{ "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 Kalman Filters - Working with Multiple State Variables" ] }, { "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": [ "In this chapter I am purposefully glossing over many aspects of the mathematics behind Kalman filters. Some things I show you will only work for special cases, others will be 'magical' - it will not be clear how I derived a certain result. I prefer that you develop an intuition for how these filters work through several worked examples. If I started with rigorous, generalized equations you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. \n", "\n", "To make this possible we will restrict ourselves to a subset of problems which we can describe with Newton's equations of motion. These filters are called **discretized continuous-time kinematic filters**. In the *Kalman Filter Math* chapter we will develop the math required for solving any kind of dynamic system. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Newton's Equations of Motion\n", "\n", "Newton's equations of motion are: given a constant velocity $v$ of a system we can compute its position $x$ after time $t$ with:\n", "\n", "$$x = vt + x_0$$\n", "\n", "For example, if we start at position 13 ($x_0=13$), our velocity is 10 m/s ($v=10$) and we travel for 12 seconds($t=12$) our final position is $133=(10\\times 12) + 13$.\n", "\n", "We can incorporate constant acceleration with this equation\n", "\n", "$$x = \\frac{1}{2}at^2 + v_0 t + x_0$$\n", "\n", "And if we assume constant jerk we get\n", "\n", "$$x = \\frac{1}{6}jt^3 + \\frac{1}{2}a_0 t^2 + v_0 t + x_0$$\n", "\n", "As a reminder, we generate these equations by integrating a differential equation. Given a constant velocity v we can compute the distance traveled over time with the equation\n", "\n", "$$\\begin{aligned} v &= \\frac{dx}{dt}\\\\\n", "dx &= v\\, dt \\\\\n", "\\int_{x_0}^x\\, dx &= \\int_0^t v\\, dt\\\\\n", "x - x_0 &= vt - 0\\\\\n", "x &= vt + x_0\\end{aligned}$$\n", "\n", "Dynamic systems are describable with differential equations. Most are not easily integrable in this way. We start with Newton because we can integrate and get a closed form solution, which makes the Kalman filter easier to design." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear Algebra with NumPy\n", "\n", "This chapter and the remainder of the book will be using linear algebra to implement the filter. I do assume some basic familiarity with linear algebra - an understanding of vectors, matrices, matrix addition and multiplication, inverses and transposes.\n", "\n", "Chapter one contains an overview of doing linear algebra in NumPy; please refer to it before going on if you are in doubt in how to use it. The main thing to know is that we will be using `numpy.array` to store matrices and arrays. Matrix multiplication of `A` and `B` requires the use of `numpy.dot(A, B)`. The asterisk performs element-wise multiplication. The Kalman filter code always uses matrix multiplication, not element-wise multiplication." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[34, 37],\n", " [78, 85]])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "A = np.array([[1, 2], [3, 4]])\n", "B = np.array([[10, 11], [12, 13]])\n", "\n", "np.dot(A, B) # matrix multiplication" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[10, 22],\n", " [36, 52]])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A*B # element-wise multiplication" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Kalman Filter Algorithm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have that under our belts we can show how the Kalman filter works. The algorithm is the same Bayesian filter algorithm that we have used in every chapter. The update step is slightly more complicated, but I will explain why when we get to it.\n", "\n", "**Initialization**\n", "\n", " 1. Initialize the state of the filter\n", " 2. Initialize our belief in the state - how accurate do we think it is\n", " \n", "**Predict**\n", "\n", " 1. Based on the system behaves, predict its state at the next time step\n", " 2. Adjust belief in that state to account for the uncertainty in prediction\n", " \n", "**Update**\n", "\n", " 1. Get a measurement and associated belief about its accuracy\n", " 2. Compute difference (residual) between our estimated state and measurement\n", " 3. Compute scaling factor (Kalman gain) based on whether the measurement or prediction is more accurate\n", " 4. set state between the prediction and measurement based on scaling factor\n", " 5. update belief in the state based on how certain we are in the measurement\n", " \n", "As a reminder, the chart below shows what the filter does. **blah about multple variables - not sure where I first introduce that such that this will make sense**." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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KS+np6W6vL1++rPbt2yspKUnPP/+8mjVrprJly8rHx0eTJ0/Wpk2bbBkTCofD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\nbLwzZpjzjRsnvfGG+z5n2Ue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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mkf_internal import show_residual_chart\n", "show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking a Dog" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of the previous chapter - that of using *hidden variables* to improve our estimates. I could spend a lot of time talking about it, but let's implement a filter, learning as we go. On the surface the math is different and perhaps more complicated than the previous chapters, but the ideas are all the same. There are more things to do, so I have broken it up into a series of steps **blah**\n", "\n", "I have programmed the equations of the Kalman filter into the `KalmanFilter` class in FilterPy. You will import it with\n", "\n", " from filterpy.kalman import KalmanFilter\n", " \n", "The class contains variables **blah**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initialization - Choose the State Variables and Set Initial Conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 1**: Design State Variable as a Multivariate Gaussian\n", "\n", "In the univariate chapter we tracked a dog in one dimension by using a Gaussian. The mean $(\\mu)$ represented the most likely position, and the variance ($\\sigma^2$) represented the probability distribution of the position. In that problem the position is the *state* of the system, and we call $\\mu$ the *state variable*.\n", "\n", "In this problem we will be tracking both the position and velocity of the dog, so we have two state variables. It is important to understand that this is a design choice with implications and assumptions that we are not yet prepared to explore. For example, we could also track acceleration, or even jerk.\n", "\n", "State variables can either be *observed variables* - directly measured by a sensor, or *hidden variables* - inferred from the observed variables. For our dog tracking problem the sensor reads position, so position is observed and velocity is hidden. \n", "\n", "In the previous chapter we would represent the dog's position as:\n", "\n", "$$\\mu = 3.2$$\n", "\n", "In the last chapter we learned to use a multivariate Gaussian. For example, if we wanted to specify a position of 10.0 m and a velocity of 4.5 m/s, we would write:\n", "\n", "$$\\mu = \\begin{bmatrix}10.0\\\\4.5\\end{bmatrix}$$\n", "\n", "The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix (usually called a **vector**) to store $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot{x}$, for velocity. The Kalman filter equations use $\\mathbf{x}$ for the state, so we define $\\mathbf{x}$ as:\n", "\n", "$$\\mathbf{x} =\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", "\n", "We use $\\mathbf{x}$ instead of $\\mu$, but recognize this is the mean of the multivariate Gaussian. It is common to use the transpose notation to write the state variable as $\\mathbf{x} =\\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathbf{T}$ because the transpose of a row vector is a column vector. This notation is easier to use in running text because it takes less vertical space.\n", "\n", "Let's code this. FilterPy's `KalmanFilter` class contains a variable `x` for the state variable. Initialization of `x` is as simple as" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 10. ],\n", " [ 4.5]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from filterpy.kalman import KalmanFilter\n", "kf = KalmanFilter(dim_x=2, dim_z=1)\n", "\n", "kf.x = np.array([[10.0],\n", " [4.5]])\n", "kf.x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I often use the transpose trick in my code to turn a row matrix into a vector:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 10. ],\n", " [ 4.5]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kf.x = np.array([[10.0, 4.5]]).T\n", "kf.x " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, NumPy recognizes 1D arrays as vectors, so I can simplify this line to use a 1D array." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "kf.x = np.array([10.0, 4.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's it; the state vector is designed and implemented.\n", "\n", "One point that might be confusing: $\\mathbf{x}$ and $x$ somewhat coincidentally have the same name. If we were tracking the dog in the y-axis we would write $\\mathbf{x} =\\begin{bmatrix}y & \\dot{y}\\end{bmatrix}^\\mathsf{T}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The other half of the multivariate Gaussian is the covariance $\\Sigma$. Kalman filter equations typically use the symbol $\\mathbf{P}$. In the one dimensional Kalman filter we specified an initial value for $\\sigma^2$, and then the filter took care of updating its value as measurements were added to the filter. The same thing happens in the multidimensional Kalman filter. We specify an initial value for $\\mathbf{P}$ and the filter updates it during each predict and update step.\n", "\n", "We need to set the variances to reasonable values. For example, we may choose $\\sigma_\\mathtt{pos}^2=500 m^2$ if we are quite uncertain about the initial position. Top speed for a dog is around 20 m/s, so in the absence of any other information about the velocity we can set $\\sigma_\\mathtt{vel}=20$, or $\\sigma_\\mathtt{vel}^2=400$. \n", "\n", "In the last chapter we showed that the position and velocities are correlated. But how correlated are they for a dog? I have no idea. As we will see the filter computes this for us, so I initialize the covariances to zero. Of course if you know the covariancies you should use them.\n", "\n", "Recall that the diagonals of the covariance matrix contains the variance of each variable, and the off-diagonal elements contains the covariances. To initialize the Kalman filter to the values in the previous paragraph we would write:\n", "\n", "$$\n", "\\mathbf{P} = \\begin{bmatrix}500 & 0 \\\\ 0&400\\end{bmatrix}\n", "$$\n", "\n", "There are better initialization schemes than this - typically we use the first measurement to determine the values for $\\mathbf{x}$, but we will need to know a bit more before I can explain it. A Kalman filter can recover from poor initialization, so for now this scheme is fine.\n", "\n", "Let's write the code for that. Here I take advantage of the function `numpy.diag` which creates a diagonal matrix from the values for the diagonal. Recall from linear algebra that a diagonal matrix is one with zeros in the off-diagonal elements." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 500., 0.],\n", " [ 0., 400.]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kf.P = np.diag([500, 400])\n", "kf.P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I could have been explicit. This creates the same value:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 500., 0.],\n", " [ 0., 400.]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kf.P = np.array([[500., 0.],\n", " [0., 400.]])\n", "kf.P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are done. We've expressed the state of the filter as a multivariate Gaussian and implemented it in code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predict Step\n", "\n", "The next step in designing a Kalman filter is telling it how to predict the state (mean and covariance) of the system for the next time step. We do this by providing it with equations that describe the physical model of the system.\n", "\n", "\n", "### **Step 2:** Design the State Transition Function\n", "\n", "In the univariate chapter we modeled the dog's motion with\n", "\n", "$$ x = v \\Delta t + x_0$$\n", "\n", "and implemented it with\n", "\n", " def predict(pos, variance, movement, movement_variance):\n", " return (pos + movement, variance + movement_variance)\n", " \n", "If the current position is 5.4 meters, and the movement is 1.1 meters over the time step, then of course the new position is 5.4 + 1.1, or 6.5 meters.\n", "\n", "We will do the same thing in this chapter, using multivariate Gaussians instead of univariate Gaussians. You might imagine this sort of implementation:\n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix}10.0\\\\4.5\\end{bmatrix}, \\, \\, \n", "d\\mathbf{x} = \\begin{bmatrix}1.2\\\\0.\\end{bmatrix} \\\\\n", "\\mathbf{x} = \\mathbf{x} + d\\mathbf{x}$$\n", "\n", "But we need to generalize this. The Kalman filter equations work with *any* linear system, not just Newtonian ones. Maybe the system you are filtering is the plumbing system in a chemical plant, and the amount of flow in a given pipe is determined by a linear combination of the settings of different valves. \n", "\n", "$$ \\mathtt{pipe_1 flow} = 0.134 (\\mathtt{valve}_1) + 0.41(\\mathtt{valve}_2 - \\mathtt{valve}_3) + .34 \\\\\n", "\\mathtt{pipe_2 flow} = 0.21 (\\mathtt{valve}_2) - 0.6(\\mathtt{valve}_1 - \\mathtt{valve}_5) + 1.86$$\n", "\n", "Linear algebra has a powerful way to express systems of equations. Take this system\n", "\n", "$$2x+3y=8\\\\3x-y=1$$\n", "\n", "We can put this in matrix form by writing:\n", "\n", "$$\\begin{bmatrix}2& 3 \\\\ 3&-1\\end{bmatrix} \\begin{bmatrix}x\\\\y\\end{bmatrix} = \\begin{bmatrix}8\\\\1\\end{bmatrix}$$\n", "\n", "If you perform the matrix multiplication in this equation the result will be the two equations above. In linear algebra we would write this as $\\mathbf{Ax}=\\mathbf{b}$, where\n", "\n", "$$\\mathbf{A} = \\begin{bmatrix}2& 3 \\\\ 3&-1\\end{bmatrix},\\, \\mathbf{x} = \\begin{bmatrix}x\\\\y\\end{bmatrix}, \\mathbf{b}=\\begin{bmatrix}8\\\\1\\end{bmatrix}$$\n", "\n", "We call the set of equations that describe how the systems behaves the **process model**. We use the process model to perform the innovation, because the equations tell us what the next state will be given the current state. Kalman filters implement this using the linear equation, where $\\mathbf{x}^-$ is the *prior*, or predicted state:\n", "\n", "$$\\mathbf{x}^- = \\mathbf{Fx}$$\n", "\n", "Our job as Kalman filters designers is to specify $\\mathbf{F}$ such that $\\mathbf{x}^- = \\mathbf{Fx}$ performs the innovation (prediction) for our system. To do this we need one equation for each state variable. In our problem $\\mathbf{x} = \\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathtt{T}$, so we need one equation for $x$ and a second one for $\\dot{x}$ . We already know the equation for the position innovation:\n", "\n", "$$x^- = \\dot{x} \\Delta t + x$$\n", "\n", "What is our equation for velocity ($\\dot{x}$)? Unfortunately, we have no predictive model for how our dog's velocity will change over time. In this case we assume that it remains constant between innovations. Of course this is not exactly true, but so long as the velocity doesn't change *too much* over each innovation you will see that the filter performs very well. So we say\n", "\n", "$$\\dot{x}^- = \\dot{x}$$\n", "\n", "This gives us the process model for our system \n", "\n", "$$\\begin{aligned}\n", "x^- &= \\dot{x} \\Delta t + x \\\\\n", "\\dot{x}^- &= \\dot{x}\n", "\\end{aligned}$$\n", "\n", "We need to express this set of equations in the form $\\mathbf{x}^- = \\mathbf{Fx}$. Let me rearrange terms to make it easier to see what to do.\n", "\n", "$$\\begin{aligned}\n", "x^- &= 1x + &\\Delta t \\dot{x} \\\\\n", "\\dot{x}^- &=0x + &\\dot{x}\n", "\\end{aligned}$$\n", "\n", "We can rewrite this in matrix form as\n", "\n", "$$\\begin{aligned}\n", "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}^- &= \\begin{bmatrix}1&\\Delta t \\\\ 0&1\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\\\\\n", "\\mathbf{x}^- &= \\mathbf{Fx}\n", "\\end{aligned}$$\n", "\n", "$\\mathbf{F}$ is often called the **state transition function**. In the `KalmanFilter` class we implement the state transition function with" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , 0.1],\n", " [ 0. , 1. ]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dt = 0.1\n", "kf.F = np.array([[1, dt],\n", " [0, 1]])\n", "kf.F" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test this! `KalmanFilter` has a `predict` method that performs the prediction by computing $\\mathbf{x}^- = \\mathbf{Fx}$. Let's call it and see what happens. We've set the position to 10.0 and the velocity to 0.45 meter/sec. We've defined `dt=0.1`, which means the time step is 0.1 seconds, so we expect the new position to be 10.45 meters after the innovation. The velocity should be unchanged." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 10.45 4.5 ]\n" ] } ], "source": [ "kf.x = np.array([10.0, 4.5])\n", "kf.Q = 0 # amount of noise in the system, we haven't learned this yet.\n", "kf.predict()\n", "print(kf.x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This worked. Note that the code does not distinguish between between the *prior* and *posterior* in the variable names, so after calling predict the prior $\\mathbf{x}^-$ is stored in `KalmanFilter.x`. If we call `predict()` several times in a row the value will be updated each time." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 10.9 4.5]\n", "[ 11.35 4.5 ]\n" ] } ], "source": [ "kf.predict()\n", "print(kf.x)\n", "kf.predict()\n", "print(kf.x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 3**: Design the Process Noise Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`KalmanFilter.predict()` computes both the mean and covariance of the innovation. This is the value of $\\mathbf{P}$ after three innovations (predictions)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 536., 120.],\n", " [ 120., 400.]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kf.P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspecting the diagonals shows us that the position variance got larger. We've performed three prediction steps with no measurements, and our uncertainty grew. The off-diagonal elements became non-zero - the Kalman filter detected a correlation between position and velocity! The variance of the velocity did not change.\n", "\n", "Here I plot the covariance before and after the predictions. The intial value is in solid red, and the final value is in dashed black." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7dsTjX7vS2e12xo4dyyuvvEKHDh2oUqUKU6dOJSkpiRkzZlhZhoi4g4QEWLrU\njF/t2PGWT7N27Vr69esHwOTJk6lVq5ZVFYq4By+vS++RzA+rIpIrOW2Md2xsLPHx8bRq1eriY35+\nfoSFhbF+/XpnlSEizjJ/vhm32qKF6c27BQkJCXTq1Im0tDQGDhzI448/bnGRIm4i87dCFgw3ERH3\n5eWshuLi4gAoUqTIZY8HBwdz9OjRq74uOjr6uue+kWPEcXT9Xcedr32FTz8lPxBbrx4Jt1jn9u3b\nOX/+PDVq1OCRRx5xu5/X3eq53eSq658nD9XvuAPvffvYMX06ZypXdnVF15Srrn0OpOvvOte79qGh\nodd83mnB+1q07JFI7uJ18iT5oqPJ8PLir6ZNb/k8VapUYdasWaSmpuLl5Rb/XIk4hqcnp1q0IHj2\nbO5YutTtg7eI3Bqn/U+WOdEjPj7+sl3m4uPjrzkJpHbt2ld9LvNTx7WOEcfR9Xcdt7/2EydCRga2\ntm2p2by5q6uxnNtf/1wu117/Pn1g9mxC1qwhZOpUswznTXr00UeJjo5m8uTJNM3Gh96rybXXPofQ\n9XedG732iYmJ13zeaWO8y5YtS0hICEuWLLn4WGpqKuvWraNBgwbOKkNEnMGi1UxEbisNG0Lx4nDw\nIPzyyy2dYvfu3ezbt488efJYXJyIWMHy5QS3bNnCli1byMjI4ODBg2zZsoXDhw9js9no378/kZGR\nzJ8/n23bttG9e3fy5ctHly5drCxDRFzp9GlYuxa8veHBB11djUjO4eFxaXWTH364pVMcPHgQgFKl\nSllVlYhYyNLgvXHjRmrVqkWtWrVITU1l6NCh1KpVi6FDhwIwZMgQBgwYQO/evalTpw7x8fEsWbKE\ngIAAK8sQEVf63/8gIwNq1oT8+W/qpQcOHGDkyJGkpaU5qDgRN9ekifm6YcNNvzQ5OZmTJ0/i6+tL\ncHCwxYWJiBUsHePdtGlTMjIyrnnM0KFDLwZxEcmFMgND/fo39bKMjAx69OjBqlWrSEpKYsSIEQ4o\nTsTNZb5vfvkF0tPNOvg36J+93f/eS0NE3IPemSJirczgfZNzNz788ENWrVpFcHAwAwYMcEBhIjlA\n0aJQpgwkJ8P27Tf10sOHDwNQunRpBxQmIlbQ+lwiYp2MjFvq8T5w4AAvv/wyAJ988gmFCxd2RHUi\nOUP9+nDgAKxfD9Wq3fDLWrduzcmTJ0lJSXFcbSKSLerxFhHr/P47/PWXWZmhZMkbftlLL71Eamoq\njz76KA8s6WiOAAAgAElEQVRqQqbc7jI/tN7kOG+bzUaBAgUuW7JXRNyLgreIWOcWhpmkpqYSHx+P\nn58fkZGRDipMJAfJfP/cwgRLEXFvCt4iYp1bGGbi5+fHypUr2bx5s5ZAEwEzvMTfH/bsgT//dHU1\nImIhBW8Rsc769ebrTa5oYrPZqFSpkgMKEsmBvL2hTh1zX73eIrmKgreIWOPMGdi504SGmjVdXY1I\nznbvvebr39tUX8/evXtJTk52YEEiYgUFbxGxxuHDYLdDqVLg6+vqakRytvLlzde/lwi8nq5duxIU\nFMTatWsdWJSIZJeCt4hY448/zNcbWFEhPj6eo0ePOrggkRws8310A8H77NmzREdHk5GRQdWqVR1c\nmIhkh4K3iFgjMyDcQPAePHgwFSpUYN68eQ4uSiSHylyOM/MD7TVER0dz4cIFqlatSlBQkIMLE5Hs\nUPAWEWtkBoTrrN8dHR3NtGnTuHDhAjVq1HBCYSI50D97vO32ax66bt06ABo1auToqkQkmxS8RcQa\nN9jj/eabbwLQt29fypUr5+iqRHKmwEDImxdSUiAx8ZqH/vjjjwCEhYU5ozIRyQYFbxGxxg2M8d62\nbRvfffcdfn5+DB482EmFieRANtul99I1hpukp6dTqVIlihUrxn333eek4kTkVil4i4g1Mnu8rzHU\nZNSoUQA89dRTBAcHO6MqkZwr8710jQmWnp6efPrppxw+fJh8+fI5qTARuVVeri5ARHKJG+jxHjRo\nEOnp6QwaNMhJRYnkYDfQ453Jw0P9aCI5gYK3iGRfSgqcOgU+PlCo0FUPq1GjBjNnznRiYSI52E0s\nKSgiOYM+IotI9iUlma9BQaCeNxFrFChgvma+v0Qkx9P/kCKSfRcumK9e+iWaiGUy30+Z7y8RyfEU\nvEUk+zKDgbe3a+sQyU0y309ZBO+tW7fSsmVLvv76aycXJSLZoeAtItmXlma+ZhG8N23axL59+5xc\nkFzPqlU397i4QOb7KfP99Q8zZ85k+fLlrNIfmEiOouAtItmXGQyyGGry4osvEhoaenGTD3EPCt45\nwFWGmqSnp/PVV18B8Oijjzq7KhHJBg3IFJHsy5xQmZFx2cN//PEHa9aswdfXV9tZu4lVq8xt+HDz\nfdOm5na1x8WF0tPNV0/Pyx7+9ttvOXToEHfeead2qxTJYRS8RST7rjIW9ZtvvsFut3P//feTP39+\nFxQm//bPQD1s2PUfFxe6yhCusWPHAtCvXz+t3y2Sw+gdKyLZd5Xgnblmt34d7n6u1putXm43ksWk\n5YSEBA4cOED+/Pnp3r27a+oSkVumHm8Ryb4sxqLu3buX6Oho8ubNy/333++iwuRqFLxzgCyW6SxY\nsCD79u1jx44d2iJeJAdS8BaR7PPzM1/PnPnHQ34MGTIEAH9/f1dUJZKznT1rvma+v/7m7e1N9erV\nXVCQiGSXgreIZF+BAiYcJCWZW758lChRgsjISFdXJpJzHTlivhYr5to6RMQyGuMtItlns0GJEub+\nH3+4thaR3OLwYfO1ZEnX1iEillHwFhFrKHiLWCvzvVSiBHa73bW1iIglFLxFxBqZvXIK3iLW+LvH\nOzF/fmrVqsWECRPI+Nda+SKSsyh4i4g1Mnu8M389LiK3LjUVTpwALy9GfPYZW7ZsYfbs2Vq3WySH\n0ztYRKzxd4/316tXU7duXT7//HMXFySSg/09sXJ/cDBjx40D4J133nFlRSJiAQVvEbHG3z3eq/bs\nYePGjfz5558uLkgkB/t7yNZL585x/vx5IiIiqFOnjouLEpHsUvAWEWv83eO97vhxABo1auTKakRy\ntj/+YA0wJyEBf39/RowY4eqKRMQCWsdbRKxRogQnge3nzuHr68s999zj6opEcq6DB/EDagUH0+65\n5yiROYdCRHI0BW8RsUbBgqwPCoK//qJu1ar4+vq6uiKRnCs6mrrAxpEjSXviCVdXIyIW0VATEbGG\nzcamkBAAGv39VURugd0OGzYA4NGwIT4+Pi4uSESs4pLg/dFHH1G2bFn8/f2pXbs269atc0UZImKx\n17t3Zy/wfFCQq0sRybkOHoS4OLjjDqhQwdXViIiFnB68Z82aRf/+/XnttdfYsmULDRo0oG3bthzW\n2r8iOZ6tYUPuBEps3erqUkRyrr97u6lfH2w219YiIpZyevB+77336NGjBz179qRixYqMGzeOokWL\nMnHiRGeXIiJWu+ce8PKCrVshKcnV1YjkKHa7nTFjxpCwfLl5oH591xYkIpZzavA+f/48MTExtGrV\n6rLHW7Vqxfr1651Ziog4gr8/1KwJGRnwv/+5uhqRHOXzzz9n8ODBhH31Femg4C2SCzl1VZM///yT\n9PR0ihQpctnjwcHBxMXFZfma6Ojo6573Ro4Rx9H1dx13vPYly5WjyMaNHJkzh2OBga4ux6Hc8frf\nTnLT9T969Ch9+/YF4OVz5/Dw8CDGy4sMN/0Zc9O1z4l0/V3netc+NDT0ms9rVRMRscTZs2ex2+0k\nV6sGQIDGeYvckIyMDN544w3OnDlDq1q1eMJu52z58mTkyePq0kTEYk7t8S5UqBCenp7Ex8df9nh8\nfDxFixbN8jW1a9e+6vkyP3Vc6xhxHF1/13HHa9+xY0d++OEHZn/0EXcCQTt2ULtmTfD0dHVplnPH\n6387yW3Xf9y4cWzatIng4GCmt2mDLSaGPC1auOXPl9uufU6j6+86N3rtExMTr/m8U3u8fXx8uOee\ne1iyZMlljy9dupQGDRo4sxQRsdjBgwc5d+4chSpVgnLl4NQp0FKhItd17NgxACZNmkThzImVzZq5\nsCIRcRSnDzUZOHAgU6ZM4bPPPmPnzp3069ePuLg4evXq5exSRMRCBw8eBKB0mTLQqZN5cNYs1xUk\nkkOMHDmSHTt28FCNGvDLL5AnD9x3n6vLEhEHcHrw7tSpE2PHjuWtt96iZs2arF+/nh9//JGSJUs6\nuxQRsciZM2f4888/8fb2JiQkBDp3Nk/MmQNpaa4tTiQHqFy5MnzzjfmmXTsICHBtQSLiEC6ZXPnc\nc88RGxtLamoqGzdupFGjRq4oQ0QscujQIQBKliyJh4cHVK9udtw7cQJWrXJtcSI5ReZviDI/uIpI\nrqNVTUQk244fP463tzelSpUyD9hsl8KDhpuIXN/evRATA/nyQdu2rq5GRBxEwVtEsi0sLIzz58+z\ncuXKSw9mBu958+D8edcUJuJmMjIy6NmzJ+v+PfE48wPqgw+Cn5/zCxMRp1DwFhHHqFLF3E6ehGXL\nXF2NiFsYPnw4n3/+OQ8//DBnzpy59ISGmYjcFhS8RcRxNNxE5KL58+fzxhtv4OHhwbRp08iTuUHO\nzp2wdSsEBUGrVq4tUkQcSsFbRBwnM3gvWAApKa6tRcSFduzYQdeuXQGIjIwkPDz80pMzZpivHTqA\nj48LqhMRZ1HwFhHHqVAB7r0XTp+GL75wdTUiLnHhwgU6duxIcnIyjz32GC+++OKlJ8+cgY8/Nve7\ndXNNgSLiNAreIpJtGRkZnD9/ngsXLlz55ODB5uu772pNb7kteXt7895779G0aVMmT56MzWa79OQX\nX8Cff0KdOhAW5roiRcQpFLxFJNtWrlyJr68vbdq0ufLJBx80Pd8HDsDs2U6vTcQdtG3blhUrVlwa\n1w3mg+iYMeb+Sy+ZZThFJFdT8BYRx/L0hEGDzP3ISLDbXVuPiIvY/h2s58wxH0hDQ+Ghh1xSk4g4\nl4K3iGSbv78/AKdPn876gIgICAmBX3+FpUudWJmIm7LbzQdRMB9MPT1dW4+IOIWCt4hkW5kyZQA4\nePBg1gf4+UG/fuZ+ZtgQyaWio6P59ttvr33QsmWwZQsUKQJ/r3YiIrmfgreIZFtISAi+vr6cOHGC\nlKstG9irl9kOe8UKiI52boEiTrJz507atGlDx44dWb169dUPzPwA2q+fdqoUuY0oeItItnl4eFC6\ndGmCg4OJj4/P+qCgIBO+AUaPdl5xIk5y8OBBwsPDSUhIoE2bNjRo0CDrAzdtguXLIW9eeO455xYp\nIi6l4C0ilti6dSvx8fGUK1fu6gf16wfe3mZSWUyM84oTcbD4+HhatmzJkSNHaNy4Md988w3e3t5X\nHmi3w3/+Y+4/+6z5QCoitw0FbxGxhM+N7LhXvDj06WPCR+/ekJHh+MJEHMxut/N///d/7N27lxo1\narBw4cLLlw38pwULYPFiE7iHDHFuoSLicgreIuJcQ4eaFU5+/hmmTnV1NSLZZrPZGD16NHXr1mXx\n4sUEBgZmfeCZM9C/v7n/5psQHOy8IkXELSh4i4hz5c9/+aYhf/3l2npELNCwYUN+/vlngq8VpkeN\ngkOHoHr1S/MdROS2ouAtIs7XpQs0bgwnTsDrr7u6GhFLXLFBzj/t23dpUvGECeDl5ZyiRMStKHiL\niGUuXLjATz/9xF/X68W22WD8eLNpyIQJZmMdkRwiPT395l/Urx+cO2fW7G7Y0PqiRCRHUPAWEct0\n7NiRRo0aERUVdf2Dq1W7NMHyhRe0lbzkCAkJCTRs2JAvv/zyxl+0cCH88IMZZqUNpERuawreImKZ\nRo0aAbD0RreFHz7cTDBbtw6++sqBlYlk39GjR2nSpAm//PILb775JufOnbv+i1JTL+3aOny4mVgs\nIrctBW8RsUx4eDhggrf9Rnqwg4Iu9QC++CLExTmwOpFbt3//fho1asT27du56667WLVqFb6+vtd/\n4euvQ2ws3H23+c2OiNzWFLxFxDLVq1enUKFCHD58mL17997Yi7p2hebN4fhxePxxuJXxsyIOtG3b\nNho1akRsbCx16tRhzZo1FC9e/Pov/PFHeOcdM5dh0iRNqBQRBW8RsY6HhwctWrQAbmK4iYcHTJ9u\nhpysWAFvv+3ACkVuXnp6OmfOnKFZs2YsX76cggULXv9Ff/xhPlSCWbP7atvHi8htRR+/RcRSDzzw\nAImJiZQsWfLGX1S0qAnfrVubcbBhYdC0qcNqFLkZ1atXZ+3atYSGhuLn53f9F6SlmSUzExLM3+mX\nXnJ8kSKSI6jHW0Qs9cQTT7Bo0SLatWt3cy8MD4dXXzWrnHTpYoaeiLiJqlWr3ljoBhg2DNauNR8o\nv/zS/FZHRAQFbxFxJ8OGmY11jh2DiAgTwkWcKD09/cYmBl/N0qUwYoQJ2zNmaFt4EbmMgreIuA8v\nL5g5EwoVgiVLzBbbIk6SkJBAq1atGDt27K2d4NgxM0HYboehQzVcSkSuoOAtIu6leHGYNs3c/+9/\nza/sRRxs69at1KlThxUrVjBmzBiSk5Nv7gTp6SZ0nzhhVun5z38cU6iI5GgK3iLiUGfOnLn5F7Vp\nYyakZWRAx46we7f1hYn8bd68edSvX5/Y2Fjuuecefv75Z/LmzXvjJ7DbzS6sK1dCkSJmMyhPT8cV\nLCI5loK3iDiE3W6nT58+hISEcPDgwZs/wZtvmgB+4gS0agVHjlhfpNz2PvnkEzp27EhKSgpdunRh\n7dq1N7ciD5hhJZMmgZ8fzJ6t3SlF5KoUvEXEIWw2GydPniQpKYmJEyfe/Am8vWHOHKhXDw4eNMuy\nnTxpfaFyW2vVqhXBwcGMHj2a6dOn4+/vf3Mn+PBD8yHR0xNmzTKTg0VErkLBW0Qcpk+fPgB8+umn\ntzbkJCAAfvgBKleG7duhXTu4lfOIXEWZMmXYs2cPgwcPxmaz3dyLZ86Evn3N/U8/hfbtrS9QRHIV\nBW8RcZh69epRt25dTp48yZgxY27tJAULmhVOSpaE9evhkUfgwgVrC5XbWv78+W/+RVFRl3amHD0a\nevSwtigRyZUUvEXEYWw2G6NHjwZg1KhRHD58+NZOVKKECd8FC8KPP8KTT2qNb7kpJ06cYPjw4WRY\n8ffm55/NpN+0NBg0CAYPzv45ReS2oC3jRcShmjRpQqdOnfD19cXb2/vWT1SpEixaBM2ame3lCxWC\n996Dmx0eILedRYsW0aNHD+Lj4wkKCqJfv363frIdO+D++82Qp+7dTW+3iMgNsqzH+5NPPqFZs2YE\nBQXh4eHBoUOHrjjm1KlTREREEBQURFBQEF27diUxMdGqEkTETX311Vd8+eWXhGR3tYc6dWDBAjPx\ncuxYs8V8dnYZlFzt7Nmz9OnTh/vuu4/4+HiaNGlChw4dbv2E27dDeLiZ5NuunRnXrQ9+InITLAve\nZ8+epU2bNgwfPvyqx3Tp0oUtW7awePFioqKiiImJISIiwqoSRMRNeXlZ+Mu1li3NVtyenmZny2ef\nNZuXiPzDkSNHqF27NuPHj8fb25tRo0axfPlySpUqdWsn/OUXCAuDo0fNjpSzZpmdVkVEboJl/2pk\n/uouOjo6y+d37tzJ4sWL+emnn6hXrx4AkyZNonHjxuzevZsKFSpYVYqI5HYPPwzffmu+fvopnDpl\nhp/4+rq6MnETRYoUITAwkIoVKzJjxgxq1ap16ydbuhQ6dICUFLNyyddfw80uOygighMnV27YsIG8\nefNSv379i481aNCAgIAANmzY4KwyRCS3uP9+M+Eyf36z3vcDD8Dp066uStyEl5cXc+bMISYmJnuh\ne9Ys83ctJcWsYjJ3rkK3iNwypwXvuLg4ChcufNljNpuN4OBg4uLinFWGiLiB7du307Rp0+y/9xs3\nhtWrITgYli2DRo3gjz+sKVJyvGLFipEnT55be7HdDpGR8OijZvnK/v3hiy80vEREsuWa/4K89tpr\njBgx4ponWLVqFWFhYZYW9U9XG7pys8eI4+j6u05OvfZ9+/Zlw4YNhIeH8/HHH+ObzSEiPpMmEdq/\nP/5bt3K+Vi32vP8+ZytWtKjaq8up1z+3iI6OZuvWrYwfP563336bQoUKWXJeW1oapSIjKbxgAQCH\n+/YlvksXiImx5Py5gf7uu5auv+tc79qHhoZe8/lr9ngPGDCAXbt2XfNWp06dGyo0JCSEEydOXPaY\n3W7n+PHj2V/pQERylGHDhhESEsK2bdt46623sGdzZZLzJUqw67PPSKpZE58TJ6j0zDMErltnUbXi\njpKSkoiMjKRnz57ExMQwZcoUS87rmZxM+QEDKLxgARm+vuwbNYr4iAitXiIilrhmj3fBggUpWLCg\nJQ3Vr1+f5ORkNmzYcHGc94YNG0hJSaFBgwZXfV3t2rWv+lzmp45rHSOOo+vvOrnh2i9evJgGDRoQ\nFRVF48aNefXVV7N/0g0boGdPPL/6itCBA+Gll+CNN8zygxbKDdc/p8rIyGD48OGMHz+ekydP4uXl\nxaBBg/jvf/9768NKMm3cCD17wv79ULgwHt99x5333mtN4bmE/u67lq6/69zotb/eMtmWjfGOi4tj\ny5Yt7N69GzBjOLds2cKpU6cAqFy5Mm3atOHZZ5/l559/ZsOGDTz77LO0a9fuut3yIpL7VKtWjRkz\nZmCz2XjttdfYvn179k/q6wvTpsHbb5seylGjzBJwBw5k/9ziFvbs2cPbb7/NyZMnadiwIZs2bWLk\nyJHZC90ZGTBmDDRoYEJ3zZpmd0qFbhGxmGXB++OPP6ZWrVo88cQT2Gw27r//fu655x4WLlx48ZgZ\nM2ZQvXp1WrduTZs2bahZsybTpk2zqgQRyWHat2/PmDFj+OKLL6hSpYo1J7XZzMY6q1dDyZImQNWo\nAbNnW3N+camKFSvy1FNPMXz4cNauXUu1atWyd8Ljx82qJYMHmy3g+/c3vzkpV86agkVE/sGy6dnD\nhg1j2LBh1zwmKChIQVtELjNw4EDHnLhRI9iyxQwdWLAAOnWCZ56B99+H7A5JEJd66qmnALMyVrYs\nWwYRERAXBwULmlVL2rWzoEIRkaw5bTlBERGnu+MOmDcPxo83w1A++QTq1jVbf4vbSk1N5f333+eZ\nZ55xTAMXLsB//gOtWpnQ3aQJ/PqrQreIOJyCt4i4pePHj1tzIpsNevc2W35XrGhCd+3a8PHHZmyv\nuI0LFy7w6aefEhoaysCBA/n000/ZunWrtY3s32+2fB8xwvzdGD4cli+H4sWtbUdEJAsK3iLidmJi\nYggNDSUyMjLbSw1eVL06bNoETz4Jqanw3HPQsKHWZnYTc+bM4a677uKZZ57hjz/+oHr16nz//ffc\nfffd1jRw9iwMHQp33QXr10OJErByJbz+Onh6WtOGiMh1KHiLiNvZtGkTSUlJvPzyywwYMIAMq3qm\nAwLgs8/MNuAhIWbiZe3aJoSfPGlNG3JLYmJi2Lt3LxUqVGDWrFnExMRw//33Z38ct90O335rAvcb\nb8C5c/DEE2b8vwM3fxMRyYqCt4i4naeffpqZM2fi7e3NBx98QKdOnS4uTWqJTp3g999h4EDw8DDD\nTipUMGPA09Ota0du2ODBg/n888/Zvn07nTp1wsPDgv+e9uyB++6Dhx4yS0pWqwZr1pglJy3ao0JE\n5GYoeIuIW+rcuTOLFi0iX758zJ07l8aNG5NuZSjOnx/efddMqmvWDBIS4NlnzdrN//ufde3IRUlJ\nSXzxxRdZDh8qUKAAPXr0wMvLgsW2UlLMkpJ33w1RURAYCB9+aIYaNW6c/fOLiNwiBW8RcVstWrRg\n06ZN1K9fn5deeglPR4zFrVLFTK6bNctMsIuOhnr14KmnzBrPkm2xsbEMHDiQEiVK8OSTT7J06VLH\nNGS3m/XaK1WCkSPh/Hkzpn/3bnjhBbAi1IuIZIOCt4i4tdDQUNauXcsTTzzhuEZsNjP8ZNcus828\nt7cZC162LAwYAH/84bi2c7GNGzfSsWNHypcvz/vvv8/p06dp0qQJAQEB1jaUng7ffGN2nOzUyfx5\n1aplNsL57DMIDra2PRGRW6TgLSJuz9PTM8tJdhkZGZw7d866hvLmNdvMb90KDzwAZ87A2LFmF8Nn\nnoG9e61r6zYQHR3NvHnz8PT0JCIigk2bNrFq1SoaNmxoTQPnz8Pnn0PlytC5sxk2FBICEyea4ULa\n8l1E3IyCt4jkWB999BF33303M2bMsHb8d8WKsHAhbN5selDT0uDTT83jXbrgrwB+Q7p27cqwYcM4\ncOAAX375JbVq1bLkvB6pqQTPmgXly5udSffsgTJlTOCOjYVevbREoIi4JQVvEcmR0tPTmTJlCnv3\n7uXxxx+nWrVqzJ4927qlBwFq1DBjv3ftMmOFPTxg5kyqPPYYd774otmU5zZ25MgR3nnnHRo3bkxq\nauoVzwcEBDB06FCKFStmTYOJiTByJFXbt6fUmDFw+LBZJnDaNBO+e/UCPz9r2hIRcQAFbxHJkTw9\nPdmwYQOTJ0+mdOnS7Nixg06dOlGrVi1OWr0md4UKZqzwvn3Qpw8Zvr4UWLPGDGVo0gSmTIGkJGvb\ndFOnT59mypQptGzZkpIlSzJkyBDWrVvHDz/84JgG7XYz4bVPHyhdGl59Fe9Tp0ipXBnmzTPDgp54\nQhMnRSRHUPAWkRzL29ubnj17snv3biZOnEjx4sUJDAykQIECjmmwVCkYN47fvvuOY927myUJ16yB\nHj3M2OKuXWHZsly9FniPHj3o0aMHy5cvx8fHh4cffpgFCxbQrl07axs6cgRGjzZLAtapA+PHmx7v\npk3ZPX48O6dOhQ4dzG8hRERyCHURiEiO5+PjQ69evejevTsnTpzIciKm3W7P/i6If0u74w6O9O5N\n0Q8+MMvXTZ0Ka9eaIQ/TppntyCMioFs3My48B0pPT89y+cYuXbqQkJDAE088wcMPP0xQUJB1jZ45\nAwsWmOu5bBlkDhsqXBi6dDHXs2ZNTkdHW9emiIgTKXiLSK7h5+dHyZIls3yuV69eHD58mG7dutG+\nfXv8/f2z32D+/GZyX8+eZhjKtGnw5Zdmgt/IkeZWr54JjA89BEWLZr9NB0lPT2fjxo0sWrSIqKgo\nihUrxvz58684rmPHjnTs2NG6hi9cgJ9+gunTzZKAmUN2vL3NNevWDdq2Nd+LiORwCt4ikuulpaUx\nd+5cEhISWLRoEYGBgXTq1ImuXbvSsGFDa3rC77wThg2D11+HdetMr+3s2WYC5i+/wPPPQ9Wq0KoV\nhIebHRTz5Ml+u9kUHx9Pv379WLJkCadOnbr4eMGCBa/a650tdruZCLlkibmtWnX5+Pi6dU3Y7txZ\n27qLSK6j4C0iuZ6Xlxc7d+7k66+/5ssvvyQ6OppPP/2UKVOmcOzYMQpaGfA8PCAszNw+/NAMnZgx\nA1auNBMBt241W9X7+kKjRpeCePXqDh2vnJ6ejoeHxxUfMoKCgvj+++9JSUmhXLlytG3bljZt2tCs\nWTPrQndCgtkddOlSE7YPHbr8+UqVTO92165mTW4RkVxKwVtEbguFCxemT58+9OnTh+3btzNt2jQS\nExOzDN0nT55k0aJFNGnShBIlStx6o3nymLHJXbrAuXOwfr0JnkuXQkyMCaPLl5vdMgsXhpYtzUop\nVatCtWq33OObkZHB3r172bhxI9HR0URHRxMTE8OuXbuuGIrj6+vLjBkzqFy5MqGhobf+s2a6cMFs\n0f7bb7Bli/nAER1terozFSxoPmxk3q4yPEhEJLdR8BaR206VKlUYNWrUVZ9fsWLFxS3q77zzTpo0\naULVqlVp0KABdevWvbVGfX2hWTNzGzkS/vzThO7MIRd//AEzZ5pbpmLFTADPvFWtanqHfXyu2VST\nJk1Yt27dFY9v3bo1yzHw7du3v/mfx26H+HgTsDNvW7fCjh1mR8l/8vExvfvh4aaHv0YNrUYiIrcl\nBW8RkX8JCgrivvvuY+3atezbt499+/YB8MILL2QZvHfs2MG+ffu48847KViwIEFBQfj6+l67kUKF\nzDjmzp1NiP39dxPEf/31Uog9ehSOHmVzVBQxwAHggM1GrL8/BzIyGBcWxv/dey8UKWJuwcFQpAiV\nypVj//791K5dmzp16lCnTh3uueceChUqdGMX4Px5OHHCBOv4eDh+/PL7R47Atm3mmKyUK3fpg0L9\n+mbYTUDAjbUtIpKLKXiLiPxLy5YtadmyJWlpaWzevJmffvqJ3bt306JFiyyP//rrr3nzzTcve8zX\n14sm3rUAAA0hSURBVJe33nqLQYMGXXH89OnTmTlzJikpKZfdhg4dypOffGIOysiA/fth61Y+fvtt\nPtm0yTxut5tl94DYzN7yfxn/d/ts3mx2d/z+e7PBTObN09OcPz0d0tIu3ZKSTLj+xyTLawoMvBSw\nM3vl774b8uW7sdeLiNxmFLxFRK7Cy8vrYo/xtZQrV47WrVsTGxvLqVOn+Ouvvzh37hw+VxkSEhMT\nw48//njF4yf+2YPs4QHly0P58oSdOUPqkiWUKVOGMkWLUiYjg7J2O8XT082QlX/1SvvGx0NKignd\nhw/f/A/u6WnGnP/dg/7P3vSLt7vuMmOzLVobXUTkdqDgLSKSTd27d6d79+4Xv7fb7aSmpl71+G7d\nutG8eXMCAgIICAggT548BAQEULhw4SyPf/zxx3n88cdvrqiUFBPGExLMhMe0tMt7uD08Lu8B9/Iy\nw0GKFDGTHzUGW0TEcgreIiIWs9ls19ygp3r16lSvXt2xRQQEQNmy5iYiIm5BXRoiIiIiIk6g4C0i\nIiIi4gQK3iIiIiIiTqDgLSIiIiLiBAreIiIiIiJOoOAtIiIiIuIECt4iIiIiIk6g4C0iIiIi4gQK\n3iIiIiIiTqDgLSIiIiLiBAreIiIiIiJOoOAtIiIiIuIECt4iIiIiIk5gSfA+deoUffr0oXLlyuTJ\nk4dSpUrx/PPPc/LkySuOi4iIICgoiKCgILp27UpiYqIVJYiIiIiIuDVLgvfRo0c5evQo77zzDtu2\nbWP69OmsWbOGxx577LLjunTpwpYtW1i8eDFRUVHExMQQERFhRQkiIiIiIm7Ny4qTVKlShblz5178\nvly5crzzzjs88MADJCcnkzdvXnbu3MnixYv56aefqFevHgCTJk2icePG7N69mwoVKlhRioiIiIiI\nW3LYGO/ExER8fX3JkycPABs2bCBv3rzUr1//4jENGjQgICCADRs2OKoMERERERG34JDg/ddff/Hf\n//6XZ555Bg8P00RcXByFCxe+7DibzUZwcDBxcXGOKENERERExG1cc6jJa6+9xogRI655glWrVhEW\nFnbx++TkZNq1a0fJkiUZPXp0tgu81uTL0NDQ6x4jjqPr7zq69q6l6+9auv6uo2vvWrr+rmPVtb9m\n8B4wYABdu3a95glKlix58X5ycjL33XcfHh4efP/99/j4+Fx8LiQkhBMnTlz2WrvdzvHjxwkJCbmV\n2kVEREREcoxrBu+CBQtSsGDBGzpRUlISbdu2xWazsWjRootjuzPVr1+f5ORkNmzYcHGc94YNG0hJ\nSaFBgwa3WL6IiIiISM5gs9vt9uyeJCkpiVatWpGUlMSCBQvImzfvxecKFiyI9/+3d/8hUd9/HMCf\nn494ac1zyUrTCnXLzc44QrOVTVswTfshbZSwrXKjJKRL2grmj8jYLrfaYLQlWVGxMegH2S/dwDEv\nTVQKNjC9Msl+glxYWh5UMn19/xA/9KHa13V97ur2fMD9ce/3y3j7vI/H6+zj+x0YCADIysrCzZs3\nsXv3bogI8vLyEBsbixMnTni6BCIiIiKiF9pzabxPnz6NefPmQVEUPPrPKYoCh8Oh3QPe29sLm82G\nkydPAgCys7Px448/wmw2e7oEIiIiIqIX2nNpvImIiIiI6J8Zto+3N5w9exbvvfceQkJCYDabkZKS\ngtu3b2vzPKLeWCKCzMxMqKqqO0AJYPZG6enpgc1mQ3x8PEaPHo3JkycjPz8fd+7ceayO+RujvLwc\nMTExCA4ORlJSEhoaGny9JL9UVlaGGTNmIDQ0FOPHj8fixYvR1tb2WF1paSmioqIwevRovPvuu3A6\nnT5YrX8rKyuDqqqw2Wy6cWZvnK6uLqxcuRLjx49HcHAwLBYL6uvrdTXM3xh///03ioqKEBsbi+Dg\nYMTGxmLTpk0YGBjQ1T1z/vKSam5ulldffVW2bt0qbW1t0tHRIceOHZO7d+9qNfPnz5eEhARpbm6W\npqYmsVgssmjRIh+u2r9s375dFixYIIqiyNGjR3VzzN4Yra2t8v7778upU6fk8uXLUldXJxaLRdLT\n03V1zN8YBw8elMDAQNm7d69cvHhRbDabvPLKK3L9+nVfL83vZGRkyIEDB6StrU3Onz8vS5YskYiI\nCLlz545W8/XXX0tISIhUVlZKa2urLFu2TCIjI6Wvr8+HK/cvTU1NEhMTI1arVWw2mzbO7I3T09Mj\nMTExsnLlSjl37pxcvXpVamtr5cKFC1oN8zfOli1bJCwsTKqqquTatWty8uRJCQsLky+//FKr8ST/\nl7bxnjVrlpSUlDx13ul0iqIo0tjYqI01NDSIoijS3t7ujSX6tbNnz8qkSZPk1q1bjzXezN67fv31\nV1FVVfuBZ/7GSU5Olry8PN3YlClTpLCw0Ecr+u9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "x = np.array([10.0, 4.5])\n", "P = np.array([[500., 0], [0, 400.]])\n", "plot_covariance_ellipse(x, P, edgecolor='r')\n", "\n", "x = np.array([11.35, 4.5])\n", "P = np.array([[564., 160], [160, 400.]])\n", "plot_covariance_ellipse(x, P, edgecolor='k', ls='dashed')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How does the filter compute new values for $\\mathbf{P}$, and what is it based on? It's a little to early to discuss this, but recall that in every filter so far the predict step entailed a loss of information. The same is true here. I will give you the details once we have covered a bit more ground." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Process Noise**\n", "\n", "A quick review on **process noise**. A car is driving along the road with the cruise control on; it should travel at a constant speed. We model this with $x=\\dot{x}\\Delta t + x_0$. However, it is affected by a number of unknown factors. The cruise control is not perfect, and cannot maintain a constant velocity. Winds affect the car, as do hills and potholes. Passengers roll down windows, changing the drag profile of the car. \n", "\n", "We can model this system with the differential equation\n", "\n", "$$\\dot{\\mathbf{x}} = \\mathbf{Fx} + w$$\n", "\n", "where $\\mathbf{Fx}$ models the state transition and $w$ is white process noise.\n", "\n", "To account for the unmodelled behavior in the system the filter adds a **process noise** covariance matrix $\\mathbf{Q}$ to the covariance $\\mathbf{P}$. We do not add anything to $\\mathbf{x}$ because the noise is *white* - which means that the mean of the noise will be 0. If the mean is 0, $\\mathbf{x}$ will not change." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The univariate Kalman filter used `variance = variance + process_noise` to compute the variance for the variance of the prediction step. The multivariate Kalman filter does exactly the same thing, essentially `P = P + Q`. I say 'essentially' because there are other terms unrelated to noise in the covariance equation that we will see later.\n", "\n", "Computing the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. For now I will say that $\\mathbf{Q}$ equals the *expected value* of the white noise $w$. ($\\mathbf{Q} = E[\\mathbf{ww}^\\mathsf{T}]$). In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter. FilterPy provides functions which compute $\\mathbf{Q}$ for the kinematic problems of this chapter." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function Q_discrete_white_noise in module filterpy.common.discretization:\n", "\n", "Q_discrete_white_noise(dim, dt=1.0, var=1.0)\n", " Returns the Q matrix for the Discrete Constant White Noise\n", " Model. dim may be either 2 or 3, dt is the time step, and sigma is the\n", " variance in the noise.\n", " \n", " Q is computed as the G * G^T * variance, where G is the process noise per\n", " time step. In other words, G = [[.5dt^2][dt]]^T for the constant velocity \n", " model.\n", " \n", " **Paramaeters**\n", " \n", " dim : int (2 or 3)\n", " dimension for Q, where the final dimension is (dim x dim)\n", " \n", " dt : float, default=1.0\n", " time step in whatever units your filter is using for time. i.e. the\n", " amount of time between innovations\n", " \n", " var : float, default=1.0\n", " variance in the noise\n", "\n" ] } ], "source": [ "from filterpy.common import Q_discrete_white_noise\n", "help(Q_discrete_white_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This code computes $\\mathbf{Q}$ for white noise with a variance of 2.35 and a time step of 0.1 seconds." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.00005875, 0.001175 ],\n", " [ 0.001175 , 0.0235 ]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kf.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=2.35)\n", "kf.Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 4**: Design the Control Function\n", "\n", "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Suppose we are controlling a robot. At each time step we would send control signals to the robot based on its current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. Remember, we *never* throw information away.\n", "\n", "For a linear system the effect of control inputs can be described as a set of linear equations, which we can express with linear algebra as\n", "\n", "$$\\mathbf{Bu}$$\n", "\n", "Here $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is the control input model. For example, $\\mathbf{u}$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf{B}$ yields $[\\begin{smallmatrix}x\\\\\\dot{x}\\end{smallmatrix}]$.\n", "\n", "\n", "Therefore the complete Kalman filter equation for the prior mean is\n", "\n", "$$\\mathbf{x^-} = \\mathbf{Fx} + \\mathbf{Bu}$$\n", "\n", "Your dog may be trained to respond to voice commands. All available evidence suggests that my dog has no control inputs, so I set $\\mathbf{B}$ to zero. In Python we write" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "kf.B = 0. # my dog doesn't listen to me!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### Prediction: Summary\n", "\n", "Your job as a designer is to specify the matrices for\n", "* $\\mathbf{x}$: the state variables and initial value\n", "* $\\mathbf{P}$: the covariance matrix initial value\n", "* $\\mathbf{F}$: the state transition function\n", "* $\\mathbf{B}$: Optionally, the control function\n", "* $\\mathbf{Q}$: the process noise matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Update Step\n", "\n", "Now we can implement the update step of the filter. The good news is that you only have to supply two more matrices, and they are easy to understand. The bad news is that the Kalman filter equations themselves are harder to understand. So for now I'll leave the equations unexplained so we can get the full Kalman filter working. After that we'll look at the equations. \n", "\n", "### **Step 5**: Design the Measurement Function\n", "\n", "The Kalman filter computes the update step in what we call **measurement space**. We mostly ignored this issue in the univariate chapter because of the complication it adds. Ee tracked our dog's position using a sensor that reported his position. Computing the *residual* was easy - subtract the filter's predicted position from the measurement:\n", "\n", "$$ \\mathtt{residual} = \\mathtt{measured\\, position} - \\mathtt{estimated\\, position}$$\n", "\n", "However, consider what would happen if we were trying to track temperature using a thermometer that outputs a voltage corresponding to the temperature reading. The equation for the residual computation would be nonsense; you can't subtract a temperature from a voltage.\n", "\n", "$$ \\mathtt{residual} = \\mathtt{voltage} - \\mathtt{temperature}\\;\\;\\;(BAD!)$$\n", "\n", "\n", "We need to convert the temperature into a voltage so we can perform the subtraction. For the thermometer it might read:\n", "\n", " CELSIUS_TO_VOLTS = 0.21475\n", " residual = measurement - CELSIUS_TO_VOLTS * predicted_state\n", " \n", "The Kalman filter generalizes this problem by having you supply a **measurement function** that converts a state into a measurement. \n", "\n", "But why are we working in measurement space? Why not work in state space? Isn't that easier? No, it is not. Consider. Our state is $\\begin{bmatrix}x&\\dot{x}\\end{bmatrix}^\\mathsf{T}$. It contains the *hidden* variable $\\dot{x}$. There is no way to directly convert a measurement of $x$ into a state $\\begin{bmatrix}x&\\dot{x}\\end{bmatrix}^\\mathsf{T}$. We have to work in measurement space to make the computation of the residual possible.\n", "\n", "Both the measurement $\\mathbf{z}$ and state $\\mathbf{x}$ are vectors so we need to use a matrix to perform the conversion. The Kalman filter equation that performs this step is:\n", "\n", "$$\\textbf{y} = \\mathbf{z} - \\mathbf{H x^-}$$\n", "\n", "where $\\textbf{y}$ is the residual, $\\mathbf{x^-}$ is the prior, $\\textbf{z}$ is the measurement, and $\\textbf{H}$ is the measurement function. So we take the prior, convert it to a measurement, and subtract it from the measurement our sensor gave us. This gives us the difference between our prediction and measurement in measurement space!\n", "\n", "We need to design $\\mathbf{H}$ so that $\\textbf{Hx}^-$ yields a measurement. For this problem we have a sensor that measures position, so $\\mathbf{z}$ will be a one variable vector:\n", "\n", "$$\\mathbf{z} = \\begin{bmatrix}z\\end{bmatrix}$$\n", "\n", "The state is $\\mathbf{x}=\\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathsf{T}$ so $\\mathbf{H}$ has to be a $1\\times 2$ matrix. Recall that multiplying matrices $m\\times n$ by $n\\times p$ yield one of size $m\\times p$. The equation will have the form\n", "\n", "$$\n", "\\begin{aligned}\n", "\\textbf{y} &= \\mathbf{z} - \\mathbf{H}\\mathbf{x^-} \\\\\n", "\\begin{bmatrix}y \\end{bmatrix} &= \\begin{bmatrix}z\\end{bmatrix} - \\begin{bmatrix}?&?\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "We will want to multiply the position $x$ by 1 to get the corresponding measurement of the position, and multiply the velocity $\\dot{x}$ by 0 to get the corresponding measurement of velocity (of which there is none).\n", "\n", "$$\n", "\\textbf{y} = \\mathbf{z} - \\begin{bmatrix}1&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", "$$\n", "\n", "And so, for our Kalman filter we set\n", "\n", "$$\\mathbf{H}=\\begin{bmatrix}1&0\\end{bmatrix}$$\n", "\n", "We implement this as" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "kf.H = np.array([[1., 0.]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Believe it or not, we have designed the majority of our Kalman filter! All that is left is to model the noise in our sensors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 6**: Design the Measurement Noise Matrix\n", "\n", "The **measurement noise matrix** models the noise in our sensors as a covariance matrix. In practice this can be difficult. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean.\n", "\n", "In the univariate chapter we used a variance of 5 meters squared for our position sensor. Let's use the same value here. The Kalman filter equations uses the symbol $\\mathbf{R}$ for this matrix. The matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is $m{\\times}m$ because it is a covariance matrix, as there may be correlations between the sensors. We have only 1 sensor here so we write:\n", "\n", "$$R = \\begin{bmatrix}5\\end{bmatrix}$$\n", "\n", "If we had two position sensors, the first with a variance of 5 meters squared, the second with a variance of 3 meters squared, we would write\n", "\n", "$$R = \\begin{bmatrix}5&0\\\\0&3\\end{bmatrix}$$\n", "\n", "We put the variances on the diagonal because this is a *covariance* matrix, where the variances lie on the diagonal, and the covariances, if any, lie in the off-diagonal elements. Here we assume there is no correlation in the noise between the two sensors, so the covariances are 0.\n", "\n", "For our problem we only have one sensor, so we can implement this as" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "kf.R = np.array([[5.]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have a few shortcuts. `KalmanFilter.R` is initialized to the identity matrix. For this simple problem we could write:\n", "\n", " kf.R *= 5.\n", "\n", "Finally, since this is a 1x1 matrix you can just use a scalar.\n", "\n", " kf.R = 5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementing the Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I've given you all of the code for the filter, but now let's collect it in one place. First we construct an `KalmanFilter` object. We have to specify the number of variable in the state with the `dim_x` parameter, and the number of sensors/measurements with `dim_z`. We have two random variables in the state and one measurement, so we write" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from filterpy.kalman import KalmanFilter\n", "dog_filter = KalmanFilter(dim_x=2, dim_z=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we initialize the filter's matrices and vectors." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dog_filter.x = np.array([0., 0.]) # state (location and velocity)\n", "dog_filter.F = np.array([[1., 1.], \n", " [0., 1.]]) # state transition function\n", "dog_filter.H = np.array([[1., 0.]]) # Measurement function\n", "dog_filter.R = 5 # measurement noise\n", "dog_filter.Q = Q_discrete_white_noise(2, dt=0.1, var=0.1) # process noise\n", "dog_filter.P = np.diag([500., 400.]) # covariance matrix " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at this line by line. \n", "\n", "**1**: We assign the initial value for our state. Here we initialize both the position and velocity to zero.\n", "\n", "**2**: We set $\\textbf{F}=\\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$, as in design step 2 above. \n", "\n", "**3**: We set $\\textbf{H}=\\begin{bmatrix}1&0\\end{bmatrix}$, as in design step 4 above.\n", "\n", "**4**: We set $\\textbf{R} = \\begin{bmatrix}5\\end{bmatrix}$. \n", "\n", "**5** We use the `Q_discrete_white_noise()` method to set $\\mathbf{Q}$'s variance to 0.1.\n", "\n", "**6**: We set $\\mathbf{P} = \\begin{bmatrix} 500&0\\\\0&400\\end{bmatrix}$\n", "\n", "I've rewritten the creation of the Kalman filter to allow you to specify different initial values for `R`, `P`, and `Q` and put it in a helper function. We will be creating and running many of these filters, and this saves us a lot of headaches." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def pos_vel_filter(x, P, R, Q=0.):\n", " dog_filter = KalmanFilter(dim_x=2, dim_z=1)\n", " dog_filter.x = np.array([x[0], x[1]]) # (location and velocity)\n", " dog_filter.F = np.array([[1, 1],\n", " [0, 1]]) # state transition matrix\n", " dog_filter.H = np.array([[1, 0]]) # Measurement function\n", " dog_filter.R *= R # measurement uncertainty\n", " dog_filter.P *= P # covariance matrix \n", " if np.isscalar(Q):\n", " dog_filter.Q = Q_discrete_white_noise(dim=2, dt=0.1, var=Q)\n", " else:\n", " dog_filter.Q = Q\n", " return dog_filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All that is left is to write the code to run the Kalman filter. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def filter_dog(data, R=0, Q=0, P=500., initial_x=(0., 0.)):\n", " \"\"\" Filters 'data' using the filter provided by \n", " dog_tracking_filter().\n", " \n", " 'initial_x' optional initializes x to some value other than [0, 0].\n", " \n", " returns a tuple of (positions, covariance)\n", " \"\"\"\n", " dog_filter = pos_vel_filter(initial_x, R=R, Q=Q, P=P)\n", " \n", " pos, cov = [], [] \n", " for z in data: \n", " # perform the kalman filter steps\n", " dog_filter.predict()\n", " dog_filter.update(z)\n", "\n", " pos.append(dog_filter.x)\n", " cov.append(dog_filter.P)\n", " \n", " pos = np.array(pos)\n", " cov = np.array(cov)\n", " return (pos, cov)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the complete code for the filter, and most of it is\n", "boilerplate. I've made it flexible enough to support several uses in this chapter, so it is a bit verbose. The first function `dog_tracking_filter()` is a helper function that creates a `KalmanFilter` object with specified $\\mathbf{R}$, $\\mathbf{Q}$ and $\\mathbf{P}$ matrices. We've shown this code already, so I will not discuss it more here. \n", "\n", "The function `filter_dog()` implements the filter itself. Lets work through it line by line. The first line creates the simulation of the DogSensor, as we have seen in the previous chapter.\n", "\n", " dog = DogSensor(velocity=1, noise=noise)\n", "\n", "The next line uses our helper function to create a Kalman filter.\n", "\n", " dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", " \n", "We will want to plot the filtered position, the measurements, and the covariance, so we will need to store them in lists. The next three lines initialize empty lists of length *count* in a Pythonic way.\n", "\n", " pos = [None] * count\n", " zs = [None] * count\n", " cov = [None] * count\n", " \n", "Finally we get to the filter. All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The `KalmanFilter` class provides the two functions `update()` and `predict()` for this purpose. `update()` performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n", "\n", "Absent the bookkeeping work of storing the filter's data, the for loop reads:\n", "\n", " for t in range(count):\n", " z = dog.sense()\n", " dog_filter.update (z)\n", " dog_filter.predict()\n", " \n", "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the `KalmanFilter` variables; executing the filter is trivial.\n", "\n", "Now let's look at the result. Here is some code that calls `filter_track()` and then plots the result. It is fairly uninteresting code, so I will not walk through it. The `DogSimulation` class from the previous chapter has been placed in `DogSimulation.py`. I have also implemented a few plot routines to visualize the data in `mkf_internal.py`. Both of these are in the *code* subdirectory if you wish to read them.\n", "\n", "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `KalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays.\n", "\n", "Here is an alternative form of the last function which uses batch filtering. `batch_filter` returns four NumPy `Array` objects; the first two contain the filtered estimates and covariances (the posteriors), and the last two contain the predicted estimates and covariances (the priors). The priors are useful for smoothing algorithms which we will learn later, but for now they are not useful to us, so I disregard them." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def filter_dog(data, R=0, Q=0, P=500., initial_x=(0., 0.)):\n", " dog_filter = pos_vel_filter(initial_x, R=R, Q=Q, P=P) \n", " pos, cov, _, _ = dog_filter.batch_filter(data)\n", " return (pos, cov)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from DogSimulation import DogSimulation\n", "from mkf_internal import plot_track\n", "\n", "def run_filter(Q, R, P, initial_x=(0.,0.), data=None, count=0, std_scale=1, **kwargs):\n", " if data is None:\n", " dog = DogSimulation(velocity=1, measurement_variance=R)\n", " zs = [dog.move_and_sense() for t in range(count)]\n", " else:\n", " zs = data\n", " ps, cov = filter_dog(data=zs, R=R, Q=Q, P=P, initial_x=initial_x)\n", " plot_track(ps[:, 0], zs, cov, std_scale, **kwargs)\n", " return ps, cov" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, call it. We will start by filtering 50 measurements with a noise variance of 10 and a process variance of 0.01." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/l5fVRueETLo0z6BT00w8LRo7d2bi5gjCbo+itNSV4GB/nJyslJXpscvXt/a7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itWrMCoUaMwfvx4nDt3DgsWLMCPP/6IzMxMKBQK/TFOnTqFIUOGICoqCmPGjOHNpY84FuZERERE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\niIiIzAALcyIiIiIiM/D/dOAu6YC7aJwAAAAASUVORK5CYII=\n", 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dqKk3SxgNEZF3YkWbiMhOVon2A9EpiNEnArD/h+D7499IHBERkfdhRZuIyE5W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\nWj+M7J+OjGnv44WxsxEdnuB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = np.diag([500., 400.])\n", "Ms, Ps = run_filter(count=50, R=10, Q=0.01, P=P, y_lim=(-20, 50))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Rudolf Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n", "\n", "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely. The yellow shaded portion between the black dotted lines shows 1 standard deviations of the filter's variance, which I explain in the next paragraph.\n", "\n", "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. The covariance matrix $\\mathbf{P}$ tells us the *theoretical* performance of the filter *assuming* everything we tell it is true. Recall from the Gaussian chapter that the standard deviation is the square root of the variance, and that approximately 68% of a Gaussian distribution occurs within one standard deviation. Therefore, if at least 68% of the filter output is within one standard deviation we can be sure that the filter is performing well. In the top chart I have displayed the one standard deviation as the yellow shaded area between the two dotted lines. To my eye it looks like perhaps the filter is slightly exceeding that bounds, so the filter probably needs some tuning. We will discuss this later in the chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I want you to get a better feel for how the Gaussians change over time, so here is a 3D plot showing the Gaussians from the plot above. I generated this by computing the probability distribution for each over a large area, and then summing them together so I can show them all in the same plot. Note that it makes no mathematical sense to add these together, it is merely a way to display them all at once. The scale of the y axis is much smaller than the x axis, so the Gaussians look very stretched horizontally, but they are not. This scaling makes it easier to see everything and minimizes the amount of computation needed. You should still be able to tell that our certainty in both the position and velocity improve over time. We know this because the Gaussian gets narrow in both axis as time increases, and it simultaneously gets taller." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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IxTU3QVkt5VxgerwHGftuoj2dTiOfzyORSARyl8m+TtdDVVXTBY5EIswFZrjC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\naxsNlicJIoqYkJJuz+NBKTkvn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Fnjwq4+Ll63nkPLVa647z68JUuYNW/e847BbXW1rdi6\nrovnedPks/3T3ta26FJKbUCAXywhatt+bRx00Q4nau9nJgne2BKtHeow0z5tU2iHHLXfIwiC6d6V\nmfvelIXZC/0sM4lq+9hejF1b+/3af5OZNm0zCWk7jW5z0LZgm1m20j6HM49Taz1dKyylnC4/2dLw\n9tJhC/l9GZHL5fjyl7/MnDlzCMOQM888k9tvv52LL76YfD7Paaedxtlnnz0dbbzttttywQUXsGzZ\nMnbYYQduv/12PvOZz3Daaaex5557bta+C4UCWmve8IY3cMQRR/Ce97yHj3zkI5x66qnk83kWLVrE\nYYcdtsHgK6WcHqjmLljAa/fbj+tuu41Ba3kilSIrJg3x70+lWJokHFapsEgIljkOR42N4WmNcF0e\nNIaW4zDheQjHYcIYfprJ4IQhi5OEA2o1bgxDPjs8zPaNBp1ac4/j0AAipYhcF98Yrg5Dns5mafo+\nh9Zq/NP3ObhcZrtKhVIQEAvJVWGKrOPy6dFhlgUBVddlv3qdu5XDL4M035sY5pyOXt7bKHOXGxAq\nwb6NCqv9FK+IWywzlrLjsSLMUhOSnE1YbQR72piCFaSEAGPoM4a0kgwZeHOlxN5JzP9kcxg/wHMc\nttGaX4QhO2rN/vU6767VuD+dZqtajR3KZRzXZUxK1gAtz2NwKj3t957HPzIZ5kjJ4ZXKpMIhBO8b\nHaUjjolclwesxUydz5RSLJeSEaU4oF7j6cBHSUFaCUYTzXaeS78nqSvFoqROzQk42EyqlYt0g685\n/RxFhdfQ5Gs6xzfMKBeTZUdPUjeGYSv4bq3Iz92Q1yiHdRZ6reVD4+Ps02xyXyaDNoaPFQq8o1aj\n6Losk5Ltmk3KjoOQkseMYWUYsjaTwQdGheCGMOToep2jqlV2jSJ+EQa0BBxvahxPk9OTHLfEaW5R\n3dxmsjze0LzbnSQttzudPCVCdnAibqk79AvNVkmTK0mzLzFrpEtBSN5pDGsEzLaGc4aGOaJeZzAM\nccz/x96bR8lV1Vv8n3PuuWONPaczQMI8gwiCCDKDzCLKExUkKjL53lMBBX3gLA4oICqKgMITBEEE\nEYjMMwJhSsIQEhIISU/V1TUPdzr390dXhyaAgj99P39rZa/VK6u7q2/dVak6d9999ndvzccKBXrC\nkIpl8RygDYOSZZEzDJ5UiuvTaZqex66+z8w4ZqFp8t3hYR51FS9KkwNVm3Sg2VV0LvDALW43hweT\natSTdoZF2Byuqtyr03y0WuEP2S7aiWSfiQnuNV3OLRa4xElzTrPB1criQMNgRCfM0DEXDQ2xZ6vF\ncsdhVZKwse/TME0SIciJgGWYnGbUMTrX91tjh7u1zaFOGyHgIZln97CBIaAkFKoWsTCTRwjYr1Tj\nukyW2X5IbJkESBZKkxmG4gEpSZsmjlLUo2iy+c62qVsWaa253HV5JZ1mLvDhSoWVrsvTIuEoWogE\nXpE2FzXL2MDTmRw7BZM3AxrB3W6eM4ujnOf2kgL2i+u4aG5UXVQw6DYidp6o83AuixHFvD8KODPX\nzR2jw2wRx/zJ9fhSocAnq1U27mT5ukGAkJLINPHjmHssi6FMhh4hmNtqscQwWKxMhpTNLcLi/NIo\n0+sCKrFmzHPZMpokHqulohQnbNVJzrjDy3Fwtcq+tToXZLp40s2yIJ1jRRRzfTrDs/k8caPBsttv\nZ6TVYrv3vW8tcbU7ld9TpNa27deR2unE9v9S5Zsi39Ob4aaI43TCNXVeU4R93fY1rfVbkswpSwe8\n1u42PXN3uv91Kt923Urmv4WpTN0pTD+Hqaa5d3K8KbxVzvAU/pG2tbfTiKe1fkNm8Vv5tdfjnwOR\n/CtqutbjLXHxxRfzgx/8gOHhYbbddlvOP/98dt99dwDmz5/Pfffdx4oVK9Y+fsmSJZx66qk89thj\ndHd3c9JJJ3H22Wf/08/rwgsv5L777uPSSy99XZvMus1BY6OjXHbKKbgrV1JUCoSg5Ps0DYNtDAM7\njsmGIfcYBl8plZgbxwTAF/v72bzVwjNNxjoqYSwEmyiFDago4rk4Zvc4Zrd6ncEo4ve9vRSThB1r\nNV72PJ61LEa0ZkPLIiMEdhxTCEMk8LVikboQXJvN8oBhkDEV36yUGEZwdXcvh7SbPBfHPGTZ7CVi\nVlo2RwcNFkuTllJ8rDzG1/KDzG+VuMjOYgLdSiKThGVBjNSaGUqxPNbME5KXdMxmyqQcR/jA3ghG\nhWRFHJMxTXo6EXFDYYitFBsB+TimqDVDQvA/ExN0xTEPpVJclMmwd7tN2XUpSslIEGAqxSaGga01\nOgh4WkpOr9XYIAgwk4TT+vvZutGg1smdFVHECmAQjYvmkUTQS8JGSrC14ZO1TR7QDr8IV+MJeBmT\nb6p+Rtshpztt9o6rHMcg2ynNcl+zb9jifJXB1aB1TF+SsAqDP4+P8d2ubpYok60NAwFUgoAVUrJv\nkjAnisj6Plem03x7fBwDWKIUP83n6QfShoEhJe0wZDRJ2EZK+rTmVqFpGQl/0UX+lNj8Qaa5SJSY\nJyYvQMcaA3zBq7KjaHEGsxmPBZ8zRvhapYuDnRZ/jTyejgRfrZf5gtfFLmieQfBYYZRf5ru5S5ns\nKiVGkhBHEY9LyRmd19NIEr48MMAelQqJUgy5Lk9qjSklG5kmTpIg45jnoogeFXE3DgcbLX4el5m+\nYfuf6Q24qDYZf3Wp28dCH07sqfGXJM9nXh3jSzNnoXXCL0ZWs1t2kCcnhtmja5BbRod5b+8gn27W\n+WytzoXd3dxuKD4EzAhDjDDkqnSa7xYK1JKEy/pT3ILHanPSqvSMVpwfpBlBsVOfybesYX4UD/CJ\nRoEZUrM4VtzSzLKiN0W/HfH1l4Y5bmAmW7QCNq03uDGTZ7NakwdNm42kZAGCxZ0YuFuyWW72PPZt\nNJjwPEakZKzznt7YMHjV93nYMFgaj3C5kWGeH3J40EIDZ/fO5DvVIQB84NTMbC4dX80xM2cxU2p+\nFEymjZwg57Df+AS/703z5ZEJHvVSPO44XDkywoE9A2SlwTwh0EnCK2EIhsHBUcScZpNnXZfFlsWX\nR0d5zjS5P5XiYaXYwFTsGkUcOT7ODwdm0J9o3lOt8HhXjnOKI7SAa3M93Gs6rA5DNrQtLCmoRhFh\nrPl43GLXdp0f52dw7tAQEljoevwuneMHQ8OsMAy+1dtLTQg2EYIJw6CeJOTnzuXsa675/7T2+O1i\nivCuq6Capvm63NvpSRPrNsNNZQuvazVoNBpryanneW9oKNNavy5tYQrrpi28FcIwXDtsOOUFfrPj\nvdO4tukIguB1iRXwmp3hnSrAU5jyWq9bMT2lOMOkwjzVFPePPs96/H2sJ7/rsRbXXHMNl156KVde\neSX5fH7tz6Moet2wQ6FQ4KJTTuGkxx6jKgTLlOKmbBbRyQO1pCSJIl6NIuYZBhtqzZww5AnDIBfH\nnFAqMWQY3JDJ8LDjsC1Q7RCp8SDAMk02Bjyt0WHIIsPg28UifVrzbKf04b2+T9V1aUlJPQgYF4Ij\nE83u5TLZOOZzvX3EAj6kYw4tFTlnYCY7RQHbVsr8ONeDZUAzgaNFAFHEo06ab5SH+FZ+kIEkoZIk\n1BPNYa0yOyQh57u9PJYoNo8DnhWKmSRUkGwZhUhD8oxQzDUVfqx5KYrYKYpIK0VNSp6KY3oMgz6l\nJvONfZ+VwG5SMjuOmdlqcVUqxWdLJTYNQ5aaJj/p6sIEepRCC0EUxxTimA2VYqCTrfuCEGS1ZrNm\nkzt7esgkCSvDgBEErkyYYRrYSiLQpHREhOCnyRiXWH08rS1+1FzDbU4Xl0c251kV/mjkWB4IdqPF\nHyMbLSSnlcf5VLqXfQzB0ihmrpB0K8XyIKCXhM10Qtk0WR7HaCHYsBOFpuKYlVHETODAdps5rRYP\n53I8Z5ocUSzyom2zyPN4FphnWbwYt2khWMQYxzuzOb4xxqpUhuOCyXrZK6we7hcml9kjfI8ZRGWf\nnboCrmvlyJqwuBGypQ55IbF5FckR7TZXOTa7JDDbNFkRBkRCMiAlSkrCKGJcawY7r+dgHLM0SbDj\nmC+Uy0jgylyOBbbNe5KEolIEWjNKgCkTmlryF8aZfsk/PT2b82qTftIHhc0TgcXLA1l2Um02eLXG\nw16aB1yXPxfW8L7cIPcVhzkt38e8WpNj2i3e19PP7oaBISTjYUgbmGOapAAjjlkVRdSAlBFSRXKn\nWSRI4ONxD1fVipzaO4c9WjWG+x26RMx7qyW2VRGjWvL9eAaIBJHVfPGVAj/P9zBuKH4wPsxh2Znc\nWxhidtcgQ6PDXJjJcr3tcDAwJ4rIBQFXp1IcVa3yPt/nWdPkwnyetpTkY5+HDJs18TCfSs/h12Ov\nrn09vtg/hx+XX/v+M7k5XDr2KvdKi1/15PktYwgBp5obcNHLq9hzcJATSmU+FLQ4sGuAAwXMiGKu\nMRTvaTSxbJtR02RFFCENg82UwtIaEYYsBo7yfXZpNnHjmC8NDNCtNUIpziwW2LSjqn26rx9DQqgs\nji4WOKjt892BGRxVKLB5Z2jwkzNmckhpgoe7u1gBGDph0LJIgNEgYEInHAVs0G6j45irMhm+PTZG\nXUqetCyu6+/nhHPO4bCjj/4nrcz/WsRxTLPZfB2pnapNnk6+ppTiqcSK6ViXtNZqtbVkLpVKvWn7\n2hT5nh5hBpM2iXUH9NaF7/tr/840TTKZzFo7wXSx5u0e782QJAmlUulNf/d2SfpbHXfdYox1j+26\n7tqdgfX412C97WE91mKbbbZh5syZnHLKKey///5kMhlg8m53+lZVKpVityOO4H8eeoh2u817Wi0+\nXK/TYxg8bxjsPzGBFAJtmjwXxzRsm4JtI5RiLEm4PJOh17bZ1vfZu9Xibsfh9NFRNmy3yQJPGAYt\nIFQK37JwtOZq12VNJoNv2xzUbPKY43BYqcR+1SqO1gzZNouEYGUmw4jjckK5hKc1f1AmCzMZvjc2\nwm2pDMOux6mlMR5MZzmkWeNKabHUsPhYs8R5uQH+s1mix29yv5tlXhxylfRY42Zom4pmFAESC6gn\nCRkpWSoN5kmDiUQTxJqPlybYp93iSS/FDo0Gny6XObjVYpHn4YYhW1arCMuiJiUvaU3DtlntunQB\n95omd6fTzJWSQ6tVBqVkmWFwwtgY2SBAmCZPJAm+lJQtC6kUq7XmccfmS+Nj3J1O827fJ2eZzFCS\njCF4PkqIohgfk8P8Ol8Sed4ftzgzLGIL2DDyecTKcY9w2TuqEgbwvOmSJIJ8EvOg6bI5CcUkYR/g\ncSn4zdAajm02aVk2i5Xi3NFRjmw0SAF/MU027ewECMNgSGsWui5DmQwNKUlHEdd5Hh9sNDikXmdz\n3+cvtk0oEyqJ5D9oscxK8cmgzFVuNwdEk+qOikKu1y47WiEmCdmqz4PpbgJh0IolOdMgloqnIsFl\nzSLfdbP8sl7lZ7bDZSPDHFuv0yMECy2Lk8fG6OtUmy4EfCGoWhaGaVLTmktTKeqpFBvEMR9oNLjb\ndTlkYoJHHJtYaJqJ5OjQZ9x12Sx+bev1fpXi/WEdyWRZwm1uD61EsoWosbopOLLd4EorzWfaNRY4\nGTby2+zht/hOuotRz2O/VpPlps3lq1fzoXqd3jjmFstiXqtFqBRaKRpJAALOkHU2kjHfN/s4ql5j\nYx1zh5fnrPIoT2qb22LF9rSZJ2NcEq4nxyfHC1xteuzst+n2A+53XI5v1fmNneFTzRp/dTyuzOaI\nXA8PWKw1qx2HIdclKwSLleLKdJotDIPZrRYPWSbvin32MSIiZZEEMe8NXrug/ymd55B2Ze33t7k5\nDm1UmZvE/K+V5hUnze66wV1Ghg+UqzyVSjFhKg5tNRk0TV5Cse9EiQ3DkJc8jyRJ+PbYGHu3WhRN\nk8elZEBrykqRkpIlUnJHOs1YOs2uYUgqimiYirnNJt8fmMEt2Rzv933GlckJhTHeH0yuZ1s1m3xr\ncCaH1aoIYNMo5OZ8FxcMD3N0rc7zrkc1itiq0cAyLcrAUiEY8TxGXZfeJOEm22ax5/F+3+c/SiVe\nXbiQO4eGePeee/7bb11LKbEs63U2CGDtej/l7Z0ielPXg+m2gCiKiKJordVgevrCW1UbT9Usv1VN\n8N+qHl7XVjFlR/hHj/dmWNdaMR3TLQvv9P93ur94+nlOYcqW8k59y+vxzrCe/K7H67DRRhux4447\nMn/+fHbbbTd6enqAyQVv+odVKcUHPvIR7lu2jNsmJngllaJmGMwNAm70PE4olzm8VmPvdpubXJdZ\njQaWlLRNk3Ycs9gwKKVSrHRd+rXmGtel1zDYtdnkuEaDNa6LDEPeVS6jTZOmYfDiNLKYkZJHleJR\nz+PAdpuP1mpsFMfcYFlEhmRJOkOfEJw8UeSPXorrvRSntmqEieZPuS6+MT7MJV19nNWqscJQ3KFc\ndtIhN7tZpGnx9eoQxQReMl1WxBpbSnYLmywWCtdUxFpTkQZz9GSixAbKJBP43OV59NsOpmHwlDK4\nKp2h5XlspDWyU1Rx+vg4H6nV2DCKuNm22azZxFeKWCnGo4inLIvRTIZxpeiKIq52XfYKQ/ZvNPhE\no8EdqRTdjQamELRNEw/4vevxiXqVRzIplIC+oMUTscDXCR8KWuygEoakYm4SM+647BFNqia2gNut\nHBfW1vBdu5+Cstg29HkCg82kwUqgV0qWJtAvJAc1anw1n2dlJkvZNJGd3OFiJkNOCA6p17nPdTmy\nVOKoapUNw5CnbZvxJAHDoGGaZIC7LYuFmQx50+S5JGFCCD5Im0ecPPObBXrR/MHu4rBokjzl0Nxr\n5llspDg4KXOPyDEqTUwD9imVuBmTrSNNlQTP8XgwEezfanJI0OaMfBer0xmqpsXsKOIq12UTrTmo\nXmd+o8Ez6TQqCNi8Xie2bWpSsixJGHddVnkePVpzv2Pzikiwgb0Nk9NqRS7K9nFw+NrE+XLl4oQB\nA2hSJPzeynHa2Ai/TeVBmBzuN7jCzvApv4anY37odjHPMOg1DTao1hkQBpGU/CCV4tlsFlcpDm42\nWeQ4bNZus2elwrOeiUfC6arBU4bLX5MUJ9bLANznptm/WWMXv8V9ysW0DHYSbaSAP8scJ1dL/NzN\nsIPvs4/2+ZXK8Cm/znPK4TIvxzaGZDRJOLFQ4L/KZd7bbvNnzyPfapEBWqaJnyTcpxSzTANpGbRN\nxQ5JwO+MNN+rFl6XnfkHN8MR/muvz+1OloMak98/5WUZqPnck8oRAXtW6uzYbPFz2+PhbDcvmxYP\nJwmPpFJUOtvMrc7AX+J5bB0EHFavc7/ncWSpxF71Ot1RxCLbZkQIypZF07axdcKdlsUHajW+XCyy\nXavFHvU6/z0wA8KQ2zIZbst38VwUcWsuz935Lp7yUhSikEsyWZanMwwkCT1RxH22zVmFAsd2bFk3\n2zZdvk+kFCjFRBxzt+uyJpulrDWpJUtY8MADbL3PPqRSqX/Ngv1PwhQhmz7nAa8Nw00RsenDcFNe\n1ekkc8o3PH1obN3s4HUx5bOFtz8MN1WaAaz1Ub+d48Vx/LaH66a8yPBaIsSbDa5N+aL/kazhNzvP\nqTY+x3H+7W+c/v+M9eR3Pd6AwcFB9t13X+bPn89WW23FrFmzgNeM+1MEWErJew88kGajwbLnnqMm\nJRXLIqs1N9g2SzMZyo7DPr7PCstiA9/nPwsFtvF9Rg2DZ6UklySUlSJtGCwGHstkeCmdxgOU1jzs\nunx+YoKjajU2DkNutm02abVoGwaRUpTjmLs7yRCRUny4VmOxbbN5tcqSVIpF6QzHNup4ccSvHJeU\nYXBMaZzv9M3ge8URLsr38gEdsFPY4h7DQQuoJgm3pbrZCM1ZzQJbC80fhM2esY+yLFZEmnlApRNd\n1hYCrWMOjkIqhuIBOVkFqzpDQyulQduyaHYG937tuqzOZhFK8YFmk4ddl/0qFT5RLrNpJ8FhOEkw\nhKBmmqSF4AGleDyTYVkqxXZhiC8ldSE4aXycl10X2zR5QUgKJKzRCSsSyYAQ7GgZPG+7nFYb5Sqv\nm+83xrjWzKITjZNoPBIqhkkpjDkuqHIZHhc2x7jaynBcpcj9jse72m3KpkWLhJmGotUhwz1A2zDQ\nQrAsSSg4Dq+mUuSAR02TW9JptgMOq1bZMkl4QimOKRSwtEbbNs9qzTNKERGTCLiSMjfaXRzvT5K5\nBSrFrlEDTyQoAQvsLpwgZjvT53aRZa9qmVu0yXn1CS62MxxfKXGn45EOIlKG5AnbIXZTWEKyWGsi\npZgwTTKdIcE7MhlWptPM1Jq01jxg23xlfJyjazVmhSE32TapOCawTJbFMS6avBB8p1ogTcLNboZd\n4wZeJ1O3rOFFJNsTIYAFTp7jqyWuynQRG5JDmzWeMW3ucXIc3yrzSCpPV6PNQjfFrabJjDCkqRSJ\nYfBCHDNsWQx7Ho6UvCAENzg2/TKmLCTjTobrSfOz8aG1hPMp22OeSTK4AAAgAElEQVSjdosMCbsG\nbb5lZNjL9MmhWSDzHFKtcEcuQ7cfsLsOuUuluNPLcVyrzEInw5lDwwzZDte4Hn/IZmm7Lu/zfZCS\nlwyD/xkbQwE1y2KJ1pQSTX+UcI9wkAkc7DdeN0y2wEnz/qDO1Ib3XXaGAxqTSn6EIA4iZCi4BYNd\nWm02TmI2k4JlyuKC1UMcX6+zwnV5Bdi6XiewbQIpeR54yfNYnU6TBxYbBgtSKQ71fT5ar/MurbnL\nsthrYgKEILQs7lCTleAL83keSafZOgi4yXX5ULXKEdUq8xsN/ppKsW21yrurVbwElivFEFBXiqpt\nk00SrnMc7stk6FOKw+t1SpZFnCScNTrKhmFI2TB4UgikEJSUIiwUuPfqq8nMm8cGm2zyL1qx/3mY\nanuL4/h1iQdhGL5hGG7qX9mZb5jCdOILvM4//FaYPgw3XQ19q2G46eT3zVIY/t7x3o4KPKXuwmuJ\nFVMK87rDf++EVK97nkqpN/iup4YJ32ls23q8fawnv+vxpujq6uLwww/n5JNPpq+vj006C/fUojJ1\nByyEYOtddyWwLPqeeIJ5hQKJUoRKsVRrap0kAyUlLycJv81kmG2a7NJqsbvvc7/r8vmREQbbbVJS\n8oSUtKTE71geTK353862eWxZHNRo8KDjcGSpxJGdiLWlts2qJKFpmqz0PLqThKcsk8PbLQZaLW7O\n5xmQkjOK4/zSS3Gzk+Ki0ihf6Z3J5xplnlQ2I5bLlypj/MXL4ugEV2uWKYsFXp7VymbfqMkl0kWZ\nNmkdszSR9CvFCwn0qslJ8wdMi17LohZHVGLN+0tltggDRpViAtii1SIyDPyO5aHUUbHTQvCEYfCn\ndJpNpOTAep2tO0UiJxUKdAUBpmnyFNASgqptE5omURxzredxZrFIxZAUXYct/QDbVDhKYSmDXesV\n5ijB9U6OE1tF+nXM1VaW27XNsOlxrZVnhTC5X5t8WtfpV5Jvqjxfak9wgdfF1+sTXJrK8fuxEX6T\nStPVbvPJapX3RCF32Q7nDw9zRK3GvI4SNthqkShFoBTNOOYRy2I0m2XIspgZRdzkOOzWarFLvU7k\nOLwoICs0vTJhBjF5KdkhmvTstaKQIcdlcz259Xi3meFrE0P8OD2DWEjOqo5zoZlht7DNq+k0a2yb\nPaKAJ22br06Mc52b4phKmTNLJQ5otbg5leajhQKbNpukhWCJUhQB3zQn0wyShP91HF7IZskpxeG1\nGk+4LkkcEaNxdMLWlskHW5ME7g7lcqWR4l63mz+bOR4XDiswOFw3kcBdVpYP1KroMOZ+y+Hj7Rrb\nhm1uNNP82csxEPokwuC8kRG2DEOuz2Q4plTi09UqB7TbLPA8kigiNiS+YTCmQ4rC4PelCX5iZtkm\nDtnHf83fWBaSlYlgKx2RIuHudBd3iRSHUOMuI8tB1SpDWvK05XBE2KRbCpp+wiN2hkVas9RQ5JME\n11SsiDWvGgZlx6GhFLbWXOm67BIGuCIB2+ZbxSK3Z3P8eGKcfet1LusbYK/25IBQE8ECZTOhTObF\nAS5wr51m72YdAQxGIZd09fHNwhhNZXKhl+HBrm4WOR4rtObSdIaV2SwDScK2vs8C1+XUYpFPVqts\nGgQssG2IY0RnrUi05k7bZlk2y2rLYtso4mHbZjAIOL1Y5JhGg1Uda9ScKGK1bYMQ3GPb3JHL8XQ2\niwsMS8ldrsvHajU+3miwfRxzm22zS6mEKSWYJiu0ZqlpUkiniQwDHcdc4nnMNQz2q9c5utHgUc9j\n83qd7Wo1iGOuu+MOnnz0UfY6/PB/ezVvao0H3pTUTleBp5TgKRvEm40QvR3yO4Up8j3ViAevKazA\n2ueePnj3VraKv3W8txOJ9lbWijeLRPtHrRVT5/NmQ4fZzhzNevxrsJ78rsdbIpVK8eEPf5izzjqL\nMAzZbrvtgNcWx+lxMJtuvz1LbZu7n32WUwsFjqjV2Knd5kbXZW6ziTCMtZaHp5ViPJ1mpePQH8f8\nznWZB+zWbPLJep3lnofj+2xdrZIoRd0wWN6xPKzyPLJS8pBpcn86zfZac3i1yjZJwoOWxbuqVV51\nHFxlsiiBxZbFxaPDLEhneDCT4avlCUIh+ZmbZfck4H4nxZZJzLb1Cj/KD3BBaYjnnRT1BKpCcnyt\nQBIGLLNTlJDU4pij/AZtpRhLBFuRsIqEPaOQspBUE82+rSbz4pg7vBRHNprs3PaZlSTcadt8rVDg\niHqdTTpRTXMbjbVksRbHPGFZjGUyrLEsZkQR17guO0QR+zUafKrR4NF0Gtv36Y8iSpaFCVzjuewe\nhfTGmqY96Sc+sF7GtRSPuGlOqI7xsJvl2FaJMzODfCRq0laKY9sTfKZV4oPtKndZGR6wM5zQLvIH\nM0vJ8bCBJy2PWVHI5Zkc+4Q+Sy2Lmmkz7rh4ScLFrsuL2SyuaXJws8ly22au7/Of4+NsFAQMK8Wz\nQmAJQaWjut5rmjznecwKQ8aVQX8SsUPK4kEzw2nN0bUJCvOI+LWZ50A9adFYqFK8q9nkXivNWAL/\n0arxUDqDr+HIeoXfOWl+VhzjZ26az1cqfLDV5Bu5Lu7IZFmWSjNHa+63bYZtmw/WanyyXiejFE9K\nyfsmJtBKEZsmS+OYVyyLgueRThKWJAmujplrWXy+UiCfaC5Ld+FJg0hZXDy8msNqVY6s1/itm+Ne\nJ8u+UY2/qhR71utsG4Vcq1xWeRn2bNe5N5XjV6tW84LlcpNpcne+i+Xp9Npc7OuyWZquyx6+T4vJ\nKuBhkWBqzXy/zdNemvfpmEWuy6HN12wFxJo7Uzn27hDie1NZjh0b5ze5PjSCA6o1dgx9Lrcz3JvK\ns0PU5nYvy8Vrhjii0eDuTAZTaz5fLPKpep2yZfFUJ7auYlmYUvKQobCk5H+KBb4yMIMfjY0wN4ro\nTRJ+nc6yxrS4MtvDn50s763WuMFK86ST5U+pPIuCmIZpYUURXYnm7nSOQ6pV3tNuYzgOw4nggMI4\neaCgFC8lCTXTpOA4dAG3WxZ/zGYZNE0Oq9XISskKw+ArIyPMCQISIXhESsLODpSnFKuF4JfpNKPZ\nLPO0Zo9mkztcl/8aG+OIWo05Ycg9joOvNXEnVlElCbc4DksyGUZtm13CkKcsi0wcc9b4OEe0Wrxs\nmiwSgllxTMWysIXgGSl5MJNhVTpNd5LQEIK7HYeTSiWOr9WYuXIlZ//lL2y+yy709vX9H6zg/zim\nFMkp5XQKUxXNU0rs9DKOKfV13aa1qd+9XSI3PY943WiwKQvGVE4u/H1bxdSO5bqWjr/n2/1b6vJb\nRaL9I7nFU+2AMEnWU6nU2iKP9fjXYT35XY+/Cdu2+chHPsIFF1zASy+9xK677rr2jn9qMZj68G+x\n/fYMbrcdZzz8MEOuS91xOKDVYolts2OjwQkTE2wRBKwyTZYLQQomLQ9S8qRh8Hg6zbJ0mm6t0UnC\nU7bNf01M8OGOsvgn22bLTjFGZJoUo4jHHYehbJY1nZKCexyHs8fG2KjZZMzzqArBr7wUp1TKbNlo\n8rPefnaPAz5SK3Olm6UCCB3zgpvm2+VhvtA9kwOjJkfXSyxw0twkHbYn4qh2hc+ENbTtcLUxWf85\nFsUYSLSAJdJgwLRYHU9mAOcti0QKrnNcip2LaDZJuKyTVWyYJgc1mzzlOOzYaHByqcRmQcBKy+Il\nwAFKpklaSh5XiocyGV5MpdgojjGThKWGwfdGRrDDkLbrcZ+QvKQU2wc+m0jN7akse9ZKdJmS33ld\nfKUyzI1OFssw+I9GkV2DOj/IzuAgf1LFTJRiTSvm7nQXeUOyRb3JMsOgJ4oZs2zqCRxfq7HaTfEY\nCVoaNDqxZcvjmDWmyZDnYSrFUJJweTrNllLy/kaDA1ot7nVdjhwfRwLatilpzdOmohBr5hpweFzj\nZeVyaCcndwLB6d4slvualpvi3VGDRiJ4IRJ8qlniPJnmpLCOF4b8wc5yervKpVaaw9tNZiaaz+d6\neTHXhSknyy0QgrJSWKZJMY65KZ1mdTZLS0q2CwL+7Hl8tFzm2EqFnYKA2x2HSpLQJyeznc/wqyzx\nUhzTqHCr7bHITvGV4ig3ehn2bk5u7QtgYSbHZ0bHOCs/yFwdYLcDZiUaaduUay1+0zVAEAWMC4OT\nymV2b7W52fN4b7FIPoowLIsVWrPKMKi7DkiDlVozEmsOikMObjW4M5Pli8UxbndS7BA0yXRsFyk0\n16a6OLyjTD9luexbr7FIOTyg4bhWHQUU3BQHjxX5q5niUSG5Lp1hYT6PVIrxJOHXqRSrslm6gT2a\nTe7slK/s3GiQmCZPGorr3BQXFcfYII55XJmcPWMms2LN41JxxZo1HF6t8q4w5LlMhjNGRzimVOGg\nRoMfZfLEicG12W6GophfpzK8kM7SEBIrirjZ8/hktcpH63X2brW40fPYolLBEwJtWQxHEUuUYiyd\npmyaZDqKdJdhsH+jwScbDZanUthBwE7lMoZpUjIMlgHjts0az6MLuMuy+FMmwzZSclSlwiwpWWIY\nnDQ6Sl9ni/9xIahLScmysE2TYpLw83SaRirF1lHE/vU697gu88fHOaBeZ0YU8Zg1ORAXSklgmrhJ\nwp8ch0cyGRqOwy7j4zx6xx00enrYaKut/i+W8P9XmJr1eLNM4Ole1ymiNz0ebQpTpPWdEMK/Nbw2\npdpOwfO8t3XcqeO9Xd/u9KE927bfoOhOkeq3yi1+uyrwdHvFVMzcP5JRvB7vDOujzv6NcO6553LD\nDTfw4osvYts2u+66K+eeey5bb7313/y7xYsX87nPfY7HH3+c7u5uTjzxxH96FrDWmtNOO40oijj3\n3HPf4L+aHtvy6iuv8LPPfhZVLuMJgaU1hSCgLCUfDUNmNxo0leLXmQxnFgqsUIoXXZdbLYt+w6Db\nMLCEwPd9VgC7rxMJ9umJCTaNIp43TS7J5wmFoFcpTCFQWjMchmwZx3y2UsYHftnVzTMCNpSSC8bH\n+J+BGfQlCSeNj3Jm/0xkHNKWBr6EH9YL3GmnWWh5fLsywgohOcPtpttUzFKTC9lw28cWkgPjFr8X\nNhuSECQwJhT7teo8ZrtUlMmgYTAWhpSThC2kxJeTxRHFOKa/kwVsaU0xCBiRkuOCgNmNBqFS/DKX\n4wtjY7xqmrzouizoPH6gE5emg4AXtOaUdpvtGw1uzOV4zHHQOsYS0BIQCsGxfoWlqRwfrI1zebaf\n8ytDCGAYyXy3n3crzWmNAh4Jp2Rn86FaiZ84GQ4KAkLT4EYUd40N84n+mQRxzGcqZfpizYW9vXxn\ndIwZccwLpsnZvb1sGARkTZMJpShGEU1gU6VIJQluHLNMa3Zot5kXhtzS28vzgc9sU5KxFVm/zXYi\n5tNBicfMFBeYXfywOMQ1+T7qUYzpKT7RKvBT1ccPKiPMT/dzWNTkQ36do5x+DjBgMPT5uXTZzDSo\nhBH7N9t8vFKhLATfnDGDzdpttmo0WKoUd2YylIRgllK4UiLjmNFOhuwHooiN63UWuC5PWyauFMxM\nYk5pVfHjmF/n+rmwMIQBXG+5GLbFkfXJwbw/pvOIdptdg4Bj+wfYod3ke80KMfDZvjn8ZtWr3Ox5\n/CyVZkPDYBOtycUxC4WgL4o4qZNecklXF3faFrMMg33aLe5zHC4tDPHJ/llcMjpEmoQnDMWj3V2c\nUi2s/ex9tmcOl4xPxovdZ3ksjQ0+26yxf/8guyQx+7XrbBa0+WrXTH69ejUJ8J2BASo6YddqlZdc\nl8dsm1KSMMs0yUqJGceMBQFIyZnFIptGEQtsm5/k82QNyV5xzKcLBTJJwpU9vViBz0frkwT8FUPx\n475+LhyZzPu9NZfnKWVyRKnEUqX4befz29eJoIuiiILW9BnGZNtcGPKsEMRJwjnFIjUhuDqX4xbH\nYSetqZkmUZJQDkMCpdhWCDytscOQBwyDb0xMsFEUMWQYnN7Xx5btNq5lUTBNhsKQUAg2VwoXsMOQ\nJUnCbr7PQY0GM7Tmor4+XpWSnatVVqfTvCAlFa3pV4qezto2EYYUDINTGw1mtVoMuy6/zmb5xPg4\nI4bBi6kUjwhBl1LMVAoLEFrTd8ABnHreeW8aA/bvhrfKBJ4ijVM5wH+LTggh3nGd8dRzr1s9PB3v\nNFP5raLGTNMklUqtvbZVKpW1wk42m/2bmbtaa5rN5hsi4BzH+bu2j1artfZcHMdZGzG3PubsX4v1\n5PffCB/4wAc45phj2HnnndFac8455/DII4/w3HPP0dXV9aZ/U61W2Wyzzdhrr70455xzeP7555k/\nfz5f//rX+eIXv/hPPb8kSfjhD3/Ik08+yS9+8YvXLWLrlmEUi0UuP/lkBpcsYdR1KRkGo2FILCWb\nq8l8TiuKWJgkHNtus3WrRV8c8/2BAfK+z5x2m9WpFIsNg1qSsIFp4gmBqTWrwxBHCA4LAjZoNFjl\nutzseXyiWOSZVIrlrsuKKMI2DPaLYw4qTRABX+jpoS0EP62VWWEobszk+MbEKFdn80xIk4KEMa35\niIw5qjbOmfmZzEgSvlAZ4eT8TDYLmuztN9gmCfhCagauEEwgGI00myuDZ6OI7WMNtsWzQchOrRbv\nDUICw+CqbJYfjo4Sy0mF9sddXezg+5i2vfa1CaVky2mvzaIk4SDf532NBgOdC/FEkrB5u82qVIpV\nQFFrNpOS4ytlnjct7stm2Kde40YvxXatBg9aDjMsRSGK+F1rjDwJ30z1UzZMPl8a4Uu5AXKGpFto\nVsUJl00Mc7fjcb6d4brSGGfnelkpFR9qNFhh2zQ1bCEEQ1KyRGuyUrJbFDEYBDxrWayRkm8UCixX\nijtdl1s8jy2FQBsGtpSMttv4UrJvFOCZkoeV4pVIMw9JvxJMCE1WGpw3MTnItciwuNnJsmkU8Gg2\nxXhicMXEatYIyXFOL18TbRYph4l6yFjapZAIrli9hp/1dPMX0yIlDTbtvG9qYcgKKflyucxgFFFX\ninN6eji0VKLiOKxxHJ6JY2yl2FoKNg1Cyn6bB70UfWh8Q+LrhKuKI2sHuzRwev8sflxYA0BJCL7S\nM5OLR9fQAD7aO0CvaZIjYVkUs3elhjIMRm2bB6RklpRkDANTCJq+zytCsC+wcRDgtNtcns8TkfCz\nyjg/7erj4/UKO7Ve+5ydNDibn0ysRgES+K/eOfykMEl+Kwi+3DWTX4ysoYFg/sBM9qtUeTKXZVWs\nQQi2EwKnk5X7mGHw9YkJNohjykLwhYEBdmg0kI7DqFIMRxGBEGwnJVsGAe8pl/lDTw8zw4BPlUo8\noxSP2TbXpNJspBRSChSC0SDAVoo5QmAmCWNhSEEITmw2mdluM+K6XJFOc1KhwGqleCGV4l7DoEdK\nZpgmNpMq3NIk4UAh2DQImNFsckl3Nx+qVJgXBDxvmvw2myWWk1nOlmGQRBGFKMI1DHbUmg2CgKWG\nwZBh8MOxMV41DG5OpfiT57ENEBoGUgjKvk/ZMNhZSnJxTCYIWGBZ/E+xyNZRxHLD4My+PmZFETml\nKElJuXOzt7Fpkk0S0lHEs0nCFkHAx2o1BrTmZ729LFSK9zWbDHseq6QkzmT41vXXs+G8ef/Utfqd\nIEmStV9TCu90MrtuBNo7gWEYb2hKs237bau10xGGIY1G4w3n8veI6VshiiLq9fob8o2nSjumZ/zm\n8/m3pcRO5QxPp1WGYZBOp9+SzNbr9bWkeaoQ5B+JUFuPd4b15PffGI1Gg1wux0033cQhhxzypo+5\n+OKLOeussxgdHV2rIHznO9/h4osvZvXq1f+S87riiiv43e9+xxVXXLE2CxjeWIZRKpX49vz5/Ncz\nzzA3DHlRKS7N5SgqxYZS0hKCpKOEdinFzCQhH8eUtWYkSfhqqUS31jziOPwon2efZpOS6zJhGIx0\nfGcbS4ndUXoel5KzJybYMopYaRh8racHpGSOYbB5EPChiSLXeB4LHJedJZwxUeCLA7M4ut2gv1Hn\nJ739HFCr8js3RdoQfK9ZxIsivpUfxBGQhAFNBLOVQQXB82HMzkmEheBuYbJn0GaRMtHKZNt2ixcM\nxRZhyEbSoCAl9wI7AtuEIV2+z5/TaeYGAcdWKixXimuzWZ6xLLYEGoaBBIpBgKEUmwHdcUwSxzxm\nGPykUKAhBH+xbf6YyeAZkuN9H9tvc2O+ixOLo1zUO8D3x4b44sAsTiyN8dN8D5aQnNyuskdna/wb\n3YMcVxwli+ar2X4mEsGvamP8b66X2xPFYUQ8aFgcVa1yXybLojBkUBo4UtIGXg1Dskox2zAwk4Q4\nCFgMfExrNmo26QtDzu/tZd9KhQnL4tl0mkYcM4EmSTS+Tug1TS6bGOGSrl7uTgwua44xmExekDTw\nme45XF54lXsth295ef7YGCVLwoldc1CxZre4yQNGitOHh/hs/wC9YcgebZ+2objFsRlMJpvltJS0\nwpDxJGErpcgkCQNhyOPA9r7PMfU6LeCn3d0sMk1mGQYHtZq8v1LmnMGZbB2EPG8a/Ge1xLb+pFLT\nBo7rHeT7pTHm6BgFnDQwm18MTX72bsjlKcbw6XKZWx2bX2VzfLxS5V1RREprfjwwgBsEbNlsssLz\neEIpasAGpklfHLOd7/NiFPGYa9MrJf9bHAXgOak4v28Go1GIKSVZaQAJo1HETFMxSMIerSq/9fL8\nfGg1Argrm+NpaXFIqcSLpslV2SxISb9hoIQgjiLGtKbXMNhUazYIQ5ZISZgkfKNYZI2U3JDJcIvj\nsKUQxGqynbHZbvOqYXBMFLFFvU4ujvlufz8XDA/TrzUvGQZf7O9nThCQMU3GlWIsDPGnVNckwe2Q\nxXf7Pkc0GsyIY37Z18cSw+C9tRpDqRQvScmE1nQrxaCUmFpTCQJWScnnGw1mt9tULYsLurr4yPg4\nJcNgZSbDQ0lCxjDYwDSxkgQdBDyXJOwPbNdqMdhuc2lvL1u32+xQr/OCUtySzVKdtjMg4pixMCTq\n3FBv0G6zSiketW0uHBnhJaW4z3G4IZViIyGwOjc0Nd9nWEp2FYIBren1fW5wHE6dmOA9QcBS0+S7\ns2ez5/HHc8Lpp//T1+q3Q2r/2RRgygYxlVcLvGkz3D/SlKa1pl6vv6Eh7R8tnUiShGaz+YY8X8uy\nXqfidnV1ve1jv1WL21u1zVWr1bWPzWQyrxuuW49/HdaT339jDA8PM2vWLB588EF22223N33Mcccd\nR6lU4uabb177s8cff5xddtmFlStXsuGGG/5Lzu3WW2/l3HPP5corr2RgYABg7SIy/Y41DEO+/IlP\nYC9fzv6+z5xmk3HL4g+pFGcVCixTiudsm1sdh1lSku1cNNpBwCvA+6RkMIqY1W7zW8/jvycm2CSO\neUEpLuzcjfcYBlGHSBfimFlSslMYsk2txirP41rHYRDQSrFbq8nepRKf6u8nAH5bLnBtrouiMvnq\n+DBn9M3i3VHAX5XJiNZspyQnV0aYmWiuNT1+ZWboMg12jNtsGvpcqTLMNhUvBiGbJhrftHgxijmn\nUmJxNsfCBELTZKY0CLRmKAxwTYuZQqCShEoQ8LKUHBtFzG61UHHMRV1dfKVQYMwwWGrb/NF1ycrJ\ndAlLCHQY8lIcs48Q7Fyvs2G7zdl9fTQE7CwSji6Oc27/DH48NsTn+mfxw4kRlknFb7NdRIbkV6U1\na4fKRoTkm12D/Ly4hgQ4rmsmSIMP+jVutjMcOTHBxdkcTpLwjfECA3HM1/tncNTEBPv4Pqul5Gv9\n/cRxzCbAqGkykiQ0tWbQNOkB7DhmPIowSfh4pcKlAwNko5jVAjZOIvYPfSzf545cNydMjHJJ3wy+\nVRpa+x76fM9sLhibJJPn5ft5QBj8oD3Bn1N5Dh0e51f9AzyUJDwwMlmXe0ZvH5kg4qh6HTNJuDOf\nZ6VSnDg+zrNK8WgqxSNKTbbRycnSkqrvM2QYHBrHbNxuEwcBV3d3MxjHCGVw5ugIg1pTAw7vH2CW\nYZAzDHJRRK7d5h7TYqY1OQy2PAjJC0FaShSwLIrYWE5GwklgPAwxlGLTzha9DkOeNgy+WywyI455\nXinO6e1lFpBWih18n4+Mj3NNVxePWSYoxZZRxAljo3hJwkmz5nDFmkm1tyoE/z1zFhetXs0fUylu\nS6VoCMlOQpAAr0YRJcPghHqdwXabNZ7Hlek0nykUWKUUL6bTPCAEvYbBDNPEAgLf5/kk4YPAZq0W\nA+02P+/r49BymVlhyAtqsuGxISWDUmJLiezYj1zDYBet2cD3WaoULxsG542O8rJS3OZ53JRKsRUQ\ndQh4xfeZMAx2FoKuOCYfBPzZtvlKscg2YchypTirr4+BKKLbNClLSTWKqCcJ80yTXJKQjSKW6skW\nxE9XqwxozaXd3dxlWby/2WTU81gjBBNxjKcUczv2o3YQ8LyUfLlaZU4YEknJOf8Pe+cdJklV7/3P\nOaeqOoeZ6YmbAzlJUAwkRUG9CnoVvAqK8KIgQTGheL0IigEFAQUxIApGwAxXQb0EQUBA4i7LsoFl\n04Seme6e6VThnPP+0TXjsiwKvODjfZ/9/jPP1vT21PRUV3/P73xDqcQh1SrGcdiYTnOPMSSVYpHj\nkARkGPKo1uxvLQc0mwwFAT/t6cFYyyHVKis9jzszGYaBoVhGooyhEgSMKcVRUcT8Vot6IsGKN7+Z\nUy688GlVwNvClhrYv0dqXwxiOxNvZq19GsGTUpJOp58y5ZxJgQiC4AWpH263209rcYOOpnemFvi5\nYqZpbluvl5TyKY2nzwbPpW2uUqnM/txCoTCbULGd/L642E5+/4Vx9NFHs2bNGu67775nfCMcdthh\nzJ8/nyuuuGL22Pr161m4cCF33XUX+++//wt2Pr7vc+ONN7Jp0yY2b97Mgw8+yO23305/fz/lcplq\ntcqnPvUpTjvttKf8P2MM3/jUp3j81lsZMgbPWlQY8lfgfe02S1steo3h8319LGk0KIUh6zMZHnAc\nmtaywHVJxHrejWFIVkoOC0Pm1eusSae5M5nk1HKZZa7LsiNp5ksAACAASURBVEyGO6Rk0HUZkJKs\n1mR9n0cTHqdOTPD93j5SWN5VqXC76/LfyST/ZiOOnK5wdmmIs6YmGDeW7xd7eGmrwV2JFAklyUjB\na9t1Xtus8dHCIK+pV6ils9xvBetQvL01zR8SaYzjsn99mt+7SRZ4HgGwOgzZr91mqdG0peQ3qTQ7\nRRF5z6Mq5azkYUfHIWktjtY8qjUvD0Ne02gwqDW/7OlhhVIcUK2yNptlleOw2Rj6XZcFxvCSVgvV\navGtriIucM3EKB8YmMPZ1TKrheL3+SIXlDdzj+PylXwP3a6DIyVJa1nnB+zgSE6ulXk4k6PZjhjx\nElyjXE6qVTneb/GZrh4eVy57A9NCsE5r6krxamMYCkMmreW2RIJvjI5SE4K7EgkuLRTY2VpwXVwp\nmQoCNgj49sQ45/UPcNrEKL/uKfHJ8WHO6J3Dd8Y6pPzE/rl8ubKJ7tjI9c18L/vXKuxtIjYKyfmF\nfppKsXfUZK1I8NXRYT7dXeLPymUP10UDm9ptItdlaTwhNGHIQ0LwgVaLJa0WRWM4t6+PPep18lqz\nPpPhXinRQrA4ngoPhCHLleTgKCTZanNjsYseY3hDrcqVXV38YPOm2Yzdjw4M8pHRUeYYQwt439Ac\nLtu0iQSw0XE4u7+fT42MEArBctflykKBPNDlOLhSEoUhm41hqZTsrDWLWy3+kkqBEMxpt7g7XyBv\nLTs0mzyQTnHF5k2z76/LevvYo1rloDCY/fdOtSleEgSsdhSf7ykxJwzJxOaviTCkKQS7xtdbOop4\nyFpe3WpxeCw/uqivj3VSsl+jweZ0mtVCMGUMPa5LvxAkYgI3rBQfqdWYE4ZUPY/zCwWOnpxk3HV5\nMpPhLmspKMW8eOpKELDMWt4I7NZsMuj7fLtUYvdWi92bTR5zHG6cmboqNavHHgtDQqV4ndYsaLfZ\n6Dj8OZHg4pERVjsOd3gev4jbEROqU7Feb7fZHE9dB4yhv93m2lSKkyoVXun7rHRdPtvTgwsMSkld\nSnytmTKGUrwT1aM1TxpDaC2fqlTo0prrCgV+mMlwYLtNNZlkQggmwhAch51jIi3DkPuk5GO1GjuG\nIa61fLi/n12aTfJCsDmV4mFjUEKwwO1UWLta054zhxMuv5wlO+20TTK75dcXGjOkdssEhy2PbWls\n2/Le3mq1tjmJ3VIWN/M7aK23Geu1pdb2H6HZbM4+hxDiKYR1ppb5+eiojTE0Go2nEXQpJYVC4XmR\n0SiKaDQaT5F+bHmOW1cod3V1zTbubceLi+3k918UH/nIR7j22mu54447WLhw4TM+7vDDD2fevHn/\nFPJbr9efInPYFk444QTOO++8bX7v55deysarr6ZuDHUh0MYwaQyDjkPJWvJaM2oMgbWcUa3SqzV3\nZjJcks9zeL3OeDrNmFJsCEPSjsMipWa3MR8Ugo/W6yzyfbqN4Yz+fgbabYJUikApEsawXGvOm6ox\nheWnpV72CAPeUS5zfG8foYBfV0e5oKuPhJScOTHMZ7sH8IGNUvGxepm7nSQPpfMgBJvbAVnPZUft\nM2w7z19zXdZGmveEIXe5Hk9aw3G1KeZpzfWFAl1ByL81Gkjg18UiylpOn5hgXZzxe0sqxb5AVSks\nHckDrsvOMGviuUMpzp+YYEhrVjoOZ/X0MADkPJf+SHN4tcJV6QyrleL9UYuEtdydzvKl8WGelJL/\nKg2RCQPeHAW8KW4Ge0K5fLHQS05YppViXWT4TXkzZSl5f7HErsqhoRwe89ssNJZux6EpJY+FIZmZ\n7WTAxlOw1wC7+D5zm01+3N3NEt9noN3mL11drBOCKR3xBqu5N5niW+VNfKBvDl8qDzPHaALgfd2D\n1K1mfiqBayyVKKKuDVdPjeECJ/fO45sbN3Bebx83CslRzSY7Bj535gssage8rVrlcdfl4q4uGlKy\nWAgqUuIbQy3eNh+ylpzWTBrDBPDpyUn6jOFP6TQX5PPsG0VMel6HfAUBTwDXjI0yc/XfnMtxbSbN\n4dUaI0qyLpniXtdjZylpCgiMYVwb5seNdq4xPBlF5ITgqEaDOe02j+Tz/D6R4JiJCVa7LiszGe4F\nBlyXAaVIGoMNAlYJwQ9HR8kDTeD8nh4edl0WSElNSpSAjUHIYtclJUAZy8owZEgIXq41/e02d6VS\ntIBPl8s87jhcn8txczLJLnS0ro4QVHyfKaXYTwhKWpOJp65fHB9nYRTxqOvyn6US88OQrOcxFU9d\np61lJ9clawyFKOIRa9klCDimXqfXGC7r6eFO1+VVrRYjqRSbhaCiNdlY/uQZQysIeExKPhUT6UAp\n/rNU4rBKBd912ZTJcJ/WJJRiSUykZ6aurwJeVa8zGIb8pFRCa83BU1M87nncmU6zGZjjuuTihVAl\nCBhViqOjiAXNJlNKcV02y+eHh9noutzvefwsk6FfSoqOQyI23z4J7Csli7VmbqvFdek0hzYaHFGv\ns8J1+VqxSFUpFgiBH+f/1rRGOQ67AANRxKQxrFCKC8pl8sZwUyrF14pF9glDQs+jLgQN4NUnnsi/\nn3TS87pPb42tyezWpHbm6/PFM5nhZpILtkyAmCHuvu8/jRA+WzNco9GYlSmkUimAp5nXPM8jnU4/\nZ93s35vYPt+p8jMZ9jzPI5lMMjXVSbiZmTDPJGxsx4uL7eT3XxAf/vCHufbaa7nlllvYcccd/+5j\njzvuOCYmJrjhhhtmj72YsodCoTD7Zt0ajuPwH//xH1x44YWzN9Uoip4ypfjFd75D87vf5aiNG3nM\ndbk/keCGVIpFSpGMUx7q7TableIVQF88sflpKsVZExMsjSLWOg7n9fSQAnqlZFpKAq2pGMNCx6HH\nWuZGERusRQHHTk7yy0KBFek05TCgKATfKY/y9e4Sq5JJTqhVuFM63JBMcqwJOLhZ45yeIU5q1ti7\nOc0ZPUOsiQzvjFoc254ijaWM5NTCAJ+aGuO2XDe3aMGgkrzcb3K1SjLfdZnTqHOfl+AIY9ioHDbq\niLLjsoeUSGuphSGPSckxWjPUbpMOQy7t6uKcsTGaUrLCcfhBoUAOKM5IHqKIDVqzi1LsrDVLGg3u\nzWSYEAKkZNpxOKjZZP9ahQ+UetFCcENllO/nu1mZSHBueZiitRzbP5dvlDeRj6erH+2dw1kjw3Rj\n+Gyhm7vdBIOOQ8pvg3L4xvAwdSE4p7ePHVst3jU9jbSWC3t7WeY47N9sMpJOs0EIJrTuTAgBzxga\nYchmKblkfJx7PI8be3pAa6YFhFbz3rDNEfUpbkikuTbfxZmVCa4qdnPW2Ga6AQ0c2zOA5znsGQWE\n1vCayRovi0J+l83xEy/JkUHIOs9jmbWMKsVRYchQu01NKX6WyXDJyAhPOg73uy4/yuUYEoJsTGza\nQcAG4GVSMk9r5rda/DyT4e1TU+zo+9yZSHBrLsd6YIHnUQRSUUQjipgSgv9Tq1HUmrWZDD/LZPju\n5s1EwK3JJF/s6uIVvk87kaCmFONBQKAUu8XGxnQQcLcQHF+vs0+8cPvkwAAqipinNRtTKcrGUDeG\nfsdhgTHs0m5TFoJVrstFo6NIYJ3j8KG+Pt41McFIIsGT6TT3xUR/juPgWUvo+ywD3hFPkEtBwNdK\nJQ6v1eiNIla6LjfkckTAkOOQjLWuM/KFg7RmQavFY57HSs/j88PDrPA8bksk+G0mwxIhUHGawXS7\nzYhSvEIIBrSmx/e5LpXizIkJdg1DHnVdPlsqkbeWkpQ0paStNTVjmOM49FpLbxSxyloSxvDRapWi\n1vywWOS6dJqD2m0mkkkmgckoQrkuO0qJpzUiDPmrUnyiUmFJFKHiqevuzSYZKdmcSvGI1ighWOS6\npAAnilgdRSwGjozLc37f3c39jsMRk5OsSSRYlkqxylr6XJe+eOFdb7dZJSXv1ZqF8cL2G11dnDY2\nRkspHvM8fp5OkxXib0ktYch6Y1gsJXtHEQtaLW7MZCgaw6nj4yzzPK4rFBhZupQvXn31361G/ntk\ndsuJ7T8DURTRarWepu2die6awcwUOAzDp6UjPBsz3PT09Ox0NpvNzsahbW1ek1LOmteeK7Y0oc3g\n/2WqDNs27G05uXYch3w+j1LqeRn4tuO5YTv5/RfDhz70Ia677jpuueUWdtppp3/4+G9+85t84hOf\nYGxsbPZN+YUvfIHLL7+cDRs2vODnd9JJJ2GMYWhoiDlz5jBnzhwGBwfJZrOcdtppHHPMMRx11FGz\nj5+JldnyRnLTL37Bd88/nzOmp5nXbNIdG2QOrNVIWcuTqRR3xJKBefGHsNSa9WFISXbSBea3WjyW\nTLLSdfn42BiPui73JJPcmEyy2HFIS9mZ2LTbPCEFX6pU2CEIuCGV5gf5PA0B5zTr7NJqcnb/EIu0\n5oTyCO8u9WME/KI2ym/SeW5JZfnPWpm+KOCI/ADdrmKe0zHZuVHIn7VgUcJjrt/gPpFgPwkPG4tr\nBSe26tyYSvOohbmOgwaeDCO6hKBXKXwhqEQRPrA0np46WrMqDNkBOLzRYCgIuLNY5D7X5cjJSVYl\nEjyWSvEInWlWSUpSWjMVRURS8InxMl/pH6DLWj4wNsafXZcrcjnegOHM6jgG+HE6x28zeSaiiF0T\nHloI6lHERm14XRhwzHSV/+ob4pJNG1mRTPL9bI61ymGPeCI9Ek/OXgEMao2Ka6e/Wi7TawyPOA6f\nKZVYGEV4rktbSvw4wurdYcDrajW+0j9AoCRvqFT4flcRx1heaTWnjI+hgFWOyze6erhofASAX+aL\nTAeaPfwWF/X2sVEbFiiHlDWs1ZpFQUh3vK3/uNY4UrI4Jn0qilihNQdYy8sbDeaEIT/r6aFhLQfV\naqxKJPhrXKM7N9ZletZSbbcpK8VHpqbYwfcRwMcHBjhxbIyKUqxNp/mD65KQkqE4ai8KQ9YYwz5S\nsiSKmNdq8et0mn3bbY6ammKF63JVocBa12WxEARKIa1lMgiwjsNu1jKkNb7W3OU4XD42hmctd3se\nn+vuZhdjkK5LIASNKGIC2CueEvdGEX8SgjdPT/O6IKCgNZ/p72dUSvb0fYaTSTZaSz2WLwwIgac1\nlTBkTEo+GqdgjCcSfL5Y5C2VCpOex8Z0mge0JuM4LHQcEtZiY/nCkVqzR6PBQBRxeW8vc32f3RsN\nViUS3JpKUaNz7adjrWs5DGlKyVvi9/Co6/K7dJovxPKFexMJfpPJMCQE+Xhx0vJ91gGvlJL5WjPU\nbPKTbJajazUOabVY7nlcVCzSUoq5QhDGCQNVrUkqxY50pq6jxvCElHx5fJysMfw2k+GyfJ6XhiG+\n53UyfYOAllLsqRSeMeSDgNuV4n1x/nPGWs4YGCAdhsw3huFEgrXWElrLkOvSTUe+sDmKQAhOqVYZ\n1JpHslm+n07ztslJNieTrE0mecRaumKz6OziRAiOjSJ2ajQ6ZH+ffXjjeeexx777Po3oAv9yutCZ\nKefW0oFEIvEUbe+WUo5Wq/Wc0hGeKYLMWkuj0XhecWNbY1vkdwbPd6r8985x5nlnTIDbY85efGwn\nv/9COPXUU/nhD3/Ir371K3bZZZfZ47lcbnb1f9ZZZ3Hvvffyxz/+Eeg4RXfaaScOOeQQPv3pT7Ny\n5crZqLMPf/jD/9Tzb7fbvPvd72b//ffnlFNOmT2+rW2xxx95hEtOP505rRZpY0gZw4YoomgM763V\n6DeGu7JZvpPJ8KZajeFMhs2uy5oooit24nvGEAYBjwjByUHAgkaDbq35fH8/B1Qq+I7DmlyO1cbg\nW8vuUvKaZoNXTk/znUyGm9JpFjqK88qj/DWR4ppiF++brvFXpbjeS/AWNKdNjXNBvsRqL8kHa2Uu\nKvTy5laNeX6LAMH/pPNsEg7Ht2r8Jp3nbiM42ER4xnCjk2Sp6zAehkQIPj9eRln4fbHAk8rhrHKZ\nDVJycybD9ek0B2pNxXVpCsFEECBdlx1FJ0vUDQLuUYr/rFRYEBddnNLfz8J2G51KUVcKpTUrjOGS\nyiTGGi7rH2C3KOS95TFOHxgkYQxJx+GNjTpvmKryy64eJo3l5NokAF/oHWBgeprRXJ41wJPGslQp\nunTEPUKyR7vNXGDS87gHcKRkbjzNElHEuihioVLsHYbMb7X4SzqND7x7cpK7PI+783ketpaFSnFO\nZYJsFHFu/wB5a9kMnDVVYTe/c40Y4Li+QT42UWY3EyGA4wfmcvWmjvHtqu4eWtrwH5Uqo0pxRVcX\nXVHEqdUq0lq+29XFb1MpXhUElOPigcmYjC+RksTMhFBKzq5UmKc1WMvpAwPsNz2NdF2Gk0lWa40R\ngh1cl7S1JLTmMa3ZOwx5UxxhdUNPD3c5Dm+sVHgimWRFIsEqaxnyPLpFJ96r7vuslZL3RhHzm01c\na/ladzcfKpeZkpKViQS/SqdJC8Fg/JraMOQJrdlVKV4ShixoNLgpnyevNSdMTrLccbghm+Vez2Op\nlAilcICK71NTiv2BIa1xt1icdOlOi+B5PT0s0Jq06+LHi5+qteziOGStpT+KOikY7TbvqtfJGcNX\nSyXucV1eHgSMJRKMA7UoIuW6LIqnrmEYslxK/qtSYY7WtIXg4729vGp6Gut5bE4kWKY1rlIsidMi\nZhYnrzSGg6anGYoiri2VGBGC11QqrE4meTCVYkNMMIuxfKHm+2xQiveEIQuaTUIp+XahwCfGxphU\nimWexy/TaQryb/nYOghYawx7KsWuUcT8RoNf5XLsGAQcW6mwzPP4cS7HKs9jkRDYeJemGoY0lGI/\nYE4UEWrNzZ7HJWNjFI3hrkSC87q62CmKcD2PthBMhSE1IdhNKTLW0heG3CklBzWbvK3ZJBfrzlcr\nxb6+z1gyybC1NIwh6zjMi69TEgl2OOkkjj7ttH85svtM2Dr7HTqkdmvSOGOG833/WacjbGkQ21YE\n2bbMa/+IUG+NLQl2Op3eZlrF850qP9M5CiHI5XJ/t655O144bCe//0KYWdlv/Sc555xzOPvsswE4\n/vjjue2221i7du3s95ctW8app57KPffcQ3d3NyeffPILXnLxbKG15rTTTiObzXLOOec85ca19Q1x\neNMmvnvyyTAyQkt0KnBnPrj3jt3ePUHArxIJzhkfZ4nWjEjJJ/v66I0iuhyHCaWY1pppY1jsumSt\nJW0M66OIOVHEKbUaFrguk+GaTIZFjkMvsH+zwX61Gqf39ZMU8EYT8Z6JMuf0DqCl5LjxMT7W04sD\nfCSs8+rGND9O5bgpU0QHPq4QvJoIz1r+iuRh6TLXUURBQNEYkq7Hg1HE4jDimPo061Ipvp9I8m+A\nj2DcGP4qJcdqTX8QkA4CLu/q4uxymawxHQ1hVxcZIehSCoRAa82o1sxXikFrmR+GrBadBIGTJya4\nPpPh3lyOTVFIUSmuKI/yhFJ8rW+AHmPYbOGDjRr7NRsEwO1ugnMLXRxgNIuaDeZpzXe6S1w7vAkF\n/KinxBMGjq1UmJCSa4tFpNa8v1Yjbwy3FQr8KJXiLdUq61MpnkwkWKk1vY7DwBbTrBVScub0NDv5\nPk3g9N5e8gJ2FILTxzomsU1SckxPL4OuQ7eQZIymOwi4RSpeqiRtqRgOQ2pKMddxMNbyhO9TcF16\nY9I31W6zXkpeLQRzw5BSu81V2Sxnj4/TbwzLXJevdHWRE4IuKbFSEsYT6XmOQ78xzNGax60FY/jU\n5CTCWq7L5/lROs0rYl23LwSTQUDouuwmBAmtScelCv85OckSrVHWcurAAAvabQpSMpJIsE5rImCh\n65IFPK15IooYsJZ3TU0xqDV3FQr8PJnkrZUKT6ZSrE0kWKE1vW6nNMWzliCeEJ4YhixqNMhrzVf6\n+jhicpKEtaxKJrkplUIKwZDqxNKJKGJDFFGSkoNj0ndfJsMGx+HMsTGWuy63pVLcmkyyUEpSM1Fd\nsWnsICGYG0V0tdv8KJPh0+PjLNSah1yXL3Z3UwC6lSKKp/yTsXyh3xiGoojHAMcYPlGpkDKGHxUK\nXJPJ8MowpOZ5TAOVMMS4LrvGC75EEHCnUnyyUmGHKMIFTu3vZ3G7TVEIhpNJVhmDBRbE731Xa9Zp\nTb+1vLNWY1Brbi8W+Z3n8ZZKhXXJZGf3xFpKjjP7mrZ9n0el5PgwZEmzScYYLuzp4W2Tk6SAxxMJ\nrk+lcKRkSMrZ13RjFNElJQdrzYJGg79kMgwrxafLZZY7Dn9Mp7k1kWBh/HdwgWnfZ5NSHBy/pnnf\n56eZDJ8aH2fHMOQh1+W8nh664tfUl5LQGLp33ZWzrr6afD7/ot/HXwjMFD9sre3durr3uZjhtmUQ\n29aC4JnixmZ0xf9oEbF1AoOU8gWbKs/AGEOtVnva530ulyObzT7n59uO54bt5Hc7XnBYa/nc5z7H\n6tWr+frXv/6UG93WZRgjIyN894Mf5MS772ZYKVYnEvwunUbQMf54QiC0ZkMYMlcpdtOdjM1lnkdV\nCD41Ps5qpbglnebX6TS7x2YTT3RikyaU4nXWslujwbxWiwv7+lhSn2Z9oUAKeGWzySOuyyYhsI7D\nh6YmKfltPtM7xAGhz3LlULEG4bq8yW9w5HQFH3hrfoBuJZgP5HXIH4XLSdMVuhIuP3RTTCmXV/gt\n1iuHiE6707g2DMekQEpJLQqpGctCzyMFKGN4IgwpCcHhsWFsRTbL3YkEHyiXecx1eSiV4lbHYa7j\ndMw4QNBu87gQnDM9zV6tFo8rxdmlEhZ4jbC8b2yMgrX8Ipni27kcOddlZ2vZo91iSb3Ol7pLnFGb\nZFMqzQqpuE0q9nMdAiHZ4PsYx2FIdXKHK75PWSn2EYKM1nSHIb9zXT4+OckeWhMCZ/T1kY0iBpRi\nxHGoxprVhUqxQxSxb73OvakUGz2PnI4YTiSZryPePDHBhb29fGvzJmZu/V/oH+TAyQkODAIscMbg\nEMeNjbFPFBECHx4cZGEsZXgileIuz6NNhwylhMDRmo1hiCclR8RRe2syGW5OJDhzbIyVjsOD6TR/\n8DyGlKIrvnbavs9q4LVSsjAuVbiyUOB9k5MsiSKWuy7fKhbRUtInJUJKrNaUtSYnJTsA86KIzdby\nhJRcUC5jhOB3qRTfzOfZzxhajkMkBLUgYFopXhIbM0u+zx8dhw9Uq+wXJwWcMTCAjCIWAqOex7Ax\ntK2l33Eo0SHS41FEWwg+VKkwoDWrMhm+mstxRKVCOZViYzLJo1FExnFY5Di4sXzhYeCYMGTXep2S\n1lzc18fiVotF7TZrUinuSCSo05EgZaREac1IEBA5Dv8eF81sSKW4MZXiv0ZGWOO63J9M8t/JJANS\n0hXrgH3fZ60QHCgEi6KIoWaTH+TzvL1W45W+z3LH4bJYvjAkOsUoVmsmtcaVkl2AOVozYQzLlOKS\nchnPGH6fTnNJocBLwhDtebSEoBaGTCvFXkKQtJaeIOA2pXjX1BQHBQEZY/j4wAANa9klDBmJJSFt\nY+hxHPriRc1kFDEhBGfG8oUnk0m+nM9zZLXKZDLJ+mSSh7UmoxSLt0i0eMRa3qI1e9Xr9GvNZb29\nDPg+e8aSkNtSqdkc4Wz8mo6HIVNScnS8OBlJJPhNOs1nR0ZY7zjcn0hwY6nEh84/n0OfIff9Xw0z\nU91t5ehumcu7pRlu6ymrEIJsNovrumitqdU6bYr/KILsmZrc/pFs4e8R7BdiqrwlqtXq05I7isXi\nrJFvO148bCe/2/Gi4dvf/jbXX389V1555VNMG1uXYbRaLT501FEc8uSTHDg9zYDW/CWf59fJJG+u\nVlkXTxWXac1AbDZx42nNY0LwHmM62uEg4IJSiZPGxztpBMkkv4/joha6LinTqZId1Zpdo4idmnWu\nLfWRFLCk2eT+VJIeHeEoh0+Wh3nATXBVd4mFQZumctm7NcXN+S56rOWt05P8OF3ksOkKO5iImpB8\nIV2kz/MAy+rIcMZ0jQfyBR6MNAmpmCcgDEJWuS4fnpigJQQrYo3joUHAdCJBVUqGg4CE67I4dsIT\nhjwgBKc3GixqtykZw9n9/SxuNslay5OZDKuBljEscRz29n0OqlZ5NJHgB/k8XVKSEnBIs8kbalU+\n0T/A8RNl9o0i6sDVhSIPugneW52kaC0/7+pmwA84qlalJSXn9fWxtNli53abJ5XiplyOlhAMyE6T\nFlozFjdp7WEMC8OQEeAR1+VrcZPWnzyPq/N5FsRazowx9MdSjq+XxxgyhtVS8eNslttSKRYoBVIg\nLGwOQ4Y8j7QQWGvYGHRSJhYAGdMpSRkTgrMmJxkwhlWJBJ/p6uLwapVaJsOI57E2DHEdh6WOQ8J0\noqgesJZjfJ89m036tObi/n7SQcAOzSbrMhkedF0qxjDf88iJTkvcmO8zrRTv9n3mNRpMJhJclcvx\n0bExnnQcVqTT3OS6dEtJv9tpJ4uCgJXWcjCwQxgyr9Hgh8UiBzabvKrRYLnrck2hwLBSzJOdml9p\nLRNBQBRvtc8LQxrGcIvncfnoKJEQ3Ol5XFgsspMxKM/DCEE9CJgQgr2UImsMg2HILVJyWKPBW1ot\nlDF8rq+PNUqxVxQx5nlUrGU61vQuiHXAQRSxUkrOmZxkSGsqSvGxUolDpqYIkkmGEwkeiyKUUuwY\nkz4nDFlmDK+JIg6s1xnUmh+USowBB9ZqrEmleMjz2ExnYdsdT3hrQcAGpTghCJgX13t/M673nlCq\n8x5JpchJ2ZnUxpKQNcawu5TsGYbMbza5IZdjIIp4b7XKMsfhF7kcy1yXhVKipERZSzUIqDkOLwfm\nhCFSa25IJPjq2Bg9xnCP5/H5rSQhjShi0lp2dhyKtlOMcp8Q7OD7nDg9Tc4YLu7p4XbP4xVBQDmR\nYAKoRhFuHLeX0BobhjwgJWdPTjLfGCLgI3197Nto4CnFcCrFw1qjpGRJnCPsRBGrooidjOGIep3B\nKOLmefOYfsc7OPHTn/5f0wK29T0ftp0J/PfMcMlkEsdxqNfrQId0FgqFZ/Wzn4sZbkuCLYR4Wrvq\nMxVtPNfM4q1J9ozR7bnWNW/H88N28rsdLyp+9atfIiv5OAAAIABJREFUcfHFF3P11VdTKpVmj89s\nS81cflEU8ZXTT2f4/vtZFGuAc0HAza7LZycmmK81Ot5K3qHVIu26jHke6+Np41LXJWEtntas1ZrF\nWvO2qSmGtOYvuRzfT6d5he+zJp1GCcF4EGAFfL88xn2Oy4/6+shqw2Ysbwta/D6dZa8o5OSJUX6V\nzvGzdJYJa7lmaoysNfzCS3NzrovNYUTec0kDNtKsBy6qllmZzvFd5TLgeRQizTLg0xPj5IGVqTRX\nJZK8r9WiGEW4WnNpVxcfjp3wq12X83t6EMAcKalukWYxGDvhC1ozbgx1a/nM5CQpY/hdKsXXi0UW\nAzmlKGrNrs0mv81m+PLYKI8qh5u6uqkqRTkIGFKKuRj6teZRKwgF7AnUheRBa4ikYh9r8axltbVU\nheADtRolrdmcTPKtfJ73l8uscxzWZrPcJgQ96m/lCCYIWG4tR1rLzs0mc9ttvtfby5x2mx7f56FC\ngTEhqEYRRcfhZVHE3tPTNB2HX+TzfGtTJ8t2WCk+MjjI+Zs2sclxWOG6fC+fZz7gOQ6OELSCgBFg\nH6UoGMO8IOAmx+HwRoO3NJvUhOCrPT087jjsbi0TjoNvTMcU5TgsBlLGoMOQR5Ti8xMTDGrNsFJ8\ntLeXl9XrmHSasuOwPorQUrJznJPrhiHLrOXQIOCQep0BY7i6VOJx1cllXpfN8rjzt1zmUkz6poKA\nJ6Xk5Hab+c0mVkq+2tPDe8tlphyH1akUN7kuaSmZGxNpwpDVWrOHlOwbT7JvLBRwrOVdExM86rr8\nTy7H/XEUYCLeaq/5PmNKcQgwPwhIBgE/yWb5ytgYaWt5wHX5cnc3A9aScxysELMmxcVK0Wctc+JF\nWI/WnFGpIK3le11dXJ9M8vIoouJ5NInlC47DrlKSjOULf3Yc/mtigiVaY4FT+vtZ0mpRUIrhRIIn\ntEYTS0KsxTWGdbEk5NhajYFYvvCbRIIjKxXWp1KsSSRYEU9q58TyBd/3WS4l/ycMWdJokNOar/T2\n8sZqlbwxPB7vLEHHiDcjX9gcRaSl5LB46vpIOs0yz+Pc0VEedRzuSCa5KZ1mnhBkYv1wI5bZHCQE\n86KIvnabH2YynDw5yX5BwHLX5Uvd3UgpGRCCQErC2IiXcxwWW8tAvDswLCVfGh8nZww3ZLNclsux\nfxB0UkJiI15bKfZwHBJa02UMk/vtx6mXX/6/hiw9UyZwMpl8ihRhhgDPTIG3JswzJNZ13X8YvTmD\nZ2py25ZsIQxDpqc7DZgzCQzber5tRaI9l8xiYwzVaiduUggxK694vmkS2/HcsJ38bseLjttvv50z\nzzyT733ve8yfP3/2+Eyo+MzNzFrLj88/n9W//CW+tbhSYqKITVqzVCkGTady9UHZKa/4UKXCtBD8\nOpvt6AeNoRKXHEwEAdpx2E0I8lrTFwT8t+fxjdFRNjkOf8zluNPzqAP/oSPeNTnBnZ7HNaVeWmHI\nfAlvqU5yeamfw/wW76xOcFUyww9TWZY6kre2GxzQ7NwgTy4N8fXxTVghuDOZ4SIvwy6ex0QUUQEu\nLY9xXz7PtdIl7zr0SEVDazZqzWCcAytinbInJa+NOo12G12XO5JJLhweZqXrcq/ncU02yyIhcOMP\n4Lbvs14IXg3sGAQsqde5slRi3+lpWlLyUC6HBCbDkMWmQ1qGjKEmBO/vH+C0iXHaUjIhJJcXCrzc\n98kpia8UtyGYKyVJpRBCUAkC6lKy+0xMV1wNfHSzyf7tNn1ac0FfH2Vgj2aTjZkMa4WgEpO+3ngr\nuR2GDEvJReUyg8awUSlO7Otj13YbkUxSUYrpKGJaCHaJt+el1jysNYeaTqFHv+/zs54e0lpzaLXK\nY67L7bkcK2WnzjoT7w5UYtL3emOYHwS4YcjVuRyXjIwwrRQPOw6XFQr0SUku1rkGUcSwMew8c80F\nAXc6DnPCkNOrVSaE4IeFAn9IJtnXWqqOgwEqQUDoOOwuBBnTiTG7xXX53Pg4i7WmJgSn9fez2PfJ\nuS6jjsOo1vjWsthxyAJJ00mvmBtFHDM1xaAx3FwocG0yyRurVTZms6x3HNZqTZfnMVd2kkf8IGCZ\nEJzabrOw2SRvLV/o6+OAWo2cMaxNpbjN6yR7zHccUkKgdCdBpSAlr/d95jebLM9mucfz+PjoKCtc\nl/vSaf4nloQU46lrq91mjRC8VggWhSEDrRZX5PO8v1JhlzBkmetyWbFIJAT9UkJMWCajiKRS7Gwt\n86KIYeBxpbh4bAxlLTdmMlyay7GP1gSuSyAl1SBgSileEv+evUHALUrx7li+kDaGj8byhZ3DkNFk\nkk3W0jKGbtdlkE7cXi0MGZWST0xOMmg6KQ2fKxZ5U6VCLZlkYzLJQ1qTUp0c4YS1iDDkYWN4o9a8\ntF5nIIr4bl8fbhTxiqkpViYS/CWdZsRa5sQpIY7p5AiPSMmxMZFuOA4/yOf5zMgIY0rxkOdxXSZD\nlxCU4kSLMAx50hj2UIpdYlPkb7JZFoUhJ01OssLt1FE/5HnsJAShlEgh0Mkk773kEl568MH/tPv5\n/wueKRPYcRxSqdSzNsPB39IRnguejWzB930ajcaz+hnPVGLxbDKLtyTZM1Ps7Rm//zxsJ7/b8U/B\n8uXLOf7447n00kvZfffdZ4/PrMi3vLldd+mldF19NXPHxljlujyayfCAELMxVC6dHNH1UvIma5kf\nBHS123yjWOTzY2OEQvCY43BFsUgS6HY6tbMy1n/uYy3/XqmwNIq4NJvlD5kMA67LoX6boycn+H0q\nyQ9yRUaxXFMdY4XjcXVXLwcHLd5UneCU0iCLo4DJRJKEkCR0xLIwYueEhy8ET/gBA8bwiakKjyTT\nfMtLslciwZQxrAojXmoNXcbStIY/uR4HxgH3NSF4ItZkzo8nWTYMedha3qk1S5tNBsOQy0ol9mo0\nmB8EPJZIcGcqRRmY7zjkpCSpNbUwxAIXl8tEwB+TSb5WKFBQiiFHkTKWbBhyD5ZjwojeMCAfBHyj\n2MVR1Sq7RxEe8PXeXvZstXhDHNP1k3yex12XnYBGrAOeCAKk47AT0KM1Ioq4w3G4cHycfq1Z7nQq\naXcJQ2QcKdWMIiasZU+l6NWaHdptbk4k2KfV4r3T02jg+8Uiv0mlOKjdZiyZZEQIxqJOM968eHo6\nU47w8XqdOb5P0lr+s7+fQysVjBBsyGa5WwgcKVngOCSFQG2R6fraVou57TZ3Fgo86rq8u1xmpevy\nYCbDPUoxR6lOxjLQaLdZLSVvsZb5vk9Pu83lXV2cOT5OylpWOA5XFAq4UlJSCkdKbBQxqjXdUrKz\ntSwIAtZIyaZYB1wWgpvSaa7K5djbGNqOg5CSmu9TVYp9pSRrDL2+z29dl9OqVV4WBPhC8LH+fowx\nLADKW2ir+1yXPiCpNZUooiLELOlbnUzy2WJxVhIy7LqsiiK8rSQhD1rL0UHA3o0GfVpzaX8/Thiy\nZ6PB2lSKv3oekzOkL5aETAYBZaU4zveZ32gw7Xl8N5/nzLExhpXi0WSS65NJClJ2DJGik3m72hj2\nlZLdgoAFzSa/KBRYEgQcXauxzHH4WS7Hyjh9QapONFwtCGYTLeZFETKKuD6R4KKxMbqN4V7P43M9\nPczXmozr4ktJMwypWMuOM/KFKOJ+a1kUhrx/aoq8MVze3c1NySSvjHOEJ4BKFOE4DjsoRUJrZBBw\nn1KcVa2yJIpwrOVDAwPs0miQE4JNqRTLjUGILdrbooi1UUQ/8I44R/jOYpE/eh5HT06yzvNYkUrx\nENDrurOGUd/3eVQIjtWaxc0mxSjia6USb65WGYiiTrV0dzc7HXggn/nWt/7XpARorWk2m0/T9qbT\n6adlAmutZ6fAW0IpRS6Xe87Sj38kW9hSJ5xMJknHOwXPhGcqsfhHmcVbkuyZKfb2jN9/HraT3+34\np2H9+vW84x3v4Nxzz+WAAw6YPb6tbMhrvvMdbr7iCj4+NsZQFJGKP2AOrlbRjsNwOs0D1iKlZNGM\n5lBrVochOwrBwTGpeSCf56+ex5ETEzySSrEqnWaF6YT/74hln2aLHep1zuvrY24UUvcSvKbV4G2V\nSa7MZLkulWYvCV+aHGOZcvhGaYABrVkOfHl6gh3jStlbEykuyhT5xsRopyii2MuwkOQdl7VhiAcc\nNTXFAh3xte4e3lOpMF9rAiG4oLub4ypVXuX7lKXkvN5eAmNYai1jnseYtUybTslBTzw9rUYRk0Lw\nsUqFQa2pOg5n9vRw6NQU5VyOMcdhOgypAAdIyT7NJnvW61zV18cc3+egWo3lrsudmQz3ui6LlESI\nzofIaBCQ8zwGhcCxnQzaTVJybBgyJ97mu7y7m88PDzPiODzqOPwkl6MgJT2qUy1rwpD1ulPGsYPu\nlCP8KZWiS2s+MDHB8jjf9ZZUih1iw9iWJsWX04npyvk+16ZSnF8us1BrVjkOn+ztpS+OvKtISSNO\n+1jkuuStJR9FrDOGvNacXKsxYAw3ZrNckcvx2rgpcFQpNoUhCfdvFcgyCPirlHywXmdpXDhxdn8/\n81ot+oKADdksD0qJD8yfITXGsCkMkVJyTKPB3FaL9ZkMP8lkOKVc5gnHYWUmwy1KUVKK/tikGPk+\nK6zl9bF2dE6jwXd7ejikXucl7TYrHIef5/OUlWJOrK2WxjARBPhK8cqYSDet5cZkkm+NjNAQgrs9\nj4uLRZZYi+u6SCFoBEFnGq8URWuZGwTcqhQvbzY5ptEgspavlkrc77rsrTXjrkvT2o5m1XFYKgTJ\nmBTfpxSfm5xknta0gNP6+3lJs4nruox4Hmu0xtCRIaXi9IXVWrOzMbx1aooBrbmxu5tbXZc3Vyqs\nS6V4PI6GKynFgFIkrKUdBKwQgvcFAQtn0hd6ezlycpKUtaxKJPhtOv20RItNUUQu3j2Z32jwSCbD\nctflc6OjLI/lC79Lp5kvBOl496QZL6QPjNMXBlotfpTNckJcg7zCdTm/u5tISuYIQVtKtDFU4knx\nUqA/ipgwhlWq097WYww3p9N8uVBgX98nSiapSslkLF/YPTY35sOQu4XgrdPTvCYI6NGacwcGGBOC\nvRoNhjMZ1gB1Yyi6LkOiUy1dDQLWS8mZcSNe3fP4wQEH8L5LLnnBi41eLGwrAx62nQlsrZ3NyN0S\nzzdy7O/JFoQQs+eUTqdJJpPP6jnDMKRerz9NpjGT3bs1Wq3W00j29ozffx62k9//D/GnP/2JCy64\ngPvvv5/Nmzfzve99j+OOO+4ZH79u3ToWL178tOM33ngjhx122At6bpOTk7z97W/n/e9/P0ccccTs\n8W3dCB+66y4u/vjH2S0ISGpNv9Y8aC07+z7vajQoaM1Pi0V+mUpxSLvNaCrFuBCMhCGZ2OjiGQNB\nwANScm6lwuIowgAf6O8nYw2e65EF5oQBK4Tk9WHA40qy3ktyeLPOm6sVjuobxAh4LZoTJsu41nJh\noYe7pCLtOOyApdsYVBTy38plb8ehLgSr/IA9hODwqSprMlnuE4qXYdmgHFbGWtM5ohNttyGKCJXi\nAK0ZCEMqQnCH63LZ2BhaCO50Xb7c1cWexmBcl1BKpoOAihDsrRQZY5gbhtwsJW+dnuaIVouVjsNV\n+TwPJBLMV4qUlCSsZardZkJK3h/rcLWUfLm3lys3bsQBVirFmX19vKTRIJFIMO66rNIapOxMB+lM\nsh6LIvYxhtc0GgyEIbd2dfGA63LEVmUcg45DKZYhtHyfx4Xg+ChiYbNJMQz5cl8fJ5TLIAQrXZfr\nYx3fYDyxF1qzKQzpUYr9YiK90vNY7bp8eWSElY7D7ckk1+Ry7AwQE/B63DK2v+jU9Q622/w8meTk\nSoVXxiar80olGkKwcEZbHeuAC47DPCCvNXWtWScEn52YYMAYHkkkOLuri1c1GrTTacYdh+HYnLZL\nLAlJRhEPWMuRrRavarU6jv++PjYKwUunplifzfK4UozHkpCeLXTA66XktGaTeTN/m54ejh0fp6YU\nT6TT/E+sVZ2plRZhyOooYg+leFlsxPtDsUhLCN49Ps6jrsufMhnui3cUUlJ2Wth8n42Ow+tik2LB\n97kyn+fcsTG6reUh1+Wiri6ydCK3rBBEsdZ8QErm2U6T4mohqFvLeRMTYC2/yGa5Mpdj/yii4XV2\nQypBQFOp2UKOLt/nfxyH06pV9g1DksZ0Ei20ZpHWs4UcvrX0OQ6leNE3GYZUheCjlQqDxrApmeSL\nhQJHVipMJhJsSKV4UGvSjjNbciLCkEeM4d+0Zp/YNPa9vj4SYcgrpqdZ6XncnU6zCWblCzM1yMNS\n8s4oms0RvjKf53Ojo0xIycOex4+zWbqlpDuWL0RBwHpj2FEpdtWdtsCbUykKxnDm+DgrHYdrcjnu\nSCTYVXSSaRTMTrL3g061dBjy34kE58Y+gFVK8Yk44rHbcagqxVQU0bCWua5Lj7UUtWaqVOKQc8/l\ngNe//gW9b7+YCMPwaUUXW27/b5kEsXUywgyeb+TYtmQLW2KmQe7ZYibebWtCn0qlnpJuAU8t0pgh\n2a7r/q8xMf5vx3by+/8hfve73/HnP/+Zvffem/e85z1cfvnlvOc973nGx8+Q35tuuom99tpr9nhX\nV9eLoj9qNpu8853v5NBDD+XEE098yvd833/K9tHalSv5wQc/SFipIEScBdxuU1WKl9KZDhZ8n5+m\nUny1XKakNStcl3NLJXqjiJzr0ooNYxPGsFQphoxh53abNY5DxVG8olrlxu4efKVoBQGugMvKo1zY\nXWJdMslhzQarHMWwlLQdlyKWd9Qq7O23OL00yA71KXqsoea43JJIkbKGE6an2EsHnNLVzxtDn9WJ\nJE9GmopyGFASawyrIs2uQFIpWkLweBiSj807LmDCkMeM4RAhWBqGzG00uLZY/L/svWecZVWZvn2t\nsPeJVedUnUqdm4YGJElWgkg0R0AZEB0VsyiYkKCjokgQGf0PKKKDSlDnFR2BUUBRYZTYqDQ0dKCb\nzl3pnIon7bTW+2GvKpqk4qu86r+fL1V1ft11du3atfeznnXf181BrRYvrddZ4RrFNZ7HQinxnCRk\nPAiYUorXJgm7T0+Ts5av9PRw9tAQG5ViZaHA7Z6XSgE8Dw/Aucr3UIolrgG/U2vmRxHvmZxEW8s1\nXV38JJfj8DCk6mQatShCbbcl7IUh9yrFeRMTLI5jisZw+sAAS5pNSlIymMux2jndd/JSo6CfJGyO\nYzqBt0xOMjeOeaxQ4D8LBd42NsZ632dDPs/91qbmJtfUJA4p9WabxvX2BwFf7+3lkHqdnYKAVVrz\ni44OakIwX2ty0qWMuRSvlyUJi9ttGkLw3/k8XxscZKPWPOi26+cLQc410kEYstVa9pWSAWNYGATc\n5vsc4GQaW5Ti6nKZ+3yfFwKTbnozFoYknseeQIcxZKKIO5XiolqNRUnKrT6zr48lQUDR8xjRmtEk\noW0tu3geBWvJJQnrjGGh0wEPJAm/KpX4Xi7HKycm2FYssllr1icJHZ7HIrfoi10AzPvbbXZptSgb\nwxf7+tinXqcvjlmXy3GX7xO4BqogUjTcYByDlJzg5Aub8nluzuc5b3iYtVqzPJvllmyWfqXodvKF\nMAhYay0vlZKdHdHi2nKZYxoNjms0WKE13ymVGNSaBUKAm2SPRRGh1uzvGukojrk9k+HykRE6jOEe\nF8ixaxzjO4xZPYqYAPbQmqIxaSCHEOzVbvO2ep1uY7i8UuFXvs/hQcBwNktVCMaiaDbkxHf0hQel\n5JyJCXaKYzxr+ejAAHvW6xSBbYUCy42ZpcXkSdPbNkQR3UJw8vQ0c6OIB0olbstkOLVaZZ3nsapQ\nYJkQT+NdPwq8yVp2abXoDQIu7+nhFdPT7Nxus9Lz+FFnJw0hmDOjs08SanFMoBTHGsPiVothpfh1\nLsfXt21jSCnuymT4VmcnOwEZrdHuXrf0Va/iQ5de+nezhT4zud2+kd2+oZ35+rnUU5n4WmsKhcJz\nnpw+mxkOUubuXzJVntEWb19PPb6pqalZ6cXM+/w5DOId9depHc3vP3l1dHRwxRVX/FnN77Jlyzjg\ngAOel+OK45j3vOc9zJkzh3PPPfePhmFs2riRH370o5z0wAMpWSCX43bPw5cybYREmjD2eByzm5Ts\nE8csaDZZls/TFIIP1mo85Hnclc3yi2yWnZwhKmstJgxZJwRXV0exwDXlMvf7GYas5fONKY5oNfk/\n5S4ezhXoDwKmPM1na0N8p7OLldk8fSZha5xwaLvJwVFA3lr+q7OLMQtdnmYcwdokoV9p5iUxK5C8\notXilKlJmkLwud4+XjY1xcubTZpSclFvL3Vg33qdbYUCa6VkxFrm+T5lNx2cMdS8s91mQaOBkJJL\nKxU+MDrKNq1Tjq1z+i/2PLLW4scxK+OYo6OIo+t15icJv+ju5k7f58RajXVas6pQ4H4pWaBT9qgv\nBFPtNlsdJWB+FFFpt/lORwfnj44yN45Z4ftc0t1NDqgoRSglSZJQTRLmaM2AMcxJErZZS81aPjs2\nRodJ2az/XipxWBhSz2Souy3hQCn2VAo/SSjFMb8VgtOmpzkgDOlJEj41MEDdGHYLArbl82yEVBKy\n3fR0Ikzjlz86McGcKCLQadzyCdUqY57H1kKBe6wlq9SsZEa583MocHCrxbx2m592d1MXglePjbFK\na5YVi6yQaapdh2tqpoOADVLyRmtZ3G7TEYZ8rauLzw4PY4RgpefxzVKJPKn23BMCmyQMJgkDUrKb\nM9StVopRKbl4ZIQRKbk1n+eajg72dTpgKQQTYZjqgEXKWB5wJs4PTExwSBgSAp/o66MNLAFGtGbS\n6YDLWjOP1FBXj2O2SsmnazXmGMM2rTm7UuHYyUka+TyDvs+aOEYrhzEzBhXHrDCG48KQwxsNBpKE\n7/X2skUIjpqYYG0ux4pMhk3GMMf36ZZpRPR0u806KXm3a4g9Ifj37m7eX60SCMFql8KWk09ERBNF\nbE4S5kjJIc78taxQYERKPjM8zArf55fZLLfm8+zsFn0zk/6tSnEYKQ+4r93m+/k8p4+N8eIwZJXW\nfL6nBwPMF4KGUoTGMOnoC4utpSdJqCUJG6TkolqNviThN7kcXyyXeVGrRZjLMa4UI+5a3cvJNIrO\n/Pmaep1jgoB+Y7ikr49NUnLg9DRb3d/y+IwRb7tJ/3ql+Pj0NPODgFApLqxUeO3YGLEQrC8WuVOm\nUe2LPI+MEMgoYl0cs4sQHNNus6DV4hddXWxTitNGR1mpNXcXi6ysVLjsxz9m0eLFf9N7+faN7VOb\n2u0b3b9meZ6H53kEQfA0s9mMdve51jOZ4aSUs1rc51p/KmhjcnJydpJdKpVQSu1ofp/H2tH8/pPX\nc2l+FyxYQLvdZunSpXzkIx/hhBNO+Jsem7WWT33qU4yMjHDZZZc96Qbz1DCMyclJTj/hBE7ZupUD\nGw36jeGnXV3c6fscNzHBhnyejb7PY04b2+sevu0gYJWUT8QfG8MXens5bnyccd9ndbE4Gyl6oIA3\njI/zwjDkqnyBGwp5BjyP909P8ZJmnR/mCvyos8RmY/h8Y5KjghYh8INMnqtzHczzdcqiBTYEIfOU\nYp+wTTmO+VWhg/NHh3ksl+emTJZtSrEPAiMEm+KYCSV5iUnlExPGcK/WXOSSybYqxZm9vby4Xidx\nuK0tcUwsBLvqlAeaSZI0IjYIeEWjwdwk4abubn7m+xwxPc3mYpFBpZ4kCck6884ypThncpJ5cUzB\nGM4bGOCY8XEywHpHCYhJQw6yMgXyb44iOqXk2ChiYaPB4/k8d2WzfG5oiEc8jz/4Pjfl88yTko7t\nyBTrgZdIyUK3QLm+o4MTJyZ4qZt+fbNcZotS7CQlgZQIaxmPIoRSvADoNwYTx/xGa77itJUP+j7n\nVSrsGUUo32dKSqaiiGkh2ENrcsbQlSQst5b92m1OdCaua7q7uSWT4ahGg22FAoNSMhxFFLeTzMRh\nyHIpOWtqioVRRIcxnDMwwAunpigYw6aODn4PGNec5Eh1wJuiiA4hOLHZZF6rxdpikRvzed43MsLj\nzsR5p1L0OS3wDA94pbW8CtjFhZx8q1Lh6Hqd/VotHnXTwSEpU7SXlLPT07ZSHGIMi8OQyBhuzue5\ncmiISAiW+T5fKpdZZC1ZzwMhaEURo9ayh9MBL4gi7pGSpUHAe6amUNZyVXc3t2YyHBLHVB0ZZTyK\nEJ7H7k6GkI0i7tKaTzmMmWdTHOHCdptukaawrXWT/oWeR4lUMrMlSchay7tcCtvKQoFvFYu8uVZj\nSzbLhmyW31tLSSkWaE3GmT8ftpY3GcOejQb9UcTXe3vZpd1m70aD1Z7Hr4tFRoD5DhGnnRGvphTH\nxzGLWi2aQvCDjg6+PDjIsErpC9/u7KQXKGlNRkrCMGSLtewuJbsYw0JnyOyLY84aG2OjUlzf2ckv\ns1n2BerO/DnhAkv2F4LuJKEjiviZ7/OZapU945gRpTizr4/uOKZXSqqex3gc07I2lQcBebc4Sqzl\n4xMTKfe8WOSrHR0cNz7ORLHIVs9jfRzjK8XSGXlHGLIcOLndZv9mkx5j+PYee7Dzhz7E60499S+6\nPwPP2Mhu/9pfu4V4ppRTIQSZTGZWkyuEmD2GOI6fMUSjUCj8RTKIqampp73+XBm+M/VsQRue5z3J\n49LV1YWU8jlJLHbU/7fa0fz+k9ef0/zWajWuueYaDjvsMLTW3HjjjVxwwQV897vf5S1vecvf5Lis\ntVSrVbZu3cqVV17Jfffdx7HHHsvQ0BCDg4MceeSRnHbaaU/6P0EQcMFpp9FYs4YFxlBI0ljZOzyP\nC2s15jkTzgcGBnhBs0nG9xn2PLYZQwAs1ZqctWSThE3GsDQMef/kJIkQ3JDPc32hwCLPY461HNZo\ncOjUFKfPGaBgEnKex3HNBq+dGOc+7fHpUhcLfZ/51nBEY5p9mw3O6pvDBaODLHDv9+7eOZw8PsZk\nvsBypblXCPb2M4TA2nabolKUpcQK2BhGFJW5wmqVAAAgAElEQVRirk65taFDH71QSvqMYX4YcqfW\n7B0EvH16mjHxBG7rIJtyaw3pNrvVmhcIQSlJKIcht/g+XxodZackYauUfLy/ny6nHaypFLs2ZQyL\nPY8Oa8kZw5Y4Jm8t756YYMAYVuXzXNrZyYnj42zN5diazfKIk5UsUmo2jGO5tZwax+xWrzOQJHyt\nr4/+IGD3RoPHslmW5XIMwRPTZWOohiE1KfkXZ1KKpeSqcpkLBgfZolOu738Vi5SEoNdNv5IoYkOS\nsKdS7JokLG61uDOXoyNJ+HCtxiqt+VmhwC/yefYAQpVizCYcReFAIehNEipBwA3ZLJ+t1XhBFLFR\nKc7t6yNnDP1KMSElrSRh0qSM5T5SHfBIkjBtLec47emybJYvlMscVa8z5XTAW6MIqxS7uemgH0X8\nHjip2eSgdpv+JOE/+vqoAftPTbGhWGS11oyaJ/OAJ8OQzVLygVaLBa0WVkq+VKnwr6OjTGvNulyO\nn3semafogB+PY3ZRikOdfOG3pRIjSnG6izP+bT7Pnb7PIqXIO/lCo91mo5QcIwQLo4jeVotvd3Zy\nRrXKHlHECt/ny11dGCmZIwSxUhg3LS0689fcOKZqDCuV4t9HR+kwhl9ns1zU1cX+UZrCVpeSiSii\nLiX7OC16JYq4Rwhe0WjwilaLXmO4qLeXR7Tm4GaTwVyOLUIwaQxFrVnorp8gDFkpJedOTDAvjhFC\ncE5fH0dMTiKFYHOhwP2AcvKFHKCThHVxzALgdY0G84KAe8tl7vY83lmt8pjWPFQscq9MyRQ9jvgR\ntNusEoI3WMvSdpveVouv9/RwwuQkS4OARzyP60ulVL7gFijCGGpRlGr63aR/HLjDGRXrQnBXJsP/\nKZVYQsquZjuj4l5SUjGGBVHEr7Vmv3ab06ansc6oeJfncXAcU/N96s6oKLRmd7fALUiJeM1reO9F\nF802VzNN65+a2P41a6ZplVIipZz9/KmvzRzfU03Q8MxM4GdLhvtjZrNnq2drfuG5MXyf6fs+NWhj\n++Msl8s7MGfPc+1ofv/J689pfp+pTj/9dH7zm9+wfPnyv/oxTU1N0dvb+zRTwPZ1/PHHc/nllz/t\n9SRJ+Oa55zL8q1/RBjwpSeKYrcbwAtcoLnSu9N445vSJCRpC8JNikR8UCrzIGMbc9GDCpXUdZS37\nNBrs0mpxSV8fCxt1tnZ0oqRglzBkI7C7NTSThEfyBXaNY15dG+WLfQOcOl7loVyetbk8Ctgahixw\nU6fQGDZEMRXPQ5Mik6SFf50cZ05i+F6lh73abU4dH2dCSq7o6WFMSo4ZH2dTJsOKXI7VPNEoejZN\nqBqSklfa1O3fGQRcWSrx5eFhAiFmY3fzQHlmGzlJ2BbHzFOK3Y1hcRCwRmuGlOLi4WG2Sskd2SxX\nlUocZAxNNx2ccNrhfZUi53TAtynFeyYmODiK8I3hvP5+xoDdjGHI96lZy1SSUPE8BkgZq60oYqOU\nnDc2xkCSEEjJmb29HDcxQTuXY1smw8NJglaKXWbIHXHMqiTh4CThyHqduXHM7V1dPOh5vGFsjDW+\nz6p8nodIjXEVJ0NoBQGrheCtzhhXCUMu6+3lHdUqWWtZpTX/XSoRCcGAowTIJGEoivCd4XChM8r9\nNpvl64ODPK419/k+V3d2srNIsWlaSlphyDbgQCnpcTrgn/o+xzUavKnRYERKLu/uZrnW7AOMKUWC\nm55qze5AIUnwHRruIhfmMikEH+jvZ7d2m7zWDHkeQ8YQWMvOTgecNYb1ScLcJOHUyUnmGMPdnZ1c\nk8/zuvFxtuTzbM5kWOXMe4uc4dAEAcuF4LQgYNdGgx5juKyvj11aLZa0WjyWzXJ3LscEzEbvek4n\nPS0lJ7lJ/5TncV1nJ58fHGSz1jzs+9xQKNAtJRU36Z9ZoOylUnbtomaT24pF+qOID46NsVKnYSa/\nyWTYA4iUQm+3QDlICPrjmM4w5MfZLOe7BcpapTinr4+OJKFfa8alpOmIH3O0ps+mITDDJg2BOW98\nnP4k4e58notLJY6s16nn8wxrzbYowjijYsYY/Cjid8CbWy1e3GqlyX8DA4wZw4FugbJSa6omRcr1\nugZ8yslfznAm0kgpLuvu5lSX5Lgmn+fnnkdWSua7644oYkMcs0hKXhqmMdH/WyqxTWs+NjzMI57H\nnfk8/+t4zkW3gGsGARuE4FgpWRSG9LbbfKezk/eMjXFgELDC87i0q4tYpTHRkZRYa9G9vbzvG99g\n3sKFf5Np7TM1stt//pds5z9VAgd/nAkchuHTGuZnMpv9sfebSZDTWmOt/YsYvs9Uz6YtFkJQLpfR\nWv/daLT/b6gdze8/ef2lze93v/td3v/+9z8NBfPXKGsthULhaTe17evQQw/lhhtuAJ6+DWat5btf\n/CK7/fCHDIyPs1prHiwW+YNMWa55mbrZp4KALUrxSpMmfvW021xZLnPRyAgtIVjueXyvVMIKwQKt\nyZFO9cbjmEVJzJsmJ7i6UmGLn03jNgVcNzrEvdrnup5ehBA8Fse8rznNa1sNMsAWKXl3ZYAPjNcY\nsIZACL7S3ct3BrcyJhW3dnZym/Z5jUkYk4pV1rBRaY61lrwxTBrDvUrxqbEx+oxBAZ/o7+c1Y2O0\npWRzocC9MgXcL/Z9fNJt5LVxzM7A0e0281stlnd0sCyT4V2jo6z0PFYUCtzpdJVdjtgQBgGrgNcB\ni4OAuc0mV1YqvHVsjCVRxKNuijWmFHPdQ0xZSzUMQSn2JdUBh0nC7ZkMVw4PI63lPt/ni93d7GoM\n2pEpmlFEzVr20JoOa5njNJJ7BQGn1ut0GMN3ymVuzOc53HF9J4WgGkVorWcjYjNRxD1KcbZjrHaa\nlBIwv92mYgzb8nlWO0rAQt+ng9SktM1NBE+bmmJuFDGUzfIfnZ38a7XKFs9jQ6HAXUBJqVlDnYhj\nHjGGl1nL3u0281otvl+p0BtFHDU1lVIUikVWu4ZmJlhjMgjYphSvdjKEfBjyzVKJS0dGSKxlhedx\neXc3ndZS1holBEkcM2IMc5RiJ7eAWyMEE0JwYbVKUwh+msvxrc5ODjCGptYYpwOeVIr9lSKfJPSH\nabLdOyYmODwMyVrLJ/v7GZOSPaKIoe3QeZ2exwLSBUo7ilgnJZ92ccZtKflYXx9HTkwQ+j6D+TzL\n4xgtJTt73mz07uokYe8k4RVugfLr7m7u15oTajUe831WFgost5Z+L40ln5EirRSCtyQJS9wC5au9\nvZwwNkZ/ksw2xW0pmSslGaUQccxoHJMoxdHOqDiqFLfncnxj2za2ac29nsdVpRKLceYvIWiHIVuB\nfaWk3y1QfuH77Ntu8+6pKcal5GtdXdzl+xxg0pCcyFomoohYp4ElRWPIhSG/1prP1WrsmiQ0SXeY\n5gcBFaUY8n22JGna5HzPo8vtMG2NYzzgg26H4CEX5PH6sTGG83k2ZTI8kiQUlGKJW/gRhjxkLSdG\n0Sxn+et9feSjiBdPT7Mmk+GeXI5BeIKz7K67LVLytjhmcaNBqBTfLJU4b3iYupQ87Pv8sLubl516\nKm/90If+7Pv1szW123/8W+pUkySh1Wo9rQnN5XJPmpTOTIFn/v32pbWmWCz+yaltu92efebNcHqf\nqWH9UwzfP1bbN9gzNRNysSPd7fmrHc3vP3n9pc3vRz7yEW6++WbWrl37NzmupUuXMjo6yrx585g7\nd+7sR8/zeOCBB3jnO9/Jy1/+8tkb6zOFYXzrkkt48IYb+FCtxpwoImctZ/X385pajbZSaaOo0nSy\nxW47WCcJj0cRS4Hjmk0WtdusKha5IZfjqKkplpdKNJQiCAKGpOSrYzV2iyNuzGa5vtxFzRiONwlv\nGa9RspYfZnP8Z76DzozHIiEpmoT5QZufKI8TbEJTKsaN4Q4kB3iaSEmGgpBpkZr1DJbNYYTnGlMl\nBM0oYtiYVK/qplgrbIp4e3O9zhxjuKWzk+vyeY6bnmawUGBQazZHEUXfZ6FIWaAiivi9EHy40WDn\ndpteYzi/v5/5zSYDYciGYpGHnClqoe9TFGlYwUgY0pKStzhD3bTvc1WpxCeHh9moNatzOX6aydAp\nJQNuymejNHb3QNdkLWw0+HlnJ51JwtvGx3lEa36Zz/ObbJZdpEQqhU8auzs6Y1KKYyrtNtcWi5w/\nOsriOGal53FBpYIP9ElJUwhiYxgzhl6lmGst/cZQTRK2SMkXqlUqxnBPJsPnurs5rNWi5UxKNcdY\n3dPJNDrjmGWk294vbbeZYwyX9/TwsNa8aHqabYUCG6RkNEno0po5KmWztsKQ1VLysXqdBUFAzlr+\nrb+fY8bGkEKwsVDgLqWw8olgDR3HbIxjuoXgNe02C5pNVhaL/DKb5eMjI6zyPB7K5bjd9+lXKp1k\nC0EUBKwBjhGCncOQ+Y0G13R1cWy9zkubTVZozQ9KJTY4GcDMAmXMocUOAhZEESKOuTmX4/LhYUrG\n8Dvf53OVCguSNASiJQTtJI3Q3kVrSsYwkCQ86q6/Mycm6DKGH3V2cnWxyBGtFuO5HGNSUg1DjNbs\nrlLiRy6KuFdK3j85yT5RRI8xnDswgIgilgYBWwoFVgtBwxgGPI9uJ++YCck4Y2qKeWFI3fP4UlcX\n/1KrMSElG4pF7hCCrFIscgs4GcesiWP2kZLDnSzktq4uakrxjtFRHtGauwsF7tOaBUqlRkUn71gn\nBK8BFruF8VXlMh+uVtkpSXjY87i8XMZISb9MOdQ2SRhzRsB9gIVRRNVafud5XDE8jLaWO7JZLimX\n2SNJkL5PIJ9AEu6tFEVrGQhD7pKSF7danNxoUDKGL/f0cLfncYijU4wAk3GM53ns7PTVRBG/V4pz\nJyZYEsf41vLR/n52bzYpW8sWF5JhhWCe1nSSLvxmGvB3Tk+nJJVymbuPO463n3/+bEjEs01sgb8L\nA9YMl/eZtL3bT3W3l0E8kxnuT01tG43G7HvkcjlyuRzw7MlwhULhL5rWbv8+M+V5HpVK5e/ifP/f\nUDua33/CajQaPPbYYwAcdthhnH322bz2ta+lUqmwYMECzjnnHJYtW8btt98OpFNe3/fZd999kVJy\n8803c95553HJJZdwxhln/E2OMQiCZ13lrl+/npNPPpmLLrqIgw8+ePb1Z9KB3fWzn3H1BRewexyT\nSZLZRnG/VovXNZsMGMNPSyX+K5fjGNfQDGnNpiii0xmbMs6YcrdS/MfICBVj+Hk2y/fLZaaAPZTk\nyGaTY6cmWSEVn6pUmKs1vQKOaDQ4enqSL/QNsKRRpz+KWJfN8bCfYauFnZUkj6WaGIaF5Pj6JANJ\nwt0dJSSCD1XTBLYfVCpsVpp/qdXYphTLcjnu8X1e4HSVnhCMBQF1rdkX6EoSesKQn/g+n6vV2C2O\nqUnJJ/v78eOYOUpR1ZrGjF7V8+ixloIxTMUxI0LMyhA2ac0neno4dmoq3Q72fR53JrMZt7/n3P4v\nDwIOazYZSBL+u6eHR5TiyIkJHs/leCyT4bEkYW4mk5IXtpMhvMc1xKUk4cK+Pk6pVlFCsCaT4bZ8\nnkgI5quUUKGShG1RRFZKjoljFrZabPM8fp3P8+/btrHK83jAMVYXSEleKTJCEIQhm4CDpGRekrCo\n3ebGbJbDm01OqddZp1Pu8QNum33aTdAnwpBQKfYSgq4koRCG3Ob7XFytsjhJGHImpTlhSNnzqKl0\nQdNwOumSteSThG1JgjaGD02mv+OH83kuLJV41fg4tWKRQc9jbRyT0Zqd3Ta7iiL+YC2nBAEvbDbp\nTxKu6u+nFcccND3N2nyehzMZthrDXM+jS0q8JEl5wErxLqfn1UJwWU8PHxwZoSklq32fGwsFfCGY\nq1MGLXHM5jimXykOjSIWNZs8lM+zzvO4YHCQlZ7Hb3yfH3d0sLNII7QzQCMI2CIEh0jJ3CRhfqvF\nD/J5/mVqile2WjyuNZd1dbFZa3YFppXCuOmp0GnyX0+SYJKEu5Xi0mqVeUnCBq35SG8vu7fbZDMZ\nqlozGse0SfX5BWspJGlIxrw45h3T0wwkCb8slfiOw7wNFYtsduavguexk1ugmDBM5R2tFnu0WlSM\n4dK+PvqCgN2aTdbl89zv+4xb+0RypDFUg4CqUrzDndeG5/HNri7OGhqiqhSP+D4/zucpSZkGlog0\npW5DkrBUKQ5wVIs7OzqIhOBcJ1+4NZ/n59ksu0qJcH/P0+02g0pxmBDMjWN6g4Af5PN8aGyMw8KQ\nx7Tms5UKoRAsEoIpJ6WaMoacUiyxlkqSUDeGR915HUgSHvZ9zq5UOKDVQmQyjGrNcBwTiDQuPGct\nRWOYWLSIf73iCnbZffe/yT3+b1FxHNNsNp9GZMjn808yTP8xM9wfm9pOT0/PPl8KhcKTnlHGGBqN\nxtNkFX+JGW7795mpSqWyw/D2PNaO5vefsO644w6OPvpo4MmSgbe//e1cffXVvOMd7+DOO+/k8ccf\nB+Caa67h4osvZuPGjSil2G233TjzzDM55ZRT/n/7GUZHRznxxBM544wzeMV2wPZnmgA88sAD3Hz2\n2SQTEzSkxBOCWhAQaM3eQHeSUApDbs5kuKRaZWEcM6wUH+/royuOKXoe0zJl744mCTtLyXGNBvs2\nGlQ9j493d7PEWqSnmRfHvHR8nK9Xenj7RI378kU2ZLOUsIwFIb3GcOr0JAMmYVM2x9c6y1wyPEhD\nCP6QL/C9bI63t1uMeT4rECxXkldakNYybgz3KMUZjQa9QYAHXNzby8eGh4mkZI3W/FephBCCHiln\nAyCG4pgupdjbGBaFIduk5CGtudzpee/NZLiiXGYPa7Faz6Z+DQvBAVJSspYFQcDPteYV9Tqvb7UI\nreXySoX7fJ/9jWFUa9pAzbFSd3HT5UwYco9SnO9Sv7S1vG9ggKXNJgWlGMxm2WAMkbUs9v1Zru/W\nKKIAvMO5/Tfmcnyls5NTajU2ZzJsyuf5nTF0KMVCJ0OQURr1/IYkYc9mk3lRxLWVCp1xzCHT06zS\nmvuLRdY4GUtBpsSPqSBgs1Kc4LbLC1HE5V1dfHFkhLbTSV9dKpGFWb2qTVLeba9S7OnO6+NK8bhS\nfGV4mBEp+bXTSe9lDInTkU8HAVUp2V9KOqxlfhBwq+fxxqkpXtVuY63lwt5eHtWafeOYkRmTUpKQ\n0ZolwqWpuQjdmTQ1ay3vHxhg72aTnFJszWRYay0GWKQ1BVLix8YkoWJtqgNOEh4tFvl2ocAptRqb\nMhnW53I84OQW82coCo6XfLxJKQpzoohv9fayMAg4aHqalVpzZ2cnG4EFnkdhRn8eBAxKyRtNyqBV\nScK3ymUuGRqiJSUPOxlChxB0uYbPxGncc/+M/jwMeUQpqkpx6fAwY1Lys3ye/3SYt9DpzyeDgLHt\nzuvcIOBWrfmXqSleHgRgLf/W18dGpdjbnddxa5mOY7KexxI3PTVxzHIp+fzYGPOdTOFDAwMcUK/j\nuet1Jpp4yQzb12EU5wInu/P6QKnEj7NZTqnVWO/7rM3n+Z21dOmU0z3DoV4BnJgkvKDZpD+KuLK3\nlz3bbQ6o13lUa27r7GQIZjnU2qSovhGleKPTnyfWcl1HB5cND9MWgt97Hl8rl6mQynQ8IYicCXOe\nUix11+uD7m/2wtFRJqXkx8Ui1xYK7G8MLc/DCkHLWo778Id58wc+8A8zcTTG0Gq1noYQm5FBbD8F\nnpkE/7lmuMnJydlp8TMxfv9YMtxzMcNt/z4zVIpisfgP8zv4Z6gdze+O+ruter3OSSedxOtf/3pO\nfQqq56lhGCsffpgbzzqLTz70EI97HquV4gelEnkh6HYTResQSztJyVKT4otWe2lE7qdHRviD73NX\nLsf/ZLPMVYp+pSgnCXs3GtxYKHBmdZQHc1nu6yyRQfB4HHFSu8nbpqeoAzdl83yz0EGXpxhQGg0E\nYcgGYA/fwyBS7BKCRZ7G2NQgZ2UqgZDAdBynW8+el26XJwnrooj5wGsaDeaGIauKRW7K5XhPtcoa\nrVlTKPC/KsVm9TpXehIEPGotrxGCXdpt5jWbfLtS4fBGg/2bTR71PG7p6GCd1ixwjbQHjAUBk0px\nuLUsiiLyQcC1HR1cMTSEEoKHPI+Lu7roJn3wGimJnV51kdb0GcO8OGY90LKWT4+NkTWG23I5/r1c\n5rAwZDqToSElE25rfm+Vcn0rccxvhOCt09O8OAjoNYYL+vpYrxT7NZtsy+XYKgRjJuXWznXb5e0o\nYrWUnDM5ydwoIgt8sr+fo8bHMVKyqVjkAQAh2Mnz0oQ6Y9gQRfQBr2s2mddus6ZY5H/yeT44MsJj\nnseqfJ5faU3vU87rKmt5mUhjiec3GlxbqfCiVovDp6d51EuDR1Z7adiEJ2VqdnQmrpcAC5wO+Ppi\nka8OD9NhDMudTrobKCtFJCVRnEbmztOafmPSaam1TFnL58bG6DSG2/J5LiuVOCQIaGazTEk5K+/Y\nW2v8JKErirhLCN48Pc0RYUhvknBJXx+PKcUBjQaD+TybpKTmzHHznYmrHYaskpJPTk2xIIrwreW8\n/n6OGB/HAzYWi9zjpm0zmDedJGyKIkpScnyzyfxWi9UdHfwsl+OMkRHWac3D+Ty/9DwqUtLnpqdx\nELAaOBrYzck7ru/uZt92m1dPTbHC8/jvjg4e9Tx2khIlJdpaJsOQqlK8xFoWxjG5MOQHhQIXj4ww\nN0lY7nl8vlKhTJpS1xaC0Mk7+rVmnrUMxDGbraUGXFCr0WVSDvWlpRKHtNu0s1nGlaI6w6GWKZ2i\nM4q4TwheV69zbBDQlyRc1tfHo0pxqGP7Pi4lNWMo6TTNMeMMoKuk5BPT0ywKQzxr+Ux/Py+ZnCRv\nDBsKBX6jFJYUD5d394EtUURWKd7UbLKg1WJVscgtuRxnDQ+zTmuW53LclsnQK2V6vbrzusZaDheC\nPcOQ+c0m3+/qYvcw5OSxMVb4PjeUy4zuuiv/8eMfUygU/gZ38r9+zZjbtn8GwHM3wz11ajs+Pj47\nLJohMDxTJUlCvV7/i8xw1lrGx8dnvy6Xy7OM3x31/NWO5ndH/V1XGIacdtpp7Lrrrnz0ox/9o2EY\no6OjfPCEE3jzxAR7NxrMjSLuLJdZ6Xm8sVZjtU6DHO6TaZBDSaV81aDdZqUQvDuOWVqvMy+KuLC/\nnznNJoHvsyWTIQeMhiF7xhFnTYwzLSXXd5b4ueeBUrxIwCH1aQ5sNLmsr5/9m3VeUZ9mREp+1Fnm\nD16Gd47XKFjLbzs7Wa99zhoZRgA/7epihefzgdFRRqRkWTbLTYUCR8Yxk24qPRKGKM9jF9eYeGHI\n/VJyer3Oru7Be2F/P9kwZKdWi03budLn+z4l8URAxqiUvNs9QIUQXNjTw/tGR6kpxdp8nl94aYDI\nfKeTlnHM+jhmFyl5cRiyoNHgD65x/sTICCs8j2WZDD/N5VjoZAizXF8hOEIIFrqwgms7Ojh5cpIj\nHNf3P8tl1ivFEiFoS4kExhwibA+gP0nwooif+z5frVaZkySsVopP9PWxyDGLx5WiHsdMWctSrSkC\nnXHMRmPoSBLeP0NDKBT4Umcnr5ycZLRYZNjJXzyl0thmY/Cc2/+trRYvbLUYMIav9fUxZQz7TU+z\noVBgpecxaFyYgzuv00HAeil5v4sXzrjz+g4X5vBYNsutLn51Rt4hk5SX3C0lRztZyJp8nvuzWS7a\nto1HfZ/7fZ8fFQoskJKCa2iCIGAD8GIpZ8/rDcUiRzYanFSvs0anaWoP+j57AA2lEKQM2rZSvFCI\nJyJ0fZ8LR0fZJUnYqhQfcRG6FaWoac1kklC3lnlaU7GWopswtoGzxscZSBIeyeX4XLnMcRMTTBcK\nDDrZjHSymZnz+pC1vCoI0pAMY7iut5d1UnL0+DjrcjlWZrOsT5InmeOa7TarpOT9joZQsJZL+vp4\nc7VKzlpWZzL8NJ/HCMFc9WR6h9CaVzl5x5ZMhttzOb6ybRuPa82yTIbrikXmypSi4IsUL7jZGF6o\nFIuTlBZySy7HrmHIhyYm2CAl15RK3JnNso+11N15nYyiWbZvV5LiBf/H9zlvbIwXRhGTQnDmwAB+\nHLNQSoa1ZtwYmsZQcWjFvDFMxjHbpOSztRpzkoRNvs+53d0cOTlJkMsxmMmwKo5RKmX7Zm1KRVlp\nDAdFEa92eMH/rlT4vda8bmyM9ZkMj+RyrLSWPs9L8WvOdPiIEJwWxyyp1yknCd87+GDeeMkl7Lnf\nfs/Pzf2vUEmS0Gw2nzTVnQm62H6qu32S3DMxd2emr9s3pV1dXX90Ejsjw3tqA/6nzHDGGCYmJp70\nPkqpHZiz57l2NL876u++jDF84hOfoN1uc/HFFz9pNT6TzT5T9Xqdi9/1LqING6hYi+/0fw8pxTkT\nE8yNIsrW8rGBAQ6anEQLwZZCgYeFSFFSvk/ePeQnnankglqVP2iPW0ud3KE0vlK8BMsxE+Ps325z\nRW8f90lJr5Q0lSIPVIOAtlS8FENnklC1lt8qjxOSmJaUbDaG+5TmVdZiBUwkCfdIxTvDkK4oIhNF\nXN7dzWdGR9k1jnlMay6sVEiEYL4QjKs0nWo8SejRmgF3zK0kYb2UfM7peYek5MN9fRw2PU2YzzPq\neWyOY2Ip2VUpsqQyhNVxzAFxzKunpxkwhjvLZX6SyfDaiQnW53JsymR4NEmoaM3c7bZ1HwLeHUUs\nca70y/r62Hd6moVRxOpMhrtzOUZIcW05+QTXd0IpTnSNG8BV5TKXDg6yVWse1ZprSyVKbmrvu6n9\n5jhmiVLs7raDH3IRy18YHWWDUvwyl+PaYpF9gFCnmLcpp+E8SAhKxjA/CLjR93nbxATHBAF1Kbmw\np4d1Tt5QdVvF41GUbpcDeWOQUcT9SvHFWo35SUIMvHdggL2aTbKex5Dvs94YImCJw5H5ScLmJKHL\nWt7mwgrWFAp8vaODk2o1NmezbMrl+L2bDM7IO0QUsdwY3pgk7NNoMBBFXNfbSy6OOXxqipVas6yj\ngzWkZIEZXvJ0ELBBKU6KYxa12xSjiJh0FUkAACAASURBVMsrFT49PAwiTZu7ulRCC0GPa/hIEobj\nmIJS7O9kCFul5Peex9eHhhiTkt9kMvyfcpkXGINwMoQZBu1+StFpLfPDkDuU4kWtFm+t1xHWckV3\nN7/KZHiRC8mYZjvMm9PaF6KI/1WKc8fG2C1JyFvL6QMDdAcBc6xlMJdjrbUEM5pnIfCThFoUMSUE\nZ7o47Krvc1FXF2+q1ah5HpsLBe6yNtXGao0HqChidZJwAKlWf34YcktXF5uV4i3VaqolLxR4QErm\nKEWXm/a3goA1QnC8tezUbtPbbvO1SoW3jo+zaxjyqDuvDSkZkBJPKYRJw0cCpTjUpljCprXcms1y\n5dAQnrXc4/tcWKmwKEk54rGUtKKIMWvZRWsqbhdlOVBKEj4+Pk6HtXyvVOKaQoHD220mslkmhJjl\nCO/ldlE6o4i7lOKdk5O8KAypGMOn5sxh0hj2abXYms/zmBDUjaHL95lDSv0wvs8e730vbz799H+Y\nLfgZWcNT0ZmZTOZJU93tQzna7fYz0iNm5Awz7N0/p6Iool6vP02H/GyM4e1ZwjOUhx2M3+e/djS/\nO+ofpi699FKWLVvGlVde+SQjwkyM5MylHEUR3/j4x/HvuIOam5y23Fbn7p5H3hhKScJ6Y+iJY949\nNZXGmObzXFIuc0S7zWAuRyKfYLmeYhJePDHBbnHM5/v6eERKytojJ6DXsUhX+z5XDg8yBdzjZ7i4\nVKZfCEpKEQjBUBSBkMzRCiwMxjEImKM0Qggm45i6tSz20iAH4baQi1JyqDEsaLXYpjV3O/7sJqVY\n5vt8rVRiKSCUQktJOwwZBPZXirJJofq/1pqDmk3e2mjQtpbvlsv8Ty7Hi5KEmucRCkEtDLFK8QIp\nyRpDOQz5pdZ8emyMXZKEgjGcPmcOhTBkjrUMZbNssZamM9R1kepOJ+KYmhB8bGKCuUlCSynOrlR4\nw/g4E77P1nyeB4zBU4qdt+P6ro5j9oOU6xtF3FUu8wfP4+RqldVa82ixyD1CMNfzUikLKa7tUeAE\nm8YLz221+HqlwhumptjVMU9v6uxkq1LMk5KMkyHUgoC6UhxhDIujCBlFfL9Y5BtDQ1gheNDzuLi7\nmz5r6dCaRAiiOGbUGHZSij5rmR9FrBWCtrX8W61Gzlpuyef5SqnEoVFEw4U5jDt5xz4qpUxUoojf\nCsFJ09O8xMk7Lu7rY5VSHNBsMpjPs0UIxpKEkufNbpeHYcgjTt4xL4rIW8s5AwMcPDlJ1lo2ucYt\nFoKFOk0b9I1hSxjiK8XJjQbzWy22FgpcVyxy5vAwG7RmlWPQdknJgJv22zBktTEcIgT7uGn/TV1d\nlJKEt46NscLzuD2f565MJo0YVmoWL7hNSo4SggXREyEZZ42Oslcc86jncVF3N6EQzJeSlpQYt4jL\nKsVSa5mTJDSM4XdK8ZXRUXqN4UHP4+yeHvYKQ7TvM64UY1FEE9hda/LW0hnHrLSWnaOIf3XmuJvL\nZa7N5Xj55CRDxSJbtWZzHJPVmp2dJlyEIQ9KybsaDfZqt+kxhi/195OJIvZuNFiXy/Gg51GD9Dp3\nZs6JIGCrUry31WJhs0miVBrdPDpKS0pWZTLclMuRkXJ2Kk0csyWOqUjJUW7a/1CxyCO+z8XbtrHS\n8/itMx0uEoKsm/a3goDNwIukZFGSsKDZ5IeFAkc2Gry1XudxpfhaVxfLPY+9SM2ckE6l21rzQqCS\npCSOW32fz1ervCCOGZGSM/r76Yoi+pVi1PMYN4be3XbjM9/7Hp2dnc/Hrf2vUlEU0Wq1nkZkyOfz\nTxqY/DEz3ExprZ/Tz/5sZrhnYgwHQTA7sPE8bzY+eQfj9/mtHc3vjvqHqmuvvZbrr7+e73znO0+6\nOc3cfGa2v4wxXHrGGRz5q19x7Pg4qxxq68ZCgX2Bppt8zQD1DxBp4teCdpvv53KcX60yEMfck8nw\nvVKJUSlZ7Hl0WsuiKCQfRdyXy3HB0BA35fM8UCoxmSSMGsvhUrJn2Ga3+jTXdfewb6PBSfVpFHB9\npZe1SvKZ4WEAburq5vZMhs8MDjKmFPfmclzb2ckJ4+NU83lGfJ8/JAk9nseAazCMMyi9zlp2dlzf\n6yoV9m42ObTR4FHP41fFIg/rNNzAdwalSYeSOtI1fOV2m2+VSnx5ZIQOa3lYa77c1YUvBBWlSEQa\nIVqLYypas9Ba5rnJ1Gql+HK1SsEY7vF9PlupcEAQEGezTMs0XnhKCPZSipy1VOKY3wGHNJu8odWi\nN0n4flcXP8lmOarRYLBQYEhKhqKInO+zRKTYNRlF/E4IPjI9zc5hSCVJOH9ggJ52m/ntNpvczznh\n5B2dpHreMZca9x6Hv4qV4kuVCh8cGWFUKdblctzi+2nogGswRByzIY7ZSUoOddvsf+jo4DHP41PD\nwzysNfdlMtxcKLBICHJOr/pMsc3f6+jgdVNTvLrZZJXWfLtc5hHPY3dSGYICxp2G9IXu2suHIf+T\nyXDJ6ChLkoTN28sQtKaqFHXn7p/nebMyhGqSMA2cPTbGHGNY7ft8qrubY6emmM7n06l0FIFS7O6m\ny36URgUfEwQc1Wgwxxh+VKnwO615xfg4j+dyrMlmWWMMfVozoFKGcei2y98Thuzk4sK/1NfH0ZOT\n9EcRq3yf2wsFpmXKPp4xcVXDkLqUvMHRO5pKpZrnwUEGleIh3+fqUoluZ8bzRco+3pok7KQUuzmz\n4gO+Twh8oVplmzPHXdfRwT7WEiiFFIKpMI0zPlAIOpOE+WHITZ7HKVNTvDIIiK3ls319rFOKfeKY\nUd9nylqmHFpsFyDnrr1lSvEFFz5ieCI9siglg7kcq4zBkhoBOwHf+Qoy1vKeyUnmJgmP5fN8vaOD\nk2s1tnkpU/o+a+lQikVu8SeiiEeThGOAg9zi7/+pVAiB42s1HvU87ikWecj5A0ruXlBvt1krBCda\ny5J2m1IQ8LXubj5YqzE/jlnheVxVLhPLFNmmpYQkRbYlSvFiN5WeBH6VyfCNoSGktdydyfDVRYt4\n3/nn87LXvvZ5uLP/dcoYQ7PZfNJUF9ImdHtN7fZmuKc2zPDcm194Qoe8/U7kzPfanjHcarVmpRfZ\nbHZWorE9rWJH/e1rR/O7o/7h6tZbb+WCCy7gmmuuob+/f/b1Z7rxXf5v/8ayW27hpDBkUbNJZxRx\nWU8P/zY8TEsIVnkeP3BBF32uUdTGsC0MKUvJa9ttdq3Xafo+F5fLvHxigofLZVpKoeKYtSbhE40G\nh7SaFK3lqlKZG7I5lgpBqBUZBNWgTVunkcMSmAhTw8thQiCAZhLzeyE53lo6TZoy9f1slo+Nj7Nb\nHFM2hvMGBpBRxNJ2m835PI/pNAZ3vufN6nknwpBBKXmva/g84ILeXt49OsqkUqzNZvlFJoMUggVu\nwqeShE1xTL8QacpUs8nj+Tx3ZbN8YXiYFVrzoEvvmiclna4xicKQx63lEClZ5BqaGwsFDmw2OdmR\nF37U0cFvs1n2JF1szODaGlqzH9CbJHQHAT/KZvl8tcruccyQlJzd14eylnlCUNWaljFMziwArKXD\nGBpxzHopOb9WYyBJqErJ6X19HDY1RZTPM+x5bEgSjBDsqvWsvGNNkrB3FPF6p4+8u1Tih7kcx4+N\nsSGXY2M2y0NJmlA3I++wYchya3lrHLO00WAgjrmyr49F7TZ7NRqs9jzuLRafREPw7ROhAyclCYua\nTTJJwhXd3VwwNERbSlZ4Ht8plci4xcYMZWI4jikpxX7GsMiRKh7yPK4YGqK2nQxhD2OwnjdL7xgB\n9lWKTjftv0NrDt5OhnBVdzc/y2Y5NIqo+j51nL5aa/aQTyD/7lCKc5wModMYzpgzh2wUsSiO2ZrL\npWZGkyac9TgZwmQUMaQUnxgfZ04cEyjFZ3p7eV21SkNrNhWL3AN4QrDYLRp0HLMujlkCvLLZZF4Q\ncH9nJ3dnMnxwdJTVXso+vsPz6JNyNmI4duEsrwB2DQLmOzPnIc0mx9XrPOx5/MhFRS92uyGaVPNc\nU4ojINWLBwHXFYtcPDLC/CThIc/j/J4eCtbSpxQtIYjcVLpbaxZZyxxn7lynFJeOjs4ypT/T3c2B\n7TaJM8fVwpCmlOypNTmTMqWXA/u325zUaNCfJHy/UuFm3+e4yUm2FYts0pqtM8g2dw3NINs+0Giw\nW7tNlzFc3N9PJQjYvdViXS7HA45sMc/z/l/23jxMrqpc+/6ttfbeNVf1VD0k6UyEBETGgIAHBFFB\nVA74qhwFBXkVQUEUFQGRSQWcmFQOAopHPerBGfUV9ciogBKGQOaZTD1Wd1d3dU1777X298de3UkA\n/Tge0O/9Tj/XlSuhkg7dO9VV937Wfd8/CjKubBuzTRwfaDSYV6vRcBy+1t7OhwcGqCnFGlvZlrIW\njyni3Hatp7fS82s11nZ1EZ15Ju++6KL/q2wQL9QJ7LouKeu7n5qpMFyz2Xxee8TfUmE29Xf+tTDc\n5OTktEUjnU6TTCZxXfdvwibPzN8+M+J3Zv7iPPTQQ3z5y1/mySefpK+vj29961uceeaZf/VjVqxY\nwfnnn8+yZctoa2vjnHPO4fLLL3/JP7fHHnuMCy64gDvuuIO99tpr+vEXgmHc+8Mf8oubb6aoNW4U\n4WrNpjBkryjihFqNWc1mnPRPpXhfqcQa12VjLscfo4h2x4lxpMbQZtPdl4+OcGAY8pDn8ZNCgdVC\nMt/z6DSGJX6Tzkad7+ULfLu/D4C1jsOn24vM8pv0itgX/JQUOMAsqQgEDIYaH+hVClfGtWv9QUDB\nceiNIlqNYVJr1kvJZ0dG6DaGQSE4r6uLoycm8K3g2641oRDTgRhPxz2p+4UhJ09OxjVNuRzfSad5\n+9gYz6ZSbEsmedoKvjl2w8cLCL5vdHbS1Wxy4OQk61yXZdksm9kl+BL2KHi7lLxTa+bW6+R8n5s7\nOrja4pfXuC7fKRSQQlC0NxtCawaDgOyU4LN+0keSSW7v76ckJX/2PG5saWFvY5CehxCCRhAwGEUc\noBQtUUSvrV1b0mzy/okJpPVH/iCd5qgwZMTzqIm4cSNwXV5phVtrEHC/Unx0bIz9w5A2Y7i4u5uq\nMSzxffpSKbYBE8ZQdF067c1G1ffZohSXjI0xKwxxiFsm3jA6Sigl27NZHhMxpGWeG1PRXK3ZGoa0\nC8Eptg1hYzbLz9JpPjo0xEbXZU0qxX/aNoQue7NhrA3hGCHY19oQftrayqww5F/GxljpOPwuk+HR\nRIKFUuLYzWCl0aDPcTgmitsQOq0N4ZLhYV4RhqxxHL7U3k5DCGYLQV3FHb1jYUjC2hC6jMHXmj9Z\nG0KXMaxxHC4qFlli+7pHpWTMhuMWO3FHb15rNhlDp9acbUOHf8hm+Uo2y5vKZYayWfrcuKPXU7tC\nh04Q8BTwznqdpTZ0eHuxyAhw1Pg4m1IpViYSbDWGbs+jXUoSxlBrNlkvJef6PvOqVdJRxBeLRf5l\nJA6arnVdfpXLoYFZjjMdjhsMYsTxm4OAefU6Q67LrzIZvrpzJzschyc9j2/k8/QIQc5+fwa+z44o\nYh8pWWQ96A8nk6SM4fJSKQ66ZrP8MJPh4Cii5lhrU7PJqFIcJiU5relpNvmV5/He8XFe32xioohP\nd3WxXUpeabfSo1FERcdVeLsDL55ScRXeXK2JgPO7u3lFtUpWCPpSKVY9Zys9DbwQgnOsJWlTOs1t\n+TynDw8z4DhszuV4JIrI7raVdoxB7L8/H7njDtra2l7y1/KXa15MJ/AUES4MQ4Ig2CM4B//1CrOp\n+WthuDAMp4VxNpvF8zw8+5o2M3+/mRG/M/MX55577uHhhx/m4IMP5owzzuDWW2/9q6S4iYkJFi9e\nzLHHHssVV1zBmjVrOOuss7jqqqv42Mc+9pJ/fuvXr+c973kPN9xwAwfvllB+IRjGsvvv5+mrryY/\nMEBfJsOQlHHXrOcxz3oqVRDwuBB8fGKCRb5PjzFc0d2NDgI6ooitySQ+UA4DUlJxkt9k6cQEeWP4\ncGcXr65MsDOXZ8xxkGHIVqM5VCrm65C5jQb3JpMUfZ93TE6SjCLubWnhKc/jCwMDOMCj6TTXFwp8\ndLjEoFJs8Tzutg0Knoxrs6b8vAdLScHEGNwHleKwep3Tq1VMFPHdlhZ+lkpxZBhScl0aNhBjdtvw\ntQYB9ynFxXbD12IMn+jpIQwC9tKavlSK7cCETd9Pbfgmg4DtUnJRucysMCZHXdTVxYmjo9SVYns2\nyzJASMkCJ4YkuFrzbBjSDZxka8U2W8F3wVSt2JTgU3HFnCcEke+zxhheKwT7WBvCz1tb6QkC3l4u\ns8J1uc/6ThdO+U6FYMLCA14TRcwNAroaDe7M5bikVOIVYchqx+GG9nYmpaRXSuoi7sIeDQISjhML\nPq3RWvNHx+FmK/jWOw4fLxZZ7Pt41ndatj7tvV2XrBV8W7SmRWvOsYLviXSazxcKnDg2RimbnbYh\nOI7D3na77AYBy6OItzUaHFar0WPiNoQtQnBsucymVIp1iQQbreDrsJvBKVTwOVbwtRjDF7u6+OeR\nEVqMYZ3r8ttslknbMpGUcUXYsN1Mnmy30lUp+X4uxy19ffQ7Ds+4LncUCtOVdp6MK+36rA1hkdbM\nbzZZ7rrUhOC64WFKUnKPRTAfpDVNN+5cnbAWlKVCkDOG2UHAbxyHUyoVTmo0UFHE5zs6eNJ1eVUQ\nMOh5lIHylA1BCFLG4Nmbm09bD3rKhuNmN5sUtWZnOs36KEZbz/I8Wu1zrxQEVITgIzYcV/Y8Pt/W\nxjtLJUaViqvFpCQpJQus4FNhjAzfB3hdvc7sRoM/tLSw0nU5f2iI1a7Lk+k0D9oGhVZlQSuWyHcC\nsNj3mV2tcmd7O6+tVuOttONwVz7PervdFTIm8k3YyrajiMlxaVvZdt3QEAu1ZpXrckVHB6kooltK\nKlIS6BhgU3Ac5hkzTTrcoBTXDw/TaQxPJRJc2tbG0nodLPBiOAhoSjntlc6GIauiiH19n9MrFXqM\n4RetrfwokeCEcpmBTIbtnhfbcG6+maNPOOElfy1/OWaK9PZcNDLsota9GPkz1cH7twTSgiDYw473\n3CkUCtM1ZzPi9+87M+J3Zl7UvBhM8q233sqll17K4ODgdCDtmmuu4dZbb2XHjh0vy+fV39/PO97x\nDi6++GJe97rXTT/+QkdfjzzwAD+6/HKue/ZZZmlNn5R8squLQhjSoRTDjkNN69g/6rq0G0O71tS0\nZpuUfHV4mBrwh0SCGwsFOmTcU5qOIjoDn6cjOL0ywZsbDUaE4K50hv/IZtlXCgIZwzdKTZ/AcVik\nJDKCmu+zVsT0rKQxJLXmPik5q15ngT3mvL1YZL96nVdVq6xxHB7IZllp/byulHhCMNZoULJHunOD\ngLZ6nW/m83xpaIhOrVntxv28Ukq6VNx3ShQxHIa0Og69xkwHjZ5Wihvske4zjsPFxSL7NxqIZJKy\nUnEwD9jXbpcLYcg6Y1gYBNNvnn/IZvlqLscby2UGs1kGXZctUw0Kdks8RTc7s17nlfU6PcbwzWKR\nUhRx+MQEm9Jp1iYSbNGa2YlEXCsWxfVX66WcFnx5Y/h8VxfvHB4mAazxPP4zk6EudtHNXGMY9H20\nUrwpDJlXrzOpFHdls/xrXx/bdhN8RRtSdK3vdIfWLFaKBcYwv9HgKc8jAK4eHmZQSn5nBd9SE8MD\npIhbJkaUYqmUseBrNrnHdXnH+DhvbDYRUcSXOjp4ynVZGsZQhnHiNoQpwZfQmmQQ8IjjcOXICAu0\nJhNFnNfdzWyLq96ZTrMBaFjPc4HY3lEKAiak5AJ7kzLpunyurY13jowwqhRbMxn+KAQJpZhv7QSO\nFXxLiAXfnEaDPxcKPO55XGAF39OpFPd5Ht1S0mpvbgLfZ10Udx8vslvpb7e1cWStxput4PtpLscK\n+28vZNwpPeVBnxJ8BWtD+NzwMHvbrfTVHR1IYJYVfKG1wGSUYiGxdWZSa1ZYwddtt9IfLxY5sF5H\nJZOUlGIo3JMcl9OaDcYwJww5a2KCHmN4KJ/n9kyGt4yNMZDJsMPzWB+GpJxdRD5pb1L+pdFgab1O\nl9bc0dXFpDEcUy6zIZFgeTrN5iiKqYr2JqXaaLBOSj4QBMyrVskYw/WdnZxeKtFqDKsdh5/m8/hS\nMktKkkohtY6FqlK8SWvm12qMKcXdmQz/2tdHSSmecGPgRZfdSjs2mNlvDAukZC97kvKE4xBEEdeV\nSlSBn2Wz3JnLcYgxNGygs2xbWA4WgmwUg0R+57qcXKnwz/U6mSji8729TL7hDVx2003/UI/qlLCd\n+vmFfv3fkTae5z2vPSKZTD7PNvFiZsqO99y/D2Y6fv+RMyN+Z+ZFzYsRv2eccQZjY2P88pe/nH5s\n2bJlHH744WzZsoV58+a9LJ/b+Pg4p556Ku9617s49dRT9/i958Iwdm7bxqfOOINXTk7SqzVzm002\nOA6DUnLd0BDD1lN5S0sL+0cRTcfBEQLf99lOXML/ykaDJdUqP25vxwtDFtSqPJEvMOA4lG2w6HBj\n2K9Rp6fR4MvtHfzrwAAtkWG7lFxe7KQ1CNg7CJjwXJ5SDlUhmCVj9KlvQ2ZFu3F1bIBrQCnOrVaZ\n1WighODajg4+OjzMiJRsTCT4dTqN2k3wKdsW0SEER9lase2JBH9Ipbixv5+1rsuTrst3czl67Rtu\nQkqCIGCrMSyVkjk6xgTfm0yy0Pf5ULnMdin5RTbLjzMZlhLjbJUQjDWbVJTiYCnJa02P73O363Lh\n2BiHBgFhFHF5VxeDQrCP1gx6HpUoYkxrco7DXBHTzYTv86RSXDMywixjpqlx+1erJJSiP5VivYlr\nxea7MYUroTV9tprufRMT9IQhpUSCL7S0cGapRJ/rxoIPyFjB5wIqDFkbhhwJHG43fPdbVO8Zw8Os\ncl2Wp1I86DjMdhxa7XZ5asP3FmCB3fDd0d7OKePjHNZosNJx+FE+zybHYa6USKWmYRcTSnEEseDL\n+j7fz2S4fnCQWcawynG4qlgkE0UUpWRSSkIdN5W0OzGUoUtrRrVmk1J80bYhrHRdPtnRwdJajSiV\noqRUjAoWgn1s6DCrNWuNYR/f552Tk/QYw335PHem05xULrMjk2Gn67JRa9KOw0IVt1OIIOBp4D2N\nBgdYwXdrsUhoDEdOTLAhmeTpZJJnYRrBnDCGyWaTDUpxtr1JyVrBd8bwMNkoYrXj8PNCgaZ97u8u\n+AKleKOOu3bHpeRnmQy39fUxpBRPui63FAp0SRkLPvuc7TeGhVKywOwinIVRxGdLJWrAL7JZ7sjl\nWGoMNSv4JqzgO8gKvh7f516lOGlykpPqdbJRxOeLRZY5Dkc2m/Qnk5SA0TDcg3To+D6PKcWlY2Ms\nCkNyUcRF3d10NJvM8n12ZjKslJKGMXS7Lu32hmzU3gBcaBs8qo7DF9rbOW14mEml2JxOc6/j4EnJ\nXMchKUR8qhQEdEvJm6y//8l8nj8lk3yqv5/1rsvjiQS/TqXoUiquCxSCoNlkI3CkELzC9+PGiEKB\nxb7P+8bGWG2fs48mEiyBaax6pdlkSCleDczWmo4g4IkjjuDcW2+lWCy+pK/lU3LkLwnal0LYvtBI\nKad/KKWQMm4haVgq49Qopchms/9l4f/XwnC5XI5kMvmSfB0z8+JnRvzOzIuaFyN+jz/+eObOncs3\nvvGN6ce2bdvG/PnzefTRRzn88MNfts+v2WxyxhlncOihh3LeeecB8Qvo+Pg4qVRqjw3w6OgoN77/\n/YQ7duAJEYMubJfnSVHEfEuYuq29nXePjdEbhiz3PH6bzbLZvgllpCRlYgrWoJRcP1JijtbskJIP\nFjspAEkn7pp1TEwTm69i9Gh3GLBKSiom4gMT42SjiPXpNP+eL3D7jh0MSslqJ+71PaJWg1SKEaXo\nC0O0lLvAAVqzTmsODENOtBvXJ/N5fpxMctroKBs8j63pNH+OIoquS7fdQkU26X+qMexdqzHb9/lu\nRwezfJ/DJyZYawNcK5RirlJk7NF8pdlkq5ScEkXMbTToaDT4Wlsblw0PkzdmGhNcV4ouGVO4pD1i\nV0pxIDDX9wm15p5UijsGBnCiiCddl6s6Oqb7ThtC0NSaEWNY5Di02K305igiMoaLx8ZoN4YHUymu\naWnhmFqNSjrNqFIMBQGBDRp5xpALYmjFiZOTvK7ZpFtrvt/ezn2ex+vGx9maybDDddkahhQ8j14h\ncG3Q6Bkh+HCtxoJ6naK1E8yp11nYaLApleKJRILBKKLXdcnJuGt3rNlkQCne22wyt1bDAW7o6OCi\ngQEmlWKt6/KTXA5HCLqtn1dqTZ+ttHuN3fBt9zweSqX4uoUyPO663FYoMA9I2OeVHwTsjCL2l5JZ\nxjC/2eQPrktXGPKJsTHKUvLjbJbvpdMcEUWMOw5GCMZ9nwm74UsbQ4/v8xvX5X3lMkf7Pqko4sqp\nNoRmk0Er+Ma1JuU4zLeCT/o+TyjFldZ3mo4iPtLTw6JqlVZj2JHJsBIIomi6icOzgb6aEJw3McEs\n36ecSHB9aytnDQ9TUopNlqyXkpK5bkzkk0HApjBkbyE4zjac/LlQYIXr8snBQVa7Lo8nk9xj6Ywt\nVvD5zSYbo4hjpYy30rUaPygUOLTR4F3j46xyXX6Yy/HYcwTfuO2HPlIIZochrY0Gd6XTXDIywtIg\nYKuUfLqzkyawQAhG7U3ruNaklGIvoEVrAq15Qim+XCoxW2sGpYy9ubUaKTfuh96hY8zyQschByS1\nZkcYko4iPlgux5jqTIbr83neOjLCUDrNdhvMTKq4LnDqJGWlMRwXhrzG+vt/0tHBZil5u4X8PJ3N\n8jTQ5cTkwinrzFopOU1rFtXrFJtNvtrZyesrFQ6s11nlOPwkn2dQyl3WGUCnUvyv667jqN3w839t\npkTrXxK0U4+9lCOEQEq5x8+7e26nxvO8PSrJdv+cfN9/XhhuKrz2X90CNxqN56GRhRB0dnbOBN7+\nzjMjfmfmRc2LEb8nnHACvb29CtyS9QAAIABJREFUf1fxu27dOlatWsXOnTvZvn07d999N/V6Hc/z\n6Ovro16vs3z5cjo7O/f4uMnJSW7/yEc48f77GRSCzakUj7suk8So1qQNNQ34PijFu6tV5tXrGKX4\nbHs77ymV2JBOsymdZrvWNITgACXpCjUHVqssS6dJRobzSiVWOC4PJxL8KJNhb6VAxRaIctOnohSv\nUAoVRURhyJPGcIIQzApDis0mP0mn+adqlX+pVvGBf2tt5Z5kkqOCID4qF4Lh3f2jOgYH/FFKPlku\nsygMKWrNFT09EATMbzTYmcmwSUpGTdzP22bFTMW+qV9YqTCr2SRlN7WnjIwQSsmWdJo/2o3ZXHcX\nfnlHEJCSkpMbDeZWq5SSSb6Xz/OZ/n42ui6rbbK8RcbY1YQQREHAZq3ZXyleaftOH8lmaQrBpUND\nrHYcHkom+VEux75AZH2n1WaTPiE4XAi6jWFOvc5PUyn+18QEJ9XrDEjJbW1tPOa6HAiMqhgTO+r7\nGMdhXyBrPc/3uC6fHRlhsdaYKOLDPT0kgoA5QjDoeQwaQ9XErQadxMKtHoZslZLLR0fp0THs4oLu\nbl47NkbgefSl0zxjDEJKFtqWCVdrtoQhPVHE2ycmmBWGbMxm+fdMhrOHh9nkOGzOZnlACFqVYpa1\nIYggYI0xHBtFHGQF3y/a2oiiiNNGRljlujyaTvMHz6NXqRh2IeJO2E1C8EZgvu8zq17nGy0tvGds\njMObzemblG2uy3xiwTdVvVZXiqXEG76U7/PTZJLrh4aYbwzrleLizk4KWlN0HMpS0rC+06Lj0BNF\ntGlNWWu2Ssm1IyN0ac1Ga0M4fHISk04zZFsNfCHYx16jVBiy3hgWBwHvrFTo0ZqHCwW+lU7zttFR\ntqfTbEskWGlPCeY7znRH7zNRxDuCgIMmJ+k2hn/r7CTQmuPKZda6LsuzWVYDs+1Weso6s05KzrA3\nG21BwI3FImeMjtJt+4h/mM8zYW0ICaVQxjDix9+zJxjDvEaDwBh+mMtxS38/CMETrssX29ooRhF5\npUDGmOqSMXQrxfwoxoZvBnZKyQ3DwySiiHuTST7f2srBvo9OJJiUcV3guBAcoBQpY+gKQx4TgoMa\nDd4zOUmHMXy3tZUfp1IcV6kwlMkwoBT9QYDjuiy2G3jX91kmJe+bmOAQ36fDGL7Y3U1da5ZWKmxO\np1nlugxHMQWuaG/kqjZAeGGtxtx6HVcIrisWOWlsjJwxrEskuDefZ/5hh/HZb30LpdRfFLRTv34p\nZ0rQ7i5unyt0/5I4fTFhONi1gdZaPy+85nne8zqE/9/mhcRvOp2mUCi86L9jZl6amRG/M/Oi5sWI\n3zPPPJORkRF+9atfTT/2ctsezjnnHG6//fa/+md+85vfcMABBzzv8SAIuPjd7+aQVat408QE3cbw\nrOdxdWsrby+X2ZlK0Z9MsioMpzcsSWNIBwFPRxGnVSq8vtEgE0V8u1Dg++k0rwSqjkNKCOqNBs9K\nyXt0yF7VKl1BwLXFTj4+PMSiMGSbcvhqWxsjQnBwEDDmeWwTggFj6HVd0jacNGIT4kcBs4OAfLPJ\nd7NZbhgcpNfEQawrOzpIRHFFU9l6I0etSJkVRbTomP62TimuLZXo0pp+KflQVxev2k2UDOoYXbvE\n+nmTxvCs1swJQ06bmKBHa9an03yhUOBUK0r6kklWhCFppWJAhzGoMOQZYzg5CDikWqVHa37R3s5W\nKTlxdJR1rsuabJbl1hvZphQJ69NeIwSnG8OCWo3OZpOvFYucND7OfN9njevy61yO7XYLlbD+0THr\nsT3exJSytO/zjXyemwcHcYEVrsuNra0kgDaliIQgMoZSGFJwHBbZcNxYFPGE6/K1wUHSUcRjnscV\n7e28IghQnkdFSqphSBnYV6m4FsvCFbrCkHPGx+k0hvuyWW7I53lDpUIpnWbYceizlpglduOWslvp\nd9RqHNlo0K013+noYLnj8LpymU3pNFs8j006pvj1WBtC4PuslJLz6nUW1Ou0G8MXOzs5eDey3sOp\nFMPEBLjM1FbanlKcbn2nEvhqWxufHRykIuImju/m83hSTjdxEIYMhCFZpTjCWmD6leKPySR39Pcz\nLCV/8jxuamlhYRTFlU0ibuIYiCL2U4qiMcwLYkJeexhy0dgYRBE/yuW4M5fjyCCgYps4dgeCJLWm\n0zZx/Mv4OK/zfdrs17pcKQ63/dB9QlAKQ9Kuy3z7tQrf5ykpuWh8nL2CgIIxXN7dTU+jQW+jwZZs\nluVKMRlFzHJdWsQu/PegUpxfrTK7XiewbRjvHxqiLiXrk0l+nUrh7BYglGHIjiAgpxRvshv/DZkM\nD6RSfHHnTja6Lk94Hj/IZumScrrHOPB9thnD/iruMZ5Xq3FvOk3OGC4rlXhWSn6ey/GTdJoDgKa1\nF000mwwrxWFAhzHMaja5O5HgnePjvLnRoAl8rrOTVUpxiG2MmCQGXkjXZYkQpLUm6fs85DhcNTrK\nYttWcn53N62+z2xj6Esm2WQDhF2uSwfxDeAUhvkyewM46bp8/fDDOfXaa1mwcOFL8rr+lwTt7qL2\nvxsQmwrDPXerm0qlcG1Yc+rPTW2s6/X6HiJeSkkmk3nRYbharTYtoqd8vlO+35n5+86M+J2ZFzUv\nRvx+/etf5+KLL2ZoaGg68Hbttddy6623sn379pfl8/rMZz7DlVde+Rd/P5VK8e1vf5tjjjlm+oUz\nCILpO/4oirjlsstYdd99LDZx4KwrCPitUny0XOZA3ycXRXzWHgPvGwTsTCSow3Q7wL7AQt+nq17n\nzkKB2/r6GJOSPyUS/KRQoC4EvbsFr7b5PikZU9u6goBBIXjEdbmuVKJgDBUp+WhXF2eUSlSVYnsy\nye8SCRK7HZWLMGRbGDJLKQ6y3shnXZcVnsdXBwZ4VkqWJRJ8rVBgCSAcBykEzSCgP4o4WEparDfy\nj47DkmaTD1QqBFHEj3M5vpPNTteDBSKuB2soxf5KkTCGLt/nP5XiA+UyrwoCWo3hus5O1inFwY0G\nfakUA1aUFFyXOTbAFQUBy6Xk0nKZ3jCk1cS1YotrNVqCgO2ZDCsch4ox9HoeOWLs6ojvM6oU51hK\nWSQl1xWLfGhoiFEpWZ9O8zvPw5ExtGLa8+z7dCrFcbYtYks6zX3pNF/YuZM1nsdy1+U/slm6pZxu\nNdBBwBZjOERK9rKi5P50moLWXDQywialuCed5q5sloOAhg0aVaZEiRC0aU1vs8nPEgneUy5zfLNJ\nDfhyRwfLXZeDbchtCqUsHYfFQpDStmvXipK9wpBUFPGhnh7yzSazopis9yxx1+60KDGGySBgh5Rx\n9ZqOK+8u6ezkxNFRfCnZmsuxDJBCsMDaCRyt2RoEtAnBOyYnme37bM5kuCub5cKBATa7LmvTaX7r\nurRISY99/hEErNeaw4Tg4GaT3mqV37e20hCCjwwOstLzeCiZ5DfpNPNFTCpLCEGt0eBZIThGSuYF\nAXNqNb6Xz/PPExOcXKuxwXH4RksLy12X/YBJpRDEHb1T/dCdWtPi+/wskeAzIyPsFwSMSsnHu7rA\nGOYCw65LRWsqxlBwXXqjiLQxBEHAKqW4bmSE2VpTFYJzu7pYWq3iOg59iQQboggDLLANHq7W7LS2\njg9YTPWWdJqb83neNTJCv+uyLZPh0SgirdQejRFrwpAjgNdMTsYtF21tbFKK/z08zFrX5YlUioet\nJand/ps0m03WRRFvARZbauE3Ozo4sl7njRMTrHDiDu3Vnsd8IXCUigOEzSaDSvFaeyPX0mzynVyO\ny4aH2c8GCK9pb6cpBHOFYNJuasthiFKKfYBurfHDkIddl5uGh5lj4k7jj3Z2srDZJOu6lByHEa2p\nRxG9jkObDRDWWlo46OMf5+i3vOWvvma/mG3t36v5YMqL+9ytruM4pNPpF+wEDoLgbw7DVSqV6Rai\nTCZDIpGYaXr4B82M+J2ZvzjVapUNGzYA8E//9E9ccsklnHTSSbS3t9Pb28ull17KsmXL+P3vfw/E\nVWdLlizh2GOP5dOf/jTr1q2brjq78MILX5bP8e677+aOO+5gzpw5zJ49e/pHT08Pa9as4ZZbbuHf\n//3f6ejomP6YF4Jh/OL229lw551UtCaQEmEMw2FITikWRhGztUbbbt/bBwenvapXtrfTjfX3Solj\nQ2YHCMEx1Sp72R7XH2YynD88xAbHZUMqxW9dlw4bRnGEoOH77IwiDpzyqhrDE1HE0Y0Gx9brdGjN\nQ62tPOR5nDYywgal2JDN8gcp6VZqGgCgm01WRxEnC8HCep059TrfbW9nab3OayoVVrsuv89kWJZI\nsEAIHHtUPt5oMOg4HBvFfbBdtRrfKBS4fHiYRbYe7KttbYwpRa+U1EQM7BjxfRzHYQnQHYY4QcDv\nEgluHhqixxi22zfO2UFAznUZUTGlrGIMc12XFhvEGtWaMnCppZT1Ow4f7ejg9RMTTKZSDCYSbAxD\nIinZ23FIRXGH8YYwZD+t+Wd7VL48l+Pb6TTvGh1lSyLB1kyGx7Wm1XGY4zi4UUzTWmkMp2jNAdUq\nPUHAXR0dGK05sVxmtevyVCbDE0ox23HIS0kCqDWbbBCCt0URCxoNeup1vtbRwXvGxljk+6x2Xe6y\nKOVe+6buENsJJpTiKLsBTfs+383luHlwkA7rlf5MeztJoKhiuIIxhtEwpMWxcAV7zZ5RcRNHh4nD\ncZ+wTRwqmWRUKcbCkCrx5n4K+bvFGFr1ruq1p9Jpri0UeMvYGMOZDH2ex8YwxFGKxdZO4IUhK4zh\nhGaT11gC3M/b23nccThpdJSNiQQbrcWj6Mb0wUQUETabrADODEMWVat0hSG3dHayX73OQZOTrHFd\nHsjn2SwEc5UibbfgE80m26Tk7cYw3/ZD39LezmVDQxSMYYW7J6lM2e/REbtNP8xe23oUcU8yyW0D\nAySiiCctfXCW1uR285OPGUOv49BpDLPDkC3AeBTxudFRWo3h4WSSz7S2cnithr+bn7whJfspFbec\n2CDgIY0Gp1pwxa/a2viPZJITx8boy2bZ7rpsslvpKZyy9H2WA++u1zm4XqfLGL7+nMaIp9NpNtub\nmylvbq3ZZK0QnBMEzK9WyWvNl7u6OHlsjNlBwGrH4Rf5PBNCMNuJe4ydqRtHKXmr1syv1wmB7+Tz\nXD8wgAGWuy43t7aSB1rt65HWmmGtySnFgfY0ZbuUPOM4fN3SKR9MJLi2tZUlYYjreTSkpGkM844+\nmo/cdBOe572gyP3/4mitqdVqe2x1hRDT9LWpmdoCT9kgdpdPjuOQyWT+6hZ3fHx8+n0nn8/jOM6M\n+P0HzYz4nZm/OA888ADHHXccEL8QTD1V3vve93LnnXdy1lln8eCDD7J58+bpj1m5ciXnnXcejz32\nGG1tbZx77rkvC+Tixc7DDz/MJz7xCe688849bBcvBMP45Xe+w+Rtt/H+LVviWifbhDBHSlL2iN0E\nAZuN4QgpWRwELKhUeKhQIGEM7xod5U+ex5PZLA9JySz7xpW04aCnhOAj1SpzGw26jeHGri72qdc5\nslLhWcfht5kMTyUS7E/coBABw7ZTdoGIe3ZFEPC4lFw8McHcIKBdaz7b3c3sWo05vs+WVIoVnsdg\nFDHX88jabfN4s0mfUpzdaNBbrZIEPt/ZyYcHB5mUknWexz2ZDKF940xIiTKGft/Hk5LXhzHFraIU\nP8pmub2vjy2OwwrX5ev5/HTy3hUCozU7tGZvKZlvg1irHYeyEFw7PExZSh5IJLippYVDjKHpukRC\nMOn7lITgICnJRRFzgoCHpOTIWo13WmjBdwsF7spkeE2jwVAyybgQlIIAXJd9ZNxhnA8C/iAl55XL\nHBAEdBrDdV1d7AQOnpxkezbLVqUY0jG5q1sIEnYDtEpKPlmp0Ov7FIzhyq4uDq1UaNWajakUyywK\nt9d1ydij8pLvM6YUZ9lrG0nJjR0dXDIwwKhSrPU8fpbJ7GrikDHYY2cQUJCSY2wTR18iwf2pFLfa\nkNsTrsvthQKzgdTUUXkYssMYXiEl80xMgHvM8/BMDFcYl5L/k05zey7HYcZQdRwiKRm3GO9DZBzU\nnOP7/F4p3jw5OV1j9ZW2Nu5NJDiq2WTAgitGpvyj9mtNWz/5J8bG2DcMaTeGy3t6CMOQJbUa27NZ\nNkjJmBXFXWIXEGSDlHyiUmGu75OMIq7s6uK4cpmMMWy03mUf6LWBUkdrBu2Jw+nWTz7hedzR2srV\nFou8ynX5US5HVgg67XZZhCHbw5BOpXh1EDCvVmON/b74Wn8/mxyHRyy4YqEQuPZ525y6AVWK2Tru\nMb4/kWBOGPKx0VEqwF0WmnKYMUxY//tUgPAQKeMAYbPJb12Xd42Pc3yzSTqK+FxnJyuU4lW2MWII\nYpCI68bgCrOrMeJTtjEiH0Vc3N1NwfeZb1Heq6Rk0uxqjPCMYdwK009UKszxfUIhuKZY5G2jowBs\nTKW41/NASnqVmvbq9wUBUilOrdeZV6uxPZ3mJ9ksn+vrY7t9/bsrm6Vgr60nBFEYslVrFirFofba\n/imTYUgprh8YYLNS/D6V4u65c7n6G99g/wMP/Lu91v93J4oiGo3G87a6iURiD9LbXwvDTQnmqZPP\n5/795XJ5+n10pubsHzsz4ndm/n8/q1ev5qyzzuIrX/kK+++///TjLwTDuP+ee7j5qqs4t15nvt0K\n3lkssm+9zgF2c/WnbJaVStHrOGSlJBlF1JtNNkvJBbUae9VqdGnN5d3d7FupkDKGzbkc66Rkwhjm\n7nacX7JHtu9uNums1TBS8rXWVm7v70dFERtclys7OuiyfbxjdnM6vtvmNGUME2HIiBB80m5Oq0Jw\nfmcnbyqXqSST9KdSrNQaKQR7uTHa2NOazWHIQq05ZXKSnjBkUybDnZkM7x8ZYZPj8Gwmw0NC0OI4\ncRAripD2OPe1QnCQhVb8vq2NshC8u1RitePweDrNfTaIlVe76sE2EGNpFwQBc6pVvt3ayomVCsdV\nq6xyXX6ay/FEIsHeQhDarXTZep4PJw5iddbrfDeT4cpSif3DGHN8bbFIWQgWCMGYUugohlYkHWc6\nee+EIX9wHL5cips5qkJwTnc38xoNco7DoOsyGEXUree6YD3P5TBkXAguGh1lljFMKMWFHR2cVC4z\n4Xn0pVIsNwalFHtZr/QURXBBFPHWSoVZYcjqbJYfZDJ8YHiYjbuH3Oy1TUQRIgxZrTWvBQ6ym/tf\nt7XREIIzhodZbUNu99trm1MxXKHebLIJOP451/bNlQpvqFZZ47p8P5djeSLBEiHw5VToMhbFrwJ6\nwpCOZpPvp9NcWSpxQBiyXUquLBapCcF8savVoGxbDRYKQUFrpO0j/tJu1/bc7m4WTl1bz2OHMfjG\nMNvzaI0iklozEoZMCsEn7PN21HH4VLHIW0ZHmXBddmYyPKE1ztS1hWks8oIo4hR7bZ/O5/l5KsW5\nQ0OxVSOT4QEpd11bmIamHGuvbW+9zt3t7Rjg7OFhVrouD6bTPOh59EpJ1orihg0QvkEIFgQBs6tV\nvt3SwkmVCm+y3dv/ZgEYi9nlzR3f/dpqTavv86NkkstLJQ4KY5T3xZ2dNIRgryhi2HFoGMPEVIuD\nEOTCkEhrlinFF0ol5mrNpBB8sLubRfU6eaUYSCTYYgxhFCOOW6OIhPWz1+zztscYBjyPz7S1cdLI\nCBXPY1s6zWNRhKcUC5SaDmdunHreWqvGY4UCv0sm+eDQEJtcl1WpFPfb8OBs+1oyRSA8mngTPqde\n596992b+hRdy4mmnvdwv8S/pBEFAvV5/XsXZc8NtU2G4MAyfh1L2PI9MJrPHRtcYQ7lcnv7v1tZW\nlFJ/EzxjZv77MyN+Z+Z/xOzYsYNTTz2VK6+8kqOPPnr68ReCYWxau5ZbzzuPdLVKJorwTNzHOSol\nH5qcpLfZxIsiPtXVFUMDpGRTPs9TQhACi1yXpPUYDgcBKa25YHycWVrTrxTnd3XxlnKZ8WSSwWSS\nZ8IQ13oFHUCGIevDkH2UYr8wZFajwfJEglEhuGZ4mArwUDLJl1pbOTIMqXkeTSmp+D7jUnKgUiS0\npktr/gwcVa3yVhuM+nGhwHcyGV43OclgJsOwUvRb68IiGafDU0HAY0JwdqXC/pZ09/XOTrYAR0xM\nsCWTYbPr8qzWdLouXfY41/d9VgnBBfU68+p1Oozh2s5ODq9U6AoC1icS/DmVYoBdSGQviuJ6MCk5\nzW6SUsZwQ0cHVw8MMCkEa12XHxQKGJjG/SpjGAwClFIcZYNYVSH4RTrNt/r7KUvJU67LF1tb6SHu\n9kUIQq0ZNDEAoNsm77cIQUkIriuVSEQRDySTXNPayqHNJn4ySUVKJoOACSFiz7MNtz0ZRezfbHLa\n5CSdxvDrfJ7bslmOn5hgMJNh0HHYEQQox2Gx9Uong4DHgdOrVQ611WvfLhZZrRTHWZLbpkSCDVrT\n4cb0sEQUETSbrBCCDzabLKhWKRrDDV1dvLJaZVG9zlrP49FMhh1CMMfelHlRxLi1E5wehsyr1chq\nzU0dHVwyOEgCWOU4fKdQIBSCThVDU6S9KQuV4mitWeD7+Mbw00yG2/v7iYCnPI9r2troBHJKYeSu\nVoMepZhjfac7ga1Kcf3QEJko4lHP48r2dg5qNIimoClBTGB7hYoDhO1hTBybF4a8b3ycLmO4L5fj\nK7kcx5fLMSXPddlmvdJLVBwETAYxFvmkRoOjazW6teauYpEnleJNo6NsSKXYmEqx9jnXNmw2eUYI\n/rfvs6Rapag1X+nsZEGjwasmJ1ntOPwxn2czcYAwZ69tpdlki4jDmfNrNXJhyFfa2/nw8DCdWrPS\ndfm3lhZqQtCz27UdCQLqSnGM9dwbrflxJsMtAwNkoojlrsvV7e20Aa1S4suY5jZmDG1KMd/EcI4h\nYK1S3DQ0RFsU8YTncWl7O/s1GriJBCPWBlMDFjsO2SiiNQzZEEW0as2Hx8fp0ppHcjluyOU4fmyM\nMYuc3hSGSKVY4sRwDy8IWAG8ttHgeHttf9bRwaOOw1tHR+PnrLXBtLkxJt2LIqQx5I47jg/fdNP/\nVV22L2SNg7iZYXexuns92wuF4bLZ7LRtIgxDJiYmgFhMT9HddrdVzMzfb2bE78z8j5nR0VHe8Y53\n8P73v5+TTz55j997LgxjoL+f7593Hns/8ww7MhmGPI/tYUgoYyxowm6u1mnNkY0GJ1WrzNKaP2ez\nfCmf54RKhe3ZLCNKMeL7NB2H/aUkqTVzgoDfS8npExMc6fu0G8P3Ozp4yHU5cWyMbYkEW5JJnooi\n5rguLTbQUrcl9ScAvWHI7GqVf2tp4Z3lMsc2GqxxHH6Qz/NkIsG+xGEhVwhGm03qjsOBxESsYrPJ\nD5NJPlsqsW8YUpaSTxeLVIAFwJDj0Ih2g08AaWNwg4A/K8XnR0aYpTUOcHZ3N4tqNbJK0Z9M8qzd\nnM7drdd11Iqbj9rOUl9KLi0WedvICONKsTWX4zFACcF8u0lytebZIGA28JZajTnNJlvTab6fyfDJ\noSHWuy7rUyl+7Xm0SjmNRJ66cThESg62IbeH83lGlOLiwUFWeB5/8jx+mskwX+4CezSbTZ4FXi0l\nvUHAvHqdn2UyHFGvc0alwhYp+Uk+z/9JpTgYmLDeyCloxVIhaLVH3j/zPM4fG+PVvk8AXGODgAfY\nkFsFKAcBnj3yTmpNOgj4g+PwmSmSmzFcYENuc7RmRzrNFnjekfek77PVBgh7bGL/0q4u3jg6SiQE\nWzIZHnUcDLtV+FnLhRSC02s15tTrjCYS3NbSwmUDA+xwHNYmEvw8lSJjrRqeEAit2RqG9ErJPwUB\ncycnWZ3NsjyR4Ia+PtY6Dss8j2/n88wTgqSKA4S+77PdGA5UigU2nHl/KkW71lwyMsKQlNydyfCd\nbDYGUNik/bht8DhMSrLGMMdS8k6uVDilXseJIm5ub+d+z+PVvs9QIsGYEIzaVoN97NeaCwIeUoqP\njY2xvw1ZXt7Tw6TW7FersTOTYaNSjGlNq+syy17bhu+zRkoumZig1/dJRxFXdXezdGKCdq3ZnErx\niOdRs9+nUxajEd9nRCnOthVhDcfhK21tXDQwQEUp1rguP87l8CD2SkuJ1Jr+ICChFMeHIfOrVXYk\nEvxnOs2/9vWxUyke9zxuzefpESLeSktJGAT0GcNCFXeITxEIK0LwpaEhqsA9mQxfy+c5UGtC143h\nHkEQt8xMWYx8n4eU4qBGg/dVKmSjiG+1tHBXKsVrajVG0mlGhGAkDAkdh/1kTKTMBwEPC8HplQpH\nN5vTN2VrpeTocplt2SybXZdyKsXn7rqLvffd92V7fX+p54UWIwCu6z4v3DYVhvN9f4+TRIhD18lk\ncg/Iheu65HK5GfH7D5wZ8Tsz/6OmXq9z2mmnceyxx3L22Wfv8XtBEOzRwTg4OMhn3vtePrZ2LQf7\nPiKKuLWtjfsSCQ4PAgYSCWpCMOL7CMdhHyHIG0NPo8HdiQSfK5V4hRWXn+vo4Fkp2dseHUfEYTHX\ncdhLiGlx+bBSXD06SqcxZI3hku5ujh4fJ681m5NJHk2lGIWY9iQlbhQx3GwyISUnax33cWrNra2t\n3Nrfz5iUrHIcbm9pwROCNicm1gljGAgC8kqxXxSxwPcZjyIeTCa5vb8fTbzdu7Ktjb20xrOBlqnt\n3mLHoRBFzApDtkQRQRTxqdFR2ozhT4kEV7S1cVStRi2dZlRKSmFIXYhp+ERea1ZGEYfW67zVbpIe\nyuf5eibDSeUyO20Qa0MY42UX2M2pE4Y8HcV42YPrdXq05oe2yP/4sTHWJxKsS6V4JtqFl00AQbPJ\nSuC9WrOwWqU7DLmlWGRprcaB1SqrXZcHs1nWqhjskZISD6jYzekpVli0NZt8ra2NT1mU7jOOwzdb\nWhhXih4hECrubB7xfQKlOJSY5Ob5Pj/KZLhlcJCiiXG2ny4WyRtDu1JUpCQwhjGtp0luU+jeVUrx\n5eFhukxMCDy/u5sDq1X1050kAAAgAElEQVRUMsmQ4zCk43q6vex2L20MO8OQhDGcNz5Oj9ZsTSb5\ndGsrp4yNMZJM0mchCa5S7G3bCdwwpt0dovU0NOVP+Ty/SiY5q1Rig+uyMZPhYSFo380GQxCwyhje\nGEUcWKsxq9nkp+3tRFHE6aUSK12XR9JpHvY85jhOvDkVgkajwQYheBNxW8rsapVvtrfzpokJTrA2\nmP+wVo0pG4wr4qqvklIcCcwJQ9obDb6XyXBpqcTSMGSHlFxVLDIqBIvs91sYRZRtqG8JsQ3GDUMe\ncBy+UCqxQGvq1k7Q4ft0CUF/IkG/1jSiiE7HoQgkjaEahmyTkqtGRugxhroQfKyzk2PGx4kchx2p\nFE8St2rMdxxSxDeB28OQjBC8d3yc2WHIs9abfW6pRJ9SbEiluNdWHM61AVZpLR5LhOA4a9V4tKWF\npz2PywcGWOM4LEsk+GU6TZe1eSREXKO2KYo4Qgj2tT3avywUKGrNx0olNjgOv8hk+EU6zb6AtjeP\nlWaTfik5Qgh6tGZOo8GPUilOqVR4e63GOHBjezt/8jyWWpuKT3wz13AcDhCCnDG0+j6/dRw+bumO\nXhRx+aJFzDr9dM7+5Cdf3hf5l3j+K53Afy0Mp5SaFtKJRIJMJjP9+Mz8/WdG/M7M/7gJw5Bzzz2X\nzs5OLrvssj3u4MMw3ANB2Wg0uPqsswg2bmSxMfQGASnf54eZDLcNDNASxZjWq4pFUsbQ6jg0bBJ9\nOAhodxyWGMPCZpNGFPGfqRTf7O/HB552XS5vb2eB1qRdl6qU1Ozx5mLXJWU9pzvDkDTw3nKZLmMY\n9Tw+19rKB4aH2e44bM1meVAI0krRazenKgzZGIa8Ughebb2jq3I5Hk0muWxggFWuy4pEgp+mUnSr\nXUQsEwRs0JojpWTvIGBurcZ92SxZY7jQUqLuSya5K5vllUIQ2I+r2jfNVwlBl9bMbTS4O5nkzZOT\nvLVWY1xKvlUo8JtEgldZf6MRcYVa03HYD8iauELt167LJ8bGOCgIyEQRV3R2sl1KXtlsMpBMMiQl\no0FA1nWZa7d0yvd5XCmuGBtjrta0GsMnu7uZVa/T6ftsz2ZZrRTj1nNaABI2LLRTSi6YnGR2s0ki\niri6q4t3lkpoIdiQTPJAMhnXQ+2WoB/wfYxSvK3RYG6tRt1xuKOlhS/39bHDcVjtOHy3UCArRNzE\nIeIg1s4wpKgUh9kN6DbX5bFEgtv6+9kpJcs8j5taW1loDI7rokRMchuIIvZVik4TJ++XK4UbRVxW\nKiGBe9JpbiwUOCIIqHoeNSljO4GUHGBDbt1hyCNCcFS1ytutLeWulha+l0rx+slJBjIZBpViZxDg\nujEkwdN62gZz5uQkS5tNuo3hjs5O1kvJa61VY2MiwSatKVo7wVQf8QohOK9eZ6H9/13f1cWSep19\nq1XWui6PZLNsZ087wYS1E7xX6xiLrDU3dnRwwdAQLVHEStfl+/k8VRk3nXhqF4CiqhSvN3EQEK35\nfjbLLQMDJKOIZ1yXa9rbyRF3PYdSorVmRGvySrG3DVmWo4gnHYdbhoYoRBFPOw6fLBZZ7PskPI8x\npaiEIZUoYqHjUDCGdq3ZFkWYKOLSsTE6tWZVMsmnWls5bmKCajrNgOuyOQxBShbbxpJkGLLOGPYL\nQ94+BfdoaeEHqRSnjoywNZHg2UyGJ7Um7zjMszccIghYpTUnGMMR1q//k44O+qXk9OFh1rguT2Qy\n/FkpepSi3Yppv9FgDfBWYEk9xq/f0dHB0nqdt0xM8Izj8MtcjqdsjVrCnjpVGg22SckJwPwgoGjB\nKR8aGeHVvs86x+GGtjb6lWIRtqIuihi3Fo+DiX3P2Shi2/HH88EbbySTyfxdXu9finmhfAjEFWe7\ntzXs3gncaDSeZ5uYmnQ6TTKZjHux5QzZ7R8xM+J3Zv5HThRFXHHFFfT393PDDTfscfSktab6/7D3\n3mGSlXXa/+c8J1QO3V3VVZ1mhmEGhkEkSg6KmNcMKCj7oq6iC4iICUFYQRAxEFSCgMi4ioBhlVUE\nFASUIAgDTE5M6ByqOlQ64XnO+8d5umcQ3N+uK/jbfft7XVxATddMcajuus/3ue/PXa/P3bkHQcCN\n551H//33ExoGMcOAIOC5IGC5abIsCFjUbLI2FmPAsrhkZIR1lsVjjsP3MhkWCjHHOVW+zyYpOdw0\n2V1vZO7NZOgMAs6qVBgVgnuSSa7PZjnG95nSonjC8/Ati720sEhq7+iJ9Tqv0t7Rn3d08KBt84bJ\nSbYkEmyLxVj9Z4Ik9H1WAh/yPJbU65Sl5MbOToquy0EahfZUKsUqIXZu6dCWC8PgvdpfW3ZdrigU\n+FClQq/vs8q2+Xk2y1YzwnzZQpdPaBLCq7W/Me+63JjL8Y3RUTqkZI1t8/W2Njwh6DIjzJcRhkwE\nUbHIHkRBLCMIuNdx+NboaLQBNU0+3tlJdxCVVIybOxFqPbZNRxiS0UHAQSG4cHycLqWYNAxOK5U4\nenqaIB5nKBZji1LP82rHNK0iH4Z8QHNdB2MxvpzP84+VCv22Tb/musbNnVxXOwhYHwTsF4a8pl6n\nx/f5UzbL72IxPj42xjrLYnUyyb2aAlLUNw6h77NOSl5tGCx3XRbU6/yyrQ0nDPnnsTGedRweiMX4\nVTLJ7qaJrZ/XdF22AUcJwcIgoK/R4LZ0muPqdd5Tq/GcEPwwl+PeeJwDiKwaQtsJprRVo11Kyp7H\nTx2Hs6pVDtNWjYs6O9lkmuwTBIzaNtPAVBBg2TZLgIRSpHw/KkmYmGD3ICAdhpzd1UXc81jo+1GT\nIJFVo2jbdBo7yQ+bheBzmvXshCGfL5c5enKSeBiyVVs1XCKrRhKwlWLM86iZJh+q1+lrNmnYNld3\ndPDp4WEqQrDWcfi3VApHiCjkpm0wA0FAUgjeoBFhO+Jx7komuXZwkB2WxZOaWNJpGGS1nUAGAYNS\nsptpsoeULGq1eNZxGBWCK0ZHqQG/SST4Ri7HPkqhbBtlGNR9n3FgH9MkH4Ys8DweNk0Wex5nTE2R\nCiOO9ncyGY5uNplMJCKqhufhmjs52nnf5xHD4K0zM7zedSkpxfcKBX5j27x+cpId6TTb7aiWO2Xb\n7CZEFJj0PJ4CPtho8MpWi06l+FaphCclR01NsSEWY6XGqJVnMWpK0fQ81hoGH/E8Ftfr5JXiG52d\nvHp6mr1aLdbYNr/KZhkCeq2oetoOQ6Y1aeI9SrGw2SQeBFzf1sZ5+vv0Gdvm6nweJSJEnRACIwyh\nrY3Trr+evf6H0SBmw3C7jmVZJBKJ/3QYDuYZv/9/mHnxOz//T8+3v/1t7r33Xm666SYSicTc40op\n6vX6XIBBKcW/XnYZr7j9drorlQiFlkrxsGmy0LLImCYO0fH6WuC9YciSep0e1+X6YpEjajWWN5us\nsm3+kErxtGWxUB+vxwyD6VaLHWZUm9obBHQ2Glyfy/H58XH2DQIGhOBrHR3ssCz2UipKhgMTQUDK\nsliwi3f096bJlyoV+qQkqxRndXXR4bp0BgH9ySRbDYMppaJmK6INaM332S6iRqxu3ycZRpilt2jv\n6JZEgsdsmxawwLZJaH/jiOfhC8HJzSYLmk0CIfi6DqsNmhHm699SKWzDoGxHEH+h1AswX2O2za9S\nKW7QCLWnLYtv53J0GwYJy5pDqA1IyRIRIdQWeh4bTJNR0+TykRGawEOxGJe1t7NfEBA4Dr4QkSAJ\nQ/YzTZJhSJ/v8yed3P+nqSnawpBfp1J8I5fjNfU6Vc11HfN9PBFxXR2lyAYBTwBvrtU4znUp6RuO\nnzsOb5icZHsqxYC2amQtiwU6LCR8n6fCkA+0WuzdaEQVvMUiU2HIMVNTrI/FWJtIsArotiw6dFjI\nc11WGwanBlFDYGcQcHVnJ0fPzLC82YyYzek0m0yTPtMkoZ835br0C8E7wpBFrRZtrRbXdHTwudFR\neoOAVY7D9fk8VdOkxzDANBFhSMXz8LRVo8/3ifs+tyeTXDUyQq+K6o3PLRaJhyFlIZg0TQIVkR8y\nlsWiMKQgJZ6UPGGaXDE+TllKxoXgo6USezSbpGybYcdhWNsJFuj3YFxKqkHANPDZapUuKanYNp8u\nFnlzpUJd33CsVAohxBxVw5KSrUFAOQw5SZMfNqZSfDed5mNjY2y3LDYmk9yvQ4C9mvwggoCNQcAr\nDYOj9cnIH/J5Vts2542MsMq2ecJxuDOZpCwEbfqGI5i1EwjBXp7HwkaDX+ZytEnJOePjbLAsfpVI\n8NN0muXstBPUXJfBXewEfa0WP0skeEO9zntrNaaBa9vbuTcW42BtJwgMg0ndeLefiDBqnZ7Hry2L\nj01OcoT2IV/Y2clG0+SgVouhRIIhYDIIiNs2i0WE/zM9j8dNk3M1Ri0XhpxXLpPyPJY2GmxLp1ll\nWUwqXZxiRPi1mkbUfUYHfe0w5KJSiTdWq+SVrjhOJmkRieJZRN2E5zFumnzAdVlYr9OyLK5rb+eC\noSFcw2CVbfODQoFD3/52PnXZZf+jBOBfYgLPNsPNzq7Vzq1W60XDcP+Ttt//22Ze/M7PyzbXXHMN\nX/3qVxkeHmbvvffmyiuv5Mgjj3zRr926dSuLX6Qq89e//jWvf/3r/6av64477uC6665jxYoVtLW1\nzT0ehiH1ev15R1fXX3YZK3/6U06vVulxXXJKcUG5zBsrFSxgYyLB4/E4VaVY5Dgk9YfIuA5GfbhW\no7fVIgZcUCpx1ugo00Kw0XG4K5lE6a2VrYkGg55H3DQ5SEVs1lYY8stEgu8OD2PqI+DPFwosCCKQ\n/owQcxD/RZZFXikKUjKhFKPAv+gj2e1CcEapxBEzM3iJBCO7CJI9tE8xLiXbNTXi/0xPU5aSgViM\nC9vaeE+lwkA8zkAyydNS4phR/fOu3tGDleI1+kh2ZTbLL+NxPqKbrTalUtwvBB2WFbXWAYbvs0ZK\njgNeof2N97S30wA+PD7Os9oicFciwQIhSOntnqsxX68Rgt10yO2OXI6Dm03eOz3NesvizlSKuxIJ\nXmEYtLQgma2JPdgw6Jz1N8bjfHBykte6LlPA1R0dPO447K8Uo5aFT9Tsp0yT5UKQUooOLUjOq1RY\nrjegnymXmQpDlnkeg4kEg8CklC9ou3tKCC6oVumTkpyK2u52azQoeh7b02me1YKkV1s1ZsXtgGly\npn4vOUSb2veNj4NhsGEXQdI36w1XihHXxTVNTvA8+up1PO0F/9rQEBNCRHSCXI6EYVDQYTUjCBgK\nonrjw7SdZVwIfptI8N2hIaaF4DHb5ittbSwgKnvBiHjEozqI1aXJD1uAUSH4ytgYiTDkYU1+OMB1\nkfE4U0Iw4/tMA3tZUUlHIYiqo7uDgI/q6ug/pFJcls3yhslJKpr8sC0IwDRZpj3lCd/n2TDkKNfl\nzY0GXVJyd3s7v3AcTqhU2BKP81w8zsowJG9ZLNA3DsKPqsvfHQTsX6vRJSW3FgpMAidMTMzZCf6o\nv0/b9U2vp296jweWNpt0N5tcXyxyaLPJG3axE6x0HBZqO4Eze9MrBK8jshOUGg1uyuf56MQER3ge\nGyyLq9va2GJFRTI100QQNd41LYv9iE5GMp7Hz+Jx/kUj6qYNg0+WSpEXPAwZtSxmwpAZKefwfyl9\nY/aYGTXeLZSSEPjncpleHV4bTCbZGIZ4amebYEwppnyfARFVHHdLiWuafKFY5PXVKgawNZ3mD0JE\nbGHLIkW0vR/0fULD4IPaZjSeTHLv617HP3/zm+Ryub/pz/WXcv4SE9hxHOLx+JyYD8OQIAiQUr7o\nBrijo2Oe8/t3mnnxOz8vy9x2222ccsopXHvttRx55JF8+9vf5uabb2bNmjX09fW94Otnxe/dd9/N\nvrscjbW1tb0kXMT777+f888/n+9973v09PTMPf5iZRgP33UX//qlL9ErJXGliCnF9iCgpBSnTE7S\npRRjts35HR2cNDFBfzxOfzLJM1JizgaMlMLRtIgDg4DjajXKUrImnebHqRRnjY6y0bLYGI/zy1iM\nohC0a5GogoDNUnKAECwJovKJRxIJBHDe+DjbheDBeJzrcjn2V4qWFVUbN3yfUeAAIcgpxQI/qtE9\npNHgffU6dhhyeybDTek0r3ZdxuJxakJQ1RvB5SJCoRWCgIcMg/dPT3O451FUihUdHdztOBwzPU1/\nOs2wZbHd90nPegeVwvJ9njAMTq/V2FNvTq8rlZiSkoNnZticSLA+HmeTlHTFYrQbunxCb0A/6nks\n0iiqb5RKHDozw+6acvGHTIbNOiiU3MU7ul0ITlARiqrddbmyWOQzo6N0KMUq2+b7uRwV06RLCCwR\nNbJNuC4N0+TwMGSR75NyXW7JZLh6eJhiGLLWsvhSRwcYBiUhaAhBGIZUgoCkabI7kSCZbQS8enSU\nslIM6xuOHs8jZ1mM2jaTUlLXW/gOHVar69DWFycmKMuImfuxcpmjJieRsRiDGteljIjZnAgjHN9g\nEBALQz6sqRoTsRiXtrfzj2NjjJgm23T5SkyIOauGJSVbfJ9FhsGbNLN5QzrNL1IpPj80xCbbZnUs\nxi8SCfJCREUSADqItY8QHKA3oI9ls5HtZ2iItVZUJPGDbJZFhoGjqQae57E9DDlACBbKqHHs3kSC\nbt/nU9UqFRGRH27W5Ie6ZREaBjOex4QQ7G8Y5LT3/h7L4vW1Gic0m8TCkJvyef4tkeDIVouxeJyq\nEIx7Hsq22VsIHG0neFAIPjg1xaH6vfvNzk6eMc05OsFW22YgCMjYNgu0nUB5Hk8bBmfo925BKb5a\nKpH2PA6q1Vgfj7MykWCrDlp26Pdgw3VZbxicpt+7ef28t1WrLNKtgP+ezTJsGPSYUeOdHYZMag/9\n8dpOkPB9rmtv5wuzdgLL4pvaLlQWAkPnDCq+j2dGTOxFngdS8rNEgquHhymFIetMk3M7O8koRadp\nMiUijNqUUqQti93CkLIOWj5pmlw5NkaXUgzo9+7SVou0FXGbh6TEDUN6LIuOMCQhJRWlmALO19v7\nIcfh3EKB4yoV3F2296YQLNY32TEpaRSLvPeKK9j3kEP+5j/bX6r5S9XIEG12d930vthYlkWhUPgf\ntfX+3zTz4nd+XpY55JBD2G+//bj++uvnHttjjz04/vjjufTSS1/w9bPi9/HHH+fAAw98WV7j008/\nzUc+8hGuvfZali1bNvf4i93lr3r8cR74/OfJDg0xFI8zKQRjnkeoEUsxpWgPAh4CPjQ9zas8j06l\n+H5HB792HI6cmWEolWLIstihw1sL9Qe08H3+BHy01WJxs0mnlNxQLJLzfQ6fmWGdZfFUKsWT5s6i\njVlf7mbD4G1hyELXpbfR4NqODk6pVtnfdVnlOPwkneZZx2GxECi9tapqGP8hROn5UrPJLek0F+gS\niW1C8LVCgQEhWAJM6HRyRTNslxoGbUFA1ve5y3G4fHycRUFACHy8qwvL9+kFhmMxxsOQKRlxVstE\nKXiCgGeE4CK9RUqFIWeWyyyv1UgB/ckka4SgoRR9swg1FbGXJ4Tg49PT9Pg+ArhAb0CbQrBZFxYE\ns2E1bdUY8jwQghN0a1jDtrm2vZ3LBgYYsCzW2DY/ymZJGDubrQwZNWLlheCIIGBhs8mIbXOP3oAO\nCsFTjsM38vm5RjbTMAiCIOIKmyZ9UkZcYSEiG8voKAbwsOPwxY4O9vN9pA6r1YOAahiy3LJIKxXd\nGIUhHVJy5uQkBaV4JJHgi/k8r52ZYSqVYtS2GfJ9AiFYrjegySBi5h7cavF2TdX4fS7HzYkE76pW\n2ZFIsEOTH9KWxW46UGX5Ps9KyZuDIApUSckvOzpYZVmcND7OOstiTTrNI4ZBybIi7yhR2cHqMOSd\nSrGs2aTHdflhoUBHEPCeSoVnbJsHdZtbn2lG713tX95iGFFJh+fR22jwvbY23jwzw1vrddZbFj/M\nZHg4FmNvw6ApdiE/WBaHAN1SUmq1uDWZ5MxKhaM9jypwabHIOstiX31T6odRAUpoWSw3DNJKkfM8\n7rEsLpiYYLmUxMKQc7q6aEjJnr7PUDxOv2EwrYNns0HLUIcPL6hUWCglyTDkc+UyuzWblF2Xrek0\nT1sWM0rR5Ti0E21AZ1vZzqnV6HZdTODSUonjx8eJAetjMe5JJvEMg27TJKm392P6BOl9rsvCRoOW\nZXF9Ps+XhoZo6e39d3M5HMOgICKUH1IyqpnYr9Y3HBOmyV3JJN8ZHCQAnnAcLu3ooBSGZEyTUOwk\nu3SaUcX7Qt+nH1hvmnx7dJRkGPK4bXNuocDenoflOEwKwbSU1MKQ3W2bvFIUpWSzUhhhyLmaZLMy\nHufCtjaOmZqilUox7DhsC0OOOv54zrjkkr97CGy2wW3XNrc//+e/dkzTxDAMMpnM/yj28f+2mRe/\n8/OSj+d5pFIpfvSjH/Hud7977vEzzjiDVatW8bvf/e4Fz5kVv319fbRaLZYuXcrZZ5/9vOe/FLN1\n61ZOOukkLr30Ug7ZZQvxYszHpx5/nO9/5jN8ZdMmeqRkRESIpSnDYDdgzLKQYciE75OwLBYRIZYy\nvs+9jsM3xsbo0ZaKf+7qIud5lMKQ4ViMQYg+MLUn0lGKGd9nhxCcPT0958s9r1TipPFxlCYTPJhI\nUGMXFJpSjHoeDSE43vdZWK9jGgZXtbfzjaEhxoVgrd6AGoYRiRgRcUeHNXf0UKVY2GrhhSE/TaW4\neWgIF1jpOFza3k4xDElbFlIIlJSMSUmXadIThvQFAZUwZJVpctXoKNkwZLVlcU6xyF6uixWLUTVN\n6nr7tNS2SStFm5QMqqi16tPVKiUp2WFZfKJY5LjpaWYSCUZiMZ4LAqQQLNXp+ZiUPBcELFCKk6am\n6FKKbYkEl+dyvG9ign7HYUcqxWNKkTBNFtk2sTDE0mG1A8KQY+t1uj2Pp3I57onFOGtsjPWWxdpk\nkntsm3a9AZ21aqyXkiMMg3205eKBfJ5JIfjUyAirbZtHYjF+mk6zyDDmgo+e67IFOEwIFgVRAcVd\n6TSLPY/Tq1X6heDOVIofptMcEIbUtZie0VaNVwlBXkoWuC6/sm3eVK/zrnodE/huPs9PkkmO8jzG\nHIcZHaia5bPGpKTg+9xvmvyT3oAW9Ab0CdPk8JkZ+lMp+k2TwSCYuzGLqaim+09C8PGZGfZ0XTqV\n4spSCVdKDpmeZmMiwZpYjOfCkE7Hoai3967rslqIuZKODqX4Wmcnh9dq7NlqscayuD+TYZsQ9MyK\n4jAqktgqBCcrxYJmkzbP46pCgY+PjbFASp61bW7J5RgzTXr09t4MQ6peVDl8TBiy0PNIeR7fy2T4\n6ugoC6VkvWVxUUcHvmHQJwQzQqDCkEldnLGX3oCaQcA9jsNVo6P0KcW4YXB6uUyb71MyTUYsi6pS\n1JWiw7LoCkNSSuFKyVoh+PLEBD1S4urn7TszQ1wIBpJJ1iqFBPpmLS1SMq6Z2J+cnKRbSmZMk4uK\nRU7QN3RbUikeNE2EECycvaELAvqDgJgQnFyv09tsMphMcks2yxeGhhg0TdbEYvwkmSQhdoYBZ2ug\nC0JwrO+zsFZjQyrF7xMJvj0wwHbT5HHH4bpcjm4gre1YfhAwpKKimGU6DPi04zBqmlypvff3xuN8\nva2N5UGAmPXeex4TwN6zYUB9EtQhJZ+pVkmFIfdkMvzrfvtxwY030tvb+zf/+T4rd14qYfvn4/s+\nlmVhWRZCRIE/0zQZHR2lWCySz+f/Zn/W/PzXZl78zs9LPoODg/T29vLggw8+z+N70UUX8cMf/pB1\n69a94DkTExOsWLGCI444Asuy+PnPf84ll1zCLbfcwvve976X9PWOjY1xwgkncOaZZ/KmN71p7nGl\nFL7vP++Ya2x0lPNOPpmFk5MslJKFetv0iOPwnZERWkQi8YL2dnZXCsuy8IUgkJIxpVhimrSFEWKp\nH5gAvqh5uRs10eDomRlaiQRjts0OKQkMg6VWVPU6K/Z6w5D3TE1RlpLhWIzL29r40Pg42y2L7ek0\nDxlGxA+1bWx93L0pCHgFcHSjQW+rxfp0ml8nEpw3MsLaXY67202TghnV6KJpFQcIwSu02Hsik2HE\nNLlIUy7+6Dh8N5tlqWEgtLfR9322hyEHCkGPipi5D8ZidAYBn6xUmALu1jD+Q5VixrJQImqtqwrB\n/iIK/PTqY+uj6nVObDTI6PT8Tek0r2k2GUskqJgmo56H0nSMmJTkgoBHgRNrNY7Qlosf6y38GyYn\n2ZpKscNx2BQEZB0nOu5WCtP3eXKXsFqXUqwoFhkHXlutsj4WY10iwdNAlw6rxYDAdVllGJwiJUt0\nTfZ1xSLLm02OnJlhlW3zYDrNU9pvmtLb+7quyX57GLLIdemu17m2UOD91SqH6NT9DzMZntXsW188\nvwJ6ln3b2WyyIpPh3LExDggChoTgskKB54RgL8NgwjQjq4bvg2WxF5CTkpze3n9pfJw9ggADOLtc\nxleKxUHAUDzOSBgyoxQZ06RPn3II3+dJ0+TiSoVevb0/p1ymt9mkpP3La4RgJgzptm3a9POmdUnH\np2Zm6PU8nDDkwlKJt1YqxMOQDfqGrk7kX07q05Fx/b74P5qOEQrBlR0dXDA8TMswWK1xaBgGJdMk\nbpoIKRnRfu3Xywg11zAMbk+nuX5wkEAInrSjVsA2wyBnRq2ASkrGZYRDW6YUi3yfShjyqONw/chI\n1MpmWXyuWGShPsWZ1CcVM0rRY1kUw5BOGbULDhsGl46PU1SKLfqG7uBaDeJxhh2H/iDAN4w5bnNC\nKfqDgHgYcqa2tGyNx7m4vZ13TExQ1Td0T2jv/WLrhTXQx+sw4LOZDLelUpw+MsI222Z9IsG9GjM3\ni0k0fJ+NQcArhOCYRoM+HQZc5ThcPDjIGsfhj7oopiwEeX06EngezynFK4VgH03WuC+bRRkGF42M\nsEMI7k4k+F42y15hSGhFzPG65zEM7C8EXUqxyHVZuXgxx33pS7zqmGP+0z+3ZxFjsyL2pRa2ENkb\nDMOYE7ZKKVzX5TBhUksAACAASURBVMknn+TUU0+lUqmQyWQ48MADUUohpUQIQWdnJ+eee+7Ldqo5\nPy+cefE7Py/5/DXi98XmjDPO4KGHHuLpp59+SV7n8PAw27Zto7+/ny1btnDdddfR0dGBZVkMDg4y\nPDzMM888QyaTed7zZmZmuPK002ht3IgwDBzDQPo+m5TiKMNgcRA1Nt2VzdLt+3ysWmWDZfG7WIzv\np9O8UghcLRIbnsewYfAqIchJyQLf527L4rhajXc0myTCkNuyWb6fTnNsvc6oJhMMex6GbbOnFgcp\n3+ePwPs1m7VLKX7a0cEDf4ZCWyMl7bZNjyYaGL7PyjDkA15U9VqWkh8Ui/hKcezkJOssi2fTaZ4Q\ngh7LIq9FW6B9uScpxW7NJt2tFjcVixxcr3NUrcYq2+a+VIrHYjF2EwJHi7aa5ofOBn5663VuyOf5\nYKXCEZof+oNcjscdh+XsbK2rui4zlsWBQElKyq0WtyYSnDsxwYG+zwxwaWcnG0yT5UoxbkXorIrv\nY9o2exC11uU9j3ttmy+Oj7NURhzSz5bL1JViD9dlIJlkwDCoSEmbZdGtN6eh77NSCM7XYbU2pTiv\nXKa30aDX83gulWK1bTOqdFhNH5PXXJfnTJOPa1xXOgz5UrnMO8bHyYQh6xyH+1MpKkJEBAe9Aa24\nLqOmGVVA1+vElOLKQoGLh4cxwpDVts338nlcIejU19cMQ8a1X/toFfGBhe/zr5kM1+kq3Wdtmy+1\ntxPXx+QtIUApJrR/eSnQ4/v4SvE7x+Ga0VE6VYSaO7Ozk27tXx6zLGpa7JUsi84wJCslDSnZZJp8\nWZMfakLwsXKZA2ZmsGyboXicjXoDusi2Sevt/VgQlaKcrb2jNcviC8Ui7xofpy4E23SgSgjBblrs\n2XJnkcRJtRq9rstIPM538nnOHRqi37JYq2/oEvr9O4tD2x4EFIXgONdlQaPBlmSS3yaTXDUwwDbL\n4inb5oZcjiKQtSxiQiB9nwEpWWCavEJvQNfaNpsti2+PjFADHozF+EpbG3sqhWnbSCFo+T6jYcRt\n7tB2gmeNCPF34cQEqTDkwUSCi/N5Dm408PX3eMX3qRtRUUxC26pWhSGLg5010LNVxW+uVhnX9JEN\nQVTusYdtE1MKOwhYqxSHeh5v0ZaW+9rb+fdYjPePj7PJttmcTvPHMHweW1j4Pquk5LVhyGG1Gt2+\nz793dPCcaXKGPuV4IpnkfsehJMQcW1h6HuvDkGMNg71bLfoaDX7S0UFWSj49NsaIEDyQTHJjPs/b\n4nHcTIYwk2FDLMalK1aQzWZfIGz/krj9W86fC1uAqakphoeH2bFjB1u3bmVgYICBgQFGR0dRKiKR\n9PX1EQQBt99++9zvZZom9913H0cfffTf9DXOz18/8+J3fl7y+Uu2h9NPP501a9Zw//33/6d+n1tu\nuYWPfexjz2th+1vOcccdx29/+9v/8GseeOABli5d+oLHm80m151zDu+55x4C32edZfFwJsMGw4iO\nJ7VIrLku20QUwlrYbNLZanFlocAnx8boUYpVlsUd2SybbJtFhoEyTSygokNY+xHB4guuy62JBJeO\njbGnlNSB80slJoClSjHiONSBShCQtqwoYS53otAumZigVynySnF2Vxdp16VHs1m3GAYVbbmYrdFt\neR4bRFT12u155MOQ80slDp2eJislmxIJntKe3j7bjo6tlYqCO6bJh7S/Nh2GXFoqceboKCGwxrL4\nVTbLlBD0aI+irTd700LwVhWF1WJBwDXt7Vw5PEwIrLZtrtH80KIZ8WtFGDLmeQjTZH8dVhO+z49T\nKb4zPExOh9W+UCySkpKCZTEjBIGKmtXylkVfGFKSEj8IeNSyuEo3q1UMg9PKZRa1WmR14GdcH3f3\n2DZtekPX0GG1C3VYTeqw2tGTkyjLYiCVYlUYzom9JNFx90gQRF87OUl3ENAyTb5YLHLq6ChTlsXm\nRIL7bRuxi3/ZUop+3ydpGLxb0zEqsRg35nJcOjjIDttmrWVx26x/WW/vhZQMBAF5IThaWy4GHYd7\nk0luHBxkSAiedByuyOcpAykzqnKWUjIsJb1mVKW70PPYZppsME2+NTKCATzqOFzQ0cGenocVi9EQ\ngpaM6CNLragQoltKtoRRK+D5lQodKuLBfrZQ4IiZGdxUilHLYigI8AyDZdrSkpKSLVJSlpIPaUvL\numSSS3I53jkxwVgiwUAiwUq9AV2iLS12EFVe7y0lb9NFEk9ls9yeTPLPo6NssW02aPpIzjTp0RtQ\n0/cjK4xhcOSuODTdrrbKsvhTLMa/JZN0ip2BVOn7bFGK/YVgH89jUaPB/dksnt6AbhGC+5JJvpdO\nsyeAZWELQct1GSAKpHbr05H7YjH69OmIB/w0neaGbJaDdZlJSwimPI8pIeZwaD36dOSwRoP31+vk\nwpDb83luSSY5bmaGUV1mMuz7hKbJXlaE5Etpdvg/1Gq8TrPDf6TZwm+rVtmaTPJcLMZaKcnYNovM\niEls+D7PhCHHuy6vajQoSckK3bB3xtgYg6bJ4/k8K2Ix3l4oYGWzkbidmWHJnnvStfvulJcto71U\noquri0wm83cRtpOTkwwPD7N9+3a2b99Of38/AwMDjI2NoZTCNE1KpRK9vb309vayYMEC+vr66O3t\npVwuv6Cp7fbbb+e0005jcnKSY489lnvvvffv7mWen50zL37n52WZQw89lH333fcFgbcTTjiBSy65\n5D/1e5x99tnceeedbNq06SV5jaeeeiq33HLLf/g1t912G8ccc8zcD7FdKRBKKS748IdxVq7kxMlJ\nunUb0AVa7I0LwaZkkvtjMZRhzB0z2kox4Hk4QvAPnkevxlDdkM9z/cAAg5bFah1sSQM5fVyIUowE\nAR2myZIwpM/zaCgVkR6Gh0mGIWtNk890drLQ90k4DlO7iJFFOpDSLiVTUjIgIsJASUqqQvCRUolD\nZmZQ8TjDsRg7pMQlKoNI7rKhU8CZ1SpdStEQgk91dvKuiQmqOt39BNGHzWItDhwp2R4EtAMnzszQ\n4/tUYzGuyOf5zPAw2y2LDckkdzkOcRGxWR3DwJSSbb5P2TA4TlsuBhIJ/i2d5uqBATZaFqsch5sz\nGdqFIK8JA2hP5ALT5JX6uPs5x+Fpx+Eajfl63HG4LJ9ncRhGNBHtbRxWimWmSTGMCgs2GwaT+tg6\nHoY8atucXyhwYKuF1MHHac2r3dvSuC4p2agUeSk5Xbf0rYnFOLejgzdOTjKpAz/PBQFKCPYwTeJA\nPAjYKCV7BgEnatG2LpXiykyG91cq7HActieTPBaGJE2TRbNhNSnZEATsrxTH1et0+z5PZrP8Oh7n\nnNFR1to2axMJ7rZt2kxzJ2pO/3kHAQfqDegjuRxbbZt/GRpirW3zmONwazrNAiFI6uvrex5bw5D9\nhWCpFtMPJZNYYcgF4+OMCME9mj7ySqXwtYive15EHzFN8vq4+yHbZnfP4/TJSWzgF+k038pkOMp1\nmYrHmRaCim5y21eLr2IQ8BhwRKPB8Y0GRaX4VS7HjakUb6pWGU6nGbRttgYBlmWxVD8vFkRV2W9q\ntXi1xqH9sqOD+2ybd1cqbI7F2JxI8KcwjCqnLYtYGNU5r1KKt0vJ/rUa3UHUrjYmBKeOjbHasngi\nmeQh26asRXGMaAO6BngLsEzfrPyoo4NSEPCh8XHW6ADlrxMJdjej5ro/LzNZ5Eeti7dlsxzeaHDq\n9DTDQvCv2Sy/SCQ4MAyZsSwMIyozqZgRyq9NSno8jzsdh3dOT/OOZhMT+FZHB3fHYhzRajEajzNp\nGFR8f84fHpeSDt/nd6bJqVNTHOV5dCjFNZ2drLEs/nFigsF8nmfTae6SkrcvXIjI5VDpNBNBwOK9\n96Zrr70o9fRQLBbJ5XKY2nLzUgrbXcVtGIZ/UdiOj4/PCdtyufwXhe1fK1q3b9/Oxz/+ca655hq6\nu7v/pv+d8/Pfm3nxOz8vy9x+++2ccsopXHPNNRx++OFcd9113HzzzaxevZq+vj7OPfdcHn/8cX7z\nm98A0ZbXcRz2228/hBDceeednHfeeVx++eWcddZZL8lrvPzyy7ntttvo7e2lp6dn7u9dXV08+uij\nrFmzhmuvvZZYLDb3nD8vwwjDkFu/8Q0e/vGP6Q0jBJUtJWul5CjP49h6nS4peTadZkU6zQc1GH9b\nJsNDYUjeNOnWGyszCFgbBBxpGOzbatHbbPJYNssW2+bzuqL4Ke0BXai3pjEhCHyf55TiQCFYIKNG\ntsdiMWJKce7EBFUhuD8W48p8noOUoqH9tQ3fZ4zIe5cOozKIx4RgmevywelpMmHIb5NJLsvleG2j\nQeXPyiCWa+tEPghYCRzVaPAPzSYlKXksk+GqTIZ3Vqv0p1IMOg7rgoCYZbHEsrD1cewqpXij63KE\nFiN/yOf5VSzGKbpaeUsmwx/CkIJl0TV7HBsErJKSN4Uhr6zX6fE8ftPWxqBlcZouLFgZj/OreJxu\nM6pyjhkG0vPYEIa8GthDi+m78nkySnHW+DhrLYsH4nF+lE6zzDAI9fVtui47gEOFoEeL6buSSV7R\nbHLa9DRTwM/SaW7KZDhMSqZsG6U3dJNCcICI+MC9nsd9pslxtRrHN5uktKVlRSrFsY0GI4kE4/r6\nStOM/MtKkfWjuuF312oco/3LP21v585YjDdPTrItkaBfb+iyVlSmEgtDTG1pObnVYn9dtnFHocBm\n0+SdmmG7LpXij0DZtuk0I/at8jxWhSEnKsWeWkzfWiiQlpITJiZYZds8rI+7F1nWnH/Zc102GAZv\nBHbX1/cH7e0c0GrxPm2h+UUqxa8TCZYbO6uyZwshDjMMeqSkr9nkx8kkb52Z4d2NBjPATW1t3BmP\nc6hSTFgW0jCo6ga4WX94j+tyl23z/qkpXue6JMOQbxUK3GfbHNVoMJRMMioEo76PZUd1zjEpSfs+\nDxsGH56Z4SDPo1NKrimVWCOiOufnkkm2OA6bVVRn3qv/v8zi0D7SbLKs0aCkFNd2dkIQ8NrpadZa\nFivTaVYZxpw/3AlDfNdlFfCPSrGkXqfk+1xbLLJvs8lx09Ossm3uSaf5k962JrRlqN5qscUweAuw\n2PPoajS4ob2dd09N8YZGg/WWxYpdLEMtbRma0qHJww2DniCgs9XiR8kkH65UOM7zcIGrCgXWxGL8\ng1IMZbOMJxI80mxy7B57YGSz2O3tiGyWZYceSldvL52dnSQSiZdlY/vnwrZarf5FYRuGIZZl/UVh\nWyqV5rex/4/OvPidn5dtrr32Wi6//HKGhobYZ599uOKKK+Y8wB/4wAd44IEH2LJlCwArVqzgK1/5\nCtu2bcM0Tfbcc08+8YlPcPLJJ//dXv8PfvADVqxYwS233EI2m517/MXKMO699VZGr74aMTnJYDLJ\nmBAM/xnSLO55PCIEn5yaYnffp0t/WE4oxUEzMzyXSLApFmOtUvQ4Dm0iYo4GrsszhsGpUrJIh6mu\n1/7ag2o11tg2v0+leNRx2E3TG2L6w3KrELwBWKg3zN9ta+OkapVXuy4bLIs7MhkejMfZG2iYUdXr\nZKtF1YzqcEsyKoO4LR7njEqFI3yfBtEG6SHH4aAgYMy2aRkGE7NhKiFISEnR87jbsvhUtco+vk9b\nGPL1zk5WmiaH1Ov0J5MMCcGwjBrDZkNnjufxmBB8cnqapZ5HWSmuLpWoKsXB09NsSibZFIuxUSnK\nVoTdiilF4Hk8Yxh8rNVisRYj3+zsZEGrFV0ny+KJdJpnRcQHnm3pa7ZarDcMTtb+5XKrxbeLRd46\nPc1BzSbP2ja/Sqd50nHYTegqZ+1f7heC12ofZ0+jwQ35PKdp//Jm0+TmfH6nf1kITMNgSpMJDgA6\npaTsutwRj3NOpcIhvo8LXFYo8LRts38QMGLbNPSGzrAslhlG5AH1PH5jWXymUmGfICAfhlxcKrFd\nCPav1ehPpdghBKOzoT5taTE8jyeF4JypKZb4PkWluLxcRvg++9VqbJolOKgI11XQPmRPh/pO1wSH\nglJ8o1Riv3qdfer16H2orT89pklahwHruir7fUqxqNmk03W5ulDgvZOT7O+6PGtZ/DiTYa0We5aI\nqrKnXJdh0+RYbWkpNRrcmM/z8fFxDvV9tgjBN9vbWWvb7EVU52wSVWw3LIv9gaKUFF2XH8fjfG5i\ngoN8Hx/4QqnEViF4pe8zEosxBUzOimIjak/MaELGeZUKewUB2TDkC11dTCrFPvU6/akUz5km41KS\nt6MyE0eL4pVC8LmpKXbzfdqU4pJymYLnsbxWY2Miwcp4nP4wpOw4FPTzmq7LWiE4w3V3MoLLZY6a\nnmZ5s8lq2+Y3mQzbRUTISGkxXdOhyZP1jVmb5/HNQoEPTUxwsL6GN7W3sz6Z5MhEAjedppVM8myt\nxkHLl+N0dFDafXcS5TJL9tyTzs5OYrHYi/ps/5bzl4Tt0NAQ27ZtY8eOHXPCdmJiYk7YdnV1vaiw\n7ezsnBe28/MXZ178zs/8/Bfm7rvv5uKLL2bFihWUy+W5x1+sDOPfb72VR66+mot37KCkFDNESLNC\nq0WH9o1WlGJa7WxPikuJDALWCcEFlQplHcI6q1zm4KkpYmHINt38NaUUCx2HlP6wrOiNzj81m/Q1\nGqS0+PnEyAiBYbDGsvh1NsukFiNxMwLqj7suM6bJW2TEAE15Ht/s6OCq4WEMYJUVNYE1TZOSiFqb\nTGDcdQm1aFugcVI/SKe5ZniYzjBki2lyQaGAArqFoDpLGNBhqt2ADimJ+T6/cRyuGBujV0p8fZ3S\nvk+ZnXzgabmTDxxXCjyPp02Tiycm6FGKpIqqnJc0GuSCgB3pNOuEYEYpuh1nrsp5xvPYbpp8amqK\nHt8npRTnl8u8sVolrhSb4nEejcepEFU5zxIGqlo4zFa2JsOQyzo7+dTICAJYY9v8TF/fbiGI6es7\noTnKb9FiL+X7XNPWxtdHRsgoxSrH4ep8npYQlIQgFCKqG/Z9AtPkwDBkQRCQ8Dx+lEpx9cgIPUrR\nLwTndnYSAH2GQdU0CfT1TZhR2UablDhBwH2WxdfGx1koJRI4o6uLpOfRE4YMxeMMhSE1pWi3bbr0\ndQp9n2eE4OJKhR4ZMWzPKZdZ3GjQ4ftsT6dZbZpM6+vbhkbyaS/wOdPT9Hq6gldX4uaUYl0sxu+T\nSarsrMR1VMS+7ReCD+ktcSIM+WqxyCdGRsgAqy2L23I5poSgW0ShPjuMapnHTZO36tBZwvf5Tlsb\nXx4epqSiMpMr2tqom1Gdc2DurHP2LYsD9ClH3Pf5cTLJ10dG2E0phoTgs52deMAsutBViintKV5q\nGOSlxPF97rdtvjI2xmJ9A3x6VxcJ32eBlAwkEgzo69tmWXRr/73ahW/dKyUJHbbcrdGgy/N4Lp3m\nGf19PssInn3/bhERI7jPdUmEIReXy7y9WmW56zLoOPygvZ3hWIzDCwXIZPASCba1Wuy9zz6Udt+d\n0h57kG9vp7e3F8dxXhZhC9FJ2dTUFJdffjmbN29m6dKlHHbYYYyMjMwJ20qlQqjtR/+RsJ0vh5if\n/87Mi9/5mZ//4jz++OOcccYZ3HDDDSxZsmTu8Rcrw1jz1FNcduaZ7Ou65FXUqrYZqAH/opPdT1oW\nn9FVqF4iQdU0mQwCZohqXuNhSEZFLXI5KfknXTU8btt8slDgpIkJRmIxBlIpnlIKSwgW6wYvW6PQ\n+sKQt+uE9lgsxrfyec4bHmazZbExkeBXsRhxESXgd/XXdhsGx+gGr+FYjJ9lMlyr/bXP2jY3ZbO0\nG8ZcAp4gYCAI6NYJ+IWtFiOmycPxODcMDVEH/uQ4XNTezkKliNs2gRAEQcCYisogimHEBx4JQ7YI\nwdfHxsiEIRvMCP32ymYToS0BNSmZVoolmhSQ12D+qTDk89UqZe1f/mipxLFTU7jxOIPxOJuUIiDy\nL8e1f3kkCDCBj2qcVN2y+HyhwPsnJpgQgq3pNI+IqE1rkfbl2ruEzt5br9PrukzbNle1t/OF4WEG\nTJP1sRi/SCaxDINufX0tKekPApJC8CbfZ0GtxpTjcGs2y3UDAwybJs/oUF8WaLMixipKMez7ZE2T\nA7RPdhq4O5nku4ODhMBK2+bCQoFOKcnqLbxUigkp6TQj/nKPlMwoxVOmydVjY3QoxQ4hOL1UYkmr\nRcJxntdA12vbtOv34UwQsN0wuHhigi6laBoG/1wuc/D0NMI0GUgmWR+G+OwkODhSMhEEzBgGZ+tQ\nn2+anF8s8q6JCTwRMWz/YJoEhsFC2yZhGNgaT+YJwQc0w7ZlWVxRKPC5oSGmTZM1lsVPs1kMIyqE\niAuBqZ8XmCZv04SMlmlycy7HtzSn+hnb5qq2toh0YZqY+vqO+z7CNDlERaE+Tyl+nkzyneFhMmHE\nqT6vWCSnQ5PTQiBVFJrMmCa7hWFU+SslD9s2V42O0qUiRvDHymW6XJd202TEtpkIQxraxlMOo4Y/\nLwiexwgOgE92d3Ps9DQLlGKwrY2f2TbE4xzY3U2YySDTaeqmySsPOYTSHnvQWS5TLBaxbfslFbaG\nYTwvOGYYBkopKpUKg4ODbN++/Xkb23w+z/j4OHfdddfc79Hd3c2FF17IQQcdRG9vL8VicV7Yzs9L\nPvPid37m56+YjRs3csopp/C1r32NAw44YO7xFyvD2LFtGyvOOINweJiGYRATgrrrMmgYHCoEpSBg\nQavFL+JxXl+r8e5GAxf4SSbD9zIZjvY8xmMxGtrX6OowiqMUHUHAw8C7Z2Y4WvsT787n+X4yyVur\nVbZr3NE6XVawSPty7SDgaaV4p+dxkPYh/7atjUcdZ67Ba3M6zYNG1HLW+SL+2r2bTXpbLe5rb2dc\nCD42Osoqy+LJWIyfJ5P0CEFW+zhn0W9HCMEeWozcl8nghCGfHR9ns2ny+1iMG7NZlhsGUhMGXN+n\nPwx5lRAUtdj7g+NQ9n3OrlaRwD2JBF/N5znc96nFYjQNgxnfp2oY7GuaJJSiOwj4E7DMdflArUa7\nihrSLsrneeP0NOPpNCOmyZAWZXvp65SSknVKcaDr8g7dkPZsKsXXMxlOrlTYHo+zI5HgKaWImxFj\nNaZvOtYFAQdJyetqNbq1z/uOZJJPjI2xwbbZkEhwj22TEzuLB4RmrO4rBIfrUNQzmQwPJxJ8eWCA\nNbbNSsfhh+k0nULQpsU0vs9zUrLMNNnH91nYbLIqHuc52+bK4WFGhOARx+Hr+Ty7hyGWbWP8Waiv\nS4u99UJQNQwuGxvDBh6zbb5QKLCf6xLqUF8tCJgKQ5ZZEYu2MwjYGoYQhnxWt3htdBw+2dHBq6en\naSWTDNk22/Rmfw87qmVOKsUObSE4Td90DMZifLGjg/eMjzNq2+zQPmRTCHbX4TFbSrYFAR3ASbr0\nZSiR4Jpcjk8PD9NvWayLx7krHo9u6mybOCCCgH4/aup7i2YE9yeT/CSd5ird8Pe0bXNTLkcOIoKD\nvqkb1ISMw1VEahmyLO5PJLhxcJAWUUvalzo66FJRVbDSN3XjSlE0TRZpO8xYGHGBrxsdJROG9AvB\nWeUyr3Vdcskkw5kMj0tJLJNhr74+wmyWZLGI1dbG3ocdRmepRKFQmBO2u4rbl0PYTkxMvKiwnZyc\nBMC2bbq7u+nt7aWvr+95f3V0dDA1NcVHPvIR7rjjDgAWL17Mk08+SS6X+5u99vmZn/+vmRe/8zM/\nf+UMDw9zwgkn8OlPf5rjjjvueb/meR7NZnPu3wcHB7n5zDO58LHHaBGhum7LZhm0LHr0h4tNhDSr\nmSYHA32+T7HV4uZMhi+PjrJUSoaF4CuFAjvMCLg/ZtsEwLjnYds2S4j4tW2exz22zUXj4yyWkrw+\nep4IQ/ZqNqMGLyEYkZJ2y6JLi2nD83hKCD4zPc1Cz6OkFF8rl4l5Hvto/+e6eJz12ofcrv2fvub8\nfsTz2K1epyQl3+zsZN9Gg/3rdVbbNo+mUvxJUwlS2v/ZbLXYYBgcH4YsarXoaTa5vlDgH6amOKrR\nYJVtc1cqxQOJBHvq0Nls2KdfCI42DHp1Av77mQwnT03xxlaLYSH4fjbLL+NxXhWGVC0LdvHX7m8Y\n5KSkz/P4hW3zj1NTHOe62MBN+Ty/SCQ4utViOB6nKqLqamXbLNehqPYg4CHD4P9MT3Oorq7+kS7N\neN3kJNvSafptm00aNTd30+H7rATe12yyf7NJl5T8tFDgWcviXRMTrHEcNqdSPBaGFG2bLu3jNHyf\nZ5TinUrxCt1A94uODqYMgw+MjbHatnkykeDuWIxu06RNXyc1y1gF9tR2gl/m8yTDkLPHxuZ40z/M\nZtkDolISEWG3tgOv0qHJRc0mv0kk6PF9PlmtUgPuSqX4ZjbLq4KApm7xqnkeE4bBfruEJh8VgqWu\ny0d1aPK+2dBkrUY1mWTCthnWPOK9TJN4GJLTDNtXui7vrdUoS8kT6TRfz2Y5vlJhMJFgIB7nGaVw\nhGCpbc+FS9cHAftLyVs1IWNlNssPkkk+OjbGc5bFJo01S5smfbuESzcGAcuBY5tN+lotns5muS+R\n4NLBQdbZNk85Dj9OpWgTguIuNx1bpWSxaXKo57GwXmdVKsXTsRjXDA4yYxistyzOLxZ5jWXhZDL4\n6TRrXJdELkdPby/JYpHSkiVke3rYc9myObb430PYjo+PMzg4OMc77+/vZ3BwkGq1imEYOI7zosJ2\nwYIFtLW1/ac3tmEYcv311/PZz36W++67b77sYX5e9pkXv/MzP/+NmZ6e5sQTT+TEE0/kve997/N+\nzff95zGJG40GZ59wArsPDXGk69JXr1OzbW7K57l2YIDnLIs1ts3NuRxJ/i975x0mVXm/7/u06bOz\nM7s7M9tpSw3VAhhDFITYEk2MEYk9xsSABTVGsYBKiSWxUmMBY8/XaDTGkiIiggk2BBYQpG7vZXba\nab8/5uyEFfCXGBDBc1/XXhd75pzdd9Z155n3PJ/n4d+7etat7qAk8Q3DoCydJmmavOp280htLQqw\nUZaZUVBALMSVgAAAIABJREFUWFXJcTjoEEVUw6BF1ymUM6UDIV1H1XU+lCTuaWoiouukBYGfRKP0\nj8dxSxL1LlfWn1jmcBCwLAEJTWOnKHJzSwuFlj/x6sJCxra2ogA7LX9iZ7cPGXCaJm2WT3ZqZycl\nqRRe0+TWSITzGxuRBIGNDgcrvF6arfxat+XjbE2lqBdFplhNUX5d5+6CAm6pr8dpmqxXFJ4LBGgU\nRYqswbxu/2ebJDFe1+mlqoQSCRYFg9zZ0ECJrrNRlnkwGKRGkugtCHSJIrIg0GLV/w61blnnpVI8\n43Yzt6mJgZpGjExkXbUoMkjXqVcUEkCrNRRVwb/fdPxVUZjV1ER/XcdvPd86YFgiwW63m2pJolHT\nyFEUSq2hPjmd5l+iyK+s4cewNdykahpHdXay1e1ms9PJVsMgqiiZoT7rTce6zwz1PRQOU5pKMaaj\ng42Kwhqfjw9EkVJZJse6LpVKsVEQmGya9InHKUomWVJQwJh4nFPb21nvcPC6x8Nyl4u+oohiiem4\nNTQ5XhDopaqUdnXxZCDApFiMH8ZiVIsiz/n9vODxcLSZid2SrISBZkniGCt2qyyV4mWHg9OtOx0i\n8HggwNNeL9+2Yrc6xUysWUKWGWq96QhrGisFgdNjMU5NJsk3DF4MBnnS7eaU1laqfT6qHQ62qyqK\nJFFh7cS7rKSLU61YsyJd59VQiFcdDqY0N7PF4WCb18sa08zkPVt3OiRVZYOuM94wGBuLUaxp/D0Y\nZK3DwazaWuokiU88Hu7KyWGiz4c3GAS/nx2pFL6CAnpVVBCpqMiI25wciouLkSQJXddRrSjEA82+\nhK2u6z2E7e7du6murqampia7Y+tyufYrbHNzcw+KFaGtrc2u+LU5JNji18bmfySVSnHhhRcycuRI\nrrjiih6PaZpGPB7P7tqoqsqD11xD3Zo1+MgIRFHT2KBpTAK+kUhQnEzybm4uWxWF6+rrWWf5a5/1\n+SgRRXyWKNZVlR2GwQhRpJc12b3W6SQGzG5qogNY5XQyNxRihK6jKQqqKJJQVZpMk6GyjNcwKNZ1\nPrF8mde1thKyfI3XFhQwLhajy+OhUVFo0DSSwIA9SgeqdJ0cw+BnVrVykyxzTUEBP2hpocnppMbj\n4WPDAFGkr7Xb69AzTVwh4LyODoo0jQ5ZZnZeHtMaG6mVZba53fxdUZAs0eYEZF2nWlXxiiJnJhKU\nJRLEFIUFwSC/ralhlyyzUZZ5OicHxbJrOAQByXrzoIgiE6yfUwp4IieHR2pqSIoi62SZu0MhPIJA\n0Bo6EwyDRlXFLUkMsW5ZG5rGyx4Pv7NKM3aIItdHIngMgwJRpEWS0AyDNl0nIGdKM/J0HUHTWCnL\n3NvURJF16//ywkLyUinCkB066zQMChSFCJnqajSNj0SR2dbQmc80uS4apVc8TkE6zU6fj0pZpmWP\noTOnYdCVTrNVFLnOGooKGAa3RaMc395OVFXZ7HTyT4+HKqBEydTbdicFfCoI/ETTKI/FyNN17gmH\nObelhT7pNOsVhZdzcthqpXF0l7d0pFLsliS+axiUp1JEEgkWhEL8vLmZ0ek0m2SZpYEAHzkcDCST\nJOIA2tNpWiSJ0UCxrlOUSPCk18svWlr4djpNJ/BAXh4rHQ6O1nUaFYW0Zf9JyjLDBQGPYRC1Ys1+\n3tbGN9Np/GYm1my5ojCuq4tqj4c6KVPs4FAUKqw7Hd50mndFkUs6OznGio17vKCAdYrCZQ0NVHu9\nbMrN5feGwZnFxSi5uZh+P42aRmGfPvQZNoxI376Ew2Fyc3O/lB3bzxY0qKq6X2Hb3t4OZIRtd3zj\nZ4VtIBCwPbY2Xzts8WtjcwAwDIOrrroKWZa54447ekTs6LpOV1dX9kXQNE2emDOH/s89hxmL8anb\nzRanM2sl6I40697Vu1TTKIvFiGoaS8JhRsbjjOnsZIOVr7rS4aC3NXDmEASSqRTbBIGTBIHy7nzV\n3FwmdXby/a4udogif/b5eM7r5Sig0xr26UynaRZFjhJFcq3dudcVhe/EYnw/HkcBXvD7WezzMT6Z\npMHtpl0UaVFVUqLIN6RMO1t36cCkWIxTkknChsFbfj8P+Hyc0dZGtcdDjdPJVk1DkST6yTIOI1M6\nsMEwGJ9KcWI8TpFh8L7fz+89Hi5pbmaLorDD6+UdwCdJlMkyCiBrGp/oOqNNk+NjMUpUlfV+P39x\nu7nVykOudDp50e0mKIpZUSxqGts0jUGiyDHWz+kTr5fVLhcP1tSwTZL4UFFYEAhQJGZKHRRBwNAz\nDWm9JIn+RqaJq0qSMre6a2vRgfet8ou+mobT4SAhCKR1nRbDoFyWyTcMijWNJtNkqzXUF7L8nz+P\nRBiSSKA4nTRawrbLMChXFAKmidcaOqsVRWY2NVFoGKTJJGSMbW8HSaLa62WjaZI2TcocDvxk3nS0\nqirNosh11tCZaJrcGI1yRksLAvCp2807TiddQLmVxKAY/04SuSwepzSRQAHmhcNMt5rdNioKf8rJ\noU0UKRH/nXTRal13lqZlky4ezMvjtvp6wrrOeoeDRbm5tEgSRYIAoogMtFn2lG+SSRIJplIs9fu5\no6GBgbpOrSgyJz+f3aLIQEGgxUoSaVVVVFlmKBDSdfLSaV50Orm5uZkRqopsrbtBljklHqcmGGSr\ny8U/VZVJ/fphWtW6msvF4NGjKezXj0gkQjAYzP6/u6e4PdAvnx0dHbz99tsEg0G+9a1vAdDY2EhN\nTQ07duzI+mtramro6OgAwO1271fY5liDgDY2Nj2xxa/NYceCBQu4++67qaurY8iQIdx3333ZvOB9\nsW7dOqZNm8aaNWsIhUL87Gc/45Zbbjng6zJNk3nz5rFhwwYWLFiQaQqz+GwZBsCDM2fS9Mor/KKx\nkahlJbiqsJATW1pAENjp87HWijrq5XDgsSLNWlMpGqxIs5J4HL+ZiTS7pr4eyAiRv/j9NIiZ/E/H\nHkKkSZI41TAoSybJTyZ5KBRidkMDxZYl4OFgkB2yTB9BICFm8mu7q5VHAkW6TjSZ5AmPh5lNTQy1\nUinusXJoh1s5tKk9cmgHCAIeXSeiqrxq5dAOs4ac7s/PZ42iMDYWY7fHQ70kUaNpeBSF3tbzdVtl\nG79ob2eIqhLVdX4fDrNOkpjU0sIWt5vtbjcf6zoFikKR5a9FVVlrmpyvqgzq6qJI03gxP59aUWRy\nUxMbFIUNHg9vyjKFkkSenGk6M9NpKg2DU/l3E9droRBp4MqGBiqtprPn/H56CQKu7p34dJpthsFo\nSaKvNXS20uPBBGY2NtIoiqxwOLg3GGSotROPIJC0ki2GiiJ5ZibD9mNRRDJNbm5qwgX80+Hgprw8\nRu+RCNKuacRMk0FypkkuT9fZYRg4DINrWlsJGwY7FYXp+flMbGujy+3OJF3omdrlCiXT1OfQdWo1\nDadpcnlbG4WGQZsl3qc0NdEiiuz0+VglSQiCQG9ZziZd1KgqkiBwQSxGSSpFl6JwT14eN9TW0iJJ\nbHI4eMnrxbR+F7NJDJbN5AfpNGWxGLoksTAY5N7aWlRgnaKwOBjEFIRMrrCYiX9rtrzB46zhR1nT\n+L3fz0P19YQNg0ZR5NaCAjyKwjccDpp9PpoUhW26ztH9+0NODqHSUhz5+QwYOZJIJJK97X4whe2+\ndmzT6XRW2DY1NREOhznnnHNoaWkBwOfzMXz4cCoqKvYrbG1sbL4Ytvi1Oax49tlnOf/881m4cCHH\nH3888+fP57HHHqOyspLS0tK9zu/o6KB///6ccMIJ3HrrrWzcuJGLL76YWbNmcc011xyUNT766KM8\n//zzPPbYY/h8vuzxfZVh/OP//o9n7r2XfpqWTRfYZhiUqirndXYS1XUaHQ6uz8vjx83N1CoK1VZl\nsCyK9O6ONDMMdqoqBcCZXV0UpVJ0Ohw8EAoxr6aGbbLMZkXhRb8fWRCIWOkCkmFQk07jFkVOtKpp\nVUFgaSDAYzU1xESRj2WZe4NBnIJASJJAEBBMkyZVxSVJDDYMylUVSdP4o9fL7+rqyDVNdokiN4TD\nKIZBRBRpliR006TVGgIrJ7M751ZV/qoo3NvURImuIwBXFhYiqSqlhkGty0UD0Krr2Rxal2GVX0gS\nt7W0UKrrhAyDWwsLcabT9I3H2eHzsVWWqTYyOcoFgpDZUU+nWScITO/qope1M/2bSITiVIphsRgb\nFYWPfT42kLEEBKyd+FQqRaWQKRfpvUe5yDCriWudorDC4+Fth4Nyy7/sFARSqRRbgO+QaeIqjcd5\nOhhkdCLBlPZ2PpUk/uLx8KzXy3BBINntr02nqRYExggCUSth4C8uF0clk/ykowMVeNnr5aGcHL6p\nqnRYiSAdqkqbKDJcFPGYJsVWSciwZJILOzsJmiarPB7m5Obynba2TNKFolClaeiiyCBZxmkYuDWN\nT0yTQek0k2OxTL2yNaw2pbmZGqeT3R4PawwDhyTR1xoeU3SdTzWNcsPgrM5OijWN3XskMeyWZTbv\nUV9d2r2Dr+vsUlVCoshpySTl8TiNLhdPBAI8WFVFUhSpliRmFRTQx+mkKCcH/H4aJYk2QaBfRQX5\nZWWEKyrwFRTQt29fcnJyskL2yxa2DQ0N+9yxjcViAHi93h47tuFwmIcffpg///nP2a992WWX9aiE\nt7GxOTDY4tfmsGL06NGMGDGixwtC//79+eEPf8jcuXP3On/hwoXceOON1NfXZ2uJ58yZw8KFC6mq\nqjpo63z55Ze55557ePzxxykoKMgeN02TRCLRY9jlgxUr+OfMmXgaG6l1uWgXRZrSaUxFYaAo4tB1\ncjWN1cDkWIwxljfx78Egz7hc/KClhW0eD9UuFx/qmUrbMmtgR7aiyb6j6xxlDeysCQR40+nk2vp6\nKhWFjW43rzidhESRAkt4iZrGVl1nhCAwwppir/T5+NDp5N7aWrZKEh91WwIEAbc1dGZqGtXW9Htf\nXadXKkW1JPGxw8GCujo0Mjm0N+Xn00dVcTgcxEURTddp7rYEmCbFmkabYVApSdzb2EjIMKgXBH4W\njTIgkcDlcFCvKLQYBp2GQZmiELSis1KaxlZRzOTQ6joScHk0yojOTpyCwG6vl08EgZhhUOpwECCz\nixlLp9klivyqrY1iTcNnWQLGt7Xh03W2uN2873JRb5qUKQpea1itM51mhyjys1SKsliMoGHw62iU\nyc3NRDWNSkXhrz4fWyWJMknCbSU4dKZS7BBFzjIy5RfRZJIH8/O5uKWFY1MpNigKf/D5+JfLRX9B\nQLN2QDuTSeokieOBUk2jpKuLJ3JyOL+tjUnJJC3AMqv+91jDoEVRMAWBtlQqk3QhivitpIu/KApn\ndXRwejKJyzR5LjeXxz0exsdi1Hu9NEkSDek0hixn6qut38U1wHdiMU62fhffzM3lYbebs1pb2eV2\nU+12s07TcO0pijWNjbrOcarKJEtMvx8I8H9eLzNramiSJHbm5HCX281Yv5+CYBAhEKBNklDdboaM\nGEGkf38i5eWEQiFCodCXJmz3FLfpdJr6+vp9Ctuuri4gs2u7LytCaWkpfr9/v9/PNE0eeughrrnm\nGvr3788///nPHm+gbQ4/amtrueGGG3j11Vfp7OykT58+LFy4kHHjxmXPmTVrFr/73e9obW1l9OjR\nzJ8/n8GDBx/CVR/52OLX5rAhnU7j9Xp55plnOOuss7LHp02bxvr161m+fPle11xwwQW0trby8ssv\nZ4+tWbOG0aNHs337dsrLyw/aeletWsW1117LI488Qq9evbLH91WG8a933uEPM2Zw56efUmgYxICb\nrWiyCtOk3uEgBjRrGl5Zplz4d+Xqckni1pYWeut6ppo2EqHRMBgVi7Hd42Gnw8Gnuk6BLBOxLAGm\nqrJWELg8kaBPIkFU11lWUICk60xoa2OjorDO6+Ud63Z10LIEGOk0G0yTM4GKRIKSRIIX8/II6DoX\nNzVRqSisdjr5g89HX1HEIUk4BQE1nWabaTJWFOmlafSKx1nu8eA3DK63SiRWOBzcEwwyyjBIyTKI\nIklVpc40GSlJBEyT8nSadZYP9caWFtymyYeKwvX5+YyJx0l5PLRImZKQmGkySFEyKQy6TrVhIBgG\n17a1EdF16iWJaeEwJ7W1kbAsAVuMf5dfuC1LQIOmYQgCV7S2UqjrqILA9ZEIk5uaiEkS271e3pVl\n0mRKHVyCgEPXaUyniUsSP7HKGSRBYHY4zPS6OtKiSKWi8GpODp1AiSRlPNtmphGuWZL4kabRq6sL\nr2Fwb34+s+rqCJomH8syj+fmUi9JFIsiUrdPNpWiVZIYZ5r0SqcpSCZZEggws6GBwbrOLjFT/7te\nURgCtEkSoiDQmkoRl2VGAPm6TqFV/3t1czNjVRUBuM+qrx6TSlHnctEmZOqrTUVhkCDgNAzy02mW\nSxKXtLdzXDpNnhX/9qbLxWUNDdTm5rItEOCpdJrTy8pwBAKQk0OXJJHfuzcVI0eSV1REMBjE5/Nl\nvard6QV7WoYOBPsStqlUKitst2/fnhW11dXV2eQWv9+/X2F7oITq6tWrCQaDDBw48IB8PZtDQ1tb\nG6NGjWLcuHFMmzaNgoICtm3bRmFhYfa/7Z133smcOXNYtmwZ/fv35/bbb2flypVs3rzZfuNzELHF\nr81hQ01NDSUlJaxYsaKHx/f222/nqaeeYtOmTXtdM2nSJMrKynj44Yezx3bt2kWvXr1YvXo1o0eP\nPqhr3rhxIxdddBH3338/w4YN6/FYKpUimUxmP6+pqmLWhRfSq6ODiK5Tpml0GgarFYUFViD+blHk\nikiE8mQSj8NBkywTMwzaDYNiWSYEePRMRXKlJDG7uTnrJ55aWMjgWAyvYbDb5+MTUaTNyLR35VgC\npmuP6tTiVIqQlRJwQlsbBZrGJkXhPZ+PbUC5kqn+dZom8VSKLZYloLyri4iqcl9BAd9rb2d4Msk6\nReFvHg//crnoLYooliWgOzprkiXYSuNxlgWDfLejg9PjcbaJIi/5fPzR62Uk0GUNncXSaeoFgWNF\nkQI90yT3itPJt7u6mNLVhQG85PPxkN/PuFSKVpeLmCjSrqrERJFhkoRL1ynSddaYJiOTSaZ0dREy\nDN53u5kZDHJ6ayuNPh91Dgc7NA1TFBlgWQJchsE2XafvHpaAKpeL24JBzm9upkaW2eXz8U8y9pQ9\nLQE7NY184ByrnKHN4eCeUIib6uqolmU2O538xe1GFARKFAWnkGmEq1VVRFHkzFQqY0+RJOaHQtxf\nU0MnsN6KzTOtHXxFEJBNk0bLJ3uCYdA7mcSpaTwSCPBgXR15hsEmWeauvDw6BYEyUaRLFBGBlnQa\nXZYZBhRrGoFUimfdbuZZ8W8qMCcSoU2SOFHTqM7NpcbpZE0qxXjLXyvl5iL6/QwcM4bCsjLC4TBe\nr7dHEkL3ru2BZF/CNplM7lfYdmdyd8eR7UvYer3eA7pGmyOfGTNm8Pbbb/P222/v83HTNCkqKuLK\nK6/kxhtvBCCZTBIOh7nnnnu47LLLvszlfq2wxa/NYcMXEb/f+c53KC0tPWTiF6Cqqoof/ehHXHHF\nFZSUlGSjiIYNG8bIkSN7eIDb2tpY8POfI2zZQqcoIltRRlWmySgx03JWnk7zkSwj6zozWlpwAO8p\nCr/Kz+e4eJyEx0OrKNKh65mKZEnCbZrk6Do1hoFsGFzZ1kZU1+mw0gW+19ZGu8NBtcdDpWmiA32t\nVixlj93Pn1kpAYIgcEM4zE8bG4mJIlvcbt52uYgDZbKcicAyDJpSKdokiQutXGOvYTA3EuGmujpM\nQaDS8iE3iiKFVkqAwzRpS6dpkCS+q+sZX24iwX0FBdzS0EAvTaNSlvl9bi6Vskw/USRpiem2VCob\nnVWi6xTH4/ze5+PKlhaOS6fpAJaEQvzV6eQYKzpLt3J+E5KU8ckaBiVWdNaP29o4yYrOes5qzpvY\n2Umt10uDNZwnSBIDJAmnYeDXND4wTU6OxTgplSKq66wKBPidx8O5LS1sc7mo8nj4QNfxSBK997AE\nbNI0jtU0TrKG8zb5fCzzermusZGtsswnHg+vW3aLEkXBCUialqmvFgQmWvFvtW43T+fkcH9VFTtk\nmQ2KwtJAAK8gkGeVWIiWmPaKIt8yDHrF48RFkWd9Ph6uqUEBaiSJm8JhSiWJUo+HLr+fBkmizjQZ\n2r8/cm4uBb1744xEGDBkSFbYfjbq60AKW9M0kazBuz3FbTKZpK6ujurqanbs2NFD2Ha/wQwEAvsV\nth6P54Ct0camm8GDB3PKKadQVVXF8uXLKSoq4tJLL2Xq1KkAbNu2jX79+rFmzZoeRR+nn346+fn5\nLF269BCt/MjHFr82hw37sz1MnTqVyspK3nzzzb2uufDCC2lubu4xRPJl2B6WL1/O4sWLsy1J1dXV\ne4XaT5s2jRkzZux1bUdHBw9MncrVK1dSaHk/X/V4+IfbzSBBIG35crtSKWpFkTGCQMTa/XzB7ea7\nHR2ckUigAy/6fCzOyeHEZJJGa/ezVVWJiyJDLQtE2PJwHt/VxfcSCcKGwYceD7Nzczm7tZUqt5ta\nl4tNuo4k/rtNy6HrbNF1hmgaZ1ptWjVOJ3cGg0xrbGSnLLPd62W55QcuVxQcZMT0LlUlH/ieZZ2I\nORw8GApxd3U1u2WZSlnm/6yYpqii4BAEZMOgLp0GSeJkVaVXIoFkmiwIBllYXQ2Q8Rbn5pKSJMKi\nmInOMk2a0mk0SeJoK00hkErxmN/PffX1maE6KzqrWhTpLwg0SxKQ2f00FIXBpknQMAinUrzgdHJL\nczNDVRUFuKuggA9kmWOSSWpdLppFkUZVRbGEudMwyFVV3hZFLm9rY6SqUmAYPJ2fz98VhVPa2tjm\ndrPb5WKjphFQFMqsNw+KprHWNDkrmeQYK/7tb8Egyx0OLmlsZJOisMXn4y1BIFeWKe4uZ7DE9Fhg\nbDxOcSrFRzk5vOV289vqahokiR2Kwqy8PMa63ZkSA7+fWtMk5XLRt6KCcO/eRAYMICcUoqysDI/H\nc1CFLdBjp7bb6pBKpZg1axYvvvginZ2dTJo0iWAwSHV1dbZGPDc3d7/C1u12H9A12tj8p7hcLgRB\n4JprruFHP/oRH374IVdccQW//vWvmTp1KqtWreL4449n165dlJSUZK+75JJLqKmp4bXXXjuEqz+y\nscWvzWHFmDFjGD58+F4Db2effTZz5szZ6/xFixbxq1/9ioaGhuzA29y5c1m4cCG7d+8+aOt8+umn\nmTJlyueec9ZZZ/Hggw/u8zFN07jlkktIVFZysjVw5jMMfpufz29qa3EC62SZZYEADbKcyUiVJGTI\nRpMdBZRoGpFEgqU+H3c0NTHYiia7Nz+f9xWFkZpGg8NBUhBoSqcz0WSiiMuKJvurJHFFWxsj02lC\npslToRCvOJ1MaG9nl9dLrcPBNlXFoyj0sSwQTlXlA9Pk7HicY5NJCnWdt3NzedHl4oLmZjYqSiY6\nyzQJyDIlewznbdR1vmkYfDMWo0hV2ej385LXy+21tWxQFDY6nfzR7cYvikS7Syw0jR2aRpkocryV\n11vncvGiz8fD1dVUiyLrFIUHQiECQMCyBAhGpvzCL0mMsKKzVMPgj14vj9bW4gI+kWVuKSjAoeuE\nZZlOUcQwTVo0Dbck0dc0ieo6XlXlZaeT+xoaKLNyd6+NRokbBn0Ngzqnk1agTdNwyzK9BQGXYZCT\nTvOmLDOzuZl+mkbINPl1JEINMKqjgx0+H7tkmZ26TlBRMhm6hoGsqrwvCPw8FmOwtcP8eDhMrShy\naUMDNYrC5mCQRbLM9woKcFjlDHWaRm5RERXf+Abh/v2JFBWRl5eHx+PZa3DsYArb7n/H43Hq6+up\nqqrqsWNbU1OTFbZDhgzh6aefprOzM/u1rr32Wu644w5b2Np8pXE4HBx77LGsXLkye+ymm27ihRde\noLKy8nPFb21tLa+++uqhWPbXAlv82hxWPPfcc5x//vksWLCA4447jkWLFvHYY4+xYcMGSktLufHG\nG1mzZg1/+9vfgMwu6oABAzjhhBO4+eab2bx5czbqbPr06QdtnStWrODb3/52j2PBYJDi4mK8Xi+h\nUIjTTz+dKVOmZAVBdxJEt+gwTZOn7rqLj154AbdpZqLJdJ2dqkqhIPAtVaWsq4sOh4OncnJ4pLqa\nOmuQ6v5gEL8gELBuEQuGQYOq4pMkBgJlqoqcTvO8FU0WMk3qRZHrw2HQdYpEkUZriKtFVfEpCuWA\nzxJsf1UU7mxqolzXs5XFLabJoESCKq+XalGkTtMIOhwUW35ihxW5dV17O/1UlYiu80gkwk7gxLY2\nPnG52O5285FhEFYUIpaYFqy83h+rKoO7uijSdf6Sl8d2SeInDQ2sVxQ2uN285nAQEUXyrRg3VJVN\nus63BIGhySRl8TjvBwJsdDj4dU0Nn8gyHzocLMnJoUgQ8FhDZ4aqUqXr9JUkBuk6vRIJqhSFNU4n\ni2prSZFJrLg1P59iXcejKCRFEUPXadZ1IpJEiWlSomkkdJ1VDgcL6usJmiatgsDl0Sh5qRR5ikK9\nLBMzTdqsGLdiK7HCoaqskiTubm6mRNdxmSY3FBZSmE5zTDxObSjEe243a4EJZWWYVuxXBzDk2GOJ\nDhhApLCQgoICHA7HIRG2XV1dWWG7c+dOqqqqssK2e9gzGAxSUlKy145tSUkJLpcr+/U3bdrED37w\nAzZu3Ijb7Wb16tUMHz78gD4Hmy+XWbNmcfvtt/c4Fo1Gqamp6XHO4ZyC0KtXLyZNmsSSJUuyx37/\n+99z+eWXE4vF9mt7OO200wiHwzz22GOHYtlfC2zxa3PYsXDhQu666y5qa2sZOnQo9957b9YDfPHF\nF/PWW2+xbdu27Pnr169n6tSp/Otf/yIUCvHzn//8oJRc7ElLSwuvvPJK9oW9uLg46ys0TZNZs2ax\ne/du7rvvPmRZzl5nGAbxeLyHD/iVRx/Fu2gRg+vq2KgobHa7+auiEN2jmEGwhN44QWCQ5a/9IBDg\nU0UZiM+UAAAcdUlEQVThztpaPpUkPlAUHgoEKBcEFFlGEQR0XadG16kQRUosP3GdILBeUXiwvh4H\n8IkkcU04TJ90GqfDQYskkdL17LBcnmEQ0nVUXecjSeI3TU1EdB0D+HlhISWJBLmCQI3LRZUg0KHr\nRBSFfEHIVPiqKh+JIrdZFb7deb35iQS9Uym2ut184nCwwzAocjrJFwQUw0Cz8nqvSCTonUgQ0XUW\nRiKE0mnGtbdTqSis9XpZLUmUyDK5lp/YSKdZb5qcBVTE45Qkk7yYl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nonlinear_plots import plot_multiple_gaussians\n", "with figsize(y=5):\n", " plot_multiple_gaussians(Ms[::7], Ps[::7], (0,52), (-1, 2), 75)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Kalman Filter Equations\n", "\n", "I've not shown you how `predict()` and `update` perform their computations. In some ways this section is optional, especially if this is your first pass through the book. You'll certainly be able to understand the rest of this section without reading it.\n", "\n", "However, most of the difficulties we encounter in Kalman filters result from these equations. If you ever plan to read any other book or paper on the Kalman filter they will not be hiding the equations behind two functions. If you want to grow past this chapter you will need this information. And, it's not that hard. \n", "\n", "A word about my notation. I'm a programmer, and I am used to statements like `x = x + 1`. That is not an equation; the sides are not equal. If we wanted to write this in correct mathematical notation we'd write\n", "$$x_k = x_{k-1} + 1$$\n", "\n", "The Kalman filter equations are traditionally *littered* with subscripts and superscripts to keep the equations mathematically consistent. I show then in the summary to this section. But in most of the book I opt for subscriptless statements. As a programmer you should understand that I am showing you an algorithm that is to be executed step by step. I'll elaborate on this once we have a concrete example.\n", "\n", "### Prediction Equations\n", "\n", "The Kalman filter uses these equations to compute the *prior* - the predicted next state of the system. They compute the mean ($\\mathbf{x}$) and covariance ($\\mathbf{P}$) of the system.\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{x}^- &= \\mathbf{Fx} + \\mathbf{Bu}\\\\\n", "\\mathbf{P}^- &= \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}\n", "\\end{aligned}$$\n", "\n", "**Mean**\n", "\n", "$\\mathbf{x}^- = \\mathbf{Fx} + \\mathbf{Bu}$\n", "\n", "We are starting out easy - you were already exposed to the first equation while designing the state transition function $\\mathbf{F}$ and control function $\\mathbf{B}$. \n", "\n", "As a reminder, the linear equation $\\mathbf{Ax} = \\mathbf{b}$ represents a system of equations, where $\\mathbf{A}$ holds the coefficients of the state $\\mathbf{x}$. Performing the multiplication $\\mathbf{Ax}$ computes the right hand side values for that set of equations.\n", "\n", "If $\\mathbf{F}$ contains the state transition for a given time step, then the product $\\mathbf{Fx}$ computes the state after that transition. Easy! Likewise, $\\mathbf{B}$ is the control function, $\\mathbf{u}$ is the control input, so $\\mathbf{Bu}$ computes the contribution of the controls to the state after the transition.\n", "\n", "**Covariance**\n", "\n", "$\\mathbf{P}^- = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$\n", "\n", "This equation is not as easy to understand so we will spend more time on it. \n", "\n", "\n", "In the univariate chapter when we added Gaussians in the predict step we did it this way:\n", "\n", "$$\\mu = \\mu + \\mu_1\\\\\n", "\\sigma^2 = \\sigma^2 + \\sigma^2_1$$\n", "\n", "We added the variance of the movement $\\mu_1$ to the variance of our estimate to reflect the loss of knowlege. We need to do the same thing here, except it isn't quite that easy with multivariate Gaussians.\n", "\n", "In a multivariate Gaussians the state variables are *correlated*. What does this imply? Our knowledge of the velocity is imperfect, but we are adding it to the position with\n", "\n", "$$x^- = \\dot{x}\\Delta t + x$$\n", "\n", "Since we do not have perfect knowledge of the value of $\\dot{x}$ the sum $x^- = \\dot{x}\\Delta t + x$ gains uncertainty. Because the positions and velocities are correlated we cannot simply add the covariance matrices. The correct equation is\n", "\n", "$$\\mathbf{P} = \\mathbf{FPF}^\\mathsf{T}$$\n", "\n", "The expression $\\mathbf{FPF}^\\mathsf{T}$ is seen all the time in linear algebra. You can think of it as *projecting* the middle term by the outer term. We will be using this many times in the rest of the book. I explain its derivation in the *Kalman Math* chapter. \n", "\n", "For now we will look at its effect. Here I use $\\mathbf{F}$ from our filter and project the state forward 6/10ths of a second. I do this five times so you can see how $\\mathbf{P}$ continues to change. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VqlViv+qcnBx8+vRJfEmrSpUqUi8nlpatrS2eP39e7LaXL19W6JikAhgD1q0T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\n2syU1ZcWFhaYMWMGGjZsiKKiIqSmpmL8+PHQarWIjY1lX5qZl19+GWv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import book_plots\n", "dt = 0.6\n", "x = np.array([0., 5.])\n", "F = np.array([[1., dt], [0, 1.]])\n", "P = np.array([[1.5, 0], [0, 3.]])\n", "plot_covariance_ellipse(x, P, edgecolor='r')\n", "\n", "for _ in range(5):\n", " x = np.dot(F, x)\n", " P = np.dot(F, P).dot(F.T)\n", " plot_covariance_ellipse(x, P, edgecolor='k', ls='dashed')\n", "book_plots.set_labels(x='position', y='velocity')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that with a velocity of 5 the position correctly moves 3 units in each 6/10ths of a second step. At each step the width of the ellipse is larger, indicating that we have lost information asbout the position due to adding $\\dot{x}\\Delta t$ to x at each step. The height has not changed - our system model say the velocity does not change, so the belief we have about the velocity cannot change. As time continues you can see that the ellipse becomes more and more tilted. Recall that a tilt indicates *correlation*. $\\mathbf{F}$ linearly correlates $x$ with $\\dot{x}$ with the expression $x^- = \\dot{x} \\Delta t + x$. The $\\mathbf{FPF}^\\mathsf{T}$ computation correctly incorporates this correlation into the covariance matrix!\n", "\n", "Here is an animation of this equation that allows you to change the design of $\\mathbf{F}$ to see how it affects shape of $\\mathbf{P}$. The `F00` slider affects the value of F[0, 0]. `covar` sets the intial covariance between the position and velocity($\\sigma_x\\sigma_{\\dot{x}}$). I recommend answering these questions at a minimum\n", "\n", "* what if $x$ is not correlated to $\\dot{x}$? (set F01 to 0, the rest at defaults)\n", "* what if $x = 2\\dot{x}\\Delta t + x_0$? (set F01 to 2, the rest at defaults)\n", "* what if $x = \\dot{x}\\Delta t + 2x_0$? (set F00 to 2, the rest at defaults)\n", "* what if $x = \\dot{x}\\Delta t$? (set F00 to 0, the rest at defaults)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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mTaSoKKluXWnLFpfvcU77jLeMYz940PzVIDlZeuUV6V//ckB1AJAzshzYz5w5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\nPr169VJkZKRWrlypsLAwRUREqE+fPjl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.html.widgets import interact, interactive, fixed\n", "import IPython.html.widgets as widgets\n", "\n", "def plot_FPFT(F00, F01, F10, F11, covar): \n", " dt = 1.\n", " x = np.array((0, 0.))\n", " P = np.array(((1, covar), (covar, 2)))\n", " F = np.array(((F00, F01), (F10, F11)))\n", " plot_covariance_ellipse(x, P)\n", " plot_covariance_ellipse(x, np.dot(F, P).dot(F.T), edgecolor='r')\n", " plt.gca().set_aspect('equal')\n", " plt.xlim(-4, 4)\n", " plt.ylim(-4, 4)\n", " plt.title(str(F))\n", " plt.xlabel('position')\n", " plt.ylabel('velocity')\n", " \n", "interact(plot_FPFT, \n", " F00=widgets.IntSliderWidget(value=1, min=0, max=2.), \n", " F01=widgets.FloatSliderWidget(value=1, min=0., max=2., description='F01(dt)'),\n", " F10=widgets.FloatSliderWidget(value=0, min=0., max=2.),\n", " F11=widgets.FloatSliderWidget(value=1, min=0., max=2.),\n", " covar=widgets.FloatSliderWidget(value=0, min=0, max=1.));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(If you are reading this in a static form: instructions to run this online are here: http://git.io/vmv6e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Equations\n", "\n", "The update equations look messier than the predict equations, but that is mostly due to the Kalman filter computing the update in **measurement space**. This is because measurement are not *invertable*. For example, later on we will be using sensors that only give you the range to a target. It is impossible to convert a range into a position - an infinite number of positions (in a circle) will yield the same range. On the other hand, we can always compute the range (measurement) given a position(state).\n", "\n", "Before I continue, recall that we are trying to do something very simple: choose a new estimate chosen somewhere between a measurement and a prediction, as in this chart:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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02ksGQ40bN8bzzz+PAwcO4MqVK5r2vLw8fPTRRzp9qtNVoqOjtdo///xz/Pbb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\na+Ui69Z+AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with figsize(y=2.5):\n", " show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equations will be complicted because our state has multiple dimensions, not one, but this is all we are doing. Don't let the equations distract you from the simplicity of this idea." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**System Uncertainty**\n", "\n", "$\\textbf{S} = \\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R}$\n", "\n", "To work in measurement space the Kalman filter has to project the covariance matrix into measurement space. The math for this is $\\mathbf{HP^-H}^\\mathsf{T}$, where $\\mathbf{P}^-$ is the *prior* covariance and $\\mathbf{H}$ is the measurement function.\n", "\n", "\n", "You should recognize this $\\mathbf{ABA}^\\mathsf{T}$ form - the prediction step used $\\mathbf{FPF}^\\mathsf{T}$ to update $\\mathbf{P}$ with the state transition function. Here, we use the same form to update it with the measurement function. In a real sense the linear algebra is changing the coordinate system for us. \n", "\n", "Once the covariace is in measurement space we need to account for the sensor noise. This is very easy - we just add matrices. The result is variously called either the **system uncertainty** or **innovation covariance**.\n", "\n", "I want you to compare the equation for the system uncertainty and the covariance\n", "\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{S} &= \\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R}\\\\\n", "\\mathbf{P} &= \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}\n", "\\end{aligned}$$\n", "\n", "You can see that they are performing the same computation. In each $\\mathbf{P}$ is put into a different space with either the function $\\mathbf{H}$ or $\\mathbf{F}$. Once that is done we add the noise matrix associated with that space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Kalman Gain**\n", "\n", "$\\mathbf{K} = \\mathbf{P^-H}^\\mathsf{T} \\mathbf{S}^{-1}$\n", "\n", "Look back at the diagram above. Once we have a prediction and a measurement we need to select an estimate somewhere between the two. If we have more certainty about the measurement the estimate will be closer to it. If instead we have more certainty about the prediction then the estimate will be closer to it. \n", "\n", "In the univariate chapter we scaled the mean using this equation\n", "\n", "$$\n", "\\mu =\\frac{\\sigma_\\mathtt{prior}^2 \\mu_2 + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} {\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2}$$\n", "\n", "which lead to this equivalent simplification\n", "\n", "$$\\mu = (1-K)\\mu_\\mathtt{prior} + K\\mu_\\mathtt{z}$$\n", "\n", "Here $K$ is the Kalman gain, and it is a scaler between 0 and 1. Examine this equation and ensure you understand how it selects a mean somewhere between the prediction and measurement. In this form the Kalman gain is essentially a *percentage* or *ratio* - if K is .9 it takes 90% of the measurement and 10% of the prediction. \n", "\n", "For the multivariate Kalman filter $\\mathbf{K}$ is a vector, not a scalar. Here is the equation again: $\\mathbf{K} = \\mathbf{P^-H}^\\mathsf{T} \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of doing matrix division. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n", "\n", "$$\\begin{aligned} \\textbf{K} &\\approx \\frac{\\textbf{P}\\textbf{H}^\\mathsf{T}}{\\mathbf{S}} \\\\\n", "\\textbf{K} &\\approx \\frac{\\mathsf{uncertainty}_\\mathsf{prediction}}{\\mathsf{uncertainty}_\\mathsf{measurement}}\\textbf{H}^\\mathsf{T}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In other words, the *Kalman gain* equation is doing nothing more than computing a ratio based on how much we trust the prediction vs the measurement. If we are confident in our measurements and unconfident in our predictions $\\mathbf{K}$ will favor the measurement, and vice versa. The equation is complicated because we are doing this in multiple dimensions via matrices, but the concept is simple - scale by a ratio, same as the univariate case.\n", "\n", "Without going into the derivation of $\\mathbf{K}$, I'll say that this equation is the result of finding a value of $\\mathbf{K}$ that optimizes the *mean-square estimation error*. It does this by finding the minimal values for $\\mathbf{P}$ along its diagonal. Recall that the diagonal of $\\mathbf{P}$ is the variance for each state variable. So, this equation for $\\mathbf{K}$ ensures that the Kalman filter output is optimal. To put this in concrete terms, for our dog tracking problem this means that the estimates for both position and velocity will be optimal in a least squares sense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Residual**\n", "\n", "$\\mathbf{y} = \\mathbf{z} - \\mathbf{Hx}$\n", "\n", "This is an easy one as we've covered this equation while designing the measurement function $\\mathbf{H}$. Recall that the measurement function converts a state into a measurement. So $\\mathbf{Hx}$ converts $\\mathbf{x}$ into an equivalent measurement. Once that is done, we can subtract it from the measurement $\\mathbf{z}$ to get the residual - the difference between the measurement and prediction.\n", "\n", "**State Update**\n", "\n", "$\\mathbf{x} = \\mathbf{x}^- + \\mathbf{Ky}$\n", "\n", "We select our new state to be along the residual, scaled by the Kalman gain. The scaling is performed by $\\mathbf{Ky}$, which then needs to be added to the prior: $\\mathbf{x} =\\mathbf{x}^- + \\mathbf{Ky}$.\n", "\n", "**Covariance Update**\n", "\n", "$\\mathbf{P} = (\\mathbf{I}-\\mathbf{KH})\\mathbf{P}^-$\n", "\n", "$\\mathbf{I}$ is the identity matrix, and is the way we represent $1$ in multiple dimensions. $\\mathbf{H}$ is our measurement function, and is a constant. So, simplified, this is simply $\\mathbf{P} = (1-c\\mathbf{K})\\mathbf{P}$. $\\mathbf{K}$ is our ratio of how much prediction vs measurement we use. So, if $\\mathbf{K}$ is large then $(1-\\mathbf{cK})$ is small, and $\\mathbf{P}$ will be made smaller than it was. If $\\mathbf{K}$ is small, then $(1-\\mathbf{cK})$ is large, and $\\mathbf{P}$ will be made larger than it was. So we adjust the size of our uncertainty by some factor of the *Kalman gain*.\n", "\n", "### Summary\n", "\n", "We have learned the Kalman filter equations. Here they are all together for your review. There was a lot to learn, but I hope that as you went through each you recognized it's kinship with the equations in the univariate filter. In the *Kalman Math* chapter I will show you that if we set the dimension of $\\mathbf{x}$ to one that these equations revert back to the equations for the univariate filter. This is not \"like\" the univariate filter - it is a multiple dimension implementation of it.\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{Predict Step}\\\\\n", "\\mathbf{x^-} &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n", "\\mathbf{P^-} &= \\mathbf{FP{F}}^\\mathsf{T} + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n", "\\\\\n", "\\text{Update Step}\\\\\n", "\\textbf{S} &= \\mathbf{HP^-H}^\\mathsf{T} + \\mathbf{R} \\;\\;\\;&(3)\\\\\n", "\\mathbf{K} &= \\mathbf{P^-H}^\\mathsf{T} \\mathbf{S}^{-1}\\;\\;\\;&(4) \\\\\n", "\\textbf{y} &= \\mathbf{z} - \\mathbf{H x^-} \\;\\;\\;&(5)\\\\\n", "\\mathbf{x} &=\\mathbf{x^-} +\\mathbf{K\\textbf{y}} \\;\\;\\;&(6)\\\\\n", "\\mathbf{P} &= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P^-}\\;\\;\\;&(7)\n", "\\end{aligned}\n", "$$\n", "\n", "While we are looking at the equations, I want to share a form of the equations that you will see in the literature. No article or book uses the same notation, but this gives you an idea of what to expect.\n", "\n", " $$\n", "\\begin{aligned}\n", "\\hat{\\mathbf{x}}_{k\\mid k-1} &= \\mathbf{F}_k\\hat{\\mathbf{x}}_{k-1\\mid k-1} + \\mathbf{B}_k \\mathbf{u}_k \\\\\n", "\\mathbf{P}_{k\\mid k-1} &= \\mathbf{F}_k \\mathbf{P}_{k-1\\mid k-1} \\mathbf{F}_k^\\mathsf{T} + \\mathbf{Q}_k \\\\ \t\n", "\\tilde{\\mathbf{y}}_k &= \\mathbf{z}_k - \\mathbf{H}_k\\hat{\\mathbf{x}}_{k\\mid k-1}\\\\\n", "\\mathbf{S}_k &= \\mathbf{H}_k \\mathbf{P}_{k\\mid k-1} \\mathbf{H}_k^\\mathsf{T} + \\mathbf{R}_k \\\\\n", "\\mathbf{K}_k &= \\mathbf{P}_{k\\mid k-1}\\mathbf{H}_k^\\mathsf{T} \\mathbf{S}_k^{-1}\\\\\n", "\\hat{\\mathbf{x}}_{k\\mid k} &= \\hat{\\mathbf{x}}_{k\\mid k-1} + \\mathbf{K}_k\\tilde{\\mathbf{y}}_k\\\\\n", "\\mathbf{P}_{k|k} &= (I - \\mathbf{K}_k \\mathbf{H}_k) \\mathbf{P}_{k|k-1}\n", "\\\\\\end{aligned}\n", "$$\n", "\n", "The notation above makes heavy use of the Bayesian a$\\mid$b notation, which means a given the evidence of b. The hat means estimate. So, $\\hat{\\mathbf{x}}_{k\\mid k}$ means the estimate of the state $\\mathbf{X}$ at time $k$ (the first k) given the evidence from time $k$ (the second k). The posterior, in other words. $\\hat{\\mathbf{x}}_{k\\mid k-1}$ means the estimate for the state $\\mathbf{x}$ at time k given the estimate from time k - 1. The prior, in other words. \n", "\n", "This notation allows a mathematician to express himself exactly, and when it comes to formal publications presenting new results this precision is necessary. As a programmer I find all of that fairly unreadable; I am used to thinking about variables changing state as a program runs, and do not use a different variable name for each new computation. There is no agreed upon format, so each author makes different choices. I find it challenging to switch quickly between books an papers, and so have adopted my admittedly less precise notation. Mathematicians will write scathing emails to me, but I hope the programmers and students will rejoice.\n", "\n", "Here are some examples for how other authors write the prior: $X^*_{n+1,n}$, $\\underline{\\hat{x}}_k(-)$ (really!), $\\hat{\\textbf{x}}^-_{k+1}$, $\\hat{x}_{k}$. If you are lucky an author defines the notation; more often you have to read the equations in context to recognize what the author is doing. Of course, people write within a tradition; papers on Kalman filters in finance are likely to use one set of notations while papers on radar tracking is likely to use a different set. Over time you will start to become familiar with trends, and also instantly recognize when somebody just copied equations wholesale from another work. For example - the equations I gave above were copied from the Wikipedia [Kalman Filter](https://en.wikipedia.org/wiki/Kalman_filter#Details) [[1]](#[wiki_article]) article.\n", "\n", "The *Symbology* Chapter lists the notation used by various authors. This brings up another difficulty. Different authors use different variable names. $\\mathbf{x}$ is fairly universal, but after that it is anybody's guess. Again, you need to read carefully, and hope that the author defines their variables (they often do not).\n", "\n", "If you are a programmer trying to understand a paper's math equations, I suggest starting by removing all of the superscripts, subscripts, and diacriticals, replacing them with a single letter. If you work with equations like this every day this is superfluous advice, but when I read I am usually trying to understand the flow of computation. To me it is far more understandable to remember that $P$ in this step represents the updated value of $P$ computed in the last step, as opposed to trying to remember what $P_{k-1}(+)$ denotes, and what its relation to $P_k(-)$ is, if any, and how any of that relates to the completely different notation used in the paper I read 5 minutes ago." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Show Effect of Hidden Variables\n", "\n", "In our filter above velocity is the hidden variable. How would a filter perform if we did not use velocity in the state?\n", "\n", "Write a Kalman filter that uses the state $\\mathbf{x}=\\begin{bmatrix}x & \\dot{x}\\end{bmatrix}^\\mathsf{T}$ and compare it against the filter in the last exercise which used the state $\\mathbf{x}=\\begin{bmatrix}x\\end{bmatrix}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution\n", "\n", "We've already implemented a Kalman filter for position and velocity, so I will provide the code without much comment, and then plot the result." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LUVJSAnf3vkcCiIiInIU9s6QYjN0oLM9FbkkGCstPwmQ29nU6AIAEEqhcPaB2\n08DdVWP1rnbztHz2UvtxFJzoLubQYP7QQw9Z/bx+/Xps27YNJ06cQHx8PDZv3oy1a9di+fLlAICd\nO3dCq9Vi165dePbZZx3ZFSIiohHR1ywpstAQXLxSiJxzGThTmoWO7nabYwWJgGjtJEwNmAa/8Bh4\nqDzh7uoJd1c1BEE62l+FiJzMiNWYm0wmfPTRR+js7ERKSgrKy8uh1+uRmppqaaNUKpGSkoKsrCwG\ncyIiGnUdXe3Yd+IfOJZ/AADw1Xk/qN084eHmCQ83L6hVPe8eN97Vbp4QROvZT6r9XJFT+AVOHTjd\n60qaQM/0hIkxCzAjKpkPYBJRnySiKPY/v9Ig5efnY+7cuejq6oKrqys++OAD3H///cjKykJycjIu\nXbqE4OBgS/tVq1ahuroae/futWxrbm62fC4tLXVk94iIiCCKIsprC3Cy4it0GK4P6lhBIoVaUEJT\npUe3TECNn1uv7dyVnpjgNxUT/KbAw9Wn1zZEdHeJioqyfNZoNIM+3uEj5jExMTh79iyam5vx0Ucf\n4fHHH8fBgwf7PYa1ckRENFoa2vQ4UbYX11qqhnS8WTSh2dSG5l5mSVG4uCLcNw4TtFPg6x7E/78R\n0aA4PJjLZDJMmDABADBjxgzk5ORgy5YteO211wAAer3easRcr9dDp9P1eb7ExERHd5HuErm5uQB4\nj1D/eJ/QTe2d17EnexeOnN0LUTRbtmtau/Gd3WcRebEezRFBaPyfd9CpkqOlvQmt7Y1oaWtCS3sj\nWtua0NLRhK7uDqvzyqRyTI2cg1kxCxATOh1SKWcivhvxdwnZ49aqj6EY8d8eJpMJZrMZERER0Ol0\nSE9Px8yZMwEAnZ2dyMzMxMaNG0e6G0RENE6ZRTOOF36FL7L+L9o6WizbBUGKlMiFuPe538DtUjUA\nQFPThgDdFKvl7m/XZejsWfSnrQkGYxdC/aPgqui9nIWIaDAcGsxfeeUVPPDAAwgODkZrayt27dqF\njIwMS/34mjVr8NZbbyEmJgZRUVFYv3491Go1nnzySUd2g4iIxqHe5havrCnFR4fexSW99fNKk0Kn\n4fsL/gN+noHo+nMUzLdOfRgS0u91FDIlFBodfDV9/2svEdFQODSY6/V6PPXUU6ipqYFGo8G0adOw\nd+9eLF26FADw8ssvo6OjA6tXr0ZjYyOSkpKQnp4OlUrlyG4QEdE4c/vc4g3bt2K/shrZhQcg4ps5\nDrzUfngdA6QPAAAgAElEQVQ45YeIj5xjqf9WpKbi0u7dAIDQ2bP7XSyIiGgkOTSYv/feewO2SUtL\nQ1pamiMvS0REd5G6phoUnzmE1q5WuPnp4Kpwg0LmCoXcFUq5KxQyVyjlbj2f5a6QClLL3OLQ1+Do\nvHB8WfBXtLt+8784F6kM35q5HEsTvwe5TGF1PUEQUOfS0zacoZyI7iA+oUJERHdUZ3cHSi/no+TS\naRRXnkZtU/U3O4sHPl4mlUMulUP5n9NgQjyavFyt9k+JmIXlKavg5xng4J4TETkWgzkREY2I3mq+\ne7abUHXtIs5dOo1zladRXlMCs9k05OsYTN0wmLrR5qW02u6r0eF7C36EuAjOokFEYwODOREROdzt\nNd817/4B5eEeKKk6g/OXzqK9q+9FfWQGEyZeqENgdQu6PNVo/+6DMMoFdHZ3oKu7A52GG+/dHegy\ndFpNfQgAMqkMqbMeweKZ34XMRT6i35OIyJEYzImIaEB9jX73pb3iIirfWINzc31RHKPFtbK/AWV9\ntw/yi0BM6HRMCpmGwMLLcH/7PwAAXe+9DUVqap/XE0UR3cYuq6Du5xkApdy11/ZERM6MwZyIiPp1\n++h313vv9RqW65prUFSRh6KKkyitOgvDYzF9ntPDzQsxYdMx6UYY91B5fnO9kHgYsrMBAIoB/hIg\nkUh6pi+UKeGh8hrO1yQiuuMYzImIqF83ZzwRamoAAIqVK2HIzoYQFIiLVwpRVNkTxq81XunzHC4S\nKSJDpmJy2HTEhE5HgE9Yn8vVC4LQ7wI/RER3KwZzIiKyW4OXKwqna1GYvR0X6i+g29DZZ1s/z0DE\n+ERhkn8soqelsLyEiGgADOZERONIX7Xioiiio6utZ6n59ia0tjfhekezZen55vWPoa6iGNd8b4Tr\nmgKbc8tc5IgKnorY8JmIDU/gyphERIPEYE5ENE6YzWZU/PMDFL//ezR6KNAydybaVDK0tjehtaMZ\nJpOx/xP42o54+2kCEBsxE5PDEjAxOA5yF0UvBxIRkT0YzImI7nLtXdeRV5KJrFNf4nJTFZAc3LOj\n7RLQNrhzuUhlN0bFEzA5LAFar0DHd5iIaJxiMCciGoMGmr7QLJpx4XIhsgsP4MyFYzCYugc8p0Km\nhNrN85uXq+bG5553D5UXgv0m2CxpT0REjsFgTkQ0xvQ3fWFjay1OFB9EdtFXqG/W2xwrlQiIL7yG\nqMoWuP7oeXjNWwCNyhtqN08GbiKiO4zBnIhojLl9+kLpj1Yh9x9bkXvtDEoqT0OEaHNMkF8E5sYt\nwYyoZMhrmwDYt1AQERGNHgZzIqI7aLArat7UKRegD/NCXkIQcmeFoi1nh00bN4U7EmNSMCd2CUK0\nE77ZEaZxRNeJiMjBGMyJiO6QgVbUNBgNqG+pwbXGatQ2VX/z3lSNlp/N6vWcEkgQHRKPpLgliI+c\nA5mLfNS+DxERDQ+DORHRHXKzJKWzuR6VoZ649sdXUGMoQr2pFbWN1WhorYUomu06l5faD3NiF2NO\n7GL4ePiPcM+JiGgkMJgTETnAUEpSWjpbcHhxKLKmJ8Igl/ZsLDts1/Wkggt8NTqEaCMxe/IiRIfG\nQ5CwXpyIaCxjMCciGqaBSlJu19zWgK9yd+No/j4YZgf0eV4JJPBS+8LPKxBazyBovQLh5xkIP88A\neHtoIRWkI/J9iIjozmAwJyIapttnSVGsXAlDdjYUYWFW7ZrbGnAg91Nk5afbzCvur9YhPCQOWq8g\naD0DofUKhK9GxxpxIqJxhMGciGiENV9vwIGTn+Jo/j4YTQarfcHaCbhvzuOYEjELEonkDvWQiIic\nAYM5EdFtBlsvLgsJ6SlfubWUJSQETdfrcSD3E2QV7LcJ5CHaSNw353HERSQykBMREQAGcyIiK4Ot\nFwcAQRCgSE2FITsbANDh5Yp/ZfwFWYXpMJmMVm1D/aNw35zHEBs+k4GciIisMJgTEd3C3nrx2wmC\ngHZvVU8NeS+BPMw/CvcykBMRUT8cNrfWr3/9a8yaNQsajQZarRYPPfQQCgsLbdqtW7cOQUFBcHNz\nw6JFi1BUVOSoLhARWTGbzfA1GuFrNMJstm8+8KFoaKnFh1//D97Y+WMcObvHKpSH6aLx4++8hp89\n9luWrRARUb8cNmKekZGBF154AbNmzYLZbMZrr72GJUuWoKioCF5eXgCADRs2YNOmTdi5cyeio6Px\nxhtvYOnSpSgpKYG7u7ujukJEZClJCR1ESQrQd714b+pb9Nif8wmOF30Nk9l6hDxcNwn3JT2OmNDp\nDONERGQXiSiK4kicuK2tDRqNBp9//jnuv/9+iKKIwMBAvPjii1i7di0AoLOzE1qtFhs3bsSzzz5r\nOba5udnyWaPRjET36C6Qm5sLAEhMTLzDPSFn1FVZCVlSkqUkxazT2VWSAgz88Gddcw3Scz7GieKD\nMJtNVvvCAybhvjkM5GMNf5/QQHiPkD2Gm2FHrMa8paUFZrPZMlpeXl4OvV6P1NRUSxulUomUlBRk\nZWVZBXMiolsNZVXN4RAEodcAf62xGvtzPkbOuUMwi9alMRMCJ+O+OY8jOiSegZyIiIZkxEbMH330\nUVy8eBG5ubmQSCTIyspCcnIyLl26hODgYEu7VatWobq6Gnv37rVsu/VvG6WlpSPRPSIaIwRBQHhl\nJTyffx4A0LR1KyrCwgasGR/qcb1pbq9H/uVMlNcWQIT1r0x/j1BMC0mBvyaMgZyIaJyLioqyfHaa\nEfOf/exnyMrKQmZmpl3/o+L/zIioL97d3fB8/nlLSYrn88/De/du1Ln0/+vLbDajIiwM3rt3AwAa\n5PJBh/Km9jrkVx1BRV2RTSDXacIRH3IPdJqBS2OIiIjs4fBg/tOf/hT/+Mc/cPDgQYSHh1u263Q6\nAIBer7caMdfr9ZZ9vWEtF/WF9X7jQ1dlpc22gIAAhNtRKw7ccp8kJNjVXhRFVOpLcejUFzh1/qhN\nIJ8UOg33zn4MkUGxdp2Pxgb+PqGB8B4he9xa9TEUDg3mL730Ej766CMcPHgQ0dHRVvsiIiKg0+mQ\nnp6OmTNnAuh5+DMzMxMbN250ZDeI6C4ymFlShqOlrQm5JYeQXfgVahqqbPZPDkvAvXMeRURAjMOv\nTUREBDgwmK9evRrvv/8+PvvsM2g0GtTc+GdntVoNlUoFiUSCNWvW4K233kJMTAyioqKwfv16qNVq\nPPnkk47qBhE5saE8xHn7qpoKBz78aTKbUFRxEseLvkJBea7NDCsAEBeeiHvnPIowXXQvZyAiInIc\nhwXzbdu2QSKR4Fvf+pbV9nXr1uG1114DALz88svo6OjA6tWr0djYiKSkJKSnp0OlUjmqG0TkpIay\n1P1Nfc2SMlT6xis4XvgVThQfREt7o81+hUyJGdHJSJ56L0L9JzrsukRERP1xWDC396GqtLQ0pKWl\nOeqyRDRGDHWpe0fp6u5AXulRHC/8CmVXi3ttMyFwMubGLcH0ifOgkLuOSr+IiIhuGrF5zImI7iSz\naEZrexOuNpWjvLYAfz+xEd2GTpt2HiovzJ68GEmxi6H1CroDPSUiIurBYE5Eo8LRD3GaRTNa25pQ\n33INDS16NLTWoqHl2jev1loYTYZejxUEKaZGzEJS3BLEhM2AVJAOuR9ERESOwmBORIPWbejC4SN/\nR+HVfBiEnpBsNptgEk0wm3s+3/5zz2cTzGvnQYQIWdkOuPxlF+RSOVxc5JBJZZC53Phs+Vlhtb3b\n0HEjiNeiofUaTCbjoPqt8w5BUtwSzIpZALWb5wj96RAREQ0NgzkR2c0smnHy3GH86+Bf0WhoHda5\nugyd6DJ0os1BfeuNm1INpVQFX3UgHlzwOEL9o7igGREROS0GcyKyy/mqs/gscwcuXyu7012xUCnV\n8PbQ9rzUfpbPPh5aeKm1cFW4WRYF4XSHRETk7BjMiahf1XUV+CLz/6CoMs9qu+p6F1L3n0dYiwTi\nezugDAyCIEghCFJIBSkEyY13QejZfsvPAGA0GWEwdsFgNMBg6obR2I1uYzeMpm4YjN09241dMJgM\nN37uhsxFBm+11hLAlZw5hYiI7iIM5kQjwCyacfFKIXLOZUDfcBmzJy/C3LglEJzwIcO+Fv1pbK3D\nnmO7cKL4oNWy9DKpHMmaOKT+fjtcu0w9D3FOnTfoRX9cpDIGayIiolswmBM5kL7hMnLOHULOuQw0\nttZatpdfPYej+fvw/YX/gQmBk+9gD631tuiPecF8fJX3GTJO/RMGU7elrQQSzI5djGVJT0Cj8oYh\nZQUMcOxKnEREROMZgznRMLW2NyPv/BHknMvAJX1pn+0u15Zh80drkThpAR5Kfhqe7j6j2Mve3bro\nj0EqIHvLK9hXHof2butHMmPDZ+Kh+T9AoG+4ZdtoLQxEREQ0XjCYEw2BwdiNgvIc5BQfQlFlHsxm\nk00bN6UaCVHz4aZU42De55bR59ySDJwtO45vz34UC6c/CJmLzCF96qskZSAmCXBqRhD+df9k1Puq\ngFtCeYg2Et9JfgbRIfEO6SMRERH1jcGcyE6iKKKsugg55w7h1Pmj6Ohut2kjFVwwJSIRsyYvRGz4\nTLhIe0L3vClL8dmRHTh9IQsA0G3oxD+P/h9kFx7AwymrEBeROKy+9VaSokhN7TOcG4zdOF91FqdK\ns1Dw8wVoN1mviOntocWD857CjOhkCBKWqRAREY0GBnOifpjMJpRVF6OwPAdnLmSjvkXfa7uIgBjM\nilmIGdHzoVKqbfZ7e2ix6v6Xcb7qLD7J+Auu1l8CANQ2VePPX6xHXHgiHl7wQ/h5Bgypn7eWpACA\nYuVKGLKzrcpNuro7UFSZhzMXslFYkYuu7g6b87gp3fHtWY8iOf4+h43kExERkX0YzIlu0955HcWV\neSgoy0FRZR46unpfAsdH449ZMQsxK2ah3YE6OiQeLz+xCZn5e7Hn2C7LqHthRS7OVZ3GohnfwdKZ\nD0PQ1wEYXElKb9o6W1FQloMzF7NxrvJUn0vUa1TemD15Eb6VuBxuCvchX4+IiIiGjsGcCIC+8QoK\nynJQWJ6DsupimEVzr+1cFSokRCVj1uSFiAiIGdIqklKpCxZMfwAJ0ffgX1nvI7vwAESIMJmMOJD7\nCU6c/je+8+lZJBTVD1iScpMsJKSn7cqVaFbJcOrNl1B08q+4cLmgz+/io/HH9IlzER85F2G6KJas\nEBER3WEM5jQumUxGXKwuRkF5DgrLc1HbVN1nW093H0yJmIW4iEREh8RD5iJ3SB/Ubho8sWQ15k/9\nNj4+tB0VNSUAgBZjO/7vQxNxIFEL9/QNMNUdgEQhhyiKMMMMiIAomi0/i6JoeRnXP4i667UQrx3p\n9ZqBPmGIn5iEaZFzEegbxuXpiYiInAiDOY0bLW2NKK48heLKPBRX5PX68CbQM193qC4KUyISMSVi\nFgJ9w4cUYO2dJSXUfyLWPPpr5J7LwOcZ76G1qwUAcDXQo6dB/YVBX/tWYbpoTItMQnxkErRegcM6\nFxEREY0cBnO6a5lMRlTUlKC48hSKKvJwubasz7ZymRIxodMRF5GIuPBEeKg8h3Xtwc6SIkgEzJ68\nCFMiZmHPP36HzLpTMEuHVloikQiYGBSHaROTMHXCHHipfYf8PYiIiGj0MJjTXaWxtc4yKn7+0pk+\nR8UBwEvtZylRiQqe4rASFcC+WVJ646Z0x8NPpWFBaSFqWq5CpvWHVCoAkECQSCCRCJDcfIfkxucb\nLwiQSACNu0+vM8MQERGRc2MwpzHNZDbifNVZFFfmoagizzINYW8EQYoJgZMxOSwBsWEJTltjLQgC\n/CZNhR+m3umuEBER0ShiMKcxxSyaUVN/CSVVZ5FTdAQ1zRUwmnufAhDoGRWPDUvA5PAZiAqOh6vC\nbWjXHeSqmrfOkgLcKGUJCRnStYmIiGh8YDAnpyaKIuqaa3C+6izOV51F6eUCXO9o7rO9VOqCiUFx\nPaPi4Qnw9woe9qj4YOvFgZ5Rb0VqKgzZ2QAAxTDnIyciIqK7H4M5OZ3G1jqUXs7vCeJV+Wi8Xtdv\nex+NP2LDZiI2PAETg6dAIVM6tD9DrRcXBGHANkREREQ3MZjTHdfedR0ll87gfFU+SqvO4lo/c4oD\ngMrVA9HBU6Ewe0CnicDie1LtvtZgS1KIiIiIRotDg/nhw4exceNG5OXlobq6Gu+99x6eeeYZqzbr\n1q3D9u3b0djYiDlz5mDLli2IjY11ZDdoDBBFERU153E0fy9OnT8Kg6m7z7YKuSuigqYgKmQqooPj\nEeAbCkEiIDc3d1DXHEpJCsB6cSIiIhodDg3mbW1tiI+PxzPPPIOnn37aprZ3w4YN2LRpE3bu3Ino\n6Gi88cYbWLp0KUpKSuDu7u7IrpCT6uzuQO65DBzN34srdRW9tpFJ5YgIjEF0SDyiQ+IRoo2EVJBa\ntTGbzfA1Gi2f7Rn5HlZJCuvFiYiIaIQ5NJjfd999uO+++wAAK1assNoniiI2b96MtWvXYvny5QCA\nnTt3QqvVYteuXXj22Wcd2RVyMldqy5GZvw+55w6hy9Bpsz/ILwJTbix5H66b1O+c4jdHvkMHOfI9\nHKwXJyIiopE2ajXm5eXl0Ov1SE39ph5YqVQiJSUFWVlZDOZ3oW5jF06XZiEzfy8qrpbY7Je5yDEz\n+h7Mn3ovQv0n2j17ylBHvlmSQkRERM5s1IJ5zY0Q5e/vb7Vdq9Wiurr/h/1odJlFM641XoHZbIZC\npoRcpoBcpoTcRWFXeL7WeAWZ+ftwouhrtHddt9nv7x2M5Kn3YlbMQrgpR6+EiSUpRERE5MycYlaW\n/sLeYB/wo6ERRRF116tRUVeEyroitHe39trORZDBRSq/8X7r5573ju7r0LdU2hwnSASE+kzGJF0C\ntB6hkBglKCo4B0EQ4N3d8+Bng1wOs9k8YF8FQUD41q3wfP55AEDT1q2oqK+HubZ2cF96sO1pTOPv\nErIH7xMaCO8R6k9UVNSwjh+1YK7T6QAAer0ewcHBlu16vd6yj0aXKIpoaKtBRV0RKuqK0NbV98I9\nNxnNhn5X2rydu8IT0boERGqnwVWustonCALCKystAdtj61ZUhIUNGM7NZjMqwsLgvXs3APsDPRER\nEZEzG7VgHhERAZ1Oh/T0dMycORMA0NnZiczMTGzcuLHP4xITE0eri+OCKIqorqvAqdKjyDufibrm\nml7buSnV8HDzRLehE13GLnQbOmEw9j2l4a0kEgFTIhIxf+q9iAmbDkHSe7lIV2UlZPffb6kV93z+\necTZUSt+081Ri8SEBLva0/hkuU/4u4T6wfuEBsJ7hOzR3DzwIGd/HD5dYmlpKYCeUc3KykqcPn0a\nPj4+CAkJwZo1a/DWW28hJiYGUVFRWL9+PdRqNZ588klHdoN6cbW+CqfOZyKvNBPXGq/02sZVoUJ8\nZBISopMRHTwVUqn17WE2m9Bt7O4J64bOG+89ob2zux3t+mpABCbFp8BHox2Nr0VERDRqXFxc0Nlp\nO7MYjQ8SiQRyudzuySqGwqHBPCcnB4sXLwbQ0/m0tDSkpaVhxYoV+N///V+8/PLL6OjowOrVq9HY\n2IikpCSkp6dDpVINcGYais7uDhw+/S+cPH8EV+sv9dpGIXdF/IQ5SIhOxqTQaXCRyvo8nyBIoZS7\nQil3tdr+zcI9PwHQM9uJmQv3EBHRXcTFxQWhoaFQKOybCIHuPiaTCZ2dnVAoFCM2eYREFEVxRM48\nDLf+M4BGo7mDPRm7Cspy8NHBP6Pxep3NPrlMiakRszAjOhmTw2bYzBk+2GXruyorIUtKspSkmHU6\nu6YvHMq1bsV/ViR78D4he/A+oYFcvXoVOp2OoXycE0URXV1dUCqVve4fboZ1illZyHGa2xrwScZf\ncLo0y2q7zEWOuIhEzIhKRlz4TMhlil6PH+qy9UPFhXuIiGgscHFxYSinEb8HGMzvEmbRjGMF+/FF\n5k50dLdbtqtcPfDgvB9gZnQyFLeVoPRmKIv3sCSFiIiIaPgYzO8CNQ1V+PtXW1FWXWy1fVbMItwf\nsQQqhTtkLr2PkDsCF+4hIiIiGj4G8zHMYDRgf+7H2J/zCUxmo2W7nyYAjyz6T4QV10CxYAkA+0tS\nhjr6zZIUIiIiouHhsOYYdeFKITbsWoO9xz+0hHJBkCJ11vfx/z+1GRHwspSkCDU1PSUpNx6y7M+t\no9+G7OwRrS8nIiIi6s2hQ4cgCAIyMjIs29atW3fXZ5K7+9vdhdo7r+PvX23BHz5+1Wo+8jBdNF5+\n4m08MO8pyIdZtnJz9FsRFnbX/wdAREQ03rW1tSEtLQ3Lli2Dn58fBEHAhg0bem27cOFCCIIAQRAg\nlUqh0WgQExODp59+GgcOHLD7mjdDdm+vt99+GxKJxPK61e0/b926FTt37hz8l3ZSLGUZI0RRxKnS\no/gk4y9obW+ybFfIXfHgvB8geeq3IQhSy3Y+kElERET2qK2txZtvvomQkBAkJCRg//79/c4+EhgY\niN/+9rcAvllc8tNPP8X777+PRx99FO+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import randn\n", "\n", "def mkf_filter(R, Q):\n", " f = KalmanFilter(dim_x=1, dim_z=1, dim_u=1)\n", " f.P = 50.\n", " f.H = np.array([[1.]])\n", " f.F = np.array([[1.]])\n", " f.B = np.array([[1.]])\n", " f.Q = Q\n", " f.R = R \n", " return f\n", "\n", "def plot_compare_pos_vel(x0, p0, R, Q, move):\n", " # storage for filter output\n", " x1, x2 = [], []\n", "\n", " # initialize the filters\n", " f1 = mkf_filter(R, Q)\n", " f1.x[0] = 0.\n", " f1.P[0, 0] = p0\n", " \n", " f2 = pos_vel_filter(x=(0., 1.), P=p0, R=R, Q=Q)\n", " f2.x[0] = 0.\n", " f2.x[1] = 1.\n", " f2.P *= p0\n", " \n", " for i in range(50):\n", " u = move + randn()\n", " f1.predict(u=u)\n", " f2.predict(u=u)\n", " \n", " z = i*move + randn()\n", " f1.update(z)\n", " f2.update(z)\n", " \n", " x1.append(f1.x[0, 0])\n", " x2.append(f2.x[0])\n", "\n", " plt.plot(x1, label='1D Filter')\n", " plt.scatter(range(len(x2)), x2, c='r', label='2D Filter')\n", " plt.title('State')\n", " plt.legend(loc=4)\n", " plt.xlim([0,50])\n", " plt.show()\n", " \n", "plot_compare_pos_vel(x0=0., p0=50., R=5., Q=.2, move=1.) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion\n", "\n", "The output of the filter that incorporates velocity into the state produces much better output than the filter that only tracks position - the output is much closer to a straight line. We've already discussed why hidden variables increase the precision of the filter, so I will not repeat that explanation here. But this exercise is intended to trigger a train of thought:\n", "\n", "1. The equations in this chapter are mathematically equivalent to the equations in the last chapter when we are only tracking one state variable.\n", " \n", "2. Therefore, the simple Bayesian reasoning we used in the last chapter applies to this chapter as well.\n", "\n", "3. Therefore, the equations in this chapter might 'look ugly', but they really implement multiplying and addition of Gaussians.\n", "\n", "> The above might not seem worth emphasizing, but as we continue in the book the mathematical demands will increase significantly. It is easy to get lost in a thicket of linear algebra equations when you read a book or paper on optimal estimation. Any time you start getting lost, go back to the basics of the predict/update cycle based on residuals between measurements and predictions and the meaning of the math will usually be much clearer. The math *looks* daunting, and can sometimes be very hard to solve analytically, but the concepts are quite simple." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adjusting the Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Your results will vary slightly depending on what numbers your random generator creates for the noise component of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n", "\n", "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the ${\\mathbf{H}}$ and ${\\mathbf{F}}$ matrices - they develop in an obvious manner based on the physics of the system we are modeling. The art comes in modeling the sensors and selecting appropriate values for the rest of our variables.\n", "\n", "Let's look at the effects of the noise parameters ${\\mathbf{R}}$ and ${\\mathbf{Q}}$. We will want to see the effect of different settings for ${\\mathbf{R}}$ and ${\\mathbf{Q}}$, so I have hard coded our measurements in `zs` based on a variance of 50 meters squared. That is very large, but it magnifies the effects of various design choices on the graphs, making it easier to recognize what is happening. The behavior of the filter is somewhat dependent on the measurements, so I have hard coded them to ensure we all see the same behavior. Note that I use `numpy.var()` to compute the variance of the data - this is an important tactic that you can use if you are running a filter *off-line*, meaning with collected data rather than real time data. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "variance 240.45554425\n" ] }, { "data": { "image/png": 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Yb1zgn7vhnle09cHnvwNP3VfkaXGJjsxaXItvV/rZpZUAKIrg/i6ZvDIkmWM7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\n", 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cYMfP7xAWiwXDCAJgwIDYk2eWARAWFlS1whI7fLvM/fx8AeYf74ZPFsKu/TBt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# I've hard coded the measurements to ensure we are all looking \n", "# at the same data. R~240\n", "zs = [3.59, 1.73, -2.575, 4.38, 9.71, 2.88, 10.08, 8.97, 3.74,\n", " 12.81, 11.15, 9.25, 3.93, 11.11, 19.29, 16.20, 19.63,\n", " 9.54, 26.27, 23.29, 25.18, 26.21, 17.1, 25.27, 26.86,\n", " 33.70, 25.92, 28.82, 32.13, 25.0, 38.56, 26.97, 22.49,\n", " 40.77, 32.95, 38.20, 40.93, 39.42, 35.49, 36.31, 31.56,\n", " 50.29, 40.20, 54.49, 50.38, 42.79, 37.89, 56.69, 41.47, 53.66]\n", " \n", "print('variance', np.var(zs))\n", "run_filter(data=zs, R=240, Q=200, P=P, plot_P=False, \n", " title='R_var = 240 $m^2$, Q_var = 20 $m^2$')\n", "\n", "run_filter(data=zs, R=240, Q=.02, P=P, plot_P=False, \n", " title='R_var = 240 $m^2$, Q_var = 0.02 $m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n", "\n", "In the Kalman filter ${\\mathbf{R}}$ is the *measurement noise* and ${\\mathbf{Q}}$ is the *process uncertainty*. ${\\mathbf{R}}$ is the same in both plots, so ignore it for the moment. Why does ${\\mathbf{Q}}$ affect the plots this way?\n", "\n", "Let's remind ourselves of what the term *process uncertainty* means. Consider the problem of tracking a ball. We can accurately model its behavior in static air with math, but if there is any wind our model will diverge from reality. \n", "\n", "In the first case we set `Q_var=20 m^2`, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\" as we are saying that the variance in the velocity is 10. Strictly speaking, we are telling the filter there is a lot of external noise that we are not modeling with $\\small{\\mathbf{F}}$, but the upshot of that is to not trust the motion prediction step. So the filter will be computing velocity ($\\dot{x}$), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n", "\n", "In the second case we set `Q_var=0.02 m^2`, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". Again, more strictly this actually says there is very small amounts of process noise (variance 0.02 $m^2$), so the motion computation will be accurate. So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our trustworthy velocity prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's set `Q_var` to $0.2\\, m^2$, and bump `R_var` up to $10,000\\, m^2$. This is telling the filter that the measurement noise is very large. " ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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teL/d8fDml9Vr+8MFcOMTsHlPzftXHQ8Og/8bAYVFqOnzKC4utrz03nvflQm8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\n7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_filter(data=zs, R=10000, Q=.2, P=P, plot_P=False, std_scale=1., \n", " title='R_var = $10,000\\, m^2$, Q_var = $20\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effect of this can be subtle. We have created an suboptimal filter because the actual measurement noise variance is 240 $m^2$, not 10,000 $m^2$. By setting the filter's noise variance so high we force the filter to favor the prediction over the measurement. This can lead to apparently very smooth and good looking results. In the chart above the track may look extremely good to you since it follows the ideal path very closely. But, the 'great' behavior at the start should give you pause - the filter has not converged yet ($\\mathbf{P}$ is still large) so it should not be able to be so close to the actual position. We can see that $\\mathbf{P}$ has not converged because the entire chart is colored with the yellow background denoting the size of $\\mathbf{P}$. Let's make $\\mathbf{R}$ larger yet. Let's see the result of a bad initial guess for the position by guessing the initial position to be 20 m and the initial velocity to be 1 m/s." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vQ1EOoKpJ3HFHV3x9bSiKHUUBX19vGYhLklQ7LFZYvk5/3rfzpbfbnwD//qRy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_filter(data=zs, R=10000, Q=.02, P=P, plot_P=False,\n", " initial_x=np.array([20., 1.]), std_scale=1.,\n", " title='R_var = $10,000\\, m^2$, Q_var = $.2\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see that the filter cannot acquire the track. This happens because even though the filter is getting reasonably good measurements it assumes that the measurements are bad, and eventually predicts forward from a bad position at each step. If you think that perhaps that bad initial position would give similar results for a smaller measurement noise, let's set it back to the correct value of 240 $m^2$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JMGkGvPjQmc9/+2vj/bFbK1xQ6GzWrNnK8eO5DBrUA4B33vmGrKwc3njjMQBs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\n5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_filter(data=zs, R=240, Q=.2, P=P, plot_P=False, \n", " initial_x=np.array([20., 1.]), std_scale=1.,\n", " title='R_var = $240\\, m^2$, Q_var = $.2\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see that the filter initially struggles for several iterations to acquire the track, but then it accurately tracks our dog. In fact, this is nearly optimum - we have not designed $\\mathbf{Q}$ optimally, but $\\mathbf{R}$ is optimal, and thus will yield optimal results. Recall that our rule of thumb for the variance of $\\mathbf{Q}$ was to set it between $\\frac{1}{2}\\Delta a$ to $\\Delta a$, where $\\Delta a$ is the maximum amount that the acceleration will change between sample period. This only applies for the assumption we are making in this chapter - that acceleration is constant and uncorrelated between each time period. In the Kalman Math chapter we will discuss several different ways of designing $\\mathbf{Q}$.\n", "\n", "To some extent you can get similar looking output by varying either ${\\mathbf{R}}$ or ${\\mathbf{Q}}$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary ${\\mathbf{R}}$ and/or ${\\mathbf{Q}}$ based on your knowledge of the system you are filtering." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Detailed Examination of the Covariance Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far I have not given a lot of coverage of the covariance matrix $\\mathbf{P}$. It is nothing more than the variance of our state - such as the position and velocity of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9{\\times}9$ covariance matrix, or even larger.\n", "\n", "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n", "\n", "$$\n", "\\Sigma = \\begin{pmatrix}\n", " \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n", " \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n", " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n", " \\end{pmatrix}\n", "$$\n", "\n", "(The Kalman filter literature uses $\\mathbf{P}$ for $\\Sigma$; they both denote the same thing.)\n", "\n", "The diagonal contains the variance of each of our state variables. So, if our state variables are\n", "\n", "$$\\textbf{x}=\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n", "\n", "and the covariance matrix happens to be\n", "\n", "$$\\textbf{P}=\\begin{bmatrix}2&0\\\\0&6\\end{bmatrix}$$\n", "\n", "we know that the variance of $x$ is 2 $m^2$ and the variance of $\\dot{x}$ is 6 $(m/s)^2$. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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QZZhyHK8rwVw4jivLMGVZ3LoA+A9XJgAdwzJNmYbF+EebolMNwM8I1QA6xu86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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import filterpy.stats as stats\n", "\n", "P = np.array([[2., 0.], \n", " [0., 6.]])\n", "stats.plot_covariance_ellipse((0, 0), P, facecolor='g', alpha=0.2,\n", " title='|2 0|\\n|0 6|')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = np.array([[2.0, 2.4],\n", " [2.4, 6.0]])\n", "stats.plot_covariance_ellipse((0, 0), P, facecolor='g', alpha=0.2, \n", " title='|2.0 2.4|\\n|2.4 6.0|')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, dependent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n", "\n", "$$\n", "\\mathbf{P} = \\begin{pmatrix}\n", " \\sigma_1^2 & \\sigma_{1,2} \\\\\n", " \\sigma_{2,1} &\\sigma_2^2 \n", " \\end{pmatrix}\n", "$$\n", "\n", "Here the notation $\\sigma_{1,2}$ means the covariance of variables 1 and 2 where that is defined as\n", "\n", "$$\\sigma_{i,j}\n", "= \\mathrm{cov}(X_i, X_j) = \\mathrm{E}\\begin{bmatrix}\n", "(X_i - \\mu_i)(X_j - \\mu_j)\n", "\\end{bmatrix}$$\n", "\n", "We can rearrange the terms to get\n", "\n", "$$\\begin{aligned}\n", "\\sigma_{i,j} &= \\mathrm{E}\\begin{bmatrix}(X_i - \\mu_i)(X_j - \\mu_j)\\end{bmatrix} \\\\ \n", "&= \\mathrm{E}\\begin{bmatrix} (X_j - \\mu_j)(X_i - \\mu_i)\\end{bmatrix} \\\\ \n", "&= \\sigma_{j,i}\n", "\\end{aligned}$$\n", "\n", "In general, we can state that $\\sigma_{i,j}=\\sigma_{j,i}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's get back to concrete terms. Let's start by revisiting plotting a track. I will hard code the data and noise to avoid being at the mercy of the random number generator, which might generate data that does not illustrate what I want to talk about. I will start with `P=500`." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gQ6+vxGIpRlU9NwDGxirExqYCnjrRfn6NJfX+t5hOD7zuef70bS0Ggq1RZ1WZ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\nrVaLf/7zn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ndU4REYGXX36Z3NxccnJyMJlMrbZvS5u2OHHyOJWXu/f0hocOHTI6wn1T5q7h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\nY+TIkZ42PUFUnxjmTl/s2T9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# guarantee the noise is the same each time so I can be sure of\n", "# what the graphs look like.\n", "zs = [-6.947, 12.467, 6.899, 2.643, 6.980, 5.820, 5.788, 10.614, 5.210, \n", " 14.338, 11.401, 19.138, 14.169, 19.572, 25.471, 13.099, 27.090,\n", " 12.209, 14.274, 21.302, 14.678, 28.655, 15.914, 28.506, 23.181, \n", " 18.981, 28.197, 39.412, 27.640, 31.465, 34.903, 28.420, 33.889, \n", " 46.123, 31.355, 30.473, 49.861, 41.310, 42.526, 38.183, 41.383, \n", " 41.919, 52.372, 42.048, 48.522, 44.681, 32.989, 37.288, 49.141, \n", " 54.235, 62.974, 61.742, 54.863, 52.831, 61.122, 61.187, 58.441, \n", " 47.769, 56.855, 53.693, 61.534, 70.665, 60.355, 65.095, 63.386]\n", "\n", "var = np.std(zs)**2\n", "run_filter(data=zs, R=var, Q=.2, P=500., plot_P=True, \n", " title='$P=500\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the output we see a very large spike in the filter output at the beginning. If you look at the data (dotted red line) you will see a corresponding, smaller spike in the beginning of the data. We set $P=500\\, m^2$, which corresponds to $\\text{P}=[\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix}]$. We now have enough information to understand what this means, and how the Kalman filter treats it. The 500 in the upper left hand corner corresponds to $\\sigma^2_x$; therefore we are saying the standard deviation of `x` is $\\sqrt{500}$, or roughly 22.36 m. If we recall how standard deviations work, roughly 99% of the samples occur withing $3\\sigma$, therefore `P=500` is telling the Kalman filter that the initial estimate could be up to 67 meters off. That is a pretty large error, so when the measurement spikes the Kalman filter distrusts its own estimate and jumps wildly to try to incorporate the measurement. Then, as the filter evolves $\\mathbf{P}$ quickly converges to a more realistic value.\n", "\n", "Now let us see the effect of a smaller initial value for `P`." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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G3ie+iLS6uo7S0moSEnoDFg4cqGL//gqGDOmHoqjExSURH6+gqvqCPoGBR30r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\nAAAAAElFTkSuQmCC\n", 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7612jUCiE18Sk1Wlxo+zmwBm2bN9ZVMgAvPD4n2EnswcAVNaUYsN/l7FLCRGZ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\nxmRENBCKaLa/cxmvzWabiIjuTXqdD56btxZzkxY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_filter(data=zs, R=var, Q=.2, P=1., plot_P=True, \n", " title='$P=1\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This *looks* good at first blush. The plot does not have the spike that the former plot did; the filter starts tracking the measurements and doesn't take any time to settle to the signal. However, if we look at the plots for P you can see that there is an initial spike for the variance in position, and that it never really converges. Poor design leads to a long convergence time, and suboptimal results. \n", "\n", "So despite the filter tracking very close to the actual signal we cannot conclude that the 'magic' is to use a small $\\text{P}$. Yes, this will avoid having the Kalman filter take time to accurately track the signal, but if we are truly uncertain about the initial measurements this can cause the filter to generate very bad results. If we are tracking a living object we are probably very uncertain about where it is before we start tracking it. On the other hand, if we are filtering the output of a thermometer, we are as certain about the first measurement as the 1000th. For your Kalman filter to perform well you must set $\\text{P}$ to a value that truly reflects your knowledge about the data. \n", "\n", "Let's see the result of a bad initial estimate coupled with a very small $\\text{P}$ We will set our initial estimate at 100 m (whereas the dog actually starts at 0m), but set `P=1 m`." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FeXkFkZF3UlZWDoCvjwfBMckUvzYLNu6GZn60+mAclZXG0hQHB3sWLJhqmZ1X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\nQjCZmjNy5P04OLhbZrHd3c+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VV86hoqKSykozTk5O6LoD27fvx8XFk/DwToAzbm6BODm5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\nbjWsorrhy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.array([100., 0.]).T\n", "\n", "run_filter(data=zs, R=var, Q=.2, P=1., initial_x=x,\n", " plot_P=False, title='$P=1\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the initial estimates are terrible and that it takes the filter a long time to start converging onto the signal . This is because we told the Kalman filter that we strongly believe in our initial estimate of 100 m and were incorrect in that belief.\n", "\n", "Now, let's provide a more reasonable value for P and see the difference." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1EBJ4CyGEEKLdud1u1q5dTY8eett0u72MJUsWct55/VEUJwEBHs4+OxFV3QuA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MmTJ0vd5uPjU+a+ZY54T506FaIolvmKi4vT2ycrKws9evSAm5sb5syZ84yXQkRERGTavvnmG10d\ntG/fvlL71KtXD6IookOHDgaOjh4VHx+PqKgok1nMo8wR73feeQeDBw8u8wBubm66r7OyshAeHg5R\nFPHTTz9BLpfrttWuXRt37tzR21eSJNy+fRu1a9d+4vEDAwPLPD8ZT/GID3Nk2pin6oF5qh6Yp2eT\nm5tr7BCqlEqlwtq1a9GmTRu99gMHDuDSpUtQKpW654+QcRQX3sOGDYNara6UY1pbWz/x74CnFfhl\nFt4ODg5wcHAoVxCZmZno1q0bBEHAL7/8opvbXaxVq1bIyspCQkKCbp53QkICsrOzERISUq5zEBER\nEZmKbt26YcOGDfjyyy9hZvZ3SbV27Vo0aNAAMpnMiNFVXHZ2NiwtLY0dRqWQJMnYIQCopJsrMzMz\nERYWhvT0dKxYsQKZmZlITk5GcnIyCgoKAAANGzZE165d8eabb+LAgQNISEjAm2++iR49ejx1PgwR\nERGRqYmIiMC9e/ewY8cOXVthYSHWr1+P119/vUR/SZIQHR2NgIAAqFQqODk5YcSIEbh7965evx9/\n/FE3bVepVMLDwwOTJk1CXl6eXr+UlBSMGDFC16927doIDw/H6dOndX1EUURUVFSJWDw8PDBs2DDd\n++LpM7GxsXj77bfh5OQEa2tr3faDBw8iPDwctra2sLCwQGhoKPbs2aN3zOnTp0MURZw9exYDBw6E\nra0tatWqhffffx8AcP36dfTq1QtqtRq1a9fGp59+WiKuvLw8REVFwcfHB0qlEnXq1MHEiRORk5Oj\n108URYwZMwZbtmxBo0aNoFQq0ahRI71cTJ8+HZMmTQIAeHp6lpgmfeTIEYSHh0Oj0UClUsHDwwOD\nBw+u0v+pqZSbKw8fPozff/8dgiDoLQsoCAJiY2PRtm1bAEW/AY4fPx5dunQBAPTq1QsLFiyojBCI\niIiIDKpOnToIDQ3F2rVr8Y9//AMA8Ouvv+L27duIiIjAd999p9d/zJgx+PrrrzF06FC8/fbbuHbt\nGqKjo/HHH3/g4MGDUCgUAIqKYJVKhcjISKjVaiQkJODzzz/H9evX9Y7Zu3dvnDx5EuPHj4enpydu\n376NuLg4nD9/Hn5+frp+pU13EQSh1Pbx48fD3t4eH3zwgW7axN69e9GlSxc0a9YM06ZNg5mZGb79\n9luEhYUhJiYG7dq10ztGREQEGjZsiNmzZ+Pnn3/GrFmzoFar8d///hedOnXCnDlzsHr1akyaNAnN\nmzfXzYOXJAmvvvoq4uLiMGrUKPj5+eH06dNYtGgRTp06pVdUA0UzJ7Zu3YqxY8fCysoKX375JV57\n7TVcu3YN9vb2eO2113D+/Hl89913mD9/PhwdHQEUDQbfuXMHnTt3hkajwbvvvgs7Oztcu3YNW7du\nxYMHD6rupmDJBKWnp+teZLoOHjwoHTx40Nhh0FMwT9UD81Q9ME/PJicn59l2AEp/VVb/SrJixQpJ\nEATp999/l5YsWSJZWlpKDx48kCRJkgYNGiS1atVKkiRJ8vf3lzp06CBJkiTt379fEgRBWr16td6x\n9u3bJwmCIC1dulTXVnysR82cOVMSRVG6fv26JEmSlJaWJgmCIH322WdlxioIghQVFVWi3cPDQxo2\nbFiJa2rZsqVUWFioa9dqtZKvr6/UuXNnvf3z8/Mlf39/KSQkRNc2bdo0SRAEacSIEbq2wsJCyc3N\nTRIEQZo5c6auPT09XbKwsJAGDhyoa1uzZo0kiqIUFxend641a9ZIgiBIO3fu1LsuhUIhXbx4UdeW\nmJgoCYIgLViwQNc2d+5cSRAE6erVq3rH3LJliyQIgnT48OFSvmtlK+tz/bQatsrW8SYiIiJ60fXp\n0wcFBQXYsmULcnJysGXLllKnmaxfvx5WVlYICwtDamqq7uXr6wuNRoPY2FhdX5VKBQDQarXIyMhA\namoqWrduDUmScPToUV0fuVyO2NhYpKWlVdr1jBw5UrcUNAAcP34cSUlJiIiI0Is7IyMDnTp1wu+/\n/15iasaIESN0X4uiiObNm0MQBAwfPlzXrlar4evri8uXL+t9j+rXrw8/Pz+9c7Vt21Y3i+JRHTp0\ngJeXl+59QEAAbGxs9I75JLa2tgCArVu34uHDh+X87lRclazjTURERPTMnvUGOBO4Yc7Ozg5dunTB\n6tWrIYoicnJy0K9fvxL9kpKSkJWVBScnp1KP8+jKbydPnsSkSZOwd+/eEnObi6d/KBQKzJ49G//6\n17/g5OSE4OBghIeHY9CgQahTp85zX4+3t3eJuAHoFc2PEgQBd+/ehaurq66tbt26en3UajXMzc2h\n0Wj02m1sbPSuOykpCefOnSvx3Jfi8zy+Ot7j5wGK8lGeX0TatWuH3r17IyoqCvPmzUO7du3Qs2dP\nDBgwoMQCIZWJhTcRERFRBQwYMACDBw/G/fv30blzZ91c4kdptVo4ODhg3bp1pR7Dzs4OQFFh3aFD\nB1hbW2PmzJmoV68eVCoVbty4gaFDh0Kr1er2iYyMRK9evfDDDz8gJiYGM2bMwMyZM/HTTz+VmHf9\nuCeN8haPtj8aNwDMnj0bzZs3L3Wfx6+3tNVcnrSsovTIL09arRb+/v744osvSu3r4uLy1PM8fsyy\nrF+/HgcPHsRPP/2EmJgYjBo1CrNmzcKBAwdKLf4rAwtvIiIiogro1asXFAoF4uPjsXLlylL7eHt7\n49dff0VwcHCZS/TFxsbi7t272Lx5M0JDQ3XtMTExpfb38PBAZGQkIiMj8eeff+Kll17Cxx9/rCu8\n7ezskJ6errdPfn4+bt26Va5rKx4Bt7KyQseOHcu1z/OqV68eDh8+XKnnedo66kFBQQgKCkJUVBS2\nb9+O8PBwLFu2DO+9916lxfAozvEmIiIiqgCVSoWvvvoK06ZNwyuvvFJqn/79+0Or1eLDDz8ssa2w\nsFBXHBeP4j46sq3VajFv3jy9fXJyckpMQ3F1dUWtWrX0HuLi7e2NvXv36vVbunSp3vHLEhgYiHr1\n6mHevHnIysoqsf3x6R9PUp4HCfXr1w8pKSn46quvSmzLy8sr9fxPU/xLzr179/Ta09PTS4yMN23a\nFMDTH4JTERzxJiIiIqqggQMHltpeXNyFhoZi3LhxmDt3LhITExEWFgaFQoELFy5g06ZNmDFjBgYP\nHow2bdrAwcEBQ4YMwfjx42FmZoaNGzciOztb77jnzp1Dx44d0bdvX/j5+UGhUGDbtm04e/YsPvvs\nM12/ESNGYPTo0ejduzc6deqE48ePY+fOnXB0dCzXlAxBELB8+XJ07doVfn5+eOONN+Dq6oqbN2/q\nCvrdu3c/9ThPOtej7QMHDsTGjRsxbtw47N27V3dD6blz57BhwwZs3LhRt0R1ec8TFBQEAJgyZQoi\nIiIgl8vx8ssvY82aNVi4cCH++c9/wsvLCzk5OVixYgXMzMzQu3fvp17P82LhTURERPSMyjOC+/ha\n2dHR0WjWrBkWL16MqVOnwszMDO7u7ujXr59ueoWdnR1+/vln/N///R+mTZsGa2trvPbaaxg9ejQa\nN26sO1bdunUxcOBA7Nq1C2vXroUgCPD19dWtE15s5MiRuHz5MpYvX47t27ejbdu2iImJwcsvv1zi\nGp50TaGhoThw4ABmzJiBRYsW4f79+3B2dkZQUJDeCiZPWhu8vO2CIGDz5s2YP38+Vq5ciR9++AEq\nlQre3t4YN24cAgICnvIdL3kNzZs3x6xZs7Bo0SK88cYbkCQJsbGxaN++PQ4dOoT169cjOTkZNjY2\naNasGRYuXKgr1quCIJV3BroBPTrEr1arjRgJleXQoUMAiv4bikwX81Q9ME/VA/P0bHJzc6vuQSRE\nRlLW5/ppNSzneBMRERERGQALbyIiIiIiA2DhTURERERkACy8iYiIiIgMgIU3EREREZEBsPAmIiIi\nIjIAFt5ERERERAbAwpuIiIiIyABYeBMRERERGQALbyIiIiIiA2DhTURERERkACy8iYiIiCrJlStX\nIIoiVq5cqWv75ptvIIoirl27ZsTIyBSw8CYiIiJ6BsWFdGmv8ePHQxAECIJQ5jHWrl2LL774wkAR\nk6kwM3YARERERNVRVFQUvL299dp8fX2xadMmmJmVXWKtXbsWp06dQmRkZFWGSCaGhTcRERHRc+jS\npQtatGjx3Ps/bVT8eeTk5EClUlX6calycKoJERERUSUpbY7349q3b49t27bp+ha/ikmShOjoaAQE\nBEClUsHJyQkjRozA3bt39Y7j4eGBbt26YdeuXQgODoZKpcKcOXOq7Nqo4jjiTURERPQc0tPTkZqa\nWuq2skazp06dikmTJuHGjRuYP39+ie1jxozB119/jaFDh+Ltt9/GtWvXEB0djT/++AMHDx6EQqHQ\nnePChQvo06cPRo0ahZEjR6Ju3bqVc3FUJVh4ExERET2Hrl276r0XBAGJiYlP3a9Tp05wcXFBeno6\nBgwYoLctPj4eS5cuxbfffovXX39d71yhoaFYtWoVRo4cCaBoZPzixYv48ccf0b1790q4IqpqLLyJ\niIjIJExfLuHDr6vu+P95A5g+vPLmVUdHR6Nhw4Z6bUqlskLHXL9+PaysrBAWFqY3mu7r6wuNRoPY\n2Fhd4Q0Abm5uLLqrkUqf4y1JErp16wZRFLFp0ya9bWlpaRg0aBBsbW1ha2uLwYMHIyMjo7JDICIi\nIqpyQUFB6Nixo95LJpNV6JhJSUnIysqCk5MTNBqN3uv27du4c+eOXn8vL68KnY8Mq9JHvD/77DPd\nh+7x+U0DBgzAjRs3sGPHDkiShBEjRmDQoEH48ccfKzsMIiIiompHq9XCwcEB69atK3W7nZ2d3nuu\nYFK9VGrhffDgQXz55Zc4fPgwnJyc9LadOXMGO3bswP79+xEcHAwAWLJkCUJDQ5GUlIT69etXZihE\nRERUzUwfLmD6cGNHYRhPuvnS29sbv/76K4KDg2FpaWngqKiqVdpUk8zMTAwYMADLli1DrVq1SmxP\nSEiAlZUVWrVqpWsLCQmBpaUlEhISKisMIiIiIpNnaWmJtLS0Eu39+/eHVqvFhx9+WGJbYWEh0tPT\nDREeVZFKG/EePXo0wsPD0aVLl1K3JycnlyjIBUGARqNBcnJyZYVBREREZPKCgoKwfv16TJgwAS1a\ntIAoiujfvz9CQ0Mxbtw4zJ07F4mJiQgLC4NCocCFCxewadMmzJgxA4MHDzZ2+PScyiy8p06dipkz\nZ5Z5gNjYWFy7dg2JiYk4dOgQgKIbLB/9syKKj0mmizmqHpin6oF5qh6Yp/Jxd3ev8CofpupZnzr5\neP+xY8fixIkTWL16NaKjowEUjXYDRaulNGvWDIsXL8bUqVNhZmYGd3d39OvXDx07dnzuGKhyZGZm\n4uTJk6Vu8/HxKXNfQSqjOr57926JpyQ9zs3NDWPHjsWqVav0nrpUWFgIURQREhKCuLg4fP3115gw\nYQLu37+v6yNJEmxsbLBgwQIMGTJE1/7oSifnz58v8/xERERkmtzd3UudfkpUnd25cwdXr14tdduj\nhbdarS6xvczCu7xu3rypN+dIkiQEBATg888/R69eveDh4YEzZ87A398f+/fv183zjo+PR5s2bXDu\n3Dm9QB8tvEsLmkxD8YhPYGCgkSOhsjBP1QPzVD0wT88mNzf3hR3xppqrrM/102rYSpnj7eLiAhcX\nlxLtbm5u8PDwAAA0bNgQXbt2xZtvvomlS5dCkiS8+eab6NGjx1OH5YmIiIiIqrtKf4BOWdauXYsm\nTZqgS5cu6Nq1K5o2bYpvv/3WkCEQERERERlFlT0yXqvVlmiztbVloU1ERERENZJBR7yJiIiIiGoq\nFt5ERERERAbAwpuIiIiIyABYeBMREVGVqYyH6RGZiop+nll4ExERUZWQy+XIzc1FYWGhsUMhqrDC\nwkLk5uZCLpc/9zGqbFUTIiIiqtlEUYRSqUR+fj4KCgoMdt7MzEwAgLW1tcHOSc+uuuVJEAQolUoI\ngvDcx2DhTURERFVGEAQoFAqDnvPkyZMA+IRRU1cT88SpJkREREREBsDCm4iIiMqQgBsAAAdJSURB\nVIjIAFh4ExEREREZAAtvIiIiIiIDYOFNRERERGQALLyJiIiIiAxAkEzwkVIZGRnGDoGIiIiI6Lmp\n1eoSbRzxJiIiIiIyABbeREREREQGYJJTTYiIiIiIXjQc8SYiIiIiMgAW3kREREREBsDCm4iIiIjI\nAEyy8F60aBE8PT2hUqkQGBiIffv2GTukGi0uLg49e/ZEnTp1IIoiVq5cWaLP9OnT4erqCgsLC3To\n0AGnT582QqQ116xZsxAUFAS1Wg2NRoOePXvi1KlTJfoxT8a1cOFCNGnSBGq1Gmq1GiEhIdi2bZte\nH+bI9MyaNQuiKGL8+PF67cyVcU2fPh2iKOq9XFxcSvRhjozv1q1bGDJkCDQaDVQqFfz9/REXF6fX\np6bkyuQK73Xr1mHChAmYOnUqjh07hpCQEHTr1g3Xr183dmg1VnZ2Nho3bowvvvgCKpUKgiDobZ89\nezbmzZuHBQsW4ODBg9BoNOjcuTOysrKMFHHNs3fvXrz11ltISEjA7t27YWZmhk6dOiEtLU3Xh3ky\nPjc3N8yZMwdHjx7F4cOH0bFjR7zyyis4fvw4AObIFB04cADLli1D48aN9f7uY65MQ4MGDZCcnKx7\nnThxQreNOTIN6enpaN26NQRBwLZt23D27FksWLAAGo1G16dG5UoyMS1atJBGjRql1+bj4yNNmTLF\nSBHRo6ysrKSVK1fq3mu1Wql27drSzJkzdW05OTmStbW1tGTJEmOESJIkZWVlSTKZTPrpp58kSWKe\nTJm9vb20dOlS5sgEpaenS97e3tKePXuk9u3bS+PHj5ckiT9PpmLatGlSo0aNSt3GHJmOKVOmSG3a\ntHni9pqWK5Ma8c7Pz8eRI0cQFham1x4WFob4+HgjRUVluXz5MlJSUvRyplQq0bZtW+bMiO7fvw+t\nVgs7OzsAzJMpKiwsxPfff4/c3Fy0bduWOTJBo0aNQp8+fdCuXTtIj6y8y1yZjkuXLsHV1RVeXl6I\niIjA5cuXATBHpmTLli1o0aIF+vXrBycnJzRt2hQLFy7Uba9puTKpwjs1NRWFhYVwcnLSa9doNEhO\nTjZSVFSW4rwwZ6YlMjISTZs2RatWrQAwT6bkxIkTsLKyglKpxKhRo7B+/Xr4+voyRyZm2bJluHTp\nEj766CMA0JtmwlyZhpYtW2LlypXYsWMHli1bhuTkZISEhODevXvMkQm5dOkSFi1ahHr16mHnzp2I\njIzE5MmTdcV3TcuVmbEDoBfX43PByTAmTpyI+Ph47Nu3r1w5YJ4Mq0GDBkhMTERGRgY2bNiA/v37\nIzY2tsx9mCPDOnfuHN5//33s27cPMpkMACBJkt6o95MwV4bTtWtX3deNGjVCq1at4OnpiZUrVyI4\nOPiJ+zFHhqXVatGiRQt8/PHHAIAmTZrg/PnzWLhwIcaNG1fmvi9irkxqxNvR0REymQwpKSl67Skp\nKXB2djZSVFSW2rVrA0CpOSveRobzzjvvYN26ddi9ezc8PDx07cyT6TA3N4eXlxeaNm2KmTNnomXL\nlli4cKHu7zjmyPgSEhKQmpoKf39/mJubw9zcHHFxcVi0aBHkcjkcHR0BMFemxsLCAv7+/rhw4QJ/\nnkyIi4sL/Pz89NoaNGiAa9euAah5/z6ZVOEtl8vRvHlz7Ny5U689JiYGISEhRoqKyuLp6YnatWvr\n5Sw3Nxf79u1jzgwsMjJSV3TXr19fbxvzZLoKCwuh1WqZIxPy6quv4uTJkzh+/DiOHz+OY8eOITAw\nEBERETh27Bh8fHyYKxOUm5uLM2fOwNnZmT9PJqR169Y4e/asXltSUpJucKim5Uo2ffr06cYO4lE2\nNjaYNm0aXFxcoFKp8NFHH2Hfvn1YsWIF1Gq1scOrkbKzs3H69GkkJydj+fLlCAgIgFqtRkFBAdRq\nNQoLC/HJJ5/A19cXhYWFmDhxIlJSUrB06VLI5XJjh18jjBs3DqtWrcKGDRtQp04dZGVlISsrC4Ig\nQC6XQxAE5skETJ48GUqlElqtFtevX8f8+fOxdu1azJkzB97e3syRiVAqlahVq5bupdFosGbNGri7\nu2PIkCH8eTIR//rXv3Q/T0lJSXjrrbdw6dIlLFmyhP82mRB3d3dERUVBJpPB2dkZu3btwtSpUzFl\nyhQEBQXVvJ8nI6+qUqpFixZJHh4ekkKhkAIDA6XffvvN2CHVaLGxsZIgCJIgCJIoirqvhw0bpusz\nffp0ydnZWVIqlVL79u2lU6dOGTHimufx3BS/oqKi9PoxT8Y1dOhQyd3dXVIoFJJGo5E6d+4s7dy5\nU68Pc2SaHl1OsBhzZVz9+/eXXFxcJLlcLrm6ukq9e/eWzpw5o9eHOTINP//8s9SkSRNJqVRKvr6+\nUnR0dIk+NSVXgiSV424RIiIiIiKqEJOa401ERERE9KJi4U1EREREZAAsvImIiIiIDICFNxERERGR\nAbDwJiIiIiIyABbeREREREQGwMKbiIiIiMgAWHgTERERERnA/wP4AE2iGoXk5AAAAABJRU5ErkJg\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run_filter(data=zs, R=var, Q=.2, P=500., initial_x=x,\n", " plot_P=False, title='$P=500\\, m^2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case the Kalman filter is very uncertain about the initial state, so it converges onto the signal much faster. It is producing good output after only 5 to 6 evolutions. With the theory we have developed so far this is about as good as we can do. However, this scenario is a bit artificial; if we do not know where the object is when we start tracking we do not initialize the filter to some arbitrary value, such as 0 m or 100 m. Instead, we would normally take the first measurement, use that to initialize the Kalman filter, and proceed from there. But this is an engineering decision. You really need to understand the domain in which you are working and initialize your filter on the best available information. For example, suppose we were trying to track horses in a horse race. The initial measurements might be very bad, and provide you with a position far from the starting gate. We know that the horse must start at the starting gate; initializing the filter to the initial measurement would lead to suboptimal results. In this scenario we would want to always initialize the Kalman filter with the starting gate position. \n", "\n", "If we have the luxury of not needing to perform the filtering in real time, as the data comes in, we can take advantage of other techniques. We can 'eyeball' the data and see that the initial measurements are giving us reasonable values for the dog's position because we can see all of the data at once. A *fixed lag smoother* will look N steps ahead before computing the state, and other filters will do things like first run forwards, than backwards over the data. This will be the subject of the Smoothing chapter. It is worthwhile to keep in mind that whenever possible we should prefer this sort of batch processing because it takes advantage of all available information. It does incur cost of additional processing time and increased storage due to the requirement to store some or all of the measurements. And, of course, batch processing does not work if we need real time results, such as when using GPS in our car." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ne6D4NUz+UyUznxlImG4EGrUmuPny5MC90FGIqzr0/NfE8ER6p/QODbgB2ren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\napVaZrkvc//85z+ZM2cOOp2O0tJStmzZ0md922w2Pvvss44Sl3ZDhw7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EVQ/ikWqPoFHkPbIQQtwPRqORIUOGALBw4UK0Wi2HDx9GuWExBEBRFLM2nU7H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\n0B9RsY1bSyZMMB+rqdLg6LWjkCBhWvi0Nu0dJyI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import book_plots as bp\n", "def plot_track_ellipses(noise, count, R, Q=0, P=20., plot_P=True, \n", " title='Kalman Filter'):\n", " dog = DogSimulation(velocity=1, measurement_variance=noise)\n", " f = pos_vel_filter(x=(0., 0.), R=R, Q=Q, P=P)\n", "\n", " ps, zs, cov = [], [], []\n", " for t in range(count):\n", " z = dog.move_and_sense()\n", " f.update(z)\n", " ps.append(f.x[0])\n", " cov.append(f.P)\n", " zs.append(z)\n", " f.predict()\n", "\n", " bp.plot_measurements(range(1,count + 1), zs)\n", " plt.plot(range(1,count + 1), ps, c='b', lw=2, label='filter')\n", " plt.legend(loc='best')\n", " plt.title(title)\n", "\n", " for i,p in enumerate(cov):\n", " stats.plot_covariance_ellipse(\n", " (i+1, ps[i]), cov=p, variance=4, axis_equal=False, \n", " edgecolor='g', alpha=0.5)\n", "\n", " if i == len(cov)-1:\n", " s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n", " plt.text (20, 5, s, fontsize=18)\n", " s = ('$\\sigma^2_{vel} = %.2f$' % p[1, 1])\n", " plt.text (20, 0, s, fontsize=18)\n", " plt.xlim(-10, 80)\n", " plt.gca().set_aspect('equal')\n", " plt.show()\n", "\n", "plot_track_ellipses(noise=5, R=5, Q=.2, count=20, title='$R = 5\\, m^2$')\n", "plot_track_ellipses(noise=.5, R=.5, Q=.2, count=20, title='$R = 0.5\\, m^2$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are viewing this in IPython Notebook or on the web, here is an animation of the filter filtering the data. I've tuned the filter parameters such that it is easy to see a change in $\\mathbf{P}$ as the filter progresses.\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $\\mathbf{P}=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slightly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n", "\n", "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n", "\n", "The first plot, with $R=5 m^2$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85 $m^2$, and the variance for velocity is 3.0 $m^2$. \n", "\n", "In contrast, the second plot, with `R=0.5` $m^2$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf{R}$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Question: Explain Ellipse Differences" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why are the ellipses for $\\mathbf{R}=5 m^2$ shorter, and more tilted than the ellipses for $\\mathbf{R}=0.5 m^2$. Hint: think about this in the context of what these ellipses mean physically, not in terms of the math. If you aren't sure about the answer,change $\\mathbf{R}$ to truly large and small numbers such as 100 $m^2$ and 0.1 $m^2$, observe the changes, and think about what this means. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $x$ axis is for position, and $y$ is velocity. An ellipse that is vertical, or nearly so, says there is no correlation between position and velocity, and an ellipse that is diagonal says that there is a lot of correlation. Phrased that way, it sounds unlikely - either they are correlated or not. But this is a measure of the *output of the filter*, not a description of the actual, physical world. When $\\mathbf{R}$ is very large we are telling the filter that there is a lot of noise in the measurements. In that case the Kalman gain $\\mathbf{K}$ is set to favor the prediction over the measurement, and the prediction comes from the velocity state variable. So, there is a large correlation between $x$ and $\\dot{x}$. Conversely, if $\\mathbf{R}$ is small, we are telling the filter that the measurement is very trustworthy, and $\\mathbf{K}$ is set to favor the measurement over the prediction. Why would the filter want to use the prediction if the measurement is nearly perfect? If the filter is not using much from the prediction there will be very little correlation reported. \n", "\n", "**This is a critical point to understand!**. The Kalman filter is a mathematical model for a real world system. A report of little correlation *does not mean* there is no correlation in the physical system, just that there was no *linear* correlation in the mathematical model. It's a report of how much measurement vs prediction was incorporated into the model. \n", "\n", "Let's bring that point home with a truly large measurement error. We will set $\\mathbf{R}=500 m^2$. Think about what the plot will look like before scrolling down. To emphasize the issue, I will set the amount of noise injected into the measurements to 0, so the measurement will exactly equal the actual position. " ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mz57Nb3/7W9xuNwaDgTfeeIOJEyeSk5MT1Xft2rW8+OKL/Pvf/+Z//ud/5PYZ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\n/tf4v7g99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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_track_ellipses(noise=0., R=500., Q=.2, count=7, title='$R = 500\\, m^2$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I hope the result was what you were expecting. The ellipse quickly became very wide and not very tall. It did this because the Kalman filter mostly used the prediction vs the measurement to produce the filtered result. We can also see how the filter output is slow to acquire the track. The Kalman filter assumes that the measurements are extremely noisy, and so it is very slow to update its estimate for $\\dot{x}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Keep looking at these plots until you grasp how to interpret the covariance matrix $\\mathbf{P}$. When you start dealing with a, say, $9{\\times}9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9{\\times}9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intuition and understanding in this simple, 2-D case. \n", "\n", "> **sidebar**: when plotting covariance ellipses, make sure to always use ax.set_aspect('equal') or plt.axis('equal') in your code (the former lets you set the xlim and ylim values). If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Filter Initialization\n", "\n", "\n", "There are many schemes for initializing the filter (i.e. choosing the initial values for $\\mathbf{x}$ and $\\mathbf{P}$. I will share a common approach that performs well in most situations. In this scheme you do not initialize the filter until you get the first measurement, $\\mathbf{z}_0$. From this you can compute the initial value for $\\mathbf{x}$ with $\\mathbf{x}_0 = \\mathbf{z}_0$. If $\\mathbf{z}$ is not of the same size, type, and units as $\\mathbf{x}$, which is usually the case, we can use our measurement function as follow.\n", "\n", "We know\n", "\n", "$$\\mathbf{z} = \\mathbf{Hx}$$\n", "\n", "Hence,\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{H}^{-1}\\mathbf{Hx} &= \\mathbf{H}^{-1}\\mathbf{z} \\\\\n", "\\mathbf{x} &= \\mathbf{H}^{-1}\\mathbf{z}\\end{aligned}$$\n", "\n", "Matrix inversion requires a square matrix, but $\\mathbf{H}$ is rarely square. SciPy will compute the Moore-Penrose pseudo-inverse of a matrix with `scipy.linalg.pinv`, so your code might look like" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 3.2],\n", " [ 0. ]])" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.linalg as la\n", "\n", "H = np.array([[1, 0.]]) \n", "z0 = 3.2\n", "\n", "x = np.dot(la.pinv(H), z0)\n", "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Specialized knowledge of your problem domain may lead you to a different computation, but this is one way to do it. \n", "\n", "Now we need to compute a value for $\\mathbf{P}$. This will vary by problem, but in general you will use the measurement error $\\mathbf{R}$ for identical terms, and maximum values for the rest of the terms. Maybe that isn't clear. In this chapter we have been tracking and object using position and velocity as the state, and the measurements have been positions. In that case we would initialize $\\mathbf{P}$ with\n", "\n", "$$\\mathbf{P} = \\begin{bmatrix}\\mathbf{R}_0 & 0 \\\\0 & vel_{max}^2\\end{bmatrix}$$\n", "\n", "The diagonal of $\\mathbf{P}$ contains the variance of each state variable, so we populate it with reasonable values. $\\mathbf{R}$ is a reasonable variance for the position, and the maximum velocity squared is a reasonable variance for the velocity. It is squared because variance is squared: $\\sigma^2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Batch Processing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `KalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It simplifies your logic and conveniently gathers all of the outputs into arrays. More importantly, this also allows you to use a smoothing method which generates far better results. I will demonstrate that in the next section. Here I will show you how perform the batch filtering step.\n", "\n", "First collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n", "\n", " zs = read_altitude_from_csv()\n", "\n", "Or maybe you will generate it using a generator:\n", "\n", " zs = [some_func(i) for i in range(1000)]\n", "\n", "Then call the `batch_filter()` method.\n", "\n", " Xs, Ps, Xs_pred, Ps_pred = kfilter.batch_filter(zs)\n", " \n", "The function takes the list/array of measurements, filters it, and returns a list of state estimates (Xs), covariance matrices (Ps), and the predictions for the same (Xs_pred, Ps_pred).\n", "\n", "Here is a complete example." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PePCASLP8/OyvMOcXuHAtaZMGleHTLjBpRCdK2ozH0rw5oHDu3LnMXclR5Ei5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dog = DogSimulation(velocity=1, measurement_variance=10.)\n", "f = pos_vel_filter(x=(0., 0.), R=3., Q=.02, P=P)\n", "count = 50\n", "zs = [dog.move_and_sense() for t in range(count)]\n", "Xs, _, _, _ = f.batch_filter(zs)\n", "\n", "bp.plot_track([0, count], [0, count])\n", "bp.plot_measurements(range(1, count + 1), zs)\n", "bp.plot_filter(range(1, count + 1), Xs[:,0])\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing the Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have an entire chapter on using the Kalman filter to smooth data; I will not repeat the chapter's information here. However, it is so easy to use, and offers such a profoundly improved output that I will tease you will a few examples. The smoothing chapter is not especially difficult; you are sufficiently prepared to read it now.\n", "\n", "Let's assume that we are tracking a car that has been traveling in a straight line. We get a measurement that implies that the car is starting to turn to the left. The Kalman filter moves the state estimate somewhat towards the measurement, but it cannot judge whether this is a particularly noisy measurement or the true start of a turn. \n", "\n", "However, if we have future measurements we can decide if a turn was made. Suppose the subsequent measurements all continue turning left. We can then be sure that that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored. Instead of making an estimate part way between the measurement and prediction the estimate will either fully incorporate the measurement or ignore it, depending on what the future measurements imply about the object's movement.\n", "\n", "FilterPy implements a form of this algorithm which is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel. The routine is `KalmanFilter.rts_smoother()`. To use it pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ratT6rbfeYtq0acTExLA4e1nVPCZOnMjnn3/OU089xYsvvsi5c+dYsmQJ+/bt\nY//+/Vje/uOm0+mIjIzk0UcfZcKECTzzzDNyAaYQQoiy0TT48EPw8IAHHoA8g0I8+ywsW6YC50cf\nwauvlu4c4eFqdUpQFxPa2uY+Nno0XLgAdeuW/jlUFAeHEs8l1+uziIo9TmhEMEciQ0i+mWiwXR0r\nOzp5dqOTZyAtm3bA1LRkUS78nMZbk6/xXbv8K7lYW8JLj6sa0/a2FViZY9iwijt2NVejw/aszzTm\nfF5xx58xDmaNL78X3sCBA/N9r9PpOHLkSLH79e3bl8aNG5OYmMjIkSPzPRYcHMzKlSv56quvGDVq\nVL5z9ejRgy+//JJnnnkGUCPgUVFR/Pzzz9x///3l8IyEEELc9S5dUpU16tdXUyfyMjNTI9IDB6rR\n6IkT8wflknr1VUhLgzFjYMCA/I+99Vbp+17F9PosIi8cJyxiN4ej9nC9kIBta21PJ49ueHsF4tm0\nPaYmpgbbGXIxXmP25/DZLxpZ+g45201NYfz9MGMsNHas+PJ3d7MaHbZrmiVLltCmTZt826ysrMp0\nzPXr12Nra0v//v3zjZq3atUKJycntm/fnhO2AVxdXSVoCyGEKD/Zi9m0LORz/QED1AWADz9cuqAN\n8Mkn4OSkFoap4bL0WURd+DdnBPt6apLBdnYp6XQ8HItPZn08Vq7CtKGjUedJStFYsBb+ux5upkHe\npSKH3QNvPwst3SRkVwYJ25XI39+/wAWSZ86cKdMxw8PDSUlJwTm7DNIdrlzJXwqoRXmWXxJCCCGK\nC9ugVk0sCxcXWLWqbMeoQln6LCJjjhEWEczhqD2kFBawberRyTMAH69APK5kYLL8QbhwBE72gt9/\nV/PVDbiVoREbD+fjIOYKnDwLS7+Ha8n52/X2hXcnlvPFj9XdhQvwww/q0xUvryrpQo0O27PG65g1\nvqp7UbX0ej0NGjTgf//7n8HHHRwc8n0vlUeEEEKUq5KE7bvN8eNkubkSeS262IBd18aBTp4BeHsF\n4tG4DSbZU0SaAiEhZAx6gNjIBM5P+oSYKW/nBOqY2/fnL0PcNTV1vjCdPOG959WqiRVR2axa+/VX\nePFFVY3khx+qpAs1OmzfTQr7x+Hh4cG2bdvo2rUrdargClshhBB3OQnbObL0WUTFHCN04UQOe9qT\nYmu4+krdOg54ewbg7RVEi0atcwP2bSfOaHz9B3y3vSmR9Q6h+engGmBk8bDmjWHO0zCiH5iYVIOQ\n/eefatWiQoyfAAAgAElEQVTMwEB4//3KOeeWLeq+CuprZ5OwXUPUqVOHhISCpX+GDx/O8uXLmTNn\nDvPvmMuWlZXF9evXqVevXmV1UwghxN1myBBwdARv7/I7ZkqKqk+dt7JJUbKy4L33YN8+NXppWvIL\nCMtKXeSo5mAfjgxRI9jeTgXaZQdsH68gmhsI2Jeuany7Ddb+AQdP5X2k+JCs00GjBtDUCVydoImj\nWjVxeF+wtKgGITubTgchISVfX72ssrJyFxbq169yzmmAhO0awt/fn/Xr1/PSSy/RpUsXTExMGD58\nOD169GDSpEksXLiQI0eO0L9/fywtLYmMjOT7779n7ty5PPnkk1XdfSGEELXVuHHqVlIXL6oKIh07\nQmGrIj/7LJw5o5YyL0ldZlNT+PxziI5Wq0yWctGUkspXRaSIixxVwA7ExyuQ5o3bYKLL/+Yh5abG\nxn9UwN6633AG1enApT64OkNTRxWos0N19n2jhmBuVkio3rULfH3Vm5eq5uur7g8fVosUFbN6dpkd\nPAgJCdCihSpNWUUkbFcSY+dI3dn++eef5+jRo3z99dcsWbIEUKPaoKqc+Pr6smLFCt566y3MzMxw\nd3fn8ccfp0+eJWLvunlaQgghqp9Dh1QwtreHUaOgYcP8j2/aBOvWGTeyDdCrlwrbf/9dIWE7pw52\neNFl+ureAu890fjcO5zm418vELAzMzX+PKgC9o874UZqwWNYmMMDQTBqAAzsWsgiM5mZsHq1eqNT\n2M8pIUFVg7GyUtN98ix0VyXq1VOhNypK1V7v2LFiz1cNppAA6DStqCn15ScpKfddn729faHt0tLS\nylwOT4jqRF7Txjtw4AAAnTt3ruKeiJpAXi81jKapyhBbtsCkSfDxx7mPJSVBu3aqgsSHH8JLL5X8\nuF9+qepwP/AA/PxzkU1L+ppRAfsEodkj2IUFbBsHvL0C8PYIoEXnezG5fEWtanl7HrumaRw6BV//\nAd9uUxc0GtLLB0b1h2G9oZ5dMQNkzz8Py5fDY4+pTwAM/T/z/vuqRnnfvrB1a9HHqyyPPQYbNqg3\nXGPHVuy5Dh2C775TU0h69y6+fSFKmmELIyPbQgghhKg8Op1a6KZjR1ixQi10066deuy111TQ7toV\nJk827ri9eqn7f/5Rc3VLOW9br+k5fTtgh0WEkHzT8FLpOQE770WOSUnQoydEROSUmdscrPHaMvj3\ntOHztW0GowfCyH7g5mLEJ9DDhsHatbB+PcTFwcaNauQ4W2Ym3P4k3Kg3LRXNz0+F7cOHK/5cvr65\nU1eqkIRtIYQQQlSudu3UvOzly+Hll1UN6f371eI15ubw6afGh2V3d2jWTM31PnIEfHxKvKsK2CcJ\niwwmNGI3yTcMB+zcOthB+cv0ZbO3VyOpqJUbX/qvxoa/Ch6nUQMY0R9G94dOXqWc5tmnj3pjMWgQ\n7NgB3bvDb7+Bq6t6fONGOHdOhf5Bg4w/fkUZM0YtcFSFc6grm4RtIYQQQpTOwoVqBHXsWLXwjDFm\nz1ajsp6ekJGhRjz/+1+1LHv79qXrz9Klag54hw7FNtU0jejYk4RG7CIsMoSklKsG29lZ29PJK7Dw\ngH0HvV5j5U/wxgpISsndXscaHuml5mH38QNT03K4jqpjR1XdY+BA+PdftVLnV1+pxxYvVvdTphg3\n972iubgY/1qp4YwK2++++y5vvvkmkyZNyrlID2DWrFmsWrWKhIQEunbtytKlS2nbtm25d1YIIUQN\n8O67kJioKk7Y2VV1b0RFWroUzp5VUxqMDVCOjuqCxrp1c7e9+KJRh7icoFHXJs8FhIMHF9ler+k5\neymc/ae3cjb+ODeDrxtsZ2ttnzOC7dmkbbEBO9uxaI1n50PIsfzbxwyChS9Aw3oVUKjAzU1VHHnj\nDViwQG3TNJgxA1auVCPJokqVOGzv2bOHVatW0bFjx3wfd8yfP59FixaxZs0aWrZsyZw5c+jXrx+n\nTp3C1ta2QjothBCimkpKUqNrAP/7n7porWfPqu2TqBipqWqagpmZmr5RGnmDthGSb2hMeh/WbgEz\nU+joqeHfBvzbQJe20MY9d+RY0zTOXApXFzlGBJOQEm/wmHWs6+LtEYBPyyA8mrTDtIQBGyA1XWPu\nF/D+OsjMyt3u5QorXoXefhVcDax+fTUFJ5tOpypwVHEVjiqjaepnUE2UKGwnJSUxevRovvjiC2bN\nmpWzXdM0Fi9ezBtvvMHQoUMBWLNmDU5OTqxbt44JEyZUSKeFEEJUU//+m/v12bNw61bV9UVUrKgo\nFWpatFDzrCvJ3n81Rs6C07Hq+8wsOHRK3T7ZqLbVsdbo3imcVu67MTcLIT3jisFj1bGyo5NnN3y8\nuuPZtL1RATvb1n0aExdCdGzuNnMzeG00TH+ykLJ9omKtWQMffQT/93/wxBNV3ZuShe0JEybw6KOP\n0qtXL/JWCjx9+jRxcXH0z/POycrKip49exIcHCxhWwgh7jbHbn9+Pny4+k+ub9+q7Y+oOJW8TLte\nr7FgLcxYlX/0OJeGU/0IPJsG4+kaTN06V9BrkJ6Rv5UOW2wt2tDSpTWjHngQM7PSvVG4nKDxykdq\ndD2v7u0yWfGGGW2bS8gukqZBbCw0aVL+x/7jDwgNVZ+0VQPFhu1Vq1YRHR3NunXrgPxXzF66dAkA\nZ2fnfPs4OTkRGxuLEEKIu4yrKzzyiKprW8z8WVHDVWLYjr2i8eRc+Otg7ra6dWD5qxodWkTy56Fg\nzlwKJkt/2eD+aem2RF/oSuT5IGIud0CvqfjzwlJo6arR2h1aukErN2jtpr62sTIcljVN4/NNMG0p\nJOSZ8l0vM4EFZ6Yxbv1cTJo0KrfnXitdv67mmmdkqEBcyjKNBun1sG2b+rqaTKMpMmyfOnWKN998\nk127dmF6+wehaRolWQenqDI22cXkDXF3d5cFQEStcv36dY4dO1Z8Q1FAUX8rRDXl6Aivv66+LuT3\n5/TNN9xs25aUTp3K9dTyeqlc1q6u1H3pJW60akVKBf7s/zlmz5x1zUi6kR1ZNALaHeXhHls5GnWM\nkOOGF5oxS4NUXQDRMYHsPeFH8k3rAm1upEJouLrdybleOs2c03BzSsPdKY1mzmlYW+r5+OcmhEbl\nv/D3vhZRfPq/IOo2rcOhi8/BxQtlfdq1XgcrKywTEzn2ww+kNW9ebse1OXmStvHxpDdqxNGkpEL/\nDhnD63bN9NIqMmyHhIQQHx9Pu+xi80BWVhb//PMPn3zySU6AiIuLo2nTpjlt4uLicLnLyroIIYQo\nns3Jk7guXgyaRtzIkVx47jk0GWCpkVJbtSK1VasKO356ho4lPzdl/U4nQMPRIQov1114e/2DielV\nzhpYhdHc1BK3+q24Z8m3tNsfycm1I0jrY41ef5zz8ZacOFeHf8/acOJ8Hc7EWZF8s/AYFJdoQVyi\nBXtPFX4RZ+MG6bz26Dke3r0I54zLXO78aDk887vDzdatsbx0CZsTJ8o1bNfdsweA5C5dqs1FkkWG\n7aFDh9KlS5ec7zVNY+zYsbRs2ZLp06fj5eWFi4sLW7Zswc/PD1BLU+/atYv333+/0OMWtTxqWlqa\nsc9BiGrNzs5OlpE2kiy/XYt16AAnT8J77+Gydi0uBw7A6tXQrVupDymvl9rnxBmNp2dqXIyPJqDD\n73i6BmNvG2ewrbWFDR08uuLjFUQrt06YmZrDr1GwJ4L28fHw+OMAdMmzz4EDB9A0aObpx6lzcOoc\nnDwL4be/jopVi1AWxtQUXhkBM8ZaYmPVEr5QQ+NOw4fjJK/Dkrn3Xvj7b1okJNCiPH9mH3wAgOOo\nUTiW03GTyjj3u8iwbW9vX2ANeBsbGxwcHHLqaL/00kvMmzeP1q1b4+Xlxdtvv42dnR0jR44sU8eE\nEELUQpaW8PbbMGSIqv974gQEBanqAaNHV3XvRBXT6/V8/P1pvv97Nx29gunpe8lgOysLGzq06HI7\nYHtjfudFjr16wbp1amXFSZMMHkOnA0cHHY4O0P2OGU23MjSiY3ND+KlzKoifuQgdPeG9idDR8/ao\naWoqBAerA2YvGS+Kd3uQloMHi25nrHXrYM4caFR95s0bvYKkTqfLNx972rRppKamMmnSJBISEujW\nrRtbtmyhTp065drRmmz16tWMGzcu53tTU1OcnZ3p06cPc+fOZebMmXz55ZfFHqdXr15s374dgN9+\n+42FCxdy4sQJkpKScHJywtvbm8cff5wRI0ZU2HMRQohy4e8Phw7BzJnwxRdSteQupmkaF+JPE3Js\nN9sPBWNmdpFOBq65zA7Y3l6BtHbzKRiw88oOvTt2lKrmsoW5jtbu0NodhvQoprGpKXz/PRw/Dg0a\nGHWeu5qfn3rzbWFRvsfV6dQS9dWITivJ1Y7lIO8Q/J2j5XmlpaXVugsks8P27Nmz8fDwIC0tjZCQ\nEFavXk2TJk345ptvOH36dE7748ePM2/ePF544QW65flo1dnZmXvvvZdFixYxdepUunfvztChQ7Gz\nsyM6OpqdO3diaWnJn3/+WRVPUxSiNr6mK5pMC6ih1q1TK0c+8ICqSlJSSUlQxP8LxZHXS82jaRqx\n8WcIjdhNaPhuriRdNNjO3MyaTp5qBLu1mzfmZiUMZpqmSsrVrw/bt6sLd/OQ10w1kZFRqTXaS6uk\nGbYwRo9si9IbMGBAzhz4cePG0bBhQ+bPn8/p06fzTbv5+++/mTdvHt27d+exxx7Ld4zMzEzmzJlD\n7969DYbqK1cMF+4XQogKt3Sp+ji9VSvjwnYZgraoIp9+Cn//DePHQ+/eJdpFBeyzKmBH7OZKouES\nwbcyrDAz6cKYwYF4e/qWPGDnpdNBRATIp+zVWw0I2uVBwnYV6t69O/Pnz+f8+fMl3ic+Pp7k5GS6\nd+9u8HHHO969CyFEpdC03NUj81SwErXUn3/Ct98WW8dY0zQuXj2bM4J9uYiAfSbWn4vxQfxnrDfD\nepfDp4EStEU1IWG7Cp05cwbAqDKJTk5OWFtb88svvzBlyhTq169fQb0TQggjXLigpoM0aAB3LHRm\nNL1ejUxWk7Jd5SozE37+WV0gWp4LeVS2Iha0UQH7XM4I9uUEwzWnswN2xPkgzsV506OjJZsWgqtz\nLfy9i4p37JgqIdOhA5iYVHVv8pGwXYkSExOJj48nLS2NvXv3Mnv2bFxcXHj44YdLfAwTExNee+01\nZs2ahZubG0FBQXTv3j3fFBUhhKh02Qs3tW9ftpA8ZQp88w3s3AmtW5dP36qTQYPU6nYbNsCwYVXd\nm9LRNINhO2/AjrsWY3DXjEwrTsd2JvJ8EGcv+ZCVZUm3drD0FRjQtegF8aqlrKya/aapujlwAEo7\nj/6992DtWjWd7fnny7dfZVSjw/bmPd/w+97/VdjxB3Z9nMHdyq+yx8CBA/N97+3tzYYNG7Czsytk\nD8NmzJhBixYtWLZsGX/99Rdbt25l5syZeHl58eWXX9K1a9dy67MQQpRI3rBdFvHxcOUK/PFH7Qzb\nDz+swvbChWpZ+5oWLgEuXYKUFGjQgIvaDUL3/EFYRDCXrhmeEqlpVkTGdCbiXCBnL/mSlWUJQFBH\nmDEW+vrXwJCdLShIhe2vvoIWLaq6NzXbuHGqMtFPP8GDDxq3b94l2u+5p9y7VlY1OmzXNEuWLKFN\nmzYkJSXxxRdfsGnTJkJCQvDw8DD6WKNHj2b06NHcvHmTAwcO8M0337Bq1Sruu+8+Tp48ScOGDSvg\nGQghRCF69oQZMyAwsGzHGThQVTX5/Xc1yl0bvP8+XLsGkyer2uL/+Q/s2we7d0Mh199UZ5cOhxA6\noBVhAZ5c/HqywTZmppakpvnz14FATsf6knk7YAP09IYZ46C3byWE7Fu3YM8euHoVhg4t32Nfu6Z+\nj2ZmIKtml12n28XOJ09WC94YM+f+6FGIi1MVaNq0qZj+lYGE7Urk7++fM9VjyJAh9OrVixdeeIFB\ngwbRoJS1OW1sbOjZsyc9e/bEycmJuXPn8ttvv/HEE0+UZ9eFEKJoXbqoW1llX3D3999qsRBr67If\nsyqlpcH8+WrE/r771EjopElq0Y33368xYfvStfOERgQTFrGbi1fPwaCCnzpYmFni6uTHkYhA1m7p\nzK0My3yP9/aF/4yFe3wrcRQ7PFzV3G7SBB56qHw/Sdi5U02pCQgAG5vyO+7datIktbhVaKj69zF/\nfsn33bpV3ffrVy0/LarRYXtwtxHlOs2jMpmYmPDee+/Ro0cPPvjgA+bNm1fmY/r7+wNw8aLheqVC\nCFHtOTuDj4/6D/eff4qtdlHtffutCtq+vrmj/pMmqSDx888qDBq4yLA6iLsWkzMH++LVcwbbmJtZ\n0K55Z7w9A1m/zY+X/2vFnat39O2sQnYP7yoIQW3bQsOG6gLeqCjw9Cy/Y//1l7rv06f8jnk3MzOD\nFSugWzdYtEitKNuhQ8n23bJF3VfTvxc1OmzXdEFBQQQEBLBixQrefPPNEq26mZqayqFDhwgKCirw\n2ObNmwFoXRvnOQoh7h4DBqiPhU+dqrb/eZaIpsFHH6mvJ0/OHXFzcoK5c8HNrdrN841LuEDY7TJ9\nsVfPGmxjbmZBu2ad8WkZRNtmfliYWTJ5ESz7IX+7/l3UdJHADlU40mhioqY4/fCDWk1Swnb11qUL\nTJwIy5bBO++oN6sl0a+f+iTs3nsrtn+lJGG7ik2dOpVHHnmETz/9lCklmJ9448YNevTogb+/P4MG\nDcLNzY3r16+zbds2fv31V7p168b9999fCT0XQogK8sor8MYbULduVfekbIKD1Qh9w4YwfHj+x159\ntWr6ZMDlhNicEezY+DMG25ibWdC2mR8+XkG0a+aHpYWa3qPXa0xcCCt/ym3b2xfeeRa6ta8mH+f3\n6pUbtsePL59jpqSoTyysrctn+pTI9c476g3p1Kkl3+fVV6vVv6k7SdiuJIVdBPLQQw/h6enJ4sWL\nmTx5Mia3a0MW1t7BwYFPP/2UX3/9lS+//JJLly6h0+nw9PRk5syZvPrqqznHEEKIGqm2XOC9Y4e6\nf/ZZsCqHRVqMpdersH/hQoHqDlcSL+YE7AtXThvc3dzUgrbNfPFp2T1fwM49vMaE+fD5ptxtw/vC\nl/8BM7NqErQhtzrF33+rTxvKY06vrS1cvAjnzoGlZfHtRcnVqwczZ1Z1L8qVTtPunF1VMUq6rnxa\nWhpWVfFHSYgKIq9p4x04cACAzqWttyoq19tvq+AxeXKVlOur1q+Xkyehfn01UlfZ/v1XlWJ0doaL\nF7mSdImwiGBCI3YTcyXa4C5mpua3R7ADad/cv0DAzpaVpfH0u7Dmt9xtowfA59OrWdAG9aZj5Ejw\n91cVbszMqvdrRlQ7Jc2whZGRbSGEEGWzfr2aY/3UU1Xdk+qnKq+haduWq22aEdrIjNAvJnH+uuGl\n0lXA9lVTRJr7Y1VIwAbgzz/JfPV1xnp8xtrY3IvXnhoMq14HU9NqFrRBzdsu6dxfISqAhG0hhBCl\nl5GhRm9BVX4QxktJUatmjhtX9tUIk5K4lpZIaEwooRG7Offs7drFdwRtU1Mz2rirgN2+uT/WliUr\nXZd55F+eTPk/vs0TtMc/AJ9MAxOTahi0Re2QlqbeNFlYVHVPSkXCthBCiNKLiFCBu0UL4xahKImU\nFNi+XY0Oe3mV77Grk1694NAhNVe9lAuvJFy/QmhEMKF/fMVZm0yDbUxNzWjj5oNPy+yAbdzvKyNT\nY9TWIL5z9M3Z9uxDaql1Cdqiwuzcqd6IjhsH06fnf2zGDEhOVlPYSrFAYGWRsC2EEKL0spdpb9eu\n/I/95puqdN5bb6lSebXVU0+psP3++0aF7cSUqzkXOZ65eEptvGOAWq83JetcQ3qERTHkh2+p41C6\ni09vZWiMmAE/JuUG7UmPwEf/V4OXWi+tv/5Si+S0bFktF1CpdW7dUjXS585VVX2yy2VqGnz6qbpe\npLyqzFQQKVshhBCi9LLDdvv25X/sAQPU/R9/lP+xK0pwMDz9tJrDXlJjx6oKDMHB6laEpJRr7Ajb\nxOINbzDjs/H8uPPz3KB9m15vypmLvmzbN5nPflrNJ/tWMPrWVnq8WI+VP2mk3DSuLkL6LY1H34Qf\nd+Zum9I/8e4M2poGY8aoT1uyX/uiYvXtqy5wTUtTC0Jl1/U4flwFbReXivn7U45kZFsIIUTpjR+v\n/qNr1ar8j92rlyqrduCAqmlcE0oCLl4MGzZAo0YlX/3O1lYt5PHuu/DBB7krTd6WfCOBsMgQQiN2\nE33hOBoFw7KmmRBzqT3hMT2IvtCV9Ft2BdqERZvy3AKYthRGD9CYOBTatSg6LKelawx7EzaH5G57\n5eIHLHhjSs0L2v/+qz49aNy41NN1iIqCmBho0KBiPs0Rhi1aBL/+Cr//Dt9/D8OG5a4aWU2XaM9L\nwrYQQojSc3dXt4pQpw706AHbtsHWrTBiRMWcp7ycP68WTzEzg+eeM27fyZNVEPzxRzhzhmTHehyO\nUgE7KuZfgwEbTLia2IHDkYFEx3Qj7VbuIkAOdjBmMPTzhw3b4dutkHZLPZZ8Q632uOwH6NFJ47mh\n8HAvsLTIH1hS0zWGvg5b9uVue31IMu8EBqCzMDfu+VUHaWmwerWahlDasJ29amTv3uqCPVE5nJ3h\nvffUm9IpU2DQIPU3AVTYruaqZdjWNK3mvWMWwoBKKmMvRO01cKAK27//Xv3D9ooVkJUFjz+u5vQa\no1Ejrr//LkeaWBB68DMiLvyLpukLNNNhQkZmO0KOBRF+tiup6fXyPR7YQV20OKw3WFuq/0cHBcAH\nL2is+Q1W/Ajh53Pb/3NY3Rzrwbj7NZ59CJo10nEzTWPIa/Dngdy2bz0Fs5+ui04XZNxzqy68vdWq\npNHRmMfFkeHsbPwxZIn2qjNhgvpbMHo0mJvnLhrVt2/V9qsEql3YtrCwyFkERAK3qMk0TSMtLQ1L\nWV1MiNIbPFhNI7ljBcRqJzUVPvlEff3iiyXeLSU1mSNRewgN300ER9HHFAzYoMPasg1HIrqzMzSg\nQMC2s4HRA+HZIdDRs5DVh+vqeOlxmPKYxvZDKnT/uFO9NwC4kgjzv4YFa2FQN43kG7DrSO7+s8bD\njHE1/P9kU1Po3h02b8bu0CGuDRpk3P6apqrjgITtqmBiAt99l/v9yZOwd6+aslXNVbuwbWJigqWl\nJenp6VXdFVFOrl+/DoCdXcE5hLWdpaUlJvJRoxCl16aNqkFd3e3fD9evg58fBAQU2fRGajJHovYS\nGrGbU+ePGBzB1jQdVxLbcOJ0EFEx3biZVr9AG99W8NxDaol0W5uSBWGdTkcfP+jjB7FXND79BVb9\nDBeuZJ83//xsgLcnwPQxNTxoZ7vnHhW2Dx40Pmynpanyc0eOqEokomq5uqpbDVDtwjaowC3LW9ce\nx25fsS3L4gohaq2ePeHcObh0yeDFWjfTUli7ZQ+Ho3aj0x1Bp8syeJjYK22IPB9EVEwANwwEbBsr\nFa6fewg6tzEiAKemwtSpEBoKu3aBiQmNHXXMGAfTn9TYFKxGu/POzwaY/zy8OqqWBG1QF90CdqGh\nhbdJTVXTRQYPzv+7tLZWF7EKYaRqGbaFEELUAE88oS4KXLxYzYe92zk7q9ttN9NSOBq9l73HdxMR\ncxidLsvgNXUX41sTcT5QBezU/BVXTE2hqSO0aAwP3wOjB4C9re72/A8jVpu0soJfflG/r8OHwccn\n5yEzMx0P9YSHekJUjMYnP8G+42oJ9qfuyxM29fqaf1Ggry/88AMn7vykNSkJNm9WF7hu3gw3b8LB\ng6q9EGUkYVsIIUTp7NypRnOtrau6J9XGzfQUjkbtU1NEzh0mS69Wc7xzsPtSfEsiYoK4eCUQx3oN\ncXOGgHbg5gzuLuBmdhX3f76j8fQJmJrfEXAzMyEoSNUhnz5dBeni6HTQvz989pkqmZYnbOfl0VTH\ngkkGHkhIUCXzvL0hJMRAgxrCzAyGDiXrQJ4rP6dOVYsnZWTkbuvcWU0LEqIcSNgWQghhvORkFbQt\nLKr1MsmV4WZ6Csei9xMavpuT58JyAvadLl31wsE2kN6+gbR2c8LNRZXoK1AMQNOgZQBERoJfU7j/\n/vyP//e/sG8fXLkCr79e8o7mDduvvWbck4yIUHOW09KM268mcHRUnxT07AkPP6zKArq5VXWvRC0i\nYVsIIYTxjh9X923aqNHCinbwILzzjrow7b33Kv58xUhNv8HRaDWCffJcGFlZhgN23FVPImOCSLkZ\nyOIpTgwKKMH8Z51O1RN+5RVVeztv2D57FmbMUF8vWwY2NoaPYci996pj79oFN26oOuYlFR6u7mvj\nhYHPPKNW8XRyquqeiFpKwrYQQgjjVeQy7YZkZqoFX5o3VxepVUFp2OyAHRYRzIlzoYUH7GueRJ4P\nJDImkOs3nHnqPlg0GerZGdHnp5+G2bNVLeH9+8HfX414v/CCmk/82GOqBrkxGjRQ0yP271flFG9f\nLFgitTls1y94IaoQ5UnCthBCCONVdtju3FmFotOn1fQKL69KOW3OFJFiRrBtrVsQfCSIsPBAkm+4\nANC4IXwzCwYHluKNQd268OyzsHChWsL922/Vm41Nm9RjixeX7gmtXKku4jS2NnF22K6kn7sQtYmE\nbSGEEMZbsEB9/F6vXvFty4OpqZpz/O23ajXJCgx92Rc5hkUEFzkHu+nVdFrtieU791V8fNw/32NP\nDYYPJqvFZErtxRfhww/h++/h8mVVw/uBB9SFkaVdyKO0VWNiYtR9bRzZFqKCSdgWQghhPAsLaNeu\nQk+RmamRkkruzXckKZsvkvLLNa63vv3YTQiPcqGOpZ76jTRaNClduM0u0xcaEZyvisidmjq2wNsr\nEJ9Ec3YP/4LnPLcQdzx3rm/jhvDJa3BfaUazC5ysqVoCPiAgdz7xTz+V/bil8c8/EBcnUy6EKAUJ\n20IIIarcxXiNVz+G3Udzw3X6rTtb3Q/t74cbwKy825sAsOhH6Nxa47F74bE+4OZSdOC9mZbCkai9\nhPoxDmsAACAASURBVN1eybHQgO3UAh/PILy9AnGs14j4RI2XHvmHda1/zNduzCBY9GIZR7PvNH58\n/u+rYK56znldXKrm3ELUcMWG7aVLl7Jy5UrOnDkDQLt27XjrrbcYPHhwTptZs2axatUqEhIS6Nq1\nK0uXLqVt27YV1mkhhBC1R8R5jYEvw+nYsh/rwEl1m7YUAtqr4P1ob2jsqEJqyu2l0sMigwk/fwS9\n3vBKjq5OHnh7BeHtGYC5qQv/HIYFX8POMI1DpzSy9D1y2jZqoEaz7w+qRSstCiHKTbFh29XVlQUL\nFuDl5YVer2f16tU89NBD7N+/n06dOjF//nwWLVrEmjVraNmyJXPmzKFfv36cOnUKW1vbyngOQggh\naqgDJzTumwpXEgs+ZmICdjZga53nluf7OrfvryddJDLWmj0n65GRZ3A65Ji6vflJIgO67cHLNYTU\nW8fQNL3Bvrg5eeLtFYi7cwBHo1zYtAte+xgOR6pCILlyQ/WTA+HDKeU8ml0ZMjJg714IDKz5q0IK\nUc0VG7YffPDBfN+//fbbLF++nH379tGxY0cWL17MG2+8wdChQwFYs2YNTk5OrFu3jgkTJlRMr4UQ\nQlSdGzdUfecyTmnYuk/jkelqygiAtSV8+R/o6a1CtqWFgQVfDDhwQA2Je7T0Y+M/sP5PCD52jWaN\n9uDZNJjGjsfR6TRuphfc183ZC4/GASSlBLLvuDOrN8HxM0WfT6cDn5Ywcxw80L2Ghexsfn5w9Kgq\nAejnV9W9EaJWM2rOdlZWFhs2bCAtLY2ePXty+vRp4uLi6N+/f04bKysrevbsSXBwsIRtIYSojQYN\nghMnYPNmVf+5FL7dpjFmLjkj0Q52sOl9CGhfhvCqi6dZ4xAGdAvBy/1Eoc0uxrcmMiaAsxe7Uc/W\niTMXiz6siQn4toSePtDLG4I6Qv2aNpJ9p27dVNjesqX4sB0XBw0bqoowQgijlShsHz16lICAANLT\n07G2tmb9+vW0atWK4OBgAJydnfO1d3JyIja28Ml3Bw4cKEOXRU0lv3dhLHnNVEOahvfhw5glJ3P4\n6lUySvE7+vZvJxb96JrzvVO9W3w0MQLztDSMPdz1tATOxp/k3NWTxO++UGg7neZB5PkAdh7uxY3U\nhjnbE68XbGtmqqet2018Pa7j45lCx+Yp1LHKnXoSHQ7RxnWz2nHw8MADSP7+e8L79Suybbthw7CM\njeX4unWkNWtWKf2rLPI3RpSEVxlLjZYobLdu3ZojR46QlJTEhg0bGD58ONu3by9yn5J89CeEEKJm\nMY+Pxyw5mUx7ezIaNDBqX02DZZsas2Zbbo3o5i6pfPRcBM4OGSU+TuLNeM5fCON8/HHi9ckG2+jQ\n4WzvjnuDNrg1aIW1hbqGKG5QLH+GprIt1IFjZ9U2S3M97d1v4HM7XHdoloKVhWbwuLVFcufOaCYm\n2B4+jMnNm+gLW/Y9MxPLmBhMsrK4JdVIhCiVEoVtc3NzWrRoAYCPjw/79+9n6dKlzJgxA4C4uDia\nNm2a0z4uLg6XIv5Rdu7cuSx9FjVM9siB/N5FSclrphrbsgUAs06d6GzEFJLMTI0JC2DNttxtgR3g\n5wXW1K/bqch9NU3jQvxpDkeGEBYZQty1GIPtTHQmtHTtiLdXIB1adMXOxt5gu/v6qvvzcRpXEqFd\ncxMsLeoCdYt+Ert3w5kzMGQI1IYCAP7+6PbuxTc5GXr2NNwmMhKyssDVFd/u3Su3fxVI/sYIYyQl\nJZVp/1LV2c7KykKv19O8eXNcXFzYsmULfrfnfKWlpbFr1y7ef//9MnVMCCFENZS9TLsRC9rcTNP4\nf/buOyyqa2vg8G/oVUAElKZUkWpHTTTVJEZNYkxveu9NTDHVGKMxUWOM6YnfjZp2Y2KK6d3YUoy9\nN1CkqzRBRARE+pzvj01VQNowgOt9nnkOc+acM3tw1DV71l7rjjmwckvNvnGXwNfzwcaq/m9BNU3j\nWFYCBxK3ciBxOyfzMus9zlRnSk9HH3o7BzH+ytuwtb5AwFyLl5sOL7cLH1etqpvjm2/C008348QO\n6qabVJMaW9uGj5E27UK02gWD7ZkzZzJu3Dg8PT0pKChgxYoVbNiwgTVr1gDw5JNPsnDhQoKCgggI\nCGDBggXY29tz1113GXzwQggh2tmpU2BmBqGhTTs8X+OGGbA1umbf5LHw4QwwM6sbaOv1FSQfj+VA\n4jYOJG7j9Jmceq9pbmZB8GlTIn7cRMj4f3FoxI0AzQq0my0vD1auVKVI7rjDcM/TnmbOVLfGVAXb\n0qZdiBa7YLCdlZXFPffcQ2ZmJg4ODkRERLBmzRpGVy6omDFjBkVFRUydOpXc3FyGDRvGunXrsG3s\nk7IQFztNg/feg6AguOIK43WFE6K5FiyAOXNUasEFpGZpjJlWt5TezHvh5Qdr1vVUVJQTnxZNVOJ2\nopJ3UHC2noLbgKWFNaF9BhPhP5x+fQZiueYPeP5rMP8Dxt3YFq+scT/+CCUl6u+rh4fhn6+jKC0F\nR0cJtoVoBZ2mae2yCqR2vouDQ/15dKJrkty4eqSmgrc3uLjAiRPGHk2HI++Zzi/miOoKmVbr7f3O\nE/DEbTpKy0uISznAgcRtRCfvpKiksN5r2FjaEeY7lAj/4fT1jsDczKLmwTNnVApERQX71q6lwtHR\nsO+X0aPhzz/ho4/g/vsN9zwdkaaBXt+lSv/JvzGiOVobw7YoZ1sI0UoxMWobHGzccQhhANsOaoyb\nDrmVZfXMzWDZc0X089nLJ6u2cejoHkrLius9197agXC/YUT4DyfAMxRT0wb+m7Kzg1tvBUtLTIqL\nufA8eyscPw5//w3m5jBxoiGfqWPS6bpUoC1Ee5NgWwhjOHRIbSXYbjsZGSrF4dFH5fdqRJv2qxnt\nohKwtCigX+9dTLxyO3sS9rMjtv7yfk72LkT4DSPCfxg+vYIwMWliYPfllwAtqvXdLM7O8NNPKn/Z\nycmwzyWE6HIk2BbCGKpmtouK4PffYexY446nK7CwgPR0uPtu2LtX8uCNIDld4655p/D13Imfx3Y8\nXaMxMdGTlXv+sS6O7kT4D6e//3C8XP06dm8GCwu44QZjj8JwVq+G77+Hxx6D/v2NPRohuhwJtoUw\nhqpg+9NPYcUKFXSbmBh1SJ2elRVs365y4FeuhPHjjT2iricmRrXtdnWts/tkXiY7Y7bz9V/bueny\nOHS6+pcCuffoQ4T/cCL8htHL2btjB9gXk19+gWXLwNdXgm0hDECCbSGM4eabwdNTzSaVlqoUiFqN\noUQL2NnBc8/Bk0/C88+rbwvkA0zbuvNOiIpC276dTP9eqkRf0nbSs48A4Gh//im9ewZWpogMx8Wx\n1/kHCOO75hr44APVsGj27Jr9VQ1tfHzU7L4QokUk2BbCGKZPV9sRI2DbNkhKkmC7LTz4oGo4EhUF\n337bfvWQ4+LUn18XLnmqlZaSUnicA+OCiYr5hBPb628yo9eb4GAbzDVDhxHuF4mTvUs7j1Q025VX\nqg+mW7dCQQHYV35qevll9e3b+++rv1tCiBaRYFsIY/L1VcF2cjJcdpmxR9P5FBWBtXXNfSsrmDsX\nHnhAbW+5RTVgMaSSEpXPW1wMixaprnxtlB5RXq6RWwAn8yAnD/IKYUg/cHVqn/SLCn0FyRkxHEjc\nTlTsZk4/NkI9kF830K6oMCM1K4Kk9GHccMkQXp7i2C7jq+L6zTd0274dfv21bRcwZmWpCiTdu7fd\nNTsiR0eIjFT/Fv3zT00KljS0EaJNSLAthDH5+qptcrJxx9EZ/fADTJsGn38Oo0bV7J80CX7+Ge67\nr33SSLKy1Ix2fLxKD7ruOvjvfxtsb11errEnDtKzIScfTp5W25zTNferguuq0nm1mZvBkqc17r/B\nMAF3WXkZ8amVNbCP7KKwKL/e4yzMrXBxGMSnvw8jOX0gZeU23DRKNaxpbw6bNuGwYwe8+KL6wNNW\nXnsNFi+GJUvUB7iu7JprVLC9dq0E20K0MQm2hTCmQYNUcFYVdIumSU9XwU9urkoZqR1sm5urBZKG\nkp2tFglWzV57e8OuXeqr9tmzYc0a1cr89dfhiScAOF2gsWYH/LYZVm+H0/UE0U1VVg5TXoMDiRpv\nPw7mZq0PuotLi4g5uoeopO0cOrqHktKieo+zKSwlTOdC+O1TsTAN55KHLDlVGYv3D4DPXgATk/Zf\n9Jj2+ON0u/dedIsXw5QpbVP6saICvv4aysogPLz11+vo7roLQkLgqqvU/dxcOHkSbGzA3d24YxOi\nk5NgWwhjuvFGdRNNp9er2evcXBgzBqZObb/nrqhQH45sbFSNZ29vtd/UVI3j1lthxgxYvpwk20B+\n/Vpj5RbYdADKW9h1xckeejiCczc4kQvJGWr/kh8g5gh8u0DD2aH5AW5hUT4Hj+ziQOJ2YlP2U15R\nfw1sB9vuqsnMvlT8VvyI6fP3kec6hOFTqA603brDL6+BnY1xqosUBQaSPWECrj/8AI8/Dn/80fpU\nng0bVDMbX18YOrRtBtqRBQbWncFOSKjZL1VjhGgVCbaFaE+aBk89BX5+8PDDhs8n7ooWLYK//lKz\ny8uWtW8g8PHHqoa3p6dqdFJLRYXGtuMu/Db0E1YWvMfhT6wavIynKwwMBOfKILpHA1snezCrNXNd\nWKTx74Xw3d/q/vq9MPR++PlVjTC/C/8eTp/JISppB1GJ20hMP4Re09d7XA+HnkT4Dyfcbxi9ewZg\nojOBK4BpL1FernHHDIg9po61tICfXwUvN+MGZOkPPYTr33+r98bPP8OECa27YGXDHO666+IMNisq\n4JJL1Lc0QohWkf/phWhPWVnwf/+nFiQ9+qixR9P5ZGSo8n6gAu2ePdvvuU+dqnnut94CW1sKCjXW\n7oSVm2HVdpVvrZwfaA/pB+OGVTA+spyIUMsW1Zi2tdbx9XyNMD+Y85HadyQDRjwIn72gMeGy8695\nIjeDqKTtHEjazrHM+Aav7d6jT3UXx17OvRsc39OLYe2OmvvLnoPIEOMHoxWOjvDSS+rDWLdurbtY\ncbFaEwAq2L4YDR8OmzcbexRCdAkSbAvRnqratIeEXJyzZa3l7g4//qhKlDW1aU1hISxdqnK8HVtR\nJWPOHMjJgSuuIP3yW1nwhsYnv0Np/dkXWFvC1YNh3KUwbgT06qGDl1+Dm5apBZQt7Bqq0+l4fjKE\n+Wnc+yKcKYLCIpj4HMz9j8bzkzQyTx3jQOJ2DiRt43hOSoPX6tOrLxF+wwn3i2xSDez3f9J497ua\n+7MnwZ2jO9D7+MEH4f77wdKyddcpKFCLXY8cgX792mZsQoiLlgTbQrSnqs6RbbGA62J1/fXq1lST\nJqlZyoICmD+/Zc958CC89x7Zlm68Oupb3rsdikvPP6yXM4y9BMZfAlcNBhurWoGoXq9K0yUnw7hx\ncPvt8OGHLZ6FvXGkjm0fatw0E5LS9fR0jufP3dvJyt2OmVlWveeY6EwI8Awj3H8Y4b6RONg1vaTd\n33s0Hnun5v7Ey+HF+1s0dMMxM2ub1CwXF/XNiVZ/J8wur7hYlbR0cDD2SIToEiTYFqI91RdsJyXB\nli3g76+a3Ii29dRTKth+5x147DEVSDVTnmcQb/17K4viIjjzR91Z03B/uOFSdRvYt5FqHCYm6mv5\nxYvVLPk336j87x9+gLCwZo+poqIcU9ODvPDvbWw/tBMzs9x6jzM3taBv7/5E+EUS6jsUW6t62jxe\nQEKqxq2zVRovqNf56fPGqTzSri7Gb5/efVct8p01S71PhRCtJsG2EO2pvmB75UrVYvzhhyXYNoRL\nLlEz4atWwauvqnzrJios0nj3e3jjS1NyC+pWpBgcBC9NgWuG0vT8a3NzFfyPHasa7kRHw9NPqzbZ\nTVBaVkJsyj4OJG7n4JFdFJUUAudP5paU2nD85GBuuzKSW68YiKWFdT1Xa5rcfI3xj5wht8AOULP3\nP7+q8sdFF+TtrWa2162TYFuINiLBthDtacYM1Rq5f/+afdLYpmGaBrGxrc+bXbBABdtLlqhg19Oz\n0cNLSjU++AVe+QyyTtV9LMQH5j8AN41qRpB9rsBA2L5dLbh85plGDz1bcoZDR/YQlbiNw8f2UVpe\nUu9xdtYOWJoP5Ys1kRzJCEevN2f1NlXTe+pErUVjLSvXuP0FiD+lAm0rcz0/v2aCp2snCbQLC1UF\nmalTVXlGcWFXXKG2W7aob14GDjTueIToAiTYFqI9jR17/sI4Pz+1TUpq//F0dB98oKq2vPGGCpJb\nasAANZP8/ffw7beq82Q9yss1lq+Glz6BlHPSnv08YN5/4I6rwdS0DYJNG5sGux3mF+YSnbyTA4nb\niE+LRq+vv0i3k70LEX7DCPcfhm+vIExMTLlmiMbE5yAzR6V9PP4OHEhUXSctzGvGrWkaJaVQUqby\nz0tKK7e17i9fDX/urnm+T5/TGNKvkwTaoGqib96sFkw+aITWlp1R7TUEV12l6tkLIVpFgm0hjK1P\nH7U9elRFR111Bu6zz1TN3oiIJr1Gq6NHVVBcUQG9Llwp44IWLlSpOldeed5Der3GN3/BvI8hIbXu\nY56u8MK/YPL1bdOtsSEn8zKJStpOVOIOjhyPRaP+xXlu3T2J8BtOhP8wPF18z5uxHh6qY9fHGjfP\ngl2H1b6Pf4OfNoCpiVYdUDdURaUhc0uWcts17dhAqC08/rgKtmfPhttuAyenxo9fvFgtYp05s973\nyUVj3jx1W7DA2CMRokuQYFsIY7OxUcHk8eOQmloTfHclp06pqiAA9vaqhu+ll6rb5ZeftxBNV1aG\nzwsvQFER3Hsv3HFH68cQEKBulc4Wa+yMgS3R8O1fEH3OFwuupnnMGhrHgy8NwcrapPXPfw5N0zie\nc4wDlU1m0k8ebfBYb7cAwv0iifAbhlv3xlNgADxcdPyzROPB1+CLtWpfVbfHlrjt5DfMGbgF6GTB\n9i23qPfXP//A3Lmq5GJjPv8cdu5U5QMvZi+8ADfcoD4YCyFaTYJtITqCSZNUqa2u2lGysBDuu0/N\nMiYnq8VX69aBj0+9ueruH3yAbWys+uCxeHGbDCEzR2NLlAqut0bD3rj6W6g72sMzA2J47PVI7KLN\nYVYiWDuff2AL6DU9xzLjq2ews/OO13ucTq/hl3SSiDxLwme/g1NQ84Mea0sdy1/QCPdXM/Zni88/\nxsIcrCzA0hysLGv9bKE6Q1qaQ3j6Bl7e/i90k15o9hiMTqdTAXb//qrW+pQpDXdETEhQgbadnSrN\neDEzMVGpV0KINtFF/2cXopN55RVjj6BtHT4MQUE1M9ZeXrB8ufo5I0MF3Zs3Q/d66jyfPk2PX35B\nMzFB98UXLapDrddrHD5aGVhHweYoSM5o/Bxba3jiNpg+oRjHoeNAXwgvvXteW/bmKq8oIyHtIFGJ\n24lO3kn+2fpzYE1NzQjy7k+E33BCc02wWzQZUlJg1ZXwxRcwZkyzn1un0zH9LnjkZo2Tp1UAXRVQ\nW5g3sXTfl+lgOl59G9EZhYWp9KElS1RDpIaC7a++Utubb1bfNgkhRBuRYFuI9nLDDeDhoUrPdeX/\nzOPjVWnDSy+FjRvPr1Xs7q7yZ2+7rf7zHR2J+fJL7HfvxveSS5r8tFmnND5dBZsPqJnr3IILnxPc\nB0aEwyVhMHYE9HDUwfw3VP58WBg89FCTn7+2ktIiYo7tJSpxO4eO7qG49Gy9x1maWxHiM5hwv2EE\n9xmEVe0SfXv3qm8DVq1SpQvXrIFrr23ReGysdHi3tLP93XerW2c2f776+3fNNfU/rmnw5Zfq54u1\nPbsQwmAk2BaiPWRnw2+/qa+oly419mgM67331Lb2zHYzlbm6cur66/Ft4vFrd2jcOx9Onm74GEsL\nGNoPRoTBpX6FDF/1Ot1TD8GzP9QcdPRozbcM777brLSegrN5HEzeSVTSDuJSD1BeUf8KRDtrB0J9\nhxDhN4xAr3DMzSzqv6Czs3rPvPaaSrm5mBfstVb37g0H2qC+bTl1ClxdVQUOIYRoQxJsC9EeDleW\nhQgO7tpd6QoL4ZNP1M8PP2zwp6uo0Jj3MSz87PzO2i6OcEm4Cq4vCYeBgWBpUfm7zymBWxapFu6b\nNsHIkWp/fr6qgR0cDJdddsHnz8nPIippB1FJO0jOOIym6es9rns3V8L9hhHhF4lPZYm+JjExUZ38\nZszoulVqOgIPDxVwJyZ23XUTQgijkX9VhGgPhw6pbe3OkV3R119DXh4MG2bwZhiZORp3z4P1e2v2\n9XKGF++HUf0hwKuRpjPOzqqs4IsvqrJwGzaoD0Hh4bBnj/rQUA9N00g/eYSopB1EJ+1otIKIe48+\n1RVE3Hv0aXkDHJBAuz2Ym7e+eZIQQtRDgm0h2kN9bdrP9fnn6rhZs1q0KNDoNE0tQgN45BGDPtX6\nPRp3zavb3fHqwfD5XHDr3sSgdto0lSqyaZNK06jKhzYzAweH6sMq9BUkpccQnawC7FMF2fVeTocO\nH/cgwv2GEe4XSQ+HliZJi3aRmQk95c9ICGF4EmwL0R6qgu2QkIaPeeMNiI5WtYEHDWqfcbWligq1\nuMzcHG691SBPoddrLPxMlbLTV2Zs6HQw59/w/KRmdnbs1k01L5kxA55/XuX0Vs4+l5QWEZuyn6ik\nHRw6spuzJWfqvYSpqRl9PcMJ9x9GqM9Qutk6tvYldixvvaW6L951V/2VYzqrF19UTY7WrlV1uIUQ\nwoAk2BaiPbz/PkRFQWRkw8f4+qpgOzm5cwbbZmYwfbq6GUB2rloEuW5nzT4XR/hyHlw9pIUpGlOn\nqpbpvr4UZKdz8MRhopJ3EJfS8AJHawsbgn0GE+4XSb/eA+tWEDG0xETVtt7cXJWxMyRNU4tFc3Jg\nwgTDPld7MzGB0lLVYXLvXsnTFkIYlPwLI0R7OKd7Yb18K2tvJCU1ftxFaPMBjTvnQnqtDI5R/WHF\nPHB3aXku9ImSXKK/fZPo9CiOfPVYgy3SHe2cCfONJNwvEj+PYMxMzVv8nK3i4AArV4KVlQoWLRqo\nZNIWUlJUoO3kpMo1diXTp8OyZerDbf/+sH49uLgYe1RCiC5Kgm0hOgo/P7Wtp6Nim5g2Tc3oTZvW\naYInvV7jza9g9gcqS6XKzHth/v1gZta8QLuqg2N00k6ik3eSlZvW4LHuzr0J8xtKmG8kXq5+rVvg\n2FZcXFTef0wM7N4NI0YY7rn++kttR43qehV0rK3h7bdVA5tDh1TDJQN9IyOEEBcMtl955RV+/PFH\n4uPjsbS0ZNiwYbzyyiuEnJN7Om/ePD766CNyc3OJjIxkyZIlBHf1ygtCtCVDzmzr9fDxx6q0XScJ\nKvIKTblpJqzcUrOvezf47AW4fkTTg7+y8lLiU6PUAsfkXRScrb8Yt05ngm+vIML8IgnzHYqLY6/W\nvgTDGDlSBdsbN7ZPsN1V607fdJMKtjdu7PxNe4QQHdoFg+0NGzbw6KOPMmTIEPR6PXPmzOHqq68m\nJiYGJycnAF577TXefvttli9fTmBgIPPnz2f06NHExcVhZ2dn8BchRJcQFgbPPgsDBrT9tZOTVaDd\nq1fbV2DIzlaL59qwPN3BozY896kvmbU6mw8Pha9eBO+eFw60C4vyOXR0D9FJOzicsp/SsuJ6jzM3\nsyDIuz9hvpGE+AzG3sah3uM6lFGj4IMPVBWVmTMN8xyaBn//rX7uqsG2Tgfffadeq5RWFEIY0AWD\n7TVr1tS5//nnn+Pg4MDWrVsZO3YsmqaxaNEiZs2axYTKRTTLly/H1dWVFStWMGXKFMOMXIiuxtMT\nXn3VMNfeW1mM2hC1rydPVl/Ff/21qq/dCkUlGm9/DS9+3JfyCpPq/dPuhFceAvNG0kZO5mVWpoeo\nBjP6BhrM2Fk7EOozmDC/SPp6RWBhbtmqMbe7qgY8u3erQNEQKR6aplIrtm7t2rWnTUwufIwQQrRS\ns3O28/Pz0ev11bPaR44cISsri2tqtcK1srJi1KhRbN26VYJtISIi1MK2n35SzVSMYd8+ta0dbJeW\nqgVwvVqRLpGcDKtXq4V6/v4tvoxer/H1n/Dc+5CSBaCCIAc7+GQ23DTq/IBSr+lJzUokOlnlXx/P\nSWnw+i6O7oRX5l/36RnY9A6OHZGXF2zbphb2GSqX2sRElUJsrMW5EEKIJml2sP3EE08wYMAAhg8f\nDkBmZiYAbm5udY5zdXUlIyOjDYYoRCd2+rQq+WdtDY5GrMF87sx2bCxMnKgqTWzc2PIZvg8+ULOg\nt90GPXq06BKbD2g8/S7sOlx3f5BXISvfssXXoyagrMm/3snBI7vIL8ylPjp09O4ZSJjvUML8huLm\n5NkxFji2lVZ+gyCEEKL9NCvYnjZtGlu3bmXz5s1N+o+roWN2797dnKcVXcTF+Odue+AA/YBCb28O\nV80uG4HVf/6D7fDh5NnaUr57N6YFBYRmZmIeE8PROXM4edNNzb6mrqSE8A8+wBw4fOWVFDbzzzc1\n25LFv3qwPsqpzn5H2zKmjDnOTSOyOXUcMlLOkp6bSOqpeDJykyjX11//2kRnirujL57dA/DqHoi1\nhVovkpacRRpZzX59ovO5GP+NEa0j7xnRFAEXKt17AU0Otp966im+/fZb1q9fT58+far396xcbJWV\nlYWnp2f1/qysrOrHhLhYWR85AkCxj49Rx1Hs60txVbUToMLenpSnn8Zv9mw8//tfTo8cSXkzU1y6\n//kn5nl5FAYFUdhYZ8xz5BWasmxdL77b5FInL9vCTM8dl51g8ujj6DlJXGY8aafiOZGf2mD9a0sz\nGzy7++PVPZBejr6Ymxqw7rQQQgjRAk0Ktp944gm+++471q9fT2BgYJ3HfHx86NmzJ+vWrWNQZde7\n4uJiNm/ezJtvvlnv9QYPHtzKYYvOpGrm4KL8c1+xAgDnUaNwbsrrT0yE994DV1dVmcSQBg2CjRsx\nW7uW/p9/Dl980bzzs7MhMhLbBx5g8JAhFzy8tExj6Y/w0ieQW1D3sTuurmDqLfGczNvFliO7nSG9\nSwAAIABJREFUyDrVcP1rF0d3lR7iOxSfXn07d/51R1RR0emqc1zU/8aIFpH3jGiOvLy8Vp1/wWB7\n6tSpfPHFF/z88884ODhU52jb29tja2uLTqfjySefZOHChQQFBREQEMCCBQuwt7fnrrvuatXghOj0\nYmPVtqk153NzVbON/v0NH2zrdLB0KYSEwJdfqtbVQ4c2/fwxY9RNX3/VjyqapvHzRnh2KSTWiqHN\nzYoYPXQ/Vw/ZRdbpPXzzd379w0RHn159CfUdSrjvUNy6e9Z73EUpOxvOnoXevdvummPGqLUGH3+s\nylEKIYRolQsG2++99x46nY6rzqm1Om/ePObMmQPAjBkzKCoqYurUqeTm5jJs2DDWrVuHra2tYUYt\nRGfxyy+qSU1TOzZWpXokJxuurNu5z/fWW2rxZhNmp+vVyOLK3YfV4sdNB9R9O+uT9HHfRYjvLly7\nR6Np5SQfP/88UxMzejn6MnLgNYT0GUw3WyMuLu2oli9XZRfvvRc++6xtrllUpBbMlpS0fT12IYS4\nSF0w2NZfYNaqyty5c5k7d26rByREl2JuDkFBTT++e3fo1k01oMnJaXGFj2Z55JE2v+SZsxpP/Rc+\n/k2Pq1MyQ0N24uO+GxenI9XHaOekYXezdSLUZzChPkM5k12Omak5g0PkK94GRUSo7caNbXfNrVtV\noB0RoVrDCyGEaLVml/4TQhiQTqdmm/fvV7PbrQ22s7JUSspll6mmM+1gV0wRTy+OwtxsN5PH7cHO\n5lSDx3r06EOo7xBCfYbi5eaHiU7Nku8+JRUCLigsTNVvP3YMUlLA27v11+zqLdqFEMIIJNgWoqPx\n86sJtpuTQ12fffsgMxOO15Or0RJ6PRQXg41Nnd2n8rM5eGQXq7btJv9sNP371l+ez9TEjADPUEJ9\nhxLqM5ju3VzbZlwXI1NTuOQSWLVKtW6/++7WX7Ort2gXQggjkGBbiI5myhS44QYYMaL112ppm/bS\nUtUV8lx//QW3347+2Rkcu+8mDh3ZzcEju8k4ebT6ELNzClnYWtkT4jOYEJ8hBHn3x9qybqAuWmHU\nqLYLtktL1QczMzN1XSGEEG1Cgm0hDOX0afU1f3MXObZli+yqYHvAgKYdr9fDO+/A//0f7N6tShBW\nKiopJPa7JRwa04dDFrsp/HZ7g5cpLPJiZPhgRkYMxqdXkJTnM5RRo8DfH87p4NsiFhZw5IhKSbGz\na/31hBBCABJsC2E4/furhY4HDoCXl3HG0NyZbZ0O1q6F1FS06U9z4v9e5dCR3cQc2U1i+iH0IQDe\nQHmd0yoqzEg7EcbR44O5bMAglk5zw9KiC7VH76iGD4eEhLa7nk7XtmUEhRBCSLAthEGcOaMWrllY\nQK9exhlDQQGkpoKVVZMropRWlJL44uPEOGVzqHcmOZ9NbfDYsnIn4lMGcTRjMGknwulma82y52D8\npRJkCyGEEFUk2BbCEA4fVtu+fVUOrDHY26uZ9eTkRseQk59FzJE9xBzdS3xaFGXlpTCi/tlN75Rc\nTH0msnTT9SSl+QCqeshlA+CLueDhIoG2EEIIUZsE20IYQkyM2ja1c6ShWFurDpG1VFSUk5RxmJij\ne4g5uofMU6kNnm5ZXEaQzpl+l4zH/60VvJT2EEu231H9uIkJzP03PHcfmJpKoC2EEEKcS4JtIQyh\ntcH24sXw++8wa1abVIY4fSaHw8f2EXN0D3EpByguPdvgsW5OnoT4DCK4wBLft/6H2ZLniLXuy7X2\nt3DAvOY4Lzf4ci5cGiFBdqf355+qY2RIiOG7lgohxEVGgm0hDOHMGdU98pxZ5SaLioI1a2Ds2BYF\n2+UVZSRnxHL42F4OH91LRs6xBo81N7UgwDOUYJ/BBPcZSA8H1aa7okJjT+87Wb0V3vgSzhbXnHPT\nKPjfLOjeTQKzDuHgQVi9Gq68EgYNat65mgb336/WGOzZ0/wykUIIIRolwbYQhrBkiSqfp9e37Hw/\nP7VNTm7yKTn5WRw+uo/Dx/YSnxpFSVlxg8d2t3ch2GcwIX0GEeAZhoW5JZqmkZQO3/2t8dcu+Hsv\nnC6oe56lBbz1GDw8AXQyA9pxLF8Ob74Js2c3P9hOTlaBtpNTTQt4IYQQbUaCbSEMpTULI3191baR\nYLusvJTE9EMcPrqXw8f2kZWb1uCxpqZm+LkH06/3QEJ8BuHm5IlOp+PkaY2fNsCfuzX+3AXHMhse\nUr8+8NWLEO4vQXaHM2qUCrY3bmz+uVUt2q+4QnWlFEII0aYk2BaiI6qa2U5Kqt6laRonTmcQe2wf\nh4/uJSH9oKoc0gDnk4X0s3Sn311TCfQMw9LCmqISjc0H4J3d8OcujX3xjQ+jlzNcPQRGD4WJl4O1\npQTaHdKll6pc6x07oLhYlXtsKmnRLoQQBiXBthAdUeXM9tmMFOITthKbso/YY/s5VZDd4Cnmphb4\ne4YS3Gcg/d7/DpcPfkG3eDH4DiW/UOORtzRWrIOShuNzbK3h8gEqwL56MAT7SLpIp+DkBGFhKtd/\n1y4YObJp5+n1EmwLIYSBSbAtRAei11dwLCuR2GP7iF16P8dKT6Jf9XqDx7s6edCv9wD69R6Iv2cI\nFmaW6oHtz6vtwIHsj9e4fQ4k1FPhz9QUhvarCa4jQ8DCXILrTmnkSBVsb9zY9GC7pAQefFCdFxho\n2PEJIcRFSoJtIdragQPg6qpKqTVhVji3IJvYY/s5nLKP+JQozpacafBYSwtrAj3DCOo9gH69B1RX\nDqmjuBgOHULT6fgwZSBPPld3Nruvd2VwPUTNYjvYSXDdJdx2G7i7w/jxTT/H2hpeeslwYxJCCCHB\n9nmSkmDGDFi4UHX/E6K5brkFEhNVObZ6Sv+VlBWTmHaQuJQDHE7ZR9aphhc26tDh5epXGVz3p0/P\nvpiaXuCv7cGDFOiteGjQV3z1X4vq3XbW8MGzcOdoCa67pFGj2qQmuxBCiLYlwfa57rkHtm9Xs5OJ\nicYejehsiorUBzZTUwgIAFRqSOqJZOJS9hObsp8jx+Oo0Jc3eAkH2+4EefcnqPcA+npHYGfdrVlD\niIot57bBB4g386neF+YH374EfXtLoC2EEEK0Jwm2z7Vvn9omJalmD7I4TDRHXBxoGjkD+xEX/w+x\nx/YTnxbN2eKCBk8przDnxKlg+vQcwKQx/Qn17d2iRYmapvHxb/D4x5EU1/qbff8N8H9PSiURIYQQ\nwhgk2K5N01THvh9/VPfj4iAoyLhjEp1CUUkhCWnRxO74jrjZV5HtYgd/LW3w+JzTvUnJ6k9qZgTp\nJ4OpqFALG5f+AP8aB9Pv1PBxb3pwfOasxiNvwhdra/bZWsP7z8Dd10qQLYQQQhiLBNu16XTwww/w\nxhsqDaB7d2OPqGvQNHXrQsrKyziaGUd86gHiUqNIyUxAr1V2i3SxO+/4bjZOBPXuj79HOI+9HcGe\nWCcA+geAlQXEV1YKKS6F936ED3+BO0aWMGPLI4QVHVT1kxtwMFnjtuchtlZH9lBf+HYBBEnaiGjI\ngw+CnR0884xazCuEEMIgJNiuzzPPGHsEXUd+PmE33ECRvz9s2mTs0bSYXtOTnn2U+NQo4lIPkJwe\nQ2l5SYPHm+tM8feOIMi7P329I+jl7I1Op+Pl5Rp7YtUx1pbw3QLo0wt+3givfg574tRjFRXw5T8W\nfMn/GJu/kpk7i7lkaN1GJZqm8ekqePQtKKo1lH+Ng3efAhsrCbQvSi+8oL6d++47CA6u/5izZ+HT\nT6GsTLV4F0IIYTASbAvDWr0ay8xMLDMzVS3f8HBjj6jJTuZlEpdygLjUAySkRlPYSN61Dh2err6V\nwXV/fHoFYW5mXueY2GMaL31Sc3/+A+DnqQLiiVfAzZdr/LUbXvsC/tpdc9zv3cfx+1NwabjGs/fC\n9cPhbDFMfRM+W1NznI0VLJ0O942RIPuilpgIMTGq3nZDwfbmzVBaCoMGyTd4QghhYBJsC8Py9q75\nedkyWLTIeGO5gIKzeSSkRVcH2KfyTzR6fA+HnvT1iiDQO5wAz7BGq4bo9RoPvAqlZer+kH7wxK11\nj9HpdNX1r3fGaLz+Bfy0QY+GCQCbo2DzM6qySHkFHD5ac25wH5U2EpyyETabwsCBYGPTgt+C6PRG\njoSvv1bfJD30UP3H/PWX2krXSCGEMDgJtoVhDR9OzOefE3zvvfD55/Daa2BpaexRAWpRY2L6IeJT\no0hIjSYj51ijx9tZO9DXK5xAr3ACvcNx7ubW5Od67yfYEqV+NjOFj2aCmVnDM9BDg3V8vxBi/72A\nNzZ68kWvSZTpTQGITqp77H3XwZLpYGutg/ueV7OWa9bAtdc2eXyiC6mqtb1hQ8MVlSTYFkKIdiPB\ndpWoKNi9Gy67DPz8jD2aLuVs376cDQjAxsICUlKq60+3t9KyEo4cjyU+NYr41ChSTiShVS1qrIeF\nuRX+HiFq9tornF49vDHRmTT7eVMyNWa9V3P/2Xsg3L9pqR5BIXZ8/Mn9zLv6GO8Ev8iHv6gUElA5\n30uehsljK6+l19eUrhwwoNnjFF1EcDA4OUF6Ohw9Cj4+dR8/fRr27gULC7j0UqMMUQghLiYSbFf5\n4QeYPx+mT1fVSDRNfQX7558qgOnWvMYiohadjrilSxlw1VXtWre8oqKcY1kJKrhOi+bI8VgqKhpu\nJmNiYkoft0ACvcPp6xVB754BmJmaN3h8U2iaxsNvwJkidT+oNzw/uRkXuPNOuPpqvPz8eNtOx+xJ\nGh/+AkeOqzSUEN9av8+EBCgsBE9P1S5eXJxMTFQqya+/qgmEc4NtR8eaDqeSaiSEEAYnwXaVqtJq\nQ4eqrU4H0dGQnKy+jh0/3nhj6wIqHB0NHmjr9RWkZR8hIe0gCalRJGbEUFpW3ODxVYsaA73CCPAM\nx8+9H5YW1i0fwO+/qxSZYcNUSTVgxTpYvb3y+XTwv1lgadGM34O7u7pVcnbQMeu+Bo7du1dtBw5s\nweBFl/LGG/D++9CrV/2P+/qqmxBCCIOTYBvULPbOnernyMia/VdfDdu2qdltCbY7HL2m5/jJFBLS\noklIiyYx/RBFJYWNnuPW3ZO+XuEEeIbj7xmCrZV92w1o+nSIjVXfhPTvT3auxpP/V/Pw1IkwIsyA\nHziqUkgk2BaBgcYegRBCiEoSbIP6+j03VzV28PKq2T96NLz0Evzxh/HG1lktX65Scx59tM1Ki2ma\nxoncdLWgMe0gCekHKSzKb/Sc7vYuakGjVzgBXmE42BqozFlpqXof6XTQty8AT/4f5OSph73dYOGD\nhnnqauHhcOONkocrhBBCdCASbENNCklkZN1Uh8hIsLWFw4fVYiMPD+OMrzP6/ntYuVIFfy0MtjVN\n42Reppq5To0mIe0g+WdzGz2nm40TAV5hBHiG0dcrHGeHplcMaZWEBNWJxs8PrK1ZuUXjq1qf0d6f\nAXY2Bs5Xv+cedRNCCCFEh3HBYHvjxo28+eab7N27l4yMDD755BMmTZpU55h58+bx0UcfkZubS2Rk\nJEuWLCG4oWYKHVFoqOoa2b9/3f0WFnD55bBqlVpoJMF205w9q1JvAK6/Xn1QqZKZCe++CyUl8Oab\n552ak5dFQtpBEtMPkpAaTe6Zk40+la11NwI8QwnwDCPQMwxXJw907bgIs9qhQ2obEkJ+ocYjtV7a\nvdfBdcPaYEwNlXEToqlSU9W/YybNr6ojhBCiZS4YbBcWFhIeHs6kSZO47777zgtkXnvtNd5++22W\nL19OYGAg8+fPZ/To0cTFxWFXuUiswxswoOFSaYsWqZQIZ+f2HVNntn49FBfD4MFqgVbtYLuoCBYu\nBCsreP55TpmUqpSQtGgS0w5yqiC70UtbW9pWB9cBnqH0dG5ZOb42FxOjtsHBzHwP0ir74bg4wtuP\nt/LaH30Ec+fC/ferijlCNFVZmfpmLjxcfVgbMUJ9GN63r27DKSGEEAZzwWB7zJgxjBkzBoDJkyfX\neUzTNBYtWsSsWbOYMGECAMuXL8fV1ZUVK1YwZcqUth9xe/P3N/YIOp+VK9V23LjzHjrlbEfipGtJ\nKM0iYfnDnKKo0UtZWljj7x5CgJcKsD169MHExLRp40hOhmefVZUZ+vRp5otoprAwuOMONnmP5/0v\nanb/9ylVQaRVzM3h+HFISrrwsUJUKSsDNzdVV/vUKThxAtLSoEcPVR5SCCFEu2hVzvaRI0fIysri\nmmuuqd5nZWXFqFGj2Lp1a9cItkXzbdyotmPHkluQTfKJaDLzjvL7wY/IycuCAVZAb6gn0LYwt8LP\nPbhy9joUT1c/TJsaXJ9r1iyVO/777zBnDkybplKDDGHiRIrH3cwDtTKsxl8Ct7VFg76qEm3JyW1w\nMXHRMDdXDW62bIGtW+FYZYfUK6+UNBIhhGhHrQq2MzMzAXBzq7sIzdXVlYyMjIZPLC5WaQSiyzmV\nn03iV++QsG89idEfkbMlq9HjLUwt8PUMIcAjFH/PULxd/TA1baN1u++8o4KKr79Wgffy5bB0KVxx\nRdtc/xzzP4H4VPVzN1vVQr1N8serOpo2NrM9fbqqgjJ5sgqyhADV3GbLFvUBODFR7ZMW7UII0a4M\nVo2ksSAja9IkUp95xlBP3Wpl5TrMzTRjD6NTOFN8mqz8Y2TmHSMr7xhnSvIaPd7MxByXbp703X+M\nAT//AzdPJmfYWABy0gvISd/fonFYHD9O74ULSX/4Yc7WXpz79NN0u/RSvF9/HavYWPRjxhD166+U\nt1E5wipxada88WU/QL3vHxl7jMyUk2SmtMHF9XoGWlhgkp3N3g0b0Nva1nnY/ORJIt56i3I7O/b3\n79+lFlHu3r3b2EPo1Lr17EkgcGbVKqxSUjADol1dKemiv1d5v4jmkveMaIqAgIBWnd+qYLtnz54A\nZGVl4VkrBzArK6v6sfq4ffst+UOHknfZZa15+jbhM3s2ZW5uZPznP+htbXnjey9+2OzC5RGnef7O\no9hZ6QHQlZRgd+AAZwYMQLtIZw41TeNMyWmy8o6RlZ9CZt4xCi8QXJuamOFq74Wbgzc9HfrgbOeO\nqYkpFt2Pc2bkPZS00SItj6VLcdi+nXIHB44sWFDnsfzISA599RU9P/8czcyszQPt8gp4+aveVOhV\nkDvQv4CbhjdeRaVZTEwo8fDA6uhRLDIzKa6a6a5kExsLwNm+fbtUoC1arzAiAs3EBLvoaM6EhGDm\n4ECJVFUSQoh21apg28fHh549e7Ju3ToGDRoEQHFxMZs3b+bNesq61RawcCHccYdxy+llZ8O6dWBj\nQ89ly9h62JTvNqmH/t7vROZpJ359HXw9dKqyxp49qnX78OHGG3M7qqpznZh2kMT0QySmHyL3AtVC\nLMws8XEPqkwLCcPbzY/9+w4AMHjwYMMMdM8eWLMGLCxwfv99nBtaDDliBABtuTRMr9d47QuITVP3\nrSzgqwX2BHi18WvdtAmcnQmtL/1q9WoAul12meF+x+2sarapq7weoxo5EqyssPvwQ/DwYLBpC9dA\ndGDyfhHNJe8Z0Rx5eY1PLF5Ik0r/JSQkAKDX6zl27Bj79+/H2dkZLy8vnnzySRYuXEhQUBABAQEs\nWLAAe3t77rrrroYvet11qivjhg3Q2HGGVtWifdAgMDNjzkd1U0dijkLkA/DdAo3LR45UQd0ff8Co\nUe0/1nZQ1aExMf1QdYCdV3iq0XMszK3w7RWEf+WCRi9XP8xM23HmX9NUjXSAxx9vedWR999XH/4c\nHevszi/USM2ClCxIPVG5rbylZGmkZUNpWc1s8rz7IcDLALPLjX0o3btXbaVNu6jP+vXyjYcQQhjR\nBYPtXbt2ceWVVwIqD3vu3LnMnTuXyZMns2zZMmbMmEFRURFTp04lNzeXYcOGsW7dOmzPySut49NP\n1WKvyplGo6nVOXL9Ho2/96i7pqZgZgolpard9jVPwuJr/sUUFqlg+6WXjDfmNqTX9GTmpFbOWh8k\nKT2GgrOnGz3HwtwKX/d+9S9o3LgRzHuo0mLtZdUqFUw4OcFzzzX79PxCjaQv/yHp+T9JeieboxHX\nkFrkQGqRPSl6F/JKGvvgUDeAGehZyLTbG3nfG4oE26IxEmgLIYRRXTDYvvzyy9Hr9Y0eUxWAN5mb\nm7oZW2WwrQ2NZM7/anZPGgP3j4cJsyDrlMrJfWh1GAd9/8vbu57G7PTp82ZAOwO9voKMnGMkpqmU\nkKT0QxQWFzR6jpWFDb7u/fD3CMHfMxQvF9/6q4WUlcH48XDmjOpS5+5uoFdxjtxc9Wfxwgsq4D6H\npmlkn4bENEhKr7zV+jn7NMDl0PdydUL6eZe4IKeKXMIs0vjwlX6YmbVzYKNp8PbbqklJYGD7PrcQ\nQgghLshg1Ug6PL2+Oo1krdUotkSp3eZm8MK/oHdPHTv/p3HTTNgXrx5b3PNR4qwC+Xr1ZpzuPL9h\nS0dTUVFOWnZydb51cnoMRaVnGz3HxtIOX49gFVx7hODp4tO0JjKbN0N+vqrr25xAW9PUzOwPP8CC\nBc2v/3vPPaolfOU3KUePa3yxFvbH1wTUZxrvm9MoSwvwdgMvV7X1dAVvpxK8e+jx8rbCq6cOO5vu\nQNsuumwynQ4mTlQ3IYQQQnQ4F2+wrdPB5s1oe/Yy52eX6t3336ACbQAvNx0bl2r862X4fr16/A/H\naxj+9Vl+vUQj0LtjfT1bVl5GSlZC9ax18vFYSsuKGz3H1rob/u7B+HuG4u8RQq8evVvW/vz339V2\n7NjmnadpcPPNkJICo0e3qAZ2sa0TP2+CZb9p/LVHXbKpLMzB1x38PMDXQ/3s7VYZYLupduvnl7E0\nYo3406ehWzdpSiKEEEJ0Eh0n2F69moqTueSMu5PsXPX1fvZpOJGrJqHvHA09HNswuNXpICSEX08F\ns/sDtcvKAmbfV/cwW2sdX8/XmP8JzF+m9sWftGHYFPhmvsboocYLuEvLSjiaGafSQjIOcex4PGUV\npY2e083GCX/PEPwqA+ye3b3apvFKIy3aG2ViohqxzJ8PH3/crGA7KlHj45Xw5Vo4ld/wcfY24O9Z\nE1D7e6if/TzAwwVMTTvWh6YGhYbCoUNw9Cj07m3s0QghhBCiCYwSbM/9n8qjPVkZTGcfLyI7bRA5\nZs5o79d/zke/wo7/aVhbtl1gpNdrzPmo5v5DE8Dd5fzrm5jomPcfCO6jZrmLSuB0AVw/Hd55XGPq\nxDbqFHgBRSWFHDkeS2J6DEnph0jJSqRCX97oOU72Lvh7hOBXmRbi4tir7ceakABxcSp3up5Frzn5\nZpTrdej1GiYm9Tx3VbD9ww+weHGj+fB5ZzS++gOWrYTdsec/rtPBNUNVm/R+vVVA3aPe2elOqOr3\nkpwswbYQQgjRSRgl2H7pk3P3WIO5daPnHEyGZ5fCf59qu3F8vx6iKztg21jBzHsbP/62q3T4eag8\n7vRsqKiAx99RY3t3moZ5Gy+OO1OUT1JlYJ2YcYj07KNoWuOLVV0ceuHnGVKdc929m2ubjqleOh08\n8ADY2IBZzVtK0zReXg7z/heOXtNhvRD8PTUCvdRMc4AXBHhCgFcf3K64Et36v1Vr9YceqnN5TdPY\ndACW/QbfrVcfds7Vuyf8ayxMvh68e3aBwLo+vr6q9XZyssFazgshhBCibXWcNJJKTmWncLErw6Wv\nG66OoAE/b1SPLf4erovUuH5E64Op8nKNubUqkDx+K7g6Xfi6g4LUwskJs2BnjNr34S8QnwLfvazh\n7NDysZ0+k6MC68oAO/NU6gXP6dndq87MtYOdERbq+fvDhx/W2VVUonH/K/DVH1BVIq+oRH24qfqA\nU5u9+Wr8w6MJXJ6Dv4lGgJfKn94SrWaxE+r5VViYa0wYpePf4+CqwdQ/a96VVHWOTKr8BW7bBjNn\nwoQJ8OSTxhuXEEIIIRpklGD7+clq4ZmLU+XWEVydwDlpL+aXDldl5J78BW64AU3TmDATft2szv33\nQjjwmYZb91YEVmVlrPjDjLgUdbebLUxvRm+dXj10rF+sMeVV+HKd2vfPPoi8H5ZM1xgRCva2jY+v\nqjtjckZMdXB9Mi+z0XN0OhM8XPrg766Ca1/3ftjbODR94O0kM0f9me2Iqdlnaa6npKzhRX0FZebs\nsxvIPoDljV8/rDCK/wTEcff/bm3Vh5tOx9dXbZOT1XbHDlXbvG9f441JCCGEEI0ySrA9/4EGAiTn\nQfDKK7BoUXXNZJ1Ox0czNXZOgswcleP9n4Xw2xtai/Nwy959j/lfjwfzPgA8dQd079aMa/30E9bf\nf89nz84k2CeU2ZULLJMzYMw0lVUR6qsxLBSGhcDwUPD31JN9Or2yUogKri/UndHUxAxvN//KWetg\nfHoFYW1phKYpzbAvXuPGZyHtRM2+CSOyeeaWFAKCBpGQCglpaqY6sXKbkAb5hY1ft5st3BGcwX8+\nvonBxKJbmwgXU6ANKtg2M4OSyjyaffvUVprZCCGEEB1Wh0sj4amn4D//qbNIzsVJx6ezNa6bpu6v\n2gZLfoBHb2nZU3y63orkykC7ezd48rZmXuC332DFCnT9+zPrmTCCfTTueREKK+s5axocTK4g69QR\ndh0+xA8bYvBwicHS4kyjlzU3taBPr77VaSF9egZiYW7Z/BfYmP37VW3q8ePVB5s29NMGjXvnw9nK\naoMmJvD24zC8Two6HTg76HB2gGGhdc9TbeI5LxBPSoceDnD3tXDLZRo2o26EM3tUB8+O0BSpvQ0b\nBkVFNXnx0jlSCCGE6PA6XrBtYlJvNYprInU8ebvGom/U/WeWwBUDNUJ8mze7WVKqsSB7LFT2aXnm\nbnCwa+YM6ejR8MknqnX7M89w40gd2z4sYelPiaSdOISJyWF6Oh/GwrzxGtfl5TZAEB4uwYyKCGF4\nqD9mpo21B28DJ06o8nGHDqn0g8mTW31JTdN45TN4vlbadjdb+Ho+XDdMx+7djZ+v0+lw6w5u3eHS\niAYO+uln2LNHNcyZNq3VY+6UTGs1Fzp7FmJi1L6wMOONSQghhBCN6njBdiNeeQj+3gNV0KO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import seed\n", "dog = DogSimulation(velocity=1, measurement_variance=40.)\n", "f = pos_vel_filter(x=(0., 0.), R=3., Q=.2, P=P)\n", "count = 50\n", "seed(8923)\n", "zs = [dog.move_and_sense() for t in range(count)]\n", "xs, Covs, _, _ = f.batch_filter(zs)\n", "Ms, Ps, _ = f.rts_smoother(Xs, Covs)\n", "\n", "bp.plot_measurements(range(1, count + 1), zs)\n", "bp.plot_filter(range(1, count + 1), xs[:, 0])\n", "plt.plot(range(1, count + 1), Ms[:, 0], label='RTS')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This output is fantastic!. Two things are very apparent to me in this chart. First, the RTS output is much, much smoother than the KF output. Second, it is almost always more accurate than the KF output (we will examine this claim in detail in the **Smoothing** chapter).\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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X43pw7uk2AD+7z4m/GBUXi/WkujLGsHCl/YL9n7m2f0RxtZPtwAUXDITXPoE3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\nwBenmA6675s29jhHihyff4i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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dog = DogSimulation(velocity=1, measurement_variance=40.)\n", "f = pos_vel_filter(x=(0., 0.), R=3., Q=.2, P=P)\n", "count = 50\n", "seed(8923)\n", "zs = [dog.move_and_sense() for t in range(count)]\n", "xs, Covs, _, _ = f.batch_filter(zs)\n", "Ms, Ps, _ = f.rts_smoother(Xs, Covs)\n", "bp.plot_filter(xs[:, 1])\n", "plt.plot(Ms[:, 1], label='RTS')\n", "plt.legend(loc='best')\n", "plt.gca().axhline(1, c='k');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The improvement in the velocity, which is an hidden variable, is even more dramatic. We will explore why this is so in the next exercise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Compare Velocities\n", "\n", "Since we are plotting velocities let's look at what the the 'raw' velocity is, which we can compute by subtracting subsequent measurements. i.e the velocity at time 1 can be approximated by xs[1] - xs[0]. Plot the raw value against the values estimated by the Kalman filter. Discuss what you see." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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U8RTnz58v9L5E0fDYnu6gUgat01RYW+XKMQMJCfDFF7B0afbbSE+3EEKIm5nN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\nuOUiyTa99RZw773yPTZ6dPXlbw1dKB94QPuxWZD9Bt1Nmkg70BMnJJC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dx = np.diff(xs[:, 0], axis=0)\n", "plt.plot(range(1,count), dx, c='r',ls='--', lw=2, label='Raw velocity')\n", "plt.plot(xs[:, 1], label='Filter')\n", "plt.plot(Ms[:, 1], label='RTS')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the noise swamps the signal, causing the raw values to be essentially worthless. The filter is maintaining a separate estimate for velocity. The Kalman gain $\\mathbf{k}$ is multidimensional. For example, it might have the value $\\mathbf{k} = [0.1274, 0.843]^\\mathsf{T}$. the first value is used to scale the residual of the position, and the second value will scale the residual of the velocity. The covariance matrix tells the filter how correlated the position and velocity are, and each will be optimally filtered. \n", "\n", "I show this to reiterate the importance of using Kalman filters to compute velocities, accelerations, and even higher order values. I use a Kalman filter even when my measurements are so accurate that I am willing to use them unfiltered because it allows me accurate estimates for velocities and accelerations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion and Summary\n", "\n", "We extended Gaussians into multiple dimensions to allow us to simultaneously handle multiple dimensions, both spacial and others (velocity, etc). This led us to use linear algebra. We made a key insight: hidden variables have the ability to significantly increase the accuracy of the filter. This counterintuitive result is because the hidden variables are correlated with the observed variables. Intuitively, I think of it as *triangulating* onto the solution - only a small number of states can be true for a given combination of a velocity Gaussian and position Gaussian, roughly described by their intersection. But of course this works for non-spatial problems as well. \n", "\n", "There is one important caveat about hidden variables. It is easy to construct a filter that produces estimates for hidden variables. Heck, I could write a filter that estimates the color of a tracked car. The designer must verify that these variables are being estimated *correctly*. If you do not have a velocity sensor and yet are estimating velocity, you will need to test that the velocity estimates are correct.; do not trust that they are. For example, suppose the velocity has a periodic component to it - it looks like a sine wave. If your sample time is less than 2 times the frequency you will not be able to accurately estimate the velocity (due to Nyquist's Theorem). Imagine that the sample period is equal to the frequency of the velocity. The filter will report that the velocity is constant because each time it will be sampling the system at the same point on the sin wave. \n", "\n", "Initialization poses a particularly difficult problem for hidden variables. If you start with a bad initialization the filter can usually recover the observed variables, but may struggle and fail with the hidden one. Estimating hidden variables is a powerful tool, but a dangerous one. \n", "\n", "I established a series of steps for designing a Kalman filter. These are not a usual part of the Kalman filter literature, and are only meant as a guide, not a prescription. Designing for a hard problem is an iterative process. You make a guess at the state vector, work out what your measurement and state models are, run some tests, and then alter the design as necessary. \n", "\n", "The design of $\\mathbf{R}$ and $\\mathbf{Q}$ is often quite challenging. I've made it appear to be quite scientific. Your sensor has Gaussian noise of $\\mathcal{N}(0, \\sigma^2)$, so set $\\mathbf{R}=\\sigma^2$. Easy! But I told you a dirty lie. Sensors are not Gaussian. We started the book with a bathroom scale. Suppose $\\sigma=1$ kg, and you try to weigh something that weighs 0.5 kg. Theory tells us we will get negative measurements, but of course the scale will never report weights less than zero. Real world sensors typically have *fat tails*, which mean they have more outlying noise than theory predicts. In some cases, such as with the scale, one or both tails are truncated.\n", "\n", "The case with $\\mathbf{Q}$ is more dire. I hope you were skeptical when I blithely assigned a noise matrix to my prediction about the movements of a dog. Who can say what a dog will do next? But this holds true for more other systems. The GPS in my car doesn't know about hills, the outside winds, or my terrible driving skills. Yet the filter in it requires a precise number to encapsulate all of that information, and it need to work while I drive off-road in the desert, and when Formula One champion Michael Schumacher drives on a closed circuit track.\n", "\n", "These problems led some researchers and engineers to derogatorily call the Kalman filter a 'ball of mud'. In other words, it doesn't always hold together so well. Another term to know - Kalman filters can become **smug**. Their estimates are based solely on what you tell it the noises are. Those values can lead to overly confident estimates. $\\mathbf{P}$ gets smaller and smaller while the filter is actually becoming more and more inaccurate! In the worst case the filter diverges. We will see a lot of that when we start studying nonlinear filters. \n", "\n", "The reality is that the Kalman filter is a mathematical model of the world. The output is only as accurate as that model. To make the math tractable we had to make some assumptions. I We assume that the sensors and motion model have Gaussian noise. We assume that everything is linear. If that is true, the Kalman filter is *optimal* in a least squares sense. This means that there is no way to make a better estimate than what the filter gives us. However, these assumption are almost never true, and hence the model is necessarily limited, and a working filter is rarely optimal.\n", "\n", "In later chapters we will deal with the problem of nonlinearity. For now I want you to understand that designing the matrices of a linear filter is an experimental procedure more than a mathematical one. Use math to establish the initial values, but then you need to experiment. If there is a lot of unaccounted noise in the world (wind, etc) you may have to make $\\mathbf{Q}$ larger. If you make it too large the filter fails to respond quickly to changes. In the **Adaptive Filters** chapter you will learn some alternative techniques that allow you to change the filter design in real time in response to the inputs and performance, but for now you need to find one set of values that works for the conditions your filter will encounter. Noise matrices for an acrobatic plane might be different if the pilot is a student than if the pilot is an expert as the dynamics will be quite different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] 'Kalman Filters'. Wikipedia\n", "https://en.wikipedia.org/wiki/Kalman_filter#Details" ] } ], "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 }