfYxTJkyhU2bNgHGZ7KCgoKyTegePnyIl5cXFy9eBKBBgwaEhIRQpkyZx35/S5LzV9skvtpmK/G12STqxo0bTJ48mRYtWtClS5c87XP27FlcXV0pW7asWpaSksKFCxcAqFChArVr1zbZ5/LlyyQmJgLGbg6ZxcTEqCtytWvXNvljqNPpOHPmDGCcN+O5554z2TciIoL79+8DxiTQweGfUNy7d4+//voLgJo1a2aZaPHUqVMYDAZKlixJgwYNTNb9/fff3L17F4CGDRuazDHy8OFDrly5AkDVqlWzzONx7tw59SDfoyMy3bx5U3U/qVu3rsmVyuTkZPWHtWLFijzzzDMm+166dImkpCTs7Ox44YUXTNZFR0cTFRUFGLu1ZB4kJD09XV3hLVu2LM8++6zJvlevXjW5opt5HpO4uDiuXbsGGK+uVq5c2WTfjGcRnJ2dqV+/vsm6a9euqa4qjRo1MrnKev/+fSIiIgCoVq0a1atXN9n37NmzpKen4+TkRKNGjUzWRUVFER0dDRjnXilVqpRal5iYyOXLlwGoVKkSLi4uJvtevHiR5ORk7O3tadq0qcm6O3fucPPmTQDq1KlDuXLl1LrU1FTOnz8PGGcAr1Onjsm+V65cUX2OmzVrZtJwxcbGcv36dQBcXFxM7gbr9XpOnz4NGJ//ePTBz8jISPV8RePGjSlevLhaFx8fT2RkJGD84Vm1alWTfc+cOYNOp6NEiRJZujhdv36d2NhYAOrXr4+zs7Nal5CQoH7QVqlShZo1a5rse+HCBVJSUnBwcMhy4eXWrVvcvn0bgGeffVbaCKSNyKmNOHToEG+++aY671xdXQkLC6Nu3bpm24hly5bx7rvvqkEb2rVrx4IFC7IkUNm1EYcOHcLPz0/N3ZRh165dHDx4kHbt2uW7jQgICGDWrFmA8QfLzJkzzQ7SdOXKFeLi4hgzZgx//PEHYPzOhYaGUqxYMfU5SRshbQRIG5FBfkcY2drviIzzNK9sMom6e/cuXl5eGAwGNm7cmOeMNT09Xf0Ry2AwGEhLS1Prze2Tsf5Rer1ercsYoSizvJb7aJ0yl6vT6cyWazAYcHR0zLJOp9M9UbnZHWvmch891syfoblyM47VXNfNvJZrLbHJ7VjT0tJIT083+53MKTZ5KTctLc3supzKzdg3t3LNyetnaG7/zHV6VG7Hmpqail6vNzu5Z0F8huY+o7yWay3fQ2kjspZbWLE5d+4cffr0UT8G69Wrx/79+9WPvkfrNH36dKZOnar279atGx988IHJD15zx2owGIiIiGDSpEls2bLF7DEYDAaOHDlCu3bt8tVG7N27lxEjRqj148eP59VXXzW7b0pKCh999JHq8le+fHl2795NnTp1iI6OljYCaSMeLfdpbyMeLVd+R9hWG5EfNpdExcXF0bFjR27cuMH+/fuzXJnJiYODQ5YT0M7OTjUi5v6oOTg4mG1kwHj1LmOduS97RvDMBThzuY/WKXO55r4Ajo6OGAwGs/W1t7d/onIz/z+7ch891syfoblyM47VXOOX13ILOjZ5LTen70tKSgrR0dEUK1ZMXV3JOM7cPsOcys0uNjqdzuy6nMrNfKzZlfukn2Fux/qo3I61ePHi6HQ6i3yGer0+z+dNbGwser3epC7W8j2UNiJrufmNTUJCgqpLXmNz4sQJ3N3diYmJAYwJ1L59+0yummfUSafT8cknn7Bq1Sq1btKkSQwePDjX73dSUhKffvopixYtIiUlRa1v0KABvXv3Jjo6muXLl5vUPa9txIULF+jdu7f6uzRmzBgGDhyotsvMYDAwZ84cQkNDAeOw7Tt37lTPK1hzG6HX67l37x7JycmqfS7oNsJcfaWNKJw2IqN9LlasmE3/jsjuM3zaf0fExsaSlpaGvb292f0s+TsiP+wM+U27LCgmJoYqVapkmScqQ1xcHG5ubkRERBAWFsZLL72UbVl6vV7dos1QpkyZQu1nGR4erm5rP3oLX9g+ia+2SXy1Lb/x/e233/D09FTdS15++WVCQ0PNDnqUkpLCkCFD1PNGAF999RXvvfderu9z/PhxBgwYoLo2gbHb1IwZMxg2bBj29va8/vrrHDx4EIDTp09n6ZqTnVu3btGqVSvVRcnb25utW7ea/RECMHPmTDX5rr29PYGBgXTr1i1P71XU5PzVNomvthVVfPObO9jGk1v8k0BdvXqVPXv25JhACSGEEAXl4MGDdOzYUSVQbdq0ISwszGwC9eDBAzp37qwSKAcHB9asWZNrAqXX65kzZw6tW7dWCVTx4sWZNGkSly9fZvjw4djb2/Pbb7+pBKpevXp5HlgpMTGRrl27qgSqRYsWrFu3LtsEKiAgQCVQAMuXL7eZBEoIIQqDVXTn27VrFwkJCSr7O3funOoD7uXlhZ2dHR4eHpw4cYIFCxaQnp7Ob7/9pvavUqWKVc5o7OLiom43C+2R+GqbxFfb8hrf3bt306NHD5KTkwHo0KEDO3bsMHmgO8OdO3fw8vLi2LFjgHGOw61bt9KpU6cc3+P69esMHTpUjTgL8K9//Yt169aZPFiu1+vx8/NTr8eOHZun7ic6nY5BgwZx9OhRwDiAwc6dO80eA8D27dt555131OtZs2bx1ltv5fo+1kTOX22T+GqbzcTXYAVcXV0NgNn/IiIiDBEREdmuBwxDhw7NUqZOpzPcu3fP5D+dTlf4ByeEEMImBQYGGhwdHdXfms6dOxuSkpLMbnv16lVD/fr11bYVKlQwHDlyJNf32LJli6FChQpqPzs7O8PkyZMNKSkpWbb9/vvv1XZNmjQxpKWl5ek43nvvPbVf2bJlDadPn852259++sng5OSkth83bpxBr9fn6X2EEMKW5Td3sKpnogqSNTwTJYQQwjatX7+eIUOGqAEYevfuzbp160yG2c1w6tQpPD091RDBLi4uhIaGZhniObPU1FTGjh3LN998o5a5uLjw/fff89prr2XZPiEhgYYNG6rhsPfs2UPHjh1zPY6lS5cyatQowPhcU0hICO7u7ma3DQ8Pp3379qrb4qBBg/juu+/k76YQ4qmg2WeihBBCiMIQEBDAoEGDVAI1ZMgQNmzYYDaBOnToEO3atVMJVKNGjThy5EiOCdSNGzdo3769SQLVp08fTp06ZTaBApg6dapKoLp06ZKnBCokJITRo0er19988022CdTVq1dNBs7w9PRk5cqVkkAJIUQ25E6UheuQQf4QaY/EV9skvtqWXXwXLlzI2LFj1esRI0awZMkSs9+BnTt30rdvX/W8VKtWrQgODjY74ESGn376ib59+6p5ppycnFiyZAk+Pj7ZPt8UFhaGm5sbYBwK+MyZM1kmSH1UeHg4//73v9UkmO+//76aXPdRd+7coW3btmoi2latWhEWFpbtM1O2QM5fbZP4altRxTe/uYNVDCyhVadPn5YhODVM4qttEl9tMxffGTNmMGXKFLXN+PHjmTNnjtnkZuPGjQwaNEhNtOnp6cmWLVuyTTwMBgNLly7Fz89P3eFydXVl69atvPzyy9nWMzY2liFDhqjXM2fOzDWBunHjBp07d1YJVO/evZkxY4bZbe/fv0+nTp1UAtW4cWOCg4NtOoECOX+1TuKrbbYSX0nfhRBCPNUMBgNTpkwxSaCmTp2abQK1atUqBgwYoBKo/v378+OPP2abeKSmpjJixAj++9//qgSqY8eOHDt2LMcEymAw4OvrS1RUFABubm6MGzcux2N5+PAhXbp0UV3/WrduzZo1a8xeSU1JSaFHjx4cP34c+OdZrpzupAkhhDCSO1EWVLp0aZVJC+2R+GqbxFfbMuLr4ODAuHHjWLhwoVr35ZdfMnHiRLP7LVmyhP/+97/qta+vL99880228y1FR0fTq1cvfv75Z7Vs4sSJzJw5M9t9MqxcuZJt27YBULFixVwHeUhLS6Nv376cPHkSgGeffZYdO3ZQsmTJLNtmDHueMax6xYoVCQ0N5ZlnnsmxTrZCzl9tk/hqm63EV56JEkII8VTS6XSMGDGCgIAAtWzx4sVqNLtHzZkzh0mTJqnXfn5+zJ8/P9tnmcLDw/H29uavv/4CjM8/ZQxakZtLly7x0ksvkZiYCEBgYCA9evTIdnu9Xs/QoUNZu3YtAOXLl+fIkSM0btw4y7YGg4FRo0apgS1KlixJWFgYr776aq71EkIIrZJnooQQQohcpKenM3ToUNavXw8YH15esWIFw4YNy7KtwWBg2rRpTJ8+XS378MMP+fzzz7NNoAIDAxk8eLBKgmrUqMH27dtp2bJlrnVLSkqif//+al9fX98cEyiDwcDEiRNVAuXk5MSOHTvMJlAA06dPVwmUg4MDW7dulQRKCCHySW7LCCGEeKqkpKTQt29flUA5ODiwfv36bBOoiRMnmiRQX3zxBV988YXZBEqv1zN9+nR69eqlkqBXXnmFo0eP5imByrhLlPGcUv369Zk/f36O+8yZM4d58+YBxmRw48aNtGvXzuy23377LdOmTVOvV61aRadOnXKtlxBCCFNyJ0oIIcRTIykpiZ49e7J7924AihcvzpYtW+jatWuWbfV6PaNGjeLbb79VyxYsWICfn5/ZspOTkxk6dCibNm1SywYNGoS/v7/Z55LM8ff3Z9WqVYCxm11OI/6BMQl6//33Tfb39vY2u+2WLVsYOXKkev3VV1/lqWuhEEKIrCSJsqDIyEh0Oh329vbUqVOnqKsjCpjEV9skvtqTkJBAly5dOHjwIAAlSpTA39/fbAKVnp7O8OHDWbNmDQB2dnb4+/vzn//8x2zZ8fHxdO/eXZVtZ2fHrFmzmDhxYrZd/h71+++/m0yOGxAQwAsvvJDt9jt37sTX11e9njFjBsOHDze77f79+xk4cCAZj0FPmjSJ9957L0/1skVy/mqbxFfbbCW+kkRZUHx8vE2MLiIej8RX2yS+2vLw4UM6d+7MoUOHAChVqhTz5883m6SkpqYyaNAgNm/eDIC9vT1r1qxhwIABZsu+desWnTp1UqPilSpVih9++IEuXbrkuX5RUVH07NmTtLQ0AMaMGZPt+wEcPnyYvn37qiHT/fz8mDx5stltjx8/jre3N6mpqQAMGzYs24l3tULOX22T+GqbrcRXkighhBCa9uDBA7y8vDh8+DBgHLlu0aJFNGrUKMu2ycnJ9O7dm+DgYAAcHR3ZuHFjtgM7XLlyBXd3d65evQpApUqVCAkJydPzTxmSkpLo0aOHmg/q//7v/5g7d262258+fZquXbuSnJwMwIABA5g3b57ZO15//vknnTp1UhPvdunSheXLl+f57pgQQgjzZIhzC8q46gfGfvdCWyS+2ibx1YYHDx7QqVMnfvnlFwAqVKjA3r17adasmdomI74PHz7E29tbzZ1UokQJtm3bhqenp9myT5w4QadOnbh9+zYAtWvXJjQ01Gxylh2DwcCQIUPUyHq1a9fmjz/+oGrVqma3j4yMpG3btirh8vDw4McffzT7Hb158yZt27YlIiICgLZt27Jnzx6cnZ3zXD9bJeevtkl8ta2o4itDnFsRObG1TeKrbRJf23f//n06derEkSNHAGMCtW/fPv71r39l2TY+Ph4vLy+1benSpQkKCqJ9+/Zmyz548CDdunVTf3CbNGnC7t27cXFxyVcd586dqxIoZ2dnfvzxx2wTqOjoaDw8PFQC1bJlS7Zs2WL2uxoXF4enp6dKoJo2bcrOnTufigQK5PzVOomvttlKfGWIcyGEEJoTHx+Ph4eHSooqVqxIWFiY2QQqNjaWDh06qG3Lly/P3r17s02gAgMD8fDwUAlUmzZtOHToUL4TqJCQEJOR9dasWUPz5s3NbpvRJfHSpUsANGzYkODgYEqXLm12W09PT06dOgWAq6sru3fvpkKFCvmqnxBCiOxJEiWEEEJTMhKo3377DfgngXrp6xgWWAAAIABJREFUpZeybHvr1i1ee+01jh07BkDlypU5cOAArVu3Nlu2v78/ffr0Ud1NOnfuzN69e6lYsWK+6nj+/Hn69++vRsubNm0avXr1MrttamoqPXv25OjRowDUqlWLPXv2ULly5SzbJiYm0qVLF/73v/8BULVqVUJDQ6lVq1a+6ieEECJn0p3PguLj4zEYDNjZ2VGuXLmiro4oYBJfbZP42qZ79+7h4eGhkohKlSoRFhaW5Q5PfHw8f//9N927d+fKlSsA1KhRg3379vH8889nKddgMPD555/zySefqGVDhw5l+fLl+R5BKi4ujm7dunH//n0AevXqxccff2x2W71ez5AhQ9i3bx9g7JIYGhpK7dq1s2ybkpJCjx491AiEGd0XGzZsmK/6aYGcv9om8dU2W4mvJFEWFBkZqYZozK6LhrBdEl9tk/janri4ONzd3dUdm8qVKxMWFmZ2GPOff/6Zt99+m5s3bwLGLm9hYWHUrVs3y7Z6vZ4xY8awZMkStWzixInMnj0736Pcpaam0rdvX/78808AmjdvznfffWf2wWWDwYCfnx8bN24EjJPvBgUF0aRJkyzbpqWl0a9fP/bs2QMYH4YODQ01GUDjaSLnr7ZJfLXNVuIrSZQQQgibFxcXR8eOHVW3vCpVqrB//36aNm2aZdvz58/j4+NDdHQ0APXr12ffvn3Z3t0ZOnSoSmQA5syZw4QJE/JdR71ez1tvvaXuKlWpUoUdO3ZQqlQps9t/8cUXLF68GDDOVbV582batGmTZTudTsfQoUPZsWMHYBygIiQkhFdeeSXfdRRCCJE3kkRZUI0aNdSMy0J7JL7aJvG1HXfv3qVjx44cP34cMD4HtH//frN3bE6dOoWbm5tKoBo1asSBAweoXr16lm0fPHhAz549VdJjb2/PypUrGTJkSL7raDAYGD9+POvXrwf+GT7d1dXV7Pb+/v4mXfxWrlxJ586ds2yn1+t555132LBhAwBOTk7s2LGDf//73/muo5bI+attEl9ts5X4yjxRQgghbFZsbCxubm6cPHkSgGrVqrF//36zzzWdPHkSNzc3YmNjAfjXv/7Fnj17qFSpUpZto6Oj8fLyUl0DS5YsyebNm80mMnkxa9YsPvjgA8CYjAUGBtKtWzez2wYGBtKnTx/0ej2Q/Z2vjO5+ixYtAsDBwYHAwEC6du36WHUUQoinmcwTJYQQ4qkQExODm5sb4eHhgDGBOnDgAI0bN86y7YkTJ3Bzc+Pu3bsAtG7dml27dlG+fPks20ZGRuLu7s7ly5cB4wANQUFBZrvS5cXKlStVAgXGu0zZJVAHDx5kwIABKoGaMGFCtl0Hp0yZohKoYsWKsW7dOkmghBCikEgSJYQQwubExMTQoUMHNRdS9erVOXDgAI0aNcqy7fHjx3FzcyMuLg4wzuu0a9cuypYtm2Xb06dP4+HhoQacqFWrFqGhoWa7BubFjz/+iK+vr3o9c+ZMfHx8zG579OhRvL29SUlJAWDIkCHMnj3b7LZffPEFM2fOVK9XrlxJ3759H6uOQggh8k/6tgkhhLApjyZQNWrU4ODBg2YTqGPHjtGhQweVQLVt25bdu3ebTaAOHz5Mu3btVALVsGFDjhw58tgJ1M8//0y/fv3UXaWxY8eaTK6bWUbyljHseefOnQkICDDbjWTBggV89NFH6vWSJUsYOnToY9VRCCHE45E7URZ05swZUlNTKV68uNkRooRtk/hqm8TXOj2aQNWsWZMDBw7QoEGDLNv+8ccfuLu7c+/ePQD+/e9/ExISQpkyZbLEd+fOnfTt25fk5GQAWrZsSXBwsNkJbfPi1KlTdO3aVZU3cOBAvvrqK7NDol+6dMmkq2G7du3YtGmT2fmn/P39GTdunHo9Z84cRo4c+Vh11DI5f7VN4qttthJfuRNlQTqdDr1ej06nK+qqCAuQ+GqbxNf6ZAwikTmBOnjwoNkE6n//+x8dO3ZUCdT//d//sWvXLsqUKQOYxnfz5s306NFDJTweHh6EhYU9dgIVERGBp6cn8fHxAHh6erJy5Uqzd5UiIyPp0KEDd+7cAaBVq1YEBQXh7OycZdu1a9cyYsQI9Xrq1KmPNdT600DOX22T+GqbrcRX7kRZUIkSJbC3t8/3bPbCNkh8tU3ia13u3r1rMohEjRo1OHDgAPXr18+y7e+//467u7vqGte+fXuCgoIoXbq02iYjvnv27GHSpEnqj3X//v1ZvXo1xYsXf6x63rlzx+SZqlatWrFlyxaz5d24cYM33niD69evA8aJdzMnepkFBgYybNgwMgbUnTBhAlOnTn2sOj4N5PzVNomvttlKfGWIcyGEEFYtI4E6ceIE8E8C1bBhwyzb/vrrr3h4eKj2/7XXXiMoKMjshLbr1q1jyJAh6pml4cOH4+/v/9h/Jx48eMDrr7+uJvxt1KgRhw8fNjuE+p07d2jfvj0XLlxQ2/70009UrVo1y7YhISF0796dtLQ0AEaOHMnixYvNdg0UQgjxePKbO0hGIYQQwmrFxcXh7u6uEqjq1auzf/9+swnUkSNHTBKoN954g+DgYLMJ1HfffcfgwYNVAvX2228/UQKVkpJCjx49VALl4uJCaGio2QTq7t27uLu7qwTqueeeY9++fWYTqAMHDtCrVy+VQA0dOpRFixZJAiWEEEVMkighhBBW6d69e7i7u6vEJGMiXXOj8P366694enqqBKpDhw7s3LnT7LNFK1eu5K233lJd40aOHMk333zz2AmUTqdjyJAhhIWFAcZ5pUJDQ6ldu3aWbe/fv0+nTp1Ut0QXFxfCwsKoVauW2WPKPDhFnz59sh2xTwghROGSllgIIYTViY+Px93dnaNHjwJQtWpV9u/fb3Yi3d9++83kDpSbm1u2CZS/vz/Dhw9XCdTo0aNZvHjxYycmBoMBPz8/Nm3aBEDJkiUJDg7m+eefz7JtYuL/Y++8w6Oovv//SqOGFjoivakUFRUEQQiBRIoh9CZNQpEqoKB0ROGLqCC9Sgmhl8QEQgkgSBFBBCmhSa+BUEzPZuf3x/5yP1l2NwUSyA7n9Tw8ZGbuvXtmzs7dec+995xomjdvzuHDhwGTKAwNDaVMmTIWZf/66y8++ugjoqKiAGjevDl+fn44O8tSZkEQhKyA9MaZyPXr10lMTMTJyYmSJUu+aHOEDEb8q2/Evy+OR48e4enpyZ9//glA4cKF2bVrl1Vh8scff1gIqMDAQHLmzGlRdu7cuWbhwHv27MkXX3zxTFPjJk2axOzZswFwcnJi/fr1vP/++xblkqb77du3DwA3Nzd27txpNbLgqVOnaNKkiYru5+Hhwbp165462MXLiNy/+kb8q2/sxb8yEpWJ3L9/n/DwcO7fv/+iTREyAfGvvhH/vhgeP36Ml5cXf/zxBwCFChVi165dVhPeHj582CwKn7u7OwEBAVYF1MyZM80EVNeuXenbt6/KzfQ0zJ8/n7Fjx6rtX375haZNm1qUS0hIoH379mzfvh2AvHnzsn37dqv5Ty5cuEDjxo3V9+6DDz5g8+bN5MiR46ntfBmR+1ffiH/1jb34V0aiBEEQhCxBkoA6dOgQAAULFmTXrl1WxcaRI0fMBFTDhg1tTuH76aefGDp0qNoeOXIk7du3x2AwPLWtGzZsoF+/fmp72rRpfPLJJxblktZLBQQEAJArVy62bNlCzZo1LcpeuXKFRo0aqfDo77zzjs3IgoIgCMKLRUKcZyLR0dFomoaDg4PVH3bBvhH/6hvx7/Plv//+w8vLiwMHDgAmARUaGkqNGjUsyh49ehQPDw+VSPfDDz+0GYXvSQE1evRoJk6cSExMzFP7d/fu3Xh5eREfHw/Al19+yf/93/9ZlDMajfj6+rJkyRIAsmfPTnBwMI0aNbIoe+vWLerXr8+FCxcAqFq1Knv27LEa3U9IHbl/9Y34V9+8KP+mWztoL5jHjx9rX3zxhda4cWOtUKFCGqCNGzfOatmjR49qjRo10nLnzq3ly5dP8/Hx0S5evGi1bGJiovbw4UOzf4mJiZl4JoIgCMLT8PjxY61u3boaoAGam5ubduzYMatljx49qhUoUECVrV+/vhYZGWm17IwZM1Q5QBs/fvwz23rkyBEtT548qs3u3btrRqPRopzRaNQGDhyoyjk7O2tBQUFW2wwPD9def/11VbZSpUra7du3n9lWQRAEIe2kVzukaVimXr16XLp06Sk0Xercv3+fBQsWEBcXR8uWLW2WCwsLo0GDBsTHx7N27VqWLFnCuXPnqFevHuHh4ZlimyAIgpC5REZG0qxZM/bv3w+YwoPv3LmTN99806LssWPH8PDw4MGDB4BpvZCtEajZs2czePBgtT1+/HjGjRv3TLYeO3aMxo0bqzeVzZs3Z+HChRaBKTRN4+uvv2bmzJkAODo64u/vT7NmzSzaTArjfvr0aQDKlClDaGgoRYsWfSZbBUEQhEwmLcqsWLFiWp48ebT58+dnlNhTGI1G9RYvPDzc5khU27ZttUKFCmmPHj1S+y5fvqy5uLhoX375pUV5GYkSBEHI2kRGRmr169dXIzD58+fXjh49arXs33//rbm5uamydevW1R4/fmy17Lx588xGoMaMGWPxuUnHbI1ipfb59erV06KioqyW/eabb8w+f9myZVbL/ffff9r777+vypUoUcLm7ApBEAQhc8mUkajTp0/TvHlz+vbty0cffaQWvWYEDg4OqYaXNRgMBAUF0bp1a/Lmzav2ly5dmoYNG7Jp06YMsycjiYqKIjIyUuX5EPSF+FffiH8zl9jYWFq2bMnevXsByJ8/Pzt37uTtt9+2KHvy5EkaNWqkIunVqVOHrVu3kidPHouyixcvpm/fvmr766+/ZsKECTbtSIt/T548iYeHh/r8unXrEhwcbDOIxZgxY9T2nDlz6Nq1q0W5mJgYPv74Yw4ePAiYwriHhoZSrly5VO0RUkfuX30j/tU39uLfNImoAgUK4O/vz4YNGzh27BhVq1Zl1apVmW2b4uLFi8TExFC9enWLY9WrV+fChQsqo3tW4sKFC4SFhamFwoK+EP/qG/Fv5pGQkEC7du3YuXMn8L+Q39Yi1p07dw4PDw8V6rZ27do2BdTSpUvx9fVV219++SWTJk1SL+qioqLUvyROnTplsS85p0+fxt3dnXv37qnP37Jli9XPX7BggVkQi2nTpplF8EsiPj6eNm3asHv3bsD0G7tjxw6qVKli1QYh/cj9q2/Ev/rGXvybrhDnPj4+fPjhh3z22Wd06dKFCRMmWCT/c3Bw4Pjx4xlqZNKPp5ubm8UxNzc3NE3jwYMHFC9ePMV2Tp06RenSpc1Gs+Li4ggLCwNMP2SlSpUyq3P+/Hmio6MBLKJE3bt3jxs3bgBQqlQpChQooI4lJiaSkJAAYDWM7qVLl1Ro3jfeeMMsC/3Dhw+5cuUKACVKlKBw4cJmdU+cOIGmaeTMmdMiUeO1a9fU29LKlSub5RaJjIzk4sWLABQpUsTiep0+fZqEhARcXFwsklreunWLu3fvAlC+fHlcXV3VsdjYWM6ePQuY/PHqq6+a1T137hwxMTE4ODhYCOHw8HBu3rwJmEYW8+fPr44ZDAZOnToFmB6yypYta1b333//VWsTqlatipOTkzr24MEDrl69CsArr7xCoUKFzOomfUdz5cpFxYoVzY5dvXpVrbmoUqUK2bNnV8ceP36s1gcmJibyJKdOncJgMJA9e3aLB6KbN2+q9XsVKlQwW8cRHR3N+fPnAVNUsieTy509e5bY2FicnJwswj3fvXtXjQ6XKVOGfPnyqWPx8fGcOXMGgHz58lGmTBmzuhcvXiQyMhKAatWqmUWguX//PtevXwegZMmSZlHCjEYj//zzDwCurq6UL1/erN3Lly+rRKGvvfaaWT/x6NEjLl++DEDx4sUpUqSIWd2TJ0+SmJhIjhw5qFy5stmx69evq/6gYsWKZiMBUVFRqsMtXLgwJUqUMKsbFhZGXFwczs7OFjmHbt++zZ07dwAoW7asWR+haZr6vmR0H3Hy5EnAFP3nyREIvfYR+fLlY8SIEfz6668A5M6dm/nz55MtWzZOnDhh1kdcvnyZhg0bKt+8/fbbhISEKP8k7yN27drFsGHD0P5/wNmhQ4fSu3dvTpw4AZj6iOQ2JeHu7q7+1pIFqz1+/DiXLl3C19dXCaj33nuPkJAQHj58qPqBpD7Cz8/PbASsX79+dO7c2eLzjh8/zvDhw5WAzJMnDyEhIdSoUUP6iP9PRvQRSb+/ycmsPiIznyNexj7iZXqOKFq0KMWKFTOrK88R/yMhIYHjx48/t+eIpPs0raQ7T1RkZCTh4eFomoabm5vZFyOzSWnaX1oyzhsMBrMfSTD9aKYkdgwGg9XOGExfgKRjRqPR5udayzKfvN0nbUrerrUH9YSEBDRNw8XFxeJYcvH2NO3aOtfk7T55rsmvobV2k87Vmo/S2m5G+yat7ab0fXF1dSV37txmnW5CQgIGg8FqOMyUfJPaNUzyjbVjKbWb/FzT6/O0XkNr9ZPb9CSpnWt8fDxGo9Hsulpr92mvobVrZK3dwoULk5iYiKZp6oc/q3wP7bWPMBqNDB8+nA0bNgCmkN+BgYEUK1aM6Ohosz7i5s2bNGrUSD0cVaxYkbVr15r9uCe1u23bNsaOHavOZ9CgQUybNo3z58/btDc1Lly4QN++fZWAqlmzJtu2bSNfvnxmD+maprF69Wq6deumPr9r16706NHD4homJiYyatQoJaBy5sxJUFAQ7733nsU1lD7i2fsINzc3MwGQ0X2EtXalj3g+zxFJ/bOTk5NdP0fYuoYv+3NE4cKFuX//PnFxcVbbzszniPSQLhG1cOFChg8fTp48ediyZQteXl7p+rCnJUm5WstcHBERgYODg9mbB1s4OztbPMg7ODioTiT5W5zkdax1MmCKuJR0zNqXPemYtchRydt90qbk7Vr7Ari4uKBpmlV7nZycnqnd5P/bavfJc01+Da21m3Su1kRUWtvNLN+k1m5K35f8+fNbvEFKOs/UrmFK7dryTdIPRnraTX6uttp91muY2rk+SWrnmi1bNhITEzPlGhqNxjTfN0lvqePi4tQbxazyPbTHPsLZ2ZnJkycrAeXi4sLGjRtxd3fn3LlzZn1EeHg4Hh4e/Pvvv4Dpzei8efMsciY5ODiwa9cuxo4dq36g+/fvz/Tp09VnJrc16W1pVFSUin63a9cuypUrZ/aW+cKFC/Tr108JqLfeeovt27er35nk7a5fv55u3bqpz/f19eWzzz7DwcHB7BomJibSo0cPgoOD1flv3ryZ+vXrW72G0kc8ex9RrFgxs7fMGd1HWGtX+ojn8xyRfBQxPDzcbp8jbF3Dl/05okSJEkoIWSMznyPSRVqiVVy/fl3z8vLSHBwctI4dO2oRERFpqZZubEXnS0hI0HLmzKn17dvXoo6np6dWsWJFi/0SnU8QBCFrYDQatS+++EJFoXN0dNTWrVtntWxERIRWo0YNVbZs2bLatWvXrJbdsGGD5uTkpMr27dvXas6mJ0kpOt/Fixe1kiVLquPVq1fX7t27Z7WdtWvXmn1+nz59rP7OGAwGrVu3bmY5owICAlK1UxAEQXh+ZEp0vqpVq3LkyBHWrFmDv7+/2Zzd54GzszMtWrRg48aNZpmEr169yu7du2nVqtVztUcQBEFIOxMnTuT7778HTG/6li5dSps2bSzK/ffff3z00UdqrcErr7xCaGioxdx+gNDQUDp06KCmcvTq1YvZs2en/01iMq5cuULDhg3VHP6qVauyc+dOixEwMI1AdezYUX2+r68vc+bMsXjbajQa8fX1ZdmyZYDp92zt2rV8/PHHT22nIAiC8OJJ03S+Dz74gEWLFmVa8r+tW7cSFRWlBNLp06dZv349AE2bNiVXrlxMmDCBd999l+bNmzNy5EhiY2MZO3YshQoVYtiwYZlilyAIgvBsTJs2jfHjx6vtuXPn8sknn1iUi46Opnnz5vzxxx+AadF6aGioxUJwgKNHj9KyZUs1r71bt27Mnz/f6nQRa+TOndti7vulS5do2LChWkj++uuvExoaarEgH2DDhg1mAu7TTz9l3rx5VgVU7969+eWXXwDTNJI1a9bg4+OTJjsFQRCErIuD9uQvyQugTJkyKorMk1y6dElFAjl69CgjRozg4MGDODs74+7uzrRp06xG9DAajWajVmCKbpPWH9mMICwsTEWpkdC1+kP8q2/Ev8/OnDlz6N+/v9r+8ccf+fzzzy3KxcXF4e3tzbZt2wBThLM9e/ZYTWtx/vx56tatqyJUeXt7s379eqvrElIiuX9dXFxwd3dXAqpy5crs2bPHYs0jwKZNm2jXrp1aTN6jRw8WLVpkVUD16dOHRYsWASYBtXr1aqsjcELGI/evvhH/6psX5d/0aod0R+fLDJLCFKZGzZo1VVQjeyApqkhKkfsE+0X8q2/Ev8/GsmXLzATUN998Y1VAJSQk0KFDByWg8uTJw7Zt26wKqJs3b9KkSRMloOrVq8eqVavSLaDgf/69dOkS/fv3V1P4XnvtNUJDQ60KqICAADMB1b17d5sCql+/fmYCatWqVSKgniNy/+ob8a++sRf/ZgkRpVecnZ1tRr8R7B/xr74R/z49a9eupWfPnmp7xIgRjBo1yqJcYmIi3bt3Z/PmzYAp5HdwcDDvvvuuRdmHDx/i5eWlXrpVq1aNwMBAcubM+VQ2Ojs7c+nSJfr06aNC2L/xxhuEhoZanboeGBhI27ZtlYDq2rWrVQGlaRr9+/dnwYIFgElArVy5krZt2z6VncLTIfevvhH/6ht78W+WmM6XGWSF6XyCIAgvG0FBQfj4+CixMXDgQGbMmGER8EHTNHr37q1Ga7Jly0ZQUBCNGze2aDMmJgZPT0/27dsHmKaA79+/3yJZano4c+YM7u7u3L59GzCJMltroIKCgmjVqpVag9WlSxeWLl1qEVpX0zQGDBjAnDlzAFNI35UrV9KhQ4entlMQBEF4PqRXO4iiEARBEDKEnTt30qZNGyWgevbsqXI2JUfTNIYMGaIElLOzM+vXr7cqoAwGAx07dlQCqnDhwmzfvv2ZBNSpU6do0KCBElBvvvkmu3btsiqggoODad26tRJQnTp1simgBg0aZCagVqxYIQJKEARBp4iIEgRBEJ6Z33//HW9vb+Li4gDo0KEDCxYssPoGb/To0fz888+ASWz4+fnRokULi3KaptGnTx8CAgIAcHV1ZevWrVSsWPGp7Txx4gQNGjRQU/jefvttQkNDzZLtJvHrr7/i4+NDfHw8AB07dmTZsmVWBdTgwYOZNWuWOqfly5fTqVOnp7ZTEARByNqIiBIEQRCeiSNHjtC0aVOio6MBU8S85cuXW80k/9133/Hdd9+p7cWLF9O+fXur7Y4aNYolS5YApoz2mzZtombNmk9t599//427uzv37t0D4N1332Xnzp24ublZlA0ICDAbgerQoQPLly+3mKOvaRqff/45M2fOBP6XB6tz585PbacgCIKQ9cnaK7bsnNu3b5OYmIiTk5PVSE+CfSP+1Tfi37Txzz//4OnpqeaRN2nShDVr1uDi4mJRdvr06WYBJmbPnk337t2ttjt9+nQmT54MmISJn58fHh4eT23nX3/9hYeHBw8ePABMI1BLly5VI2fJeTKMeadOnVi2bJlVATV06FBmzJih7Pzll1+s5sESni9y/+ob8a++sRf/iojKRO7cuaPi3GflL4HwdIh/9Y34N3XOnTtH48aNiYiIAKB+/fps2rSJ7NmzW5RduHChWYjzqVOn8tlnn1ltd+XKlWZlZ82aRbt27Z7azoMHD9K0aVMePnwIQJ06dZg6dSrR0dEkJCSY+Xfjxo20b99eCaiUgkgMHz6c6dOnAyYBtWTJErp16/bUdgoZh9y/+kb8q2/sxb8ynU8QBEFIN5cvX6ZRo0bcuXMHgPfee4+goCBy5cplUXblypX06dNHbY8bN44vvvjCarshISFmo1Njx461KbbSQnBwMI0aNVIC6oMPPiAkJARXV1eLsuvXrzcbgfrkk09sCqgRI0bw448/qn2LFi2yOaomCIIg6A8JcZ6JPH78GE3TcHBwIG/evM/tc4Xng/hX34h/bXPjxg3q1avHpUuXAKhRowa7d++mQIECFmU3bdpE27ZtSUxMBGDYsGF8//33FhH7AP744w/c3d3V2qo+ffowd+5cq2XTwvLly+nZs6f6bA8PDzZt2oSrq6uFf9etW0fHjh1V2W7durF48WKrAurLL79k2rRpat/ChQvp1avXU9koZA5y/+ob8a++eVH+Ta92EBElCIIgpJm7d+/y4YcfEhYWBkCVKlX47bffKFKkiEXZnTt30rRpUxWcoV+/fsyePduqKDpz5gz16tXj/v37ALRu3Zo1a9ZYDU6RFqZNm2Y22tW+fXuWL19OtmzZLMquWbOGzp07KwHVvXt3Fi1aZHMKX/IRqPnz59O7d++nslEQBEHIOkieKEEQBCFTiIiIoEmTJkpAlStXjp07d1oVUEeOHKFly5ZKQHXr1o1Zs2ZZFVDXrl3D09NTCagGDRrg5+f3VAIqaaQouYAaMGAA/v7+VgXUqlWr6NSpkxJQPXv2tDkCNXToUDMBtWDBAhFQgiAILykSWEIQBEFIlcePH/PRRx9x/PhxAEqWLEloaCivvPKKRdlz587x0UcfERUVBZhCni9atMjq27yIiAi8vLy4du0aAG+99RYBAQHkyJEj3TYmJCTg6+vLsmXL1L5vvvmGUaNGWRVv/v7+fPLJJxiNRgB69erF/PnzLexMSg6clNvKwcGBhQsX8umnn6bbRkEQBEEfiIjKROLi4tScTmvRqgT7Rvyrb8S//yM6OpoWLVpw+PBhAIoWLUpoaChlypSxKHvz5k2aNGmicjHVr1+fVatWWYQHT2q3efPmnD59GoDy5cuzdevWp5oDHx0dTbt27QgODgar5Z/AAAAgAElEQVRMCW/nzp1rc6Ro3rx5fPbZZyTNaPf19WXevHlWBdSgQYNUIl0HBwcWLVpEz549022j8PyQ+1ffiH/1jb34V0RUJhIWFqZCNNaoUeNFmyNkMOJffSP+NREXF4ePjw979+4FwM3NjR07dlCpUiWLsg8ePMDT05MrV64AUL16dQICAsiZM6dF2YSEBNq2bcvBgwcBkzDbvn07RYsWTbeNERERNG/eXLWVPXt2/P39adWqldXyM2fOZNCgQWq7T58+zJkzx6qAGjBgAHPmzAH+F8ZcovBlfeT+1TfiX31jL/4VESUIgiBYJSEhgfbt27N9+3YA8ubNy7Zt26hWrZpF2ZiYGD7++GNOnjwJQNmyZQkJCSF//vxW2x42bBhbtmxR7YaEhFCuXLl023j9+nU8PT3VaFbevHkJCAigQYMGVstPmTKFr776Sm137tzZagRAo9HIgAEDmDt3LmASUEuXLqVr167ptlEQBEHQHyKiMpECBQpgMBisTmMR7B/xr7552f2bmJhI165dCQgIACBXrlxs2bKFd955x6KswWCgffv2/P777wAULlyYbdu2Ubx4cattL1y4kJkzZwLg4uJCQEAAb775ZrptDAsLo0mTJmo9VdGiRQkJCbHalqZpjBkzhm+//Vbt69+/P1988YVVAfXZZ58xf/58wDQ1cNmyZXTp0iXdNgovhpf9/tU74l99Yy/+lRDngiAIghlGoxFfX1+WLFkCmKbHJSWtfRJN0+jVq5cq6+rqyp49e6hZs6bVtvft20ejRo1U1L5FixY9VYCGP/74g2bNmqmIfuXLl2fbtm2UL1/eqo1Dhw5l+vTpat93331nNiKVhNFopG/fvixcuBAwCajly5fTuXPndNsoCIIg2A/p1Q5ZW+IJgiAIz5WkSHRJosjZ2Zn169dbFVAAX3/9tSqbLVs2AgICbAqoK1eu0Lp1ayWgBg8e/FQCatu2bbRq1Uol5X3zzTcJCQmxup7KaDTSr18/FixYoPbNmDHDbE1U8rK9e/dm8eLFgElArVixgk6dOqXbRkEQBEHfiIgSBEEQFBMmTFBT7RwdHfH396d58+ZWy/70009MmTIFMK0ZWrlyJe7u7lbLRkVF4e3tTXh4OAAeHh5MmzYt3fb5+/vTrVs3DAYDYMoptXnzZvLly2dR1mAw0KNHD/z8/JSNtkKTG41GevXqxS+//AKYzn3lypV06NAh3TYKgiAI+kfmtgmCIAgAzJ07lwkTJqjtJUuW0LZtW6tl/fz8GDp0qNqePXs2bdq0sVpW0zS6d++uckxVqFCBNWvWpHu++4wZM+jcubMSUK1atWLr1q1WBVR8fDzt27dXAsrJyYmVK1daFVCJiYl8+umnSkA5OTnh7+8vAkoQBEGwiYxEZSLnz59XC+MqVqz4os0RMhjxr7552fy7bt06+vfvr7Z/+uknunXrZrXs1q1b6dGjh9oeN24c/fr1s9n2pEmTWL9+PWCaXx4YGIibm1uabdM0jVGjRjF58mS1r3fv3syZMwcnJyeL8jExMbRu3ZqtW7cCpmmGa9euxdvbW5VJ8q+DgwOTJ09m+fLlgElArVq1yqZ4FOyDl+3+fdkQ/+obe/GviKhMJDo6WsW5F/SH+FffvEz+DQ0NpUuXLirx7MiRIxkyZIjVsocOHaJNmzZqNKhfv36MGzfOZtubNm1i7NixgGk63apVq3jttdfSbJvBYKBv375qnRLAmDFjmDBhgkVUPYDIyEg+/vhjdu/eDUCOHDnYvHkznp6eZuWio6OJjY1l0qRJBAUFAab1X6tXr6Z169Zptk/ImrxM9+/LiPhX39iLf0VECYIgvMQcPXqUli1bEh8fD0DPnj357rvvrJY9c+YMzZo1UwEd2rRpw8yZM62KGTCFIE+eV2nKlCk0a9YszbZFRUXRuXNnFWbdwcGBn3/+mQEDBlgt//DhQ5o2baqS7rq6uhIUFMSHH35oUTYhIYHRo0ezc+dOwCSg1qxZYzNBryAIgiAkR0KcC4IgvKScP3+eunXrqmAPH3/8MRs2bLC6VunatWvUqVOH69evA+Du7s6WLVvInj271bb/++8/3nvvPcLCwgDo2LEjK1eutCm4nuTq1au0bNmSY8eOAaZ8UitWrKB9+/ZWy9+7d48mTZqo8vnz5yckJIRatWpZlI2NjaVt27ZqBMrFxYU1a9bg4+OTJtsEQRAE/SEhzgVBEIRUuXXrFk2aNFEC6oMPPmD16tVWBdT9+/fx9PRUAurtt99m06ZNNgWUpmn06NFDCahq1aqxcOHCNAuo/fv306pVK+7evQuYfsQ2bNhA48aNbZ6Lh4cHp0+fBkzJfnfs2EGNGjUsykZFRdGyZUs1ApU9e3Y2btxI06ZN02SbIAiCIIBE5xMEQXjpePjwIV5eXly+fBmAqlWrEhgYSM6cOS3KRkVF0bx5c86cOQOYIutt2bKFvHnz2mx/xowZbNiwAYB8+fKxceNGcufOnSbblixZQsOGDZWAKl++PIcOHbIpoK5evUr9+vWVgCpRogS//fabVQH16NEjPD09lYDKnTs3W7ZsEQElCIIgpBsRUYIgCC8RMTExeHt7c+LECQBKly7Ntm3bKFCggEXZhIQE2rZty6FDhwAoVqwY27dvt5rUNonjx48zYsQIte3n50eFChVStctgMDBkyBA+/fRTlYy3UaNGHD58mNdff91qnQsXLlCvXj0uXLgAQJkyZdi3b5/VwBX379/Hw8OD/fv3A5A3b162b99uM6+VIAiCIKSETOfLRO7du4fRaMTR0ZFChQq9aHOEDEb8q2/06F+DwUCnTp3Yu3cvAIUKFWL79u2UKFHCoqymafTu3VuFCc+bNy8hISGULVvWZvsxMTF06tRJBakYPny4zUS9yYmIiKB9+/ZqhAhg4MCB/PDDDzajM50+fRoPDw9u3boFQKVKldi5cyevvvqqRdk7d+7g4eHByZMnAShYsCBr1qyhQoUK3Lt3Tzf+Ff6HHu9f4X+If/WNvfhXRFQmcuPGDRWiMSt/CYSnQ/yrb/TmX03T6Nu3L5s3bwZMkeu2bt1KpUqVrJb/7rvvWLp0KWBaNxQYGGh1ilxyvvzySzWt7s0332TSpEmp2nXmzBk+/vhjNZrk4uLC7Nmz8fX1tVnn2LFjNGnShHv37gGm6Yg7duygWLFiFmWvX79Oo0aNOHfuHGAaTduxYweJiYlcvXpVN/4VzNHb/SuYI/7VN/biX5nOJwiC8BIwevRolWvJxcWFTZs28c4771gtu2rVKkaPHq22V6xYYTVMeHKCg4OZNWsWYMrN5O/vbzPwRBKbNm2iVq1aSkAVLlyY0NDQFAXUwYMHadiwoRJQNWvWZM+ePVYF1L///ku9evWUgHr11VfZu3cvVatWTdEuQRAEQUgNGYnKREqVKqWGIwX9If7VN3ry788//6xyPzk4OLBixQo8PDyslv3999/p3r272p4yZQpt27ZNsf07d+7Qo0cPtf3jjz+mmFA3MTGR0aNHM2XKFLWvRo0aBAQEULp0aZv1tmzZQps2bYiJiQGgbt26BAcHky9fPouyYWFhNGrUiJs3bwKmABWhoaGqfT35V7BE/KtvxL/6xl78K3miBEEQdMyqVavo1KmT2p45c6bNZLXnz5/n/fff5/79+wD4+voyf/78VEOTe3t7ExgYCEDz5s0JDAy0WSc8PJxOnTqZrX/q0KEDixYtSjGC34oVK+jRoweJiYkAeHh4sHnzZqt1Tpw4gYeHhwrf/tprr7Fz506ra78EQRAEAdKvHURRCIIg6JRt27bRtWtXtT1mzBibAur+/fs0a9ZMCajGjRsze/bsVAXUtm3blIAqWrQoixcvtlln+/btVK9eXQkoJycnpk+fjr+/f4oC6ocffqBr165KQLVr146goCCrdQ4fPkyDBg2UgHrzzTf57bffREAJgiAIGYqIKEEQBB1y+PBhWrdujcFgAKB3795MmDDBatm4uDh8fHw4f/48AG+88Qbr1q2zGRkvCYPBwNChQ9X2tGnTKFKkiEW52NhYhg4diqenJ7dv3wZMgmvXrl0MHjzYpujSNI0vv/yS4cOHq339+/e3ud5q7969eHh48ODBAwBq167N7t27KVy4cIrnIQiCIAjpRdZEZSJJb03B9MZV0BfiX31jz/4NCwujadOmREVFAdCqVSvmzJljVaxomkbPnj3Zt28fYIpeZ2ud0ZPMnz9fReOrVauW2bTBJE6dOkWnTp1UXioAT09Pli5dajUYRBIGgwFfX18VIRBgwoQJjBkzxup5bN++nZYtW6r1Ug0aNCAwMJA8efJYbd+e/SukjvhX34h/9Y29+NeuRNSxY8eYMGEChw8f5uHDh5QqVYpOnToxfPhwcuXK9aLNs+DkyZMqRGNqoYEF+0P8q2/s1b/Xr1/H09NTTctr0KABK1eutPlDNH78ePz9/QHImTMnv/76a4rBHZKIiIhg7Nixanv69Olm88Y1TWP27Nl88cUXxMbGAqZQ6VOnTmXAgAEprk+Njo6mffv2BAUFAaZgGHPmzKFv375WywcGBtK2bVuVn8rLy4uNGzeSM2dOm59hr/4V0ob4V9+If/WNvfjXbkTU6dOnqVOnDpUrV2b69OkUKlSIvXv3MnHiRI4ePUpAQMCLNlEQBOGFEhERgZeXF1evXgVMEe82b95Mjhw5rJZftmwZEydOBExCxd/f32bY8ydZsGABERERAHTu3JnatWurY8eOHWPIkCEqqS+Ycjn5+/tTrVq1FNt98OABLVq0YP/+/QBky5YNf39/WrdubbX86tWr6dKli3pz6ePjw6pVq1INry4IgiAIz4LdiCh/f39iY2PZsGED5cuXB8Dd3Z1bt26xYMECHjx4QIECBV6wlebkyZMHg8GAs7PdXGYhHYh/9Y29+Tc6OpoWLVpw6tQpAMqVK0dISIjNaXm7d+82y8f0ww8/0LJlyzR/3saNG9Xf48ePB0yhzkeNGsWSJUtIHvh10KBBTJkyJcWRITAlWPT09FTnkCdPHgICAmjYsKHV8kuWLKFXr17qszp37szSpUvT5DN786+QPsS/+kb8q2/sxb9Z27pkJC1wfvKBIH/+/Dg6OpItW7YXYVaKlCtX7kWbIGQi4l99Y0/+TUhIoF27dhw4cAAwBW3Yvn27zTVHYWFhtGrVioSEBMAUrGHIkCFp/rybN2/y559/AqbRLk3TmDhxItOmTTMLD1uhQgVmzZqFp6dnqm2ePXuWJk2aqFG0IkWKEBISwltvvWW1/KxZsxg4cKDa9vX1Ze7cuWmeP29P/hXSj/hX34h/9Y29+NduovN169aN/Pnz069fP/7991/+++8/goKCmD9/Pv37908xPK4gCIJe0TQNX19fgoODAdMbvK1bt6oR+ycJDw+nadOmPHz4EICmTZsyffr0VEOZJycyMlL9ffz4cSpVqsS4ceOUgMqbNy/Tpk3j1KlTaRJQf/75Jx988IESUOXKlWP//v02BdTUqVPNBNTgwYOZP39+ll6ALAiCIOgLu0q2GxYWho+PD2FhYWrfoEGDrD4AWEuYdfXqVUqXLk3evHnVvri4ONVegQIFKFWqlFmd8+fPEx0dDWCxuO3evXvcuHEDMGVXTj6dMDExkZMnTwKmh5onVfWlS5d4/PgxYAonnHzI8uHDh1y5cgWAEiVKWITnPXHiBJqmkTNnTipVqmR27Nq1a2qdQuXKlc3WQkRGRnLx4kXA9Ja3ePHiZnVPnz6tFvK9/vrrZsdu3brF3bt3AShfvjyurq7qWGxsLGfPngXAzc2NV1991azuuXPniImJwcHBgerVq5sdCw8P5+bNmwCULl2a/Pnzq2MGg0FN68mbNy9ly5Y1q5skpsG03iL5A9SDBw/UA9krr7xCoUKFzOoeP34cgFy5clGxYkWzY1evXlUhkqtUqWK2tuLx48dcunQJML3tf/JN/6lTpzAYDGTPnp0qVaqYHbt586bKXVOhQgUz4R8dHa3CSxcsWJCSJUua1T179iyxsbE4OTlRtWpVs2N3797l1q1bAJQpU8ZstDY+Pp4zZ84AplHcMmXKmNW9ePGieiCuVq2a2WL/+/fvc/36dQBKlixJwYIF1TGj0cg///wDgKurq8UD++XLl3n06BFgSnSafKT40aNHXL58GYDixYtbhMQ+efIkiYmJ5MiRg8qVK5sdu379ugqYULFiRbOAMlFRUVy4cAGAwoULW+QFCgsLIy4uDmdnZ9544w2zY7dv3+bOnTsAlC1b1q76iIULFzJ79mzAtH4oJCSEggULWu0jYmJi+OCDD/jrr78AqF69Or///ruKYJfWPiIuLg5PT08lxJJwdHSkVatWTJ061ex+TamP2L59Oz4+PmbXMCQkRN1byfuIUqVK8dNPP/HNN9+o+r169aJ///7ky5dP+gjpI6SP+P/Ic4QJeY74H9JHmEipj4iMjDSLDAgpJ9u1m+l8ly9fpkWLFhQtWpT169dTuHBh/vjjDyZNmkRkZCSLFy9OtQ2DwcCTmlHTNDWlJSmfypN1ko4/idFoVMeMRqPF8bS2+6RNydt90plJ7WqaZjWHS2Ji4jO1a+tck7f75Lkmv4bW2k06V2tvutPablbxTWrnmpCQgMFgsHrDpeSbtLSbkJBg9VhK7SbVTa1da6T1Glqrn9ymJ0ntXOPj4zEajVZHFTLiGlq7RmltN6t8D5Pa9fPzUwIqKTBEw4YNOXr0qEUfYTQa6datmxJQhQsXZv369WYhwNPaR2TPnp3AwED69+/P7du3qVChAu7u7rzzzjsWP5RJ9ltrd9WqVXTr1k0de/vtt9m1a5fZD3iSbzRNY/To0cyZM0cdmzhxIh999BEGgyHL+Eb6CMt2pY+Q54gn25XnCOkjkreblfqI9GA3ImrkyJE8fvyYv//+Wynv+vXrU6hQIXr27EnXrl358MMPU2zD2dnZ4gZ0cHBQnYi1BWzOzs42E046OjqqY9a+7I6OjmiapsL72mr3SZuSt2vtC+Di4oKmaVbtdXJyeqZ2k/9vq90nzzX5NbTWbtK5Wuv80tpuRvsmre2m9H159OgR0dHRODs7q7dbSeeZ2jVMqV1bvklMTLR6LKV2k5+rrXaf9Rqmdq5Pktq5ZsuWjcTExEy5hkajMc33zaVLlzAYDFnye+jo6EhISAgzZsxQ++bOnasi2FnrI0aNGsW6desAUyjzmTNnWrztTU8fUa9ePbPcT8nfMqelj/j5558ZPHiwKuPu7s6UKVMs1r06OTnh5OTE5MmTlf1gCqnev39/9ZY5vb4JDw/HwcEBBweHTOsjbF1D6SMyv49ITEzk2rVrZM+eXfXPGd1HWLM3K/URen6OSOqfnZ2dcXV1tdvnCOkjrH9fLl26RFRUFI6OjlY/MzOfI9KD3Uznq1KlCsWLF2f37t1m+0+ePEm1atWYNWsW/fv3V/utTedLaUguMzh+/LhdxLkXng7xr77Jyv4NDg7G29tbvYGbOHEiY8aMsVl+0aJFKhKfo6MjgYGBNGvW7LnY+iSapjFmzBi+/fZbtS+loBAGg4GePXuyYsUKwPQjt2DBAnr16vVMdmRl/wrPjvhX34h/9c2L8m96tYPdBJYoUaIEp06dMlvQDHDw4EEAi7mfgiAIeuTgwYO0bdtWCaj+/fszevRom+X37t1Lv3791PbPP//8wgSUwWCgT58+ZgJq9OjRNoNCxMfH07FjRyWgnJyc8PPze2YBJQiCIAjPit2MRAUGBtKyZUtq1arF559/TqFChTh06BCTJ0+mVKlSHDt2zGzRWVYYiUpag+Xg4JDlY90L6Uf8q2+yon8vXLhA7dq11aLYdu3a4e/vbzMq3dWrV3nnnXfUQuTBgwczffr052ZvcmJjY+nUqRObNm0CTCNKM2bMMIuy92T5Nm3aqKiDLi4urFmzBh8fnwyxJyv6V8g4xL/6Rvyrb16Uf9OrHexGRIEpOeSUKVM4ceIEjx494tVXX6VFixZ89dVXFguZs4KIEgRByCju37/P+++/r6IvNWrUiODgYLOoT8mJjo6mXr16KpBE48aN2bJlywt54Lh37x4tW7Zk//79gEkQLV++nA4dOlgtHxkZibe3N7t27QIgR44cbNq0CS8vr+dmsyAIgvByoWsRlR5ERAmCoBfi4uJo3Lgx+/btA0zhjPfv328RhCEJTdPo3Lkzq1atAkx5l/7880/c3Nyem81JnDt3jqZNm6qwyLlz52bTpk00btzYavlHjx7RtGlTlTjY1dWVoKCgVAMHCYIgCMKzkF7tIGOggiAIWRhN0+jZs6cSUEWLFiU4ONimgAKYNm2aElC5c+cmICDghQiovXv34uPjo3LOFCtWjKCgIGrWrGm1/L179/Dy8uLo0aMA5M+fn61bt1K7du3nZrMgCIIgpAURUZnIw4cPMRqNODo6miV/E/SB+FffZBX/jh8/Hn9/f8AUmvzXX3+ldOnSNstv27aNkSNHqu0VK1ZYJFZ8HqxcuZKePXsSHx8PmJIwBgUFWSQiTeLKlSt4enqqhJuFChVix44dvPnmm5liX1bxr5A5iH/1jfhX39iLf0VEZSJXrlxRIRqz8pdAeDrEv/omK/h3+fLlTJw4EfhfMt13333XZvkLFy7QoUMHldRw3LhxGRaIIa1omsY333zDuHHj1D5PT0/Wrl1L3rx5rdY5deoUnp6e3LhxAzBFY92xYwevv/56ptmZFfwrZB7iX30j/tU39uJfWSAkCIKQBdmzZ49ZKO8ffviBli1b2iz/33//4e3tzcOHDwFo2bIlY8eOzXQ7kxMfH0/37t3NBFSfPn349ddfbQqoAwcOUK9ePSWgKlWqxIEDBzJVQAmCIAjCsyIjUZlIiRIlbGaHFuwf8a++eZH+DQsLw8fHh4SEBAA+++wzhgwZYrO8pmn06NGD06dPA/D666+zfPny5xpIJyIigtatW7Nnzx617/vvv2fYsGE2s8AHBwfTtm1bYmJiAHj33XcJDg6mcOHCmW6v3L/6Rvyrb8S/+sZe/CvR+QRBELIQ4eHh1KpVi0uXLgHQtGlTAgICUgxN/v333/Pll18CkC9fPv78808qVqz4XOwFuHjxIs2aNVPrmXLkyIGfnx+tW7e2WWfZsmV8+umnKmlw48aN2bhxI66urs/FZkEQBEFITnq1gygKQRCELEJMTAze3t5KQNWoUYPVq1enKKB27dplFkjCz8/vuQqoAwcOULt2bSWgihQpwp49e1IUUN9//z3du3dXAqpDhw4EBQWJgBIEQRDsBhFRgiAIWQCj0Uj37t05ePAgYJrOEBQURJ48eWzWuXbtGu3bt1eBJMaMGUPz5s2fi70Aa9euxd3dnXv37gHw2muvcejQIWrVqmW1vNFoZPjw4WrUDGDgwIGsXLmSbNmyPRebBUEQBCEjEBElCIKQBRg1ahRr164FTLmdgoODKVmypM3ycXFxtGnTRgkYLy8vs4AOmYmmaUyZMoX27dsTFxcHgLu7OwcOHKBs2bJW6yQkJNC9e3d++OEHtW/SpEnMmDFDplkLgiAIdocElshETpw4oUI0Vq9e/UWbI2Qw4l998zz9u2jRIqZMmQKAo6Mja9asSTU/0qBBgzh8+DAAZcuWZeXKlc9lEW5CQgL9+vVj8eLFal+PHj2YN2+ezdGkqKgo2rVrx5YtWwDTOc6bNw9fX99Mt9cWcv/qG/GvvhH/6ht78a+IqExE0zT1T9Af4l9987z8u2PHDvr27au2f/75Z5o1a5ZinSVLlrBgwQLAFMRhw4YNuLm5ZaqdAI8ePaJNmzbs3LlT7fv222/56quvbEbgi4iIoFmzZhw6dAiA7Nmzs2rVqueev+pJ5P7VN+JffSP+1Tf24l8RUZlIzpw5cXFxSXFRuGC/iH/1zfPw78mTJ2nTpo0KsDBkyBD69++fYp0zZ84wYMAAtT1//nzeeuutTLMxiStXrtC0aVMVRj179uwsXbqUDh062Kxz/fp1PD09VZ28efMSGBjIhx9+mOn2pobcv/pG/KtvxL/6xl78KyHOBUEQXgC3b9+mVq1aXL16FQBvb282bNiQ4pS8uLg4ateuzd9//w2YEtnOmzcv0209ePAgPj4+3LlzB4CCBQsSEBBA3bp1bdY5c+YMnp6eXLt2DYCiRYsSEhKS6jRFQRAEQXgRSIhzQRCELE50dDQtWrRQAqpmzZppWtM0ZswYJaBee+01fvzxx0y3dfHixTRo0EAJqIoVK3Lo0KEUBdQff/zBBx98oARU+fLlOXDggAgoQRAEQTeIiBIEQXiOJCYm0qVLF44cOQJAqVKl+PXXX8mdO3eK9UJDQ/n+++8BcHFxwd/fn1y5cmWanQkJCQwYMIBevXoRHx8PQIMGDTh48CAVKlSwWS8kJAR3d3ciIiIAeOutt9i/fz/lypXLNFsFQRAE4XkjIkoQBOE58uWXX7Jp0ybAtEYoODiY4sWLp1jn/v37dOvWTW1Pnjw5U0d1wsPDady4MbNnz1b7Bg4cyPbt2ylYsKDNeitXrqRFixZER0cD0LBhQ/bs2UPRokUzzVZBEARBeBFk7RVbds61a9dITEzEycmJV1999UWbI2Qw4l99kxn+nTNnjpqC5+TkxLp166hatWqKdTRNo3fv3ty4cQOARo0a8fnnn2eIPdb4+++/8fb2VlMNs2XLxrx58+jRo0eK9aZPn25mV+vWrfHz8yNHjhyZZuuzIPevvhH/6hvxr76xF//KSFQmEhERwb1799S0FkFfiH/1TUb7d8uWLQwcOFBtz507lyZNmqRab8mSJWzcuBEANzc3li1blmkBclavXk2dOnWUgCpevDi//fZbigJK0zS++uorMwHVt29f1qxZk2UFFMj9q3fEv/pG/Ktv7MW/IqIEQRAymePHj9O+fXuMRiNgmtKXlkSz586dY9CgQWp70aJFvPLKKxlun8FgYOTIkXTs2JGYmBgAatWqxZEjR6hdu3aK9QG7if0AACAASURBVHr16qUSBQOMGzeOOXPmPJfEv4IgCILwopAQ55lIbGwsmqbh4OCQpd/ICk+H+FffZJR/b9y4Qa1atdR0vDZt2rBmzZpU+6KEhATq1KmjAlD4+vqqBLsZSXh4OB07diQ0NFTt69GjB3PmzEnxvGNiYujQoQOBgYEAODg4MGvWLD777LMMtzEzkPtX34h/9Y34V9+8KP+mVzvImqhMRG5sfSP+1TcZ4d/IyEiaN2+uBFStWrVYvnx5ml7mjB8/XgmoSpUq8dNPPz2zPU/y559/0rp1axWK3NnZmR9//JEBAwbg4OBgs97Dhw/5+OOP2bdvH2CKFujn50e7du0y3MbMQu5ffSP+1TfiX31jL/4VESUIgpAJJCYm0qFDB5XXqWzZsgQGBpIzZ85U6+7du5fJkycDJmGzcuXKVEOgp5dFixbRv39/Fb68aNGirFu3jnr16qVY7+bNm3h5efHPP/8A4OrqyubNm2nUqFGG2icIgiAIWRkRUYIgCJnAiBEjCA4OBiB//vwEBwdTpEiRVOs9fPiQLl26kDTT+ptvvuGdd97JMLtiY2MZOHAgixYtUvvq1KnDunXrKFGiRIp1z507h6enJ5cvXwagcOHCbN26lZo1a2aYfYIgCIJgD4iIykQiIyMxGo04Ojri6ur6os0RMhjxr755Fv/6+fnxww8/AKaRpA0bNvDaa6+lqe7IkSPV9LoPP/yQL774In2Gp8DVq1dp3bq1miYI0L9/f3788UeyZcuWYt2jR4/y0UcfER4eDkCZMmXYvn07FStWzDD7nidy/+ob8a++Ef/qG3vxr4ioTOTixYskJCTg4uJCjRo1XrQ5QgYj/tU3T+vfI0eO0KtXL7X9888/4+7unqa6x44dU8EjXF1dWb58eYZFuQsICODTTz/l/v37gGnO+YIFC/jkk09Srbtz5058fHyIjIwEoFq1aoSEhKQ6cpWVkftX34h/9Y34V9/Yi38lxLkgCEIGcefOHXx8fIiLiwOgd+/e9O3bN011NU1j4MCBahrf2LFjKVWq1DPbFBUVRd++fWnZsqUSUGXLluXgwYNpElB+fn40bdpUCah69eqxd+9euxZQgiAIgvCsyEhUJlKkSBGVcVnQH+JffZNe/8bHx9O6dWuuX78OQN26dZk5c2aKUe6S4+/vz/79+wFTNL7Bgwc/neHJ+Ouvv+jUqRNnz55V+7y9vVmyZAlubm4p1tU0jYkTJzJ+/HizuqtWrUpTcIysjty/+kb8q2/Ev/rGXvwreaIEQRAygL59+zJ//nwAXnnlFY4cOUKxYsXSVPe///6jcuXK3Lp1C4CtW7fi5eX11LYYjUZ++OEHRo0aRUJCAgC5cuVi+vTp9OrVK1VhFxcXh6+vLytWrFD7+vTpw6xZs3B2lndvgiAIgv6QPFGCIAjPmXnz5ikBlT17djZv3pxmAQXw3XffKQHVokWLZxJQ169fp1u3buzatUvtq1mzJitXrqRy5cqp1o+IiKBVq1b89ttvgCmJ7tSpUxk2bFiaR9UEQRAEQe/ISJQgCMIzsG/fPtzd3TEYDAAsX748TWuNkjh//jxVq1YlPj6ebNmycfr0acqXL/9UtmzYsAFfX18ePHgAmATQiBEjmDBhQqrR98C0mLdZs2Zq+l+OHDnw8/OjdevWT2WPIAiCINgLMhIlCILwnLh27Rpt2rRRAmro0KHpElBgCiCRlPB2+PDhTyWgIiMjGTx4MEuWLFH7SpYsyYoVK2jQoEGa2jhw4ADe3t7cu3cPMM1JDwwMpFatWum2RxAEQRD0joxEZSKnT59WIRpff/315/a5wvNB/KtvUvNvdHQ09erV46+//gKgcePGbNmyJV1rhi5dukSFChUwGo0ULlyYS5cukTt37nTZefjwYTp37syFCxfUvrZt2zJ//nwKFCiQpjbWrFlDt27dVFTB1157jS1btlCmTJl02WJPyP2rb8S/+kb8q29elH/Tqx1kblsmkpCQoP4J+kP8q29S8q+mafj6+ioBVa5cOVavXp3uoAs//vgjRqMRgEGDBqVLQMXHxzNp0iTq1KmjBFTu3Ln55ZdfWLNmTZoElKZpTJ48mQ4dOigB5e7uzoEDB3QtoEDuX70j/tU34l99Yy/+lel8mYiLi4vZ/4K+EP/qm5T8++OPP+Lv7w+YhEtAQECqIcOf5N69eyxevBgwRc777LPP0lx3+/btDB48mLCwMLXvvffeY+XKlVSoUCFNbSQkJNCvXz9lA0CPHj2YN29emtZP2Tty/+ob8a++Ef/qG3vxr0znEwRBSAe7d+/Gw8NDjSBt3LgRHx+fdLczf/58lYh30KBBzJgxI9U6//77L8OGDWPz5s1qn6OjI6NGjWLMmDFp/sF59OgRbdq0YefOnWrft99+y1dffSUR+ARBEISXEt1P5/v9999p2rQpBQoUIGfOnFSsWJFvvvnmRZslCMJLwLVr12jfvr0SUKNHj34qAQWwbds29XdqwSiio6MZO3Ysr7/+upmAql27Nn/88QcTJ05Ms4C6cuUKderUUQIqe/bsrF69mq+//loElCAIgiCkEbuazufv788nn3xCu3btWL58Oa6urly8eJGbN2++aNMEQdA5cXFxtGnThvDwcAA8PT0ZP378U7WVkJCgREyhQoV4++23rZYzGo2sW7eOL774gmvXrqn9xYoV4//+7//o0qVLukbX//zzT1q0aMGdO3cAKFiwIAEBAdStW/epzkMQBEEQXlbsRkTduHGD3r1706dPH+bMmaP2N2zY8AVaJQjCy8LgwYM5fPgwAGXKlMHf3x8nJ6enauvGjRtqysD7779vIYRiY2Px8/Pj+++/59y5c2q/i4sLQ4YMYfTo0eTNmzddn7lp0yY6d+5MTEwMAJUqVSI4ODjNa6gEQRAEQfgfdiOiFi1aRFRUFCNGjHjRpqSZW7dukZiYiJOTE8WLF3/R5ggZjPhX3yT3b0hICPPnzwdMCWg3btyY7kASycmXL5/6OykvU3x8PAcOHCAkJISlS5eq0aIkPD09mTFjBpUrV07XZ2maxk8//cTw4cNJWgJbv359Nm3a9EznYO/I/atvxL/6Rvyrb+zFv3Yjovbu3YubmxthYWF4e3tz8uRJ3NzcaNWqFVOnTk33W9nnwd27d1Wc+6z8JRCeDvGvvkny7/nz5+nXr5/aP2/ePN56661najtv3rw4OTmRmJjIwYMHyZEjB46OjmqUKDkNGzZkxIgRNGnSJN1rlgwGA4MGDWLu3LlqX5cuXVi0aBHZs2d/pnOwd+T+1TfiX30j/tU39uJfuxFRN27cIDo6mrZt2/LVV18xffp0/vzzT8aNG8fJkyfZt29fqg8Yp06donTp0maCKy4uToUJLlCgAKVKlTKrc/78eaKjowGoUaOG2bF79+5x48YNAEqVKmWWlyUxMVHFtzcYDBa2XLp0icePHwPwxhtvmOWXefjwIVeuXAGgRIkSFC5c2KzuiRMn0DSNnDlzUqlSJbNj165dIyIiAoDKlSuTI0cOdSwyMpKLFy8CUKRIEYsvZkrJzW7dusXdu3cBKF++PK6urupYbGwsZ8+eBcDNzY1XX33VrO65c+eIiYnBwcGB6tWrmx0LDw9Xa9pKly5N/vz51TGDwcCpU6cA00Nn2bJlzer++++/akpU1apVzaZWPXjwgKtXrwLwyiuvUKhQIbO6x48fB0yhpStWrGh27OrVqzx48ACAKlWqmD1sPn78mEuXLgEmHz/JqVOnMBgMZM+enSpVqpgdu3nzplpPU6FCBbOcQNHR0Zw/fx4wrVMpWbKkWd2zZ88SGxuLk5MTVatWNTt29+5dbt26BZimmSUf5YiPj+fMmTOAafTjydw/Fy9eJDIyEoBq1aqZTSu7f/8+169fB6BkyZIULFhQHTMajfzzzz8AuLq6Ur58ebN2L1++zKNHjwBT4tbkIbMfPXrE5cuXAShevDhFihQxq3vy5EkSExPJkSOHxajL9evXuX//PgAVK1YkV65c6lhUVJTKl1S4cGFKlChhVjcsLIy4uDicnZ154403zI7dvn1bjfyULVtW9REPHz5k2LBhKodSly5d6Natm1ndp+kjnJycmDBhAqNHjwZQ7Sfh6OiIl5cXnTp1omrVqrzxxhtm/Vta+ojIyEi++uor9u7dq/aPHz+eHj16qD7vZe4jkoKDJCQkcO/evUzpI4oWLUqxYsXM6kofYSKz+whr+WUyo4+AzH2OOHnyJGCKEFauXDmzuvIcYcKenyOkj7DdR4Cpfz5+/Phze45Iuk/Tit2IKKPRSGxsLOPGjWPkyJEANGjQgGzZsjFkyBBCQ0Px8PBIsQ2DwcCTEd01TUtR7BgMBpvJvoxGozqW9INsjeQOstbukzYlb9fag3pCQgKaplmNxpVcvD1Nu7bONXm7T55r8mtord2kc7UmctPabkb7Jq3tpvR9KViwIAULFjTrMBISEjAYDFYX+6fkm9SuYZJvrB1Lqd3k55pen6f1Glqrn9ymJ0ntXOPj4zEajVbXG2XENbR2jay1W6ZMGT7//HP1w1KtWjVGjRplUfdpv4cjRowgMjKSrVu3Eh0dTWJiInXq1MHLy4vGjRvz6NEjHj16ZNXm1O7l69evM2TIEPWD6uLiwuLFi/nkk0+4fPmy9BGYHgCTfJtZfYStayh9xPPpI0qVKmX2+5vRfYS1drPKb5XenyPKly+P0WjE0dGRyMhIu32OkD7Ceh9Rvnx5rl+/bubb5GTmc0R6sBsRVbBgQc6fP4+np6fZ/o8++oghQ4bw119/pSqinJ2dLX6kHRwcVCeS/C1O8jq2Qgc7OjqqY9a+7EnHrE2bSd7ukzYlb9faF8DFxQVN06za6+Tk9EztJv/fVrtPnmvya2it3aRztfaAlNZ2M8s3qbWb0vclZ86cFtNIk84ztWuYUru2fJM0Pzg97SY/V1vtPus1TO1cnyS1c82WLRuJiYmZcg2NRmOa75upU6eye/duwPRmdNq0aVZfiDzt99DBwYEOHTrQoUMHq2+Zo6KinupePnbsGN27d1dvKwsUKMCmTZv48MMPbZ5rWtoFffURuXLlyvQ+wtY1lD7i+fQRrq6uZvdsRvcR1trNKr9Ven+OSD6KFRMTY7fPEdJHWP++uLq6kiNHDotZGklk5nNEerCbZLt9+vRhwYIF/PXXX2brEc6ePUuVKlX4/vvvGT58uNovyXYFQXhaAgICaNmyJWDqcENDQ5UIycoEBQXRoUMHoqKiAChXrhxbtmxJdzAKQRAEQXjZ0G2y3datWwOwdetWs/1btmwBTEknBUEQnpV///2Xrl27qu2pU6fahYCaNWsW3t7eSkDVqVOHQ4cOiYASBEEQhEzAbqbzNWnShBYtWjBx4kSMRiO1a9fmyJEjTJgwgebNm/PBBx+8aBMtiI2NRdM0HBwczBZmCvpA/Ks/EhIS6NSpk1qs3aZNG7PIfFmRxMREhg0bxowZM9S+9u3bs3TpUvlepoDcv/pG/KtvxL/6xl78azfT+cA073XChAn4+/tz69YtSpQoQefOnRk3bpzFuqOsMJ3v+PHjKkrNkxF5BPtH/Ks/Ro8ezbfffgvAq6++yooVK8ifP3+W9W9kZCSdO3cmMDBQ7fv666/55ptvZOpyKsj9q2/Ev/pG/KtvXpR/06sd7GYkCkwL+adMmcKUKVNetCmCIOiMPXv28N133wGmRcGTJ082Cx+b1fj3339p2bKlChHr7OzM/Pnz6dmz5wu2TBAEQRD0j12JKHvDzc3NZiQUwf4R/+qHiIgIunTposKbTpo0ifr162dZ/4aGhtKuXTuVyyVfvnysX78+1Qilwv+Q+1ffiH/1jfhX39iLf+1qOl96yArT+QRByPpomkabNm3YuHEjAO7u7uzYsSNL9hWapjFjxgyGDx+ucmNUrlyZgIAACSAhCIIgCM+ArqfzCYIgZDQLFy5UAqpgwYIsX748Swqo2NhY+vbty7Jly9S+Zs2asXLlSrPs8oIgCIIgZD5Z70lBEAThOXHmzBmGDBmithcvXswrr7zyAi2yzo0bN6hfv76ZgPr6668JCAgQASUIgiAILwAZiRIE4aUkLi6Ojh07EhMTA0C/fv3w9vZ+wVZZcuDAAVq3bs3t27cByJUrF0uXLqVt27Yv2DJBEARBeHkREZWJnDt3DoPBgLOzM5UqVXrR5ggZjPjXvhk5ciTHjx/n/7V3//E53ff/x5+XJMgP+SlEaKkf8zto1431o+NWwY2tQ2dtTVWVVfUH2i6r0eKm1O/Z2mF+tJgyqnStNrTqx2ZDWbGEUvFjiTLSJH7kF7lyne8fvs5cEuQiV07OyeN+u+Umzvs67/O6rtf1Piev633OuSSpVatWmjlzpld7ZcjvokWLNGLECBUVFUmSGjVqpA8//JBb+paDypBf+A/5dTby62x2yS9FlB8VFBSY97mH85Bf+0pOTtacOXMkSTVq1NDKlSsVEhLi9Rgr81tUVKTRo0frj3/8o7msa9euWr16tWrXrl3h8TgR49fZyK+zkV9ns0t+uSbKj1wul/kD5yG/9nTmzBkNHjzY/P+MGTOUkJBQ4nFW5TczM1OJiYleBdSLL76ojRs3UkCVI8avs5FfZyO/zmaX/HKLcwBVhsfjUe/evbVhwwZJUq9evbR+/fpKs6PevXu3HnnkEWVkZEiSqlevrvnz5+upp56yODIAAJzN19qBigJAlfGHP/zBLKDq1q2rd999t9IUUAsXLtT//d//mQVUvXr1tG3bNgooAAAqIYooAFVCamqqfvOb35j/X7ZsmerUqWNhRFcUFhZq6NCh+tWvfqXLly9Lkh544AHt2bNHHTt2tDg6AABQGoooAI5XXFysp59+2ixSXnrpJXXv3t3iqKT09HR17txZixcvNpe98MIL2rx5s+Lj4y2MDAAA3Ax35/OjzMxMFRcXKyAgQLGxsVaHg3JGfu1jzpw5+vLLLyVJLVq00OTJk2+5jr/zu2nTJj322GPKysqSJAUHB2vBggUaOHBguW8LJTF+nY38Ohv5dTa75Jciyo9OnTpl3qKxMr8JcHvIrz2kpaVp3Lhxkq7c8Wfx4sWqWbPmLdfzV34Nw9C0adM0duxYeTweSVLjxo21du1avv+pAjF+nY38Ohv5dTa75JciCoBjeTweDR06VIWFhZKunCr3ox/9yLJ4Lly4oMGDB2vdunXmsl69emn58uWKioqyLC4AAOAbiig/atiwoTweD7dVdyjyW/ktWLBA27ZtkyQ1atSoTKfxXVXe+f3666/Vt29fHT58WNKVWbHx48frtdde4z1kAcavs5FfZyO/zmaX/PI9UQAcKSMjQ61btzb3A5999pkSExMtiWXVqlUaOnSocnNzJUmRkZF677331KtXL0viAQAA3nytHZiJAuA4hmHomWeeMXeGQ4YMsaSAys3N1QsvvKAlS5aYyxISErR27Vo1adKkwuMBAADlg2kZAI6zatUqJScnS7rypbWzZs2q8Bj27Nmje++916uAeuKJJ7Rjxw4KKAAAbI4iyo/cbreKiorkdrutDgV+QH4rp/z8fCUlJZn/nzt3riIjI33u53bz6/F4NH36dHXq1ElHjhyRJIWFhWnZsmVatmyZQkJCfI4F5Y/x62zk19nIr7PZJb+czudHBw4cMG/RyK2LnYf8Vk4zZ85URkaGJKlnz57q06fPbfVzO/k9deqUBg0apC+++MJc9oMf/EArVqxg9qmSYfw6G/l1NvLrbHbJLzNRABzj5MmTmjZtmiQpICBAs2fPrrBtf/TRR0pISDALKJfLpTFjxmj79u0UUAAAOAwzUX4UHh4ut9utwEBeZiciv5XPmDFjlJ+fL0kaMWKEWrZsedt9lTW/BQUFeuWVVzR37lxzWf369fXnP/9ZXbt2ve3tw78Yv85Gfp2N/DqbXfLLLc4BOMKuXbvUsWNHSVJUVJTS0tIUHR3t122mpKTo8ccf14EDB8xlffr00aJFixQTE+PXbQMAgPLja+1ARQHA9gzD0KhRo8z/T5w40a8FlGEYevvtt3X//febBVRwcLDmz5+vtWvXUkABAOBwlXueDADK4MMPP9TOnTslSS1bttTw4cP9tq3MzEwNGTJE69evN5clJCRo5cqVatWqld+2CwAAKg9mogDYmmEY5s0kJGn69OkKCgryy7Y+/fRTJSQkeBVQI0eO1K5duyigAACoQpiJ8qNjx46ZF8Y1btzY6nBQzshv5bB9+3bt2rVLktS2bVv17t27XPq9Nr8REREaNWqUli9fbrbHxsZqyZIl6tWrV7lsDxWL8ets5NfZyK+z2SW/FFF+dPHiRfM+93Ae8ls5TJ8+3fw9KSlJLperXPq9ePGiLl++rC1btmjmzJnKzMw023r06KElS5YoLi6uXLaFisf4dTby62zk19nskl+KKAC2dfDgQfPUurvuukuPPvpoufWdmZmpyZMna+vWreayyMhIzZ49W4MHDy63Yg0AANgPRZQftWnTxuoQ4Efk13ozZ840fx89enS5fGplGIaWLFmil156SefOnTOX9+nTR3PnzlW9evXueBuwHuPX2civs5FfZ7NLfvmeKAC2dPnyZUVHRysvL08RERHKyMhQrVq17qjPo0eP6tlnn9Xnn39uLouNjdXbb7+t/v37M/sEAIBD8T1RAKqEf/zjH8rLy5MkPfzww3dUQJ0/f15JSUlq2bKlVwE1cOBAHTx4UL/4xS8ooAAAgInT+QDY0oYNG8zfe/bseVt9FBcX65133tG4ceN09uxZc3n9+vX1pz/9qdzu9AcAAJyFIsqPcnJy5PF4VK1aNUVFRVkdDsoZ+bXWxo0bJUkul0uJiYk+r79161aNGjVK+/fvN5fVqFFDL7/8sl599VW53W5lZWWRX4di/Dob+XU28utsdsmvrYuoRYsWadiwYQoNDVVubq7V4ZSQnp5u3qKxMr8JcHvIr3XOnTtnFj/33nuvYmNjy7zu3r17NWnSJK1bt85ref/+/TVt2jTdc889kqT9+/eTXwdj/Dob+XU28utsdsmvbYuob7/9Vq+88ori4+N1/vx5q8MBUIHcbrf5e1nulmcYhjZt2qTp06dr06ZNXm0dOnTQnDlz9OCDD5Z7nAAAwJlsW0QNHz5cDz74oKKjo7VmzRqrwylV/fr1zelIOA/5tU716tXN3282C11UVKT3339fM2bM0L59+7za6tatqylTpujJJ59UQEBAiXXJr7ORX2cjv85Gfp3NLvm1ZRG1fPlybdu2TQcPHtS4ceOsDueGateubXUI8CPya52QkBBFRUUpJydHO3bs0M6dO9WxY0dJV04D2LhxozZs2KBNmzbpwoULXus2adJEL7/8sgYPHqzg4OAbboP8Ohv5dTby62zk19nskl/bFVFnz57VqFGjNHXqVDVo0MCndQ8cOKCGDRsqPDzcXHbp0iUdOnRIkhQVFaW7777ba50jR44oPz9fktSuXTuvtu+++07ffvutJOnuu+/2Om+zuLhYqampkq7cY75x48Ze6x4/ftz8465169YKDPxfKs6dO6f//Oc/kqT4+PgS13v8+9//lmEYCg4O1ve+9z2vtoyMDGVnZ0uSmjdvrpo1a5ptubm5Onr0qCSpTp06JU6DOnjwoHkOaqtWrbzaTp8+bd69rEmTJgoLCzPbCgsLdfjwYUlSdHS07rrrLq91v/nmGxUUFMjlcikhIcGrLTMzU6dOnZIkNWzYUJGRkWab2+3WgQMHJEnh4eHmtSpXHTt2zLyff5s2bbxmE3JycpSeni7pyica1w/Iq9fThISEqFmzZl5t6enpysnJkSS1aNFCNWrUMNsuXLig48ePS7oykxEXF+e17oEDB+R2u1WjRg21aNHCq+3UqVPKzMyUJDVt2lShoaFmW35+vo4cOSJJiomJKfHePnz4sAoLCxUQEFDiS+jOnj2r06dPS5IaNWqkiIgIs+3y5cv6+uuvJUkRERFq1KiR17pHjx41Z3Latm3r9alPVlaWTp48KUlq0KCBYmJizDaPx6OUlBRJUlhYmJo0aeLV74kTJ8zTbFu2bOk1c3T+/HmdOHFC0pVT8erUqeO1bmpqqoqLi1WzZk01b97cq+3kyZPKysqSJD322GOaN2+eLl26pE6dOikoKEhBQUHmeL1e27ZtNWjQIHXv3r3E+/C///2vzpw5I0m655572EeIfQT7iCvsvI9o1qyZQkJCzLa8vDylpaVJuvL9b/Hx8V7rHjp0SJcuXVJgYKBat27t1cY+4gr2Ef/DPuIKJ+0jbvT3w43YrogaMWKEmjdvrmeffdbndd1ut67/bmHDMFRUVGS2l7bO1fbreTwes83j8ZRoL2u/18d0bb/FxcWl9msYhoKCgkq0FRcX31G/N3qu1/Z7/XO99jUsrd+rz7W079kpa7+VJTe3eq5FRUVyu92lTkHfLDdl6beoqKjUtpv1e3XdW/VbmrK+hqWtf21M17vVc718+bI8Hk+pp9hd2+/YsWO1c+dO7d2794bPJSYmRomJiXrmmWcUHR1t9n2zftlHsI+Q2Edc329pKvs+4nZfw9JeI/YRZe+XfQT7iKvsuI/wha2KqA8++EAff/yx9u7de1tffBkYGFhiPZfLZe5Erv0U59p1StvJSFK1atXMttLe7GXt9/qYru23tDdAUFCQDMMotd+AgIA76vfaf2/U7/XP9drXsLR+rz7X0nJW1n4rS25u9VyvPs9bvYa3029xcXGpbTfr9+q6N+v3Tl/DWz3X693quVavXl3FxcW37DcqKkp///vftXTpUq1evVo5OTnKy8tTrVq11K1bN/Xv31/33XefuY1Dhw7d1ripjO9D9hEl+60suWEfUbJfq/YRt/Maejwe9hHsI8y+2Ef8b92b9eukfYQvXIavZZdFcnNz1bRpUw0cONDrOqgRI0boo48+0smTJxUUFGRObXo8HnOK9qpatWpV6EVq194i+fopfNgf+XU2698HlgAACwNJREFU8uts5NfZyK+zkV9nsyq/vtYOlfu2F9f47rvvdObMGc2aNUtRUVHmz8qVK5WXl6eoqCj98pe/tDpMAAAAAA5nm9P54uLitGXLlhLLp06dqm3btik5ObnS3c0jJCREbre71Kle2B/5dTby62zk19nIr7ORX2ezS35tczrfjQwePFhr1qwp8V0xleF0PgAAAACVn2NP5wMAAACAysD2M1E3wkwUAAAAgLJgJgoAAAAA/KhyX7Flc+np6eaFcdd/gznsj/w6G/l1NvLrbOTX2civs9klv8xE+VFOTo6ys7OVk5NjdSjwA/LrbOTX2civs5FfZyO/zmaX/FJEAQAAAIAPuLGEH126dEmGYcjlcqlGjRoVtl1UDPLrbOTX2civs5FfZyO/zmZVfn2tHbgmyo8Y2M5Gfp2N/Dob+XU28uts5NfZ7JJfTucDAAAAAB9QRAEAAACADxx7Ol9pl3p5PJ4KjeHa8ypr1apVoduG/5FfZyO/zkZ+nY38Ohv5dTar8ltanXCzW0c49sYSbrdbeXl5VocBAAAAwIZCQ0MVGFj6nBOn8wEAAACADyiiAAAAAMAHFFEAAAAA4APHXhPl8XhKXCDmcrnkcrksiggAAABAZWQYRokbSVSrVu2GX7br2CIKAAAAAPyB0/kAAAAAwAcUUX5y8eJFJSUlqXv37oqNjZXL5dKECRNu+PivvvpK3bp1U1hYmCIjI9WvXz8dO3as4gLGHdu6dat5yuj1Pzt37rQ6PJRRbm6uRo0apfj4eNWsWVPt27fXX/7yF6vDQjlgjDqHL8dYjq/2U9b8Dh48uNTx3KJFi4oPGmW2efNmDRkyRC1atFBoaKjq16+vn/3sZ/rXv/5V4rGVefxSRPlJVlaWFixYoEuXLqlPnz43feyhQ4fUpUsXXb58WatXr9Y777yjb775Rp07d1ZmZmYFRYzyMmXKFO3YscPrp02bNlaHhTLq16+fli5dqvHjxys5OVn333+/Hn/8ca1YscLq0FBOGKP2V9ZjLMdXe/Llb6jg4OAS43nVqlUVFClux7x583TixAmNHDlSn376qX7/+9/r7Nmz6tixozZv3mw+rtKPXwN+4fF4DI/HYxiGYWRmZhqSjPHjx5f62P79+xu1a9c2zp8/by47ceKEERQUZCQlJVVEuCgHW7ZsMSQZ77//vtWh4DZ98sknhiRjxYoVXssTExON+Ph4w+12WxQZygNj1DnKeozl+GpPZc3vk08+aYSGhlZwdLhTZ86cKbHs4sWLRt26dY2HHnrIXFbZxy8zUX5S1jsBut1urV+/Xo888ojCw8PN5Q0bNlTXrl21bt06f4YJ4Brr1q1TWFiY+vfv77X8qaee0qlTp7Rr1y6LIgNwrbIcYzm+2hd3U3a2OnXqlFgWFhamVq1aKSMjQ5I9xi9FlMWOHj2qgoICJSQklGhLSEhQWlqaCgsLLYgMt+u5555TYGCgwsPD1aNHD23fvt3qkFBGqampatmypQIDA72WXx2fqampVoSFcsYYrRo4vlYNBQUFiouLU0BAgBo0aKDnn39e2dnZVocFH50/f15fffWVWrduLcke4zfw1g+BP2VlZUmSoqOjS7RFR0fLMAzl5OSoXr16FR0afBQREaGRI0eqS5cuiomJUVpammbMmKEuXbrok08+UY8ePawOEbeQlZWlxo0bl1h+dXxeHa+wJ8Zo1cLx1fnatWundu3amdc0btu2Tb/73e/0xRdfaPfu3QoLC7M4QpTVc889p7y8PI0dO1aSPcYvRVQZbN26VV27di3TY/fu3av27dv7vI2bTVszpV3xbifnHTp0UIcOHczlnTt3Vt++fdW2bVslJSXxB5pNMBadizFaNTGmnWv06NFe/09MTFSHDh3085//XAsXLizRjsrptdde03vvvae33npL9913n1dbZR6/FFFl0Lx5cy1cuLBMj7377rt96jsmJkZS6Z9wZ2dny+VyKTIy0qc+cefKK+eRkZH6yU9+ovnz56ugoEDBwcHlFSL8ICYm5oZjUSr9EzHYG2PUuTi+Vk19+/ZVaGgoX1tgExMnTtQbb7yhyZMn6/nnnzeX22H8UkSVQb169TR06FC/9N2kSRMFBwcrJSWlRFtKSoqaNm2qmjVr+mXbuLHyzLlhGJKs/8QEt9a2bVutXLlSbrfb67qoq+OT22A7E2PUmTi+Vl2GYahaNS77r+wmTpyoCRMmaMKECfrtb3/r1WaH8cs7zGKBgYH66U9/qrVr1+rixYvm8vT0dG3ZskX9+vWzMDrcqZycHK1fv17t27e3fLDj1vr27avc3Fx98MEHXsuXLl2q+Ph4/fCHP7QoMvgLY9S5OL5WTWvWrFF+fr46duxodSi4iUmTJmnChAkaN26cxo8fX6LdDuM3YMKNvuIbdyw5OVn79+9XSkqK/vrXv6pOnTpyuVw6ePCgGjVqpKCgIElXPv2eO3eutmzZori4OKWmpmrYsGFyuVxatmyZQkNDLX4mKIsBAwZo9+7dOnfunM6ePavPP/9cTz/9tDIyMrR06dJSb1iAyqVZs2b65z//qYULFyo6OloXLlzQm2++qdWrV2vevHlq166d1SHiDjBGnaUsx1iOr/Z1q/yeOnVKvXv3Vn5+vrKzs3X06FEtXrxYr776qpo3b6558+apevXqVj8NlGLWrFkaM2aMevbsqWHDhunkyZNePw0aNJBkg7+PrfySKqdr2LChIanUn+PHj3s9ds+ePcZDDz1khISEGOHh4UafPn2MtLQ0awLHbXnzzTeN9u3bGxEREUZAQIARGxtr9O3b1/jyyy+tDg0+uHjxovHiiy8acXFxRvXq1Y2EhARj5cqVVoeFcsAYdZayHmM5vtrTrfKbnZ1t9O3b12jUqJERHBxsVK9e3WjWrJmRlJRknDt3zurwcRM//vGPb5jb60uTyjx+XYbx/08GBwAAAADcEtdEAQAAAIAPKKIAAAAAwAcUUQAAAADgA4ooAAAAAPABRRQAAAAA+IAiCgAAAAB8QBEFAAAAAD6giAIAVAlDhgxRjRo1lJKSUqJt6tSpcrlc+vjjjy2IDABgN3zZLgCgSrhw4YLatm2rmJgY7dq1S0FBQZKklJQUff/739eAAQP07rvvWhwlAMAOmIkCAFQJ4eHhWrx4sfbt26c33nhDklRUVKQnnnhCdevW1Zw5cyyOEABgF4FWBwAAQEXp1q2bhg8frilTpujhhx/W2rVrtX//fn322WeKiIiwOjwAgE1wOh8AoErJy8tTQkKCPB6PMjIyNGzYMM2bN8/qsAAANkIRBQCoclauXKkBAwYoLi5OR44cUVhYmNUhAQBshGuiAABVisfj0VtvvaVq1arp7Nmz2r9/v9UhAQBshiIKAFClzJw5Uzt27NCKFSvUrFkzDRkyRAUFBVaHBQCwEYooAECVcfDgQb3++usaNGiQHn30US1ZskRpaWkaO3as1aEBAGyEa6IAAFWC2+1Wp06ddPr0aaWmpioyMlKS9Otf/1qzZ8/W3/72Nz3wwAMWRwkAsAOKKABAlTBp0iS9/vrrSk5OVs+ePc3lhYWFat++vQzD0L59+xQcHGxhlAAAO+B0PgCA4+3fv1+TJk3SsGHDvAooSapZsyan9QEAfMJMFAAAAAD4gJkoAAAAAPABRRQAAAAA+IAiCgAAAAB8QBEFAAAAAD6giAIAAAAAH1BEAQAAAIAPKKIAAAAAwAcUUQAAAADgA4ooAAAAAPABRRQAAAAA+IAiCgAAAAB8QBEFAAAAAD74f9Nkaa3jlTDZAAAAAElFTkSuQmCC\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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gVvr+vxzINtCW5K8tyV9bi5F/2Hwit7W1+acwlJ136Un+2lrp+aemphJliEJVVZyjTkyJoTWJxNjYmL/zjkwO/nyTKdFExW0VDDQO0HS0iY+6PiIvIY+XX36Zd999l3vuuYe1a9cucctXhpW+/y8Hsg20JflrS/LX1mLkHzYDKCHEyjUxgAJwjDpCbgA1WxMTTSTlJdH2QRstp1rotfZS4izhySef5NJLL2XPnj0kJiZq3VQhhBAibIXNAConJ8f/DbBYepK/tlZ6/qmpqUTqI1FQcIw4tG7ONDHRMaioKMxuUghDhIGiq4vIWJvB2cNnqeypJCMmA9f7Lqqqqrj99tu5/vrrV+z2XGgrff9fDmQbaEvy15bkr63FyD9s3gMlhFi5ampqeOqpp/ig8wPSNqRReGWh1k1aMKqq0lvXS/M7zagulYLEArJisygsLGTfvn1kZWVp3UQhhBBiWZnv2EFGGEKIZW9iprooQ1RIXoGaD0VRyFybyaX3XkpaWRqNlkYqeyupPVvLI488wuuvv47P59O6mUIIIUTYkAGUEGLZS0lJQVEUogxR2C12rZuzKIxRRkquK2Hjro14TB4+7v6YZnMzL774Iv/0T/9EV1eX1k0UQgghwoIMoIQQy57BYCAnJ4eEyASsg1ZcNpfWTVo08VnxbL57M9mbsmkZbuFkz0lON5zm0Ucf5eDBg3I1SgghhFhkYTOJRGVlpX8Kw40bN2rdnLAj+WsrHPJft24dja2NqKrKUOcQ6SXpWjfJzzxo9j/AmpKcMu/6dAYdRVcVkVqUypk/nuHj7o/JT8jnpZdeorKykvvuu4+MjIwFaPnKEA77f6iTbaAtyV9bkr+2FiN/uQIlhFgR1q1bR6Q+khhjDENtQ1o3Z0nEZ8az+a7N5FySQ8twy/izUWdq+fa3v80f//hHVsAcQUIIIUTICZsrUNHR0Xg8HgyGsFnlkCL5aysc8l+9evX4S/JMSfS396OqKooyu2nDF5vBYFi0KWx1Bh2FVxaSUphC/aF6jncfpzCpkP/+7/+msrKSz3/+8yQnJy/4311OwmH/D3WyDbQl+WtL8tfWYuQv05gLIVaMp556iqMfHaWqr4pLP3Mp0cnRWjdpSXndXprfbaarqovEqERKU0pJiE3gM5/5DFdccUXIDCiFEEIILck05kII8Wfr1q0jISoBnaLD0m7RujlLTm/Us/ra1Wz41AbsBjvHu4/TOtDKT37yE37yk5/gcKysKd6FEEIILcgASgixYqxbtw6doiM+Mj4sB1ATEnMT2bJ3C6lrUqk311M3UMc7777Do48+Smtrq9bNE0IIIZY1GUAJIVaMrKwsEhISSDGlMNQxhMfp0bpJmjFEGlhzwxrW3ryWQfcgx7uP09jeyGOPPcahQ4dkggkhhBDiIoXN02xtbW3+B8jy8vK0bk7Ykfy1FS75K4rCli1b6B/sp8nSRP/ZfrIqsrRuFmNjY/hUHzpFR2xs7JL+7bSSNOIy4jj9+9NU9lZSkFjA888/z+nTp9m3bx9xcXFL2h4thMv+H8pkG2hL8teW5K+txcg/bK5AWSwWBgcHsVjC97YeLUn+2gqn/K+66ioi9BEkm5LpOd2jdXMAcLqcOJ1OnC6nJn8/Kj6Kjbs3krMphyZLEzX9NZyoPMG3v/1t6urqNGnTUgqn/T9UyTbQluSvLclfW4uRf9gMoIQQ4WHVqlWsWrWKjNgMRvtGsZqtWjcpJOj0OgqvKmT9besZY4zj3cdp6WnhySef5OWXX8bn82ndRCGEEGJZCJtpzJ1Op/+9MJGRkUvdxLAn+Wsr3PJ/6623eO6553i/833SK9IpurpI0/Z4fV5QAQX0Or2mbQFw2VzUv1HPUMcQufG5FCQWsHr1ar74xS+SkpKidfMWXLjt/6FItoG2JH9tSf7aCpb/fKcxD5sBlBAifFitVh588EHO9J+hz93H5Z+/HJ1e+oPJVFWl40QHLe+1EBcRR1lqGcnxyXz2s59l8+bNWjdPCCGEWDTzHTuEzSQSQojwERMTw6ZNmxh+d5iOrg4GWwZJLU7VulkhRVEUVm1eRUJ2AnV/qOPj7o8pcZbwox/9iG3btnHXXXct6FvbRXhxuVx0dHTQ1tZGW1sbnZ2deL1edDodiqKg0+nIy8vj8ssvp6ioSF7yLIRYVuQKlBBiRaqpqeGpp57iRPcJIrIjKP9kudZNClkep4ezh8/S39BPVmwWxcnFFBcV8+Uvf5mkpCStmyeWia6uLj788ENOnTpFZ2cnqqqiqj58PhterxVV9QIKoKAoCgZDIjpdJElJSVx77bXs2LFDPreFEEtCrkDN0sjIiP/+x/j4eK2bE3Ykf22FY/5r164lKSmJzNFMGlobcI45iYzV5t5zl9vlfwYqwhihSRsuxBBpoOzmMhJzE2l8u5GxnjHcXjePPvoo999/P6WlpVo3cV7Ccf9fKr29vXz00Ud89NFHdHV1oaoe3G4zHs8IXu8oPp8NVfWhqj4URfnzdpg4QVEwGOJxOtN5+eVBWlpauP/++zEajZqu00okx4C2JH9tLUb+YTOAam5uxu12YzQa2bhxo9bNCTuSv7bCMX+dTseVV15Jv7mfpqEmuqu7KdhaoElbRkdH8fl86HQ6UpJDc5IGRVHIKs8iLj2O2oO1fNz9MWXuMn7wgx+we/dubrrppmV7m1U47v+LyePx8MEHH/DWW2/R1taGqnpxu8243f14PBZAJSMjhqysWLKzM8nOjsVodKLXjx+XKSkpOJ0eTp82U1XVT0NDAx6PmZMnVf7rv/6L++67b9nua6FKjgFtSf7aWoz8w2YAJYQIP9deey2vv/46mbGZdFV3kbs5F0OEdHsXEpsWyyV3XUL9G/VUt1VTkFjACy+8QHNzM5///OeJiorSuolCI1arlSNHjvDWW28xPDyMxzOIy9WLxzOIqvrIy4unoqKQdetSiY8PvNprNpsDpsqPjDSwaVMGmzZl0Nho4Re/qMFmq+f993VcdtllrF+/fqlXTwghZi1sziQyMjLwer3o9dpPIRyOJH9thWv+SUlJbN26Ffuf7HSPdtNT20Puptwlb4fJZPLfPrAcGKOMlH+ynNYPWmk+3syoaxTfRz66urr4yle+QmZmptZNnJNw3f8XSm9vL4cOHeLdd9/F5XLicvXicnXi9drIzo5jw4YCysvTSEg4/y2y0dEmfD4VnW76MVBcnMTtt5fw4ov1eL35fPjhhzKAWmByDGhL8tfWYuQvk0gIIVa07u5uHn74Yc6Yz2BRLVz22ctkSvM5MDebqT9UT4Qawdq0tSTHJrNv3z6Z6jwMdHV18Zvf/IYTJ07g87lwubpwOrsBD2vXpvCJT+SyatXCPE/g8fh44on3UNVsEhJK2b9/PxERofe8oBBiZZjv2GHOZxGjo6M8+OCD3HzzzaSlpaEoCg8//PC03zt69Chf+tKX2LJlC5GRkSiKQktLy5z+1qFDh7jyyiuJjo4mNTWVffv20dfXN9cmCyHCWFZWFhs3biQ3PheX1UXfGelD5iKlMIVL9lyCEqdwsuckHYMd/OhHP+J//ud/Am7JEiuH2Wzmpz/9Kf/4j//IRx+9i812htHRD/D5Otm6NZ2/+ZvL2Lt33YINngAMBh1r16bidvfjdDqpra1dsLqFEGKhzXkAZTabOXDgAE6nkzvuuOO8v/fmm29y6NAh8vLyuOqqq+bcsCNHjnDLLbeQkZHBK6+8wj//8z9z6NAhbrjhBpxO55zrE0KErx07dhBtjCYlOoWOjztYARfel5Qp0cSmOzeRUpzC6YHTNFma+P3vf8+TTz457Rs8sXyNjo7y/PPP861vfYtjx45gs51lbOwjIiMHuemmAr7+9Su45ZZikpIW5zm4vLx4vF47qqrKfiWECGlzfgYqPz8fi8WCoigMDAzw9NNPB/29f/iHf+Chhx4CYP/+/Rw+fHhOf+cb3/gGa9as4YUXXvC/zLGwsJBPfOITPPPMM3zlK1+Za9OFEGGqqKiINWvWMOoc5UTPCcxNZnmx7hzpjXpKbyolLiOOpmNNjLpGcfvGpzr/8pe/TGFhodZNFBfJ4XBw6NAh/vCHP+BwWHE4OnC5OomKUrjxxnyuuCKbiIjFf3Zj8jOCcnVTCBHK5jyAmu1D0PN5/qizs5MPP/yQ7373u/7BE8BVV13FmjVreOmll+Y8gKqpqfFPYVheLi/UXGqSv7Yk//GrUGfOnCExKpH2j9tJKUpZskkdLBaLfxrz5fxiWkVRyNmYQ2xaLKd/f5oT3SdY61nL/v37uffeey/qboOlIPt/cKqqcuzYMV5++WVGRoZxubpwONrR671cc00un/hELibTwsw1NZtj4NwEE6oMoBaYHAPakvy1tRj5h+QsfNXV1QBs2LBhWtmGDRs4duzYjHXU1NSQn5/vf2GWx+Px/6usrCQpKYm8vLyAZc6ePYvNZgOYNk/8wMAAnZ2dAOTl5QV8AHi9Xn+b4+LiKCoqCli2ubmZkZERAMrLywMGhUNDQ7S2tgKQnZ1NWlpawLKnTp1CVVVMJhNr1qwJKGtvb2dwcBCA0tLSgOmFx8bGaGxsBCA9PZ2srKyAZWtra/0707p16wLKuru7/c+aFRcXExsb6y9zOBzU19cDkJyczKpVqwKWPXPmDHa7HUVRArbf1Pzz8/NJTEwMKK+pqQEgPj5+2rfZTU1N/ls6KioqAmZSsVgstLW1AZCTk0NqauCVhcrKSgCio6MpKSkJKGtra8NisQBQVlZGZOS5WaRGRkZobm4GxmdwmTrzWE1NDR6Ph8jISMrKygLKurq66O/vB2D16tXExMT4y2w2G2fPngUgJSWF3NzAWeHq6+txOBzo9XoqKioCyvr6+uju7gagoKCAhIQEf5nL5eL06dMAJCQkUFBQ4C+bmv/69esDvuQwm810dHQAkJubS0rKuXcV+Xw+qqqqAIiNjaW4uDigTS0tLQwPDwPjL6+d/OD38PCw/9nHrKws0tPTA5atrq7G6/USFRU17WWtHR0dmM1mAEpKSoiOjvaXWa1WGhoaAEhLSyM7Oztg2bq6OpxOJwaDwd9Zrlu3jtzcXLot3VS3V9N6upXskuyAF9t6fV6GhoYAiIyIDNj3AYZHhvF4PADT3ufkcDiw2qz+nCIjzu1LPp8Pn+rD5/UxMjpCfFzgsyOjo6PjL9tlfOZAnXJu2zhdTsbGxoDxfdgUZQpY1jw4npFBbwjYHwDGrGP+W54TExIDjhu3x+3vl0xRpoB8ASxDk054EwNPeI2JRgpuKqDpcBMnu09SklLCs88+S1dXFzt37vTv33PpIwD6+/vp6uoCWNA+wuVy4fV68Xg8DAwMSB/B+D539OhRmpqacLv7cDhacLmsVFQkcdVVmeTnZwZ8weB0Ohgbm9i/Y4iMPPd5o6qq/7PIaDROe1Hl6Oio/7iZyuVy+bebyzVxe77qv812KfuICT09PfT29gLjd75MXh+n00ldXR3AsjqPcLnG+5epXxotp/MIWLw+YrHPI9xuNzA9/1DuI6aeRwA0Njb6P4+W03lEsPwnjtOLFZIDqIkOMTk5eVpZcnKyv/xCPB5PwHMOExNZuFwu3G530M7c4/H4Q57K5/P5y4J9MzZRNlO9U5+9mFyv1+sNWq+qqkHfzO71eudV7/nWdXK9U9dVVdUL1juxrlM7icjISHw+n7/uC9UbKttmpnWd2I+CXW290LaZTb1utzto2YXqnVg2WL2RkZH+YyJYjrPNMNiyk9s01Uzr6nK58Pl8QacWXYgMJy+nKAo7duygvr6eKF0U3ZXdZK8OPKlCPbf+PnV6Dj6f77zfjKuTvjWf2l6dXofP8+cy3/Tt5lMn1asCkw+fSW0Kts397dVNb5eqTmoT0zOcqd7zrquqoo/Ss/rm1QxWD3L29FlsbhvqH1Ta2tq44ooriIyMnFMfAbPve+baRxgMBn9bwr2PGBkZ4ciRI9TW1hIdrcNub8DjGaa8PI3LLssnLi74rXqz2V8m/3fqshOmZ3Gu3qEhB4piQFH0/pPFpewj5lpvqHxWzebzHsb7wMkn9xO/v1zOI+ZSb6hsm8lt0uv10/IPxT7iYrd5qJ9HGI3GgPzn+yx0SA6gJpzv9prZ3HZjMBgCfq+srEPcmd4AACAASURBVCzgm6PJ395MXibYQAXGO/2JsmA7+kTZTPVObfvkeoNtfKPRiKqqQevV6/Xzqnfyf89X79R1VRTlgvVOrOvU9pSVlQV8c3ShekNl28y0rhPrOVOGF1Pv+d5XcKF6J5YNVm9ZWVnAN0dTzTbDmdZ1qpnWNSIiAq/XuygZ+ny+adt8y5YtpKSkkDWSRXN3MyPdI6TmT/qmUTm3/pOvAk3Q6XTnvT1ZQfGXTW1vYkIig5bxb3mVIO/B0SmT6p1aPKlNwbb5hdqrKJPaxPQMZ1VvkPX1L6uD4muLiU+Pp/FPjdjcNlweF2fPnuXuu+8mIyNj2rLn6yNg9n3PXPuI3Nxc/7fL4dpHqKrKO++8wzPPPIPNNopO18/Y2CCpqSY++ckNFBUlMjIyct6TmAXZX4CEhKkz950r6+mxodePX6mYuLKz1H3EXOoNlc+q2Z5HBLuTZTmdR8yl3lDZNpPbFOwqdSj1EVPX9Xz1zjdDrc4jpl6lnu8t/PN6D9TAwABpaWk89NBDQacyn7B//36+8Y1v0NzcPO1yYDC///3v2bFjB6+++io7d+4MKNuzZw/Hjh3zn4iDvAdKCDF777zzDj/96U852XMSJVlh4+6Ny+YFt6FsqGOI2tdrifBFUJ5WTmpiKg888MC0Ezax9Nra2njuuedoamrC5erF4WjGYPCyfXs+W7dmYzCExmfl97//AXZ7KomJa3nyySflM1wIsWiW/D1QS2Hifs2J+yUnq6qqmnY/pxBCzNbWrVvJycmhMKmQkZ4RzM0z3xIsZpaYm8gld14CMXCy5ySd5k5+8IMfzOqZVbE4nE4nzz//PN/5znc4e7aKsbFKbLZ61q1L4K//+lKuvjo3ZAZPNpuboSEHen0subm5MngSQoS0kOyhcnJyuPzyy/n5z38ecL/je++9R319Pbt379awdUKI5Uyn07Fr1y4SoxJJikqi5b2WoM8libmbeF9UbE4sVb1VdA538rOf/Yxf//rXMqvaEqurq+Mf//EfOXToD9hsjYyNfUxiopt9+zZw111rSUiInLmSJdTZOf5NsF4fN21iBiGECDUX9QzUwYMHsVqt/ktftbW1vPDCCwDs3LmT6Oho+vv7OXLkCHDuStLBgwdJS0sjLS2Nbdu2nWuEwcC2bdt48803/T977LHHuOmmm9izZw9f/epX6evr4+///u+pqKjgvvvum3Obu7q6/PeDTp2NRyw+yV9bkn+g9evXs3r1asZcY5zoPkFvXS+Z6zJnXvAiWW1WVFVFURRiomNmXmAZM0QaqLi1gqZjTZw9dRar24r6hkp3dzf3338/JpNp5koWWDjt/3a7nRdeeIGjR4/i8Qxjs51Bp3Ny440FXHlljmZXnGyTjoHoIMdAXZ0ZnS4Kvd7E6tWrNWjhyhZOx0Aokvy1tRj5X9QA6itf+Yp/ykyAX//61/z6178G8D/nVFNTw549ewKW++pXvwrAtm3bAl6s6/V6p82ssX37dl577TW+9a1vcdtttxEdHc2tt97KE088MW0Wk9no7+/3T7cpO+/Sk/y1JfkHUhSF3bt309DQQFpMGq0ftJJWkobeuDgvC3U4HP4pwVf6AArGJ8oovqaY6ORoGo40YHfb8VZ5eeyxx/hf/+t/TZtmebGFy/5fU1PDz372MywWM3Z7Ey5XD/n58XzqU+WkpkbPXMEistvPHQNTB1A+n0pNzQBGYyZGo5H169dr1MqVK1yOgVAl+WtrMfK/qAHUxHzsF7J9+/ZZTxF4vt+76aabuOmmm+bSNCGEmJXi4mI2btyI47iDj7o+outUF6u2rJp5QTFrWeVZmBJMnP79aU72nMTtdfPd735XJpdYYE6nkxdeeIE//elPuN0W7PYzGAwebr21mMsuywr5SVKamoaw2dzExaWxYcOGi/qSVAghltK8ZuELFbOZScNqnXQLTczK/wY41Ej+2pL8g+vu7ub//b//R4O5gV5nL5d99jKMUcGnUp0Pt+fc1NBGw8LXH+rsQ3ZqXqvBNexibepaUmJSuOeee7jmmmuW5O+v5P3/7Nmz/PSnP6W/vxeHowmns5vi4iQ+9akSEhOjZq5giXg8blQVFAUMU46Bl18+Q2XlMHFxl/HlL3+ZzZs3a9TKlWslHwPLgeSvrWD5z3cWvpB+D9RCkh1WW5K/tiT/4LKysrjqqqtw/clFb1cv7cfbKfpE0YL/nXAcNE1mSjSx6dObqHujjurWaoqTi/n5z39Of38/u3btWvQrJCtx/3e73bz88su8+eabuN1D2Gz16PVubr11dUhedZo6aJrg8fg4fXoAozGbyMhIuX1vkazEY2A5kfy1tRj5h80ASgghgrntttv44IMPyI3Ppa2qjez12UTFh8439yuFIdJA+c5ymt9ppqGyAbvHzuuvv47ZbGbfvn3nfYmimK6lpYVnnnmGnp5uHI4WnM5O8vPj2bVrPcnJSz9Jx3zU1w9it3uIi0tj06ZNsh8IIZYFGUAJIcJaUlIS119/PY6DDrpGu2j9oJXSG0u1btaKpOgUiq4uIioxisY/NeL0OFE/VBkeHuYrX/mKfEs7A4/Hw6uvvsrBgwdxu0ew2+tRFAc7dhSydWsOOl1oXXWajXff7cBgSECvj2Hr1q1aN0cIIWYlbAZQNptt0hSq2s5GFI4kf21J/he2Y8cO3n77bfIT8jlbf5bs9dnEZcQtWP0ejwcVFQUFgyFsut3zyq7IJjImkro/1HGq9xRen5cnnniCv/7rvyYlJWXB/95K2P/7+vo4cOAAbW1tOJ2tOJ3tZGXFsnv3ZtLTQ3+dPB4PoMKkY6CjY4S2thFiYsrJzs5m7dq1mrZxJVsJx8ByJvlrazHy1z/88MMPL0hNGlJVFZfLFfCzyMjIgHvAa2tr6e3tZWhoiMzMxXvfiwhO8teW5H9hRqMRo9FI69lWBu2DWHotZK7LXLDnSCxDFux2Oy6Xi2iTfHgCRCdFk7Qqie6GbvpG+jB6jJz8+CSlpaUkJiYu6N9a7vv/xx9/zL/8y7/Q39+J1VqF1zvAddfls2vXGuLiIrRu3qxYLJOOgT+fwLz+ehNms0pUVDG7d++WF+guouV+DCx3kr+2guU/m7HDhWjzRj0hhAgx27dvJycnh9XJqxntG6X3dK/WTVrx4jLi2HTnJpRYhcreSjr7O/ne975HdXW11k0LCR6Ph+eff54f/ehHjI62MzZ2gqQkH1/+8iVs356HXr98P8ItFgc1NQNEROQQHx/P5ZdfrnWThBBi1sLmCpTH48FkMhETE0N8fPxSNzHsSf7akvxnptPpyMrK4uMPP8bhcdDT3kPmukx0hvmfpKo+Fb1Bj9FgJCJieVwxWCqGSANpa9KwdFpo720nShdFTWUNCQkJ5OfnL8jfWI77/+DgID/84Q85fvwjHI4m7PYmKipSuPfe8pCanny2VFXFYNBjNI4fA4cPt9LRYSc6upQdO26hrKxM6yauaMvxGFhJJH9tBct/vlegwuY9UEIIMRs//vGPeef9d/io6yMyKjIovqZY6yaFBZ/HR/2hegYaByhOLiY7LptbbrmFT33qUyE3Jfdiq66u5plnnmF01IzVehpFsfIXf1HE5ZeH3vTkF8Nu9/C9772PouQQH1/Cd7/7XeLiFu6ZQyGEmIm8B0oIIRbQnXfeyalTp8hLyKO5qpmMtRnEpsZq3awVT2fQUfYXZePTnJ9swOFx8NprrzE4OMjnPve5sJh8w+fz8dvf/pbXXnsNt3sQm62ehAQ9d9+9kZyclTPAeOedDtxulbi4bLZu3SqDJyHEsrPyP5GEEGIOkpKSuOWWW3j55ZfpGeuh4UgDG3dvXBHf/Ic6RVEo+kQRUXFRNB798zTn76kMDQ3xwAMPrOjZq0ZGRvjxj39MfX39n9/t1EFpaTK7d5diMq2cj+qxMRfvvNNJREQORqOJHTt2aN0kIYSYM7nHTQghprj55pvJyMhgdfJqRnpG6K2TCSWWUvaGbNbuWIvZaaaqt4rq2mqeeOIJBgcHtW7aojhz5gzf/va3qaurxmo9hdvdwc03F3LPPetW1OAJ4MiRNjwehaioVVx77bWkpqZq3SQhhJizsHkGqr6+HrfbjdFopLRUXpK51CR/bUn+c1dbW8s///M/Uz9Qz6B3kEvvvRRjlPGi6hoaHsLn86HT6UhMWNgpuleykZ4Ral6tweg1UpFeQUZKBv/7f/9vcnNz51RPqO7/qqry+uuv88orr+ByWbDb64iNVbjzzjIKChK0bt6CGh4eYnDQztNP1xITs4aEhNU88sgj8kD9EgnVYyBcSP7aCpb/fJ+BCpsrUA6Hw/9PLD3JX1uS/9ytW7eOSy+9lMKkQlSXSst7LRddl9fr9f8TsxefGc+mT29CjVY52XPSP815Y2PjnOoJxf3farXywx/+kJdeegm7vRWrtYrCwhgeeOCSFTd4AvB4vBw50oHHoycyMpsbbrhBBk9LKBSPgXAi+WtrMfIPmwGUXq9Hp9Oh1+u1bkpYkvy1JflfnD179hAXHUdBYgE9tT2M9IxcVD2KoqCgyHNUF8GUaGLj7o1EpkRyqvcU3YPd/OAHP5jTu6JCbf9vbm7mkUce4dSpE9hsNTidrVx3XR6f/WwFsbErc5r7gQE7p08PoddnERsbz80336x1k8JKqB0D4Uby19Zi5B82t/AJIcTFePPNN/nVr37FiZ4TEA+X7LkERScDoaXmdXupfa2W4c5h1qauJS02jX379nHFFVdo3bRZU1WVP/7xj/zP//wPTqcFm+00UVE+9uwpo7g4SevmLapf/KKGhgYbsbGXsmfPHm666SatmySECGNyC58QQiyi6667jlWrVlGSXIJ1wErHiQ6tmxSW9EY95beWk1KcQm1/Ld0j3TzzzDP88Y9/1Lpps2K32zlw4ADPP/88NlsbVuspcnMj+epXN6/4wVNT0xD19WYiIwtITk5m+/btWjdJCCHmRQZQQghxATqdjs9+9rPER8WTG59L64et2Cw2rZsVlnR6HWU3lZFZnkm9uZ6OkQ5+9atf8Zvf/IZQvpmivb2d73znOxw//gFWay12eyNXXZXNffdtID4+UuvmLSqPx8fvfteAwZBAREQat99+O0bjxU3GIoQQoUL/8MMPP6x1I+ZLVVVcLlfAzyIjI+V5AyHEgkhMTMThcDDQOUC/tR9Lr4WMsgzpYzSgKArJ+cmgQktTCz7VR397P6Ojo5SXl4fUNlFVlWPHjvEf//EfDA11MzZ2iogIG3fdtZatW3PQhcGtoMeOdVBTM0BMTDnFxaXs3bs3pLaRECI8zXfssLJeMHEBfX19eL1e9Ho96enpWjcn7Ej+2pL85+/222+nsrKSEmcJp3pO0VXVRc7GnFkta3fYUX0qik7BFGVa5JaufIqiUHBFAcYoI41HG3H73KiHVaxWK/fddx8GQ+BHmxb7v8/n41e/+hWHDx/G6ezG4WgkKyuGu+/eQFJS1JK0QWvDw06OHGkjIiIbt1vPDTfcQH9/v/RBGpDPAG1J/tpajPzDZgDV3d3tnwNedt6lJ/lrS/Kfv4iICD73uc+xf/9+suKyaHmvhZTCFKLiZz4Zttls/vdAyQBq4eRszMEYZaT+zXo8Pg/qhyo2m40HHniAyMhzt8Yt9f5vs9n48Y9/TE1NDXZ7Ay5XN5dfns2OHUUYDOFz5/zvf9+Ex6MnLq6AoqLVKIpCd3e39EEakM8AbUn+2lqM/MOnJxdCiHkqKSlh27ZtFCYWYsTImbfOhPSzN+EgvTSd8p3lDDoHqe6rpqq6iieffBKr1apJewYGBnj88cepqTmF1VqF19vLrl2l3Hrr6rAaPDU2Wqiu7icqqoi4uASZOEIIsaKEzRWogoICVFWVe681IvlrS/JfOLt376aqqooSZwlVHVX0nu4lc13mBZeJi41DRUVB8l8MyQXJrL99PTWv1nCq9xQ+1cf+/fv52te+RmJi4pLt/w0NDfz7v/87w8P92Gw1RES4+cxn1q/IF+NeiMfj49VXG/88cUQ6n/70p1m7dq30QRqSzwBtSf7aWoz85T1QQggxRzU1NTz11FOcMZ9hwDXAls9sITJ2Zc+mthyMDYxR/dtqDG4D69PXk52Rzd/8zd8syS0z7733Hv/1X/+Fw2HGaq0lJcXIX/5lOcnJ4XfL5ttvt3PoUAuxsZspKVnPgw8+KCeOQoiQIu+BEkKIJVZeXs6VV15JUVIROq+OhiMNcitfCIhNjWXj7o34TD5O9p6kvaedxx9/nPb29kX7m6qq8sorr/CTn/wEm60Dq7WKoqJY7r9/U1gOniwWB4cPj08cYTDEcs8998jgSQix4sgASgghLsKePXtITkymJLkEc4uZ/rP9WjdJAKYEE5t2b8KYYKSyp5KugS6+//3v09zcvOB/y+VyceDAAV599VXs9mZstjNcemkGf/mX5ZhMYXOHvJ+qqvzmN2fxeo1ERRWwbds2Vq1apXWzhBBiwYXNAMrlcvn/iaUn+WtL8l94MTEx3HPPPaREp5AWnUbj2424bMHz9fq8/n9i8UXERLBh1wZM6Saq+qroHOhk//791NTULNjfGB4eZv/+/Rw//iE2Wy0uVwc7dxZz662r0evD5qM1wIkTvTQ2WjCZSkhOTmXXrl3+MumDtCX5a0vy19Zi5B82L9Ktrq6mu7ubwcFBMjMv/MC3WHiSv7Yk/8WRlZVFT08PtkEbXUNd2EftpK1Om/Z7FosFm82G0+kk2hStQUvDj86gI60kjeHuYRrbGvHZfXz03kdUVFSQmpo6r7rb29v5/ve/T1dXK1ZrFXq9lb1717FxY/i+XHlkxMkvf1mLTpdGVFQu999/P9nZ2f5y6YO0JflrS/LXVrD85/si3fD8mkwIIRbI3r17SYxPZHXyavob+uVWvhCiN+qpuLWC2OxYmkabMFvN/Mu//AvV1dUXXWdlZSVPPPEEAwNtjI2dJC7Ow5e+tJE1a5IXsOXLi6qq/O53DbhcOkymYrZu3UpFRYXWzRJCiEUTNjdpJyQk+N9CLJae5K8tyX/xxMXF8ZnPfIann34as93M2SNnic+KD5iVLyIiAtWnoujC8+qElnQGHWU7ymg41EBzRzPxI/H827/9G/fffz+XXHLJrOtRVZU33niDF198EZerH5utjtzcWD7zmXXExkYs4hqEvsrKPurqzMTElBMfn8Rdd9017XekD9KW5K8tyV9bi5G/TGMuhBDzpKoq//mf/8m777/L8e7jmDJNrL99fdjezhWKfF4f9YfqGWgYoCy1jIy4DL7whS9w2WWXzbisx+Phueee4+jRozgc7TgcLaxfn8Ydd6zBaAzvz5nhYSf/+q/H8flSiI4u5YEHHpjTwFQIIbQg05gLIYTGFEXhnnvuIS0ljdKUUoY7hums7NS6WWISnV5H2U1lpJelUzdQR/dIN//5n//JO++8c8HlrFYrTz31FG+//Sdstnocjmauuy6PO+8sDfvB0/gU7mdwufSYTMVcccUVMngSQoSF8O79hRBigURHR7Nv3z4SoxLJic+h5b0WxgbGtG6WmETRKay5fg2Z5ZmcMZ+ha6SLZ599liNHjgT9/d7eXv7pn/6JurpqrNYqfL5+9uwp47rr8uXqIvDRRz00NFgwmdaQlJTK3r17tW6SEEIsibCZhU8IIRZbamoqTqcTc6cZs83MQMcAmWsz5dmnEKIoCsn5yXhcHlpaWjDoDLSeacVkMlFUVOT/vfr6ep588knM5i7Gxk4RFeXmc5+roKQkfCeLmMxicfDcc7Xo9ZlEReXwV3/1V+Tk5GjdLCGEmJX5jh3CZhKJxsZG3G43RqOR4uJirZsTdiR/bUn+S+eOO+6gtrYWu8fOie4TtLzXQuqGVHw+Hzqdjvj4eK2bGHZGRkYC8lcUhaJPFKE36Gk83ohP9fHrX/8al8vFzp07OXbsGD//+c9xOs3YbKdJS4vk3ns3kJQUpfWqhARVVXnxxXo8HiNxcUVcc801lJeXX3AZ6YO0JflrS/LX1mLkP+db+EZHR3nwwQe5+eabSUtLQ1EUzncR6+OPP+bGG28kNjaWxMREdu/eTVNT06z+zvbt21EUZdq/HTt2zLXJAIyNjfn/iaUn+WtL8l86BoOBL37xiySYEihMLKSjsgNzmxm3x43b49a6eWFpIvvJ+SuKQsHWAgquKKB5qJmWoRZefvll/u7v/o5nn30Wu70Tm62a1avjuf/+jTJ4muTddztpbR0hOrqU1NR07rzzzhmXkT5IW5K/tiR/bS1G/nO+AmU2mzlw4AAbN27kjjvu4Omnnw76e3V1dWzfvp1Nmzbx/PPP43A4+Na3vsU111zDyZMnSUub/rLJqYqKivjFL34R8LPExMS5NlkIIZZUTk4Ou3bt4vnnn8dsN9N6tJXS20qJMIX3dNehKO/SPHR6HU3HmmhrbwMLpKcbyMhwc9VVufzFXxShk1sw/fr6bBw61EJkZDYGQwL79u0jKkoGl0KI8DLnAVR+fj4WiwVFURgYGDjvAOpb3/oWkZGR/O53v/PfsrJlyxZKSkrYv38/jz322Ix/y2QysXXr1rk2Maj169cvSD3i4kj+2pL8l94NN9xAVVUVLp+L413HGaoeovTmUq2bFZaSky/83FLWhiya25rp/rCbSEXF1alQUVHEjh1F8iztJB6Pj5deqkdVo4iKKuSGG25gzZo1s1pW+iBtSf7akvy1tRj5z/kWvolb6S7E4/Hwu9/9jk9/+tMB9/vn5+dz3XXX8dJLL829pfOk0+n8/8TSk/y1JfkvPUVR2LdvH0lxSZQkl9Df0M/AmQGtmxWWlEn/N5Xb7eZU1SnUZB8xZWA32IlZZWRgwMZrrzWyAl6VuGDeeKOZri4rJlMpmZlZ3HHHHbNeVvogbUn+2pL8tbUY+S/KJBKNjY3Y7XY2bNgwrWzDhg288cYbOByOGS/7NzY2kpyczMjICPn5+ezdu5dvfvObmEymGdtQU1NDfn5+wADO6XRSV1cHQFJSEnl5eQHLnD17FpvNBsDGjRsDygYGBujsHH+vS15eHklJSf4yr9dLdXU1MP4SrskzOQE0NzczMjICQHl5OQbDudiHhoZobW0FIDs7e9qtjadOnUJVVUwm07Rv+trb2xkcHASgtLQ0IM+xsTEaGxsBSE9PJysrK2DZ2tpa/wN169atCyjr7u6mr68PgOLiYmJjY/1lDoeD+vp6YPxb3VWrVgUse+bMGex2O4qiTNv+/f39dHV1AeOD6cm3Y3o8HmpqagCIj4+nsLAwYNmmpib/C88qKioC3iZtsVhoa2sDxm+dSk1NDVi2srISGJ9muqSkJKCsra0Ni8UCQFlZGZGRkf6ykZERmpubAcjIyCAzMzNg2ZqaGjweD5GRkZSVlQWUdXV10d/fD8Dq1auJiYnxl9lsNs6ePQtASkoKubm5AcvW19fjcDjQ6/VUVFQElPX19dHd3Q1AQUEBCQkJ/jKXy8Xp06eB8bduFxQUBCzb2Njov/93/fr1AR2J2Wymo6MDgNzcXFJSUvxlPp+PqqoqAGJjY6c9gNnS0sLw8DAAa9euJSLi3G1qw8PDtLS0AJCVlUV6enrAstXV1Xi9XqKioigtDbw609HRgdlsBqCkpITo6Gh/mdVqpaGhAYC0tDSys7MDlq2rq8PpdGIwGKY93N7T00Nvby8AhYWFi9pHJCUlce+993LgwAFiiKHqD1VsiNtAWnbgcT46OorL7fL/XZ1ybts4XU7/douOjsYUFdj/mQfHMzLoDQH7A8CYdQyn0wlAYkJiwHHj9rj9/ZIpyhSQL4BlyOKfeCEpMSmgzGazYXfYgfHj1Wgw+su8Xi9Dw0PA+IxGsTGxAcsODw/j8XoASElOCSizO+z+fGNjY4mMOHc8+lSf/1iNMEYQFxcXsOzI6Ahu9/gzTslJyQFf9E3OMCY6xt9XOp1OqqqqsFjM+NRhorJV8gvT6PnQSuvoCLw//jvXXpuBoigkJk7J0O1iZGS8X4qONmEyTcnQMp6hXq+fdvu5zWbFbncAkJAQj2FShh6Px39MRUVFBfQf4xkO4fF40ekUkpICr67Z7ecyjIuLCzgefT4vFsv4tomICJLhyKQMkwMzPHmyk8OHm9DpVhETY+KLX/yiv27pI86R84hxch4xTs4jxoViHzFxnF6sRRlATTQ22G0TycnJqKqKxWKZdjBOdvXVV3P33XdTVlaG3W7n4MGDPP744xw9epS33nprxlGkx+OZ9s2hqqr+DwePxxN0mYnyqXw+n7/M5/NNK59tvVPbNLler9cbtF5VVTEajdPKvF7vvOo937pOrnfquk7OMFi9E+sa7CrlbOsNlW0z07q63W48Hk/QffFC22Y29brd7qBlF6p3YtmZ6g1mthkGW35ym6aaaV1dLpf/BPNC9V5shsEymm29C7UfXnrppVRWVtLb38vo8ChNh5tI3ZsaMLW5T/WdW0aFgAsl6rn6gq3PRJlPN327qap6blmmr+tM9QbbF2ZaVmWGetXZ1cvURSfl4FODrKtPnV17/1yxzWajqroKh8OGzzeE0aiyenUi8QnRmKIMNL89/mHu/tCF2+3iuuumT9GtTm6T7/wZBusPAzOcVjqpbPo6TdSrqheud3qIM+9LwTI0m+288kojkACkcNttt5Gfnx/wO9JH4P+ZnEfIeUSwNsl5ROj1EfOxqNOYX+hWv5luA3zkkUcC/vfOnTspKCjgb//2b3nllVfYtWvXBZc3GAwBf8NsNuN0OtHr9eh0uoBvbyYvE6yDgfHLfxNlwXb0ibKZ6p263pPrDbbxjUYjqqoGrVev18+r3sn/PV+9U9dVUZQL1juxrlPbYzabsdls/vwvVG+obJuZ1nViPWfK8GLq9Xq9QcsuVO/EssHqNZvN/g4mWEazzXCmdZ1qpnWNiIjA6/UuSoY+n2/Ox81i7Yc33XQTx44do8BbQFNfE23H28i/7NwJqE6ZdExM3azKq0kyDgAAIABJREFUufqCbfOJsslXrSavj39Zpq/rrOoNsj9caFmFGepVzn8bxeR6L5RD0HXVKeet1+P2+NuioDA6Nkp1VTUutx2Pe5DIKIXiogQio8a3ecpqE6oKLUeH8Xo9eI+PX4nbtSvwS0FlcpuCTDQx+wynlU4qC3686nRq0L8ZkGGQWxZn2uZT2+p2+3j++dN4PBEYDAWUl6/n6quvnrbsTH3ExHFqsVjIyMgIaK/0EefaNJt6L+bz3uv14vP5MJvNAVcGltN5xFzqDZVtM9Emn8+Hw+GYlv9yOo+YKJtvhlqcR/h8PoaGhnA4HP785/t8q6LOYwg2MDBAWloaDz30UMBU5vX19ZSVlfGv//qvfPWrXw1Y5hvf+Abf+973sNlsc565p7e3l8zMTB588MGASSh8Pp//suyEuLi4gA1YWVnpv9Q89bK6WHySv7Ykf21VVlbS2NjIc889x6h+lLbhNtbfvp7EXJlVdCmYB83+2xF1Oh21tbV43A7cnkGio/WUlCRjNE7/wB84Y6Pl2AjpUdHkxcb/eVa+wrCaWOI3vznL8eO9xMZeQnZ2Ef/3//7fi5p1T/ogbUn+2pL8tRUs/9mMHS5kUZ5mKy4uxmQy+e93nKyqqorVq1fPa9pTeQhPCLHc5OXlsW3bNvLi80iITKDujTpcNtfMC4oFM2QZoqa6BrfbhtszSFyskdLSlKCDJ4DUNdEUfCKePruNtrER3nmngzfeaAmbiSVOnuzlo4+6MZlWExWVyAMPPCBTlgshBIt0C5/BYOC2227jxRdf5PHHH/c/qNrW1sZbb73F//k//+ei6n322WcBLmpq89zcXP83kGLpSf7akvy1NZF/fn7++P3yPjcfd39M/Rv1VNxeEVZXNLQQExNDb08v7e3toLjweIZITIyiqCiRmQ6J1DXRqCq0Hht/gP/o0XYUBW68sWBFb7feXiu//W0DERGZRERkcu+9906biGEupA/SluSvLclfW4uR/0Xdwnfw4EGsViujo6N84QtfYM+ePdx1113A+LNK0dHR1NXVcdlll7F582b+/u//3v8i3cHBwWkv0jUYDGzbto0333wTgLfffptHH32UXbt2UVRUhMPh4ODBgxw4cIBt27bxxhtvBIQw38twQgixVEZGRvj2t79NW18bVb1V5F+RT96leTMvKC6KikpHewfNLc34vDY83hFSU03k5ycEefbo/PrrbbQeGyHDFM2q2HiuvTaPG27IX5GDKJfLy49+dILBQYXY2E1cffW1fO5zn9O6WUIIsWDmO3a4qAFUQUGBf8rMqZqbm/3THh4/fpy/+7u/491338VgMHD99dezf//+adMXKorCtm3bOHz4MAANDQ187Wtfo7KykoGBARRFoaSkhL179/L1r389YIpIkAGUEGJ5qaur48knn6TF0kLbSBsb7thAQnbCzAuKOVFRaW5qpqOzA693DK93jMyMGHJz44LNrzCj/8/encfHUd55Hv9U35eu1n1f1m3ZBiecgWAIZ8IZMiEZQxIICUzIbnZ3BrKzr8mS187uTshkZjM7hAGSADaQ5QiEADGHE0MSiAMMIOuw7ss6rLPVkvo+av+QJast2ZJttUqyfu/Xy8NE1fXUU9/uru5f11NPjTR76Xl3kkyrnXxHAp/+dAGXXnpmFVGqqvLLX7ZQXz+Ow3EWhYVlfPe73z3uBd5CCLEeaVJArTVSQAkh1puXX36Zl19+mfrhenx6H2f9xVmYbKalVxTLoqoqrW2tDA0NEQlPEol6yctNICvbvvTKJzB80EPvn6bIstnJsydwySWFXHpp4dIrrhPvvz/Iyy+3YbNVkZiYz9/+7d/GzJonhBBngjU5icRaNHt/i+PdJ0TEl+SvLclfW4vl/9nPfpbKykoq0ipQ/Sqtv23dMJMTxFs0GqXpYBNDQ0OEwxNEol6KChPJyjq94gkgo8pOwXkJHPZ66PNM8dZbPezbt/iIjPVmYGCaPXs6MJtzMJnSue2221aseJJjkLYkf21J/tqKR/5xvQ/UWlJfXy9TSGpI8teW5K+txfLX6XTccccd/I//8T+oCFbQ0NtA30d95J+dr3Fv17dwJExjYyNu9wTh8ASoAfLzbTgcOgKBAGaLeelGlpBRbUdV4dCfp1CAfft60OkUPv3p9Xstm88X5plnmlBVOxZLCTt27GD79u0r1r4cg7Ql+WtL8tdWPPLfMGeghBBirUlKSuKOO+7AaXOSn5RP9/5uJgcnte7WuhUMBTlQdwC320U4NA4EKStzkpx0+kXTsTJr7OSfk8Cg10O/Z5rf/rab3/++d8W3sxpUVeVXv2plYiKM3V5FcXEJN998s9bdEkKINWvDnIFyOBxz1adYfZK/tiR/bZ0o/6qqKq6++mpeffVV3H43B984yNlfPBujRZ6rk+H3+6mvr8fn8xAKj6PXRykrc2K3GwkFQ6iquuKTPWRunjkT1ff+zJmovXu7MRh0XHBB3opuJ97+9Kd+Dh4cw26vxuFw8o1vfAODYWW/HsgxSFuSv7Ykf23FI3+ZREIIITQWjUb5p3/6JxoONvDh4IckFiRSfU31GTW7Wzx5vB7q6+sJBHyEQ+MYTSrl5U4sltX5jfBwvYe+96fItTvItjm49toyPvnJ7FXZ9unq7Z3k5z+vw2jMw2ot5p577qG2tlbrbgkhRFzJJBJCCLHO6XQ6vv71r5OanEpFWgXj3eP0f9yvdbfWhcnJSerq6ggEvIRCY5gtCpWVaatWPAFk1drJOdtBv2eaIZ+Xl19u4+OPh1Zt+6dqejrIs88eRKdLxGIp4qqrrpLiSQghlkEKKCGEWAOSk5O5/fbbcVqd5CXm0fWnLrkeagnjrnEO1B8gFJwpnuw2PZUVTkym1f9oy95qJ6vWzqHpSUb9Pl58sZXGxtFV78dyqarKCy+0MjWlYrNVUl5ezvXXX691t4QQYl2QAkoIIdaImpoarrrqKoqSi0g0J9L0WhNBb1Drbq1JI6MjNDY2Eg77CIXHSUw0Ul7hxGDU5mNNURRyP+Ego8pG95SbUb+P5547SEvLuCb9Wcrbbx+ivd2FzVZBUlIad955pwx7F0KIZdowk0h0d3cTiUTQ6/UUFRVp3Z0NR/LXluSvrZPJ//rrr6ezs5NQNMRHgx9x8LWD1F5fi04vX25nDQ8P09LSQiTqJRx2k5JioaQ4GeU4EYVCIVABhbhexK0oCvnnJRANq3S3TaADnnmmiZ07N1NSkhy37Z6szs4J9u3rwWIpwGRy8vWvf52kpKS4blOOQdqS/LUl+WsrHvlvmE9kt9uNy+XC7XZr3ZUNSfLXluSvrZPJX6fT8Y1vfIPMtEyq0quYOjxF17tdq9DL9WFoeCimeEpLs1JScvziCSAaiRKJRIhG4n8TS0VRKLwwkZQSC12TE4x5fTz9dCO9vWtjOObYmI9nnjmIwZCM2VzAddddR2VlZdy3K8cgbUn+2pL8tRWP/DdMASWEEOtFQkICd911F067k5KUEvoP9DPcMqx1tzQ3NDREa0srkYiHcNhNerqNosIk1tpkhYpOoejiJBILzHRMuhjz+HjyyQYGB6c17ZfPF+appxoJBo3YbFXU1tZy9dVXa9onIYRYjzbMNObB4NHrCEwm06r1TcyQ/LUl+WvrVPP/wx/+wJNPPknrWCvDvmG23bwNR5ojHl1c8w4fPkxrWyvRiJdwZJKMDBsF+YmwjOJp/sfcak4NHw2rtO914RkMUZ7kJD3Jxh13bCU93bZqfZgViUTZvbuBri4PDsc28vJKuO+++7BarauyfTkGaUvy15bkr63F8pdpzJfJZDLN/ROrT/LXluSvrVPN/6KLLuJTn/oUm5ybsOltNO1pIuQPxamXa9fg4cGY4ikzc/nFE8wUTbP/VpPOoFB6WTLWdANtky7Gpnw88UQ9Lpd/VfuhqiqvvtpBV9ckdns1yckZ3HPPPatWPIEcg7Qm+WtL8tdWPPLfMAWUEEKsR7fccgvFRcVUp1cTmY7Q8mYLanTdDxxYtoHBAdra2uYVT3by85ZfPGlNb9Sx6fIUTMk6WifGGXF5eeKJeqamVm92xf37B/jgg0Gs1jIsllTuvvtu0tLSVm37QghxppECSggh1jCj0chdd91FWnIalWmVuHpd9Lzfo3W3VkX/QD/t7e1zxVNWlp38vIR1UzzNMph1lF2Zgj5BoWVinMOjHp54oh6vN/5nE1taxnjttU7M5nxMpkxuu+02SktL475dIYQ4k22YAsrtdjMxMSEzoGhE8teW5K+t083f6XRy55134rQ5KUouoveDXsa6xla4l2tLf38/HR0dRCMewpFJsrMd5OWeWvEUjUTn/mnFaNVTfpUTbNA6MU7/4Sl2724gEAjHbZuHD0/z3HPNGAypWCxFfPazn+Xcc8+N2/ZORI5B2pL8tSX5ayse+W+YAqq7u5v29na6u7u17sqGJPlrS/LX1krkX1lZyU033UR+Uj5ptjRa9rbgm/CtXCfXkL6+Pjo6O2Zm24tMkZPtIDfHccpnnkKhEMFgcOZ+UBoy2fWUX5lCxBSlzT1Ob98kTz3VRCi08oXd9HSQp55qJBKxYrNV8MlPfpJrr712xbezXHIM0pbkry3JX1vxyH/DFFBCCLHeXX755Wzfvp2K1ApMqommPU1EQhGtu7WiDvUdorOrk0hkmkhkipwcBzm5p148rTWWJAPlV6UQ1Edoc4/T2eXi+eebia7gdW2hUJSnnmpkagrs9hqKi0v56le/uuqTaAghxJnKoHUHVkt2dvbcXYjF6pP8tSX5a2ul8lcUhdtuu42BgQECkQAfH/6Y1t+1UnlF5Rnx5fhQ3yG6urqOFE/T5OY6yM4+/WnbDQYDKirKGqnCrClGyq5IoWWPi47JCZSDCq+80s6112467edRVVVefLGFgQEvDsdWUlOz+Na3voXRaFyh3p8aOQZpS/LXluSvrXjkv2HuAyWEEGeKoaEh/tf/+l/0jffRNNJEyQUl5J2Vp3W3Tktffx+dnZ1zxVNebgJZ2XatuxVXk/0B2t504TRZKU5I4tOfLuCyy4pOq83f/a6Ht97qxW6vwuHI5d577yUvb32/NoQQYqXJfaCEEGKDyczM5PbbbyfNlkZ+Yj5df+rC1evSulunrH+g/0jx5Jk783SmF08Aiblmii9OYizgo88zxdtv97J//8Apt1dXN8xbb/VgsRRhMqXz9a9/XYonIYSIAymghBBiHdq6dSvXXHMNRclFOC1ODr5+EK/Lq3W3TtrAwMDcbHuRyBS5OSszbG+9cJZYKTg3gcNeD0M+D3v2dFBfP3LS7fT2TvLSS62YTFlYLPncfPPNbNmyJQ49FkIIIQWUEEKsU9dddx3btm2jMq0Ss2qm8dVGwnGcFnulDQ4O0t7RfmSq8pnZ9rJzNk7xNCuj2k72FjuHpqcY9ft44YUWOjsnlr2+y+XnF79oAhKwWjdx0UUXcdlll8Wvw0IIscFtmEkkGhoaCAaDmEwmNm/erHV3NhzJX1uSv7bilb+iKNxxxx2MPTBGKBrio8GPOPjaQTZfuxlFtzYmTDiewcODtLW3HblJ7hTZ2Q5y4lQ8BQIBVFVFURTMZnNctnG6crY7CPmjdLdOYFAUnn66kdtv37pkJoFAmKeeasTv1+NwVFNVVc2XvvSlNTepiByDtCX5a0vy11Y88t8wZ6AikQjRaJRI5Mya8ne9kPy1JflrK575m81m/uqv/or0lHSq06tx97vp+GPHim9nJR0eOkxb22zxNEl2lv207vO0JHXevzVKURQKL0gkqcBMx+QELo+f3bsbGBs7/r2+olGVZ59tZmQkgM22maysPL75zW+uyZm+5BikLclfW5K/tuKR/4YpoCwWy9w/sfokf21J/tqKd/6pqancddddOO1OSlNKGagfYLBhMC7bOl1DQ0O0tR4tnrIy7eTmJsT1Pk+KTpn7t5YpOoWSS5KxZRhom3QxNull1656pqeDiz7+tdc6aW93YbNVk5iYxj333IPNZlvlXi+PHIO0JflrS/LXVjzyl2nMhRDiDPHOO++wa9cuOsY7GJgeoPb6WpJzk7Xu1pyh4SFaW1qJRDyEI5NkZtrJz4tv8bQehQNRWl4dJzKpUpWSSn5OIrffvgWL5eio+z//eYBXX23Hai3DZsvjO9/5DuXl5Rr2Wggh1g+ZxlwIIQQAF154IZ/5zGcoSSkh2ZzMwdcO4nMffwjYahoeGT5SPM2cecrIsEnxdBwGs46yK1PAqtLqHqd/cIqnn24iFIoC0NY2zp49HZjNuZjN2ezcuVOKJyGEWEVSQAkhxBnk85//PJs3b6YqvQpjxDgzM19Q25n5RkdHaWluIRL1Eo64yUi3UZCfKMXTCZjsesqudBLSR2hzj9PZNcEvf9nM4cMenn22Gb3eicVSwpVXXskFF1ygdXeFEGJDkQJKCCHOIDqdjjvvvJO8nDxq0msIuoM0v9GMGtVmtPbExATNLc1Eoj7CYTfp6TYKCqR4Wg5rsoGyK1LwqiE6J118/PEQ3//+HwiFzNhslZx11lnceOONWndTCCE2nA1zDVRfXx+RSAS9Xi93ZteA5K8tyV9bWuQ/PDzM//7f/5v+sX4ahhvIPSuXkgtKVmXbs6ampzhw4AChkI9weJzUVCvFRUmrXjyFQ2FUVBQUDMb1d/cOd1+A1jfGCY5FsHhMlJZu46KLdvA3f/M3a3Za9mPJMUhbkr+2JH9tLZa/XAO1TGNjY4yMjDA2NqZ1VzYkyV9bkr+2tMg/IyODb37zm6TaUylJKaHvoz4OHzy8atv3+rw01DcQDvkJh10kJ5sp0qB4gpkpbCPhyLqdQjgh24S+QGEyGsJnMTM8PM4nP/nJdVM8gRyDtCb5a0vy11Y88t8wBZQQQmw0lZWV3HLLLeQm5pLtyKb97XYmByfjvt1AIEB9fT3BkI9QeJwEh5GSkhTW2L1d1wU1Cu0dE0STFZKqnPhNATJLM/nVr35Fc3Oz1t0TQogNacMM4fN6vXN3ol+r98k4k0n+2pL8taV1/r/4xS/Yt28fB4YP4FN8bLt5G5bE+NyPJBQKUVdXh8c7RTg0htWmo6IiFb1eu+pp5vovFVj794KKoUJn1wTj434MBidGo5VkTzLjrePUZNSQk5LDfffdR05OjtY9XZLW74GNTvLXluSvrcXyP90hfBumgBJCiI0qEonwL//yL9Q31vPR4Y/QJ+rZetNWDOaVvR4oEolwoP4AU5NuQuExzCaoqEzFaJRj8UlToffQJMPDXgyGZAwGG7W1tSQ6Emna08RE7wRbM7eSn5nPd7/7XZKT1879voQQYq1b9WugpqamuPfee7niiitIT09HURTuv//+RR/74Ycf8pnPfAaHw0FycjI33XQTnZ2dy97W3r17Of/887HZbKSlpfHVr36V4eHhk+2yEEJsaHq9nm984xvkZueyOWMzgYkATa81EY1EV2wbUTVKY1MjU1OThMLjGA0qZeVOKZ5O0cDg9EzxpE9Cr7dSVVVFUmISik6h8opKbKk2GocbOTxymAcffJBAIKB1l4UQYsM46U+2sbExHnnkEQKBADfccMNxH9fc3Mwll1xCMBjk2Wef5ec//zmtra1cdNFFjIyMLLmdt99+m6uvvprMzExeeuklfvzjH7N3714uu+wy+aAQQoiTZLfb+fa3v016cjo16TVM9k/S/lY7KzEIQUWlubmZiYkJwiEXel2EsnInZrN+BXp+eiLhCAcPNnPwYDOR8PqYRGJ4yMvAwDR6fQI6vZXy8nJSnalzy/VGPTWfq0GxKTSONNLV3cWjjz5KNLpyBbEQQojjO+khfLMPVxSF0dFR0tPT+e///b8vOAv1F3/xF+zbt4+Ojg4SExMB6OnpoaysjP/0n/4TP/jBD064nXPOOQePx0NdXR0Gw8wwk3fffZcLL7yQn/zkJ9x9991zj13OaTiPxzM3/tFut5/MLosVIPlrS/LX1lrKv6Ojg3/6p39iwD1Ay2gLhecUUvDJglNuT0Wlvb2dwcFBwmEXEKSi3IndYVy5Tp+GSDhCa1sbAJs2lWI0ro1+Hc/4mJ/Orgn0Ojt6QwKlpaXk5uQu+ljPmIe6F+pI1CdSk17Djh07uOWWW1DW4Gwda+k9sBFJ/tqS/LW1WP6rPoRPUZQlD87hcJhXXnmFz3/+83PFE0BhYSE7duzgxRdfPOH6/f39vP/++9x6661zxRPABRdcQHl5+ZLrL6a9vZ3m5mba29tPel1x+iR/bUn+2lpL+ZeWlnL77beTYc+gMLmQ7ve6GW459aHRPd09R4onN6oaoLQ0eU0UT5HwzNTl4XlTl/v9/rm/r0Vud4Curgl0Oit6QwIFBQXHLZ4A7Kl2qq+uZiIwQft4O2+99RZ79+5dxR4v31p6D2xEkr+2JH9txSP/uNxRsKOjA5/Px5YtWxYs27JlC2+++SZ+vx+LZfFZoBoaGuYeu9j677zzzpJ9aGxspLCwMKaAg6MzRKWkpFBQEPura1tbG16vF4CtW7fGLBsdHaW/vx+AgoICUlJS5pZFIpG5PickJFBSEnuzyq6uLiYnZ6YOrqmpiSkKJyYm6OnpASAnJ4f09PSYdQ8cOICqqlitM8M45jt06BDj4+MAVFRUxOQ5PT1NR0cHMHM/mOzs7Jh1m5qaCIVCGI1GqqurY5YNDg7OXWtWWlqKw+GYW+b3+2lpaQHA6XSSn58fs25rays+nw9FURZ9/mbzLywsjLnoORwO09jYCEBiYiLFxcUx63V2ds79UrB582b0+qNDg1wuF729vQDk5uaSlpYWs25dXR0ANpuNsrKymGW9vb24XC5gZsrn+fdVmZycpKurC4DMzEyysrJi1m1sbCQcDmM2m6msrIxZNjAwMDdUddOmTTG/OHm9XtqO/CKempq64KZ6LS0t+P1+9Ho9mzdvjlk2PDzM4OAgAEVFRSQlJc0tCwaDHDx4EICkpCSKioo41mz+tbW1Mb+yjI2N0dfXB0BeXh6pqUeHC0WjUerr6wFwOByUlpbGtNnd3Y3b7QagqqoKk8k0t8ztdtPd3Q1AdnY2GRkZMes2NDQQiUSwWCxUVFTELOvr65u7Z0NZWVnMzEUej2fuQJienr5gFrLm5mYCgQAGg4GampqYZYcPH2ZoaAiA4uLimGNEIBCYmxp6JY8Rs2fuQ6EQnZ2dmh8jtm/fzjXXXMPu3btx4KDpjSZMdhPJeUffk64JF9FoFJ1OR0pySky7Xq8Xn9/H0NAQw8PDqFEP0aiPkpJkEhNNBPwzw6z1ev2CG9cGg8GZWfEUFtzHKBKJEA6FATAajej0837jU5kbvq3T6xacSQqFQnPXdJnN5rmzTvP19fXP/f9VVUffs7P9VXRKzOt3pt0w0SNFmMlsivkBMRqNEgqGADAY9OgNsfsaCAThyK+eJnNsu+FweK6QM5mMeLwROtpdKDozOl0CCQkJJDgS8Hg8C36xnnBPEIlEUBQFZ56Tsh1ltPy2BYvBwu7duxkbG6OqquqkjxEdHR1MT08DrPgxIhSayenYQS9yjJgR7+8Rs/kfa719jxgZGWFgYABgXX2POF7+6+17RDyPEfH8HrFY/rPv01MVlwJq9oDmdDoXLHM6naiqisvlWvBmXO76y7kRVjgcjjlQp6enEwgE5oIMh8OLrnO8F3k0Gp1bttg489llS7V77IfH/HYXu8ljKBRCVdVFh51EIpHTavd4+zq/3WP3VVXVE7Y7u6/HnqVMT09ncnKS6enpmS86J2h3rTw3S+3r7OtosdO9J3pultNuKBRadNmJ2p1dd7F209PTGRkZOe7zvtwMF1t3fp+OtdS+BoNBotFozAfZYu2eaoaLZbTcdlfydZiWlsbhw4eX1e5qHSMuueQS6uvriXwYodffS9OeJrZ9fhs259EpXo93TY2qqoyMjNDX14dBHyKqeigsSMTptKCq6ty2VBbmr6qLv3ZnFx5d95hF8/ZhsfXnb/dkzQ1NVxcbXXGCdtX5fVq04Znlizc7t67XF6a9zQWYMBhScDqdZGRkEFWjRNWFz8Hsc6McaTizMhP/lJ/u97rBAS+88AJf/vKXKSwsXLDuqX4unO4xYtb8L1Ugx4hj+7Scdk/lGAFgMBgWFFfr6XvEybS7Vp6b+X2y2+0xxcpsu+vle8T8dhez1r9HOJ3OmB8ITvf637gUULNONNRvOWO0j/eY5axrMBhiHpeTk0MgEJj7BcdgWLjrBoPhuOPjdbqjv3gu9kKfXbZUu8f2fX67iz35RqMRVVUXbVev159Wu/P/e7x2j91XRVFO2O7svh7bn5ycHIxG49FfkE/Q7lp5bpba19n9XCrDU2k3EoksuuxE7c6uu1i7OTk5+Hy+uV+OjrXcDJfa12Mtta8mk4lIJBKXDKPR6Em/b+L1OszOzp774WetHCP0ej2f/exnmZ6exnrISutUKw2vNLDt5m2YbKa5fVjs9TAxMUHfoT4gQCTqJS83gfSMo7/+z25LWaRyUJQj/2exw/i8IeLHLlbmt7vIa//Y4eXlR34lDkcic7O/5uXlYjaZF+Q4t96iHy0nGLauzO/TcfaHxXOYXTcQjNDZ6SYS1WM0ppCSkkJ5efncL+U6ZWH+Op1ubjz/rIJPFOB3++lo6qDYVswLL7xAbW3tgunNl3otne5xdqn3cmZmZmwMcoyI6dNy2j3VY4TVal1wJm49fY84mXbXynMzv08pKSkLRrKsp+8Rs8vifYw41kodI7KysmLOUp/utaKndR+o400i0dLSQmVlJQ8++CB/9Vd/FbPO3/zN3/CjH/0Ir9d73CF8r7/+OldddRWvvvoq11xzTcyyL3zhC7zzzjtzp3BB7gMlhBCnKhAI8MMf/pD2rnY+PvwxJqeJLTduQW9cfAY9t9tNfUM94bCXcHiCjAwbBfmJxyk+tDd/EonysjL0Bu1nBpwVCkVpbh4jGFQwGpwkJCaxZcsW9LpT62M0EqXh5QY8gx68LlzZAAAgAElEQVS2ZW2jKK+I++67Ty5aF0KIY6z6JBLLUVpaitVqnRvvOF99fT2bNm06bvEEzI3XPN76x47nFEIIcWrMZjP33HMPWelZ1GTU4B3z0vxm88x1SseY9kwfGbPvJxyeIDXVsqaLp7UsElZpax0nGFAxGlKw2R0z12WcYvEEM9eGVV9djTHJSMNwA30DffzkJz857tAYIYQQpyYuBZTBYODaa6/lhRdeiKnuent72bdvHzfddNMJ18/NzeWcc87hySefjBnvuH//flpaWpZcXwghxPIlJyfz7W9/m7TENKrSqhjvGqfz3dibnvt8PhrqGwiFfITDLpKSzBQVJa/54klv0FNVVUlVVeWaOfsUjai0tbvw+qIYjE4sFju1tbUYDac/e6HBbGDz5zYTMUVoHGmkta2VJ554YkXu9yWEEGKG/v5jb+C0DHv27KGuro76+npeeuklMjIyUBSFpqYmioqKMBqN1NbW8pOf/IR9+/aRlZVFQ0MDd955J4qisGvXrpghBQaDgbfffpuvfOUrc38rKyvjn//5n6mrqyM1NZX9+/fzzW9+k4KCAh566KGYcaiqqhIMBmP6aDabY8Y3Njc3Mzg4iMvlWjC7iog/yV9bkr+21kP+iYmJFBUVUf9RPUadke7ubgxmA4lZiQSCAQ7UH8Af8BAKu3A4DJRtSkGnW+PV0xHBQJBwJEw0EtW8iFJV6OyYYHIqhNHgxGy2s2XLlhOOyjhZBrOBpNwk+pr68Aa8BFwBdDrdglkaV9N6eA+cySR/bUn+2los/+XUDidySpNI3H333XNTZgI899xzPPfcc8DMVJtFRUVUVlby1ltvcd9993HzzTdjMBi49NJL+cd//MdFZ4E5dmaNSy65hN/85jd873vf49prr8Vms/G5z32OH/7whwumvl2OQCCw6OxvYnVI/tqS/LW1XvKvqqpi586d7Nq1C3/YT+c7nehtevom+/D7vIRD49isOso2OdHp10fxBPNm6NO6yyp0d08w4Q5gMDgxGq3UbK7BarWu+KYSMhKovKKSpj1N9Lh7ePnll8nJyeHss89e8W0tx3p5D5ypJH9tSf7aikf+p1RAzc7HvpTt27cv66Z+xxtacPnll3P55ZefTNeOy2AwHHemKhF/kr+2JH9traf8L7zwQkZHR3n11Vfxhrzsf3Y/jlo7imMKk0mhrNyJ3qB1JXKSjsyGt/hUeatEhUN9k4yN+TEYkjEYLNTU1JDgSIjbJlOLUyk6r4iuP3VhN9r5+c9/Tnp6+oL77qyG9fQeOBNJ/tqS/LUVj/xPaxa+tUJm4RNCiJWjqiqPPvoojz3+GB3THQSN06SdY2bzJ9Ixm9fGdUTrzeDgNP390xj0iej1dqqrqxfcEykeVFWl9betjLSOsDVzKwVZBfzt3/7tgpvMCyHERrImZ+ETQgixvimKghqNkuADfVBF6VZQFt5DUizDyIiX/v5p9HoHOr2NsvKyVSmeYOZ5LLukDEemg6aRJg6PHuahhx6SmfmEEOI0SAElhBAixp49e3j//fcpKjJgt8L2vCwMIYW2112EAzKG/2SMjfno6ZlEr7Oh1zsoKS4hKzNr6RVXkM4wM705VmgabqK9o50nn3xSZuYTQohTJAWUEEKIOR988AEvvfQSgUAP4OLee8+jpDCZ8mQnocko7XtdRMPyxXs5xsf8dHW50els6A2J5Oflk5eXp0lfTDYTNdfU4I16aR1rZf/+/bzxxhua9EUIIda7DXM12+HDh4lEIuj1erKyVvfXPyH5a03y19Z6yb+7u5vHH3+cYHAYv7+Xyy8v5pOfzKakJJmf/rSOsqhKy/A4nW9NUHppMso6mcY8Eg6jqjNzSOhX6SLu8XE/nV0T6HRWDIZEcnJyKCouWpVtH48j3UHFZypoeq0Jm9HGiy++SHZ2Nlu2bIn7ttfLe+BMJflrS/LXVjzy3zBnoIaGhhgcHGRoaEjrrmxIkr+2JH9trYf8x8fHefDBB/H5xvD5Wjn77Cw+9amZsyWpqVZ27qwhxW6hNDEZd2+Anncn180QsHA4QjgcJhyOLP3gFeAa99PVOVs8JZGdnU1paSmK5vOoQ1ppGoXnFNIz0cOIZ4Sf/vSnDAwMxH276+E9cCaT/LUl+WsrHvlvmAJKCCHE4vx+Pw8++CAu1zAeTxOFhYl87nObYm4omJubwJe+VI3TaqUoIYnRVh8DH05r2Ou1yeXy09k5gTKveNq0adOaKJ5mFXyigLRNabSMtTA+Nc6//uu/LpiNSgghxPFtmGnMJydnfi1VFEWmb9WA5K8tyV9bazn/aDTKQw89RF3dR0xPf0xycpQ779yGzWZc9PH19SM8/3wzg55p+jxTFJyXQEa1fZV7fXKi0SiogEJcb28xMRGgo92ForNgMCSTlZVFWVnZmiqeZkVCEeperCPsCnNW1llUV1bzne98J273qVnL74GNQPLXluSvrcXyP91pzDdMASWEEGKh5557jjfffBOvtxGDYZI779xGWprthOvs3z/Ab37TziHPFEM+DyWfTsJZYl2lHq9N7okA7R0uFGWmeMrMzKS8vHxNFk+zAtMBPnruIywRC1syt3DxRRezc+fOmDOPQghxJpL7QAkhhDglf/jDH9i7dy9+fweRiIsvfrF6yeIJ4Lzzcvj0pwvItyeQarbS9Xs3k/2BVejx2uR2B+iYXzxlrP3iCcDsMFN9dTXT4Wnaxtv44x//yL59+7TulhBCrHlSQAkhxAbU3NzM008/TSAwQCAwwOc+t4mSkuRlr3/ppYWcfXYWRQlJJBrMtP92As/oxrs5q9s9M2yPI8VTRnoG5RVrv3ialZiVSPmOcoamh+ib7OPZZ5+lqalJ624JIcSatmEKqEAggN/vJxDYuL+Sakny15bkr621lv/Q0BAPP/wwgcAYfn8HF1yQxyc+kX1SbSiKwnXXlVFVmUppYjJWDLS94cLvDsep16dOVdW5fytpcjJ4pHgyYzAkk56eTkVlxbopnmZlVGRQsL2ALlcXY94xHn30UUZHR1d0G2vtPbDRSP7akvy1FY/89ffff//9K9aaRlRVJRgMxvzNbDbHjONubGzk8OHDuFwumYNfA5K/tiR/ba2l/D0eDz/60Y8YHx/A42mgvDyFG24oP6XrXhRFobIyjd6eSRQ/jHv8jPX6cJZY0BvXzu9zwUCQcDhMNBJdsUkSpiaDtLeNHymeUkhPS6eysnLdXj+UlJvE9Mg0/YP9JBmT6Oro4rzzzkOv169I+2vpPbARSf7akvy1tVj+y6kdTmTtfMIJIYSIq3A4zEMPPcTQ0AAeTyOZmRZuvrkC3WncENdo1PHlL9eQk5lAeVIKqkel9XUX4UB0BXu+tky6g7TNK57SUtPWdfEEM8VwxWcqMCYYOTh6kO7ebp566ql1c68vIYRYTatzS/Y1ICUlhXA4HLcpWsWJSf7akvy1tRbyV1WVp556itbWFrzeRmy2KF/+cjVm8+n3yWo1cNttm/npT+uIoNIyMU77my7KrkxZE2eidHo9c/OYn6aj1zzNFE+pqalUVq3v4mmWwWyg+upqPn7+Y9rG2tDv11NcXMwll1xy2m2vhffARib5a0vy11Y88pdpzIUQYgN4/fXXeeGFF/B6W4hGR7j99q3k5SWs6DZGR7389Kd1jLi9tLjHceQY2fSZFHT69V9cwMLiKS1t5syTTjmzPmtG2kY4+MZBSlNKyU/O56//+q8pLS3VultCCLFiZBpzIYQQJ/TRRx/x4osv4vf3EgwOceONFStePAGkpdm47bZanA4rZUkpTA8E6XxrAjW67n+nm7nP09xsezPXPFVVVp1xxRNAelk6edvy6HR14vK6ePjhh3G73Vp3Swgh1owz78gvhBBiTm9vLz//+c8JBIbx+3u47LIiamvT47a9nBwHO3fWkGK1UJqYgrsnQPcf3ev6WpoJlz/mJrnp6et7wojlKD6/mKScJA6OHmR4fJiHH36YcHjtzbAohBBakAJKCCHOUBMTEzz44IN4vWP4fC1s3ZrOxRfnx327hYVJfPnLNaTarBQnJjPW7ufQ/ql1WUS5XH46OibmiqeMjIwzvngCUHQKlVdWolgUDo4cpK29jeeff17rbgkhxJqwYa5ma2trm7uArKysTOvubDiSv7Ykf21pkX8gEODBBx9kfHwIr7eR/HwH1113atOVn4pNm1K4+eZKnnnmIJFolJ6Dk+hNCrnbV37o4FKCweDcHBImk2nZ67nG/XR2TqDoZoqnzMxMysvXz01yT5fJZqLqqioO/OoAna5OdPt0FBcXc+655550W3IM0pbkry3JX1vxyH/DFFBer5dQKITRaNS6KxuS5K8tyV9bq52/qqo89thj9PR04fE0kpio45ZbqjGu8ox41dVp3HBDOS++2EJEVemrm0Jv0pFVa1/VfqjRmZvonkzxOD7up6tzAkVnxWBIIiszi7Lysg1TPM1KzEqk9KJS2t5qI8GUwO7du8nJySE//+TOZMoxSFuSv7Ykf23FI38ZwieEEGeYl156iQ8//BCvtxmDwc9f/mUNDsfyz7yspLPOyuSaazaRZbOTY3PQ9/4Uwwc9mvRlucbGZs88HSmesjZm8TQruyabrKos2sbbcHlc/Nu//Rsez9p+DoUQIp5kGnMhhDiD1NXV8ZOf/ASfr4tgsI+dO2soK3Nq3S1+//te9u7t5tD0FEM+D0UXJZFWZtW6WwuMjfro6najO1I8ZWdns2nTpg1bPM2KhqPUvVBHyBXirKyz2LZlG/fcc498zgoh1iWZxlwIIQQAo6OjPPbYY4RCowQCh7jqqpI1UTwBXHxxARdfXEC+I4F0i43uP7oZ7/Rp3a0Yw0PeI8WTDYMhiZzsHCmejtAZdFRdXUXEEKF5tJmGhgZeeeUVrbslhBCakAJKCCHOAKFQiIcffpjp6XG83lZqatI577wcrbsV47LLCjnvvFwKExJJNVvpetvNRK9f626BCgP90/QemkSvs2MwJJKbk0vpplIpnuaxJFiourKKicAE3RPdvPrqqxw4cEDrbgkhxKqTAkoIIc4Azz33HD093Xi9B3E6jdxwQ9mam2pbURSuvrqEs8/OoighiWSThY7fTTDZH9CsT6oKPb2TDAxOY9AnoDckUFhYSElpiRRPi0jOS6b4/GIOTR5izDvG448/jsvl0rpbQgixqjbMLHyjo6NEo1F0Oh1paWlad2fDkfy1JflrK975v/fee7z99tv4fB0oipcvfnEbZvPaPLwrisJ115URDkehDtonXbT/1kXZlU4SMuMz0UUkEpmbxlyv18/9XY1CV9cE4y4/BkMSOp2V0tJScnNy49KPM0Xutlzcg25aelpwmBw8+uij/Jf/8l9isj2WHIO0JflrS/LXVjzyX5ufsHHQ398/N4WhvHhXn+SvLclfW/HMf3BwkCeffJJgcJhgcJAbbignK8uxottYaTqdwo03lhMKRVGboM09TvsbLsqvSsGevvJFVDgUnpvGfPZLfjSi0t7hYnIyiMGQgl5voaK8goyMjBXf/plGURTKLy3no2c+4uDoQUx6E7/+9a+58cYbj7uOHIO0JflrS/LXVjzylyF8QgixTgUCAR555BG8Xhc+XxvbtmVy1lmZWndrWfR6HV/4QiXlZU7KklKwYqD1dRee0VDctx0OR2lpHWdyMoTR4MRgsFJTXSPF00kwWoxUXlnJVHCK7oluXnvtNRobG7XulhBCrAr9/ffff7/WnThdqqrO3Gl+HrPZHDP+32w2k5ycTHJyMlbr2ps690wn+WtL8tdWPPJXVZXdu3fT1NSAx1NPWpqRL32pGoNh/fwuptMpVFWlcujQFIpPYdIfYKjDQ2KOGZPt+MPBTpai6NDrdej0eiJhlZaWcXy+KEajE6PJxubNm0lJTlmx7W0UZocZvUFPb3svCeYEOls7Offcc7FYLAsfK8cgTUn+2pL8tbVY/supHU5E7gMlhBDr0B//+Ed2796N19sCjPLNb55FerpN626dkmAwwu7dDXR2T9DmHsenhKm42oktdeXuGg/g94dpbXURCoLB6MRstlK7uRa73b6i29lIVFWl6TdNTPZOcnb22Wyu2sx//s//WT5/hRBrmtwHSgghNphDhw7xi1/8gkBgkGBwiOuvL1u3xROAyaTn1ls3U1KUTFmSE0vUQOtr43jHVm44n9cbprl5nFBIwWhMxWq1s3XrVimeTpOiKJRfVo7OpqN5tJnW1lZefvllrbslhBBxJQWUEEKsIz6fj0ceeYRAYAK/v4Nzzsmhtnb9X7szv4gqT3ZijhwposZPv4iamgrS0jxGJKLHaHTicCSybes2rBYZSrMSjBYjVVdUMRmcpMfdw549ezh48KDW3RJCiLjZMAVUJBKZ+ydWn+SvLclfWyuVv6qq7Nq1i6GhATyeJrKz7Vx1VckK9VJ7JpOenTtrKC5MojzZiSlioHXP6RVRExMBWlvHUVUjRoOTxMRktmzZgskUnynTN6rE7ESKzivikPsQ495xfvazn+F2u+eWyzFIW5K/tiR/bcUj/w0zjXlDQ8PcFIZbt27VujsbjuSvLclfWyuV/+9+9zs+/PBDvN5WzOYwX/zilnU1acRymM0Gbr11M7t2NQDQMjFG62vjVFztxJpyctdEjY766O52E43oQbFid1iora1Fr1u5CSrEUXln5eEecNPS14LNZONnP/sZ3/nOd9DpdHIM0pjkry3JX1vxyD+un7zvvfceV155JQkJCTgcDnbs2ME777yzrHXvv/9+FEVZ8G+x2X2EEOJM19nZyfPPP08g0E8oNMqNN1aQknJmHg9ni6jC/CNnosJ6Wva48LmWfyZq6LCH7m43ep0NRUnEmZJKaUmpFE9xNHt/KMWi0DLaQnNzM7/5zW+07pYQQqy4uJ2Bev/997n44os555xz2L17N6qq8sADD3DZZZexb98+zj///GW189prr5GUlDT3v091Zp+EhATC4TAGw4Y56bamSP7akvy1dbr5ezweHnnkEYLBCfz+Li68MI/KytQV7uXaYrEYuO22zTzxRD0ArRPjtOxxUXGNE2vyCXJUob9/isHDHvR6B3q9g/R0J3n5eTIz3Cow2UxUXlHJgV8doNfdyyuvvEJZWZkcgzQm+WtL8tdWPPKP2zTmV111FR9//DGdnZ3YbDOzQ01NTVFSUkJ5efmSZ6Luv/9+vv/97zMyMrLkXYNlGnMhxJlKVVX+9V//lQMHPmJ6+kPy8y189au16PUb4/jm84V54ol6evvdtE6MEzJGKb968SJKVaGnx83oqA+DPhGd3kZRURH5+fkoLO/eHmJl9H7QS8+fe6jNrKUgo4C/+7u/IzExUetuCSEEsIanMX/nnXe45JJL5oqn2Y5dfPHFvPvuuwwODsZr00IIccZ47bXXqK+vx+drwWKJ8oUvVG6Y4gnAajXwla/UUpCbRHmSE0NIR+uecfzucMzj1Ch0dk7MFE+GJPR6O2WbyijIL5DiSQP52/NJzkumebSZUdcou3bt4gy47aQQQgBxHMIXDAYxm80L/j77t/r6erKzs5dsp7a2luHhYdLS0rjyyiv5+7//ewoKCpZcr7GxkcLCwphfvAKBAM3NzQCkpKQsaKetrQ2v1wuw4CKz0dFR+vv7ASgoKCAl5ehd6yORCA0NMxc8JyQkUFISOytWV1cXk5OTANTU1MScQpyYmKCnpweAnJwc0tPTY9Y9cOAAqqpitVopLy+PWXbo0CHGx8cBqKioiLk+bHp6mo6ODgAyMjIWZN3U1DR3QV11dXXMssHBQYaHhwEoLS3F4XDMLfP7/bS0tADgdDrJz8+PWbe1tRWfz4eiKGzZsiVm2cjICAMDAwAUFhaSnJw8tywcDtPY2AhAYmIixcXFMet2dnbO/VKwefNm9Pqj1zG4XC56e3sByM3NXXDGsq6uDgCbzUZZWVnMst7eXlwuFwCVlZUxr9nJyUm6uroAyMzMJCsrK2bdxsZGwuEwZrOZysrKmGUDAwOMjIwAsGnTpph7zXi9Xtra2gBITU0lLy8vZt2Wlhb8fj96vZ7NmzfHLBseHp778aGoqChmeGswGJybOjgpKYmioqKYdTs6OpiengZm3lfzf2UZGxujr68PgLy8PFJTjw4Pi0aj1NfPDKNyOByUlpbGtNvd3T0321ZVVVXM7GZut5vu7m4AsrOzyciInW67oaGBSCSCxWKhoqIiZllfXx9jY2MAlJWVxfwY4/F4aG9vByA9PZ2cnJyYdZubmwkEAhgMBmpqamKWHT58mKGhIQCKi4vX9DGitbWVZ599Fre7jWh0kK98pZbExNjj6vj4GKoKBoMh5vUwk9M0fn8AgOTk5Jj3TSgUmtum1WqNyRdm3lfRaBSdThezLzDzGvb5fMDM+9VoPDq5QyQSYWJiAgCLxYzd7ohZ1+12Ew6HURRwOmOHIfr9Pjwe75GcHJhM5iP9M3DbbTX827+9jz9gp9MzSctvxqm4xoklyUAkotLaMsrkVBBFSUSvt1FZWUl62szxNBAMzL327Tb7gmtpx8ZnXmcGg4GkxNgMp6enCQTnZTjvGqpgKDh3XLJardisi2SoRtHr9DHHOwCP14Pf7z+aoeFohuFwGPfkzHvKYrYsuFfVhHuCSCSCoig4U5wxy3x+39xrNMGREPN+jESPPjcmk4kER0LMupOTk4TCM9eZOZ3OmMLTH/Dj8XgAsNvtWMxHM1RR5z6LjAYjiYmJKIpCxeUVfPj/PqR+oJ6piSlsNhs7d+6UYwTyPUK+R8yQ7xEztPgeMfs+PVVxK6Cqq6vZv3//3AcwzLy4//znPwPM7dDxlJaW8j//5//krLPOwmKx8N577/HAAw/wxhtv8O///u/k5uaecP1wOLzg1y5VVQmFQnPLF1tndvmxotHo3LJoNLpg+XLbPbZP89tdbHrFUCiEqqoxX1BmRSKR02r3ePs6v91j93V+hou1O7uvirLwF9/ltrtWnpul9jUUChEOhxc93Xui52Y57YZCoUWXnajd2XWXancxy81wsfXn9+lYS+1rMBgkGo3GfJAt1u6pZrhYRsttV+vX4eTkJI8++iihkItIpJ8LLsiiuHjhEKhoNIqqLr7NaFSd9/djszi6bLGcotHoom3OPn457Uajx293kUNETLvHdsliMXDzzSU8+2w7uhGFTs80LXvGKb08md6hKaanQygkotOZqa6uJnVecRbT7oL+Mq+/i2Sozsth4a4unaEaXfQMWGyGxzY7L0N1sef1SIaLtRtd3r6qJ3huFu2TuvTrZf5/YeZ6qPJLy/noxY8YZpjXXnuNyy+/POYLsxwjYvu0nHble4R8j5DvEUedzjHidMStgPr2t7/NHXfcwT333MN/+2//jWg0yve///25X0mWGmN46623xvzvHTt2sGPHDs4//3weeOABfvzjH59wfYPBEPPm6+rqIhgMotPp0Ov1i15IZjAYFj3AzPZ3dtlifZ9dtlS7xx4Q5re72JNvNBpRVXXRdvV6/Wm1O/+/x2v32H1VFOWE7c7u67H96erqwuv1zuV/onbXynOz1L7O7udSGZ5Ku5FIZNFlJ2p3dt3F2u3q6sLv98/lf6zlZrjUvh5rqX01mUxEIpG4ZBiNRk/6fROv12FPT8/cTKLLeR2qqspjjz3GxMQowWA7RUWJXHhhzqLPuU6nQ1UXf950OmXe349d9+iy47W72L7MPn457ep0i7er0+kWLaDmt3vsckUBu93ELbeU89xznRjHTBwcG+XPTw/i2GJGb09BpzOyqXTTgrMyfp//SM+URYuOE+2rTtEd/fvCXV06w+M8N7EZHtvsvAyVxZ5XHaqqLrpNZd5zfqJ9VU7w3CzaJ+XUXi/OIicZ1Rn0N/aTYErg//yf/8MDDzww976VY0Rsn5bT7ql83ofDYYLBIF1dXTFnZtbT94iTaXetPDezfYpEIrhcLoLBYEz+6+l7xOyy081Qi+8RkUiEQ4cOYTab5/JfbN9PRtwmkQD4wQ9+wN///d/Pne47//zzufjii/nBD37AH/7wBz71qU+ddJtVVVUkJibOncmC5V0IVldXJ3Pwa0jy15bkr62Tzf/3v/89Tz31FB5PAxbLNHfffTYOh9z4dZbHE+L//t8PeGd/H6M6P1jNZF2QzdkXno3dZl/w+LHxsbnREKnOM3v2wrUoEorwzhPvoPPoqEyu5LZbb+P666/XulsbinwGaEvy19Zi+a/ZSSQA7rvvPkZHR6mvr6e7u5t3330Xl8uF3W5n+/btp9Smqqoyu54Q4ow1Ojp65H5Pg4RC49xwQ7kUT8fo6XHj9YawmuykR3OxqFbohOjU4sPPhLb0Rj1FFxfhi/gY9A6yZ8+euWtrhBBiPYrrGahj9fb2smXLFr72ta/xz//8zye9/v79+7nwwgv5D//hP8Ssv5wqcvaaqOMNoRHxJflrS/LX1nLzV1WVH/3oRzQ31zM9/e9s357BddeVHffxG42qqvzxj328+WYXRmMGJlMJhw8PkZaRRourBa/qZfPnNpOYHXutWFSNzly/pCw+JE7EX1SNcuj9Q/S838O2rG2U5Jbwd3/3dwsm9BDxIZ8B2pL8tbVY/qd7BipuBVRDQwO//OUv+cQnPoHZbKauro5/+Id/oKioiH379sXMyHLZZZfx9ttvx1yct3XrVnbu3ElVVdXcJBI//OEPsdlsfPDBBzGzwch9oIQQZ4K9e/fy7LPP4vEcwOEI8K1vnY3ZLB+2AOFwlF//uo2PPx7CYinEbC7g/PPP5wtf+AIPP/wwB5sP0jjSyFRkipprakjOS166UbGq1KhK3Yt1BEeDbM/ezkWfuoivfOUrWndLCLEBnW7tELdPZpPJxO9+9zv+5V/+henpaQoKCrjrrrv47ne/u2BK1kgksmBmjerqah555BEGBwcJBoPk5ORwyy238L3vfW9Z058LIcR6Mjg4yIsvvkgwOEA47ObGG7dI8Ue21FgAACAASURBVHSExxPi//2/Jnp7p7DZKjGZMrjhhhu46qqrUBSFb3/72zz00EMojQpNI000vNJA9TXVOAucSzcuVo2iU6i8vJIPn/mQDlcH+nf11NbWcvbZZ2vdNSGEOCmrOoQvXuQMlBBiPYtGo/zgBz+go6OJ6ekPOe+8bK6+unTpFTeAkREvTz3ViMsVwW6vxmpN5fbbb1/wpTsUCvHII4/wcd3HHBw9iMvvouqqKlKLZdKItebwwcO0/q6V6vRqCtML+d73vrfgPllCCBFPp1s76O+///7749CvVaWqKsFgMOZvZrM5ZorCiYkJvF4vgUBAxlxrQPLXluSvraXy37NnD/v378fjacTp1PPFL1aj15/eFKtngo4OF7t2NeD1GnE4tpCSks13vvMdqqqqFjxWr9dz9tlnM3R4iLA7jDfopedgD7ZkG4YEA5FwhEg0gkEvZ/W0EAgG5p6DpMwkvONeBgYGSDGlMDQ4xLnnnnva0wqL45PPAG1J/tpaLP/l1A4nsmE+SXp6euamMJRfulaf5K8tyV9bJ8r/0KFDvPLKKwQCh4hGp7nppq0YjXL2/P33B3n11Xb0+hQcjioKCor41re+RUpKynHXMRgM3HnnnTP3A9kPrWOtNL/ZTOYnMkkpSUGn02F2mldxL8Ss6enpmKnkyy4p498H/52W0RaMjUbeeustduzYoXU3z1jyGaAtyV9b8ch/wxRQQgix1kQiER5//HGCwUkCgV4uuiifvLzEpVc8g0WjKq+/3smf/tSP2ZyLxVLCtm3buOOOOzCbly5+dDodX/va12aKqD/MzLrX/cduIuEIGZUZq7AHYjmMFiMVl1VQ/3I9g9ODPP/881RWVso1zkKIdWHDFFA5OTnHvSuziD/JX1uSv7aOl//rr7/OoUOH8HpbyMiwcsklBRr1cG0IBMI891wzbW0urNZNmM05XHHFFdx4440ndU2roijs3Llzpoj63cwUtoPvD2I2muVGuhqx2Wxz0wjPSilIIXdLLp31nSRbknn88ce577775PrlOJDPAG1J/tqKR/4bpoBKT0/XugsbmuSvLclfW4vlPzg4yKuvvkog0Ec06uGGG7ZhMGzcL44ul5+nn25keDiAzbYZszmVv/zLv+RTn/rUKbWnKApf/OIXMZlMKK8rWEwWDr13CKPOSP72/BXuvViK1WJd9O/F5xfj6nXROtaK1WDlt7/9LZdffvkq9+7MJ58B2pL8tRWP/DdMASWEEGtFNBpl165dBAKTBAI9XHhhHrm5CVp3SzOHDk3y9NNN+Hw6HI5tJCSkcdddd1FRUXFa7SqKwo033ojRaOSVV15Bp+jo2t9FJByh8JxCmbRgDdAZdJRfWk7di3UMTA3w0ksvsXXrVjIyZLilEGLt2rg/dwohhEbeeustOjo68PlacTrN7NhRqHWXNFNfP8xjjx0gELDicJxFdnYR3/3ud0+7eJqlKArXXnstN910E4XJhRQnF9P7QS8df+jgDLiLxxkhMTuRnNocuie6mfJNsWvXLnluhBBrmpyBEkKIVeR2u3nppZcIBgcJhye5/vqNOeueqqq89VYv+/b1YDJlYrWWUVFRyV133bXgZusr4corr8RoNPLMM89g0Blor28n7A9Tflk5Ov3Gy3+tKTqviLHuMVrHWjG3mvn973/Ppz/9aa27JYQQi9owBdSBAwfmpjDcsmWL1t3ZcCR/bUn+2pqf/wcffIDXO4Xf38327VkUFSVp3b1VFwpF+dWvWqmvH8FiKcJiKeDCCy/ky1/+MgbDyn8szeaflpbG1772NZ544gmMeiPN7c2EA2GqrqpCb5SLu+NpbHwsZhrzY+mNesp3lHPgpQMcnj7ML3/5S2pra3E6nRr09swjnwHakvy1FY/8N8zPbqqqzv0Tq0/y15bkr63Z7Lu7u/nzn/+M39+JxaLwmc8Ua921VTc9HeTxxw/Q0DCK3V6F1VrI5z//eW699da4FE8Q+/o/77zzuPvuu8lOymZzxmbcfW7qf11PyB+Ky7bF8iXnJZNdnU3XRBeTnkmefPJJOWatEPkM0Jbkr6145L9hCiir1YrNZsNqXXwmIBFfkr+2JH9tWa1WzGYze/fuJRyeJBgc5vLLi7DbjVp3bVUNDXl45JGP6e/343BsxW7P4e677+aKK66I64QOx77+t2zZwn/8j/+RrOQstmRswTfs48CLBwhMB+LWh43OoDdgMBgw6E9cJBdfUIzeqqdtvI3Gxkb279+/Sj08s8lngLYkf23FI39FPQPK4Wg0ytTUVMzfEhIS5F4SQog1Y+/evTz77LNMT39EVpbCnXduQ6fbOLPANTSM8KtftRKJWLHba3A6M7nnnnvIz9duSvFDhw7x4x//mKHxIeqH61GsCrXX1WJNli85WhrrGqPxN41UpFVQnF7M/fffT1LSxhvqKoSIn9OtHaTCEEKIOJuYmODXv/41weAA0aiHz35204YpnsLhKK++2s6zzx5EVVNxOLZSXFzOf/2v/1XT4gkgPz+fe++9l/ysfLZlbkPn11H3Qh3TI9Oa9mujSy1OJaM8g87xTiamJvjFL34hQ5+EEGuKFFBCCBFnzz//PD7fFH5/D5/4RBZ5eRvjnk8ul5+f/ayO9947jNW6Cbu9knPPPZ+//uu/Jjk5WevuAZCRkcG9995LcUExWzO3Yo6YOfCrA7gH3Fp3bUMr/VQpilmhY7yDjz766P+3d+fxUdX3/sdfZzKZSSaTfSMhJIEQCBAWWRTQRhAQVGhB663e+tCKS+1Vb9uHe9G20t6r9fZxH9RH29tqrbb0Z8Ui4m4FZFEW2ZckhBCSkJWQPZlkJrOd3x9pxgwJECAzJ5n5PB8PHrZzcr7zmfecc2a+c875fjl48KDWJQkhhId0oIQQwoeKi4vZt28fNlsZYWEKCxZkal2SX5w40cgf/nCQ2lrHv+53Sueuu+5i5cqVGAwGrcvzEhMTwxNPPEHOuBymJE/BrDNz7P1jNJY1al1a0AoNDyUrL4v6znoaOhv4+9//jsUiZwaFEENDyM9//vOfa13ElVJVFbvd7vWY0Wj0uim5srKS5uZm2tvb5VpqDUj+2pL8taGqKq+88gqVlSewWk+xcGEaWVkJWpflU263yqZN5Xz0UQmKEovZPJmkpFH88Ic/ZMqUKT4dLOJ8BrL9h4aGMnPmTKqrqlE7VDrtnZw+fpqwyDDMCWY/Vxx4LB0WuuxdOByOAXegTbEmOhs7qT1TS2xoLJZ2C1dddZWPKw1M8hmgLclfW/3lP5C+w4UEzRmopqYmGhoaaGpq0rqUoCT5a0vy18bBgwc5ffo0NlspcXEGcnKitC7Jp9raunj99aPs3FlFePgYIiImMX36LFatWkV6erpmdQ10+zcajfzHf/wHs6+ZTU5CDiMiRnBiywmqDlf5qdLA1dXVhc1mo6tr4CMdKorC2LyxuPVuylrK2LNnD8XFxT6sMnDJZ4C2JH9t+SL/oJlIVwgh/MnlcrFx40YcjiZUtYO8vDGanH3xl9LSFv7xjyKsVoWIiCkYDLHcdtttLFiwYFi97pCQEFauXElERATKVoXQkFBKd5bitDnJuCZjWL2WQGCIMDB69mhKtpcwwjyCN998k+eee46QEJn4WAihnaDpQI0fPx5VVeXDTyOSv7Ykf//btWsXdXV12GzlZGcnMmNGOooSeCf9VVVl+/ZKtm49TUhIDGZzDvHxSTzwwANkZWVpXR5w6du/oih85zvfwWw288EHHxCqC6X0QCldli6y52ejCwm899HXYqJjUFFRuPRj0IiJIzhz/AwlTSVEGiLZsmULN954ow+qDFzyGaAtyV9bvsg/aDpQYWFhWpcQ1CR/bUn+/mW32/nwww9xOOpxuSzceOM09PrAmzTXYrGzYUMxJSXNhIWlYzSmk5uby8qVKzGbh859Q5ez/SuKwtKlSzGbzbz11lsYQgycKD6BvcPOhCUT0BuD5uNzUFzJGSNFpzD2+rEcXn+YmvYaPvjgA2bOnElcXNwgVhjY5DNAW5K/tnyRv/yMJoQQg2zr1q00Nzdjs5WTkxNPenrg3ftUUdHGH/5wiFOnLERE5BIensny5ct59NFHh1Tn6UrNmzePBx98kNSYVCYnTaa9pp2j7x6lyzLwe3nElYtMiiQlN4XTradpt7bz9ttva12SECKIyU9oQggxiDo7O/n000+x22tR1S4WLJikdUmDSlVVdu+u5rPPytDpooiMzCE6OoH777+fnJwcrcvzienTpxMdHc3vfvc7QkNCyT+bz+H1h5m0dJKM0OdHmddk0nCqgdKmUoyHjOTn55Obm6t1WUKIIBQ0Z6AsFgttbW0yj4RGJH9tSf7+s2XLFjo62unqqmDq1CSSkyNwOBw4HHYcDofW5V0Rq9XJW28d59NPywgNTSMiYgrjx+fy7LPPDunO02Bs/1lZWTz11FOkp6QzbcQ0Qh2hHH33KM2VzYNYaeByOB3YHXYczsvfB/RGPWPmjqG+s54WWwvr1q3D6XQOYpWBSz4DtCX5a8sX+QfNGahTp07hcDgIDQ1l6tSpWpcTdCR/bUn+/uFwONi2bRt2ex3gYP78DADa2tpwu93odDri4+O1LfIyVVe38/bbx2lpcRIRMZHQ0HiWLFnCt771LXS6of1b3GBt/8nJyTz99NP89re/JUQJ4XjDcfI/yGfcDeNIzkkexIoDj9c+EHf5+0DiuERqC2opaSgh2hjNli1bWLx48SBWGpjkM0Bbkr+2fJH/0P7UE0KIYWTPnj20t7fT1VXNpEmJxMYO/xuHVVVl375aXnvtCG1toURGTic6ehQPP/wwK1asGPKdp8EWGRnJY489xvSrpjMpcZJnrqiKfRWoqqp1eQFPURSyvpGF1Wmlpr2Gjz76iJaWFq3LEkIEmaA5A5WUlITL5ZK5IzQi+WtL8vc9VVXZvHkzTmcjbreVuXO/vqQtPDx8WA5h29Xl5IMPSjh69CxGYyphYWMYPXoMDz744LA6kzbY27/BYOChhx5i3bp1KNsUjHoj5XvLsbXbGHv9WBnmvB/hYYO3D5gTzaRMSuF04WkSIxJZv349999//yBUGbjkM0Bbkr+2fJF/0HSgUlJStC4hqEn+2pL8fa+goIAzZ87Q1VVFRkY0I0dGepaZTCYNK7s85eWtvPvuCVpaHJhMEzAYEpk/fz7f/va30euH10eHL7Z/nU7HHXfcQUJCAuvXrydMH0ZxUTH2Djs5i3PQG4ZXRr422PtAxjUZ1JfUU95SjmGfgeuvv57s7OxBfY5AIp8B2pL8teWTz4BBb1EIIYLQpk2bcDrbcTrbuPbaNK3LuWwOh5tPPy3l9deP0t5uxGyeQVTUKB588EHuuOOOYdd58iVFUVi0aBEPPPAAqdGp5Cbl0lbVJsOc+0FoWCiZ12RSZ6mjrauNdevWySWUQgi/kU9CIYS4QpWVlRQVFdHVVUV8fDjjxw/PCT6rqtrZsOEEjY02wsLGYDCkkp2dzfe+9z0SExO1Lm/ImjlzJtHR0fz+97//epjzdw6TuzSXiPgIrcsLWCMmjqC2oJbS5lKiKqPYv38/s2bN0rosIUQQkDNQQghxhb788kvc7i6czgZmzx457O51cjrdbNlSzquvHqa5OQSzeToRERncfvvtPPbYY9J5GoDs7OzuYc5H/GuYc3soRzYckWHOfUjRKYyeO5q2rjYaOxvZuHGjDGsuhPCLoDkDVVhY6BnCcOLEiVqXE3Qkf21J/r7jdrs5ePAgDkc9ISEK06Yl9fmb5uZmzxDOsbGxGlR5fmfOWNiwoZi6uk6MxgyMxlFkZmZy7733Bsx1+/7a/keMGOEZ5lyv6D3DnGddl0XK5JRh17EeTM0tvfaBmMHbB2JHxRKbFktZXRlx4XF88cUXzJ8/f9DaDxTyGaAtyV9bvsg/aDpQ3RNZDu9JLIczyV9bkr/vFBcX09bWht1ez/jxcRiNfQ+rbrcbt9utQXXn53arfPllJVu3VgAmzOZphIZGsXTpUpYsWRJQo0X5c/uPioriscce47XXXkN3WEdZSxklX5TQ0dRB1jeygnaEPl/uA5lzMjn0j0PUddTx4YcfMmfOHMLChv8UAoNJPgO0Jflryxf5B00HKjQ01Ou/wr8kf21J/r6zf/9+XC4bLlc7kyb1P3hEz1xJQ2XOpDNnLGzceJLaWgsGwyjCwtJJSxvFvffey6hRo7Qub9D5e/s3Go384Ac/YOPGjXz66aeYQk2UFJZgbbUyYfEEQsOCbz/05T4QmRRJUnYSp8tOkxSRxKZNm1i2bNmgP89wJp8B2pL8teWL/BU1AIatcbvdtLe3ez0WGRk5ZL6sCCECk8vl4oknnqCxsQiXq4KnnpqNwTB0z9w4nW527Khgx45KFMVEePg4QkOjWLJkCUuXLpUR9nxgz549rF27lkZLI4X1hegj9Uy6ZRKm2OE3tP1QZm21sv//7SczOpOxSWP55S9/SVRUlNZlCSGGqCvtO8inpRBCXKaioiI6OjpwOOqZMCFuSHeeKivb2LixmIYGG0ZjOkbjKFJTR3L33XczZswYrcsLWLNnzyYpKYnf//73GPVGCs4WcHj9YXIW5xCXPjxHaxyKwqPDSclNobKgkpTIFD766CPuvPNOrcsSQgQon56i2bt3L4sXLyYyMhKz2cz8+fPZuXPngNcvLS3l1ltvJSYmBrPZzKJFizh48KAPKxZCiIE7fvw4brcNl8vCpElDc6S6jg4H771XzKuvHqapKQSz+SpMptEsXbqMZ599VjpPfjBmzBieeeYZxmaOZdqIaUSHRFPwYQHVR6pl7qJBlD4zHTVEpbK1kh07dnD27FmtSxJCBCifdaD27dtHXl4eVquVtWvXsnbtWmw2GwsWLGD37t0XXb++vp5vfOMbFBcX8+c//5m3334bm83GvHnzOHHihK/KFkKIAauoqMDlsgCQkTG0Lhdyu1X27avl5Zf3cfBgA+HhYzGbpzFmzERWrVrFN7/5Tblkz4/i4+N58sknmTF9BhMTJ5IWmcapL09Rsq0Et2toDTAyXBlMBtKuSqO6vRqr3cp7772ndUlCiADls3uglixZwuHDhyktLcVk6r7Wu729nTFjxjBu3LiLnol68sknWbNmDSdPniQjIwOAtrY2srKyuOGGG1i3bp3nbwdyHWNtbS0ul4uQkJCAGZp3OJH8tSX5Dz5VVfnxj39MU9NxjMY6Hn/8mvP+bWdnJ6qqoiiK53joS1VV7Xz4YQk1NRYMhmTCwkZjMkXyzW9+k/nz5wfd/aFDaftXVZX33nuPTz75hDpLHSebThKVEsWEmwJ7cAl/7QNOu5P9f9tPXEgc4+LH8cwzz5CZmemz5xsuhtI+EIwkf231l/+V3gPls0/RnTt3Mm/ePK8DZWRkJHl5eezatYva2toLrv/uu+9yww03eDpP0D087K233soHH3xwyZPlnT17ljNnzsgpfY1I/tqS/AdfQ0MDVqsVt9tCSor5gn9rtVrp7OzEarX6tKbOTgfvv3+SV189TF2ditk8FZNpHHPmXMfq1atZsGBB0HWeYGht/4qisHz5clauXMnImJFMSZ5CZ10nh/5xiM6mTq3L8xmrzUqntROrzbf7gN6gJ31WOnWWOjocHbz//vs+fb7hYijtA8FI8teWL/L32fUbdrsdo9HY5/Gex44dO3beXrjVauXUqVOsWLGiz7IpU6ZgtVopLS1l3Lhx533+goICMjIy+ozC43A4OHLkCLGxsaSnp3stO3nyJJ2d3R9gU6dO9VrW0NBAdXU1AOnp6V6TYbpcLvLz84HuTuK59xSUlZXR1tYGwKRJk7wum2lpaeH06dMApKamkpjofR/F0aNHUVWV8PDwPq+3srKSpqYmAMaPH+8174XFYuHUqVMAJCUl9cn6QpOK1dbWejayrKwszOavvxzabDbPJZRxcXF9hjwuLi7GarWiKApTpkzhXD35Z2RkEBMT43nc6XRSUFAAdHeUR48e7bVeaWmp55eC3NxcrzlqmpubqaioAGDkyJEkJCR4rXvkyBEATCYT2dnZXssqKipobm4GICcnx2ubbWtro6ysDIDk5GRGjBjhtW5BQQFOpxOj0UhOTo7XspqaGurr6wEYO3YsERERnmWdnZ2cPHkS6L6sJy3Ne+jrEydOYLPZCAkJITc312vZ2bNnPT8+ZGZmEh0d7Vlmt9s5fvw4ANHR0f3+6tqT/+TJk72+SDc2NlJVVQVAWloa8fHxnmVut5tjx44BYDabycrK8mqzvLyc1tZWACZMmIDBYPAsa21tpby8HICUlBSSkrwnmc3Pz8flchEWFsb48eO9llVVVdHY2AhAdna2148xHR0dlJSUAJCYmEhqaqrXukVFRXR1daHX65k0aZLXsjNnzlBXVwfA6NGjvY4RXV1dFBUVAVz0GNEzp4TTaSElJQWbzUZHR4cnp/6Of92/eLURGel9XGpvb8dutwMQFxeLonz93tjtXbS3d18mGBFhIiws3GvdpqZGXC6VgoJmdu9uwGZTCQvLwmBIwWw2M2/ePDIyMvrUMxSPEfX19dTU1AAM6jGiZ/4hh8NBQ0PDkDhGjBo1iltuuYV169aRm5DLieYTHH7nMDk35hA1MorWtu59KswY5nX8AGhpbcHlcqEoCnGx3gNRWG1WzzYaaY702h9dbhctLS0AGAwGIs2RXuu2tbXhcHZv13FxcSh8PfGvrevr7TsiIoIw49efNyqq57MoVB/a53O33dL+9RxQ51zzYrfbabd0v28mk4nwc7fv5iZUVSUkJISY6BivZR0dHdi6bABER0V7PltHTBxBxYEKjlcfx9ZmY86cOcyaNctrXX8cI4bS94jzzYEz3L5H+OoY4evvEefLf7h9jzh16hQWS/fn0XD6HtFf/j376eXyWQdq4sSJ7NmzxzPzOHRv3F999RWA54tRf5qbm1FVlbi4viMU9Tx2ofV7nqv31YlZWVnYbDbKy8txOBz9nsFyOp3n3cjdbrdnWX+TAX79ZerC7Z57xWTvdl0uV7/tqqra79j1Lpfrito932vt3e65r1VV1Qu22/NaFUXxejwrK4vGxkbq6+txOBwXbHeovDcXe60921F/v+hf6L0ZSLsOh6PfZRdqt2fd/trNysri9OnTWK3WfnMcaIb9rdu7pnNd7LXa7Xbcbne/k7YORob9ZTTQdi+2vTQ2NqKqTlTVTmKiCVVVe2Xn3W5kZKTnw8Ht7ltT70lGVRV67z6qSq9lfestLGzkiy9qaWlxEBk5isjIMZhMkSxbtozRo0fT3NzcbxZD7RhxKe1e6jEiKSnJ84VhKB0jkpKSuOeee9i2bRvhhnCKGoso+KiAkTNGYh5jRlEU3Grfenu2l94dHE9N7q+3Q/Xc3kqv169eZDvs026v7bu//apnWX/r934uc6T32VoV9cI1udyoqP1uL27V3e9r1YXoSJ2WyoktJ0gJT2Hr1q19OlD+OEb0qVfD7xHQ/QP2uZ2K4fQ94lLaHSrvTe+a4uLi+nz5H07fI3q325+h/j0iPT3d64fYK72DyWcdqEcffZT77ruPRx55hFWrVuF2u3n++ec9v5IM5DKS/naegSwD0Ov1Xn9jNpsJDQ31dET6u3lar9efd5ItnU7nWdZf7QNt99y6e7fb35sfGhqKqqr9thsSEnJF7fb+7/naPfe1KopywXZ7Xuu59ZjNZqxW64DaHSrvzcVea8/rvFiGl9Nuz7W6l9Juz7r9tWs2mwkLCzvvpa8DzfBir/VcF3utBoMBl8vlkwzdbvcl7zeXsh32XlenU1AUpVd23u2Ghob2mki07/um0+k8y899WxWFXsu6F6qqSmlpC5s2lVNW1oCiRGEwjMNkSuHqq6/mtttuIyYmhsrKymFzjLiUdi/1GGEymYbsMSI+Pp4f/ehHvP322+gO6qhoraB8XznhFeFkfiMTndK3Xp1O57mf6FyK7uvtsL8OlmfZRbbDPu322r77e94LTZTbu6ZzM1ZQLlxTSPdr7a9dnaI772tNzknm1K5TnLWd5dixY9TX13udmfHHMaJPvRp/jzAajV5ngnr+Xo4R/vkeYTKZ+uQ/nL5H9Cy70gy1+h5hNpu9OlAX60dcjE8n0v3Vr37FL3/5S8/pvjlz5pCXl8evfvUrvvjiC6677rp+17NarURERPD444/z0ksveS373e9+xyOPPMKJEyc8l7TJRLpCCH/bvHkzb7/9Fq2tO7n99glMnuyfYcyrqtrZvLmM0tIW9PoowsJGo9dHk52dzYoVK/pcGiGGB1VV+eSTT3j//fdp7GykqKGI0MhQJt40kYj4iIs3IPqo2F9Bxd4Krhl5DQvmL+C73/2u1iUJIYaIITuIBMBTTz1FQ0MDx44do7y8nF27dtHc3ExERAQzZsw473rh4eGMHTvWc71kb8eOHSM8PFzmLhFCaMr71yvfz+VTU2PhrbcKeeWVQ5w+7SAiYhJm8zQyMyfx6KOP8thjj0nnaRhTFIWbb76ZRx99lLT4NKanTCfEGsLh9Yc5e1JuPL8cqZNTUfQK1e3V7Nq1y3MPkRBCXCmfTwJiNBo9N7BVVFSwbt06HnjgAcLDwy+43ooVK1izZg2VlZWeGwzb29vZsGHDZc1fYrPZPJc89L5JUviH5K8tyX/wdd/kqkNR9DQ22i74t93XbauA0u8lCOejqirFxU3s3FlNeXkLOl0YJtN4QkOTSExMZPny5cycOfOKL0UIdMNp+580aRKrVq3iD3/4A4YQAycbT1L0WRHtde2MnjMaXcjwvLLC5XJ138t0ifvAldAb9aTkplBzpIZRUaP4/PPPWb58uV+ee6gZTvtAIJL8teWL/H12CV9+fj7vvPMOM2fOxGg0cuTIEV588UUyMzPZunWr13WgCxYsYPv27V73Z9TX1zN16lQSEhJYvXo1RqORF198kUOHDrF3716v0UoGchruyJEjntFizh0ZR/ie5K8tyX/woC2ESQAAIABJREFUNTU18cwzz9DZeYLo6HYeeWTGeTsyjY2NngF1eo9MdD52u4sjR86ye3c1DQ2d6PVRGI1p6PXxREdHc8stt3DdddfJRLgDNBy3f4fDwZtvvsmuXbuoaa+htLmUyBGRTFg8AUOE4eINDDGNTb32gbiL7wODpcvSxb6/7SMjMoPs5GxefPHFi/6AG4iG4z4QSCR/bfWX/5VewuezT1+DwcDnn3/Oyy+/jMViIT09nYceeoinn366z5CsLperz8gaiYmJfPHFFzz++OPcc889OJ1O5syZw7Zt2/oM9SiEEP4WFxdHVlYWRUWN1NfXceZMx0Xng7oQVVWpq+vg6NF6Dhw4g83mRK9PwGweh14fRXJyMgsXLmT27NleQ7yKwBQaGsrdd9/N6NGjeeuttzAbzBw/e5yDbx9k4pKJRKVEXbwRgdFsJGl8EtUnqhkZNZIdO3awePFircsSQgxzPutAjRs3ju3btw/ob7dt29bv41lZWbz77ruDUk9cXNx5RyQRvif5a0vy941Zs2ZRUlJCSEg469cXce+9UzCb+3ZuwsKMuN1qvyPwnT3bSX5+Pfn59TQ0dKIooRgMSZjNIwkJ6Z7XYuHChUyePFku1btMw3X7VxSFvLw8Ro0axR//+EfC9GEcbzjOkXePMObaMaROSR0224TRaDzvyIG+ljYtjbrjddRZ6ti8eTM33HDDeUf8ClTDdR8IFJK/tnyRv09H4fMXGYVPCKEFq9XKCy+8QE1NOR0dR4iK0jF3bhq5uQn9dqRUVaWx0UptrYWaGgslJc3U1XWgKHpCQxMIDU1Er48hJCSEWbNmsWjRoj6TTIrg1N7ezquvvkpRURFlLWVUtVWRlJ1E9vxsQkLlS9nFFH5aSMfpDmamzuTee+9lzpw5WpckhNDQlfYdpAMlhBBXoL6+nl//+tc0NZ3Baj2F09kMqKSlRWI0hqAoCooCXV0uzpzpoKur+15PnS4MvT6a0NAE9PpYdLoQxo4dy8yZM5kxYwaRkZHavjAx5LjdbjZu3Mg///lP6jvqKW4qJiw2jAmLJ2CKNV28gSDWdqaNw+8cZnLSZK6ecjWPP/641iUJITQkHSikAyWE0FZLSwt//OMfKS0tRVUd2O2NuFwt/5rpvOdfCHp9BDqdGb3ejKJ0X0I0ZswYT6cpJiZGy5chhomDBw/yxhtv0GRp4nj9cbroYmzeWJJzkrUubchSVZUDfz+A2W4mJyGHX/ziFyQlJWldlhBCI9KBQjpQQoihoaamhn379rFv3z7q6+v7LI+NjSUjI4P09HTPf6OiZDAAcenOnDnD//3f/1FdU01JUwl1HXUkj08mKy8LvUFGZ+xP1aEqyneXMzttNstuWRa0Q5oLIaQDBQwshOLiYpxOJ3q9nnHjxvm7xKAn+WtL8vcvVVWx2+243W7cbjfFxcW43W4iIyMlfw0E6vbf1dXFW2+9xa5duzjbcZaTTScxRBqYsHgC5sTLHxHSF1pbW3GrbnSKjujoaE1qsHfa+eqNr8iKzWLiqIm88MILQfNDa6DuA8OF5K+t/vK/0g5UcBw56L7Zu7OzE6vVqnUpQUny15bk71+KomA0GgkPDyciIgKdToeqqpK/RgJ1+zcajdxzzz3cd999pMenM33EdPRWPYffOUz1kWqG0u+jTpcTp9OJ0+W8+B/7iMFkIC4zjjpLHS0tLRQWFmpWi78F6j4wXEj+2vJF/kHTgeq+kVsZNkO+BhrJX1uSv7Ykf20Fev5XX301q1atImdsDlNHTCU1IpXSL0sp/LgQh9WhdXlDyogJI2i3t9Nh72Dnzp1al+M3gb4PDHWSv7Z8kX/QXMInhBBCBDKn08nGjRvZtGkTTdYmTjScQBeuY/yi8cSMlAFKANwuN3v/spfE0ETGJYzjpZdewmweWpc7CiF8Ty7hE0IIIQR6vZ5vf/vbPProo2QkZTA9dTrhrnCOvXeM8q/KUd3D/vfSK6YL0ZE0PomzlrM4nU727t2rdUlCiGFIOlBCCCFEAMnNzeW5555j6qSpTE6aTEZ0BpX7Kzm68Shdli6ty9Ncck4yDreDRmsjX331ldblCCGGIelACSGEEAEmOjqaH/7wh6xYsYLM2EymjphKV30XB946QMOpBq3L01REfAQR8RE0WZs4ffo0HR0dWpckhBhmgmayiPr6elwuFyEhISQmJmpdTtCR/LUl+WtL8tdWsOav0+m46aabGDduHK+99hqmUBMnG09S+GkhSeOSGJs3Fr3RP18DrDYrqqqiKArhYeF+ec4LiU2Ppf5oPaqqcvz4cWbOnKl1ST4VrPvAUCH5a8sX+QdNB6qmpgaHw0FoaKhsvBqQ/LUl+WtL8tdWsOeflZXFs88+y9q1a9Ef1BPfEU9JSQkHqg+QfUM2celxPq+hs7MTt9uNTqcbGh2oUbFUHaqiw9FBYWFhwHeggn0f0Jrkry1f5C+X8AkhhBABzmQy8eCDD7Jy5UoyEzOZkToDk8tE/gf5nNx2EpfDpXWJfhWdEo0uREeLtXs+qAAYkFgI4UdBcwYqIyPD8+uX8D/JX1uSv7Ykf21J/t0UReGaa65h3Lhx/PWvf8VYaKS2vZbS46W0VLUw7oZxRKdG++S5zWYzqMAQmQZHp9cRnRpNc0Mzzc3N1NXVMWLECK3L8hnZB7Ql+WvLF/nLPFBCCCFEkFFVlR07drB+/XpaO1opbiymzd5G6uRUMmdnEhIaonWJPld1qIry3eXMHTWXO++4kxtuuEHrkoQQfiLzQAkhhBDikiiKwvXXX89zzz1Hbk4uU5KnMCZmDGeOneHAWwdoqW7RukSfi02Pxa26abW1UlhYqHU5QohhRDpQQgghRJBKSkri8ccf5zvf+Q6Z8ZlMT5mO0W7k6MajlGwvCeh7o0xxJgwmAy22Fk6ePCn3QQkhBixo7oFyOp2eIVT1+qB52UOG5K8tyV9bkr+2JP8L0+l0LFiwgMmTJ/OXv/yFsJNh1FpqKSsso+l0E1nfyCJ+dPwVPYdbdXvugdIpQ+O3W0VRiIiPwNpoxWazYbFYiIyM1Losn5B9QFuSv7Z8kX/QvIsFBQWeIQynTp2qdTlBR/LXluSvLclfW5L/wPScjdq6dSsbNmwgLjyOkqYSCj4uIH50PFnXZREWFXZZbTc3N3tu4o6Pu7LO2GAKiwqjva77PojGxsaA7UDJPqAtyV9bvsh/aPwMJIQQQgjNKYrCDTfcwE9/+lOm5U4jNymXiYkTsVRa2P/mfioOVOB2ubUuc9CERYVhc9oAaGho0LgaIcRwETRnoKKionA6nXLqVCOSv7Ykf21J/tqS/C9dUlISP/rRj9i/fz9vv/02sWGxnG49zek9pzl74ixj88YSkxYz4PYMoQbcqnvIXL7XIywyDKfbidPtDOgOlOwD2pL8teWL/GUYcyGEEEKcl9Vq5YMPPuDzzz/HYrdQ0lRCq62VpOwkxlw7BkOEQesSL1t7XTuH1h9iesp0blpwE3fddZfWJQkh/OBK+w7SFRZCCCHEeYWHh/Nv//ZvzJkzhzfffJOI0gjqLHWUlZax//R+Mq7OIHVyKopuiMySewl67umyOW0BfQZKCDG45BSNEEIIIS5q1KhRPPnkk9x9992MSR7DzNSZJBoSKf2ylEP/OERrTavWJV4yfZgeRVFwuBxYLBatyxFCDBNyBkoIIYQQA6IoCtdeey1Tp05lw4YN6HfqGWEeQUlTCUfePUJcRhyZszMxJ5i1LnVAVJeKqqqE6EIIDw/XuhwhxDARNB2o0tJSzw1kY8aM0bqcoCP5a0vy15bkry3Jf/CZzWbuvvturr32Wt58803MBjMNnQ2UV5dz6O1DJGYnknlNpucSubb2NlS3iqJTiIqM0rj6rzntTgBCdCGEhV3eEO3DgewD2pL8teWL/IOmA9Xe3u4ZA174n+SvLclfW5K/tiR/38nKymLVqlXs2bOH999/nwRTAmcsZzh96jT7S/YzYtII0mem43A4PPNADSXOru4OlF7RB/QZKNkHtCX5a8sX+QdNB0oIIYQQg0+n0zF37lxmzZrF9u3b+fjjj0kyJ1HTVkNlQSV1RXVEZUWRODERnXFodaDsnXYAQkNCMZlMGlcjhBgugmYYc5fL5fnfISEhfqtNdJP8tSX5a0vy15bk719Wq5XPPvuMzZs302HtoKqtiur2akKMIYyaMYqUSSmEhA6N96HyYCUVX1UwN20u99xzD9dee63WJfmE7APakvy11V/+Moz5AMkGqy3JX1uSv7Ykf21J/v4VHh7Ot771LebNm8fHH3/Mjh07SI1KpaKlgrKdZVQeqCRlUgopuSkYzUZNa22taSXSEImiKAF9b4rsA9qS/LXli/yDpgMlhBBCCP+Jjo7mzjvvZMGCBbz//vvs27ePUdGjqGmvoeZQDVWHqkjMTmTk1JGYE/0/al+XpYvmimbGxo4lJiaGESNG+L0GIcTwJB0oIYQQQvhMUlIS999/P0uWLGHTpk3s3buXjOgMzljOUH2qmroTdcSkxjBy2kjiMuNQFP9MyFt9uJoQJYSkiCSuu+46vz2vEGL4C5p7oJqbmz0jAMXGxvq7xKAn+WtL8teW5K8tyV97vd8DRVHYtm0bO3bswGKx0GhtpKqtirauNsKjw0mdnEpCVoJPL+9rO9PGkQ1HyIzOJDMuk//+7/8mJibGZ8+nNdkHtCX5a6u//OUeqAGqqKjwDGEoG6//Sf7akvy1JflrS/LXXu/3YOrUqSxfvpybb76ZPXv2sHnzZhLqEmjvaqeqrYqynWWU7iwlakQUCVkJg96Z6mzu5Pinx4k0RJIWlcayZcsCuvMEsg9oTfLXli/y9+l4oocOHWL58uWkpqZiMpnIyclh9erVdHZ2XnC9N954A0VR+v135swZX5YshBBCCD8wGAzk5eXx/PPP88gjjzBr6iwmJE5gdtpsxsWNQ9+ip2xnGV/95SsOv3OY6iPVdFm6Lvv5VFXlTOEZDr9zGL1dz6TESWRlZbF48eJBfFVCiGDgszNQhYWFzJ07l/Hjx7NmzRoSEhLYsWMHq1ev5sCBA7z33nsXbeP1118nJyfH67H4+PjLqmfkyJFDchK/YCH5a0vy15bkry3JX3sXeg8URWHy5MlMnjyZ2tpa9u/fz4EDB6itrcXpdtJobaShrYGynWWc+vIUphgTEfERRCREeP5rNBv7vYdJVVVsrTYayxqpK6qjs6mTJHMSWbFZZKZn8vDDDwfFdiH7gLYkf235In+f3QP17LPP8l//9V+UlJSQlZXlefz73/8+r7zyCk1NTec9jfbGG29w7733sm/fPmbOnHnR57rS6xiFEEIIMbTU1NRw8OBBDhw4QE1NDS63iyZrE232NjrsHVjsFpxuJwB6ox5TrPdEuG6Hm86WTtwuNzpFR3x4PCOjRhJljGLWrFncddddhIWFafHShBAaG7L3QIWGhgLdw5j2FhMTg06nw2Aw+OqphRBCCDHMpaamkpqaytKlS6mtreXgwYMcPXqU6upqHA4HAF3OLiwOC532TqwWKyoqCt1nohQUkqOSMYWaiDJGEaILYfTo0axYsYLx48dr+dKEEMOcz85AlZeXc9VVV7Fw4UJ+9atfkZiYyPbt27nrrru4++67efnll8+7bs8ZqOTkZOrr64mOjmbevHmsXr2a3NzcPn/fXy+yoqKCjIwMoqKiPI91dXVRVFQEQGxsLOnp6V7rnDx50nN/1tSpU72WNTQ0UF1dDUB6errX2TOXy0V+fj7Q3Xs9dzK+srIy2traAJg0aRJ6/df91paWFk6fPg10f1gkJiZ6rXv06FFUVSU8PJxx48Z5LausrKSpqQmA8ePHe/2SZrFYOHXqFNA9hGxKSorXuoWFhZ4b6iZOnOi1rLa2lrNnzwKQlZWF2fz1/Bw2m40TJ04AEBcXx6hRo7zWLS4uxmq1oigKU6ZM8VpWX19PTU0NABkZGV437TqdTgoKCgCIiopi9OjRXuuWlpZ63uPc3FyvSdGam5upqKgAuk/TJiQkeK175MgRAEwmE9nZ2V7LKioqaG5uBiAnJwej8esbldva2igrKwMgOTm5zxwhBQUFOJ1OjEZjn0tNa2pqqK+vB2Ds2LFERER4lnV2dnLy5Emg+5LUtLQ0r3VPnDiBzWYjJCSkz/Z+9uxZamtrAcjMzPT6gcJut3P8+HGg+4eLzMxMr3VPnTqFxWIBYPLkyV6/sjQ2NlJVVQVAWlqa16WybrebY8eOAWA2m73OKEP3vt7a2grAhAkTvH4caW1tpby8HICUlBSSkpK81s3Pz8flchEWFtbnC01VVRWNjY0AZGdnYzJ9/etyR0cHJSUlACQmJpKamuq1blFREV1dXej1eiZNmuS17MyZM9TV1QEwevRoOUYgxwg5RnQbLscIt9tNXV0dBw4c4OTJk9TV1WG32+no6PCs53A4aG9vJzY2lszMTKZNm8bMmTM97csxopscI7rJMaJboBwjelzoe4TFYsHlcnn9/ZA4A5WZmcnu3btZsWKFV1D/+Z//yZo1ay647ogRI1i1ahWzZ88mKiqKY8eO8eKLLzJ79mx27tzZ56DUH6fTybl9Q1VVPb9aOZ3OftfpWX4ut9vtWeZ2u/ssH2i759bUu91z38iedlVV9ZzR683lcl1Ru+d7rb3bPfe19s6wv3Z7Xmt/16IPtN2h8t5c7LU6HA6cTme/O9uF3puBtOtwOPpddqF2e9a9WLv9GWiG/a3fu6ZzXey12u123G53v7OED0aG/WU00HaHynYox4i+7Q6V90aOEX3b9ccxQqfTkZKSwuTJkz1fSCdMmEB4eDjQfU+VxWLxfElPTk7u8yVdjhF4/l6OEXKMOHfdi7Xbn6F0jOiv3f4yvBI+60CVl5ezbNkykpOTWb9+PYmJiXz11Vf88pe/xGKx8Nprr5133SVLlrBkyRLP/8/Ly+OWW25h8uTJ/PSnPx3QABR6vd5r5zty5IgnxNDQUK9fb3qv098BBroP2D3L+tvQe5ZdrN1zDwi92+3vzQ8NDUVV1X7bDQkJuaJ2e//3fO2e+1oVRblguz2v9dx6zs3/Qu0OlffmYq+153VeLMPLadflcvW77ELt9qzbX7vn5n+ugWZ4sdd6rou9VoPBgMvl8kmGbrf7kvcbX22HPb+8DaTdYD1GXEq7l/re9Pyy3F+7IMeI3suu9Dh7vtfao7CwkGnTpnn+/2AeI3rXNZDteygdI3pqGki7l7Mv2+12Ojs7OXLkiNeP0HKMwNOWL79HOBwOamtraWho8MpfjhF9azrXYBwjHA4Hx48f90yj0NPulfDZJXx33HEHW7dupbS01Ou04+uvv87KlSvZtm0b119//SW1edNNN3Hw4EHPqfUeA7kRrOcLZO/whP9I/tqS/LUl+WtL8teevAfakvy1Jflrq7/8h+wgEocPH2bixIlenSeAWbNmAd3XLF5qB0pV1cseWc9kMuF0Ovv99UD4nuSvLclfW5K/tiR/7cl7oC3JX1uSv7Z8kb/P3snU1FTy8/OxWCxeNw/u3r0boM8NbxdTVlbGzp07Wbhw4WXVc+5Nf8K/JH9tSf7akvy1JflrT94DbUn+2pL8teWL/H12Cd/777/P8uXLueaaa/jxj39MQkICe/bs4YUXXiA9PZ1Dhw5hMBi47777+Mtf/sKpU6fIyMgAYOHCheTl5TFlyhTPIBIvvfQS7e3t7Nq1q8+IIjIPlBBCCCGEEGIghuwlfN/85jfZsmULL774Ij/84Q9pbW1l1KhRfP/73+eZZ57xDFHocrlwuVxeo2FMnjyZdevW8etf/xqr1UpSUhI33HADzz33XJ8hOIUQQgghhBDCX3x2Bsqf5AyUEEIIIYQQYiCG7BmooaaiosJzA9m5E98J35P8tSX5a0vy15bkrz15D7Ql+WtL8teWL/IPmlM0zc3NNDU1eWaLFv4l+WtL8teW5K8tyV978h5oS/LXluSvLV/kHzQdKCGEEEIIIYS4UkFzD1RXVxeqqqIoCkaj0d8lBj3JX1uSv7Ykf21J/tqT90Bbkr+2JH9t9Zf/ld4DFTQdKCGEEEIIIYS40r6D9DCEEEIIIYQQYoCkAyWEEEIIIYQQAxQQw5j3dxWi2+32+v+9T9NFRkb6vCbhTfLXluSvLclfW5K/9uQ90Jbkry3JX1v95X9uPwH670+cT0DcA+V0Ouno6NC6DCGEEEIIIcQwFBERgV4/sHNLcgmfEEIIIYQQQgyQdKCEEEIIIYQQYoCkAyWEEEIIIYQQAxQQ90C53e4+N4MpioKiKBpVJIQQQgghhBiKVFXtM2iETqcLrol0hRBCCCGEEMIf5BI+IYQQQgghhBgg6UAJIYQQQgghxAAFRQfqyy+/5OabbyY2Npbw8HCys7P5xS9+oXVZAe973/ue5160/v7t2bNH6xID3qFDh1i+fDmpqamYTCZycnJYvXo1nZ2dWpcWFPbu3cvixYuJjIzEbDYzf/58du7cqXVZAam9vZ0nn3ySG2+8kcTERBRF4ec//3m/f3vw4EEWLlyI2WwmJiaGW2+9ldLSUv8WHGAGmv+XX37J/fffz4wZMzAajSiKQnl5ud/rDTQDyd/lcvG///u/LFmyhLS0NEwmExMmTODpp5+mpaVFm8IDxEC3/5dffpnZs2eTkJCA0WgkPT2dO+64g4KCAv8XHUAu5fjfQ1VV8vLyUBSFRx555JKfM+A7UG+++SbXX3890dHR/PWvf+Xjjz/mqaeeuqTZhsXlee6559i9e3effwkJCYwcOZJZs2ZpXWJAKywsZO7cuZSXl7NmzRo+/PBD7rjjDlavXs2dd96pdXkBb9++feTl5WG1Wlm7di1r167FZrOxYMECdu/erXV5AaexsZFXXnmFrq4uli9fft6/KyoqYt68edjtdt5++23+/Oc/U1xczDe+8Q3q6+v9WHFgGWj+W7ZsYfPmzaSnpzN37lw/VhjYBpK/1Wrl5z//ORkZGaxZs4aPP/6YBx54gFdeeYVrr70Wq9Xq56oDx0C3/8bGRm666Sb+9Kc/8dlnn/H8889z6NAhrrnmGk6cOOHHigPLQPPv7Xe/+x0lJSWX/6RqAKuqqlIjIiLUH/zgB1qXIv5l27ZtKqA+++yzWpcS8FatWqUCaklJidfjDz74oAqoTU1NGlUWHBYvXqwmJyerHR0dnsfa2trUhIQEde7cuRpWFpjcbrfqdrtVVVXV+vp6FVB/9rOf9fm722+/XU1ISFBbW1s9j5WXl6uhoaHqk08+6a9yA85A83e5XJ7//T//8z8qoJaVlfmpysA1kPydTqfa0NDQZ91//OMfKqCuXbvWH6UGpIFu//0pLCxUAfW5557zYYWB7VLzLysrU81ms7phwwYVUB9++OFLfs6APgP1pz/9iY6ODp566imtSxH/8tprr6EoCitXrtS6lIAXGhoKQHR0tNfjMTEx6HQ6DAaDFmUFjZ07dzJv3jxMJpPnscjISPLy8ti1axe1tbUaVhd4BjJ1hdPp5MMPP+S2224jKirK83hGRgbz58/n3Xff9XWZAWugU4cMdIhgcWkGkn9ISAjx8fF9Hr/66qsBqKys9EltweBKps5JTEwEQK/XD2ZJQeVS83/wwQdZtGgRK1asuOznDOgj2Y4dO4iLi6OoqIhp06ah1+tJSkrioYceoq2tTevygk5rayvr169nwYIFjB49WutyAt4999xDTEwMP/jBDygtLaW9vZ0PP/yQP/7xjzz88MNERERoXWJAs9vtGI3GPo/3PHbs2DF/lxT0Tp06hdVqZcqUKX2WTZkyhZKSEmw2mwaVCaGdzz//HIBJkyZpXEnwcLlcdHV1UVRUxP33309SUhL33nuv1mUFhT/96U/s3buX3/72t1fUTkB3oKqrq+ns7OT222/nO9/5Dps3b+aJJ57gr3/9KzfffLPcB+Vnf//737Fardx3331alxIUMjMz2b17N/n5+WRlZREVFcWyZcu45557+M1vfqN1eQFv4sSJ7Nmzx2uSb6fTyVdffQV0X7Mt/Ksn87i4uD7L4uLiUFWV5uZmf5clhGaqq6t5+umnmTlzJkuXLtW6nKARERFBWFgYEyZM4Pjx42zbto1Ro0ZpXVbAq66u5vHHH+ell14iNTX1itoK6A6U2+3GZrPxk5/8hGeeeYZ58+bxxBNP8MILL7Bz5062bNmidYlB5bXXXiM+Pv6KTpmKgSsvL2fZsmXEx8ezfv16tm/fzksvvcQbb7zB/fffr3V5Ae/RRx+luLiYRx55hOrqaiorK3nooYc4ffo0IJcyaelCl3pc7mU4Qgw3TU1Nnh+T161bJ8ckP9q1axe7d+/mb3/7G5GRkcyfP19G4vODhx56iKlTp/LAAw9ccVsBvbf0XOu7ePFir8dvuukmoHsoW+EfR48eZf/+/dx11139XtYkBt/TTz9NW1sb//znP7ntttvIy8vjiSeeYM2aNfz5z39m+/btWpcY0FauXMmLL77I2rVrSUtLIz09ncLCQh5//HEARo4cqXGFwafnM6G/s39NTU0oikJMTIy/yxLC75qbm1m0aBHV1dVs2rSJMWPGaF1SUJk+fTqzZ8/mu9/9Llu3bkVVVX7yk59oXVZAW79+PZ9++ikvvfQSra2ttLS0eIbvt9vttLS04HA4BtxeQHeg+rvOHfBcuie/tvjPa6+9BiBnPvzo8OHDTJw4sc+9Tj3Dx+fn52tRVlB56qmnaGho4NixY5SXl7Nr1y6am5uJiIhgxowZWpcXdLKysggPD+/3/rNjx44xduxYwsLCNKhMCP9pbm5m4cKFlJWVsWnTpvN+VxL+ERkZSU5ODsXFxVqXEtDy8/NxOp3Mnj2b2NhYzz+AV199ldjYWD766KMBtxfQPYjbbrsNgE8++cTr8Y8//hiA2bNn+72mYNTV1cXf/vY3rr76anJzc7UuJ2ikpqZSUFCAxWLxerxnDqK0tDQtygo6RqOR3NxcMjL1MUuvAAADCklEQVQyqKioYN26dTzwwAOEh4drXVrQ0ev1LFu2jA0bNtDe3u55vKKigq1bt3LrrbdqWJ0QvtfTeSotLeWzzz7jqquu0rqkoNfzI9vYsWO1LiWgfe9732Pr1q19/gEsX76crVu3ct111w24vYAeM/HGG29k2bJlrF69GrfbzezZs9m/fz/PP/88S5cuvaSgxOXbuHEjTU1NcvbJz370ox+xfPlyFi1axI9//GMSEhLYs2cPL7zwAhMnTvRcyip8Iz8/n3feeYeZM2diNBo5cuQIL774ItnZ2fziF7/QuryA9Mknn9DR0eHpHBUWFrJ+/XoAbr75ZkwmE88//zyzZs1i6dKlPP3009hsNn7605+SkJDAY489pmX5w95A8q+vr/dcPtxzJvCTTz4hMTGRxMRErr/+em2KDwAXy19RFBYvXsyhQ4dYs2YNTqeTPXv2eNZPTEwkKytLk9oDwcXydzgcLFq0iH//938nOzub8PBwiouL+c1vfkNXVxc/+9nPtCx/2LtY/pmZmWRmZva77siRI5k3b96lPeFlzFc1rHR2dqpPPfWUOmrUKFWv16vp6enqM888o9psNq1LCxqLFi1SIyIi1La2Nq1LCTqff/65euONN6ojRoxQw8PD1XHjxqmPPfZYv5MpisF14sQJNS8vT42Li1MNBoM6duxY9dlnn1UtFovWpQWsjIwMFej3X+/JWvfv368uWLBANZlMalRUlLp8+fI+E06LSzeQ/Ldu3Xrev7n++us1rX+4u1j+ZWVl510OqPfcc4/WL2FYu1j+NptNvf/++9UJEyaoZrNZ1ev1alpamnrXXXepBQUFWpc/7A30+H8uLnMiXeVfKwshhBBCCCGEuIiAvgdKCCGEEEIIIQaTdKCEEEIIIYQQYoCkAyWEEEIIIYQQAyQdKCGEEEIIIYQYIOlACSGEEEIIIcQASQdKCCGEEEIIIQZIOlBCCCGEEEIIMUDSgRJCCCGEEEKIAZIOlBBCCCGEEEIMkHSghBBCCCGEEGKApAMlhBBCCCGEEAP0/wH6N5qusj5qmwAAAABJRU5ErkJggg==\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": { "scrolled": true }, "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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\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')\n", "plt.xlim(6, 14);" ] }, { "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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PSFhMqwMAAEhQNTU1WrdunSSptLRUhmHIMAzt2LHjiv6ewsJCSZLfz/fmSG5kAAAAQIJau3atOjo6tHnzZr3xxhuaNWuWJGnZsmUyTVOmaU7Yh2EY8vl84x4Ph8MaHh7WwYMH9bd/+7davHixvvzlL1/xfQC8hJEjwOOGhoaiP0CyIx8w1RQXFysUCkmSbrjhBlVWVqqyslLBYFBVVVUKBAIT/nz+858f129LS4sCgYAyMzP1e7/3ewqHw9q+fbuys7Ov9S4CCYWRI8DjDhw4EF2utaKiwu1wAFeRD0gmNTU1qq6ujtt2+PBhhcNh+f1+3XjjjePaCwoK9Jvf/EaDg4M6cOCAvve97+n222/Xjh07oqNTQDKiOAIAAPCgUCik4uLiuG2GYUS/KFi4cOG4dr/fr5tuukmSdMstt+jOO+9UaWmpnnvuOW3atOmqxg0kMoojwOOmTZsWvQs6kOzIBySTqqoqbdu2bcLn3XbbbRMu4FBcXKzZs2fr8OHDVyg6wJsojgCPKykpcTsEIGGQD5iK0tLSJEn9/f0xj19sWt1oOTk5Ez7n6NGjamxs1Be+8AVnQQJTBMURAABAAisvL5ckbdq0SWvWrFEgENCSJUtUUlJyyV8I7NmzR3/3d3+nP//zP9f8+fOVkpKivXv36h//8R+Vn5+vRx555CrsAeAdhmVZlttBTJZpmurp6Yl5LCcnRykpLLoHAACmrvXr12vbtm1qaWmRaZravn27Vq1adcn9nD59Wo888og++eQTNTc3KxwOq7i4WHfccYfWr1+vuXPnXvngAZc4qR0ojgAAAABMOU5qB6bVAR537Nix6IpECxYscDscwFXkA2AjFwBnKI4Aj+vt7Y2eAIFkRz4ANnIBcIb5aAAAAAAgrjkCPM80zei/yQUkO/IBsJELANccAUmJkx5wHvkA2MgFwBkyBwAAAABEcQQAAAAAkphWB3jemTNnZJqmUlJSlJ+f73Y4gKvIB8BGLgDOUBwBHtfY2BhdrpUTIJId+QDYyAXAGabVAQAAAIAYOQI8r7i4ODp1Akh25ANgIxcAZyiOAI9jugRwHvkA2MgFwBm+TgAAAAAAURwBAAAAgCSm1QGeZ5pm9N/MLUeyIx8AG7kAOENxBHjc3r17o8u1VlRUuB0O4CryAbCRC4AzfJUAAAAAAGLkCPC87Ozs6LeDQLIjHwAbuQA4Y1iWZbkdxGSZpqmenp6Yx3JycphLCwAAACCGk9qBqgIAAAAARHEEAAAAAJIojgAAAABAEgsyAJ5XX1+vSCQin8+nkpISt8MBXEU+ADZyAXCG4gjwuLNnz7IiEfD/kQ+AjVwAnGFaHQAAAACIpbwBzxsaGor+OzU11cVIAPeRD4CNXACc1Q5MqwM8jpMecB75ANjIBcAZhlwAAAAAQBRHAAAAACCJaXWA5509e1aWZckwDE2bNs3tcABXkQ+AjVwAnKE4Ajyuvr4+ulxrRUWF2+EAriIfABu5ADjDtDoAAAAAECNHgOfNmjUrehd0INmRD4CNXACc4T5HAAAAAKYcJ7UDVQUAAAAAiOIIAAAAACRRHAEAAACAJBZkADxv3759GhoaUmpqqsrKytwOB3AV+QDYyAXAGUaOAI+LRCIyTVORSMTtUADXkQ+AjVwAnGHkCPC49PR0+Xw+BQIBt0MBXEc+ADZyAXCGpbwBAAAATDks5Q0AAAAADlEcAQAAAIAojgAAAABAEgsyAJ7X2NioSCQin8+n4uJit8MBXEU+ADZyAXCG4gjwuDNnzmh4eFiBQIATIJIe+QDYyAXAGYojAIDndXT3a8ubn+qtX+9V70BY2el+/emtXaq+Z6XyghluhwcA8AiW8gY87ty5c7IsS4ZhKDMz0+1wgGuqsa1bD/3gbe062qKWjl5FzPOnNL8vRUW5Wbp+4Uz9y7fuVnFh0MVIgWuLcwPg0aW8P/jgA1VVVWnp0qXKysrSnDlz9MUvflGfffaZ26EBnpCZmamsrCxOfkg6e4+f1i3VL+qdnUd0qr0npjCSpHDE1Kn2Hr2z84huqX5Re4+fdilS4Nrj3AA4M6ni6A//8A9VV1d3VQJ44YUXVF9fr29+85t69913tWnTJrW2tqqyslIffPDBVfmdAABva2zr1t2PvqKG1u5JPb+h1X5+Y9vkng8ASE6TmlY3a9Ys9fX16fnnn9eDDz54RQNobW3VjBkzYh7r7e3VwoULVVZWpl/96lfRx5lWBwCQpLsffUXv7Dxyydutrlykt5+99ypEBABINFdtWt3+/ft1991366GHHtKf/MmfqLm5+fIiHWVsYSRJ2dnZWrZsmU6ePHnFfg8wVfX19am3t1d9fX1uhwJcEx3d/dp1tMXRtruOtqizp/8KRwQkHs4NgDOTKo5yc3P1yiuv6F//9V/1u9/9TmVlZfrlL3951YI6e/asfvvb32r58uVX7XcAU8XRo0d18OBBHT161O1QgGtiy5ufqqWj19G2pzv7tPmNT69wREDi4dwAOHNJS3nfc889uu222/Twww/rvvvu04YNG5SamhrzHMMwtHv37ssK6hvf+Ib6+vr02GOPTfjc2tpazZs3T8Hg+VWIBgcHdfDgQUl2YRcKhWK2OXLkiM6dOydJqqioiGlrb2/XqVOnJEmhUEi5ubnRtkgkon379kmyh+Tmz58fs21dXZ26u+357MuXL5fff/7l7erq0okTJyRJs2fPVmFhYcy2e/bskWVZysjI0OLFi2PaTp48qY6ODknSkiVLlJ6eHm3r7e3VsWPHJNmjcLNmzYrZdv/+/dH7HCxbtiymrbm5Wa2trZKkBQsWKDs7O9o2MDCgQ4cOSZLy8vI0d+7cmG0PHz6s/v5+GYahFStWxLS1tbWpqalJkjRv3jxNnz492hYOh1VbWytJCgaDKi0tjdn2+PHj0eHPsrIy+Xy+aFtnZ6caGhokSXPmzFFBQUHMtiN/d5mZmVq0aFFMW0NDgzo7OyVJS5cuVVpaWrStu7s7ek1dUVGRZs6cGbNtbW2twuGw0tLStHTp0pi2pqYmtbW1SZIWLlyorKysaNu5c+d05Ig97Sc/P3/cfSYOHTqkgYEB+Xw+lZWVxbS1trZGR2hLSko0bdq0aNvQ0JAOHDggSTGPjzh27Jh6e+0PjuXl5TFDx2fOnFFjY6Mkqbi4WPn5+dE20zS1d+9eSfbo7YIFC2L6ra+v19mzZyVJ1113XUzunz17VvX19ZLsabhjR4T37dunSCSi9PR0LVmyJKatsbFRZ86ckSQtWrQo5uLhvr6+6Im9sLBQs2fPjtn24MGDGhwclN/vH/dlSktLi06fti/ALy0t5RihqXOMeOvXe8ctvjBZ4Yipdz/ZryfW3Bbz+FQ+RpSUlMRsyzHCxjHCNhWPEXyO4BgxYiRPL8Ul3+eot7dXbW1tsixLeXl5MX8cV8Ljjz+uX/ziF9q8ebNuvPHGCZ8fDoc19rIpy7I0PDwcbY+3zUj7WKZpRttM0xzXPtl+x8Y0ut9IJBK3X8uyFAgExrVFIpHL6vdC+zq637H7Ovo1jNfvyL4ahuG430R5byba1+HhYYXD4bjzUy/23kym3+Hh4bhtF+t3ZNuR5xUWFkbvgj6633gm+xrG2350TGNNtK9DQ0MyTTPmJBWvX6evYbzXaLL9JsrfIceI8f1e6DXsHRj/+KXo7R+/v1P5GHGhfuPhGDG+X68eI0afG4aGhpLqGMHnCI4Ro/u9VJdUHP30pz/VI488opycHL377ru68847L/kXXsyGDRu0ceNGPf3006qurp7UNn6/f1xiGYYRPTiM/tZl9DbxPmBIUkpKSrQt3h/xZPsdG9PofuO9sYFAQJZlxe3X5/NdVr+j/3uhfsfu6+jXMF6/I/sa76A22X4T5b2ZaF9H9nOi19BJv6OLmsn2O7LtyPPGflMaCAQu+zWcaF/HmmhfU1NTFYlErspraJrmJedNIv4dcowY3++FXsPs9Mu7f3l2xvh9ncrHiHhtHCOm/jFi9Lnh5MmTSXWM4HMEx4jR/V6qSa1Wd+rUKa1du1bvv/++/vIv/1I/+tGPYoaJr4QNGzaopqZGNTU1evLJJ+M+h9XqAADf3fahvvvyh46m1vl9KXr8/j8aN60OADD1XLXV6srKyvR///d/evXVV/XKK69c8cLoqaeeUk1Njb7zne9csDACAECSqu9ZqZl52RM/MY6i3Cz9zZdXXuGIAABTxaTmJtx666362c9+pqKioisewPe//3098cQTuvPOO7V69Wrt3Lkzpr2ysvKK/04AgHflBTN0/cKZOtXeM/GTx7h+4Uzl5mRchagAAFPBpKbVXU2rVq3Shx9+eMH20eExrQ4Y7+DBg9GVhMauggNMVY1t3fqD6hd1srV70tuEZgT10ZYHVFwYnPjJgMdxbgCu4rS6q2nHjh2yLOuCPwAubnBwMPoDJIviwqDeefZehWZMrtAJzQjq7WfvpTBC0uDcADjjenEE4PL4/f7oD5BMyucX6aMtD2h15SLNKciR3xd7SvP7UjSnIEerKxfpoy0PqHz+lZ8aDiQqzg2AM65Pq7sUTKsDAMTT0d2vLW9+qh276tXTP6ScjFStur5E1fesVF6Qa4wAIBk5qR0ojgAAAABMOZ685ggAAAAAEgHFEQAAAABokvc5ApC4WlpaFIlE5PP5NHPmTLfDAVxFPgA2cgFwhuII8LjTp09H72XBCRDJjnwAbOQC4AzT6gAACefjjz9WTU2Nurq6Lruv7u5uPf3001q1apVmzpyp7OxslZeX6x/+4R80MDBwBaIFAEwVrFYHeFx3d7csy5JhGAoGucElpobnn39e69atU11dnUpKSia9Xbx82Ldvn26//Xbdf//9WrVqlbKzs/U///M/eu6553TLLbfoP//zP2UYxlXaE8AdnBsAZ7UD0+oAj+OkB5wXLx9KS0tVX1+vrKys6GOf+9znlJWVpXXr1umjjz7Srbfeei3DBK46zg2AMwy5AAASSk1NjdatWyfJLmwMw5BhGNqxY4ej/rKysmIKoxErV66UJJ08edJxrACAqYWRIwBAQlm7dq06Ojq0efNmvfHGG5o1a5YkadmyZTJNU6ZpTtiHYRjy+XwXfc4HH3wgSVq+fPnlBw0AmBIYOQI8bnBwUAMDAxocHHQ7FOCKKC4uVigUkiTdcMMNqqysVGVlpYLBoKqqqhQIBCb8uf322y/6O/bs2aPvfe97uueee7RixYprsVvANcW5AXCGkSPA4w4ePBhdrrWiosLtcICrqqamRtXV1RdsP3z4sMLhsKZNm3bB59TX1+vuu+/W3Llz9bOf/exqhAm4jnMD4AzFEQDAM0KhkIqLiy/YbhiGhoeHlZqaGrf9xIkTuv322+X3+/Vf//VfysvLu1qhAgA8iOII8Ljc3FyFw2H5/aQzpr6qqipt27ZtwudVVlbqk08+iXnsxIkTWrVqlSzL0o4dOy5aZAFex7kBcIaMATxu5NoMYCpJS0uTJPX398c8PtG0uhE5OTkx/9/Q0KBVq1YpEolox44dmjdv3pULFkhAnBsAZyiOAAAJp7y8XJK0adMmrVmzRoFAQEuWLFFJSckl3RRWklpbW3X77berublZL774olpbW9Xa2hptLy4uZhQJACBJMizLstwOYrKc3OUWAOBN69ev17Zt29TS0iLTNLV9+3atWrXqkvvZsWPHRVeve/LJJ1VTU+M8UABAQnJSO1AcAQAAAJhynNQOTKsDPO7IkSPRi24XLVrkdjiAq8gHwEYuAM5QHAEed+7cuei9LIBkRz4ANnIBcIb5aAAAAAAgrjkCAAAAMAU5qR2oKgAAAABAFEcAAAAAIIniCAAAAAAksVod4Hnt7e0yTVMpKSkqKChwOxzAVeQDYCMXAGcojgCPO3XqVHS5Vk6ASHbkA2AjFwBnmFYHAAAAAGLkCPC8UCgUnToBJDvyAbCRC4AzFEeAx+Xm5rodApAwyAfARi4AzvB1AgAAAACI4ggAAAAAJDGtDvC8SCQS/bfP53MxEsB95ANgIxcAZyiOAI/bt29fdLnWiooKt8MBXEU+ADZyAXCGaXUAAAAAIEaOAM/LyclROByW3086A+QDYCMXAGcMy7Ist4OYLNM01dPTE/NYTk4Oa/gDAAAAiOGkdrDZy1UAABQuSURBVKCqAAAAAABRHAEAAACAJIojAAAAAJDEggyA59XV1UUvui0tLXU7HMBV5ANgIxcAZyiOAI/r7u6O3ssCSHbkA2AjFwBnmFYHAAAAAGIpb8DzwuGwLMuSYRjczwJJj3wAbOQC4Kx2IFsAj+OkB5xHPgA2cgFwhiEXAAAAABDFEQAAAABIYlod4HldXV0yTVMpKSmaPn262+EAriIfABu5ADhDcQR43IkTJ6LLtXICRLIjHwAbuQA4w7Q6AAAAABAjR4DnzZ49W5FIRD6fz+1QANeRD4CNXACc4T5HAAAAAKYcJ7UDVQUAAAAAiOIIAAAAACRRHAEAAACAJBZkADxvz5490eVaV6xY4XY4gKvIB8BGLgDOMHIEeJxlWdEfINmRD4CNXACcYeQI8LiMjAwFAgH5/aQzQD4ANnIBcIalvAEAAABMOSzlDQAAAAAOURwBAAAAgCiOAAAAAEASCzIAnnfy5ElFIhH5fD7NnTvX7XAAV5EPgI1cAJxh5AjwuI6ODrW3t6ujo8PtUADXkQ+AjVwAnGHkCPCoju5+bXnzU731673qHQgrO92vP721S9X3rFReMMPt8AAAADyHpbwBj2ls69ZDP3hbu462qKWjVxHzfAr7fSkqys3S9Qtn6l++dbeKC4MuRgpcewMDA7IsS4ZhKD093e1wANeQC4BHl/Lu6enRt7/9bd1xxx0qLCyUYRiqqalxOywgIe09flq3VL+od3Ye0an2npjCSJLCEVOn2nv0zs4juqX6Re09ftqlSAF3pKenKyMjgw+DSHrkAuCM68XRmTNn9JOf/ESDg4P60pe+5HY4QMJqbOvW3Y++oobW7kk9v6HVfn5j2+SeDwAAkOxcL47mzZunzs5Offjhh3r22WfdDgdIWA/94O1JF0YjGlrtKXgAAACYmOsLMhiG4XYIQMLr6O7XrqMtjrbddbRFnT39ys1hkQZMfb29vTJNUykpKcrOznY7HMA15ALgjOsjRwAmtuXNT9XS0eto29Odfdr8xqdXOCIgMR07dkyHDx/WsWPH3A4FcBW5ADjj+sjR5aqtrdW8efMUDJ5flWtwcFAHDx6UJOXm5ioUCsVsc+TIEZ07d06SVFFREdPW3t6uU6dOSZJCoZByc3OjbZFIRPv27ZNkr3Qxf/78mG3r6urU3W1Pe1q+fLn8/vMvb1dXl06cOCFJmj17tgoLC2O23bNnjyzLUkZGhhYvXhzTdvLkyeh9CpYsWRJzcWVvb2/0wDdjxgzNmjUrZtv9+/dreHhYgUBAy5Yti2lrbm5Wa2urJGnBggUx3ywNDAzo0KFDkqS8vLxxN5A7fPiw+vv7ZRiGVqxYEdPW1tampqYmSfa0yenTp0fbwuGwamtrJUnBYFClpaUx2x4/fjy6qkhZWZl8Pl+0rbOzUw0NDZKkOXPmqKCgIGbb3bt3S5IyMzO1aNGimLaGhgZ1dnZKkpYuXaq0tLRoW3d3t+rq6iRJRUVFmjlzZsy2tbW1CofDSktL09KlS2Pampqa1NbWJklauHChsrKyom3nzp3TkSNHJEn5+fkqLi6O2fbQoUMaGBiQz+dTWVlZTFtra6uam5slSSUlJdr+u7pxiy9MVjhiaseuej2x5jadOXNGjY2NkqTi4mLl5+dHn2eapvbu3StJys7O1oIFC2L6qa+v19mzZyVJ1113nVJTU6NtZ8+eVX19vSRp1qxZmjFjRsy2+/btUyQSUXp6upYsWRLT1tjYqDNnzkiSFi1apMzMzGhbX1+fjh49KkkqLCzU7NmzY7Y9ePCgBgcH5ff7tXz58pi2lpYWnT5tL0hRWlrKMULJcYwYHh6WZP89jzWVjxHTpk2Ltg0NDenAgQOSpGnTpqmkpCRm22PHjqm31/6ypby8PGbVJo4RNo4R5021Y0Syfo5I1mPESJ5eCs8XR+FwWGNXI7csK3qCDIfDcbcZaR/LNM2Lnlwn2+/YmEb3G4lE4vZrWZYCgcC4tkgkcln9XmhfR/c7dl9Hv4bx+h3Z13jTIifbb6K8NxPt6/DwsMLhcNxlHy/23kym3+Hh4bhtY/vt6R8a95xLMbL9ZF/DeO/B6JjGmmhfh4aGZJpmzEkqXr9OX8N4dySYbL+J8nfIMWJ8v07emxHxphFN5WNEvG0n6jcejhHj+/XqMWLGjBmKRCLy+XwaHBzkGKHk/hwRb9uJ+o3Hi8eIS+X54sjv949LLMMwogeH0d+6jN4m3gcMSUpJSYm2xfsjnmy/Y2Ma3W+8NzYQCMiyrLj9+ny+y+p39H8v1O/YfR39Gsbrd2Rf4x3UJttvorw3E+3ryH5O9Bo66XfkxDVRvzkZqeOecylGtp/sazjRvo410b6mpqYqEolcldfQNM1LzptE/DvkGDG+38t5b0Z/Wz9iKh8j4m17sX4v9++bY0TiHyNGjwCdPHmSY4SS+3NEvG0v1u9UOkZcqoS6CWx7e7sKCwv15JNPxr3XETeBRbL67rYP9d2XP3Q0tc7vS9Hj9/+Rnlhz21WIDAAAIDF58iawACZWfc9KzcxzttpQUW6W/ubLK69wRAAAAFNPQkyre++999TX1xet7Pbv36/XX39dknTXXXfFXFgFJKO8YIauXzhTp9p7Jn7yGNcvnMky3gAAAJOQENPqSkpKoiuwjFVXVxddRYNpdUhmjW3d+oPqF3XyEm4EG5oR1EdbHlBxYXDiJwNTwMVW1gKSCbkAeHhaXX19vSzLivszdnlBIFkVFwb1zrP3KjRjcoVOaEZQbz97L4URksrIKksXWhEJSBbkAuBMQhRHACanfH6RPtrygFZXLtKcghz5fbEp7PelaE5BjlZXLtJHWx5Q+fwilyIF3DGyytKFVkQCkgW5ADiTENPqJotpdcB5Hd392vLmp9qxq149/UPKyUjVqutLVH3PSuUFucYIAAAkNye1A8URAAAAgCnHs9ccAQAAAIDbKI4AAAAAQAlynyMAzjU3NysSicjn82nWrFluhwO4inwAbOQC4AzFEeBxra2t0XtZcAJEsiMfABu5ADjDtDoggXz88ceqqalRV1fXFenv7bff1le+8hWVl5crEAjIMIwr0i8AAMBUxMgRkEA+/vhjbdiwQV/96lc1ffr0SW2zYMECmaYZd+WVN998Uzt37tQNN9ygtLQ0ffbZZ1c6ZCChXCwfgGRCLgDOUBwBHpednX3Btp/+9KfRE2N1dTXFEaa8i+UDkEzIBcAZvk4AEkRNTY3WrVsnSSotLZVhGDIMQzt27HDcJ98YAgAATB4jR0CCWLt2rTo6OrR582a98cYb0Qtoly1bJtM0ZZrmhH0YhiGfz3e1QwUAAJiS+FoZSBDFxcUKhUKSpBtuuEGVlZWqrKxUMBhUVVWVAoHAhD+f//znXd4LwF0DAwPq7+/XwMCA26EAriIXAGcYOQI8oKamRtXV1XHbDh8+rHA4LL/frxtvvPEaRwYklkOHDkWXL66oqHA7HMA15ALgDMUR4AGhUEjFxcVx2wzDiJ4AFy5ceI0jAwAAmDoojgAPqKqq0rZt2yZ83m233XZZCzgAXpeXl6dIJMK1d0h65ALgDMURkEDS0tIkSf39/TGPX2xa3Wg5OTlXJS7AK+bOnet2CEBCIBcAZyiOgARSXl4uSdq0aZPWrFmjQCCgJUuWqKSkRCUlJZfc34kTJ/Sb3/xGknTs2DFJ0uuvvy5JKikp0U033XRlAgcAAJgCDMuyLLeDmCzTNNXT0xPzWE5ODvdywZSyfv16bdu2TS0tLTJNU9u3b9eqVasc9fXSSy/pr//6r+O2rVmzRi+99JLzQAEAABKYk9qB4ggAAADAlOOkdmBaHeBxo5fyXrx4sdvhAK4iHwAbuQA4Q3EEeFx/f390KW8g2ZEPgI1cAJxhPhrgcYZhRH+AZEc+ADZyAXCGa44AAAAATDlOageqCgAAAAAQxREAAAAASKI4AgAAAABJrFYHeF5bW5sikYh8Pp8KCwvdDgdwFfkA2MgFwBmKI8Djmpqaosu1cgJEsiMfABu5ADjDtDoAAAAAECNHgOfNmzdPpmmypD0g8gEYQS4AzlAcAR43ffp0t0MAEgb5ANjIBcAZvk4AAAAAAFEcAQAAAIAkptUBnhcOh2VZlgzDkN9PSiO5kQ+AjVwAnCFbAI+rra2NLtdaUVHhdjiAq8gHwEYuAM4wrQ4AAAAAxMgR4HnBYFDhcJhpE4DIB2AEuQA4Y1iWZbkdxGSZpqmenp6Yx3JycljDHwAAAEAMJ7UDVQUAAAAAiOIIAAAAACRRHAEAAACAJBZkADzv+PHj0Ytu58+f73Y4gKvIB8BGLgDOUBwBHtfT0xO9lwWQ7MgHwEYuAM4wrQ4AAAAAxFLegOdFIpHov30+n4uRAO4jHwAbuQA4qx2YVgd4HCc94DzyAbCRC4AzDLkAAAAAgCiOAAAAAEAS0+oAz+vs7JRpmkpJSVFubq7b4QCuIh8AG7kAOENxBHhcQ0NDdLlWToBIduQDYCMXAGeYVgcAAAAAYuQI8Lw5c+ZEp04AyY58AGzkAuAMxRHgcQUFBW6HACQM8gGwkQuAM3ydAAAAAACiOAIAAAAASRRHAAAAACCJa44Az9u9e3d0udaKigq3wwFcRT4ANnIBcIaRIwAAAAAQI0eA52VmZiocDsvvJ50B8gGwkQuAM4ZlWZbbQUyWaZrq6emJeSwnJ4c1/AEAAADEcFI7UFUAAAAAgCiOAAAAAEASxREAAAAASGJBBsDzGhoaohfdhkIht8MBXEU+ADZyAXCGkSPA4zo7O9XR0aHOzk63QwFcRz4ANnIBcIbiCAAAAADEUt6A5w0ODsqyLBmGobS0NLfDAVxFPgA2cgFwVjtwzRHgcZz0gPPIB8BGLgDOMOQCAAAAAKI4AgAAAABJHptWF+/yKNM0XYgESByj59Lm5OS4GAngPvIBsJELQPw6YaLlFjy1IEM4HFZfX5/bYQAAAADwoKysLPn9Fx4fYlodAAAAAIjiCAAAAAAkURwBAAAAgCSPXXNkmua4C6sMw5BhGC5FBAAAACARWZY1bgGGlJSUi94E1lPFEQAAAABcLUyrAwAAAABRHAGe1NPTo29/+9u64447VFhYKMMwVFNT43ZYwDX3wQcfqKqqSkuXLlVWVpbmzJmjL37xi/rss8/cDg245nbt2qXVq1crFAopIyNDeXl5uvnmm/Xzn//c7dAAz6A4AjzozJkz+slPfqLBwUF96UtfcjscwDUvvPCC6uvr9c1vflPvvvuuNm3apNbWVlVWVuqDDz5wOzzgmurq6tLcuXP1zDPP6N1339XLL7+skpIS3X///dq4caPb4QGewDVHgAeNpK1hGGpvb1dhYaGefPJJRo+QdFpbWzVjxoyYx3p7e7Vw4UKVlZXpV7/6lUuRAYmjsrJSTU1NamhocDsUIOExcgR4EKs0AraxhZEkZWdna9myZTp58qQLEQGJp6CgQH6/3+0wAE8gUwAAU8rZs2f129/+Vp/73OfcDgVwxcitTzo7O/Xaa6/p/fff15YtW9wOC/AEiiMAwJTyjW98Q319fXrsscfcDgVwxcMPP6wf//jHkqTU1FT98Ic/1Ne//nWXowK8geIIADBlPP744/rFL36hzZs368Ybb3Q7HMAV69ev19q1a9Xa2qq33npL1dXV6uvr0yOPPOJ2aEDCozgCAEwJGzZs0MaNG/X000+rurra7XAA14RCIYVCIUnSXXfdJUl69NFHtWbNGhUWFroZGpDwWJABAOB5GzZsUE1NjWpqarR+/Xq3wwESysqVKxUOh3X8+HG3QwESHsURAMDTnnrqKdXU1Og73/mOnnzySbfDARLO9u3blZKSovnz57sdCpDwmFYHeNR7772nvr4+9fT0SJL279+v119/XZI9jSIzM9PN8IBr4vvf/76eeOIJ3XnnnVq9erV27twZ015ZWelSZMC19+CDDyoYDGrlypUqKipSe3u7XnvtNb366qtat24dU+qASeAmsIBHlZSU6MSJE3Hb6urqVFJScm0DAlywatUqffjhhxds5xSHZLJ161Zt3bpVBw4cUFdXl7Kzs1VRUaG1a9fqvvvuczs8wBMojgAAAABAXHMEAAAAAJIojgAAAABAEsURAAAAAEiiOAIAAAAASRRHAAAAACCJ4ggAAAAAJFEcAQAAAIAkiiMAgIdVVVUpLS1Ne/fuHdf23HPPyTAMvfXWWy5EBgDwIm4CCwDwrO7ubpWXlys/P1//+7//q0AgIEnau3evbrrpJt17773aunWry1ECALyCkSMAgGcFg0G9+OKL2rVrlzZu3ChJGh4e1v3336+ioiL90z/9k8sRAgC8xO92AAAAXI4//uM/1kMPPaRnnnlGX/jCF/TGG29o9+7d+o//+A9NmzbN7fAAAB7CtDoAgOf19fVpxYoVMk1TJ0+e1Ne+9jW98MILbocFAPAYiiMAwJTwy1/+Uvfee69mzpypI0eOKDs72+2QAAAewzVHAADPM01TmzdvVkpKilpbW7V79263QwIAeBDFEQDA855//nl98skneuWVV7Ro0SJVVVWpv7/f7bAAAB5DcQQA8LT9+/friSee0Fe+8hX9xV/8hV566SUdPXpUjz32mNuhAQA8hmuOAACeFQ6HdfPNN6u5uVn79u3T9OnTJUnr1q3TD37wA/33f/+3brnlFpejBAB4BcURAMCznnrqKT3xxBN67733dOedd0YfHxgY0PXXXy/LsrRr1y5lZGS4GCUAwCuYVgcA8KTdu3frqaee0te+9rWYwkiS0tPTmV4HALhkjBwBAAAAgBg5AgAAAABJFEcAAAAAIIniCAAAAAAkURwBAAAAgCSKIwAAAACQRHEEAAAAAJIojgAAAABAEsURAAAAAEiiOAIAAAAASRRHAAAAACCJ4ggAAAAAJFEcAQAAAIAk6f8B5yUfzpj8ZD8AAAAASUVORK5CYII=\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 narrower 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": [ "However, position and velocity are correlated. If the velocity is 5 m/s, then in 1 second the position will be 5 m. If the velocity is -10 m/s then in 1 second the position will be -10 m. Let's visualize this with a velocity covariance drawn on the diagonal. " ] }, { "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": [ "At this point the velocity covariance doesn't help us. We can't predict a new position because we have no idea what the velocity is. But after one second we get a position update of x=5." ] }, { "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 what I'm about to say. 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 velocity covariance and measurement covariance! 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": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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2NzcHRVFcf+koJRAIrPqHqyiKffOR/2okH+N1cwIAVVXtbV7/SDZ63uJrks/rNXCCwSBM0/Q8r6Zpt3Ve+f+lzlv8WuX30Ou81mv1umlu9Lzl8rNZ77Var3O99/BWzqvruue2tc5rHbvWeW/3PVzvtRZb77WGQiHour4t76FhGJv+d1OO45D3iNXnLZefTbncI+RuhOFQAEFVHKsbpr1Icjzi/nlax1rPA0DOACKhwnvhmvNlIBbenfeIwMwMIqOjgFVNEw4Dx49DuXEDwUwGAVUFLl50Wsp3dkKNRBAs/FWc9wjeI4Ddf4/Y6HmtY9c67176HLEZirkHFt2YmZlBY2MjPvzhD7vW+srn86iqqsKv/Mqv4JOf/KTrmJ/92Z/FlStXcPnyZdfzhmHYqWRLZWWl5w+fdrfR0VHk83kEAoFV5R7kbxwbVMpeHxsLy2k8PzQBAGhvrMKhtrpVz7fWV+Lw/vpVxy4mM/jJ4PiqfZZTWTx7SZR3tdRVoLejYdWxZc00xfyuQpkfAKC6Gjh2THQ1LLj51FPA5CQ0TcO+AweAu+8WzTbI9/b6fcPvNhs77Om7QiAQwOtf/3r80z/9k+tNGR0dxbe//W28+c1v3sGro52WSCQwNzdn11cTWTg2qJS9Pjbkhhhyo4yVjFPGI2e4ZDHpeatEsfg8u67hRjYLvPCCO/BqawP6+12BF8bGsDIygqWlJSytrABHjzLwIttev2/Q5uzqssNvfOMbSCaTdmB1/vx5PPHEEwCA1772tYjFYnj44Yfx4he/GK973evw0EMPIZ1O40Mf+hAaGhrwB3/wBzt5+URERGVFbgUvr8eVTDvBV6xE8BXQVISDGjI53bW/e52vXdRqfmkJOHfONb8LPT1AcZOu+Xmg0EwCANJdXYDU0ICISLaryw67urrsrjzFRkZG7M4qzz33HP7oj/4IP/jBDxAIBPCqV70KH//4x1d1SAFYdugnmUwGpmlCURRXRyEijg0qZa+PjdHJBVwZF3+dP9bViMYaEUScHpqw1++659h+hILeCyWfGZ7EXGEh5pcdbUc4JP7G+70z16AbJuKRIF7c1+Z5bFmZmAAuXxYt5QExv+vYMUDqVggASKeB554Dcjlks1mY+/cDBw7sybFBt26v3zf8brOxw67OfFntItdz991341vf+tb2XgztOrwBUikcG1TKXh8bcsMNr8xXUFNLBl6AKEm0gq+VTM4OvgKaCt3QXd0Uy9IG53cBAHRdZMYKHdBCzc1AXx+wycn3tPft9fsGbQ7TOURERATAXRZodSnM6wayhefj0ZDncRb3vK/VpYdlXXao68DZs+7Aq7V19fwuy+XLorU8AESjYp4XAy8iWseuznwRERHR1vFquJGSmm1EQ2t/bIiFneBLPs46l4nCWl9amf3tN5MRgZcVTCkKcPjw6vldluvXgcIC69A04PhxwKN1OBFRMd4pyLcWFxftGuyq4jp+8jWODSplr48Nr4Yb1vpeABBZJ/iSt8vHySWMZRd8JZPAmTNOY41AQARTpdYBTSSAK1ecx319QDy+58cG3TqODZIx+CLfGhkZQS6XQzAYRH9//05fDpURjg0qZa+PDWvOl6YqUFVRQpfO5u3t6wVfoaAGBSLDJR/nXmhZX/c8d0wiAQwMAPnCtUYiwMmTQCzmvX86DZw/71pIGY2NAPb+2KBbx7FBsjK5+xEREdFOsxpiyMGSHESF1wmaFEVBOBRAOptHRjouGJCDrzJpujExAVy65ARSlZXAiRPe87uAVQ02UF8PFLoqExFtFIMv8q19+/ZB13VoWunOXeRPHBtUyl4fG1bZoVwmmNlE5svaJ53NI6cb0HUDmqaW31pfV6+K/yz19aJhxlo/10uX3A02jhxxNdjY62ODbh3HBskYfJFvNTc37/QlUJni2KBS9vLY0HUD1sKfcuZLnrsVXqPNvNc+mZyOmKa6zie3s7/jDEN0KZyYcJ5rawMOHVq7U+HVq8DUlPi6RIONvTw26PZwbJCMwRcRERFBN0z7a3fwJTJfoYAGZQOt1MNBuelGHrFIEJrqHCd/nzsqnxfzuxIJ57mDB4H9+9c+bmLCnSU7cgSIx7flEolo72PwRURERNANJyOlFoIs0zSRLWS+NpL1Kt7PypppqhPMyd/njslkREfDZFI8VlURRBWaZZSUSIhyQ8vBg0BDw/ZdJxHteQy+iIiIyJWRsjJV2ZxulyKGNhh8yftl7eDLyXwZdzrztbws1vCyWskHg6JssLp67eOSSZEpsxpytLWtnyUjIloHgy/yrYGBAbv167Fjx3b6cqiMcGxQKXt5bOjSXCytUHaYzcvzvTb2kaG47FA+H3CHyw7n5kQApRdeRzQqWslHo2sfl82KgM1qQV9fL+aFrWEvjw26PRwbJGPwRb6Vz+eRz+c3NIeB/IVjg7yYpomF5RQy2Rwq4zs0b2kbeWW+Nttso3i/jEfm646VHY6Pi+YaVuaqqkq0kg8G1z5O10WJYjotHldWik6I69wPeN+gUjg2SMbgi3wrHA5DVVUE1/tFTL7DsUHFdN3AuZEpDE2uIJ/PI7qoo3clg8pYeKcvbcvIQZE1R0tuCy+3i1+LV1t595yvOxC4jowA1645jxsbxRwv6To8maZYRNlqKR+JiIBtAy3Ced+gUjg2SMbgi3yrr69vpy+ByhTHBslM08QLQxNYSmXR0dFhP//C0ARO9bSgIlpiUd5dxivzJS+ILC+UvBZVVaCpCnTDtNvKuzJf29lq3jBEg4zJSee5/fuBAwfWzVwBAAYHgdlZ8XUgsPaiy0V436BSODZItrE7KRERkU/dnFnCUioLQLRgtxYa1g0TQzfmdvLStpTXnC95Ta6NZr4Ap1W9Fbypd6LVfD4vygWtwEtRgJ4e0aFwI4HX6Chw86Zz7PHjbClPRFuOwRcREVEJed3A1Yl5+/HJA/vwkr42RAsB2PxyGjMLKzt1eVvKO/MllR1qG//IYAVq1vGKotjn3JY5X9ks8MILwHzhZ6WqwLFjokPhRkxNAVeuOI/7+oCamq2/TiLyPQZfREREJUzMLSNXyP7sq42jKh6Gqio42FZn73N9amGnLm9LGaYcfBUyV1LmK7CZ4KuwrwlIpYfiuS3PfKVSwPPPO/O0gkHgrrs2vh7XwgJw8aLzuLsb2Ldva6+RiKiAc77It27evAld16FpGlpbW3f6cqiMcGyQZXJu2f66o6naNTbikSCS6RwWkhmkMjlEw7t7Mr2r7NAr87WJskN537xuIKCpTuZrK+d8LS2JlvBZURaKcBjo7wdisY0dv7IijreycS0tQGfnLV0K7xtUCscGyRh8kW9NT0/b627wZkgyjg0CgGQqa8/1qoyGEI+GMHTZGRv7mrtwZTwBAJhMJNHVvLvL1Fxlh0VztjRVcc3bWo/cnCOX1xEJBexzblnmK5EAzp1z1vCKx8UaXuENdqDMZsUcMWstr7o64PDhW74c3jeoFI4NkrHskIiIyMPUfNL+urmuYtX2fbVOM4apRHLV9t3G3WpeBFpWyeBmsl6Au0RRDuAAUd5omrcZgE1NiYyVFXhVVwOnTm088NJ1EbhZa3lVVGxoLS8iotvFzBf51qFDh2CaJhc9pFU4NggAEktp++vGGhFoyWMjHAqgOh7GQjKDlUwOmWwe4dDu/bXqbrjhXufLa75XOptHYimFWDiIqnjY9e9lI2t9BbRb/Pd144ZoCW9paBCB03preFlME7hwAVhcFI/DYdFSPnB7PzveN6gUjg2S7d7fEkS3Kc4WwlQCxwbldQNLKxkAQDwSRCgogonisVFbGcVCUuyXWE57Zsh2i+I5X3ndgBWOFXc6zOV1PHvppp0Z6+tocL12ef9cibW+NtPAw1a8eHJLiygV3MyH2uFhYGZGfK1pIvDaaMZsDbxvUCkcGyRj2SEREVGRheW0HXjUVERK7idvm19Ol9xvN5AzX6qqrNls49rkgmsNsJHxhCt4K264ATjzyIq/14aYplg8WQ68OjuB3t7NBV7XrwNjY+JrRRHt6Ct2b8BMRLsPgy8iIqIiciBVWxktuV9VLAy18OE/sZTa9uvaTtacL01VoChK0QLLzscF0zQxPrvkOjaT0zG76Lx+95wvq+xQXmh5Ex0PDQMYGADGx53nenpES/jNmJwUWS/L4cOiyQYR0R3EskPyrZWVFbsGO7bRtsTkCxwblJCCr+q4U5JWPDZUVUF1PIzEchqZnL6rW85b2Shrbla+xBpfSytZe9+gptplhfPLaTQVmpDIwVrxOl/y91pXPi8aY1iLJysKcOQI0NS0mZcGzM251/Lq6hIli1uI9w0qhWODZAy+yLcGBwft1q/9/f07fTlURjg2/C2X17EstZiXS+i8xkZtZdQO1hJL6d0bfBXNzfJqwAG4s4KdzTUYvjEHs+h5VZGzXFZQ557ztS6rFby1eLKmAcePA7W1G39RgGisMTAgShcBoLVVBF9bjPcNKoVjg2QsOyQiIpIsFhpoAGvP9/LaZ3Els8ae5c0Okqz1uKQASV7jSw6y6iqjqIyJzOBKJodsTnedAwCMovPK36ukdBp4/nkn8AoGgbvu2nzgZS2ibLWkb2wUJYtERDuEmS/yrfr6envFeSIZx4a/JdM5++uKaMi1zWtsxCNOpitZyJjtRkYhM2RlrQxTznyJ50zTxEJSBF+hgIZYJIiaiogddC4k02isiXvO75KzYcZa63wlk8Dp0yLzBYhOhP39wGbLtTIZkTnLFX6eNTWiZHGb2n3zvkGlcGyQjMEX+VZ7e/tOXwKVKY4Nf0umnQAqXhR8eY0NTVMRDQWQyuaxksntyvV85EWPrUv3KjtMZ/P289ZcuCppTtxyKovGmjgURYECwJTOI78lJRdZXlgQmap8XjyOxUTgtdlW8Pm8CLzkRZSPH9/4WmC3gPcNKoVjg2QsOyQiIpKsFDJfCoDYBudvWUGabpjI5PR19i4/htxmvhAleZUdprN5+zlrbltUWlha3m6VGRp28OVEX56x1+ysyHhZgVdVFXDq1OYDL8MQAVwyKR5HIsDJk7e9iDIR0VZg8EVERFRgmqZddhgJBVxzndYiB2m7sfRQjoWUNcoO5eAqUgi6IqWCL7txxwbKDicnRVdDqwV9ba3IeAU32bzENIHz50UGDRDH9/cDodDaxxER3SEMvoiIiArS2bwdGBSXHK7FNe9LmjO2W8iZr7XKDlOZ1cGXpqkIFTpCysGXnUFbr+xwbAy4cMFJhzU1ASdOiO6Gm3X5MjAzU7hoTWS8oqXXaSMiutOYgyffunTpkt36tbe3d6cvh8oIx4Z/yYGTHFBZSo0NOVCT54ztFnIwtNGyQznjFQkFkM3ryOR0GIYJVVVWdU10Zb6swG5kBLh2zbmQ1lbRjVCO1LJZYGlJLIi81ly6K1echZgVRczxqqzcwKvfGrxvUCkcGyRj8EW+lU6nkcvloOu7b34GbS+ODf9acQVfqzNfpcZGLBy0G0ys7MLMl1fZoTvzJZ7L5EoHX1bHw0wuj2g46HRIBFY1ITFNExgcBG7ccL5xV5d7/a1UChgeFnPBTFMEUnff7f0CxsaA0VHn8ZEjm29Lf5t436BSODZIxuCLfEvTNLZ+JU8cG/4lZ61iHpmvUmNDVRVECh0Pk+nd1/HQ1XBD9ZrzJbJY1jpeAU11zYcLBZ33I5vTC8GXe10ve3/ThHb5EmA664Whpwdoa7O348YNkckypMWYl5ZEE4143H3xk5PA0JD7XE1NG3/xW4T3DSqFY4NkDL7It44fP77Tl0BlimPDv5LrdDpca2zEoyGkCnPG0tm83Q1wN3C1mi/8Xy47tLJY2bwIvsJB94dIa86XvI8cnOm6Ic5rGIhfGYRqZoDGKlEe2NcH7NsndlxZAS5eBBYXV19kJLJ6ra/ZWbG/pavLCeLuMN43qBSODZKx4QYRERFEAGKVDEbDwQ13OrTIc8R2W+mhnOVS1dVlh6qqIK8b9nNysAW4gzErOyYvtGyYJhTDQHzwIoLzCeukwLFjTuA1MwM895x34AWI+WByNnFhARgYcBp1tLW5yxaJiMoQgy8iIiK4Ox16lRyux9VufpcFX3LzweJW86qiQFEUO6gC3GWGxY8zdvAllR1mcwicOx1NooEAACAASURBVIvgkgisDEUVHQ0bGsQ3HxkRreatOTHRKFBf73yDeByQF6pNJsVaXlZZYlMTcOjQrb14IqI7iMEXERER1u90uJ7d3PHQWKPssLjkEFid+Vqr7FDJZYHnn4dSCLxMTUO676hoiJHPi6BL7njY1AQcPQokChkyRQF6e0WmDADSafdizHV1onRxF82xIyL/4pwv8q2pqSl7AmzTDkzOpvLFseFPcht1r/lewNpjQz5GPtduYK5Rdmg9zktzwIJFwZf8OC8FbWomg/jgBZh1UagBDUYgiOThPkQqK8X8rnPnxP8BETwdOAC0tIjyQyur1d4OVFWJr7NZEXhlC8FtVZUoXVR3/m/JvG9QKRwbJGPwRb41Pj5ur7vBmyHJODb8SQ6YwiHvX49rjQ1VVRDUVOR0YxcGX87XxWWHVvmgVwMOr8fWfoF0GhUXB6DmsjCMCBAJY7n3KIxoFOrsLDB60SkzDAZFtqumRgRkqZR4vqLCmceVzwNnzjjbYrFbX4x5G/C+QaVwbJCMwRcRERGATIkFhDcjEgogl8oim9N3Vbt5Y41FljWPBhzWAsr2MXLwZZh49vkhfOWJ/8BTQzPI6Cbaaqfx4M+cwtGDQVTeHENoYRpoKazDFY+LBZGjUTH3a3ZWPB8Miuc1TWTBzp0DlpfFtnAY6O8X+xAR7SIMvsi3urq6dtWHI7pzODb8ycpWKVjdSt2y3tiIhAJYSmVhQjSeuNUg7k5ztZpXxLpf1jNOGWLpzJeiKFAVBeevTePzX3sOP7w84dp+bjaNbw49hSNNcXzyFS0wa6NiQ1OTmM+lacD0tDP3S1FEJiwSEWm58+eB+XmxLRgUgVc4vHVvwBbgfYNK4dgg2e74rUC0Daqrq3f6EqhMcWz4kxV8hYJayQ9J640NuVwxnc3vmuDLtciyongusOzKfBXNsVpJ5/B/fuUH+B9PX1rz+1yYSuITp2fwsfs6xPyujg6xIZl0r9d14IBoyGGawKVLog09IIK0kydXr/dVBnjfoFI4Nki2O34rEBERbSNdN5ArlNndTsAkH5vZRfO+pClfUBTFc35XqTlfI+MJvOFP/gFnr0zZz3XVRPC+e7vRdqIXTbEg5s9dwH/9x/NYyRl4YnAev/yGl+KgFXhZHQ+t+V/79gH794uvh4aAiUIWTVVFGWJl5da9cCKiO2zn2wMRERHtsIy0htVWBV+7qemGnPlSlKLW80rpOV9PPXcFL/qtv7EDr4im4H+9uwmXPvwgfu2d/zPaoipqBs/jZQ0h/OHLxDpdJoBnJwsdDq2SQrnBxuHD4uuREeDGDeeijhba0xMR7WIMvsi3stms/R+RjGPDf1ydDoOlg6/1xoY8V2w3BV+mR8MNi/WweM7X1384iNd84IuYWxSBU3d1CF96sBM/f08PgiePQ03MouLSeaiF9bhedaTFPv78tWnxxZUrwNyc+FpusHH9unvtr95esSBzGeN9g0rh2CAZyw7Jty5cuGC3fu3v79/py6EywrHhP/ICwqWabQDrjw05cJPPWe6Kyw69Ws/Lma8Xhibwtoe/Yj/32p46vOtoLb4+mcN3n7+Aqc/8GM2xAN58oBJv7amBUV2Dzr4jwKd/BABYSGaAmzdFkCW+idNg4+ZNYHjYuYCeHqC5eVte91bifYNK4dggGYMvIiLyvcwG1vjaiGBAhQLY3Q53C1fDDdW72Yg152tibhnv/+t/RTKdAwD8/NEGHGmI4W3/cgV56TwLqRw+NpvCnBbBBx48irwU0IWNPDA46DzR0yNKCqemgMuXnee7u4G2ti14hURE5YHBF/lWdXW1veI8kYxjw3/kQGmtzFdlZRVy+TzCIe/1pRRFQTgUQDqb310NN+RUV9FjKxTTDRNLKxn80ae/hclEEgDwkrZKXF/I4InzM67jm+NBTCRFcPa3z93AO5fSCAacmQ7R5JKzsnNHB9DaKtb3unDBOcn+/UBn5xa9wu3H+waVwrFBMgZf5FtdXV07fQlUpjg2/CeTcwKlUMD7A9L47BKuLyowEURjMAbDMD2zRKGAhnQ2j5xulNynnJW62lQmhz/57LcxOrUAAOiuieD6QhrjyyLI0hTg147W4ecP1+Devhb85n9M4otPDyGb03FuZBKxSMg+V3tFIXhtahLZrfl5YGDACchaW4GDB7frJW4L3jeoFI4NkjH4IiIi38sWMl8KxDpfxabnk7h0fdZ5vLACZXQGR7saV+0rZ86y+d2z0LJs9RwwEw9//rs4c2USANAQCyKrG3bg1V4dwace6EBbRIGpacgdOYZ7UtX44tNDAIDhmwmk0k6zgZ6aMFBdDfT1AUtLwNmzgNXQY98+UYZIRLQHsdshERH5nlV26LXAsmmauHIzseqYqfkkllYyq54P79K1vtbyua89h3977goA0U6+IRbEjSURTPU3V+DZd51Ce3UEGTWApb5j0KtrUB2P2Mcvr2Tw9H86c7n699eKzoapFHDmjLPGV329CMhKLHJNRLTbMfgiIiJfM03T7kzoVXI4mUgiVQiiaioi6Gmrs7eNjM+v2l8+x25pumEWP5bmfE1Oz+P3P/FN+/HBmjAuzoh1uvZXhfGm3nq88vEXcNfnzuDBrw7j6StzME0TVyec96Ylt4yfjBXKFavDCJ48LhZXPn1a/B8AamqAY8cYeBHRnrb7aiGItsjw8LDd+vXgLptbQNuLY8NfsnKzDY8SwfHZJedBKoGFbAIzUwtoaGrG3FIKmWzedVxx2eFu48r8ZTP48Ke+icW0CJAO1oQxMJsGAFSFNXRUh/GR7zrrcSWW0/jw49/Gr76mH6eHJ+3nx27M2p0Q+3tbAVUVgZe17lFVFXDihHh+l+J9g0rh2CDZ7r3LbcJ3vvMdKIri+d8Pf/jDnb482iHLy8v2f0Qyjg1/kQOk4sxXXjewmBSlhbFwEIqRxcpKErGAs+BwYjntOkaeM5bdJZmvYqYJKNkMnv7GM/j2iCi5rAlrGJ4X70VQVdBdE8HT1xdXHZvLGxi4No0fDIg1vMIq8NQ1Z7/XvvQwohfPA+nC+xaPi8Brl3eC432DSuHYIJmvMl8f/ehHcf/997ueO378+A5dDRERlYNc3gmk5HboADC/nLZL8morI1gp9NyojAZhhVWJpRSa6yqkczhBRG4XZr4AAOk01HNn8X/96Kb9VDAcBDLi9RxviuH5CdFuHqaJJ/7sbfjXHw/jM1/7CQDge2eu4fq0CLgO1IRxYU4EWsc6G/BTK1PQchkAlUA0CvT3A0Hv1v1ERHuNr4Kvnp4evPSlL93py6AyceLEiZ2+BCpTHBv+kted4CuguYOvxFLK/rq2MoqDrWJsGIaJH5wfg26YSCy5M19B6RzyuXeNVArawFn87XPjmE6JcsO+9jpcHJsDINrE24EXACgK7j3Rgf/jK04lydMvjNhfB6VW++84VAUttQIENCAcFoFXyGlBv5vxvkGlcGyQzFfBF5FM3cVzC2h7cWz4i5ydChaVHVqBlQLRbMMaG6oqHs8uppDN60imsohHRRAhB3C5XRJ8WQ021FQKgTMjGJpexBcvinLDoKbi2qRonqECSKRXd3A8PTSJHw6MAQAaqyL4zllRclgXVjEwJ0oVGytC+NlmkeEyAgEReEUiq861W/G+QaVwbJDMV8HXe9/7XvziL/4iYrEYXvayl+FP//RP8fKXv3zd4wYGBtDZ2Ymqqir7uUwmg4sXLwIAamtr0dHR4TpmcHAQKyuiG1R/f79r28zMDG7cuAEA6OjoQG1trb1N13WcO3cOAFBZWYkDBw64jh0ZGcHioijlOHbsGAIB50c4Pz+Pa9fExOfW1lY0NrrXnzlz5gxM00Q0GsXhw4dd265fv465OfFXzd7eXkSkX4jLy8sYHh4GADQ1NaGlpcV17Pnz5+2JpEePHnVtGx8fx9TUFADg4MGDqKhwSnPS6TQuXboEAKirq8P+/ftdx16+fBmpVAqKouDkyZOubdPT07h5U5TDdHZ2oqamxt6Wz+cxMDAAAKiqqkJ3d7fr2CtXrmBpSUygP378uGvF+UQigdHRUQBAW1sbGhoaXMeePn0aABCLxdBTtA7N6OgoEgnxYaWvrw/hcNjetri4iJER8Zfgffv2obm52XXswMAA8vk8wuEw+vr6XNtu3ryJ6elpAMChQ4cQj8ftbSsrKxgcHAQA1NfXo7293XXspUuXkE6noWnaqhLbqakpjI+PAxALQFZXV9vbstksLly4AACorq5etUDk8PCwXbt+4sQJ1y+W2dlZjI2JD2Ht7e2or6+3txmGgbNnzwIAKioqVk08vnr1KhYWREe0I0eOICT9RXxhYQFXr14FALS0tKCpqcl17Llz56DrOiKRCHp7e13bxsbGMDsr6sV6enoQi8XsbclkEkNDYi2ixsZGtLa2uo69ePEiMpkMAoEAjh075to2MTGByUnRVKC7u5v3COzOe4QSdd7foKba94hMTseSUg1N01AVDyOgqa57hBJx/s3MLaUQj4bse8TNG8tobWtzBXblfI8YT6QRD1UgfvkClKZK/PV/jiNXaJBxoCqASwnRGKOnNoxLidXt9V/9gS/aX++PaihUHKIlrmFuTqwF9u67mhHSVCSWV3A9XgV9cJD3CN4jAJT/PYKfI/g5Yq17hPXvdKN8EXxVV1fj937v93Dfffehvr4eQ0ND+Iu/+Avcd999+NrXvobXvOY1ax6fz+ddbXcB8VfCXC5nb/c6xtpezDAMe5thrP6r6EbPW3xN8nl1ffU8g1wuB9M0EfSordd1/bbOW+q1yuctfq3ye+h1Xuu1Fq+5s5nzlsvPZr3XmsvlkM/nPf86ttbPZiPnzeVyntvWOq917Hrn9bLR99DrePmaiq33WrPZLAzDcP0S9Drvrb6HXu/RRs9bLuOQ94jV583n80BR5ss678JyBmql+DBRUxFZ9Vrra4OYS4mvl1ay9msFAAXie8rzycr5HmEsLCCeuA41n8diJo9/OD8DAAhrwPXFbOFrBWMr68xhM00MzolSTQ3AtZVCRk0BfvNFLVicX8ZC90Gk02nxfXmPAMB7RNnfI0qc1ws/R7iPXe+8Xnbj54jN8EXwderUKZw6dcp+fO+99+JNb3oTTpw4gQ984APrBl+BQGDVP1xFUeybj/xXI/kYr5sTINLP1javfyQbPW/xNcnn9Ro4wWAQpml6nlfTtNs6r/z/Uuctfq3ye+h1Xuu1et00N3retd5DwzAwMzODQCBg/1Vlu342671W63Wu9x7eynl1XffcttZ5rWPXOu/tju/1Xmux9V5rKBSCrutb8h7Ozs7CMAz7tRiGsel/N7xHrL7ecr1HpIvmfFnnzRlZWH93riiUFCaTSfta4pEQFORgAkims67XGA6JD1au+WRleo8wFxZQNzoCNSoCzb8fXsJyVnwwOVShYmBBvIa+9nqcviaCsre+8gh+8aUteMuf/7vrfN1VIYwsiQ8onU1xXJkSc8Me7K5BR00UP25og543EMjnEQwGd+09ovh6rQ+I09PTUFXV/p3Ce8TGzyv/v9R5y+1zhBevn03x75SNnLec7hH8HLH+e7gZirnZcG0P+e3f/m186lOfwsrKCqLRKAARYVupZEtlZSXrdfeg06dP22UOxSUd5G8cG/5yZngSc4XGGj99fL897+v81WlMzYvg4SV9bYhFgqvGxn9evIFkOgcFwCv6O+1fwqeHJuwW9Pee6ICmlenvkPl54OxZjE/NYzKRRC5egV96chiDN8Ucr/aKAMaWRSB59+EWPHdZlBj94BO/jgMtNdj35r+0T1Ub1jCf0WECiIUCyOk6crqJkKrgqbcfwcvfcB+emUwjm9cRCQXw0qPtqy5nN+N9g0rh2NjbNhs7lOlvgzvDijs3G7ESEdHeYc3LUuBulmFlsxQA0bB3oUgsLP4SagJIZZwyol3RdGNuDjhzBtB1KIqCXGUVnk6H7cDrcE3YDrx++vh+TMyJ+RmRUAAv7m2128pbokHVbsvfUhNFTheP/pejdWg5dQwomj9ERORHvig79JJIJPDkk0/irrvuck0KJf9ob2+3ywCIZBwb/mIFRwFNtf8YZ5omVtKifC4WccqWisdGPBrC9IKYbJ1MZxGLFMphitb6ioTK7Nft7CwwMAAUyuX02lpkEMU//+237V1aqiO4XFhU+Tdffzf+8JP/HwAgnc3jTR/6f/Evz1y29315RxW+P7poHzc8Jf4K3BwL4O0/ewrGvn135GXtJN43qBSODZKV2W+D7fGOd7wDHR0deNGLXoSGhgYMDg7iL//yLzE5OYnHH398py+PdojcPYdIxrHhL9a8LDlgWknn7CxOPOJ0yyoeG/GIMzcgmc7Byu3IizXLTTfKwvQ0cP48YM06aGiAbgSx/J0f47tjIrvVUhXGrOK8tv/yooM4vL8BU/Oii5sceD3QXYNvjYhsmaYAi8msve2/veYo1LY2+/FenunA+waVwrFBMl+E4CdPnsQ3v/lNvOtd78IDDzyAP/7jP8bRo0fxzDPP4IEHHtjpyyMioh1imqYdfMmlgisZp1uWHGAVkwMzK1MGuAO5slpoeXLSHXg1NQG1tQgNDeIHN5ModJfHf33wp3BlXLRrbmuoRHNdBd5ybx/CQed11UYCeP//1IanCoEXABysCSNZCDbfencHXvIK0exq1QT17Xp9RERlzheZr4ceeggPPfTQTl8GERGVGTkrJWerklIgFVsj+IqGA1AAV8dDoGjOV36d9ux3yvg4UFgTCQDQ3CwWOS6s8XN6OmVvuruvDSuZHwAAupvF+kcv7mvD4w+9ET969jIerFegKcDr/v6cnSF8WVsFfnBDZM4aK8L43//gTbg66QRmRETkk8wXkRfDMOz/iGQcG/6RK1rjyyJnseTsVvHYUBTFDs5W0s5aT8Fya7hx44Y78GppATQNKCw4CgDPJ8RrDgU0HG6rs58PFrJdqqqgLWjg15sMzKdz+Ll/OId0IXi9Z3+VHXgBwH//vdeittJf86l536BSODZI5ovMF5GXs2fPsvUreeLY8A+5JFAOmNJZp3Oh3CzDa2xEQgEkC3PEsjkd4VBgVcONHXX9OjA87DxuawN0XQRkBfNNrRhNPAcAOHGgCQdb6xAOasjkdFy+PisW1k2loF84jz97dgJfGVywjz3VXIEf33DaLP/2z92N19/TC8Nw5ndZZYZ7d8YX7xtUGscGyRh8ERGRb+WKFli2ZHIi+AoFNKjq2jOU5OAsYwdfzrl2dM7XtWvAyIjzuL0dSKeBGbFYMhQFOHwYQyOL9i5HOhuhqgo699Xg8tgsbsws4Zce/goS18fx/euLWM45r+f1fQ34zpUE8oVA600v78Vb7zsGTVVhGKWDTi7xQkR+xbJD8q2Kigr7PyIZx4Z/eJUdGoaJTE48X9wi3mtsyPtYGTP3nK8dCr5GRtyBV0cHsLzsBF6qChw7BrS0YFkqs6yrikJRFLzjgRP2c3//3Qv41yvzduAVCwfwvz1wAD+5sYilrHivXnVXF977ppdAURRoquLKcvkh2OJ9g0rh2CAZM1/kWwcPHtzpS6AyxbHhH14NN6ysFwBXdz/Ae2yEg97Bl9WIY0fKDoeHRbmhpbMTmJ8HFgrlgpoGHD8O1NYCRdcYKrwPrzjZgV/9Lyfwd0+dQ66Q2aoMaXhZXwv+2131eP/XLuPGkmgy8pK+Vnz03T+DVOH1a5r333atOXF7MRbjfYNK4dggGYMvIiLyLdecr0Lmy8p6AaszX17cZYci+FAUBQFNRU437mzDDdMEhoZc87nQ1SUWVV4qzMsKBICTJ4GqKnsXeb7bUjILRQEUw8B7u0N4zy8dQVoL4uZSFk3HejDwzGm8/cvnMJ8W79OBlhr8y0ffgRszi3bwpSqKa00vK9iy5oGpezH6IiLaAAZfRETkW3LwpRXmdmWkZhvhDQRfcnZMDty0QvCl36ngyzSBy5dFS3lLd7dYVHm50IkwGAT6+4Gi8qejXU321y8MTwCGgfjwZQSSy6itiKCzowkD0Tr8989/G587M2WvB3a0swH/8tF3oKk2jtEpkVVTgJLz5KxwzA9liEREXhh8ERGRb+mGHHxZZYdOAFVcduglFNTsEkM5cLOCOd24Az3+TBO4eFEsogyIVFN3NzAxAaysFC40JAKveHzV4Y01MeyrjWMykcSPLtzA9772fTQtimAqp6j44iTwx5//HxhdyNjHvOFlh/GFP3kzKmNhALCDTKvk0NXtUFFcj9drYkJEtFdtOvg6ffo022TSnnD16lXoug5N09DV1bXTl0NlhGPDP+SAwM58SXO+QgF38OU1NhRFQTCgIZvX3ZmvQjBnmCZM09y+bI9pAufPiwyXuCAReI2PA6nCwsnhsAi8YjHPU6iKgl941XH83//4IwDAGz79DH6qMQpNBV6YzWJJasihKcBDv3gP/uxdD7iCKCvItN5Hw3S/t64yxNt/1WWH9w0qhWODZJsOvk6dOoWf/umfxvve9z685S1vQSDA5BntTgsLC/a6G0Qyjg3/kLNSVsYmK2e+isoOS42NcFAEX7m8bgdaWlFgEtC2IeQwDBF4yR0Mu7vFnK90WjwXiQB33SX+X4KiKPi5ew7jqWcuYGB8Eem8gWfGk6v2e0lLBX795+/Bm3+mf1X2ysoiWkGn671VVVcwthfLDnnfoFI4Nki26Vbzn/nMZ5BKpfD2t78dHR0dePjhhzEu15cTERHtEu6yQyvzJXf+W7/sEHCCNGuhZcDd8W9b5n3pOnDunDvwOnBAdDm0Aq9YDDh1as3ASxyqIDY1gb95xT78xl1NCEuBYk1Yw88fbcATv3Acf/F7r8PhAy2er8coynzJ+6iqAin2YtkhEfnWptNW73znO/HOd74TzzzzDP76r/8aH/vYx/DRj34Ub3zjG/G+970P995773ZcJ9GWO3LkyE5fApUpjg3/0KXue1Y2Jltoux7U1FVBQqmxIQdp2bxYaLk487WldB04e1a0jwdE6/iuLrGocq5QIhiPi1LDUEiUH05OAtEo0NgoAjWJOj6O6NgoEFDx8L378f/8zmvw7e+cxsrCEg7VRXD08H5MdBzCxemk5+sxDNNupmHP+fJZ2SHvG1QKxwbJbrlm8J577sE999yDyclJfPrTn8bf/M3f4IknnsCJEyfwO7/zO/jlX/5lhMPhrbxWoi0VCoV2+hKoTHFs+IfdJEIKlKw1r4IeWa9SY8NaI0wc7y6/A9wZttuWz4vAS16zq7sbuHpVbAOAykrRTj4QAEZHgStXnOMjEaC62nk8MYHglSHn+lvboC0sYB+y0CtDMAKiUYeWNQE7+HK/Hq8M4lplh3sx88X7BpXCsUGyTZcdFovH46irq0M8Hodpmpibm8O73/1u9Pb24sc//vFWXCMREdG2sJtESB36rOcCJRYK9iIHanmPgG7LMl+5HHD6tBN4BQIi4yUHXlVVIuNlGMBPfuIOvAAg43QsxNQUcOmSnfVLNzVDWVwCFhZEwBQIYLnnCBCLuYLJfFHZobtlf2HO1xplh3txzhcR0UbccvB1/vx5vPe970VbWxt+//d/H3fddReefvppjI6O4rnnnkNTUxN+4zd+YyuvlYiIaEs5TSJEMOBedHkTwZcmZ75Wz/kytiL4sgIva7HkYBDo7HQHXjU1IvBKJoHnnnP2tUSjQEOD+HpmBrhwAVZUlGlogpZOQVkQpYxKMIBkTx9yhfliIantvtyUpPixtV9x2aEr88Xgi4h8atNlh//4j/+IT3ziE/jud7+Luro6vO9978N73vMetLW12fucOnUKH/vYx/Dggw9u6cUSbaWFhQW7K1m1XIJDvsex4Q+maUrt0UWgZAVOgHfZYamxIWfJcp6Zr9ssO8xmgRdecK/ZtX8/MDIiMlwAUFcHHDsmslmXL8OVarL09Yn5XnNzwMCAs09LC9ShmwguLsCsjgKahnTfUehaGNaKysXz2lyXl1/dpKS47FB+D/Zi7MX7BpXCsUGyTQdfb33rW3Hy5Ek89thja87r6u7uxi/8wi/c9gUSbZerV6/arV+5dh3JODb8wWuNr5yc+fIoOyw1NuRAzc58ueZ83UbmK5MRgZe8ZldbmygntIKn+nrg6FHx3I0b3udpbxdzvRIJ0SXROrapCepKBsH5BADAVDTg5Eko0ylgWXRN1HUDwYBqLyZdnPnyWpi6uOxQjtf2Ytkh7xtUCscGyTYdfP37v/877rvvvnX3O3DgAL7whS/cyjURERFtO681vtxlhxtrMy/29Wq4IWW+brXVfDotAi95za7WVpHxsoKnxkbg0CERUCUS3ueprQUOHhRzxc6dc7JlhRJEdW4WAGAqClK9fUB1NbTZtH24YZrQFBWhoIZMzr2YNOBddqgbLDskIiq26eDrS1/6Erq6ujxX6B4dHcWjjz6Kxx57bCuujWhbtbS02CvOE8k4NvzBq0OfXHbo1XCj1NjwbLih3Wbma2VFzPGyGmREo0Bzszvw2rdPzPuSM2OK4i45jEREVmx5GThzRrSpB0TgFQgAExN2Rit5qBeRKlEWVZy5C0KUFGZy7sWkAe+yQ/ecL9Xdan4Pxl68b1ApHBsk23Tw9dnPfhbvete7PIOv6elpfPazn2XwRbtCU1PTTl8ClSmODX8onpMEOFkrwLvhRqmxoamKHcA4ZYe3MecrmRSBVzYrHsfjIsM1MuLs09oqgrHnn3fW9gqFRJv52dnChWnAiRMigDt92gm86upEw47xcfFYVbFy8DDy1TV2OabqkbkLhwJYSmXt0kNrcelMNm/vaz1nHaMUziWXee7FzBfvG1QKxwbJNh18mV4TeAsSiQTX9iIiol1B19fOfBWXHS6tZDB0Yw65vIG2hkq0NVbZ2xRFQUBTkdMNqeHGLWa+lpdFoGQFVBUVYk7X1avOPu3tIoCSA6p4XMwFu3zZ2e/IEZFmeuEFd0fESAS4edO6eChHjiA3LTJsS6JkJQAAIABJREFU9mLJUvBlZbEiIedjQzqbtwOtdCH4CmiqnTHUi4I4+R3Yi3O+iIg2YkPB1/e//338x3/8h/348ccfx7e+9S3XPqlUCl/96lfR19e3tVdIRES0Ddad81VUdjg4NofFFRGgDN2YQ11VFNFw0Nk/oIngyyvztdE5X0tLIqCSF0uurgauXXP26egQgdbZs055YU2NKD88d87Zr6tL7CdnxqqqxDmvX3f26+2F0tAITIvnjKIOkIDzXhUHX9UQf5S1gi95uxWwWedxZb724CLLREQbsaHg66mnnsLDDz8MQPy16lOf+pTnfm1tbXj88ce37OKIiIi2i+ecLylIkud8zSys2IEXILI4VyfmcaSz0X4uGFCBjAhUDMPc/JyvhQX3nKzqapH1Ghtz9unuFq3iL1xwnmtsFIHWCy84xzY2ivlgculiZaUI0kZHnWMPHwaam6FKr9uqcPEqO5SDq1Qh4MrkdDurJW/Xi1ruu+Z8rf9uEBHtSRsKvv7wD/8Qv/VbvwXTNNHa2oqvf/3rOHXqlGufcDiMmpqabblIou1w7tw5ZLNZhEIhHD9+fKcvh8oIx4Y/eM/58i47nF0Q62uNjIzYLaMD2kFX0wk5WMvrxubmfM3Pi0yWFTzV1IgGG3Lb+AMHRCAlB2OtrSLjJWe3amrEvmfOOF0S43FRpihn0A4dEsfDXQa4mbJD+f/F2/1Wdsj7BpXCsUGyDQVf8Xgc8XgcADA4OIj9+/cjFApt64URbTdd12EYBnRdX39n8hWODX/wmvNlBQxWkwjLfGG9K9M0UBkJIJnVkdcNJNM5VETF78OAK9NlIBxcHYh4mptzt3+vrRVreVnNMAARKC0tAZOTznPd3WKOl9yKPh4X2ayzZ53uh7GYyITJc8YOHBDzxgrkWGitssNoKGA3FlkqZAKXpIxgrFCGaZqm78oOed+gUjg2SLbphhsHDx7cjusguuMikQg0TUMwGFx/Z/IVjg1/8JrzpXu0ic9k83aJXW1lHJURFbmECHbml9N28CV38NMNE6rUAbHknK/ZWWBgwAm86utFh8KJCWefQ4fE+l1WB0NFEQHWvn0iyFpeFs9HIqLBxvnzok299dy+fe4uiV1dYt6YRFGcazXWKDvUNBUV0RCWUlkk0znk8rodmAJAdVw03fJawHqvlx3yvkGlcGyQbEPB16tf/Wr81V/9FXp7e/HqV796zX0VRcE3v/nNLbk4ou3U29u705dAZYpjwx/kUkArcHKyNauzXgBw1/FeNNbE8eylm/a29kLXQzlgk9u164bpnfkqDrwaGkRgNTUlHiuKCLympsR8MHFCsWZXfb2Y92UtqhwMiucvXXKCsXBYlBVeueJ8z44OEXx50DQVed2QMl+ryw4BoKYigqVU1n79C0mR+QpqKuKFQFT3yHJ5Bbt7Ce8bVArHBsk2FHylUin7L1YrKyt7slabiIj8RV45pThAkEvu5EYbNRURxCNBBAtt5RekwMxrjpeqKNBhrl6mxSvwMk1gZkY8tgKv8XEnmLLW7KqpAYaGnCDNCsiGh0VpIiDW+2prc2e82ttFuWEJmqogrzvXXqpVfnVFBNenFwEAN2aW7A6RNRURe5/iBZbl96T4vSIi8pMNBV/f+9737K+///3vb9vFEBER3SleZXBWeZ1ccpfKOA0lKqIhKIqCeDSE+eU0crqBvG4goKmryg4Bp7GEK/SanRVzvKzv39AgGm1YWSxVFUHS2JgzbysYBPr7RffDa9ecphuKIkoNr11zsmPBoAi0Rkac79HaKoK5NYggSZcCUOf1yC345SDLVXIoPZ9fYz6d872IiPyHdz8iIvIlOTujqgpM0/Ts9JfK5OznrA6IXl3/XK3li4I4ew7UzIw78KqvF10KiwOv0VEn8IpEgFOnROB144Y7m9XTI7Jj8/PicSAgSguvXnW+R3Oz2G8ddpBUuHa522O+qAV/rRRoASJ4baiO2Y+9ukZ6NTghIvKbTTfc+MY3voGRkRG85z3vWbXtk5/8JA4cOIDXvOY1W3JxRNtpbGwMuq5D0zS0S12/iDg2/EGuBFQUxTMzY5omMjkRSERCAXtsJOZWACUKQARfFdGQ5xwp6xnTKikcGFgdeC0uFr6pJtrGX73qLLIcjwMnT4r5W1NTwOCgc9EHDohOiXNzzvEdHSI4s0r8mpqA3l53O8MSrODRhAgWgwEnmJSDKQA42FZnz3sDgLbGKldA6lqsOmCVHe7tOV+8b1ApHBsk2/Td75FHHsG89Re2IouLi3j00Udv+6KI7oTZ2VlMT09j1uogRlTAseEPrsyXorgyM1bGKpvTXWtcWWNjZXnR3tfOfHnMkbLOo87NugOvujogk3ECLytjde2aE3hVVQF33SUCr7k598LK+/eLuWDWHDFNE400rl1zzyM7cmRDgZe4fvecNbl1fi7v7tZYEQ2hd389aisiaGuoRFeze51PeX8787XH53zxvkGlcGyQbNPB14ULF3D33Xd7bjt16hTOnz9/2xdFRES03VxzvpTiJhEiOCi1gHBIygpZ+3i1ZlcUBcG5WcSGLjuBV22tWJfLaqQRDDqBl7UOUG2tmOMVDIq5XHKpYkuLyJjJDTc6O93H19WJJhybaJBVHDwqimIHYMWZLwBoqa9E/6Fm9LTXuwK14v2tbZzzRUR0C2WHmUwGuVzOc1sul8OKtbYIUZnr6emBaZrs3kmrcGz4g7wWlaIoRU0iRHCQlYKIcDCAtsLYSGfzOHtNzNPKFsoSvcoOg3Oz0K4MOg036urEXC5rPpfclVBuwHH0qAiqkkmxlpeVNWpsFP+31gFTFJHxun7dyZjV1gLHj4vjN0HzCB6DhfbzuVLrlJUg7x8sWkOteAHrvYL3DSqFY4Nkmw6+Dh8+jK9//et43etet2rb1772NfRsYFIvUTmIxWLr70S+xLHhD3IHwlJlh9Z8LwAIBzV7bESjJoBEYZ8SZYfT04hdGUTS+n41NVBWVkTWC3DW4ZKbYzQ2OhmrVAo4fdodVAWDwM3CXCsr8BobE5kwAKiuvqXACyhqGFIITIMBDalsHnnd2NSHR8+GG1YXxT043wvgfYNK49gg2abvgL/2a7+Gxx57DI888ohduzo7O4tHH30Ujz32GN75zndu+UUSERFttY2UHWal4CsUdLr/qapTkmft48rmTE4C58/bDTdyFVUwk1LgFYmI8kE549Xc7ARe6bQIvLJiMWNUVYnmGzedJhfo7BSP5X1OnBDzv26B1zplcjlhfhPZL++GG9b6YfzrPxH516YzX7/7u7+LH/3oR/jwhz+Mj3zkIwiFQshmszBNE29/+9vx/ve/fzuuk4iIaEvJZYdqiW6HctlhKOAOakIBDXndsPexgorg3AyC0zeAfdVQIAIvLZ2CmY4AmgrEYqK08OpV52StraIdvKKIRhynTzuBWjwuAitrbS9ABF4TE2JfQLShP3lSNO64RV7rlLk7Hhqu9vNrkRtuFM/54nwvIvKzTd+lFUXBl770Jbz73e/GN77xDczMzKCxsREPPvgg7rvvvm24RKLtkUwm7TKaeDy+05dDZYRjwx/kskOlVNmh1HAjFNRcYyMU1LCSyUE3TOR1A5qqIjg3g9iVIRjxMABAr66GNp2AqudhwhSBVF2dWMfL0t7uLICczYrAy5oTFouJlvTy/h0dotmGHJz1999W4AV4r1MmB1uilDC4oXNZZYcBTbVLFa1z7tXMF+8bVArHBslu+U59//334/7779/KayG6o4aGhpDL5RAMBtHf37/Tl0NlhGPDH9wNN4q78YkAISc1iQgGNJwfcMZGqLrV3j+X1xGcFYGXgsK5amoQmB6DqosAzojFxbyt69edi+joEOt1AWLe1pkzgNW4KhIRc8CuXXP2b28HpqfdwZnVFfE2ucsOC5mvWyw7zEkNOwDxXtsLWO/ROV+8b1ApHBsku+Xg67vf/S6eeuopzM7OoqGhAQ888ADuvfferbw2IiKibWNKCyErilI058vdoa+4lXrxc8b4BLSrw84cr8oqIJm0Ay89GoNZWVQ62N0tygcB0VTjzBmn/Xw4LOaAyaWJLS3A7KwTeEWjIvAKhW7tDSjibhjikfnaYPBlmqYdqPlljS8ioo3adPCVy+Xwtre9Df/8z/9sp1BN08Sjjz6KN7zhDfjyl7+MwG2WPhDdCY2NjfaK80Qyjg1/sIKt4rI4wAkQijv0yWMjZRbmeM1Ow5yYhxIJQgGQraxCeHkZqAqILFg0JoKvmzcBa62wgwfFQsniG4t28ktL4nEoJAItOeO1bx8wP+8OvKwFmLeIV+bLvdDy6rW+vHg329j7a3zxvkGlcGyQbNNR0iOPPIInn3wSjz76KH71V38Vzc3NmJiYwOc//3l86EMfwiOPPIKHH354O66VaEu1trauvxP5EseGP1iJLrUo0HI/JwIJqxmFPDZGxhMIzUwjdnUYRkut2L+6GlpyBSbEcWY8Dj1rIjQ3AzNeLw7s6RFrewFi/a6zZ8VCyoAoH2xrc7efb2oSgdk2Bl6A95wvucOj3HZ/LfJ+VpMSr8B2r+F9g0rh2CDZpv/89Hd/93f44Ac/iA9+8INoaWmBoihoaWnBQw89hIceeghf/OIXt+M6iYiItpRcdggUt5pXYZqm1KFvdcAQLARe4lgDqK1FKJ2Cms+Jc1VUwIxEEUrMOQf19roDr3PnREYLEA0z9u93B14NDaIUUZ4H1t+/5YFX8Wu0XndYCr6yGwy+vNrzuzJfe3TOFxHRRmz6Djg2NoZXvvKVntte8YpXYEyuZyciIipTVrBlZ7mKsjPGWgHDxATCw4P2w3zV/8/em8ZGlp513/+z1e59X9puu727292jJCLwJrwzCQkTASMSiLJDwkSIKEiED4TRo5cECWmUiCDBh4hAYAARkgAvSYAMCkJ6Ez0QeIaQzHRPu9u92G67vW/lpfY6y/vhqnPOfWqxy91tu8p1/aRW+9Q55/Y5Vbfvqn9d1/W/GoFYDIpJwiMbDAE+H3y7JLwsAPrIGKUTAiSubt0CdnbsX1AovJqagHjcK7yuXaP/T4BiNV9+zU2QsZtJH4V4nH2+WPMll9momWEY5jxybPHV2tqKmzdvFt1369YttLa2PvZFMQzDMMxJY2scu+ZLjHzJcn7fL0EwrK4CMzNuL7CGBlj7B0A2C1mSoAeD0CXZEVYWgMTgMMy2NvcX374NbG3Zv4xcDxcXKRoGAI2NZCVvpxqesPDKv0dbeMqy5DgWPkraob9Y5Oucph0yDMOUw7Frvn7u534On/nMZzAwMIDnnnvOefzll1/GZz/7Wbz//e9/ohfIMCfFzMyMY/06NjZ21pfDVBA8N2oDJ/KVE1+C9qK+Xx6HPhIg9/73/4Zy/z5UVUV9cxuy9Q1Q43GYSgCAD0YoBCtrQjvYBzpCkFUF8aFR6I1N9PssC7hzh/p0ASS8+vtJeBk50VJfT82TT1F4AXk1X4JY8mkKsoZZdtqh2BvNnzMY8UQVz2naIa8bTCl4bjAixxZfL774Ir7//e/j3e9+N+rr69HV1YW1tTXs7e1hcnISL7744klcJ8M8cdLpNLLZLEyz/N41TG3Ac6M2cGq+JO82QHVgen60ZnUV0t27yBoGzY2mZihbDyHrOgmrcBjSTgpafD93koLs+CT0lD0+gHv3gLU1OL/4wgWv8Kqro35fpyy8nHvMIToW+jUV8RTVsWWyhseEoxhFDTeE57KYbf95gNcNphQ8NxiRY4uv5uZm/Pd//zdeeuklfPe738X29jYmJibw9re/HR/96EcRDAZP4joZ5omjqiosy+LWCEwBPDdqAzu1TipRgyRGa3yb68DBpmsV3dICNRGHrFOURw/Qe58SjwMALFkGpqZgJS1gLWeoMTcL7OZSDW3htbTkFV667govv5/MNU5BeNElSVAVGbphemzlAz5v3dfR4oueE1mSnGPF8c6r+OJ1gykFzw1G5JFmQTAYxCc/+Ul88pOffNLXwzCnxuTk5FlfAlOh8NyoDexYjJS3Ddhph/SIb2MdgYMNoKUOAwMDQHMzcHCAZIyMMIxAkIRaPA5JAixFQWxkHFZ9PeQ0RcECyw8hWzEgkvuCsqcHWF52hVckUii8rl0jW/lTRLPFlyfy5YqtVEZHXehwp8VULu1QFG3ieNo5FV+8bjCl4LnBiJzPFZBhGIZhyqRk5Ms04dtYR2hx3nXoa2oC9vcdcw0jGCTRlnMktFQVsdEJGOGIM45/ZQmB1WV34O5uSj2sMOEFAFouTVA3TCcN0xv5OrzuK6sbRW3qxciX/TsYhmFqkbIiX+985zvLHlCSJPzrv/7rI18QwzAMw5wFnpovCcDSMkKL8wBydvTNzSS8cqmGcl0drM041FQSVtgPaBpS45dhWEpuPEBZWUZwRWjB0tlJZhu5MRCJkAhL5QrDzlB4Ad6UQN0woamKR3ylMofbzYviTDxPrCHTVP7el2GY2qUs8ZVIJEp+M8gwDMMw1YYotIqyvAxp9r6zKbW0eIQXwmHIugE1F63SZQW4dg3m6gEQywmplRWo83POGEZrO9nLC2PAMCoi4mUjCqOsTuLLL4ioZDp76Pnifk/aoe6Kr/Na88UwDFMOZYmv//iP/zjp62CYU2dtbQ2GYUBRFHR2dp715TAVBM+N2sJ1O6T/fRtrkLcTjkDLNDRCiR0AQQ07OzvQ/X7IiQRaciLJVFXERyfJ7RAHuTHWYW3HnS8uM43NkKM7QFCjXxIOU08vW3j5fGSuccamVWJKIKUKavBrCpRc37NE6nDxFRf2hwJa3lgkvM7rl7m8bjCl4LnBiPDXT0zNsr6+jtXVVayvr5/1pTAVBs+N2sW3sYbQ4gMAFB3L1DdAix1AMihatZlKYWtrC7srK5AkCaaqITY6ATMUcsfY3HDSFQEgU98I7WDPG/HKF17XrgHCGGeFaIZhm2RIkoSQn4RUMqN7XCDzEcVZOOArGOu8mm0AvG4wpeG5wYg80iqYyWTw53/+5/jIRz6Cd73rXbh/n1IzXn75ZczPzx9x9ukTi8XwqU99Ct3d3QgEArh27Rq+/vWvn/VlMQzDMBWEsrriCC8AMJqaoMVjkGxjjHAYkmVBseuzfD7ERsdhBl3RpG1uILQgpBo2NEKLH7hjRCIUYqtA4QV4I19inVY46AqpxCGph/FUBgA5SAb9lFxjWZYzFpttMAxT6xzban57extvf/vbcePGDbS2tmJ7exv7+2Sl+/d///cIh8P44he/+MQv9HF4z3vegx/84Af43Oc+h5GREXz1q1/FBz7wAZimiQ9+8INnfXnMGTEwMADLss5tCgzz6PDcOP8UlHytrMC/MA9HVrS0QF5cdUSTFY4ApomexkZYDQ2Qcj24rHubufEsYHUV/rn7yNi/o7kZ8tK6M4YZClHEK+eMWGnCC/DWY4kOhWEhhTCeyha1m7csNy0xFNCcv59aMdvgdYMpBc8NRuTY4uu3f/u3sbm5iVdeeQVPPfUUfD7327C3ve1t+PznP/9EL/Bx+Zd/+Rf827/9myO4AOCZZ57BwsICfuu3fgvve9/73KaZTE1RX19/1pfAVCg8N2oLdX0N0Pec7Wx9A7DnpgnqwSAk00RybQPhn38OABBfWKL0QZD4Ujc3gNVdp34sW9cA7O876Yp6MESNxCpYeAGFhhs2YgphqbqvRCrr9ErzpBzWiNkGrxtMKXhuMCLHXgX/+Z//Gb/3e7+HN73pTQUKvqenB0tLSyXOPBu++c1vIhKJ4L3vfa/n8Y997GNYWVnBK6+8ckZXxjAMw5w1vs0NBBfcdPlsfQPUXKqhBVd4SXaaoE1ONEmSBN/WJgJzrjNitq4BSjIO6CRSSHhZkEThdfVqxQkvoJjhBhHyRL4yKIaYjhguYraRPz7DMEwtcmzxtbe3h4sXLxbdp+s6dP3wHiCnzc2bNzE+Pg5V9Qb5pqamnP0MwzBM7eHLq8/SGxod4QXk0gQtC/p2FKmDGFLJtHNsYmcX8a0ojPl5hB7MOo8bjU1QknHIug7LAqxQEJJlQU3lxJumkfAKh0/nJo+JltfnyybgU6HI9IVrvETkq6TToZh2eI4jXwzDMOVw7LTDixcv4pVXXsHb3va2gn3/8z//g5GRkSdyYU+K7e1tDA4OFjze3Nzs7D+K6elp9Pf3e8LG6XQaMzMzAICmpib09fV5zrl37x4SuW85r1696tm3tbWF5eVlAEBfXx+ampqcfYZhOIKwrq6u4Nrn5+edGrvJyUmPqNzd3cXCwgIAoLu7G21tbZ5zb9y4AcuyEAwGC16nhw8fYmdnBwAwOjqKQCDg7IvFYpidpQ8X7e3t6Orq8px769YtZLNZaJqGiYkJz77V1VVsbGwAAC5duoRIJOLsS6VSuHPnDgB6PS5cuOA59+7du0gmk5AkyRHLNpubm1hZWQEA9Pf3o7Gx0dmn6zqmp6cBUKh/YGDAc+7c3BwODg5gWRaGh4ehqir8fqpfiEajWFxcBECR3NbWVs+5169fBwCEQiEMDw979i0uLiIajQIAxsbGnDEBYH9/3zGj6ejoKLCanZ6ehq7r8Pv9GBsb8+xbWVnB5ialNg0NDSEsfGhLJBK4d+8eAKClpQW9vb2ec+/cuYNUKgVFUXD58mXPvo2NDayurgKgv+uGhgZnXyaTwe3btwEADQ0NBV+4zM7OIhaLAQCuXLkCWXY/UG1vbzsR8N7eXrS0tDj7TNPE66+/DgCIRCK4dOmSZ9wHDx5gb4/Sv8bHxz1pzXt7e3jw4AEAoKurC+3t7Z5zb968CcMwEAgEMDo66tm3tLTk/K0PDw8jJEQc4vG4YxrU1taG7u5upNNpJz9/fn4e6XQaqqpicnLSM+7a2prjXjUwMMBrBKpnjbj9/30X0f+6gWQggEhvF9DUBHl1HpJhYGtrC/eCBjb3kggqQfj/n/+FQCqKBsON+LSN0vPeEm6H+Yd/BAsW0NSE5R9+H/FYkubuRD9wkIKSE14b0SiW25tg3r9fsWuEmBa4vrkFfd9dI8IBH/YTaaQyOhLJFO7dpdfGXiNiSff5WV9ZwsoCGZO09bhrsKYq52KNEJmZmUE6nYaiKBgaGoIkSc5ry2sEUY1rRDmfIwDg8uXLnvKVYp8jxPcU+zXnzxHn53OE/XdaLscWXx/84Afxuc99DlNTU3j22WcBUNrFq6++ij/8wz/ECy+8cNwhT5zDChzLKX7Udb2gIadlWchms87+YufY+/MxTdPZZ5qFlr3ljpt/TeK4hmEUnJvNZmFZFjRNK9hnGMZjjVvqXsVx8+9VfA6LjWvfa7HXqNxxj3oOb9++DU3TnDe2k3ptjrrXbDYLXdc9i0+xe32UcbPZbNF9h41rn3vUuMUo9zksdr54Tfkcda+ZTAamaRat4TzuczgzM+N8EJBl2fnbedRxeY2osDVidRXq7CwMw4BpmtAbGoED15Ew7fNBz2YhJ+JAXRCmJEEvkShiIWcq0dAIxGIwM2kYhoG0qgGQICXpTdlUVcSG+wFVAorMp0pZIxRFhixJMC0L6UwWWdkdtz7sx36Con/Rg5RnXMuysJtrLq0pMhTJRMr+W/ekHcows9W/RuRfr/3v5s2bnvcUXiPKH7ei1ogn/NqI7yn8OcI7bjGq8XPEcTi2+HrhhRfw7//+73juueccJfozP/MzWF9fxzve8Q586lOfOu6QJ0pLS0vR6Jb97YwdATsMVVUL/nAlSXIWn/yURvuxYosTAMiy7Owr9kdS7rj51ySOW2ziaJoGy7KKjqsoymONK/5fatz8exWfw2Lj2vdabNEsd9zDnsNif5wn9docda/2fR71HD7KuHZjx+OMa5972LiPO7+Putd8jrpXn88HwzBO5Dk0TfPYfze8RhReb0WsEWtrkO/ehaqqUBQF2foGKPEYEKmHJEkwgkHIBzH4sjoURYWl+bD1//4jWkd6YWbTTsTr1d97Ed39fUjvZCDV1SOQSABZDYoswwiFqZlwMg4g14R5ZByhOhWqmSr6HFbSGqGpMtJZA6YlecZtigSwtEkRk2gs6Rn3IJFx0hSb6oLwGVlkMhQJyzfcMI3zuUYUe0/hNaL8ccX/S41baZ8jisGfI7znHjbuefoccRwkqwy5trm56Qk9m6aJr371q3j55Zexvr6O1tZW/OzP/iw+9KEPVZxz4K/+6q/ia1/7GqLRqGeif/3rX8cHPvABfP/738dP/MRPOI+bpumEkm3q6uqKvvhMdbO4uAhd16GqakG6B1Pb8Nw4p6ytAbmUH9O08MOtFJREHPWajKGeZtzZSeEgmYaaTGJqsAMbiSzutvTCDIZweaAdwWwa4Tb6wm7xy3+OvqFB/M96HHIyhbBsYbSvFfd2kthPZqAkk7g80IZo0sBMcw+MUBjjfa3oaI4cdoUVwf/cWUEsmYEE4P++dtF53DBM/Mfri7AABH0qfmzCTU9aWNvF/NouAGD0Qgu6WuqcfXcWt7C6Q+lFbxztRkToGXae4HWDKQXPjfPNcbVDWZGvnp4ePPfcc3j++efx7LPPQpZlfPjDH8aHP/zhx7/iE+bd7343vvzlL+Mf/uEf8L73vc95/K/+6q/Q3d2NH/uxHzvDq2POEl4AmVLw3DiHrK87wgsA0NQEZfE+GWOoGjVQ3klCzbkaWqqK7MQozH23jknK1e4AVPuDxkYoD7Yh6VnApwKhEKxoGortjKj5kBm8BGOvuDtgpWKbYlggwaXkthVFRkMkgN1YCsmMjlRGR8BHHyN2Dlw3yKa6oGe8WjHc4HWDKQXPDUakLPH13ve+F9/61rfwzW9+E11dXfjoRz+Kj33sYwVFbpXIu971LrzjHe/AJz7xCezv72NoaAhf+9rX8J3vfAdf+cpXKi5SxzAMwzxh1teBXOE3AKCpCdLBAeRczYURDAKWBTknmkxVBa5dg5U0AVt8ra0htLkGfPe7AIBgUxMQi5HwAmAGgoAkQUlQqqGlKNQB4OumAAAgAElEQVSEOQNgj9Lcq6XBqqfRsiC+AKApJ74AYGc/ie7WOhiGif041YKF/JojyGy8TZb5PZdhmNqmrK+g/uZv/garq6v44he/iJ6eHrz44osYGRnBM888g6985StIpVInfZ2PxTe+8Q185CMfwWc+8xk8++yzeOWVV/C1r30NH/rQh8760hiGYZiTpEjEC7EYYBddB3JRmkQCEnLGGKMTsMJhp2Gyb2sT6r07JcfQAwFAkYF4HBZIeMVGxiFFKj/FsBg+zRVImay3KL253o1qLW/tw7IsrGwfOM2Vm+oCyMceQ5ElyHJ1CFCGYZiTouz4f319PX7t134Nr7zyCqanp/Gbv/mbmJmZwS/90i+hs7MTn/jEJ/CDH/zgJK/1kYlEIvijP/ojrK6uIp1O4/r163j/+99/1pfFMAzDnCQbGyS87NLmfNEUDMKSJCdN0NI0xEfGYQZdC2Hf5oanjxeamwuElyRJUGyr4ZzwMsLVKbwAwK+5kat01uvIVhfyoz5E9tfxVBYrWwdYXN9z9ncLtV75Y4jjMgzD1CqPlHw9Pj6OL3zhC1haWsK3vvUtPP3003jppZfw5je/uaCPAsNUKvfu3cPt27ed/hYMY8Nz4xywsUGphrbwamwE4nFHNCEchiXJUJMJOkTTkB6fhBGi/jeWZUHZWHeaMJsmgKYmPLx1Cwv372NpaQlmMETCK5mkKJmqIjE26RFex7UgrgTEyFc6W2jHPNDl9kO6t7zj1HR1NIURzjPT0A0ThknPgV873ymHvG4wpeC5wYg8VuWroih47rnn8Cd/8if49V//dQBwmtIxTKWTSCQQj8eP3RyPOf/w3Khy8oVXUxMJr5z1OcJhSJoGTazPmpqCKTQexcoK/LP3nU29vgGIxZCOxZBKpZCQJBiW5UTNJE0Drl6FKaQaFtoRn8C9ngD+Q9IOATLUaM4z1VAVGRc7GwuOTWfcyJnvnIsvXjeYUvDcYEQeOQfAMAz80z/9E/7iL/4C3/nOd6DrOqampvD8888/yetjGIZhmPLZ3CwUXkKaICIRQNOAaBQAYMkykmMTQF0dpC0SUr6NdWAr5tQnZeobYMUOgAil2xmBAFQA1gHZp5uqiuzkFaCuDliPn969nhCHpR3aXB5ox52HW9jZT8LvUzHW14qgv7A3TkZosMxphwzDMI8gvqanp/HSSy/hK1/5Cra2tlBfX4+Pf/zjeP755/GGN7zhJK6RYU6Eq1evnvUlMBUKz40qZXMTuHXLm2qYL7z8fmB7GwBgSRLiw2MIRdw6Jd/GGkKLD4CLbZAlCZn6BmjxGCw1CMCPITu1PpFAMp11GyjX0xhimmG1RLry8R+RdggAsixhvL+t6D4R8fzznnbI6wZTCp4bjEhZ4mt/fx9f/epX8dJLL+GHP/whAOAnf/In8fzzz+MXf/EXEQgUuhsxDMMwzKlRTHjl1XghEAC2tmhblpEYGoVeV+8IJm1lmYQXaBiptRXa7XlIhgHDMGkMywJyqUOmQsLLCIWhlHDxE0u+qsVqXlFkKLIEw7SKph0eBzHt0O/jyBfDMExZK2FnZyfS6TS6urrwwgsv4Fd+5VeqoscXwzAMUwNsbR0uvCIRIBSiWjCAQlKTkzCWYoBlkU36gwfwLT6A3SrYam6GGo1CMkh86LYDol2zoWnIjI7AyKUZKnKuMXGe2PJEwp7wbZ8kfk1FIp0tmXZYLmLaoY97fDEMw5Qnvp599lk8//zzeNe73gVZPr/d6RmGYZgqY2sLmJ72Cq9Ewiu8IhFgbY22JQmYmABaWiCvxGEaFrSFB4Av40Sm0o3NwP4eZJNc/PRgCKZpkqADqGbs2jWYugTAFl/FpZUpiK9q6nHl1xQk0lkYpgXdMD2Nl49DLaUdMgzDlENZ4usb3/jGSV8Hw5w6W1tbME0TsiyjtbX1rC+HqSB4blQJ+cKrudnrahiJAA0NwPKye87YGNBGtUoSgODiA2g7m8BFeizd0grfbhRSQzMkSaKIl2XRuPU+7MbjyExMQE4mYSqu45+i2JEvyxmbtt1fXS1ph4A3RTCV0RHJs5Avl1Qu7VDC+Xc75HWDKQXPDUaEE7CZmmV5eRnZbBaapvFiyHjguVEFFBNeiQSQTtN2OExOhw8fuueMjAAdHfSzZSG0MAdpYw1WTjgZHZ3wPXgIyTBgWhbUhnpgPQY1lYQZ9AGahoctLUhvb0Pb30d776AztB35siNdct42AMhVJL4CgvhKPwHx5fepVSU+HwVeN5hS8NxgRDiHkGEYhqkutrcLhVcqRf8AIBgEWlq8wmtoCOjupp8tC5iZgX9rkzYhAT098EW3nRovIxiCAgtqiqrADFWlVMOgG+2ymwcDbs2X/ZgttKrV/TCQF/l6FAzDhJ5rwBxgsw2GYRgAHPliapi+vj4nDYBhRHhuVDD5wqulhUSXbYQRCADt7cDCgnvO4CDQ20s/myb1Adu0hReQau8A1tYgC8LLNAxIyQwkAIaqITYyAYTDnrmxnzadX2FHvoyc2LDTEE1TFF/Vo77E+qxHFV/iebUgvnjdYErBc4MROf+rIcOUoKmp6awvgalQeG5UKLbwyhlhoKWF6rtsIwy/H+jsBB48cM+5eBHo66OfTZPOz/X5kmUJ6c5uBDfXgXAbFEWGEQwBpgkrngDCfkh+H2JD4/D7qaWKODeiK1HnZ0ds5UShLcaEkq/qTTt8RLt5UXzVgtkGrxtMKXhuMCIswRmGYZjKZ2enUHhls8DBAW37fJRWKEa8Llwg8QUAhgHcvOkIL8gy0j298G+sAbYdel0EME0o6RRMywR8PqQmrsAMBj0phjaGWSTyZdriy2vAAVRX2qFfe/y0Q1G01ULki2EYphxYfDEMwzCVTTRKwskWO62tJKb292lb04CeHop42WKnpwew+1EaBvD66yTgAEBRgP5+BNbXIJkmRaciEcgGCS+AUg1x7RqkMPX3smuXRPJrvgzhGMdww6xOww1Zlpy+XE8i7VAUcwzDMLUMr4ZMzWIY7reyinL+U2KY8uG5UUHs7pJwEoWXadLjAKCqVM+1sOAKr64uMtgAAF0HbtxwhZqqUkRscRGy6TZQtnQdaoacEk3Nh/T4ZSAUgqrs0WOWBdO0YFmuwMoKDYRVRfY4GxZLO6ymmi8ACPpVZHQDGd14pF5fiXTWM9Z5h9cNphQ8NxiR878aMkwJbt686Vi/Xr169awvh6kgeG5UCPv7hcIL8Eaw+voo4mUf09FBlvKSRGmJ168DsRjtU1XP8dTHKwjJNGHGE5BlEl6x0QkYOVdDO/oDAOmsjrszt5y5kQ24/cI0Vfak2dlph57IVxU1WQaAcMCHvTgJ0kQqi/qw/1jnx5PUb02WpJpIO+R1gykFzw1GhNMOGYZhmMrj4IAiVvY3xs3NJKi2tmhblqmea2HBFV5tbdREWZLIiOO111zhpWkU8RKEmhmOQDItJ9VQDgQRG52AGQg4KYVis+FMnvGEve3TFEiSVDTt0FPz9dhPyukSCmjOz/FU5ljnmqblpB2GA1rVRf0YhmFOivP/VRTDlKCurg66rkNV+c+A8cJz44yJxUh46bmaocZGEk/r67Qty2Qfv7DgirOWFmB8nIRXOk0RL9t+3ucrrAlraIC8s+YIL9Pngzk2CXOZ0gxtISVGvjK64cwNRVGwe2B4jimWdmha1Wk1D5BosomnsoccWUginXVSLkURd57hdYMpBc8NRoRnAVOzDA4OnvUlMBUKz40zJJEg4ZTNfdhvbKTeXWtrtC1JJLwePvQeMzlJoiyVooiX3XA5EHDt520h1NgIpNOu8NJ8MKeuQtF8ANwaL4CiWjaZrOHMjUzWwMPph55jijVdFrRXVaYd2iSOKb7slMP8cc4zvG4wpeC5wYhw2iHDMAxTGSSTJJxsUVVfD4TDXuE1NASsrFB0CwAiEeDyZRJeiQTw6quu8AoGqQZMFF7NzXRuMglJkmD6/IiNTsAKBh3BBLhCylvzZQg/u05+9jGHpR1Wl+wifJrimGwcN+1QNNsI10jki2EYphxYfDEMwzBnTypFEa9M7kN+XR2Jr+Vl95ihIRJidjphMAhMTZGRxsEBCS9blIVCVAMm9v1qbSWBl0zSdiDg1HiZpuWJTNlCSjSKEK3TxZ/tYw5LO6y2qJeNLZzSWaOo3X4pxDTFWkk7ZBiGKQcWXwzDMMzZYtdo2RGrcJhSA5eW3GOGhshsw26q7PcDV69SPdfurjdiFolQhGtx0T2/rY1EmyC8MhOXYfrJwc+yLEcwAa5oOo74OiztsNrqvWzElEExlfAo7GMVuTacDhmGYcqFV0SmZpmfn3cKYAcGBs76cpgKgufGKZLJkPCyRVEoRBEqMWJ16RIJrGiUtlWVIl6BAAmyW7dcx8OGBoqaicKts5Ns6+2IWSBADZS34kCCxJxpWUXTDu1mwxndQCqjO3Pj4XYCcqCBhrPFV7Emy3bkq2rFlxu1SqSzaIgEjjzHNC0kc+I05K8dp0NeN5hS8NxgRFh8MTXL/v6+03eDYUR4bpwSdh8uMY2wvZ1qtGwGB2m/bTGvKCS87FqwO3fc8FJLCwkrUXh1d5NoEyJeuHYNCAQgSQnnMMtC0bRDgMSV3Ww4ursH09CxE02gtStPfJlFmizbNV9Vqj9Cj+B46Kn3CtaG2QbA6wZTGp4bjAinHTIMwzCnj66T8IrHaVt0JbTp7ycr+dVV2pYkcjWsrye3w5kZV3i1t1MqolgjduFCSeEFeE0w7AhVMYv4oN/9ntI23UhlSZzJkuS4HXprvrxNlqs1+vMoaYficSE/f9hkGIYR4cgXU7NMTk7Csqyq/VDEnBw8N04Yw6A+XnYDZL+fIlTz8+4xFy7Q43fvuo+Nj1Mt19yct56rp4fGXFlxH+vvBzY2XOEVDFKNWMBNmxMjXZYjvmQYpuGJYkWCPqxHSSR29w2gtT6EPWnZ2WfPEzFa5kS+7N9VpXPJpynQFBlZwyw78iUeV0tOh7xuMKXgucGIsPhiahZudsiUgufGCWILr/192vb5gN5eElR25Kinh6Jb09PueUNDZJpx544bCQOAixdJYNkNmCWJhNfamtdy/to1EnMCoiAyTa8roSikGoU6p1hSRyhgQFGUgn2iYHNqvszqdjsEKHVwN5ZCRjeQzujwH2GgcZBIe86tFXjdYErBc4MR4bRDhmEY5nQwTeDmTWCPGhlD04C+Pop42cKrq4sMN27fds/r66PHb970Cq+hIUpbzBdeq6tHCi8AUJRCgw07YpUf+bIf34unET1IOftE8ZWfdmhZVkE6YzXSEHafu91Y6pAjSWzuxUl8+TWFnQ4ZhmHyYPHFMAzDnDymSZEs0bGwr48iXrZTYUcHRb2mp93HOjspBfH6dWB7mx6TJGBsjMba3HQfu3jR24A5FCopvACvIDJyv8+p1bIswSxDQkOYRFZGN7CyTQ6JEoB6QZjkpx0Ws56vRprqgs7PR4mv/UTaEZzieQzDMAzBX0kxNcvu7i5M04Qsy2hsbDzry2EqCJ4bTxjLIjt4WzwpCgml+XlXZLW10WOvvUZmHADVd/X3U/Nk2xFRUaj2a3nZFXKyTOc+fOjt9TU1RWmNJShmLa8K0TDdMKGplF7YVBfAzkESsVjMmRvd7S0Fx9uoiuzZrubIV33ID1mSYFoWokeIL1GcNZZhS3+e4HWDKQXPDUaExRdTsywsLDjWr7wYMiI8N54glkUphLZVvC2UHjyg+i+ALOJHRii6ZUet6upcMWY/5vOR2+HcnJu6qCgk0BYXXdFWV0fC6whbZ6WItbymumIqq7viq7M5goX1PaytrcEwqObrxy57+/VkDdcBUVFkxxmRLrN6I1+yLKEh7Ec0lkIqoyOZziJYwsUwepB0fm6qMfHF6wZTCp4bjEj1vhswDMMwlY1lkUHGxgZtyzL17RKFUlMTCaq7d133w2CQBNWNG67wCgZJUM3OusJLVem4hQV3vPp6cjUso59OsZqvUpEsTVVwsdP90FQX1NDWGPaMl9UNzxh2KiNQ3ZEvwBvFKpV6aBgm9nP1XkGfeqQxB8MwTC3CKyNTs3R3dzvfYDOMCM+NJ8S9e+Q6CFBN1sAACS87NbChAbh8mdIF7dotRaEUxFu33JTEujpKNbx1yxVotvASI2iNjcCVKzRGGRSr+bIjXYArpmx62+rxzh+fRCqdQWOksJ4pq3ujZ+el5gug+q35tV0AQPQgha6WuoJj9uJpx1q/Fuu9eN1gSsFzgxFh8cXULG1tbWd9CUyFwnPjCXD/vtt3S5KAS5dIZGVyDXjr6kgoRaPe/l4+n7eHV3MzMDxMTod2Q2ZNIxMOsWasuZkiaMf4cFOs5ksTIl9ZIfJl09fTVXQswzAdowlbwBXr+1Wt1IV8Th3b9n4ChmEWpFJu7Madn5vqaivlEOB1gykNzw1GpLq/imMYhmEqj7k5YGnJ3R4cpG07hdA2w0invZbygNsUGSDnw5ERSj+0hZffT8LrwQNXeLW0UATtmN8qF6/5Kh35OgxPiqJSJPJVxTVfADk+tufSLA3TwtZewrPfMExs5sSXqshoqQ+d+jUyDMNUA9X9bsAwDMNUFg8eeCNXg4PevluhENVkARTNMooIHEki0XXhAhlu2IIsECBBlu+SODlJ9WTHpFjNl2i4oReJfJUim+d0SGO6j4kNnauVjia3xm1tJ+bZt7mXcJ7DtoZQVTeVZhiGOUlYfDEMwzBPhsVFEl82AwPUANm2ibcbHmsa1YOJUS4bTSNx1thIFvNis+SuLm9D5o4OYGLikYQX4BVEtlASDTfsGq5yEKNkTtqhp+ar+sVIQySAYM5EIxpLOcYbpmlhIVcPBpAzJMMwDFMcrvliapYbN2441q9TU1NnfTlMBcFz4xFYWqJ0Q5uLF8lEw04XDARIVPl81O/LdkAUiUQofdAwKOJl14eFQkB7u7c2rKuLomOPEVGSZcnpX+VGvg5POyw1N0Sh5hhuiDVfVZ52aNPX0YA7D6lf2+zyDp4a7sLS5j6SGXKbbAj70VBjFvM2vG4wpeC5wYiw+GJqFsuynH8MI8Jz45isrJDBhk1/P7Cz4zoT+v0kvAIBilrdu1c4RlsbMDZGUbIbN7zNkltavBG1nh5gaOixhJeNIkswDcut+TrCcKPU3Mi3pQfOX+QLoKjW8tYBYskMDpIZfP/mouc+h3qaz/DqzhZeN5hS8NxgRFh8MTVLMBiEpmlQVf4zYLzw3DgGa2vUo8vmwgXqw7W/T9s+HwmvoGA9bgsrgEwyBgdJUO3vk/ASmyU3NVEfL3H8S5ee2OXLsgQYrlBSFNmJhhWr+So1Nzxph0X7fJ2PyJckSRjuacaNuXUYpuURXhfa6lEX8p/h1Z0tvG4wpeC5wYjwLGBqlpGRkbO+BKZC4blRJhsb1ETZpqeH0gx3c/U/mkauhiHB+U6SgM5OspgPhchG3u+nc15/3TXgaGighsmieUd/P9WRPUFIFBkeoaQqMjK6UTTtsNTcKG64cf4iXwDVfl0b6sTrcxvI5J6jgc5G9AtNqGsRXjeYUvDcYERYfDEMwzDHZ2uLbOLtNJrubqrR2tmhbVUl4RUpYr4wPOzdjkZJeNkCqKkJCIepL5jNwACJryeMLYpEoeTTFGR0A5msAcuyIJWR3pjJFjHcOIc1XzZ1IT9+fLIX6awBTZHP3f0xDMOcFLxaMgzDMMdjZweYnnaFV1eu8fDmJv0vy9RAua7u6LG2t73Cq7mZUhTFPmGXLp2I8ALy7OZzYsmXE08Wync8zAhRMr9G55vW+Yx82UiShIBPZeHFMAxzDHjFZBiGYconGqX+XKLdu6aR6QZAaYWXL1Pa4FFsbtJYYrNkn88dC6Ao2YULT/YeBDyNlnPRL1s8AV5RdRjpnNufKkSBvGmH/HbLMAzDcNohU8M8fPgQhmFAURRcOMEPd0z1wXOjBHt7XrHU3k5phbOz7jHj4xS9Oor1dWBmxhVxbW0UMVtbc48ZHXWjaieEKIqo7kuB3+e+NaYzOiJBn7Ndam6kc2mHonCzI2kSwE2HawBeN5hS8NxgRPirOKZm2dnZwdbWFnbsGhWGycFzowi2E6FtiNHaSrVZovAaHiZBdhSrq956sY4Oipitr9O2JJGIO2HhBRSPfPmEXl/prDfyVWxuZHXDSTEUzxUdFJnzD68bTCl4bjAiHPliGIZhDicW8wqv5mYSWbdvu8dcvEhuh0exvOzt89XZSdbyW1u0LUnAxARFwk6BYjVfx007FM02xKiZ7aB4Huu9GIZhmEeDxRdTs4yOjpbtZMbUFjw3BOJx4Pp1t/dWYyPQ2+ut++rpIfF1FIuLwNycu93TA6RSZLoBUNrh5CTVfp0SqiC+7L5eooBK5Wq5bIrNDfEYUbjZZh0qR75qAl43mFLw3GBEWHwxNUsgEDjrS2AqFJ4bORIJEl52U+SGBrJ8v3HDrfvq6ACGho4ea3bWax3f20vCLhqlbVkmo45y6sWeIJogjOxeXYG8mi+RYnNDTE20zzUM00lF1IRUROb8wusGUwqeG4wIiy+GYRimkGSShFcmQ9t1dWT5LjZCbmkBxsYoVbAUlkWNmEUjjf5+Mu+wmzErClnTN55+k15RGNlNlVVFhqrI0A2zIPJVDPEYW3zpQo8vjSNfDMMwTA5+R2AYhmG8pFIkvNJp2o5EyHnw1i1vFGxi4nDhZZrUD0wUXoODFO2yhZfdjPkMhBcAaGph2iHgpg+mc42WD8ObdkjiKyuMxWmHDMMwjA1HvpiaJRaLwTRNyLKMSCRy1pfDVBA1PTfSaRJeqRRth8Mksqan3cciEYpUKYek0+k61YXZIkuSyA1xdRU4OKDHVBW4erW8ZswnhCiMxIbKAZ+KeCoL07KQyRpOHVixuZHOFka+soJRB6cd1gY1vW4wh8JzgxFh8cXULLOzs8hms9A0DVevXj3ry2EqiJqdG9ks1XMlk7QdDFId1u3bVJ9lPzY1RcKpFJkMpSfaIktRgJERMtywx9E0El5n/EGkWNohAAT9GgB6HhLprCO+is2NeIqigX5Ncfp5iUJOjK4x55eaXTeYI+G5wYjwOwLDMAxDkaobN1xxFAiQyLp7l3p8AYDPR4/5fKXHSaWA115zhZemUV3YwoI7ts8HPPXUmQsvoLjhBgCEA5rzcyInroqRyRpOumI44D4vHPliGIZhisGRL6ZmaW9vdzrOM4xIzc0Nw/BGqvx+Ellzc64boZ0iGAyWHsd2R7Rrxfx+injdv+9G0/x+4Nq1w8c5RRRFhixJMC3LI5hCfld8xQXxlT834qmMe44g2Nhwo/aouXWDKRueG4zIuRdf3/ve9/DMM88U3fdf//VfePOb33zKV8RUCl1dXWd9CUyFUlNzwzbF2NujbU0j4bW8DGxu0mOyTDVe4XDpcfb3ScDZhhyhENV43bnj1ooFAiS8Ksx2WVNlpIUIFgCEg24USxRY+XNDFGZitIwNN2qPmlo3mGPBc4MROffiy+bFF18sEGGXL18+o6thGIapACyL6rl2dmjbdh7c3CTxBZBRxuXL5G5YimiUzDVsC3rblv72bTcKFgpR5MzvP7n7eURUhcSXWKelKjL8moJ01jg07TDhEV+cdsgwDMMcTs2Ir+HhYY5yMQzDiNy9WxjdOjgAHjxwjxkbO7zx8eYmiSy76XJjIzVinp52e4SFwyS8DqsVO0NIHJGzoWGYUHKRqnDAh3Q2iaxhIpM14NMKRVSptEM23GAYhmGKwe8IDMMwtcj9+2T7DrjRrUwGuHfPPebSJaCjo/QYq6vU+8sWXq2tJLxu3nSFVyRCqYYVKryA0qYbopgSRZaI6HQophfqnHbIMAzDFKFmIl+f/OQn8f73vx+hUAg//uM/jt/5nd/BW97ylrLOnZ6eRn9/P+rr653H0uk0ZmZmAABNTU3o6+vznHPv3j0kEgkAKLAV3drawnIupaevrw9NTU3OPsMwcPPmTQBAXV0dBgcHPefOz89jP+c8Njk5CVWwe97d3cXCwgIAoLu7G21tbZ5zb9y4AcuyEAwGMTIy4tn38OFD7ORSj0ZHRxEQajJisRhmZ2cBUNFofu7yrVu3HAvViYkJz77V1VVsbGwAAC5duuTpb5FKpXDnzh0AQHNzMy5cuOA59+7du0gmk5AkCVNTU559m5ubWFlZAQD09/ejUWjQqus6pqenAQD19fUYGBjwnDs3N4eDgwPoug5FUeDz+ZzrjkajWFxcBAD09PSgtbXVc+7169cBAKFQCMPDw559i4uLiObMCcbGxuAX0qv29/cxPz8PAOjo6EBnZ6fn3Onpaei6Dr/fj7GxMc++lZUVbOaiE0NDQwgLdTeJRAL3ch+WW1pa0Nvb6zn3zp07SKVSUBSlIM12Y2MDq7kP3xcvXkSDkFaWyWRw+/ZtAEBDQwMuXrzoOXd2dhaxWAwAcOXKFciy++Fye3sbS0tLAIDe3l60tLQ4+0zTxOuvvw4AiEQiuHTpkmfcBw8eYC9XezQ+Pg6f8IF9b28PD3IRma6uLrS3t3vOvXnzJgzDQCAQwOjoqGff0tIStre3AVAUPBQKOfvi8Tju378PAGhra0N3d7dnTsuyjHQ6DVVVMTk56Rl3bW0N6+vrAICBgYGqWSO05WV0ZzL0dyNJ1MdLljH7j/8IyzDg9/tx4Sd+AhD+JgvWiI0NMuQAkEwmsZBOI6uq6Lp/H63232N9PTA1hVt371b0GqGp7uumG6azRmzupSCFW6EoCuKpLJrqgrhx4wYymQwkSUJnd2+B06G9RsytJdDa0QVNkSHlGlHzGkGchzVCZGZmBul0GrquQ1VVzzyv1jUC4M8R5XyOAKiERTTSKPY5Qry/bK4ulj9HnJ81wv47LZdzL74aGhrwG7/xG3j66afR0tKC+/fv4/d///fx9NNP4+WXX8ZP//RPHzmGruuwLMvzmGVZzh+QrutFz7H352OaprPPNM2C/eWOm39N4o4WsFwAACAASURBVLiGYRScm81mYVkWNE0r2GcYxmONW+pexXHz71V8DouNa9+r/cHlUcY96jnUdd0z/km9Nkfdazabha7rnsWn2L0+yrjZbLbovsPGtc89atxilPscFjtfvKZ8jrrXTCYD0zSLukkd9zkU70+WZedv51HHraQ1AktLUJaWYNofqkZGyHnwtdeg56JV6aYmIO8Dm+e1mZ110xUB6F1dSEajCN6+Dcv+ANPQQGmMqlrxa4TqFxstG864mmzBfob342mgzb0Oy7KwF08559lmG/a4qQz974mG8RoB4HysEfnXW+qaq3GN4M8RT/61KTZH+HPE+VojjkNVia/DnAvzefXVV3Ht2jU89dRTeOqpp5zH3/rWt+Ld7343rly5gk9/+tNliS9VVQv+cCVJchYftUizUfvbr2LIsuzsK/ZHUu64+dckjlts4miaBsuyio6rKMpjjSv+X2rc/HsVn8Ni49r3WmzRLHfcw55DO/IlXvdJvTZH3at9n0c9h48ybil728PGtc89bNzHnd9H3Ws+R92rz+eDYRhP5DkUr1GWZZimeey/m0pcI5SNDYRXVwFFoXGHhoCmJuBHPwJy39rr9fUwh4cpIpZ/r6oK/4MHkEMhN41wcBCSJKHu1VcBSaJxm5oojbHI85lPJawRqiqKL9MZt0FVsQcZFoDoQRKWZUFRFBiGAUmSsB/PAKBxmuqCzj1algVINKZotsFrBHEe1oj86zVN0xP5Ou64lbJG8OeIwnGfxGtT7P74c8T5WiOOg2QdV66dIaurq3j55ZfLOvY973kPmg8pEv/EJz6BL33pS0gkEggK/WZM03RCyTZ1dXVFX3yGYZiqYXOT6rPsJf/iRaC3l4SXnTJRX0/GGMV60RgGnZ9LuwBAUTO/n8w17G8nm5tJeFXRmrm2E8PM4hYAYLinGT1tbmrYzfkNbO3R8/OGkS7Uhdw0oP9zawmpjA5ZkvB/Xb7gGHVksgb+c/ohAKClPogrg4fUzTEMwzBVzXG1Q1VFvrq6uvDxj3/8iYxla87jqlWGYZiqY2fHK7x6e4G+PuDGDVd4hUKUJlhMeGWz1MMrVycCWQbGx+nnmzfdcVtbnfqxaqKU4QYANNcFHfEVPUg54iuZziKVobShhrDfEV5AXoNltplnGIZhBKrrHfIJEY1G8e1vfxvXrl3zFIQyDMOcO3Z3vQKpq4vSDe/coX0ANVa+coX+zyeVAl591RVedi8wOxJmj9veDkxOVp3wAlDSpRAAmurc94joQVL4OSUcE/ScI/b4YqdDhmEYRqSqIl+Pwgc/+EH09fXhjW98I1pbW3Hv3j38wR/8AdbX1/GXf/mXZ315DMMwJ8fBAUWs7JTAtjZKFZyfB3IObE5/r2Cw8Px4nKJjdqNkn4+E196e15K+sxMYHS2oE6sWxOhUJustwg76NQR8KlIZHXvxtNPva3M37hwjCjTAGz3TWHwxDMMwAudefE1NTeFv//Zv8aUvfQmxWAzNzc14y1vegr/+67/Gm970prO+POYMWV1ddYpI821vmdrmXMwNWzjZjk7NzZQquLYG5KykAVCaoGB/7bC3R8LNduQKBqkebH2dxJtNTw9F0qpUeAHUo8smoxc6YLU2hLC0uQ/TsvDD6ftoDGu4vxhFS0sLAj4VkaC3h1k647qY+X3n/m2WyXEu1g3mROC5wYic+3eFF154AS+88MJZXwZTgWxsbDh9N3gxZESqfm6kUiS8bLvdhgZKCdzdBe7edY8bGqI6rXw2N4Hbt92IWV0dRbwWF4GHD93j+vupqXKVoygyVEWGbpge4WTT196Ala0DmJaF6fsPAcsEJBktLS3o72goqB1OC9EzUdgx55uqXzeYE4PnBiPC+RAMwzDniXQauH7dTRWsq6O0wmSSXAlF0428ZpoASFyJ7oVNTRTxmp/3Cq9Ll86F8LLx5VIP09nCyJdPU9DTWudsGyY9h0Gfis7mSMHxYvTMx4YbDMMwjMC5j3wxTCkuXboE0zS5jQBTQNXOjWyWIl7JnDFEOOyaY7z+upuC2NpK4knEsoD794HlZfexzk5geJjMOTY23MdHRoDu7pO9l1PGrylIpLMwLQu6YRYYZfR3NuIgmUFPTw9M04RPUzHe31bUMZfTDmuTql03mBOH5wYjwu8KTM0SiRR+Y80wQJXODV0n4RXPGUEEAiS8JImElx0Jq6+n2i9RNBgGpRlubbmPXbxIdvTT025vL0mic9vbT+WWThNRJKUzOtS8Oi5VkTE12IGOpjAM00JLfRBBf/FGnnb0TJEldjusIapy3WBOBZ4bjAiLL4ZhmGrHNMlO3m7y6PNRqqDPR4IsFqPHg0FqgCz28spkSJzZ50oSORe2tdG5th29LFPdWEvL6d3XKSKmB6azBsJFzB9lWUJXS13hjjzSWb1gTIZhGIYBWHwxDMNUN6ZJ0SmxZ9fVqyS07t4FolH38StXSJDZJBIksFK5nlWqSgIrEgFee80VZIpC5zY2nt59nTJHOR6Wi2GYTk0YpxwyDMMw+fA7A1OzpFIpWJYFSZK42TbjoWrmhmUBMzNuWqCiUKphOAysrNA/gKJWly8DoZB7rt182baS9/vpXE0j4WWnL9qirZgd/TkiP+2wFEfNDXY6rF2qZt1gTh2eG4wIiy+mZrlz545j/Xr16tWzvhymgqiauXH3rmuEYTdLrqsrbII8Okp28zbr62SiYTsaRiJ0rmUBr77qGnbY6Yvh8OnczxkiCqVijoc2R80NO+WQxuS32FqiatYN5tThucGI8DsDwzBMNTI7C6yu0s+SROmCjY1krCFayl+4AHR0uOctLgJzc+52czOdm29RHwi46Ys1QECIfKUOiXwdhXhugNMOGYZhmDz4nYGpWZqbm52O8wwjUvFzY2HB23NrfJyMMOz6r0yGHm9qAgYH6WfTpEjZ2pp7Xnc3WcnHYt6mzKEQCS+//3TupwLQVAWyJMG0rEPF11FzQzyX0w5ri4pfN5gzg+cGI8Lii6lZLly4cNaXwFQoFT03Vlao4bHN6Khr/X7vHrC/Tz8HAsDEBEXF7GiYvQ8gUdbXRymKr7/u1n5FIiS8tOI26ueZgE9FIp31pA7mc9TcEFMWOfJVW1T0usGcKTw3GBF+Z2AYhqkWNje9tVyDg0BXF/28suKmIdoGG5pG4kqMhskyMDZGgm1nh0w37Nqvhgaq/VJr863BFl+GaSGrG9AewSqe0w4ZhmGYw+B3BoZhmGogGqVGyGItV18f/ZxvsDE2RhGs5WXg/n33nECARFkkQkLu1i13n137VcNpMWKaYCqjP5b4UhUZCjdYZhiGYfJg8cUwDFPpHBx4I1SdncClS/SzrhcabLS2kpuhHQkDqP5rYoKiYWtrtN8+p62N6sbk2hYLYqQqnTVwdDtlL5ZlOTb1HPViGIZhisHvDkzNcvfuXei6DlVVMTIyctaXw1QQFTU37EbIRq6WqKWF6rxs7t/3Gmz09FCfLrG+68IFSlGUJGBpic6x6eyk8STp5O+lwhEFUzKdLXrMYXMjnTVgFRmLqQ0qat1gKgqeG4wIvzswNUsymXT6bjCMSMXMjXTa60LY0ECpgbZQ2tlx3QtVleq4fvQjb33X6KhrNb+w4DXr6O2lCBoLLwBAKOC+3olUcfF12NwQzwn5eV2pNSpm3WAqDp4bjAiLL6ZmkSTJ+ccwIhUxN7JZEl6pFG3bjZDt1EDDIOt4G12nVEIbsb4LoL5goj39xYv0j3EQBVO8hPg6bG7EUxl3rAB/yKo1KmLdYCoSnhuMCIsvpmaZmpo660tgKpQznxuGQfbv8ThtB4PA1JTXhXB93RVm+TQ3Uw2XplFd19273vqvS5coFZHxoCgyAj4VqYzuEVIih80NUbCFWXzVHGe+bjAVC88NRoTFF8MwTCVhN0q2a7Z8PhJePp/3OLFZso2qkrCy7edNE5iZATY23GNGR939TAHhgIZURodhUrPl49RuxZNC5IvTDhmGYZgisPhiGIapFCyLxNLODm2rKgmvYLDwWL/fu93aCgwPu48bBok4eyxJomiY3ZCZKUo44MP2fhIA1XCVK74sy0IiZ9IR9KlsM88wDMMUhcUXwzBMpTA760apZJlqvOyarXyGhiitUJLIUKO+3t2XzVLaoh09k2Uy6mhpOdnrPweItVrxVAbN9UWEbxHSWQOGaRWMwTAMwzAiLL6YmmVzcxOGYUBRFLS1tZ315TAVxJnMjcVFsoEHSFBNTJC7YSn8fqCYZXE6DVy/Thb1AEXPrlw5fCzGIRw43HSj1NwQUw7DAV/Becz5h99TmFLw3GBEWHwxNcvKyopj/cqLISNy6nNjbQ2Ym3O3R0YojfC42D3BbCMOu16sVPSMKcDjeJgsNN0oNTfYbIPh9xSmFDw3GBEWXwzDMGfJ9rbXIn5w8NEMMQ4OvD3BbIfEYvViTEkURUbQpyKZ0ZFIZ2FZVln20AmhKTOnHTIMwzClYPHF1Cz9/f0wTROyzIXxjJdTmxt7e2SKYVGtEHp7gb6+448TjQI3b5LJBkCRrmIOiUxZhAIakjnHw3TW8JhulJob7HTI8HsKUwqeG4wIiy+mZmlsbDzrS2AqlFOZG/E4mWKYJm23t5NN/HHZ3ARu33bHaWyk5soqL++Piuh4GE9mPOKr2Nxgp0MG4PcUpjQ8NxgRfodgGIY5bdJpShHUddpuagLGxsho4zisrFDkzBZera2FzZiZY3OU6UY+dl8wAAgHOdrIMAzDlIbfoRmGYU6TbJbcCNNp2q6ro0jVcdNRFhaA+Xl3u7OTGigfV8AxBUQEAbUXTwE43ClyL54uei7DMAzD5MPii6lZdF13iulVjhQwAic2NwyDUg1tG/hgkGzgFaX8MSyL+oHZtvQAcOHCo6UsMkUJB33wqQoyuoHdWMpjulFsbkQPks65jZHAmVwzc/bwewpTCp4bjAjPAKZmmZ6edqxfr169etaXw1QQJzI3LAu4dcttfOzzAVevHs8UwzSBmRm3ETNAouvChSdzjYxDYySAjd04DNPCQSKD+rAfQPG5sRsja39ZklAf8p/ZNTNnC7+nMKXgucGIcM0XwzDMaXDvHtnKA1STNTUFBI4RJbGjZrbwkiRKM2ThdSI01bmvjRjZyieRyiKdJZfJxkgAssxpnwzDMExpOPLF1Cz19fXQdZ1TAJgCnvjcWFwkcwyARNPly8drfJzNkkHHwQFtyzIwOQm0tDyZ62MKENMHd2Mp9Od+zp8bdtQr/xym9uD3FKYUPDcYEZ4FTM0yMDBw1pfAVChPdG5sbABzc+722BjZwZdLKkUGHclc9EVVqU6s4XATCObxCPo1BHwqUhkde/E0TNOCLEsFc0OMionRMqb24PcUphQ8NxgRTjtkGIY5Kfb2qEbLZmAA6Ogo//xYDPjRj1zh5fcDTz3FwuuUsCNZpmV5Ilw2pmkhmntcVWR2OmQYhmGOhMUXwzDMSZBIADdvuj24urqA/v7DzxHZ3QVeew3IZGg7FCLhFQ4/+WtlitLaEHJ+XtuJFezf3k9AN+j1bakPOo6IDMMwDFMKTjtkGIZ50mQyZI6RzTXobW4GRkbKP39zE7h92xVu9fWUaqhph5/HPFGa64LQFBlZw8TWHgktVXG/s1yPxp2fO5uPUcPHMAzD1CwsvpiaZW5uzimAHRwcPOvLYSqIx5obhkERLztVMBIBJibKb368skLOiJZF2y0tdP5xeoExTwRZltDeFMby1gFMy8LaTgyZgy3oug7DkrCdJDHs1xQ222D4PYUpCc8NRoTFF1OzHBwcOH03GEbkkeeGZVHEyu7l5fdTxKpch6sHD+ifTWcn2clzOtuZ0dVSh+UtcplcWNtFILsHyzSwuJ1EcwfZ/Hc2RzjlkOH3FKYkPDcYEa75YhiGeVLMzgJbW/SzopDw8pfRdNduniwKrwsXyBmRP9SfKZGgDx1NVGeXNUzMrR9gZSeBnYM0AEBTZFxoZwMUhmEYpjwky7JzWxgAME0TB3YvnRx1dXWQZdap5w3DMJyfFU7pYgQeaW4sLQH379PPkkTCq7n56PN0HZieBqJR97GhIaC39xhXzJwk6YyOV24vw7Ssgrkx0tuC7ta6M7w6plLg9xSmFDw3zjfH1Q6cdsjULLwAMqU49tzY2nKFF0DmGuUIr1SKjDniOeMGWQbGx4G2tuP9fuZE8ftUXBlsx835DQDu3Ohrb0BXCxttMAS/pzCl4LnBiLD4YhiGeRz294Fbt9zt/n6ylT+KWAy4ccO1ktc0ipbV15/MdTKPRVNdEE8Nd2F1+wCGaaEpEkAHOxwyDMMwx4TFF8MwzKOSTFLkyraE7+igRspHsbNDqYZ2KkowCExN0f9MxRIJ+jDc23LWl8EwDMNUMSy+mJolGo3CNE3IsoympqazvhymgihrbmSzFLmye3k1NpIz4VHkW8lzD6+qgtcNphQ8N5hS8NxgRFh8MTXL4uKiY/3KiyEjcuTcME1vL69wGLh8mWq2SmFZwPw8sLjoPtbWRjVebOhTNfC6wZSC5wZTCp4bjAiLL4ZhmOMyMwPs7dHPPt/RvbxsK/mNDfexCxeAwUG2kmcYhmGYGoLFF1Oz9PT0OGkADCNy6NxYWHBFlN3LKxAoPVg2S/Vdu7u0LUlkJd/T8+QvnDlxeN1gSsFzgykFzw1GhPt85cF9vhiGKcn2Nhls2Fy5ArQcYsCQSlFdWCJB24oCTEwcfg7DMAzDMFUD9/liGIY5CZJJ4PZtd3tg4HARdXBAQs22krfTE+u4IS/DMAzD1CosvhiGYY7CMMhgQ9dpu7UV6OsrffzWFvX+si3oQyGykj8sPZFhGIZhmHMPiy+GYZjDsCyKeMXjtB0Ok0NhKaOM5WXg/n3XSr6xkZwQDzPkYBiGYRimJuBPA0zNcv36dcf69erVq2d9OUwF4ZkbjY0UyQJIQF2+TLVb+VgWMDsLLC25j3V0UO8vrhk9N/C6wZSC5wZTCp4bjAiLL4ZhmBIou7tANOo+MDEBBIOFB2azlGYoHtvfD1y8yFbyDMMwDMM4sPhiapZQKARd16FyOhiTRygUgnFwgPDKCtDVRQ8ODADNzYUHx2JUD5ZK0bYkASMj7nnMuYLXDaYUPDeYUvDcYETYaj4PtppnGAa6DvzoR65FfFsbMDlZeNzGBjVPto01fD46rqHh9K6VYRiGYZgz47jaoSoVxcHBAT796U/jne98J9ra2iBJEn73d3+35PE/+tGP8FM/9VOIRCJobGzEe97zHszNzZ3eBTMMUz1YFgkqW3iFw8DYWOExs7NeR8O6OuANb2DhxTAMwzBMSapSfG1vb+NP//RPkU6n8fM///OHHjszM4Onn34amUwGf/d3f4eXXnoJd+/exVvf+lZsbm6e0hUzDFM1LC4ebrCRzVLj5IcP3cc6O4GnngL8/tO9VoZhGIZhqoqqTD7t7+9HNBqFJEnY2trCn/3Zn5U89jOf+Qz8fj++/e1vo76+HgDwhje8AcPDw/jCF76Az3/+86d12QzDVDrRKDA/727nG2zEYsD0NDVcBqi+a2gI6Ok53etkGIZhGKYqqcrIlyRJkMpwENN1Hd/+9rfxC7/wC47wAki8PfPMM/jmN795kpfJVDiLi4uYm5vD4uLiWV8KUwkYBnDnDgBgfX0dC6qKxVjM3b+xAbz6qiu8NA24epWFV43B6wZTCp4bTCl4bjAiVSm+ymV2dhbJZBJTU1MF+6ampnD//n2kbIcypuaIRqPY2dlBVLQHZ2qXuTnHsXAXwGYgQHPDsmjfrVsk0ACq73rjG6mBMlNT8LrBlILnBlMKnhuMSFWmHZbL9vY2AKC5iD10c3MzLMtCNBpF1xGW0NPT0+jv7/dEz9LpNGZmZgAATU1N6Ovr85xz7949JHIF+/kN9ba2trC8vAwA6OvrQ1NTk7PPMAzcvHkTADmlDA4Oes6dn5/H/v4+AGByctJjW7q7u4uFhQUAQHd3N9ra2jzn3rhxA5ZlIRgMYmRkxLPv4cOH2NnZAQCMjo4iEAg4+2KxGGZnZwEA7e3tBc/XrVu3nOaBExMTnn2rq6vY2NgAAFy6dAmRSMTZl0qlcCcXaWhubsaFCxc85969exfJZBKSJBUI6M3NTaysrACgSGaj8CFY13VMT08DAOrr6zEwMOA5d25uDgcHB8hms8gnGo0630z19PSgtbXVs//69esAyDZ2eHjYs29xcdFZWMfGxuAX6n/29/cxn0tn6+joQGdnp+fc6elp6LoOv9+PsTxzh5WVFac+cWhoCOFw2NmXSCRw7949AEBLSwt6e3s95965cwepVAqKouDy5cuefRsbG1hdXQUAXLx4EQ2CUUQmk8Ht27cBAA0NDbh48aLn3NnZWcRyUaErV654HH22t7exlGs03Nvbi5aWFmefaZp4/fXXAQCRSASXLl3yjPvgwQPs7e0BAMbHx+Hz+Zx9e3t7ePDgAQCgq6sL7e3tnnNv3rwJwzAQCAQwOjrq2be0tOSsB8PDwwiFQs6+eDyOuVdfRXBmBo2NjWhtb0favt9sFvP/9E8wNjehKArNpc5OspKXZaytrWF9fR0AMDAwwGsEztcaAQCXL1+GItT8mTmDlWw2i62tLV4jUBtrxP379wEAbW1t6O7u9pw7MzODdDpd9D2F1wiiltYI/hxB1NIaYf+dlsuZi6/vfe97eOaZZ8o69tVXX8W1a9eO/TsOS1EsN30x35HfsixnodV1veg5xRZigCaOvc9+Ixcpd9z8axLHNexv6PPGtSwLmqYV7DMM47HGLXWv4rj59yo+h8XGte+12GtU7rhHPYfj4+OeN56Tem2OutdsNgtd14vakh722pQzbjabLbrvsHHtc48atxjlPofFzhevKZ+j7jWTycA0Tc+bYLFxC55Dw4A6OwvDMOh6Bwcx2tYGa2MD8uwslra3YRgGLAAYHvakGZb72vAaUb1rRD5dXV3OhwJeI2pkjSjzOVQUBePj4575yGtE+eOelzWi2GszNjYGy7IgSZIjHHiNOF9rxHE4c/E1OjqKL3/5y2Udm/+t0FHYStlWqiI7OzuQJMnzTUcpVFUt+MOVJMlZfIo1zVNVtejiBACyLDv7iv2RlDtu/jWJ4xabOJqmwbKsouMqivJY44r/lxo3/17F57DYuPa9Fls0yx33qOcwEAh4fvdJvTZH3at9n0c9h48yrmEYRfcdNq597mHjPu78Pupe8znqXn0+HwzDOPZzKC8uQstmAUWB1NAAtLXBf++e43ioqioMWYY+OlpQ31Xua8NrRPWuEfn4/X5eI4RzDxv3vKwR5TyHpmlCVVVPtOc44/IacX7WiGKvjRjB4jXC3Xee1ojjUPVNlre2ttDW1obPfvazBb2+dF1HfX09fvmXfxl//Md/7Nn37LPPYm5uDnfv3vU8zk2WGaaGMAzgP/+T/pckoLf3/2/v/mOiruM4jr9ODkF+dQEnSCZt2RAVxlKK1TIJfzQSNQq35j/oWm3RklVDQ4Vj0pqulvZHtmwZDrnWEvpDYv0D2laspcwGFTZM0KUzg0BEyJBvf7i7PA7wVPwecM/Hdpv3uc/d9y339uPnzffz/Xyl8+ev32TZJTb2+jLDG5YuAAAASAFyk2VfWa1W5eTkqLq62uOHcubMGTU0NCg3N9eP0QHwu7/++n8TDcO4fu8uV+E1fbq0YMH1+3xReAEAgHHg92WHt6uurk59fX3uouqXX37Rl19+KUnKzs52XwhXVlam9PR0rVq1Slu2bNHAwIBKSkoUGxurN954w+tzRzoRONJ6U0x+NxbkkZGRfowEftPdff1GysP0hYVpaM4cKThYkfz7xw0YNzAacgOjITemtpHqhLEWFk7aZYcPPPCAe0ee4U6fPu2xq8rx48e1efNmNTY2ymq16qmnntK7777rtUOKdH2pYl9f390KGwAAAMAUFh4ePuJ1fdIkLr7uFoovAAAAALdrrOJrSl/zBQAAAAATBcUXAAAAAJiAZYfDDA0NeV04Z7FYbnkPfwAAAABTm2EYXhtsTJs2bdSt5im+AAAAAMAELDsEAAAAABNQfCHg1NfXa+PGjZo3b57Cw8N13333ac2aNTp+/PiI/ZuamrRs2TJFRETIZrMpNzdXv//+u8lRwwy9vb0qKirSihUrZLfbZbFY5HA4Ru1PbgSOy5cvq7CwUAkJCQoNDVVaWpo+//xzf4cFE93K+MDYEFhuZV5BboDiCwFn7969am9v16ZNm/T1119rz549+vPPP5WRkaH6+nqPvq2trVq6dKmuXr2qL774Qp9++ql+++03PfHEE7p48aKf/ga4Wzo7O/Xxxx/rn3/+0dq1a8fsS24EltzcXFVUVKi0tFR1dXVKT0/XCy+8oKqqKn+HBpP4Oj4wNgQeX+cV5AYkSQYQYC5cuODV1tvba8TFxRlZWVke7Xl5eUZsbKzR09PjbmtvbzeCg4ONoqKiux4rzDU0NGQMDQ0ZhmEYFy9eNCQZpaWlI/YlNwJHbW2tIcmoqqryaF++fLmRkJBgDA4O+ikymMnX8YGxIfD4Oq8gN2AYhsGZLwScmTNnerVFRERo/vz5Onv2rLttcHBQhw8f1nPPPaeoqCh3e2JiojIzM1VTU2NKvDCPrzubkhuBpaamRhEREcrLy/No37Bhg86dO6cffvjBT5HBTL6MD4wNgcmXeQW5AReKL0BST0+PmpqatGDBAnfbqVOn1N/fr9TUVK/+qampamtr08DAgJlhYoIgNwJLS0uLkpOTZbVaPdpd339LS4s/wsIExNgAl+HzCnIDLhRfgKSCggL19fVp69at7rbOzk5JUnR0tFf/6OhoGYahv//+27QYMXGQG4Gls7Nz1O/a9TogMTbgf8PnFeQGXCi+MKkdOXLEvRTkZo8TJ06M+Bnbt2/XwYMH9f7772vRokVer4+1zISbb09c45EbN0NuBA6+a9wK8iWwjTWvIDdgvXkXYOJKSkrSvn37fOo7qb9ntgAABsRJREFUZ84cr7aysjKVl5fr7bff1quvvurxWkxMjKSRf6vd1dUli8Uim812G1HDDHeaG2MhNwJLTEzMqN+1NPJvshGYGBsw2ryC3IALxRcmtVmzZunFF1+8rfeWlZXJ4XDI4XCouLjY6/UHH3xQM2bMUHNzs9drzc3Nmjt3rkJDQ2/r2Lj77iQ3bobcCCwpKSlyOp0aHBz0uO7L9f0vXLjQX6FhgmFsCGxjzSvIDbiw7BABaceOHXI4HNq2bZtKS0tH7GO1WpWTk6Pq6mr19va628+cOaOGhgbl5uaaFS4mGHIjsDz77LO6fPmyDh065NFeUVGhhIQEPfroo36KDBMNY0Pgutm8gtyAi8UwDMPfQQBmeu+99/Tmm2/q6aefHnGAzMjIcP+5tbVV6enpevjhh7VlyxYNDAyopKREXV1dOnHihOx2u5mhwwR1dXXq6+tTb2+vNm7cqLy8PK1bt06SlJ2drbCwMEnkRqBZsWKFjh07pp07d2ru3LlyOp3at2+fKisrtX79en+HB5P4Mj4wNgQeX+cV5AYkcZNlBJ4nn3zSkDTqY7hjx44ZWVlZRlhYmBEVFWWsXbvWaGtr80PkMENiYuKouXH69GmPvuRG4Ojt7TVee+01Iz4+3pg+fbqRmppqOJ1Of4cFk/k6PjA2BJZbmVeQG+DMFwAAAACYgGu+AAAAAMAEFF8AAAAAYAKKLwAAAAAwAcUXAAAAAJiA4gsAAAAATEDxBQAAAAAmoPgCAAAAABNQfAEAJp3PPvtMFovF/bBarZo9e7Y2bNigP/74464dr7293d1WVVWl3bt3j9jfYrHI4XCMexwAgMnN6u8AAAC4Xfv379e8efPU39+vb7/9Vu+8846OHj2q5uZmhYeHj9txnnnmGTU2NmrWrFnutqqqKrW0tKiwsNCrf2Njo2bPnj1uxwcATA0UXwCASWvhwoVavHixJCkzM1PXrl3Tjh079NVXX2n9+vXjdhy73S673e5z/4yMjHE7NgBg6mDZIQBgynAVPR0dHZKklpYWrVmzRvfee69CQ0OVlpamiooKj/cMDQ2pvLxcSUlJmjFjhmw2m1JTU7Vnzx53n+HLDpcuXara2lp1dHR4LH90GWnZoS+xHDlyRBaLRU6nU1u3blVCQoKioqK0bNkynTx5crx+TAAAP+HMFwBgymhra5N0/UzVyZMn9dhjj2nmzJn64IMPFBMTo8rKSuXn5+vChQsqKiqSJO3atUsOh0Pbtm3TkiVL9O+//6q1tVXd3d2jHufDDz/USy+9pFOnTqmmpuamcfkai0txcbEef/xxffLJJ7p06ZI2b96snJwc/frrrwoKCrqDnxAAwJ8ovgAAk9a1a9c0ODiogYEBHT16VOXl5YqMjNTq1atVWFioq1evqqGhQffff78kKTs7W93d3SorK9PLL7+se+65R999951SUlI8zlStXLlyzOPOnz9fNptNISEhPi0xdDgcPsVy4+dXVla6nwcFBWndunX68ccfWdIIAJMYyw4BAJNWRkaGgoODFRkZqVWrVik+Pl51dXWKi4tTfX29srKy3MWOS35+vq5cuaLGxkZJ0iOPPKKffvpJr7zyir755htdunRp3OP0NRaX1atXezxPTU2V9P9ySgDA5MSZLwDApHXgwAElJyfLarUqLi7OYzfCzs5Oj+cuCQkJ7tcl6a233lJ4eLgqKyv10UcfKSgoSEuWLNHOnTvdm3ncKV9jcYmJifF4HhISIknq7+8fl3gAAP7BmS8AwKSVnJysxYsXKy0tzau4iYmJ0fnz573ec+7cOUlSbGysJMlqter1119XU1OTurq65HQ6dfbsWa1cuVJXrlwZlzh9jQUAMLVRfAEApqSsrCzV19e7CxyXAwcOKCwsbMRrp2w2m55//nkVFBSoq6vL46bKw4WEhPh8Jup2YgEATD0sOwQATEmlpaU6fPiwMjMzVVJSoujoaB08eFC1tbXatWuXe4OLnJwc9/3C7Ha7Ojo6tHv3biUmJuqhhx4a9fNTUlJUXV2tvXv3atGiRZo2bdqoyxR9jQUAMLVRfAEApqSkpCR9//33Ki4uVkFBgfr7+5WcnKz9+/crPz/f3S8zM1OHDh1yb+seHx+v5cuXa/v27QoODh718zdt2qSff/5ZxcXF6unpkWEYMgzjjmIBAExtFmO0/ykAAAAAAOOGa74AAAAAwAQUXwAAAABgAoovAAAAADABxRcAAAAAmIDiCwAAAABMQPEFAAAAACag+AIAAAAAE1B8AQAAAIAJKL4AAAAAwAQUXwAAAABgAoovAAAAADABxRcAAAAAmOA/oFQzBn51l78AAAAASUVORK5CYII=\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. It is not easy to see in this diagram, but the uncertainty in position has become smaller. We know this because the new covariance doesn't reach as far in the x-axis as the measurement covariance at t=1. So we are not just more certain about velocity, but we are also more certain about the position than we would be if we only used position measurement without considering the velocity!" ] }, { "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.\n", "\n", "The effect of including velocity appears to me minor if only care about the position. But this is only after one update. In the next chapter we will see what a dramatic increase in certainty we have after multiple updates. The measurment variance will be large, but the estimated position variance will be small. Each time you intersect the velocity covariance with position it gets narrower on the x-axis, hence the variance is also smaller each time." ] }, { "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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\n", "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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