{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multivariate Gaussians - Modeling Uncertainty in Multiple Dimensions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "from __future__ import division, print_function\n", "from book_format import load_style, set_figsize, figsize\n", "load_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. Gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters from the last chapter. One would track the x coordinate and the other the y coordinate. That does work, but suppose we want to track position, velocity, acceleration, and attitude. These values are related to each other, and as we learned in the g-h chapter we should never throw away information. Through one key insight we will achieve markedly better filter performance than was possible with the equations from the last chapter.\n", "\n", "In this chapter I will introduce you to multivariate Gaussians - Gaussians for more than one variable, and the key insight I mention above. Then, in the next chapter we will use the math from this chapter to write a complete filter in just a few lines of code. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last two chapters we used Gaussians for a scalar (one dimensional) 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 across multiple dimensions. I don't necessarily mean spatial dimensions - it could be position, velocity, and acceleration. Consider a two dimensional case. Let's say we believe that $x = 2$ and $y = 17$. This might be the *x* and *y* coordinates for the position of our dog, it might be the position and velocity of our dog on the x-axis, or the temperature and wind speed at our weather station. 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", "Therefore for this example 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 incorrect because it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are **correlated**. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. The **covariance** describes how two variables are correlated. **Covariance** is short for **correlated variances**\n", "\n", "We use a **covariance matrix** to denote **covariances** with multivariate normal distributions, and it looks like this:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\Sigma = \\begin{bmatrix}\n", " \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n", " \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n", " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n", " \\end{bmatrix}\n", "$$\n", "\n", "If you haven't seen this before it is probably a bit confusing. Instead of starting with the mathematical definition I will build your intuition with thought experiments. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements (covariances) are represent how much the $i$th (horizontal row) and $j$th (vertical column) state variable are linearly correlated to each other. In other words, covariance is a *measure for how much they change together*. \n", "\n", "A couple of examples. Generally speaking as the square footage of a house increases the price increases. These variables are correlated. As the temperature of an engine increases its life expectancy lowers. These are **inversely correlated**. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are not correlated - each can change independent of the other.\n", "\n", "Correlation implies *prediction*. If our houses are in the same neighborhood, and you have twice the square footage I can predict that the price is likely to be higher. This is not guaranteed as there are other factors such as proximity to garbage dumps which also affect the price. If my car engine significantly overheats I start planning on replacing it soon. If my dog wags his tail grocery I don't conclude that tea prices will be increasing.\n", "\n", "A covariance of 0 indicates no correlation. So, for example, 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 say\n", "\n", "$$\\Sigma = \\begin{bmatrix}10&0\\\\0&4\\end{bmatrix}$$\n", "\n", "If there was a small amount of 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. Note that this is always symmetric - 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": [ "Now, without explanation, here is the multivariate normal distribution in $n$ dimensions.\n", "\n", "$$f(\\mathbf{x},\\, \\mu,\\,\\Sigma) = \\frac{1}{(2\\pi)^{\\frac{n}{2}}|\\Sigma|^{\\frac{1}{2}}}\\, \\exp \\Big [{ -\\frac{1}{2}(\\mathbf{x}-\\mu)^\\mathsf{T}\\Sigma^{-1}(\\mathbf{x}-\\mu) \\Big ]}\n", "$$\n", "\n", "I urge you to not try to remember this function. We will program it in a Python function and then call it if we need to compute a specific value. Plus, the Kalman filter equations compute this for us automatically; we never have to explicitly compute it. However, note that it has the same form as the univariate normal distribution. It uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. If you set n=1 then it turns into the univarate equation. Here is the univariate equation for reference:\n", "\n", "$$ \n", "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp \\Big [{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 \\Big ]\n", "$$\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! Let's plot it and see what it looks like." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OiSiBZwCQu5+E7f+EeR8siu3lKn4T43ZLFcpQSaTzRFn6duTYGkzXkcjhF3GH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H6rp1Ah5rx/iapnQHl5XhNGuGm56OUlCA+dVXEuVbLS/q2o0J4VNOIXTddeImUFoaS2GLRWIW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\nOnel+snn8I5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Hj6Lu2oWyfj1O8+bYgwejb9uGZ/z4WIpenTEBp1Urqp97DhIS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\nn7zQskwCXFUBx4VFdrZ+YQE/PzS9/DLk5GQIZ87A8PHHEAoLXS4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import mkf_internal\n", "mkf_internal.plot_3d_covariance((2, 17), [[10., 0], [0, 4.]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a plot of two dimensional 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 of 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 normal 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 curve is centered over (2, 17), the means for x and y. \n", "\n", "All multivariate Gaussians form this shape. If we think of this as a the Gaussian for the position of a dog, the z-value at each point of (x, y) is the probability density of it being at that position. So, he 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).\n", "\n", "More details are in the *Kalman Filter Math* chapter. Here we need to understand the following.\n", "\n", "1. The diagonal of the matrix contains the variance for each variable. This is because the covariance between x and itself is the variance of x: $\\sigma_{xx} = \\sigma_x^2$.\n", "\n", "\n", "2. Each off-diagonal element contains $\\sigma_{ij}$ - the covariance between *i* and *j*. This tells us how much linear correlation there is between the two variables. 0 means no correlation, and as the number gets higher the correlation gets greater.\n", "\n", "3. $\\sigma_{ij} = \\sigma_{ji}$: if i gets larger when j gets larger, then it must be true that j gets larger when i gets larger.\n", "\n", "4. This chart only shows a 2 dimensional Gaussian, but the equation works for any number of dimensions > 0." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FilterPy [2] implements the equation with the function `filterpy.stats.multivariate_gaussian`. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of NumPy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner.\n", "\n", "In the last chapter we did not have to explicitly program the univariate equation into our filter. The filter equations were generated by substituting the univariate equation into Bayes' equation. The same is true for the multivariate case. You will not be using this function very often in this book, so I would not spend a lot of time mastering it unless it interests you." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use `scipy.version.version` to get the version number. I named my function `multivariate_gaussian()` to ensure it is never confused with the SciPy version. I will say that for a single call, where the frozen variables do not matter, mine consistently runs faster as measured by the `timeit` function.\n", "\n", "> The tutorial[1] for the `scipy.stats` module explains 'freezing' distributions and other very useful features." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "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 4 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": 43, "metadata": { "collapsed": false }, "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": 44, "metadata": { "collapsed": false }, "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. If there is no correlation between the values place the variances in the diagonal, and set off-diagonal elements to zero. I will use 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": 45, "metadata": { "collapsed": false }, "outputs": [], "source": [ "P = [[8., 0.], [0., 4.]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now call the function" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.02739\n" ] } ], "source": [ "print('{:.4}'.format(multivariate_gaussian(x, mu, P)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These numbers are not easy to interpret. Let's view a plot of it." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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AMpD11XiCP0SmKT4t7Po+PvMHKZcNy1fhMa9POR3AxIPBaGQacWv3omlT8Xsf\nwa3eiap8lLxPZjWByEP4QmcSVH8Gkh9JiWAamzBLIA2iLtDCwq3LMfaJ/uHOMs4cMbukKrf1VChn\nsoYb7PRx2rAZLGpYDcDGwF7ead7KsTUTkrad7XXdGmhcao4X/YVSe5Coq6sruI/uVVddxZNPPsmL\nL75IZWUlDQ2xfPvy8vJ4gZSbb76Z5cuX8/rrrwOwcOFCnE4nBx54ILIs8/LLL3Pfffdx5513FrRv\nhUKI3wIjy3JJvvrNRfwmFpbIxn4s8XV8sS8KcsNb8b/Dg49Ese9zw0D5562o/+486cyKEUQv/Svm\n2HkQDSFtfg957WKUD59A8u9FCjSh/uk0ote/DWWD48vps2+Ki1958zNw4E+hbHzKfuXjtwvEo/Ju\ntxu3253tbigJco382m3asjm+rGXyya1MFw3rjRuXoe1EMv34gqejmJu7TmMIMruQCCZfFi8Sbci0\nJJ1uEZHOwRlZGP+ssgFv4LuEXH8k6vgabvUOJKlzHxtmDcHIA3hDVyCzE692DQH1ITzhs9CUk4nK\np2FwQJ8J4KZwgD9v/oCIETsnqhwezht5IC65/+a1Z3u8JVrDzXWNYWe0g3f2bgHgrabNjPFUMtk7\nKO/7TGIF0HT9zfZnoJC4z0th2+vr6wue83v//fcjSRLHH398l+9vvfVWbrnlFgAaGhrYvLnzmiZJ\nErfddhvbtm1DURSmTZvGo48+yjnnnFPQvhUKUd64wFiRvlIjHA7HSzI6nU7KyjpHedu9drPxjLW/\njldVtfcjlIaOc9FopEgzALuPfQvX8Lm4XDGPX/md+3E83xktM0bOJnrZC1Dd/QIhbfsIx70nxCPB\nxsQjiF71L3B0+gU7XjsRueEdAPRpl6Mddnd8Wq5CLlnebiAQiOf6ejwePJ7CG9sXk/b29nhUu6ys\nrFvZ3lwHQdpvqMW05st0Q++ppZWhNQAOHNrzeCM3dZvud92Hi9+gSpu7LwwEpFtxmn9HlT5JuQ4T\nCEjP4gt9N+n0sHwqUff5eBzXosg7MMwaApEH8YauQWanrR0vAcfDeLQbgDB+9TkM5aBeF8ABLcK9\nG9+Nl/v1KA6unHgEFWYsTiPLcr8tz54vumnw4Bfvs6ljDxDbJzdO+wpVjthDcroock9SL7Kl2OdR\nKVGKZaK//vWvZxyMJuiOiPwOEOw3MbsQydZrt69stJIhNX8aF766ayha2RSc1sU9EkT996/i8+oz\nvo524RMBUyx6AAAgAElEQVTgLk/aljnuYLQLHkN95Cwk00TevBT16UvRLngsXthCm3UTzn3iV960\nkOjsHxOVygqWt1vInNlSIddUGWv/WAMgo9FofL8UK7eyJyP1M+ZXGi1IRhtK9H2cxv3d2jMAJCcq\nyYUvgClNRCW18AXQzMOR9c9TTncZL+EIvEvAfR8O9R9E9VPwhrsKXwCJAJ7oVQQcD+LVLsSrXUCA\nJzGY22sCOGroPLzlw7jwVSWZiyYcylBXWdqBoPs7iiRz3riD+d2Gt2iNhgjqURZt/4RLJx2BbDse\n09HR0Zn/bQUJ9gdruN6m1PJ9LUqpL/0FIX4LTCkehFbkzULXddrb29MuY3nslqKNlmzP9x18JEid\nbgPyBwuR2mL5SWblSLQfLOoSxU2GMedU9FN+ifrSzQAoHy/CHDIZ/aSfxQZgDT0WpWoWSstnSHoQ\nY80jhCZdmrK9XB8U+rv4tfc/FAoRCAQyRmzT2bQle7WYzyvjnlQTS9Z2tst4PTJydC2+PScTHPo4\nari7wI2qF+HgxZRtRMyvobI047qinI9buy7tPDJNlIXOot35dxzG292Er30+T/R6Ao5H8Wpn4tEv\nI8jDGMwuugA2TJOnt33MVn8sH1oCzhl3EBPLBnV5wCyl61BvUu5wcd64g7lv0xJMYGPHHt7bs4Wj\nh0zMua1M1/NMEWT7uZUrPRXKqR46e4tSE7/hcDj+MCPIDSF+C0wpnBD218y9aT/WW0gJ+b6w7/W4\nFkH9z13xafrxN2QUvvF5j7sOafcmlKX7Clu8ejvB8lH4Z30rltow9ntUtcReXXu3PY5/4sWwb/BN\nT/127fP3dQW+bElMZbBIFQm38sKLOggyIWKUqZpYthHlXPB6PKjB5/E1X0LItwBn9NGk82nqcXi5\nIGU7Ufk8vGbqBywAg6GYpgOZSMZ+GdJwZK0BQ68hop6B03wu6XwKtbi1nxNUH8ejnYdHu5og92MU\nuSLcyzs+49PWTlF+yshZzKkqzVHifcXEskEcO3Qyb+7aBMArOz5navkQhqV4q2WR6zHc04F8qc6l\nXCnWm5meUIqD3UaNGtXX3eiXCPFbYPrihLAuMn1tP9YrGFHkxiXxj5HBRwGxfSAvfxqpuTb2uWwI\n+hEXZdWklbfrP+l2fI1f4PriLQDK/nYDwZEHoVePITTqWxhrfoGstaH6N+Nr+QBGn1AQIddfIr+5\nDuYrpVSZRHpyg08VUfZ4PDjbfoOn/TYAdM98XNF7urWnyTNQWI1E8gcdgyFI1KccCGcRNi/BFf11\nVtsQVq7D3XI7irGNQOU9SHIbDvO1pPOq5meY2oME1QfwaZfj1m4iJP0W5AOyWleuLNm9mXd2d0bH\njxkyiWOGTop/LpVom2EayH3sNvH14dNZ17aLnaE2NNPgmW2fcM3Uo3NywSjkPiyEUC6ENVw+QjnT\nYNhk22VfRyncM+vq6hg7tmfV/wYqQvwWAcn2Gr5Y5GM/Zn9qLS8vL1qVt2Ii7VmOpMUG7hm+ceje\n2IlvaFGU1zuFgP6Va7sXrtiHaab2242c8QCDHj4Fx+4NSFqI8sW30Xrmg6ieSqITzsG18QEAfNsW\nok3KUFUu220qUfFr30+55IZ7PJ4ep8r0J6FsnVfu5qtwBZ4CIOo8DtV4N6l/b9hxEy4eJMrRmIzG\nYBwGNWA6ASe6NAHJbCUo3YKTRcis79aOiYrBAahsyNh/Ew+6ORrF2AaAt3UB/qqHQGrDYb6fdBmH\n+Q6mPpSA8mu8+k2Y2v8R4v+Q1ClJ58+XdW2NvFi/Ov75S5Uj+ebImQVdRzpM02R7eyPLGtfxedNW\n/NEgIT1KOP4Tif+OGjpDPJXMqBnPzJrxzKgZz6TKkahy711HVVnhnHHzuHvDO+imQW2whdcbN/C1\n4an9x0vl4aGnQjmTNVy22NvLps92kWy/Blpt9HbqhR0hfvNHiN8iUAzxm6/9mN2Roa2tLS70ilni\nuJjY833tVd2cq19E3v0FAKanCv2oy+LTrFf02fjtmu4KWr/5awY/cioAnjUvI+/5DKYcjTTzStgn\nfuW6f0DHdijr+YXHHkHoS/GbmMqQzWA+h8MRj5xDZ7R3oBBLt6nH23wZjojtjUT59/Fql3WZV2MS\nEfU6DMYTCXwDJVKLHN2AM/wGstEYn69j+FP4Gs9FV6cQrvwBhmcCslSPymIc0ltIBImap6Bq/8yq\njxHlfFwdXasseVouIVjzJJLZgcrqpMs5jefR5GMIKHfj1v8fbu0uQvwPkjo+y72Tnp3BNh7f+lG8\nfMdYbzXnjJtX1CIWAEEtzIrdm1jeuI5ljWvZFUxvJWdnd7CVt+tX8XZ9rPiGW3EwrXrsPkE8jlmD\nJuJzFNeqcKSnkq8Pn84/dq4B4PWGDRxQMYyx3uqk85eK+M2FUsjzt9pN9dBvv5dkiiAXK0e5rq6O\no446qmDtDSSE+C0ChTi47fZj2YrdTK4CPSl0USrY/X2N4V/e94eB9+1O+zH9y1diuMqIhsM5+e3G\nHxbmnIh+0HdRPo5Vd3O88EOiNy3FrJyKMeI45J1vIJkGyoaH0Of9osfb1JeR30KkMgSDwfhNoBD9\n7y83aMMwkMJrcQUf7yJ8DXkMMtuQiFkiadIcIsoVEI6gtixGca/G1fZg8jZxI2t7kQBV24i693/2\nfe8kWnYWgfL7kZQghjwer3FSxj6agCYdgy/adX0y4Gm6gEDNM7iNm5O6TkT5GmbUh2H68CsPoEi7\nkM1aomEVQxraoxH67dEQD2/+gPC+AjTVDg8XTTgER5IoaiHE255gK2/Vr2R54zpW791M1Mj8FiMb\nQnqUVXu+YNWe2IO3R3VxyoQj+M7kY6h2pc/F7QnHDp3MmrYGtvibMDB5etsn3Djt2KLtv1Il1zx/\n63ehreF6OpAvWb6yfbtSUVdXV7TSxvs7QvyWCFb0zBK82bxitg9Qyyanst+LXy2ItOuD+EdzxLEQ\nBtf613DsWh/7zumj6cDz0FvSR3My5Txrp9yO/OnLSNEgcv0q5A8WYhxxEfr0y5F3vgGAsvEx9Dk/\nBaVno217U/zmmspg30+pBkLubzfUbJHDa5GMepz+h7t8H6r8MW79l0SV44hI5yEFG3E3XIdMiMDI\nB3C3/Cxlm5HyC3D4/959XURwdTyOq+NxDHkwHUMeIag+iUv7WVq7NE0+ASWUPLVBxsDbdD6BQU/j\n0a5FkXZ09kP6Npp2LL6mH2BK5fgHP41r16VonnMwyy8mGHWjm90jnNkMOtJMg0e2LKN5n7e2S1b5\nwcTDKC9CxHRXoIW/bHyDV7d9mFLwelU3Bw2dwsFDpzPcV4NbceBSnLgUB+59v12KE0WS2NLWwOdN\nW1nTtJXP926lMdjcpa2gFmbRxjd5cfMSvjH+cE6f/GUGeyoLvl2yJHH22Hnctf5NwobO7nAH/9ix\nhtNGzy74uvYX7IIyU75uKkEciXQOLrXa622h3NTUxLvvvsvw4cPZuXMnFRUVmKY5YK/D+SLEbxHI\n9nVNqrzTVNitx/LJqezv4lfaswzJiF18jMppaM4hEG6n7N3fx+fxH3wBuruq+7KS1O1hIS3VY9CP\nvwH11dsBUP9xK5G5p2OMPgnTNxrJX4cU2o287QWMiWcXbiOhoBeyxMGQmZw/kqXLZKJUc5aLiRn6\nAiX8CbK5A8nmtqCjojvnEDB+i9L6EZ49FyPbBraZkoqs707Zru4+EtfehSmnA0S9J+PZ+zuUwIcE\nR9+Dpn6OS7836QC6iHwmnsDFKduSieDdexGBQQ/j1S9DpomwdAF6dAbe5msBkMx2XK13EKp6AF/L\n5TiDzyDVLKKd7q9b7Tf2ZA9WhmnyfONnbA/ERKMEnDnyS9TILiKRSNLoVz7sCjTzzIY3eHXbMjSz\nez8mVIzgkGHTmT9sOjNrxmedtzu5ahSTq0Zx6sSYy8yeYGtMCDdtZXnjOmo7Yv/bsB7lr1+8w9+3\nLOXr4w7hzCnHMsxbk/f2JGOQy8cpo2bzXO1KAN7ds5kZlcOYWj60y3z7c+S3WCRLT0gUv16vN57i\nmK3rRa4kE8orVqzg4os7z+nRo0fjcrkYNmwYw4cPZ/jw4SxcuJCqqu73QUEnQvwWgVSjRHPJp4Se\nW2il61d/E7+maSI1dkZ9g5XzaW9vR9m9EeeO2MXfVFz4D+/Ms+yp24D+1RtRPngMqaUeqX0Xyr//\nH/qpv0SfejHqilsBUNb9qcfi17rQ2l/L9eR/nej8kel/XUhXhkKJ394YNJovRqQBZ/Df6M5ZuJtv\njn9vSmX4q5/C0bIY1+7/JTG2ZKgjkPXtaduWTD+SGU47j+4+FFdTTCD76i4hUvYNAkOexKXd2mUA\nnMY0JK21Wz8SkWnD23w1wer7kVkJQRVv6/90mccRWYqmHU/E9Q2c4VfwtlyFUfNXgubUnCJZbzZt\n5vOOXfHPXx88lUnu6qzsGCEmqO0iOfGnMdDEMxve4LVty7uJ3gOqx/H1cfOZP2w6QzyFEQaDPZUc\nM2oOx4yaw2Wzvsl7Oz/n6fWvs6m1HoCoofHylqX8c+sHnDD2YM6eehwjfYMztJo9h9aM5fPWnaxp\ni+WM/2X7Cm6adhwetTPvXojfwpC4H+2R5J46XiTLWU7Fnj17un0XDofZvn0727fHri/5VEG84447\neOGFF9iwYQMul4vDDjuMO+64g5kz0w9AXb16NVdffTXLly+npqaGyy67jJ/9LPXbrVJBiN8iYN24\n7YOssrEfUxSlS3S30FYq/S3ymxixrNrZafofrZ4LgHvtv+Lfhacej3PI2MIV5nB60U79JY6F3wNA\neev36Ef8AH3K91FW3Y5kRJF3f4DUtAqzZk6PVpUofnOhGKkMuTCQbqiG3oEafBvD9KJoK5HMNgA0\nZTKhijuQNAn37tuSuzxUXYKj46WUbWuuQ5Ajn6Zdv4kDUyrr8p2z4xXUjn8TGvV7os5a3NodSOhE\n1MtxN/1vVtslG404OhYR8i6gvPXLSedxt91OoOZx1PASZGM3nvbbMCt/g+wan9XAoxWt9bzTvDXe\n3iGVozmsqnvJ8XQYhtEl+maxK9jMc1ve5c2dK9HNrte2A6rHce7U4zloyNSiDvKVJZmjR87mqBGz\nWNa4lifXv8665pgY0U2DV7ct4z+1n3DpzG9w6sQjC3LeSJLEGWMO5Nfr3iSgR2iNhvhb/aecM+6g\n+DxC/BaGQuzHQgjlESNGcPLJJ9PY2MimTZuIRCLxkssANTU13UrMZ8Pbb7/N1Vdfzfz58zEMg1tu\nuYWvfvWrrFmzhurq5IMp29raOOGEEzj22GP56KOPWLt2Ld///vfx+XzccMMNOfehNxHitwjouk5L\nS0tW9mP2V/HF9g0sFVeBVKQd5GeaOFpWxD9Gq+chyzKetZ0j3s2538rriTdtn+Z9F+Od+5G3fICk\nR1Ff/B+0S57DGPctlC2xAXHKuj+hHXFfj9aTS+pAPqkMidHdQjJQ0h4Mw0AOr0OKNmMow3B1xPx8\nI+7vEHV+B89n5xKeci8Syf8fhnsySntqcRspOx93669STgfQ3EehdnTP4ZWJ4K2/jIjva/iHLsKl\n34NpVCLTlvX2aa7/wrHnAcLlN+Fu7+4fLGHgbvkRweo/4ms+F0f43zjCrxBVL0JWYuddqoFHmzv2\n8mLj2vjnaeVD+NaYLyEjpYx8ZXMs6YbO37e/zzOb3+yW03tA1VjOnPBlvlQzEUmSupRITjfQqKcj\n8yVJ4tDhMzhk2AGs2L2RJ9e/zuq9sbzsqKHxx9UvsmzXOm6aeybVGQpUZEOFw80ZY+awcOtyAD5u\nrmNO1ShmVg7vcduCTnr7ISLV8XfCCSdwwgknsHr1ah5//HEeeOABOjo6aGxspKGhAb/fn9f6Xn31\n1S6fn3jiCSorK1m6dCknn3xy0mWeeuopQqEQCxcuxOVyMWPGDNatW8dvf/tbIX4HIqnERT75lIUk\nMfLb10nyueQ9K8F6lHDsdanpqMA36mCU1nocO2NiwpQdRKefSMELPUoS2rd/g/OuWH6jsvpl9PX/\nQZ9+eVz8ylv+Agf/Epz5v0rNJCBzdf/oq/LU+6v4NQwDKVqL6v8A5467CI/7CZKxi2DZTzGDDnxf\nnEOk6r9Qg+8kXx4ZyWhCIvX+MWUfsl6Xth9R7zdwN/wk5XSn/zXULf/BP/5V1PC/Us6XiKbOhnAz\nnpZn8Jf9Gc15EGrk427zKUY9Dv/zhHw34fb/Gk/rzzDU2ejuo1M+vO8Jd/DolmXxiOxwdznnj5+P\nU8lsiWeaJqFQKP42wzqWTdNkc9tO7v3sb3zRtqPLMjOqxnHmxC8zu3pCyuM+n0FHuRZFkCSJeUOn\nMm/oVD7d8wV//PQlNu/r6/LGdVz65l38cO6ZHDq858VDvlQ1knnVo/mkOXb8PF+7kgm+4/CqThH5\nLRClVt2ttrY27vFbVlZGWVkZkyZNyrBU9rS1tWEYRsqoL8D777/P0Ucf3aXE8oknnsjPfvYztm3b\nVtJOFH1fomQ/RJIknE5nXOx6vV4qKyupqqqirKwMl8vVJx67iRfo3hYqltgNhUK0t7fT3NxMe3s7\noVAopfC1iiZUhDujRubgg1BUB8qqzlfI4YlHY7gqitPvcQejH3JeZ59evBlz0KEY1bGR1ZIWQNn0\nZI/Wkfh/sdw/AoEAbW1ttLS00NHRQTgcTip8ZVnG5XJRVlZGVVUVFRUVeL3eXilVXQo3gmISE77b\nce59DHfdjwmP+l+cwScJVD6CsmsV3u2x1ILo4DNR25N770bLT0cNvpV6HXIVsr4z5XSI2ZYZ6mhk\nQmnnk9GQw42YkZGEXd9LO69F2Hsd7p23AuCpu5hQ+Y8xpeQuBc7Q3zCUEWjqLCR0PM2XIYeTR7Q7\ntDAPffEBAT2WqlCmuvjBhMPwZCF8ofs1S1EUJFXhL1ve4ob37+8ifCdXjuRXh1/KXUddwfwRB+By\nubqkkOV7nFoRaevhMxKJEA6HCYVCBINBAoEAfr8fv99PIBAgGAwSCoUIh8NEIhE0TWNm9XjuOfpq\nTp90TLzdlnAHP/3gYf746YtE9OxyntNx2qjZlKsxEdKmhXmp/rN4/y3293O1mNj3YylUd6uvry+q\nuFywYAFz587l8MMPTzlPQ0MDw4YN6/Kd9bmhoaFofSsEIvJbJHw+X3w0aCkhy3I8imIYRtFP4lx9\nZFMN8lOaOqNQxuD5AMifvhj/LjTjpKKKee2bv0Be+QJSJIBc/ynyZ6+gT78M+f2rY31Z/yf0A66E\nPMuf2o+TYDCI3+/PuD32vN2ejo7vCft72oMUqce56w+49z6IgRPdewAh7cd4Nt2IEtnWOR9hZCO5\nxZ5WcRLevVenXEe4/GJU/ytp+6Gr05Cj9Rn7ayjDQAvi3XYjgdG/IOz8Hq5IagcJXZ6AFAkhm7G8\nQRnw1N1AYOSdeJsvS5q/7Gn9Kf6ax/A2n4Vi7MDV8VtCym1Izs6iL1FD55HNH7InEnsNq0oyF004\nhBpX/qlJ61tquefTv7K1vbMoiENWOX/6CZwx+disXBsyDTQqptfruROOY2bFOO79/EWaI+0AvLh5\nCSt2beS/557FxMoReadd+FQn3xk9h8e2LgPgo+Za5lSNZLyjMyhQavej/kSpPUTU1dUxf/78orR9\nww03sHTpUpYsWZJ2W0thP+RL3z++7Kf0dNR8sSj2oDdrQIrf76elpYWWlhb8fj+RSCTpjSExYllZ\nWZk0YinvXhb/2xxyKLTuRNoSc38wJZnwtK8VdxBf5Qj0o6+If1RevR1j3JmYjlh0TG7biLTP/zdb\nLOscv9/fJW9X1/Wk+0pRFNxuN+Xl5VRXV1NeXo7b7e7zY63Q4teKsum6nrdFUKEwAnU4d/0R995Y\nkYjA6D8iRZrxrjmri/DVPDOQI+tSNyQZSGZHysm6+1DUyLKU0wE032m49v4+7TwAkbJv4doVq+jm\nrfsZRmQ8YVdqu7Ow51rcO7uOzlai21DalhEuSy7YJTOAu/U2QpV/AMAZehFH6F8YesypwjBNnt72\nMdtslmbnjjuIcb7c7b5M0ySsR3hsw2vc+N79XYTvjJrxPPCVGzh76vFZ25VZKQz2AcYulwu3243H\n48Hr9eLz+eI/Ho8Ht9uNy+XC6XR2SVvL57w7cNAk7j7scuYPnhb/bltHI9e99wf+tvGdrKLJ1sDW\nRHeA2VUjOLBqVLzd5+pWEdC6DxAU5E4pit9iRH6vv/56Fi1axBtvvMH48ePTzjt8+PBuEd7Gxsb4\ntFJGRH6LRCmcHMkotN1Zrk4DOfvtAugRpL2dg92MwfORP/ob0r6LUWTc4Ri+QUUXSfpx16G8e39n\n9HfdG+iTz0ddGxMAyro/oY38asrlc7W76+0BkX1FtsdQptxLa/8U6twztBBqaDWufcI3Uv5foA6l\nbN2p3eaNDL0YV/u9SdvRnDOQoxtTrweQjFYk0p87ujoJt7Ylc79dc1H9D8Q/e+p/TnDUTwi5rsAd\nvr/rvPIITKMM2Wjq1o67+WH8vofRHAehRrvn/6rap2jRdYRdp+MKP4+79cfo6nR099G8snMNn7Z2\npnGcMnIWX6oambHvydjYWsdvVj3HzmBnH92Kg4tmnMQpE49EyfNtSyZSDd5LRjbWVXaRWuH0cfOc\ns3it/iMe3fAaEUMjaug8uP6f7Aw2ceGUE5ElOa/c5P8aNIWN7bvx6xHaoiFe3b2B04bNyH9HCIDS\ny/ltaGhg5Mj8zqlULFiwgOeee44333yTqVOnZpz/8MMP50c/+hHhcDie97t48WJGjRpV0vm+IMRv\n0SiFkyMZPY382gWcJVgy0VMfWal5NZIRiyiZZePBMxRlVdeUB+gF+7byIehHX476n98CseivdtkT\nsE/8ynX/gI5tUNZ50tvt7rJJ+4DY/vL5fH2aypAL+UR+c02Hsdq2BEWm/mQzij/dvjUMA7ljFWrr\ni0hoRMu+QqT8bBT/iqTzm85qlOjWpNPCNZfjbr876TQA3XNi2nxgAEOuxpQypwuYcgWm2T2f1lN/\nO8ERPyLkvQZ3qDN6HHZfg2fn/6Vsz1N3CYFxi/C1XIRktidZoUak7Go099eR9a24On5Li1nB27s7\n/YyPHjyRY4bmPhDHNE3+tnkJD332ShfP3rlDpnD9gaczwjco5zaLRbYpCnZLOMMwOHXSURw4dAq/\nXrGIze2xh4WXt39AU7idBTO/hUPO/hZtnR9uSeEbQ6axqGE1ACvadzKzbBhTfIMIBmNV9dKdE7mU\n1x1IlFrOr67rqGrhJNxVV13Fk08+yYsvvkhlZWU8olteXo7P5wPg5ptvZvny5bz++usAnHPOOfz8\n5z/nwgsv5Kc//Snr16/nV7/6FbfeemvB+lUs+v4/uJ9SqheNfMSvruuEw2E6OjpoaWmhra2NYDCY\nUvgmvp6vqKjA4/Hk7Tog2VIejMHzwb8XaVPnqPrQ9K8DvZNvqh93HaYzJkLk+k+Rtq3DGHF8rJ+m\ngbL+oS5pH62trWnTPqx9ZR8tqyhKn6cy9IRk22kfwNfa2ppVOky+4t8SFtaDRz4DlOT2VSjBlThb\nFhH1HUWk/Hxk/3Yce5/rtj5DrUHW0uTiKhUoWuoSxFHf6TiC6Z0Zot7TcLY8kXHbo96TcDS9mHSa\nZ+evIOAg5I5ZEBlSNYY0ElmrTdmejIF7548JVNzZxafCRCJYcRtSB3jXXwhhcNQ+T4TTcMsKC8ZN\nB2BW5XBOGTUrY78TaY8E+Pmyhdy/+qW48PUqLq6b8x1+dcSlJSV8c8EuMK2gwOSa0dx77LUcNaKz\nNPF7jZ9z26qnMRxS0rQLRVHSnh8zyoYys6yz0tvfd68lpHe+abKfH4mD+OznR+I5YqVclEpaUm9R\natuo63rBBfj9999PR0cHxx9/PCNHjoz/3HXXXfF5Ghoa2Ly581pWUVHB4sWL2bFjBwcffDDXXHMN\nP/zhD7n++usL2rdiICK/A4xsvH5ztdWyF00oSnGOPfZ830OQV7+CtM/TUx9/KEbFiHi/i0750G7R\n38gZN+Pe+R8ApA2P0DH2SlDcSRe3293ZUxnC4TDh8L7odoldaDOR6gZsT/HIxovYnk9pGEb8/5kY\nLUv3ejkXUr1SdhkNOHY9i6w2oXsOJlJ1KZ6PLiB48EKUXZ93mz889FLUFMUrDLxI+q6k0+L9QEI2\n9qadR3cchLvp0bTzAGjeo3E3XJVyunvnbwkNu4ZQ+X9jymW4Gv5fxjbVyEb09o+IeH6AK/gwJi4C\nNQ/i2PE8zuaXAVACazGc4/BtXQDA+ElPcVTNOE4ePQs5xweYtU3buH35kzQGm+PfTSofwY2zz2Di\noFH99qEwHS7FwU8POZ/7P32Jl7a8B8Cnezdz45L7uP3wSxjqTW2jmKrAyKkjZrFl87sE9ChtWpjX\n9m7k1KG52arlmnaRKaJszdffSMz37ettaGhoKHhObTb3z0cf7X4NmjVrFm+//XZB+9IbCPFbJKwT\npNSETLLIb6/k7fYAac/yzj4POQTl3c4btjHntC7z9oZ3cfTYa1HeeQApGsv9DezoQPWMQg3Wo0Sa\n8Ox4heCY0+PzZ5P2Uehc7N7Gfqz7/f4el1VOll9nv4GmIttR/KnOS9mM4Gl+CaNiOmrzY4QH3Yhn\n+TngHIIcqU3qfGD4ZqA2JC9OEan+AY5gV/N4U3JjylWYcjWGOgbJDGBC0rYBTFRMqSLjazpTcmFS\nnnE+d+PvCZpXow/6Mp7ILRnmjuFqeRj/qAeRneuJeK/AueXXOAIrO6fvvJvA1CdR2xYjY+DZejXf\nmvYyRg4vF03T5K9fvMOfP/9HlyptJ489lO9NPiGnFID+iCLJXPWl0xjireLPn/8DgK3tjSx45/f8\n8vCLmVA5IulyiSkK1vV4kNPJt0d9iSe3x/K1P2nbwUGDxzK1bEhWOcq5YqXEZSJdqkW+ThfFZqAM\ndhtI7N9XE0E37OJB13Xa29t7JW83b0J7kds2AbFCFqZ3IvK6/8QnGwee1kV4FUP8dn84cFI+/3uU\nLRmrwaoAACAASURBVI0NHip/+3cEjj+fivUxUe7b9hjmlPNyKjDRH+3CrJtlYs5usvKzUPiyysnI\nJfcy2Y+r7T2Ujo/QnfMIDf4R3mVnIQPBCVfiaHq+WzupileYyGierxAtPxVNP5SI+2xil1sV9ChS\ntB0iLWieLyGHmghUPY4ktSJr63AGX0HWbE4SriNQQsvJRNRzLGrbWxnnA1AitejBdsIV38XV9mxW\ny3jqr8I/6T94130PJdJ14J2Ejqvu/xEcdy++bVcj6804G+8jNPJm8GS+SbdFAvz6k7/wQcOa+Hc+\n1c2N885kXuXE+PFVCsKjmEiSxJlTvsJgdyW/+WQRmqmzJ9TKde/+kZ8feiEHDpmcU3uzK4YzwzeE\nNf7dADxXu4qbpn8Fd5YFRnryIJmp3WzIJm+/N4RyqQ12sxe4EOSHEL9FpJQiv/b8Rzvp8naT+e32\nNvKej+J/m9VzkDd/iLTPMN8Y9SUYNAG5tbWg3sXZuDL4j7gC7/LHkKNBHI1rCBlXYspOJCOCo/kT\nfIG1mIMPynqd/UX8Wrm72abE5OtFbJ07xTruEm+YhmEgt6/C0fAI4Qk/Qwrtwvvh6cjEtk+vnIl7\n98+7tRMdfDaqf3FnO45xhCsvxpDHozZ8gKxuxPf5Fd2Ws/Af+DjeTy9F2pfXqlUdTnDMTeArQ5Ja\nUCMfoLmPxt1wU8Zt0nz/hXvLD7Pafq3iRLwrziIw9xmU0BrUyGeZlyn/NkrDm0SGXoin7n+7TVcD\nq4hqTUQ9B+EIfoxr79No1aegOYYiq56U7a5t2sZty59gV7DTI3la1Rh+Mv88RvgG5V2utT9z/Jh5\nVLvL+fmHjxHQwgS0ED9+/yF+dNDZfHnUgTm1dfKQaWwNthAworREg7xU/xlnjp2bcbmePkgWKpqc\nzyDXdKI5H0ptsFt9fT2zZuWeSy/oRIjfItKXT4illrebL9KeD+N/G0MOQV5rExoHnBibpwDCMVf3\nAblqOJHDf4D7nZjTg+/dhzCOOB1l89MAKOseQDvqoazXn00udl+Qqz0bgNPpxOVy9elDU65IwW0o\nwS+IDP4eGOBd/l1kYttqqNXI0R1J0xK06hPw7L6ecMX5aL4TwO/Hs+qXyMFadO8ETIcv/Xq1jrjw\nBVBb3kdteT+2XkAbejLRybOQan6Cu+VXSEZb0nZMZEx5ULzP6TBlLyZlyIB3xbkEDvkb3h3fR9a7\n2511tq8QLT8V34pzCEz/HZpvHqr/k27zuevvwD/lGZSNp8WKZWy9mo5p/8CQp3W7ppimyStb3+e+\nT1/q4ubw7UlHc/HMk+NpDqV0PvQm84ZM4bdHX8WP3/8zTaE2oobOL5c/hW4YHDdmXlZtmKZJmeri\npCFTeb4xlq++rGk7sytHMKOyMDmjuYjKbO3geiOanE1E2d6+ffm+pra2lpNPPrmvu9GvKQ2Fs5/S\nmydJstH06crhWrhcrnjpZZ/Ph9PpLBnhCyDv7nzdaw6Zj7T+9fhnY3rMUzcfB4t83AesYhyWg4X0\ntf/GdMQiWnL9Kkyl00tT3vochNIPYrJTSpFfwzCSunukEr6JHsRWWdlSuElkgxHtANmFWv88OIfg\ne++ryEbnG5LwhGtx7Hmq+3LqEAzXZII19yDtaMH37gX4PrkCORhzT4iMOQ91z2sp16t5JyEHU/v2\nyoAcrMNV+1cca54kUHM/4YpLMJNctjX3oSj+5CWGE4lWfgNHw0v71mHgXXk5weH3YqaJhUSqLsRR\ntwgA97obCY/4Eabk7DafZARx7fw9odG3x9rX9uBq+ANEdneZL6RF+PUnf+HeVS/EhW+Zw8Oth1zI\nFbNPTZnf21+OqUIxqXIkvz/mGsaWx5wbDEx+9fEzvFHb/cEjGda1ZFbZMGaVd5ahfbZ2Jf4+KH5h\nCc5CFBjJ9z5ld4PJtly1/dpnLduTiHZPqa+vF2kPPaR0VM5+SDEv1FYeajAYpL29nebmZtrb2wmF\nQikHHaiqGrccs39X7AFreWMaXQe7KSOQd38Rm+T0Yk6I1RzPRjhaEcxQKJTV/rLcB3w+X7eHg/j6\n9jk/WMjvLsKoib1OlPQQyqbUJWUzbnovXlDtx1JbW1vGB4FkleZK6YEpFwzDQArW4Vt2EuGxV+Jo\n/AeyEegyj141E9VvewgDIoPOJTDuz6jb/obv/QtwNrzcve3yqSjtq1OuOzrqPNTdqcUxQGTE2Th2\nvYrasRbfB+ci7dxLYOhTRN3HdJlP852Kc9efsthi0Mq/gtr4QvyzHNmJ84v7CQ67I+n8puRC8x6P\nc3enYHZtvpvQyP9JOr+j7T+Y6lB0ZyzX17n3CZTgpxj7HgZ3+Pew4J0/sLi2s3DGxIqR3HfsdRw5\nUrzKTWSot5rfHHUF4/eJV0sA/ydLAQyx69mpw2dSrsYsFdu1MC/UZfew1BdYkVe7SLbeKNmFcllZ\nGT6fD6/X200o20VyTy0T7ddB61rZl5Zwzc3N1NTkXi1R0En/vGMNUArlt2sXu6XsLCC1bUKKxPIA\nTdcg5NoN8WnG5GPAEbuQp3IJsEcwW1tbaW1tJRAIpNxf1sNBRUUFVVVVlJWV4XK50j4c6Mdfb/P9\nXY3hOzQ+TVn/IBiZRz9b29Cb0d9corv2B4FUJahLKXKdC3LrZ/g+PoPw+OuRNA1n/ZNdphtyGXJ4\nazzlQXeMJDDhMYz2CuTm9Th3/i1l25LWhkTq80uvmJ1WHAOYrpHIHZ3HvXPnC3iWno2mH4t/yEPo\njgmYgKGORE6REtGlPbkcE3e3C7+j+T2Ups2Eqy7ptkxo0AIcW7sKa7XtfUxpMJo3eV67Z9tNBMf8\nGoi5WHi3XolktLCicT1XvXUPm9t2xOc9YczB3Pvla5J69/anY6mYVLvKufOoyxlfEUtVMDC58+Nn\neL22e+U9O/b9V+ZwccaYznzhlS31rGxO40/dT0gWTXY6nSmjyV6vt6jR5HTe4h0dHSnLVVsOOdlG\nkwfaW5BCI3J+i0hPD85i5e2Wan5pItLuhHzf9W/EP5vTO8sIJzpYWAI3k+1OQdwHEnx/5WXvYo6r\nQYo0IXVsRa5/DWPMSVk1lehaUUhytbNTFKWLoX6mfVNo8dsbF3bDvwPn7leJDv8WcsNnmCNcyJGu\nnrzh8VfiaH4hFu0dfDGa+xg8S65DjjTR8eW/IPuTF6/QymciBzYknWYhBxu7uUR06R8gRVu65RrL\ngGft/2GoFQTn3ovkDCOF6jJvMBCpPg1H/aKk01zb7ycw426i3mNwBGJFZEy5DN15EJ7mO7vN7153\nHYG5z+LbdDbS/2fvvOOrqNI3/p12axKSkNB7E1FAEBDFihXXrqtiQbBi+63ddddd0bWXVVfXXrDr\n2svaGygiRUClIyUQSEIIqbdOOb8/Jvfm3tySGwhJcPN8PnzInTlz5szcuTPvvOd5n0fEv1DKZhVa\n5YcEu1yOa+u/kfUynGX/Zq/CP1Gn2y5jqqQwfa/jmNRnP2QhxQn3p/r+/5cf+HnObO6bMJ3r5zzB\nhppSLAT3/fQ6AEf0Tv4S0pirulenbozN78OC7bYD39vFPzMgqzM5WnJd8t8TdkYyMRgMRtcpirLD\n3GTIPOHUmH88f/58Vq1aRX5+PoqiUFRURNeuXXG5fv/f3a5AR+Z3F6K5N+rm8nYjGTmPx9Ms3u7O\nWhy3FuQYZzfReQzy6m+in62hR0SpDLHZSl3X01IZNE1Ler525qEa5/q2ZRlWpwOi65SVj2fcT0sH\nkLE0j6qqqoxpHpHs7s648rV3WIaOUrsUxbcKS+6D5C9F2/5NYrvc4ch6Gf7+L0K5H+93U5DD2+sD\n05qU2rzh3mehpaE0GFl7I/vSB8dm/mEoVamntmWjBu+CqYgaA9OxB6aaXAc2br85R+LY9mnK9a7l\nVxHKvQJTtSkLofwrcP2WGPhChP7wIMFeM5Kud2x7CTNrfyzFnp51lD+DU1/NfaOOpcCZwx1jpnF4\nt1GEw+FohqzxNHJs0AH8zzmLNUauM4v7Jkynf8TYB8G9P72eMgOcrFDrxJ57k1dfq+A3dd7ctOR/\n8lymQ2w2ufHMn8vlSppNdrvdKbPJO0u7MAyDDz/8kGuvvZZp06bx3Xff0a9fP9xuN3l5eQwbNmy3\ncFVrT+gIfncx0l30O8PbjZ2ad7lczeLt7i7BrxTr7GZ1QgpUA2B16kldVq8olSGVriw0nK/s7Gxy\nc3PJzs5u9vlqEtldMA9qkLOSlq5C1IdF8pYvkLZnxq3b2eC38ctTLM0jWX+paB47MvW3O9EeLMtC\nqvoVpW45euEpeOZdgzHwVLTSeFtgU/ZiZu9FsPBvuGdfhnPDq9F1Rs8/oG1L7WokPL2RfStTrg93\nPxNt++dpxxnuPhmt/Iu0bQDQOuGddQGBXv/CcI9M2cxSciGcXtPbVoCYSqD7I1haL0zHKNTa1FPr\nWvUcLLkQwz0iYZ0EuIpuwN//aYTSCQlwb/g/Rhb05pHxFzKkU6+U/cY++GOR6TTy7zlIznVmce+E\nS6IBsKgPgL/YmJ4CEYFb0Tg9RupseU1ZNBPcgUQ0foGIvdfFqkZE5EGTcZMbB8nJaBdNBcllZWVJ\nl1dVVbFixQpKSkp26Phmz57NCSecQK9evZBlmRdeSF+rsmHDhqj9fOy/zz9Pfz9rb+igPexiNNb6\njfVTz0RSa1fo7e4Wwa/uQ6q0+ZACCWPjJiKy7MEBBxFKE/BG1AZaU7LNnHgVyndPIIV9yMVrsIaM\nQ6q2g3dl6f0YB7/YZB87EkA2x0J4V5pM7E7Br1S9EiVcgpk1HM/np2LJKpJVjWQFom2E7Ma3z2s4\nlj+B67enEvrQ+5yKe8UNqfdhVKfMCgMId1/kuhVNDNSBHEzPyRRKFggZ2ajC8/Xp+A96Gc33Hs6q\nNxPahnNPx7G56etQtvy4ll5H3aj38Px8VpPt3cumJ6U/CCBceD7CclHX/w1kvQSEH8msJt/hwNAc\nSSWvmovmTiMnk7eKDTx2h5mOSAb4+jlPsL6mBIHgvkWvI0nxFIhUEl1DsguZUNCfOdtstZH3Ni9l\nUHYh+fUzWB1oQEvJnO2MJJxlWRx22GF4vV6KiorYtGkTuq5TVlYWfUHcUbtjn8/HiBEjOO+885gy\nZUrGY/zss88YObLhZTsvL2+H9t9W6Ah+dzGEEFFCe3vR220c/O5KM4EdgWmaWCVzcdZbnBrZQ1BW\nfx9dHxp4SFx7VVXjqA9eb3pt1V2C7ELMgy9F/fJ++/Nv26DQ/lPe8BaMmgHZA9J2kalqRXNMJlRV\njWYXdnT6rbloz5xfK1COWrUYK39fvJ9MQsYiOPQKtBj1A8vRhcCe/0LWdZzrZqboSSCHtyVdY+Tt\nh1LbhGmE6UsbHFvISOHUursR6IVHoGy2aQwygqzvzsY/YgbBwr44y++P24eZdUDSQD4ZlMB68JVi\n5B2F2hR3GQvHhkcJdr8B9xZb4kzIXvx9/ola/C1ZRXfiG/8K7nkXIGOh5wwnMPYpNGs9UvYeCf3F\nPvRN04yb2dkZvuWOGCZkqgPbFujk9HLfhOncMOcJ1kUC4J9eR5NVDulpByXpArfjegxjVe1WtoV8\nhCyDNzYu5pKBByC3o2dBe0BbuLslu76mTZvGtGnTuPPOO5k4cSJHHnkklmVRUVFBSUkJ2dnZO7Sv\nSZMmMWnSJACmTp2a8Xb5+fl06dJlh/bZHtBBe9jF8Pv9GfF2k0lqtVbWsq0zdZEXBJ/PR1VVFdXV\n1Vilc6Pr9ey90TYvttsiYQw6JEFqq3F/bQFz4lUIZxYA8sZ1WFm2bJMkLNRlDzW5fbLgt7EMWWVl\nZdrrKZkecYTmsStv3G0dCGQCy7KQy3/ELJyA6/tLkMO29JbZbRxqhU1hMLKG4R/2GO4vLkcOlSFZ\niTMMluxCShH4AoR7/hG1IjVdwei0L4p/VdqxGl1OQa34rsljMvIPwRFDxwDw/DIDqXQLgZ7/imrx\nWmoBwsr8fqIXHI9z7atYzr0xvImUhsZwVH6LUHpguIdjOvrh7z8T5y8P4ix6DQkL18p7CYywXwy1\nml/xzD8fFA8isCWhr1R8S1mWM5pGbkmuZaY6sBHKxa6Ut0qGTk4v9zbiAN+18BV+KFkWPZYIGp8L\nh6wyuc/o6AvSb3XbopngDjSgvbm7FRcX07evzcmXZZnCwkJGjBhB//79W3Ucp5xyCl27duXAAw/k\n7bffbtV9twTa/pv8nUPTEj3UNU1rtqRWS6JxtWtrUx8yCegclTGFPoYXqT4LLHqPIqfHgDiprdaW\nCUuJrALMg2OsbNc3SE/Ja16AQGnazWOPwTAMfD4f1dXVGZlMtHQRX3PRLs5/GliWhVzxE5Ks4lxy\nN1qF/TJluQqR9DIkLPTCYwj1vQnPR2di5QxErkrO1db7n41W/mXSdQDCVYjsT64CARDuejra1g/S\njlcvPBq1IrEAL2Ffam5SVzdn0as4lr2Ev89MLLUz4U6n4yr6d5P9RWAUHIO2/lVcP15GsN/NCKXp\n2RTXij8R7HMPgR534v7+PNTaBs6zWrUYSRgYWUPsz7Ur0IreRCDv8P2nuRJXO8q1TIXGBUm6rjdb\n3qolzBI6Ob3cM+FiemfZWThTWNy+4EUWlKXmnEfQz5vPYV0GRz9/tGUZW+prKzpgo725u23evJne\nvXu32f6zs7N54IEHePPNN/nkk084/PDDOeOMM3jllUQjoPaMjuB3FyMS1DbOVLZ1JX1ry52l0ihO\nGtAJgaOyoXjDUVkX/dva84jE9rSf4Cs++7sRy21THSQrhLL80aTbRF4GYs9FJNuULDBIdj21eBHf\nTmBnzn+E1hEIBAiFQi2WTZNq16Nteg/JtwXnuoZMaXCva3FsfJZQn8sI556E95NzkS2D8LBzcGz+\nKGlfRpeDUCvnJF1nq0A0wfd1dkP2r00/YAGyXpW2ienphxSqTLle3b4A99yr8fd8EiPnMNTqeSnb\nxsJydAPD9pGTsXAtmkFgQHIDjFhIsoYwDNTynxKMQgDcy28nNOzW6GfXytuR69ZDYPMufQFvyjAh\nEiQ3NkxoSR3YxkFy5PedyiwhmQZsxGwh2fWf58zm3gmX0KNeK1m3TGbMm8mv2xsyuameNUd324Me\nrhwADGHx4oYFhMymbbL/V9Degt9QKITb7W6z/Xfu3Jmrr76acePGMXr0aG699VamT5/OvfcmV4Vp\nr+gIfncxFEVJagrQ1tjVmd9kVIaMXcMcdcghW29VqFkoqxc2jHWP5MFvuyni83bGPOSyhs+bQtE/\nlVVPQbhesSKJyUSqzG4mJhNtjZ0ZR+NzEVE8SZdNa86Us6X7QJIJ9zkD17JH4vYtcnqg9zoHK+DF\n+1WDW59wZCH7k2vnSiKIZCYGdwBmwaEodamNKyyaLoazZE9KPnEs9MJjcWxIn22Rg2W4f7gCS+mG\n4RnSZJ8A4e5TcCx/OPpZrV6OXLGGcNfJabcL9L8Z1/zbMHJGYHoTp2AlowZty3uE+l1sfxYGrqV/\nRQ6UQiB5pXprBx6ZVO6nchVrSXmrxkFyKim4WEexTqqHu8ZfRBe3XXgUtgzuWPIqK6o2ph2LKiuc\n228MDtl+eS4P+Xi7+Od2OYPTFmhPwW97/U7Gjh3LmjVr2noYzUJH8LuL0dY/llRo6WCxudzUdAGd\nUhFjJdtpL6R6GR7h8CL6j0+6//aS+QUwD7sK4bR5yHLRZoTDrsKV9BrMpY9FNZzTvQxIkhR9GdhZ\nGbLWQHPOf+y1ksm5SNVHJlPOPp8PyV8GtVtQatej1DXQEfTOozHzxyKvXYj7p/uiyy01C0lPnlG1\nXN2R0igwhHtNRitPraNr5R2AUrMk7bHpPc5CLf86bRsAK2sv1Mqm5a2MHsfgmnsbwf63Y7rTF10K\nwMwagVq9PG65a+Uj6J2OwXQPTLqd6eyLpfRGq1iIZ86lBIbfk9S+Q9v0BkbBAViyrSqgVS5E2b4Q\npXIZVnD3mW5PRrlorrxVS2rARoLkHMnFjFHn0rn+/hOydP6x+GVWVW1KKwXXxZXNab0aKvd/qixm\nwfZNLXa+dme0RcFbKlRUVFBQUNCmY0iGJUuW0KNHj7YeRrPQPp+kvzO09Q8mGVoi+G2ORS5krisr\nxZpbGA3FbNaQQ0F1JO07lcVxm8Cbj3noFdGPYlODhJZz9WOY4bqETSRJQlUbxFcURWl32d1MkSyA\nTXWtpDPcaAmxeI9ZjuQvR1v3LVpRg6KDUNwE9r0H92fn4Vz3Ttw2+p5T0Db/N2l/oYFTUMs+Trk/\noeUgB1MHDeGup6FVfpV2zEbniSlpFdH9SCpCyay628wbg2PzF3g+nUJgyIOYztT6ukbOfkhVyTM4\n7rnTCQy6DyEl1jEE+/8Nz/f2NS8bftT1HxAecGlCOwlwLr+NwD4NBaDulf9AkkyUinlt/9ttYaTi\nJTudzmZb72Z67Xf35HPr6PPIddg87YAZ5rbFL7OmclM0m5yMlzzUmc/onIYA5p3iXyiu3d5s293f\nG9pTwVtxcTG9eqX+/e4IfD4fS5YsYcmSJViWRVFREUuWLGHTJvs+dtNNN3HEEQ0zri+88AKvvfYa\nK1asYNWqVdx///089thjXHnllS06rl2NjuC3FdAeg5cdCX6TOdBlTGWoVx7IhOsc6+zGtgbeozU0\nOeWh8fG01Q069vxUjr0Q02trncmbq7EkmweshMrxbLI1WBu/DMTyuHa3h0zj77PxTEBT10rjcxEp\n2ss0m5YsSHZadaC4cP7wAGafcWib3rfHpnjwH/A0cqAKbev8hLEY3cajln+fsBzA6rQXaorMrYVN\nM0gHoeYjB4rStiEcSEmriI4xdz+UysXp+wGE7IgGybIVxPPx2QSGPoblSC5RpHebjGtpCkc3M4Dz\n5/sIDLwjfrj5xyCXr0Y2Ggo8XetexsibgOVM3I/qW4fi24Cetz8AklGHtvFl5Jp1SJXxGef2NOW8\nKxErrZaMl+x2u5Pykl0uV9KXxF5ZhcwYPYXseic3nxFkxqKXKKpLfX0KIZhUMIRCzc7K68LklU2L\nqPH7kvKSI7z8xrzk35OxSHs7jk2bNkWVHloKCxYsYPTo0YwePZpgMMgtt9zC6NGjueWWWwAoLS1l\n3bqGGTNJkrj99tsZO3Ys48aN4z//+Q/PP/88f/rTn1p0XLsaHTq/rYD2eNPOJFMa0dmMaMqmyujG\n9hlrorBDb8lmGKmi4aEu/9bwMBRDj0y77wgyCuaFCfomJBEGEQah2//L2QjnnpDhd5bSZEJ1U3v4\njeR+cB0IkIqD0NNelb3+CRwjLkNulMVuT9SN5iJ27KZpUlVVlfYYmrpWmtq2qd+UZYQgJKP98jxy\ndRHK9p+QhIVQvfj3fwptwYuY/fdNuq1k1iWVOLPX1SKJ5O6LRu+zQDIIF56AULMADRQ3QnEjZI/9\nt7sHeu4E1JpFcaYa0XE7uiAHmnbbMgqPwbn8wQzaHYy6uSGQl406PJ9OJXDUk7hXXoKsN2gJC9mD\nUPKRzcRxRaBtm0u49wnoeUejVX6GkByEu03F8+WZCW3d868lOOZWPIsTM8DO1ffjG/cSyry5yICj\n5EP07sfj2PAaIdeVyN4dE+z/X0CmGsODtd7cMupcbln0Ij4jSI3u55ZFL3LH2PPpk9UlqV6yQ1b4\nY7fhPFW8AENYbA37+HTbak7osme0Tew2qZxIY8eZiW5ye0U6d7e2wObNm1s8+D300EPTPjOff/75\nuM9TpkxhypQpLTqGtkBH8Ps/ilSZX8uy4oK5poKwSJYiwmHb2ZuDVPkLkmUXiQlndyS/XQgj8vsi\nCpPzDaEZmV9hIFe+iLr1diQjUWMUwHIOw+x8KVanyaBkxW/eDJOJwD5n4F0wE61kKdJWA9HTgUQY\nuW4D6sa3sQbEFxC1h+x1cxDhHUamUmOXJ0NsEVFT18rOFtBJ/q3IW3/G/f0d+E58AfeS6xBqFv79\nn8T5+a2E9rsC14qHE7Y1uoxDrksuEWXkjYxzZRNKFnrh4RiFRyJEFkZWPxwr3gS/AzlcgRSuBb0O\nKVSNFK7F6L4fUu5WTGk04UEXgaQjWTUodQvRtn+DHCol3H0KavlnTR+jsztyJiYY3Y7GNeevccvk\n8HbcX11BYOLjeFZejGTYXNtwl1PR1v2nyT69i2+i7tA3UHxLCHedgvPXx5NOIcrBMuTKdYS7/QFH\naTyNRLLCONc+QWjPGbhXzADAvexm/CMfQS2fi+E+sc2nmH8PGJjTg7+POodbF7+E3whRHfZx88Ln\nuX/CdPrm2C8Y0cLQ+oxtH6eTE7oN450S26jlp5ot9PfkMzyra7P23RyaRKqguPHy1kZ7m3koLi5m\nwoQJbT2M3wU6gt9WQHv40TRG40DL5/NFp62a2m5XWeRCI76vyEXCDn6tPY9Mm41tMvMrBHLtJyhl\nf0UOpbeVlUPLkbdciSi9GTP3XPS8iwlLfXbIQlicej88egxYIG0JQz2lTl30d8J9TgS1wU50d8j8\nNif4b5GZgB1BbSnodXjePQdL1pCED8kM4j/gaZyf3oxauZaQOxulOlFuLDRsGu5VdyTpFML9zkat\n+YHgoD9jufojJC/K6k9xzbkK2TLwHfss7iWptXSNAX/A9eMdyL4SqJextmQVfcBxBAbfBg4HVk5f\nlIof0x6epeVDBrMbAhDOQuQkWWw5UIZ71nX4D3kCz4oLkUwfRt4heJde2GS/AJ4fLsN/4GNIoQCu\nsvtStnMtuw/fYa+jbZuNZNTGrdPKv0Hv/UcsZ1fkUBlyaCtaxSxE2MLy9MIq2LfdBR+7EyLnbkin\nXtw6Ziq3LJyJ3whRFarj+jlPct+B0+mb3TV6XmOlEg/oMoD1gUoWV9nFnR9uXcHgvK50dngT7KiT\nWfE2Fy1hUR2rX99S10p7KnaDeIOLDuwcOl6tWwHt4UcTQYTKEAqF4paHQqG0xUfJHOh2xXHJ5TEP\n/m0NHEIrDeUB0mdNpcAvaBuORtt4SlzgK+RcLMcgLOcwLNdILPcYhNyQ6ZWsatTtj+JeOwJtKLSK\ntgAAIABJREFUy+UYoeTV6LEmE506dYo7P2LIoZjDj7cbbgVh2e+bkm8TytJ/pj2m9hIAm6ZJMBik\ntra2SRWPCNpKpcKqKUGSBVn/OQkZi9D4a1GL38e//9O4PvkLauVaLG8XZF/yojThzkuQOBOyRnDQ\npRid98VgH7QfXsXz7iV43zkH19KXkS0DS1aRgqk1dwGE5rED3xjIloHzt/fwfnIx3venIm9ZjaFN\nxDd8Jnrnw5MqJhiFR6EVpzfJADBz9kKqSU2hkOs24fz+FvxDn8D07oEUSk13SNg2XIFUV4NU2bS8\nkXPRDAJD/5Z0nWvZDPz7PBI9TsfaxzF6HYlz+YNIdR1qAy2FYfl9uXP/i3CrTgAqQ7Vc//0TbKzd\nmrS9JEmc1nskneuL5kKWyUsbFmIIa7eVgtsRXnJ7KnYD2Lp1K927d2/rYfwu0JH5bQW0dfAbS2WI\nVO6mQ0tTGTKGEMilMfzEzXbWQciKrfSQBqmyppLvB7QNxyGJhgIiIWdhFlyLWfB/IHvjuM1GqAKt\n5lW8vpmoZgPJ3+N/BUd4HpV5TyBcw6PnJxOjEvPEu5CXf4pk6kibDKh/cVeW3o856FzI6hs9BkmS\n4qyN22qqLyKf1FR2F4ieC7/fH7estWGZOsgyro8vjQaZZu9xWNY+uD6+EaXaLjQLjbkUbV2iHael\nZiHXNRSjCdlBqP/5mJ0PRlvwCop7LZ7ZM5LuWx98CurmWanHhowUTG9aYeQNQalcjWvBA1hAeNxV\nhEdMRSt9B23re0j1IaKRdyCu365I2xeA3vMkXEufSttGrV6NmHcfviNfx/vNaU32GYHQcgAHOHph\n5A1HrUytbaxWryRsgp63H1plvNGGmbMXQsulbsLnyHUbkUQIkAkPmopW/F/C/aZmPKYOxKNx1nyv\nzv24c/8LuemHpwma4foA+HHuP/BSemcnFia6FI0p/cbwrzXfYQqL4kA1b2xczNl9923yvpQpTSFZ\n5jhVZrm5x57JNsmyx7GZ5faW+bUsq10E4b8HdJzF3yHSqTKkCmQ0TSMrK6tZqgwtDalmDVLA5uEK\n2Q31sZToNw7cndJu25jDLIRACixBKzo5GvgKFMz8SwgPWY5ecCMhXU2Q3tItD/6sCynvMpuK/FcJ\nOg+N9qsav1Gw7Q/kGa/hcbszpn2ILoMwD643vtgGImQXuklmEHXhX+LPQRtRHyzLisvu1tbWpszu\nyrKc4DDndDrj2rTE2Jtz7VmWBaaBc8kzOIpsjdzQwGOxcvfA/d/ro4EvgFUwCGXbzwl9hIeeh1by\nMUJ2Ehx0Gf4xz6OsXY/31bNACLSi1Nq7xoAj0Ypnp1yvDzgetSS9w1p4+AWo622NYBlwzX8I71vn\nImry8I94iVCPKQhJw3J1yejGbWUNQPYlN+qIhVrxC9K2DYQGXZY005wMocGX4Fzwb1yfXU5wxN8Q\niitte9fCGwgPvjoqkyYklcDQGej5J+B97Wgkfw3uTy7D8/HlZL15MtRsBUnGWd1gc94ego/dCcko\nI3t37s+d+1+IS7HvQdtDtVw35wmK68qT9tHLk8sJPfaKfl5ctZkvyla32BjbQgouFsn0wmOl4GKL\nvCPOk8nc91pDCk7X9Tg5zA7sHDqC31bAribrRzKXjYOXYDCYksoQuWlEELnptOUDRiqNyZxZ+Q1/\nNkF5SNpXaDXahuORLJuqIJQuBPr/QG3e3dT4XU3LtKkacu4xGH0/QO/xFEKyubmSCKGVXIW68XQw\nKjIej3n0TYh661FpfQMHUyl6O+64Wyv4TfaC5Pf7U3KaY6kdubm5CRrEbR2YSL5y5JKfcC56AgDh\nyCE89hq8Lx2DXNMwfW6pHqRQeVKHNaPnBMz8Mfj3fQ5l1Uq8r56N9ptdfGYMOxF1w5fpx5CCFgNg\nDDkJdWP67a1OA1C2LU9Y7vzlObxvnYO0uRbfqDfBCCXZulFfzkKElaFiSd5eKFuXoWz8ldDgpuWK\nhCRj5I9HLZ2PjIVzzt0E9rk17TYy4Fj2b0JDrsf09MW/70uoK7/F89XVyAhcc24hMLHB/tv79f+h\n545GEibuUAf9YUeQii89vGAAd+x/AS7FfhHZHqzhuu8fTxkATyjoz/6d+0U/f1a6ksWVTb9UtSRa\nWgpuRwPlZBbVwWCwVaTgtmzZstsZSbRndAS/rYSWDg4sy4raB1dXV1NdXZ02eInoqEa4mNnZ2XHB\nb3sQl5djg9/yWL5van3fCGKLHRSjGG3DsUimfTO35E5UdH6N6lDvlCYcKR3nHA6s/Cnog+ZiuUZE\n2yu1H+JYOx4pmBisJIUnF2NSPe/RB6Ky4aenzr8WLCM6jghaOvhNZSOc7AVJlmWcTmd0NiA7OxuX\nyxVXFNMYbZa1rtuG0DwoZYuRQtUILQvfMU+ibF+LUhMfOIX3vRht3XsJfYT7HIdwdUNZuhDva2ej\nrY/P8gqnBzmQ3HLYUlOva+gA5ED6lyXZVx6lNiSDY827qOt+QN6yAd+Yp7G03JRt9R4n4Vw5M/2Y\nIm0HnIFrwSM4f5mJZXUm3OOk9O27/wFtdYPRh1a2CEIWes9JabfTtn6H6d0D/8jHcX90EVrxt9F1\nasUy5OA2jG712r+Wgefb6xC6jOzORzaDGR1LBzLDiIKB3L7/hdEAuCJYw7XfP876mkSbaUmSOLnX\ncIZkF0aXvb5xMRt8TauNtAUaZ5OboxfucDjiguQdQWw2ORkveUcs2sGWOevdu3dLnab/eXQEv7sJ\nYjN1EdOAdIVHscFLbm5ulMoQm61raYvjnYIQyKUN08ZSuV0ZLjx5iD7J9ViTQTbLya84A9mw+cKW\n5GF7/kvo6p4JbRVFychxDkA490AfMBuj8+UNY9Q3oa07DKnu24zGZk24EKvHcHvbTRbCsvcjVy5F\nXv2svbwFA8gIdzdTUxJVVVMW7rVXWEYYPPko677FNf8BhOrGf8wTKBuXo658J6G92WNf1BheueXM\nx3/QY+iFR+NY8gZaUSJv11I9SP7Uwa0+7EzUjald2yzZgRSuSbkewOhxAErZorRtAKzcgXi++hvu\nT27DP/Z5wj2OT9rO7LQPWklqGkYEArC8fZH9tvmBZ9bf0bseh5GX+jen9zoZ7ddn45Z5Zt1EaNBF\nWM78FFuB0DoBLqRAEKzEYNb1w60Ex91A5E6kli9BrfgFbc4DuKRANJj4vRkp7Co0pZQxsmAg/xh/\nAc6YDPC13z3Giu2JJiyKJDOl71i6Ou2CYENYPL9+HttD6c1Y2jNSUS5ig+RYJLOoVlW1xSyqU1m0\nn3nmmYwbN44ZM2Ywa9YsbrzxRh566CHeeOMNZs+ezbZtTbx4dyApOoLfVsKO/DhiqQyxmbpUZhOp\nVAdSvcG2p+BXqlqBFLQrj4XshvrCc2vIRJBTZxtjz5Fl6uRVXohqrrf7wUFl/nPojjH2PpJkd5vF\nbZZdmN0fQO/zZlQVQrKq0YqOR656tentFRVjykyE6gQdpJKGc64ungHBip0OfpPZCGea3c3JyYlm\nd3fkem3tzK9lWSCruJ89DcW/GSnsw3/0Ezj/exdW9yFo6+NpBpasIoW3Iwn7vIcGTcZ/8DO4PrgL\nCdBWfZR0P+F9zkVbm3wdgNHrINQtP6Rcrw8+FXXTt2mPJTzkj2gbPk/bRqgehGZfd3L1JrJePBlT\n2gf/8PsRirehnexENNKnTgUzfwRS5Ya4Ze4PLyS4x42Y7kQbVSNnGFLNtqQPDs/nVxIYdW/K3HVg\n1O24Pvszrlm3EDj88YT1khnCufhRggfeFV3mmjsDc9DReN46FVfNGkKhUIItr8/nS8rF/F8PkjOR\niduncBB37H8hnnoViFo9wA1znmTR1kRer1vVuGDAeLz1fOE6I8yz638kYKaXf9xd0fi6SUW5SMZL\ndrvdSXnJO5JNXrNmDStXruTHH39k/vz53HvvvVx99dWceeaZHHLIIbzzTuJLfgeaRkfw20rItPI1\nQmWoqqqKozJkYh8cOzWdyf7ak6lCHN833PDgtvaMpzw05qrGniNv3RM4wgvsdihU5j2O5Z2YcXY3\nU1g5x6P3/xKh2pIzktDRis9H2Xo3NHEeRY+9ME662/5QBtTTN6VwJeriGc0OIHfGRrils7utGfxG\nXtZcb16JPv5cnAsfxn/04zg/fxC5ajNSaFuCE5s+/BzU4s+w3F3wHf4iIphP1tOnIFdvQrg7Iddu\nTrovs/f+qJtTB7dYYSQjdQbM6D0RbWPqYjkA4chFTiNLBqD3m4jy2xdxy9yz/oHj+5n49n0ePW+8\n3a7gENQtTWd9AcJDzsW18NG4ZTLg+eB8gqMeRKjZ8e0HXoxr7u1J+5LrNqMW/UB4wPmJ++lzCnLZ\nBpSq9ahbf0Wu3YreI1GsX9v4FTg6YebUK6CYIZyL/ok+6mKci5/CaSRm0FNxMf+Xg+TmHMvIgoHc\nd+CldKqXNQuaYW7+8Vm+35Ko4NHZ6WVq/3Eokn3/LA3W8tKGhZii7WlzLY3murvF8pJbUgpu69bk\ncnQR7Kj02ezZsznhhBPo1asXsizzwgsvNLnNr7/+yiGHHILH46FXr1784x//2KF9twd0lA62EpL9\ncJprHxwxUIi8fe6s5El7yvzG8X3LGvRSraFHpLYQjoGqryC7tkFsP5B7HZ4eZ+2yKXvh3ofwgFlo\nRSchh2zer7p1BpJehNHjXyCllvqyDpqOufwzlOWfwiZgkL1cWf00js4HECo42t5HigdYROcy8vDO\nxEY4wmXbnWRyYmXfEqAHUVd8grbma4yh+xOYMAPnN0+ibl6C/w//wPHLS4mbDJiIVjob/4TH8bx+\nGXKdPdVvuXKQgqn5i5IZRDKSa+BarvwoZSDtsYRTF8NZyEih9DJoAEbPQ3F98ZeE5Wr5Ujyvnk7w\nmPswuh2DcHbG9f21TfZnm2B0Q/YnFjrJ4Tpcn9+A//BH8cw/H0mYWI58hJyDnIbC4Vz6HL5jZ6Ju\n/Qalzp6BsZwFhPudTdbrp0bbuWbfiu/kl1G2zEUm/t7j+v4v+I98mqz//hEAbfN36P2PRyldhLNk\nLnqfY+yx74D8VVMmPtAwHd7e3MaagwSt8ybGOyS3F/886HL+/MOTlAeq0S2Tf8x/kWtGnc7RfcfG\ntR2Q1Zkzeu/Dqxttms6q2q28v3kpp/Qakazr3Ra7UuasOVJw8+bNo7S0lHvuuYdJkyZRVVVFSUkJ\npaWllJSU0K9fvx0ag8/nY8SIEZx33nlMmTKlyfHU1NRw5JFHcuihh7Jw4UJWrFjBtGnT8Hq9XHPN\nNTs0hrZER/DbSohcWLEZikzsgxs7ZLXkj7Bxpq6tdGURFnJZDN+3yn4JMLruSZWUjVWdOnAAUBWL\n/G1XIWGrKIS1kYTyrsGzq4/F0Qd9wNdoG89E9n0LgFL5PJK+Cb33q6DkJN9OkjDOfgr57jFI1Vuh\nCqivXfLOv5zAhPcxOu0Vp/fbnJekttJpbq3MrxWoQQrV4n1lGnVTXwGXG+cXD6EW2VJiVvc9UObG\n82dNd2eszkMRa34k65lT49aFx0xDW/Zm8n116o1cmzojGx5+HmpRarpCJsVwxsATUIvnpG0DINwF\nSd3aoD5b++n16L33J3jUnQhnAQSS23dHYOaPRK5IdLmLQKlaj2PBcwTGPIx7wRWEB1yEc/6DTY7T\n/fllBI57Fs/354AwCYy6C8+Hl8e1kcwwrh8eIHjw/Xhmxz845VAVjjXvEBx+Ka5fbXqEe96t+I58\nDs9HF2Cd/iFWt1HR6y2Z09jOasT+noLkTMfQJ7sLDx50OTfOeYrNvm1YCO5f/AY+PcApgw6Oa7tv\nfm+2hur4sl72bM629XR2eDiky6AWH39boT24C0qSRI8ePejRowfV1dVceeWVLdb3pEmTmDTJLlKd\nOnVqk+1feeUVgsEgL7zwAk6nk2HDhrFy5Ur++c9/7pbB7+6TBtrNYZpmlMqQVmJrJ6kMzUGsQgK0\nYfZ3+69IITvzJoQT6mthAnsc3WQxX15eHnnBR1HC9hSdwEl17r+wRGqecItCyUXv+wFm7tkN46v7\nEm3dRAinkWjK7oJx9tP23xuIHrNk+slbMA0pVIFhGFE1j4gOcSZKFW2m05wu+NWTB23pkOz3YQUD\n4Mwi6449Mb0FWL3H4Pz6MbS19suTUTgYtXRxnJSZ3msC/lPexDnrEVxzHkvo0+y7L2pxcg3e0Mgp\nqOs+TroOwOwyCrV0fsr1+h6TUTelpzzo/Y9FbYIWYeX0RQo0nR2Wwj6UtfMIjH8II3+f9Psd8Eec\nCx9J20bbOAt5wy+Ehl6P2WkE6rbUZhYRyIYfx6JnCO71Z8KDpqGsX4DsK01op26ZhxSswygck7jf\nVa9hdh+H5bBfICXdh/PXpwjtdy2ub/+KVLUhGlxmqhGbrGBpV0hfJaNb+P3+tPqwLY0dDdy6evJ5\n8KDLGdipQVLr8aUfMHPFpwnjPLrbUEbmNrT7YMsyZpenfpna3dDe3N3aGnPnzuWggw6K03Q/6qij\n2LJlC0VFiUWS7R0d32grQVGUpDe5lBJbGRoo7CzaKviNlWoLb/isYUVNQ8YluOex0b8b68xGi/kC\nC1DK7422q825CUMb3Lr8PdmB0fMZjMK/NiwKLcWx7hCkwJKUm1nDjsY45HIwgbUQoaiqgWLyfroE\nIxxIqeYReUlqSS5zi6N4Huqzg3A85sIxMweWZlAUGIPG179lWUi1W8ie0R9JkvCd8xKud65HW91Q\n2BY+7CocS18GQCAR3O9a9P6nIVWV4fg1UeIMQArXIVnJs+lW4R4o5b+kHqRsZzFTweh5IGpJGr4w\ngKwip6FdAIT7H4tj6Svp+wH0PU7CNfthPM+dTmjwlYT7JJcts1Ue+jQpvwbgWvwURs5Y5PLMzQ20\njV8hHN3Re56Ia3FqlznXnDsJjvszja9wCXD9MIPAIQ2ZZm3TVwhPHnJdCdqaD7BCdUn7FEJgCouw\nZRK0DAKWQcAyCSMwZBCKjKQqKA4Nh8uJq14jdlcGyakseXdVkLwzWcs8Vzb3T7iUvfL7RZe9supL\n7l/8BmGz4XciSxKT+4ymn7dB4eP9zUuZtfX3EQC3h8xvBLW1tWRlZVbEuqtQWlpK165d45ZFPpeW\nJr7ctnd00B5aCRHuZTgcbjv74BTjimBXBr/ppu495Q3SUxHKg5nbG7XfvrjruapJz5EVQC2+AKn+\n0Wm6D8TnvTC6v1aFJGF2/RvC0Q9186VIGEjGFrT1h2P0fgUr+5iETYQQBI65Bfeqb1BLlyOtBzEQ\nJAmcFT+Qs2wGNcPvqO9eSqDAtDdIkoT3x9vI2jATSQqCCySV6F1Gm3Md+t5n7VDflmWBvxL3W1ci\nBavwnfYYcqASx7IP4ttl5SLXbMJy5RI44gHUBR/j+ekB/NOeQgrVJvSrDzgYpWRh6mMK1UTVIRLG\nlNUTeduq9AM3w0i6L/VxqR4IJ44roV3B3qjzEhUSEtrl9EWutbVava9fgH/SbVgjBuP85b64bLiZ\nPxJ5229N9heBZISxvP0x8oehbs9Q2zoUwHIJhCMnpdSbZARxLniE4MEP4Jkdz1NWaotQyn8l3PcY\nHEW285177i34D38Cz/tnY3Yfy9ycAYSEhSksLASmEBm71MVCRkKTZRySjCbJaLJi/y/JaLKMW1bt\nf4qKhhS1vt0VlrxN3YdT0Sta0pY3y+Hm7gMu5rb5L7Bgq32Nf75xIcV15dwy7jzyXXZGXpMVLhow\nnqfX/RjV/f1gy1IEgkN3cwpEewp+i4uL21zjt63PQUujI/htRUQyC+3pItqVmV/LsuIK1ZI+DISJ\no+LHhs/1cYAYdQoerzexfQyU8nuQw2vs9nIW4R5PQkCO7rstYOWdi671RNs4GcmqRrJ8qEWnYHb9\nB2bB1ZiWSCjeC5z+DJ1nnopSXYK0Behp9+Xd8Dx0HonY44JWpzBkjNoylPePR6leSr5mITmBFF+b\nZO6YKH7ku1TXfoe6fg6B0x4DS8M55+m4dvrgiWjrv0bvOZ7QAX/BM/Ny5MpN6EMOQdmYnNagjzoT\n1/e3JV1n9ByHkmaaPzTsHNT6oCzpuF35yP70ldrhoZNx/JZaRg1AyCpCy07bBsDK6o6kx+vnej75\nO6ExUwgc9DjuOf+HZNnXnD7gDJzf3d9knwBWdk8IhXG/cTH+aa/j+fLiJjPVVlZPhJqL573rCBz9\nAO7/XpTUVQ9AK5qFPvgEjM57o1YsjVvnXPIIvuPeQLLCSGYQjADKtp8Jjrsa98cXM/bUt/hC9qTo\nOXNYCEKWSYimub4KEm7FDoY99f9nqxrZqgN3jCxj5H7XVkFyBKZpEgqFkgbJkDqocakObh0/jQcX\nv8UXm+wXxOXbi7hi1sPcut80BufaUnguReOiAeN5Zt2PrK8PgD/csgyB4LAug5t1bO0Ju7Lgrblo\nD8Fvt27dEjK8ZWVl0XW7GzqC31aEqqoZFVK0Jloy+I3IbkUCu6aOVVEUXLUrkOvli4QhI4XsMVgj\nTki7rRT6DWXbP6OfjW53gbM/1PMiM36glG9G2vQb0uZ1SMVrkbasR6ooReR3RXTri+jWB7r1QfTo\nh+g7FNI4nEUgsiaiD/gGrehEJH0TEhZq2V8xq7+mttNDWErnuPZmfj8qpr5N55mnoZRuATdQP5Po\nWXQtJgHMva7K7HhaA7+8gDb3z0hWJThBUoAUM3IiBOgSZqe9Mc/5sMmuo4GBYWCtX4/YsAEmHIC8\nZSmuj/5K4LR/o8z7BHHgH1HXfhO3bXjcucjVqzFz98Hz4AlRTlf4gHNwf/rnpPuzsvKQ65JP2YVG\nnYd7wb1J1wFYBXuhLk4dQOpDz0LdmF671+x+EM5ll6VtY3Qbh1K6OG0bAH2PE3EsTFS5cC58EX3b\nb/gnPo97zhVI4Sqb8tBEABtBaOSFOL+8C9ky8PznSgKn/gvPZ9OigXQyBEdfg/u/f0euLcHYsIjw\nqItwLn46ZXv3rL/jO/45PJ+cEf3ehOIkOOZGCAQIjroJ7df3ELnZCN2L2XcskmniXvQ4o8dewyIR\nH5zISMiShIKELNUrW1AfODb622pmrthEUGfq1Jk6NDoFTlkhR3GQrWr1/zvwyOlfXGMLW5sKlHcE\nEXnIVEiXSVZkmetGnU7/nG48s+y/WAjKA9Vc/d2/uX70GRzS0+aV2wHw/jyz7kfW+WwqzUdblmMJ\nweFdh+zQuNsa7YnzW1xcTN++fdt0DPvvvz833ngjoVAoyvv94osv6NmzZ5uPbUfQEfy2Itr67TEZ\ndlbrN6Psbj2STd0rmxqyvlK1HfiK7C6I/uNT71QI1JKrkYTNtbTcY7HyLkAivuAqpXqFHkb++m2U\n/zyKvPKnjI9V5BZiTZiEdeBxWGMPB3fyFKdlWejSQGq7fkJ22Xk4dHsfzuBXFISPpCrvMcJO+/gi\n8nWOvsMxrvoK6ZGjkYs2ggvwgCRM1J9uQto6F+PAp8CR2tJ2lyEUQPnodJSyb0Ax7IDXlbypsIAg\nCOFCHzwVjnyoye4jlBiruhpp40ak9etB15E1DWPiwcir56CWLCR05F9Q5n2C7K9G2TAnLpNoObMx\ne41C/eULnPPuit+B043sS+S2Wp58lDRqB6ge5JrkhRxCVkESiKweCGEBwj54Uf8/AqP7eDy/pg74\nwNaxTacRDGAMPgnnrLvTtgEwu+6Dc/YTSddpG35AeasI/+SXcKx7BXn7uib7A5s3beUNRS23Z1jk\n2hIcsx4ncNhDuL+6PGk218rujVByovQL1w+PUzfldZT1X6FWJd+vpPtw/vQUwf1m4Jk3A73HBEJj\nbsT18R24N95G8LDrUcrXoq22M+3C1Ym6qe8g6RV09W3hsO5jkWUFWZKQad69VgiBiUC3LHRhoQsT\n3bIIC/tzhDvsN23+sJHmHheyTMqtAOV6gzSegkSu5iRXdZKnOsnVnKhSw303NgObLsjaVUFyJpnk\nSd3H0M2RywO/voXPCBIydW5f8DJrK7dwzh5HoCoqDlnhgv778dz6eayt/719XLICARyxGwbA7Y32\nEFFmaCn4fD7WrLF/15ZlUVRUxJIlS+jcuTO9e/fmpptuYsGCBXz5pV1TcdZZZ3HrrbcydepUbr75\nZlatWsU999zDjBkzWnRcrQVJ/J6Uvds5IoFie4Ku69TW2lwDVVXJyUkhz1WP5mZ3m+I3ax8filxe\nHwBvACrAPOACjDP/nbJPueZ9tI1n2ONBQh84B+EeDUBlZWX0ppWbmxv/MKnahvL+syjvPIm0Lb0M\nVFMQDhfW2IlYh/8R85ATMRQt+TkROtk1d5Pla+BrCmRC+X/G6vJnFNUR32/FBtSHj0Kt2wgDicuo\niuwB6Ie+hsgfuVNjzwir30Ob/SckvQwc9dzdFBA6EAZL607F+Ecwex4QdT5KuU3E2rO4GLZvRzid\nyKtWoc6Zg7JsGcrSpdQumItSsgzMIJJeizr3A5yLPsB3xUt43p6OFLa5tEbBYAJnPInj0/tx/hqv\nzGD0Gokx/FBc3z+cMIbAIdeilsxB2/xjwjoLmeAx9+OedQ3C2xWzcCRm4WgsTzeE6kW48hGqC6Vk\npU3SlqX6/1WEqiGZOma3oci1W0AykAJbUYu/Qy1fhOQrQQIsTxdCwy/D/cOMtF9F3fGvkvVmeq60\n0Dz4//AU3lfOSdvOUh3UXfo1rtm34ChKbckcgd7rIMy8cbhmPRC3PDT+EvBKOJcmBtv+iY/g+ugf\nyHUNlA9LdeE/92W8701OmzH2H/kwQpGQfAFcH9zYkAWWFfxnv4T79fORDZvaoQ86jPCwExEFfbC6\nDUNkddvlGTohBLqw7CI608BfHxTXGGHqTD2jLLIEZCsO8jQ7GM7TXDjTuFjuyBhjXR0j+t4tkUne\n7NvGHT+/Som/YdZgv8Kh/Gmvk3HXu8TpwuKVLUtYH2jQaz+ycDBHdB2SEd2iPUAIgc/XwNVva7ri\n9OnTue222xg4cGCL9fntt98yceJEIF5TferUqTz33HNMmzaNWbNmsW5dwwvr0qVLufzQ+jiwAAAg\nAElEQVTyy5k/fz75+flMnz6dv/3tby02ptZER/DbimiPwa9pmlTX6+jKskxubmJmMROTiQgi6hWx\nvucp4SvG+ZZdFCEESD8DJoSnf4AYdlTybSw/jjUjkXRbRszMv9g2lahHVVVVNIORk5ODqqpgmigv\n3Yvywj1I4XhOpHA4EYNGInr2R/QcgOg1EFHQHWl7GVLpRqSSIvv/tUuRtic3M7Cycgkcegr+o87C\n6D8sYb0sy3j0b/GWX4ZsNTw0LNdwjK53IrKPbBiPEFSv/5XOL5yOWrXB5v/GFNgKxYWx751Yg84D\nLT0nulmoKUb9cjpy2SxQdJu7mwJCYGd3LRWz60SsE94CzUEgECAQsDNeTqcTbwxnO/LQtUIhREkJ\n0oYNaJ99hvb668hbtyK8Xqxu3bB69sQcPJjQjJuRa0pRv3sZ/ahLcL5+M85FH2DldCV42g143reL\no8J7n4S+18kIZLwvTEtQbfCf9Qiu2XcjVye6t/nOegnPB1MTnOCMvIGExv8Jq8ueSP4qpKptKOsW\n4Fj6OXJlsd3v6Q/gnPUoyrb1Sc+R0W0o+uhTcH98J2Abaegj/oA5aH+ENwfJ9GHm9cax5l0cvz6f\nkg9ruTsTOPAevB9emPoLAcJDT8ESXlyLEmkPsRCA7/SXkLBwLH8erfjbtO39hz+K691rkI1ERQv/\nif9EK/4QrbiBfmJm9yE45u9430gcr97/IIy9j8Q9++8px+Y/5glMbx+ynjk2QYrI6DyA0JF/xfvG\nBdFlgePuRv3lv1gFgwkecR3k9mizKWpLCPymTo2pU2uEqTXD1Bhhwhm4n2UpGp01FwWam7xGmeEd\nQTAYjBYVR9zDGmNHM8l1eoD7f32Tn2NmD/p4u3DN8FPpm2XfrMKWyWslP7MuJgAek9OTSYVDoseW\nSeFepF1rw7Is/H5/dP/eJupPdjWOP/54PvvssziZsQ7sHDqC31aEELZ9cXuCEILKyoYbVF5eHkBc\nsNsUF3hH1SuUFf9GnV9f4V0DrAHhyiF8ZzE0yohGtym7BbX8HnvsSgHhwb+A2iC1U1NTE73pZ2dn\no1WUoN02DfnneBMB0bkb5imXYJ54IeQVNjlWYZqIZfORvvsQdc5/UYuSV/mHh4yyg+DDTkXtlGfL\nsUVu5Hox2qbzkP3xY7G8h2N0uwvhth2SKisrkaq3kPvun3Cu/x7ygL5ATHJIaNlY/f6IOXgqomCs\nnXXMFMJC2roEednzKL+9DtTa2d00XUSyu0LJRd/vTtgn0cI2It0E9jXhcNjfoVRdjbxxI/Lq1aif\nforIycEaMACRn49wu8HhwPJ6EZ06gcOB6NsTyQji/fM++O5aiPPVv+Bc9D4A/gsexzn7XuTKIoJH\n3gxBcH74EMHJf8fz1nUJY/JNexbvWxckLLeA4Gn/xvOJbb5g5vZD32syZv4eUFmBVTiArGenIAWT\nKzH4zp+J94WpKc+X/4yHcX7zKMrWNSnb1J7/Csr2dVg9BqBuXYRjxYsJbmvhPSZDXRWOtZ+k7Afs\njKnrg6uRm/it6n32w+gzEfend+E/5wnUog9wrE+uYywcOfgP+xfe16am7M937iu4frwZpWZ9/Tie\nxPXuX5D9ySXU/H+4E23Tl2hFibrGwbFXI5WWIVcUoY86Ec9HNyS2OWA6UqAS55I37DEqGr7z3sTz\nzOmED7yU0OHXIHvz0p6D1kbANKg0QlTpQSqNELVmEwkEIE910llzU+BwkaM03348EAhEM78ul8tO\nAuwgkgXJhmnw7MpPeX9Dw71MlRTOGXQ4x/cZjyzJ6JbJayW/sDbQ8MLf29WJM7oNJ1vNPIhLFyTH\nUkVaMkg2DINg0E6UyLKcdharNTBp0iS+//77pht2IGN0cH5bEe1xmqfxmGprazO2WY7829Hjkje8\n0/ChPv629pqUMvCVQmtQtjXofhrdbo8LfCH+eORv3sHxzz8h1TaYA1iDRmCedRXWxNNAS76faNvG\nfOZee8DkPWDydSglG3DPfh/3F6+hljU4gDlWL8axejHimVuwDj8N87ipiOH72yu1Xuj9P0Mpvx+l\n/F4kYQeKsu8rtLX7YeWehZk/HYlBWDnd2T7lDfI3fI3j/T8jrdhs0yDc9cep16KseQ5lzXNY2YMR\nPQ5HeHsiPD0Qnp7gKgS9GqlmE1LlWqSaIqTtS5FqloEcJJpYSvUMsuqL1UwZs9MIzJPfg5zMKnol\nQNmyBYqLUaqr7YBWCMz8fMSxxyJt2oSyfDlUV6MffzxkZaEUFaG9+SbBW25GaE6yrxpI3XXv4Xrj\n7zjqA19LkhDeLKRAJf4zn0P75j84lnxM4PRbcSx4PWEcZkF/lIrkcl7mkCOQ/KUE978Bs/NQpNpq\nHJ8+iqvM5gD7Lno2ZeBrqS6kukRL4Lg23gLkNIGvBSi+Sjxv21OGRu+RBI66E0m1UNd9iFb0KZJl\nYPQ8ANfH6V2dBBLCld9k4AugD/8jrvdtdQvPy9Pxn/4gaF4cqxMd7sJ7nolj3nNp+3O/dgH+c1/C\n++UFWM48LFNNGfgCeP77F+oufA9l689xGsP6gGMwnb3wLrB/38bQw9EHHoq29tu47Z1zn8Q/eSba\nys+Qg1VIpo7rwxvwn/sC3ucnY/bZF2PI4cieptUxWgtuxZZI6+G0s4e6ZVFlhKg0glTqIaqMUBxZ\nQgDbjRDbjRBrAqBJMgWai0KHhwLNhSMDikRL8lWTcZI1TeOKfU5mUF5PHvn5HcKWgSFMZq75nCWV\n67hm5GkUuDtxXt8xvL3lV36usfnfm4LVPLlpAWd0H05vV6eM9t9cCbh02eTY42lqnxG0dbFbm5lP\n/c7RkfltZaRydmttRCqAdV0nFAo12b7FbZb9JTjeHICEsCkPvwAG6NNexRp1SrIBoxWdgFz3BQCW\nez/0Ad9Ao+lBn89HqKaKTk/9Dc/nDaYKQpYxp/0Vc8qNkCILskM2woqC89cfcHz8AvLsD5CSOJlZ\nfffAOnoy1kEnIPrvaadY9S2oW29HrpwZ1SmOwFR6E3AdR9B9PO7OB6FaIZTP70H59kGkfAMKsAvi\nWhIiEuyCkHPQR1wPB1zf9GYROoPfjyguRkgSUlkZ2ltvoc6di7xyJXL9ebRkGf2CCwifeiqSz4e8\nejU4nYisLITTibn3UGTfRryPnYd/+vNIRgjvE1Oi+woeey14FYx+E/A8eQVyhU19qbv+P3ifPD2B\nOuA/7V6cPz2FEqNnKyQJfcgkQgf/CXn7Fpzv34VaEm/eYPQZgbHXRFxfJS/WCx5yCcq239BWJufM\nWqqD4Il34Xn72qTrAcLDjgFPPo558cYfFhA+aBrGqKORAyVYOX3IeuPU5J3UQ+8+FqP3Ebi/uStt\nOyFJ+E97Ae/zU+KW+0++EyWwBufS5+OW+yY9j/eVaWn7BDDz+xP8w9+RwnW4ProF2d+EDFp2dwIn\n3I3no/OQALNTXwIH303W05Mbxiqr+Ke+hPuNaVGOb3R/OT0JnPQAWS+dGV0WHH8JhMM4f3qduss/\nYb0jl626jxynl2ynlzx3Dh7N1S4TEKaw2K6HqNADbNODtopEGuSqTgodbrpobrKU5MkHn88Xfc54\nPJ5dGsAV1ZZx98JX+S2GWpSlubly5ClM7DUKIQSzytfy0ZZl0SBfkWRO6TmcMbm9WlzdoilkEiRH\nDEbAfva1Jd2grKyMG264gXfeeafpxh3IGB3BbysjExrBrkBzAztFUaLB7q7QmJVXPok270/2h1pg\nNQjNZVMenIm6WXL1u2ib7IejQK4vchuV0M5fXornr2fgXNag6yq69UG/ZSZixAEJ7WNfApp6MWnS\naKJqG8qnryJ/NBN5fXIjAKv3IKyDTsA6+HjEnmORjNUoZTej1CaferbUHuDcE+EcgKjNRv7hJ6Q1\nPyOJKjsIziOODpExdMCoFyZAwcobj3HU09B5QJObRtUZKipg/XqUVavQXnsN9YcfELm5iO7dMfv3\nxxo8GGPIEMwxY5Cqq5H8fvB4kCorkTZvRlm7FnnFCtRly/DNuAnGjcTz73MJnPtPCARwvXszalmD\nGkPNbXNRipfjfvyiaJbT6D4Y/ZAzcH98e8I4fZe8gvdV23ZaKA7C+5yFMfAI1KVzMAbui/e55Dxa\n3zkP4/7qn8gVyZUe6i57E++zZyMl4cEChPafilRdimN5ag1g3zlP437rBmRfZco2gQMvQB9zMmrl\nKlw/3ovsS845Dxz8D5yzHkqbcQXQe4/H7HUQri/uS+zjmL8gaTW4Fj8KgFEwjPCQqUmpB8kQGnUW\nof3OI+fJozNrv89kRG4+zqXP4zvxVTxPnYUcjle9MAoGEDr2b3jfSAzAg+PORzi9uL+37ZkF4J/8\nAu53bkA4PPgufo/Jnz/GrA0Nai4ORSPPnUOeO4dcd3b073xPJwq9eXTx5lPozaMwK58u3nw6ubLa\nJFgOWgYVepCKcJAKPUhIpC4qdskKhZqbLg4P+ZoLpX68dXUN7ne7OvgF0C2Dl1Z+wRurv44r+ju0\n5z7838hTyHZ4WF27lZc2LMQfE9wfUNCPE3sMR00xvlS6yK0RJEcgSVL0Gbir6RbJ8NNPP/Huu+/y\n8MOJRbsd2HF0BL+tDMMwWk3rtzkyZBE4HA7cbjdKBnq2OwPts6ORS2fZHzYC/8/eeYdJUaXf/3Mr\ndZqcAww5KSiSRFTM6BqRYAAVdM0BxbQq7q5pMYc1oyjwRRdFVEwsrq6YEyooMOQZmMwkJnWuqvv7\noyYwTM+A2f09nOfpZ6arbldXV4c69d7znlMF1rDJmNNjNOxYTU6Tm+lUFqyUSzFzYlTldlaiXXMy\n6pa2OFrr2MmY1z8G8U4jX8uP5q7RoV1BVdV2Ead79UMnJSJ/Jepb81DefwUR7CSG1XAj+x6AHHgQ\n8oA4RM4GFD5ByNhpWG0PBGqBEqAUCOAImAxAb/6r4sQmWzg6BMUZ0/IJkK7uWANmYB98OexhGrX1\nRGNZyKIixLZtKKtWQSiEzM52dLsuF9IwQNOQigJeLzIlBWXHDownnkBfvhzRTFil243MzCR6wAFE\nLr8cOzsFQRjXR/OIjpqA+9mbiJx6Md4XnIsjqeoEzn0UEfLjXdhe1xv48xO437+7tRGtBXZcOuET\nr8P9wWzCB1+MlXUQ+kcvYXzzFmaPAzAPPBr3f2JXdv2XzMc3b3qnx8M/fS6+hZ03oPmnLcD7r0sR\nu9hddRgz9Vl8/3dRp+ud55mHd8EVSF8ywTPuRPFvx/3Nw4hw+8+H/6R5+BbvuUIb+NN9uN+4AyUS\n+/MYOnoGJHlxfX0PwWMfcRwb9kCoWxD80z3QFEAJleD6pmupROt+T5qDjEvGvfQ2tPLYF4vhQ85H\nagrur59rt9whu/PxvHOL46iBIzXxT36G+GcmEDlgPMHx9zL4ucvZGarfq/3ZHYaqk+ZLJjMuhez4\ndLIT0slNSG/9Pychnay4NHT111MPSilptKJURQJURoPUd3LBBY6lWqruJt3w4ItKjOZZsd/SqWBt\nTSH3fruIil2q/+meRGYOnczIzIHUhP3MK/ya8lDbZ7iXL4VpPUcSr//06ayuSPKuy38N/JJyi1hY\nunQplZWVXHdd5zNJ+/DjsU/z+xvj1/wR2rW6G4lE9ipkQtf1VjLYsuzXJr4EKxE7PmneZxDNxS/r\n0NhkQK26u5X4SjUdM/O2joMqitCvOQmluE1n6b/odrRpNyKBaDPZ3VPl/ReJERYCuf8ozP1HwYz7\nUT59G+WTt1C+eLcdERaRECL/a8j/GlpmtFRgEMhRKhxgIzwxfrAFkNp8OxCHCViAucvNBpqAapAW\nSDMeO+UYrMNvh4wBe3wJrXKGpibYtg0qK5GGgQiHob4edB1l61bU999H5OdjnnYa5umnQyiE+sMP\nGMuWYScnY/fvj3X44Zinnop0u7G7dwe3GykEuN2gRtHXf4rMzCU6cgLe2VMJXXQfrncclwQrOZfQ\n2Q8gDS/ex6Z23E+XqwPxBQgfMwM7rReBkx/D9eajuAvawigix12M+53YEgHblxJzey0wex+MWvJ9\nl8dORINdEl8rtUdM94kO24mEEJEAIhLAN+cCzG6D8Y9/ArVuHe4vH0JYEezEPAjt4WIJkEJxrMA6\nIb4A7g8eJTzmfIKHz0a60vea+Ep3IrYvC9+L0wlMfZho76PQC1bs8XHaxv8SHnMZahfH2/hiHoEp\nz2Jv/A9KfXHrcgF43ryOwJnPETdvPACKvxrXl3MJnHQH3nf+hpU3gu/PeYDDFt9KZWAnoS6IYyxE\nrChlDZWUNVSyig0xxwgEmXEpdE/KJi8pix5JOeQlZdE9KZseydlkxaWi/gwbMyEECZpBgmbQhyQi\ntkVVNEhVxJFImLs4SVhIKqNBKps/e3FCI0XR6WYZxHcij/ilMTi1F08fdS1Pr3mT5UVfA1AVrOeW\nL+ZycOYgLhl8Clf1O5zFxatZXed8Bwr9tTyw8UPG5w5maFLuT9rP3YlmZ+gqZe+nkuRdq89dnXN/\nKkkuKSmhX7//3aS8Pyr2kd//cfzckAlwuvRbyO9vIclQit9ENP9oiybABDtzALLv4R33ObQetbpt\nusfMmg1qezs2sX0T+swTETuck6hUFOqvvJ/w8VNRm5r2aM/2q0o8vHHY487CHncWhEMo336I8vEb\nKF+/17q/7WABa0GstRwinAGk73Zz4xBca5e/DTjVYB1IBomOnXQA9pA/Yw+eCvqeNWut3rsVFchg\nEFFTg/Hss+iLF6M0fz4kIJOSsA44gPCMGUSmT0cpKoJIBPx+pGFgjRxJaNQoqK5GbNsGponVrRui\nsRF92TKMRYsQ5eU0fv8lxtJ/Epl8LUptGd7bT4eEdLCCqDVFRAePI3LY+bjmziJy2qWIUHviFh18\nDNrW3ZwzvEmE/jQLs9fB+B6eilpTzO6QCSkoO2OTz/BxV6B9/2anxyhy8Dm437u30/Vm7gEo5es7\nXQ8QHnsZxmf/1+WY6ICxqIXftFumlawl7vFziQw6Ev/4RegblyI9qbhW7rnSauYdglK0eo/jXJ/P\nw5/zIFIqjn57L4hAeNSFuP7jyA+8L87Ef9mLiIYStOrOG/6k4cMcfDq+ORcQmPAQ3kUXxXwuAXiW\n3khwyhw8C89oZ3+m+Gswvp5P8Nhb8bzvyF6MDcswB55ANOcA3Mv+jpW1H19M/Dtk9SdkRdgZbGBn\noIG6UAM7gw3UBhqoCdRT7a+l0r+TKv9OqppqqfLvpCnSdfgIgERS0VRDRVMNK0vWdlivKxrdk7Lo\nndKNXim59E5u/pvajdyEDJQfaWlmKCq5rjhyXXHYUlJnhqmMBKmKBPDvZvPXJE2aLJOi+mCrPCLd\n8JCqu1F/ppVaV/Dpbq4bdgYHZw3ikdVLqG/24/5qx3q+qdzI+N6HMbX/seR6EllWno8EmswwL2z/\nlm9qi5nY7UBSXL+Ou0IL0QS6LPLsKhtpca35rUnyjBkziIuLo7a2lkAgQHx8PNnZ2eTk5JCamvqH\n1K//L2Gf7OE3xs/1+v2xIRN7M20fiURav+y6rhMf/+t2Suv/OQmlvLlZqFnyYJ5+P9ZRu3W1S4m+\n7QQUvyOPsL1jiPb6bztPLlG4Hv3KcYg6p/te6gZ11z1B6NCTut4HXW89Lr9bN+/OSsTG1SgbVyE2\nrkIU5iMaaqGhtlUi0AEKkAB0a3+TBshgT2ztBKyBl0C3QXt8+paZAmmasH07orAQ9Ysv0F97zfHd\nbdbt2t26Ib1ex57M43GIbnw8ytataJ98grphA+ratYiyMie8ITub8MyZWPvvjygvR/vqK+y0NGRO\njrMdlws5cgieZ24kNOkaRDiA986JKEDTDfPxvjqLyGHTsJU4vM/fQuCKR3G9+whqZft0MP8V8/G+\nchUi1Ig0vISPvhorbRDGO89ijjgGzyu3dXjNZnY/zDETcb8TOzHNf9mLeJ8/t/XirMP66c/jW9jR\n5q0FgYkP4frosU79fwH80/4P7/PndertC+A/5xk8S25BaazudEx49FmET7gc79Jr0Mq+62Jr4B//\nBJ7FN3TQ1cZC4Kw5qN8uwxp+NJ63rumSAEtFwz/1ZeL+2daUZ2sGgStfwrvkzyjB2JrmwEn3Y3zw\nAlrR90RGTsTO7oX7gy6iogcdT3TI8XjfuLbD8zdd+i5K6VrQ3Y6ER6jYqT1xffg4WsGn+M9fRFi4\nWGskYlsmmhC4NZ14t5dkXzxuTXdS4Xbfx2iIqqZadjTVUtZQSXljFaUNVZQ3VDXfr6ayqRb5I+OR\nW+BSdXok59AntTt9U/Pom5pHv9Tu9E3LI971431l/VaUykiQyrCfnVbnVW5lF3lEuu7B8yvKNnaG\nGnl+/b95d/vKdscp0fAxbdDx9E3tzSvF31MfbWtqNBSVE7IGclh671+VpHeGHxNw8WtUksE5J/fs\n2bPT9YZhsH79enr33nOPxj7Exr7K72+Mn3K1tnuj2s9qyoqBXcf86pXfUDWi4sO2+3UgNRfWqI5T\n2kr94lbiK1GdMItdjp+9bSOuGSe0El/b7WXnLc8ROeiIDtv6tRv4fhKS05Gj+yHHhEGYYIYRdjXC\nbTs63nogiGNv5m3+68I5S5eC/C4JOzAaK2Eq8qDTwOjaug12aVarq3OihAsKUJqakC4XuFyYI0Zg\njh6N8PsRZWVIw8AeMABRV4f+1lsYL72EUl6O9HicUIqcHOz+/Qn/+c/Y/fujlJRANAq67pBklwu7\nd2+UjRtRP/iAiN+PXPICnkcuIzL6RERdJXEPTAPAyuyBUCF45t3o/12M+8u3sQGZlNKB+NqK4sQC\nR4KEjroKK280rlcfwb3pbgIXPYTxfuyEwMi4y3B98FjMdbaiIPw1nRJf252AUl/R9fGNT+uS+Nqa\ngWiq6ZL4AuD2dkl8AfS17xEd8ifCB15IZGgTnv/8DbGbMwI4kgf0hL0ivnZiNpg2rm/fIGJGCU54\nGs9rl3V6TCLDz0X/dFG7ZYoZwTv/KgLnz8X34lmI3dwLzLT+SDUerciRjxgrXyVw5r1E+x2Nvrmj\n/y+Avv5dzP5HEu05Bn3b5wBE+x3rVJ3f/CeRI6bjfXwKSnOIjZnVj8DFz6IeMAGloQJXXCZDcFPf\nrX3MbqD5BtAUaMIfbCISCSNtC1UIPJpB98RuHJAzCF1VO5DkiBWlvKGK7XXlFNWVU1RXQXHz36L6\nCqq7aGgMW1E2VW9nU3XHxsqsuFT6prUQ4jz6p/dgQFpP0nzJnf52+VSdXh6dPMNHQ8DPTjvKThll\npx1tJ4+wkY50okUeoeqk6R7SDTfJmhvlF/xtTHbHc91BZ3BqrzE8ueYN1tY43436iJ9Hv3+NXgnZ\n/Hn/kyiNRvi8uhCJE5DxZtk6vttZwqTuQ+nu/R0i3fcSe1tJ/rEkubKystNtgUOOMzIyfvJ+P/nk\nk9x///1UVFSw//7788gjj3DYYYfFHLtt27aYJHv58uWMG9dJGNX/APZVfn8H7Mla7JeOEN4Tdk15\nE0K0Bl38GlA2z0P//DLnThOwEaxRUzHPad/QglWPsXkownT8Ic3UGZhZ97YeF6tkK8k3nIpa7ay3\nPT5q71hEdOCIdpvxer2tx+X3QwQhChFiU/Nto/OXtQilcw1mOxSAXOlC1g3BSj4Ve+RUyMndq4e2\n/LDaxcXIqiqkx4NSXIz67beoGzagrF2LsmkTim1j5eURvvpq7H79EBUVaB9+CMnJ2D17IhMSkG63\nQ2hdLkhIQBoGMiEBbf16jKeeQv3ss1ZrsxaJRHTiRCJTpmADIjsJz6NXEjnxz8ikdHx3jG+tLDbe\n+Q5oOr57p6PUOk1MoYnXolblo69u75wQHHcZ9sCRoHjQ/70A49u29f5rn8f3dOzqrP/K+fjmTo+5\nLjz6bIRiYnzT0fMWIHTsTNTtX6MXfBZzva25CU26D+9LMzp5JyA05nyUhiqM79/udIyZ2Z/oQZPw\nvDW70zHO/lyFtvEbtM1fYPYeQWjSjbg+fRi95It246J9jsRKPgD3h492sqVdtnncTWifvYZW4di/\nRYYcR/Sos/EuuQhht/8dkkDgzBfwPRU7UtnsM5rIMefjefWSVsIoAf/Ul/E+MQ0l2p6o+69YhHvp\nDaj1sTXAUjXwX7gY1zt/ITLuryjb8nG9NhsFMDP7Ep7wN3xPtdm4RUaMx+w1En3VckJT7kCaYULJ\n3WhK77HH49AZbNumMdBIIOgnGg2DbaMrKl7DRaLHR6LHh6YoCByS7I8E2bazjMLaEgpqSymsLWFr\nbQmFO0u7JMadIdmTQL+0HvRvvg1I70n/tB5kxrVNg+8a0KCqKi63mzozTFXEIbxdWampCFJ0N2m6\nmzTDg0/tmAz3UyGl5OOyH3h27dvs2G1GYGhaX47uMZq1/loqdvHXFsDY9D6MyxqA+xfcl67we6a7\ntZDhhoYG3nvvPcrLy1myZAmDBw+mrKyM8vJyysrKsG2bhoY9a/1j4eWXX+bcc8/lqaee4rDDDuOJ\nJ55g3rx55Ofn07179w7jW8jvu+++y4EHHti6PDk5OWZy4P8K9pHf3wGxLLV+TITwLxUy0YJYKW+/\nSmVUSvS3x6DUrnLuFwOVELlmBbL3Ie2GaiWXoNYtAMBWs9iZ8zlR24OUEqW6jNSbJrSGS9guD7W3\n/wtryCHout7u4iIpKek3kjXUNxPcgl1uzn0oRogfUVH3A9+C/E7Fqu8PKadgj5qAPOAA2IvX0qrd\nDQZhxw4nSvjtt9FfeQWluhqpqsj0dOzsbKw+fTAnTsQaOLBNu6vrYNtgWSgVFShbtqBu3Aj19UTO\nPBOZl4dSWYn+xhuo33+PnZHRJpHIzcVOTMQePBjR7DUqPB5koAmyUjDefBLzkFMgHMa98Ba00s1I\nRSF09t+wcvvhvWdqO12n/6aFeJ88t121LXrAcQTHz8JYPhf3By+0e+1mn2GYI4/G/WbHKXQ7tTvh\nky7Hs/jm2If9ovl4X7oCEfbHXn/BQrwLO0YotyA09hLUmm3o697t9L3xnzcf78g+1J8AACAASURB\nVAuXIqIdK7StY85+FPfyjjKP3RGY9gzeORe33reB0NR7wAOeFXcgos4JPDD+SdwvzUQx93DRLQSB\nc/8P3+Pntlse2e9IosdNw/vKRe1ee7TXWMzMQ/As61wDHTr0XGROdzwfOEQ+MngykhRcK+Z0GGu7\n4wheOBfvC9MQnexr6MhriIw4g7i7TkDZrdEvPGoidu5+eF6/s3VZ8PRZKCWbML54heAFjxIdehxb\nqyr4vrEJRdVIik8iLTmN9KQ0tF9w+j8SjdDobyAYDmKZUYSUuFQNn+Em2RdPnMuNP+ynsLaUrbXF\nbKkuYnNNEVtqiiioKSHayWesMyS645oJcU/6pnSnZ0I2/VLzyEnMwOPxtBsbsKKtRLgmGupStOFR\nNNJ0N6m6m5S9DNjYE8JWlCVbPuKlTR8Q2k2e0Tshm+HdhrM12NiuWu1Vdcam9+Gw9N54fmUS/EdK\ndwuHw0yaNIkPP/yw3fJQKITb/dPcMQ4++GCGDh3KnDlt38H+/fszadIkZs/ueMHdQn5XrlzJ8OHD\nf9Jz/hGxT/bwO0AI0aFRbW8ihHfVqP6S5LRl6qaFkNu2/atUSkXFh23E1wZqwc4ZjOw1unWMlBJZ\n93Yr8QWoT7idiOUGJMrOSlJvPaOV+ErdReDORXhHH9e6z7sez1/22i6MEFubK7ctt83NJHfvOuM7\noBr4HvgB5DqBDO5PtNs4mkaMJnLaCPT4+L3SYLe6M1RVIbZvR2zciGvZMmRKCnafPlgHHIA5apRT\ntfX5kElJTthHXBzKxo24b74Z7fPPUXapJtgeD5Hzzyc6YQLmkUeiFBUhDAPq6pDx8YQvuABUFcJh\nqKuD7GzstDSUbdtw33IL+ocfIiMRmj7/EJLcqEXrMYeNQ3/pMeTQkWilm7EyexI6bzbSm4D3/nPa\nEd/o/oehbv6ilfiaOQMIj58FVVVo+V90IL4AoQlXd7BDa113/OUYn3TeaCaioU6Jrw1gBjslvgBW\nzzG4Pp/f6XoAEQ51SXwB0BP2SHzthAznAmUXKID3xZswuw/Gf9Y8XF89hVb0CbYWv0fiC2D2ORy1\noGNTnJH/IcK2CEx8Bu9rl7TKGKIHnYv7+Uu63Kb7s4UEJt9NZPBE9E3LiQ6eiO+xs2KOVUJNGO88\nQHDCA3gXd0y1iwz6E3ZCL1xvPEr4xJl4Xru93XrX168SnDiE6ODj0Nc6YTju1/9B4PIFqEVr8My7\nBnvGC/TpN4r+61ag+CPY8fFEvSWEDJ1ISjIRAWXBJmo0gV9aRG2JbhgkxSeTmZJBWlLaHo8jgKEb\npHYyNkpzoKU7nsSkbvQ3EumR3Jej+pioCHRVoSHcRE2wluL6cjZXb2dzszzCH4ntIlIfamJlyTpW\nlqxrtzzBFceAdIcU909vrhan9SQvPo0engRMaVMbDVEdDVEdCRLY7fMdtE2Kw00Uh50ZqnhVJ6WZ\nDCdrbvSfUFhwqTpTBxzL8Xkjmbf+37xf/B12M9EtaCinIP9tsuMy6Ju5P/WWsz8BK8ryig18WLmF\nw9N7Mza9D95OkkB/Lv5I6W6lpaV069atw/KfSnwjkQjfffcdN97Y3r973LhxfP75510+dsKECYRC\nIfr168fMmTOZOLHr8J0/OvaR398BTU1NrVeWneGXru7uCYqitMorfq3JAG1dWzQx1YAJ1pgLsaVs\ntSIzw5Wk7biydVjQfQohzykAiPoaUv56FlqpQwykpmPOfgl9zAntnmfXY/XTiXwAIb5HiFUoyncI\nsQohNiDET/RoLgI2ABvb/spNCjJrGPbYI5Bjx2KfcwgkJDhWdY2NrfsfC61k1zSh2XuXYBBU1ank\npKYSPeEElG3bUFeuRIZCRCdNAl13ooQfegh17VpkRgZ29+7Y/foRPuYYrJwc7EGDEPX1YFlIrxel\nqAi1sBBl0ybUjRtR8vOhqYnIlClYp54KQqCUlaG98gp2z57YvXphjh9P8MILUQb0RNnwHfaooxHf\nfoDn6b8SuP81fPecRfi48zH3OwJj8eOYh45Daapr9xojJ12Md95l2PGphCb8FUwNzz2XErr8Qdyv\nPBTzuIhIGKUhdvSwnd0btRMnBrP3CJTSNZ2+fdbAo9CKvul0PYAI+zutWAKYPUehVG7scht2XCpK\nbUeHit0RGXEGxgdzY67Titfivf9MQmf8nfBhV6Fu/GiP2wOIjD4Pz5zLYq7TN3wCVoTAhDl4X7sU\nK7kH+Jv2KlLZ+8rNNF32ItHBp+N6o+sUOr3wG6w+owkfegmuz9oqU9E+YzH3H4/3SYdsB6feTeSg\nkzFWtZePuF+/k8Cl81GLf0Cp34EAvM9djv+qRXgfOgPfkxfgv+4VrLGHoTy3EG3tOjj7bIxIFHXF\nRxgvv0wfVXVmRfr2dWYzcnKwMkNYGEQ2b6HBitKoCmqxqVUVgnYUG4Hb4yU1MZXM5AzifXvXNBzn\njSPO2zHUJ3uX/6NmlIamBvzBJsrrKiiuK6WsvoKyxkpKGsop3FlCYzi2nrshHJsUx7t8rUS4X1pe\n860HKYnZ1DZLJGqjIazd6sKNVpRGK8r2ZmlComaQorlJ0l0ka64fVRlO8yRyw7CzOG/gOF7d8gn/\n3v4loeYLq/KmSsqbKslKyCU3pTctc6Eh2+S9HZv4uGorY9J6cUR6X+L3wsnmx+CXjIb+uSgtLY0p\nRfipqK6uxrIsMjMz2y3PyMigoiJ2P0N8fDwPPvgghx56KJqm8cYbb3DmmWeyYMECpk7t2Kvzv4J9\n5Pd3QGdfqF3J7m+tUd2V/P4aTW9i51qU0v84dyRQCVL3UjfgJMy6NtKTVHcrqu0kWVlKGvWJs52q\nd8hP/O1TUbY7fptSVTFvX4g95k9dvpa9J/IhhPgCRfkQRfkQIb75UURXhkAUAC23rbvcCoGw40kr\nR47EPvRQ7GsOQ44eDTGqurt+Pnbd/1Y5Q10dsrISNA119WqMF15AXbkSpbbNWN72+QhfdRXWMcdg\nDxuGUlCAEgg4lfXkZMKXXw6ahgBkOIxMS0MmJaEWFuK+5hr0Tz9F2DZSCGRyMjIrC/PQQwnefTfY\nttPYBhCNIlUV66CDsAYPRqmsRJSUED3+WNRADdqb84icfRXuB2dgfLmcwLX/xHh/AYGrnkFd9Sm+\nO6bTdO+r+B6c3u4Y2EkZCNNP6IQZ2JmDcD97K+qOIqcBztBRajpalUVGnYK29cuY748dn4patqnT\nRrPwURfjefuOmOskEBlxNp7ldyDp6AoAYOYNR9nRtcVZZOS5uN/tXCIAED78UvTvXu9yDIDd/UC0\nZY93ul4BvItvp3HGC5j9j8Es+AJt+8pOx0t3AlLzoXShB9U3fwWWReCsBU6U8cI9x1+3wP3KLQQu\newkR2HPghPv9xwmcPwczdyha6WqivccQOfRyfA+0VYzd/5pF4Or/Qy1Zg1rV1jAmbAvPwmsIXDwX\n74OnOw1qYT+eBVcTuGohcQ9Oxvv4NPxXLcQ8eSyMGoVWXuHEa48cSWDMGNB1REMDVFVh9+4Nycmo\n33+Pd9Ys1HXryATHDSUrCzs3F2vQIKJTpiCFC9ZvIawUEHTpBFwGjdjUCkmdrhAxTWxVJd4bT0Zy\nOunJ6ejanqfwdU0nNSmV1KRU8rJ7cPBu66WUVDZWs6Z0PRvKNlFQvZ3tO0spbSgn0MksQ2PYz7el\n+Xxb2j5cxK256JvavZkM96RfVl9SEzORuotGK9pBIlFvRpzgjean8SoaybqL5GZC7FP23Fyc6U3h\n8gNO45yBx/JmwecsLfi01R6toqGUioZSknwZdE/pjWiWPIRtixWVW/i0qpBD0noyJq0n6TGSQX8K\n/kjkt7i4mB49frpG/ZdAamoqM2fObL0/bNgwampquO+++/aR3334cXC5XASDwT+UA8Gv7figrN2l\n6lsHhCEwfAKm3tZM4Ar+G0+wLb88kvUYScl9EYFG9FlnoGx2ktukEJi3Pod95PiYz9UZeeyIMhTl\nTVT1DYT4HCH21IgooCYO1kv4pgmxHqeSuwVEOex+ZpApKdiHHII85xDn74gRsBcZ8btXruvr69Gr\nqlCLi9Hy8/EsXIhaWOicfLt1w+7bF/PII7H69cPu0wdR1Vz5dLkQFRWI0lJESQna5s2o+fnIpiYi\nl16KNWoUNDSgf/UV6ldfORXgPn2wxo8nOnWqc4Lv1w8RibSGUqibNqGuWuWQ6S1bUDZvhkCA6Gmn\nEZ0yhWiPHnDiOPSP3oBImMiJU4i74hiUmnLMvAFYQw7GTs/B+8AMlJpyokMOQdv4FSLY1uQihcB/\n3fNguHC/9SL6mrZqYWTSDPQvYpPD6JFn4n029jR8+Pgr0L9d0vE9Bez0XtiZvQmPOhuZlI1UXc3J\neCqoBqg6Vlo3gifchdSbp1q15otT2wJsZFIWSkMlQW8q6vZv0CrWIGqL2tmESXd8lwEaAHbOfqh7\naHSzE7Ow9+LiWLrjUCImnvtPJ3TJo5i9DsP10SMxrcsiw6fgWt45mW6BXvANctkcwpNu7TTeORYi\nJ96M786JBK94HO+CS1Eauu5md8+/lMCVi3F9/DjhI67Ge8+EduuFtPE+cwX+K57D+8QUlF32RWms\nwfX63QQveQ7fnD8DoFYV4vrvHALnPoB34fV4n7uS4LSHkHERKC/D84/ZKKaJud9+hK+7zrkQLC5G\nf/ZZZO/e2D16EL76auf7axjYbjckJjpphXFx6CtWYMybh7J2LQm7N3yeeiqR6dMR9UFEeRF4PJi+\nUkIug6DLIGho1COp0wRBTSNgRdE0g4T4RDKTM0iK79rtQAhBZkI6mQnpHDtobOtyKSU7GqsoqN7O\n1qptbK3ezpaqQrZWbcPfifNHyAyzdscW1u7Y0v45EPRJy+PgXiMYmDuQzOQcdMPTzn0HIGCbBMIm\npc3yIUMoJGouEjWj9W9n1eEEw8c5A49jcr8j+U/RSl7Z/BHlzUErdf5K6vyVJPrSyUzMw204Otyo\ntPi4aisfV22lpy+FkSndOTAp92fpgv9I5LekpIQxY8b8YttLS0tDVVV27Ggflb5jxw6ys7M7eVRH\njBw5kuef37skxz8q9jW8/Q6wLItIJPK764l2RTAYJBh09GRut/tni/x3TZuzGraT8u4IhGzWk60H\nGXFTedWn2Ik5AOiijpTysSi2Y+9kJU3B7PY8BJrQrzsF5Ye2DvboLXOwT5rW6XMHAoFWWYnH49mt\n4aMYVV2KoryGEF8iROyPv5QCGnOQG3zwQQPKOxWwGsehohPYffsiD2kmumPGIPv336sGtfbP6xw3\nf00NelkZWlER6ubNjkbX7XYsyXQd2dJlKyUyLQ18PpT8fNwPP4y6erVT0QWIj8fKzCR6+umYp52G\naGhAlJU5+9WyHU1zqsBNTeD3Y+fkINPSUKqq0BctwnjjDUQggPT5kGlp2BkZmCecQOTEExGhkFMF\nlhJzUH+EW0d/dxHm8KPA0In7y3hEKIAdn4T/wbdRv/kA7zN/a329/rsW4X34AkSzljE69BjCx18I\nkTBxd0/vcHya7lqC7+7JHQicrSgEZzyN75mLOzwGoOnGV/E9NgmZmke036FYvUYiVQ/oXkezrGi4\nXrobpbyg1a2iBebAkZgHHoH7lc59aP23LMJ399nYCalEDzoWc9BIZHquYz1mBRFNVciM3nifm97B\nNaH1NWgGwTP/iW9+bOlBC4J/ugF91fto21Z1OS589EUoJYXo378PQOSQiUTHnopn6fUoTe2lIf6p\n8/A9teeIZIDghNtQ164ketxUvAsvRewhYc7MHUJ4zEX45szATkglcN08fE+fgwju4XE9hhKc/hTe\nvx+HGor9xTO7DSI86VZ8T3asQIWPuggpFNwftMknQn+aCTsrcH+6CLPfaELjLkcoGmb3A1E3bYVQ\nyPk+gOO1XVHhSH7y8xGFhUQnTsQeOdJp+FyyBHXNGuzMTKfhs2/fNk/s/v2RqgqmifB6UdatQ127\nFmXDBtQ1axBFRSiAnZpK6IYbsPffH2X7dtRPP0Xm5WHn5WEnJBD1egi5dIIuF9F4H/VmlB3CJiQE\nUggMt4fUxBQykjP2qooMzm9MVVMNBc1kuLC6iIKa7RRUF7EzULfnDTTDa3gZkDOA/XIGMSh3INnJ\nOSh7IXtwK+ouhNggQTXQYzzOkjafl63l3aKVrKzc2KoLBkjwppKZmIcnRrVXEwpDErMZkZJH//j0\nH23dFggEWgtAbrcbTfv9aoRXX3011113Hfvvv/8vts3Ro0dz4IEHdmh4mzx5Mv/4xz/2ahszZ87k\nrbfeYsuWLXse/AfFPvL7O0BK2Zqo9kdBOBxuNfY2DIO4uB8/hSSljNnEF59/B3Fbn3YGNQKboOnw\nGYT/9Den8q2pGCVnoTY6+j2p5RDp9y2YbvTrx6N816ZZjF7/GPbpsWOQW9CRyKvNFd75CPFB54Q3\nkIdcmwGv1yPmbkFUd2Hur6rIoUOxDz0Ueeih2KNHw246qr1Fq353xw4oKnJIq5SI4mKUkhLULVsc\nve369eD1ErziCsdTt7YW7b33UDdtck6WPXs6J9/4eCdauE8fRGMjqCrC5UJs3YpSWOicZLdtQ2zd\nivD7iVx4IdaI4YgmP+qqVahffYnMzcXOzUVmZTvby8nBzuuOqKuHSBg8XggEEPV1WPEJ0DMXoiHU\nyjKUogKsHn3wPnYdSnkh4fGXEjnuLFyLH8W1oq36Gjn4eOwB++F+/WHM3gcSnnQjyub12EmpuN7/\nP7TN7cmd2Wsw0WMn4nmxfaMTQOjky1HqtmN8907bcQWsvCFED5mMecAxiJoyRFUF+tfvoX21vLVa\n6L95Hp75f0Wpil2VbbrlRbxPXY1SH9t31+w/guiwY/C83LmkoenyxxC2iczMRZhNaBs/xFj9BiLY\nJgMIHXEZ6o5C9DXLO90OgP/ihfgePbfLMQD+qxfhu+fsdsvsxHQCVz+N64u56Pn/dvY/ezCR4efh\n/deNsTbTDlJ3E7hgLr77zsHK7EHwovvwvnApShe2Xf7pz+N59NLW421l9CB0wT14507vVCMthSBw\n4QKMxQ8RPusWvA+3T3fbFZHREzEHjMa7qL0MQwLB8x5DX/EsevEPrcsC5z+J69+Po5XkExl1OtH+\nh0NiOnxdgO+vf297vMuFtd9+hK+/HjsrC6WgwPGwbrb7k4bhSCQCASgtRUSj2EOHQjCI/sEH6P/6\nF8rOnY4dYFYWVnY2sm9fzGHDMI89FlFZ6cgrDMMhyaEQoqzM+a43WxCaRx1F9KyzEKEQ2n//i7Zi\nBTI93dEj9+3ruKvExxNNS8VKTcPfWEedtKlXJY2GQUSAUDXifAmkJ6eR4Evo8v2tC9RTUFNEQfV2\nttUUUVBdxLaaYsrqK9qRz1jQVZ2e6T3pl9WPftn96JvZlzj33p1H3IpKvGoQr+nNfw28itZKXHeG\nGllRupr3i79lc13b9zTek0xKfBYJnhREjECMRN3NsORu7JeQRQ9f8l6FZvibXWrAscr8PYtUEydO\n5NVXX/1Fg6cWL17Mueeey5NPPsmYMWN4+umnmTdvHuvWraN79+7cfPPNrFy5kvffdy6aFyxYgGEY\nDB06FEVReOutt5g1axb33XcfV1999S+2X7819ske9gHoONW+N2ghbdFolEgkgml27IQX0Qa823fp\nyt8BMi4N7eRZ6B7nh1HdcUcr8QUwc5+CkIb+l9NQVn3ctnzG/XskvtAm4dC0jbjdL2EYS2K6MUip\nIHcMhGUexCMFiDVFCIpiv1ZNQ44ahX344diHH448+OCYet29hW3bWJGIo92tq0NdsQLPE0+gFjW7\nWAjhyCaysoiccw7hiy5y9LRVVU6V1u9HxsURmTwZoSjIxkanQa1bN0hIQNm+Hc8tt6C//76j3dU0\nZGoqdnY2kfPOIzptGqKqCtEy/VVTi9Q158Q8ahQyMdFJc9NUcHscne+ataibNiJqahD1dZg9emBe\ndBHKhtVIM4pSW43r2fuInjAZ17L52CmZBGc8iLbiHdSKonbEFyAy+TLcz/0F//XzoaEJz1+ng2UR\nnP1iB+ILEJo2C+/THV0AAMwR4/A9MBHpTSQy/GTMIccgvcko2zZhJ2TiufsitG35MR+Lx9sp8QUQ\nqtIp8QUIT7oWz5N7OAmk5+L9+wQnAQ8wDzkV/9Q5CEWiVGzA+PIFzMHH4VpxZpebsZNzoQtdbgus\njJ7Q2LGKp9RXEXfHRALTZ2P2HYv7nb8ROfxi3Iv+3nEjMRA+6iL09+YDoO7YjvfJawjMnI93/kUx\npQzR/mNRyra1kyWoldsxXr6PwHlP4Z3f0T8YIHTyzWifvIG+dTXi5XsJXrmwgwVbC4wvX8XOGUh4\n5CRcK9s+YwLwvHQj/isXYX3zJjKjF3ZiBrjjCF7wGGrharQNH6MEqqGmDHvYfjR88hFKVQ129+6I\nhgZkfDyiqgrtiy9Q1q9HXb8eJT8fJRTCBqJnnEF0yhREbi7qp5+iFhVh9+yJNWQI5sMPOyRZ05wZ\nG7cbmZSECAZx3X03+muvtcaGA8i4OKycHCIXXkj0vPMc68GGBoTfD7pO9MQTiZ56KqKx0VlXUYHd\npw/4fLhXrcaYN4/0jRsduVJmpnPBOmAAZt++WEcdBfVFRKt2ENA1Qi4XTQrUawpNLh1LCDTdRVJ8\nEkOyBzKs+5D277sZoXhnKYU1DhluvdUW09hclY9aUTZXbGZzxWZY7UglspOz6Znek17pveiZ3pMe\naT1iVqhDtkXIbgveACeJLk7VidN04lSdw7oP5/ieo6lsquGDku/4b8m3VAV30hjciaroJPnSSYnL\nbFcNro+GWFG5hRWVW/CoOv3j0xkYn8nAhAwS9I6OCbtGEMPvL3vw+/2/eOLqGWecQU1NDXfddRfl\n5eUMGTKEZcuWtTbWVVRUUFDQ5jYjhOCuu+5i+/btqKrKgAEDmDdvHlOmTPlF9+u3xr7K7++EWF6/\nvydM02w1zVYUhaSk2Dqzzqq7sSCEIL7gaXxrmyt1QSAfopMewR57qfNc9a+jF7dVp8zUq7C8N6Ff\ndxrK+rbuevOyu7DOiW1h1R4Wtv0mivIELtenMfZfIIv7wxIF8cBmRHls6yopBHLYMOyjjsI+4gjk\nmDHwM8zOW6u7tbVQVISyeTPa0qWI+nrsZk2hTEtDulzYycnI3FxEMIj0+RDhMMrq1aibNqFs29aq\ntyU9nfBll2Httx+ivh7to49QNm3Ezu2GzM3BzsxExsVj9+uHTEtF7KgEKR17slDQqS5HIoimJmQk\n6jx/VhYyIQGlqhLtk09QNm9CWDZSUzEHD8EaOQqZng7xPtTSbWiL5xKdNgPt43/jfmY2kXETsA4+\nFGl4EIEg7ntmEnjkFbwPXI5S26YzC580nfBZM1AK8vHOvrLV6SFwxT/Qv3sX/fuP2x0/W9MI3vI8\nvgfOY3dEeh1I6IYFqKUbkJZA/89i9I9eb3Ui8N/9Cr6/TY75vkRGn4jM7o7rrY6+swCRMachk1Jx\nLe9c3+aftQjf7LM7XW/m9iN63HQ8z8+Kvb57f8KTrsHuORAt/wNc7z2O0sn0c3D8X9E/fwOt6IdO\nnw8gcN79uF97FKWqc+eI6JCxhM64DiElcffH1s/vCikEgasW47uz/bG0E1Lx/2UB3gWXou6iaZaA\n/8pX8d4xMWbVNjL0OMxDT8Hz4ox2TYRmz5GEx16C76EL2/Z15IlExpyC79nYkhApBIFLn8W17D60\nciegw0rNIzThb2AKrNRu+O6cjOpvaNvnG55H//RtzOFHILv1Q131PjIlCzNjP3znno+6YQMIgUxN\nRWZnY/XsiTVgAObpp4MQjnzIMMCyHIlEVRXq1q1OmuGaNUghCN9wAzIjA3XrVvQXXkAAVo8ezncy\nL8+xHXS7nVka00R6PIjGRrQVK1B/+MEJoNm6tfX4Wb16EbrtNmRyskPCy8qw8/KQ8fFOAI2uOxVp\nIUBRHEmUYWAsWYLxxBMozeENEiAxETs7G3PMGMIXXoior0fs2IHlcRN2uQh6XAQNA78C9YZOyNAR\nqorucqQWiXGJSCmpCzZQVFvC9toSimpLKdrZ9v/u2mJVUclJzqFXRi96pTu3nJQc9B+j0ZXSqRRr\nBhUN5Wyo3sqa6i2UNkt53LqP5LgMkuIy0NXO7dByPYkMTMhgQHwGed5kdEX9UdHGvwVOOOEEPvss\ndqjOPvw87CO/vxP2xtv3t4Rt29Q1uy7snvL2YwI42jXxRWtwvTkcEW6uum4DW+1H9ObvQNURoTXo\nW49ASOcH0vYdQzTuafRrx6MUtFnzmJf/A2vqdXt4BfWo6nxU9SmE2NZhraxPRi72odxZ4oRrxIDM\nzMQ+7jjsceOwjz4a0vbO07Mz2LbtpKtt3+5Yke3cCZqGVBRHiqAoUFuLKC2FaBR72DCky4Wan4/x\n0kuo337r7FdyMjItDSs9neg552APH44oL2+uAquOflfTHY2hpjknQa/X0fPGxyHq6lC//Q6lsMA5\nwdXVId0uzKOPwRo4CKSNUlSE9vnnYJlOpapHT8yDD4bkFOdkGo2CxwWKgvA3oC97GavPfsjMLLx3\nXIFaUojZoz+BOW+jbF2H964ZKDuKCZ12HqQm4V7spIvZKZkEp8/C7j0E723TUcvbOvVtIPDgEuL+\nOqnDsQye/ze09Z+g/7ACaCaUx/8ZK7sfVmI63kdvQF/3VYfHRQ49EZnTA9fSp2K+R/67XsV7z3mI\nUCfBFre/hveecxCdWElFDj4JmZ6L651nOv0c+G+Yj+e5W1GqO68uhyZcg1q0EVGzg/C0m8DyY3w4\nF23zZ+2Iof+qxfjuP6PT7UBzw+D1rxF3x+ldjgMInngZ5mETMT5dgOuThV2OjRw8CdvIwP32kx3W\n2d4EArMW4XlxBmrVVmf8sInYegbuf8c+9gDhI6di9x+CZ/FNzr674vBfOB/v7ZM6EObw0edhZ+bg\neeOemNuS7jj8V8zD86/rCR93JegJuOfejNJQi9ljP0LTb8d7x+Q2IpmSwQ3NMwAAIABJREFURfDa\nuXhvOwMRChC68B+YQw6BuERsqSG++R6lpbktPh48HqTPh7Z8Oe45c5xo8Jbn1nVkZibmkUcSvugi\nRFOTQ441DQzD+S7qOoRCKOXliM2bkRkZWMOHo9TWoi9bhv7mm87sTWYmdnY2dt++WH36YA0ejD1w\noPM7oWkO2W7W7qtbt6Lm56OuXQs1NUSmTcM85RREYyP622+jbN3qXFw3SySkx+N4faemIhMTnQth\nTUN77z30jz5CXbcOiotbX5etaYRnzMA84QQn8GbDBmROTrM/soewyyDkcRM0dAK6SsDjpUnYKKqG\nzxuP0FUqm6op3lnm3OpKKdlZRsnOcqr9jjuNqqhkJmbSPbV7u1uy78cljdaH6tlaXcD2nUUUNZRh\n2hbxnmQSvCnEe1IwtM6bjRUg0x1PH18aWZqX7u5EknTPT5L//VKor6/n4osvZtmyZb/bPvz/jH3k\n93fCH4387p7yFhcXh2maRCKRPe5nC9k1DKNNHyUl2odnoxYtde6HgXUQveBl7ANPA7MaY+uhiKhD\nfqTRm4jvXxgzpyBafHyFwLzu0T1IHbajqk+gqs8jRPumGGkryA8SUe7dCf+lgxsDgD10KPbJJ2Of\nfPJeJ6h1Bdu2MRsaYMcOpKIgCgsxXnsN9bvvnAjh5kY8OyGB8OWXYx1+OGLnTrQvv4Rw2Gk2S01t\nreLYaWnI9HREMID0+hCWiVK4DVFViaiuQdlRAdXVWAMHYR1+OCBRN29G/9eLqAUF4PEifV6sgQOJ\nnnkWdmYWyo4KlI0bEFXVSEPHjovDHj0aO6cbqIojowgFITHR0TdGo06gQsCPUlmGaGpAeuIQKviu\nOwtpmgSuvw978Ajc8+/DeN95z22Xh8ADL+C7ZRIyLYfg9FlIXwqisgL92/cwPn2n3bELTr8JtWgN\nxpfv7H5YabpnKZ5nryNywoVYOf0QlTvwPHcPVBQTfGAxvlmxCWHTva/ju3MKItwxHMDWDIJ/mYPv\n3tiNXraiELxxHr77Om+u9P/9Vbz3TUN00pAF4L/1ZXx3dC1naLp9Kb6/TnAqiIBtuAlPuxWr335o\nWz7D9d85SF8ywdNvx/dE7OjmFkSHHIuVNwz3kvu6HAfgv2UJvlsnETz/NuzMdLwLZ3bq4tB0zZKY\npLQFtuEmcNtruF++HrViI/6rXifu76fucR9Cp1wN8QbuZfcTmD4H46UH0Uo2xR476S/QWIa7E6Ie\nGn8jkVGn47v9TNTK9hImc+AowpNm4vtHW5XeSs8jeOU/8f79TBQzQuisG4nufzAybwBS1WHdJvRt\n25zmtm3bHB/svn0dQpmZ2Vq1RdOc74jHg7pyJdpXXzm63TVrUJoribZhEL72WswjjkCpqEBdvdqZ\naUlObo0Nl7rePDMTQiYlOY2n+fm4Z89G29jmEd1itWbl5RG55BLsHj1QCgsRluVcADc3soqGBpSS\nEpQNG6C6muj48YiUFJRNmzCefRalvNxxjWl5XX36YGdkYB10ECIahUAA3G5EeTlKcXFr74G6di1K\nXR129+4Eb7nFqW5v2IC+bBlWs294ix454nYR9riw0tIJmlFqsWhyuwhgURtupD7qpz7SSGldBWX1\nFZTWlVNaV4FQFLqldCM7OZvc5Fyyk7LJTs7eK1Js2iYl9WUU1m6ntKGMyqYqXLqHeE8K8Z5kfO6E\nmBrhXWEIhW6eRAYkZNLNm0y2J54Ezf2bVYLXrl3L/Pnz2zWm7cMvh33k93eCaZqtXrR/BLRYau3N\nx0FRlNa0uc4s2pRtS9A/OqdtwSaw0w8hevUHgIm+7SQUvzO1LZU4TGUO2k03Iqoc/1apqpiz5mIf\nH3s6WYjVqOrDKMqSDn68skGDp0zEE3So8kpVRY4di3XqqdgnnQR5eXt8vV2hxZ1B7tiB2L4dJT8f\n7cUX0dascTS2GRmtzWjWyJFYgwYhysqcJhnDcOKEVdW5X1uLqKgAXccaMQK8HpT16zHmzkVbtcpx\ncHC5kAkJmIcdTuS888BlILYXoeWvc9Z5PODxYqckY40YgbAsRFERoq7OOTHaNtJlYA4eAh6P45pg\n28iWRp5mlw9hmUgJwoqirP8BOyUdklPQ8r9He+tlIudfjuf2ywhddSfobuyMTDyzr0Ir3NB6bJru\nfxHX8gVEjpqMNLx477ke/I0EZs8l7pb2KV8S8D/0Gr5bJ7SrdNrp3Qie8xfsgSNR1n+H+7l721WL\nQ1NmoFQVYXy8tMN7Y8clEbrqXrwPxLY/C029CXXLt+jfvhd7/fgrnG1/8VbM9TYQvGkhvns7bz6L\nHHAEdu+huF/7Z6dj7NRcRzf8ROzZjejQsUTOvBo7MRXX6/dhrOq6EuS/Yj6ehy9EsbqOyI0OPITo\n8FPxPuvEPUf3G03o/FvwLrgataqw3VizzygiI87A+0zX0iNb0wjcvhSlaivqqk9wfdrRXi4WAuff\njczKQ1m/Cs+Szl01JBC84gm0b17HWPN+u+XhP12N1JLQP3uL0LRb8d42oQNRjw49mugRk/A+ennb\na8vtS+iC2XhvPwvFtglNmontjnd0tuOmwLr1qA1NSF13vkM7diCEwOrfH+H3o7//PsZLLyFqahzC\nmp2NnZeH1a8f5n77YY0Z43hw+/2O/WBTE6KqCqWwsLWxTdmyBfvAAwlfcw3S50PNz0d/++3WCrDd\nowfS63W+4243MivLuVCPi3OI7Msvo373HWLbtrZqNGANH07o5pvB7UZZv95JF01IcIi2y+UQZEVB\n1tQgpMTu1w8CAYyFCzGWLkWEmuOPExJarRXNMWOITpiAUlnpzGa1OM+oKqK+HqWoCGXDBpT16zH7\n98c64wxEIID2zjvoy5cjk5MdYty/v0O2MzMx09McO7naGvwC/KpCtWJRQpjKQC0VgVpqQw1U+Wuo\n8dchFYUEbwI5STlkJmaSmZhJRmIGRiepbxErQkVjJWUN5ZQ1lFPRVImuex0i7EpstU7bE1QgQTPI\ndifQJz6d3nHpZLrjcf2C0dgtePfdd9m4cSOzZsWWS+3Dz8M+8vs7wbKsmA1ivxWklJim2Spl2BMR\n/1EBHMFKjDeGIcLNTUJVIIsF0Ws+RPYYilY8tc3ZAYFVOwP1tmdaq3NSNzDvfBH78FN232sU5T+o\n6iMoyoqOr2k9iIeBF3D0xS3LVRV55JFYEyZgn3oqpKd3vf97gG3b2NGoI2coLEQUFLSdTFqmODXN\nqeCoKnZiIiQloRYUoC9YgPbxx+0DKZKTnYrQ8OEo1VVon30GwRAyJQWZkgyJSdheL9bQoYhoxCHI\nUjrTn5aFVBTHhzc7xzkhBvyOnjccdizKbBu7Rw/QdZQdFchQGJmYgExKRvh8UFeLjEtAaBqivBg7\nOR3FDKN98RHqd18SvuIvqOu/x/3YXdgeL8F/PIGor0X4A7ievo/IWReibViJsfzl1tcUOvlcIpfc\nhLL2G7yzr0Wpc6QvTfcvxD33DrTize2OaXDyZSjBGlwfLMaOTybyp/MxBx2M8PuxU7OIu35izOpt\n48OvE3fzhJjetYGZj2D8+3m0rbH1sU13L8X3t9NjPhag6c6l+G6f2Kk1WeiEC1AC/4+99w6Pqszf\n/1+nTk2DhBQIkFBFbAsqq6y9rr03VCy4YkNFFKQIWMBdK+oKdlERUbErYK+oFKV3EtJIDyHT55zz\n/P54JpPEJKD73c/6x4/3deWCzHnmzDkzk+fc537u933vxvy2c4AXnLQA78OjUIKdhzsEb3sG92sz\n0So6jzR2gNDUt1BiTWBquN6diV7WvoFPuP2EbnwJ333tpSPtX/clPA9e16YZzXF7CU15DWP5m7i+\nn9cy9oa5eB4ahRrfe0yy4/ISePBzPK/dg7FyyV7HAzgZOQQmvIVryUu4FnWcXNdcQtUIjZuL6937\n0UvXIxSV8FWPom7ZiDshb4kPPoLY+bfgue/idgA49rfzsPoPxfvChORjVuGBRC6egHf6JahA5Nyb\ncVK6oW9dReTaKYjtOzC2FOH07Ckb4L74Ajwe7D595N9pK+ZWeDxyHkhPRw2HMZ97DuP115MWekLT\nktKG2PnnY514ImpZGUpjo3SGSNgQKtEoSnk52pYtKJs3Yx94IPbRR6Pu2oXx7rsYn3+ebIp1+vXD\nLiyUwDsvD6dHDylv8vtR6+okGN2ypYW1ra+XDXuXXEL8wgtRAgH0xYtRIpEWy7bmc0rcVIuE9AMh\nMF96CfP996GiogVsKwpOZiaxESOwzj5byjuqqhBeb1t3DEWBmhooKYGEHENdtw7Xc89J2QUk9chO\nfr68iTjlFLkqVlZGVBFE3S4Cpk6NE6XUiVBqN1HeVE19tAlH01A1HbfpISs1i6yULLJSs/CYLZaX\nQgjqQw1JVrgmVE/IiuMyvXhdKXhdKWjqHwC0jo1P0+lqesn1pFHgz6S3P5MuLt/vcpjoqJ577jky\nMzO5/PK9O7vsqz9e+9we/qT6M0T0zc4MzT97uu9RFCXJ7v7ReGX9p9tagG8MKAP7lImIXgdglJyP\nGmhh2pyiI9BntrBiwpdK/IH5iKHHtdpjFFWdj6Y9jqp20LH/BfAQKItIShuEohA74gjCZ5+NeeGF\naP+hDRm0albbvRtRUiLlDKEQ6qpVsglt2zYpaSgqgowMojfdJJcN6+sxFi9GW7VKauzy8nB69yZ6\n+OHYAwfiFBaglldIb1FNTTo4xE89VTo0xOLSdSEjHbxe1K3b0NatQWkKSLsx28Y66CDEoP1xUtNQ\nq6tQi4tBOPJi1a2bfG40ilpTDbt34xT2kR3nQqDsagBNskeKFUepr0OkpmF++TFORlfiRxyD3asA\n36izUOtqiP/1GCITHkRbuxL3kw+g7iwl+vfzQUQxF72B0HRip15E7PhzEL4U/BcdidrKccDqOwh1\nd1074AtgHX0G5pcLCE6eh0DF/fIs3E8/QnzI37AOP6pD4BsbejTG6u86Ba9Ot+6dAl8nsztqxbbO\nn+v2ozZUdgp8QTo2+O7ruJEOJGAlHtsj8AXAn75H4AsQO+8WzEVzMb99H8ebSvi2R4j63bje+yf6\njpZzjB1zJcaHs/f8eoCTno3QzDbAF0CNhPDffQ7ha6YTGjkLzytjEem5YPO7gC9A9PxxuGeNI3bW\ndTgZubg+f3mP4wUQHvUo/nFnE7lqEtEzbsL1QeeBG4pj431sFMGJ8/E8dxORETMxPnoF88dPkmOM\ntT+A20do/Cv4Z7YFD+a3b+N0zSF0+RS8r8hUP337atzvPE546ht4pl6Ee+ETRE+7FuugI/FOvozw\nhDnEDxmC8tU3qGlpEjAmXBfU775DpKdjH3MMajyOunYt5ltvga5jFxbi9OtH5OGHpVTB7UYUFMib\nVo9H2qItWID+44+ywa1V2qXdrRvR8eOJX3ABakmJZIurqxFuN7GLLiJ6xRUoqipBbk2N9BVPSUH7\n+Wc8Y8dK2RNIq8IEa2sPGkR00iSctDTpGGEYcuXH78c6/ngpbdiwAfOTT1Bqa4nedhuisBB982aM\nl15CCQQkuO7Xj+g//iHnGLdbJuFpGkJRUADt559R165F37BBMtuJZmrH7yc6fjz2IYegxmJon30m\nWe28PKK3394CknVd9h6kpEBGBvry5XjuvBNl40bSmr83isKAzEzs3r2J3n47Iu+vqDt2IGyB5fUQ\n0Vw0xVR2NdhU1BVRSpQm1aYuFiKmOLgMD35PCoOz9qOrvyu6prMr0khNoJbqYC11gVpCVgxFNXCb\nXtymr3NArGoEhSAYDVISDfLTrgp5jEJg2zFU4eBRdXI9qfRNzaa3P4uevq749hDNXFZWxpAhQzrd\nvq/+32of8/sn1f/C67d5ST4Wi/0udldRlCQg/k+DLtTitzG+bmU4vwXsHqdgXTMXo+z8pNQBQKzu\njfJUcfJ3p2d/rJlvIXr1TzxSg6Y9j6bNQVF2tn0hC3gTeAhY2fKwM3QozkUXseukk4gnGN7U1NQ/\nbFTe/N45lZUoxcVoa9dizJ2LtjLxYmlpUtKQk4N1/PHETz8dtbZWWodpsglNtGJ/CUhNqNO9O2Rk\noG7fjvn662grlks9XUILbB1xBNHRo8HlQt2yBePNN2T4hGGAbuD07El05Ejwp6Bu34a+6BPU+jqI\nRKS+7uprcQYOBFVDLdkBVhzRVbpIqNVVqJUVUFSMffwJkJKCWl6GumoF9qHDcPoNQC3ejrZ1E05e\nD9SijbheforIjROwBx+CEgnjHXcVap3sqrbzCwhPeADvQ+OIjLgFu2c/zI/eJnbCGXiemIJevKnN\nexqY/T6+ySNQEh33wjCJDz+d6BlXgseH+fpsjMVvtWHqAv9+D9/4izsEv4FH38E39TKUSPtmtNhh\nJ+IUDsT99hMdfr7BO2bjevMh9PKOTdpDV03H+OkjjI3tm+hA6lvDtzyF7+FrOtwOEDnpKtRwEPPr\nBZ2OiQ09GZHXD9fCPaerBe5/F9/4Fk0wSJY2POZhyEjH9eHD6NuWE7ztDXwP7FlfDBC66kHMd59B\nL9/W6Zj44COIXjkeJdKE5+k7UOt3djq2uYQvjeDtL+O/U7pHhG7+F0q0Ac+CzlProsdfgXB1wz1P\nyh1CNz6IGqjC/fYje3wtJyuf4MQ3cD15J+aa9s4uALHhZxEffga+h65tty182SSUYAPu955qOecD\njiJ20lVJHXj0uEuwDhiOZ84UQpNfxMnqgbLsV4zFi7HOO1/KGKqqUIuKpH7X55OWZs0sZzCIsnOn\nvPnt2ROlrAzjo48wP5K69iS72b8/TmEhdo8eiP32Q6mvl/MGyJvrbdukzVpCIqEC1gEHSHCamoq2\nbh3ar79i9+2L6NFD3vwmjkMYhpQzpaQgUlIwvvwS1+OPS41w8+eWcLWw99+fyNix8ma7uFi6RhhG\ni0QCoLoabft2RCSCddxxKJEIxjffYM6bB42NLaxtz56Ske7XD+voo1EaGuQ8aBjS07ihQd48tLKQ\ncxK+yrhcaMuWSelH165SIlFYKB1p3G4JuHv1kjcRPh9qURH6J5+gr18vddZNLYmRdr9+hKdNA58P\nbdUqiMVkMqbPR8zjJmDqNBoKu1RByONiuxNkN3EiwkEzTEzDhaKphK0IdeFGdseCRB0LBxWX4cVl\neP5jMst2LEQszOPDRrTbNmrUKGbOnEnv3r3/o33vqz3XPvD7J9X/Ffj9I+yuqqpt5AyRSCQZDuFy\nufD9UWuvUAXm+4e1sL61IAK9id22CKNmJGr4x+RQ8VU6yuutWI4jTsW65yXwp6Eoa9G0J1HV19tH\nDjcBzwKPQ7Mlr9O3L87FF+NcfDGib18Adu/enZSVpKSkYBh7t9JJyhmKi1GKilCXLZNWRzk5cvJP\npKs5hgHp6Qk3hRSUpibMt95CW7pUXpgS7I1jmsRGjZKG9oEm9C++RFu9CpGahuiWheiaid2lC/Yx\nRyPSM1CLiyTQbS5FBVXB6dIVkZ2NUl0lLxqxGMRjkrExDOz9D0CtrUEtLkKtrEAtLkapriJ68aWI\nQYMhlmB+YzGcwj5oG9dhzH0WxecncvEVkJ6BtnEt5mvPo5YUE3z2dZSmXeBNQS0vRf/+C2IXXoHv\n1hEoYdm8Y7ndhBZ+j1qxAwIBPA9NQSsrJnzJKJQUH+65j7V5b6OnXQzZWZhvPo3115OIHX8Bwp+O\n9sUn2Mf9Hd9NZ/Pby0d8yHCsYUfjea596pCTnU9k5Fi8j93a4WcZeHAhvvsu79TFITB9Af7pnbsm\nNE1fiH/que2OqbnCF49H3/gTxqr28pvka0x9B9/0C1Gszh1Sgve8jfeBK1HCnTfMWQWDiR9zEZ5n\nJne43dFNwrf8E5HXA+JR/A+2TztrXUI3CE54C/+Es/Y4DsDO7knwnvm4Pvg3ri9f3ev40HWPYr75\nNHpJS8Na5MIxOAV98Dwzpn0ynz+D0G1z8Y9tK3EKj5oOIoJnfsegWagqobtew1gwh9jld+KdeRVq\nQ1WHY6MnXIJ18FH4Hmtvkxa6/mG0zStwfSklHk5KF6IX3YnV52Bc789BrS7FGnwkVuHB+GZeR2js\nEzjd+yIycxE/LUfXpbWYoqoSFG7ahLJ5E3b//ogjh8vwih070JcuxenVC6d3b5mU2Aogo2mSBe7a\nFbW4GPPhhzGWLpUa/1YSCbtvX+JnnCHT4EpKwLKkRAJQQiEpkdi0CX3DBpQ1a4iffba0ZWtqwli8\nGP3HHyUo7ddPNuw1A8m0NERurmzY8/nQ1qxB/+wzCUjXrUvaowHEjzmG6K23Qjwu3WgMQ86PCReJ\nJGsbjaLoOqJ7dwgEcD35JMb77yc/f5GwYRO5ucSPPprYiBHSx7y2Vu5T1yVIFgKqqtC2b0fZuBE7\nPx/7pJNQGxsx3n4bY9Ei8HrbgG2nd2/ZmLjffijV1WCa0tKxoqIt2N64ETUWI3bSScRGjYJoFOOT\nT1CLi7H79UP07YuTnY3t8xF2GTR5pA1ldbiRciVGnUtllx2hIRYkLCziikPMtokLB6FomLoLYw8O\nE8nvZ2Q3Tw5rL204/fTT+eyzz37XtWtf/fHaB37/xPpveP22jhGOx+N71RHrut5Gu9v6jrV1ypth\nGH/MXDtchbHoJNTdCbYvBmKzi/jo19Cde1Ejq1rGvg20kgJaV9yJfe3dqMYiNO1pVPVr2lU5EvA+\nAzQiU44uuADnkksQQ4e2y5gPBALJmwufz4fL1X4SapYziEAAUVSECIelLra4WC4zbtuGltDJ0dRE\n7LrrsI49FmX3bvQvv8RYvFg2oXTtipOfL5cV+/SR3dz19dKKTNPAtqUWV9PkBS3RQe1kZSLSM9CK\ntqN/9RVKbQ1KIIgSDOC43cQvuQTRqwClugpj8WKU2hqEoSNMF9Zhh+P85RDw+mRYRdNuaZPUNRMM\nHXVHMeqOYvSflqKUFBG5axL24APRKspRdjcirDhO70Jc78zHfO4JREoakVE3Yx93Mur2LZjvvI7+\nzWfYffoTmfgAvttGIOIxYhePIjb8JERud8xP3sL1zENJP10nK5fwtEfx3n5xG9BoqyqhN5aibV2L\nk9YV/bvPMV97GtWyCN77b1zvvYy+uj3DuifWN3j/K3ieHo+aaJBsXY7XT+S2R/H+s2OXkPiBw7EH\nHYr7rUc73O5k5RM57xa8z4zrcDtA07R38E/rWGsMCVb2+sfwPdJx3DIkQOttc/DN2HOscOCe+Xgf\nugl1V+dBGwBNY58CTUP1e3HPm4ZW2TGrGz35WqhvxPX1m3vcH0D4xkcwXn+a+GmXIbKz8TxzG0os\n0vH5dMkjNOpR/JPaM8+xv51F/KQL8M66BqWVfCJ460t4np6MWtXefzB85d3gMfG8OrXN4wII3/Rv\n9M/ew/xxMU5qF0LT5uJ9dHSH+wGInj4Ku2A/vE/f3nZfnhQCD30GlTtQNA2CIfRVS1GadhE7dxTa\n0k8R3fIQ2T1wPD60rashIwtheBAZmTipmWg//Jjw03Wh7mqQqz/xuGx+S2qBTRkFvmMHyrZtSUZU\nCwTQVq7E+OILGUzRv7+MSk5NlXOE2w3Z2VLT7/ejVFbievZZ6emd6Bto9uy1e/YkevPNOIMGSdY2\nHG4Th64oSrLRTi0uJn744Ti9e6OXlGAmVrVERoaUZzWz0b16Ye+3HyIzUwJTjwcCAdSKinYNe+i6\nvNk/+WSU2lrMhQshHJaAtKCgxdXCNHHS06WkwTBAUTDfeAP9yy8l2G5FCjmmSeyqq7AuuACluhp1\n2zapsW4G260s5JTKSinDyM9H3bAB16xZ6AkNcWuwbffuTfzUU7EPP7wltU9VEZom5WA1NWjbt6Nu\n2oSycSPWqadiH3ssys6dmK++ir52bVJG4vTvL6UtXbti5eRgZXejsbaKes2hjjjlusVO3aY+HqLR\nimAJgVBUFFXD0FyoqkY8tItZR7R3lNnn8ft/W/vA759Y/yn4dRwnaUP2e7S7zTZkuq7vMaoxHo/T\nlFgu0nWd1NQ9R2EmK1IjgW/jBvm7ALaAdeJ1aN1eR3FalqCYDyTIMpGSjnXXdJQTdqIpL6BoHTA3\ny5CgdwEIw4tz5pnYl16KOO442VTWSQWDQaJReZH1er243TLNJylnqK2F0lL0X39Ff+UV9GXLUIRI\nJquJ7Gysgw6Snp2KIpkWIZJaNBI/SigEu3bJZoy8PNSaGoyXX8J4/33UaMtF3tF1Ytdei3XyKSiN\nuzA+/EA2d5guhFt2cDu9C4iNGIESj6OuWS3T3hIsrxKPY/cfgHXMsajl5RjvLUymrdFQT+z6G4if\nfCpq4y6UbVsReT3kBSYzE7W8FG3LJvTPFqH/uoLITXdIzd2GNYiBB0A8hpOTh1pahPeuG1DCkumx\n+g8iPGUm2sql2AcehtpQj/HRQmLnXIS5cC7m95+1ec8DL36Ad8JI1F11CI+P+LFnEB9+ClZ+IebS\nL3HNnoEabQFOTnZ3ImOn453UXjoQP+QIrCOPw/Psfe22OaZJeOpz+Ka1D7wACI55GGPtd6jVZTg5\nvXByCxBZ3XFcXjBcONm9UJoaWpLSmhtSFAVQsLtmo+6ulyDPseWPHUexLfkcK47T5yDcr96LVrpB\nxib/5m8wPGIK+sovMNZ2vBwPEL5sIvrqHzB+6Zw9dnSd8LgX8E3v+FyT41LSCd31LP5xF+D4Ugnd\n/SSqHcT96hTUxpq278/Et/FNPG+P+wNwUrsQvv1ZfOPk2PjAIURvmo77hXHoO9pr70O3Pof7qYlt\nwkxaV3zAEKKjJuN79EqUYCOxv56D3XMInjmTOj2GyMW3I7KycL84IXlDFR4xBaWiCvfCFgso4Usj\nOG0u7qfHdWqTFr1gDHZGFt4XJuGkZBC9ZDx2Xn9cz83EOuVilOpy3HNbnCaswkFEbn8I791XojbU\nYPfoQ2j84yiV5YjC/oACoSZEz36IjVvRt22R0gK3B+FySYlKxU7Uulqc3gU4mV1Rm5pQd5SgNu7C\nye8pm8HcboRpoGg61NailJdLHWx2NmpFBcaiRehffIFIT5eAa8BdxvrXAAAgAElEQVQAnL595e/p\n6TgFBbKx1e9Hra1F++ortFWr0NeubePZa+fnE546FZGbi7Z1K0pNDU52tvQvbgUklVAI0dSEKCgA\ntxv9889xz56NWiO/R0LXk2y01b8/8csvR6Sloe7YIVlskHNjNIqyc2cLgVBZSfz663F69kTbvBnj\n+edl/HMCkDp9+8rgD79fuk4Yhpz/3G7U9esl0N60CW3t2qTHsuN2E731VumoUVqK/sknsumvsFCC\n7eZkvUQjovB4EOnpaGVluGbNQvvuu6TkDKRfs5ObS/T667GHD5fSkECg5Samma2PRlF37oTSUpwD\nDkB064a+ahWuOXOk7rh1OEqvXjj9+2MdcQT2oYdSHQ+xoraE0lAtVbEm8r1dufrgk9t8V23b5owz\nzuDbb7/t9G9jX/2/1T7w+yfW7/X6/W+yu3sq27ZpbJTNOXtKeWtTkTqMRSeiNiYuhgLYDk7BQNRD\nW2yvsIDXgB/kr87woYhxftTcr1HU33wFLSQ7/DiIZRrOCSfiXHihdGr4nabj4XA4KeFQFAVdVTF2\n7kTdsQP9559Ra2vlBaYVGyEMA5GaKidMvx+EkEtrH3+MumlTG0bCarYlSklB27wZ/eOPJGjOycHp\nlg2ZmTg+n2x8C4VQ6uskyIpFk3IG+a+K8PvlRdDjRikpRd1Vn6BzEmA8NxeRli6bWyp3yguC4yB0\nA9EjH7W8VDI6VTvRNm5A2b6V2NXXgd+H6+EHUHfuxBp+NPGjjsU5+C8oNdVoO4rQF3+E9vMPhB96\nEnXbRtz/fggFsA78C+FLr4EB+6Nu24T53gL0H75CsW1Ckx9E27EJ14K2iWeh8TNRK4vB48Me9BfQ\nXegfvgU1VTgnnopn5p3tPqPg0wvxTPsHan1Nu217Yn3DY2agL/0ItbYCu/cg7IFDEFl5CLcPx3Aj\n0jLRtq5FK9uBumMravEW1B2bUWMxnNx8IteOw/vALR1+bxzTTfi+5/Hd1bl0IHD/SxgfzUN07409\neAgisxvYMZRYGCXUiFa8jviRZ+ObfNYeJQ9N097BP/GcTqUVAOErp6Cv+Abjl6/2MErKBIxFb6Fv\nbWl+c7LzCd/1KGrVVtzz70OJBLAGHE7s8HPxzr5rj/sDCN/wMMb82W0aFB3DJHT/qxjrv8b84Knk\nsVs9BxE9+w589+/Zg9jJyic0cQ7uF8YRGfkg/ttP3+txRM65AdG7EPezdxA7dRR2lwK8T93dbpxw\n+whOfwXXS1MxOml0DF91D3a/g1HiNq4nJ6Nv39DyOleOw8npgfefLVHVTnomoanP43pqKsbGXxAu\nD6FJ/0b79SeMLz8gPHEWdo/eKB4fwhEQjqFWVyLSMhAeN9q2behLFiMyuuDk58vwGZdbWhQGAihb\ntqKVl2PtPwhRUIgSDMrm2eIimQKXlYVwt0gKFMdBNDZKhjMtTQbivPwy+k8/SeCZkyOX/Pv3lyEZ\n++8v0+OqqpLNbWpZGWrCllFbu1Yu/zsO1rBhRG6+GQwDfflyqSFOyAiS86Jp4pgmpKbKOSs1Ff2L\nL3A984xMnGv9efj92IMGEb7zTkhLkyyrEEkJWbMrjtrYiFJSgtrURPyII1DicYyvv8Z89VXpgJEI\nEGm2fbP698f6+98luK6tlZaR8bgEpBUVbVwt8HikD3FmJtq6dZivvQZuN3bPni0Wcn4/uFzYvXvL\na6XHA01N6F99hbZmjWSjt25tWeHyeolOnCgJhC1b0Naule/Rb1w/0HX5Ge/aJW9Y+vRBdO0q35vf\nwC4hRPI6LYRg69atzJgxg4ULF+7172Nf/We1D/z+ibUnr98/GiPcWru7J3Z3T/XboIuMjIw9A+do\nA8Ynx7cFvkUgemSgHN5AciasRup0S0D4TRijopwdod1VfyfwnBzr9BqOfdFFOOec84eT1oQQRCIR\nYo2NmBUVqIGAbCCrrpa6uK1b0TZuRFu/HlFRgX3mmcQuvRQcB231asz58+V+unXD6d072Y1sHXCA\nZDgqK+UyomWBFZdShbo6lIpylLIynP0GYR96KEpVJa4Fb6AvWSLHJsrRdWKjb8A67jjUnTsx5r6M\ntilxo6AooCjEzzyL+Hnno5aVYj47B23rVggFURwHa7/9iE6ZjrJ7F+ZjD6NWVuD0LsDuWUD8vPNx\nBg5Cqa+TjXAheWz2wYegFW3Dc8+dUiIBOOldCDwzF33lT4i8fJyMTJTdjfJz9Hvx3XwlSiumNnLV\nDYisrnhm3Sufn9GV2Hkjif/tRCnf2LoB10uz0X+R2m7HNAk99za+0ee2A4Gx4SdiDzkcz9Ptmd3W\nrK8ARG4vrEFDsQ/8K3ZGJiK3N2pjHcrOMtRff8ZY/h1aufT+Dd86XYLFHz5rt1+AwGNv4H3gFtS6\njtnJ0ITHMD94BX3dig63O6ab8LRn8U3o2H7IMU1iZ11N/ISzUONhsKIojVUYy5egr/kOJSTfeyu3\nD7FTr8X7zIQO95M83nvfwTd+zwBZGCaBe98g5baOE92sAQcTuXEq+sYfsAsOwDNzFGon0oXkeaRk\nEB77XJL1/W1FLr0VZ/AheJ66ESUSIHjX63juuwa1g+bDdvv2+AnOWoz59hxci+budTxA5LSrsP52\nGkpTE75pnctEhOkmNPVlzLcexVj3Y5tt1n6HERk5FXXtCkSXLHz3Xd/u+dFTL8Y6+kw8Ey5tsfAy\nXYSmPIv+1Ye4Fi+QnsJX3oFVsB/eidcQu/wW4secjnAcyMyRK0P+dNncFY9BIAg+L0osDsGgDBHx\neCEQlHrgbdsQqSlyWd7jkWDX0FEadqFu3oS6bRv2AQfiDB6MEgyirV6Ntnx5i09uWppkb02zRXPr\n9UJGBtr69bhmzGhZ/lcU+Tp5ediFhcTPPhv7gAMka2tZUp6lqjKJrrxchlokmsis008nft55Mn75\no48wli6VgRh9+kggmZcnpRppaTj5+bI3we9H3bQJ/euvJSBds6aNzaN14IGE774bxTDQli+XVmv5\n+ZIQaI5rbqV5dXJyUBQF19y5kjluNa8Kv182IA8aRGzMGAn0S0tbki8T743S2IhaVoa2aRPEYsTO\nPhsV0L/6SjbthcMSbOfk4PTpg52wY7MPOwwlGISEPE5paGgB2xs3Ska6shJSU2XS3imn4PTti5KX\n97uuyZFIhE8//ZQFCxZQWVnJjBkzOOqoo/b6vH31n9U+8Psn1m+9fpvZ3Vgstld2tzlG2DTNP8Tu\n7q0aGhqSd6Xp6emd/tEqjZvQP7sANZBYYhRAMYi+CspBogXY/oxkfCPA34C7gd/a7H4GPA1OxRCc\ncy7EPvdcyM//Q8edlDPU10vvyV9+wZw3D/2HH6QxPYlUpOxs7MJCoqNHI3JzZXNYPC6X8hKTpAJS\nR1taCi4X1qGHogQCko14/fU2k7dQFJysLKK334Y9ZKhcevtlpdTspWdITbChI3QDZ8AAaZ3VuBsF\nIS3OIMkEC9NEpKZJ2zPHQamrBduRb64QiMws6d/btBulqQmiUdnIEWjC2n8wihCYLz2LvvR7qR8G\n4n87muitd+Ca9S+0zRuwhh9D/NC/YvffD0XTUMtK0JYtxfxiCWp5KdELLsM6+hi8465Pvm8AseNO\nIX7OhWjrfsU+7GiIxVAry1GX/0z8/Evwjb5QJkK1quC/5+H69/3oW9a1eVwAwec/xHfzOW1AsXB5\nsPrtT2TSE6glW2Rks+FGqarEWPol+jdLiNxxL+YH89B/WdruO+DoOqHHXsc/pmP7MScrl8hNU/BO\nb9/4BIlEt4fn47u980a40PjHMN+bi75hZadjArPewTf+yqSrheNPJXbKhVhHngC6ihrahZ3VA+/T\n49G2d8xQAliDjyC+/3A8r+45qS1y3o2oZSWY33QcxtFc0TNHEj37KlwfPIP52Wt7BNSh0Q9hLnim\nTeNau+Pr1Z/InY9hLP8Yu0tvvE/sOQCjueJDTyA27AxISUPf9gvmgsf3eCwAdl4hwXGzUeMW3vuu\n6lRaAbKhLzTlRYxFL2Gu+EyC1cvGY+cPwnP3SFTHIX706cTOvQbPnRe0AVAA8b/8jejIO/GOuyB5\nkyAUhfAtMyEYxDtH2qPFhh5NdOQ4fHddifCnEr7rEfSlX2IfMgyr/2Dw+EE44PJAOCQ9wR1baldL\nSuS8k9ddzhFuD6gKys4KlPp6nN6FkJYm7dRKSxCKiujSRS7hJ3S8yu5G1K3bUDdtwho4EHHIIbIf\nYelS9G+/lUzpwIGyuS0lRQJTlwuysuRcl5qKumMH5uzZ6N9+K0mC5vfQ78fu3p3Y9ddjH3ooammp\nBPOtvMwVVYWEhljZuhX7kENwBg1CKy/HmDtXstEJQOokUt/sggLZTFZQIIGi2y0Z28pKlJKSJCmh\nrl8PloV1xhnErrwSQiGMjz9G275dgtE+fXBycpJMq+P1SpLEMMDjkXHNH37YDmwLEo46d90lyY51\n62TDnN/f1qVDURA1cg51BgyA3bsxn3sO8+OPk0SG8HqlTrt7d5zBg4ldeSWiWzeUWAy1Rw/5/uyl\nHMfh+++/Z8GCBaxdu5aTTz6ZESNG0L9//70+d1/9v9U+8Psnlm3bhEKh/ym7u7dqbGxMstEdWoQJ\ngbrh3+jL7kKh1V33DlAGA81/szGkvvd7YABwMzCs1X7KgLng/DQQ57AR2OedBwUFv/s4hRCyYc22\nEaWl0p1h+XLUzZtlc0VubovZvGnKC0xCX4fbjfHee5gvviiX21rt1zFNYjfeSPyEE1Dr6tB++EFO\nrt27I1JS5ORompKhycmROmCfD6WyUkYYl5ZINqC0FLW0FHvgQKK33ILiOOhLFmMuWIASblnKd4DY\nqOuwTjsNtWg7rqeeSPpzJrffOR5r2DCMzz/FfOE5lFZa4sjlV2Kdcy7GG/PQV/yEU9gXu1chdkEh\n9mHDZANUeZm0XKqpQvtlJfG/n47aUIdn2vg2jHTkxrGI7rm4p96B0HXs4ccRP+5U7P77owgbdfNG\njE8/RP/pe5RoRDK7r7yH96ZLUBtbnDsAomdejCjojXv2zHafXfjGSWg1pSgVO7AOOxYntyfC60dx\nZICBvuw7zOcfaRdO4GRmE54wA99dHS+thyY/hvnRfPRVP3a4PfDwPLwPjUOtbt8kBxC+YQr6r0sx\nlnac+OYA4UcW7BEcW736Eb/wejz/7DitDcB2ewk98Q5KYx0YKlrpRswlr6L9xnYtMO0tfPddnWSL\nOyoBBGe+i/+2szsd01zBKc/heXgC0b9fjH3kcbje+Jf0w/3teaZkEBr7LP5xew/KcDSNwAvfo/+0\nBM8L0/boiwzyBid431t4R58mwyRGjMEZOBjPwze1aYRr8xy3l+C9C/DeeiG4PYSmP4/rtX9irG5/\n7MnnqBrhic+i/fol1l//jvbVYtzvvdRmjNV3fyJj/4V3stT0ti67Zz/Cdz3eblvkgtFYg4binXKN\n1Jx26UZoyhxcLz+GvuwbItdNwOl3AMabLxAbeSt2agaK2yOdOJp2QywOuxpQXB6IReSyvcuFSM8A\nRUFbvhxt6Q+IPn1wsnOSMglFUVB2FKMtW4a6cSP2iSdi/e1vEI2hlpagBILSQcbjQZgucJlyW0kJ\nysaNkpndbz/pkvDpp+hLlkjNcM+eEiAnmuyEx4PTrx9KNIrw+VDq6tAXLUL/9VfpQ1xX1/LZp6YS\nmTIF+8ADpRtDWVnLvNs61CIUgpoaRK9eOF26oP/8M+4nnpBsMwk2OitL6mMLCoifdRb2gQdKmYTj\nSMcdTZOEQFUV2rZtqAlrtPhZZ8kVtKoqzNdeQ1+1SgLSHj2kZKOgQJ5nohFO2b1bOvQ0yz42b0Zb\nt07uLyFrix17LPEbb4RYTK7ahULSQi4vr9254TgoloXo1w8KC2VQ0O8gotasWcOCBQv49ttvGTZs\nGJdffjlDhw79U/z///9a+8Dvn1ihUCipse2omtndPcUI/7ertUWY3+/HNFvFRYYrMT69CLWhVWe+\ng3RiGAr0SDy2HngDKXsYDZyc+H8EeBecH/rj5F2Bfda5UFj4u48tGTYRCsGOHVBbi3C7ZXRvWRla\nwgtTW7MGystxDjuM6A03QMIH0pg3T5q0N0eGFhQgMjNl00j//lJf5nKh2LbUwRUVyYl282bUTZtA\nVYmOGYN12GGoNdWYCxagf/WVXHJMT0ekZ+BkdsUaNoz42edINmPnTsmCawlmWdNAU3G6ZspJOBKW\nbO7u3W0cK4RuyIAKTUeJhGUghSMkkyQETm4eSjQiGepgUFqg1VSjlpViHXEkoksX3NMno21cn2TV\nnMwsgrNfwDX3WcxP3m/5CHO7E5o6E6ewH2rVTpRwCKVxF9ovKxCWhX3yqXhvulIuY7aqwCvv4n7g\nLvRtbf18ndR0Qo++gO/G8yRj3b0X1kGHYx98OHZWLiI7D7WqAm3ZUoxP30crlRdBx59K6LEX8I0+\nv0MmMPj0W3im34RaU9lum+P2Ep75HL6xl3b43XG6ZBG5/X6893TsvuAAoVnv4BvTucQg/I9J6GuX\nYXy/uJMREHzkTTzTR6M2dO7MEJz0JK43n0ff8AsgAXN05Bic7By0+gqML99E27aa8A2P4Hugcx9h\nkC4KTk4h7lc7dq5oLju/D5Frp+CbILvKHVUlfOfDkNUV9wuT0SpbIqNDox/CfPMZ9B2ds77NFTl/\nNOwOou5qIHbxtbifvAO9rH2ISXOFxzyK/s6rGOtbZCXxQUOI3jQVzyM3olWWtBkvgNDkubjmPIi+\nLbF0rxuEJz6JWrQG95ud+yNb+f0JTXkBfeUPeB9przkHcDKyCN37PK6nJmNsXtV2W3pXgtNexDNr\nPPp2Ke1yunQjct0UrP2GoG1eLd1bDBf2oCEoZUVopdtA1bCGDMd8cRaKYRA/8WzJ5vbsjdOlG0ow\ngPB4JXiqrkJtqIdoFK2kFGX3btmw1TVThtHsaoRQQKYx2jbK7t0o9fWJGHOP1A/rOkptLdraNejL\nlqOsXIF9wgnELpfx52pJKWpZqZQTNPsQGwkJQEMDSnGx7FUoKEApK8P17rvoS5bIdMrcXMlsJprs\nnJwc7IMOkp69qirJkGYf4vXr0daskUQE0sM4Mn48Tq9esi/iiy8kY9usIW7utTBN8Hiks0WXLlLH\n/OijaCtWJHW2AMLlws7NJTZ6NPZf/ypDhUKhNjaUwjCkzraiAmX7dpyDDsLp3h190yYZE795c0sz\nWl6ebEbr2xfriCNw+vRBLSmRshXLQrEslISnsbpxozy3HTtwDjuM2HXX4QwejCgsRPF4fhcZVVJS\nwoIFC1i0aBF9+/ZlxIgRHH/88XtPTN1X/ye1D/z+iWXbNtXV1W0e+0Mxwv8H1doiLOmS4Niom15E\n//kOFFppBUPALuBIoAtQiQyeqAZGAOcDOogvQSzrg+MZgX3qpdCr1+8+nqScoaEBKitRf/1V3uF/\n913L8pPLhcjJwcrPJ3bNNUkfTCUclhOrqsqJPhhEKS9H3bgRpbYW69RTEd26oZaVYcyb1+L44HJJ\nvW+3btj770/sask0qiUlkoVI7A9Nk4xEIACNjTg9e0JuDuq27bifegr155/a2vZ4vUTGj8c+4AD0\n1atwzX4atart8q11+DAid9yBUlOD6/HH0De3BZbRCy8ifullGIs+xnzh2TbShPghQ4hMvgfzzfmY\nC+bJJTuA7vlEz72A+OUj0datRnh8UqsciUIkgn3gQZhvzsN8/22U8tIk+IsdewLxS0fivWVkG4YY\nIPjIM5hL3sX44uPkY3bPAuJHHkfssuvQqsohFkWYbpTKnRjffoH25RLCz76O9+bLZVPfbyr47Fu4\n778drbyk3bb40COxjjkFz2Mde90GH3hWsm9b13W8/V+v4J41Ea2i/b4BIhf+AzXQiPnJ/A63AwRn\nvYP3ls7BsZOZS+SGe/BOa68lTY4xTUL3vYT/jk5Auj+V6KU3ED/uDNSGKlxvPoH+y1edWqoF738T\nzx0XtGPJ242b9hKeB25tk7gHCZeIe55CbarB8+I90j937HP4O9H6ti7hTyMwdS4pN0q/YMflITTj\nRbTNy3DPf6TdMVv7DyN6ylX4pv2j/Xl7/YT+OQ/X+3Mwfvgo+Xj4ykko5RW432nbYCmA6FXjsHv1\nxfdg+/1ZAw4h8o/78d5wLvFzriD+1+Px3nVJGzCV3JfLTWjqM+hff4jr07aBJMKbQmD2YkRtJaoj\npN718w/R1q4gMv6f6F9+jPvNFwGI//UYoqPuQPviE5RQCGe/g7AHHwSREKJwANTVoG3agOiejzBc\n0FCPyO2OsmuXBLIpqZLttOKI7FyEpqKvWI721Vc4gwbh9OwlmWCPByUURluzGv3rr1G2bCZ21dVY\nJ50MtoVaJa8pwu0GXUNBQSkrRV21Gn3lCtQ1a3AOOojojTchunZFLSlBW7lSkgHdurVhNxVFQdTX\nSxeLvDyU4mJcc+agf/+9nCtbOT84/fphDR0qfc0rK6U+1jAkkAwEZKPdhg1S1rB2LU7fvkTHjQO3\nG23FCoyFCxGpqVJn269fkmkVLpeMlUZK15SaGimBWL1ayhpas9FuN9FJk7CGDJHExaZNOD17tjTs\nuVwIXZe2drt343TrBl27oi1fjvu++9B2tgS5CNOUNwU5OcRPPpnYyJEQixE1DOxWAVCqqqIoCqtX\nr+aDDz4gNzeX/Px88vLycLvd/PDDD3z44YekpqZy6aWXcsYZZ/xHAVL76r9b+8Dvn1x1dXXJKOH/\nFbu7pwqFQkQSWlS3y8RfsgB9+WQUp67twGqgOzAYCAMfIBvWLgVOBLFKQazoj+26Aue4EfA744WT\n3rvNcobiYtTly2VEcHPmfNIeyJQTfOKCgNeL8cknmLNmoVW2ZQcFEP/734mOHi2Z3c2b5WSalpbs\nYm7u0CUWkzKJnByUhgZcs2ejv/MO6m8N+lszG5s2oX/4QYvjQ1aW9P91e3AOPFA2X9TWIhCyM1lR\nZbSwogIC4fVBWpqUKWxcjxIKS39gy5L+vdnZ2P36oYQjaNu3InQDTB10E8c0IC0DxY7LZdR4DGLx\npAbXPvhgjC8+RV/0EVpxEUpVJYoQOPn5hGbNwT19IvqaX9qcW+yU07DOvgDPrde0AdiOrhOecC/O\n4INR62sRHh9KJALBAGpFGfbQwzEWzsN467V2gCz46LOYC1/FWNrexzl6xoWIXr1wz/lXh9+LwAsf\n4LvpfJRY+6VxJzWd8OTH8I0f2eFzndQMwhMexjepcyeCwJPv4bvl7E5BZuScq1GsOK4PXul0H8EH\nX8XzyATUyo69ZgGCEx7H9e7cThvqQALB8LQ5eMZfQ/Tq27D/chhqVQnme8+gF7WAe2vAEGInXY73\noY6DPpLjCgcRvWwsvsmds8hWwQAidzwIXi/uh25H37Z2j/sECI57AtfcJ9CL2zLE0TMvJ37iWXhm\n3YpWXQYkmvLuX4jvpjM7BKDJfU58EnV3Fe4X7yV+xN+JH346vuk3dDo+ftRpRC+4Du+ki5L63PjQ\nY4leMAbvjecmX8va7xAit9+P5/7RyebI1iUUhfCtMyESxPvMdOl7femt2AMPQf94ISI3H6ffIDx3\nXJnUCEsAfiv20OF47hiJGgogdIPITZOw+wzAO/ZaFE0jcts92Dk9cM1+iPhp52EfcnjCwcENkbCU\nKYBsUK2uRPGlIFRNsqlbNmEPPhCnoAA8Xpn8Fg4jUlKkDGD3bgiFWlwkEo4w2vLl6N99J+c5lwv7\nkEOI3DIG0asnSlk5RKPgdoEqvceVnRWo69ajr1qFunIlTn6+jAzu1g21pATj44+TALe5Ma+1z65w\nuSSQrq/HfPhh9CVLWhoGQa6M5eURP+ooYiNHyjTMmpr2gRbV1bIhef167ITXuWJZ6J99hmuBvDFx\ncnNbZA2FhThduuAkXHWaPdXV4mLpaNFKQ6xaFk7XrkQmTJAs78aNmO+9J+3j+vSR0javV55Lgo0W\nloXw+Yj37k18L773L774IhMnTuxwW1ZWFhdeeCFPPrnnJMd99b+rfeD3T67/RtDFf7MikQihYBDP\n1ldJ3TgTlYa2A2JIxvdwpCXZl0g5w0UghIrYNBjbfyXO8Mvhd/oEt5YziKIilGY5Q1MTSkUF2tat\nqOvWoa9ejVJRIfPpb7kFkZUlPW8XLECtrpZNFQMGyGW1tDScZv1aPC4nattG//ZbaXW2bp2UMzRf\nHAcMIDp2LKJLF7SiIvS335Za34IC6faQlSW9eDMypHasqSnpq6kWFaFUlKMWF6MV70DdukUazo8d\niwLoixZhvrlAgsRWZfXtS+SeqVLP/cZ89B++b4lDVjWEoRO5eQyibz+Mdxeif/+tlB7EovLihUL4\ngZlgGrjvmyp9gVt/lpddgXXmWXgm34W2ra2eNHb6WcQvvgzvmFEoraQ3jttN7LKriV96BdqyHxB5\n+QhVRYnGJEvctx/6+jUYC15F27xBLtkmKnzXPagNdbheaD/BR8+9FKewEM9jHfj2ut2Enp6P7x/n\ndAg+IyNvQWmqx/VexwljwYdfwT1rMlpZccfbZ76Ie859aCWdhD6ccC5k5eKa/1SH2wECT7wnJRGd\nADfHn0p4/OP4JnbuROCYJqH7X8Y/9pJOxwAE738R15yZ6NtbWH+nSxaRmybi9MhH274W17tzCN8w\nQ1rF7cW5IXjfq3imXo8a6jxFDsDO7Ulw2rOoVhTjy4WYH77c6c2A1fcAopfcju/ujs/XSUknOOMF\njJ8X4XrvGcLXz8D4chHGig4CbH5TkdMvwzruDBy3n9TRe7dCs3r1I3zXY3gfuQm7/yHEjj4f7+2X\ntrv5Ev40gvc+g/H527gWdxw5Hb52AvEjT0Gpr8HzxP3o61tuCq2BBxEZdz+up2dgLG8JH7B79CY8\n6VGMDxfg+uB1+Vh+AeHx/0T/6TvcLzyOk9Od8B33guPgmTaO2CVXYw07Cu3n7xGagTPkcBlBvnkT\nIq87Ts9eKMEQ6oYNEjjm5kE0hr5kEerWLTiHD8PJzkZ4fcRMjHMAACAASURBVLJxddNm9M8/Rfvh\ne0R2DvHzziN+7vkIVUGtrEJ4vSi6hrJ1K9qvv8o58JdfUB0HYZqyue2aa7CPP0HeHO9qlHNmcxNw\nYyPq9u2Sbf3lF4SqEh03DpGdjbZ9O8brr4OqytCHfv0Q2dktzWgZGUk7MYTANW8e2mefJS3Wkp+P\ny0X81FMlQREIyECLZteHZoJC0+R1oawMRVGwhwxBqanBXLAAI9GM1sbRoqAAe9Ag4ueeKyUjdXUt\nWl3HgcrKpIZYX7sWEQgQv/pq7OOPl+Ec3bq19Jc4Trt/W9eMGTN44omO49QBrr76ap5//vm9fp/3\n1f+m9oHfP7l+r9fv/6RC1SjfTcAofRNF/030sg00AgWAG1gO9ATRw0AED8XqMgpx6HnSc/F3VIdy\nhrlz27oz6LqUM/ToQfyqq7CHDJFdx8GgfJ3m1LSGBgk8169HKSoifuqpOEOHotTXY3z8McbHH0M0\nisjKkqxBYSFOIonNyclBLS+XVjhCSMPzmhrUHTvQNm9G3bABJRAgevvtOPn5aEVFGC++KLuEAfx+\nyfBmZmIdeiixK65AbWhAKS+XXr660SoYQ0NoOqSlSs2faaL+uhKtvBylrh6loQ6lvgF2NxG7fASi\nZy+MV1/B/PgDCAZRE++LA0Sm3YvTvz/uB2eir5YXaEdRZPxyt2xCT85BK9qKufhjnIwu0me0ayZO\nairO/oMhLR2lvAzicSlpiMVQYlHsAw9CW7sa48P30LZtkR7CCdAevnMS6Bqef05r93lGL7kSp/8A\nPPe39191croTvu8RvKMv7hBMBZ96DdeT96Jv3dj+uYZB6Mn5+G48r43cQOg6eHxYPQqI3XA37scm\nJW4c9ERak5SlOF4/sVF34n7sbpR4DKIRyR7Hool/IwQfXYDv1vM79eSNDT8Fp2Ag7lce63A7QHDq\ns7hefjSpDe2oQnc9hvnRPPTVP3c6xumaTWTM/XjvvrbTMVafgYQn/Av8fswP5mIumtchIw5y+T96\nznX4OnG4aHMO/5qHZ9INqLt3EbnkH1jH/x3Xm09h/LikzTgBBP+5EO/Yi9vIejqqyOVjsIcdhYjE\n8N+5Z9Cf3L/LQ9MjC1F21aNvWonn5Yf3/hxfKoFZ7yJCAVKvP7PzcYpC5OapOGnp+Ga2+PkKIHbJ\njcQPPwnz1dnErrgR1+yZGMvbhpQIwyRy5wwclxvPlBtb2E1FIfqPO7H2PwTvHSNRIxG5z/NGEj/1\nPNzTbkcv2oI18ACiYybJ5taZE7HOOJ/4mRehbt2M/tbrxC+7Gqdnb7SVK1C3bcY+5gScLl1RS0sx\nPvkIp09frIP/IpfxAW3tGohEcI44EpHRVfYGRKKIjHQU20H7ZSX6N1+jffMNSiSCyOuO3bcv9kEH\nYR15JE7ffij1dQjdQNE0tJ9+Ql+6FG3ZMrnqlnhvRGYm8dNPJ3bVVRJ8VlbKOVjXZZ9EwvlB27IF\nde1alNpaYtdcA5mZqJs2YT7/vNQzd+8uE9H69ZOreD6f/DclRbK2LhfqypXoK1eir1uHumYN6u6W\nhs/YyScTGz0aJRRC/+YbGc/cs6d0s3C55CpeoklbaJp0X4jHMWfPxpg/v83qXbNczu7TRybjHXSQ\nDBjq3v13rcA6jsPKlSv5/PPPqayspGvXrkQiERobG6murmbnzp2Ul5dTVVWFEILJkyczffr0ve53\nX/1vah/4/ZNrT16//5MSAnXDa2g/TkBRapJhV8mygQCQDwSBJhCpXpyux2H3ugkx8Oh20cIdv0zi\njtlxEDt2yIn1p5+knKFfP6nLam7GaJYzuN1S4uD1oi9ejOvxx9vLGRQF68gj5RKdx4NWVCRlAl5v\nm6x5olGUigoAnP33RwkE0L/9FnPevGRyEZA0VLeGDZMMRCyGUlYmz9EwWuQRmiaX2erqED164OTm\nom3ejGvGA+ib2up0IWGvc+ttEIlgLngD/dtvEV6PPE6fH+HzYR0+jPh558oGko0b5MXFNGVzimni\n6DrOEUei7qxAKSuVzIUg2QQnBNjDh8sL0Ib1KLsaUBp3odTVoTY04OR1J3rNtbj+PQvj8yVtrMkc\nXSf00jz0JR/jfu2ldscfmjYDpaEWz5PtgUj8yKOJX3Q5ntuvbaeHdYDQ6x/hvXkE6q6WVQQnNR2n\nZwGxE05D7H8gxqKFOJk5iK5ZiJQ0ec6Ggd2jADUShuBuebOjyB/FcSAcxs7vjb56RTIFD9uWzHg8\njmLFiZ10ptQlqyp4/fI9d3mk64dp4uTkybHhANi2BMBWTGqio2GU+hqsYSfgefxu1KKNKI317c+x\nWcc7rmMdb/P7G37wNXy3tY/+bV2BR97Ae99tqNUVne8LCD3zIb7rziF20lnEz70MtX4n5ltPo29Z\n02ZscMZ8PBNG7pUdjh97JtaAoXgen9LmdaJ3PIBd2Af3C/ejb5G2bNEzRiJ0P+55e1/CFaaLwKx3\nIBrBWPUDrlce6ZQ9h0SD230v45r9EPqmNUTPG0n8lHPwTr+uU29mgOjpI7AGH4lasg374EPxTrhq\nj57DsWPPIHrhKHzjL8XJySdyy/3oiz9I6neFbhAZdz9Oegaeif9oJ9WIH3Ec0WvH4r7vNvTtLbIP\nq6A/kQn/wnjnNfSt67H7DMT6yzCsE86EkiLUuloUx8bJ742wHZRYVILPvB4IXwoiFEKNxWRTnG4k\nmto8KNU7k3/vols2js+PvmIZ2urVUnObWLLHttGXL0f/4H20khIJlv/yF+yDD8beX/qUJ50c6usx\nn/43RkLSJVJScHr2xB4wQIZj9MjHPvBAyaY6jtTmLluG/v330tlm48YW8K9pxI8+Wq52CSHjlRNy\niGZ5hKKqUFsr0+WqqogffzzC7UZfvRrXCy+gVlTIY8jNbYlXLijAPuAAKamoqZF650AApbJSMtEb\nN0qAvE2u6sQvugjrootg9255Xjt3Sou1vn0lG90s10gEGSnRqFzJKyyUc/rvuJZt3ryZN954gy++\n+IKDDz6YESNGMHz48E6fa1kWlZWVmKZJt27d9rr/ffW/qX3g90+u33r9/q9K2fIuxjdjwKlC6Yis\ntZFyhhQQMRBOGk7vs7EPGAs5v8+DMClnCASguFgCRZdLTl7l5TL2ct06tFWrUKuqsAYNInrzzVJn\nVlGB8eabqFVVOL16STlDQQFOSoqUHxQUSJuxBNOsL1mC8dln7XwdHb+f2A03YA0fjlJfj/7NN5Id\nLSyUet9WiTzC75dgOS0Nta4O8+mn0T/5pE38JYCTnU3kzjtx+vZF3bYN46OPklY6IicH4fPx/7H3\n3tFRlH/7/2vKzpYUkkBIQoBAgFAFKSI2ml0soCIoiCBFmoCCCAIW7IogqFiwoIACIk0QxIYd6T1A\ngBQgIYQSIMmWab8/7s0mMRvke85zHj+f58f7HA7KzN4zOzs7e93Xfb2vy9Y0rOrVBfPg9WK73ci5\nx0QS24kTSEeOIucegyNHMLp2xezUGXXHNpxvv1Xh/CEY5/vKa5BUC+2D2TjWr690rX0jRmJ0vR7n\n9Gk4/qyYB28BvmlvgubAPWk8UklxxY+6bl1KZr6L+5mJqHsq+84WvzYL5WA6ro/frTSu2bwV3hen\n4ZozCzs+ATOptgCw1WKx3R7s6jXKwjZ0XQDNoDexDZjNL8Ox9mvk47nIuUeRj+XAyQJhDjJoJDg1\nXO9OD3t/lUx+GXXnZrRVX4Xd7rv/YYiOxjUnPGNruT2UvDOfiEH3hGWkLVXFN3w81ExEKsjHbJiG\nHRklQgr8XiRfCfLRw5hpLdG+XYK2vmqf3ZLx09HWfom6vbI/cWkZKY0IPDASz/Ojq9wHwDtiCsq+\nXWjfLi871+gYfI8/h52cjLLjd5zLPsRs0ILAjb3wvHJhTbDt0Ch+cymeQbeHbZyznC68z76F5FBw\nfvoy3semEzn0jguOWVolk97GsWgujl2b8d92L/q9/XDNeRF1119h9/cOnoSUl49r0Ydlx69eE+/T\nM1F2bcD1+cxKr/Hf9gBG645ETBSNhkb9RngnvoZz+adoPyyvtH9pmbXrUfzGF0iFp4kYek+l7zmA\n0aYDvpGTcc58FseuzRW22RFRlEyZgXwsB9f7r2K0vw69653YNZOwZRU7Jg7H96vRln6BfOwIZr0G\n+EdPxHa6cU95HLkgH+PytvgHjsR2R+B69Vnk/OMEHhyE2eYKOHMG1xuvYNWth37X3VgJSUgFJ3DO\neQ8cDvRud2DVT8WOiELOzkL7YgFKejp6mzbog4ZgtGiJXHReyOqiolF278L55pso27ZiJyZhpjXC\nbNMGK7WBeGa53YKAkBXs2Fiks2fR5s5FW7ECqbhYANM6dUSoRfPmIYBqR0WFtisZGcKubdculG3b\nKjSjGU2a4HvmGfB4BDscCAjpRvnoYEVBPnsWTp3CatIEnE5BfHzySWisCk12DRsKa7SGDQXgBkFU\nKAqS1ysanPfvR927F3nPHswWLdAHDcJq3hy7QQMkTbsop4a8vDyWLFnCqlWrqFWrFn369OHWW2/F\nUS6A41L9d9Ul8Psv1/8m+JV2foz65wQk6RySs4qdvIAEtgKmFY/d5BGs9mPAdXGxwiE5w8mTkJ+P\nsnmzMDzftCnE+NgOB3ZSkpAz9O+P2aaNcFLwegWYlaQyA/WghY60bx/GHXdgduwoOq7Xr8exdCmS\n3x9qgCi14zHr1xda35MnQ0tg8sGDyAcPCiu0nTuRgg9Ko1s39H79wDRRtm/H8dVXEBGBGTRlL82a\nt2vUEKlFQa2vlJ+PumeP0NAdOICSno5cUIAVHY1/wgTMpk1RDh7EMecD1IwMkVYcESHilGNiMa7q\nQODBfki5uchZWYK1UdWypjtVwY6uhl2jhpAdGLpgmkEASL9fNL543FiNmyKdLEDd9BfowdS5QEA0\n7lWvgX5Xd5Rtm1H27gk2mAjmGtUhkuGat0DZuV0EbThdwQmFhIUN8TVFqMbZs4JVNU0xvmFgJSaJ\nZKb1PyCfOI58PA/51CnBOBeeofi1mWg/fou2dFGl+8SKjqHkowVEDL4/lDhXvvTLWqMPGYl79MCw\n7gp66yvQe/XD89SjYe9DKyaOkjfeJ2JwzyrdGYreW4j7tckomQfDbrc8kZS8OZeIIeGt1yxZxri6\nC/5RTyHn5WBHV0PylyCdP4uSvhV16+/IORmimerVz4l4rGp/YIDit5binjAQ+eyZKvexPJF4X/6I\niBFVM8iBDp0IPPwodlw8zllTcGz55cIRyiOeQ/ljPdqGny54flaNBIreW4acm43nxUcvaOcGELih\nB0bzK/G8MqFsDFnG+8JsJNnG/eYEpKIyvbnesRuBa24nYnJliYYNBHoPQe96G55nByIXCiAUuKUX\ngfY3EDl+cMX9ZRnf8ImYac3wTBpQSZ5hxdag5Ln30JYswExrjtm0JZ6nhiCfq+iGAYK99j75Mram\n4X5mZIVGLuOaG/A+NhUCOsreHbhfmoxcJO5nOzIK7+insBo0xvXcE6hZgp20kmrje3wyVrVYPM+M\nQz52BCuuOv5hj2M2aYG68itcCz/DTKlP4OFhmA0aoezZjXPGq9g14gnc1wejdVtwuZAPHBBsZp26\n2EhI589hR0VDtWoomzbhfG82ckYGVmoqZuu2mG3bYtWoge32IDlUOHoMJAmrbl3k8+eQ9+/H8fXX\nAui2bInZSIDbUIKcZSH7/Zi1aolGtDVrcC5YgHzihAClSUmYtWtjNW0qGNcmTYRTw4kTgm0+f148\nh/ftKyM+gj0HRqNG+CdOFLHN27ah7N0rVgVLWe1yIRQQbKKLjUX94w+cL72EcvRohfuF6GispCT0\nW24hMHSoAMTR0ciRkRfF8BYWFrJixQqWLVuGw+GgV69e9OjRg6h/aHy7VP8ddQn8/stlWRa6Hl5r\n+D8wOPJ3w1EPfQ5qoGrAa4It+qew3amcTRuLL+0ukGSqVat2Qcu1kJzBMLCzspCyslB+/12ETaSl\nCW/JchKE0mUwKyoKSdNwrFqFc9Ys5DMVf/BtRcHs0AHf449jR0eLWb1hiOXq0mU0RYEzZ4TfY1ER\n5tVXA6BkZOCYNw9l3z7h6FCOKTCbNiXQr58YMztbgMBgpLBUUoJ09KhgCtLTsYqK0EeMELnwhw/j\nmDsXZe9eYXcWEyNcHWrVwmzWjMADD4is+aB+GBB/yzLSubNIx/ORjhzBvKwFVmoD1A0bcL39FvLf\nrO4AArfdRmDwEOScbFzTpyPnlHWn25IELhf+/v0xbr8D9bt1OL5dG2qUsxUZFFVIHB4dhbJlE9rq\n1WCZwjA+CGDt6Gh8Tz6FY/2POJYtEQDb50Xyir/NevXxzXgL10tTUTdVDo3w398Xo3NXPGOGVvL/\nBSia/THa92vQln9ZaZulqhQvXIln9CCU45WX962ISIrnfE7kwPsqxCuHtmsaJZ98RcTA8O4PAEVz\nl+GeOAIlP7x8IHDLXZhNLsM9s3IDXmiM9xbhfmkCSk5m1ft8vBzPuMHIp8qkM5bDgXlVZ/TON2Gn\nNsCKjkHyleD4cQWO39chHcuuBEb1Fu0wunbHPX1ylccCKH5jAa7pT6Nkh2/eK62S595C/W415pXX\nYTZpirpzA85F74VS50rLrJmMb8JMIkb8c6CF3uk29KtvxPnRLHxPv46cfwTnu1ORz1UG61ZcPCXP\nf0zkw+EZYqNeI3xPv4Fj/Uq0pR9iJdfDO34WkYOq1usCWPGJlDw9E2XzDyiFpwhc3Y3IJ6p28TDS\nmuN78mW0L95B+1X4M+sduuIfMA7PmAHIJ4WUwkyui3fyayi7t+J+P3yiXuDKTviHjsf13isY7Tti\ntGiHuuUvnG+/huTQ8A0fh9GqLe4XJ6JmlOnXrZhYfI8/jZVYC8/kMcj5ecH3koBvzFNYCbVwvTgJ\n9dABbFUl0OshAj37wtlC8eyIisZyuZECumBoa9RA2bQRddNGKC7GvPoa7Oo1QJZR1v+EtvBzJN3A\naN0ao3NX0QAcEQk2yBkHRAxwnbrIJcUijGfvXmGlFh8fdI1wIvkDyPvSUf/4A3n/fgIPDxT+voVn\nUH/4Aens2ZD9mu3xgFt4B0u2jX3mDHbt2kKG9ttvuOfMKQu0cLmwatUKNScbV16J2a4dcilwtW3h\nWZ6XF4pWVnbsQD55EiMtDf/EicK3fetWtFWrRKBFuSbnkHdwsNla8niwGzZEio29KMDr8/n49ttv\n+fLLLzl9+jQ9evSgd+/eJFykW9Gl+u+pS+D3Xy7btkO+uv8jVXQCdfkdyOd2gWYhVbUqY4HtA2wZ\nK7olxvUfQFJLoGLKW1RUVKWlnVLAaxYWIuXkQGk4xOnT4mGanl42qz9/HuOyy4ScIS5OuDMsWYJ8\n5oxgaJs0CZmv2y4Xdu3aomEpyAA7Vq7EsWoV8u7dFWJILVUl0L8/RvfuSOfPiw5kh6NyCo+qCiN0\nlwtq1UI6dQpHaUxluetuA1SrRqC0qSMIhKXSTPjyurXCQqRjx4QXcMOGyJmZaJ9+KryH/26Hpqr4\nx47F6NIZOTsHZdNG4RyRkCDsjoK6XisyErtmTfHwV1XkfekiBvX4cWFDdPQoHDmC3qMHVufOIqFu\n/mcVbMhAeAl733oHKRDA9eyUsODa99g4zHbtcE0Yh3LsaOXtQ0ditm+PZ8wIpKLzlbZ7n54KioJr\n6qTwYRTvzcXx7Wq0FWGAL1D8+XLcL01BTd9V+cXA+QUr8Ex8FOVoeE/eog8W4pr+HOqB9LDbfYNG\nIwVKcM6fE3a7pWmUfPAlEQOrdm8I3HwXZlpz3G+9FHY7gO/hR5F8XpwLPqxyH71ZK/S+g3FNHInZ\n8QYCt9+DnZCAVFKEfPQw6s+rUdO3UzxzCRGj70e6gE7VaNwSvcdDuF+oOj0OwGjSksD9Q/BMGln2\nb+2uxj90LBQX4lzyAcrOv5CA4pfn4Z46JsSkVlVWdAwlb8zH069MGmGkpuF/6mXkY4dwvf8i0nnB\n4NlAyfTFuCePRD5V+f4rX74+QzE634jtjiRicI8L6nRLywZKXv8Eo34aEY/3R82qOlQDxETaN+ZZ\nrNp14MhhqJGMe/wjld0ggED3+9F79MH1ynjUjIrNi3ZEFN5xL2CmNgHDIOLxQSEgG9onqhresU9j\n1aqDZ8roCtutmol4xz2D7YnEM/FRpKJzWKmNCNzanUDfQUhHc4Se/dQp5CPZqLt3Yl52OVbdFOTM\nw7hmvI50Ih+zWQv0nvdjpTYAWUZdtgTH0iVILjfGVddg3HwLVmISVmQkUmGhkOrounhO7t+PLUvY\n9eqLxEq3G+lMIcrGjajffYt6+DAWoPfqjf7QQ6AborlNVYNaWQ3JsgXJsW0bysa/kA8dwrz+evwD\nB4mUuh07UDdtwmzcWMjLgoEWtqYhaRq2zwfR0QLE792L88UXUQ+Wrb6EGtFq18a47jr0Xr2Q8/Kg\nsLCMUJBlOHVK6H6Dq3kUFaEPHozZqRN2w4YQH39RkgbLsvj1119ZvHgx6enp3HrrrfTt25cGDRr8\n42sv1X9vXQK//3L9j4DffUtx/Pyo8OJ1glQVURsCvCpm0u2Yt30IzspyhvPnz4fYaI/HgyOYdW6a\nJnZ+PuTmogblDMr27SEAZLvdggmtWxd94EDMxo2FO0MgUOYCYZrIwaAJZfdu5AMH0Hv3xujSRTSh\n/fYbjiVLxLJ6crIAyI0bC91vQgJmWhrymTPioR0IiBSgXbtQd+8WADmo2zNatMA/ejR2bKzolF6+\nXBiop6WVNdc5naGse2QZOzoa6fhxnHPmoP74I3Lh3wIB4uLwjxsnojePHEH55Reh8a1TBysiIuQX\nbGkaxMaKiNGoaJTNm9EWfiGS5/LzQz+6FqA/8AB6z/uQjx9Hm/MBytatwbjTmNAfs0lT/IMHI5/I\nF9czmGQkgjaERMIK/mBgmkheL3JJCbbfLxLkiouFJg8wu3RFPpiB45tVAuAXFwk5RVERtq8E3wuv\nom7bgnP2TPB6KzT6WID3g09Q//oT59wPwt5ixR98hmPNCrQV4XW4xe/NRVvyOY6f1oXf/vo7Qif5\n3Tdht3v7D0PSVFwfhrcUsuITKJk6nYgRfaqWO8z6DNfs11D3h/eytVSV4jlfEXkBcGzFVsf70mw8\nQ3tVHXoBlMxbTcSge8Xn8LcyU1IJ3PMA+tWdkBwa6o6/UL9bjrpzY6VQEYCi91cS8egDSBewLLOA\nko9XEfHIfUjeykDScnvwj5mCldYY6cQx8AfwvHRhMG0DJdPm4X7lKeRjlT2MjbRm+Ca8iJK1D9cH\nL+PvPRTpWC7OZeGt6SqMLcsUz/oCOTMTq0lznLNfwLE9vB64tAI33EXgprvxTB6N74mpWHFxeKYM\nD8kNwh7HHUHx2wuxZQXH7z/hei+8nzSA7YnEO+ElbLcb95RhSJKMf9DjGK074HrladQ9O7ESkvCN\nfxbb5cH91KOV5BJWQhLe8c+B6hDbi4vE969RU/zDx2E2ayk+n5wcXJ99iPLHr0iqSuCue9BvvgMk\nG9eM11B37Qhp4wN9+mOm1EfOysQ9/TXkE/nYUdH4b74V/YGHsGNjRaCEroso5OxslC2bMVtejtWg\ngZBryQryju04vl6BvDOYUFezJoF7exLo9xBSUTHSubPYUdFIhWeELdoff6D8+SdyUHZlu1yY9evj\nHz0Gs1UrIVnT9TIrMp9PuO/s2CF0vwcOYKek4JswAbtmTZH2tny5SLIrXR0MPo8rNDvHxCCdO4dz\nxgzUb76paIsWdHIwgxaVVpMmSJKEnJh4UQyvbdvs3LmThQsX8ueff3LNNdfQt29f2rRp86977V+q\n/526BH7/A+r/2evXNJHWDkLN/gpJDoCrasMF2wD8YEsRGK2exL46fMxn+SouLsbvF8vJsmmi5eWh\nZGXh+O034RrQqJFYInO5xIMq6H5gOxwQFwemiWPxYpxz5yKdr8gc2m43xlVXCWAaESEenJZVMQve\nNIUWdv9+OH9eJAZ5PMhZWTi++AJl2zbR7BYdLZbQUlIwmjbFuO02iI0VrKymCRb1/HkBtvfvFwB5\n504IBAgMGYJx/fXBxKYfcKxZI8BxnTrigZyaGsqEt5KTkYqKBDjOzUXduFF0GQfBu2xZAsj27o3e\nsycUF+NYuxbHjz9ix8aKc0xNFaC7enXMBg1E1/WZM6BpwjqosFCwvFnBSOWMDPSmzTAeGYJ8LBdt\n5owK7EhpWbXr4H35FdADON+cjrpLsKm2JIXCP8xmzfFPmIi8Zzfa8mXYzjIXjdK/9ZtvAUVB2bZF\nAOoguLZlWfh3JiRgJyQI6zfbFtKP8nHMmobVuAnKvr3i8/zbDWlLElbT5iiHMoRmGcr2Cf5tpDZA\nPpEvgGLp+OX+2NHRIhjgzGkhU5EQEyu/TzQVeoux2nXA9e7rKJkHhdPF+bNQXFSWWnft9ZjXdMb9\nWvikOIDimXNxvj8Dde+Oqvf5aBnuCcORT+RVvc9r76F9OR/Hxt+q3MdKTMb73HQ8g3thxyfg7zsQ\ns/UVopku+wCOtUtRMnbjv3cgEhLOL8Kz2aVVMukNHD+vw7G+6ghmEGl8JVPfRtJ9SCXn0L78CHXz\nb2GBvL/XEGxnBK45F45QNpq1wjfpFSy3h4ix/VGOVC0XAQGqvc/PRl2zEu3HtdhuD76RT2I0b4l7\n2kTUQ5Wt7wJdbyfQrTeRw/uWvZd6DfCNn4p0IhfXy09UYnTN5Lp4n38X1zNjUTL2od9xL4H7+uFY\nOh/n1+H9fgGMlm3xvvg2diCAa/qLaOsrT9jMlFR8454B3Y970qhKTXNGwyZ43/hA+HL7vCiHD6F9\n8DZq5iGs2Dj8g0dgtmqDsmUTzpmvhVa3rBrx+AcMwWzZBiknE/erLyKfPRO0T+uFb/R4JK8XNAfS\n2bOo677F8ct6pKIi9Btuwmx1OVZUNJLfj/rtWrTlS8WE2OXCaHEZ+v19MDp3CT2DbFlG+/JLtM/m\nljWWRUVjNkgVTXHNW2DWqoVVPxV8PuGUkJWFc948AMptYgAAIABJREFU1J9/rtCkW9oYp99wA4EH\nHxRuOoWFIQJEkiTIy0PZvz/kG4yq4n/iCcwmTZCzstDmzUMyDGGLlpYWskULOQBFRIhrWr8+UkqK\nYIIvojIzM1m8eDHr1q2jcePG9O3bly5dulyKGP7/YV0Cv/8BdVFev6cyUFfdjVx8EBx2eIeGYNkB\nIACWszbGLfOhdoeLOo9SOYNeUADZ2ciGga2qYhZ/6BDKnj3IO3aI5jHAaNMG/4gRQj979KhoFtN1\nAY7T0gRAdrsFK5mUFLSb8iAFAjjmz0cLWtGUL0uWCQwYgHHPPQK47t0rQFpMjFg6C7KrkmVBfr5Y\nIktNFZGXa9agLVtWIbTBjojASkrCaNtWND1IkmBPS4GdwyGSksppzGxdRx8wACIjkQ8eFAx3eroA\n+DVrCu1waipmo0YYt9+OJElIx4+LcwsIyy0paJ6u7N+PsmcPZkQEgQkTwO1G2bQJrXz3siyLRria\nNcU1HTq0zCtYVUFzgEPDdgimV5IkbNPAqpUMTifOTz4WDEt2FuTlljHLtevgfWM6Um4urhenVui8\nLi29bTv8U57BsWIp2txPwlqV+V5/AyIicT85LqwMQr+2I/7Hx+IeOxolO6vSdisykpLPFuGcNQ3H\nz+GbqkremIWcnYXr7fDODvoVVxIY+TieR/qJZj+CAN/pEjIXt4eSGbNRfv0JyTAFWK9eHTsqWshL\nbAskGTuuOnJujmDd/D7RqHc0CzknE7ngOEbdBpgdr8fz0sSw5wHg6/0wuDy4Pqna6ku/8jqMm+/C\n/dy4KvexgJL5q/GM7CccMf5WRoM0An0HYaU1waoej3PZfBzfLAnpVCvt37AJgQFj8DxZdbwyiO9Y\nydxVRAzpLZbeXS78o5/CbHYZyt4tOBfMDsVPm8kp+J6aQcSguy84JoBZMwnvtI9wjx5IYMQ4zHqp\nON9/Fce2yppxAO/IyUinTuP6ZHaFf7ejq+F9/Gms2nWE7Vv+MQD0zrfhv6sPkUP7hB1Pv7oz/kfG\noP64GtfCOcF/64J/4Fg8Q3ojF5cx5raiEOg/DL3zzTjffgnHloouHGatOvimTEPZsgk59yiBHr1R\nN/2G9s60sI4YRtMW+MdMQirIx/XcOKgWi3/ACMzmrVB27UBdvRy9/yNYCYloc95BW/992bkARseu\nBB54CNvpxDXtJdTdwnXFkmX8j45Dv6c3nDuLHRMros2/XIiSvhc7IZHA7XditG2HXS0G+cgRnJ9+\njLpTTNysuDiMazsSuOc+zEZpAjBHRSJnHMD52quo27aJhreUFIzL22C2a4ddMwE7wgOaE86fw65e\nHRQVZc8etEULUTZvFiFC9ephtmiB2ay5+K55PFgJCSKQwu1G8vnQZs/GsXIlcnGZw0ypPM1o1gz/\nY4+Bw1H2TFaUUCSyfOxYKHxC3rsXo3NnjPvvx0pLg/r1hTPERYDegoICli5dyooVK4iLi+OBBx6g\nW7duuN3uf3ztpfq/W5fA739AVen1u2kWji3PI9nnLyxnsEXDmm0omDU7Yd35FTj/+YsdsiIzTey8\nPKHj2ro1BPYkCKXlWMnJGGlp6P36CQYwJ0dIBWRZSBkKC4X+au9e5B07kHJz0QcNQi8nZ9CWL4dg\nmlCpM4MVH48dF4eVmirY1agowWT8+CPKli0ibrMcQDZTUvCPHo1Vvz5yXh7qunXi/Bo0ENHCpQA5\n6MlruVwQF4ecm4s2fTqOn36qDPCcTgIPPYTeq5dgYI8cCfprOsvGkmWkkyeRsrKw4+IwmzUTUoXV\nq3GsXl0hvc12u7ESEjA6diQwWCSoSXl5QSBbLkbZMJDz85GyssS1aNAAZft2XLPfCTWIVDjPyEh8\nzzyL3SAV5fc/cKxeJX6EkpJEKlRiInZsLGZqKsTEIOUfFw1uIGJMZUlEoRaegbNnMa+9DrmkGOe0\n15AzD4sJQDkJjt6yFf7nX8T5ziwc34WXKZS88jqSquCa9GQF3+DSMpo0w/fSa7hHD0M5WnnJ3AK8\nH89HXbcG5+IFYY+hX9ORwMCheIY+FPYYEJRbLFuMtnZV2O1WZCTFcxcT8Ug/5FPCpcCSZaz6DbAa\nNcaq3wCjmWhGlM4VikAMnw/J70POP4Z8IB310H44exrvczOJGBzeAQKCsomPlxP58N1inCqq5IVZ\nOL7/BsePa6vcRwDkVbjGDsWu34BAnwFixaQgD8e3y1A3/RYK5yj6eBURw+5HKq48QalwrWbNx/nB\nTNTtmyptM1q2xT9qPBgBtOXz8PcZhmfUQxeUFADYLjfF7y7CM6xfSAJgR0Tie2QMZusrcKxcgHN1\nGcvqv7sfRqPLiHjuiarfe3wCvieew4qKxPH9SvSb7ibykd4XPg9JItCrP3q3u5GzDmBHxeEePSAs\nYC09b9+jEzCbt8T1whMoOYfxDX8Sq0Vb3KMGlb0XQL/1LgK9H0JJ34lz2nOV4s4B/A+PwN9nIPh8\nuJ57Cu239RWP54nA328Q5rWdkDP243z1uQpssRUbh/e5VzCbtwIk5KzDaGtWoa5bi3TqFGar1ug9\ne2HVrYdtWWhfzEddszoURmE1bESg+90YV16FXSM+eFJ+1PXr0VYsQ9m3Dys1Ff2qq7Fat8GKiRH3\nU2Ehym+/4vjpR/Tb70Tv3AWpuBh161aRWNmmTZnrgtMpnofZOaibN0EggH73PUiyjLxjB84F4nts\npqQIS7RGjbCiowUREhkp5BnB+GDH4sU4582DI0cqfEa2x4NVuzaBBx9E79VLNG/HxyM5nRclSygq\nKmLVqlV89dVX6LpOz549uffee4mNjf3H1/5v1y+//MK0adPYunUrubm5fPLJJzz00EOh7f379+ez\nzz6r8JoOHTrwxx9//G+f6v+pugR+/wMqBH59Rchf34ty4lck1URyVf0a2yQoZ4hEv3wCdKiaYarw\nulLA6/VCVhZSZibKb78JoFiqvXK5QpntoWaxpCQ4dQrHggU4v/4aqfxMXpKw4+NFMMTIkWJGfuSI\nWKoup0+VT58OWZfZJSVCIhATI1jjhQtRN24U7GpiogDIaWlYjRphdOiAHReHlJ8PHg8EAoKNzsgQ\nscc7diDn5grpQc+eGPfdB7ourMtWrcKKiRFgu1GjMoDs8YjmONsWS3hHj+L89FPU33+vzEZXr45v\n7Fih9T12DPWvv4SUITER3O6K18s0RddxXBzKrl2imSOjckOOpWn4x44V1m1HjqBu2IBVq5bQEJfz\nvbRVFaKixPlGRaGtWYO6ehXK/v0VwjksIDBqFEbXriibNuF6661KFmK2JGFccQX+KU8j5xzB8dUS\nwdjEx2PVqAExsdgup7heqQ2Qjx5B0nXBsCqK+MGTJPCWYPn82M2bIefk4PhuLdLJk8gFJ5AK8gWI\n9vnw93oA4+Zb8Yx8JLz+VJYp+WIpzvffxlGOCStfgc43oPd5CM/wAWF1sADFb3+I47s1aCvD64wt\nTaPk8+W4Rz+CEkazCmBFRVPyyUI8g/pUDOMA7LopmK2vQG95OWanrkgn84WHqLcY6dQJlB1bUfft\nRM7JRDIMimZ+imvOm6i7toU9FkDguhswOt2IZ+qTVe4DUDztfbSvl+L4saKMwYqMJtBvMMbV1yB5\ni7GiY9C+W4Vz/vsXHM/34DDQXLjev7CEwVJVipb+JGQo2GhzZ+H469ew+9qSRMmbn+Gc+Srqvso6\naltVCdw/AP2G21C2/oG8ezP6vQ8TOeLBC55D6JwfHol+2z1IJ/NxvToFNfOfG9y8L72N5Y6AqGgc\nq77CuWTehd9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EaH03bhTnF9T6ltq8SYqCXVwsmJUaNVD270d7803UbdsqXS+iown06CEm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\nAKk1ZIjUrefmgu2AquJ69130b79G3batzSxjs1cvmn4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zq4BSXo5aWIi+YUPoPBTTxPjo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\nragoLGXDiY5uvj969cLMzZXno6ZGSl9UVerNKyvRNm9GDxSiqPX1AmKvvRZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import mkf_internal\n", "import matplotlib.pyplot as plt\n", "\n", "ax = mkf_internal.plot_3d_covariance(mu, P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is clearly a 3D bell shaped curve. We can see that the Gaussian is centered around (2,7), and that the probability density quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange." ] }, { "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 $[\\begin{smallmatrix}8&0\\\\0&4\\end{smallmatrix}]$." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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n5+NyuaJuIx3bheul4wDQnYV4v3YA5MC7oLzhrzgfvzq4rlY6js5vP4t3yPge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\ncxorHD+6D3m6+vv7ceLECXz++efw9vZGZmYmUlJS4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"text/plain": [ "" ] }, "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 variance in the points for $x$ and $y$ only. 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 this is, it is hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance. In most of the book I'll display Gaussians using contour plots. Helper functions in FilterPy plot them for us. If you are interested in linear algebra look at the code used to produce these contours, otherwise feel free to ignore it. " ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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cZyGi4GNhTkQEsFvuU22ZGOqWipLagGU7XodDRLSsWJgTUei5rkClrkM1VLSl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\nWCIaM+OeBbIsIeFZCMoBiuUysknezGZYWmEHrRbgex4SvKn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with figsize(y=5):\n", " mkf_internal.plot_3_covariances()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For those of you viewing this online or in IPython Notebook on your computer, here is an animation.\n", "\n", "\n", "(source: http://git.io/vqxLS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From a mathematical perspective these display the values that the multivariate Gaussian takes for a specific standard deviation. This is like taking a horizontal slice out of the 3D plot. By default it displays one standard deviation, but you can use the `variance` parameter to control what is displayed. For example, `variance=3**2` would display the 3rd standard deviation, and `variance=[1,4,9]` would display the 1st, 2nd, and 3rd standard deviations as in the chart below. This takes 3 different horizontal slices of the multivariate Gaussian chart and displays them in 2D." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HX0FG3atgsl7Coak67A4rxYbe6o02YzxwqMgiHN+Ntd05EdF80HalutFo4Omn\nnwYABEGA/fv3Y9euXejv78fy5ctx00034Y477sBZZ52F1atXY+vWrchms7j66qvnbPFERKea6/lw\nfA+CEEKKWHG1HA+OZ0PV49czQoQYm25gqlGG6dcxUNBOOoFElUUMFHSUKiYmGj6CMMSygWzsirWm\nSKjX7VibwGiKCNd3YLs+DE2JdX0iol7W9jf7jh07sGbNGqxZswaWZWHz5s1Ys2YNNm/eDAD4wAc+\ngJtvvhk33ngjzjvvPIyPj+P+++9HOt2bD6UQEcVhuz4c34EasUoNtEK17TvQYkwNmTFdM1Gx6i8a\nqGeIgoBiQQNEFxWzgolKM/a1FUWEG7iwHA9hGEY7VhZh+w5nVRPRgtV2pfqiiy5CEAQv+JnNmzfP\nhmwiooWoVW2OHqrDMITlekcDebTpGTNMx0W5ZqJiVVDMa8ftGXAyAgQUsgomSg1UmjoMTUEhHa0n\nGmgFdFlCKxy7PnS1/cdyVEWEHXOrcyKi+SCRnmoiosXCdjy4gQM14qYvttea0CHLrXAaVYgQk5Um\nSlYZaUOMHOpFUUQ+o6JslTBVbcSexKGqEhw/ejhWFeloTzUngBDRwsRQTUQUge36sH0Hqhr9IcVW\nhTte60e16aBuN+ELNrJpNdY5dE2CpgmoO3WU61asc6iyCMeL3letKiIc3+aDikS0YDFUExFF4Hg+\nPN+FEmFOM9Aap2f7NrQYvdghQlTqFqp2FblUvEA9I5uS0XAbqJkW3BjVak2VYMeoVCuyCC/04Lh+\n5H5sIqL5gKGaiCgC1/PhBd6LPiD4fJY9008dvVLdsBw0j25tHmUu9olIkghDk9BwGqg27cjHK4rY\nav9woz+sKIkCvMCD57/w8zlERPMRQzURUQSuF8ALfMhSxHF6rgfHtyO3jQBAteGg4daRSSUzii5t\nHK1WN20EiBiMBQGyjNYOjhEr3bLUCtWux1BNRAsPQzURUZs8vxWoRREQIjxsaLseHM+FKLZCabRr\n+jCd1hbknW4aM0ORRUgyYHo2TMuJfLyqSHA8B5YdrQVElkR4oR+r7YSIqNcxVBMRtakVqr3IVWrH\n81tV6hj91A3bg+VZ0FQRApLb3ttQJVieiYYV/cFBVRHg+E7khw5lSYDns/2DiBYmhmoiojbN9FNL\nEUO15wXwQx9ym3Oln6tpObA8C0aHvdTPZ2i/33I8jNoCIorwQx9+EPE4SYAXenAZqoloAWKoJiJq\nU6uf2oOFXJM5AAAgAElEQVQccfKH5wfwAx9Rdwf3wwCm47amhnSwC+OJSJIIUQpheTbMiG0ckijA\nD3x4ftSeahGe77H9g4gWJIZqIqI2zU7+iFqp9gMEQQAp6hg+24XlWVBlIdaGMS/GUCVYrgXTcSMd\nJ8kC/NCD50erVMvy0Uo1H1QkogWIoZqIqE2/rzhHDNVBAC/0IIlRJ4b4cD03Vi92OxRZghO4sJ2I\nFWdRgBf48CJWnCVRPFrhZqgmooWHoZqIqE1BGCIIg8jh2PfDWGHccX24gQdFTrb1Y4aqCHADJ3I7\nhiSKCBHAD8JIs6olUUAQ+vADhmoiWngYqomI2uQHIQIEkcbpAa2xeH7oRw7jrVDtQJWTb/0AAFEU\nIQJwfA9OxGAtCq2+6igBWRSP/sEk4gOORETzAUM1EVGbgiBepdrzQ/hBEKlS7fkzDwKGECP2Ykeh\nKCJc34HjRXxYUQK8iH3VoiAgDAME3KaciBYghmoiojb5QeuBwyiFai9obRgjiIg0Z9r2fDiBAzXi\nduhRKbIAN3DhuFH7qsXIE0AEUYAfBpFH8RERzQcM1UREbYpTqfb8mRnV0a7l+WGrZWSOWj9mSEd3\nOYw6yUOSWgE5ynGSeLRSzVBNRAsQQzURUZuCMESIAEKEUO0fnRgiRmwZCYKjx81tpm49dHj0DwuR\njpME+GH0WdUQgCAMIj3gSEQ0HzBUExG1yQ9C+GEQKei2WkZ8iBEnf/h+0KqKz2E/NQAIIuCHHvyI\nleqZBxW9iFVnUWALCBEtTAzVRERtCoIQYRhEqjqHIRACkTdv8Y+O75uLTV+eSxZxtI0jWqVaEND6\n4SISRbAFhIgWJIZqIqI2hWGIMESkkXqtUB1GeESxxTu6JXrUCndU4szM6TBAiPaD7uw9iJiNBUFo\n3RO2fxDRAsNQTUTUphCIFDyPPTKaAK0AP8eZGgAgQkAYhpFH3YWItvnLMcdFPoqIqLcxVBMRRRQl\n54ZheLRSHTEdh63/iZOp9+yL9nlh5nqRQ3WcPy4QES1MDNVERKdC1Ewdxq2KA/v2Rj8mPFoZb5cg\nxKtUn4LCOxFRV8jdXgAR0XwRr9Xh1NmzrxWoH3qg9d+nrwRWnd7GgV1IuuypJqKFhqGaiKhNUR5Q\nnD1m5l8iP9AXbQdGoBWgZ0L0xesjHBi2rhX1x2sdEy+Rxz2OiKhXsf2DiCiiKPlYEAQIEKK3cgit\n/4lTzz19ZbTPhzPXizjVRED0Ijfr00S0UDFUExG1qRUi41RYox8jHq0cR9yTBUCbLR/PESCEIAiR\nZ2LHrVQLMe8iEVEvY6gmImqTILSCbpR+4Jk2jqjZWJIEyKKMIE6qjiAIW5NJJEGMFHXj9kSHYRi5\nzYSIaD5gqCYiapMoChAEMfJGgnE2H5REEYIgRp4dHZXvh5AgQYo4EHt2WTGmmgiCOOfbrxMRnWr8\nViMiapMoCBAFEX6ELbYlUYQgigiCaNuAS6IACSL8iMdFFQSAKEqQxGi/HQRhCEmUIEfYsh0A/CCE\nKIhzvv06EdGpxlBNRNQmSRQgQkQYIVTLsghJkOBHbOOQJAmiJGGOMzX8IIAoipFDte8fDdWSFO2C\nISAJIsSIYZyIqNcxVBMRtUkUo1eqZUmELErwIoZjWWyFz6hhPCo/CCDHaP/wgxCSIEGOcFwQhBAY\nqIlogWKoJiJqk3h0QkaUNmdZFCGLMsIgjDRWT5FlKKIK153bUrXrhZAlBaocreLsB61KdZQKdxCE\ns/eQiGihYagmImqTJIkQRSnyw4OSKEAUxUiTPFRZgirJCCBE7seOwnUDKJICVYm2F5jvzVSqI4Tq\nMIQoSJBYqSaiBYihmoioTaIgQISAIEL7B9BqAZEECV7E4xRZgiIqcNy5aQEJwhBBCKiSAlWO2FMd\nzPRUR6lUH72HDNVEtAAxVBMRtUkSBYiChIjZGLLcagGJ2h+tqa1Q7flzU6n2vBCy0Gr9iDKj2g8C\nCIIIWRQjbf4yU6lm+wcRLUQM1UREbZIlEZIowY8YcmXx6ASQiGm81QKiwJmjvmrb9aBKKjQlej+1\nLEqRZ03/fmIIf+shooUn0W+2LVu2QBTFY/5ZsmRJkpcgIuqa1iQPGV7U8Xii0ArjEXujU5oMTdZg\nu8GcbAJjOQF0WYeuReyn9gFJkCOHY88PIAsSlIgPRRIRzQfRvknbcNZZZ+Ghhx6a/W8p6gxTIqIe\npcgSJFGC50SsVB89zvWjXU8SJRiqCtXU4DgBdC2579PAD+B5gK6rMDQl0rGt2dZxQnUIWZShROzf\nJiKaDxIP1ZIkYWhoKOnTEhF1nSKLkAUZnhf1QUUBkiDBjDHFI6Ur0JsaTKeRaKi23FaV2tAViBH3\nGvf96JM/AMDzAhiizEo1ES1IiZcL9uzZg6VLl2LVqlW46qqrsHfv3qQvQUTUFYosQZait3+oigxF\nijdzOqUpMCQDlh2xzP0iTMuDLmtIRaxSA4DjBUd7saPVZWYr1eypJqIFSAjD5Br17rvvPtTrdZx1\n1lkYHx/H1q1b8etf/xpPPvkkisUiAKBSqcx+/umnn07q0kREp8Svn61gb30fThtR2p58EYYhnplo\n4GDzEEb65UgTMwBgomxhwizBMHxoaueB1A9ClKsBimoRo30piBF3U5wouSjIAzh9oABVaX89hyYd\nDMijOHO0H7rKajURzS+rV6+e/fd8Pn/c+4m2f1x++eWz//7yl78cF1xwAVauXIlt27bh5ptvTvJS\nRERdIYnC0UkeQLtdDIIgHG0dUeB6IdSIxeGULsFwdZh2LZFQbVkBdElHSlciB+owDOH5gKIoUOSo\nW5sDEjd/IaIFKvGe6udKpVI4++yz8dvf/vaE769du3YuLx/Zzp07AfTeuhYD3vvu4v1vX3r/BJQx\nDaNDSqQe5+J0Hfp4BrJuI59RZ1/fs28PAGDV6atOemyAELnxCsZq4yjk5UjV4ePOFQQ4Mm1jKDWM\nZUMFaBH7m23Hh5Hysap/BVaO9kU6VjQqOLP/TPzRGUsiV+vnCn/tdxfvf/fw3kf33G6LE5nTxjbL\nsvCrX/0Ko6Ojc3kZIqJTRpWlVn+0F60/WldlqLIGJ+JxACBCQD6tIaNlUG04kY9/rnrTgyGnkElp\nkQM1ANiuD03SoKsR+6m9AJIgQZWjt78QEc0HiYbq973vfXj44Yexd+9e/OxnP8PrXvc6mKaJN7/5\nzUlehoioazRVhiqqsCPOx9NVGaqkwnHiPXCYTWvIqGkEvoim5cU6h+MFaFoBsmoWhYwR7xxuAFVW\nI4fq1sONWuSNZoiI5otE2z8OHjyIq666CpOTkxgcHMQFF1yAn/70p1i+fHmSlyEi6hpNae1yaEac\n5KEpEjRJhefPbNcdrVorCSIG8gZsv4jJ+gRUWYQcYd5zEIYoV23ktQIKWSNWlRpoVaqzeoxQ7R6d\nGBLxOCKi+SLRb7f/+I//SPJ0REQ9Z6aNo2JFC9WCIEBTZSiiAtcNoMWYfpHWNfSlU3D9PEr1KgYK\nGoQ2Z0xX6y4U0UDeyKCYjVelDhHC9UJokhY5HDuuD0WKHsaJiOYLDgslIopAU2SoogInxsxpXZWh\nSVrk1pHnKuYM5IwMFOiYLNsIXmRDmRAhyjUHriOgT89joJBuO4g/n+MGUEQFqiJFrrQ7XgBNUtn+\nQUQLFkM1EVEEqiJBlRX4PhAE0cb8t6rcaqxAPkMSRAwXMhhIF6EJKUyW7ZM+/Bj4AabLNgJPxmB6\nAMN9mdhtH8BMC0f0hxQBwHECKGL0DWOIiOYLfrsREUWkKUfDsRdE2sQkpSnQZB3l+nRH11dlCUv6\nMxAFAWVTRqlcgyiHSOsyREFAiBCm7cN2AqSVNPpSBQwXOwvUANC0PaTkbPxdGGM84EhENF/w242I\nKKLWw4oqHNeLFKp1VUZK0SBAbo2m66AVQhIljA5koddkZJppNNwmTMtCGIQQRAGaZKAvk0JG11DM\n6pClzgJ1iBCWHWAgayBjqC9+wHPMjNPTZBkiN34hogWKoZqIKKJWb7QKx3GAdLRjsykNqXoKTavZ\ncX+xCAH92RT6sgbqTQOm4yEMg9ZDkbKEbEqFJCbTw2xaPlRRQ1rToESseFuOD03SWaUmogWN33BE\nRBGldAW6rKPivPDuWieSMVSk1RQmzSr6sloi6xEhIJfSkEslc74TaVoeUmoO2VS0KjXQCtW6nEFK\nj942QkQ0X/BBRSKiiFJaK1RbdvQpHmldgaHo8AMBrhd/Csip1rR8pI/uxBhVK1TrsXqxiYjmC4Zq\nIqKINFWGrmgIAhGeH31edcZQkZbTaFrzI1Rbjg9JkGFoGvQY0zss+2ioZqWaiBYwhmoiohg6qVZn\nUyoMNYVGzO3GT7WG6SGtpJGN+IAiAPhBCN8XoCuc/EFECxtDNRFRDDN91ZYTPVRnDA1pxYDrhZFn\nXXdD0/JgKClk47R+2Gz9IKLFgaGaiCiG2Up1jFAtHm0BMeQULKe3Q7Xt+UAoIa3GC8az/dRs/SCi\nBY6hmogohtlKdYz2D2CmWp3q+b7qRrPV+hF1NvUMVqqJaLFgqCYiikFXZRiqhjAQ4Z5km/AXkktr\nyGoZ+J4E1+vNanUQhqg1PeS0LPqyRqxzNC0PKcVAOmYoJyKaLxiqiYhiyhoqDCWFZowHDkVBQCGj\nIy2nUDd7s1pdb7rQZQNZw4j1kKHj+hBCCSmVG78Q0cLHUE1EFFM2dbSFw4w3xaOYNZCW07DsEH7E\n0XynQqXuoqDl0Z+PW6X2kVLjt44QEc0nDNVERDFlDBUpJR17NJ4iS8jorZnVlYab8Oo607A8SFCQ\n0VPIGvF2amyYHlJyKtYujERE8w1DNRFRTCldQVrVY/dVA0AhrSIjZ1BrevCD3qlWl6s2CnoB/TF7\nqYFWP3VajTeKj4hovmGoJiLqwGy1OmYLiKqIyOqtYF2u9Ua1umG5EEIFeSODQkaPdQ7b8SFAZj81\nES0aDNVERB2Y7avuYHfEQlpDQS+gbvZGtbpcdVAw+jCQT0MQhFjnMG0fKYWtH0S0eDBUExF1IJvq\nrFINtKrVhYyBrJLDVMVJcHXRVeoOhFBFXk8jn47ftlFvuq2tzdn6QUSLBEM1EVEHDE1B1jAgCSrM\nDqrVQ4U0+lN9cGwBDas7bSCu56NcdzGYHsRwMRO7Sh0EIRqWj4ya6SiYExHNJwzVREQdKmR0ZNUM\nas34YVhVZAz3ZTCYHsBU2elKG8hE2Uaf3oeBXCb2xA+gNfXDkFLIp3QospTgComIehdDNRFRh1qh\nOotaM36lGgD6sgaKmQyyag6TZTuh1bWnXLchBhr6UwUM96U7Olet6SKrxX/IkYhoPmKoJiLqUMZQ\nkdFSCH0RttPZ7ohL+rMoporwXLGjyncUtuejUvcwmBrAaH8Wkhj/t4YwDNEwPWTVLEM1ES0qDNVE\nRAkoZHRk1GzHQViWJIwWMxhMD6FUdWB1GNJfjO8HODJlYcAYwEAhg7Te2bSOpuVDETRkDQMaR+kR\n0SLCUE1ElIBCRkdWy6LeYQsIAOTTOoYLOQymhnFk2oLjzU2w9sMQY1MmcmoBg9kChgudtX0ArdaP\njMYqNREtPgzVREQJyKU15PQMXBdw3M5D8EhfBkO5PPr1AYxPJR+s/TDE+JQJXcxgKNuPZYO52NM+\nZoRhiFrDRU7NMVQT0aLDUE1ElABBENCX0ZHXCijXkpk1vXQgi8FcAUVtAGOTFkw7mWDt+QEOTzSh\nC1mM5AaxfDDXUR/1jHrTgyoayKdSSOlKAislIpo/GKqJiBIykE+hoBdQqbsIw7Dj8wmCgBVDeYwU\nihhKj2CiZKNS7yywNy0PhydN5NQ+LMkP4vSRQmJj78o1BwW9gIF8KpHzERHNJ3yKhIgoIWlDRc4w\noNR0NEwPmVTn1VpBELBsMAdFFiEJEiabk2hYTfQXNGgRwrDvB5iqOnBsAYPpEfRnMlg2mIfYYcvH\nDM8LYNoBlqWzKOaMRM5JRDSfMFQTESVoIJ9CoVpAuTaRSKieMdyXQVpXkJpWMd2sYnxyGqoCZNMq\nUroEAScOx7bjo9JwYdo+skoOw4UihgppFLPJBt9y3UFOzaGYTUGW+JegRLT4MFQTESWoP59CfiKH\nI9Pj8LwAspxcwMwYGlYtUZEta8jVMqjZDVSrNUyUGlBkAaoiQRQEhGEI1wvgeCFkQUZGy2Egm0E+\nbWC4Lz0nuxyWaw6WZUbZ+kFEixZDNRFRgmRJRF/GQK6eQ7luYqCQ7BQMURAw3JfBQD6FSiODSj0P\ny/Fg+zYc30UYBhAgIK0qUA0VuqogZ6joyxpztmV4w/QgQkXOSCOXjr+9ORHRfMZQTUSUsMFCGmPl\nPhyoVtCf1zoeVXcikiiimDVQzBoIwhCW48FxfYRhCEEQIEsidE2GnMBUjxczXbFR1AdYpSaiRY2h\nmogoYbm0hmImg4lmCpW6i0K2s10KX4woCEhpClLaqR9jZzs+LDvEiv4CBhPYPIaIaL7i0yRERHNg\nuC+DotGP6Yrd7aXMqamKjT6jiMFCmg8oEtGilvg34Kc//WmsXLkShmFg7dq12L59e9KXICLqeX1Z\nHX2pLMRQRa3hdns5c8L1AtSbPop6H4ZYpSaiRS7RUH3PPffgpptuwm233YZdu3Zh3bp12LBhAw4c\nOJDkZYiIep4gCBgpZjCQGsBk2er2cubEVNlGn96HwUIGmspuQiJa3BIN1XfddReuv/56vPWtb8WZ\nZ56Jf/mXf8Ho6Cg+85nPJHkZIqJ5YSCfQl8qDwTKgqtWu16AWsND0ShipJjp9nKIiLousVDtOA5+\n8Ytf4LLLLjvm9csuuwyPPPJIUpchIpo3BEHAaH8GQ+lhjE+biWxd3ivGp0306UUMFbLQWaUmIkou\nVE9OTsL3fQwPDx/z+tDQEMbGxpK6DBHRvDKQT2Egk4cupjFddbq9nEQ0LQ+WCQymB7B0INvt5RAR\n9YSulhd27tzZzcufVK+uazHgve8u3v+5UbdcTI1XMGYdwpIhGZJ4/Nzq3b/a3YWVxXNw0kFBGsAR\ncw8erx7q9nISwV/73cX73z289+1bvXr1C76fWKV6YGAAkiRhfHz8mNfHx8cxOjqa1GWIiOadjK6g\nmDaQlrMoVb1uL6cjtaYP0ddQ0LIoZrh7IhHRjMQq1aqq4o/+6I9w//33Y9OmTbOv//CHP8TrX//6\nEx6zdu3apC6fiJk/rfXauhYD3vvu4v2fe3/oePi/veP4Xel3WDasQ9daW4bPVKhf9tKXdXN5bfGD\nEHsP1nHOqhV42YpR9GWNbi+pY/y13128/93Dex9dpVJ5wfcTbf9473vfi2uvvRavfOUrsW7dOnz2\ns5/F2NgY3vGOdyR5GSKieUdTZYwUs6jaQzg0MYaVSzNzsn35XBqbNJGR8xjI5hZEoCYiSlKiofoN\nb3gDpqamsHXrVhw+fBh/+Id/iO9973tYvnx5kpchIpqXlvRnUakXUXfqGJ+2MNI/f4Jppe7AtkX8\nQd8wTh8pdHs5REQ9J/EHFd/5znfine98Z9KnJSKa90RRwMrRPjRtB3tKe1A35sfsatcLcGTKxvLc\naVgxXOBGL0REJ5D4NuVERHRyKV3B8qECluSWYmzKgh/0/uzqQxNNFI0BjBTyGMinur0cIqKexFBN\nRHSKjRQzGM4VkFP6MFnu7WkgEyUL8DWMZAdxGts+iIhOiqGaiKgLTh8pYEluGPA0TFZ6M1iXaw4q\ntQDLckuxcrQAWeJvGUREJ8NvSCKiLlAVCS9ZWsSwMQTHkjFZsrq9pGPUmy4mph2syK3AqtF+ZFOc\nSU1E9EL4tAkRUZekDRXL+jMIwmGUawFk2UEhq3Z7WbBsH4cmLCzPLcdpQ0X2URMRtYGVaiKiLsoa\nCpb0pbEitwIT0w4qdaer67FsHwfGG1iSWYJl/f1YMpDt6nqIiOYLVqqJiLqsL6NhyVARIUIcmHoG\nrhdgoKCf8nXUmy4OTVhYklmKpcUBnDacP+VrICKarxiqiYh6wJKBLGRJhCxKeKbyDDzPxMjAqdsc\nplS1MVX2sCK3Asv6i1gxnJ93Oz4SEXUTQzURUY8Y6ktDVSRIoogDlWfxzFgdowMpKPLcdeoFQYgj\nJQuNBnBa/jScNlTEaD9bPoiIomKoJiLqIYWMjrOWD0IWJYzVJ7Dv4BQG+lT05ZKfvlFvuhibNJFW\nclhZGMaq0SL6+VAiEVEsDNVERD0mbag4e+UQsuMaxss5HK4eRqVex0i/AV2TOj6/6wWYKFlomsBo\nZjmGcgWcNpyHoSkJrJ6IaHFiqCYi6kGyJGLVkj4UcwbS4zom6lN4dnwKshygL6cil1Yi9zw3TA+l\nqg3TClHQC3hJcQDLBvIYLmbm6KcgIlo8GKqJiHpYIaMja6gYmzYwWSmibFYxXS7hyHQNaUOGoUkw\nNBmaKh4Xsm3Hh2n7sGwfDcuDECoo6gNYWsxjIJ/GaDEDTeVvA0RESeC3KRFRj5MkEUsHcxjtz2K6\nlsORUh8qzSaabgNWw0K5YsL2bYiCAEEAwhAIwhCKqEKXdRhKDoW0gZyRxkA+hcFCmluOExEljKGa\niGieEEUBA/kUBvIpmLaLuumgabloWC5M24UfBgjDABAESIIITZGR1lWkdQVpo/X/HJNHRDQ3GKqJ\niOYhQ1OOebAwDEMEQYggDCEIAkRBgCgyQBMRnSoM1UREC4AgCJAkAZ3PBiEiojjYVEdERERE1CGG\naiIiIiKiDjFUExERERF1iKGaiIiIiKhDDNVERERERB1iqCYiIiIi6hBDNRERERFRhxiqiYiIiIg6\nxFBNRERERNQhhmoiIiIiog4xVBMRERERdYihmoiIiIioQwzVREREREQdYqgmIiIiIuoQQzURERER\nUYcYqomIiIiIOsRQTURERETUIYZqIiIiIqIOMVQTEREREXWIoZqIiIiIqEOJheqLLroIoige88/V\nV1+d1OmJiIiIiHqWnNSJBEHAX/3VX+GOO+6Yfc0wjKROT0RERETUsxIL1UArRA8NDSV5SiIiIiKi\nnpdoT/XXvvY1DA4O4uUvfzne//73o16vJ3l6IiIiIqKelFil+uqrr8bpp5+OJUuW4IknnsCtt96K\nX/7yl/jBD36Q1CWIiIiIiHqSEIZheLI3b7vttmN6pE/koYcewoUXXnjc6zt37sQrX/lKPPbYYzj3\n3HNnX69UKh0sl4iIiIiou/L5/HGvvWConpqawtTU1AuedPny5Sd8IDEIAmiahq9+9at4/etfP/s6\nQzURERERzWcnCtUv2P7R39+P/v7+WBf7v//7P/i+j9HR0VjHExERERHNFy9YqW7Xnj178JWvfAVX\nXHEF+vv7sXv3btxyyy1Ip9PYsWMHBEFIYq1ERERERD0pkVD97LPP4i//8i/xxBNPoF6vY/ny5fiz\nP/szbN68GYVCIYl1EhERERH1rERCNRERERHRYpbonOr56m1vexte8pKXIJVKYWhoCK997Wvxq1/9\n6pjPlEolXHvttSgUCigUCrjuuuv40GUCSqUS3v3ud+OlL30pUqkUVqxYgb/+67/G9PT0cZ/j/U/e\n5z73Oaxfvx6FQgGiKOKZZ5457jO893Pr05/+NFauXAnDMLB27Vps376920takB5++GFs3LgRy5Yt\ngyiK2LZt23Gf2bJlC5YuXYpUKoX169dj9+7dXVjpwvPRj34U5513HvL5PIaGhrBx40Y8+eSTx32O\n9z95d999N8455xzk83nk83msW7cO3/ve9475DO97chiqAZx33nnYtm0bfv3rX+MHP/gBwjDEq171\nKnieN/uZq6++Grt27cIPfvAD3HffffjFL36Ba6+9tourXhgOHTqEQ4cO4R/+4R/wxBNP4Ctf+Qoe\nfvhhXHXVVcd8jvd/bpimicsvvxwf+tCHTvoZ3vu5c8899+Cmm27Cbbfdhl27dmHdunXYsGEDDhw4\n0O2lLTiNRgOveMUr8IlPfAKGYRz3rM+dd96Ju+66C5/61KewY8cODA0N4dJLL+UmZgn40Y9+hHe9\n61149NFH8cADD0CWZbzqVa9CqVSa/Qzv/9xYvnw5Pvaxj+F///d/8dhjj+Hiiy/Ga1/7Wjz++OMA\neN8TF9JxHn/88VAQhPA3v/lNGIZhuHv37lAQhPCRRx6Z/cz27dtDQRDCp556qlvLXLC+973vhaIo\nhrVaLQxD3v9TYceOHaEgCOH+/fuPeZ33fm698pWvDG+44YZjXlu9enV46623dmlFi0Mmkwm3bds2\n+99BEIQjIyPhHXfcMfuaaZphNpsN//Vf/7UbS1zQ6vV6KElS+N3vfjcMQ97/U61YLIaf+9zneN/n\nACvVz9NoNPBv//ZvWL16NVauXAkAePTRR5HJZHDBBRfMfm7dunVIp9N49NFHu7XUBatSqUDTNKRS\n/7+9+wdtoo3jAP69iybpvwsFm0ZpaWuhFcEh1KF2CC4NpOBUCg6x1KUOLYRm6qA2goMUBxHMoIjg\nUEKKulSEOIT+ocU/iCiRDopDBu9aobVJILRcHgffHm98pbxpcj0avx8ICU+ewC/fO45f/vA8tQCY\nv5WYvXm2t7fx7t07+P3+onG/34/l5WWLqvo7ff36FZqmFR0Lp9MJn8/HY2GCra0tFAoFNDY2AmD+\nB0XXdcRiMeTzefh8PuZuAjbV/4hGo2hoaEBDQwPm5ubw/PlzHDnyaxlvVVXR1NRUNF+SJLjdbqiq\nakW5VWtzcxPXrl3D6OgoZPnX6cn8rcPszfP9+3fouo7m5uaicWZ78Hbz5rE4GKFQCF6v1/iwzvzN\n9fHjR9TX18PpdGJ0dBTxeBzd3d3M3QRV21RfvXoVsizveVtYWDDmB4NBvH//HvPz8zh9+jQCgQAy\nmYyF7+BwKzV/AMhms7hw4YLxHzDan/1kT0R/xn0WKiscDmN5eRlPnjz5X9ky//KdOnUKHz58wOvX\nrzE+Po6LFy/i7du3e76Gue/PnjsqHmYTExMYHh7ec05ra6vxWFEUKIqCzs5O9Pb2orGxEc+ePcPw\n8L0tSE4AAAM3SURBVDA8Hg/W19eLXiuEwNraGjwejyn1H3al5p/NZjEwMABZljE3Nwe73W48x/xL\nU2r2e2H25jl27BhsNhs0TSsa1zSNO9EesN1zWdM0tLS0GOOapvE8r6CJiQnE43Ekk0m0t7cb48zf\nXEePHsXJkycBAF6vF2/evMG9e/dw/fp1AMy9kqq2qS5ni/VCoQAhBHRdBwCcO3cO2WwWKysrxs9V\nKysryOVy6Ovrq1jN1aSU/DOZDAKBACRJwosXL4z/Uu9i/qUp59z/HbM3j91uR09PDxKJBAYHB43x\nly9fYmhoyMLK/j4dHR3weDxIJBLo6ekBAOTzeSwtLeH27dsWV1cdQqEQZmdnkUwm0dXVVfQc8z9Y\nuq6jUCgwdxPYIpFIxOoirPTlyxc8ePAAtbW12NnZQSqVQigUwrdv33D37l3U1dWhqakJr169wszM\nDLxeL9LpNK5cuYLe3l6MjY1Z/RYOtUwmA7/fj62tLcRiMQC/vrXOZrNwOByw2WzM30SqquLz589Y\nXV3F06dP0d/fj1wuB4fDgZqaGmZvMkVRMDU1hRMnTqCmpgY3b97E0tISHj16BJfLZXV5VSWXy+HT\np09QVRUPHz7EmTNn4HK5sLOzA5fLBV3XcevWLXR3d0PXdYTDYWiahvv37xf9ckalGxsbw+PHjzE7\nO4uWlhbjGi9JEux2OyRJYv4mmZychNPpRKFQQDqdxp07dzAzM4Pp6Wl0dnYy90qzdvER66XTaREI\nBITb7RZ2u120traKYDD4n+XCNjY2RDAYFIqiCEVRxKVLl8SPHz8sqrp6JJNJIUmSkGVZSJJk3GRZ\nFvPz88Y85m+Oqamposx37/+93BizN1c0GhXt7e3C4XCIs2fPisXFRatLqkq715rfrzeXL1825kQi\nEXH8+HHhdDrF+fPnRSqVsrDi6vGna7wkSeLGjRtF85h/5Y2MjIi2tjbhcDiE2+0W/f39IpFIFM1h\n7pXDbcqJiIiIiMpUtat/EBEREREdFDbVRERERERlYlNNRERERFQmNtVERERERGViU01EREREVCY2\n1UREREREZWJTTURERERUJjbVRERERERlYlNNRERERFSmn70sbo08tT2gAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "P = [[2, 0], [0, 9]]\n", "plot_covariance_ellipse((2, 7), P, facecolor='g', alpha=0.2, \n", " variance=[1, 2**2, 3**2],\n", " axis_equal=True, title='|2 0|\\n|0 9|')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the solid colors may suggest 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 ($\\begin{smallmatrix}2&1.2\\\\1.2&1.3\\end{smallmatrix})$." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7PmbZBfsOWA/wR0iXfJHntdIZVM5zRZ1dx7rbFT/AHzE9jXu/okd9\n4HJ3x6LqAH8U6ZYv8nbrihnrZ693dLRLD1uyU4911b7f9SOZ04kcZbrk/9Pf/eI90vLfVf9Rxzz6\nfmp/hjvGvS791JXLVneBe4A/eqS2/OUcq0cu23WO9R1m1Q/wRxVtd+8f8QJeZaF338uZ3Dt6Bl0y\npt+tqz/c2XWeHcc7wB9drTL0P37U/q9c9diPON6zfP12gD+6Q62JvGd5OWcH9EyTe109S5sefX89\ntXu/+yepzwb6o8539N56Suhf2c0/Onp2fTz6Ao6Oju7Vgf7o6M10oD86ejNJY/o///zz6us4Ojq6\nScfSHx29mQ70R0dvph9fj/ip3NHR0cN0LP3R0ZvpQH909GY60B8dvZkO9EdHb6b/BxE2UFIjB6Qj\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from 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 fist plot is\n", "\n", "$$\n", "\\mathbf{\\mu} =\\begin{bmatrix}2\\\\7\\end{bmatrix},\\, \\,\n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&2 \\end{bmatrix}\n", "$$ \n", "\n", "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for $1\\sigma$. As in the univariate case 68% of the data will fall within this ellipse. Recall from the Gaussians chapter the the 68-95-99.7 rule - 68% of all values will fall within 1 standard deviation ($1\\sigma$), 95% within $2\\sigma$, and 99.7% within $3\\sigma$. This rule applies for any dimensional size. The dog could be at (356443, 58483), but the chances for values that far away from the mean are infinitesimally small.\n", "\n", "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. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second plot is for the mean and covariance\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n", "$$\n", "\n", "This time we use a different variance for $x$ ($\\sigma_x^2=2$) vs $y$ ($\\sigma^2_y=9$). The result is a tall and narrow ellipse. We can see that a lot more uncertainty in $y$ value vs $x$. Our belief that the value is (2, 7) is the same in both cases, but the uncertainties are different. In this case the standard deviation in $x$ is $\\sigma_x = \\sqrt{2}=1.414$ and the standard deviation for $y$ is $\\sigma_y = \\sqrt{9}=3$. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object or is closer than another sensor, resulting in different uncertainties in each axis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The third plot shows the mean and covariance\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", "$$\n", "\n", "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**. We denote that in the covariance matrix with values off the diagonal.\n", "\n", "What does this mean in physical terms? Think of parallel parking a car. You can not pull up beside the spot and then move sideways into the space because cars cannot drive sideways. $x$ and $y$ are not independent. This is a consequence of the steering mechanism. When the steering wheel is turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk in a straight line or a zig zag. If $x$ changes, $y$ must also change in a defined way. \n", "\n", "When we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how the relative sizes of the variance in $x$ and $y$. For example, a very long and narrow ellipse tilted almost to the horizontal has a strong correlation between $x$ and $y$ (because the ellipse is narrow), and the variance of $x$ is much larger than that of $y$ (because the ellipse is much longer in $x$)." ] }, { "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": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ail6TLiIiKYe3tzctW7Y0dwqdPXu2GdBXrFiBu7s7cXFxdO7cmbVr11oF9IUL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\n2xMTE1WnTh35+vpq7969dqwQAJwfK+kAABulS5fWvHnzFBc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "P = [[4, 3.9], [3.9, 4]]\n", "plot_covariance_ellipse((5, 10), P, edgecolor='k', \n", " variance=[1, 2**2, 3**2])\n", "plt.xlabel('X')\n", "plt.ylabel('Y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose I were to tell you that the actual position of the dog in the x-axis is 7.5, what can we infer about his position in the y-axis? 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 roughly illustrated the likely value for y as a blue filled circle." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YsEHe/SGEeCWjrEkXQgghnqcoCvfva7h0SSEszIRHj9SA/t3m0dE38PP7kseP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_correlation_covariance()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. " ] }, { "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": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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S5rJly5bKHfAR2NmqGG1U4v/DH9UeghA1jiToQggh6pQ9e/YYSj1atmxpmHjP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_gaussian_multiply()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The combination of measurement 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. They are generated by plugging the Gaussians for the prior and the estimate into Bayes Theorem. I gave you the algebra for the univariate case in the last section of the last chapter. 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", "$$\\begin{aligned}\n", "\\mu &= \\Sigma_2(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_1 + \\Sigma_1(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_2 \\\\\n", "\\Sigma &= \\Sigma_1(\\Sigma_1+\\Sigma_2)^{-1}\\Sigma_2\n", "\\end{aligned}$$\n", "\n", "To give you some intuition about this, recall the equations for multiplying univariate Gaussians:\n", "\n", "$$\\begin{aligned}\n", "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}} = \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n", "\\end{aligned}$$\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* division since $AA^{-1} =I$. I will rewrite the inversions as divisions - this is not a mathematically correct thing to do but it does help us see what is going on.\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 we can surmise that these equations are the linear algebra form of the univariate equations.\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. Radars give us 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": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7MxnvQNLp6E2R05mlypIcu6MAsAFFGkDMKotzzo939FCkkVw63rUiDSD5UKQB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\nvgZHDL2636VdJzKUmjZFebk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P0 = [[6, 0], [0, 6]]\n", "plot_covariance_ellipse((10, 10), P0, facecolor='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 is very accurate in the bearing measurement, but not very accurate at the range. That covariance, which is the uncertainty in the reading might look like this (plotted in blue):" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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PXj9FTeni/8GqNC9+sb2jfyzZpYhIEihIi8iMdfjGiMenKFOQToo2n4tf7Cvi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\nWfjF3nR6R0vIzVnOY59Zz6aG8mSXJSI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 1.9], [1.9, 2]]\n", "plot_covariance_ellipse((10, 10), P0, facecolor='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P1, facecolor='b', alpha=0.6)" ] }, { "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 he 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 of incorporating the evidence into the prior. As in every chapter so far we multiply them together. I have the equations for this and we could use those, but I will use FilterPy's `multivariate_multiply` method." ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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+efPvGJrIE/Gn+cq7/4cTWwdmZWzLgq/d8Sb6J2rx2r2cf1qQt13QzImLFn6b\nj8/jIJXPks4VFKRFqpCCtIhMWzpXwDJz+BSkK2Lb/iyfunmIRNakMRzna++5kY76sVkb/0ePvooH\nd63Cjp3XrGjgtadHWXdK/ayNX0l+j4NENkcmpz5pkWqkIC0i02JZFtl8CdPK4fcs/BnIueZnvxvg\n724cJFOw6Kgf4WtX3URjJDFr4+/sbec/77kEgNXtjZx/eoB3XrgwFxe+GL/XgWnmtOBQpEopSIvI\ntGihYeX8z6+O8LH/fIpcwWJFax9ffvfNRPyZWRs/nvHxj7dtxDAdtIajXPqaIB+4fDEup33Waqg0\nLTgUqW4K0iIyLVpoWBn/9uMDfPbG3RQNi9OXHuBzb/8Bfk9h1sY3LRtf+vFbGE5ECLi9vPG8KB98\nQyfhKjuQRwsORaqbgrSITIsWGs6+z9+8h/932z4MEy5Y9TSfuuJ23E5jVmu45eFzeXR/Fw6bnctf\nXc8H39i5YI7/fqV8Hgfp/GR7h4K0SHVRkBaRackXS1hmAberet7OrxTLsvj0t3dx3R0HsazJg1Y+\ncvldOOzWrNax/dASvnPfhQCcd1I9f/HmJSxrDcxqDXOJ120nmSuQL5QqXYqIzDIFaRGZlmLJxKKE\n26mZuJlkWRZ//62n+cbPDgPwrnMf4v0X/XpWDlr5Y4OxKJ/74UZMy87K9ggfeVsnpy2Pzm4Rc4zT\nYcc0SxSNmT85UkTmFgVpEZmWYsnAskq4nAv34I1KsyyLv/3m03zzrsMAvO/Ce3nP+Q/Oeh3pvIdP\n3vIuYpkAjWEvH93YyYWnVsc2d8fictrAKlEszW57jYhUnoK0iEyZZVmUDBMwcDrU2jETLMviY994\niv/+ZQ8A77/oV7z7vIdnvQ7DtPN/f/g2Do80EvS6+Ou3dvL2C9q0SwXgctixKFIsaUZapNooSIvI\nlBVLJqZVwuVQmJoJlmXx4f94iu/ePRmi/+x1W3jnOb+tSC3/cfclPLq/C5fDzvtev4g/e8MSbXf4\nDJfThqUZaZGqpCAtIlP2XFuHZqPLzbIsPvKN50L0hy65m7e/5ncVqeUnW8/k9sdejc0Gbz2/hb97\nZxcel3ZpedbkuzEGRcPQXtIiVUZ3PxGZsqJhYlklnJqRLivLsvib63fwnWfaOf7i0l9WLERvPbCM\nf/vFegAuPLWez29aVXV7RR8Pl+PZWWm1d4hUEwVpEZmyyRnpomaky8iyLD7xX0/zXz/vBuBDF9/N\n2179SEUa2IpZAAAgAElEQVRqOTzSwGdvm9yh49RlEb7+wZOrdq/ol+Ny2tXeIVKFdPcTkSkrliZn\npNUjXT6f/vZO/vPOwwD8n9few9vPrsxMdCzt51O3vItM3sviRj/f+PApLG2p3r2iX47TYcPSFngi\nVeeYQfrBBx9kw4YNtLe3Y7fbueGGG17wOZ/97Gdpa2vD7/dz4YUXsnPnzhkrVkTmlpJhYlmGWjvK\n5LM37uK6nx4C4E8v+jVXnvubitSRLzr5zA/eyUCshrqQm//6+KmsXhKuSC3zhctpx8LQjLRIlTlm\nkE6n06xZs4Zrr70Wn8/3ggUUX/nKV/j617/Ov//7v7N161YaGxu5+OKLSaVSM1q0iMwNlmUBWlxV\nDl//4X7+5UcHsICrL7ifq857qCJ1lAw7n/vhRnYc6cDvcXDdX6/h1StrK1LLfDL5HWBhze4hkyJS\nYccM0uvXr+fzn/88b33rW7Hbn/+plmXxL//yL3zyk5/kiiuuYPXq1dxwww0kk0luueWWGS1aROYG\nC7AsZv10vYXm27/s5vM378G04IqzHuXqC+6vSB2mZeOrd7yJ3+49EbfTztf+z2oue1VzRWqZb579\nHrCUpEWqypR7pA8dOsTQ0BCXXHLJ0Y95vV7OP/98fvvbyuxzKiKz67kZ6UpXMn/96KE+PvFfT1My\nLF578pP85et/WZG/T8uCb9x9Cfc8eQpOu41/eO+JvOfijtkvZJ6a/DdTiBapNlPeR3pwcBCApqam\n5328sbGR/v7+l/xz27Ztm+qQIoCeQ3NJ71iGeLqXzFiBsF/7Cr9Sj+xJ8/f/M0y+aPGq5fv4+zf9\nBLutMmHs5ofP44ePvgabDa66IMJru3Ja8/IKjCRKjCXDxIZi1Ie9lS5H/hfdN2Squrq6jvn4jOza\noX5Jkeqib/lX7snuLNd8b4Rc0eKkRT189u234nRUZseHO7adzn/f+1oA3vKqMH92SY1ex0VEjsOU\nZ6Sbmyf75oaGhmhvbz/68aGhoaOPvZgzzjhjqkNKlXt2RkHPobmjbmCC/hE/ixqK1ATdlS5n3nj6\ncIJP3/IIqZzJ0sYhvnjlLXhdxYrUcv/Tq/iXu94AwMYLWvmvj56mo7+noH8sS10qQmdrJ821wUqX\nI8/QfUOmKx6PH/PxKc9Id3Z20tzczJYtW45+LJfL8fDDD3P22WdP9bIiMg9pfdXx6x7MsPFzjzES\nL9ASneCrV91EyJerSC3bDizlC7e/FQsbl57RyPUfOVUhehpsNhv62xOpLseckU6n0+zbtw8A0zTp\n7u7miSeeoK6ujkWLFvGRj3yEL37xi6xYsYKuri4+//nPEwqFeNe73jUrxYtIZU2+/W9TkD5OQxM5\nrvjso/SO5qgJpPjae26kLlSZ7UJ39rbxmR+8k5Lp4DWrarnp79fidOiMrqma/B6wqSVGpMocM0hv\n3bqViy66CJi8YW7evJnNmzezadMmvv3tb/N3f/d3ZLNZ/uIv/oKJiQle/epXs2XLFgIBnX4lUg1s\nqD/6eE2kClz5hW3s708T8OT46lU30VY7UZFa9g828/c3X0Wu6GZNZ5gfbT4Lr3vKnX7Cc+/K6PtB\npLoc85Vz3bp1mOaxF788G65FpPpMtgE4ME1NSR9LMlPiz/75CbbtjeGwG/zfd3yf5c1DFanlwFAT\nH7/xvSRzPk5oD3LnF15N0KcQPV2GaWHDjl1JWqSq6H08EZkyl9OB3e6kaFRmt4n5IJs3+MS3dnD3\n1mEAPnr5nZzWebgitRwabuTjN76XRNbP8tYAW75yNlEtEi2LomGCzYnLqW0gRaqJgrSITJnLYceG\nk2JJM9IvpmSYfPl7e/j+ff1YwDvO/g2Xr91ekVoOjzTwsRuuJp4JsLTFz5avnE1tSCG6XEolC5vN\nicup26pINdF3vIhMmcvpAJtmpF+MZVl8887DfPOuHkqGyTkn7uYDr/1VRWrpHqnnYzdcTSwToLPZ\nzz1fOYf6iKcitSxURePZIK0ZaZFqoiAtIlPmdjmw2ZyUNCP9Aj/5TT//77aDpPMlljcP8Om33I7D\nPvt/T4eGG/jIDZuYSAdZ0uTnnq+eQ0NUIbqcLMuiZIDD7tTOJyJVRt/xIjJlLocdu91JoaQZ6T/2\n8FOjfPaGfYwkctQFk3zxyu/hcxdmvY6DQ4189IZNxNJBOpv9/Oqr59CoEF12xZKFzeZQW4dIFdJ3\nvYhMmcNhx2F3YJg27dzxjB2HElzznd0cGkrhcRb5wpXfoyGcmPU69g828dEbNh3tib7nq+fQWKMQ\nPROKhond5lJbh0gVUpAWkWlxOSfbO9QnDT3DGf7xpt38fn8MgE9e8WNObO2f9Tr2DrTwsRuvPro7\nh2aiZ1axZE3u2KG2DpGqo81DRWRaXA47dtvkzh0eV6WrqZyxRIF/unU/v/79KAB/su5eLli1c9br\neOLwEj79vSvJFDx0tQW456vnaHeOGVYyTGw2j2akRaqQgrSITMtzO3eUKl1KxaRzJa776UF+9OAw\nJdPkVV17uer8h2a9jod3n8jnfriRouFk1eIQv/jSa6jRPtEzrlAytfWdSJXSd72ITIvX7cRu95DN\nG5UupSJKhsm3f9HNrfeOkMzlaIrE+OSbf4zdNrs947/Yfiqbb30HRcPJmSdGuecr5yhEz5Js3sRu\n9+Cr5rdkRKqUZqRFZFr8Xhd2u49MfqLSpcw6y7K4+de93P7AGD1jcZx2g394221E/NlZrePW376G\nb9xzKQAXnVbP9z99Bl63Xt5nSyZv4HJ78StIi1QdvdKKyLQEvC7sdi/ZfPUtNrzzkUHufHic7Ycm\n+6I/eMkWVrX3zdr4lgXf+vVrueU35wHw5nNa+O+Pn6YWg1lUKJoYpp2A043bpR5pkWqjIC0i0+Jy\nOvC43ORyDgpFE7erOkLco7vG+fFDIzzw1AimZXL+yp285axHZ218w7Txz3e+gbu2n44N2HBmkO/8\nzVocDtus1SCTs9F2mxe/V7PRItVIQVpEps3vdZFMe8nkjaoI0ocHM9zy637u3RYnZ+Rpqx3jbzf8\nFNssZdhCycnnb38LD+1ahcMOV54b4S/W1ypEV0A2b2B3hAh41Y8uUo0UpEVk2vyeyfaOTD5BNLiw\nZ+bi6SL//ctuHno8x3gujttZ5LMbbyXozc/K+Kmch3+49R1sP7QUl8PGJ991AutXFbDNVoqX58nk\nDex2zUiLVKuFP3UkIjPuuQWHC3vnjpJh8p1fdvP4kwaHxkcA+MvX/5LlzUOzMn7/RA1/+e0/Zfuh\npXjddr7ygdX8zcYuhegKOhqktdBQpCppRlpEpq0aFhxalsVtD/azdUeeJw6PY1gGr+rayxvWPj4r\n4z/Vs4jP/OCdxDMBIgEX1/75SbzlvLZZGVtenBYaioiCtIhMWzUsOPzN0+Pcuy3G4zsLpEoJQt4s\nf/PGn81KX/Q9T67hq3dsoGQ4aa3zcv1HT+WCNfUzP7AckxYaioiCtIiURcDrIpn2k8wWqXMtrIVX\n+/tT/OC+fv6ww8lwbhiAv77s59SHkjM6rmnZ+O5967jpoQsAWNkR4psfPZVTlkVmdFw5PslsCYcz\nStC3sJ7vInL8FKRFpCwiQS+jsRDx9BB14YUTLCZSBb7zyx527vQwkp6gZJU458TdvPakp2Z03FzR\nxZd/8mYe2LkagLNX1/Jvf7mGrrbgjI4rxy+RLmJ3BokEvJUuRUQqREFaRMoiGvTicAZIZgxM08Ju\nn/8L4Iolk2/9vJsdu+yMx2CsMILfk+PDl901oy0dY8kg13z/Snb3t+Gw23jjq5v50vtX0Vbvm7lB\n5RXJ5A1KpouIx6fWDpEqpiAtImXhdNgJ+rzkc36S2RKRwPwOF5Zl8f37etm+s8hQf5De7F4APnjx\nPTSEZ66lY/9gM5/+3pUMJyL4XE6uuriNa646kZrgwpnlXwgS6SJ2u2ajRaqdgrSIlE006CWWDBJP\nj8/7IP2bp8e5f3uCQweDGBjkzRxrOrq5fO3vZ2Q8y4Kfbz+Nf/3FZRRKLmqDHj60YTF/fcUyfB7t\nCDHXxNNFHI4Q0aCCtEg1U5AWkbKJBDw4HEES6eFKlzItvSNZbrt/gD17vLR4Orhv+G4APnTJ3dht\nVtnHyxZc/MvPL2fLH04FYEljkI9t7OSq1y3C6Vh4O6DMd8WSSbZgIxQMEPLrnQKRaqYgLSJl4/O4\n8Hl8xPJu0rkSAe/8e4nJFw2+u6WHvfvcRGmjJ3MYwzK4YNXTrGjrL/t4PaP1bL717RweacSOjbNO\nrOWjG5fy+jMbddDKHBV/pq0j7Pfo30ikys2/u5yIzGmRgIdkOkg8nZyXQfq2B/rZsccgM1HH4kA9\nD43ci91m8r4L7y37WL9+6iT+6WcbyBXdeJ1uLjmjnr+6YgmvWllb9rGkfOLpEk5HHZGAp9KliEiF\nzb+7nIjMadGgl4GxIIn0BK11la7mlXls9wQPbI/TfTjISaFVPDr+MBYWl522nY76sbKNUyg5uO7u\n13PHtjMBqA+EeOM5NXxoQycrOkJlG0fKzzQtUlkTny9IRP3RIlVPQVpEyiroc+NxBUikHGTyBv55\nslBuNJ7n1vv72LPXy2JfFxkjzeH0AdzOIldf8EDZxumfqOEfb9vI3oFWbNjoaqrn9WeH+OAbOmlv\n0PZ2c91EqojN7ifk96p/XUQUpEWkvGw2G3URP9l8DaPxCToa/ZUu6WWZpsVNvzrCnv0u/KVmGkPN\nPDQ62crx5jO30hBOTHsMy4I7f38639hyCdmCB5fNzZnLG1l3pp8/e8MSbW83T4zG8zidbdRH5v7z\nWkRm3rR/nE4mk3zkIx9hyZIl+P1+zjnnHLZt21aO2kRknmqI+HE6o0wkDQyj/LtclNvd24bZvivP\nxHCQZcEuDMugJ30IgDeePv3Xs5FEmE/cfBVfv/ONZAsewu4wl57ezBUXRvjwFcsUoueJdK5ErujE\n6w5RE1Jbh4iUYUb6/e9/Pzt27ODGG2+kvb2dm266ide97nXs3LmT1tbWctQoIvOMx+0kGvQzlA8x\nnszTEJ27i7IODqS563fD7D/g54TgSpx2F93pQxStAl3NA7TXjU/52pYFv3ziVK67+/Wk816cNift\n4UZec5qLDWc3sP6spgVxAmS1GI0XcDprqY/4tVuHiADTnJHOZrPcfvvtfPnLX+b8889n6dKlbN68\nmeXLl/ONb3yjXDWKyDzUEPHjckUZTRQqXcpLKpZMbv51L3v3e2hwdBBxRQE4nN4PwIWrd0z52n3j\nNXz8pvfy1TveTDrvJeyKclp7Bxef4+ZDb+rg8lc3K0TPIyXDJJYycDkjNEQDlS5HROaIac1Il0ol\nDMPA43n+bJPX6+Xhhx+eVmEiMr9Fgl58niDxpItEpkjYP/dOOvzV70fYfdAgF6/jxGgnACWzSE9m\nsq1j3eqnX/E1CyUnP3rkVdzwwDryJRduu5tGTzMrlzo5ZZWd91/WSWudFhXON+OJInZHiGjQj9s1\nPxbQisjMs1mWNa0GxnPOOQeHw8H3v/99mpqa+N73vsemTZvo6upi165dAMTj8aOfv2/fvulVLCLz\nxmgix3B8lIBnnPa6uRWkx1MG39wS4+mna1lsX03QMbntXNyY4L7kL1lUN8qNf/nvx309w7TzyydO\n4YYH1jGSiADQ4Gwi6PSxtDPJycvgTWeF8Lm108N8dGCwQMlsoaOhhqB3bj2XRWTmdHV1Hf11JBJ5\nwePT7pG+6aabeN/73kd7ezsOh4PTTz+dK6+8kscff3y6lxaReS4acDMSD5DKjVEsWbicc6OVwbIs\n7nkiRV+/n5DVeDREAxiWAUDAkz/Oa8FDu1fy3/deRM9oAwBhe4RGVwtOT5bOzhjnneRm3eqAWjnm\nqXTOpGi48bh9CtEi8jzTDtJLly7l/vvvJ5vNkkgkaGpq4h3veAfLli170c8/44wzpjukVKlnd4PR\nc2h+aRqYYGC0gbpQas60NPx+X4y+mEUmGea0hpNx2Z/bNSOfzUAKbLZjv1lnWjZ+f7CT/77vInb3\ntQMQcoY5ObKWvJHDHR1n5Yk23v261Zx5Ys2Mfj07d+4EYNWqVTM6TrU60J8mUN/AkpZFNNUGK12O\nvAK6b8h0/XFXxYsp2z7SPp8Pn8/HxMQEW7Zs4Wtf+1q5Li0i81hjNMBovIaRWIzGqFnxQyxyBYPb\nH+7n4EEPHf6lzwvRAGFXDTZs7BtoYTgepjHy3B7SlgW7+tq5b8dq7t+5mtFkGACfw8cp0TNp9DRx\nML2X5rY0J62weP9lS+fFPtry0lLZEsmsjWAgSp32jhaR/2XaQXrLli0YhsGKFSvYv38/f/u3f8vK\nlSv5kz/5k3LUJyLzXMDnpjYUYqgYZXA8VfHT++56dIj9h8DK1tAUaXnB436nn3ZfB0ey3Xzg+g9y\n9ol7cNoN8iUXT3YvZigePfq5QWeIE0KrWBE6iYFcL4fyOzhhZY4zV/t4z8WL5uQCS3llBsZyuF1N\nNNcGK/5DoIjMPdMO0vF4nE9+8pP09vZSW1vL2972Nr7whS/gcGhVs4hMamsIM5GsYzQxOSvtdlUm\nkPSOZLlv+xg9PQFWBrteci/gcxsu4ldDP2ckO8QvnzjteY/5HQE6A8vpDCyn3tNI3syzJ/k0rtA4\np52QZ8M5TVy8tkH7DC8A8XSRTMFJKBClqUYtHSLyQtMO0hs3bmTjxo3lqEVEFiiv20lDNET/aC39\nY3GWNFfmLfJ7Hh+mp8dNnaONoDP0kp/ndfi4vOUtjBVGGM4NYrc5cNgchF0RGj3NR0PySH6IQ+m9\ntHdkWHUCXH3JUpa2aI/hhWJgLIfL1UpLXUgLRUXkRZWtR1pE5Fha6kKMJeqIpSfI5g18ntl912os\nUeD3+xIMDwc4Ndzxsp9vs9mo9zRS72l8wWMls8TB9D5S9gFWnZTjNScHufKidgJevaQuFOPJAoWS\nh0g4SkNUvdEi8uL0qi8is8LtctBYE6K3WE//2BjLWmd35vahp0YZGHBS42zC45j6keWJYpx9yV1E\nG5Kc2VXkree1cPbqWrVyLCCWZTE4nsPl7qC1LqR/WxF5SQrSIjJrmmuDjMRqSabHSWVLBH2z8xKU\nKxj89ukJBgY9rPC1T+kaJbNEb7abkdIRlp2Q45QTXbz34i4aa6YeymVuGo0XKJkBaoJhasNzY8tG\nEZmbFKRFZNY4HXaaa4P0FBoYGBuiq312FnA9umuCvgEbXrP2mL3RL8ayLMYKoxxO7ydSl+a0zjyv\nP6ue9Wc1aReHBcg0LQYn8rhcrbTVv7LniohUHwVpEZlVTTVBRmI1JFLjjCUK1IXdL/+HpsGyLB54\napT+fhdt3lc2G50zshxM7SPvHKVrZZ6TuzxsvGCZ9oZewPrGcmALEwkEiQS9lS5HROY4BWkRmVV2\nu41FjWH2FVrpGz1MyOec0e3wktkSg6NFsmk/tbV1x/VnTMukL9vDQL6H1vYcy5YYbDi7mbNX1Wr3\nhgUsmSkxljDx+5roaIpUuhwRmQcUpEVk1tWEfNRHIgyN19EzMs7y1plr8RiO5clmbfgc/pddNGZZ\nFrHiBIfS+/FFEqxZmefckyO86ZwWHa6ywJmmxZGRDG53O631EXwe/XuLyMtTkBaRiuhoipDM5Emm\nkzPa4jESK5DL2fE5XnrRmGmZjOaH6c/2YrkTLOkqsGKZg7ef3zlrfdxSWX1jOQwrTE0gSnOt/s1F\n5PgoSItIRTgddjqaIuzrndkWD4fdht0OJct4wWNFs8Bgrp/BXD/+cIbFJxRZ1GrjwlPrWXdKvRYT\nVok/bulY0hzVdncictwUpEWkYmajxWNZa4BwxOCQNcrB1D68Dh85I0vWyJAy4tTV51l9QpHli9ys\nO7WV07siCtBVRC0dIjIdCtIiUlEz3eJRF3bzxtc0YBqjjIwcIle04fWa1PhMgiGTU5eHWHdKG11t\nAc1EViG1dIjIdChIi0hFzUaLx2WvaqarPci+3hSJTInGqIfGqIeWOu+Mb78nc5daOkRkuhSkRaTi\nnm3xGJ5o4NDgCF1twbJvM9fVFqSrTTOOMqlQNOkeyqqlQ0SmRY2AIjInLG6KEPQ3kC+F6BnOVroc\nWcBM0+LQYBqbo4HacA0tdTrBUESmRkFaROYEh8PO8rZa/L5WEhknQxO5SpckC1T3cIaCESLkb2Bp\nS02lyxGReUxBWkTmDK/bydKWGjyedgbGDeLpYqVLkgVmcDxHMuPC521lWVstDu3QIiLToFcQEZlT\nIkEv7Y2TYbp7KEeu8ML9n0WmIpYqMjhh4PG0s6y1Fq9by4REZHoUpEVkzmmuDdIQrcHpbObgQBrD\nsCpdksxz2bxBz3AOj6edRY01hAOeSpckIguAgrSIzElLmqNEQvWY1HJwMI1lKUzL1JQMk0ODaZzO\nFhpramnSftEiUiYK0iIyJ9lsNpa11hDwNZMt+LSTh0yJaVocGshgUkskVMfipkilSxKRBURBWkTm\nLJfTwbLWGnzeduJpF0dGFKbl+JmmxYG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MdLNsbAEEaQAAAKAN9EgDAAAAbSBIAwAAAG0g\nSAMAAABtIEgDAAAAbSBIAwAAAG0gSAMAAABtIEgDAAAAbSBIAwAAAG0gSAMAAABt+A/ZGNyW36Os\nXwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "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, facecolor='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, facecolor='b', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P2, facecolor='y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I have plotted the original estimate (prior) it a very transparent yellow, the radar reading in blue (evidence), and the finale estimate (posterior) in yellow.\n", "\n", "The Gaussian 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. But the main point I want to make is that the covariance shape reflects the physical layout of the aircraft and the radar system.\n", "\n", "Now lets say we get a measurement from a second radar, this one to the lower right, which I will plot in blue against the yellow covariance of our current belief. " ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PpLMvmLiIIFL0E/P+/9drIf8t5i8Z28CWlZU1436v/I3ub2vFPys7O5vs7Ozp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\nsQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P3 = [[2, -1.9], [-1.9, 2.2]]\n", "plot_covariance_ellipse((10, 10), P2, facecolor='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P3, facecolor='b', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, to incorporate this new information we will multiply the Gaussians together." ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OqrPWoVNSt+PH1Toz8p2Vlc24P0SaMYBOUUi3paHTZZMVzaCp7whNDj+5+Ta2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\nqqurkZycDKVSCbvdjszMTKxevVruaDTA7t0QLTw8vNdxvV6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", "plot_covariance_ellipse((10, 10), P2, facecolor='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P3, facecolor='b', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, facecolor='y')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see how the multivariate Gaussian's shape reflects the geometry of the problem. The first radar system was at a 45 degree angle to the aircraft, and its error in the bearing measurement was much smaller than the error in the range. This resulted in a long and narrow covariance ellipse whose major axis was aligned with the angle to the radar system. The next radar system was also at a 45 degree angle, but to the right, so the two measurements were orthogonal to each other. This allowed 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", "To make sure you understand this, what would the Gaussian look like if we only had one radar station, and we received several measurements from it over a short period of time? Clearly the Gaussian would remain elongated in the axis of the bearing angle. Without a second radar station no information would be provided to reduce the error on that axis, so it would remain quite large. As the aircraft moves the bearing will typically change by a small amount, so over time some of the error will be reduced, but it will never be reduced as much as a second radar station would provide.\n", "\n", "To round this out lets quickly redo this example but with the first radar system in a different position. I will position it directly to the left of the aircraft. The only change I need to make is to the Gaussian for the measurement from the radar. In the previsous example I used\n", "\n", "$$\\Sigma = \\begin{bmatrix}2&1.9\\\\1.9&2\\end{bmatrix}$$\n", "\n", "Why did this result in a 45 degree ellipse? Think about that before reading on. It was 45 degrees because the values in the diagonal were identical. So if x=10 then y=10, and so on. We can alter the angle by making the variance for x or y different, like so:" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QyNCALyCLJaAEh9lposPpNxkuL5vO1D0AUIRGpLu7u/UXf/EXWrBggW666Sat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\n8XK/okiP4Fe/+pXuuusu3Xv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 1.9], [1.9, 8]]\n", "plot_covariance_ellipse((10, 10), P1, facecolor='y', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The radar is to the left of the aircraft, so I can use a covariance of \n", "\n", "$$\\Sigma = \\begin{bmatrix}2&0\\\\0&0.2\\end{bmatrix}$$\n", "\n", "to model the measurement. Incidentally, I invented those values. We haven't learned how to transform a matrix from one coordinate system to another. \n", "\n", "In the next graph I plot the original estimate in a very light yellow, the radar measurement in blue, and the new estimate based on multiplying the two Gaussians together in yellow." ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PpodskwBPCw5FdpkrBul6vc6tt97KAw88QCwWu+zltU984hP8/u//Pn/0R3/E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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, facecolor='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, facecolor='b', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P2, facecolor='y')" ] }, { "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": 85, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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+i68ewzDwBSL4Al6G/QOMBHQCAQuDXjua6kTV7FjNVtyODwK53Wq++D+OEELM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\nfF6F3HGIyIGwgBMRkewCBnlg06uT8NL0QESPboX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"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, facecolor='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P3, facecolor='b', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, facecolor='y')" ] }, { "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. Imagine standing on the ground and trying to triangulate on an aircraft in the sky with a transit. If you took a measurement, moved the transit 5 meters and took a second measurement the tiny change in angle between the two measurements would result in a very poor measurement because a very small error in either measurement would give a wildly different result. Think of the measurements as two nearly parallel lines. Changing the angle between them slightly will move the intersection between the two by a large amount. If you were to take the measurements from positions 100 km apart the lines might be nearly perpendicular to each other, in which case a small measurement error would result in a very small shift in the intersection point." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hidden Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can probably already see why a multivariate Kalman filter can perform better than a univariate one. The last section demonstrated how we can use correlations between variables to 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": 86, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import mkf_internal\n", "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": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "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* assumption is that the aircraft is moving one unit each in *x* and *y* per time step.\n", "\n", "Think back to the g-h filter chapter when we were trying to improve the weight predictions of a noisy scale. We incorporated *weight gain* into the equations because it allowed us to make a better prediction of the weight the next day. The g-h filter uses the *g* parameter to scale the amount of significance given to the current weight measurement, and the *h* parameter scaled the amount of significance given to the weight gain.\n", "\n", "We are going to do the same thing with our Kalman filter. After all, the Kalman filter is a form of a g-h filter. In this case we are tracking an airplane, so instead of weight and weight gain we need to track position and velocity. Weight gain is the *derivative* of weight, and of course velocity is the derivative of position. It's impossible to plot and understand the 4D chart that would be needed to plot *x* and *y* and their respective velocities so let's do it for $x$, knowing that the math generalizes to more dimensions.\n", "\n", "At time 1 we might be fairly certain about the position (x=0) but have no idea about the velocity. We can plot that with a covariance matrix like this. The narrow width expresses our relative certainty about position, and the tall height expresses our lack of knowledge about velocity." ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now after one second we get a position update of x=5." ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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E12mn/qqrrnK2QDsajz/++HEVBAA4fvasefvXbTv1SX6f0+luv94L7E59Wmqy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\nSU8//bT69++vU045Rbfeeqt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This implies that our velocity is roughly 5 m/s. But of course position and velocity are correlated. If the velocity is 5 m/s the position would be 5, but if the velocity was 10 m/s the position would be 10. So let's draw a velocity covariance matrix in red." ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2QWSkCewZGXDBBaWBftMm04KTkADZ2aXVeh8f+OADc+KsiIiUU+mdrX379nXj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\nkSSd/+KiztU0yb+/n4YOItQDAAj1AOD1RgwJlyQ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IzZkzR6+//vplW2+ux5Vq+eqxmMOH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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This superposition of the two covariances is where the magic happens. The only reasonable estimate at time t=1 (where position=5) is roughly the *intersection* between the two covariance matrices! More exactly, we can use the math from the last section and *multiply* the two covariances together. From a Bayesian point of view we multiply the prior with the evidence to get the posterior. If we multiply the position covariance with the velocity covariance using the Bayesian equations we get the result shown in the next chart." ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CDNgoG0uHjp0f7sO6f9mBluEALDLg14DXmofQG9Sjgb6mBmhrOz/Qu90M9ERE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\nYagnIkoZfsclIpqss2dFf7wkiR76vLz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that 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 thing happens here. However, the amount by which the covariance got smaller by is much larger in this chapter. This is because we are using two different kinds of information which are nevertheless correlated. Knowing the velocity approximately and the position approximately allows us to very quickly hone in on the correct answer. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a *key point* in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). This is called an **observed variable**. It does not have a sensor that provides velocity. But based on the position estimates we can compute velocity. In Kalman filters we would 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 measurement, and use Bayes theorem to and produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you grasp this point the rest is straightforward. If you do not you will quickly find it impossible to reason about what you will learn in the rest of this chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In summary 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 zombies. I showed you this in terms of geometry and talked about *triangulation*. That was just to build your intuition. 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 evidence 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": { "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }